import numba
import numpy as np
from scipy import constants
from numba.experimental import jitclass

from pynucastro.rates import TableIndex, TableInterpolator, TabularRate, Tfactors
from pynucastro.screening import PlasmaState, ScreenFactors

jn = 0
jp = 1
jd = 2
jt = 3
jhe3 = 4
jhe4 = 5
jhe6 = 6
jhe8 = 7
jli5 = 8
jli6 = 9
jli7 = 10
jli8 = 11
jli9 = 12
jli11 = 13
jbe7 = 14
jbe9 = 15
jbe10 = 16
jbe11 = 17
jbe12 = 18
jbe14 = 19
jbe15 = 20
jbe16 = 21
jb8 = 22
jb10 = 23
jb11 = 24
jb12 = 25
jb13 = 26
jb14 = 27
jb15 = 28
jb17 = 29
jb18 = 30
jb19 = 31
jc9 = 32
jc10 = 33
jc11 = 34
jc12 = 35
jc13 = 36
jc14 = 37
jc15 = 38
jc16 = 39
jc17 = 40
jc18 = 41
jc19 = 42
jc20 = 43
jc21 = 44
jc22 = 45
jn11 = 46
jn12 = 47
jn13 = 48
jn14 = 49
jn15 = 50
jn16 = 51
jn17 = 52
jn18 = 53
jn19 = 54
jn20 = 55
jn21 = 56
jn22 = 57
jn23 = 58
jn24 = 59
jo12 = 60
jo13 = 61
jo14 = 62
jo15 = 63
jo16 = 64
jo17 = 65
jo18 = 66
jo19 = 67
jo20 = 68
jo21 = 69
jo22 = 70
jo23 = 71
jo24 = 72
jo25 = 73
jo26 = 74
jo27 = 75
jo28 = 76
jf14 = 77
jf15 = 78
jf16 = 79
jf17 = 80
jf18 = 81
jf19 = 82
jf20 = 83
jf21 = 84
jf22 = 85
jf23 = 86
jf24 = 87
jf25 = 88
jf26 = 89
jf27 = 90
jf28 = 91
jf29 = 92
jf30 = 93
jf31 = 94
jne16 = 95
jne17 = 96
jne18 = 97
jne19 = 98
jne20 = 99
jne21 = 100
jne22 = 101
jne23 = 102
jne24 = 103
jne25 = 104
jne26 = 105
jne27 = 106
jne28 = 107
jne29 = 108
jne30 = 109
jne31 = 110
jne32 = 111
jne33 = 112
jne34 = 113
jna19 = 114
jna20 = 115
jna21 = 116
jna22 = 117
jna23 = 118
jna24 = 119
jna25 = 120
jna26 = 121
jna27 = 122
jna28 = 123
jna29 = 124
jna30 = 125
jna31 = 126
jna32 = 127
jna33 = 128
jna34 = 129
jna35 = 130
jna36 = 131
jna37 = 132
jna38 = 133
jna39 = 134
jmg19 = 135
jmg20 = 136
jmg21 = 137
jmg22 = 138
jmg23 = 139
jmg24 = 140
jmg25 = 141
jmg26 = 142
jmg27 = 143
jmg28 = 144
jmg29 = 145
jmg30 = 146
jmg31 = 147
jmg32 = 148
jmg33 = 149
jmg34 = 150
jmg35 = 151
jmg36 = 152
jmg37 = 153
jmg38 = 154
jmg39 = 155
jmg40 = 156
jmg41 = 157
jal21 = 158
jal22 = 159
jal23 = 160
jal24 = 161
jal25 = 162
jal26 = 163
jal27 = 164
jal28 = 165
jal29 = 166
jal30 = 167
jal31 = 168
jal32 = 169
jal33 = 170
jal34 = 171
jal35 = 172
jal36 = 173
jal37 = 174
jal38 = 175
jal39 = 176
jal40 = 177
jal41 = 178
jal42 = 179
jal43 = 180
jsi22 = 181
jsi23 = 182
jsi24 = 183
jsi25 = 184
jsi26 = 185
jsi27 = 186
jsi28 = 187
jsi29 = 188
jsi30 = 189
jsi31 = 190
jsi32 = 191
jsi33 = 192
jsi34 = 193
jsi35 = 194
jsi36 = 195
jsi37 = 196
jsi38 = 197
jsi39 = 198
jsi40 = 199
jsi41 = 200
jsi42 = 201
jsi43 = 202
jsi44 = 203
jsi45 = 204
jp24 = 205
jp25 = 206
jp26 = 207
jp27 = 208
jp28 = 209
jp29 = 210
jp30 = 211
jp31 = 212
jp32 = 213
jp33 = 214
jp34 = 215
jp35 = 216
jp36 = 217
jp37 = 218
jp38 = 219
jp39 = 220
jp40 = 221
jp41 = 222
jp42 = 223
jp43 = 224
jp44 = 225
jp45 = 226
jp46 = 227
jp47 = 228
js26 = 229
js27 = 230
js28 = 231
js29 = 232
js30 = 233
js31 = 234
js32 = 235
js33 = 236
js34 = 237
js35 = 238
js36 = 239
js37 = 240
js38 = 241
js39 = 242
js40 = 243
js41 = 244
js42 = 245
js43 = 246
js44 = 247
js45 = 248
js46 = 249
js47 = 250
js48 = 251
js49 = 252
jcl28 = 253
jcl29 = 254
jcl30 = 255
jcl31 = 256
jcl32 = 257
jcl33 = 258
jcl34 = 259
jcl35 = 260
jcl36 = 261
jcl37 = 262
jcl38 = 263
jcl39 = 264
jcl40 = 265
jcl41 = 266
jcl42 = 267
jcl43 = 268
jcl44 = 269
jcl45 = 270
jcl46 = 271
jcl47 = 272
jcl48 = 273
jcl49 = 274
jcl50 = 275
jcl51 = 276
jcl52 = 277
jar29 = 278
jar30 = 279
jar31 = 280
jar32 = 281
jar33 = 282
jar34 = 283
jar35 = 284
jar36 = 285
jar37 = 286
jar38 = 287
jar39 = 288
jar40 = 289
jar41 = 290
jar42 = 291
jar43 = 292
jar44 = 293
jar45 = 294
jar46 = 295
jar47 = 296
jar48 = 297
jar49 = 298
jar50 = 299
jar51 = 300
jar52 = 301
jar53 = 302
jar54 = 303
jk31 = 304
jk32 = 305
jk33 = 306
jk34 = 307
jk35 = 308
jk36 = 309
jk37 = 310
jk38 = 311
jk39 = 312
jk40 = 313
jk41 = 314
jk42 = 315
jk43 = 316
jk44 = 317
jk45 = 318
jk46 = 319
jk47 = 320
jk48 = 321
jk49 = 322
jk50 = 323
jk51 = 324
jk52 = 325
jk53 = 326
jk54 = 327
jk55 = 328
jk56 = 329
jk57 = 330
jk58 = 331
jk59 = 332
jca33 = 333
jca34 = 334
jca35 = 335
jca36 = 336
jca37 = 337
jca38 = 338
jca39 = 339
jca40 = 340
jca41 = 341
jca42 = 342
jca43 = 343
jca44 = 344
jca45 = 345
jca46 = 346
jca47 = 347
jca48 = 348
jca49 = 349
jca50 = 350
jca51 = 351
jca52 = 352
jca53 = 353
jca54 = 354
jca55 = 355
jca56 = 356
jca57 = 357
jca58 = 358
jca59 = 359
jca60 = 360
jca61 = 361
jsc35 = 362
jsc36 = 363
jsc37 = 364
jsc38 = 365
jsc39 = 366
jsc40 = 367
jsc41 = 368
jsc42 = 369
jsc43 = 370
jsc44 = 371
jsc45 = 372
jsc46 = 373
jsc47 = 374
jsc48 = 375
jsc49 = 376
jsc50 = 377
jsc51 = 378
jsc52 = 379
jsc53 = 380
jsc54 = 381
jsc55 = 382
jsc56 = 383
jsc57 = 384
jsc58 = 385
jsc59 = 386
jsc60 = 387
jsc61 = 388
jsc62 = 389
jsc63 = 390
jti37 = 391
jti38 = 392
jti39 = 393
jti40 = 394
jti41 = 395
jti42 = 396
jti43 = 397
jti44 = 398
jti45 = 399
jti46 = 400
jti47 = 401
jti48 = 402
jti49 = 403
jti50 = 404
jti51 = 405
jti52 = 406
jti53 = 407
jti54 = 408
jti55 = 409
jti56 = 410
jti57 = 411
jti58 = 412
jti59 = 413
jti60 = 414
jti61 = 415
jti62 = 416
jti63 = 417
jti64 = 418
jti65 = 419
jv39 = 420
jv40 = 421
jv41 = 422
jv42 = 423
jv43 = 424
jv44 = 425
jv45 = 426
jv46 = 427
jv47 = 428
jv48 = 429
jv49 = 430
jv50 = 431
jv51 = 432
jv52 = 433
jv53 = 434
jv54 = 435
jv55 = 436
jv56 = 437
jv57 = 438
jv58 = 439
jv59 = 440
jv60 = 441
jv61 = 442
jv62 = 443
jv63 = 444
jv64 = 445
jv65 = 446
jv66 = 447
jv67 = 448
jcr41 = 449
jcr42 = 450
jcr43 = 451
jcr44 = 452
jcr45 = 453
jcr46 = 454
jcr47 = 455
jcr48 = 456
jcr49 = 457
jcr50 = 458
jcr51 = 459
jcr52 = 460
jcr53 = 461
jcr54 = 462
jcr55 = 463
jcr56 = 464
jcr57 = 465
jcr58 = 466
jcr59 = 467
jcr60 = 468
jcr61 = 469
jcr62 = 470
jcr63 = 471
jcr64 = 472
jcr65 = 473
jcr66 = 474
jcr67 = 475
jcr68 = 476
jcr69 = 477
jcr70 = 478
jmn43 = 479
jmn44 = 480
jmn45 = 481
jmn46 = 482
jmn47 = 483
jmn48 = 484
jmn49 = 485
jmn50 = 486
jmn51 = 487
jmn52 = 488
jmn53 = 489
jmn54 = 490
jmn55 = 491
jmn56 = 492
jmn57 = 493
jmn58 = 494
jmn59 = 495
jmn60 = 496
jmn61 = 497
jmn62 = 498
jmn63 = 499
jmn64 = 500
jmn65 = 501
jmn66 = 502
jmn67 = 503
jmn68 = 504
jmn69 = 505
jmn70 = 506
jmn71 = 507
jmn72 = 508
jmn73 = 509
jfe45 = 510
jfe46 = 511
jfe47 = 512
jfe48 = 513
jfe49 = 514
jfe50 = 515
jfe51 = 516
jfe52 = 517
jfe53 = 518
jfe54 = 519
jfe55 = 520
jfe56 = 521
jfe57 = 522
jfe58 = 523
jfe59 = 524
jfe60 = 525
jfe61 = 526
jfe62 = 527
jfe63 = 528
jfe64 = 529
jfe65 = 530
jfe66 = 531
jfe67 = 532
jfe68 = 533
jfe69 = 534
jfe70 = 535
jfe71 = 536
jfe72 = 537
jfe73 = 538
jfe74 = 539
jfe75 = 540
jfe76 = 541
jco47 = 542
jco48 = 543
jco49 = 544
jco50 = 545
jco51 = 546
jco52 = 547
jco53 = 548
jco54 = 549
jco55 = 550
jco56 = 551
jco57 = 552
jco58 = 553
jco59 = 554
jco60 = 555
jco61 = 556
jco62 = 557
jco63 = 558
jco64 = 559
jco65 = 560
jco66 = 561
jco67 = 562
jco68 = 563
jco69 = 564
jco70 = 565
jco71 = 566
jco72 = 567
jco73 = 568
jco74 = 569
jco75 = 570
jco76 = 571
jco77 = 572
jni49 = 573
jni50 = 574
jni51 = 575
jni52 = 576
jni53 = 577
jni54 = 578
jni55 = 579
jni56 = 580
jni57 = 581
jni58 = 582
jni59 = 583
jni60 = 584
jni61 = 585
jni62 = 586
jni63 = 587
jni64 = 588
jni65 = 589
jni66 = 590
jni67 = 591
jni68 = 592
jni69 = 593
jni70 = 594
jni71 = 595
jni72 = 596
jni73 = 597
jni74 = 598
jni75 = 599
jni76 = 600
jni77 = 601
jni78 = 602
jni79 = 603
jni80 = 604
nnuc = 605

A = np.zeros((nnuc), dtype=np.int32)

A[jn] = 1
A[jp] = 1
A[jd] = 2
A[jt] = 3
A[jhe3] = 3
A[jhe4] = 4
A[jhe6] = 6
A[jhe8] = 8
A[jli5] = 5
A[jli6] = 6
A[jli7] = 7
A[jli8] = 8
A[jli9] = 9
A[jli11] = 11
A[jbe7] = 7
A[jbe9] = 9
A[jbe10] = 10
A[jbe11] = 11
A[jbe12] = 12
A[jbe14] = 14
A[jbe15] = 15
A[jbe16] = 16
A[jb8] = 8
A[jb10] = 10
A[jb11] = 11
A[jb12] = 12
A[jb13] = 13
A[jb14] = 14
A[jb15] = 15
A[jb17] = 17
A[jb18] = 18
A[jb19] = 19
A[jc9] = 9
A[jc10] = 10
A[jc11] = 11
A[jc12] = 12
A[jc13] = 13
A[jc14] = 14
A[jc15] = 15
A[jc16] = 16
A[jc17] = 17
A[jc18] = 18
A[jc19] = 19
A[jc20] = 20
A[jc21] = 21
A[jc22] = 22
A[jn11] = 11
A[jn12] = 12
A[jn13] = 13
A[jn14] = 14
A[jn15] = 15
A[jn16] = 16
A[jn17] = 17
A[jn18] = 18
A[jn19] = 19
A[jn20] = 20
A[jn21] = 21
A[jn22] = 22
A[jn23] = 23
A[jn24] = 24
A[jo12] = 12
A[jo13] = 13
A[jo14] = 14
A[jo15] = 15
A[jo16] = 16
A[jo17] = 17
A[jo18] = 18
A[jo19] = 19
A[jo20] = 20
A[jo21] = 21
A[jo22] = 22
A[jo23] = 23
A[jo24] = 24
A[jo25] = 25
A[jo26] = 26
A[jo27] = 27
A[jo28] = 28
A[jf14] = 14
A[jf15] = 15
A[jf16] = 16
A[jf17] = 17
A[jf18] = 18
A[jf19] = 19
A[jf20] = 20
A[jf21] = 21
A[jf22] = 22
A[jf23] = 23
A[jf24] = 24
A[jf25] = 25
A[jf26] = 26
A[jf27] = 27
A[jf28] = 28
A[jf29] = 29
A[jf30] = 30
A[jf31] = 31
A[jne16] = 16
A[jne17] = 17
A[jne18] = 18
A[jne19] = 19
A[jne20] = 20
A[jne21] = 21
A[jne22] = 22
A[jne23] = 23
A[jne24] = 24
A[jne25] = 25
A[jne26] = 26
A[jne27] = 27
A[jne28] = 28
A[jne29] = 29
A[jne30] = 30
A[jne31] = 31
A[jne32] = 32
A[jne33] = 33
A[jne34] = 34
A[jna19] = 19
A[jna20] = 20
A[jna21] = 21
A[jna22] = 22
A[jna23] = 23
A[jna24] = 24
A[jna25] = 25
A[jna26] = 26
A[jna27] = 27
A[jna28] = 28
A[jna29] = 29
A[jna30] = 30
A[jna31] = 31
A[jna32] = 32
A[jna33] = 33
A[jna34] = 34
A[jna35] = 35
A[jna36] = 36
A[jna37] = 37
A[jna38] = 38
A[jna39] = 39
A[jmg19] = 19
A[jmg20] = 20
A[jmg21] = 21
A[jmg22] = 22
A[jmg23] = 23
A[jmg24] = 24
A[jmg25] = 25
A[jmg26] = 26
A[jmg27] = 27
A[jmg28] = 28
A[jmg29] = 29
A[jmg30] = 30
A[jmg31] = 31
A[jmg32] = 32
A[jmg33] = 33
A[jmg34] = 34
A[jmg35] = 35
A[jmg36] = 36
A[jmg37] = 37
A[jmg38] = 38
A[jmg39] = 39
A[jmg40] = 40
A[jmg41] = 41
A[jal21] = 21
A[jal22] = 22
A[jal23] = 23
A[jal24] = 24
A[jal25] = 25
A[jal26] = 26
A[jal27] = 27
A[jal28] = 28
A[jal29] = 29
A[jal30] = 30
A[jal31] = 31
A[jal32] = 32
A[jal33] = 33
A[jal34] = 34
A[jal35] = 35
A[jal36] = 36
A[jal37] = 37
A[jal38] = 38
A[jal39] = 39
A[jal40] = 40
A[jal41] = 41
A[jal42] = 42
A[jal43] = 43
A[jsi22] = 22
A[jsi23] = 23
A[jsi24] = 24
A[jsi25] = 25
A[jsi26] = 26
A[jsi27] = 27
A[jsi28] = 28
A[jsi29] = 29
A[jsi30] = 30
A[jsi31] = 31
A[jsi32] = 32
A[jsi33] = 33
A[jsi34] = 34
A[jsi35] = 35
A[jsi36] = 36
A[jsi37] = 37
A[jsi38] = 38
A[jsi39] = 39
A[jsi40] = 40
A[jsi41] = 41
A[jsi42] = 42
A[jsi43] = 43
A[jsi44] = 44
A[jsi45] = 45
A[jp24] = 24
A[jp25] = 25
A[jp26] = 26
A[jp27] = 27
A[jp28] = 28
A[jp29] = 29
A[jp30] = 30
A[jp31] = 31
A[jp32] = 32
A[jp33] = 33
A[jp34] = 34
A[jp35] = 35
A[jp36] = 36
A[jp37] = 37
A[jp38] = 38
A[jp39] = 39
A[jp40] = 40
A[jp41] = 41
A[jp42] = 42
A[jp43] = 43
A[jp44] = 44
A[jp45] = 45
A[jp46] = 46
A[jp47] = 47
A[js26] = 26
A[js27] = 27
A[js28] = 28
A[js29] = 29
A[js30] = 30
A[js31] = 31
A[js32] = 32
A[js33] = 33
A[js34] = 34
A[js35] = 35
A[js36] = 36
A[js37] = 37
A[js38] = 38
A[js39] = 39
A[js40] = 40
A[js41] = 41
A[js42] = 42
A[js43] = 43
A[js44] = 44
A[js45] = 45
A[js46] = 46
A[js47] = 47
A[js48] = 48
A[js49] = 49
A[jcl28] = 28
A[jcl29] = 29
A[jcl30] = 30
A[jcl31] = 31
A[jcl32] = 32
A[jcl33] = 33
A[jcl34] = 34
A[jcl35] = 35
A[jcl36] = 36
A[jcl37] = 37
A[jcl38] = 38
A[jcl39] = 39
A[jcl40] = 40
A[jcl41] = 41
A[jcl42] = 42
A[jcl43] = 43
A[jcl44] = 44
A[jcl45] = 45
A[jcl46] = 46
A[jcl47] = 47
A[jcl48] = 48
A[jcl49] = 49
A[jcl50] = 50
A[jcl51] = 51
A[jcl52] = 52
A[jar29] = 29
A[jar30] = 30
A[jar31] = 31
A[jar32] = 32
A[jar33] = 33
A[jar34] = 34
A[jar35] = 35
A[jar36] = 36
A[jar37] = 37
A[jar38] = 38
A[jar39] = 39
A[jar40] = 40
A[jar41] = 41
A[jar42] = 42
A[jar43] = 43
A[jar44] = 44
A[jar45] = 45
A[jar46] = 46
A[jar47] = 47
A[jar48] = 48
A[jar49] = 49
A[jar50] = 50
A[jar51] = 51
A[jar52] = 52
A[jar53] = 53
A[jar54] = 54
A[jk31] = 31
A[jk32] = 32
A[jk33] = 33
A[jk34] = 34
A[jk35] = 35
A[jk36] = 36
A[jk37] = 37
A[jk38] = 38
A[jk39] = 39
A[jk40] = 40
A[jk41] = 41
A[jk42] = 42
A[jk43] = 43
A[jk44] = 44
A[jk45] = 45
A[jk46] = 46
A[jk47] = 47
A[jk48] = 48
A[jk49] = 49
A[jk50] = 50
A[jk51] = 51
A[jk52] = 52
A[jk53] = 53
A[jk54] = 54
A[jk55] = 55
A[jk56] = 56
A[jk57] = 57
A[jk58] = 58
A[jk59] = 59
A[jca33] = 33
A[jca34] = 34
A[jca35] = 35
A[jca36] = 36
A[jca37] = 37
A[jca38] = 38
A[jca39] = 39
A[jca40] = 40
A[jca41] = 41
A[jca42] = 42
A[jca43] = 43
A[jca44] = 44
A[jca45] = 45
A[jca46] = 46
A[jca47] = 47
A[jca48] = 48
A[jca49] = 49
A[jca50] = 50
A[jca51] = 51
A[jca52] = 52
A[jca53] = 53
A[jca54] = 54
A[jca55] = 55
A[jca56] = 56
A[jca57] = 57
A[jca58] = 58
A[jca59] = 59
A[jca60] = 60
A[jca61] = 61
A[jsc35] = 35
A[jsc36] = 36
A[jsc37] = 37
A[jsc38] = 38
A[jsc39] = 39
A[jsc40] = 40
A[jsc41] = 41
A[jsc42] = 42
A[jsc43] = 43
A[jsc44] = 44
A[jsc45] = 45
A[jsc46] = 46
A[jsc47] = 47
A[jsc48] = 48
A[jsc49] = 49
A[jsc50] = 50
A[jsc51] = 51
A[jsc52] = 52
A[jsc53] = 53
A[jsc54] = 54
A[jsc55] = 55
A[jsc56] = 56
A[jsc57] = 57
A[jsc58] = 58
A[jsc59] = 59
A[jsc60] = 60
A[jsc61] = 61
A[jsc62] = 62
A[jsc63] = 63
A[jti37] = 37
A[jti38] = 38
A[jti39] = 39
A[jti40] = 40
A[jti41] = 41
A[jti42] = 42
A[jti43] = 43
A[jti44] = 44
A[jti45] = 45
A[jti46] = 46
A[jti47] = 47
A[jti48] = 48
A[jti49] = 49
A[jti50] = 50
A[jti51] = 51
A[jti52] = 52
A[jti53] = 53
A[jti54] = 54
A[jti55] = 55
A[jti56] = 56
A[jti57] = 57
A[jti58] = 58
A[jti59] = 59
A[jti60] = 60
A[jti61] = 61
A[jti62] = 62
A[jti63] = 63
A[jti64] = 64
A[jti65] = 65
A[jv39] = 39
A[jv40] = 40
A[jv41] = 41
A[jv42] = 42
A[jv43] = 43
A[jv44] = 44
A[jv45] = 45
A[jv46] = 46
A[jv47] = 47
A[jv48] = 48
A[jv49] = 49
A[jv50] = 50
A[jv51] = 51
A[jv52] = 52
A[jv53] = 53
A[jv54] = 54
A[jv55] = 55
A[jv56] = 56
A[jv57] = 57
A[jv58] = 58
A[jv59] = 59
A[jv60] = 60
A[jv61] = 61
A[jv62] = 62
A[jv63] = 63
A[jv64] = 64
A[jv65] = 65
A[jv66] = 66
A[jv67] = 67
A[jcr41] = 41
A[jcr42] = 42
A[jcr43] = 43
A[jcr44] = 44
A[jcr45] = 45
A[jcr46] = 46
A[jcr47] = 47
A[jcr48] = 48
A[jcr49] = 49
A[jcr50] = 50
A[jcr51] = 51
A[jcr52] = 52
A[jcr53] = 53
A[jcr54] = 54
A[jcr55] = 55
A[jcr56] = 56
A[jcr57] = 57
A[jcr58] = 58
A[jcr59] = 59
A[jcr60] = 60
A[jcr61] = 61
A[jcr62] = 62
A[jcr63] = 63
A[jcr64] = 64
A[jcr65] = 65
A[jcr66] = 66
A[jcr67] = 67
A[jcr68] = 68
A[jcr69] = 69
A[jcr70] = 70
A[jmn43] = 43
A[jmn44] = 44
A[jmn45] = 45
A[jmn46] = 46
A[jmn47] = 47
A[jmn48] = 48
A[jmn49] = 49
A[jmn50] = 50
A[jmn51] = 51
A[jmn52] = 52
A[jmn53] = 53
A[jmn54] = 54
A[jmn55] = 55
A[jmn56] = 56
A[jmn57] = 57
A[jmn58] = 58
A[jmn59] = 59
A[jmn60] = 60
A[jmn61] = 61
A[jmn62] = 62
A[jmn63] = 63
A[jmn64] = 64
A[jmn65] = 65
A[jmn66] = 66
A[jmn67] = 67
A[jmn68] = 68
A[jmn69] = 69
A[jmn70] = 70
A[jmn71] = 71
A[jmn72] = 72
A[jmn73] = 73
A[jfe45] = 45
A[jfe46] = 46
A[jfe47] = 47
A[jfe48] = 48
A[jfe49] = 49
A[jfe50] = 50
A[jfe51] = 51
A[jfe52] = 52
A[jfe53] = 53
A[jfe54] = 54
A[jfe55] = 55
A[jfe56] = 56
A[jfe57] = 57
A[jfe58] = 58
A[jfe59] = 59
A[jfe60] = 60
A[jfe61] = 61
A[jfe62] = 62
A[jfe63] = 63
A[jfe64] = 64
A[jfe65] = 65
A[jfe66] = 66
A[jfe67] = 67
A[jfe68] = 68
A[jfe69] = 69
A[jfe70] = 70
A[jfe71] = 71
A[jfe72] = 72
A[jfe73] = 73
A[jfe74] = 74
A[jfe75] = 75
A[jfe76] = 76
A[jco47] = 47
A[jco48] = 48
A[jco49] = 49
A[jco50] = 50
A[jco51] = 51
A[jco52] = 52
A[jco53] = 53
A[jco54] = 54
A[jco55] = 55
A[jco56] = 56
A[jco57] = 57
A[jco58] = 58
A[jco59] = 59
A[jco60] = 60
A[jco61] = 61
A[jco62] = 62
A[jco63] = 63
A[jco64] = 64
A[jco65] = 65
A[jco66] = 66
A[jco67] = 67
A[jco68] = 68
A[jco69] = 69
A[jco70] = 70
A[jco71] = 71
A[jco72] = 72
A[jco73] = 73
A[jco74] = 74
A[jco75] = 75
A[jco76] = 76
A[jco77] = 77
A[jni49] = 49
A[jni50] = 50
A[jni51] = 51
A[jni52] = 52
A[jni53] = 53
A[jni54] = 54
A[jni55] = 55
A[jni56] = 56
A[jni57] = 57
A[jni58] = 58
A[jni59] = 59
A[jni60] = 60
A[jni61] = 61
A[jni62] = 62
A[jni63] = 63
A[jni64] = 64
A[jni65] = 65
A[jni66] = 66
A[jni67] = 67
A[jni68] = 68
A[jni69] = 69
A[jni70] = 70
A[jni71] = 71
A[jni72] = 72
A[jni73] = 73
A[jni74] = 74
A[jni75] = 75
A[jni76] = 76
A[jni77] = 77
A[jni78] = 78
A[jni79] = 79
A[jni80] = 80

Z = np.zeros((nnuc), dtype=np.int32)

Z[jn] = 0
Z[jp] = 1
Z[jd] = 1
Z[jt] = 1
Z[jhe3] = 2
Z[jhe4] = 2
Z[jhe6] = 2
Z[jhe8] = 2
Z[jli5] = 3
Z[jli6] = 3
Z[jli7] = 3
Z[jli8] = 3
Z[jli9] = 3
Z[jli11] = 3
Z[jbe7] = 4
Z[jbe9] = 4
Z[jbe10] = 4
Z[jbe11] = 4
Z[jbe12] = 4
Z[jbe14] = 4
Z[jbe15] = 4
Z[jbe16] = 4
Z[jb8] = 5
Z[jb10] = 5
Z[jb11] = 5
Z[jb12] = 5
Z[jb13] = 5
Z[jb14] = 5
Z[jb15] = 5
Z[jb17] = 5
Z[jb18] = 5
Z[jb19] = 5
Z[jc9] = 6
Z[jc10] = 6
Z[jc11] = 6
Z[jc12] = 6
Z[jc13] = 6
Z[jc14] = 6
Z[jc15] = 6
Z[jc16] = 6
Z[jc17] = 6
Z[jc18] = 6
Z[jc19] = 6
Z[jc20] = 6
Z[jc21] = 6
Z[jc22] = 6
Z[jn11] = 7
Z[jn12] = 7
Z[jn13] = 7
Z[jn14] = 7
Z[jn15] = 7
Z[jn16] = 7
Z[jn17] = 7
Z[jn18] = 7
Z[jn19] = 7
Z[jn20] = 7
Z[jn21] = 7
Z[jn22] = 7
Z[jn23] = 7
Z[jn24] = 7
Z[jo12] = 8
Z[jo13] = 8
Z[jo14] = 8
Z[jo15] = 8
Z[jo16] = 8
Z[jo17] = 8
Z[jo18] = 8
Z[jo19] = 8
Z[jo20] = 8
Z[jo21] = 8
Z[jo22] = 8
Z[jo23] = 8
Z[jo24] = 8
Z[jo25] = 8
Z[jo26] = 8
Z[jo27] = 8
Z[jo28] = 8
Z[jf14] = 9
Z[jf15] = 9
Z[jf16] = 9
Z[jf17] = 9
Z[jf18] = 9
Z[jf19] = 9
Z[jf20] = 9
Z[jf21] = 9
Z[jf22] = 9
Z[jf23] = 9
Z[jf24] = 9
Z[jf25] = 9
Z[jf26] = 9
Z[jf27] = 9
Z[jf28] = 9
Z[jf29] = 9
Z[jf30] = 9
Z[jf31] = 9
Z[jne16] = 10
Z[jne17] = 10
Z[jne18] = 10
Z[jne19] = 10
Z[jne20] = 10
Z[jne21] = 10
Z[jne22] = 10
Z[jne23] = 10
Z[jne24] = 10
Z[jne25] = 10
Z[jne26] = 10
Z[jne27] = 10
Z[jne28] = 10
Z[jne29] = 10
Z[jne30] = 10
Z[jne31] = 10
Z[jne32] = 10
Z[jne33] = 10
Z[jne34] = 10
Z[jna19] = 11
Z[jna20] = 11
Z[jna21] = 11
Z[jna22] = 11
Z[jna23] = 11
Z[jna24] = 11
Z[jna25] = 11
Z[jna26] = 11
Z[jna27] = 11
Z[jna28] = 11
Z[jna29] = 11
Z[jna30] = 11
Z[jna31] = 11
Z[jna32] = 11
Z[jna33] = 11
Z[jna34] = 11
Z[jna35] = 11
Z[jna36] = 11
Z[jna37] = 11
Z[jna38] = 11
Z[jna39] = 11
Z[jmg19] = 12
Z[jmg20] = 12
Z[jmg21] = 12
Z[jmg22] = 12
Z[jmg23] = 12
Z[jmg24] = 12
Z[jmg25] = 12
Z[jmg26] = 12
Z[jmg27] = 12
Z[jmg28] = 12
Z[jmg29] = 12
Z[jmg30] = 12
Z[jmg31] = 12
Z[jmg32] = 12
Z[jmg33] = 12
Z[jmg34] = 12
Z[jmg35] = 12
Z[jmg36] = 12
Z[jmg37] = 12
Z[jmg38] = 12
Z[jmg39] = 12
Z[jmg40] = 12
Z[jmg41] = 12
Z[jal21] = 13
Z[jal22] = 13
Z[jal23] = 13
Z[jal24] = 13
Z[jal25] = 13
Z[jal26] = 13
Z[jal27] = 13
Z[jal28] = 13
Z[jal29] = 13
Z[jal30] = 13
Z[jal31] = 13
Z[jal32] = 13
Z[jal33] = 13
Z[jal34] = 13
Z[jal35] = 13
Z[jal36] = 13
Z[jal37] = 13
Z[jal38] = 13
Z[jal39] = 13
Z[jal40] = 13
Z[jal41] = 13
Z[jal42] = 13
Z[jal43] = 13
Z[jsi22] = 14
Z[jsi23] = 14
Z[jsi24] = 14
Z[jsi25] = 14
Z[jsi26] = 14
Z[jsi27] = 14
Z[jsi28] = 14
Z[jsi29] = 14
Z[jsi30] = 14
Z[jsi31] = 14
Z[jsi32] = 14
Z[jsi33] = 14
Z[jsi34] = 14
Z[jsi35] = 14
Z[jsi36] = 14
Z[jsi37] = 14
Z[jsi38] = 14
Z[jsi39] = 14
Z[jsi40] = 14
Z[jsi41] = 14
Z[jsi42] = 14
Z[jsi43] = 14
Z[jsi44] = 14
Z[jsi45] = 14
Z[jp24] = 15
Z[jp25] = 15
Z[jp26] = 15
Z[jp27] = 15
Z[jp28] = 15
Z[jp29] = 15
Z[jp30] = 15
Z[jp31] = 15
Z[jp32] = 15
Z[jp33] = 15
Z[jp34] = 15
Z[jp35] = 15
Z[jp36] = 15
Z[jp37] = 15
Z[jp38] = 15
Z[jp39] = 15
Z[jp40] = 15
Z[jp41] = 15
Z[jp42] = 15
Z[jp43] = 15
Z[jp44] = 15
Z[jp45] = 15
Z[jp46] = 15
Z[jp47] = 15
Z[js26] = 16
Z[js27] = 16
Z[js28] = 16
Z[js29] = 16
Z[js30] = 16
Z[js31] = 16
Z[js32] = 16
Z[js33] = 16
Z[js34] = 16
Z[js35] = 16
Z[js36] = 16
Z[js37] = 16
Z[js38] = 16
Z[js39] = 16
Z[js40] = 16
Z[js41] = 16
Z[js42] = 16
Z[js43] = 16
Z[js44] = 16
Z[js45] = 16
Z[js46] = 16
Z[js47] = 16
Z[js48] = 16
Z[js49] = 16
Z[jcl28] = 17
Z[jcl29] = 17
Z[jcl30] = 17
Z[jcl31] = 17
Z[jcl32] = 17
Z[jcl33] = 17
Z[jcl34] = 17
Z[jcl35] = 17
Z[jcl36] = 17
Z[jcl37] = 17
Z[jcl38] = 17
Z[jcl39] = 17
Z[jcl40] = 17
Z[jcl41] = 17
Z[jcl42] = 17
Z[jcl43] = 17
Z[jcl44] = 17
Z[jcl45] = 17
Z[jcl46] = 17
Z[jcl47] = 17
Z[jcl48] = 17
Z[jcl49] = 17
Z[jcl50] = 17
Z[jcl51] = 17
Z[jcl52] = 17
Z[jar29] = 18
Z[jar30] = 18
Z[jar31] = 18
Z[jar32] = 18
Z[jar33] = 18
Z[jar34] = 18
Z[jar35] = 18
Z[jar36] = 18
Z[jar37] = 18
Z[jar38] = 18
Z[jar39] = 18
Z[jar40] = 18
Z[jar41] = 18
Z[jar42] = 18
Z[jar43] = 18
Z[jar44] = 18
Z[jar45] = 18
Z[jar46] = 18
Z[jar47] = 18
Z[jar48] = 18
Z[jar49] = 18
Z[jar50] = 18
Z[jar51] = 18
Z[jar52] = 18
Z[jar53] = 18
Z[jar54] = 18
Z[jk31] = 19
Z[jk32] = 19
Z[jk33] = 19
Z[jk34] = 19
Z[jk35] = 19
Z[jk36] = 19
Z[jk37] = 19
Z[jk38] = 19
Z[jk39] = 19
Z[jk40] = 19
Z[jk41] = 19
Z[jk42] = 19
Z[jk43] = 19
Z[jk44] = 19
Z[jk45] = 19
Z[jk46] = 19
Z[jk47] = 19
Z[jk48] = 19
Z[jk49] = 19
Z[jk50] = 19
Z[jk51] = 19
Z[jk52] = 19
Z[jk53] = 19
Z[jk54] = 19
Z[jk55] = 19
Z[jk56] = 19
Z[jk57] = 19
Z[jk58] = 19
Z[jk59] = 19
Z[jca33] = 20
Z[jca34] = 20
Z[jca35] = 20
Z[jca36] = 20
Z[jca37] = 20
Z[jca38] = 20
Z[jca39] = 20
Z[jca40] = 20
Z[jca41] = 20
Z[jca42] = 20
Z[jca43] = 20
Z[jca44] = 20
Z[jca45] = 20
Z[jca46] = 20
Z[jca47] = 20
Z[jca48] = 20
Z[jca49] = 20
Z[jca50] = 20
Z[jca51] = 20
Z[jca52] = 20
Z[jca53] = 20
Z[jca54] = 20
Z[jca55] = 20
Z[jca56] = 20
Z[jca57] = 20
Z[jca58] = 20
Z[jca59] = 20
Z[jca60] = 20
Z[jca61] = 20
Z[jsc35] = 21
Z[jsc36] = 21
Z[jsc37] = 21
Z[jsc38] = 21
Z[jsc39] = 21
Z[jsc40] = 21
Z[jsc41] = 21
Z[jsc42] = 21
Z[jsc43] = 21
Z[jsc44] = 21
Z[jsc45] = 21
Z[jsc46] = 21
Z[jsc47] = 21
Z[jsc48] = 21
Z[jsc49] = 21
Z[jsc50] = 21
Z[jsc51] = 21
Z[jsc52] = 21
Z[jsc53] = 21
Z[jsc54] = 21
Z[jsc55] = 21
Z[jsc56] = 21
Z[jsc57] = 21
Z[jsc58] = 21
Z[jsc59] = 21
Z[jsc60] = 21
Z[jsc61] = 21
Z[jsc62] = 21
Z[jsc63] = 21
Z[jti37] = 22
Z[jti38] = 22
Z[jti39] = 22
Z[jti40] = 22
Z[jti41] = 22
Z[jti42] = 22
Z[jti43] = 22
Z[jti44] = 22
Z[jti45] = 22
Z[jti46] = 22
Z[jti47] = 22
Z[jti48] = 22
Z[jti49] = 22
Z[jti50] = 22
Z[jti51] = 22
Z[jti52] = 22
Z[jti53] = 22
Z[jti54] = 22
Z[jti55] = 22
Z[jti56] = 22
Z[jti57] = 22
Z[jti58] = 22
Z[jti59] = 22
Z[jti60] = 22
Z[jti61] = 22
Z[jti62] = 22
Z[jti63] = 22
Z[jti64] = 22
Z[jti65] = 22
Z[jv39] = 23
Z[jv40] = 23
Z[jv41] = 23
Z[jv42] = 23
Z[jv43] = 23
Z[jv44] = 23
Z[jv45] = 23
Z[jv46] = 23
Z[jv47] = 23
Z[jv48] = 23
Z[jv49] = 23
Z[jv50] = 23
Z[jv51] = 23
Z[jv52] = 23
Z[jv53] = 23
Z[jv54] = 23
Z[jv55] = 23
Z[jv56] = 23
Z[jv57] = 23
Z[jv58] = 23
Z[jv59] = 23
Z[jv60] = 23
Z[jv61] = 23
Z[jv62] = 23
Z[jv63] = 23
Z[jv64] = 23
Z[jv65] = 23
Z[jv66] = 23
Z[jv67] = 23
Z[jcr41] = 24
Z[jcr42] = 24
Z[jcr43] = 24
Z[jcr44] = 24
Z[jcr45] = 24
Z[jcr46] = 24
Z[jcr47] = 24
Z[jcr48] = 24
Z[jcr49] = 24
Z[jcr50] = 24
Z[jcr51] = 24
Z[jcr52] = 24
Z[jcr53] = 24
Z[jcr54] = 24
Z[jcr55] = 24
Z[jcr56] = 24
Z[jcr57] = 24
Z[jcr58] = 24
Z[jcr59] = 24
Z[jcr60] = 24
Z[jcr61] = 24
Z[jcr62] = 24
Z[jcr63] = 24
Z[jcr64] = 24
Z[jcr65] = 24
Z[jcr66] = 24
Z[jcr67] = 24
Z[jcr68] = 24
Z[jcr69] = 24
Z[jcr70] = 24
Z[jmn43] = 25
Z[jmn44] = 25
Z[jmn45] = 25
Z[jmn46] = 25
Z[jmn47] = 25
Z[jmn48] = 25
Z[jmn49] = 25
Z[jmn50] = 25
Z[jmn51] = 25
Z[jmn52] = 25
Z[jmn53] = 25
Z[jmn54] = 25
Z[jmn55] = 25
Z[jmn56] = 25
Z[jmn57] = 25
Z[jmn58] = 25
Z[jmn59] = 25
Z[jmn60] = 25
Z[jmn61] = 25
Z[jmn62] = 25
Z[jmn63] = 25
Z[jmn64] = 25
Z[jmn65] = 25
Z[jmn66] = 25
Z[jmn67] = 25
Z[jmn68] = 25
Z[jmn69] = 25
Z[jmn70] = 25
Z[jmn71] = 25
Z[jmn72] = 25
Z[jmn73] = 25
Z[jfe45] = 26
Z[jfe46] = 26
Z[jfe47] = 26
Z[jfe48] = 26
Z[jfe49] = 26
Z[jfe50] = 26
Z[jfe51] = 26
Z[jfe52] = 26
Z[jfe53] = 26
Z[jfe54] = 26
Z[jfe55] = 26
Z[jfe56] = 26
Z[jfe57] = 26
Z[jfe58] = 26
Z[jfe59] = 26
Z[jfe60] = 26
Z[jfe61] = 26
Z[jfe62] = 26
Z[jfe63] = 26
Z[jfe64] = 26
Z[jfe65] = 26
Z[jfe66] = 26
Z[jfe67] = 26
Z[jfe68] = 26
Z[jfe69] = 26
Z[jfe70] = 26
Z[jfe71] = 26
Z[jfe72] = 26
Z[jfe73] = 26
Z[jfe74] = 26
Z[jfe75] = 26
Z[jfe76] = 26
Z[jco47] = 27
Z[jco48] = 27
Z[jco49] = 27
Z[jco50] = 27
Z[jco51] = 27
Z[jco52] = 27
Z[jco53] = 27
Z[jco54] = 27
Z[jco55] = 27
Z[jco56] = 27
Z[jco57] = 27
Z[jco58] = 27
Z[jco59] = 27
Z[jco60] = 27
Z[jco61] = 27
Z[jco62] = 27
Z[jco63] = 27
Z[jco64] = 27
Z[jco65] = 27
Z[jco66] = 27
Z[jco67] = 27
Z[jco68] = 27
Z[jco69] = 27
Z[jco70] = 27
Z[jco71] = 27
Z[jco72] = 27
Z[jco73] = 27
Z[jco74] = 27
Z[jco75] = 27
Z[jco76] = 27
Z[jco77] = 27
Z[jni49] = 28
Z[jni50] = 28
Z[jni51] = 28
Z[jni52] = 28
Z[jni53] = 28
Z[jni54] = 28
Z[jni55] = 28
Z[jni56] = 28
Z[jni57] = 28
Z[jni58] = 28
Z[jni59] = 28
Z[jni60] = 28
Z[jni61] = 28
Z[jni62] = 28
Z[jni63] = 28
Z[jni64] = 28
Z[jni65] = 28
Z[jni66] = 28
Z[jni67] = 28
Z[jni68] = 28
Z[jni69] = 28
Z[jni70] = 28
Z[jni71] = 28
Z[jni72] = 28
Z[jni73] = 28
Z[jni74] = 28
Z[jni75] = 28
Z[jni76] = 28
Z[jni77] = 28
Z[jni78] = 28
Z[jni79] = 28
Z[jni80] = 28

# masses in ergs
mass = np.zeros((nnuc), dtype=np.float64)

mass[jn] = 0.001505349762871528
mass[jp] = 0.0015040963047307696
mass[jd] = 0.0030058819195053215
mass[jt] = 0.004501206494525079
mass[jhe3] = 0.004501176706825056
mass[jhe4] = 0.0059735574859708365
mass[jhe6] = 0.008982694165199753
mass[jhe8] = 0.01198998897555323
mass[jli5] = 0.007480803851115754
mass[jli6] = 0.008977078184259593
mass[jli7] = 0.010470810414554471
mass[jli8] = 0.01197290355618945
mass[jli9] = 0.013471744944160714
mass[jli11] = 0.016481852872269935
mass[jbe7] = 0.010472191322584432
mass[jbe9] = 0.013449944991877256
mass[jbe10] = 0.014944380281952656
mass[jbe11] = 0.01644892633198164
mass[jbe12] = 0.017949196092465647
mass[jbe14] = 0.020957860155014076
mass[jbe15] = 0.02246610774576412
mass[jbe16] = 0.023970734417321324
mass[jb8] = 0.011976069136782909
mass[jb10] = 0.01494348806343089
mass[jb11] = 0.016430486140895328
mass[jb12] = 0.01793043716756412
mass[jb13] = 0.019427970202074294
mass[jb14] = 0.02093176710635275
mass[jb15] = 0.022432665512882637
mass[jb17] = 0.025441154617742635
mass[jb18] = 0.02694650226878514
mass[jb19] = 0.028451705723930583
mass[jc9] = 0.013478083299120714
mass[jc10] = 0.014949332898320143
mass[jc11] = 0.016433661161513517
mass[jc12] = 0.017909017027273523
mass[jc13] = 0.01940644192976114
mass[jc14] = 0.020898691600487556
mass[jc15] = 0.022402089734217045
mass[jc16] = 0.023900629576524023
mass[jc17] = 0.025404804434270442
mass[jc18] = 0.026903451782629557
mass[jc19] = 0.02840787017122435
mass[jc20] = 0.029908443335897532
mass[jc21] = 0.03141390313930442
mass[jc22] = 0.032919090572683524
mass[jn11] = 0.016455637577531438
mass[jn12] = 0.017936795725971476
mass[jn13] = 0.01940999951603316
mass[jn14] = 0.020898440897976135
mass[jn15] = 0.022386433805845516
mass[jn16] = 0.023887795981468018
mass[jn17] = 0.025383716585413735
mass[jn18] = 0.026884534883111922
mass[jn19] = 0.028381347739225113
mass[jn20] = 0.029883241097444713
mass[jn21] = 0.03138120271420448
mass[jn22] = 0.032884083013230626
mass[jn23] = 0.03438444789494139
mass[jn24] = 0.035893240225747
mass[jo12] = 0.01796030750785776
mass[jo13] = 0.019438469425774554
mass[jo14] = 0.020906683078094165
mass[jo15] = 0.02239084645968795
mass[jo16] = 0.023871099855618198
mass[jo17] = 0.025369811672200496
mass[jo18] = 0.026862271330925704
mass[jo19] = 0.028361283521019864
mass[jo20] = 0.029854443895060524
mass[jo21] = 0.031353696545751965
mass[jo22] = 0.0328480660824983
mass[jo23] = 0.03434903979132999
mass[jo24] = 0.03584767432227604
mass[jo25] = 0.03735423962756038
mass[jo26] = 0.038858401667893734
mass[jo27] = 0.040366857541606196
mass[jo28] = 0.041871147756070266
mass[jf14] = 0.02094505876370841
mass[jf15] = 0.02241281454438738
mass[jf16] = 0.023895792605265975
mass[jf17] = 0.025374234423440733
mass[jf18] = 0.026864924401329426
mass[jf19] = 0.028353560476732827
mass[jf20] = 0.02984833373331198
mass[jf21] = 0.03134070353412088
mass[jf22] = 0.03283767276267355
mass[jf23] = 0.034330887130066774
mass[jf24] = 0.0358301144663674
mass[jf25] = 0.037328604801416386
mass[jf26] = 0.038832782863516074
mass[jf27] = 0.04033555101017784
mass[jf28] = 0.04184121909654715
mass[jf29] = 0.043344451874432775
mass[jf30] = 0.04485098513618444
mass[jf31] = 0.04635602837366649
mass[jne16] = 0.023917120780617786
mass[jne17] = 0.025397544170853475
mass[jne18] = 0.026872045275379234
mass[jne19] = 0.02835875072008801
mass[jne20] = 0.029837079292893483
mass[jne21] = 0.03133159647374143
mass[jne22] = 0.032820340870865106
mass[jne23] = 0.03431735827046045
mass[jne24] = 0.035808498540092125
mass[jne25] = 0.037307190108526345
mass[jne26] = 0.03880364087272025
mass[jne27] = 0.04030658365663512
mass[jne28] = 0.041805810992935746
mass[jne29] = 0.04330960453264327
mass[jne30] = 0.044809841240223316
mass[jne31] = 0.04631491652123804
mass[jne32] = 0.04781665927485406
mass[jne33] = 0.0493237052331286
mass[jne34] = 0.05082687392394886
mass[jna19] = 0.02837665816821739
mass[jna20] = 0.02985933742315375
mass[jna21] = 0.0313372792660881
mass[jna22] = 0.03282489638134515
mass[jna23] = 0.03431034746033777
mass[jna24] = 0.03580454709025751
mass[jna25] = 0.03729545929164752
mass[jna26] = 0.03879187769187342
mass[jna27] = 0.040286447500699006
mass[jna28] = 0.04178612344645716
mass[jna29] = 0.0432844183159568
mass[jna30] = 0.04478612101515695
mass[jna31] = 0.04628458090884989
mass[jna32] = 0.047787243311853814
mass[jna33] = 0.049287896585358704
mass[jna34] = 0.050792971866373424
mass[jna35] = 0.05229524333827865
mass[jna36] = 0.05380059098932116
mass[jna37] = 0.055304592811991106
mass[jna38] = 0.056811078008443754
mass[jna39] = 0.05831642565948626
mass[jmg19] = 0.02840695693054297
mass[jmg20] = 0.029876364074678592
mass[jmg21] = 0.03135824977152814
mass[jmg22] = 0.032832557028702955
mass[jmg23] = 0.03431684618276469
mass[jmg24] = 0.03579571000144743
mass[jmg25] = 0.03728931497629966
mass[jmg26] = 0.03877689166223153
mass[jmg27] = 0.04027191801769768
mass[jmg28] = 0.0417636417840377
mass[jmg29] = 0.043263121543267016
mass[jmg30] = 0.044758312996626595
mass[jmg31] = 0.04625995865833858
mass[jmg32] = 0.04775605053496647
mass[jmg33] = 0.04925774826741906
mass[jmg34] = 0.050755549826733096
mass[jmg35] = 0.05225969103877019
mass[jmg36] = 0.053759703441621474
mass[jmg37] = 0.05526466657027183
mass[jmg38] = 0.056766473410953186
mass[jmg39] = 0.058272846455041466
mass[jmg40] = 0.05977611127645977
mass[jmg41] = 0.06128222797228659
mass[jal21] = 0.03138418276274372
mass[jal22] = 0.032862357498073584
mass[jal23] = 0.03433642761708481
mass[jal24] = 0.03581795585230553
mass[jal25] = 0.03729616718134972
mass[jal26] = 0.03878330742475342
mass[jal27] = 0.040267735904095256
mass[jal28] = 0.041760708567121475
mass[jal29] = 0.04325095237086113
mass[jal30] = 0.04474712547784436
mass[jal31] = 0.046241006991587986
mass[jal32] = 0.04773959618093528
mass[jal33] = 0.04923618313014308
mass[jal34] = 0.05073741222593022
mass[jal35] = 0.05223427410864842
mass[jal36] = 0.053736584032792856
mass[jal37] = 0.055235186520206224
mass[jal38] = 0.0567382751021948
mass[jal39] = 0.05823873611450359
mass[jal40] = 0.05974289815483696
mass[jal41] = 0.06124456079962125
mass[jal42] = 0.06274883499231898
mass[jal43] = 0.06425131474718662
mass[jsi22] = 0.03288709510530254
mass[jsi23] = 0.03436398809932521
mass[jsi24] = 0.035835249442479365
mass[jsi25] = 0.037316583670131485
mass[jsi26] = 0.0387914290824159
mass[jsi27] = 0.04027544613881988
mass[jsi28] = 0.041753271139658626
mass[jsi29] = 0.04324504469459885
mass[jsi30] = 0.044733396647367994
mass[jsi31] = 0.04622819223812919
mass[jsi32] = 0.04771880202707735
mass[jsi33] = 0.049216929292879304
mass[jsi34] = 0.05071018467599437
mass[jsi35] = 0.05221157767445117
mass[jsi36] = 0.053707120004493604
mass[jsi37] = 0.05520894286694131
mass[jsi38] = 0.05670520617646904
mass[jsi39] = 0.05820802238842983
mass[jsi40] = 0.059705807765759844
mass[jsi41] = 0.06121029024142
mass[jsi42] = 0.06270854024997388
mass[jsi43] = 0.06421295863856867
mass[jsi44] = 0.06571335556381211
mass[jsi45] = 0.06721823858363075
mass[jp24] = 0.035872540103635726
mass[jp25] = 0.037342800086393624
mass[jp26] = 0.03882044610343427
mass[jp27] = 0.040294232476963614
mass[jp28] = 0.04177625419860938
mass[jp29] = 0.0432529631025368
mass[jp30] = 0.0447401772223051
mass[jp31] = 0.04622580258463001
mass[jp32] = 0.04771843802856788
mass[jp33] = 0.04920759965812187
mass[jp34] = 0.050702883557073225
mass[jp35] = 0.052194806409881785
mass[jp36] = 0.05369460540280542
mass[jp37] = 0.055189027811380686
mass[jp38] = 0.05668846343064373
mass[jp39] = 0.05818384554302276
mass[jp40] = 0.05968368170644431
mass[jp41] = 0.06118116267021387
mass[jp42] = 0.06268330596798838
mass[jp43] = 0.06418205265129881
mass[jp44] = 0.0656841959490733
mass[jp45] = 0.06718438459135434
mass[jp46] = 0.0686878256522024
mass[jp47] = 0.0701898087323135
mass[js26] = 0.03884721847498842
mass[js27] = 0.04032331038069408
mass[js28] = 0.04179422725587193
mass[js29] = 0.043275167348072074
mass[js30] = 0.04475001716634224
mass[js31] = 0.04623445115717168
mass[js32] = 0.04771569725373347
mass[js33] = 0.04920720158403909
mass[js34] = 0.05069425905627418
mass[js35] = 0.05218841627257298
mass[js36] = 0.053677921713210855
mass[js37] = 0.05517637633574267
mass[js38] = 0.05666885118646694
mass[js39] = 0.0581671989277955
mass[js40] = 0.059660132914277776
mass[js41] = 0.06115868573421549
mass[js42] = 0.06265330088463983
mass[js43] = 0.06415443913701183
mass[js44] = 0.06565164933293023
mass[js45] = 0.06715346258231815
mass[js46] = 0.06865225733092759
mass[js47] = 0.07015518569525275
mass[js48] = 0.07165591907758934
mass[js49] = 0.07316115457626746
mass[jcl28] = 0.04183299993041473
mass[jcl29] = 0.04330258699898635
mass[jcl30] = 0.04478003274394775
mass[jcl31] = 0.04625368934116973
mass[jcl32] = 0.047736014194634656
mass[jcl33] = 0.04921614582850528
mass[jcl34] = 0.05070305756947744
mass[jcl35] = 0.05218814819637857
mass[jcl36] = 0.05367975160720986
mass[jcl37] = 0.05516858155415706
mass[jcl38] = 0.05666414540143169
mass[jcl39] = 0.058156560154510414
mass[jcl40] = 0.059652567436212015
mass[jcl41] = 0.061145386065976644
mass[jcl42] = 0.0626417775496351
mass[jcl43] = 0.06413526909358601
mass[jcl44] = 0.06563358318920526
mass[jcl45] = 0.06712955810693887
mass[jcl46] = 0.06862923405269701
mass[jcl47] = 0.07012830117133423
mass[jcl48] = 0.07162921079310057
mass[jcl49] = 0.07312967180540937
mass[jcl50] = 0.07463324104038813
mass[jcl51] = 0.07613621747001233
mass[jcl52] = 0.07764156512105483
mass[jar29] = 0.04334095912937065
mass[jar30] = 0.04480790260649618
mass[jar31] = 0.046283113315053144
mass[jar32] = 0.0477538533099306
mass[jar33] = 0.04923476151881573
mass[jar34] = 0.05071276964379744
mass[jar35] = 0.05219770715067765
mass[jar36] = 0.05367861481161837
mass[jar37] = 0.055169885517654185
mass[jar38] = 0.056656267963553525
mass[jar39] = 0.05815104578297151
mass[jar40] = 0.059640583315207364
mass[jar41] = 0.06113616153400639
mass[jar42] = 0.06262640786918514
mass[jar43] = 0.06412269200700911
mass[jar44] = 0.0656140473688539
mass[jar45] = 0.06711111577214021
mass[jar46] = 0.06860353305665802
mass[jar47] = 0.0701030071281603
mass[jar48] = 0.07160025145044101
mass[jar49] = 0.07310115306132417
mass[jar50] = 0.07459970748343851
mass[jar51] = 0.07610292423955779
mass[jar52] = 0.07760352944776366
mass[jar53] = 0.07910903731646958
mass[jar54] = 0.08061069996125388
mass[jk31] = 0.04631985122527077
mass[jk32] = 0.04779261060357771
mass[jk33] = 0.049261877236822536
mass[jk34] = 0.05074026025511483
mass[jk35] = 0.05221673203690041
mass[jk36] = 0.05369914565095086
mass[jk37] = 0.05517973486646816
mass[jk38] = 0.05666574334831938
mass[jk39] = 0.05815014024074886
mass[jk40] = 0.05964299362973556
mass[jk41] = 0.06113216883132782
mass[jk42] = 0.06262544811731607
mass[jk43] = 0.06411537742980425
mass[jk44] = 0.0656090674834401
mass[jk45] = 0.06710014919351581
mass[jk46] = 0.06859449261478301
mass[jk47] = 0.07008643309153453
mass[jk48] = 0.07158434263755371
mass[jk49] = 0.07308104334130251
mass[jk50] = 0.07457968347986679
mass[jk51] = 0.07607724935899796
mass[jk52] = 0.07757827914401183
mass[jk53] = 0.07907845176452652
mass[jk54] = 0.08058232541306573
mass[jk55] = 0.08208374773135495
mass[jk56] = 0.08358819816348241
mass[jk57] = 0.08509046963538765
mass[jk58] = 0.08659538469873897
mass[jk59] = 0.08809872962898897
mass[jca33] = 0.04929951236595519
mass[jca34] = 0.05076607132068857
mass[jca35] = 0.0522429482929449
mass[jca36] = 0.05371671704253126
mass[jca37] = 0.05519842281494481
mass[jca38] = 0.05667654563975173
mass[jca39] = 0.05816059363418651
mass[jca40] = 0.05964089333318169
mass[jca41] = 0.0611328443714816
mass[jca42] = 0.06261980002811529
mass[jca43] = 0.0641124398870111
mass[jca44] = 0.06559995558448722
mass[jca45] = 0.06709342549905357
mass[jca46] = 0.06858211467876173
mass[jca47] = 0.07007580633457422
mass[jca48] = 0.07156521205894274
mass[jca49] = 0.073062316299716
mass[jca50] = 0.07455747538910759
mass[jca51] = 0.07605511160379298
mass[jca52] = 0.07755083978632495
mass[jca53] = 0.07905107056585146
mass[jca54] = 0.08055026585861941
mass[jca55] = 0.08205311411411287
mass[jca56] = 0.08355376738761776
mass[jca57] = 0.08505732060083018
mass[jca58] = 0.08655779763490533
mass[jca59] = 0.08806197569700501
mass[jca60] = 0.08956270907934161
mass[jca61] = 0.09106796059978606
mass[jsc35] = 0.052278051982995836
mass[jsc36] = 0.05375292623445966
mass[jsc37] = 0.055225525395103205
mass[jsc38] = 0.056705078002338316
mass[jsc39] = 0.058181597689205264
mass[jsc40] = 0.05966384131231483
mass[jsc41] = 0.06114325138991658
mass[jsc42] = 0.06263009607979661
mass[jsc43] = 0.06411599795281459
mass[jsc44] = 0.06560580785507823
mass[jsc45] = 0.06709300877291106
mass[jsc46] = 0.06858432247816337
mass[jsc47] = 0.07007261463850162
mass[jsc48] = 0.07156476484017454
mass[jsc49] = 0.07305388500539725
mass[jsc50] = 0.07454954797934021
mass[jsc51] = 0.0760440275856213
mass[jsc52] = 0.07754081384560237
mass[jsc53] = 0.07903604214902453
mass[jsc54] = 0.08053540086380914
mass[jsc55] = 0.08203358358094441
mass[jsc56] = 0.08353452524624341
mass[jsc57] = 0.08503357634311431
mass[jsc58] = 0.08653544727086103
mass[jsc59] = 0.08803531547781525
mass[jsc60] = 0.0895377952326829
mass[jsc61] = 0.09103830431029074
mass[jsc62] = 0.09254163321877439
mass[jsc63] = 0.09404327984179237
mass[jti37] = 0.055259795953304464
mass[jti38] = 0.0567301040013614
mass[jti39] = 0.05820831078022393
mass[jti40] = 0.059682319856305406
mass[jti41] = 0.06116399054105066
mass[jti42] = 0.06264133799247557
mass[jti43] = 0.0641270082708611
mass[jti44] = 0.06560623627711017
mass[jti45] = 0.06709631246113038
mass[jti46] = 0.06858053065478899
mass[jti47] = 0.07007165203475815
mass[jti48] = 0.07155837383769034
mass[jti49] = 0.07305067807262486
mass[jti50] = 0.07453850133994942
mass[jti51] = 0.07603364131537374
mass[jti52] = 0.07752646843667453
mass[jti53] = 0.0790230462534755
mass[jti54] = 0.08051728665478515
mass[jti55] = 0.08201597245538347
mass[jti56] = 0.08351225499103081
mass[jti57] = 0.08501271600333962
mass[jti58] = 0.08651070966363207
mass[jti59] = 0.08801120271947355
mass[jti60] = 0.08950967703275621
mass[jti61] = 0.09101127559047514
mass[jti62] = 0.09251037475264505
mass[jti63] = 0.09401295063811074
mass[jti64] = 0.09551238625737378
mass[jti65] = 0.09701552290466137
mass[jv39] = 0.05824046646526833
mass[jv40] = 0.05971670256687105
mass[jv41] = 0.06118963818460774
mass[jv42] = 0.06266935100950624
mass[jv43] = 0.06414526667578216
mass[jv44] = 0.0656282511453673
mass[jv45] = 0.06710772620725332
mass[jv46] = 0.0685918297972173
mass[jv47] = 0.07007634727747114
mass[jv48] = 0.07156480649676702
mass[jv49] = 0.07305164227854496
mass[jv50] = 0.07454203995532856
mass[jv51] = 0.07602968376284833
mass[jv52] = 0.07752331963087043
mass[jv53] = 0.07901508247429856
mass[jv54] = 0.08051063121304751
mass[jv55] = 0.08200428778119172
mass[jv56] = 0.08350142427698498
mass[jv57] = 0.08499663014993426
mass[jv58] = 0.08649547296384273
mass[jv59] = 0.08799240918755673
mass[jv60] = 0.08949206911154854
mass[jv61] = 0.09098914953115961
mass[jv62] = 0.09248953043463672
mass[jv63] = 0.09398750807316282
mass[jv64] = 0.09548860995612522
mass[jv65] = 0.09698777320536049
mass[jv66] = 0.09848949993721016
mass[jv67] = 0.09998922394826734
mass[jcr41] = 0.061221841934951136
mass[jcr42] = 0.06269287096249337
mass[jcr43] = 0.06417082139309448
mass[jcr44] = 0.0656448945562413
mass[jcr45] = 0.06712755538614636
mass[jcr46] = 0.06860401258812458
mass[jcr47] = 0.07008827399248702
mass[jcr48] = 0.07156746130344957
mass[jcr49] = 0.07305585568265706
mass[jcr50] = 0.07454037670372128
mass[jcr51] = 0.07603088924054774
mass[jcr52] = 0.07751694860752885
mass[jcr53] = 0.07900957800421124
mass[jcr54] = 0.08049935608724694
mass[jcr55] = 0.0819946982413407
mass[jcr56] = 0.08348683629851474
mass[jcr57] = 0.08498367655184837
mass[jcr58] = 0.08647694891803574
mass[jcr59] = 0.0879755768800576
mass[jcr60] = 0.08946992943373161
mass[jcr61] = 0.09096941632264695
mass[jcr62] = 0.09246446758555106
mass[jcr63] = 0.09396437264256786
mass[jcr64] = 0.09546086025682435
mass[jcr65] = 0.0969618179438897
mass[jcr66] = 0.09845931492942561
mass[jcr67] = 0.09996113779187331
mass[jcr68] = 0.10145929166982914
mass[jcr69] = 0.10296141894583731
mass[jcr70] = 0.10446022971621312
mass[jmn43] = 0.06420180748919603
mass[jmn44] = 0.0656783480043592
mass[jmn45] = 0.06715083501263837
mass[jmn46] = 0.06863133290408754
mass[jmn47] = 0.07010748889685857
mass[jmn48] = 0.07158912914024777
mass[jmn49] = 0.0730682124699468
mass[jmn50] = 0.07455260847316825
mass[jmn51] = 0.07603602823812308
mass[jmn52] = 0.07752449184738293
mass[jmn53] = 0.07901053501635827
mass[jmn54] = 0.08050156257286374
mass[jmn55] = 0.08199052902526018
mass[jmn56] = 0.08348423024606717
mass[jmn57] = 0.0849757276729141
mass[jmn58] = 0.08647080328890305
mass[jmn59] = 0.08796370571250563
mass[jmn60] = 0.08946022120463555
mass[jmn61] = 0.09095460323835963
mass[jmn62] = 0.09245217728859163
mass[jmn63] = 0.09394721813734763
mass[jmn64] = 0.09544588150747307
mass[jmn65] = 0.09694153919423316
mass[jmn66] = 0.09844071365870487
mass[jmn67] = 0.09993821064424077
mass[jmn68] = 0.10143809487296133
mass[jmn69] = 0.1029362167073845
mass[jmn70] = 0.10443650148026355
mass[jmn71] = 0.10593505590237791
mass[jmn72] = 0.10743620585063934
mass[jmn73] = 0.10893578566579944
mass[jfe45] = 0.06718190121757164
mass[jfe46] = 0.06865317057160897
mass[jfe47] = 0.07013222650408754
mass[jfe48] = 0.07160721290791573
mass[jfe49] = 0.07308883072083208
mass[jfe50] = 0.07456566763867255
mass[jfe51] = 0.0760489321687333
mass[jfe52] = 0.07752830389022643
mass[jfe53] = 0.079016531643064
mass[jfe54] = 0.08050044681705582
mass[jfe55] = 0.08199089935236736
mass[jfe56] = 0.083478309418338
mass[jfe57] = 0.0849714086533183
mass[jfe58] = 0.08646066519581609
mass[jfe59] = 0.08795547100525987
mass[jfe60] = 0.08944669066274376
mass[jfe61] = 0.09094310217361014
mass[jfe62] = 0.09243558819150555
mass[jfe63] = 0.09393320069397676
mass[jfe64] = 0.09542668582922112
mass[jfe65] = 0.09692511528155802
mass[jfe66] = 0.09841937587029324
mass[jfe67] = 0.09991877944602362
mass[jfe68] = 0.10141409426698401
mass[jfe69] = 0.10291404258276994
mass[jfe70] = 0.1044101616964006
mass[jfe71] = 0.10591052657811137
mass[jfe72] = 0.10740723849709662
mass[jfe73] = 0.1089080840317976
mass[jfe74] = 0.11040583736559495
mass[jfe75] = 0.1119078044239397
mass[jfe76] = 0.11340680745551156
mass[jco47] = 0.07016066513934104
mass[jco48] = 0.0716388398746709
mass[jco49] = 0.07311281690721969
mass[jco50] = 0.07459272199331426
mass[jco51] = 0.07606951885673889
mass[jco52] = 0.07755071529720049
mass[jco53] = 0.07902981064322426
mass[jco54] = 0.08051365596231484
mass[jco55] = 0.08199642910480195
mass[jco56] = 0.08348562601428541
mass[jco57] = 0.08497274858568084
mass[jco58] = 0.08646436301948736
mass[jco59] = 0.087952963919263
mass[jco60] = 0.08944631030601086
mass[jco61] = 0.09093672919561306
mass[jco62] = 0.09243150921001304
mass[jco63] = 0.09392324156401981
mass[jco64] = 0.09541896013349198
mass[jco65] = 0.09691235041987961
mass[jco66] = 0.09840921646825705
mass[jco67] = 0.09990337611986433
mass[jco68] = 0.10140168861330695
mass[jco69] = 0.10289611422623549
mass[jco70] = 0.10439472472453201
mass[jco71] = 0.1058905955007844
mass[jco72] = 0.10738953444529094
mass[jco73] = 0.10888568560245428
mass[jco74] = 0.11038520133054902
mass[jco75] = 0.11188239390252445
mass[jco76] = 0.1133826626536372
mass[jco77] = 0.11488108890162081
mass[jni49] = 0.07314215276138823
mass[jni50] = 0.07461536074915269
mass[jni51] = 0.07609465700812636
mass[jni52] = 0.07756959534665554
mass[jni53] = 0.07905068444128266
mass[jni54] = 0.0805276463289006
mass[jni55] = 0.08201035842845794
mass[jni56] = 0.08348904329682807
mass[jni57] = 0.08497797440520796
mass[jni58] = 0.08646375162888383
mass[jni59] = 0.08795468305479126
mass[jni60] = 0.0894417876818084
mass[jni61] = 0.09093460823418498
mass[jni62] = 0.09242298178509624
mass[jni63] = 0.0939173761555804
mass[jni64] = 0.09540725302882734
mass[jni65] = 0.09690283252936768
mass[jni66] = 0.09839383989844756
mass[jni67] = 0.09988988467108241
mass[jni68] = 0.10138274960375177
mass[jni69] = 0.10288075095449205
mass[jni70] = 0.10437439486544087
mass[jni71] = 0.10587291355901628
mass[jni72] = 0.10736722237326816
mass[jni73] = 0.10886623806203544
mass[jni74] = 0.11036091233277756
mass[jni75] = 0.11186047612617135
mass[jni76] = 0.11335617867387715
mass[jni77] = 0.11485635129439187
mass[jni78] = 0.11635272675628397
mass[jni79] = 0.11785591146887056
mass[jni80] = 0.11935621226351596

names = []
names.append("n")
names.append("H1")
names.append("H2")
names.append("H3")
names.append("He3")
names.append("He4")
names.append("He6")
names.append("He8")
names.append("Li5")
names.append("Li6")
names.append("Li7")
names.append("Li8")
names.append("Li9")
names.append("Li11")
names.append("Be7")
names.append("Be9")
names.append("Be10")
names.append("Be11")
names.append("Be12")
names.append("Be14")
names.append("Be15")
names.append("Be16")
names.append("B8")
names.append("B10")
names.append("B11")
names.append("B12")
names.append("B13")
names.append("B14")
names.append("B15")
names.append("B17")
names.append("B18")
names.append("B19")
names.append("C9")
names.append("C10")
names.append("C11")
names.append("C12")
names.append("C13")
names.append("C14")
names.append("C15")
names.append("C16")
names.append("C17")
names.append("C18")
names.append("C19")
names.append("C20")
names.append("C21")
names.append("C22")
names.append("N11")
names.append("N12")
names.append("N13")
names.append("N14")
names.append("N15")
names.append("N16")
names.append("N17")
names.append("N18")
names.append("N19")
names.append("N20")
names.append("N21")
names.append("N22")
names.append("N23")
names.append("N24")
names.append("O12")
names.append("O13")
names.append("O14")
names.append("O15")
names.append("O16")
names.append("O17")
names.append("O18")
names.append("O19")
names.append("O20")
names.append("O21")
names.append("O22")
names.append("O23")
names.append("O24")
names.append("O25")
names.append("O26")
names.append("O27")
names.append("O28")
names.append("F14")
names.append("F15")
names.append("F16")
names.append("F17")
names.append("F18")
names.append("F19")
names.append("F20")
names.append("F21")
names.append("F22")
names.append("F23")
names.append("F24")
names.append("F25")
names.append("F26")
names.append("F27")
names.append("F28")
names.append("F29")
names.append("F30")
names.append("F31")
names.append("Ne16")
names.append("Ne17")
names.append("Ne18")
names.append("Ne19")
names.append("Ne20")
names.append("Ne21")
names.append("Ne22")
names.append("Ne23")
names.append("Ne24")
names.append("Ne25")
names.append("Ne26")
names.append("Ne27")
names.append("Ne28")
names.append("Ne29")
names.append("Ne30")
names.append("Ne31")
names.append("Ne32")
names.append("Ne33")
names.append("Ne34")
names.append("Na19")
names.append("Na20")
names.append("Na21")
names.append("Na22")
names.append("Na23")
names.append("Na24")
names.append("Na25")
names.append("Na26")
names.append("Na27")
names.append("Na28")
names.append("Na29")
names.append("Na30")
names.append("Na31")
names.append("Na32")
names.append("Na33")
names.append("Na34")
names.append("Na35")
names.append("Na36")
names.append("Na37")
names.append("Na38")
names.append("Na39")
names.append("Mg19")
names.append("Mg20")
names.append("Mg21")
names.append("Mg22")
names.append("Mg23")
names.append("Mg24")
names.append("Mg25")
names.append("Mg26")
names.append("Mg27")
names.append("Mg28")
names.append("Mg29")
names.append("Mg30")
names.append("Mg31")
names.append("Mg32")
names.append("Mg33")
names.append("Mg34")
names.append("Mg35")
names.append("Mg36")
names.append("Mg37")
names.append("Mg38")
names.append("Mg39")
names.append("Mg40")
names.append("Mg41")
names.append("Al21")
names.append("Al22")
names.append("Al23")
names.append("Al24")
names.append("Al25")
names.append("Al26")
names.append("Al27")
names.append("Al28")
names.append("Al29")
names.append("Al30")
names.append("Al31")
names.append("Al32")
names.append("Al33")
names.append("Al34")
names.append("Al35")
names.append("Al36")
names.append("Al37")
names.append("Al38")
names.append("Al39")
names.append("Al40")
names.append("Al41")
names.append("Al42")
names.append("Al43")
names.append("Si22")
names.append("Si23")
names.append("Si24")
names.append("Si25")
names.append("Si26")
names.append("Si27")
names.append("Si28")
names.append("Si29")
names.append("Si30")
names.append("Si31")
names.append("Si32")
names.append("Si33")
names.append("Si34")
names.append("Si35")
names.append("Si36")
names.append("Si37")
names.append("Si38")
names.append("Si39")
names.append("Si40")
names.append("Si41")
names.append("Si42")
names.append("Si43")
names.append("Si44")
names.append("Si45")
names.append("P24")
names.append("P25")
names.append("P26")
names.append("P27")
names.append("P28")
names.append("P29")
names.append("P30")
names.append("P31")
names.append("P32")
names.append("P33")
names.append("P34")
names.append("P35")
names.append("P36")
names.append("P37")
names.append("P38")
names.append("P39")
names.append("P40")
names.append("P41")
names.append("P42")
names.append("P43")
names.append("P44")
names.append("P45")
names.append("P46")
names.append("P47")
names.append("S26")
names.append("S27")
names.append("S28")
names.append("S29")
names.append("S30")
names.append("S31")
names.append("S32")
names.append("S33")
names.append("S34")
names.append("S35")
names.append("S36")
names.append("S37")
names.append("S38")
names.append("S39")
names.append("S40")
names.append("S41")
names.append("S42")
names.append("S43")
names.append("S44")
names.append("S45")
names.append("S46")
names.append("S47")
names.append("S48")
names.append("S49")
names.append("Cl28")
names.append("Cl29")
names.append("Cl30")
names.append("Cl31")
names.append("Cl32")
names.append("Cl33")
names.append("Cl34")
names.append("Cl35")
names.append("Cl36")
names.append("Cl37")
names.append("Cl38")
names.append("Cl39")
names.append("Cl40")
names.append("Cl41")
names.append("Cl42")
names.append("Cl43")
names.append("Cl44")
names.append("Cl45")
names.append("Cl46")
names.append("Cl47")
names.append("Cl48")
names.append("Cl49")
names.append("Cl50")
names.append("Cl51")
names.append("Cl52")
names.append("Ar29")
names.append("Ar30")
names.append("Ar31")
names.append("Ar32")
names.append("Ar33")
names.append("Ar34")
names.append("Ar35")
names.append("Ar36")
names.append("Ar37")
names.append("Ar38")
names.append("Ar39")
names.append("Ar40")
names.append("Ar41")
names.append("Ar42")
names.append("Ar43")
names.append("Ar44")
names.append("Ar45")
names.append("Ar46")
names.append("Ar47")
names.append("Ar48")
names.append("Ar49")
names.append("Ar50")
names.append("Ar51")
names.append("Ar52")
names.append("Ar53")
names.append("Ar54")
names.append("K31")
names.append("K32")
names.append("K33")
names.append("K34")
names.append("K35")
names.append("K36")
names.append("K37")
names.append("K38")
names.append("K39")
names.append("K40")
names.append("K41")
names.append("K42")
names.append("K43")
names.append("K44")
names.append("K45")
names.append("K46")
names.append("K47")
names.append("K48")
names.append("K49")
names.append("K50")
names.append("K51")
names.append("K52")
names.append("K53")
names.append("K54")
names.append("K55")
names.append("K56")
names.append("K57")
names.append("K58")
names.append("K59")
names.append("Ca33")
names.append("Ca34")
names.append("Ca35")
names.append("Ca36")
names.append("Ca37")
names.append("Ca38")
names.append("Ca39")
names.append("Ca40")
names.append("Ca41")
names.append("Ca42")
names.append("Ca43")
names.append("Ca44")
names.append("Ca45")
names.append("Ca46")
names.append("Ca47")
names.append("Ca48")
names.append("Ca49")
names.append("Ca50")
names.append("Ca51")
names.append("Ca52")
names.append("Ca53")
names.append("Ca54")
names.append("Ca55")
names.append("Ca56")
names.append("Ca57")
names.append("Ca58")
names.append("Ca59")
names.append("Ca60")
names.append("Ca61")
names.append("Sc35")
names.append("Sc36")
names.append("Sc37")
names.append("Sc38")
names.append("Sc39")
names.append("Sc40")
names.append("Sc41")
names.append("Sc42")
names.append("Sc43")
names.append("Sc44")
names.append("Sc45")
names.append("Sc46")
names.append("Sc47")
names.append("Sc48")
names.append("Sc49")
names.append("Sc50")
names.append("Sc51")
names.append("Sc52")
names.append("Sc53")
names.append("Sc54")
names.append("Sc55")
names.append("Sc56")
names.append("Sc57")
names.append("Sc58")
names.append("Sc59")
names.append("Sc60")
names.append("Sc61")
names.append("Sc62")
names.append("Sc63")
names.append("Ti37")
names.append("Ti38")
names.append("Ti39")
names.append("Ti40")
names.append("Ti41")
names.append("Ti42")
names.append("Ti43")
names.append("Ti44")
names.append("Ti45")
names.append("Ti46")
names.append("Ti47")
names.append("Ti48")
names.append("Ti49")
names.append("Ti50")
names.append("Ti51")
names.append("Ti52")
names.append("Ti53")
names.append("Ti54")
names.append("Ti55")
names.append("Ti56")
names.append("Ti57")
names.append("Ti58")
names.append("Ti59")
names.append("Ti60")
names.append("Ti61")
names.append("Ti62")
names.append("Ti63")
names.append("Ti64")
names.append("Ti65")
names.append("V39")
names.append("V40")
names.append("V41")
names.append("V42")
names.append("V43")
names.append("V44")
names.append("V45")
names.append("V46")
names.append("V47")
names.append("V48")
names.append("V49")
names.append("V50")
names.append("V51")
names.append("V52")
names.append("V53")
names.append("V54")
names.append("V55")
names.append("V56")
names.append("V57")
names.append("V58")
names.append("V59")
names.append("V60")
names.append("V61")
names.append("V62")
names.append("V63")
names.append("V64")
names.append("V65")
names.append("V66")
names.append("V67")
names.append("Cr41")
names.append("Cr42")
names.append("Cr43")
names.append("Cr44")
names.append("Cr45")
names.append("Cr46")
names.append("Cr47")
names.append("Cr48")
names.append("Cr49")
names.append("Cr50")
names.append("Cr51")
names.append("Cr52")
names.append("Cr53")
names.append("Cr54")
names.append("Cr55")
names.append("Cr56")
names.append("Cr57")
names.append("Cr58")
names.append("Cr59")
names.append("Cr60")
names.append("Cr61")
names.append("Cr62")
names.append("Cr63")
names.append("Cr64")
names.append("Cr65")
names.append("Cr66")
names.append("Cr67")
names.append("Cr68")
names.append("Cr69")
names.append("Cr70")
names.append("Mn43")
names.append("Mn44")
names.append("Mn45")
names.append("Mn46")
names.append("Mn47")
names.append("Mn48")
names.append("Mn49")
names.append("Mn50")
names.append("Mn51")
names.append("Mn52")
names.append("Mn53")
names.append("Mn54")
names.append("Mn55")
names.append("Mn56")
names.append("Mn57")
names.append("Mn58")
names.append("Mn59")
names.append("Mn60")
names.append("Mn61")
names.append("Mn62")
names.append("Mn63")
names.append("Mn64")
names.append("Mn65")
names.append("Mn66")
names.append("Mn67")
names.append("Mn68")
names.append("Mn69")
names.append("Mn70")
names.append("Mn71")
names.append("Mn72")
names.append("Mn73")
names.append("Fe45")
names.append("Fe46")
names.append("Fe47")
names.append("Fe48")
names.append("Fe49")
names.append("Fe50")
names.append("Fe51")
names.append("Fe52")
names.append("Fe53")
names.append("Fe54")
names.append("Fe55")
names.append("Fe56")
names.append("Fe57")
names.append("Fe58")
names.append("Fe59")
names.append("Fe60")
names.append("Fe61")
names.append("Fe62")
names.append("Fe63")
names.append("Fe64")
names.append("Fe65")
names.append("Fe66")
names.append("Fe67")
names.append("Fe68")
names.append("Fe69")
names.append("Fe70")
names.append("Fe71")
names.append("Fe72")
names.append("Fe73")
names.append("Fe74")
names.append("Fe75")
names.append("Fe76")
names.append("Co47")
names.append("Co48")
names.append("Co49")
names.append("Co50")
names.append("Co51")
names.append("Co52")
names.append("Co53")
names.append("Co54")
names.append("Co55")
names.append("Co56")
names.append("Co57")
names.append("Co58")
names.append("Co59")
names.append("Co60")
names.append("Co61")
names.append("Co62")
names.append("Co63")
names.append("Co64")
names.append("Co65")
names.append("Co66")
names.append("Co67")
names.append("Co68")
names.append("Co69")
names.append("Co70")
names.append("Co71")
names.append("Co72")
names.append("Co73")
names.append("Co74")
names.append("Co75")
names.append("Co76")
names.append("Co77")
names.append("Ni49")
names.append("Ni50")
names.append("Ni51")
names.append("Ni52")
names.append("Ni53")
names.append("Ni54")
names.append("Ni55")
names.append("Ni56")
names.append("Ni57")
names.append("Ni58")
names.append("Ni59")
names.append("Ni60")
names.append("Ni61")
names.append("Ni62")
names.append("Ni63")
names.append("Ni64")
names.append("Ni65")
names.append("Ni66")
names.append("Ni67")
names.append("Ni68")
names.append("Ni69")
names.append("Ni70")
names.append("Ni71")
names.append("Ni72")
names.append("Ni73")
names.append("Ni74")
names.append("Ni75")
names.append("Ni76")
names.append("Ni77")
names.append("Ni78")
names.append("Ni79")
names.append("Ni80")

def to_composition(Y):
    """Convert an array of molar fractions to a Composition object."""
    from pynucastro import Composition, Nucleus
    nuclei = [Nucleus.from_cache(name) for name in names]
    comp = Composition(nuclei)
    for i, nuc in enumerate(nuclei):
        comp.X[nuc] = Y[i] * A[i]
    return comp


def energy_release(dY):
    """return the energy release in erg/g (/s if dY is actually dY/dt)"""
    enuc = 0.0
    for i, y in enumerate(dY):
        enuc += y * mass[i]
    enuc *= -1*constants.Avogadro
    return enuc

@jitclass([
    ("Fe45__p_p_p_Ti42__weak__wc12", numba.float64),
    ("Cr43__p_p_p_Ca40__weak__wc12", numba.float64),
    ("Fe75__n_n_n_Co72__weak__mo03", numba.float64),
    ("Mn73__n_n_n_Fe70__weak__mo03", numba.float64),
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    ("n_V45__p_Ti45", numba.float64),
    ("p_O18__F19", numba.float64),
    ("p_P36__S37", numba.float64),
    ("Na35__Mg35__weak__wc17", numba.float64),
    ("He4_Fe72__Ni76", numba.float64),
    ("Na24__Mg24__weak__wc12", numba.float64),
    ("V59__Cr59__weak__wc12", numba.float64),
    ("Ar41__K41__weak__wc12", numba.float64),
    ("Cr65__Mn65__weak__wc17", numba.float64),
    ("Cr46__V46__weak__wc12", numba.float64),
    ("n_F24__F25", numba.float64),
    ("Ar37__Cl37__weak__wc12", numba.float64),
    ("Be10__B10__weak__wc12", numba.float64),
    ("Ar32__Cl32__weak__wc12", numba.float64),
    ("p_Mg39__He4_Na36", numba.float64),
    ("n_S27__p_P27", numba.float64),
    ("Ti63__n_n_V61__weak__mp17", numba.float64),
    ("He4_Al30__n_P33", numba.float64),
    ("Ar29__Cl29__weak__bqa_pos_", numba.float64),
    ("Na31__Mg31__weak__wc12", numba.float64),
    ("n_V60__V61", numba.float64),
    ("p_Sc44__Ti45", numba.float64),
    ("n_V40__V41", numba.float64),
    ("B15__C15__weak__wc12", numba.float64),
    ("Cl44__Ar44__weak__wc17", numba.float64),
    ("He4_Ca33__p_Sc36", numba.float64),
    ("Na33__Mg33__weak__wc12", numba.float64),
    ("Ar44__K44__weak__wc12", numba.float64),
    ("p_V66__He4_Ti63", numba.float64),
    ("Sc60__n_n_n_Ti57__weak__mo03", numba.float64),
    ("Cl31__S31__weak__wc12", numba.float64),
    ("V53__Cr53__weak__wc12", numba.float64),
    ("n_V39__He4_Sc36", numba.float64),
    ("V44__Ti44__weak__wc12", numba.float64),
    ("Fe49__p_Cr48__weak__wc12", numba.float64),
    ("n_Sc60__Sc61", numba.float64),
    ("Mn63__n_Fe62__weak__mp17", numba.float64),
    ("Si37__P37__weak__wc12", numba.float64),
    ("Al39__Si39__weak__wc17", numba.float64),
    ("Fe76__Co76__weak__mo03", numba.float64),
    ("He4_Na38__Al42", numba.float64),
    ("Mg30__Al30__weak__wc12", numba.float64),
    ("He4_Ar49__Ca53", numba.float64),
    ("Al33__n_Si32__weak__wc12", numba.float64),
    ("N19__O19__weak__wc12", numba.float64),
    ("S38__Cl38__weak__wc12", numba.float64),
    ("He4_K46__Sc50", numba.float64),
    ("He4_Sc50__n_V53", numba.float64),
    ("n_Sc39__p_Ca39", numba.float64),
    ("Mg31__n_Al30__weak__wc12", numba.float64),
    ("P39__S39__weak__wc12", numba.float64),
    ("n_Sc40__He4_K37", numba.float64),
    ("n_Ca39__Ca40", numba.float64),
    ("n_Ne33__Ne34", numba.float64),
    ("He4_O16__Ne20", numba.float64),
    ("p_Ar51__n_K51", numba.float64),
    ("p_Cr67__Mn68", numba.float64),
    ("F30__n_n_n_Ne27__weak__mo03", numba.float64),
    ("p_P41__He4_Si38", numba.float64),
    ("p_Mg34__n_Al34", numba.float64),
    ("p_Na39__Mg40", numba.float64),
    ("Si22__Al22__weak__wc12", numba.float64),
    ("Si39__P39__weak__wc17", numba.float64),
    ("Al40__n_n_Si38__weak__mp17", numba.float64),
    ("He4_Ca56__n_Ti59", numba.float64),
    ("p_Be10__He4_Li7", numba.float64),
    ("p_Mg35__Al36", numba.float64),
    ("Cr45__V45__weak__wc12", numba.float64),
    ("p_Ar50__K51", numba.float64),
    ("K50__n_n_Ca48__weak__mp17", numba.float64),
    ("Sc60__Ti60__weak__mo03", numba.float64),
    ("p_Ca47__Sc48", numba.float64),
    ("N18__He4_C14__weak__wc12", numba.float64),
    ("He4_Cr68__Fe72", numba.float64),
    ("N20__O20__weak__wc12", numba.float64),
    ("p_Cl44__He4_S41", numba.float64),
    ("Ar54__K54__weak__mo03", numba.float64),
    ("n_Ca38__He4_Ar35", numba.float64),
    ("p_Sc54__He4_Ca51", numba.float64),
    ("n_Be9__Be10", numba.float64),
    ("He4_Ne21__Mg25", numba.float64),
    ("p_Cr70__He4_V67", numba.float64),
    ("p_Mg40__Al41", numba.float64),
    ("p_Ti55__He4_Sc52", numba.float64),
    ("Ar51__n_n_K49__weak__mp17", numba.float64),
    ("p_Mg33__Al34", numba.float64),
    ("p_Al29__Si30", numba.float64),
    ("p_Mn56__n_Fe56", numba.float64),
    ("n_Sc47__Sc48", numba.float64),
    ("p_V59__He4_Ti56", numba.float64),
    ("Na37__n_n_Mg35__weak__mp17", numba.float64),
    ("p_Ar49__He4_Cl46", numba.float64),
    ("F28__Ne28__weak__mo03", numba.float64),
    ("Mg35__Al35__weak__wc17", numba.float64),
    ("He4_K52__Sc56", numba.float64),
    ("p_Al32__Si33", numba.float64),
    ("Ne23__Na23__weak__wc12", numba.float64),
    ("Mn45__Cr45__weak__bqa_pos_", numba.float64),
    ("Na33__n_n_Mg31__weak__wc12", numba.float64),
    ("p_Na19__Mg20", numba.float64),
    ("Mg20__Na20__weak__wc12", numba.float64),
    ("Ne26__Na26__weak__wc12", numba.float64),
    ("Ti60__V60__weak__wc17", numba.float64),
    ("p_Fe62__Co63", numba.float64),
    ("p_P39__S40", numba.float64),
    ("K56__n_n_Ca54__weak__mp17", numba.float64),
    ("Cl38__Ar38__weak__wc12", numba.float64),
    ("He4_Na32__Al36", numba.float64),
    ("Sc55__Ti55__weak__wc12", numba.float64),
    ("He4_P30__Cl34", numba.float64),
    ("p_F26__He4_O23", numba.float64),
    ("F28__n_Ne27__weak__mp17", numba.float64),
    ("n_S32__He4_Si29", numba.float64),
    ("n_Si37__Si38", numba.float64),
    ("Ca56__Sc56__weak__wc17", numba.float64),
    ("p_S48__Cl49", numba.float64),
    ("Cl42__Ar42__weak__wc12", numba.float64),
    ("p_Sc42__He4_Ca39", numba.float64),
    ("n_Sc38__He4_K35", numba.float64),
    ("n_Al42__Al43", numba.float64),
    ("O19__F19__weak__wc12", numba.float64),
    ("n_Na28__Na29", numba.float64),
    ("p_Si38__He4_Al35", numba.float64),
    ("n_Al25__He4_Na22", numba.float64),
    ("p_F30__Ne31", numba.float64),
    ("N22__n_O21__weak__wc17", numba.float64),
    ("Na29__Mg29__weak__wc12", numba.float64),
    ("He4_K37__Sc41", numba.float64),
    ("n_K34__p_Ar34", numba.float64),
    ("He4_Si45__n_S48", numba.float64),
    ("He4_Fe69__n_Ni72", numba.float64),
    ("Mn72__Fe72__weak__mo03", numba.float64),
    ("He4_S40__Ar44", numba.float64),
    ("n_P28__He4_Al25", numba.float64),
    ("p_O23__F24", numba.float64),
    ("K49__n_Ca48__weak__wc12", numba.float64),
    ("p_Fe75__Co76", numba.float64),
    ("O27__n_F26__weak__mp17", numba.float64),
    ("Ne33__Na33__weak__mo03", numba.float64),
    ("p_Mn65__Fe66", numba.float64),
    ("Na28__n_Mg27__weak__wc12", numba.float64),
    ("Ti52__V52__weak__wc12", numba.float64),
    ("He4_Mn50__p_Fe53", numba.float64),
    ("Fe45__Mn45__weak__wc17", numba.float64),
    ("Al35__Si35__weak__wc12", numba.float64),
    ("F17__O17__weak__wc12", numba.float64),
    ("n_Mn66__Mn67", numba.float64),
    ("Al40__Si40__weak__mo03", numba.float64),
    ("F26__Ne26__weak__wc12", numba.float64),
    ("n_Ar49__Ar50", numba.float64),
    ("Cl47__Ar47__weak__wc17", numba.float64),
    ("p_Cr61__n_Mn61", numba.float64),
    ("p_Na35__Mg36", numba.float64),
    ("n_O20__O21", numba.float64),
    ("He4_Ar32__p_K35", numba.float64),
    ("Sc36__Ca36__weak__bqa_pos_", numba.float64),
    ("n_Mg37__Mg38", numba.float64),
    ("Al36__n_Si35__weak__mp17", numba.float64),
    ("He4_K56__Sc60", numba.float64),
    ("p_Na30__n_Mg30", numba.float64),
    ("K34__Ar34__weak__bqa_pos_", numba.float64),
    ("K42__Ca42__weak__wc12", numba.float64),
    ("Na37__n_Mg36__weak__mp17", numba.float64),
    ("n_S29__S30", numba.float64),
    ("n_Cr48__He4_Ti45", numba.float64),
    ("Cl30__S30__weak__bqa_pos_", numba.float64),
    ("n_C16__C17", numba.float64),
    ("K40__Ca40__weak__wc12", numba.float64),
    ("P30__Si30__weak__wc12", numba.float64),
    ("p_V62__Cr63", numba.float64),
    ("p_Ar46__n_K46", numba.float64),
    ("He4_K46__n_Sc49", numba.float64),
    ("B19__n_n_C17__weak__wc12", numba.float64),
    ("V49__Ti49__weak__wc12", numba.float64),
    ("Ar30__Cl30__weak__bqa_pos_", numba.float64),
    ("P29__Si29__weak__wc12", numba.float64),
    ("He4_K34__Sc38", numba.float64),
])
class RateEval:
    def __init__(self):
        self.Fe45__p_p_p_Ti42__weak__wc12 = np.nan
        self.Cr43__p_p_p_Ca40__weak__wc12 = np.nan
        self.Fe75__n_n_n_Co72__weak__mo03 = np.nan
        self.Mn73__n_n_n_Fe70__weak__mo03 = np.nan
        self.Mn71__n_n_n_Fe68__weak__mo03 = np.nan
        self.Cr70__n_n_n_Mn67__weak__mo03 = np.nan
        self.V66__n_n_n_Cr63__weak__mo03 = np.nan
        self.V65__n_n_n_Cr62__weak__mo03 = np.nan
        self.Ti65__n_n_n_V62__weak__mo03 = np.nan
        self.Sc63__n_n_n_Ti60__weak__mo03 = np.nan
        self.Sc62__n_n_n_Ti59__weak__mo03 = np.nan
        self.Sc61__n_n_n_Ti58__weak__mo03 = np.nan
        self.Sc59__n_n_n_Ti56__weak__mo03 = np.nan
        self.Sc58__n_n_n_Ti55__weak__mo03 = np.nan
        self.Sc57__n_n_n_Ti54__weak__mo03 = np.nan
        self.Ca60__n_n_n_Sc57__weak__mo03 = np.nan
        self.Ca59__n_n_n_Sc56__weak__mo03 = np.nan
        self.Ca58__n_n_n_Sc55__weak__mo03 = np.nan
        self.Ca57__n_n_n_Sc54__weak__mo03 = np.nan
        self.K59__n_n_n_Ca56__weak__mo03 = np.nan
        self.K58__n_n_n_Ca55__weak__mo03 = np.nan
        self.K55__n_n_n_Ca52__weak__mo03 = np.nan
        self.K53__n_n_n_Ca50__weak__mo03 = np.nan
        self.Ar54__n_n_n_K51__weak__mo03 = np.nan
        self.Ar53__n_n_n_K50__weak__mo03 = np.nan
        self.Ar52__n_n_n_K49__weak__mo03 = np.nan
        self.Cl50__n_n_n_Ar47__weak__mo03 = np.nan
        self.S48__n_n_n_Cl45__weak__mo03 = np.nan
        self.S47__n_n_n_Cl44__weak__mo03 = np.nan
        self.K56__n_n_n_Ca53__weak__mo03 = np.nan
        self.P44__n_n_n_S41__weak__mo03 = np.nan
        self.Si42__n_n_n_P39__weak__mo03 = np.nan
        self.Al43__n_n_n_Si40__weak__mo03 = np.nan
        self.Al42__n_n_n_Si39__weak__mo03 = np.nan
        self.Al41__n_n_n_Si38__weak__mo03 = np.nan
        self.Al39__n_n_n_Si36__weak__mo03 = np.nan
        self.Al38__n_n_n_Si35__weak__mo03 = np.nan
        self.Al37__n_n_n_Si34__weak__mo03 = np.nan
        self.Mg40__n_n_n_Al37__weak__mo03 = np.nan
        self.Mg36__n_n_n_Al33__weak__mo03 = np.nan
        self.Mg35__n_n_n_Al32__weak__mo03 = np.nan
        self.Na34__n_n_n_Mg31__weak__mo03 = np.nan
        self.Na33__n_n_n_Mg30__weak__mo03 = np.nan
        self.Na32__n_n_n_Mg29__weak__mo03 = np.nan
        self.Ne31__n_n_n_Na28__weak__mo03 = np.nan
        self.F31__n_n_n_Ne28__weak__mo03 = np.nan
        self.F29__n_n_n_Ne26__weak__mo03 = np.nan
        self.K54__n_n_n_Ca51__weak__mo03 = np.nan
        self.F28__n_n_n_Ne25__weak__mo03 = np.nan
        self.F27__n_n_n_Ne24__weak__mo03 = np.nan
        self.O27__n_n_n_F24__weak__mo03 = np.nan
        self.n_p_p__p_d = np.nan
        self.n_n_He4__He6 = np.nan
        self.p_Be9__n_p_He4_He4 = np.nan
        self.He3_Be7__p_p_He4_He4 = np.nan
        self.t_Be7__n_p_He4_He4 = np.nan
        self.He4_Ca36__p_p_Ca38 = np.nan
        self.He4_O13__p_p_O15 = np.nan
        self.p_B11__He4_He4_He4 = np.nan
        self.n_B8__p_He4_He4 = np.nan
        self.p_Be9__d_He4_He4 = np.nan
        self.d_Li7__n_He4_He4 = np.nan
        self.He3_He3__p_p_He4 = np.nan
        self.He4_Fe76__n_Ni79 = np.nan
        self.p_Fe76__He4_Mn73 = np.nan
        self.He4_Fe75__n_Ni78 = np.nan
        self.p_Fe75__He4_Mn72 = np.nan
        self.p_Fe75__n_Co75 = np.nan
        self.He4_Fe74__n_Ni77 = np.nan
        self.p_Fe74__He4_Mn71 = np.nan
        self.p_Fe74__n_Co74 = np.nan
        self.Mg37__n_n_n_Al34__weak__mo03 = np.nan
        self.p_Fe73__He4_Mn70 = np.nan
        self.p_Fe73__n_Co73 = np.nan
        self.p_Fe72__He4_Mn69 = np.nan
        self.p_Fe72__n_Co72 = np.nan
        self.He4_Fe71__n_Ni74 = np.nan
        self.p_Fe71__He4_Mn68 = np.nan
        self.p_Fe71__n_Co71 = np.nan
        self.He4_Fe70__n_Ni73 = np.nan
        self.p_Fe70__He4_Mn67 = np.nan
        self.p_Fe70__n_Co70 = np.nan
        self.p_Fe69__He4_Mn66 = np.nan
        self.p_Fe69__n_Co69 = np.nan
        self.He4_Fe68__n_Ni71 = np.nan
        self.p_Fe68__He4_Mn65 = np.nan
        self.p_Fe67__He4_Mn64 = np.nan
        self.p_Fe65__He4_Mn62 = np.nan
        self.He4_Fe64__n_Ni67 = np.nan
        self.He4_Fe63__n_Ni66 = np.nan
        self.p_Fe63__He4_Mn60 = np.nan
        self.p_Fe62__He4_Mn59 = np.nan
        self.p_Fe61__He4_Mn58 = np.nan
        self.p_Fe61__n_Co61 = np.nan
        self.p_Fe60__He4_Mn57 = np.nan
        self.He4_Fe59__n_Ni62 = np.nan
        self.p_Fe59__He4_Mn56 = np.nan
        self.p_Fe59__n_Co59 = np.nan
        self.p_Fe57__He4_Mn54 = np.nan
        self.n_Fe56__He4_Cr53 = np.nan
        self.O28__n_O27 = np.nan
        self.p_Ar34__K35 = np.nan
        self.n_Fe55__p_Mn55 = np.nan
        self.n_Sc40__Sc41 = np.nan
        self.n_Fe54__p_Mn54 = np.nan
        self.He4_Sc59__V63 = np.nan
        self.n_Fe53__He4_Cr50 = np.nan
        self.Fe67__Co67__weak__wc12 = np.nan
        self.He4_S30__Ar34 = np.nan
        self.n_Fe53__p_Mn53 = np.nan
        self.He4_Fe52__p_Co55 = np.nan
        self.n_Al25__Al26 = np.nan
        self.p_Ca61__Sc62 = np.nan
        self.n_Fe52__He4_Cr49 = np.nan
        self.Mn58__Fe58__weak__wc12 = np.nan
        self.n_Fe51__He4_Cr48 = np.nan
        self.He4_Cr66__Fe70 = np.nan
        self.n_Fe50__He4_Cr47 = np.nan
        self.He4_Fe49__p_Co52 = np.nan
        self.n_Fe49__He4_Cr46 = np.nan
        self.n_Fe49__p_Mn49 = np.nan
        self.He4_Fe48__p_Co51 = np.nan
        self.p_Sc50__Ti51 = np.nan
        self.n_Fe47__He4_Cr44 = np.nan
        self.Al37__Si37__weak__wc17 = np.nan
        self.n_Fe46__He4_Cr43 = np.nan
        self.n_Fe46__p_Mn46 = np.nan
        self.He4_Mn73__n_Co76 = np.nan
        self.p_Mn73__He4_Cr70 = np.nan
        self.p_Mg34__Al35 = np.nan
        self.He4_Mn72__n_Co75 = np.nan
        self.p_Mn72__He4_Cr69 = np.nan
        self.p_Mn71__He4_Cr68 = np.nan
        self.Ca56__n_n_n_Sc53__weak__mo03 = np.nan
        self.He4_Mn69__n_Co72 = np.nan
        self.p_Mn69__He4_Cr66 = np.nan
        self.He4_Mn68__n_Co71 = np.nan
        self.p_Mn68__n_Fe68 = np.nan
        self.He4_Si33__n_S36 = np.nan
        self.p_Mn67__He4_Cr64 = np.nan
        self.p_Mn66__He4_Cr63 = np.nan
        self.p_Mn66__n_Fe66 = np.nan
        self.p_K48__Ca49 = np.nan
        self.p_P46__S47 = np.nan
        self.He4_Ca52__Ti56 = np.nan
        self.He4_Mn65__n_Co68 = np.nan
        self.p_Mn65__He4_Cr62 = np.nan
        self.p_Si44__n_P44 = np.nan
        self.He4_Mn68__Co72 = np.nan
        self.p_Mn64__He4_Cr61 = np.nan
        self.p_Mn62__He4_Cr59 = np.nan
        self.He4_Mn60__n_Co63 = np.nan
        self.p_Mn60__He4_Cr57 = np.nan
        self.p_Mn60__n_Fe60 = np.nan
        self.He4_Fe65__Ni69 = np.nan
        self.p_Mn59__He4_Cr56 = np.nan
        self.p_Mn57__n_Fe57 = np.nan
        self.p_Fe64__He4_Mn61 = np.nan
        self.p_Mn56__He4_Cr53 = np.nan
        self.p_Mn54__He4_Cr51 = np.nan
        self.S49__n_n_n_Cl46__weak__mo03 = np.nan
        self.He4_Mn53__p_Fe56 = np.nan
        self.p_Mn53__He4_Cr50 = np.nan
        self.n_Mn52__He4_V49 = np.nan
        self.Ar48__n_K47__weak__mp17 = np.nan
        self.n_Mn52__p_Cr52 = np.nan
        self.He4_Mn51__p_Fe54 = np.nan
        self.p_Ca53__n_Sc53 = np.nan
        self.n_Mn51__p_Cr51 = np.nan
        self.p_O22__n_F22 = np.nan
        self.n_Mn50__He4_V47 = np.nan
        self.He4_Mn49__p_Fe52 = np.nan
        self.n_Cl37__Cl38 = np.nan
        self.n_Mn48__He4_V45 = np.nan
        self.He4_Mn47__p_Fe50 = np.nan
        self.n_Ne20__Ne21 = np.nan
        self.n_Mn47__p_Cr47 = np.nan
        self.He4_Mn46__p_Fe49 = np.nan
        self.p_Ca44__Sc45 = np.nan
        self.n_Mn46__He4_V43 = np.nan
        self.n_Mn46__p_Cr46 = np.nan
        self.n_Mn45__p_Cr45 = np.nan
        self.He4_Mn44__p_Fe47 = np.nan
        self.He4_Cr70__n_Fe73 = np.nan
        self.n_F26__F27 = np.nan
        self.He4_Cr69__n_Fe72 = np.nan
        self.p_Cr68__He4_V65 = np.nan
        self.p_Cr68__n_Mn68 = np.nan
        self.p_Cr67__n_Mn67 = np.nan
        self.He4_Cr66__n_Fe69 = np.nan
        self.p_Cr66__He4_V63 = np.nan
        self.He4_Cr65__n_Fe68 = np.nan
        self.p_Cr65__He4_V62 = np.nan
        self.p_Mn72__n_Fe72 = np.nan
        self.He4_Cr64__n_Fe67 = np.nan
        self.p_O25__n_F25 = np.nan
        self.He4_Cr63__n_Fe66 = np.nan
        self.p_Cr63__n_Mn63 = np.nan
        self.He4_Cr62__n_Fe65 = np.nan
        self.p_Cr62__He4_V59 = np.nan
        self.N21__O21__weak__wc12 = np.nan
        self.He4_Mn48__Co52 = np.nan
        self.He4_Cr61__n_Fe64 = np.nan
        self.p_Cr60__He4_V57 = np.nan
        self.He4_Cr59__n_Fe62 = np.nan
        self.n_Ca50__Ca51 = np.nan
        self.p_Cr59__n_Mn59 = np.nan
        self.p_Fe62__n_Co62 = np.nan
        self.n_O18__O19 = np.nan
        self.p_Cr57__n_Mn57 = np.nan
        self.Mg22__Na22__weak__wc12 = np.nan
        self.He4_Cr55__n_Fe58 = np.nan
        self.Cr43__p_p_Sc41__weak__wc12 = np.nan
        self.n_Cr55__He4_Ti52 = np.nan
        self.p_Cr54__He4_V51 = np.nan
        self.p_Ne32__Na33 = np.nan
        self.p_Mg24__He4_Na21 = np.nan
        self.p_Si38__n_P38 = np.nan
        self.Mn54__Cr54__weak__wc12 = np.nan
        self.p_Mn55__He4_Cr52 = np.nan
        self.n_Cr51__He4_Ti48 = np.nan
        self.n_Cr50__He4_Ti47 = np.nan
        self.He4_Cr49__p_Mn52 = np.nan
        self.He4_Cr48__p_Mn51 = np.nan
        self.n_Cr48__p_V48 = np.nan
        self.p_Ti57__He4_Sc54 = np.nan
        self.n_Cr46__He4_Ti43 = np.nan
        self.He4_Cr45__p_Mn48 = np.nan
        self.n_B13__B14 = np.nan
        self.He4_Ne29__Mg33 = np.nan
        self.He4_Ti59__n_Cr62 = np.nan
        self.He4_P44__n_Cl47 = np.nan
        self.n_Cr45__He4_Ti42 = np.nan
        self.He4_Cr44__p_Mn47 = np.nan
        self.He4_Cr43__p_Mn46 = np.nan
        self.n_Cr43__p_V43 = np.nan
        self.He4_Cr42__p_Mn45 = np.nan
        self.n_Cr42__He4_Ti39 = np.nan
        self.n_Cr42__p_V42 = np.nan
        self.n_Cr41__He4_Ti38 = np.nan
        self.Ne26__n_Na25__weak__wc12 = np.nan
        self.He4_V67__n_Mn70 = np.nan
        self.He4_Sc37__p_Ti40 = np.nan
        self.p_V67__n_Cr67 = np.nan
        self.He4_V66__n_Mn69 = np.nan
        self.p_V66__n_Cr66 = np.nan
        self.He4_V50__p_Cr53 = np.nan
        self.p_K47__He4_Ar44 = np.nan
        self.p_V65__He4_Ti62 = np.nan
        self.He4_V64__n_Mn67 = np.nan
        self.n_Cr49__p_V49 = np.nan
        self.p_V64__He4_Ti61 = np.nan
        self.p_V63__n_Cr63 = np.nan
        self.He4_Mn60__Co64 = np.nan
        self.He4_V62__n_Mn65 = np.nan
        self.He4_V61__n_Mn64 = np.nan
        self.p_V61__n_Cr61 = np.nan
        self.p_P32__n_S32 = np.nan
        self.He4_Al32__n_P35 = np.nan
        self.He4_V63__Mn67 = np.nan
        self.p_V60__He4_Ti57 = np.nan
        self.t_He3__n_p_He4 = np.nan
        self.p_V60__n_Cr60 = np.nan
        self.p_O27__He4_N24 = np.nan
        self.p_Si43__n_P43 = np.nan
        self.He4_V59__n_Mn62 = np.nan
        self.He4_V58__n_Mn61 = np.nan
        self.p_V58__He4_Ti55 = np.nan
        self.p_V58__n_Cr58 = np.nan
        self.p_V57__He4_Ti54 = np.nan
        self.p_V57__n_Cr57 = np.nan
        self.n_Cr53__He4_Ti50 = np.nan
        self.He4_V56__n_Mn59 = np.nan
        self.Mn43__Cr43__weak__bqa_pos_ = np.nan
        self.He4_Al40__p_Si43 = np.nan
        self.He4_V55__n_Mn58 = np.nan
        self.Ne28__Na28__weak__wc17 = np.nan
        self.He4_Cr47__p_Mn50 = np.nan
        self.p_V55__n_Cr55 = np.nan
        self.He4_V54__n_Mn57 = np.nan
        self.He4_Ar52__Ca56 = np.nan
        self.p_V53__n_Cr53 = np.nan
        self.p_V52__He4_Ti49 = np.nan
        self.p_V52__n_Cr52 = np.nan
        self.He4_S45__n_Ar48 = np.nan
        self.He4_Ca43__Ti47 = np.nan
        self.p_V51__He4_Ti48 = np.nan
        self.p_F23__Ne24 = np.nan
        self.n_Mn69__Mn70 = np.nan
        self.p_V50__He4_Ti47 = np.nan
        self.p_V50__n_Cr50 = np.nan
        self.n_V50__p_Ti50 = np.nan
        self.p_F24__Ne25 = np.nan
        self.p_V49__He4_Ti46 = np.nan
        self.He4_N15__F19 = np.nan
        self.He4_V47__p_Cr50 = np.nan
        self.He4_V46__p_Cr49 = np.nan
        self.n_V46__He4_Sc43 = np.nan
        self.n_V46__p_Ti46 = np.nan
        self.He4_V58__Mn62 = np.nan
        self.p_Sc52__Ti53 = np.nan
        self.n_V44__He4_Sc41 = np.nan
        self.n_V44__p_Ti44 = np.nan
        self.Cl49__n_n_Ar47__weak__mp17 = np.nan
        self.He4_V43__p_Cr46 = np.nan
        self.n_V43__p_Ti43 = np.nan
        self.He4_V42__p_Cr45 = np.nan
        self.He4_Si43__n_S46 = np.nan
        self.Sc47__Ti47__weak__wc12 = np.nan
        self.He4_Ne33__n_Mg36 = np.nan
        self.n_V42__He4_Sc39 = np.nan
        self.n_V41__He4_Sc38 = np.nan
        self.n_V40__p_Ti40 = np.nan
        self.He4_V39__p_Cr42 = np.nan
        self.p_Sc53__n_Ti53 = np.nan
        self.He4_Ti65__n_Cr68 = np.nan
        self.p_Cr57__He4_V54 = np.nan
        self.p_Ne27__He4_F24 = np.nan
        self.He4_Ti64__n_Cr67 = np.nan
        self.p_Ti64__He4_Sc61 = np.nan
        self.He4_Ti63__n_Cr66 = np.nan
        self.p_Ti63__He4_Sc60 = np.nan
        self.p_Ti63__n_V63 = np.nan
        self.p_Ti61__n_V61 = np.nan
        self.He4_Ti60__n_Cr63 = np.nan
        self.n_O12__O13 = np.nan
        self.p_Ti60__n_V60 = np.nan
        self.p_Ti59__n_V59 = np.nan
        self.He4_Ti58__n_Cr61 = np.nan
        self.p_Ti58__n_V58 = np.nan
        self.K32__Ar32__weak__bqa_pos_ = np.nan
        self.He4_Ti55__n_Cr58 = np.nan
        self.p_Ti55__n_V55 = np.nan
        self.He4_Ti54__n_Cr57 = np.nan
        self.p_Ti54__He4_Sc51 = np.nan
        self.p_Ti54__n_V54 = np.nan
        self.p_F23__He4_O20 = np.nan
        self.He4_Ti53__n_Cr56 = np.nan
        self.p_Ti53__He4_Sc50 = np.nan
        self.n_Na33__Na34 = np.nan
        self.He4_Be10__C14 = np.nan
        self.p_Ti52__He4_Sc49 = np.nan
        self.p_Ti52__n_V52 = np.nan
        self.He4_Ti51__n_Cr54 = np.nan
        self.Ti43__Sc43__weak__wc12 = np.nan
        self.p_Ti51__n_V51 = np.nan
        self.n_Ti51__He4_Ca48 = np.nan
        self.He4_F26__Na30 = np.nan
        self.n_Ti49__He4_Ca46 = np.nan
        self.Sc61__n_n_Ti59__weak__mp17 = np.nan
        self.He4_Fe73__n_Ni76 = np.nan
        self.He4_K36__p_Ca39 = np.nan
        self.Sc56__n_Ti55__weak__mp17 = np.nan
        self.He4_Ar35__Ca39 = np.nan
        self.p_Ar51__He4_Cl48 = np.nan
        self.He4_Na19__Al23 = np.nan
        self.n_Na35__Na36 = np.nan
        self.n_Ti45__p_Sc45 = np.nan
        self.He4_Ti43__p_V46 = np.nan
        self.n_Ti43__He4_Ca40 = np.nan
        self.He4_F28__n_Na31 = np.nan
        self.He4_F31__n_Na34 = np.nan
        self.n_Ti41__He4_Ca38 = np.nan
        self.n_Ti41__p_Sc41 = np.nan
        self.He4_Ti40__p_V43 = np.nan
        self.n_K55__K56 = np.nan
        self.p_Cr55__n_Mn55 = np.nan
        self.p_F31__He4_O28 = np.nan
        self.He4_Ti39__p_V42 = np.nan
        self.n_Ti39__p_Sc39 = np.nan
        self.He4_Ti38__p_V41 = np.nan
        self.n_Ti38__He4_Ca35 = np.nan
        self.n_Ti38__p_Sc38 = np.nan
        self.He4_Ti37__p_V40 = np.nan
        self.Ti65__n_V64__weak__mp17 = np.nan
        self.He4_Sc62__n_V65 = np.nan
        self.He4_Sc61__n_V64 = np.nan
        self.p_Sc61__n_Ti61 = np.nan
        self.He4_Sc40__p_Ti43 = np.nan
        self.He4_Sc60__n_V63 = np.nan
        self.Ne34__n_n_n_Na31__weak__mo03 = np.nan
        self.p_Sc60__He4_Ca57 = np.nan
        self.p_Sc60__n_Ti60 = np.nan
        self.n_Fe48__p_Mn48 = np.nan
        self.He4_Sc59__n_V62 = np.nan
        self.n_Mn53__p_Cr53 = np.nan
        self.He4_Sc58__n_V61 = np.nan
        self.p_Sc58__He4_Ca55 = np.nan
        self.p_Sc58__n_Ti58 = np.nan
        self.He4_Sc57__n_V60 = np.nan
        self.Cr58__Mn58__weak__wc12 = np.nan
        self.He4_Sc56__n_V59 = np.nan
        self.He4_Sc55__n_V58 = np.nan
        self.p_Sc55__He4_Ca52 = np.nan
        self.n_Cr41__Cr42 = np.nan
        self.He4_Sc54__n_V57 = np.nan
        self.p_Sc54__n_Ti54 = np.nan
        self.n_Ar36__He4_S33 = np.nan
        self.He4_Sc52__n_V55 = np.nan
        self.p_Sc52__He4_Ca49 = np.nan
        self.p_S47__Cl48 = np.nan
        self.He4_C9__p_N12 = np.nan
        self.p_Sc52__n_Ti52 = np.nan
        self.He4_Sc51__n_V54 = np.nan
        self.p_Sc50__n_Ti50 = np.nan
        self.He4_Ar29__Ca33 = np.nan
        self.p_Sc49__He4_Ca46 = np.nan
        self.p_Sc48__He4_Ca45 = np.nan
        self.He4_Sc47__p_Ti50 = np.nan
        self.p_Sc47__He4_Ca44 = np.nan
        self.He4_Sc46__p_Ti49 = np.nan
        self.p_Sc46__He4_Ca43 = np.nan
        self.n_Sc46__p_Ca46 = np.nan
        self.n_V56__V57 = np.nan
        self.He4_Sc45__p_Ti48 = np.nan
        self.n_Si24__p_Al24 = np.nan
        self.n_Mg22__He4_Ne19 = np.nan
        self.p_Sc45__He4_Ca42 = np.nan
        self.n_Sc45__p_Ca45 = np.nan
        self.He4_Sc44__p_Ti47 = np.nan
        self.p_Sc44__He4_Ca41 = np.nan
        self.n_Sc44__p_Ca44 = np.nan
        self.He4_Sc43__p_Ti46 = np.nan
        self.n_Sc43__He4_K40 = np.nan
        self.n_Sc43__p_Ca43 = np.nan
        self.He4_Sc42__p_Ti45 = np.nan
        self.n_Sc42__He4_K39 = np.nan
        self.n_Sc42__p_Ca42 = np.nan
        self.p_Cr56__n_Mn56 = np.nan
        self.n_Sc41__He4_K38 = np.nan
        self.p_Si36__He4_Al33 = np.nan
        self.He4_Sc39__p_Ti42 = np.nan
        self.p_P31__S32 = np.nan
        self.n_Sc39__He4_K36 = np.nan
        self.p_Si45__P46 = np.nan
        self.He4_Sc38__p_Ti41 = np.nan
        self.n_Ti47__He4_Ca44 = np.nan
        self.p_Na36__n_Mg36 = np.nan
        self.n_Sc37__He4_K34 = np.nan
        self.He4_Sc36__p_Ti39 = np.nan
        self.Mg36__n_n_Al34__weak__mp17 = np.nan
        self.He4_Sc35__p_Ti38 = np.nan
        self.n_Sc35__He4_K32 = np.nan
        self.n_Sc35__p_Ca35 = np.nan
        self.p_Ca61__He4_K58 = np.nan
        self.p_Ca61__n_Sc61 = np.nan
        self.p_Ca60__n_Sc60 = np.nan
        self.n_Fe48__Fe49 = np.nan
        self.p_Ca59__n_Sc59 = np.nan
        self.He4_Ca58__n_Ti61 = np.nan
        self.p_Ca58__He4_K55 = np.nan
        self.n_Cr46__p_V46 = np.nan
        self.p_Ca58__n_Sc58 = np.nan
        self.He4_Al25__P29 = np.nan
        self.p_Ca56__He4_K53 = np.nan
        self.p_Ca55__He4_K52 = np.nan
        self.p_Ca55__n_Sc55 = np.nan
        self.He4_Ca53__n_Ti56 = np.nan
        self.He8__Li8__weak__wc12 = np.nan
        self.p_Ca52__n_Sc52 = np.nan
        self.p_P45__S46 = np.nan
        self.p_Cr56__He4_V53 = np.nan
        self.He4_Ca51__n_Ti54 = np.nan
        self.p_Ca51__He4_K48 = np.nan
        self.n_Si24__He4_Mg21 = np.nan
        self.p_Al39__He4_Mg36 = np.nan
        self.He4_Ca47__n_Ti50 = np.nan
        self.p_Ca47__n_Sc47 = np.nan
        self.S45__n_Cl44__weak__wc12 = np.nan
        self.C12_C12__He4_Ne20 = np.nan
        self.He4_Ca57__n_Ti60 = np.nan
        self.He4_Ca43__n_Ti46 = np.nan
        self.O24__F24__weak__wc12 = np.nan
        self.He4_Ti45__p_V48 = np.nan
        self.Na39__n_Mg38__weak__mp17 = np.nan
        self.p_Ca42__He4_K39 = np.nan
        self.n_Mn43__He4_V40 = np.nan
        self.He4_F16__Na20 = np.nan
        self.n_Ca40__He4_Ar37 = np.nan
        self.p_P42__n_S42 = np.nan
        self.He4_V63__n_Mn66 = np.nan
        self.n_Ca38__p_K38 = np.nan
        self.He4_Fe66__n_Ni69 = np.nan
        self.Ca53__n_Sc52__weak__wc12 = np.nan
        self.n_Ca37__He4_Ar34 = np.nan
        self.n_Ca37__p_K37 = np.nan
        self.n_Ca36__p_K36 = np.nan
        self.n_Cl35__p_S35 = np.nan
        self.He4_P39__n_Cl42 = np.nan
        self.n_Ca35__He4_Ar32 = np.nan
        self.n_Ca35__p_K35 = np.nan
        self.Cr67__Mn67__weak__mo03 = np.nan
        self.n_Ca34__He4_Ar31 = np.nan
        self.n_Ca34__p_K34 = np.nan
        self.He4_Ca48__Ti52 = np.nan
        self.He4_K57__n_Sc60 = np.nan
        self.p_K57__He4_Ar54 = np.nan
        self.He4_Si42__S46 = np.nan
        self.p_K57__n_Ca57 = np.nan
        self.He4_K56__n_Sc59 = np.nan
        self.p_K56__n_Ca56 = np.nan
        self.He4_K54__n_Sc57 = np.nan
        self.p_K54__n_Ca54 = np.nan
        self.Cl49__n_Ar48__weak__mp17 = np.nan
        self.He4_K53__n_Sc56 = np.nan
        self.n_O14__O15 = np.nan
        self.p_K53__n_Ca53 = np.nan
        self.n_K31__K32 = np.nan
        self.He4_K52__n_Sc55 = np.nan
        self.p_P29__S30 = np.nan
        self.He4_K51__n_Sc54 = np.nan
        self.p_K51__n_Ca51 = np.nan
        self.He4_Cr57__n_Fe60 = np.nan
        self.He4_K50__n_Sc53 = np.nan
        self.p_S42__Cl43 = np.nan
        self.He4_K48__n_Sc51 = np.nan
        self.n_Fe50__Fe51 = np.nan
        self.n_Cr44__He4_Ti41 = np.nan
        self.p_K48__He4_Ar45 = np.nan
        self.He4_Sc35__V39 = np.nan
        self.p_K45__He4_Ar42 = np.nan
        self.p_K45__n_Ca45 = np.nan
        self.p_K44__He4_Ar41 = np.nan
        self.Ne31__n_Na30__weak__mp17 = np.nan
        self.He4_K43__p_Ca46 = np.nan
        self.p_K43__n_Ca43 = np.nan
        self.n_V45__He4_Sc42 = np.nan
        self.He4_K42__p_Ca45 = np.nan
        self.He8__n_Li7__weak__wc12 = np.nan
        self.He4_K42__n_Sc45 = np.nan
        self.He4_K41__n_Sc44 = np.nan
        self.p_K41__He4_Ar38 = np.nan
        self.p_K41__n_Ca41 = np.nan
        self.He4_K46__p_Ca49 = np.nan
        self.p_K40__He4_Ar37 = np.nan
        self.p_K40__n_Ca40 = np.nan
        self.p_S37__Cl38 = np.nan
        self.n_K40__He4_Cl37 = np.nan
        self.n_K40__p_Ar40 = np.nan
        self.n_K39__p_Ar39 = np.nan
        self.p_O14__F15 = np.nan
        self.He4_Sc43__V47 = np.nan
        self.n_K38__p_Ar38 = np.nan
        self.n_Ar31__He4_S28 = np.nan
        self.He4_K37__p_Ca40 = np.nan
        self.He4_K44__p_Ca47 = np.nan
        self.n_K37__He4_Cl34 = np.nan
        self.n_K36__He4_Cl33 = np.nan
        self.n_K36__p_Ar36 = np.nan
        self.n_Sc46__He4_K43 = np.nan
        self.n_K35__p_Ar35 = np.nan
        self.He4_K34__p_Ca37 = np.nan
        self.p_Al39__n_Si39 = np.nan
        self.He4_Sc54__V58 = np.nan
        self.p_Cr61__He4_V58 = np.nan
        self.K52__Ca52__weak__wc17 = np.nan
        self.n_K33__p_Ar33 = np.nan
        self.p_Mn51__Fe52 = np.nan
        self.n_K32__He4_Cl29 = np.nan
        self.p_Mn56__Fe57 = np.nan
        self.n_K32__p_Ar32 = np.nan
        self.He4_K31__p_Ca34 = np.nan
        self.p_Ti38__V39 = np.nan
        self.n_K31__p_Ar31 = np.nan
        self.p_Ar54__n_K54 = np.nan
        self.p_Ar52__He4_Cl49 = np.nan
        self.p_Ar52__n_K52 = np.nan
        self.n_Ti39__He4_Ca36 = np.nan
        self.p_K59__n_Ca59 = np.nan
        self.p_Ar50__He4_Cl47 = np.nan
        self.n_Ca36__He4_Ar33 = np.nan
        self.V67__n_n_n_Cr64__weak__mo03 = np.nan
        self.He4_F20__n_Na23 = np.nan
        self.p_Ar48__He4_Cl45 = np.nan
        self.p_Ar48__n_K48 = np.nan
        self.He4_Ar46__n_Ca49 = np.nan
        self.p_F28__n_Ne28 = np.nan
        self.He4_Fe50__p_Co53 = np.nan
        self.n_d__t = np.nan
        self.He4_Si35__n_S38 = np.nan
        self.p_Ar44__n_K44 = np.nan
        self.He4_Ar43__n_Ca46 = np.nan
        self.n_V39__V40 = np.nan
        self.p_Cr55__He4_V52 = np.nan
        self.p_Ar43__n_K43 = np.nan
        self.p_Fe47__Co48 = np.nan
        self.He4_Cl47__K51 = np.nan
        self.p_Ar41__n_K41 = np.nan
        self.n_Mn52__Mn53 = np.nan
        self.p_Ar40__He4_Cl37 = np.nan
        self.He4_Mn54__Co58 = np.nan
        self.He4_Fe68__Ni72 = np.nan
        self.p_Ar39__He4_Cl36 = np.nan
        self.p_Cr62__Mn63 = np.nan
        self.He4_Mn62__n_Co65 = np.nan
        self.n_Mn49__He4_V46 = np.nan
        self.n_Ar37__p_Cl37 = np.nan
        self.n_Ar35__He4_S32 = np.nan
        self.n_Ar35__p_Cl35 = np.nan
        self.He4_Ar34__p_K37 = np.nan
        self.n_Ar34__p_Cl34 = np.nan
        self.He4_Ar33__p_K36 = np.nan
        self.n_Ar33__p_Cl33 = np.nan
        self.n_Ar32__He4_S29 = np.nan
        self.n_Fe75__Fe76 = np.nan
        self.n_Ar32__p_Cl32 = np.nan
        self.He4_Ar31__p_K34 = np.nan
        self.n_Ar31__p_Cl31 = np.nan
        self.P27__p_Al26__weak__wc12 = np.nan
        self.n_Ar30__He4_S27 = np.nan
        self.n_Ar30__p_Cl30 = np.nan
        self.He4_Ar29__p_K32 = np.nan
        self.n_Ar29__He4_S26 = np.nan
        self.n_Ar29__p_Cl29 = np.nan
        self.p_Cl52__He4_S49 = np.nan
        self.p_Cl52__n_Ar52 = np.nan
        self.p_O16__F17 = np.nan
        self.He4_Cl51__n_K54 = np.nan
        self.n_Ti58__Ti59 = np.nan
        self.He4_Cl50__K54 = np.nan
        self.p_Cl51__He4_S48 = np.nan
        self.p_Cl50__He4_S47 = np.nan
        self.p_Cl50__n_Ar50 = np.nan
        self.n_Ar34__Ar35 = np.nan
        self.p_B12__n_C12 = np.nan
        self.He4_Cl49__n_K52 = np.nan
        self.He4_Ar36__Ca40 = np.nan
        self.p_Cl48__He4_S45 = np.nan
        self.He4_Ca50__n_Ti53 = np.nan
        self.p_Cl48__n_Ar48 = np.nan
        self.p_Ti62__n_V62 = np.nan
        self.He4_Cl47__n_K50 = np.nan
        self.p_Cl45__He4_S42 = np.nan
        self.p_Cl45__n_Ar45 = np.nan
        self.He4_Cl43__p_Ar46 = np.nan
        self.p_Cl43__He4_S40 = np.nan
        self.p_Mn61__n_Fe61 = np.nan
        self.He4_V49__Mn53 = np.nan
        self.p_V55__Cr56 = np.nan
        self.He4_Cl42__n_K45 = np.nan
        self.p_Cl42__He4_S39 = np.nan
        self.p_S47__n_Cl47 = np.nan
        self.n_Fe72__Fe73 = np.nan
        self.He4_Cl41__n_K44 = np.nan
        self.p_Cl41__He4_S38 = np.nan
        self.He4_Cl40__n_K43 = np.nan
        self.p_Cl40__n_Ar40 = np.nan
        self.p_O19__He4_N16 = np.nan
        self.n_Cl36__p_S36 = np.nan
        self.He4_F17__Na21 = np.nan
        self.n_Cl35__He4_P32 = np.nan
        self.He4_Cl34__p_Ar37 = np.nan
        self.n_C11__He4_He4_He4 = np.nan
        self.n_Cl34__He4_P31 = np.nan
        self.P42__n_n_S40__weak__mp17 = np.nan
        self.n_Cl34__p_S34 = np.nan
        self.n_Cl33__He4_P30 = np.nan
        self.p_Ti43__V44 = np.nan
        self.n_Cl33__p_S33 = np.nan
        self.p_Na34__Mg35 = np.nan
        self.He4_S48__n_Ar51 = np.nan
        self.n_Cl31__p_S31 = np.nan
        self.He4_Ar35__p_K38 = np.nan
        self.He4_Cl30__p_Ar33 = np.nan
        self.Ca35__K35__weak__wc17 = np.nan
        self.n_Cl29__He4_P26 = np.nan
        self.He4_Na25__Al29 = np.nan
        self.n_Cl29__p_S29 = np.nan
        self.He4_Cl28__p_Ar31 = np.nan
        self.n_V49__p_Ti49 = np.nan
        self.n_Cl28__He4_P25 = np.nan
        self.d_Li8__n_Be9 = np.nan
        self.Cr44__V44__weak__wc12 = np.nan
        self.n_Cr57__Cr58 = np.nan
        self.p_S49__n_Cl49 = np.nan
        self.He4_Mg38__n_Si41 = np.nan
        self.n_Ca52__Ca53 = np.nan
        self.p_S48__n_Cl48 = np.nan
        self.p_N15__O16 = np.nan
        self.p_S47__He4_P44 = np.nan
        self.p_K52__He4_Ar49 = np.nan
        self.p_S46__n_Cl46 = np.nan
        self.Na25__Mg25__weak__wc12 = np.nan
        self.d_Be7__p_He4_He4 = np.nan
        self.p_S45__He4_P42 = np.nan
        self.He4_S43__n_Ar46 = np.nan
        self.p_Mn64__n_Fe64 = np.nan
        self.p_S43__He4_P40 = np.nan
        self.He4_Mn67__n_Co70 = np.nan
        self.p_Cr60__Mn61 = np.nan
        self.p_Sc57__He4_Ca54 = np.nan
        self.He4_Fe56__Ni60 = np.nan
        self.He4_S42__n_Ar45 = np.nan
        self.He4_S41__n_Ar44 = np.nan
        self.He4_Sc63__n_V66 = np.nan
        self.p_S41__He4_P38 = np.nan
        self.p_Al30__He4_Mg27 = np.nan
        self.p_S40__n_Cl40 = np.nan
        self.p_Cl40__He4_S37 = np.nan
        self.He4_Fe47__Ni51 = np.nan
        self.d_Li8__t_Li7 = np.nan
        self.p_S39__He4_P36 = np.nan
        self.He4_S38__n_Ar41 = np.nan
        self.p_S38__He4_P35 = np.nan
        self.p_S38__n_Cl38 = np.nan
        self.He4_Mn47__Co51 = np.nan
        self.He4_S37__n_Ar40 = np.nan
        self.He4_K49__n_Sc52 = np.nan
        self.p_V56__He4_Ti53 = np.nan
        self.p_S37__n_Cl37 = np.nan
        self.p_K49__n_Ca49 = np.nan
        self.p_Cl45__Ar46 = np.nan
        self.p_Li6__Be7 = np.nan
        self.p_S36__He4_P33 = np.nan
        self.p_Cr69__He4_V66 = np.nan
        self.p_Sc51__He4_Ca48 = np.nan
        self.p_K51__He4_Ar48 = np.nan
        self.He4_P34__n_Cl37 = np.nan
        self.He4_S35__n_Ar38 = np.nan
        self.p_S35__He4_P32 = np.nan
        self.n_Si43__Si44 = np.nan
        self.p_Sc57__n_Ti57 = np.nan
        self.n_S35__He4_Si32 = np.nan
        self.He4_S34__p_Cl37 = np.nan
        self.n_Al36__Al37 = np.nan
        self.p_Cl35__He4_S32 = np.nan
        self.He4_Ti60__Cr64 = np.nan
        self.Cr68__Mn68__weak__mo03 = np.nan
        self.n_S33__He4_Si30 = np.nan
        self.He4_S31__p_Cl34 = np.nan
        self.He4_S30__p_Cl33 = np.nan
        self.n_S30__He4_Si27 = np.nan
        self.n_S30__p_P30 = np.nan
        self.Cl49__n_n_n_Ar46__weak__mo03 = np.nan
        self.He4_S28__p_Cl31 = np.nan
        self.n_Cr43__He4_Ti40 = np.nan
        self.n_S28__He4_Si25 = np.nan
        self.Ca53__Sc53__weak__wc12 = np.nan
        self.He4_S26__p_Cl29 = np.nan
        self.n_S26__He4_Si23 = np.nan
        self.p_V65__Cr66 = np.nan
        self.He4_P47__n_Cl50 = np.nan
        self.p_P47__n_S47 = np.nan
        self.p_P45__n_S45 = np.nan
        self.n_Si33__Si34 = np.nan
        self.He4_P43__n_Cl46 = np.nan
        self.p_P43__He4_Si40 = np.nan
        self.He4_Al38__n_P41 = np.nan
        self.p_P43__n_S43 = np.nan
        self.p_Sc55__n_Ti55 = np.nan
        self.p_P42__He4_Si39 = np.nan
        self.Ne27__n_Na26__weak__wc12 = np.nan
        self.He4_P41__p_S44 = np.nan
        self.He4_P41__n_Cl44 = np.nan
        self.p_O20__He4_N17 = np.nan
        self.p_Ar43__He4_Cl40 = np.nan
        self.p_P38__He4_Si35 = np.nan
        self.p_P38__n_S38 = np.nan
        self.n_S33__p_P33 = np.nan
        self.p_F18__He4_O15 = np.nan
        self.He4_P37__n_Cl40 = np.nan
        self.p_P37__He4_Si34 = np.nan
        self.p_P36__He4_Si33 = np.nan
        self.n_Ti54__Ti55 = np.nan
        self.p_P36__n_S36 = np.nan
        self.p_Mn69__n_Fe69 = np.nan
        self.p_P34__n_S34 = np.nan
        self.p_Ca56__n_Sc56 = np.nan
        self.He4_Cl44__p_Ar47 = np.nan
        self.p_Al25__Si26 = np.nan
        self.p_Sc45__Ti46 = np.nan
        self.p_P32__He4_Si29 = np.nan
        self.n_P32__p_Si32 = np.nan
        self.He4_P31__p_S34 = np.nan
        self.n_F25__F26 = np.nan
        self.He4_P30__p_S33 = np.nan
        self.Mg39__n_n_n_Al36__weak__mo03 = np.nan
        self.He4_K55__n_Sc58 = np.nan
        self.n_V47__He4_Sc44 = np.nan
        self.n_P28__p_Si28 = np.nan
        self.He4_P27__p_S30 = np.nan
        self.n_P27__He4_Al24 = np.nan
        self.n_P27__p_Si27 = np.nan
        self.He4_P26__p_S29 = np.nan
        self.n_Cr47__He4_Ti44 = np.nan
        self.n_P26__He4_Al23 = np.nan
        self.n_P26__p_Si26 = np.nan
        self.He4_P25__p_S28 = np.nan
        self.He4_P24__p_S27 = np.nan
        self.n_P24__He4_Al21 = np.nan
        self.n_P24__p_Si24 = np.nan
        self.p_Si45__He4_Al42 = np.nan
        self.p_Si45__n_P45 = np.nan
        self.He4_Si44__n_S47 = np.nan
        self.He4_P42__n_Cl45 = np.nan
        self.He4_Si42__n_S45 = np.nan
        self.Na26__Mg26__weak__wc12 = np.nan
        self.p_Si42__n_P42 = np.nan
        self.n_Mn54__p_Cr54 = np.nan
        self.Sc38__Ca38__weak__mo97 = np.nan
        self.He4_Si40__n_S43 = np.nan
        self.He4_Si39__n_S42 = np.nan
        self.Mn68__Fe68__weak__wc17 = np.nan
        self.p_S38__Cl39 = np.nan
        self.p_Si39__n_P39 = np.nan
        self.p_Sc62__n_Ti62 = np.nan
        self.n_Cr47__p_V47 = np.nan
        self.He4_Si38__n_S41 = np.nan
        self.p_Ti65__He4_Sc62 = np.nan
        self.He4_Si37__n_S40 = np.nan
        self.He4_Ca40__Ti44 = np.nan
        self.p_Si37__He4_Al34 = np.nan
        self.O14__N14__weak__wc12 = np.nan
        self.p_Si37__n_P37 = np.nan
        self.p_Si35__He4_Al32 = np.nan
        self.He3__t__weak__electron_capture = np.nan
        self.p_Si33__n_P33 = np.nan
        self.He4_Mn45__p_Fe48 = np.nan
        self.He4_Cr41__p_Mn44 = np.nan
        self.He4_Mn43__Co47 = np.nan
        self.He4_V57__n_Mn60 = np.nan
        self.n_Mn51__He4_V48 = np.nan
        self.p_V49__Cr50 = np.nan
        self.B18__n_B17 = np.nan
        self.n_Ti37__He4_Ca34 = np.nan
        self.n_O24__O25 = np.nan
        self.He4_Ti61__n_Cr64 = np.nan
        self.Sc62__Ti62__weak__mo03 = np.nan
        self.He4_Si25__p_P28 = np.nan
        self.n_Ar35__Ar36 = np.nan
        self.p_Mn58__Fe59 = np.nan
        self.n_Si25__p_Al25 = np.nan
        self.He4_V40__p_Cr43 = np.nan
        self.He4_Si24__p_P27 = np.nan
        self.V64__n_n_Cr62__weak__mp17 = np.nan
        self.He4_Be7__C11 = np.nan
        self.He4_Ca54__Ti58 = np.nan
        self.He4_K40__p_Ca43 = np.nan
        self.He4_Si23__p_P26 = np.nan
        self.He4_Ar42__n_Ca45 = np.nan
        self.p_V61__He4_Ti58 = np.nan
        self.n_Si23__p_Al23 = np.nan
        self.He4_Si22__p_P25 = np.nan
        self.n_Si22__He4_Mg19 = np.nan
        self.n_Si22__p_Al22 = np.nan
        self.p_Al43__n_Si43 = np.nan
        self.Mg27__Al27__weak__wc12 = np.nan
        self.He4_Al42__n_P45 = np.nan
        self.p_Al41__He4_Mg38 = np.nan
        self.He4_Al40__n_P43 = np.nan
        self.p_Al40__He4_Mg37 = np.nan
        self.p_Al40__n_Si40 = np.nan
        self.He4_Al39__p_Si42 = np.nan
        self.He4_Al38__p_Si41 = np.nan
        self.He4_Mn49__Co53 = np.nan
        self.p_Al38__He4_Mg35 = np.nan
        self.p_V59__n_Cr59 = np.nan
        self.n_V48__p_Ti48 = np.nan
        self.p_Al37__He4_Mg34 = np.nan
        self.He4_Al36__p_Si39 = np.nan
        self.n_Si44__Si45 = np.nan
        self.He4_Al36__n_P39 = np.nan
        self.p_Al36__He4_Mg33 = np.nan
        self.C22__N22__weak__wc17 = np.nan
        self.He4_Mn59__Co63 = np.nan
        self.p_Al36__n_Si36 = np.nan
        self.p_Al41__n_Si41 = np.nan
        self.p_V64__n_Cr64 = np.nan
        self.He4_Al35__n_P38 = np.nan
        self.p_Al35__He4_Mg32 = np.nan
        self.He4_Al34__n_P37 = np.nan
        self.p_Al34__He4_Mg31 = np.nan
        self.p_Al34__n_Si34 = np.nan
        self.He4_K50__Sc54 = np.nan
        self.He4_Al33__n_P36 = np.nan
        self.p_Al33__He4_Mg30 = np.nan
        self.Si43__n_n_P41__weak__mp17 = np.nan
        self.He4_Si27__p_P30 = np.nan
        self.p_Cl46__He4_S43 = np.nan
        self.p_Al33__n_Si33 = np.nan
        self.p_Ne26__n_Na26 = np.nan
        self.p_Al32__He4_Mg29 = np.nan
        self.p_Al32__n_Si32 = np.nan
        self.n_Cr66__Cr67 = np.nan
        self.He4_Al31__p_Si34 = np.nan
        self.He4_Al31__n_P34 = np.nan
        self.p_Cl38__He4_S35 = np.nan
        self.p_Al31__He4_Mg28 = np.nan
        self.p_Al30__n_Si30 = np.nan
        self.He4_Al29__n_P32 = np.nan
        self.p_Al29__He4_Mg26 = np.nan
        self.p_Al29__n_Si29 = np.nan
        self.He4_Al37__n_P40 = np.nan
        self.p_Ne34__He4_F31 = np.nan
        self.n_Ti44__p_Sc44 = np.nan
        self.p_Al28__He4_Mg25 = np.nan
        self.n_Ti59__Ti60 = np.nan
        self.He4_K41__p_Ca44 = np.nan
        self.He4_Al27__p_Si30 = np.nan
        self.He4_Al27__n_P30 = np.nan
        self.p_Ca49__Sc50 = np.nan
        self.n_Al26__He4_Na23 = np.nan
        self.n_Al26__p_Mg26 = np.nan
        self.He4_Al32__P36 = np.nan
        self.n_Al25__p_Mg25 = np.nan
        self.He4_Al24__p_Si27 = np.nan
        self.p_S46__Cl47 = np.nan
        self.He4_Al25__p_Si28 = np.nan
        self.F31__n_n_Ne29__weak__mp17 = np.nan
        self.n_Al23__He4_Na20 = np.nan
        self.p_Na37__Mg38 = np.nan
        self.He4_Al22__p_Si25 = np.nan
        self.p_V67__He4_Ti64 = np.nan
        self.n_Al22__He4_Na19 = np.nan
        self.O28__n_n_n_F25__weak__mo03 = np.nan
        self.n_Al22__p_Mg22 = np.nan
        self.He4_Al21__p_Si24 = np.nan
        self.n_Sc48__p_Ca48 = np.nan
        self.He4_Mg40__n_Si43 = np.nan
        self.p_Mg40__n_Al40 = np.nan
        self.He4_Mg39__n_Si42 = np.nan
        self.p_Mg39__n_Al39 = np.nan
        self.Ca33__K33__weak__bqa_pos_ = np.nan
        self.p_Mg38__n_Al38 = np.nan
        self.p_Al27__He4_Mg24 = np.nan
        self.He4_Mg37__n_Si40 = np.nan
        self.p_Al38__n_Si38 = np.nan
        self.p_Na31__Mg32 = np.nan
        self.p_Ar45__He4_Cl42 = np.nan
        self.He4_Mg35__n_Si38 = np.nan
        self.He4_Mg34__n_Si37 = np.nan
        self.p_Mg34__He4_Na31 = np.nan
        self.p_Ti53__n_V53 = np.nan
        self.p_Mg33__He4_Na30 = np.nan
        self.Fe49__Mn49__weak__wc12 = np.nan
        self.p_Fe66__He4_Mn63 = np.nan
        self.He4_Mg32__n_Si35 = np.nan
        self.n_Mn47__He4_V44 = np.nan
        self.p_Mg32__He4_Na29 = np.nan
        self.n_Na19__p_Ne19 = np.nan
        self.p_Mn59__n_Fe59 = np.nan
        self.He4_Mg30__n_Si33 = np.nan
        self.p_Mg30__n_Al30 = np.nan
        self.n_P29__He4_Al26 = np.nan
        self.p_Ca45__Sc46 = np.nan
        self.He4_Cr46__p_Mn49 = np.nan
        self.p_Cl46__n_Ar46 = np.nan
        self.p_Mg29__He4_Na26 = np.nan
        self.p_Mg29__n_Al29 = np.nan
        self.p_Cr60__n_Mn60 = np.nan
        self.n_S29__He4_Si26 = np.nan
        self.n_K58__K59 = np.nan
        self.He4_K57__Sc61 = np.nan
        self.He4_Ne23__n_Mg26 = np.nan
        self.p_Ne31__He4_F28 = np.nan
        self.He4_Mg27__n_Si30 = np.nan
        self.He4_O23__n_Ne26 = np.nan
        self.He4_K35__p_Ca38 = np.nan
        self.He4_Mg26__n_Si29 = np.nan
        self.p_Ti59__V60 = np.nan
        self.n_Fe54__He4_Cr51 = np.nan
        self.n_Mn68__Mn69 = np.nan
        self.He4_Fe53__p_Co56 = np.nan
        self.n_Fe55__He4_Cr52 = np.nan
        self.He4_Mg25__n_Si28 = np.nan
        self.p_Fe69__Co70 = np.nan
        self.P40__S40__weak__wc12 = np.nan
        self.n_Cl43__Cl44 = np.nan
        self.n_Mg23__C12_C12 = np.nan
        self.n_Mg23__He4_Ne20 = np.nan
        self.n_Fe66__Fe67 = np.nan
        self.He4_Mg22__p_Al25 = np.nan
        self.n_Cl30__p_S30 = np.nan
        self.n_Mg21__He4_Ne18 = np.nan
        self.He4_Mg20__p_Al23 = np.nan
        self.Ca57__n_n_Sc55__weak__mp17 = np.nan
        self.He4_Na36__n_Al39 = np.nan
        self.n_Mg20__p_Na20 = np.nan
        self.p_Na39__n_Mg39 = np.nan
        self.Na27__n_Mg26__weak__wc12 = np.nan
        self.He4_Na38__n_Al41 = np.nan
        self.He4_Na37__p_Mg40 = np.nan
        self.He4_K33__Sc37 = np.nan
        self.p_Na37__He4_Ne34 = np.nan
        self.He4_Na35__n_Al38 = np.nan
        self.p_Na35__n_Mg35 = np.nan
        self.Mg37__n_Al36__weak__mp17 = np.nan
        self.n_V43__He4_Sc40 = np.nan
        self.He4_Na34__n_Al37 = np.nan
        self.He4_V60__n_Mn63 = np.nan
        self.He4_Na33__p_Mg36 = np.nan
        self.p_Na33__n_Mg33 = np.nan
        self.n_N18__N19 = np.nan
        self.S30__P30__weak__wc12 = np.nan
        self.n_Mn43__p_Cr43 = np.nan
        self.He4_Sc44__V48 = np.nan
        self.He4_Na31__n_Al34 = np.nan
        self.p_Na31__He4_Ne28 = np.nan
        self.p_Na31__n_Mg31 = np.nan
        self.p_Fe66__n_Co66 = np.nan
        self.p_Na30__He4_Ne27 = np.nan
        self.p_Cl40__Ar41 = np.nan
        self.n_S31__p_P31 = np.nan
        self.p_Na29__He4_Ne26 = np.nan
        self.He4_Na28__n_Al31 = np.nan
        self.p_Na28__n_Mg28 = np.nan
        self.Ar49__K49__weak__wc12 = np.nan
        self.p_Na27__n_Mg27 = np.nan
        self.n_Ar39__He4_S36 = np.nan
        self.He4_Na26__n_Al29 = np.nan
        self.p_Sc49__n_Ti49 = np.nan
        self.Ar52__n_n_K50__weak__mp17 = np.nan
        self.He4_Na24__p_Mg27 = np.nan
        self.p_Na24__He4_Ne21 = np.nan
        self.n_Ti42__p_Sc42 = np.nan
        self.p_K56__He4_Ar53 = np.nan
        self.p_K46__Ca47 = np.nan
        self.He4_Na23__p_Mg26 = np.nan
        self.p_Fe67__n_Co67 = np.nan
        self.n_Fe50__p_Mn50 = np.nan
        self.n_Sc43__Sc44 = np.nan
        self.n_S26__p_P26 = np.nan
        self.p_Na23__He4_Ne20 = np.nan
        self.p_Na23__n_Mg23 = np.nan
        self.He4_Na22__p_Mg25 = np.nan
        self.He4_S41__Ar45 = np.nan
        self.p_V56__Cr57 = np.nan
        self.n_Na21__He4_F18 = np.nan
        self.He4_S29__p_Cl32 = np.nan
        self.n_Na20__He4_F17 = np.nan
        self.n_V40__He4_Sc37 = np.nan
        self.He4_Cl35__p_Ar38 = np.nan
        self.p_Ne34__n_Na34 = np.nan
        self.n_Mn54__He4_V51 = np.nan
        self.n_Cl32__He4_P29 = np.nan
        self.p_Cl36__Ar37 = np.nan
        self.He4_S46__n_Ar49 = np.nan
        self.He4_Ne31__n_Mg34 = np.nan
        self.p_Al35__n_Si35 = np.nan
        self.He4_Ne30__n_Mg33 = np.nan
        self.p_Ne30__He4_F27 = np.nan
        self.n_Sc40__p_Ca40 = np.nan
        self.p_Ne29__He4_F26 = np.nan
        self.He4_Ar43__Ca47 = np.nan
        self.p_Ne29__n_Na29 = np.nan
        self.He4_Ne28__n_Mg31 = np.nan
        self.p_Ne28__n_Na28 = np.nan
        self.Si35__P35__weak__wc17 = np.nan
        self.He4_Ne27__n_Mg30 = np.nan
        self.p_Ne27__n_Na27 = np.nan
        self.He4_Ca39__Ti43 = np.nan
        self.N23__O23__weak__wc12 = np.nan
        self.He4_Ti54__Cr58 = np.nan
        self.He4_S39__n_Ar42 = np.nan
        self.p_Ne25__He4_F22 = np.nan
        self.p_Ne25__n_Na25 = np.nan
        self.K59__Ca59__weak__mo03 = np.nan
        self.He4_S27__p_Cl30 = np.nan
        self.He4_Ne24__n_Mg27 = np.nan
        self.p_Ne24__n_Na24 = np.nan
        self.Cl39__Ar39__weak__wc12 = np.nan
        self.p_S30__Cl31 = np.nan
        self.n_Ti45__He4_Ca42 = np.nan
        self.Cr69__Mn69__weak__mo03 = np.nan
        self.P33__S33__weak__wc12 = np.nan
        self.He4_Ca61__n_Ti64 = np.nan
        self.He4_K39__Sc43 = np.nan
        self.p_Ne23__n_Na23 = np.nan
        self.He4_Sc62__V66 = np.nan
        self.He4_Ne22__n_Mg25 = np.nan
        self.n_Cl38__He4_P35 = np.nan
        self.p_Al43__He4_Mg40 = np.nan
        self.He4_Ne21__n_Mg24 = np.nan
        self.n_Si27__Si28 = np.nan
        self.p_V42__Cr43 = np.nan
        self.C12_Ne20__He4_Si28 = np.nan
        self.C12_Ne20__p_P31 = np.nan
        self.n_Na30__Na31 = np.nan
        self.p_V54__n_Cr54 = np.nan
        self.p_Ne20__He4_F17 = np.nan
        self.p_Ne22__Na23 = np.nan
        self.He4_Al26__p_Si29 = np.nan
        self.p_K33__Ca34 = np.nan
        self.He4_Ne19__p_Na22 = np.nan
        self.He4_Ne18__p_Na21 = np.nan
        self.n_Si25__He4_Mg22 = np.nan
        self.n_Ne18__He4_O15 = np.nan
        self.n_Ne18__p_F18 = np.nan
        self.He4_Ne17__p_Na20 = np.nan
        self.n_Be7__He4_He4 = np.nan
        self.He4_Ne16__p_Na19 = np.nan
        self.He4_Cl49__K53 = np.nan
        self.n_Ne16__p_F16 = np.nan
        self.p_Cr67__He4_V64 = np.nan
        self.He4_Ar53__n_Ca56 = np.nan
        self.p_F31__n_Ne31 = np.nan
        self.He4_F30__p_Ne33 = np.nan
        self.p_Ar45__n_K45 = np.nan
        self.p_Mn47__Fe48 = np.nan
        self.p_F30__He4_O27 = np.nan
        self.He4_F29__n_Na32 = np.nan
        self.p_F29__He4_O26 = np.nan
        self.He4_F27__n_Na30 = np.nan
        self.p_F27__He4_O24 = np.nan
        self.p_F27__n_Ne27 = np.nan
        self.S27__p_Si26__weak__wc17 = np.nan
        self.He4_F26__n_Na29 = np.nan
        self.p_F26__n_Ne26 = np.nan
        self.p_Na34__He4_Ne31 = np.nan
        self.p_F25__He4_O22 = np.nan
        self.n_S30__S31 = np.nan
        self.p_F25__n_Ne25 = np.nan
        self.He4_Ca38__Ti42 = np.nan
        self.He4_F24__n_Na27 = np.nan
        self.p_F24__n_Ne24 = np.nan
        self.He4_Ti42__p_V45 = np.nan
        self.p_Na26__He4_Ne23 = np.nan
        self.p_F22__He4_O19 = np.nan
        self.p_F22__n_Ne22 = np.nan
        self.Cl48__n_Ar47__weak__mp17 = np.nan
        self.He4_F21__p_Ne24 = np.nan
        self.He4_F21__n_Na24 = np.nan
        self.p_Ne26__He4_F23 = np.nan
        self.He4_F20__p_Ne23 = np.nan
        self.n_Si26__p_Al26 = np.nan
        self.p_Al39__Si40 = np.nan
        self.p_F20__He4_O17 = np.nan
        self.He4_F19__p_Ne22 = np.nan
        self.p_F19__n_Ne19 = np.nan
        self.p_O21__n_F21 = np.nan
        self.He4_F18__p_Ne21 = np.nan
        self.p_O15__F16 = np.nan
        self.Al40__n_n_n_Si37__weak__mo03 = np.nan
        self.n_F18__He4_N15 = np.nan
        self.n_F15__He4_N12 = np.nan
        self.Fe76__n_n_n_Co73__weak__mo03 = np.nan
        self.n_Al41__Al42 = np.nan
        self.n_F14__He4_N11 = np.nan
        self.n_Ca33__p_K33 = np.nan
        self.S37__Cl37__weak__wc12 = np.nan
        self.He4_O28__n_Ne31 = np.nan
        self.He4_O26__n_Ne29 = np.nan
        self.p_O26__He4_N23 = np.nan
        self.He4_Ti44__p_V47 = np.nan
        self.Ne34__Na34__weak__mo03 = np.nan
        self.p_O26__n_F26 = np.nan
        self.He4_O24__n_Ne27 = np.nan
        self.p_O24__n_F24 = np.nan
        self.Na31__n_Mg30__weak__wc17 = np.nan
        self.He4_F30__n_Na33 = np.nan
        self.He4_O22__n_Ne25 = np.nan
        self.He4_Ar52__n_Ca55 = np.nan
        self.p_Ti57__n_V57 = np.nan
        self.p_O20__n_F20 = np.nan
        self.He4_O19__n_Ne22 = np.nan
        self.He4_Cl32__p_Ar35 = np.nan
        self.p_Cr62__n_Mn62 = np.nan
        self.p_O18__He4_N15 = np.nan
        self.He4_O17__n_Ne20 = np.nan
        self.p_S49__Cl50 = np.nan
        self.p_O17__He4_N14 = np.nan
        self.O16_O16__He4_Si28 = np.nan
        self.O16_O16__p_P31 = np.nan
        self.He4_Ne26__n_Mg29 = np.nan
        self.Cl32__S32__weak__wc12 = np.nan
        self.O16_O16__n_S31 = np.nan
        self.He4_Al28__n_P31 = np.nan
        self.C12_O16__He4_Mg24 = np.nan
        self.C12_O16__p_Al27 = np.nan
        self.p_K48__n_Ca48 = np.nan
        self.p_Ne28__He4_F25 = np.nan
        self.p_Al26__Si27 = np.nan
        self.p_Ca36__Sc37 = np.nan
        self.p_Na28__He4_Ne25 = np.nan
        self.n_K33__He4_Cl30 = np.nan
        self.He4_Cr45__Fe49 = np.nan
        self.p_Cr70__Mn71 = np.nan
        self.n_O14__He4_C11 = np.nan
        self.He4_O13__p_F16 = np.nan
        self.He4_Sc57__V61 = np.nan
        self.n_Ca33__He4_Ar30 = np.nan
        self.n_O13__He4_C10 = np.nan
        self.n_O13__p_N13 = np.nan
        self.n_O12__p_N12 = np.nan
        self.p_N15__He4_C12 = np.nan
        self.p_N15__n_O15 = np.nan
        self.n_Sc37__p_Ca37 = np.nan
        self.n_Mg19__He4_Ne16 = np.nan
        self.p_F28__He4_O25 = np.nan
        self.He4_Ar41__n_Ca44 = np.nan
        self.p_F29__Ne30 = np.nan
        self.n_N14__p_C14 = np.nan
        self.He4_N13__p_O16 = np.nan
        self.He4_C15__n_O18 = np.nan
        self.p_C15__n_N15 = np.nan
        self.He4_Cl50__n_K53 = np.nan
        self.He4_Si31__n_S34 = np.nan
        self.n_V39__p_Ti39 = np.nan
        self.He4_Cl45__n_K48 = np.nan
        self.Al36__Si36__weak__wc17 = np.nan
        self.He4_C13__n_O16 = np.nan
        self.Na38__Mg38__weak__mo03 = np.nan
        self.d_C13__n_N14 = np.nan
        self.p_C13__n_N13 = np.nan
        self.Sc53__Ti53__weak__wc12 = np.nan
        self.p_K44__n_Ca44 = np.nan
        self.n_Mn50__Mn51 = np.nan
        self.n_C11__p_B11 = np.nan
        self.He4_B13__n_N16 = np.nan
        self.n_K35__He4_Cl32 = np.nan
        self.p_Ar53__He4_Cl50 = np.nan
        self.He4_B12__n_N15 = np.nan
        self.p_B12__He4_Be9 = np.nan
        self.p_Ti56__He4_Sc53 = np.nan
        self.He4_B11__p_C14 = np.nan
        self.S44__n_Cl43__weak__wc12 = np.nan
        self.p_Ar41__K42 = np.nan
        self.He4_Fe46__p_Co49 = np.nan
        self.He4_B10__p_C13 = np.nan
        self.He4_B8__p_C11 = np.nan
        self.p_V63__He4_Ti60 = np.nan
        self.He4_Mn70__Co74 = np.nan
        self.He4_Li8__n_B11 = np.nan
        self.Si24__p_Mg23__weak__wc12 = np.nan
        self.n_Ti42__He4_Ca39 = np.nan
        self.n_Fe48__He4_Cr45 = np.nan
        self.He4_V49__p_Cr52 = np.nan
        self.n_Mn53__He4_V50 = np.nan
        self.d_Li7__p_Li8 = np.nan
        self.P45__n_n_n_S42__weak__mo03 = np.nan
        self.Be11__B11__weak__wc12 = np.nan
        self.n_Mn65__Mn66 = np.nan
        self.n_Li6__He4_t = np.nan
        self.Na35__n_n_n_Mg32__weak__mo03 = np.nan
        self.p_Li6__He4_He3 = np.nan
        self.t_He3__d_He4 = np.nan
        self.d_He3__p_He4 = np.nan
        self.Cl51__Ar51__weak__mo03 = np.nan
        self.He4_V51__Mn55 = np.nan
        self.p_P34__S35 = np.nan
        self.n_He3__p_t = np.nan
        self.d_t__n_He4 = np.nan
        self.d_d__p_t = np.nan
        self.He4_Fe76__Ni80 = np.nan
        self.p_Fe76__Co77 = np.nan
        self.n_Cr61__Cr62 = np.nan
        self.n_V50__He4_Sc47 = np.nan
        self.He4_Fe73__Ni77 = np.nan
        self.p_Fe73__Co74 = np.nan
        self.p_Fe72__Co73 = np.nan
        self.p_Mg31__n_Al31 = np.nan
        self.n_Fe71__Fe72 = np.nan
        self.He4_Fe70__Ni74 = np.nan
        self.n_Cl28__Cl29 = np.nan
        self.He4_Ne18__Mg22 = np.nan
        self.p_Fe70__Co71 = np.nan
        self.Sc62__n_n_Ti60__weak__mp17 = np.nan
        self.n_Fe70__Fe71 = np.nan
        self.He4_Fe69__Ni73 = np.nan
        self.n_F16__p_O16 = np.nan
        self.n_Mn62__Mn63 = np.nan
        self.n_Fe69__Fe70 = np.nan
        self.p_P32__S33 = np.nan
        self.p_Fe68__Co69 = np.nan
        self.n_Fe68__Fe69 = np.nan
        self.He4_Fe67__Ni71 = np.nan
        self.C17__N17__weak__wc12 = np.nan
        self.n_Fe67__Fe68 = np.nan
        self.n_Na21__p_Ne21 = np.nan
        self.p_Fe66__Co67 = np.nan
        self.p_Fe65__Co66 = np.nan
        self.n_Fe65__Fe66 = np.nan
        self.Mg20__p_Ne19__weak__wc12 = np.nan
        self.He4_Fe64__Ni68 = np.nan
        self.p_Fe63__Co64 = np.nan
        self.He4_Sc48__n_V51 = np.nan
        self.n_Fe63__Fe64 = np.nan
        self.n_Fe62__Fe63 = np.nan
        self.n_S29__p_P29 = np.nan
        self.He4_P36__n_Cl39 = np.nan
        self.p_Fe61__Co62 = np.nan
        self.p_S46__He4_P43 = np.nan
        self.p_Fe60__Co61 = np.nan
        self.p_Al34__Si35 = np.nan
        self.He4_Fe59__Ni63 = np.nan
        self.p_Fe59__Co60 = np.nan
        self.He4_Fe58__Ni62 = np.nan
        self.n_Fe58__Fe59 = np.nan
        self.p_Fe57__Co58 = np.nan
        self.n_Fe57__Fe58 = np.nan
        self.p_Fe56__Co57 = np.nan
        self.Sc54__Ti54__weak__wc17 = np.nan
        self.n_Fe56__Fe57 = np.nan
        self.p_Fe55__Co56 = np.nan
        self.He4_Fe54__Ni58 = np.nan
        self.Ti38__Sc38__weak__mo97 = np.nan
        self.n_Fe54__Fe55 = np.nan
        self.He4_Fe52__Ni56 = np.nan
        self.p_Fe52__Co53 = np.nan
        self.He4_Fe51__Ni55 = np.nan
        self.p_Si36__n_P36 = np.nan
        self.p_Fe50__Co51 = np.nan
        self.p_Ne32__n_Na32 = np.nan
        self.n_Fe49__Fe50 = np.nan
        self.n_Ne30__Ne31 = np.nan
        self.p_Fe48__Co49 = np.nan
        self.He4_O25__n_Ne28 = np.nan
        self.n_Fe47__Fe48 = np.nan
        self.n_Cr55__Cr56 = np.nan
        self.He4_Fe46__Ni50 = np.nan
        self.He4_Fe57__Ni61 = np.nan
        self.He4_Fe45__Ni49 = np.nan
        self.p_Mn73__Fe74 = np.nan
        self.He4_Mn72__Co76 = np.nan
        self.n_Mn72__Mn73 = np.nan
        self.n_Mn71__Mn72 = np.nan
        self.n_Mn70__Mn71 = np.nan
        self.B12__C12__weak__wc17 = np.nan
        self.He4_Mn69__Co73 = np.nan
        self.p_Mn69__Fe70 = np.nan
        self.p_Mn68__Fe69 = np.nan
        self.Fe53__Mn53__weak__wc12 = np.nan
        self.p_Mn73__n_Fe73 = np.nan
        self.He4_Mn67__Co71 = np.nan
        self.He4_Cl30__K34 = np.nan
        self.p_Mn67__Fe68 = np.nan
        self.n_Mn67__Mn68 = np.nan
        self.He4_Mn66__Co70 = np.nan
        self.p_Mn66__Fe67 = np.nan
        self.He4_Mn64__Co68 = np.nan
        self.He4_Mn63__Co67 = np.nan
        self.n_Mn63__Mn64 = np.nan
        self.He4_Cl29__p_Ar32 = np.nan
        self.p_Ne33__n_Na33 = np.nan
        self.p_Mn62__Fe63 = np.nan
        self.He4_Mn61__Co65 = np.nan
        self.p_Mn61__Fe62 = np.nan
        self.Mg38__Al38__weak__mo03 = np.nan
        self.n_Fe51__p_Mn51 = np.nan
        self.P25__Si25__weak__bqa_pos_ = np.nan
        self.n_Mn60__Mn61 = np.nan
        self.p_Ca58__Sc59 = np.nan
        self.n_Mn59__Mn60 = np.nan
        self.n_Mn58__Mn59 = np.nan
        self.n_Mn56__Mn57 = np.nan
        self.p_K42__n_Ca42 = np.nan
        self.n_Mn55__Mn56 = np.nan
        self.p_Fe64__n_Co64 = np.nan
        self.He4_Mn53__Co57 = np.nan
        self.He4_Mn52__Co56 = np.nan
        self.He4_Mn50__Co54 = np.nan
        self.p_Mn50__Fe51 = np.nan
        self.p_Mn49__Fe50 = np.nan
        self.n_Mn49__Mn50 = np.nan
        self.He4_Si23__S27 = np.nan
        self.p_Mn48__Fe49 = np.nan
        self.He4_Mn46__Co50 = np.nan
        self.p_Mn46__Fe47 = np.nan
        self.He4_Mn45__Co49 = np.nan
        self.p_Mn45__Fe46 = np.nan
        self.n_Mn44__Mn45 = np.nan
        self.He4_Cr70__Fe74 = np.nan
        self.p_V53__He4_Ti50 = np.nan
        self.p_Cr69__Mn70 = np.nan
        self.n_Cr69__Cr70 = np.nan
        self.n_Cl40__Cl41 = np.nan
        self.He4_Cr67__Fe71 = np.nan
        self.K38__Ar38__weak__wc12 = np.nan
        self.p_Cr66__Mn67 = np.nan
        self.p_Cr65__Mn66 = np.nan
        self.He4_Cr63__Fe67 = np.nan
        self.p_Ca52__Sc53 = np.nan
        self.p_Cr63__Mn64 = np.nan
        self.O25__n_F24__weak__mp17 = np.nan
        self.He4_Cr62__Fe66 = np.nan
        self.n_Cr62__Cr63 = np.nan
        self.p_Sc48__n_Ti48 = np.nan
        self.p_Cr61__Mn62 = np.nan
        self.Al30__Si30__weak__wc12 = np.nan
        self.n_Ca43__He4_Ar40 = np.nan
        self.He4_Cr60__Fe64 = np.nan
        self.n_Fe51__Fe52 = np.nan
        self.Cr70__Mn70__weak__mo03 = np.nan
        self.n_Cr60__Cr61 = np.nan
        self.He4_Cr59__Fe63 = np.nan
        self.p_Cr59__Mn60 = np.nan
        self.He4_Mg19__p_Al22 = np.nan
        self.n_Cr59__Cr60 = np.nan
        self.He4_Cr58__Fe62 = np.nan
        self.p_Cr58__Mn59 = np.nan
        self.He4_Cr57__Fe61 = np.nan
        self.p_Cr57__Mn58 = np.nan
        self.p_Cr56__Mn57 = np.nan
        self.n_Cr56__Cr57 = np.nan
        self.He4_Cr54__Fe58 = np.nan
        self.p_Cr54__Mn55 = np.nan
        self.Cr47__V47__weak__wc12 = np.nan
        self.n_Mn49__p_Cr49 = np.nan
        self.He4_Cr53__Fe57 = np.nan
        self.p_Cr53__Mn54 = np.nan
        self.He4_Sc48__V52 = np.nan
        self.n_Cr53__Cr54 = np.nan
        self.p_Cl39__He4_S36 = np.nan
        self.p_Cr52__Mn53 = np.nan
        self.p_Cr51__Mn52 = np.nan
        self.p_Cr50__Mn51 = np.nan
        self.p_Cr49__Mn50 = np.nan
        self.n_O17__O18 = np.nan
        self.He4_Cr48__Fe52 = np.nan
        self.He4_Ar45__Ca49 = np.nan
        self.He4_K38__p_Ca41 = np.nan
        self.He4_P40__n_Cl43 = np.nan
        self.n_Cr48__Cr49 = np.nan
        self.Fe66__Co66__weak__wc12 = np.nan
        self.He4_Cr47__Fe51 = np.nan
        self.He4_Cr46__Fe50 = np.nan
        self.n_Ne19__He4_O16 = np.nan
        self.p_Cr46__Mn47 = np.nan
        self.n_Cr46__Cr47 = np.nan
        self.n_Cr45__Cr46 = np.nan
        self.He4_Cr44__Fe48 = np.nan
        self.n_Cr44__Cr45 = np.nan
        self.n_Sc55__Sc56 = np.nan
        self.He4_Cr43__Fe47 = np.nan
        self.n_Cr43__Cr44 = np.nan
        self.He4_Cr42__Fe46 = np.nan
        self.He4_Cr41__Fe45 = np.nan
        self.p_P44__He4_Si41 = np.nan
        self.He4_Mg22__Si26 = np.nan
        self.He4_V67__Mn71 = np.nan
        self.p_V67__Cr68 = np.nan
        self.He4_V66__Mn70 = np.nan
        self.p_V66__Cr67 = np.nan
        self.n_Mg27__Mg28 = np.nan
        self.He4_V64__Mn68 = np.nan
        self.n_Al37__Al38 = np.nan
        self.p_V64__Cr65 = np.nan
        self.He4_O14__p_F17 = np.nan
        self.p_K58__n_Ca58 = np.nan
        self.p_V63__Cr64 = np.nan
        self.n_V62__V63 = np.nan
        self.He4_V61__Mn65 = np.nan
        self.He4_V60__Mn64 = np.nan
        self.p_Ne32__He4_F29 = np.nan
        self.p_V60__Cr61 = np.nan
        self.p_V59__Cr60 = np.nan
        self.Na36__n_Mg35__weak__mp17 = np.nan
        self.n_V59__V60 = np.nan
        self.p_V58__Cr59 = np.nan
        self.He4_V57__Mn61 = np.nan
        self.p_V57__Cr58 = np.nan
        self.He4_V56__Mn60 = np.nan
        self.He4_Na37__n_Al40 = np.nan
        self.n_V55__V56 = np.nan
        self.He4_V54__Mn58 = np.nan
        self.p_V54__Cr55 = np.nan
        self.He4_V53__Mn57 = np.nan
        self.p_V53__Cr54 = np.nan
        self.n_V53__V54 = np.nan
        self.He4_V52__Mn56 = np.nan
        self.p_V62__n_Cr62 = np.nan
        self.He4_Ne25__Mg29 = np.nan
        self.p_V52__Cr53 = np.nan
        self.n_V51__V52 = np.nan
        self.He4_V50__Mn54 = np.nan
        self.He4_V65__Mn69 = np.nan
        self.p_V50__Cr51 = np.nan
        self.He4_Ne32__n_Mg35 = np.nan
        self.He4_F16__p_Ne19 = np.nan
        self.n_V49__V50 = np.nan
        self.p_V48__Cr49 = np.nan
        self.n_V48__V49 = np.nan
        self.n_S28__S29 = np.nan
        self.He4_V47__Mn51 = np.nan
        self.p_S42__n_Cl42 = np.nan
        self.p_Sc46__n_Ti46 = np.nan
        self.n_V47__V48 = np.nan
        self.He4_V46__Mn50 = np.nan
        self.p_V46__Cr47 = np.nan
        self.p_Si38__P39 = np.nan
        self.n_V46__V47 = np.nan
        self.He4_V45__Mn49 = np.nan
        self.p_Mn63__Fe64 = np.nan
        self.n_V45__V46 = np.nan
        self.He4_V43__Mn47 = np.nan
        self.p_V43__Cr44 = np.nan
        self.p_P40__n_S40 = np.nan
        self.p_Al42__He4_Mg39 = np.nan
        self.n_V42__V43 = np.nan
        self.He4_V41__Mn45 = np.nan
        self.n_Fe57__He4_Cr54 = np.nan
        self.p_V41__Cr42 = np.nan
        self.C16__n_N15__weak__wc12 = np.nan
        self.n_V41__V42 = np.nan
        self.He4_V39__Mn43 = np.nan
        self.n_Mn54__Mn55 = np.nan
        self.n_Ti64__Ti65 = np.nan
        self.He4_Ti63__Cr67 = np.nan
        self.p_Ti63__V64 = np.nan
        self.p_Ti62__V63 = np.nan
        self.He4_Ti61__Cr65 = np.nan
        self.Al39__n_Si38__weak__mp17 = np.nan
        self.n_Ne16__He4_O13 = np.nan
        self.p_N12__O13 = np.nan
        self.p_Ti61__V62 = np.nan
        self.p_Ti60__V61 = np.nan
        self.n_Ti60__Ti61 = np.nan
        self.p_Ti58__V59 = np.nan
        self.C21__n_C20 = np.nan
        self.p_Ti57__V58 = np.nan
        self.p_Ti56__V57 = np.nan
        self.p_Fe63__n_Co63 = np.nan
        self.p_Ti55__V56 = np.nan
        self.p_Cr58__n_Mn58 = np.nan
        self.p_Ar47__n_K47 = np.nan
        self.n_Ti55__Ti56 = np.nan
        self.p_Ar36__K37 = np.nan
        self.p_Ti54__V55 = np.nan
        self.He4_Ti53__Cr57 = np.nan
        self.p_Ti53__V54 = np.nan
        self.n_Ti57__Ti58 = np.nan
        self.He4_Ti52__Cr56 = np.nan
        self.C12_Ne20__n_S31 = np.nan
        self.p_Ti52__V53 = np.nan
        self.n_Ti52__Ti53 = np.nan
        self.n_V43__V44 = np.nan
        self.He4_Ti51__Cr55 = np.nan
        self.p_Ti49__V50 = np.nan
        self.t_Be9__n_B11 = np.nan
        self.n_Ti49__Ti50 = np.nan
        self.He4_Na39__n_Al42 = np.nan
        self.He4_Ti48__Cr52 = np.nan
        self.p_Ti47__V48 = np.nan
        self.He4_Ti57__n_Cr60 = np.nan
        self.n_Ti47__Ti48 = np.nan
        self.He4_Ti46__Cr50 = np.nan
        self.n_Ti46__Ti47 = np.nan
        self.He4_Ti45__Cr49 = np.nan
        self.n_Ti45__Ti46 = np.nan
        self.He4_Ti44__Cr48 = np.nan
        self.p_Ti44__V45 = np.nan
        self.n_Ti44__Ti45 = np.nan
        self.n_Mn44__p_Cr44 = np.nan
        self.He4_Al29__p_Si32 = np.nan
        self.He4_Ti43__Cr47 = np.nan
        self.n_Ti43__Ti44 = np.nan
        self.p_Ti42__V43 = np.nan
        self.He4_Ti41__Cr45 = np.nan
        self.He4_Na32__n_Al35 = np.nan
        self.p_Ti41__V42 = np.nan
        self.p_S28__Cl29 = np.nan
        self.n_Ti41__Ti42 = np.nan
        self.He4_Ti40__Cr44 = np.nan
        self.p_Ti40__V41 = np.nan
        self.p_Mn72__Fe73 = np.nan
        self.n_Ti40__Ti41 = np.nan
        self.He4_Ti38__Cr42 = np.nan
        self.p_Ar50__n_K50 = np.nan
        self.n_Ti38__Ti39 = np.nan
        self.n_Ti37__Ti38 = np.nan
        self.n_Ar34__He4_S31 = np.nan
        self.p_Sc63__Ti64 = np.nan
        self.n_Sc62__Sc63 = np.nan
        self.He4_Al35__P39 = np.nan
        self.p_Mn44__Fe45 = np.nan
        self.p_Sc61__Ti62 = np.nan
        self.He4_Sc60__V64 = np.nan
        self.n_Sc59__Sc60 = np.nan
        self.N16__O16__weak__wc12 = np.nan
        self.Si44__n_P43__weak__mp17 = np.nan
        self.He4_Sc58__V62 = np.nan
        self.p_Sc58__Ti59 = np.nan
        self.n_Sc58__Sc59 = np.nan
        self.He4_Ca60__n_Ti63 = np.nan
        self.p_Sc57__Ti58 = np.nan
        self.He4_Sc56__V60 = np.nan
        self.He4_Ti49__n_Cr52 = np.nan
        self.N17__n_O16__weak__wc12 = np.nan
        self.p_Sc56__Ti57 = np.nan
        self.n_Sc56__Sc57 = np.nan
        self.p_Sc37__Ti38 = np.nan
        self.He4_Sc55__V59 = np.nan
        self.p_Sc55__Ti56 = np.nan
        self.He4_K45__p_Ca48 = np.nan
        self.n_Sc54__Sc55 = np.nan
        self.p_Sc53__Ti54 = np.nan
        self.n_Sc53__Sc54 = np.nan
        self.n_Sc50__Sc51 = np.nan
        self.p_Mn57__He4_Cr54 = np.nan
        self.p_He3__He4__weak__bet_pos_ = np.nan
        self.He4_Sc49__V53 = np.nan
        self.He4_Mn44__Co48 = np.nan
        self.p_Mg31__Al32 = np.nan
        self.p_Sc49__Ti50 = np.nan
        self.n_Sc49__Sc50 = np.nan
        self.p_Sc48__Ti49 = np.nan
        self.n_Sc48__Sc49 = np.nan
        self.p_Ne21__Na22 = np.nan
        self.He4_Sc47__V51 = np.nan
        self.p_Sc46__Ti47 = np.nan
        self.n_Sc46__Sc47 = np.nan
        self.n_V47__p_Ti47 = np.nan
        self.He4_Sc45__V49 = np.nan
        self.He4_Mg20__Si24 = np.nan
        self.n_Sc45__Sc46 = np.nan
        self.p_Ca50__He4_K47 = np.nan
        self.p_Sc43__Ti44 = np.nan
        self.Cl52__n_n_n_Ar49__weak__mo03 = np.nan
        self.n_Cr63__Cr64 = np.nan
        self.F23__Ne23__weak__wc12 = np.nan
        self.He4_Sc42__V46 = np.nan
        self.p_Sc42__Ti43 = np.nan
        self.n_Sc42__Sc43 = np.nan
        self.He4_Sc41__V45 = np.nan
        self.p_Mn60__Fe61 = np.nan
        self.p_Sc41__Ti42 = np.nan
        self.n_Sc41__Sc42 = np.nan
        self.p_Sc40__Ti41 = np.nan
        self.He4_Sc39__V43 = np.nan
        self.n_Sc39__Sc40 = np.nan
        self.Mg36__Al36__weak__wc17 = np.nan
        self.He4_Sc38__V42 = np.nan
        self.p_Sc38__Ti39 = np.nan
        self.n_Sc38__Sc39 = np.nan
        self.p_Na33__He4_Ne30 = np.nan
        self.n_Sc37__Sc38 = np.nan
        self.He4_Cr55__Fe59 = np.nan
        self.p_Ca60__Sc61 = np.nan
        self.F27__n_n_Ne25__weak__mp17 = np.nan
        self.n_Ca60__Ca61 = np.nan
        self.He4_F25__n_Na28 = np.nan
        self.p_Ti51__V52 = np.nan
        self.He4_Ca59__Ti63 = np.nan
        self.n_Ar39__Ar40 = np.nan
        self.p_Ca59__Sc60 = np.nan
        self.He4_Cr64__Fe68 = np.nan
        self.p_Ca57__Sc58 = np.nan
        self.P47__n_n_n_S44__weak__mo03 = np.nan
        self.p_Na20__Mg21 = np.nan
        self.n_Ca57__Ca58 = np.nan
        self.Cl41__Ar41__weak__wc12 = np.nan
        self.C12_C12__p_Na23 = np.nan
        self.n_Ca56__Ca57 = np.nan
        self.n_Ca55__Ca56 = np.nan
        self.He4_Na27__n_Al30 = np.nan
        self.He4_Mn59__n_Co62 = np.nan
        self.He4_O27__Ne31 = np.nan
        self.Sc40__Ca40__weak__wc12 = np.nan
        self.p_Ca54__Sc55 = np.nan
        self.He4_V48__p_Cr51 = np.nan
        self.n_Ca54__Ca55 = np.nan
        self.Al39__n_n_Si37__weak__mp17 = np.nan
        self.n_Ca53__Ca54 = np.nan
        self.p_Fe58__Co59 = np.nan
        self.p_Mn71__Fe72 = np.nan
        self.P36__S36__weak__wc12 = np.nan
        self.He4_Ca51__Ti55 = np.nan
        self.S47__Cl47__weak__mo03 = np.nan
        self.p_Ca51__Sc52 = np.nan
        self.O27__F27__weak__mo03 = np.nan
        self.p_K42__He4_Ar39 = np.nan
        self.He4_Be11__n_C14 = np.nan
        self.n_Ca51__Ca52 = np.nan
        self.He4_Ca50__Ti54 = np.nan
        self.n_Ca49__Ca50 = np.nan
        self.He4_Ca47__Ti51 = np.nan
        self.B17__n_n_n_C14__weak__wc12 = np.nan
        self.He4_Na36__Al40 = np.nan
        self.He4_Ca46__Ti50 = np.nan
        self.Ca36__K36__weak__wc12 = np.nan
        self.Ca34__K34__weak__bqa_pos_ = np.nan
        self.C17__n_N16__weak__wc12 = np.nan
        self.n_Ca46__Ca47 = np.nan
        self.He4_Ca45__Ti49 = np.nan
        self.t_Li7__n_Be9 = np.nan
        self.He4_Li7__B11 = np.nan
        self.He4_Ca44__Ti48 = np.nan
        self.He4_Ca42__Ti46 = np.nan
        self.p_Ca42__Sc43 = np.nan
        self.p_Ca41__Sc42 = np.nan
        self.Si34__P34__weak__wc12 = np.nan
        self.n_Cr51__Cr52 = np.nan
        self.n_Ca41__Ca42 = np.nan
        self.p_Ca52__He4_K49 = np.nan
        self.n_F16__He4_N13 = np.nan
        self.p_Ca40__Sc41 = np.nan
        self.Al41__n_Si40__weak__mp17 = np.nan
        self.n_Ca40__Ca41 = np.nan
        self.He4_Ca37__Ti41 = np.nan
        self.n_Ca37__Ca38 = np.nan
        self.p_Fe64__Co65 = np.nan
        self.n_Na27__Na28 = np.nan
        self.n_Ca36__Ca37 = np.nan
        self.p_Si37__P38 = np.nan
        self.He4_Ca35__Ti39 = np.nan
        self.P37__S37__weak__wc12 = np.nan
        self.Ar54__n_K53__weak__mp17 = np.nan
        self.p_Ca35__Sc36 = np.nan
        self.He4_Ca34__Ti38 = np.nan
        self.He4_Cl46__n_K49 = np.nan
        self.p_Ca34__Sc35 = np.nan
        self.p_Be11__He4_Li8 = np.nan
        self.n_Fe47__p_Mn47 = np.nan
        self.He4_Ca33__Ti37 = np.nan
        self.He4_Na27__Al31 = np.nan
        self.p_K59__Ca60 = np.nan
        self.He4_K58__Sc62 = np.nan
        self.p_K50__n_Ca50 = np.nan
        self.Na27__Mg27__weak__wc12 = np.nan
        self.p_P30__S31 = np.nan
        self.p_K57__Ca58 = np.nan
        self.He4_Cl44__n_K47 = np.nan
        self.He4_Na29__Al33 = np.nan
        self.p_K56__Ca57 = np.nan
        self.He4_Si45__S49 = np.nan
        self.He4_K55__Sc59 = np.nan
        self.V60__Cr60__weak__wc17 = np.nan
        self.Fe60__Co60__weak__wc12 = np.nan
        self.p_Cl36__He4_S33 = np.nan
        self.n_K56__K57 = np.nan
        self.Sc55__n_Ti54__weak__wc12 = np.nan
        self.n_K53__K54 = np.nan
        self.He4_S27__Ar31 = np.nan
        self.p_K52__Ca53 = np.nan
        self.n_K52__K53 = np.nan
        self.He4_K51__Sc55 = np.nan
        self.p_F20__n_Ne20 = np.nan
        self.p_K51__Ca52 = np.nan
        self.n_K50__K51 = np.nan
        self.He4_K49__Sc53 = np.nan
        self.n_K46__K47 = np.nan
        self.p_Ti65__V66 = np.nan
        self.p_Ne26__Na27 = np.nan
        self.p_K45__Ca46 = np.nan
        self.He4_Ne17__Mg21 = np.nan
        self.Sc54__n_Ti53__weak__mp17 = np.nan
        self.n_K45__K46 = np.nan
        self.p_Ar38__K39 = np.nan
        self.He4_K44__Sc48 = np.nan
        self.n_K44__K45 = np.nan
        self.He4_K43__Sc47 = np.nan
        self.p_K43__Ca44 = np.nan
        self.n_K39__He4_Cl36 = np.nan
        self.p_Cr45__Mn46 = np.nan
        self.He4_Ti47__Cr51 = np.nan
        self.He4_Ne27__Mg31 = np.nan
        self.Mn70__n_Fe69__weak__mp17 = np.nan
        self.p_Sc62__Ti63 = np.nan
        self.n_K43__K44 = np.nan
        self.n_Al28__Al29 = np.nan
        self.p_K41__Ca42 = np.nan
        self.p_S34__Cl35 = np.nan
        self.n_K41__K42 = np.nan
        self.Ca35__p_p_Cl33__weak__wc12 = np.nan
        self.n_K40__K41 = np.nan
        self.p_K38__Ca39 = np.nan
        self.He4_Ca36__p_Sc39 = np.nan
        self.p_K37__Ca38 = np.nan
        self.He4_Sc48__p_Ti51 = np.nan
        self.n_Mn45__Mn46 = np.nan
        self.p_V56__n_Cr56 = np.nan
        self.n_K37__K38 = np.nan
        self.He4_P28__Cl32 = np.nan
        self.p_K36__Ca37 = np.nan
        self.n_K36__K37 = np.nan
        self.n_O15__He4_C12 = np.nan
        self.He4_K35__Sc39 = np.nan
        self.n_K34__K35 = np.nan
        self.n_K33__K34 = np.nan
        self.He4_K32__Sc36 = np.nan
        self.n_Si40__Si41 = np.nan
        self.n_K32__K33 = np.nan
        self.He4_Ar53__Ca57 = np.nan
        self.p_Ar51__K52 = np.nan
        self.Mn66__Fe66__weak__wc17 = np.nan
        self.p_Cl42__n_Ar42 = np.nan
        self.n_Ar51__Ar52 = np.nan
        self.n_Ar47__Ar48 = np.nan
        self.He4_Ar46__Ca50 = np.nan
        self.n_Ar46__Ar47 = np.nan
        self.n_F18__p_O18 = np.nan
        self.p_S41__Cl42 = np.nan
        self.p_Ar47__K48 = np.nan
        self.n_Ar45__Ar46 = np.nan
        self.Fe50__Mn50__weak__wc12 = np.nan
        self.p_Ar44__K45 = np.nan
        self.n_Ar44__Ar45 = np.nan
        self.p_Ar43__K44 = np.nan
        self.P46__n_n_n_S43__weak__mo03 = np.nan
        self.K53__n_Ca52__weak__wc17 = np.nan
        self.p_Ar42__K43 = np.nan
        self.n_Li7__Li8 = np.nan
        self.n_Ar42__Ar43 = np.nan
        self.n_Mg26__Mg27 = np.nan
        self.He4_Ar40__Ca44 = np.nan
        self.He4_Cr51__Fe55 = np.nan
        self.p_Ar40__K41 = np.nan
        self.n_Ar40__Ar41 = np.nan
        self.He4_Ar39__Ca43 = np.nan
        self.He4_Ar37__Ca41 = np.nan
        self.p_Ar37__K38 = np.nan
        self.He4_Ca36__Ti40 = np.nan
        self.Ne28__n_Na27__weak__wc12 = np.nan
        self.He4_Fe50__Ni54 = np.nan
        self.p_Ar35__K36 = np.nan
        self.Cl43__n_Ar42__weak__mp17 = np.nan
        self.p_F20__Ne21 = np.nan
        self.p_Si25__P26 = np.nan
        self.He4_Ar33__Ca37 = np.nan
        self.p_Ar33__K34 = np.nan
        self.He4_Ar32__Ca36 = np.nan
        self.p_Cl43__Ar44 = np.nan
        self.p_Ar32__K33 = np.nan
        self.Al41__Si41__weak__mo03 = np.nan
        self.n_Ar32__Ar33 = np.nan
        self.p_P33__He4_Si30 = np.nan
        self.p_Si44__He4_Al41 = np.nan
        self.Na32__n_n_Mg30__weak__wc12 = np.nan
        self.p_P28__S29 = np.nan
        self.He4_Ar31__Ca35 = np.nan
        self.p_Ar31__K32 = np.nan
        self.n_Ar31__Ar32 = np.nan
        self.He4_Ne20__Mg24 = np.nan
        self.Ne24__Na24__weak__wc12 = np.nan
        self.He4_Ar30__Ca34 = np.nan
        self.n_Ar29__Ar30 = np.nan
        self.He4_Cl51__K55 = np.nan
        self.He4_Mg34__Si38 = np.nan
        self.p_Cl51__Ar52 = np.nan
        self.n_Cl51__Cl52 = np.nan
        self.p_Mn57__Fe58 = np.nan
        self.He4_Cr60__n_Fe63 = np.nan
        self.p_Cl49__Ar50 = np.nan
        self.p_Ar53__n_K53 = np.nan
        self.Ca51__Sc51__weak__wc12 = np.nan
        self.n_Cl49__Cl50 = np.nan
        self.V46__Ti46__weak__wc12 = np.nan
        self.He4_Cl46__K50 = np.nan
        self.n_Cl46__Cl47 = np.nan
        self.Ti45__Sc45__weak__wc12 = np.nan
        self.n_Cl45__Cl46 = np.nan
        self.V62__n_Cr61__weak__mp17 = np.nan
        self.n_Cl44__Cl45 = np.nan
        self.He4_P26__Cl30 = np.nan
        self.He4_Cl42__K46 = np.nan
        self.n_Cl42__Cl43 = np.nan
        self.p_Cl41__Ar42 = np.nan
        self.He4_Cl39__K43 = np.nan
        self.Ne31__Na31__weak__wc17 = np.nan
        self.p_Cl46__Ar47 = np.nan
        self.p_Cl39__Ar40 = np.nan
        self.p_Cr64__n_Mn64 = np.nan
        self.Si45__n_P44__weak__mp17 = np.nan
        self.He4_Cl38__K42 = np.nan
        self.He4_Cl36__K40 = np.nan
        self.Na20__Ne20__weak__wc12 = np.nan
        self.He4_Cl35__K39 = np.nan
        self.p_Cl35__Ar36 = np.nan
        self.p_Ti39__V40 = np.nan
        self.p_Mg35__n_Al35 = np.nan
        self.He4_Cl33__K37 = np.nan
        self.n_Cl33__Cl34 = np.nan
        self.He4_Cl32__K36 = np.nan
        self.He4_O21__Ne25 = np.nan
        self.n_Mg32__Mg33 = np.nan
        self.p_Cl32__Ar33 = np.nan
        self.n_Ca44__Ca45 = np.nan
        self.p_Al42__Si43 = np.nan
        self.n_Cl32__Cl33 = np.nan
        self.He4_Cl31__K35 = np.nan
        self.He4_K45__Sc49 = np.nan
        self.p_Cl31__Ar32 = np.nan
        self.p_Cl30__Ar31 = np.nan
        self.p_Cl29__Ar30 = np.nan
        self.n_K47__K48 = np.nan
        self.K47__Ca47__weak__wc12 = np.nan
        self.He4_S49__Ar53 = np.nan
        self.He4_S48__Ar52 = np.nan
        self.p_Si34__P35 = np.nan
        self.He4_S47__Ar51 = np.nan
        self.Fe72__n_Co71__weak__mp17 = np.nan
        self.n_S47__S48 = np.nan
        self.He4_S44__Ar48 = np.nan
        self.p_S44__Cl45 = np.nan
        self.n_S44__S45 = np.nan
        self.n_Fe73__Fe74 = np.nan
        self.n_K49__K50 = np.nan
        self.n_Mg28__Mg29 = np.nan
        self.He4_S43__Ar47 = np.nan
        self.He4_S46__Ar50 = np.nan
        self.He4_S42__Ar46 = np.nan
        self.Mn61__Fe61__weak__wc12 = np.nan
        self.n_S42__S43 = np.nan
        self.Si33__P33__weak__wc12 = np.nan
        self.B17__n_n_C15__weak__wc12 = np.nan
        self.Al37__n_Si36__weak__mp17 = np.nan
        self.p_S40__Cl41 = np.nan
        self.n_S40__S41 = np.nan
        self.He4_F28__Na32 = np.nan
        self.p_Cl50__Ar51 = np.nan
        self.He4_S39__Ar43 = np.nan
        self.He4_Ar47__Ca51 = np.nan
        self.p_S39__Cl40 = np.nan
        self.n_S38__S39 = np.nan
        self.V47__Ti47__weak__wc12 = np.nan
        self.p_K34__Ca35 = np.nan
        self.He4_S36__Ar40 = np.nan
        self.He4_Mg36__Si40 = np.nan
        self.p_Na32__n_Mg32 = np.nan
        self.Cl47__n_n_Ar45__weak__mp17 = np.nan
        self.Ti51__V51__weak__wc12 = np.nan
        self.p_S36__Cl37 = np.nan
        self.He4_Ar54__n_Ca57 = np.nan
        self.p_S35__Cl36 = np.nan
        self.V45__Ti45__weak__wc12 = np.nan
        self.n_S34__S35 = np.nan
        self.He4_Ca45__n_Ti48 = np.nan
        self.n_S33__S34 = np.nan
        self.He4_S32__Ar36 = np.nan
        self.n_Ar52__Ar53 = np.nan
        self.p_S32__Cl33 = np.nan
        self.n_S32__S33 = np.nan
        self.p_S31__Cl32 = np.nan
        self.p_S29__Cl30 = np.nan
        self.He4_O22__Ne26 = np.nan
        self.He4_Ne24__Mg28 = np.nan
        self.He4_P37__Cl41 = np.nan
        self.Mg39__n_Al38__weak__mp17 = np.nan
        self.n_S27__S28 = np.nan
        self.p_Si33__P34 = np.nan
        self.n_S26__S27 = np.nan
        self.He4_Fe71__Ni75 = np.nan
        self.n_P45__P46 = np.nan
        self.n_P44__P45 = np.nan
        self.Al32__Si32__weak__wc12 = np.nan
        self.n_P42__P43 = np.nan
        self.n_P41__P42 = np.nan
        self.He4_O21__n_Ne24 = np.nan
        self.He4_P40__Cl44 = np.nan
        self.He4_K41__Sc45 = np.nan
        self.p_P40__S41 = np.nan
        self.C19__N19__weak__wc07 = np.nan
        self.He4_Cl37__K41 = np.nan
        self.He4_Mg33__n_Si36 = np.nan
        self.t__He3__weak__wc12 = np.nan
        self.p_P38__S39 = np.nan
        self.He4_Cl38__n_K41 = np.nan
        self.n_Na31__Na32 = np.nan
        self.n_P38__P39 = np.nan
        self.He4_P36__Cl40 = np.nan
        self.n_P36__P37 = np.nan
        self.He4_P35__Cl39 = np.nan
        self.C20__n_N19__weak__wc12 = np.nan
        self.He4_Cl44__K48 = np.nan
        self.p_P35__S36 = np.nan
        self.n_P35__P36 = np.nan
        self.n_P33__P34 = np.nan
        self.p_Fe58__He4_Mn55 = np.nan
        self.n_Ca38__Ca39 = np.nan
        self.He4_P32__Cl36 = np.nan
        self.n_P32__P33 = np.nan
        self.n_Mn45__He4_V42 = np.nan
        self.n_Cl32__p_S32 = np.nan
        self.n_Ar30__Ar31 = np.nan
        self.n_P28__P29 = np.nan
        self.He4_S26__Ar30 = np.nan
        self.B19__C19__weak__wc12 = np.nan
        self.He4_P27__Cl31 = np.nan
        self.n_P27__P28 = np.nan
        self.p_P26__S27 = np.nan
        self.n_P26__P27 = np.nan
        self.V55__Cr55__weak__wc12 = np.nan
        self.He4_Na31__Al35 = np.nan
        self.He4_P24__Cl28 = np.nan
        self.p_Mn70__Fe71 = np.nan
        self.He4_Cl33__p_Ar36 = np.nan
        self.S49__n_Cl48__weak__mp17 = np.nan
        self.p_Ca56__Sc57 = np.nan
        self.p_K55__n_Ca55 = np.nan
        self.p_Si42__P43 = np.nan
        self.K49__Ca49__weak__wc12 = np.nan
        self.Si31__P31__weak__wc12 = np.nan
        self.Mg37__Al37__weak__mo03 = np.nan
        self.n_Si42__Si43 = np.nan
        self.He4_Si41__S45 = np.nan
        self.He4_Si40__S44 = np.nan
        self.Ca59__n_n_Sc57__weak__mp17 = np.nan
        self.p_Si40__P41 = np.nan
        self.p_Si39__P40 = np.nan
        self.He4_Si38__S42 = np.nan
        self.p_Ar54__He4_Cl51 = np.nan
        self.F31__Ne31__weak__mo03 = np.nan
        self.S27__P27__weak__wc12 = np.nan
        self.Al34__n_Si33__weak__wc12 = np.nan
        self.n_Si38__Si39 = np.nan
        self.n_Si36__Si37 = np.nan
        self.n_Cr42__Cr43 = np.nan
        self.n_Al24__He4_Na21 = np.nan
        self.He4_Si34__S38 = np.nan
        self.He4_Si33__S37 = np.nan
        self.n_S45__S46 = np.nan
        self.He4_Cl29__K33 = np.nan
        self.p_Si32__P33 = np.nan
        self.p_Cl47__Ar48 = np.nan
        self.p_Mg37__n_Al37 = np.nan
        self.n_Si32__Si33 = np.nan
        self.n_Si22__Si23 = np.nan
        self.p_Si31__P32 = np.nan
        self.p_Si30__P31 = np.nan
        self.Cl29__S29__weak__bqa_pos_ = np.nan
        self.p_Si28__P29 = np.nan
        self.n_S41__S42 = np.nan
        self.p_Si26__P27 = np.nan
        self.n_Ne17__He4_O14 = np.nan
        self.n_Si26__Si27 = np.nan
        self.He4_Si24__S28 = np.nan
        self.Ca54__n_Sc53__weak__mp17 = np.nan
        self.p_Si24__P25 = np.nan
        self.p_Sc56__He4_Ca53 = np.nan
        self.p_Ca54__n_Sc54 = np.nan
        self.n_Si24__Si25 = np.nan
        self.Ca57__Sc57__weak__mo03 = np.nan
        self.He4_Al43__P47 = np.nan
        self.He4_Cl34__K38 = np.nan
        self.Mn62__Fe62__weak__mo03 = np.nan
        self.He4_Al42__P46 = np.nan
        self.He4_Ca38__p_Sc41 = np.nan
        self.p_O17__F18 = np.nan
        self.He4_Al40__P44 = np.nan
        self.p_Al40__Si41 = np.nan
        self.V65__Cr65__weak__mo03 = np.nan
        self.n_Al40__Al41 = np.nan
        self.p_Ti64__n_V64 = np.nan
        self.n_Al39__Al40 = np.nan
        self.He4_Al38__P42 = np.nan
        self.p_K40__Ca41 = np.nan
        self.n_Al38__Al39 = np.nan
        self.He4_Al37__P41 = np.nan
        self.p_Cl51__n_Ar51 = np.nan
        self.p_Al37__Si38 = np.nan
        self.P32__S32__weak__wc12 = np.nan
        self.Ne19__F19__weak__wc12 = np.nan
        self.n_Ar38__Ar39 = np.nan
        self.p_Sc59__He4_Ca56 = np.nan
        self.p_K44__Ca45 = np.nan
        self.S49__Cl49__weak__mo03 = np.nan
        self.He4_Al36__P40 = np.nan
        self.p_Si40__n_P40 = np.nan
        self.He4_Mg37__Si41 = np.nan
        self.p_Al36__Si37 = np.nan
        self.n_Al35__Al36 = np.nan
        self.He4_N14__n_F17 = np.nan
        self.n_V61__V62 = np.nan
        self.He4_Al34__P38 = np.nan
        self.n_Al34__Al35 = np.nan
        self.He4_Cr56__Fe60 = np.nan
        self.p_Al33__Si34 = np.nan
        self.p_Al31__Si32 = np.nan
        self.n_Al31__Al32 = np.nan
        self.Li11__n_n_Be9__weak__wc12 = np.nan
        self.He4_Al30__P34 = np.nan
        self.p_S49__He4_P46 = np.nan
        self.p_Al30__Si31 = np.nan
        self.n_V50__V51 = np.nan
        self.p_Al28__Si29 = np.nan
        self.He4_Ti62__n_Cr65 = np.nan
        self.p_Cr68__Mn69 = np.nan
        self.He4_Al27__P31 = np.nan
        self.Al25__Mg25__weak__wc12 = np.nan
        self.He4_Al26__P30 = np.nan
        self.n_Al26__Al27 = np.nan
        self.p_Al24__Si25 = np.nan
        self.n_Al24__Al25 = np.nan
        self.He4_Ti56__Cr60 = np.nan
        self.Fe69__Co69__weak__wc17 = np.nan
        self.He4_Mg41__Si45 = np.nan
        self.p_Cl39__n_Ar39 = np.nan
        self.He4_Mg39__Si43 = np.nan
        self.p_Mg39__Al40 = np.nan
        self.p_Mg37__Al38 = np.nan
        self.n_Sc44__Sc45 = np.nan
        self.n_Mg36__Mg37 = np.nan
        self.He4_Al41__P45 = np.nan
        self.d_Li6__n_Be7 = np.nan
        self.n_Mg35__Mg36 = np.nan
        self.p_Sc60__Ti61 = np.nan
        self.p_P46__He4_Si43 = np.nan
        self.n_Mg34__Mg35 = np.nan
        self.p_Cr47__Mn48 = np.nan
        self.He4_Si39__S43 = np.nan
        self.He4_Mg40__Si44 = np.nan
        self.p_Ca43__Sc44 = np.nan
        self.He4_Mg33__Si37 = np.nan
        self.He4_Mg31__Si35 = np.nan
        self.p_S48__He4_P45 = np.nan
        self.n_Si35__Si36 = np.nan
        self.He4_Al29__P33 = np.nan
        self.n_K37__p_Ar37 = np.nan
        self.n_Mg31__Mg32 = np.nan
        self.p_Fe49__Co50 = np.nan
        self.He4_K47__Sc51 = np.nan
        self.p_Mg30__Al31 = np.nan
        self.p_Si44__P45 = np.nan
        self.He4_Mg29__Si33 = np.nan
        self.p_Mg33__n_Al33 = np.nan
        self.n_Mg29__Mg30 = np.nan
        self.He4_Mg30__Si34 = np.nan
        self.n_Ca45__Ca46 = np.nan
        self.p_Mg32__Al33 = np.nan
        self.He4_Mg28__Si32 = np.nan
        self.p_Fe54__Co55 = np.nan
        self.p_Mg27__Al28 = np.nan
        self.He4_Mn65__Co69 = np.nan
        self.Mn70__Fe70__weak__mo03 = np.nan
        self.B17__C17__weak__wc17 = np.nan
        self.Ti64__n_n_V62__weak__mp17 = np.nan
        self.P44__S44__weak__wc17 = np.nan
        self.p_Fe46__Co47 = np.nan
        self.p_Mg26__Al27 = np.nan
        self.p_K49__Ca50 = np.nan
        self.Ne25__Na25__weak__wc12 = np.nan
        self.p_Mg24__Al25 = np.nan
        self.n_Mg24__Mg25 = np.nan
        self.n_Ca43__Ca44 = np.nan
        self.Fe68__n_Co67__weak__mp17 = np.nan
        self.He4_Mg23__Si27 = np.nan
        self.p_Mg23__Al24 = np.nan
        self.n_Mn44__He4_V41 = np.nan
        self.S45__n_n_Cl43__weak__mp17 = np.nan
        self.n_Mg23__Mg24 = np.nan
        self.He4_Mg31__n_Si34 = np.nan
        self.He4_Ca53__Ti57 = np.nan
        self.Cl28__S28__weak__bqa_pos_ = np.nan
        self.n_Cl34__Cl35 = np.nan
        self.p_Mg22__Al23 = np.nan
        self.n_Mg22__Mg23 = np.nan
        self.n_C14__C15 = np.nan
        self.He4_Mg21__Si25 = np.nan
        self.He4_Mn48__p_Fe51 = np.nan
        self.He4_He4_He4__C12 = np.nan
        self.He4_Cl43__K47 = np.nan
        self.He4_Mg19__Si23 = np.nan
        self.p_Na38__Mg39 = np.nan
        self.He4_Si31__S35 = np.nan
        self.p_Sc36__Ti37 = np.nan
        self.He4_Na37__Al41 = np.nan
        self.n_Na37__Na38 = np.nan
        self.n_Mn51__Mn52 = np.nan
        self.He4_S49__n_Ar52 = np.nan
        self.n_Na36__Na37 = np.nan
        self.p_Cl47__n_Ar47 = np.nan
        self.Ca38__K38__weak__wc12 = np.nan
        self.He4_Na34__Al38 = np.nan
        self.n_Na34__Na35 = np.nan
        self.He4_Na33__Al37 = np.nan
        self.n_He3__He4 = np.nan
        self.p_F21__n_Ne21 = np.nan
        self.He4_Na39__Al43 = np.nan
        self.Mg32__n_Al31__weak__wc12 = np.nan
        self.p_Na32__Mg33 = np.nan
        self.He4_Al28__p_Si31 = np.nan
        self.He4_Ne29__n_Mg32 = np.nan
        self.He4_P25__Cl29 = np.nan
        self.p_Na36__Mg37 = np.nan
        self.Cl50__Ar50__weak__mo03 = np.nan
        self.He4_Na28__Al32 = np.nan
        self.n_F15__F16 = np.nan
        self.p_Na26__Mg27 = np.nan
        self.He4_Ti56__n_Cr59 = np.nan
        self.Si45__P45__weak__mo03 = np.nan
        self.p_Na25__Mg26 = np.nan
        self.n_Na24__Na25 = np.nan
        self.Na36__Mg36__weak__mo03 = np.nan
        self.p_Ar52__K53 = np.nan
        self.Na28__Mg28__weak__wc12 = np.nan
        self.He4_F15__p_Ne18 = np.nan
        self.He4_Na23__Al27 = np.nan
        self.p_Ca51__n_Sc51 = np.nan
        self.p_Sc63__He4_Ca60 = np.nan
        self.p_Na23__Mg24 = np.nan
        self.Sc62__n_Ti61__weak__mp17 = np.nan
        self.p_Na22__Mg23 = np.nan
        self.n_Na22__Na23 = np.nan
        self.He4_V55__Mn59 = np.nan
        self.He4_Ar50__Ca54 = np.nan
        self.p_Na21__Mg22 = np.nan
        self.Ar53__n_n_K51__weak__mp17 = np.nan
        self.He4_Ti42__Cr46 = np.nan
        self.n_Na21__Na22 = np.nan
        self.p_Ti65__n_V65 = np.nan
        self.He4_Na20__Al24 = np.nan
        self.p_S33__Cl34 = np.nan
        self.n_Na20__Na21 = np.nan
        self.Sc63__Ti63__weak__mo03 = np.nan
        self.n_Na19__Na20 = np.nan
        self.p_Mg31__He4_Na28 = np.nan
        self.Al42__Si42__weak__mo03 = np.nan
        self.He4_K58__n_Sc61 = np.nan
        self.n_Mg40__Mg41 = np.nan
        self.He4_Ne34__Mg38 = np.nan
        self.p_Sc54__Ti55 = np.nan
        self.n_Ne32__Ne33 = np.nan
        self.p_Si29__P30 = np.nan
        self.Cr68__n_Mn67__weak__mp17 = np.nan
        self.He4_Ne31__Mg35 = np.nan
        self.p_Ne31__Na32 = np.nan
        self.He4_Ne30__Mg34 = np.nan
        self.He4_Ca58__Ti62 = np.nan
        self.Mg41__n_Al40__weak__mp17 = np.nan
        self.p_Ne30__Na31 = np.nan
        self.p_Mn71__n_Fe71 = np.nan
        self.Mn52__Cr52__weak__wc12 = np.nan
        self.Ti58__V58__weak__wc12 = np.nan
        self.Ne17__p_O16__weak__wc12 = np.nan
        self.p_Cl44__Ar45 = np.nan
        self.p_Ne28__Na29 = np.nan
        self.p_Na35__He4_Ne32 = np.nan
        self.n_Fe74__Fe75 = np.nan
        self.p_Ne27__Na28 = np.nan
        self.He4_Ne26__Mg30 = np.nan
        self.Ti41__p_Ca40__weak__wc12 = np.nan
        self.n_Ne26__Ne27 = np.nan
        self.S28__p_Si27__weak__wc12 = np.nan
        self.He4_Cl52__n_K55 = np.nan
        self.p_Ne25__Na26 = np.nan
        self.n_Mg19__Mg20 = np.nan
        self.n_Ne24__Ne25 = np.nan
        self.p_Ne23__Na24 = np.nan
        self.Sc42__Ca42__weak__wc12 = np.nan
        self.p_Al43__Si44 = np.nan
        self.p_Ne33__Na34 = np.nan
        self.p_F27__Ne28 = np.nan
        self.p_Ne20__Na21 = np.nan
        self.p_K53__Ca54 = np.nan
        self.p_Cr70__n_Mn70 = np.nan
        self.p_Ne19__Na20 = np.nan
        self.p_F24__He4_O21 = np.nan
        self.F24__Ne24__weak__wc12 = np.nan
        self.p_Mn52__Fe53 = np.nan
        self.n_Ne19__Ne20 = np.nan
        self.p_Ne18__Na19 = np.nan
        self.Ne32__n_Na31__weak__mp17 = np.nan
        self.p_Cr64__Mn65 = np.nan
        self.Sc61__n_Ti60__weak__mp17 = np.nan
        self.n_S46__S47 = np.nan
        self.Ca39__K39__weak__wc12 = np.nan
        self.n_Ne18__Ne19 = np.nan
        self.p_Cl48__Ar49 = np.nan
        self.n_Ne17__Ne18 = np.nan
        self.He4_Cr65__Fe69 = np.nan
        self.F25__Ne25__weak__wc12 = np.nan
        self.He4_Ne16__Mg20 = np.nan
        self.He4_Na30__Al34 = np.nan
        self.He4_O28__Ne32 = np.nan
        self.n_Ne16__Ne17 = np.nan
        self.He4_F31__Na35 = np.nan
        self.n_O13__O14 = np.nan
        self.p_F28__Ne29 = np.nan
        self.p_F19__He4_O16 = np.nan
        self.p_Mg38__Al39 = np.nan
        self.He4_Mg29__n_Si32 = np.nan
        self.He4_Ar41__Ca45 = np.nan
        self.n_V41__p_Ti41 = np.nan
        self.n_P39__P40 = np.nan
        self.n_Si34__Si35 = np.nan
        self.He4_F24__Na28 = np.nan
        self.He4_Al31__P35 = np.nan
        self.n_F23__F24 = np.nan
        self.He4_Mn51__Co55 = np.nan
        self.p_F22__Ne23 = np.nan
        self.n_F22__F23 = np.nan
        self.p_F21__Ne22 = np.nan
        self.n_Cr54__Cr55 = np.nan
        self.p_Fe51__Co52 = np.nan
        self.n_F21__F22 = np.nan
        self.Na30__n_Mg29__weak__wc17 = np.nan
        self.n_Al23__Al24 = np.nan
        self.n_F20__F21 = np.nan
        self.N22__O22__weak__wc12 = np.nan
        self.He4_F18__Na22 = np.nan
        self.n_F18__F19 = np.nan
        self.n_F17__F18 = np.nan
        self.He4_K59__Sc63 = np.nan
        self.n_F16__F17 = np.nan
        self.n_F14__F15 = np.nan
        self.p_O27__F28 = np.nan
        self.He4_Ar42__Ca46 = np.nan
        self.p_O26__F27 = np.nan
        self.p_Cl43__n_Ar43 = np.nan
        self.Cr67__n_Mn66__weak__mp17 = np.nan
        self.He4_O24__Ne28 = np.nan
        self.p_K35__Ca36 = np.nan
        self.n_Ne23__Ne24 = np.nan
        self.He4_O23__Ne27 = np.nan
        self.K36__He4_S32__weak__wc12 = np.nan
        self.n_O23__O24 = np.nan
        self.He4_F27__Na31 = np.nan
        self.n_K57__K58 = np.nan
        self.p_O22__F23 = np.nan
        self.n_O22__O23 = np.nan
        self.n_O21__O22 = np.nan
        self.n_Cl31__He4_P28 = np.nan
        self.He4_O20__Ne24 = np.nan
        self.p_O20__F21 = np.nan
        self.He4_O20__n_Ne23 = np.nan
        self.n_Ar48__Ar49 = np.nan
        self.He4_O19__Ne23 = np.nan
        self.He4_S28__Ar32 = np.nan
        self.K58__n_n_Ca56__weak__mp17 = np.nan
        self.He4_Ar44__n_Ca47 = np.nan
        self.He4_O17__Ne21 = np.nan
        self.n_O16__O17 = np.nan
        self.p_S44__n_Cl44 = np.nan
        self.n_O15__O16 = np.nan
        self.n_N19__N20 = np.nan
        self.n_Si27__He4_Mg24 = np.nan
        self.Sc63__n_Ti62__weak__mp17 = np.nan
        self.V58__n_Cr57__weak__mp17 = np.nan
        self.n_N17__N18 = np.nan
        self.Ar45__K45__weak__wc12 = np.nan
        self.He4_P33__Cl37 = np.nan
        self.n_N16__N17 = np.nan
        self.n_Cl29__Cl30 = np.nan
        self.n_Ti53__Ti54 = np.nan
        self.n_N15__N16 = np.nan
        self.Ti60__n_V59__weak__mp17 = np.nan
        self.p_N14__O15 = np.nan
        self.n_N13__N14 = np.nan
        self.Mg38__n_n_Al36__weak__mp17 = np.nan
        self.n_Fe53__Fe54 = np.nan
        self.p_C14__N15 = np.nan
        self.p_C13__N14 = np.nan
        self.p_C12__N13 = np.nan
        self.p_C11__N12 = np.nan
        self.n_V42__p_Ti42 = np.nan
        self.n_B12__B13 = np.nan
        self.n_p__d = np.nan
        self.n_B11__B12 = np.nan
        self.p_B10__C11 = np.nan
        self.p_Na28__Mg29 = np.nan
        self.n_B10__B11 = np.nan
        self.n_Be11__Be12 = np.nan
        self.p_Be10__B11 = np.nan
        self.p_Sc39__Ti40 = np.nan
        self.He4_Ti64__Cr68 = np.nan
        self.n_Mg20__Mg21 = np.nan
        self.p_Be7__B8 = np.nan
        self.He4_Li9__B13 = np.nan
        self.He4_Mg26__Si30 = np.nan
        self.He4_Fe45__p_Co48 = np.nan
        self.p_P35__n_S35 = np.nan
        self.He4_Na24__Al28 = np.nan
        self.He4_Li8__B12 = np.nan
        self.He4_He3__Be7 = np.nan
        self.He4_Fe75__Ni79 = np.nan
        self.p_Ne24__Na25 = np.nan
        self.p_t__He4 = np.nan
        self.He4_d__Li6 = np.nan
        self.p_P27__S28 = np.nan
        self.He4_Cr49__Fe53 = np.nan
        self.He4_C12__O16 = np.nan
        self.Fe75__n_n_Co73__weak__mp17 = np.nan
        self.V61__n_Cr60__weak__wc12 = np.nan
        self.Fe73__n_n_Co71__weak__mp17 = np.nan
        self.Mn73__n_n_Fe71__weak__mp17 = np.nan
        self.He4_Fe62__n_Ni65 = np.nan
        self.F27__n_Ne26__weak__wc12 = np.nan
        self.Mn72__n_n_Fe70__weak__mp17 = np.nan
        self.Al22__Mg22__weak__wc12 = np.nan
        self.Mn71__n_n_Fe69__weak__mp17 = np.nan
        self.He4_Mg27__Si31 = np.nan
        self.Fe59__Co59__weak__wc12 = np.nan
        self.Mn70__n_n_Fe68__weak__mp17 = np.nan
        self.Ca61__n_n_n_Sc58__weak__mo03 = np.nan
        self.n_Ti47__p_Sc47 = np.nan
        self.p_Ca49__n_Sc49 = np.nan
        self.Mn68__n_n_Fe66__weak__mp17 = np.nan
        self.p_Si35__P36 = np.nan
        self.p_Ti46__V47 = np.nan
        self.He4_P34__Cl38 = np.nan
        self.p_Fe71__Co72 = np.nan
        self.Ti65__n_n_V63__weak__mp17 = np.nan
        self.Ar35__Cl35__weak__wc12 = np.nan
        self.Si42__P42__weak__wc17 = np.nan
        self.n_K51__K52 = np.nan
        self.Fe48__Mn48__weak__wc12 = np.nan
        self.He4_Ca49__n_Ti52 = np.nan
        self.Sc60__n_n_Ti58__weak__mp17 = np.nan
        self.n_V48__He4_Sc45 = np.nan
        self.p_F18__Ne19 = np.nan
        self.p_Mg36__Al37 = np.nan
        self.Ar49__n_K48__weak__wc12 = np.nan
        self.n_Ne28__Ne29 = np.nan
        self.n_Si25__Si26 = np.nan
        self.K59__n_n_Ca57__weak__mp17 = np.nan
        self.n_S31__He4_Si28 = np.nan
        self.K56__Ca56__weak__mo03 = np.nan
        self.n_P29__P30 = np.nan
        self.Mn67__Fe67__weak__wc17 = np.nan
        self.K53__n_n_Ca51__weak__mp17 = np.nan
        self.n_Cr58__Cr59 = np.nan
        self.He4_Mn73__Co77 = np.nan
        self.K52__n_n_Ca50__weak__mp17 = np.nan
        self.Ar54__n_n_K52__weak__mp17 = np.nan
        self.p_Ar42__He4_Cl39 = np.nan
        self.N21__n_O20__weak__wc12 = np.nan
        self.Cl52__n_n_Ar50__weak__mp17 = np.nan
        self.Cl50__n_n_Ar48__weak__mp17 = np.nan
        self.S49__n_n_Cl47__weak__mp17 = np.nan
        self.S47__n_n_Cl45__weak__mp17 = np.nan
        self.n_Cl30__He4_P27 = np.nan
        self.S27__p_p_Al25__weak__wc12 = np.nan
        self.P47__n_n_S45__weak__mp17 = np.nan
        self.O20__F20__weak__wc12 = np.nan
        self.He4_K42__Sc46 = np.nan
        self.P45__n_n_S43__weak__mp17 = np.nan
        self.He4_Na19__p_Mg22 = np.nan
        self.p_F25__Ne26 = np.nan
        self.P44__n_n_S42__weak__mp17 = np.nan
        self.P43__n_n_S41__weak__mp17 = np.nan
        self.Cr61__Mn61__weak__wc12 = np.nan
        self.Si44__n_n_P42__weak__mp17 = np.nan
        self.He4_Mn61__n_Co64 = np.nan
        self.Sc57__Ti57__weak__wc17 = np.nan
        self.He4_Si28__S32 = np.nan
        self.Si41__n_n_P39__weak__mp17 = np.nan
        self.p_K42__Ca43 = np.nan
        self.Si39__n_n_P37__weak__mp17 = np.nan
        self.Si23__p_p_Na21__weak__wc12 = np.nan
        self.He4_Sc41__p_Ti44 = np.nan
        self.He4_Sc36__V40 = np.nan
        self.p_S37__He4_P34 = np.nan
        self.Al43__n_n_Si41__weak__mp17 = np.nan
        self.Al41__n_n_Si39__weak__mp17 = np.nan
        self.He4_Mn43__p_Fe46 = np.nan
        self.n_K42__K43 = np.nan
        self.Al38__n_n_Si36__weak__mp17 = np.nan
        self.P41__n_S40__weak__wc12 = np.nan
        self.p_V40__Cr41 = np.nan
        self.Mg33__n_Al32__weak__wc12 = np.nan
        self.He4_K36__Sc40 = np.nan
        self.Mg37__n_n_Al35__weak__mp17 = np.nan
        self.p_K39__Ca40 = np.nan
        self.He4_Sc40__V44 = np.nan
        self.Cr43__p_Ti42__weak__wc17 = np.nan
        self.Al24__p_Na23__weak__wc12 = np.nan
        self.Mg33__n_n_Al31__weak__mp17 = np.nan
        self.Na35__n_n_Mg33__weak__mp17 = np.nan
        self.p_Sc51__n_Ti51 = np.nan
        self.Na31__n_n_Mg29__weak__wc12 = np.nan
        self.Sc59__n_n_Ti57__weak__mp17 = np.nan
        self.He4_K47__n_Sc50 = np.nan
        self.F24__n_Ne23__weak__wc12 = np.nan
        self.Na30__n_n_Mg28__weak__wc12 = np.nan
        self.Mn69__n_Fe68__weak__mp17 = np.nan
        self.Ne32__n_n_Na30__weak__mp17 = np.nan
        self.He4_O14__Ne18 = np.nan
        self.Al22__p_p_Ne20__weak__wc12 = np.nan
        self.p_Ti50__V51 = np.nan
        self.Ne29__n_n_Na27__weak__wc12 = np.nan
        self.F30__n_n_Ne28__weak__mp17 = np.nan
        self.O27__n_n_F25__weak__mp17 = np.nan
        self.n_Ar36__Ar37 = np.nan
        self.O26__n_n_F24__weak__mp17 = np.nan
        self.p_Mn53__Fe54 = np.nan
        self.C14__N14__weak__wc12 = np.nan
        self.He4_Mg38__Si42 = np.nan
        self.O25__n_n_F23__weak__mp17 = np.nan
        self.B15__n_n_C13__weak__wc12 = np.nan
        self.n_Ar43__Ar44 = np.nan
        self.He4_Si26__S30 = np.nan
        self.p_P33__S34 = np.nan
        self.Be16__n_n_Be14 = np.nan
        self.Be14__n_n_B12__weak__wc12 = np.nan
        self.He4_Na20__p_Mg23 = np.nan
        self.p_Al28__n_Si28 = np.nan
        self.Fe75__n_Co74__weak__mp17 = np.nan
        self.P43__n_S42__weak__wc12 = np.nan
        self.Fe73__n_Co72__weak__mp17 = np.nan
        self.Fe74__Co74__weak__mo03 = np.nan
        self.p_Cl41__n_Ar41 = np.nan
        self.n_Mg25__Mg26 = np.nan
        self.n_C11__C12 = np.nan
        self.Fe70__n_Co69__weak__mp17 = np.nan
        self.Mg35__n_Al34__weak__wc12 = np.nan
        self.n_Cl30__Cl31 = np.nan
        self.Fe69__n_Co68__weak__mp17 = np.nan
        self.He4_Fe74__Ni78 = np.nan
        self.p_K55__Ca56 = np.nan
        self.p_K47__n_Ca47 = np.nan
        self.p_Ca50__n_Sc50 = np.nan
        self.He4_V44__p_Cr47 = np.nan
        self.n_S35__S36 = np.nan
        self.He4_Mg36__n_Si39 = np.nan
        self.n_Ca48__Ca49 = np.nan
        self.He4_B11__n_N14 = np.nan
        self.He4_Mn58__Co62 = np.nan
        self.He4_Si32__S36 = np.nan
        self.p_V45__Cr46 = np.nan
        self.V60__n_Cr59__weak__mp17 = np.nan
        self.He4_S29__Ar33 = np.nan
        self.Sc44__Ca44__weak__wc12 = np.nan
        self.p_p__d__weak__bet_pos_ = np.nan
        self.p_p__d__weak__electron_capture = np.nan
        self.Ti57__V57__weak__wc12 = np.nan
        self.p_Cl38__n_Ar38 = np.nan
        self.He4_F30__Na34 = np.nan
        self.He4_Fe63__Ni67 = np.nan
        self.n_Cl31__Cl32 = np.nan
        self.p_Al23__Si24 = np.nan
        self.n_Cl48__Cl49 = np.nan
        self.V65__n_Cr64__weak__mp17 = np.nan
        self.He4_F20__Na24 = np.nan
        self.He4_K59__n_Sc62 = np.nan
        self.He4_S47__n_Ar50 = np.nan
        self.p_Al41__Si42 = np.nan
        self.K48__n_Ca47__weak__wc12 = np.nan
        self.n_Mg19__p_Na19 = np.nan
        self.p_Cl38__Ar39 = np.nan
        self.p_Mg32__n_Al32 = np.nan
        self.He4_Cl28__K32 = np.nan
        self.Fe48__p_Cr47__weak__wc12 = np.nan
        self.p_Na27__Mg28 = np.nan
        self.p_P46__n_S46 = np.nan
        self.p_P41__n_S41 = np.nan
        self.Al43__n_Si42__weak__mp17 = np.nan
        self.Si23__Al23__weak__wc12 = np.nan
        self.Fe46__p_Cr45__weak__wc12 = np.nan
        self.p_P39__n_S39 = np.nan
        self.p_Cr55__Mn56 = np.nan
        self.n_Cl38__Cl39 = np.nan
        self.Ne18__F18__weak__wc12 = np.nan
        self.Fe45__p_Cr44__weak__wc17 = np.nan
        self.He4_Mg28__n_Si31 = np.nan
        self.Mn73__n_Fe72__weak__mp17 = np.nan
        self.Mn72__n_Fe71__weak__mp17 = np.nan
        self.p_Mn63__He4_Cr60 = np.nan
        self.n_Al23__p_Mg23 = np.nan
        self.Ar52__K52__weak__mo03 = np.nan
        self.Mn65__n_Fe64__weak__mp17 = np.nan
        self.Fe74__n_Co73__weak__mp17 = np.nan
        self.n_P40__P41 = np.nan
        self.S26__P26__weak__bqa_pos_ = np.nan
        self.n_Al24__p_Mg24 = np.nan
        self.He4_Cr68__n_Fe71 = np.nan
        self.He4_Fe66__Ni70 = np.nan
        self.p_Ca50__Sc51 = np.nan
        self.He4_Si29__S33 = np.nan
        self.p_Mn64__Fe65 = np.nan
        self.p_V44__Cr45 = np.nan
        self.Li11__Be11__weak__wc12 = np.nan
        self.Ca61__n_Sc60__weak__mp17 = np.nan
        self.n_Fe60__Fe61 = np.nan
        self.n_Si23__He4_Mg20 = np.nan
        self.Ti61__V61__weak__wc17 = np.nan
        self.n_Cl41__Cl42 = np.nan
        self.Al23__Mg23__weak__wc12 = np.nan
        self.p_N14__n_O14 = np.nan
        self.p_Na36__He4_Ne33 = np.nan
        self.He4_O18__n_Ne21 = np.nan
        self.He4_Be9__n_C12 = np.nan
        self.p_Cl34__Ar35 = np.nan
        self.K55__n_n_Ca53__weak__mp17 = np.nan
        self.He4_Fe61__Ni65 = np.nan
        self.p_Mg37__He4_Na34 = np.nan
        self.p_Na34__n_Mg34 = np.nan
        self.Mg39__n_n_Al37__weak__mp17 = np.nan
        self.n_Mg22__p_Na22 = np.nan
        self.He4_Ca35__p_Sc38 = np.nan
        self.Ne32__Na32__weak__wc17 = np.nan
        self.He4_Ar54__Ca58 = np.nan
        self.He4_V59__Mn63 = np.nan
        self.p_K58__Ca59 = np.nan
        self.Si32__P32__weak__wc12 = np.nan
        self.p_Fe53__Co54 = np.nan
        self.He4_P41__Cl45 = np.nan
        self.He4_P46__n_Cl49 = np.nan
        self.He4_K53__Sc57 = np.nan
        self.Mn46__p_V45__weak__wc12 = np.nan
        self.K57__n_n_Ca55__weak__mp17 = np.nan
        self.He4_S34__Ar38 = np.nan
        self.He4_Ca37__p_Sc40 = np.nan
        self.Be12__B12__weak__wc12 = np.nan
        self.N19__n_O18__weak__wc12 = np.nan
        self.p_P31__He4_Si28 = np.nan
        self.n_Ti37__p_Sc37 = np.nan
        self.Cr70__n_Mn69__weak__mp17 = np.nan
        self.O24__n_F23__weak__wc12 = np.nan
        self.Sc41__Ca41__weak__wc12 = np.nan
        self.Mn68__n_Fe67__weak__mp17 = np.nan
        self.p_P41__S42 = np.nan
        self.p_Cl44__n_Ar44 = np.nan
        self.Cr69__n_Mn68__weak__mp17 = np.nan
        self.n_Li8__Li9 = np.nan
        self.He4_N12__p_O15 = np.nan
        self.Cr66__n_Mn65__weak__mp17 = np.nan
        self.n_C13__C14 = np.nan
        self.n_Mg21__p_Na21 = np.nan
        self.Cr63__n_Mn62__weak__mp17 = np.nan
        self.He4_Mn71__Co75 = np.nan
        self.n_Ca59__Ca60 = np.nan
        self.N13__C13__weak__wc12 = np.nan
        self.p_Ca48__Sc49 = np.nan
        self.Sc37__Ca37__weak__bqa_pos_ = np.nan
        self.F29__Ne29__weak__wc17 = np.nan
        self.He4_V65__n_Mn68 = np.nan
        self.Cr62__n_Mn61__weak__mp17 = np.nan
        self.F30__n_Ne29__weak__mp17 = np.nan
        self.Cr61__n_Mn60__weak__mp17 = np.nan
        self.n_Si23__Si24 = np.nan
        self.p_Mg41__Al42 = np.nan
        self.He4_Be10__n_C13 = np.nan
        self.n_Be7__p_Li7 = np.nan
        self.n_Al21__Al22 = np.nan
        self.n_Si26__He4_Mg23 = np.nan
        self.n_Na32__Na33 = np.nan
        self.Mn44__Cr44__weak__bqa_pos_ = np.nan
        self.Fe73__Co73__weak__mo03 = np.nan
        self.He4_Ca55__n_Ti58 = np.nan
        self.He4_Ar44__Ca48 = np.nan
        self.Cr45__p_Ti44__weak__wc12 = np.nan
        self.n_P34__P35 = np.nan
        self.He4_P28__p_S31 = np.nan
        self.He4_Si25__S29 = np.nan
        self.n_Sc35__Sc36 = np.nan
        self.p_Sc47__Ti48 = np.nan
        self.He4_P38__Cl42 = np.nan
        self.n_Cl28__p_S28 = np.nan
        self.Ar51__n_K50__weak__mp17 = np.nan
        self.Cr42__p_Ti41__weak__wc12 = np.nan
        self.He4_Mg25__Si29 = np.nan
        self.He4_Mn52__p_Fe55 = np.nan
        self.n_Mn50__p_Cr50 = np.nan
        self.C15__N15__weak__wc12 = np.nan
        self.V63__n_Cr62__weak__wc12 = np.nan
        self.Ar52__n_K51__weak__mp17 = np.nan
        self.n_Cr41__p_V41 = np.nan
        self.p_Ar46__K47 = np.nan
        self.V59__n_Cr58__weak__wc12 = np.nan
        self.p_S42__He4_P39 = np.nan
        self.He4_N14__F18 = np.nan
        self.He4_Si36__n_S39 = np.nan
        self.p_Li8__n_He4_He4 = np.nan
        self.n_Ca47__Ca48 = np.nan
        self.p_Fe67__Co68 = np.nan
        self.Fe76__n_n_Co74__weak__mp17 = np.nan
        self.n_Cr47__Cr48 = np.nan
        self.He4_V48__Mn52 = np.nan
        self.He4_Ca61__Ti65 = np.nan
        self.He4_Fe62__Ni66 = np.nan
        self.He4_Ca55__Ti59 = np.nan
        self.n_S28__p_P28 = np.nan
        self.He4_P46__Cl50 = np.nan
        self.Ti56__V56__weak__wc12 = np.nan
        self.K55__n_Ca54__weak__mp17 = np.nan
        self.n_Mg20__He4_Ne17 = np.nan
        self.F22__Ne22__weak__wc17 = np.nan
        self.Sc39__Ca39__weak__mo97 = np.nan
        self.Fe75__Co75__weak__mo03 = np.nan
        self.He4_Al24__P28 = np.nan
        self.p_Si40__He4_Al37 = np.nan
        self.p_Mg41__n_Al41 = np.nan
        self.Mg39__Al39__weak__mo03 = np.nan
        self.p_Cl42__Ar43 = np.nan
        self.He4_Ti50__Cr54 = np.nan
        self.n_Sc52__Sc53 = np.nan
        self.p_Sc51__Ti52 = np.nan
        self.n_Ti40__p_Sc40 = np.nan
        self.He4_Al43__n_P46 = np.nan
        self.n_P30__p_Si30 = np.nan
        self.n_P46__P47 = np.nan
        self.O28__n_n_F26__weak__mp17 = np.nan
        self.He4_Fe51__p_Co54 = np.nan
        self.Cl31__p_P30__weak__wc12 = np.nan
        self.Mg40__n_n_Al38__weak__mp17 = np.nan
        self.p_F19__Ne20 = np.nan
        self.He4_Ne25__n_Mg28 = np.nan
        self.Cr70__n_n_Mn68__weak__mp17 = np.nan
        self.p_K50__He4_Ar47 = np.nan
        self.Ti64__n_V63__weak__mp17 = np.nan
        self.He4_O27__n_Ne30 = np.nan
        self.n_Mn57__Mn58 = np.nan
        self.He4_Ca60__Ti64 = np.nan
        self.n_P25__He4_Al22 = np.nan
        self.Ti63__n_V62__weak__mp17 = np.nan
        self.n_F19__F20 = np.nan
        self.V52__Cr52__weak__wc12 = np.nan
        self.Ti61__n_V60__weak__mp17 = np.nan
        self.He4_P39__Cl43 = np.nan
        self.V65__n_n_Cr63__weak__mp17 = np.nan
        self.n_Na22__p_Ne22 = np.nan
        self.p_S45__n_Cl45 = np.nan
        self.n_Cr52__Cr53 = np.nan
        self.n_P30__P31 = np.nan
        self.Ca55__n_Sc54__weak__mp17 = np.nan
        self.Sc57__n_Ti56__weak__mp17 = np.nan
        self.He4_S38__Ar42 = np.nan
        self.He4_Ar30__p_K33 = np.nan
        self.Ti58__n_V57__weak__mp17 = np.nan
        self.p_Ar30__K31 = np.nan
        self.Al37__n_n_Si35__weak__mp17 = np.nan
        self.Cr69__n_n_Mn67__weak__mp17 = np.nan
        self.He4_P31__Cl35 = np.nan
        self.p_Mn58__n_Fe58 = np.nan
        self.p_Ca57__He4_K54 = np.nan
        self.p_Cr65__n_Mn65 = np.nan
        self.p_F29__n_Ne29 = np.nan
        self.He4_Mg32__Si36 = np.nan
        self.Na21__Ne21__weak__wc12 = np.nan
        self.He4_Cl41__K45 = np.nan
        self.n_Ca39__He4_Ar36 = np.nan
        self.O26__n_O25 = np.nan
        self.d_d__He4 = np.nan
        self.Al40__n_Si39__weak__mp17 = np.nan
        self.p_N13__O14 = np.nan
        self.n_C12__C13 = np.nan
        self.Ar31__p_S30__weak__wc17 = np.nan
        self.p_Mn63__n_Fe63 = np.nan
        self.n_Al27__Al28 = np.nan
        self.Mn49__Cr49__weak__wc12 = np.nan
        self.He4_Cl43__n_K46 = np.nan
        self.Al42__n_n_Si40__weak__mo03 = np.nan
        self.He4_Na33__n_Al36 = np.nan
        self.Cl32__He4_Si28__weak__wc12 = np.nan
        self.S28__P28__weak__wc12 = np.nan
        self.n_K48__K49 = np.nan
        self.He4_Ti55__Cr59 = np.nan
        self.He4_V45__p_Cr48 = np.nan
        self.He4_Al39__P43 = np.nan
        self.p_Ne30__n_Na30 = np.nan
        self.p_F30__n_Ne30 = np.nan
        self.p_Na27__He4_Ne24 = np.nan
        self.n_Ti50__Ti51 = np.nan
        self.He4_Na25__n_Al28 = np.nan
        self.n_S27__He4_Si24 = np.nan
        self.Mn66__n_Fe65__weak__mp17 = np.nan
        self.C22__n_N21__weak__wc17 = np.nan
        self.p_Si33__He4_Al30 = np.nan
        self.p_B11__C12 = np.nan
        self.Ti39__p_Ca38__weak__wc12 = np.nan
        self.Ti44__Sc44__weak__wc12 = np.nan
        self.n_V64__V65 = np.nan
        self.Mg23__Na23__weak__wc12 = np.nan
        self.Ar39__K39__weak__wc12 = np.nan
        self.n_Sc36__p_Ca36 = np.nan
        self.p_K46__He4_Ar43 = np.nan
        self.p_S41__n_Cl41 = np.nan
        self.Sc59__n_Ti58__weak__mp17 = np.nan
        self.He4_t__Li7 = np.nan
        self.p_Mg36__n_Al36 = np.nan
        self.Sc58__n_Ti57__weak__mp17 = np.nan
        self.n_He4_He4__Be9 = np.nan
        self.He4_P47__Cl51 = np.nan
        self.K54__n_n_Ca52__weak__mp17 = np.nan
        self.p_Cr69__n_Mn69 = np.nan
        self.Sc59__Ti59__weak__mo03 = np.nan
        self.He4_Cl48__K52 = np.nan
        self.He4_Ar47__n_Ca50 = np.nan
        self.n_Al32__Al33 = np.nan
        self.n_Cr65__Cr66 = np.nan
        self.p_V51__Cr52 = np.nan
        self.Ca49__Sc49__weak__wc12 = np.nan
        self.p_Al38__Si39 = np.nan
        self.He4_S40__n_Ar43 = np.nan
        self.V54__Cr54__weak__wc12 = np.nan
        self.Na31__n_n_n_Mg28__weak__wc12 = np.nan
        self.He4_Si35__S39 = np.nan
        self.He4_P43__Cl47 = np.nan
        self.Ne17__F17__weak__wc17 = np.nan
        self.He4_Na29__n_Al32 = np.nan
        self.n_Ne21__Ne22 = np.nan
        self.n_Ca41__He4_Ar38 = np.nan
        self.P24__Si24__weak__bqa_pos_ = np.nan
        self.O26__n_F25__weak__mp17 = np.nan
        self.Sc40__He4_Ar36__weak__wc12 = np.nan
        self.He4_Mg35__Si39 = np.nan
        self.Na22__Ne22__weak__wc12 = np.nan
        self.He4_F23__Na27 = np.nan
        self.p_K49__He4_Ar46 = np.nan
        self.p_P25__S26 = np.nan
        self.p_Na24__Mg25 = np.nan
        self.Al34__Si34__weak__wc12 = np.nan
        self.S46__Cl46__weak__wc17 = np.nan
        self.n_Mg38__Mg39 = np.nan
        self.N20__n_O19__weak__wc12 = np.nan
        self.Ca59__n_Sc58__weak__mp17 = np.nan
        self.Mn73__Fe73__weak__mo03 = np.nan
        self.Al24__He4_Ne20__weak__wc12 = np.nan
        self.He4_Na21__Al25 = np.nan
        self.Ca55__Sc55__weak__wc12 = np.nan
        self.Ca58__n_Sc57__weak__mp17 = np.nan
        self.He4_P45__n_Cl48 = np.nan
        self.n_Ne31__Ne32 = np.nan
        self.He4_Sc52__V56 = np.nan
        self.Ar32__p_S31__weak__wc12 = np.nan
        self.Ca57__n_Sc56__weak__mp17 = np.nan
        self.He4_Mg41__n_Si44 = np.nan
        self.n_Cl39__Cl40 = np.nan
        self.He4_C14__O18 = np.nan
        self.Ca52__n_Sc51__weak__wc12 = np.nan
        self.He4_O18__Ne22 = np.nan
        self.Si24__Al24__weak__wc12 = np.nan
        self.n_V54__V55 = np.nan
        self.p_S39__n_Cl39 = np.nan
        self.Cl34__S34__weak__wc12 = np.nan
        self.He4_Mn62__Co66 = np.nan
        self.Al42__n_Si41__weak__mp17 = np.nan
        self.Si42__n_P41__weak__mp17 = np.nan
        self.He4_K44__n_Sc47 = np.nan
        self.n_Na19__He4_F16 = np.nan
        self.V62__Cr62__weak__wc17 = np.nan
        self.Cl46__n_Ar45__weak__wc12 = np.nan
        self.He4_Al28__P32 = np.nan
        self.He4_Mn70__n_Co73 = np.nan
        self.Cl51__n_Ar50__weak__mp17 = np.nan
        self.p_Cl33__Ar34 = np.nan
        self.Ca37__p_Ar36__weak__wc12 = np.nan
        self.n_Mg30__Mg31 = np.nan
        self.p_Ca46__Sc47 = np.nan
        self.Ca36__p_Ar35__weak__wc12 = np.nan
        self.p_Fe68__n_Co68 = np.nan
        self.n_Ti42__Ti43 = np.nan
        self.Ca35__p_Ar34__weak__wc17 = np.nan
        self.C18__N18__weak__wc12 = np.nan
        self.Si26__Al26__weak__wc12 = np.nan
        self.O26__F26__weak__mo03 = np.nan
        self.Cr48__V48__weak__wc12 = np.nan
        self.p_Na29__n_Mg29 = np.nan
        self.B14__C14__weak__wc12 = np.nan
        self.n_p_He4__Li6 = np.nan
        self.K58__n_Ca57__weak__mp17 = np.nan
        self.He4_Na25__p_Mg28 = np.nan
        self.He4_Cl52__K56 = np.nan
        self.n_Ar33__Ar34 = np.nan
        self.n_Ca33__Ca34 = np.nan
        self.K57__n_Ca56__weak__mp17 = np.nan
        self.He4_Sc53__n_V56 = np.nan
        self.p_V55__He4_Ti52 = np.nan
        self.p_Ca60__He4_K57 = np.nan
        self.p_Mn58__He4_Cr55 = np.nan
        self.n_Si39__Si40 = np.nan
        self.n_Fe46__Fe47 = np.nan
        self.n_Cr64__Cr65 = np.nan
        self.He4_K31__Sc35 = np.nan
        self.V39__Ti39__weak__bqa_pos_ = np.nan
        self.K59__n_Ca58__weak__mp17 = np.nan
        self.He4_S31__Ar35 = np.nan
        self.p_Al37__n_Si37 = np.nan
        self.S35__Cl35__weak__wc12 = np.nan
        self.K52__n_Ca51__weak__wc12 = np.nan
        self.He4_F15__Na19 = np.nan
        self.N18__O18__weak__wc12 = np.nan
        self.p_Ti48__V49 = np.nan
        self.K51__n_Ca50__weak__wc12 = np.nan
        self.Sc35__Ca35__weak__bqa_pos_ = np.nan
        self.Mg32__Al32__weak__wc12 = np.nan
        self.F20__Ne20__weak__wc12 = np.nan
        self.p_Ar41__He4_Cl38 = np.nan
        self.He4_Mg21__p_Al24 = np.nan
        self.K50__n_Ca49__weak__wc12 = np.nan
        self.He4_Ca41__Ti45 = np.nan
        self.He4_Cl40__K44 = np.nan
        self.p_Cl49__He4_S46 = np.nan
        self.Sc56__Ti56__weak__wc17 = np.nan
        self.He4_Ar45__n_Ca48 = np.nan
        self.He4_P29__Cl33 = np.nan
        self.K37__Ar37__weak__wc12 = np.nan
        self.n_Ca34__Ca35 = np.nan
        self.n_Sc38__p_Ca38 = np.nan
        self.p_Ar39__K40 = np.nan
        self.n_Ti51__Ti52 = np.nan
        self.He4_F25__Na29 = np.nan
        self.p_K47__Ca48 = np.nan
        self.p_O23__n_F23 = np.nan
        self.He4_Mn63__n_Co66 = np.nan
        self.He4_C11__p_N14 = np.nan
        self.He4_Fe61__n_Ni64 = np.nan
        self.K36__p_Cl35__weak__wc12 = np.nan
        self.He4_Si37__S41 = np.nan
        self.K35__p_Cl34__weak__wc12 = np.nan
        self.Ca58__n_n_Sc56__weak__mp17 = np.nan
        self.p_Ne34__Na35 = np.nan
        self.p_Ti61__He4_Sc58 = np.nan
        self.n_Si31__Si32 = np.nan
        self.n_Cl36__He4_P33 = np.nan
        self.n_S37__S38 = np.nan
        self.He4_Sc51__V55 = np.nan
        self.p_Ti60__He4_Sc57 = np.nan
        self.He4_Ti41__p_V44 = np.nan
        self.p_B10__He4_Be7 = np.nan
        self.n_Ar50__Ar51 = np.nan
        self.Ar31__Cl31__weak__wc12 = np.nan
        self.Ca59__Sc59__weak__mo03 = np.nan
        self.C9__He4_Li5__weak__wc12 = np.nan
        self.Mn67__n_Fe66__weak__mp17 = np.nan
        self.V66__Cr66__weak__mo03 = np.nan
        self.p_Cr42__Mn43 = np.nan
        self.n_Ca58__Ca59 = np.nan
        self.p_S40__He4_P37 = np.nan
        self.n_Ar41__Ar42 = np.nan
        self.He4_S35__Ar39 = np.nan
        self.p_K54__Ca55 = np.nan
        self.n_K42__He4_Cl39 = np.nan
        self.He4_S45__Ar49 = np.nan
        self.p_V61__Cr62 = np.nan
        self.p_Mg27__n_Al27 = np.nan
        self.P26__Si26__weak__wc12 = np.nan
        self.p_Mn70__He4_Cr67 = np.nan
        self.P38__S38__weak__wc12 = np.nan
        self.Ca41__K41__weak__wc12 = np.nan
        self.He4_K45__n_Sc48 = np.nan
        self.n_Ne29__Ne30 = np.nan
        self.Si22__p_Mg21__weak__wc12 = np.nan
        self.He4_P38__n_Cl41 = np.nan
        self.C18__n_N17__weak__wc12 = np.nan
        self.He4_Cl48__n_K51 = np.nan
        self.Sc63__n_n_Ti61__weak__mp17 = np.nan
        self.He4_Ne23__Mg27 = np.nan
        self.Si41__P41__weak__wc17 = np.nan
        self.n_F27__F28 = np.nan
        self.n_Cr51__p_V51 = np.nan
        self.n_V65__V66 = np.nan
        self.p_K46__n_Ca46 = np.nan
        self.V66__n_Cr65__weak__mp17 = np.nan
        self.Si38__P38__weak__mo03 = np.nan
        self.P47__n_S46__weak__mp17 = np.nan
        self.p_Sc59__Ti60 = np.nan
        self.p_Be9__B10 = np.nan
        self.He4_Ar50__n_Ca53 = np.nan
        self.Ne27__Na27__weak__wc12 = np.nan
        self.Si44__n_n_n_P41__weak__mo03 = np.nan
        self.p_P39__He4_Si36 = np.nan
        self.He4_Ti49__Cr53 = np.nan
        self.He4_K33__p_Ca36 = np.nan
        self.n_K31__He4_Cl28 = np.nan
        self.Ar50__n_K49__weak__wc12 = np.nan
        self.S39__Cl39__weak__wc12 = np.nan
        self.p_F26__Ne27 = np.nan
        self.Ar33__p_S32__weak__wc12 = np.nan
        self.Ca47__Sc47__weak__wc12 = np.nan
        self.He4_Li6__B10 = np.nan
        self.He4_S33__Ar37 = np.nan
        self.Mg34__n_Al33__weak__mp17 = np.nan
        self.S29__p_Si28__weak__wc12 = np.nan
        self.O28__n_F27__weak__mp17 = np.nan
        self.He4_Cr69__Fe73 = np.nan
        self.p_Li7__He4_He4 = np.nan
        self.Cl51__n_n_Ar49__weak__mp17 = np.nan
        self.n_O12__He4_C9 = np.nan
        self.He4_Ca56__Ti60 = np.nan
        self.p_Fe65__n_Co65 = np.nan
        self.p_Fe76__n_Co76 = np.nan
        self.n_O19__O20 = np.nan
        self.Ar47__K47__weak__wc12 = np.nan
        self.p_Na33__Mg34 = np.nan
        self.Cl52__n_Ar51__weak__mp17 = np.nan
        self.n_Cr45__p_V45 = np.nan
        self.Cl50__n_Ar49__weak__mp17 = np.nan
        self.S45__Cl45__weak__wc12 = np.nan
        self.n_Sc41__p_Ca41 = np.nan
        self.p_Mn67__n_Fe67 = np.nan
        self.n_Fe52__p_Mn52 = np.nan
        self.Ne34__n_n_Na32__weak__mp17 = np.nan
        self.Al33__Si33__weak__wc12 = np.nan
        self.n_S36__S37 = np.nan
        self.Cl47__n_Ar46__weak__wc12 = np.nan
        self.P46__n_S45__weak__mp17 = np.nan
        self.p_Ca57__n_Sc57 = np.nan
        self.Cl45__n_Ar44__weak__wc12 = np.nan
        self.Be11__He4_Li7__weak__wc12 = np.nan
        self.n_Ne27__Ne28 = np.nan
        self.He4_B10__n_N13 = np.nan
        self.p_Ca59__He4_K56 = np.nan
        self.n_Mn64__Mn65 = np.nan
        self.Sc48__Ti48__weak__wc12 = np.nan
        self.Cl44__n_Ar43__weak__mp17 = np.nan
        self.n_V44__V45 = np.nan
        self.Sc60__n_Ti59__weak__mp17 = np.nan
        self.Ti63__V63__weak__mo03 = np.nan
        self.He4_O15__Ne19 = np.nan
        self.d_d__n_He3 = np.nan
        self.Na32__Mg32__weak__wc12 = np.nan
        self.Si43__n_P42__weak__mp17 = np.nan
        self.Sc58__n_n_Ti56__weak__mp17 = np.nan
        self.Fe70__Co70__weak__wc17 = np.nan
        self.p_Ne31__n_Na31 = np.nan
        self.p_F21__He4_O18 = np.nan
        self.Mn64__Fe64__weak__wc12 = np.nan
        self.Ar48__K48__weak__wc17 = np.nan
        self.He4_Ne28__Mg32 = np.nan
        self.p_Sc61__He4_Ca58 = np.nan
        self.S48__n_n_Cl46__weak__mp17 = np.nan
        self.He4_Na35__Al39 = np.nan
        self.Al29__Si29__weak__wc12 = np.nan
        self.p_V65__n_Cr65 = np.nan
        self.p_Be9__He4_Li6 = np.nan
        self.He4_Cr61__Fe65 = np.nan
        self.Cl32__p_P31__weak__wc12 = np.nan
        self.p_Na26__n_Mg26 = np.nan
        self.He4_Ne32__Mg36 = np.nan
        self.p_Si27__P28 = np.nan
        self.Si36__P36__weak__wc12 = np.nan
        self.n_Si27__p_Al27 = np.nan
        self.n_Cl47__Cl48 = np.nan
        self.p_Ca54__He4_K51 = np.nan
        self.Sc40__p_K39__weak__wc12 = np.nan
        self.He4_Ne22__Mg26 = np.nan
        self.p_Fe74__Co75 = np.nan
        self.He4_Mn58__n_Co61 = np.nan
        self.S46__n_Cl45__weak__mp17 = np.nan
        self.Ti41__Sc41__weak__wc17 = np.nan
        self.p_O21__F22 = np.nan
        self.He4_Ti62__Cr66 = np.nan
        self.He4_Li9__n_B12 = np.nan
        self.Mg35__n_n_Al33__weak__mp17 = np.nan
        self.p_P42__S43 = np.nan
        self.p_Cr66__n_Mn66 = np.nan
        self.O13__N13__weak__wc17 = np.nan
        self.He4_Al23__p_Si26 = np.nan
        self.p_O27__n_F27 = np.nan
        self.n_Ti61__Ti62 = np.nan
        self.n_Mn46__Mn47 = np.nan
        self.p_Al31__n_Si31 = np.nan
        self.Cl48__n_n_Ar46__weak__mp17 = np.nan
        self.Na19__Ne19__weak__bqa_pos_ = np.nan
        self.F28__n_n_Ne26__weak__mp17 = np.nan
        self.n_Li6__Li7 = np.nan
        self.p_Ca53__He4_K50 = np.nan
        self.p_Ar45__K46 = np.nan
        self.Al23__p_Na22__weak__wc12 = np.nan
        self.O25__F25__weak__mo03 = np.nan
        self.p_Cr64__He4_V61 = np.nan
        self.He4_N16__n_F19 = np.nan
        self.Mg41__Al41__weak__mo03 = np.nan
        self.Mn48__Cr48__weak__wc12 = np.nan
        self.He4_Cl41__p_Ar44 = np.nan
        self.p_Si41__P42 = np.nan
        self.n_Mn48__p_Cr48 = np.nan
        self.He4_Si36__S40 = np.nan
        self.n_Cr49__He4_Ti46 = np.nan
        self.He4_Sc46__n_V49 = np.nan
        self.n_K38__He4_Cl35 = np.nan
        self.p_Mg30__He4_Na27 = np.nan
        self.N24__n_N23 = np.nan
        self.He4_Fe65__n_Ni68 = np.nan
        self.n_K34__He4_Cl31 = np.nan
        self.n_Ne17__p_F17 = np.nan
        self.p_Al35__Si36 = np.nan
        self.n_Ti43__p_Sc43 = np.nan
        self.Mg29__Al29__weak__wc12 = np.nan
        self.p_F17__Ne18 = np.nan
        self.p_Sc53__He4_Ca50 = np.nan
        self.P39__n_S38__weak__wc12 = np.nan
        self.P44__n_S43__weak__mp17 = np.nan
        self.Ca56__n_Sc55__weak__mp17 = np.nan
        self.K46__Ca46__weak__wc12 = np.nan
        self.P42__n_S41__weak__wc12 = np.nan
        self.Na35__n_Mg34__weak__mp17 = np.nan
        self.Na33__n_Mg32__weak__wc17 = np.nan
        self.Fe76__n_Co75__weak__mp17 = np.nan
        self.Mg38__n_n_n_Al35__weak__mo03 = np.nan
        self.Ar31__p_p_P29__weak__wc12 = np.nan
        self.He4_B13__N17 = np.nan
        self.p_Na25__n_Mg25 = np.nan
        self.n_Sc57__Sc58 = np.nan
        self.He4_P42__Cl46 = np.nan
        self.n_Na23__Na24 = np.nan
        self.p_N16__n_O16 = np.nan
        self.n_Cr44__p_V44 = np.nan
        self.p_Mn70__n_Fe70 = np.nan
        self.S44__Cl44__weak__wc12 = np.nan
        self.He4_Cl45__K49 = np.nan
        self.p_Mg41__He4_Na38 = np.nan
        self.Fe71__n_Co70__weak__mp17 = np.nan
        self.n_O17__He4_C14 = np.nan
        self.He4_F21__Na25 = np.nan
        self.P28__He4_Mg24__weak__wc12 = np.nan
        self.P43__S43__weak__wc17 = np.nan
        self.P28__p_Al27__weak__wc12 = np.nan
        self.Al31__Si31__weak__wc12 = np.nan
        self.p_P37__S38 = np.nan
        self.He4_Al39__n_P42 = np.nan
        self.He4_Ca49__Ti53 = np.nan
        self.Cr42__V42__weak__wc12 = np.nan
        self.t_Li7__n_n_He4_He4 = np.nan
        self.n_V66__V67 = np.nan
        self.He4_K48__Sc52 = np.nan
        self.Cl49__Ar49__weak__mo03 = np.nan
        self.n_Ar33__He4_S30 = np.nan
        self.p_Mn59__Fe60 = np.nan
        self.K54__n_Ca53__weak__mp17 = np.nan
        self.p_P44__n_S44 = np.nan
        self.p_Cl28__Ar29 = np.nan
        self.p_S27__Cl28 = np.nan
        self.He4_P45__Cl49 = np.nan
        self.p_B8__C9 = np.nan
        self.n_Sc61__Sc62 = np.nan
        self.p_K55__He4_Ar52 = np.nan
        self.Si41__n_P40__weak__mp17 = np.nan
        self.Mn57__Fe57__weak__wc12 = np.nan
        self.Si40__n_P39__weak__mp17 = np.nan
        self.Si38__n_P37__weak__mp17 = np.nan
        self.p_Mg29__Al30 = np.nan
        self.He4_Mn64__n_Co67 = np.nan
        self.He4_Cl31__p_Ar34 = np.nan
        self.He4_Na22__Al26 = np.nan
        self.Fe52__Mn52__weak__wc12 = np.nan
        self.K43__Ca43__weak__wc12 = np.nan
        self.Mg33__Al33__weak__wc12 = np.nan
        self.n_Sc36__He4_K33 = np.nan
        self.N11__C11__weak__btyk = np.nan
        self.Ca60__n_Sc59__weak__mp17 = np.nan
        self.Al21__Mg21__weak__bqa_pos_ = np.nan
        self.O15__N15__weak__wc12 = np.nan
        self.V67__Cr67__weak__mo03 = np.nan
        self.n_K38__K39 = np.nan
        self.He4_Ti37__Cr41 = np.nan
        self.p_Si31__n_P31 = np.nan
        self.Ne33__n_n_n_Na30__weak__mo03 = np.nan
        self.He4_Na26__Al30 = np.nan
        self.He4_F22__Na26 = np.nan
        self.He4_Sc63__V67 = np.nan
        self.Cl46__Ar46__weak__wc12 = np.nan
        self.He4_Ti57__Cr61 = np.nan
        self.Ti62__n_V61__weak__mp17 = np.nan
        self.p_Mn68__He4_Cr65 = np.nan
        self.Cr64__n_Mn63__weak__mp17 = np.nan
        self.Mn60__Fe60__weak__wc12 = np.nan
        self.Si25__p_Mg24__weak__wc12 = np.nan
        self.n_Mg21__Mg22 = np.nan
        self.n_Fe61__Fe62 = np.nan
        self.P42__S42__weak__wc17 = np.nan
        self.He4_Fe67__n_Ni70 = np.nan
        self.O22__F22__weak__wc17 = np.nan
        self.He4_K40__Sc44 = np.nan
        self.K31__Ar31__weak__bqa_pos_ = np.nan
        self.He4_Ne34__n_Mg37 = np.nan
        self.n_V63__V64 = np.nan
        self.Na39__n_n_Mg37__weak__mp17 = np.nan
        self.Si23__p_Mg22__weak__wc17 = np.nan
        self.He4_Fe48__Ni52 = np.nan
        self.n_N14__N15 = np.nan
        self.n_F17__p_O17 = np.nan
        self.n_Fe45__p_Mn45 = np.nan
        self.He4_Na30__n_Al33 = np.nan
        self.p_Mg38__He4_Na35 = np.nan
        self.Fe47__p_Cr46__weak__wc12 = np.nan
        self.Al38__n_Si37__weak__mp17 = np.nan
        self.He4_Ar49__n_Ca52 = np.nan
        self.p_O24__F25 = np.nan
        self.p_Mg21__Al22 = np.nan
        self.n_Si30__Si31 = np.nan
        self.He4_Mn55__Co59 = np.nan
        self.Cr60__Mn60__weak__wc12 = np.nan
        self.p_Cr48__Mn49 = np.nan
        self.p_K52__n_Ca52 = np.nan
        self.He4_Si30__S34 = np.nan
        self.n_P31__P32 = np.nan
        self.He4_Si43__S47 = np.nan
        self.Al35__n_Si34__weak__wc12 = np.nan
        self.Cl52__Ar52__weak__mo03 = np.nan
        self.Mn69__Fe69__weak__wc17 = np.nan
        self.p_Mg35__He4_Na32 = np.nan
        self.Si39__n_P38__weak__mp17 = np.nan
        self.He4_Mn56__Co60 = np.nan
        self.Ne29__Na29__weak__wc12 = np.nan
        self.He4_P44__Cl48 = np.nan
        self.n_Fe45__Fe46 = np.nan
        self.He4_Sc37__V41 = np.nan
        self.N16__He4_C12__weak__wc12 = np.nan
        self.p_Cl37__Ar38 = np.nan
        self.P40__n_S39__weak__wc12 = np.nan
        self.Al32__n_Si31__weak__wc12 = np.nan
        self.p_K32__Ca33 = np.nan
        self.C10__B10__weak__wc12 = np.nan
        self.Cr57__Mn57__weak__wc12 = np.nan
        self.Cl36__Ar36__weak__wc12 = np.nan
        self.n_Fe59__Fe60 = np.nan
        self.He4_Na24__n_Al27 = np.nan
        self.B13__C13__weak__wc12 = np.nan
        self.p_Ar54__K55 = np.nan
        self.He4_O25__Ne29 = np.nan
        self.p_Sc50__He4_Ca47 = np.nan
        self.Fe61__Co61__weak__wc12 = np.nan
        self.p_P45__He4_Si42 = np.nan
        self.p_K43__He4_Ar40 = np.nan
        self.n_P37__P38 = np.nan
        self.He4_Si44__S48 = np.nan
        self.Na20__He4_O16__weak__wc12 = np.nan
        self.Si43__n_n_n_P40__weak__mo03 = np.nan
        self.P47__S47__weak__mo03 = np.nan
        self.Ti54__V54__weak__wc12 = np.nan
        self.K51__Ca51__weak__wc12 = np.nan
        self.Ti39__Sc39__weak__wc17 = np.nan
        self.Mg40__n_Al39__weak__mp17 = np.nan
        self.He4_K38__Sc42 = np.nan
        self.Mn72__n_n_n_Fe69__weak__mo03 = np.nan
        self.Mg38__n_Al37__weak__mp17 = np.nan
        self.p_S43__n_Cl43 = np.nan
        self.He4_Ti59__Cr63 = np.nan
        self.n_Ti62__Ti63 = np.nan
        self.Cr44__p_Ti43__weak__wc12 = np.nan
        self.O27__n_O26 = np.nan
        self.p_Mn54__Fe55 = np.nan
        self.Ca60__Sc60__weak__mo03 = np.nan
        self.p_P40__He4_Si37 = np.nan
        self.n_Mg33__Mg34 = np.nan
        self.p_P44__S45 = np.nan
        self.Ca58__Sc58__weak__mo03 = np.nan
        self.He4_V52__n_Mn55 = np.nan
        self.V61__Cr61__weak__wc12 = np.nan
        self.O21__F21__weak__wc12 = np.nan
        self.O13__p_C12__weak__wc12 = np.nan
        self.P45__S45__weak__mo03 = np.nan
        self.K56__n_Ca55__weak__mp17 = np.nan
        self.C20__N20__weak__wc12 = np.nan
        self.p_d__He3 = np.nan
        self.n_C15__C16 = np.nan
        self.Si25__Al25__weak__wc12 = np.nan
        self.K57__Ca57__weak__mo03 = np.nan
        self.S42__Cl42__weak__wc12 = np.nan
        self.p_V47__Cr48 = np.nan
        self.Mg21__p_Ne20__weak__wc12 = np.nan
        self.S31__P31__weak__wc12 = np.nan
        self.He4_Mn71__n_Co74 = np.nan
        self.K45__Ca45__weak__wc12 = np.nan
        self.Cr55__Mn55__weak__wc12 = np.nan
        self.n_Ca42__Ca43 = np.nan
        self.He4_Ar34__Ca38 = np.nan
        self.p_Na38__n_Mg38 = np.nan
        self.p_V54__He4_Ti51 = np.nan
        self.p_Ca53__Sc54 = np.nan
        self.n_Mn53__Mn54 = np.nan
        self.S43__Cl43__weak__wc12 = np.nan
        self.p_Na37__n_Mg37 = np.nan
        self.Ti62__V62__weak__mo03 = np.nan
        self.p_Mn62__n_Fe62 = np.nan
        self.n_Mn48__Mn49 = np.nan
        self.P27__Si27__weak__wc12 = np.nan
        self.n_Ti56__Ti57 = np.nan
        self.Mg28__Al28__weak__wc12 = np.nan
        self.Na38__n_Mg37__weak__mp17 = np.nan
        self.He4_Si22__S26 = np.nan
        self.Ar53__n_K52__weak__mp17 = np.nan
        self.n_S43__S44 = np.nan
        self.V67__n_Cr66__weak__mp17 = np.nan
        self.p_F23__n_Ne23 = np.nan
        self.Ti64__V64__weak__mo03 = np.nan
        self.S41__Cl41__weak__wc12 = np.nan
        self.Na34__n_Mg33__weak__wc12 = np.nan
        self.p_Ca38__Sc39 = np.nan
        self.n_Ti39__Ti40 = np.nan
        self.n_Ca39__p_K39 = np.nan
        self.He4_Ar51__Ca55 = np.nan
        self.n_Ti44__He4_Ca41 = np.nan
        self.Si37__n_P36__weak__wc12 = np.nan
        self.Mn64__n_Fe63__weak__wc12 = np.nan
        self.Ne33__n_Na32__weak__mp17 = np.nan
        self.He4_Mn66__n_Co69 = np.nan
        self.Na30__He4_Ne26__weak__wc12 = np.nan
        self.He4_Ca52__n_Ti55 = np.nan
        self.p_Cr43__Mn44 = np.nan
        self.He4_Ne19__Mg23 = np.nan
        self.Na29__n_Mg28__weak__wc12 = np.nan
        self.p_Sc56__n_Ti56 = np.nan
        self.n_Mg39__Mg40 = np.nan
        self.p_Si36__P37 = np.nan
        self.He4_Fe60__Ni64 = np.nan
        self.He4_Ar48__Ca52 = np.nan
        self.p_S43__Cl44 = np.nan
        self.Mg34__Al34__weak__wc17 = np.nan
        self.Ca48__Sc48__weak__mo03 = np.nan
        self.p_V62__He4_Ti59 = np.nan
        self.p_P47__He4_Si44 = np.nan
        self.He4_Ca54__n_Ti57 = np.nan
        self.n_S48__S49 = np.nan
        self.n_P43__P44 = np.nan
        self.n_P25__p_Si25 = np.nan
        self.Ar33__Cl33__weak__wc12 = np.nan
        self.p_Ar49__n_K49 = np.nan
        self.p_Cr44__Mn45 = np.nan
        self.V50__Ti50__weak__mo03 = np.nan
        self.p_Ti62__He4_Sc59 = np.nan
        self.Ca37__K37__weak__wc12 = np.nan
        self.O23__F23__weak__wc12 = np.nan
        self.He4_V42__Mn46 = np.nan
        self.p_Al22__Si23 = np.nan
        self.n_B10__He4_Li7 = np.nan
        self.Al26__Mg26__weak__wc12 = np.nan
        self.p_Ca55__Sc56 = np.nan
        self.n_Si27__C12_O16 = np.nan
        self.n_Si28__Si29 = np.nan
        self.He4_Fe55__Ni59 = np.nan
        self.Mn71__n_Fe70__weak__mp17 = np.nan
        self.Cl45__Ar45__weak__wc12 = np.nan
        self.Al24__Mg24__weak__wc12 = np.nan
        self.p_Na30__Mg31 = np.nan
        self.N18__n_O17__weak__wc12 = np.nan
        self.t_t__n_n_He4 = np.nan
        self.V67__n_n_Cr65__weak__mp17 = np.nan
        self.p_Cr59__He4_V56 = np.nan
        self.p_P35__He4_Si32 = np.nan
        self.p_Ar48__K49 = np.nan
        self.He6__Li6__weak__wc12 = np.nan
        self.p_Ne29__Na30 = np.nan
        self.p_Ar53__K54 = np.nan
        self.p_P34__He4_Si31 = np.nan
        self.n_Si41__Si42 = np.nan
        self.Ca61__Sc61__weak__mo03 = np.nan
        self.p_K39__He4_Ar36 = np.nan
        self.V40__Ti40__weak__bqa_pos_ = np.nan
        self.Cl43__Ar43__weak__wc12 = np.nan
        self.Fe71__Co71__weak__wc17 = np.nan
        self.He3_Li7__n_p_He4_He4 = np.nan
        self.P35__S35__weak__wc12 = np.nan
        self.n_K35__K36 = np.nan
        self.Fe45__p_p_V43__weak__wc12 = np.nan
        self.P46__S46__weak__mo03 = np.nan
        self.F18__O18__weak__wc12 = np.nan
        self.n_K39__K40 = np.nan
        self.Sc49__Ti49__weak__wc12 = np.nan
        self.He4_P29__p_S32 = np.nan
        self.p_Mn55__Fe56 = np.nan
        self.n_Al33__Al34 = np.nan
        self.p_Ar49__K50 = np.nan
        self.p_Mn65__n_Fe65 = np.nan
        self.d_C14__n_N15 = np.nan
        self.He4_Ti58__Cr62 = np.nan
        self.n_P29__p_Si29 = np.nan
        self.p_N16__He4_C13 = np.nan
        self.n_Na26__Na27 = np.nan
        self.n_K54__K55 = np.nan
        self.n_Ti63__Ti64 = np.nan
        self.Be12__n_B11__weak__wc12 = np.nan
        self.p_Ca39__Sc40 = np.nan
        self.p_Na32__He4_Ne29 = np.nan
        self.n_Cl50__Cl51 = np.nan
        self.Ti42__Sc42__weak__wc12 = np.nan
        self.p_Ti64__V65 = np.nan
        self.F31__n_Ne30__weak__mp17 = np.nan
        self.F26__n_Ne25__weak__wc12 = np.nan
        self.Ne29__n_Na28__weak__wc17 = np.nan
        self.He4_Cr52__Fe56 = np.nan
        self.K48__Ca48__weak__wc12 = np.nan
        self.V63__Cr63__weak__wc12 = np.nan
        self.n_V52__V53 = np.nan
        self.He4_Al21__P25 = np.nan
        self.n_Be10__Be11 = np.nan
        self.n_Al29__Al30 = np.nan
        self.Be7__Li7__weak__electron_capture = np.nan
        self.Al38__Si38__weak__wc17 = np.nan
        self.n_Ar36__p_Cl36 = np.nan
        self.n_Ar53__Ar54 = np.nan
        self.Mg31__Al31__weak__wc12 = np.nan
        self.Ca60__n_n_Sc58__weak__mp17 = np.nan
        self.Ti40__p_Ca39__weak__wc12 = np.nan
        self.He4_Mg23__p_Al26 = np.nan
        self.He4_Ca34__p_Sc37 = np.nan
        self.n_Ne22__Ne23 = np.nan
        self.He4_Sc61__V65 = np.nan
        self.V48__Ti48__weak__wc12 = np.nan
        self.P34__S34__weak__wc12 = np.nan
        self.S29__P29__weak__wc12 = np.nan
        self.Ar43__K43__weak__wc12 = np.nan
        self.p_Cl49__n_Ar49 = np.nan
        self.p_Cl52__Ar53 = np.nan
        self.n_Sc36__Sc37 = np.nan
        self.P46__n_n_S44__weak__mp17 = np.nan
        self.n_Ca35__Ca36 = np.nan
        self.p_O25__F26 = np.nan
        self.V41__Ti41__weak__bqa_pos_ = np.nan
        self.He4_V44__Mn48 = np.nan
        self.O23__n_F22__weak__wc12 = np.nan
        self.V64__n_Cr63__weak__mp17 = np.nan
        self.Ti53__V53__weak__wc12 = np.nan
        self.p_K54__He4_Ar51 = np.nan
        self.He4_Fe53__Ni57 = np.nan
        self.p_Sc59__n_Ti59 = np.nan
        self.p_Ca37__Sc38 = np.nan
        self.Cr56__Mn56__weak__wc12 = np.nan
        self.p_P37__n_S37 = np.nan
        self.Fe72__Co72__weak__mo03 = np.nan
        self.He4_Al41__n_P44 = np.nan
        self.p_Mn61__He4_Cr58 = np.nan
        self.He4_F19__Na23 = np.nan
        self.He4_Si41__n_S44 = np.nan
        self.p_P43__S44 = np.nan
        self.p_Ti45__V46 = np.nan
        self.Fe47__Mn47__weak__wc12 = np.nan
        self.P28__Si28__weak__wc12 = np.nan
        self.Cr51__V51__weak__wc12 = np.nan
        self.Fe55__Mn55__weak__wc12 = np.nan
        self.p_Cl47__He4_S44 = np.nan
        self.n_Cl36__Cl37 = np.nan
        self.C19__n_N18__weak__wc12 = np.nan
        self.He4_Ti65__Cr69 = np.nan
        self.Ca52__Sc52__weak__wc12 = np.nan
        self.p_Al27__Si28 = np.nan
        self.He4_V62__Mn66 = np.nan
        self.Si43__P43__weak__mo03 = np.nan
        self.n_Na22__He4_F19 = np.nan
        self.Ne34__n_Na33__weak__mp17 = np.nan
        self.Sc52__Ti52__weak__wc12 = np.nan
        self.P45__n_S44__weak__mp17 = np.nan
        self.He4_V40__Mn44 = np.nan
        self.Ar51__K51__weak__mo03 = np.nan
        self.B19__n_C18__weak__wc17 = np.nan
        self.p_Ti56__n_V56 = np.nan
        self.B15__n_C14__weak__wc12 = np.nan
        self.He4_Ar51__n_Ca54 = np.nan
        self.n_S39__S40 = np.nan
        self.K40__Ar40__weak__wc12 = np.nan
        self.He4_K54__Sc58 = np.nan
        self.He4_Sc53__V57 = np.nan
        self.He4_Si27__S31 = np.nan
        self.F30__Ne30__weak__mo03 = np.nan
        self.p_Na29__Mg30 = np.nan
        self.Be15__n_Be14 = np.nan
        self.Ne30__Na30__weak__wc17 = np.nan
        self.Be14__n_B13__weak__wc17 = np.nan
        self.n_Mn56__He4_V53 = np.nan
        self.Li11__n_Be10__weak__wc17 = np.nan
        self.Al22__He4_Ne18__weak__wc12 = np.nan
        self.Ti37__Sc37__weak__bqa_pos_ = np.nan
        self.K33__Ar33__weak__bqa_pos_ = np.nan
        self.Cr64__Mn64__weak__wc12 = np.nan
        self.p_Ti59__He4_Sc56 = np.nan
        self.n_Ar37__Ar38 = np.nan
        self.He4_F29__Na33 = np.nan
        self.N17__O17__weak__wc12 = np.nan
        self.Fe63__Co63__weak__wc12 = np.nan
        self.Si27__Al27__weak__wc12 = np.nan
        self.B8__He4_He4__weak__wc12 = np.nan
        self.He4_Cr50__Fe54 = np.nan
        self.Fe68__Co68__weak__wc12 = np.nan
        self.n_Al22__Al23 = np.nan
        self.n_V57__V58 = np.nan
        self.He4_Ar38__Ca42 = np.nan
        self.Fe64__Co64__weak__wc12 = np.nan
        self.He4_Al23__P27 = np.nan
        self.He4_F22__n_Na25 = np.nan
        self.Cr62__Mn62__weak__wc12 = np.nan
        self.n_Al21__p_Mg21 = np.nan
        self.p_K50__Ca51 = np.nan
        self.Sc58__Ti58__weak__wc17 = np.nan
        self.O26__n_n_n_F23__weak__mo03 = np.nan
        self.Si36__n_P35__weak__wc12 = np.nan
        self.He4_Mg24__Si28 = np.nan
        self.He4_Si34__n_S37 = np.nan
        self.Ti59__V59__weak__wc12 = np.nan
        self.C11__B11__weak__wc12 = np.nan
        self.p_Si34__n_P34 = np.nan
        self.He4_Ne33__Mg37 = np.nan
        self.Fe46__Mn46__weak__wc12 = np.nan
        self.n_Na29__Na30 = np.nan
        self.Cr65__n_Mn64__weak__mp17 = np.nan
        self.p_O19__n_F19 = np.nan
        self.F21__Ne21__weak__wc12 = np.nan
        self.Mn65__Fe65__weak__wc17 = np.nan
        self.Mn63__Fe63__weak__wc12 = np.nan
        self.Mn59__Fe59__weak__wc12 = np.nan
        self.He4_Ca57__Ti61 = np.nan
        self.Mn56__Fe56__weak__wc12 = np.nan
        self.p_Mg25__Al26 = np.nan
        self.B17__n_C16__weak__wc17 = np.nan
        self.Mn50__Cr50__weak__wc12 = np.nan
        self.n_Cr67__Cr68 = np.nan
        self.Cr66__Mn66__weak__wc17 = np.nan
        self.P41__S41__weak__wc12 = np.nan
        self.Mn47__Cr47__weak__wc17 = np.nan
        self.Mn46__Cr46__weak__wc12 = np.nan
        self.Ar42__K42__weak__wc12 = np.nan
        self.He4_Ar48__n_Ca51 = np.nan
        self.Na30__Mg30__weak__wc12 = np.nan
        self.n_F14__p_O14 = np.nan
        self.n_Cr49__Cr50 = np.nan
        self.n_P25__P26 = np.nan
        self.Cr63__Mn63__weak__wc17 = np.nan
        self.Fe62__Co62__weak__wc12 = np.nan
        self.n_Al30__Al31 = np.nan
        self.Al36__n_n_Si34__weak__mp17 = np.nan
        self.C16__N16__weak__wc12 = np.nan
        self.Ar34__Cl34__weak__wc12 = np.nan
        self.Sc46__Ti46__weak__wc12 = np.nan
        self.p_Sc63__n_Ti63 = np.nan
        self.P38__n_S37__weak__wc12 = np.nan
        self.Cr59__Mn59__weak__wc12 = np.nan
        self.n_Ti48__Ti49 = np.nan
        self.n_Mn47__Mn48 = np.nan
        self.Cr49__V49__weak__wc12 = np.nan
        self.p_Al42__n_Si42 = np.nan
        self.Ca61__n_n_Sc59__weak__mp17 = np.nan
        self.n_Fe55__Fe56 = np.nan
        self.Mn48__p_V47__weak__wc12 = np.nan
        self.n_Cr68__Cr69 = np.nan
        self.He4_K32__p_Ca35 = np.nan
        self.Cr43__V43__weak__wc12 = np.nan
        self.He4_Mn57__Co61 = np.nan
        self.p_S45__Cl46 = np.nan
        self.n_Ne25__Ne26 = np.nan
        self.n_S31__S32 = np.nan
        self.He4_Cr58__n_Fe61 = np.nan
        self.He4_Si26__p_P29 = np.nan
        self.Mn71__Fe71__weak__mo03 = np.nan
        self.Mg36__n_Al35__weak__mp17 = np.nan
        self.Ne30__n_Na29__weak__wc12 = np.nan
        self.Be14__B14__weak__wc12 = np.nan
        self.Cr41__V41__weak__bqa_pos_ = np.nan
        self.Fe65__Co65__weak__wc12 = np.nan
        self.V58__Cr58__weak__wc17 = np.nan
        self.Cl51__n_n_n_Ar48__weak__mo03 = np.nan
        self.He4_Cr67__n_Fe70 = np.nan
        self.He4_Sc46__V50 = np.nan
        self.He4_Ca59__n_Ti62 = np.nan
        self.He4_S34__n_Ar37 = np.nan
        self.p_Ti58__He4_Sc55 = np.nan
        self.K44__Ca44__weak__wc12 = np.nan
        self.V43__Ti43__weak__wc12 = np.nan
        self.Sc50__Ti50__weak__wc12 = np.nan
        self.K53__Ca53__weak__wc17 = np.nan
        self.S47__n_Cl46__weak__mp17 = np.nan
        self.p_F31__Ne32 = np.nan
        self.p_Sc43__He4_Ca40 = np.nan
        self.S48__Cl48__weak__mo03 = np.nan
        self.n_K42__p_Ar42 = np.nan
        self.He4_V41__p_Cr44 = np.nan
        self.n_Fe45__He4_Cr42 = np.nan
        self.He4_Ti39__Cr43 = np.nan
        self.V66__n_n_Cr64__weak__mp17 = np.nan
        self.K54__Ca54__weak__wc17 = np.nan
        self.Cl48__Ar48__weak__mo03 = np.nan
        self.p_Sc62__He4_Ca59 = np.nan
        self.Ar46__K46__weak__wc12 = np.nan
        self.Li9__Be9__weak__wc12 = np.nan
        self.Ca50__Sc50__weak__wc12 = np.nan
        self.He4_Sc50__V54 = np.nan
        self.n_Fe52__Fe53 = np.nan
        self.n_Fe64__Fe65 = np.nan
        self.Al22__p_Na21__weak__wc17 = np.nan
        self.V64__Cr64__weak__wc17 = np.nan
        self.Cl40__Ar40__weak__wc12 = np.nan
        self.Na34__n_n_Mg32__weak__wc12 = np.nan
        self.Na34__Mg34__weak__wc12 = np.nan
        self.Ar53__K53__weak__mo03 = np.nan
        self.He4_F23__n_Na26 = np.nan
        self.Al28__Si28__weak__wc12 = np.nan
        self.K35__Ar35__weak__wc12 = np.nan
        self.Sc61__Ti61__weak__mo03 = np.nan
        self.Li8__He4_He4__weak__wc12 = np.nan
        self.K58__Ca58__weak__mo03 = np.nan
        self.Ti64__n_n_n_V61__weak__mo03 = np.nan
        self.n_Sc51__Sc52 = np.nan
        self.F29__n_Ne28__weak__wc12 = np.nan
        self.n_Fe59__He4_Cr56 = np.nan
        self.He4_S37__Ar41 = np.nan
        self.p_P47__S48 = np.nan
        self.Sc51__Ti51__weak__wc12 = np.nan
        self.K55__Ca55__weak__mo03 = np.nan
        self.Ti65__V65__weak__mo03 = np.nan
        self.d_Li6__p_Li7 = np.nan
        self.n_Si29__Si30 = np.nan
        self.N22__n_n_O20__weak__wc12 = np.nan
        self.n_Cl35__Cl36 = np.nan
        self.F25__n_Ne24__weak__wc12 = np.nan
        self.p_Mg28__Al29 = np.nan
        self.n_F15__p_O15 = np.nan
        self.Sc43__Ca43__weak__wc12 = np.nan
        self.n_Na20__p_Ne20 = np.nan
        self.n_Na38__Na39 = np.nan
        self.n_V52__He4_Sc49 = np.nan
        self.He4_Fe49__Ni53 = np.nan
        self.n_Cr50__Cr51 = np.nan
        self.N12__C12__weak__wc12 = np.nan
        self.Ne31__n_n_Na29__weak__mp17 = np.nan
        self.Fe51__Mn51__weak__wc12 = np.nan
        self.n_P24__P25 = np.nan
        self.p_O19__F20 = np.nan
        self.Ne32__n_n_n_Na29__weak__mo03 = np.nan
        self.p_Cr58__He4_V55 = np.nan
        self.V42__Ti42__weak__mo97 = np.nan
        self.Cl36__S36__weak__wc12 = np.nan
        self.p_Si41__n_P41 = np.nan
        self.Mn51__Cr51__weak__wc12 = np.nan
        self.He4_Fe47__p_Co50 = np.nan
        self.Ca54__Sc54__weak__wc17 = np.nan
        self.n_Ca42__He4_Ar39 = np.nan
        self.Ca45__Sc45__weak__wc12 = np.nan
        self.p_Na24__n_Mg24 = np.nan
        self.n_Na25__Na26 = np.nan
        self.p_Cr63__He4_V60 = np.nan
        self.Ne33__n_n_Na31__weak__mp17 = np.nan
        self.p_Si35__n_P35 = np.nan
        self.S40__Cl40__weak__wc12 = np.nan
        self.Na32__n_Mg31__weak__wc17 = np.nan
        self.n_V58__V59 = np.nan
        self.p_Si43__P44 = np.nan
        self.K50__Ca50__weak__wc12 = np.nan
        self.n_Mn61__Mn62 = np.nan
        self.Mg21__Na21__weak__wc12 = np.nan
        self.V57__Cr57__weak__wc12 = np.nan
        self.He4_Fe72__n_Ni75 = np.nan
        self.K57__n_n_n_Ca54__weak__mo03 = np.nan
        self.He4_Al33__P37 = np.nan
        self.Cl33__S33__weak__wc12 = np.nan
        self.S48__n_Cl47__weak__mp17 = np.nan
        self.n_Mn43__Mn44 = np.nan
        self.He4_Al22__P26 = np.nan
        self.Si40__P40__weak__wc17 = np.nan
        self.p_K53__He4_Ar50 = np.nan
        self.K36__Ar36__weak__wc12 = np.nan
        self.S43__n_Cl42__weak__wc12 = np.nan
        self.Mn53__Cr53__weak__wc12 = np.nan
        self.F27__Ne27__weak__wc17 = np.nan
        self.Ti55__V55__weak__wc12 = np.nan
        self.He4_O26__Ne30 = np.nan
        self.n_Ti40__He4_Ca37 = np.nan
        self.V56__Cr56__weak__wc12 = np.nan
        self.Ar50__K50__weak__wc12 = np.nan
        self.p_Na25__He4_Ne22 = np.nan
        self.He4_S44__n_Ar47 = np.nan
        self.p_Mg28__n_Al28 = np.nan
        self.n_V45__p_Ti45 = np.nan
        self.p_O18__F19 = np.nan
        self.p_P36__S37 = np.nan
        self.Na35__Mg35__weak__wc17 = np.nan
        self.He4_Fe72__Ni76 = np.nan
        self.Na24__Mg24__weak__wc12 = np.nan
        self.V59__Cr59__weak__wc12 = np.nan
        self.Ar41__K41__weak__wc12 = np.nan
        self.Cr65__Mn65__weak__wc17 = np.nan
        self.Cr46__V46__weak__wc12 = np.nan
        self.n_F24__F25 = np.nan
        self.Ar37__Cl37__weak__wc12 = np.nan
        self.Be10__B10__weak__wc12 = np.nan
        self.Ar32__Cl32__weak__wc12 = np.nan
        self.p_Mg39__He4_Na36 = np.nan
        self.n_S27__p_P27 = np.nan
        self.Ti63__n_n_V61__weak__mp17 = np.nan
        self.He4_Al30__n_P33 = np.nan
        self.Ar29__Cl29__weak__bqa_pos_ = np.nan
        self.Na31__Mg31__weak__wc12 = np.nan
        self.n_V60__V61 = np.nan
        self.p_Sc44__Ti45 = np.nan
        self.n_V40__V41 = np.nan
        self.B15__C15__weak__wc12 = np.nan
        self.Cl44__Ar44__weak__wc17 = np.nan
        self.He4_Ca33__p_Sc36 = np.nan
        self.Na33__Mg33__weak__wc12 = np.nan
        self.Ar44__K44__weak__wc12 = np.nan
        self.p_V66__He4_Ti63 = np.nan
        self.Sc60__n_n_n_Ti57__weak__mo03 = np.nan
        self.Cl31__S31__weak__wc12 = np.nan
        self.V53__Cr53__weak__wc12 = np.nan
        self.n_V39__He4_Sc36 = np.nan
        self.V44__Ti44__weak__wc12 = np.nan
        self.Fe49__p_Cr48__weak__wc12 = np.nan
        self.n_Sc60__Sc61 = np.nan
        self.Mn63__n_Fe62__weak__mp17 = np.nan
        self.Si37__P37__weak__wc12 = np.nan
        self.Al39__Si39__weak__wc17 = np.nan
        self.Fe76__Co76__weak__mo03 = np.nan
        self.He4_Na38__Al42 = np.nan
        self.Mg30__Al30__weak__wc12 = np.nan
        self.He4_Ar49__Ca53 = np.nan
        self.Al33__n_Si32__weak__wc12 = np.nan
        self.N19__O19__weak__wc12 = np.nan
        self.S38__Cl38__weak__wc12 = np.nan
        self.He4_K46__Sc50 = np.nan
        self.He4_Sc50__n_V53 = np.nan
        self.n_Sc39__p_Ca39 = np.nan
        self.Mg31__n_Al30__weak__wc12 = np.nan
        self.P39__S39__weak__wc12 = np.nan
        self.n_Sc40__He4_K37 = np.nan
        self.n_Ca39__Ca40 = np.nan
        self.n_Ne33__Ne34 = np.nan
        self.He4_O16__Ne20 = np.nan
        self.p_Ar51__n_K51 = np.nan
        self.p_Cr67__Mn68 = np.nan
        self.F30__n_n_n_Ne27__weak__mo03 = np.nan
        self.p_P41__He4_Si38 = np.nan
        self.p_Mg34__n_Al34 = np.nan
        self.p_Na39__Mg40 = np.nan
        self.Si22__Al22__weak__wc12 = np.nan
        self.Si39__P39__weak__wc17 = np.nan
        self.Al40__n_n_Si38__weak__mp17 = np.nan
        self.He4_Ca56__n_Ti59 = np.nan
        self.p_Be10__He4_Li7 = np.nan
        self.p_Mg35__Al36 = np.nan
        self.Cr45__V45__weak__wc12 = np.nan
        self.p_Ar50__K51 = np.nan
        self.K50__n_n_Ca48__weak__mp17 = np.nan
        self.Sc60__Ti60__weak__mo03 = np.nan
        self.p_Ca47__Sc48 = np.nan
        self.N18__He4_C14__weak__wc12 = np.nan
        self.He4_Cr68__Fe72 = np.nan
        self.N20__O20__weak__wc12 = np.nan
        self.p_Cl44__He4_S41 = np.nan
        self.Ar54__K54__weak__mo03 = np.nan
        self.n_Ca38__He4_Ar35 = np.nan
        self.p_Sc54__He4_Ca51 = np.nan
        self.n_Be9__Be10 = np.nan
        self.He4_Ne21__Mg25 = np.nan
        self.p_Cr70__He4_V67 = np.nan
        self.p_Mg40__Al41 = np.nan
        self.p_Ti55__He4_Sc52 = np.nan
        self.Ar51__n_n_K49__weak__mp17 = np.nan
        self.p_Mg33__Al34 = np.nan
        self.p_Al29__Si30 = np.nan
        self.p_Mn56__n_Fe56 = np.nan
        self.n_Sc47__Sc48 = np.nan
        self.p_V59__He4_Ti56 = np.nan
        self.Na37__n_n_Mg35__weak__mp17 = np.nan
        self.p_Ar49__He4_Cl46 = np.nan
        self.F28__Ne28__weak__mo03 = np.nan
        self.Mg35__Al35__weak__wc17 = np.nan
        self.He4_K52__Sc56 = np.nan
        self.p_Al32__Si33 = np.nan
        self.Ne23__Na23__weak__wc12 = np.nan
        self.Mn45__Cr45__weak__bqa_pos_ = np.nan
        self.Na33__n_n_Mg31__weak__wc12 = np.nan
        self.p_Na19__Mg20 = np.nan
        self.Mg20__Na20__weak__wc12 = np.nan
        self.Ne26__Na26__weak__wc12 = np.nan
        self.Ti60__V60__weak__wc17 = np.nan
        self.p_Fe62__Co63 = np.nan
        self.p_P39__S40 = np.nan
        self.K56__n_n_Ca54__weak__mp17 = np.nan
        self.Cl38__Ar38__weak__wc12 = np.nan
        self.He4_Na32__Al36 = np.nan
        self.Sc55__Ti55__weak__wc12 = np.nan
        self.He4_P30__Cl34 = np.nan
        self.p_F26__He4_O23 = np.nan
        self.F28__n_Ne27__weak__mp17 = np.nan
        self.n_S32__He4_Si29 = np.nan
        self.n_Si37__Si38 = np.nan
        self.Ca56__Sc56__weak__wc17 = np.nan
        self.p_S48__Cl49 = np.nan
        self.Cl42__Ar42__weak__wc12 = np.nan
        self.p_Sc42__He4_Ca39 = np.nan
        self.n_Sc38__He4_K35 = np.nan
        self.n_Al42__Al43 = np.nan
        self.O19__F19__weak__wc12 = np.nan
        self.n_Na28__Na29 = np.nan
        self.p_Si38__He4_Al35 = np.nan
        self.n_Al25__He4_Na22 = np.nan
        self.p_F30__Ne31 = np.nan
        self.N22__n_O21__weak__wc17 = np.nan
        self.Na29__Mg29__weak__wc12 = np.nan
        self.He4_K37__Sc41 = np.nan
        self.n_K34__p_Ar34 = np.nan
        self.He4_Si45__n_S48 = np.nan
        self.He4_Fe69__n_Ni72 = np.nan
        self.Mn72__Fe72__weak__mo03 = np.nan
        self.He4_S40__Ar44 = np.nan
        self.n_P28__He4_Al25 = np.nan
        self.p_O23__F24 = np.nan
        self.K49__n_Ca48__weak__wc12 = np.nan
        self.p_Fe75__Co76 = np.nan
        self.O27__n_F26__weak__mp17 = np.nan
        self.Ne33__Na33__weak__mo03 = np.nan
        self.p_Mn65__Fe66 = np.nan
        self.Na28__n_Mg27__weak__wc12 = np.nan
        self.Ti52__V52__weak__wc12 = np.nan
        self.He4_Mn50__p_Fe53 = np.nan
        self.Fe45__Mn45__weak__wc17 = np.nan
        self.Al35__Si35__weak__wc12 = np.nan
        self.F17__O17__weak__wc12 = np.nan
        self.n_Mn66__Mn67 = np.nan
        self.Al40__Si40__weak__mo03 = np.nan
        self.F26__Ne26__weak__wc12 = np.nan
        self.n_Ar49__Ar50 = np.nan
        self.Cl47__Ar47__weak__wc17 = np.nan
        self.p_Cr61__n_Mn61 = np.nan
        self.p_Na35__Mg36 = np.nan
        self.n_O20__O21 = np.nan
        self.He4_Ar32__p_K35 = np.nan
        self.Sc36__Ca36__weak__bqa_pos_ = np.nan
        self.n_Mg37__Mg38 = np.nan
        self.Al36__n_Si35__weak__mp17 = np.nan
        self.He4_K56__Sc60 = np.nan
        self.p_Na30__n_Mg30 = np.nan
        self.K34__Ar34__weak__bqa_pos_ = np.nan
        self.K42__Ca42__weak__wc12 = np.nan
        self.Na37__n_Mg36__weak__mp17 = np.nan
        self.n_S29__S30 = np.nan
        self.n_Cr48__He4_Ti45 = np.nan
        self.Cl30__S30__weak__bqa_pos_ = np.nan
        self.n_C16__C17 = np.nan
        self.K40__Ca40__weak__wc12 = np.nan
        self.P30__Si30__weak__wc12 = np.nan
        self.p_V62__Cr63 = np.nan
        self.p_Ar46__n_K46 = np.nan
        self.He4_K46__n_Sc49 = np.nan
        self.B19__n_n_C17__weak__wc12 = np.nan
        self.V49__Ti49__weak__wc12 = np.nan
        self.Ar30__Cl30__weak__bqa_pos_ = np.nan
        self.P29__Si29__weak__wc12 = np.nan
        self.He4_K34__Sc38 = np.nan

@numba.njit()
def ye(Y):
    return np.sum(Z * Y)/np.sum(A * Y)

@numba.njit()
def Fe45__p_p_p_Ti42__weak__wc12(rate_eval, tf):
    # Fe45 --> 3 p + Ti42
    rate = 0.0

    # wc12w
    rate += np.exp(  2.49342)

    rate_eval.Fe45__p_p_p_Ti42__weak__wc12 = rate

@numba.njit()
def Cr43__p_p_p_Ca40__weak__wc12(rate_eval, tf):
    # Cr43 --> 3 p + Ca40
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.61495)

    rate_eval.Cr43__p_p_p_Ca40__weak__wc12 = rate

@numba.njit()
def Fe75__n_n_n_Co72__weak__mo03(rate_eval, tf):
    # Fe75 --> 3 n + Co72
    rate = 0.0

    # mo03w
    rate += np.exp(  -6.16924)

    rate_eval.Fe75__n_n_n_Co72__weak__mo03 = rate

@numba.njit()
def Mn73__n_n_n_Fe70__weak__mo03(rate_eval, tf):
    # Mn73 --> 3 n + Fe70
    rate = 0.0

    # mo03w
    rate += np.exp(  1.25617)

    rate_eval.Mn73__n_n_n_Fe70__weak__mo03 = rate

@numba.njit()
def Mn71__n_n_n_Fe68__weak__mo03(rate_eval, tf):
    # Mn71 --> 3 n + Fe68
    rate = 0.0

    # mo03w
    rate += np.exp(  -1.86812)

    rate_eval.Mn71__n_n_n_Fe68__weak__mo03 = rate

@numba.njit()
def Cr70__n_n_n_Mn67__weak__mo03(rate_eval, tf):
    # Cr70 --> 3 n + Mn67
    rate = 0.0

    # mo03w
    rate += np.exp(  -3.2107)

    rate_eval.Cr70__n_n_n_Mn67__weak__mo03 = rate

@numba.njit()
def V66__n_n_n_Cr63__weak__mo03(rate_eval, tf):
    # V66 --> 3 n + Cr63
    rate = 0.0

    # mo03w
    rate += np.exp(  -1.79174)

    rate_eval.V66__n_n_n_Cr63__weak__mo03 = rate

@numba.njit()
def V65__n_n_n_Cr62__weak__mo03(rate_eval, tf):
    # V65 --> 3 n + Cr62
    rate = 0.0

    # mo03w
    rate += np.exp(  -2.30248)

    rate_eval.V65__n_n_n_Cr62__weak__mo03 = rate

@numba.njit()
def Ti65__n_n_n_V62__weak__mo03(rate_eval, tf):
    # Ti65 --> 3 n + V62
    rate = 0.0

    # mo03w
    rate += np.exp(  0.116914)

    rate_eval.Ti65__n_n_n_V62__weak__mo03 = rate

@numba.njit()
def Sc63__n_n_n_Ti60__weak__mo03(rate_eval, tf):
    # Sc63 --> 3 n + Ti60
    rate = 0.0

    # mo03w
    rate += np.exp(  2.91766)

    rate_eval.Sc63__n_n_n_Ti60__weak__mo03 = rate

@numba.njit()
def Sc62__n_n_n_Ti59__weak__mo03(rate_eval, tf):
    # Sc62 --> 3 n + Ti59
    rate = 0.0

    # mo03w
    rate += np.exp(  2.14442)

    rate_eval.Sc62__n_n_n_Ti59__weak__mo03 = rate

@numba.njit()
def Sc61__n_n_n_Ti58__weak__mo03(rate_eval, tf):
    # Sc61 --> 3 n + Ti58
    rate = 0.0

    # mo03w
    rate += np.exp(  1.07453)

    rate_eval.Sc61__n_n_n_Ti58__weak__mo03 = rate

@numba.njit()
def Sc59__n_n_n_Ti56__weak__mo03(rate_eval, tf):
    # Sc59 --> 3 n + Ti56
    rate = 0.0

    # mo03w
    rate += np.exp(  -0.453068)

    rate_eval.Sc59__n_n_n_Ti56__weak__mo03 = rate

@numba.njit()
def Sc58__n_n_n_Ti55__weak__mo03(rate_eval, tf):
    # Sc58 --> 3 n + Ti55
    rate = 0.0

    # mo03w
    rate += np.exp(  -1.54759)

    rate_eval.Sc58__n_n_n_Ti55__weak__mo03 = rate

@numba.njit()
def Sc57__n_n_n_Ti54__weak__mo03(rate_eval, tf):
    # Sc57 --> 3 n + Ti54
    rate = 0.0

    # mo03w
    rate += np.exp(  -4.56522)

    rate_eval.Sc57__n_n_n_Ti54__weak__mo03 = rate

@numba.njit()
def Ca60__n_n_n_Sc57__weak__mo03(rate_eval, tf):
    # Ca60 --> 3 n + Sc57
    rate = 0.0

    # mo03w
    rate += np.exp(  0.956082)

    rate_eval.Ca60__n_n_n_Sc57__weak__mo03 = rate

@numba.njit()
def Ca59__n_n_n_Sc56__weak__mo03(rate_eval, tf):
    # Ca59 --> 3 n + Sc56
    rate = 0.0

    # mo03w
    rate += np.exp(  -0.322213)

    rate_eval.Ca59__n_n_n_Sc56__weak__mo03 = rate

@numba.njit()
def Ca58__n_n_n_Sc55__weak__mo03(rate_eval, tf):
    # Ca58 --> 3 n + Sc55
    rate = 0.0

    # mo03w
    rate += np.exp(  -3.70937)

    rate_eval.Ca58__n_n_n_Sc55__weak__mo03 = rate

@numba.njit()
def Ca57__n_n_n_Sc54__weak__mo03(rate_eval, tf):
    # Ca57 --> 3 n + Sc54
    rate = 0.0

    # mo03w
    rate += np.exp(  0.004129)

    rate_eval.Ca57__n_n_n_Sc54__weak__mo03 = rate

@numba.njit()
def K59__n_n_n_Ca56__weak__mo03(rate_eval, tf):
    # K59 --> 3 n + Ca56
    rate = 0.0

    # mo03w
    rate += np.exp(  5.35769)

    rate_eval.K59__n_n_n_Ca56__weak__mo03 = rate

@numba.njit()
def K58__n_n_n_Ca55__weak__mo03(rate_eval, tf):
    # K58 --> 3 n + Ca55
    rate = 0.0

    # mo03w
    rate += np.exp(  4.66428)

    rate_eval.K58__n_n_n_Ca55__weak__mo03 = rate

@numba.njit()
def K55__n_n_n_Ca52__weak__mo03(rate_eval, tf):
    # K55 --> 3 n + Ca52
    rate = 0.0

    # mo03w
    rate += np.exp(  2.19566)

    rate_eval.K55__n_n_n_Ca52__weak__mo03 = rate

@numba.njit()
def K53__n_n_n_Ca50__weak__mo03(rate_eval, tf):
    # K53 --> 3 n + Ca50
    rate = 0.0

    # mo03w
    rate += np.exp(  -1.57696)

    rate_eval.K53__n_n_n_Ca50__weak__mo03 = rate

@numba.njit()
def Ar54__n_n_n_K51__weak__mo03(rate_eval, tf):
    # Ar54 --> 3 n + K51
    rate = 0.0

    # mo03w
    rate += np.exp(  1.75093)

    rate_eval.Ar54__n_n_n_K51__weak__mo03 = rate

@numba.njit()
def Ar53__n_n_n_K50__weak__mo03(rate_eval, tf):
    # Ar53 --> 3 n + K50
    rate = 0.0

    # mo03w
    rate += np.exp(  0.924686)

    rate_eval.Ar53__n_n_n_K50__weak__mo03 = rate

@numba.njit()
def Ar52__n_n_n_K49__weak__mo03(rate_eval, tf):
    # Ar52 --> 3 n + K49
    rate = 0.0

    # mo03w
    rate += np.exp(  -2.60082)

    rate_eval.Ar52__n_n_n_K49__weak__mo03 = rate

@numba.njit()
def Cl50__n_n_n_Ar47__weak__mo03(rate_eval, tf):
    # Cl50 --> 3 n + Ar47
    rate = 0.0

    # mo03w
    rate += np.exp(  2.22262)

    rate_eval.Cl50__n_n_n_Ar47__weak__mo03 = rate

@numba.njit()
def S48__n_n_n_Cl45__weak__mo03(rate_eval, tf):
    # S48 --> 3 n + Cl45
    rate = 0.0

    # mo03w
    rate += np.exp(  1.77318)

    rate_eval.S48__n_n_n_Cl45__weak__mo03 = rate

@numba.njit()
def S47__n_n_n_Cl44__weak__mo03(rate_eval, tf):
    # S47 --> 3 n + Cl44
    rate = 0.0

    # mo03w
    rate += np.exp(  -1.8386)

    rate_eval.S47__n_n_n_Cl44__weak__mo03 = rate

@numba.njit()
def K56__n_n_n_Ca53__weak__mo03(rate_eval, tf):
    # K56 --> 3 n + Ca53
    rate = 0.0

    # mo03w
    rate += np.exp(  2.52914)

    rate_eval.K56__n_n_n_Ca53__weak__mo03 = rate

@numba.njit()
def P44__n_n_n_S41__weak__mo03(rate_eval, tf):
    # P44 --> 3 n + S41
    rate = 0.0

    # mo03w
    rate += np.exp(  -0.462988)

    rate_eval.P44__n_n_n_S41__weak__mo03 = rate

@numba.njit()
def Si42__n_n_n_P39__weak__mo03(rate_eval, tf):
    # Si42 --> 3 n + P39
    rate = 0.0

    # mo03w
    rate += np.exp(  -6.44002)

    rate_eval.Si42__n_n_n_P39__weak__mo03 = rate

@numba.njit()
def Al43__n_n_n_Si40__weak__mo03(rate_eval, tf):
    # Al43 --> 3 n + Si40
    rate = 0.0

    # mo03w
    rate += np.exp(  5.64619)

    rate_eval.Al43__n_n_n_Si40__weak__mo03 = rate

@numba.njit()
def Al42__n_n_n_Si39__weak__mo03(rate_eval, tf):
    # Al42 --> 3 n + Si39
    rate = 0.0

    # mo03w
    rate += np.exp(  4.83671)

    rate_eval.Al42__n_n_n_Si39__weak__mo03 = rate

@numba.njit()
def Al41__n_n_n_Si38__weak__mo03(rate_eval, tf):
    # Al41 --> 3 n + Si38
    rate = 0.0

    # mo03w
    rate += np.exp(  2.99069)

    rate_eval.Al41__n_n_n_Si38__weak__mo03 = rate

@numba.njit()
def Al39__n_n_n_Si36__weak__mo03(rate_eval, tf):
    # Al39 --> 3 n + Si36
    rate = 0.0

    # mo03w
    rate += np.exp(  2.28185)

    rate_eval.Al39__n_n_n_Si36__weak__mo03 = rate

@numba.njit()
def Al38__n_n_n_Si35__weak__mo03(rate_eval, tf):
    # Al38 --> 3 n + Si35
    rate = 0.0

    # mo03w
    rate += np.exp(  0.802749)

    rate_eval.Al38__n_n_n_Si35__weak__mo03 = rate

@numba.njit()
def Al37__n_n_n_Si34__weak__mo03(rate_eval, tf):
    # Al37 --> 3 n + Si34
    rate = 0.0

    # mo03w
    rate += np.exp(  -1.05163)

    rate_eval.Al37__n_n_n_Si34__weak__mo03 = rate

@numba.njit()
def Mg40__n_n_n_Al37__weak__mo03(rate_eval, tf):
    # Mg40 --> 3 n + Al37
    rate = 0.0

    # mo03w
    rate += np.exp(  3.04479)

    rate_eval.Mg40__n_n_n_Al37__weak__mo03 = rate

@numba.njit()
def Mg36__n_n_n_Al33__weak__mo03(rate_eval, tf):
    # Mg36 --> 3 n + Al33
    rate = 0.0

    # mo03w
    rate += np.exp(  -1.63001)

    rate_eval.Mg36__n_n_n_Al33__weak__mo03 = rate

@numba.njit()
def Mg35__n_n_n_Al32__weak__mo03(rate_eval, tf):
    # Mg35 --> 3 n + Al32
    rate = 0.0

    # mo03w
    rate += np.exp(  -2.75658)

    rate_eval.Mg35__n_n_n_Al32__weak__mo03 = rate

@numba.njit()
def Na34__n_n_n_Mg31__weak__mo03(rate_eval, tf):
    # Na34 --> 3 n + Mg31
    rate = 0.0

    # mo03w
    rate += np.exp(  1.64594)

    rate_eval.Na34__n_n_n_Mg31__weak__mo03 = rate

@numba.njit()
def Na33__n_n_n_Mg30__weak__mo03(rate_eval, tf):
    # Na33 --> 3 n + Mg30
    rate = 0.0

    # mo03w
    rate += np.exp(  2.16251)

    rate_eval.Na33__n_n_n_Mg30__weak__mo03 = rate

@numba.njit()
def Na32__n_n_n_Mg29__weak__mo03(rate_eval, tf):
    # Na32 --> 3 n + Mg29
    rate = 0.0

    # mo03w
    rate += np.exp(  -1.88116)

    rate_eval.Na32__n_n_n_Mg29__weak__mo03 = rate

@numba.njit()
def Ne31__n_n_n_Na28__weak__mo03(rate_eval, tf):
    # Ne31 --> 3 n + Na28
    rate = 0.0

    # mo03w
    rate += np.exp(  -0.975243)

    rate_eval.Ne31__n_n_n_Na28__weak__mo03 = rate

@numba.njit()
def F31__n_n_n_Ne28__weak__mo03(rate_eval, tf):
    # F31 --> 3 n + Ne28
    rate = 0.0

    # mo03w
    rate += np.exp(  5.01759)

    rate_eval.F31__n_n_n_Ne28__weak__mo03 = rate

@numba.njit()
def F29__n_n_n_Ne26__weak__mo03(rate_eval, tf):
    # F29 --> 3 n + Ne26
    rate = 0.0

    # mo03w
    rate += np.exp(  4.06247)

    rate_eval.F29__n_n_n_Ne26__weak__mo03 = rate

@numba.njit()
def K54__n_n_n_Ca51__weak__mo03(rate_eval, tf):
    # K54 --> 3 n + Ca51
    rate = 0.0

    # mo03w
    rate += np.exp(  0.803491)

    rate_eval.K54__n_n_n_Ca51__weak__mo03 = rate

@numba.njit()
def F28__n_n_n_Ne25__weak__mo03(rate_eval, tf):
    # F28 --> 3 n + Ne25
    rate = 0.0

    # mo03w
    rate += np.exp(  2.36227)

    rate_eval.F28__n_n_n_Ne25__weak__mo03 = rate

@numba.njit()
def F27__n_n_n_Ne24__weak__mo03(rate_eval, tf):
    # F27 --> 3 n + Ne24
    rate = 0.0

    # mo03w
    rate += np.exp(  0.308411)

    rate_eval.F27__n_n_n_Ne24__weak__mo03 = rate

@numba.njit()
def O27__n_n_n_F24__weak__mo03(rate_eval, tf):
    # O27 --> 3 n + F24
    rate = 0.0

    # mo03w
    rate += np.exp(  3.58072)

    rate_eval.O27__n_n_n_F24__weak__mo03 = rate

@numba.njit()
def n_p_p__p_d(rate_eval, tf):
    # n + p + p --> p + d
    rate = 0.0

    # cf88n
    rate += np.exp(  -4.24034 + -3.72*tf.T913i + 0.946313*tf.T913
                  + 0.105406*tf.T9 + -0.0149431*tf.T953 + -1.5*tf.lnT9)

    rate_eval.n_p_p__p_d = rate

@numba.njit()
def n_n_He4__He6(rate_eval, tf):
    # n + n + He4 --> He6
    rate = 0.0

    # cf88r
    rate += np.exp(  -23.9322 + -9.585*tf.T9i + 0.694279*tf.T913i + -3.33326*tf.T913
                  + 0.507932*tf.T9 + -0.0427342*tf.T953 + -1.0*tf.lnT9)

    rate_eval.n_n_He4__He6 = rate

@numba.njit()
def p_Be9__n_p_He4_He4(rate_eval, tf):
    # Be9 + p --> n + p + He4 + He4
    rate = 0.0

    # cf88r
    rate += np.exp(  20.7431 + -26.725*tf.T9i + 1.40505e-06*tf.T913i + -1.47128e-06*tf.T913
                  + 6.89313e-08*tf.T9 + -3.55179e-09*tf.T953 + -1.5*tf.lnT9)
    # cf88n
    rate += np.exp(  14.6035 + -21.4742*tf.T9i + -0.634849*tf.T913i + 4.82033*tf.T913
                  + -0.257317*tf.T9 + 0.0134206*tf.T953 + -1.08885*tf.lnT9)

    rate_eval.p_Be9__n_p_He4_He4 = rate

@numba.njit()
def He3_Be7__p_p_He4_He4(rate_eval, tf):
    # Be7 + He3 --> p + p + He4 + He4
    rate = 0.0

    # mafon
    rate += np.exp(  31.7435 + -5.45213e-12*tf.T9i + -21.793*tf.T913i + -1.98126e-09*tf.T913
                  + 1.84204e-10*tf.T9 + -1.46403e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He3_Be7__p_p_He4_He4 = rate

@numba.njit()
def t_Be7__n_p_He4_He4(rate_eval, tf):
    # Be7 + t --> n + p + He4 + He4
    rate = 0.0

    # mafon
    rate += np.exp(  28.6992 + -6.9004e-12*tf.T9i + -13.792*tf.T913i + -2.92021e-09*tf.T913
                  + 2.89378e-10*tf.T9 + -2.40287e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.t_Be7__n_p_He4_He4 = rate

@numba.njit()
def He4_Ca36__p_p_Ca38(rate_eval, tf):
    # Ca36 + He4 --> p + p + Ca38
    rate = 0.0

    # fkthr
    rate += np.exp(  60.9026 + -1.47986*tf.T9i + -27.3832*tf.T913i + -55.6339*tf.T913
                  + 2.1009*tf.T9 + -0.113521*tf.T953 + 30.0739*tf.lnT9)

    rate_eval.He4_Ca36__p_p_Ca38 = rate

@numba.njit()
def He4_O13__p_p_O15(rate_eval, tf):
    # O13 + He4 --> p + p + O15
    rate = 0.0

    # wiesn
    rate += np.exp(  -709.294)
    # wiesr
    rate += np.exp(  459.951 + -33.7936*tf.T9i + 1162.8*tf.T913i + -1683.98*tf.T913
                  + 95.2669*tf.T9 + -5.52244*tf.T953 + 841.006*tf.lnT9)
    # wiesr
    rate += np.exp(  -33.9128 + -2.437*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.He4_O13__p_p_O15 = rate

@numba.njit()
def p_B11__He4_He4_He4(rate_eval, tf):
    # B11 + p --> 3 He4
    rate = 0.0

    # nacrr
    rate += np.exp(  -14.9395 + -1.724*tf.T9i + 8.49175*tf.T913i + 27.3254*tf.T913
                  + -3.72071*tf.T9 + 0.275516*tf.T953 + -1.5*tf.lnT9)
    # nacrn
    rate += np.exp(  28.6442 + -12.097*tf.T913i + -0.0496312*tf.T913
                  + 0.687736*tf.T9 + -0.564229*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_B11__He4_He4_He4 = rate

@numba.njit()
def n_B8__p_He4_He4(rate_eval, tf):
    # B8 + n --> p + He4 + He4
    rate = 0.0

    #  wagn
    rate += np.exp(  19.812 + -1.13869e-12*tf.T9i + 1.5368e-10*tf.T913i + -5.36043e-10*tf.T913
                  + 5.80628e-11*tf.T9 + -5.23778e-12*tf.T953 + 1.77211e-10*tf.lnT9)

    rate_eval.n_B8__p_He4_He4 = rate

@numba.njit()
def p_Be9__d_He4_He4(rate_eval, tf):
    # Be9 + p --> d + He4 + He4
    rate = 0.0

    # cf88r
    rate += np.exp(  20.5607 + -5.8*tf.T9i
                  + -0.75*tf.lnT9)
    # cf88r
    rate += np.exp(  20.1768 + -3.046*tf.T9i
                  + -1.0*tf.lnT9)
    # cf88n
    rate += np.exp(  26.0751 + -10.359*tf.T913i + 0.103955*tf.T913
                  + 4.4262*tf.T9 + -5.95664*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Be9__d_He4_He4 = rate

@numba.njit()
def d_Li7__n_He4_He4(rate_eval, tf):
    # Li7 + d --> n + He4 + He4
    rate = 0.0

    # cf88n
    rate += np.exp(  26.4 + -10.259*tf.T913i
                  + -0.666667*tf.lnT9)

    rate_eval.d_Li7__n_He4_He4 = rate

@numba.njit()
def He3_He3__p_p_He4(rate_eval, tf):
    # He3 + He3 --> p + p + He4
    rate = 0.0

    # nacrn
    rate += np.exp(  24.7788 + -12.277*tf.T913i + -0.103699*tf.T913
                  + -0.0649967*tf.T9 + 0.0168191*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He3_He3__p_p_He4 = rate

@numba.njit()
def He4_Fe76__n_Ni79(rate_eval, tf):
    # Fe76 + He4 --> n + Ni79
    rate = 0.0

    # rath 
    rate += np.exp(  -1297.01 + 26.9302*tf.T9i + -2671.49*tf.T913i + 4133.83*tf.T913
                  + -234.269*tf.T9 + 12.96*tf.T953 + -2005.12*tf.lnT9)

    rate_eval.He4_Fe76__n_Ni79 = rate

@numba.njit()
def p_Fe76__He4_Mn73(rate_eval, tf):
    # Fe76 + p --> He4 + Mn73
    rate = 0.0

    # rath 
    rate += np.exp(  -385.124 + 11.2515*tf.T9i + -1130.28*tf.T913i + 1540.81*tf.T913
                  + -81.7783*tf.T9 + 4.34253*tf.T953 + -777.383*tf.lnT9)

    rate_eval.p_Fe76__He4_Mn73 = rate

@numba.njit()
def He4_Fe75__n_Ni78(rate_eval, tf):
    # Fe75 + He4 --> n + Ni78
    rate = 0.0

    # rath 
    rate += np.exp(  -1290.25 + 26.7832*tf.T9i + -2657.11*tf.T913i + 4111.69*tf.T913
                  + -233.04*tf.T9 + 12.8907*tf.T953 + -1994.17*tf.lnT9)

    rate_eval.He4_Fe75__n_Ni78 = rate

@numba.njit()
def p_Fe75__He4_Mn72(rate_eval, tf):
    # Fe75 + p --> He4 + Mn72
    rate = 0.0

    # rath 
    rate += np.exp(  -763.839 + 14.9322*tf.T9i + -1507.83*tf.T913i + 2346.68*tf.T913
                  + -134.046*tf.T9 + 7.47008*tf.T953 + -1126.9*tf.lnT9)

    rate_eval.p_Fe75__He4_Mn72 = rate

@numba.njit()
def p_Fe75__n_Co75(rate_eval, tf):
    # Fe75 + p --> n + Co75
    rate = 0.0

    # rath 
    rate += np.exp(  160.786 + -7.7204*tf.T9i + 295.41*tf.T913i + -472.698*tf.T913
                  + 26.2436*tf.T9 + -1.47439*tf.T953 + 236.283*tf.lnT9)

    rate_eval.p_Fe75__n_Co75 = rate

@numba.njit()
def He4_Fe74__n_Ni77(rate_eval, tf):
    # Fe74 + He4 --> n + Ni77
    rate = 0.0

    # rath 
    rate += np.exp(  -1282.01 + 26.6081*tf.T9i + -2640.31*tf.T913i + 4085.66*tf.T913
                  + -231.704*tf.T9 + 12.8274*tf.T953 + -1981.29*tf.lnT9)

    rate_eval.He4_Fe74__n_Ni77 = rate

@numba.njit()
def p_Fe74__He4_Mn71(rate_eval, tf):
    # Fe74 + p --> He4 + Mn71
    rate = 0.0

    # rath 
    rate += np.exp(  -709.472 + 14.3181*tf.T9i + -1446.74*tf.T913i + 2224.73*tf.T913
                  + -126.134*tf.T9 + 6.98216*tf.T953 + -1072.91*tf.lnT9)

    rate_eval.p_Fe74__He4_Mn71 = rate

@numba.njit()
def p_Fe74__n_Co74(rate_eval, tf):
    # Fe74 + p --> n + Co74
    rate = 0.0

    # rath 
    rate += np.exp(  159.406 + -7.67135*tf.T9i + 293.023*tf.T913i + -468.733*tf.T913
                  + 25.981*tf.T9 + -1.45689*tf.T953 + 234.447*tf.lnT9)

    rate_eval.p_Fe74__n_Co74 = rate

@numba.njit()
def Mg37__n_n_n_Al34__weak__mo03(rate_eval, tf):
    # Mg37 --> 3 n + Al34
    rate = 0.0

    # mo03w
    rate += np.exp(  0.866354)

    rate_eval.Mg37__n_n_n_Al34__weak__mo03 = rate

@numba.njit()
def p_Fe73__He4_Mn70(rate_eval, tf):
    # Fe73 + p --> He4 + Mn70
    rate = 0.0

    # rath 
    rate += np.exp(  -882.49 + 12.4878*tf.T9i + -1384.34*tf.T913i + 2353.68*tf.T913
                  + -142.004*tf.T9 + 8.18519*tf.T953 + -1085.96*tf.lnT9)

    rate_eval.p_Fe73__He4_Mn70 = rate

@numba.njit()
def p_Fe73__n_Co73(rate_eval, tf):
    # Fe73 + p --> n + Co73
    rate = 0.0

    # rath 
    rate += np.exp(  159.846 + -7.63286*tf.T9i + 291.831*tf.T913i + -467.982*tf.T913
                  + 25.9813*tf.T9 + -1.45835*tf.T953 + 233.819*tf.lnT9)

    rate_eval.p_Fe73__n_Co73 = rate

@numba.njit()
def p_Fe72__He4_Mn69(rate_eval, tf):
    # Fe72 + p --> He4 + Mn69
    rate = 0.0

    # rath 
    rate += np.exp(  -665.668 + 13.8269*tf.T9i + -1398.27*tf.T913i + 2127.37*tf.T913
                  + -119.358*tf.T9 + 6.55048*tf.T953 + -1030.93*tf.lnT9)

    rate_eval.p_Fe72__He4_Mn69 = rate

@numba.njit()
def p_Fe72__n_Co72(rate_eval, tf):
    # Fe72 + p --> n + Co72
    rate = 0.0

    # rath 
    rate += np.exp(  157.053 + -7.57523*tf.T9i + 288.547*tf.T913i + -461.403*tf.T913
                  + 25.4395*tf.T9 + -1.41817*tf.T953 + 231.063*tf.lnT9)

    rate_eval.p_Fe72__n_Co72 = rate

@numba.njit()
def He4_Fe71__n_Ni74(rate_eval, tf):
    # Fe71 + He4 --> n + Ni74
    rate = 0.0

    # rath 
    rate += np.exp(  -1256.95 + 26.1008*tf.T9i + -2590.99*tf.T913i + 4007.43*tf.T913
                  + -227.238*tf.T9 + 12.5732*tf.T953 + -1943.21*tf.lnT9)

    rate_eval.He4_Fe71__n_Ni74 = rate

@numba.njit()
def p_Fe71__He4_Mn68(rate_eval, tf):
    # Fe71 + p --> He4 + Mn68
    rate = 0.0

    # rath 
    rate += np.exp(  -862.73 + 12.3191*tf.T9i + -1364.89*tf.T913i + 2314.14*tf.T913
                  + -139.442*tf.T9 + 8.02759*tf.T953 + -1069.0*tf.lnT9)

    rate_eval.p_Fe71__He4_Mn68 = rate

@numba.njit()
def p_Fe71__n_Co71(rate_eval, tf):
    # Fe71 + p --> n + Co71
    rate = 0.0

    # rath 
    rate += np.exp(  157.912 + -7.53873*tf.T9i + 287.636*tf.T913i + -461.412*tf.T913
                  + 25.5269*tf.T9 + -1.42945*tf.T953 + 230.727*tf.lnT9)

    rate_eval.p_Fe71__n_Co71 = rate

@numba.njit()
def He4_Fe70__n_Ni73(rate_eval, tf):
    # Fe70 + He4 --> n + Ni73
    rate = 0.0

    # rath 
    rate += np.exp(  -1245.54 + 25.8903*tf.T9i + -2570.71*tf.T913i + 3973.91*tf.T913
                  + -225.313*tf.T9 + 12.4695*tf.T953 + -1927.2*tf.lnT9)

    rate_eval.He4_Fe70__n_Ni73 = rate

@numba.njit()
def p_Fe70__He4_Mn67(rate_eval, tf):
    # Fe70 + p --> He4 + Mn67
    rate = 0.0

    # rath 
    rate += np.exp(  -803.625 + 11.7554*tf.T9i + -1308.88*tf.T913i + 2191.08*tf.T913
                  + -130.418*tf.T9 + 7.44678*tf.T953 + -1018.19*tf.lnT9)

    rate_eval.p_Fe70__He4_Mn67 = rate

@numba.njit()
def p_Fe70__n_Co70(rate_eval, tf):
    # Fe70 + p --> n + Co70
    rate = 0.0

    # rath 
    rate += np.exp(  155.472 + -7.48743*tf.T9i + 285.037*tf.T913i + -455.907*tf.T913
                  + 25.0181*tf.T9 + -1.39017*tf.T953 + 228.565*tf.lnT9)

    rate_eval.p_Fe70__n_Co70 = rate

@numba.njit()
def p_Fe69__He4_Mn66(rate_eval, tf):
    # Fe69 + p --> He4 + Mn66
    rate = 0.0

    # rath 
    rate += np.exp(  -824.585 + 11.7956*tf.T9i + -1309.23*tf.T913i + 2215.97*tf.T913
                  + -134.406*tf.T9 + 7.76017*tf.T953 + -1021.0*tf.lnT9)

    rate_eval.p_Fe69__He4_Mn66 = rate

@numba.njit()
def p_Fe69__n_Co69(rate_eval, tf):
    # Fe69 + p --> n + Co69
    rate = 0.0

    # rath 
    rate += np.exp(  153.777 + -7.43957*tf.T9i + 282.843*tf.T913i + -451.815*tf.T913
                  + 24.7401*tf.T9 + -1.37595*tf.T953 + 226.842*tf.lnT9)

    rate_eval.p_Fe69__n_Co69 = rate

@numba.njit()
def He4_Fe68__n_Ni71(rate_eval, tf):
    # Fe68 + He4 --> n + Ni71
    rate = 0.0

    # rath 
    rate += np.exp(  -1225.0 + 25.505*tf.T9i + -2533.35*tf.T913i + 3912.79*tf.T913
                  + -221.728*tf.T9 + 12.2634*tf.T953 + -1897.92*tf.lnT9)

    rate_eval.He4_Fe68__n_Ni71 = rate

@numba.njit()
def p_Fe68__He4_Mn65(rate_eval, tf):
    # Fe68 + p --> He4 + Mn65
    rate = 0.0

    # rath 
    rate += np.exp(  -688.213 + 10.6195*tf.T9i + -1188.19*tf.T913i + 1941.19*tf.T913
                  + -114.356*tf.T9 + 6.4664*tf.T953 + -908.064*tf.lnT9)

    rate_eval.p_Fe68__He4_Mn65 = rate

@numba.njit()
def p_Fe67__He4_Mn64(rate_eval, tf):
    # Fe67 + p --> He4 + Mn64
    rate = 0.0

    # rath 
    rate += np.exp(  -423.135 + 0.455063*tf.T9i + -426.242*tf.T913i + 879.303*tf.T913
                  + -60.8802*tf.T9 + 3.77721*tf.T953 + -360.699*tf.lnT9)

    rate_eval.p_Fe67__He4_Mn64 = rate

@numba.njit()
def p_Fe65__He4_Mn62(rate_eval, tf):
    # Fe65 + p --> He4 + Mn62
    rate = 0.0

    # rath 
    rate += np.exp(  -92.611 + -5.39031*tf.T9i + 74.3492*tf.T913i + 8.16774*tf.T913
                  + -7.34152*tf.T9 + 0.633197*tf.T953 + 41.1042*tf.lnT9)

    rate_eval.p_Fe65__He4_Mn62 = rate

@numba.njit()
def He4_Fe64__n_Ni67(rate_eval, tf):
    # Fe64 + He4 --> n + Ni67
    rate = 0.0

    # rath 
    rate += np.exp(  -1189.7 + 24.7714*tf.T9i + -2462.4*tf.T913i + 3801.36*tf.T913
                  + -215.594*tf.T9 + 11.9342*tf.T953 + -1843.31*tf.lnT9)

    rate_eval.He4_Fe64__n_Ni67 = rate

@numba.njit()
def He4_Fe63__n_Ni66(rate_eval, tf):
    # Fe63 + He4 --> n + Ni66
    rate = 0.0

    # rath 
    rate += np.exp(  -1172.56 + 24.5452*tf.T9i + -2439.75*tf.T913i + 3759.43*tf.T913
                  + -212.815*tf.T9 + 11.7555*tf.T953 + -1824.57*tf.lnT9)

    rate_eval.He4_Fe63__n_Ni66 = rate

@numba.njit()
def p_Fe63__He4_Mn60(rate_eval, tf):
    # Fe63 + p --> He4 + Mn60
    rate = 0.0

    # rath 
    rate += np.exp(  -60.1788 + -5.50115*tf.T9i + 92.339*tf.T913i + -44.1217*tf.T913
                  + -3.12206*tf.T9 + 0.353686*tf.T953 + 59.9237*tf.lnT9)

    rate_eval.p_Fe63__He4_Mn60 = rate

@numba.njit()
def p_Fe62__He4_Mn59(rate_eval, tf):
    # Fe62 + p --> He4 + Mn59
    rate = 0.0

    # rath 
    rate += np.exp(  -45.0453 + -5.76933*tf.T9i + 125.258*tf.T913i + -94.3055*tf.T913
                  + -2.53048*tf.T9 + 0.468679*tf.T953 + 89.2569*tf.lnT9)

    rate_eval.p_Fe62__He4_Mn59 = rate

@numba.njit()
def p_Fe61__He4_Mn58(rate_eval, tf):
    # Fe61 + p --> He4 + Mn58
    rate = 0.0

    # rath 
    rate += np.exp(  -66.9263 + -5.43116*tf.T9i + 91.6649*tf.T913i + -35.1979*tf.T913
                  + -4.47436*tf.T9 + 0.452231*tf.T953 + 59.0677*tf.lnT9)

    rate_eval.p_Fe61__He4_Mn58 = rate

@numba.njit()
def p_Fe61__n_Co61(rate_eval, tf):
    # Fe61 + p --> n + Co61
    rate = 0.0

    # rath 
    rate += np.exp(  140.882 + -7.00746*tf.T9i + 261.817*tf.T913i + -416.833*tf.T913
                  + 22.7128*tf.T9 + -1.27086*tf.T953 + 210.682*tf.lnT9)

    rate_eval.p_Fe61__n_Co61 = rate

@numba.njit()
def p_Fe60__He4_Mn57(rate_eval, tf):
    # Fe60 + p --> He4 + Mn57
    rate = 0.0

    # rath 
    rate += np.exp(  -507.122 + 0.984911*tf.T9i + -470.65*tf.T913i + 1021.57*tf.T913
                  + -73.9191*tf.T9 + 4.71971*tf.T953 + -409.342*tf.lnT9)

    rate_eval.p_Fe60__He4_Mn57 = rate

@numba.njit()
def He4_Fe59__n_Ni62(rate_eval, tf):
    # Fe59 + He4 --> n + Ni62
    rate = 0.0

    # rath 
    rate += np.exp(  -1134.9 + 23.7432*tf.T9i + -2362.65*tf.T913i + 3638.95*tf.T913
                  + -206.196*tf.T9 + 11.3991*tf.T953 + -1765.29*tf.lnT9)

    rate_eval.He4_Fe59__n_Ni62 = rate

@numba.njit()
def p_Fe59__He4_Mn56(rate_eval, tf):
    # Fe59 + p --> He4 + Mn56
    rate = 0.0

    # rath 
    rate += np.exp(  -370.402 + -0.386959*tf.T9i + -334.106*tf.T913i + 733.915*tf.T913
                  + -55.0482*tf.T9 + 3.57766*tf.T953 + -285.783*tf.lnT9)

    rate_eval.p_Fe59__He4_Mn56 = rate

@numba.njit()
def p_Fe59__n_Co59(rate_eval, tf):
    # Fe59 + p --> n + Co59
    rate = 0.0

    # rath 
    rate += np.exp(  139.281 + -6.90072*tf.T9i + 257.214*tf.T913i + -410.785*tf.T913
                  + 22.5007*tf.T9 + -1.26753*tf.T953 + 207.488*tf.lnT9)

    rate_eval.p_Fe59__n_Co59 = rate

@numba.njit()
def p_Fe57__He4_Mn54(rate_eval, tf):
    # Fe57 + p --> He4 + Mn54
    rate = 0.0

    # ths8r
    rate += np.exp(  -88.432 + -37.1663*tf.T913i + 123.946*tf.T913
                  + -27.2803*tf.T9 + 2.75453*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Fe57__He4_Mn54 = rate

@numba.njit()
def n_Fe56__He4_Cr53(rate_eval, tf):
    # Fe56 + n --> He4 + Cr53
    rate = 0.0

    # ths8r
    rate += np.exp(  -115.917 + 108.603*tf.T913
                  + -15.5995*tf.T9 + 1.14343*tf.T953)

    rate_eval.n_Fe56__He4_Cr53 = rate

@numba.njit()
def O28__n_O27(rate_eval, tf):
    # O28 --> n + O27
    rate = 0.0

    # wc12s
    rate += np.exp(  15.7516)

    rate_eval.O28__n_O27 = rate

@numba.njit()
def p_Ar34__K35(rate_eval, tf):
    # Ar34 + p --> K35
    rate = 0.0

    # il10n
    rate += np.exp(  18.9679 + -28.9336*tf.T913i + 0.251249*tf.T913
                  + -0.0326331*tf.T9 + -0.00253518*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ar34__K35 = rate

@numba.njit()
def n_Fe55__p_Mn55(rate_eval, tf):
    # Fe55 + n --> p + Mn55
    rate = 0.0

    # ths8r
    rate += np.exp(  4.70639 + 7.03052*tf.T913
                  + 0.260509*tf.T9 + -0.0813397*tf.T953)

    rate_eval.n_Fe55__p_Mn55 = rate

@numba.njit()
def n_Sc40__Sc41(rate_eval, tf):
    # Sc40 + n --> Sc41
    rate = 0.0

    # ths8r
    rate += np.exp(  11.0811 + 0.753376*tf.T913
                  + -0.0291255*tf.T9 + 0.00291754*tf.T953)

    rate_eval.n_Sc40__Sc41 = rate

@numba.njit()
def n_Fe54__p_Mn54(rate_eval, tf):
    # Fe54 + n --> p + Mn54
    rate = 0.0

    # ths8r
    rate += np.exp(  -43.1319 + 51.9922*tf.T913
                  + -7.26639*tf.T9 + 0.502147*tf.T953)

    rate_eval.n_Fe54__p_Mn54 = rate

@numba.njit()
def He4_Sc59__V63(rate_eval, tf):
    # Sc59 + He4 --> V63
    rate = 0.0

    # rath 
    rate += np.exp(  -993.291 + 20.6514*tf.T9i + -2053.96*tf.T913i + 3163.69*tf.T913
                  + -179.302*tf.T9 + 9.90166*tf.T953 + -1534.9*tf.lnT9)

    rate_eval.He4_Sc59__V63 = rate

@numba.njit()
def n_Fe53__He4_Cr50(rate_eval, tf):
    # Fe53 + n --> He4 + Cr50
    rate = 0.0

    # ths8r
    rate += np.exp(  11.025 + -0.146952*tf.T913
                  + 1.12217*tf.T9 + -0.10318*tf.T953)

    rate_eval.n_Fe53__He4_Cr50 = rate

@numba.njit()
def Fe67__Co67__weak__wc12(rate_eval, tf):
    # Fe67 --> Co67
    rate = 0.0

    # wc12w
    rate += np.exp(  0.539828)

    rate_eval.Fe67__Co67__weak__wc12 = rate

@numba.njit()
def He4_S30__Ar34(rate_eval, tf):
    # S30 + He4 --> Ar34
    rate = 0.0

    # ths8r
    rate += np.exp(  43.1127 + -65.211*tf.T913i + -1.41447*tf.T913
                  + -0.542976*tf.T9 + 0.0211165*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S30__Ar34 = rate

@numba.njit()
def n_Fe53__p_Mn53(rate_eval, tf):
    # Fe53 + n --> p + Mn53
    rate = 0.0

    # ths8r
    rate += np.exp(  21.1239 + -1.19445*tf.T913
                  + 0.393603*tf.T9 + -0.0404022*tf.T953)

    rate_eval.n_Fe53__p_Mn53 = rate

@numba.njit()
def He4_Fe52__p_Co55(rate_eval, tf):
    # Fe52 + He4 --> p + Co55
    rate = 0.0

    # ths8r
    rate += np.exp(  62.2207 + -91.6819*tf.T913i + -0.329235*tf.T913
                  + -0.780924*tf.T9 + 0.0425179*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe52__p_Co55 = rate

@numba.njit()
def n_Al25__Al26(rate_eval, tf):
    # Al25 + n --> Al26
    rate = 0.0

    # ths8r
    rate += np.exp(  7.92587 + 1.17141*tf.T913
                  + -0.162515*tf.T9 + 0.0126275*tf.T953)

    rate_eval.n_Al25__Al26 = rate

@numba.njit()
def p_Ca61__Sc62(rate_eval, tf):
    # Ca61 + p --> Sc62
    rate = 0.0

    # rath 
    rate += np.exp(  102.513 + -5.80507*tf.T9i + 211.367*tf.T913i + -331.918*tf.T913
                  + 17.8601*tf.T9 + -0.980418*tf.T953 + 168.809*tf.lnT9)

    rate_eval.p_Ca61__Sc62 = rate

@numba.njit()
def n_Fe52__He4_Cr49(rate_eval, tf):
    # Fe52 + n --> He4 + Cr49
    rate = 0.0

    # ths8r
    rate += np.exp(  -11.1596 + 14.3781*tf.T913
                  + 0.0859569*tf.T9 + -0.0900604*tf.T953)

    rate_eval.n_Fe52__He4_Cr49 = rate

@numba.njit()
def Mn58__Fe58__weak__wc12(rate_eval, tf):
    # Mn58 --> Fe58
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.46512)

    rate_eval.Mn58__Fe58__weak__wc12 = rate

@numba.njit()
def n_Fe51__He4_Cr48(rate_eval, tf):
    # Fe51 + n --> He4 + Cr48
    rate = 0.0

    # ths8r
    rate += np.exp(  13.9918 + 2.70632*tf.T913
                  + -0.705789*tf.T9 + 0.0921714*tf.T953)

    rate_eval.n_Fe51__He4_Cr48 = rate

@numba.njit()
def He4_Cr66__Fe70(rate_eval, tf):
    # Cr66 + He4 --> Fe70
    rate = 0.0

    # rath 
    rate += np.exp(  -1147.39 + 23.7928*tf.T9i + -2364.09*tf.T913i + 3646.1*tf.T913
                  + -206.265*tf.T9 + 11.3488*tf.T953 + -1769.53*tf.lnT9)

    rate_eval.He4_Cr66__Fe70 = rate

@numba.njit()
def n_Fe50__He4_Cr47(rate_eval, tf):
    # Fe50 + n --> He4 + Cr47
    rate = 0.0

    # ths8r
    rate += np.exp(  10.6338 + 2.18154*tf.T913
                  + 0.0570322*tf.T9 + 0.00399649*tf.T953)

    rate_eval.n_Fe50__He4_Cr47 = rate

@numba.njit()
def He4_Fe49__p_Co52(rate_eval, tf):
    # Fe49 + He4 --> p + Co52
    rate = 0.0

    # ths8r
    rate += np.exp(  62.8817 + -91.5495*tf.T913i + -1.49042*tf.T913
                  + -0.460075*tf.T9 + 0.0090969*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe49__p_Co52 = rate

@numba.njit()
def n_Fe49__He4_Cr46(rate_eval, tf):
    # Fe49 + n --> He4 + Cr46
    rate = 0.0

    # ths8r
    rate += np.exp(  11.2463 + 7.06445*tf.T913
                  + -2.56841*tf.T9 + 0.304677*tf.T953)

    rate_eval.n_Fe49__He4_Cr46 = rate

@numba.njit()
def n_Fe49__p_Mn49(rate_eval, tf):
    # Fe49 + n --> p + Mn49
    rate = 0.0

    # ths8r
    rate += np.exp(  21.9022 + -1.04539*tf.T913
                  + 0.279661*tf.T9 + -0.0257187*tf.T953)

    rate_eval.n_Fe49__p_Mn49 = rate

@numba.njit()
def He4_Fe48__p_Co51(rate_eval, tf):
    # Fe48 + He4 --> p + Co51
    rate = 0.0

    # ths8r
    rate += np.exp(  62.4878 + -91.5018*tf.T913i + -1.34844*tf.T913
                  + -0.443194*tf.T9 + 0.00570378*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe48__p_Co51 = rate

@numba.njit()
def p_Sc50__Ti51(rate_eval, tf):
    # Sc50 + p --> Ti51
    rate = 0.0

    # rath 
    rate += np.exp(  116.516 + -5.59095*tf.T9i + 208.759*tf.T913i + -343.038*tf.T913
                  + 19.191*tf.T9 + -1.09756*tf.T953 + 171.101*tf.lnT9)

    rate_eval.p_Sc50__Ti51 = rate

@numba.njit()
def n_Fe47__He4_Cr44(rate_eval, tf):
    # Fe47 + n --> He4 + Cr44
    rate = 0.0

    # ths8r
    rate += np.exp(  14.7023 + -0.950512*tf.T913
                  + 0.258138*tf.T9 + 0.00640087*tf.T953)

    rate_eval.n_Fe47__He4_Cr44 = rate

@numba.njit()
def Al37__Si37__weak__wc17(rate_eval, tf):
    # Al37 --> Si37
    rate = 0.0

    # wc17w
    rate += np.exp(  4.07669)

    rate_eval.Al37__Si37__weak__wc17 = rate

@numba.njit()
def n_Fe46__He4_Cr43(rate_eval, tf):
    # Fe46 + n --> He4 + Cr43
    rate = 0.0

    # ths8r
    rate += np.exp(  15.1479 + -0.891531*tf.T913
                  + 0.157287*tf.T9 + 0.0221599*tf.T953)

    rate_eval.n_Fe46__He4_Cr43 = rate

@numba.njit()
def n_Fe46__p_Mn46(rate_eval, tf):
    # Fe46 + n --> p + Mn46
    rate = 0.0

    # ths8r
    rate += np.exp(  21.7502 + -0.922836*tf.T913
                  + 0.251022*tf.T9 + -0.0225837*tf.T953)

    rate_eval.n_Fe46__p_Mn46 = rate

@numba.njit()
def He4_Mn73__n_Co76(rate_eval, tf):
    # Mn73 + He4 --> n + Co76
    rate = 0.0

    # rath 
    rate += np.exp(  -1236.56 + 25.7552*tf.T9i + -2555.45*tf.T913i + 3950.57*tf.T913
                  + -223.893*tf.T9 + 12.3882*tf.T953 + -1916.65*tf.lnT9)

    rate_eval.He4_Mn73__n_Co76 = rate

@numba.njit()
def p_Mn73__He4_Cr70(rate_eval, tf):
    # Mn73 + p --> He4 + Cr70
    rate = 0.0

    # rath 
    rate += np.exp(  140.589 + -7.53238*tf.T9i + 294.043*tf.T913i + -469.414*tf.T913
                  + 25.9261*tf.T9 + -1.36117*tf.T953 + 235.982*tf.lnT9)

    rate_eval.p_Mn73__He4_Cr70 = rate

@numba.njit()
def p_Mg34__Al35(rate_eval, tf):
    # Mg34 + p --> Al35
    rate = 0.0

    # rath 
    rate += np.exp(  67.1527 + -3.18341*tf.T9i + 112.857*tf.T913i + -187.377*tf.T913
                  + 10.0708*tf.T9 + -0.550368*tf.T953 + 94.4743*tf.lnT9)

    rate_eval.p_Mg34__Al35 = rate

@numba.njit()
def He4_Mn72__n_Co75(rate_eval, tf):
    # Mn72 + He4 --> n + Co75
    rate = 0.0

    # rath 
    rate += np.exp(  -1228.97 + 25.6201*tf.T9i + -2541.97*tf.T913i + 3928.53*tf.T913
                  + -222.582*tf.T9 + 12.3135*tf.T953 + -1906.22*tf.lnT9)

    rate_eval.He4_Mn72__n_Co75 = rate

@numba.njit()
def p_Mn72__He4_Cr69(rate_eval, tf):
    # Mn72 + p --> He4 + Cr69
    rate = 0.0

    # rath 
    rate += np.exp(  129.484 + -7.43163*tf.T9i + 285.907*tf.T913i + -448.415*tf.T913
                  + 24.456*tf.T9 + -1.2893*tf.T953 + 228.164*tf.lnT9)

    rate_eval.p_Mn72__He4_Cr69 = rate

@numba.njit()
def p_Mn71__He4_Cr68(rate_eval, tf):
    # Mn71 + p --> He4 + Cr68
    rate = 0.0

    # rath 
    rate += np.exp(  146.663 + -7.49513*tf.T9i + 295.68*tf.T913i + -477.221*tf.T913
                  + 26.6555*tf.T9 + -1.40986*tf.T953 + 238.526*tf.lnT9)

    rate_eval.p_Mn71__He4_Cr68 = rate

@numba.njit()
def Ca56__n_n_n_Sc53__weak__mo03(rate_eval, tf):
    # Ca56 --> 3 n + Sc53
    rate = 0.0

    # mo03w
    rate += np.exp(  -4.0205)

    rate_eval.Ca56__n_n_n_Sc53__weak__mo03 = rate

@numba.njit()
def He4_Mn69__n_Co72(rate_eval, tf):
    # Mn69 + He4 --> n + Co72
    rate = 0.0

    # rath 
    rate += np.exp(  -1203.89 + 25.0773*tf.T9i + -2489.93*tf.T913i + 3847.39*tf.T913
                  + -218.108*tf.T9 + 12.0692*tf.T953 + -1866.22*tf.lnT9)

    rate_eval.He4_Mn69__n_Co72 = rate

@numba.njit()
def p_Mn69__He4_Cr66(rate_eval, tf):
    # Mn69 + p --> He4 + Cr66
    rate = 0.0

    # rath 
    rate += np.exp(  165.18 + -7.54471*tf.T9i + 306.514*tf.T913i + -508.077*tf.T913
                  + 29.1009*tf.T9 + -1.56482*tf.T953 + 250.023*tf.lnT9)

    rate_eval.p_Mn69__He4_Cr66 = rate

@numba.njit()
def He4_Mn68__n_Co71(rate_eval, tf):
    # Mn68 + He4 --> n + Co71
    rate = 0.0

    # rath 
    rate += np.exp(  -1192.35 + 24.9696*tf.T9i + -2477.55*tf.T913i + 3822.3*tf.T913
                  + -216.342*tf.T9 + 11.9589*tf.T953 + -1855.69*tf.lnT9)

    rate_eval.He4_Mn68__n_Co71 = rate

@numba.njit()
def p_Mn68__n_Fe68(rate_eval, tf):
    # Mn68 + p --> n + Fe68
    rate = 0.0

    # rath 
    rate += np.exp(  155.902 + -7.22416*tf.T9i + 276.498*tf.T913i + -446.982*tf.T913
                  + 24.7466*tf.T9 + -1.38274*tf.T953 + 222.848*tf.lnT9)

    rate_eval.p_Mn68__n_Fe68 = rate

@numba.njit()
def He4_Si33__n_S36(rate_eval, tf):
    # Si33 + He4 --> n + S36
    rate = 0.0

    # rath 
    rate += np.exp(  -7.14215 + -2.85375*tf.T9i + -21.0117*tf.T913i + 24.4946*tf.T913
                  + -4.89433*tf.T9 + 0.383037*tf.T953 + 4.78192*tf.lnT9)

    rate_eval.He4_Si33__n_S36 = rate

@numba.njit()
def p_Mn67__He4_Cr64(rate_eval, tf):
    # Mn67 + p --> He4 + Cr64
    rate = 0.0

    # rath 
    rate += np.exp(  150.619 + -7.37289*tf.T9i + 293.274*tf.T913i + -475.461*tf.T913
                  + 25.8926*tf.T9 + -1.30638*tf.T953 + 237.468*tf.lnT9)

    rate_eval.p_Mn67__He4_Cr64 = rate

@numba.njit()
def p_Mn66__He4_Cr63(rate_eval, tf):
    # Mn66 + p --> He4 + Cr63
    rate = 0.0

    # rath 
    rate += np.exp(  108.089 + -6.88064*tf.T9i + 247.251*tf.T913i + -379.638*tf.T913
                  + 20.3335*tf.T9 + -1.07138*tf.T953 + 195.997*tf.lnT9)

    rate_eval.p_Mn66__He4_Cr63 = rate

@numba.njit()
def p_Mn66__n_Fe66(rate_eval, tf):
    # Mn66 + p --> n + Fe66
    rate = 0.0

    # rath 
    rate += np.exp(  138.455 + -6.90587*tf.T9i + 251.03*tf.T913i + -401.61*tf.T913
                  + 22.211*tf.T9 + -1.24722*tf.T953 + 201.382*tf.lnT9)

    rate_eval.p_Mn66__n_Fe66 = rate

@numba.njit()
def p_K48__Ca49(rate_eval, tf):
    # K48 + p --> Ca49
    rate = 0.0

    # rath 
    rate += np.exp(  99.8981 + -5.10058*tf.T9i + 187.269*tf.T913i + -302.167*tf.T913
                  + 16.1113*tf.T9 + -0.833227*tf.T953 + 152.839*tf.lnT9)

    rate_eval.p_K48__Ca49 = rate

@numba.njit()
def p_P46__S47(rate_eval, tf):
    # P46 + p --> S47
    rate = 0.0

    # rath 
    rate += np.exp(  92.554 + -4.28619*tf.T9i + 159.147*tf.T913i + -264.029*tf.T913
                  + 14.4613*tf.T9 + -0.795835*tf.T953 + 131.525*tf.lnT9)

    rate_eval.p_P46__S47 = rate

@numba.njit()
def He4_Ca52__Ti56(rate_eval, tf):
    # Ca52 + He4 --> Ti56
    rate = 0.0

    # rath 
    rate += np.exp(  -942.635 + 14.9961*tf.T9i + -1629.11*tf.T913i + 2674.78*tf.T913
                  + -159.656*tf.T9 + 9.12532*tf.T953 + -1255.04*tf.lnT9)

    rate_eval.He4_Ca52__Ti56 = rate

@numba.njit()
def He4_Mn65__n_Co68(rate_eval, tf):
    # Mn65 + He4 --> n + Co68
    rate = 0.0

    # rath 
    rate += np.exp(  -1164.43 + 24.4023*tf.T9i + -2423.02*tf.T913i + 3735.81*tf.T913
                  + -211.505*tf.T9 + 11.6929*tf.T953 + -1813.52*tf.lnT9)

    rate_eval.He4_Mn65__n_Co68 = rate

@numba.njit()
def p_Mn65__He4_Cr62(rate_eval, tf):
    # Mn65 + p --> He4 + Cr62
    rate = 0.0

    # rath 
    rate += np.exp(  123.182 + -7.05068*tf.T9i + 266.128*tf.T913i + -414.92*tf.T913
                  + 21.8582*tf.T9 + -1.11278*tf.T953 + 212.697*tf.lnT9)

    rate_eval.p_Mn65__He4_Cr62 = rate

@numba.njit()
def p_Si44__n_P44(rate_eval, tf):
    # Si44 + p --> n + P44
    rate = 0.0

    # rath 
    rate += np.exp(  94.6444 + -4.01103*tf.T9i + 147.445*tf.T913i + -242.151*tf.T913
                  + 13.2161*tf.T9 + -0.733916*tf.T953 + 121.438*tf.lnT9)

    rate_eval.p_Si44__n_P44 = rate

@numba.njit()
def He4_Mn68__Co72(rate_eval, tf):
    # Mn68 + He4 --> Co72
    rate = 0.0

    # rath 
    rate += np.exp(  -1200.13 + 24.9433*tf.T9i + -2475.26*tf.T913i + 3817.73*tf.T913
                  + -215.963*tf.T9 + 11.9117*tf.T953 + -1853.74*tf.lnT9)

    rate_eval.He4_Mn68__Co72 = rate

@numba.njit()
def p_Mn64__He4_Cr61(rate_eval, tf):
    # Mn64 + p --> He4 + Cr61
    rate = 0.0

    # rath 
    rate += np.exp(  127.299 + -6.98069*tf.T9i + 263.187*tf.T913i + -416.12*tf.T913
                  + 22.5475*tf.T9 + -1.19187*tf.T953 + 211.54*tf.lnT9)

    rate_eval.p_Mn64__He4_Cr61 = rate

@numba.njit()
def p_Mn62__He4_Cr59(rate_eval, tf):
    # Mn62 + p --> He4 + Cr59
    rate = 0.0

    # rath 
    rate += np.exp(  113.448 + -6.88744*tf.T9i + 257.744*tf.T913i + -395.57*tf.T913
                  + 20.6726*tf.T9 + -1.06926*tf.T953 + 205.517*tf.lnT9)

    rate_eval.p_Mn62__He4_Cr59 = rate

@numba.njit()
def He4_Mn60__n_Co63(rate_eval, tf):
    # Mn60 + He4 --> n + Co63
    rate = 0.0

    # rath 
    rate += np.exp(  -1114.99 + 23.3754*tf.T9i + -2324.6*tf.T913i + 3580.14*tf.T913
                  + -202.83*tf.T9 + 11.2172*tf.T953 + -1737.33*tf.lnT9)

    rate_eval.He4_Mn60__n_Co63 = rate

@numba.njit()
def p_Mn60__He4_Cr57(rate_eval, tf):
    # Mn60 + p --> He4 + Cr57
    rate = 0.0

    # rath 
    rate += np.exp(  96.175 + -6.69031*tf.T9i + 242.315*tf.T913i + -358.25*tf.T913
                  + 17.3082*tf.T9 + -0.77883*tf.T953 + 190.96*tf.lnT9)

    rate_eval.p_Mn60__He4_Cr57 = rate

@numba.njit()
def p_Mn60__n_Fe60(rate_eval, tf):
    # Mn60 + p --> n + Fe60
    rate = 0.0

    # rath 
    rate += np.exp(  138.738 + -6.78821*tf.T9i + 254.173*tf.T913i + -405.828*tf.T913
                  + 22.0704*tf.T9 + -1.23139*tf.T953 + 204.9*tf.lnT9)

    rate_eval.p_Mn60__n_Fe60 = rate

@numba.njit()
def He4_Fe65__Ni69(rate_eval, tf):
    # Fe65 + He4 --> Ni69
    rate = 0.0

    # rath 
    rate += np.exp(  -974.922 + 24.8608*tf.T9i + -2402.09*tf.T913i + 3493.94*tf.T913
                  + -189.396*tf.T9 + 10.1116*tf.T953 + -1742.53*tf.lnT9)

    rate_eval.He4_Fe65__Ni69 = rate

@numba.njit()
def p_Mn59__He4_Cr56(rate_eval, tf):
    # Mn59 + p --> He4 + Cr56
    rate = 0.0

    # rath 
    rate += np.exp(  107.84 + -6.67809*tf.T9i + 244.922*tf.T913i + -372.516*tf.T913
                  + 18.8733*tf.T9 + -0.958194*tf.T953 + 194.879*tf.lnT9)

    rate_eval.p_Mn59__He4_Cr56 = rate

@numba.njit()
def p_Mn57__n_Fe57(rate_eval, tf):
    # Mn57 + p --> n + Fe57
    rate = 0.0

    # rath 
    rate += np.exp(  134.717 + -6.61769*tf.T9i + 245.956*tf.T913i + -393.919*tf.T913
                  + 21.6464*tf.T9 + -1.22314*tf.T953 + 198.818*tf.lnT9)

    rate_eval.p_Mn57__n_Fe57 = rate

@numba.njit()
def p_Fe64__He4_Mn61(rate_eval, tf):
    # Fe64 + p --> He4 + Mn61
    rate = 0.0

    # rath 
    rate += np.exp(  -7.11368 + -6.02982*tf.T9i + 147.907*tf.T913i + -164.057*tf.T913
                  + 5.27678*tf.T9 + -0.208568*tf.T953 + 112.692*tf.lnT9)

    rate_eval.p_Fe64__He4_Mn61 = rate

@numba.njit()
def p_Mn56__He4_Cr53(rate_eval, tf):
    # Mn56 + p --> He4 + Cr53
    rate = 0.0

    # rath 
    rate += np.exp(  64.0275 + -6.32885*tf.T9i + 217.009*tf.T913i + -298.559*tf.T913
                  + 13.5402*tf.T9 + -0.639577*tf.T953 + 167.958*tf.lnT9)

    rate_eval.p_Mn56__He4_Cr53 = rate

@numba.njit()
def p_Mn54__He4_Cr51(rate_eval, tf):
    # Mn54 + p --> He4 + Cr51
    rate = 0.0

    # ths8r
    rate += np.exp(  -40.6329 + -36.1955*tf.T913i + 69.5086*tf.T913
                  + -14.1484*tf.T9 + 1.38598*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn54__He4_Cr51 = rate

@numba.njit()
def S49__n_n_n_Cl46__weak__mo03(rate_eval, tf):
    # S49 --> 3 n + Cl46
    rate = 0.0

    # mo03w
    rate += np.exp(  2.869)

    rate_eval.S49__n_n_n_Cl46__weak__mo03 = rate

@numba.njit()
def He4_Mn53__p_Fe56(rate_eval, tf):
    # Mn53 + He4 --> p + Fe56
    rate = 0.0

    # ths8r
    rate += np.exp(  54.0176 + -89.3558*tf.T913i + 9.25287*tf.T913
                  + -3.70352*tf.T9 + 0.372202*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn53__p_Fe56 = rate

@numba.njit()
def p_Mn53__He4_Cr50(rate_eval, tf):
    # Mn53 + p --> He4 + Cr50
    rate = 0.0

    # ths8r
    rate += np.exp(  -68.3424 + -36.1913*tf.T913i + 99.0857*tf.T913
                  + -20.8943*tf.T9 + 2.06209*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn53__He4_Cr50 = rate

@numba.njit()
def n_Mn52__He4_V49(rate_eval, tf):
    # Mn52 + n --> He4 + V49
    rate = 0.0

    # ths8r
    rate += np.exp(  -2.29492 + 5.72895*tf.T913
                  + 1.74506*tf.T9 + -0.232362*tf.T953)

    rate_eval.n_Mn52__He4_V49 = rate

@numba.njit()
def Ar48__n_K47__weak__mp17(rate_eval, tf):
    # Ar48 --> n + K47
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.671895)

    rate_eval.Ar48__n_K47__weak__mp17 = rate

@numba.njit()
def n_Mn52__p_Cr52(rate_eval, tf):
    # Mn52 + n --> p + Cr52
    rate = 0.0

    # ths8r
    rate += np.exp(  17.9487 + 0.50599*tf.T913
                  + 0.283832*tf.T9 + -0.0422814*tf.T953)

    rate_eval.n_Mn52__p_Cr52 = rate

@numba.njit()
def He4_Mn51__p_Fe54(rate_eval, tf):
    # Mn51 + He4 --> p + Fe54
    rate = 0.0

    # ths8r
    rate += np.exp(  62.2777 + -89.274*tf.T913i + -0.862452*tf.T913
                  + -0.635672*tf.T9 + 0.0196464*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn51__p_Fe54 = rate

@numba.njit()
def p_Ca53__n_Sc53(rate_eval, tf):
    # Ca53 + p --> n + Sc53
    rate = 0.0

    # rath 
    rate += np.exp(  118.262 + -5.52673*tf.T9i + 205.013*tf.T913i + -331.19*tf.T913
                  + 18.2023*tf.T9 + -1.02201*tf.T953 + 166.644*tf.lnT9)

    rate_eval.p_Ca53__n_Sc53 = rate

@numba.njit()
def n_Mn51__p_Cr51(rate_eval, tf):
    # Mn51 + n --> p + Cr51
    rate = 0.0

    # ths8r
    rate += np.exp(  20.982 + -1.37768*tf.T913
                  + 0.466991*tf.T9 + -0.0461074*tf.T953)

    rate_eval.n_Mn51__p_Cr51 = rate

@numba.njit()
def p_O22__n_F22(rate_eval, tf):
    # O22 + p --> n + F22
    rate = 0.0

    # rpsmr
    rate += np.exp(  57.5626 + -1.95273*tf.T9i + 65.7674*tf.T913i + -115.133*tf.T913
                  + 6.29937*tf.T9 + -0.351353*tf.T953 + 57.6081*tf.lnT9)

    rate_eval.p_O22__n_F22 = rate

@numba.njit()
def n_Mn50__He4_V47(rate_eval, tf):
    # Mn50 + n --> He4 + V47
    rate = 0.0

    # ths8r
    rate += np.exp(  12.7581 + 0.0723126*tf.T913
                  + 0.772457*tf.T9 + -0.0591176*tf.T953)

    rate_eval.n_Mn50__He4_V47 = rate

@numba.njit()
def He4_Mn49__p_Fe52(rate_eval, tf):
    # Mn49 + He4 --> p + Fe52
    rate = 0.0

    # ths8r
    rate += np.exp(  62.437 + -89.1861*tf.T913i + -1.31711*tf.T913
                  + -0.507338*tf.T9 + 0.0108137*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn49__p_Fe52 = rate

@numba.njit()
def n_Cl37__Cl38(rate_eval, tf):
    # Cl37 + n --> Cl38
    rate = 0.0

    # ks03 
    rate += np.exp(  30.0579 + -0.0331935*tf.T9i + 5.04212*tf.T913i + -25.9267*tf.T913
                  + 3.22991*tf.T9 + -0.274968*tf.T953 + 6.92921*tf.lnT9)

    rate_eval.n_Cl37__Cl38 = rate

@numba.njit()
def n_Mn48__He4_V45(rate_eval, tf):
    # Mn48 + n --> He4 + V45
    rate = 0.0

    # ths8r
    rate += np.exp(  14.3171 + 2.32856*tf.T913
                  + -0.789334*tf.T9 + 0.110052*tf.T953)

    rate_eval.n_Mn48__He4_V45 = rate

@numba.njit()
def He4_Mn47__p_Fe50(rate_eval, tf):
    # Mn47 + He4 --> p + Fe50
    rate = 0.0

    # ths8r
    rate += np.exp(  61.593 + -89.0914*tf.T913i + -1.32264*tf.T913
                  + -0.430879*tf.T9 + 0.00385075*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn47__p_Fe50 = rate

@numba.njit()
def n_Ne20__Ne21(rate_eval, tf):
    # Ne20 + n --> Ne21
    rate = 0.0

    # ka02r
    rate += np.exp(  12.7344 + -1.70393*tf.T9i
                  + -1.5*tf.lnT9)
    # ka02n
    rate += np.exp(  8.57651)

    rate_eval.n_Ne20__Ne21 = rate

@numba.njit()
def n_Mn47__p_Cr47(rate_eval, tf):
    # Mn47 + n --> p + Cr47
    rate = 0.0

    # ths8r
    rate += np.exp(  22.0927 + -1.38963*tf.T913
                  + 0.380929*tf.T9 + -0.036173*tf.T953)

    rate_eval.n_Mn47__p_Cr47 = rate

@numba.njit()
def He4_Mn46__p_Fe49(rate_eval, tf):
    # Mn46 + He4 --> p + Fe49
    rate = 0.0

    # ths8r
    rate += np.exp(  61.9247 + -89.0414*tf.T913i + -1.53993*tf.T913
                  + -0.452496*tf.T9 + 0.010938*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn46__p_Fe49 = rate

@numba.njit()
def p_Ca44__Sc45(rate_eval, tf):
    # Ca44 + p --> Sc45
    rate = 0.0

    # ths8r
    rate += np.exp(  35.0037 + -31.1491*tf.T913i + 0.402181*tf.T913
                  + -1.30287*tf.T9 + 0.135535*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ca44__Sc45 = rate

@numba.njit()
def n_Mn46__He4_V43(rate_eval, tf):
    # Mn46 + n --> He4 + V43
    rate = 0.0

    # ths8r
    rate += np.exp(  16.567 + -1.0356*tf.T913
                  + 0.296535*tf.T9 + -0.0101152*tf.T953)

    rate_eval.n_Mn46__He4_V43 = rate

@numba.njit()
def n_Mn46__p_Cr46(rate_eval, tf):
    # Mn46 + n --> p + Cr46
    rate = 0.0

    # ths8r
    rate += np.exp(  21.8309 + -0.983674*tf.T913
                  + 0.251607*tf.T9 + -0.0217666*tf.T953)

    rate_eval.n_Mn46__p_Cr46 = rate

@numba.njit()
def n_Mn45__p_Cr45(rate_eval, tf):
    # Mn45 + n --> p + Cr45
    rate = 0.0

    # ths8r
    rate += np.exp(  21.7309 + -0.999122*tf.T913
                  + 0.281323*tf.T9 + -0.0252854*tf.T953)

    rate_eval.n_Mn45__p_Cr45 = rate

@numba.njit()
def He4_Mn44__p_Fe47(rate_eval, tf):
    # Mn44 + He4 --> p + Fe47
    rate = 0.0

    # ths8r
    rate += np.exp(  63.3625 + -88.9347*tf.T913i + -2.86881*tf.T913
                  + -0.327748*tf.T9 + 0.012567*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn44__p_Fe47 = rate

@numba.njit()
def He4_Cr70__n_Fe73(rate_eval, tf):
    # Cr70 + He4 --> n + Fe73
    rate = 0.0

    # rath 
    rate += np.exp(  -1231.37 + 19.483*tf.T9i + -2113.1*tf.T913i + 3495.37*tf.T913
                  + -208.966*tf.T9 + 12.0034*tf.T953 + -1638.74*tf.lnT9)

    rate_eval.He4_Cr70__n_Fe73 = rate

@numba.njit()
def n_F26__F27(rate_eval, tf):
    # F26 + n --> F27
    rate = 0.0

    # rpsmr
    rate += np.exp(  8.89778 + -0.0335857*tf.T9i + 2.38036*tf.T913i + -6.31021*tf.T913
                  + 0.756594*tf.T9 + -0.0493664*tf.T953 + 1.91014*tf.lnT9)

    rate_eval.n_F26__F27 = rate

@numba.njit()
def He4_Cr69__n_Fe72(rate_eval, tf):
    # Cr69 + He4 --> n + Fe72
    rate = 0.0

    # rath 
    rate += np.exp(  -1222.25 + 19.3535*tf.T9i + -2099.16*tf.T913i + 3470.99*tf.T913
                  + -207.475*tf.T9 + 11.9152*tf.T953 + -1627.41*tf.lnT9)

    rate_eval.He4_Cr69__n_Fe72 = rate

@numba.njit()
def p_Cr68__He4_V65(rate_eval, tf):
    # Cr68 + p --> He4 + V65
    rate = 0.0

    # rath 
    rate += np.exp(  -742.032 + 10.8828*tf.T9i + -1214.07*tf.T913i + 2028.63*tf.T913
                  + -121.064*tf.T9 + 6.95196*tf.T953 + -942.965*tf.lnT9)

    rate_eval.p_Cr68__He4_V65 = rate

@numba.njit()
def p_Cr68__n_Mn68(rate_eval, tf):
    # Cr68 + p --> n + Mn68
    rate = 0.0

    # rath 
    rate += np.exp(  150.018 + -7.01848*tf.T9i + 267.584*tf.T913i + -431.195*tf.T913
                  + 23.9161*tf.T9 + -1.34311*tf.T953 + 215.295*tf.lnT9)

    rate_eval.p_Cr68__n_Mn68 = rate

@numba.njit()
def p_Cr67__n_Mn67(rate_eval, tf):
    # Cr67 + p --> n + Mn67
    rate = 0.0

    # rath 
    rate += np.exp(  147.547 + -6.96693*tf.T9i + 264.889*tf.T913i + -425.592*tf.T913
                  + 23.4279*tf.T9 + -1.30686*tf.T953 + 213.046*tf.lnT9)

    rate_eval.p_Cr67__n_Mn67 = rate

@numba.njit()
def He4_Cr66__n_Fe69(rate_eval, tf):
    # Cr66 + He4 --> n + Fe69
    rate = 0.0

    # rath 
    rate += np.exp(  -1194.5 + 18.9516*tf.T9i + -2056.05*tf.T913i + 3395.75*tf.T913
                  + -202.875*tf.T9 + 11.645*tf.T953 + -1592.38*tf.lnT9)

    rate_eval.He4_Cr66__n_Fe69 = rate

@numba.njit()
def p_Cr66__He4_V63(rate_eval, tf):
    # Cr66 + p --> He4 + V63
    rate = 0.0

    # rath 
    rate += np.exp(  17.7385 + -6.02505*tf.T9i + 160.926*tf.T913i + -204.684*tf.T913
                  + 8.72083*tf.T9 + -0.372341*tf.T953 + 124.309*tf.lnT9)

    rate_eval.p_Cr66__He4_V63 = rate

@numba.njit()
def He4_Cr65__n_Fe68(rate_eval, tf):
    # Cr65 + He4 --> n + Fe68
    rate = 0.0

    # rath 
    rate += np.exp(  -1185.32 + 18.8731*tf.T9i + -2045.7*tf.T913i + 3374.76*tf.T913
                  + -201.36*tf.T9 + 11.5459*tf.T953 + -1583.42*tf.lnT9)

    rate_eval.He4_Cr65__n_Fe68 = rate

@numba.njit()
def p_Cr65__He4_V62(rate_eval, tf):
    # Cr65 + p --> He4 + V62
    rate = 0.0

    # rath 
    rate += np.exp(  82.9718 + -6.84858*tf.T9i + 256.905*tf.T913i + -372.259*tf.T913
                  + 19.0256*tf.T9 + -1.02571*tf.T953 + 201.921*tf.lnT9)

    rate_eval.p_Cr65__He4_V62 = rate

@numba.njit()
def p_Mn72__n_Fe72(rate_eval, tf):
    # Mn72 + p --> n + Fe72
    rate = 0.0

    # rath 
    rate += np.exp(  156.036 + -7.39199*tf.T9i + 282.579*tf.T913i + -453.639*tf.T913
                  + 25.139*tf.T9 + -1.40864*tf.T953 + 226.635*tf.lnT9)

    rate_eval.p_Mn72__n_Fe72 = rate

@numba.njit()
def He4_Cr64__n_Fe67(rate_eval, tf):
    # Cr64 + He4 --> n + Fe67
    rate = 0.0

    # rath 
    rate += np.exp(  -1174.06 + 18.658*tf.T9i + -2024.9*tf.T913i + 3341.1*tf.T913
                  + -199.535*tf.T9 + 11.4497*tf.T953 + -1567.01*tf.lnT9)

    rate_eval.He4_Cr64__n_Fe67 = rate

@numba.njit()
def p_O25__n_F25(rate_eval, tf):
    # O25 + p --> n + F25
    rate = 0.0

    # rpsmr
    rate += np.exp(  60.0843 + -2.11782*tf.T9i + 73.9791*tf.T913i + -125.775*tf.T913
                  + 6.71755*tf.T9 + -0.366672*tf.T953 + 63.4126*tf.lnT9)

    rate_eval.p_O25__n_F25 = rate

@numba.njit()
def He4_Cr63__n_Fe66(rate_eval, tf):
    # Cr63 + He4 --> n + Fe66
    rate = 0.0

    # rath 
    rate += np.exp(  -1162.81 + 18.6501*tf.T9i + -2019.87*tf.T913i + 3324.84*tf.T913
                  + -198.209*tf.T9 + 11.3634*tf.T953 + -1561.59*tf.lnT9)

    rate_eval.He4_Cr63__n_Fe66 = rate

@numba.njit()
def p_Cr63__n_Mn63(rate_eval, tf):
    # Cr63 + p --> n + Mn63
    rate = 0.0

    # rath 
    rate += np.exp(  148.522 + -6.78926*tf.T9i + 258.487*tf.T913i + -419.776*tf.T913
                  + 23.174*tf.T9 + -1.29292*tf.T953 + 209.31*tf.lnT9)

    rate_eval.p_Cr63__n_Mn63 = rate

@numba.njit()
def He4_Cr62__n_Fe65(rate_eval, tf):
    # Cr62 + He4 --> n + Fe65
    rate = 0.0

    # rath 
    rate += np.exp(  -1161.11 + 18.4499*tf.T9i + -2001.78*tf.T913i + 3303.95*tf.T913
                  + -197.563*tf.T9 + 11.3465*tf.T953 + -1548.9*tf.lnT9)

    rate_eval.He4_Cr62__n_Fe65 = rate

@numba.njit()
def p_Cr62__He4_V59(rate_eval, tf):
    # Cr62 + p --> He4 + V59
    rate = 0.0

    # rath 
    rate += np.exp(  -51.9502 + -5.29217*tf.T9i + 100.397*tf.T913i + -62.6975*tf.T913
                  + -2.92178*tf.T9 + 0.435787*tf.T953 + 68.9004*tf.lnT9)

    rate_eval.p_Cr62__He4_V59 = rate

@numba.njit()
def N21__O21__weak__wc12(rate_eval, tf):
    # N21 --> O21
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.231477)

    rate_eval.N21__O21__weak__wc12 = rate

@numba.njit()
def He4_Mn48__Co52(rate_eval, tf):
    # Mn48 + He4 --> Co52
    rate = 0.0

    # ths8r
    rate += np.exp(  49.9642 + -89.1398*tf.T913i + 4.36566*tf.T913
                  + -2.1732*tf.T9 + 0.160209*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn48__Co52 = rate

@numba.njit()
def He4_Cr61__n_Fe64(rate_eval, tf):
    # Cr61 + He4 --> n + Fe64
    rate = 0.0

    # rath 
    rate += np.exp(  -1145.71 + 18.3143*tf.T9i + -1985.93*tf.T913i + 3270.95*tf.T913
                  + -195.291*tf.T9 + 11.2064*tf.T953 + -1534.97*tf.lnT9)

    rate_eval.He4_Cr61__n_Fe64 = rate

@numba.njit()
def p_Cr60__He4_V57(rate_eval, tf):
    # Cr60 + p --> He4 + V57
    rate = 0.0

    # rath 
    rate += np.exp(  118.793 + -6.85143*tf.T9i + 272.268*tf.T913i + -421.55*tf.T913
                  + 22.4813*tf.T9 + -1.21234*tf.T953 + 219.606*tf.lnT9)

    rate_eval.p_Cr60__He4_V57 = rate

@numba.njit()
def He4_Cr59__n_Fe62(rate_eval, tf):
    # Cr59 + He4 --> n + Fe62
    rate = 0.0

    # rath 
    rate += np.exp(  -1127.14 + 18.0239*tf.T9i + -1955.06*tf.T913i + 3218.39*tf.T913
                  + -192.156*tf.T9 + 11.0261*tf.T953 + -1510.15*tf.lnT9)

    rate_eval.He4_Cr59__n_Fe62 = rate

@numba.njit()
def n_Ca50__Ca51(rate_eval, tf):
    # Ca50 + n --> Ca51
    rate = 0.0

    # rath 
    rate += np.exp(  1.50354 + 0.0483998*tf.T9i + -5.79254*tf.T913i + 16.6033*tf.T913
                  + -1.53844*tf.T9 + 0.0986748*tf.T953 + -6.10404*tf.lnT9)

    rate_eval.n_Ca50__Ca51 = rate

@numba.njit()
def p_Cr59__n_Mn59(rate_eval, tf):
    # Cr59 + p --> n + Mn59
    rate = 0.0

    # rath 
    rate += np.exp(  134.344 + -6.54981*tf.T9i + 244.603*tf.T913i + -390.793*tf.T913
                  + 21.2575*tf.T9 + -1.1858*tf.T953 + 197.337*tf.lnT9)

    rate_eval.p_Cr59__n_Mn59 = rate

@numba.njit()
def p_Fe62__n_Co62(rate_eval, tf):
    # Fe62 + p --> n + Co62
    rate = 0.0

    # rath 
    rate += np.exp(  142.131 + -7.06833*tf.T9i + 264.85*tf.T913i + -421.016*tf.T913
                  + 22.8391*tf.T9 + -1.27057*tf.T953 + 212.889*tf.lnT9)

    rate_eval.p_Fe62__n_Co62 = rate

@numba.njit()
def n_O18__O19(rate_eval, tf):
    # O18 + n --> O19
    rate = 0.0

    # ks03 
    rate += np.exp(  -2.99721 + 0.0120002*tf.T9i + -2.77409*tf.T913i + 15.9457*tf.T913
                  + -1.62022*tf.T9 + 0.113592*tf.T953 + -3.26167*tf.lnT9)

    rate_eval.n_O18__O19 = rate

@numba.njit()
def p_Cr57__n_Mn57(rate_eval, tf):
    # Cr57 + p --> n + Mn57
    rate = 0.0

    # rath 
    rate += np.exp(  131.475 + -6.44172*tf.T9i + 239.421*tf.T913i + -382.812*tf.T913
                  + 20.911*tf.T9 + -1.17383*tf.T953 + 193.42*tf.lnT9)

    rate_eval.p_Cr57__n_Mn57 = rate

@numba.njit()
def Mg22__Na22__weak__wc12(rate_eval, tf):
    # Mg22 --> Na22
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.72235)

    rate_eval.Mg22__Na22__weak__wc12 = rate

@numba.njit()
def He4_Cr55__n_Fe58(rate_eval, tf):
    # Cr55 + He4 --> n + Fe58
    rate = 0.0

    # rath 
    rate += np.exp(  -1089.53 + 17.4221*tf.T9i + -1891.42*tf.T913i + 3111.38*tf.T913
                  + -185.891*tf.T9 + 10.6686*tf.T953 + -1459.23*tf.lnT9)

    rate_eval.He4_Cr55__n_Fe58 = rate

@numba.njit()
def Cr43__p_p_Sc41__weak__wc12(rate_eval, tf):
    # Cr43 --> p + p + Sc41
    rate = 0.0

    # wc12w
    rate += np.exp(  0.870876)

    rate_eval.Cr43__p_p_Sc41__weak__wc12 = rate

@numba.njit()
def n_Cr55__He4_Ti52(rate_eval, tf):
    # Cr55 + n --> He4 + Ti52
    rate = 0.0

    # rath 
    rate += np.exp(  -33.2778 + -16.7469*tf.T9i + 270.247*tf.T913i + -250.369*tf.T913
                  + 6.16556*tf.T9 + -0.113544*tf.T953 + 176.038*tf.lnT9)

    rate_eval.n_Cr55__He4_Ti52 = rate

@numba.njit()
def p_Cr54__He4_V51(rate_eval, tf):
    # Cr54 + p --> He4 + V51
    rate = 0.0

    # ths8r
    rate += np.exp(  -94.698 + -35.2237*tf.T913i + 131.726*tf.T913
                  + -29.7395*tf.T9 + 3.03809*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cr54__He4_V51 = rate

@numba.njit()
def p_Ne32__Na33(rate_eval, tf):
    # Ne32 + p --> Na33
    rate = 0.0

    # rath 
    rate += np.exp(  60.5308 + -2.74784*tf.T9i + 97.6532*tf.T913i + -164.334*tf.T913
                  + 8.9214*tf.T9 + -0.490449*tf.T953 + 82.3496*tf.lnT9)

    rate_eval.p_Ne32__Na33 = rate

@numba.njit()
def p_Mg24__He4_Na21(rate_eval, tf):
    # Mg24 + p --> He4 + Na21
    rate = 0.0

    # nacr 
    rate += np.exp(  42.3867 + -79.897*tf.T9i + -49.9621*tf.T913i + 5.90498*tf.T913
                  + -1.6598*tf.T9 + 0.117817*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mg24__He4_Na21 = rate

@numba.njit()
def p_Si38__n_P38(rate_eval, tf):
    # Si38 + p --> n + P38
    rate = 0.0

    # rath 
    rate += np.exp(  89.2838 + -3.73533*tf.T9i + 135.079*tf.T913i + -224.321*tf.T913
                  + 12.2609*tf.T9 + -0.681458*tf.T953 + 112.487*tf.lnT9)

    rate_eval.p_Si38__n_P38 = rate

@numba.njit()
def Mn54__Cr54__weak__wc12(rate_eval, tf):
    # Mn54 --> Cr54
    rate = 0.0

    # wc12w
    rate += np.exp(  -17.4779)

    rate_eval.Mn54__Cr54__weak__wc12 = rate

@numba.njit()
def p_Mn55__He4_Cr52(rate_eval, tf):
    # Mn55 + p --> He4 + Cr52
    rate = 0.0

    # ths8r
    rate += np.exp(  17.7897 + -36.1995*tf.T913i + 11.023*tf.T913
                  + -2.435*tf.T9 + 0.306933*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn55__He4_Cr52 = rate

@numba.njit()
def n_Cr51__He4_Ti48(rate_eval, tf):
    # Cr51 + n --> He4 + Ti48
    rate = 0.0

    # ths8r
    rate += np.exp(  -0.304828 + 1.94389*tf.T913
                  + 2.5871*tf.T9 + -0.307303*tf.T953)

    rate_eval.n_Cr51__He4_Ti48 = rate

@numba.njit()
def n_Cr50__He4_Ti47(rate_eval, tf):
    # Cr50 + n --> He4 + Ti47
    rate = 0.0

    # ths8r
    rate += np.exp(  -108.708 + 104.649*tf.T913
                  + -15.3856*tf.T9 + 1.13897*tf.T953)

    rate_eval.n_Cr50__He4_Ti47 = rate

@numba.njit()
def He4_Cr49__p_Mn52(rate_eval, tf):
    # Cr49 + He4 --> p + Mn52
    rate = 0.0

    # ths8r
    rate += np.exp(  52.5075 + -86.7913*tf.T913i + 10.6892*tf.T913
                  + -4.01586*tf.T9 + 0.411275*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr49__p_Mn52 = rate

@numba.njit()
def He4_Cr48__p_Mn51(rate_eval, tf):
    # Cr48 + He4 --> p + Mn51
    rate = 0.0

    # ths8r
    rate += np.exp(  59.2276 + -86.7459*tf.T913i + 1.05653*tf.T913
                  + -1.15757*tf.T9 + 0.0877546*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr48__p_Mn51 = rate

@numba.njit()
def n_Cr48__p_V48(rate_eval, tf):
    # Cr48 + n --> p + V48
    rate = 0.0

    # ths8r
    rate += np.exp(  16.9 + 0.783544*tf.T913
                  + 0.521131*tf.T9 + -0.0677724*tf.T953)

    rate_eval.n_Cr48__p_V48 = rate

@numba.njit()
def p_Ti57__He4_Sc54(rate_eval, tf):
    # Ti57 + p --> He4 + Sc54
    rate = 0.0

    # rath 
    rate += np.exp(  116.795 + -6.1124*tf.T9i + 229.394*tf.T913i + -365.189*tf.T913
                  + 19.8746*tf.T9 + -1.07643*tf.T953 + 185.34*tf.lnT9)

    rate_eval.p_Ti57__He4_Sc54 = rate

@numba.njit()
def n_Cr46__He4_Ti43(rate_eval, tf):
    # Cr46 + n --> He4 + Ti43
    rate = 0.0

    # ths8r
    rate += np.exp(  8.19581 + 6.9271*tf.T913
                  + -1.75348*tf.T9 + 0.251716*tf.T953)

    rate_eval.n_Cr46__He4_Ti43 = rate

@numba.njit()
def He4_Cr45__p_Mn48(rate_eval, tf):
    # Cr45 + He4 --> p + Mn48
    rate = 0.0

    # ths8r
    rate += np.exp(  60.8786 + -86.5991*tf.T913i + -1.44024*tf.T913
                  + -0.441577*tf.T9 + 0.00862524*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr45__p_Mn48 = rate

@numba.njit()
def n_B13__B14(rate_eval, tf):
    # B13 + n --> B14
    rate = 0.0

    # wiesr
    rate += np.exp(  3.90197
                  + 1.0*tf.lnT9)
    # wiesr
    rate += np.exp(  10.8077 + -4.76*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.n_B13__B14 = rate

@numba.njit()
def He4_Ne29__Mg33(rate_eval, tf):
    # Ne29 + He4 --> Mg33
    rate = 0.0

    # rath 
    rate += np.exp(  58.0319 + -2.84882*tf.T9i + 60.7286*tf.T913i + -135.727*tf.T913
                  + 6.14192*tf.T9 + -0.302454*tf.T953 + 71.8246*tf.lnT9)

    rate_eval.He4_Ne29__Mg33 = rate

@numba.njit()
def He4_Ti59__n_Cr62(rate_eval, tf):
    # Ti59 + He4 --> n + Cr62
    rate = 0.0

    # rath 
    rate += np.exp(  -1065.33 + 16.9949*tf.T9i + -1844.54*tf.T913i + 3040.22*tf.T913
                  + -181.775*tf.T9 + 10.4392*tf.T953 + -1425.53*tf.lnT9)

    rate_eval.He4_Ti59__n_Cr62 = rate

@numba.njit()
def He4_P44__n_Cl47(rate_eval, tf):
    # P44 + He4 --> n + Cl47
    rate = 0.0

    # rath 
    rate += np.exp(  -18.1274 + -3.42941*tf.T9i + -24.0571*tf.T913i + 39.8981*tf.T913
                  + -6.11044*tf.T9 + 0.460677*tf.T953 + -0.427182*tf.lnT9)

    rate_eval.He4_P44__n_Cl47 = rate

@numba.njit()
def n_Cr45__He4_Ti42(rate_eval, tf):
    # Cr45 + n --> He4 + Ti42
    rate = 0.0

    # ths8r
    rate += np.exp(  16.7093 + -0.137642*tf.T913
                  + -0.0231495*tf.T9 + 0.0180586*tf.T953)

    rate_eval.n_Cr45__He4_Ti42 = rate

@numba.njit()
def He4_Cr44__p_Mn47(rate_eval, tf):
    # Cr44 + He4 --> p + Mn47
    rate = 0.0

    # ths8r
    rate += np.exp(  60.4623 + -86.5458*tf.T913i + -1.34458*tf.T913
                  + -0.395743*tf.T9 + 0.00170088*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr44__p_Mn47 = rate

@numba.njit()
def He4_Cr43__p_Mn46(rate_eval, tf):
    # Cr43 + He4 --> p + Mn46
    rate = 0.0

    # ths8r
    rate += np.exp(  60.6886 + -86.4906*tf.T913i + -1.51497*tf.T913
                  + -0.408829*tf.T9 + 0.00630284*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr43__p_Mn46 = rate

@numba.njit()
def n_Cr43__p_V43(rate_eval, tf):
    # Cr43 + n --> p + V43
    rate = 0.0

    # ths8r
    rate += np.exp(  21.4361 + -0.770688*tf.T913
                  + 0.227518*tf.T9 + -0.0198496*tf.T953)

    rate_eval.n_Cr43__p_V43 = rate

@numba.njit()
def He4_Cr42__p_Mn45(rate_eval, tf):
    # Cr42 + He4 --> p + Mn45
    rate = 0.0

    # ths8r
    rate += np.exp(  59.88 + -86.4328*tf.T913i + -0.906774*tf.T913
                  + -0.512178*tf.T9 + 0.0163552*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr42__p_Mn45 = rate

@numba.njit()
def n_Cr42__He4_Ti39(rate_eval, tf):
    # Cr42 + n --> He4 + Ti39
    rate = 0.0

    # ths8r
    rate += np.exp(  15.0825 + -0.103933*tf.T913
                  + 0.0975842*tf.T9 + 0.0144018*tf.T953)

    rate_eval.n_Cr42__He4_Ti39 = rate

@numba.njit()
def n_Cr42__p_V42(rate_eval, tf):
    # Cr42 + n --> p + V42
    rate = 0.0

    # ths8r
    rate += np.exp(  21.3888 + -0.827392*tf.T913
                  + 0.264441*tf.T9 + -0.0247629*tf.T953)

    rate_eval.n_Cr42__p_V42 = rate

@numba.njit()
def n_Cr41__He4_Ti38(rate_eval, tf):
    # Cr41 + n --> He4 + Ti38
    rate = 0.0

    # ths8r
    rate += np.exp(  14.989 + -0.173252*tf.T913
                  + 0.197779*tf.T9 + -0.00880003*tf.T953)

    rate_eval.n_Cr41__He4_Ti38 = rate

@numba.njit()
def Ne26__n_Na25__weak__wc12(rate_eval, tf):
    # Ne26 --> n + Na25
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.38735)

    rate_eval.Ne26__n_Na25__weak__wc12 = rate

@numba.njit()
def He4_V67__n_Mn70(rate_eval, tf):
    # V67 + He4 --> n + Mn70
    rate = 0.0

    # rath 
    rate += np.exp(  -1169.03 + 18.5975*tf.T9i + -2016.32*tf.T913i + 3329.41*tf.T913
                  + -198.867*tf.T9 + 11.4177*tf.T953 + -1561.98*tf.lnT9)

    rate_eval.He4_V67__n_Mn70 = rate

@numba.njit()
def He4_Sc37__p_Ti40(rate_eval, tf):
    # Sc37 + He4 --> p + Ti40
    rate = 0.0

    # ths8r
    rate += np.exp(  56.9345 + -78.7634*tf.T913i + -1.03282*tf.T913
                  + -0.424405*tf.T9 + 0.00880205*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc37__p_Ti40 = rate

@numba.njit()
def p_V67__n_Cr67(rate_eval, tf):
    # V67 + p --> n + Cr67
    rate = 0.0

    # rath 
    rate += np.exp(  146.244 + -6.7797*tf.T9i + 258.511*tf.T913i + -416.999*tf.T913
                  + 23.0283*tf.T9 + -1.28572*tf.T953 + 208.231*tf.lnT9)

    rate_eval.p_V67__n_Cr67 = rate

@numba.njit()
def He4_V66__n_Mn69(rate_eval, tf):
    # V66 + He4 --> n + Mn69
    rate = 0.0

    # rath 
    rate += np.exp(  -1158.8 + 18.6039*tf.T9i + -2012.57*tf.T913i + 3314.41*tf.T913
                  + -197.36*tf.T9 + 11.3064*tf.T953 + -1557.47*tf.lnT9)

    rate_eval.He4_V66__n_Mn69 = rate

@numba.njit()
def p_V66__n_Cr66(rate_eval, tf):
    # V66 + p --> n + Cr66
    rate = 0.0

    # rath 
    rate += np.exp(  149.341 + -6.71985*tf.T9i + 256.272*tf.T913i + -417.945*tf.T913
                  + 23.3053*tf.T9 + -1.30909*tf.T953 + 207.483*tf.lnT9)

    rate_eval.p_V66__n_Cr66 = rate

@numba.njit()
def He4_V50__p_Cr53(rate_eval, tf):
    # V50 + He4 --> p + Cr53
    rate = 0.0

    # ths8r
    rate += np.exp(  43.0514 + -84.4058*tf.T913i + 13.5454*tf.T913
                  + -3.26175*tf.T9 + 0.249401*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V50__p_Cr53 = rate

@numba.njit()
def p_K47__He4_Ar44(rate_eval, tf):
    # K47 + p --> He4 + Ar44
    rate = 0.0

    # rath 
    rate += np.exp(  22.0652 + -4.96355*tf.T9i + 173.383*tf.T913i + -208.555*tf.T913
                  + 4.4353*tf.T9 + 0.222238*tf.T953 + 132.713*tf.lnT9)

    rate_eval.p_K47__He4_Ar44 = rate

@numba.njit()
def p_V65__He4_Ti62(rate_eval, tf):
    # V65 + p --> He4 + Ti62
    rate = 0.0

    # rath 
    rate += np.exp(  159.116 + -6.87015*tf.T9i + 274.74*tf.T913i + -465.267*tf.T913
                  + 27.3216*tf.T9 + -1.51497*tf.T953 + 225.79*tf.lnT9)

    rate_eval.p_V65__He4_Ti62 = rate

@numba.njit()
def He4_V64__n_Mn67(rate_eval, tf):
    # V64 + He4 --> n + Mn67
    rate = 0.0

    # rath 
    rate += np.exp(  -1138.85 + 18.3021*tf.T9i + -1980.71*tf.T913i + 3259.38*tf.T913
                  + -194.09*tf.T9 + 11.1191*tf.T953 + -1531.56*tf.lnT9)

    rate_eval.He4_V64__n_Mn67 = rate

@numba.njit()
def n_Cr49__p_V49(rate_eval, tf):
    # Cr49 + n --> p + V49
    rate = 0.0

    # ths8r
    rate += np.exp(  21.1065 + -1.62261*tf.T913
                  + 0.507111*tf.T9 + -0.0492268*tf.T953)

    rate_eval.n_Cr49__p_V49 = rate

@numba.njit()
def p_V64__He4_Ti61(rate_eval, tf):
    # V64 + p --> He4 + Ti61
    rate = 0.0

    # rath 
    rate += np.exp(  131.29 + -6.64912*tf.T9i + 254.024*tf.T913i + -411.87*tf.T913
                  + 23.1723*tf.T9 + -1.26652*tf.T953 + 205.65*tf.lnT9)

    rate_eval.p_V64__He4_Ti61 = rate

@numba.njit()
def p_V63__n_Cr63(rate_eval, tf):
    # V63 + p --> n + Cr63
    rate = 0.0

    # rath 
    rate += np.exp(  136.222 + -6.56889*tf.T9i + 247.174*tf.T913i + -394.698*tf.T913
                  + 21.5032*tf.T9 + -1.19595*tf.T953 + 198.82*tf.lnT9)

    rate_eval.p_V63__n_Cr63 = rate

@numba.njit()
def He4_Mn60__Co64(rate_eval, tf):
    # Mn60 + He4 --> Co64
    rate = 0.0

    # rath 
    rate += np.exp(  -1120.79 + 23.4074*tf.T9i + -2326.7*tf.T913i + 3579.85*tf.T913
                  + -202.652*tf.T9 + 11.1818*tf.T953 + -1738.33*tf.lnT9)

    rate_eval.He4_Mn60__Co64 = rate

@numba.njit()
def He4_V62__n_Mn65(rate_eval, tf):
    # V62 + He4 --> n + Mn65
    rate = 0.0

    # rath 
    rate += np.exp(  -1122.48 + 17.9516*tf.T9i + -1946.01*tf.T913i + 3205.59*tf.T913
                  + -191.312*tf.T9 + 10.977*tf.T953 + -1504.56*tf.lnT9)

    rate_eval.He4_V62__n_Mn65 = rate

@numba.njit()
def He4_V61__n_Mn64(rate_eval, tf):
    # V61 + He4 --> n + Mn64
    rate = 0.0

    # rath 
    rate += np.exp(  -1115.79 + 17.8372*tf.T9i + -1933.21*tf.T913i + 3185.06*tf.T913
                  + -190.202*tf.T9 + 10.9155*tf.T953 + -1494.39*tf.lnT9)

    rate_eval.He4_V61__n_Mn64 = rate

@numba.njit()
def p_V61__n_Cr61(rate_eval, tf):
    # V61 + p --> n + Cr61
    rate = 0.0

    # rath 
    rate += np.exp(  134.982 + -6.47628*tf.T9i + 243.317*tf.T913i + -389.311*tf.T913
                  + 21.1812*tf.T9 + -1.17718*tf.T953 + 196.127*tf.lnT9)

    rate_eval.p_V61__n_Cr61 = rate

@numba.njit()
def p_P32__n_S32(rate_eval, tf):
    # P32 + p --> n + S32
    rate = 0.0

    # rath 
    rate += np.exp(  82.294 + -3.56696*tf.T9i + 124.605*tf.T913i + -206.844*tf.T913
                  + 11.0016*tf.T9 + -0.612898*tf.T953 + 104.905*tf.lnT9)

    rate_eval.p_P32__n_S32 = rate

@numba.njit()
def He4_Al32__n_P35(rate_eval, tf):
    # Al32 + He4 --> n + P35
    rate = 0.0

    # rath 
    rate += np.exp(  -7.21665 + -2.62742*tf.T9i + -24.1732*tf.T913i + 29.6237*tf.T913
                  + -5.0512*tf.T9 + 0.389215*tf.T953 + 1.36789*tf.lnT9)

    rate_eval.He4_Al32__n_P35 = rate

@numba.njit()
def He4_V63__Mn67(rate_eval, tf):
    # V63 + He4 --> Mn67
    rate = 0.0

    # rath 
    rate += np.exp(  -1088.34 + 22.6124*tf.T9i + -2247.83*tf.T913i + 3463.65*tf.T913
                  + -196.043*tf.T9 + 10.8088*tf.T953 + -1681.11*tf.lnT9)

    rate_eval.He4_V63__Mn67 = rate

@numba.njit()
def p_V60__He4_Ti57(rate_eval, tf):
    # V60 + p --> He4 + Ti57
    rate = 0.0

    # rath 
    rate += np.exp(  125.184 + -6.45034*tf.T9i + 244.583*tf.T913i + -393.801*tf.T913
                  + 21.8284*tf.T9 + -1.18499*tf.T953 + 198.17*tf.lnT9)

    rate_eval.p_V60__He4_Ti57 = rate

@numba.njit()
def t_He3__n_p_He4(rate_eval, tf):
    # He3 + t --> n + p + He4
    rate = 0.0

    # cf88n
    rate += np.exp(  22.7658 + -7.733*tf.T913i + -0.118902*tf.T913
                  + -0.267393*tf.T9 + 0.0275387*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.t_He3__n_p_He4 = rate

@numba.njit()
def p_V60__n_Cr60(rate_eval, tf):
    # V60 + p --> n + Cr60
    rate = 0.0

    # rath 
    rate += np.exp(  138.574 + -6.42655*tf.T9i + 242.105*tf.T913i + -391.894*tf.T913
                  + 21.5382*tf.T9 + -1.20385*tf.T953 + 196.22*tf.lnT9)

    rate_eval.p_V60__n_Cr60 = rate

@numba.njit()
def p_O27__He4_N24(rate_eval, tf):
    # O27 + p --> He4 + N24
    rate = 0.0

    # rpsmr
    rate += np.exp(  52.5176 + -2.15418*tf.T9i + 73.9656*tf.T913i + -127.131*tf.T913
                  + 6.97025*tf.T9 + -0.387233*tf.T953 + 63.4835*tf.lnT9)

    rate_eval.p_O27__He4_N24 = rate

@numba.njit()
def p_Si43__n_P43(rate_eval, tf):
    # Si43 + p --> n + P43
    rate = 0.0

    # rath 
    rate += np.exp(  92.1887 + -3.95724*tf.T9i + 144.393*tf.T913i + -236.393*tf.T913
                  + 12.8139*tf.T9 + -0.707076*tf.T953 + 118.918*tf.lnT9)

    rate_eval.p_Si43__n_P43 = rate

@numba.njit()
def He4_V59__n_Mn62(rate_eval, tf):
    # V59 + He4 --> n + Mn62
    rate = 0.0

    # rath 
    rate += np.exp(  -1093.71 + 17.4978*tf.T9i + -1898.55*tf.T913i + 3124.89*tf.T913
                  + -186.464*tf.T9 + 10.6928*tf.T953 + -1466.42*tf.lnT9)

    rate_eval.He4_V59__n_Mn62 = rate

@numba.njit()
def He4_V58__n_Mn61(rate_eval, tf):
    # V58 + He4 --> n + Mn61
    rate = 0.0

    # rath 
    rate += np.exp(  -1086.39 + 17.39*tf.T9i + -1886.41*tf.T913i + 3104.85*tf.T913
                  + -185.438*tf.T9 + 10.6435*tf.T953 + -1456.77*tf.lnT9)

    rate_eval.He4_V58__n_Mn61 = rate

@numba.njit()
def p_V58__He4_Ti55(rate_eval, tf):
    # V58 + p --> He4 + Ti55
    rate = 0.0

    # rath 
    rate += np.exp(  121.765 + -6.3335*tf.T9i + 237.431*tf.T913i + -379.459*tf.T913
                  + 20.8542*tf.T9 + -1.14004*tf.T953 + 191.871*tf.lnT9)

    rate_eval.p_V58__He4_Ti55 = rate

@numba.njit()
def p_V58__n_Cr58(rate_eval, tf):
    # V58 + p --> n + Cr58
    rate = 0.0

    # rath 
    rate += np.exp(  131.273 + -6.3232*tf.T9i + 236.223*tf.T913i + -378.273*tf.T913
                  + 20.5841*tf.T9 + -1.14751*tf.T953 + 190.846*tf.lnT9)

    rate_eval.p_V58__n_Cr58 = rate

@numba.njit()
def p_V57__He4_Ti54(rate_eval, tf):
    # V57 + p --> He4 + Ti54
    rate = 0.0

    # rath 
    rate += np.exp(  131.244 + -6.3133*tf.T9i + 239.332*tf.T913i + -392.33*tf.T913
                  + 22.3046*tf.T9 + -1.24739*tf.T953 + 195.215*tf.lnT9)

    rate_eval.p_V57__He4_Ti54 = rate

@numba.njit()
def p_V57__n_Cr57(rate_eval, tf):
    # V57 + p --> n + Cr57
    rate = 0.0

    # rath 
    rate += np.exp(  129.757 + -6.26824*tf.T9i + 233.519*tf.T913i + -374.007*tf.T913
                  + 20.374*tf.T9 + -1.13853*tf.T953 + 188.791*tf.lnT9)

    rate_eval.p_V57__n_Cr57 = rate

@numba.njit()
def n_Cr53__He4_Ti50(rate_eval, tf):
    # Cr53 + n --> He4 + Ti50
    rate = 0.0

    # ths8r
    rate += np.exp(  -23.5895 + 21.17*tf.T913
                  + -0.195248*tf.T9 + -0.121068*tf.T953)

    rate_eval.n_Cr53__He4_Ti50 = rate

@numba.njit()
def He4_V56__n_Mn59(rate_eval, tf):
    # V56 + He4 --> n + Mn59
    rate = 0.0

    # rath 
    rate += np.exp(  -1066.31 + 17.1164*tf.T9i + -1856.54*tf.T913i + 3052.15*tf.T913
                  + -182.223*tf.T9 + 10.4558*tf.T953 + -1432.4*tf.lnT9)

    rate_eval.He4_V56__n_Mn59 = rate

@numba.njit()
def Mn43__Cr43__weak__bqa_pos_(rate_eval, tf):
    # Mn43 --> Cr43
    rate = 0.0

    # bqa+w
    rate += np.exp(  3.96863)

    rate_eval.Mn43__Cr43__weak__bqa_pos_ = rate

@numba.njit()
def He4_Al40__p_Si43(rate_eval, tf):
    # Al40 + He4 --> p + Si43
    rate = 0.0

    # rath 
    rate += np.exp(  -289.2 + 1.58359*tf.T9i + -411.585*tf.T913i + 722.777*tf.T913
                  + -48.6385*tf.T9 + 3.02238*tf.T953 + -315.024*tf.lnT9)

    rate_eval.He4_Al40__p_Si43 = rate

@numba.njit()
def He4_V55__n_Mn58(rate_eval, tf):
    # V55 + He4 --> n + Mn58
    rate = 0.0

    # rath 
    rate += np.exp(  -1057.99 + 16.9423*tf.T9i + -1839.13*tf.T913i + 3024.89*tf.T913
                  + -180.731*tf.T9 + 10.374*tf.T953 + -1418.86*tf.lnT9)

    rate_eval.He4_V55__n_Mn58 = rate

@numba.njit()
def Ne28__Na28__weak__wc17(rate_eval, tf):
    # Ne28 --> Na28
    rate = 0.0

    # wc17w
    rate += np.exp(  3.47425)

    rate_eval.Ne28__Na28__weak__wc17 = rate

@numba.njit()
def He4_Cr47__p_Mn50(rate_eval, tf):
    # Cr47 + He4 --> p + Mn50
    rate = 0.0

    # ths8r
    rate += np.exp(  60.7276 + -86.6989*tf.T913i + -1.15472*tf.T913
                  + -0.484509*tf.T9 + 0.0105851*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr47__p_Mn50 = rate

@numba.njit()
def p_V55__n_Cr55(rate_eval, tf):
    # V55 + p --> n + Cr55
    rate = 0.0

    # rath 
    rate += np.exp(  127.744 + -6.16171*tf.T9i + 228.628*tf.T913i + -367.338*tf.T913
                  + 20.1562*tf.T9 + -1.13523*tf.T953 + 185.272*tf.lnT9)

    rate_eval.p_V55__n_Cr55 = rate

@numba.njit()
def He4_V54__n_Mn57(rate_eval, tf):
    # V54 + He4 --> n + Mn57
    rate = 0.0

    # rath 
    rate += np.exp(  -1049.72 + 16.7997*tf.T9i + -1824.0*tf.T913i + 3000.14*tf.T913
                  + -179.322*tf.T9 + 10.2954*tf.T953 + -1406.89*tf.lnT9)

    rate_eval.He4_V54__n_Mn57 = rate

@numba.njit()
def He4_Ar52__Ca56(rate_eval, tf):
    # Ar52 + He4 --> Ca56
    rate = 0.0

    # rath 
    rate += np.exp(  -890.349 + 14.1139*tf.T9i + -1531.13*tf.T913i + 2520.76*tf.T913
                  + -151.109*tf.T9 + 8.68767*tf.T953 + -1181.17*tf.lnT9)

    rate_eval.He4_Ar52__Ca56 = rate

@numba.njit()
def p_V53__n_Cr53(rate_eval, tf):
    # V53 + p --> n + Cr53
    rate = 0.0

    # rath 
    rate += np.exp(  131.597 + -6.09475*tf.T9i + 228.066*tf.T913i + -371.873*tf.T913
                  + 20.7886*tf.T9 + -1.18461*tf.T953 + 186.026*tf.lnT9)

    rate_eval.p_V53__n_Cr53 = rate

@numba.njit()
def p_V52__He4_Ti49(rate_eval, tf):
    # V52 + p --> He4 + Ti49
    rate = 0.0

    # rath 
    rate += np.exp(  60.9203 + -5.89339*tf.T9i + 209.633*tf.T913i + -291.46*tf.T913
                  + 13.4258*tf.T9 + -0.668366*tf.T953 + 164.685*tf.lnT9)

    rate_eval.p_V52__He4_Ti49 = rate

@numba.njit()
def p_V52__n_Cr52(rate_eval, tf):
    # V52 + p --> n + Cr52
    rate = 0.0

    # rath 
    rate += np.exp(  130.283 + -6.04059*tf.T9i + 225.572*tf.T913i + -367.914*tf.T913
                  + 20.4967*tf.T9 + -1.16016*tf.T953 + 184.15*tf.lnT9)

    rate_eval.p_V52__n_Cr52 = rate

@numba.njit()
def He4_S45__n_Ar48(rate_eval, tf):
    # S45 + He4 --> n + Ar48
    rate = 0.0

    # rath 
    rate += np.exp(  -353.151 + 1.90069*tf.T9i + -504.872*tf.T913i + 897.889*tf.T913
                  + -59.4835*tf.T9 + 3.62786*tf.T953 + -393.026*tf.lnT9)

    rate_eval.He4_S45__n_Ar48 = rate

@numba.njit()
def He4_Ca43__Ti47(rate_eval, tf):
    # Ca43 + He4 --> Ti47
    rate = 0.0

    # ths8r
    rate += np.exp(  60.4703 + -76.5897*tf.T913i + -7.46117*tf.T913
                  + -0.574977*tf.T9 + 0.115742*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca43__Ti47 = rate

@numba.njit()
def p_V51__He4_Ti48(rate_eval, tf):
    # V51 + p --> He4 + Ti48
    rate = 0.0

    # ths8r
    rate += np.exp(  -13.7548 + -34.2261*tf.T913i + 38.6574*tf.T913
                  + -7.18743*tf.T9 + 0.692255*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V51__He4_Ti48 = rate

@numba.njit()
def p_F23__Ne24(rate_eval, tf):
    # F23 + p --> Ne24
    rate = 0.0

    # rpsmr
    rate += np.exp(  48.076 + -2.14691*tf.T9i + 71.6037*tf.T913i + -122.175*tf.T913
                  + 6.49572*tf.T9 + -0.354485*tf.T953 + 62.0993*tf.lnT9)

    rate_eval.p_F23__Ne24 = rate

@numba.njit()
def n_Mn69__Mn70(rate_eval, tf):
    # Mn69 + n --> Mn70
    rate = 0.0

    # rath 
    rate += np.exp(  18.0282 + -0.0327505*tf.T9i + 3.55335*tf.T913i + -12.7242*tf.T913
                  + 1.47019*tf.T9 + -0.158246*tf.T953 + 3.87674*tf.lnT9)

    rate_eval.n_Mn69__Mn70 = rate

@numba.njit()
def p_V50__He4_Ti47(rate_eval, tf):
    # V50 + p --> He4 + Ti47
    rate = 0.0

    # ths8r
    rate += np.exp(  -50.621 + -34.2216*tf.T913i + 78.8919*tf.T913
                  + -16.0561*tf.T9 + 1.55251*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V50__He4_Ti47 = rate

@numba.njit()
def p_V50__n_Cr50(rate_eval, tf):
    # V50 + p --> n + Cr50
    rate = 0.0

    # ths8r
    rate += np.exp(  17.9003 + -34.2216*tf.T913i + 18.9337*tf.T913
                  + -4.3348*tf.T9 + 0.409807*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V50__n_Cr50 = rate

@numba.njit()
def n_V50__p_Ti50(rate_eval, tf):
    # V50 + n --> p + Ti50
    rate = 0.0

    # ths8r
    rate += np.exp(  2.14011 + 13.156*tf.T913
                  + -2.27428*tf.T9 + 0.204692*tf.T953)

    rate_eval.n_V50__p_Ti50 = rate

@numba.njit()
def p_F24__Ne25(rate_eval, tf):
    # F24 + p --> Ne25
    rate = 0.0

    # rpsmr
    rate += np.exp(  52.8391 + -2.21162*tf.T9i + 75.7353*tf.T913i + -131.568*tf.T913
                  + 7.18977*tf.T9 + -0.39952*tf.T953 + 65.8254*tf.lnT9)

    rate_eval.p_F24__Ne25 = rate

@numba.njit()
def p_V49__He4_Ti46(rate_eval, tf):
    # V49 + p --> He4 + Ti46
    rate = 0.0

    # ths8r
    rate += np.exp(  -20.0996 + -34.217*tf.T913i + 47.2584*tf.T913
                  + -9.18871*tf.T9 + 0.87823*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V49__He4_Ti46 = rate

@numba.njit()
def He4_N15__F19(rate_eval, tf):
    # N15 + He4 --> F19
    rate = 0.0

    # il10r
    rate += np.exp(  -28.7989 + -4.19986*tf.T9i + 35.4292*tf.T913
                  + -5.5767*tf.T9 + 0.441293*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  3.5342 + -6.98462*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -9.41892 + -4.17795*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  25.3916 + -36.2324*tf.T913i
                  + -2.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_N15__F19 = rate

@numba.njit()
def He4_V47__p_Cr50(rate_eval, tf):
    # V47 + He4 --> p + Cr50
    rate = 0.0

    # ths8r
    rate += np.exp(  59.9106 + -84.2732*tf.T913i + -1.10027*tf.T913
                  + -0.487084*tf.T9 + 0.00453269*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V47__p_Cr50 = rate

@numba.njit()
def He4_V46__p_Cr49(rate_eval, tf):
    # V46 + He4 --> p + Cr49
    rate = 0.0

    # ths8r
    rate += np.exp(  59.798 + -84.2255*tf.T913i + -1.09776*tf.T913
                  + -0.495216*tf.T9 + 0.0124719*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V46__p_Cr49 = rate

@numba.njit()
def n_V46__He4_Sc43(rate_eval, tf):
    # V46 + n --> He4 + Sc43
    rate = 0.0

    # ths8r
    rate += np.exp(  7.52435 + 6.99126*tf.T913
                  + -0.552826*tf.T9 + 0.0272052*tf.T953)

    rate_eval.n_V46__He4_Sc43 = rate

@numba.njit()
def n_V46__p_Ti46(rate_eval, tf):
    # V46 + n --> p + Ti46
    rate = 0.0

    # ths8r
    rate += np.exp(  21.15 + -0.663329*tf.T913
                  + 0.174849*tf.T9 + -0.0157869*tf.T953)

    rate_eval.n_V46__p_Ti46 = rate

@numba.njit()
def He4_V58__Mn62(rate_eval, tf):
    # V58 + He4 --> Mn62
    rate = 0.0

    # rath 
    rate += np.exp(  -1043.64 + 21.7498*tf.T9i + -2163.68*tf.T913i + 3330.03*tf.T913
                  + -188.697*tf.T9 + 10.4167*tf.T953 + -1616.08*tf.lnT9)

    rate_eval.He4_V58__Mn62 = rate

@numba.njit()
def p_Sc52__Ti53(rate_eval, tf):
    # Sc52 + p --> Ti53
    rate = 0.0

    # rath 
    rate += np.exp(  114.282 + -5.67647*tf.T9i + 211.542*tf.T913i + -344.346*tf.T913
                  + 19.1043*tf.T9 + -1.08459*tf.T953 + 172.594*tf.lnT9)

    rate_eval.p_Sc52__Ti53 = rate

@numba.njit()
def n_V44__He4_Sc41(rate_eval, tf):
    # V44 + n --> He4 + Sc41
    rate = 0.0

    # ths8r
    rate += np.exp(  18.1942 + -0.272328*tf.T913
                  + 0.0776173*tf.T9 + 0.00870707*tf.T953)

    rate_eval.n_V44__He4_Sc41 = rate

@numba.njit()
def n_V44__p_Ti44(rate_eval, tf):
    # V44 + n --> p + Ti44
    rate = 0.0

    # ths8r
    rate += np.exp(  21.2863 + -0.782579*tf.T913
                  + 0.235148*tf.T9 + -0.0215934*tf.T953)

    rate_eval.n_V44__p_Ti44 = rate

@numba.njit()
def Cl49__n_n_Ar47__weak__mp17(rate_eval, tf):
    # Cl49 --> n + n + Ar47
    rate = 0.0

    # mp17w
    rate += np.exp(  1.63862)

    rate_eval.Cl49__n_n_Ar47__weak__mp17 = rate

@numba.njit()
def He4_V43__p_Cr46(rate_eval, tf):
    # V43 + He4 --> p + Cr46
    rate = 0.0

    # ths8r
    rate += np.exp(  59.4783 + -84.0702*tf.T913i + -1.24277*tf.T913
                  + -0.410682*tf.T9 + 0.0037765*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V43__p_Cr46 = rate

@numba.njit()
def n_V43__p_Ti43(rate_eval, tf):
    # V43 + n --> p + Ti43
    rate = 0.0

    # ths8r
    rate += np.exp(  21.0451 + -0.53342*tf.T913
                  + 0.192011*tf.T9 + -0.0170537*tf.T953)

    rate_eval.n_V43__p_Ti43 = rate

@numba.njit()
def He4_V42__p_Cr45(rate_eval, tf):
    # V42 + He4 --> p + Cr45
    rate = 0.0

    # ths8r
    rate += np.exp(  59.7431 + -84.014*tf.T913i + -1.34916*tf.T913
                  + -0.471184*tf.T9 + 0.0150191*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V42__p_Cr45 = rate

@numba.njit()
def He4_Si43__n_S46(rate_eval, tf):
    # Si43 + He4 --> n + S46
    rate = 0.0

    # rath 
    rate += np.exp(  -10.4618 + -3.39675*tf.T9i + -9.43765*tf.T913i + 18.079*tf.T913
                  + -5.12606*tf.T9 + 0.421776*tf.T953 + 10.4046*tf.lnT9)

    rate_eval.He4_Si43__n_S46 = rate

@numba.njit()
def Sc47__Ti47__weak__wc12(rate_eval, tf):
    # Sc47 --> Ti47
    rate = 0.0

    # wc12w
    rate += np.exp(  -12.9407)

    rate_eval.Sc47__Ti47__weak__wc12 = rate

@numba.njit()
def He4_Ne33__n_Mg36(rate_eval, tf):
    # Ne33 + He4 --> n + Mg36
    rate = 0.0

    # rath 
    rate += np.exp(  76.308 + -3.10092*tf.T9i + 71.7129*tf.T913i + -154.39*tf.T913
                  + 7.20947*tf.T9 + -0.360388*tf.T953 + 80.3755*tf.lnT9)

    rate_eval.He4_Ne33__n_Mg36 = rate

@numba.njit()
def n_V42__He4_Sc39(rate_eval, tf):
    # V42 + n --> He4 + Sc39
    rate = 0.0

    # ths8r
    rate += np.exp(  14.1565 + 0.333223*tf.T913
                  + -0.658289*tf.T9 + 0.178865*tf.T953)

    rate_eval.n_V42__He4_Sc39 = rate

@numba.njit()
def n_V41__He4_Sc38(rate_eval, tf):
    # V41 + n --> He4 + Sc38
    rate = 0.0

    # ths8r
    rate += np.exp(  15.5404 + 0.00133845*tf.T913
                  + 0.160704*tf.T9 + -0.00319207*tf.T953)

    rate_eval.n_V41__He4_Sc38 = rate

@numba.njit()
def n_V40__p_Ti40(rate_eval, tf):
    # V40 + n --> p + Ti40
    rate = 0.0

    # ths8r
    rate += np.exp(  21.5569 + -0.766287*tf.T913
                  + 0.208517*tf.T9 + -0.017311*tf.T953)

    rate_eval.n_V40__p_Ti40 = rate

@numba.njit()
def He4_V39__p_Cr42(rate_eval, tf):
    # V39 + He4 --> p + Cr42
    rate = 0.0

    # ths8r
    rate += np.exp(  59.4023 + -83.8293*tf.T913i + -1.14751*tf.T913
                  + -0.443214*tf.T9 + 0.00733154*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V39__p_Cr42 = rate

@numba.njit()
def p_Sc53__n_Ti53(rate_eval, tf):
    # Sc53 + p --> n + Ti53
    rate = 0.0

    # rath 
    rate += np.exp(  121.677 + -5.7115*tf.T9i + 212.013*tf.T913i + -342.781*tf.T913
                  + 18.8962*tf.T9 + -1.06508*tf.T953 + 172.4*tf.lnT9)

    rate_eval.p_Sc53__n_Ti53 = rate

@numba.njit()
def He4_Ti65__n_Cr68(rate_eval, tf):
    # Ti65 + He4 --> n + Cr68
    rate = 0.0

    # rath 
    rate += np.exp(  -1117.58 + 17.7881*tf.T9i + -1929.09*tf.T913i + 3184.39*tf.T913
                  + -190.25*tf.T9 + 10.9214*tf.T953 + -1493.56*tf.lnT9)

    rate_eval.He4_Ti65__n_Cr68 = rate

@numba.njit()
def p_Cr57__He4_V54(rate_eval, tf):
    # Cr57 + p --> He4 + V54
    rate = 0.0

    # rath 
    rate += np.exp(  73.2665 + -6.41774*tf.T9i + 235.034*tf.T913i + -332.023*tf.T913
                  + 15.9052*tf.T9 + -0.825836*tf.T953 + 184.346*tf.lnT9)

    rate_eval.p_Cr57__He4_V54 = rate

@numba.njit()
def p_Ne27__He4_F24(rate_eval, tf):
    # Ne27 + p --> He4 + F24
    rate = 0.0

    # rath 
    rate += np.exp(  57.519 + -2.51138*tf.T9i + 86.0249*tf.T913i + -142.955*tf.T913
                  + 7.59259*tf.T9 + -0.411175*tf.T953 + 73.0575*tf.lnT9)

    rate_eval.p_Ne27__He4_F24 = rate

@numba.njit()
def He4_Ti64__n_Cr67(rate_eval, tf):
    # Ti64 + He4 --> n + Cr67
    rate = 0.0

    # rath 
    rate += np.exp(  -1111.62 + 17.657*tf.T9i + -1915.7*tf.T913i + 3164.13*tf.T913
                  + -189.257*tf.T9 + 10.8743*tf.T953 + -1483.28*tf.lnT9)

    rate_eval.He4_Ti64__n_Cr67 = rate

@numba.njit()
def p_Ti64__He4_Sc61(rate_eval, tf):
    # Ti64 + p --> He4 + Sc61
    rate = 0.0

    # rath 
    rate += np.exp(  -26.382 + -5.34152*tf.T9i + 120.321*tf.T913i + -115.344*tf.T913
                  + 2.23079*tf.T9 + 0.0726172*tf.T953 + 86.8127*tf.lnT9)

    rate_eval.p_Ti64__He4_Sc61 = rate

@numba.njit()
def He4_Ti63__n_Cr66(rate_eval, tf):
    # Ti63 + He4 --> n + Cr66
    rate = 0.0

    # rath 
    rate += np.exp(  -1102.48 + 17.5319*tf.T9i + -1902.09*tf.T913i + 3140.07*tf.T913
                  + -187.744*tf.T9 + 10.7814*tf.T953 + -1472.18*tf.lnT9)

    rate_eval.He4_Ti63__n_Cr66 = rate

@numba.njit()
def p_Ti63__He4_Sc60(rate_eval, tf):
    # Ti63 + p --> He4 + Sc60
    rate = 0.0

    # rath 
    rate += np.exp(  91.8947 + -6.45227*tf.T9i + 247.738*tf.T913i + -373.506*tf.T913
                  + 20.2863*tf.T9 + -1.13006*tf.T953 + 197.466*tf.lnT9)

    rate_eval.p_Ti63__He4_Sc60 = rate

@numba.njit()
def p_Ti63__n_V63(rate_eval, tf):
    # Ti63 + p --> n + V63
    rate = 0.0

    # rath 
    rate += np.exp(  135.398 + -6.38799*tf.T9i + 241.218*tf.T913i + -387.006*tf.T913
                  + 21.1642*tf.T9 + -1.17765*tf.T953 + 194.334*tf.lnT9)

    rate_eval.p_Ti63__n_V63 = rate

@numba.njit()
def p_Ti61__n_V61(rate_eval, tf):
    # Ti61 + p --> n + V61
    rate = 0.0

    # rath 
    rate += np.exp(  130.928 + -6.28041*tf.T9i + 235.496*tf.T913i + -376.488*tf.T913
                  + 20.5109*tf.T9 + -1.14197*tf.T953 + 189.715*tf.lnT9)

    rate_eval.p_Ti61__n_V61 = rate

@numba.njit()
def He4_Ti60__n_Cr63(rate_eval, tf):
    # Ti60 + He4 --> n + Cr63
    rate = 0.0

    # rath 
    rate += np.exp(  -1075.47 + 17.1307*tf.T9i + -1859.27*tf.T913i + 3066.49*tf.T913
                  + -183.413*tf.T9 + 10.5376*tf.T953 + -1437.61*tf.lnT9)

    rate_eval.He4_Ti60__n_Cr63 = rate

@numba.njit()
def n_O12__O13(rate_eval, tf):
    # O12 + n --> O13
    rate = 0.0

    # rpsmr
    rate += np.exp(  11.3989 + 0.00877921*tf.T9i + -0.540715*tf.T913i + -0.683761*tf.T913
                  + 0.136266*tf.T9 + -0.00213797*tf.T953 + -0.171372*tf.lnT9)

    rate_eval.n_O12__O13 = rate

@numba.njit()
def p_Ti60__n_V60(rate_eval, tf):
    # Ti60 + p --> n + V60
    rate = 0.0

    # rath 
    rate += np.exp(  129.961 + -6.23386*tf.T9i + 233.433*tf.T913i + -373.23*tf.T913
                  + 20.2701*tf.T9 + -1.12399*tf.T953 + 188.187*tf.lnT9)

    rate_eval.p_Ti60__n_V60 = rate

@numba.njit()
def p_Ti59__n_V59(rate_eval, tf):
    # Ti59 + p --> n + V59
    rate = 0.0

    # rath 
    rate += np.exp(  128.206 + -6.17882*tf.T9i + 230.574*tf.T913i + -368.472*tf.T913
                  + 20.0263*tf.T9 + -1.11486*tf.T953 + 185.958*tf.lnT9)

    rate_eval.p_Ti59__n_V59 = rate

@numba.njit()
def He4_Ti58__n_Cr61(rate_eval, tf):
    # Ti58 + He4 --> n + Cr61
    rate = 0.0

    # rath 
    rate += np.exp(  -1057.13 + 16.8672*tf.T9i + -1830.8*tf.T913i + 3017.1*tf.T913
                  + -180.439*tf.T9 + 10.365*tf.T953 + -1414.54*tf.lnT9)

    rate_eval.He4_Ti58__n_Cr61 = rate

@numba.njit()
def p_Ti58__n_V58(rate_eval, tf):
    # Ti58 + p --> n + V58
    rate = 0.0

    # rath 
    rate += np.exp(  127.398 + -6.13315*tf.T9i + 228.687*tf.T913i + -365.797*tf.T913
                  + 19.8857*tf.T9 + -1.10644*tf.T953 + 184.626*tf.lnT9)

    rate_eval.p_Ti58__n_V58 = rate

@numba.njit()
def K32__Ar32__weak__bqa_pos_(rate_eval, tf):
    # K32 --> Ar32
    rate = 0.0

    # bqa+w
    rate += np.exp(  5.34732)

    rate_eval.K32__Ar32__weak__bqa_pos_ = rate

@numba.njit()
def He4_Ti55__n_Cr58(rate_eval, tf):
    # Ti55 + He4 --> n + Cr58
    rate = 0.0

    # rath 
    rate += np.exp(  -1028.82 + 16.4601*tf.T9i + -1786.83*tf.T913i + 2940.76*tf.T913
                  + -175.81*tf.T9 + 10.0932*tf.T953 + -1378.92*tf.lnT9)

    rate_eval.He4_Ti55__n_Cr58 = rate

@numba.njit()
def p_Ti55__n_V55(rate_eval, tf):
    # Ti55 + p --> n + V55
    rate = 0.0

    # rath 
    rate += np.exp(  123.48 + -5.9723*tf.T9i + 220.929*tf.T913i + -354.09*tf.T913
                  + 19.3657*tf.T9 + -1.08927*tf.T953 + 178.843*tf.lnT9)

    rate_eval.p_Ti55__n_V55 = rate

@numba.njit()
def He4_Ti54__n_Cr57(rate_eval, tf):
    # Ti54 + He4 --> n + Cr57
    rate = 0.0

    # rath 
    rate += np.exp(  -1016.57 + 16.2898*tf.T9i + -1768.85*tf.T913i + 2908.37*tf.T913
                  + -173.745*tf.T9 + 9.96909*tf.T953 + -1364.1*tf.lnT9)

    rate_eval.He4_Ti54__n_Cr57 = rate

@numba.njit()
def p_Ti54__He4_Sc51(rate_eval, tf):
    # Ti54 + p --> He4 + Sc51
    rate = 0.0

    # rath 
    rate += np.exp(  89.9444 + -5.95599*tf.T9i + 222.269*tf.T913i + -337.08*tf.T913
                  + 18.4168*tf.T9 + -1.06903*tf.T953 + 178.307*tf.lnT9)

    rate_eval.p_Ti54__He4_Sc51 = rate

@numba.njit()
def p_Ti54__n_V54(rate_eval, tf):
    # Ti54 + p --> n + V54
    rate = 0.0

    # rath 
    rate += np.exp(  124.755 + -5.93773*tf.T9i + 220.42*tf.T913i + -355.516*tf.T913
                  + 19.5653*tf.T9 + -1.09854*tf.T953 + 178.959*tf.lnT9)

    rate_eval.p_Ti54__n_V54 = rate

@numba.njit()
def p_F23__He4_O20(rate_eval, tf):
    # F23 + p --> He4 + O20
    rate = 0.0

    # rpsmr
    rate += np.exp(  56.8593 + -2.16807*tf.T9i + 73.8811*tf.T913i + -127.554*tf.T913
                  + 6.84937*tf.T9 + -0.369383*tf.T953 + 64.3029*tf.lnT9)

    rate_eval.p_F23__He4_O20 = rate

@numba.njit()
def He4_Ti53__n_Cr56(rate_eval, tf):
    # Ti53 + He4 --> n + Cr56
    rate = 0.0

    # rath 
    rate += np.exp(  -1007.28 + 16.1473*tf.T9i + -1753.62*tf.T913i + 2882.52*tf.T913
                  + -172.261*tf.T9 + 9.88845*tf.T953 + -1351.87*tf.lnT9)

    rate_eval.He4_Ti53__n_Cr56 = rate

@numba.njit()
def p_Ti53__He4_Sc50(rate_eval, tf):
    # Ti53 + p --> He4 + Sc50
    rate = 0.0

    # rath 
    rate += np.exp(  48.9374 + -5.73537*tf.T9i + 199.206*tf.T913i + -265.132*tf.T913
                  + 10.6945*tf.T9 + -0.373299*tf.T953 + 153.686*tf.lnT9)

    rate_eval.p_Ti53__He4_Sc50 = rate

@numba.njit()
def n_Na33__Na34(rate_eval, tf):
    # Na33 + n --> Na34
    rate = 0.0

    # rath 
    rate += np.exp(  11.8182 + -0.07527*tf.T9i + 6.26692*tf.T913i + -14.5879*tf.T913
                  + 1.40359*tf.T9 + -0.0963501*tf.T953 + 5.34762*tf.lnT9)

    rate_eval.n_Na33__Na34 = rate

@numba.njit()
def He4_Be10__C14(rate_eval, tf):
    # Be10 + He4 --> C14
    rate = 0.0

    # fkthr
    rate += np.exp(  35.2348 + -1.46291*tf.T9i + 29.2642*tf.T913i + -67.302*tf.T913
                  + 2.97191*tf.T9 + -0.134701*tf.T953 + 35.1235*tf.lnT9)

    rate_eval.He4_Be10__C14 = rate

@numba.njit()
def p_Ti52__He4_Sc49(rate_eval, tf):
    # Ti52 + p --> He4 + Sc49
    rate = 0.0

    # rath 
    rate += np.exp(  12.2908 + -5.44526*tf.T9i + 172.967*tf.T913i + -199.918*tf.T913
                  + 6.08335*tf.T9 + -0.144711*tf.T953 + 128.91*tf.lnT9)

    rate_eval.p_Ti52__He4_Sc49 = rate

@numba.njit()
def p_Ti52__n_V52(rate_eval, tf):
    # Ti52 + p --> n + V52
    rate = 0.0

    # rath 
    rate += np.exp(  125.382 + -5.85008*tf.T9i + 217.545*tf.T913i + -353.559*tf.T913
                  + 19.6066*tf.T9 + -1.10699*tf.T953 + 177.37*tf.lnT9)

    rate_eval.p_Ti52__n_V52 = rate

@numba.njit()
def He4_Ti51__n_Cr54(rate_eval, tf):
    # Ti51 + He4 --> n + Cr54
    rate = 0.0

    # rath 
    rate += np.exp(  -987.778 + 15.8616*tf.T9i + -1722.81*tf.T913i + 2829.38*tf.T913
                  + -169.068*tf.T9 + 9.70315*tf.T953 + -1326.98*tf.lnT9)

    rate_eval.He4_Ti51__n_Cr54 = rate

@numba.njit()
def Ti43__Sc43__weak__wc12(rate_eval, tf):
    # Ti43 --> Sc43
    rate = 0.0

    # wc12w
    rate += np.exp(  0.308794)

    rate_eval.Ti43__Sc43__weak__wc12 = rate

@numba.njit()
def p_Ti51__n_V51(rate_eval, tf):
    # Ti51 + p --> n + V51
    rate = 0.0

    # rath 
    rate += np.exp(  121.807 + -5.7807*tf.T9i + 213.317*tf.T913i + -345.382*tf.T913
                  + 19.0423*tf.T9 + -1.06972*tf.T953 + 173.788*tf.lnT9)

    rate_eval.p_Ti51__n_V51 = rate

@numba.njit()
def n_Ti51__He4_Ca48(rate_eval, tf):
    # Ti51 + n --> He4 + Ca48
    rate = 0.0

    # rath 
    rate += np.exp(  72.4516 + -12.4162*tf.T9i + 343.859*tf.T913i + -441.137*tf.T913
                  + 18.781*tf.T9 + -0.911515*tf.T953 + 254.789*tf.lnT9)

    rate_eval.n_Ti51__He4_Ca48 = rate

@numba.njit()
def He4_F26__Na30(rate_eval, tf):
    # F26 + He4 --> Na30
    rate = 0.0

    # rpsmr
    rate += np.exp(  49.7686 + -2.44085*tf.T9i + 46.6522*tf.T913i + -111.547*tf.T913
                  + 4.84476*tf.T9 + -0.227867*tf.T953 + 59.511*tf.lnT9)

    rate_eval.He4_F26__Na30 = rate

@numba.njit()
def n_Ti49__He4_Ca46(rate_eval, tf):
    # Ti49 + n --> He4 + Ca46
    rate = 0.0

    # ths8r
    rate += np.exp(  -106.775 + 100.098*tf.T913
                  + -14.6121*tf.T9 + 1.09235*tf.T953)

    rate_eval.n_Ti49__He4_Ca46 = rate

@numba.njit()
def Sc61__n_n_Ti59__weak__mp17(rate_eval, tf):
    # Sc61 --> n + n + Ti59
    rate = 0.0

    # mp17w
    rate += np.exp(  0.939124)

    rate_eval.Sc61__n_n_Ti59__weak__mp17 = rate

@numba.njit()
def He4_Fe73__n_Ni76(rate_eval, tf):
    # Fe73 + He4 --> n + Ni76
    rate = 0.0

    # rath 
    rate += np.exp(  -1272.54 + 26.4329*tf.T9i + -2623.21*tf.T913i + 4057.68*tf.T913
                  + -230.034*tf.T9 + 12.7278*tf.T953 + -1967.91*tf.lnT9)

    rate_eval.He4_Fe73__n_Ni76 = rate

@numba.njit()
def He4_K36__p_Ca39(rate_eval, tf):
    # K36 + He4 --> p + Ca39
    rate = 0.0

    # ths8r
    rate += np.exp(  54.1563 + -73.6116*tf.T913i + 0.485828*tf.T913
                  + -0.890495*tf.T9 + 0.0643941*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K36__p_Ca39 = rate

@numba.njit()
def Sc56__n_Ti55__weak__mp17(rate_eval, tf):
    # Sc56 --> n + Ti55
    rate = 0.0

    # mp17w
    rate += np.exp(  1.07587)

    rate_eval.Sc56__n_Ti55__weak__mp17 = rate

@numba.njit()
def He4_Ar35__Ca39(rate_eval, tf):
    # Ar35 + He4 --> Ca39
    rate = 0.0

    # ths8r
    rate += np.exp(  56.5167 + -70.9375*tf.T913i + -10.7059*tf.T913
                  + 1.44501*tf.T9 + -0.179044*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar35__Ca39 = rate

@numba.njit()
def p_Ar51__He4_Cl48(rate_eval, tf):
    # Ar51 + p --> He4 + Cl48
    rate = 0.0

    # rath 
    rate += np.exp(  85.0923 + -5.12839*tf.T9i + 194.009*tf.T913i + -300.034*tf.T913
                  + 15.5824*tf.T9 + -0.803063*tf.T953 + 156.969*tf.lnT9)

    rate_eval.p_Ar51__He4_Cl48 = rate

@numba.njit()
def He4_Na19__Al23(rate_eval, tf):
    # Na19 + He4 --> Al23
    rate = 0.0

    # ths8r
    rate += np.exp(  32.9864 + -49.6957*tf.T913i + 0.620856*tf.T913
                  + -0.773759*tf.T9 + 0.0591118*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Na19__Al23 = rate

@numba.njit()
def n_Na35__Na36(rate_eval, tf):
    # Na35 + n --> Na36
    rate = 0.0

    # rath 
    rate += np.exp(  -471.085 + -27.4533*tf.T9i + -162.425*tf.T913i + 693.711*tf.T913
                  + -49.9732*tf.T9 + 3.09284*tf.T953 + -254.463*tf.lnT9)

    rate_eval.n_Na35__Na36 = rate

@numba.njit()
def n_Ti45__p_Sc45(rate_eval, tf):
    # Ti45 + n --> p + Sc45
    rate = 0.0

    # ths8r
    rate += np.exp(  20.2443 + -1.6182*tf.T913
                  + 0.577281*tf.T9 + -0.0582774*tf.T953)

    rate_eval.n_Ti45__p_Sc45 = rate

@numba.njit()
def He4_Ti43__p_V46(rate_eval, tf):
    # Ti43 + He4 --> p + V46
    rate = 0.0

    # ths8r
    rate += np.exp(  58.6358 + -81.6147*tf.T913i + -1.14195*tf.T913
                  + -0.422296*tf.T9 + 0.00129531*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti43__p_V46 = rate

@numba.njit()
def n_Ti43__He4_Ca40(rate_eval, tf):
    # Ti43 + n --> He4 + Ca40
    rate = 0.0

    # ths8r
    rate += np.exp(  18.5905 + -0.195471*tf.T913
                  + 0.0674919*tf.T9 + 0.00712608*tf.T953)

    rate_eval.n_Ti43__He4_Ca40 = rate

@numba.njit()
def He4_F28__n_Na31(rate_eval, tf):
    # F28 + He4 --> n + Na31
    rate = 0.0

    # rpsmr
    rate += np.exp(  65.8444 + -2.56615*tf.T9i + 52.141*tf.T913i + -121.81*tf.T913
                  + 5.5056*tf.T9 + -0.269289*tf.T953 + 63.9552*tf.lnT9)

    rate_eval.He4_F28__n_Na31 = rate

@numba.njit()
def He4_F31__n_Na34(rate_eval, tf):
    # F31 + He4 --> n + Na34
    rate = 0.0

    # rpsmr
    rate += np.exp(  70.2562 + -2.76505*tf.T9i + 61.1517*tf.T913i + -135.264*tf.T913
                  + 6.16538*tf.T9 + -0.299277*tf.T953 + 70.6457*tf.lnT9)

    rate_eval.He4_F31__n_Na34 = rate

@numba.njit()
def n_Ti41__He4_Ca38(rate_eval, tf):
    # Ti41 + n --> He4 + Ca38
    rate = 0.0

    # ths8r
    rate += np.exp(  15.738 + 0.382387*tf.T913
                  + -0.0265151*tf.T9 + 0.0262384*tf.T953)

    rate_eval.n_Ti41__He4_Ca38 = rate

@numba.njit()
def n_Ti41__p_Sc41(rate_eval, tf):
    # Ti41 + n --> p + Sc41
    rate = 0.0

    # ths8r
    rate += np.exp(  20.7008 + -0.435315*tf.T913
                  + 0.195941*tf.T9 + -0.0175409*tf.T953)

    rate_eval.n_Ti41__p_Sc41 = rate

@numba.njit()
def He4_Ti40__p_V43(rate_eval, tf):
    # Ti40 + He4 --> p + V43
    rate = 0.0

    # ths8r
    rate += np.exp(  58.1621 + -81.4428*tf.T913i + -1.03371*tf.T913
                  + -0.443809*tf.T9 + 0.0080546*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti40__p_V43 = rate

@numba.njit()
def n_K55__K56(rate_eval, tf):
    # K55 + n --> K56
    rate = 0.0

    # rath 
    rate += np.exp(  17.0572 + -0.0611973*tf.T9i + 5.81455*tf.T913i + -17.2695*tf.T913
                  + 1.65342*tf.T9 + -0.134453*tf.T953 + 5.69124*tf.lnT9)

    rate_eval.n_K55__K56 = rate

@numba.njit()
def p_Cr55__n_Mn55(rate_eval, tf):
    # Cr55 + p --> n + Mn55
    rate = 0.0

    # rath 
    rate += np.exp(  129.895 + -6.33134*tf.T9i + 234.432*tf.T913i + -376.509*tf.T913
                  + 20.722*tf.T9 + -1.17059*tf.T953 + 189.935*tf.lnT9)

    rate_eval.p_Cr55__n_Mn55 = rate

@numba.njit()
def p_F31__He4_O28(rate_eval, tf):
    # F31 + p --> He4 + O28
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.3002 + -2.51603*tf.T9i + 88.6434*tf.T913i + -148.224*tf.T913
                  + 7.9198*tf.T9 + -0.420208*tf.T953 + 74.7343*tf.lnT9)

    rate_eval.p_F31__He4_O28 = rate

@numba.njit()
def He4_Ti39__p_V42(rate_eval, tf):
    # Ti39 + He4 --> p + V42
    rate = 0.0

    # ths8r
    rate += np.exp(  58.2902 + -81.3803*tf.T913i + -1.17167*tf.T913
                  + -0.443349*tf.T9 + 0.0108529*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti39__p_V42 = rate

@numba.njit()
def n_Ti39__p_Sc39(rate_eval, tf):
    # Ti39 + n --> p + Sc39
    rate = 0.0

    # ths8r
    rate += np.exp(  20.4692 + -0.113431*tf.T913
                  + 0.116686*tf.T9 + -0.00974852*tf.T953)

    rate_eval.n_Ti39__p_Sc39 = rate

@numba.njit()
def He4_Ti38__p_V41(rate_eval, tf):
    # Ti38 + He4 --> p + V41
    rate = 0.0

    # ths8r
    rate += np.exp(  57.8741 + -81.3145*tf.T913i + -1.04661*tf.T913
                  + -0.416359*tf.T9 + 0.00621366*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti38__p_V41 = rate

@numba.njit()
def n_Ti38__He4_Ca35(rate_eval, tf):
    # Ti38 + n --> He4 + Ca35
    rate = 0.0

    # ths8r
    rate += np.exp(  13.5418 + 1.81677*tf.T913
                  + -0.314025*tf.T9 + 0.0450868*tf.T953)

    rate_eval.n_Ti38__He4_Ca35 = rate

@numba.njit()
def n_Ti38__p_Sc38(rate_eval, tf):
    # Ti38 + n --> p + Sc38
    rate = 0.0

    # ths8r
    rate += np.exp(  20.4355 + -0.136901*tf.T913
                  + 0.142987*tf.T9 + -0.0143227*tf.T953)

    rate_eval.n_Ti38__p_Sc38 = rate

@numba.njit()
def He4_Ti37__p_V40(rate_eval, tf):
    # Ti37 + He4 --> p + V40
    rate = 0.0

    # ths8r
    rate += np.exp(  57.7678 + -81.2459*tf.T913i + -1.12457*tf.T913
                  + -0.390635*tf.T9 + 0.00486405*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti37__p_V40 = rate

@numba.njit()
def Ti65__n_V64__weak__mp17(rate_eval, tf):
    # Ti65 --> n + V64
    rate = 0.0

    # mp17w
    rate += np.exp(  4.2701)

    rate_eval.Ti65__n_V64__weak__mp17 = rate

@numba.njit()
def He4_Sc62__n_V65(rate_eval, tf):
    # Sc62 + He4 --> n + V65
    rate = 0.0

    # rath 
    rate += np.exp(  -1060.75 + 17.0804*tf.T9i + -1847.24*tf.T913i + 3040.13*tf.T913
                  + -181.109*tf.T9 + 10.3779*tf.T953 + -1428.38*tf.lnT9)

    rate_eval.He4_Sc62__n_V65 = rate

@numba.njit()
def He4_Sc61__n_V64(rate_eval, tf):
    # Sc61 + He4 --> n + V64
    rate = 0.0

    # rath 
    rate += np.exp(  -1049.1 + 16.7134*tf.T9i + -1814.37*tf.T913i + 2993.06*tf.T913
                  + -179.007*tf.T9 + 10.2842*tf.T953 + -1403.29*tf.lnT9)

    rate_eval.He4_Sc61__n_V64 = rate

@numba.njit()
def p_Sc61__n_Ti61(rate_eval, tf):
    # Sc61 + p --> n + Ti61
    rate = 0.0

    # rath 
    rate += np.exp(  129.666 + -6.09959*tf.T9i + 229.503*tf.T913i + -368.286*tf.T913
                  + 20.1203*tf.T9 + -1.1209*tf.T953 + 185.117*tf.lnT9)

    rate_eval.p_Sc61__n_Ti61 = rate

@numba.njit()
def He4_Sc40__p_Ti43(rate_eval, tf):
    # Sc40 + He4 --> p + Ti43
    rate = 0.0

    # ths8r
    rate += np.exp(  57.4355 + -78.955*tf.T913i + -1.01222*tf.T913
                  + -0.448952*tf.T9 + 0.00782836*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc40__p_Ti43 = rate

@numba.njit()
def He4_Sc60__n_V63(rate_eval, tf):
    # Sc60 + He4 --> n + V63
    rate = 0.0

    # rath 
    rate += np.exp(  -1039.24 + 16.6813*tf.T9i + -1807.7*tf.T913i + 2975.75*tf.T913
                  + -177.636*tf.T9 + 10.1939*tf.T953 + -1396.85*tf.lnT9)

    rate_eval.He4_Sc60__n_V63 = rate

@numba.njit()
def Ne34__n_n_n_Na31__weak__mo03(rate_eval, tf):
    # Ne34 --> 3 n + Na31
    rate = 0.0

    # mo03w
    rate += np.exp(  3.90682)

    rate_eval.Ne34__n_n_n_Na31__weak__mo03 = rate

@numba.njit()
def p_Sc60__He4_Ca57(rate_eval, tf):
    # Sc60 + p --> He4 + Ca57
    rate = 0.0

    # rath 
    rate += np.exp(  110.959 + -6.05556*tf.T9i + 227.631*tf.T913i + -362.086*tf.T913
                  + 19.8528*tf.T9 + -1.0618*tf.T953 + 183.411*tf.lnT9)

    rate_eval.p_Sc60__He4_Ca57 = rate

@numba.njit()
def p_Sc60__n_Ti60(rate_eval, tf):
    # Sc60 + p --> n + Ti60
    rate = 0.0

    # rath 
    rate += np.exp(  131.298 + -6.06127*tf.T9i + 228.678*tf.T913i + -369.033*tf.T913
                  + 20.1766*tf.T9 + -1.12144*tf.T953 + 185.047*tf.lnT9)

    rate_eval.p_Sc60__n_Ti60 = rate

@numba.njit()
def n_Fe48__p_Mn48(rate_eval, tf):
    # Fe48 + n --> p + Mn48
    rate = 0.0

    # ths8r
    rate += np.exp(  22.0173 + -1.24123*tf.T913
                  + 0.345246*tf.T9 + -0.0336185*tf.T953)

    rate_eval.n_Fe48__p_Mn48 = rate

@numba.njit()
def He4_Sc59__n_V62(rate_eval, tf):
    # Sc59 + He4 --> n + V62
    rate = 0.0

    # rath 
    rate += np.exp(  -1029.78 + 16.4853*tf.T9i + -1788.46*tf.T913i + 2945.48*tf.T913
                  + -176.028*tf.T9 + 10.1076*tf.T953 + -1381.75*tf.lnT9)

    rate_eval.He4_Sc59__n_V62 = rate

@numba.njit()
def n_Mn53__p_Cr53(rate_eval, tf):
    # Mn53 + n --> p + Cr53
    rate = 0.0

    # ths8r
    rate += np.exp(  11.6975 + 0.167386*tf.T913
                  + 1.15594*tf.T9 + -0.119143*tf.T953)

    rate_eval.n_Mn53__p_Cr53 = rate

@numba.njit()
def He4_Sc58__n_V61(rate_eval, tf):
    # Sc58 + He4 --> n + V61
    rate = 0.0

    # rath 
    rate += np.exp(  -1019.13 + 16.3613*tf.T9i + -1774.79*tf.T913i + 2919.95*tf.T913
                  + -174.393*tf.T9 + 10.0109*tf.T953 + -1370.39*tf.lnT9)

    rate_eval.He4_Sc58__n_V61 = rate

@numba.njit()
def p_Sc58__He4_Ca55(rate_eval, tf):
    # Sc58 + p --> He4 + Ca55
    rate = 0.0

    # rath 
    rate += np.exp(  112.691 + -5.94583*tf.T9i + 222.07*tf.T913i + -356.165*tf.T913
                  + 19.6325*tf.T9 + -1.06025*tf.T953 + 179.523*tf.lnT9)

    rate_eval.p_Sc58__He4_Ca55 = rate

@numba.njit()
def p_Sc58__n_Ti58(rate_eval, tf):
    # Sc58 + p --> n + Ti58
    rate = 0.0

    # rath 
    rate += np.exp(  128.08 + -5.96495*tf.T9i + 223.997*tf.T913i + -360.822*tf.T913
                  + 19.6628*tf.T9 + -1.09217*tf.T953 + 181.356*tf.lnT9)

    rate_eval.p_Sc58__n_Ti58 = rate

@numba.njit()
def He4_Sc57__n_V60(rate_eval, tf):
    # Sc57 + He4 --> n + V60
    rate = 0.0

    # rath 
    rate += np.exp(  -1010.73 + 16.1977*tf.T9i + -1758.25*tf.T913i + 2893.53*tf.T913
                  + -172.929*tf.T9 + 9.92951*tf.T953 + -1357.38*tf.lnT9)

    rate_eval.He4_Sc57__n_V60 = rate

@numba.njit()
def Cr58__Mn58__weak__wc12(rate_eval, tf):
    # Cr58 --> Mn58
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.31242)

    rate_eval.Cr58__Mn58__weak__wc12 = rate

@numba.njit()
def He4_Sc56__n_V59(rate_eval, tf):
    # Sc56 + He4 --> n + V59
    rate = 0.0

    # rath 
    rate += np.exp(  -1003.59 + 16.137*tf.T9i + -1749.85*tf.T913i + 2877.18*tf.T913
                  + -171.837*tf.T9 + 9.8636*tf.T953 + -1350.31*tf.lnT9)

    rate_eval.He4_Sc56__n_V59 = rate

@numba.njit()
def He4_Sc55__n_V58(rate_eval, tf):
    # Sc55 + He4 --> n + V58
    rate = 0.0

    # rath 
    rate += np.exp(  -994.76 + 15.9478*tf.T9i + -1731.29*tf.T913i + 2848.14*tf.T913
                  + -170.261*tf.T9 + 9.77735*tf.T953 + -1335.84*tf.lnT9)

    rate_eval.He4_Sc55__n_V58 = rate

@numba.njit()
def p_Sc55__He4_Ca52(rate_eval, tf):
    # Sc55 + p --> He4 + Ca52
    rate = 0.0

    # rath 
    rate += np.exp(  111.662 + -5.79596*tf.T9i + 215.095*tf.T913i + -345.142*tf.T913
                  + 19.017*tf.T9 + -1.0431*tf.T953 + 174.308*tf.lnT9)

    rate_eval.p_Sc55__He4_Ca52 = rate

@numba.njit()
def n_Cr41__Cr42(rate_eval, tf):
    # Cr41 + n --> Cr42
    rate = 0.0

    # ths8r
    rate += np.exp(  9.29573 + 0.590266*tf.T913
                  + 0.0774057*tf.T9 + -0.00974136*tf.T953)

    rate_eval.n_Cr41__Cr42 = rate

@numba.njit()
def He4_Sc54__n_V57(rate_eval, tf):
    # Sc54 + He4 --> n + V57
    rate = 0.0

    # rath 
    rate += np.exp(  -983.628 + 15.902*tf.T9i + -1723.16*tf.T913i + 2827.77*tf.T913
                  + -168.632*tf.T9 + 9.66754*tf.T953 + -1328.13*tf.lnT9)

    rate_eval.He4_Sc54__n_V57 = rate

@numba.njit()
def p_Sc54__n_Ti54(rate_eval, tf):
    # Sc54 + p --> n + Ti54
    rate = 0.0

    # rath 
    rate += np.exp(  125.289 + -5.7638*tf.T9i + 215.079*tf.T913i + -349.334*tf.T913
                  + 19.2485*tf.T9 + -1.08155*tf.T953 + 175.179*tf.lnT9)

    rate_eval.p_Sc54__n_Ti54 = rate

@numba.njit()
def n_Ar36__He4_S33(rate_eval, tf):
    # Ar36 + n --> He4 + S33
    rate = 0.0

    # ths8r
    rate += np.exp(  3.04033 + 5.44923*tf.T913
                  + 1.17359*tf.T9 + -0.175811*tf.T953)

    rate_eval.n_Ar36__He4_S33 = rate

@numba.njit()
def He4_Sc52__n_V55(rate_eval, tf):
    # Sc52 + He4 --> n + V55
    rate = 0.0

    # rath 
    rate += np.exp(  -967.065 + 15.5566*tf.T9i + -1688.47*tf.T913i + 2773.54*tf.T913
                  + -165.749*tf.T9 + 9.51523*tf.T953 + -1301.08*tf.lnT9)

    rate_eval.He4_Sc52__n_V55 = rate

@numba.njit()
def p_Sc52__He4_Ca49(rate_eval, tf):
    # Sc52 + p --> He4 + Ca49
    rate = 0.0

    # rath 
    rate += np.exp(  115.419 + -5.72184*tf.T9i + 215.683*tf.T913i + -347.332*tf.T913
                  + 18.2843*tf.T9 + -0.909461*tf.T953 + 175.665*tf.lnT9)

    rate_eval.p_Sc52__He4_Ca49 = rate

@numba.njit()
def p_S47__Cl48(rate_eval, tf):
    # S47 + p --> Cl48
    rate = 0.0

    # rath 
    rate += np.exp(  92.0956 + -4.53666*tf.T9i + 168.441*tf.T913i + -274.086*tf.T913
                  + 14.7667*tf.T9 + -0.804162*tf.T953 + 137.997*tf.lnT9)

    rate_eval.p_S47__Cl48 = rate

@numba.njit()
def He4_C9__p_N12(rate_eval, tf):
    # C9 + He4 --> p + N12
    rate = 0.0

    # wiesr
    rate += np.exp(  12.0436 + -14.08*tf.T9i
                  + -1.5*tf.lnT9)
    # wiesr
    rate += np.exp(  4.03954 + -5.292*tf.T9i
                  + -1.5*tf.lnT9)
    # wiesn
    rate += np.exp(  35.0504 + -31.272*tf.T913i + -0.623937*tf.T913
                  + 11.6326*tf.T9 + -19.1574*tf.T953 + 0.333333*tf.lnT9)
    # wiesn
    rate += np.exp(  35.0504 + -31.272*tf.T913i + -0.63045*tf.T913
                  + -18.1435*tf.T9 + -1.94515*tf.T953 + -0.666667*tf.lnT9)
    # wiesr
    rate += np.exp(  17.993 + -23.09*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.He4_C9__p_N12 = rate

@numba.njit()
def p_Sc52__n_Ti52(rate_eval, tf):
    # Sc52 + p --> n + Ti52
    rate = 0.0

    # rath 
    rate += np.exp(  121.927 + -5.66696*tf.T9i + 210.515*tf.T913i + -341.638*tf.T913
                  + 18.8721*tf.T9 + -1.06395*tf.T953 + 171.572*tf.lnT9)

    rate_eval.p_Sc52__n_Ti52 = rate

@numba.njit()
def He4_Sc51__n_V54(rate_eval, tf):
    # Sc51 + He4 --> n + V54
    rate = 0.0

    # rath 
    rate += np.exp(  -958.007 + 15.3895*tf.T9i + -1671.44*tf.T913i + 2745.87*tf.T913
                  + -164.178*tf.T9 + 9.42788*tf.T953 + -1287.64*tf.lnT9)

    rate_eval.He4_Sc51__n_V54 = rate

@numba.njit()
def p_Sc50__n_Ti50(rate_eval, tf):
    # Sc50 + p --> n + Ti50
    rate = 0.0

    # rath 
    rate += np.exp(  120.45 + -5.56968*tf.T9i + 206.419*tf.T913i + -336.131*tf.T913
                  + 18.5966*tf.T9 + -1.04704*tf.T953 + 168.679*tf.lnT9)

    rate_eval.p_Sc50__n_Ti50 = rate

@numba.njit()
def He4_Ar29__Ca33(rate_eval, tf):
    # Ar29 + He4 --> Ca33
    rate = 0.0

    # ths8r
    rate += np.exp(  40.6154 + -70.4479*tf.T913i + -0.338552*tf.T913
                  + -0.410332*tf.T9 + 0.000116775*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar29__Ca33 = rate

@numba.njit()
def p_Sc49__He4_Ca46(rate_eval, tf):
    # Sc49 + p --> He4 + Ca46
    rate = 0.0

    # rath 
    rate += np.exp(  73.2396 + -5.66716*tf.T9i + 218.203*tf.T913i + -316.114*tf.T913
                  + 14.9186*tf.T9 + -0.720017*tf.T953 + 174.788*tf.lnT9)

    rate_eval.p_Sc49__He4_Ca46 = rate

@numba.njit()
def p_Sc48__He4_Ca45(rate_eval, tf):
    # Sc48 + p --> He4 + Ca45
    rate = 0.0

    # rath 
    rate += np.exp(  72.7227 + -5.86977*tf.T9i + 239.338*tf.T913i + -335.863*tf.T913
                  + 14.1283*tf.T9 + -0.596544*tf.T953 + 190.967*tf.lnT9)

    rate_eval.p_Sc48__He4_Ca45 = rate

@numba.njit()
def He4_Sc47__p_Ti50(rate_eval, tf):
    # Sc47 + He4 --> p + Ti50
    rate = 0.0

    # rath 
    rate += np.exp(  -980.428 + 14.926*tf.T9i + -1637.36*tf.T913i + 2730.59*tf.T913
                  + -164.393*tf.T9 + 9.47988*tf.T953 + -1271.98*tf.lnT9)

    rate_eval.He4_Sc47__p_Ti50 = rate

@numba.njit()
def p_Sc47__He4_Ca44(rate_eval, tf):
    # Sc47 + p --> He4 + Ca44
    rate = 0.0

    # rath 
    rate += np.exp(  74.4575 + -5.79201*tf.T9i + 224.282*tf.T913i + -318.978*tf.T913
                  + 15.9466*tf.T9 + -0.877308*tf.T953 + 174.938*tf.lnT9)

    rate_eval.p_Sc47__He4_Ca44 = rate

@numba.njit()
def He4_Sc46__p_Ti49(rate_eval, tf):
    # Sc46 + He4 --> p + Ti49
    rate = 0.0

    # rath 
    rate += np.exp(  -938.441 + 14.7159*tf.T9i + -1603.15*tf.T913i + 2650.58*tf.T913
                  + -159.776*tf.T9 + 9.24163*tf.T953 + -1237.15*tf.lnT9)

    rate_eval.He4_Sc46__p_Ti49 = rate

@numba.njit()
def p_Sc46__He4_Ca43(rate_eval, tf):
    # Sc46 + p --> He4 + Ca43
    rate = 0.0

    # rath 
    rate += np.exp(  70.6373 + -5.26809*tf.T9i + 189.856*tf.T913i + -278.908*tf.T913
                  + 13.9142*tf.T9 + -0.770736*tf.T953 + 153.141*tf.lnT9)

    rate_eval.p_Sc46__He4_Ca43 = rate

@numba.njit()
def n_Sc46__p_Ca46(rate_eval, tf):
    # Sc46 + n --> p + Ca46
    rate = 0.0

    # rath 
    rate += np.exp(  74.17 + -0.632473*tf.T9i + 65.2318*tf.T913i + -132.177*tf.T913
                  + 8.05925*tf.T9 + -0.425861*tf.T953 + 59.0907*tf.lnT9)

    rate_eval.n_Sc46__p_Ca46 = rate

@numba.njit()
def n_V56__V57(rate_eval, tf):
    # V56 + n --> V57
    rate = 0.0

    # rath 
    rate += np.exp(  19.2063 + -0.0300554*tf.T9i + 3.02609*tf.T913i + -8.69678*tf.T913
                  + 0.506788*tf.T9 + -0.0512755*tf.T953 + 3.01387*tf.lnT9)

    rate_eval.n_V56__V57 = rate

@numba.njit()
def He4_Sc45__p_Ti48(rate_eval, tf):
    # Sc45 + He4 --> p + Ti48
    rate = 0.0

    # ths8r
    rate += np.exp(  57.207 + -79.222*tf.T913i + 0.0710184*tf.T913
                  + -1.47173*tf.T9 + 0.15944*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc45__p_Ti48 = rate

@numba.njit()
def n_Si24__p_Al24(rate_eval, tf):
    # Si24 + n --> p + Al24
    rate = 0.0

    # ths8r
    rate += np.exp(  18.4448 + 2.22761*tf.T913
                  + -0.339393*tf.T9 + 0.0256302*tf.T953)

    rate_eval.n_Si24__p_Al24 = rate

@numba.njit()
def n_Mg22__He4_Ne19(rate_eval, tf):
    # Mg22 + n --> He4 + Ne19
    rate = 0.0

    # ths8r
    rate += np.exp(  16.2584 + 2.08592*tf.T913
                  + -0.188654*tf.T9 + 0.0101103*tf.T953)

    rate_eval.n_Mg22__He4_Ne19 = rate

@numba.njit()
def p_Sc45__He4_Ca42(rate_eval, tf):
    # Sc45 + p --> He4 + Ca42
    rate = 0.0

    # ths8r
    rate += np.exp(  17.8284 + -32.1843*tf.T913i + 14.0733*tf.T913
                  + -3.38786*tf.T9 + 0.349494*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc45__He4_Ca42 = rate

@numba.njit()
def n_Sc45__p_Ca45(rate_eval, tf):
    # Sc45 + n --> p + Ca45
    rate = 0.0

    # ths8r
    rate += np.exp(  -3.98017 + 14.7265*tf.T913
                  + -1.41914*tf.T9 + 0.0785177*tf.T953)

    rate_eval.n_Sc45__p_Ca45 = rate

@numba.njit()
def He4_Sc44__p_Ti47(rate_eval, tf):
    # Sc44 + He4 --> p + Ti47
    rate = 0.0

    # ths8r
    rate += np.exp(  59.5285 + -79.1731*tf.T913i + -3.93328*tf.T913
                  + 0.112908*tf.T9 + -0.0385366*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc44__p_Ti47 = rate

@numba.njit()
def p_Sc44__He4_Ca41(rate_eval, tf):
    # Sc44 + p --> He4 + Ca41
    rate = 0.0

    # ths8r
    rate += np.exp(  19.102 + -32.179*tf.T913i + 13.8907*tf.T913
                  + -3.30408*tf.T9 + 0.332186*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc44__He4_Ca41 = rate

@numba.njit()
def n_Sc44__p_Ca44(rate_eval, tf):
    # Sc44 + n --> p + Ca44
    rate = 0.0

    # ths8r
    rate += np.exp(  20.9033 + -1.95318*tf.T913
                  + 0.326277*tf.T9 + -0.0205095*tf.T953)

    rate_eval.n_Sc44__p_Ca44 = rate

@numba.njit()
def He4_Sc43__p_Ti46(rate_eval, tf):
    # Sc43 + He4 --> p + Ti46
    rate = 0.0

    # ths8r
    rate += np.exp(  57.3723 + -79.122*tf.T913i + -0.495539*tf.T913
                  + -0.618414*tf.T9 + 0.0175873*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc43__p_Ti46 = rate

@numba.njit()
def n_Sc43__He4_K40(rate_eval, tf):
    # Sc43 + n --> He4 + K40
    rate = 0.0

    # ths8r
    rate += np.exp(  10.3424 + -0.653091*tf.T913
                  + 1.79632*tf.T9 + -0.19216*tf.T953)

    rate_eval.n_Sc43__He4_K40 = rate

@numba.njit()
def n_Sc43__p_Ca43(rate_eval, tf):
    # Sc43 + n --> p + Ca43
    rate = 0.0

    # ths8r
    rate += np.exp(  19.4535 + -0.494422*tf.T913
                  + 0.261414*tf.T9 + -0.0285528*tf.T953)

    rate_eval.n_Sc43__p_Ca43 = rate

@numba.njit()
def He4_Sc42__p_Ti45(rate_eval, tf):
    # Sc42 + He4 --> p + Ti45
    rate = 0.0

    # ths8r
    rate += np.exp(  57.6956 + -79.0687*tf.T913i + -0.981235*tf.T913
                  + -0.48951*tf.T9 + 0.0114272*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc42__p_Ti45 = rate

@numba.njit()
def n_Sc42__He4_K39(rate_eval, tf):
    # Sc42 + n --> He4 + K39
    rate = 0.0

    # ths8r
    rate += np.exp(  20.4355 + -2.41191*tf.T913
                  + 0.477161*tf.T9 + -0.0129902*tf.T953)

    rate_eval.n_Sc42__He4_K39 = rate

@numba.njit()
def n_Sc42__p_Ca42(rate_eval, tf):
    # Sc42 + n --> p + Ca42
    rate = 0.0

    # ths8r
    rate += np.exp(  21.0655 + -1.56085*tf.T913
                  + 0.451674*tf.T9 + -0.0433207*tf.T953)

    rate_eval.n_Sc42__p_Ca42 = rate

@numba.njit()
def p_Cr56__n_Mn56(rate_eval, tf):
    # Cr56 + p --> n + Mn56
    rate = 0.0

    # rath 
    rate += np.exp(  132.525 + -6.40137*tf.T9i + 238.436*tf.T913i + -383.268*tf.T913
                  + 21.1075*tf.T9 + -1.19385*tf.T953 + 193.114*tf.lnT9)

    rate_eval.p_Cr56__n_Mn56 = rate

@numba.njit()
def n_Sc41__He4_K38(rate_eval, tf):
    # Sc41 + n --> He4 + K38
    rate = 0.0

    # ths8r
    rate += np.exp(  15.843 + 1.40375*tf.T913
                  + -0.354997*tf.T9 + 0.0693393*tf.T953)

    rate_eval.n_Sc41__He4_K38 = rate

@numba.njit()
def p_Si36__He4_Al33(rate_eval, tf):
    # Si36 + p --> He4 + Al33
    rate = 0.0

    # rath 
    rate += np.exp(  63.5181 + -3.85488*tf.T9i + 154.833*tf.T913i + -232.698*tf.T913
                  + 10.4388*tf.T9 + -0.477846*tf.T953 + 128.564*tf.lnT9)

    rate_eval.p_Si36__He4_Al33 = rate

@numba.njit()
def He4_Sc39__p_Ti42(rate_eval, tf):
    # Sc39 + He4 --> p + Ti42
    rate = 0.0

    # ths8r
    rate += np.exp(  57.2081 + -78.8941*tf.T913i + -0.997143*tf.T913
                  + -0.438738*tf.T9 + 0.00785094*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc39__p_Ti42 = rate

@numba.njit()
def p_P31__S32(rate_eval, tf):
    # P31 + p --> S32
    rate = 0.0

    # il10r
    rate += np.exp(  0.821556 + -3.77704*tf.T9i + 8.09341*tf.T913
                  + -0.615971*tf.T9 + 0.031159*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -2.66839 + -2.25958*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  19.2596 + -25.3278*tf.T913i + 6.4931*tf.T913
                  + -9.27513*tf.T9 + -0.610439*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_P31__S32 = rate

@numba.njit()
def n_Sc39__He4_K36(rate_eval, tf):
    # Sc39 + n --> He4 + K36
    rate = 0.0

    # ths8r
    rate += np.exp(  13.3101 + 2.4921*tf.T913
                  + -0.532733*tf.T9 + 0.0631129*tf.T953)

    rate_eval.n_Sc39__He4_K36 = rate

@numba.njit()
def p_Si45__P46(rate_eval, tf):
    # Si45 + p --> P46
    rate = 0.0

    # rath 
    rate += np.exp(  84.0805 + -4.04455*tf.T9i + 148.714*tf.T913i + -243.803*tf.T913
                  + 13.1769*tf.T9 + -0.720405*tf.T953 + 122.383*tf.lnT9)

    rate_eval.p_Si45__P46 = rate

@numba.njit()
def He4_Sc38__p_Ti41(rate_eval, tf):
    # Sc38 + He4 --> p + Ti41
    rate = 0.0

    # ths8r
    rate += np.exp(  57.4703 + -78.8304*tf.T913i + -1.17649*tf.T913
                  + -0.449846*tf.T9 + 0.0124757*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc38__p_Ti41 = rate

@numba.njit()
def n_Ti47__He4_Ca44(rate_eval, tf):
    # Ti47 + n --> He4 + Ca44
    rate = 0.0

    # ths8r
    rate += np.exp(  -3.94695 + 4.6504*tf.T913
                  + 2.25932*tf.T9 + -0.286843*tf.T953)

    rate_eval.n_Ti47__He4_Ca44 = rate

@numba.njit()
def p_Na36__n_Mg36(rate_eval, tf):
    # Na36 + p --> n + Mg36
    rate = 0.0

    # rath 
    rate += np.exp(  79.9558 + -3.11066*tf.T9i + 112.741*tf.T913i + -188.905*tf.T913
                  + 10.3231*tf.T9 + -0.572745*tf.T953 + 94.3764*tf.lnT9)

    rate_eval.p_Na36__n_Mg36 = rate

@numba.njit()
def n_Sc37__He4_K34(rate_eval, tf):
    # Sc37 + n --> He4 + K34
    rate = 0.0

    # ths8r
    rate += np.exp(  14.1165 + 1.02388*tf.T913
                  + 0.000982349*tf.T9 + 0.00678714*tf.T953)

    rate_eval.n_Sc37__He4_K34 = rate

@numba.njit()
def He4_Sc36__p_Ti39(rate_eval, tf):
    # Sc36 + He4 --> p + Ti39
    rate = 0.0

    # ths8r
    rate += np.exp(  56.9288 + -78.6932*tf.T913i + -1.07636*tf.T913
                  + -0.414773*tf.T9 + 0.00798428*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc36__p_Ti39 = rate

@numba.njit()
def Mg36__n_n_Al34__weak__mp17(rate_eval, tf):
    # Mg36 --> n + n + Al34
    rate = 0.0

    # mp17w
    rate += np.exp(  0.575096)

    rate_eval.Mg36__n_n_Al34__weak__mp17 = rate

@numba.njit()
def He4_Sc35__p_Ti38(rate_eval, tf):
    # Sc35 + He4 --> p + Ti38
    rate = 0.0

    # ths8r
    rate += np.exp(  56.5879 + -78.6193*tf.T913i + -0.982362*tf.T913
                  + -0.398633*tf.T9 + 0.00532429*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc35__p_Ti38 = rate

@numba.njit()
def n_Sc35__He4_K32(rate_eval, tf):
    # Sc35 + n --> He4 + K32
    rate = 0.0

    # ths8r
    rate += np.exp(  11.7358 + 1.52461*tf.T913
                  + -0.117566*tf.T9 + 0.0215375*tf.T953)

    rate_eval.n_Sc35__He4_K32 = rate

@numba.njit()
def n_Sc35__p_Ca35(rate_eval, tf):
    # Sc35 + n --> p + Ca35
    rate = 0.0

    # ths8r
    rate += np.exp(  19.939 + 0.308891*tf.T913
                  + 0.0503038*tf.T9 + -0.00448393*tf.T953)

    rate_eval.n_Sc35__p_Ca35 = rate

@numba.njit()
def p_Ca61__He4_K58(rate_eval, tf):
    # Ca61 + p --> He4 + K58
    rate = 0.0

    # rath 
    rate += np.exp(  -227.447 + -0.499232*tf.T9i + -243.077*tf.T913i + 473.543*tf.T913
                  + -33.3872*tf.T9 + 2.14053*tf.T953 + -190.812*tf.lnT9)

    rate_eval.p_Ca61__He4_K58 = rate

@numba.njit()
def p_Ca61__n_Sc61(rate_eval, tf):
    # Ca61 + p --> n + Sc61
    rate = 0.0

    # rath 
    rate += np.exp(  126.742 + -5.90592*tf.T9i + 222.329*tf.T913i + -357.042*tf.T913
                  + 19.4653*tf.T9 + -1.07866*tf.T953 + 179.355*tf.lnT9)

    rate_eval.p_Ca61__n_Sc61 = rate

@numba.njit()
def p_Ca60__n_Sc60(rate_eval, tf):
    # Ca60 + p --> n + Sc60
    rate = 0.0

    # rath 
    rate += np.exp(  125.861 + -5.86168*tf.T9i + 220.395*tf.T913i + -354.245*tf.T913
                  + 19.3571*tf.T9 + -1.07763*tf.T953 + 177.968*tf.lnT9)

    rate_eval.p_Ca60__n_Sc60 = rate

@numba.njit()
def n_Fe48__Fe49(rate_eval, tf):
    # Fe48 + n --> Fe49
    rate = 0.0

    # ths8r
    rate += np.exp(  13.9988 + -1.27601*tf.T913
                  + 0.326562*tf.T9 + -0.0442988*tf.T953)

    rate_eval.n_Fe48__Fe49 = rate

@numba.njit()
def p_Ca59__n_Sc59(rate_eval, tf):
    # Ca59 + p --> n + Sc59
    rate = 0.0

    # rath 
    rate += np.exp(  124.044 + -5.8156*tf.T9i + 218.145*tf.T913i + -349.962*tf.T913
                  + 19.021*tf.T9 + -1.05233*tf.T953 + 176.151*tf.lnT9)

    rate_eval.p_Ca59__n_Sc59 = rate

@numba.njit()
def He4_Ca58__n_Ti61(rate_eval, tf):
    # Ca58 + He4 --> n + Ti61
    rate = 0.0

    # rath 
    rate += np.exp(  -988.642 + 15.8078*tf.T9i + -1716.18*tf.T913i + 2827.54*tf.T913
                  + -169.108*tf.T9 + 9.71424*tf.T953 + -1325.84*tf.lnT9)

    rate_eval.He4_Ca58__n_Ti61 = rate

@numba.njit()
def p_Ca58__He4_K55(rate_eval, tf):
    # Ca58 + p --> He4 + K55
    rate = 0.0

    # rath 
    rate += np.exp(  -438.434 + 7.2785*tf.T9i + -819.308*tf.T913i + 1293.27*tf.T913
                  + -77.0412*tf.T9 + 4.45426*tf.T953 + -606.682*tf.lnT9)

    rate_eval.p_Ca58__He4_K55 = rate

@numba.njit()
def n_Cr46__p_V46(rate_eval, tf):
    # Cr46 + n --> p + V46
    rate = 0.0

    # ths8r
    rate += np.exp(  21.9848 + -1.49972*tf.T913
                  + 0.432805*tf.T9 + -0.0418945*tf.T953)

    rate_eval.n_Cr46__p_V46 = rate

@numba.njit()
def p_Ca58__n_Sc58(rate_eval, tf):
    # Ca58 + p --> n + Sc58
    rate = 0.0

    # rath 
    rate += np.exp(  123.032 + -5.76618*tf.T9i + 215.797*tf.T913i + -346.626*tf.T913
                  + 18.9103*tf.T9 + -1.05298*tf.T953 + 174.443*tf.lnT9)

    rate_eval.p_Ca58__n_Sc58 = rate

@numba.njit()
def He4_Al25__P29(rate_eval, tf):
    # Al25 + He4 --> P29
    rate = 0.0

    # ths8r
    rate += np.exp(  37.9099 + -56.3424*tf.T913i + 0.542998*tf.T913
                  + -0.721716*tf.T9 + 0.0469712*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al25__P29 = rate

@numba.njit()
def p_Ca56__He4_K53(rate_eval, tf):
    # Ca56 + p --> He4 + K53
    rate = 0.0

    # rath 
    rate += np.exp(  76.9237 + -5.83254*tf.T9i + 227.778*tf.T913i + -332.268*tf.T913
                  + 15.6071*tf.T9 + -0.714846*tf.T953 + 181.904*tf.lnT9)

    rate_eval.p_Ca56__He4_K53 = rate

@numba.njit()
def p_Ca55__He4_K52(rate_eval, tf):
    # Ca55 + p --> He4 + K52
    rate = 0.0

    # rath 
    rate += np.exp(  77.1416 + -5.60302*tf.T9i + 206.981*tf.T913i + -308.539*tf.T913
                  + 15.8318*tf.T9 + -0.81781*tf.T953 + 165.025*tf.lnT9)

    rate_eval.p_Ca55__He4_K52 = rate

@numba.njit()
def p_Ca55__n_Sc55(rate_eval, tf):
    # Ca55 + p --> n + Sc55
    rate = 0.0

    # rath 
    rate += np.exp(  119.407 + -5.62016*tf.T9i + 208.941*tf.T913i + -336.117*tf.T913
                  + 18.3787*tf.T9 + -1.02738*tf.T953 + 169.337*tf.lnT9)

    rate_eval.p_Ca55__n_Sc55 = rate

@numba.njit()
def He4_Ca53__n_Ti56(rate_eval, tf):
    # Ca53 + He4 --> n + Ti56
    rate = 0.0

    # rath 
    rate += np.exp(  -945.157 + 15.1653*tf.T9i + -1646.96*tf.T913i + 2708.51*tf.T913
                  + -162.016*tf.T9 + 9.3075*tf.T953 + -1269.98*tf.lnT9)

    rate_eval.He4_Ca53__n_Ti56 = rate

@numba.njit()
def He8__Li8__weak__wc12(rate_eval, tf):
    # He8 --> Li8
    rate = 0.0

    # wc12w
    rate += np.exp(  1.58776)

    rate_eval.He8__Li8__weak__wc12 = rate

@numba.njit()
def p_Ca52__n_Sc52(rate_eval, tf):
    # Ca52 + p --> n + Sc52
    rate = 0.0

    # rath 
    rate += np.exp(  117.976 + -5.4845*tf.T9i + 203.485*tf.T913i + -329.448*tf.T913
                  + 18.1344*tf.T9 + -1.01884*tf.T953 + 165.659*tf.lnT9)

    rate_eval.p_Ca52__n_Sc52 = rate

@numba.njit()
def p_P45__S46(rate_eval, tf):
    # P45 + p --> S46
    rate = 0.0

    # rath 
    rate += np.exp(  87.3953 + -4.24875*tf.T9i + 156.749*tf.T913i + -256.359*tf.T913
                  + 13.9073*tf.T9 + -0.766565*tf.T953 + 128.869*tf.lnT9)

    rate_eval.p_P45__S46 = rate

@numba.njit()
def p_Cr56__He4_V53(rate_eval, tf):
    # Cr56 + p --> He4 + V53
    rate = 0.0

    # rath 
    rate += np.exp(  -104.787 + -4.82681*tf.T9i + 68.971*tf.T913i + 31.7713*tf.T913
                  + -11.8858*tf.T9 + 1.0916*tf.T953 + 37.6028*tf.lnT9)

    rate_eval.p_Cr56__He4_V53 = rate

@numba.njit()
def He4_Ca51__n_Ti54(rate_eval, tf):
    # Ca51 + He4 --> n + Ti54
    rate = 0.0

    # rath 
    rate += np.exp(  -926.683 + 14.897*tf.T9i + -1618.0*tf.T913i + 2658.38*tf.T913
                  + -158.996*tf.T9 + 9.13187*tf.T953 + -1246.54*tf.lnT9)

    rate_eval.He4_Ca51__n_Ti54 = rate

@numba.njit()
def p_Ca51__He4_K48(rate_eval, tf):
    # Ca51 + p --> He4 + K48
    rate = 0.0

    # rath 
    rate += np.exp(  97.0062 + -5.80159*tf.T9i + 243.953*tf.T913i + -370.396*tf.T913
                  + 17.67*tf.T9 + -0.859615*tf.T953 + 200.653*tf.lnT9)

    rate_eval.p_Ca51__He4_K48 = rate

@numba.njit()
def n_Si24__He4_Mg21(rate_eval, tf):
    # Si24 + n --> He4 + Mg21
    rate = 0.0

    # ths8r
    rate += np.exp(  14.52 + 2.08623*tf.T913
                  + -0.283593*tf.T9 + 0.0231677*tf.T953)

    rate_eval.n_Si24__He4_Mg21 = rate

@numba.njit()
def p_Al39__He4_Mg36(rate_eval, tf):
    # Al39 + p --> He4 + Mg36
    rate = 0.0

    # rath 
    rate += np.exp(  71.5558 + -3.57933*tf.T9i + 128.07*tf.T913i + -207.897*tf.T913
                  + 11.1104*tf.T9 + -0.589493*tf.T953 + 105.709*tf.lnT9)

    rate_eval.p_Al39__He4_Mg36 = rate

@numba.njit()
def He4_Ca47__n_Ti50(rate_eval, tf):
    # Ca47 + He4 --> n + Ti50
    rate = 0.0

    # ths8r
    rate += np.exp(  57.426 + -76.7758*tf.T913i + -0.981924*tf.T913
                  + -0.52791*tf.T9 + 0.0150723*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca47__n_Ti50 = rate

@numba.njit()
def p_Ca47__n_Sc47(rate_eval, tf):
    # Ca47 + p --> n + Sc47
    rate = 0.0

    # ths8r
    rate += np.exp(  34.8341 + -31.164*tf.T913i + -0.314533*tf.T913
                  + -0.0979736*tf.T9 + 0.00385901*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ca47__n_Sc47 = rate

@numba.njit()
def S45__n_Cl44__weak__wc12(rate_eval, tf):
    # S45 --> n + Cl44
    rate = 0.0

    # wc12w
    rate += np.exp(  1.70555)

    rate_eval.S45__n_Cl44__weak__wc12 = rate

@numba.njit()
def C12_C12__He4_Ne20(rate_eval, tf):
    # C12 + C12 --> He4 + Ne20
    rate = 0.0

    # cf88r
    rate += np.exp(  61.2863 + -84.165*tf.T913i + -1.56627*tf.T913
                  + -0.0736084*tf.T9 + -0.072797*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.C12_C12__He4_Ne20 = rate

@numba.njit()
def He4_Ca57__n_Ti60(rate_eval, tf):
    # Ca57 + He4 --> n + Ti60
    rate = 0.0

    # rath 
    rate += np.exp(  -981.031 + 15.7028*tf.T9i + -1704.4*tf.T913i + 2807.21*tf.T913
                  + -167.895*tf.T9 + 9.64364*tf.T953 + -1316.33*tf.lnT9)

    rate_eval.He4_Ca57__n_Ti60 = rate

@numba.njit()
def He4_Ca43__n_Ti46(rate_eval, tf):
    # Ca43 + He4 --> n + Ti46
    rate = 0.0

    # ths8r
    rate += np.exp(  53.4643 + -76.5897*tf.T913i + 3.69244*tf.T913
                  + -1.90131*tf.T9 + 0.171994*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca43__n_Ti46 = rate

@numba.njit()
def O24__F24__weak__wc12(rate_eval, tf):
    # O24 --> F24
    rate = 0.0

    # wc12w
    rate += np.exp(  1.49935)

    rate_eval.O24__F24__weak__wc12 = rate

@numba.njit()
def He4_Ti45__p_V48(rate_eval, tf):
    # Ti45 + He4 --> p + V48
    rate = 0.0

    # ths8r
    rate += np.exp(  54.1979 + -81.7175*tf.T913i + 5.07471*tf.T913
                  + -2.34907*tf.T9 + 0.226169*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti45__p_V48 = rate

@numba.njit()
def Na39__n_Mg38__weak__mp17(rate_eval, tf):
    # Na39 --> n + Mg38
    rate = 0.0

    # mp17w
    rate += np.exp(  5.00977)

    rate_eval.Na39__n_Mg38__weak__mp17 = rate

@numba.njit()
def p_Ca42__He4_K39(rate_eval, tf):
    # Ca42 + p --> He4 + K39
    rate = 0.0

    # ths8r
    rate += np.exp(  -78.212 + -31.1381*tf.T913i + 117.868*tf.T913
                  + -27.0455*tf.T9 + 2.75661*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ca42__He4_K39 = rate

@numba.njit()
def n_Mn43__He4_V40(rate_eval, tf):
    # Mn43 + n --> He4 + V40
    rate = 0.0

    # ths8r
    rate += np.exp(  14.8919 + 0.0254304*tf.T913
                  + 0.0671978*tf.T9 + 0.0133268*tf.T953)

    rate_eval.n_Mn43__He4_V40 = rate

@numba.njit()
def He4_F16__Na20(rate_eval, tf):
    # F16 + He4 --> Na20
    rate = 0.0

    # rpsmr
    rate += np.exp(  39.9493 + -1.72407*tf.T9i + 19.3405*tf.T913i + -72.9392*tf.T913
                  + 2.63998*tf.T9 + -0.100006*tf.T953 + 40.0259*tf.lnT9)

    rate_eval.He4_F16__Na20 = rate

@numba.njit()
def n_Ca40__He4_Ar37(rate_eval, tf):
    # Ca40 + n --> He4 + Ar37
    rate = 0.0

    # ths8r
    rate += np.exp(  -9.43576 + 13.8882*tf.T913
                  + 0.260223*tf.T9 + -0.108063*tf.T953)

    rate_eval.n_Ca40__He4_Ar37 = rate

@numba.njit()
def p_P42__n_S42(rate_eval, tf):
    # P42 + p --> n + S42
    rate = 0.0

    # rath 
    rate += np.exp(  96.5215 + -4.10871*tf.T9i + 150.54*tf.T913i + -248.512*tf.T913
                  + 13.613*tf.T9 + -0.757924*tf.T953 + 124.543*tf.lnT9)

    rate_eval.p_P42__n_S42 = rate

@numba.njit()
def He4_V63__n_Mn66(rate_eval, tf):
    # V63 + He4 --> n + Mn66
    rate = 0.0

    # rath 
    rate += np.exp(  -1130.97 + 18.0204*tf.T9i + -1955.26*tf.T913i + 3223.91*tf.T913
                  + -192.467*tf.T9 + 11.0425*tf.T953 + -1512.45*tf.lnT9)

    rate_eval.He4_V63__n_Mn66 = rate

@numba.njit()
def n_Ca38__p_K38(rate_eval, tf):
    # Ca38 + n --> p + K38
    rate = 0.0

    # ths8r
    rate += np.exp(  19.6123 + 0.26913*tf.T913
                  + 0.0847781*tf.T9 + -0.00889117*tf.T953)

    rate_eval.n_Ca38__p_K38 = rate

@numba.njit()
def He4_Fe66__n_Ni69(rate_eval, tf):
    # Fe66 + He4 --> n + Ni69
    rate = 0.0

    # rath 
    rate += np.exp(  -1207.57 + 25.1398*tf.T9i + -2498.07*tf.T913i + 3857.37*tf.T913
                  + -218.666*tf.T9 + 12.0989*tf.T953 + -1870.77*tf.lnT9)

    rate_eval.He4_Fe66__n_Ni69 = rate

@numba.njit()
def Ca53__n_Sc52__weak__wc12(rate_eval, tf):
    # Ca53 --> n + Sc52
    rate = 0.0

    # wc12w
    rate += np.exp(  0.83746)

    rate_eval.Ca53__n_Sc52__weak__wc12 = rate

@numba.njit()
def n_Ca37__He4_Ar34(rate_eval, tf):
    # Ca37 + n --> He4 + Ar34
    rate = 0.0

    # ths8r
    rate += np.exp(  17.1109 + -0.44039*tf.T913
                  + 0.143523*tf.T9 + 0.0047869*tf.T953)

    rate_eval.n_Ca37__He4_Ar34 = rate

@numba.njit()
def n_Ca37__p_K37(rate_eval, tf):
    # Ca37 + n --> p + K37
    rate = 0.0

    # ths8r
    rate += np.exp(  19.6017 + 0.432093*tf.T913
                  + 0.0436066*tf.T9 + -0.00558044*tf.T953)

    rate_eval.n_Ca37__p_K37 = rate

@numba.njit()
def n_Ca36__p_K36(rate_eval, tf):
    # Ca36 + n --> p + K36
    rate = 0.0

    # ths8r
    rate += np.exp(  19.6162 + 0.415205*tf.T913
                  + 0.0597582*tf.T9 + -0.00804379*tf.T953)

    rate_eval.n_Ca36__p_K36 = rate

@numba.njit()
def n_Cl35__p_S35(rate_eval, tf):
    # Cl35 + n --> p + S35
    rate = 0.0

    # ths8r
    rate += np.exp(  7.51079 + 6.51754*tf.T913
                  + -0.295846*tf.T9 + -0.00271436*tf.T953)

    rate_eval.n_Cl35__p_S35 = rate

@numba.njit()
def He4_P39__n_Cl42(rate_eval, tf):
    # P39 + He4 --> n + Cl42
    rate = 0.0

    # rath 
    rate += np.exp(  -15.2296 + -3.27412*tf.T9i + -20.3941*tf.T913i + 32.1452*tf.T913
                  + -5.85211*tf.T9 + 0.455148*tf.T953 + 3.76404*tf.lnT9)

    rate_eval.He4_P39__n_Cl42 = rate

@numba.njit()
def n_Ca35__He4_Ar32(rate_eval, tf):
    # Ca35 + n --> He4 + Ar32
    rate = 0.0

    # ths8r
    rate += np.exp(  16.4976 + 0.0241353*tf.T913
                  + -0.0293507*tf.T9 + 0.0140919*tf.T953)

    rate_eval.n_Ca35__He4_Ar32 = rate

@numba.njit()
def n_Ca35__p_K35(rate_eval, tf):
    # Ca35 + n --> p + K35
    rate = 0.0

    # ths8r
    rate += np.exp(  19.5184 + 0.603195*tf.T913
                  + 0.00345943*tf.T9 + -0.00153592*tf.T953)

    rate_eval.n_Ca35__p_K35 = rate

@numba.njit()
def Cr67__Mn67__weak__mo03(rate_eval, tf):
    # Cr67 --> Mn67
    rate = 0.0

    # mo03w
    rate += np.exp(  3.08528)

    rate_eval.Cr67__Mn67__weak__mo03 = rate

@numba.njit()
def n_Ca34__He4_Ar31(rate_eval, tf):
    # Ca34 + n --> He4 + Ar31
    rate = 0.0

    # ths8r
    rate += np.exp(  14.1632 + 0.747566*tf.T913
                  + -0.1651*tf.T9 + 0.0363316*tf.T953)

    rate_eval.n_Ca34__He4_Ar31 = rate

@numba.njit()
def n_Ca34__p_K34(rate_eval, tf):
    # Ca34 + n --> p + K34
    rate = 0.0

    # ths8r
    rate += np.exp(  19.5543 + 0.609638*tf.T913
                  + 0.00842823*tf.T9 + -0.00304902*tf.T953)

    rate_eval.n_Ca34__p_K34 = rate

@numba.njit()
def He4_Ca48__Ti52(rate_eval, tf):
    # Ca48 + He4 --> Ti52
    rate = 0.0

    # ths8r
    rate += np.exp(  57.3374 + -76.8177*tf.T913i + -9.55565*tf.T913
                  + 1.18188*tf.T9 + -0.157384*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca48__Ti52 = rate

@numba.njit()
def He4_K57__n_Sc60(rate_eval, tf):
    # K57 + He4 --> n + Sc60
    rate = 0.0

    # rath 
    rate += np.exp(  -441.266 + 2.21954*tf.T9i + -616.258*tf.T913i + 1105.23*tf.T913
                  + -72.7542*tf.T9 + 4.42414*tf.T953 + -485.012*tf.lnT9)

    rate_eval.He4_K57__n_Sc60 = rate

@numba.njit()
def p_K57__He4_Ar54(rate_eval, tf):
    # K57 + p --> He4 + Ar54
    rate = 0.0

    # rath 
    rate += np.exp(  104.593 + -5.44949*tf.T9i + 200.377*tf.T913i + -325.656*tf.T913
                  + 18.0933*tf.T9 + -0.969057*tf.T953 + 162.786*tf.lnT9)

    rate_eval.p_K57__He4_Ar54 = rate

@numba.njit()
def He4_Si42__S46(rate_eval, tf):
    # Si42 + He4 --> S46
    rate = 0.0

    # rath 
    rate += np.exp(  -324.756 + 1.72482*tf.T9i + -451.507*tf.T913i + 802.833*tf.T913
                  + -53.5723*tf.T9 + 3.28238*tf.T953 + -350.754*tf.lnT9)

    rate_eval.He4_Si42__S46 = rate

@numba.njit()
def p_K57__n_Ca57(rate_eval, tf):
    # K57 + p --> n + Ca57
    rate = 0.0

    # rath 
    rate += np.exp(  125.114 + -5.55793*tf.T9i + 210.118*tf.T913i + -341.967*tf.T913
                  + 18.7603*tf.T9 + -1.04283*tf.T953 + 170.828*tf.lnT9)

    rate_eval.p_K57__n_Ca57 = rate

@numba.njit()
def He4_K56__n_Sc59(rate_eval, tf):
    # K56 + He4 --> n + Sc59
    rate = 0.0

    # rath 
    rate += np.exp(  -440.017 + 2.20507*tf.T9i + -612.074*tf.T913i + 1099.41*tf.T913
                  + -72.5513*tf.T9 + 4.41829*tf.T953 + -481.726*tf.lnT9)

    rate_eval.He4_K56__n_Sc59 = rate

@numba.njit()
def p_K56__n_Ca56(rate_eval, tf):
    # K56 + p --> n + Ca56
    rate = 0.0

    # rath 
    rate += np.exp(  121.918 + -5.50726*tf.T9i + 207.219*tf.T913i + -335.618*tf.T913
                  + 18.3067*tf.T9 + -1.01488*tf.T953 + 168.272*tf.lnT9)

    rate_eval.p_K56__n_Ca56 = rate

@numba.njit()
def He4_K54__n_Sc57(rate_eval, tf):
    # K54 + He4 --> n + Sc57
    rate = 0.0

    # rath 
    rate += np.exp(  -434.301 + 2.20718*tf.T9i + -605.579*tf.T913i + 1086.75*tf.T913
                  + -71.83*tf.T9 + 4.37833*tf.T953 + -475.942*tf.lnT9)

    rate_eval.He4_K54__n_Sc57 = rate

@numba.njit()
def p_K54__n_Ca54(rate_eval, tf):
    # K54 + p --> n + Ca54
    rate = 0.0

    # rath 
    rate += np.exp(  120.313 + -5.41541*tf.T9i + 203.079*tf.T913i + -329.515*tf.T913
                  + 17.9429*tf.T9 + -0.993017*tf.T953 + 165.243*tf.lnT9)

    rate_eval.p_K54__n_Ca54 = rate

@numba.njit()
def Cl49__n_Ar48__weak__mp17(rate_eval, tf):
    # Cl49 --> n + Ar48
    rate = 0.0

    # mp17w
    rate += np.exp(  3.45391)

    rate_eval.Cl49__n_Ar48__weak__mp17 = rate

@numba.njit()
def He4_K53__n_Sc56(rate_eval, tf):
    # K53 + He4 --> n + Sc56
    rate = 0.0

    # rath 
    rate += np.exp(  -428.263 + 2.18986*tf.T9i + -600.333*tf.T913i + 1074.61*tf.T913
                  + -70.9323*tf.T9 + 4.31972*tf.T953 + -471.014*tf.lnT9)

    rate_eval.He4_K53__n_Sc56 = rate

@numba.njit()
def n_O14__O15(rate_eval, tf):
    # O14 + n --> O15
    rate = 0.0

    # rpsmr
    rate += np.exp(  9.87196 + 0.0160481*tf.T9i + -1.38986*tf.T913i + 1.74662*tf.T913
                  + -0.0276897*tf.T9 + 0.00321014*tf.T953 + -1.06122*tf.lnT9)

    rate_eval.n_O14__O15 = rate

@numba.njit()
def p_K53__n_Ca53(rate_eval, tf):
    # K53 + p --> n + Ca53
    rate = 0.0

    # rath 
    rate += np.exp(  119.335 + -5.36915*tf.T9i + 201.077*tf.T913i + -326.499*tf.T913
                  + 17.7869*tf.T9 + -0.98655*tf.T953 + 163.803*tf.lnT9)

    rate_eval.p_K53__n_Ca53 = rate

@numba.njit()
def n_K31__K32(rate_eval, tf):
    # K31 + n --> K32
    rate = 0.0

    # ths8r
    rate += np.exp(  9.64661 + -0.620638*tf.T913
                  + 0.307498*tf.T9 + -0.0256787*tf.T953)

    rate_eval.n_K31__K32 = rate

@numba.njit()
def He4_K52__n_Sc55(rate_eval, tf):
    # K52 + He4 --> n + Sc55
    rate = 0.0

    # rath 
    rate += np.exp(  -425.424 + 2.1933*tf.T9i + -597.039*tf.T913i + 1067.58*tf.T913
                  + -70.4233*tf.T9 + 4.28644*tf.T953 + -467.959*tf.lnT9)

    rate_eval.He4_K52__n_Sc55 = rate

@numba.njit()
def p_P29__S30(rate_eval, tf):
    # P29 + p --> S30
    rate = 0.0

    # il10r
    rate += np.exp(  -26.0 + -3.71938*tf.T9i + 8.48834*tf.T913i + 25.65*tf.T913
                  + -3.79773*tf.T9 + 0.320391*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  20.9731 + -25.6007*tf.T913i
                  + -2.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_P29__S30 = rate

@numba.njit()
def He4_K51__n_Sc54(rate_eval, tf):
    # K51 + He4 --> n + Sc54
    rate = 0.0

    # rath 
    rate += np.exp(  -422.332 + 2.19901*tf.T9i + -593.895*tf.T913i + 1060.69*tf.T913
                  + -69.9389*tf.T9 + 4.25559*tf.T953 + -465.005*tf.lnT9)

    rate_eval.He4_K51__n_Sc54 = rate

@numba.njit()
def p_K51__n_Ca51(rate_eval, tf):
    # K51 + p --> n + Ca51
    rate = 0.0

    # rath 
    rate += np.exp(  115.211 + -5.25904*tf.T9i + 195.316*tf.T913i + -316.994*tf.T913
                  + 17.3764*tf.T9 + -0.972506*tf.T953 + 159.309*tf.lnT9)

    rate_eval.p_K51__n_Ca51 = rate

@numba.njit()
def He4_Cr57__n_Fe60(rate_eval, tf):
    # Cr57 + He4 --> n + Fe60
    rate = 0.0

    # rath 
    rate += np.exp(  -1104.42 + 17.6993*tf.T9i + -1920.7*tf.T913i + 3157.65*tf.T913
                  + -188.306*tf.T9 + 10.788*tf.T953 + -1482.08*tf.lnT9)

    rate_eval.He4_Cr57__n_Fe60 = rate

@numba.njit()
def He4_K50__n_Sc53(rate_eval, tf):
    # K50 + He4 --> n + Sc53
    rate = 0.0

    # rath 
    rate += np.exp(  -418.515 + 2.27957*tf.T9i + -596.546*tf.T913i + 1059.24*tf.T913
                  + -69.4458*tf.T9 + 4.21085*tf.T953 + -466.04*tf.lnT9)

    rate_eval.He4_K50__n_Sc53 = rate

@numba.njit()
def p_S42__Cl43(rate_eval, tf):
    # S42 + p --> Cl43
    rate = 0.0

    # rath 
    rate += np.exp(  88.2456 + -4.27454*tf.T9i + 155.508*tf.T913i + -255.726*tf.T913
                  + 14.0345*tf.T9 + -0.79028*tf.T953 + 128.448*tf.lnT9)

    rate_eval.p_S42__Cl43 = rate

@numba.njit()
def He4_K48__n_Sc51(rate_eval, tf):
    # K48 + He4 --> n + Sc51
    rate = 0.0

    # rath 
    rate += np.exp(  -864.496 + 14.0164*tf.T9i + -1521.47*tf.T913i + 2493.14*tf.T913
                  + -148.997*tf.T9 + 8.554*tf.T953 + -1170.0*tf.lnT9)

    rate_eval.He4_K48__n_Sc51 = rate

@numba.njit()
def n_Fe50__Fe51(rate_eval, tf):
    # Fe50 + n --> Fe51
    rate = 0.0

    # ths8r
    rate += np.exp(  13.2307 + -1.43737*tf.T913
                  + 0.511909*tf.T9 + -0.0531273*tf.T953)

    rate_eval.n_Fe50__Fe51 = rate

@numba.njit()
def n_Cr44__He4_Ti41(rate_eval, tf):
    # Cr44 + n --> He4 + Ti41
    rate = 0.0

    # ths8r
    rate += np.exp(  15.5371 + -0.0787441*tf.T913
                  + -0.0435765*tf.T9 + 0.0419458*tf.T953)

    rate_eval.n_Cr44__He4_Ti41 = rate

@numba.njit()
def p_K48__He4_Ar45(rate_eval, tf):
    # K48 + p --> He4 + Ar45
    rate = 0.0

    # rath 
    rate += np.exp(  67.2404 + -5.08309*tf.T9i + 183.977*tf.T913i + -268.577*tf.T913
                  + 12.8076*tf.T9 + -0.564651*tf.T953 + 146.485*tf.lnT9)

    rate_eval.p_K48__He4_Ar45 = rate

@numba.njit()
def He4_Sc35__V39(rate_eval, tf):
    # Sc35 + He4 --> V39
    rate = 0.0

    # ths8r
    rate += np.exp(  44.5395 + -78.6193*tf.T913i + -0.900781*tf.T913
                  + -0.324011*tf.T9 + -0.0113464*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc35__V39 = rate

@numba.njit()
def p_K45__He4_Ar42(rate_eval, tf):
    # K45 + p --> He4 + Ar42
    rate = 0.0

    # rath 
    rate += np.exp(  67.6367 + -4.85769*tf.T9i + 170.619*tf.T913i + -251.954*tf.T913
                  + 12.4668*tf.T9 + -0.661536*tf.T953 + 136.535*tf.lnT9)

    rate_eval.p_K45__He4_Ar42 = rate

@numba.njit()
def p_K45__n_Ca45(rate_eval, tf):
    # K45 + p --> n + Ca45
    rate = 0.0

    # rath 
    rate += np.exp(  111.508 + -4.96802*tf.T9i + 183.001*tf.T913i + -301.16*tf.T913
                  + 16.6421*tf.T9 + -0.933366*tf.T953 + 150.762*tf.lnT9)

    rate_eval.p_K45__n_Ca45 = rate

@numba.njit()
def p_K44__He4_Ar41(rate_eval, tf):
    # K44 + p --> He4 + Ar41
    rate = 0.0

    # rath 
    rate += np.exp(  49.9687 + -4.8552*tf.T9i + 171.063*tf.T913i + -233.078*tf.T913
                  + 9.71453*tf.T9 + -0.42409*tf.T953 + 134.334*tf.lnT9)

    rate_eval.p_K44__He4_Ar41 = rate

@numba.njit()
def Ne31__n_Na30__weak__mp17(rate_eval, tf):
    # Ne31 --> n + Na30
    rate = 0.0

    # mp17w
    rate += np.exp(  3.01488)

    rate_eval.Ne31__n_Na30__weak__mp17 = rate

@numba.njit()
def He4_K43__p_Ca46(rate_eval, tf):
    # K43 + He4 --> p + Ca46
    rate = 0.0

    # rath 
    rate += np.exp(  -821.804 + 13.1871*tf.T9i + -1437.68*tf.T913i + 2355.37*tf.T913
                  + -140.919*tf.T9 + 8.10266*tf.T953 + -1104.1*tf.lnT9)

    rate_eval.He4_K43__p_Ca46 = rate

@numba.njit()
def p_K43__n_Ca43(rate_eval, tf):
    # K43 + p --> n + Ca43
    rate = 0.0

    # rath 
    rate += np.exp(  110.363 + -4.86758*tf.T9i + 178.812*tf.T913i + -295.417*tf.T913
                  + 16.2625*tf.T9 + -0.908893*tf.T953 + 147.813*tf.lnT9)

    rate_eval.p_K43__n_Ca43 = rate

@numba.njit()
def n_V45__He4_Sc42(rate_eval, tf):
    # V45 + n --> He4 + Sc42
    rate = 0.0

    # ths8r
    rate += np.exp(  11.9312 + 2.45165*tf.T913
                  + -0.370637*tf.T9 + 0.0836828*tf.T953)

    rate_eval.n_V45__He4_Sc42 = rate

@numba.njit()
def He4_K42__p_Ca45(rate_eval, tf):
    # K42 + He4 --> p + Ca45
    rate = 0.0

    # rath 
    rate += np.exp(  -793.981 + 12.8488*tf.T9i + -1400.12*tf.T913i + 2286.39*tf.T913
                  + -137.138*tf.T9 + 7.89768*tf.T953 + -1071.24*tf.lnT9)

    rate_eval.He4_K42__p_Ca45 = rate

@numba.njit()
def He8__n_Li7__weak__wc12(rate_eval, tf):
    # He8 --> n + Li7
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.0704626)

    rate_eval.He8__n_Li7__weak__wc12 = rate

@numba.njit()
def He4_K42__n_Sc45(rate_eval, tf):
    # K42 + He4 --> n + Sc45
    rate = 0.0

    # rath 
    rate += np.exp(  -811.023 + 13.1551*tf.T9i + -1429.89*tf.T913i + 2339.64*tf.T913
                  + -140.001*tf.T9 + 8.04164*tf.T953 + -1096.96*tf.lnT9)

    rate_eval.He4_K42__n_Sc45 = rate

@numba.njit()
def He4_K41__n_Sc44(rate_eval, tf):
    # K41 + He4 --> n + Sc44
    rate = 0.0

    # SM91 
    rate += np.exp(  12.8237 + -39.3393*tf.T9i + -7.79828*tf.T913
                  + 4.55188*tf.T9 + -0.667478*tf.T953 + 1.0*tf.lnT9)
    # SM91 
    rate += np.exp(  12.4167 + -39.3393*tf.T9i + -2.89121*tf.T913
                  + 2.26347*tf.T9 + -0.251579*tf.T953)

    rate_eval.He4_K41__n_Sc44 = rate

@numba.njit()
def p_K41__He4_Ar38(rate_eval, tf):
    # K41 + p --> He4 + Ar38
    rate = 0.0

    # tb18 
    rate += np.exp(  64.4107 + -0.681143*tf.T9i + 9.28681*tf.T913i + -73.161*tf.T913
                  + 4.26053*tf.T9 + -0.235892*tf.T953 + 31.8226*tf.lnT9)

    rate_eval.p_K41__He4_Ar38 = rate

@numba.njit()
def p_K41__n_Ca41(rate_eval, tf):
    # K41 + p --> n + Ca41
    rate = 0.0

    # SM86 
    rate += np.exp(  8.69806 + -13.9718*tf.T9i + 6.52588*tf.T913
                  + -1.55272*tf.T9 + 0.150334*tf.T953 + 1.0*tf.lnT9)
    # SM86 
    rate += np.exp(  15.9784 + -13.9718*tf.T9i + -2.82146*tf.T913
                  + 1.71734*tf.T9 + -0.187775*tf.T953)

    rate_eval.p_K41__n_Ca41 = rate

@numba.njit()
def He4_K46__p_Ca49(rate_eval, tf):
    # K46 + He4 --> p + Ca49
    rate = 0.0

    # rath 
    rate += np.exp(  -819.96 + 13.206*tf.T9i + -1441.13*tf.T913i + 2355.2*tf.T913
                  + -142.84*tf.T9 + 8.44153*tf.T953 + -1103.03*tf.lnT9)

    rate_eval.He4_K46__p_Ca49 = rate

@numba.njit()
def p_K40__He4_Ar37(rate_eval, tf):
    # K40 + p --> He4 + Ar37
    rate = 0.0

    # ths8r
    rate += np.exp(  23.7792 + -30.0795*tf.T913i + 8.28189*tf.T913
                  + -2.15178*tf.T9 + 0.242064*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_K40__He4_Ar37 = rate

@numba.njit()
def p_K40__n_Ca40(rate_eval, tf):
    # K40 + p --> n + Ca40
    rate = 0.0

    # ths8r
    rate += np.exp(  32.1312 + -30.0795*tf.T913i + 2.76095*tf.T913
                  + -1.51745*tf.T9 + 0.191236*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_K40__n_Ca40 = rate

@numba.njit()
def p_S37__Cl38(rate_eval, tf):
    # S37 + p --> Cl38
    rate = 0.0

    # rath 
    rate += np.exp(  87.315 + -4.02559*tf.T9i + 144.546*tf.T913i + -241.034*tf.T913
                  + 13.0821*tf.T9 + -0.729868*tf.T953 + 120.609*tf.lnT9)

    rate_eval.p_S37__Cl38 = rate

@numba.njit()
def n_K40__He4_Cl37(rate_eval, tf):
    # K40 + n --> He4 + Cl37
    rate = 0.0

    # ths8r
    rate += np.exp(  16.0992 + -0.86425*tf.T913
                  + 0.646211*tf.T9 + -0.0583195*tf.T953)

    rate_eval.n_K40__He4_Cl37 = rate

@numba.njit()
def n_K40__p_Ar40(rate_eval, tf):
    # K40 + n --> p + Ar40
    rate = 0.0

    # ths8r
    rate += np.exp(  14.133 + -0.499903*tf.T913
                  + 0.849663*tf.T9 + -0.0834774*tf.T953)

    rate_eval.n_K40__p_Ar40 = rate

@numba.njit()
def n_K39__p_Ar39(rate_eval, tf):
    # K39 + n --> p + Ar39
    rate = 0.0

    # ths8r
    rate += np.exp(  -15.2094 + 26.5209*tf.T913
                  + -3.63684*tf.T9 + 0.276163*tf.T953)

    rate_eval.n_K39__p_Ar39 = rate

@numba.njit()
def p_O14__F15(rate_eval, tf):
    # O14 + p --> F15
    rate = 0.0

    # rpsmr
    rate += np.exp(  3.69607 + -19.5633*tf.T9i + 71.6134*tf.T913i + -76.9654*tf.T913
                  + 3.54377*tf.T9 + -0.159804*tf.T953 + 46.3922*tf.lnT9)

    rate_eval.p_O14__F15 = rate

@numba.njit()
def He4_Sc43__V47(rate_eval, tf):
    # Sc43 + He4 --> V47
    rate = 0.0

    # ths8r
    rate += np.exp(  59.0195 + -79.122*tf.T913i + -7.07006*tf.T913
                  + 0.424183*tf.T9 + -0.0665231*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc43__V47 = rate

@numba.njit()
def n_K38__p_Ar38(rate_eval, tf):
    # K38 + n --> p + Ar38
    rate = 0.0

    # ths8r
    rate += np.exp(  19.6025 + -0.5015*tf.T913
                  + 0.324921*tf.T9 + -0.0393691*tf.T953)

    rate_eval.n_K38__p_Ar38 = rate

@numba.njit()
def n_Ar31__He4_S28(rate_eval, tf):
    # Ar31 + n --> He4 + S28
    rate = 0.0

    # ths8r
    rate += np.exp(  16.2096 + -0.556664*tf.T913
                  + 0.20583*tf.T9 + -0.00877773*tf.T953)

    rate_eval.n_Ar31__He4_S28 = rate

@numba.njit()
def He4_K37__p_Ca40(rate_eval, tf):
    # K37 + He4 --> p + Ca40
    rate = 0.0

    # ths8r
    rate += np.exp(  54.2966 + -73.6776*tf.T913i + 0.493294*tf.T913
                  + -0.902307*tf.T9 + 0.0641391*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K37__p_Ca40 = rate

@numba.njit()
def He4_K44__p_Ca47(rate_eval, tf):
    # K44 + He4 --> p + Ca47
    rate = 0.0

    # rath 
    rate += np.exp(  -805.073 + 13.2156*tf.T9i + -1435.79*tf.T913i + 2333.14*tf.T913
                  + -138.772*tf.T9 + 7.95617*tf.T953 + -1097.52*tf.lnT9)

    rate_eval.He4_K44__p_Ca47 = rate

@numba.njit()
def n_K37__He4_Cl34(rate_eval, tf):
    # K37 + n --> He4 + Cl34
    rate = 0.0

    # ths8r
    rate += np.exp(  15.9641 + 1.35231*tf.T913
                  + -0.147095*tf.T9 + 0.0306549*tf.T953)

    rate_eval.n_K37__He4_Cl34 = rate

@numba.njit()
def n_K36__He4_Cl33(rate_eval, tf):
    # K36 + n --> He4 + Cl33
    rate = 0.0

    # ths8r
    rate += np.exp(  17.5697 + 0.275133*tf.T913
                  + 0.00444428*tf.T9 + 0.0117689*tf.T953)

    rate_eval.n_K36__He4_Cl33 = rate

@numba.njit()
def n_K36__p_Ar36(rate_eval, tf):
    # K36 + n --> p + Ar36
    rate = 0.0

    # ths8r
    rate += np.exp(  19.1136 + 0.752718*tf.T913
                  + -0.00478822*tf.T9 + -0.00297178*tf.T953)

    rate_eval.n_K36__p_Ar36 = rate

@numba.njit()
def n_Sc46__He4_K43(rate_eval, tf):
    # Sc46 + n --> He4 + K43
    rate = 0.0

    # rath 
    rate += np.exp(  166.614 + -3.81386*tf.T9i + 288.57*tf.T913i + -490.272*tf.T913
                  + 26.4459*tf.T9 + -1.47391*tf.T953 + 249.343*tf.lnT9)

    rate_eval.n_Sc46__He4_K43 = rate

@numba.njit()
def n_K35__p_Ar35(rate_eval, tf):
    # K35 + n --> p + Ar35
    rate = 0.0

    # ths8r
    rate += np.exp(  19.1611 + 0.87581*tf.T913
                  + -0.0495026*tf.T9 + 0.00329552*tf.T953)

    rate_eval.n_K35__p_Ar35 = rate

@numba.njit()
def He4_K34__p_Ca37(rate_eval, tf):
    # K34 + He4 --> p + Ca37
    rate = 0.0

    # ths8r
    rate += np.exp(  54.6796 + -73.4689*tf.T913i + -0.350491*tf.T913
                  + -0.675654*tf.T9 + 0.0423497*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K34__p_Ca37 = rate

@numba.njit()
def p_Al39__n_Si39(rate_eval, tf):
    # Al39 + p --> n + Si39
    rate = 0.0

    # rath 
    rate += np.exp(  87.3159 + -3.60395*tf.T9i + 130.919*tf.T913i + -217.045*tf.T913
                  + 11.86*tf.T9 + -0.658659*tf.T953 + 108.786*tf.lnT9)

    rate_eval.p_Al39__n_Si39 = rate

@numba.njit()
def He4_Sc54__V58(rate_eval, tf):
    # Sc54 + He4 --> V58
    rate = 0.0

    # rath 
    rate += np.exp(  -948.544 + 19.8149*tf.T9i + -1972.08*tf.T913i + 3031.21*tf.T913
                  + -171.808*tf.T9 + 9.4915*tf.T953 + -1471.3*tf.lnT9)

    rate_eval.He4_Sc54__V58 = rate

@numba.njit()
def p_Cr61__He4_V58(rate_eval, tf):
    # Cr61 + p --> He4 + V58
    rate = 0.0

    # rath 
    rate += np.exp(  103.902 + -6.76211*tf.T9i + 260.348*tf.T913i + -394.424*tf.T913
                  + 20.612*tf.T9 + -1.08871*tf.T953 + 208.154*tf.lnT9)

    rate_eval.p_Cr61__He4_V58 = rate

@numba.njit()
def K52__Ca52__weak__wc17(rate_eval, tf):
    # K52 --> Ca52
    rate = 0.0

    # wc17w
    rate += np.exp(  0.384263)

    rate_eval.K52__Ca52__weak__wc17 = rate

@numba.njit()
def n_K33__p_Ar33(rate_eval, tf):
    # K33 + n --> p + Ar33
    rate = 0.0

    # ths8r
    rate += np.exp(  19.1471 + 1.00911*tf.T913
                  + -0.0738768*tf.T9 + 0.00468015*tf.T953)

    rate_eval.n_K33__p_Ar33 = rate

@numba.njit()
def p_Mn51__Fe52(rate_eval, tf):
    # Mn51 + p --> Fe52
    rate = 0.0

    # ths8r
    rate += np.exp(  36.2596 + -36.1825*tf.T913i + 0.873042*tf.T913
                  + -2.89731*tf.T9 + 0.364394*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn51__Fe52 = rate

@numba.njit()
def n_K32__He4_Cl29(rate_eval, tf):
    # K32 + n --> He4 + Cl29
    rate = 0.0

    # ths8r
    rate += np.exp(  16.0515 + -0.46558*tf.T913
                  + 0.246355*tf.T9 + -0.0166775*tf.T953)

    rate_eval.n_K32__He4_Cl29 = rate

@numba.njit()
def p_Mn56__Fe57(rate_eval, tf):
    # Mn56 + p --> Fe57
    rate = 0.0

    # rath 
    rate += np.exp(  116.344 + -6.46579*tf.T9i + 232.952*tf.T913i + -368.183*tf.T913
                  + 20.251*tf.T9 + -1.16222*tf.T953 + 187.086*tf.lnT9)

    rate_eval.p_Mn56__Fe57 = rate

@numba.njit()
def n_K32__p_Ar32(rate_eval, tf):
    # K32 + n --> p + Ar32
    rate = 0.0

    # ths8r
    rate += np.exp(  19.1597 + 1.12687*tf.T913
                  + -0.113013*tf.T9 + 0.00780576*tf.T953)

    rate_eval.n_K32__p_Ar32 = rate

@numba.njit()
def He4_K31__p_Ca34(rate_eval, tf):
    # K31 + He4 --> p + Ca34
    rate = 0.0

    # ths8r
    rate += np.exp(  53.3263 + -73.2242*tf.T913i + 0.510478*tf.T913
                  + -0.82791*tf.T9 + 0.0592067*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K31__p_Ca34 = rate

@numba.njit()
def p_Ti38__V39(rate_eval, tf):
    # Ti38 + p --> V39
    rate = 0.0

    # ths8r
    rate += np.exp(  -13.9122 + -39.0031*tf.T9i + 14.9455*tf.T913
                  + -1.13381*tf.T9 + 0.0537045*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ti38__V39 = rate

@numba.njit()
def n_K31__p_Ar31(rate_eval, tf):
    # K31 + n --> p + Ar31
    rate = 0.0

    # ths8r
    rate += np.exp(  19.2213 + 1.014*tf.T913
                  + -0.0782201*tf.T9 + 0.00462463*tf.T953)

    rate_eval.n_K31__p_Ar31 = rate

@numba.njit()
def p_Ar54__n_K54(rate_eval, tf):
    # Ar54 + p --> n + K54
    rate = 0.0

    # rath 
    rate += np.exp(  117.106 + -5.22146*tf.T9i + 195.679*tf.T913i + -317.954*tf.T913
                  + 17.3682*tf.T9 + -0.96238*tf.T953 + 159.238*tf.lnT9)

    rate_eval.p_Ar54__n_K54 = rate

@numba.njit()
def p_Ar52__He4_Cl49(rate_eval, tf):
    # Ar52 + p --> He4 + Cl49
    rate = 0.0

    # rath 
    rate += np.exp(  74.5249 + -5.15576*tf.T9i + 194.181*tf.T913i + -289.492*tf.T913
                  + 13.818*tf.T9 + -0.647377*tf.T953 + 155.77*tf.lnT9)

    rate_eval.p_Ar52__He4_Cl49 = rate

@numba.njit()
def p_Ar52__n_K52(rate_eval, tf):
    # Ar52 + p --> n + K52
    rate = 0.0

    # rath 
    rate += np.exp(  112.729 + -5.11656*tf.T9i + 190.078*tf.T913i + -307.597*tf.T913
                  + 16.7175*tf.T9 + -0.927139*tf.T953 + 154.706*tf.lnT9)

    rate_eval.p_Ar52__n_K52 = rate

@numba.njit()
def n_Ti39__He4_Ca36(rate_eval, tf):
    # Ti39 + n --> He4 + Ca36
    rate = 0.0

    # ths8r
    rate += np.exp(  14.77 + 1.4416*tf.T913
                  + -0.169682*tf.T9 + 0.0206434*tf.T953)

    rate_eval.n_Ti39__He4_Ca36 = rate

@numba.njit()
def p_K59__n_Ca59(rate_eval, tf):
    # K59 + p --> n + Ca59
    rate = 0.0

    # rath 
    rate += np.exp(  123.986 + -5.63676*tf.T9i + 212.759*tf.T913i + -343.571*tf.T913
                  + 18.7675*tf.T9 + -1.04193*tf.T953 + 172.225*tf.lnT9)

    rate_eval.p_K59__n_Ca59 = rate

@numba.njit()
def p_Ar50__He4_Cl47(rate_eval, tf):
    # Ar50 + p --> He4 + Cl47
    rate = 0.0

    # rath 
    rate += np.exp(  72.6737 + -5.09644*tf.T9i + 191.954*tf.T913i + -283.401*tf.T913
                  + 13.2661*tf.T9 + -0.608131*tf.T953 + 153.542*tf.lnT9)

    rate_eval.p_Ar50__He4_Cl47 = rate

@numba.njit()
def n_Ca36__He4_Ar33(rate_eval, tf):
    # Ca36 + n --> He4 + Ar33
    rate = 0.0

    # ths8r
    rate += np.exp(  16.4495 + 0.565687*tf.T913
                  + -0.206204*tf.T9 + 0.0427835*tf.T953)

    rate_eval.n_Ca36__He4_Ar33 = rate

@numba.njit()
def V67__n_n_n_Cr64__weak__mo03(rate_eval, tf):
    # V67 --> 3 n + Cr64
    rate = 0.0

    # mo03w
    rate += np.exp(  1.55541)

    rate_eval.V67__n_n_n_Cr64__weak__mo03 = rate

@numba.njit()
def He4_F20__n_Na23(rate_eval, tf):
    # F20 + He4 --> n + Na23
    rate = 0.0

    # rpsmr
    rate += np.exp(  55.1346 + -2.00307*tf.T9i + 28.2992*tf.T913i + -86.0503*tf.T913
                  + 3.48915*tf.T9 + -0.157188*tf.T953 + 46.29*tf.lnT9)

    rate_eval.He4_F20__n_Na23 = rate

@numba.njit()
def p_Ar48__He4_Cl45(rate_eval, tf):
    # Ar48 + p --> He4 + Cl45
    rate = 0.0

    # rath 
    rate += np.exp(  80.8635 + -5.23065*tf.T9i + 215.993*tf.T913i + -322.071*tf.T913
                  + 14.7168*tf.T9 + -0.688286*tf.T953 + 176.83*tf.lnT9)

    rate_eval.p_Ar48__He4_Cl45 = rate

@numba.njit()
def p_Ar48__n_K48(rate_eval, tf):
    # Ar48 + p --> n + K48
    rate = 0.0

    # rath 
    rate += np.exp(  108.711 + -4.92617*tf.T9i + 181.541*tf.T913i + -295.304*tf.T913
                  + 16.1827*tf.T9 + -0.906087*tf.T953 + 148.529*tf.lnT9)

    rate_eval.p_Ar48__n_K48 = rate

@numba.njit()
def He4_Ar46__n_Ca49(rate_eval, tf):
    # Ar46 + He4 --> n + Ca49
    rate = 0.0

    # rath 
    rate += np.exp(  -385.358 + 2.03481*tf.T9i + -547.571*tf.T913i + 973.209*tf.T913
                  + -64.2434*tf.T9 + 3.90783*tf.T953 + -426.243*tf.lnT9)

    rate_eval.He4_Ar46__n_Ca49 = rate

@numba.njit()
def p_F28__n_Ne28(rate_eval, tf):
    # F28 + p --> n + Ne28
    rate = 0.0

    # rpsmr
    rate += np.exp(  66.6584 + -2.40366*tf.T9i + 84.6259*tf.T913i + -144.357*tf.T913
                  + 7.81107*tf.T9 + -0.432664*tf.T953 + 72.2972*tf.lnT9)

    rate_eval.p_F28__n_Ne28 = rate

@numba.njit()
def He4_Fe50__p_Co53(rate_eval, tf):
    # Fe50 + He4 --> p + Co53
    rate = 0.0

    # ths8r
    rate += np.exp(  62.7305 + -91.5952*tf.T913i + -1.33713*tf.T913
                  + -0.465416*tf.T9 + 0.00761392*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe50__p_Co53 = rate

@numba.njit()
def n_d__t(rate_eval, tf):
    # d + n --> t
    rate = 0.0

    # nk06n
    rate += np.exp(  6.60935
                  + 1.0*tf.lnT9)
    # nk06n
    rate += np.exp(  5.36598
                  + 0.075*tf.lnT9)

    rate_eval.n_d__t = rate

@numba.njit()
def He4_Si35__n_S38(rate_eval, tf):
    # Si35 + He4 --> n + S38
    rate = 0.0

    # rath 
    rate += np.exp(  -7.79415 + -2.96803*tf.T9i + -18.6461*tf.T913i + 23.0048*tf.T913
                  + -4.88241*tf.T9 + 0.384187*tf.T953 + 5.9573*tf.lnT9)

    rate_eval.He4_Si35__n_S38 = rate

@numba.njit()
def p_Ar44__n_K44(rate_eval, tf):
    # Ar44 + p --> n + K44
    rate = 0.0

    # rath 
    rate += np.exp(  109.334 + -4.78797*tf.T9i + 178.118*tf.T913i + -293.069*tf.T913
                  + 16.1211*tf.T9 + -0.898816*tf.T953 + 146.748*tf.lnT9)

    rate_eval.p_Ar44__n_K44 = rate

@numba.njit()
def He4_Ar43__n_Ca46(rate_eval, tf):
    # Ar43 + He4 --> n + Ca46
    rate = 0.0

    # rath 
    rate += np.exp(  -371.194 + 2.00159*tf.T9i + -533.145*tf.T913i + 942.459*tf.T913
                  + -62.1006*tf.T9 + 3.76713*tf.T953 + -413.111*tf.lnT9)

    rate_eval.He4_Ar43__n_Ca46 = rate

@numba.njit()
def n_V39__V40(rate_eval, tf):
    # V39 + n --> V40
    rate = 0.0

    # ths8r
    rate += np.exp(  9.74196 + 0.00897837*tf.T913
                  + 0.175529*tf.T9 + -0.015058*tf.T953)

    rate_eval.n_V39__V40 = rate

@numba.njit()
def p_Cr55__He4_V52(rate_eval, tf):
    # Cr55 + p --> He4 + V52
    rate = 0.0

    # rath 
    rate += np.exp(  -56.4636 + -5.15446*tf.T9i + 108.901*tf.T913i + -62.9908*tf.T913
                  + -4.88848*tf.T9 + 0.564223*tf.T953 + 76.8961*tf.lnT9)

    rate_eval.p_Cr55__He4_V52 = rate

@numba.njit()
def p_Ar43__n_K43(rate_eval, tf):
    # Ar43 + p --> n + K43
    rate = 0.0

    # rath 
    rate += np.exp(  107.453 + -4.69558*tf.T9i + 172.587*tf.T913i + -285.357*tf.T913
                  + 15.7704*tf.T9 + -0.885823*tf.T953 + 142.696*tf.lnT9)

    rate_eval.p_Ar43__n_K43 = rate

@numba.njit()
def p_Fe47__Co48(rate_eval, tf):
    # Fe47 + p --> Co48
    rate = 0.0

    # ths8r
    rate += np.exp(  -19.3572 + -9.377*tf.T9i + 20.4773*tf.T913
                  + -2.90303*tf.T9 + 0.254241*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Fe47__Co48 = rate

@numba.njit()
def He4_Cl47__K51(rate_eval, tf):
    # Cl47 + He4 --> K51
    rate = 0.0

    # rath 
    rate += np.exp(  -805.456 + 12.9056*tf.T9i + -1400.83*tf.T913i + 2296.23*tf.T913
                  + -137.374*tf.T9 + 7.88754*tf.T953 + -1077.13*tf.lnT9)

    rate_eval.He4_Cl47__K51 = rate

@numba.njit()
def p_Ar41__n_K41(rate_eval, tf):
    # Ar41 + p --> n + K41
    rate = 0.0

    # rath 
    rate += np.exp(  106.213 + -4.59286*tf.T9i + 168.194*tf.T913i + -279.253*tf.T913
                  + 15.3712*tf.T9 + -0.860285*tf.T953 + 139.589*tf.lnT9)

    rate_eval.p_Ar41__n_K41 = rate

@numba.njit()
def n_Mn52__Mn53(rate_eval, tf):
    # Mn52 + n --> Mn53
    rate = 0.0

    # ths8r
    rate += np.exp(  17.0941 + -0.91084*tf.T913
                  + 0.162511*tf.T9 + -0.0279619*tf.T953)

    rate_eval.n_Mn52__Mn53 = rate

@numba.njit()
def p_Ar40__He4_Cl37(rate_eval, tf):
    # Ar40 + p --> He4 + Cl37
    rate = 0.0

    # ths8r
    rate += np.exp(  16.62 + -29.0146*tf.T913i + 15.2952*tf.T913
                  + -3.22171*tf.T9 + 0.283382*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ar40__He4_Cl37 = rate

@numba.njit()
def He4_Mn54__Co58(rate_eval, tf):
    # Mn54 + He4 --> Co58
    rate = 0.0

    # ths8r
    rate += np.exp(  67.6083 + -89.3946*tf.T913i + -8.26476*tf.T913
                  + -0.766622*tf.T9 + 0.135181*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn54__Co58 = rate

@numba.njit()
def He4_Fe68__Ni72(rate_eval, tf):
    # Fe68 + He4 --> Ni72
    rate = 0.0

    # rath 
    rate += np.exp(  -991.65 + 25.3739*tf.T9i + -2449.65*tf.T913i + 3559.85*tf.T913
                  + -192.376*tf.T9 + 10.2174*tf.T953 + -1777.07*tf.lnT9)

    rate_eval.He4_Fe68__Ni72 = rate

@numba.njit()
def p_Ar39__He4_Cl36(rate_eval, tf):
    # Ar39 + p --> He4 + Cl36
    rate = 0.0

    # ths8r
    rate += np.exp(  8.20001 + -29.0085*tf.T913i + 15.2414*tf.T913
                  + -1.01027*tf.T9 + -0.0165013*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ar39__He4_Cl36 = rate

@numba.njit()
def p_Cr62__Mn63(rate_eval, tf):
    # Cr62 + p --> Mn63
    rate = 0.0

    # rath 
    rate += np.exp(  135.354 + -6.73507*tf.T9i + 255.064*tf.T913i + -411.976*tf.T913
                  + 22.7675*tf.T9 + -1.29593*tf.T953 + 206.104*tf.lnT9)

    rate_eval.p_Cr62__Mn63 = rate

@numba.njit()
def He4_Mn62__n_Co65(rate_eval, tf):
    # Mn62 + He4 --> n + Co65
    rate = 0.0

    # rath 
    rate += np.exp(  -1133.43 + 23.7743*tf.T9i + -2362.84*tf.T913i + 3639.94*tf.T913
                  + -206.157*tf.T9 + 11.3997*tf.T953 + -1766.75*tf.lnT9)

    rate_eval.He4_Mn62__n_Co65 = rate

@numba.njit()
def n_Mn49__He4_V46(rate_eval, tf):
    # Mn49 + n --> He4 + V46
    rate = 0.0

    # ths8r
    rate += np.exp(  10.2545 + -1.43898*tf.T913
                  + 1.62371*tf.T9 + -0.168368*tf.T953)

    rate_eval.n_Mn49__He4_V46 = rate

@numba.njit()
def n_Ar37__p_Cl37(rate_eval, tf):
    # Ar37 + n --> p + Cl37
    rate = 0.0

    # ths8r
    rate += np.exp(  16.2094 + 1.64495*tf.T913
                  + -0.154677*tf.T9 + 0.0083347*tf.T953)

    rate_eval.n_Ar37__p_Cl37 = rate

@numba.njit()
def n_Ar35__He4_S32(rate_eval, tf):
    # Ar35 + n --> He4 + S32
    rate = 0.0

    # ths8r
    rate += np.exp(  18.2388 + 0.502191*tf.T913
                  + -0.0974026*tf.T9 + 0.0167829*tf.T953)

    rate_eval.n_Ar35__He4_S32 = rate

@numba.njit()
def n_Ar35__p_Cl35(rate_eval, tf):
    # Ar35 + n --> p + Cl35
    rate = 0.0

    # ths8r
    rate += np.exp(  19.5533 + 0.0970999*tf.T913
                  + 0.139648*tf.T9 + -0.0149442*tf.T953)

    rate_eval.n_Ar35__p_Cl35 = rate

@numba.njit()
def He4_Ar34__p_K37(rate_eval, tf):
    # Ar34 + He4 --> p + K37
    rate = 0.0

    # ths8r
    rate += np.exp(  53.1837 + -70.8666*tf.T913i + 0.263069*tf.T913
                  + -0.802985*tf.T9 + 0.0550287*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar34__p_K37 = rate

@numba.njit()
def n_Ar34__p_Cl34(rate_eval, tf):
    # Ar34 + n --> p + Cl34
    rate = 0.0

    # ths8r
    rate += np.exp(  18.8161 + 1.04995*tf.T913
                  + -0.0436573*tf.T9 + -0.00168124*tf.T953)

    rate_eval.n_Ar34__p_Cl34 = rate

@numba.njit()
def He4_Ar33__p_K36(rate_eval, tf):
    # Ar33 + He4 --> p + K36
    rate = 0.0

    # ths8r
    rate += np.exp(  53.0357 + -70.792*tf.T913i + 0.244377*tf.T913
                  + -0.779786*tf.T9 + 0.0523787*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar33__p_K36 = rate

@numba.njit()
def n_Ar33__p_Cl33(rate_eval, tf):
    # Ar33 + n --> p + Cl33
    rate = 0.0

    # ths8r
    rate += np.exp(  18.8096 + 1.27279*tf.T913
                  + -0.118189*tf.T9 + 0.00691897*tf.T953)

    rate_eval.n_Ar33__p_Cl33 = rate

@numba.njit()
def n_Ar32__He4_S29(rate_eval, tf):
    # Ar32 + n --> He4 + S29
    rate = 0.0

    # ths8r
    rate += np.exp(  16.3565 + -0.483147*tf.T913
                  + 0.187432*tf.T9 + -0.00355391*tf.T953)

    rate_eval.n_Ar32__He4_S29 = rate

@numba.njit()
def n_Fe75__Fe76(rate_eval, tf):
    # Fe75 + n --> Fe76
    rate = 0.0

    # rath 
    rate += np.exp(  0.484399 + 0.066106*tf.T9i + -7.5661*tf.T913i + 13.8743*tf.T913
                  + 0.128258*tf.T9 + -0.102522*tf.T953 + -7.10014*tf.lnT9)

    rate_eval.n_Fe75__Fe76 = rate

@numba.njit()
def n_Ar32__p_Cl32(rate_eval, tf):
    # Ar32 + n --> p + Cl32
    rate = 0.0

    # ths8r
    rate += np.exp(  19.663 + 0.487736*tf.T913
                  + 0.0231795*tf.T9 + -0.00292297*tf.T953)

    rate_eval.n_Ar32__p_Cl32 = rate

@numba.njit()
def He4_Ar31__p_K34(rate_eval, tf):
    # Ar31 + He4 --> p + K34
    rate = 0.0

    # ths8r
    rate += np.exp(  53.4441 + -70.6299*tf.T913i + 0.133959*tf.T913
                  + -0.787144*tf.T9 + 0.0534655*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar31__p_K34 = rate

@numba.njit()
def n_Ar31__p_Cl31(rate_eval, tf):
    # Ar31 + n --> p + Cl31
    rate = 0.0

    # ths8r
    rate += np.exp(  19.5303 + 0.71865*tf.T913
                  + -0.0339555*tf.T9 + 0.00249097*tf.T953)

    rate_eval.n_Ar31__p_Cl31 = rate

@numba.njit()
def P27__p_Al26__weak__wc12(rate_eval, tf):
    # P27 --> p + Al26
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.28387)

    rate_eval.P27__p_Al26__weak__wc12 = rate

@numba.njit()
def n_Ar30__He4_S27(rate_eval, tf):
    # Ar30 + n --> He4 + S27
    rate = 0.0

    # ths8r
    rate += np.exp(  14.1231 + 0.617593*tf.T913
                  + -0.0271873*tf.T9 + 0.0140215*tf.T953)

    rate_eval.n_Ar30__He4_S27 = rate

@numba.njit()
def n_Ar30__p_Cl30(rate_eval, tf):
    # Ar30 + n --> p + Cl30
    rate = 0.0

    # ths8r
    rate += np.exp(  19.632 + 0.587038*tf.T913
                  + 0.0100556*tf.T9 + -0.00250624*tf.T953)

    rate_eval.n_Ar30__p_Cl30 = rate

@numba.njit()
def He4_Ar29__p_K32(rate_eval, tf):
    # Ar29 + He4 --> p + K32
    rate = 0.0

    # ths8r
    rate += np.exp(  53.0952 + -70.4479*tf.T913i + 0.121469*tf.T913
                  + -0.753019*tf.T9 + 0.0503531*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar29__p_K32 = rate

@numba.njit()
def n_Ar29__He4_S26(rate_eval, tf):
    # Ar29 + n --> He4 + S26
    rate = 0.0

    # ths8r
    rate += np.exp(  14.3896 + 0.44445*tf.T913
                  + 0.0861791*tf.T9 + -0.00502699*tf.T953)

    rate_eval.n_Ar29__He4_S26 = rate

@numba.njit()
def n_Ar29__p_Cl29(rate_eval, tf):
    # Ar29 + n --> p + Cl29
    rate = 0.0

    # ths8r
    rate += np.exp(  19.5297 + 0.798542*tf.T913
                  + -0.0474751*tf.T9 + 0.00299523*tf.T953)

    rate_eval.n_Ar29__p_Cl29 = rate

@numba.njit()
def p_Cl52__He4_S49(rate_eval, tf):
    # Cl52 + p --> He4 + S49
    rate = 0.0

    # rath 
    rate += np.exp(  102.542 + -4.89782*tf.T9i + 182.387*tf.T913i + -303.383*tf.T913
                  + 17.3268*tf.T9 + -0.957701*tf.T953 + 150.06*tf.lnT9)

    rate_eval.p_Cl52__He4_S49 = rate

@numba.njit()
def p_Cl52__n_Ar52(rate_eval, tf):
    # Cl52 + p --> n + Ar52
    rate = 0.0

    # rath 
    rate += np.exp(  112.38 + -4.94206*tf.T9i + 184.844*tf.T913i + -301.023*tf.T913
                  + 16.4034*tf.T9 + -0.907826*tf.T953 + 150.786*tf.lnT9)

    rate_eval.p_Cl52__n_Ar52 = rate

@numba.njit()
def p_O16__F17(rate_eval, tf):
    # O16 + p --> F17
    rate = 0.0

    # ia08n
    rate += np.exp(  19.0904 + -16.696*tf.T913i + -1.16252*tf.T913
                  + 0.267703*tf.T9 + -0.0338411*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_O16__F17 = rate

@numba.njit()
def He4_Cl51__n_K54(rate_eval, tf):
    # Cl51 + He4 --> n + K54
    rate = 0.0

    # rath 
    rate += np.exp(  -390.709 + 2.07225*tf.T9i + -554.157*tf.T913i + 989.176*tf.T913
                  + -65.3015*tf.T9 + 3.97861*tf.T953 + -434.012*tf.lnT9)

    rate_eval.He4_Cl51__n_K54 = rate

@numba.njit()
def n_Ti58__Ti59(rate_eval, tf):
    # Ti58 + n --> Ti59
    rate = 0.0

    # rath 
    rate += np.exp(  24.5873 + -0.0659348*tf.T9i + 7.3448*tf.T913i + -25.5757*tf.T913
                  + 3.30665*tf.T9 + -0.332656*tf.T953 + 7.99934*tf.lnT9)

    rate_eval.n_Ti58__Ti59 = rate

@numba.njit()
def He4_Cl50__K54(rate_eval, tf):
    # Cl50 + He4 --> K54
    rate = 0.0

    # rath 
    rate += np.exp(  -836.74 + 13.2492*tf.T9i + -1440.88*tf.T913i + 2371.37*tf.T913
                  + -142.182*tf.T9 + 8.17865*tf.T953 + -1110.98*tf.lnT9)

    rate_eval.He4_Cl50__K54 = rate

@numba.njit()
def p_Cl51__He4_S48(rate_eval, tf):
    # Cl51 + p --> He4 + S48
    rate = 0.0

    # rath 
    rate += np.exp(  107.998 + -4.90732*tf.T9i + 185.585*tf.T913i + -311.942*tf.T913
                  + 17.8128*tf.T9 + -0.974338*tf.T953 + 153.326*tf.lnT9)

    rate_eval.p_Cl51__He4_S48 = rate

@numba.njit()
def p_Cl50__He4_S47(rate_eval, tf):
    # Cl50 + p --> He4 + S47
    rate = 0.0

    # rath 
    rate += np.exp(  111.66 + -4.92563*tf.T9i + 189.69*tf.T913i + -319.21*tf.T913
                  + 18.126*tf.T9 + -0.992779*tf.T953 + 157.094*tf.lnT9)

    rate_eval.p_Cl50__He4_S47 = rate

@numba.njit()
def p_Cl50__n_Ar50(rate_eval, tf):
    # Cl50 + p --> n + Ar50
    rate = 0.0

    # rath 
    rate += np.exp(  109.788 + -4.85014*tf.T9i + 180.6*tf.T913i + -294.027*tf.T913
                  + 15.9798*tf.T9 + -0.884012*tf.T953 + 147.586*tf.lnT9)

    rate_eval.p_Cl50__n_Ar50 = rate

@numba.njit()
def n_Ar34__Ar35(rate_eval, tf):
    # Ar34 + n --> Ar35
    rate = 0.0

    # ths8r
    rate += np.exp(  10.6999 + 1.14834*tf.T913
                  + -0.142306*tf.T9 + 0.00918793*tf.T953)

    rate_eval.n_Ar34__Ar35 = rate

@numba.njit()
def p_B12__n_C12(rate_eval, tf):
    # B12 + p --> n + C12
    rate = 0.0

    #  wagn
    rate += np.exp(  26.7197 + -3.77039e-12*tf.T9i + -12.12*tf.T913i + -1.83547e-09*tf.T913
                  + 2.0104e-10*tf.T9 + -1.82499e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_B12__n_C12 = rate

@numba.njit()
def He4_Cl49__n_K52(rate_eval, tf):
    # Cl49 + He4 --> n + K52
    rate = 0.0

    # rath 
    rate += np.exp(  -384.269 + 2.04612*tf.T9i + -545.33*tf.T913i + 972.659*tf.T913
                  + -64.2949*tf.T9 + 3.91949*tf.T953 + -426.36*tf.lnT9)

    rate_eval.He4_Cl49__n_K52 = rate

@numba.njit()
def He4_Ar36__Ca40(rate_eval, tf):
    # Ar36 + He4 --> Ca40
    rate = 0.0

    # ths8r
    rate += np.exp(  52.3486 + -71.0046*tf.T913i + 4.0656*tf.T913
                  + -5.26509*tf.T9 + 0.683546*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar36__Ca40 = rate

@numba.njit()
def p_Cl48__He4_S45(rate_eval, tf):
    # Cl48 + p --> He4 + S45
    rate = 0.0

    # rath 
    rate += np.exp(  108.155 + -4.80168*tf.T9i + 182.266*tf.T913i + -306.461*tf.T913
                  + 17.4043*tf.T9 + -0.958839*tf.T953 + 151.06*tf.lnT9)

    rate_eval.p_Cl48__He4_S45 = rate

@numba.njit()
def He4_Ca50__n_Ti53(rate_eval, tf):
    # Ca50 + He4 --> n + Ti53
    rate = 0.0

    # rath 
    rate += np.exp(  -917.002 + 14.7544*tf.T9i + -1602.76*tf.T913i + 2632.06*tf.T913
                  + -157.413*tf.T9 + 9.04042*tf.T953 + -1234.22*tf.lnT9)

    rate_eval.He4_Ca50__n_Ti53 = rate

@numba.njit()
def p_Cl48__n_Ar48(rate_eval, tf):
    # Cl48 + p --> n + Ar48
    rate = 0.0

    # rath 
    rate += np.exp(  110.873 + -4.75597*tf.T9i + 176.993*tf.T913i + -291.851*tf.T913
                  + 16.0962*tf.T9 + -0.900847*tf.T953 + 145.618*tf.lnT9)

    rate_eval.p_Cl48__n_Ar48 = rate

@numba.njit()
def p_Ti62__n_V62(rate_eval, tf):
    # Ti62 + p --> n + V62
    rate = 0.0

    # rath 
    rate += np.exp(  133.398 + -6.33786*tf.T9i + 238.707*tf.T913i + -382.433*tf.T913
                  + 20.8962*tf.T9 + -1.16449*tf.T953 + 192.337*tf.lnT9)

    rate_eval.p_Ti62__n_V62 = rate

@numba.njit()
def He4_Cl47__n_K50(rate_eval, tf):
    # Cl47 + He4 --> n + K50
    rate = 0.0

    # rath 
    rate += np.exp(  -377.606 + 2.02674*tf.T9i + -536.786*tf.T913i + 955.891*tf.T913
                  + -63.1638*tf.T9 + 3.84755*tf.T953 + -418.806*tf.lnT9)

    rate_eval.He4_Cl47__n_K50 = rate

@numba.njit()
def p_Cl45__He4_S42(rate_eval, tf):
    # Cl45 + p --> He4 + S42
    rate = 0.0

    # rath 
    rate += np.exp(  76.9625 + -4.60442*tf.T9i + 167.822*tf.T913i + -258.225*tf.T913
                  + 12.7184*tf.T9 + -0.607547*tf.T953 + 135.806*tf.lnT9)

    rate_eval.p_Cl45__He4_S42 = rate

@numba.njit()
def p_Cl45__n_Ar45(rate_eval, tf):
    # Cl45 + p --> n + Ar45
    rate = 0.0

    # rath 
    rate += np.exp(  103.77 + -4.60366*tf.T9i + 168.931*tf.T913i + -276.691*tf.T913
                  + 15.2175*tf.T9 + -0.85335*tf.T953 + 138.921*tf.lnT9)

    rate_eval.p_Cl45__n_Ar45 = rate

@numba.njit()
def He4_Cl43__p_Ar46(rate_eval, tf):
    # Cl43 + He4 --> p + Ar46
    rate = 0.0

    # rath 
    rate += np.exp(  -727.908 + 11.8827*tf.T9i + -1295.55*tf.T913i + 2107.37*tf.T913
                  + -127.401*tf.T9 + 7.50276*tf.T953 + -988.7*tf.lnT9)

    rate_eval.He4_Cl43__p_Ar46 = rate

@numba.njit()
def p_Cl43__He4_S40(rate_eval, tf):
    # Cl43 + p --> He4 + S40
    rate = 0.0

    # rath 
    rate += np.exp(  92.1459 + -4.56337*tf.T9i + 169.946*tf.T913i + -273.015*tf.T913
                  + 13.9318*tf.T9 + -0.683285*tf.T953 + 139.643*tf.lnT9)

    rate_eval.p_Cl43__He4_S40 = rate

@numba.njit()
def p_Mn61__n_Fe61(rate_eval, tf):
    # Mn61 + p --> n + Fe61
    rate = 0.0

    # rath 
    rate += np.exp(  140.367 + -6.84597*tf.T9i + 257.042*tf.T913i + -410.336*tf.T913
                  + 22.276*tf.T9 + -1.23765*tf.T953 + 207.067*tf.lnT9)

    rate_eval.p_Mn61__n_Fe61 = rate

@numba.njit()
def He4_V49__Mn53(rate_eval, tf):
    # V49 + He4 --> Mn53
    rate = 0.0

    # ths8r
    rate += np.exp(  62.4555 + -84.3633*tf.T913i + -5.28933*tf.T913
                  + -1.3103*tf.T9 + 0.187088*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V49__Mn53 = rate

@numba.njit()
def p_V55__Cr56(rate_eval, tf):
    # V55 + p --> Cr56
    rate = 0.0

    # rath 
    rate += np.exp(  121.808 + -6.17197*tf.T9i + 229.86*tf.T913i + -371.592*tf.T913
                  + 20.6013*tf.T9 + -1.18205*tf.T953 + 186.645*tf.lnT9)

    rate_eval.p_V55__Cr56 = rate

@numba.njit()
def He4_Cl42__n_K45(rate_eval, tf):
    # Cl42 + He4 --> n + K45
    rate = 0.0

    # rath 
    rate += np.exp(  -358.55 + 2.00004*tf.T9i + -516.376*tf.T913i + 913.718*tf.T913
                  + -60.3971*tf.T9 + 3.67834*tf.T953 + -400.413*tf.lnT9)

    rate_eval.He4_Cl42__n_K45 = rate

@numba.njit()
def p_Cl42__He4_S39(rate_eval, tf):
    # Cl42 + p --> He4 + S39
    rate = 0.0

    # rath 
    rate += np.exp(  72.6263 + -4.4143*tf.T9i + 157.212*tf.T913i + -239.866*tf.T913
                  + 11.8441*tf.T9 + -0.587598*tf.T953 + 127.369*tf.lnT9)

    rate_eval.p_Cl42__He4_S39 = rate

@numba.njit()
def p_S47__n_Cl47(rate_eval, tf):
    # S47 + p --> n + Cl47
    rate = 0.0

    # rath 
    rate += np.exp(  101.738 + -4.51142*tf.T9i + 166.027*tf.T913i + -270.201*tf.T913
                  + 14.6959*tf.T9 + -0.81544*tf.T953 + 135.953*tf.lnT9)

    rate_eval.p_S47__n_Cl47 = rate

@numba.njit()
def n_Fe72__Fe73(rate_eval, tf):
    # Fe72 + n --> Fe73
    rate = 0.0

    # rath 
    rate += np.exp(  13.262 + 0.00850199*tf.T9i + -0.198495*tf.T913i + -6.45725*tf.T913
                  + 2.06933*tf.T9 + -0.282534*tf.T953 + 0.740142*tf.lnT9)

    rate_eval.n_Fe72__Fe73 = rate

@numba.njit()
def He4_Cl41__n_K44(rate_eval, tf):
    # Cl41 + He4 --> n + K44
    rate = 0.0

    # rath 
    rate += np.exp(  -351.91 + 1.96937*tf.T9i + -509.725*tf.T913i + 899.467*tf.T913
                  + -59.4051*tf.T9 + 3.61598*tf.T953 + -394.389*tf.lnT9)

    rate_eval.He4_Cl41__n_K44 = rate

@numba.njit()
def p_Cl41__He4_S38(rate_eval, tf):
    # Cl41 + p --> He4 + S38
    rate = 0.0

    # rath 
    rate += np.exp(  91.4618 + -4.39559*tf.T9i + 159.473*tf.T913i + -259.637*tf.T913
                  + 13.7718*tf.T9 + -0.728043*tf.T953 + 131.756*tf.lnT9)

    rate_eval.p_Cl41__He4_S38 = rate

@numba.njit()
def He4_Cl40__n_K43(rate_eval, tf):
    # Cl40 + He4 --> n + K43
    rate = 0.0

    # rath 
    rate += np.exp(  -349.439 + 2.01444*tf.T9i + -509.277*tf.T913i + 896.042*tf.T913
                  + -59.0474*tf.T9 + 3.5861*tf.T953 + -393.346*tf.lnT9)

    rate_eval.He4_Cl40__n_K43 = rate

@numba.njit()
def p_Cl40__n_Ar40(rate_eval, tf):
    # Cl40 + p --> n + Ar40
    rate = 0.0

    # rath 
    rate += np.exp(  102.3 + -4.37055*tf.T9i + 159.805*tf.T913i + -265.883*tf.T913
                  + 14.6628*tf.T9 + -0.822704*tf.T953 + 132.884*tf.lnT9)

    rate_eval.p_Cl40__n_Ar40 = rate

@numba.njit()
def p_O19__He4_N16(rate_eval, tf):
    # O19 + p --> He4 + N16
    rate = 0.0

    #  wagn
    rate += np.exp(  28.2781 + -3.40423e-12*tf.T9i + -16.75*tf.T913i + -1.70953e-09*tf.T913
                  + 1.89875e-10*tf.T9 + -1.73971e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_O19__He4_N16 = rate

@numba.njit()
def n_Cl36__p_S36(rate_eval, tf):
    # Cl36 + n --> p + S36
    rate = 0.0

    # ths8r
    rate += np.exp(  15.1404 + 2.26066*tf.T913
                  + -0.487956*tf.T9 + 0.0471708*tf.T953)

    rate_eval.n_Cl36__p_S36 = rate

@numba.njit()
def He4_F17__Na21(rate_eval, tf):
    # F17 + He4 --> Na21
    rate = 0.0

    # rpsmr
    rate += np.exp(  41.1529 + -1.72817*tf.T9i + 15.559*tf.T913i + -68.3231*tf.T913
                  + 2.54275*tf.T9 + -0.0989207*tf.T953 + 36.8877*tf.lnT9)

    rate_eval.He4_F17__Na21 = rate

@numba.njit()
def n_Cl35__He4_P32(rate_eval, tf):
    # Cl35 + n --> He4 + P32
    rate = 0.0

    # ths8r
    rate += np.exp(  -32.0685 + 35.1367*tf.T913
                  + -3.30169*tf.T9 + 0.150699*tf.T953)

    rate_eval.n_Cl35__He4_P32 = rate

@numba.njit()
def He4_Cl34__p_Ar37(rate_eval, tf):
    # Cl34 + He4 --> p + Ar37
    rate = 0.0

    # ths8r
    rate += np.exp(  52.795 + -68.2165*tf.T913i + 0.330057*tf.T913
                  + -0.873334*tf.T9 + 0.0592127*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl34__p_Ar37 = rate

@numba.njit()
def n_C11__He4_He4_He4(rate_eval, tf):
    # C11 + n --> 3 He4
    rate = 0.0

    # bb92r
    rate += np.exp(  22.7448 + -5.58*tf.T9i
                  + -1.5*tf.lnT9)
    # bb92n
    rate += np.exp(  18.9275)
    # bb92r
    rate += np.exp(  14.7197 + -0.917*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.n_C11__He4_He4_He4 = rate

@numba.njit()
def n_Cl34__He4_P31(rate_eval, tf):
    # Cl34 + n --> He4 + P31
    rate = 0.0

    # ths8r
    rate += np.exp(  18.8653 + -0.466069*tf.T913
                  + 0.167169*tf.T9 + -0.00537463*tf.T953)

    rate_eval.n_Cl34__He4_P31 = rate

@numba.njit()
def P42__n_n_S40__weak__mp17(rate_eval, tf):
    # P42 --> n + n + S40
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.153732)

    rate_eval.P42__n_n_S40__weak__mp17 = rate

@numba.njit()
def n_Cl34__p_S34(rate_eval, tf):
    # Cl34 + n --> p + S34
    rate = 0.0

    # ths8r
    rate += np.exp(  18.4445 + 0.847427*tf.T913
                  + 0.000125282*tf.T9 + -0.00573985*tf.T953)

    rate_eval.n_Cl34__p_S34 = rate

@numba.njit()
def n_Cl33__He4_P30(rate_eval, tf):
    # Cl33 + n --> He4 + P30
    rate = 0.0

    # ths8r
    rate += np.exp(  15.9018 + 1.33535*tf.T913
                  + -0.149988*tf.T9 + 0.0279218*tf.T953)

    rate_eval.n_Cl33__He4_P30 = rate

@numba.njit()
def p_Ti43__V44(rate_eval, tf):
    # Ti43 + p --> V44
    rate = 0.0

    # ths8r
    rate += np.exp(  38.9726 + -33.1869*tf.T913i + -3.81513*tf.T913
                  + -2.20092*tf.T9 + 0.338712*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ti43__V44 = rate

@numba.njit()
def n_Cl33__p_S33(rate_eval, tf):
    # Cl33 + n --> p + S33
    rate = 0.0

    # ths8r
    rate += np.exp(  18.5772 + 1.39633*tf.T913
                  + -0.136457*tf.T9 + 0.00585594*tf.T953)

    rate_eval.n_Cl33__p_S33 = rate

@numba.njit()
def p_Na34__Mg35(rate_eval, tf):
    # Na34 + p --> Mg35
    rate = 0.0

    # rath 
    rate += np.exp(  69.5413 + -3.02709*tf.T9i + 109.431*tf.T913i + -185.728*tf.T913
                  + 10.2181*tf.T9 + -0.565824*tf.T953 + 92.3148*tf.lnT9)

    rate_eval.p_Na34__Mg35 = rate

@numba.njit()
def He4_S48__n_Ar51(rate_eval, tf):
    # S48 + He4 --> n + Ar51
    rate = 0.0

    # rath 
    rate += np.exp(  -362.477 + 1.89468*tf.T9i + -514.56*tf.T913i + 918.478*tf.T913
                  + -60.8722*tf.T9 + 3.71441*tf.T953 + -401.925*tf.lnT9)

    rate_eval.He4_S48__n_Ar51 = rate

@numba.njit()
def n_Cl31__p_S31(rate_eval, tf):
    # Cl31 + n --> p + S31
    rate = 0.0

    # ths8r
    rate += np.exp(  18.5484 + 1.72683*tf.T913
                  + -0.223785*tf.T9 + 0.0160054*tf.T953)

    rate_eval.n_Cl31__p_S31 = rate

@numba.njit()
def He4_Ar35__p_K38(rate_eval, tf):
    # Ar35 + He4 --> p + K38
    rate = 0.0

    # ths8r
    rate += np.exp(  53.7318 + -70.9375*tf.T913i + 0.516471*tf.T913
                  + -0.946325*tf.T9 + 0.0684713*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar35__p_K38 = rate

@numba.njit()
def He4_Cl30__p_Ar33(rate_eval, tf):
    # Cl30 + He4 --> p + Ar33
    rate = 0.0

    # ths8r
    rate += np.exp(  52.3051 + -67.9024*tf.T913i + 0.19456*tf.T913
                  + -0.781433*tf.T9 + 0.0533255*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl30__p_Ar33 = rate

@numba.njit()
def Ca35__K35__weak__wc17(rate_eval, tf):
    # Ca35 --> K35
    rate = 0.0

    # wc17w
    rate += np.exp(  -111.835)

    rate_eval.Ca35__K35__weak__wc17 = rate

@numba.njit()
def n_Cl29__He4_P26(rate_eval, tf):
    # Cl29 + n --> He4 + P26
    rate = 0.0

    # ths8r
    rate += np.exp(  15.5353 + -0.4078*tf.T913
                  + 0.267622*tf.T9 + -0.01407*tf.T953)

    rate_eval.n_Cl29__He4_P26 = rate

@numba.njit()
def He4_Na25__Al29(rate_eval, tf):
    # Na25 + He4 --> Al29
    rate = 0.0

    # rath 
    rate += np.exp(  -1.9634 + -2.06673*tf.T9i + -21.1952*tf.T913i + 14.8785*tf.T913
                  + -3.54907*tf.T9 + 0.287791*tf.T953 + 4.1834*tf.lnT9)

    rate_eval.He4_Na25__Al29 = rate

@numba.njit()
def n_Cl29__p_S29(rate_eval, tf):
    # Cl29 + n --> p + S29
    rate = 0.0

    # ths8r
    rate += np.exp(  18.6093 + 1.79806*tf.T913
                  + -0.241061*tf.T9 + 0.0173929*tf.T953)

    rate_eval.n_Cl29__p_S29 = rate

@numba.njit()
def He4_Cl28__p_Ar31(rate_eval, tf):
    # Cl28 + He4 --> p + Ar31
    rate = 0.0

    # ths8r
    rate += np.exp(  51.7571 + -67.7158*tf.T913i + 0.0464732*tf.T913
                  + -0.729512*tf.T9 + 0.0522057*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl28__p_Ar31 = rate

@numba.njit()
def n_V49__p_Ti49(rate_eval, tf):
    # V49 + n --> p + Ti49
    rate = 0.0

    # ths8r
    rate += np.exp(  15.9391 + -2.17107*tf.T913
                  + 1.10014*tf.T9 + -0.0944408*tf.T953)

    rate_eval.n_V49__p_Ti49 = rate

@numba.njit()
def n_Cl28__He4_P25(rate_eval, tf):
    # Cl28 + n --> He4 + P25
    rate = 0.0

    # ths8r
    rate += np.exp(  15.0961 + 1.10577*tf.T913
                  + 0.016606*tf.T9 + -0.00777096*tf.T953)

    rate_eval.n_Cl28__He4_P25 = rate

@numba.njit()
def d_Li8__n_Be9(rate_eval, tf):
    # Li8 + d --> n + Be9
    rate = 0.0

    # mafon
    rate += np.exp(  26.4 + -5.94754e-12*tf.T9i + -10.259*tf.T913i + -2.53711e-09*tf.T913
                  + 2.5234e-10*tf.T9 + -2.10055e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.d_Li8__n_Be9 = rate

@numba.njit()
def Cr44__V44__weak__wc12(rate_eval, tf):
    # Cr44 --> V44
    rate = 0.0

    # wc12w
    rate += np.exp(  2.63388)

    rate_eval.Cr44__V44__weak__wc12 = rate

@numba.njit()
def n_Cr57__Cr58(rate_eval, tf):
    # Cr57 + n --> Cr58
    rate = 0.0

    # rath 
    rate += np.exp(  13.7287 + -0.0116238*tf.T9i + 0.445653*tf.T913i + -0.831281*tf.T913
                  + 0.190958*tf.T9 + -0.0551895*tf.T953 + 0.110994*tf.lnT9)

    rate_eval.n_Cr57__Cr58 = rate

@numba.njit()
def p_S49__n_Cl49(rate_eval, tf):
    # S49 + p --> n + Cl49
    rate = 0.0

    # rath 
    rate += np.exp(  104.197 + -4.60521*tf.T9i + 170.458*tf.T913i + -277.137*tf.T913
                  + 15.0679*tf.T9 + -0.835079*tf.T953 + 139.278*tf.lnT9)

    rate_eval.p_S49__n_Cl49 = rate

@numba.njit()
def He4_Mg38__n_Si41(rate_eval, tf):
    # Mg38 + He4 --> n + Si41
    rate = 0.0

    # rath 
    rate += np.exp(  88.8621 + -3.85591*tf.T9i + 96.704*tf.T913i + -196.883*tf.T913
                  + 9.42041*tf.T9 + -0.482148*tf.T953 + 102.248*tf.lnT9)

    rate_eval.He4_Mg38__n_Si41 = rate

@numba.njit()
def n_Ca52__Ca53(rate_eval, tf):
    # Ca52 + n --> Ca53
    rate = 0.0

    # rath 
    rate += np.exp(  23.521 + -0.075544*tf.T9i + 8.1754*tf.T913i + -25.3734*tf.T913
                  + 2.90468*tf.T9 + -0.267136*tf.T953 + 8.51375*tf.lnT9)

    rate_eval.n_Ca52__Ca53 = rate

@numba.njit()
def p_S48__n_Cl48(rate_eval, tf):
    # S48 + p --> n + Cl48
    rate = 0.0

    # rath 
    rate += np.exp(  103.613 + -4.56189*tf.T9i + 168.637*tf.T913i + -274.809*tf.T913
                  + 14.9912*tf.T9 + -0.833689*tf.T953 + 138.027*tf.lnT9)

    rate_eval.p_S48__n_Cl48 = rate

@numba.njit()
def p_N15__O16(rate_eval, tf):
    # N15 + p --> O16
    rate = 0.0

    # li10r
    rate += np.exp(  14.5444 + -10.2295*tf.T9i
                  + 0.0459037*tf.T9 + -1.5*tf.lnT9)
    # li10r
    rate += np.exp(  6.59056 + -2.92315*tf.T9i
                  + -1.5*tf.lnT9)
    # li10n
    rate += np.exp(  20.0176 + -15.24*tf.T913i + 0.334926*tf.T913
                  + 4.59088*tf.T9 + -4.78468*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_N15__O16 = rate

@numba.njit()
def p_S47__He4_P44(rate_eval, tf):
    # S47 + p --> He4 + P44
    rate = 0.0

    # rath 
    rate += np.exp(  76.3562 + -4.56962*tf.T9i + 171.314*tf.T913i + -264.552*tf.T913
                  + 13.6715*tf.T9 + -0.708584*tf.T953 + 138.837*tf.lnT9)

    rate_eval.p_S47__He4_P44 = rate

@numba.njit()
def p_K52__He4_Ar49(rate_eval, tf):
    # K52 + p --> He4 + Ar49
    rate = 0.0

    # rath 
    rate += np.exp(  110.633 + -5.35783*tf.T9i + 202.937*tf.T913i + -331.123*tf.T913
                  + 18.2787*tf.T9 + -0.991237*tf.T953 + 165.963*tf.lnT9)

    rate_eval.p_K52__He4_Ar49 = rate

@numba.njit()
def p_S46__n_Cl46(rate_eval, tf):
    # S46 + p --> n + Cl46
    rate = 0.0

    # rath 
    rate += np.exp(  101.62 + -4.47029*tf.T9i + 164.508*tf.T913i + -268.737*tf.T913
                  + 14.6947*tf.T9 + -0.81941*tf.T953 + 135.012*tf.lnT9)

    rate_eval.p_S46__n_Cl46 = rate

@numba.njit()
def Na25__Mg25__weak__wc12(rate_eval, tf):
    # Na25 --> Mg25
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.44574)

    rate_eval.Na25__Mg25__weak__wc12 = rate

@numba.njit()
def d_Be7__p_He4_He4(rate_eval, tf):
    # Be7 + d --> p + He4 + He4
    rate = 0.0

    # cf88n
    rate += np.exp(  27.6987 + -12.428*tf.T913i
                  + -0.666667*tf.lnT9)

    rate_eval.d_Be7__p_He4_He4 = rate

@numba.njit()
def p_S45__He4_P42(rate_eval, tf):
    # S45 + p --> He4 + P42
    rate = 0.0

    # rath 
    rate += np.exp(  44.7691 + -4.37862*tf.T9i + 156.594*tf.T913i + -217.803*tf.T913
                  + 10.0339*tf.T9 + -0.507067*tf.T953 + 123.97*tf.lnT9)

    rate_eval.p_S45__He4_P42 = rate

@numba.njit()
def He4_S43__n_Ar46(rate_eval, tf):
    # S43 + He4 --> n + Ar46
    rate = 0.0

    # rath 
    rate += np.exp(  -345.315 + 1.89089*tf.T9i + -496.86*tf.T913i + 880.929*tf.T913
                  + -58.3769*tf.T9 + 3.56283*tf.T953 + -385.703*tf.lnT9)

    rate_eval.He4_S43__n_Ar46 = rate

@numba.njit()
def p_Mn64__n_Fe64(rate_eval, tf):
    # Mn64 + p --> n + Fe64
    rate = 0.0

    # rath 
    rate += np.exp(  154.01 + -7.00352*tf.T9i + 266.242*tf.T913i + -434.204*tf.T913
                  + 24.1467*tf.T9 + -1.35501*tf.T953 + 215.83*tf.lnT9)

    rate_eval.p_Mn64__n_Fe64 = rate

@numba.njit()
def p_S43__He4_P40(rate_eval, tf):
    # S43 + p --> He4 + P40
    rate = 0.0

    # rath 
    rate += np.exp(  96.4986 + -4.68822*tf.T9i + 206.251*tf.T913i + -329.277*tf.T913
                  + 15.9646*tf.T9 + -0.794453*tf.T953 + 175.778*tf.lnT9)

    rate_eval.p_S43__He4_P40 = rate

@numba.njit()
def He4_Mn67__n_Co70(rate_eval, tf):
    # Mn67 + He4 --> n + Co70
    rate = 0.0

    # rath 
    rate += np.exp(  -1185.9 + 24.7112*tf.T9i + -2454.4*tf.T913i + 3790.54*tf.T913
                  + -214.812*tf.T9 + 11.8815*tf.T953 + -1838.61*tf.lnT9)

    rate_eval.He4_Mn67__n_Co70 = rate

@numba.njit()
def p_Cr60__Mn61(rate_eval, tf):
    # Cr60 + p --> Mn61
    rate = 0.0

    # rath 
    rate += np.exp(  128.005 + -6.59991*tf.T9i + 246.869*tf.T913i + -395.565*tf.T913
                  + 21.7443*tf.T9 + -1.24714*tf.T953 + 199.157*tf.lnT9)

    rate_eval.p_Cr60__Mn61 = rate

@numba.njit()
def p_Sc57__He4_Ca54(rate_eval, tf):
    # Sc57 + p --> He4 + Ca54
    rate = 0.0

    # rath 
    rate += np.exp(  107.102 + -5.87811*tf.T9i + 217.443*tf.T913i + -345.749*tf.T913
                  + 18.9095*tf.T9 + -1.0109*tf.T953 + 175.296*tf.lnT9)

    rate_eval.p_Sc57__He4_Ca54 = rate

@numba.njit()
def He4_Fe56__Ni60(rate_eval, tf):
    # Fe56 + He4 --> Ni60
    rate = 0.0

    # ths8r
    rate += np.exp(  60.6673 + -91.8383*tf.T913i + 3.63237*tf.T913
                  + -2.73367*tf.T9 + 0.179684*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe56__Ni60 = rate

@numba.njit()
def He4_S42__n_Ar45(rate_eval, tf):
    # S42 + He4 --> n + Ar45
    rate = 0.0

    # rath 
    rate += np.exp(  -339.692 + 1.87683*tf.T9i + -491.791*tf.T913i + 869.49*tf.T913
                  + -57.5275*tf.T9 + 3.50529*tf.T953 + -380.971*tf.lnT9)

    rate_eval.He4_S42__n_Ar45 = rate

@numba.njit()
def He4_S41__n_Ar44(rate_eval, tf):
    # S41 + He4 --> n + Ar44
    rate = 0.0

    # rath 
    rate += np.exp(  -337.058 + 1.88676*tf.T9i + -489.063*tf.T913i + 863.743*tf.T913
                  + -57.1744*tf.T9 + 3.48575*tf.T953 + -378.459*tf.lnT9)

    rate_eval.He4_S41__n_Ar44 = rate

@numba.njit()
def He4_Sc63__n_V66(rate_eval, tf):
    # Sc63 + He4 --> n + V66
    rate = 0.0

    # rath 
    rate += np.exp(  -1066.3 + 17.1647*tf.T9i + -1856.07*tf.T913i + 3055.24*tf.T913
                  + -182.176*tf.T9 + 10.4468*tf.T953 + -1435.07*tf.lnT9)

    rate_eval.He4_Sc63__n_V66 = rate

@numba.njit()
def p_S41__He4_P38(rate_eval, tf):
    # S41 + p --> He4 + P38
    rate = 0.0

    # rath 
    rate += np.exp(  94.2713 + -4.58935*tf.T9i + 201.022*tf.T913i + -319.243*tf.T913
                  + 15.1788*tf.T9 + -0.745201*tf.T953 + 171.34*tf.lnT9)

    rate_eval.p_S41__He4_P38 = rate

@numba.njit()
def p_Al30__He4_Mg27(rate_eval, tf):
    # Al30 + p --> He4 + Mg27
    rate = 0.0

    # rath 
    rate += np.exp(  59.8043 + -3.1291*tf.T9i + 106.635*tf.T913i + -167.777*tf.T913
                  + 8.38429*tf.T9 + -0.42631*tf.T953 + 88.7407*tf.lnT9)

    rate_eval.p_Al30__He4_Mg27 = rate

@numba.njit()
def p_S40__n_Cl40(rate_eval, tf):
    # S40 + p --> n + Cl40
    rate = 0.0

    # rath 
    rate += np.exp(  97.5174 + -4.18842*tf.T9i + 152.466*tf.T913i + -252.54*tf.T913
                  + 13.8763*tf.T9 + -0.77506*tf.T953 + 126.56*tf.lnT9)

    rate_eval.p_S40__n_Cl40 = rate

@numba.njit()
def p_Cl40__He4_S37(rate_eval, tf):
    # Cl40 + p --> He4 + S37
    rate = 0.0

    # rath 
    rate += np.exp(  85.3025 + -4.33906*tf.T9i + 156.004*tf.T913i + -248.469*tf.T913
                  + 12.7563*tf.T9 + -0.644632*tf.T953 + 128.199*tf.lnT9)

    rate_eval.p_Cl40__He4_S37 = rate

@numba.njit()
def He4_Fe47__Ni51(rate_eval, tf):
    # Fe47 + He4 --> Ni51
    rate = 0.0

    # ths8r
    rate += np.exp(  52.7481 + -91.4525*tf.T913i + -2.06127*tf.T913
                  + -0.453483*tf.T9 + 0.00852766*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe47__Ni51 = rate

@numba.njit()
def d_Li8__t_Li7(rate_eval, tf):
    # Li8 + d --> t + Li7
    rate = 0.0

    # hi09r
    rate += np.exp(  19.5259 + -3.51*tf.T9i
                  + -0.624*tf.lnT9)
    # hi09n
    rate += np.exp(  27.0897 + -19.72*tf.T913i + 0.264846*tf.T913
                  + -0.0181997*tf.T9 + 0.00188655*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.d_Li8__t_Li7 = rate

@numba.njit()
def p_S39__He4_P36(rate_eval, tf):
    # S39 + p --> He4 + P36
    rate = 0.0

    # rath 
    rate += np.exp(  56.2454 + -4.09349*tf.T9i + 144.626*tf.T913i + -211.411*tf.T913
                  + 10.1211*tf.T9 + -0.518303*tf.T953 + 116.675*tf.lnT9)

    rate_eval.p_S39__He4_P36 = rate

@numba.njit()
def He4_S38__n_Ar41(rate_eval, tf):
    # S38 + He4 --> n + Ar41
    rate = 0.0

    # rath 
    rate += np.exp(  -324.636 + 1.86591*tf.T9i + -475.72*tf.T913i + 835.509*tf.T913
                  + -55.211*tf.T9 + 3.36118*tf.T953 + -366.298*tf.lnT9)

    rate_eval.He4_S38__n_Ar41 = rate

@numba.njit()
def p_S38__He4_P35(rate_eval, tf):
    # S38 + p --> He4 + P35
    rate = 0.0

    # rath 
    rate += np.exp(  66.9801 + -3.9963*tf.T9i + 137.678*tf.T913i + -207.992*tf.T913
                  + 9.46974*tf.T9 + -0.439218*tf.T953 + 111.758*tf.lnT9)

    rate_eval.p_S38__He4_P35 = rate

@numba.njit()
def p_S38__n_Cl38(rate_eval, tf):
    # S38 + p --> n + Cl38
    rate = 0.0

    # rath 
    rate += np.exp(  97.0425 + -4.09417*tf.T9i + 148.765*tf.T913i + -247.939*tf.T913
                  + 13.5583*tf.T9 + -0.753868*tf.T953 + 124.078*tf.lnT9)

    rate_eval.p_S38__n_Cl38 = rate

@numba.njit()
def He4_Mn47__Co51(rate_eval, tf):
    # Mn47 + He4 --> Co51
    rate = 0.0

    # ths8r
    rate += np.exp(  50.1959 + -89.0914*tf.T913i + 4.21122*tf.T913
                  + -2.14662*tf.T9 + 0.151912*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn47__Co51 = rate

@numba.njit()
def He4_S37__n_Ar40(rate_eval, tf):
    # S37 + He4 --> n + Ar40
    rate = 0.0

    # rath 
    rate += np.exp(  -319.687 + 1.8535*tf.T9i + -470.638*tf.T913i + 824.747*tf.T913
                  + -54.4776*tf.T9 + 3.31464*tf.T953 + -361.678*tf.lnT9)

    rate_eval.He4_S37__n_Ar40 = rate

@numba.njit()
def He4_K49__n_Sc52(rate_eval, tf):
    # K49 + He4 --> n + Sc52
    rate = 0.0

    # rath 
    rate += np.exp(  -877.189 + 14.1509*tf.T9i + -1536.71*tf.T913i + 2522.54*tf.T913
                  + -150.912*tf.T9 + 8.66999*tf.T953 + -1182.94*tf.lnT9)

    rate_eval.He4_K49__n_Sc52 = rate

@numba.njit()
def p_V56__He4_Ti53(rate_eval, tf):
    # V56 + p --> He4 + Ti53
    rate = 0.0

    # rath 
    rate += np.exp(  120.272 + -6.23852*tf.T9i + 233.67*tf.T913i + -372.915*tf.T913
                  + 20.2301*tf.T9 + -1.09449*tf.T953 + 189.17*tf.lnT9)

    rate_eval.p_V56__He4_Ti53 = rate

@numba.njit()
def p_S37__n_Cl37(rate_eval, tf):
    # S37 + p --> n + Cl37
    rate = 0.0

    # rath 
    rate += np.exp(  95.8943 + -4.04288*tf.T9i + 146.519*tf.T913i + -244.233*tf.T913
                  + 13.298*tf.T9 + -0.739039*tf.T953 + 122.402*tf.lnT9)

    rate_eval.p_S37__n_Cl37 = rate

@numba.njit()
def p_K49__n_Ca49(rate_eval, tf):
    # K49 + p --> n + Ca49
    rate = 0.0

    # rath 
    rate += np.exp(  112.673 + -5.15665*tf.T9i + 190.43*tf.T913i + -309.696*tf.T913
                  + 17.0431*tf.T9 + -0.957188*tf.T953 + 155.657*tf.lnT9)

    rate_eval.p_K49__n_Ca49 = rate

@numba.njit()
def p_Cl45__Ar46(rate_eval, tf):
    # Cl45 + p --> Ar46
    rate = 0.0

    # rath 
    rate += np.exp(  94.235 + -4.60975*tf.T9i + 169.412*tf.T913i + -277.251*tf.T913
                  + 15.2305*tf.T9 + -0.854359*tf.T953 + 139.265*tf.lnT9)

    rate_eval.p_Cl45__Ar46 = rate

@numba.njit()
def p_Li6__Be7(rate_eval, tf):
    # Li6 + p --> Be7
    rate = 0.0

    # nacrn
    rate += np.exp(  14.2792 + -8.4372*tf.T913i + -0.515473*tf.T913
                  + 0.0285578*tf.T9 + 0.00879731*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Li6__Be7 = rate

@numba.njit()
def p_S36__He4_P33(rate_eval, tf):
    # S36 + p --> He4 + P33
    rate = 0.0

    # ths8r
    rate += np.exp(  -14.1346 + -26.7991*tf.T913i + 44.6374*tf.T913
                  + -9.82916*tf.T9 + 0.995523*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_S36__He4_P33 = rate

@numba.njit()
def p_Cr69__He4_V66(rate_eval, tf):
    # Cr69 + p --> He4 + V66
    rate = 0.0

    # rath 
    rate += np.exp(  -47.8424 + -5.54795*tf.T9i + 108.729*tf.T913i + -84.0797*tf.T913
                  + 0.475381*tf.T9 + 0.100534*tf.T953 + 76.0546*tf.lnT9)

    rate_eval.p_Cr69__He4_V66 = rate

@numba.njit()
def p_Sc51__He4_Ca48(rate_eval, tf):
    # Sc51 + p --> He4 + Ca48
    rate = 0.0

    # rath 
    rate += np.exp(  139.539 + -5.86703*tf.T9i + 233.531*tf.T913i + -392.514*tf.T913
                  + 21.6584*tf.T9 + -1.05361*tf.T953 + 193.23*tf.lnT9)

    rate_eval.p_Sc51__He4_Ca48 = rate

@numba.njit()
def p_K51__He4_Ar48(rate_eval, tf):
    # K51 + p --> He4 + Ar48
    rate = 0.0

    # rath 
    rate += np.exp(  109.684 + -5.27976*tf.T9i + 197.774*tf.T913i + -324.812*tf.T913
                  + 18.1732*tf.T9 + -0.991361*tf.T953 + 161.97*tf.lnT9)

    rate_eval.p_K51__He4_Ar48 = rate

@numba.njit()
def He4_P34__n_Cl37(rate_eval, tf):
    # P34 + He4 --> n + Cl37
    rate = 0.0

    # rath 
    rate += np.exp(  -9.62296 + -3.04057*tf.T9i + -21.4264*tf.T913i + 25.9604*tf.T913
                  + -5.1221*tf.T9 + 0.397294*tf.T953 + 5.1141*tf.lnT9)

    rate_eval.He4_P34__n_Cl37 = rate

@numba.njit()
def He4_S35__n_Ar38(rate_eval, tf):
    # S35 + He4 --> n + Ar38
    rate = 0.0

    # ths8r
    rate += np.exp(  51.1473 + -65.58*tf.T913i + 0.762185*tf.T913
                  + -0.938779*tf.T9 + 0.0668864*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S35__n_Ar38 = rate

@numba.njit()
def p_S35__He4_P32(rate_eval, tf):
    # S35 + p --> He4 + P32
    rate = 0.0

    # ths8r
    rate += np.exp(  -30.5654 + -26.7922*tf.T913i + 56.581*tf.T913
                  + -10.5304*tf.T9 + 0.9493*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_S35__He4_P32 = rate

@numba.njit()
def n_Si43__Si44(rate_eval, tf):
    # Si43 + n --> Si44
    rate = 0.0

    # rath 
    rate += np.exp(  12.252 + -0.0920857*tf.T9i + 7.67153*tf.T913i + -16.9954*tf.T913
                  + 1.45839*tf.T9 + -0.0890566*tf.T953 + 6.46873*tf.lnT9)

    rate_eval.n_Si43__Si44 = rate

@numba.njit()
def p_Sc57__n_Ti57(rate_eval, tf):
    # Sc57 + p --> n + Ti57
    rate = 0.0

    # rath 
    rate += np.exp(  124.879 + -5.90712*tf.T9i + 220.596*tf.T913i + -354.099*tf.T913
                  + 19.2718*tf.T9 + -1.07297*tf.T953 + 178.45*tf.lnT9)

    rate_eval.p_Sc57__n_Ti57 = rate

@numba.njit()
def n_S35__He4_Si32(rate_eval, tf):
    # S35 + n --> He4 + Si32
    rate = 0.0

    # ths8r
    rate += np.exp(  -30.1276 + 32.5444*tf.T913
                  + -2.95994*tf.T9 + 0.119682*tf.T953)

    rate_eval.n_S35__He4_Si32 = rate

@numba.njit()
def He4_S34__p_Cl37(rate_eval, tf):
    # S34 + He4 --> p + Cl37
    rate = 0.0

    # SM93 
    rate += np.exp(  80.8229 + -35.2081*tf.T9i + -47.5185*tf.T913i + -32.046*tf.T913
                  + 4.43077*tf.T9 + -0.368628*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S34__p_Cl37 = rate

@numba.njit()
def n_Al36__Al37(rate_eval, tf):
    # Al36 + n --> Al37
    rate = 0.0

    # rath 
    rate += np.exp(  12.8754 + -0.0348531*tf.T9i + 2.49795*tf.T913i + -5.6662*tf.T913
                  + 0.421542*tf.T9 + -0.0320373*tf.T953 + 1.93084*tf.lnT9)

    rate_eval.n_Al36__Al37 = rate

@numba.njit()
def p_Cl35__He4_S32(rate_eval, tf):
    # Cl35 + p --> He4 + S32
    rate = 0.0

    # il10r
    rate += np.exp(  -1.01202 + -3.93495*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -57.5294 + -0.532931*tf.T9i + 25.5338*tf.T913
                  + 6.45824*tf.T9 + -0.950294*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  32.12 + -30.9147*tf.T913i + -1.2345*tf.T913
                  + 22.5118*tf.T9 + -33.0589*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  2.29121 + -6.00976*tf.T9i + 5.33756*tf.T913
                  + 1.64418*tf.T9 + -0.246167*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Cl35__He4_S32 = rate

@numba.njit()
def He4_Ti60__Cr64(rate_eval, tf):
    # Ti60 + He4 --> Cr64
    rate = 0.0

    # rath 
    rate += np.exp(  -1032.83 + 21.4366*tf.T9i + -2132.56*tf.T913i + 3285.69*tf.T913
                  + -186.146*tf.T9 + 10.258*tf.T953 + -1594.06*tf.lnT9)

    rate_eval.He4_Ti60__Cr64 = rate

@numba.njit()
def Cr68__Mn68__weak__mo03(rate_eval, tf):
    # Cr68 --> Mn68
    rate = 0.0

    # mo03w
    rate += np.exp(  3.34908)

    rate_eval.Cr68__Mn68__weak__mo03 = rate

@numba.njit()
def n_S33__He4_Si30(rate_eval, tf):
    # S33 + n --> He4 + Si30
    rate = 0.0

    # ths8r
    rate += np.exp(  17.1798 + -0.725571*tf.T913
                  + 0.430731*tf.T9 + -0.0323663*tf.T953)

    rate_eval.n_S33__He4_Si30 = rate

@numba.njit()
def He4_S31__p_Cl34(rate_eval, tf):
    # S31 + He4 --> p + Cl34
    rate = 0.0

    # ths8r
    rate += np.exp(  50.2997 + -65.2934*tf.T913i + 1.2687*tf.T913
                  + -1.08925*tf.T9 + 0.0898609*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S31__p_Cl34 = rate

@numba.njit()
def He4_S30__p_Cl33(rate_eval, tf):
    # S30 + He4 --> p + Cl33
    rate = 0.0

    # ths8r
    rate += np.exp(  50.7513 + -65.211*tf.T913i + 0.403887*tf.T913
                  + -0.808239*tf.T9 + 0.0581461*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S30__p_Cl33 = rate

@numba.njit()
def n_S30__He4_Si27(rate_eval, tf):
    # S30 + n --> He4 + Si27
    rate = 0.0

    # ths8r
    rate += np.exp(  14.3423 + 1.55858*tf.T913
                  + -0.0243677*tf.T9 + 0.00835247*tf.T953)

    rate_eval.n_S30__He4_Si27 = rate

@numba.njit()
def n_S30__p_P30(rate_eval, tf):
    # S30 + n --> p + P30
    rate = 0.0

    # ths8r
    rate += np.exp(  18.4197 + 1.95764*tf.T913
                  + -0.276549*tf.T9 + 0.0196548*tf.T953)

    rate_eval.n_S30__p_P30 = rate

@numba.njit()
def Cl49__n_n_n_Ar46__weak__mo03(rate_eval, tf):
    # Cl49 --> 3 n + Ar46
    rate = 0.0

    # mo03w
    rate += np.exp(  0.408104)

    rate_eval.Cl49__n_n_n_Ar46__weak__mo03 = rate

@numba.njit()
def He4_S28__p_Cl31(rate_eval, tf):
    # S28 + He4 --> p + Cl31
    rate = 0.0

    # ths8r
    rate += np.exp(  51.0447 + -65.031*tf.T913i + 0.337267*tf.T913
                  + -0.794128*tf.T9 + 0.0547785*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S28__p_Cl31 = rate

@numba.njit()
def n_Cr43__He4_Ti40(rate_eval, tf):
    # Cr43 + n --> He4 + Ti40
    rate = 0.0

    # ths8r
    rate += np.exp(  15.7166 + -0.721603*tf.T913
                  + 0.265678*tf.T9 + -0.00766693*tf.T953)

    rate_eval.n_Cr43__He4_Ti40 = rate

@numba.njit()
def n_S28__He4_Si25(rate_eval, tf):
    # S28 + n --> He4 + Si25
    rate = 0.0

    # ths8r
    rate += np.exp(  14.0683 + 1.06141*tf.T913
                  + 0.00205462*tf.T9 + -0.000783957*tf.T953)

    rate_eval.n_S28__He4_Si25 = rate

@numba.njit()
def Ca53__Sc53__weak__wc12(rate_eval, tf):
    # Ca53 --> Sc53
    rate = 0.0

    # wc12w
    rate += np.exp(  1.68476)

    rate_eval.Ca53__Sc53__weak__wc12 = rate

@numba.njit()
def He4_S26__p_Cl29(rate_eval, tf):
    # S26 + He4 --> p + Cl29
    rate = 0.0

    # ths8r
    rate += np.exp(  50.0756 + -64.8267*tf.T913i + 0.330659*tf.T913
                  + -0.706924*tf.T9 + 0.0473324*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S26__p_Cl29 = rate

@numba.njit()
def n_S26__He4_Si23(rate_eval, tf):
    # S26 + n --> He4 + Si23
    rate = 0.0

    # ths8r
    rate += np.exp(  13.4675 + 2.25556*tf.T913
                  + -0.36566*tf.T9 + 0.0347657*tf.T953)

    rate_eval.n_S26__He4_Si23 = rate

@numba.njit()
def p_V65__Cr66(rate_eval, tf):
    # V65 + p --> Cr66
    rate = 0.0

    # rath 
    rate += np.exp(  133.77 + -6.68767*tf.T9i + 254.344*tf.T913i + -410.75*tf.T913
                  + 22.7856*tf.T9 + -1.28766*tf.T953 + 205.152*tf.lnT9)

    rate_eval.p_V65__Cr66 = rate

@numba.njit()
def He4_P47__n_Cl50(rate_eval, tf):
    # P47 + He4 --> n + Cl50
    rate = 0.0

    # rath 
    rate += np.exp(  -14.5287 + -3.75324*tf.T9i + -6.11353*tf.T913i + 17.4039*tf.T913
                  + -5.346*tf.T9 + 0.439886*tf.T953 + 12.5608*tf.lnT9)

    rate_eval.He4_P47__n_Cl50 = rate

@numba.njit()
def p_P47__n_S47(rate_eval, tf):
    # P47 + p --> n + S47
    rate = 0.0

    # rath 
    rate += np.exp(  98.8619 + -4.32374*tf.T9i + 159.308*tf.T913i + -259.654*tf.T913
                  + 14.1466*tf.T9 + -0.785091*tf.T953 + 130.492*tf.lnT9)

    rate_eval.p_P47__n_S47 = rate

@numba.njit()
def p_P45__n_S45(rate_eval, tf):
    # P45 + p --> n + S45
    rate = 0.0

    # rath 
    rate += np.exp(  100.157 + -4.25326*tf.T9i + 157.403*tf.T913i + -259.083*tf.T913
                  + 14.2109*tf.T9 + -0.794423*tf.T953 + 129.68*tf.lnT9)

    rate_eval.p_P45__n_S45 = rate

@numba.njit()
def n_Si33__Si34(rate_eval, tf):
    # Si33 + n --> Si34
    rate = 0.0

    # rath 
    rate += np.exp(  11.3312 + -0.0203928*tf.T9i + 0.794684*tf.T913i + -1.37796*tf.T913
                  + 0.211696*tf.T9 + -0.0230196*tf.T953 + 0.202766*tf.lnT9)

    rate_eval.n_Si33__Si34 = rate

@numba.njit()
def He4_P43__n_Cl46(rate_eval, tf):
    # P43 + He4 --> n + Cl46
    rate = 0.0

    # rath 
    rate += np.exp(  -13.4929 + -3.54578*tf.T9i + -10.9436*tf.T913i + 21.1952*tf.T913
                  + -5.42994*tf.T9 + 0.438392*tf.T953 + 9.95521*tf.lnT9)

    rate_eval.He4_P43__n_Cl46 = rate

@numba.njit()
def p_P43__He4_Si40(rate_eval, tf):
    # P43 + p --> He4 + Si40
    rate = 0.0

    # rath 
    rate += np.exp(  73.3535 + -4.14003*tf.T9i + 150.266*tf.T913i + -235.103*tf.T913
                  + 11.9624*tf.T9 + -0.604865*tf.T953 + 122.404*tf.lnT9)

    rate_eval.p_P43__He4_Si40 = rate

@numba.njit()
def He4_Al38__n_P41(rate_eval, tf):
    # Al38 + He4 --> n + P41
    rate = 0.0

    # rath 
    rate += np.exp(  -10.5326 + -2.89329*tf.T9i + -22.3873*tf.T913i + 32.8145*tf.T913
                  + -5.46011*tf.T9 + 0.422344*tf.T953 + 0.767048*tf.lnT9)

    rate_eval.He4_Al38__n_P41 = rate

@numba.njit()
def p_P43__n_S43(rate_eval, tf):
    # P43 + p --> n + S43
    rate = 0.0

    # rath 
    rate += np.exp(  96.1628 + -4.14931*tf.T9i + 151.829*tf.T913i + -249.231*tf.T913
                  + 13.5941*tf.T9 + -0.75438*tf.T953 + 125.19*tf.lnT9)

    rate_eval.p_P43__n_S43 = rate

@numba.njit()
def p_Sc55__n_Ti55(rate_eval, tf):
    # Sc55 + p --> n + Ti55
    rate = 0.0

    # rath 
    rate += np.exp(  123.082 + -5.80976*tf.T9i + 216.271*tf.T913i + -348.159*tf.T913
                  + 19.0674*tf.T9 + -1.07032*tf.T953 + 175.362*tf.lnT9)

    rate_eval.p_Sc55__n_Ti55 = rate

@numba.njit()
def p_P42__He4_Si39(rate_eval, tf):
    # P42 + p --> He4 + Si39
    rate = 0.0

    # rath 
    rate += np.exp(  83.7449 + -4.10853*tf.T9i + 150.341*tf.T913i + -244.673*tf.T913
                  + 13.1497*tf.T9 + -0.695127*tf.T953 + 123.939*tf.lnT9)

    rate_eval.p_P42__He4_Si39 = rate

@numba.njit()
def Ne27__n_Na26__weak__wc12(rate_eval, tf):
    # Ne27 --> n + Na26
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.820768)

    rate_eval.Ne27__n_Na26__weak__wc12 = rate

@numba.njit()
def He4_P41__p_S44(rate_eval, tf):
    # P41 + He4 --> p + S44
    rate = 0.0

    # rath 
    rate += np.exp(  -595.673 + 10.0584*tf.T9i + -1102.34*tf.T913i + 1764.1*tf.T913
                  + -106.119*tf.T9 + 6.20118*tf.T953 + -831.275*tf.lnT9)

    rate_eval.He4_P41__p_S44 = rate

@numba.njit()
def He4_P41__n_Cl44(rate_eval, tf):
    # P41 + He4 --> n + Cl44
    rate = 0.0

    # rath 
    rate += np.exp(  -12.9153 + -3.43895*tf.T9i + -13.321*tf.T913i + 22.6066*tf.T913
                  + -5.39776*tf.T9 + 0.433821*tf.T953 + 8.74959*tf.lnT9)

    rate_eval.He4_P41__n_Cl44 = rate

@numba.njit()
def p_O20__He4_N17(rate_eval, tf):
    # O20 + p --> He4 + N17
    rate = 0.0

    # rpsmr
    rate += np.exp(  50.1346 + -1.99648*tf.T9i + 76.8633*tf.T913i + -125.555*tf.T913
                  + 5.80402*tf.T9 + -0.267067*tf.T953 + 67.444*tf.lnT9)

    rate_eval.p_O20__He4_N17 = rate

@numba.njit()
def p_Ar43__He4_Cl40(rate_eval, tf):
    # Ar43 + p --> He4 + Cl40
    rate = 0.0

    # rath 
    rate += np.exp(  25.4799 + -3.41754*tf.T9i + 81.7144*tf.T913i + -123.912*tf.T913
                  + 2.05502*tf.T9 + 0.114428*tf.T953 + 83.0788*tf.lnT9)

    rate_eval.p_Ar43__He4_Cl40 = rate

@numba.njit()
def p_P38__He4_Si35(rate_eval, tf):
    # P38 + p --> He4 + Si35
    rate = 0.0

    # rath 
    rate += np.exp(  80.2435 + -3.88719*tf.T9i + 138.751*tf.T913i + -225.258*tf.T913
                  + 11.7274*tf.T9 + -0.586389*tf.T953 + 114.847*tf.lnT9)

    rate_eval.p_P38__He4_Si35 = rate

@numba.njit()
def p_P38__n_S38(rate_eval, tf):
    # P38 + p --> n + S38
    rate = 0.0

    # rath 
    rate += np.exp(  93.3568 + -3.91729*tf.T9i + 142.121*tf.T913i + -236.634*tf.T913
                  + 12.9636*tf.T9 + -0.722236*tf.T953 + 118.496*tf.lnT9)

    rate_eval.p_P38__n_S38 = rate

@numba.njit()
def n_S33__p_P33(rate_eval, tf):
    # S33 + n --> p + P33
    rate = 0.0

    # ths8r
    rate += np.exp(  5.10143 + 8.02978*tf.T913
                  + -0.479244*tf.T9 + 0.0134889*tf.T953)

    rate_eval.n_S33__p_P33 = rate

@numba.njit()
def p_F18__He4_O15(rate_eval, tf):
    # F18 + p --> He4 + O15
    rate = 0.0

    # il10r
    rate += np.exp(  1.75704 + -3.01675*tf.T9i + 13.3223*tf.T913
                  + -1.36696*tf.T9 + 0.0757363*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -31.7388 + -0.376432*tf.T9i + 61.738*tf.T913
                  + -108.29*tf.T9 + -34.2365*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  62.0058 + -21.4023*tf.T913i + -80.8891*tf.T913
                  + 134.6*tf.T9 + -126.504*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_F18__He4_O15 = rate

@numba.njit()
def He4_P37__n_Cl40(rate_eval, tf):
    # P37 + He4 --> n + Cl40
    rate = 0.0

    # rath 
    rate += np.exp(  -7.64169 + -3.25742*tf.T9i + -14.054*tf.T913i + 16.5702*tf.T913
                  + -4.66091*tf.T9 + 0.374758*tf.T953 + 10.0889*tf.lnT9)

    rate_eval.He4_P37__n_Cl40 = rate

@numba.njit()
def p_P37__He4_Si34(rate_eval, tf):
    # P37 + p --> He4 + Si34
    rate = 0.0

    # rath 
    rate += np.exp(  89.0153 + -3.87172*tf.T9i + 140.439*tf.T913i + -236.101*tf.T913
                  + 12.9434*tf.T9 + -0.690996*tf.T953 + 117.574*tf.lnT9)

    rate_eval.p_P37__He4_Si34 = rate

@numba.njit()
def p_P36__He4_Si33(rate_eval, tf):
    # P36 + p --> He4 + Si33
    rate = 0.0

    # rath 
    rate += np.exp(  85.7361 + -3.81554*tf.T9i + 137.531*tf.T913i + -228.055*tf.T913
                  + 12.2388*tf.T9 + -0.656682*tf.T953 + 114.943*tf.lnT9)

    rate_eval.p_P36__He4_Si33 = rate

@numba.njit()
def n_Ti54__Ti55(rate_eval, tf):
    # Ti54 + n --> Ti55
    rate = 0.0

    # rath 
    rate += np.exp(  16.568 + 0.00252315*tf.T9i + 0.266251*tf.T913i + -6.8382*tf.T913
                  + 1.54978*tf.T9 + -0.198682*tf.T953 + 1.06287*tf.lnT9)

    rate_eval.n_Ti54__Ti55 = rate

@numba.njit()
def p_P36__n_S36(rate_eval, tf):
    # P36 + p --> n + S36
    rate = 0.0

    # rath 
    rate += np.exp(  92.0298 + -3.81916*tf.T9i + 137.976*tf.T913i + -230.615*tf.T913
                  + 12.5465*tf.T9 + -0.696639*tf.T953 + 115.549*tf.lnT9)

    rate_eval.p_P36__n_S36 = rate

@numba.njit()
def p_Mn69__n_Fe69(rate_eval, tf):
    # Mn69 + p --> n + Fe69
    rate = 0.0

    # rath 
    rate += np.exp(  153.394 + -7.25641*tf.T9i + 276.681*tf.T913i + -444.58*tf.T913
                  + 24.5373*tf.T9 + -1.37062*tf.T953 + 222.315*tf.lnT9)

    rate_eval.p_Mn69__n_Fe69 = rate

@numba.njit()
def p_P34__n_S34(rate_eval, tf):
    # P34 + p --> n + S34
    rate = 0.0

    # rath 
    rate += np.exp(  88.2872 + -3.71317*tf.T9i + 132.972*tf.T913i + -221.404*tf.T913
                  + 11.9005*tf.T9 + -0.656698*tf.T953 + 111.582*tf.lnT9)

    rate_eval.p_P34__n_S34 = rate

@numba.njit()
def p_Ca56__n_Sc56(rate_eval, tf):
    # Ca56 + p --> n + Sc56
    rate = 0.0

    # rath 
    rate += np.exp(  121.491 + -5.67535*tf.T9i + 211.882*tf.T913i + -341.216*tf.T913
                  + 18.6836*tf.T9 + -1.04509*tf.T953 + 171.67*tf.lnT9)

    rate_eval.p_Ca56__n_Sc56 = rate

@numba.njit()
def He4_Cl44__p_Ar47(rate_eval, tf):
    # Cl44 + He4 --> p + Ar47
    rate = 0.0

    # rath 
    rate += np.exp(  -764.144 + 12.2087*tf.T9i + -1330.51*tf.T913i + 2180.59*tf.T913
                  + -131.432*tf.T9 + 7.67696*tf.T953 + -1020.12*tf.lnT9)

    rate_eval.He4_Cl44__p_Ar47 = rate

@numba.njit()
def p_Al25__Si26(rate_eval, tf):
    # Al25 + p --> Si26
    rate = 0.0

    # li20r
    rate += np.exp(  8.74592 + -4.78862*tf.T9i
                  + -1.48545*tf.lnT9)
    # li20r
    rate += np.exp(  5.38793 + -12.4587*tf.T9i
                  + 1.48721*tf.lnT9)
    # li20r
    rate += np.exp(  -6.20781 + -1.73102*tf.T9i
                  + -0.244294*tf.lnT9)

    rate_eval.p_Al25__Si26 = rate

@numba.njit()
def p_Sc45__Ti46(rate_eval, tf):
    # Sc45 + p --> Ti46
    rate = 0.0

    # ths8r
    rate += np.exp(  34.8383 + -32.1843*tf.T913i + 1.38642*tf.T913
                  + -1.64811*tf.T9 + 0.157323*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc45__Ti46 = rate

@numba.njit()
def p_P32__He4_Si29(rate_eval, tf):
    # P32 + p --> He4 + Si29
    rate = 0.0

    # rath 
    rate += np.exp(  118.233 + -3.89928*tf.T9i + 160.025*tf.T913i + -285.126*tf.T913
                  + 16.3226*tf.T9 + -0.928477*tf.T953 + 138.458*tf.lnT9)

    rate_eval.p_P32__He4_Si29 = rate

@numba.njit()
def n_P32__p_Si32(rate_eval, tf):
    # P32 + n --> p + Si32
    rate = 0.0

    # rath 
    rate += np.exp(  -33.9397 + 0.296332*tf.T9i + -31.4944*tf.T913i + 82.7906*tf.T913
                  + -5.28792*tf.T9 + 0.278753*tf.T953 + -31.7623*tf.lnT9)

    rate_eval.n_P32__p_Si32 = rate

@numba.njit()
def He4_P31__p_S34(rate_eval, tf):
    # P31 + He4 --> p + S34
    rate = 0.0

    # ths8r
    rate += np.exp(  49.0993 + -62.5433*tf.T913i + 1.69339*tf.T913
                  + -1.27872*tf.T9 + 0.106616*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P31__p_S34 = rate

@numba.njit()
def n_F25__F26(rate_eval, tf):
    # F25 + n --> F26
    rate = 0.0

    # rpsmr
    rate += np.exp(  9.56516 + -0.00738971*tf.T9i + 0.941501*tf.T913i + -5.61593*tf.T913
                  + 0.783472*tf.T9 + -0.0543499*tf.T953 + 1.30401*tf.lnT9)

    rate_eval.n_F25__F26 = rate

@numba.njit()
def He4_P30__p_S33(rate_eval, tf):
    # P30 + He4 --> p + S33
    rate = 0.0

    # ths8r
    rate += np.exp(  49.813 + -62.4643*tf.T913i + 0.492934*tf.T913
                  + -0.841855*tf.T9 + 0.059263*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P30__p_S33 = rate

@numba.njit()
def Mg39__n_n_n_Al36__weak__mo03(rate_eval, tf):
    # Mg39 --> 3 n + Al36
    rate = 0.0

    # mo03w
    rate += np.exp(  3.0915)

    rate_eval.Mg39__n_n_n_Al36__weak__mo03 = rate

@numba.njit()
def He4_K55__n_Sc58(rate_eval, tf):
    # K55 + He4 --> n + Sc58
    rate = 0.0

    # rath 
    rate += np.exp(  -437.103 + 2.17622*tf.T9i + -606.905*tf.T913i + 1091.34*tf.T913
                  + -72.1745*tf.T9 + 4.40073*tf.T953 + -477.684*tf.lnT9)

    rate_eval.He4_K55__n_Sc58 = rate

@numba.njit()
def n_V47__He4_Sc44(rate_eval, tf):
    # V47 + n --> He4 + Sc44
    rate = 0.0

    # ths8r
    rate += np.exp(  -34.4416 + 31.743*tf.T913
                  + -1.66241*tf.T9 + -0.0278854*tf.T953)

    rate_eval.n_V47__He4_Sc44 = rate

@numba.njit()
def n_P28__p_Si28(rate_eval, tf):
    # P28 + n --> p + Si28
    rate = 0.0

    # ths8r
    rate += np.exp(  18.4738 + 1.78908*tf.T913
                  + -0.241511*tf.T9 + 0.0173924*tf.T953)

    rate_eval.n_P28__p_Si28 = rate

@numba.njit()
def He4_P27__p_S30(rate_eval, tf):
    # P27 + He4 --> p + S30
    rate = 0.0

    # ths8r
    rate += np.exp(  49.3493 + -62.196*tf.T913i + 0.402585*tf.T913
                  + -0.751414*tf.T9 + 0.0523684*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P27__p_S30 = rate

@numba.njit()
def n_P27__He4_Al24(rate_eval, tf):
    # P27 + n --> He4 + Al24
    rate = 0.0

    # ths8r
    rate += np.exp(  15.378 + 0.325917*tf.T913
                  + 0.234222*tf.T9 + -0.0161401*tf.T953)

    rate_eval.n_P27__He4_Al24 = rate

@numba.njit()
def n_P27__p_Si27(rate_eval, tf):
    # P27 + n --> p + Si27
    rate = 0.0

    # ths8r
    rate += np.exp(  18.3615 + 2.31646*tf.T913
                  + -0.344644*tf.T9 + 0.0239329*tf.T953)

    rate_eval.n_P27__p_Si27 = rate

@numba.njit()
def He4_P26__p_S29(rate_eval, tf):
    # P26 + He4 --> p + S29
    rate = 0.0

    # ths8r
    rate += np.exp(  49.8282 + -62.0947*tf.T913i + 0.336874*tf.T913
                  + -0.779016*tf.T9 + 0.0552547*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P26__p_S29 = rate

@numba.njit()
def n_Cr47__He4_Ti44(rate_eval, tf):
    # Cr47 + n --> He4 + Ti44
    rate = 0.0

    # ths8r
    rate += np.exp(  18.428 + -1.39278*tf.T913
                  + 0.393768*tf.T9 + -0.0353577*tf.T953)

    rate_eval.n_Cr47__He4_Ti44 = rate

@numba.njit()
def n_P26__He4_Al23(rate_eval, tf):
    # P26 + n --> He4 + Al23
    rate = 0.0

    # ths8r
    rate += np.exp(  15.9759 + 0.519692*tf.T913
                  + -0.049713*tf.T9 + -0.000276202*tf.T953)

    rate_eval.n_P26__He4_Al23 = rate

@numba.njit()
def n_P26__p_Si26(rate_eval, tf):
    # P26 + n --> p + Si26
    rate = 0.0

    # ths8r
    rate += np.exp(  18.6214 + 1.84629*tf.T913
                  + -0.256577*tf.T9 + 0.0190237*tf.T953)

    rate_eval.n_P26__p_Si26 = rate

@numba.njit()
def He4_P25__p_S28(rate_eval, tf):
    # P25 + He4 --> p + S28
    rate = 0.0

    # ths8r
    rate += np.exp(  48.979 + -61.9857*tf.T913i + 0.396878*tf.T913
                  + -0.717028*tf.T9 + 0.0494789*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P25__p_S28 = rate

@numba.njit()
def He4_P24__p_S27(rate_eval, tf):
    # P24 + He4 --> p + S27
    rate = 0.0

    # ths8r
    rate += np.exp(  48.8414 + -61.8692*tf.T913i + 0.363684*tf.T913
                  + -0.699459*tf.T9 + 0.0481254*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P24__p_S27 = rate

@numba.njit()
def n_P24__He4_Al21(rate_eval, tf):
    # P24 + n --> He4 + Al21
    rate = 0.0

    # ths8r
    rate += np.exp(  13.7427 + 0.904608*tf.T913
                  + -0.0752674*tf.T9 + -0.00327894*tf.T953)

    rate_eval.n_P24__He4_Al21 = rate

@numba.njit()
def n_P24__p_Si24(rate_eval, tf):
    # P24 + n --> p + Si24
    rate = 0.0

    # ths8r
    rate += np.exp(  18.3093 + 2.37382*tf.T913
                  + -0.349306*tf.T9 + 0.0255632*tf.T953)

    rate_eval.n_P24__p_Si24 = rate

@numba.njit()
def p_Si45__He4_Al42(rate_eval, tf):
    # Si45 + p --> He4 + Al42
    rate = 0.0

    # rath 
    rate += np.exp(  62.9281 + -4.05755*tf.T9i + 148.947*tf.T913i + -225.718*tf.T913
                  + 10.9392*tf.T9 + -0.524746*tf.T953 + 120.272*tf.lnT9)

    rate_eval.p_Si45__He4_Al42 = rate

@numba.njit()
def p_Si45__n_P45(rate_eval, tf):
    # Si45 + p --> n + P45
    rate = 0.0

    # rath 
    rate += np.exp(  97.9305 + -4.05899*tf.T9i + 150.349*tf.T913i + -248.355*tf.T913
                  + 13.5631*tf.T9 + -0.750267*tf.T953 + 124.063*tf.lnT9)

    rate_eval.p_Si45__n_P45 = rate

@numba.njit()
def He4_Si44__n_S47(rate_eval, tf):
    # Si44 + He4 --> n + S47
    rate = 0.0

    # rath 
    rate += np.exp(  -10.0265 + -3.45151*tf.T9i + -7.83572*tf.T913i + 15.9748*tf.T913
                  + -4.96986*tf.T9 + 0.409294*tf.T953 + 11.46*tf.lnT9)

    rate_eval.He4_Si44__n_S47 = rate

@numba.njit()
def He4_P42__n_Cl45(rate_eval, tf):
    # P42 + He4 --> n + Cl45
    rate = 0.0

    # rath 
    rate += np.exp(  -13.7109 + -3.46368*tf.T9i + -14.4684*tf.T913i + 24.8295*tf.T913
                  + -5.5129*tf.T9 + 0.43951*tf.T953 + 7.63165*tf.lnT9)

    rate_eval.He4_P42__n_Cl45 = rate

@numba.njit()
def He4_Si42__n_S45(rate_eval, tf):
    # Si42 + He4 --> n + S45
    rate = 0.0

    # rath 
    rate += np.exp(  -10.3132 + -3.34295*tf.T9i + -10.843*tf.T913i + 19.3003*tf.T913
                  + -5.13226*tf.T9 + 0.41797*tf.T953 + 9.59422*tf.lnT9)

    rate_eval.He4_Si42__n_S45 = rate

@numba.njit()
def Na26__Mg26__weak__wc12(rate_eval, tf):
    # Na26 --> Mg26
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.434172)

    rate_eval.Na26__Mg26__weak__wc12 = rate

@numba.njit()
def p_Si42__n_P42(rate_eval, tf):
    # Si42 + p --> n + P42
    rate = 0.0

    # rath 
    rate += np.exp(  91.7916 + -3.91717*tf.T9i + 142.849*tf.T913i + -234.452*tf.T913
                  + 12.7323*tf.T9 + -0.704172*tf.T953 + 117.883*tf.lnT9)

    rate_eval.p_Si42__n_P42 = rate

@numba.njit()
def n_Mn54__p_Cr54(rate_eval, tf):
    # Mn54 + n --> p + Cr54
    rate = 0.0

    # ths8r
    rate += np.exp(  15.9581 + -1.70783*tf.T913
                  + 0.767763*tf.T9 + -0.0572818*tf.T953)

    rate_eval.n_Mn54__p_Cr54 = rate

@numba.njit()
def Sc38__Ca38__weak__mo97(rate_eval, tf):
    # Sc38 --> Ca38
    rate = 0.0

    # mo97w
    rate += np.exp(  2.79645)

    rate_eval.Sc38__Ca38__weak__mo97 = rate

@numba.njit()
def He4_Si40__n_S43(rate_eval, tf):
    # Si40 + He4 --> n + S43
    rate = 0.0

    # rath 
    rate += np.exp(  -14.1303 + -3.21462*tf.T9i + -15.9489*tf.T913i + 28.901*tf.T913
                  + -5.85248*tf.T9 + 0.464963*tf.T953 + 5.49878*tf.lnT9)

    rate_eval.He4_Si40__n_S43 = rate

@numba.njit()
def He4_Si39__n_S42(rate_eval, tf):
    # Si39 + He4 --> n + S42
    rate = 0.0

    # rath 
    rate += np.exp(  -9.37792 + -3.18629*tf.T9i + -14.2192*tf.T913i + 21.2303*tf.T913
                  + -5.07971*tf.T9 + 0.408479*tf.T953 + 7.94724*tf.lnT9)

    rate_eval.He4_Si39__n_S42 = rate

@numba.njit()
def Mn68__Fe68__weak__wc17(rate_eval, tf):
    # Mn68 --> Fe68
    rate = 0.0

    # wc17w
    rate += np.exp(  2.98589)

    rate_eval.Mn68__Fe68__weak__wc17 = rate

@numba.njit()
def p_S38__Cl39(rate_eval, tf):
    # S38 + p --> Cl39
    rate = 0.0

    # rath 
    rate += np.exp(  90.7866 + -4.08329*tf.T9i + 147.719*tf.T913i + -247.717*tf.T913
                  + 13.5477*tf.T9 + -0.759751*tf.T953 + 123.349*tf.lnT9)

    rate_eval.p_S38__Cl39 = rate

@numba.njit()
def p_Si39__n_P39(rate_eval, tf):
    # Si39 + p --> n + P39
    rate = 0.0

    # rath 
    rate += np.exp(  88.4175 + -3.78628*tf.T9i + 137.011*tf.T913i + -225.252*tf.T913
                  + 12.2053*tf.T9 + -0.673417*tf.T953 + 113.474*tf.lnT9)

    rate_eval.p_Si39__n_P39 = rate

@numba.njit()
def p_Sc62__n_Ti62(rate_eval, tf):
    # Sc62 + p --> n + Ti62
    rate = 0.0

    # rath 
    rate += np.exp(  137.069 + -6.13362*tf.T9i + 232.04*tf.T913i + -378.581*tf.T913
                  + 20.992*tf.T9 + -1.17602*tf.T953 + 188.343*tf.lnT9)

    rate_eval.p_Sc62__n_Ti62 = rate

@numba.njit()
def n_Cr47__p_V47(rate_eval, tf):
    # Cr47 + n --> p + V47
    rate = 0.0

    # ths8r
    rate += np.exp(  21.912 + -1.31295*tf.T913
                  + 0.354332*tf.T9 + -0.0323899*tf.T953)

    rate_eval.n_Cr47__p_V47 = rate

@numba.njit()
def He4_Si38__n_S41(rate_eval, tf):
    # Si38 + He4 --> n + S41
    rate = 0.0

    # rath 
    rate += np.exp(  -9.04786 + -3.13237*tf.T9i + -15.3868*tf.T913i + 21.9218*tf.T913
                  + -5.06898*tf.T9 + 0.405614*tf.T953 + 7.37058*tf.lnT9)

    rate_eval.He4_Si38__n_S41 = rate

@numba.njit()
def p_Ti65__He4_Sc62(rate_eval, tf):
    # Ti65 + p --> He4 + Sc62
    rate = 0.0

    # rath 
    rate += np.exp(  84.7363 + -6.54553*tf.T9i + 252.546*tf.T913i + -372.371*tf.T913
                  + 19.4601*tf.T9 + -1.06587*tf.T953 + 200.417*tf.lnT9)

    rate_eval.p_Ti65__He4_Sc62 = rate

@numba.njit()
def He4_Si37__n_S40(rate_eval, tf):
    # Si37 + He4 --> n + S40
    rate = 0.0

    # rath 
    rate += np.exp(  -8.80871 + -3.07577*tf.T9i + -16.7225*tf.T913i + 22.878*tf.T913
                  + -5.07082*tf.T9 + 0.403909*tf.T953 + 6.66362*tf.lnT9)

    rate_eval.He4_Si37__n_S40 = rate

@numba.njit()
def He4_Ca40__Ti44(rate_eval, tf):
    # Ca40 + He4 --> Ti44
    rate = 0.0

    # chw0 
    rate += np.exp(  53.75 + -76.4273*tf.T913i + 3.87451*tf.T913
                  + -3.61477*tf.T9 + 0.367451*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca40__Ti44 = rate

@numba.njit()
def p_Si37__He4_Al34(rate_eval, tf):
    # Si37 + p --> He4 + Al34
    rate = 0.0

    # rath 
    rate += np.exp(  48.7001 + -3.75416*tf.T9i + 139.74*tf.T913i + -201.413*tf.T913
                  + 9.07386*tf.T9 + -0.435051*tf.T953 + 113.661*tf.lnT9)

    rate_eval.p_Si37__He4_Al34 = rate

@numba.njit()
def O14__N14__weak__wc12(rate_eval, tf):
    # O14 --> N14
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.62354)

    rate_eval.O14__N14__weak__wc12 = rate

@numba.njit()
def p_Si37__n_P37(rate_eval, tf):
    # Si37 + p --> n + P37
    rate = 0.0

    # rath 
    rate += np.exp(  88.7651 + -3.68934*tf.T9i + 133.165*tf.T913i + -221.822*tf.T913
                  + 12.1308*tf.T9 + -0.674612*tf.T953 + 111.161*tf.lnT9)

    rate_eval.p_Si37__n_P37 = rate

@numba.njit()
def p_Si35__He4_Al32(rate_eval, tf):
    # Si35 + p --> He4 + Al32
    rate = 0.0

    # rath 
    rate += np.exp(  48.9826 + -3.59676*tf.T9i + 128.567*tf.T913i + -187.588*tf.T913
                  + 8.66696*tf.T9 + -0.421968*tf.T953 + 104.632*tf.lnT9)

    rate_eval.p_Si35__He4_Al32 = rate

@numba.njit()
def He3__t__weak__electron_capture(rate_eval, tf):
    # He3 --> t
    rate = 0.0

    #   ecw
    rate += np.exp(  -32.462 + -0.21338*tf.T9i + -0.821581*tf.T913i + 11.1241*tf.T913
                  + -0.577338*tf.T9 + 0.0290471*tf.T953 + -0.262705*tf.lnT9)

    rate_eval.He3__t__weak__electron_capture = rate

@numba.njit()
def p_Si33__n_P33(rate_eval, tf):
    # Si33 + p --> n + P33
    rate = 0.0

    # rath 
    rate += np.exp(  83.9132 + -3.48814*tf.T9i + 124.1*tf.T913i + -206.932*tf.T913
                  + 11.1244*tf.T9 + -0.614581*tf.T953 + 104.349*tf.lnT9)

    rate_eval.p_Si33__n_P33 = rate

@numba.njit()
def He4_Mn45__p_Fe48(rate_eval, tf):
    # Mn45 + He4 --> p + Fe48
    rate = 0.0

    # ths8r
    rate += np.exp(  61.3147 + -88.989*tf.T913i + -1.30257*tf.T913
                  + -0.417112*tf.T9 + 0.00356355*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn45__p_Fe48 = rate

@numba.njit()
def He4_Cr41__p_Mn44(rate_eval, tf):
    # Cr41 + He4 --> p + Mn44
    rate = 0.0

    # ths8r
    rate += np.exp(  60.5435 + -86.3725*tf.T913i + -1.31678*tf.T913
                  + -0.416126*tf.T9 + 0.00367425*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr41__p_Mn44 = rate

@numba.njit()
def He4_Mn43__Co47(rate_eval, tf):
    # Mn43 + He4 --> Co47
    rate = 0.0

    # ths8r
    rate += np.exp(  49.8765 + -88.8778*tf.T913i + -0.521752*tf.T913
                  + -0.660682*tf.T9 + 0.0195998*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn43__Co47 = rate

@numba.njit()
def He4_V57__n_Mn60(rate_eval, tf):
    # V57 + He4 --> n + Mn60
    rate = 0.0

    # rath 
    rate += np.exp(  -1076.95 + 17.2446*tf.T9i + -1870.98*tf.T913i + 3078.62*tf.T913
                  + -183.891*tf.T9 + 10.5547*tf.T953 + -1444.37*tf.lnT9)

    rate_eval.He4_V57__n_Mn60 = rate

@numba.njit()
def n_Mn51__He4_V48(rate_eval, tf):
    # Mn51 + n --> He4 + V48
    rate = 0.0

    # ths8r
    rate += np.exp(  -23.8508 + 20.8632*tf.T913
                  + 0.466645*tf.T9 + -0.196969*tf.T953)

    rate_eval.n_Mn51__He4_V48 = rate

@numba.njit()
def p_V49__Cr50(rate_eval, tf):
    # V49 + p --> Cr50
    rate = 0.0

    # ths8r
    rate += np.exp(  35.2335 + -34.217*tf.T913i + 1.28258*tf.T913
                  + -1.5098*tf.T9 + 0.142011*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V49__Cr50 = rate

@numba.njit()
def B18__n_B17(rate_eval, tf):
    # B18 --> n + B17
    rate = 0.0

    # wc12s
    rate += np.exp(  17.0987)

    rate_eval.B18__n_B17 = rate

@numba.njit()
def n_Ti37__He4_Ca34(rate_eval, tf):
    # Ti37 + n --> He4 + Ca34
    rate = 0.0

    # ths8r
    rate += np.exp(  13.2757 + 0.806485*tf.T913
                  + 0.0761172*tf.T9 + -0.00311309*tf.T953)

    rate_eval.n_Ti37__He4_Ca34 = rate

@numba.njit()
def n_O24__O25(rate_eval, tf):
    # O24 + n --> O25
    rate = 0.0

    # rpsmr
    rate += np.exp(  50.195 + -4.13365*tf.T9i + 130.467*tf.T913i + -187.727*tf.T913
                  + 10.7481*tf.T9 + -0.622883*tf.T953 + 96.0339*tf.lnT9)

    rate_eval.n_O24__O25 = rate

@numba.njit()
def He4_Ti61__n_Cr64(rate_eval, tf):
    # Ti61 + He4 --> n + Cr64
    rate = 0.0

    # rath 
    rate += np.exp(  -1083.81 + 17.2608*tf.T9i + -1873.12*tf.T913i + 3089.67*tf.T913
                  + -184.707*tf.T9 + 10.6063*tf.T953 + -1448.66*tf.lnT9)

    rate_eval.He4_Ti61__n_Cr64 = rate

@numba.njit()
def Sc62__Ti62__weak__mo03(rate_eval, tf):
    # Sc62 --> Ti62
    rate = 0.0

    # mo03w
    rate += np.exp(  4.54315)

    rate_eval.Sc62__Ti62__weak__mo03 = rate

@numba.njit()
def He4_Si25__p_P28(rate_eval, tf):
    # Si25 + He4 --> p + P28
    rate = 0.0

    # ths8r
    rate += np.exp(  48.6133 + -59.1975*tf.T913i + 0.4596*tf.T913
                  + -0.796605*tf.T9 + 0.0579722*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si25__p_P28 = rate

@numba.njit()
def n_Ar35__Ar36(rate_eval, tf):
    # Ar35 + n --> Ar36
    rate = 0.0

    # ths8r
    rate += np.exp(  8.76542 + 0.542023*tf.T913
                  + 0.0223868*tf.T9 + -0.0120062*tf.T953)

    rate_eval.n_Ar35__Ar36 = rate

@numba.njit()
def p_Mn58__Fe59(rate_eval, tf):
    # Mn58 + p --> Fe59
    rate = 0.0

    # rath 
    rate += np.exp(  129.748 + -6.67599*tf.T9i + 248.931*tf.T913i + -398.8*tf.T913
                  + 21.8363*tf.T9 + -1.24332*tf.T953 + 201.148*tf.lnT9)

    rate_eval.p_Mn58__Fe59 = rate

@numba.njit()
def n_Si25__p_Al25(rate_eval, tf):
    # Si25 + n --> p + Al25
    rate = 0.0

    # ths8r
    rate += np.exp(  18.4512 + 2.14473*tf.T913
                  + -0.326805*tf.T9 + 0.0250005*tf.T953)

    rate_eval.n_Si25__p_Al25 = rate

@numba.njit()
def He4_V40__p_Cr43(rate_eval, tf):
    # V40 + He4 --> p + Cr43
    rate = 0.0

    # ths8r
    rate += np.exp(  59.9001 + -83.8937*tf.T913i + -1.36185*tf.T913
                  + -0.476387*tf.T9 + 0.0148535*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V40__p_Cr43 = rate

@numba.njit()
def He4_Si24__p_P27(rate_eval, tf):
    # Si24 + He4 --> p + P27
    rate = 0.0

    # ths8r
    rate += np.exp(  48.3498 + -59.0853*tf.T913i + 0.453417*tf.T913
                  + -0.77107*tf.T9 + 0.0556093*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si24__p_P27 = rate

@numba.njit()
def V64__n_n_Cr62__weak__mp17(rate_eval, tf):
    # V64 --> n + n + Cr62
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.31522)

    rate_eval.V64__n_n_Cr62__weak__mp17 = rate

@numba.njit()
def He4_Be7__C11(rate_eval, tf):
    # Be7 + He4 --> C11
    rate = 0.0

    # nacrr
    rate += np.exp(  11.8776 + -10.177*tf.T9i + 0.685881*tf.T913
                  + -0.697071*tf.T9 + 0.13274*tf.T953 + -1.5*tf.lnT9)
    # nacrr
    rate += np.exp(  9.43348 + -6.498*tf.T9i
                  + -1.5*tf.lnT9)
    # nacrn
    rate += np.exp(  24.2273 + -23.214*tf.T913i + -3.74943*tf.T913
                  + 1.23242*tf.T9 + -0.195665*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Be7__C11 = rate

@numba.njit()
def He4_Ca54__Ti58(rate_eval, tf):
    # Ca54 + He4 --> Ti58
    rate = 0.0

    # rath 
    rate += np.exp(  -965.051 + 15.2868*tf.T9i + -1660.5*tf.T913i + 2732.15*tf.T913
                  + -163.312*tf.T9 + 9.35233*tf.T953 + -1281.03*tf.lnT9)

    rate_eval.He4_Ca54__Ti58 = rate

@numba.njit()
def He4_K40__p_Ca43(rate_eval, tf):
    # K40 + He4 --> p + Ca43
    rate = 0.0

    # ths8r
    rate += np.exp(  43.3098 + -73.858*tf.T913i + 16.1645*tf.T913
                  + -5.93343*tf.T9 + 0.650563*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K40__p_Ca43 = rate

@numba.njit()
def He4_Si23__p_P26(rate_eval, tf):
    # Si23 + He4 --> p + P26
    rate = 0.0

    # ths8r
    rate += np.exp(  48.1583 + -58.9653*tf.T913i + 0.422257*tf.T913
                  + -0.745726*tf.T9 + 0.0532908*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si23__p_P26 = rate

@numba.njit()
def He4_Ar42__n_Ca45(rate_eval, tf):
    # Ar42 + He4 --> n + Ca45
    rate = 0.0

    # rath 
    rate += np.exp(  -371.201 + 2.04544*tf.T9i + -533.182*tf.T913i + 942.514*tf.T913
                  + -62.2175*tf.T9 + 3.78577*tf.T953 + -412.991*tf.lnT9)

    rate_eval.He4_Ar42__n_Ca45 = rate

@numba.njit()
def p_V61__He4_Ti58(rate_eval, tf):
    # V61 + p --> He4 + Ti58
    rate = 0.0

    # rath 
    rate += np.exp(  137.804 + -6.60493*tf.T9i + 257.155*tf.T913i + -421.374*tf.T913
                  + 23.6522*tf.T9 + -1.27128*tf.T953 + 209.44*tf.lnT9)

    rate_eval.p_V61__He4_Ti58 = rate

@numba.njit()
def n_Si23__p_Al23(rate_eval, tf):
    # Si23 + n --> p + Al23
    rate = 0.0

    # ths8r
    rate += np.exp(  18.4141 + 2.28254*tf.T913
                  + -0.341354*tf.T9 + 0.0252389*tf.T953)

    rate_eval.n_Si23__p_Al23 = rate

@numba.njit()
def He4_Si22__p_P25(rate_eval, tf):
    # Si22 + He4 --> p + P25
    rate = 0.0

    # ths8r
    rate += np.exp(  48.4633 + -58.835*tf.T913i + 0.194096*tf.T913
                  + -0.402765*tf.T9 + -0.0002567*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si22__p_P25 = rate

@numba.njit()
def n_Si22__He4_Mg19(rate_eval, tf):
    # Si22 + n --> He4 + Mg19
    rate = 0.0

    # ths8r
    rate += np.exp(  11.2915 + 3.30579*tf.T913
                  + -0.00938888*tf.T9 + -0.047435*tf.T953)

    rate_eval.n_Si22__He4_Mg19 = rate

@numba.njit()
def n_Si22__p_Al22(rate_eval, tf):
    # Si22 + n --> p + Al22
    rate = 0.0

    # ths8r
    rate += np.exp(  17.6661 + 3.02177*tf.T913
                  + -0.0149754*tf.T9 + -0.0407512*tf.T953)

    rate_eval.n_Si22__p_Al22 = rate

@numba.njit()
def p_Al43__n_Si43(rate_eval, tf):
    # Al43 + p --> n + Si43
    rate = 0.0

    # rath 
    rate += np.exp(  92.0313 + -3.78742*tf.T9i + 139.719*tf.T913i + -230.703*tf.T913
                  + 12.6155*tf.T9 + -0.701934*tf.T953 + 115.409*tf.lnT9)

    rate_eval.p_Al43__n_Si43 = rate

@numba.njit()
def Mg27__Al27__weak__wc12(rate_eval, tf):
    # Mg27 --> Al27
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.70687)

    rate_eval.Mg27__Al27__weak__wc12 = rate

@numba.njit()
def He4_Al42__n_P45(rate_eval, tf):
    # Al42 + He4 --> n + P45
    rate = 0.0

    # rath 
    rate += np.exp(  -9.08978 + -3.16737*tf.T9i + -11.5952*tf.T913i + 20.4972*tf.T913
                  + -5.07781*tf.T9 + 0.414142*tf.T953 + 8.05967*tf.lnT9)

    rate_eval.He4_Al42__n_P45 = rate

@numba.njit()
def p_Al41__He4_Mg38(rate_eval, tf):
    # Al41 + p --> He4 + Mg38
    rate = 0.0

    # rath 
    rate += np.exp(  65.799 + -3.71047*tf.T9i + 135.964*tf.T913i + -212.331*tf.T913
                  + 10.4432*tf.T9 + -0.500609*tf.T953 + 111.072*tf.lnT9)

    rate_eval.p_Al41__He4_Mg38 = rate

@numba.njit()
def He4_Al40__n_P43(rate_eval, tf):
    # Al40 + He4 --> n + P43
    rate = 0.0

    # rath 
    rate += np.exp(  -10.6819 + -3.02196*tf.T9i + -17.8953*tf.T913i + 28.412*tf.T913
                  + -5.36304*tf.T9 + 0.423227*tf.T953 + 3.61698*tf.lnT9)

    rate_eval.He4_Al40__n_P43 = rate

@numba.njit()
def p_Al40__He4_Mg37(rate_eval, tf):
    # Al40 + p --> He4 + Mg37
    rate = 0.0

    # rath 
    rate += np.exp(  76.0513 + -3.65251*tf.T9i + 133.231*tf.T913i + -218.469*tf.T913
                  + 11.7339*tf.T9 + -0.621053*tf.T953 + 110.271*tf.lnT9)

    rate_eval.p_Al40__He4_Mg37 = rate

@numba.njit()
def p_Al40__n_Si40(rate_eval, tf):
    # Al40 + p --> n + Si40
    rate = 0.0

    # rath 
    rate += np.exp(  90.5818 + -3.66076*tf.T9i + 134.417*tf.T913i + -223.965*tf.T913
                  + 12.2746*tf.T9 + -0.680964*tf.T953 + 111.802*tf.lnT9)

    rate_eval.p_Al40__n_Si40 = rate

@numba.njit()
def He4_Al39__p_Si42(rate_eval, tf):
    # Al39 + He4 --> p + Si42
    rate = 0.0

    # rath 
    rate += np.exp(  -23.9293 + -3.04631*tf.T9i + -12.6275*tf.T913i + 25.2075*tf.T913
                  + -5.72605*tf.T9 + 0.474455*tf.T953 + 7.45274*tf.lnT9)

    rate_eval.He4_Al39__p_Si42 = rate

@numba.njit()
def He4_Al38__p_Si41(rate_eval, tf):
    # Al38 + He4 --> p + Si41
    rate = 0.0

    # rath 
    rate += np.exp(  -247.865 + 1.45126*tf.T9i + -387.753*tf.T913i + 654.95*tf.T913
                  + -43.5386*tf.T9 + 2.71422*tf.T953 + -289.958*tf.lnT9)

    rate_eval.He4_Al38__p_Si41 = rate

@numba.njit()
def He4_Mn49__Co53(rate_eval, tf):
    # Mn49 + He4 --> Co53
    rate = 0.0

    # ths8r
    rate += np.exp(  53.7894 + -89.1861*tf.T913i + -0.631651*tf.T913
                  + -0.826494*tf.T9 + 0.0355619*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn49__Co53 = rate

@numba.njit()
def p_Al38__He4_Mg35(rate_eval, tf):
    # Al38 + p --> He4 + Mg35
    rate = 0.0

    # rath 
    rate += np.exp(  79.8791 + -3.56008*tf.T9i + 129.468*tf.T913i + -216.723*tf.T913
                  + 11.927*tf.T9 + -0.644262*tf.T953 + 108.153*tf.lnT9)

    rate_eval.p_Al38__He4_Mg35 = rate

@numba.njit()
def p_V59__n_Cr59(rate_eval, tf):
    # V59 + p --> n + Cr59
    rate = 0.0

    # rath 
    rate += np.exp(  132.305 + -6.37366*tf.T9i + 238.477*tf.T913i + -381.573*tf.T913
                  + 20.7433*tf.T9 + -1.15441*tf.T953 + 192.478*tf.lnT9)

    rate_eval.p_V59__n_Cr59 = rate

@numba.njit()
def n_V48__p_Ti48(rate_eval, tf):
    # V48 + n --> p + Ti48
    rate = 0.0

    # ths8r
    rate += np.exp(  19.5486 + -0.307045*tf.T913
                  + 0.0615476*tf.T9 + -0.00172407*tf.T953)

    rate_eval.n_V48__p_Ti48 = rate

@numba.njit()
def p_Al37__He4_Mg34(rate_eval, tf):
    # Al37 + p --> He4 + Mg34
    rate = 0.0

    # rath 
    rate += np.exp(  74.9525 + -3.50137*tf.T9i + 125.548*tf.T913i + -206.961*tf.T913
                  + 11.1721*tf.T9 + -0.605464*tf.T953 + 104.435*tf.lnT9)

    rate_eval.p_Al37__He4_Mg34 = rate

@numba.njit()
def He4_Al36__p_Si39(rate_eval, tf):
    # Al36 + He4 --> p + Si39
    rate = 0.0

    # rath 
    rate += np.exp(  -244.32 + 1.60773*tf.T9i + -388.873*tf.T913i + 652.139*tf.T913
                  + -43.5065*tf.T9 + 2.70535*tf.T953 + -287.913*tf.lnT9)

    rate_eval.He4_Al36__p_Si39 = rate

@numba.njit()
def n_Si44__Si45(rate_eval, tf):
    # Si44 + n --> Si45
    rate = 0.0

    # rath 
    rate += np.exp(  -518.789 + -29.3214*tf.T9i + -190.191*tf.T913i + 775.352*tf.T913
                  + -55.441*tf.T9 + 3.39952*tf.T953 + -286.861*tf.lnT9)

    rate_eval.n_Si44__Si45 = rate

@numba.njit()
def He4_Al36__n_P39(rate_eval, tf):
    # Al36 + He4 --> n + P39
    rate = 0.0

    # rath 
    rate += np.exp(  -9.2024 + -2.84795*tf.T9i + -19.7072*tf.T913i + 28.0989*tf.T913
                  + -5.25553*tf.T9 + 0.412616*tf.T953 + 3.32675*tf.lnT9)

    rate_eval.He4_Al36__n_P39 = rate

@numba.njit()
def p_Al36__He4_Mg33(rate_eval, tf):
    # Al36 + p --> He4 + Mg33
    rate = 0.0

    # rath 
    rate += np.exp(  75.7645 + -3.46344*tf.T9i + 124.305*tf.T913i + -206.13*tf.T913
                  + 11.2172*tf.T9 + -0.60179*tf.T953 + 103.718*tf.lnT9)

    rate_eval.p_Al36__He4_Mg33 = rate

@numba.njit()
def C22__N22__weak__wc17(rate_eval, tf):
    # C22 --> N22
    rate = 0.0

    # wc17w
    rate += np.exp(  3.79134)

    rate_eval.C22__N22__weak__wc17 = rate

@numba.njit()
def He4_Mn59__Co63(rate_eval, tf):
    # Mn59 + He4 --> Co63
    rate = 0.0

    # rath 
    rate += np.exp(  -1128.64 + 23.4528*tf.T9i + -2331.05*tf.T913i + 3593.97*tf.T913
                  + -203.611*tf.T9 + 11.236*tf.T953 + -1744.04*tf.lnT9)

    rate_eval.He4_Mn59__Co63 = rate

@numba.njit()
def p_Al36__n_Si36(rate_eval, tf):
    # Al36 + p --> n + Si36
    rate = 0.0

    # rath 
    rate += np.exp(  85.3135 + -3.47066*tf.T9i + 125.255*tf.T913i + -209.188*tf.T913
                  + 11.4144*tf.T9 + -0.633229*tf.T953 + 104.785*tf.lnT9)

    rate_eval.p_Al36__n_Si36 = rate

@numba.njit()
def p_Al41__n_Si41(rate_eval, tf):
    # Al41 + p --> n + Si41
    rate = 0.0

    # rath 
    rate += np.exp(  88.3808 + -3.68911*tf.T9i + 134.473*tf.T913i + -221.43*tf.T913
                  + 12.0041*tf.T9 + -0.66113*tf.T953 + 111.209*tf.lnT9)

    rate_eval.p_Al41__n_Si41 = rate

@numba.njit()
def p_V64__n_Cr64(rate_eval, tf):
    # V64 + p --> n + Cr64
    rate = 0.0

    # rath 
    rate += np.exp(  144.787 + -6.63355*tf.T9i + 252.251*tf.T913i + -408.877*tf.T913
                  + 22.5629*tf.T9 + -1.26058*tf.T953 + 204.038*tf.lnT9)

    rate_eval.p_V64__n_Cr64 = rate

@numba.njit()
def He4_Al35__n_P38(rate_eval, tf):
    # Al35 + He4 --> n + P38
    rate = 0.0

    # rath 
    rate += np.exp(  -5.71843 + -2.82945*tf.T9i + -17.5031*tf.T913i + 21.8889*tf.T913
                  + -4.79185*tf.T9 + 0.382946*tf.T953 + 5.74251*tf.lnT9)

    rate_eval.He4_Al35__n_P38 = rate

@numba.njit()
def p_Al35__He4_Mg32(rate_eval, tf):
    # Al35 + p --> He4 + Mg32
    rate = 0.0

    # rath 
    rate += np.exp(  74.5204 + -3.41073*tf.T9i + 121.66*tf.T913i + -201.61*tf.T913
                  + 10.7818*tf.T9 + -0.569199*tf.T953 + 101.668*tf.lnT9)

    rate_eval.p_Al35__He4_Mg32 = rate

@numba.njit()
def He4_Al34__n_P37(rate_eval, tf):
    # Al34 + He4 --> n + P37
    rate = 0.0

    # rath 
    rate += np.exp(  -6.63714 + -2.75355*tf.T9i + -20.5068*tf.T913i + 25.4979*tf.T913
                  + -4.88939*tf.T9 + 0.383492*tf.T953 + 3.6877*tf.lnT9)

    rate_eval.He4_Al34__n_P37 = rate

@numba.njit()
def p_Al34__He4_Mg31(rate_eval, tf):
    # Al34 + p --> He4 + Mg31
    rate = 0.0

    # rath 
    rate += np.exp(  75.452 + -3.37311*tf.T9i + 120.647*tf.T913i + -200.885*tf.T913
                  + 10.8777*tf.T9 + -0.586833*tf.T953 + 101.167*tf.lnT9)

    rate_eval.p_Al34__He4_Mg31 = rate

@numba.njit()
def p_Al34__n_Si34(rate_eval, tf):
    # Al34 + p --> n + Si34
    rate = 0.0

    # rath 
    rate += np.exp(  84.4454 + -3.38177*tf.T9i + 121.739*tf.T913i + -204.394*tf.T913
                  + 11.0895*tf.T9 + -0.613462*tf.T953 + 102.379*tf.lnT9)

    rate_eval.p_Al34__n_Si34 = rate

@numba.njit()
def He4_K50__Sc54(rate_eval, tf):
    # K50 + He4 --> Sc54
    rate = 0.0

    # rath 
    rate += np.exp(  -897.581 + 14.4341*tf.T9i + -1562.95*tf.T913i + 2561.07*tf.T913
                  + -152.715*tf.T9 + 8.7449*tf.T953 + -1203.06*tf.lnT9)

    rate_eval.He4_K50__Sc54 = rate

@numba.njit()
def He4_Al33__n_P36(rate_eval, tf):
    # Al33 + He4 --> n + P36
    rate = 0.0

    # rath 
    rate += np.exp(  -4.23553 + -2.7313*tf.T9i + -18.707*tf.T913i + 20.8143*tf.T913
                  + -4.54184*tf.T9 + 0.360313*tf.T953 + 5.6032*tf.lnT9)

    rate_eval.He4_Al33__n_P36 = rate

@numba.njit()
def p_Al33__He4_Mg30(rate_eval, tf):
    # Al33 + p --> He4 + Mg30
    rate = 0.0

    # rath 
    rate += np.exp(  71.9196 + -3.32691*tf.T9i + 118.231*tf.T913i + -193.182*tf.T913
                  + 10.0162*tf.T9 + -0.531441*tf.T953 + 98.7526*tf.lnT9)

    rate_eval.p_Al33__He4_Mg30 = rate

@numba.njit()
def Si43__n_n_P41__weak__mp17(rate_eval, tf):
    # Si43 --> n + n + P41
    rate = 0.0

    # mp17w
    rate += np.exp(  2.67765)

    rate_eval.Si43__n_n_P41__weak__mp17 = rate

@numba.njit()
def He4_Si27__p_P30(rate_eval, tf):
    # Si27 + He4 --> p + P30
    rate = 0.0

    # ths8r
    rate += np.exp(  49.1273 + -59.3989*tf.T913i + 0.529139*tf.T913
                  + -0.885635*tf.T9 + 0.0664556*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si27__p_P30 = rate

@numba.njit()
def p_Cl46__He4_S43(rate_eval, tf):
    # Cl46 + p --> He4 + S43
    rate = 0.0

    # rath 
    rate += np.exp(  73.3473 + -4.67488*tf.T9i + 172.051*tf.T913i + -259.78*tf.T913
                  + 12.6131*tf.T9 + -0.613486*tf.T953 + 138.584*tf.lnT9)

    rate_eval.p_Cl46__He4_S43 = rate

@numba.njit()
def p_Al33__n_Si33(rate_eval, tf):
    # Al33 + p --> n + Si33
    rate = 0.0

    # rath 
    rate += np.exp(  83.0436 + -3.34253*tf.T9i + 120.219*tf.T913i + -201.337*tf.T913
                  + 10.8728*tf.T9 + -0.600584*tf.T953 + 101.138*tf.lnT9)

    rate_eval.p_Al33__n_Si33 = rate

@numba.njit()
def p_Ne26__n_Na26(rate_eval, tf):
    # Ne26 + p --> n + Na26
    rate = 0.0

    # rath 
    rate += np.exp(  64.9754 + -2.46508*tf.T9i + 84.5414*tf.T913i + -143.623*tf.T913
                  + 7.74648*tf.T9 + -0.430456*tf.T953 + 72.5326*tf.lnT9)

    rate_eval.p_Ne26__n_Na26 = rate

@numba.njit()
def p_Al32__He4_Mg29(rate_eval, tf):
    # Al32 + p --> He4 + Mg29
    rate = 0.0

    # rath 
    rate += np.exp(  71.3763 + -3.25454*tf.T9i + 114.202*tf.T913i + -187.75*tf.T913
                  + 9.70015*tf.T9 + -0.495027*tf.T953 + 95.8224*tf.lnT9)

    rate_eval.p_Al32__He4_Mg29 = rate

@numba.njit()
def p_Al32__n_Si32(rate_eval, tf):
    # Al32 + p --> n + Si32
    rate = 0.0

    # rath 
    rate += np.exp(  80.8216 + -3.27371*tf.T9i + 116.376*tf.T913i + -194.953*tf.T913
                  + 10.4891*tf.T9 + -0.57975*tf.T953 + 98.171*tf.lnT9)

    rate_eval.p_Al32__n_Si32 = rate

@numba.njit()
def n_Cr66__Cr67(rate_eval, tf):
    # Cr66 + n --> Cr67
    rate = 0.0

    # rath 
    rate += np.exp(  26.0245 + -0.0586384*tf.T9i + 7.08816*tf.T913i + -27.5401*tf.T913
                  + 3.83289*tf.T9 + -0.406612*tf.T953 + 8.19698*tf.lnT9)

    rate_eval.n_Cr66__Cr67 = rate

@numba.njit()
def He4_Al31__p_Si34(rate_eval, tf):
    # Al31 + He4 --> p + Si34
    rate = 0.0

    # rath 
    rate += np.exp(  -210.072 + 1.49767*tf.T9i + -359.324*tf.T913i + 588.347*tf.T913
                  + -39.6662*tf.T9 + 2.49741*tf.T953 + -260.684*tf.lnT9)

    rate_eval.He4_Al31__p_Si34 = rate

@numba.njit()
def He4_Al31__n_P34(rate_eval, tf):
    # Al31 + He4 --> n + P34
    rate = 0.0

    # rath 
    rate += np.exp(  -7.17077 + -2.57225*tf.T9i + -25.3799*tf.T913i + 31.1021*tf.T913
                  + -5.16173*tf.T9 + 0.396463*tf.T953 + 0.607853*tf.lnT9)

    rate_eval.He4_Al31__n_P34 = rate

@numba.njit()
def p_Cl38__He4_S35(rate_eval, tf):
    # Cl38 + p --> He4 + S35
    rate = 0.0

    # rath 
    rate += np.exp(  91.1244 + -4.26643*tf.T9i + 154.934*tf.T913i + -251.267*tf.T913
                  + 12.9301*tf.T9 + -0.662415*tf.T953 + 128.434*tf.lnT9)

    rate_eval.p_Cl38__He4_S35 = rate

@numba.njit()
def p_Al31__He4_Mg28(rate_eval, tf):
    # Al31 + p --> He4 + Mg28
    rate = 0.0

    # rath 
    rate += np.exp(  70.9778 + -3.20904*tf.T9i + 112.302*tf.T913i + -184.128*tf.T913
                  + 9.21545*tf.T9 + -0.447333*tf.T953 + 94.3323*tf.lnT9)

    rate_eval.p_Al31__He4_Mg28 = rate

@numba.njit()
def p_Al30__n_Si30(rate_eval, tf):
    # Al30 + p --> n + Si30
    rate = 0.0

    # rath 
    rate += np.exp(  78.5586 + -3.16982*tf.T9i + 111.65*tf.T913i + -187.623*tf.T913
                  + 10.0584*tf.T9 + -0.55738*tf.T953 + 94.643*tf.lnT9)

    rate_eval.p_Al30__n_Si30 = rate

@numba.njit()
def He4_Al29__n_P32(rate_eval, tf):
    # Al29 + He4 --> n + P32
    rate = 0.0

    # rath 
    rate += np.exp(  -3.75067 + -2.48408*tf.T9i + -24.8199*tf.T913i + 25.9762*tf.T913
                  + -4.64239*tf.T9 + 0.358101*tf.T953 + 2.1695*tf.lnT9)

    rate_eval.He4_Al29__n_P32 = rate

@numba.njit()
def p_Al29__He4_Mg26(rate_eval, tf):
    # Al29 + p --> He4 + Mg26
    rate = 0.0

    # cf88r
    rate += np.exp(  16.3373 + -8.11632*tf.T9i
                  + -4.0*tf.lnT9)
    # cf88n
    rate += np.exp(  24.7307 + -23.28*tf.T913i
                  + -0.666667*tf.lnT9)
    # cf88r
    rate += np.exp(  11.8599 + -5.60132*tf.T9i
                  + 1.75*tf.lnT9)

    rate_eval.p_Al29__He4_Mg26 = rate

@numba.njit()
def p_Al29__n_Si29(rate_eval, tf):
    # Al29 + p --> n + Si29
    rate = 0.0

    # rath 
    rate += np.exp(  74.6331 + -3.09997*tf.T9i + 107.539*tf.T913i + -179.861*tf.T913
                  + 9.66559*tf.T9 + -0.539683*tf.T953 + 91.2227*tf.lnT9)

    rate_eval.p_Al29__n_Si29 = rate

@numba.njit()
def He4_Al37__n_P40(rate_eval, tf):
    # Al37 + He4 --> n + P40
    rate = 0.0

    # rath 
    rate += np.exp(  -2.61091 + -2.98046*tf.T9i + -11.1226*tf.T913i + 12.2437*tf.T913
                  + -4.2554*tf.T9 + 0.353052*tf.T953 + 10.4522*tf.lnT9)

    rate_eval.He4_Al37__n_P40 = rate

@numba.njit()
def p_Ne34__He4_F31(rate_eval, tf):
    # Ne34 + p --> He4 + F31
    rate = 0.0

    # rath 
    rate += np.exp(  48.3237 + -2.96071*tf.T9i + 115.194*tf.T913i + -171.472*tf.T913
                  + 7.08862*tf.T9 + -0.292998*tf.T953 + 95.2178*tf.lnT9)

    rate_eval.p_Ne34__He4_F31 = rate

@numba.njit()
def n_Ti44__p_Sc44(rate_eval, tf):
    # Ti44 + n --> p + Sc44
    rate = 0.0

    # ths8r
    rate += np.exp(  10.2889 + 4.3491*tf.T913
                  + 0.421585*tf.T9 + -0.0855256*tf.T953)

    rate_eval.n_Ti44__p_Sc44 = rate

@numba.njit()
def p_Al28__He4_Mg25(rate_eval, tf):
    # Al28 + p --> He4 + Mg25
    rate = 0.0

    # cf88n
    rate += np.exp(  20.6553 + -23.271*tf.T913i + 1.22438*tf.T913
                  + 1.57567*tf.T9 + -0.209975*tf.T953 + -0.666667*tf.lnT9)
    # cf88r
    rate += np.exp(  20.1444 + -23.271*tf.T913i + 5.6671*tf.T913
                  + -0.708839*tf.T9 + -0.0561047*tf.T953 + 1.33333*tf.lnT9)

    rate_eval.p_Al28__He4_Mg25 = rate

@numba.njit()
def n_Ti59__Ti60(rate_eval, tf):
    # Ti59 + n --> Ti60
    rate = 0.0

    # rath 
    rate += np.exp(  7.82366 + 0.0194093*tf.T9i + -3.03326*tf.T913i + 5.87347*tf.T913
                  + 0.101687*tf.T9 + -0.0810031*tf.T953 + -3.15886*tf.lnT9)

    rate_eval.n_Ti59__Ti60 = rate

@numba.njit()
def He4_K41__p_Ca44(rate_eval, tf):
    # K41 + He4 --> p + Ca44
    rate = 0.0

    # SM91n
    rate += np.exp(  55.5 + -73.9*tf.T913i + -0.410794*tf.T913
                  + 0.365336*tf.T9 + -0.607187*tf.T953 + -0.666667*tf.lnT9)
    # SM91n
    rate += np.exp(  48.7841 + -73.9*tf.T913i + 5.43181*tf.T913
                  + -2.12763*tf.T9 + 0.134461*tf.T953 + 0.333333*tf.lnT9)

    rate_eval.He4_K41__p_Ca44 = rate

@numba.njit()
def He4_Al27__p_Si30(rate_eval, tf):
    # Al27 + He4 --> p + Si30
    rate = 0.0

    # ths8r
    rate += np.exp(  47.4856 + -56.5351*tf.T913i + 1.60477*tf.T913
                  + -1.40594*tf.T9 + 0.127353*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al27__p_Si30 = rate

@numba.njit()
def He4_Al27__n_P30(rate_eval, tf):
    # Al27 + He4 --> n + P30
    rate = 0.0

    # nacr 
    rate += np.exp(  6.09163 + -30.667*tf.T9i + 5.40982*tf.T913
                  + -0.265676*tf.T9 + 1.0*tf.lnT9)
    # nacr 
    rate += np.exp(  11.3074 + -30.667*tf.T9i + 0.311974*tf.T913
                  + -2.02044*tf.T9)

    rate_eval.He4_Al27__n_P30 = rate

@numba.njit()
def p_Ca49__Sc50(rate_eval, tf):
    # Ca49 + p --> Sc50
    rate = 0.0

    # rath 
    rate += np.exp(  109.628 + -5.34377*tf.T9i + 197.859*tf.T913i + -324.035*tf.T913
                  + 17.9116*tf.T9 + -1.00255*tf.T953 + 162.032*tf.lnT9)

    rate_eval.p_Ca49__Sc50 = rate

@numba.njit()
def n_Al26__He4_Na23(rate_eval, tf):
    # Al26 + n --> He4 + Na23
    rate = 0.0

    # ol11r
    rate += np.exp(  13.62 + -0.0661138*tf.T9i
                  + -1.5*tf.lnT9)
    # ol11n
    rate += np.exp(  11.6414 + 5.07134*tf.T913
                  + -0.557537*tf.T9 + 0.0451737*tf.T953)
    # ol11r
    rate += np.exp(  14.7127 + -0.41015*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.n_Al26__He4_Na23 = rate

@numba.njit()
def n_Al26__p_Mg26(rate_eval, tf):
    # Al26 + n --> p + Mg26
    rate = 0.0

    # ol11r
    rate += np.exp(  13.565 + -0.203581*tf.T9i + 3.87515*tf.T913
                  + 0.228327*tf.T9 + -0.045872*tf.T953 + -1.5*tf.lnT9)
    # ol11r
    rate += np.exp(  12.501 + -0.0608268*tf.T9i
                  + -1.5*tf.lnT9)
    # ol11n
    rate += np.exp(  11.1387 + 7.36773*tf.T913
                  + -2.42424*tf.T9 + 0.313743*tf.T953)

    rate_eval.n_Al26__p_Mg26 = rate

@numba.njit()
def He4_Al32__P36(rate_eval, tf):
    # Al32 + He4 --> P36
    rate = 0.0

    # rath 
    rate += np.exp(  -17.1021 + -2.63229*tf.T9i + -23.8523*tf.T913i + 29.4142*tf.T913
                  + -5.0319*tf.T9 + 0.385174*tf.T953 + 1.5501*tf.lnT9)

    rate_eval.He4_Al32__P36 = rate

@numba.njit()
def n_Al25__p_Mg25(rate_eval, tf):
    # Al25 + n --> p + Mg25
    rate = 0.0

    # ths8r
    rate += np.exp(  18.4104 + 2.28536*tf.T913
                  + -0.38512*tf.T9 + 0.0288056*tf.T953)

    rate_eval.n_Al25__p_Mg25 = rate

@numba.njit()
def He4_Al24__p_Si27(rate_eval, tf):
    # Al24 + He4 --> p + Si27
    rate = 0.0

    # ths8r
    rate += np.exp(  47.4359 + -56.2358*tf.T913i + 0.540959*tf.T913
                  + -0.817566*tf.T9 + 0.061438*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al24__p_Si27 = rate

@numba.njit()
def p_S46__Cl47(rate_eval, tf):
    # S46 + p --> Cl47
    rate = 0.0

    # rath 
    rate += np.exp(  88.8001 + -4.46866*tf.T9i + 164.072*tf.T913i + -266.078*tf.T913
                  + 14.3791*tf.T9 + -0.791926*tf.T953 + 134.332*tf.lnT9)

    rate_eval.p_S46__Cl47 = rate

@numba.njit()
def He4_Al25__p_Si28(rate_eval, tf):
    # Al25 + He4 --> p + Si28
    rate = 0.0

    # ths8r
    rate += np.exp(  47.6167 + -56.3424*tf.T913i + 0.553763*tf.T913
                  + -0.84072*tf.T9 + 0.0634219*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al25__p_Si28 = rate

@numba.njit()
def F31__n_n_Ne29__weak__mp17(rate_eval, tf):
    # F31 --> n + n + Ne29
    rate = 0.0

    # mp17w
    rate += np.exp(  4.77587)

    rate_eval.F31__n_n_Ne29__weak__mp17 = rate

@numba.njit()
def n_Al23__He4_Na20(rate_eval, tf):
    # Al23 + n --> He4 + Na20
    rate = 0.0

    # ths8r
    rate += np.exp(  14.9347 + 2.64587*tf.T913
                  + -0.373409*tf.T9 + 0.0281886*tf.T953)

    rate_eval.n_Al23__He4_Na20 = rate

@numba.njit()
def p_Na37__Mg38(rate_eval, tf):
    # Na37 + p --> Mg38
    rate = 0.0

    # rath 
    rate += np.exp(  69.8005 + -3.14979*tf.T9i + 114.351*tf.T913i + -191.316*tf.T913
                  + 10.4851*tf.T9 + -0.581039*tf.T953 + 95.5262*tf.lnT9)

    rate_eval.p_Na37__Mg38 = rate

@numba.njit()
def He4_Al22__p_Si25(rate_eval, tf):
    # Al22 + He4 --> p + Si25
    rate = 0.0

    # ths8r
    rate += np.exp(  46.9722 + -55.9969*tf.T913i + 0.52429*tf.T913
                  + -0.765107*tf.T9 + 0.0564007*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al22__p_Si25 = rate

@numba.njit()
def p_V67__He4_Ti64(rate_eval, tf):
    # V67 + p --> He4 + Ti64
    rate = 0.0

    # rath 
    rate += np.exp(  181.261 + -7.11027*tf.T9i + 294.65*tf.T913i + -511.345*tf.T913
                  + 30.5848*tf.T9 + -1.69931*tf.T953 + 244.301*tf.lnT9)

    rate_eval.p_V67__He4_Ti64 = rate

@numba.njit()
def n_Al22__He4_Na19(rate_eval, tf):
    # Al22 + n --> He4 + Na19
    rate = 0.0

    # ths8r
    rate += np.exp(  15.1864 + 2.44085*tf.T913
                  + -0.354822*tf.T9 + 0.0272546*tf.T953)

    rate_eval.n_Al22__He4_Na19 = rate

@numba.njit()
def O28__n_n_n_F25__weak__mo03(rate_eval, tf):
    # O28 --> 3 n + F25
    rate = 0.0

    # mo03w
    rate += np.exp(  5.54351)

    rate_eval.O28__n_n_n_F25__weak__mo03 = rate

@numba.njit()
def n_Al22__p_Mg22(rate_eval, tf):
    # Al22 + n --> p + Mg22
    rate = 0.0

    # ths8r
    rate += np.exp(  18.2127 + 2.44004*tf.T913
                  + -0.354244*tf.T9 + 0.0249166*tf.T953)

    rate_eval.n_Al22__p_Mg22 = rate

@numba.njit()
def He4_Al21__p_Si24(rate_eval, tf):
    # Al21 + He4 --> p + Si24
    rate = 0.0

    # ths8r
    rate += np.exp(  46.5939 + -55.8622*tf.T913i + 0.52302*tf.T913
                  + -0.731539*tf.T9 + 0.0530999*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al21__p_Si24 = rate

@numba.njit()
def n_Sc48__p_Ca48(rate_eval, tf):
    # Sc48 + n --> p + Ca48
    rate = 0.0

    # rath 
    rate += np.exp(  193.674 + -1.20143*tf.T9i + 149.725*tf.T913i + -359.287*tf.T913
                  + 24.8127*tf.T9 + -1.57647*tf.T953 + 151.916*tf.lnT9)

    rate_eval.n_Sc48__p_Ca48 = rate

@numba.njit()
def He4_Mg40__n_Si43(rate_eval, tf):
    # Mg40 + He4 --> n + Si43
    rate = 0.0

    # rath 
    rate += np.exp(  91.7906 + -3.98783*tf.T9i + 102.626*tf.T913i + -205.944*tf.T913
                  + 9.92705*tf.T9 + -0.509839*tf.T953 + 106.658*tf.lnT9)

    rate_eval.He4_Mg40__n_Si43 = rate

@numba.njit()
def p_Mg40__n_Al40(rate_eval, tf):
    # Mg40 + p --> n + Al40
    rate = 0.0

    # rath 
    rate += np.exp(  84.4379 + -3.45875*tf.T9i + 125.889*tf.T913i + -207.634*tf.T913
                  + 11.2184*tf.T9 + -0.614112*tf.T953 + 104.262*tf.lnT9)

    rate_eval.p_Mg40__n_Al40 = rate

@numba.njit()
def He4_Mg39__n_Si42(rate_eval, tf):
    # Mg39 + He4 --> n + Si42
    rate = 0.0

    # rath 
    rate += np.exp(  91.1526 + -3.9149*tf.T9i + 99.1578*tf.T913i + -201.637*tf.T913
                  + 9.77528*tf.T9 + -0.506412*tf.T953 + 104.205*tf.lnT9)

    rate_eval.He4_Mg39__n_Si42 = rate

@numba.njit()
def p_Mg39__n_Al39(rate_eval, tf):
    # Mg39 + p --> n + Al39
    rate = 0.0

    # rath 
    rate += np.exp(  84.9295 + -3.41986*tf.T9i + 124.568*tf.T913i + -206.824*tf.T913
                  + 11.233*tf.T9 + -0.61817*tf.T953 + 103.578*tf.lnT9)

    rate_eval.p_Mg39__n_Al39 = rate

@numba.njit()
def Ca33__K33__weak__bqa_pos_(rate_eval, tf):
    # Ca33 --> K33
    rate = 0.0

    # bqa+w
    rate += np.exp(  5.89939)

    rate_eval.Ca33__K33__weak__bqa_pos_ = rate

@numba.njit()
def p_Mg38__n_Al38(rate_eval, tf):
    # Mg38 + p --> n + Al38
    rate = 0.0

    # rath 
    rate += np.exp(  83.876 + -3.37608*tf.T9i + 122.501*tf.T913i + -203.903*tf.T913
                  + 11.1553*tf.T9 + -0.619364*tf.T953 + 102.042*tf.lnT9)

    rate_eval.p_Mg38__n_Al38 = rate

@numba.njit()
def p_Al27__He4_Mg24(rate_eval, tf):
    # Al27 + p --> He4 + Mg24
    rate = 0.0

    # il10r
    rate += np.exp(  -7.02789 + -4.2425*tf.T9i + 18.0416*tf.T913
                  + -1.54137*tf.T9 + 0.0847506*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -26.8683 + -0.963012*tf.T9i + 5.18642*tf.T913i + -34.7936*tf.T913
                  + 168.225*tf.T9 + -115.825*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  29.4576 + -26.4162*tf.T913i
                  + -2.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Al27__He4_Mg24 = rate

@numba.njit()
def He4_Mg37__n_Si40(rate_eval, tf):
    # Mg37 + He4 --> n + Si40
    rate = 0.0

    # rath 
    rate += np.exp(  88.6396 + -3.79294*tf.T9i + 94.2453*tf.T913i + -194.201*tf.T913
                  + 9.36142*tf.T9 + -0.483781*tf.T953 + 100.632*tf.lnT9)

    rate_eval.He4_Mg37__n_Si40 = rate

@numba.njit()
def p_Al38__n_Si38(rate_eval, tf):
    # Al38 + p --> n + Si38
    rate = 0.0

    # rath 
    rate += np.exp(  90.6369 + -3.57573*tf.T9i + 131.14*tf.T913i + -220.733*tf.T913
                  + 12.1683*tf.T9 + -0.677376*tf.T953 + 109.771*tf.lnT9)

    rate_eval.p_Al38__n_Si38 = rate

@numba.njit()
def p_Na31__Mg32(rate_eval, tf):
    # Na31 + p --> Mg32
    rate = 0.0

    # rath 
    rate += np.exp(  62.7678 + -2.88976*tf.T9i + 102.426*tf.T913i + -171.597*tf.T913
                  + 9.24941*tf.T9 + -0.507094*tf.T953 + 86.4046*tf.lnT9)

    rate_eval.p_Na31__Mg32 = rate

@numba.njit()
def p_Ar45__He4_Cl42(rate_eval, tf):
    # Ar45 + p --> He4 + Cl42
    rate = 0.0

    # rath 
    rate += np.exp(  -320.925 + 5.67065*tf.T9i + -634.307*tf.T913i + 984.474*tf.T913
                  + -60.8007*tf.T9 + 3.5761*tf.T953 + -457.191*tf.lnT9)

    rate_eval.p_Ar45__He4_Cl42 = rate

@numba.njit()
def He4_Mg35__n_Si38(rate_eval, tf):
    # Mg35 + He4 --> n + Si38
    rate = 0.0

    # rath 
    rate += np.exp(  86.286 + -3.6586*tf.T9i + 88.4816*tf.T913i + -185.894*tf.T913
                  + 8.92934*tf.T9 + -0.461649*tf.T953 + 96.446*tf.lnT9)

    rate_eval.He4_Mg35__n_Si38 = rate

@numba.njit()
def He4_Mg34__n_Si37(rate_eval, tf):
    # Mg34 + He4 --> n + Si37
    rate = 0.0

    # rath 
    rate += np.exp(  85.3524 + -3.59446*tf.T9i + 85.9801*tf.T913i + -182.42*tf.T913
                  + 8.75551*tf.T9 + -0.453192*tf.T953 + 94.6838*tf.lnT9)

    rate_eval.He4_Mg34__n_Si37 = rate

@numba.njit()
def p_Mg34__He4_Na31(rate_eval, tf):
    # Mg34 + p --> He4 + Na31
    rate = 0.0

    # rath 
    rate += np.exp(  61.7545 + -3.39807*tf.T9i + 141.43*tf.T913i + -217.812*tf.T913
                  + 9.85371*tf.T9 + -0.481108*tf.T953 + 120.249*tf.lnT9)

    rate_eval.p_Mg34__He4_Na31 = rate

@numba.njit()
def p_Ti53__n_V53(rate_eval, tf):
    # Ti53 + p --> n + V53
    rate = 0.0

    # rath 
    rate += np.exp(  126.844 + -5.9233*tf.T9i + 221.542*tf.T913i + -359.17*tf.T913
                  + 19.8965*tf.T9 + -1.12369*tf.T953 + 180.282*tf.lnT9)

    rate_eval.p_Ti53__n_V53 = rate

@numba.njit()
def p_Mg33__He4_Na30(rate_eval, tf):
    # Mg33 + p --> He4 + Na30
    rate = 0.0

    # rath 
    rate += np.exp(  45.353 + -3.1697*tf.T9i + 113.286*tf.T913i + -166.635*tf.T913
                  + 7.59182*tf.T9 + -0.353381*tf.T953 + 92.5726*tf.lnT9)

    rate_eval.p_Mg33__He4_Na30 = rate

@numba.njit()
def Fe49__Mn49__weak__wc12(rate_eval, tf):
    # Fe49 --> Mn49
    rate = 0.0

    # wc12w
    rate += np.exp(  1.53446)

    rate_eval.Fe49__Mn49__weak__wc12 = rate

@numba.njit()
def p_Fe66__He4_Mn63(rate_eval, tf):
    # Fe66 + p --> He4 + Mn63
    rate = 0.0

    # rath 
    rate += np.exp(  -371.975 + 0.0997908*tf.T9i + -385.08*tf.T913i + 779.343*tf.T913
                  + -53.2233*tf.T9 + 3.26695*tf.T953 + -320.568*tf.lnT9)

    rate_eval.p_Fe66__He4_Mn63 = rate

@numba.njit()
def He4_Mg32__n_Si35(rate_eval, tf):
    # Mg32 + He4 --> n + Si35
    rate = 0.0

    # rath 
    rate += np.exp(  81.9308 + -3.45077*tf.T9i + 79.7221*tf.T913i + -173.152*tf.T913
                  + 8.3224*tf.T9 + -0.433155*tf.T953 + 90.0865*tf.lnT9)

    rate_eval.He4_Mg32__n_Si35 = rate

@numba.njit()
def n_Mn47__He4_V44(rate_eval, tf):
    # Mn47 + n --> He4 + V44
    rate = 0.0

    # ths8r
    rate += np.exp(  7.46454 + 7.81721*tf.T913
                  + -2.51681*tf.T9 + 0.367766*tf.T953)

    rate_eval.n_Mn47__He4_V44 = rate

@numba.njit()
def p_Mg32__He4_Na29(rate_eval, tf):
    # Mg32 + p --> He4 + Na29
    rate = 0.0

    # rath 
    rate += np.exp(  32.0228 + -3.03033*tf.T9i + 101.377*tf.T913i + -137.641*tf.T913
                  + 5.26912*tf.T9 + -0.215711*tf.T953 + 81.3125*tf.lnT9)

    rate_eval.p_Mg32__He4_Na29 = rate

@numba.njit()
def n_Na19__p_Ne19(rate_eval, tf):
    # Na19 + n --> p + Ne19
    rate = 0.0

    # ths8r
    rate += np.exp(  18.2257 + 1.58349*tf.T913
                  + -0.107577*tf.T9 + 0.00299512*tf.T953)

    rate_eval.n_Na19__p_Ne19 = rate

@numba.njit()
def p_Mn59__n_Fe59(rate_eval, tf):
    # Mn59 + p --> n + Fe59
    rate = 0.0

    # rath 
    rate += np.exp(  136.472 + -6.72617*tf.T9i + 250.84*tf.T913i + -400.205*tf.T913
                  + 21.7908*tf.T9 + -1.21911*tf.T953 + 202.27*tf.lnT9)

    rate_eval.p_Mn59__n_Fe59 = rate

@numba.njit()
def He4_Mg30__n_Si33(rate_eval, tf):
    # Mg30 + He4 --> n + Si33
    rate = 0.0

    # rath 
    rate += np.exp(  80.0121 + -3.30902*tf.T9i + 73.9106*tf.T913i + -164.85*tf.T913
                  + 7.8382*tf.T9 + -0.405091*tf.T953 + 85.8967*tf.lnT9)

    rate_eval.He4_Mg30__n_Si33 = rate

@numba.njit()
def p_Mg30__n_Al30(rate_eval, tf):
    # Mg30 + p --> n + Al30
    rate = 0.0

    # rath 
    rate += np.exp(  76.3685 + -3.00508*tf.T9i + 105.937*tf.T913i + -178.71*tf.T913
                  + 9.60226*tf.T9 + -0.528158*tf.T953 + 89.8752*tf.lnT9)

    rate_eval.p_Mg30__n_Al30 = rate

@numba.njit()
def n_P29__He4_Al26(rate_eval, tf):
    # P29 + n --> He4 + Al26
    rate = 0.0

    # ths8r
    rate += np.exp(  -39.2446 + 41.9938*tf.T913
                  + -4.54859*tf.T9 + 0.243841*tf.T953)

    rate_eval.n_P29__He4_Al26 = rate

@numba.njit()
def p_Ca45__Sc46(rate_eval, tf):
    # Ca45 + p --> Sc46
    rate = 0.0

    # ths8r
    rate += np.exp(  38.986 + -31.1543*tf.T913i + -6.97397*tf.T913
                  + -0.344025*tf.T9 + 0.128258*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ca45__Sc46 = rate

@numba.njit()
def He4_Cr46__p_Mn49(rate_eval, tf):
    # Cr46 + He4 --> p + Mn49
    rate = 0.0

    # ths8r
    rate += np.exp(  60.5689 + -86.6499*tf.T913i + -1.08241*tf.T913
                  + -0.516569*tf.T9 + 0.0131721*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr46__p_Mn49 = rate

@numba.njit()
def p_Cl46__n_Ar46(rate_eval, tf):
    # Cl46 + p --> n + Ar46
    rate = 0.0

    # rath 
    rate += np.exp(  108.776 + -4.66698*tf.T9i + 173.145*tf.T913i + -286.021*tf.T913
                  + 15.8037*tf.T9 + -0.885781*tf.T953 + 142.772*tf.lnT9)

    rate_eval.p_Cl46__n_Ar46 = rate

@numba.njit()
def p_Mg29__He4_Na26(rate_eval, tf):
    # Mg29 + p --> He4 + Na26
    rate = 0.0

    # rath 
    rate += np.exp(  37.4336 + -3.04746*tf.T9i + 111.895*tf.T913i + -153.93*tf.T913
                  + 5.58386*tf.T9 + -0.196356*tf.T953 + 91.3161*tf.lnT9)

    rate_eval.p_Mg29__He4_Na26 = rate

@numba.njit()
def p_Mg29__n_Al29(rate_eval, tf):
    # Mg29 + p --> n + Al29
    rate = 0.0

    # rath 
    rate += np.exp(  72.8772 + -2.95332*tf.T9i + 103.177*tf.T913i + -172.537*tf.T913
                  + 9.24904*tf.T9 + -0.513102*tf.T953 + 87.4281*tf.lnT9)

    rate_eval.p_Mg29__n_Al29 = rate

@numba.njit()
def p_Cr60__n_Mn60(rate_eval, tf):
    # Cr60 + p --> n + Mn60
    rate = 0.0

    # rath 
    rate += np.exp(  133.571 + -6.59259*tf.T9i + 245.829*tf.T913i + -391.025*tf.T913
                  + 21.1256*tf.T9 + -1.16826*tf.T953 + 197.853*tf.lnT9)

    rate_eval.p_Cr60__n_Mn60 = rate

@numba.njit()
def n_S29__He4_Si26(rate_eval, tf):
    # S29 + n --> He4 + Si26
    rate = 0.0

    # ths8r
    rate += np.exp(  15.0939 + 1.23363*tf.T913
                  + -0.138791*tf.T9 + 0.0145343*tf.T953)

    rate_eval.n_S29__He4_Si26 = rate

@numba.njit()
def n_K58__K59(rate_eval, tf):
    # K58 + n --> K59
    rate = 0.0

    # rath 
    rate += np.exp(  17.5963 + -0.0215618*tf.T9i + 2.85191*tf.T913i + -13.1088*tf.T913
                  + 1.05669*tf.T9 + -0.0770766*tf.T953 + 3.61409*tf.lnT9)

    rate_eval.n_K58__K59 = rate

@numba.njit()
def He4_K57__Sc61(rate_eval, tf):
    # K57 + He4 --> Sc61
    rate = 0.0

    # rath 
    rate += np.exp(  -957.776 + 15.1954*tf.T9i + -1649.09*tf.T913i + 2714.23*tf.T913
                  + -162.131*tf.T9 + 9.2993*tf.T953 + -1273.56*tf.lnT9)

    rate_eval.He4_K57__Sc61 = rate

@numba.njit()
def He4_Ne23__n_Mg26(rate_eval, tf):
    # Ne23 + He4 --> n + Mg26
    rate = 0.0

    # rath 
    rate += np.exp(  63.2103 + -2.4071*tf.T9i + 42.1177*tf.T913i + -110.734*tf.T913
                  + 4.88447*tf.T9 + -0.238446*tf.T953 + 58.6262*tf.lnT9)

    rate_eval.He4_Ne23__n_Mg26 = rate

@numba.njit()
def p_Ne31__He4_F28(rate_eval, tf):
    # Ne31 + p --> He4 + F28
    rate = 0.0

    # rath 
    rate += np.exp(  51.5779 + -2.92372*tf.T9i + 118.88*tf.T913i + -180.175*tf.T913
                  + 7.81026*tf.T9 + -0.335196*tf.T953 + 99.4731*tf.lnT9)

    rate_eval.p_Ne31__He4_F28 = rate

@numba.njit()
def He4_Mg27__n_Si30(rate_eval, tf):
    # Mg27 + He4 --> n + Si30
    rate = 0.0

    # rath 
    rate += np.exp(  75.4975 + -3.07638*tf.T9i + 63.9974*tf.T913i + -150.564*tf.T913
                  + 7.14815*tf.T9 + -0.372762*tf.T953 + 78.6784*tf.lnT9)

    rate_eval.He4_Mg27__n_Si30 = rate

@numba.njit()
def He4_O23__n_Ne26(rate_eval, tf):
    # O23 + He4 --> n + Ne26
    rate = 0.0

    # rpsmr
    rate += np.exp(  56.4566 + -2.04953*tf.T9i + 34.1468*tf.T913i + -91.6241*tf.T913
                  + 3.88406*tf.T9 + -0.177485*tf.T953 + 48.6899*tf.lnT9)

    rate_eval.He4_O23__n_Ne26 = rate

@numba.njit()
def He4_K35__p_Ca38(rate_eval, tf):
    # K35 + He4 --> p + Ca38
    rate = 0.0

    # ths8r
    rate += np.exp(  54.0018 + -73.542*tf.T913i + 0.488909*tf.T913
                  + -0.879*tf.T9 + 0.0634783*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K35__p_Ca38 = rate

@numba.njit()
def He4_Mg26__n_Si29(rate_eval, tf):
    # Mg26 + He4 --> n + Si29
    rate = 0.0

    # nacrn
    rate += np.exp(  45.8397 + -53.505*tf.T913i + 0.045598*tf.T913
                  + -0.194481*tf.T9 + -0.0748153*tf.T953 + -0.666667*tf.lnT9)
    # nacrr
    rate += np.exp(  15.7057 + -18.73*tf.T9i + -9.54056*tf.T913
                  + 4.71712*tf.T9 + -0.461053*tf.T953 + -1.5*tf.lnT9)

    rate_eval.He4_Mg26__n_Si29 = rate

@numba.njit()
def p_Ti59__V60(rate_eval, tf):
    # Ti59 + p --> V60
    rate = 0.0

    # rath 
    rate += np.exp(  120.079 + -6.18473*tf.T9i + 231.293*tf.T913i + -371.542*tf.T913
                  + 20.4824*tf.T9 + -1.16486*tf.T953 + 186.82*tf.lnT9)

    rate_eval.p_Ti59__V60 = rate

@numba.njit()
def n_Fe54__He4_Cr51(rate_eval, tf):
    # Fe54 + n --> He4 + Cr51
    rate = 0.0

    # ths8r
    rate += np.exp(  -83.0822 + 77.6519*tf.T913
                  + -9.70923*tf.T9 + 0.625406*tf.T953)

    rate_eval.n_Fe54__He4_Cr51 = rate

@numba.njit()
def n_Mn68__Mn69(rate_eval, tf):
    # Mn68 + n --> Mn69
    rate = 0.0

    # rath 
    rate += np.exp(  23.3934 + -0.0452578*tf.T9i + 5.16378*tf.T913i + -16.7905*tf.T913
                  + 1.16991*tf.T9 + -0.0965304*tf.T953 + 5.57685*tf.lnT9)

    rate_eval.n_Mn68__Mn69 = rate

@numba.njit()
def He4_Fe53__p_Co56(rate_eval, tf):
    # Fe53 + He4 --> p + Co56
    rate = 0.0

    # ths8r
    rate += np.exp(  54.8614 + -91.7231*tf.T913i + 10.052*tf.T913
                  + -3.86332*tf.T9 + 0.391105*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe53__p_Co56 = rate

@numba.njit()
def n_Fe55__He4_Cr52(rate_eval, tf):
    # Fe55 + n --> He4 + Cr52
    rate = 0.0

    # ths8r
    rate += np.exp(  10.6453 + -4.54346*tf.T913
                  + 2.79557*tf.T9 + -0.273997*tf.T953)

    rate_eval.n_Fe55__He4_Cr52 = rate

@numba.njit()
def He4_Mg25__n_Si28(rate_eval, tf):
    # Mg25 + He4 --> n + Si28
    rate = 0.0

    # nacrn
    rate += np.exp(  45.7613 + -53.415*tf.T913i + -1.46489*tf.T913
                  + 1.7777*tf.T9 + -0.903499*tf.T953 + -0.666667*tf.lnT9)
    # nacr 
    rate += np.exp(  38.337 + -53.416*tf.T913i + 8.01209*tf.T913
                  + -2.64791*tf.T9 + 0.218637*tf.T953 + 0.333333*tf.lnT9)

    rate_eval.He4_Mg25__n_Si28 = rate

@numba.njit()
def p_Fe69__Co70(rate_eval, tf):
    # Fe69 + p --> Co70
    rate = 0.0

    # rath 
    rate += np.exp(  147.486 + -7.4516*tf.T9i + 284.265*tf.T913i + -456.852*tf.T913
                  + 25.3706*tf.T9 + -1.4473*tf.T953 + 228.431*tf.lnT9)

    rate_eval.p_Fe69__Co70 = rate

@numba.njit()
def P40__S40__weak__wc12(rate_eval, tf):
    # P40 --> S40
    rate = 0.0

    # wc12w
    rate += np.exp(  1.54095)

    rate_eval.P40__S40__weak__wc12 = rate

@numba.njit()
def n_Cl43__Cl44(rate_eval, tf):
    # Cl43 + n --> Cl44
    rate = 0.0

    # rath 
    rate += np.exp(  6.14122 + 0.0283739*tf.T9i + -3.62747*tf.T913i + 9.24735*tf.T913
                  + -0.465005*tf.T9 + -0.00433101*tf.T953 + -3.79359*tf.lnT9)

    rate_eval.n_Cl43__Cl44 = rate

@numba.njit()
def n_Mg23__C12_C12(rate_eval, tf):
    # Mg23 + n --> C12 + C12
    rate = 0.0

    # cf88r
    rate += np.exp(  -12.8267 + 11.4826*tf.T913
                  + 1.82849*tf.T9 + -0.34844*tf.T953)

    rate_eval.n_Mg23__C12_C12 = rate

@numba.njit()
def n_Mg23__He4_Ne20(rate_eval, tf):
    # Mg23 + n --> He4 + Ne20
    rate = 0.0

    # ths8r
    rate += np.exp(  17.7448 + 1.83199*tf.T913
                  + -0.290485*tf.T9 + 0.0242929*tf.T953)

    rate_eval.n_Mg23__He4_Ne20 = rate

@numba.njit()
def n_Fe66__Fe67(rate_eval, tf):
    # Fe66 + n --> Fe67
    rate = 0.0

    # rath 
    rate += np.exp(  24.9999 + -0.0044362*tf.T9i + 2.35972*tf.T913i + -17.5239*tf.T913
                  + 2.91566*tf.T9 + -0.331484*tf.T953 + 4.15574*tf.lnT9)

    rate_eval.n_Fe66__Fe67 = rate

@numba.njit()
def He4_Mg22__p_Al25(rate_eval, tf):
    # Mg22 + He4 --> p + Al25
    rate = 0.0

    # ths8r
    rate += np.exp(  46.0189 + -53.0847*tf.T913i + 0.634581*tf.T913
                  + -0.829647*tf.T9 + 0.0650313*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg22__p_Al25 = rate

@numba.njit()
def n_Cl30__p_S30(rate_eval, tf):
    # Cl30 + n --> p + S30
    rate = 0.0

    # ths8r
    rate += np.exp(  19.0661 + 1.13666*tf.T913
                  + -0.105309*tf.T9 + 0.0069057*tf.T953)

    rate_eval.n_Cl30__p_S30 = rate

@numba.njit()
def n_Mg21__He4_Ne18(rate_eval, tf):
    # Mg21 + n --> He4 + Ne18
    rate = 0.0

    # ths8r
    rate += np.exp(  15.9862 + 2.49883*tf.T913
                  + -0.356413*tf.T9 + 0.0232661*tf.T953)

    rate_eval.n_Mg21__He4_Ne18 = rate

@numba.njit()
def He4_Mg20__p_Al23(rate_eval, tf):
    # Mg20 + He4 --> p + Al23
    rate = 0.0

    # ths8r
    rate += np.exp(  45.3138 + -52.8179*tf.T913i + 0.692999*tf.T913
                  + -0.798677*tf.T9 + 0.0616104*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg20__p_Al23 = rate

@numba.njit()
def Ca57__n_n_Sc55__weak__mp17(rate_eval, tf):
    # Ca57 --> n + n + Sc55
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.0254301)

    rate_eval.Ca57__n_n_Sc55__weak__mp17 = rate

@numba.njit()
def He4_Na36__n_Al39(rate_eval, tf):
    # Na36 + He4 --> n + Al39
    rate = 0.0

    # rath 
    rate += np.exp(  85.7743 + -3.53074*tf.T9i + 87.636*tf.T913i + -182.532*tf.T913
                  + 8.79102*tf.T9 + -0.451808*tf.T953 + 94.258*tf.lnT9)

    rate_eval.He4_Na36__n_Al39 = rate

@numba.njit()
def n_Mg20__p_Na20(rate_eval, tf):
    # Mg20 + n --> p + Na20
    rate = 0.0

    # ths8r
    rate += np.exp(  18.1295 + 2.03889*tf.T913
                  + -0.215808*tf.T9 + 0.0125129*tf.T953)

    rate_eval.n_Mg20__p_Na20 = rate

@numba.njit()
def p_Na39__n_Mg39(rate_eval, tf):
    # Na39 + p --> n + Mg39
    rate = 0.0

    # rath 
    rate += np.exp(  83.623 + -3.23816*tf.T9i + 118.834*tf.T913i + -198.598*tf.T913
                  + 10.8177*tf.T9 + -0.594766*tf.T953 + 99.025*tf.lnT9)

    rate_eval.p_Na39__n_Mg39 = rate

@numba.njit()
def Na27__n_Mg26__weak__wc12(rate_eval, tf):
    # Na27 --> n + Mg26
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.81126)

    rate_eval.Na27__n_Mg26__weak__wc12 = rate

@numba.njit()
def He4_Na38__n_Al41(rate_eval, tf):
    # Na38 + He4 --> n + Al41
    rate = 0.0

    # rath 
    rate += np.exp(  84.9874 + -3.62112*tf.T9i + 89.7358*tf.T913i + -183.525*tf.T913
                  + 8.72107*tf.T9 + -0.442424*tf.T953 + 95.2571*tf.lnT9)

    rate_eval.He4_Na38__n_Al41 = rate

@numba.njit()
def He4_Na37__p_Mg40(rate_eval, tf):
    # Na37 + He4 --> p + Mg40
    rate = 0.0

    # rath 
    rate += np.exp(  -18.9436 + -2.64097*tf.T9i + -12.4924*tf.T913i + 21.1083*tf.T913
                  + -5.00883*tf.T9 + 0.423076*tf.T953 + 6.44693*tf.lnT9)

    rate_eval.He4_Na37__p_Mg40 = rate

@numba.njit()
def He4_K33__Sc37(rate_eval, tf):
    # K33 + He4 --> Sc37
    rate = 0.0

    # ths8r
    rate += np.exp(  43.4914 + -73.3916*tf.T913i + -0.362928*tf.T913
                  + -0.500382*tf.T9 + 0.00594182*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K33__Sc37 = rate

@numba.njit()
def p_Na37__He4_Ne34(rate_eval, tf):
    # Na37 + p --> He4 + Ne34
    rate = 0.0

    # rath 
    rate += np.exp(  70.125 + -3.15074*tf.T9i + 114.387*tf.T913i + -190.852*tf.T913
                  + 10.4389*tf.T9 + -0.571305*tf.T953 + 95.4815*tf.lnT9)

    rate_eval.p_Na37__He4_Ne34 = rate

@numba.njit()
def He4_Na35__n_Al38(rate_eval, tf):
    # Na35 + He4 --> n + Al38
    rate = 0.0

    # rath 
    rate += np.exp(  81.3245 + -3.43281*tf.T9i + 81.6379*tf.T913i + -171.584*tf.T913
                  + 8.08732*tf.T9 + -0.408947*tf.T953 + 89.3354*tf.lnT9)

    rate_eval.He4_Na35__n_Al38 = rate

@numba.njit()
def p_Na35__n_Mg35(rate_eval, tf):
    # Na35 + p --> n + Mg35
    rate = 0.0

    # rath 
    rate += np.exp(  78.7953 + -3.06538*tf.T9i + 110.569*tf.T913i + -185.491*tf.T913
                  + 10.1196*tf.T9 + -0.560812*tf.T953 + 92.7405*tf.lnT9)

    rate_eval.p_Na35__n_Mg35 = rate

@numba.njit()
def Mg37__n_Al36__weak__mp17(rate_eval, tf):
    # Mg37 --> n + Al36
    rate = 0.0

    # mp17w
    rate += np.exp(  4.13462)

    rate_eval.Mg37__n_Al36__weak__mp17 = rate

@numba.njit()
def n_V43__He4_Sc40(rate_eval, tf):
    # V43 + n --> He4 + Sc40
    rate = 0.0

    # ths8r
    rate += np.exp(  15.9373 + 0.0397161*tf.T913
                  + -0.0236614*tf.T9 + 0.0380802*tf.T953)

    rate_eval.n_V43__He4_Sc40 = rate

@numba.njit()
def He4_Na34__n_Al37(rate_eval, tf):
    # Na34 + He4 --> n + Al37
    rate = 0.0

    # rath 
    rate += np.exp(  80.8111 + -3.35966*tf.T9i + 78.2647*tf.T913i + -167.594*tf.T913
                  + 7.95366*tf.T9 + -0.405558*tf.T953 + 86.9921*tf.lnT9)

    rate_eval.He4_Na34__n_Al37 = rate

@numba.njit()
def He4_V60__n_Mn63(rate_eval, tf):
    # V60 + He4 --> n + Mn63
    rate = 0.0

    # rath 
    rate += np.exp(  -1103.52 + 17.7726*tf.T9i + -1924.07*tf.T913i + 3162.52*tf.T913
                  + -188.352*tf.T9 + 10.7906*tf.T953 + -1486.0*tf.lnT9)

    rate_eval.He4_V60__n_Mn63 = rate

@numba.njit()
def He4_Na33__p_Mg36(rate_eval, tf):
    # Na33 + He4 --> p + Mg36
    rate = 0.0

    # rath 
    rate += np.exp(  6.81811 + -2.26255*tf.T9i + -18.7355*tf.T913i + -0.490442*tf.T913
                  + -2.94237*tf.T9 + 0.289202*tf.T953 + 11.313*tf.lnT9)

    rate_eval.He4_Na33__p_Mg36 = rate

@numba.njit()
def p_Na33__n_Mg33(rate_eval, tf):
    # Na33 + p --> n + Mg33
    rate = 0.0

    # rath 
    rate += np.exp(  77.6231 + -2.98108*tf.T9i + 107.027*tf.T913i + -180.645*tf.T913
                  + 9.85481*tf.T9 + -0.546564*tf.T953 + 90.2562*tf.lnT9)

    rate_eval.p_Na33__n_Mg33 = rate

@numba.njit()
def n_N18__N19(rate_eval, tf):
    # N18 + n --> N19
    rate = 0.0

    # wiesr
    rate += np.exp(  5.77765 + -1.99922e-13*tf.T9i + 2.42748e-11*tf.T913i + -7.21863e-11*tf.T913
                  + 6.61152e-12*tf.T9 + -5.20015e-13*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_N18__N19 = rate

@numba.njit()
def S30__P30__weak__wc12(rate_eval, tf):
    # S30 --> P30
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.532027)

    rate_eval.S30__P30__weak__wc12 = rate

@numba.njit()
def n_Mn43__p_Cr43(rate_eval, tf):
    # Mn43 + n --> p + Cr43
    rate = 0.0

    # ths8r
    rate += np.exp(  21.7529 + -0.903049*tf.T913
                  + 0.246557*tf.T9 + -0.0218448*tf.T953)

    rate_eval.n_Mn43__p_Cr43 = rate

@numba.njit()
def He4_Sc44__V48(rate_eval, tf):
    # Sc44 + He4 --> V48
    rate = 0.0

    # ths8r
    rate += np.exp(  56.6322 + -79.1731*tf.T913i + -4.22583*tf.T913
                  + -0.427863*tf.T9 + 0.0235817*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc44__V48 = rate

@numba.njit()
def He4_Na31__n_Al34(rate_eval, tf):
    # Na31 + He4 --> n + Al34
    rate = 0.0

    # rath 
    rate += np.exp(  79.2115 + -3.20334*tf.T9i + 73.7692*tf.T913i + -162.246*tf.T913
                  + 7.77707*tf.T9 + -0.402119*tf.T953 + 84.1513*tf.lnT9)

    rate_eval.He4_Na31__n_Al34 = rate

@numba.njit()
def p_Na31__He4_Ne28(rate_eval, tf):
    # Na31 + p --> He4 + Ne28
    rate = 0.0

    # rath 
    rate += np.exp(  64.5778 + -2.88635*tf.T9i + 101.978*tf.T913i + -169.438*tf.T913
                  + 9.05785*tf.T9 + -0.485106*tf.T953 + 85.8272*tf.lnT9)

    rate_eval.p_Na31__He4_Ne28 = rate

@numba.njit()
def p_Na31__n_Mg31(rate_eval, tf):
    # Na31 + p --> n + Mg31
    rate = 0.0

    # rath 
    rate += np.exp(  74.7447 + -2.88516*tf.T9i + 102.392*tf.T913i + -172.732*tf.T913
                  + 9.33885*tf.T9 + -0.516607*tf.T953 + 86.6648*tf.lnT9)

    rate_eval.p_Na31__n_Mg31 = rate

@numba.njit()
def p_Fe66__n_Co66(rate_eval, tf):
    # Fe66 + p --> n + Co66
    rate = 0.0

    # rath 
    rate += np.exp(  146.047 + -7.26776*tf.T9i + 273.568*tf.T913i + -434.13*tf.T913
                  + 23.5663*tf.T9 + -1.30694*tf.T953 + 219.247*tf.lnT9)

    rate_eval.p_Fe66__n_Co66 = rate

@numba.njit()
def p_Na30__He4_Ne27(rate_eval, tf):
    # Na30 + p --> He4 + Ne27
    rate = 0.0

    # rath 
    rate += np.exp(  64.9865 + -2.82752*tf.T9i + 98.9108*tf.T913i + -164.757*tf.T913
                  + 8.71015*tf.T9 + -0.456984*tf.T953 + 83.5467*tf.lnT9)

    rate_eval.p_Na30__He4_Ne27 = rate

@numba.njit()
def p_Cl40__Ar41(rate_eval, tf):
    # Cl40 + p --> Ar41
    rate = 0.0

    # rath 
    rate += np.exp(  92.6777 + -4.35853*tf.T9i + 158.484*tf.T913i + -262.339*tf.T913
                  + 14.3146*tf.T9 + -0.795769*tf.T953 + 131.556*tf.lnT9)

    rate_eval.p_Cl40__Ar41 = rate

@numba.njit()
def n_S31__p_P31(rate_eval, tf):
    # S31 + n --> p + P31
    rate = 0.0

    # ths8r
    rate += np.exp(  17.7037 + 2.15006*tf.T913
                  + -0.300369*tf.T9 + 0.0229589*tf.T953)

    rate_eval.n_S31__p_P31 = rate

@numba.njit()
def p_Na29__He4_Ne26(rate_eval, tf):
    # Na29 + p --> He4 + Ne26
    rate = 0.0

    # rath 
    rate += np.exp(  61.41 + -2.77705*tf.T9i + 96.0757*tf.T913i + -159.071*tf.T913
                  + 8.50847*tf.T9 + -0.460169*tf.T953 + 81.0616*tf.lnT9)

    rate_eval.p_Na29__He4_Ne26 = rate

@numba.njit()
def He4_Na28__n_Al31(rate_eval, tf):
    # Na28 + He4 --> n + Al31
    rate = 0.0

    # rath 
    rate += np.exp(  73.2091 + -2.95903*tf.T9i + 61.8209*tf.T913i + -143.248*tf.T913
                  + 6.64766*tf.T9 + -0.336996*tf.T953 + 75.0102*tf.lnT9)

    rate_eval.He4_Na28__n_Al31 = rate

@numba.njit()
def p_Na28__n_Mg28(rate_eval, tf):
    # Na28 + p --> n + Mg28
    rate = 0.0

    # rath 
    rate += np.exp(  72.0831 + -2.74346*tf.T9i + 96.2006*tf.T913i + -163.39*tf.T913
                  + 8.77419*tf.T9 + -0.48397*tf.T953 + 82.1555*tf.lnT9)

    rate_eval.p_Na28__n_Mg28 = rate

@numba.njit()
def Ar49__K49__weak__wc12(rate_eval, tf):
    # Ar49 --> K49
    rate = 0.0

    # wc12w
    rate += np.exp(  0.355622)

    rate_eval.Ar49__K49__weak__wc12 = rate

@numba.njit()
def p_Na27__n_Mg27(rate_eval, tf):
    # Na27 + p --> n + Mg27
    rate = 0.0

    # rath 
    rate += np.exp(  69.9864 + -2.68746*tf.T9i + 93.2971*tf.T913i + -158.212*tf.T913
                  + 8.46169*tf.T9 + -0.466818*tf.T953 + 79.8304*tf.lnT9)

    rate_eval.p_Na27__n_Mg27 = rate

@numba.njit()
def n_Ar39__He4_S36(rate_eval, tf):
    # Ar39 + n --> He4 + S36
    rate = 0.0

    # ths8r
    rate += np.exp(  13.3069 + -1.97008*tf.T913
                  + 1.52238*tf.T9 + -0.159721*tf.T953)

    rate_eval.n_Ar39__He4_S36 = rate

@numba.njit()
def He4_Na26__n_Al29(rate_eval, tf):
    # Na26 + He4 --> n + Al29
    rate = 0.0

    # rath 
    rate += np.exp(  70.422 + -2.81287*tf.T9i + 55.7606*tf.T913i + -134.247*tf.T913
                  + 6.15683*tf.T9 + -0.310068*tf.T953 + 70.5619*tf.lnT9)

    rate_eval.He4_Na26__n_Al29 = rate

@numba.njit()
def p_Sc49__n_Ti49(rate_eval, tf):
    # Sc49 + p --> n + Ti49
    rate = 0.0

    # rath 
    rate += np.exp(  120.282 + -5.52132*tf.T9i + 204.555*tf.T913i + -334.141*tf.T913
                  + 18.5078*tf.T9 + -1.04158*tf.T953 + 167.483*tf.lnT9)

    rate_eval.p_Sc49__n_Ti49 = rate

@numba.njit()
def Ar52__n_n_K50__weak__mp17(rate_eval, tf):
    # Ar52 --> n + n + K50
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.703699)

    rate_eval.Ar52__n_n_K50__weak__mp17 = rate

@numba.njit()
def He4_Na24__p_Mg27(rate_eval, tf):
    # Na24 + He4 --> p + Mg27
    rate = 0.0

    # rath 
    rate += np.exp(  -9.11451 + -2.09128*tf.T9i + -14.1355*tf.T913i + 19.7349*tf.T913
                  + -5.35946*tf.T9 + 0.449186*tf.T953 + 8.72434*tf.lnT9)

    rate_eval.He4_Na24__p_Mg27 = rate

@numba.njit()
def p_Na24__He4_Ne21(rate_eval, tf):
    # Na24 + p --> He4 + Ne21
    rate = 0.0

    # rath 
    rate += np.exp(  47.365 + -2.4679*tf.T9i + 79.8849*tf.T913i + -124.834*tf.T913
                  + 6.1655*tf.T9 + -0.339742*tf.T953 + 67.7826*tf.lnT9)

    rate_eval.p_Na24__He4_Ne21 = rate

@numba.njit()
def n_Ti42__p_Sc42(rate_eval, tf):
    # Ti42 + n --> p + Sc42
    rate = 0.0

    # ths8r
    rate += np.exp(  20.6632 + -0.497079*tf.T913
                  + 0.222253*tf.T9 + -0.0205254*tf.T953)

    rate_eval.n_Ti42__p_Sc42 = rate

@numba.njit()
def p_K56__He4_Ar53(rate_eval, tf):
    # K56 + p --> He4 + Ar53
    rate = 0.0

    # rath 
    rate += np.exp(  123.324 + -5.55483*tf.T9i + 214.054*tf.T913i + -358.621*tf.T913
                  + 20.4961*tf.T9 + -1.12836*tf.T953 + 176.189*tf.lnT9)

    rate_eval.p_K56__He4_Ar53 = rate

@numba.njit()
def p_K46__Ca47(rate_eval, tf):
    # K46 + p --> Ca47
    rate = 0.0

    # rath 
    rate += np.exp(  94.1858 + -4.96051*tf.T9i + 178.672*tf.T913i + -285.662*tf.T913
                  + 14.9223*tf.T9 + -0.761834*tf.T953 + 145.614*tf.lnT9)

    rate_eval.p_K46__Ca47 = rate

@numba.njit()
def He4_Na23__p_Mg26(rate_eval, tf):
    # Na23 + He4 --> p + Mg26
    rate = 0.0

    # ths8r
    rate += np.exp(  44.527 + -50.2042*tf.T913i + 1.76141*tf.T913
                  + -1.36813*tf.T9 + 0.123087*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Na23__p_Mg26 = rate

@numba.njit()
def p_Fe67__n_Co67(rate_eval, tf):
    # Fe67 + p --> n + Co67
    rate = 0.0

    # rath 
    rate += np.exp(  150.136 + -7.34093*tf.T9i + 278.185*tf.T913i + -443.111*tf.T913
                  + 24.1283*tf.T9 + -1.33898*tf.T953 + 223.143*tf.lnT9)

    rate_eval.p_Fe67__n_Co67 = rate

@numba.njit()
def n_Fe50__p_Mn50(rate_eval, tf):
    # Fe50 + n --> p + Mn50
    rate = 0.0

    # ths8r
    rate += np.exp(  22.0069 + -1.18881*tf.T913
                  + 0.315591*tf.T9 + -0.0282979*tf.T953)

    rate_eval.n_Fe50__p_Mn50 = rate

@numba.njit()
def n_Sc43__Sc44(rate_eval, tf):
    # Sc43 + n --> Sc44
    rate = 0.0

    # ths8r
    rate += np.exp(  15.7633 + -0.575865*tf.T913
                  + 0.0565199*tf.T9 + -0.0129886*tf.T953)

    rate_eval.n_Sc43__Sc44 = rate

@numba.njit()
def n_S26__p_P26(rate_eval, tf):
    # S26 + n --> p + P26
    rate = 0.0

    # ths8r
    rate += np.exp(  18.5465 + 2.04242*tf.T913
                  + -0.282959*tf.T9 + 0.0190726*tf.T953)

    rate_eval.n_S26__p_P26 = rate

@numba.njit()
def p_Na23__He4_Ne20(rate_eval, tf):
    # Na23 + p --> He4 + Ne20
    rate = 0.0

    # il10r
    rate += np.exp(  -6.58736 + -2.31577*tf.T9i + 19.7297*tf.T913
                  + -2.20987*tf.T9 + 0.153374*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  0.0178295 + -1.86103*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  18.9756 + -20.0024*tf.T913i + 11.5988*tf.T913
                  + -1.37398*tf.T9 + -1.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Na23__He4_Ne20 = rate

@numba.njit()
def p_Na23__n_Mg23(rate_eval, tf):
    # Na23 + p --> n + Mg23
    rate = 0.0

    # nacr 
    rate += np.exp(  19.4638 + -56.1542*tf.T9i + 0.993488*tf.T913
                  + -0.257094*tf.T9 + 0.0284334*tf.T953)

    rate_eval.p_Na23__n_Mg23 = rate

@numba.njit()
def He4_Na22__p_Mg25(rate_eval, tf):
    # Na22 + He4 --> p + Mg25
    rate = 0.0

    # ths8r
    rate += np.exp(  44.973 + -50.0924*tf.T913i + 0.807739*tf.T913
                  + -0.956029*tf.T9 + 0.0793321*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Na22__p_Mg25 = rate

@numba.njit()
def He4_S41__Ar45(rate_eval, tf):
    # S41 + He4 --> Ar45
    rate = 0.0

    # rath 
    rate += np.exp(  -344.523 + 1.87056*tf.T9i + -487.664*tf.T913i + 860.632*tf.T913
                  + -56.9346*tf.T9 + 3.46483*tf.T953 + -377.236*tf.lnT9)

    rate_eval.He4_S41__Ar45 = rate

@numba.njit()
def p_V56__Cr57(rate_eval, tf):
    # V56 + p --> Cr57
    rate = 0.0

    # rath 
    rate += np.exp(  121.96 + -6.21697*tf.T9i + 231.518*tf.T913i + -372.997*tf.T913
                  + 20.5345*tf.T9 + -1.16811*tf.T953 + 187.678*tf.lnT9)

    rate_eval.p_V56__Cr57 = rate

@numba.njit()
def n_Na21__He4_F18(rate_eval, tf):
    # Na21 + n --> He4 + F18
    rate = 0.0

    # ths8r
    rate += np.exp(  15.7482 + 1.06229*tf.T913
                  + 0.212448*tf.T9 + -0.020685*tf.T953)

    rate_eval.n_Na21__He4_F18 = rate

@numba.njit()
def He4_S29__p_Cl32(rate_eval, tf):
    # S29 + He4 --> p + Cl32
    rate = 0.0

    # ths8r
    rate += np.exp(  51.2648 + -65.124*tf.T913i + 0.280931*tf.T913
                  + -0.79903*tf.T9 + 0.0557124*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S29__p_Cl32 = rate

@numba.njit()
def n_Na20__He4_F17(rate_eval, tf):
    # Na20 + n --> He4 + F17
    rate = 0.0

    # ths8r
    rate += np.exp(  16.8663 + 2.29236*tf.T913
                  + -0.234144*tf.T9 + 0.0119218*tf.T953)

    rate_eval.n_Na20__He4_F17 = rate

@numba.njit()
def n_V40__He4_Sc37(rate_eval, tf):
    # V40 + n --> He4 + Sc37
    rate = 0.0

    # ths8r
    rate += np.exp(  15.9518 + -0.0590932*tf.T913
                  + 0.191809*tf.T9 + -0.0119029*tf.T953)

    rate_eval.n_V40__He4_Sc37 = rate

@numba.njit()
def He4_Cl35__p_Ar38(rate_eval, tf):
    # Cl35 + He4 --> p + Ar38
    rate = 0.0

    # ths8r
    rate += np.exp(  51.1272 + -68.2848*tf.T913i + 2.5993*tf.T913
                  + -1.59144*tf.T9 + 0.137745*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl35__p_Ar38 = rate

@numba.njit()
def p_Ne34__n_Na34(rate_eval, tf):
    # Ne34 + p --> n + Na34
    rate = 0.0

    # rath 
    rate += np.exp(  74.1777 + -2.83263*tf.T9i + 101.585*tf.T913i + -170.557*tf.T913
                  + 9.26496*tf.T9 + -0.509169*tf.T953 + 85.3205*tf.lnT9)

    rate_eval.p_Ne34__n_Na34 = rate

@numba.njit()
def n_Mn54__He4_V51(rate_eval, tf):
    # Mn54 + n --> He4 + V51
    rate = 0.0

    # ths8r
    rate += np.exp(  -7.40385 + 7.07865*tf.T913
                  + 2.24997*tf.T9 + -0.318964*tf.T953)

    rate_eval.n_Mn54__He4_V51 = rate

@numba.njit()
def n_Cl32__He4_P29(rate_eval, tf):
    # Cl32 + n --> He4 + P29
    rate = 0.0

    # ths8r
    rate += np.exp(  16.9536 + 1.0254*tf.T913
                  + -0.188653*tf.T9 + 0.0264376*tf.T953)

    rate_eval.n_Cl32__He4_P29 = rate

@numba.njit()
def p_Cl36__Ar37(rate_eval, tf):
    # Cl36 + p --> Ar37
    rate = 0.0

    # ths8r
    rate += np.exp(  34.0223 + -27.9044*tf.T913i + -0.481331*tf.T913
                  + -1.50793*tf.T9 + 0.182531*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cl36__Ar37 = rate

@numba.njit()
def He4_S46__n_Ar49(rate_eval, tf):
    # S46 + He4 --> n + Ar49
    rate = 0.0

    # rath 
    rate += np.exp(  -358.386 + 1.91489*tf.T9i + -509.786*tf.T913i + 908.94*tf.T913
                  + -60.3275*tf.T9 + 3.6866*tf.T953 + -397.604*tf.lnT9)

    rate_eval.He4_S46__n_Ar49 = rate

@numba.njit()
def He4_Ne31__n_Mg34(rate_eval, tf):
    # Ne31 + He4 --> n + Mg34
    rate = 0.0

    # rath 
    rate += np.exp(  73.6087 + -2.97105*tf.T9i + 66.0008*tf.T913i + -145.696*tf.T913
                  + 6.71551*tf.T9 + -0.332811*tf.T953 + 76.1282*tf.lnT9)

    rate_eval.He4_Ne31__n_Mg34 = rate

@numba.njit()
def p_Al35__n_Si35(rate_eval, tf):
    # Al35 + p --> n + Si35
    rate = 0.0

    # rath 
    rate += np.exp(  84.5097 + -3.42217*tf.T9i + 123.062*tf.T913i + -206.07*tf.T913
                  + 11.2417*tf.T9 + -0.624036*tf.T953 + 103.201*tf.lnT9)

    rate_eval.p_Al35__n_Si35 = rate

@numba.njit()
def He4_Ne30__n_Mg33(rate_eval, tf):
    # Ne30 + He4 --> n + Mg33
    rate = 0.0

    # rath 
    rate += np.exp(  74.34 + -2.92019*tf.T9i + 64.8266*tf.T913i + -146.024*tf.T913
                  + 6.96081*tf.T9 + -0.357295*tf.T953 + 75.723*tf.lnT9)

    rate_eval.He4_Ne30__n_Mg33 = rate

@numba.njit()
def p_Ne30__He4_F27(rate_eval, tf):
    # Ne30 + p --> He4 + F27
    rate = 0.0

    # rath 
    rate += np.exp(  53.2811 + -2.69403*tf.T9i + 96.0623*tf.T913i + -152.54*tf.T913
                  + 7.66452*tf.T9 + -0.391518*tf.T953 + 80.086*tf.lnT9)

    rate_eval.p_Ne30__He4_F27 = rate

@numba.njit()
def n_Sc40__p_Ca40(rate_eval, tf):
    # Sc40 + n --> p + Ca40
    rate = 0.0

    # ths8r
    rate += np.exp(  20.4372 + -0.332049*tf.T913
                  + 0.18829*tf.T9 + -0.0179201*tf.T953)

    rate_eval.n_Sc40__p_Ca40 = rate

@numba.njit()
def p_Ne29__He4_F26(rate_eval, tf):
    # Ne29 + p --> He4 + F26
    rate = 0.0

    # rath 
    rate += np.exp(  61.1866 + -2.61621*tf.T9i + 91.5003*tf.T913i + -153.028*tf.T913
                  + 8.17097*tf.T9 + -0.43989*tf.T953 + 77.4787*tf.lnT9)

    rate_eval.p_Ne29__He4_F26 = rate

@numba.njit()
def He4_Ar43__Ca47(rate_eval, tf):
    # Ar43 + He4 --> Ca47
    rate = 0.0

    # rath 
    rate += np.exp(  -783.994 + 12.7001*tf.T9i + -1381.96*tf.T913i + 2254.15*tf.T913
                  + -134.525*tf.T9 + 7.74614*tf.T953 + -1058.85*tf.lnT9)

    rate_eval.He4_Ar43__Ca47 = rate

@numba.njit()
def p_Ne29__n_Na29(rate_eval, tf):
    # Ne29 + p --> n + Na29
    rate = 0.0

    # rath 
    rate += np.exp(  69.349 + -2.61578*tf.T9i + 91.8282*tf.T913i + -155.422*tf.T913
                  + 8.3852*tf.T9 + -0.463574*tf.T953 + 78.0988*tf.lnT9)

    rate_eval.p_Ne29__n_Na29 = rate

@numba.njit()
def He4_Ne28__n_Mg31(rate_eval, tf):
    # Ne28 + He4 --> n + Mg31
    rate = 0.0

    # rath 
    rate += np.exp(  71.106 + -2.77934*tf.T9i + 58.4126*tf.T913i + -135.681*tf.T913
                  + 6.28722*tf.T9 + -0.314638*tf.T953 + 70.8239*tf.lnT9)

    rate_eval.He4_Ne28__n_Mg31 = rate

@numba.njit()
def p_Ne28__n_Na28(rate_eval, tf):
    # Ne28 + p --> n + Na28
    rate = 0.0

    # rath 
    rate += np.exp(  71.5277 + -2.58754*tf.T9i + 91.7257*tf.T913i + -157.676*tf.T913
                  + 8.64403*tf.T9 + -0.481943*tf.T953 + 78.5687*tf.lnT9)

    rate_eval.p_Ne28__n_Na28 = rate

@numba.njit()
def Si35__P35__weak__wc17(rate_eval, tf):
    # Si35 --> P35
    rate = 0.0

    # wc17w
    rate += np.exp(  -0.118052)

    rate_eval.Si35__P35__weak__wc17 = rate

@numba.njit()
def He4_Ne27__n_Mg30(rate_eval, tf):
    # Ne27 + He4 --> n + Mg30
    rate = 0.0

    # rath 
    rate += np.exp(  68.4379 + -2.70101*tf.T9i + 54.5879*tf.T913i + -129.313*tf.T913
                  + 5.93936*tf.T9 + -0.297298*tf.T953 + 67.8421*tf.lnT9)

    rate_eval.He4_Ne27__n_Mg30 = rate

@numba.njit()
def p_Ne27__n_Na27(rate_eval, tf):
    # Ne27 + p --> n + Na27
    rate = 0.0

    # rath 
    rate += np.exp(  66.246 + -2.51621*tf.T9i + 86.9709*tf.T913i + -147.292*tf.T913
                  + 7.91961*tf.T9 + -0.438407*tf.T953 + 74.346*tf.lnT9)

    rate_eval.p_Ne27__n_Na27 = rate

@numba.njit()
def He4_Ca39__Ti43(rate_eval, tf):
    # Ca39 + He4 --> Ti43
    rate = 0.0

    # ths8r
    rate += np.exp(  57.6074 + -76.3683*tf.T913i + -1.90759*tf.T913
                  + -2.91291*tf.T9 + 0.389632*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca39__Ti43 = rate

@numba.njit()
def N23__O23__weak__wc12(rate_eval, tf):
    # N23 --> O23
    rate = 0.0

    # wc12w
    rate += np.exp(  3.86709)

    rate_eval.N23__O23__weak__wc12 = rate

@numba.njit()
def He4_Ti54__Cr58(rate_eval, tf):
    # Ti54 + He4 --> Cr58
    rate = 0.0

    # rath 
    rate += np.exp(  -982.592 + 20.4387*tf.T9i + -2035.1*tf.T913i + 3132.13*tf.T913
                  + -177.645*tf.T9 + 9.79827*tf.T953 + -1519.17*tf.lnT9)

    rate_eval.He4_Ti54__Cr58 = rate

@numba.njit()
def He4_S39__n_Ar42(rate_eval, tf):
    # S39 + He4 --> n + Ar42
    rate = 0.0

    # rath 
    rate += np.exp(  -330.836 + 1.88979*tf.T9i + -481.992*tf.T913i + 849.342*tf.T913
                  + -56.2061*tf.T9 + 3.42324*tf.T953 + -372.105*tf.lnT9)

    rate_eval.He4_S39__n_Ar42 = rate

@numba.njit()
def p_Ne25__He4_F22(rate_eval, tf):
    # Ne25 + p --> He4 + F22
    rate = 0.0

    # rath 
    rate += np.exp(  17.9847 + -0.300689*tf.T9i + -48.0684*tf.T913i + 23.499*tf.T913
                  + -3.2844*tf.T9 + 0.237953*tf.T953 + -4.51773*tf.lnT9)

    rate_eval.p_Ne25__He4_F22 = rate

@numba.njit()
def p_Ne25__n_Na25(rate_eval, tf):
    # Ne25 + p --> n + Na25
    rate = 0.0

    # rath 
    rate += np.exp(  64.1027 + -2.41421*tf.T9i + 82.2523*tf.T913i + -140.548*tf.T913
                  + 7.61913*tf.T9 + -0.425362*tf.T953 + 70.9022*tf.lnT9)

    rate_eval.p_Ne25__n_Na25 = rate

@numba.njit()
def K59__Ca59__weak__mo03(rate_eval, tf):
    # K59 --> Ca59
    rate = 0.0

    # mo03w
    rate += np.exp(  -109.666)

    rate_eval.K59__Ca59__weak__mo03 = rate

@numba.njit()
def He4_S27__p_Cl30(rate_eval, tf):
    # S27 + He4 --> p + Cl30
    rate = 0.0

    # ths8r
    rate += np.exp(  50.9855 + -64.9324*tf.T913i + 0.257107*tf.T913
                  + -0.76833*tf.T9 + 0.0530446*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S27__p_Cl30 = rate

@numba.njit()
def He4_Ne24__n_Mg27(rate_eval, tf):
    # Ne24 + He4 --> n + Mg27
    rate = 0.0

    # rath 
    rate += np.exp(  64.7039 + -2.48477*tf.T9i + 45.4852*tf.T913i + -115.792*tf.T913
                  + 5.15572*tf.T9 + -0.251338*tf.T953 + 61.1354*tf.lnT9)

    rate_eval.He4_Ne24__n_Mg27 = rate

@numba.njit()
def p_Ne24__n_Na24(rate_eval, tf):
    # Ne24 + p --> n + Na24
    rate = 0.0

    # rath 
    rate += np.exp(  64.0799 + -2.37082*tf.T9i + 80.7458*tf.T913i + -138.809*tf.T913
                  + 7.52269*tf.T9 + -0.42014*tf.T953 + 69.9474*tf.lnT9)

    rate_eval.p_Ne24__n_Na24 = rate

@numba.njit()
def Cl39__Ar39__weak__wc12(rate_eval, tf):
    # Cl39 --> Ar39
    rate = 0.0

    # wc12w
    rate += np.exp(  -8.48918)

    rate_eval.Cl39__Ar39__weak__wc12 = rate

@numba.njit()
def p_S30__Cl31(rate_eval, tf):
    # S30 + p --> Cl31
    rate = 0.0

    # il10n
    rate += np.exp(  16.9482 + -26.5445*tf.T913i + 2.36819*tf.T913
                  + -0.795998*tf.T9 + 0.0151029*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  4.83062 + -5.35737*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_S30__Cl31 = rate

@numba.njit()
def n_Ti45__He4_Ca42(rate_eval, tf):
    # Ti45 + n --> He4 + Ca42
    rate = 0.0

    # ths8r
    rate += np.exp(  16.4413 + -1.31041*tf.T913
                  + 0.516347*tf.T9 + -0.0189198*tf.T953)

    rate_eval.n_Ti45__He4_Ca42 = rate

@numba.njit()
def Cr69__Mn69__weak__mo03(rate_eval, tf):
    # Cr69 --> Mn69
    rate = 0.0

    # mo03w
    rate += np.exp(  3.68364)

    rate_eval.Cr69__Mn69__weak__mo03 = rate

@numba.njit()
def P33__S33__weak__wc12(rate_eval, tf):
    # P33 --> S33
    rate = 0.0

    # wc12w
    rate += np.exp(  -14.9659)

    rate_eval.P33__S33__weak__wc12 = rate

@numba.njit()
def He4_Ca61__n_Ti64(rate_eval, tf):
    # Ca61 + He4 --> n + Ti64
    rate = 0.0

    # rath 
    rate += np.exp(  -1016.21 + 16.2017*tf.T9i + -1758.31*tf.T913i + 2901.26*tf.T913
                  + -173.605*tf.T9 + 9.97799*tf.T953 + -1360.1*tf.lnT9)

    rate_eval.He4_Ca61__n_Ti64 = rate

@numba.njit()
def He4_K39__Sc43(rate_eval, tf):
    # K39 + He4 --> Sc43
    rate = 0.0

    # ths8r
    rate += np.exp(  54.1202 + -73.8006*tf.T913i + 1.87885*tf.T913
                  + -2.75862*tf.T9 + 0.279678*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K39__Sc43 = rate

@numba.njit()
def p_Ne23__n_Na23(rate_eval, tf):
    # Ne23 + p --> n + Na23
    rate = 0.0

    # rath 
    rate += np.exp(  59.1181 + -2.29126*tf.T9i + 75.4476*tf.T913i + -128.085*tf.T913
                  + 6.80309*tf.T9 + -0.377154*tf.T953 + 65.3401*tf.lnT9)

    rate_eval.p_Ne23__n_Na23 = rate

@numba.njit()
def He4_Sc62__V66(rate_eval, tf):
    # Sc62 + He4 --> V66
    rate = 0.0

    # rath 
    rate += np.exp(  -1027.76 + 21.3863*tf.T9i + -2123.03*tf.T913i + 3272.12*tf.T913
                  + -185.058*tf.T9 + 10.2083*tf.T953 + -1588.76*tf.lnT9)

    rate_eval.He4_Sc62__V66 = rate

@numba.njit()
def He4_Ne22__n_Mg25(rate_eval, tf):
    # Ne22 + He4 --> n + Mg25
    rate = 0.0

    # li12r
    rate += np.exp(  -27.5027 + -7.38607*tf.T9i + 35.987*tf.T913
                  + -4.12183*tf.T9 + 0.263326*tf.T953 + -1.5*tf.lnT9)
    # li12n
    rate += np.exp(  -10.4729 + -5.55032*tf.T9i + 15.4898*tf.T913
                  + -30.8154*tf.T9 + -3.0*tf.T953 + 2.0*tf.lnT9)
    # li12n
    rate += np.exp(  -52.326 + -5.55032*tf.T9i + 88.2725*tf.T913
                  + -40.1578*tf.T9 + -3.0*tf.T953)

    rate_eval.He4_Ne22__n_Mg25 = rate

@numba.njit()
def n_Cl38__He4_P35(rate_eval, tf):
    # Cl38 + n --> He4 + P35
    rate = 0.0

    # rath 
    rate += np.exp(  -80.1414 + -1.02651*tf.T9i + 67.0126*tf.T913i + 17.6873*tf.T913
                  + -8.53544*tf.T9 + 0.724666*tf.T953 + 33.8438*tf.lnT9)

    rate_eval.n_Cl38__He4_P35 = rate

@numba.njit()
def p_Al43__He4_Mg40(rate_eval, tf):
    # Al43 + p --> He4 + Mg40
    rate = 0.0

    # rath 
    rate += np.exp(  77.1429 + -3.76644*tf.T9i + 137.373*tf.T913i + -223.937*tf.T913
                  + 12.0772*tf.T9 + -0.660326*tf.T953 + 112.982*tf.lnT9)

    rate_eval.p_Al43__He4_Mg40 = rate

@numba.njit()
def He4_Ne21__n_Mg24(rate_eval, tf):
    # Ne21 + He4 --> n + Mg24
    rate = 0.0

    # nacrr
    rate += np.exp(  -7.26831 + -13.2638*tf.T9i + 18.0748*tf.T913
                  + -0.981883*tf.T9 + -1.5*tf.lnT9)
    # nacrn
    rate += np.exp(  43.9762 + -46.88*tf.T913i + -0.536629*tf.T913
                  + 0.144715*tf.T9 + -0.197624*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ne21__n_Mg24 = rate

@numba.njit()
def n_Si27__Si28(rate_eval, tf):
    # Si27 + n --> Si28
    rate = 0.0

    # ths8r
    rate += np.exp(  9.14054 + 0.559804*tf.T913
                  + -0.0233808*tf.T9 + -0.00121313*tf.T953)

    rate_eval.n_Si27__Si28 = rate

@numba.njit()
def p_V42__Cr43(rate_eval, tf):
    # V42 + p --> Cr43
    rate = 0.0

    # ths8r
    rate += np.exp(  38.0125 + -34.179*tf.T913i + -2.19491*tf.T913
                  + -2.95824*tf.T9 + 0.424276*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V42__Cr43 = rate

@numba.njit()
def C12_Ne20__He4_Si28(rate_eval, tf):
    # Ne20 + C12 --> He4 + Si28
    rate = 0.0

    # rolfr
    rate += np.exp(  -308.905 + -47.2175*tf.T9i + 514.197*tf.T913i + -200.896*tf.T913
                  + -6.42713*tf.T9 + 0.758256*tf.T953 + 236.359*tf.lnT9)

    rate_eval.C12_Ne20__He4_Si28 = rate

@numba.njit()
def C12_Ne20__p_P31(rate_eval, tf):
    # Ne20 + C12 --> p + P31
    rate = 0.0

    # rolfr
    rate += np.exp(  -268.136 + -38.7624*tf.T9i + 361.154*tf.T913i + -92.643*tf.T913
                  + -9.98738*tf.T9 + 0.892737*tf.T953 + 161.042*tf.lnT9)

    rate_eval.C12_Ne20__p_P31 = rate

@numba.njit()
def n_Na30__Na31(rate_eval, tf):
    # Na30 + n --> Na31
    rate = 0.0

    # rath 
    rate += np.exp(  12.9465 + -0.04274*tf.T9i + 3.0932*tf.T913i + -6.47721*tf.T913
                  + 0.407861*tf.T9 + -0.0239584*tf.T953 + 2.3532*tf.lnT9)

    rate_eval.n_Na30__Na31 = rate

@numba.njit()
def p_V54__n_Cr54(rate_eval, tf):
    # V54 + p --> n + Cr54
    rate = 0.0

    # rath 
    rate += np.exp(  129.852 + -6.14822*tf.T9i + 229.859*tf.T913i + -371.233*tf.T913
                  + 20.5354*tf.T9 + -1.16657*tf.T953 + 186.685*tf.lnT9)

    rate_eval.p_V54__n_Cr54 = rate

@numba.njit()
def p_Ne20__He4_F17(rate_eval, tf):
    # Ne20 + p --> He4 + F17
    rate = 0.0

    # nacr 
    rate += np.exp(  41.563 + -47.9266*tf.T9i + -43.18*tf.T913i + 4.46827*tf.T913
                  + -1.63915*tf.T9 + 0.123483*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ne20__He4_F17 = rate

@numba.njit()
def p_Ne22__Na23(rate_eval, tf):
    # Ne22 + p --> Na23
    rate = 0.0

    # ke17r
    rate += np.exp(  -0.599331 + -1.72007*tf.T9i
                  + -0.310765*tf.lnT9)
    # ke17r
    rate += np.exp(  -21.4345 + -0.410962*tf.T9i
                  + -1.49019*tf.lnT9)
    # ke17r
    rate += np.exp(  -4.09035 + -0.799756*tf.T9i
                  + 3.23558*tf.lnT9)
    # ke17r
    rate += np.exp(  14.0373 + -8.72377*tf.T9i
                  + -0.767467*tf.lnT9)
    # ke17r
    rate += np.exp(  11.6408 + -4.59936*tf.T9i
                  + 0.156226*tf.lnT9)
    # ke17r
    rate += np.exp(  -4.00597 + -2.6179*tf.T9i
                  + -4.29964*tf.lnT9)

    rate_eval.p_Ne22__Na23 = rate

@numba.njit()
def He4_Al26__p_Si29(rate_eval, tf):
    # Al26 + He4 --> p + Si29
    rate = 0.0

    # ths8r
    rate += np.exp(  47.7092 + -56.4422*tf.T913i + 0.705353*tf.T913
                  + -0.957427*tf.T9 + 0.0756045*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al26__p_Si29 = rate

@numba.njit()
def p_K33__Ca34(rate_eval, tf):
    # K33 + p --> Ca34
    rate = 0.0

    # ths8r
    rate += np.exp(  36.6172 + -30.0277*tf.T913i + -7.85883*tf.T913
                  + -0.941155*tf.T9 + 0.206608*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_K33__Ca34 = rate

@numba.njit()
def He4_Ne19__p_Na22(rate_eval, tf):
    # Ne19 + He4 --> p + Na22
    rate = 0.0

    # ths8r
    rate += np.exp(  43.1874 + -46.6346*tf.T913i + 0.866532*tf.T913
                  + -0.893541*tf.T9 + 0.0747971*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ne19__p_Na22 = rate

@numba.njit()
def He4_Ne18__p_Na21(rate_eval, tf):
    # Ne18 + He4 --> p + Na21
    rate = 0.0

    # mo14r
    rate += np.exp(  -23.5811 + -5.76874*tf.T9i + 8.5632e-08*tf.T913i + 24.8579*tf.T913
                  + 0.0823845*tf.T9 + -0.365374*tf.T953 + -2.21415e-06*tf.lnT9)
    # mo14r
    rate += np.exp(  -22.4389 + -10.2598*tf.T9i + 4.73034e-07*tf.T913i + 36.29*tf.T913
                  + -6.56565*tf.T9 + -2.96287e-06*tf.T953 + -9.00373e-07*tf.lnT9)
    # mo14r
    rate += np.exp(  -37.3979 + -3.8681*tf.T9i + 7.09521e-06*tf.T913i + 34.1789*tf.T913
                  + -1.72974*tf.T9 + -0.0395081*tf.T953 + -7.82759e-07*tf.lnT9)

    rate_eval.He4_Ne18__p_Na21 = rate

@numba.njit()
def n_Si25__He4_Mg22(rate_eval, tf):
    # Si25 + n --> He4 + Mg22
    rate = 0.0

    # ths8r
    rate += np.exp(  15.3902 + 1.72545*tf.T913
                  + -0.244135*tf.T9 + 0.0193897*tf.T953)

    rate_eval.n_Si25__He4_Mg22 = rate

@numba.njit()
def n_Ne18__He4_O15(rate_eval, tf):
    # Ne18 + n --> He4 + O15
    rate = 0.0

    # ths8r
    rate += np.exp(  18.0529 + 0.377325*tf.T913
                  + 0.0968945*tf.T9 + -0.007769*tf.T953)

    rate_eval.n_Ne18__He4_O15 = rate

@numba.njit()
def n_Ne18__p_F18(rate_eval, tf):
    # Ne18 + n --> p + F18
    rate = 0.0

    # ths8r
    rate += np.exp(  18.5429 + 0.590026*tf.T913
                  + 0.0742242*tf.T9 + -0.0116856*tf.T953)

    rate_eval.n_Ne18__p_F18 = rate

@numba.njit()
def He4_Ne17__p_Na20(rate_eval, tf):
    # Ne17 + He4 --> p + Na20
    rate = 0.0

    # ths8r
    rate += np.exp(  42.4434 + -46.3234*tf.T913i + 0.713497*tf.T913
                  + -0.737825*tf.T9 + 0.059715*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ne17__p_Na20 = rate

@numba.njit()
def n_Be7__He4_He4(rate_eval, tf):
    # Be7 + n --> He4 + He4
    rate = 0.0

    #  wagn
    rate += np.exp(  18.1614 + -0.00210045*tf.T913
                  + 0.000176541*tf.T9 + -1.36797e-05*tf.T953 + 1.00083*tf.lnT9)

    rate_eval.n_Be7__He4_He4 = rate

@numba.njit()
def He4_Ne16__p_Na19(rate_eval, tf):
    # Ne16 + He4 --> p + Na19
    rate = 0.0

    # ths8r
    rate += np.exp(  42.1092 + -46.1429*tf.T913i + 0.783955*tf.T913
                  + -0.73972*tf.T9 + 0.0598405*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ne16__p_Na19 = rate

@numba.njit()
def He4_Cl49__K53(rate_eval, tf):
    # Cl49 + He4 --> K53
    rate = 0.0

    # rath 
    rate += np.exp(  -829.676 + 13.262*tf.T9i + -1437.48*tf.T913i + 2360.34*tf.T913
                  + -141.244*tf.T9 + 8.11234*tf.T953 + -1107.08*tf.lnT9)

    rate_eval.He4_Cl49__K53 = rate

@numba.njit()
def n_Ne16__p_F16(rate_eval, tf):
    # Ne16 + n --> p + F16
    rate = 0.0

    # ths8r
    rate += np.exp(  19.6492 + 0.0686744*tf.T913
                  + 0.110401*tf.T9 + -0.00999667*tf.T953)

    rate_eval.n_Ne16__p_F16 = rate

@numba.njit()
def p_Cr67__He4_V64(rate_eval, tf):
    # Cr67 + p --> He4 + V64
    rate = 0.0

    # rath 
    rate += np.exp(  -404.19 + 0.520413*tf.T9i + -410.078*tf.T913i + 838.688*tf.T913
                  + -57.2839*tf.T9 + 3.523*tf.T953 + -345.674*tf.lnT9)

    rate_eval.p_Cr67__He4_V64 = rate

@numba.njit()
def He4_Ar53__n_Ca56(rate_eval, tf):
    # Ar53 + He4 --> n + Ca56
    rate = 0.0

    # rath 
    rate += np.exp(  -414.484 + 2.08949*tf.T9i + -577.725*tf.T913i + 1037.78*tf.T913
                  + -68.7582*tf.T9 + 4.19622*tf.T953 + -453.891*tf.lnT9)

    rate_eval.He4_Ar53__n_Ca56 = rate

@numba.njit()
def p_F31__n_Ne31(rate_eval, tf):
    # F31 + p --> n + Ne31
    rate = 0.0

    # rpsmr
    rate += np.exp(  68.5013 + -2.52278*tf.T9i + 89.5013*tf.T913i + -151.354*tf.T913
                  + 8.18591*tf.T9 + -0.449289*tf.T953 + 75.7251*tf.lnT9)

    rate_eval.p_F31__n_Ne31 = rate

@numba.njit()
def He4_F30__p_Ne33(rate_eval, tf):
    # F30 + He4 --> p + Ne33
    rate = 0.0

    # rpsmr
    rate += np.exp(  44.6089 + -2.62921*tf.T9i + 50.9142*tf.T913i + -110.569*tf.T913
                  + 4.40742*tf.T9 + -0.179343*tf.T953 + 61.209*tf.lnT9)

    rate_eval.He4_F30__p_Ne33 = rate

@numba.njit()
def p_Ar45__n_K45(rate_eval, tf):
    # Ar45 + p --> n + K45
    rate = 0.0

    # rath 
    rate += np.exp(  106.5 + -4.78009*tf.T9i + 175.241*tf.T913i + -286.905*tf.T913
                  + 15.7883*tf.T9 + -0.885732*tf.T953 + 144.106*tf.lnT9)

    rate_eval.p_Ar45__n_K45 = rate

@numba.njit()
def p_Mn47__Fe48(rate_eval, tf):
    # Mn47 + p --> Fe48
    rate = 0.0

    # nfisn
    rate += np.exp(  12644.8 + -37.7402*tf.T9i + 4124.11*tf.T913i + -20307.8*tf.T913
                  + 4924.7*tf.T9 + -1413.68*tf.T953 + 5310.56*tf.lnT9)
    # nfisn
    rate += np.exp(  386.521 + -5.83182*tf.T9i + 242.062*tf.T913i + -699.29*tf.T913
                  + 76.5578*tf.T9 + -8.92043*tf.T953 + 249.844*tf.lnT9)
    # nfisn
    rate += np.exp(  22.4249 + 0.0392138*tf.T9i + -38.9353*tf.T913i + 3.32414*tf.T913
                  + -0.0398256*tf.T9 + -0.0321214*tf.T953 + -2.36463*tf.lnT9)
    # nfisn
    rate += np.exp(  54.8121 + -0.773117*tf.T9i + -132.912*tf.T913i + 72.2283*tf.T913
                  + 2.45509*tf.T9 + -0.364613*tf.T953 + -65.2383*tf.lnT9)
    # nfisn
    rate += np.exp(  98.8237 + -2.83967*tf.T9i + -3.77566*tf.T913i + -103.572*tf.T913
                  + 8.60296*tf.T9 + -0.609341*tf.T953 + 32.2966*tf.lnT9)

    rate_eval.p_Mn47__Fe48 = rate

@numba.njit()
def p_F30__He4_O27(rate_eval, tf):
    # F30 + p --> He4 + O27
    rate = 0.0

    # rpsmr
    rate += np.exp(  51.5741 + -2.41991*tf.T9i + 81.128*tf.T913i + -133.734*tf.T913
                  + 7.1079*tf.T9 + -0.383258*tf.T953 + 68.1613*tf.lnT9)

    rate_eval.p_F30__He4_O27 = rate

@numba.njit()
def He4_F29__n_Na32(rate_eval, tf):
    # F29 + He4 --> n + Na32
    rate = 0.0

    # rpsmr
    rate += np.exp(  66.7117 + -2.62933*tf.T9i + 54.7657*tf.T913i + -125.371*tf.T913
                  + 5.66994*tf.T9 + -0.276336*tf.T953 + 65.8238*tf.lnT9)

    rate_eval.He4_F29__n_Na32 = rate

@numba.njit()
def p_F29__He4_O26(rate_eval, tf):
    # F29 + p --> He4 + O26
    rate = 0.0

    # rpsmr
    rate += np.exp(  59.1087 + -2.40478*tf.T9i + 82.3942*tf.T913i + -139.275*tf.T913
                  + 7.54891*tf.T9 + -0.416948*tf.T953 + 70.0068*tf.lnT9)

    rate_eval.p_F29__He4_O26 = rate

@numba.njit()
def He4_F27__n_Na30(rate_eval, tf):
    # F27 + He4 --> n + Na30
    rate = 0.0

    # rpsmr
    rate += np.exp(  65.2123 + -2.50634*tf.T9i + 49.8363*tf.T913i + -118.526*tf.T913
                  + 5.29288*tf.T9 + -0.255208*tf.T953 + 62.3065*tf.lnT9)

    rate_eval.He4_F27__n_Na30 = rate

@numba.njit()
def p_F27__He4_O24(rate_eval, tf):
    # F27 + p --> He4 + O24
    rate = 0.0

    # rpsmr
    rate += np.exp(  60.3399 + -2.34979*tf.T9i + 81.778*tf.T913i + -140.409*tf.T913
                  + 7.61924*tf.T9 + -0.41875*tf.T953 + 70.1812*tf.lnT9)

    rate_eval.p_F27__He4_O24 = rate

@numba.njit()
def p_F27__n_Ne27(rate_eval, tf):
    # F27 + p --> n + Ne27
    rate = 0.0

    # rpsmr
    rate += np.exp(  65.5701 + -2.35602*tf.T9i + 82.2832*tf.T913i + -140.709*tf.T913
                  + 7.58307*tf.T9 + -0.417673*tf.T953 + 70.5184*tf.lnT9)

    rate_eval.p_F27__n_Ne27 = rate

@numba.njit()
def S27__p_Si26__weak__wc17(rate_eval, tf):
    # S27 --> p + Si26
    rate = 0.0

    # wc17w
    rate += np.exp(  0.0281413)

    rate_eval.S27__p_Si26__weak__wc17 = rate

@numba.njit()
def He4_F26__n_Na29(rate_eval, tf):
    # F26 + He4 --> n + Na29
    rate = 0.0

    # rpsmr
    rate += np.exp(  63.3008 + -2.43649*tf.T9i + 46.6888*tf.T913i + -113.668*tf.T913
                  + 5.06188*tf.T9 + -0.244801*tf.T953 + 59.9416*tf.lnT9)

    rate_eval.He4_F26__n_Na29 = rate

@numba.njit()
def p_F26__n_Ne26(rate_eval, tf):
    # F26 + p --> n + Ne26
    rate = 0.0

    # rpsmr
    rate += np.exp(  63.4806 + -2.30615*tf.T9i + 79.7246*tf.T913i + -136.127*tf.T913
                  + 7.35507*tf.T9 + -0.408647*tf.T953 + 68.4742*tf.lnT9)

    rate_eval.p_F26__n_Ne26 = rate

@numba.njit()
def p_Na34__He4_Ne31(rate_eval, tf):
    # Na34 + p --> He4 + Ne31
    rate = 0.0

    # rath 
    rate += np.exp(  70.4712 + -3.02451*tf.T9i + 109.125*tf.T913i + -184.77*tf.T913
                  + 10.1165*tf.T9 + -0.544248*tf.T953 + 91.9855*tf.lnT9)

    rate_eval.p_Na34__He4_Ne31 = rate

@numba.njit()
def p_F25__He4_O22(rate_eval, tf):
    # F25 + p --> He4 + O22
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.7325 + -2.26392*tf.T9i + 78.1968*tf.T913i + -134.952*tf.T913
                  + 7.39144*tf.T9 + -0.412479*tf.T953 + 67.5834*tf.lnT9)

    rate_eval.p_F25__He4_O22 = rate

@numba.njit()
def n_S30__S31(rate_eval, tf):
    # S30 + n --> S31
    rate = 0.0

    # ths8r
    rate += np.exp(  10.3285 + 1.62298*tf.T913
                  + -0.278802*tf.T9 + 0.0210647*tf.T953)

    rate_eval.n_S30__S31 = rate

@numba.njit()
def p_F25__n_Ne25(rate_eval, tf):
    # F25 + p --> n + Ne25
    rate = 0.0

    # rpsmr
    rate += np.exp(  62.366 + -2.25808*tf.T9i + 77.4751*tf.T913i + -132.818*tf.T913
                  + 7.20802*tf.T9 + -0.402463*tf.T953 + 66.8086*tf.lnT9)

    rate_eval.p_F25__n_Ne25 = rate

@numba.njit()
def He4_Ca38__Ti42(rate_eval, tf):
    # Ca38 + He4 --> Ti42
    rate = 0.0

    # ths8r
    rate += np.exp(  58.4869 + -76.3063*tf.T913i + -10.7213*tf.T913
                  + 0.926161*tf.T9 + -0.0855699*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca38__Ti42 = rate

@numba.njit()
def He4_F24__n_Na27(rate_eval, tf):
    # F24 + He4 --> n + Na27
    rate = 0.0

    # rpsmr
    rate += np.exp(  60.1571 + -2.28962*tf.T9i + 39.9617*tf.T913i + -103.44*tf.T913
                  + 4.50349*tf.T9 + -0.214767*tf.T953 + 54.8788*tf.lnT9)

    rate_eval.He4_F24__n_Na27 = rate

@numba.njit()
def p_F24__n_Ne24(rate_eval, tf):
    # F24 + p --> n + Ne24
    rate = 0.0

    # rpsmr
    rate += np.exp(  62.6297 + -2.21638*tf.T9i + 76.0843*tf.T913i + -131.759*tf.T913
                  + 7.18481*tf.T9 + -0.401301*tf.T953 + 66.0387*tf.lnT9)

    rate_eval.p_F24__n_Ne24 = rate

@numba.njit()
def He4_Ti42__p_V45(rate_eval, tf):
    # Ti42 + He4 --> p + V45
    rate = 0.0

    # ths8r
    rate += np.exp(  58.4447 + -81.5598*tf.T913i + -1.03231*tf.T913
                  + -0.471149*tf.T9 + 0.0112292*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti42__p_V45 = rate

@numba.njit()
def p_Na26__He4_Ne23(rate_eval, tf):
    # Na26 + p --> He4 + Ne23
    rate = 0.0

    # rath 
    rate += np.exp(  60.597 + -2.61919*tf.T9i + 89.3507*tf.T913i + -148.891*tf.T913
                  + 7.9457*tf.T9 + -0.430979*tf.T953 + 76.3971*tf.lnT9)

    rate_eval.p_Na26__He4_Ne23 = rate

@numba.njit()
def p_F22__He4_O19(rate_eval, tf):
    # F22 + p --> He4 + O19
    rate = 0.0

    # rpsmr
    rate += np.exp(  55.0585 + -2.09806*tf.T9i + 69.5566*tf.T913i + -119.907*tf.T913
                  + 6.55038*tf.T9 + -0.366208*tf.T953 + 60.7212*tf.lnT9)

    rate_eval.p_F22__He4_O19 = rate

@numba.njit()
def p_F22__n_Ne22(rate_eval, tf):
    # F22 + p --> n + Ne22
    rate = 0.0

    # rpsmr
    rate += np.exp(  59.0738 + -2.10661*tf.T9i + 70.4584*tf.T913i + -122.313*tf.T913
                  + 6.61596*tf.T9 + -0.369133*tf.T953 + 61.6195*tf.lnT9)

    rate_eval.p_F22__n_Ne22 = rate

@numba.njit()
def Cl48__n_Ar47__weak__mp17(rate_eval, tf):
    # Cl48 --> n + Ar47
    rate = 0.0

    # mp17w
    rate += np.exp(  3.10766)

    rate_eval.Cl48__n_Ar47__weak__mp17 = rate

@numba.njit()
def He4_F21__p_Ne24(rate_eval, tf):
    # F21 + He4 --> p + Ne24
    rate = 0.0

    # rpsmr
    rate += np.exp(  36.6732 + -1.93402*tf.T9i + 18.4351*tf.T913i + -61.9233*tf.T913
                  + 1.84567*tf.T9 + -0.0610043*tf.T953 + 37.1531*tf.lnT9)

    rate_eval.He4_F21__p_Ne24 = rate

@numba.njit()
def He4_F21__n_Na24(rate_eval, tf):
    # F21 + He4 --> n + Na24
    rate = 0.0

    # rpsmr
    rate += np.exp(  57.3827 + -2.08564*tf.T9i + 32.1286*tf.T913i + -92.3717*tf.T913
                  + 3.88845*tf.T9 + -0.179974*tf.T953 + 49.2678*tf.lnT9)

    rate_eval.He4_F21__n_Na24 = rate

@numba.njit()
def p_Ne26__He4_F23(rate_eval, tf):
    # Ne26 + p --> He4 + F23
    rate = 0.0

    # rath 
    rate += np.exp(  46.1811 + -2.46281*tf.T9i + 83.5003*tf.T913i + -128.942*tf.T913
                  + 5.99688*tf.T9 + -0.29294*tf.T953 + 69.985*tf.lnT9)

    rate_eval.p_Ne26__He4_F23 = rate

@numba.njit()
def He4_F20__p_Ne23(rate_eval, tf):
    # F20 + He4 --> p + Ne23
    rate = 0.0

    # rpsmr
    rate += np.exp(  76.9378 + -2.12457*tf.T9i + 47.7125*tf.T913i + -134.323*tf.T913
                  + 6.38555*tf.T9 + -0.319981*tf.T953 + 67.6003*tf.lnT9)

    rate_eval.He4_F20__p_Ne23 = rate

@numba.njit()
def n_Si26__p_Al26(rate_eval, tf):
    # Si26 + n --> p + Al26
    rate = 0.0

    # ths8r
    rate += np.exp(  18.3907 + 2.01618*tf.T913
                  + -0.300371*tf.T9 + 0.0228631*tf.T953)

    rate_eval.n_Si26__p_Al26 = rate

@numba.njit()
def p_Al39__Si40(rate_eval, tf):
    # Al39 + p --> Si40
    rate = 0.0

    # rath 
    rate += np.exp(  75.7866 + -3.59734*tf.T9i + 130.146*tf.T913i + -214.975*tf.T913
                  + 11.7228*tf.T9 + -0.648379*tf.T953 + 107.991*tf.lnT9)

    rate_eval.p_Al39__Si40 = rate

@numba.njit()
def p_F20__He4_O17(rate_eval, tf):
    # F20 + p --> He4 + O17
    rate = 0.0

    #  wagn
    rate += np.exp(  29.27 + -4.58659e-12*tf.T9i + -18.13*tf.T913i + -2.20482e-09*tf.T913
                  + 2.4033e-10*tf.T9 + -2.17403e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_F20__He4_O17 = rate

@numba.njit()
def He4_F19__p_Ne22(rate_eval, tf):
    # F19 + He4 --> p + Ne22
    rate = 0.0

    # da18r
    rate += np.exp(  52.9317 + -2.8444*tf.T9i + -38.7722*tf.T913i + -13.3654*tf.T913
                  + 0.863648*tf.T9 + -0.0451491*tf.T953 + 1.33333*tf.lnT9)
    # da18r
    rate += np.exp(  51.6709 + -45.7808*tf.T9i + -34.5008*tf.T913i + 56.9316*tf.T913
                  + 2.09613*tf.T9 + -32.496*tf.T953 + 0.333333*tf.lnT9)
    # da18r
    rate += np.exp(  29430.6 + -133.026*tf.T9i + 12625.1*tf.T913i + -49107.1*tf.T913
                  + 9227.53*tf.T9 + -2086.65*tf.T953 + 14520.2*tf.lnT9)

    rate_eval.He4_F19__p_Ne22 = rate

@numba.njit()
def p_F19__n_Ne19(rate_eval, tf):
    # F19 + p --> n + Ne19
    rate = 0.0

    # nacr 
    rate += np.exp(  15.6732 + -46.6617*tf.T9i + 4.34441*tf.T913
                  + -1.71268*tf.T9)
    # nacr 
    rate += np.exp(  20.353 + -46.6617*tf.T9i + -1.58171*tf.T913
                  + 0.0324472*tf.T9 + 1.0*tf.lnT9)

    rate_eval.p_F19__n_Ne19 = rate

@numba.njit()
def p_O21__n_F21(rate_eval, tf):
    # O21 + p --> n + F21
    rate = 0.0

    # rpsmr
    rate += np.exp(  54.5936 + -1.89323*tf.T9i + 62.2103*tf.T913i + -108.311*tf.T913
                  + 5.82993*tf.T9 + -0.320966*tf.T953 + 54.5882*tf.lnT9)

    rate_eval.p_O21__n_F21 = rate

@numba.njit()
def He4_F18__p_Ne21(rate_eval, tf):
    # F18 + He4 --> p + Ne21
    rate = 0.0

    # rpsmr
    rate += np.exp(  49.7863 + -1.84559*tf.T9i + 21.4461*tf.T913i + -73.252*tf.T913
                  + 2.42329*tf.T9 + -0.077278*tf.T953 + 40.7604*tf.lnT9)

    rate_eval.He4_F18__p_Ne21 = rate

@numba.njit()
def p_O15__F16(rate_eval, tf):
    # O15 + p --> F16
    rate = 0.0

    # rpsmr
    rate += np.exp(  -3.01222 + -8.51539*tf.T9i + 74.5955*tf.T913i + -73.794*tf.T913
                  + 2.87936*tf.T9 + -0.117988*tf.T953 + 47.5366*tf.lnT9)

    rate_eval.p_O15__F16 = rate

@numba.njit()
def Al40__n_n_n_Si37__weak__mo03(rate_eval, tf):
    # Al40 --> 3 n + Si37
    rate = 0.0

    # mo03w
    rate += np.exp(  2.76325)

    rate_eval.Al40__n_n_n_Si37__weak__mo03 = rate

@numba.njit()
def n_F18__He4_N15(rate_eval, tf):
    # F18 + n --> He4 + N15
    rate = 0.0

    # cf88n
    rate += np.exp(  18.8011 + 1.74308*tf.T913
                  + -1.15123*tf.T9 + 0.135196*tf.T953)

    rate_eval.n_F18__He4_N15 = rate

@numba.njit()
def n_F15__He4_N12(rate_eval, tf):
    # F15 + n --> He4 + N12
    rate = 0.0

    # rpsmr
    rate += np.exp(  17.7992 + -0.00409112*tf.T9i + -0.532821*tf.T913i + 0.582145*tf.T913
                  + 0.141968*tf.T9 + -0.013595*tf.T953 + -0.423928*tf.lnT9)

    rate_eval.n_F15__He4_N12 = rate

@numba.njit()
def Fe76__n_n_n_Co73__weak__mo03(rate_eval, tf):
    # Fe76 --> 3 n + Co73
    rate = 0.0

    # mo03w
    rate += np.exp(  -3.48594)

    rate_eval.Fe76__n_n_n_Co73__weak__mo03 = rate

@numba.njit()
def n_Al41__Al42(rate_eval, tf):
    # Al41 + n --> Al42
    rate = 0.0

    # rath 
    rate += np.exp(  -1271.65 + -43.3228*tf.T9i + -1768.7*tf.T913i + 3225.98*tf.T913
                  + -183.025*tf.T9 + 9.96587*tf.T953 + -1512.79*tf.lnT9)

    rate_eval.n_Al41__Al42 = rate

@numba.njit()
def n_F14__He4_N11(rate_eval, tf):
    # F14 + n --> He4 + N11
    rate = 0.0

    # rpsmr
    rate += np.exp(  18.2109 + 0.000827571*tf.T9i + -0.609374*tf.T913i + 0.404936*tf.T913
                  + 0.0365943*tf.T9 + -0.0027444*tf.T953 + -0.425329*tf.lnT9)

    rate_eval.n_F14__He4_N11 = rate

@numba.njit()
def n_Ca33__p_K33(rate_eval, tf):
    # Ca33 + n --> p + K33
    rate = 0.0

    # ths8r
    rate += np.exp(  19.4834 + 0.750089*tf.T913
                  + -0.038398*tf.T9 + 0.00301504*tf.T953)

    rate_eval.n_Ca33__p_K33 = rate

@numba.njit()
def S37__Cl37__weak__wc12(rate_eval, tf):
    # S37 --> Cl37
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.08025)

    rate_eval.S37__Cl37__weak__wc12 = rate

@numba.njit()
def He4_O28__n_Ne31(rate_eval, tf):
    # O28 + He4 --> n + Ne31
    rate = 0.0

    # rpsmr
    rate += np.exp(  55.1828 + -2.2214*tf.T9i + 35.0335*tf.T913i + -89.9489*tf.T913
                  + 4.11746*tf.T9 + -0.24834*tf.T953 + 48.3159*tf.lnT9)

    rate_eval.He4_O28__n_Ne31 = rate

@numba.njit()
def He4_O26__n_Ne29(rate_eval, tf):
    # O26 + He4 --> n + Ne29
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.6902 + -2.14501*tf.T9i + 34.5397*tf.T913i + -93.7084*tf.T913
                  + 4.59067*tf.T9 + -0.281231*tf.T953 + 49.007*tf.lnT9)

    rate_eval.He4_O26__n_Ne29 = rate

@numba.njit()
def p_O26__He4_N23(rate_eval, tf):
    # O26 + p --> He4 + N23
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.194 + -2.14995*tf.T9i + 76.6636*tf.T913i + -134.681*tf.T913
                  + 7.93313*tf.T9 + -0.494523*tf.T953 + 66.6488*tf.lnT9)

    rate_eval.p_O26__He4_N23 = rate

@numba.njit()
def He4_Ti44__p_V47(rate_eval, tf):
    # Ti44 + He4 --> p + V47
    rate = 0.0

    # chw0r
    rate += np.exp(  -76.5154 + -10.7931*tf.T9i + 70.2835*tf.T913
                  + -7.99061*tf.T9 + 0.486213*tf.T953 + -1.5*tf.lnT9)

    rate_eval.He4_Ti44__p_V47 = rate

@numba.njit()
def Ne34__Na34__weak__mo03(rate_eval, tf):
    # Ne34 --> Na34
    rate = 0.0

    # mo03w
    rate += np.exp(  2.78939)

    rate_eval.Ne34__Na34__weak__mo03 = rate

@numba.njit()
def p_O26__n_F26(rate_eval, tf):
    # O26 + p --> n + F26
    rate = 0.0

    # rpsmr
    rate += np.exp(  67.9408 + -2.14615*tf.T9i + 76.6335*tf.T913i + -136.515*tf.T913
                  + 8.04131*tf.T9 + -0.507801*tf.T953 + 66.9549*tf.lnT9)

    rate_eval.p_O26__n_F26 = rate

@numba.njit()
def He4_O24__n_Ne27(rate_eval, tf):
    # O24 + He4 --> n + Ne27
    rate = 0.0

    # rpsmr
    rate += np.exp(  57.8778 + -2.11575*tf.T9i + 36.9995*tf.T913i + -96.0134*tf.T913
                  + 4.13241*tf.T9 + -0.192316*tf.T953 + 50.8296*tf.lnT9)

    rate_eval.He4_O24__n_Ne27 = rate

@numba.njit()
def p_O24__n_F24(rate_eval, tf):
    # O24 + p --> n + F24
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.6527 + -2.04262*tf.T9i + 69.6111*tf.T913i + -119.941*tf.T913
                  + 6.4986*tf.T9 + -0.360902*tf.T953 + 60.2693*tf.lnT9)

    rate_eval.p_O24__n_F24 = rate

@numba.njit()
def Na31__n_Mg30__weak__wc17(rate_eval, tf):
    # Na31 --> n + Mg30
    rate = 0.0

    # wc17w
    rate += np.exp(  2.71378)

    rate_eval.Na31__n_Mg30__weak__wc17 = rate

@numba.njit()
def He4_F30__n_Na33(rate_eval, tf):
    # F30 + He4 --> n + Na33
    rate = 0.0

    # rpsmr
    rate += np.exp(  67.5685 + -2.68412*tf.T9i + 56.7353*tf.T913i + -128.202*tf.T913
                  + 5.8305*tf.T9 + -0.28544*tf.T953 + 67.2062*tf.lnT9)

    rate_eval.He4_F30__n_Na33 = rate

@numba.njit()
def He4_O22__n_Ne25(rate_eval, tf):
    # O22 + He4 --> n + Ne25
    rate = 0.0

    # rpsmr
    rate += np.exp(  55.4222 + -1.98369*tf.T9i + 31.4729*tf.T913i + -87.8568*tf.T913
                  + 3.6968*tf.T9 + -0.168553*tf.T953 + 46.7593*tf.lnT9)

    rate_eval.He4_O22__n_Ne25 = rate

@numba.njit()
def He4_Ar52__n_Ca55(rate_eval, tf):
    # Ar52 + He4 --> n + Ca55
    rate = 0.0

    # rath 
    rate += np.exp(  -411.06 + 2.08161*tf.T9i + -573.658*tf.T913i + 1029.63*tf.T913
                  + -68.2177*tf.T9 + 4.16252*tf.T953 + -450.26*tf.lnT9)

    rate_eval.He4_Ar52__n_Ca55 = rate

@numba.njit()
def p_Ti57__n_V57(rate_eval, tf):
    # Ti57 + p --> n + V57
    rate = 0.0

    # rath 
    rate += np.exp(  127.299 + -6.0898*tf.T9i + 227.117*tf.T913i + -364.2*tf.T913
                  + 19.8625*tf.T9 + -1.10919*tf.T953 + 183.649*tf.lnT9)

    rate_eval.p_Ti57__n_V57 = rate

@numba.njit()
def p_O20__n_F20(rate_eval, tf):
    # O20 + p --> n + F20
    rate = 0.0

    # rpsmr
    rate += np.exp(  57.8051 + -1.8634*tf.T9i + 62.3972*tf.T913i + -112.053*tf.T913
                  + 6.18399*tf.T9 + -0.345778*tf.T953 + 55.5269*tf.lnT9)

    rate_eval.p_O20__n_F20 = rate

@numba.njit()
def He4_O19__n_Ne22(rate_eval, tf):
    # O19 + He4 --> n + Ne22
    rate = 0.0

    #  wagn
    rate += np.exp(  41.2444 + -40.19*tf.T913i
                  + -0.666667*tf.lnT9)

    rate_eval.He4_O19__n_Ne22 = rate

@numba.njit()
def He4_Cl32__p_Ar35(rate_eval, tf):
    # Cl32 + He4 --> p + Ar35
    rate = 0.0

    # ths8r
    rate += np.exp(  52.3543 + -68.0682*tf.T913i + 0.0983684*tf.T913
                  + -0.783598*tf.T9 + 0.0556457*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl32__p_Ar35 = rate

@numba.njit()
def p_Cr62__n_Mn62(rate_eval, tf):
    # Cr62 + p --> n + Mn62
    rate = 0.0

    # rath 
    rate += np.exp(  140.671 + -6.71489*tf.T9i + 252.874*tf.T913i + -405.637*tf.T913
                  + 22.1295*tf.T9 + -1.22846*tf.T953 + 203.865*tf.lnT9)

    rate_eval.p_Cr62__n_Mn62 = rate

@numba.njit()
def p_O18__He4_N15(rate_eval, tf):
    # O18 + p --> He4 + N15
    rate = 0.0

    # il10r
    rate += np.exp(  -27.9044 + -0.245884*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  26.9671 + -16.6979*tf.T913i
                  + -3.0*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  8.94352 + -5.32335*tf.T9i + 11.6568*tf.T913
                  + -2.16303*tf.T9 + 0.209965*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  10.2725 + -1.663*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_O18__He4_N15 = rate

@numba.njit()
def He4_O17__n_Ne20(rate_eval, tf):
    # O17 + He4 --> n + Ne20
    rate = 0.0

    # nacrr
    rate += np.exp(  1.80342 + -13.8*tf.T9i + 12.6501*tf.T913
                  + -1.10938*tf.T9 + 0.0696232*tf.T953 + -1.5*tf.lnT9)
    # nacrr
    rate += np.exp(  7.45588 + -8.55*tf.T9i
                  + -1.5*tf.lnT9)
    # nacrn
    rate += np.exp(  40.621 + -39.918*tf.T913i
                  + 0.227017*tf.T9 + -0.900234*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_O17__n_Ne20 = rate

@numba.njit()
def p_S49__Cl50(rate_eval, tf):
    # S49 + p --> Cl50
    rate = 0.0

    # rath 
    rate += np.exp(  98.3208 + -4.65565*tf.T9i + 175.704*tf.T913i + -288.434*tf.T913
                  + 15.6933*tf.T9 + -0.857588*tf.T953 + 144.176*tf.lnT9)

    rate_eval.p_S49__Cl50 = rate

@numba.njit()
def p_O17__He4_N14(rate_eval, tf):
    # O17 + p --> He4 + N14
    rate = 0.0

    # il10r
    rate += np.exp(  -7.20763 + -0.753395*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  19.579 + -16.9078*tf.T913i
                  + -2.0*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  10.174 + -4.95865*tf.T9i + 5.10182*tf.T913
                  + 0.379373*tf.T9 + -0.0672515*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  5.5336 + -2.11477*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_O17__He4_N14 = rate

@numba.njit()
def O16_O16__He4_Si28(rate_eval, tf):
    # O16 + O16 --> He4 + Si28
    rate = 0.0

    # cf88r
    rate += np.exp(  97.2435 + -0.268514*tf.T9i + -119.324*tf.T913i + -32.2497*tf.T913
                  + 1.46214*tf.T9 + -0.200893*tf.T953 + 13.2148*tf.lnT9)

    rate_eval.O16_O16__He4_Si28 = rate

@numba.njit()
def O16_O16__p_P31(rate_eval, tf):
    # O16 + O16 --> p + P31
    rate = 0.0

    # cf88r
    rate += np.exp(  85.2628 + 0.223453*tf.T9i + -145.844*tf.T913i + 8.72612*tf.T913
                  + -0.554035*tf.T9 + -0.137562*tf.T953 + -6.88807*tf.lnT9)

    rate_eval.O16_O16__p_P31 = rate

@numba.njit()
def He4_Ne26__n_Mg29(rate_eval, tf):
    # Ne26 + He4 --> n + Mg29
    rate = 0.0

    # rath 
    rate += np.exp(  67.0078 + -2.63003*tf.T9i + 51.5556*tf.T913i + -124.744*tf.T913
                  + 5.69194*tf.T9 + -0.284117*tf.T953 + 65.5918*tf.lnT9)

    rate_eval.He4_Ne26__n_Mg29 = rate

@numba.njit()
def Cl32__S32__weak__wc12(rate_eval, tf):
    # Cl32 --> S32
    rate = 0.0

    # wc12w
    rate += np.exp(  0.843349)

    rate_eval.Cl32__S32__weak__wc12 = rate

@numba.njit()
def O16_O16__n_S31(rate_eval, tf):
    # O16 + O16 --> n + S31
    rate = 0.0

    # cf88r
    rate += np.exp(  77.5491 + -0.373641*tf.T9i + -120.83*tf.T913i + -7.72334*tf.T913
                  + -2.27939*tf.T9 + 0.167655*tf.T953 + 7.62001*tf.lnT9)

    rate_eval.O16_O16__n_S31 = rate

@numba.njit()
def He4_Al28__n_P31(rate_eval, tf):
    # Al28 + He4 --> n + P31
    rate = 0.0

    # rath 
    rate += np.exp(  -4.29707 + -2.4128*tf.T9i + -27.1835*tf.T913i + 29.3511*tf.T913
                  + -4.90371*tf.T9 + 0.376759*tf.T953 + 0.485028*tf.lnT9)

    rate_eval.He4_Al28__n_P31 = rate

@numba.njit()
def C12_O16__He4_Mg24(rate_eval, tf):
    # O16 + C12 --> He4 + Mg24
    rate = 0.0

    # cf88r
    rate += np.exp(  48.5341 + 0.37204*tf.T9i + -133.413*tf.T913i + 50.1572*tf.T913
                  + -3.15987*tf.T9 + 0.0178251*tf.T953 + -23.7027*tf.lnT9)

    rate_eval.C12_O16__He4_Mg24 = rate

@numba.njit()
def C12_O16__p_Al27(rate_eval, tf):
    # O16 + C12 --> p + Al27
    rate = 0.0

    # cf88r
    rate += np.exp(  68.5253 + 0.205134*tf.T9i + -119.242*tf.T913i + 13.3667*tf.T913
                  + 0.295425*tf.T9 + -0.267288*tf.T953 + -9.91729*tf.lnT9)

    rate_eval.C12_O16__p_Al27 = rate

@numba.njit()
def p_K48__n_Ca48(rate_eval, tf):
    # K48 + p --> n + Ca48
    rate = 0.0

    # rath 
    rate += np.exp(  113.715 + -5.11788*tf.T9i + 189.487*tf.T913i + -309.913*tf.T913
                  + 17.1184*tf.T9 + -0.963187*tf.T953 + 155.356*tf.lnT9)

    rate_eval.p_K48__n_Ca48 = rate

@numba.njit()
def p_Ne28__He4_F25(rate_eval, tf):
    # Ne28 + p --> He4 + F25
    rate = 0.0

    # rath 
    rate += np.exp(  64.1345 + -2.58799*tf.T9i + 91.3342*tf.T913i + -155.158*tf.T913
                  + 8.40741*tf.T9 + -0.456403*tf.T953 + 77.8663*tf.lnT9)

    rate_eval.p_Ne28__He4_F25 = rate

@numba.njit()
def p_Al26__Si27(rate_eval, tf):
    # Al26 + p --> Si27
    rate = 0.0

    # il01n
    rate += np.exp(  17.0284 + -1.51551*tf.T9i + -9.85794*tf.T913
                  + 0.100748*tf.T9 + 5.94209*tf.lnT9)
    # il01n
    rate += np.exp(  -12.9989 + -0.750435*tf.T9i
                  + 0.803967*tf.lnT9)
    # il01n
    rate += np.exp(  21.1233 + -23.1959*tf.T913i
                  + -0.666667*tf.lnT9)

    rate_eval.p_Al26__Si27 = rate

@numba.njit()
def p_Ca36__Sc37(rate_eval, tf):
    # Ca36 + p --> Sc37
    rate = 0.0

    # ths8r
    rate += np.exp(  -14.5883 + -23.1091*tf.T9i + 16.7352*tf.T913
                  + -1.67848*tf.T9 + 0.120144*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ca36__Sc37 = rate

@numba.njit()
def p_Na28__He4_Ne25(rate_eval, tf):
    # Na28 + p --> He4 + Ne25
    rate = 0.0

    # rath 
    rate += np.exp(  64.9719 + -2.73456*tf.T9i + 95.0298*tf.T913i + -159.333*tf.T913
                  + 8.35573*tf.T9 + -0.433156*tf.T953 + 80.8158*tf.lnT9)

    rate_eval.p_Na28__He4_Ne25 = rate

@numba.njit()
def n_K33__He4_Cl30(rate_eval, tf):
    # K33 + n --> He4 + Cl30
    rate = 0.0

    # ths8r
    rate += np.exp(  14.902 + 0.051684*tf.T913
                  + 0.0959087*tf.T9 + 0.00539958*tf.T953)

    rate_eval.n_K33__He4_Cl30 = rate

@numba.njit()
def He4_Cr45__Fe49(rate_eval, tf):
    # Cr45 + He4 --> Fe49
    rate = 0.0

    # ths8r
    rate += np.exp(  50.2436 + -86.5991*tf.T913i + 2.84539*tf.T913
                  + -1.73453*tf.T9 + 0.106073*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr45__Fe49 = rate

@numba.njit()
def p_Cr70__Mn71(rate_eval, tf):
    # Cr70 + p --> Mn71
    rate = 0.0

    # rath 
    rate += np.exp(  142.778 + -7.11267*tf.T9i + 272.021*tf.T913i + -439.466*tf.T913
                  + 24.6837*tf.T9 + -1.41564*tf.T953 + 218.782*tf.lnT9)

    rate_eval.p_Cr70__Mn71 = rate

@numba.njit()
def n_O14__He4_C11(rate_eval, tf):
    # O14 + n --> He4 + C11
    rate = 0.0

    # rpsmr
    rate += np.exp(  17.5737 + 0.00781138*tf.T9i + -1.31632*tf.T913i + 2.06431*tf.T913
                  + 0.0585225*tf.T9 + -0.00948426*tf.T953 + -1.11933*tf.lnT9)

    rate_eval.n_O14__He4_C11 = rate

@numba.njit()
def He4_O13__p_F16(rate_eval, tf):
    # O13 + He4 --> p + F16
    rate = 0.0

    # rpsmr
    rate += np.exp(  41.2681 + -1.27751*tf.T9i + 1.81381*tf.T913i + -42.9086*tf.T913
                  + 1.30615*tf.T9 + -0.0418392*tf.T953 + 24.4506*tf.lnT9)

    rate_eval.He4_O13__p_F16 = rate

@numba.njit()
def He4_Sc57__V61(rate_eval, tf):
    # Sc57 + He4 --> V61
    rate = 0.0

    # rath 
    rate += np.exp(  -974.059 + 20.2773*tf.T9i + -2018.02*tf.T913i + 3106.15*tf.T913
                  + -176.075*tf.T9 + 9.72327*tf.T953 + -1507.02*tf.lnT9)

    rate_eval.He4_Sc57__V61 = rate

@numba.njit()
def n_Ca33__He4_Ar30(rate_eval, tf):
    # Ca33 + n --> He4 + Ar30
    rate = 0.0

    # ths8r
    rate += np.exp(  14.2381 + -0.529423*tf.T913
                  + 0.322002*tf.T9 + -0.0241468*tf.T953)

    rate_eval.n_Ca33__He4_Ar30 = rate

@numba.njit()
def n_O13__He4_C10(rate_eval, tf):
    # O13 + n --> He4 + C10
    rate = 0.0

    # rpsmr
    rate += np.exp(  18.6727 + -0.00165492*tf.T9i + -0.322485*tf.T913i + -0.644258*tf.T913
                  + 0.164962*tf.T9 + -0.0116628*tf.T953 + -0.094256*tf.lnT9)

    rate_eval.n_O13__He4_C10 = rate

@numba.njit()
def n_O13__p_N13(rate_eval, tf):
    # O13 + n --> p + N13
    rate = 0.0

    # rpsmr
    rate += np.exp(  20.1706 + 0.0531441*tf.T9i + -2.68865*tf.T913i + 2.79084*tf.T913
                  + -0.0461798*tf.T9 + 0.00157148*tf.T953 + -1.79162*tf.lnT9)

    rate_eval.n_O13__p_N13 = rate

@numba.njit()
def n_O12__p_N12(rate_eval, tf):
    # O12 + n --> p + N12
    rate = 0.0

    # rpsmr
    rate += np.exp(  20.4261 + 0.0519523*tf.T9i + -2.60944*tf.T913i + 2.5239*tf.T913
                  + -0.0302444*tf.T9 + 0.00117817*tf.T953 + -1.72422*tf.lnT9)

    rate_eval.n_O12__p_N12 = rate

@numba.njit()
def p_N15__He4_C12(rate_eval, tf):
    # N15 + p --> He4 + C12
    rate = 0.0

    # nacrn
    rate += np.exp(  27.4764 + -15.253*tf.T913i + 1.59318*tf.T913
                  + 2.4479*tf.T9 + -2.19708*tf.T953 + -0.666667*tf.lnT9)
    # nacrr
    rate += np.exp(  -6.57522 + -1.1638*tf.T9i + 22.7105*tf.T913
                  + -2.90707*tf.T9 + 0.205754*tf.T953 + -1.5*tf.lnT9)
    # nacrr
    rate += np.exp(  20.8972 + -7.406*tf.T9i
                  + -1.5*tf.lnT9)
    # nacrr
    rate += np.exp(  -4.87347 + -2.02117*tf.T9i + 30.8497*tf.T913
                  + -8.50433*tf.T9 + -1.54426*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_N15__He4_C12 = rate

@numba.njit()
def p_N15__n_O15(rate_eval, tf):
    # N15 + p --> n + O15
    rate = 0.0

    # nacrn
    rate += np.exp(  18.3942 + -41.0335*tf.T9i + 0.331392*tf.T913
                  + 0.0171473*tf.T9)

    rate_eval.p_N15__n_O15 = rate

@numba.njit()
def n_Sc37__p_Ca37(rate_eval, tf):
    # Sc37 + n --> p + Ca37
    rate = 0.0

    # ths8r
    rate += np.exp(  20.0061 + 0.191687*tf.T913
                  + 0.0745727*tf.T9 + -0.00666777*tf.T953)

    rate_eval.n_Sc37__p_Ca37 = rate

@numba.njit()
def n_Mg19__He4_Ne16(rate_eval, tf):
    # Mg19 + n --> He4 + Ne16
    rate = 0.0

    # ths8r
    rate += np.exp(  13.6808 + 1.3782*tf.T913
                  + -0.105439*tf.T9 + 0.000490626*tf.T953)

    rate_eval.n_Mg19__He4_Ne16 = rate

@numba.njit()
def p_F28__He4_O25(rate_eval, tf):
    # F28 + p --> He4 + O25
    rate = 0.0

    # rpsmr
    rate += np.exp(  56.4692 + -2.4184*tf.T9i + 84.6892*tf.T913i + -139.956*tf.T913
                  + 7.32996*tf.T9 + -0.390796*tf.T953 + 71.3393*tf.lnT9)

    rate_eval.p_F28__He4_O25 = rate

@numba.njit()
def He4_Ar41__n_Ca44(rate_eval, tf):
    # Ar41 + He4 --> n + Ca44
    rate = 0.0

    # rath 
    rate += np.exp(  -366.5 + 2.03318*tf.T9i + -528.173*tf.T913i + 932.091*tf.T913
                  + -61.5117*tf.T9 + 3.74155*tf.T953 + -408.491*tf.lnT9)

    rate_eval.He4_Ar41__n_Ca44 = rate

@numba.njit()
def p_F29__Ne30(rate_eval, tf):
    # F29 + p --> Ne30
    rate = 0.0

    # rpsmr
    rate += np.exp(  54.1011 + -2.41151*tf.T9i + 83.1475*tf.T913i + -141.312*tf.T913
                  + 7.71707*tf.T9 + -0.42936*tf.T953 + 70.7715*tf.lnT9)

    rate_eval.p_F29__Ne30 = rate

@numba.njit()
def n_N14__p_C14(rate_eval, tf):
    # N14 + n --> p + C14
    rate = 0.0

    # cf88 
    rate += np.exp(  4.13728 + 12.3428*tf.T913
                  + -2.70025*tf.T9 + 0.236625*tf.T953 + 1.0*tf.lnT9)
    # cf88n
    rate += np.exp(  13.6622 + -4.33989*tf.T913
                  + 11.4311*tf.T9 + -11.7764*tf.T953)

    rate_eval.n_N14__p_C14 = rate

@numba.njit()
def He4_N13__p_O16(rate_eval, tf):
    # N13 + He4 --> p + O16
    rate = 0.0

    # cf88n
    rate += np.exp(  40.4644 + -35.829*tf.T913i + -0.530275*tf.T913
                  + -0.982462*tf.T9 + 0.0808059*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_N13__p_O16 = rate

@numba.njit()
def He4_C15__n_O18(rate_eval, tf):
    # C15 + He4 --> n + O18
    rate = 0.0

    #  wagn
    rate += np.exp(  37.7735 + -32.68*tf.T913i + 3.27973e-09*tf.T913
                  + -3.3161e-10*tf.T9 + 2.86029e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_C15__n_O18 = rate

@numba.njit()
def p_C15__n_N15(rate_eval, tf):
    # C15 + p --> n + N15
    rate = 0.0

    #  wagn
    rate += np.exp(  27.9675 + -4.16059e-12*tf.T9i + -13.76*tf.T913i + -2.02952e-09*tf.T913
                  + 2.22438e-10*tf.T9 + -2.01977e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_C15__n_N15 = rate

@numba.njit()
def He4_Cl50__n_K53(rate_eval, tf):
    # Cl50 + He4 --> n + K53
    rate = 0.0

    # rath 
    rate += np.exp(  -387.378 + 2.04139*tf.T9i + -548.332*tf.T913i + 979.321*tf.T913
                  + -64.7709*tf.T9 + 3.95022*tf.T953 + -429.166*tf.lnT9)

    rate_eval.He4_Cl50__n_K53 = rate

@numba.njit()
def He4_Si31__n_S34(rate_eval, tf):
    # Si31 + He4 --> n + S34
    rate = 0.0

    # rath 
    rate += np.exp(  -5.10649 + -2.7438*tf.T9i + -22.4045*tf.T913i + 23.4647*tf.T913
                  + -4.73922*tf.T9 + 0.371237*tf.T953 + 4.62837*tf.lnT9)

    rate_eval.He4_Si31__n_S34 = rate

@numba.njit()
def n_V39__p_Ti39(rate_eval, tf):
    # V39 + n --> p + Ti39
    rate = 0.0

    # ths8r
    rate += np.exp(  21.6121 + -0.868337*tf.T913
                  + 0.232608*tf.T9 + -0.0188134*tf.T953)

    rate_eval.n_V39__p_Ti39 = rate

@numba.njit()
def He4_Cl45__n_K48(rate_eval, tf):
    # Cl45 + He4 --> n + K48
    rate = 0.0

    # rath 
    rate += np.exp(  -364.38 + 1.92234*tf.T9i + -520.539*tf.T913i + 924.544*tf.T913
                  + -61.1912*tf.T9 + 3.73012*tf.T953 + -404.731*tf.lnT9)

    rate_eval.He4_Cl45__n_K48 = rate

@numba.njit()
def Al36__Si36__weak__wc17(rate_eval, tf):
    # Al36 --> Si36
    rate = 0.0

    # wc17w
    rate += np.exp(  1.90217)

    rate_eval.Al36__Si36__weak__wc17 = rate

@numba.njit()
def He4_C13__n_O16(rate_eval, tf):
    # C13 + He4 --> n + O16
    rate = 0.0

    # gl12 
    rate += np.exp(  62.5775 + -0.0277331*tf.T9i + -32.3917*tf.T913i + -48.934*tf.T913
                  + 44.1843*tf.T9 + -20.8743*tf.T953 + 2.02494*tf.lnT9)
    # gl12 
    rate += np.exp(  79.3008 + -0.30489*tf.T9i + 7.43132*tf.T913i + -84.8689*tf.T913
                  + 3.65083*tf.T9 + -0.148015*tf.T953 + 37.6008*tf.lnT9)

    rate_eval.He4_C13__n_O16 = rate

@numba.njit()
def Na38__Mg38__weak__mo03(rate_eval, tf):
    # Na38 --> Mg38
    rate = 0.0

    # mo03w
    rate += np.exp(  -108.881)

    rate_eval.Na38__Mg38__weak__mo03 = rate

@numba.njit()
def d_C13__n_N14(rate_eval, tf):
    # C13 + d --> n + N14
    rate = 0.0

    # bb92n
    rate += np.exp(  27.1993 + -0.00261944*tf.T9i + -16.8935*tf.T913i + 4.06445*tf.T913
                  + -1.1715*tf.T9 + 0.118556*tf.T953 + -1.13937*tf.lnT9)

    rate_eval.d_C13__n_N14 = rate

@numba.njit()
def p_C13__n_N13(rate_eval, tf):
    # C13 + p --> n + N13
    rate = 0.0

    # nacrn
    rate += np.exp(  17.7625 + -34.8483*tf.T9i + 1.26126*tf.T913
                  + -0.204952*tf.T9 + 0.0310523*tf.T953)

    rate_eval.p_C13__n_N13 = rate

@numba.njit()
def Sc53__Ti53__weak__wc12(rate_eval, tf):
    # Sc53 --> Ti53
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.24198)

    rate_eval.Sc53__Ti53__weak__wc12 = rate

@numba.njit()
def p_K44__n_Ca44(rate_eval, tf):
    # K44 + p --> n + Ca44
    rate = 0.0

    # rath 
    rate += np.exp(  111.388 + -4.93613*tf.T9i + 182.35*tf.T913i + -300.324*tf.T913
                  + 16.5628*tf.T9 + -0.927966*tf.T953 + 150.358*tf.lnT9)

    rate_eval.p_K44__n_Ca44 = rate

@numba.njit()
def n_Mn50__Mn51(rate_eval, tf):
    # Mn50 + n --> Mn51
    rate = 0.0

    # ths8r
    rate += np.exp(  15.4434 + -0.538879*tf.T913
                  + 0.284528*tf.T9 + -0.0459849*tf.T953)

    rate_eval.n_Mn50__Mn51 = rate

@numba.njit()
def n_C11__p_B11(rate_eval, tf):
    # C11 + n --> p + B11
    rate = 0.0

    # cf88n
    rate += np.exp(  18.8963)

    rate_eval.n_C11__p_B11 = rate

@numba.njit()
def He4_B13__n_N16(rate_eval, tf):
    # B13 + He4 --> n + N16
    rate = 0.0

    # wiesr
    rate += np.exp(  217.518 + -13.8689*tf.T9i + 280.275*tf.T913i + -519.678*tf.T913
                  + 35.7143*tf.T9 + -2.28948*tf.T953 + 230.853*tf.lnT9)
    # wiesr
    rate += np.exp(  -20.2453 + -2.5531*tf.T9i + 2.32491e-09*tf.T913i + -6.08007e-09*tf.T913
                  + 5.35337e-10*tf.T9 + -4.1727e-11*tf.T953 + -1.5*tf.lnT9)

    rate_eval.He4_B13__n_N16 = rate

@numba.njit()
def n_K35__He4_Cl32(rate_eval, tf):
    # K35 + n --> He4 + Cl32
    rate = 0.0

    # ths8r
    rate += np.exp(  16.3542 + 0.0704425*tf.T913
                  + 0.107442*tf.T9 + -0.00114597*tf.T953)

    rate_eval.n_K35__He4_Cl32 = rate

@numba.njit()
def p_Ar53__He4_Cl50(rate_eval, tf):
    # Ar53 + p --> He4 + Cl50
    rate = 0.0

    # rath 
    rate += np.exp(  54.6674 + -5.01256*tf.T9i + 175.31*tf.T913i + -249.528*tf.T913
                  + 11.7471*tf.T9 + -0.538997*tf.T953 + 137.491*tf.lnT9)

    rate_eval.p_Ar53__He4_Cl50 = rate

@numba.njit()
def He4_B12__n_N15(rate_eval, tf):
    # B12 + He4 --> n + N15
    rate = 0.0

    #  wagn
    rate += np.exp(  35.6506 + -28.45*tf.T913i + 2.82044e-10*tf.T913
                  + -2.59013e-11*tf.T9 + 2.07893e-12*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_B12__n_N15 = rate

@numba.njit()
def p_B12__He4_Be9(rate_eval, tf):
    # B12 + p --> He4 + Be9
    rate = 0.0

    #  wagn
    rate += np.exp(  26.0266 + -2.55368e-12*tf.T9i + -12.12*tf.T913i + -1.22842e-09*tf.T913
                  + 1.34011e-10*tf.T9 + -1.21412e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_B12__He4_Be9 = rate

@numba.njit()
def p_Ti56__He4_Sc53(rate_eval, tf):
    # Ti56 + p --> He4 + Sc53
    rate = 0.0

    # rath 
    rate += np.exp(  102.386 + -6.03552*tf.T9i + 223.475*tf.T913i + -344.695*tf.T913
                  + 17.7976*tf.T9 + -0.902084*tf.T953 + 179.009*tf.lnT9)

    rate_eval.p_Ti56__He4_Sc53 = rate

@numba.njit()
def He4_B11__p_C14(rate_eval, tf):
    # B11 + He4 --> p + C14
    rate = 0.0

    # bb92r
    rate += np.exp(  5.48852 + -5.147*tf.T9i + -5.81643e-09*tf.T913i + 1.24374e-08*tf.T913
                  + -9.55069e-10*tf.T9 + 6.81706e-11*tf.T953 + -1.5*tf.lnT9)
    # bb92r
    rate += np.exp(  6.1942 + -5.157*tf.T9i + -2.8504e-09*tf.T913i + 5.85721e-09*tf.T913
                  + -4.34052e-10*tf.T9 + 3.01373e-11*tf.T953 + -1.5*tf.lnT9)
    # bb92n
    rate += np.exp(  178.316 + -0.19519*tf.T9i + 4.28912*tf.T913i + -214.72*tf.T913
                  + 57.4073*tf.T9 + -25.5329*tf.T953 + 53.0473*tf.lnT9)
    # bb92r
    rate += np.exp(  15.4137 + -11.26*tf.T9i + -1.87598e-08*tf.T913i + 3.26423e-08*tf.T913
                  + -2.18782e-09*tf.T9 + 1.43323e-10*tf.T953 + 0.6*tf.lnT9)
    # bb92r
    rate += np.exp(  -5.21398 + -2.868*tf.T9i + 2.62625e-09*tf.T913i + -6.58921e-09*tf.T913
                  + 5.62244e-10*tf.T9 + -4.28925e-11*tf.T953 + -1.5*tf.lnT9)

    rate_eval.He4_B11__p_C14 = rate

@numba.njit()
def S44__n_Cl43__weak__wc12(rate_eval, tf):
    # S44 --> n + Cl43
    rate = 0.0

    # wc12w
    rate += np.exp(  0.221274)

    rate_eval.S44__n_Cl43__weak__wc12 = rate

@numba.njit()
def p_Ar41__K42(rate_eval, tf):
    # Ar41 + p --> K42
    rate = 0.0

    # rath 
    rate += np.exp(  116.312 + -4.62829*tf.T9i + 173.571*tf.T913i + -303.052*tf.T913
                  + 17.7025*tf.T9 + -1.0355*tf.T953 + 146.474*tf.lnT9)

    rate_eval.p_Ar41__K42 = rate

@numba.njit()
def He4_Fe46__p_Co49(rate_eval, tf):
    # Fe46 + He4 --> p + Co49
    rate = 0.0

    # ths8r
    rate += np.exp(  62.2446 + -91.401*tf.T913i + -1.38716*tf.T913
                  + -0.407203*tf.T9 + 0.00261659*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe46__p_Co49 = rate

@numba.njit()
def He4_B10__p_C13(rate_eval, tf):
    # B10 + He4 --> p + C13
    rate = 0.0

    #  wagn
    rate += np.exp(  34.498 + -27.99*tf.T913i
                  + -0.666667*tf.lnT9)

    rate_eval.He4_B10__p_C13 = rate

@numba.njit()
def He4_B8__p_C11(rate_eval, tf):
    # B8 + He4 --> p + C11
    rate = 0.0

    # wiesr
    rate += np.exp(  207.835 + -9.09757*tf.T9i + 381.949*tf.T913i + -608.493*tf.T913
                  + 34.7229*tf.T9 + -2.02465*tf.T953 + 297.922*tf.lnT9)
    # wiesr
    rate += np.exp(  13.8524 + -1.0296*tf.T9i + 3.19293*tf.T913i + -37.5025*tf.T913
                  + 4.4781*tf.T9 + -0.401587*tf.T953 + 8.35133*tf.lnT9)

    rate_eval.He4_B8__p_C11 = rate

@numba.njit()
def p_V63__He4_Ti60(rate_eval, tf):
    # V63 + p --> He4 + Ti60
    rate = 0.0

    # rath 
    rate += np.exp(  162.576 + -6.8592*tf.T9i + 278.501*tf.T913i + -471.876*tf.T913
                  + 27.2898*tf.T9 + -1.48194*tf.T953 + 229.477*tf.lnT9)

    rate_eval.p_V63__He4_Ti60 = rate

@numba.njit()
def He4_Mn70__Co74(rate_eval, tf):
    # Mn70 + He4 --> Co74
    rate = 0.0

    # rath 
    rate += np.exp(  -1232.93 + 25.6147*tf.T9i + -2537.43*tf.T913i + 3917.03*tf.T913
                  + -221.178*tf.T9 + 12.1828*tf.T953 + -1902.82*tf.lnT9)

    rate_eval.He4_Mn70__Co74 = rate

@numba.njit()
def He4_Li8__n_B11(rate_eval, tf):
    # Li8 + He4 --> n + B11
    rate = 0.0

    # ld11 
    rate += np.exp(  35.63 + -2.51*tf.T9i + -32.33*tf.T913i + 13.17*tf.T913
                  + -0.01816*tf.T9 + -0.02032*tf.T953 + -12.38*tf.lnT9)

    rate_eval.He4_Li8__n_B11 = rate

@numba.njit()
def Si24__p_Mg23__weak__wc12(rate_eval, tf):
    # Si24 --> p + Mg23
    rate = 0.0

    # wc12w
    rate += np.exp(  0.793975)

    rate_eval.Si24__p_Mg23__weak__wc12 = rate

@numba.njit()
def n_Ti42__He4_Ca39(rate_eval, tf):
    # Ti42 + n --> He4 + Ca39
    rate = 0.0

    # ths8r
    rate += np.exp(  18.5163 + -1.305*tf.T913
                  + 0.292886*tf.T9 + -0.00227446*tf.T953)

    rate_eval.n_Ti42__He4_Ca39 = rate

@numba.njit()
def n_Fe48__He4_Cr45(rate_eval, tf):
    # Fe48 + n --> He4 + Cr45
    rate = 0.0

    # ths8r
    rate += np.exp(  11.7818 + 2.24493*tf.T913
                  + -0.719479*tf.T9 + 0.144026*tf.T953)

    rate_eval.n_Fe48__He4_Cr45 = rate

@numba.njit()
def He4_V49__p_Cr52(rate_eval, tf):
    # V49 + He4 --> p + Cr52
    rate = 0.0

    # ths8r
    rate += np.exp(  57.428 + -84.3633*tf.T913i + 2.73419*tf.T913
                  + -2.05655*tf.T9 + 0.203834*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V49__p_Cr52 = rate

@numba.njit()
def n_Mn53__He4_V50(rate_eval, tf):
    # Mn53 + n --> He4 + V50
    rate = 0.0

    # ths8r
    rate += np.exp(  -122.895 + 115.52*tf.T913
                  + -16.7944*tf.T9 + 1.23427*tf.T953)

    rate_eval.n_Mn53__He4_V50 = rate

@numba.njit()
def d_Li7__p_Li8(rate_eval, tf):
    # Li7 + d --> p + Li8
    rate = 0.0

    # mafor
    rate += np.exp(  20.5381 + -6.998*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.d_Li7__p_Li8 = rate

@numba.njit()
def P45__n_n_n_S42__weak__mo03(rate_eval, tf):
    # P45 --> 3 n + S42
    rate = 0.0

    # mo03w
    rate += np.exp(  2.38266)

    rate_eval.P45__n_n_n_S42__weak__mo03 = rate

@numba.njit()
def Be11__B11__weak__wc12(rate_eval, tf):
    # Be11 --> B11
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.02267)

    rate_eval.Be11__B11__weak__wc12 = rate

@numba.njit()
def n_Mn65__Mn66(rate_eval, tf):
    # Mn65 + n --> Mn66
    rate = 0.0

    # rath 
    rate += np.exp(  27.785 + -0.0595381*tf.T9i + 7.3828*tf.T913i + -24.8039*tf.T913
                  + 2.07223*tf.T9 + -0.16587*tf.T953 + 8.24832*tf.lnT9)

    rate_eval.n_Mn65__Mn66 = rate

@numba.njit()
def n_Li6__He4_t(rate_eval, tf):
    # Li6 + n --> He4 + t
    rate = 0.0

    # cf88r
    rate += np.exp(  21.665 + -2.39128*tf.T9i
                  + -1.5*tf.lnT9)
    # cf88n
    rate += np.exp(  18.9496 + -0.001281*tf.T9i)

    rate_eval.n_Li6__He4_t = rate

@numba.njit()
def Na35__n_n_n_Mg32__weak__mo03(rate_eval, tf):
    # Na35 --> 3 n + Mg32
    rate = 0.0

    # mo03w
    rate += np.exp(  4.09157)

    rate_eval.Na35__n_n_n_Mg32__weak__mo03 = rate

@numba.njit()
def p_Li6__He4_He3(rate_eval, tf):
    # Li6 + p --> He4 + He3
    rate = 0.0

    # pt05n
    rate += np.exp(  24.3475 + -8.39481*tf.T913i + -0.165254*tf.T913
                  + -0.16936*tf.T9 + 0.0533676*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Li6__He4_He3 = rate

@numba.njit()
def t_He3__d_He4(rate_eval, tf):
    # He3 + t --> d + He4
    rate = 0.0

    # cf88n
    rate += np.exp(  22.4207 + -7.733*tf.T913i + -0.133473*tf.T913
                  + -0.294412*tf.T9 + 0.0310968*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.t_He3__d_He4 = rate

@numba.njit()
def d_He3__p_He4(rate_eval, tf):
    # He3 + d --> p + He4
    rate = 0.0

    # de04 
    rate += np.exp(  41.2969 + -7.182*tf.T913i + -17.1349*tf.T913
                  + 1.36908*tf.T9 + -0.0814423*tf.T953 + 3.35395*tf.lnT9)
    # de04 
    rate += np.exp(  24.6839 + -7.182*tf.T913i + 0.473288*tf.T913
                  + 1.46847*tf.T9 + -27.9603*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.d_He3__p_He4 = rate

@numba.njit()
def Cl51__Ar51__weak__mo03(rate_eval, tf):
    # Cl51 --> Ar51
    rate = 0.0

    # mo03w
    rate += np.exp(  -110.409)

    rate_eval.Cl51__Ar51__weak__mo03 = rate

@numba.njit()
def He4_V51__Mn55(rate_eval, tf):
    # V51 + He4 --> Mn55
    rate = 0.0

    # ths8r
    rate += np.exp(  61.6131 + -84.4467*tf.T913i + -1.29542*tf.T913
                  + -3.56909*tf.T9 + 0.513926*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V51__Mn55 = rate

@numba.njit()
def p_P34__S35(rate_eval, tf):
    # P34 + p --> S35
    rate = 0.0

    # rath 
    rate += np.exp(  78.6008 + -3.69428*tf.T9i + 131.034*tf.T913i + -217.078*tf.T913
                  + 11.6341*tf.T9 + -0.651346*tf.T953 + 109.768*tf.lnT9)

    rate_eval.p_P34__S35 = rate

@numba.njit()
def n_He3__p_t(rate_eval, tf):
    # He3 + n --> p + t
    rate = 0.0

    # de04 
    rate += np.exp(  19.2762 + 0.0438557*tf.T913
                  + -0.201527*tf.T9 + 0.0153433*tf.T953 + 1.0*tf.lnT9)
    # de04 
    rate += np.exp(  20.3787 + -0.332788*tf.T913
                  + -0.700485*tf.T9 + 0.0976521*tf.T953)

    rate_eval.n_He3__p_t = rate

@numba.njit()
def d_t__n_He4(rate_eval, tf):
    # t + d --> n + He4
    rate = 0.0

    # de04 
    rate += np.exp(  39.3457 + -4.5244*tf.T913i + -16.4028*tf.T913
                  + 1.73103*tf.T9 + -0.122966*tf.T953 + 2.31304*tf.lnT9)
    # de04 
    rate += np.exp(  25.1794 + -4.5244*tf.T913i + 0.350337*tf.T913
                  + 0.58747*tf.T9 + -8.84909*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.d_t__n_He4 = rate

@numba.njit()
def d_d__p_t(rate_eval, tf):
    # d + d --> p + t
    rate = 0.0

    # go17n
    rate += np.exp(  18.8052 + 4.36209e-05*tf.T9i + -4.32296*tf.T913i + 1.91572*tf.T913
                  + -0.081562*tf.T9 + -3.28804e-22*tf.T953 + -0.879518*tf.lnT9)

    rate_eval.d_d__p_t = rate

@numba.njit()
def He4_Fe76__Ni80(rate_eval, tf):
    # Fe76 + He4 --> Ni80
    rate = 0.0

    # rath 
    rate += np.exp(  -1054.05 + 26.7954*tf.T9i + -2583.2*tf.T913i + 3762.66*tf.T913
                  + -203.479*tf.T9 + 10.8349*tf.T953 + -1877.68*tf.lnT9)

    rate_eval.He4_Fe76__Ni80 = rate

@numba.njit()
def p_Fe76__Co77(rate_eval, tf):
    # Fe76 + p --> Co77
    rate = 0.0

    # rath 
    rate += np.exp(  156.36 + -7.79284*tf.T9i + 300.51*tf.T913i + -485.112*tf.T913
                  + 27.435*tf.T9 + -1.57957*tf.T953 + 241.009*tf.lnT9)

    rate_eval.p_Fe76__Co77 = rate

@numba.njit()
def n_Cr61__Cr62(rate_eval, tf):
    # Cr61 + n --> Cr62
    rate = 0.0

    # rath 
    rate += np.exp(  25.3451 + -0.0707066*tf.T9i + 7.85781*tf.T913i + -21.27*tf.T913
                  + 1.61205*tf.T9 + -0.141702*tf.T953 + 7.9626*tf.lnT9)

    rate_eval.n_Cr61__Cr62 = rate

@numba.njit()
def n_V50__He4_Sc47(rate_eval, tf):
    # V50 + n --> He4 + Sc47
    rate = 0.0

    # ths8r
    rate += np.exp(  -71.6649 + 66.0687*tf.T913
                  + -8.06344*tf.T9 + 0.527546*tf.T953)

    rate_eval.n_V50__He4_Sc47 = rate

@numba.njit()
def He4_Fe73__Ni77(rate_eval, tf):
    # Fe73 + He4 --> Ni77
    rate = 0.0

    # rath 
    rate += np.exp(  -1037.1 + 26.3331*tf.T9i + -2540.18*tf.T913i + 3702.39*tf.T913
                  + -200.617*tf.T9 + 10.7124*tf.T953 + -1846.38*tf.lnT9)

    rate_eval.He4_Fe73__Ni77 = rate

@numba.njit()
def p_Fe73__Co74(rate_eval, tf):
    # Fe73 + p --> Co74
    rate = 0.0

    # rath 
    rate += np.exp(  152.829 + -7.6465*tf.T9i + 293.401*tf.T913i + -473.252*tf.T913
                  + 26.6147*tf.T9 + -1.52397*tf.T953 + 235.529*tf.lnT9)

    rate_eval.p_Fe73__Co74 = rate

@numba.njit()
def p_Fe72__Co73(rate_eval, tf):
    # Fe72 + p --> Co73
    rate = 0.0

    # rath 
    rate += np.exp(  151.467 + -7.59264*tf.T9i + 290.627*tf.T913i + -468.443*tf.T913
                  + 26.2847*tf.T9 + -1.51157*tf.T953 + 233.36*tf.lnT9)

    rate_eval.p_Fe72__Co73 = rate

@numba.njit()
def p_Mg31__n_Al31(rate_eval, tf):
    # Mg31 + p --> n + Al31
    rate = 0.0

    # rath 
    rate += np.exp(  76.8055 + -3.05314*tf.T9i + 107.973*tf.T913i + -181.418*tf.T913
                  + 9.77621*tf.T9 + -0.540265*tf.T953 + 91.3012*tf.lnT9)

    rate_eval.p_Mg31__n_Al31 = rate

@numba.njit()
def n_Fe71__Fe72(rate_eval, tf):
    # Fe71 + n --> Fe72
    rate = 0.0

    # rath 
    rate += np.exp(  12.4089 + 0.0143169*tf.T9i + -1.40841*tf.T913i + -0.936054*tf.T913
                  + 0.761864*tf.T9 + -0.133288*tf.T953 + -0.890283*tf.lnT9)

    rate_eval.n_Fe71__Fe72 = rate

@numba.njit()
def He4_Fe70__Ni74(rate_eval, tf):
    # Fe70 + He4 --> Ni74
    rate = 0.0

    # rath 
    rate += np.exp(  -1015.73 + 25.8143*tf.T9i + -2491.37*tf.T913i + 3629.0*tf.T913
                  + -196.6*tf.T9 + 10.4777*tf.T953 + -1809.78*tf.lnT9)

    rate_eval.He4_Fe70__Ni74 = rate

@numba.njit()
def n_Cl28__Cl29(rate_eval, tf):
    # Cl28 + n --> Cl29
    rate = 0.0

    # ths8r
    rate += np.exp(  9.5469 + 0.919021*tf.T913
                  + 0.03556*tf.T9 + -0.0104944*tf.T953)

    rate_eval.n_Cl28__Cl29 = rate

@numba.njit()
def He4_Ne18__Mg22(rate_eval, tf):
    # Ne18 + He4 --> Mg22
    rate = 0.0

    # ths8r
    rate += np.exp(  32.8865 + -46.4859*tf.T913i + 0.956741*tf.T913
                  + -0.914402*tf.T9 + 0.0722478*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ne18__Mg22 = rate

@numba.njit()
def p_Fe70__Co71(rate_eval, tf):
    # Fe70 + p --> Co71
    rate = 0.0

    # rath 
    rate += np.exp(  150.433 + -7.50455*tf.T9i + 287.097*tf.T913i + -463.046*tf.T913
                  + 25.9035*tf.T9 + -1.49253*tf.T953 + 230.86*tf.lnT9)

    rate_eval.p_Fe70__Co71 = rate

@numba.njit()
def Sc62__n_n_Ti60__weak__mp17(rate_eval, tf):
    # Sc62 --> n + n + Ti60
    rate = 0.0

    # mp17w
    rate += np.exp(  4.30953)

    rate_eval.Sc62__n_n_Ti60__weak__mp17 = rate

@numba.njit()
def n_Fe70__Fe71(rate_eval, tf):
    # Fe70 + n --> Fe71
    rate = 0.0

    # rath 
    rate += np.exp(  18.5671 + 0.0104915*tf.T9i + 0.289139*tf.T913i + -11.0956*tf.T913
                  + 2.52465*tf.T9 + -0.320575*tf.T953 + 1.82579*tf.lnT9)

    rate_eval.n_Fe70__Fe71 = rate

@numba.njit()
def He4_Fe69__Ni73(rate_eval, tf):
    # Fe69 + He4 --> Ni73
    rate = 0.0

    # rath 
    rate += np.exp(  -1005.29 + 25.6067*tf.T9i + -2471.82*tf.T913i + 3597.83*tf.T913
                  + -194.872*tf.T9 + 10.3964*tf.T953 + -1794.69*tf.lnT9)

    rate_eval.He4_Fe69__Ni73 = rate

@numba.njit()
def n_F16__p_O16(rate_eval, tf):
    # F16 + n --> p + O16
    rate = 0.0

    # rpsmr
    rate += np.exp(  18.9074 + 0.0532742*tf.T9i + -2.69385*tf.T913i + 3.18271*tf.T913
                  + -0.0491204*tf.T9 + 0.000327601*tf.T953 + -1.83412*tf.lnT9)

    rate_eval.n_F16__p_O16 = rate

@numba.njit()
def n_Mn62__Mn63(rate_eval, tf):
    # Mn62 + n --> Mn63
    rate = 0.0

    # rath 
    rate += np.exp(  21.156 + -0.0407298*tf.T9i + 4.13088*tf.T913i + -11.3959*tf.T913
                  + 0.767989*tf.T9 + -0.0801338*tf.T953 + 4.07144*tf.lnT9)

    rate_eval.n_Mn62__Mn63 = rate

@numba.njit()
def n_Fe69__Fe70(rate_eval, tf):
    # Fe69 + n --> Fe70
    rate = 0.0

    # rath 
    rate += np.exp(  7.6699 + 0.0344878*tf.T9i + -4.04856*tf.T913i + 8.56302*tf.T913
                  + -0.327831*tf.T9 + -0.0455967*tf.T953 + -3.93752*tf.lnT9)

    rate_eval.n_Fe69__Fe70 = rate

@numba.njit()
def p_P32__S33(rate_eval, tf):
    # P32 + p --> S33
    rate = 0.0

    # rath 
    rate += np.exp(  107.354 + -3.79249*tf.T9i + 147.624*tf.T913i + -261.318*tf.T913
                  + 14.2732*tf.T9 + -0.776243*tf.T953 + 126.747*tf.lnT9)

    rate_eval.p_P32__S33 = rate

@numba.njit()
def p_Fe68__Co69(rate_eval, tf):
    # Fe68 + p --> Co69
    rate = 0.0

    # rath 
    rate += np.exp(  149.666 + -7.41635*tf.T9i + 283.706*tf.T913i + -458.439*tf.T913
                  + 25.7256*tf.T9 + -1.49799*tf.T953 + 228.563*tf.lnT9)

    rate_eval.p_Fe68__Co69 = rate

@numba.njit()
def n_Fe68__Fe69(rate_eval, tf):
    # Fe68 + n --> Fe69
    rate = 0.0

    # rath 
    rate += np.exp(  32.6352 + -0.0847694*tf.T9i + 10.2871*tf.T913i + -36.6781*tf.T913
                  + 4.62125*tf.T9 + -0.45954*tf.T953 + 11.5912*tf.lnT9)

    rate_eval.n_Fe68__Fe69 = rate

@numba.njit()
def He4_Fe67__Ni71(rate_eval, tf):
    # Fe67 + He4 --> Ni71
    rate = 0.0

    # rath 
    rate += np.exp(  -991.333 + 25.304*tf.T9i + -2442.64*tf.T913i + 3553.04*tf.T913
                  + -192.295*tf.T9 + 10.2483*tf.T953 + -1772.78*tf.lnT9)

    rate_eval.He4_Fe67__Ni71 = rate

@numba.njit()
def C17__N17__weak__wc12(rate_eval, tf):
    # C17 --> N17
    rate = 0.0

    # wc12w
    rate += np.exp(  0.89289)

    rate_eval.C17__N17__weak__wc12 = rate

@numba.njit()
def n_Fe67__Fe68(rate_eval, tf):
    # Fe67 + n --> Fe68
    rate = 0.0

    # rath 
    rate += np.exp(  7.12522 + 0.0408225*tf.T9i + -4.59102*tf.T913i + 11.0647*tf.T913
                  + -0.826513*tf.T9 + 0.00453315*tf.T953 + -4.52555*tf.lnT9)

    rate_eval.n_Fe67__Fe68 = rate

@numba.njit()
def n_Na21__p_Ne21(rate_eval, tf):
    # Na21 + n --> p + Ne21
    rate = 0.0

    # ths8r
    rate += np.exp(  17.9167 + 2.17917*tf.T913
                  + -0.303135*tf.T9 + 0.019321*tf.T953)

    rate_eval.n_Na21__p_Ne21 = rate

@numba.njit()
def p_Fe66__Co67(rate_eval, tf):
    # Fe66 + p --> Co67
    rate = 0.0

    # rath 
    rate += np.exp(  140.547 + -7.27704*tf.T9i + 274.78*tf.T913i + -439.065*tf.T913
                  + 24.2363*tf.T9 + -1.39448*tf.T953 + 220.7*tf.lnT9)

    rate_eval.p_Fe66__Co67 = rate

@numba.njit()
def p_Fe65__Co66(rate_eval, tf):
    # Fe65 + p --> Co66
    rate = 0.0

    # rath 
    rate += np.exp(  139.759 + -7.22883*tf.T9i + 272.75*tf.T913i + -436.205*tf.T913
                  + 24.0865*tf.T9 + -1.37897*tf.T953 + 219.265*tf.lnT9)

    rate_eval.p_Fe65__Co66 = rate

@numba.njit()
def n_Fe65__Fe66(rate_eval, tf):
    # Fe65 + n --> Fe66
    rate = 0.0

    # rath 
    rate += np.exp(  2.62324 + 0.0416578*tf.T9i + -5.76484*tf.T913i + 18.241*tf.T913
                  + -1.54755*tf.T9 + 0.056958*tf.T953 + -6.50886*tf.lnT9)

    rate_eval.n_Fe65__Fe66 = rate

@numba.njit()
def Mg20__p_Ne19__weak__wc12(rate_eval, tf):
    # Mg20 --> p + Ne19
    rate = 0.0

    # wc12w
    rate += np.exp(  0.72325)

    rate_eval.Mg20__p_Ne19__weak__wc12 = rate

@numba.njit()
def He4_Fe64__Ni68(rate_eval, tf):
    # Fe64 + He4 --> Ni68
    rate = 0.0

    # rath 
    rate += np.exp(  -1193.82 + 24.7922*tf.T9i + -2463.33*tf.T913i + 3797.95*tf.T913
                  + -215.064*tf.T9 + 11.8478*tf.T953 + -1843.16*tf.lnT9)

    rate_eval.He4_Fe64__Ni68 = rate

@numba.njit()
def p_Fe63__Co64(rate_eval, tf):
    # Fe63 + p --> Co64
    rate = 0.0

    # rath 
    rate += np.exp(  138.053 + -7.12802*tf.T9i + 268.27*tf.T913i + -429.082*tf.T913
                  + 23.5898*tf.T9 + -1.34853*tf.T953 + 215.939*tf.lnT9)

    rate_eval.p_Fe63__Co64 = rate

@numba.njit()
def He4_Sc48__n_V51(rate_eval, tf):
    # Sc48 + He4 --> n + V51
    rate = 0.0

    # rath 
    rate += np.exp(  -925.664 + 14.9263*tf.T9i + -1621.99*tf.T913i + 2659.5*tf.T913
                  + -158.959*tf.T9 + 9.12514*tf.T953 + -1247.44*tf.lnT9)

    rate_eval.He4_Sc48__n_V51 = rate

@numba.njit()
def n_Fe63__Fe64(rate_eval, tf):
    # Fe63 + n --> Fe64
    rate = 0.0

    # rath 
    rate += np.exp(  17.9444 + -0.0180028*tf.T9i + 1.80625*tf.T913i + -6.82631*tf.T913
                  + 0.816536*tf.T9 + -0.110855*tf.T953 + 1.95329*tf.lnT9)

    rate_eval.n_Fe63__Fe64 = rate

@numba.njit()
def n_Fe62__Fe63(rate_eval, tf):
    # Fe62 + n --> Fe63
    rate = 0.0

    # rath 
    rate += np.exp(  24.655 + -0.0409112*tf.T9i + 5.27507*tf.T913i + -19.1022*tf.T913
                  + 2.30844*tf.T9 + -0.22992*tf.T953 + 6.07933*tf.lnT9)

    rate_eval.n_Fe62__Fe63 = rate

@numba.njit()
def n_S29__p_P29(rate_eval, tf):
    # S29 + n --> p + P29
    rate = 0.0

    # ths8r
    rate += np.exp(  18.8264 + 1.39543*tf.T913
                  + -0.160998*tf.T9 + 0.012068*tf.T953)

    rate_eval.n_S29__p_P29 = rate

@numba.njit()
def He4_P36__n_Cl39(rate_eval, tf):
    # P36 + He4 --> n + Cl39
    rate = 0.0

    # rath 
    rate += np.exp(  -10.806 + -3.14434*tf.T9i + -20.2012*tf.T913i + 26.3511*tf.T913
                  + -5.23585*tf.T9 + 0.408499*tf.T953 + 5.34466*tf.lnT9)

    rate_eval.He4_P36__n_Cl39 = rate

@numba.njit()
def p_Fe61__Co62(rate_eval, tf):
    # Fe61 + p --> Co62
    rate = 0.0

    # rath 
    rate += np.exp(  136.616 + -7.0169*tf.T9i + 262.952*tf.T913i + -421.376*tf.T913
                  + 23.2334*tf.T9 + -1.33783*tf.T953 + 212.009*tf.lnT9)

    rate_eval.p_Fe61__Co62 = rate

@numba.njit()
def p_S46__He4_P43(rate_eval, tf):
    # S46 + p --> He4 + P43
    rate = 0.0

    # rath 
    rate += np.exp(  77.2024 + -4.47096*tf.T9i + 163.554*tf.T913i + -253.034*tf.T913
                  + 12.4595*tf.T9 + -0.593809*tf.T953 + 132.354*tf.lnT9)

    rate_eval.p_S46__He4_P43 = rate

@numba.njit()
def p_Fe60__Co61(rate_eval, tf):
    # Fe60 + p --> Co61
    rate = 0.0

    # rath 
    rate += np.exp(  214.087 + -7.0055*tf.T9i + 277.194*tf.T913i + -518.374*tf.T913
                  + 33.721*tf.T9 + -2.12994*tf.T953 + 236.936*tf.lnT9)

    rate_eval.p_Fe60__Co61 = rate

@numba.njit()
def p_Al34__Si35(rate_eval, tf):
    # Al34 + p --> Si35
    rate = 0.0

    # rath 
    rate += np.exp(  73.6762 + -3.37682*tf.T9i + 121.039*tf.T913i + -202.664*tf.T913
                  + 11.0069*tf.T9 + -0.607487*tf.T953 + 101.633*tf.lnT9)

    rate_eval.p_Al34__Si35 = rate

@numba.njit()
def He4_Fe59__Ni63(rate_eval, tf):
    # Fe59 + He4 --> Ni63
    rate = 0.0

    # rath 
    rate += np.exp(  -1188.67 + 24.6958*tf.T9i + -2446.52*tf.T913i + 3777.2*tf.T913
                  + -213.37*tf.T9 + 11.734*tf.T953 + -1833.56*tf.lnT9)

    rate_eval.He4_Fe59__Ni63 = rate

@numba.njit()
def p_Fe59__Co60(rate_eval, tf):
    # Fe59 + p --> Co60
    rate = 0.0

    # rath 
    rate += np.exp(  101.376 + -6.74452*tf.T9i + 235.267*tf.T913i + -353.388*tf.T913
                  + 18.6683*tf.T9 + -1.06059*tf.T953 + 183.906*tf.lnT9)

    rate_eval.p_Fe59__Co60 = rate

@numba.njit()
def He4_Fe58__Ni62(rate_eval, tf):
    # Fe58 + He4 --> Ni62
    rate = 0.0

    # ths8r
    rate += np.exp(  59.393 + -91.9089*tf.T913i + 8.18581*tf.T913
                  + -6.00824*tf.T9 + 0.693434*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe58__Ni62 = rate

@numba.njit()
def n_Fe58__Fe59(rate_eval, tf):
    # Fe58 + n --> Fe59
    rate = 0.0

    # ks03 
    rate += np.exp(  12.9299 + 0.00302175*tf.T9i + -0.461754*tf.T913i + 2.44181*tf.T913
                  + -0.318228*tf.T9 + 0.0109977*tf.T953 + -0.598723*tf.lnT9)

    rate_eval.n_Fe58__Fe59 = rate

@numba.njit()
def p_Fe57__Co58(rate_eval, tf):
    # Fe57 + p --> Co58
    rate = 0.0

    # ths8r
    rate += np.exp(  35.269 + -37.1663*tf.T913i + 3.48503*tf.T913
                  + -2.56204*tf.T9 + 0.272972*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Fe57__Co58 = rate

@numba.njit()
def n_Fe57__Fe58(rate_eval, tf):
    # Fe57 + n --> Fe58
    rate = 0.0

    # ks03 
    rate += np.exp(  20.2493 + -0.0214497*tf.T9i + 2.1643*tf.T913i + -7.49584*tf.T913
                  + 0.656354*tf.T9 + -0.0549855*tf.T953 + 2.38149*tf.lnT9)

    rate_eval.n_Fe57__Fe58 = rate

@numba.njit()
def p_Fe56__Co57(rate_eval, tf):
    # Fe56 + p --> Co57
    rate = 0.0

    # ths8r
    rate += np.exp(  36.0665 + -37.1625*tf.T913i + 1.06776*tf.T913
                  + -1.31689*tf.T9 + 0.122089*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Fe56__Co57 = rate

@numba.njit()
def Sc54__Ti54__weak__wc17(rate_eval, tf):
    # Sc54 --> Ti54
    rate = 0.0

    # wc17w
    rate += np.exp(  0.255738)

    rate_eval.Sc54__Ti54__weak__wc17 = rate

@numba.njit()
def n_Fe56__Fe57(rate_eval, tf):
    # Fe56 + n --> Fe57
    rate = 0.0

    # ks03 
    rate += np.exp(  35.834 + -0.0600873*tf.T9i + 9.79414*tf.T913i + -33.7366*tf.T913
                  + 2.97173*tf.T9 + -0.236498*tf.T953 + 11.8711*tf.lnT9)

    rate_eval.n_Fe56__Fe57 = rate

@numba.njit()
def p_Fe55__Co56(rate_eval, tf):
    # Fe55 + p --> Co56
    rate = 0.0

    # ths8r
    rate += np.exp(  35.7333 + -37.1585*tf.T913i + 1.66198*tf.T913
                  + -1.60842*tf.T9 + 0.148916*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Fe55__Co56 = rate

@numba.njit()
def He4_Fe54__Ni58(rate_eval, tf):
    # Fe54 + He4 --> Ni58
    rate = 0.0

    # ths8r
    rate += np.exp(  60.2478 + -91.7628*tf.T913i + 4.23027*tf.T913
                  + -3.31305*tf.T9 + 0.271293*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe54__Ni58 = rate

@numba.njit()
def Ti38__Sc38__weak__mo97(rate_eval, tf):
    # Ti38 --> Sc38
    rate = 0.0

    # mo97w
    rate += np.exp(  2.39494)

    rate_eval.Ti38__Sc38__weak__mo97 = rate

@numba.njit()
def n_Fe54__Fe55(rate_eval, tf):
    # Fe54 + n --> Fe55
    rate = 0.0

    # ks03 
    rate += np.exp(  -0.80864 + 0.0591716*tf.T9i + -8.66617*tf.T913i + 26.4472*tf.T913
                  + -1.9222*tf.T9 + 0.0986404*tf.T953 + -9.78317*tf.lnT9)

    rate_eval.n_Fe54__Fe55 = rate

@numba.njit()
def He4_Fe52__Ni56(rate_eval, tf):
    # Fe52 + He4 --> Ni56
    rate = 0.0

    # ths8r
    rate += np.exp(  66.6417 + -91.6819*tf.T913i + -9.51885*tf.T913
                  + -0.533014*tf.T9 + 0.0892607*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe52__Ni56 = rate

@numba.njit()
def p_Fe52__Co53(rate_eval, tf):
    # Fe52 + p --> Co53
    rate = 0.0

    # ths8r
    rate += np.exp(  39.2879 + -37.1457*tf.T913i + -5.67417*tf.T913
                  + -0.559644*tf.T9 + 0.102768*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Fe52__Co53 = rate

@numba.njit()
def He4_Fe51__Ni55(rate_eval, tf):
    # Fe51 + He4 --> Ni55
    rate = 0.0

    # ths8r
    rate += np.exp(  63.8701 + -91.6394*tf.T913i + -9.83814*tf.T913
                  + 0.710874*tf.T9 + -0.0603943*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe51__Ni55 = rate

@numba.njit()
def p_Si36__n_P36(rate_eval, tf):
    # Si36 + p --> n + P36
    rate = 0.0

    # rath 
    rate += np.exp(  89.001 + -3.64827*tf.T9i + 131.812*tf.T913i + -220.537*tf.T913
                  + 12.0451*tf.T9 + -0.668764*tf.T953 + 110.365*tf.lnT9)

    rate_eval.p_Si36__n_P36 = rate

@numba.njit()
def p_Fe50__Co51(rate_eval, tf):
    # Fe50 + p --> Co51
    rate = 0.0

    # nfisn
    rate += np.exp(  -1029.07 + -207.829*tf.T9i + 3087.39*tf.T913i + -1915.13*tf.T913
                  + 54.2128*tf.T9 + -1.75436*tf.T953 + 1427.4*tf.lnT9)
    # nfisn
    rate += np.exp(  27.4974 + 0.280683*tf.T9i + -50.0866*tf.T913i + 11.6066*tf.T913
                  + 0.232922*tf.T9 + -0.107431*tf.T953 + -8.40452*tf.lnT9)
    # nfisn
    rate += np.exp(  1136.79 + -10.1797*tf.T9i + 597.505*tf.T913i + -1960.57*tf.T913
                  + 269.151*tf.T9 + -41.4909*tf.T953 + 647.448*tf.lnT9)

    rate_eval.p_Fe50__Co51 = rate

@numba.njit()
def p_Ne32__n_Na32(rate_eval, tf):
    # Ne32 + p --> n + Na32
    rate = 0.0

    # rath 
    rate += np.exp(  72.3337 + -2.74903*tf.T9i + 97.8264*tf.T913i + -164.792*tf.T913
                  + 8.91821*tf.T9 + -0.489538*tf.T953 + 82.5399*tf.lnT9)

    rate_eval.p_Ne32__n_Na32 = rate

@numba.njit()
def n_Fe49__Fe50(rate_eval, tf):
    # Fe49 + n --> Fe50
    rate = 0.0

    # ths8r
    rate += np.exp(  16.6027 + -1.16093*tf.T913
                  + 0.138525*tf.T9 + -0.0406634*tf.T953)

    rate_eval.n_Fe49__Fe50 = rate

@numba.njit()
def n_Ne30__Ne31(rate_eval, tf):
    # Ne30 + n --> Ne31
    rate = 0.0

    # rath 
    rate += np.exp(  14.0244 + -0.0271499*tf.T9i + 3.40874*tf.T913i + -11.975*tf.T913
                  + 1.35505*tf.T9 + -0.112482*tf.T953 + 3.85903*tf.lnT9)

    rate_eval.n_Ne30__Ne31 = rate

@numba.njit()
def p_Fe48__Co49(rate_eval, tf):
    # Fe48 + p --> Co49
    rate = 0.0

    # ths8r
    rate += np.exp(  -17.0528 + -10.5047*tf.T9i + 19.0735*tf.T913
                  + -2.23228*tf.T9 + 0.159842*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Fe48__Co49 = rate

@numba.njit()
def He4_O25__n_Ne28(rate_eval, tf):
    # O25 + He4 --> n + Ne28
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.9547 + -2.17947*tf.T9i + 39.6574*tf.T913i + -99.8114*tf.T913
                  + 4.31935*tf.T9 + -0.200471*tf.T953 + 52.7619*tf.lnT9)

    rate_eval.He4_O25__n_Ne28 = rate

@numba.njit()
def n_Fe47__Fe48(rate_eval, tf):
    # Fe47 + n --> Fe48
    rate = 0.0

    # ths8r
    rate += np.exp(  13.0127 + -1.46478*tf.T913
                  + 0.354233*tf.T9 + -0.0323023*tf.T953)

    rate_eval.n_Fe47__Fe48 = rate

@numba.njit()
def n_Cr55__Cr56(rate_eval, tf):
    # Cr55 + n --> Cr56
    rate = 0.0

    # rath 
    rate += np.exp(  26.1281 + -0.0937138*tf.T9i + 9.21329*tf.T913i + -22.7172*tf.T913
                  + 1.67667*tf.T9 + -0.12049*tf.T953 + 8.6839*tf.lnT9)

    rate_eval.n_Cr55__Cr56 = rate

@numba.njit()
def He4_Fe46__Ni50(rate_eval, tf):
    # Fe46 + He4 --> Ni50
    rate = 0.0

    # ths8r
    rate += np.exp(  51.9636 + -91.401*tf.T913i + -1.45212*tf.T913
                  + -0.454692*tf.T9 + -0.0111654*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe46__Ni50 = rate

@numba.njit()
def He4_Fe57__Ni61(rate_eval, tf):
    # Fe57 + He4 --> Ni61
    rate = 0.0

    # ths8r
    rate += np.exp(  66.184 + -91.8742*tf.T913i + -4.07595*tf.T913
                  + -1.93027*tf.T9 + 0.240619*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe57__Ni61 = rate

@numba.njit()
def He4_Fe45__Ni49(rate_eval, tf):
    # Fe45 + He4 --> Ni49
    rate = 0.0

    # ths8r
    rate += np.exp(  51.2465 + -91.3476*tf.T913i + -1.11579*tf.T913
                  + -0.471526*tf.T9 + -0.000721251*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe45__Ni49 = rate

@numba.njit()
def p_Mn73__Fe74(rate_eval, tf):
    # Mn73 + p --> Fe74
    rate = 0.0

    # rath 
    rate += np.exp(  146.915 + -7.43692*tf.T9i + 284.56*tf.T913i + -457.679*tf.T913
                  + 25.626*tf.T9 + -1.45984*tf.T953 + 228.187*tf.lnT9)

    rate_eval.p_Mn73__Fe74 = rate

@numba.njit()
def He4_Mn72__Co76(rate_eval, tf):
    # Mn72 + He4 --> Co76
    rate = 0.0

    # rath 
    rate += np.exp(  -1237.02 + 25.584*tf.T9i + -2538.79*tf.T913i + 3922.28*tf.T913
                  + -222.069*tf.T9 + 12.2617*tf.T953 + -1903.51*tf.lnT9)

    rate_eval.He4_Mn72__Co76 = rate

@numba.njit()
def n_Mn72__Mn73(rate_eval, tf):
    # Mn72 + n --> Mn73
    rate = 0.0

    # rath 
    rate += np.exp(  16.4783 + -0.0136509*tf.T9i + 1.72754*tf.T913i + -7.99795*tf.T913
                  + 0.649899*tf.T9 + -0.070122*tf.T953 + 2.17191*tf.lnT9)

    rate_eval.n_Mn72__Mn73 = rate

@numba.njit()
def n_Mn71__Mn72(rate_eval, tf):
    # Mn71 + n --> Mn72
    rate = 0.0

    # rath 
    rate += np.exp(  18.4457 + -0.0409609*tf.T9i + 4.46054*tf.T913i + -15.388*tf.T913
                  + 1.69053*tf.T9 + -0.168635*tf.T953 + 4.81487*tf.lnT9)

    rate_eval.n_Mn71__Mn72 = rate

@numba.njit()
def n_Mn70__Mn71(rate_eval, tf):
    # Mn70 + n --> Mn71
    rate = 0.0

    # rath 
    rate += np.exp(  22.6058 + 0.154964*tf.T9i + -10.2741*tf.T913i + -0.208968*tf.T913
                  + 0.748926*tf.T9 + -0.089311*tf.T953 + -5.0552*tf.lnT9)

    rate_eval.n_Mn70__Mn71 = rate

@numba.njit()
def B12__C12__weak__wc17(rate_eval, tf):
    # B12 --> C12
    rate = 0.0

    # wc17w
    rate += np.exp(  3.53556)

    rate_eval.B12__C12__weak__wc17 = rate

@numba.njit()
def He4_Mn69__Co73(rate_eval, tf):
    # Mn69 + He4 --> Co73
    rate = 0.0

    # rath 
    rate += np.exp(  -1209.74 + 25.0387*tf.T9i + -2486.29*tf.T913i + 3839.15*tf.T913
                  + -217.402*tf.T9 + 11.9949*tf.T953 + -1862.91*tf.lnT9)

    rate_eval.He4_Mn69__Co73 = rate

@numba.njit()
def p_Mn69__Fe70(rate_eval, tf):
    # Mn69 + p --> Fe70
    rate = 0.0

    # rath 
    rate += np.exp(  146.781 + -7.27054*tf.T9i + 278.322*tf.T913i + -450.226*tf.T913
                  + 25.2214*tf.T9 + -1.44155*tf.T953 + 224.121*tf.lnT9)

    rate_eval.p_Mn69__Fe70 = rate

@numba.njit()
def p_Mn68__Fe69(rate_eval, tf):
    # Mn68 + p --> Fe69
    rate = 0.0

    # rath 
    rate += np.exp(  147.885 + -7.22369*tf.T9i + 276.537*tf.T913i + -448.673*tf.T913
                  + 25.1081*tf.T9 + -1.42695*tf.T953 + 223.079*tf.lnT9)

    rate_eval.p_Mn68__Fe69 = rate

@numba.njit()
def Fe53__Mn53__weak__wc12(rate_eval, tf):
    # Fe53 --> Mn53
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.60288)

    rate_eval.Fe53__Mn53__weak__wc12 = rate

@numba.njit()
def p_Mn73__n_Fe73(rate_eval, tf):
    # Mn73 + p --> n + Fe73
    rate = 0.0

    # rath 
    rate += np.exp(  156.112 + -7.43489*tf.T9i + 284.225*tf.T913i + -455.499*tf.T913
                  + 25.2569*tf.T9 + -1.41754*tf.T953 + 227.684*tf.lnT9)

    rate_eval.p_Mn73__n_Fe73 = rate

@numba.njit()
def He4_Mn67__Co71(rate_eval, tf):
    # Mn67 + He4 --> Co71
    rate = 0.0

    # rath 
    rate += np.exp(  -1191.11 + 24.6779*tf.T9i + -2451.14*tf.T913i + 3782.48*tf.T913
                  + -214.092*tf.T9 + 11.8009*tf.T953 + -1835.52*tf.lnT9)

    rate_eval.He4_Mn67__Co71 = rate

@numba.njit()
def He4_Cl30__K34(rate_eval, tf):
    # Cl30 + He4 --> K34
    rate = 0.0

    # ths8r
    rate += np.exp(  41.9433 + -67.9024*tf.T913i + -0.618087*tf.T913
                  + -0.498925*tf.T9 + 0.0172983*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl30__K34 = rate

@numba.njit()
def p_Mn67__Fe68(rate_eval, tf):
    # Mn67 + p --> Fe68
    rate = 0.0

    # rath 
    rate += np.exp(  142.507 + -7.16882*tf.T9i + 273.219*tf.T913i + -440.164*tf.T913
                  + 24.4717*tf.T9 + -1.39514*tf.T953 + 219.96*tf.lnT9)

    rate_eval.p_Mn67__Fe68 = rate

@numba.njit()
def n_Mn67__Mn68(rate_eval, tf):
    # Mn67 + n --> Mn68
    rate = 0.0

    # rath 
    rate += np.exp(  13.8767 + -0.00793296*tf.T9i + 0.487717*tf.T913i + -4.38895*tf.T913
                  + 0.955202*tf.T9 + -0.136518*tf.T953 + 0.654872*tf.lnT9)

    rate_eval.n_Mn67__Mn68 = rate

@numba.njit()
def He4_Mn66__Co70(rate_eval, tf):
    # Mn66 + He4 --> Co70
    rate = 0.0

    # rath 
    rate += np.exp(  -1214.15 + 25.1148*tf.T9i + -2489.28*tf.T913i + 3848.05*tf.T913
                  + -217.48*tf.T9 + 11.9815*tf.T953 + -1867.89*tf.lnT9)

    rate_eval.He4_Mn66__Co70 = rate

@numba.njit()
def p_Mn66__Fe67(rate_eval, tf):
    # Mn66 + p --> Fe67
    rate = 0.0

    # rath 
    rate += np.exp(  131.151 + -6.90547*tf.T9i + 251.032*tf.T913i + -403.125*tf.T913
                  + 22.5545*tf.T9 + -1.29123*tf.T953 + 201.551*tf.lnT9)

    rate_eval.p_Mn66__Fe67 = rate

@numba.njit()
def He4_Mn64__Co68(rate_eval, tf):
    # Mn64 + He4 --> Co68
    rate = 0.0

    # rath 
    rate += np.exp(  -1162.15 + 24.3746*tf.T9i + -2416.92*tf.T913i + 3717.72*tf.T913
                  + -209.816*tf.T9 + 11.5496*tf.T953 + -1807.49*tf.lnT9)

    rate_eval.He4_Mn64__Co68 = rate

@numba.njit()
def He4_Mn63__Co67(rate_eval, tf):
    # Mn63 + He4 --> Co67
    rate = 0.0

    # rath 
    rate += np.exp(  -1147.08 + 23.9708*tf.T9i + -2380.64*tf.T913i + 3663.61*tf.T913
                  + -207.223*tf.T9 + 11.4222*tf.T953 + -1779.54*tf.lnT9)

    rate_eval.He4_Mn63__Co67 = rate

@numba.njit()
def n_Mn63__Mn64(rate_eval, tf):
    # Mn63 + n --> Mn64
    rate = 0.0

    # rath 
    rate += np.exp(  24.0021 + -0.060428*tf.T9i + 6.47496*tf.T913i + -18.3209*tf.T913
                  + 1.49244*tf.T9 + -0.134903*tf.T953 + 6.55541*tf.lnT9)

    rate_eval.n_Mn63__Mn64 = rate

@numba.njit()
def He4_Cl29__p_Ar32(rate_eval, tf):
    # Cl29 + He4 --> p + Ar32
    rate = 0.0

    # ths8r
    rate += np.exp(  51.5091 + -67.8117*tf.T913i + 0.267424*tf.T913
                  + -0.726288*tf.T9 + 0.0481218*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl29__p_Ar32 = rate

@numba.njit()
def p_Ne33__n_Na33(rate_eval, tf):
    # Ne33 + p --> n + Na33
    rate = 0.0

    # rath 
    rate += np.exp(  73.2941 + -2.79166*tf.T9i + 99.765*tf.T913i + -167.797*tf.T913
                  + 9.10199*tf.T9 + -0.499868*tf.T953 + 83.9805*tf.lnT9)

    rate_eval.p_Ne33__n_Na33 = rate

@numba.njit()
def p_Mn62__Fe63(rate_eval, tf):
    # Mn62 + p --> Fe63
    rate = 0.0

    # rath 
    rate += np.exp(  138.801 + -6.92118*tf.T9i + 262.193*tf.T913i + -422.722*tf.T913
                  + 23.2306*tf.T9 + -1.31212*tf.T953 + 211.833*tf.lnT9)

    rate_eval.p_Mn62__Fe63 = rate

@numba.njit()
def He4_Mn61__Co65(rate_eval, tf):
    # Mn61 + He4 --> Co65
    rate = 0.0

    # rath 
    rate += np.exp(  -1129.76 + 23.6003*tf.T9i + -2345.26*tf.T913i + 3608.75*tf.T913
                  + -204.204*tf.T9 + 11.2584*tf.T953 + -1752.58*tf.lnT9)

    rate_eval.He4_Mn61__Co65 = rate

@numba.njit()
def p_Mn61__Fe62(rate_eval, tf):
    # Mn61 + p --> Fe62
    rate = 0.0

    # rath 
    rate += np.exp(  134.208 + -6.8533*tf.T9i + 257.956*tf.T913i + -414.013*tf.T913
                  + 22.7299*tf.T9 + -1.29243*tf.T953 + 208.149*tf.lnT9)

    rate_eval.p_Mn61__Fe62 = rate

@numba.njit()
def Mg38__Al38__weak__mo03(rate_eval, tf):
    # Mg38 --> Al38
    rate = 0.0

    # mo03w
    rate += np.exp(  -110.746)

    rate_eval.Mg38__Al38__weak__mo03 = rate

@numba.njit()
def n_Fe51__p_Mn51(rate_eval, tf):
    # Fe51 + n --> p + Mn51
    rate = 0.0

    # ths8r
    rate += np.exp(  21.3823 + -0.733491*tf.T913
                  + 0.250569*tf.T9 + -0.0245564*tf.T953)

    rate_eval.n_Fe51__p_Mn51 = rate

@numba.njit()
def P25__Si25__weak__bqa_pos_(rate_eval, tf):
    # P25 --> Si25
    rate = 0.0

    # bqa+w
    rate += np.exp(  3.35077)

    rate_eval.P25__Si25__weak__bqa_pos_ = rate

@numba.njit()
def n_Mn60__Mn61(rate_eval, tf):
    # Mn60 + n --> Mn61
    rate = 0.0

    # rath 
    rate += np.exp(  18.9433 + -0.0283764*tf.T9i + 2.663*tf.T913i + -7.12176*tf.T913
                  + 0.463155*tf.T9 + -0.0602925*tf.T953 + 2.51827*tf.lnT9)

    rate_eval.n_Mn60__Mn61 = rate

@numba.njit()
def p_Ca58__Sc59(rate_eval, tf):
    # Ca58 + p --> Sc59
    rate = 0.0

    # rath 
    rate += np.exp(  108.925 + -5.72813*tf.T9i + 212.001*tf.T913i + -339.649*tf.T913
                  + 18.6725*tf.T9 + -1.05517*tf.T953 + 171.087*tf.lnT9)

    rate_eval.p_Ca58__Sc59 = rate

@numba.njit()
def n_Mn59__Mn60(rate_eval, tf):
    # Mn59 + n --> Mn60
    rate = 0.0

    # rath 
    rate += np.exp(  20.5786 + -0.0424123*tf.T9i + 4.41995*tf.T913i + -11.9252*tf.T913
                  + 0.956911*tf.T9 + -0.0995306*tf.T953 + 4.36904*tf.lnT9)

    rate_eval.n_Mn59__Mn60 = rate

@numba.njit()
def n_Mn58__Mn59(rate_eval, tf):
    # Mn58 + n --> Mn59
    rate = 0.0

    # rath 
    rate += np.exp(  19.5045 + -0.0289757*tf.T9i + 2.76912*tf.T913i + -7.50491*tf.T913
                  + 0.551149*tf.T9 + -0.0676596*tf.T953 + 2.64724*tf.lnT9)

    rate_eval.n_Mn58__Mn59 = rate

@numba.njit()
def n_Mn56__Mn57(rate_eval, tf):
    # Mn56 + n --> Mn57
    rate = 0.0

    # rath 
    rate += np.exp(  32.7254 + -0.114637*tf.T9i + 11.6073*tf.T913i + -31.0965*tf.T913
                  + 2.42836*tf.T9 + -0.167953*tf.T953 + 11.3269*tf.lnT9)

    rate_eval.n_Mn56__Mn57 = rate

@numba.njit()
def p_K42__n_Ca42(rate_eval, tf):
    # K42 + p --> n + Ca42
    rate = 0.0

    # rath 
    rate += np.exp(  109.636 + -4.815*tf.T9i + 176.559*tf.T913i + -292.118*tf.T913
                  + 16.0165*tf.T9 + -0.893402*tf.T953 + 146.195*tf.lnT9)

    rate_eval.p_K42__n_Ca42 = rate

@numba.njit()
def n_Mn55__Mn56(rate_eval, tf):
    # Mn55 + n --> Mn56
    rate = 0.0

    # ks03 
    rate += np.exp(  23.5376 + -0.101456*tf.T9i + 8.83153*tf.T913i + -18.3753*tf.T913
                  + 1.43799*tf.T9 + -0.112154*tf.T953 + 7.38141*tf.lnT9)

    rate_eval.n_Mn55__Mn56 = rate

@numba.njit()
def p_Fe64__n_Co64(rate_eval, tf):
    # Fe64 + p --> n + Co64
    rate = 0.0

    # rath 
    rate += np.exp(  145.157 + -7.17111*tf.T9i + 269.61*tf.T913i + -429.298*tf.T913
                  + 23.4373*tf.T9 + -1.3114*tf.T953 + 216.576*tf.lnT9)

    rate_eval.p_Fe64__n_Co64 = rate

@numba.njit()
def He4_Mn53__Co57(rate_eval, tf):
    # Mn53 + He4 --> Co57
    rate = 0.0

    # ths8r
    rate += np.exp(  62.0252 + -89.3558*tf.T913i + 0.000882861*tf.T913
                  + -2.79327*tf.T9 + 0.309057*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn53__Co57 = rate

@numba.njit()
def He4_Mn52__Co56(rate_eval, tf):
    # Mn52 + He4 --> Co56
    rate = 0.0

    # ths8r
    rate += np.exp(  63.5657 + -89.3157*tf.T913i + -1.95982*tf.T913
                  + -2.45671*tf.T9 + 0.296095*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn52__Co56 = rate

@numba.njit()
def He4_Mn50__Co54(rate_eval, tf):
    # Mn50 + He4 --> Co54
    rate = 0.0

    # ths8r
    rate += np.exp(  54.3174 + -89.2309*tf.T913i + -1.30702*tf.T913
                  + -1.30543*tf.T9 + 0.141679*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn50__Co54 = rate

@numba.njit()
def p_Mn50__Fe51(rate_eval, tf):
    # Mn50 + p --> Fe51
    rate = 0.0

    # ths8r
    rate += np.exp(  35.7518 + -36.1778*tf.T913i + 1.40937*tf.T913
                  + -2.23863*tf.T9 + 0.244817*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn50__Fe51 = rate

@numba.njit()
def p_Mn49__Fe50(rate_eval, tf):
    # Mn49 + p --> Fe50
    rate = 0.0

    # ths8r
    rate += np.exp(  36.0838 + -36.173*tf.T913i + 1.28192*tf.T913
                  + -3.04331*tf.T9 + 0.393688*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn49__Fe50 = rate

@numba.njit()
def n_Mn49__Mn50(rate_eval, tf):
    # Mn49 + n --> Mn50
    rate = 0.0

    # ths8r
    rate += np.exp(  11.269 + -0.759512*tf.T913
                  + 0.246336*tf.T9 + -0.0261234*tf.T953)

    rate_eval.n_Mn49__Mn50 = rate

@numba.njit()
def He4_Si23__S27(rate_eval, tf):
    # Si23 + He4 --> S27
    rate = 0.0

    # ths8r
    rate += np.exp(  35.83 + -58.9653*tf.T913i + 0.637856*tf.T913
                  + -0.686203*tf.T9 + 0.0421532*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si23__S27 = rate

@numba.njit()
def p_Mn48__Fe49(rate_eval, tf):
    # Mn48 + p --> Fe49
    rate = 0.0

    # nfisn
    rate += np.exp(  26.4123 + -0.0354336*tf.T9i + -36.0158*tf.T913i + -1.4389*tf.T913
                  + 0.200517*tf.T9 + -0.0424345*tf.T953 + -0.0810949*tf.lnT9)
    # nfisn
    rate += np.exp(  -45.645 + -7.6769*tf.T9i + 46.0077*tf.T913i + 6.51511*tf.T913
                  + -2.27848*tf.T9 + 0.120343*tf.T953 + 15.9481*tf.lnT9)
    # nfisn
    rate += np.exp(  -0.767721 + -20.0015*tf.T9i + 19.7008*tf.T913i + -7.20576*tf.T913
                  + 3.25685*tf.T9 + -0.585917*tf.T953 + 1.9698*tf.lnT9)
    # nfisn
    rate += np.exp(  24646.4 + -145.752*tf.T9i + 12456.4*tf.T913i + -42516.9*tf.T913
                  + 6842.27*tf.T9 + -1296.21*tf.T953 + 13456.9*tf.lnT9)
    # nfisn
    rate += np.exp(  -678.403 + -140.01*tf.T9i + 633.483*tf.T913i + 64.7273*tf.T913
                  + 149.03*tf.T9 + -35.9858*tf.T953 + -35.8098*tf.lnT9)

    rate_eval.p_Mn48__Fe49 = rate

@numba.njit()
def He4_Mn46__Co50(rate_eval, tf):
    # Mn46 + He4 --> Co50
    rate = 0.0

    # ths8r
    rate += np.exp(  51.9123 + -89.0414*tf.T913i + -1.56171*tf.T913
                  + -0.559047*tf.T9 + 0.017378*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn46__Co50 = rate

@numba.njit()
def p_Mn46__Fe47(rate_eval, tf):
    # Mn46 + p --> Fe47
    rate = 0.0

    # nfisn
    rate += np.exp(  93.9757 + -19.6336*tf.T9i + 551.123*tf.T913i + -658.393*tf.T913
                  + 31.1478*tf.T9 + -1.6152*tf.T953 + 364.223*tf.lnT9)
    # nfisn
    rate += np.exp(  262.987 + -4.02713*tf.T9i + 230.847*tf.T913i + -523.116*tf.T913
                  + 32.0722*tf.T9 + -1.73303*tf.T953 + 227.075*tf.lnT9)
    # nfisn
    rate += np.exp(  19.5875 + -0.0108102*tf.T9i + -36.8881*tf.T913i + 3.27542*tf.T913
                  + -0.280996*tf.T9 + -0.00370294*tf.T953 + -1.50657*tf.lnT9)

    rate_eval.p_Mn46__Fe47 = rate

@numba.njit()
def He4_Mn45__Co49(rate_eval, tf):
    # Mn45 + He4 --> Co49
    rate = 0.0

    # ths8r
    rate += np.exp(  51.4799 + -88.989*tf.T913i + -1.46275*tf.T913
                  + -0.528983*tf.T9 + 0.0100936*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn45__Co49 = rate

@numba.njit()
def p_Mn45__Fe46(rate_eval, tf):
    # Mn45 + p --> Fe46
    rate = 0.0

    # ths8r
    rate += np.exp(  41.2369 + -36.1516*tf.T913i + -11.3353*tf.T913
                  + 0.290321*tf.T9 + 0.0486483*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn45__Fe46 = rate

@numba.njit()
def n_Mn44__Mn45(rate_eval, tf):
    # Mn44 + n --> Mn45
    rate = 0.0

    # ths8r
    rate += np.exp(  13.7554 + -2.59703*tf.T913
                  + 0.547478*tf.T9 + -0.0432276*tf.T953)

    rate_eval.n_Mn44__Mn45 = rate

@numba.njit()
def He4_Cr70__Fe74(rate_eval, tf):
    # Cr70 + He4 --> Fe74
    rate = 0.0

    # rath 
    rate += np.exp(  -1188.53 + 24.5224*tf.T9i + -2435.27*tf.T913i + 3764.11*tf.T913
                  + -213.379*tf.T9 + 11.782*tf.T953 + -1825.59*tf.lnT9)

    rate_eval.He4_Cr70__Fe74 = rate

@numba.njit()
def p_V53__He4_Ti50(rate_eval, tf):
    # V53 + p --> He4 + Ti50
    rate = 0.0

    # rath 
    rate += np.exp(  85.9748 + -5.9584*tf.T9i + 211.655*tf.T913i + -313.047*tf.T913
                  + 14.8539*tf.T9 + -0.642528*tf.T953 + 167.503*tf.lnT9)

    rate_eval.p_V53__He4_Ti50 = rate

@numba.njit()
def p_Cr69__Mn70(rate_eval, tf):
    # Cr69 + p --> Mn70
    rate = 0.0

    # rath 
    rate += np.exp(  142.742 + -7.06997*tf.T9i + 270.349*tf.T913i + -437.614*tf.T913
                  + 24.6077*tf.T9 + -1.41108*tf.T953 + 217.696*tf.lnT9)

    rate_eval.p_Cr69__Mn70 = rate

@numba.njit()
def n_Cr69__Cr70(rate_eval, tf):
    # Cr69 + n --> Cr70
    rate = 0.0

    # rath 
    rate += np.exp(  16.225 + 0.00298474*tf.T9i + 0.381774*tf.T913i + -9.03601*tf.T913
                  + 1.78083*tf.T9 + -0.216927*tf.T953 + 1.43616*tf.lnT9)

    rate_eval.n_Cr69__Cr70 = rate

@numba.njit()
def n_Cl40__Cl41(rate_eval, tf):
    # Cl40 + n --> Cl41
    rate = 0.0

    # rath 
    rate += np.exp(  14.5399 + -0.0190647*tf.T9i + 0.983938*tf.T913i + -1.49503*tf.T913
                  + 0.00631608*tf.T9 + -0.0103406*tf.T953 + 0.479579*tf.lnT9)

    rate_eval.n_Cl40__Cl41 = rate

@numba.njit()
def He4_Cr67__Fe71(rate_eval, tf):
    # Cr67 + He4 --> Fe71
    rate = 0.0

    # rath 
    rate += np.exp(  -1162.85 + 24.0184*tf.T9i + -2386.41*tf.T913i + 3686.67*tf.T913
                  + -208.969*tf.T9 + 11.5314*tf.T953 + -1787.88*tf.lnT9)

    rate_eval.He4_Cr67__Fe71 = rate

@numba.njit()
def K38__Ar38__weak__wc12(rate_eval, tf):
    # K38 --> Ar38
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.49338)

    rate_eval.K38__Ar38__weak__wc12 = rate

@numba.njit()
def p_Cr66__Mn67(rate_eval, tf):
    # Cr66 + p --> Mn67
    rate = 0.0

    # rath 
    rate += np.exp(  138.57 + -6.92938*tf.T9i + 263.913*tf.T913i + -426.024*tf.T913
                  + 23.7517*tf.T9 + -1.3649*tf.T953 + 212.723*tf.lnT9)

    rate_eval.p_Cr66__Mn67 = rate

@numba.njit()
def p_Cr65__Mn66(rate_eval, tf):
    # Cr65 + p --> Mn66
    rate = 0.0

    # rath 
    rate += np.exp(  135.466 + -6.87354*tf.T9i + 260.735*tf.T913i + -419.124*tf.T913
                  + 23.1679*tf.T9 + -1.31468*tf.T953 + 209.969*tf.lnT9)

    rate_eval.p_Cr65__Mn66 = rate

@numba.njit()
def He4_Cr63__Fe67(rate_eval, tf):
    # Cr63 + He4 --> Fe67
    rate = 0.0

    # rath 
    rate += np.exp(  -1115.29 + 23.3438*tf.T9i + -2318.34*tf.T913i + 3566.99*tf.T913
                  + -201.678*tf.T9 + 11.1177*tf.T953 + -1733.05*tf.lnT9)

    rate_eval.He4_Cr63__Fe67 = rate

@numba.njit()
def p_Ca52__Sc53(rate_eval, tf):
    # Ca52 + p --> Sc53
    rate = 0.0

    # rath 
    rate += np.exp(  112.429 + -5.51426*tf.T9i + 206.74*tf.T913i + -337.891*tf.T913
                  + 18.8846*tf.T9 + -1.08195*tf.T953 + 168.898*tf.lnT9)

    rate_eval.p_Ca52__Sc53 = rate

@numba.njit()
def p_Cr63__Mn64(rate_eval, tf):
    # Cr63 + p --> Mn64
    rate = 0.0

    # rath 
    rate += np.exp(  142.178 + -6.79867*tf.T9i + 259.647*tf.T913i + -424.139*tf.T913
                  + 23.7056*tf.T9 + -1.35004*tf.T953 + 210.648*tf.lnT9)

    rate_eval.p_Cr63__Mn64 = rate

@numba.njit()
def O25__n_F24__weak__mp17(rate_eval, tf):
    # O25 --> n + F24
    rate = 0.0

    # mp17w
    rate += np.exp(  2.40038)

    rate_eval.O25__n_F24__weak__mp17 = rate

@numba.njit()
def He4_Cr62__Fe66(rate_eval, tf):
    # Cr62 + He4 --> Fe66
    rate = 0.0

    # rath 
    rate += np.exp(  -1112.91 + 23.0685*tf.T9i + -2294.7*tf.T913i + 3539.05*tf.T913
                  + -200.833*tf.T9 + 11.0983*tf.T953 + -1716.47*tf.lnT9)

    rate_eval.He4_Cr62__Fe66 = rate

@numba.njit()
def n_Cr62__Cr63(rate_eval, tf):
    # Cr62 + n --> Cr63
    rate = 0.0

    # rath 
    rate += np.exp(  -6.99173 + 0.127778*tf.T9i + -13.8522*tf.T913i + 33.9859*tf.T913
                  + -2.35157*tf.T9 + 0.110531*tf.T953 + -13.5516*tf.lnT9)

    rate_eval.n_Cr62__Cr63 = rate

@numba.njit()
def p_Sc48__n_Ti48(rate_eval, tf):
    # Sc48 + p --> n + Ti48
    rate = 0.0

    # rath 
    rate += np.exp(  118.891 + -5.45559*tf.T9i + 201.123*tf.T913i + -329.189*tf.T913
                  + 18.2769*tf.T9 + -1.03382*tf.T953 + 164.945*tf.lnT9)

    rate_eval.p_Sc48__n_Ti48 = rate

@numba.njit()
def p_Cr61__Mn62(rate_eval, tf):
    # Cr61 + p --> Mn62
    rate = 0.0

    # rath 
    rate += np.exp(  135.751 + -6.69488*tf.T9i + 254.02*tf.T913i + -411.47*tf.T913
                  + 22.7563*tf.T9 + -1.29257*tf.T953 + 205.678*tf.lnT9)

    rate_eval.p_Cr61__Mn62 = rate

@numba.njit()
def Al30__Si30__weak__wc12(rate_eval, tf):
    # Al30 --> Si30
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.65299)

    rate_eval.Al30__Si30__weak__wc12 = rate

@numba.njit()
def n_Ca43__He4_Ar40(rate_eval, tf):
    # Ca43 + n --> He4 + Ar40
    rate = 0.0

    # ths8r
    rate += np.exp(  0.325905 + 4.3289*tf.T913
                  + 1.46375*tf.T9 + -0.180625*tf.T953)

    rate_eval.n_Ca43__He4_Ar40 = rate

@numba.njit()
def He4_Cr60__Fe64(rate_eval, tf):
    # Cr60 + He4 --> Fe64
    rate = 0.0

    # rath 
    rate += np.exp(  -1094.69 + 22.7539*tf.T9i + -2262.97*tf.T913i + 3486.13*tf.T913
                  + -197.51*tf.T9 + 10.8833*tf.T953 + -1691.53*tf.lnT9)

    rate_eval.He4_Cr60__Fe64 = rate

@numba.njit()
def n_Fe51__Fe52(rate_eval, tf):
    # Fe51 + n --> Fe52
    rate = 0.0

    # ths8r
    rate += np.exp(  11.0052 + -0.566649*tf.T913
                  + 0.19001*tf.T9 + -0.0219395*tf.T953)

    rate_eval.n_Fe51__Fe52 = rate

@numba.njit()
def Cr70__Mn70__weak__mo03(rate_eval, tf):
    # Cr70 --> Mn70
    rate = 0.0

    # mo03w
    rate += np.exp(  3.34038)

    rate_eval.Cr70__Mn70__weak__mo03 = rate

@numba.njit()
def n_Cr60__Cr61(rate_eval, tf):
    # Cr60 + n --> Cr61
    rate = 0.0

    # rath 
    rate += np.exp(  22.069 + 0.00212518*tf.T9i + 1.28549*tf.T913i + -13.6658*tf.T913
                  + 2.50621*tf.T9 + -0.293466*tf.T953 + 2.85177*tf.lnT9)

    rate_eval.n_Cr60__Cr61 = rate

@numba.njit()
def He4_Cr59__Fe63(rate_eval, tf):
    # Cr59 + He4 --> Fe63
    rate = 0.0

    # rath 
    rate += np.exp(  -1082.06 + 22.5743*tf.T9i + -2244.96*tf.T913i + 3455.14*tf.T913
                  + -195.802*tf.T9 + 10.8146*tf.T953 + -1677.12*tf.lnT9)

    rate_eval.He4_Cr59__Fe63 = rate

@numba.njit()
def p_Cr59__Mn60(rate_eval, tf):
    # Cr59 + p --> Mn60
    rate = 0.0

    # rath 
    rate += np.exp(  127.333 + -6.55601*tf.T9i + 245.378*tf.T913i + -393.847*tf.T913
                  + 21.6472*tf.T9 + -1.23268*tf.T953 + 198.246*tf.lnT9)

    rate_eval.p_Cr59__Mn60 = rate

@numba.njit()
def He4_Mg19__p_Al22(rate_eval, tf):
    # Mg19 + He4 --> p + Al22
    rate = 0.0

    # ths8r
    rate += np.exp(  44.8898 + -52.6672*tf.T913i + 0.580705*tf.T913
                  + -0.696974*tf.T9 + 0.0518569*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg19__p_Al22 = rate

@numba.njit()
def n_Cr59__Cr60(rate_eval, tf):
    # Cr59 + n --> Cr60
    rate = 0.0

    # rath 
    rate += np.exp(  18.8256 + -0.0340561*tf.T9i + 3.41134*tf.T913i + -9.50349*tf.T913
                  + 0.72232*tf.T9 + -0.0831589*tf.T953 + 3.353*tf.lnT9)

    rate_eval.n_Cr59__Cr60 = rate

@numba.njit()
def He4_Cr58__Fe62(rate_eval, tf):
    # Cr58 + He4 --> Fe62
    rate = 0.0

    # rath 
    rate += np.exp(  -1076.84 + 22.419*tf.T9i + -2230.1*tf.T913i + 3433.8*tf.T913
                  + -194.609*tf.T9 + 10.7292*tf.T953 + -1666.2*tf.lnT9)

    rate_eval.He4_Cr58__Fe62 = rate

@numba.njit()
def p_Cr58__Mn59(rate_eval, tf):
    # Cr58 + p --> Mn59
    rate = 0.0

    # rath 
    rate += np.exp(  126.92 + -6.49724*tf.T9i + 242.318*tf.T913i + -389.478*tf.T913
                  + 21.5166*tf.T9 + -1.24314*tf.T953 + 195.927*tf.lnT9)

    rate_eval.p_Cr58__Mn59 = rate

@numba.njit()
def He4_Cr57__Fe61(rate_eval, tf):
    # Cr57 + He4 --> Fe61
    rate = 0.0

    # rath 
    rate += np.exp(  -1056.15 + 22.0523*tf.T9i + -2195.85*tf.T913i + 3376.81*tf.T913
                  + -191.798*tf.T9 + 10.6664*tf.T953 + -1638.75*tf.lnT9)

    rate_eval.He4_Cr57__Fe61 = rate

@numba.njit()
def p_Cr57__Mn58(rate_eval, tf):
    # Cr57 + p --> Mn58
    rate = 0.0

    # rath 
    rate += np.exp(  125.826 + -6.45332*tf.T9i + 240.736*tf.T913i + -387.018*tf.T913
                  + 21.3525*tf.T9 + -1.22551*tf.T953 + 194.824*tf.lnT9)

    rate_eval.p_Cr57__Mn58 = rate

@numba.njit()
def p_Cr56__Mn57(rate_eval, tf):
    # Cr56 + p --> Mn57
    rate = 0.0

    # rath 
    rate += np.exp(  117.626 + -6.36162*tf.T9i + 233.611*tf.T913i + -369.964*tf.T913
                  + 20.0026*tf.T9 + -1.12378*tf.T953 + 188.055*tf.lnT9)

    rate_eval.p_Cr56__Mn57 = rate

@numba.njit()
def n_Cr56__Cr57(rate_eval, tf):
    # Cr56 + n --> Cr57
    rate = 0.0

    # rath 
    rate += np.exp(  15.8676 + 0.0159805*tf.T9i + -0.919066*tf.T913i + -2.46732*tf.T913
                  + 0.726089*tf.T9 + -0.100137*tf.T953 + -0.130039*tf.lnT9)

    rate_eval.n_Cr56__Cr57 = rate

@numba.njit()
def He4_Cr54__Fe58(rate_eval, tf):
    # Cr54 + He4 --> Fe58
    rate = 0.0

    # ths8r
    rate += np.exp(  63.2926 + -86.9945*tf.T913i + -1.05674*tf.T913
                  + -4.13443*tf.T9 + 0.599141*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr54__Fe58 = rate

@numba.njit()
def p_Cr54__Mn55(rate_eval, tf):
    # Cr54 + p --> Mn55
    rate = 0.0

    # ths8r
    rate += np.exp(  34.9354 + -35.2237*tf.T913i + 2.60768*tf.T913
                  + -1.7864*tf.T9 + 0.134189*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cr54__Mn55 = rate

@numba.njit()
def Cr47__V47__weak__wc12(rate_eval, tf):
    # Cr47 --> V47
    rate = 0.0

    # wc12w
    rate += np.exp(  0.326634)

    rate_eval.Cr47__V47__weak__wc12 = rate

@numba.njit()
def n_Mn49__p_Cr49(rate_eval, tf):
    # Mn49 + n --> p + Cr49
    rate = 0.0

    # ths8r
    rate += np.exp(  21.6064 + -0.816586*tf.T913
                  + 0.240254*tf.T9 + -0.0214987*tf.T953)

    rate_eval.n_Mn49__p_Cr49 = rate

@numba.njit()
def He4_Cr53__Fe57(rate_eval, tf):
    # Cr53 + He4 --> Fe57
    rate = 0.0

    # ths8r
    rate += np.exp(  65.95 + -86.9567*tf.T913i + -12.0579*tf.T913
                  + 1.33466*tf.T9 + -0.14709*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr53__Fe57 = rate

@numba.njit()
def p_Cr53__Mn54(rate_eval, tf):
    # Cr53 + p --> Mn54
    rate = 0.0

    # ths8r
    rate += np.exp(  34.2032 + -35.2197*tf.T913i + 3.74805*tf.T913
                  + -2.77987*tf.T9 + 0.296885*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cr53__Mn54 = rate

@numba.njit()
def He4_Sc48__V52(rate_eval, tf):
    # Sc48 + He4 --> V52
    rate = 0.0

    # rath 
    rate += np.exp(  -957.316 + 15.0869*tf.T9i + -1642.74*tf.T913i + 2707.58*tf.T913
                  + -162.101*tf.T9 + 9.30824*tf.T953 + -1268.27*tf.lnT9)

    rate_eval.He4_Sc48__V52 = rate

@numba.njit()
def n_Cr53__Cr54(rate_eval, tf):
    # Cr53 + n --> Cr54
    rate = 0.0

    # ks03 
    rate += np.exp(  10.8793 + -0.00984544*tf.T9i + -1.26805*tf.T913i + 6.34126*tf.T913
                  + -0.39287*tf.T9 + 0.000487041*tf.T953 + -2.46456*tf.lnT9)

    rate_eval.n_Cr53__Cr54 = rate

@numba.njit()
def p_Cl39__He4_S36(rate_eval, tf):
    # Cl39 + p --> He4 + S36
    rate = 0.0

    # rath 
    rate += np.exp(  100.157 + -4.32864*tf.T9i + 158.557*tf.T913i + -265.12*tf.T913
                  + 14.2241*tf.T9 + -0.729508*tf.T953 + 132.24*tf.lnT9)

    rate_eval.p_Cl39__He4_S36 = rate

@numba.njit()
def p_Cr52__Mn53(rate_eval, tf):
    # Cr52 + p --> Mn53
    rate = 0.0

    # ths8r
    rate += np.exp(  35.6954 + -35.2154*tf.T913i + 0.73019*tf.T913
                  + -1.26018*tf.T9 + 0.121141*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cr52__Mn53 = rate

@numba.njit()
def p_Cr51__Mn52(rate_eval, tf):
    # Cr51 + p --> Mn52
    rate = 0.0

    # ths8r
    rate += np.exp(  35.265 + -35.2111*tf.T913i + 1.49375*tf.T913
                  + -1.48209*tf.T9 + 0.131902*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cr51__Mn52 = rate

@numba.njit()
def p_Cr50__Mn51(rate_eval, tf):
    # Cr50 + p --> Mn51
    rate = 0.0

    # ths8r
    rate += np.exp(  35.8532 + -35.2065*tf.T913i + 0.884621*tf.T913
                  + -1.76421*tf.T9 + 0.202494*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cr50__Mn51 = rate

@numba.njit()
def p_Cr49__Mn50(rate_eval, tf):
    # Cr49 + p --> Mn50
    rate = 0.0

    # ths8r
    rate += np.exp(  36.3884 + -35.2018*tf.T913i + 0.168579*tf.T913
                  + -2.87983*tf.T9 + 0.378768*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cr49__Mn50 = rate

@numba.njit()
def n_O17__O18(rate_eval, tf):
    # O17 + n --> O18
    rate = 0.0

    # bb92n
    rate += np.exp(  4.27026 + -5.69067e-13*tf.T9i + 7.48144e-11*tf.T913i + -2.47239e-10*tf.T913
                  + 2.48052e-11*tf.T9 + -2.07736e-12*tf.T953 + 8.43048e-11*tf.lnT9)
    # bb92r
    rate += np.exp(  20.1798 + -2.12961*tf.T9i + 16.8052*tf.T913i + -30.138*tf.T913
                  + 1.14711*tf.T9 + -0.0220312*tf.T953 + 13.7452*tf.lnT9)

    rate_eval.n_O17__O18 = rate

@numba.njit()
def He4_Cr48__Fe52(rate_eval, tf):
    # Cr48 + He4 --> Fe52
    rate = 0.0

    # ths8r
    rate += np.exp(  65.1754 + -86.7459*tf.T913i + -9.79373*tf.T913
                  + -0.772169*tf.T9 + 0.155883*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr48__Fe52 = rate

@numba.njit()
def He4_Ar45__Ca49(rate_eval, tf):
    # Ar45 + He4 --> Ca49
    rate = 0.0

    # rath 
    rate += np.exp(  -808.583 + 13.0047*tf.T9i + -1414.83*tf.T913i + 2314.15*tf.T913
                  + -138.457*tf.T9 + 7.99912*tf.T953 + -1086.03*tf.lnT9)

    rate_eval.He4_Ar45__Ca49 = rate

@numba.njit()
def He4_K38__p_Ca41(rate_eval, tf):
    # K38 + He4 --> p + Ca41
    rate = 0.0

    # ths8r
    rate += np.exp(  54.4204 + -73.7407*tf.T913i + 0.600725*tf.T913
                  + -0.957475*tf.T9 + 0.0689286*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K38__p_Ca41 = rate

@numba.njit()
def He4_P40__n_Cl43(rate_eval, tf):
    # P40 + He4 --> n + Cl43
    rate = 0.0

    # rath 
    rate += np.exp(  -8.28858 + -3.41403*tf.T9i + -11.4451*tf.T913i + 15.6481*tf.T913
                  + -4.79808*tf.T9 + 0.391308*tf.T953 + 11.1173*tf.lnT9)

    rate_eval.He4_P40__n_Cl43 = rate

@numba.njit()
def n_Cr48__Cr49(rate_eval, tf):
    # Cr48 + n --> Cr49
    rate = 0.0

    # ths8r
    rate += np.exp(  15.8544 + -0.000452357*tf.T913
                  + 0.0412838*tf.T9 + -0.0160865*tf.T953)

    rate_eval.n_Cr48__Cr49 = rate

@numba.njit()
def Fe66__Co66__weak__wc12(rate_eval, tf):
    # Fe66 --> Co66
    rate = 0.0

    # wc12w
    rate += np.exp(  0.454468)

    rate_eval.Fe66__Co66__weak__wc12 = rate

@numba.njit()
def He4_Cr47__Fe51(rate_eval, tf):
    # Cr47 + He4 --> Fe51
    rate = 0.0

    # ths8r
    rate += np.exp(  55.4642 + -86.6989*tf.T913i + -4.56938*tf.T913
                  + 0.0468303*tf.T9 + -0.0433688*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr47__Fe51 = rate

@numba.njit()
def He4_Cr46__Fe50(rate_eval, tf):
    # Cr46 + He4 --> Fe50
    rate = 0.0

    # ths8r
    rate += np.exp(  56.3568 + -86.6499*tf.T913i + -6.44312*tf.T913
                  + 1.15026*tf.T9 + -0.173961*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr46__Fe50 = rate

@numba.njit()
def n_Ne19__He4_O16(rate_eval, tf):
    # Ne19 + n --> He4 + O16
    rate = 0.0

    # ths8r
    rate += np.exp(  17.6409 + 1.70736*tf.T913
                  + -0.132579*tf.T9 + 0.00454218*tf.T953)

    rate_eval.n_Ne19__He4_O16 = rate

@numba.njit()
def p_Cr46__Mn47(rate_eval, tf):
    # Cr46 + p --> Mn47
    rate = 0.0

    # nfisn
    rate += np.exp(  86.3356 + -8.10299*tf.T9i + 10.1754*tf.T913i + -101.635*tf.T913
                  + 6.38471*tf.T9 + -0.370109*tf.T953 + 38.2798*tf.lnT9)
    # nfisn
    rate += np.exp(  -77.4493 + -6.07975*tf.T9i + -51.0865*tf.T913i + 148.149*tf.T913
                  + -22.0328*tf.T9 + 2.39024*tf.T953 + -47.3621*tf.lnT9)
    # nfisn
    rate += np.exp(  41.1709 + -0.513301*tf.T9i + -8.34902*tf.T913i + -49.016*tf.T913
                  + 3.67612*tf.T9 + -0.282377*tf.T953 + 20.8502*tf.lnT9)

    rate_eval.p_Cr46__Mn47 = rate

@numba.njit()
def n_Cr46__Cr47(rate_eval, tf):
    # Cr46 + n --> Cr47
    rate = 0.0

    # ths8r
    rate += np.exp(  15.4822 + -1.5945*tf.T913
                  + 0.39528*tf.T9 + -0.0372417*tf.T953)

    rate_eval.n_Cr46__Cr47 = rate

@numba.njit()
def n_Cr45__Cr46(rate_eval, tf):
    # Cr45 + n --> Cr46
    rate = 0.0

    # ths8r
    rate += np.exp(  13.1792 + -1.49037*tf.T913
                  + 0.393966*tf.T9 + -0.0350405*tf.T953)

    rate_eval.n_Cr45__Cr46 = rate

@numba.njit()
def He4_Cr44__Fe48(rate_eval, tf):
    # Cr44 + He4 --> Fe48
    rate = 0.0

    # ths8r
    rate += np.exp(  52.0335 + -86.5458*tf.T913i + 1.97255*tf.T913
                  + -1.56115*tf.T9 + 0.065487*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr44__Fe48 = rate

@numba.njit()
def n_Cr44__Cr45(rate_eval, tf):
    # Cr44 + n --> Cr45
    rate = 0.0

    # ths8r
    rate += np.exp(  13.5726 + -1.6015*tf.T913
                  + 0.456139*tf.T9 + -0.0493003*tf.T953)

    rate_eval.n_Cr44__Cr45 = rate

@numba.njit()
def n_Sc55__Sc56(rate_eval, tf):
    # Sc55 + n --> Sc56
    rate = 0.0

    # rath 
    rate += np.exp(  16.2134 + -0.0329892*tf.T9i + 3.0244*tf.T913i + -10.37*tf.T913
                  + 1.18614*tf.T9 + -0.115517*tf.T953 + 3.05336*tf.lnT9)

    rate_eval.n_Sc55__Sc56 = rate

@numba.njit()
def He4_Cr43__Fe47(rate_eval, tf):
    # Cr43 + He4 --> Fe47
    rate = 0.0

    # ths8r
    rate += np.exp(  50.9622 + -86.4906*tf.T913i + -1.66143*tf.T913
                  + -0.451078*tf.T9 + 6.28872e-05*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr43__Fe47 = rate

@numba.njit()
def n_Cr43__Cr44(rate_eval, tf):
    # Cr43 + n --> Cr44
    rate = 0.0

    # ths8r
    rate += np.exp(  10.6873 + -0.30956*tf.T913
                  + 0.21955*tf.T9 + -0.0204641*tf.T953)

    rate_eval.n_Cr43__Cr44 = rate

@numba.njit()
def He4_Cr42__Fe46(rate_eval, tf):
    # Cr42 + He4 --> Fe46
    rate = 0.0

    # ths8r
    rate += np.exp(  50.1167 + -86.4328*tf.T913i + -1.84864*tf.T913
                  + -0.274763*tf.T9 + -0.032258*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr42__Fe46 = rate

@numba.njit()
def He4_Cr41__Fe45(rate_eval, tf):
    # Cr41 + He4 --> Fe45
    rate = 0.0

    # ths8r
    rate += np.exp(  48.9964 + -86.3725*tf.T913i + -0.651549*tf.T913
                  + -0.589344*tf.T9 + 0.0069321*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr41__Fe45 = rate

@numba.njit()
def p_P44__He4_Si41(rate_eval, tf):
    # P44 + p --> He4 + Si41
    rate = 0.0

    # rath 
    rate += np.exp(  88.229 + -4.15642*tf.T9i + 151.12*tf.T913i + -251.013*tf.T913
                  + 14.0122*tf.T9 + -0.769527*tf.T953 + 125.064*tf.lnT9)

    rate_eval.p_P44__He4_Si41 = rate

@numba.njit()
def He4_Mg22__Si26(rate_eval, tf):
    # Mg22 + He4 --> Si26
    rate = 0.0

    # ths8r
    rate += np.exp(  35.9065 + -53.0847*tf.T913i + 0.625592*tf.T913
                  + -0.893632*tf.T9 + 0.0691552*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg22__Si26 = rate

@numba.njit()
def He4_V67__Mn71(rate_eval, tf):
    # V67 + He4 --> Mn71
    rate = 0.0

    # rath 
    rate += np.exp(  -1128.38 + 23.3854*tf.T9i + -2322.43*tf.T913i + 3584.73*tf.T913
                  + -203.052*tf.T9 + 11.2091*tf.T953 + -1739.51*tf.lnT9)

    rate_eval.He4_V67__Mn71 = rate

@numba.njit()
def p_V67__Cr68(rate_eval, tf):
    # V67 + p --> Cr68
    rate = 0.0

    # rath 
    rate += np.exp(  138.363 + -6.78881*tf.T9i + 259.615*tf.T913i + -421.364*tf.T913
                  + 23.5947*tf.T9 + -1.33984*tf.T953 + 209.519*tf.lnT9)

    rate_eval.p_V67__Cr68 = rate

@numba.njit()
def He4_V66__Mn70(rate_eval, tf):
    # V66 + He4 --> Mn70
    rate = 0.0

    # rath 
    rate += np.exp(  -1119.61 + 23.3585*tf.T9i + -2316.95*tf.T913i + 3569.61*tf.T913
                  + -201.658*tf.T9 + 11.1093*tf.T953 + -1734.32*tf.lnT9)

    rate_eval.He4_V66__Mn70 = rate

@numba.njit()
def p_V66__Cr67(rate_eval, tf):
    # V66 + p --> Cr67
    rate = 0.0

    # rath 
    rate += np.exp(  140.507 + -6.71815*tf.T9i + 256.212*tf.T913i + -419.494*tf.T913
                  + 23.6658*tf.T9 + -1.34899*tf.T953 + 207.638*tf.lnT9)

    rate_eval.p_V66__Cr67 = rate

@numba.njit()
def n_Mg27__Mg28(rate_eval, tf):
    # Mg27 + n --> Mg28
    rate = 0.0

    # rath 
    rate += np.exp(  4.73336 + 0.0227938*tf.T9i + -4.06138*tf.T913i + 12.6524*tf.T913
                  + -1.01849*tf.T9 + 0.0573214*tf.T953 + -4.82565*tf.lnT9)

    rate_eval.n_Mg27__Mg28 = rate

@numba.njit()
def He4_V64__Mn68(rate_eval, tf):
    # V64 + He4 --> Mn68
    rate = 0.0

    # rath 
    rate += np.exp(  -1100.27 + 22.9853*tf.T9i + -2280.54*tf.T913i + 3511.06*tf.T913
                  + -198.37*tf.T9 + 10.9316*tf.T953 + -1705.82*tf.lnT9)

    rate_eval.He4_V64__Mn68 = rate

@numba.njit()
def n_Al37__Al38(rate_eval, tf):
    # Al37 + n --> Al38
    rate = 0.0

    # rath 
    rate += np.exp(  11.3092 + -0.0501116*tf.T9i + 4.35306*tf.T913i + -12.1723*tf.T913
                  + 1.45015*tf.T9 + -0.109466*tf.T953 + 4.00141*tf.lnT9)

    rate_eval.n_Al37__Al38 = rate

@numba.njit()
def p_V64__Cr65(rate_eval, tf):
    # V64 + p --> Cr65
    rate = 0.0

    # rath 
    rate += np.exp(  135.041 + -6.62609*tf.T9i + 251.455*tf.T913i + -408.186*tf.T913
                  + 22.7269*tf.T9 + -1.28528*tf.T953 + 203.389*tf.lnT9)

    rate_eval.p_V64__Cr65 = rate

@numba.njit()
def He4_O14__p_F17(rate_eval, tf):
    # O14 + He4 --> p + F17
    rate = 0.0

    # Ha96r
    rate += np.exp(  12.1289 + -12.0223*tf.T9i
                  + -1.5*tf.lnT9)
    # Ha96r
    rate += np.exp(  18.6518 + -26.0*tf.T9i
                  + -1.5*tf.lnT9)
    # Ha96n
    rate += np.exp(  40.8358 + -39.388*tf.T913i + -17.4673*tf.T913
                  + 35.3029*tf.T9 + -24.8162*tf.T953 + -0.666667*tf.lnT9)
    # Ha96r
    rate += np.exp(  16.3087 + -22.51*tf.T9i
                  + -1.5*tf.lnT9)
    # Ha96r
    rate += np.exp(  11.1184 + -13.6*tf.T9i
                  + -1.5*tf.lnT9)
    # Ha96r
    rate += np.exp(  -106.091 + -0.453036*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.He4_O14__p_F17 = rate

@numba.njit()
def p_K58__n_Ca58(rate_eval, tf):
    # K58 + p --> n + Ca58
    rate = 0.0

    # rath 
    rate += np.exp(  126.158 + -5.6044*tf.T9i + 212.248*tf.T913i + -345.247*tf.T913
                  + 18.9497*tf.T9 + -1.05275*tf.T953 + 172.39*tf.lnT9)

    rate_eval.p_K58__n_Ca58 = rate

@numba.njit()
def p_V63__Cr64(rate_eval, tf):
    # V63 + p --> Cr64
    rate = 0.0

    # rath 
    rate += np.exp(  128.459 + -6.58293*tf.T9i + 248.772*tf.T913i + -399.693*tf.T913
                  + 22.0581*tf.T9 + -1.25104*tf.T953 + 200.517*tf.lnT9)

    rate_eval.p_V63__Cr64 = rate

@numba.njit()
def n_V62__V63(rate_eval, tf):
    # V62 + n --> V63
    rate = 0.0

    # rath 
    rate += np.exp(  18.4702 + -0.0203914*tf.T9i + 2.24389*tf.T913i + -8.72955*tf.T913
                  + 0.571733*tf.T9 + -0.0571194*tf.T953 + 2.54796*tf.lnT9)

    rate_eval.n_V62__V63 = rate

@numba.njit()
def He4_V61__Mn65(rate_eval, tf):
    # V61 + He4 --> Mn65
    rate = 0.0

    # rath 
    rate += np.exp(  -1073.14 + 22.3172*tf.T9i + -2218.55*tf.T913i + 3418.12*tf.T913
                  + -193.623*tf.T9 + 10.6816*tf.T953 + -1658.71*tf.lnT9)

    rate_eval.He4_V61__Mn65 = rate

@numba.njit()
def He4_V60__Mn64(rate_eval, tf):
    # V60 + He4 --> Mn64
    rate = 0.0

    # rath 
    rate += np.exp(  -1062.95 + 22.2478*tf.T9i + -2209.74*tf.T913i + 3398.65*tf.T913
                  + -192.115*tf.T9 + 10.5887*tf.T953 + -1651.15*tf.lnT9)

    rate_eval.He4_V60__Mn64 = rate

@numba.njit()
def p_Ne32__He4_F29(rate_eval, tf):
    # Ne32 + p --> He4 + F29
    rate = 0.0

    # rpsmr
    rate += np.exp(  47.525 + -2.74706*tf.T9i + 96.9329*tf.T913i + -148.992*tf.T913
                  + 7.03634*tf.T9 + -0.335939*tf.T953 + 80.0235*tf.lnT9)

    rate_eval.p_Ne32__He4_F29 = rate

@numba.njit()
def p_V60__Cr61(rate_eval, tf):
    # V60 + p --> Cr61
    rate = 0.0

    # rath 
    rate += np.exp(  130.202 + -6.42196*tf.T9i + 241.698*tf.T913i + -392.335*tf.T913
                  + 21.7775*tf.T9 + -1.23681*tf.T953 + 195.997*tf.lnT9)

    rate_eval.p_V60__Cr61 = rate

@numba.njit()
def p_V59__Cr60(rate_eval, tf):
    # V59 + p --> Cr60
    rate = 0.0

    # rath 
    rate += np.exp(  124.563 + -6.37984*tf.T9i + 239.251*tf.T913i + -384.715*tf.T913
                  + 21.1691*tf.T9 + -1.20211*tf.T953 + 193.396*tf.lnT9)

    rate_eval.p_V59__Cr60 = rate

@numba.njit()
def Na36__n_Mg35__weak__mp17(rate_eval, tf):
    # Na36 --> n + Mg35
    rate = 0.0

    # mp17w
    rate += np.exp(  5.07133)

    rate_eval.Na36__n_Mg35__weak__mp17 = rate

@numba.njit()
def n_V59__V60(rate_eval, tf):
    # V59 + n --> V60
    rate = 0.0

    # rath 
    rate += np.exp(  18.7823 + -0.0471284*tf.T9i + 4.66058*tf.T913i + -12.9053*tf.T913
                  + 1.19361*tf.T9 + -0.12209*tf.T953 + 4.54137*tf.lnT9)

    rate_eval.n_V59__V60 = rate

@numba.njit()
def p_V58__Cr59(rate_eval, tf):
    # V58 + p --> Cr59
    rate = 0.0

    # rath 
    rate += np.exp(  123.269 + -6.32093*tf.T9i + 236.096*tf.T913i + -379.371*tf.T913
                  + 20.8536*tf.T9 + -1.18323*tf.T953 + 190.906*tf.lnT9)

    rate_eval.p_V58__Cr59 = rate

@numba.njit()
def He4_V57__Mn61(rate_eval, tf):
    # V57 + He4 --> Mn61
    rate = 0.0

    # rath 
    rate += np.exp(  -1032.94 + 21.5814*tf.T9i + -2146.89*tf.T913i + 3301.76*tf.T913
                  + -187.021*tf.T9 + 10.3185*tf.T953 + -1602.84*tf.lnT9)

    rate_eval.He4_V57__Mn61 = rate

@numba.njit()
def p_V57__Cr58(rate_eval, tf):
    # V57 + p --> Cr58
    rate = 0.0

    # rath 
    rate += np.exp(  121.756 + -6.26939*tf.T9i + 233.79*tf.T913i + -375.918*tf.T913
                  + 20.6777*tf.T9 + -1.177*tf.T953 + 189.234*tf.lnT9)

    rate_eval.p_V57__Cr58 = rate

@numba.njit()
def He4_V56__Mn60(rate_eval, tf):
    # V56 + He4 --> Mn60
    rate = 0.0

    # rath 
    rate += np.exp(  -1020.61 + 21.3578*tf.T9i + -2125.18*tf.T913i + 3265.59*tf.T913
                  + -184.962*tf.T9 + 10.2108*tf.T953 + -1585.62*tf.lnT9)

    rate_eval.He4_V56__Mn60 = rate

@numba.njit()
def He4_Na37__n_Al40(rate_eval, tf):
    # Na37 + He4 --> n + Al40
    rate = 0.0

    # rath 
    rate += np.exp(  83.5009 + -3.55614*tf.T9i + 86.7654*tf.T913i + -179.064*tf.T913
                  + 8.50648*tf.T9 + -0.432823*tf.T953 + 93.0433*tf.lnT9)

    rate_eval.He4_Na37__n_Al40 = rate

@numba.njit()
def n_V55__V56(rate_eval, tf):
    # V55 + n --> V56
    rate = 0.0

    # rath 
    rate += np.exp(  18.6471 + -0.0277628*tf.T9i + 2.70956*tf.T913i + -9.42123*tf.T913
                  + 1.02955*tf.T9 + -0.105149*tf.T953 + 2.82123*tf.lnT9)

    rate_eval.n_V55__V56 = rate

@numba.njit()
def He4_V54__Mn58(rate_eval, tf):
    # V54 + He4 --> Mn58
    rate = 0.0

    # rath 
    rate += np.exp(  -1006.32 + 21.021*tf.T9i + -2092.84*tf.T913i + 3217.31*tf.T913
                  + -182.365*tf.T9 + 10.0724*tf.T953 + -1561.39*tf.lnT9)

    rate_eval.He4_V54__Mn58 = rate

@numba.njit()
def p_V54__Cr55(rate_eval, tf):
    # V54 + p --> Cr55
    rate = 0.0

    # rath 
    rate += np.exp(  117.58 + -6.13155*tf.T9i + 227.736*tf.T913i + -363.747*tf.T913
                  + 19.5042*tf.T9 + -1.04096*tf.T953 + 184.273*tf.lnT9)

    rate_eval.p_V54__Cr55 = rate

@numba.njit()
def He4_V53__Mn57(rate_eval, tf):
    # V53 + He4 --> Mn57
    rate = 0.0

    # rath 
    rate += np.exp(  -981.042 + 21.3911*tf.T9i + -2108.54*tf.T913i + 3205.86*tf.T913
                  + -179.713*tf.T9 + 9.84449*tf.T953 + -1565.22*tf.lnT9)

    rate_eval.He4_V53__Mn57 = rate

@numba.njit()
def p_V53__Cr54(rate_eval, tf):
    # V53 + p --> Cr54
    rate = 0.0

    # rath 
    rate += np.exp(  118.487 + -6.02482*tf.T9i + 221.178*tf.T913i + -358.083*tf.T913
                  + 19.6168*tf.T9 + -1.07563*tf.T953 + 179.858*tf.lnT9)

    rate_eval.p_V53__Cr54 = rate

@numba.njit()
def n_V53__V54(rate_eval, tf):
    # V53 + n --> V54
    rate = 0.0

    # rath 
    rate += np.exp(  25.1798 + -0.0520468*tf.T9i + 5.66438*tf.T913i + -18.9001*tf.T913
                  + 1.86255*tf.T9 + -0.152791*tf.T953 + 6.0526*tf.lnT9)

    rate_eval.n_V53__V54 = rate

@numba.njit()
def He4_V52__Mn56(rate_eval, tf):
    # V52 + He4 --> Mn56
    rate = 0.0

    # rath 
    rate += np.exp(  -1005.63 + 20.9554*tf.T9i + -2084.52*tf.T913i + 3208.64*tf.T913
                  + -181.758*tf.T9 + 10.0347*tf.T953 + -1556.85*tf.lnT9)

    rate_eval.He4_V52__Mn56 = rate

@numba.njit()
def p_V62__n_Cr62(rate_eval, tf):
    # V62 + p --> n + Cr62
    rate = 0.0

    # rath 
    rate += np.exp(  137.103 + -6.52801*tf.T9i + 246.042*tf.T913i + -394.365*tf.T913
                  + 21.4898*tf.T9 + -1.19367*tf.T953 + 198.374*tf.lnT9)

    rate_eval.p_V62__n_Cr62 = rate

@numba.njit()
def He4_Ne25__Mg29(rate_eval, tf):
    # Ne25 + He4 --> Mg29
    rate = 0.0

    # rath 
    rate += np.exp(  51.7119 + -2.54003*tf.T9i + 46.3681*tf.T913i + -113.493*tf.T913
                  + 4.77744*tf.T9 + -0.209114*tf.T953 + 61.0263*tf.lnT9)

    rate_eval.He4_Ne25__Mg29 = rate

@numba.njit()
def p_V52__Cr53(rate_eval, tf):
    # V52 + p --> Cr53
    rate = 0.0

    # rath 
    rate += np.exp(  129.295 + -6.02127*tf.T9i + 224.733*tf.T913i + -373.356*tf.T913
                  + 21.346*tf.T9 + -1.24075*tf.T953 + 184.549*tf.lnT9)

    rate_eval.p_V52__Cr53 = rate

@numba.njit()
def n_V51__V52(rate_eval, tf):
    # V51 + n --> V52
    rate = 0.0

    # ks03 
    rate += np.exp(  3.43672 + 0.00903385*tf.T9i + -4.14102*tf.T913i + 17.4073*tf.T913
                  + -1.59715*tf.T9 + 0.114181*tf.T953 + -5.93987*tf.lnT9)

    rate_eval.n_V51__V52 = rate

@numba.njit()
def He4_V50__Mn54(rate_eval, tf):
    # V50 + He4 --> Mn54
    rate = 0.0

    # ths8r
    rate += np.exp(  63.3156 + -84.4058*tf.T913i + -6.25173*tf.T913
                  + -1.31339*tf.T9 + 0.208695*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V50__Mn54 = rate

@numba.njit()
def He4_V65__Mn69(rate_eval, tf):
    # V65 + He4 --> Mn69
    rate = 0.0

    # rath 
    rate += np.exp(  -1110.8 + 23.0448*tf.T9i + -2289.14*tf.T913i + 3531.08*tf.T913
                  + -199.964*tf.T9 + 11.035*tf.T953 + -1713.57*tf.lnT9)

    rate_eval.He4_V65__Mn69 = rate

@numba.njit()
def p_V50__Cr51(rate_eval, tf):
    # V50 + p --> Cr51
    rate = 0.0

    # ths8r
    rate += np.exp(  34.5894 + -34.2216*tf.T913i + 2.39774*tf.T913
                  + -2.15306*tf.T9 + 0.232283*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V50__Cr51 = rate

@numba.njit()
def He4_Ne32__n_Mg35(rate_eval, tf):
    # Ne32 + He4 --> n + Mg35
    rate = 0.0

    # rath 
    rate += np.exp(  74.8548 + -3.03648*tf.T9i + 68.8699*tf.T913i + -150.02*tf.T913
                  + 6.96002*tf.T9 + -0.345295*tf.T953 + 78.2557*tf.lnT9)

    rate_eval.He4_Ne32__n_Mg35 = rate

@numba.njit()
def He4_F16__p_Ne19(rate_eval, tf):
    # F16 + He4 --> p + Ne19
    rate = 0.0

    # rpsmr
    rate += np.exp(  48.4419 + -1.67449*tf.T9i + 14.6635*tf.T913i + -65.6394*tf.T913
                  + 2.4479*tf.T9 + -0.102505*tf.T953 + 36.1187*tf.lnT9)

    rate_eval.He4_F16__p_Ne19 = rate

@numba.njit()
def n_V49__V50(rate_eval, tf):
    # V49 + n --> V50
    rate = 0.0

    # ths8r
    rate += np.exp(  17.5445 + -1.8725*tf.T913
                  + 0.291609*tf.T9 + -0.0370216*tf.T953)

    rate_eval.n_V49__V50 = rate

@numba.njit()
def p_V48__Cr49(rate_eval, tf):
    # V48 + p --> Cr49
    rate = 0.0

    # ths8r
    rate += np.exp(  34.5168 + -34.2123*tf.T913i + 2.51264*tf.T913
                  + -2.09211*tf.T9 + 0.219444*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V48__Cr49 = rate

@numba.njit()
def n_V48__V49(rate_eval, tf):
    # V48 + n --> V49
    rate = 0.0

    # ths8r
    rate += np.exp(  17.8835 + -0.917026*tf.T913
                  + -0.109162*tf.T9 + 0.0127488*tf.T953)

    rate_eval.n_V48__V49 = rate

@numba.njit()
def n_S28__S29(rate_eval, tf):
    # S28 + n --> S29
    rate = 0.0

    # ths8r
    rate += np.exp(  7.8907 + 1.8911*tf.T913
                  + -0.229084*tf.T9 + 0.0178048*tf.T953)

    rate_eval.n_S28__S29 = rate

@numba.njit()
def He4_V47__Mn51(rate_eval, tf):
    # V47 + He4 --> Mn51
    rate = 0.0

    # ths8r
    rate += np.exp(  56.8618 + -84.2732*tf.T913i + -2.98061*tf.T913
                  + -0.531361*tf.T9 + 0.023612*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V47__Mn51 = rate

@numba.njit()
def p_S42__n_Cl42(rate_eval, tf):
    # S42 + p --> n + Cl42
    rate = 0.0

    # rath 
    rate += np.exp(  97.4651 + -4.27377*tf.T9i + 155.442*tf.T913i + -255.372*tf.T913
                  + 13.9608*tf.T9 + -0.77733*tf.T953 + 128.372*tf.lnT9)

    rate_eval.p_S42__n_Cl42 = rate

@numba.njit()
def p_Sc46__n_Ti46(rate_eval, tf):
    # Sc46 + p --> n + Ti46
    rate = 0.0

    # rath 
    rate += np.exp(  120.144 + -5.3851*tf.T9i + 200.092*tf.T913i + -329.451*tf.T913
                  + 18.1752*tf.T9 + -1.01788*tf.T953 + 164.827*tf.lnT9)

    rate_eval.p_Sc46__n_Ti46 = rate

@numba.njit()
def n_V47__V48(rate_eval, tf):
    # V47 + n --> V48
    rate = 0.0

    # ths8r
    rate += np.exp(  17.5513 + -2.40159*tf.T913
                  + 0.594573*tf.T9 + -0.0682896*tf.T953)

    rate_eval.n_V47__V48 = rate

@numba.njit()
def He4_V46__Mn50(rate_eval, tf):
    # V46 + He4 --> Mn50
    rate = 0.0

    # ths8r
    rate += np.exp(  54.311 + -84.2255*tf.T913i + -4.85634*tf.T913
                  + 0.0528515*tf.T9 + -0.0425496*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V46__Mn50 = rate

@numba.njit()
def p_V46__Cr47(rate_eval, tf):
    # V46 + p --> Cr47
    rate = 0.0

    # nfisn
    rate += np.exp(  -109.212 + -23.6545*tf.T9i + 210.899*tf.T913i + -78.1586*tf.T913
                  + 0.307833*tf.T9 + 0.0410555*tf.T953 + 80.7382*tf.lnT9)
    # nfisn
    rate += np.exp(  -85.0084 + -6.64565*tf.T9i + -17.9114*tf.T913i + 122.683*tf.T913
                  + -13.2648*tf.T9 + 0.972426*tf.T953 + -33.5469*tf.lnT9)
    # nfisn
    rate += np.exp(  3.35155 + -1.35204*tf.T9i + -91.1518*tf.T913i + 93.9165*tf.T913
                  + -6.05277*tf.T9 + 0.426188*tf.T953 + -53.3212*tf.lnT9)
    # nfisn
    rate += np.exp(  130.692 + 0.525361*tf.T9i + -112.367*tf.T913i + 154.173*tf.T913
                  + 2221.52*tf.T9 + -7249.28*tf.T953 + 31.2256*tf.lnT9)
    # nfisn
    rate += np.exp(  23.554 + -0.53633*tf.T9i + -14.4186*tf.T913i + -17.3717*tf.T913
                  + -0.352764*tf.T9 + 0.0837867*tf.T953 + 11.5594*tf.lnT9)

    rate_eval.p_V46__Cr47 = rate

@numba.njit()
def p_Si38__P39(rate_eval, tf):
    # Si38 + p --> P39
    rate = 0.0

    # rath 
    rate += np.exp(  79.1232 + -3.73242*tf.T9i + 134.775*tf.T913i + -223.727*tf.T913
                  + 12.2594*tf.T9 + -0.68539*tf.T953 + 112.208*tf.lnT9)

    rate_eval.p_Si38__P39 = rate

@numba.njit()
def n_V46__V47(rate_eval, tf):
    # V46 + n --> V47
    rate = 0.0

    # ths8r
    rate += np.exp(  15.7405 + -0.692996*tf.T913
                  + 0.316873*tf.T9 + -0.0417235*tf.T953)

    rate_eval.n_V46__V47 = rate

@numba.njit()
def He4_V45__Mn49(rate_eval, tf):
    # V45 + He4 --> Mn49
    rate = 0.0

    # ths8r
    rate += np.exp(  51.8178 + -84.1758*tf.T913i + -2.09835*tf.T913
                  + -0.662318*tf.T9 + 0.0293536*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V45__Mn49 = rate

@numba.njit()
def p_Mn63__Fe64(rate_eval, tf):
    # Mn63 + p --> Fe64
    rate = 0.0

    # rath 
    rate += np.exp(  141.222 + -6.98455*tf.T9i + 265.829*tf.T913i + -430.135*tf.T913
                  + 23.8055*tf.T9 + -1.35225*tf.T953 + 214.893*tf.lnT9)

    rate_eval.p_Mn63__Fe64 = rate

@numba.njit()
def n_V45__V46(rate_eval, tf):
    # V45 + n --> V46
    rate = 0.0

    # ths8r
    rate += np.exp(  12.5642 + -1.62632*tf.T913
                  + 0.391829*tf.T9 + -0.0403093*tf.T953)

    rate_eval.n_V45__V46 = rate

@numba.njit()
def He4_V43__Mn47(rate_eval, tf):
    # V43 + He4 --> Mn47
    rate = 0.0

    # ths8r
    rate += np.exp(  48.5003 + -84.0702*tf.T913i + 8.01358*tf.T913
                  + -4.00362*tf.T9 + 0.362668*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V43__Mn47 = rate

@numba.njit()
def p_V43__Cr44(rate_eval, tf):
    # V43 + p --> Cr44
    rate = 0.0

    # ths8r
    rate += np.exp(  38.5903 + -34.1852*tf.T913i + -2.59134*tf.T913
                  + -2.59126*tf.T9 + 0.357806*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V43__Cr44 = rate

@numba.njit()
def p_P40__n_S40(rate_eval, tf):
    # P40 + p --> n + S40
    rate = 0.0

    # rath 
    rate += np.exp(  94.6429 + -4.01217*tf.T9i + 146.158*tf.T913i + -242.083*tf.T913
                  + 13.2582*tf.T9 + -0.738242*tf.T953 + 121.34*tf.lnT9)

    rate_eval.p_P40__n_S40 = rate

@numba.njit()
def p_Al42__He4_Mg39(rate_eval, tf):
    # Al42 + p --> He4 + Mg39
    rate = 0.0

    # rath 
    rate += np.exp(  72.327 + -3.7063*tf.T9i + 133.512*tf.T913i + -214.898*tf.T913
                  + 11.3233*tf.T9 + -0.590721*tf.T953 + 109.52*tf.lnT9)

    rate_eval.p_Al42__He4_Mg39 = rate

@numba.njit()
def n_V42__V43(rate_eval, tf):
    # V42 + n --> V43
    rate = 0.0

    # ths8r
    rate += np.exp(  11.2785 + 0.054772*tf.T913
                  + 0.0806926*tf.T9 + -0.00361548*tf.T953)

    rate_eval.n_V42__V43 = rate

@numba.njit()
def He4_V41__Mn45(rate_eval, tf):
    # V41 + He4 --> Mn45
    rate = 0.0

    # ths8r
    rate += np.exp(  49.1422 + -83.9551*tf.T913i + -1.22789*tf.T913
                  + -0.494458*tf.T9 + 0.00588069*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V41__Mn45 = rate

@numba.njit()
def n_Fe57__He4_Cr54(rate_eval, tf):
    # Fe57 + n --> He4 + Cr54
    rate = 0.0

    # ths8r
    rate += np.exp(  -6.72376 + 4.48478*tf.T913
                  + 2.88431*tf.T9 + -0.366076*tf.T953)

    rate_eval.n_Fe57__He4_Cr54 = rate

@numba.njit()
def p_V41__Cr42(rate_eval, tf):
    # V41 + p --> Cr42
    rate = 0.0

    # ths8r
    rate += np.exp(  38.0351 + -34.1725*tf.T913i + -3.8815*tf.T913
                  + -2.57735*tf.T9 + 0.377253*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V41__Cr42 = rate

@numba.njit()
def C16__n_N15__weak__wc12(rate_eval, tf):
    # C16 --> n + N15
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.0848732)

    rate_eval.C16__n_N15__weak__wc12 = rate

@numba.njit()
def n_V41__V42(rate_eval, tf):
    # V41 + n --> V42
    rate = 0.0

    # ths8r
    rate += np.exp(  9.98584 + 0.260614*tf.T913
                  + 0.122073*tf.T9 + -0.0123217*tf.T953)

    rate_eval.n_V41__V42 = rate

@numba.njit()
def He4_V39__Mn43(rate_eval, tf):
    # V39 + He4 --> Mn43
    rate = 0.0

    # ths8r
    rate += np.exp(  47.2727 + -83.8293*tf.T913i + -0.483402*tf.T913
                  + -0.591152*tf.T9 + 0.00876387*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V39__Mn43 = rate

@numba.njit()
def n_Mn54__Mn55(rate_eval, tf):
    # Mn54 + n --> Mn55
    rate = 0.0

    # ths8r
    rate += np.exp(  18.4705 + -2.56572*tf.T913
                  + 0.352447*tf.T9 + -0.0375878*tf.T953)

    rate_eval.n_Mn54__Mn55 = rate

@numba.njit()
def n_Ti64__Ti65(rate_eval, tf):
    # Ti64 + n --> Ti65
    rate = 0.0

    # rath 
    rate += np.exp(  25.4803 + -0.107219*tf.T9i + 11.7974*tf.T913i + -38.1994*tf.T913
                  + 5.11414*tf.T9 + -0.490145*tf.T953 + 12.4894*tf.lnT9)

    rate_eval.n_Ti64__Ti65 = rate

@numba.njit()
def He4_Ti63__Cr67(rate_eval, tf):
    # Ti63 + He4 --> Cr67
    rate = 0.0

    # rath 
    rate += np.exp(  -1061.16 + 21.9568*tf.T9i + -2183.64*tf.T913i + 3369.58*tf.T913
                  + -191.003*tf.T9 + 10.5457*tf.T953 + -1634.14*tf.lnT9)

    rate_eval.He4_Ti63__Cr67 = rate

@numba.njit()
def p_Ti63__V64(rate_eval, tf):
    # Ti63 + p --> V64
    rate = 0.0

    # rath 
    rate += np.exp(  125.937 + -6.39307*tf.T9i + 241.699*tf.T913i + -389.165*tf.T913
                  + 21.5524*tf.T9 + -1.21526*tf.T953 + 194.879*tf.lnT9)

    rate_eval.p_Ti63__V64 = rate

@numba.njit()
def p_Ti62__V63(rate_eval, tf):
    # Ti62 + p --> V63
    rate = 0.0

    # rath 
    rate += np.exp(  125.068 + -6.34634*tf.T9i + 239.654*tf.T913i + -386.117*tf.T913
                  + 21.433*tf.T9 + -1.22281*tf.T953 + 193.41*tf.lnT9)

    rate_eval.p_Ti62__V63 = rate

@numba.njit()
def He4_Ti61__Cr65(rate_eval, tf):
    # Ti61 + He4 --> Cr65
    rate = 0.0

    # rath 
    rate += np.exp(  -1046.75 + 21.6345*tf.T9i + -2152.49*tf.T913i + 3322.28*tf.T913
                  + -188.535*tf.T9 + 10.417*tf.T953 + -1610.49*tf.lnT9)

    rate_eval.He4_Ti61__Cr65 = rate

@numba.njit()
def Al39__n_Si38__weak__mp17(rate_eval, tf):
    # Al39 --> n + Si38
    rate = 0.0

    # mp17w
    rate += np.exp(  4.47227)

    rate_eval.Al39__n_Si38__weak__mp17 = rate

@numba.njit()
def n_Ne16__He4_O13(rate_eval, tf):
    # Ne16 + n --> He4 + O13
    rate = 0.0

    # ths8r
    rate += np.exp(  16.5763 + 0.149648*tf.T913
                  + 0.156816*tf.T9 + -0.0192189*tf.T953)

    rate_eval.n_Ne16__He4_O13 = rate

@numba.njit()
def p_N12__O13(rate_eval, tf):
    # N12 + p --> O13
    rate = 0.0

    # wiesr
    rate += np.exp(  7.95997 + -14.32*tf.T9i + 1.46937e-08*tf.T913i + -2.46688e-08*tf.T913
                  + 1.64945e-09*tf.T9 + -1.09914e-10*tf.T953 + -1.5*tf.lnT9)
    # wiesn
    rate += np.exp(  20.2322 + -1.43389e-12*tf.T9i + -15.13*tf.T913i + -8.09285e-10*tf.T913
                  + 9.41522e-11*tf.T9 + -8.88739e-12*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_N12__O13 = rate

@numba.njit()
def p_Ti61__V62(rate_eval, tf):
    # Ti61 + p --> V62
    rate = 0.0

    # rath 
    rate += np.exp(  121.935 + -6.2852*tf.T9i + 236.014*tf.T913i + -378.819*tf.T913
                  + 20.8948*tf.T9 + -1.18502*tf.T953 + 190.326*tf.lnT9)

    rate_eval.p_Ti61__V62 = rate

@numba.njit()
def p_Ti60__V61(rate_eval, tf):
    # Ti60 + p --> V61
    rate = 0.0

    # rath 
    rate += np.exp(  122.621 + -6.24428*tf.T9i + 234.706*tf.T913i + -377.957*tf.T913
                  + 20.8952*tf.T9 + -1.19278*tf.T953 + 189.645*tf.lnT9)

    rate_eval.p_Ti60__V61 = rate

@numba.njit()
def n_Ti60__Ti61(rate_eval, tf):
    # Ti60 + n --> Ti61
    rate = 0.0

    # rath 
    rate += np.exp(  28.0507 + -0.101343*tf.T9i + 10.8885*tf.T913i + -34.3955*tf.T913
                  + 4.0236*tf.T9 + -0.378264*tf.T953 + 11.3678*tf.lnT9)

    rate_eval.n_Ti60__Ti61 = rate

@numba.njit()
def p_Ti58__V59(rate_eval, tf):
    # Ti58 + p --> V59
    rate = 0.0

    # rath 
    rate += np.exp(  121.167 + -6.14764*tf.T9i + 230.439*tf.T913i + -371.772*tf.T913
                  + 20.6048*tf.T9 + -1.18339*tf.T953 + 186.572*tf.lnT9)

    rate_eval.p_Ti58__V59 = rate

@numba.njit()
def C21__n_C20(rate_eval, tf):
    # C21 --> n + C20
    rate = 0.0

    # wc12s
    rate += np.exp(  16.9556)

    rate_eval.C21__n_C20 = rate

@numba.njit()
def p_Ti57__V58(rate_eval, tf):
    # Ti57 + p --> V58
    rate = 0.0

    # rath 
    rate += np.exp(  118.754 + -6.09336*tf.T9i + 227.643*tf.T913i + -366.674*tf.T913
                  + 20.236*tf.T9 + -1.1504*tf.T953 + 184.332*tf.lnT9)

    rate_eval.p_Ti57__V58 = rate

@numba.njit()
def p_Ti56__V57(rate_eval, tf):
    # Ti56 + p --> V57
    rate = 0.0

    # rath 
    rate += np.exp(  119.017 + -6.04264*tf.T9i + 225.48*tf.T913i + -364.381*tf.T913
                  + 20.2408*tf.T9 + -1.16629*tf.T953 + 182.915*tf.lnT9)

    rate_eval.p_Ti56__V57 = rate

@numba.njit()
def p_Fe63__n_Co63(rate_eval, tf):
    # Fe63 + p --> n + Co63
    rate = 0.0

    # rath 
    rate += np.exp(  143.038 + -7.11455*tf.T9i + 266.727*tf.T913i + -423.91*tf.T913
                  + 23.017*tf.T9 + -1.28153*tf.T953 + 214.263*tf.lnT9)

    rate_eval.p_Fe63__n_Co63 = rate

@numba.njit()
def p_Ti55__V56(rate_eval, tf):
    # Ti55 + p --> V56
    rate = 0.0

    # rath 
    rate += np.exp(  114.93 + -5.96945*tf.T9i + 220.842*tf.T913i + -355.152*tf.T913
                  + 19.6015*tf.T9 + -1.12286*tf.T953 + 178.965*tf.lnT9)

    rate_eval.p_Ti55__V56 = rate

@numba.njit()
def p_Cr58__n_Mn58(rate_eval, tf):
    # Cr58 + p --> n + Mn58
    rate = 0.0

    # rath 
    rate += np.exp(  132.022 + -6.49066*tf.T9i + 241.396*tf.T913i + -385.207*tf.T913
                  + 20.9639*tf.T9 + -1.17136*tf.T953 + 194.749*tf.lnT9)

    rate_eval.p_Cr58__n_Mn58 = rate

@numba.njit()
def p_Ar47__n_K47(rate_eval, tf):
    # Ar47 + p --> n + K47
    rate = 0.0

    # rath 
    rate += np.exp(  107.864 + -4.8811*tf.T9i + 179.683*tf.T913i + -292.631*tf.T913
                  + 16.0213*tf.T9 + -0.894668*tf.T953 + 147.2*tf.lnT9)

    rate_eval.p_Ar47__n_K47 = rate

@numba.njit()
def n_Ti55__Ti56(rate_eval, tf):
    # Ti55 + n --> Ti56
    rate = 0.0

    # rath 
    rate += np.exp(  1.25912 + 0.0550371*tf.T9i + -7.13219*tf.T913i + 17.8487*tf.T913
                  + -1.02831*tf.T9 + 0.00957004*tf.T953 + -7.44593*tf.lnT9)

    rate_eval.n_Ti55__Ti56 = rate

@numba.njit()
def p_Ar36__K37(rate_eval, tf):
    # Ar36 + p --> K37
    rate = 0.0

    # il10r
    rate += np.exp(  3.18278 + -8.98031*tf.T9i + 7.50962*tf.T913
                  + -1.68675*tf.T9 + 0.189725*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  4.69769 + -3.6251*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  21.4923 + -28.9682*tf.T913i
                  + -1.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ar36__K37 = rate

@numba.njit()
def p_Ti54__V55(rate_eval, tf):
    # Ti54 + p --> V55
    rate = 0.0

    # rath 
    rate += np.exp(  118.152 + -5.94369*tf.T9i + 221.254*tf.T913i + -359.065*tf.T913
                  + 20.026*tf.T9 + -1.15636*tf.T953 + 179.991*tf.lnT9)

    rate_eval.p_Ti54__V55 = rate

@numba.njit()
def He4_Ti53__Cr57(rate_eval, tf):
    # Ti53 + He4 --> Cr57
    rate = 0.0

    # rath 
    rate += np.exp(  -962.487 + 20.1057*tf.T9i + -2003.6*tf.T913i + 3078.78*tf.T913
                  + -174.653*tf.T9 + 9.64876*tf.T953 + -1493.8*tf.lnT9)

    rate_eval.He4_Ti53__Cr57 = rate

@numba.njit()
def p_Ti53__V54(rate_eval, tf):
    # Ti53 + p --> V54
    rate = 0.0

    # rath 
    rate += np.exp(  110.037 + -5.87119*tf.T9i + 215.907*tf.T913i + -344.234*tf.T913
                  + 18.5032*tf.T9 + -1.00772*tf.T953 + 174.662*tf.lnT9)

    rate_eval.p_Ti53__V54 = rate

@numba.njit()
def n_Ti57__Ti58(rate_eval, tf):
    # Ti57 + n --> Ti58
    rate = 0.0

    # rath 
    rate += np.exp(  9.66558 + 0.00646072*tf.T9i + -1.68336*tf.T913i + 3.1453*tf.T913
                  + 0.155107*tf.T9 + -0.0696797*tf.T953 + -1.91212*tf.lnT9)

    rate_eval.n_Ti57__Ti58 = rate

@numba.njit()
def He4_Ti52__Cr56(rate_eval, tf):
    # Ti52 + He4 --> Cr56
    rate = 0.0

    # rath 
    rate += np.exp(  -981.905 + 20.1341*tf.T9i + -2009.07*tf.T913i + 3105.59*tf.T913
                  + -176.936*tf.T9 + 9.80074*tf.T953 + -1502.61*tf.lnT9)

    rate_eval.He4_Ti52__Cr56 = rate

@numba.njit()
def C12_Ne20__n_S31(rate_eval, tf):
    # Ne20 + C12 --> n + S31
    rate = 0.0

    # rolfr
    rate += np.exp(  -342.129 + -54.118*tf.T9i + 638.957*tf.T913i + -289.04*tf.T913
                  + -3.53144*tf.T9 + 0.648991*tf.T953 + 297.721*tf.lnT9)

    rate_eval.C12_Ne20__n_S31 = rate

@numba.njit()
def p_Ti52__V53(rate_eval, tf):
    # Ti52 + p --> V53
    rate = 0.0

    # rath 
    rate += np.exp(  116.703 + -5.83346*tf.T9i + 215.615*tf.T913i + -350.828*tf.T913
                  + 19.6134*tf.T9 + -1.12863*tf.T953 + 175.637*tf.lnT9)

    rate_eval.p_Ti52__V53 = rate

@numba.njit()
def n_Ti52__Ti53(rate_eval, tf):
    # Ti52 + n --> Ti53
    rate = 0.0

    # rath 
    rate += np.exp(  12.8478 + 0.00523058*tf.T9i + -0.589214*tf.T913i + 0.239212*tf.T913
                  + 0.267487*tf.T9 + -0.0579114*tf.T953 + -0.470838*tf.lnT9)

    rate_eval.n_Ti52__Ti53 = rate

@numba.njit()
def n_V43__V44(rate_eval, tf):
    # V43 + n --> V44
    rate = 0.0

    # ths8r
    rate += np.exp(  12.7778 + -0.887122*tf.T913
                  + 0.238853*tf.T9 + -0.0224821*tf.T953)

    rate_eval.n_V43__V44 = rate

@numba.njit()
def He4_Ti51__Cr55(rate_eval, tf):
    # Ti51 + He4 --> Cr55
    rate = 0.0

    # rath 
    rate += np.exp(  -947.708 + 19.9121*tf.T9i + -1981.84*tf.T913i + 3040.8*tf.T913
                  + -172.074*tf.T9 + 9.48364*tf.T953 + -1476.66*tf.lnT9)

    rate_eval.He4_Ti51__Cr55 = rate

@numba.njit()
def p_Ti49__V50(rate_eval, tf):
    # Ti49 + p --> V50
    rate = 0.0

    # ths8r
    rate += np.exp(  34.0041 + -33.2179*tf.T913i + 3.05321*tf.T913
                  + -2.48884*tf.T9 + 0.254524*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ti49__V50 = rate

@numba.njit()
def t_Be9__n_B11(rate_eval, tf):
    # Be9 + t --> n + B11
    rate = 0.0

    # bb92n
    rate += np.exp(  28.966 + -5.61387e-12*tf.T9i + -14.02*tf.T913i + -2.37143e-09*tf.T913
                  + 2.34748e-10*tf.T9 + -1.94782e-11*tf.T953 + -0.666667*tf.lnT9)
    # bb92r
    rate += np.exp(  18.6438 + -4.43*tf.T9i + -4.68045e-09*tf.T913i + 1.05992e-08*tf.T913
                  + -8.43414e-10*tf.T9 + 6.15011e-11*tf.T953 + -1.5*tf.lnT9)

    rate_eval.t_Be9__n_B11 = rate

@numba.njit()
def n_Ti49__Ti50(rate_eval, tf):
    # Ti49 + n --> Ti50
    rate = 0.0

    # ks03 
    rate += np.exp(  13.6326 + 0.0289531*tf.T9i + -2.8384*tf.T913i + 4.10103*tf.T913
                  + -0.0325714*tf.T9 + -0.0305035*tf.T953 + -2.3012*tf.lnT9)

    rate_eval.n_Ti49__Ti50 = rate

@numba.njit()
def He4_Na39__n_Al42(rate_eval, tf):
    # Na39 + He4 --> n + Al42
    rate = 0.0

    # rath 
    rate += np.exp(  86.6284 + -3.67783*tf.T9i + 92.0547*tf.T913i + -187.46*tf.T913
                  + 8.96169*tf.T9 + -0.45592*tf.T953 + 97.0113*tf.lnT9)

    rate_eval.He4_Na39__n_Al42 = rate

@numba.njit()
def He4_Ti48__Cr52(rate_eval, tf):
    # Ti48 + He4 --> Cr52
    rate = 0.0

    # ths8r
    rate += np.exp(  56.6787 + -81.8569*tf.T913i + 4.92305*tf.T913
                  + -5.04112*tf.T9 + 0.6175*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti48__Cr52 = rate

@numba.njit()
def p_Ti47__V48(rate_eval, tf):
    # Ti47 + p --> V48
    rate = 0.0

    # ths8r
    rate += np.exp(  35.1951 + -33.2084*tf.T913i + 1.06738*tf.T913
                  + -1.55342*tf.T9 + 0.159225*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ti47__V48 = rate

@numba.njit()
def He4_Ti57__n_Cr60(rate_eval, tf):
    # Ti57 + He4 --> n + Cr60
    rate = 0.0

    # rath 
    rate += np.exp(  -1049.69 + 16.7533*tf.T9i + -1818.24*tf.T913i + 2996.03*tf.T913
                  + -179.173*tf.T9 + 10.2882*tf.T953 + -1404.54*tf.lnT9)

    rate_eval.He4_Ti57__n_Cr60 = rate

@numba.njit()
def n_Ti47__Ti48(rate_eval, tf):
    # Ti47 + n --> Ti48
    rate = 0.0

    # ks03 
    rate += np.exp(  14.8734 + 0.0181751*tf.T9i + -2.34945*tf.T913i + 3.2238*tf.T913
                  + -0.0455487*tf.T9 + -0.0153771*tf.T953 + -2.10785*tf.lnT9)

    rate_eval.n_Ti47__Ti48 = rate

@numba.njit()
def He4_Ti46__Cr50(rate_eval, tf):
    # Ti46 + He4 --> Cr50
    rate = 0.0

    # ths8r
    rate += np.exp(  57.0372 + -81.7658*tf.T913i + 3.48637*tf.T913
                  + -3.9188*tf.T9 + 0.440356*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti46__Cr50 = rate

@numba.njit()
def n_Ti46__Ti47(rate_eval, tf):
    # Ti46 + n --> Ti47
    rate = 0.0

    # ks03 
    rate += np.exp(  12.2761 + 0.0882347*tf.T9i + -7.30817*tf.T913i + 10.713*tf.T913
                  + -0.537251*tf.T9 + 0.0187304*tf.T953 + -5.38893*tf.lnT9)

    rate_eval.n_Ti46__Ti47 = rate

@numba.njit()
def He4_Ti45__Cr49(rate_eval, tf):
    # Ti45 + He4 --> Cr49
    rate = 0.0

    # ths8r
    rate += np.exp(  64.023 + -81.7175*tf.T913i + -10.1755*tf.T913
                  + 0.364167*tf.T9 + -0.000317666*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti45__Cr49 = rate

@numba.njit()
def n_Ti45__Ti46(rate_eval, tf):
    # Ti45 + n --> Ti46
    rate = 0.0

    # ths8r
    rate += np.exp(  17.133 + -1.55633*tf.T913
                  + 0.300783*tf.T9 + -0.0373696*tf.T953)

    rate_eval.n_Ti45__Ti46 = rate

@numba.njit()
def He4_Ti44__Cr48(rate_eval, tf):
    # Ti44 + He4 --> Cr48
    rate = 0.0

    # ths8r
    rate += np.exp(  64.7958 + -81.667*tf.T913i + -10.6333*tf.T913
                  + -0.672613*tf.T9 + 0.161209*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti44__Cr48 = rate

@numba.njit()
def p_Ti44__V45(rate_eval, tf):
    # Ti44 + p --> V45
    rate = 0.0

    # nfisn
    rate += np.exp(  14.2807 + -1.40579*tf.T9i + -22.1209*tf.T913i + 2.87067*tf.T913
                  + -0.0200651*tf.T9 + -0.0194061*tf.T953 + -6.51065*tf.lnT9)
    # nfisn
    rate += np.exp(  18.7183 + 0.159399*tf.T9i + -41.059*tf.T913i + 12.0361*tf.T913
                  + -0.649888*tf.T9 + 0.0175707*tf.T953 + -6.46732*tf.lnT9)
    # nfisn
    rate += np.exp(  21.7795 + -1.8856*tf.T9i + -155.515*tf.T913i + 135.903*tf.T913
                  + -3.34812*tf.T9 + -0.0139974*tf.T953 + -87.4481*tf.lnT9)
    # nfisn
    rate += np.exp(  -118.107 + -34.8499*tf.T9i + 84.8583*tf.T913i + 64.855*tf.T913
                  + -6.59381*tf.T9 + 0.413146*tf.T953 + -1.42502*tf.lnT9)
    # nfisn
    rate += np.exp(  2.92559 + -2.45693*tf.T9i + -27.0951*tf.T913i + 22.7374*tf.T913
                  + -2.18213*tf.T9 + 0.223757*tf.T953 + -15.3241*tf.lnT9)

    rate_eval.p_Ti44__V45 = rate

@numba.njit()
def n_Ti44__Ti45(rate_eval, tf):
    # Ti44 + n --> Ti45
    rate = 0.0

    # ths8r
    rate += np.exp(  15.2506 + 1.01203*tf.T913
                  + -0.201174*tf.T9 + 0.00360954*tf.T953)

    rate_eval.n_Ti44__Ti45 = rate

@numba.njit()
def n_Mn44__p_Cr44(rate_eval, tf):
    # Mn44 + n --> p + Cr44
    rate = 0.0

    # ths8r
    rate += np.exp(  22.054 + -1.11477*tf.T913
                  + 0.23741*tf.T9 + -0.0177883*tf.T953)

    rate_eval.n_Mn44__p_Cr44 = rate

@numba.njit()
def He4_Al29__p_Si32(rate_eval, tf):
    # Al29 + He4 --> p + Si32
    rate = 0.0

    # rath 
    rate += np.exp(  -37.3386 + -2.15562*tf.T9i + -53.766*tf.T913i + 88.2856*tf.T913
                  + -9.45663*tf.T9 + 0.68414*tf.T953 + -23.0343*tf.lnT9)

    rate_eval.He4_Al29__p_Si32 = rate

@numba.njit()
def He4_Ti43__Cr47(rate_eval, tf):
    # Ti43 + He4 --> Cr47
    rate = 0.0

    # ths8r
    rate += np.exp(  55.7123 + -81.6147*tf.T913i + -5.62703*tf.T913
                  + 0.409671*tf.T9 + -0.0680118*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti43__Cr47 = rate

@numba.njit()
def n_Ti43__Ti44(rate_eval, tf):
    # Ti43 + n --> Ti44
    rate = 0.0

    # ths8r
    rate += np.exp(  11.5528 + -1.09388*tf.T913
                  + 0.248209*tf.T9 + -0.02653*tf.T953)

    rate_eval.n_Ti43__Ti44 = rate

@numba.njit()
def p_Ti42__V43(rate_eval, tf):
    # Ti42 + p --> V43
    rate = 0.0

    # hg95n
    rate += np.exp(  -20.6408 + -33.0969*tf.T913i
                  + -0.666667*tf.lnT9)
    # hg95r
    rate += np.exp(  -0.047476 + -5.33807*tf.T9i
                  + -1.5*tf.lnT9)
    # hg95r
    rate += np.exp(  -14.5281 + -3.13321*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Ti42__V43 = rate

@numba.njit()
def He4_Ti41__Cr45(rate_eval, tf):
    # Ti41 + He4 --> Cr45
    rate = 0.0

    # ths8r
    rate += np.exp(  52.2528 + -81.5027*tf.T913i + -3.88825*tf.T913
                  + 0.0374822*tf.T9 + -0.0480125*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti41__Cr45 = rate

@numba.njit()
def He4_Na32__n_Al35(rate_eval, tf):
    # Na32 + He4 --> n + Al35
    rate = 0.0

    # rath 
    rate += np.exp(  78.9831 + -3.22534*tf.T9i + 72.5432*tf.T913i + -159.803*tf.T913
                  + 7.5769*tf.T9 + -0.387166*tf.T953 + 82.904*tf.lnT9)

    rate_eval.He4_Na32__n_Al35 = rate

@numba.njit()
def p_Ti41__V42(rate_eval, tf):
    # Ti41 + p --> V42
    rate = 0.0

    # ths8r
    rate += np.exp(  -24.1067 + -2.80863*tf.T9i + 26.896*tf.T913
                  + -4.66268*tf.T9 + 0.444358*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ti41__V42 = rate

@numba.njit()
def p_S28__Cl29(rate_eval, tf):
    # S28 + p --> Cl29
    rate = 0.0

    # ths8r
    rate += np.exp(  -16.9432 + -20.6656*tf.T9i + 19.1618*tf.T913
                  + -2.43847*tf.T9 + 0.194115*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_S28__Cl29 = rate

@numba.njit()
def n_Ti41__Ti42(rate_eval, tf):
    # Ti41 + n --> Ti42
    rate = 0.0

    # ths8r
    rate += np.exp(  10.1987 + 0.551571*tf.T913
                  + 0.0621682*tf.T9 + -0.00960812*tf.T953)

    rate_eval.n_Ti41__Ti42 = rate

@numba.njit()
def He4_Ti40__Cr44(rate_eval, tf):
    # Ti40 + He4 --> Cr44
    rate = 0.0

    # ths8r
    rate += np.exp(  50.2229 + -81.4428*tf.T913i + -3.13395*tf.T913
                  + 0.0095614*tf.T9 + -0.0629252*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti40__Cr44 = rate

@numba.njit()
def p_Ti40__V41(rate_eval, tf):
    # Ti40 + p --> V41
    rate = 0.0

    # ths8r
    rate += np.exp(  -16.7267 + -15.7392*tf.T9i + 17.7727*tf.T913
                  + -1.89337*tf.T9 + 0.124478*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ti40__V41 = rate

@numba.njit()
def p_Mn72__Fe73(rate_eval, tf):
    # Mn72 + p --> Fe73
    rate = 0.0

    # rath 
    rate += np.exp(  146.514 + -7.38827*tf.T9i + 282.25*tf.T913i + -454.134*tf.T913
                  + 25.3843*tf.T9 + -1.4423*tf.T953 + 226.468*tf.lnT9)

    rate_eval.p_Mn72__Fe73 = rate

@numba.njit()
def n_Ti40__Ti41(rate_eval, tf):
    # Ti40 + n --> Ti41
    rate = 0.0

    # ths8r
    rate += np.exp(  9.27057 + 1.52793*tf.T913
                  + -0.244329*tf.T9 + 0.0280298*tf.T953)

    rate_eval.n_Ti40__Ti41 = rate

@numba.njit()
def He4_Ti38__Cr42(rate_eval, tf):
    # Ti38 + He4 --> Cr42
    rate = 0.0

    # ths8r
    rate += np.exp(  47.5327 + -81.3145*tf.T913i + -1.63184*tf.T913
                  + -0.264622*tf.T9 + -0.0300755*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti38__Cr42 = rate

@numba.njit()
def p_Ar50__n_K50(rate_eval, tf):
    # Ar50 + p --> n + K50
    rate = 0.0

    # rath 
    rate += np.exp(  110.169 + -5.02009*tf.T9i + 185.571*tf.T913i + -300.573*tf.T913
                  + 16.3709*tf.T9 + -0.911533*tf.T953 + 151.338*tf.lnT9)

    rate_eval.p_Ar50__n_K50 = rate

@numba.njit()
def n_Ti38__Ti39(rate_eval, tf):
    # Ti38 + n --> Ti39
    rate = 0.0

    # ths8r
    rate += np.exp(  8.27063 + 1.46816*tf.T913
                  + -0.125632*tf.T9 + 0.0080463*tf.T953)

    rate_eval.n_Ti38__Ti39 = rate

@numba.njit()
def n_Ti37__Ti38(rate_eval, tf):
    # Ti37 + n --> Ti38
    rate = 0.0

    # ths8r
    rate += np.exp(  8.04474 + 1.1098*tf.T913
                  + 0.0111233*tf.T9 + -0.0049613*tf.T953)

    rate_eval.n_Ti37__Ti38 = rate

@numba.njit()
def n_Ar34__He4_S31(rate_eval, tf):
    # Ar34 + n --> He4 + S31
    rate = 0.0

    # ths8r
    rate += np.exp(  16.1614 + 1.91616*tf.T913
                  + -0.544035*tf.T9 + 0.0771515*tf.T953)

    rate_eval.n_Ar34__He4_S31 = rate

@numba.njit()
def p_Sc63__Ti64(rate_eval, tf):
    # Sc63 + p --> Ti64
    rate = 0.0

    # rath 
    rate += np.exp(  125.287 + -6.20199*tf.T9i + 235.265*tf.T913i + -381.76*tf.T913
                  + 21.2425*tf.T9 + -1.19654*tf.T953 + 190.235*tf.lnT9)

    rate_eval.p_Sc63__Ti64 = rate

@numba.njit()
def n_Sc62__Sc63(rate_eval, tf):
    # Sc62 + n --> Sc63
    rate = 0.0

    # rath 
    rate += np.exp(  23.1276 + 0.0191985*tf.T9i + 0.207862*tf.T913i + -14.6845*tf.T913
                  + 1.51152*tf.T9 + -0.118503*tf.T953 + 2.49981*tf.lnT9)

    rate_eval.n_Sc62__Sc63 = rate

@numba.njit()
def He4_Al35__P39(rate_eval, tf):
    # Al35 + He4 --> P39
    rate = 0.0

    # rath 
    rate += np.exp(  -16.7168 + -2.82642*tf.T9i + -17.9426*tf.T913i + 23.3677*tf.T913
                  + -4.89456*tf.T9 + 0.387208*tf.T953 + 5.2315*tf.lnT9)

    rate_eval.He4_Al35__P39 = rate

@numba.njit()
def p_Mn44__Fe45(rate_eval, tf):
    # Mn44 + p --> Fe45
    rate = 0.0

    # ths8r
    rate += np.exp(  40.6028 + -36.1457*tf.T913i + -6.20399*tf.T913
                  + -2.04399*tf.T9 + 0.328581*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn44__Fe45 = rate

@numba.njit()
def p_Sc61__Ti62(rate_eval, tf):
    # Sc61 + p --> Ti62
    rate = 0.0

    # rath 
    rate += np.exp(  115.345 + -6.07072*tf.T9i + 226.344*tf.T913i + -361.842*tf.T913
                  + 19.8781*tf.T9 + -1.11646*tf.T953 + 182.151*tf.lnT9)

    rate_eval.p_Sc61__Ti62 = rate

@numba.njit()
def He4_Sc60__V64(rate_eval, tf):
    # Sc60 + He4 --> V64
    rate = 0.0

    # rath 
    rate += np.exp(  -1003.3 + 20.8639*tf.T9i + -2074.31*tf.T913i + 3195.57*tf.T913
                  + -181.018*tf.T9 + 9.99851*tf.T953 + -1550.74*tf.lnT9)

    rate_eval.He4_Sc60__V64 = rate

@numba.njit()
def n_Sc59__Sc60(rate_eval, tf):
    # Sc59 + n --> Sc60
    rate = 0.0

    # rath 
    rate += np.exp(  15.7084 + -0.0427062*tf.T9i + 3.88904*tf.T913i + -12.503*tf.T913
                  + 1.47801*tf.T9 + -0.146101*tf.T953 + 3.82569*tf.lnT9)

    rate_eval.n_Sc59__Sc60 = rate

@numba.njit()
def N16__O16__weak__wc12(rate_eval, tf):
    # N16 --> O16
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.33084)

    rate_eval.N16__O16__weak__wc12 = rate

@numba.njit()
def Si44__n_P43__weak__mp17(rate_eval, tf):
    # Si44 --> n + P43
    rate = 0.0

    # mp17w
    rate += np.exp(  3.53485)

    rate_eval.Si44__n_P43__weak__mp17 = rate

@numba.njit()
def He4_Sc58__V62(rate_eval, tf):
    # Sc58 + He4 --> V62
    rate = 0.0

    # rath 
    rate += np.exp(  -984.859 + 20.4932*tf.T9i + -2038.66*tf.T913i + 3139.09*tf.T913
                  + -177.901*tf.T9 + 9.82714*tf.T953 + -1523.14*tf.lnT9)

    rate_eval.He4_Sc58__V62 = rate

@numba.njit()
def p_Sc58__Ti59(rate_eval, tf):
    # Sc58 + p --> Ti59
    rate = 0.0

    # rath 
    rate += np.exp(  114.772 + -5.93259*tf.T9i + 220.65*tf.T913i + -354.372*tf.T913
                  + 19.4385*tf.T9 + -1.09239*tf.T953 + 178.317*tf.lnT9)

    rate_eval.p_Sc58__Ti59 = rate

@numba.njit()
def n_Sc58__Sc59(rate_eval, tf):
    # Sc58 + n --> Sc59
    rate = 0.0

    # rath 
    rate += np.exp(  17.4603 + -0.0188125*tf.T9i + 1.97083*tf.T913i + -8.24667*tf.T913
                  + 0.562447*tf.T9 + -0.0513237*tf.T953 + 2.26354*tf.lnT9)

    rate_eval.n_Sc58__Sc59 = rate

@numba.njit()
def He4_Ca60__n_Ti63(rate_eval, tf):
    # Ca60 + He4 --> n + Ti63
    rate = 0.0

    # rath 
    rate += np.exp(  -1005.84 + 16.0648*tf.T9i + -1743.62*tf.T913i + 2874.62*tf.T913
                  + -171.878*tf.T9 + 9.8695*tf.T953 + -1347.98*tf.lnT9)

    rate_eval.He4_Ca60__n_Ti63 = rate

@numba.njit()
def p_Sc57__Ti58(rate_eval, tf):
    # Sc57 + p --> Ti58
    rate = 0.0

    # rath 
    rate += np.exp(  113.047 + -5.88594*tf.T9i + 218.511*tf.T913i + -350.953*tf.T913
                  + 19.3092*tf.T9 + -1.09188*tf.T953 + 176.686*tf.lnT9)

    rate_eval.p_Sc57__Ti58 = rate

@numba.njit()
def He4_Sc56__V60(rate_eval, tf):
    # Sc56 + He4 --> V60
    rate = 0.0

    # rath 
    rate += np.exp(  -966.999 + 20.1488*tf.T9i + -2005.1*tf.T913i + 3085.46*tf.T913
                  + -174.888*tf.T9 + 9.66056*tf.T953 + -1497.13*tf.lnT9)

    rate_eval.He4_Sc56__V60 = rate

@numba.njit()
def He4_Ti49__n_Cr52(rate_eval, tf):
    # Ti49 + He4 --> n + Cr52
    rate = 0.0

    # ths8r
    rate += np.exp(  58.814 + -81.8999*tf.T913i + -0.331496*tf.T913
                  + -0.758416*tf.T9 + 0.0413394*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti49__n_Cr52 = rate

@numba.njit()
def N17__n_O16__weak__wc12(rate_eval, tf):
    # N17 --> n + O16
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.84467)

    rate_eval.N17__n_O16__weak__wc12 = rate

@numba.njit()
def p_Sc56__Ti57(rate_eval, tf):
    # Sc56 + p --> Ti57
    rate = 0.0

    # rath 
    rate += np.exp(  111.961 + -5.82105*tf.T9i + 215.011*tf.T913i + -345.931*tf.T913
                  + 19.0486*tf.T9 + -1.07651*tf.T953 + 174.115*tf.lnT9)

    rate_eval.p_Sc56__Ti57 = rate

@numba.njit()
def n_Sc56__Sc57(rate_eval, tf):
    # Sc56 + n --> Sc57
    rate = 0.0

    # rath 
    rate += np.exp(  18.7721 + -0.0247977*tf.T9i + 2.63174*tf.T913i + -9.78581*tf.T913
                  + 0.639582*tf.T9 + -0.0527231*tf.T953 + 2.90641*tf.lnT9)

    rate_eval.n_Sc56__Sc57 = rate

@numba.njit()
def p_Sc37__Ti38(rate_eval, tf):
    # Sc37 + p --> Ti38
    rate = 0.0

    # ths8r
    rate += np.exp(  36.3087 + -32.1339*tf.T913i + -9.1348*tf.T913
                  + 0.11336*tf.T9 + 0.045814*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc37__Ti38 = rate

@numba.njit()
def He4_Sc55__V59(rate_eval, tf):
    # Sc55 + He4 --> V59
    rate = 0.0

    # rath 
    rate += np.exp(  -956.051 + 19.9165*tf.T9i + -1983.25*tf.T913i + 3051.03*tf.T913
                  + -172.976*tf.T9 + 9.55204*tf.T953 + -1480.2*tf.lnT9)

    rate_eval.He4_Sc55__V59 = rate

@numba.njit()
def p_Sc55__Ti56(rate_eval, tf):
    # Sc55 + p --> Ti56
    rate = 0.0

    # rath 
    rate += np.exp(  112.22 + -5.79054*tf.T9i + 214.728*tf.T913i + -346.866*tf.T913
                  + 19.2208*tf.T9 + -1.09296*tf.T953 + 174.296*tf.lnT9)

    rate_eval.p_Sc55__Ti56 = rate

@numba.njit()
def He4_K45__p_Ca48(rate_eval, tf):
    # K45 + He4 --> p + Ca48
    rate = 0.0

    # rath 
    rate += np.exp(  -828.995 + 13.5228*tf.T9i + -1467.91*tf.T913i + 2391.89*tf.T913
                  + -142.442*tf.T9 + 8.19342*tf.T953 + -1124.89*tf.lnT9)

    rate_eval.He4_K45__p_Ca48 = rate

@numba.njit()
def n_Sc54__Sc55(rate_eval, tf):
    # Sc54 + n --> Sc55
    rate = 0.0

    # rath 
    rate += np.exp(  19.1379 + -0.018177*tf.T9i + 2.62076*tf.T913i + -13.4451*tf.T913
                  + 1.10543*tf.T9 + -0.0799585*tf.T953 + 3.53093*tf.lnT9)

    rate_eval.n_Sc54__Sc55 = rate

@numba.njit()
def p_Sc53__Ti54(rate_eval, tf):
    # Sc53 + p --> Ti54
    rate = 0.0

    # rath 
    rate += np.exp(  117.472 + -5.74326*tf.T9i + 215.596*tf.T913i + -352.542*tf.T913
                  + 19.7383*tf.T9 + -1.1313*tf.T953 + 176.053*tf.lnT9)

    rate_eval.p_Sc53__Ti54 = rate

@numba.njit()
def n_Sc53__Sc54(rate_eval, tf):
    # Sc53 + n --> Sc54
    rate = 0.0

    # rath 
    rate += np.exp(  18.2633 + -0.0420072*tf.T9i + 4.0652*tf.T913i + -13.3843*tf.T913
                  + 1.65313*tf.T9 + -0.152463*tf.T953 + 4.13399*tf.lnT9)

    rate_eval.n_Sc53__Sc54 = rate

@numba.njit()
def n_Sc50__Sc51(rate_eval, tf):
    # Sc50 + n --> Sc51
    rate = 0.0

    # rath 
    rate += np.exp(  22.7961 + -0.0818207*tf.T9i + 7.74992*tf.T913i + -19.1066*tf.T913
                  + 1.6014*tf.T9 + -0.121029*tf.T953 + 7.18054*tf.lnT9)

    rate_eval.n_Sc50__Sc51 = rate

@numba.njit()
def p_Mn57__He4_Cr54(rate_eval, tf):
    # Mn57 + p --> He4 + Cr54
    rate = 0.0

    # rath 
    rate += np.exp(  93.0973 + -6.525*tf.T9i + 234.549*tf.T913i + -345.603*tf.T913
                  + 17.1019*tf.T9 + -0.890297*tf.T953 + 185.072*tf.lnT9)

    rate_eval.p_Mn57__He4_Cr54 = rate

@numba.njit()
def p_He3__He4__weak__bet_pos_(rate_eval, tf):
    # He3 + p --> He4
    rate = 0.0

    # bet+w
    rate += np.exp(  -27.7611 + -4.30107e-12*tf.T9i + -6.141*tf.T913i + -1.93473e-09*tf.T913
                  + 2.04145e-10*tf.T9 + -1.80372e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_He3__He4__weak__bet_pos_ = rate

@numba.njit()
def He4_Sc49__V53(rate_eval, tf):
    # Sc49 + He4 --> V53
    rate = 0.0

    # rath 
    rate += np.exp(  -1034.46 + 14.947*tf.T9i + -1662.68*tf.T913i + 2812.64*tf.T913
                  + -170.886*tf.T9 + 9.89784*tf.T953 + -1302.87*tf.lnT9)

    rate_eval.He4_Sc49__V53 = rate

@numba.njit()
def He4_Mn44__Co48(rate_eval, tf):
    # Mn44 + He4 --> Co48
    rate = 0.0

    # ths8r
    rate += np.exp(  52.4663 + -88.9347*tf.T913i + -2.41015*tf.T913
                  + -0.458817*tf.T9 + 0.0164617*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn44__Co48 = rate

@numba.njit()
def p_Mg31__Al32(rate_eval, tf):
    # Mg31 + p --> Al32
    rate = 0.0

    # rath 
    rate += np.exp(  65.8507 + -3.05027*tf.T9i + 107.555*tf.T913i + -180.171*tf.T913
                  + 9.69496*tf.T9 + -0.532886*tf.T953 + 90.8291*tf.lnT9)

    rate_eval.p_Mg31__Al32 = rate

@numba.njit()
def p_Sc49__Ti50(rate_eval, tf):
    # Sc49 + p --> Ti50
    rate = 0.0

    # rath 
    rate += np.exp(  106.943 + -5.43496*tf.T9i + 195.561*tf.T913i + -317.373*tf.T913
                  + 17.5352*tf.T9 + -0.999861*tf.T953 + 159.384*tf.lnT9)

    rate_eval.p_Sc49__Ti50 = rate

@numba.njit()
def n_Sc49__Sc50(rate_eval, tf):
    # Sc49 + n --> Sc50
    rate = 0.0

    # rath 
    rate += np.exp(  23.5242 + -0.0831821*tf.T9i + 7.90963*tf.T913i + -20.481*tf.T913
                  + 1.92991*tf.T9 + -0.147799*tf.T953 + 7.4351*tf.lnT9)

    rate_eval.n_Sc49__Sc50 = rate

@numba.njit()
def p_Sc48__Ti49(rate_eval, tf):
    # Sc48 + p --> Ti49
    rate = 0.0

    # rath 
    rate += np.exp(  101.172 + -5.49324*tf.T9i + 198.826*tf.T913i + -313.844*tf.T913
                  + 17.0251*tf.T9 + -0.945704*tf.T953 + 159.404*tf.lnT9)

    rate_eval.p_Sc48__Ti49 = rate

@numba.njit()
def n_Sc48__Sc49(rate_eval, tf):
    # Sc48 + n --> Sc49
    rate = 0.0

    # rath 
    rate += np.exp(  17.731 + -0.026995*tf.T9i + 2.32858*tf.T913i + -6.44325*tf.T913
                  + 0.608389*tf.T9 + -0.0534156*tf.T953 + 2.13196*tf.lnT9)

    rate_eval.n_Sc48__Sc49 = rate

@numba.njit()
def p_Ne21__Na22(rate_eval, tf):
    # Ne21 + p --> Na22
    rate = 0.0

    # il10n
    rate += np.exp(  19.0696 + -19.2096*tf.T913i
                  + -1.0*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  -39.4862 + -4.21385*tf.T9i + 21.1176*tf.T913i + 34.0411*tf.T913
                  + -4.45593*tf.T9 + 0.328613*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  1.75704 + -1.39957*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -47.6554 + -0.19618*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Ne21__Na22 = rate

@numba.njit()
def He4_Sc47__V51(rate_eval, tf):
    # Sc47 + He4 --> V51
    rate = 0.0

    # rath 
    rate += np.exp(  -1038.06 + 15.2937*tf.T9i + -1682.84*tf.T913i + 2838.54*tf.T913
                  + -171.874*tf.T9 + 9.93236*tf.T953 + -1317.42*tf.lnT9)

    rate_eval.He4_Sc47__V51 = rate

@numba.njit()
def p_Sc46__Ti47(rate_eval, tf):
    # Sc46 + p --> Ti47
    rate = 0.0

    # rath 
    rate += np.exp(  134.507 + -5.50507*tf.T9i + 212.079*tf.T913i + -358.599*tf.T913
                  + 19.2793*tf.T9 + -1.01913*tf.T953 + 176.254*tf.lnT9)

    rate_eval.p_Sc46__Ti47 = rate

@numba.njit()
def n_Sc46__Sc47(rate_eval, tf):
    # Sc46 + n --> Sc47
    rate = 0.0

    # rath 
    rate += np.exp(  17.7335 + -0.0211697*tf.T9i + 1.157*tf.T913i + -3.39674*tf.T913
                  + 0.179575*tf.T9 + -0.00780135*tf.T953 + 0.783491*tf.lnT9)

    rate_eval.n_Sc46__Sc47 = rate

@numba.njit()
def n_V47__p_Ti47(rate_eval, tf):
    # V47 + n --> p + Ti47
    rate = 0.0

    # ths8r
    rate += np.exp(  20.3911 + -0.897943*tf.T913
                  + 0.233018*tf.T9 + -0.0170844*tf.T953)

    rate_eval.n_V47__p_Ti47 = rate

@numba.njit()
def He4_Sc45__V49(rate_eval, tf):
    # Sc45 + He4 --> V49
    rate = 0.0

    # ths8r
    rate += np.exp(  60.1427 + -79.222*tf.T913i + -5.31022*tf.T913
                  + -1.37323*tf.T9 + 0.21679*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc45__V49 = rate

@numba.njit()
def He4_Mg20__Si24(rate_eval, tf):
    # Mg20 + He4 --> Si24
    rate = 0.0

    # ths8r
    rate += np.exp(  34.2811 + -52.8179*tf.T913i + 1.14732*tf.T913
                  + -0.637933*tf.T9 + 0.0355077*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg20__Si24 = rate

@numba.njit()
def n_Sc45__Sc46(rate_eval, tf):
    # Sc45 + n --> Sc46
    rate = 0.0

    # ks03 
    rate += np.exp(  6.62692 + 0.0466836*tf.T9i + -6.18502*tf.T913i + 16.5806*tf.T913
                  + -1.45949*tf.T9 + 0.0995696*tf.T953 + -6.53696*tf.lnT9)

    rate_eval.n_Sc45__Sc46 = rate

@numba.njit()
def p_Ca50__He4_K47(rate_eval, tf):
    # Ca50 + p --> He4 + K47
    rate = 0.0

    # rath 
    rate += np.exp(  39.1391 + -5.35518*tf.T9i + 201.1*tf.T913i + -260.145*tf.T913
                  + 7.87655*tf.T9 + -0.152999*tf.T953 + 159.37*tf.lnT9)

    rate_eval.p_Ca50__He4_K47 = rate

@numba.njit()
def p_Sc43__Ti44(rate_eval, tf):
    # Sc43 + p --> Ti44
    rate = 0.0

    # ths8r
    rate += np.exp(  36.8432 + -32.1734*tf.T913i + -1.77078*tf.T913
                  + -2.21706*tf.T9 + 0.298499*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc43__Ti44 = rate

@numba.njit()
def Cl52__n_n_n_Ar49__weak__mo03(rate_eval, tf):
    # Cl52 --> 3 n + Ar49
    rate = 0.0

    # mo03w
    rate += np.exp(  4.41991)

    rate_eval.Cl52__n_n_n_Ar49__weak__mo03 = rate

@numba.njit()
def n_Cr63__Cr64(rate_eval, tf):
    # Cr63 + n --> Cr64
    rate = 0.0

    # rath 
    rate += np.exp(  28.2916 + -0.0600706*tf.T9i + 7.2821*tf.T913i + -25.5234*tf.T913
                  + 2.11258*tf.T9 + -0.164229*tf.T953 + 8.1937*tf.lnT9)

    rate_eval.n_Cr63__Cr64 = rate

@numba.njit()
def F23__Ne23__weak__wc12(rate_eval, tf):
    # F23 --> Ne23
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.16851)

    rate_eval.F23__Ne23__weak__wc12 = rate

@numba.njit()
def He4_Sc42__V46(rate_eval, tf):
    # Sc42 + He4 --> V46
    rate = 0.0

    # ths8r
    rate += np.exp(  51.7727 + -79.0687*tf.T913i + -4.25493*tf.T913
                  + 0.184703*tf.T9 + -0.0785452*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc42__V46 = rate

@numba.njit()
def p_Sc42__Ti43(rate_eval, tf):
    # Sc42 + p --> Ti43
    rate = 0.0

    # ths8r
    rate += np.exp(  35.7889 + -32.1676*tf.T913i + 1.2856*tf.T913
                  + -2.95494*tf.T9 + 0.378749*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc42__Ti43 = rate

@numba.njit()
def n_Sc42__Sc43(rate_eval, tf):
    # Sc42 + n --> Sc43
    rate = 0.0

    # ths8r
    rate += np.exp(  14.9443 + -0.921604*tf.T913
                  + 0.333782*tf.T9 + -0.0404241*tf.T953)

    rate_eval.n_Sc42__Sc43 = rate

@numba.njit()
def He4_Sc41__V45(rate_eval, tf):
    # Sc41 + He4 --> V45
    rate = 0.0

    # ths8r
    rate += np.exp(  53.2525 + -79.013*tf.T913i + -6.64623*tf.T913
                  + 1.10793*tf.T9 + -0.169427*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc41__V45 = rate

@numba.njit()
def p_Mn60__Fe61(rate_eval, tf):
    # Mn60 + p --> Fe61
    rate = 0.0

    # rath 
    rate += np.exp(  124.879 + -6.7489*tf.T9i + 249.906*tf.T913i + -394.714*tf.T913
                  + 21.0349*tf.T9 + -1.14923*tf.T953 + 200.658*tf.lnT9)

    rate_eval.p_Mn60__Fe61 = rate

@numba.njit()
def p_Sc41__Ti42(rate_eval, tf):
    # Sc41 + p --> Ti42
    rate = 0.0

    # ths8r
    rate += np.exp(  38.3524 + -32.1615*tf.T913i + -3.68811*tf.T913
                  + -2.01234*tf.T9 + 0.3232*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc41__Ti42 = rate

@numba.njit()
def n_Sc41__Sc42(rate_eval, tf):
    # Sc41 + n --> Sc42
    rate = 0.0

    # ths8r
    rate += np.exp(  10.6014 + -1.01509*tf.T913
                  + 0.362316*tf.T9 + -0.0412181*tf.T953)

    rate_eval.n_Sc41__Sc42 = rate

@numba.njit()
def p_Sc40__Ti41(rate_eval, tf):
    # Sc40 + p --> Ti41
    rate = 0.0

    # ths8r
    rate += np.exp(  38.6297 + -32.1551*tf.T913i + -4.65671*tf.T913
                  + -1.9518*tf.T9 + 0.316964*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc40__Ti41 = rate

@numba.njit()
def He4_Sc39__V43(rate_eval, tf):
    # Sc39 + He4 --> V43
    rate = 0.0

    # ths8r
    rate += np.exp(  45.9631 + -78.8941*tf.T913i + 0.407416*tf.T913
                  + -0.76983*tf.T9 + 0.0430663*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc39__V43 = rate

@numba.njit()
def n_Sc39__Sc40(rate_eval, tf):
    # Sc39 + n --> Sc40
    rate = 0.0

    # ths8r
    rate += np.exp(  9.20064 + 1.24481*tf.T913
                  + -0.0745803*tf.T9 + 0.00467306*tf.T953)

    rate_eval.n_Sc39__Sc40 = rate

@numba.njit()
def Mg36__Al36__weak__wc17(rate_eval, tf):
    # Mg36 --> Al36
    rate = 0.0

    # wc17w
    rate += np.exp(  4.66944)

    rate_eval.Mg36__Al36__weak__wc17 = rate

@numba.njit()
def He4_Sc38__V42(rate_eval, tf):
    # Sc38 + He4 --> V42
    rate = 0.0

    # ths8r
    rate += np.exp(  46.8314 + -78.8304*tf.T913i + -0.806462*tf.T913
                  + -0.549318*tf.T9 + 0.00970364*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc38__V42 = rate

@numba.njit()
def p_Sc38__Ti39(rate_eval, tf):
    # Sc38 + p --> Ti39
    rate = 0.0

    # ths8r
    rate += np.exp(  37.621 + -32.1413*tf.T913i + -4.55276*tf.T913
                  + -2.24702*tf.T9 + 0.357394*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc38__Ti39 = rate

@numba.njit()
def n_Sc38__Sc39(rate_eval, tf):
    # Sc38 + n --> Sc39
    rate = 0.0

    # ths8r
    rate += np.exp(  7.54137 + 2.29167*tf.T913
                  + -0.309687*tf.T9 + 0.0332207*tf.T953)

    rate_eval.n_Sc38__Sc39 = rate

@numba.njit()
def p_Na33__He4_Ne30(rate_eval, tf):
    # Na33 + p --> He4 + Ne30
    rate = 0.0

    # rath 
    rate += np.exp(  68.441 + -2.98104*tf.T9i + 106.706*tf.T913i + -178.868*tf.T913
                  + 9.71435*tf.T9 + -0.526021*tf.T953 + 89.726*tf.lnT9)

    rate_eval.p_Na33__He4_Ne30 = rate

@numba.njit()
def n_Sc37__Sc38(rate_eval, tf):
    # Sc37 + n --> Sc38
    rate = 0.0

    # ths8r
    rate += np.exp(  8.49009 + 0.773035*tf.T913
                  + 0.0524431*tf.T9 + -0.00439746*tf.T953)

    rate_eval.n_Sc37__Sc38 = rate

@numba.njit()
def He4_Cr55__Fe59(rate_eval, tf):
    # Cr55 + He4 --> Fe59
    rate = 0.0

    # rath 
    rate += np.exp(  -1055.12 + 21.8055*tf.T9i + -2173.8*tf.T913i + 3353.55*tf.T913
                  + -190.637*tf.T9 + 10.5473*tf.T953 + -1624.74*tf.lnT9)

    rate_eval.He4_Cr55__Fe59 = rate

@numba.njit()
def p_Ca60__Sc61(rate_eval, tf):
    # Ca60 + p --> Sc61
    rate = 0.0

    # rath 
    rate += np.exp(  108.204 + -5.80337*tf.T9i + 214.386*tf.T913i + -341.779*tf.T913
                  + 18.7004*tf.T9 + -1.0484*tf.T953 + 172.436*tf.lnT9)

    rate_eval.p_Ca60__Sc61 = rate

@numba.njit()
def F27__n_n_Ne25__weak__mp17(rate_eval, tf):
    # F27 --> n + n + Ne25
    rate = 0.0

    # mp17w
    rate += np.exp(  1.71293)

    rate_eval.F27__n_n_Ne25__weak__mp17 = rate

@numba.njit()
def n_Ca60__Ca61(rate_eval, tf):
    # Ca60 + n --> Ca61
    rate = 0.0

    # rath 
    rate += np.exp(  25.3694 + 0.185843*tf.T9i + -6.2167*tf.T913i + -17.5061*tf.T913
                  + 3.14354*tf.T9 + -0.33536*tf.T953 + 2.31692*tf.lnT9)

    rate_eval.n_Ca60__Ca61 = rate

@numba.njit()
def He4_F25__n_Na28(rate_eval, tf):
    # F25 + He4 --> n + Na28
    rate = 0.0

    # rpsmr
    rate += np.exp(  61.4884 + -2.36449*tf.T9i + 43.3812*tf.T913i + -108.444*tf.T913
                  + 4.77171*tf.T9 + -0.228787*tf.T953 + 57.4185*tf.lnT9)

    rate_eval.He4_F25__n_Na28 = rate

@numba.njit()
def p_Ti51__V52(rate_eval, tf):
    # Ti51 + p --> V52
    rate = 0.0

    # rath 
    rate += np.exp(  130.346 + -5.83918*tf.T9i + 220.953*tf.T913i + -370.119*tf.T913
                  + 21.0839*tf.T9 + -1.22336*tf.T953 + 182.332*tf.lnT9)

    rate_eval.p_Ti51__V52 = rate

@numba.njit()
def He4_Ca59__Ti63(rate_eval, tf):
    # Ca59 + He4 --> Ti63
    rate = 0.0

    # rath 
    rate += np.exp(  -1011.61 + 15.9092*tf.T9i + -1728.72*tf.T913i + 2853.27*tf.T913
                  + -170.759*tf.T9 + 9.80068*tf.T953 + -1336.86*tf.lnT9)

    rate_eval.He4_Ca59__Ti63 = rate

@numba.njit()
def n_Ar39__Ar40(rate_eval, tf):
    # Ar39 + n --> Ar40
    rate = 0.0

    # ks03 
    rate += np.exp(  15.8265 + -0.0317703*tf.T9i + 2.09789*tf.T913i + -4.77242*tf.T913
                  + 0.64032*tf.T9 + -0.0694485*tf.T953 + 1.51561*tf.lnT9)

    rate_eval.n_Ar39__Ar40 = rate

@numba.njit()
def p_Ca59__Sc60(rate_eval, tf):
    # Ca59 + p --> Sc60
    rate = 0.0

    # rath 
    rate += np.exp(  107.14 + -5.76038*tf.T9i + 212.354*tf.T913i + -338.106*tf.T913
                  + 18.4559*tf.T9 + -1.03217*tf.T953 + 170.799*tf.lnT9)

    rate_eval.p_Ca59__Sc60 = rate

@numba.njit()
def He4_Cr64__Fe68(rate_eval, tf):
    # Cr64 + He4 --> Fe68
    rate = 0.0

    # rath 
    rate += np.exp(  -1114.16 + 23.2926*tf.T9i + -2315.68*tf.T913i + 3559.86*tf.T913
                  + -200.779*tf.T9 + 11.0125*tf.T953 + -1730.06*tf.lnT9)

    rate_eval.He4_Cr64__Fe68 = rate

@numba.njit()
def p_Ca57__Sc58(rate_eval, tf):
    # Ca57 + p --> Sc58
    rate = 0.0

    # rath 
    rate += np.exp(  107.93 + -5.66518*tf.T9i + 208.632*tf.T913i + -335.23*tf.T913
                  + 18.4839*tf.T9 + -1.04516*tf.T953 + 168.676*tf.lnT9)

    rate_eval.p_Ca57__Sc58 = rate

@numba.njit()
def P47__n_n_n_S44__weak__mo03(rate_eval, tf):
    # P47 --> 3 n + S44
    rate = 0.0

    # mo03w
    rate += np.exp(  3.66366)

    rate_eval.P47__n_n_n_S44__weak__mo03 = rate

@numba.njit()
def p_Na20__Mg21(rate_eval, tf):
    # Na20 + p --> Mg21
    rate = 0.0

    # ku92r
    rate += np.exp(  9.35824 + -7.94908*tf.T9i
                  + -1.5*tf.lnT9)
    # ku92r
    rate += np.exp(  8.79863 + -6.23046*tf.T9i
                  + -1.5*tf.lnT9)
    # ku92r
    rate += np.exp(  3.23895 + -4.95512*tf.T9i
                  + -1.5*tf.lnT9)
    # ku92r
    rate += np.exp(  -1.81414 + -1.52019*tf.T9i
                  + -1.5*tf.lnT9)
    # ku92r
    rate += np.exp(  9.58481 + -9.21397*tf.T9i
                  + -1.5*tf.lnT9)
    # ku92n
    rate += np.exp(  17.6614 + -20.67*tf.T913i
                  + -0.666667*tf.lnT9)

    rate_eval.p_Na20__Mg21 = rate

@numba.njit()
def n_Ca57__Ca58(rate_eval, tf):
    # Ca57 + n --> Ca58
    rate = 0.0

    # rath 
    rate += np.exp(  12.0267 + -0.0473973*tf.T9i + 3.25034*tf.T913i + -6.64268*tf.T913
                  + 0.662637*tf.T9 + -0.0861883*tf.T953 + 2.35096*tf.lnT9)

    rate_eval.n_Ca57__Ca58 = rate

@numba.njit()
def Cl41__Ar41__weak__wc12(rate_eval, tf):
    # Cl41 --> Ar41
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.01457)

    rate_eval.Cl41__Ar41__weak__wc12 = rate

@numba.njit()
def C12_C12__p_Na23(rate_eval, tf):
    # C12 + C12 --> p + Na23
    rate = 0.0

    # cf88r
    rate += np.exp(  60.9649 + -84.165*tf.T913i + -1.4191*tf.T913
                  + -0.114619*tf.T9 + -0.070307*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.C12_C12__p_Na23 = rate

@numba.njit()
def n_Ca56__Ca57(rate_eval, tf):
    # Ca56 + n --> Ca57
    rate = 0.0

    # rath 
    rate += np.exp(  24.3732 + -0.157915*tf.T9i + 15.5102*tf.T913i + -39.5705*tf.T913
                  + 4.43974*tf.T9 + -0.388075*tf.T953 + 14.6898*tf.lnT9)

    rate_eval.n_Ca56__Ca57 = rate

@numba.njit()
def n_Ca55__Ca56(rate_eval, tf):
    # Ca55 + n --> Ca56
    rate = 0.0

    # rath 
    rate += np.exp(  19.3757 + -0.0425057*tf.T9i + 5.10188*tf.T913i + -17.6781*tf.T913
                  + 1.97268*tf.T9 + -0.183766*tf.T953 + 5.68599*tf.lnT9)

    rate_eval.n_Ca55__Ca56 = rate

@numba.njit()
def He4_Na27__n_Al30(rate_eval, tf):
    # Na27 + He4 --> n + Al30
    rate = 0.0

    # rath 
    rate += np.exp(  70.9624 + -2.87933*tf.T9i + 58.0736*tf.T913i + -137.03*tf.T913
                  + 6.26957*tf.T9 + -0.314558*tf.T953 + 72.105*tf.lnT9)

    rate_eval.He4_Na27__n_Al30 = rate

@numba.njit()
def He4_Mn59__n_Co62(rate_eval, tf):
    # Mn59 + He4 --> n + Co62
    rate = 0.0

    # rath 
    rate += np.exp(  -1102.63 + 23.1561*tf.T9i + -2303.09*tf.T913i + 3544.46*tf.T913
                  + -200.779*tf.T9 + 11.1026*tf.T953 + -1720.26*tf.lnT9)

    rate_eval.He4_Mn59__n_Co62 = rate

@numba.njit()
def He4_O27__Ne31(rate_eval, tf):
    # O27 + He4 --> Ne31
    rate = 0.0

    # rpsmr
    rate += np.exp(  42.3359 + -2.28579*tf.T9i + 41.7887*tf.T913i + -96.5441*tf.T913
                  + 3.77425*tf.T9 + -0.152953*tf.T953 + 52.8029*tf.lnT9)

    rate_eval.He4_O27__Ne31 = rate

@numba.njit()
def Sc40__Ca40__weak__wc12(rate_eval, tf):
    # Sc40 --> Ca40
    rate = 0.0

    # wc12w
    rate += np.exp(  1.33263)

    rate_eval.Sc40__Ca40__weak__wc12 = rate

@numba.njit()
def p_Ca54__Sc55(rate_eval, tf):
    # Ca54 + p --> Sc55
    rate = 0.0

    # rath 
    rate += np.exp(  110.448 + -5.57956*tf.T9i + 208.342*tf.T913i + -339.492*tf.T913
                  + 18.9362*tf.T9 + -1.07742*tf.T953 + 169.833*tf.lnT9)

    rate_eval.p_Ca54__Sc55 = rate

@numba.njit()
def He4_V48__p_Cr51(rate_eval, tf):
    # V48 + He4 --> p + Cr51
    rate = 0.0

    # ths8r
    rate += np.exp(  60.9483 + -84.3192*tf.T913i + -1.84683*tf.T913
                  + -0.459124*tf.T9 + 0.00700566*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V48__p_Cr51 = rate

@numba.njit()
def n_Ca54__Ca55(rate_eval, tf):
    # Ca54 + n --> Ca55
    rate = 0.0

    # rath 
    rate += np.exp(  13.5476 + -0.0370465*tf.T9i + 3.56991*tf.T913i + -10.7607*tf.T913
                  + 1.64898*tf.T9 + -0.185387*tf.T953 + 3.51288*tf.lnT9)

    rate_eval.n_Ca54__Ca55 = rate

@numba.njit()
def Al39__n_n_Si37__weak__mp17(rate_eval, tf):
    # Al39 --> n + n + Si37
    rate = 0.0

    # mp17w
    rate += np.exp(  1.29422)

    rate_eval.Al39__n_n_Si37__weak__mp17 = rate

@numba.njit()
def n_Ca53__Ca54(rate_eval, tf):
    # Ca53 + n --> Ca54
    rate = 0.0

    # rath 
    rate += np.exp(  12.0416 + -0.0233799*tf.T9i + 1.30858*tf.T913i + -4.12723*tf.T913
                  + 0.782238*tf.T9 + -0.10254*tf.T953 + 0.914902*tf.lnT9)

    rate_eval.n_Ca53__Ca54 = rate

@numba.njit()
def p_Fe58__Co59(rate_eval, tf):
    # Fe58 + p --> Co59
    rate = 0.0

    # ths8r
    rate += np.exp(  36.2182 + -37.17*tf.T913i + 1.63285*tf.T913
                  + -1.16636*tf.T9 + 0.0508619*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Fe58__Co59 = rate

@numba.njit()
def p_Mn71__Fe72(rate_eval, tf):
    # Mn71 + p --> Fe72
    rate = 0.0

    # rath 
    rate += np.exp(  147.158 + -7.35491*tf.T9i + 281.542*tf.T913i + -454.387*tf.T913
                  + 25.4738*tf.T9 + -1.45499*tf.T953 + 226.276*tf.lnT9)

    rate_eval.p_Mn71__Fe72 = rate

@numba.njit()
def P36__S36__weak__wc12(rate_eval, tf):
    # P36 --> S36
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.08928)

    rate_eval.P36__S36__weak__wc12 = rate

@numba.njit()
def He4_Ca51__Ti55(rate_eval, tf):
    # Ca51 + He4 --> Ti55
    rate = 0.0

    # rath 
    rate += np.exp(  -932.655 + 14.8636*tf.T9i + -1614.89*tf.T913i + 2650.59*tf.T913
                  + -158.32*tf.T9 + 9.06552*tf.T953 + -1243.63*tf.lnT9)

    rate_eval.He4_Ca51__Ti55 = rate

@numba.njit()
def S47__Cl47__weak__mo03(rate_eval, tf):
    # S47 --> Cl47
    rate = 0.0

    # mo03w
    rate += np.exp(  4.67611)

    rate_eval.S47__Cl47__weak__mo03 = rate

@numba.njit()
def p_Ca51__Sc52(rate_eval, tf):
    # Ca51 + p --> Sc52
    rate = 0.0

    # rath 
    rate += np.exp(  110.298 + -5.45035*tf.T9i + 203.049*tf.T913i + -331.437*tf.T913
                  + 18.469*tf.T9 + -1.05349*tf.T953 + 165.913*tf.lnT9)

    rate_eval.p_Ca51__Sc52 = rate

@numba.njit()
def O27__F27__weak__mo03(rate_eval, tf):
    # O27 --> F27
    rate = 0.0

    # mo03w
    rate += np.exp(  5.21949)

    rate_eval.O27__F27__weak__mo03 = rate

@numba.njit()
def p_K42__He4_Ar39(rate_eval, tf):
    # K42 + p --> He4 + Ar39
    rate = 0.0

    # rath 
    rate += np.exp(  88.9962 + -4.83199*tf.T9i + 177.047*tf.T913i + -276.563*tf.T913
                  + 14.2618*tf.T9 + -0.760444*tf.T953 + 144.452*tf.lnT9)

    rate_eval.p_K42__He4_Ar39 = rate

@numba.njit()
def He4_Be11__n_C14(rate_eval, tf):
    # Be11 + He4 --> n + C14
    rate = 0.0

    #  wagn
    rate += np.exp(  33.7425 + -24.33*tf.T913i + -9.14417e-10*tf.T913
                  + 9.48721e-11*tf.T9 + -8.2792e-12*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Be11__n_C14 = rate

@numba.njit()
def n_Ca51__Ca52(rate_eval, tf):
    # Ca51 + n --> Ca52
    rate = 0.0

    # rath 
    rate += np.exp(  20.005 + -0.0825837*tf.T9i + 7.54703*tf.T913i + -20.2616*tf.T913
                  + 2.09021*tf.T9 + -0.169361*tf.T953 + 7.03609*tf.lnT9)

    rate_eval.n_Ca51__Ca52 = rate

@numba.njit()
def He4_Ca50__Ti54(rate_eval, tf):
    # Ca50 + He4 --> Ti54
    rate = 0.0

    # rath 
    rate += np.exp(  -928.574 + 14.77*tf.T9i + -1604.6*tf.T913i + 2636.52*tf.T913
                  + -157.907*tf.T9 + 9.06815*tf.T953 + -1236.04*tf.lnT9)

    rate_eval.He4_Ca50__Ti54 = rate

@numba.njit()
def n_Ca49__Ca50(rate_eval, tf):
    # Ca49 + n --> Ca50
    rate = 0.0

    # rath 
    rate += np.exp(  21.0163 + -0.0697085*tf.T9i + 6.48681*tf.T913i + -17.1936*tf.T913
                  + 1.69568*tf.T9 + -0.131467*tf.T953 + 6.07819*tf.lnT9)

    rate_eval.n_Ca49__Ca50 = rate

@numba.njit()
def He4_Ca47__Ti51(rate_eval, tf):
    # Ca47 + He4 --> Ti51
    rate = 0.0

    # ths8r
    rate += np.exp(  50.6782 + -76.7758*tf.T913i + -1.97823*tf.T913
                  + -0.552991*tf.T9 + 0.0318371*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca47__Ti51 = rate

@numba.njit()
def B17__n_n_n_C14__weak__wc12(rate_eval, tf):
    # B17 --> 3 n + C14
    rate = 0.0

    # wc12w
    rate += np.exp(  1.56352)

    rate_eval.B17__n_n_n_C14__weak__wc12 = rate

@numba.njit()
def He4_Na36__Al40(rate_eval, tf):
    # Na36 + He4 --> Al40
    rate = 0.0

    # rath 
    rate += np.exp(  -11.3944 + -2.61648*tf.T9i + -11.6493*tf.T913i + 14.7777*tf.T913
                  + -4.22295*tf.T9 + 0.351429*tf.T953 + 7.81712*tf.lnT9)

    rate_eval.He4_Na36__Al40 = rate

@numba.njit()
def He4_Ca46__Ti50(rate_eval, tf):
    # Ca46 + He4 --> Ti50
    rate = 0.0

    # ths8r
    rate += np.exp(  62.9052 + -76.732*tf.T913i + -13.6546*tf.T913
                  + 1.61796*tf.T9 + -0.159*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca46__Ti50 = rate

@numba.njit()
def Ca36__K36__weak__wc12(rate_eval, tf):
    # Ca36 --> K36
    rate = 0.0

    # wc12w
    rate += np.exp(  1.1332)

    rate_eval.Ca36__K36__weak__wc12 = rate

@numba.njit()
def Ca34__K34__weak__bqa_pos_(rate_eval, tf):
    # Ca34 --> K34
    rate = 0.0

    # bqa+w
    rate += np.exp(  3.13672)

    rate_eval.Ca34__K34__weak__bqa_pos_ = rate

@numba.njit()
def C17__n_N16__weak__wc12(rate_eval, tf):
    # C17 --> n + N16
    rate = 0.0

    # wc12w
    rate += np.exp(  0.139118)

    rate_eval.C17__n_N16__weak__wc12 = rate

@numba.njit()
def n_Ca46__Ca47(rate_eval, tf):
    # Ca46 + n --> Ca47
    rate = 0.0

    # ks03 
    rate += np.exp(  -0.886174 + 0.206974*tf.T9i + -19.7417*tf.T913i + 35.2401*tf.T913
                  + -1.61262*tf.T9 + 0.0443701*tf.T953 + -16.7507*tf.lnT9)

    rate_eval.n_Ca46__Ca47 = rate

@numba.njit()
def He4_Ca45__Ti49(rate_eval, tf):
    # Ca45 + He4 --> Ti49
    rate = 0.0

    # ths8r
    rate += np.exp(  57.6604 + -76.6866*tf.T913i + -9.95306*tf.T913
                  + 1.72367*tf.T9 + -0.226004*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca45__Ti49 = rate

@numba.njit()
def t_Li7__n_Be9(rate_eval, tf):
    # Li7 + t --> n + Be9
    rate = 0.0

    # bk91 
    rate += np.exp(  30.2619 + -11.333*tf.T913i + -0.170964*tf.T913
                  + -6.30572*tf.T9 + 1.2248*tf.T953 + -0.666667*tf.lnT9)
    # bk91 
    rate += np.exp(  34.634 + -11.333*tf.T913i + -7.3964*tf.T913
                  + 0.947759*tf.T9 + -0.0839008*tf.T953 + 0.333333*tf.lnT9)

    rate_eval.t_Li7__n_Be9 = rate

@numba.njit()
def He4_Li7__B11(rate_eval, tf):
    # Li7 + He4 --> B11
    rate = 0.0

    # nacrr
    rate += np.exp(  10.6937 + -6.44203*tf.T9i
                  + 0.190698*tf.T9 + -1.5*tf.lnT9)
    # nacrr
    rate += np.exp(  5.81084 + -2.95915*tf.T9i
                  + -1.5*tf.lnT9)
    # nacrn
    rate += np.exp(  18.4284 + -19.163*tf.T913i + 0.0587651*tf.T913
                  + 0.773338*tf.T9 + -0.201519*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Li7__B11 = rate

@numba.njit()
def He4_Ca44__Ti48(rate_eval, tf):
    # Ca44 + He4 --> Ti48
    rate = 0.0

    # ths8r
    rate += np.exp(  55.9169 + -76.6391*tf.T913i + 2.70825*tf.T913
                  + -4.48808*tf.T9 + 0.582872*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca44__Ti48 = rate

@numba.njit()
def He4_Ca42__Ti46(rate_eval, tf):
    # Ca42 + He4 --> Ti46
    rate = 0.0

    # ths8r
    rate += np.exp(  54.833 + -76.5379*tf.T913i + 2.80099*tf.T913
                  + -2.34788*tf.T9 + 0.150014*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca42__Ti46 = rate

@numba.njit()
def p_Ca42__Sc43(rate_eval, tf):
    # Ca42 + p --> Sc43
    rate = 0.0

    # ths8r
    rate += np.exp(  35.8192 + -31.1381*tf.T913i + -0.151667*tf.T913
                  + -1.76926*tf.T9 + 0.219569*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ca42__Sc43 = rate

@numba.njit()
def p_Ca41__Sc42(rate_eval, tf):
    # Ca41 + p --> Sc42
    rate = 0.0

    # ths8r
    rate += np.exp(  39.315 + -31.1321*tf.T913i + -6.33393*tf.T913
                  + -1.39316*tf.T9 + 0.255024*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ca41__Sc42 = rate

@numba.njit()
def Si34__P34__weak__wc12(rate_eval, tf):
    # Si34 --> P34
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.38536)

    rate_eval.Si34__P34__weak__wc12 = rate

@numba.njit()
def n_Cr51__Cr52(rate_eval, tf):
    # Cr51 + n --> Cr52
    rate = 0.0

    # ks03 
    rate += np.exp(  20.1253 + -0.0860167*tf.T9i + 6.95563*tf.T913i + -11.4485*tf.T913
                  + 0.736956*tf.T9 + -0.0695323*tf.T953 + 5.31244*tf.lnT9)

    rate_eval.n_Cr51__Cr52 = rate

@numba.njit()
def n_Ca41__Ca42(rate_eval, tf):
    # Ca41 + n --> Ca42
    rate = 0.0

    # ks03 
    rate += np.exp(  20.4461 + -0.0409481*tf.T9i + 3.7037*tf.T913i + -9.99246*tf.T913
                  + 1.05894*tf.T9 + -0.0978564*tf.T953 + 3.43604*tf.lnT9)

    rate_eval.n_Ca41__Ca42 = rate

@numba.njit()
def p_Ca52__He4_K49(rate_eval, tf):
    # Ca52 + p --> He4 + K49
    rate = 0.0

    # rath 
    rate += np.exp(  79.7478 + -5.49469*tf.T9i + 202.955*tf.T913i + -302.078*tf.T913
                  + 14.914*tf.T9 + -0.733585*tf.T953 + 161.878*tf.lnT9)

    rate_eval.p_Ca52__He4_K49 = rate

@numba.njit()
def n_F16__He4_N13(rate_eval, tf):
    # F16 + n --> He4 + N13
    rate = 0.0

    # rpsmr
    rate += np.exp(  16.7588 + 0.00426483*tf.T9i + -1.70176*tf.T913i + 3.84453*tf.T913
                  + -0.121351*tf.T9 + 0.00264846*tf.T953 + -1.63623*tf.lnT9)

    rate_eval.n_F16__He4_N13 = rate

@numba.njit()
def p_Ca40__Sc41(rate_eval, tf):
    # Ca40 + p --> Sc41
    rate = 0.0

    # il10n
    rate += np.exp(  20.0077 + -31.1711*tf.T913i
                  + -1.0*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  50.687 + -33.5123*tf.T9i + -33.7287*tf.T913
                  + 5.22449*tf.T9 + -0.357104*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  5.62969 + -7.32236*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Ca40__Sc41 = rate

@numba.njit()
def Al41__n_Si40__weak__mp17(rate_eval, tf):
    # Al41 --> n + Si40
    rate = 0.0

    # mp17w
    rate += np.exp(  4.81848)

    rate_eval.Al41__n_Si40__weak__mp17 = rate

@numba.njit()
def n_Ca40__Ca41(rate_eval, tf):
    # Ca40 + n --> Ca41
    rate = 0.0

    # ks03 
    rate += np.exp(  3.04601 + 0.0855375*tf.T9i + -9.18636*tf.T913i + 21.0095*tf.T913
                  + -1.33326*tf.T9 + 0.0769347*tf.T953 + -8.66245*tf.lnT9)

    rate_eval.n_Ca40__Ca41 = rate

@numba.njit()
def He4_Ca37__Ti41(rate_eval, tf):
    # Ca37 + He4 --> Ti41
    rate = 0.0

    # ths8r
    rate += np.exp(  51.8981 + -76.2415*tf.T913i + -6.81204*tf.T913
                  + 0.91107*tf.T9 + -0.146955*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca37__Ti41 = rate

@numba.njit()
def n_Ca37__Ca38(rate_eval, tf):
    # Ca37 + n --> Ca38
    rate = 0.0

    # ths8r
    rate += np.exp(  10.5086 + -0.222812*tf.T913
                  + 0.169715*tf.T9 + -0.0108234*tf.T953)

    rate_eval.n_Ca37__Ca38 = rate

@numba.njit()
def p_Fe64__Co65(rate_eval, tf):
    # Fe64 + p --> Co65
    rate = 0.0

    # rath 
    rate += np.exp(  140.405 + -7.17982*tf.T9i + 270.774*tf.T913i + -434.346*tf.T913
                  + 24.1172*tf.T9 + -1.40265*tf.T953 + 218.01*tf.lnT9)

    rate_eval.p_Fe64__Co65 = rate

@numba.njit()
def n_Na27__Na28(rate_eval, tf):
    # Na27 + n --> Na28
    rate = 0.0

    # rath 
    rate += np.exp(  11.7825 + -0.0412645*tf.T9i + 2.92915*tf.T913i + -6.38197*tf.T913
                  + 0.530499*tf.T9 + -0.028775*tf.T953 + 2.21943*tf.lnT9)

    rate_eval.n_Na27__Na28 = rate

@numba.njit()
def n_Ca36__Ca37(rate_eval, tf):
    # Ca36 + n --> Ca37
    rate = 0.0

    # ths8r
    rate += np.exp(  11.7923 + -0.659533*tf.T913
                  + 0.236318*tf.T9 + -0.0257033*tf.T953)

    rate_eval.n_Ca36__Ca37 = rate

@numba.njit()
def p_Si37__P38(rate_eval, tf):
    # Si37 + p --> P38
    rate = 0.0

    # rath 
    rate += np.exp(  78.6076 + -3.68821*tf.T9i + 132.966*tf.T913i + -221.198*tf.T913
                  + 12.1055*tf.T9 + -0.672511*tf.T953 + 110.924*tf.lnT9)

    rate_eval.p_Si37__P38 = rate

@numba.njit()
def He4_Ca35__Ti39(rate_eval, tf):
    # Ca35 + He4 --> Ti39
    rate = 0.0

    # ths8r
    rate += np.exp(  45.1043 + -76.1016*tf.T913i + -0.913501*tf.T913
                  + -0.502372*tf.T9 + 0.00757111*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca35__Ti39 = rate

@numba.njit()
def P37__S37__weak__wc12(rate_eval, tf):
    # P37 --> S37
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.20376)

    rate_eval.P37__S37__weak__wc12 = rate

@numba.njit()
def Ar54__n_K53__weak__mp17(rate_eval, tf):
    # Ar54 --> n + K53
    rate = 0.0

    # mp17w
    rate += np.exp(  4.31544)

    rate_eval.Ar54__n_K53__weak__mp17 = rate

@numba.njit()
def p_Ca35__Sc36(rate_eval, tf):
    # Ca35 + p --> Sc36
    rate = 0.0

    # ths8r
    rate += np.exp(  -17.041 + -23.2906*tf.T9i + 19.5625*tf.T913
                  + -2.69513*tf.T9 + 0.226635*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ca35__Sc36 = rate

@numba.njit()
def He4_Ca34__Ti38(rate_eval, tf):
    # Ca34 + He4 --> Ti38
    rate = 0.0

    # ths8r
    rate += np.exp(  45.2875 + -76.0259*tf.T913i + -1.81643*tf.T913
                  + -0.299807*tf.T9 + -0.0115079*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca34__Ti38 = rate

@numba.njit()
def He4_Cl46__n_K49(rate_eval, tf):
    # Cl46 + He4 --> n + K49
    rate = 0.0

    # rath 
    rate += np.exp(  -372.934 + 2.09659*tf.T9i + -538.545*tf.T913i + 952.912*tf.T913
                  + -62.6512*tf.T9 + 3.80599*tf.T953 + -419.097*tf.lnT9)

    rate_eval.He4_Cl46__n_K49 = rate

@numba.njit()
def p_Ca34__Sc35(rate_eval, tf):
    # Ca34 + p --> Sc35
    rate = 0.0

    # ths8r
    rate += np.exp(  -16.0974 + -47.5904*tf.T9i + 18.7003*tf.T913
                  + -2.23638*tf.T9 + 0.185081*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ca34__Sc35 = rate

@numba.njit()
def p_Be11__He4_Li8(rate_eval, tf):
    # Be11 + p --> He4 + Li8
    rate = 0.0

    #  wagn
    rate += np.exp(  25.1949 + -2.37082e-12*tf.T9i + -10.42*tf.T913i + -1.12148e-09*tf.T913
                  + 1.21029e-10*tf.T9 + -1.08657e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Be11__He4_Li8 = rate

@numba.njit()
def n_Fe47__p_Mn47(rate_eval, tf):
    # Fe47 + n --> p + Mn47
    rate = 0.0

    # ths8r
    rate += np.exp(  21.9011 + -1.08015*tf.T913
                  + 0.290465*tf.T9 + -0.0265093*tf.T953)

    rate_eval.n_Fe47__p_Mn47 = rate

@numba.njit()
def He4_Ca33__Ti37(rate_eval, tf):
    # Ca33 + He4 --> Ti37
    rate = 0.0

    # ths8r
    rate += np.exp(  43.1496 + -75.9466*tf.T913i + -0.908393*tf.T913
                  + -0.276939*tf.T9 + -0.0164977*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca33__Ti37 = rate

@numba.njit()
def He4_Na27__Al31(rate_eval, tf):
    # Na27 + He4 --> Al31
    rate = 0.0

    # rath 
    rate += np.exp(  -11.474 + -2.09682*tf.T9i + -26.2446*tf.T913i + 29.279*tf.T913
                  + -4.66098*tf.T9 + 0.358776*tf.T953 + -1.05227*tf.lnT9)

    rate_eval.He4_Na27__Al31 = rate

@numba.njit()
def p_K59__Ca60(rate_eval, tf):
    # K59 + p --> Ca60
    rate = 0.0

    # rath 
    rate += np.exp(  116.154 + -5.57558*tf.T9i + 208.528*tf.T913i + -343.539*tf.T913
                  + 19.4983*tf.T9 + -1.11951*tf.T953 + 169.992*tf.lnT9)

    rate_eval.p_K59__Ca60 = rate

@numba.njit()
def He4_K58__Sc62(rate_eval, tf):
    # K58 + He4 --> Sc62
    rate = 0.0

    # rath 
    rate += np.exp(  -971.992 + 15.3689*tf.T9i + -1667.34*tf.T913i + 2749.18*tf.T913
                  + -164.41*tf.T9 + 9.43889*tf.T953 + -1289.01*tf.lnT9)

    rate_eval.He4_K58__Sc62 = rate

@numba.njit()
def p_K50__n_Ca50(rate_eval, tf):
    # K50 + p --> n + Ca50
    rate = 0.0

    # rath 
    rate += np.exp(  117.94 + -5.21683*tf.T9i + 194.379*tf.T913i + -319.081*tf.T913
                  + 17.691*tf.T9 + -0.996329*tf.T953 + 159.361*tf.lnT9)

    rate_eval.p_K50__n_Ca50 = rate

@numba.njit()
def Na27__Mg27__weak__wc12(rate_eval, tf):
    # Na27 --> Mg27
    rate = 0.0

    # wc12w
    rate += np.exp(  0.832831)

    rate_eval.Na27__Mg27__weak__wc12 = rate

@numba.njit()
def p_P30__S31(rate_eval, tf):
    # P30 + p --> S31
    rate = 0.0

    # mb07 
    rate += np.exp(  -7756.63 + 10.5093*tf.T9i + -1999.51*tf.T913i + 11886.5*tf.T913
                  + -2668.72*tf.T9 + 354.294*tf.T953 + -2900.45*tf.lnT9)
    # mb07 
    rate += np.exp(  24.3866 + -8.98316*tf.T9i + 156.029*tf.T913i + -174.377*tf.T913
                  + 7.4644*tf.T9 + -0.342232*tf.T953 + 99.2579*tf.lnT9)

    rate_eval.p_P30__S31 = rate

@numba.njit()
def p_K57__Ca58(rate_eval, tf):
    # K57 + p --> Ca58
    rate = 0.0

    # rath 
    rate += np.exp(  113.028 + -5.47718*tf.T9i + 203.566*tf.T913i + -335.501*tf.T913
                  + 18.9835*tf.T9 + -1.08723*tf.T953 + 166.179*tf.lnT9)

    rate_eval.p_K57__Ca58 = rate

@numba.njit()
def He4_Cl44__n_K47(rate_eval, tf):
    # Cl44 + He4 --> n + K47
    rate = 0.0

    # rath 
    rate += np.exp(  -364.556 + 1.97627*tf.T9i + -521.841*tf.T913i + 926.034*tf.T913
                  + -61.2362*tf.T9 + 3.73051*tf.T953 + -405.625*tf.lnT9)

    rate_eval.He4_Cl44__n_K47 = rate

@numba.njit()
def He4_Na29__Al33(rate_eval, tf):
    # Na29 + He4 --> Al33
    rate = 0.0

    # rath 
    rate += np.exp(  -12.9058 + -2.21816*tf.T9i + -23.1197*tf.T913i + 27.1418*tf.T913
                  + -4.65852*tf.T9 + 0.364013*tf.T953 + 0.651521*tf.lnT9)

    rate_eval.He4_Na29__Al33 = rate

@numba.njit()
def p_K56__Ca57(rate_eval, tf):
    # K56 + p --> Ca57
    rate = 0.0

    # rath 
    rate += np.exp(  125.426 + -5.54271*tf.T9i + 212.718*tf.T913i + -356.919*tf.T913
                  + 20.4313*tf.T9 + -1.17354*tf.T953 + 175.036*tf.lnT9)

    rate_eval.p_K56__Ca57 = rate

@numba.njit()
def He4_Si45__S49(rate_eval, tf):
    # Si45 + He4 --> S49
    rate = 0.0

    # rath 
    rate += np.exp(  -319.806 + 1.69707*tf.T9i + -455.881*tf.T913i + 801.849*tf.T913
                  + -52.9328*tf.T9 + 3.22892*tf.T953 + -352.752*tf.lnT9)

    rate_eval.He4_Si45__S49 = rate

@numba.njit()
def He4_K55__Sc59(rate_eval, tf):
    # K55 + He4 --> Sc59
    rate = 0.0

    # rath 
    rate += np.exp(  -944.63 + 14.9465*tf.T9i + -1623.31*tf.T913i + 2674.42*tf.T913
                  + -160.09*tf.T9 + 9.19352*tf.T953 + -1253.64*tf.lnT9)

    rate_eval.He4_K55__Sc59 = rate

@numba.njit()
def V60__Cr60__weak__wc17(rate_eval, tf):
    # V60 --> Cr60
    rate = 0.0

    # wc17w
    rate += np.exp(  2.24916)

    rate_eval.V60__Cr60__weak__wc17 = rate

@numba.njit()
def Fe60__Co60__weak__wc12(rate_eval, tf):
    # Fe60 --> Co60
    rate = 0.0

    # wc12w
    rate += np.exp(  -32.4128)

    rate_eval.Fe60__Co60__weak__wc12 = rate

@numba.njit()
def p_Cl36__He4_S33(rate_eval, tf):
    # Cl36 + p --> He4 + S33
    rate = 0.0

    # ths8r
    rate += np.exp(  24.6393 + -27.9044*tf.T913i + 7.06482*tf.T913
                  + -1.77458*tf.T9 + 0.192878*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cl36__He4_S33 = rate

@numba.njit()
def n_K56__K57(rate_eval, tf):
    # K56 + n --> K57
    rate = 0.0

    # rath 
    rate += np.exp(  16.2953 + -0.0257247*tf.T9i + 2.61778*tf.T913i + -9.92324*tf.T913
                  + 0.757424*tf.T9 + -0.0612534*tf.T953 + 2.86588*tf.lnT9)

    rate_eval.n_K56__K57 = rate

@numba.njit()
def Sc55__n_Ti54__weak__wc12(rate_eval, tf):
    # Sc55 --> n + Ti54
    rate = 0.0

    # wc12w
    rate += np.exp(  0.204937)

    rate_eval.Sc55__n_Ti54__weak__wc12 = rate

@numba.njit()
def n_K53__K54(rate_eval, tf):
    # K53 + n --> K54
    rate = 0.0

    # rath 
    rate += np.exp(  18.0981 + -0.0397892*tf.T9i + 4.5787*tf.T913i + -17.4588*tf.T913
                  + 1.84174*tf.T9 + -0.144478*tf.T953 + 5.208*tf.lnT9)

    rate_eval.n_K53__K54 = rate

@numba.njit()
def He4_S27__Ar31(rate_eval, tf):
    # S27 + He4 --> Ar31
    rate = 0.0

    # ths8r
    rate += np.exp(  38.4676 + -64.9324*tf.T913i + 0.663455*tf.T913
                  + -0.753231*tf.T9 + 0.0464906*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S27__Ar31 = rate

@numba.njit()
def p_K52__Ca53(rate_eval, tf):
    # K52 + p --> Ca53
    rate = 0.0

    # rath 
    rate += np.exp(  112.368 + -5.35583*tf.T9i + 202.695*tf.T913i + -332.534*tf.T913
                  + 18.3814*tf.T9 + -1.02949*tf.T953 + 165.926*tf.lnT9)

    rate_eval.p_K52__Ca53 = rate

@numba.njit()
def n_K52__K53(rate_eval, tf):
    # K52 + n --> K53
    rate = 0.0

    # rath 
    rate += np.exp(  16.9699 + -0.0205834*tf.T9i + 2.31648*tf.T913i + -8.84146*tf.T913
                  + 0.589922*tf.T9 + -0.0475069*tf.T953 + 2.6301*tf.lnT9)

    rate_eval.n_K52__K53 = rate

@numba.njit()
def He4_K51__Sc55(rate_eval, tf):
    # K51 + He4 --> Sc55
    rate = 0.0

    # rath 
    rate += np.exp(  -910.38 + 14.457*tf.T9i + -1569.15*tf.T913i + 2578.85*tf.T913
                  + -154.196*tf.T9 + 8.84634*tf.T953 + -1209.33*tf.lnT9)

    rate_eval.He4_K51__Sc55 = rate

@numba.njit()
def p_F20__n_Ne20(rate_eval, tf):
    # F20 + p --> n + Ne20
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.4299 + -2.00863*tf.T9i + 66.6612*tf.T913i + -118.432*tf.T913
                  + 6.47602*tf.T9 + -0.36471*tf.T953 + 59.1958*tf.lnT9)

    rate_eval.p_F20__n_Ne20 = rate

@numba.njit()
def p_K51__Ca52(rate_eval, tf):
    # K51 + p --> Ca52
    rate = 0.0

    # rath 
    rate += np.exp(  111.184 + -5.30773*tf.T9i + 200.505*tf.T913i + -329.445*tf.T913
                  + 18.2784*tf.T9 + -1.0279*tf.T953 + 164.328*tf.lnT9)

    rate_eval.p_K51__Ca52 = rate

@numba.njit()
def n_K50__K51(rate_eval, tf):
    # K50 + n --> K51
    rate = 0.0

    # rath 
    rate += np.exp(  24.8722 + 0.0273876*tf.T9i + 0.424229*tf.T913i + -14.3581*tf.T913
                  + 1.2293*tf.T9 + -0.0878978*tf.T953 + 3.02981*tf.lnT9)

    rate_eval.n_K50__K51 = rate

@numba.njit()
def He4_K49__Sc53(rate_eval, tf):
    # K49 + He4 --> Sc53
    rate = 0.0

    # rath 
    rate += np.exp(  -885.068 + 14.1342*tf.T9i + -1534.93*tf.T913i + 2518.16*tf.T913
                  + -150.563*tf.T9 + 8.63625*tf.T953 + -1181.2*tf.lnT9)

    rate_eval.He4_K49__Sc53 = rate

@numba.njit()
def n_K46__K47(rate_eval, tf):
    # K46 + n --> K47
    rate = 0.0

    # rath 
    rate += np.exp(  13.3 + -0.0526583*tf.T9i + 3.435*tf.T913i + -3.6976*tf.T913
                  + -0.176925*tf.T9 + 0.0212584*tf.T953 + 2.06442*tf.lnT9)

    rate_eval.n_K46__K47 = rate

@numba.njit()
def p_Ti65__V66(rate_eval, tf):
    # Ti65 + p --> V66
    rate = 0.0

    # rath 
    rate += np.exp(  129.876 + -6.49302*tf.T9i + 246.852*tf.T913i + -399.033*tf.T913
                  + 22.2248*tf.T9 + -1.25715*tf.T953 + 199.075*tf.lnT9)

    rate_eval.p_Ti65__V66 = rate

@numba.njit()
def p_Ne26__Na27(rate_eval, tf):
    # Ne26 + p --> Na27
    rate = 0.0

    # rath 
    rate += np.exp(  53.0388 + -2.45835*tf.T9i + 83.6568*tf.T913i + -141.082*tf.T913
                  + 7.57753*tf.T9 + -0.418521*tf.T953 + 71.5722*tf.lnT9)

    rate_eval.p_Ne26__Na27 = rate

@numba.njit()
def p_K45__Ca46(rate_eval, tf):
    # K45 + p --> Ca46
    rate = 0.0

    # rath 
    rate += np.exp(  105.864 + -4.97604*tf.T9i + 183.874*tf.T913i + -304.097*tf.T913
                  + 16.8925*tf.T9 + -0.961336*tf.T953 + 151.699*tf.lnT9)

    rate_eval.p_K45__Ca46 = rate

@numba.njit()
def He4_Ne17__Mg21(rate_eval, tf):
    # Ne17 + He4 --> Mg21
    rate = 0.0

    # ths8r
    rate += np.exp(  32.2147 + -46.3234*tf.T913i + 0.343364*tf.T913
                  + -0.65908*tf.T9 + 0.0503969*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ne17__Mg21 = rate

@numba.njit()
def Sc54__n_Ti53__weak__mp17(rate_eval, tf):
    # Sc54 --> n + Ti53
    rate = 0.0

    # mp17w
    rate += np.exp(  -3.63608)

    rate_eval.Sc54__n_Ti53__weak__mp17 = rate

@numba.njit()
def n_K45__K46(rate_eval, tf):
    # K45 + n --> K46
    rate = 0.0

    # rath 
    rate += np.exp(  11.2022 + -0.0224398*tf.T9i + 0.846638*tf.T913i + 0.963526*tf.T913
                  + -0.0713414*tf.T9 + -0.013947*tf.T953 + -0.0632809*tf.lnT9)

    rate_eval.n_K45__K46 = rate

@numba.njit()
def p_Ar38__K39(rate_eval, tf):
    # Ar38 + p --> K39
    rate = 0.0

    # ths8r
    rate += np.exp(  35.2834 + -29.0021*tf.T913i + -0.525968*tf.T913
                  + -1.94216*tf.T9 + 0.267346*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ar38__K39 = rate

@numba.njit()
def He4_K44__Sc48(rate_eval, tf):
    # K44 + He4 --> Sc48
    rate = 0.0

    # rath 
    rate += np.exp(  -832.035 + 13.4129*tf.T9i + -1457.62*tf.T913i + 2383.2*tf.T913
                  + -142.4*tf.T9 + 8.16278*tf.T953 + -1118.51*tf.lnT9)

    rate_eval.He4_K44__Sc48 = rate

@numba.njit()
def n_K44__K45(rate_eval, tf):
    # K44 + n --> K45
    rate = 0.0

    # rath 
    rate += np.exp(  22.8112 + -0.0494145*tf.T9i + 4.82096*tf.T913i + -13.7693*tf.T913
                  + 1.12152*tf.T9 + -0.0895938*tf.T953 + 4.71976*tf.lnT9)

    rate_eval.n_K44__K45 = rate

@numba.njit()
def He4_K43__Sc47(rate_eval, tf):
    # K43 + He4 --> Sc47
    rate = 0.0

    # rath 
    rate += np.exp(  -852.619 + 13.3039*tf.T9i + -1456.98*tf.T913i + 2406.08*tf.T913
                  + -144.317*tf.T9 + 8.28842*tf.T953 + -1125.17*tf.lnT9)

    rate_eval.He4_K43__Sc47 = rate

@numba.njit()
def p_K43__Ca44(rate_eval, tf):
    # K43 + p --> Ca44
    rate = 0.0

    # rath 
    rate += np.exp(  113.428 + -4.92141*tf.T9i + 184.43*tf.T913i + -311.657*tf.T913
                  + 17.5759*tf.T9 + -1.0033*tf.T953 + 153.486*tf.lnT9)

    rate_eval.p_K43__Ca44 = rate

@numba.njit()
def n_K39__He4_Cl36(rate_eval, tf):
    # K39 + n --> He4 + Cl36
    rate = 0.0

    # ths8r
    rate += np.exp(  -18.3419 + 20.3122*tf.T913
                  + -0.37149*tf.T9 + -0.0867942*tf.T953)

    rate_eval.n_K39__He4_Cl36 = rate

@numba.njit()
def p_Cr45__Mn46(rate_eval, tf):
    # Cr45 + p --> Mn46
    rate = 0.0

    # nfisn
    rate += np.exp(  28.0461 + -0.0910014*tf.T9i + -30.449*tf.T913i + -10.9197*tf.T913
                  + 0.947957*tf.T9 + -0.0867724*tf.T953 + 3.78308*tf.lnT9)
    # nfisn
    rate += np.exp(  -57.8292 + -30.903*tf.T9i + 460.107*tf.T913i + -389.006*tf.T913
                  + 15.0962*tf.T9 + -0.649315*tf.T953 + 248.102*tf.lnT9)
    # nfisn
    rate += np.exp(  162.07 + -19.6375*tf.T9i + 528.326*tf.T913i + -714.758*tf.T913
                  + 44.2716*tf.T9 + -3.80935*tf.T953 + 364.631*tf.lnT9)
    # nfisn
    rate += np.exp(  6100.51 + -6.70231*tf.T9i + 812.772*tf.T913i + -9847.77*tf.T913
                  + 5483.87*tf.T9 + -3072.96*tf.T953 + 1623.06*tf.lnT9)
    # nfisn
    rate += np.exp(  1615.36 + -51.085*tf.T9i + 2122.65*tf.T913i + -4024.61*tf.T913
                  + 369.083*tf.T9 + -40.3015*tf.T953 + 1700.1*tf.lnT9)

    rate_eval.p_Cr45__Mn46 = rate

@numba.njit()
def He4_Ti47__Cr51(rate_eval, tf):
    # Ti47 + He4 --> Cr51
    rate = 0.0

    # ths8r
    rate += np.exp(  63.333 + -81.8123*tf.T913i + -8.91821*tf.T913
                  + -0.0329369*tf.T9 + 0.039179*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti47__Cr51 = rate

@numba.njit()
def He4_Ne27__Mg31(rate_eval, tf):
    # Ne27 + He4 --> Mg31
    rate = 0.0

    # rath 
    rate += np.exp(  54.3633 + -2.68892*tf.T9i + 53.0168*tf.T913i + -123.838*tf.T913
                  + 5.39601*tf.T9 + -0.248316*tf.T953 + 66.0472*tf.lnT9)

    rate_eval.He4_Ne27__Mg31 = rate

@numba.njit()
def Mn70__n_Fe69__weak__mp17(rate_eval, tf):
    # Mn70 --> n + Fe69
    rate = 0.0

    # mp17w
    rate += np.exp(  2.83546)

    rate_eval.Mn70__n_Fe69__weak__mp17 = rate

@numba.njit()
def p_Sc62__Ti63(rate_eval, tf):
    # Sc62 + p --> Ti63
    rate = 0.0

    # rath 
    rate += np.exp(  118.715 + -6.08397*tf.T9i + 226.145*tf.T913i + -364.519*tf.T913
                  + 20.1886*tf.T9 + -1.13498*tf.T953 + 182.434*tf.lnT9)

    rate_eval.p_Sc62__Ti63 = rate

@numba.njit()
def n_K43__K44(rate_eval, tf):
    # K43 + n --> K44
    rate = 0.0

    # rath 
    rate += np.exp(  6.00908 + 0.0258062*tf.T9i + -4.17838*tf.T913i + 13.6934*tf.T913
                  + -1.34815*tf.T9 + 0.0902499*tf.T953 + -4.93285*tf.lnT9)

    rate_eval.n_K43__K44 = rate

@numba.njit()
def n_Al28__Al29(rate_eval, tf):
    # Al28 + n --> Al29
    rate = 0.0

    # rath 
    rate += np.exp(  9.47835 + 0.0133004*tf.T9i + -3.00881*tf.T913i + 7.20606*tf.T913
                  + -0.364428*tf.T9 + 0.0101722*tf.T953 + -3.49316*tf.lnT9)

    rate_eval.n_Al28__Al29 = rate

@numba.njit()
def p_K41__Ca42(rate_eval, tf):
    # K41 + p --> Ca42
    rate = 0.0

    # SM86n
    rate += np.exp(  32.2014 + -30.08*tf.T913i + 2.93877*tf.T913
                  + 2.77388*tf.T9 + -4.8284*tf.T953 + -0.666667*tf.lnT9)
    # SM86r
    rate += np.exp(  16.0218 + -12.0*tf.T9i + -1.68317*tf.T913
                  + 0.692171*tf.T9 + -0.0831029*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_K41__Ca42 = rate

@numba.njit()
def p_S34__Cl35(rate_eval, tf):
    # S34 + p --> Cl35
    rate = 0.0

    # se19r
    rate += np.exp(  -7.70046 + -2.02615*tf.T9i
                  + -1.5*tf.lnT9)
    # se19r
    rate += np.exp(  8.25443 + -5.75583*tf.T9i
                  + -1.5*tf.lnT9)
    # se19r
    rate += np.exp(  -14.8781 + -1.40414*tf.T9i
                  + -1.5*tf.lnT9)
    # se19r
    rate += np.exp(  7.00142 + -5.10598*tf.T9i
                  + -1.5*tf.lnT9)
    # se19r
    rate += np.exp(  -17.9366 + -1.17205*tf.T9i
                  + -1.5*tf.lnT9)
    # se19r
    rate += np.exp(  5.80604 + -4.6418*tf.T9i
                  + -1.5*tf.lnT9)
    # se19r
    rate += np.exp(  0.43449 + -3.16803*tf.T9i
                  + -1.5*tf.lnT9)
    # se19r
    rate += np.exp(  -60.0247 + -27.689*tf.T9i + 454.53*tf.T913i + -375.557*tf.T913
                  + 12.6533*tf.T9 + -0.408677*tf.T953 + 245.118*tf.lnT9)

    rate_eval.p_S34__Cl35 = rate

@numba.njit()
def n_K41__K42(rate_eval, tf):
    # K41 + n --> K42
    rate = 0.0

    # ks03 
    rate += np.exp(  13.5369 + -0.0421838*tf.T9i + 2.7759*tf.T913i + -1.20231*tf.T913
                  + -0.0812946*tf.T9 + -0.0149075*tf.T953 + 1.4088*tf.lnT9)

    rate_eval.n_K41__K42 = rate

@numba.njit()
def Ca35__p_p_Cl33__weak__wc12(rate_eval, tf):
    # Ca35 --> p + p + Cl33
    rate = 0.0

    # wc12w
    rate += np.exp(  0.100568)

    rate_eval.Ca35__p_p_Cl33__weak__wc12 = rate

@numba.njit()
def n_K40__K41(rate_eval, tf):
    # K40 + n --> K41
    rate = 0.0

    # ks03 
    rate += np.exp(  17.4542 + -0.0277342*tf.T9i + 1.90527*tf.T913i + -4.8523*tf.T913
                  + 0.552061*tf.T9 + -0.0570777*tf.T953 + 1.46777*tf.lnT9)

    rate_eval.n_K40__K41 = rate

@numba.njit()
def p_K38__Ca39(rate_eval, tf):
    # K38 + p --> Ca39
    rate = 0.0

    # ths8r
    rate += np.exp(  36.0112 + -30.0666*tf.T913i + -1.25895*tf.T913
                  + -2.18714*tf.T9 + 0.305897*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_K38__Ca39 = rate

@numba.njit()
def He4_Ca36__p_Sc39(rate_eval, tf):
    # Ca36 + He4 --> p + Sc39
    rate = 0.0

    # ths8r
    rate += np.exp(  55.7563 + -76.1732*tf.T913i + -0.623677*tf.T913
                  + -0.571836*tf.T9 + 0.0260149*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca36__p_Sc39 = rate

@numba.njit()
def p_K37__Ca38(rate_eval, tf):
    # K37 + p --> Ca38
    rate = 0.0

    # ths8r
    rate += np.exp(  36.2122 + -30.0596*tf.T913i + -2.56332*tf.T913
                  + -2.026*tf.T9 + 0.289027*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_K37__Ca38 = rate

@numba.njit()
def He4_Sc48__p_Ti51(rate_eval, tf):
    # Sc48 + He4 --> p + Ti51
    rate = 0.0

    # rath 
    rate += np.exp(  -846.099 + 17.271*tf.T9i + -1740.8*tf.T913i + 2683.45*tf.T913
                  + -154.78*tf.T9 + 8.68561*tf.T953 + -1291.82*tf.lnT9)

    rate_eval.He4_Sc48__p_Ti51 = rate

@numba.njit()
def n_Mn45__Mn46(rate_eval, tf):
    # Mn45 + n --> Mn46
    rate = 0.0

    # ths8r
    rate += np.exp(  12.8383 + -1.59471*tf.T913
                  + 0.415909*tf.T9 + -0.0371426*tf.T953)

    rate_eval.n_Mn45__Mn46 = rate

@numba.njit()
def p_V56__n_Cr56(rate_eval, tf):
    # V56 + p --> n + Cr56
    rate = 0.0

    # rath 
    rate += np.exp(  129.408 + -6.21765*tf.T9i + 231.441*tf.T913i + -371.678*tf.T913
                  + 20.3152*tf.T9 + -1.13861*tf.T953 + 187.434*tf.lnT9)

    rate_eval.p_V56__n_Cr56 = rate

@numba.njit()
def n_K37__K38(rate_eval, tf):
    # K37 + n --> K38
    rate = 0.0

    # ths8r
    rate += np.exp(  8.98129 + 0.538174*tf.T913
                  + -0.0208079*tf.T9 + -0.00404949*tf.T953)

    rate_eval.n_K37__K38 = rate

@numba.njit()
def He4_P28__Cl32(rate_eval, tf):
    # P28 + He4 --> Cl32
    rate = 0.0

    # ths8r
    rate += np.exp(  40.827 + -62.2912*tf.T913i + -0.0652088*tf.T913
                  + -0.754179*tf.T9 + 0.0521034*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P28__Cl32 = rate

@numba.njit()
def p_K36__Ca37(rate_eval, tf):
    # K36 + p --> Ca37
    rate = 0.0

    # laurr
    rate += np.exp(  -38.3067 + -0.731*tf.T9i
                  + -1.5*tf.lnT9)
    # laurr
    rate += np.exp(  8.10168 + -8.332*tf.T9i
                  + -1.5*tf.lnT9)
    # laurr
    rate += np.exp(  7.87853 + -7.938*tf.T9i
                  + -1.5*tf.lnT9)
    # laurr
    rate += np.exp(  6.96602 + -6.963*tf.T9i
                  + -1.5*tf.lnT9)
    # laurr
    rate += np.exp(  7.59085 + -11.512*tf.T9i
                  + -1.5*tf.lnT9)
    # laurr
    rate += np.exp(  -31.0423 + -0.928*tf.T9i
                  + -1.5*tf.lnT9)
    # laurr
    rate += np.exp(  8.10168 + -11.466*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_K36__Ca37 = rate

@numba.njit()
def n_K36__K37(rate_eval, tf):
    # K36 + n --> K37
    rate = 0.0

    # ths8r
    rate += np.exp(  11.7972 + -0.0219877*tf.T913
                  + 0.0899246*tf.T9 + -0.00523424*tf.T953)

    rate_eval.n_K36__K37 = rate

@numba.njit()
def n_O15__He4_C12(rate_eval, tf):
    # O15 + n --> He4 + C12
    rate = 0.0

    # cf88n
    rate += np.exp(  17.3699 + 0.124787*tf.T913
                  + 0.0588937*tf.T9 + -0.00679206*tf.T953)

    rate_eval.n_O15__He4_C12 = rate

@numba.njit()
def He4_K35__Sc39(rate_eval, tf):
    # K35 + He4 --> Sc39
    rate = 0.0

    # ths8r
    rate += np.exp(  44.3089 + -73.542*tf.T913i + -2.20522*tf.T913
                  + -0.0580847*tf.T9 + -0.0436294*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K35__Sc39 = rate

@numba.njit()
def n_K34__K35(rate_eval, tf):
    # K34 + n --> K35
    rate = 0.0

    # ths8r
    rate += np.exp(  9.5425 + -0.0436317*tf.T913
                  + 0.125768*tf.T9 + -0.00193909*tf.T953)

    rate_eval.n_K34__K35 = rate

@numba.njit()
def n_K33__K34(rate_eval, tf):
    # K33 + n --> K34
    rate = 0.0

    # ths8r
    rate += np.exp(  9.79792 + -0.0599437*tf.T913
                  + 0.109216*tf.T9 + -0.00467937*tf.T953)

    rate_eval.n_K33__K34 = rate

@numba.njit()
def He4_K32__Sc36(rate_eval, tf):
    # K32 + He4 --> Sc36
    rate = 0.0

    # ths8r
    rate += np.exp(  42.4397 + -73.3104*tf.T913i + -0.542268*tf.T913
                  + -0.401874*tf.T9 + 0.00126369*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K32__Sc36 = rate

@numba.njit()
def n_Si40__Si41(rate_eval, tf):
    # Si40 + n --> Si41
    rate = 0.0

    # rath 
    rate += np.exp(  9.69718 + -0.0367264*tf.T9i + 2.49706*tf.T913i + -3.43064*tf.T913
                  + -0.141913*tf.T9 + 0.025872*tf.T953 + 1.64157*tf.lnT9)

    rate_eval.n_Si40__Si41 = rate

@numba.njit()
def n_K32__K33(rate_eval, tf):
    # K32 + n --> K33
    rate = 0.0

    # ths8r
    rate += np.exp(  10.5853 + -0.477681*tf.T913
                  + 0.232368*tf.T9 + -0.0198295*tf.T953)

    rate_eval.n_K32__K33 = rate

@numba.njit()
def He4_Ar53__Ca57(rate_eval, tf):
    # Ar53 + He4 --> Ca57
    rate = 0.0

    # rath 
    rate += np.exp(  -907.202 + 14.3084*tf.T9i + -1552.51*tf.T913i + 2562.07*tf.T913
                  + -153.602*tf.T9 + 8.83033*tf.T953 + -1199.73*tf.lnT9)

    rate_eval.He4_Ar53__Ca57 = rate

@numba.njit()
def p_Ar51__K52(rate_eval, tf):
    # Ar51 + p --> K52
    rate = 0.0

    # rath 
    rate += np.exp(  109.945 + -5.13634*tf.T9i + 195.22*tf.T913i + -321.983*tf.T913
                  + 17.751*tf.T9 + -0.985569*tf.T953 + 160.251*tf.lnT9)

    rate_eval.p_Ar51__K52 = rate

@numba.njit()
def Mn66__Fe66__weak__wc17(rate_eval, tf):
    # Mn66 --> Fe66
    rate = 0.0

    # wc17w
    rate += np.exp(  2.2615)

    rate_eval.Mn66__Fe66__weak__wc17 = rate

@numba.njit()
def p_Cl42__n_Ar42(rate_eval, tf):
    # Cl42 + p --> n + Ar42
    rate = 0.0

    # rath 
    rate += np.exp(  102.584 + -4.46563*tf.T9i + 163.493*tf.T913i + -269.974*tf.T913
                  + 14.8618*tf.T9 + -0.832266*tf.T953 + 135.282*tf.lnT9)

    rate_eval.p_Cl42__n_Ar42 = rate

@numba.njit()
def n_Ar51__Ar52(rate_eval, tf):
    # Ar51 + n --> Ar52
    rate = 0.0

    # rath 
    rate += np.exp(  17.5775 + -0.0280034*tf.T9i + 3.2005*tf.T913i + -11.9075*tf.T913
                  + 0.978775*tf.T9 + -0.0741144*tf.T953 + 3.61267*tf.lnT9)

    rate_eval.n_Ar51__Ar52 = rate

@numba.njit()
def n_Ar47__Ar48(rate_eval, tf):
    # Ar47 + n --> Ar48
    rate = 0.0

    # rath 
    rate += np.exp(  10.1065 + -0.0131785*tf.T9i + 0.213763*tf.T913i + -0.642259*tf.T913
                  + 0.326153*tf.T9 + -0.050865*tf.T953 + -0.228163*tf.lnT9)

    rate_eval.n_Ar47__Ar48 = rate

@numba.njit()
def He4_Ar46__Ca50(rate_eval, tf):
    # Ar46 + He4 --> Ca50
    rate = 0.0

    # rath 
    rate += np.exp(  -843.362 + 13.3845*tf.T9i + -1452.87*tf.T913i + 2391.15*tf.T913
                  + -143.971*tf.T9 + 8.35655*tf.T953 + -1119.15*tf.lnT9)

    rate_eval.He4_Ar46__Ca50 = rate

@numba.njit()
def n_Ar46__Ar47(rate_eval, tf):
    # Ar46 + n --> Ar47
    rate = 0.0

    # rath 
    rate += np.exp(  22.1744 + -0.0702247*tf.T9i + 7.33561*tf.T913i + -20.3761*tf.T913
                  + 2.13377*tf.T9 + -0.187336*tf.T953 + 7.30146*tf.lnT9)

    rate_eval.n_Ar46__Ar47 = rate

@numba.njit()
def n_F18__p_O18(rate_eval, tf):
    # F18 + n --> p + O18
    rate = 0.0

    #  wagn
    rate += np.exp(  19.0085)

    rate_eval.n_F18__p_O18 = rate

@numba.njit()
def p_S41__Cl42(rate_eval, tf):
    # S41 + p --> Cl42
    rate = 0.0

    # rath 
    rate += np.exp(  88.7085 + -4.23598*tf.T9i + 154.417*tf.T913i + -255.161*tf.T913
                  + 14.0489*tf.T9 + -0.788924*tf.T953 + 127.909*tf.lnT9)

    rate_eval.p_S41__Cl42 = rate

@numba.njit()
def p_Ar47__K48(rate_eval, tf):
    # Ar47 + p --> K48
    rate = 0.0

    # rath 
    rate += np.exp(  92.1807 + -4.82795*tf.T9i + 173.532*tf.T913i + -277.314*tf.T913
                  + 14.3714*tf.T9 + -0.732591*tf.T953 + 141.031*tf.lnT9)

    rate_eval.p_Ar47__K48 = rate

@numba.njit()
def n_Ar45__Ar46(rate_eval, tf):
    # Ar45 + n --> Ar46
    rate = 0.0

    # rath 
    rate += np.exp(  9.45759 + 0.00340504*tf.T9i + -1.57724*tf.T913i + 5.10096*tf.T913
                  + -0.259571*tf.T9 + -0.0137837*tf.T953 + -2.11345*tf.lnT9)

    rate_eval.n_Ar45__Ar46 = rate

@numba.njit()
def Fe50__Mn50__weak__wc12(rate_eval, tf):
    # Fe50 --> Mn50
    rate = 0.0

    # wc12w
    rate += np.exp(  1.49782)

    rate_eval.Fe50__Mn50__weak__wc12 = rate

@numba.njit()
def p_Ar44__K45(rate_eval, tf):
    # Ar44 + p --> K45
    rate = 0.0

    # rath 
    rate += np.exp(  103.496 + -4.79384*tf.T9i + 178.779*tf.T913i + -295.855*tf.T913
                  + 16.444*tf.T9 + -0.939254*tf.T953 + 147.521*tf.lnT9)

    rate_eval.p_Ar44__K45 = rate

@numba.njit()
def n_Ar44__Ar45(rate_eval, tf):
    # Ar44 + n --> Ar45
    rate = 0.0

    # rath 
    rate += np.exp(  19.1521 + -0.0463184*tf.T9i + 4.46461*tf.T913i + -12.8562*tf.T913
                  + 1.61075*tf.T9 + -0.165487*tf.T953 + 4.3409*tf.lnT9)

    rate_eval.n_Ar44__Ar45 = rate

@numba.njit()
def p_Ar43__K44(rate_eval, tf):
    # Ar43 + p --> K44
    rate = 0.0

    # rath 
    rate += np.exp(  95.3433 + -4.66951*tf.T9i + 169.747*tf.T913i + -277.855*tf.T913
                  + 15.0691*tf.T9 + -0.82997*tf.T953 + 139.859*tf.lnT9)

    rate_eval.p_Ar43__K44 = rate

@numba.njit()
def P46__n_n_n_S43__weak__mo03(rate_eval, tf):
    # P46 --> 3 n + S43
    rate = 0.0

    # mo03w
    rate += np.exp(  3.14754)

    rate_eval.P46__n_n_n_S43__weak__mo03 = rate

@numba.njit()
def K53__n_Ca52__weak__wc17(rate_eval, tf):
    # K53 --> n + Ca52
    rate = 0.0

    # wc17w
    rate += np.exp(  2.85236)

    rate_eval.K53__n_Ca52__weak__wc17 = rate

@numba.njit()
def p_Ar42__K43(rate_eval, tf):
    # Ar42 + p --> K43
    rate = 0.0

    # rath 
    rate += np.exp(  102.707 + -4.70123*tf.T9i + 171.849*tf.T913i + -282.869*tf.T913
                  + 15.2206*tf.T9 + -0.828672*tf.T953 + 140.551*tf.lnT9)

    rate_eval.p_Ar42__K43 = rate

@numba.njit()
def n_Li7__Li8(rate_eval, tf):
    # Li7 + n --> Li8
    rate = 0.0

    # ks03 
    rate += np.exp(  2.50071 + 0.0248641*tf.T9i + -3.24071*tf.T913i + 10.225*tf.T913
                  + -0.540218*tf.T9 + 0.0265361*tf.T953 + -3.61209*tf.lnT9)

    rate_eval.n_Li7__Li8 = rate

@numba.njit()
def n_Ar42__Ar43(rate_eval, tf):
    # Ar42 + n --> Ar43
    rate = 0.0

    # rath 
    rate += np.exp(  7.98561 + 0.021426*tf.T9i + -3.02977*tf.T913i + 8.06247*tf.T913
                  + -0.414467*tf.T9 + 0.00295853*tf.T953 + -3.29131*tf.lnT9)

    rate_eval.n_Ar42__Ar43 = rate

@numba.njit()
def n_Mg26__Mg27(rate_eval, tf):
    # Mg26 + n --> Mg27
    rate = 0.0

    # ks03 
    rate += np.exp(  -9.15466 + 0.0267177*tf.T9i + -4.22578*tf.T913i + 27.9161*tf.T913
                  + -3.93743*tf.T9 + 0.339693*tf.T953 + -6.22982*tf.lnT9)

    rate_eval.n_Mg26__Mg27 = rate

@numba.njit()
def He4_Ar40__Ca44(rate_eval, tf):
    # Ar40 + He4 --> Ca44
    rate = 0.0

    # ths8r
    rate += np.exp(  51.2366 + -71.2432*tf.T913i + 6.75101*tf.T913
                  + -5.53183*tf.T9 + 0.667023*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar40__Ca44 = rate

@numba.njit()
def He4_Cr51__Fe55(rate_eval, tf):
    # Cr51 + He4 --> Fe55
    rate = 0.0

    # ths8r
    rate += np.exp(  61.6085 + -86.8771*tf.T913i + -0.0873902*tf.T913
                  + -3.40716*tf.T9 + 0.441679*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr51__Fe55 = rate

@numba.njit()
def p_Ar40__K41(rate_eval, tf):
    # Ar40 + p --> K41
    rate = 0.0

    # ths8r
    rate += np.exp(  34.4108 + -29.0146*tf.T913i + 0.65181*tf.T913
                  + -1.50557*tf.T9 + 0.139974*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ar40__K41 = rate

@numba.njit()
def n_Ar40__Ar41(rate_eval, tf):
    # Ar40 + n --> Ar41
    rate = 0.0

    # ks03 
    rate += np.exp(  23.2118 + -0.0179675*tf.T9i + 3.79891*tf.T913i + -15.4616*tf.T913
                  + 1.64739*tf.T9 + -0.155712*tf.T953 + 5.13139*tf.lnT9)

    rate_eval.n_Ar40__Ar41 = rate

@numba.njit()
def He4_Ar39__Ca43(rate_eval, tf):
    # Ar39 + He4 --> Ca43
    rate = 0.0

    # ths8r
    rate += np.exp(  53.0126 + -71.1879*tf.T913i + 2.58821*tf.T913
                  + -3.67809*tf.T9 + 0.431537*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar39__Ca43 = rate

@numba.njit()
def He4_Ar37__Ca41(rate_eval, tf):
    # Ar37 + He4 --> Ca41
    rate = 0.0

    # ths8r
    rate += np.exp(  52.7522 + -71.0688*tf.T913i + 2.71847*tf.T913
                  + -3.17333*tf.T9 + 0.335323*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar37__Ca41 = rate

@numba.njit()
def p_Ar37__K38(rate_eval, tf):
    # Ar37 + p --> K38
    rate = 0.0

    # ths8r
    rate += np.exp(  37.7254 + -28.9954*tf.T913i + -5.57966*tf.T913
                  + -1.27516*tf.T9 + 0.217568*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ar37__K38 = rate

@numba.njit()
def He4_Ca36__Ti40(rate_eval, tf):
    # Ca36 + He4 --> Ti40
    rate = 0.0

    # ths8r
    rate += np.exp(  49.6465 + -76.1732*tf.T913i + -4.87682*tf.T913
                  + 1.31056*tf.T9 + -0.240342*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca36__Ti40 = rate

@numba.njit()
def Ne28__n_Na27__weak__wc12(rate_eval, tf):
    # Ne28 --> n + Na27
    rate = 0.0

    # wc12w
    rate += np.exp(  1.48182)

    rate_eval.Ne28__n_Na27__weak__wc12 = rate

@numba.njit()
def He4_Fe50__Ni54(rate_eval, tf):
    # Fe50 + He4 --> Ni54
    rate = 0.0

    # ths8r
    rate += np.exp(  57.348 + -91.5952*tf.T913i + -0.120496*tf.T913
                  + -2.1148*tf.T9 + 0.207344*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe50__Ni54 = rate

@numba.njit()
def p_Ar35__K36(rate_eval, tf):
    # Ar35 + p --> K36
    rate = 0.0

    # il10r
    rate += np.exp(  1.92933 + -5.89587*tf.T9i + 1.23472*tf.T913
                  + 0.677432*tf.T9 + -0.0712254*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -3.06454 + -2.59171*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  21.6289 + -28.9685*tf.T913i
                  + -1.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ar35__K36 = rate

@numba.njit()
def Cl43__n_Ar42__weak__mp17(rate_eval, tf):
    # Cl43 --> n + Ar42
    rate = 0.0

    # mp17w
    rate += np.exp(  -6.11272)

    rate_eval.Cl43__n_Ar42__weak__mp17 = rate

@numba.njit()
def p_F20__Ne21(rate_eval, tf):
    # F20 + p --> Ne21
    rate = 0.0

    # rpsmr
    rate += np.exp(  45.5657 + -1.99314*tf.T9i + 64.666*tf.T913i + -111.609*tf.T913
                  + 5.88114*tf.T9 + -0.322771*tf.T953 + 56.9335*tf.lnT9)

    rate_eval.p_F20__Ne21 = rate

@numba.njit()
def p_Si25__P26(rate_eval, tf):
    # Si25 + p --> P26
    rate = 0.0

    # ths8r
    rate += np.exp(  40.5114 + -24.4196*tf.T913i + -20.0928*tf.T913
                  + 2.99587*tf.T9 + -0.214034*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Si25__P26 = rate

@numba.njit()
def He4_Ar33__Ca37(rate_eval, tf):
    # Ar33 + He4 --> Ca37
    rate = 0.0

    # ths8r
    rate += np.exp(  45.9124 + -70.792*tf.T913i + -3.32023*tf.T913
                  + 0.874694*tf.T9 + -0.191591*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar33__Ca37 = rate

@numba.njit()
def p_Ar33__K34(rate_eval, tf):
    # Ar33 + p --> K34
    rate = 0.0

    # ths8r
    rate += np.exp(  -18.9682 + -7.12714*tf.T9i + 20.7703*tf.T913
                  + -2.95588*tf.T9 + 0.257828*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ar33__K34 = rate

@numba.njit()
def He4_Ar32__Ca36(rate_eval, tf):
    # Ar32 + He4 --> Ca36
    rate = 0.0

    # ths8r
    rate += np.exp(  43.8241 + -70.713*tf.T913i + -0.0778489*tf.T913
                  + -0.466075*tf.T9 + -0.00979269*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar32__Ca36 = rate

@numba.njit()
def p_Cl43__Ar44(rate_eval, tf):
    # Cl43 + p --> Ar44
    rate = 0.0

    # rath 
    rate += np.exp(  93.7241 + -4.50978*tf.T9i + 165.004*tf.T913i + -271.609*tf.T913
                  + 14.9625*tf.T9 + -0.843801*tf.T953 + 136.192*tf.lnT9)

    rate_eval.p_Cl43__Ar44 = rate

@numba.njit()
def p_Ar32__K33(rate_eval, tf):
    # Ar32 + p --> K33
    rate = 0.0

    # ths8r
    rate += np.exp(  -17.7268 + -19.4286*tf.T9i + 20.2635*tf.T913
                  + -2.76523*tf.T9 + 0.235117*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ar32__K33 = rate

@numba.njit()
def Al41__Si41__weak__mo03(rate_eval, tf):
    # Al41 --> Si41
    rate = 0.0

    # mo03w
    rate += np.exp(  3.93992)

    rate_eval.Al41__Si41__weak__mo03 = rate

@numba.njit()
def n_Ar32__Ar33(rate_eval, tf):
    # Ar32 + n --> Ar33
    rate = 0.0

    # ths8r
    rate += np.exp(  10.4093 + -0.214074*tf.T913
                  + 0.129622*tf.T9 + -0.00588429*tf.T953)

    rate_eval.n_Ar32__Ar33 = rate

@numba.njit()
def p_P33__He4_Si30(rate_eval, tf):
    # P33 + p --> He4 + Si30
    rate = 0.0

    # rath 
    rate += np.exp(  81.5654 + -3.41491*tf.T9i + 110.297*tf.T913i + -193.863*tf.T913
                  + 11.4977*tf.T9 + -0.687235*tf.T953 + 94.819*tf.lnT9)

    rate_eval.p_P33__He4_Si30 = rate

@numba.njit()
def p_Si44__He4_Al41(rate_eval, tf):
    # Si44 + p --> He4 + Al41
    rate = 0.0

    # rath 
    rate += np.exp(  76.3423 + -3.99875*tf.T9i + 145.948*tf.T913i + -232.953*tf.T913
                  + 11.9572*tf.T9 + -0.608502*tf.T953 + 119.355*tf.lnT9)

    rate_eval.p_Si44__He4_Al41 = rate

@numba.njit()
def Na32__n_n_Mg30__weak__wc12(rate_eval, tf):
    # Na32 --> n + n + Mg30
    rate = 0.0

    # wc12w
    rate += np.exp(  1.4353)

    rate_eval.Na32__n_n_Mg30__weak__wc12 = rate

@numba.njit()
def p_P28__S29(rate_eval, tf):
    # P28 + p --> S29
    rate = 0.0

    # ths8r
    rate += np.exp(  34.9605 + -25.6044*tf.T913i + -4.80892*tf.T913
                  + -1.47704*tf.T9 + 0.246699*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_P28__S29 = rate

@numba.njit()
def He4_Ar31__Ca35(rate_eval, tf):
    # Ar31 + He4 --> Ca35
    rate = 0.0

    # ths8r
    rate += np.exp(  43.0178 + -70.6299*tf.T913i + -1.02898*tf.T913
                  + -0.325359*tf.T9 + -0.00845154*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar31__Ca35 = rate

@numba.njit()
def p_Ar31__K32(rate_eval, tf):
    # Ar31 + p --> K32
    rate = 0.0

    # ths8r
    rate += np.exp(  -17.8606 + -21.3062*tf.T9i + 17.7736*tf.T913
                  + -2.18701*tf.T9 + 0.179851*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ar31__K32 = rate

@numba.njit()
def n_Ar31__Ar32(rate_eval, tf):
    # Ar31 + n --> Ar32
    rate = 0.0

    # ths8r
    rate += np.exp(  9.85492 + -0.324027*tf.T913
                  + 0.191147*tf.T9 + -0.0127061*tf.T953)

    rate_eval.n_Ar31__Ar32 = rate

@numba.njit()
def He4_Ne20__Mg24(rate_eval, tf):
    # Ne20 + He4 --> Mg24
    rate = 0.0

    # il10r
    rate += np.exp(  -8.79827 + -12.7809*tf.T9i + 16.9229*tf.T913
                  + -2.57325*tf.T9 + 0.208997*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  1.98307 + -9.22026*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -38.7055 + -2.50605*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  24.5058 + -46.2525*tf.T913i + 5.58901*tf.T913
                  + 7.61843*tf.T9 + -3.683*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ne20__Mg24 = rate

@numba.njit()
def Ne24__Na24__weak__wc12(rate_eval, tf):
    # Ne24 --> Na24
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.67972)

    rate_eval.Ne24__Na24__weak__wc12 = rate

@numba.njit()
def He4_Ar30__Ca34(rate_eval, tf):
    # Ar30 + He4 --> Ca34
    rate = 0.0

    # ths8r
    rate += np.exp(  41.4584 + -70.5413*tf.T913i + -0.80342*tf.T913
                  + -0.316762*tf.T9 + -0.0129266*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar30__Ca34 = rate

@numba.njit()
def n_Ar29__Ar30(rate_eval, tf):
    # Ar29 + n --> Ar30
    rate = 0.0

    # ths8r
    rate += np.exp(  7.67812 + 0.78454*tf.T913
                  + 0.0158791*tf.T9 + -0.00114403*tf.T953)

    rate_eval.n_Ar29__Ar30 = rate

@numba.njit()
def He4_Cl51__K55(rate_eval, tf):
    # Cl51 + He4 --> K55
    rate = 0.0

    # rath 
    rate += np.exp(  -840.81 + 13.4003*tf.T9i + -1455.16*tf.T913i + 2391.07*tf.T913
                  + -143.143*tf.T9 + 8.22758*tf.T953 + -1121.44*tf.lnT9)

    rate_eval.He4_Cl51__K55 = rate

@numba.njit()
def He4_Mg34__Si38(rate_eval, tf):
    # Mg34 + He4 --> Si38
    rate = 0.0

    # rath 
    rate += np.exp(  -18.8218 + -2.60733*tf.T9i + -20.3215*tf.T913i + 29.0152*tf.T913
                  + -5.28831*tf.T9 + 0.414765*tf.T953 + 2.14088*tf.lnT9)

    rate_eval.He4_Mg34__Si38 = rate

@numba.njit()
def p_Cl51__Ar52(rate_eval, tf):
    # Cl51 + p --> Ar52
    rate = 0.0

    # rath 
    rate += np.exp(  114.174 + -4.93783*tf.T9i + 188.937*tf.T913i + -320.171*tf.T913
                  + 18.2878*tf.T9 + -1.04135*tf.T953 + 156.628*tf.lnT9)

    rate_eval.p_Cl51__Ar52 = rate

@numba.njit()
def n_Cl51__Cl52(rate_eval, tf):
    # Cl51 + n --> Cl52
    rate = 0.0

    # rath 
    rate += np.exp(  100.004 + -7.98944*tf.T9i + 247.79*tf.T913i + -361.368*tf.T913
                  + 20.5235*tf.T9 + -1.18412*tf.T953 + 181.263*tf.lnT9)

    rate_eval.n_Cl51__Cl52 = rate

@numba.njit()
def p_Mn57__Fe58(rate_eval, tf):
    # Mn57 + p --> Fe58
    rate = 0.0

    # rath 
    rate += np.exp(  129.635 + -6.63166*tf.T9i + 247.383*tf.T913i + -397.449*tf.T913
                  + 21.986*tf.T9 + -1.2738*tf.T953 + 200.183*tf.lnT9)

    rate_eval.p_Mn57__Fe58 = rate

@numba.njit()
def He4_Cr60__n_Fe63(rate_eval, tf):
    # Cr60 + He4 --> n + Fe63
    rate = 0.0

    # rath 
    rate += np.exp(  -1139.57 + 18.1499*tf.T9i + -1969.61*tf.T913i + 3246.82*tf.T913
                  + -194.025*tf.T9 + 11.1385*tf.T953 + -1522.55*tf.lnT9)

    rate_eval.He4_Cr60__n_Fe63 = rate

@numba.njit()
def p_Cl49__Ar50(rate_eval, tf):
    # Cl49 + p --> Ar50
    rate = 0.0

    # rath 
    rate += np.exp(  107.386 + -4.86581*tf.T9i + 185.445*tf.T913i + -308.922*tf.T913
                  + 17.1756*tf.T9 + -0.957437*tf.T953 + 153.026*tf.lnT9)

    rate_eval.p_Cl49__Ar50 = rate

@numba.njit()
def p_Ar53__n_K53(rate_eval, tf):
    # Ar53 + p --> n + K53
    rate = 0.0

    # rath 
    rate += np.exp(  115.375 + -5.17331*tf.T9i + 193.298*tf.T913i + -313.636*tf.T913
                  + 17.0818*tf.T9 + -0.946087*tf.T953 + 157.355*tf.lnT9)

    rate_eval.p_Ar53__n_K53 = rate

@numba.njit()
def Ca51__Sc51__weak__wc12(rate_eval, tf):
    # Ca51 --> Sc51
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.6691)

    rate_eval.Ca51__Sc51__weak__wc12 = rate

@numba.njit()
def n_Cl49__Cl50(rate_eval, tf):
    # Cl49 + n --> Cl50
    rate = 0.0

    # rath 
    rate += np.exp(  14.3223 + -0.028602*tf.T9i + 3.22415*tf.T913i + -13.5389*tf.T913
                  + 1.67622*tf.T9 + -0.141047*tf.T953 + 3.76331*tf.lnT9)

    rate_eval.n_Cl49__Cl50 = rate

@numba.njit()
def V46__Ti46__weak__wc12(rate_eval, tf):
    # V46 --> Ti46
    rate = 0.0

    # wc12w
    rate += np.exp(  0.49387)

    rate_eval.V46__Ti46__weak__wc12 = rate

@numba.njit()
def He4_Cl46__K50(rate_eval, tf):
    # Cl46 + He4 --> K50
    rate = 0.0

    # rath 
    rate += np.exp(  -796.437 + 12.8769*tf.T9i + -1394.65*tf.T913i + 2280.45*tf.T913
                  + -136.102*tf.T9 + 7.80238*tf.T953 + -1071.27*tf.lnT9)

    rate_eval.He4_Cl46__K50 = rate

@numba.njit()
def n_Cl46__Cl47(rate_eval, tf):
    # Cl46 + n --> Cl47
    rate = 0.0

    # rath 
    rate += np.exp(  23.1603 + 0.0101918*tf.T9i + 1.52574*tf.T913i + -14.6735*tf.T913
                  + 1.17381*tf.T9 + -0.078759*tf.T953 + 3.58367*tf.lnT9)

    rate_eval.n_Cl46__Cl47 = rate

@numba.njit()
def Ti45__Sc45__weak__wc12(rate_eval, tf):
    # Ti45 --> Sc45
    rate = 0.0

    # wc12w
    rate += np.exp(  -9.68121)

    rate_eval.Ti45__Sc45__weak__wc12 = rate

@numba.njit()
def n_Cl45__Cl46(rate_eval, tf):
    # Cl45 + n --> Cl46
    rate = 0.0

    # rath 
    rate += np.exp(  11.875 + -0.040315*tf.T9i + 3.03579*tf.T913i + -7.70777*tf.T913
                  + 1.02399*tf.T9 + -0.094149*tf.T953 + 2.49616*tf.lnT9)

    rate_eval.n_Cl45__Cl46 = rate

@numba.njit()
def V62__n_Cr61__weak__mp17(rate_eval, tf):
    # V62 --> n + Cr61
    rate = 0.0

    # mp17w
    rate += np.exp(  1.36897)

    rate_eval.V62__n_Cr61__weak__mp17 = rate

@numba.njit()
def n_Cl44__Cl45(rate_eval, tf):
    # Cl44 + n --> Cl45
    rate = 0.0

    # rath 
    rate += np.exp(  16.3654 + -0.023248*tf.T9i + 2.3592*tf.T913i + -7.02607*tf.T913
                  + 0.416968*tf.T9 + -0.0340408*tf.T953 + 2.38165*tf.lnT9)

    rate_eval.n_Cl44__Cl45 = rate

@numba.njit()
def He4_P26__Cl30(rate_eval, tf):
    # P26 + He4 --> Cl30
    rate = 0.0

    # ths8r
    rate += np.exp(  38.3859 + -62.0947*tf.T913i + 0.561637*tf.T913
                  + -0.733357*tf.T9 + 0.0461301*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P26__Cl30 = rate

@numba.njit()
def He4_Cl42__K46(rate_eval, tf):
    # Cl42 + He4 --> K46
    rate = 0.0

    # rath 
    rate += np.exp(  -759.054 + 12.2111*tf.T9i + -1327.57*tf.T913i + 2172.39*tf.T913
                  + -130.117*tf.T9 + 7.47431*tf.T953 + -1018.59*tf.lnT9)

    rate_eval.He4_Cl42__K46 = rate

@numba.njit()
def n_Cl42__Cl43(rate_eval, tf):
    # Cl42 + n --> Cl43
    rate = 0.0

    # rath 
    rate += np.exp(  15.1521 + -0.029449*tf.T9i + 2.11225*tf.T913i + -4.54775*tf.T913
                  + 0.299096*tf.T9 + -0.0327172*tf.T953 + 1.61095*tf.lnT9)

    rate_eval.n_Cl42__Cl43 = rate

@numba.njit()
def p_Cl41__Ar42(rate_eval, tf):
    # Cl41 + p --> Ar42
    rate = 0.0

    # rath 
    rate += np.exp(  94.7152 + -4.42239*tf.T9i + 162.064*tf.T913i + -268.945*tf.T913
                  + 14.805*tf.T9 + -0.833847*tf.T953 + 134.48*tf.lnT9)

    rate_eval.p_Cl41__Ar42 = rate

@numba.njit()
def He4_Cl39__K43(rate_eval, tf):
    # Cl39 + He4 --> K43
    rate = 0.0

    # rath 
    rate += np.exp(  -358.725 + 1.8487*tf.T9i + -500.49*tf.T913i + 889.176*tf.T913
                  + -58.0768*tf.T9 + 3.48991*tf.T953 + -390.498*tf.lnT9)

    rate_eval.He4_Cl39__K43 = rate

@numba.njit()
def Ne31__Na31__weak__wc17(rate_eval, tf):
    # Ne31 --> Na31
    rate = 0.0

    # wc17w
    rate += np.exp(  5.18963)

    rate_eval.Ne31__Na31__weak__wc17 = rate

@numba.njit()
def p_Cl46__Ar47(rate_eval, tf):
    # Cl46 + p --> Ar47
    rate = 0.0

    # rath 
    rate += np.exp(  99.2048 + -4.6651*tf.T9i + 172.872*tf.T913i + -285.373*tf.T913
                  + 15.7696*tf.T9 + -0.884022*tf.T953 + 142.484*tf.lnT9)

    rate_eval.p_Cl46__Ar47 = rate

@numba.njit()
def p_Cl39__Ar40(rate_eval, tf):
    # Cl39 + p --> Ar40
    rate = 0.0

    # rath 
    rate += np.exp(  93.1696 + -4.3033*tf.T9i + 155.882*tf.T913i + -259.84*tf.T913
                  + 14.2407*tf.T9 + -0.797757*tf.T953 + 129.767*tf.lnT9)

    rate_eval.p_Cl39__Ar40 = rate

@numba.njit()
def p_Cr64__n_Mn64(rate_eval, tf):
    # Cr64 + p --> n + Mn64
    rate = 0.0

    # rath 
    rate += np.exp(  140.601 + -6.80832*tf.T9i + 256.659*tf.T913i + -409.808*tf.T913
                  + 22.3714*tf.T9 + -1.24655*tf.T953 + 206.347*tf.lnT9)

    rate_eval.p_Cr64__n_Mn64 = rate

@numba.njit()
def Si45__n_P44__weak__mp17(rate_eval, tf):
    # Si45 --> n + P44
    rate = 0.0

    # mp17w
    rate += np.exp(  1.71962)

    rate_eval.Si45__n_P44__weak__mp17 = rate

@numba.njit()
def He4_Cl38__K42(rate_eval, tf):
    # Cl38 + He4 --> K42
    rate = 0.0

    # rath 
    rate += np.exp(  -430.223 + 3.44161*tf.T9i + -628.615*tf.T913i + 1098.74*tf.T913
                  + -69.8207*tf.T9 + 4.1307*tf.T953 + -491.691*tf.lnT9)

    rate_eval.He4_Cl38__K42 = rate

@numba.njit()
def He4_Cl36__K40(rate_eval, tf):
    # Cl36 + He4 --> K40
    rate = 0.0

    # ths8r
    rate += np.exp(  55.7157 + -68.3499*tf.T913i + -4.69433*tf.T913
                  + -1.24812*tf.T9 + 0.169306*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl36__K40 = rate

@numba.njit()
def Na20__Ne20__weak__wc12(rate_eval, tf):
    # Na20 --> Ne20
    rate = 0.0

    # wc12w
    rate += np.exp(  0.21268)

    rate_eval.Na20__Ne20__weak__wc12 = rate

@numba.njit()
def He4_Cl35__K39(rate_eval, tf):
    # Cl35 + He4 --> K39
    rate = 0.0

    # ths8r
    rate += np.exp(  52.718 + -68.2848*tf.T913i + 0.0178545*tf.T913
                  + -2.06783*tf.T9 + 0.199659*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl35__K39 = rate

@numba.njit()
def p_Cl35__Ar36(rate_eval, tf):
    # Cl35 + p --> Ar36
    rate = 0.0

    # il10r
    rate += np.exp(  -42.5249 + -0.564651*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  35.6868 + -27.8971*tf.T913i + -16.2304*tf.T913
                  + 35.255*tf.T9 + -25.8411*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  -7.84699 + -3.65092*tf.T9i + 18.0179*tf.T913
                  + -2.86304*tf.T9 + 0.250854*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -9.03294 + -2.00996*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Cl35__Ar36 = rate

@numba.njit()
def p_Ti39__V40(rate_eval, tf):
    # Ti39 + p --> V40
    rate = 0.0

    # ths8r
    rate += np.exp(  -17.7509 + -17.8829*tf.T9i + 18.7676*tf.T913
                  + -2.45087*tf.T9 + 0.201364*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ti39__V40 = rate

@numba.njit()
def p_Mg35__n_Al35(rate_eval, tf):
    # Mg35 + p --> n + Al35
    rate = 0.0

    # rath 
    rate += np.exp(  81.2033 + -3.24427*tf.T9i + 116.661*tf.T913i + -195.138*tf.T913
                  + 10.6166*tf.T9 + -0.586734*tf.T953 + 97.777*tf.lnT9)

    rate_eval.p_Mg35__n_Al35 = rate

@numba.njit()
def He4_Cl33__K37(rate_eval, tf):
    # Cl33 + He4 --> K37
    rate = 0.0

    # ths8r
    rate += np.exp(  46.6859 + -68.1442*tf.T913i + -2.72746*tf.T913
                  + -0.317537*tf.T9 + 0.0162782*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl33__K37 = rate

@numba.njit()
def n_Cl33__Cl34(rate_eval, tf):
    # Cl33 + n --> Cl34
    rate = 0.0

    # ths8r
    rate += np.exp(  8.14947 + 0.921411*tf.T913
                  + -0.0823764*tf.T9 + 0.000852746*tf.T953)

    rate_eval.n_Cl33__Cl34 = rate

@numba.njit()
def He4_Cl32__K36(rate_eval, tf):
    # Cl32 + He4 --> K36
    rate = 0.0

    # ths8r
    rate += np.exp(  42.6778 + -68.0682*tf.T913i + -1.44981*tf.T913
                  + -0.556621*tf.T9 + 0.023385*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl32__K36 = rate

@numba.njit()
def He4_O21__Ne25(rate_eval, tf):
    # O21 + He4 --> Ne25
    rate = 0.0

    # rpsmr
    rate += np.exp(  41.7593 + -1.9019*tf.T9i + 27.2088*tf.T913i + -79.9315*tf.T913
                  + 3.18711*tf.T9 + -0.138465*tf.T953 + 43.2582*tf.lnT9)

    rate_eval.He4_O21__Ne25 = rate

@numba.njit()
def n_Mg32__Mg33(rate_eval, tf):
    # Mg32 + n --> Mg33
    rate = 0.0

    # rath 
    rate += np.exp(  11.1923 + -0.0750393*tf.T9i + 6.4854*tf.T913i + -9.76339*tf.T913
                  + 0.239537*tf.T9 + 0.0132113*tf.T953 + 5.11626*tf.lnT9)

    rate_eval.n_Mg32__Mg33 = rate

@numba.njit()
def p_Cl32__Ar33(rate_eval, tf):
    # Cl32 + p --> Ar33
    rate = 0.0

    # il10n
    rate += np.exp(  20.34 + -27.8029*tf.T913i
                  + -1.0*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  -1.71607 + -5.07091*tf.T9i + 7.33571*tf.T913
                  + -0.458163*tf.T9 + -0.014725*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -23.1312 + -1.30777*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -84.7811 + -0.259849*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Cl32__Ar33 = rate

@numba.njit()
def n_Ca44__Ca45(rate_eval, tf):
    # Ca44 + n --> Ca45
    rate = 0.0

    # ks03 
    rate += np.exp(  2.03089 + 0.19047*tf.T9i + -17.5809*tf.T913i + 30.835*tf.T913
                  + -1.52658*tf.T9 + 0.0495163*tf.T953 + -14.5794*tf.lnT9)

    rate_eval.n_Ca44__Ca45 = rate

@numba.njit()
def p_Al42__Si43(rate_eval, tf):
    # Al42 + p --> Si43
    rate = 0.0

    # rath 
    rate += np.exp(  76.319 + -3.72078*tf.T9i + 135.135*tf.T913i + -220.463*tf.T913
                  + 11.8476*tf.T9 + -0.649118*tf.T953 + 111.289*tf.lnT9)

    rate_eval.p_Al42__Si43 = rate

@numba.njit()
def n_Cl32__Cl33(rate_eval, tf):
    # Cl32 + n --> Cl33
    rate = 0.0

    # ths8r
    rate += np.exp(  10.2432 + 1.33999*tf.T913
                  + -0.226447*tf.T9 + 0.0236307*tf.T953)

    rate_eval.n_Cl32__Cl33 = rate

@numba.njit()
def He4_Cl31__K35(rate_eval, tf):
    # Cl31 + He4 --> K35
    rate = 0.0

    # ths8r
    rate += np.exp(  41.8813 + -67.9875*tf.T913i + -1.49266*tf.T913
                  + -0.486213*tf.T9 + 0.0122537*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl31__K35 = rate

@numba.njit()
def He4_K45__Sc49(rate_eval, tf):
    # K45 + He4 --> Sc49
    rate = 0.0

    # rath 
    rate += np.exp(  -845.662 + 13.5827*tf.T9i + -1475.89*tf.T913i + 2416.42*tf.T913
                  + -144.458*tf.T9 + 8.28494*tf.T953 + -1133.69*tf.lnT9)

    rate_eval.He4_K45__Sc49 = rate

@numba.njit()
def p_Cl31__Ar32(rate_eval, tf):
    # Cl31 + p --> Ar32
    rate = 0.0

    # il10n
    rate += np.exp(  20.7113 + -27.8568*tf.T913i
                  + -0.666667*tf.lnT9)

    rate_eval.p_Cl31__Ar32 = rate

@numba.njit()
def p_Cl30__Ar31(rate_eval, tf):
    # Cl30 + p --> Ar31
    rate = 0.0

    # ths8r
    rate += np.exp(  38.6523 + -27.8542*tf.T913i + -11.9372*tf.T913
                  + 0.258101*tf.T9 + 0.0855887*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cl30__Ar31 = rate

@numba.njit()
def p_Cl29__Ar30(rate_eval, tf):
    # Cl29 + p --> Ar30
    rate = 0.0

    # ths8r
    rate += np.exp(  38.4837 + -27.8439*tf.T913i + -13.6678*tf.T913
                  + 0.743042*tf.T9 + 0.0358561*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cl29__Ar30 = rate

@numba.njit()
def n_K47__K48(rate_eval, tf):
    # K47 + n --> K48
    rate = 0.0

    # rath 
    rate += np.exp(  21.6563 + -0.0784677*tf.T9i + 7.74515*tf.T913i + -18.7786*tf.T913
                  + 1.40252*tf.T9 + -0.0758241*tf.T953 + 7.27806*tf.lnT9)

    rate_eval.n_K47__K48 = rate

@numba.njit()
def K47__Ca47__weak__wc12(rate_eval, tf):
    # K47 --> Ca47
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.22871)

    rate_eval.K47__Ca47__weak__wc12 = rate

@numba.njit()
def He4_S49__Ar53(rate_eval, tf):
    # S49 + He4 --> Ar53
    rate = 0.0

    # rath 
    rate += np.exp(  -810.057 + 12.6909*tf.T9i + -1381.07*tf.T913i + 2281.96*tf.T913
                  + -137.255*tf.T9 + 7.91153*tf.T953 + -1066.94*tf.lnT9)

    rate_eval.He4_S49__Ar53 = rate

@numba.njit()
def He4_S48__Ar52(rate_eval, tf):
    # S48 + He4 --> Ar52
    rate = 0.0

    # rath 
    rate += np.exp(  -796.145 + 12.6206*tf.T9i + -1369.74*tf.T913i + 2254.68*tf.T913
                  + -135.22*tf.T9 + 7.77373*tf.T953 + -1055.95*tf.lnT9)

    rate_eval.He4_S48__Ar52 = rate

@numba.njit()
def p_Si34__P35(rate_eval, tf):
    # Si34 + p --> P35
    rate = 0.0

    # rath 
    rate += np.exp(  77.0384 + -3.55945*tf.T9i + 127.961*tf.T913i + -213.326*tf.T913
                  + 11.5251*tf.T9 + -0.64022*tf.T953 + 107.273*tf.lnT9)

    rate_eval.p_Si34__P35 = rate

@numba.njit()
def He4_S47__Ar51(rate_eval, tf):
    # S47 + He4 --> Ar51
    rate = 0.0

    # rath 
    rate += np.exp(  -784.052 + 12.5083*tf.T9i + -1356.32*tf.T913i + 2228.37*tf.T913
                  + -133.534*tf.T9 + 7.67611*tf.T953 + -1044.36*tf.lnT9)

    rate_eval.He4_S47__Ar51 = rate

@numba.njit()
def Fe72__n_Co71__weak__mp17(rate_eval, tf):
    # Fe72 --> n + Co71
    rate = 0.0

    # mp17w
    rate += np.exp(  0.0196399)

    rate_eval.Fe72__n_Co71__weak__mp17 = rate

@numba.njit()
def n_S47__S48(rate_eval, tf):
    # S47 + n --> S48
    rate = 0.0

    # rath 
    rate += np.exp(  7.46522 + -0.0336681*tf.T9i + 1.62487*tf.T913i + -1.26306*tf.T913
                  + 0.161481*tf.T9 + -0.0318581*tf.T953 + 0.569263*tf.lnT9)

    rate_eval.n_S47__S48 = rate

@numba.njit()
def He4_S44__Ar48(rate_eval, tf):
    # S44 + He4 --> Ar48
    rate = 0.0

    # rath 
    rate += np.exp(  -744.164 + 11.9412*tf.T9i + -1298.29*tf.T913i + 2124.76*tf.T913
                  + -127.151*tf.T9 + 7.29826*tf.T953 + -996.567*tf.lnT9)

    rate_eval.He4_S44__Ar48 = rate

@numba.njit()
def p_S44__Cl45(rate_eval, tf):
    # S44 + p --> Cl45
    rate = 0.0

    # rath 
    rate += np.exp(  86.2735 + -4.35825*tf.T9i + 158.18*tf.T913i + -257.287*tf.T913
                  + 14.0077*tf.T9 + -0.779948*tf.T953 + 129.817*tf.lnT9)

    rate_eval.p_S44__Cl45 = rate

@numba.njit()
def n_S44__S45(rate_eval, tf):
    # S44 + n --> S45
    rate = 0.0

    # rath 
    rate += np.exp(  21.3458 + -0.106757*tf.T9i + 10.2394*tf.T913i + -28.0387*tf.T913
                  + 3.06535*tf.T9 + -0.255697*tf.T953 + 9.80188*tf.lnT9)

    rate_eval.n_S44__S45 = rate

@numba.njit()
def n_Fe73__Fe74(rate_eval, tf):
    # Fe73 + n --> Fe74
    rate = 0.0

    # rath 
    rate += np.exp(  13.1327 + -0.0100272*tf.T9i + 0.763989*tf.T913i + -5.49607*tf.T913
                  + 1.17808*tf.T9 + -0.157336*tf.T953 + 0.98221*tf.lnT9)

    rate_eval.n_Fe73__Fe74 = rate

@numba.njit()
def n_K49__K50(rate_eval, tf):
    # K49 + n --> K50
    rate = 0.0

    # rath 
    rate += np.exp(  13.5721 + -0.0459114*tf.T9i + 3.71546*tf.T913i + -8.28367*tf.T913
                  + 0.745259*tf.T9 + -0.0640668*tf.T953 + 3.08787*tf.lnT9)

    rate_eval.n_K49__K50 = rate

@numba.njit()
def n_Mg28__Mg29(rate_eval, tf):
    # Mg28 + n --> Mg29
    rate = 0.0

    # rath 
    rate += np.exp(  9.54437 + -0.0345286*tf.T9i + 2.00104*tf.T913i + -1.07948*tf.T913
                  + -0.0276825*tf.T9 + 0.00202272*tf.T953 + 0.927324*tf.lnT9)

    rate_eval.n_Mg28__Mg29 = rate

@numba.njit()
def He4_S43__Ar47(rate_eval, tf):
    # S43 + He4 --> Ar47
    rate = 0.0

    # rath 
    rate += np.exp(  -352.618 + 1.86101*tf.T9i + -494.226*tf.T913i + 875.904*tf.T913
                  + -58.0354*tf.T9 + 3.53956*tf.T953 + -383.474*tf.lnT9)

    rate_eval.He4_S43__Ar47 = rate

@numba.njit()
def He4_S46__Ar50(rate_eval, tf):
    # S46 + He4 --> Ar50
    rate = 0.0

    # rath 
    rate += np.exp(  -768.927 + 12.308*tf.T9i + -1335.41*tf.T913i + 2189.99*tf.T913
                  + -131.21*tf.T9 + 7.54*tf.T953 + -1026.78*tf.lnT9)

    rate_eval.He4_S46__Ar50 = rate

@numba.njit()
def He4_S42__Ar46(rate_eval, tf):
    # S42 + He4 --> Ar46
    rate = 0.0

    # rath 
    rate += np.exp(  -348.216 + 1.86621*tf.T9i + -490.828*tf.T913i + 867.358*tf.T913
                  + -57.3716*tf.T9 + 3.48826*tf.T953 + -380.113*tf.lnT9)

    rate_eval.He4_S42__Ar46 = rate

@numba.njit()
def Mn61__Fe61__weak__wc12(rate_eval, tf):
    # Mn61 --> Fe61
    rate = 0.0

    # wc12w
    rate += np.exp(  0.0339646)

    rate_eval.Mn61__Fe61__weak__wc12 = rate

@numba.njit()
def n_S42__S43(rate_eval, tf):
    # S42 + n --> S43
    rate = 0.0

    # rath 
    rate += np.exp(  12.548 + -0.015715*tf.T9i + 2.00961*tf.T913i + -6.33956*tf.T913
                  + 1.03082*tf.T9 + -0.116596*tf.T953 + 2.20129*tf.lnT9)

    rate_eval.n_S42__S43 = rate

@numba.njit()
def Si33__P33__weak__wc12(rate_eval, tf):
    # Si33 --> P33
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.17644)

    rate_eval.Si33__P33__weak__wc12 = rate

@numba.njit()
def B17__n_n_C15__weak__wc12(rate_eval, tf):
    # B17 --> n + n + C15
    rate = 0.0

    # wc12w
    rate += np.exp(  2.70866)

    rate_eval.B17__n_n_C15__weak__wc12 = rate

@numba.njit()
def Al37__n_Si36__weak__mp17(rate_eval, tf):
    # Al37 --> n + Si36
    rate = 0.0

    # mp17w
    rate += np.exp(  1.64527)

    rate_eval.Al37__n_Si36__weak__mp17 = rate

@numba.njit()
def p_S40__Cl41(rate_eval, tf):
    # S40 + p --> Cl41
    rate = 0.0

    # rath 
    rate += np.exp(  89.8932 + -4.18894*tf.T9i + 152.601*tf.T913i + -253.723*tf.T913
                  + 14.05*tf.T9 + -0.799299*tf.T953 + 126.807*tf.lnT9)

    rate_eval.p_S40__Cl41 = rate

@numba.njit()
def n_S40__S41(rate_eval, tf):
    # S40 + n --> S41
    rate = 0.0

    # rath 
    rate += np.exp(  15.2234 + -0.0241856*tf.T9i + 2.65819*tf.T913i + -8.38527*tf.T913
                  + 1.10835*tf.T9 + -0.112549*tf.T953 + 2.78929*tf.lnT9)

    rate_eval.n_S40__S41 = rate

@numba.njit()
def He4_F28__Na32(rate_eval, tf):
    # F28 + He4 --> Na32
    rate = 0.0

    # rpsmr
    rate += np.exp(  56.3346 + -2.62629*tf.T9i + 57.2686*tf.T913i + -129.448*tf.T913
                  + 5.85944*tf.T9 + -0.281886*tf.T953 + 67.9559*tf.lnT9)

    rate_eval.He4_F28__Na32 = rate

@numba.njit()
def p_Cl50__Ar51(rate_eval, tf):
    # Cl50 + p --> Ar51
    rate = 0.0

    # rath 
    rate += np.exp(  113.607 + -4.92369*tf.T9i + 189.331*tf.T913i + -319.324*tf.T913
                  + 18.0737*tf.T9 + -1.02131*tf.T953 + 156.796*tf.lnT9)

    rate_eval.p_Cl50__Ar51 = rate

@numba.njit()
def He4_S39__Ar43(rate_eval, tf):
    # S39 + He4 --> Ar43
    rate = 0.0

    # rath 
    rate += np.exp(  -339.618 + 1.8952*tf.T9i + -482.557*tf.T913i + 850.761*tf.T913
                  + -56.4169*tf.T9 + 3.44005*tf.T953 + -372.648*tf.lnT9)

    rate_eval.He4_S39__Ar43 = rate

@numba.njit()
def He4_Ar47__Ca51(rate_eval, tf):
    # Ar47 + He4 --> Ca51
    rate = 0.0

    # rath 
    rate += np.exp(  -836.496 + 13.37*tf.T9i + -1452.53*tf.T913i + 2382.34*tf.T913
                  + -142.613*tf.T9 + 8.18703*tf.T953 + -1117.07*tf.lnT9)

    rate_eval.He4_Ar47__Ca51 = rate

@numba.njit()
def p_S39__Cl40(rate_eval, tf):
    # S39 + p --> Cl40
    rate = 0.0

    # rath 
    rate += np.exp(  88.2699 + -4.13866*tf.T9i + 150.322*tf.T913i + -249.917*tf.T913
                  + 13.7849*tf.T9 + -0.777739*tf.T953 + 125.075*tf.lnT9)

    rate_eval.p_S39__Cl40 = rate

@numba.njit()
def n_S38__S39(rate_eval, tf):
    # S38 + n --> S39
    rate = 0.0

    # rath 
    rate += np.exp(  7.01358 + 0.00420188*tf.T9i + -1.59474*tf.T913i + 6.13833*tf.T913
                  + -0.409248*tf.T9 + 0.0144884*tf.T953 + -2.20685*tf.lnT9)

    rate_eval.n_S38__S39 = rate

@numba.njit()
def V47__Ti47__weak__wc12(rate_eval, tf):
    # V47 --> Ti47
    rate = 0.0

    # wc12w
    rate += np.exp(  -7.94721)

    rate_eval.V47__Ti47__weak__wc12 = rate

@numba.njit()
def p_K34__Ca35(rate_eval, tf):
    # K34 + p --> Ca35
    rate = 0.0

    # ths8r
    rate += np.exp(  36.6033 + -30.0364*tf.T913i + -5.6016*tf.T913
                  + -1.67829*tf.T9 + 0.284814*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_K34__Ca35 = rate

@numba.njit()
def He4_S36__Ar40(rate_eval, tf):
    # S36 + He4 --> Ar40
    rate = 0.0

    # ths8r
    rate += np.exp(  49.9867 + -65.6425*tf.T913i + 4.12861*tf.T913
                  + -3.33119*tf.T9 + 0.31889*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S36__Ar40 = rate

@numba.njit()
def He4_Mg36__Si40(rate_eval, tf):
    # Mg36 + He4 --> Si40
    rate = 0.0

    # rath 
    rate += np.exp(  -17.5586 + -2.72044*tf.T9i + -17.0199*tf.T913i + 24.8162*tf.T913
                  + -5.0215*tf.T9 + 0.398153*tf.T953 + 4.3226*tf.lnT9)

    rate_eval.He4_Mg36__Si40 = rate

@numba.njit()
def p_Na32__n_Mg32(rate_eval, tf):
    # Na32 + p --> n + Mg32
    rate = 0.0

    # rath 
    rate += np.exp(  79.0885 + -2.94321*tf.T9i + 106.124*tf.T913i + -181.193*tf.T913
                  + 9.91612*tf.T9 + -0.548558*tf.T953 + 90.0747*tf.lnT9)

    rate_eval.p_Na32__n_Mg32 = rate

@numba.njit()
def Cl47__n_n_Ar45__weak__mp17(rate_eval, tf):
    # Cl47 --> n + n + Ar45
    rate = 0.0

    # mp17w
    rate += np.exp(  -2.67905)

    rate_eval.Cl47__n_n_Ar45__weak__mp17 = rate

@numba.njit()
def Ti51__V51__weak__wc12(rate_eval, tf):
    # Ti51 --> V51
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.21295)

    rate_eval.Ti51__V51__weak__wc12 = rate

@numba.njit()
def p_S36__Cl37(rate_eval, tf):
    # S36 + p --> Cl37
    rate = 0.0

    # ths8r
    rate += np.exp(  33.9758 + -26.7991*tf.T913i + 0.0770118*tf.T913
                  + -1.71514*tf.T9 + 0.205981*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_S36__Cl37 = rate

@numba.njit()
def He4_Ar54__n_Ca57(rate_eval, tf):
    # Ar54 + He4 --> n + Ca57
    rate = 0.0

    # rath 
    rate += np.exp(  -419.799 + 2.0998*tf.T9i + -582.271*tf.T913i + 1048.36*tf.T913
                  + -69.5181*tf.T9 + 4.24419*tf.T953 + -458.21*tf.lnT9)

    rate_eval.He4_Ar54__n_Ca57 = rate

@numba.njit()
def p_S35__Cl36(rate_eval, tf):
    # S35 + p --> Cl36
    rate = 0.0

    # ths8r
    rate += np.exp(  35.1122 + -26.7922*tf.T913i + -1.83516*tf.T913
                  + -2.03932*tf.T9 + 0.322305*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_S35__Cl36 = rate

@numba.njit()
def V45__Ti45__weak__wc12(rate_eval, tf):
    # V45 --> Ti45
    rate = 0.0

    # wc12w
    rate += np.exp(  0.236794)

    rate_eval.V45__Ti45__weak__wc12 = rate

@numba.njit()
def n_S34__S35(rate_eval, tf):
    # S34 + n --> S35
    rate = 0.0

    # ks03 
    rate += np.exp(  41.4131 + -0.229262*tf.T9i + 25.2182*tf.T913i + -59.2704*tf.T913
                  + 4.22256*tf.T9 + -0.274247*tf.T953 + 24.532*tf.lnT9)

    rate_eval.n_S34__S35 = rate

@numba.njit()
def He4_Ca45__n_Ti48(rate_eval, tf):
    # Ca45 + He4 --> n + Ti48
    rate = 0.0

    # ths8r
    rate += np.exp(  57.1268 + -76.6866*tf.T913i + -0.885239*tf.T913
                  + -0.554755*tf.T9 + 0.0189393*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca45__n_Ti48 = rate

@numba.njit()
def n_S33__S34(rate_eval, tf):
    # S33 + n --> S34
    rate = 0.0

    # ks03 
    rate += np.exp(  -4.17932 + 0.24641*tf.T9i + -23.1351*tf.T913i + 43.3623*tf.T913
                  + -2.74733*tf.T9 + 0.159045*tf.T953 + -19.6332*tf.lnT9)

    rate_eval.n_S33__S34 = rate

@numba.njit()
def He4_S32__Ar36(rate_eval, tf):
    # S32 + He4 --> Ar36
    rate = 0.0

    # ths8r
    rate += np.exp(  48.901 + -65.3709*tf.T913i + 5.68294*tf.T913
                  + -5.00388*tf.T9 + 0.571407*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S32__Ar36 = rate

@numba.njit()
def n_Ar52__Ar53(rate_eval, tf):
    # Ar52 + n --> Ar53
    rate = 0.0

    # rath 
    rate += np.exp(  -8.22023 + 0.0685781*tf.T9i + -4.3758*tf.T913i + 17.4237*tf.T913
                  + -1.94579*tf.T9 + 0.145722*tf.T953 + -3.82839*tf.lnT9)

    rate_eval.n_Ar52__Ar53 = rate

@numba.njit()
def p_S32__Cl33(rate_eval, tf):
    # S32 + p --> Cl33
    rate = 0.0

    # il10n
    rate += np.exp(  52.47 + -29.7741*tf.T913i + -87.4473*tf.T913
                  + 182.189*tf.T9 + -128.625*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  69.3346 + -3.00371*tf.T9i + -33.7204*tf.T913i + -32.7355*tf.T913
                  + 3.92526*tf.T9 + -0.250479*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -27.2382 + -0.874107*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_S32__Cl33 = rate

@numba.njit()
def n_S32__S33(rate_eval, tf):
    # S32 + n --> S33
    rate = 0.0

    # ks03 
    rate += np.exp(  12.4466 + 0.198828*tf.T9i + -15.0178*tf.T913i + 16.3567*tf.T913
                  + -0.436839*tf.T9 + -0.00574462*tf.T953 + -9.78034*tf.lnT9)

    rate_eval.n_S32__S33 = rate

@numba.njit()
def p_S31__Cl32(rate_eval, tf):
    # S31 + p --> Cl32
    rate = 0.0

    # mm11r
    rate += np.exp(  -11.7529 + -1.77549*tf.T9i
                  + -1.5*tf.lnT9)
    # mm11n
    rate += np.exp(  6.30412 + -25.3278*tf.T913i + 42.7226*tf.T913
                  + -102.23*tf.T9 + -2.0*tf.T953 + -0.666667*tf.lnT9)
    # mm11r
    rate += np.exp(  3.272 + -6.35927*tf.T9i + 3.202*tf.T913
                  + 0.101684*tf.T9 + -0.0334894*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_S31__Cl32 = rate

@numba.njit()
def p_S29__Cl30(rate_eval, tf):
    # S29 + p --> Cl30
    rate = 0.0

    # ths8r
    rate += np.exp(  -19.6182 + -3.6393*tf.T9i + 21.3406*tf.T913
                  + -3.25229*tf.T9 + 0.307741*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_S29__Cl30 = rate

@numba.njit()
def He4_O22__Ne26(rate_eval, tf):
    # O22 + He4 --> Ne26
    rate = 0.0

    # rpsmr
    rate += np.exp(  43.2123 + -1.9769*tf.T9i + 30.7632*tf.T913i + -85.8468*tf.T913
                  + 3.53959*tf.T9 + -0.162431*tf.T953 + 46.0452*tf.lnT9)

    rate_eval.He4_O22__Ne26 = rate

@numba.njit()
def He4_Ne24__Mg28(rate_eval, tf):
    # Ne24 + He4 --> Mg28
    rate = 0.0

    # rath 
    rate += np.exp(  32.9465 + -2.30403*tf.T9i + 26.2241*tf.T913i + -71.9124*tf.T913
                  + 2.14361*tf.T9 + -0.0676422*tf.T953 + 42.7812*tf.lnT9)

    rate_eval.He4_Ne24__Mg28 = rate

@numba.njit()
def He4_P37__Cl41(rate_eval, tf):
    # P37 + He4 --> Cl41
    rate = 0.0

    # rath 
    rate += np.exp(  -311.748 + 1.74853*tf.T9i + -448.772*tf.T913i + 786.018*tf.T913
                  + -51.9413*tf.T9 + 3.15343*tf.T953 + -344.849*tf.lnT9)

    rate_eval.He4_P37__Cl41 = rate

@numba.njit()
def Mg39__n_Al38__weak__mp17(rate_eval, tf):
    # Mg39 --> n + Al38
    rate = 0.0

    # mp17w
    rate += np.exp(  4.20835)

    rate_eval.Mg39__n_Al38__weak__mp17 = rate

@numba.njit()
def n_S27__S28(rate_eval, tf):
    # S27 + n --> S28
    rate = 0.0

    # ths8r
    rate += np.exp(  7.62531 + 1.97289*tf.T913
                  + -0.223151*tf.T9 + 0.0169858*tf.T953)

    rate_eval.n_S27__S28 = rate

@numba.njit()
def p_Si33__P34(rate_eval, tf):
    # Si33 + p --> P34
    rate = 0.0

    # rath 
    rate += np.exp(  75.3859 + -3.48026*tf.T9i + 123.357*tf.T913i + -205.966*tf.T913
                  + 11.0352*tf.T9 + -0.607806*tf.T953 + 103.75*tf.lnT9)

    rate_eval.p_Si33__P34 = rate

@numba.njit()
def n_S26__S27(rate_eval, tf):
    # S26 + n --> S27
    rate = 0.0

    # ths8r
    rate += np.exp(  7.37517 + 2.35524*tf.T913
                  + -0.35361*tf.T9 + 0.0286977*tf.T953)

    rate_eval.n_S26__S27 = rate

@numba.njit()
def He4_Fe71__Ni75(rate_eval, tf):
    # Fe71 + He4 --> Ni75
    rate = 0.0

    # rath 
    rate += np.exp(  -1024.87 + 26.0002*tf.T9i + -2509.1*tf.T913i + 3657.33*tf.T913
                  + -198.266*tf.T9 + 10.5846*tf.T953 + -1823.44*tf.lnT9)

    rate_eval.He4_Fe71__Ni75 = rate

@numba.njit()
def n_P45__P46(rate_eval, tf):
    # P45 + n --> P46
    rate = 0.0

    # rath 
    rate += np.exp(  -8.76868 + 0.0481882*tf.T9i + -6.7613*tf.T913i + 18.4891*tf.T913
                  + -0.639893*tf.T9 + -0.00793701*tf.T953 + -7.39694*tf.lnT9)

    rate_eval.n_P45__P46 = rate

@numba.njit()
def n_P44__P45(rate_eval, tf):
    # P44 + n --> P45
    rate = 0.0

    # rath 
    rate += np.exp(  21.5481 + 0.0244726*tf.T9i + -0.0177662*tf.T913i + -14.0463*tf.T913
                  + 1.4007*tf.T9 + -0.0954339*tf.T953 + 2.39574*tf.lnT9)

    rate_eval.n_P44__P45 = rate

@numba.njit()
def Al32__Si32__weak__wc12(rate_eval, tf):
    # Al32 --> Si32
    rate = 0.0

    # wc12w
    rate += np.exp(  3.03771)

    rate_eval.Al32__Si32__weak__wc12 = rate

@numba.njit()
def n_P42__P43(rate_eval, tf):
    # P42 + n --> P43
    rate = 0.0

    # rath 
    rate += np.exp(  14.7299 + -0.0165412*tf.T9i + 1.79491*tf.T913i + -6.34857*tf.T913
                  + 0.322345*tf.T9 + -0.0223143*tf.T953 + 1.96455*tf.lnT9)

    rate_eval.n_P42__P43 = rate

@numba.njit()
def n_P41__P42(rate_eval, tf):
    # P41 + n --> P42
    rate = 0.0

    # rath 
    rate += np.exp(  4.1257 + -0.0123571*tf.T9i + -0.224959*tf.T913i + 4.80007*tf.T913
                  + -0.331656*tf.T9 + 0.00634316*tf.T953 + -1.23293*tf.lnT9)

    rate_eval.n_P41__P42 = rate

@numba.njit()
def He4_O21__n_Ne24(rate_eval, tf):
    # O21 + He4 --> n + Ne24
    rate = 0.0

    # rpsmr
    rate += np.exp(  53.9135 + -1.9125*tf.T9i + 28.3617*tf.T913i + -83.1293*tf.T913
                  + 3.44917*tf.T9 + -0.155723*tf.T953 + 44.4254*tf.lnT9)

    rate_eval.He4_O21__n_Ne24 = rate

@numba.njit()
def He4_P40__Cl44(rate_eval, tf):
    # P40 + He4 --> Cl44
    rate = 0.0

    # rath 
    rate += np.exp(  -324.381 + 1.7696*tf.T9i + -461.432*tf.T913i + 812.453*tf.T913
                  + -53.7722*tf.T9 + 3.27546*tf.T953 + -356.218*tf.lnT9)

    rate_eval.He4_P40__Cl44 = rate

@numba.njit()
def He4_K41__Sc45(rate_eval, tf):
    # K41 + He4 --> Sc45
    rate = 0.0

    # ths8r
    rate += np.exp(  54.8015 + -73.9127*tf.T913i + 0.81435*tf.T913
                  + -2.90813*tf.T9 + 0.335176*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K41__Sc45 = rate

@numba.njit()
def p_P40__S41(rate_eval, tf):
    # P40 + p --> S41
    rate = 0.0

    # rath 
    rate += np.exp(  84.618 + -4.0103*tf.T9i + 145.85*tf.T913i + -241.07*tf.T913
                  + 13.1823*tf.T9 + -0.733677*tf.T953 + 120.975*tf.lnT9)

    rate_eval.p_P40__S41 = rate

@numba.njit()
def C19__N19__weak__wc07(rate_eval, tf):
    # C19 --> N19
    rate = 0.0

    # wc07w
    rate += np.exp(  1.70781)

    rate_eval.C19__N19__weak__wc07 = rate

@numba.njit()
def He4_Cl37__K41(rate_eval, tf):
    # Cl37 + He4 --> K41
    rate = 0.0

    # ths8r
    rate += np.exp(  51.2462 + -68.4116*tf.T913i + 3.55194*tf.T913
                  + -2.84942*tf.T9 + 0.24958*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl37__K41 = rate

@numba.njit()
def He4_Mg33__n_Si36(rate_eval, tf):
    # Mg33 + He4 --> n + Si36
    rate = 0.0

    # rath 
    rate += np.exp(  82.9749 + -3.52045*tf.T9i + 82.597*tf.T913i + -177.119*tf.T913
                  + 8.50879*tf.T9 + -0.441818*tf.T953 + 92.1362*tf.lnT9)

    rate_eval.He4_Mg33__n_Si36 = rate

@numba.njit()
def t__He3__weak__wc12(rate_eval, tf):
    # t --> He3
    rate = 0.0

    # wc12w
    rate += np.exp(  -20.1456)

    rate_eval.t__He3__weak__wc12 = rate

@numba.njit()
def p_P38__S39(rate_eval, tf):
    # P38 + p --> S39
    rate = 0.0

    # rath 
    rate += np.exp(  81.0107 + -3.897*tf.T9i + 139.893*tf.T913i + -230.594*tf.T913
                  + 12.3874*tf.T9 + -0.668382*tf.T953 + 116.249*tf.lnT9)

    rate_eval.p_P38__S39 = rate

@numba.njit()
def He4_Cl38__n_K41(rate_eval, tf):
    # Cl38 + He4 --> n + K41
    rate = 0.0

    # rath 
    rate += np.exp(  -336.469 + 1.91622*tf.T9i + -492.641*tf.T913i + 864.166*tf.T913
                  + -57.0822*tf.T9 + 3.47394*tf.T953 + -378.89*tf.lnT9)

    rate_eval.He4_Cl38__n_K41 = rate

@numba.njit()
def n_Na31__Na32(rate_eval, tf):
    # Na31 + n --> Na32
    rate = 0.0

    # rath 
    rate += np.exp(  11.6232 + -0.0490285*tf.T9i + 3.76697*tf.T913i + -8.75898*tf.T913
                  + 0.795599*tf.T9 + -0.0491848*tf.T953 + 3.06686*tf.lnT9)

    rate_eval.n_Na31__Na32 = rate

@numba.njit()
def n_P38__P39(rate_eval, tf):
    # P38 + n --> P39
    rate = 0.0

    # rath 
    rate += np.exp(  13.5697 + -0.0269225*tf.T9i + 1.76024*tf.T913i + -3.54025*tf.T913
                  + 0.160121*tf.T9 + -0.0164326*tf.T953 + 1.22522*tf.lnT9)

    rate_eval.n_P38__P39 = rate

@numba.njit()
def He4_P36__Cl40(rate_eval, tf):
    # P36 + He4 --> Cl40
    rate = 0.0

    # rath 
    rate += np.exp(  -310.434 + 1.78815*tf.T9i + -448.258*tf.T913i + 783.782*tf.T913
                  + -51.779*tf.T9 + 3.14591*tf.T953 + -344.032*tf.lnT9)

    rate_eval.He4_P36__Cl40 = rate

@numba.njit()
def n_P36__P37(rate_eval, tf):
    # P36 + n --> P37
    rate = 0.0

    # rath 
    rate += np.exp(  13.6214 + -0.0317342*tf.T9i + 2.02264*tf.T913i + -3.49412*tf.T913
                  + 0.116927*tf.T9 + -0.0108357*tf.T953 + 1.31756*tf.lnT9)

    rate_eval.n_P36__P37 = rate

@numba.njit()
def He4_P35__Cl39(rate_eval, tf):
    # P35 + He4 --> Cl39
    rate = 0.0

    # rath 
    rate += np.exp(  -104.351 + -2.19677*tf.T9i + -114.707*tf.T913i + 218.798*tf.T913
                  + -16.8301*tf.T9 + 1.05305*tf.T953 + -81.377*tf.lnT9)

    rate_eval.He4_P35__Cl39 = rate

@numba.njit()
def C20__n_N19__weak__wc12(rate_eval, tf):
    # C20 --> n + N19
    rate = 0.0

    # wc12w
    rate += np.exp(  3.57368)

    rate_eval.C20__n_N19__weak__wc12 = rate

@numba.njit()
def He4_Cl44__K48(rate_eval, tf):
    # Cl44 + He4 --> K48
    rate = 0.0

    # rath 
    rate += np.exp(  -785.941 + 12.5737*tf.T9i + -1365.9*tf.T913i + 2240.98*tf.T913
                  + -134.492*tf.T9 + 7.78063*tf.T953 + -1050.32*tf.lnT9)

    rate_eval.He4_Cl44__K48 = rate

@numba.njit()
def p_P35__S36(rate_eval, tf):
    # P35 + p --> S36
    rate = 0.0

    # rath 
    rate += np.exp(  86.6555 + -3.77127*tf.T9i + 136.559*tf.T913i + -231.994*tf.T913
                  + 12.8603*tf.T9 + -0.734984*tf.T953 + 115.168*tf.lnT9)

    rate_eval.p_P35__S36 = rate

@numba.njit()
def n_P35__P36(rate_eval, tf):
    # P35 + n --> P36
    rate = 0.0

    # rath 
    rate += np.exp(  20.2815 + -0.0892849*tf.T9i + 8.37783*tf.T913i + -20.0009*tf.T913
                  + 1.82869*tf.T9 + -0.135224*tf.T953 + 7.65394*tf.lnT9)

    rate_eval.n_P35__P36 = rate

@numba.njit()
def n_P33__P34(rate_eval, tf):
    # P33 + n --> P34
    rate = 0.0

    # rath 
    rate += np.exp(  11.2327 + -0.010288*tf.T9i + -0.209588*tf.T913i + 1.56877*tf.T913
                  + 0.0878171*tf.T9 + -0.0260999*tf.T953 + -0.800608*tf.lnT9)

    rate_eval.n_P33__P34 = rate

@numba.njit()
def p_Fe58__He4_Mn55(rate_eval, tf):
    # Fe58 + p --> He4 + Mn55
    rate = 0.0

    # ths8r
    rate += np.exp(  -74.5149 + -37.17*tf.T913i + 110.878*tf.T913
                  + -24.5555*tf.T9 + 2.47003*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Fe58__He4_Mn55 = rate

@numba.njit()
def n_Ca38__Ca39(rate_eval, tf):
    # Ca38 + n --> Ca39
    rate = 0.0

    # ths8r
    rate += np.exp(  12.0675 + -0.418748*tf.T913
                  + 0.243656*tf.T9 + -0.0268305*tf.T953)

    rate_eval.n_Ca38__Ca39 = rate

@numba.njit()
def He4_P32__Cl36(rate_eval, tf):
    # P32 + He4 --> Cl36
    rate = 0.0

    # rath 
    rate += np.exp(  -119.479 + -1.48992*tf.T9i + -158.272*tf.T913i + 281.836*tf.T913
                  + -20.652*tf.T9 + 1.28543*tf.T953 + -112.725*tf.lnT9)

    rate_eval.He4_P32__Cl36 = rate

@numba.njit()
def n_P32__P33(rate_eval, tf):
    # P32 + n --> P33
    rate = 0.0

    # rath 
    rate += np.exp(  10.8477 + 0.0572362*tf.T9i + -6.14814*tf.T913i + 9.5582*tf.T913
                  + -0.244744*tf.T9 + -0.012887*tf.T953 + -5.42926*tf.lnT9)

    rate_eval.n_P32__P33 = rate

@numba.njit()
def n_Mn45__He4_V42(rate_eval, tf):
    # Mn45 + n --> He4 + V42
    rate = 0.0

    # ths8r
    rate += np.exp(  15.2163 + -1.10483*tf.T913
                  + 0.295654*tf.T9 + 0.00469897*tf.T953)

    rate_eval.n_Mn45__He4_V42 = rate

@numba.njit()
def n_Cl32__p_S32(rate_eval, tf):
    # Cl32 + n --> p + S32
    rate = 0.0

    # ths8r
    rate += np.exp(  18.3866 + 1.81434*tf.T913
                  + -0.244818*tf.T9 + 0.0169659*tf.T953)

    rate_eval.n_Cl32__p_S32 = rate

@numba.njit()
def n_Ar30__Ar31(rate_eval, tf):
    # Ar30 + n --> Ar31
    rate = 0.0

    # ths8r
    rate += np.exp(  8.65601 + 0.496438*tf.T913
                  + 0.0367452*tf.T9 + -0.00135434*tf.T953)

    rate_eval.n_Ar30__Ar31 = rate

@numba.njit()
def n_P28__P29(rate_eval, tf):
    # P28 + n --> P29
    rate = 0.0

    # ths8r
    rate += np.exp(  10.1198 + 1.02998*tf.T913
                  + -0.0525896*tf.T9 + 0.00405559*tf.T953)

    rate_eval.n_P28__P29 = rate

@numba.njit()
def He4_S26__Ar30(rate_eval, tf):
    # S26 + He4 --> Ar30
    rate = 0.0

    # ths8r
    rate += np.exp(  37.255 + -64.8264*tf.T913i + 0.430868*tf.T913
                  + -0.647762*tf.T9 + 0.0303891*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S26__Ar30 = rate

@numba.njit()
def B19__C19__weak__wc12(rate_eval, tf):
    # B19 --> C19
    rate = 0.0

    # wc12w
    rate += np.exp(  3.3494)

    rate_eval.B19__C19__weak__wc12 = rate

@numba.njit()
def He4_P27__Cl31(rate_eval, tf):
    # P27 + He4 --> Cl31
    rate = 0.0

    # ths8r
    rate += np.exp(  38.9613 + -62.196*tf.T913i + 0.447106*tf.T913
                  + -0.73871*tf.T9 + 0.0474553*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P27__Cl31 = rate

@numba.njit()
def n_P27__P28(rate_eval, tf):
    # P27 + n --> P28
    rate = 0.0

    # ths8r
    rate += np.exp(  9.89904 + 0.826735*tf.T913
                  + -0.0340403*tf.T9 + 0.00548843*tf.T953)

    rate_eval.n_P27__P28 = rate

@numba.njit()
def p_P26__S27(rate_eval, tf):
    # P26 + p --> S27
    rate = 0.0

    # ths8r
    rate += np.exp(  37.6971 + -25.5819*tf.T913i + -11.9827*tf.T913
                  + 0.333997*tf.T9 + 0.0772567*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_P26__S27 = rate

@numba.njit()
def n_P26__P27(rate_eval, tf):
    # P26 + n --> P27
    rate = 0.0

    # ths8r
    rate += np.exp(  10.5084 + -0.0118188*tf.T913
                  + 0.154886*tf.T9 + -0.00988297*tf.T953)

    rate_eval.n_P26__P27 = rate

@numba.njit()
def V55__Cr55__weak__wc12(rate_eval, tf):
    # V55 --> Cr55
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.24445)

    rate_eval.V55__Cr55__weak__wc12 = rate

@numba.njit()
def He4_Na31__Al35(rate_eval, tf):
    # Na31 + He4 --> Al35
    rate = 0.0

    # rath 
    rate += np.exp(  -9.3975 + -2.38499*tf.T9i + -15.3524*tf.T913i + 14.8029*tf.T913
                  + -3.87514*tf.T9 + 0.315976*tf.T953 + 6.55754*tf.lnT9)

    rate_eval.He4_Na31__Al35 = rate

@numba.njit()
def He4_P24__Cl28(rate_eval, tf):
    # P24 + He4 --> Cl28
    rate = 0.0

    # ths8r
    rate += np.exp(  36.5732 + -61.8692*tf.T913i + 0.896017*tf.T913
                  + -0.688903*tf.T9 + 0.0410111*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P24__Cl28 = rate

@numba.njit()
def p_Mn70__Fe71(rate_eval, tf):
    # Mn70 + p --> Fe71
    rate = 0.0

    # rath 
    rate += np.exp(  148.231 + -7.2359*tf.T9i + 273.952*tf.T913i + -446.852*tf.T913
                  + 25.3545*tf.T9 + -1.45801*tf.T953 + 221.137*tf.lnT9)

    rate_eval.p_Mn70__Fe71 = rate

@numba.njit()
def He4_Cl33__p_Ar36(rate_eval, tf):
    # Cl33 + He4 --> p + Ar36
    rate = 0.0

    # ths8r
    rate += np.exp(  52.1588 + -68.1442*tf.T913i + 0.291238*tf.T913
                  + -0.791384*tf.T9 + 0.0524823*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl33__p_Ar36 = rate

@numba.njit()
def S49__n_Cl48__weak__mp17(rate_eval, tf):
    # S49 --> n + Cl48
    rate = 0.0

    # mp17w
    rate += np.exp(  3.91793)

    rate_eval.S49__n_Cl48__weak__mp17 = rate

@numba.njit()
def p_Ca56__Sc57(rate_eval, tf):
    # Ca56 + p --> Sc57
    rate = 0.0

    # rath 
    rate += np.exp(  112.194 + -5.65834*tf.T9i + 210.865*tf.T913i + -342.153*tf.T913
                  + 19.058*tf.T9 + -1.08931*tf.T953 + 171.32*tf.lnT9)

    rate_eval.p_Ca56__Sc57 = rate

@numba.njit()
def p_K55__n_Ca55(rate_eval, tf):
    # K55 + p --> n + Ca55
    rate = 0.0

    # rath 
    rate += np.exp(  123.069 + -5.46968*tf.T9i + 206.109*tf.T913i + -335.58*tf.T913
                  + 18.3697*tf.T9 + -1.01989*tf.T953 + 167.789*tf.lnT9)

    rate_eval.p_K55__n_Ca55 = rate

@numba.njit()
def p_Si42__P43(rate_eval, tf):
    # Si42 + p --> P43
    rate = 0.0

    # rath 
    rate += np.exp(  77.8751 + -3.90304*tf.T9i + 141.263*tf.T913i + -229.957*tf.T913
                  + 12.335*tf.T9 + -0.67626*tf.T953 + 116.251*tf.lnT9)

    rate_eval.p_Si42__P43 = rate

@numba.njit()
def K49__Ca49__weak__wc12(rate_eval, tf):
    # K49 --> Ca49
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.56374)

    rate_eval.K49__Ca49__weak__wc12 = rate

@numba.njit()
def Si31__P31__weak__wc12(rate_eval, tf):
    # Si31 --> P31
    rate = 0.0

    # wc12w
    rate += np.exp(  -9.51922)

    rate_eval.Si31__P31__weak__wc12 = rate

@numba.njit()
def Mg37__Al37__weak__mo03(rate_eval, tf):
    # Mg37 --> Al37
    rate = 0.0

    # mo03w
    rate += np.exp(  -33.8021)

    rate_eval.Mg37__Al37__weak__mo03 = rate

@numba.njit()
def n_Si42__Si43(rate_eval, tf):
    # Si42 + n --> Si43
    rate = 0.0

    # rath 
    rate += np.exp(  -715.028 + -40.5824*tf.T9i + -264.114*tf.T913i + 1072.05*tf.T913
                  + -77.0324*tf.T9 + 4.7674*tf.T953 + -397.546*tf.lnT9)

    rate_eval.n_Si42__Si43 = rate

@numba.njit()
def He4_Si41__S45(rate_eval, tf):
    # Si41 + He4 --> S45
    rate = 0.0

    # rath 
    rate += np.exp(  -318.877 + 1.71286*tf.T9i + -446.901*tf.T913i + 792.166*tf.T913
                  + -52.7046*tf.T9 + 3.22317*tf.T953 + -346.424*tf.lnT9)

    rate_eval.He4_Si41__S45 = rate

@numba.njit()
def He4_Si40__S44(rate_eval, tf):
    # Si40 + He4 --> S44
    rate = 0.0

    # rath 
    rate += np.exp(  -313.748 + 1.68464*tf.T9i + -441.137*tf.T913i + 781.33*tf.T913
                  + -52.1616*tf.T9 + 3.19948*tf.T953 + -341.453*tf.lnT9)

    rate_eval.He4_Si40__S44 = rate

@numba.njit()
def Ca59__n_n_Sc57__weak__mp17(rate_eval, tf):
    # Ca59 --> n + n + Sc57
    rate = 0.0

    # mp17w
    rate += np.exp(  1.79805)

    rate_eval.Ca59__n_n_Sc57__weak__mp17 = rate

@numba.njit()
def p_Si40__P41(rate_eval, tf):
    # Si40 + p --> P41
    rate = 0.0

    # rath 
    rate += np.exp(  79.0994 + -3.82988*tf.T9i + 139.061*tf.T913i + -228.491*tf.T913
                  + 12.3202*tf.T9 + -0.674089*tf.T953 + 115.085*tf.lnT9)

    rate_eval.p_Si40__P41 = rate

@numba.njit()
def p_Si39__P40(rate_eval, tf):
    # Si39 + p --> P40
    rate = 0.0

    # rath 
    rate += np.exp(  78.161 + -3.78355*tf.T9i + 136.711*tf.T913i + -224.549*tf.T913
                  + 12.1759*tf.T9 + -0.671186*tf.T953 + 113.183*tf.lnT9)

    rate_eval.p_Si39__P40 = rate

@numba.njit()
def He4_Si38__S42(rate_eval, tf):
    # Si38 + He4 --> S42
    rate = 0.0

    # rath 
    rate += np.exp(  -304.553 + 1.69091*tf.T9i + -434.128*tf.T913i + 763.63*tf.T913
                  + -50.6707*tf.T9 + 3.0897*tf.T953 + -334.517*tf.lnT9)

    rate_eval.He4_Si38__S42 = rate

@numba.njit()
def p_Ar54__He4_Cl51(rate_eval, tf):
    # Ar54 + p --> He4 + Cl51
    rate = 0.0

    # rath 
    rate += np.exp(  74.3635 + -5.20251*tf.T9i + 192.266*tf.T913i + -286.702*tf.T913
                  + 13.8358*tf.T9 + -0.639389*tf.T953 + 153.07*tf.lnT9)

    rate_eval.p_Ar54__He4_Cl51 = rate

@numba.njit()
def F31__Ne31__weak__mo03(rate_eval, tf):
    # F31 --> Ne31
    rate = 0.0

    # mo03w
    rate += np.exp(  4.97369)

    rate_eval.F31__Ne31__weak__mo03 = rate

@numba.njit()
def S27__P27__weak__wc12(rate_eval, tf):
    # S27 --> P27
    rate = 0.0

    # wc12w
    rate += np.exp(  3.76581)

    rate_eval.S27__P27__weak__wc12 = rate

@numba.njit()
def Al34__n_Si33__weak__wc12(rate_eval, tf):
    # Al34 --> n + Si33
    rate = 0.0

    # wc12w
    rate += np.exp(  1.49424)

    rate_eval.Al34__n_Si33__weak__wc12 = rate

@numba.njit()
def n_Si38__Si39(rate_eval, tf):
    # Si38 + n --> Si39
    rate = 0.0

    # rath 
    rate += np.exp(  18.4767 + -0.123122*tf.T9i + 11.63*tf.T913i + -25.1146*tf.T913
                  + 2.18422*tf.T9 + -0.164289*tf.T953 + 10.3818*tf.lnT9)

    rate_eval.n_Si38__Si39 = rate

@numba.njit()
def n_Si36__Si37(rate_eval, tf):
    # Si36 + n --> Si37
    rate = 0.0

    # rath 
    rate += np.exp(  18.6093 + -0.0921576*tf.T9i + 8.61852*tf.T913i + -20.6215*tf.T913
                  + 1.93986*tf.T9 + -0.147204*tf.T953 + 7.86284*tf.lnT9)

    rate_eval.n_Si36__Si37 = rate

@numba.njit()
def n_Cr42__Cr43(rate_eval, tf):
    # Cr42 + n --> Cr43
    rate = 0.0

    # ths8r
    rate += np.exp(  10.2293 + -0.0358726*tf.T913
                  + 0.19898*tf.T9 + -0.0212086*tf.T953)

    rate_eval.n_Cr42__Cr43 = rate

@numba.njit()
def n_Al24__He4_Na21(rate_eval, tf):
    # Al24 + n --> He4 + Na21
    rate = 0.0

    # ths8r
    rate += np.exp(  16.9713 + 1.96316*tf.T913
                  + -0.325682*tf.T9 + 0.0271663*tf.T953)

    rate_eval.n_Al24__He4_Na21 = rate

@numba.njit()
def He4_Si34__S38(rate_eval, tf):
    # Si34 + He4 --> S38
    rate = 0.0

    # rath 
    rate += np.exp(  -271.715 + 1.57156*tf.T9i + -407.711*tf.T913i + 701.313*tf.T913
                  + -45.984*tf.T9 + 2.77802*tf.T953 + -309.729*tf.lnT9)

    rate_eval.He4_Si34__S38 = rate

@numba.njit()
def He4_Si33__S37(rate_eval, tf):
    # Si33 + He4 --> S37
    rate = 0.0

    # rath 
    rate += np.exp(  -289.453 + 1.6465*tf.T9i + -414.921*tf.T913i + 728.172*tf.T913
                  + -48.246*tf.T9 + 2.9343*tf.T953 + -318.798*tf.lnT9)

    rate_eval.He4_Si33__S37 = rate

@numba.njit()
def n_S45__S46(rate_eval, tf):
    # S45 + n --> S46
    rate = 0.0

    # rath 
    rate += np.exp(  5.99369 + -0.00540108*tf.T9i + -0.99403*tf.T913i + 3.45885*tf.T913
                  + -0.103868*tf.T9 + -0.0179374*tf.T953 + -1.65608*tf.lnT9)

    rate_eval.n_S45__S46 = rate

@numba.njit()
def He4_Cl29__K33(rate_eval, tf):
    # Cl29 + He4 --> K33
    rate = 0.0

    # ths8r
    rate += np.exp(  40.6053 + -67.8117*tf.T913i + -0.294831*tf.T913
                  + -0.394384*tf.T9 + 0.0004138*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl29__K33 = rate

@numba.njit()
def p_Si32__P33(rate_eval, tf):
    # Si32 + p --> P33
    rate = 0.0

    # rath 
    rate += np.exp(  178.753 + -3.87095*tf.T9i + 174.94*tf.T913i + -365.37*tf.T913
                  + 23.1636*tf.T9 + -1.3429*tf.T953 + 160.075*tf.lnT9)

    rate_eval.p_Si32__P33 = rate

@numba.njit()
def p_Cl47__Ar48(rate_eval, tf):
    # Cl47 + p --> Ar48
    rate = 0.0

    # rath 
    rate += np.exp(  98.4022 + -4.73203*tf.T9i + 176.544*tf.T913i + -289.967*tf.T913
                  + 15.9313*tf.T9 + -0.884872*tf.T953 + 145.112*tf.lnT9)

    rate_eval.p_Cl47__Ar48 = rate

@numba.njit()
def p_Mg37__n_Al37(rate_eval, tf):
    # Mg37 + p --> n + Al37
    rate = 0.0

    # rath 
    rate += np.exp(  82.5854 + -3.33114*tf.T9i + 120.379*tf.T913i + -200.335*tf.T913
                  + 10.9016*tf.T9 + -0.60201*tf.T953 + 100.416*tf.lnT9)

    rate_eval.p_Mg37__n_Al37 = rate

@numba.njit()
def n_Si32__Si33(rate_eval, tf):
    # Si32 + n --> Si33
    rate = 0.0

    # rath 
    rate += np.exp(  12.845 + -0.0507754*tf.T9i + 3.87479*tf.T913i + -6.3252*tf.T913
                  + 0.491329*tf.T9 + -0.0341576*tf.T953 + 2.86561*tf.lnT9)

    rate_eval.n_Si32__Si33 = rate

@numba.njit()
def n_Si22__Si23(rate_eval, tf):
    # Si22 + n --> Si23
    rate = 0.0

    # ths8r
    rate += np.exp(  7.31374 + 2.70789*tf.T913
                  + 0.00973014*tf.T9 + -0.0387347*tf.T953)

    rate_eval.n_Si22__Si23 = rate

@numba.njit()
def p_Si31__P32(rate_eval, tf):
    # Si31 + p --> P32
    rate = 0.0

    # rath 
    rate += np.exp(  100.968 + -3.38247*tf.T9i + 123.4*tf.T913i + -231.734*tf.T913
                  + 14.2724*tf.T9 + -0.867645*tf.T953 + 108.469*tf.lnT9)

    rate_eval.p_Si31__P32 = rate

@numba.njit()
def p_Si30__P31(rate_eval, tf):
    # Si30 + p --> P31
    rate = 0.0

    # de20r
    rate += np.exp(  12.3695 + -6.64105*tf.T9i
                  + -1.1191*tf.lnT9)
    # de20r
    rate += np.exp(  8.79766 + -5.18231*tf.T9i
                  + 1.2883*tf.lnT9)
    # de20r
    rate += np.exp(  -334.266 + -1.13327*tf.T9i
                  + -78.547*tf.lnT9)
    # de20r
    rate += np.exp(  -4.24208 + -1.25174*tf.T9i
                  + 4.99034*tf.lnT9)
    # de20r
    rate += np.exp(  -18.9198 + -0.945261*tf.T9i
                  + 1.30331*tf.lnT9)
    # de20r
    rate += np.exp(  -1138.34 + -95.8769*tf.T9i
                  + -896.758*tf.lnT9)
    # de20r
    rate += np.exp(  9.96544 + -5.58963*tf.T9i
                  + -1.57082*tf.lnT9)
    # de20r
    rate += np.exp(  -34.8594 + -0.592934*tf.T9i
                  + -1.62839*tf.lnT9)

    rate_eval.p_Si30__P31 = rate

@numba.njit()
def Cl29__S29__weak__bqa_pos_(rate_eval, tf):
    # Cl29 --> S29
    rate = 0.0

    # bqa+w
    rate += np.exp(  4.1343)

    rate_eval.Cl29__S29__weak__bqa_pos_ = rate

@numba.njit()
def p_Si28__P29(rate_eval, tf):
    # Si28 + p --> P29
    rate = 0.0

    # il10n
    rate += np.exp(  16.1779 + -23.8173*tf.T913i + 7.08203*tf.T913
                  + -1.44753*tf.T9 + 0.0804296*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  5.73975 + -4.14232*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Si28__P29 = rate

@numba.njit()
def n_S41__S42(rate_eval, tf):
    # S41 + n --> S42
    rate = 0.0

    # rath 
    rate += np.exp(  13.1609 + -0.0313402*tf.T9i + 2.27591*tf.T913i + -4.95255*tf.T913
                  + 0.439305*tf.T9 + -0.0399335*tf.T953 + 1.75276*tf.lnT9)

    rate_eval.n_S41__S42 = rate

@numba.njit()
def p_Si26__P27(rate_eval, tf):
    # Si26 + p --> P27
    rate = 0.0

    # il10n
    rate += np.exp(  19.9961 + -24.3506*tf.T913i + 1.57777*tf.T913
                  + -0.796182*tf.T9 + 0.0805265*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  3.93294 + -3.01616*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Si26__P27 = rate

@numba.njit()
def n_Ne17__He4_O14(rate_eval, tf):
    # Ne17 + n --> He4 + O14
    rate = 0.0

    # ths8r
    rate += np.exp(  17.0541 + 0.263528*tf.T913
                  + 0.0627555*tf.T9 + -0.0118345*tf.T953)

    rate_eval.n_Ne17__He4_O14 = rate

@numba.njit()
def n_Si26__Si27(rate_eval, tf):
    # Si26 + n --> Si27
    rate = 0.0

    # ths8r
    rate += np.exp(  10.2624 + 1.48358*tf.T913
                  + -0.270432*tf.T9 + 0.0230319*tf.T953)

    rate_eval.n_Si26__Si27 = rate

@numba.njit()
def He4_Si24__S28(rate_eval, tf):
    # Si24 + He4 --> S28
    rate = 0.0

    # ths8r
    rate += np.exp(  37.2722 + -59.0853*tf.T913i + 0.510911*tf.T913
                  + -0.742518*tf.T9 + 0.0431572*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si24__S28 = rate

@numba.njit()
def Ca54__n_Sc53__weak__mp17(rate_eval, tf):
    # Ca54 --> n + Sc53
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.908837)

    rate_eval.Ca54__n_Sc53__weak__mp17 = rate

@numba.njit()
def p_Si24__P25(rate_eval, tf):
    # Si24 + p --> P25
    rate = 0.0

    # ths8r
    rate += np.exp(  -19.9988 + -9.61266*tf.T9i + 22.6594*tf.T913
                  + -3.60616*tf.T9 + 0.344666*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Si24__P25 = rate

@numba.njit()
def p_Sc56__He4_Ca53(rate_eval, tf):
    # Sc56 + p --> He4 + Ca53
    rate = 0.0

    # rath 
    rate += np.exp(  108.766 + -5.82165*tf.T9i + 215.059*tf.T913i + -343.753*tf.T913
                  + 18.8901*tf.T9 + -1.02614*tf.T953 + 173.917*tf.lnT9)

    rate_eval.p_Sc56__He4_Ca53 = rate

@numba.njit()
def p_Ca54__n_Sc54(rate_eval, tf):
    # Ca54 + p --> n + Sc54
    rate = 0.0

    # rath 
    rate += np.exp(  118.682 + -5.57375*tf.T9i + 206.962*tf.T913i + -333.466*tf.T913
                  + 18.2683*tf.T9 + -1.02297*tf.T953 + 167.947*tf.lnT9)

    rate_eval.p_Ca54__n_Sc54 = rate

@numba.njit()
def n_Si24__Si25(rate_eval, tf):
    # Si24 + n --> Si25
    rate = 0.0

    # ths8r
    rate += np.exp(  7.37464 + 2.52249*tf.T913
                  + -0.341976*tf.T9 + 0.0289094*tf.T953)

    rate_eval.n_Si24__Si25 = rate

@numba.njit()
def Ca57__Sc57__weak__mo03(rate_eval, tf):
    # Ca57 --> Sc57
    rate = 0.0

    # mo03w
    rate += np.exp(  4.44048)

    rate_eval.Ca57__Sc57__weak__mo03 = rate

@numba.njit()
def He4_Al43__P47(rate_eval, tf):
    # Al43 + He4 --> P47
    rate = 0.0

    # rath 
    rate += np.exp(  -21.4642 + -3.24196*tf.T9i + -8.48842*tf.T913i + 17.932*tf.T913
                  + -5.09137*tf.T9 + 0.423723*tf.T953 + 9.99614*tf.lnT9)

    rate_eval.He4_Al43__P47 = rate

@numba.njit()
def He4_Cl34__K38(rate_eval, tf):
    # Cl34 + He4 --> K38
    rate = 0.0

    # ths8r
    rate += np.exp(  47.9589 + -68.2165*tf.T913i + -2.18792*tf.T913
                  + -1.25322*tf.T9 + 0.140901*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl34__K38 = rate

@numba.njit()
def Mn62__Fe62__weak__mo03(rate_eval, tf):
    # Mn62 --> Fe62
    rate = 0.0

    # mo03w
    rate += np.exp(  1.35974)

    rate_eval.Mn62__Fe62__weak__mo03 = rate

@numba.njit()
def He4_Al42__P46(rate_eval, tf):
    # Al42 + He4 --> P46
    rate = 0.0

    # rath 
    rate += np.exp(  -19.8598 + -3.19891*tf.T9i + -8.93998*tf.T913i + 17.1222*tf.T913
                  + -4.99355*tf.T9 + 0.416069*tf.T953 + 10.0695*tf.lnT9)

    rate_eval.He4_Al42__P46 = rate

@numba.njit()
def He4_Ca38__p_Sc41(rate_eval, tf):
    # Ca38 + He4 --> p + Sc41
    rate = 0.0

    # ths8r
    rate += np.exp(  56.0864 + -76.3063*tf.T913i + -0.741136*tf.T913
                  + -0.511467*tf.T9 + 0.0171615*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca38__p_Sc41 = rate

@numba.njit()
def p_O17__F18(rate_eval, tf):
    # O17 + p --> F18
    rate = 0.0

    # il10r
    rate += np.exp(  9.39048 + -6.22828*tf.T9i + 2.31435*tf.T913
                  + -0.302835*tf.T9 + 0.020133*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -13.077 + -0.746296*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  15.8929 + -16.4035*tf.T913i + 4.31885*tf.T913
                  + -0.709921*tf.T9 + -2.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_O17__F18 = rate

@numba.njit()
def He4_Al40__P44(rate_eval, tf):
    # Al40 + He4 --> P44
    rate = 0.0

    # rath 
    rate += np.exp(  -19.738 + -3.05489*tf.T9i + -14.8355*tf.T913i + 23.2811*tf.T913
                  + -5.08956*tf.T9 + 0.410532*tf.T953 + 6.1861*tf.lnT9)

    rate_eval.He4_Al40__P44 = rate

@numba.njit()
def p_Al40__Si41(rate_eval, tf):
    # Al40 + p --> Si41
    rate = 0.0

    # rath 
    rate += np.exp(  76.488 + -3.6517*tf.T9i + 133.246*tf.T913i + -219.732*tf.T913
                  + 11.8806*tf.T9 + -0.650929*tf.T953 + 110.45*tf.lnT9)

    rate_eval.p_Al40__Si41 = rate

@numba.njit()
def V65__Cr65__weak__mo03(rate_eval, tf):
    # V65 --> Cr65
    rate = 0.0

    # mo03w
    rate += np.exp(  3.89662)

    rate_eval.V65__Cr65__weak__mo03 = rate

@numba.njit()
def n_Al40__Al41(rate_eval, tf):
    # Al40 + n --> Al41
    rate = 0.0

    # rath 
    rate += np.exp(  17.6883 + -0.0131199*tf.T9i + 2.29881*tf.T913i + -10.6935*tf.T913
                  + 0.630094*tf.T9 + -0.0362621*tf.T953 + 3.09966*tf.lnT9)

    rate_eval.n_Al40__Al41 = rate

@numba.njit()
def p_Ti64__n_V64(rate_eval, tf):
    # Ti64 + p --> n + V64
    rate = 0.0

    # rath 
    rate += np.exp(  136.822 + -6.43648*tf.T9i + 243.556*tf.T913i + -390.94*tf.T913
                  + 21.4083*tf.T9 + -1.19124*tf.T953 + 196.134*tf.lnT9)

    rate_eval.p_Ti64__n_V64 = rate

@numba.njit()
def n_Al39__Al40(rate_eval, tf):
    # Al39 + n --> Al40
    rate = 0.0

    # rath 
    rate += np.exp(  20.9952 + -1.39288*tf.T9i + 50.6873*tf.T913i + -75.7653*tf.T913
                  + 4.51516*tf.T9 + -0.28038*tf.T953 + 39.5043*tf.lnT9)

    rate_eval.n_Al39__Al40 = rate

@numba.njit()
def He4_Al38__P42(rate_eval, tf):
    # Al38 + He4 --> P42
    rate = 0.0

    # rath 
    rate += np.exp(  -20.274 + -2.91462*tf.T9i + -20.6394*tf.T913i + 30.4781*tf.T913
                  + -5.36026*tf.T9 + 0.417901*tf.T953 + 2.08181*tf.lnT9)

    rate_eval.He4_Al38__P42 = rate

@numba.njit()
def p_K40__Ca41(rate_eval, tf):
    # K40 + p --> Ca41
    rate = 0.0

    # ths8r
    rate += np.exp(  35.0973 + -30.0795*tf.T913i + 0.0447475*tf.T913
                  + -1.69565*tf.T9 + 0.20173*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_K40__Ca41 = rate

@numba.njit()
def n_Al38__Al39(rate_eval, tf):
    # Al38 + n --> Al39
    rate = 0.0

    # rath 
    rate += np.exp(  20.7695 + 0.0408663*tf.T9i + -0.67887*tf.T913i + -11.1275*tf.T913
                  + 0.908505*tf.T9 + -0.0579717*tf.T953 + 2.02937*tf.lnT9)

    rate_eval.n_Al38__Al39 = rate

@numba.njit()
def He4_Al37__P41(rate_eval, tf):
    # Al37 + He4 --> P41
    rate = 0.0

    # rath 
    rate += np.exp(  -15.1223 + -2.98046*tf.T9i + -11.4158*tf.T913i + 14.2618*tf.T913
                  + -4.45274*tf.T9 + 0.367687*tf.T953 + 9.9289*tf.lnT9)

    rate_eval.He4_Al37__P41 = rate

@numba.njit()
def p_Cl51__n_Ar51(rate_eval, tf):
    # Cl51 + p --> n + Ar51
    rate = 0.0

    # rath 
    rate += np.exp(  113.508 + -4.9067*tf.T9i + 184.072*tf.T913i + -301.46*tf.T913
                  + 16.4812*tf.T9 + -0.913802*tf.T953 + 150.648*tf.lnT9)

    rate_eval.p_Cl51__n_Ar51 = rate

@numba.njit()
def p_Al37__Si38(rate_eval, tf):
    # Al37 + p --> Si38
    rate = 0.0

    # rath 
    rate += np.exp(  74.4912 + -3.51182*tf.T9i + 126.713*tf.T913i + -210.724*tf.T913
                  + 11.5119*tf.T9 + -0.636968*tf.T953 + 105.68*tf.lnT9)

    rate_eval.p_Al37__Si38 = rate

@numba.njit()
def P32__S32__weak__wc12(rate_eval, tf):
    # P32 --> S32
    rate = 0.0

    # wc12w
    rate += np.exp(  -14.389)

    rate_eval.P32__S32__weak__wc12 = rate

@numba.njit()
def Ne19__F19__weak__wc12(rate_eval, tf):
    # Ne19 --> F19
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.21142)

    rate_eval.Ne19__F19__weak__wc12 = rate

@numba.njit()
def n_Ar38__Ar39(rate_eval, tf):
    # Ar38 + n --> Ar39
    rate = 0.0

    # ks03 
    rate += np.exp(  14.726 + -0.0331959*tf.T9i + 2.38837*tf.T913i + -4.76536*tf.T913
                  + 0.701311*tf.T9 + -0.0705226*tf.T953 + 1.80517*tf.lnT9)

    rate_eval.n_Ar38__Ar39 = rate

@numba.njit()
def p_Sc59__He4_Ca56(rate_eval, tf):
    # Sc59 + p --> He4 + Ca56
    rate = 0.0

    # rath 
    rate += np.exp(  112.48 + -6.00853*tf.T9i + 225.339*tf.T913i + -361.117*tf.T913
                  + 19.8114*tf.T9 + -1.04429*tf.T953 + 181.909*tf.lnT9)

    rate_eval.p_Sc59__He4_Ca56 = rate

@numba.njit()
def p_K44__Ca45(rate_eval, tf):
    # K44 + p --> Ca45
    rate = 0.0

    # rath 
    rate += np.exp(  102.892 + -4.93046*tf.T9i + 181.641*tf.T913i + -298.012*tf.T913
                  + 16.3694*tf.T9 + -0.923139*tf.T953 + 149.57*tf.lnT9)

    rate_eval.p_K44__Ca45 = rate

@numba.njit()
def S49__Cl49__weak__mo03(rate_eval, tf):
    # S49 --> Cl49
    rate = 0.0

    # mo03w
    rate += np.exp(  4.38402)

    rate_eval.S49__Cl49__weak__mo03 = rate

@numba.njit()
def He4_Al36__P40(rate_eval, tf):
    # Al36 + He4 --> P40
    rate = 0.0

    # rath 
    rate += np.exp(  -19.845 + -2.85002*tf.T9i + -19.7136*tf.T913i + 28.9337*tf.T913
                  + -5.31878*tf.T9 + 0.415424*tf.T953 + 3.1547*tf.lnT9)

    rate_eval.He4_Al36__P40 = rate

@numba.njit()
def p_Si40__n_P40(rate_eval, tf):
    # Si40 + p --> n + P40
    rate = 0.0

    # rath 
    rate += np.exp(  89.428 + -3.82258*tf.T9i + 138.389*tf.T913i + -227.326*tf.T913
                  + 12.2953*tf.T9 + -0.678347*tf.T953 + 114.519*tf.lnT9)

    rate_eval.p_Si40__n_P40 = rate

@numba.njit()
def He4_Mg37__Si41(rate_eval, tf):
    # Mg37 + He4 --> Si41
    rate = 0.0

    # rath 
    rate += np.exp(  -15.4106 + -2.808*tf.T9i + -12.2861*tf.T913i + 16.6306*tf.T913
                  + -4.58926*tf.T9 + 0.381567*tf.T953 + 8.15242*tf.lnT9)

    rate_eval.He4_Mg37__Si41 = rate

@numba.njit()
def p_Al36__Si37(rate_eval, tf):
    # Al36 + p --> Si37
    rate = 0.0

    # rath 
    rate += np.exp(  74.4574 + -3.46549*tf.T9i + 124.586*tf.T913i + -207.662*tf.T913
                  + 11.3652*tf.T9 + -0.629977*tf.T953 + 104.102*tf.lnT9)

    rate_eval.p_Al36__Si37 = rate

@numba.njit()
def n_Al35__Al36(rate_eval, tf):
    # Al35 + n --> Al36
    rate = 0.0

    # rath 
    rate += np.exp(  11.8256 + -0.0491523*tf.T9i + 3.71581*tf.T913i + -8.81203*tf.T913
                  + 0.859254*tf.T9 + -0.0584268*tf.T953 + 3.01071*tf.lnT9)

    rate_eval.n_Al35__Al36 = rate

@numba.njit()
def He4_N14__n_F17(rate_eval, tf):
    # N14 + He4 --> n + F17
    rate = 0.0

    # nacr 
    rate += np.exp(  19.2094 + -54.9473*tf.T9i + -0.712285*tf.T913
                  + 0.240317*tf.T9 + -0.0201705*tf.T953)

    rate_eval.He4_N14__n_F17 = rate

@numba.njit()
def n_V61__V62(rate_eval, tf):
    # V61 + n --> V62
    rate = 0.0

    # rath 
    rate += np.exp(  17.2298 + -0.0282061*tf.T9i + 2.78006*tf.T913i + -10.2184*tf.T913
                  + 1.21058*tf.T9 + -0.134955*tf.T953 + 2.95881*tf.lnT9)

    rate_eval.n_V61__V62 = rate

@numba.njit()
def He4_Al34__P38(rate_eval, tf):
    # Al34 + He4 --> P38
    rate = 0.0

    # rath 
    rate += np.exp(  -17.7125 + -2.75247*tf.T9i + -20.8731*tf.T913i + 27.2021*tf.T913
                  + -5.00402*tf.T9 + 0.388001*tf.T953 + 3.15885*tf.lnT9)

    rate_eval.He4_Al34__P38 = rate

@numba.njit()
def n_Al34__Al35(rate_eval, tf):
    # Al34 + n --> Al35
    rate = 0.0

    # rath 
    rate += np.exp(  15.2917 + -0.0439939*tf.T9i + 3.49634*tf.T913i + -7.88533*tf.T913
                  + 0.389571*tf.T9 + -0.0210598*tf.T953 + 2.89354*tf.lnT9)

    rate_eval.n_Al34__Al35 = rate

@numba.njit()
def He4_Cr56__Fe60(rate_eval, tf):
    # Cr56 + He4 --> Fe60
    rate = 0.0

    # rath 
    rate += np.exp(  -1066.0 + 22.003*tf.T9i + -2193.28*tf.T913i + 3385.09*tf.T913
                  + -192.502*tf.T9 + 10.6491*tf.T953 + -1640.01*tf.lnT9)

    rate_eval.He4_Cr56__Fe60 = rate

@numba.njit()
def p_Al33__Si34(rate_eval, tf):
    # Al33 + p --> Si34
    rate = 0.0

    # rath 
    rate += np.exp(  72.1442 + -3.33898*tf.T9i + 119.685*tf.T913i + -199.893*tf.T913
                  + 10.79*tf.T9 + -0.594055*tf.T953 + 100.547*tf.lnT9)

    rate_eval.p_Al33__Si34 = rate

@numba.njit()
def p_Al31__Si32(rate_eval, tf):
    # Al31 + p --> Si32
    rate = 0.0

    # rath 
    rate += np.exp(  69.4315 + -3.2117*tf.T9i + 112.86*tf.T913i + -188.573*tf.T913
                  + 9.94128*tf.T9 + -0.529924*tf.T953 + 95.2811*tf.lnT9)

    rate_eval.p_Al31__Si32 = rate

@numba.njit()
def n_Al31__Al32(rate_eval, tf):
    # Al31 + n --> Al32
    rate = 0.0

    # rath 
    rate += np.exp(  13.6594 + -0.0440933*tf.T9i + 3.28487*tf.T913i + -7.10674*tf.T913
                  + 0.545425*tf.T9 + -0.0354725*tf.T953 + 2.57129*tf.lnT9)

    rate_eval.n_Al31__Al32 = rate

@numba.njit()
def Li11__n_n_Be9__weak__wc12(rate_eval, tf):
    # Li11 --> n + n + Be9
    rate = 0.0

    # wc12w
    rate += np.exp(  1.178)

    rate_eval.Li11__n_n_Be9__weak__wc12 = rate

@numba.njit()
def He4_Al30__P34(rate_eval, tf):
    # Al30 + He4 --> P34
    rate = 0.0

    # rath 
    rate += np.exp(  -21.2887 + -2.44693*tf.T9i + -33.4724*tf.T913i + 45.3034*tf.T913
                  + -6.00406*tf.T9 + 0.449284*tf.T953 + -6.21939*tf.lnT9)

    rate_eval.He4_Al30__P34 = rate

@numba.njit()
def p_S49__He4_P46(rate_eval, tf):
    # S49 + p --> He4 + P46
    rate = 0.0

    # rath 
    rate += np.exp(  79.2358 + -4.68681*tf.T9i + 178.59*tf.T913i + -277.529*tf.T913
                  + 14.433*tf.T9 + -0.739892*tf.T953 + 144.956*tf.lnT9)

    rate_eval.p_S49__He4_P46 = rate

@numba.njit()
def p_Al30__Si31(rate_eval, tf):
    # Al30 + p --> Si31
    rate = 0.0

    # rath 
    rate += np.exp(  69.5909 + -3.16685*tf.T9i + 111.379*tf.T913i + -187.151*tf.T913
                  + 10.0525*tf.T9 + -0.54397*tf.T953 + 94.4147*tf.lnT9)

    rate_eval.p_Al30__Si31 = rate

@numba.njit()
def n_V50__V51(rate_eval, tf):
    # V50 + n --> V51
    rate = 0.0

    # ks03 
    rate += np.exp(  26.4771 + -0.118554*tf.T9i + 10.9535*tf.T913i + -23.1254*tf.T913
                  + 1.53091*tf.T9 + -0.0992995*tf.T953 + 9.62203*tf.lnT9)

    rate_eval.n_V50__V51 = rate

@numba.njit()
def p_Al28__Si29(rate_eval, tf):
    # Al28 + p --> Si29
    rate = 0.0

    # rath 
    rate += np.exp(  82.7866 + -3.13386*tf.T9i + 114.903*tf.T913i + -203.401*tf.T913
                  + 11.5793*tf.T9 + -0.672783*tf.T953 + 99.4177*tf.lnT9)

    rate_eval.p_Al28__Si29 = rate

@numba.njit()
def He4_Ti62__n_Cr65(rate_eval, tf):
    # Ti62 + He4 --> n + Cr65
    rate = 0.0

    # rath 
    rate += np.exp(  -1091.12 + 17.3721*tf.T9i + -1885.38*tf.T913i + 3110.26*tf.T913
                  + -185.9*tf.T9 + 10.6737*tf.T953 + -1458.45*tf.lnT9)

    rate_eval.He4_Ti62__n_Cr65 = rate

@numba.njit()
def p_Cr68__Mn69(rate_eval, tf):
    # Cr68 + p --> Mn69
    rate = 0.0

    # rath 
    rate += np.exp(  143.342 + -7.03381*tf.T9i + 269.371*tf.T913i + -437.086*tf.T913
                  + 24.6203*tf.T9 + -1.41897*tf.T953 + 217.238*tf.lnT9)

    rate_eval.p_Cr68__Mn69 = rate

@numba.njit()
def He4_Al27__P31(rate_eval, tf):
    # Al27 + He4 --> P31
    rate = 0.0

    # ths8r
    rate += np.exp(  47.2333 + -56.5351*tf.T913i + -0.896208*tf.T913
                  + -1.72024*tf.T9 + 0.185409*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al27__P31 = rate

@numba.njit()
def Al25__Mg25__weak__wc12(rate_eval, tf):
    # Al25 --> Mg25
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.33781)

    rate_eval.Al25__Mg25__weak__wc12 = rate

@numba.njit()
def He4_Al26__P30(rate_eval, tf):
    # Al26 + He4 --> P30
    rate = 0.0

    # ths8r
    rate += np.exp(  42.9778 + -56.4422*tf.T913i + -2.44848*tf.T913
                  + -1.17578*tf.T9 + 0.150757*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al26__P30 = rate

@numba.njit()
def n_Al26__Al27(rate_eval, tf):
    # Al26 + n --> Al27
    rate = 0.0

    # ks03 
    rate += np.exp(  14.7625 + 0.00350938*tf.T9i + -0.171158*tf.T913i + -1.77283*tf.T913
                  + 0.206192*tf.T9 + -0.0191705*tf.T953 + 0.139609*tf.lnT9)

    rate_eval.n_Al26__Al27 = rate

@numba.njit()
def p_Al24__Si25(rate_eval, tf):
    # Al24 + p --> Si25
    rate = 0.0

    # lg18 
    rate += np.exp(  547.839 + -132.723*tf.T913i + -719.687*tf.T913
                  + 516.917*tf.T9 + -229.626*tf.T953 + -0.6667*tf.lnT9)
    # lg18 
    rate += np.exp(  -240.327 + -69.5212*tf.T9i + 1215.44*tf.T913i + -937.305*tf.T913
                  + 34.6876*tf.T9 + -1.518*tf.T953 + 620.869*tf.lnT9)
    # lg18 
    rate += np.exp(  -94.6498 + -64.3537*tf.T9i + 114.231*tf.T913i + 29.9722*tf.T913
                  + -0.912192*tf.T9 + 0.0157024*tf.T953 + -0.66667*tf.lnT9)
    # lg18 
    rate += np.exp(  -40.1405 + -12.4124*tf.T9i + 36.6405*tf.T913i + 19.0341*tf.T913
                  + -1.25438*tf.T9 + 0.0290137*tf.T953 + -0.667*tf.lnT9)
    # lg18 
    rate += np.exp(  57.5226 + -26.19*tf.T9i + -44.1969*tf.T913
                  + 7.42869*tf.T9 + -0.637559*tf.T953 + -0.66667*tf.lnT9)
    # lg18 
    rate += np.exp(  626.421 + -16.7058*tf.T9i + 701.368*tf.T913i + -1424.23*tf.T913
                  + 126.754*tf.T9 + -12.3375*tf.T953 + 586.976*tf.lnT9)
    # lg18 
    rate += np.exp(  -102.436 + -16.9734*tf.T9i + 74.395*tf.T913i + 49.2327*tf.T913
                  + -3.43351*tf.T9 + -1.5*tf.lnT9)
    # lg18 
    rate += np.exp(  -56.0488 + -1.25412*tf.T9i + -105.339*tf.T913i + 174.554*tf.T913
                  + -9.87771*tf.T9 + 0.297539*tf.T953 + -83.529*tf.lnT9)
    # lg18 
    rate += np.exp(  -88.3633 + -24.7611*tf.T9i + 221.948*tf.T913i + -111.276*tf.T913
                  + 2.1968*tf.T9 + -0.03973*tf.T953 + 92.3269*tf.lnT9)

    rate_eval.p_Al24__Si25 = rate

@numba.njit()
def n_Al24__Al25(rate_eval, tf):
    # Al24 + n --> Al25
    rate = 0.0

    # ths8r
    rate += np.exp(  9.14197 + 1.8985*tf.T913
                  + -0.177554*tf.T9 + 0.0119186*tf.T953)

    rate_eval.n_Al24__Al25 = rate

@numba.njit()
def He4_Ti56__Cr60(rate_eval, tf):
    # Ti56 + He4 --> Cr60
    rate = 0.0

    # rath 
    rate += np.exp(  -997.91 + 20.7465*tf.T9i + -2065.47*tf.T913i + 3179.82*tf.T913
                  + -180.302*tf.T9 + 9.94132*tf.T953 + -1542.37*tf.lnT9)

    rate_eval.He4_Ti56__Cr60 = rate

@numba.njit()
def Fe69__Co69__weak__wc17(rate_eval, tf):
    # Fe69 --> Co69
    rate = 0.0

    # wc17w
    rate += np.exp(  1.76819)

    rate_eval.Fe69__Co69__weak__wc17 = rate

@numba.njit()
def He4_Mg41__Si45(rate_eval, tf):
    # Mg41 + He4 --> Si45
    rate = 0.0

    # rath 
    rate += np.exp(  -20.2309 + -2.96858*tf.T9i + -11.441*tf.T913i + 22.1416*tf.T913
                  + -5.23535*tf.T9 + 0.431186*tf.T953 + 7.03753*tf.lnT9)

    rate_eval.He4_Mg41__Si45 = rate

@numba.njit()
def p_Cl39__n_Ar39(rate_eval, tf):
    # Cl39 + p --> n + Ar39
    rate = 0.0

    # rath 
    rate += np.exp(  100.827 + -4.3126*tf.T9i + 156.901*tf.T913i + -261.097*tf.T913
                  + 14.3284*tf.T9 + -0.802391*tf.T953 + 130.639*tf.lnT9)

    rate_eval.p_Cl39__n_Ar39 = rate

@numba.njit()
def He4_Mg39__Si43(rate_eval, tf):
    # Mg39 + He4 --> Si43
    rate = 0.0

    # rath 
    rate += np.exp(  -16.2334 + -2.89193*tf.T9i + -11.4655*tf.T913i + 17.7696*tf.T913
                  + -4.79642*tf.T9 + 0.400447*tf.T953 + 8.09301*tf.lnT9)

    rate_eval.He4_Mg39__Si43 = rate

@numba.njit()
def p_Mg39__Al40(rate_eval, tf):
    # Mg39 + p --> Al40
    rate = 0.0

    # rath 
    rate += np.exp(  74.256 + -3.41531*tf.T9i + 124.066*tf.T913i + -205.751*tf.T913
                  + 11.1702*tf.T9 + -0.612859*tf.T953 + 103.1*tf.lnT9)

    rate_eval.p_Mg39__Al40 = rate

@numba.njit()
def p_Mg37__Al38(rate_eval, tf):
    # Mg37 + p --> Al38
    rate = 0.0

    # rath 
    rate += np.exp(  70.8202 + -3.3247*tf.T9i + 119.665*tf.T913i + -198.607*tf.T913
                  + 10.7985*tf.T9 + -0.593799*tf.T953 + 99.7133*tf.lnT9)

    rate_eval.p_Mg37__Al38 = rate

@numba.njit()
def n_Sc44__Sc45(rate_eval, tf):
    # Sc44 + n --> Sc45
    rate = 0.0

    # ths8r
    rate += np.exp(  17.0705 + -1.31922*tf.T913
                  + 0.167096*tf.T9 + -0.0191676*tf.T953)

    rate_eval.n_Sc44__Sc45 = rate

@numba.njit()
def n_Mg36__Mg37(rate_eval, tf):
    # Mg36 + n --> Mg37
    rate = 0.0

    # rath 
    rate += np.exp(  137.935 + -12.521*tf.T9i + 375.663*tf.T913i + -532.551*tf.T913
                  + 29.9603*tf.T9 + -1.72041*tf.T953 + 269.94*tf.lnT9)

    rate_eval.n_Mg36__Mg37 = rate

@numba.njit()
def He4_Al41__P45(rate_eval, tf):
    # Al41 + He4 --> P45
    rate = 0.0

    # rath 
    rate += np.exp(  -22.3347 + -3.13191*tf.T9i + -11.9135*tf.T913i + 22.4364*tf.T913
                  + -5.30904*tf.T9 + 0.431*tf.T953 + 7.69018*tf.lnT9)

    rate_eval.He4_Al41__P45 = rate

@numba.njit()
def d_Li6__n_Be7(rate_eval, tf):
    # Li6 + d --> n + Be7
    rate = 0.0

    # mafon
    rate += np.exp(  28.0095 + -4.77456e-12*tf.T9i + -10.259*tf.T913i + -2.01559e-09*tf.T913
                  + 1.99542e-10*tf.T9 + -1.65595e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.d_Li6__n_Be7 = rate

@numba.njit()
def n_Mg35__Mg36(rate_eval, tf):
    # Mg35 + n --> Mg36
    rate = 0.0

    # rath 
    rate += np.exp(  13.6088 + -0.0980639*tf.T9i + 7.90448*tf.T913i + -14.1879*tf.T913
                  + 0.901873*tf.T9 + -0.0509823*tf.T953 + 6.20343*tf.lnT9)

    rate_eval.n_Mg35__Mg36 = rate

@numba.njit()
def p_Sc60__Ti61(rate_eval, tf):
    # Sc60 + p --> Ti61
    rate = 0.0

    # rath 
    rate += np.exp(  117.025 + -6.03225*tf.T9i + 225.319*tf.T913i + -361.747*tf.T913
                  + 19.8698*tf.T9 + -1.11433*tf.T953 + 181.78*tf.lnT9)

    rate_eval.p_Sc60__Ti61 = rate

@numba.njit()
def p_P46__He4_Si43(rate_eval, tf):
    # P46 + p --> He4 + Si43
    rate = 0.0

    # rath 
    rate += np.exp(  92.1219 + -4.28791*tf.T9i + 159.195*tf.T913i + -263.353*tf.T913
                  + 14.3854*tf.T9 + -0.770793*tf.T953 + 131.441*tf.lnT9)

    rate_eval.p_P46__He4_Si43 = rate

@numba.njit()
def n_Mg34__Mg35(rate_eval, tf):
    # Mg34 + n --> Mg35
    rate = 0.0

    # rath 
    rate += np.exp(  -31.9839 + -29.1496*tf.T9i + 513.969*tf.T913i + -481.173*tf.T913
                  + 18.9985*tf.T9 + -0.820243*tf.T953 + 297.583*tf.lnT9)

    rate_eval.n_Mg34__Mg35 = rate

@numba.njit()
def p_Cr47__Mn48(rate_eval, tf):
    # Cr47 + p --> Mn48
    rate = 0.0

    # nfisn
    rate += np.exp(  6124.88 + -10.277*tf.T9i + 804.191*tf.T913i + -9710.91*tf.T913
                  + 6159.65*tf.T9 + -6070.73*tf.T953 + 1640.27*tf.lnT9)
    # nfisn
    rate += np.exp(  154.881 + -2.56422*tf.T9i + -5.3389*tf.T913i + -179.804*tf.T913
                  + 30.5046*tf.T9 + -4.62095*tf.T953 + 36.7896*tf.lnT9)
    # nfisn
    rate += np.exp(  32.0165 + -0.146551*tf.T9i + -28.0121*tf.T913i + -15.026*tf.T913
                  + 1.113*tf.T9 + -0.0981393*tf.T953 + 5.7578*tf.lnT9)
    # nfisn
    rate += np.exp(  39.7225 + -3.63746*tf.T9i + -39.9182*tf.T913i + 2.57325*tf.T913
                  + 1.37645*tf.T9 + -0.147521*tf.T953 + -10.8212*tf.lnT9)

    rate_eval.p_Cr47__Mn48 = rate

@numba.njit()
def He4_Si39__S43(rate_eval, tf):
    # Si39 + He4 --> S43
    rate = 0.0

    # rath 
    rate += np.exp(  -307.259 + 1.67612*tf.T9i + -436.431*tf.T913i + 769.291*tf.T913
                  + -51.1015*tf.T9 + 3.12234*tf.T953 + -336.796*tf.lnT9)

    rate_eval.He4_Si39__S43 = rate

@numba.njit()
def He4_Mg40__Si44(rate_eval, tf):
    # Mg40 + He4 --> Si44
    rate = 0.0

    # rath 
    rate += np.exp(  -22.01 + -2.92376*tf.T9i + -12.5531*tf.T913i + 24.2084*tf.T913
                  + -5.4222*tf.T9 + 0.442611*tf.T953 + 6.20069*tf.lnT9)

    rate_eval.He4_Mg40__Si44 = rate

@numba.njit()
def p_Ca43__Sc44(rate_eval, tf):
    # Ca43 + p --> Sc44
    rate = 0.0

    # ths8r
    rate += np.exp(  34.9383 + -31.1437*tf.T913i + 1.02701*tf.T913
                  + -1.81612*tf.T9 + 0.197287*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ca43__Sc44 = rate

@numba.njit()
def He4_Mg33__Si37(rate_eval, tf):
    # Mg33 + He4 --> Si37
    rate = 0.0

    # rath 
    rate += np.exp(  -16.6333 + -2.57249*tf.T9i + -19.7679*tf.T913i + 25.8703*tf.T913
                  + -4.85241*tf.T9 + 0.381233*tf.T953 + 3.09806*tf.lnT9)

    rate_eval.He4_Mg33__Si37 = rate

@numba.njit()
def He4_Mg31__Si35(rate_eval, tf):
    # Mg31 + He4 --> Si35
    rate = 0.0

    # rath 
    rate += np.exp(  -16.6141 + -2.45843*tf.T9i + -22.7075*tf.T913i + 28.9413*tf.T913
                  + -4.94973*tf.T9 + 0.381403*tf.T953 + 1.30257*tf.lnT9)

    rate_eval.He4_Mg31__Si35 = rate

@numba.njit()
def p_S48__He4_P45(rate_eval, tf):
    # S48 + p --> He4 + P45
    rate = 0.0

    # rath 
    rate += np.exp(  82.3312 + -4.75193*tf.T9i + 187.659*tf.T913i + -290.059*tf.T913
                  + 14.4449*tf.T9 + -0.699636*tf.T953 + 152.855*tf.lnT9)

    rate_eval.p_S48__He4_P45 = rate

@numba.njit()
def n_Si35__Si36(rate_eval, tf):
    # Si35 + n --> Si36
    rate = 0.0

    # rath 
    rate += np.exp(  11.4651 + -0.0402582*tf.T9i + 2.75728*tf.T913i + -4.94062*tf.T913
                  + 0.440231*tf.T9 + -0.0344186*tf.T953 + 1.92218*tf.lnT9)

    rate_eval.n_Si35__Si36 = rate

@numba.njit()
def He4_Al29__P33(rate_eval, tf):
    # Al29 + He4 --> P33
    rate = 0.0

    # rath 
    rate += np.exp(  -3.10838 + -2.56506*tf.T9i + -18.1499*tf.T913i + 12.7893*tf.T913
                  + -4.43703*tf.T9 + 0.390981*tf.T953 + 7.70771*tf.lnT9)

    rate_eval.He4_Al29__P33 = rate

@numba.njit()
def n_K37__p_Ar37(rate_eval, tf):
    # K37 + n --> p + Ar37
    rate = 0.0

    # ths8r
    rate += np.exp(  19.3703 + 0.399131*tf.T913
                  + 0.0819317*tf.T9 + -0.0133489*tf.T953)

    rate_eval.n_K37__p_Ar37 = rate

@numba.njit()
def n_Mg31__Mg32(rate_eval, tf):
    # Mg31 + n --> Mg32
    rate = 0.0

    # rath 
    rate += np.exp(  11.9333 + -0.0433286*tf.T9i + 2.7546*tf.T913i + -4.54919*tf.T913
                  + 0.30283*tf.T9 + -0.0231067*tf.T953 + 1.76173*tf.lnT9)

    rate_eval.n_Mg31__Mg32 = rate

@numba.njit()
def p_Fe49__Co50(rate_eval, tf):
    # Fe49 + p --> Co50
    rate = 0.0

    # ths8r
    rate += np.exp(  41.6706 + -37.1314*tf.T913i + -6.88094*tf.T913
                  + -1.43009*tf.T9 + 0.255202*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Fe49__Co50 = rate

@numba.njit()
def He4_K47__Sc51(rate_eval, tf):
    # K47 + He4 --> Sc51
    rate = 0.0

    # rath 
    rate += np.exp(  -876.404 + 13.9826*tf.T9i + -1517.41*tf.T913i + 2491.61*tf.T913
                  + -149.171*tf.T9 + 8.57652*tf.T953 + -1168.1*tf.lnT9)

    rate_eval.He4_K47__Sc51 = rate

@numba.njit()
def p_Mg30__Al31(rate_eval, tf):
    # Mg30 + p --> Al31
    rate = 0.0

    # rath 
    rate += np.exp(  65.7998 + -3.00057*tf.T9i + 105.396*tf.T913i + -177.145*tf.T913
                  + 9.4872*tf.T9 + -0.520738*tf.T953 + 89.301*tf.lnT9)

    rate_eval.p_Mg30__Al31 = rate

@numba.njit()
def p_Si44__P45(rate_eval, tf):
    # Si44 + p --> P45
    rate = 0.0

    # rath 
    rate += np.exp(  79.3616 + -3.99027*tf.T9i + 145.068*tf.T913i + -235.33*tf.T913
                  + 12.6472*tf.T9 + -0.694154*tf.T953 + 118.964*tf.lnT9)

    rate_eval.p_Si44__P45 = rate

@numba.njit()
def He4_Mg29__Si33(rate_eval, tf):
    # Mg29 + He4 --> Si33
    rate = 0.0

    # rath 
    rate += np.exp(  -16.0165 + -2.32395*tf.T9i + -26.8646*tf.T913i + 33.2636*tf.T913
                  + -5.1927*tf.T9 + 0.404201*tf.T953 + -1.27387*tf.lnT9)

    rate_eval.He4_Mg29__Si33 = rate

@numba.njit()
def p_Mg33__n_Al33(rate_eval, tf):
    # Mg33 + p --> n + Al33
    rate = 0.0

    # rath 
    rate += np.exp(  79.4081 + -3.15228*tf.T9i + 112.579*tf.T913i + -188.962*tf.T913
                  + 10.2266*tf.T9 + -0.564297*tf.T953 + 94.7873*tf.lnT9)

    rate_eval.p_Mg33__n_Al33 = rate

@numba.njit()
def n_Mg29__Mg30(rate_eval, tf):
    # Mg29 + n --> Mg30
    rate = 0.0

    # rath 
    rate += np.exp(  9.41174 + 0.00271002*tf.T9i + -1.6451*tf.T913i + 3.1692*tf.T913
                  + -0.0540245*tf.T9 + -0.00438893*tf.T953 + -2.01214*tf.lnT9)

    rate_eval.n_Mg29__Mg30 = rate

@numba.njit()
def He4_Mg30__Si34(rate_eval, tf):
    # Mg30 + He4 --> Si34
    rate = 0.0

    # rath 
    rate += np.exp(  -17.2786 + -2.38428*tf.T9i + -25.5448*tf.T913i + 33.0132*tf.T913
                  + -5.29701*tf.T9 + 0.406523*tf.T953 + -0.718156*tf.lnT9)

    rate_eval.He4_Mg30__Si34 = rate

@numba.njit()
def n_Ca45__Ca46(rate_eval, tf):
    # Ca45 + n --> Ca46
    rate = 0.0

    # ks03 
    rate += np.exp(  22.6116 + -0.0524788*tf.T9i + 5.01526*tf.T913i + -14.4226*tf.T913
                  + 1.37087*tf.T9 + -0.111582*tf.T953 + 4.87661*tf.lnT9)

    rate_eval.n_Ca45__Ca46 = rate

@numba.njit()
def p_Mg32__Al33(rate_eval, tf):
    # Mg32 + p --> Al33
    rate = 0.0

    # rath 
    rate += np.exp(  65.8813 + -3.09475*tf.T9i + 109.171*tf.T913i + -181.832*tf.T913
                  + 9.73463*tf.T9 + -0.533099*tf.T953 + 91.8164*tf.lnT9)

    rate_eval.p_Mg32__Al33 = rate

@numba.njit()
def He4_Mg28__Si32(rate_eval, tf):
    # Mg28 + He4 --> Si32
    rate = 0.0

    # rath 
    rate += np.exp(  -23.1473 + -2.1929*tf.T9i + -35.2693*tf.T913i + 50.8633*tf.T913
                  + -6.49947*tf.T9 + 0.472061*tf.T953 + -8.59373*tf.lnT9)

    rate_eval.He4_Mg28__Si32 = rate

@numba.njit()
def p_Fe54__Co55(rate_eval, tf):
    # Fe54 + p --> Co55
    rate = 0.0

    # ths8r
    rate += np.exp(  36.2304 + -37.1544*tf.T913i + 0.950364*tf.T913
                  + -1.77529*tf.T9 + 0.198562*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Fe54__Co55 = rate

@numba.njit()
def p_Mg27__Al28(rate_eval, tf):
    # Mg27 + p --> Al28
    rate = 0.0

    # rath 
    rate += np.exp(  65.9571 + -2.86222*tf.T9i + 100.284*tf.T913i + -171.46*tf.T913
                  + 9.44978*tf.T9 + -0.536212*tf.T953 + 86.0023*tf.lnT9)

    rate_eval.p_Mg27__Al28 = rate

@numba.njit()
def He4_Mn65__Co69(rate_eval, tf):
    # Mn65 + He4 --> Co69
    rate = 0.0

    # rath 
    rate += np.exp(  -1168.52 + 24.3649*tf.T9i + -2419.32*tf.T913i + 3726.62*tf.T913
                  + -210.777*tf.T9 + 11.6205*tf.T953 + -1809.99*tf.lnT9)

    rate_eval.He4_Mn65__Co69 = rate

@numba.njit()
def Mn70__Fe70__weak__mo03(rate_eval, tf):
    # Mn70 --> Fe70
    rate = 0.0

    # mo03w
    rate += np.exp(  4.06191)

    rate_eval.Mn70__Fe70__weak__mo03 = rate

@numba.njit()
def B17__C17__weak__wc17(rate_eval, tf):
    # B17 --> C17
    rate = 0.0

    # wc17w
    rate += np.exp(  3.56886)

    rate_eval.B17__C17__weak__wc17 = rate

@numba.njit()
def Ti64__n_n_V62__weak__mp17(rate_eval, tf):
    # Ti64 --> n + n + V62
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.689321)

    rate_eval.Ti64__n_n_V62__weak__mp17 = rate

@numba.njit()
def P44__S44__weak__wc17(rate_eval, tf):
    # P44 --> S44
    rate = 0.0

    # wc17w
    rate += np.exp(  -111.506)

    rate_eval.P44__S44__weak__wc17 = rate

@numba.njit()
def p_Fe46__Co47(rate_eval, tf):
    # Fe46 + p --> Co47
    rate = 0.0

    # ths8r
    rate += np.exp(  -18.5553 + -17.6735*tf.T9i + 20.309*tf.T913
                  + -2.64768*tf.T9 + 0.201647*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Fe46__Co47 = rate

@numba.njit()
def p_Mg26__Al27(rate_eval, tf):
    # Mg26 + p --> Al27
    rate = 0.0

    # il10r
    rate += np.exp(  -27.2168 + -0.888689*tf.T9i + 35.6312*tf.T913
                  + -5.27265*tf.T9 + 0.392932*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -84.493 + -0.469464*tf.T9i + 251.281*tf.T913
                  + -730.009*tf.T9 + -224.016*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  5.26056 + -3.35921*tf.T9i + 6.78105*tf.T913
                  + -1.25771*tf.T9 + 0.140754*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Mg26__Al27 = rate

@numba.njit()
def p_K49__Ca50(rate_eval, tf):
    # K49 + p --> Ca50
    rate = 0.0

    # rath 
    rate += np.exp(  93.2617 + -5.10049*tf.T9i + 184.177*tf.T913i + -292.024*tf.T913
                  + 15.3032*tf.T9 + -0.798175*tf.T953 + 149.246*tf.lnT9)

    rate_eval.p_K49__Ca50 = rate

@numba.njit()
def Ne25__Na25__weak__wc12(rate_eval, tf):
    # Ne25 --> Na25
    rate = 0.0

    # wc12w
    rate += np.exp(  0.140985)

    rate_eval.Ne25__Na25__weak__wc12 = rate

@numba.njit()
def p_Mg24__Al25(rate_eval, tf):
    # Mg24 + p --> Al25
    rate = 0.0

    # il10r
    rate += np.exp(  8.24021 + -2.48451*tf.T9i + -1.57811*tf.T913
                  + 1.52232*tf.T9 + -0.183001*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  19.8966 + -22.0227*tf.T913i + 0.361297*tf.T913
                  + 2.61292*tf.T9 + -1.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mg24__Al25 = rate

@numba.njit()
def n_Mg24__Mg25(rate_eval, tf):
    # Mg24 + n --> Mg25
    rate = 0.0

    # ks03 
    rate += np.exp(  64.622 + 0.161296*tf.T9i + -0.142939*tf.T913i + -57.7499*tf.T913
                  + 7.01981*tf.T9 + -0.582057*tf.T953 + 12.8133*tf.lnT9)

    rate_eval.n_Mg24__Mg25 = rate

@numba.njit()
def n_Ca43__Ca44(rate_eval, tf):
    # Ca43 + n --> Ca44
    rate = 0.0

    # ks03 
    rate += np.exp(  10.6877 + -0.00587516*tf.T9i + -1.26512*tf.T913i + 6.74718*tf.T913
                  + -0.673582*tf.T9 + 0.0412245*tf.T953 + -2.30362*tf.lnT9)

    rate_eval.n_Ca43__Ca44 = rate

@numba.njit()
def Fe68__n_Co67__weak__mp17(rate_eval, tf):
    # Fe68 --> n + Co67
    rate = 0.0

    # mp17w
    rate += np.exp(  -3.25689)

    rate_eval.Fe68__n_Co67__weak__mp17 = rate

@numba.njit()
def He4_Mg23__Si27(rate_eval, tf):
    # Mg23 + He4 --> Si27
    rate = 0.0

    # ths8r
    rate += np.exp(  43.7008 + -53.203*tf.T913i + -4.6318*tf.T913
                  + -0.130951*tf.T9 + 0.014691*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg23__Si27 = rate

@numba.njit()
def p_Mg23__Al24(rate_eval, tf):
    # Mg23 + p --> Al24
    rate = 0.0

    # il10r
    rate += np.exp(  7.24404 + -5.41079*tf.T9i + 0.871175*tf.T913
                  + 0.261915*tf.T9 + -0.0107798*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  19.8512 + -22.0099*tf.T913i + -0.366127*tf.T913
                  + 0.554403*tf.T9 + -1.09855*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mg23__Al24 = rate

@numba.njit()
def n_Mn44__He4_V41(rate_eval, tf):
    # Mn44 + n --> He4 + V41
    rate = 0.0

    # ths8r
    rate += np.exp(  18.0733 + -2.63761*tf.T913
                  + 0.581739*tf.T9 + -0.033943*tf.T953)

    rate_eval.n_Mn44__He4_V41 = rate

@numba.njit()
def S45__n_n_Cl43__weak__mp17(rate_eval, tf):
    # S45 --> n + n + Cl43
    rate = 0.0

    # mp17w
    rate += np.exp(  -2.28344)

    rate_eval.S45__n_n_Cl43__weak__mp17 = rate

@numba.njit()
def n_Mg23__Mg24(rate_eval, tf):
    # Mg23 + n --> Mg24
    rate = 0.0

    # ths8r
    rate += np.exp(  7.00613 + 2.66964*tf.T913
                  + -0.448904*tf.T9 + 0.0326505*tf.T953)

    rate_eval.n_Mg23__Mg24 = rate

@numba.njit()
def He4_Mg31__n_Si34(rate_eval, tf):
    # Mg31 + He4 --> n + Si34
    rate = 0.0

    # rath 
    rate += np.exp(  80.2697 + -3.377*tf.T9i + 76.4682*tf.T913i + -168.102*tf.T913
                  + 8.04665*tf.T9 + -0.419551*tf.T953 + 87.6461*tf.lnT9)

    rate_eval.He4_Mg31__n_Si34 = rate

@numba.njit()
def He4_Ca53__Ti57(rate_eval, tf):
    # Ca53 + He4 --> Ti57
    rate = 0.0

    # rath 
    rate += np.exp(  -957.886 + 15.1479*tf.T9i + -1646.26*tf.T913i + 2709.91*tf.T913
                  + -162.164*tf.T9 + 9.30266*tf.T953 + -1270.0*tf.lnT9)

    rate_eval.He4_Ca53__Ti57 = rate

@numba.njit()
def Cl28__S28__weak__bqa_pos_(rate_eval, tf):
    # Cl28 --> S28
    rate = 0.0

    # bqa+w
    rate += np.exp(  6.01061)

    rate_eval.Cl28__S28__weak__bqa_pos_ = rate

@numba.njit()
def n_Cl34__Cl35(rate_eval, tf):
    # Cl34 + n --> Cl35
    rate = 0.0

    # ths8r
    rate += np.exp(  12.6539 + 0.990222*tf.T913
                  + -0.146686*tf.T9 + 0.00560251*tf.T953)

    rate_eval.n_Cl34__Cl35 = rate

@numba.njit()
def p_Mg22__Al23(rate_eval, tf):
    # Mg22 + p --> Al23
    rate = 0.0

    # il10r
    rate += np.exp(  -2.25379 + -4.64045*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  15.6143 + -21.965*tf.T913i + 0.526407*tf.T913
                  + 0.062416*tf.T9 + -0.0212869*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mg22__Al23 = rate

@numba.njit()
def n_Mg22__Mg23(rate_eval, tf):
    # Mg22 + n --> Mg23
    rate = 0.0

    # ths8r
    rate += np.exp(  9.32079 + 2.72435*tf.T913
                  + -0.470498*tf.T9 + 0.0357362*tf.T953)

    rate_eval.n_Mg22__Mg23 = rate

@numba.njit()
def n_C14__C15(rate_eval, tf):
    # C14 + n --> C15
    rate = 0.0

    # ks03 
    rate += np.exp(  11.0666 + -0.0227107*tf.T9i + 1.58295*tf.T913i + -4.89363*tf.T913
                  + 0.382862*tf.T9 + -0.0225403*tf.T953 + 2.63942*tf.lnT9)

    rate_eval.n_C14__C15 = rate

@numba.njit()
def He4_Mg21__Si25(rate_eval, tf):
    # Mg21 + He4 --> Si25
    rate = 0.0

    # ths8r
    rate += np.exp(  35.0521 + -52.9572*tf.T913i + 0.491853*tf.T913
                  + -0.774204*tf.T9 + 0.0589171*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg21__Si25 = rate

@numba.njit()
def He4_Mn48__p_Fe51(rate_eval, tf):
    # Mn48 + He4 --> p + Fe51
    rate = 0.0

    # ths8r
    rate += np.exp(  62.2973 + -89.1398*tf.T913i + -1.32805*tf.T913
                  + -0.491734*tf.T9 + 0.00938461*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn48__p_Fe51 = rate

@numba.njit()
def He4_He4_He4__C12(rate_eval, tf):
    # 3 He4 --> C12
    rate = 0.0

    # fy05r
    rate += np.exp(  -11.7884 + -1.02446*tf.T9i + -23.57*tf.T913i + 20.4886*tf.T913
                  + -12.9882*tf.T9 + -20.0*tf.T953 + -2.16667*tf.lnT9)
    # fy05n
    rate += np.exp(  -0.971052 + -37.06*tf.T913i + 29.3493*tf.T913
                  + -115.507*tf.T9 + -10.0*tf.T953 + -1.33333*tf.lnT9)
    # fy05r
    rate += np.exp(  -24.3505 + -4.12656*tf.T9i + -13.49*tf.T913i + 21.4259*tf.T913
                  + -1.34769*tf.T9 + 0.0879816*tf.T953 + -13.1653*tf.lnT9)

    rate_eval.He4_He4_He4__C12 = rate

@numba.njit()
def He4_Cl43__K47(rate_eval, tf):
    # Cl43 + He4 --> K47
    rate = 0.0

    # rath 
    rate += np.exp(  -786.001 + 12.4889*tf.T9i + -1356.6*tf.T913i + 2231.31*tf.T913
                  + -134.366*tf.T9 + 7.78044*tf.T953 + -1043.95*tf.lnT9)

    rate_eval.He4_Cl43__K47 = rate

@numba.njit()
def He4_Mg19__Si23(rate_eval, tf):
    # Mg19 + He4 --> Si23
    rate = 0.0

    # ths8r
    rate += np.exp(  33.831 + -52.6672*tf.T913i + 0.676276*tf.T913
                  + -0.667318*tf.T9 + 0.045782*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg19__Si23 = rate

@numba.njit()
def p_Na38__Mg39(rate_eval, tf):
    # Na38 + p --> Mg39
    rate = 0.0

    # rath 
    rate += np.exp(  70.2562 + -3.18883*tf.T9i + 115.916*tf.T913i + -192.98*tf.T913
                  + 10.5121*tf.T9 + -0.578584*tf.T953 + 96.543*tf.lnT9)

    rate_eval.p_Na38__Mg39 = rate

@numba.njit()
def He4_Si31__S35(rate_eval, tf):
    # Si31 + He4 --> S35
    rate = 0.0

    # rath 
    rate += np.exp(  -73.2581 + -1.94072*tf.T9i + -98.5176*tf.T913i + 171.207*tf.T913
                  + -14.3839*tf.T9 + 0.960708*tf.T953 + -61.9936*tf.lnT9)

    rate_eval.He4_Si31__S35 = rate

@numba.njit()
def p_Sc36__Ti37(rate_eval, tf):
    # Sc36 + p --> Ti37
    rate = 0.0

    # ths8r
    rate += np.exp(  -19.8508 + -7.78696*tf.T9i + 19.4414*tf.T913
                  + -2.68762*tf.T9 + 0.237237*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Sc36__Ti37 = rate

@numba.njit()
def He4_Na37__Al41(rate_eval, tf):
    # Na37 + He4 --> Al41
    rate = 0.0

    # rath 
    rate += np.exp(  -18.4736 + -2.59184*tf.T9i + -17.1283*tf.T913i + 26.5556*tf.T913
                  + -5.0366*tf.T9 + 0.402782*tf.T953 + 2.77995*tf.lnT9)

    rate_eval.He4_Na37__Al41 = rate

@numba.njit()
def n_Na37__Na38(rate_eval, tf):
    # Na37 + n --> Na38
    rate = 0.0

    # rath 
    rate += np.exp(  -19.2663 + -32.373*tf.T9i + 585.822*tf.T913i + -569.205*tf.T913
                  + 23.5019*tf.T9 + -1.05607*tf.T953 + 344.552*tf.lnT9)

    rate_eval.n_Na37__Na38 = rate

@numba.njit()
def n_Mn51__Mn52(rate_eval, tf):
    # Mn51 + n --> Mn52
    rate = 0.0

    # ths8r
    rate += np.exp(  17.2055 + -1.83611*tf.T913
                  + 0.460384*tf.T9 + -0.0584947*tf.T953)

    rate_eval.n_Mn51__Mn52 = rate

@numba.njit()
def He4_S49__n_Ar52(rate_eval, tf):
    # S49 + He4 --> n + Ar52
    rate = 0.0

    # rath 
    rate += np.exp(  -367.41 + 1.90752*tf.T9i + -519.19*tf.T913i + 928.806*tf.T913
                  + -61.6364*tf.T9 + 3.76617*tf.T953 + -406.231*tf.lnT9)

    rate_eval.He4_S49__n_Ar52 = rate

@numba.njit()
def n_Na36__Na37(rate_eval, tf):
    # Na36 + n --> Na37
    rate = 0.0

    # rath 
    rate += np.exp(  9.45679 + -0.0718194*tf.T9i + 5.54615*tf.T913i + -11.7091*tf.T913
                  + 1.17143*tf.T9 + -0.0828531*tf.T953 + 4.40166*tf.lnT9)

    rate_eval.n_Na36__Na37 = rate

@numba.njit()
def p_Cl47__n_Ar47(rate_eval, tf):
    # Cl47 + p --> n + Ar47
    rate = 0.0

    # rath 
    rate += np.exp(  104.949 + -4.69387*tf.T9i + 172.601*tf.T913i + -281.391*tf.T913
                  + 15.415*tf.T9 + -0.861626*tf.T953 + 141.431*tf.lnT9)

    rate_eval.p_Cl47__n_Ar47 = rate

@numba.njit()
def Ca38__K38__weak__wc12(rate_eval, tf):
    # Ca38 --> K38
    rate = 0.0

    # wc12w
    rate += np.exp(  0.454468)

    rate_eval.Ca38__K38__weak__wc12 = rate

@numba.njit()
def He4_Na34__Al38(rate_eval, tf):
    # Na34 + He4 --> Al38
    rate = 0.0

    # rath 
    rate += np.exp(  -14.8477 + -2.45169*tf.T9i + -19.5924*tf.T913i + 25.8897*tf.T913
                  + -4.78096*tf.T9 + 0.380296*tf.T953 + 2.02258*tf.lnT9)

    rate_eval.He4_Na34__Al38 = rate

@numba.njit()
def n_Na34__Na35(rate_eval, tf):
    # Na34 + n --> Na35
    rate = 0.0

    # rath 
    rate += np.exp(  18.6548 + -0.0255448*tf.T9i + 4.11362*tf.T913i + -15.8736*tf.T913
                  + 1.19059*tf.T9 + -0.0703139*tf.T953 + 5.11007*tf.lnT9)

    rate_eval.n_Na34__Na35 = rate

@numba.njit()
def He4_Na33__Al37(rate_eval, tf):
    # Na33 + He4 --> Al37
    rate = 0.0

    # rath 
    rate += np.exp(  -15.6782 + -2.39871*tf.T9i + -21.2578*tf.T913i + 29.0671*tf.T913
                  + -5.0007*tf.T9 + 0.392819*tf.T953 + 0.704809*tf.lnT9)

    rate_eval.He4_Na33__Al37 = rate

@numba.njit()
def n_He3__He4(rate_eval, tf):
    # He3 + n --> He4
    rate = 0.0

    # ka02n
    rate += np.exp(  9.04572 + -1.50147*tf.T913
                  + 1.0*tf.lnT9)
    # ka02n
    rate += np.exp(  5.51711)

    rate_eval.n_He3__He4 = rate

@numba.njit()
def p_F21__n_Ne21(rate_eval, tf):
    # F21 + p --> n + Ne21
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.8402 + -2.05757*tf.T9i + 68.5042*tf.T913i + -120.301*tf.T913
                  + 6.5642*tf.T9 + -0.368059*tf.T953 + 60.3558*tf.lnT9)

    rate_eval.p_F21__n_Ne21 = rate

@numba.njit()
def He4_Na39__Al43(rate_eval, tf):
    # Na39 + He4 --> Al43
    rate = 0.0

    # rath 
    rate += np.exp(  -16.3934 + -2.70934*tf.T9i + -12.826*tf.T913i + 21.0375*tf.T913
                  + -4.85727*tf.T9 + 0.401366*tf.T953 + 5.75044*tf.lnT9)

    rate_eval.He4_Na39__Al43 = rate

@numba.njit()
def Mg32__n_Al31__weak__wc12(rate_eval, tf):
    # Mg32 --> n + Al31
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.813527)

    rate_eval.Mg32__n_Al31__weak__wc12 = rate

@numba.njit()
def p_Na32__Mg33(rate_eval, tf):
    # Na32 + p --> Mg33
    rate = 0.0

    # rath 
    rate += np.exp(  68.1904 + -2.94651*tf.T9i + 106.119*tf.T913i + -180.591*tf.T913
                  + 9.90422*tf.T9 + -0.54607*tf.T953 + 89.8762*tf.lnT9)

    rate_eval.p_Na32__Mg33 = rate

@numba.njit()
def He4_Al28__p_Si31(rate_eval, tf):
    # Al28 + He4 --> p + Si31
    rate = 0.0

    # rath 
    rate += np.exp(  -2.43395 + -2.38203*tf.T9i + -26.9479*tf.T913i + 24.6543*tf.T913
                  + -4.64894*tf.T9 + 0.36237*tf.T953 + 2.30351*tf.lnT9)

    rate_eval.He4_Al28__p_Si31 = rate

@numba.njit()
def He4_Ne29__n_Mg32(rate_eval, tf):
    # Ne29 + He4 --> n + Mg32
    rate = 0.0

    # rath 
    rate += np.exp(  70.7686 + -2.83828*tf.T9i + 60.3541*tf.T913i + -137.563*tf.T913
                  + 6.36561*tf.T9 + -0.319468*tf.T953 + 72.0218*tf.lnT9)

    rate_eval.He4_Ne29__n_Mg32 = rate

@numba.njit()
def He4_P25__Cl29(rate_eval, tf):
    # P25 + He4 --> Cl29
    rate = 0.0

    # ths8r
    rate += np.exp(  37.4807 + -61.9857*tf.T913i + 0.825832*tf.T913
                  + -0.695885*tf.T9 + 0.0383237*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P25__Cl29 = rate

@numba.njit()
def p_Na36__Mg37(rate_eval, tf):
    # Na36 + p --> Mg37
    rate = 0.0

    # rath 
    rate += np.exp(  69.1633 + -3.10759*tf.T9i + 112.428*tf.T913i + -188.419*tf.T913
                  + 10.3431*tf.T9 + -0.574214*tf.T953 + 94.1051*tf.lnT9)

    rate_eval.p_Na36__Mg37 = rate

@numba.njit()
def Cl50__Ar50__weak__mo03(rate_eval, tf):
    # Cl50 --> Ar50
    rate = 0.0

    # mo03w
    rate += np.exp(  -110.07)

    rate_eval.Cl50__Ar50__weak__mo03 = rate

@numba.njit()
def He4_Na28__Al32(rate_eval, tf):
    # Na28 + He4 --> Al32
    rate = 0.0

    # rath 
    rate += np.exp(  -12.5093 + -2.1579*tf.T9i + -24.6789*tf.T913i + 28.2904*tf.T913
                  + -4.66715*tf.T9 + 0.361197*tf.T953 + -0.205513*tf.lnT9)

    rate_eval.He4_Na28__Al32 = rate

@numba.njit()
def n_F15__F16(rate_eval, tf):
    # F15 + n --> F16
    rate = 0.0

    # rpsmr
    rate += np.exp(  8.54244 + 0.0214707*tf.T9i + -1.8316*tf.T913i + 2.8333*tf.T913
                  + -0.0925718*tf.T9 + 0.00805423*tf.T953 + -1.44099*tf.lnT9)

    rate_eval.n_F15__F16 = rate

@numba.njit()
def p_Na26__Mg27(rate_eval, tf):
    # Na26 + p --> Mg27
    rate = 0.0

    # rath 
    rate += np.exp(  57.2505 + -2.63351*tf.T9i + 90.399*tf.T913i + -151.46*tf.T913
                  + 8.01175*tf.T9 + -0.432414*tf.T953 + 77.2484*tf.lnT9)

    rate_eval.p_Na26__Mg27 = rate

@numba.njit()
def He4_Ti56__n_Cr59(rate_eval, tf):
    # Ti56 + He4 --> n + Cr59
    rate = 0.0

    # rath 
    rate += np.exp(  -1039.47 + 16.6032*tf.T9i + -1802.31*tf.T913i + 2968.47*tf.T913
                  + -177.586*tf.T9 + 10.204*tf.T953 + -1391.62*tf.lnT9)

    rate_eval.He4_Ti56__n_Cr59 = rate

@numba.njit()
def Si45__P45__weak__mo03(rate_eval, tf):
    # Si45 --> P45
    rate = 0.0

    # mo03w
    rate += np.exp(  -110.596)

    rate_eval.Si45__P45__weak__mo03 = rate

@numba.njit()
def p_Na25__Mg26(rate_eval, tf):
    # Na25 + p --> Mg26
    rate = 0.0

    # rath 
    rate += np.exp(  57.191 + -2.55927*tf.T9i + 86.33*tf.T913i + -147.225*tf.T913
                  + 8.01031*tf.T9 + -0.452387*tf.T953 + 74.4214*tf.lnT9)

    rate_eval.p_Na25__Mg26 = rate

@numba.njit()
def n_Na24__Na25(rate_eval, tf):
    # Na24 + n --> Na25
    rate = 0.0

    # rath 
    rate += np.exp(  7.19787 + 0.0157997*tf.T9i + -3.03801*tf.T913i + 8.89891*tf.T913
                  + -0.684955*tf.T9 + 0.0415126*tf.T953 + -3.59954*tf.lnT9)

    rate_eval.n_Na24__Na25 = rate

@numba.njit()
def Na36__Mg36__weak__mo03(rate_eval, tf):
    # Na36 --> Mg36
    rate = 0.0

    # mo03w
    rate += np.exp(  -109.214)

    rate_eval.Na36__Mg36__weak__mo03 = rate

@numba.njit()
def p_Ar52__K53(rate_eval, tf):
    # Ar52 + p --> K53
    rate = 0.0

    # rath 
    rate += np.exp(  109.577 + -5.16061*tf.T9i + 195.301*tf.T913i + -321.749*tf.T913
                  + 17.7802*tf.T9 + -0.991923*tf.T953 + 160.116*tf.lnT9)

    rate_eval.p_Ar52__K53 = rate

@numba.njit()
def Na28__Mg28__weak__wc12(rate_eval, tf):
    # Na28 --> Mg28
    rate = 0.0

    # wc12w
    rate += np.exp(  3.1177)

    rate_eval.Na28__Mg28__weak__wc12 = rate

@numba.njit()
def He4_F15__p_Ne18(rate_eval, tf):
    # F15 + He4 --> p + Ne18
    rate = 0.0

    # rpsmr
    rate += np.exp(  46.8138 + -1.58356*tf.T9i + 10.8535*tf.T913i + -60.1083*tf.T913
                  + 2.19998*tf.T9 + -0.0925197*tf.T953 + 33.282*tf.lnT9)

    rate_eval.He4_F15__p_Ne18 = rate

@numba.njit()
def He4_Na23__Al27(rate_eval, tf):
    # Na23 + He4 --> Al27
    rate = 0.0

    # ths8r
    rate += np.exp(  44.7724 + -50.2042*tf.T913i + -1.64239*tf.T913
                  + -1.59995*tf.T9 + 0.184933*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Na23__Al27 = rate

@numba.njit()
def p_Ca51__n_Sc51(rate_eval, tf):
    # Ca51 + p --> n + Sc51
    rate = 0.0

    # rath 
    rate += np.exp(  117.106 + -5.43097*tf.T9i + 200.983*tf.T913i + -326.087*tf.T913
                  + 17.9788*tf.T9 + -1.01095*tf.T953 + 163.877*tf.lnT9)

    rate_eval.p_Ca51__n_Sc51 = rate

@numba.njit()
def p_Sc63__He4_Ca60(rate_eval, tf):
    # Sc63 + p --> He4 + Ca60
    rate = 0.0

    # rath 
    rate += np.exp(  132.137 + -6.23613*tf.T9i + 239.981*tf.T913i + -400.083*tf.T913
                  + 23.4242*tf.T9 + -1.30639*tf.T953 + 195.889*tf.lnT9)

    rate_eval.p_Sc63__He4_Ca60 = rate

@numba.njit()
def p_Na23__Mg24(rate_eval, tf):
    # Na23 + p --> Mg24
    rate = 0.0

    # il10r
    rate += np.exp(  9.0594 + -3.28029*tf.T9i + -0.360588*tf.T913
                  + 1.4187*tf.T9 + -0.184061*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -5.02585 + -1.61219*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  18.9075 + -20.6428*tf.T913i + 1.52954*tf.T913
                  + 2.7487*tf.T9 + -1.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Na23__Mg24 = rate

@numba.njit()
def Sc62__n_Ti61__weak__mp17(rate_eval, tf):
    # Sc62 --> n + Ti61
    rate = 0.0

    # mp17w
    rate += np.exp(  3.311)

    rate_eval.Sc62__n_Ti61__weak__mp17 = rate

@numba.njit()
def p_Na22__Mg23(rate_eval, tf):
    # Na22 + p --> Mg23
    rate = 0.0

    # il10r
    rate += np.exp(  -11.2731 + -2.42669*tf.T9i + 4.86658*tf.T913i + 16.4592*tf.T913
                  + -1.95129*tf.T9 + 0.132972*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -16.2423 + -0.777841*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -25.2739 + -0.499888*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Na22__Mg23 = rate

@numba.njit()
def n_Na22__Na23(rate_eval, tf):
    # Na22 + n --> Na23
    rate = 0.0

    # ths8r
    rate += np.exp(  12.8678 + 1.02148*tf.T913
                  + -0.334638*tf.T9 + 0.0258708*tf.T953)

    rate_eval.n_Na22__Na23 = rate

@numba.njit()
def He4_V55__Mn59(rate_eval, tf):
    # V55 + He4 --> Mn59
    rate = 0.0

    # rath 
    rate += np.exp(  -1016.3 + 21.2678*tf.T9i + -2116.01*tf.T913i + 3252.34*tf.T913
                  + -184.152*tf.T9 + 10.1584*tf.T953 + -1579.15*tf.lnT9)

    rate_eval.He4_V55__Mn59 = rate

@numba.njit()
def He4_Ar50__Ca54(rate_eval, tf):
    # Ar50 + He4 --> Ca54
    rate = 0.0

    # rath 
    rate += np.exp(  -868.991 + 13.8186*tf.T9i + -1499.88*tf.T913i + 2465.65*tf.T913
                  + -147.725*tf.T9 + 8.48558*tf.T953 + -1155.64*tf.lnT9)

    rate_eval.He4_Ar50__Ca54 = rate

@numba.njit()
def p_Na21__Mg22(rate_eval, tf):
    # Na21 + p --> Mg22
    rate = 0.0

    # il10r
    rate += np.exp(  6.28009 + -7.47826*tf.T9i + 4.75873*tf.T913
                  + -0.708067*tf.T9 + 0.0523665*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  5.07923 + -2.38741*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  18.6558 + -20.7329*tf.T913i
                  + -1.5*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Na21__Mg22 = rate

@numba.njit()
def Ar53__n_n_K51__weak__mp17(rate_eval, tf):
    # Ar53 --> n + n + K51
    rate = 0.0

    # mp17w
    rate += np.exp(  2.12154)

    rate_eval.Ar53__n_n_K51__weak__mp17 = rate

@numba.njit()
def He4_Ti42__Cr46(rate_eval, tf):
    # Ti42 + He4 --> Cr46
    rate = 0.0

    # ths8r
    rate += np.exp(  54.5788 + -81.5598*tf.T913i + -7.76887*tf.T913
                  + 1.52445*tf.T9 + -0.287125*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti42__Cr46 = rate

@numba.njit()
def n_Na21__Na22(rate_eval, tf):
    # Na21 + n --> Na22
    rate = 0.0

    # ths8r
    rate += np.exp(  7.58321 + 1.31089*tf.T913
                  + -0.164931*tf.T9 + 0.00903374*tf.T953)

    rate_eval.n_Na21__Na22 = rate

@numba.njit()
def p_Ti65__n_V65(rate_eval, tf):
    # Ti65 + p --> n + V65
    rate = 0.0

    # rath 
    rate += np.exp(  138.718 + -6.48486*tf.T9i + 245.945*tf.T913i + -395.438*tf.T913
                  + 21.7277*tf.T9 + -1.21078*tf.T953 + 198.042*tf.lnT9)

    rate_eval.p_Ti65__n_V65 = rate

@numba.njit()
def He4_Na20__Al24(rate_eval, tf):
    # Na20 + He4 --> Al24
    rate = 0.0

    # ths8r
    rate += np.exp(  33.805 + -49.8396*tf.T913i + 0.898266*tf.T913
                  + -0.795853*tf.T9 + 0.0591478*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Na20__Al24 = rate

@numba.njit()
def p_S33__Cl34(rate_eval, tf):
    # S33 + p --> Cl34
    rate = 0.0

    # ths8r
    rate += np.exp(  36.4908 + -26.777*tf.T913i + -5.96882*tf.T913
                  + -1.0706*tf.T9 + 0.19692*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_S33__Cl34 = rate

@numba.njit()
def n_Na20__Na21(rate_eval, tf):
    # Na20 + n --> Na21
    rate = 0.0

    # ths8r
    rate += np.exp(  8.25037 + 2.95276*tf.T913
                  + -0.404532*tf.T9 + 0.028855*tf.T953)

    rate_eval.n_Na20__Na21 = rate

@numba.njit()
def Sc63__Ti63__weak__mo03(rate_eval, tf):
    # Sc63 --> Ti63
    rate = 0.0

    # mo03w
    rate += np.exp(  1.43833)

    rate_eval.Sc63__Ti63__weak__mo03 = rate

@numba.njit()
def n_Na19__Na20(rate_eval, tf):
    # Na19 + n --> Na20
    rate = 0.0

    # ths8r
    rate += np.exp(  7.85008 + 1.9478*tf.T913
                  + -0.159986*tf.T9 + 0.00901359*tf.T953)

    rate_eval.n_Na19__Na20 = rate

@numba.njit()
def p_Mg31__He4_Na28(rate_eval, tf):
    # Mg31 + p --> He4 + Na28
    rate = 0.0

    # rath 
    rate += np.exp(  62.1981 + -3.05673*tf.T9i + 108.004*tf.T913i + -173.87*tf.T913
                  + 8.87333*tf.T9 + -0.458406*tf.T953 + 90.4178*tf.lnT9)

    rate_eval.p_Mg31__He4_Na28 = rate

@numba.njit()
def Al42__Si42__weak__mo03(rate_eval, tf):
    # Al42 --> Si42
    rate = 0.0

    # mo03w
    rate += np.exp(  -108.924)

    rate_eval.Al42__Si42__weak__mo03 = rate

@numba.njit()
def He4_K58__n_Sc61(rate_eval, tf):
    # K58 + He4 --> n + Sc61
    rate = 0.0

    # rath 
    rate += np.exp(  -451.264 + 2.31406*tf.T9i + -627.834*tf.T913i + 1128.16*tf.T913
                  + -74.2839*tf.T9 + 4.51829*tf.T953 + -495.026*tf.lnT9)

    rate_eval.He4_K58__n_Sc61 = rate

@numba.njit()
def n_Mg40__Mg41(rate_eval, tf):
    # Mg40 + n --> Mg41
    rate = 0.0

    # rath 
    rate += np.exp(  -1283.65 + -71.956*tf.T9i + -3183.28*tf.T913i + 4704.67*tf.T913
                  + -229.47*tf.T9 + 11.1305*tf.T953 + -2427.1*tf.lnT9)

    rate_eval.n_Mg40__Mg41 = rate

@numba.njit()
def He4_Ne34__Mg38(rate_eval, tf):
    # Ne34 + He4 --> Mg38
    rate = 0.0

    # rath 
    rate += np.exp(  64.2125 + -3.15348*tf.T9i + 73.2439*tf.T913i + -155.072*tf.T913
                  + 7.17112*tf.T9 + -0.358143*tf.T953 + 81.1316*tf.lnT9)

    rate_eval.He4_Ne34__Mg38 = rate

@numba.njit()
def p_Sc54__Ti55(rate_eval, tf):
    # Sc54 + p --> Ti55
    rate = 0.0

    # rath 
    rate += np.exp(  121.76 + -5.78494*tf.T9i + 218.064*tf.T913i + -359.658*tf.T913
                  + 20.2482*tf.T9 + -1.16039*tf.T953 + 178.65*tf.lnT9)

    rate_eval.p_Sc54__Ti55 = rate

@numba.njit()
def n_Ne32__Ne33(rate_eval, tf):
    # Ne32 + n --> Ne33
    rate = 0.0

    # rath 
    rate += np.exp(  -660.761 + -38.1096*tf.T9i + -244.132*tf.T913i + 990.592*tf.T913
                  + -70.5651*tf.T9 + 4.35282*tf.T953 + -368.247*tf.lnT9)

    rate_eval.n_Ne32__Ne33 = rate

@numba.njit()
def p_Si29__P30(rate_eval, tf):
    # Si29 + p --> P30
    rate = 0.0

    # il10r
    rate += np.exp(  -1.24791 + -3.33929*tf.T9i + 14.0921*tf.T913
                  + -3.92096*tf.T9 + 0.447706*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -13.4701 + -1.25026*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  16.5182 + -23.9101*tf.T913i + 10.7796*tf.T913
                  + -3.04181*tf.T9 + 0.274565*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Si29__P30 = rate

@numba.njit()
def Cr68__n_Mn67__weak__mp17(rate_eval, tf):
    # Cr68 --> n + Mn67
    rate = 0.0

    # mp17w
    rate += np.exp(  1.35665)

    rate_eval.Cr68__n_Mn67__weak__mp17 = rate

@numba.njit()
def He4_Ne31__Mg35(rate_eval, tf):
    # Ne31 + He4 --> Mg35
    rate = 0.0

    # rath 
    rate += np.exp(  60.4854 + -2.96528*tf.T9i + 65.1074*tf.T913i + -142.518*tf.T913
                  + 6.45995*tf.T9 + -0.316442*tf.T953 + 75.0558*tf.lnT9)

    rate_eval.He4_Ne31__Mg35 = rate

@numba.njit()
def p_Ne31__Na32(rate_eval, tf):
    # Ne31 + p --> Na32
    rate = 0.0

    # rath 
    rate += np.exp(  59.4404 + -2.73012*tf.T9i + 97.4968*tf.T913i + -162.577*tf.T913
                  + 8.69904*tf.T9 + -0.470703*tf.T953 + 81.9845*tf.lnT9)

    rate_eval.p_Ne31__Na32 = rate

@numba.njit()
def He4_Ne30__Mg34(rate_eval, tf):
    # Ne30 + He4 --> Mg34
    rate = 0.0

    # rath 
    rate += np.exp(  61.0087 + -2.92215*tf.T9i + 64.5574*tf.T913i + -143.768*tf.T913
                  + 6.7451*tf.T9 + -0.344163*tf.T953 + 75.1201*tf.lnT9)

    rate_eval.He4_Ne30__Mg34 = rate

@numba.njit()
def He4_Ca58__Ti62(rate_eval, tf):
    # Ca58 + He4 --> Ti62
    rate = 0.0

    # rath 
    rate += np.exp(  -998.774 + 15.7528*tf.T9i + -1711.98*tf.T913i + 2821.55*tf.T913
                  + -168.653*tf.T9 + 9.6649*tf.T953 + -1322.76*tf.lnT9)

    rate_eval.He4_Ca58__Ti62 = rate

@numba.njit()
def Mg41__n_Al40__weak__mp17(rate_eval, tf):
    # Mg41 --> n + Al40
    rate = 0.0

    # mp17w
    rate += np.exp(  4.17412)

    rate_eval.Mg41__n_Al40__weak__mp17 = rate

@numba.njit()
def p_Ne30__Na31(rate_eval, tf):
    # Ne30 + p --> Na31
    rate = 0.0

    # rath 
    rate += np.exp(  56.133 + -2.65789*tf.T9i + 92.6958*tf.T913i + -153.858*tf.T913
                  + 8.21645*tf.T9 + -0.448107*tf.T953 + 77.9749*tf.lnT9)

    rate_eval.p_Ne30__Na31 = rate

@numba.njit()
def p_Mn71__n_Fe71(rate_eval, tf):
    # Mn71 + p --> n + Fe71
    rate = 0.0

    # rath 
    rate += np.exp(  154.889 + -7.34712*tf.T9i + 280.54*tf.T913i + -450.299*tf.T913
                  + 24.9278*tf.T9 + -1.3962*tf.T953 + 225.076*tf.lnT9)

    rate_eval.p_Mn71__n_Fe71 = rate

@numba.njit()
def Mn52__Cr52__weak__wc12(rate_eval, tf):
    # Mn52 --> Cr52
    rate = 0.0

    # wc12w
    rate += np.exp(  -13.4543)

    rate_eval.Mn52__Cr52__weak__wc12 = rate

@numba.njit()
def Ti58__V58__weak__wc12(rate_eval, tf):
    # Ti58 --> V58
    rate = 0.0

    # wc12w
    rate += np.exp(  2.49819)

    rate_eval.Ti58__V58__weak__wc12 = rate

@numba.njit()
def Ne17__p_O16__weak__wc12(rate_eval, tf):
    # Ne17 --> p + O16
    rate = 0.0

    # wc12w
    rate += np.exp(  1.84989)

    rate_eval.Ne17__p_O16__weak__wc12 = rate

@numba.njit()
def p_Cl44__Ar45(rate_eval, tf):
    # Cl44 + p --> Ar45
    rate = 0.0

    # rath 
    rate += np.exp(  94.4939 + -4.56138*tf.T9i + 167.388*tf.T913i + -274.898*tf.T913
                  + 15.1256*tf.T9 + -0.848796*tf.T953 + 137.914*tf.lnT9)

    rate_eval.p_Cl44__Ar45 = rate

@numba.njit()
def p_Ne28__Na29(rate_eval, tf):
    # Ne28 + p --> Na29
    rate = 0.0

    # rath 
    rate += np.exp(  58.9021 + -2.58578*tf.T9i + 91.113*tf.T913i + -154.914*tf.T913
                  + 8.41738*tf.T9 + -0.464993*tf.T953 + 77.6862*tf.lnT9)

    rate_eval.p_Ne28__Na29 = rate

@numba.njit()
def p_Na35__He4_Ne32(rate_eval, tf):
    # Na35 + p --> He4 + Ne32
    rate = 0.0

    # rath 
    rate += np.exp(  69.1622 + -3.06387*tf.T9i + 110.355*tf.T913i + -184.751*tf.T913
                  + 10.0811*tf.T9 + -0.551116*tf.T953 + 92.4888*tf.lnT9)

    rate_eval.p_Na35__He4_Ne32 = rate

@numba.njit()
def n_Fe74__Fe75(rate_eval, tf):
    # Fe74 + n --> Fe75
    rate = 0.0

    # rath 
    rate += np.exp(  -8.1469 + 0.101668*tf.T9i + -11.7775*tf.T913i + 27.5566*tf.T913
                  + -0.542782*tf.T9 + -0.113755*tf.T953 + -11.7043*tf.lnT9)

    rate_eval.n_Fe74__Fe75 = rate

@numba.njit()
def p_Ne27__Na28(rate_eval, tf):
    # Ne27 + p --> Na28
    rate = 0.0

    # rath 
    rate += np.exp(  53.7777 + -2.51504*tf.T9i + 86.4601*tf.T913i + -145.066*tf.T913
                  + 7.76109*tf.T9 + -0.425661*tf.T953 + 73.6058*tf.lnT9)

    rate_eval.p_Ne27__Na28 = rate

@numba.njit()
def He4_Ne26__Mg30(rate_eval, tf):
    # Ne26 + He4 --> Mg30
    rate = 0.0

    # rath 
    rate += np.exp(  54.5552 + -2.634*tf.T9i + 51.4663*tf.T913i + -122.853*tf.T913
                  + 5.51313*tf.T9 + -0.275266*tf.T953 + 65.1458*tf.lnT9)

    rate_eval.He4_Ne26__Mg30 = rate

@numba.njit()
def Ti41__p_Ca40__weak__wc12(rate_eval, tf):
    # Ti41 --> p + Ca40
    rate = 0.0

    # wc12w
    rate += np.exp(  2.15423)

    rate_eval.Ti41__p_Ca40__weak__wc12 = rate

@numba.njit()
def n_Ne26__Ne27(rate_eval, tf):
    # Ne26 + n --> Ne27
    rate = 0.0

    # wiesr
    rate += np.exp(  6.36475 + -4.42336e-13*tf.T9i + 5.57757e-11*tf.T913i + -1.74727e-10*tf.T913
                  + 1.67647e-11*tf.T9 + -1.36248e-12*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_Ne26__Ne27 = rate

@numba.njit()
def S28__p_Si27__weak__wc12(rate_eval, tf):
    # S28 --> p + Si27
    rate = 0.0

    # wc12w
    rate += np.exp(  0.137892)

    rate_eval.S28__p_Si27__weak__wc12 = rate

@numba.njit()
def He4_Cl52__n_K55(rate_eval, tf):
    # Cl52 + He4 --> n + K55
    rate = 0.0

    # rath 
    rate += np.exp(  -393.835 + 2.00998*tf.T9i + -552.688*tf.T913i + 991.131*tf.T913
                  + -65.693*tf.T9 + 4.0119*tf.T953 + -433.719*tf.lnT9)

    rate_eval.He4_Cl52__n_K55 = rate

@numba.njit()
def p_Ne25__Na26(rate_eval, tf):
    # Ne25 + p --> Na26
    rate = 0.0

    # rath 
    rate += np.exp(  52.8288 + -2.40558*tf.T9i + 81.3234*tf.T913i + -138.185*tf.T913
                  + 7.46267*tf.T9 + -0.414385*tf.T953 + 69.9862*tf.lnT9)

    rate_eval.p_Ne25__Na26 = rate

@numba.njit()
def n_Mg19__Mg20(rate_eval, tf):
    # Mg19 + n --> Mg20
    rate = 0.0

    # ths8r
    rate += np.exp(  8.28643 + 1.39502*tf.T913
                  + -0.0418443*tf.T9 + -0.00337632*tf.T953)

    rate_eval.n_Mg19__Mg20 = rate

@numba.njit()
def n_Ne24__Ne25(rate_eval, tf):
    # Ne24 + n --> Ne25
    rate = 0.0

    # wiesr
    rate += np.exp(  8.50309 + -1.66068e-12*tf.T9i + 2.18942e-10*tf.T913i + -7.26379e-10*tf.T913
                  + 7.31316e-11*tf.T9 + -6.13925e-12*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_Ne24__Ne25 = rate

@numba.njit()
def p_Ne23__Na24(rate_eval, tf):
    # Ne23 + p --> Na24
    rate = 0.0

    # rath 
    rate += np.exp(  43.5658 + -2.22177*tf.T9i + 68.3965*tf.T913i + -113.974*tf.T913
                  + 6.08328*tf.T9 + -0.34487*tf.T953 + 58.9352*tf.lnT9)

    rate_eval.p_Ne23__Na24 = rate

@numba.njit()
def Sc42__Ca42__weak__wc12(rate_eval, tf):
    # Sc42 --> Ca42
    rate = 0.0

    # wc12w
    rate += np.exp(  0.0176801)

    rate_eval.Sc42__Ca42__weak__wc12 = rate

@numba.njit()
def p_Al43__Si44(rate_eval, tf):
    # Al43 + p --> Si44
    rate = 0.0

    # rath 
    rate += np.exp(  77.6465 + -3.76858*tf.T9i + 137.672*tf.T913i + -225.25*tf.T913
                  + 12.2352*tf.T9 + -0.679383*tf.T953 + 113.358*tf.lnT9)

    rate_eval.p_Al43__Si44 = rate

@numba.njit()
def p_Ne33__Na34(rate_eval, tf):
    # Ne33 + p --> Na34
    rate = 0.0

    # rath 
    rate += np.exp(  61.6835 + -2.78977*tf.T9i + 99.5038*tf.T913i + -167.039*tf.T913
                  + 9.05642*tf.T9 + -0.495337*tf.T953 + 83.6929*tf.lnT9)

    rate_eval.p_Ne33__Na34 = rate

@numba.njit()
def p_F27__Ne28(rate_eval, tf):
    # F27 + p --> Ne28
    rate = 0.0

    # rpsmr
    rate += np.exp(  55.6601 + -2.35656*tf.T9i + 82.556*tf.T913i + -142.599*tf.T913
                  + 7.83119*tf.T9 + -0.434709*tf.T953 + 70.9847*tf.lnT9)

    rate_eval.p_F27__Ne28 = rate

@numba.njit()
def p_Ne20__Na21(rate_eval, tf):
    # Ne20 + p --> Na21
    rate = 0.0

    # ly18 
    rate += np.exp(  195297.0 + -61.14*tf.T9i + 21894.7*tf.T913i + -319153.0*tf.T913
                  + 224369.0*tf.T9 + -188049.0*tf.T953 + 48703.4*tf.lnT9)
    # ly18 
    rate += np.exp(  207.877 + -0.152711*tf.T9i + 15.325*tf.T913i + -294.859*tf.T913
                  + 107.692*tf.T9 + -46.2072*tf.T953 + 57.8398*tf.lnT9)
    # ly18 
    rate += np.exp(  5.83103 + -8.838*tf.T9i + 20.5893*tf.T913i + -17.5841*tf.T913
                  + 0.243226*tf.T9 + -0.000231418*tf.T953 + 12.8398*tf.lnT9)
    # ly18 
    rate += np.exp(  230.019 + -4.45358*tf.T9i + 258.57*tf.T913i + -506.387*tf.T913
                  + 22.1576*tf.T9 + -0.721182*tf.T953 + 230.288*tf.lnT9)

    rate_eval.p_Ne20__Na21 = rate

@numba.njit()
def p_K53__Ca54(rate_eval, tf):
    # K53 + p --> Ca54
    rate = 0.0

    # rath 
    rate += np.exp(  117.594 + -5.42527*tf.T9i + 207.416*tf.T913i + -343.075*tf.T913
                  + 19.0432*tf.T9 + -1.06432*tf.T953 + 170.202*tf.lnT9)

    rate_eval.p_K53__Ca54 = rate

@numba.njit()
def p_Cr70__n_Mn70(rate_eval, tf):
    # Cr70 + p --> n + Mn70
    rate = 0.0

    # rath 
    rate += np.exp(  150.045 + -7.09953*tf.T9i + 270.472*tf.T913i + -434.255*tf.T913
                  + 24.0578*tf.T9 + -1.34892*tf.T953 + 217.081*tf.lnT9)

    rate_eval.p_Cr70__n_Mn70 = rate

@numba.njit()
def p_Ne19__Na20(rate_eval, tf):
    # Ne19 + p --> Na20
    rate = 0.0

    # il10r
    rate += np.exp(  5.63289 + -5.07623*tf.T9i + 1.23704*tf.T913
                  + 0.337618*tf.T9 + -0.0562825*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  17.822 + -19.5908*tf.T913i + -2.37696*tf.T913
                  + 3.26815*tf.T9 + -1.06524*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ne19__Na20 = rate

@numba.njit()
def p_F24__He4_O21(rate_eval, tf):
    # F24 + p --> He4 + O21
    rate = 0.0

    # rpsmr
    rate += np.exp(  59.1645 + -2.21452*tf.T9i + 76.1002*tf.T913i + -133.238*tf.T913
                  + 7.38318*tf.T9 + -0.410733*tf.T953 + 66.2799*tf.lnT9)

    rate_eval.p_F24__He4_O21 = rate

@numba.njit()
def F24__Ne24__weak__wc12(rate_eval, tf):
    # F24 --> Ne24
    rate = 0.0

    # wc12w
    rate += np.exp(  0.514283)

    rate_eval.F24__Ne24__weak__wc12 = rate

@numba.njit()
def p_Mn52__Fe53(rate_eval, tf):
    # Mn52 + p --> Fe53
    rate = 0.0

    # ths8r
    rate += np.exp(  35.4319 + -36.187*tf.T913i + 1.79171*tf.T913
                  + -1.77786*tf.T9 + 0.179936*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn52__Fe53 = rate

@numba.njit()
def n_Ne19__Ne20(rate_eval, tf):
    # Ne19 + n --> Ne20
    rate = 0.0

    # ths8r
    rate += np.exp(  6.40633 + 1.57592*tf.T913
                  + -0.11175*tf.T9 + 0.00226473*tf.T953)

    rate_eval.n_Ne19__Ne20 = rate

@numba.njit()
def p_Ne18__Na19(rate_eval, tf):
    # Ne18 + p --> Na19
    rate = 0.0

    # rath 
    rate += np.exp(  63.5156 + -7.09035*tf.T9i + 162.52*tf.T913i + -241.186*tf.T913
                  + 13.3329*tf.T9 + -0.751035*tf.T953 + 123.881*tf.lnT9)

    rate_eval.p_Ne18__Na19 = rate

@numba.njit()
def Ne32__n_Na31__weak__mp17(rate_eval, tf):
    # Ne32 --> n + Na31
    rate = 0.0

    # mp17w
    rate += np.exp(  4.67229)

    rate_eval.Ne32__n_Na31__weak__mp17 = rate

@numba.njit()
def p_Cr64__Mn65(rate_eval, tf):
    # Cr64 + p --> Mn65
    rate = 0.0

    # rath 
    rate += np.exp(  140.702 + -6.85963*tf.T9i + 262.391*tf.T913i + -426.54*tf.T913
                  + 24.0867*tf.T9 + -1.41036*tf.T953 + 212.283*tf.lnT9)

    rate_eval.p_Cr64__Mn65 = rate

@numba.njit()
def Sc61__n_Ti60__weak__mp17(rate_eval, tf):
    # Sc61 --> n + Ti60
    rate = 0.0

    # mp17w
    rate += np.exp(  4.05264)

    rate_eval.Sc61__n_Ti60__weak__mp17 = rate

@numba.njit()
def n_S46__S47(rate_eval, tf):
    # S46 + n --> S47
    rate = 0.0

    # rath 
    rate += np.exp(  11.1983 + -0.0649442*tf.T9i + 5.31831*tf.T913i + -14.892*tf.T913
                  + 2.43192*tf.T9 + -0.242185*tf.T953 + 4.71935*tf.lnT9)

    rate_eval.n_S46__S47 = rate

@numba.njit()
def Ca39__K39__weak__wc12(rate_eval, tf):
    # Ca39 --> K39
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.21569)

    rate_eval.Ca39__K39__weak__wc12 = rate

@numba.njit()
def n_Ne18__Ne19(rate_eval, tf):
    # Ne18 + n --> Ne19
    rate = 0.0

    # ths8r
    rate += np.exp(  9.249 + 0.937162*tf.T913
                  + -0.0221952*tf.T9 + -0.00101206*tf.T953)

    rate_eval.n_Ne18__Ne19 = rate

@numba.njit()
def p_Cl48__Ar49(rate_eval, tf):
    # Cl48 + p --> Ar49
    rate = 0.0

    # rath 
    rate += np.exp(  109.554 + -4.81569*tf.T9i + 183.575*tf.T913i + -308.79*tf.T913
                  + 17.3629*tf.T9 + -0.976735*tf.T953 + 152.178*tf.lnT9)

    rate_eval.p_Cl48__Ar49 = rate

@numba.njit()
def n_Ne17__Ne18(rate_eval, tf):
    # Ne17 + n --> Ne18
    rate = 0.0

    # ths8r
    rate += np.exp(  10.2447 + -0.126871*tf.T913
                  + 0.0997419*tf.T9 + -0.00483163*tf.T953)

    rate_eval.n_Ne17__Ne18 = rate

@numba.njit()
def He4_Cr65__Fe69(rate_eval, tf):
    # Cr65 + He4 --> Fe69
    rate = 0.0

    # rath 
    rate += np.exp(  -1140.14 + 23.66*tf.T9i + -2350.7*tf.T913i + 3625.11*tf.T913
                  + -205.176*tf.T9 + 11.3111*tf.T953 + -1759.28*tf.lnT9)

    rate_eval.He4_Cr65__Fe69 = rate

@numba.njit()
def F25__Ne25__weak__wc12(rate_eval, tf):
    # F25 --> Ne25
    rate = 0.0

    # wc12w
    rate += np.exp(  1.89655)

    rate_eval.F25__Ne25__weak__wc12 = rate

@numba.njit()
def He4_Ne16__Mg20(rate_eval, tf):
    # Ne16 + He4 --> Mg20
    rate = 0.0

    # ths8r
    rate += np.exp(  30.6507 + -46.1429*tf.T913i + 0.891484*tf.T913
                  + -0.690732*tf.T9 + 0.0468149*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ne16__Mg20 = rate

@numba.njit()
def He4_Na30__Al34(rate_eval, tf):
    # Na30 + He4 --> Al34
    rate = 0.0

    # rath 
    rate += np.exp(  -14.8779 + -2.2635*tf.T9i + -22.8181*tf.T913i + 28.3219*tf.T913
                  + -4.72984*tf.T9 + 0.367567*tf.T953 + 0.445877*tf.lnT9)

    rate_eval.He4_Na30__Al34 = rate

@numba.njit()
def He4_O28__Ne32(rate_eval, tf):
    # O28 + He4 --> Ne32
    rate = 0.0

    # rpsmr
    rate += np.exp(  42.6153 + -2.22943*tf.T9i + 35.4288*tf.T913i + -89.6224*tf.T913
                  + 4.05831*tf.T9 + -0.242523*tf.T953 + 48.3979*tf.lnT9)

    rate_eval.He4_O28__Ne32 = rate

@numba.njit()
def n_Ne16__Ne17(rate_eval, tf):
    # Ne16 + n --> Ne17
    rate = 0.0

    # ths8r
    rate += np.exp(  9.30084 + 0.172144*tf.T913
                  + 0.053108*tf.T9 + -0.00328348*tf.T953)

    rate_eval.n_Ne16__Ne17 = rate

@numba.njit()
def He4_F31__Na35(rate_eval, tf):
    # F31 + He4 --> Na35
    rate = 0.0

    # rpsmr
    rate += np.exp(  56.4044 + -2.75746*tf.T9i + 60.1387*tf.T913i + -131.905*tf.T913
                  + 5.88749*tf.T9 + -0.279913*tf.T953 + 69.4955*tf.lnT9)

    rate_eval.He4_F31__Na35 = rate

@numba.njit()
def n_O13__O14(rate_eval, tf):
    # O13 + n --> O14
    rate = 0.0

    # rpsmr
    rate += np.exp(  11.4461 + 0.0124752*tf.T9i + -0.898885*tf.T913i + 0.322012*tf.T913
                  + 0.0603352*tf.T9 + -0.000451895*tf.T953 + -0.519828*tf.lnT9)

    rate_eval.n_O13__O14 = rate

@numba.njit()
def p_F28__Ne29(rate_eval, tf):
    # F28 + p --> Ne29
    rate = 0.0

    # rpsmr
    rate += np.exp(  52.6227 + -2.41975*tf.T9i + 84.9815*tf.T913i + -141.324*tf.T913
                  + 7.47373*tf.T9 + -0.404652*tf.T953 + 71.7438*tf.lnT9)

    rate_eval.p_F28__Ne29 = rate

@numba.njit()
def p_F19__He4_O16(rate_eval, tf):
    # F19 + p --> He4 + O16
    rate = 0.0

    # nacr 
    rate += np.exp(  -52.7043 + -0.12765*tf.T9i
                  + -1.5*tf.lnT9)
    # nacr 
    rate += np.exp(  26.2916 + -18.116*tf.T913i
                  + 1.86674*tf.T9 + -7.5666*tf.T953 + -0.666667*tf.lnT9)
    # nacrr
    rate += np.exp(  14.3586 + -3.286*tf.T9i
                  + -0.21103*tf.T9 + 2.87702*tf.lnT9)
    # nacr 
    rate += np.exp(  15.1955 + -3.75185*tf.T9i
                  + -1.5*tf.lnT9)
    # nacr 
    rate += np.exp(  8.239 + -2.46828*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_F19__He4_O16 = rate

@numba.njit()
def p_Mg38__Al39(rate_eval, tf):
    # Mg38 + p --> Al39
    rate = 0.0

    # rath 
    rate += np.exp(  71.1947 + -3.36521*tf.T9i + 121.285*tf.T913i + -200.672*tf.T913
                  + 10.9066*tf.T9 + -0.602417*tf.T953 + 100.813*tf.lnT9)

    rate_eval.p_Mg38__Al39 = rate

@numba.njit()
def He4_Mg29__n_Si32(rate_eval, tf):
    # Mg29 + He4 --> n + Si32
    rate = 0.0

    # rath 
    rate += np.exp(  78.4289 + -3.23217*tf.T9i + 70.6419*tf.T913i + -160.363*tf.T913
                  + 7.68097*tf.T9 + -0.401497*tf.T953 + 83.5589*tf.lnT9)

    rate_eval.He4_Mg29__n_Si32 = rate

@numba.njit()
def He4_Ar41__Ca45(rate_eval, tf):
    # Ar41 + He4 --> Ca45
    rate = 0.0

    # rath 
    rate += np.exp(  -781.106 + 12.5449*tf.T9i + -1364.94*tf.T913i + 2234.39*tf.T913
                  + -133.787*tf.T9 + 7.67449*tf.T953 + -1047.29*tf.lnT9)

    rate_eval.He4_Ar41__Ca45 = rate

@numba.njit()
def n_V41__p_Ti41(rate_eval, tf):
    # V41 + n --> p + Ti41
    rate = 0.0

    # ths8r
    rate += np.exp(  20.9142 + -0.4032*tf.T913
                  + 0.158495*tf.T9 + -0.0130779*tf.T953)

    rate_eval.n_V41__p_Ti41 = rate

@numba.njit()
def n_P39__P40(rate_eval, tf):
    # P39 + n --> P40
    rate = 0.0

    # rath 
    rate += np.exp(  7.13676 + -0.00444454*tf.T9i + -0.772213*tf.T913i + 4.7424*tf.T913
                  + -0.425866*tf.T9 + 0.0160923*tf.T953 + -1.50349*tf.lnT9)

    rate_eval.n_P39__P40 = rate

@numba.njit()
def n_Si34__Si35(rate_eval, tf):
    # Si34 + n --> Si35
    rate = 0.0

    # rath 
    rate += np.exp(  18.8713 + -0.104803*tf.T9i + 10.0174*tf.T913i + -21.8284*tf.T913
                  + 1.74873*tf.T9 + -0.114634*tf.T953 + 9.01771*tf.lnT9)

    rate_eval.n_Si34__Si35 = rate

@numba.njit()
def He4_F24__Na28(rate_eval, tf):
    # F24 + He4 --> Na28
    rate = 0.0

    # rpsmr
    rate += np.exp(  47.7442 + -2.29858*tf.T9i + 40.4166*tf.T913i + -102.626*tf.T913
                  + 4.36702*tf.T9 + -0.202307*tf.T953 + 54.9379*tf.lnT9)

    rate_eval.He4_F24__Na28 = rate

@numba.njit()
def He4_Al31__P35(rate_eval, tf):
    # Al31 + He4 --> P35
    rate = 0.0

    # rath 
    rate += np.exp(  -17.0716 + -2.56832*tf.T9i + -25.9161*tf.T913i + 32.2972*tf.T913
                  + -5.22279*tf.T9 + 0.396137*tf.T953 + 0.060593*tf.lnT9)

    rate_eval.He4_Al31__P35 = rate

@numba.njit()
def n_F23__F24(rate_eval, tf):
    # F23 + n --> F24
    rate = 0.0

    # wiesr
    rate += np.exp(  8.16622 + -9.70523e-13*tf.T9i + 1.25912e-10*tf.T913i + -4.09236e-10*tf.T913
                  + 4.04765e-11*tf.T9 + -3.35602e-12*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_F23__F24 = rate

@numba.njit()
def He4_Mn51__Co55(rate_eval, tf):
    # Mn51 + He4 --> Co55
    rate = 0.0

    # ths8r
    rate += np.exp(  65.9219 + -89.274*tf.T913i + -10.4373*tf.T913
                  + 1.00492*tf.T9 + -0.125548*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn51__Co55 = rate

@numba.njit()
def p_F22__Ne23(rate_eval, tf):
    # F22 + p --> Ne23
    rate = 0.0

    # rpsmr
    rate += np.exp(  48.3287 + -2.10387*tf.T9i + 70.1221*tf.T913i + -121.103*tf.T913
                  + 6.54255*tf.T9 + -0.355294*tf.T953 + 61.2341*tf.lnT9)

    rate_eval.p_F22__Ne23 = rate

@numba.njit()
def n_F22__F23(rate_eval, tf):
    # F22 + n --> F23
    rate = 0.0

    # wiesr
    rate += np.exp(  5.27811
                  + 1.0*tf.lnT9)

    rate_eval.n_F22__F23 = rate

@numba.njit()
def p_F21__Ne22(rate_eval, tf):
    # F21 + p --> Ne22
    rate = 0.0

    # rpsmr
    rate += np.exp(  49.6296 + -2.05922*tf.T9i + 68.6237*tf.T913i + -120.332*tf.T913
                  + 6.5752*tf.T9 + -0.368955*tf.T953 + 60.4231*tf.lnT9)

    rate_eval.p_F21__Ne22 = rate

@numba.njit()
def n_Cr54__Cr55(rate_eval, tf):
    # Cr54 + n --> Cr55
    rate = 0.0

    # ks03 
    rate += np.exp(  5.37244 + 0.0398429*tf.T9i + -4.85575*tf.T913i + 14.5994*tf.T913
                  + -1.39135*tf.T9 + 0.0963933*tf.T953 + -5.17163*tf.lnT9)

    rate_eval.n_Cr54__Cr55 = rate

@numba.njit()
def p_Fe51__Co52(rate_eval, tf):
    # Fe51 + p --> Co52
    rate = 0.0

    # nfisn
    rate += np.exp(  24.7165 + 0.393894*tf.T9i + -22.4773*tf.T913i + 56.2612*tf.T913
                  + -117.254*tf.T9 + 21.0689*tf.T953 + 15.6248*tf.lnT9)
    # nfisn
    rate += np.exp(  38.4292 + -0.24474*tf.T9i + -23.922*tf.T913i + -27.2343*tf.T913
                  + 1.98546*tf.T9 + -0.14183*tf.T953 + 10.9094*tf.lnT9)
    # nfisn
    rate += np.exp(  59.6498 + -1.08255*tf.T9i + -77.2631*tf.T913i + 16.7898*tf.T913
                  + 0.998444*tf.T9 + -0.100098*tf.T953 + -24.6804*tf.lnT9)
    # nfisn
    rate += np.exp(  17.7892 + -3.43838*tf.T9i + -23.4454*tf.T913i + 0.21076*tf.T913
                  + 1.02763*tf.T9 + -0.103588*tf.T953 + -8.53789*tf.lnT9)

    rate_eval.p_Fe51__Co52 = rate

@numba.njit()
def n_F21__F22(rate_eval, tf):
    # F21 + n --> F22
    rate = 0.0

    # wiesr
    rate += np.exp(  4.95583 + -1.19407e-13*tf.T9i + 1.5462e-11*tf.T913i + -5.04619e-11*tf.T913
                  + 5.05685e-12*tf.T9 + -4.25539e-13*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_F21__F22 = rate

@numba.njit()
def Na30__n_Mg29__weak__wc17(rate_eval, tf):
    # Na30 --> n + Mg29
    rate = 0.0

    # wc17w
    rate += np.exp(  1.46607)

    rate_eval.Na30__n_Mg29__weak__wc17 = rate

@numba.njit()
def n_Al23__Al24(rate_eval, tf):
    # Al23 + n --> Al24
    rate = 0.0

    # ths8r
    rate += np.exp(  8.06744 + 2.57879*tf.T913
                  + -0.381593*tf.T9 + 0.0300709*tf.T953)

    rate_eval.n_Al23__Al24 = rate

@numba.njit()
def n_F20__F21(rate_eval, tf):
    # F20 + n --> F21
    rate = 0.0

    # fkthr
    rate += np.exp(  4.77528 + 0.021153*tf.T9i + -3.71688*tf.T913i + 12.6698*tf.T913
                  + -1.47692*tf.T9 + 0.119962*tf.T953 + -4.49967*tf.lnT9)

    rate_eval.n_F20__F21 = rate

@numba.njit()
def N22__O22__weak__wc12(rate_eval, tf):
    # N22 --> O22
    rate = 0.0

    # wc12w
    rate += np.exp(  2.94767)

    rate_eval.N22__O22__weak__wc12 = rate

@numba.njit()
def He4_F18__Na22(rate_eval, tf):
    # F18 + He4 --> Na22
    rate = 0.0

    # rpsmr
    rate += np.exp(  35.3786 + -1.82957*tf.T9i + 18.8956*tf.T913i + -65.6134*tf.T913
                  + 1.71114*tf.T9 + -0.0260999*tf.T953 + 37.8396*tf.lnT9)

    rate_eval.He4_F18__Na22 = rate

@numba.njit()
def n_F18__F19(rate_eval, tf):
    # F18 + n --> F19
    rate = 0.0

    # rpsmr
    rate += np.exp(  0.814964 + 0.0604483*tf.T9i + -6.65988*tf.T913i + 18.3243*tf.T913
                  + -1.47263*tf.T9 + 0.0955082*tf.T953 + -6.75505*tf.lnT9)

    rate_eval.n_F18__F19 = rate

@numba.njit()
def n_F17__F18(rate_eval, tf):
    # F17 + n --> F18
    rate = 0.0

    # rpsmr
    rate += np.exp(  3.42798 + 0.0273799*tf.T9i + -2.71353*tf.T913i + 6.19871*tf.T913
                  + -0.26836*tf.T9 + 0.0115489*tf.T953 + -2.52002*tf.lnT9)

    rate_eval.n_F17__F18 = rate

@numba.njit()
def He4_K59__Sc63(rate_eval, tf):
    # K59 + He4 --> Sc63
    rate = 0.0

    # rath 
    rate += np.exp(  -974.432 + 15.4641*tf.T9i + -1676.49*tf.T913i + 2760.47*tf.T913
                  + -164.855*tf.T9 + 9.45317*tf.T953 + -1295.25*tf.lnT9)

    rate_eval.He4_K59__Sc63 = rate

@numba.njit()
def n_F16__F17(rate_eval, tf):
    # F16 + n --> F17
    rate = 0.0

    # rpsmr
    rate += np.exp(  9.36454 + 0.00885357*tf.T9i + -0.79526*tf.T913i + 1.84363*tf.T913
                  + -0.123684*tf.T9 + 0.0149635*tf.T953 + -0.704695*tf.lnT9)

    rate_eval.n_F16__F17 = rate

@numba.njit()
def n_F14__F15(rate_eval, tf):
    # F14 + n --> F15
    rate = 0.0

    # rpsmr
    rate += np.exp(  5.04324 + 0.0206573*tf.T9i + -2.19515*tf.T913i + 8.79719*tf.T913
                  + -0.630523*tf.T9 + 0.0348628*tf.T953 + -2.48832*tf.lnT9)

    rate_eval.n_F14__F15 = rate

@numba.njit()
def p_O27__F28(rate_eval, tf):
    # O27 + p --> F28
    rate = 0.0

    # rpsmr
    rate += np.exp(  49.4133 + -2.15265*tf.T9i + 73.7526*tf.T913i + -126.23*tf.T913
                  + 6.85077*tf.T9 + -0.377893*tf.T953 + 63.2206*tf.lnT9)

    rate_eval.p_O27__F28 = rate

@numba.njit()
def He4_Ar42__Ca46(rate_eval, tf):
    # Ar42 + He4 --> Ca46
    rate = 0.0

    # rath 
    rate += np.exp(  -808.273 + 12.7365*tf.T9i + -1390.87*tf.T913i + 2290.85*tf.T913
                  + -137.476*tf.T9 + 7.89918*tf.T953 + -1071.92*tf.lnT9)

    rate_eval.He4_Ar42__Ca46 = rate

@numba.njit()
def p_O26__F27(rate_eval, tf):
    # O26 + p --> F27
    rate = 0.0

    # rpsmr
    rate += np.exp(  56.9415 + -2.15274*tf.T9i + 77.2069*tf.T913i + -137.543*tf.T913
                  + 8.10506*tf.T9 + -0.507871*tf.T953 + 67.4271*tf.lnT9)

    rate_eval.p_O26__F27 = rate

@numba.njit()
def p_Cl43__n_Ar43(rate_eval, tf):
    # Cl43 + p --> n + Ar43
    rate = 0.0

    # rath 
    rate += np.exp(  102.346 + -4.50746*tf.T9i + 164.815*tf.T913i + -271.069*tf.T913
                  + 14.9037*tf.T9 + -0.833869*tf.T953 + 136.022*tf.lnT9)

    rate_eval.p_Cl43__n_Ar43 = rate

@numba.njit()
def Cr67__n_Mn66__weak__mp17(rate_eval, tf):
    # Cr67 --> n + Mn66
    rate = 0.0

    # mp17w
    rate += np.exp(  0.888052)

    rate_eval.Cr67__n_Mn66__weak__mp17 = rate

@numba.njit()
def He4_O24__Ne28(rate_eval, tf):
    # O24 + He4 --> Ne28
    rate = 0.0

    # rpsmr
    rate += np.exp(  43.862 + -2.10406*tf.T9i + 35.81*tf.T913i + -92.8306*tf.T913
                  + 3.89374*tf.T9 + -0.181213*tf.T953 + 49.6642*tf.lnT9)

    rate_eval.He4_O24__Ne28 = rate

@numba.njit()
def p_K35__Ca36(rate_eval, tf):
    # K35 + p --> Ca36
    rate = 0.0

    # il10r
    rate += np.exp(  3.05288 + -5.30233*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  19.5074 + -29.9725*tf.T913i + 1.17665*tf.T913
                  + -0.431989*tf.T9 + 0.0488304*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_K35__Ca36 = rate

@numba.njit()
def n_Ne23__Ne24(rate_eval, tf):
    # Ne23 + n --> Ne24
    rate = 0.0

    # wiesn
    rate += np.exp(  6.1506
                  + 1.0*tf.lnT9)
    # wiesn
    rate += np.exp(  6.85961)

    rate_eval.n_Ne23__Ne24 = rate

@numba.njit()
def He4_O23__Ne27(rate_eval, tf):
    # O23 + He4 --> Ne27
    rate = 0.0

    # rpsmr
    rate += np.exp(  44.0547 + -2.04333*tf.T9i + 33.5114*tf.T913i + -89.9067*tf.T913
                  + 3.75404*tf.T9 + -0.170703*tf.T953 + 48.0648*tf.lnT9)

    rate_eval.He4_O23__Ne27 = rate

@numba.njit()
def K36__He4_S32__weak__wc12(rate_eval, tf):
    # K36 --> He4 + S32
    rate = 0.0

    # wc12w
    rate += np.exp(  -9.58272)

    rate_eval.K36__He4_S32__weak__wc12 = rate

@numba.njit()
def n_O23__O24(rate_eval, tf):
    # O23 + n --> O24
    rate = 0.0

    # rpsmr
    rate += np.exp(  6.82629 + -0.0358493*tf.T9i + 1.42488*tf.T913i + -0.795927*tf.T913
                  + 0.171867*tf.T9 + -0.00587905*tf.T953 + 0.214416*tf.lnT9)

    rate_eval.n_O23__O24 = rate

@numba.njit()
def He4_F27__Na31(rate_eval, tf):
    # F27 + He4 --> Na31
    rate = 0.0

    # rpsmr
    rate += np.exp(  52.4766 + -2.54017*tf.T9i + 52.0194*tf.T913i + -119.174*tf.T913
                  + 5.17118*tf.T9 + -0.239209*tf.T953 + 63.4256*tf.lnT9)

    rate_eval.He4_F27__Na31 = rate

@numba.njit()
def n_K57__K58(rate_eval, tf):
    # K57 + n --> K58
    rate = 0.0

    # rath 
    rate += np.exp(  -4.26906 + 0.0575629*tf.T9i + -6.36338*tf.T913i + 13.9304*tf.T913
                  + -0.238568*tf.T9 + -0.0480796*tf.T953 + -6.12326*tf.lnT9)

    rate_eval.n_K57__K58 = rate

@numba.njit()
def p_O22__F23(rate_eval, tf):
    # O22 + p --> F23
    rate = 0.0

    # rpsmr
    rate += np.exp(  48.3519 + -1.95421*tf.T9i + 65.954*tf.T913i + -116.092*tf.T913
                  + 6.41174*tf.T9 + -0.360634*tf.T953 + 57.8512*tf.lnT9)

    rate_eval.p_O22__F23 = rate

@numba.njit()
def n_O22__O23(rate_eval, tf):
    # O22 + n --> O23
    rate = 0.0

    # rpsmr
    rate += np.exp(  13.8238 + -0.0519084*tf.T9i + 4.69424*tf.T913i + -11.3507*tf.T913
                  + 0.946785*tf.T9 + -0.0604058*tf.T953 + 4.22971*tf.lnT9)

    rate_eval.n_O22__O23 = rate

@numba.njit()
def n_O21__O22(rate_eval, tf):
    # O21 + n --> O22
    rate = 0.0

    # wiesr
    rate += np.exp(  2.85647
                  + 1.0*tf.lnT9)

    rate_eval.n_O21__O22 = rate

@numba.njit()
def n_Cl31__He4_P28(rate_eval, tf):
    # Cl31 + n --> He4 + P28
    rate = 0.0

    # ths8r
    rate += np.exp(  15.4971 + 0.267342*tf.T913
                  + 0.110853*tf.T9 + 1.83478e-05*tf.T953)

    rate_eval.n_Cl31__He4_P28 = rate

@numba.njit()
def He4_O20__Ne24(rate_eval, tf):
    # O20 + He4 --> Ne24
    rate = 0.0

    # rpsmr
    rate += np.exp(  37.0999 + -1.78935*tf.T9i + 19.8987*tf.T913i + -67.2522*tf.T913
                  + 2.55528*tf.T9 + -0.114106*tf.T953 + 37.1166*tf.lnT9)

    rate_eval.He4_O20__Ne24 = rate

@numba.njit()
def p_O20__F21(rate_eval, tf):
    # O20 + p --> F21
    rate = 0.0

    # rpsmr
    rate += np.exp(  49.0863 + -1.86828*tf.T9i + 62.8872*tf.T913i + -113.054*tf.T913
                  + 6.16844*tf.T9 + -0.342827*tf.T953 + 55.9731*tf.lnT9)

    rate_eval.p_O20__F21 = rate

@numba.njit()
def He4_O20__n_Ne23(rate_eval, tf):
    # O20 + He4 --> n + Ne23
    rate = 0.0

    # rpsmr
    rate += np.exp(  53.1902 + -1.84694*tf.T9i + 25.9281*tf.T913i + -79.9483*tf.T913
                  + 3.29894*tf.T9 + -0.148546*tf.T953 + 42.7276*tf.lnT9)

    rate_eval.He4_O20__n_Ne23 = rate

@numba.njit()
def n_Ar48__Ar49(rate_eval, tf):
    # Ar48 + n --> Ar49
    rate = 0.0

    # rath 
    rate += np.exp(  17.2385 + -0.0644221*tf.T9i + 6.10943*tf.T913i + -17.9891*tf.T913
                  + 2.20222*tf.T9 + -0.198579*tf.T953 + 5.94252*tf.lnT9)

    rate_eval.n_Ar48__Ar49 = rate

@numba.njit()
def He4_O19__Ne23(rate_eval, tf):
    # O19 + He4 --> Ne23
    rate = 0.0

    # rpsmr
    rate += np.exp(  40.7895 + -1.77725*tf.T9i + 22.6586*tf.T913i + -73.6119*tf.T913
                  + 2.87611*tf.T9 + -0.122329*tf.T953 + 39.9182*tf.lnT9)

    rate_eval.He4_O19__Ne23 = rate

@numba.njit()
def He4_S28__Ar32(rate_eval, tf):
    # S28 + He4 --> Ar32
    rate = 0.0

    # ths8r
    rate += np.exp(  40.0908 + -65.031*tf.T913i + 0.269344*tf.T913
                  + -0.818256*tf.T9 + 0.0515944*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S28__Ar32 = rate

@numba.njit()
def K58__n_n_Ca56__weak__mp17(rate_eval, tf):
    # K58 --> n + n + Ca56
    rate = 0.0

    # mp17w
    rate += np.exp(  5.47835)

    rate_eval.K58__n_n_Ca56__weak__mp17 = rate

@numba.njit()
def He4_Ar44__n_Ca47(rate_eval, tf):
    # Ar44 + He4 --> n + Ca47
    rate = 0.0

    # rath 
    rate += np.exp(  -372.746 + 1.97707*tf.T9i + -534.703*tf.T913i + 945.852*tf.T913
                  + -62.2947*tf.T9 + 3.77807*tf.T953 + -414.604*tf.lnT9)

    rate_eval.He4_Ar44__n_Ca47 = rate

@numba.njit()
def He4_O17__Ne21(rate_eval, tf):
    # O17 + He4 --> Ne21
    rate = 0.0

    # be13r
    rate += np.exp(  -25.0898 + -5.50926*tf.T9i + 123.363*tf.T913i + -87.4351*tf.T913
                  + -3.40974e-06*tf.T9 + -57.0469*tf.T953 + 82.2218*tf.lnT9)
    # be13r
    rate += np.exp(  -117.134 + -13.6759*tf.T9i + 3.31162e-08*tf.T913i + 130.258*tf.T913
                  + -7.92551e-05*tf.T9 + -4.13772*tf.T953 + -42.7753*tf.lnT9)
    # be13r
    rate += np.exp(  2.14 + -5.99952*tf.T9i + 2.87641*tf.T913i + -3.54489*tf.T913
                  + -2.11222e-08*tf.T9 + -3.90649e-09*tf.T953 + 4.75778*tf.lnT9)

    rate_eval.He4_O17__Ne21 = rate

@numba.njit()
def n_O16__O17(rate_eval, tf):
    # O16 + n --> O17
    rate = 0.0

    # ks03 
    rate += np.exp(  7.21546 + 0.0235015*tf.T9i + -2.11246*tf.T913i + 4.87742*tf.T913
                  + -0.314426*tf.T9 + 0.0169515*tf.T953 + -0.984784*tf.lnT9)

    rate_eval.n_O16__O17 = rate

@numba.njit()
def p_S44__n_Cl44(rate_eval, tf):
    # S44 + p --> n + Cl44
    rate = 0.0

    # rath 
    rate += np.exp(  96.6849 + -4.35904*tf.T9i + 158.282*tf.T913i + -257.515*tf.T913
                  + 13.9909*tf.T9 + -0.774713*tf.T953 + 129.922*tf.lnT9)

    rate_eval.p_S44__n_Cl44 = rate

@numba.njit()
def n_O15__O16(rate_eval, tf):
    # O15 + n --> O16
    rate = 0.0

    # rpsmr
    rate += np.exp(  8.08476 + 0.0135346*tf.T9i + -1.11761*tf.T913i + 1.0167*tf.T913
                  + 0.0449976*tf.T9 + -0.00204682*tf.T953 + -0.789217*tf.lnT9)

    rate_eval.n_O15__O16 = rate

@numba.njit()
def n_N19__N20(rate_eval, tf):
    # N19 + n --> N20
    rate = 0.0

    # wiesr
    rate += np.exp(  7.33954
                  + 1.0*tf.lnT9)

    rate_eval.n_N19__N20 = rate

@numba.njit()
def n_Si27__He4_Mg24(rate_eval, tf):
    # Si27 + n --> He4 + Mg24
    rate = 0.0

    # ths8r
    rate += np.exp(  18.0785 + 0.942981*tf.T913
                  + -0.104624*tf.T9 + 0.00723421*tf.T953)

    rate_eval.n_Si27__He4_Mg24 = rate

@numba.njit()
def Sc63__n_Ti62__weak__mp17(rate_eval, tf):
    # Sc63 --> n + Ti62
    rate = 0.0

    # mp17w
    rate += np.exp(  5.10189)

    rate_eval.Sc63__n_Ti62__weak__mp17 = rate

@numba.njit()
def V58__n_Cr57__weak__mp17(rate_eval, tf):
    # V58 --> n + Cr57
    rate = 0.0

    # mp17w
    rate += np.exp(  -2.62305)

    rate_eval.V58__n_Cr57__weak__mp17 = rate

@numba.njit()
def n_N17__N18(rate_eval, tf):
    # N17 + n --> N18
    rate = 0.0

    # wiesr
    rate += np.exp(  5.67332 + -9.10209e-13*tf.T9i + 1.19836e-10*tf.T913i + -3.97338e-10*tf.T913
                  + 4.00366e-11*tf.T9 + -3.36506e-12*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_N17__N18 = rate

@numba.njit()
def Ar45__K45__weak__wc12(rate_eval, tf):
    # Ar45 --> K45
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.43457)

    rate_eval.Ar45__K45__weak__wc12 = rate

@numba.njit()
def He4_P33__Cl37(rate_eval, tf):
    # P33 + He4 --> Cl37
    rate = 0.0

    # rath 
    rate += np.exp(  50.9267 + -3.38505*tf.T9i + 21.2001*tf.T913i + -84.0086*tf.T913
                  + 1.39426*tf.T9 + 0.0896178*tf.T953 + 47.8178*tf.lnT9)

    rate_eval.He4_P33__Cl37 = rate

@numba.njit()
def n_N16__N17(rate_eval, tf):
    # N16 + n --> N17
    rate = 0.0

    # wiesr
    rate += np.exp(  2.00917 + -0.0280287*tf.T9i + 2.705*tf.T913i + 3.26418*tf.T913
                  + -1.12414*tf.T9 + 0.130302*tf.T953 + 1.66263*tf.lnT9)

    rate_eval.n_N16__N17 = rate

@numba.njit()
def n_Cl29__Cl30(rate_eval, tf):
    # Cl29 + n --> Cl30
    rate = 0.0

    # ths8r
    rate += np.exp(  9.8331 + -0.350513*tf.T913
                  + 0.230344*tf.T9 + -0.0154565*tf.T953)

    rate_eval.n_Cl29__Cl30 = rate

@numba.njit()
def n_Ti53__Ti54(rate_eval, tf):
    # Ti53 + n --> Ti54
    rate = 0.0

    # rath 
    rate += np.exp(  15.8394 + -0.0209702*tf.T9i + 1.5765*tf.T913i + -5.63788*tf.T913
                  + 0.867082*tf.T9 + -0.105018*tf.T953 + 1.4587*tf.lnT9)

    rate_eval.n_Ti53__Ti54 = rate

@numba.njit()
def n_N15__N16(rate_eval, tf):
    # N15 + n --> N16
    rate = 0.0

    # ks03 
    rate += np.exp(  8.25143 + 0.00106711*tf.T9i + 0.0770439*tf.T913i + -0.667735*tf.T913
                  + 0.135465*tf.T9 + -0.0130951*tf.T953 + 1.13171*tf.lnT9)

    rate_eval.n_N15__N16 = rate

@numba.njit()
def Ti60__n_V59__weak__mp17(rate_eval, tf):
    # Ti60 --> n + V59
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.479842)

    rate_eval.Ti60__n_V59__weak__mp17 = rate

@numba.njit()
def p_N14__O15(rate_eval, tf):
    # N14 + p --> O15
    rate = 0.0

    # im05r
    rate += np.exp(  6.73578 + -4.891*tf.T9i
                  + 0.0682*tf.lnT9)
    # im05r
    rate += np.exp(  7.65444 + -2.998*tf.T9i
                  + -1.5*tf.lnT9)
    # im05n
    rate += np.exp(  20.1169 + -15.193*tf.T913i + -4.63975*tf.T913
                  + 9.73458*tf.T9 + -9.55051*tf.T953 + 0.333333*tf.lnT9)
    # im05n
    rate += np.exp(  17.01 + -15.193*tf.T913i + -0.161954*tf.T913
                  + -7.52123*tf.T9 + -0.987565*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_N14__O15 = rate

@numba.njit()
def n_N13__N14(rate_eval, tf):
    # N13 + n --> N14
    rate = 0.0

    # wiesn
    rate += np.exp(  13.9377 + -0.0054652*tf.T9i + 1.72241e-10*tf.T913i + -5.62522e-10*tf.T913
                  + 5.59212e-11*tf.T9 + -4.6549e-12*tf.T953)
    # wiesr
    rate += np.exp(  -3.63074 + -2.99547*tf.T9i + 9.44873e-10*tf.T913i + -2.33713e-09*tf.T913
                  + 1.97507e-10*tf.T9 + -1.49747e-11*tf.T953 + -1.5*tf.lnT9)

    rate_eval.n_N13__N14 = rate

@numba.njit()
def Mg38__n_n_Al36__weak__mp17(rate_eval, tf):
    # Mg38 --> n + n + Al36
    rate = 0.0

    # mp17w
    rate += np.exp(  2.41757)

    rate_eval.Mg38__n_n_Al36__weak__mp17 = rate

@numba.njit()
def n_Fe53__Fe54(rate_eval, tf):
    # Fe53 + n --> Fe54
    rate = 0.0

    # ths8r
    rate += np.exp(  16.4534 + -1.10421*tf.T913
                  + 0.379905*tf.T9 + -0.0581878*tf.T953)

    rate_eval.n_Fe53__Fe54 = rate

@numba.njit()
def p_C14__N15(rate_eval, tf):
    # C14 + p --> N15
    rate = 0.0

    # il10r
    rate += np.exp(  17.1024 + -1.52341*tf.T9i + -10.658*tf.T913i + 1.73644*tf.T913
                  + -0.350498*tf.T9 + 0.0279902*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  20.119 + -13.9619*tf.T913i + -4.34315*tf.T913
                  + 6.64922*tf.T9 + -3.22592*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_C14__N15 = rate

@numba.njit()
def p_C13__N14(rate_eval, tf):
    # C13 + p --> N14
    rate = 0.0

    # nacrn
    rate += np.exp(  18.5155 + -13.72*tf.T913i + -0.450018*tf.T913
                  + 3.70823*tf.T9 + -1.70545*tf.T953 + -0.666667*tf.lnT9)
    # nacrr
    rate += np.exp(  13.9637 + -5.78147*tf.T9i + -0.196703*tf.T913
                  + 0.142126*tf.T9 + -0.0238912*tf.T953 + -1.5*tf.lnT9)
    # nacrr
    rate += np.exp(  15.1825 + -13.5543*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_C13__N14 = rate

@numba.njit()
def p_C12__N13(rate_eval, tf):
    # C12 + p --> N13
    rate = 0.0

    # ls09n
    rate += np.exp(  17.1482 + -13.692*tf.T913i + -0.230881*tf.T913
                  + 4.44362*tf.T9 + -3.15898*tf.T953 + -0.666667*tf.lnT9)
    # ls09r
    rate += np.exp(  17.5428 + -3.77849*tf.T9i + -5.10735*tf.T913i + -2.24111*tf.T913
                  + 0.148883*tf.T9 + -1.5*tf.lnT9)

    rate_eval.p_C12__N13 = rate

@numba.njit()
def p_C11__N12(rate_eval, tf):
    # C11 + p --> N12
    rate = 0.0

    # gl07r
    rate += np.exp(  5.791 + -4.16602*tf.T9i
                  + -1.5*tf.lnT9)
    # gl07n
    rate += np.exp(  14.0918 + -13.6275*tf.T913i
                  + 0.722849*tf.T9 + -0.666667*tf.lnT9)

    rate_eval.p_C11__N12 = rate

@numba.njit()
def n_V42__p_Ti42(rate_eval, tf):
    # V42 + n --> p + Ti42
    rate = 0.0

    # ths8r
    rate += np.exp(  21.0479 + -0.480103*tf.T913
                  + 0.167051*tf.T9 + -0.0137602*tf.T953)

    rate_eval.n_V42__p_Ti42 = rate

@numba.njit()
def n_B12__B13(rate_eval, tf):
    # B12 + n --> B13
    rate = 0.0

    # wiesr
    rate += np.exp(  3.26473 + -0.0228289*tf.T9i + 1.76541*tf.T913i + 4.43298*tf.T913
                  + -1.46879*tf.T9 + 0.163093*tf.T953 + 0.586188*tf.lnT9)

    rate_eval.n_B12__B13 = rate

@numba.njit()
def n_p__d(rate_eval, tf):
    # n + p --> d
    rate = 0.0

    # an06n
    rate += np.exp(  12.3687 + -2.70618*tf.T913
                  + 0.11718*tf.T9 + -0.00312788*tf.T953 + 0.469127*tf.lnT9)
    # an06n
    rate += np.exp(  10.7548 + -2.30472*tf.T913
                  + -0.887862*tf.T9 + 0.137663*tf.T953)
    # an06n
    rate += np.exp(  8.84688 + -0.0102082*tf.T913
                  + -0.0893959*tf.T9 + 0.00696704*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_p__d = rate

@numba.njit()
def n_B11__B12(rate_eval, tf):
    # B11 + n --> B12
    rate = 0.0

    # bb92n
    rate += np.exp(  6.59167 + -2.1598e-13*tf.T9i + 2.18692e-11*tf.T913i + -4.50377e-11*tf.T913
                  + 2.23428e-12*tf.T9 + -5.80147e-14*tf.T953 + 2.002e-11*tf.lnT9)
    # bb92r
    rate += np.exp(  -1.59362 + -0.180671*tf.T9i + -5.3754*tf.T913i + 15.15*tf.T913
                  + -0.151605*tf.T9 + -0.0619668*tf.T953 + -7.35999*tf.lnT9)

    rate_eval.n_B11__B12 = rate

@numba.njit()
def p_B10__C11(rate_eval, tf):
    # B10 + p --> C11
    rate = 0.0

    # nacrn
    rate += np.exp(  40.3933 + -13.4089*tf.T913i + -66.1173*tf.T913
                  + 163.12*tf.T9 + -250.002*tf.T953 + -0.666667*tf.lnT9)
    # nacrr
    rate += np.exp(  -13.1188 + -4.45749*tf.T9i + 105.797*tf.T913i + -86.6739*tf.T913
                  + 1.95564*tf.T9 + -0.0113213*tf.T953 + 60.9579*tf.lnT9)

    rate_eval.p_B10__C11 = rate

@numba.njit()
def p_Na28__Mg29(rate_eval, tf):
    # Na28 + p --> Mg29
    rate = 0.0

    # rath 
    rate += np.exp(  60.7218 + -2.73631*tf.T9i + 95.2602*tf.T913i + -160.314*tf.T913
                  + 8.44708*tf.T9 + -0.447733*tf.T953 + 81.099*tf.lnT9)

    rate_eval.p_Na28__Mg29 = rate

@numba.njit()
def n_B10__B11(rate_eval, tf):
    # B10 + n --> B11
    rate = 0.0

    #  wagn
    rate += np.exp(  11.1004 + -1.9027e-12*tf.T9i + 2.65756e-10*tf.T913i + -9.63588e-10*tf.T913
                  + 1.07466e-10*tf.T9 + -9.87569e-12*tf.T953 + 3.12603e-10*tf.lnT9)

    rate_eval.n_B10__B11 = rate

@numba.njit()
def n_Be11__Be12(rate_eval, tf):
    # Be11 + n --> Be12
    rate = 0.0

    # wiesr
    rate += np.exp(  5.87493 + -8.61413e-13*tf.T9i + 1.14538e-10*tf.T913i + -3.83949e-10*tf.T913
                  + 3.89769e-11*tf.T9 + -3.28959e-12*tf.T953 + 1.29988e-10*tf.lnT9)

    rate_eval.n_Be11__Be12 = rate

@numba.njit()
def p_Be10__B11(rate_eval, tf):
    # Be10 + p --> B11
    rate = 0.0

    #  wag 
    rate += np.exp(  14.7116 + -2.21365e-12*tf.T9i + -10.39*tf.T913i + -1.04664e-09*tf.T913
                  + 1.13067e-10*tf.T9 + -1.01639e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Be10__B11 = rate

@numba.njit()
def p_Sc39__Ti40(rate_eval, tf):
    # Sc39 + p --> Ti40
    rate = 0.0

    # ths8r
    rate += np.exp(  42.3709 + -32.1484*tf.T913i + -15.0165*tf.T913
                  + 1.54165*tf.T9 + -0.0793546*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc39__Ti40 = rate

@numba.njit()
def He4_Ti64__Cr68(rate_eval, tf):
    # Ti64 + He4 --> Cr68
    rate = 0.0

    # rath 
    rate += np.exp(  -1066.8 + 22.1057*tf.T9i + -2197.8*tf.T913i + 3389.57*tf.T913
                  + -191.91*tf.T9 + 10.5739*tf.T953 + -1644.55*tf.lnT9)

    rate_eval.He4_Ti64__Cr68 = rate

@numba.njit()
def n_Mg20__Mg21(rate_eval, tf):
    # Mg20 + n --> Mg21
    rate = 0.0

    # ths8r
    rate += np.exp(  7.94633 + 2.12404*tf.T913
                  + -0.197137*tf.T9 + 0.00958753*tf.T953)

    rate_eval.n_Mg20__Mg21 = rate

@numba.njit()
def p_Be7__B8(rate_eval, tf):
    # Be7 + p --> B8
    rate = 0.0

    # nacrr
    rate += np.exp(  7.73399 + -7.345*tf.T9i
                  + -1.5*tf.lnT9)
    # nacrn
    rate += np.exp(  12.5315 + -10.264*tf.T913i + -0.203472*tf.T913
                  + 0.121083*tf.T9 + -0.00700063*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Be7__B8 = rate

@numba.njit()
def He4_Li9__B13(rate_eval, tf):
    # Li9 + He4 --> B13
    rate = 0.0

    # fkthr
    rate += np.exp(  32.9641 + -1.26928*tf.T9i + 26.71*tf.T913i + -61.4797*tf.T913
                  + 2.9043*tf.T9 + -0.133977*tf.T953 + 30.9994*tf.lnT9)

    rate_eval.He4_Li9__B13 = rate

@numba.njit()
def He4_Mg26__Si30(rate_eval, tf):
    # Mg26 + He4 --> Si30
    rate = 0.0

    # cf88r
    rate += np.exp(  1.32941 + -18.7164*tf.T9i + -1.87411*tf.T913
                  + 3.41299*tf.T9 + -0.43226*tf.T953 + -1.5*tf.lnT9)
    # cf88n
    rate += np.exp(  45.8787 + -53.7518*tf.T913i + -4.8647*tf.T913
                  + -1.51467*tf.T9 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg26__Si30 = rate

@numba.njit()
def He4_Fe45__p_Co48(rate_eval, tf):
    # Fe45 + He4 --> p + Co48
    rate = 0.0

    # ths8r
    rate += np.exp(  62.1224 + -91.3476*tf.T913i + -1.40215*tf.T913
                  + -0.406715*tf.T9 + 0.00387095*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe45__p_Co48 = rate

@numba.njit()
def p_P35__n_S35(rate_eval, tf):
    # P35 + p --> n + S35
    rate = 0.0

    # rath 
    rate += np.exp(  89.7904 + -3.76609*tf.T9i + 135.343*tf.T913i + -225.471*tf.T913
                  + 12.1778*tf.T9 + -0.67271*tf.T953 + 113.379*tf.lnT9)

    rate_eval.p_P35__n_S35 = rate

@numba.njit()
def He4_Na24__Al28(rate_eval, tf):
    # Na24 + He4 --> Al28
    rate = 0.0

    # rath 
    rate += np.exp(  1.63055 + -2.00108*tf.T9i + -22.0373*tf.T913i + 12.2654*tf.T913
                  + -3.20073*tf.T9 + 0.258909*tf.T953 + 4.52728*tf.lnT9)

    rate_eval.He4_Na24__Al28 = rate

@numba.njit()
def He4_Li8__B12(rate_eval, tf):
    # Li8 + He4 --> B12
    rate = 0.0

    # fkthr
    rate += np.exp(  37.5639 + -1.04393*tf.T9i + 19.45*tf.T913i + -57.5572*tf.T913
                  + 3.09288*tf.T9 + -0.164411*tf.T953 + 27.0775*tf.lnT9)

    rate_eval.He4_Li8__B12 = rate

@numba.njit()
def He4_He3__Be7(rate_eval, tf):
    # He3 + He4 --> Be7
    rate = 0.0

    # cd08n
    rate += np.exp(  17.7075 + -12.8271*tf.T913i + -3.8126*tf.T913
                  + 0.0942285*tf.T9 + -0.00301018*tf.T953 + 1.33333*tf.lnT9)
    # cd08n
    rate += np.exp(  15.6099 + -12.8271*tf.T913i + -0.0308225*tf.T913
                  + -0.654685*tf.T9 + 0.0896331*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_He3__Be7 = rate

@numba.njit()
def He4_Fe75__Ni79(rate_eval, tf):
    # Fe75 + He4 --> Ni79
    rate = 0.0

    # rath 
    rate += np.exp(  -1052.35 + 26.6697*tf.T9i + -2572.04*tf.T913i + 3751.29*tf.T913
                  + -203.295*tf.T9 + 10.8599*tf.T953 + -1870.47*tf.lnT9)

    rate_eval.He4_Fe75__Ni79 = rate

@numba.njit()
def p_Ne24__Na25(rate_eval, tf):
    # Ne24 + p --> Na25
    rate = 0.0

    # rath 
    rate += np.exp(  53.4535 + -2.35472*tf.T9i + 78.8934*tf.T913i + -134.618*tf.T913
                  + 7.13077*tf.T9 + -0.392746*tf.T953 + 68.1357*tf.lnT9)

    rate_eval.p_Ne24__Na25 = rate

@numba.njit()
def p_t__He4(rate_eval, tf):
    # t + p --> He4
    rate = 0.0

    # cf88n
    rate += np.exp(  9.76526 + -3.869*tf.T913i + 1.45482*tf.T913
                  + 0.577246*tf.T9 + -0.112199*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_t__He4 = rate

@numba.njit()
def He4_d__Li6(rate_eval, tf):
    # d + He4 --> Li6
    rate = 0.0

    # tu19r
    rate += np.exp(  4.12313 + -7.889*tf.T9i
                  + -1.5*tf.lnT9)
    # tu19n
    rate += np.exp(  -0.676485 + 6.3911e-05*tf.T9i + -7.55198*tf.T913i + 5.77546*tf.T913
                  + -0.487854*tf.T9 + 0.032833*tf.T953 + -1.12305*tf.lnT9)

    rate_eval.He4_d__Li6 = rate

@numba.njit()
def p_P27__S28(rate_eval, tf):
    # P27 + p --> S28
    rate = 0.0

    # il10n
    rate += np.exp(  19.691 + -25.5915*tf.T913i
                  + -0.666667*tf.lnT9)

    rate_eval.p_P27__S28 = rate

@numba.njit()
def He4_Cr49__Fe53(rate_eval, tf):
    # Cr49 + He4 --> Fe53
    rate = 0.0

    # ths8r
    rate += np.exp(  65.1467 + -86.7913*tf.T913i + -6.51572*tf.T913
                  + -1.21249*tf.T9 + 0.185473*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr49__Fe53 = rate

@numba.njit()
def He4_C12__O16(rate_eval, tf):
    # C12 + He4 --> O16
    rate = 0.0

    # nac2 
    rate += np.exp(  254.634 + -1.84097*tf.T9i + 103.411*tf.T913i + -420.567*tf.T913
                  + 64.0874*tf.T9 + -12.4624*tf.T953 + 137.303*tf.lnT9)
    # nac2 
    rate += np.exp(  69.6526 + -1.39254*tf.T9i + 58.9128*tf.T913i + -148.273*tf.T913
                  + 9.08324*tf.T9 + -0.541041*tf.T953 + 70.3554*tf.lnT9)

    rate_eval.He4_C12__O16 = rate

@numba.njit()
def Fe75__n_n_Co73__weak__mp17(rate_eval, tf):
    # Fe75 --> n + n + Co73
    rate = 0.0

    # mp17w
    rate += np.exp(  0.515376)

    rate_eval.Fe75__n_n_Co73__weak__mp17 = rate

@numba.njit()
def V61__n_Cr60__weak__wc12(rate_eval, tf):
    # V61 --> n + Cr60
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.234885)

    rate_eval.V61__n_Cr60__weak__wc12 = rate

@numba.njit()
def Fe73__n_n_Co71__weak__mp17(rate_eval, tf):
    # Fe73 --> n + n + Co71
    rate = 0.0

    # mp17w
    rate += np.exp(  -2.09053)

    rate_eval.Fe73__n_n_Co71__weak__mp17 = rate

@numba.njit()
def Mn73__n_n_Fe71__weak__mp17(rate_eval, tf):
    # Mn73 --> n + n + Fe71
    rate = 0.0

    # mp17w
    rate += np.exp(  1.75375)

    rate_eval.Mn73__n_n_Fe71__weak__mp17 = rate

@numba.njit()
def He4_Fe62__n_Ni65(rate_eval, tf):
    # Fe62 + He4 --> n + Ni65
    rate = 0.0

    # rath 
    rate += np.exp(  -1167.64 + 24.3681*tf.T9i + -2423.19*tf.T913i + 3737.09*tf.T913
                  + -211.842*tf.T9 + 11.7186*tf.T953 + -1812.57*tf.lnT9)

    rate_eval.He4_Fe62__n_Ni65 = rate

@numba.njit()
def F27__n_Ne26__weak__wc12(rate_eval, tf):
    # F27 --> n + Ne26
    rate = 0.0

    # wc12w
    rate += np.exp(  4.67044)

    rate_eval.F27__n_Ne26__weak__wc12 = rate

@numba.njit()
def Mn72__n_n_Fe70__weak__mp17(rate_eval, tf):
    # Mn72 --> n + n + Fe70
    rate = 0.0

    # mp17w
    rate += np.exp(  2.25078)

    rate_eval.Mn72__n_n_Fe70__weak__mp17 = rate

@numba.njit()
def Al22__Mg22__weak__wc12(rate_eval, tf):
    # Al22 --> Mg22
    rate = 0.0

    # wc12w
    rate += np.exp(  1.21645)

    rate_eval.Al22__Mg22__weak__wc12 = rate

@numba.njit()
def Mn71__n_n_Fe69__weak__mp17(rate_eval, tf):
    # Mn71 --> n + n + Fe69
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.15332)

    rate_eval.Mn71__n_n_Fe69__weak__mp17 = rate

@numba.njit()
def He4_Mg27__Si31(rate_eval, tf):
    # Mg27 + He4 --> Si31
    rate = 0.0

    # rath 
    rate += np.exp(  -15.6982 + -2.20841*tf.T9i + -29.3833*tf.T913i + 36.5079*tf.T913
                  + -5.51379*tf.T9 + 0.423403*tf.T953 + -2.81347*tf.lnT9)

    rate_eval.He4_Mg27__Si31 = rate

@numba.njit()
def Fe59__Co59__weak__wc12(rate_eval, tf):
    # Fe59 --> Co59
    rate = 0.0

    # wc12w
    rate += np.exp(  -15.5275)

    rate_eval.Fe59__Co59__weak__wc12 = rate

@numba.njit()
def Mn70__n_n_Fe68__weak__mp17(rate_eval, tf):
    # Mn70 --> n + n + Fe68
    rate = 0.0

    # mp17w
    rate += np.exp(  0.843031)

    rate_eval.Mn70__n_n_Fe68__weak__mp17 = rate

@numba.njit()
def Ca61__n_n_n_Sc58__weak__mo03(rate_eval, tf):
    # Ca61 --> 3 n + Sc58
    rate = 0.0

    # mo03w
    rate += np.exp(  2.19063)

    rate_eval.Ca61__n_n_n_Sc58__weak__mo03 = rate

@numba.njit()
def n_Ti47__p_Sc47(rate_eval, tf):
    # Ti47 + n --> p + Sc47
    rate = 0.0

    # ths8r
    rate += np.exp(  -22.6984 + 30.6942*tf.T913
                  + -3.81514*tf.T9 + 0.263484*tf.T953)

    rate_eval.n_Ti47__p_Sc47 = rate

@numba.njit()
def p_Ca49__n_Sc49(rate_eval, tf):
    # Ca49 + p --> n + Sc49
    rate = 0.0

    # rath 
    rate += np.exp(  117.166 + -5.34459*tf.T9i + 197.997*tf.T913i + -323.315*tf.T913
                  + 17.9092*tf.T9 + -1.00926*tf.T953 + 162.074*tf.lnT9)

    rate_eval.p_Ca49__n_Sc49 = rate

@numba.njit()
def Mn68__n_n_Fe66__weak__mp17(rate_eval, tf):
    # Mn68 --> n + n + Fe66
    rate = 0.0

    # mp17w
    rate += np.exp(  -1.39613)

    rate_eval.Mn68__n_n_Fe66__weak__mp17 = rate

@numba.njit()
def p_Si35__P36(rate_eval, tf):
    # Si35 + p --> P36
    rate = 0.0

    # rath 
    rate += np.exp(  77.5173 + -3.59427*tf.T9i + 129.108*tf.T913i + -215.818*tf.T913
                  + 11.7406*tf.T9 + -0.649927*tf.T953 + 108.236*tf.lnT9)

    rate_eval.p_Si35__P36 = rate

@numba.njit()
def p_Ti46__V47(rate_eval, tf):
    # Ti46 + p --> V47
    rate = 0.0

    # ths8r
    rate += np.exp(  35.7683 + -33.2034*tf.T913i + 0.505619*tf.T913
                  + -1.73654*tf.T9 + 0.207342*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ti46__V47 = rate

@numba.njit()
def He4_P34__Cl38(rate_eval, tf):
    # P34 + He4 --> Cl38
    rate = 0.0

    # rath 
    rate += np.exp(  -285.664 + 1.84071*tf.T9i + -440.51*tf.T913i + 749.938*tf.T913
                  + -48.8067*tf.T9 + 2.93472*tf.T953 + -333.294*tf.lnT9)

    rate_eval.He4_P34__Cl38 = rate

@numba.njit()
def p_Fe71__Co72(rate_eval, tf):
    # Fe71 + p --> Co72
    rate = 0.0

    # rath 
    rate += np.exp(  151.634 + -7.55342*tf.T9i + 289.333*tf.T913i + -467.144*tf.T913
                  + 26.2195*tf.T9 + -1.5042*tf.T953 + 232.581*tf.lnT9)

    rate_eval.p_Fe71__Co72 = rate

@numba.njit()
def Ti65__n_n_V63__weak__mp17(rate_eval, tf):
    # Ti65 --> n + n + V63
    rate = 0.0

    # mp17w
    rate += np.exp(  2.03651)

    rate_eval.Ti65__n_n_V63__weak__mp17 = rate

@numba.njit()
def Ar35__Cl35__weak__wc12(rate_eval, tf):
    # Ar35 --> Cl35
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.943126)

    rate_eval.Ar35__Cl35__weak__wc12 = rate

@numba.njit()
def Si42__P42__weak__wc17(rate_eval, tf):
    # Si42 --> P42
    rate = 0.0

    # wc17w
    rate += np.exp(  3.39933)

    rate_eval.Si42__P42__weak__wc17 = rate

@numba.njit()
def n_K51__K52(rate_eval, tf):
    # K51 + n --> K52
    rate = 0.0

    # rath 
    rate += np.exp(  17.2342 + -0.0141804*tf.T9i + 2.25449*tf.T913i + -11.4628*tf.T913
                  + 1.15112*tf.T9 + -0.0960463*tf.T953 + 3.07642*tf.lnT9)

    rate_eval.n_K51__K52 = rate

@numba.njit()
def Fe48__Mn48__weak__wc12(rate_eval, tf):
    # Fe48 --> Mn48
    rate = 0.0

    # wc12w
    rate += np.exp(  2.55477)

    rate_eval.Fe48__Mn48__weak__wc12 = rate

@numba.njit()
def He4_Ca49__n_Ti52(rate_eval, tf):
    # Ca49 + He4 --> n + Ti52
    rate = 0.0

    # rath 
    rate += np.exp(  -907.359 + 14.6154*tf.T9i + -1587.73*tf.T913i + 2606.0*tf.T913
                  + -155.845*tf.T9 + 8.94969*tf.T953 + -1222.05*tf.lnT9)

    rate_eval.He4_Ca49__n_Ti52 = rate

@numba.njit()
def Sc60__n_n_Ti58__weak__mp17(rate_eval, tf):
    # Sc60 --> n + n + Ti58
    rate = 0.0

    # mp17w
    rate += np.exp(  2.49819)

    rate_eval.Sc60__n_n_Ti58__weak__mp17 = rate

@numba.njit()
def n_V48__He4_Sc45(rate_eval, tf):
    # V48 + n --> He4 + Sc45
    rate = 0.0

    # ths8r
    rate += np.exp(  -5.87552 + 8.18067*tf.T913
                  + 1.50465*tf.T9 + -0.224564*tf.T953)

    rate_eval.n_V48__He4_Sc45 = rate

@numba.njit()
def p_F18__Ne19(rate_eval, tf):
    # F18 + p --> Ne19
    rate = 0.0

    # il10r
    rate += np.exp(  -5.85727 + -2.89147*tf.T9i + 13.1683*tf.T913
                  + -1.92023*tf.T9 + 0.16901*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -29.449 + -0.39895*tf.T9i + 22.4903*tf.T913
                  + 0.307872*tf.T9 + -0.296226*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  57.4084 + -21.4023*tf.T913i + -93.766*tf.T913
                  + 179.258*tf.T9 + -202.561*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_F18__Ne19 = rate

@numba.njit()
def p_Mg36__Al37(rate_eval, tf):
    # Mg36 + p --> Al37
    rate = 0.0

    # rath 
    rate += np.exp(  68.2159 + -3.27422*tf.T9i + 116.667*tf.T913i + -192.148*tf.T913
                  + 10.3264*tf.T9 + -0.56577*tf.T953 + 97.048*tf.lnT9)

    rate_eval.p_Mg36__Al37 = rate

@numba.njit()
def Ar49__n_K48__weak__wc12(rate_eval, tf):
    # Ar49 --> n + K48
    rate = 0.0

    # wc12w
    rate += np.exp(  0.974661)

    rate_eval.Ar49__n_K48__weak__wc12 = rate

@numba.njit()
def n_Ne28__Ne29(rate_eval, tf):
    # Ne28 + n --> Ne29
    rate = 0.0

    # rath 
    rate += np.exp(  13.8902 + -0.0532286*tf.T9i + 5.14293*tf.T913i + -14.506*tf.T913
                  + 1.57272*tf.T9 + -0.121871*tf.T953 + 4.97968*tf.lnT9)

    rate_eval.n_Ne28__Ne29 = rate

@numba.njit()
def n_Si25__Si26(rate_eval, tf):
    # Si25 + n --> Si26
    rate = 0.0

    # ths8r
    rate += np.exp(  8.02363 + 2.44812*tf.T913
                  + -0.378302*tf.T9 + 0.0297493*tf.T953)

    rate_eval.n_Si25__Si26 = rate

@numba.njit()
def K59__n_n_Ca57__weak__mp17(rate_eval, tf):
    # K59 --> n + n + Ca57
    rate = 0.0

    # mp17w
    rate += np.exp(  5.10616)

    rate_eval.K59__n_n_Ca57__weak__mp17 = rate

@numba.njit()
def n_S31__He4_Si28(rate_eval, tf):
    # S31 + n --> He4 + Si28
    rate = 0.0

    # ths8r
    rate += np.exp(  18.0599 + 1.12938*tf.T913
                  + -0.122539*tf.T9 + 0.00424404*tf.T953)

    rate_eval.n_S31__He4_Si28 = rate

@numba.njit()
def K56__Ca56__weak__mo03(rate_eval, tf):
    # K56 --> Ca56
    rate = 0.0

    # mo03w
    rate += np.exp(  -109.735)

    rate_eval.K56__Ca56__weak__mo03 = rate

@numba.njit()
def n_P29__P30(rate_eval, tf):
    # P29 + n --> P30
    rate = 0.0

    # ths8r
    rate += np.exp(  8.78841 + 0.15555*tf.T913
                  + 0.155359*tf.T9 + -0.0208019*tf.T953)

    rate_eval.n_P29__P30 = rate

@numba.njit()
def Mn67__Fe67__weak__wc17(rate_eval, tf):
    # Mn67 --> Fe67
    rate = 0.0

    # wc17w
    rate += np.exp(  2.49288)

    rate_eval.Mn67__Fe67__weak__wc17 = rate

@numba.njit()
def K53__n_n_Ca51__weak__mp17(rate_eval, tf):
    # K53 --> n + n + Ca51
    rate = 0.0

    # mp17w
    rate += np.exp(  -1.46512)

    rate_eval.K53__n_n_Ca51__weak__mp17 = rate

@numba.njit()
def n_Cr58__Cr59(rate_eval, tf):
    # Cr58 + n --> Cr59
    rate = 0.0

    # rath 
    rate += np.exp(  18.2318 + 0.0167192*tf.T9i + -0.57235*tf.T913i + -7.12732*tf.T913
                  + 1.73095*tf.T9 + -0.218414*tf.T953 + 0.73649*tf.lnT9)

    rate_eval.n_Cr58__Cr59 = rate

@numba.njit()
def He4_Mn73__Co77(rate_eval, tf):
    # Mn73 + He4 --> Co77
    rate = 0.0

    # rath 
    rate += np.exp(  -1243.98 + 25.7071*tf.T9i + -2551.27*tf.T913i + 3942.56*tf.T913
                  + -223.255*tf.T9 + 12.3281*tf.T953 + -1913.14*tf.lnT9)

    rate_eval.He4_Mn73__Co77 = rate

@numba.njit()
def K52__n_n_Ca50__weak__mp17(rate_eval, tf):
    # K52 --> n + n + Ca50
    rate = 0.0

    # mp17w
    rate += np.exp(  -2.14146)

    rate_eval.K52__n_n_Ca50__weak__mp17 = rate

@numba.njit()
def Ar54__n_n_K52__weak__mp17(rate_eval, tf):
    # Ar54 --> n + n + K52
    rate = 0.0

    # mp17w
    rate += np.exp(  1.8731)

    rate_eval.Ar54__n_n_K52__weak__mp17 = rate

@numba.njit()
def p_Ar42__He4_Cl39(rate_eval, tf):
    # Ar42 + p --> He4 + Cl39
    rate = 0.0

    # rath 
    rate += np.exp(  6.0655 + -2.1123*tf.T9i + -11.7148*tf.T913i + -6.72101*tf.T913
                  + -2.53798*tf.T9 + 0.209033*tf.T953 + 18.6006*tf.lnT9)

    rate_eval.p_Ar42__He4_Cl39 = rate

@numba.njit()
def N21__n_O20__weak__wc12(rate_eval, tf):
    # N21 --> n + O20
    rate = 0.0

    # wc12w
    rate += np.exp(  2.02258)

    rate_eval.N21__n_O20__weak__wc12 = rate

@numba.njit()
def Cl52__n_n_Ar50__weak__mp17(rate_eval, tf):
    # Cl52 --> n + n + Ar50
    rate = 0.0

    # mp17w
    rate += np.exp(  5.01519)

    rate_eval.Cl52__n_n_Ar50__weak__mp17 = rate

@numba.njit()
def Cl50__n_n_Ar48__weak__mp17(rate_eval, tf):
    # Cl50 --> n + n + Ar48
    rate = 0.0

    # mp17w
    rate += np.exp(  3.49899)

    rate_eval.Cl50__n_n_Ar48__weak__mp17 = rate

@numba.njit()
def S49__n_n_Cl47__weak__mp17(rate_eval, tf):
    # S49 --> n + n + Cl47
    rate = 0.0

    # mp17w
    rate += np.exp(  3.28541)

    rate_eval.S49__n_n_Cl47__weak__mp17 = rate

@numba.njit()
def S47__n_n_Cl45__weak__mp17(rate_eval, tf):
    # S47 --> n + n + Cl45
    rate = 0.0

    # mp17w
    rate += np.exp(  2.07342)

    rate_eval.S47__n_n_Cl45__weak__mp17 = rate

@numba.njit()
def n_Cl30__He4_P27(rate_eval, tf):
    # Cl30 + n --> He4 + P27
    rate = 0.0

    # ths8r
    rate += np.exp(  16.4342 + -0.389151*tf.T913
                  + 0.217707*tf.T9 + -0.011547*tf.T953)

    rate_eval.n_Cl30__He4_P27 = rate

@numba.njit()
def S27__p_p_Al25__weak__wc12(rate_eval, tf):
    # S27 --> p + p + Al25
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.709458)

    rate_eval.S27__p_p_Al25__weak__wc12 = rate

@numba.njit()
def P47__n_n_S45__weak__mp17(rate_eval, tf):
    # P47 --> n + n + S45
    rate = 0.0

    # mp17w
    rate += np.exp(  3.68612)

    rate_eval.P47__n_n_S45__weak__mp17 = rate

@numba.njit()
def O20__F20__weak__wc12(rate_eval, tf):
    # O20 --> F20
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.9692)

    rate_eval.O20__F20__weak__wc12 = rate

@numba.njit()
def He4_K42__Sc46(rate_eval, tf):
    # K42 + He4 --> Sc46
    rate = 0.0

    # rath 
    rate += np.exp(  -837.782 + 13.276*tf.T9i + -1444.93*tf.T913i + 2377.02*tf.T913
                  + -142.659*tf.T9 + 8.19872*tf.T953 + -1112.22*tf.lnT9)

    rate_eval.He4_K42__Sc46 = rate

@numba.njit()
def P45__n_n_S43__weak__mp17(rate_eval, tf):
    # P45 --> n + n + S43
    rate = 0.0

    # mp17w
    rate += np.exp(  2.84181)

    rate_eval.P45__n_n_S43__weak__mp17 = rate

@numba.njit()
def He4_Na19__p_Mg22(rate_eval, tf):
    # Na19 + He4 --> p + Mg22
    rate = 0.0

    # ths8r
    rate += np.exp(  44.1954 + -49.6957*tf.T913i + 0.681792*tf.T913
                  + -0.776421*tf.T9 + 0.0612047*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Na19__p_Mg22 = rate

@numba.njit()
def p_F25__Ne26(rate_eval, tf):
    # F25 + p --> Ne26
    rate = 0.0

    # rpsmr
    rate += np.exp(  52.7117 + -2.26189*tf.T9i + 77.9767*tf.T913i + -134.223*tf.T913
                  + 7.29865*tf.T9 + -0.405396*tf.T953 + 67.3504*tf.lnT9)

    rate_eval.p_F25__Ne26 = rate

@numba.njit()
def P44__n_n_S42__weak__mp17(rate_eval, tf):
    # P44 --> n + n + S42
    rate = 0.0

    # mp17w
    rate += np.exp(  2.45229)

    rate_eval.P44__n_n_S42__weak__mp17 = rate

@numba.njit()
def P43__n_n_S41__weak__mp17(rate_eval, tf):
    # P43 --> n + n + S41
    rate = 0.0

    # mp17w
    rate += np.exp(  -1.66124)

    rate_eval.P43__n_n_S41__weak__mp17 = rate

@numba.njit()
def Cr61__Mn61__weak__wc12(rate_eval, tf):
    # Cr61 --> Mn61
    rate = 0.0

    # wc12w
    rate += np.exp(  1.04818)

    rate_eval.Cr61__Mn61__weak__wc12 = rate

@numba.njit()
def Si44__n_n_P42__weak__mp17(rate_eval, tf):
    # Si44 --> n + n + P42
    rate = 0.0

    # mp17w
    rate += np.exp(  2.68756)

    rate_eval.Si44__n_n_P42__weak__mp17 = rate

@numba.njit()
def He4_Mn61__n_Co64(rate_eval, tf):
    # Mn61 + He4 --> n + Co64
    rate = 0.0

    # rath 
    rate += np.exp(  -1123.56 + 23.561*tf.T9i + -2342.33*tf.T913i + 3607.74*tf.T913
                  + -204.367*tf.T9 + 11.3005*tf.T953 + -1750.85*tf.lnT9)

    rate_eval.He4_Mn61__n_Co64 = rate

@numba.njit()
def Sc57__Ti57__weak__wc17(rate_eval, tf):
    # Sc57 --> Ti57
    rate = 0.0

    # wc17w
    rate += np.exp(  3.17576)

    rate_eval.Sc57__Ti57__weak__wc17 = rate

@numba.njit()
def He4_Si28__S32(rate_eval, tf):
    # Si28 + He4 --> S32
    rate = 0.0

    # ths8r
    rate += np.exp(  47.9212 + -59.4896*tf.T913i + 4.47205*tf.T913
                  + -4.78989*tf.T9 + 0.557201*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si28__S32 = rate

@numba.njit()
def Si41__n_n_P39__weak__mp17(rate_eval, tf):
    # Si41 --> n + n + P39
    rate = 0.0

    # mp17w
    rate += np.exp(  0.326634)

    rate_eval.Si41__n_n_P39__weak__mp17 = rate

@numba.njit()
def p_K42__Ca43(rate_eval, tf):
    # K42 + p --> Ca43
    rate = 0.0

    # rath 
    rate += np.exp(  109.902 + -4.83953*tf.T9i + 179.421*tf.T913i + -302.216*tf.T913
                  + 16.9087*tf.T9 + -0.956536*tf.T953 + 149.386*tf.lnT9)

    rate_eval.p_K42__Ca43 = rate

@numba.njit()
def Si39__n_n_P37__weak__mp17(rate_eval, tf):
    # Si39 --> n + n + P37
    rate = 0.0

    # mp17w
    rate += np.exp(  -1.92466)

    rate_eval.Si39__n_n_P37__weak__mp17 = rate

@numba.njit()
def Si23__p_p_Na21__weak__wc12(rate_eval, tf):
    # Si23 --> p + p + Na21
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.527781)

    rate_eval.Si23__p_p_Na21__weak__wc12 = rate

@numba.njit()
def He4_Sc41__p_Ti44(rate_eval, tf):
    # Sc41 + He4 --> p + Ti44
    rate = 0.0

    # ths8r
    rate += np.exp(  57.4853 + -79.013*tf.T913i + -0.989013*tf.T913
                  + -0.463943*tf.T9 + 0.00902542*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc41__p_Ti44 = rate

@numba.njit()
def He4_Sc36__V40(rate_eval, tf):
    # Sc36 + He4 --> V40
    rate = 0.0

    # ths8r
    rate += np.exp(  44.4873 + -78.6932*tf.T913i + -0.0530652*tf.T913
                  + -0.629411*tf.T9 + 0.0237465*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc36__V40 = rate

@numba.njit()
def p_S37__He4_P34(rate_eval, tf):
    # S37 + p --> He4 + P34
    rate = 0.0

    # rath 
    rate += np.exp(  63.3363 + -3.9836*tf.T9i + 139.312*tf.T913i + -209.583*tf.T913
                  + 10.0342*tf.T9 + -0.488175*tf.T953 + 113.317*tf.lnT9)

    rate_eval.p_S37__He4_P34 = rate

@numba.njit()
def Al43__n_n_Si41__weak__mp17(rate_eval, tf):
    # Al43 --> n + n + Si41
    rate = 0.0

    # mp17w
    rate += np.exp(  5.85815)

    rate_eval.Al43__n_n_Si41__weak__mp17 = rate

@numba.njit()
def Al41__n_n_Si39__weak__mp17(rate_eval, tf):
    # Al41 --> n + n + Si39
    rate = 0.0

    # mp17w
    rate += np.exp(  2.72353)

    rate_eval.Al41__n_n_Si39__weak__mp17 = rate

@numba.njit()
def He4_Mn43__p_Fe46(rate_eval, tf):
    # Mn43 + He4 --> p + Fe46
    rate = 0.0

    # ths8r
    rate += np.exp(  61.5275 + -88.8778*tf.T913i + -1.28933*tf.T913
                  + -0.447927*tf.T9 + 0.00657827*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn43__p_Fe46 = rate

@numba.njit()
def n_K42__K43(rate_eval, tf):
    # K42 + n --> K43
    rate = 0.0

    # rath 
    rate += np.exp(  17.0706 + 0.00011464*tf.T9i + -0.278167*tf.T913i + -1.18798*tf.T913
                  + -0.154964*tf.T9 + 0.0229314*tf.T953 + -0.166561*tf.lnT9)

    rate_eval.n_K42__K43 = rate

@numba.njit()
def Al38__n_n_Si36__weak__mp17(rate_eval, tf):
    # Al38 --> n + n + Si36
    rate = 0.0

    # mp17w
    rate += np.exp(  1.98737)

    rate_eval.Al38__n_n_Si36__weak__mp17 = rate

@numba.njit()
def P41__n_S40__weak__wc12(rate_eval, tf):
    # P41 --> n + S40
    rate = 0.0

    # wc12w
    rate += np.exp(  0.732099)

    rate_eval.P41__n_S40__weak__wc12 = rate

@numba.njit()
def p_V40__Cr41(rate_eval, tf):
    # V40 + p --> Cr41
    rate = 0.0

    # ths8r
    rate += np.exp(  -36.1192 + -2.2168*tf.T9i + 40.938*tf.T913
                  + -8.73297*tf.T9 + 0.899164*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_V40__Cr41 = rate

@numba.njit()
def Mg33__n_Al32__weak__wc12(rate_eval, tf):
    # Mg33 --> n + Al32
    rate = 0.0

    # wc12w
    rate += np.exp(  0.0697796)

    rate_eval.Mg33__n_Al32__weak__wc12 = rate

@numba.njit()
def He4_K36__Sc40(rate_eval, tf):
    # K36 + He4 --> Sc40
    rate = 0.0

    # ths8r
    rate += np.exp(  46.095 + -73.6116*tf.T913i + -1.73961*tf.T913
                  + -0.20965*tf.T9 + -0.0277671*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K36__Sc40 = rate

@numba.njit()
def Mg37__n_n_Al35__weak__mp17(rate_eval, tf):
    # Mg37 --> n + n + Al35
    rate = 0.0

    # mp17w
    rate += np.exp(  2.549)

    rate_eval.Mg37__n_n_Al35__weak__mp17 = rate

@numba.njit()
def p_K39__Ca40(rate_eval, tf):
    # K39 + p --> Ca40
    rate = 0.0

    # lo18r
    rate += np.exp(  2761.38 + -5.22234*tf.T9i + 802.18*tf.T913i + -4010.27*tf.T913
                  + 1136.19*tf.lnT9)
    # lo18r
    rate += np.exp(  588.099 + -12.5647*tf.T9i + 641.844*tf.T913i + -1248.49*tf.T913
                  + 564.926*tf.lnT9)
    # lo18r
    rate += np.exp(  102.252 + -1.66508*tf.T9i + 41.1723*tf.T913i + -149.299*tf.T913
                  + 10.5229*tf.T9 + -0.68208*tf.T953 + 59.2367*tf.lnT9)

    rate_eval.p_K39__Ca40 = rate

@numba.njit()
def He4_Sc40__V44(rate_eval, tf):
    # Sc40 + He4 --> V44
    rate = 0.0

    # ths8r
    rate += np.exp(  48.2611 + -78.955*tf.T913i + -0.0421316*tf.T913
                  + -1.05779*tf.T9 + 0.0805568*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc40__V44 = rate

@numba.njit()
def Cr43__p_Ti42__weak__wc17(rate_eval, tf):
    # Cr43 --> p + Ti42
    rate = 0.0

    # wc17w
    rate += np.exp(  3.30523)

    rate_eval.Cr43__p_Ti42__weak__wc17 = rate

@numba.njit()
def Al24__p_Na23__weak__wc12(rate_eval, tf):
    # Al24 --> p + Na23
    rate = 0.0

    # wc12w
    rate += np.exp(  -12.1273)

    rate_eval.Al24__p_Na23__weak__wc12 = rate

@numba.njit()
def Mg33__n_n_Al31__weak__mp17(rate_eval, tf):
    # Mg33 --> n + n + Al31
    rate = 0.0

    # mp17w
    rate += np.exp(  -2.56928)

    rate_eval.Mg33__n_n_Al31__weak__mp17 = rate

@numba.njit()
def Na35__n_n_Mg33__weak__mp17(rate_eval, tf):
    # Na35 --> n + n + Mg33
    rate = 0.0

    # mp17w
    rate += np.exp(  3.61005)

    rate_eval.Na35__n_n_Mg33__weak__mp17 = rate

@numba.njit()
def p_Sc51__n_Ti51(rate_eval, tf):
    # Sc51 + p --> n + Ti51
    rate = 0.0

    # rath 
    rate += np.exp(  122.882 + -5.62973*tf.T9i + 209.648*tf.T913i + -342.092*tf.T913
                  + 19.0522*tf.T9 + -1.08324*tf.T953 + 171.297*tf.lnT9)

    rate_eval.p_Sc51__n_Ti51 = rate

@numba.njit()
def Na31__n_n_Mg29__weak__wc12(rate_eval, tf):
    # Na31 --> n + n + Mg29
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.0364)

    rate_eval.Na31__n_n_Mg29__weak__wc12 = rate

@numba.njit()
def Sc59__n_n_Ti57__weak__mp17(rate_eval, tf):
    # Sc59 --> n + n + Ti57
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.138357)

    rate_eval.Sc59__n_n_Ti57__weak__mp17 = rate

@numba.njit()
def He4_K47__n_Sc50(rate_eval, tf):
    # K47 + He4 --> n + Sc50
    rate = 0.0

    # rath 
    rate += np.exp(  -856.672 + 13.8624*tf.T9i + -1505.5*tf.T913i + 2467.7*tf.T913
                  + -147.579*tf.T9 + 8.47471*tf.T953 + -1157.43*tf.lnT9)

    rate_eval.He4_K47__n_Sc50 = rate

@numba.njit()
def F24__n_Ne23__weak__wc12(rate_eval, tf):
    # F24 --> n + Ne23
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.25512)

    rate_eval.F24__n_Ne23__weak__wc12 = rate

@numba.njit()
def Na30__n_n_Mg28__weak__wc12(rate_eval, tf):
    # Na30 --> n + n + Mg28
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.79537)

    rate_eval.Na30__n_n_Mg28__weak__wc12 = rate

@numba.njit()
def Mn69__n_Fe68__weak__mp17(rate_eval, tf):
    # Mn69 --> n + Fe68
    rate = 0.0

    # mp17w
    rate += np.exp(  2.09022)

    rate_eval.Mn69__n_Fe68__weak__mp17 = rate

@numba.njit()
def Ne32__n_n_Na30__weak__mp17(rate_eval, tf):
    # Ne32 --> n + n + Na30
    rate = 0.0

    # mp17w
    rate += np.exp(  1.37646)

    rate_eval.Ne32__n_n_Na30__weak__mp17 = rate

@numba.njit()
def He4_O14__Ne18(rate_eval, tf):
    # O14 + He4 --> Ne18
    rate = 0.0

    # wh87n
    rate += np.exp(  26.4429 + -39.38*tf.T913i + -0.0772187*tf.T913
                  + -0.635361*tf.T9 + 0.106236*tf.T953 + -0.666667*tf.lnT9)
    # wh87r
    rate += np.exp(  -4.69948 + -12.159*tf.T9i
                  + 5.0*tf.lnT9)
    # wh87r
    rate += np.exp(  3.52636 + -22.61*tf.T9i
                  + -1.5*tf.lnT9)
    # wh87r
    rate += np.exp(  -2.15417 + -11.73*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.He4_O14__Ne18 = rate

@numba.njit()
def Al22__p_p_Ne20__weak__wc12(rate_eval, tf):
    # Al22 --> p + p + Ne20
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.48058)

    rate_eval.Al22__p_p_Ne20__weak__wc12 = rate

@numba.njit()
def p_Ti50__V51(rate_eval, tf):
    # Ti50 + p --> V51
    rate = 0.0

    # ths8r
    rate += np.exp(  35.1261 + -33.2224*tf.T913i + 0.579407*tf.T913
                  + -0.949378*tf.T9 + 0.0567069*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ti50__V51 = rate

@numba.njit()
def Ne29__n_n_Na27__weak__wc12(rate_eval, tf):
    # Ne29 --> n + n + Na27
    rate = 0.0

    # wc12w
    rate += np.exp(  0.627739)

    rate_eval.Ne29__n_n_Na27__weak__wc12 = rate

@numba.njit()
def F30__n_n_Ne28__weak__mp17(rate_eval, tf):
    # F30 --> n + n + Ne28
    rate = 0.0

    # mp17w
    rate += np.exp(  5.50949)

    rate_eval.F30__n_n_Ne28__weak__mp17 = rate

@numba.njit()
def O27__n_n_F25__weak__mp17(rate_eval, tf):
    # O27 --> n + n + F25
    rate = 0.0

    # mp17w
    rate += np.exp(  3.95097)

    rate_eval.O27__n_n_F25__weak__mp17 = rate

@numba.njit()
def n_Ar36__Ar37(rate_eval, tf):
    # Ar36 + n --> Ar37
    rate = 0.0

    # ks03 
    rate += np.exp(  12.0149 + 0.0317044*tf.T9i + -3.1764*tf.T913i + 5.13191*tf.T913
                  + -0.00639688*tf.T9 + -0.0292833*tf.T953 + -2.74683*tf.lnT9)

    rate_eval.n_Ar36__Ar37 = rate

@numba.njit()
def O26__n_n_F24__weak__mp17(rate_eval, tf):
    # O26 --> n + n + F24
    rate = 0.0

    # mp17w
    rate += np.exp(  1.45895)

    rate_eval.O26__n_n_F24__weak__mp17 = rate

@numba.njit()
def p_Mn53__Fe54(rate_eval, tf):
    # Mn53 + p --> Fe54
    rate = 0.0

    # ths8r
    rate += np.exp(  35.586 + -36.1913*tf.T913i + 1.44056*tf.T913
                  + -1.50734*tf.T9 + 0.142124*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn53__Fe54 = rate

@numba.njit()
def C14__N14__weak__wc12(rate_eval, tf):
    # C14 --> N14
    rate = 0.0

    # wc12w
    rate += np.exp(  -26.2827)

    rate_eval.C14__N14__weak__wc12 = rate

@numba.njit()
def He4_Mg38__Si42(rate_eval, tf):
    # Mg38 + He4 --> Si42
    rate = 0.0

    # rath 
    rate += np.exp(  -19.3959 + -2.81916*tf.T9i + -15.2097*tf.T913i + 25.0728*tf.T913
                  + -5.24335*tf.T9 + 0.421579*tf.T953 + 4.90461*tf.lnT9)

    rate_eval.He4_Mg38__Si42 = rate

@numba.njit()
def O25__n_n_F23__weak__mp17(rate_eval, tf):
    # O25 --> n + n + F23
    rate = 0.0

    # mp17w
    rate += np.exp(  0.454468)

    rate_eval.O25__n_n_F23__weak__mp17 = rate

@numba.njit()
def B15__n_n_C13__weak__wc12(rate_eval, tf):
    # B15 --> n + n + C13
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.27578)

    rate_eval.B15__n_n_C13__weak__wc12 = rate

@numba.njit()
def n_Ar43__Ar44(rate_eval, tf):
    # Ar43 + n --> Ar44
    rate = 0.0

    # rath 
    rate += np.exp(  12.5467 + -0.0115428*tf.T9i + 0.124333*tf.T913i + 0.450934*tf.T913
                  + 0.0479574*tf.T9 + -0.0245619*tf.T953 + -0.366215*tf.lnT9)

    rate_eval.n_Ar43__Ar44 = rate

@numba.njit()
def He4_Si26__S30(rate_eval, tf):
    # Si26 + He4 --> S30
    rate = 0.0

    # ths8r
    rate += np.exp(  38.8701 + -59.3013*tf.T913i + 0.642868*tf.T913
                  + -0.958008*tf.T9 + 0.0715476*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si26__S30 = rate

@numba.njit()
def p_P33__S34(rate_eval, tf):
    # P33 + p --> S34
    rate = 0.0

    # rath 
    rate += np.exp(  173.854 + -3.84298*tf.T9i + 161.691*tf.T913i + -350.015*tf.T913
                  + 24.3597*tf.T9 + -1.56396*tf.T953 + 149.963*tf.lnT9)

    rate_eval.p_P33__S34 = rate

@numba.njit()
def Be16__n_n_Be14(rate_eval, tf):
    # Be16 --> n + n + Be14
    rate = 0.0

    # wc12s
    rate += np.exp(  15.0584)

    rate_eval.Be16__n_n_Be14 = rate

@numba.njit()
def Be14__n_n_B12__weak__wc12(rate_eval, tf):
    # Be14 --> n + n + B12
    rate = 0.0

    # wc12w
    rate += np.exp(  2.07533)

    rate_eval.Be14__n_n_B12__weak__wc12 = rate

@numba.njit()
def He4_Na20__p_Mg23(rate_eval, tf):
    # Na20 + He4 --> p + Mg23
    rate = 0.0

    # ths8r
    rate += np.exp(  44.5495 + -49.8396*tf.T913i + 0.681842*tf.T913
                  + -0.805773*tf.T9 + 0.0635389*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Na20__p_Mg23 = rate

@numba.njit()
def p_Al28__n_Si28(rate_eval, tf):
    # Al28 + p --> n + Si28
    rate = 0.0

    # rath 
    rate += np.exp(  72.7891 + -3.04903*tf.T9i + 105.263*tf.T913i + -174.93*tf.T913
                  + 9.08555*tf.T9 + -0.495072*tf.T953 + 89.3425*tf.lnT9)

    rate_eval.p_Al28__n_Si28 = rate

@numba.njit()
def Fe75__n_Co74__weak__mp17(rate_eval, tf):
    # Fe75 --> n + Co74
    rate = 0.0

    # mp17w
    rate += np.exp(  2.38718)

    rate_eval.Fe75__n_Co74__weak__mp17 = rate

@numba.njit()
def P43__n_S42__weak__wc12(rate_eval, tf):
    # P43 --> n + S42
    rate = 0.0

    # wc12w
    rate += np.exp(  2.94393)

    rate_eval.P43__n_S42__weak__wc12 = rate

@numba.njit()
def Fe73__n_Co72__weak__mp17(rate_eval, tf):
    # Fe73 --> n + Co72
    rate = 0.0

    # mp17w
    rate += np.exp(  1.16757)

    rate_eval.Fe73__n_Co72__weak__mp17 = rate

@numba.njit()
def Fe74__Co74__weak__mo03(rate_eval, tf):
    # Fe74 --> Co74
    rate = 0.0

    # mo03w
    rate += np.exp(  2.34797)

    rate_eval.Fe74__Co74__weak__mo03 = rate

@numba.njit()
def p_Cl41__n_Ar41(rate_eval, tf):
    # Cl41 + p --> n + Ar41
    rate = 0.0

    # rath 
    rate += np.exp(  102.505 + -4.42029*tf.T9i + 161.841*tf.T913i + -268.169*tf.T913
                  + 14.7453*tf.T9 + -0.823578*tf.T953 + 134.238*tf.lnT9)

    rate_eval.p_Cl41__n_Ar41 = rate

@numba.njit()
def n_Mg25__Mg26(rate_eval, tf):
    # Mg25 + n --> Mg26
    rate = 0.0

    # ks03 
    rate += np.exp(  38.34 + -0.0457591*tf.T9i + 9.392*tf.T913i + -36.6784*tf.T913
                  + 3.09567*tf.T9 + -0.223882*tf.T953 + 12.3852*tf.lnT9)

    rate_eval.n_Mg25__Mg26 = rate

@numba.njit()
def n_C11__C12(rate_eval, tf):
    # C11 + n --> C12
    rate = 0.0

    # bb92n
    rate += np.exp(  10.3672 + -0.0095137*tf.T9i + 1.18875e-10*tf.T913i + -3.10977e-10*tf.T913
                  + 2.0423e-11*tf.T9 + -6.59293e-13*tf.T953)
    # bb92r
    rate += np.exp(  13.8643 + -5.57951*tf.T9i + 1.38808e-09*tf.T913i + -3.66292e-09*tf.T913
                  + 2.41904e-10*tf.T9 + -7.82223e-12*tf.T953 + -1.5*tf.lnT9)
    # bb92r
    rate += np.exp(  8.10155 + -0.926514*tf.T9i + -5.21741e-12*tf.T913i + 2.32794e-11*tf.T913
                  + -2.03119e-12*tf.T9 + 7.09452e-14*tf.T953 + -1.5*tf.lnT9)

    rate_eval.n_C11__C12 = rate

@numba.njit()
def Fe70__n_Co69__weak__mp17(rate_eval, tf):
    # Fe70 --> n + Co69
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.0240226)

    rate_eval.Fe70__n_Co69__weak__mp17 = rate

@numba.njit()
def Mg35__n_Al34__weak__wc12(rate_eval, tf):
    # Mg35 --> n + Al34
    rate = 0.0

    # wc12w
    rate += np.exp(  1.63882)

    rate_eval.Mg35__n_Al34__weak__wc12 = rate

@numba.njit()
def n_Cl30__Cl31(rate_eval, tf):
    # Cl30 + n --> Cl31
    rate = 0.0

    # ths8r
    rate += np.exp(  10.553 + -0.282928*tf.T913
                  + 0.19149*tf.T9 + -0.0132922*tf.T953)

    rate_eval.n_Cl30__Cl31 = rate

@numba.njit()
def Fe69__n_Co68__weak__mp17(rate_eval, tf):
    # Fe69 --> n + Co68
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.818498)

    rate_eval.Fe69__n_Co68__weak__mp17 = rate

@numba.njit()
def He4_Fe74__Ni78(rate_eval, tf):
    # Fe74 + He4 --> Ni78
    rate = 0.0

    # rath 
    rate += np.exp(  -1050.01 + 26.5551*tf.T9i + -2561.07*tf.T913i + 3736.66*tf.T913
                  + -202.632*tf.T9 + 10.8243*tf.T953 + -1862.74*tf.lnT9)

    rate_eval.He4_Fe74__Ni78 = rate

@numba.njit()
def p_K55__Ca56(rate_eval, tf):
    # K55 + p --> Ca56
    rate = 0.0

    # rath 
    rate += np.exp(  123.907 + -5.53578*tf.T9i + 213.821*tf.T913i + -356.989*tf.T913
                  + 20.1315*tf.T9 + -1.13793*tf.T953 + 175.783*tf.lnT9)

    rate_eval.p_K55__Ca56 = rate

@numba.njit()
def p_K47__n_Ca47(rate_eval, tf):
    # K47 + p --> n + Ca47
    rate = 0.0

    # rath 
    rate += np.exp(  112.827 + -5.06884*tf.T9i + 187.331*tf.T913i + -307.027*tf.T913
                  + 16.9954*tf.T9 + -0.956993*tf.T953 + 153.81*tf.lnT9)

    rate_eval.p_K47__n_Ca47 = rate

@numba.njit()
def p_Ca50__n_Sc50(rate_eval, tf):
    # Ca50 + p --> n + Sc50
    rate = 0.0

    # rath 
    rate += np.exp(  116.916 + -5.38725*tf.T9i + 199.398*tf.T913i + -324.367*tf.T913
                  + 17.9133*tf.T9 + -1.00773*tf.T953 + 162.87*tf.lnT9)

    rate_eval.p_Ca50__n_Sc50 = rate

@numba.njit()
def He4_V44__p_Cr47(rate_eval, tf):
    # V44 + He4 --> p + Cr47
    rate = 0.0

    # ths8r
    rate += np.exp(  60.0879 + -84.1242*tf.T913i + -1.41443*tf.T913
                  + -0.479017*tf.T9 + 0.014919*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V44__p_Cr47 = rate

@numba.njit()
def n_S35__S36(rate_eval, tf):
    # S35 + n --> S36
    rate = 0.0

    # ths8r
    rate += np.exp(  15.0579 + -2.51293*tf.T913
                  + 0.668068*tf.T9 + -0.0786735*tf.T953)

    rate_eval.n_S35__S36 = rate

@numba.njit()
def He4_Mg36__n_Si39(rate_eval, tf):
    # Mg36 + He4 --> n + Si39
    rate = 0.0

    # rath 
    rate += np.exp(  88.3976 + -3.73414*tf.T9i + 92.1979*tf.T913i + -192.028*tf.T913
                  + 9.32024*tf.T9 + -0.486149*tf.T953 + 99.333*tf.lnT9)

    rate_eval.He4_Mg36__n_Si39 = rate

@numba.njit()
def n_Ca48__Ca49(rate_eval, tf):
    # Ca48 + n --> Ca49
    rate = 0.0

    # ks03 
    rate += np.exp(  18.5919 + -0.0358582*tf.T9i + 4.02743*tf.T913i + -11.8316*tf.T913
                  + 1.05086*tf.T9 + -0.0717238*tf.T953 + 4.24851*tf.lnT9)

    rate_eval.n_Ca48__Ca49 = rate

@numba.njit()
def He4_B11__n_N14(rate_eval, tf):
    # B11 + He4 --> n + N14
    rate = 0.0

    # cf88n
    rate += np.exp(  29.5726 + -28.234*tf.T913i + -0.325987*tf.T913
                  + 30.135*tf.T9 + -78.4165*tf.T953 + -0.666667*tf.lnT9)
    # cf88r
    rate += np.exp(  15.3084 + -8.596*tf.T9i
                  + 0.6*tf.lnT9)
    # cf88r
    rate += np.exp(  7.44425 + -5.178*tf.T9i
                  + -1.5*tf.lnT9)
    # cf88r
    rate += np.exp(  0.582216 + -2.827*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.He4_B11__n_N14 = rate

@numba.njit()
def He4_Mn58__Co62(rate_eval, tf):
    # Mn58 + He4 --> Co62
    rate = 0.0

    # rath 
    rate += np.exp(  -1111.84 + 23.1816*tf.T9i + -2304.52*tf.T913i + 3548.25*tf.T913
                  + -200.935*tf.T9 + 11.0892*tf.T953 + -1722.52*tf.lnT9)

    rate_eval.He4_Mn58__Co62 = rate

@numba.njit()
def He4_Si32__S36(rate_eval, tf):
    # Si32 + He4 --> S36
    rate = 0.0

    # rath 
    rate += np.exp(  -152.93 + -0.462221*tf.T9i + -232.306*tf.T913i + 393.438*tf.T913
                  + -25.2071*tf.T9 + 1.4457*tf.T953 + -171.471*tf.lnT9)

    rate_eval.He4_Si32__S36 = rate

@numba.njit()
def p_V45__Cr46(rate_eval, tf):
    # V45 + p --> Cr46
    rate = 0.0

    # ths8r
    rate += np.exp(  35.927 + -34.1967*tf.T913i + -1.70253*tf.T913
                  + -2.38375*tf.T9 + 0.33421*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V45__Cr46 = rate

@numba.njit()
def V60__n_Cr59__weak__mp17(rate_eval, tf):
    # V60 --> n + Cr59
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.337525)

    rate_eval.V60__n_Cr59__weak__mp17 = rate

@numba.njit()
def He4_S29__Ar33(rate_eval, tf):
    # S29 + He4 --> Ar33
    rate = 0.0

    # ths8r
    rate += np.exp(  41.2275 + -65.124*tf.T913i + -0.021112*tf.T913
                  + -0.799069*tf.T9 + 0.0579505*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S29__Ar33 = rate

@numba.njit()
def Sc44__Ca44__weak__wc12(rate_eval, tf):
    # Sc44 --> Ca44
    rate = 0.0

    # wc12w
    rate += np.exp(  -9.93453)

    rate_eval.Sc44__Ca44__weak__wc12 = rate

@numba.njit()
def p_p__d__weak__bet_pos_(rate_eval, tf):
    # p + p --> d
    rate = 0.0

    # bet+w
    rate += np.exp(  -34.7863 + -3.51193*tf.T913i + 3.10086*tf.T913
                  + -0.198314*tf.T9 + 0.0126251*tf.T953 + -1.02517*tf.lnT9)

    rate_eval.p_p__d__weak__bet_pos_ = rate

@numba.njit()
def p_p__d__weak__electron_capture(rate_eval, tf):
    # p + p --> d
    rate = 0.0

    #   ecw
    rate += np.exp(  -43.6499 + -0.00246064*tf.T9i + -2.7507*tf.T913i + -0.424877*tf.T913
                  + 0.015987*tf.T9 + -0.000690875*tf.T953 + -0.207625*tf.lnT9)

    rate_eval.p_p__d__weak__electron_capture = rate

@numba.njit()
def Ti57__V57__weak__wc12(rate_eval, tf):
    # Ti57 --> V57
    rate = 0.0

    # wc12w
    rate += np.exp(  1.95627)

    rate_eval.Ti57__V57__weak__wc12 = rate

@numba.njit()
def p_Cl38__n_Ar38(rate_eval, tf):
    # Cl38 + p --> n + Ar38
    rate = 0.0

    # rath 
    rate += np.exp(  100.633 + -4.26684*tf.T9i + 155.297*tf.T913i + -259.064*tf.T913
                  + 14.1608*tf.T9 + -0.789512*tf.T953 + 129.598*tf.lnT9)

    rate_eval.p_Cl38__n_Ar38 = rate

@numba.njit()
def He4_F30__Na34(rate_eval, tf):
    # F30 + He4 --> Na34
    rate = 0.0

    # rpsmr
    rate += np.exp(  53.862 + -2.6743*tf.T9i + 55.4794*tf.T913i + -124.467*tf.T913
                  + 5.57609*tf.T9 + -0.269925*tf.T953 + 65.8403*tf.lnT9)

    rate_eval.He4_F30__Na34 = rate

@numba.njit()
def He4_Fe63__Ni67(rate_eval, tf):
    # Fe63 + He4 --> Ni67
    rate = 0.0

    # rath 
    rate += np.exp(  -1166.73 + 24.3913*tf.T9i + -2425.54*tf.T913i + 3730.34*tf.T913
                  + -211.349*tf.T9 + 11.7334*tf.T953 + -1812.04*tf.lnT9)

    rate_eval.He4_Fe63__Ni67 = rate

@numba.njit()
def n_Cl31__Cl32(rate_eval, tf):
    # Cl31 + n --> Cl32
    rate = 0.0

    # ths8r
    rate += np.exp(  9.97368 + 0.499463*tf.T913
                  + -0.0171976*tf.T9 + 0.00471987*tf.T953)

    rate_eval.n_Cl31__Cl32 = rate

@numba.njit()
def p_Al23__Si24(rate_eval, tf):
    # Al23 + p --> Si24
    rate = 0.0

    # il10n
    rate += np.exp(  20.0403 + -23.5155*tf.T913i
                  + -5.0*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  -50.6937 + -1.97147*tf.T9i + 15.7029*tf.T913i + 38.841*tf.T913
                  + -4.61856*tf.T9 + 0.272968*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -0.518114 + -1.63122*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Al23__Si24 = rate

@numba.njit()
def n_Cl48__Cl49(rate_eval, tf):
    # Cl48 + n --> Cl49
    rate = 0.0

    # rath 
    rate += np.exp(  22.2591 + 0.0190747*tf.T9i + 0.522734*tf.T913i + -13.2979*tf.T913
                  + 1.16767*tf.T9 + -0.0828858*tf.T953 + 2.70019*tf.lnT9)

    rate_eval.n_Cl48__Cl49 = rate

@numba.njit()
def V65__n_Cr64__weak__mp17(rate_eval, tf):
    # V65 --> n + Cr64
    rate = 0.0

    # mp17w
    rate += np.exp(  3.29309)

    rate_eval.V65__n_Cr64__weak__mp17 = rate

@numba.njit()
def He4_F20__Na24(rate_eval, tf):
    # F20 + He4 --> Na24
    rate = 0.0

    # rpsmr
    rate += np.exp(  41.5328 + -2.01462*tf.T9i + 28.3636*tf.T913i + -80.775*tf.T913
                  + 2.71447*tf.T9 + -0.0909008*tf.T953 + 45.3782*tf.lnT9)

    rate_eval.He4_F20__Na24 = rate

@numba.njit()
def He4_K59__n_Sc62(rate_eval, tf):
    # K59 + He4 --> n + Sc62
    rate = 0.0

    # rath 
    rate += np.exp(  -449.145 + 2.18683*tf.T9i + -620.449*tf.T913i + 1117.92*tf.T913
                  + -73.7881*tf.T9 + 4.4943*tf.T953 + -489.576*tf.lnT9)

    rate_eval.He4_K59__n_Sc62 = rate

@numba.njit()
def He4_S47__n_Ar50(rate_eval, tf):
    # S47 + He4 --> n + Ar50
    rate = 0.0

    # rath 
    rate += np.exp(  -359.869 + 1.8994*tf.T9i + -511.669*tf.T913i + 912.596*tf.T913
                  + -60.5284*tf.T9 + 3.69681*tf.T953 + -399.303*tf.lnT9)

    rate_eval.He4_S47__n_Ar50 = rate

@numba.njit()
def p_Al41__Si42(rate_eval, tf):
    # Al41 + p --> Si42
    rate = 0.0

    # rath 
    rate += np.exp(  76.1218 + -3.68126*tf.T9i + 133.551*tf.T913i + -218.815*tf.T913
                  + 11.806*tf.T9 + -0.649373*tf.T953 + 110.244*tf.lnT9)

    rate_eval.p_Al41__Si42 = rate

@numba.njit()
def K48__n_Ca47__weak__wc12(rate_eval, tf):
    # K48 --> n + Ca47
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.75758)

    rate_eval.K48__n_Ca47__weak__wc12 = rate

@numba.njit()
def n_Mg19__p_Na19(rate_eval, tf):
    # Mg19 + n --> p + Na19
    rate = 0.0

    # ths8r
    rate += np.exp(  18.6682 + 1.26547*tf.T913
                  + -0.0558898*tf.T9 + -0.000405301*tf.T953)

    rate_eval.n_Mg19__p_Na19 = rate

@numba.njit()
def p_Cl38__Ar39(rate_eval, tf):
    # Cl38 + p --> Ar39
    rate = 0.0

    # rath 
    rate += np.exp(  91.4874 + -4.23956*tf.T9i + 152.452*tf.T913i + -253.385*tf.T913
                  + 13.739*tf.T9 + -0.768182*tf.T953 + 126.994*tf.lnT9)

    rate_eval.p_Cl38__Ar39 = rate

@numba.njit()
def p_Mg32__n_Al32(rate_eval, tf):
    # Mg32 + p --> n + Al32
    rate = 0.0

    # rath 
    rate += np.exp(  77.5139 + -3.09813*tf.T9i + 109.779*tf.T913i + -183.987*tf.T913
                  + 9.90143*tf.T9 + -0.545357*tf.T953 + 92.5681*tf.lnT9)

    rate_eval.p_Mg32__n_Al32 = rate

@numba.njit()
def He4_Cl28__K32(rate_eval, tf):
    # Cl28 + He4 --> K32
    rate = 0.0

    # ths8r
    rate += np.exp(  39.95 + -67.7156*tf.T913i + -0.446636*tf.T913
                  + -0.40884*tf.T9 + 0.00635512*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl28__K32 = rate

@numba.njit()
def Fe48__p_Cr47__weak__wc12(rate_eval, tf):
    # Fe48 --> p + Cr47
    rate = 0.0

    # wc12w
    rate += np.exp(  0.889084)

    rate_eval.Fe48__p_Cr47__weak__wc12 = rate

@numba.njit()
def p_Na27__Mg28(rate_eval, tf):
    # Na27 + p --> Mg28
    rate = 0.0

    # rath 
    rate += np.exp(  60.0313 + -2.68806*tf.T9i + 93.3597*tf.T913i + -158.208*tf.T913
                  + 8.43184*tf.T9 + -0.44949*tf.T953 + 79.8757*tf.lnT9)

    rate_eval.p_Na27__Mg28 = rate

@numba.njit()
def p_P46__n_S46(rate_eval, tf):
    # P46 + p --> n + S46
    rate = 0.0

    # rath 
    rate += np.exp(  104.047 + -4.27677*tf.T9i + 158.462*tf.T913i + -264.114*tf.T913
                  + 14.6493*tf.T9 + -0.821394*tf.T953 + 131.151*tf.lnT9)

    rate_eval.p_P46__n_S46 = rate

@numba.njit()
def p_P41__n_S41(rate_eval, tf):
    # P41 + p --> n + S41
    rate = 0.0

    # rath 
    rate += np.exp(  94.7201 + -4.05636*tf.T9i + 147.792*tf.T913i + -243.863*tf.T913
                  + 13.3558*tf.T9 + -0.743847*tf.T953 + 122.354*tf.lnT9)

    rate_eval.p_P41__n_S41 = rate

@numba.njit()
def Al43__n_Si42__weak__mp17(rate_eval, tf):
    # Al43 --> n + Si42
    rate = 0.0

    # mp17w
    rate += np.exp(  5.85815)

    rate_eval.Al43__n_Si42__weak__mp17 = rate

@numba.njit()
def Si23__Al23__weak__wc12(rate_eval, tf):
    # Si23 --> Al23
    rate = 0.0

    # wc12w
    rate += np.exp(  1.42603)

    rate_eval.Si23__Al23__weak__wc12 = rate

@numba.njit()
def Fe46__p_Cr45__weak__wc12(rate_eval, tf):
    # Fe46 --> p + Cr45
    rate = 0.0

    # wc12w
    rate += np.exp(  3.73677)

    rate_eval.Fe46__p_Cr45__weak__wc12 = rate

@numba.njit()
def p_P39__n_S39(rate_eval, tf):
    # P39 + p --> n + S39
    rate = 0.0

    # rath 
    rate += np.exp(  93.3945 + -3.96243*tf.T9i + 143.788*tf.T913i + -238.445*tf.T913
                  + 13.0695*tf.T9 + -0.728563*tf.T953 + 119.538*tf.lnT9)

    rate_eval.p_P39__n_S39 = rate

@numba.njit()
def p_Cr55__Mn56(rate_eval, tf):
    # Cr55 + p --> Mn56
    rate = 0.0

    # rath 
    rate += np.exp(  127.801 + -6.35771*tf.T9i + 237.169*tf.T913i + -384.755*tf.T913
                  + 21.4843*tf.T9 + -1.24375*tf.T953 + 192.725*tf.lnT9)

    rate_eval.p_Cr55__Mn56 = rate

@numba.njit()
def n_Cl38__Cl39(rate_eval, tf):
    # Cl38 + n --> Cl39
    rate = 0.0

    # rath 
    rate += np.exp(  8.16108 + 0.00308986*tf.T9i + -2.10317*tf.T913i + 8.96391*tf.T913
                  + -1.03255*tf.T9 + 0.0781774*tf.T953 + -3.07748*tf.lnT9)

    rate_eval.n_Cl38__Cl39 = rate

@numba.njit()
def Ne18__F18__weak__wc12(rate_eval, tf):
    # Ne18 --> F18
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.879336)

    rate_eval.Ne18__F18__weak__wc12 = rate

@numba.njit()
def Fe45__p_Cr44__weak__wc17(rate_eval, tf):
    # Fe45 --> p + Cr44
    rate = 0.0

    # wc17w
    rate += np.exp(  4.24393)

    rate_eval.Fe45__p_Cr44__weak__wc17 = rate

@numba.njit()
def He4_Mg28__n_Si31(rate_eval, tf):
    # Mg28 + He4 --> n + Si31
    rate = 0.0

    # rath 
    rate += np.exp(  77.2311 + -3.15586*tf.T9i + 67.3601*tf.T913i + -155.207*tf.T913
                  + 7.29762*tf.T9 + -0.373971*tf.T953 + 81.0946*tf.lnT9)

    rate_eval.He4_Mg28__n_Si31 = rate

@numba.njit()
def Mn73__n_Fe72__weak__mp17(rate_eval, tf):
    # Mn73 --> n + Fe72
    rate = 0.0

    # mp17w
    rate += np.exp(  4.44838)

    rate_eval.Mn73__n_Fe72__weak__mp17 = rate

@numba.njit()
def Mn72__n_Fe71__weak__mp17(rate_eval, tf):
    # Mn72 --> n + Fe71
    rate = 0.0

    # mp17w
    rate += np.exp(  3.30684)

    rate_eval.Mn72__n_Fe71__weak__mp17 = rate

@numba.njit()
def p_Mn63__He4_Cr60(rate_eval, tf):
    # Mn63 + p --> He4 + Cr60
    rate = 0.0

    # rath 
    rate += np.exp(  140.404 + -7.08572*tf.T9i + 275.977*tf.T913i + -444.553*tf.T913
                  + 24.3992*tf.T9 + -1.28431*tf.T953 + 223.464*tf.lnT9)

    rate_eval.p_Mn63__He4_Cr60 = rate

@numba.njit()
def n_Al23__p_Mg23(rate_eval, tf):
    # Al23 + n --> p + Mg23
    rate = 0.0

    # ths8r
    rate += np.exp(  18.2162 + 2.53022*tf.T913
                  + -0.402992*tf.T9 + 0.0309763*tf.T953)

    rate_eval.n_Al23__p_Mg23 = rate

@numba.njit()
def Ar52__K52__weak__mo03(rate_eval, tf):
    # Ar52 --> K52
    rate = 0.0

    # mo03w
    rate += np.exp(  3.37384)

    rate_eval.Ar52__K52__weak__mo03 = rate

@numba.njit()
def Mn65__n_Fe64__weak__mp17(rate_eval, tf):
    # Mn65 --> n + Fe64
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.885307)

    rate_eval.Mn65__n_Fe64__weak__mp17 = rate

@numba.njit()
def Fe74__n_Co73__weak__mp17(rate_eval, tf):
    # Fe74 --> n + Co73
    rate = 0.0

    # mp17w
    rate += np.exp(  1.45258)

    rate_eval.Fe74__n_Co73__weak__mp17 = rate

@numba.njit()
def n_P40__P41(rate_eval, tf):
    # P40 + n --> P41
    rate = 0.0

    # rath 
    rate += np.exp(  13.9939 + -0.0347651*tf.T9i + 2.81924*tf.T913i + -7.10447*tf.T913
                  + 0.451043*tf.T9 + -0.0323533*tf.T953 + 2.43555*tf.lnT9)

    rate_eval.n_P40__P41 = rate

@numba.njit()
def S26__P26__weak__bqa_pos_(rate_eval, tf):
    # S26 --> P26
    rate = 0.0

    # bqa+w
    rate += np.exp(  3.00319)

    rate_eval.S26__P26__weak__bqa_pos_ = rate

@numba.njit()
def n_Al24__p_Mg24(rate_eval, tf):
    # Al24 + n --> p + Mg24
    rate = 0.0

    # ths8r
    rate += np.exp(  18.1035 + 2.51366*tf.T913
                  + -0.398291*tf.T9 + 0.0295976*tf.T953)

    rate_eval.n_Al24__p_Mg24 = rate

@numba.njit()
def He4_Cr68__n_Fe71(rate_eval, tf):
    # Cr68 + He4 --> n + Fe71
    rate = 0.0

    # rath 
    rate += np.exp(  -1213.67 + 19.2274*tf.T9i + -2085.54*tf.T913i + 3447.53*tf.T913
                  + -206.084*tf.T9 + 11.8363*tf.T953 + -1616.4*tf.lnT9)

    rate_eval.He4_Cr68__n_Fe71 = rate

@numba.njit()
def He4_Fe66__Ni70(rate_eval, tf):
    # Fe66 + He4 --> Ni70
    rate = 0.0

    # rath 
    rate += np.exp(  -984.896 + 25.0891*tf.T9i + -2423.24*tf.T913i + 3526.23*tf.T913
                  + -191.096*tf.T9 + 10.1847*tf.T953 + -1758.62*tf.lnT9)

    rate_eval.He4_Fe66__Ni70 = rate

@numba.njit()
def p_Ca50__Sc51(rate_eval, tf):
    # Ca50 + p --> Sc51
    rate = 0.0

    # rath 
    rate += np.exp(  105.794 + -5.37207*tf.T9i + 197.625*tf.T913i + -320.222*tf.T913
                  + 17.5567*tf.T9 + -0.983143*tf.T953 + 161.112*tf.lnT9)

    rate_eval.p_Ca50__Sc51 = rate

@numba.njit()
def He4_Si29__S33(rate_eval, tf):
    # Si29 + He4 --> S33
    rate = 0.0

    # ths8r
    rate += np.exp(  49.5657 + -59.5755*tf.T913i + 1.06274*tf.T913
                  + -3.07529*tf.T9 + 0.372011*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si29__S33 = rate

@numba.njit()
def p_Mn64__Fe65(rate_eval, tf):
    # Mn64 + p --> Fe65
    rate = 0.0

    # rath 
    rate += np.exp(  146.867 + -7.00604*tf.T9i + 266.608*tf.T913i + -436.63*tf.T913
                  + 24.5377*tf.T9 + -1.40296*tf.T953 + 216.374*tf.lnT9)

    rate_eval.p_Mn64__Fe65 = rate

@numba.njit()
def p_V44__Cr45(rate_eval, tf):
    # V44 + p --> Cr45
    rate = 0.0

    # ths8r
    rate += np.exp(  37.5012 + -34.1911*tf.T913i + -0.0426412*tf.T913
                  + -2.96145*tf.T9 + 0.385581*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V44__Cr45 = rate

@numba.njit()
def Li11__Be11__weak__wc12(rate_eval, tf):
    # Li11 --> Be11
    rate = 0.0

    # wc12w
    rate += np.exp(  2.32215)

    rate_eval.Li11__Be11__weak__wc12 = rate

@numba.njit()
def Ca61__n_Sc60__weak__mp17(rate_eval, tf):
    # Ca61 --> n + Sc60
    rate = 0.0

    # mp17w
    rate += np.exp(  5.12251)

    rate_eval.Ca61__n_Sc60__weak__mp17 = rate

@numba.njit()
def n_Fe60__Fe61(rate_eval, tf):
    # Fe60 + n --> Fe61
    rate = 0.0

    # ks03 
    rate += np.exp(  22.9192 + -0.0645698*tf.T9i + 6.56814*tf.T913i + -17.4936*tf.T913
                  + 1.7125*tf.T9 + -0.166243*tf.T953 + 6.44679*tf.lnT9)

    rate_eval.n_Fe60__Fe61 = rate

@numba.njit()
def n_Si23__He4_Mg20(rate_eval, tf):
    # Si23 + n --> He4 + Mg20
    rate = 0.0

    # ths8r
    rate += np.exp(  14.7148 + 2.32067*tf.T913
                  + -0.363272*tf.T9 + 0.0261485*tf.T953)

    rate_eval.n_Si23__He4_Mg20 = rate

@numba.njit()
def Ti61__V61__weak__wc17(rate_eval, tf):
    # Ti61 --> V61
    rate = 0.0

    # wc17w
    rate += np.exp(  3.81299)

    rate_eval.Ti61__V61__weak__wc17 = rate

@numba.njit()
def n_Cl41__Cl42(rate_eval, tf):
    # Cl41 + n --> Cl42
    rate = 0.0

    # rath 
    rate += np.exp(  19.9592 + -0.0709336*tf.T9i + 6.85772*tf.T913i + -14.5057*tf.T913
                  + 0.785318*tf.T9 + -0.0531943*tf.T953 + 6.17292*tf.lnT9)

    rate_eval.n_Cl41__Cl42 = rate

@numba.njit()
def Al23__Mg23__weak__wc12(rate_eval, tf):
    # Al23 --> Mg23
    rate = 0.0

    # wc12w
    rate += np.exp(  0.428648)

    rate_eval.Al23__Mg23__weak__wc12 = rate

@numba.njit()
def p_N14__n_O14(rate_eval, tf):
    # N14 + p --> n + O14
    rate = 0.0

    # nacr 
    rate += np.exp(  11.3432 + -68.7567*tf.T9i + 5.48024*tf.T913
                  + -0.764072*tf.T9 + 0.0587804*tf.T953)

    rate_eval.p_N14__n_O14 = rate

@numba.njit()
def p_Na36__He4_Ne33(rate_eval, tf):
    # Na36 + p --> He4 + Ne33
    rate = 0.0

    # rath 
    rate += np.exp(  70.4873 + -3.11245*tf.T9i + 112.892*tf.T913i + -189.079*tf.T913
                  + 10.4071*tf.T9 + -0.570065*tf.T953 + 94.4863*tf.lnT9)

    rate_eval.p_Na36__He4_Ne33 = rate

@numba.njit()
def He4_O18__n_Ne21(rate_eval, tf):
    # O18 + He4 --> n + Ne21
    rate = 0.0

    # nacr 
    rate += np.exp(  2.51575 + -8.41969*tf.T9i + 6.51299*tf.T913
                  + -0.334277*tf.T9 + 2.0*tf.lnT9)
    # nacr 
    rate += np.exp(  1.3415 + -15.444*tf.T9i + 11.656*tf.T913
                  + -1.24869*tf.T9 + 1.0*tf.lnT9)
    # nacrn
    rate += np.exp(  2.82796 + -8.085*tf.T9i)

    rate_eval.He4_O18__n_Ne21 = rate

@numba.njit()
def He4_Be9__n_C12(rate_eval, tf):
    # Be9 + He4 --> n + C12
    rate = 0.0

    # cf88r
    rate += np.exp(  11.744 + -4.179*tf.T9i
                  + -1.5*tf.lnT9)
    # cf88r
    rate += np.exp(  -1.48281 + -1.834*tf.T9i
                  + -1.5*tf.lnT9)
    # cf88r
    rate += np.exp(  -9.51959 + -1.184*tf.T9i
                  + -1.5*tf.lnT9)
    # cf88n
    rate += np.exp(  31.464 + -23.87*tf.T913i + 0.566698*tf.T913
                  + 44.0957*tf.T9 + -314.232*tf.T953 + -0.666667*tf.lnT9)
    # cf88r
    rate += np.exp(  19.2962 + -12.732*tf.T9i)

    rate_eval.He4_Be9__n_C12 = rate

@numba.njit()
def p_Cl34__Ar35(rate_eval, tf):
    # Cl34 + p --> Ar35
    rate = 0.0

    # ths8r
    rate += np.exp(  34.946 + -27.8896*tf.T913i + -0.491144*tf.T913
                  + -2.47595*tf.T9 + 0.34035*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cl34__Ar35 = rate

@numba.njit()
def K55__n_n_Ca53__weak__mp17(rate_eval, tf):
    # K55 --> n + n + Ca53
    rate = 0.0

    # mp17w
    rate += np.exp(  2.2618)

    rate_eval.K55__n_n_Ca53__weak__mp17 = rate

@numba.njit()
def He4_Fe61__Ni65(rate_eval, tf):
    # Fe61 + He4 --> Ni65
    rate = 0.0

    # rath 
    rate += np.exp(  -1151.54 + 24.098*tf.T9i + -2396.07*tf.T913i + 3684.45*tf.T913
                  + -208.563*tf.T9 + 11.5032*tf.T953 + -1789.58*tf.lnT9)

    rate_eval.He4_Fe61__Ni65 = rate

@numba.njit()
def p_Mg37__He4_Na34(rate_eval, tf):
    # Mg37 + p --> He4 + Na34
    rate = 0.0

    # rath 
    rate += np.exp(  56.9293 + -3.31989*tf.T9i + 118.554*tf.T913i + -184.516*tf.T913
                  + 9.36827*tf.T9 + -0.476261*tf.T953 + 97.2392*tf.lnT9)

    rate_eval.p_Mg37__He4_Na34 = rate

@numba.njit()
def p_Na34__n_Mg34(rate_eval, tf):
    # Na34 + p --> n + Mg34
    rate = 0.0

    # rath 
    rate += np.exp(  79.5298 + -3.02672*tf.T9i + 109.392*tf.T913i + -185.038*tf.T913
                  + 10.1069*tf.T9 + -0.558679*tf.T953 + 92.2178*tf.lnT9)

    rate_eval.p_Na34__n_Mg34 = rate

@numba.njit()
def Mg39__n_n_Al37__weak__mp17(rate_eval, tf):
    # Mg39 --> n + n + Al37
    rate = 0.0

    # mp17w
    rate += np.exp(  4.12831)

    rate_eval.Mg39__n_n_Al37__weak__mp17 = rate

@numba.njit()
def n_Mg22__p_Na22(rate_eval, tf):
    # Mg22 + n --> p + Na22
    rate = 0.0

    # ths8r
    rate += np.exp(  17.8512 + 2.67784*tf.T913
                  + -0.418718*tf.T9 + 0.031411*tf.T953)

    rate_eval.n_Mg22__p_Na22 = rate

@numba.njit()
def He4_Ca35__p_Sc38(rate_eval, tf):
    # Ca35 + He4 --> p + Sc38
    rate = 0.0

    # ths8r
    rate += np.exp(  55.7921 + -76.1016*tf.T913i + -0.977608*tf.T913
                  + -0.399735*tf.T9 + 0.00566881*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca35__p_Sc38 = rate

@numba.njit()
def Ne32__Na32__weak__wc17(rate_eval, tf):
    # Ne32 --> Na32
    rate = 0.0

    # wc17w
    rate += np.exp(  4.4675)

    rate_eval.Ne32__Na32__weak__wc17 = rate

@numba.njit()
def He4_Ar54__Ca58(rate_eval, tf):
    # Ar54 + He4 --> Ca58
    rate = 0.0

    # rath 
    rate += np.exp(  -912.66 + 14.2819*tf.T9i + -1553.94*tf.T913i + 2568.39*tf.T913
                  + -154.333*tf.T9 + 8.88952*tf.T953 + -1201.6*tf.lnT9)

    rate_eval.He4_Ar54__Ca58 = rate

@numba.njit()
def He4_V59__Mn63(rate_eval, tf):
    # V59 + He4 --> Mn63
    rate = 0.0

    # rath 
    rate += np.exp(  -1051.35 + 21.9262*tf.T9i + -2180.69*tf.T913i + 3355.65*tf.T913
                  + -189.926*tf.T9 + 10.4689*tf.T953 + -1629.0*tf.lnT9)

    rate_eval.He4_V59__Mn63 = rate

@numba.njit()
def p_K58__Ca59(rate_eval, tf):
    # K58 + p --> Ca59
    rate = 0.0

    # rath 
    rate += np.exp(  121.933 + -5.5596*tf.T9i + 209.958*tf.T913i + -350.944*tf.T913
                  + 20.1898*tf.T9 + -1.16673*tf.T953 + 172.209*tf.lnT9)

    rate_eval.p_K58__Ca59 = rate

@numba.njit()
def Si32__P32__weak__wc12(rate_eval, tf):
    # Si32 --> P32
    rate = 0.0

    # wc12w
    rate += np.exp(  -22.6646)

    rate_eval.Si32__P32__weak__wc12 = rate

@numba.njit()
def p_Fe53__Co54(rate_eval, tf):
    # Fe53 + p --> Co54
    rate = 0.0

    # ths8r
    rate += np.exp(  36.8739 + -37.1501*tf.T913i + 0.211459*tf.T913
                  + -2.79493*tf.T9 + 0.358657*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Fe53__Co54 = rate

@numba.njit()
def He4_P41__Cl45(rate_eval, tf):
    # P41 + He4 --> Cl45
    rate = 0.0

    # rath 
    rate += np.exp(  -331.482 + 1.77158*tf.T9i + -465.811*tf.T913i + 824.257*tf.T913
                  + -54.7268*tf.T9 + 3.34274*tf.T953 + -360.7*tf.lnT9)

    rate_eval.He4_P41__Cl45 = rate

@numba.njit()
def He4_P46__n_Cl49(rate_eval, tf):
    # P46 + He4 --> n + Cl49
    rate = 0.0

    # rath 
    rate += np.exp(  -17.6699 + -3.55056*tf.T9i + -20.1355*tf.T913i + 35.6771*tf.T913
                  + -5.98814*tf.T9 + 0.459161*tf.T953 + 2.0777*tf.lnT9)

    rate_eval.He4_P46__n_Cl49 = rate

@numba.njit()
def He4_K53__Sc57(rate_eval, tf):
    # K53 + He4 --> Sc57
    rate = 0.0

    # rath 
    rate += np.exp(  -924.529 + 14.6923*tf.T9i + -1595.26*tf.T913i + 2623.54*tf.T913
                  + -156.928*tf.T9 + 9.0065*tf.T953 + -1230.43*tf.lnT9)

    rate_eval.He4_K53__Sc57 = rate

@numba.njit()
def Mn46__p_V45__weak__wc12(rate_eval, tf):
    # Mn46 --> p + V45
    rate = 0.0

    # wc12w
    rate += np.exp(  2.39006)

    rate_eval.Mn46__p_V45__weak__wc12 = rate

@numba.njit()
def K57__n_n_Ca55__weak__mp17(rate_eval, tf):
    # K57 --> n + n + Ca55
    rate = 0.0

    # mp17w
    rate += np.exp(  4.16904)

    rate_eval.K57__n_n_Ca55__weak__mp17 = rate

@numba.njit()
def He4_S34__Ar38(rate_eval, tf):
    # S34 + He4 --> Ar38
    rate = 0.0

    # cn18 
    rate += np.exp(  228.729 + -17.9675*tf.T9i + 635.332*tf.T913i + -902.05*tf.T913
                  + 42.5623*tf.T9 + -2.08434*tf.T953 + 477.35*tf.lnT9)

    rate_eval.He4_S34__Ar38 = rate

@numba.njit()
def He4_Ca37__p_Sc40(rate_eval, tf):
    # Ca37 + He4 --> p + Sc40
    rate = 0.0

    # ths8r
    rate += np.exp(  56.068 + -76.2415*tf.T913i + -0.922288*tf.T913
                  + -0.439136*tf.T9 + 0.00881062*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca37__p_Sc40 = rate

@numba.njit()
def Be12__B12__weak__wc12(rate_eval, tf):
    # Be12 --> B12
    rate = 0.0

    # wc12w
    rate += np.exp(  3.46314)

    rate_eval.Be12__B12__weak__wc12 = rate

@numba.njit()
def N19__n_O18__weak__wc12(rate_eval, tf):
    # N19 --> n + O18
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.148143)

    rate_eval.N19__n_O18__weak__wc12 = rate

@numba.njit()
def p_P31__He4_Si28(rate_eval, tf):
    # P31 + p --> He4 + Si28
    rate = 0.0

    # il10r
    rate += np.exp(  -10.893 + -3.42575*tf.T9i + 21.521*tf.T913
                  + -1.90355*tf.T9 + 0.092724*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -12.919 + -1.87716*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  60.8829 + -31.932*tf.T913i + -77.0334*tf.T913
                  + -43.6847*tf.T9 + -4.28955*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_P31__He4_Si28 = rate

@numba.njit()
def n_Ti37__p_Sc37(rate_eval, tf):
    # Ti37 + n --> p + Sc37
    rate = 0.0

    # ths8r
    rate += np.exp(  20.3919 + -0.0751036*tf.T913
                  + 0.122755*tf.T9 + -0.0109931*tf.T953)

    rate_eval.n_Ti37__p_Sc37 = rate

@numba.njit()
def Cr70__n_Mn69__weak__mp17(rate_eval, tf):
    # Cr70 --> n + Mn69
    rate = 0.0

    # mp17w
    rate += np.exp(  3.07623)

    rate_eval.Cr70__n_Mn69__weak__mp17 = rate

@numba.njit()
def O24__n_F23__weak__wc12(rate_eval, tf):
    # O24 --> n + F23
    rate = 0.0

    # wc12w
    rate += np.exp(  1.82213)

    rate_eval.O24__n_F23__weak__wc12 = rate

@numba.njit()
def Sc41__Ca41__weak__wc12(rate_eval, tf):
    # Sc41 --> Ca41
    rate = 0.0

    # wc12w
    rate += np.exp(  0.151002)

    rate_eval.Sc41__Ca41__weak__wc12 = rate

@numba.njit()
def Mn68__n_Fe67__weak__mp17(rate_eval, tf):
    # Mn68 --> n + Fe67
    rate = 0.0

    # mp17w
    rate += np.exp(  1.54831)

    rate_eval.Mn68__n_Fe67__weak__mp17 = rate

@numba.njit()
def p_P41__S42(rate_eval, tf):
    # P41 + p --> S42
    rate = 0.0

    # rath 
    rate += np.exp(  83.2615 + -4.05176*tf.T9i + 147.176*tf.T913i + -241.809*tf.T913
                  + 13.1661*tf.T9 + -0.729183*tf.T953 + 121.654*tf.lnT9)

    rate_eval.p_P41__S42 = rate

@numba.njit()
def p_Cl44__n_Ar44(rate_eval, tf):
    # Cl44 + p --> n + Ar44
    rate = 0.0

    # rath 
    rate += np.exp(  103.635 + -4.55947*tf.T9i + 167.317*tf.T913i + -274.92*tf.T913
                  + 15.1087*tf.T9 + -0.845196*tf.T953 + 137.915*tf.lnT9)

    rate_eval.p_Cl44__n_Ar44 = rate

@numba.njit()
def Cr69__n_Mn68__weak__mp17(rate_eval, tf):
    # Cr69 --> n + Mn68
    rate = 0.0

    # mp17w
    rate += np.exp(  2.06178)

    rate_eval.Cr69__n_Mn68__weak__mp17 = rate

@numba.njit()
def n_Li8__Li9(rate_eval, tf):
    # Li8 + n --> Li9
    rate = 0.0

    # wiesr
    rate += np.exp(  11.0553 + -2.866*tf.T9i
                  + -1.5*tf.lnT9)
    # wiesn
    rate += np.exp(  8.08948)

    rate_eval.n_Li8__Li9 = rate

@numba.njit()
def He4_N12__p_O15(rate_eval, tf):
    # N12 + He4 --> p + O15
    rate = 0.0

    #  wfhn
    rate += np.exp(  39.3263 + -35.6*tf.T913i
                  + -0.666667*tf.lnT9)

    rate_eval.He4_N12__p_O15 = rate

@numba.njit()
def Cr66__n_Mn65__weak__mp17(rate_eval, tf):
    # Cr66 --> n + Mn65
    rate = 0.0

    # mp17w
    rate += np.exp(  0.880019)

    rate_eval.Cr66__n_Mn65__weak__mp17 = rate

@numba.njit()
def n_C13__C14(rate_eval, tf):
    # C13 + n --> C14
    rate = 0.0

    # ks03 
    rate += np.exp(  35.3048 + -0.133687*tf.T9i + 18.3578*tf.T913i + -46.5786*tf.T913
                  + 2.58472*tf.T9 + -0.118622*tf.T953 + 19.9142*tf.lnT9)

    rate_eval.n_C13__C14 = rate

@numba.njit()
def n_Mg21__p_Na21(rate_eval, tf):
    # Mg21 + n --> p + Na21
    rate = 0.0

    # ths8r
    rate += np.exp(  17.8634 + 2.57325*tf.T913
                  + -0.35666*tf.T9 + 0.024981*tf.T953)

    rate_eval.n_Mg21__p_Na21 = rate

@numba.njit()
def Cr63__n_Mn62__weak__mp17(rate_eval, tf):
    # Cr63 --> n + Mn62
    rate = 0.0

    # mp17w
    rate += np.exp(  -2.23059)

    rate_eval.Cr63__n_Mn62__weak__mp17 = rate

@numba.njit()
def He4_Mn71__Co75(rate_eval, tf):
    # Mn71 + He4 --> Co75
    rate = 0.0

    # rath 
    rate += np.exp(  -1227.61 + 25.3867*tf.T9i + -2520.05*tf.T913i + 3893.0*tf.T913
                  + -220.452*tf.T9 + 12.1684*tf.T953 + -1889.06*tf.lnT9)

    rate_eval.He4_Mn71__Co75 = rate

@numba.njit()
def n_Ca59__Ca60(rate_eval, tf):
    # Ca59 + n --> Ca60
    rate = 0.0

    # rath 
    rate += np.exp(  9.31747 + -0.00609877*tf.T9i + -0.294385*tf.T913i + -1.46586*tf.T913
                  + 0.823214*tf.T9 + -0.134837*tf.T953 + -0.4325*tf.lnT9)

    rate_eval.n_Ca59__Ca60 = rate

@numba.njit()
def N13__C13__weak__wc12(rate_eval, tf):
    # N13 --> C13
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.7601)

    rate_eval.N13__C13__weak__wc12 = rate

@numba.njit()
def p_Ca48__Sc49(rate_eval, tf):
    # Ca48 + p --> Sc49
    rate = 0.0

    # ths8r
    rate += np.exp(  33.8574 + -31.1685*tf.T913i + 2.20987*tf.T913
                  + -2.24347*tf.T9 + 0.239302*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ca48__Sc49 = rate

@numba.njit()
def Sc37__Ca37__weak__bqa_pos_(rate_eval, tf):
    # Sc37 --> Ca37
    rate = 0.0

    # bqa+w
    rate += np.exp(  2.51589)

    rate_eval.Sc37__Ca37__weak__bqa_pos_ = rate

@numba.njit()
def F29__Ne29__weak__wc17(rate_eval, tf):
    # F29 --> Ne29
    rate = 0.0

    # wc17w
    rate += np.exp(  -109.504)

    rate_eval.F29__Ne29__weak__wc17 = rate

@numba.njit()
def He4_V65__n_Mn68(rate_eval, tf):
    # V65 + He4 --> n + Mn68
    rate = 0.0

    # rath 
    rate += np.exp(  -1151.7 + 18.4136*tf.T9i + -1993.47*tf.T913i + 3286.45*tf.T913
                  + -196.12*tf.T9 + 11.2519*tf.T953 + -1542.58*tf.lnT9)

    rate_eval.He4_V65__n_Mn68 = rate

@numba.njit()
def Cr62__n_Mn61__weak__mp17(rate_eval, tf):
    # Cr62 --> n + Mn61
    rate = 0.0

    # mp17w
    rate += np.exp(  -3.3918)

    rate_eval.Cr62__n_Mn61__weak__mp17 = rate

@numba.njit()
def F30__n_Ne29__weak__mp17(rate_eval, tf):
    # F30 --> n + Ne29
    rate = 0.0

    # mp17w
    rate += np.exp(  4.80131)

    rate_eval.F30__n_Ne29__weak__mp17 = rate

@numba.njit()
def Cr61__n_Mn60__weak__mp17(rate_eval, tf):
    # Cr61 --> n + Mn60
    rate = 0.0

    # mp17w
    rate += np.exp(  -3.55699)

    rate_eval.Cr61__n_Mn60__weak__mp17 = rate

@numba.njit()
def n_Si23__Si24(rate_eval, tf):
    # Si23 + n --> Si24
    rate = 0.0

    # ths8r
    rate += np.exp(  8.11262 + 2.77143*tf.T913
                  + -0.441407*tf.T9 + 0.0315224*tf.T953)

    rate_eval.n_Si23__Si24 = rate

@numba.njit()
def p_Mg41__Al42(rate_eval, tf):
    # Mg41 + p --> Al42
    rate = 0.0

    # rath 
    rate += np.exp(  75.2538 + -3.50095*tf.T9i + 127.995*tf.T913i + -211.626*tf.T913
                  + 11.5611*tf.T9 + -0.63925*tf.T953 + 105.985*tf.lnT9)

    rate_eval.p_Mg41__Al42 = rate

@numba.njit()
def He4_Be10__n_C13(rate_eval, tf):
    # Be10 + He4 --> n + C13
    rate = 0.0

    # wiesr
    rate += np.exp(  -165.229 + -5.11523*tf.T9i + -127.827*tf.T913i + 325.824*tf.T913
                  + -24.5074*tf.T9 + 1.59405*tf.T953 + -125.936*tf.lnT9)

    rate_eval.He4_Be10__n_C13 = rate

@numba.njit()
def n_Be7__p_Li7(rate_eval, tf):
    # Be7 + n --> p + Li7
    rate = 0.0

    # db18 
    rate += np.exp(  21.7899 + 0.000728098*tf.T9i + -0.30254*tf.T913i + -0.3602*tf.T913
                  + 0.17472*tf.T9 + -0.0223*tf.T953 + -0.4581*tf.lnT9)

    rate_eval.n_Be7__p_Li7 = rate

@numba.njit()
def n_Al21__Al22(rate_eval, tf):
    # Al21 + n --> Al22
    rate = 0.0

    # rath 
    rate += np.exp(  10.2784 + 0.0112332*tf.T9i + 0.752504*tf.T913i + -4.00178*tf.T913
                  + 0.376581*tf.T9 + -0.0232922*tf.T953 + 1.66693*tf.lnT9)

    rate_eval.n_Al21__Al22 = rate

@numba.njit()
def n_Si26__He4_Mg23(rate_eval, tf):
    # Si26 + n --> He4 + Mg23
    rate = 0.0

    # ths8r
    rate += np.exp(  16.107 + 1.08923*tf.T913
                  + -0.0248723*tf.T9 + 0.00450822*tf.T953)

    rate_eval.n_Si26__He4_Mg23 = rate

@numba.njit()
def n_Na32__Na33(rate_eval, tf):
    # Na32 + n --> Na33
    rate = 0.0

    # rath 
    rate += np.exp(  13.4297 + -0.00118844*tf.T9i + 1.04335*tf.T913i + -9.89504*tf.T913
                  + 1.16638*tf.T9 + -0.0825067*tf.T953 + 2.10483*tf.lnT9)

    rate_eval.n_Na32__Na33 = rate

@numba.njit()
def Mn44__Cr44__weak__bqa_pos_(rate_eval, tf):
    # Mn44 --> Cr44
    rate = 0.0

    # bqa+w
    rate += np.exp(  3.95348)

    rate_eval.Mn44__Cr44__weak__bqa_pos_ = rate

@numba.njit()
def Fe73__Co73__weak__mo03(rate_eval, tf):
    # Fe73 --> Co73
    rate = 0.0

    # mo03w
    rate += np.exp(  2.19993)

    rate_eval.Fe73__Co73__weak__mo03 = rate

@numba.njit()
def He4_Ca55__n_Ti58(rate_eval, tf):
    # Ca55 + He4 --> n + Ti58
    rate = 0.0

    # rath 
    rate += np.exp(  -963.406 + 15.4333*tf.T9i + -1675.73*tf.T913i + 2758.16*tf.T913
                  + -164.98*tf.T9 + 9.47727*tf.T953 + -1293.23*tf.lnT9)

    rate_eval.He4_Ca55__n_Ti58 = rate

@numba.njit()
def He4_Ar44__Ca48(rate_eval, tf):
    # Ar44 + He4 --> Ca48
    rate = 0.0

    # rath 
    rate += np.exp(  -788.696 + 12.8*tf.T9i + -1393.31*tf.T913i + 2270.52*tf.T913
                  + -135.316*tf.T9 + 7.79989*tf.T953 + -1067.49*tf.lnT9)

    rate_eval.He4_Ar44__Ca48 = rate

@numba.njit()
def Cr45__p_Ti44__weak__wc12(rate_eval, tf):
    # Cr45 --> p + Ti44
    rate = 0.0

    # wc12w
    rate += np.exp(  1.3649)

    rate_eval.Cr45__p_Ti44__weak__wc12 = rate

@numba.njit()
def n_P34__P35(rate_eval, tf):
    # P34 + n --> P35
    rate = 0.0

    # rath 
    rate += np.exp(  16.9359 + -0.0486639*tf.T9i + 3.84594*tf.T913i + -8.51058*tf.T913
                  + 0.668536*tf.T9 + -0.0564735*tf.T953 + 3.14979*tf.lnT9)

    rate_eval.n_P34__P35 = rate

@numba.njit()
def He4_P28__p_S31(rate_eval, tf):
    # P28 + He4 --> p + S31
    rate = 0.0

    # ths8r
    rate += np.exp(  50.0703 + -62.2912*tf.T913i + 0.389674*tf.T913
                  + -0.809909*tf.T9 + 0.0572187*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P28__p_S31 = rate

@numba.njit()
def He4_Si25__S29(rate_eval, tf):
    # Si25 + He4 --> S29
    rate = 0.0

    # ths8r
    rate += np.exp(  37.383 + -59.1975*tf.T913i + 0.483925*tf.T913
                  + -0.724803*tf.T9 + 0.0455403*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si25__S29 = rate

@numba.njit()
def n_Sc35__Sc36(rate_eval, tf):
    # Sc35 + n --> Sc36
    rate = 0.0

    # ths8r
    rate += np.exp(  7.75928 + 1.24799*tf.T913
                  + -0.0704306*tf.T9 + 0.00810055*tf.T953)

    rate_eval.n_Sc35__Sc36 = rate

@numba.njit()
def p_Sc47__Ti48(rate_eval, tf):
    # Sc47 + p --> Ti48
    rate = 0.0

    # rath 
    rate += np.exp(  50.4169 + -5.06842*tf.T9i + 155.189*tf.T913i + -211.783*tf.T913
                  + 9.70286*tf.T9 + -0.48757*tf.T953 + 117.307*tf.lnT9)

    rate_eval.p_Sc47__Ti48 = rate

@numba.njit()
def He4_P38__Cl42(rate_eval, tf):
    # P38 + He4 --> Cl42
    rate = 0.0

    # rath 
    rate += np.exp(  -316.411 + 1.7649*tf.T9i + -453.685*tf.T913i + 795.907*tf.T913
                  + -52.6415*tf.T9 + 3.2027*tf.T953 + -349.132*tf.lnT9)

    rate_eval.He4_P38__Cl42 = rate

@numba.njit()
def n_Cl28__p_S28(rate_eval, tf):
    # Cl28 + n --> p + S28
    rate = 0.0

    # ths8r
    rate += np.exp(  18.6859 + 1.86816*tf.T913
                  + -0.276845*tf.T9 + 0.0211542*tf.T953)

    rate_eval.n_Cl28__p_S28 = rate

@numba.njit()
def Ar51__n_K50__weak__mp17(rate_eval, tf):
    # Ar51 --> n + K50
    rate = 0.0

    # mp17w
    rate += np.exp(  2.47827)

    rate_eval.Ar51__n_K50__weak__mp17 = rate

@numba.njit()
def Cr42__p_Ti41__weak__wc12(rate_eval, tf):
    # Cr42 --> p + Ti41
    rate = 0.0

    # wc12w
    rate += np.exp(  3.89585)

    rate_eval.Cr42__p_Ti41__weak__wc12 = rate

@numba.njit()
def He4_Mg25__Si29(rate_eval, tf):
    # Mg25 + He4 --> Si29
    rate = 0.0

    # cf88n
    rate += np.exp(  40.3715 + -53.41*tf.T913i + -1.83266*tf.T913
                  + -0.573073*tf.T9 + 0.0462678*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg25__Si29 = rate

@numba.njit()
def He4_Mn52__p_Fe55(rate_eval, tf):
    # Mn52 + He4 --> p + Fe55
    rate = 0.0

    # ths8r
    rate += np.exp(  56.6689 + -89.3157*tf.T913i + 5.65639*tf.T913
                  + -2.28952*tf.T9 + 0.186017*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn52__p_Fe55 = rate

@numba.njit()
def n_Mn50__p_Cr50(rate_eval, tf):
    # Mn50 + n --> p + Cr50
    rate = 0.0

    # ths8r
    rate += np.exp(  21.5859 + -1.04612*tf.T913
                  + 0.340541*tf.T9 + -0.0370932*tf.T953)

    rate_eval.n_Mn50__p_Cr50 = rate

@numba.njit()
def C15__N15__weak__wc12(rate_eval, tf):
    # C15 --> N15
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.2626)

    rate_eval.C15__N15__weak__wc12 = rate

@numba.njit()
def V63__n_Cr62__weak__wc12(rate_eval, tf):
    # V63 --> n + Cr62
    rate = 0.0

    # wc12w
    rate += np.exp(  2.53651)

    rate_eval.V63__n_Cr62__weak__wc12 = rate

@numba.njit()
def Ar52__n_K51__weak__mp17(rate_eval, tf):
    # Ar52 --> n + K51
    rate = 0.0

    # mp17w
    rate += np.exp(  2.98518)

    rate_eval.Ar52__n_K51__weak__mp17 = rate

@numba.njit()
def n_Cr41__p_V41(rate_eval, tf):
    # Cr41 + n --> p + V41
    rate = 0.0

    # ths8r
    rate += np.exp(  21.7352 + -0.923025*tf.T913
                  + 0.257942*tf.T9 + -0.0232513*tf.T953)

    rate_eval.n_Cr41__p_V41 = rate

@numba.njit()
def p_Ar46__K47(rate_eval, tf):
    # Ar46 + p --> K47
    rate = 0.0

    # rath 
    rate += np.exp(  94.9231 + -4.80019*tf.T9i + 174.216*tf.T913i + -282.727*tf.T913
                  + 15.1369*tf.T9 + -0.809787*tf.T953 + 142.599*tf.lnT9)

    rate_eval.p_Ar46__K47 = rate

@numba.njit()
def V59__n_Cr58__weak__wc12(rate_eval, tf):
    # V59 --> n + Cr58
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.54003)

    rate_eval.V59__n_Cr58__weak__wc12 = rate

@numba.njit()
def p_S42__He4_P39(rate_eval, tf):
    # S42 + p --> He4 + P39
    rate = 0.0

    # rath 
    rate += np.exp(  63.2675 + -2.82193*tf.T9i + 68.539*tf.T913i + -151.803*tf.T913
                  + 5.51565*tf.T9 + -0.162474*tf.T953 + 84.6826*tf.lnT9)

    rate_eval.p_S42__He4_P39 = rate

@numba.njit()
def He4_N14__F18(rate_eval, tf):
    # N14 + He4 --> F18
    rate = 0.0

    # il10r
    rate += np.exp(  13.8995 + -10.9656*tf.T9i + -5.6227*tf.T913i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  0.196838 + -5.16034*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  21.5339 + -36.2504*tf.T913i
                  + -5.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_N14__F18 = rate

@numba.njit()
def He4_Si36__n_S39(rate_eval, tf):
    # Si36 + He4 --> n + S39
    rate = 0.0

    # rath 
    rate += np.exp(  -8.34587 + -3.02347*tf.T9i + -17.5525*tf.T913i + 22.6173*tf.T913
                  + -4.92797*tf.T9 + 0.390132*tf.T953 + 6.43709*tf.lnT9)

    rate_eval.He4_Si36__n_S39 = rate

@numba.njit()
def p_Li8__n_He4_He4(rate_eval, tf):
    # Li8 + p --> n + He4 + He4
    rate = 0.0

    # bb92r
    rate += np.exp(  20.8455 + -3.982*tf.T9i + -3.90706e-09*tf.T913i + 9.14745e-09*tf.T913
                  + -7.44527e-10*tf.T9 + 5.50866e-11*tf.T953 + -0.433*tf.lnT9)
    # bb92n
    rate += np.exp(  23.0564 + -4.7809e-12*tf.T9i + -8.429*tf.T913i + -2.04701e-09*tf.T913
                  + 2.04027e-10*tf.T9 + -1.70107e-11*tf.T953 + -0.666667*tf.lnT9)
    # bb92r
    rate += np.exp(  13.4284 + -1.02*tf.T9i + -1.56584e-10*tf.T913i + 4.97791e-10*tf.T913
                  + -4.88505e-11*tf.T9 + 4.04166e-12*tf.T953 + -1.5*tf.lnT9)
    # bb92r
    rate += np.exp(  19.6085 + -7.024*tf.T9i + -1.51325e-10*tf.T913i + 4.9858e-10*tf.T913
                  + -4.87305e-11*tf.T9 + 4.0038e-12*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Li8__n_He4_He4 = rate

@numba.njit()
def n_Ca47__Ca48(rate_eval, tf):
    # Ca47 + n --> Ca48
    rate = 0.0

    # ths8r
    rate += np.exp(  15.2216 + -2.88636*tf.T913
                  + 0.79581*tf.T9 + -0.0872236*tf.T953)

    rate_eval.n_Ca47__Ca48 = rate

@numba.njit()
def p_Fe67__Co68(rate_eval, tf):
    # Fe67 + p --> Co68
    rate = 0.0

    # rath 
    rate += np.exp(  143.974 + -7.34825*tf.T9i + 279.139*tf.T913i + -446.914*tf.T913
                  + 24.6287*tf.T9 + -1.40241*tf.T953 + 224.279*tf.lnT9)

    rate_eval.p_Fe67__Co68 = rate

@numba.njit()
def Fe76__n_n_Co74__weak__mp17(rate_eval, tf):
    # Fe76 --> n + n + Co74
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.672526)

    rate_eval.Fe76__n_n_Co74__weak__mp17 = rate

@numba.njit()
def n_Cr47__Cr48(rate_eval, tf):
    # Cr47 + n --> Cr48
    rate = 0.0

    # ths8r
    rate += np.exp(  12.5822 + -1.36332*tf.T913
                  + 0.288027*tf.T9 + -0.0333017*tf.T953)

    rate_eval.n_Cr47__Cr48 = rate

@numba.njit()
def He4_V48__Mn52(rate_eval, tf):
    # V48 + He4 --> Mn52
    rate = 0.0

    # ths8r
    rate += np.exp(  62.5923 + -84.3192*tf.T913i + -8.32959*tf.T913
                  + 0.33994*tf.T9 + -0.0359909*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V48__Mn52 = rate

@numba.njit()
def He4_Ca61__Ti65(rate_eval, tf):
    # Ca61 + He4 --> Ti65
    rate = 0.0

    # rath 
    rate += np.exp(  -1026.75 + 16.148*tf.T9i + -1754.44*tf.T913i + 2896.66*tf.T913
                  + -173.299*tf.T9 + 9.94858*tf.T953 + -1357.46*tf.lnT9)

    rate_eval.He4_Ca61__Ti65 = rate

@numba.njit()
def He4_Fe62__Ni66(rate_eval, tf):
    # Fe62 + He4 --> Ni66
    rate = 0.0

    # rath 
    rate += np.exp(  -1154.63 + 24.1953*tf.T9i + -2406.3*tf.T913i + 3697.43*tf.T913
                  + -208.985*tf.T9 + 11.5004*tf.T953 + -1796.79*tf.lnT9)

    rate_eval.He4_Fe62__Ni66 = rate

@numba.njit()
def He4_Ca55__Ti59(rate_eval, tf):
    # Ca55 + He4 --> Ti59
    rate = 0.0

    # rath 
    rate += np.exp(  -973.538 + 15.3908*tf.T9i + -1672.67*tf.T913i + 2754.31*tf.T913
                  + -164.703*tf.T9 + 9.44182*tf.T953 + -1291.12*tf.lnT9)

    rate_eval.He4_Ca55__Ti59 = rate

@numba.njit()
def n_S28__p_P28(rate_eval, tf):
    # S28 + n --> p + P28
    rate = 0.0

    # ths8r
    rate += np.exp(  18.8891 + 1.38045*tf.T913
                  + -0.160175*tf.T9 + 0.0121871*tf.T953)

    rate_eval.n_S28__p_P28 = rate

@numba.njit()
def He4_P46__Cl50(rate_eval, tf):
    # P46 + He4 --> Cl50
    rate = 0.0

    # rath 
    rate += np.exp(  -359.467 + 2.12995*tf.T9i + -511.772*tf.T913i + 901.065*tf.T913
                  + -58.8153*tf.T9 + 3.55568*tf.T953 + -398.151*tf.lnT9)

    rate_eval.He4_P46__Cl50 = rate

@numba.njit()
def Ti56__V56__weak__wc12(rate_eval, tf):
    # Ti56 --> V56
    rate = 0.0

    # wc12w
    rate += np.exp(  1.24293)

    rate_eval.Ti56__V56__weak__wc12 = rate

@numba.njit()
def K55__n_Ca54__weak__mp17(rate_eval, tf):
    # K55 --> n + Ca54
    rate = 0.0

    # mp17w
    rate += np.exp(  4.20771)

    rate_eval.K55__n_Ca54__weak__mp17 = rate

@numba.njit()
def n_Mg20__He4_Ne17(rate_eval, tf):
    # Mg20 + n --> He4 + Ne17
    rate = 0.0

    # ths8r
    rate += np.exp(  15.4618 + 1.73831*tf.T913
                  + -0.161321*tf.T9 + 0.00841019*tf.T953)

    rate_eval.n_Mg20__He4_Ne17 = rate

@numba.njit()
def F22__Ne22__weak__wc17(rate_eval, tf):
    # F22 --> Ne22
    rate = 0.0

    # wc17w
    rate += np.exp(  -1.80871)

    rate_eval.F22__Ne22__weak__wc17 = rate

@numba.njit()
def Sc39__Ca39__weak__mo97(rate_eval, tf):
    # Sc39 --> Ca39
    rate = 0.0

    # mo97w
    rate += np.exp(  2.19484)

    rate_eval.Sc39__Ca39__weak__mo97 = rate

@numba.njit()
def Fe75__Co75__weak__mo03(rate_eval, tf):
    # Fe75 --> Co75
    rate = 0.0

    # mo03w
    rate += np.exp(  2.12481)

    rate_eval.Fe75__Co75__weak__mo03 = rate

@numba.njit()
def He4_Al24__P28(rate_eval, tf):
    # Al24 + He4 --> P28
    rate = 0.0

    # ths8r
    rate += np.exp(  37.3847 + -56.2358*tf.T913i + 0.584307*tf.T913
                  + -0.757779*tf.T9 + 0.0528976*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al24__P28 = rate

@numba.njit()
def p_Si40__He4_Al37(rate_eval, tf):
    # Si40 + p --> He4 + Al37
    rate = 0.0

    # rath 
    rate += np.exp(  61.804 + -4.07892*tf.T9i + 170.41*tf.T913i + -250.461*tf.T913
                  + 10.0747*tf.T9 + -0.405578*tf.T953 + 141.702*tf.lnT9)

    rate_eval.p_Si40__He4_Al37 = rate

@numba.njit()
def p_Mg41__n_Al41(rate_eval, tf):
    # Mg41 + p --> n + Al41
    rate = 0.0

    # rath 
    rate += np.exp(  86.3691 + -3.50368*tf.T9i + 128.241*tf.T913i + -211.989*tf.T913
                  + 11.5061*tf.T9 + -0.63285*tf.T953 + 106.186*tf.lnT9)

    rate_eval.p_Mg41__n_Al41 = rate

@numba.njit()
def Mg39__Al39__weak__mo03(rate_eval, tf):
    # Mg39 --> Al39
    rate = 0.0

    # mo03w
    rate += np.exp(  -110.267)

    rate_eval.Mg39__Al39__weak__mo03 = rate

@numba.njit()
def p_Cl42__Ar43(rate_eval, tf):
    # Cl42 + p --> Ar43
    rate = 0.0

    # rath 
    rate += np.exp(  94.5354 + -4.46554*tf.T9i + 163.48*tf.T913i + -270.148*tf.T913
                  + 14.888*tf.T9 + -0.838752*tf.T953 + 135.289*tf.lnT9)

    rate_eval.p_Cl42__Ar43 = rate

@numba.njit()
def He4_Ti50__Cr54(rate_eval, tf):
    # Ti50 + He4 --> Cr54
    rate = 0.0

    # ths8r
    rate += np.exp(  63.4244 + -81.9411*tf.T913i + -6.28155*tf.T913
                  + -2.0416*tf.T9 + 0.332085*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti50__Cr54 = rate

@numba.njit()
def n_Sc52__Sc53(rate_eval, tf):
    # Sc52 + n --> Sc53
    rate = 0.0

    # rath 
    rate += np.exp(  16.5877 + -0.0286004*tf.T9i + 2.38883*tf.T913i + -6.59918*tf.T913
                  + 0.475574*tf.T9 + -0.0480182*tf.T953 + 2.15686*tf.lnT9)

    rate_eval.n_Sc52__Sc53 = rate

@numba.njit()
def p_Sc51__Ti52(rate_eval, tf):
    # Sc51 + p --> Ti52
    rate = 0.0

    # rath 
    rate += np.exp(  119.454 + -5.67361*tf.T9i + 214.069*tf.T913i + -352.444*tf.T913
                  + 19.6199*tf.T9 + -1.05951*tf.T953 + 175.464*tf.lnT9)

    rate_eval.p_Sc51__Ti52 = rate

@numba.njit()
def n_Ti40__p_Sc40(rate_eval, tf):
    # Ti40 + n --> p + Sc40
    rate = 0.0

    # ths8r
    rate += np.exp(  20.4956 + -0.187561*tf.T913
                  + 0.138966*tf.T9 + -0.0131344*tf.T953)

    rate_eval.n_Ti40__p_Sc40 = rate

@numba.njit()
def He4_Al43__n_P46(rate_eval, tf):
    # Al43 + He4 --> n + P46
    rate = 0.0

    # rath 
    rate += np.exp(  -11.2472 + -3.20071*tf.T9i + -12.0926*tf.T913i + 23.337*tf.T913
                  + -5.30636*tf.T9 + 0.42941*tf.T953 + 7.123*tf.lnT9)

    rate_eval.He4_Al43__n_P46 = rate

@numba.njit()
def n_P30__p_Si30(rate_eval, tf):
    # P30 + n --> p + Si30
    rate = 0.0

    # ths8r
    rate += np.exp(  18.3359 + 1.88379*tf.T913
                  + -0.330243*tf.T9 + 0.0239836*tf.T953)

    rate_eval.n_P30__p_Si30 = rate

@numba.njit()
def n_P46__P47(rate_eval, tf):
    # P46 + n --> P47
    rate = 0.0

    # rath 
    rate += np.exp(  23.9694 + -0.101917*tf.T9i + 8.71231*tf.T913i + -26.6056*tf.T913
                  + 2.58547*tf.T9 + -0.198551*tf.T953 + 8.1919*tf.lnT9)

    rate_eval.n_P46__P47 = rate

@numba.njit()
def O28__n_n_F26__weak__mp17(rate_eval, tf):
    # O28 --> n + n + F26
    rate = 0.0

    # mp17w
    rate += np.exp(  3.73184)

    rate_eval.O28__n_n_F26__weak__mp17 = rate

@numba.njit()
def He4_Fe51__p_Co54(rate_eval, tf):
    # Fe51 + He4 --> p + Co54
    rate = 0.0

    # ths8r
    rate += np.exp(  63.4592 + -91.6394*tf.T913i + -1.41694*tf.T913
                  + -0.483608*tf.T9 + 0.00513039*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe51__p_Co54 = rate

@numba.njit()
def Cl31__p_P30__weak__wc12(rate_eval, tf):
    # Cl31 --> p + P30
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.43124)

    rate_eval.Cl31__p_P30__weak__wc12 = rate

@numba.njit()
def Mg40__n_n_Al38__weak__mp17(rate_eval, tf):
    # Mg40 --> n + n + Al38
    rate = 0.0

    # mp17w
    rate += np.exp(  3.02366)

    rate_eval.Mg40__n_n_Al38__weak__mp17 = rate

@numba.njit()
def p_F19__Ne20(rate_eval, tf):
    # F19 + p --> Ne20
    rate = 0.0

    # nacrr
    rate += np.exp(  -5.63093 + -7.74414*tf.T9i + 31.6442*tf.T913i + -58.6563*tf.T913
                  + 67.7365*tf.T9 + -22.9721*tf.T953 + -1.5*tf.lnT9)
    # nacrr
    rate += np.exp(  12.3816 + -1.71383*tf.T9i + -11.3832*tf.T913i + 5.47872*tf.T913
                  + -1.07203*tf.T9 + 0.11196*tf.T953 + -1.5*tf.lnT9)
    # nacrn
    rate += np.exp(  18.2807 + -18.116*tf.T913i + -1.4622*tf.T913
                  + 6.95113*tf.T9 + -2.90366*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_F19__Ne20 = rate

@numba.njit()
def He4_Ne25__n_Mg28(rate_eval, tf):
    # Ne25 + He4 --> n + Mg28
    rate = 0.0

    # rath 
    rate += np.exp(  64.802 + -2.55158*tf.T9i + 47.8634*tf.T913i + -118.627*tf.T913
                  + 5.31295*tf.T9 + -0.26149*tf.T953 + 62.7247*tf.lnT9)

    rate_eval.He4_Ne25__n_Mg28 = rate

@numba.njit()
def Cr70__n_n_Mn68__weak__mp17(rate_eval, tf):
    # Cr70 --> n + n + Mn68
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.684967)

    rate_eval.Cr70__n_n_Mn68__weak__mp17 = rate

@numba.njit()
def p_K50__He4_Ar47(rate_eval, tf):
    # K50 + p --> He4 + Ar47
    rate = 0.0

    # rath 
    rate += np.exp(  113.024 + -5.2502*tf.T9i + 198.202*tf.T913i + -327.515*tf.T913
                  + 18.336*tf.T9 + -1.00814*tf.T953 + 163.077*tf.lnT9)

    rate_eval.p_K50__He4_Ar47 = rate

@numba.njit()
def Ti64__n_V63__weak__mp17(rate_eval, tf):
    # Ti64 --> n + V63
    rate = 0.0

    # mp17w
    rate += np.exp(  3.87503)

    rate_eval.Ti64__n_V63__weak__mp17 = rate

@numba.njit()
def He4_O27__n_Ne30(rate_eval, tf):
    # O27 + He4 --> n + Ne30
    rate = 0.0

    # rpsmr
    rate += np.exp(  61.9723 + -2.30767*tf.T9i + 45.3796*tf.T913i + -108.806*tf.T913
                  + 4.83385*tf.T9 + -0.229646*tf.T953 + 57.0947*tf.lnT9)

    rate_eval.He4_O27__n_Ne30 = rate

@numba.njit()
def n_Mn57__Mn58(rate_eval, tf):
    # Mn57 + n --> Mn58
    rate = 0.0

    # rath 
    rate += np.exp(  20.5429 + 0.010252*tf.T9i + -0.339016*tf.T913i + -7.15139*tf.T913
                  + 1.33648*tf.T9 + -0.153399*tf.T953 + 0.75148*tf.lnT9)

    rate_eval.n_Mn57__Mn58 = rate

@numba.njit()
def He4_Ca60__Ti64(rate_eval, tf):
    # Ca60 + He4 --> Ti64
    rate = 0.0

    # rath 
    rate += np.exp(  -1020.2 + 16.0556*tf.T9i + -1743.54*tf.T913i + 2877.13*tf.T913
                  + -172.044*tf.T9 + 9.8641*tf.T953 + -1348.49*tf.lnT9)

    rate_eval.He4_Ca60__Ti64 = rate

@numba.njit()
def n_P25__He4_Al22(rate_eval, tf):
    # P25 + n --> He4 + Al22
    rate = 0.0

    # ths8r
    rate += np.exp(  14.3746 + 0.609339*tf.T913
                  + 0.0613057*tf.T9 + 0.00883458*tf.T953)

    rate_eval.n_P25__He4_Al22 = rate

@numba.njit()
def Ti63__n_V62__weak__mp17(rate_eval, tf):
    # Ti63 --> n + V62
    rate = 0.0

    # mp17w
    rate += np.exp(  0.868779)

    rate_eval.Ti63__n_V62__weak__mp17 = rate

@numba.njit()
def n_F19__F20(rate_eval, tf):
    # F19 + n --> F20
    rate = 0.0

    # ks03 
    rate += np.exp(  -7.04662 + 0.178459*tf.T9i + -27.3483*tf.T913i + 49.1814*tf.T913
                  + -2.50685*tf.T9 + 0.101505*tf.T953 + -23.4737*tf.lnT9)

    rate_eval.n_F19__F20 = rate

@numba.njit()
def V52__Cr52__weak__wc12(rate_eval, tf):
    # V52 --> Cr52
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.78261)

    rate_eval.V52__Cr52__weak__wc12 = rate

@numba.njit()
def Ti61__n_V60__weak__mp17(rate_eval, tf):
    # Ti61 --> n + V60
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.0788309)

    rate_eval.Ti61__n_V60__weak__mp17 = rate

@numba.njit()
def He4_P39__Cl43(rate_eval, tf):
    # P39 + He4 --> Cl43
    rate = 0.0

    # rath 
    rate += np.exp(  -323.056 + 1.76759*tf.T9i + -458.313*tf.T913i + 807.931*tf.T913
                  + -53.5702*tf.T9 + 3.26486*tf.T953 + -353.827*tf.lnT9)

    rate_eval.He4_P39__Cl43 = rate

@numba.njit()
def V65__n_n_Cr63__weak__mp17(rate_eval, tf):
    # V65 --> n + n + Cr63
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.262263)

    rate_eval.V65__n_n_Cr63__weak__mp17 = rate

@numba.njit()
def n_Na22__p_Ne22(rate_eval, tf):
    # Na22 + n --> p + Ne22
    rate = 0.0

    # cf88n
    rate += np.exp(  19.6489 + -0.0514777*tf.T913
                  + 0.0274055*tf.T9 + -0.00690277*tf.T953)

    rate_eval.n_Na22__p_Ne22 = rate

@numba.njit()
def p_S45__n_Cl45(rate_eval, tf):
    # S45 + p --> n + Cl45
    rate = 0.0

    # rath 
    rate += np.exp(  99.6587 + -4.41368*tf.T9i + 161.448*tf.T913i + -263.684*tf.T913
                  + 14.4175*tf.T9 + -0.804671*tf.T953 + 132.623*tf.lnT9)

    rate_eval.p_S45__n_Cl45 = rate

@numba.njit()
def n_Cr52__Cr53(rate_eval, tf):
    # Cr52 + n --> Cr53
    rate = 0.0

    # ks03 
    rate += np.exp(  27.3183 + -0.0314027*tf.T9i + 5.71728*tf.T913i + -20.4149*tf.T913
                  + 1.95304*tf.T9 + -0.175538*tf.T953 + 7.18293*tf.lnT9)

    rate_eval.n_Cr52__Cr53 = rate

@numba.njit()
def n_P30__P31(rate_eval, tf):
    # P30 + n --> P31
    rate = 0.0

    # ths8r
    rate += np.exp(  12.8187 + 0.909911*tf.T913
                  + -0.162367*tf.T9 + 0.00668293*tf.T953)

    rate_eval.n_P30__P31 = rate

@numba.njit()
def Ca55__n_Sc54__weak__mp17(rate_eval, tf):
    # Ca55 --> n + Sc54
    rate = 0.0

    # mp17w
    rate += np.exp(  -1.15497)

    rate_eval.Ca55__n_Sc54__weak__mp17 = rate

@numba.njit()
def Sc57__n_Ti56__weak__mp17(rate_eval, tf):
    # Sc57 --> n + Ti56
    rate = 0.0

    # mp17w
    rate += np.exp(  2.02308)

    rate_eval.Sc57__n_Ti56__weak__mp17 = rate

@numba.njit()
def He4_S38__Ar42(rate_eval, tf):
    # S38 + He4 --> Ar42
    rate = 0.0

    # rath 
    rate += np.exp(  -347.741 + 1.93148*tf.T9i + -486.121*tf.T913i + 862.975*tf.T913
                  + -57.0727*tf.T9 + 3.46173*tf.T953 + -377.669*tf.lnT9)

    rate_eval.He4_S38__Ar42 = rate

@numba.njit()
def He4_Ar30__p_K33(rate_eval, tf):
    # Ar30 + He4 --> p + K33
    rate = 0.0

    # ths8r
    rate += np.exp(  53.1239 + -70.5413*tf.T913i + 0.19281*tf.T913
                  + -0.760461*tf.T9 + 0.0492121*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar30__p_K33 = rate

@numba.njit()
def Ti58__n_V57__weak__mp17(rate_eval, tf):
    # Ti58 --> n + V57
    rate = 0.0

    # mp17w
    rate += np.exp(  -2.10698)

    rate_eval.Ti58__n_V57__weak__mp17 = rate

@numba.njit()
def p_Ar30__K31(rate_eval, tf):
    # Ar30 + p --> K31
    rate = 0.0

    # ths8r
    rate += np.exp(  -13.6055 + -57.1061*tf.T9i + 14.893*tf.T913
                  + -1.26754*tf.T9 + 0.079807*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ar30__K31 = rate

@numba.njit()
def Al37__n_n_Si35__weak__mp17(rate_eval, tf):
    # Al37 --> n + n + Si35
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.434172)

    rate_eval.Al37__n_n_Si35__weak__mp17 = rate

@numba.njit()
def Cr69__n_n_Mn67__weak__mp17(rate_eval, tf):
    # Cr69 --> n + n + Mn67
    rate = 0.0

    # mp17w
    rate += np.exp(  0.387801)

    rate_eval.Cr69__n_n_Mn67__weak__mp17 = rate

@numba.njit()
def He4_P31__Cl35(rate_eval, tf):
    # P31 + He4 --> Cl35
    rate = 0.0

    # ths8r
    rate += np.exp(  50.451 + -62.5433*tf.T913i + -2.95026*tf.T913
                  + -0.89652*tf.T9 + 0.0774126*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P31__Cl35 = rate

@numba.njit()
def p_Mn58__n_Fe58(rate_eval, tf):
    # Mn58 + p --> n + Fe58
    rate = 0.0

    # rath 
    rate += np.exp(  135.714 + -6.67266*tf.T9i + 248.49*tf.T913i + -397.232*tf.T913
                  + 21.7192*tf.T9 + -1.22142*tf.T953 + 200.637*tf.lnT9)

    rate_eval.p_Mn58__n_Fe58 = rate

@numba.njit()
def p_Ca57__He4_K54(rate_eval, tf):
    # Ca57 + p --> He4 + K54
    rate = 0.0

    # rath 
    rate += np.exp(  58.6449 + -5.60629*tf.T9i + 200.545*tf.T913i + -283.333*tf.T913
                  + 13.8424*tf.T9 + -0.70711*tf.T953 + 156.838*tf.lnT9)

    rate_eval.p_Ca57__He4_K54 = rate

@numba.njit()
def p_Cr65__n_Mn65(rate_eval, tf):
    # Cr65 + p --> n + Mn65
    rate = 0.0

    # rath 
    rate += np.exp(  142.252 + -6.86016*tf.T9i + 259.178*tf.T913i + -413.965*tf.T913
                  + 22.5699*tf.T9 + -1.25323*tf.T953 + 208.272*tf.lnT9)

    rate_eval.p_Cr65__n_Mn65 = rate

@numba.njit()
def p_F29__n_Ne29(rate_eval, tf):
    # F29 + p --> n + Ne29
    rate = 0.0

    # rpsmr
    rate += np.exp(  66.9917 + -2.44125*tf.T9i + 85.9943*tf.T913i + -146.12*tf.T913
                  + 7.89728*tf.T9 + -0.43604*tf.T953 + 73.2008*tf.lnT9)

    rate_eval.p_F29__n_Ne29 = rate

@numba.njit()
def He4_Mg32__Si36(rate_eval, tf):
    # Mg32 + He4 --> Si36
    rate = 0.0

    # rath 
    rate += np.exp(  -16.4744 + -2.51536*tf.T9i + -21.1547*tf.T913i + 26.9707*tf.T913
                  + -4.90865*tf.T9 + 0.383083*tf.T953 + 2.35208*tf.lnT9)

    rate_eval.He4_Mg32__Si36 = rate

@numba.njit()
def Na21__Ne21__weak__wc12(rate_eval, tf):
    # Na21 --> Ne21
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.48003)

    rate_eval.Na21__Ne21__weak__wc12 = rate

@numba.njit()
def He4_Cl41__K45(rate_eval, tf):
    # Cl41 + He4 --> K45
    rate = 0.0

    # rath 
    rate += np.exp(  -747.554 + 12.0839*tf.T9i + -1313.51*tf.T913i + 2146.25*tf.T913
                  + -128.456*tf.T9 + 7.37203*tf.T953 + -1006.97*tf.lnT9)

    rate_eval.He4_Cl41__K45 = rate

@numba.njit()
def n_Ca39__He4_Ar36(rate_eval, tf):
    # Ca39 + n --> He4 + Ar36
    rate = 0.0

    # ths8r
    rate += np.exp(  17.6944 + 1.04999*tf.T913
                  + -0.263031*tf.T9 + 0.0384098*tf.T953)

    rate_eval.n_Ca39__He4_Ar36 = rate

@numba.njit()
def O26__n_O25(rate_eval, tf):
    # O26 --> n + O25
    rate = 0.0

    # wc12s
    rate += np.exp(  16.6679)

    rate_eval.O26__n_O25 = rate

@numba.njit()
def d_d__He4(rate_eval, tf):
    # d + d --> He4
    rate = 0.0

    # nacrn
    rate += np.exp(  3.78177 + -4.26166*tf.T913i + -0.119233*tf.T913
                  + 0.778829*tf.T9 + -0.0925203*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.d_d__He4 = rate

@numba.njit()
def Al40__n_Si39__weak__mp17(rate_eval, tf):
    # Al40 --> n + Si39
    rate = 0.0

    # mp17w
    rate += np.exp(  4.77855)

    rate_eval.Al40__n_Si39__weak__mp17 = rate

@numba.njit()
def p_N13__O14(rate_eval, tf):
    # N13 + p --> O14
    rate = 0.0

    # lg06r
    rate += np.exp(  10.9971 + -6.12602*tf.T9i + 1.57122*tf.T913i
                  + -1.5*tf.lnT9)
    # lg06n
    rate += np.exp(  18.1356 + -15.1676*tf.T913i + 0.0955166*tf.T913
                  + 3.0659*tf.T9 + -0.507339*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_N13__O14 = rate

@numba.njit()
def n_C12__C13(rate_eval, tf):
    # C12 + n --> C13
    rate = 0.0

    # ks03 
    rate += np.exp(  7.98821 + -0.00836732*tf.T9i + 1.49573*tf.T913i + -0.841102*tf.T913
                  + 0.0340543*tf.T9 + -0.0026392*tf.T953 + 1.6662*tf.lnT9)

    rate_eval.n_C12__C13 = rate

@numba.njit()
def Ar31__p_S30__weak__wc17(rate_eval, tf):
    # Ar31 --> p + S30
    rate = 0.0

    # wc17w
    rate += np.exp(  3.39598)

    rate_eval.Ar31__p_S30__weak__wc17 = rate

@numba.njit()
def p_Mn63__n_Fe63(rate_eval, tf):
    # Mn63 + p --> n + Fe63
    rate = 0.0

    # rath 
    rate += np.exp(  147.406 + -6.9713*tf.T9i + 264.325*tf.T913i + -425.141*tf.T913
                  + 23.2301*tf.T9 + -1.28905*tf.T953 + 213.268*tf.lnT9)

    rate_eval.p_Mn63__n_Fe63 = rate

@numba.njit()
def n_Al27__Al28(rate_eval, tf):
    # Al27 + n --> Al28
    rate = 0.0

    # ks03 
    rate += np.exp(  19.7971 + -0.0784751*tf.T9i + 7.49524*tf.T913i + -14.6211*tf.T913
                  + 0.721304*tf.T9 + -0.0288351*tf.T953 + 6.58346*tf.lnT9)

    rate_eval.n_Al27__Al28 = rate

@numba.njit()
def Mn49__Cr49__weak__wc12(rate_eval, tf):
    # Mn49 --> Cr49
    rate = 0.0

    # wc12w
    rate += np.exp(  0.595822)

    rate_eval.Mn49__Cr49__weak__wc12 = rate

@numba.njit()
def He4_Cl43__n_K46(rate_eval, tf):
    # Cl43 + He4 --> n + K46
    rate = 0.0

    # rath 
    rate += np.exp(  -360.894 + 1.95672*tf.T9i + -516.607*tf.T913i + 916.522*tf.T913
                  + -60.6798*tf.T9 + 3.69911*tf.T953 + -401.154*tf.lnT9)

    rate_eval.He4_Cl43__n_K46 = rate

@numba.njit()
def Al42__n_n_Si40__weak__mo03(rate_eval, tf):
    # Al42 --> n + n + Si40
    rate = 0.0

    # mo03w
    rate += np.exp(  5.0955)

    rate_eval.Al42__n_n_Si40__weak__mo03 = rate

@numba.njit()
def He4_Na33__n_Al36(rate_eval, tf):
    # Na33 + He4 --> n + Al36
    rate = 0.0

    # rath 
    rate += np.exp(  78.5725 + -3.29537*tf.T9i + 75.4152*tf.T913i + -162.334*tf.T913
                  + 7.60184*tf.T9 + -0.38408*tf.T953 + 84.7196*tf.lnT9)

    rate_eval.He4_Na33__n_Al36 = rate

@numba.njit()
def Cl32__He4_Si28__weak__wc12(rate_eval, tf):
    # Cl32 --> He4 + Si28
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.75675)

    rate_eval.Cl32__He4_Si28__weak__wc12 = rate

@numba.njit()
def S28__P28__weak__wc12(rate_eval, tf):
    # S28 --> P28
    rate = 0.0

    # wc12w
    rate += np.exp(  1.481)

    rate_eval.S28__P28__weak__wc12 = rate

@numba.njit()
def n_K48__K49(rate_eval, tf):
    # K48 + n --> K49
    rate = 0.0

    # rath 
    rate += np.exp(  17.3896 + -0.0353762*tf.T9i + 3.18892*tf.T913i + -8.24022*tf.T913
                  + 0.425119*tf.T9 + -0.0299774*tf.T953 + 2.93541*tf.lnT9)

    rate_eval.n_K48__K49 = rate

@numba.njit()
def He4_Ti55__Cr59(rate_eval, tf):
    # Ti55 + He4 --> Cr59
    rate = 0.0

    # rath 
    rate += np.exp(  -991.179 + 20.581*tf.T9i + -2049.68*tf.T913i + 3157.3*tf.T913
                  + -179.323*tf.T9 + 9.9115*tf.T953 + -1530.69*tf.lnT9)

    rate_eval.He4_Ti55__Cr59 = rate

@numba.njit()
def He4_V45__p_Cr48(rate_eval, tf):
    # V45 + He4 --> p + Cr48
    rate = 0.0

    # ths8r
    rate += np.exp(  59.6809 + -84.1758*tf.T913i + -1.12403*tf.T913
                  + -0.469581*tf.T9 + 0.00932056*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V45__p_Cr48 = rate

@numba.njit()
def He4_Al39__P43(rate_eval, tf):
    # Al39 + He4 --> P43
    rate = 0.0

    # rath 
    rate += np.exp(  -22.7481 + -3.01751*tf.T9i + -15.5543*tf.T913i + 26.6872*tf.T913
                  + -5.43254*tf.T9 + 0.433402*tf.T953 + 5.27413*tf.lnT9)

    rate_eval.He4_Al39__P43 = rate

@numba.njit()
def p_Ne30__n_Na30(rate_eval, tf):
    # Ne30 + p --> n + Na30
    rate = 0.0

    # rath 
    rate += np.exp(  71.8495 + -2.66899*tf.T9i + 94.7716*tf.T913i + -161.174*tf.T913
                  + 8.78653*tf.T9 + -0.487268*tf.T953 + 80.5481*tf.lnT9)

    rate_eval.p_Ne30__n_Na30 = rate

@numba.njit()
def p_F30__n_Ne30(rate_eval, tf):
    # F30 + p --> n + Ne30
    rate = 0.0

    # rpsmr
    rate += np.exp(  68.7928 + -2.48866*tf.T9i + 88.4973*tf.T913i + -150.592*tf.T913
                  + 8.16946*tf.T9 + -0.451427*tf.T953 + 75.2162*tf.lnT9)

    rate_eval.p_F30__n_Ne30 = rate

@numba.njit()
def p_Na27__He4_Ne24(rate_eval, tf):
    # Na27 + p --> He4 + Ne24
    rate = 0.0

    # rath 
    rate += np.exp(  64.7054 + -2.68837*tf.T9i + 93.4181*tf.T913i + -157.624*tf.T913
                  + 8.33945*tf.T9 + -0.434929*tf.T953 + 79.8664*tf.lnT9)

    rate_eval.p_Na27__He4_Ne24 = rate

@numba.njit()
def n_Ti50__Ti51(rate_eval, tf):
    # Ti50 + n --> Ti51
    rate = 0.0

    # ks03 
    rate += np.exp(  40.4047 + -0.00979462*tf.T9i + 7.07296*tf.T913i + -37.8514*tf.T913
                  + 4.03187*tf.T9 + -0.339274*tf.T953 + 11.4094*tf.lnT9)

    rate_eval.n_Ti50__Ti51 = rate

@numba.njit()
def He4_Na25__n_Al28(rate_eval, tf):
    # Na25 + He4 --> n + Al28
    rate = 0.0

    # rath 
    rate += np.exp(  69.8281 + -2.74048*tf.T9i + 53.0695*tf.T913i + -130.953*tf.T913
                  + 6.01184*tf.T9 + -0.303477*tf.T953 + 68.7494*tf.lnT9)

    rate_eval.He4_Na25__n_Al28 = rate

@numba.njit()
def n_S27__He4_Si24(rate_eval, tf):
    # S27 + n --> He4 + Si24
    rate = 0.0

    # ths8r
    rate += np.exp(  14.3889 + 1.22015*tf.T913
                  + -0.100274*tf.T9 + 0.0100944*tf.T953)

    rate_eval.n_S27__He4_Si24 = rate

@numba.njit()
def Mn66__n_Fe65__weak__mp17(rate_eval, tf):
    # Mn66 --> n + Fe65
    rate = 0.0

    # mp17w
    rate += np.exp(  0.06427)

    rate_eval.Mn66__n_Fe65__weak__mp17 = rate

@numba.njit()
def C22__n_N21__weak__wc17(rate_eval, tf):
    # C22 --> n + N21
    rate = 0.0

    # wc17w
    rate += np.exp(  4.23866)

    rate_eval.C22__n_N21__weak__wc17 = rate

@numba.njit()
def p_Si33__He4_Al30(rate_eval, tf):
    # Si33 + p --> He4 + Al30
    rate = 0.0

    # rath 
    rate += np.exp(  118.604 + -3.01386*tf.T9i + 129.736*tf.T913i + -270.032*tf.T913
                  + 13.7517*tf.T9 + -0.707932*tf.T953 + 135.663*tf.lnT9)

    rate_eval.p_Si33__He4_Al30 = rate

@numba.njit()
def p_B11__C12(rate_eval, tf):
    # B11 + p --> C12
    rate = 0.0

    # nw00n
    rate += np.exp(  25.5647 + -12.095*tf.T913i + -6.68421*tf.T913
                  + -0.0148736*tf.T9 + 0.0364288*tf.T953 + 1.33333*tf.lnT9)
    # nw00n
    rate += np.exp(  18.6165 + -12.095*tf.T913i + -1.95046*tf.T913
                  + 9.56928*tf.T9 + -10.0637*tf.T953 + -0.666667*tf.lnT9)
    # nw00r
    rate += np.exp(  8.67352 + -1.71197*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_B11__C12 = rate

@numba.njit()
def Ti39__p_Ca38__weak__wc12(rate_eval, tf):
    # Ti39 --> p + Ca38
    rate = 0.0

    # wc12w
    rate += np.exp(  3.10725)

    rate_eval.Ti39__p_Ca38__weak__wc12 = rate

@numba.njit()
def Ti44__Sc44__weak__wc12(rate_eval, tf):
    # Ti44 --> Sc44
    rate = 0.0

    # wc12w
    rate += np.exp(  -21.7264)

    rate_eval.Ti44__Sc44__weak__wc12 = rate

@numba.njit()
def n_V64__V65(rate_eval, tf):
    # V64 + n --> V65
    rate = 0.0

    # rath 
    rate += np.exp(  25.5595 + -0.0146508*tf.T9i + 3.21714*tf.T913i + -17.7545*tf.T913
                  + 1.42071*tf.T9 + -0.10887*tf.T953 + 4.76349*tf.lnT9)

    rate_eval.n_V64__V65 = rate

@numba.njit()
def Mg23__Na23__weak__wc12(rate_eval, tf):
    # Mg23 --> Na23
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.79132)

    rate_eval.Mg23__Na23__weak__wc12 = rate

@numba.njit()
def Ar39__K39__weak__wc12(rate_eval, tf):
    # Ar39 --> K39
    rate = 0.0

    # wc12w
    rate += np.exp(  -23.2287)

    rate_eval.Ar39__K39__weak__wc12 = rate

@numba.njit()
def n_Sc36__p_Ca36(rate_eval, tf):
    # Sc36 + n --> p + Ca36
    rate = 0.0

    # ths8r
    rate += np.exp(  19.9351 + 0.328677*tf.T913
                  + 0.0400666*tf.T9 + -0.00350258*tf.T953)

    rate_eval.n_Sc36__p_Ca36 = rate

@numba.njit()
def p_K46__He4_Ar43(rate_eval, tf):
    # K46 + p --> He4 + Ar43
    rate = 0.0

    # rath 
    rate += np.exp(  55.2854 + -5.10364*tf.T9i + 192.512*tf.T913i + -266.324*tf.T913
                  + 10.684*tf.T9 + -0.344051*tf.T953 + 153.097*tf.lnT9)

    rate_eval.p_K46__He4_Ar43 = rate

@numba.njit()
def p_S41__n_Cl41(rate_eval, tf):
    # S41 + p --> n + Cl41
    rate = 0.0

    # rath 
    rate += np.exp(  97.7412 + -4.23425*tf.T9i + 154.237*tf.T913i + -254.526*tf.T913
                  + 13.9662*tf.T9 + -0.779968*tf.T953 + 127.715*tf.lnT9)

    rate_eval.p_S41__n_Cl41 = rate

@numba.njit()
def Sc59__n_Ti58__weak__mp17(rate_eval, tf):
    # Sc59 --> n + Ti58
    rate = 0.0

    # mp17w
    rate += np.exp(  3.41699)

    rate_eval.Sc59__n_Ti58__weak__mp17 = rate

@numba.njit()
def He4_t__Li7(rate_eval, tf):
    # t + He4 --> Li7
    rate = 0.0

    # de04 
    rate += np.exp(  13.6162 + -8.0805*tf.T913i + -0.217514*tf.T913
                  + -0.114859*tf.T9 + 0.0470043*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_t__Li7 = rate

@numba.njit()
def p_Mg36__n_Al36(rate_eval, tf):
    # Mg36 + p --> n + Al36
    rate = 0.0

    # rath 
    rate += np.exp(  79.9963 + -3.28357*tf.T9i + 117.705*tf.T913i + -194.872*tf.T913
                  + 10.5284*tf.T9 + -0.578482*tf.T953 + 98.0921*tf.lnT9)

    rate_eval.p_Mg36__n_Al36 = rate

@numba.njit()
def Sc58__n_Ti57__weak__mp17(rate_eval, tf):
    # Sc58 --> n + Ti57
    rate = 0.0

    # mp17w
    rate += np.exp(  2.22375)

    rate_eval.Sc58__n_Ti57__weak__mp17 = rate

@numba.njit()
def n_He4_He4__Be9(rate_eval, tf):
    # n + He4 + He4 --> Be9
    rate = 0.0

    # ac12r
    rate += np.exp(  -6.81178 + -1.01953*tf.T9i + -1.56673*tf.T913i + -5.43497*tf.T913
                  + 0.673807*tf.T9 + -0.041014*tf.T953 + -1.5*tf.lnT9)
    # ac12n
    rate += np.exp(  -8.22898 + -13.3317*tf.T913i + 13.2237*tf.T913
                  + -9.06339*tf.T9 + -0.666667*tf.lnT9)

    rate_eval.n_He4_He4__Be9 = rate

@numba.njit()
def He4_P47__Cl51(rate_eval, tf):
    # P47 + He4 --> Cl51
    rate = 0.0

    # rath 
    rate += np.exp(  -363.482 + 2.00662*tf.T9i + -505.261*tf.T913i + 898.102*tf.T913
                  + -59.205*tf.T9 + 3.59835*tf.T953 + -394.27*tf.lnT9)

    rate_eval.He4_P47__Cl51 = rate

@numba.njit()
def K54__n_n_Ca52__weak__mp17(rate_eval, tf):
    # K54 --> n + n + Ca52
    rate = 0.0

    # mp17w
    rate += np.exp(  2.27254)

    rate_eval.K54__n_n_Ca52__weak__mp17 = rate

@numba.njit()
def p_Cr69__n_Mn69(rate_eval, tf):
    # Cr69 + p --> n + Mn69
    rate = 0.0

    # rath 
    rate += np.exp(  149.281 + -7.05451*tf.T9i + 268.51*tf.T913i + -431.354*tf.T913
                  + 23.8686*tf.T9 + -1.33702*tf.T953 + 215.665*tf.lnT9)

    rate_eval.p_Cr69__n_Mn69 = rate

@numba.njit()
def Sc59__Ti59__weak__mo03(rate_eval, tf):
    # Sc59 --> Ti59
    rate = 0.0

    # mo03w
    rate += np.exp(  4.02053)

    rate_eval.Sc59__Ti59__weak__mo03 = rate

@numba.njit()
def He4_Cl48__K52(rate_eval, tf):
    # Cl48 + He4 --> K52
    rate = 0.0

    # rath 
    rate += np.exp(  -818.935 + 13.2132*tf.T9i + -1429.24*tf.T913i + 2340.12*tf.T913
                  + -139.626*tf.T9 + 8.00311*tf.T953 + -1099.3*tf.lnT9)

    rate_eval.He4_Cl48__K52 = rate

@numba.njit()
def He4_Ar47__n_Ca50(rate_eval, tf):
    # Ar47 + He4 --> n + Ca50
    rate = 0.0

    # rath 
    rate += np.exp(  -391.307 + 2.05901*tf.T9i + -553.669*tf.T913i + 986.653*tf.T913
                  + -65.2529*tf.T9 + 3.97502*tf.T953 + -431.877*tf.lnT9)

    rate_eval.He4_Ar47__n_Ca50 = rate

@numba.njit()
def n_Al32__Al33(rate_eval, tf):
    # Al32 + n --> Al33
    rate = 0.0

    # rath 
    rate += np.exp(  15.9939 + -0.0490794*tf.T9i + 4.08203*tf.T913i + -8.76952*tf.T913
                  + 0.464289*tf.T9 + -0.027472*tf.T953 + 3.41954*tf.lnT9)

    rate_eval.n_Al32__Al33 = rate

@numba.njit()
def n_Cr65__Cr66(rate_eval, tf):
    # Cr65 + n --> Cr66
    rate = 0.0

    # rath 
    rate += np.exp(  4.87744 + 0.0355606*tf.T9i + -4.56361*tf.T913i + 12.0708*tf.T913
                  + -0.960483*tf.T9 + 0.0179911*tf.T953 + -4.8037*tf.lnT9)

    rate_eval.n_Cr65__Cr66 = rate

@numba.njit()
def p_V51__Cr52(rate_eval, tf):
    # V51 + p --> Cr52
    rate = 0.0

    # ths8r
    rate += np.exp(  34.1505 + -34.2261*tf.T913i + 3.30454*tf.T913
                  + -2.61654*tf.T9 + 0.283602*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_V51__Cr52 = rate

@numba.njit()
def Ca49__Sc49__weak__wc12(rate_eval, tf):
    # Ca49 --> Sc49
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.62609)

    rate_eval.Ca49__Sc49__weak__wc12 = rate

@numba.njit()
def p_Al38__Si39(rate_eval, tf):
    # Al38 + p --> Si39
    rate = 0.0

    # rath 
    rate += np.exp(  79.4524 + -3.56575*tf.T9i + 130.072*tf.T913i + -218.534*tf.T913
                  + 12.0568*tf.T9 + -0.670415*tf.T953 + 108.775*tf.lnT9)

    rate_eval.p_Al38__Si39 = rate

@numba.njit()
def He4_S40__n_Ar43(rate_eval, tf):
    # S40 + He4 --> n + Ar43
    rate = 0.0

    # rath 
    rate += np.exp(  -332.115 + 1.86974*tf.T9i + -483.79*tf.T913i + 852.785*tf.T913
                  + -56.4277*tf.T9 + 3.4384*tf.T953 + -373.713*tf.lnT9)

    rate_eval.He4_S40__n_Ar43 = rate

@numba.njit()
def V54__Cr54__weak__wc12(rate_eval, tf):
    # V54 --> Cr54
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.27453)

    rate_eval.V54__Cr54__weak__wc12 = rate

@numba.njit()
def Na31__n_n_n_Mg28__weak__wc12(rate_eval, tf):
    # Na31 --> 3 n + Mg28
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.89287)

    rate_eval.Na31__n_n_n_Mg28__weak__wc12 = rate

@numba.njit()
def He4_Si35__S39(rate_eval, tf):
    # Si35 + He4 --> S39
    rate = 0.0

    # rath 
    rate += np.exp(  -294.898 + 1.71815*tf.T9i + -425.766*tf.T913i + 745.236*tf.T913
                  + -49.4711*tf.T9 + 3.03018*tf.T953 + -326.744*tf.lnT9)

    rate_eval.He4_Si35__S39 = rate

@numba.njit()
def He4_P43__Cl47(rate_eval, tf):
    # P43 + He4 --> Cl47
    rate = 0.0

    # rath 
    rate += np.exp(  -339.859 + 1.783*tf.T9i + -473.613*tf.T913i + 840.777*tf.T913
                  + -55.8555*tf.T9 + 3.41197*tf.T953 + -367.739*tf.lnT9)

    rate_eval.He4_P43__Cl47 = rate

@numba.njit()
def Ne17__F17__weak__wc17(rate_eval, tf):
    # Ne17 --> F17
    rate = 0.0

    # wc17w
    rate += np.exp(  -113.281)

    rate_eval.Ne17__F17__weak__wc17 = rate

@numba.njit()
def He4_Na29__n_Al32(rate_eval, tf):
    # Na29 + He4 --> n + Al32
    rate = 0.0

    # rath 
    rate += np.exp(  73.9992 + -3.02929*tf.T9i + 64.629*tf.T913i + -146.923*tf.T913
                  + 6.81086*tf.T9 + -0.343383*tf.T953 + 76.9734*tf.lnT9)

    rate_eval.He4_Na29__n_Al32 = rate

@numba.njit()
def n_Ne21__Ne22(rate_eval, tf):
    # Ne21 + n --> Ne22
    rate = 0.0

    # ks03 
    rate += np.exp(  23.5205 + 0.0482005*tf.T9i + -0.238173*tf.T913i + -12.2336*tf.T913
                  + 1.14968*tf.T9 + -0.0768882*tf.T953 + 2.63636*tf.lnT9)

    rate_eval.n_Ne21__Ne22 = rate

@numba.njit()
def n_Ca41__He4_Ar38(rate_eval, tf):
    # Ca41 + n --> He4 + Ar38
    rate = 0.0

    # ta18 
    rate += np.exp(  16.972 + -1.36064e-05*tf.T9i + -0.0142*tf.T913i + -0.10052*tf.T913
                  + 0.27737*tf.T9 + -0.00483*tf.T953 + -0.2165*tf.lnT9)

    rate_eval.n_Ca41__He4_Ar38 = rate

@numba.njit()
def P24__Si24__weak__bqa_pos_(rate_eval, tf):
    # P24 --> Si24
    rate = 0.0

    # bqa+w
    rate += np.exp(  4.53976)

    rate_eval.P24__Si24__weak__bqa_pos_ = rate

@numba.njit()
def O26__n_F25__weak__mp17(rate_eval, tf):
    # O26 --> n + F25
    rate = 0.0

    # mp17w
    rate += np.exp(  4.04564)

    rate_eval.O26__n_F25__weak__mp17 = rate

@numba.njit()
def Sc40__He4_Ar36__weak__wc12(rate_eval, tf):
    # Sc40 --> He4 + Ar36
    rate = 0.0

    # wc12w
    rate += np.exp(  -7.17996)

    rate_eval.Sc40__He4_Ar36__weak__wc12 = rate

@numba.njit()
def He4_Mg35__Si39(rate_eval, tf):
    # Mg35 + He4 --> Si39
    rate = 0.0

    # rath 
    rate += np.exp(  -17.1668 + -2.66771*tf.T9i + -18.3034*tf.T913i + 25.7595*tf.T913
                  + -5.0369*tf.T9 + 0.400292*tf.T953 + 3.61445*tf.lnT9)

    rate_eval.He4_Mg35__Si39 = rate

@numba.njit()
def Na22__Ne22__weak__wc12(rate_eval, tf):
    # Na22 --> Ne22
    rate = 0.0

    # wc12w
    rate += np.exp(  -18.59)

    rate_eval.Na22__Ne22__weak__wc12 = rate

@numba.njit()
def He4_F23__Na27(rate_eval, tf):
    # F23 + He4 --> Na27
    rate = 0.0

    # rpsmr
    rate += np.exp(  47.6827 + -2.23118*tf.T9i + 37.7851*tf.T913i + -98.9875*tf.T913
                  + 4.16371*tf.T9 + -0.192076*tf.T953 + 53.0679*tf.lnT9)

    rate_eval.He4_F23__Na27 = rate

@numba.njit()
def p_K49__He4_Ar46(rate_eval, tf):
    # K49 + p --> He4 + Ar46
    rate = 0.0

    # rath 
    rate += np.exp(  82.276 + -5.12538*tf.T9i + 185.462*tf.T913i + -281.034*tf.T913
                  + 12.9103*tf.T9 + -0.472953*tf.T953 + 148.584*tf.lnT9)

    rate_eval.p_K49__He4_Ar46 = rate

@numba.njit()
def p_P25__S26(rate_eval, tf):
    # P25 + p --> S26
    rate = 0.0

    # ths8r
    rate += np.exp(  40.0996 + -25.5693*tf.T913i + -17.8904*tf.T913
                  + 2.11195*tf.T9 + -0.111747*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_P25__S26 = rate

@numba.njit()
def p_Na24__Mg25(rate_eval, tf):
    # Na24 + p --> Mg25
    rate = 0.0

    # rath 
    rate += np.exp(  63.7099 + -2.54619*tf.T9i + 88.4533*tf.T913i + -156.066*tf.T913
                  + 8.77114*tf.T9 + -0.500891*tf.T953 + 77.2574*tf.lnT9)

    rate_eval.p_Na24__Mg25 = rate

@numba.njit()
def Al34__Si34__weak__wc12(rate_eval, tf):
    # Al34 --> Si34
    rate = 0.0

    # wc12w
    rate += np.exp(  2.48886)

    rate_eval.Al34__Si34__weak__wc12 = rate

@numba.njit()
def S46__Cl46__weak__wc17(rate_eval, tf):
    # S46 --> Cl46
    rate = 0.0

    # wc17w
    rate += np.exp(  1.35625)

    rate_eval.S46__Cl46__weak__wc17 = rate

@numba.njit()
def n_Mg38__Mg39(rate_eval, tf):
    # Mg38 + n --> Mg39
    rate = 0.0

    # rath 
    rate += np.exp(  131.799 + -11.7151*tf.T9i + 355.175*tf.T913i + -506.241*tf.T913
                  + 28.5319*tf.T9 + -1.64067*tf.T953 + 256.168*tf.lnT9)

    rate_eval.n_Mg38__Mg39 = rate

@numba.njit()
def N20__n_O19__weak__wc12(rate_eval, tf):
    # N20 --> n + O19
    rate = 0.0

    # wc12w
    rate += np.exp(  0.782289)

    rate_eval.N20__n_O19__weak__wc12 = rate

@numba.njit()
def Ca59__n_Sc58__weak__mp17(rate_eval, tf):
    # Ca59 --> n + Sc58
    rate = 0.0

    # mp17w
    rate += np.exp(  4.37827)

    rate_eval.Ca59__n_Sc58__weak__mp17 = rate

@numba.njit()
def Mn73__Fe73__weak__mo03(rate_eval, tf):
    # Mn73 --> Fe73
    rate = 0.0

    # mo03w
    rate += np.exp(  3.18883)

    rate_eval.Mn73__Fe73__weak__mo03 = rate

@numba.njit()
def Al24__He4_Ne20__weak__wc12(rate_eval, tf):
    # Al24 --> He4 + Ne20
    rate = 0.0

    # wc12w
    rate += np.exp(  -8.9084)

    rate_eval.Al24__He4_Ne20__weak__wc12 = rate

@numba.njit()
def He4_Na21__Al25(rate_eval, tf):
    # Na21 + He4 --> Al25
    rate = 0.0

    # ths8r
    rate += np.exp(  35.3006 + -49.9709*tf.T913i + 1.63835*tf.T913
                  + -1.18562*tf.T9 + 0.101965*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Na21__Al25 = rate

@numba.njit()
def Ca55__Sc55__weak__wc12(rate_eval, tf):
    # Ca55 --> Sc55
    rate = 0.0

    # wc12w
    rate += np.exp(  3.4502)

    rate_eval.Ca55__Sc55__weak__wc12 = rate

@numba.njit()
def Ca58__n_Sc57__weak__mp17(rate_eval, tf):
    # Ca58 --> n + Sc57
    rate = 0.0

    # mp17w
    rate += np.exp(  1.11894)

    rate_eval.Ca58__n_Sc57__weak__mp17 = rate

@numba.njit()
def He4_P45__n_Cl48(rate_eval, tf):
    # P45 + He4 --> n + Cl48
    rate = 0.0

    # rath 
    rate += np.exp(  -14.1389 + -3.61866*tf.T9i + -11.118*tf.T913i + 22.3087*tf.T913
                  + -5.48403*tf.T9 + 0.44282*tf.T953 + 9.368*tf.lnT9)

    rate_eval.He4_P45__n_Cl48 = rate

@numba.njit()
def n_Ne31__Ne32(rate_eval, tf):
    # Ne31 + n --> Ne32
    rate = 0.0

    # rath 
    rate += np.exp(  10.9102 + -0.0647456*tf.T9i + 4.55381*tf.T913i + -8.5975*tf.T913
                  + 0.689026*tf.T9 + -0.0367362*tf.T953 + 3.28893*tf.lnT9)

    rate_eval.n_Ne31__Ne32 = rate

@numba.njit()
def He4_Sc52__V56(rate_eval, tf):
    # Sc52 + He4 --> V56
    rate = 0.0

    # rath 
    rate += np.exp(  -971.675 + 15.4954*tf.T9i + -1683.12*tf.T913i + 2762.77*tf.T913
                  + -165.081*tf.T9 + 9.46536*tf.T953 + -1296.48*tf.lnT9)

    rate_eval.He4_Sc52__V56 = rate

@numba.njit()
def Ar32__p_S31__weak__wc12(rate_eval, tf):
    # Ar32 --> p + S31
    rate = 0.0

    # wc12w
    rate += np.exp(  0.893297)

    rate_eval.Ar32__p_S31__weak__wc12 = rate

@numba.njit()
def Ca57__n_Sc56__weak__mp17(rate_eval, tf):
    # Ca57 --> n + Sc56
    rate = 0.0

    # mp17w
    rate += np.exp(  2.45948)

    rate_eval.Ca57__n_Sc56__weak__mp17 = rate

@numba.njit()
def He4_Mg41__n_Si44(rate_eval, tf):
    # Mg41 + He4 --> n + Si44
    rate = 0.0

    # rath 
    rate += np.exp(  93.4316 + -4.04555*tf.T9i + 104.982*tf.T913i + -209.997*tf.T913
                  + 10.2123*tf.T9 + -0.529395*tf.T953 + 108.45*tf.lnT9)

    rate_eval.He4_Mg41__n_Si44 = rate

@numba.njit()
def n_Cl39__Cl40(rate_eval, tf):
    # Cl39 + n --> Cl40
    rate = 0.0

    # rath 
    rate += np.exp(  12.8602 + -0.0270037*tf.T9i + 1.38817*tf.T913i + -1.52329*tf.T913
                  + 0.0974117*tf.T9 + -0.015701*tf.T953 + 0.606824*tf.lnT9)

    rate_eval.n_Cl39__Cl40 = rate

@numba.njit()
def He4_C14__O18(rate_eval, tf):
    # C14 + He4 --> O18
    rate = 0.0

    # il10r
    rate += np.exp(  11.8309 + -10.3983*tf.T9i + -3.83188*tf.T913
                  + 1.64358*tf.T9 + -0.177785*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -23.805 + -2.06876*tf.T9i
                  + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  18.4877 + -31.7222*tf.T913i + 11.3923*tf.T913
                  + -9.92249*tf.T9 + -2.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_C14__O18 = rate

@numba.njit()
def Ca52__n_Sc51__weak__wc12(rate_eval, tf):
    # Ca52 --> n + Sc51
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.80459)

    rate_eval.Ca52__n_Sc51__weak__wc12 = rate

@numba.njit()
def He4_O18__Ne22(rate_eval, tf):
    # O18 + He4 --> Ne22
    rate = 0.0

    # il10r
    rate += np.exp(  -31.9126 + -2.00306*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -81.3036 + -0.676112*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  14.9748 + -31.0468*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  82.2053 + -1.58534*tf.T9i + -44.3823*tf.T913i + -46.6617*tf.T913
                  + 7.88059*tf.T9 + -0.590829*tf.T953 + -1.5*tf.lnT9)

    rate_eval.He4_O18__Ne22 = rate

@numba.njit()
def Si24__Al24__weak__wc12(rate_eval, tf):
    # Si24 --> Al24
    rate = 0.0

    # wc12w
    rate += np.exp(  0.994645)

    rate_eval.Si24__Al24__weak__wc12 = rate

@numba.njit()
def n_V54__V55(rate_eval, tf):
    # V54 + n --> V55
    rate = 0.0

    # rath 
    rate += np.exp(  23.9166 + -0.0665381*tf.T9i + 6.64826*tf.T913i + -17.0191*tf.T913
                  + 1.18584*tf.T9 + -0.094242*tf.T953 + 6.37461*tf.lnT9)

    rate_eval.n_V54__V55 = rate

@numba.njit()
def p_S39__n_Cl39(rate_eval, tf):
    # S39 + p --> n + Cl39
    rate = 0.0

    # rath 
    rate += np.exp(  96.6137 + -4.13703*tf.T9i + 150.143*tf.T913i + -249.165*tf.T913
                  + 13.676*tf.T9 + -0.764085*tf.T953 + 124.867*tf.lnT9)

    rate_eval.p_S39__n_Cl39 = rate

@numba.njit()
def Cl34__S34__weak__wc12(rate_eval, tf):
    # Cl34 --> S34
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.791781)

    rate_eval.Cl34__S34__weak__wc12 = rate

@numba.njit()
def He4_Mn62__Co66(rate_eval, tf):
    # Mn62 + He4 --> Co66
    rate = 0.0

    # rath 
    rate += np.exp(  -1138.32 + 23.7704*tf.T9i + -2361.87*tf.T913i + 3634.93*tf.T913
                  + -205.682*tf.T9 + 11.3441*tf.T953 + -1765.33*tf.lnT9)

    rate_eval.He4_Mn62__Co66 = rate

@numba.njit()
def Al42__n_Si41__weak__mp17(rate_eval, tf):
    # Al42 --> n + Si41
    rate = 0.0

    # mp17w
    rate += np.exp(  5.80429)

    rate_eval.Al42__n_Si41__weak__mp17 = rate

@numba.njit()
def Si42__n_P41__weak__mp17(rate_eval, tf):
    # Si42 --> n + P41
    rate = 0.0

    # mp17w
    rate += np.exp(  3.23899)

    rate_eval.Si42__n_P41__weak__mp17 = rate

@numba.njit()
def He4_K44__n_Sc47(rate_eval, tf):
    # K44 + He4 --> n + Sc47
    rate = 0.0

    # rath 
    rate += np.exp(  -826.107 + 13.4076*tf.T9i + -1457.3*tf.T913i + 2384.49*tf.T913
                  + -142.567*tf.T9 + 8.18434*tf.T953 + -1118.53*tf.lnT9)

    rate_eval.He4_K44__n_Sc47 = rate

@numba.njit()
def n_Na19__He4_F16(rate_eval, tf):
    # Na19 + n --> He4 + F16
    rate = 0.0

    # ths8r
    rate += np.exp(  16.4381 + 1.52115*tf.T913
                  + -0.0816609*tf.T9 + -0.00073752*tf.T953)

    rate_eval.n_Na19__He4_F16 = rate

@numba.njit()
def V62__Cr62__weak__wc17(rate_eval, tf):
    # V62 --> Cr62
    rate = 0.0

    # wc17w
    rate += np.exp(  2.81898)

    rate_eval.V62__Cr62__weak__wc17 = rate

@numba.njit()
def Cl46__n_Ar45__weak__wc12(rate_eval, tf):
    # Cl46 --> n + Ar45
    rate = 0.0

    # wc12w
    rate += np.exp(  0.583679)

    rate_eval.Cl46__n_Ar45__weak__wc12 = rate

@numba.njit()
def He4_Al28__P32(rate_eval, tf):
    # Al28 + He4 --> P32
    rate = 0.0

    # rath 
    rate += np.exp(  -0.522392 + -2.59086*tf.T9i + -14.2992*tf.T913i + 6.40835*tf.T913
                  + -3.59742*tf.T9 + 0.308804*tf.T953 + 10.094*tf.lnT9)

    rate_eval.He4_Al28__P32 = rate

@numba.njit()
def He4_Mn70__n_Co73(rate_eval, tf):
    # Mn70 + He4 --> n + Co73
    rate = 0.0

    # rath 
    rate += np.exp(  -1274.07 + 20.4461*tf.T9i + -2205.68*tf.T913i + 3635.85*tf.T913
                  + -216.137*tf.T9 + 12.3656*tf.T953 + -1709.31*tf.lnT9)

    rate_eval.He4_Mn70__n_Co73 = rate

@numba.njit()
def Cl51__n_Ar50__weak__mp17(rate_eval, tf):
    # Cl51 --> n + Ar50
    rate = 0.0

    # mp17w
    rate += np.exp(  4.37743)

    rate_eval.Cl51__n_Ar50__weak__mp17 = rate

@numba.njit()
def p_Cl33__Ar34(rate_eval, tf):
    # Cl33 + p --> Ar34
    rate = 0.0

    # ths8r
    rate += np.exp(  35.1297 + -27.8815*tf.T913i + -3.18731*tf.T913
                  + -1.76254*tf.T9 + 0.264735*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cl33__Ar34 = rate

@numba.njit()
def Ca37__p_Ar36__weak__wc12(rate_eval, tf):
    # Ca37 --> p + Ar36
    rate = 0.0

    # wc12w
    rate += np.exp(  1.14551)

    rate_eval.Ca37__p_Ar36__weak__wc12 = rate

@numba.njit()
def n_Mg30__Mg31(rate_eval, tf):
    # Mg30 + n --> Mg31
    rate = 0.0

    # rath 
    rate += np.exp(  3.9008 + 0.0137958*tf.T9i + -2.22936*tf.T913i + 7.58235*tf.T913
                  + -0.668788*tf.T9 + 0.0394569*tf.T953 + -2.67122*tf.lnT9)

    rate_eval.n_Mg30__Mg31 = rate

@numba.njit()
def p_Ca46__Sc47(rate_eval, tf):
    # Ca46 + p --> Sc47
    rate = 0.0

    # ths8r
    rate += np.exp(  34.3625 + -31.1593*tf.T913i + 0.979497*tf.T913
                  + -1.14947*tf.T9 + 0.064347*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ca46__Sc47 = rate

@numba.njit()
def Ca36__p_Ar35__weak__wc12(rate_eval, tf):
    # Ca36 --> p + Ar35
    rate = 0.0

    # wc12w
    rate += np.exp(  1.30562)

    rate_eval.Ca36__p_Ar35__weak__wc12 = rate

@numba.njit()
def p_Fe68__n_Co68(rate_eval, tf):
    # Fe68 + p --> n + Co68
    rate = 0.0

    # rath 
    rate += np.exp(  151.682 + -7.38518*tf.T9i + 280.061*tf.T913i + -446.726*tf.T913
                  + 24.4004*tf.T9 + -1.35581*tf.T953 + 224.626*tf.lnT9)

    rate_eval.p_Fe68__n_Co68 = rate

@numba.njit()
def n_Ti42__Ti43(rate_eval, tf):
    # Ti42 + n --> Ti43
    rate = 0.0

    # ths8r
    rate += np.exp(  13.6337 + -1.00856*tf.T913
                  + 0.342738*tf.T9 + -0.0367066*tf.T953)

    rate_eval.n_Ti42__Ti43 = rate

@numba.njit()
def Ca35__p_Ar34__weak__wc17(rate_eval, tf):
    # Ca35 --> p + Ar34
    rate = 0.0

    # wc17w
    rate += np.exp(  3.25289)

    rate_eval.Ca35__p_Ar34__weak__wc17 = rate

@numba.njit()
def C18__N18__weak__wc12(rate_eval, tf):
    # C18 --> N18
    rate = 0.0

    # wc12w
    rate += np.exp(  1.64112)

    rate_eval.C18__N18__weak__wc12 = rate

@numba.njit()
def Si26__Al26__weak__wc12(rate_eval, tf):
    # Si26 --> Al26
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.16851)

    rate_eval.Si26__Al26__weak__wc12 = rate

@numba.njit()
def O26__F26__weak__mo03(rate_eval, tf):
    # O26 --> F26
    rate = 0.0

    # mo03w
    rate += np.exp(  -111.011)

    rate_eval.O26__F26__weak__mo03 = rate

@numba.njit()
def Cr48__V48__weak__wc12(rate_eval, tf):
    # Cr48 --> V48
    rate = 0.0

    # wc12w
    rate += np.exp(  -11.6258)

    rate_eval.Cr48__V48__weak__wc12 = rate

@numba.njit()
def p_Na29__n_Mg29(rate_eval, tf):
    # Na29 + p --> n + Mg29
    rate = 0.0

    # rath 
    rate += np.exp(  73.6982 + -2.79531*tf.T9i + 98.6921*tf.T913i + -167.725*tf.T913
                  + 9.06416*tf.T9 + -0.50175*tf.T953 + 84.0854*tf.lnT9)

    rate_eval.p_Na29__n_Mg29 = rate

@numba.njit()
def B14__C14__weak__wc12(rate_eval, tf):
    # B14 --> C14
    rate = 0.0

    # wc12w
    rate += np.exp(  4.01551)

    rate_eval.B14__C14__weak__wc12 = rate

@numba.njit()
def n_p_He4__Li6(rate_eval, tf):
    # n + p + He4 --> Li6
    rate = 0.0

    # cf88r
    rate += np.exp(  -12.2851 + -19.353*tf.T9i + 1.44987*tf.T913i + -1.42759*tf.T913
                  + 0.0454035*tf.T9 + 0.00471161*tf.T953 + -1.0*tf.lnT9)

    rate_eval.n_p_He4__Li6 = rate

@numba.njit()
def K58__n_Ca57__weak__mp17(rate_eval, tf):
    # K58 --> n + Ca57
    rate = 0.0

    # mp17w
    rate += np.exp(  2.53391)

    rate_eval.K58__n_Ca57__weak__mp17 = rate

@numba.njit()
def He4_Na25__p_Mg28(rate_eval, tf):
    # Na25 + He4 --> p + Mg28
    rate = 0.0

    # rath 
    rate += np.exp(  56.9522 + -2.7407*tf.T9i + 53.8715*tf.T913i + -122.485*tf.T913
                  + 4.30488*tf.T9 + -0.147151*tf.T953 + 68.7524*tf.lnT9)

    rate_eval.He4_Na25__p_Mg28 = rate

@numba.njit()
def He4_Cl52__K56(rate_eval, tf):
    # Cl52 + He4 --> K56
    rate = 0.0

    # rath 
    rate += np.exp(  -850.831 + 13.4877*tf.T9i + -1465.79*tf.T913i + 2412.13*tf.T913
                  + -144.52*tf.T9 + 8.30881*tf.T953 + -1130.51*tf.lnT9)

    rate_eval.He4_Cl52__K56 = rate

@numba.njit()
def n_Ar33__Ar34(rate_eval, tf):
    # Ar33 + n --> Ar34
    rate = 0.0

    # ths8r
    rate += np.exp(  9.72602 + 0.607673*tf.T913
                  + -0.00457904*tf.T9 + 0.000938744*tf.T953)

    rate_eval.n_Ar33__Ar34 = rate

@numba.njit()
def n_Ca33__Ca34(rate_eval, tf):
    # Ca33 + n --> Ca34
    rate = 0.0

    # ths8r
    rate += np.exp(  9.57736 + -0.622548*tf.T913
                  + 0.340351*tf.T9 + -0.0307837*tf.T953)

    rate_eval.n_Ca33__Ca34 = rate

@numba.njit()
def K57__n_Ca56__weak__mp17(rate_eval, tf):
    # K57 --> n + Ca56
    rate = 0.0

    # mp17w
    rate += np.exp(  4.4509)

    rate_eval.K57__n_Ca56__weak__mp17 = rate

@numba.njit()
def He4_Sc53__n_V56(rate_eval, tf):
    # Sc53 + He4 --> n + V56
    rate = 0.0

    # rath 
    rate += np.exp(  -976.796 + 15.6715*tf.T9i + -1701.63*tf.T913i + 2797.67*tf.T913
                  + -167.256*tf.T9 + 9.60298*tf.T953 + -1311.97*tf.lnT9)

    rate_eval.He4_Sc53__n_V56 = rate

@numba.njit()
def p_V55__He4_Ti52(rate_eval, tf):
    # V55 + p --> He4 + Ti52
    rate = 0.0

    # rath 
    rate += np.exp(  98.8858 + -6.0963*tf.T9i + 220.951*tf.T913i + -337.473*tf.T913
                  + 17.3244*tf.T9 + -0.894517*tf.T953 + 176.416*tf.lnT9)

    rate_eval.p_V55__He4_Ti52 = rate

@numba.njit()
def p_Ca60__He4_K57(rate_eval, tf):
    # Ca60 + p --> He4 + K57
    rate = 0.0

    # rath 
    rate += np.exp(  4.42696 + -5.09714*tf.T9i + 136.832*tf.T913i + -165.047*tf.T913
                  + 5.65895*tf.T9 + -0.169671*tf.T953 + 106.625*tf.lnT9)

    rate_eval.p_Ca60__He4_K57 = rate

@numba.njit()
def p_Mn58__He4_Cr55(rate_eval, tf):
    # Mn58 + p --> He4 + Cr55
    rate = 0.0

    # rath 
    rate += np.exp(  79.3997 + -6.49259*tf.T9i + 227.765*tf.T913i + -323.709*tf.T913
                  + 14.9325*tf.T9 + -0.701658*tf.T953 + 177.593*tf.lnT9)

    rate_eval.p_Mn58__He4_Cr55 = rate

@numba.njit()
def n_Si39__Si40(rate_eval, tf):
    # Si39 + n --> Si40
    rate = 0.0

    # rath 
    rate += np.exp(  12.3036 + -0.0447623*tf.T9i + 3.4152*tf.T913i + -7.46054*tf.T913
                  + 0.753255*tf.T9 + -0.0606452*tf.T953 + 2.71684*tf.lnT9)

    rate_eval.n_Si39__Si40 = rate

@numba.njit()
def n_Fe46__Fe47(rate_eval, tf):
    # Fe46 + n --> Fe47
    rate = 0.0

    # ths8r
    rate += np.exp(  12.725 + -1.33686*tf.T913
                  + 0.342524*tf.T9 + -0.0330094*tf.T953)

    rate_eval.n_Fe46__Fe47 = rate

@numba.njit()
def n_Cr64__Cr65(rate_eval, tf):
    # Cr64 + n --> Cr65
    rate = 0.0

    # rath 
    rate += np.exp(  40.9795 + -0.194122*tf.T9i + 20.6551*tf.T913i + -59.1043*tf.T913
                  + 6.25177*tf.T9 + -0.540374*tf.T953 + 20.8844*tf.lnT9)

    rate_eval.n_Cr64__Cr65 = rate

@numba.njit()
def He4_K31__Sc35(rate_eval, tf):
    # K31 + He4 --> Sc35
    rate = 0.0

    # ths8r
    rate += np.exp(  42.5338 + -73.2242*tf.T913i + -0.850282*tf.T913
                  + -0.22634*tf.T9 + -0.022833*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K31__Sc35 = rate

@numba.njit()
def V39__Ti39__weak__bqa_pos_(rate_eval, tf):
    # V39 --> Ti39
    rate = 0.0

    # bqa+w
    rate += np.exp(  4.14335)

    rate_eval.V39__Ti39__weak__bqa_pos_ = rate

@numba.njit()
def K59__n_Ca58__weak__mp17(rate_eval, tf):
    # K59 --> n + Ca58
    rate = 0.0

    # mp17w
    rate += np.exp(  4.25886)

    rate_eval.K59__n_Ca58__weak__mp17 = rate

@numba.njit()
def He4_S31__Ar35(rate_eval, tf):
    # S31 + He4 --> Ar35
    rate = 0.0

    # ths8r
    rate += np.exp(  56.1418 + -65.2934*tf.T913i + -13.3991*tf.T913
                  + 1.97512*tf.T9 + -0.208606*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S31__Ar35 = rate

@numba.njit()
def p_Al37__n_Si37(rate_eval, tf):
    # Al37 + p --> n + Si37
    rate = 0.0

    # rath 
    rate += np.exp(  85.8909 + -3.51449*tf.T9i + 127.055*tf.T913i + -211.635*tf.T913
                  + 11.5592*tf.T9 + -0.641909*tf.T953 + 106.042*tf.lnT9)

    rate_eval.p_Al37__n_Si37 = rate

@numba.njit()
def S35__Cl35__weak__wc12(rate_eval, tf):
    # S35 --> Cl35
    rate = 0.0

    # wc12w
    rate += np.exp(  -16.2036)

    rate_eval.S35__Cl35__weak__wc12 = rate

@numba.njit()
def K52__n_Ca51__weak__wc12(rate_eval, tf):
    # K52 --> n + Ca51
    rate = 0.0

    # wc12w
    rate += np.exp(  1.45585)

    rate_eval.K52__n_Ca51__weak__wc12 = rate

@numba.njit()
def He4_F15__Na19(rate_eval, tf):
    # F15 + He4 --> Na19
    rate = 0.0

    # rpsmr
    rate += np.exp(  29.0728 + -1.55503*tf.T9i + 7.57892*tf.T913i + -50.2495*tf.T913
                  + 1.3919*tf.T9 + -0.0410995*tf.T953 + 29.8231*tf.lnT9)

    rate_eval.He4_F15__Na19 = rate

@numba.njit()
def N18__O18__weak__wc12(rate_eval, tf):
    # N18 --> O18
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.10167)

    rate_eval.N18__O18__weak__wc12 = rate

@numba.njit()
def p_Ti48__V49(rate_eval, tf):
    # Ti48 + p --> V49
    rate = 0.0

    # ths8r
    rate += np.exp(  35.2907 + -33.2133*tf.T913i + 0.564373*tf.T913
                  + -1.18789*tf.T9 + 0.110892*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ti48__V49 = rate

@numba.njit()
def K51__n_Ca50__weak__wc12(rate_eval, tf):
    # K51 --> n + Ca50
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.113678)

    rate_eval.K51__n_Ca50__weak__wc12 = rate

@numba.njit()
def Sc35__Ca35__weak__bqa_pos_(rate_eval, tf):
    # Sc35 --> Ca35
    rate = 0.0

    # bqa+w
    rate += np.exp(  3.83319)

    rate_eval.Sc35__Ca35__weak__bqa_pos_ = rate

@numba.njit()
def Mg32__Al32__weak__wc12(rate_eval, tf):
    # Mg32 --> Al32
    rate = 0.0

    # wc12w
    rate += np.exp(  2.03032)

    rate_eval.Mg32__Al32__weak__wc12 = rate

@numba.njit()
def F20__Ne20__weak__wc12(rate_eval, tf):
    # F20 --> Ne20
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.77346)

    rate_eval.F20__Ne20__weak__wc12 = rate

@numba.njit()
def p_Ar41__He4_Cl38(rate_eval, tf):
    # Ar41 + p --> He4 + Cl38
    rate = 0.0

    # rath 
    rate += np.exp(  47.7691 + -4.47424*tf.T9i + 155.497*tf.T913i + -215.661*tf.T913
                  + 9.46177*tf.T9 + -0.445691*tf.T953 + 123.859*tf.lnT9)

    rate_eval.p_Ar41__He4_Cl38 = rate

@numba.njit()
def He4_Mg21__p_Al24(rate_eval, tf):
    # Mg21 + He4 --> p + Al24
    rate = 0.0

    # ths8r
    rate += np.exp(  45.8014 + -52.9572*tf.T913i + 0.606361*tf.T913
                  + -0.788873*tf.T9 + 0.0605992*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg21__p_Al24 = rate

@numba.njit()
def K50__n_Ca49__weak__wc12(rate_eval, tf):
    # K50 --> n + Ca49
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.853611)

    rate_eval.K50__n_Ca49__weak__wc12 = rate

@numba.njit()
def He4_Ca41__Ti45(rate_eval, tf):
    # Ca41 + He4 --> Ti45
    rate = 0.0

    # ths8r
    rate += np.exp(  54.6305 + -76.4839*tf.T913i + 3.03748*tf.T913
                  + -2.59814*tf.T9 + 0.210582*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca41__Ti45 = rate

@numba.njit()
def He4_Cl40__K44(rate_eval, tf):
    # Cl40 + He4 --> K44
    rate = 0.0

    # rath 
    rate += np.exp(  -744.31 + 11.9824*tf.T9i + -1302.22*tf.T913i + 2130.94*tf.T913
                  + -127.97*tf.T9 + 7.38594*tf.T953 + -998.569*tf.lnT9)

    rate_eval.He4_Cl40__K44 = rate

@numba.njit()
def p_Cl49__He4_S46(rate_eval, tf):
    # Cl49 + p --> He4 + S46
    rate = 0.0

    # rath 
    rate += np.exp(  106.372 + -4.85375*tf.T9i + 184.323*tf.T913i + -307.746*tf.T913
                  + 17.244*tf.T9 + -0.923489*tf.T953 + 152.155*tf.lnT9)

    rate_eval.p_Cl49__He4_S46 = rate

@numba.njit()
def Sc56__Ti56__weak__wc17(rate_eval, tf):
    # Sc56 --> Ti56
    rate = 0.0

    # wc17w
    rate += np.exp(  3.16661)

    rate_eval.Sc56__Ti56__weak__wc17 = rate

@numba.njit()
def He4_Ar45__n_Ca48(rate_eval, tf):
    # Ar45 + He4 --> n + Ca48
    rate = 0.0

    # rath 
    rate += np.exp(  -382.941 + 2.05001*tf.T9i + -545.327*tf.T913i + 968.664*tf.T913
                  + -64.0187*tf.T9 + 3.89673*tf.T953 + -424.198*tf.lnT9)

    rate_eval.He4_Ar45__n_Ca48 = rate

@numba.njit()
def He4_P29__Cl33(rate_eval, tf):
    # P29 + He4 --> Cl33
    rate = 0.0

    # ths8r
    rate += np.exp(  41.9979 + -62.3802*tf.T913i + 0.593062*tf.T913
                  + -1.14226*tf.T9 + 0.0934776*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P29__Cl33 = rate

@numba.njit()
def K37__Ar37__weak__wc12(rate_eval, tf):
    # K37 --> Ar37
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.573527)

    rate_eval.K37__Ar37__weak__wc12 = rate

@numba.njit()
def n_Ca34__Ca35(rate_eval, tf):
    # Ca34 + n --> Ca35
    rate = 0.0

    # ths8r
    rate += np.exp(  9.89442 + 0.0618685*tf.T913
                  + 0.0394201*tf.T9 + 0.00182409*tf.T953)

    rate_eval.n_Ca34__Ca35 = rate

@numba.njit()
def n_Sc38__p_Ca38(rate_eval, tf):
    # Sc38 + n --> p + Ca38
    rate = 0.0

    # ths8r
    rate += np.exp(  20.2342 + 0.0106931*tf.T913
                  + 0.110569*tf.T9 + -0.0107232*tf.T953)

    rate_eval.n_Sc38__p_Ca38 = rate

@numba.njit()
def p_Ar39__K40(rate_eval, tf):
    # Ar39 + p --> K40
    rate = 0.0

    # ths8r
    rate += np.exp(  35.9873 + -29.0085*tf.T913i + -2.81753*tf.T913
                  + -0.757962*tf.T9 + 0.099462*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ar39__K40 = rate

@numba.njit()
def n_Ti51__Ti52(rate_eval, tf):
    # Ti51 + n --> Ti52
    rate = 0.0

    # rath 
    rate += np.exp(  16.4033 + -0.0269137*tf.T9i + 2.01467*tf.T913i + -5.81229*tf.T913
                  + 0.818451*tf.T9 + -0.0947064*tf.T953 + 1.71924*tf.lnT9)

    rate_eval.n_Ti51__Ti52 = rate

@numba.njit()
def He4_F25__Na29(rate_eval, tf):
    # F25 + He4 --> Na29
    rate = 0.0

    # rpsmr
    rate += np.exp(  48.9345 + -2.37*tf.T9i + 43.5404*tf.T913i + -107.096*tf.T913
                  + 4.60699*tf.T9 + -0.216463*tf.T953 + 57.2381*tf.lnT9)

    rate_eval.He4_F25__Na29 = rate

@numba.njit()
def p_K47__Ca48(rate_eval, tf):
    # K47 + p --> Ca48
    rate = 0.0

    # rath 
    rate += np.exp(  92.3806 + -4.99171*tf.T9i + 178.903*tf.T913i + -284.453*tf.T913
                  + 14.721*tf.T9 + -0.738219*tf.T953 + 145.355*tf.lnT9)

    rate_eval.p_K47__Ca48 = rate

@numba.njit()
def p_O23__n_F23(rate_eval, tf):
    # O23 + p --> n + F23
    rate = 0.0

    # rpsmr
    rate += np.exp(  57.5625 + -1.99509*tf.T9i + 67.3606*tf.T913i + -116.607*tf.T913
                  + 6.32667*tf.T9 + -0.350938*tf.T953 + 58.5983*tf.lnT9)

    rate_eval.p_O23__n_F23 = rate

@numba.njit()
def He4_Mn63__n_Co66(rate_eval, tf):
    # Mn63 + He4 --> n + Co66
    rate = 0.0

    # rath 
    rate += np.exp(  -1142.79 + 23.9883*tf.T9i + -2382.67*tf.T913i + 3670.54*tf.T913
                  + -207.844*tf.T9 + 11.4905*tf.T953 + -1781.81*tf.lnT9)

    rate_eval.He4_Mn63__n_Co66 = rate

@numba.njit()
def He4_C11__p_N14(rate_eval, tf):
    # C11 + He4 --> p + N14
    rate = 0.0

    # cf88n
    rate += np.exp(  36.613 + -31.883*tf.T913i + -0.361593*tf.T913
                  + -0.394216*tf.T9 + 0.0239162*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_C11__p_N14 = rate

@numba.njit()
def He4_Fe61__n_Ni64(rate_eval, tf):
    # Fe61 + He4 --> n + Ni64
    rate = 0.0

    # rath 
    rate += np.exp(  -1156.69 + 24.1754*tf.T9i + -2404.19*tf.T913i + 3705.47*tf.T913
                  + -209.946*tf.T9 + 11.6078*tf.T953 + -1797.58*tf.lnT9)

    rate_eval.He4_Fe61__n_Ni64 = rate

@numba.njit()
def K36__p_Cl35__weak__wc12(rate_eval, tf):
    # K36 --> p + Cl35
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.89447)

    rate_eval.K36__p_Cl35__weak__wc12 = rate

@numba.njit()
def He4_Si37__S41(rate_eval, tf):
    # Si37 + He4 --> S41
    rate = 0.0

    # rath 
    rate += np.exp(  -300.004 + 1.68648*tf.T9i + -430.174*tf.T913i + 755.371*tf.T913
                  + -50.1254*tf.T9 + 3.05814*tf.T953 + -330.938*tf.lnT9)

    rate_eval.He4_Si37__S41 = rate

@numba.njit()
def K35__p_Cl34__weak__wc12(rate_eval, tf):
    # K35 --> p + Cl34
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.23996)

    rate_eval.K35__p_Cl34__weak__wc12 = rate

@numba.njit()
def Ca58__n_n_Sc56__weak__mp17(rate_eval, tf):
    # Ca58 --> n + n + Sc56
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.490499)

    rate_eval.Ca58__n_n_Sc56__weak__mp17 = rate

@numba.njit()
def p_Ne34__Na35(rate_eval, tf):
    # Ne34 + p --> Na35
    rate = 0.0

    # rath 
    rate += np.exp(  62.6012 + -2.82738*tf.T9i + 100.969*tf.T913i + -168.983*tf.T913
                  + 9.16462*tf.T9 + -0.503843*tf.T953 + 84.6924*tf.lnT9)

    rate_eval.p_Ne34__Na35 = rate

@numba.njit()
def p_Ti61__He4_Sc58(rate_eval, tf):
    # Ti61 + p --> He4 + Sc58
    rate = 0.0

    # rath 
    rate += np.exp(  -74.8844 + -4.72375*tf.T9i + 71.795*tf.T913i + -11.558*tf.T913
                  + -4.76135*tf.T9 + 0.41245*tf.T953 + 44.7258*tf.lnT9)

    rate_eval.p_Ti61__He4_Sc58 = rate

@numba.njit()
def n_Si31__Si32(rate_eval, tf):
    # Si31 + n --> Si32
    rate = 0.0

    # rath 
    rate += np.exp(  11.9451 + -0.0144696*tf.T9i + 0.154735*tf.T913i + 0.304696*tf.T913
                  + 0.0236238*tf.T9 + -0.00396359*tf.T953 + -0.432171*tf.lnT9)

    rate_eval.n_Si31__Si32 = rate

@numba.njit()
def n_Cl36__He4_P33(rate_eval, tf):
    # Cl36 + n --> He4 + P33
    rate = 0.0

    # ths8r
    rate += np.exp(  11.4695 + -0.927614*tf.T913
                  + 1.68083*tf.T9 + -0.183233*tf.T953)

    rate_eval.n_Cl36__He4_P33 = rate

@numba.njit()
def n_S37__S38(rate_eval, tf):
    # S37 + n --> S38
    rate = 0.0

    # rath 
    rate += np.exp(  12.1887 + -0.0331592*tf.T9i + 1.83701*tf.T913i + -2.55851*tf.T913
                  + 0.29562*tf.T9 + -0.0325916*tf.T953 + 0.955056*tf.lnT9)

    rate_eval.n_S37__S38 = rate

@numba.njit()
def He4_Sc51__V55(rate_eval, tf):
    # Sc51 + He4 --> V55
    rate = 0.0

    # rath 
    rate += np.exp(  -965.478 + 15.4104*tf.T9i + -1673.44*tf.T913i + 2746.58*tf.T913
                  + -164.048*tf.T9 + 9.40104*tf.T953 + -1289.01*tf.lnT9)

    rate_eval.He4_Sc51__V55 = rate

@numba.njit()
def p_Ti60__He4_Sc57(rate_eval, tf):
    # Ti60 + p --> He4 + Sc57
    rate = 0.0

    # rath 
    rate += np.exp(  6.14624 + -5.42474*tf.T9i + 144.914*tf.T913i + -175.459*tf.T913
                  + 6.48826*tf.T9 + -0.247105*tf.T953 + 112.915*tf.lnT9)

    rate_eval.p_Ti60__He4_Sc57 = rate

@numba.njit()
def He4_Ti41__p_V44(rate_eval, tf):
    # Ti41 + He4 --> p + V44
    rate = 0.0

    # ths8r
    rate += np.exp(  58.4326 + -81.5027*tf.T913i + -1.24684*tf.T913
                  + -0.426368*tf.T9 + 0.00982333*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti41__p_V44 = rate

@numba.njit()
def p_B10__He4_Be7(rate_eval, tf):
    # B10 + p --> He4 + Be7
    rate = 0.0

    # nacrr
    rate += np.exp(  -6.45503 + -0.560753*tf.T9i + 0.532995*tf.T913i + 22.8893*tf.T913
                  + -3.08149*tf.T9 + 0.218269*tf.T953 + -1.5*tf.lnT9)
    # nacrn
    rate += np.exp(  44.213 + -12.9754*tf.T913i + -44.3224*tf.T913
                  + 62.9626*tf.T9 + -49.5228*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_B10__He4_Be7 = rate

@numba.njit()
def n_Ar50__Ar51(rate_eval, tf):
    # Ar50 + n --> Ar51
    rate = 0.0

    # rath 
    rate += np.exp(  6.95975 + -0.0191957*tf.T9i + 0.760171*tf.T913i + -2.59622*tf.T913
                  + 0.977858*tf.T9 + -0.118595*tf.T953 + 0.30932*tf.lnT9)

    rate_eval.n_Ar50__Ar51 = rate

@numba.njit()
def Ar31__Cl31__weak__wc12(rate_eval, tf):
    # Ar31 --> Cl31
    rate = 0.0

    # wc12w
    rate += np.exp(  2.65323)

    rate_eval.Ar31__Cl31__weak__wc12 = rate

@numba.njit()
def Ca59__Sc59__weak__mo03(rate_eval, tf):
    # Ca59 --> Sc59
    rate = 0.0

    # mo03w
    rate += np.exp(  3.55591)

    rate_eval.Ca59__Sc59__weak__mo03 = rate

@numba.njit()
def C9__He4_Li5__weak__wc12(rate_eval, tf):
    # C9 --> He4 + Li5
    rate = 0.0

    # wc12w
    rate += np.exp(  0.739942)

    rate_eval.C9__He4_Li5__weak__wc12 = rate

@numba.njit()
def Mn67__n_Fe66__weak__mp17(rate_eval, tf):
    # Mn67 --> n + Fe66
    rate = 0.0

    # mp17w
    rate += np.exp(  0.402142)

    rate_eval.Mn67__n_Fe66__weak__mp17 = rate

@numba.njit()
def V66__Cr66__weak__mo03(rate_eval, tf):
    # V66 --> Cr66
    rate = 0.0

    # mo03w
    rate += np.exp(  3.91204)

    rate_eval.V66__Cr66__weak__mo03 = rate

@numba.njit()
def p_Cr42__Mn43(rate_eval, tf):
    # Cr42 + p --> Mn43
    rate = 0.0

    # ths8r
    rate += np.exp(  -15.1542 + -26.5862*tf.T9i + 16.933*tf.T913
                  + -1.57481*tf.T9 + 0.0792914*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Cr42__Mn43 = rate

@numba.njit()
def n_Ca58__Ca59(rate_eval, tf):
    # Ca58 + n --> Ca59
    rate = 0.0

    # rath 
    rate += np.exp(  19.2763 + -0.0787846*tf.T9i + 8.41684*tf.T913i + -27.7207*tf.T913
                  + 3.83183*tf.T9 + -0.364461*tf.T953 + 8.86453*tf.lnT9)

    rate_eval.n_Ca58__Ca59 = rate

@numba.njit()
def p_S40__He4_P37(rate_eval, tf):
    # S40 + p --> He4 + P37
    rate = 0.0

    # rath 
    rate += np.exp(  71.9311 + -4.42929*tf.T9i + 179.698*tf.T913i + -268.332*tf.T913
                  + 11.7848*tf.T9 + -0.524888*tf.T953 + 148.385*tf.lnT9)

    rate_eval.p_S40__He4_P37 = rate

@numba.njit()
def n_Ar41__Ar42(rate_eval, tf):
    # Ar41 + n --> Ar42
    rate = 0.0

    # rath 
    rate += np.exp(  20.0136 + -0.0496343*tf.T9i + 4.39661*tf.T913i + -11.9273*tf.T913
                  + 1.05979*tf.T9 + -0.0809476*tf.T953 + 4.05719*tf.lnT9)

    rate_eval.n_Ar41__Ar42 = rate

@numba.njit()
def He4_S35__Ar39(rate_eval, tf):
    # S35 + He4 --> Ar39
    rate = 0.0

    # ths8r
    rate += np.exp(  50.161 + -65.58*tf.T913i + 0.163229*tf.T913
                  + -2.20138*tf.T9 + 0.232938*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S35__Ar39 = rate

@numba.njit()
def p_K54__Ca55(rate_eval, tf):
    # K54 + p --> Ca55
    rate = 0.0

    # rath 
    rate += np.exp(  122.476 + -5.48443*tf.T9i + 211.12*tf.T913i + -352.078*tf.T913
                  + 19.8166*tf.T9 + -1.11917*tf.T953 + 173.598*tf.lnT9)

    rate_eval.p_K54__Ca55 = rate

@numba.njit()
def n_K42__He4_Cl39(rate_eval, tf):
    # K42 + n --> He4 + Cl39
    rate = 0.0

    # rath 
    rate += np.exp(  169.3 + -3.66787*tf.T9i + 282.168*tf.T913i + -482.28*tf.T913
                  + 25.516*tf.T9 + -1.38768*tf.T953 + 244.455*tf.lnT9)

    rate_eval.n_K42__He4_Cl39 = rate

@numba.njit()
def He4_S45__Ar49(rate_eval, tf):
    # S45 + He4 --> Ar49
    rate = 0.0

    # rath 
    rate += np.exp(  -757.329 + 12.1565*tf.T9i + -1319.42*tf.T913i + 2161.45*tf.T913
                  + -129.424*tf.T9 + 7.43493*tf.T953 + -1013.66*tf.lnT9)

    rate_eval.He4_S45__Ar49 = rate

@numba.njit()
def p_V61__Cr62(rate_eval, tf):
    # V61 + p --> Cr62
    rate = 0.0

    # rath 
    rate += np.exp(  127.918 + -6.4863*tf.T9i + 244.487*tf.T913i + -393.52*tf.T913
                  + 21.7085*tf.T9 + -1.23403*tf.T953 + 197.434*tf.lnT9)

    rate_eval.p_V61__Cr62 = rate

@numba.njit()
def p_Mg27__n_Al27(rate_eval, tf):
    # Mg27 + p --> n + Al27
    rate = 0.0

    # rath 
    rate += np.exp(  71.5956 + -2.8412*tf.T9i + 98.1772*tf.T913i + -166.557*tf.T913
                  + 9.06485*tf.T9 + -0.510065*tf.T953 + 84.0299*tf.lnT9)

    rate_eval.p_Mg27__n_Al27 = rate

@numba.njit()
def P26__Si26__weak__wc12(rate_eval, tf):
    # P26 --> Si26
    rate = 0.0

    # wc12w
    rate += np.exp(  2.76389)

    rate_eval.P26__Si26__weak__wc12 = rate

@numba.njit()
def p_Mn70__He4_Cr67(rate_eval, tf):
    # Mn70 + p --> He4 + Cr67
    rate = 0.0

    # rath 
    rate += np.exp(  130.584 + -7.25056*tf.T9i + 274.871*tf.T913i + -437.462*tf.T913
                  + 24.5681*tf.T9 + -1.3407*tf.T953 + 220.59*tf.lnT9)

    rate_eval.p_Mn70__He4_Cr67 = rate

@numba.njit()
def P38__S38__weak__wc12(rate_eval, tf):
    # P38 --> S38
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.0480592)

    rate_eval.P38__S38__weak__wc12 = rate

@numba.njit()
def Ca41__K41__weak__wc12(rate_eval, tf):
    # Ca41 --> K41
    rate = 0.0

    # wc12w
    rate += np.exp(  -29.1669)

    rate_eval.Ca41__K41__weak__wc12 = rate

@numba.njit()
def He4_K45__n_Sc48(rate_eval, tf):
    # K45 + He4 --> n + Sc48
    rate = 0.0

    # rath 
    rate += np.exp(  -836.906 + 13.5493*tf.T9i + -1472.89*tf.T913i + 2412.45*tf.T913
                  + -144.321*tf.T9 + 8.2899*tf.T953 + -1131.33*tf.lnT9)

    rate_eval.He4_K45__n_Sc48 = rate

@numba.njit()
def n_Ne29__Ne30(rate_eval, tf):
    # Ne29 + n --> Ne30
    rate = 0.0

    # rath 
    rate += np.exp(  11.0238 + -0.0420812*tf.T9i + 2.8689*tf.T913i + -5.84275*tf.T913
                  + 0.586466*tf.T9 + -0.0474768*tf.T953 + 2.06173*tf.lnT9)

    rate_eval.n_Ne29__Ne30 = rate

@numba.njit()
def Si22__p_Mg21__weak__wc12(rate_eval, tf):
    # Si22 --> p + Mg21
    rate = 0.0

    # wc12w
    rate += np.exp(  2.03451)

    rate_eval.Si22__p_Mg21__weak__wc12 = rate

@numba.njit()
def He4_P38__n_Cl41(rate_eval, tf):
    # P38 + He4 --> n + Cl41
    rate = 0.0

    # rath 
    rate += np.exp(  -7.43603 + -3.30747*tf.T9i + -13.4081*tf.T913i + 16.4054*tf.T913
                  + -4.73675*tf.T9 + 0.383484*tf.T953 + 10.2806*tf.lnT9)

    rate_eval.He4_P38__n_Cl41 = rate

@numba.njit()
def C18__n_N17__weak__wc12(rate_eval, tf):
    # C18 --> n + N17
    rate = 0.0

    # wc12w
    rate += np.exp(  0.864271)

    rate_eval.C18__n_N17__weak__wc12 = rate

@numba.njit()
def He4_Cl48__n_K51(rate_eval, tf):
    # Cl48 + He4 --> n + K51
    rate = 0.0

    # rath 
    rate += np.exp(  -382.12 + 2.1369*tf.T9i + -549.199*tf.T913i + 974.222*tf.T913
                  + -64.0261*tf.T9 + 3.88924*tf.T953 + -428.565*tf.lnT9)

    rate_eval.He4_Cl48__n_K51 = rate

@numba.njit()
def Sc63__n_n_Ti61__weak__mp17(rate_eval, tf):
    # Sc63 --> n + n + Ti61
    rate = 0.0

    # mp17w
    rate += np.exp(  3.74092)

    rate_eval.Sc63__n_n_Ti61__weak__mp17 = rate

@numba.njit()
def He4_Ne23__Mg27(rate_eval, tf):
    # Ne23 + He4 --> Mg27
    rate = 0.0

    # rath 
    rate += np.exp(  57.7882 + -2.44077*tf.T9i + 45.5696*tf.T913i + -118.234*tf.T913
                  + 5.33664*tf.T9 + -0.259841*tf.T953 + 61.8337*tf.lnT9)

    rate_eval.He4_Ne23__Mg27 = rate

@numba.njit()
def Si41__P41__weak__wc17(rate_eval, tf):
    # Si41 --> P41
    rate = 0.0

    # wc17w
    rate += np.exp(  2.81154)

    rate_eval.Si41__P41__weak__wc17 = rate

@numba.njit()
def n_F27__F28(rate_eval, tf):
    # F27 + n --> F28
    rate = 0.0

    # rpsmr
    rate += np.exp(  49.8354 + -4.38025*tf.T9i + 137.683*tf.T913i + -196.815*tf.T913
                  + 11.0588*tf.T9 + -0.629653*tf.T953 + 100.974*tf.lnT9)

    rate_eval.n_F27__F28 = rate

@numba.njit()
def n_Cr51__p_V51(rate_eval, tf):
    # Cr51 + n --> p + V51
    rate = 0.0

    # ths8r
    rate += np.exp(  15.1388 + -0.462299*tf.T913
                  + 0.925265*tf.T9 + -0.103818*tf.T953)

    rate_eval.n_Cr51__p_V51 = rate

@numba.njit()
def n_V65__V66(rate_eval, tf):
    # V65 + n --> V66
    rate = 0.0

    # rath 
    rate += np.exp(  16.7468 + -0.0199804*tf.T9i + 2.49021*tf.T913i + -11.1207*tf.T913
                  + 1.17846*tf.T9 + -0.122085*tf.T953 + 3.06481*tf.lnT9)

    rate_eval.n_V65__V66 = rate

@numba.njit()
def p_K46__n_Ca46(rate_eval, tf):
    # K46 + p --> n + Ca46
    rate = 0.0

    # rath 
    rate += np.exp(  112.573 + -5.0225*tf.T9i + 185.556*tf.T913i + -304.954*tf.T913
                  + 16.9162*tf.T9 + -0.955475*tf.T953 + 152.645*tf.lnT9)

    rate_eval.p_K46__n_Ca46 = rate

@numba.njit()
def V66__n_Cr65__weak__mp17(rate_eval, tf):
    # V66 --> n + Cr65
    rate = 0.0

    # mp17w
    rate += np.exp(  3.59113)

    rate_eval.V66__n_Cr65__weak__mp17 = rate

@numba.njit()
def Si38__P38__weak__mo03(rate_eval, tf):
    # Si38 --> P38
    rate = 0.0

    # mo03w
    rate += np.exp(  0.857782)

    rate_eval.Si38__P38__weak__mo03 = rate

@numba.njit()
def P47__n_S46__weak__mp17(rate_eval, tf):
    # P47 --> n + S46
    rate = 0.0

    # mp17w
    rate += np.exp(  2.4778)

    rate_eval.P47__n_S46__weak__mp17 = rate

@numba.njit()
def p_Sc59__Ti60(rate_eval, tf):
    # Sc59 + p --> Ti60
    rate = 0.0

    # rath 
    rate += np.exp(  115.448 + -5.99145*tf.T9i + 223.65*tf.T913i + -358.838*tf.T913
                  + 19.7163*tf.T9 + -1.10972*tf.T953 + 180.502*tf.lnT9)

    rate_eval.p_Sc59__Ti60 = rate

@numba.njit()
def p_Be9__B10(rate_eval, tf):
    # Be9 + p --> B10
    rate = 0.0

    # nacrr
    rate += np.exp(  7.68698 + -2.59506*tf.T9i
                  + -1.5*tf.lnT9)
    # nacrn
    rate += np.exp(  16.2908 + -10.361*tf.T913i + 0.695179*tf.T913
                  + 0.342365*tf.T9 + -0.356569*tf.T953 + -0.666667*tf.lnT9)
    # nacrr
    rate += np.exp(  14.9657 + -11.5391*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Be9__B10 = rate

@numba.njit()
def He4_Ar50__n_Ca53(rate_eval, tf):
    # Ar50 + He4 --> n + Ca53
    rate = 0.0

    # rath 
    rate += np.exp(  -403.11 + 2.07369*tf.T9i + -565.841*tf.T913i + 1012.54*tf.T913
                  + -67.0126*tf.T9 + 4.08486*tf.T953 + -443.014*tf.lnT9)

    rate_eval.He4_Ar50__n_Ca53 = rate

@numba.njit()
def Ne27__Na27__weak__wc12(rate_eval, tf):
    # Ne27 --> Na27
    rate = 0.0

    # wc12w
    rate += np.exp(  3.07105)

    rate_eval.Ne27__Na27__weak__wc12 = rate

@numba.njit()
def Si44__n_n_n_P41__weak__mo03(rate_eval, tf):
    # Si44 --> 3 n + P41
    rate = 0.0

    # mo03w
    rate += np.exp(  2.46399)

    rate_eval.Si44__n_n_n_P41__weak__mo03 = rate

@numba.njit()
def p_P39__He4_Si36(rate_eval, tf):
    # P39 + p --> He4 + Si36
    rate = 0.0

    # rath 
    rate += np.exp(  93.8463 + -4.0221*tf.T9i + 150.186*tf.T913i + -253.602*tf.T913
                  + 13.904*tf.T9 + -0.729543*tf.T953 + 125.733*tf.lnT9)

    rate_eval.p_P39__He4_Si36 = rate

@numba.njit()
def He4_Ti49__Cr53(rate_eval, tf):
    # Ti49 + He4 --> Cr53
    rate = 0.0

    # ths8r
    rate += np.exp(  65.4688 + -81.8999*tf.T913i + -15.3695*tf.T913
                  + 2.51758*tf.T9 + -0.283455*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti49__Cr53 = rate

@numba.njit()
def He4_K33__p_Ca36(rate_eval, tf):
    # K33 + He4 --> p + Ca36
    rate = 0.0

    # ths8r
    rate += np.exp(  53.6861 + -73.3916*tf.T913i + 0.478953*tf.T913
                  + -0.846479*tf.T9 + 0.0605207*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K33__p_Ca36 = rate

@numba.njit()
def n_K31__He4_Cl28(rate_eval, tf):
    # K31 + n --> He4 + Cl28
    rate = 0.0

    # ths8r
    rate += np.exp(  15.4919 + -0.602318*tf.T913
                  + 0.315733*tf.T9 + -0.0226688*tf.T953)

    rate_eval.n_K31__He4_Cl28 = rate

@numba.njit()
def Ar50__n_K49__weak__wc12(rate_eval, tf):
    # Ar50 --> n + K49
    rate = 0.0

    # wc12w
    rate += np.exp(  1.04877)

    rate_eval.Ar50__n_K49__weak__wc12 = rate

@numba.njit()
def S39__Cl39__weak__wc12(rate_eval, tf):
    # S39 --> Cl39
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.80886)

    rate_eval.S39__Cl39__weak__wc12 = rate

@numba.njit()
def p_F26__Ne27(rate_eval, tf):
    # F26 + p --> Ne27
    rate = 0.0

    # rpsmr
    rate += np.exp(  53.6903 + -2.30784*tf.T9i + 80.0647*tf.T913i + -137.557*tf.T913
                  + 7.50384*tf.T9 + -0.417011*tf.T953 + 68.9238*tf.lnT9)

    rate_eval.p_F26__Ne27 = rate

@numba.njit()
def Ar33__p_S32__weak__wc12(rate_eval, tf):
    # Ar33 --> p + S32
    rate = 0.0

    # wc12w
    rate += np.exp(  0.43862)

    rate_eval.Ar33__p_S32__weak__wc12 = rate

@numba.njit()
def Ca47__Sc47__weak__wc12(rate_eval, tf):
    # Ca47 --> Sc47
    rate = 0.0

    # wc12w
    rate += np.exp(  -13.2455)

    rate_eval.Ca47__Sc47__weak__wc12 = rate

@numba.njit()
def He4_Li6__B10(rate_eval, tf):
    # Li6 + He4 --> B10
    rate = 0.0

    # cf88r
    rate += np.exp(  1.04267 + -3.71313*tf.T9i + 3.33334*tf.T913i + 3.25335*tf.T913
                  + 0.374434*tf.T9 + -0.0706244*tf.T953 + -1.5*tf.lnT9)
    # cf88n
    rate += np.exp(  15.2167 + -18.79*tf.T913i + 0.234225*tf.T913
                  + 3.23344*tf.T9 + -1.14529*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Li6__B10 = rate

@numba.njit()
def He4_S33__Ar37(rate_eval, tf):
    # S33 + He4 --> Ar37
    rate = 0.0

    # ths8r
    rate += np.exp(  49.9315 + -65.4446*tf.T913i + 3.59607*tf.T913
                  + -3.40501*tf.T9 + 0.363961*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_S33__Ar37 = rate

@numba.njit()
def Mg34__n_Al33__weak__mp17(rate_eval, tf):
    # Mg34 --> n + Al33
    rate = 0.0

    # mp17w
    rate += np.exp(  2.23618)

    rate_eval.Mg34__n_Al33__weak__mp17 = rate

@numba.njit()
def S29__p_Si28__weak__wc12(rate_eval, tf):
    # S29 --> p + Si28
    rate = 0.0

    # wc12w
    rate += np.exp(  0.555111)

    rate_eval.S29__p_Si28__weak__wc12 = rate

@numba.njit()
def O28__n_F27__weak__mp17(rate_eval, tf):
    # O28 --> n + F27
    rate = 0.0

    # mp17w
    rate += np.exp(  5.46644)

    rate_eval.O28__n_F27__weak__mp17 = rate

@numba.njit()
def He4_Cr69__Fe73(rate_eval, tf):
    # Cr69 + He4 --> Fe73
    rate = 0.0

    # rath 
    rate += np.exp(  -1177.01 + 24.3314*tf.T9i + -2416.76*tf.T913i + 3733.06*tf.T913
                  + -211.489*tf.T9 + 11.6711*tf.T953 + -1810.94*tf.lnT9)

    rate_eval.He4_Cr69__Fe73 = rate

@numba.njit()
def p_Li7__He4_He4(rate_eval, tf):
    # Li7 + p --> He4 + He4
    rate = 0.0

    # de04r
    rate += np.exp(  21.8999 + -26.1527*tf.T9i
                  + -1.5*tf.lnT9)
    # de04 
    rate += np.exp(  20.4438 + -8.4727*tf.T913i + 0.297934*tf.T913
                  + 0.0582335*tf.T9 + -0.00413383*tf.T953 + -0.666667*tf.lnT9)
    # de04r
    rate += np.exp(  14.2538 + -4.478*tf.T9i
                  + -1.5*tf.lnT9)
    # de04 
    rate += np.exp(  11.9576 + -8.4727*tf.T913i + 0.417943*tf.T913
                  + 5.34565*tf.T9 + -4.8684*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Li7__He4_He4 = rate

@numba.njit()
def Cl51__n_n_Ar49__weak__mp17(rate_eval, tf):
    # Cl51 --> n + n + Ar49
    rate = 0.0

    # mp17w
    rate += np.exp(  3.48205)

    rate_eval.Cl51__n_n_Ar49__weak__mp17 = rate

@numba.njit()
def n_O12__He4_C9(rate_eval, tf):
    # O12 + n --> He4 + C9
    rate = 0.0

    # rpsmr
    rate += np.exp(  19.0199 + 0.00219342*tf.T9i + -0.439611*tf.T913i + -0.667179*tf.T913
                  + 0.179908*tf.T9 + -0.0123022*tf.T953 + -0.158557*tf.lnT9)

    rate_eval.n_O12__He4_C9 = rate

@numba.njit()
def He4_Ca56__Ti60(rate_eval, tf):
    # Ca56 + He4 --> Ti60
    rate = 0.0

    # rath 
    rate += np.exp(  -979.171 + 15.4996*tf.T9i + -1684.23*tf.T913i + 2771.82*tf.T913
                  + -165.576*tf.T9 + 9.4798*tf.T953 + -1299.95*tf.lnT9)

    rate_eval.He4_Ca56__Ti60 = rate

@numba.njit()
def p_Fe65__n_Co65(rate_eval, tf):
    # Fe65 + p --> n + Co65
    rate = 0.0

    # rath 
    rate += np.exp(  146.122 + -7.22091*tf.T9i + 271.809*tf.T913i + -432.675*tf.T913
                  + 23.6408*tf.T9 + -1.32197*tf.T953 + 218.192*tf.lnT9)

    rate_eval.p_Fe65__n_Co65 = rate

@numba.njit()
def p_Fe76__n_Co76(rate_eval, tf):
    # Fe76 + p --> n + Co76
    rate = 0.0

    # rath 
    rate += np.exp(  162.786 + -7.77239*tf.T9i + 298.154*tf.T913i + -477.776*tf.T913
                  + 26.6248*tf.T9 + -1.50058*tf.T953 + 238.501*tf.lnT9)

    rate_eval.p_Fe76__n_Co76 = rate

@numba.njit()
def n_O19__O20(rate_eval, tf):
    # O19 + n --> O20
    rate = 0.0

    # wiesr
    rate += np.exp(  -11.4948 + -0.174902*tf.T9i + -6.25138*tf.T913i + 30.6974*tf.T913
                  + -3.28583*tf.T9 + 0.260902*tf.T953 + -10.1207*tf.lnT9)
    # wiesr
    rate += np.exp(  6.59578 + -1.14557e-13*tf.T9i + 1.4372e-11*tf.T913i + -4.48188e-11*tf.T913
                  + 4.29278e-12*tf.T9 + -3.49005e-13*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_O19__O20 = rate

@numba.njit()
def Ar47__K47__weak__wc12(rate_eval, tf):
    # Ar47 --> K47
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.575529)

    rate_eval.Ar47__K47__weak__wc12 = rate

@numba.njit()
def p_Na33__Mg34(rate_eval, tf):
    # Na33 + p --> Mg34
    rate = 0.0

    # rath 
    rate += np.exp(  65.7178 + -2.98165*tf.T9i + 106.81*tf.T913i + -179.541*tf.T913
                  + 9.7802*tf.T9 + -0.53872*tf.T953 + 89.8848*tf.lnT9)

    rate_eval.p_Na33__Mg34 = rate

@numba.njit()
def Cl52__n_Ar51__weak__mp17(rate_eval, tf):
    # Cl52 --> n + Ar51
    rate = 0.0

    # mp17w
    rate += np.exp(  3.28059)

    rate_eval.Cl52__n_Ar51__weak__mp17 = rate

@numba.njit()
def n_Cr45__p_V45(rate_eval, tf):
    # Cr45 + n --> p + V45
    rate = 0.0

    # ths8r
    rate += np.exp(  21.611 + -0.921918*tf.T913
                  + 0.256378*tf.T9 + -0.0225542*tf.T953)

    rate_eval.n_Cr45__p_V45 = rate

@numba.njit()
def Cl50__n_Ar49__weak__mp17(rate_eval, tf):
    # Cl50 --> n + Ar49
    rate = 0.0

    # mp17w
    rate += np.exp(  4.82392)

    rate_eval.Cl50__n_Ar49__weak__mp17 = rate

@numba.njit()
def S45__Cl45__weak__wc12(rate_eval, tf):
    # S45 --> Cl45
    rate = 0.0

    # wc12w
    rate += np.exp(  1.54521)

    rate_eval.S45__Cl45__weak__wc12 = rate

@numba.njit()
def n_Sc41__p_Ca41(rate_eval, tf):
    # Sc41 + n --> p + Ca41
    rate = 0.0

    # ths8r
    rate += np.exp(  20.4268 + -0.504964*tf.T913
                  + 0.256795*tf.T9 + -0.0265109*tf.T953)

    rate_eval.n_Sc41__p_Ca41 = rate

@numba.njit()
def p_Mn67__n_Fe67(rate_eval, tf):
    # Mn67 + p --> n + Fe67
    rate = 0.0

    # rath 
    rate += np.exp(  149.232 + -7.15561*tf.T9i + 271.702*tf.T913i + -434.971*tf.T913
                  + 23.8378*tf.T9 + -1.32753*tf.T953 + 218.3*tf.lnT9)

    rate_eval.p_Mn67__n_Fe67 = rate

@numba.njit()
def n_Fe52__p_Mn52(rate_eval, tf):
    # Fe52 + n --> p + Mn52
    rate = 0.0

    # ths8r
    rate += np.exp(  17.9485 + 0.569856*tf.T913
                  + 0.390117*tf.T9 + -0.0479043*tf.T953)

    rate_eval.n_Fe52__p_Mn52 = rate

@numba.njit()
def Ne34__n_n_Na32__weak__mp17(rate_eval, tf):
    # Ne34 --> n + n + Na32
    rate = 0.0

    # mp17w
    rate += np.exp(  3.19485)

    rate_eval.Ne34__n_n_Na32__weak__mp17 = rate

@numba.njit()
def Al33__Si33__weak__wc12(rate_eval, tf):
    # Al33 --> Si33
    rate = 0.0

    # wc12w
    rate += np.exp(  2.72191)

    rate_eval.Al33__Si33__weak__wc12 = rate

@numba.njit()
def n_S36__S37(rate_eval, tf):
    # S36 + n --> S37
    rate = 0.0

    # ks03 
    rate += np.exp(  14.0632 + -0.0187455*tf.T9i + 2.00012*tf.T913i + -6.63204*tf.T913
                  + 0.787709*tf.T9 + -0.0605455*tf.T953 + 2.19399*tf.lnT9)

    rate_eval.n_S36__S37 = rate

@numba.njit()
def Cl47__n_Ar46__weak__wc12(rate_eval, tf):
    # Cl47 --> n + Ar46
    rate = 0.0

    # wc12w
    rate += np.exp(  1.92612)

    rate_eval.Cl47__n_Ar46__weak__wc12 = rate

@numba.njit()
def P46__n_S45__weak__mp17(rate_eval, tf):
    # P46 --> n + S45
    rate = 0.0

    # mp17w
    rate += np.exp(  4.42348)

    rate_eval.P46__n_S45__weak__mp17 = rate

@numba.njit()
def p_Ca57__n_Sc57(rate_eval, tf):
    # Ca57 + p --> n + Sc57
    rate = 0.0

    # rath 
    rate += np.exp(  121.881 + -5.71889*tf.T9i + 213.583*tf.T913i + -343.03*tf.T913
                  + 18.6671*tf.T9 + -1.0372*tf.T953 + 172.766*tf.lnT9)

    rate_eval.p_Ca57__n_Sc57 = rate

@numba.njit()
def Cl45__n_Ar44__weak__wc12(rate_eval, tf):
    # Cl45 --> n + Ar44
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.909322)

    rate_eval.Cl45__n_Ar44__weak__wc12 = rate

@numba.njit()
def Be11__He4_Li7__weak__wc12(rate_eval, tf):
    # Be11 --> He4 + Li7
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.46495)

    rate_eval.Be11__He4_Li7__weak__wc12 = rate

@numba.njit()
def n_Ne27__Ne28(rate_eval, tf):
    # Ne27 + n --> Ne28
    rate = 0.0

    # rath 
    rate += np.exp(  9.59951 + -0.0335771*tf.T9i + 1.99165*tf.T913i + -4.16827*tf.T913
                  + 0.342698*tf.T9 + -0.0150053*tf.T953 + 1.27551*tf.lnT9)

    rate_eval.n_Ne27__Ne28 = rate

@numba.njit()
def He4_B10__n_N13(rate_eval, tf):
    # B10 + He4 --> n + N13
    rate = 0.0

    # cf88n
    rate += np.exp(  30.5042 + -27.8719*tf.T913i + -0.599503*tf.T913
                  + 0.122849*tf.T9 + -0.0393717*tf.T953 + -0.507333*tf.lnT9)

    rate_eval.He4_B10__n_N13 = rate

@numba.njit()
def p_Ca59__He4_K56(rate_eval, tf):
    # Ca59 + p --> He4 + K56
    rate = 0.0

    # rath 
    rate += np.exp(  83.9015 + -5.97843*tf.T9i + 235.627*tf.T913i + -352.614*tf.T913
                  + 18.4948*tf.T9 + -1.01377*tf.T953 + 189.021*tf.lnT9)

    rate_eval.p_Ca59__He4_K56 = rate

@numba.njit()
def n_Mn64__Mn65(rate_eval, tf):
    # Mn64 + n --> Mn65
    rate = 0.0

    # rath 
    rate += np.exp(  32.895 + 0.0181267*tf.T9i + 2.32645*tf.T913i + -22.4674*tf.T913
                  + 2.0339*tf.T9 + -0.163873*tf.T953 + 5.56154*tf.lnT9)

    rate_eval.n_Mn64__Mn65 = rate

@numba.njit()
def Sc48__Ti48__weak__wc12(rate_eval, tf):
    # Sc48 --> Ti48
    rate = 0.0

    # wc12w
    rate += np.exp(  -12.3305)

    rate_eval.Sc48__Ti48__weak__wc12 = rate

@numba.njit()
def Cl44__n_Ar43__weak__mp17(rate_eval, tf):
    # Cl44 --> n + Ar43
    rate = 0.0

    # mp17w
    rate += np.exp(  -3.29325)

    rate_eval.Cl44__n_Ar43__weak__mp17 = rate

@numba.njit()
def n_V44__V45(rate_eval, tf):
    # V44 + n --> V45
    rate = 0.0

    # ths8r
    rate += np.exp(  14.4686 + -0.964661*tf.T913
                  + 0.258915*tf.T9 + -0.026119*tf.T953)

    rate_eval.n_V44__V45 = rate

@numba.njit()
def Sc60__n_Ti59__weak__mp17(rate_eval, tf):
    # Sc60 --> n + Ti59
    rate = 0.0

    # mp17w
    rate += np.exp(  3.73495)

    rate_eval.Sc60__n_Ti59__weak__mp17 = rate

@numba.njit()
def Ti63__V63__weak__mo03(rate_eval, tf):
    # Ti63 --> V63
    rate = 0.0

    # mo03w
    rate += np.exp(  4.01508)

    rate_eval.Ti63__V63__weak__mo03 = rate

@numba.njit()
def He4_O15__Ne19(rate_eval, tf):
    # O15 + He4 --> Ne19
    rate = 0.0

    # dc11r
    rate += np.exp(  -32.2496 + -4.20439*tf.T9i + -3.24609*tf.T913i + 44.4647*tf.T913
                  + -9.79962*tf.T9 + 0.841782*tf.T953 + -1.5*tf.lnT9)
    # dc11r
    rate += np.exp(  -0.0452465 + -5.88439*tf.T9i
                  + -1.5*tf.lnT9)
    # dc11n
    rate += np.exp(  26.2914 + -39.578*tf.T913i
                  + -3.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_O15__Ne19 = rate

@numba.njit()
def d_d__n_He3(rate_eval, tf):
    # d + d --> n + He3
    rate = 0.0

    # gi17n
    rate += np.exp(  19.0876 + -0.00019002*tf.T9i + -4.2292*tf.T913i + 1.6932*tf.T913
                  + -0.0855529*tf.T9 + -1.35709e-25*tf.T953 + -0.734513*tf.lnT9)

    rate_eval.d_d__n_He3 = rate

@numba.njit()
def Na32__Mg32__weak__wc12(rate_eval, tf):
    # Na32 --> Mg32
    rate = 0.0

    # wc12w
    rate += np.exp(  3.57536)

    rate_eval.Na32__Mg32__weak__wc12 = rate

@numba.njit()
def Si43__n_P42__weak__mp17(rate_eval, tf):
    # Si43 --> n + P42
    rate = 0.0

    # mp17w
    rate += np.exp(  3.57559)

    rate_eval.Si43__n_P42__weak__mp17 = rate

@numba.njit()
def Sc58__n_n_Ti56__weak__mp17(rate_eval, tf):
    # Sc58 --> n + n + Ti56
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.548835)

    rate_eval.Sc58__n_n_Ti56__weak__mp17 = rate

@numba.njit()
def Fe70__Co70__weak__wc17(rate_eval, tf):
    # Fe70 --> Co70
    rate = 0.0

    # wc17w
    rate += np.exp(  2.1732)

    rate_eval.Fe70__Co70__weak__wc17 = rate

@numba.njit()
def p_Ne31__n_Na31(rate_eval, tf):
    # Ne31 + p --> n + Na31
    rate = 0.0

    # rath 
    rate += np.exp(  71.7477 + -2.70498*tf.T9i + 95.8826*tf.T913i + -162.158*tf.T913
                  + 8.78348*tf.T9 + -0.483181*tf.T953 + 81.1724*tf.lnT9)

    rate_eval.p_Ne31__n_Na31 = rate

@numba.njit()
def p_F21__He4_O18(rate_eval, tf):
    # F21 + p --> He4 + O18
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.1532 + -2.06844*tf.T9i + 69.62*tf.T913i + -122.856*tf.T913
                  + 6.82433*tf.T9 + -0.38602*tf.T953 + 61.4033*tf.lnT9)

    rate_eval.p_F21__He4_O18 = rate

@numba.njit()
def Mn64__Fe64__weak__wc12(rate_eval, tf):
    # Mn64 --> Fe64
    rate = 0.0

    # wc12w
    rate += np.exp(  1.64095)

    rate_eval.Mn64__Fe64__weak__wc12 = rate

@numba.njit()
def Ar48__K48__weak__wc17(rate_eval, tf):
    # Ar48 --> K48
    rate = 0.0

    # wc17w
    rate += np.exp(  -0.0528554)

    rate_eval.Ar48__K48__weak__wc17 = rate

@numba.njit()
def He4_Ne28__Mg32(rate_eval, tf):
    # Ne28 + He4 --> Mg32
    rate = 0.0

    # rath 
    rate += np.exp(  57.7278 + -2.78315*tf.T9i + 58.2126*tf.T913i + -132.977*tf.T913
                  + 6.00608*tf.T9 + -0.29646*tf.T953 + 70.1773*tf.lnT9)

    rate_eval.He4_Ne28__Mg32 = rate

@numba.njit()
def p_Sc61__He4_Ca58(rate_eval, tf):
    # Sc61 + p --> He4 + Ca58
    rate = 0.0

    # rath 
    rate += np.exp(  122.41 + -6.18921*tf.T9i + 238.698*tf.T913i + -388.265*tf.T913
                  + 21.614*tf.T9 + -1.12626*tf.T953 + 193.678*tf.lnT9)

    rate_eval.p_Sc61__He4_Ca58 = rate

@numba.njit()
def S48__n_n_Cl46__weak__mp17(rate_eval, tf):
    # S48 --> n + n + Cl46
    rate = 0.0

    # mp17w
    rate += np.exp(  1.94429)

    rate_eval.S48__n_n_Cl46__weak__mp17 = rate

@numba.njit()
def He4_Na35__Al39(rate_eval, tf):
    # Na35 + He4 --> Al39
    rate = 0.0

    # rath 
    rate += np.exp(  -16.0474 + -2.51437*tf.T9i + -17.557*tf.T913i + 25.0129*tf.T913
                  + -4.88459*tf.T9 + 0.392549*tf.T953 + 3.11135*tf.lnT9)

    rate_eval.He4_Na35__Al39 = rate

@numba.njit()
def Al29__Si29__weak__wc12(rate_eval, tf):
    # Al29 --> Si29
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.34286)

    rate_eval.Al29__Si29__weak__wc12 = rate

@numba.njit()
def p_V65__n_Cr65(rate_eval, tf):
    # V65 + p --> n + Cr65
    rate = 0.0

    # rath 
    rate += np.exp(  142.592 + -6.68499*tf.T9i + 253.963*tf.T913i + -408.288*tf.T913
                  + 22.3685*tf.T9 + -1.24366*tf.T953 + 204.593*tf.lnT9)

    rate_eval.p_V65__n_Cr65 = rate

@numba.njit()
def p_Be9__He4_Li6(rate_eval, tf):
    # Be9 + p --> He4 + Li6
    rate = 0.0

    # cf88n
    rate += np.exp(  26.0751 + -10.359*tf.T913i + 0.102577*tf.T913
                  + 4.43544*tf.T9 + -5.97105*tf.T953 + -0.666667*tf.lnT9)
    # cf88r
    rate += np.exp(  20.3228 + -5.16*tf.T9i
                  + -0.75*tf.lnT9)
    # cf88r
    rate += np.exp(  19.927 + -3.046*tf.T9i
                  + -1.0*tf.lnT9)

    rate_eval.p_Be9__He4_Li6 = rate

@numba.njit()
def He4_Cr61__Fe65(rate_eval, tf):
    # Cr61 + He4 --> Fe65
    rate = 0.0

    # rath 
    rate += np.exp(  -1096.79 + 22.9011*tf.T9i + -2276.83*tf.T913i + 3503.59*tf.T913
                  + -198.342*tf.T9 + 10.94*tf.T953 + -1701.29*tf.lnT9)

    rate_eval.He4_Cr61__Fe65 = rate

@numba.njit()
def Cl32__p_P31__weak__wc12(rate_eval, tf):
    # Cl32 --> p + P31
    rate = 0.0

    # wc12w
    rate += np.exp(  -7.26758)

    rate_eval.Cl32__p_P31__weak__wc12 = rate

@numba.njit()
def p_Na26__n_Mg26(rate_eval, tf):
    # Na26 + p --> n + Mg26
    rate = 0.0

    # rath 
    rate += np.exp(  67.779 + -2.62795*tf.T9i + 90.1615*tf.T913i + -152.844*tf.T913
                  + 8.18062*tf.T9 + -0.454812*tf.T953 + 77.35*tf.lnT9)

    rate_eval.p_Na26__n_Mg26 = rate

@numba.njit()
def He4_Ne32__Mg36(rate_eval, tf):
    # Ne32 + He4 --> Mg36
    rate = 0.0

    # rath 
    rate += np.exp(  62.3899 + -3.03352*tf.T9i + 68.3903*tf.T913i + -148.236*tf.T913
                  + 6.82502*tf.T9 + -0.339432*tf.T953 + 77.6664*tf.lnT9)

    rate_eval.He4_Ne32__Mg36 = rate

@numba.njit()
def p_Si27__P28(rate_eval, tf):
    # Si27 + p --> P28
    rate = 0.0

    # il10r
    rate += np.exp(  -20.3199 + -0.884101*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -36.1271 + -0.442864*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  2.60003 + -3.68994*tf.T9i + 3.66074*tf.T913
                  + -0.101312*tf.T9 + 0.0145387*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -5.54084 + -1.72835*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_Si27__P28 = rate

@numba.njit()
def Si36__P36__weak__wc12(rate_eval, tf):
    # Si36 --> P36
    rate = 0.0

    # wc12w
    rate += np.exp(  0.326634)

    rate_eval.Si36__P36__weak__wc12 = rate

@numba.njit()
def n_Si27__p_Al27(rate_eval, tf):
    # Si27 + n --> p + Al27
    rate = 0.0

    # ths8r
    rate += np.exp(  17.84 + 2.10552*tf.T913
                  + -0.318695*tf.T9 + 0.0257496*tf.T953)

    rate_eval.n_Si27__p_Al27 = rate

@numba.njit()
def n_Cl47__Cl48(rate_eval, tf):
    # Cl47 + n --> Cl48
    rate = 0.0

    # rath 
    rate += np.exp(  11.8484 + -0.0693258*tf.T9i + 5.7267*tf.T913i + -11.7144*tf.T913
                  + 1.05037*tf.T9 + -0.0851855*tf.T953 + 4.7042*tf.lnT9)

    rate_eval.n_Cl47__Cl48 = rate

@numba.njit()
def p_Ca54__He4_K51(rate_eval, tf):
    # Ca54 + p --> He4 + K51
    rate = 0.0

    # rath 
    rate += np.exp(  77.3664 + -5.62937*tf.T9i + 211.79*tf.T913i + -313.688*tf.T913
                  + 15.2785*tf.T9 + -0.723738*tf.T953 + 169.0*tf.lnT9)

    rate_eval.p_Ca54__He4_K51 = rate

@numba.njit()
def Sc40__p_K39__weak__wc12(rate_eval, tf):
    # Sc40 --> p + K39
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.08891)

    rate_eval.Sc40__p_K39__weak__wc12 = rate

@numba.njit()
def He4_Ne22__Mg26(rate_eval, tf):
    # Ne22 + He4 --> Mg26
    rate = 0.0

    # li12r
    rate += np.exp(  -29.3146 + -6.44772*tf.T9i + 43.2654*tf.T913
                  + -18.5982*tf.T9 + 2.80101*tf.T953 + -1.5*tf.lnT9)
    # li12r
    rate += np.exp(  -23.7527 + -3.88217*tf.T9i
                  + -1.5*tf.lnT9)
    # li12r
    rate += np.exp(  -42.864 + -2.22115*tf.T9i
                  + -1.5*tf.lnT9)
    # li12r
    rate += np.exp(  -92.4077 + -0.910477*tf.T9i
                  + -1.5*tf.lnT9)
    # li12r
    rate += np.exp(  -34.7254 + -6.36421*tf.T9i + 35.9878*tf.T913
                  + -4.10684*tf.T9 + 0.259345*tf.T953 + -1.5*tf.lnT9)

    rate_eval.He4_Ne22__Mg26 = rate

@numba.njit()
def p_Fe74__Co75(rate_eval, tf):
    # Fe74 + p --> Co75
    rate = 0.0

    # rath 
    rate += np.exp(  151.753 + -7.68187*tf.T9i + 294.272*tf.T913i + -473.072*tf.T913
                  + 26.5281*tf.T9 + -1.51924*tf.T953 + 235.834*tf.lnT9)

    rate_eval.p_Fe74__Co75 = rate

@numba.njit()
def He4_Mn58__n_Co61(rate_eval, tf):
    # Mn58 + He4 --> n + Co61
    rate = 0.0

    # rath 
    rate += np.exp(  -1094.05 + 22.9634*tf.T9i + -2284.78*tf.T913i + 3516.19*tf.T913
                  + -199.19*tf.T9 + 11.014*tf.T953 + -1706.35*tf.lnT9)

    rate_eval.He4_Mn58__n_Co61 = rate

@numba.njit()
def S46__n_Cl45__weak__mp17(rate_eval, tf):
    # S46 --> n + Cl45
    rate = 0.0

    # mp17w
    rate += np.exp(  2.30071)

    rate_eval.S46__n_Cl45__weak__mp17 = rate

@numba.njit()
def Ti41__Sc41__weak__wc17(rate_eval, tf):
    # Ti41 --> Sc41
    rate = 0.0

    # wc17w
    rate += np.exp(  -112.975)

    rate_eval.Ti41__Sc41__weak__wc17 = rate

@numba.njit()
def p_O21__F22(rate_eval, tf):
    # O21 + p --> F22
    rate = 0.0

    # rpsmr
    rate += np.exp(  43.4654 + -1.89087*tf.T9i + 61.9533*tf.T913i + -107.365*tf.T913
                  + 5.77593*tf.T9 + -0.314725*tf.T953 + 54.3016*tf.lnT9)

    rate_eval.p_O21__F22 = rate

@numba.njit()
def He4_Ti62__Cr66(rate_eval, tf):
    # Ti62 + He4 --> Cr66
    rate = 0.0

    # rath 
    rate += np.exp(  -1048.45 + 21.7539*tf.T9i + -2163.62*tf.T913i + 3334.39*tf.T913
                  + -188.753*tf.T9 + 10.3965*tf.T953 + -1617.93*tf.lnT9)

    rate_eval.He4_Ti62__Cr66 = rate

@numba.njit()
def He4_Li9__n_B12(rate_eval, tf):
    # Li9 + He4 --> n + B12
    rate = 0.0

    # wiesr
    rate += np.exp(  -19.8289 + -1.21363*tf.T9i + 2.99884*tf.T913i + 15.6696*tf.T913
                  + -3.21146*tf.T9 + 0.319384*tf.T953 + -1.81905*tf.lnT9)
    # wiesr
    rate += np.exp(  5.3494 + -4.642*tf.T9i + -1.36024e-09*tf.T913i + 2.78823e-09*tf.T913
                  + -2.04303e-10*tf.T9 + 1.40054e-11*tf.T953 + -1.5*tf.lnT9)

    rate_eval.He4_Li9__n_B12 = rate

@numba.njit()
def Mg35__n_n_Al33__weak__mp17(rate_eval, tf):
    # Mg35 --> n + n + Al33
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.366513)

    rate_eval.Mg35__n_n_Al33__weak__mp17 = rate

@numba.njit()
def p_P42__S43(rate_eval, tf):
    # P42 + p --> S43
    rate = 0.0

    # rath 
    rate += np.exp(  84.5195 + -4.10166*tf.T9i + 149.62*tf.T913i + -245.348*tf.T913
                  + 13.3379*tf.T9 + -0.737155*tf.T953 + 123.494*tf.lnT9)

    rate_eval.p_P42__S43 = rate

@numba.njit()
def p_Cr66__n_Mn66(rate_eval, tf):
    # Cr66 + p --> n + Mn66
    rate = 0.0

    # rath 
    rate += np.exp(  144.388 + -6.9116*tf.T9i + 261.798*tf.T913i + -418.96*tf.T913
                  + 22.914*tf.T9 + -1.27364*tf.T953 + 210.4*tf.lnT9)

    rate_eval.p_Cr66__n_Mn66 = rate

@numba.njit()
def O13__N13__weak__wc17(rate_eval, tf):
    # O13 --> N13
    rate = 0.0

    # wc17w
    rate += np.exp(  -110.737)

    rate_eval.O13__N13__weak__wc17 = rate

@numba.njit()
def He4_Al23__p_Si26(rate_eval, tf):
    # Al23 + He4 --> p + Si26
    rate = 0.0

    # ths8r
    rate += np.exp(  47.218 + -56.1207*tf.T913i + 0.534839*tf.T913
                  + -0.793195*tf.T9 + 0.0590135*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al23__p_Si26 = rate

@numba.njit()
def p_O27__n_F27(rate_eval, tf):
    # O27 + p --> n + F27
    rate = 0.0

    # rpsmr
    rate += np.exp(  62.322 + -2.17816*tf.T9i + 76.1012*tf.T913i + -130.247*tf.T913
                  + 7.04522*tf.T9 + -0.388453*tf.T953 + 65.1922*tf.lnT9)

    rate_eval.p_O27__n_F27 = rate

@numba.njit()
def n_Ti61__Ti62(rate_eval, tf):
    # Ti61 + n --> Ti62
    rate = 0.0

    # rath 
    rate += np.exp(  1.17194 + 0.0480733*tf.T9i + -6.54275*tf.T913i + 16.2722*tf.T913
                  + -0.816751*tf.T9 + -0.0205595*tf.T953 + -6.92097*tf.lnT9)

    rate_eval.n_Ti61__Ti62 = rate

@numba.njit()
def n_Mn46__Mn47(rate_eval, tf):
    # Mn46 + n --> Mn47
    rate = 0.0

    # ths8r
    rate += np.exp(  13.6489 + -1.32187*tf.T913
                  + 0.300442*tf.T9 + -0.0264098*tf.T953)

    rate_eval.n_Mn46__Mn47 = rate

@numba.njit()
def p_Al31__n_Si31(rate_eval, tf):
    # Al31 + p --> n + Si31
    rate = 0.0

    # rath 
    rate += np.exp(  81.183 + -3.22724*tf.T9i + 114.635*tf.T913i + -193.512*tf.T913
                  + 10.4609*tf.T9 + -0.579218*tf.T953 + 97.107*tf.lnT9)

    rate_eval.p_Al31__n_Si31 = rate

@numba.njit()
def Cl48__n_n_Ar46__weak__mp17(rate_eval, tf):
    # Cl48 --> n + n + Ar46
    rate = 0.0

    # mp17w
    rate += np.exp(  1.72136)

    rate_eval.Cl48__n_n_Ar46__weak__mp17 = rate

@numba.njit()
def Na19__Ne19__weak__bqa_pos_(rate_eval, tf):
    # Na19 --> Ne19
    rate = 0.0

    # bqa+w
    rate += np.exp(  1.5017)

    rate_eval.Na19__Ne19__weak__bqa_pos_ = rate

@numba.njit()
def F28__n_n_Ne26__weak__mp17(rate_eval, tf):
    # F28 --> n + n + Ne26
    rate = 0.0

    # mp17w
    rate += np.exp(  4.14904)

    rate_eval.F28__n_n_Ne26__weak__mp17 = rate

@numba.njit()
def n_Li6__Li7(rate_eval, tf):
    # Li6 + n --> Li7
    rate = 0.0

    # jz10n
    rate += np.exp(  9.04782)

    rate_eval.n_Li6__Li7 = rate

@numba.njit()
def p_Ca53__He4_K50(rate_eval, tf):
    # Ca53 + p --> He4 + K50
    rate = 0.0

    # rath 
    rate += np.exp(  83.1361 + -5.50161*tf.T9i + 202.216*tf.T913i + -306.925*tf.T913
                  + 16.1811*tf.T9 + -0.872714*tf.T953 + 162.063*tf.lnT9)

    rate_eval.p_Ca53__He4_K50 = rate

@numba.njit()
def p_Ar45__K46(rate_eval, tf):
    # Ar45 + p --> K46
    rate = 0.0

    # rath 
    rate += np.exp(  98.0378 + -4.78076*tf.T9i + 175.358*tf.T913i + -287.506*tf.T913
                  + 15.9092*tf.T9 + -0.9027*tf.T953 + 144.267*tf.lnT9)

    rate_eval.p_Ar45__K46 = rate

@numba.njit()
def Al23__p_Na22__weak__wc12(rate_eval, tf):
    # Al23 --> p + Na22
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.9654)

    rate_eval.Al23__p_Na22__weak__wc12 = rate

@numba.njit()
def O25__F25__weak__mo03(rate_eval, tf):
    # O25 --> F25
    rate = 0.0

    # mo03w
    rate += np.exp(  4.97832)

    rate_eval.O25__F25__weak__mo03 = rate

@numba.njit()
def p_Cr64__He4_V61(rate_eval, tf):
    # Cr64 + p --> He4 + V61
    rate = 0.0

    # rath 
    rate += np.exp(  -254.119 + -0.996394*tf.T9i + -256.002*tf.T913i + 516.989*tf.T913
                  + -36.5618*tf.T9 + 2.35485*tf.T953 + -206.713*tf.lnT9)

    rate_eval.p_Cr64__He4_V61 = rate

@numba.njit()
def He4_N16__n_F19(rate_eval, tf):
    # N16 + He4 --> n + F19
    rate = 0.0

    #  wagn
    rate += np.exp(  39.3908 + -36.37*tf.T913i + 5.0946e-09*tf.T913
                  + -5.15247e-10*tf.T9 + 4.45482e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_N16__n_F19 = rate

@numba.njit()
def Mg41__Al41__weak__mo03(rate_eval, tf):
    # Mg41 --> Al41
    rate = 0.0

    # mo03w
    rate += np.exp(  -108.835)

    rate_eval.Mg41__Al41__weak__mo03 = rate

@numba.njit()
def Mn48__Cr48__weak__wc12(rate_eval, tf):
    # Mn48 --> Cr48
    rate = 0.0

    # wc12w
    rate += np.exp(  1.47584)

    rate_eval.Mn48__Cr48__weak__wc12 = rate

@numba.njit()
def He4_Cl41__p_Ar44(rate_eval, tf):
    # Cl41 + He4 --> p + Ar44
    rate = 0.0

    # rath 
    rate += np.exp(  -628.93 + 10.9627*tf.T9i + -1194.49*tf.T913i + 1894.83*tf.T913
                  + -112.89*tf.T9 + 6.51933*tf.T953 + -896.37*tf.lnT9)

    rate_eval.He4_Cl41__p_Ar44 = rate

@numba.njit()
def p_Si41__P42(rate_eval, tf):
    # Si41 + p --> P42
    rate = 0.0

    # rath 
    rate += np.exp(  78.3145 + -3.85319*tf.T9i + 138.911*tf.T913i + -227.158*tf.T913
                  + 12.3082*tf.T9 + -0.680323*tf.T953 + 114.615*tf.lnT9)

    rate_eval.p_Si41__P42 = rate

@numba.njit()
def n_Mn48__p_Cr48(rate_eval, tf):
    # Mn48 + n --> p + Cr48
    rate = 0.0

    # ths8r
    rate += np.exp(  21.7901 + -0.997603*tf.T913
                  + 0.288307*tf.T9 + -0.0271046*tf.T953)

    rate_eval.n_Mn48__p_Cr48 = rate

@numba.njit()
def He4_Si36__S40(rate_eval, tf):
    # Si36 + He4 --> S40
    rate = 0.0

    # rath 
    rate += np.exp(  -294.811 + 1.6787*tf.T9i + -425.566*tf.T913i + 744.167*tf.T913
                  + -49.1979*tf.T9 + 2.98724*tf.T953 + -326.507*tf.lnT9)

    rate_eval.He4_Si36__S40 = rate

@numba.njit()
def n_Cr49__He4_Ti46(rate_eval, tf):
    # Cr49 + n --> He4 + Ti46
    rate = 0.0

    # ths8r
    rate += np.exp(  13.4786 + -2.81456*tf.T913
                  + 1.61029*tf.T9 + -0.138467*tf.T953)

    rate_eval.n_Cr49__He4_Ti46 = rate

@numba.njit()
def He4_Sc46__n_V49(rate_eval, tf):
    # Sc46 + He4 --> n + V49
    rate = 0.0

    # rath 
    rate += np.exp(  -907.911 + 14.6583*tf.T9i + -1592.71*tf.T913i + 2609.63*tf.T913
                  + -155.96*tf.T9 + 8.94971*tf.T953 + -1223.97*tf.lnT9)

    rate_eval.He4_Sc46__n_V49 = rate

@numba.njit()
def n_K38__He4_Cl35(rate_eval, tf):
    # K38 + n --> He4 + Cl35
    rate = 0.0

    # ths8r
    rate += np.exp(  17.5346 + 1.15173*tf.T913
                  + -0.190157*tf.T9 + 0.0305104*tf.T953)

    rate_eval.n_K38__He4_Cl35 = rate

@numba.njit()
def p_Mg30__He4_Na27(rate_eval, tf):
    # Mg30 + p --> He4 + Na27
    rate = 0.0

    # rath 
    rate += np.exp(  54.5455 + -3.0354*tf.T9i + 109.007*tf.T913i + -168.827*tf.T913
                  + 8.58405*tf.T9 + -0.487105*tf.T953 + 90.982*tf.lnT9)

    rate_eval.p_Mg30__He4_Na27 = rate

@numba.njit()
def N24__n_N23(rate_eval, tf):
    # N24 --> n + N23
    rate = 0.0

    # wc12s
    rate += np.exp(  16.4055)

    rate_eval.N24__n_N23 = rate

@numba.njit()
def He4_Fe65__n_Ni68(rate_eval, tf):
    # Fe65 + He4 --> n + Ni68
    rate = 0.0

    # rath 
    rate += np.exp(  -1196.89 + 24.9722*tf.T9i + -2481.04*tf.T913i + 3828.0*tf.T913
                  + -216.801*tf.T9 + 11.9842*tf.T953 + -1857.15*tf.lnT9)

    rate_eval.He4_Fe65__n_Ni68 = rate

@numba.njit()
def n_K34__He4_Cl31(rate_eval, tf):
    # K34 + n --> He4 + Cl31
    rate = 0.0

    # ths8r
    rate += np.exp(  16.7538 + -0.23303*tf.T913
                  + 0.118815*tf.T9 + -0.000480329*tf.T953)

    rate_eval.n_K34__He4_Cl31 = rate

@numba.njit()
def n_Ne17__p_F17(rate_eval, tf):
    # Ne17 + n --> p + F17
    rate = 0.0

    # ths8r
    rate += np.exp(  19.411 + 0.192921*tf.T913
                  + 0.106839*tf.T9 + -0.010471*tf.T953)

    rate_eval.n_Ne17__p_F17 = rate

@numba.njit()
def p_Al35__Si36(rate_eval, tf):
    # Al35 + p --> Si36
    rate = 0.0

    # rath 
    rate += np.exp(  73.4441 + -3.41957*tf.T9i + 122.637*tf.T913i + -204.857*tf.T913
                  + 11.1822*tf.T9 + -0.618307*tf.T953 + 102.714*tf.lnT9)

    rate_eval.p_Al35__Si36 = rate

@numba.njit()
def n_Ti43__p_Sc43(rate_eval, tf):
    # Ti43 + n --> p + Sc43
    rate = 0.0

    # ths8r
    rate += np.exp(  20.8603 + -0.798735*tf.T913
                  + 0.299178*tf.T9 + -0.0302647*tf.T953)

    rate_eval.n_Ti43__p_Sc43 = rate

@numba.njit()
def Mg29__Al29__weak__wc12(rate_eval, tf):
    # Mg29 --> Al29
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.628877)

    rate_eval.Mg29__Al29__weak__wc12 = rate

@numba.njit()
def p_F17__Ne18(rate_eval, tf):
    # F17 + p --> Ne18
    rate = 0.0

    # cb09 
    rate += np.exp(  -7.84708 + -0.0323504*tf.T9i + -14.2191*tf.T913i + 34.0647*tf.T913
                  + -16.5698*tf.T9 + 2.48116*tf.T953 + -2.13376*tf.lnT9)
    # cb09 
    rate += np.exp(  27.5778 + -4.95969*tf.T9i + -21.3249*tf.T913i + -0.230774*tf.T913
                  + 0.917931*tf.T9 + -0.0440377*tf.T953 + -7.36014*tf.lnT9)

    rate_eval.p_F17__Ne18 = rate

@numba.njit()
def p_Sc53__He4_Ca50(rate_eval, tf):
    # Sc53 + p --> He4 + Ca50
    rate = 0.0

    # rath 
    rate += np.exp(  103.708 + -5.69492*tf.T9i + 209.878*tf.T913i + -329.827*tf.T913
                  + 17.3502*tf.T9 + -0.912223*tf.T953 + 169.401*tf.lnT9)

    rate_eval.p_Sc53__He4_Ca50 = rate

@numba.njit()
def P39__n_S38__weak__wc12(rate_eval, tf):
    # P39 --> n + S38
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.440621)

    rate_eval.P39__n_S38__weak__wc12 = rate

@numba.njit()
def P44__n_S43__weak__mp17(rate_eval, tf):
    # P44 --> n + S43
    rate = 0.0

    # mp17w
    rate += np.exp(  3.25241)

    rate_eval.P44__n_S43__weak__mp17 = rate

@numba.njit()
def Ca56__n_Sc55__weak__mp17(rate_eval, tf):
    # Ca56 --> n + Sc55
    rate = 0.0

    # mp17w
    rate += np.exp(  0.924471)

    rate_eval.Ca56__n_Sc55__weak__mp17 = rate

@numba.njit()
def K46__Ca46__weak__wc12(rate_eval, tf):
    # K46 --> Ca46
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.02047)

    rate_eval.K46__Ca46__weak__wc12 = rate

@numba.njit()
def P42__n_S41__weak__wc12(rate_eval, tf):
    # P42 --> n + S41
    rate = 0.0

    # wc12w
    rate += np.exp(  1.96653)

    rate_eval.P42__n_S41__weak__wc12 = rate

@numba.njit()
def Na35__n_Mg34__weak__mp17(rate_eval, tf):
    # Na35 --> n + Mg34
    rate = 0.0

    # mp17w
    rate += np.exp(  5.7791)

    rate_eval.Na35__n_Mg34__weak__mp17 = rate

@numba.njit()
def Na33__n_Mg32__weak__wc17(rate_eval, tf):
    # Na33 --> n + Mg32
    rate = 0.0

    # wc17w
    rate += np.exp(  3.70678)

    rate_eval.Na33__n_Mg32__weak__wc17 = rate

@numba.njit()
def Fe76__n_Co75__weak__mp17(rate_eval, tf):
    # Fe76 --> n + Co75
    rate = 0.0

    # mp17w
    rate += np.exp(  3.12296)

    rate_eval.Fe76__n_Co75__weak__mp17 = rate

@numba.njit()
def Mg38__n_n_n_Al35__weak__mo03(rate_eval, tf):
    # Mg38 --> 3 n + Al35
    rate = 0.0

    # mo03w
    rate += np.exp(  2.30264)

    rate_eval.Mg38__n_n_n_Al35__weak__mo03 = rate

@numba.njit()
def Ar31__p_p_P29__weak__wc12(rate_eval, tf):
    # Ar31 --> p + p + P29
    rate = 0.0

    # wc12w
    rate += np.exp(  1.40891)

    rate_eval.Ar31__p_p_P29__weak__wc12 = rate

@numba.njit()
def He4_B13__N17(rate_eval, tf):
    # B13 + He4 --> N17
    rate = 0.0

    # fkthr
    rate += np.exp(  36.1324 + -1.52254*tf.T9i + 25.5955*tf.T913i + -66.2284*tf.T913
                  + 2.75655*tf.T9 + -0.115482*tf.T953 + 35.0643*tf.lnT9)

    rate_eval.He4_B13__N17 = rate

@numba.njit()
def p_Na25__n_Mg25(rate_eval, tf):
    # Na25 + p --> n + Mg25
    rate = 0.0

    # rath 
    rate += np.exp(  66.4596 + -2.57433*tf.T9i + 87.7105*tf.T913i + -149.186*tf.T913
                  + 8.00169*tf.T9 + -0.444746*tf.T953 + 75.5389*tf.lnT9)

    rate_eval.p_Na25__n_Mg25 = rate

@numba.njit()
def n_Sc57__Sc58(rate_eval, tf):
    # Sc57 + n --> Sc58
    rate = 0.0

    # rath 
    rate += np.exp(  15.8392 + -0.0388071*tf.T9i + 3.51354*tf.T913i + -11.4275*tf.T913
                  + 1.29815*tf.T9 + -0.12705*tf.T953 + 3.46351*tf.lnT9)

    rate_eval.n_Sc57__Sc58 = rate

@numba.njit()
def He4_P42__Cl46(rate_eval, tf):
    # P42 + He4 --> Cl46
    rate = 0.0

    # rath 
    rate += np.exp(  -335.218 + 1.80498*tf.T9i + -471.662*tf.T913i + 833.837*tf.T913
                  + -55.1918*tf.T9 + 3.36509*tf.T953 + -365.41*tf.lnT9)

    rate_eval.He4_P42__Cl46 = rate

@numba.njit()
def n_Na23__Na24(rate_eval, tf):
    # Na23 + n --> Na24
    rate = 0.0

    # ks03 
    rate += np.exp(  21.496 + -0.185436*tf.T9i + 16.0285*tf.T913i + -25.7668*tf.T913
                  + 1.07385*tf.T9 + -0.0293163*tf.T953 + 12.6777*tf.lnT9)

    rate_eval.n_Na23__Na24 = rate

@numba.njit()
def p_N16__n_O16(rate_eval, tf):
    # N16 + p --> n + O16
    rate = 0.0

    #  wagn
    rate += np.exp(  27.9675 + -4.18974e-12*tf.T9i + -15.27*tf.T913i + -2.03739e-09*tf.T913
                  + 2.22909e-10*tf.T9 + -2.02151e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_N16__n_O16 = rate

@numba.njit()
def n_Cr44__p_V44(rate_eval, tf):
    # Cr44 + n --> p + V44
    rate = 0.0

    # ths8r
    rate += np.exp(  21.4629 + -0.839566*tf.T913
                  + 0.253205*tf.T9 + -0.0235124*tf.T953)

    rate_eval.n_Cr44__p_V44 = rate

@numba.njit()
def p_Mn70__n_Fe70(rate_eval, tf):
    # Mn70 + p --> n + Fe70
    rate = 0.0

    # rath 
    rate += np.exp(  156.731 + -7.23849*tf.T9i + 274.105*tf.T913i + -445.48*tf.T913
                  + 25.0055*tf.T9 + -1.41387*tf.T953 + 221.066*tf.lnT9)

    rate_eval.p_Mn70__n_Fe70 = rate

@numba.njit()
def S44__Cl44__weak__wc12(rate_eval, tf):
    # S44 --> Cl44
    rate = 0.0

    # wc12w
    rate += np.exp(  1.73762)

    rate_eval.S44__Cl44__weak__wc12 = rate

@numba.njit()
def He4_Cl45__K49(rate_eval, tf):
    # Cl45 + He4 --> K49
    rate = 0.0

    # rath 
    rate += np.exp(  -783.958 + 12.5715*tf.T9i + -1366.71*tf.T913i + 2238.4*tf.T913
                  + -133.991*tf.T9 + 7.69486*tf.T953 + -1049.74*tf.lnT9)

    rate_eval.He4_Cl45__K49 = rate

@numba.njit()
def p_Mg41__He4_Na38(rate_eval, tf):
    # Mg41 + p --> He4 + Na38
    rate = 0.0

    # rath 
    rate += np.exp(  46.7826 + -3.5033*tf.T9i + 127.022*tf.T913i + -185.958*tf.T913
                  + 8.63634*tf.T9 + -0.406835*tf.T953 + 102.194*tf.lnT9)

    rate_eval.p_Mg41__He4_Na38 = rate

@numba.njit()
def Fe71__n_Co70__weak__mp17(rate_eval, tf):
    # Fe71 --> n + Co70
    rate = 0.0

    # mp17w
    rate += np.exp(  0.906453)

    rate_eval.Fe71__n_Co70__weak__mp17 = rate

@numba.njit()
def n_O17__He4_C14(rate_eval, tf):
    # O17 + n --> He4 + C14
    rate = 0.0

    # kg91r
    rate += np.exp(  13.73 + -1.961*tf.T9i
                  + -1.5*tf.lnT9)
    # kg91n
    rate += np.exp(  10.345)
    # kg91r
    rate += np.exp(  18.0922 + -2.759*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.n_O17__He4_C14 = rate

@numba.njit()
def He4_F21__Na25(rate_eval, tf):
    # F21 + He4 --> Na25
    rate = 0.0

    # rpsmr
    rate += np.exp(  49.0227 + -2.05398*tf.T9i + 29.6051*tf.T913i + -90.8761*tf.T913
                  + 4.01979*tf.T9 + -0.194878*tf.T953 + 47.6042*tf.lnT9)

    rate_eval.He4_F21__Na25 = rate

@numba.njit()
def P28__He4_Mg24__weak__wc12(rate_eval, tf):
    # P28 --> He4 + Mg24
    rate = 0.0

    # wc12w
    rate += np.exp(  -10.7209)

    rate_eval.P28__He4_Mg24__weak__wc12 = rate

@numba.njit()
def P43__S43__weak__wc17(rate_eval, tf):
    # P43 --> S43
    rate = 0.0

    # wc17w
    rate += np.exp(  -112.185)

    rate_eval.P43__S43__weak__wc17 = rate

@numba.njit()
def P28__p_Al27__weak__wc12(rate_eval, tf):
    # P28 --> p + Al27
    rate = 0.0

    # wc12w
    rate += np.exp(  -10.3077)

    rate_eval.P28__p_Al27__weak__wc12 = rate

@numba.njit()
def Al31__Si31__weak__wc12(rate_eval, tf):
    # Al31 --> Si31
    rate = 0.0

    # wc12w
    rate += np.exp(  0.0735436)

    rate_eval.Al31__Si31__weak__wc12 = rate

@numba.njit()
def p_P37__S38(rate_eval, tf):
    # P37 + p --> S38
    rate = 0.0

    # rath 
    rate += np.exp(  82.246 + -3.8629*tf.T9i + 139.329*tf.T913i + -231.71*tf.T913
                  + 12.5863*tf.T9 + -0.697055*tf.T953 + 116.26*tf.lnT9)

    rate_eval.p_P37__S38 = rate

@numba.njit()
def He4_Al39__n_P42(rate_eval, tf):
    # Al39 + He4 --> n + P42
    rate = 0.0

    # rath 
    rate += np.exp(  -10.0617 + -3.01481*tf.T9i + -15.4698*tf.T913i + 25.0235*tf.T913
                  + -5.25789*tf.T9 + 0.420234*tf.T953 + 5.63726*tf.lnT9)

    rate_eval.He4_Al39__n_P42 = rate

@numba.njit()
def He4_Ca49__Ti53(rate_eval, tf):
    # Ca49 + He4 --> Ti53
    rate = 0.0

    # rath 
    rate += np.exp(  -913.506 + 14.6277*tf.T9i + -1588.83*tf.T913i + 2604.09*tf.T913
                  + -155.396*tf.T9 + 8.89479*tf.T953 + -1222.49*tf.lnT9)

    rate_eval.He4_Ca49__Ti53 = rate

@numba.njit()
def Cr42__V42__weak__wc12(rate_eval, tf):
    # Cr42 --> V42
    rate = 0.0

    # wc12w
    rate += np.exp(  1.07107)

    rate_eval.Cr42__V42__weak__wc12 = rate

@numba.njit()
def t_Li7__n_n_He4_He4(rate_eval, tf):
    # Li7 + t --> n + n + He4 + He4
    rate = 0.0

    # mafon
    rate += np.exp(  27.5043 + -5.31692e-12*tf.T9i + -11.333*tf.T913i + -2.24192e-09*tf.T913
                  + 2.21773e-10*tf.T9 + -1.83941e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.t_Li7__n_n_He4_He4 = rate

@numba.njit()
def n_V66__V67(rate_eval, tf):
    # V66 + n --> V67
    rate = 0.0

    # rath 
    rate += np.exp(  24.5562 + 0.0651678*tf.T9i + -2.61124*tf.T913i + -11.5083*tf.T913
                  + 1.32195*tf.T9 + -0.12057*tf.T953 + 0.915787*tf.lnT9)

    rate_eval.n_V66__V67 = rate

@numba.njit()
def He4_K48__Sc52(rate_eval, tf):
    # K48 + He4 --> Sc52
    rate = 0.0

    # rath 
    rate += np.exp(  -875.269 + 14.0285*tf.T9i + -1522.64*tf.T913i + 2495.5*tf.T913
                  + -149.14*tf.T9 + 8.55442*tf.T953 + -1171.04*tf.lnT9)

    rate_eval.He4_K48__Sc52 = rate

@numba.njit()
def Cl49__Ar49__weak__mo03(rate_eval, tf):
    # Cl49 --> Ar49
    rate = 0.0

    # mo03w
    rate += np.exp(  -111.524)

    rate_eval.Cl49__Ar49__weak__mo03 = rate

@numba.njit()
def n_Ar33__He4_S30(rate_eval, tf):
    # Ar33 + n --> He4 + S30
    rate = 0.0

    # ths8r
    rate += np.exp(  16.6191 + 0.0542245*tf.T913
                  + 0.0507365*tf.T9 + 0.00645723*tf.T953)

    rate_eval.n_Ar33__He4_S30 = rate

@numba.njit()
def p_Mn59__Fe60(rate_eval, tf):
    # Mn59 + p --> Fe60
    rate = 0.0

    # rath 
    rate += np.exp(  131.636 + -6.73792*tf.T9i + 252.226*tf.T913i + -404.909*tf.T913
                  + 22.2538*tf.T9 + -1.27354*tf.T953 + 203.799*tf.lnT9)

    rate_eval.p_Mn59__Fe60 = rate

@numba.njit()
def K54__n_Ca53__weak__mp17(rate_eval, tf):
    # K54 --> n + Ca53
    rate = 0.0

    # mp17w
    rate += np.exp(  2.72453)

    rate_eval.K54__n_Ca53__weak__mp17 = rate

@numba.njit()
def p_P44__n_S44(rate_eval, tf):
    # P44 + p --> n + S44
    rate = 0.0

    # rath 
    rate += np.exp(  102.26 + -4.17936*tf.T9i + 153.871*tf.T913i + -257.827*tf.T913
                  + 14.3794*tf.T9 + -0.810037*tf.T953 + 127.863*tf.lnT9)

    rate_eval.p_P44__n_S44 = rate

@numba.njit()
def p_Cl28__Ar29(rate_eval, tf):
    # Cl28 + p --> Ar29
    rate = 0.0

    # ths8r
    rate += np.exp(  38.6666 + -27.833*tf.T913i + -13.0739*tf.T913
                  + 0.606952*tf.T9 + 0.0419218*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cl28__Ar29 = rate

@numba.njit()
def p_S27__Cl28(rate_eval, tf):
    # S27 + p --> Cl28
    rate = 0.0

    # ths8r
    rate += np.exp(  -18.6528 + -20.0181*tf.T9i + 18.7376*tf.T913
                  + -2.43715*tf.T9 + 0.208536*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_S27__Cl28 = rate

@numba.njit()
def He4_P45__Cl49(rate_eval, tf):
    # P45 + He4 --> Cl49
    rate = 0.0

    # rath 
    rate += np.exp(  -343.911 + 1.84392*tf.T9i + -484.165*tf.T913i + 855.93*tf.T913
                  + -56.5208*tf.T9 + 3.4428*tf.T953 + -375.826*tf.lnT9)

    rate_eval.He4_P45__Cl49 = rate

@numba.njit()
def p_B8__C9(rate_eval, tf):
    # B8 + p --> C9
    rate = 0.0

    # De99 
    rate += np.exp(  13.4227 + -0.00169909*tf.T9i + -12.028*tf.T913i + 0.710892*tf.T913
                  + -0.207352*tf.T9 + 0.0303647*tf.T953 + -0.837743*tf.lnT9)

    rate_eval.p_B8__C9 = rate

@numba.njit()
def n_Sc61__Sc62(rate_eval, tf):
    # Sc61 + n --> Sc62
    rate = 0.0

    # rath 
    rate += np.exp(  -1.57564 + 0.00629914*tf.T9i + -2.05786*tf.T913i + 5.17579*tf.T913
                  + 1.07765*tf.T9 + -0.182021*tf.T953 + -2.58*tf.lnT9)

    rate_eval.n_Sc61__Sc62 = rate

@numba.njit()
def p_K55__He4_Ar52(rate_eval, tf):
    # K55 + p --> He4 + Ar52
    rate = 0.0

    # rath 
    rate += np.exp(  120.764 + -5.53173*tf.T9i + 213.243*tf.T913i + -353.534*tf.T913
                  + 19.6577*tf.T9 + -1.05638*tf.T953 + 174.963*tf.lnT9)

    rate_eval.p_K55__He4_Ar52 = rate

@numba.njit()
def Si41__n_P40__weak__mp17(rate_eval, tf):
    # Si41 --> n + P40
    rate = 0.0

    # mp17w
    rate += np.exp(  2.81154)

    rate_eval.Si41__n_P40__weak__mp17 = rate

@numba.njit()
def Mn57__Fe57__weak__wc12(rate_eval, tf):
    # Mn57 --> Fe57
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.81386)

    rate_eval.Mn57__Fe57__weak__wc12 = rate

@numba.njit()
def Si40__n_P39__weak__mp17(rate_eval, tf):
    # Si40 --> n + P39
    rate = 0.0

    # mp17w
    rate += np.exp(  2.5667)

    rate_eval.Si40__n_P39__weak__mp17 = rate

@numba.njit()
def Si38__n_P37__weak__mp17(rate_eval, tf):
    # Si38 --> n + P37
    rate = 0.0

    # mp17w
    rate += np.exp(  0.575931)

    rate_eval.Si38__n_P37__weak__mp17 = rate

@numba.njit()
def p_Mg29__Al30(rate_eval, tf):
    # Mg29 + p --> Al30
    rate = 0.0

    # rath 
    rate += np.exp(  60.2566 + -2.93858*tf.T9i + 101.479*tf.T913i + -167.449*tf.T913
                  + 8.768*tf.T9 + -0.470827*tf.T953 + 85.6357*tf.lnT9)

    rate_eval.p_Mg29__Al30 = rate

@numba.njit()
def He4_Mn64__n_Co67(rate_eval, tf):
    # Mn64 + He4 --> n + Co67
    rate = 0.0

    # rath 
    rate += np.exp(  -1207.4 + 19.427*tf.T9i + -2100.67*tf.T913i + 3455.05*tf.T913
                  + -205.506*tf.T9 + 11.7624*tf.T953 + -1624.29*tf.lnT9)

    rate_eval.He4_Mn64__n_Co67 = rate

@numba.njit()
def He4_Cl31__p_Ar34(rate_eval, tf):
    # Cl31 + He4 --> p + Ar34
    rate = 0.0

    # ths8r
    rate += np.exp(  51.845 + -67.9875*tf.T913i + 0.27813*tf.T913
                  + -0.759929*tf.T9 + 0.0510649*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cl31__p_Ar34 = rate

@numba.njit()
def He4_Na22__Al26(rate_eval, tf):
    # Na22 + He4 --> Al26
    rate = 0.0

    # ths8r
    rate += np.exp(  36.3797 + -50.0924*tf.T913i + -0.390826*tf.T913
                  + -0.99531*tf.T9 + 0.101354*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Na22__Al26 = rate

@numba.njit()
def Fe52__Mn52__weak__wc12(rate_eval, tf):
    # Fe52 --> Mn52
    rate = 0.0

    # wc12w
    rate += np.exp(  -10.6688)

    rate_eval.Fe52__Mn52__weak__wc12 = rate

@numba.njit()
def K43__Ca43__weak__wc12(rate_eval, tf):
    # K43 --> Ca43
    rate = 0.0

    # wc12w
    rate += np.exp(  -11.66)

    rate_eval.K43__Ca43__weak__wc12 = rate

@numba.njit()
def Mg33__Al33__weak__wc12(rate_eval, tf):
    # Mg33 --> Al33
    rate = 0.0

    # wc12w
    rate += np.exp(  1.88507)

    rate_eval.Mg33__Al33__weak__wc12 = rate

@numba.njit()
def n_Sc36__He4_K33(rate_eval, tf):
    # Sc36 + n --> He4 + K33
    rate = 0.0

    # ths8r
    rate += np.exp(  13.3191 + 2.08838*tf.T913
                  + -0.233992*tf.T9 + 0.0244627*tf.T953)

    rate_eval.n_Sc36__He4_K33 = rate

@numba.njit()
def N11__C11__weak__btyk(rate_eval, tf):
    # N11 --> C11
    rate = 0.0

    # btykw
    rate += np.exp(  2.62922)

    rate_eval.N11__C11__weak__btyk = rate

@numba.njit()
def Ca60__n_Sc59__weak__mp17(rate_eval, tf):
    # Ca60 --> n + Sc59
    rate = 0.0

    # mp17w
    rate += np.exp(  2.34907)

    rate_eval.Ca60__n_Sc59__weak__mp17 = rate

@numba.njit()
def Al21__Mg21__weak__bqa_pos_(rate_eval, tf):
    # Al21 --> Mg21
    rate = 0.0

    # bqa+w
    rate += np.exp(  3.00028)

    rate_eval.Al21__Mg21__weak__bqa_pos_ = rate

@numba.njit()
def O15__N15__weak__wc12(rate_eval, tf):
    # O15 --> N15
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.17053)

    rate_eval.O15__N15__weak__wc12 = rate

@numba.njit()
def V67__Cr67__weak__mo03(rate_eval, tf):
    # V67 --> Cr67
    rate = 0.0

    # mo03w
    rate += np.exp(  4.24301)

    rate_eval.V67__Cr67__weak__mo03 = rate

@numba.njit()
def n_K38__K39(rate_eval, tf):
    # K38 + n --> K39
    rate = 0.0

    # ths8r
    rate += np.exp(  13.7596 + -0.161985*tf.T913
                  + 0.187817*tf.T9 + -0.0320464*tf.T953)

    rate_eval.n_K38__K39 = rate

@numba.njit()
def He4_Ti37__Cr41(rate_eval, tf):
    # Ti37 + He4 --> Cr41
    rate = 0.0

    # ths8r
    rate += np.exp(  45.2564 + -81.2459*tf.T913i + -0.538602*tf.T913
                  + -0.48691*tf.T9 + 0.00347636*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti37__Cr41 = rate

@numba.njit()
def p_Si31__n_P31(rate_eval, tf):
    # Si31 + p --> n + P31
    rate = 0.0

    # rath 
    rate += np.exp(  80.5195 + -3.3832*tf.T9i + 119.352*tf.T913i + -198.709*tf.T913
                  + 10.5994*tf.T9 + -0.583506*tf.T953 + 100.693*tf.lnT9)

    rate_eval.p_Si31__n_P31 = rate

@numba.njit()
def Ne33__n_n_n_Na30__weak__mo03(rate_eval, tf):
    # Ne33 --> 3 n + Na30
    rate = 0.0

    # mo03w
    rate += np.exp(  2.82291)

    rate_eval.Ne33__n_n_n_Na30__weak__mo03 = rate

@numba.njit()
def He4_Na26__Al30(rate_eval, tf):
    # Na26 + He4 --> Al30
    rate = 0.0

    # rath 
    rate += np.exp(  -11.6811 + -2.05219*tf.T9i + -26.5814*tf.T913i + 29.7541*tf.T913
                  + -4.77654*tf.T9 + 0.381704*tf.T953 + -1.17784*tf.lnT9)

    rate_eval.He4_Na26__Al30 = rate

@numba.njit()
def He4_F22__Na26(rate_eval, tf):
    # F22 + He4 --> Na26
    rate = 0.0

    # rpsmr
    rate += np.exp(  46.528 + -2.14982*tf.T9i + 33.9836*tf.T913i + -93.4887*tf.T913
                  + 3.85153*tf.T9 + -0.17122*tf.T953 + 50.2431*tf.lnT9)

    rate_eval.He4_F22__Na26 = rate

@numba.njit()
def He4_Sc63__V67(rate_eval, tf):
    # Sc63 + He4 --> V67
    rate = 0.0

    # rath 
    rate += np.exp(  -1076.67 + 17.1462*tf.T9i + -1854.81*tf.T913i + 3053.69*tf.T913
                  + -181.969*tf.T9 + 10.4144*tf.T953 + -1434.24*tf.lnT9)

    rate_eval.He4_Sc63__V67 = rate

@numba.njit()
def Cl46__Ar46__weak__wc12(rate_eval, tf):
    # Cl46 --> Ar46
    rate = 0.0

    # wc12w
    rate += np.exp(  0.178214)

    rate_eval.Cl46__Ar46__weak__wc12 = rate

@numba.njit()
def He4_Ti57__Cr61(rate_eval, tf):
    # Ti57 + He4 --> Cr61
    rate = 0.0

    # rath 
    rate += np.exp(  -1009.63 + 20.9283*tf.T9i + -2083.81*tf.T913i + 3212.27*tf.T913
                  + -182.336*tf.T9 + 10.0721*tf.T953 + -1557.22*tf.lnT9)

    rate_eval.He4_Ti57__Cr61 = rate

@numba.njit()
def Ti62__n_V61__weak__mp17(rate_eval, tf):
    # Ti62 --> n + V61
    rate = 0.0

    # mp17w
    rate += np.exp(  0.665189)

    rate_eval.Ti62__n_V61__weak__mp17 = rate

@numba.njit()
def p_Mn68__He4_Cr65(rate_eval, tf):
    # Mn68 + p --> He4 + Cr65
    rate = 0.0

    # rath 
    rate += np.exp(  124.152 + -7.21613*tf.T9i + 275.142*tf.T913i + -431.013*tf.T913
                  + 23.8436*tf.T9 + -1.30044*tf.T953 + 220.017*tf.lnT9)

    rate_eval.p_Mn68__He4_Cr65 = rate

@numba.njit()
def Cr64__n_Mn63__weak__mp17(rate_eval, tf):
    # Cr64 --> n + Mn63
    rate = 0.0

    # mp17w
    rate += np.exp(  -1.8016)

    rate_eval.Cr64__n_Mn63__weak__mp17 = rate

@numba.njit()
def Mn60__Fe60__weak__wc12(rate_eval, tf):
    # Mn60 --> Fe60
    rate = 0.0

    # wc12w
    rate += np.exp(  0.906453)

    rate_eval.Mn60__Fe60__weak__wc12 = rate

@numba.njit()
def Si25__p_Mg24__weak__wc12(rate_eval, tf):
    # Si25 --> p + Mg24
    rate = 0.0

    # wc12w
    rate += np.exp(  0.0977927)

    rate_eval.Si25__p_Mg24__weak__wc12 = rate

@numba.njit()
def n_Mg21__Mg22(rate_eval, tf):
    # Mg21 + n --> Mg22
    rate = 0.0

    # ths8r
    rate += np.exp(  7.48238 + 3.2428*tf.T913
                  + -0.456424*tf.T9 + 0.0316531*tf.T953)

    rate_eval.n_Mg21__Mg22 = rate

@numba.njit()
def n_Fe61__Fe62(rate_eval, tf):
    # Fe61 + n --> Fe62
    rate = 0.0

    # rath 
    rate += np.exp(  16.0889 + -0.0218589*tf.T9i + 1.50793*tf.T913i + -4.03509*tf.T913
                  + 0.621602*tf.T9 + -0.0997712*tf.T953 + 1.18519*tf.lnT9)

    rate_eval.n_Fe61__Fe62 = rate

@numba.njit()
def P42__S42__weak__wc17(rate_eval, tf):
    # P42 --> S42
    rate = 0.0

    # wc17w
    rate += np.exp(  1.8387)

    rate_eval.P42__S42__weak__wc17 = rate

@numba.njit()
def He4_Fe67__n_Ni70(rate_eval, tf):
    # Fe67 + He4 --> n + Ni70
    rate = 0.0

    # rath 
    rate += np.exp(  -1215.24 + 25.398*tf.T9i + -2521.15*tf.T913i + 3889.12*tf.T913
                  + -219.947*tf.T9 + 12.1419*tf.T953 + -1887.78*tf.lnT9)

    rate_eval.He4_Fe67__n_Ni70 = rate

@numba.njit()
def O22__F22__weak__wc17(rate_eval, tf):
    # O22 --> F22
    rate = 0.0

    # wc17w
    rate += np.exp(  -1.17744)

    rate_eval.O22__F22__weak__wc17 = rate

@numba.njit()
def He4_K40__Sc44(rate_eval, tf):
    # K40 + He4 --> Sc44
    rate = 0.0

    # ths8r
    rate += np.exp(  55.9694 + -73.858*tf.T913i + -1.10691*tf.T913
                  + -2.42921*tf.T9 + 0.294*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K40__Sc44 = rate

@numba.njit()
def K31__Ar31__weak__bqa_pos_(rate_eval, tf):
    # K31 --> Ar31
    rate = 0.0

    # bqa+w
    rate += np.exp(  5.08263)

    rate_eval.K31__Ar31__weak__bqa_pos_ = rate

@numba.njit()
def He4_Ne34__n_Mg37(rate_eval, tf):
    # Ne34 + He4 --> n + Mg37
    rate = 0.0

    # rath 
    rate += np.exp(  78.2853 + -3.1686*tf.T9i + 74.9617*tf.T913i + -159.759*tf.T913
                  + 7.53213*tf.T9 + -0.379044*tf.T953 + 82.8901*tf.lnT9)

    rate_eval.He4_Ne34__n_Mg37 = rate

@numba.njit()
def n_V63__V64(rate_eval, tf):
    # V63 + n --> V64
    rate = 0.0

    # rath 
    rate += np.exp(  11.5014 + -0.0354858*tf.T9i + 2.55504*tf.T913i + -6.30333*tf.T913
                  + 0.975892*tf.T9 + -0.124996*tf.T953 + 2.01941*tf.lnT9)

    rate_eval.n_V63__V64 = rate

@numba.njit()
def Na39__n_n_Mg37__weak__mp17(rate_eval, tf):
    # Na39 --> n + n + Mg37
    rate = 0.0

    # mp17w
    rate += np.exp(  6.16245)

    rate_eval.Na39__n_n_Mg37__weak__mp17 = rate

@numba.njit()
def Si23__p_Mg22__weak__wc17(rate_eval, tf):
    # Si23 --> p + Mg22
    rate = 0.0

    # wc17w
    rate += np.exp(  2.45396)

    rate_eval.Si23__p_Mg22__weak__wc17 = rate

@numba.njit()
def He4_Fe48__Ni52(rate_eval, tf):
    # Fe48 + He4 --> Ni52
    rate = 0.0

    # ths8r
    rate += np.exp(  54.9667 + -91.5018*tf.T913i + -3.67127*tf.T913
                  + -0.0674993*tf.T9 + -0.0496256*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe48__Ni52 = rate

@numba.njit()
def n_N14__N15(rate_eval, tf):
    # N14 + n --> N15
    rate = 0.0

    # ks03 
    rate += np.exp(  10.1651 + -0.0114078*tf.T9i + 1.396*tf.T913i + -3.47552*tf.T913
                  + 0.351773*tf.T9 + -0.0229344*tf.T953 + 1.02161*tf.lnT9)

    rate_eval.n_N14__N15 = rate

@numba.njit()
def n_F17__p_O17(rate_eval, tf):
    # F17 + n --> p + O17
    rate = 0.0

    #  wagn
    rate += np.exp(  19.0085)

    rate_eval.n_F17__p_O17 = rate

@numba.njit()
def n_Fe45__p_Mn45(rate_eval, tf):
    # Fe45 + n --> p + Mn45
    rate = 0.0

    # ths8r
    rate += np.exp(  21.7502 + -0.952904*tf.T913
                  + 0.270134*tf.T9 + -0.0250414*tf.T953)

    rate_eval.n_Fe45__p_Mn45 = rate

@numba.njit()
def He4_Na30__n_Al33(rate_eval, tf):
    # Na30 + He4 --> n + Al33
    rate = 0.0

    # rath 
    rate += np.exp(  74.6338 + -3.0965*tf.T9i + 67.2883*tf.T913i + -150.651*tf.T913
                  + 7.0499*tf.T9 + -0.358836*tf.T953 + 78.8655*tf.lnT9)

    rate_eval.He4_Na30__n_Al33 = rate

@numba.njit()
def p_Mg38__He4_Na35(rate_eval, tf):
    # Mg38 + p --> He4 + Na35
    rate = 0.0

    # rath 
    rate += np.exp(  48.2629 + -3.40569*tf.T9i + 124.616*tf.T913i + -183.168*tf.T913
                  + 8.40042*tf.T9 + -0.400413*tf.T953 + 101.051*tf.lnT9)

    rate_eval.p_Mg38__He4_Na35 = rate

@numba.njit()
def Fe47__p_Cr46__weak__wc12(rate_eval, tf):
    # Fe47 --> p + Cr46
    rate = 0.0

    # wc12w
    rate += np.exp(  3.33146)

    rate_eval.Fe47__p_Cr46__weak__wc12 = rate

@numba.njit()
def Al38__n_Si37__weak__mp17(rate_eval, tf):
    # Al38 --> n + Si37
    rate = 0.0

    # mp17w
    rate += np.exp(  1.85383)

    rate_eval.Al38__n_Si37__weak__mp17 = rate

@numba.njit()
def He4_Ar49__n_Ca52(rate_eval, tf):
    # Ar49 + He4 --> n + Ca52
    rate = 0.0

    # rath 
    rate += np.exp(  -400.588 + 2.11803*tf.T9i + -565.869*tf.T913i + 1009.37*tf.T913
                  + -66.5668*tf.T9 + 4.04841*tf.T953 + -442.389*tf.lnT9)

    rate_eval.He4_Ar49__n_Ca52 = rate

@numba.njit()
def p_O24__F25(rate_eval, tf):
    # O24 + p --> F25
    rate = 0.0

    # rpsmr
    rate += np.exp(  48.0802 + -2.04633*tf.T9i + 69.9576*tf.T913i + -120.442*tf.T913
                  + 6.55606*tf.T9 + -0.367162*tf.T953 + 60.5512*tf.lnT9)

    rate_eval.p_O24__F25 = rate

@numba.njit()
def p_Mg21__Al22(rate_eval, tf):
    # Mg21 + p --> Al22
    rate = 0.0

    # rath 
    rate += np.exp(  -14.0669 + -13.7906*tf.T9i + 104.078*tf.T913i + -100.163*tf.T913
                  + 4.2268*tf.T9 + -0.193473*tf.T953 + 64.454*tf.lnT9)

    rate_eval.p_Mg21__Al22 = rate

@numba.njit()
def n_Si30__Si31(rate_eval, tf):
    # Si30 + n --> Si31
    rate = 0.0

    # ks03 
    rate += np.exp(  -9.19438 + 0.0685821*tf.T9i + -12.3502*tf.T913i + 34.6486*tf.T913
                  + -1.89409*tf.T9 + 0.0781979*tf.T953 + -14.4601*tf.lnT9)

    rate_eval.n_Si30__Si31 = rate

@numba.njit()
def He4_Mn55__Co59(rate_eval, tf):
    # Mn55 + He4 --> Co59
    rate = 0.0

    # ths8r
    rate += np.exp(  60.0838 + -89.432*tf.T913i + 5.33428*tf.T913
                  + -5.11461*tf.T9 + 0.613808*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn55__Co59 = rate

@numba.njit()
def Cr60__Mn60__weak__wc12(rate_eval, tf):
    # Cr60 --> Mn60
    rate = 0.0

    # wc12w
    rate += np.exp(  0.346837)

    rate_eval.Cr60__Mn60__weak__wc12 = rate

@numba.njit()
def p_Cr48__Mn49(rate_eval, tf):
    # Cr48 + p --> Mn49
    rate = 0.0

    # ths8r
    rate += np.exp(  38.5336 + -35.1969*tf.T913i + -3.36393*tf.T913
                  + -1.55965*tf.T9 + 0.237119*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cr48__Mn49 = rate

@numba.njit()
def p_K52__n_Ca52(rate_eval, tf):
    # K52 + p --> n + Ca52
    rate = 0.0

    # rath 
    rate += np.exp(  115.907 + -5.30681*tf.T9i + 197.373*tf.T913i + -319.496*tf.T913
                  + 17.4234*tf.T9 + -0.970284*tf.T953 + 160.718*tf.lnT9)

    rate_eval.p_K52__n_Ca52 = rate

@numba.njit()
def He4_Si30__S34(rate_eval, tf):
    # Si30 + He4 --> S34
    rate = 0.0

    # ths8r
    rate += np.exp(  47.5008 + -59.6559*tf.T913i + 3.70141*tf.T913
                  + -3.12537*tf.T9 + 0.307626*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si30__S34 = rate

@numba.njit()
def n_P31__P32(rate_eval, tf):
    # P31 + n --> P32
    rate = 0.0

    # ka02r
    rate += np.exp(  9.48567 + -0.246803*tf.T9i + 2.13185*tf.T913
                  + -1.5*tf.lnT9)
    # ka02n
    rate += np.exp(  12.5332 + 0.327031*tf.T913
                  + 1.0*tf.lnT9)

    rate_eval.n_P31__P32 = rate

@numba.njit()
def He4_Si43__S47(rate_eval, tf):
    # Si43 + He4 --> S47
    rate = 0.0

    # rath 
    rate += np.exp(  -319.123 + 1.64423*tf.T9i + -446.801*tf.T913i + 791.93*tf.T913
                  + -52.7379*tf.T9 + 3.23138*tf.T953 + -346.368*tf.lnT9)

    rate_eval.He4_Si43__S47 = rate

@numba.njit()
def Al35__n_Si34__weak__wc12(rate_eval, tf):
    # Al35 --> n + Si34
    rate = 0.0

    # wc12w
    rate += np.exp(  1.95735)

    rate_eval.Al35__n_Si34__weak__wc12 = rate

@numba.njit()
def Cl52__Ar52__weak__mo03(rate_eval, tf):
    # Cl52 --> Ar52
    rate = 0.0

    # mo03w
    rate += np.exp(  -109.951)

    rate_eval.Cl52__Ar52__weak__mo03 = rate

@numba.njit()
def Mn69__Fe69__weak__wc17(rate_eval, tf):
    # Mn69 --> Fe69
    rate = 0.0

    # wc17w
    rate += np.exp(  3.41515)

    rate_eval.Mn69__Fe69__weak__wc17 = rate

@numba.njit()
def p_Mg35__He4_Na32(rate_eval, tf):
    # Mg35 + p --> He4 + Na32
    rate = 0.0

    # rath 
    rate += np.exp(  68.5318 + -3.23152*tf.T9i + 115.183*tf.T913i + -189.051*tf.T913
                  + 10.1128*tf.T9 + -0.535469*tf.T953 + 96.0402*tf.lnT9)

    rate_eval.p_Mg35__He4_Na32 = rate

@numba.njit()
def Si39__n_P38__weak__mp17(rate_eval, tf):
    # Si39 --> n + P38
    rate = 0.0

    # mp17w
    rate += np.exp(  1.76422)

    rate_eval.Si39__n_P38__weak__mp17 = rate

@numba.njit()
def He4_Mn56__Co60(rate_eval, tf):
    # Mn56 + He4 --> Co60
    rate = 0.0

    # rath 
    rate += np.exp(  -1146.62 + 23.4336*tf.T9i + -2329.36*tf.T913i + 3612.59*tf.T913
                  + -205.203*tf.T9 + 11.3472*tf.T953 + -1748.94*tf.lnT9)

    rate_eval.He4_Mn56__Co60 = rate

@numba.njit()
def Ne29__Na29__weak__wc12(rate_eval, tf):
    # Ne29 --> Na29
    rate = 0.0

    # wc12w
    rate += np.exp(  3.46095)

    rate_eval.Ne29__Na29__weak__wc12 = rate

@numba.njit()
def He4_P44__Cl48(rate_eval, tf):
    # P44 + He4 --> Cl48
    rate = 0.0

    # rath 
    rate += np.exp(  -346.068 + 2.01745*tf.T9i + -495.439*tf.T913i + 869.766*tf.T913
                  + -56.8483*tf.T9 + 3.43979*tf.T953 + -384.101*tf.lnT9)

    rate_eval.He4_P44__Cl48 = rate

@numba.njit()
def n_Fe45__Fe46(rate_eval, tf):
    # Fe45 + n --> Fe46
    rate = 0.0

    # ths8r
    rate += np.exp(  10.8073 + -0.571423*tf.T913
                  + 0.259964*tf.T9 + -0.0231634*tf.T953)

    rate_eval.n_Fe45__Fe46 = rate

@numba.njit()
def He4_Sc37__V41(rate_eval, tf):
    # Sc37 + He4 --> V41
    rate = 0.0

    # ths8r
    rate += np.exp(  46.1396 + -78.7634*tf.T913i + -0.810841*tf.T913
                  + -0.485009*tf.T9 + 0.00342062*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Sc37__V41 = rate

@numba.njit()
def N16__He4_C12__weak__wc12(rate_eval, tf):
    # N16 --> He4 + C12
    rate = 0.0

    # wc12w
    rate += np.exp(  -13.6614)

    rate_eval.N16__He4_C12__weak__wc12 = rate

@numba.njit()
def p_Cl37__Ar38(rate_eval, tf):
    # Cl37 + p --> Ar38
    rate = 0.0

    # ths8r
    rate += np.exp(  34.0095 + -27.9113*tf.T913i + 0.282028*tf.T913
                  + -1.80122*tf.T9 + 0.21751*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Cl37__Ar38 = rate

@numba.njit()
def P40__n_S39__weak__wc12(rate_eval, tf):
    # P40 --> n + S39
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.132232)

    rate_eval.P40__n_S39__weak__wc12 = rate

@numba.njit()
def Al32__n_Si31__weak__wc12(rate_eval, tf):
    # Al32 --> n + Si31
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.91711)

    rate_eval.Al32__n_Si31__weak__wc12 = rate

@numba.njit()
def p_K32__Ca33(rate_eval, tf):
    # K32 + p --> Ca33
    rate = 0.0

    # ths8r
    rate += np.exp(  -18.5413 + -10.1079*tf.T9i + 20.0035*tf.T913
                  + -2.93832*tf.T9 + 0.261291*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_K32__Ca33 = rate

@numba.njit()
def C10__B10__weak__wc12(rate_eval, tf):
    # C10 --> B10
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.32662)

    rate_eval.C10__B10__weak__wc12 = rate

@numba.njit()
def Cr57__Mn57__weak__wc12(rate_eval, tf):
    # Cr57 --> Mn57
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.41579)

    rate_eval.Cr57__Mn57__weak__wc12 = rate

@numba.njit()
def Cl36__Ar36__weak__wc12(rate_eval, tf):
    # Cl36 --> Ar36
    rate = 0.0

    # wc12w
    rate += np.exp(  -30.268)

    rate_eval.Cl36__Ar36__weak__wc12 = rate

@numba.njit()
def n_Fe59__Fe60(rate_eval, tf):
    # Fe59 + n --> Fe60
    rate = 0.0

    # rath 
    rate += np.exp(  30.2038 + -0.129283*tf.T9i + 12.6507*tf.T913i + -30.044*tf.T913
                  + 2.26106*tf.T9 + -0.169674*tf.T953 + 11.7782*tf.lnT9)

    rate_eval.n_Fe59__Fe60 = rate

@numba.njit()
def He4_Na24__n_Al27(rate_eval, tf):
    # Na24 + He4 --> n + Al27
    rate = 0.0

    # rath 
    rate += np.exp(  67.5936 + -2.6585*tf.T9i + 49.3636*tf.T913i + -124.715*tf.T913
                  + 5.57965*tf.T9 + -0.275543*tf.T953 + 65.8717*tf.lnT9)

    rate_eval.He4_Na24__n_Al27 = rate

@numba.njit()
def B13__C13__weak__wc12(rate_eval, tf):
    # B13 --> C13
    rate = 0.0

    # wc12w
    rate += np.exp(  3.69054)

    rate_eval.B13__C13__weak__wc12 = rate

@numba.njit()
def p_Ar54__K55(rate_eval, tf):
    # Ar54 + p --> K55
    rate = 0.0

    # rath 
    rate += np.exp(  101.68 + -5.191*tf.T9i + 192.245*tf.T913i + -309.848*tf.T913
                  + 16.8377*tf.T9 + -0.928495*tf.T953 + 155.868*tf.lnT9)

    rate_eval.p_Ar54__K55 = rate

@numba.njit()
def He4_O25__Ne29(rate_eval, tf):
    # O25 + He4 --> Ne29
    rate = 0.0

    # rpsmr
    rate += np.exp(  47.3192 + -2.23051*tf.T9i + 43.6401*tf.T913i + -104.531*tf.T913
                  + 4.49177*tf.T9 + -0.206869*tf.T953 + 55.5763*tf.lnT9)

    rate_eval.He4_O25__Ne29 = rate

@numba.njit()
def p_Sc50__He4_Ca47(rate_eval, tf):
    # Sc50 + p --> He4 + Ca47
    rate = 0.0

    # rath 
    rate += np.exp(  50.6253 + -5.36756*tf.T9i + 182.865*tf.T913i + -247.316*tf.T913
                  + 10.1756*tf.T9 + -0.411074*tf.T953 + 141.853*tf.lnT9)

    rate_eval.p_Sc50__He4_Ca47 = rate

@numba.njit()
def Fe61__Co61__weak__wc12(rate_eval, tf):
    # Fe61 --> Co61
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.24984)

    rate_eval.Fe61__Co61__weak__wc12 = rate

@numba.njit()
def p_P45__He4_Si42(rate_eval, tf):
    # P45 + p --> He4 + Si42
    rate = 0.0

    # rath 
    rate += np.exp(  87.6697 + -4.24318*tf.T9i + 156.051*tf.T913i + -254.005*tf.T913
                  + 13.6688*tf.T9 + -0.742295*tf.T953 + 128.085*tf.lnT9)

    rate_eval.p_P45__He4_Si42 = rate

@numba.njit()
def p_K43__He4_Ar40(rate_eval, tf):
    # K43 + p --> He4 + Ar40
    rate = 0.0

    # rath 
    rate += np.exp(  96.4572 + -4.86878*tf.T9i + 178.819*tf.T913i + -287.676*tf.T913
                  + 15.6682*tf.T9 + -0.87433*tf.T953 + 146.958*tf.lnT9)

    rate_eval.p_K43__He4_Ar40 = rate

@numba.njit()
def n_P37__P38(rate_eval, tf):
    # P37 + n --> P38
    rate = 0.0

    # rath 
    rate += np.exp(  9.00321 + -0.0196806*tf.T9i + 0.76408*tf.T913i + 0.62817*tf.T913
                  + 0.0123045*tf.T9 + -0.018321*tf.T953 + -0.0134263*tf.lnT9)

    rate_eval.n_P37__P38 = rate

@numba.njit()
def He4_Si44__S48(rate_eval, tf):
    # Si44 + He4 --> S48
    rate = 0.0

    # rath 
    rate += np.exp(  -322.441 + 1.65236*tf.T9i + -450.635*tf.T913i + 799.422*tf.T913
                  + -53.1802*tf.T9 + 3.25335*tf.T953 + -349.732*tf.lnT9)

    rate_eval.He4_Si44__S48 = rate

@numba.njit()
def Na20__He4_O16__weak__wc12(rate_eval, tf):
    # Na20 --> He4 + O16
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.17049)

    rate_eval.Na20__He4_O16__weak__wc12 = rate

@numba.njit()
def Si43__n_n_n_P40__weak__mo03(rate_eval, tf):
    # Si43 --> 3 n + P40
    rate = 0.0

    # mo03w
    rate += np.exp(  0.668409)

    rate_eval.Si43__n_n_n_P40__weak__mo03 = rate

@numba.njit()
def P47__S47__weak__mo03(rate_eval, tf):
    # P47 --> S47
    rate = 0.0

    # mo03w
    rate += np.exp(  -111.182)

    rate_eval.P47__S47__weak__mo03 = rate

@numba.njit()
def Ti54__V54__weak__wc12(rate_eval, tf):
    # Ti54 --> V54
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.771978)

    rate_eval.Ti54__V54__weak__wc12 = rate

@numba.njit()
def K51__Ca51__weak__wc12(rate_eval, tf):
    # K51 --> Ca51
    rate = 0.0

    # wc12w
    rate += np.exp(  0.00646673)

    rate_eval.K51__Ca51__weak__wc12 = rate

@numba.njit()
def Ti39__Sc39__weak__wc17(rate_eval, tf):
    # Ti39 --> Sc39
    rate = 0.0

    # wc17w
    rate += np.exp(  -112.022)

    rate_eval.Ti39__Sc39__weak__wc17 = rate

@numba.njit()
def Mg40__n_Al39__weak__mp17(rate_eval, tf):
    # Mg40 --> n + Al39
    rate = 0.0

    # mp17w
    rate += np.exp(  3.55588)

    rate_eval.Mg40__n_Al39__weak__mp17 = rate

@numba.njit()
def He4_K38__Sc42(rate_eval, tf):
    # K38 + He4 --> Sc42
    rate = 0.0

    # ths8r
    rate += np.exp(  53.2593 + -73.7407*tf.T913i + -7.08848*tf.T913
                  + 0.322473*tf.T9 + -0.0523557*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K38__Sc42 = rate

@numba.njit()
def Mn72__n_n_n_Fe69__weak__mo03(rate_eval, tf):
    # Mn72 --> 3 n + Fe69
    rate = 0.0

    # mo03w
    rate += np.exp(  -0.878481)

    rate_eval.Mn72__n_n_n_Fe69__weak__mo03 = rate

@numba.njit()
def Mg38__n_Al37__weak__mp17(rate_eval, tf):
    # Mg38 --> n + Al37
    rate = 0.0

    # mp17w
    rate += np.exp(  4.23286)

    rate_eval.Mg38__n_Al37__weak__mp17 = rate

@numba.njit()
def p_S43__n_Cl43(rate_eval, tf):
    # S43 + p --> n + Cl43
    rate = 0.0

    # rath 
    rate += np.exp(  99.1273 + -4.32761*tf.T9i + 158.17*tf.T913i + -259.971*tf.T913
                  + 14.265*tf.T9 + -0.796869*tf.T953 + 130.495*tf.lnT9)

    rate_eval.p_S43__n_Cl43 = rate

@numba.njit()
def He4_Ti59__Cr63(rate_eval, tf):
    # Ti59 + He4 --> Cr63
    rate = 0.0

    # rath 
    rate += np.exp(  -1025.76 + 21.273*tf.T9i + -2117.1*tf.T913i + 3263.75*tf.T913
                  + -185.169*tf.T9 + 10.2264*tf.T953 + -1582.64*tf.lnT9)

    rate_eval.He4_Ti59__Cr63 = rate

@numba.njit()
def n_Ti62__Ti63(rate_eval, tf):
    # Ti62 + n --> Ti63
    rate = 0.0

    # rath 
    rate += np.exp(  46.3835 + -0.336234*tf.T9i + 35.4343*tf.T913i + -83.0087*tf.T913
                  + 7.27301*tf.T9 + -0.596398*tf.T953 + 33.8266*tf.lnT9)

    rate_eval.n_Ti62__Ti63 = rate

@numba.njit()
def Cr44__p_Ti43__weak__wc12(rate_eval, tf):
    # Cr44 --> p + Ti43
    rate = 0.0

    # wc12w
    rate += np.exp(  0.818591)

    rate_eval.Cr44__p_Ti43__weak__wc12 = rate

@numba.njit()
def O27__n_O26(rate_eval, tf):
    # O27 --> n + O26
    rate = 0.0

    # wc12s
    rate += np.exp(  14.7961)

    rate_eval.O27__n_O26 = rate

@numba.njit()
def p_Mn54__Fe55(rate_eval, tf):
    # Mn54 + p --> Fe55
    rate = 0.0

    # ths8r
    rate += np.exp(  35.55 + -36.1955*tf.T913i + 1.08481*tf.T913
                  + -1.46703*tf.T9 + 0.13789*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn54__Fe55 = rate

@numba.njit()
def Ca60__Sc60__weak__mo03(rate_eval, tf):
    # Ca60 --> Sc60
    rate = 0.0

    # mo03w
    rate += np.exp(  5.05712)

    rate_eval.Ca60__Sc60__weak__mo03 = rate

@numba.njit()
def p_P40__He4_Si37(rate_eval, tf):
    # P40 + p --> He4 + Si37
    rate = 0.0

    # rath 
    rate += np.exp(  73.9018 + -4.01099*tf.T9i + 145.384*tf.T913i + -229.259*tf.T913
                  + 11.7199*tf.T9 + -0.596758*tf.T953 + 119.231*tf.lnT9)

    rate_eval.p_P40__He4_Si37 = rate

@numba.njit()
def n_Mg33__Mg34(rate_eval, tf):
    # Mg33 + n --> Mg34
    rate = 0.0

    # rath 
    rate += np.exp(  13.3198 + -0.0646979*tf.T9i + 5.11926*tf.T913i + -10.2798*tf.T913
                  + 0.856609*tf.T9 + -0.0603661*tf.T953 + 4.07722*tf.lnT9)

    rate_eval.n_Mg33__Mg34 = rate

@numba.njit()
def p_P44__S45(rate_eval, tf):
    # P44 + p --> S45
    rate = 0.0

    # rath 
    rate += np.exp(  90.052 + -4.1709*tf.T9i + 152.801*tf.T913i + -254.895*tf.T913
                  + 14.176*tf.T9 + -0.795282*tf.T953 + 126.727*tf.lnT9)

    rate_eval.p_P44__S45 = rate

@numba.njit()
def Ca58__Sc58__weak__mo03(rate_eval, tf):
    # Ca58 --> Sc58
    rate = 0.0

    # mo03w
    rate += np.exp(  4.0528)

    rate_eval.Ca58__Sc58__weak__mo03 = rate

@numba.njit()
def He4_V52__n_Mn55(rate_eval, tf):
    # V52 + He4 --> n + Mn55
    rate = 0.0

    # rath 
    rate += np.exp(  -1026.77 + 16.489*tf.T9i + -1790.25*tf.T913i + 2939.64*tf.T913
                  + -175.533*tf.T9 + 10.0701*tf.T953 + -1379.09*tf.lnT9)

    rate_eval.He4_V52__n_Mn55 = rate

@numba.njit()
def V61__Cr61__weak__wc12(rate_eval, tf):
    # V61 --> Cr61
    rate = 0.0

    # wc12w
    rate += np.exp(  2.51665)

    rate_eval.V61__Cr61__weak__wc12 = rate

@numba.njit()
def O21__F21__weak__wc12(rate_eval, tf):
    # O21 --> F21
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.59615)

    rate_eval.O21__F21__weak__wc12 = rate

@numba.njit()
def O13__p_C12__weak__wc12(rate_eval, tf):
    # O13 --> p + C12
    rate = 0.0

    # wc12w
    rate += np.exp(  4.39181)

    rate_eval.O13__p_C12__weak__wc12 = rate

@numba.njit()
def P45__S45__weak__mo03(rate_eval, tf):
    # P45 --> S45
    rate = 0.0

    # mo03w
    rate += np.exp(  -111.179)

    rate_eval.P45__S45__weak__mo03 = rate

@numba.njit()
def K56__n_Ca55__weak__mp17(rate_eval, tf):
    # K56 --> n + Ca55
    rate = 0.0

    # mp17w
    rate += np.exp(  4.9318)

    rate_eval.K56__n_Ca55__weak__mp17 = rate

@numba.njit()
def C20__N20__weak__wc12(rate_eval, tf):
    # C20 --> N20
    rate = 0.0

    # wc12w
    rate += np.exp(  2.62922)

    rate_eval.C20__N20__weak__wc12 = rate

@numba.njit()
def p_d__He3(rate_eval, tf):
    # d + p --> He3
    rate = 0.0

    # de04 
    rate += np.exp(  8.93525 + -3.7208*tf.T913i + 0.198654*tf.T913
                  + 0.333333*tf.lnT9)
    # de04n
    rate += np.exp(  7.52898 + -3.7208*tf.T913i + 0.871782*tf.T913
                  + -0.666667*tf.lnT9)

    rate_eval.p_d__He3 = rate

@numba.njit()
def n_C15__C16(rate_eval, tf):
    # C15 + n --> C16
    rate = 0.0

    # wiesr
    rate += np.exp(  6.55407 + -0.000690046*tf.T9i + 0.106378*tf.T913i + -0.445016*tf.T913
                  + 0.056356*tf.T9 + -0.00488392*tf.T953 + 1.13388*tf.lnT9)

    rate_eval.n_C15__C16 = rate

@numba.njit()
def Si25__Al25__weak__wc12(rate_eval, tf):
    # Si25 --> Al25
    rate = 0.0

    # wc12w
    rate += np.exp(  0.716832)

    rate_eval.Si25__Al25__weak__wc12 = rate

@numba.njit()
def K57__Ca57__weak__mo03(rate_eval, tf):
    # K57 --> Ca57
    rate = 0.0

    # mo03w
    rate += np.exp(  -32.4169)

    rate_eval.K57__Ca57__weak__mo03 = rate

@numba.njit()
def S42__Cl42__weak__wc12(rate_eval, tf):
    # S42 --> Cl42
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.396072)

    rate_eval.S42__Cl42__weak__wc12 = rate

@numba.njit()
def p_V47__Cr48(rate_eval, tf):
    # V47 + p --> Cr48
    rate = 0.0

    # nfisn
    rate += np.exp(  42.6798 + -6.0593*tf.T9i + -34.0548*tf.T913i + -3.41973*tf.T913
                  + 1.16501*tf.T9 + -0.105543*tf.T953 + -7.70886*tf.lnT9)
    # nfisn
    rate += np.exp(  511.463 + -5.29491*tf.T9i + 317.171*tf.T913i + -911.679*tf.T913
                  + 94.4245*tf.T9 + -10.1973*tf.T953 + 330.727*tf.lnT9)
    # nfisn
    rate += np.exp(  23.8315 + 0.246665*tf.T9i + -45.9868*tf.T913i + 13.6822*tf.T913
                  + -0.376902*tf.T9 + -0.0194875*tf.T953 + -8.42325*tf.lnT9)
    # nfisn
    rate += np.exp(  40.5626 + -0.514414*tf.T9i + -110.655*tf.T913i + 83.0232*tf.T913
                  + -19.7762*tf.T9 + 3.03961*tf.T953 + -49.4742*tf.lnT9)

    rate_eval.p_V47__Cr48 = rate

@numba.njit()
def Mg21__p_Ne20__weak__wc12(rate_eval, tf):
    # Mg21 --> p + Ne20
    rate = 0.0

    # wc12w
    rate += np.exp(  0.616363)

    rate_eval.Mg21__p_Ne20__weak__wc12 = rate

@numba.njit()
def S31__P31__weak__wc12(rate_eval, tf):
    # S31 --> P31
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.31042)

    rate_eval.S31__P31__weak__wc12 = rate

@numba.njit()
def He4_Mn71__n_Co74(rate_eval, tf):
    # Mn71 + He4 --> n + Co74
    rate = 0.0

    # rath 
    rate += np.exp(  -1221.46 + 25.433*tf.T9i + -2524.31*tf.T913i + 3902.06*tf.T913
                  + -221.196*tf.T9 + 12.2405*tf.T953 + -1892.83*tf.lnT9)

    rate_eval.He4_Mn71__n_Co74 = rate

@numba.njit()
def K45__Ca45__weak__wc12(rate_eval, tf):
    # K45 --> Ca45
    rate = 0.0

    # wc12w
    rate += np.exp(  -7.34193)

    rate_eval.K45__Ca45__weak__wc12 = rate

@numba.njit()
def Cr55__Mn55__weak__wc12(rate_eval, tf):
    # Cr55 --> Mn55
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.71362)

    rate_eval.Cr55__Mn55__weak__wc12 = rate

@numba.njit()
def n_Ca42__Ca43(rate_eval, tf):
    # Ca42 + n --> Ca43
    rate = 0.0

    # ks03 
    rate += np.exp(  15.996 + 0.0365498*tf.T9i + -2.75867*tf.T913i + 0.860871*tf.T913
                  + 0.583467*tf.T9 + -0.094473*tf.T953 + -1.59357*tf.lnT9)

    rate_eval.n_Ca42__Ca43 = rate

@numba.njit()
def He4_Ar34__Ca38(rate_eval, tf):
    # Ar34 + He4 --> Ca38
    rate = 0.0

    # ths8r
    rate += np.exp(  48.8813 + -70.8666*tf.T913i + -5.98563*tf.T913
                  + 0.582779*tf.T9 + -0.093842*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar34__Ca38 = rate

@numba.njit()
def p_Na38__n_Mg38(rate_eval, tf):
    # Na38 + p --> n + Mg38
    rate = 0.0

    # rath 
    rate += np.exp(  81.487 + -3.19251*tf.T9i + 116.336*tf.T913i + -193.958*tf.T913
                  + 10.5546*tf.T9 + -0.581585*tf.T953 + 96.9573*tf.lnT9)

    rate_eval.p_Na38__n_Mg38 = rate

@numba.njit()
def p_V54__He4_Ti51(rate_eval, tf):
    # V54 + p --> He4 + Ti51
    rate = 0.0

    # rath 
    rate += np.exp(  121.253 + -6.23669*tf.T9i + 238.091*tf.T913i + -379.077*tf.T913
                  + 20.4701*tf.T9 + -1.06622*tf.T953 + 193.002*tf.lnT9)

    rate_eval.p_V54__He4_Ti51 = rate

@numba.njit()
def p_Ca53__Sc54(rate_eval, tf):
    # Ca53 + p --> Sc54
    rate = 0.0

    # rath 
    rate += np.exp(  115.443 + -5.55939*tf.T9i + 209.109*tf.T913i + -343.474*tf.T913
                  + 19.2938*tf.T9 + -1.10445*tf.T953 + 171.077*tf.lnT9)

    rate_eval.p_Ca53__Sc54 = rate

@numba.njit()
def n_Mn53__Mn54(rate_eval, tf):
    # Mn53 + n --> Mn54
    rate = 0.0

    # ths8r
    rate += np.exp(  17.3501 + -1.70171*tf.T913
                  + 0.386422*tf.T9 + -0.0536858*tf.T953)

    rate_eval.n_Mn53__Mn54 = rate

@numba.njit()
def S43__Cl43__weak__wc12(rate_eval, tf):
    # S43 --> Cl43
    rate = 0.0

    # wc12w
    rate += np.exp(  0.395627)

    rate_eval.S43__Cl43__weak__wc12 = rate

@numba.njit()
def p_Na37__n_Mg37(rate_eval, tf):
    # Na37 + p --> n + Mg37
    rate = 0.0

    # rath 
    rate += np.exp(  80.8302 + -3.15277*tf.T9i + 114.634*tf.T913i + -191.697*tf.T913
                  + 10.4764*tf.T9 + -0.5812*tf.T953 + 95.7577*tf.lnT9)

    rate_eval.p_Na37__n_Mg37 = rate

@numba.njit()
def Ti62__V62__weak__mo03(rate_eval, tf):
    # Ti62 --> V62
    rate = 0.0

    # mo03w
    rate += np.exp(  3.60963)

    rate_eval.Ti62__V62__weak__mo03 = rate

@numba.njit()
def p_Mn62__n_Fe62(rate_eval, tf):
    # Mn62 + p --> n + Fe62
    rate = 0.0

    # rath 
    rate += np.exp(  145.165 + -6.91452*tf.T9i + 261.393*tf.T913i + -419.717*tf.T913
                  + 22.8647*tf.T9 + -1.2676*tf.T953 + 210.918*tf.lnT9)

    rate_eval.p_Mn62__n_Fe62 = rate

@numba.njit()
def n_Mn48__Mn49(rate_eval, tf):
    # Mn48 + n --> Mn49
    rate = 0.0

    # ths8r
    rate += np.exp(  13.2623 + -1.31295*tf.T913
                  + 0.415426*tf.T9 + -0.0400473*tf.T953)

    rate_eval.n_Mn48__Mn49 = rate

@numba.njit()
def P27__Si27__weak__wc12(rate_eval, tf):
    # P27 --> Si27
    rate = 0.0

    # wc12w
    rate += np.exp(  0.97986)

    rate_eval.P27__Si27__weak__wc12 = rate

@numba.njit()
def n_Ti56__Ti57(rate_eval, tf):
    # Ti56 + n --> Ti57
    rate = 0.0

    # rath 
    rate += np.exp(  20.3333 + -0.0515965*tf.T9i + 5.47806*tf.T913i + -19.2753*tf.T913
                  + 2.64371*tf.T9 + -0.27063*tf.T953 + 5.88617*tf.lnT9)

    rate_eval.n_Ti56__Ti57 = rate

@numba.njit()
def Mg28__Al28__weak__wc12(rate_eval, tf):
    # Mg28 --> Al28
    rate = 0.0

    # wc12w
    rate += np.exp(  -11.5957)

    rate_eval.Mg28__Al28__weak__wc12 = rate

@numba.njit()
def Na38__n_Mg37__weak__mp17(rate_eval, tf):
    # Na38 --> n + Mg37
    rate = 0.0

    # mp17w
    rate += np.exp(  3.0297)

    rate_eval.Na38__n_Mg37__weak__mp17 = rate

@numba.njit()
def He4_Si22__S26(rate_eval, tf):
    # Si22 + He4 --> S26
    rate = 0.0

    # ths8r
    rate += np.exp(  36.1196 + -58.835*tf.T913i + 0.507628*tf.T913
                  + -0.415163*tf.T9 + -0.00683594*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si22__S26 = rate

@numba.njit()
def Ar53__n_K52__weak__mp17(rate_eval, tf):
    # Ar53 --> n + K52
    rate = 0.0

    # mp17w
    rate += np.exp(  3.45278)

    rate_eval.Ar53__n_K52__weak__mp17 = rate

@numba.njit()
def n_S43__S44(rate_eval, tf):
    # S43 + n --> S44
    rate = 0.0

    # rath 
    rate += np.exp(  11.483 + -0.0477472*tf.T9i + 3.68525*tf.T913i + -7.17964*tf.T913
                  + 0.68614*tf.T9 + -0.0552856*tf.T953 + 2.86443*tf.lnT9)

    rate_eval.n_S43__S44 = rate

@numba.njit()
def V67__n_Cr66__weak__mp17(rate_eval, tf):
    # V67 --> n + Cr66
    rate = 0.0

    # mp17w
    rate += np.exp(  4.3462)

    rate_eval.V67__n_Cr66__weak__mp17 = rate

@numba.njit()
def p_F23__n_Ne23(rate_eval, tf):
    # F23 + p --> n + Ne23
    rate = 0.0

    # rpsmr
    rate += np.exp(  60.0236 + -2.15766*tf.T9i + 72.7507*tf.T913i + -125.48*tf.T913
                  + 6.78174*tf.T9 + -0.377806*tf.T953 + 63.2653*tf.lnT9)

    rate_eval.p_F23__n_Ne23 = rate

@numba.njit()
def Ti64__V64__weak__mo03(rate_eval, tf):
    # Ti64 --> V64
    rate = 0.0

    # mo03w
    rate += np.exp(  0.409292)

    rate_eval.Ti64__V64__weak__mo03 = rate

@numba.njit()
def S41__Cl41__weak__wc12(rate_eval, tf):
    # S41 --> Cl41
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.05465)

    rate_eval.S41__Cl41__weak__wc12 = rate

@numba.njit()
def Na34__n_Mg33__weak__wc12(rate_eval, tf):
    # Na34 --> n + Mg33
    rate = 0.0

    # wc12w
    rate += np.exp(  2.93937)

    rate_eval.Na34__n_Mg33__weak__wc12 = rate

@numba.njit()
def p_Ca38__Sc39(rate_eval, tf):
    # Ca38 + p --> Sc39
    rate = 0.0

    # ths8r
    rate += np.exp(  -17.7938 + -6.98055*tf.T9i + 20.4307*tf.T913
                  + -2.70468*tf.T9 + 0.242514*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ca38__Sc39 = rate

@numba.njit()
def n_Ti39__Ti40(rate_eval, tf):
    # Ti39 + n --> Ti40
    rate = 0.0

    # ths8r
    rate += np.exp(  8.66613 + 1.79839*tf.T913
                  + -0.215433*tf.T9 + 0.0145212*tf.T953)

    rate_eval.n_Ti39__Ti40 = rate

@numba.njit()
def n_Ca39__p_K39(rate_eval, tf):
    # Ca39 + n --> p + K39
    rate = 0.0

    # ths8r
    rate += np.exp(  19.7695 + -0.222885*tf.T913
                  + 0.234029*tf.T9 + -0.0256002*tf.T953)

    rate_eval.n_Ca39__p_K39 = rate

@numba.njit()
def He4_Ar51__Ca55(rate_eval, tf):
    # Ar51 + He4 --> Ca55
    rate = 0.0

    # rath 
    rate += np.exp(  -880.976 + 14.0637*tf.T9i + -1523.44*tf.T913i + 2503.34*tf.T913
                  + -149.695*tf.T9 + 8.58941*tf.T953 + -1174.31*tf.lnT9)

    rate_eval.He4_Ar51__Ca55 = rate

@numba.njit()
def n_Ti44__He4_Ca41(rate_eval, tf):
    # Ti44 + n --> He4 + Ca41
    rate = 0.0

    # ths8r
    rate += np.exp(  7.51125 + 2.68094*tf.T913
                  + 1.34285*tf.T9 + -0.18134*tf.T953)

    rate_eval.n_Ti44__He4_Ca41 = rate

@numba.njit()
def Si37__n_P36__weak__wc12(rate_eval, tf):
    # Si37 --> n + P36
    rate = 0.0

    # wc12w
    rate += np.exp(  0.269476)

    rate_eval.Si37__n_P36__weak__wc12 = rate

@numba.njit()
def Mn64__n_Fe63__weak__wc12(rate_eval, tf):
    # Mn64 --> n + Fe63
    rate = 0.0

    # wc12w
    rate += np.exp(  0.93277)

    rate_eval.Mn64__n_Fe63__weak__wc12 = rate

@numba.njit()
def Ne33__n_Na32__weak__mp17(rate_eval, tf):
    # Ne33 --> n + Na32
    rate = 0.0

    # mp17w
    rate += np.exp(  3.98525)

    rate_eval.Ne33__n_Na32__weak__mp17 = rate

@numba.njit()
def He4_Mn66__n_Co69(rate_eval, tf):
    # Mn66 + He4 --> n + Co69
    rate = 0.0

    # rath 
    rate += np.exp(  -1256.84 + 20.0428*tf.T9i + -2164.21*tf.T913i + 3574.53*tf.T913
                  + -212.739*tf.T9 + 12.1775*tf.T953 + -1678.74*tf.lnT9)

    rate_eval.He4_Mn66__n_Co69 = rate

@numba.njit()
def Na30__He4_Ne26__weak__wc12(rate_eval, tf):
    # Na30 --> He4 + Ne26
    rate = 0.0

    # wc12w
    rate += np.exp(  -11.7433)

    rate_eval.Na30__He4_Ne26__weak__wc12 = rate

@numba.njit()
def He4_Ca52__n_Ti55(rate_eval, tf):
    # Ca52 + He4 --> n + Ti55
    rate = 0.0

    # rath 
    rate += np.exp(  -935.609 + 15.0302*tf.T9i + -1632.36*tf.T913i + 2682.97*tf.T913
                  + -160.445*tf.T9 + 9.21395*tf.T953 + -1258.11*tf.lnT9)

    rate_eval.He4_Ca52__n_Ti55 = rate

@numba.njit()
def p_Cr43__Mn44(rate_eval, tf):
    # Cr43 + p --> Mn44
    rate = 0.0

    # ths8r
    rate += np.exp(  -19.4919 + -14.4247*tf.T9i + 19.201*tf.T913
                  + -2.67118*tf.T9 + 0.226275*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Cr43__Mn44 = rate

@numba.njit()
def He4_Ne19__Mg23(rate_eval, tf):
    # Ne19 + He4 --> Mg23
    rate = 0.0

    # ths8r
    rate += np.exp(  37.1998 + -46.6346*tf.T913i + -1.1007*tf.T913
                  + -0.794097*tf.T9 + 0.0813036*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ne19__Mg23 = rate

@numba.njit()
def Na29__n_Mg28__weak__wc12(rate_eval, tf):
    # Na29 --> n + Mg28
    rate = 0.0

    # wc12w
    rate += np.exp(  1.19969)

    rate_eval.Na29__n_Mg28__weak__wc12 = rate

@numba.njit()
def p_Sc56__n_Ti56(rate_eval, tf):
    # Sc56 + p --> n + Ti56
    rate = 0.0

    # rath 
    rate += np.exp(  125.46 + -5.86439*tf.T9i + 219.239*tf.T913i + -353.391*tf.T913
                  + 19.2885*tf.T9 + -1.07539*tf.T953 + 177.787*tf.lnT9)

    rate_eval.p_Sc56__n_Ti56 = rate

@numba.njit()
def n_Mg39__Mg40(rate_eval, tf):
    # Mg39 + n --> Mg40
    rate = 0.0

    # rath 
    rate += np.exp(  16.2 + -0.0306628*tf.T9i + 3.56734*tf.T913i + -13.1106*tf.T913
                  + 0.938357*tf.T9 + -0.0303484*tf.T953 + 4.04011*tf.lnT9)

    rate_eval.n_Mg39__Mg40 = rate

@numba.njit()
def p_Si36__P37(rate_eval, tf):
    # Si36 + p --> P37
    rate = 0.0

    # rath 
    rate += np.exp(  79.5185 + -3.64958*tf.T9i + 131.934*tf.T913i + -221.008*tf.T913
                  + 12.1313*tf.T9 + -0.679016*tf.T953 + 110.494*tf.lnT9)

    rate_eval.p_Si36__P37 = rate

@numba.njit()
def He4_Fe60__Ni64(rate_eval, tf):
    # Fe60 + He4 --> Ni64
    rate = 0.0

    # rath 
    rate += np.exp(  -1410.99 + 27.6568*tf.T9i + -2724.93*tf.T913i + 4305.01*tf.T913
                  + -245.036*tf.T9 + 13.5075*tf.T953 + -2073.35*tf.lnT9)

    rate_eval.He4_Fe60__Ni64 = rate

@numba.njit()
def He4_Ar48__Ca52(rate_eval, tf):
    # Ar48 + He4 --> Ca52
    rate = 0.0

    # rath 
    rate += np.exp(  -849.187 + 13.5349*tf.T9i + -1469.84*tf.T913i + 2413.43*tf.T913
                  + -144.549*tf.T9 + 8.29782*tf.T953 + -1131.31*tf.lnT9)

    rate_eval.He4_Ar48__Ca52 = rate

@numba.njit()
def p_S43__Cl44(rate_eval, tf):
    # S43 + p --> Cl44
    rate = 0.0

    # rath 
    rate += np.exp(  88.6632 + -4.32758*tf.T9i + 158.027*tf.T913i + -259.169*tf.T913
                  + 14.1899*tf.T9 + -0.790328*tf.T953 + 130.259*tf.lnT9)

    rate_eval.p_S43__Cl44 = rate

@numba.njit()
def Mg34__Al34__weak__wc17(rate_eval, tf):
    # Mg34 --> Al34
    rate = 0.0

    # wc17w
    rate += np.exp(  3.2308)

    rate_eval.Mg34__Al34__weak__wc17 = rate

@numba.njit()
def Ca48__Sc48__weak__mo03(rate_eval, tf):
    # Ca48 --> Sc48
    rate = 0.0

    # mo03w
    rate += np.exp(  -20.9981)

    rate_eval.Ca48__Sc48__weak__mo03 = rate

@numba.njit()
def p_V62__He4_Ti59(rate_eval, tf):
    # V62 + p --> He4 + Ti59
    rate = 0.0

    # rath 
    rate += np.exp(  124.618 + -6.57863*tf.T9i + 251.274*tf.T913i + -401.549*tf.T913
                  + 22.1056*tf.T9 + -1.19012*tf.T953 + 202.813*tf.lnT9)

    rate_eval.p_V62__He4_Ti59 = rate

@numba.njit()
def p_P47__He4_Si44(rate_eval, tf):
    # P47 + p --> He4 + Si44
    rate = 0.0

    # rath 
    rate += np.exp(  81.4894 + -4.3094*tf.T9i + 157.399*tf.T913i + -252.054*tf.T913
                  + 13.184*tf.T9 + -0.664069*tf.T953 + 128.208*tf.lnT9)

    rate_eval.p_P47__He4_Si44 = rate

@numba.njit()
def He4_Ca54__n_Ti57(rate_eval, tf):
    # Ca54 + He4 --> n + Ti57
    rate = 0.0

    # rath 
    rate += np.exp(  -954.504 + 15.3051*tf.T9i + -1661.82*tf.T913i + 2734.06*tf.T913
                  + -163.531*tf.T9 + 9.39369*tf.T953 + -1281.97*tf.lnT9)

    rate_eval.He4_Ca54__n_Ti57 = rate

@numba.njit()
def n_S48__S49(rate_eval, tf):
    # S48 + n --> S49
    rate = 0.0

    # rath 
    rate += np.exp(  62.2989 + -5.34374*tf.T9i + 165.072*tf.T913i + -236.382*tf.T913
                  + 13.7513*tf.T9 + -0.849775*tf.T953 + 120.45*tf.lnT9)

    rate_eval.n_S48__S49 = rate

@numba.njit()
def n_P43__P44(rate_eval, tf):
    # P43 + n --> P44
    rate = 0.0

    # rath 
    rate += np.exp(  157.006 + -14.361*tf.T9i + 432.273*tf.T913i + -614.303*tf.T913
                  + 34.3843*tf.T9 + -1.94823*tf.T953 + 310.785*tf.lnT9)

    rate_eval.n_P43__P44 = rate

@numba.njit()
def n_P25__p_Si25(rate_eval, tf):
    # P25 + n --> p + Si25
    rate = 0.0

    # ths8r
    rate += np.exp(  18.2873 + 2.40397*tf.T913
                  + -0.360164*tf.T9 + 0.0260578*tf.T953)

    rate_eval.n_P25__p_Si25 = rate

@numba.njit()
def Ar33__Cl33__weak__wc12(rate_eval, tf):
    # Ar33 --> Cl33
    rate = 0.0

    # wc12w
    rate += np.exp(  0.89856)

    rate_eval.Ar33__Cl33__weak__wc12 = rate

@numba.njit()
def p_Ar49__n_K49(rate_eval, tf):
    # Ar49 + p --> n + K49
    rate = 0.0

    # rath 
    rate += np.exp(  109.673 + -4.97759*tf.T9i + 183.988*tf.T913i + -298.561*tf.T913
                  + 16.2719*tf.T9 + -0.906214*tf.T953 + 150.298*tf.lnT9)

    rate_eval.p_Ar49__n_K49 = rate

@numba.njit()
def p_Cr44__Mn45(rate_eval, tf):
    # Cr44 + p --> Mn45
    rate = 0.0

    # ths8r
    rate += np.exp(  -16.0243 + -12.3249*tf.T9i + 17.9363*tf.T913
                  + -1.84483*tf.T9 + 0.126945*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Cr44__Mn45 = rate

@numba.njit()
def V50__Ti50__weak__mo03(rate_eval, tf):
    # V50 --> Ti50
    rate = 0.0

    # mo03w
    rate += np.exp(  -16.3221)

    rate_eval.V50__Ti50__weak__mo03 = rate

@numba.njit()
def p_Ti62__He4_Sc59(rate_eval, tf):
    # Ti62 + p --> He4 + Sc59
    rate = 0.0

    # rath 
    rate += np.exp(  34.4836 + -5.7277*tf.T9i + 173.667*tf.T913i + -238.794*tf.T913
                  + 10.7723*tf.T9 + -0.512302*tf.T953 + 140.405*tf.lnT9)

    rate_eval.p_Ti62__He4_Sc59 = rate

@numba.njit()
def Ca37__K37__weak__wc12(rate_eval, tf):
    # Ca37 --> K37
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.377624)

    rate_eval.Ca37__K37__weak__wc12 = rate

@numba.njit()
def O23__F23__weak__wc12(rate_eval, tf):
    # O23 --> F23
    rate = 0.0

    # wc12w
    rate += np.exp(  1.89396)

    rate_eval.O23__F23__weak__wc12 = rate

@numba.njit()
def He4_V42__Mn46(rate_eval, tf):
    # V42 + He4 --> Mn46
    rate = 0.0

    # ths8r
    rate += np.exp(  49.7673 + -84.014*tf.T913i + -1.21569*tf.T913
                  + -0.5402*tf.T9 + 0.0103754*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V42__Mn46 = rate

@numba.njit()
def p_Al22__Si23(rate_eval, tf):
    # Al22 + p --> Si23
    rate = 0.0

    # ths8r
    rate += np.exp(  36.8523 + -23.2019*tf.T913i + -11.249*tf.T913
                  + 0.342464*tf.T9 + 0.0654342*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Al22__Si23 = rate

@numba.njit()
def n_B10__He4_Li7(rate_eval, tf):
    # B10 + n --> He4 + Li7
    rate = 0.0

    # cf88n
    rate += np.exp(  20.0438)

    rate_eval.n_B10__He4_Li7 = rate

@numba.njit()
def Al26__Mg26__weak__wc12(rate_eval, tf):
    # Al26 --> Mg26
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.62175 + -2.64931*tf.T9i + -0.025978*tf.T913
                  + -0.0291284*tf.T9 + 0.00389774*tf.T953)

    rate_eval.Al26__Mg26__weak__wc12 = rate

@numba.njit()
def p_Ca55__Sc56(rate_eval, tf):
    # Ca55 + p --> Sc56
    rate = 0.0

    # rath 
    rate += np.exp(  112.607 + -5.61256*tf.T9i + 209.196*tf.T913i + -341.215*tf.T913
                  + 19.1038*tf.T9 + -1.09117*tf.T953 + 170.425*tf.lnT9)

    rate_eval.p_Ca55__Sc56 = rate

@numba.njit()
def n_Si27__C12_O16(rate_eval, tf):
    # Si27 + n --> C12 + O16
    rate = 0.0

    # cf88r
    rate += np.exp(  -131.755 + 3.44391*tf.T9i + -293.089*tf.T913i + 414.404*tf.T913
                  + -28.0562*tf.T9 + 1.61807*tf.T953 + -178.28*tf.lnT9)

    rate_eval.n_Si27__C12_O16 = rate

@numba.njit()
def n_Si28__Si29(rate_eval, tf):
    # Si28 + n --> Si29
    rate = 0.0

    # ka02r
    rate += np.exp(  6.9158 + -0.38*tf.T9i + 7.68863*tf.T913
                  + -1.7991*tf.T9 + -1.5*tf.lnT9)
    # ka02 
    rate += np.exp(  8.77553)

    rate_eval.n_Si28__Si29 = rate

@numba.njit()
def He4_Fe55__Ni59(rate_eval, tf):
    # Fe55 + He4 --> Ni59
    rate = 0.0

    # ths8r
    rate += np.exp(  60.7732 + -91.8012*tf.T913i + 4.12067*tf.T913
                  + -4.13271*tf.T9 + 0.450006*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe55__Ni59 = rate

@numba.njit()
def Mn71__n_Fe70__weak__mp17(rate_eval, tf):
    # Mn71 --> n + Fe70
    rate = 0.0

    # mp17w
    rate += np.exp(  3.06556)

    rate_eval.Mn71__n_Fe70__weak__mp17 = rate

@numba.njit()
def Cl45__Ar45__weak__wc12(rate_eval, tf):
    # Cl45 --> Ar45
    rate = 0.0

    # wc12w
    rate += np.exp(  0.243358)

    rate_eval.Cl45__Ar45__weak__wc12 = rate

@numba.njit()
def Al24__Mg24__weak__wc12(rate_eval, tf):
    # Al24 --> Mg24
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.08477)

    rate_eval.Al24__Mg24__weak__wc12 = rate

@numba.njit()
def p_Na30__Mg31(rate_eval, tf):
    # Na30 + p --> Mg31
    rate = 0.0

    # rath 
    rate += np.exp(  61.5752 + -2.83142*tf.T9i + 99.3459*tf.T913i + -166.269*tf.T913
                  + 8.84597*tf.T9 + -0.474488*tf.T953 + 84.0221*tf.lnT9)

    rate_eval.p_Na30__Mg31 = rate

@numba.njit()
def N18__n_O17__weak__wc12(rate_eval, tf):
    # N18 --> n + O17
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.54774)

    rate_eval.N18__n_O17__weak__wc12 = rate

@numba.njit()
def t_t__n_n_He4(rate_eval, tf):
    # t + t --> n + n + He4
    rate = 0.0

    # cf88r
    rate += np.exp(  21.2361 + -4.872*tf.T913i + -1.72398*tf.T913
                  + 0.684775*tf.T9 + -0.0702582*tf.T953 + 0.333333*tf.lnT9)
    # cf88n
    rate += np.exp(  21.2361 + -4.872*tf.T913i + -0.0328579*tf.T913
                  + -1.13588*tf.T9 + 0.250064*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.t_t__n_n_He4 = rate

@numba.njit()
def V67__n_n_Cr65__weak__mp17(rate_eval, tf):
    # V67 --> n + n + Cr65
    rate = 0.0

    # mp17w
    rate += np.exp(  1.51298)

    rate_eval.V67__n_n_Cr65__weak__mp17 = rate

@numba.njit()
def p_Cr59__He4_V56(rate_eval, tf):
    # Cr59 + p --> He4 + V56
    rate = 0.0

    # rath 
    rate += np.exp(  96.1676 + -6.52507*tf.T9i + 241.032*tf.T913i + -361.043*tf.T913
                  + 18.7085*tf.T9 + -1.00098*tf.T953 + 191.344*tf.lnT9)

    rate_eval.p_Cr59__He4_V56 = rate

@numba.njit()
def p_P35__He4_Si32(rate_eval, tf):
    # P35 + p --> He4 + Si32
    rate = 0.0

    # rath 
    rate += np.exp(  86.3787 + -3.75284*tf.T9i + 134.693*tf.T913i + -224.657*tf.T913
                  + 11.991*tf.T9 + -0.653211*tf.T953 + 113.109*tf.lnT9)

    rate_eval.p_P35__He4_Si32 = rate

@numba.njit()
def p_Ar48__K49(rate_eval, tf):
    # Ar48 + p --> K49
    rate = 0.0

    # rath 
    rate += np.exp(  97.9444 + -4.92522*tf.T9i + 181.334*tf.T913i + -294.283*tf.T913
                  + 16.0977*tf.T9 + -0.902749*tf.T953 + 148.236*tf.lnT9)

    rate_eval.p_Ar48__K49 = rate

@numba.njit()
def He6__Li6__weak__wc12(rate_eval, tf):
    # He6 --> Li6
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.144619)

    rate_eval.He6__Li6__weak__wc12 = rate

@numba.njit()
def p_Ne29__Na30(rate_eval, tf):
    # Ne29 + p --> Na30
    rate = 0.0

    # rath 
    rate += np.exp(  56.6854 + -2.61408*tf.T9i + 91.2933*tf.T913i + -153.072*tf.T913
                  + 8.19744*tf.T9 + -0.447933*tf.T953 + 77.3408*tf.lnT9)

    rate_eval.p_Ne29__Na30 = rate

@numba.njit()
def p_Ar53__K54(rate_eval, tf):
    # Ar53 + p --> K54
    rate = 0.0

    # rath 
    rate += np.exp(  96.5537 + -5.08525*tf.T9i + 184.746*tf.T913i + -297.314*tf.T913
                  + 16.2354*tf.T9 + -0.901588*tf.T953 + 149.82*tf.lnT9)

    rate_eval.p_Ar53__K54 = rate

@numba.njit()
def p_P34__He4_Si31(rate_eval, tf):
    # P34 + p --> He4 + Si31
    rate = 0.0

    # rath 
    rate += np.exp(  73.3465 + -3.69523*tf.T9i + 130.57*tf.T913i + -206.355*tf.T913
                  + 10.2448*tf.T9 + -0.535064*tf.T953 + 108.131*tf.lnT9)

    rate_eval.p_P34__He4_Si31 = rate

@numba.njit()
def n_Si41__Si42(rate_eval, tf):
    # Si41 + n --> Si42
    rate = 0.0

    # rath 
    rate += np.exp(  16.3642 + -0.0856671*tf.T9i + 7.04472*tf.T913i + -15.1446*tf.T913
                  + 1.38126*tf.T9 + -0.0977829*tf.T953 + 5.8474*tf.lnT9)

    rate_eval.n_Si41__Si42 = rate

@numba.njit()
def Ca61__Sc61__weak__mo03(rate_eval, tf):
    # Ca61 --> Sc61
    rate = 0.0

    # mo03w
    rate += np.exp(  -109.912)

    rate_eval.Ca61__Sc61__weak__mo03 = rate

@numba.njit()
def p_K39__He4_Ar36(rate_eval, tf):
    # K39 + p --> He4 + Ar36
    rate = 0.0

    # ths8r
    rate += np.exp(  20.5166 + -30.0732*tf.T913i + 7.03263*tf.T913
                  + -1.10085*tf.T9 + 0.133768*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_K39__He4_Ar36 = rate

@numba.njit()
def V40__Ti40__weak__bqa_pos_(rate_eval, tf):
    # V40 --> Ti40
    rate = 0.0

    # bqa+w
    rate += np.exp(  4.50002)

    rate_eval.V40__Ti40__weak__bqa_pos_ = rate

@numba.njit()
def Cl43__Ar43__weak__wc12(rate_eval, tf):
    # Cl43 --> Ar43
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.50755)

    rate_eval.Cl43__Ar43__weak__wc12 = rate

@numba.njit()
def Fe71__Co71__weak__wc17(rate_eval, tf):
    # Fe71 --> Co71
    rate = 0.0

    # wc17w
    rate += np.exp(  3.10368)

    rate_eval.Fe71__Co71__weak__wc17 = rate

@numba.njit()
def He3_Li7__n_p_He4_He4(rate_eval, tf):
    # Li7 + He3 --> n + p + He4 + He4
    rate = 0.0

    # mafon
    rate += np.exp(  30.038 + -4.24733e-12*tf.T9i + -17.989*tf.T913i + -1.57523e-09*tf.T913
                  + 1.45934e-10*tf.T9 + -1.15341e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He3_Li7__n_p_He4_He4 = rate

@numba.njit()
def P35__S35__weak__wc12(rate_eval, tf):
    # P35 --> S35
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.22302)

    rate_eval.P35__S35__weak__wc12 = rate

@numba.njit()
def n_K35__K36(rate_eval, tf):
    # K35 + n --> K36
    rate = 0.0

    # ths8r
    rate += np.exp(  8.92778 + 0.684453*tf.T913
                  + 0.0116013*tf.T9 + 0.00286458*tf.T953)

    rate_eval.n_K35__K36 = rate

@numba.njit()
def Fe45__p_p_V43__weak__wc12(rate_eval, tf):
    # Fe45 --> p + p + V43
    rate = 0.0

    # wc12w
    rate += np.exp(  3.35362)

    rate_eval.Fe45__p_p_V43__weak__wc12 = rate

@numba.njit()
def P46__S46__weak__mo03(rate_eval, tf):
    # P46 --> S46
    rate = 0.0

    # mo03w
    rate += np.exp(  -109.972)

    rate_eval.P46__S46__weak__mo03 = rate

@numba.njit()
def F18__O18__weak__wc12(rate_eval, tf):
    # F18 --> O18
    rate = 0.0

    # wc12w
    rate += np.exp(  -9.15982)

    rate_eval.F18__O18__weak__wc12 = rate

@numba.njit()
def n_K39__K40(rate_eval, tf):
    # K39 + n --> K40
    rate = 0.0

    # ks03 
    rate += np.exp(  17.6161 + 0.0316194*tf.T9i + -2.2227*tf.T913i + -1.88579*tf.T913
                  + 0.714904*tf.T9 + -0.0774902*tf.T953 + -0.859473*tf.lnT9)

    rate_eval.n_K39__K40 = rate

@numba.njit()
def Sc49__Ti49__weak__wc12(rate_eval, tf):
    # Sc49 --> Ti49
    rate = 0.0

    # wc12w
    rate += np.exp(  -8.50683)

    rate_eval.Sc49__Ti49__weak__wc12 = rate

@numba.njit()
def He4_P29__p_S32(rate_eval, tf):
    # P29 + He4 --> p + S32
    rate = 0.0

    # ths8r
    rate += np.exp(  50.2824 + -62.3802*tf.T913i + 0.459085*tf.T913
                  + -0.870169*tf.T9 + 0.0631143*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P29__p_S32 = rate

@numba.njit()
def p_Mn55__Fe56(rate_eval, tf):
    # Mn55 + p --> Fe56
    rate = 0.0

    # ths8r
    rate += np.exp(  36.1888 + -36.1995*tf.T913i + 1.15346*tf.T913
                  + -1.94437*tf.T9 + 0.218429*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Mn55__Fe56 = rate

@numba.njit()
def n_Al33__Al34(rate_eval, tf):
    # Al33 + n --> Al34
    rate = 0.0

    # rath 
    rate += np.exp(  13.6978 + -0.0547878*tf.T9i + 4.41006*tf.T913i + -10.276*tf.T913
                  + 0.890107*tf.T9 + -0.0583745*tf.T953 + 3.69726*tf.lnT9)

    rate_eval.n_Al33__Al34 = rate

@numba.njit()
def p_Ar49__K50(rate_eval, tf):
    # Ar49 + p --> K50
    rate = 0.0

    # rath 
    rate += np.exp(  102.965 + -5.01165*tf.T9i + 187.502*tf.T913i + -306.316*tf.T913
                  + 16.7677*tf.T9 + -0.931527*tf.T953 + 153.586*tf.lnT9)

    rate_eval.p_Ar49__K50 = rate

@numba.njit()
def p_Mn65__n_Fe65(rate_eval, tf):
    # Mn65 + p --> n + Fe65
    rate = 0.0

    # rath 
    rate += np.exp(  152.845 + -7.08196*tf.T9i + 270.275*tf.T913i + -437.153*tf.T913
                  + 24.0945*tf.T9 + -1.34275*tf.T953 + 218.264*tf.lnT9)

    rate_eval.p_Mn65__n_Fe65 = rate

@numba.njit()
def d_C14__n_N15(rate_eval, tf):
    # C14 + d --> n + N15
    rate = 0.0

    # bk92 
    rate += np.exp(  33.5637 + -16.939*tf.T913i + -4.14392*tf.T913
                  + 0.438623*tf.T9 + -0.0354193*tf.T953 + 0.333333*tf.lnT9)
    # bk92 
    rate += np.exp(  30.6841 + -16.939*tf.T913i + -0.582342*tf.T913
                  + -8.17066*tf.T9 + 1.70865*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.d_C14__n_N15 = rate

@numba.njit()
def He4_Ti58__Cr62(rate_eval, tf):
    # Ti58 + He4 --> Cr62
    rate = 0.0

    # rath 
    rate += np.exp(  -1013.17 + 21.0882*tf.T9i + -2098.5*tf.T913i + 3230.44*tf.T913
                  + -182.965*tf.T9 + 10.0743*tf.T953 + -1567.52*tf.lnT9)

    rate_eval.He4_Ti58__Cr62 = rate

@numba.njit()
def n_P29__p_Si29(rate_eval, tf):
    # P29 + n --> p + Si29
    rate = 0.0

    # ths8r
    rate += np.exp(  18.5351 + 1.48018*tf.T913
                  + -0.177129*tf.T9 + 0.0127163*tf.T953)

    rate_eval.n_P29__p_Si29 = rate

@numba.njit()
def p_N16__He4_C13(rate_eval, tf):
    # N16 + p --> He4 + C13
    rate = 0.0

    #  wagn
    rate += np.exp(  27.9675 + -4.18974e-12*tf.T9i + -15.27*tf.T913i + -2.03739e-09*tf.T913
                  + 2.22909e-10*tf.T9 + -2.02151e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_N16__He4_C13 = rate

@numba.njit()
def n_Na26__Na27(rate_eval, tf):
    # Na26 + n --> Na27
    rate = 0.0

    # rath 
    rate += np.exp(  14.9788 + -0.0305848*tf.T9i + 2.10701*tf.T913i + -6.01861*tf.T913
                  + 0.490595*tf.T9 + -0.0300421*tf.T953 + 1.71117*tf.lnT9)

    rate_eval.n_Na26__Na27 = rate

@numba.njit()
def n_K54__K55(rate_eval, tf):
    # K54 + n --> K55
    rate = 0.0

    # rath 
    rate += np.exp(  13.9484 + -0.00886369*tf.T9i + 0.892612*tf.T913i + -5.82373*tf.T913
                  + 0.557574*tf.T9 + -0.0520647*tf.T953 + 1.22698*tf.lnT9)

    rate_eval.n_K54__K55 = rate

@numba.njit()
def n_Ti63__Ti64(rate_eval, tf):
    # Ti63 + n --> Ti64
    rate = 0.0

    # rath 
    rate += np.exp(  1.72462 + 0.0321469*tf.T9i + -4.63134*tf.T913i + 10.2175*tf.T913
                  + 0.0802695*tf.T9 + -0.0909413*tf.T953 + -4.85435*tf.lnT9)

    rate_eval.n_Ti63__Ti64 = rate

@numba.njit()
def Be12__n_B11__weak__wc12(rate_eval, tf):
    # Be12 --> n + B11
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.13198)

    rate_eval.Be12__n_B11__weak__wc12 = rate

@numba.njit()
def p_Ca39__Sc40(rate_eval, tf):
    # Ca39 + p --> Sc40
    rate = 0.0

    # il10r
    rate += np.exp(  -6.57956 + -2.732*tf.T9i + -5.8648*tf.T913
                  + 8.4718*tf.T9 + -1.79344*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  16.5177 + -30.6064*tf.T913i + 7.64941*tf.T913
                  + -1.29835*tf.T9 + -1.0*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  -112.187 + -9.14242*tf.T9i + 57.3343*tf.T913i + 63.0638*tf.T913
                  + -6.14113*tf.T9 + 0.364866*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ca39__Sc40 = rate

@numba.njit()
def p_Na32__He4_Ne29(rate_eval, tf):
    # Na32 + p --> He4 + Ne29
    rate = 0.0

    # rath 
    rate += np.exp(  70.8342 + -2.94716*tf.T9i + 106.168*tf.T913i + -180.738*tf.T913
                  + 9.95631*tf.T9 + -0.538839*tf.T953 + 89.9177*tf.lnT9)

    rate_eval.p_Na32__He4_Ne29 = rate

@numba.njit()
def n_Cl50__Cl51(rate_eval, tf):
    # Cl50 + n --> Cl51
    rate = 0.0

    # rath 
    rate += np.exp(  15.8363 + -0.0313943*tf.T9i + 3.20451*tf.T913i + -11.1319*tf.T913
                  + 0.908524*tf.T9 + -0.0684158*tf.T953 + 3.40295*tf.lnT9)

    rate_eval.n_Cl50__Cl51 = rate

@numba.njit()
def Ti42__Sc42__weak__wc12(rate_eval, tf):
    # Ti42 --> Sc42
    rate = 0.0

    # wc12w
    rate += np.exp(  1.24794)

    rate_eval.Ti42__Sc42__weak__wc12 = rate

@numba.njit()
def p_Ti64__V65(rate_eval, tf):
    # Ti64 + p --> V65
    rate = 0.0

    # rath 
    rate += np.exp(  128.743 + -6.44846*tf.T9i + 244.886*tf.T913i + -395.472*tf.T913
                  + 21.9853*tf.T9 + -1.2484*tf.T953 + 197.574*tf.lnT9)

    rate_eval.p_Ti64__V65 = rate

@numba.njit()
def F31__n_Ne30__weak__mp17(rate_eval, tf):
    # F31 --> n + Ne30
    rate = 0.0

    # mp17w
    rate += np.exp(  4.67743)

    rate_eval.F31__n_Ne30__weak__mp17 = rate

@numba.njit()
def F26__n_Ne25__weak__wc12(rate_eval, tf):
    # F26 --> n + Ne25
    rate = 0.0

    # wc12w
    rate += np.exp(  2.06184)

    rate_eval.F26__n_Ne25__weak__wc12 = rate

@numba.njit()
def Ne29__n_Na28__weak__wc17(rate_eval, tf):
    # Ne29 --> n + Na28
    rate = 0.0

    # wc17w
    rate += np.exp(  2.57365)

    rate_eval.Ne29__n_Na28__weak__wc17 = rate

@numba.njit()
def He4_Cr52__Fe56(rate_eval, tf):
    # Cr52 + He4 --> Fe56
    rate = 0.0

    # ths8r
    rate += np.exp(  58.0146 + -86.9175*tf.T913i + 5.655*tf.T913
                  + -4.53625*tf.T9 + 0.479806*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr52__Fe56 = rate

@numba.njit()
def K48__Ca48__weak__wc12(rate_eval, tf):
    # K48 --> Ca48
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.2949)

    rate_eval.K48__Ca48__weak__wc12 = rate

@numba.njit()
def V63__Cr63__weak__wc12(rate_eval, tf):
    # V63 --> Cr63
    rate = 0.0

    # wc12w
    rate += np.exp(  3.15555)

    rate_eval.V63__Cr63__weak__wc12 = rate

@numba.njit()
def n_V52__V53(rate_eval, tf):
    # V52 + n --> V53
    rate = 0.0

    # rath 
    rate += np.exp(  19.3966 + -0.0585613*tf.T9i + 4.28927*tf.T913i + -10.0007*tf.T913
                  + 0.901745*tf.T9 + -0.0728569*tf.T953 + 3.39008*tf.lnT9)

    rate_eval.n_V52__V53 = rate

@numba.njit()
def He4_Al21__P25(rate_eval, tf):
    # Al21 + He4 --> P25
    rate = 0.0

    # ths8r
    rate += np.exp(  34.7794 + -55.8622*tf.T913i + 0.986345*tf.T913
                  + -0.712033*tf.T9 + 0.0435366*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al21__P25 = rate

@numba.njit()
def n_Be10__Be11(rate_eval, tf):
    # Be10 + n --> Be11
    rate = 0.0

    # wiesr
    rate += np.exp(  6.17132 + -0.000253955*tf.T9i + 0.0399864*tf.T913i + -0.173221*tf.T913
                  + 0.0229657*tf.T9 + -0.00202838*tf.T953 + 0.0511151*tf.lnT9)

    rate_eval.n_Be10__Be11 = rate

@numba.njit()
def n_Al29__Al30(rate_eval, tf):
    # Al29 + n --> Al30
    rate = 0.0

    # rath 
    rate += np.exp(  13.522 + -0.0313171*tf.T9i + 1.89136*tf.T913i + -4.12426*tf.T913
                  + 0.476396*tf.T9 + -0.0400788*tf.T953 + 1.24629*tf.lnT9)

    rate_eval.n_Al29__Al30 = rate

@numba.njit()
def Be7__Li7__weak__electron_capture(rate_eval, tf):
    # Be7 --> Li7
    rate = 0.0

    #   ecw
    rate += np.exp(  -23.8328 + 3.02033*tf.T913
                  + -0.0742132*tf.T9 + -0.00792386*tf.T953 + -0.650113*tf.lnT9)

    rate_eval.Be7__Li7__weak__electron_capture = rate

@numba.njit()
def Al38__Si38__weak__wc17(rate_eval, tf):
    # Al38 --> Si38
    rate = 0.0

    # wc17w
    rate += np.exp(  4.35057)

    rate_eval.Al38__Si38__weak__wc17 = rate

@numba.njit()
def n_Ar36__p_Cl36(rate_eval, tf):
    # Ar36 + n --> p + Cl36
    rate = 0.0

    # ths8r
    rate += np.exp(  -22.6757 + 34.7356*tf.T913
                  + -5.0791*tf.T9 + 0.381814*tf.T953)

    rate_eval.n_Ar36__p_Cl36 = rate

@numba.njit()
def n_Ar53__Ar54(rate_eval, tf):
    # Ar53 + n --> Ar54
    rate = 0.0

    # rath 
    rate += np.exp(  14.7286 + -0.0396349*tf.T9i + 3.89634*tf.T913i + -12.7103*tf.T913
                  + 1.35875*tf.T9 + -0.106822*tf.T953 + 3.98207*tf.lnT9)

    rate_eval.n_Ar53__Ar54 = rate

@numba.njit()
def Mg31__Al31__weak__wc12(rate_eval, tf):
    # Mg31 --> Al31
    rate = 0.0

    # wc12w
    rate += np.exp(  1.07736)

    rate_eval.Mg31__Al31__weak__wc12 = rate

@numba.njit()
def Ca60__n_n_Sc58__weak__mp17(rate_eval, tf):
    # Ca60 --> n + n + Sc58
    rate = 0.0

    # mp17w
    rate += np.exp(  1.9436)

    rate_eval.Ca60__n_n_Sc58__weak__mp17 = rate

@numba.njit()
def Ti40__p_Ca39__weak__wc12(rate_eval, tf):
    # Ti40 --> p + Ca39
    rate = 0.0

    # wc12w
    rate += np.exp(  2.55702)

    rate_eval.Ti40__p_Ca39__weak__wc12 = rate

@numba.njit()
def He4_Mg23__p_Al26(rate_eval, tf):
    # Mg23 + He4 --> p + Al26
    rate = 0.0

    # ths8r
    rate += np.exp(  46.215 + -53.203*tf.T913i + 0.71292*tf.T913
                  + -0.892548*tf.T9 + 0.0709813*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mg23__p_Al26 = rate

@numba.njit()
def He4_Ca34__p_Sc37(rate_eval, tf):
    # Ca34 + He4 --> p + Sc37
    rate = 0.0

    # ths8r
    rate += np.exp(  55.5931 + -76.0259*tf.T913i + -0.911844*tf.T913
                  + -0.405886*tf.T9 + 0.00643383*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca34__p_Sc37 = rate

@numba.njit()
def n_Ne22__Ne23(rate_eval, tf):
    # Ne22 + n --> Ne23
    rate = 0.0

    # ks03 
    rate += np.exp(  1.55374 + -0.0726658*tf.T9i + 4.92331*tf.T913i + 5.00204*tf.T913
                  + -1.71949*tf.T9 + 0.174168*tf.T953 + 2.02225*tf.lnT9)

    rate_eval.n_Ne22__Ne23 = rate

@numba.njit()
def He4_Sc61__V65(rate_eval, tf):
    # Sc61 + He4 --> V65
    rate = 0.0

    # rath 
    rate += np.exp(  -1009.58 + 20.9214*tf.T9i + -2081.73*tf.T913i + 3209.53*tf.T913
                  + -181.924*tf.T9 + 10.047*tf.T953 + -1556.73*tf.lnT9)

    rate_eval.He4_Sc61__V65 = rate

@numba.njit()
def V48__Ti48__weak__wc12(rate_eval, tf):
    # V48 --> Ti48
    rate = 0.0

    # wc12w
    rate += np.exp(  -14.5041)

    rate_eval.V48__Ti48__weak__wc12 = rate

@numba.njit()
def P34__S34__weak__wc12(rate_eval, tf):
    # P34 --> S34
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.88421)

    rate_eval.P34__S34__weak__wc12 = rate

@numba.njit()
def S29__P29__weak__wc12(rate_eval, tf):
    # S29 --> P29
    rate = 0.0

    # wc12w
    rate += np.exp(  0.675255)

    rate_eval.S29__P29__weak__wc12 = rate

@numba.njit()
def Ar43__K43__weak__wc12(rate_eval, tf):
    # Ar43 --> K43
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.14106)

    rate_eval.Ar43__K43__weak__wc12 = rate

@numba.njit()
def p_Cl49__n_Ar49(rate_eval, tf):
    # Cl49 + p --> n + Ar49
    rate = 0.0

    # rath 
    rate += np.exp(  108.521 + -4.8018*tf.T9i + 178.309*tf.T913i + -290.501*tf.T913
                  + 15.8156*tf.T9 + -0.877587*tf.T953 + 145.877*tf.lnT9)

    rate_eval.p_Cl49__n_Ar49 = rate

@numba.njit()
def p_Cl52__Ar53(rate_eval, tf):
    # Cl52 + p --> Ar53
    rate = 0.0

    # rath 
    rate += np.exp(  107.135 + -4.90092*tf.T9i + 182.718*tf.T913i + -306.188*tf.T913
                  + 17.5251*tf.T9 + -1.00679*tf.T953 + 150.59*tf.lnT9)

    rate_eval.p_Cl52__Ar53 = rate

@numba.njit()
def n_Sc36__Sc37(rate_eval, tf):
    # Sc36 + n --> Sc37
    rate = 0.0

    # ths8r
    rate += np.exp(  7.99403 + 1.91207*tf.T913
                  + -0.183511*tf.T9 + 0.0145845*tf.T953)

    rate_eval.n_Sc36__Sc37 = rate

@numba.njit()
def P46__n_n_S44__weak__mp17(rate_eval, tf):
    # P46 --> n + n + S44
    rate = 0.0

    # mp17w
    rate += np.exp(  4.50352)

    rate_eval.P46__n_n_S44__weak__mp17 = rate

@numba.njit()
def n_Ca35__Ca36(rate_eval, tf):
    # Ca35 + n --> Ca36
    rate = 0.0

    # ths8r
    rate += np.exp(  10.61 + -0.017717*tf.T913
                  + -0.0105587*tf.T9 + 0.00737899*tf.T953)

    rate_eval.n_Ca35__Ca36 = rate

@numba.njit()
def p_O25__F26(rate_eval, tf):
    # O25 + p --> F26
    rate = 0.0

    # rpsmr
    rate += np.exp(  48.6892 + -2.12107*tf.T9i + 74.2652*tf.T913i + -125.968*tf.T913
                  + 6.72292*tf.T9 + -0.365088*tf.T953 + 63.6156*tf.lnT9)

    rate_eval.p_O25__F26 = rate

@numba.njit()
def V41__Ti41__weak__bqa_pos_(rate_eval, tf):
    # V41 --> Ti41
    rate = 0.0

    # bqa+w
    rate += np.exp(  3.34666)

    rate_eval.V41__Ti41__weak__bqa_pos_ = rate

@numba.njit()
def He4_V44__Mn48(rate_eval, tf):
    # V44 + He4 --> Mn48
    rate = 0.0

    # ths8r
    rate += np.exp(  50.1421 + -84.1242*tf.T913i + -0.842623*tf.T913
                  + -0.963843*tf.T9 + 0.0981395*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V44__Mn48 = rate

@numba.njit()
def O23__n_F22__weak__wc12(rate_eval, tf):
    # O23 --> n + F22
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.692729)

    rate_eval.O23__n_F22__weak__wc12 = rate

@numba.njit()
def V64__n_Cr63__weak__mp17(rate_eval, tf):
    # V64 --> n + Cr63
    rate = 0.0

    # mp17w
    rate += np.exp(  2.39283)

    rate_eval.V64__n_Cr63__weak__mp17 = rate

@numba.njit()
def Ti53__V53__weak__wc12(rate_eval, tf):
    # Ti53 --> V53
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.85389)

    rate_eval.Ti53__V53__weak__wc12 = rate

@numba.njit()
def p_K54__He4_Ar51(rate_eval, tf):
    # K54 + p --> He4 + Ar51
    rate = 0.0

    # rath 
    rate += np.exp(  120.962 + -5.494*tf.T9i + 212.106*tf.T913i + -352.461*tf.T913
                  + 19.8121*tf.T9 + -1.08099*tf.T953 + 174.332*tf.lnT9)

    rate_eval.p_K54__He4_Ar51 = rate

@numba.njit()
def He4_Fe53__Ni57(rate_eval, tf):
    # Fe53 + He4 --> Ni57
    rate = 0.0

    # ths8r
    rate += np.exp(  69.0636 + -91.7231*tf.T913i + -10.1816*tf.T913
                  + -0.0406303*tf.T9 + 0.0345056*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe53__Ni57 = rate

@numba.njit()
def p_Sc59__n_Ti59(rate_eval, tf):
    # Sc59 + p --> n + Ti59
    rate = 0.0

    # rath 
    rate += np.exp(  127.603 + -6.00633*tf.T9i + 225.319*tf.T913i + -361.694*tf.T913
                  + 19.6879*tf.T9 + -1.09379*tf.T953 + 182.029*tf.lnT9)

    rate_eval.p_Sc59__n_Ti59 = rate

@numba.njit()
def p_Ca37__Sc38(rate_eval, tf):
    # Ca37 + p --> Sc38
    rate = 0.0

    # ths8r
    rate += np.exp(  -18.4754 + -10.557*tf.T9i + 19.6599*tf.T913
                  + -2.5569*tf.T9 + 0.213755*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Ca37__Sc38 = rate

@numba.njit()
def Cr56__Mn56__weak__wc12(rate_eval, tf):
    # Cr56 --> Mn56
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.24144)

    rate_eval.Cr56__Mn56__weak__wc12 = rate

@numba.njit()
def p_P37__n_S37(rate_eval, tf):
    # P37 + p --> n + S37
    rate = 0.0

    # rath 
    rate += np.exp(  93.0261 + -3.872*tf.T9i + 140.331*tf.T913i + -234.297*tf.T913
                  + 12.809*tf.T9 + -0.712919*tf.T953 + 117.259*tf.lnT9)

    rate_eval.p_P37__n_S37 = rate

@numba.njit()
def Fe72__Co72__weak__mo03(rate_eval, tf):
    # Fe72 --> Co72
    rate = 0.0

    # mo03w
    rate += np.exp(  1.75424)

    rate_eval.Fe72__Co72__weak__mo03 = rate

@numba.njit()
def He4_Al41__n_P44(rate_eval, tf):
    # Al41 + He4 --> n + P44
    rate = 0.0

    # rath 
    rate += np.exp(  -7.88719 + -3.13913*tf.T9i + -10.8654*tf.T913i + 18.3404*tf.T913
                  + -4.94187*tf.T9 + 0.406591*tf.T953 + 8.96793*tf.lnT9)

    rate_eval.He4_Al41__n_P44 = rate

@numba.njit()
def p_Mn61__He4_Cr58(rate_eval, tf):
    # Mn61 + p --> He4 + Cr58
    rate = 0.0

    # rath 
    rate += np.exp(  129.842 + -6.91179*tf.T9i + 263.596*tf.T913i + -417.977*tf.T913
                  + 22.5326*tf.T9 + -1.18821*tf.T953 + 212.41*tf.lnT9)

    rate_eval.p_Mn61__He4_Cr58 = rate

@numba.njit()
def He4_F19__Na23(rate_eval, tf):
    # F19 + He4 --> Na23
    rate = 0.0

    # rpsmr
    rate += np.exp(  52.7856 + -2.11408*tf.T9i + 39.7219*tf.T913i + -100.401*tf.T913
                  + 3.15808*tf.T9 + -0.0629822*tf.T953 + 54.4823*tf.lnT9)

    rate_eval.He4_F19__Na23 = rate

@numba.njit()
def He4_Si41__n_S44(rate_eval, tf):
    # Si41 + He4 --> n + S44
    rate = 0.0

    # rath 
    rate += np.exp(  -10.2965 + -3.28994*tf.T9i + -12.1245*tf.T913i + 20.4395*tf.T913
                  + -5.16986*tf.T9 + 0.419168*tf.T953 + 8.87672*tf.lnT9)

    rate_eval.He4_Si41__n_S44 = rate

@numba.njit()
def p_P43__S44(rate_eval, tf):
    # P43 + p --> S44
    rate = 0.0

    # rath 
    rate += np.exp(  83.4876 + -4.14027*tf.T9i + 150.724*tf.T913i + -245.794*tf.T913
                  + 13.2908*tf.T9 + -0.731658*tf.T953 + 123.991*tf.lnT9)

    rate_eval.p_P43__S44 = rate

@numba.njit()
def p_Ti45__V46(rate_eval, tf):
    # Ti45 + p --> V46
    rate = 0.0

    # ths8r
    rate += np.exp(  37.4468 + -33.1981*tf.T913i + -1.66837*tf.T913
                  + -2.50285*tf.T9 + 0.349152*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ti45__V46 = rate

@numba.njit()
def Fe47__Mn47__weak__wc12(rate_eval, tf):
    # Fe47 --> Mn47
    rate = 0.0

    # wc12w
    rate += np.exp(  1.30059)

    rate_eval.Fe47__Mn47__weak__wc12 = rate

@numba.njit()
def P28__Si28__weak__wc12(rate_eval, tf):
    # P28 --> Si28
    rate = 0.0

    # wc12w
    rate += np.exp(  0.942799)

    rate_eval.P28__Si28__weak__wc12 = rate

@numba.njit()
def Cr51__V51__weak__wc12(rate_eval, tf):
    # Cr51 --> V51
    rate = 0.0

    # wc12w
    rate += np.exp(  -15.0533)

    rate_eval.Cr51__V51__weak__wc12 = rate

@numba.njit()
def Fe55__Mn55__weak__wc12(rate_eval, tf):
    # Fe55 --> Mn55
    rate = 0.0

    # wc12w
    rate += np.exp(  -18.6433)

    rate_eval.Fe55__Mn55__weak__wc12 = rate

@numba.njit()
def p_Cl47__He4_S44(rate_eval, tf):
    # Cl47 + p --> He4 + S44
    rate = 0.0

    # rath 
    rate += np.exp(  104.254 + -4.75917*tf.T9i + 179.728*tf.T913i + -299.534*tf.T913
                  + 16.7332*tf.T9 + -0.897714*tf.T953 + 148.495*tf.lnT9)

    rate_eval.p_Cl47__He4_S44 = rate

@numba.njit()
def n_Cl36__Cl37(rate_eval, tf):
    # Cl36 + n --> Cl37
    rate = 0.0

    # ks03 
    rate += np.exp(  14.7404 + -0.00175231*tf.T9i + -0.17256*tf.T913i + -0.577904*tf.T913
                  + 0.229273*tf.T9 + -0.0412624*tf.T953 + -0.214457*tf.lnT9)

    rate_eval.n_Cl36__Cl37 = rate

@numba.njit()
def C19__n_N18__weak__wc12(rate_eval, tf):
    # C19 --> n + N18
    rate = 0.0

    # wc12w
    rate += np.exp(  2.15513)

    rate_eval.C19__n_N18__weak__wc12 = rate

@numba.njit()
def He4_Ti65__Cr69(rate_eval, tf):
    # Ti65 + He4 --> Cr69
    rate = 0.0

    # rath 
    rate += np.exp(  -1078.3 + 22.3257*tf.T9i + -2218.77*tf.T913i + 3424.3*tf.T913
                  + -194.015*tf.T9 + 10.7092*tf.T953 + -1661.13*tf.lnT9)

    rate_eval.He4_Ti65__Cr69 = rate

@numba.njit()
def Ca52__Sc52__weak__wc12(rate_eval, tf):
    # Ca52 --> Sc52
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.91277)

    rate_eval.Ca52__Sc52__weak__wc12 = rate

@numba.njit()
def p_Al27__Si28(rate_eval, tf):
    # Al27 + p --> Si28
    rate = 0.0

    # il10r
    rate += np.exp(  -13.6664 + -1.90396*tf.T9i + 23.8634*tf.T913
                  + -3.70135*tf.T9 + 0.28964*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  86.0234 + -0.387313*tf.T9i + -26.8327*tf.T913i + -116.137*tf.T913
                  + 0.00950567*tf.T9 + 0.00999755*tf.T953 + -1.5*tf.lnT9)
    # il10n
    rate += np.exp(  21.1065 + -23.2205*tf.T913i
                  + -2.0*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Al27__Si28 = rate

@numba.njit()
def He4_V62__Mn66(rate_eval, tf):
    # V62 + He4 --> Mn66
    rate = 0.0

    # rath 
    rate += np.exp(  -1081.15 + 22.4962*tf.T9i + -2235.73*tf.T913i + 3443.99*tf.T913
                  + -194.98*tf.T9 + 10.7603*tf.T953 + -1671.76*tf.lnT9)

    rate_eval.He4_V62__Mn66 = rate

@numba.njit()
def Si43__P43__weak__mo03(rate_eval, tf):
    # Si43 --> P43
    rate = 0.0

    # mo03w
    rate += np.exp(  2.76466)

    rate_eval.Si43__P43__weak__mo03 = rate

@numba.njit()
def n_Na22__He4_F19(rate_eval, tf):
    # Na22 + n --> He4 + F19
    rate = 0.0

    # cf88 
    rate += np.exp(  6.59038 + 6.22036*tf.T913
                  + -0.0209891*tf.T9 + -0.0689843*tf.T953 + 1.0*tf.lnT9)
    # cf88n
    rate += np.exp(  15.0061 + -0.0532251*tf.T913
                  + 1.00044*tf.T9 + -0.13238*tf.T953)

    rate_eval.n_Na22__He4_F19 = rate

@numba.njit()
def Ne34__n_Na33__weak__mp17(rate_eval, tf):
    # Ne34 --> n + Na33
    rate = 0.0

    # mp17w
    rate += np.exp(  4.80429)

    rate_eval.Ne34__n_Na33__weak__mp17 = rate

@numba.njit()
def Sc52__Ti52__weak__wc12(rate_eval, tf):
    # Sc52 --> Ti52
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.47065)

    rate_eval.Sc52__Ti52__weak__wc12 = rate

@numba.njit()
def P45__n_S44__weak__mp17(rate_eval, tf):
    # P45 --> n + S44
    rate = 0.0

    # mp17w
    rate += np.exp(  3.55)

    rate_eval.P45__n_S44__weak__mp17 = rate

@numba.njit()
def He4_V40__Mn44(rate_eval, tf):
    # V40 + He4 --> Mn44
    rate = 0.0

    # ths8r
    rate += np.exp(  48.0646 + -83.8937*tf.T913i + -0.548514*tf.T913
                  + -0.638906*tf.T9 + 0.0171963*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V40__Mn44 = rate

@numba.njit()
def Ar51__K51__weak__mo03(rate_eval, tf):
    # Ar51 --> K51
    rate = 0.0

    # mo03w
    rate += np.exp(  3.06278)

    rate_eval.Ar51__K51__weak__mo03 = rate

@numba.njit()
def B19__n_C18__weak__wc17(rate_eval, tf):
    # B19 --> n + C18
    rate = 0.0

    # wc17w
    rate += np.exp(  5.14115)

    rate_eval.B19__n_C18__weak__wc17 = rate

@numba.njit()
def p_Ti56__n_V56(rate_eval, tf):
    # Ti56 + p --> n + V56
    rate = 0.0

    # rath 
    rate += np.exp(  126.406 + -6.03852*tf.T9i + 224.799*tf.T913i + -361.067*tf.T913
                  + 19.7624*tf.T9 + -1.10877*tf.T953 + 182.0*tf.lnT9)

    rate_eval.p_Ti56__n_V56 = rate

@numba.njit()
def B15__n_C14__weak__wc12(rate_eval, tf):
    # B15 --> n + C14
    rate = 0.0

    # wc12w
    rate += np.exp(  4.17526)

    rate_eval.B15__n_C14__weak__wc12 = rate

@numba.njit()
def He4_Ar51__n_Ca54(rate_eval, tf):
    # Ar51 + He4 --> n + Ca54
    rate = 0.0

    # rath 
    rate += np.exp(  -406.48 + 2.11543*tf.T9i + -572.596*tf.T913i + 1023.57*tf.T913
                  + -67.6302*tf.T9 + 4.12043*tf.T953 + -448.524*tf.lnT9)

    rate_eval.He4_Ar51__n_Ca54 = rate

@numba.njit()
def n_S39__S40(rate_eval, tf):
    # S39 + n --> S40
    rate = 0.0

    # rath 
    rate += np.exp(  11.2871 + -0.00891711*tf.T9i + -0.173344*tf.T913i + 0.973676*tf.T913
                  + 0.0385544*tf.T9 + -0.0217221*tf.T953 + -0.641922*tf.lnT9)

    rate_eval.n_S39__S40 = rate

@numba.njit()
def K40__Ar40__weak__wc12(rate_eval, tf):
    # K40 --> Ar40
    rate = 0.0

    # wc12w
    rate += np.exp(  -40.8121)

    rate_eval.K40__Ar40__weak__wc12 = rate

@numba.njit()
def He4_K54__Sc58(rate_eval, tf):
    # K54 + He4 --> Sc58
    rate = 0.0

    # rath 
    rate += np.exp(  -936.175 + 14.8052*tf.T9i + -1608.5*tf.T913i + 2649.45*tf.T913
                  + -158.607*tf.T9 + 9.10779*tf.T953 + -1241.76*tf.lnT9)

    rate_eval.He4_K54__Sc58 = rate

@numba.njit()
def He4_Sc53__V57(rate_eval, tf):
    # Sc53 + He4 --> V57
    rate = 0.0

    # rath 
    rate += np.exp(  -981.27 + 15.6178*tf.T9i + -1697.1*tf.T913i + 2787.5*tf.T913
                  + -166.516*tf.T9 + 9.53982*tf.T953 + -1308.01*tf.lnT9)

    rate_eval.He4_Sc53__V57 = rate

@numba.njit()
def He4_Si27__S31(rate_eval, tf):
    # Si27 + He4 --> S31
    rate = 0.0

    # ths8r
    rate += np.exp(  45.1874 + -59.3989*tf.T913i + -2.288*tf.T913
                  + -0.914054*tf.T9 + 0.0959821*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si27__S31 = rate

@numba.njit()
def F30__Ne30__weak__mo03(rate_eval, tf):
    # F30 --> Ne30
    rate = 0.0

    # mo03w
    rate += np.exp(  -109.219)

    rate_eval.F30__Ne30__weak__mo03 = rate

@numba.njit()
def p_Na29__Mg30(rate_eval, tf):
    # Na29 + p --> Mg30
    rate = 0.0

    # rath 
    rate += np.exp(  60.2412 + -2.78503*tf.T9i + 97.0846*tf.T913i + -162.772*tf.T913
                  + 8.68252*tf.T9 + -0.475692*tf.T953 + 82.2333*tf.lnT9)

    rate_eval.p_Na29__Mg30 = rate

@numba.njit()
def Be15__n_Be14(rate_eval, tf):
    # Be15 --> n + Be14
    rate = 0.0

    # wc12s
    rate += np.exp(  15.0584)

    rate_eval.Be15__n_Be14 = rate

@numba.njit()
def Ne30__Na30__weak__wc17(rate_eval, tf):
    # Ne30 --> Na30
    rate = 0.0

    # wc17w
    rate += np.exp(  4.41411)

    rate_eval.Ne30__Na30__weak__wc17 = rate

@numba.njit()
def Be14__n_B13__weak__wc17(rate_eval, tf):
    # Be14 --> n + B13
    rate = 0.0

    # wc17w
    rate += np.exp(  4.86034)

    rate_eval.Be14__n_B13__weak__wc17 = rate

@numba.njit()
def n_Mn56__He4_V53(rate_eval, tf):
    # Mn56 + n --> He4 + V53
    rate = 0.0

    # rath 
    rate += np.exp(  182.721 + -4.15286*tf.T9i + 341.11*tf.T913i + -565.103*tf.T913
                  + 29.3652*tf.T9 + -1.59083*tf.T953 + 291.219*tf.lnT9)

    rate_eval.n_Mn56__He4_V53 = rate

@numba.njit()
def Li11__n_Be10__weak__wc17(rate_eval, tf):
    # Li11 --> n + Be10
    rate = 0.0

    # wc17w
    rate += np.exp(  4.18586)

    rate_eval.Li11__n_Be10__weak__wc17 = rate

@numba.njit()
def Al22__He4_Ne18__weak__wc12(rate_eval, tf):
    # Al22 --> He4 + Ne18
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.79476)

    rate_eval.Al22__He4_Ne18__weak__wc12 = rate

@numba.njit()
def Ti37__Sc37__weak__bqa_pos_(rate_eval, tf):
    # Ti37 --> Sc37
    rate = 0.0

    # bqa+w
    rate += np.exp(  4.58115)

    rate_eval.Ti37__Sc37__weak__bqa_pos_ = rate

@numba.njit()
def K33__Ar33__weak__bqa_pos_(rate_eval, tf):
    # K33 --> Ar33
    rate = 0.0

    # bqa+w
    rate += np.exp(  2.81555)

    rate_eval.K33__Ar33__weak__bqa_pos_ = rate

@numba.njit()
def Cr64__Mn64__weak__wc12(rate_eval, tf):
    # Cr64 --> Mn64
    rate = 0.0

    # wc12w
    rate += np.exp(  2.80357)

    rate_eval.Cr64__Mn64__weak__wc12 = rate

@numba.njit()
def p_Ti59__He4_Sc56(rate_eval, tf):
    # Ti59 + p --> He4 + Sc56
    rate = 0.0

    # rath 
    rate += np.exp(  82.1989 + -6.20778*tf.T9i + 232.909*tf.T913i + -343.475*tf.T913
                  + 17.9002*tf.T9 + -0.979591*tf.T953 + 184.752*tf.lnT9)

    rate_eval.p_Ti59__He4_Sc56 = rate

@numba.njit()
def n_Ar37__Ar38(rate_eval, tf):
    # Ar37 + n --> Ar38
    rate = 0.0

    # ths8r
    rate += np.exp(  14.7933 + -0.825362*tf.T913
                  + 0.336634*tf.T9 + -0.0509617*tf.T953)

    rate_eval.n_Ar37__Ar38 = rate

@numba.njit()
def He4_F29__Na33(rate_eval, tf):
    # F29 + He4 --> Na33
    rate = 0.0

    # rpsmr
    rate += np.exp(  54.3661 + -2.62527*tf.T9i + 54.1099*tf.T913i + -122.974*tf.T913
                  + 5.48374*tf.T9 + -0.263998*tf.T953 + 65.0224*tf.lnT9)

    rate_eval.He4_F29__Na33 = rate

@numba.njit()
def N17__O17__weak__wc12(rate_eval, tf):
    # N17 --> O17
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.81036)

    rate_eval.N17__O17__weak__wc12 = rate

@numba.njit()
def Fe63__Co63__weak__wc12(rate_eval, tf):
    # Fe63 --> Co63
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.1748)

    rate_eval.Fe63__Co63__weak__wc12 = rate

@numba.njit()
def Si27__Al27__weak__wc12(rate_eval, tf):
    # Si27 --> Al27
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.78962)

    rate_eval.Si27__Al27__weak__wc12 = rate

@numba.njit()
def B8__He4_He4__weak__wc12(rate_eval, tf):
    # B8 --> He4 + He4
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.105148)

    rate_eval.B8__He4_He4__weak__wc12 = rate

@numba.njit()
def He4_Cr50__Fe54(rate_eval, tf):
    # Cr50 + He4 --> Fe54
    rate = 0.0

    # ths8r
    rate += np.exp(  59.7193 + -86.8349*tf.T913i + 2.37343*tf.T913
                  + -3.65677*tf.T9 + 0.412128*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Cr50__Fe54 = rate

@numba.njit()
def Fe68__Co68__weak__wc12(rate_eval, tf):
    # Fe68 --> Co68
    rate = 0.0

    # wc12w
    rate += np.exp(  1.34829)

    rate_eval.Fe68__Co68__weak__wc12 = rate

@numba.njit()
def n_Al22__Al23(rate_eval, tf):
    # Al22 + n --> Al23
    rate = 0.0

    # ths8r
    rate += np.exp(  6.77097 + 3.22221*tf.T913
                  + -0.512308*tf.T9 + 0.0424663*tf.T953)

    rate_eval.n_Al22__Al23 = rate

@numba.njit()
def n_V57__V58(rate_eval, tf):
    # V57 + n --> V58
    rate = 0.0

    # rath 
    rate += np.exp(  18.2095 + -0.0259892*tf.T9i + 2.77722*tf.T913i + -9.7122*tf.T913
                  + 0.915793*tf.T9 + -0.097007*tf.T953 + 2.99876*tf.lnT9)

    rate_eval.n_V57__V58 = rate

@numba.njit()
def He4_Ar38__Ca42(rate_eval, tf):
    # Ar38 + He4 --> Ca42
    rate = 0.0

    # ths8r
    rate += np.exp(  52.6394 + -71.1296*tf.T913i + 2.75299*tf.T913
                  + -2.43406*tf.T9 + 0.199511*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar38__Ca42 = rate

@numba.njit()
def Fe64__Co64__weak__wc12(rate_eval, tf):
    # Fe64 --> Co64
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.05966)

    rate_eval.Fe64__Co64__weak__wc12 = rate

@numba.njit()
def He4_Al23__P27(rate_eval, tf):
    # Al23 + He4 --> P27
    rate = 0.0

    # ths8r
    rate += np.exp(  36.3761 + -56.1207*tf.T913i + 0.958833*tf.T913
                  + -0.777348*tf.T9 + 0.0516482*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al23__P27 = rate

@numba.njit()
def He4_F22__n_Na25(rate_eval, tf):
    # F22 + He4 --> n + Na25
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.3149 + -2.15745*tf.T9i + 34.9592*tf.T913i + -96.2142*tf.T913
                  + 4.07004*tf.T9 + -0.188338*tf.T953 + 51.2829*tf.lnT9)

    rate_eval.He4_F22__n_Na25 = rate

@numba.njit()
def Cr62__Mn62__weak__wc12(rate_eval, tf):
    # Cr62 --> Mn62
    rate = 0.0

    # wc12w
    rate += np.exp(  1.21337)

    rate_eval.Cr62__Mn62__weak__wc12 = rate

@numba.njit()
def n_Al21__p_Mg21(rate_eval, tf):
    # Al21 + n --> p + Mg21
    rate = 0.0

    # rath 
    rate += np.exp(  20.3212 + 0.0457653*tf.T9i + -0.640193*tf.T913i + -1.55275*tf.T913
                  + 0.123721*tf.T9 + -0.00447852*tf.T953 + 0.593339*tf.lnT9)

    rate_eval.n_Al21__p_Mg21 = rate

@numba.njit()
def p_K50__Ca51(rate_eval, tf):
    # K50 + p --> Ca51
    rate = 0.0

    # rath 
    rate += np.exp(  112.194 + -5.24908*tf.T9i + 197.78*tf.T913i + -327.253*tf.T913
                  + 18.3019*tf.T9 + -1.0354*tf.T953 + 162.637*tf.lnT9)

    rate_eval.p_K50__Ca51 = rate

@numba.njit()
def Sc58__Ti58__weak__wc17(rate_eval, tf):
    # Sc58 --> Ti58
    rate = 0.0

    # wc17w
    rate += np.exp(  3.87001)

    rate_eval.Sc58__Ti58__weak__wc17 = rate

@numba.njit()
def O26__n_n_n_F23__weak__mo03(rate_eval, tf):
    # O26 --> 3 n + F23
    rate = 0.0

    # mo03w
    rate += np.exp(  -0.150487)

    rate_eval.O26__n_n_n_F23__weak__mo03 = rate

@numba.njit()
def Si36__n_P35__weak__wc12(rate_eval, tf):
    # Si36 --> n + P35
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.87059)

    rate_eval.Si36__n_P35__weak__wc12 = rate

@numba.njit()
def He4_Mg24__Si28(rate_eval, tf):
    # Mg24 + He4 --> Si28
    rate = 0.0

    # st08r
    rate += np.exp(  8.03977 + -15.629*tf.T9i
                  + -1.5*tf.lnT9)
    # st08r
    rate += np.exp(  -50.5494 + -12.8332*tf.T9i + 21.3721*tf.T913i + 37.7649*tf.T913
                  + -4.10635*tf.T9 + 0.249618*tf.T953 + -1.5*tf.lnT9)

    rate_eval.He4_Mg24__Si28 = rate

@numba.njit()
def He4_Si34__n_S37(rate_eval, tf):
    # Si34 + He4 --> n + S37
    rate = 0.0

    # rath 
    rate += np.exp(  -7.96464 + -2.90658*tf.T9i + -20.2824*tf.T913i + 24.7693*tf.T913
                  + -4.96759*tf.T9 + 0.389004*tf.T953 + 4.95303*tf.lnT9)

    rate_eval.He4_Si34__n_S37 = rate

@numba.njit()
def Ti59__V59__weak__wc12(rate_eval, tf):
    # Ti59 --> V59
    rate = 0.0

    # wc12w
    rate += np.exp(  3.22706)

    rate_eval.Ti59__V59__weak__wc12 = rate

@numba.njit()
def C11__B11__weak__wc12(rate_eval, tf):
    # C11 --> B11
    rate = 0.0

    # wc12w
    rate += np.exp(  -7.47312)

    rate_eval.C11__B11__weak__wc12 = rate

@numba.njit()
def p_Si34__n_P34(rate_eval, tf):
    # Si34 + p --> n + P34
    rate = 0.0

    # rath 
    rate += np.exp(  84.998 + -3.55365*tf.T9i + 127.331*tf.T913i + -211.365*tf.T913
                  + 11.3268*tf.T9 + -0.62125*tf.T953 + 106.614*tf.lnT9)

    rate_eval.p_Si34__n_P34 = rate

@numba.njit()
def He4_Ne33__Mg37(rate_eval, tf):
    # Ne33 + He4 --> Mg37
    rate = 0.0

    # rath 
    rate += np.exp(  63.1589 + -3.09356*tf.T9i + 70.708*tf.T913i + -151.061*tf.T913
                  + 6.94368*tf.T9 + -0.343296*tf.T953 + 79.2283*tf.lnT9)

    rate_eval.He4_Ne33__Mg37 = rate

@numba.njit()
def Fe46__Mn46__weak__wc12(rate_eval, tf):
    # Fe46 --> Mn46
    rate = 0.0

    # wc12w
    rate += np.exp(  2.42983)

    rate_eval.Fe46__Mn46__weak__wc12 = rate

@numba.njit()
def n_Na29__Na30(rate_eval, tf):
    # Na29 + n --> Na30
    rate = 0.0

    # rath 
    rate += np.exp(  11.6606 + -0.0415731*tf.T9i + 3.19324*tf.T913i + -7.933*tf.T913
                  + 0.750695*tf.T9 + -0.0475852*tf.T953 + 2.6517*tf.lnT9)

    rate_eval.n_Na29__Na30 = rate

@numba.njit()
def Cr65__n_Mn64__weak__mp17(rate_eval, tf):
    # Cr65 --> n + Mn64
    rate = 0.0

    # mp17w
    rate += np.exp(  0.549778)

    rate_eval.Cr65__n_Mn64__weak__mp17 = rate

@numba.njit()
def p_O19__n_F19(rate_eval, tf):
    # O19 + p --> n + F19
    rate = 0.0

    #  wagn
    rate += np.exp(  28.9687 + -16.75*tf.T913i + 1.31666e-09*tf.T913
                  + -1.43045e-10*tf.T9 + 1.29148e-11*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_O19__n_F19 = rate

@numba.njit()
def F21__Ne21__weak__wc12(rate_eval, tf):
    # F21 --> Ne21
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.79203)

    rate_eval.F21__Ne21__weak__wc12 = rate

@numba.njit()
def Mn65__Fe65__weak__wc17(rate_eval, tf):
    # Mn65 --> Fe65
    rate = 0.0

    # wc17w
    rate += np.exp(  2.05913)

    rate_eval.Mn65__Fe65__weak__wc17 = rate

@numba.njit()
def Mn63__Fe63__weak__wc12(rate_eval, tf):
    # Mn63 --> Fe63
    rate = 0.0

    # wc12w
    rate += np.exp(  0.924471)

    rate_eval.Mn63__Fe63__weak__wc12 = rate

@numba.njit()
def Mn59__Fe59__weak__wc12(rate_eval, tf):
    # Mn59 --> Fe59
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.89039)

    rate_eval.Mn59__Fe59__weak__wc12 = rate

@numba.njit()
def He4_Ca57__Ti61(rate_eval, tf):
    # Ca57 + He4 --> Ti61
    rate = 0.0

    # rath 
    rate += np.exp(  -993.557 + 15.6739*tf.T9i + -1702.8*tf.T913i + 2807.38*tf.T913
                  + -167.977*tf.T9 + 9.63883*tf.T953 + -1315.69*tf.lnT9)

    rate_eval.He4_Ca57__Ti61 = rate

@numba.njit()
def Mn56__Fe56__weak__wc12(rate_eval, tf):
    # Mn56 --> Fe56
    rate = 0.0

    # wc12w
    rate += np.exp(  -9.50213)

    rate_eval.Mn56__Fe56__weak__wc12 = rate

@numba.njit()
def p_Mg25__Al26(rate_eval, tf):
    # Mg25 + p --> Al26
    rate = 0.0

    # il10r
    rate += np.exp(  4.21826 + -0.71983*tf.T9i + -88.9297*tf.T913
                  + 302.948*tf.T9 + -346.461*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -37.1963 + -0.429366*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  2.22778 + -3.22353*tf.T9i + 8.46334*tf.T913
                  + -0.907024*tf.T9 + 0.0642981*tf.T953 + -1.5*tf.lnT9)

    rate_eval.p_Mg25__Al26 = rate

@numba.njit()
def B17__n_C16__weak__wc17(rate_eval, tf):
    # B17 --> n + C16
    rate = 0.0

    # wc17w
    rate += np.exp(  4.4539)

    rate_eval.B17__n_C16__weak__wc17 = rate

@numba.njit()
def Mn50__Cr50__weak__wc12(rate_eval, tf):
    # Mn50 --> Cr50
    rate = 0.0

    # wc12w
    rate += np.exp(  0.895796)

    rate_eval.Mn50__Cr50__weak__wc12 = rate

@numba.njit()
def n_Cr67__Cr68(rate_eval, tf):
    # Cr67 + n --> Cr68
    rate = 0.0

    # rath 
    rate += np.exp(  5.29466 + 0.0475389*tf.T9i + -5.40685*tf.T913i + 10.4626*tf.T913
                  + -0.242255*tf.T9 + -0.0623331*tf.T953 + -5.10527*tf.lnT9)

    rate_eval.n_Cr67__Cr68 = rate

@numba.njit()
def Cr66__Mn66__weak__wc17(rate_eval, tf):
    # Cr66 --> Mn66
    rate = 0.0

    # wc17w
    rate += np.exp(  3.32237)

    rate_eval.Cr66__Mn66__weak__wc17 = rate

@numba.njit()
def P41__S41__weak__wc12(rate_eval, tf):
    # P41 --> S41
    rate = 0.0

    # wc12w
    rate += np.exp(  1.5794)

    rate_eval.P41__S41__weak__wc12 = rate

@numba.njit()
def Mn47__Cr47__weak__wc17(rate_eval, tf):
    # Mn47 --> Cr47
    rate = 0.0

    # wc17w
    rate += np.exp(  2.06391)

    rate_eval.Mn47__Cr47__weak__wc17 = rate

@numba.njit()
def Mn46__Cr46__weak__wc12(rate_eval, tf):
    # Mn46 --> Cr46
    rate = 0.0

    # wc12w
    rate += np.exp(  2.10821)

    rate_eval.Mn46__Cr46__weak__wc12 = rate

@numba.njit()
def Ar42__K42__weak__wc12(rate_eval, tf):
    # Ar42 --> K42
    rate = 0.0

    # wc12w
    rate += np.exp(  -21.129)

    rate_eval.Ar42__K42__weak__wc12 = rate

@numba.njit()
def He4_Ar48__n_Ca51(rate_eval, tf):
    # Ar48 + He4 --> n + Ca51
    rate = 0.0

    # rath 
    rate += np.exp(  -397.555 + 2.08384*tf.T9i + -559.718*tf.T913i + 999.918*tf.T913
                  + -66.2243*tf.T9 + 4.03997*tf.T953 + -437.439*tf.lnT9)

    rate_eval.He4_Ar48__n_Ca51 = rate

@numba.njit()
def Na30__Mg30__weak__wc12(rate_eval, tf):
    # Na30 --> Mg30
    rate = 0.0

    # wc12w
    rate += np.exp(  2.2968)

    rate_eval.Na30__Mg30__weak__wc12 = rate

@numba.njit()
def n_F14__p_O14(rate_eval, tf):
    # F14 + n --> p + O14
    rate = 0.0

    # rpsmr
    rate += np.exp(  18.9775 + 0.0571208*tf.T9i + -3.14434*tf.T913i + 4.11547*tf.T913
                  + -0.0954563*tf.T9 + 0.00192658*tf.T953 + -2.27004*tf.lnT9)

    rate_eval.n_F14__p_O14 = rate

@numba.njit()
def n_Cr49__Cr50(rate_eval, tf):
    # Cr49 + n --> Cr50
    rate = 0.0

    # ths8r
    rate += np.exp(  17.8355 + -1.98927*tf.T913
                  + 0.465124*tf.T9 + -0.0582249*tf.T953)

    rate_eval.n_Cr49__Cr50 = rate

@numba.njit()
def n_P25__P26(rate_eval, tf):
    # P25 + n --> P26
    rate = 0.0

    # ths8r
    rate += np.exp(  9.29597 + 0.783618*tf.T913
                  + -0.0753412*tf.T9 + 0.0129432*tf.T953)

    rate_eval.n_P25__P26 = rate

@numba.njit()
def Cr63__Mn63__weak__wc17(rate_eval, tf):
    # Cr63 --> Mn63
    rate = 0.0

    # wc17w
    rate += np.exp(  1.66123)

    rate_eval.Cr63__Mn63__weak__wc17 = rate

@numba.njit()
def Fe62__Co62__weak__wc12(rate_eval, tf):
    # Fe62 --> Co62
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.58602)

    rate_eval.Fe62__Co62__weak__wc12 = rate

@numba.njit()
def n_Al30__Al31(rate_eval, tf):
    # Al30 + n --> Al31
    rate = 0.0

    # rath 
    rate += np.exp(  11.9756 + -0.0214587*tf.T9i + 0.805255*tf.T913i + -0.599033*tf.T913
                  + -0.00441225*tf.T9 + -0.00214759*tf.T953 + 0.0963631*tf.lnT9)

    rate_eval.n_Al30__Al31 = rate

@numba.njit()
def Al36__n_n_Si34__weak__mp17(rate_eval, tf):
    # Al36 --> n + n + Si34
    rate = 0.0

    # mp17w
    rate += np.exp(  -1.87059)

    rate_eval.Al36__n_n_Si34__weak__mp17 = rate

@numba.njit()
def C16__N16__weak__wc12(rate_eval, tf):
    # C16 --> N16
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.67999)

    rate_eval.C16__N16__weak__wc12 = rate

@numba.njit()
def Ar34__Cl34__weak__wc12(rate_eval, tf):
    # Ar34 --> Cl34
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.198094)

    rate_eval.Ar34__Cl34__weak__wc12 = rate

@numba.njit()
def Sc46__Ti46__weak__wc12(rate_eval, tf):
    # Sc46 --> Ti46
    rate = 0.0

    # wc12w
    rate += np.exp(  -16.1616)

    rate_eval.Sc46__Ti46__weak__wc12 = rate

@numba.njit()
def p_Sc63__n_Ti63(rate_eval, tf):
    # Sc63 + p --> n + Ti63
    rate = 0.0

    # rath 
    rate += np.exp(  137.337 + -6.20818*tf.T9i + 236.177*tf.T913i + -383.131*tf.T913
                  + 21.1154*tf.T9 + -1.17692*tf.T953 + 191.129*tf.lnT9)

    rate_eval.p_Sc63__n_Ti63 = rate

@numba.njit()
def P38__n_S37__weak__wc12(rate_eval, tf):
    # P38 --> n + S37
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.04049)

    rate_eval.P38__n_S37__weak__wc12 = rate

@numba.njit()
def Cr59__Mn59__weak__wc12(rate_eval, tf):
    # Cr59 --> Mn59
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.415303)

    rate_eval.Cr59__Mn59__weak__wc12 = rate

@numba.njit()
def n_Ti48__Ti49(rate_eval, tf):
    # Ti48 + n --> Ti49
    rate = 0.0

    # ks03 
    rate += np.exp(  -16.7879 + 0.320502*tf.T9i + -32.4895*tf.T913i + 67.9234*tf.T913
                  + -4.27126*tf.T9 + 0.230364*tf.T953 + -29.4521*tf.lnT9)

    rate_eval.n_Ti48__Ti49 = rate

@numba.njit()
def n_Mn47__Mn48(rate_eval, tf):
    # Mn47 + n --> Mn48
    rate = 0.0

    # ths8r
    rate += np.exp(  12.3359 + -0.80997*tf.T913
                  + 0.187769*tf.T9 + -0.0100652*tf.T953)

    rate_eval.n_Mn47__Mn48 = rate

@numba.njit()
def Cr49__V49__weak__wc12(rate_eval, tf):
    # Cr49 --> V49
    rate = 0.0

    # wc12w
    rate += np.exp(  -8.20643)

    rate_eval.Cr49__V49__weak__wc12 = rate

@numba.njit()
def p_Al42__n_Si42(rate_eval, tf):
    # Al42 + p --> n + Si42
    rate = 0.0

    # rath 
    rate += np.exp(  89.9632 + -3.73598*tf.T9i + 136.872*tf.T913i + -225.525*tf.T913
                  + 12.2556*tf.T9 + -0.676605*tf.T953 + 113.104*tf.lnT9)

    rate_eval.p_Al42__n_Si42 = rate

@numba.njit()
def Ca61__n_n_Sc59__weak__mp17(rate_eval, tf):
    # Ca61 --> n + n + Sc59
    rate = 0.0

    # mp17w
    rate += np.exp(  2.80888)

    rate_eval.Ca61__n_n_Sc59__weak__mp17 = rate

@numba.njit()
def n_Fe55__Fe56(rate_eval, tf):
    # Fe55 + n --> Fe56
    rate = 0.0

    # ks03 
    rate += np.exp(  21.7202 + -0.0955677*tf.T9i + 8.06062*tf.T913i + -14.4809*tf.T913
                  + 0.94252*tf.T9 + -0.0776007*tf.T953 + 6.47093*tf.lnT9)

    rate_eval.n_Fe55__Fe56 = rate

@numba.njit()
def Mn48__p_V47__weak__wc12(rate_eval, tf):
    # Mn48 --> p + V47
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.39949)

    rate_eval.Mn48__p_V47__weak__wc12 = rate

@numba.njit()
def n_Cr68__Cr69(rate_eval, tf):
    # Cr68 + n --> Cr69
    rate = 0.0

    # rath 
    rate += np.exp(  6.70418 + 0.0505619*tf.T9i + -4.9319*tf.T913i + 5.23408*tf.T913
                  + 1.01795*tf.T9 + -0.198498*tf.T953 + -3.95065*tf.lnT9)

    rate_eval.n_Cr68__Cr69 = rate

@numba.njit()
def He4_K32__p_Ca35(rate_eval, tf):
    # K32 + He4 --> p + Ca35
    rate = 0.0

    # ths8r
    rate += np.exp(  54.3243 + -73.3104*tf.T913i + -0.335753*tf.T913
                  + -0.647882*tf.T9 + 0.0397535*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K32__p_Ca35 = rate

@numba.njit()
def Cr43__V43__weak__wc12(rate_eval, tf):
    # Cr43 --> V43
    rate = 0.0

    # wc12w
    rate += np.exp(  1.38057)

    rate_eval.Cr43__V43__weak__wc12 = rate

@numba.njit()
def He4_Mn57__Co61(rate_eval, tf):
    # Mn57 + He4 --> Co61
    rate = 0.0

    # rath 
    rate += np.exp(  -1311.37 + 26.1125*tf.T9i + -2570.95*tf.T913i + 4040.0*tf.T913
                  + -229.258*tf.T9 + 12.6222*tf.T953 + -1949.92*tf.lnT9)

    rate_eval.He4_Mn57__Co61 = rate

@numba.njit()
def p_S45__Cl46(rate_eval, tf):
    # S45 + p --> Cl46
    rate = 0.0

    # rath 
    rate += np.exp(  87.5116 + -4.41291*tf.T9i + 161.102*tf.T913i + -261.478*tf.T913
                  + 14.1615*tf.T9 + -0.782123*tf.T953 + 132.052*tf.lnT9)

    rate_eval.p_S45__Cl46 = rate

@numba.njit()
def n_Ne25__Ne26(rate_eval, tf):
    # Ne25 + n --> Ne26
    rate = 0.0

    # wiesr
    rate += np.exp(  6.66058 + -1.91659e-14*tf.T9i + -8.35918e-14*tf.T913i + 1.13647e-11*tf.T913
                  + -2.09721e-12*tf.T9 + 2.30781e-13*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_Ne25__Ne26 = rate

@numba.njit()
def n_S31__S32(rate_eval, tf):
    # S31 + n --> S32
    rate = 0.0

    # ths8r
    rate += np.exp(  7.56582 + 1.71463*tf.T913
                  + -0.221804*tf.T9 + 0.00880104*tf.T953)

    rate_eval.n_S31__S32 = rate

@numba.njit()
def He4_Cr58__n_Fe61(rate_eval, tf):
    # Cr58 + He4 --> n + Fe61
    rate = 0.0

    # rath 
    rate += np.exp(  -1118.25 + 17.8527*tf.T9i + -1937.73*tf.T913i + 3190.56*tf.T913
                  + -190.536*tf.T9 + 10.9293*tf.T953 + -1496.53*tf.lnT9)

    rate_eval.He4_Cr58__n_Fe61 = rate

@numba.njit()
def He4_Si26__p_P29(rate_eval, tf):
    # Si26 + He4 --> p + P29
    rate = 0.0

    # ths8r
    rate += np.exp(  48.8732 + -59.3013*tf.T913i + 0.480742*tf.T913
                  + -0.834505*tf.T9 + 0.0621841*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Si26__p_P29 = rate

@numba.njit()
def Mn71__Fe71__weak__mo03(rate_eval, tf):
    # Mn71 --> Fe71
    rate = 0.0

    # mo03w
    rate += np.exp(  4.15074)

    rate_eval.Mn71__Fe71__weak__mo03 = rate

@numba.njit()
def Mg36__n_Al35__weak__mp17(rate_eval, tf):
    # Mg36 --> n + Al35
    rate = 0.0

    # mp17w
    rate += np.exp(  4.23866)

    rate_eval.Mg36__n_Al35__weak__mp17 = rate

@numba.njit()
def Ne30__n_Na29__weak__wc12(rate_eval, tf):
    # Ne30 --> n + Na29
    rate = 0.0

    # wc12w
    rate += np.exp(  2.51315)

    rate_eval.Ne30__n_Na29__weak__wc12 = rate

@numba.njit()
def Be14__B14__weak__wc12(rate_eval, tf):
    # Be14 --> B14
    rate = 0.0

    # wc12w
    rate += np.exp(  3.10495)

    rate_eval.Be14__B14__weak__wc12 = rate

@numba.njit()
def Cr41__V41__weak__bqa_pos_(rate_eval, tf):
    # Cr41 --> V41
    rate = 0.0

    # bqa+w
    rate += np.exp(  4.30053)

    rate_eval.Cr41__V41__weak__bqa_pos_ = rate

@numba.njit()
def Fe65__Co65__weak__wc12(rate_eval, tf):
    # Fe65 --> Co65
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.155792)

    rate_eval.Fe65__Co65__weak__wc12 = rate

@numba.njit()
def V58__Cr58__weak__wc17(rate_eval, tf):
    # V58 --> Cr58
    rate = 0.0

    # wc17w
    rate += np.exp(  1.26877)

    rate_eval.V58__Cr58__weak__wc17 = rate

@numba.njit()
def Cl51__n_n_n_Ar48__weak__mo03(rate_eval, tf):
    # Cl51 --> 3 n + Ar48
    rate = 0.0

    # mo03w
    rate += np.exp(  3.48926)

    rate_eval.Cl51__n_n_n_Ar48__weak__mo03 = rate

@numba.njit()
def He4_Cr67__n_Fe70(rate_eval, tf):
    # Cr67 + He4 --> n + Fe70
    rate = 0.0

    # rath 
    rate += np.exp(  -1207.91 + 19.1299*tf.T9i + -2074.61*tf.T913i + 3429.77*tf.T913
                  + -205.039*tf.T9 + 11.7741*tf.T953 + -1607.81*tf.lnT9)

    rate_eval.He4_Cr67__n_Fe70 = rate

@numba.njit()
def He4_Sc46__V50(rate_eval, tf):
    # Sc46 + He4 --> V50
    rate = 0.0

    # rath 
    rate += np.exp(  -953.322 + 15.73*tf.T9i + -1681.31*tf.T913i + 2743.27*tf.T913
                  + -162.405*tf.T9 + 9.24681*tf.T953 + -1292.78*tf.lnT9)

    rate_eval.He4_Sc46__V50 = rate

@numba.njit()
def He4_Ca59__n_Ti62(rate_eval, tf):
    # Ca59 + He4 --> n + Ti62
    rate = 0.0

    # rath 
    rate += np.exp(  -998.949 + 15.9516*tf.T9i + -1731.42*tf.T913i + 2854.56*tf.T913
                  + -170.77*tf.T9 + 9.81153*tf.T953 + -1338.31*tf.lnT9)

    rate_eval.He4_Ca59__n_Ti62 = rate

@numba.njit()
def He4_S34__n_Ar37(rate_eval, tf):
    # S34 + He4 --> n + Ar37
    rate = 0.0

    # SM93 
    rate += np.exp(  18.5358 + -53.7288*tf.T9i + -1.69894*tf.T913
                  + 0.371187*tf.T9 + -0.0457242*tf.T953 + 1.0*tf.lnT9)
    # SM93 
    rate += np.exp(  18.5358 + -53.7288*tf.T9i + 0.522368*tf.T913
                  + -1.03944*tf.T9 + 0.142735*tf.T953)

    rate_eval.He4_S34__n_Ar37 = rate

@numba.njit()
def p_Ti58__He4_Sc55(rate_eval, tf):
    # Ti58 + p --> He4 + Sc55
    rate = 0.0

    # rath 
    rate += np.exp(  110.1 + -6.45088*tf.T9i + 261.715*tf.T913i + -405.18*tf.T913
                  + 21.8054*tf.T9 + -1.1922*tf.T953 + 212.139*tf.lnT9)

    rate_eval.p_Ti58__He4_Sc55 = rate

@numba.njit()
def K44__Ca44__weak__wc12(rate_eval, tf):
    # K44 --> Ca44
    rate = 0.0

    # wc12w
    rate += np.exp(  -7.55945)

    rate_eval.K44__Ca44__weak__wc12 = rate

@numba.njit()
def V43__Ti43__weak__wc12(rate_eval, tf):
    # V43 --> Ti43
    rate = 0.0

    # wc12w
    rate += np.exp(  2.168)

    rate_eval.V43__Ti43__weak__wc12 = rate

@numba.njit()
def Sc50__Ti50__weak__wc12(rate_eval, tf):
    # Sc50 --> Ti50
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.99149)

    rate_eval.Sc50__Ti50__weak__wc12 = rate

@numba.njit()
def K53__Ca53__weak__wc17(rate_eval, tf):
    # K53 --> Ca53
    rate = 0.0

    # wc17w
    rate += np.exp(  1.75375)

    rate_eval.K53__Ca53__weak__wc17 = rate

@numba.njit()
def S47__n_Cl46__weak__mp17(rate_eval, tf):
    # S47 --> n + Cl46
    rate = 0.0

    # mp17w
    rate += np.exp(  2.84661)

    rate_eval.S47__n_Cl46__weak__mp17 = rate

@numba.njit()
def p_F31__Ne32(rate_eval, tf):
    # F31 + p --> Ne32
    rate = 0.0

    # rpsmr
    rate += np.exp(  56.082 + -2.51696*tf.T9i + 88.8078*tf.T913i + -149.583*tf.T913
                  + 8.06052*tf.T9 + -0.439476*tf.T953 + 75.0167*tf.lnT9)

    rate_eval.p_F31__Ne32 = rate

@numba.njit()
def p_Sc43__He4_Ca40(rate_eval, tf):
    # Sc43 + p --> He4 + Ca40
    rate = 0.0

    # ths8r
    rate += np.exp(  34.8559 + -32.1734*tf.T913i + 0.0296879*tf.T913
                  + -0.95232*tf.T9 + 0.129022*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc43__He4_Ca40 = rate

@numba.njit()
def S48__Cl48__weak__mo03(rate_eval, tf):
    # S48 --> Cl48
    rate = 0.0

    # mo03w
    rate += np.exp(  -110.978)

    rate_eval.S48__Cl48__weak__mo03 = rate

@numba.njit()
def n_K42__p_Ar42(rate_eval, tf):
    # K42 + n --> p + Ar42
    rate = 0.0

    # rath 
    rate += np.exp(  71.4565 + -0.680203*tf.T9i + 80.1678*tf.T913i + -153.649*tf.T913
                  + 8.1015*tf.T9 + -0.409126*tf.T953 + 76.0874*tf.lnT9)

    rate_eval.n_K42__p_Ar42 = rate

@numba.njit()
def He4_V41__p_Cr44(rate_eval, tf):
    # V41 + He4 --> p + Cr44
    rate = 0.0

    # ths8r
    rate += np.exp(  59.3909 + -83.9551*tf.T913i + -1.57038*tf.T913
                  + -0.345223*tf.T9 + 0.0032652*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_V41__p_Cr44 = rate

@numba.njit()
def n_Fe45__He4_Cr42(rate_eval, tf):
    # Fe45 + n --> He4 + Cr42
    rate = 0.0

    # ths8r
    rate += np.exp(  15.0101 + -0.754308*tf.T913
                  + 0.25012*tf.T9 + -0.0022928*tf.T953)

    rate_eval.n_Fe45__He4_Cr42 = rate

@numba.njit()
def He4_Ti39__Cr43(rate_eval, tf):
    # Ti39 + He4 --> Cr43
    rate = 0.0

    # ths8r
    rate += np.exp(  48.236 + -81.3803*tf.T913i + -1.18001*tf.T913
                  + -0.50423*tf.T9 + 0.00423975*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ti39__Cr43 = rate

@numba.njit()
def V66__n_n_Cr64__weak__mp17(rate_eval, tf):
    # V66 --> n + n + Cr64
    rate = 0.0

    # mp17w
    rate += np.exp(  2.46512)

    rate_eval.V66__n_n_Cr64__weak__mp17 = rate

@numba.njit()
def K54__Ca54__weak__wc17(rate_eval, tf):
    # K54 --> Ca54
    rate = 0.0

    # wc17w
    rate += np.exp(  3.79237)

    rate_eval.K54__Ca54__weak__wc17 = rate

@numba.njit()
def Cl48__Ar48__weak__mo03(rate_eval, tf):
    # Cl48 --> Ar48
    rate = 0.0

    # mo03w
    rate += np.exp(  -111.799)

    rate_eval.Cl48__Ar48__weak__mo03 = rate

@numba.njit()
def p_Sc62__He4_Ca59(rate_eval, tf):
    # Sc62 + p --> He4 + Ca59
    rate = 0.0

    # rath 
    rate += np.exp(  114.09 + -6.08772*tf.T9i + 226.56*tf.T913i + -365.457*tf.T913
                  + 20.5825*tf.T9 + -1.11836*tf.T953 + 182.824*tf.lnT9)

    rate_eval.p_Sc62__He4_Ca59 = rate

@numba.njit()
def Ar46__K46__weak__wc12(rate_eval, tf):
    # Ar46 --> K46
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.49475)

    rate_eval.Ar46__K46__weak__wc12 = rate

@numba.njit()
def Li9__Be9__weak__wc12(rate_eval, tf):
    # Li9 --> Be9
    rate = 0.0

    # wc12w
    rate += np.exp(  0.650182)

    rate_eval.Li9__Be9__weak__wc12 = rate

@numba.njit()
def Ca50__Sc50__weak__wc12(rate_eval, tf):
    # Ca50 --> Sc50
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.9984)

    rate_eval.Ca50__Sc50__weak__wc12 = rate

@numba.njit()
def He4_Sc50__V54(rate_eval, tf):
    # Sc50 + He4 --> V54
    rate = 0.0

    # rath 
    rate += np.exp(  -973.617 + 15.4691*tf.T9i + -1677.84*tf.T913i + 2760.39*tf.T913
                  + -165.157*tf.T9 + 9.49393*tf.T953 + -1294.31*tf.lnT9)

    rate_eval.He4_Sc50__V54 = rate

@numba.njit()
def n_Fe52__Fe53(rate_eval, tf):
    # Fe52 + n --> Fe53
    rate = 0.0

    # ths8r
    rate += np.exp(  15.8885 + -0.344319*tf.T913
                  + 0.178277*tf.T9 + -0.0334326*tf.T953)

    rate_eval.n_Fe52__Fe53 = rate

@numba.njit()
def n_Fe64__Fe65(rate_eval, tf):
    # Fe64 + n --> Fe65
    rate = 0.0

    # rath 
    rate += np.exp(  27.3951 + -0.0321138*tf.T9i + 4.96628*tf.T913i + -22.8795*tf.T913
                  + 3.30376*tf.T9 + -0.360971*tf.T953 + 6.45301*tf.lnT9)

    rate_eval.n_Fe64__Fe65 = rate

@numba.njit()
def Al22__p_Na21__weak__wc17(rate_eval, tf):
    # Al22 --> p + Na21
    rate = 0.0

    # wc17w
    rate += np.exp(  1.42232)

    rate_eval.Al22__p_Na21__weak__wc17 = rate

@numba.njit()
def V64__Cr64__weak__wc17(rate_eval, tf):
    # V64 --> Cr64
    rate = 0.0

    # wc17w
    rate += np.exp(  3.21114)

    rate_eval.V64__Cr64__weak__wc17 = rate

@numba.njit()
def Cl40__Ar40__weak__wc12(rate_eval, tf):
    # Cl40 --> Ar40
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.76096)

    rate_eval.Cl40__Ar40__weak__wc12 = rate

@numba.njit()
def Na34__n_n_Mg32__weak__wc12(rate_eval, tf):
    # Na34 --> n + n + Mg32
    rate = 0.0

    # wc12w
    rate += np.exp(  4.14335)

    rate_eval.Na34__n_n_Mg32__weak__wc12 = rate

@numba.njit()
def Na34__Mg34__weak__wc12(rate_eval, tf):
    # Na34 --> Mg34
    rate = 0.0

    # wc12w
    rate += np.exp(  3.78667)

    rate_eval.Na34__Mg34__weak__wc12 = rate

@numba.njit()
def Ar53__K53__weak__mo03(rate_eval, tf):
    # Ar53 --> K53
    rate = 0.0

    # mo03w
    rate += np.exp(  2.97899)

    rate_eval.Ar53__K53__weak__mo03 = rate

@numba.njit()
def He4_F23__n_Na26(rate_eval, tf):
    # F23 + He4 --> n + Na26
    rate = 0.0

    # rpsmr
    rate += np.exp(  59.8878 + -2.23146*tf.T9i + 38.1642*tf.T913i + -101.179*tf.T913
                  + 4.37127*tf.T9 + -0.20678*tf.T953 + 53.6931*tf.lnT9)

    rate_eval.He4_F23__n_Na26 = rate

@numba.njit()
def Al28__Si28__weak__wc12(rate_eval, tf):
    # Al28 --> Si28
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.26435)

    rate_eval.Al28__Si28__weak__wc12 = rate

@numba.njit()
def K35__Ar35__weak__wc12(rate_eval, tf):
    # K35 --> Ar35
    rate = 0.0

    # wc12w
    rate += np.exp(  1.35575)

    rate_eval.K35__Ar35__weak__wc12 = rate

@numba.njit()
def Sc61__Ti61__weak__mo03(rate_eval, tf):
    # Sc61 --> Ti61
    rate = 0.0

    # mo03w
    rate += np.exp(  4.21627)

    rate_eval.Sc61__Ti61__weak__mo03 = rate

@numba.njit()
def Li8__He4_He4__weak__wc12(rate_eval, tf):
    # Li8 --> He4 + He4
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.19216)

    rate_eval.Li8__He4_He4__weak__wc12 = rate

@numba.njit()
def K58__Ca58__weak__mo03(rate_eval, tf):
    # K58 --> Ca58
    rate = 0.0

    # mo03w
    rate += np.exp(  -109.6)

    rate_eval.K58__Ca58__weak__mo03 = rate

@numba.njit()
def Ti64__n_n_n_V61__weak__mo03(rate_eval, tf):
    # Ti64 --> 3 n + V61
    rate = 0.0

    # mo03w
    rate += np.exp(  -3.50273)

    rate_eval.Ti64__n_n_n_V61__weak__mo03 = rate

@numba.njit()
def n_Sc51__Sc52(rate_eval, tf):
    # Sc51 + n --> Sc52
    rate = 0.0

    # rath 
    rate += np.exp(  10.363 + 0.00909831*tf.T9i + -1.80515*tf.T913i + 4.00225*tf.T913
                  + -0.0935958*tf.T9 + -0.0239033*tf.T953 + -2.02516*tf.lnT9)

    rate_eval.n_Sc51__Sc52 = rate

@numba.njit()
def F29__n_Ne28__weak__wc12(rate_eval, tf):
    # F29 --> n + Ne28
    rate = 0.0

    # wc12w
    rate += np.exp(  5.62495)

    rate_eval.F29__n_Ne28__weak__wc12 = rate

@numba.njit()
def n_Fe59__He4_Cr56(rate_eval, tf):
    # Fe59 + n --> He4 + Cr56
    rate = 0.0

    # rath 
    rate += np.exp(  -17.7857 + -15.03*tf.T9i + 317.257*tf.T913i + -317.332*tf.T913
                  + 9.65534*tf.T9 + -0.305116*tf.T953 + 211.072*tf.lnT9)

    rate_eval.n_Fe59__He4_Cr56 = rate

@numba.njit()
def He4_S37__Ar41(rate_eval, tf):
    # S37 + He4 --> Ar41
    rate = 0.0

    # rath 
    rate += np.exp(  -390.646 + 2.13075*tf.T9i + -510.702*tf.T913i + 935.276*tf.T913
                  + -62.4031*tf.T9 + 3.80291*tf.T953 + -405.196*tf.lnT9)

    rate_eval.He4_S37__Ar41 = rate

@numba.njit()
def p_P47__S48(rate_eval, tf):
    # P47 + p --> S48
    rate = 0.0

    # rath 
    rate += np.exp(  85.4425 + -4.32534*tf.T9i + 159.15*tf.T913i + -256.882*tf.T913
                  + 13.7128*tf.T9 + -0.743534*tf.T953 + 129.979*tf.lnT9)

    rate_eval.p_P47__S48 = rate

@numba.njit()
def Sc51__Ti51__weak__wc12(rate_eval, tf):
    # Sc51 --> Ti51
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.88421)

    rate_eval.Sc51__Ti51__weak__wc12 = rate

@numba.njit()
def K55__Ca55__weak__mo03(rate_eval, tf):
    # K55 --> Ca55
    rate = 0.0

    # mo03w
    rate += np.exp(  4.74671)

    rate_eval.K55__Ca55__weak__mo03 = rate

@numba.njit()
def Ti65__V65__weak__mo03(rate_eval, tf):
    # Ti65 --> V65
    rate = 0.0

    # mo03w
    rate += np.exp(  1.78519)

    rate_eval.Ti65__V65__weak__mo03 = rate

@numba.njit()
def d_Li6__p_Li7(rate_eval, tf):
    # Li6 + d --> p + Li7
    rate = 0.0

    # mafon
    rate += np.exp(  28.0231 + -10.135*tf.T913i
                  + -0.666667*tf.lnT9)

    rate_eval.d_Li6__p_Li7 = rate

@numba.njit()
def n_Si29__Si30(rate_eval, tf):
    # Si29 + n --> Si30
    rate = 0.0

    # ka02r
    rate += np.exp(  9.60115 + -0.179366*tf.T9i + 5.50678*tf.T913
                  + -2.85656*tf.T9 + -1.5*tf.lnT9)
    # ka02n
    rate += np.exp(  11.8023 + 0.650904*tf.T913)

    rate_eval.n_Si29__Si30 = rate

@numba.njit()
def N22__n_n_O20__weak__wc12(rate_eval, tf):
    # N22 --> n + n + O20
    rate = 0.0

    # wc12w
    rate += np.exp(  1.42525)

    rate_eval.N22__n_n_O20__weak__wc12 = rate

@numba.njit()
def n_Cl35__Cl36(rate_eval, tf):
    # Cl35 + n --> Cl36
    rate = 0.0

    # ks03 
    rate += np.exp(  2.77768 + 0.10548*tf.T9i + -11.2145*tf.T913i + 23.5701*tf.T913
                  + -1.44059*tf.T9 + 0.0755834*tf.T953 + -10.3832*tf.lnT9)

    rate_eval.n_Cl35__Cl36 = rate

@numba.njit()
def F25__n_Ne24__weak__wc12(rate_eval, tf):
    # F25 --> n + Ne24
    rate = 0.0

    # wc12w
    rate += np.exp(  0.693878)

    rate_eval.F25__n_Ne24__weak__wc12 = rate

@numba.njit()
def p_Mg28__Al29(rate_eval, tf):
    # Mg28 + p --> Al29
    rate = 0.0

    # rath 
    rate += np.exp(  62.342 + -2.81936*tf.T9i + 93.444*tf.T913i + -159.755*tf.T913
                  + 8.80233*tf.T9 + -0.501558*tf.T953 + 79.9139*tf.lnT9)

    rate_eval.p_Mg28__Al29 = rate

@numba.njit()
def n_F15__p_O15(rate_eval, tf):
    # F15 + n --> p + O15
    rate = 0.0

    # rpsmr
    rate += np.exp(  18.6182 + 0.0583936*tf.T9i + -3.25485*tf.T913i + 4.5547*tf.T913
                  + -0.151514*tf.T9 + 0.0064577*tf.T953 + -2.38438*tf.lnT9)

    rate_eval.n_F15__p_O15 = rate

@numba.njit()
def Sc43__Ca43__weak__wc12(rate_eval, tf):
    # Sc43 --> Ca43
    rate = 0.0

    # wc12w
    rate += np.exp(  -9.91333)

    rate_eval.Sc43__Ca43__weak__wc12 = rate

@numba.njit()
def n_Na20__p_Ne20(rate_eval, tf):
    # Na20 + n --> p + Ne20
    rate = 0.0

    # ths8r
    rate += np.exp(  17.5853 + 2.18811*tf.T913
                  + -0.25904*tf.T9 + 0.015993*tf.T953)

    rate_eval.n_Na20__p_Ne20 = rate

@numba.njit()
def n_Na38__Na39(rate_eval, tf):
    # Na38 + n --> Na39
    rate = 0.0

    # rath 
    rate += np.exp(  8.55642 + -0.0840739*tf.T9i + 6.34065*tf.T913i + -12.2887*tf.T913
                  + 1.17463*tf.T9 + -0.0702496*tf.T953 + 4.84438*tf.lnT9)

    rate_eval.n_Na38__Na39 = rate

@numba.njit()
def n_V52__He4_Sc49(rate_eval, tf):
    # V52 + n --> He4 + Sc49
    rate = 0.0

    # rath 
    rate += np.exp(  -13.0046 + -2.2017*tf.T9i + 174.784*tf.T913i + -175.991*tf.T913
                  + 2.92402*tf.T9 + 0.0459501*tf.T953 + 127.478*tf.lnT9)

    rate_eval.n_V52__He4_Sc49 = rate

@numba.njit()
def He4_Fe49__Ni53(rate_eval, tf):
    # Fe49 + He4 --> Ni53
    rate = 0.0

    # ths8r
    rate += np.exp(  60.1749 + -91.5495*tf.T913i + -7.98638*tf.T913
                  + 0.532406*tf.T9 + -0.0748555*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe49__Ni53 = rate

@numba.njit()
def n_Cr50__Cr51(rate_eval, tf):
    # Cr50 + n --> Cr51
    rate = 0.0

    # ks03 
    rate += np.exp(  15.1066 + -0.0225613*tf.T9i + 0.815037*tf.T913i + -0.708732*tf.T913
                  + 0.386295*tf.T9 + -0.0615661*tf.T953 + 0.0454627*tf.lnT9)

    rate_eval.n_Cr50__Cr51 = rate

@numba.njit()
def N12__C12__weak__wc12(rate_eval, tf):
    # N12 --> C12
    rate = 0.0

    # wc12w
    rate += np.exp(  4.14335)

    rate_eval.N12__C12__weak__wc12 = rate

@numba.njit()
def Ne31__n_n_Na29__weak__mp17(rate_eval, tf):
    # Ne31 --> n + n + Na29
    rate = 0.0

    # mp17w
    rate += np.exp(  1.40544)

    rate_eval.Ne31__n_n_Na29__weak__mp17 = rate

@numba.njit()
def Fe51__Mn51__weak__wc12(rate_eval, tf):
    # Fe51 --> Mn51
    rate = 0.0

    # wc12w
    rate += np.exp(  0.820931)

    rate_eval.Fe51__Mn51__weak__wc12 = rate

@numba.njit()
def n_P24__P25(rate_eval, tf):
    # P24 + n --> P25
    rate = 0.0

    # ths8r
    rate += np.exp(  9.06533 + 0.893122*tf.T913
                  + -0.00195618*tf.T9 + 0.000477175*tf.T953)

    rate_eval.n_P24__P25 = rate

@numba.njit()
def p_O19__F20(rate_eval, tf):
    # O19 + p --> F20
    rate = 0.0

    # rpsmr
    rate += np.exp(  47.7492 + -1.81205*tf.T9i + 60.1623*tf.T913i + -109.271*tf.T913
                  + 6.05007*tf.T9 + -0.336208*tf.T953 + 53.9799*tf.lnT9)

    rate_eval.p_O19__F20 = rate

@numba.njit()
def Ne32__n_n_n_Na29__weak__mo03(rate_eval, tf):
    # Ne32 --> 3 n + Na29
    rate = 0.0

    # mo03w
    rate += np.exp(  -0.66407)

    rate_eval.Ne32__n_n_n_Na29__weak__mo03 = rate

@numba.njit()
def p_Cr58__He4_V55(rate_eval, tf):
    # Cr58 + p --> He4 + V55
    rate = 0.0

    # rath 
    rate += np.exp(  93.9821 + -6.59674*tf.T9i + 252.24*tf.T913i + -374.34*tf.T913
                  + 19.3303*tf.T9 + -1.06257*tf.T953 + 201.234*tf.lnT9)

    rate_eval.p_Cr58__He4_V55 = rate

@numba.njit()
def V42__Ti42__weak__mo97(rate_eval, tf):
    # V42 --> Ti42
    rate = 0.0

    # mo97w
    rate += np.exp(  3.05387)

    rate_eval.V42__Ti42__weak__mo97 = rate

@numba.njit()
def Cl36__S36__weak__wc12(rate_eval, tf):
    # Cl36 --> S36
    rate = 0.0

    # wc12w
    rate += np.exp(  -34.2121)

    rate_eval.Cl36__S36__weak__wc12 = rate

@numba.njit()
def p_Si41__n_P41(rate_eval, tf):
    # Si41 + p --> n + P41
    rate = 0.0

    # rath 
    rate += np.exp(  89.3899 + -3.85806*tf.T9i + 139.444*tf.T913i + -228.534*tf.T913
                  + 12.3839*tf.T9 + -0.68453*tf.T953 + 115.147*tf.lnT9)

    rate_eval.p_Si41__n_P41 = rate

@numba.njit()
def Mn51__Cr51__weak__wc12(rate_eval, tf):
    # Mn51 --> Cr51
    rate = 0.0

    # wc12w
    rate += np.exp(  -8.29312)

    rate_eval.Mn51__Cr51__weak__wc12 = rate

@numba.njit()
def He4_Fe47__p_Co50(rate_eval, tf):
    # Fe47 + He4 --> p + Co50
    rate = 0.0

    # ths8r
    rate += np.exp(  62.4487 + -91.4525*tf.T913i + -1.48823*tf.T913
                  + -0.426296*tf.T9 + 0.00754483*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Fe47__p_Co50 = rate

@numba.njit()
def Ca54__Sc54__weak__wc17(rate_eval, tf):
    # Ca54 --> Sc54
    rate = 0.0

    # wc17w
    rate += np.exp(  2.0356)

    rate_eval.Ca54__Sc54__weak__wc17 = rate

@numba.njit()
def n_Ca42__He4_Ar39(rate_eval, tf):
    # Ca42 + n --> He4 + Ar39
    rate = 0.0

    # ths8r
    rate += np.exp(  -88.517 + 88.8565*tf.T913
                  + -12.9534*tf.T9 + 0.93832*tf.T953)

    rate_eval.n_Ca42__He4_Ar39 = rate

@numba.njit()
def Ca45__Sc45__weak__wc12(rate_eval, tf):
    # Ca45 --> Sc45
    rate = 0.0

    # wc12w
    rate += np.exp(  -16.8211)

    rate_eval.Ca45__Sc45__weak__wc12 = rate

@numba.njit()
def p_Na24__n_Mg24(rate_eval, tf):
    # Na24 + p --> n + Mg24
    rate = 0.0

    # rath 
    rate += np.exp(  64.9407 + -2.51894*tf.T9i + 85.1374*tf.T913i + -145.038*tf.T913
                  + 7.70922*tf.T9 + -0.427731*tf.T953 + 73.5924*tf.lnT9)

    rate_eval.p_Na24__n_Mg24 = rate

@numba.njit()
def n_Na25__Na26(rate_eval, tf):
    # Na25 + n --> Na26
    rate = 0.0

    # rath 
    rate += np.exp(  13.4685 + -0.00934395*tf.T9i + 0.141321*tf.T913i + -2.73028*tf.T913
                  + 0.425637*tf.T9 + -0.0292701*tf.T953 + 0.0632137*tf.lnT9)

    rate_eval.n_Na25__Na26 = rate

@numba.njit()
def p_Cr63__He4_V60(rate_eval, tf):
    # Cr63 + p --> He4 + V60
    rate = 0.0

    # rath 
    rate += np.exp(  -65.7699 + -5.14867*tf.T9i + 82.9504*tf.T913i + -31.0385*tf.T913
                  + -3.85439*tf.T9 + 0.409181*tf.T953 + 53.1774*tf.lnT9)

    rate_eval.p_Cr63__He4_V60 = rate

@numba.njit()
def Ne33__n_n_Na31__weak__mp17(rate_eval, tf):
    # Ne33 --> n + n + Na31
    rate = 0.0

    # mp17w
    rate += np.exp(  3.18513)

    rate_eval.Ne33__n_n_Na31__weak__mp17 = rate

@numba.njit()
def p_Si35__n_P35(rate_eval, tf):
    # Si35 + p --> n + P35
    rate = 0.0

    # rath 
    rate += np.exp(  87.5181 + -3.59582*tf.T9i + 129.299*tf.T913i + -216.238*tf.T913
                  + 11.7484*tf.T9 + -0.650973*tf.T953 + 108.425*tf.lnT9)

    rate_eval.p_Si35__n_P35 = rate

@numba.njit()
def S40__Cl40__weak__wc12(rate_eval, tf):
    # S40 --> Cl40
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.54127)

    rate_eval.S40__Cl40__weak__wc12 = rate

@numba.njit()
def Na32__n_Mg31__weak__wc17(rate_eval, tf):
    # Na32 --> n + Mg31
    rate = 0.0

    # wc17w
    rate += np.exp(  2.53391)

    rate_eval.Na32__n_Mg31__weak__wc17 = rate

@numba.njit()
def n_V58__V59(rate_eval, tf):
    # V58 + n --> V59
    rate = 0.0

    # rath 
    rate += np.exp(  16.2014 + -0.0138221*tf.T9i + 1.20475*tf.T913i + -4.14429*tf.T913
                  + 0.25264*tf.T9 + -0.0458318*tf.T953 + 1.1993*tf.lnT9)

    rate_eval.n_V58__V59 = rate

@numba.njit()
def p_Si43__P44(rate_eval, tf):
    # Si43 + p --> P44
    rate = 0.0

    # rath 
    rate += np.exp(  78.1735 + -3.94344*tf.T9i + 142.769*tf.T913i + -231.206*tf.T913
                  + 12.337*tf.T9 + -0.670626*tf.T953 + 117.16*tf.lnT9)

    rate_eval.p_Si43__P44 = rate

@numba.njit()
def K50__Ca50__weak__wc12(rate_eval, tf):
    # K50 --> Ca50
    rate = 0.0

    # wc12w
    rate += np.exp(  0.0417731)

    rate_eval.K50__Ca50__weak__wc12 = rate

@numba.njit()
def n_Mn61__Mn62(rate_eval, tf):
    # Mn61 + n --> Mn62
    rate = 0.0

    # rath 
    rate += np.exp(  19.5893 + -0.0345542*tf.T9i + 3.43888*tf.T913i + -10.3494*tf.T913
                  + 0.96169*tf.T9 + -0.107022*tf.T953 + 3.44602*tf.lnT9)

    rate_eval.n_Mn61__Mn62 = rate

@numba.njit()
def Mg21__Na21__weak__wc12(rate_eval, tf):
    # Mg21 --> Na21
    rate = 0.0

    # wc12w
    rate += np.exp(  1.33525)

    rate_eval.Mg21__Na21__weak__wc12 = rate

@numba.njit()
def V57__Cr57__weak__wc12(rate_eval, tf):
    # V57 --> Cr57
    rate = 0.0

    # wc12w
    rate += np.exp(  0.772921)

    rate_eval.V57__Cr57__weak__wc12 = rate

@numba.njit()
def He4_Fe72__n_Ni75(rate_eval, tf):
    # Fe72 + He4 --> n + Ni75
    rate = 0.0

    # rath 
    rate += np.exp(  -1265.82 + 26.2694*tf.T9i + -2607.51*tf.T913i + 4034.23*tf.T913
                  + -228.869*tf.T9 + 12.6744*tf.T953 + -1956.06*tf.lnT9)

    rate_eval.He4_Fe72__n_Ni75 = rate

@numba.njit()
def K57__n_n_n_Ca54__weak__mo03(rate_eval, tf):
    # K57 --> 3 n + Ca54
    rate = 0.0

    # mo03w
    rate += np.exp(  3.77583)

    rate_eval.K57__n_n_n_Ca54__weak__mo03 = rate

@numba.njit()
def He4_Al33__P37(rate_eval, tf):
    # Al33 + He4 --> P37
    rate = 0.0

    # rath 
    rate += np.exp(  -14.7864 + -2.732*tf.T9i + -18.825*tf.T913i + 21.649*tf.T913
                  + -4.60082*tf.T9 + 0.361068*tf.T953 + 5.36465*tf.lnT9)

    rate_eval.He4_Al33__P37 = rate

@numba.njit()
def Cl33__S33__weak__wc12(rate_eval, tf):
    # Cl33 --> S33
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.2868)

    rate_eval.Cl33__S33__weak__wc12 = rate

@numba.njit()
def S48__n_Cl47__weak__mp17(rate_eval, tf):
    # S48 --> n + Cl47
    rate = 0.0

    # mp17w
    rate += np.exp(  4.03503)

    rate_eval.S48__n_Cl47__weak__mp17 = rate

@numba.njit()
def n_Mn43__Mn44(rate_eval, tf):
    # Mn43 + n --> Mn44
    rate = 0.0

    # ths8r
    rate += np.exp(  10.084 + -0.187747*tf.T913
                  + 0.182708*tf.T9 + -0.0142531*tf.T953)

    rate_eval.n_Mn43__Mn44 = rate

@numba.njit()
def He4_Al22__P26(rate_eval, tf):
    # Al22 + He4 --> P26
    rate = 0.0

    # ths8r
    rate += np.exp(  35.7301 + -55.9969*tf.T913i + 0.906087*tf.T913
                  + -0.793083*tf.T9 + 0.0568671*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Al22__P26 = rate

@numba.njit()
def Si40__P40__weak__wc17(rate_eval, tf):
    # Si40 --> P40
    rate = 0.0

    # wc17w
    rate += np.exp(  2.07715)

    rate_eval.Si40__P40__weak__wc17 = rate

@numba.njit()
def p_K53__He4_Ar50(rate_eval, tf):
    # K53 + p --> He4 + Ar50
    rate = 0.0

    # rath 
    rate += np.exp(  111.59 + -5.40029*tf.T9i + 204.525*tf.T913i + -333.516*tf.T913
                  + 18.064*tf.T9 + -0.947681*tf.T953 + 167.058*tf.lnT9)

    rate_eval.p_K53__He4_Ar50 = rate

@numba.njit()
def K36__Ar36__weak__wc12(rate_eval, tf):
    # K36 --> Ar36
    rate = 0.0

    # wc12w
    rate += np.exp(  0.705898)

    rate_eval.K36__Ar36__weak__wc12 = rate

@numba.njit()
def S43__n_Cl42__weak__wc12(rate_eval, tf):
    # S43 --> n + Cl42
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.00983798)

    rate_eval.S43__n_Cl42__weak__wc12 = rate

@numba.njit()
def Mn53__Cr53__weak__wc12(rate_eval, tf):
    # Mn53 --> Cr53
    rate = 0.0

    # wc12w
    rate += np.exp(  -32.7682)

    rate_eval.Mn53__Cr53__weak__wc12 = rate

@numba.njit()
def F27__Ne27__weak__wc17(rate_eval, tf):
    # F27 --> Ne27
    rate = 0.0

    # wc17w
    rate += np.exp(  3.27107)

    rate_eval.F27__Ne27__weak__wc17 = rate

@numba.njit()
def Ti55__V55__weak__wc12(rate_eval, tf):
    # Ti55 --> V55
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.628877)

    rate_eval.Ti55__V55__weak__wc12 = rate

@numba.njit()
def He4_O26__Ne30(rate_eval, tf):
    # O26 + He4 --> Ne30
    rate = 0.0

    # rpsmr
    rate += np.exp(  40.1773 + -2.11302*tf.T9i + 30.571*tf.T913i + -82.5903*tf.T913
                  + 3.71386*tf.T9 + -0.221168*tf.T953 + 44.8077*tf.lnT9)

    rate_eval.He4_O26__Ne30 = rate

@numba.njit()
def n_Ti40__He4_Ca37(rate_eval, tf):
    # Ti40 + n --> He4 + Ca37
    rate = 0.0

    # ths8r
    rate += np.exp(  14.5582 + 2.05075*tf.T913
                  + -0.502525*tf.T9 + 0.0806055*tf.T953)

    rate_eval.n_Ti40__He4_Ca37 = rate

@numba.njit()
def V56__Cr56__weak__wc12(rate_eval, tf):
    # V56 --> Cr56
    rate = 0.0

    # wc12w
    rate += np.exp(  1.16596)

    rate_eval.V56__Cr56__weak__wc12 = rate

@numba.njit()
def Ar50__K50__weak__wc12(rate_eval, tf):
    # Ar50 --> K50
    rate = 0.0

    # wc12w
    rate += np.exp(  1.66781)

    rate_eval.Ar50__K50__weak__wc12 = rate

@numba.njit()
def p_Na25__He4_Ne22(rate_eval, tf):
    # Na25 + p --> He4 + Ne22
    rate = 0.0

    # rath 
    rate += np.exp(  56.4251 + -2.54705*tf.T9i + 84.6517*tf.T913i + -138.407*tf.T913
                  + 7.06005*tf.T9 + -0.380108*tf.T953 + 72.1689*tf.lnT9)

    rate_eval.p_Na25__He4_Ne22 = rate

@numba.njit()
def He4_S44__n_Ar47(rate_eval, tf):
    # S44 + He4 --> n + Ar47
    rate = 0.0

    # rath 
    rate += np.exp(  -346.994 + 1.87088*tf.T9i + -498.475*tf.T913i + 884.015*tf.T913
                  + -58.4707*tf.T9 + 3.56291*tf.T953 + -387.169*tf.lnT9)

    rate_eval.He4_S44__n_Ar47 = rate

@numba.njit()
def p_Mg28__n_Al28(rate_eval, tf):
    # Mg28 + p --> n + Al28
    rate = 0.0

    # rath 
    rate += np.exp(  73.3906 + -2.89942*tf.T9i + 101.006*tf.T913i + -170.466*tf.T913
                  + 9.09841*tf.T9 + -0.50058*tf.T953 + 86.1098*tf.lnT9)

    rate_eval.p_Mg28__n_Al28 = rate

@numba.njit()
def n_V45__p_Ti45(rate_eval, tf):
    # V45 + n --> p + Ti45
    rate = 0.0

    # ths8r
    rate += np.exp(  21.516 + -1.1034*tf.T913
                  + 0.332295*tf.T9 + -0.0307723*tf.T953)

    rate_eval.n_V45__p_Ti45 = rate

@numba.njit()
def p_O18__F19(rate_eval, tf):
    # O18 + p --> F19
    rate = 0.0

    # il10n
    rate += np.exp(  19.917 + -16.7246*tf.T913i
                  + -3.0*tf.T953 + -0.666667*tf.lnT9)
    # il10r
    rate += np.exp(  7.26876 + -6.7253*tf.T9i + 3.99059*tf.T913
                  + -0.593127*tf.T9 + 0.0877534*tf.T953 + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  5.07648 + -1.65681*tf.T9i
                  + -1.5*tf.lnT9)
    # il10r
    rate += np.exp(  -35.0079 + -0.244743*tf.T9i
                  + -1.5*tf.lnT9)

    rate_eval.p_O18__F19 = rate

@numba.njit()
def p_P36__S37(rate_eval, tf):
    # P36 + p --> S37
    rate = 0.0

    # rath 
    rate += np.exp(  82.836 + -3.81687*tf.T9i + 137.687*tf.T913i + -229.892*tf.T913
                  + 12.4864*tf.T9 + -0.692224*tf.T953 + 115.25*tf.lnT9)

    rate_eval.p_P36__S37 = rate

@numba.njit()
def Na35__Mg35__weak__wc17(rate_eval, tf):
    # Na35 --> Mg35
    rate = 0.0

    # wc17w
    rate += np.exp(  4.62165)

    rate_eval.Na35__Mg35__weak__wc17 = rate

@numba.njit()
def He4_Fe72__Ni76(rate_eval, tf):
    # Fe72 + He4 --> Ni76
    rate = 0.0

    # rath 
    rate += np.exp(  -1032.35 + 26.1854*tf.T9i + -2526.28*tf.T913i + 3682.76*tf.T913
                  + -199.615*tf.T9 + 10.6507*tf.T953 + -1836.26*tf.lnT9)

    rate_eval.He4_Fe72__Ni76 = rate

@numba.njit()
def Na24__Mg24__weak__wc12(rate_eval, tf):
    # Na24 --> Mg24
    rate = 0.0

    # wc12w
    rate += np.exp(  -11.2633)

    rate_eval.Na24__Mg24__weak__wc12 = rate

@numba.njit()
def V59__Cr59__weak__wc12(rate_eval, tf):
    # V59 --> Cr59
    rate = 0.0

    # wc12w
    rate += np.exp(  1.93607)

    rate_eval.V59__Cr59__weak__wc12 = rate

@numba.njit()
def Ar41__K41__weak__wc12(rate_eval, tf):
    # Ar41 --> K41
    rate = 0.0

    # wc12w
    rate += np.exp(  -9.1583)

    rate_eval.Ar41__K41__weak__wc12 = rate

@numba.njit()
def Cr65__Mn65__weak__wc17(rate_eval, tf):
    # Cr65 --> Mn65
    rate = 0.0

    # wc17w
    rate += np.exp(  3.13647)

    rate_eval.Cr65__Mn65__weak__wc17 = rate

@numba.njit()
def Cr46__V46__weak__wc12(rate_eval, tf):
    # Cr46 --> V46
    rate = 0.0

    # wc12w
    rate += np.exp(  0.980561)

    rate_eval.Cr46__V46__weak__wc12 = rate

@numba.njit()
def n_F24__F25(rate_eval, tf):
    # F24 + n --> F25
    rate = 0.0

    # wiesr
    rate += np.exp(  7.09008 + -7.26011e-13*tf.T9i + 9.33078e-11*tf.T913i + -2.99521e-10*tf.T913
                  + 2.93124e-11*tf.T9 + -2.41296e-12*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_F24__F25 = rate

@numba.njit()
def Ar37__Cl37__weak__wc12(rate_eval, tf):
    # Ar37 --> Cl37
    rate = 0.0

    # wc12w
    rate += np.exp(  -15.2906)

    rate_eval.Ar37__Cl37__weak__wc12 = rate

@numba.njit()
def Be10__B10__weak__wc12(rate_eval, tf):
    # Be10 --> B10
    rate = 0.0

    # wc12w
    rate += np.exp(  -31.7772)

    rate_eval.Be10__B10__weak__wc12 = rate

@numba.njit()
def Ar32__Cl32__weak__wc12(rate_eval, tf):
    # Ar32 --> Cl32
    rate = 0.0

    # wc12w
    rate += np.exp(  1.48607)

    rate_eval.Ar32__Cl32__weak__wc12 = rate

@numba.njit()
def p_Mg39__He4_Na36(rate_eval, tf):
    # Mg39 + p --> He4 + Na36
    rate = 0.0

    # rath 
    rate += np.exp(  72.5443 + -3.705*tf.T9i + 161.462*tf.T913i + -252.797*tf.T913
                  + 11.3933*tf.T9 + -0.523812*tf.T953 + 137.264*tf.lnT9)

    rate_eval.p_Mg39__He4_Na36 = rate

@numba.njit()
def n_S27__p_P27(rate_eval, tf):
    # S27 + n --> p + P27
    rate = 0.0

    # ths8r
    rate += np.exp(  18.9082 + 1.4499*tf.T913
                  + -0.175534*tf.T9 + 0.0130298*tf.T953)

    rate_eval.n_S27__p_P27 = rate

@numba.njit()
def Ti63__n_n_V61__weak__mp17(rate_eval, tf):
    # Ti63 --> n + n + V61
    rate = 0.0

    # mp17w
    rate += np.exp(  0.581096)

    rate_eval.Ti63__n_n_V61__weak__mp17 = rate

@numba.njit()
def He4_Al30__n_P33(rate_eval, tf):
    # Al30 + He4 --> n + P33
    rate = 0.0

    # rath 
    rate += np.exp(  -9.03362 + -2.47665*tf.T9i + -29.7556*tf.T913i + 37.3866*tf.T913
                  + -5.4804*tf.T9 + 0.412129*tf.T953 + -2.55968*tf.lnT9)

    rate_eval.He4_Al30__n_P33 = rate

@numba.njit()
def Ar29__Cl29__weak__bqa_pos_(rate_eval, tf):
    # Ar29 --> Cl29
    rate = 0.0

    # bqa+w
    rate += np.exp(  5.13026)

    rate_eval.Ar29__Cl29__weak__bqa_pos_ = rate

@numba.njit()
def Na31__Mg31__weak__wc12(rate_eval, tf):
    # Na31 --> Mg31
    rate = 0.0

    # wc12w
    rate += np.exp(  3.23128)

    rate_eval.Na31__Mg31__weak__wc12 = rate

@numba.njit()
def n_V60__V61(rate_eval, tf):
    # V60 + n --> V61
    rate = 0.0

    # rath 
    rate += np.exp(  28.1775 + -0.00165722*tf.T9i + 2.91277*tf.T913i + -18.632*tf.T913
                  + 1.44558*tf.T9 + -0.110532*tf.T953 + 5.03472*tf.lnT9)

    rate_eval.n_V60__V61 = rate

@numba.njit()
def p_Sc44__Ti45(rate_eval, tf):
    # Sc44 + p --> Ti45
    rate = 0.0

    # ths8r
    rate += np.exp(  35.1446 + -32.179*tf.T913i + 1.40668*tf.T913
                  + -2.02828*tf.T9 + 0.230326*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc44__Ti45 = rate

@numba.njit()
def n_V40__V41(rate_eval, tf):
    # V40 + n --> V41
    rate = 0.0

    # ths8r
    rate += np.exp(  10.0887 + 0.233884*tf.T913
                  + 0.137287*tf.T9 + -0.0140006*tf.T953)

    rate_eval.n_V40__V41 = rate

@numba.njit()
def B15__C15__weak__wc12(rate_eval, tf):
    # B15 --> C15
    rate = 0.0

    # wc12w
    rate += np.exp(  1.43227)

    rate_eval.B15__C15__weak__wc12 = rate

@numba.njit()
def Cl44__Ar44__weak__wc17(rate_eval, tf):
    # Cl44 --> Ar44
    rate = 0.0

    # wc17w
    rate += np.exp(  0.182846)

    rate_eval.Cl44__Ar44__weak__wc17 = rate

@numba.njit()
def He4_Ca33__p_Sc36(rate_eval, tf):
    # Ca33 + He4 --> p + Sc36
    rate = 0.0

    # ths8r
    rate += np.exp(  55.4681 + -75.9466*tf.T913i + -0.97384*tf.T913
                  + -0.392451*tf.T9 + 0.00701362*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ca33__p_Sc36 = rate

@numba.njit()
def Na33__Mg33__weak__wc12(rate_eval, tf):
    # Na33 --> Mg33
    rate = 0.0

    # wc12w
    rate += np.exp(  3.54551)

    rate_eval.Na33__Mg33__weak__wc12 = rate

@numba.njit()
def Ar44__K44__weak__wc12(rate_eval, tf):
    # Ar44 --> K44
    rate = 0.0

    # wc12w
    rate += np.exp(  -6.93459)

    rate_eval.Ar44__K44__weak__wc12 = rate

@numba.njit()
def p_V66__He4_Ti63(rate_eval, tf):
    # V66 + p --> He4 + Ti63
    rate = 0.0

    # rath 
    rate += np.exp(  134.089 + -6.7987*tf.T9i + 264.69*tf.T913i + -429.034*tf.T913
                  + 24.0723*tf.T9 + -1.30372*tf.T953 + 214.682*tf.lnT9)

    rate_eval.p_V66__He4_Ti63 = rate

@numba.njit()
def Sc60__n_n_n_Ti57__weak__mo03(rate_eval, tf):
    # Sc60 --> 3 n + Ti57
    rate = 0.0

    # mo03w
    rate += np.exp(  -0.114549)

    rate_eval.Sc60__n_n_n_Ti57__weak__mo03 = rate

@numba.njit()
def Cl31__S31__weak__wc12(rate_eval, tf):
    # Cl31 --> S31
    rate = 0.0

    # wc12w
    rate += np.exp(  1.52358)

    rate_eval.Cl31__S31__weak__wc12 = rate

@numba.njit()
def V53__Cr53__weak__wc12(rate_eval, tf):
    # V53 --> Cr53
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.8948)

    rate_eval.V53__Cr53__weak__wc12 = rate

@numba.njit()
def n_V39__He4_Sc36(rate_eval, tf):
    # V39 + n --> He4 + Sc36
    rate = 0.0

    # ths8r
    rate += np.exp(  14.9161 + 0.0786948*tf.T913
                  + 0.150463*tf.T9 + -0.0043423*tf.T953)

    rate_eval.n_V39__He4_Sc36 = rate

@numba.njit()
def V44__Ti44__weak__wc12(rate_eval, tf):
    # V44 --> Ti44
    rate = 0.0

    # wc12w
    rate += np.exp(  1.83171)

    rate_eval.V44__Ti44__weak__wc12 = rate

@numba.njit()
def Fe49__p_Cr48__weak__wc12(rate_eval, tf):
    # Fe49 --> p + Cr48
    rate = 0.0

    # wc12w
    rate += np.exp(  1.80409)

    rate_eval.Fe49__p_Cr48__weak__wc12 = rate

@numba.njit()
def n_Sc60__Sc61(rate_eval, tf):
    # Sc60 + n --> Sc61
    rate = 0.0

    # rath 
    rate += np.exp(  17.8433 + -0.0154682*tf.T9i + 1.93524*tf.T913i + -9.71256*tf.T913
                  + 0.672853*tf.T9 + -0.0559046*tf.T953 + 2.50982*tf.lnT9)

    rate_eval.n_Sc60__Sc61 = rate

@numba.njit()
def Mn63__n_Fe62__weak__mp17(rate_eval, tf):
    # Mn63 --> n + Fe62
    rate = 0.0

    # mp17w
    rate += np.exp(  -3.6807)

    rate_eval.Mn63__n_Fe62__weak__mp17 = rate

@numba.njit()
def Si37__P37__weak__wc12(rate_eval, tf):
    # Si37 --> P37
    rate = 0.0

    # wc12w
    rate += np.exp(  1.8551)

    rate_eval.Si37__P37__weak__wc12 = rate

@numba.njit()
def Al39__Si39__weak__wc17(rate_eval, tf):
    # Al39 --> Si39
    rate = 0.0

    # wc17w
    rate += np.exp(  -110.616)

    rate_eval.Al39__Si39__weak__wc17 = rate

@numba.njit()
def Fe76__Co76__weak__mo03(rate_eval, tf):
    # Fe76 --> Co76
    rate = 0.0

    # mo03w
    rate += np.exp(  0.831551)

    rate_eval.Fe76__Co76__weak__mo03 = rate

@numba.njit()
def He4_Na38__Al42(rate_eval, tf):
    # Na38 + He4 --> Al42
    rate = 0.0

    # rath 
    rate += np.exp(  -16.2006 + -2.66578*tf.T9i + -13.6236*tf.T913i + 21.7693*tf.T913
                  + -4.86348*tf.T9 + 0.3986*tf.T953 + 5.36186*tf.lnT9)

    rate_eval.He4_Na38__Al42 = rate

@numba.njit()
def Mg30__Al30__weak__wc12(rate_eval, tf):
    # Mg30 --> Al30
    rate = 0.0

    # wc12w
    rate += np.exp(  0.727112)

    rate_eval.Mg30__Al30__weak__wc12 = rate

@numba.njit()
def He4_Ar49__Ca53(rate_eval, tf):
    # Ar49 + He4 --> Ca53
    rate = 0.0

    # rath 
    rate += np.exp(  -856.258 + 13.6985*tf.T9i + -1485.99*tf.T913i + 2437.61*tf.T913
                  + -145.7*tf.T9 + 8.3569*tf.T953 + -1143.68*tf.lnT9)

    rate_eval.He4_Ar49__Ca53 = rate

@numba.njit()
def Al33__n_Si32__weak__wc12(rate_eval, tf):
    # Al33 --> n + Si32
    rate = 0.0

    # wc12w
    rate += np.exp(  0.345637)

    rate_eval.Al33__n_Si32__weak__wc12 = rate

@numba.njit()
def N19__O19__weak__wc12(rate_eval, tf):
    # N19 --> O19
    rate = 0.0

    # wc12w
    rate += np.exp(  0.182846)

    rate_eval.N19__O19__weak__wc12 = rate

@numba.njit()
def S38__Cl38__weak__wc12(rate_eval, tf):
    # S38 --> Cl38
    rate = 0.0

    # wc12w
    rate += np.exp(  -9.59666)

    rate_eval.S38__Cl38__weak__wc12 = rate

@numba.njit()
def He4_K46__Sc50(rate_eval, tf):
    # K46 + He4 --> Sc50
    rate = 0.0

    # rath 
    rate += np.exp(  -867.353 + 13.8141*tf.T9i + -1500.09*tf.T913i + 2464.55*tf.T913
                  + -147.906*tf.T9 + 8.52911*tf.T953 + -1154.49*tf.lnT9)

    rate_eval.He4_K46__Sc50 = rate

@numba.njit()
def He4_Sc50__n_V53(rate_eval, tf):
    # Sc50 + He4 --> n + V53
    rate = 0.0

    # rath 
    rate += np.exp(  -946.883 + 15.2309*tf.T9i + -1654.62*tf.T913i + 2716.37*tf.T913
                  + -162.381*tf.T9 + 9.32253*tf.T953 + -1273.94*tf.lnT9)

    rate_eval.He4_Sc50__n_V53 = rate

@numba.njit()
def n_Sc39__p_Ca39(rate_eval, tf):
    # Sc39 + n --> p + Ca39
    rate = 0.0

    # ths8r
    rate += np.exp(  20.1594 + -0.00924302*tf.T913
                  + 0.115322*tf.T9 + -0.00923487*tf.T953)

    rate_eval.n_Sc39__p_Ca39 = rate

@numba.njit()
def Mg31__n_Al30__weak__wc12(rate_eval, tf):
    # Mg31 --> n + Al30
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.98004)

    rate_eval.Mg31__n_Al30__weak__wc12 = rate

@numba.njit()
def P39__S39__weak__wc12(rate_eval, tf):
    # P39 --> S39
    rate = 0.0

    # wc12w
    rate += np.exp(  0.605348)

    rate_eval.P39__S39__weak__wc12 = rate

@numba.njit()
def n_Sc40__He4_K37(rate_eval, tf):
    # Sc40 + n --> He4 + K37
    rate = 0.0

    # ths8r
    rate += np.exp(  16.275 + 1.18245*tf.T913
                  + -0.167228*tf.T9 + 0.032039*tf.T953)

    rate_eval.n_Sc40__He4_K37 = rate

@numba.njit()
def n_Ca39__Ca40(rate_eval, tf):
    # Ca39 + n --> Ca40
    rate = 0.0

    # ths8r
    rate += np.exp(  9.33485 + 0.436603*tf.T913
                  + 0.098368*tf.T9 + -0.0226294*tf.T953)

    rate_eval.n_Ca39__Ca40 = rate

@numba.njit()
def n_Ne33__Ne34(rate_eval, tf):
    # Ne33 + n --> Ne34
    rate = 0.0

    # rath 
    rate += np.exp(  8.26217 + -0.0756096*tf.T9i + 5.4903*tf.T913i + -10.3076*tf.T913
                  + 0.941721*tf.T9 + -0.0522087*tf.T953 + 4.04993*tf.lnT9)

    rate_eval.n_Ne33__Ne34 = rate

@numba.njit()
def He4_O16__Ne20(rate_eval, tf):
    # O16 + He4 --> Ne20
    rate = 0.0

    # co10r
    rate += np.exp(  3.88571 + -10.3585*tf.T9i
                  + -1.5*tf.lnT9)
    # co10n
    rate += np.exp(  23.903 + -39.7262*tf.T913i + -0.210799*tf.T913
                  + 0.442879*tf.T9 + -0.0797753*tf.T953 + -0.666667*tf.lnT9)
    # co10r
    rate += np.exp(  9.50848 + -12.7643*tf.T9i + -3.65925*tf.T913
                  + 0.714224*tf.T9 + -0.00107508*tf.T953 + -1.5*tf.lnT9)

    rate_eval.He4_O16__Ne20 = rate

@numba.njit()
def p_Ar51__n_K51(rate_eval, tf):
    # Ar51 + p --> n + K51
    rate = 0.0

    # rath 
    rate += np.exp(  112.66 + -5.07903*tf.T9i + 188.923*tf.T913i + -306.335*tf.T913
                  + 16.6301*tf.T9 + -0.920564*tf.T953 + 154.037*tf.lnT9)

    rate_eval.p_Ar51__n_K51 = rate

@numba.njit()
def p_Cr67__Mn68(rate_eval, tf):
    # Cr67 + p --> Mn68
    rate = 0.0

    # rath 
    rate += np.exp(  140.73 + -6.98021*tf.T9i + 266.406*tf.T913i + -430.773*tf.T913
                  + 24.062*tf.T9 + -1.37118*tf.T953 + 214.705*tf.lnT9)

    rate_eval.p_Cr67__Mn68 = rate

@numba.njit()
def F30__n_n_n_Ne27__weak__mo03(rate_eval, tf):
    # F30 --> 3 n + Ne27
    rate = 0.0

    # mo03w
    rate += np.exp(  4.83116)

    rate_eval.F30__n_n_n_Ne27__weak__mo03 = rate

@numba.njit()
def p_P41__He4_Si38(rate_eval, tf):
    # P41 + p --> He4 + Si38
    rate = 0.0

    # rath 
    rate += np.exp(  87.3348 + -4.11289*tf.T9i + 153.444*tf.T913i + -251.853*tf.T913
                  + 13.1129*tf.T9 + -0.645636*tf.T953 + 127.134*tf.lnT9)

    rate_eval.p_P41__He4_Si38 = rate

@numba.njit()
def p_Mg34__n_Al34(rate_eval, tf):
    # Mg34 + p --> n + Al34
    rate = 0.0

    # rath 
    rate += np.exp(  80.1851 + -3.19651*tf.T9i + 114.427*tf.T913i + -191.793*tf.T913
                  + 10.4241*tf.T9 + -0.575376*tf.T953 + 96.1224*tf.lnT9)

    rate_eval.p_Mg34__n_Al34 = rate

@numba.njit()
def p_Na39__Mg40(rate_eval, tf):
    # Na39 + p --> Mg40
    rate = 0.0

    # rath 
    rate += np.exp(  71.929 + -3.23588*tf.T9i + 118.593*tf.T913i + -198.205*tf.T913
                  + 10.8172*tf.T9 + -0.594296*tf.T953 + 98.8098*tf.lnT9)

    rate_eval.p_Na39__Mg40 = rate

@numba.njit()
def Si22__Al22__weak__wc12(rate_eval, tf):
    # Si22 --> Al22
    rate = 0.0

    # wc12w
    rate += np.exp(  2.78828)

    rate_eval.Si22__Al22__weak__wc12 = rate

@numba.njit()
def Si39__P39__weak__wc17(rate_eval, tf):
    # Si39 --> P39
    rate = 0.0

    # wc17w
    rate += np.exp(  2.15288)

    rate_eval.Si39__P39__weak__wc17 = rate

@numba.njit()
def Al40__n_n_Si38__weak__mp17(rate_eval, tf):
    # Al40 --> n + n + Si38
    rate = 0.0

    # mp17w
    rate += np.exp(  4.20318)

    rate_eval.Al40__n_n_Si38__weak__mp17 = rate

@numba.njit()
def He4_Ca56__n_Ti59(rate_eval, tf):
    # Ca56 + He4 --> n + Ti59
    rate = 0.0

    # rath 
    rate += np.exp(  -970.064 + 15.5409*tf.T9i + -1687.61*tf.T913i + 2777.74*tf.T913
                  + -166.087*tf.T9 + 9.53807*tf.T953 + -1302.65*tf.lnT9)

    rate_eval.He4_Ca56__n_Ti59 = rate

@numba.njit()
def p_Be10__He4_Li7(rate_eval, tf):
    # Be10 + p --> He4 + Li7
    rate = 0.0

    #  wagn
    rate += np.exp(  26.2245 + -1.76998e-12*tf.T9i + -10.39*tf.T913i + -8.45661e-10*tf.T913
                  + 9.17492e-11*tf.T9 + -8.2685e-12*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Be10__He4_Li7 = rate

@numba.njit()
def p_Mg35__Al36(rate_eval, tf):
    # Mg35 + p --> Al36
    rate = 0.0

    # rath 
    rate += np.exp(  70.1535 + -3.24168*tf.T9i + 116.314*tf.T913i + -194.254*tf.T913
                  + 10.5695*tf.T9 + -0.58179*tf.T953 + 97.41*tf.lnT9)

    rate_eval.p_Mg35__Al36 = rate

@numba.njit()
def Cr45__V45__weak__wc12(rate_eval, tf):
    # Cr45 --> V45
    rate = 0.0

    # wc12w
    rate += np.exp(  2.01042)

    rate_eval.Cr45__V45__weak__wc12 = rate

@numba.njit()
def p_Ar50__K51(rate_eval, tf):
    # Ar50 + p --> K51
    rate = 0.0

    # rath 
    rate += np.exp(  99.5036 + -5.03269*tf.T9i + 186.652*tf.T913i + -301.692*tf.T913
                  + 16.3445*tf.T9 + -0.904892*tf.T953 + 152.138*tf.lnT9)

    rate_eval.p_Ar50__K51 = rate

@numba.njit()
def K50__n_n_Ca48__weak__mp17(rate_eval, tf):
    # K50 --> n + n + Ca48
    rate = 0.0

    # mp17w
    rate += np.exp(  -4.22091)

    rate_eval.K50__n_n_Ca48__weak__mp17 = rate

@numba.njit()
def Sc60__Ti60__weak__mo03(rate_eval, tf):
    # Sc60 --> Ti60
    rate = 0.0

    # mo03w
    rate += np.exp(  4.39531)

    rate_eval.Sc60__Ti60__weak__mo03 = rate

@numba.njit()
def p_Ca47__Sc48(rate_eval, tf):
    # Ca47 + p --> Sc48
    rate = 0.0

    # ths8r
    rate += np.exp(  29.5755 + -31.164*tf.T913i + -2.03245*tf.T913
                  + 0.0494826*tf.T9 + 0.00201831*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Ca47__Sc48 = rate

@numba.njit()
def N18__He4_C14__weak__wc12(rate_eval, tf):
    # N18 --> He4 + C14
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.99221)

    rate_eval.N18__He4_C14__weak__wc12 = rate

@numba.njit()
def He4_Cr68__Fe72(rate_eval, tf):
    # Cr68 + He4 --> Fe72
    rate = 0.0

    # rath 
    rate += np.exp(  -1169.22 + 24.1749*tf.T9i + -2401.32*tf.T913i + 3708.37*tf.T913
                  + -210.057*tf.T9 + 11.5796*tf.T953 + -1798.97*tf.lnT9)

    rate_eval.He4_Cr68__Fe72 = rate

@numba.njit()
def N20__O20__weak__wc12(rate_eval, tf):
    # N20 --> O20
    rate = 0.0

    # wc12w
    rate += np.exp(  1.06822)

    rate_eval.N20__O20__weak__wc12 = rate

@numba.njit()
def p_Cl44__He4_S41(rate_eval, tf):
    # Cl44 + p --> He4 + S41
    rate = 0.0

    # rath 
    rate += np.exp(  79.6904 + -4.54538*tf.T9i + 164.936*tf.T913i + -256.875*tf.T913
                  + 13.2238*tf.T9 + -0.68518*tf.T953 + 134.021*tf.lnT9)

    rate_eval.p_Cl44__He4_S41 = rate

@numba.njit()
def Ar54__K54__weak__mo03(rate_eval, tf):
    # Ar54 --> K54
    rate = 0.0

    # mo03w
    rate += np.exp(  -110.73)

    rate_eval.Ar54__K54__weak__mo03 = rate

@numba.njit()
def n_Ca38__He4_Ar35(rate_eval, tf):
    # Ca38 + n --> He4 + Ar35
    rate = 0.0

    # ths8r
    rate += np.exp(  17.3855 + 0.246287*tf.T913
                  + -0.00159747*tf.T9 + 0.0158206*tf.T953)

    rate_eval.n_Ca38__He4_Ar35 = rate

@numba.njit()
def p_Sc54__He4_Ca51(rate_eval, tf):
    # Sc54 + p --> He4 + Ca51
    rate = 0.0

    # rath 
    rate += np.exp(  126.885 + -5.78947*tf.T9i + 219.01*tf.T913i + -365.024*tf.T913
                  + 20.9429*tf.T9 + -1.17926*tf.T953 + 180.046*tf.lnT9)

    rate_eval.p_Sc54__He4_Ca51 = rate

@numba.njit()
def n_Be9__Be10(rate_eval, tf):
    # Be9 + n --> Be10
    rate = 0.0

    # wa19r
    rate += np.exp(  12.0471 + -7.087*tf.T9i
                  + -1.5*tf.lnT9)
    # wa19n
    rate += np.exp(  4.275 + 0.000436012*tf.T9i + -0.272382*tf.T913i + 4.15476*tf.T913
                  + -0.397072*tf.T9 + 0.0165704*tf.T953 + -0.672889*tf.lnT9)

    rate_eval.n_Be9__Be10 = rate

@numba.njit()
def He4_Ne21__Mg25(rate_eval, tf):
    # Ne21 + He4 --> Mg25
    rate = 0.0

    # cf88r
    rate += np.exp(  26.2429 + -22.049*tf.T9i + -29.4583*tf.T913
                  + 14.6328*tf.T9 + -3.47392*tf.T953 + -1.5*tf.lnT9)
    # cf88n
    rate += np.exp(  36.6927 + -46.89*tf.T913i + -0.72642*tf.T913
                  + -0.76406*tf.T9 + 0.0797483*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ne21__Mg25 = rate

@numba.njit()
def p_Cr70__He4_V67(rate_eval, tf):
    # Cr70 + p --> He4 + V67
    rate = 0.0

    # rath 
    rate += np.exp(  -671.303 + 10.2506*tf.T9i + -1140.62*tf.T913i + 1872.85*tf.T913
                  + -112.439*tf.T9 + 6.50232*tf.T953 + -871.51*tf.lnT9)

    rate_eval.p_Cr70__He4_V67 = rate

@numba.njit()
def p_Mg40__Al41(rate_eval, tf):
    # Mg40 + p --> Al41
    rate = 0.0

    # rath 
    rate += np.exp(  70.6493 + -3.44716*tf.T9i + 124.619*tf.T913i + -204.267*tf.T913
                  + 10.945*tf.T9 + -0.596085*tf.T953 + 102.99*tf.lnT9)

    rate_eval.p_Mg40__Al41 = rate

@numba.njit()
def p_Ti55__He4_Sc52(rate_eval, tf):
    # Ti55 + p --> He4 + Sc52
    rate = 0.0

    # rath 
    rate += np.exp(  85.4954 + -5.88983*tf.T9i + 211.568*tf.T913i + -315.992*tf.T913
                  + 16.3333*tf.T9 + -0.883095*tf.T953 + 167.954*tf.lnT9)

    rate_eval.p_Ti55__He4_Sc52 = rate

@numba.njit()
def Ar51__n_n_K49__weak__mp17(rate_eval, tf):
    # Ar51 --> n + n + K49
    rate = 0.0

    # mp17w
    rate += np.exp(  0.561344)

    rate_eval.Ar51__n_n_K49__weak__mp17 = rate

@numba.njit()
def p_Mg33__Al34(rate_eval, tf):
    # Mg33 + p --> Al34
    rate = 0.0

    # rath 
    rate += np.exp(  67.2672 + -3.1467*tf.T9i + 111.773*tf.T913i + -186.551*tf.T913
                  + 10.0635*tf.T9 + -0.549775*tf.T953 + 93.8802*tf.lnT9)

    rate_eval.p_Mg33__Al34 = rate

@numba.njit()
def p_Al29__Si30(rate_eval, tf):
    # Al29 + p --> Si30
    rate = 0.0

    # rath 
    rate += np.exp(  67.9653 + -3.10598*tf.T9i + 107.905*tf.T913i + -181.56*tf.T913
                  + 9.96524*tf.T9 + -0.56986*tf.T953 + 91.557*tf.lnT9)

    rate_eval.p_Al29__Si30 = rate

@numba.njit()
def p_Mn56__n_Fe56(rate_eval, tf):
    # Mn56 + p --> n + Fe56
    rate = 0.0

    # rath 
    rate += np.exp(  135.805 + -6.57489*tf.T9i + 244.833*tf.T913i + -394.296*tf.T913
                  + 21.8589*tf.T9 + -1.24691*tf.T953 + 198.424*tf.lnT9)

    rate_eval.p_Mn56__n_Fe56 = rate

@numba.njit()
def n_Sc47__Sc48(rate_eval, tf):
    # Sc47 + n --> Sc48
    rate = 0.0

    # rath 
    rate += np.exp(  14.3286 + -0.0127821*tf.T9i + 0.297987*tf.T913i + 0.438296*tf.T913
                  + 0.0468739*tf.T9 + -0.0255895*tf.T953 + -0.227277*tf.lnT9)

    rate_eval.n_Sc47__Sc48 = rate

@numba.njit()
def p_V59__He4_Ti56(rate_eval, tf):
    # V59 + p --> He4 + Ti56
    rate = 0.0

    # rath 
    rate += np.exp(  138.654 + -6.47257*tf.T9i + 249.839*tf.T913i + -412.755*tf.T913
                  + 23.3953*tf.T9 + -1.2765*tf.T953 + 204.165*tf.lnT9)

    rate_eval.p_V59__He4_Ti56 = rate

@numba.njit()
def Na37__n_n_Mg35__weak__mp17(rate_eval, tf):
    # Na37 --> n + n + Mg35
    rate = 0.0

    # mp17w
    rate += np.exp(  5.33343)

    rate_eval.Na37__n_n_Mg35__weak__mp17 = rate

@numba.njit()
def p_Ar49__He4_Cl46(rate_eval, tf):
    # Ar49 + p --> He4 + Cl46
    rate = 0.0

    # rath 
    rate += np.exp(  81.1482 + -5.01333*tf.T9i + 186.954*tf.T913i + -286.425*tf.T913
                  + 14.7215*tf.T9 + -0.760791*tf.T953 + 150.869*tf.lnT9)

    rate_eval.p_Ar49__He4_Cl46 = rate

@numba.njit()
def F28__Ne28__weak__mo03(rate_eval, tf):
    # F28 --> Ne28
    rate = 0.0

    # mo03w
    rate += np.exp(  5.26828)

    rate_eval.F28__Ne28__weak__mo03 = rate

@numba.njit()
def Mg35__Al35__weak__wc17(rate_eval, tf):
    # Mg35 --> Al35
    rate = 0.0

    # wc17w
    rate += np.exp(  1.40115)

    rate_eval.Mg35__Al35__weak__wc17 = rate

@numba.njit()
def He4_K52__Sc56(rate_eval, tf):
    # K52 + He4 --> Sc56
    rate = 0.0

    # rath 
    rate += np.exp(  -918.503 + 14.5961*tf.T9i + -1584.2*tf.T913i + 2604.95*tf.T913
                  + -155.772*tf.T9 + 8.93662*tf.T953 + -1221.6*tf.lnT9)

    rate_eval.He4_K52__Sc56 = rate

@numba.njit()
def p_Al32__Si33(rate_eval, tf):
    # Al32 + p --> Si33
    rate = 0.0

    # rath 
    rate += np.exp(  69.5437 + -3.26337*tf.T9i + 115.138*tf.T913i + -191.33*tf.T913
                  + 10.1373*tf.T9 + -0.546421*tf.T953 + 96.8591*tf.lnT9)

    rate_eval.p_Al32__Si33 = rate

@numba.njit()
def Ne23__Na23__weak__wc12(rate_eval, tf):
    # Ne23 --> Na23
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.98282)

    rate_eval.Ne23__Na23__weak__wc12 = rate

@numba.njit()
def Mn45__Cr45__weak__bqa_pos_(rate_eval, tf):
    # Mn45 --> Cr45
    rate = 0.0

    # bqa+w
    rate += np.exp(  3.63982)

    rate_eval.Mn45__Cr45__weak__bqa_pos_ = rate

@numba.njit()
def Na33__n_n_Mg31__weak__wc12(rate_eval, tf):
    # Na33 --> n + n + Mg31
    rate = 0.0

    # wc12w
    rate += np.exp(  2.42158)

    rate_eval.Na33__n_n_Mg31__weak__wc12 = rate

@numba.njit()
def p_Na19__Mg20(rate_eval, tf):
    # Na19 + p --> Mg20
    rate = 0.0

    # ths8r
    rate += np.exp(  37.9931 + -20.709*tf.T913i + -15.3107*tf.T913
                  + 1.56476*tf.T9 + -0.0774232*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Na19__Mg20 = rate

@numba.njit()
def Mg20__Na20__weak__wc12(rate_eval, tf):
    # Mg20 --> Na20
    rate = 0.0

    # wc12w
    rate += np.exp(  1.71787)

    rate_eval.Mg20__Na20__weak__wc12 = rate

@numba.njit()
def Ne26__Na26__weak__wc12(rate_eval, tf):
    # Ne26 --> Na26
    rate = 0.0

    # wc12w
    rate += np.exp(  1.25674)

    rate_eval.Ne26__Na26__weak__wc12 = rate

@numba.njit()
def Ti60__V60__weak__wc17(rate_eval, tf):
    # Ti60 --> V60
    rate = 0.0

    # wc17w
    rate += np.exp(  3.41198)

    rate_eval.Ti60__V60__weak__wc17 = rate

@numba.njit()
def p_Fe62__Co63(rate_eval, tf):
    # Fe62 + p --> Co63
    rate = 0.0

    # rath 
    rate += np.exp(  144.207 + -7.11595*tf.T9i + 270.02*tf.T913i + -436.697*tf.T913
                  + 24.393*tf.T9 + -1.42312*tf.T953 + 218.254*tf.lnT9)

    rate_eval.p_Fe62__Co63 = rate

@numba.njit()
def p_P39__S40(rate_eval, tf):
    # P39 + p --> S40
    rate = 0.0

    # rath 
    rate += np.exp(  83.5043 + -3.96136*tf.T9i + 143.616*tf.T913i + -237.974*tf.T913
                  + 13.0387*tf.T9 + -0.728036*tf.T953 + 119.346*tf.lnT9)

    rate_eval.p_P39__S40 = rate

@numba.njit()
def K56__n_n_Ca54__weak__mp17(rate_eval, tf):
    # K56 --> n + n + Ca54
    rate = 0.0

    # mp17w
    rate += np.exp(  4.39959)

    rate_eval.K56__n_n_Ca54__weak__mp17 = rate

@numba.njit()
def Cl38__Ar38__weak__wc12(rate_eval, tf):
    # Cl38 --> Ar38
    rate = 0.0

    # wc12w
    rate += np.exp(  -8.07627)

    rate_eval.Cl38__Ar38__weak__wc12 = rate

@numba.njit()
def He4_Na32__Al36(rate_eval, tf):
    # Na32 + He4 --> Al36
    rate = 0.0

    # rath 
    rate += np.exp(  -14.1339 + -2.34509*tf.T9i + -22.2583*tf.T913i + 27.7717*tf.T913
                  + -4.76346*tf.T9 + 0.373372*tf.T953 + 0.561282*tf.lnT9)

    rate_eval.He4_Na32__Al36 = rate

@numba.njit()
def Sc55__Ti55__weak__wc12(rate_eval, tf):
    # Sc55 --> Ti55
    rate = 0.0

    # wc12w
    rate += np.exp(  1.79057)

    rate_eval.Sc55__Ti55__weak__wc12 = rate

@numba.njit()
def He4_P30__Cl34(rate_eval, tf):
    # P30 + He4 --> Cl34
    rate = 0.0

    # ths8r
    rate += np.exp(  45.3321 + -62.4643*tf.T913i + -3.19028*tf.T913
                  + -0.832633*tf.T9 + 0.0987525*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_P30__Cl34 = rate

@numba.njit()
def p_F26__He4_O23(rate_eval, tf):
    # F26 + p --> He4 + O23
    rate = 0.0

    # rpsmr
    rate += np.exp(  58.9707 + -2.30723*tf.T9i + 79.9764*tf.T913i + -137.227*tf.T913
                  + 7.46566*tf.T9 + -0.412252*tf.T953 + 68.8176*tf.lnT9)

    rate_eval.p_F26__He4_O23 = rate

@numba.njit()
def F28__n_Ne27__weak__mp17(rate_eval, tf):
    # F28 --> n + Ne27
    rate = 0.0

    # mp17w
    rate += np.exp(  4.9318)

    rate_eval.F28__n_Ne27__weak__mp17 = rate

@numba.njit()
def n_S32__He4_Si29(rate_eval, tf):
    # S32 + n --> He4 + Si29
    rate = 0.0

    # ths8r
    rate += np.exp(  -0.947538 + 9.48125*tf.T913
                  + 0.4472*tf.T9 + -0.119237*tf.T953)

    rate_eval.n_S32__He4_Si29 = rate

@numba.njit()
def n_Si37__Si38(rate_eval, tf):
    # Si37 + n --> Si38
    rate = 0.0

    # rath 
    rate += np.exp(  10.3304 + -0.0311147*tf.T9i + 1.70855*tf.T913i + -3.00677*tf.T913
                  + 0.335432*tf.T9 + -0.0341001*tf.T953 + 0.941376*tf.lnT9)

    rate_eval.n_Si37__Si38 = rate

@numba.njit()
def Ca56__Sc56__weak__wc17(rate_eval, tf):
    # Ca56 --> Sc56
    rate = 0.0

    # wc17w
    rate += np.exp(  4.10253)

    rate_eval.Ca56__Sc56__weak__wc17 = rate

@numba.njit()
def p_S48__Cl49(rate_eval, tf):
    # S48 + p --> Cl49
    rate = 0.0

    # rath 
    rate += np.exp(  93.8403 + -4.5871*tf.T9i + 171.07*tf.T913i + -278.699*tf.T913
                  + 15.0657*tf.T9 + -0.82435*tf.T953 + 140.091*tf.lnT9)

    rate_eval.p_S48__Cl49 = rate

@numba.njit()
def Cl42__Ar42__weak__wc12(rate_eval, tf):
    # Cl42 --> Ar42
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.28344)

    rate_eval.Cl42__Ar42__weak__wc12 = rate

@numba.njit()
def p_Sc42__He4_Ca39(rate_eval, tf):
    # Sc42 + p --> He4 + Ca39
    rate = 0.0

    # ths8r
    rate += np.exp(  -87.527 + -32.1676*tf.T913i + 127.281*tf.T913
                  + -29.4503*tf.T9 + 3.00671*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.p_Sc42__He4_Ca39 = rate

@numba.njit()
def n_Sc38__He4_K35(rate_eval, tf):
    # Sc38 + n --> He4 + K35
    rate = 0.0

    # ths8r
    rate += np.exp(  11.8478 + 4.29506*tf.T913
                  + -1.39225*tf.T9 + 0.209719*tf.T953)

    rate_eval.n_Sc38__He4_K35 = rate

@numba.njit()
def n_Al42__Al43(rate_eval, tf):
    # Al42 + n --> Al43
    rate = 0.0

    # rath 
    rate += np.exp(  130.403 + -11.4607*tf.T9i + 348.243*tf.T913i + -498.163*tf.T913
                  + 27.9721*tf.T9 + -1.5933*tf.T953 + 251.581*tf.lnT9)

    rate_eval.n_Al42__Al43 = rate

@numba.njit()
def O19__F19__weak__wc12(rate_eval, tf):
    # O19 --> F19
    rate = 0.0

    # wc12w
    rate += np.exp(  -3.65864)

    rate_eval.O19__F19__weak__wc12 = rate

@numba.njit()
def n_Na28__Na29(rate_eval, tf):
    # Na28 + n --> Na29
    rate = 0.0

    # rath 
    rate += np.exp(  13.9669 + -0.0420769*tf.T9i + 3.2661*tf.T913i + -7.21616*tf.T913
                  + 0.443974*tf.T9 + -0.026085*tf.T953 + 2.6443*tf.lnT9)

    rate_eval.n_Na28__Na29 = rate

@numba.njit()
def p_Si38__He4_Al35(rate_eval, tf):
    # Si38 + p --> He4 + Al35
    rate = 0.0

    # rath 
    rate += np.exp(  50.6847 + -3.83788*tf.T9i + 145.315*tf.T913i + -209.296*tf.T913
                  + 9.08316*tf.T9 + -0.403199*tf.T953 + 118.063*tf.lnT9)

    rate_eval.p_Si38__He4_Al35 = rate

@numba.njit()
def n_Al25__He4_Na22(rate_eval, tf):
    # Al25 + n --> He4 + Na22
    rate = 0.0

    # ths8r
    rate += np.exp(  8.93927 + 2.92382*tf.T913
                  + 0.706669*tf.T9 + -0.0950292*tf.T953)

    rate_eval.n_Al25__He4_Na22 = rate

@numba.njit()
def p_F30__Ne31(rate_eval, tf):
    # F30 + p --> Ne31
    rate = 0.0

    # rpsmr
    rate += np.exp(  49.2844 + -2.42098*tf.T9i + 81.2665*tf.T913i + -134.408*tf.T913
                  + 7.15063*tf.T9 + -0.390877*tf.T953 + 68.339*tf.lnT9)

    rate_eval.p_F30__Ne31 = rate

@numba.njit()
def N22__n_O21__weak__wc17(rate_eval, tf):
    # N22 --> n + O21
    rate = 0.0

    # wc17w
    rate += np.exp(  2.43685)

    rate_eval.N22__n_O21__weak__wc17 = rate

@numba.njit()
def Na29__Mg29__weak__wc12(rate_eval, tf):
    # Na29 --> Mg29
    rate = 0.0

    # wc12w
    rate += np.exp(  2.49473)

    rate_eval.Na29__Mg29__weak__wc12 = rate

@numba.njit()
def He4_K37__Sc41(rate_eval, tf):
    # K37 + He4 --> Sc41
    rate = 0.0

    # ths8r
    rate += np.exp(  50.601 + -73.6776*tf.T913i + -5.3733*tf.T913
                  + 0.685776*tf.T9 + -0.123735*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K37__Sc41 = rate

@numba.njit()
def n_K34__p_Ar34(rate_eval, tf):
    # K34 + n --> p + Ar34
    rate = 0.0

    # ths8r
    rate += np.exp(  19.131 + 1.05197*tf.T913
                  + -0.0985354*tf.T9 + 0.00694168*tf.T953)

    rate_eval.n_K34__p_Ar34 = rate

@numba.njit()
def He4_Si45__n_S48(rate_eval, tf):
    # Si45 + He4 --> n + S48
    rate = 0.0

    # rath 
    rate += np.exp(  -11.1799 + -3.44751*tf.T9i + -11.1891*tf.T913i + 21.0637*tf.T913
                  + -5.20621*tf.T9 + 0.421932*tf.T953 + 8.6538*tf.lnT9)

    rate_eval.He4_Si45__n_S48 = rate

@numba.njit()
def He4_Fe69__n_Ni72(rate_eval, tf):
    # Fe69 + He4 --> n + Ni72
    rate = 0.0

    # rath 
    rate += np.exp(  -1232.98 + 25.6987*tf.T9i + -2551.59*tf.T913i + 3940.24*tf.T913
                  + -223.159*tf.T9 + 12.338*tf.T953 + -1911.74*tf.lnT9)

    rate_eval.He4_Fe69__n_Ni72 = rate

@numba.njit()
def Mn72__Fe72__weak__mo03(rate_eval, tf):
    # Mn72 --> Fe72
    rate = 0.0

    # mo03w
    rate += np.exp(  4.40545)

    rate_eval.Mn72__Fe72__weak__mo03 = rate

@numba.njit()
def He4_S40__Ar44(rate_eval, tf):
    # S40 + He4 --> Ar44
    rate = 0.0

    # rath 
    rate += np.exp(  -339.52 + 1.86226*tf.T9i + -483.188*tf.T913i + 850.68*tf.T913
                  + -56.2165*tf.T9 + 3.4106*tf.T953 + -373.114*tf.lnT9)

    rate_eval.He4_S40__Ar44 = rate

@numba.njit()
def n_P28__He4_Al25(rate_eval, tf):
    # P28 + n --> He4 + Al25
    rate = 0.0

    # ths8r
    rate += np.exp(  16.5385 + 0.960875*tf.T913
                  + -0.0874064*tf.T9 + 0.0120785*tf.T953)

    rate_eval.n_P28__He4_Al25 = rate

@numba.njit()
def p_O23__F24(rate_eval, tf):
    # O23 + p --> F24
    rate = 0.0

    # rpsmr
    rate += np.exp(  47.3567 + -1.99863*tf.T9i + 67.7655*tf.T913i + -117.54*tf.T913
                  + 6.40951*tf.T9 + -0.355218*tf.T953 + 58.9948*tf.lnT9)

    rate_eval.p_O23__F24 = rate

@numba.njit()
def K49__n_Ca48__weak__wc12(rate_eval, tf):
    # K49 --> n + Ca48
    rate = 0.0

    # wc12w
    rate += np.exp(  -0.748447)

    rate_eval.K49__n_Ca48__weak__wc12 = rate

@numba.njit()
def p_Fe75__Co76(rate_eval, tf):
    # Fe75 + p --> Co76
    rate = 0.0

    # rath 
    rate += np.exp(  152.238 + -7.7261*tf.T9i + 296.175*tf.T913i + -476.009*tf.T913
                  + 26.7057*tf.T9 + -1.52336*tf.T953 + 237.227*tf.lnT9)

    rate_eval.p_Fe75__Co76 = rate

@numba.njit()
def O27__n_F26__weak__mp17(rate_eval, tf):
    # O27 --> n + F26
    rate = 0.0

    # mp17w
    rate += np.exp(  3.95097)

    rate_eval.O27__n_F26__weak__mp17 = rate

@numba.njit()
def Ne33__Na33__weak__mo03(rate_eval, tf):
    # Ne33 --> Na33
    rate = 0.0

    # mo03w
    rate += np.exp(  -33.0736)

    rate_eval.Ne33__Na33__weak__mo03 = rate

@numba.njit()
def p_Mn65__Fe66(rate_eval, tf):
    # Mn65 + p --> Fe66
    rate = 0.0

    # rath 
    rate += np.exp(  146.201 + -7.09126*tf.T9i + 271.39*tf.T913i + -441.394*tf.T913
                  + 24.6343*tf.T9 + -1.40243*tf.T953 + 219.544*tf.lnT9)

    rate_eval.p_Mn65__Fe66 = rate

@numba.njit()
def Na28__n_Mg27__weak__wc12(rate_eval, tf):
    # Na28 --> n + Mg27
    rate = 0.0

    # wc12w
    rate += np.exp(  -2.02638)

    rate_eval.Na28__n_Mg27__weak__wc12 = rate

@numba.njit()
def Ti52__V52__weak__wc12(rate_eval, tf):
    # Ti52 --> V52
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.99149)

    rate_eval.Ti52__V52__weak__wc12 = rate

@numba.njit()
def He4_Mn50__p_Fe53(rate_eval, tf):
    # Mn50 + He4 --> p + Fe53
    rate = 0.0

    # ths8r
    rate += np.exp(  62.6721 + -89.2309*tf.T913i + -1.4758*tf.T913
                  + -0.437831*tf.T9 + -0.00354594*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Mn50__p_Fe53 = rate

@numba.njit()
def Fe45__Mn45__weak__wc17(rate_eval, tf):
    # Fe45 --> Mn45
    rate = 0.0

    # wc17w
    rate += np.exp(  5.59269)

    rate_eval.Fe45__Mn45__weak__wc17 = rate

@numba.njit()
def Al35__Si35__weak__wc12(rate_eval, tf):
    # Al35 --> Si35
    rate = 0.0

    # wc12w
    rate += np.exp(  2.4469)

    rate_eval.Al35__Si35__weak__wc12 = rate

@numba.njit()
def F17__O17__weak__wc12(rate_eval, tf):
    # F17 --> O17
    rate = 0.0

    # wc12w
    rate += np.exp(  -4.53318)

    rate_eval.F17__O17__weak__wc12 = rate

@numba.njit()
def n_Mn66__Mn67(rate_eval, tf):
    # Mn66 + n --> Mn67
    rate = 0.0

    # rath 
    rate += np.exp(  6.69214 + 0.344296*tf.T9i + -29.2465*tf.T913i + 37.7918*tf.T913
                  + -1.49565*tf.T9 + 0.0364966*tf.T953 + -22.1649*tf.lnT9)

    rate_eval.n_Mn66__Mn67 = rate

@numba.njit()
def Al40__Si40__weak__mo03(rate_eval, tf):
    # Al40 --> Si40
    rate = 0.0

    # mo03w
    rate += np.exp(  -109.904)

    rate_eval.Al40__Si40__weak__mo03 = rate

@numba.njit()
def F26__Ne26__weak__wc12(rate_eval, tf):
    # F26 --> Ne26
    rate = 0.0

    # wc12w
    rate += np.exp(  4.15258)

    rate_eval.F26__Ne26__weak__wc12 = rate

@numba.njit()
def n_Ar49__Ar50(rate_eval, tf):
    # Ar49 + n --> Ar50
    rate = 0.0

    # rath 
    rate += np.exp(  22.3457 + -0.103097*tf.T9i + 10.2177*tf.T913i + -23.5363*tf.T913
                  + 1.54899*tf.T9 + -0.107143*tf.T953 + 9.48962*tf.lnT9)

    rate_eval.n_Ar49__Ar50 = rate

@numba.njit()
def Cl47__Ar47__weak__wc17(rate_eval, tf):
    # Cl47 --> Ar47
    rate = 0.0

    # wc17w
    rate += np.exp(  -113.203)

    rate_eval.Cl47__Ar47__weak__wc17 = rate

@numba.njit()
def p_Cr61__n_Mn61(rate_eval, tf):
    # Cr61 + p --> n + Mn61
    rate = 0.0

    # rath 
    rate += np.exp(  141.771 + -6.68199*tf.T9i + 252.503*tf.T913i + -406.378*tf.T913
                  + 22.1737*tf.T9 + -1.2306*tf.T953 + 204.014*tf.lnT9)

    rate_eval.p_Cr61__n_Mn61 = rate

@numba.njit()
def p_Na35__Mg36(rate_eval, tf):
    # Na35 + p --> Mg36
    rate = 0.0

    # rath 
    rate += np.exp(  68.0438 + -3.06456*tf.T9i + 110.464*tf.T913i + -185.444*tf.T913
                  + 10.1445*tf.T9 + -0.56138*tf.T953 + 92.6532*tf.lnT9)

    rate_eval.p_Na35__Mg36 = rate

@numba.njit()
def n_O20__O21(rate_eval, tf):
    # O20 + n --> O21
    rate = 0.0

    # wiesr
    rate += np.exp(  7.10661 + -1.1501e-12*tf.T9i + 1.51183e-10*tf.T913i + -4.99989e-10*tf.T913
                  + 5.02412e-11*tf.T9 + -4.21356e-12*tf.T953 + 1.0*tf.lnT9)

    rate_eval.n_O20__O21 = rate

@numba.njit()
def He4_Ar32__p_K35(rate_eval, tf):
    # Ar32 + He4 --> p + K35
    rate = 0.0

    # ths8r
    rate += np.exp(  53.4423 + -70.713*tf.T913i + 0.311198*tf.T913
                  + -0.858287*tf.T9 + 0.0608499*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_Ar32__p_K35 = rate

@numba.njit()
def Sc36__Ca36__weak__bqa_pos_(rate_eval, tf):
    # Sc36 --> Ca36
    rate = 0.0

    # bqa+w
    rate += np.exp(  4.36649)

    rate_eval.Sc36__Ca36__weak__bqa_pos_ = rate

@numba.njit()
def n_Mg37__Mg38(rate_eval, tf):
    # Mg37 + n --> Mg38
    rate = 0.0

    # rath 
    rate += np.exp(  15.1523 + -0.0694815*tf.T9i + 6.51684*tf.T913i + -16.875*tf.T913
                  + 1.45713*tf.T9 + -0.0900118*tf.T953 + 6.08986*tf.lnT9)

    rate_eval.n_Mg37__Mg38 = rate

@numba.njit()
def Al36__n_Si35__weak__mp17(rate_eval, tf):
    # Al36 --> n + Si35
    rate = 0.0

    # mp17w
    rate += np.exp(  -0.165842)

    rate_eval.Al36__n_Si35__weak__mp17 = rate

@numba.njit()
def He4_K56__Sc60(rate_eval, tf):
    # K56 + He4 --> Sc60
    rate = 0.0

    # rath 
    rate += np.exp(  -949.745 + 15.0384*tf.T9i + -1633.31*tf.T913i + 2689.59*tf.T913
                  + -160.846*tf.T9 + 9.23252*tf.T953 + -1261.24*tf.lnT9)

    rate_eval.He4_K56__Sc60 = rate

@numba.njit()
def p_Na30__n_Mg30(rate_eval, tf):
    # Na30 + p --> n + Mg30
    rate = 0.0

    # rath 
    rate += np.exp(  73.6567 + -2.83869*tf.T9i + 100.34*tf.T913i + -169.454*tf.T913
                  + 9.14256*tf.T9 + -0.506229*tf.T953 + 85.145*tf.lnT9)

    rate_eval.p_Na30__n_Mg30 = rate

@numba.njit()
def K34__Ar34__weak__bqa_pos_(rate_eval, tf):
    # K34 --> Ar34
    rate = 0.0

    # bqa+w
    rate += np.exp(  2.79646)

    rate_eval.K34__Ar34__weak__bqa_pos_ = rate

@numba.njit()
def K42__Ca42__weak__wc12(rate_eval, tf):
    # K42 --> Ca42
    rate = 0.0

    # wc12w
    rate += np.exp(  -11.0675)

    rate_eval.K42__Ca42__weak__wc12 = rate

@numba.njit()
def Na37__n_Mg36__weak__mp17(rate_eval, tf):
    # Na37 --> n + Mg36
    rate = 0.0

    # mp17w
    rate += np.exp(  5.25339)

    rate_eval.Na37__n_Mg36__weak__mp17 = rate

@numba.njit()
def n_S29__S30(rate_eval, tf):
    # S29 + n --> S30
    rate = 0.0

    # ths8r
    rate += np.exp(  8.4841 + 1.86133*tf.T913
                  + -0.226269*tf.T9 + 0.019372*tf.T953)

    rate_eval.n_S29__S30 = rate

@numba.njit()
def n_Cr48__He4_Ti45(rate_eval, tf):
    # Cr48 + n --> He4 + Ti45
    rate = 0.0

    # ths8r
    rate += np.exp(  -27.4028 + 29.3634*tf.T913
                  + -2.63599*tf.T9 + 0.159116*tf.T953)

    rate_eval.n_Cr48__He4_Ti45 = rate

@numba.njit()
def Cl30__S30__weak__bqa_pos_(rate_eval, tf):
    # Cl30 --> S30
    rate = 0.0

    # bqa+w
    rate += np.exp(  3.05693)

    rate_eval.Cl30__S30__weak__bqa_pos_ = rate

@numba.njit()
def n_C16__C17(rate_eval, tf):
    # C16 + n --> C17
    rate = 0.0

    # wiesr
    rate += np.exp(  5.90263
                  + 1.0*tf.lnT9)

    rate_eval.n_C16__C17 = rate

@numba.njit()
def K40__Ca40__weak__wc12(rate_eval, tf):
    # K40 --> Ca40
    rate = 0.0

    # wc12w
    rate += np.exp(  -38.6925)

    rate_eval.K40__Ca40__weak__wc12 = rate

@numba.njit()
def P30__Si30__weak__wc12(rate_eval, tf):
    # P30 --> Si30
    rate = 0.0

    # wc12w
    rate += np.exp(  -5.37715)

    rate_eval.P30__Si30__weak__wc12 = rate

@numba.njit()
def p_V62__Cr63(rate_eval, tf):
    # V62 + p --> Cr63
    rate = 0.0

    # rath 
    rate += np.exp(  129.308 + -6.52964*tf.T9i + 246.32*tf.T913i + -396.503*tf.T913
                  + 21.8535*tf.T9 + -1.23517*tf.T953 + 198.829*tf.lnT9)

    rate_eval.p_V62__Cr63 = rate

@numba.njit()
def p_Ar46__n_K46(rate_eval, tf):
    # Ar46 + p --> n + K46
    rate = 0.0

    # rath 
    rate += np.exp(  107.816 + -4.83276*tf.T9i + 177.74*tf.T913i + -291.034*tf.T913
                  + 16.0398*tf.T9 + -0.899149*tf.T953 + 146.006*tf.lnT9)

    rate_eval.p_Ar46__n_K46 = rate

@numba.njit()
def He4_K46__n_Sc49(rate_eval, tf):
    # K46 + He4 --> n + Sc49
    rate = 0.0

    # rath 
    rate += np.exp(  -846.669 + 13.6922*tf.T9i + -1488.31*tf.T913i + 2439.25*tf.T913
                  + -145.957*tf.T9 + 8.38535*tf.T953 + -1143.84*tf.lnT9)

    rate_eval.He4_K46__n_Sc49 = rate

@numba.njit()
def B19__n_n_C17__weak__wc12(rate_eval, tf):
    # B19 --> n + n + C17
    rate = 0.0

    # wc12w
    rate += np.exp(  3.63708)

    rate_eval.B19__n_n_C17__weak__wc12 = rate

@numba.njit()
def V49__Ti49__weak__wc12(rate_eval, tf):
    # V49 --> Ti49
    rate = 0.0

    # wc12w
    rate += np.exp(  -17.5319)

    rate_eval.V49__Ti49__weak__wc12 = rate

@numba.njit()
def Ar30__Cl30__weak__bqa_pos_(rate_eval, tf):
    # Ar30 --> Cl30
    rate = 0.0

    # bqa+w
    rate += np.exp(  2.84489)

    rate_eval.Ar30__Cl30__weak__bqa_pos_ = rate

@numba.njit()
def P29__Si29__weak__wc12(rate_eval, tf):
    # P29 --> Si29
    rate = 0.0

    # wc12w
    rate += np.exp(  -1.78721)

    rate_eval.P29__Si29__weak__wc12 = rate

@numba.njit()
def He4_K34__Sc38(rate_eval, tf):
    # K34 + He4 --> Sc38
    rate = 0.0

    # ths8r
    rate += np.exp(  44.1795 + -73.4689*tf.T913i + -1.11837*tf.T913
                  + -0.423848*tf.T9 + 0.00242462*tf.T953 + -0.666667*tf.lnT9)

    rate_eval.He4_K34__Sc38 = rate

def rhs(t, Y, rho, T, screen_func=None):
    return rhs_eq(t, Y, rho, T, screen_func)

@numba.njit()
def rhs_eq(t, Y, rho, T, screen_func):

    tf = Tfactors(T)
    rate_eval = RateEval()

    # reaclib rates
    Fe45__p_p_p_Ti42__weak__wc12(rate_eval, tf)
    Cr43__p_p_p_Ca40__weak__wc12(rate_eval, tf)
    Fe75__n_n_n_Co72__weak__mo03(rate_eval, tf)
    Mn73__n_n_n_Fe70__weak__mo03(rate_eval, tf)
    Mn71__n_n_n_Fe68__weak__mo03(rate_eval, tf)
    Cr70__n_n_n_Mn67__weak__mo03(rate_eval, tf)
    V66__n_n_n_Cr63__weak__mo03(rate_eval, tf)
    V65__n_n_n_Cr62__weak__mo03(rate_eval, tf)
    Ti65__n_n_n_V62__weak__mo03(rate_eval, tf)
    Sc63__n_n_n_Ti60__weak__mo03(rate_eval, tf)
    Sc62__n_n_n_Ti59__weak__mo03(rate_eval, tf)
    Sc61__n_n_n_Ti58__weak__mo03(rate_eval, tf)
    Sc59__n_n_n_Ti56__weak__mo03(rate_eval, tf)
    Sc58__n_n_n_Ti55__weak__mo03(rate_eval, tf)
    Sc57__n_n_n_Ti54__weak__mo03(rate_eval, tf)
    Ca60__n_n_n_Sc57__weak__mo03(rate_eval, tf)
    Ca59__n_n_n_Sc56__weak__mo03(rate_eval, tf)
    Ca58__n_n_n_Sc55__weak__mo03(rate_eval, tf)
    Ca57__n_n_n_Sc54__weak__mo03(rate_eval, tf)
    K59__n_n_n_Ca56__weak__mo03(rate_eval, tf)
    K58__n_n_n_Ca55__weak__mo03(rate_eval, tf)
    K55__n_n_n_Ca52__weak__mo03(rate_eval, tf)
    K53__n_n_n_Ca50__weak__mo03(rate_eval, tf)
    Ar54__n_n_n_K51__weak__mo03(rate_eval, tf)
    Ar53__n_n_n_K50__weak__mo03(rate_eval, tf)
    Ar52__n_n_n_K49__weak__mo03(rate_eval, tf)
    Cl50__n_n_n_Ar47__weak__mo03(rate_eval, tf)
    S48__n_n_n_Cl45__weak__mo03(rate_eval, tf)
    S47__n_n_n_Cl44__weak__mo03(rate_eval, tf)
    K56__n_n_n_Ca53__weak__mo03(rate_eval, tf)
    P44__n_n_n_S41__weak__mo03(rate_eval, tf)
    Si42__n_n_n_P39__weak__mo03(rate_eval, tf)
    Al43__n_n_n_Si40__weak__mo03(rate_eval, tf)
    Al42__n_n_n_Si39__weak__mo03(rate_eval, tf)
    Al41__n_n_n_Si38__weak__mo03(rate_eval, tf)
    Al39__n_n_n_Si36__weak__mo03(rate_eval, tf)
    Al38__n_n_n_Si35__weak__mo03(rate_eval, tf)
    Al37__n_n_n_Si34__weak__mo03(rate_eval, tf)
    Mg40__n_n_n_Al37__weak__mo03(rate_eval, tf)
    Mg36__n_n_n_Al33__weak__mo03(rate_eval, tf)
    Mg35__n_n_n_Al32__weak__mo03(rate_eval, tf)
    Na34__n_n_n_Mg31__weak__mo03(rate_eval, tf)
    Na33__n_n_n_Mg30__weak__mo03(rate_eval, tf)
    Na32__n_n_n_Mg29__weak__mo03(rate_eval, tf)
    Ne31__n_n_n_Na28__weak__mo03(rate_eval, tf)
    F31__n_n_n_Ne28__weak__mo03(rate_eval, tf)
    F29__n_n_n_Ne26__weak__mo03(rate_eval, tf)
    K54__n_n_n_Ca51__weak__mo03(rate_eval, tf)
    F28__n_n_n_Ne25__weak__mo03(rate_eval, tf)
    F27__n_n_n_Ne24__weak__mo03(rate_eval, tf)
    O27__n_n_n_F24__weak__mo03(rate_eval, tf)
    n_p_p__p_d(rate_eval, tf)
    n_n_He4__He6(rate_eval, tf)
    p_Be9__n_p_He4_He4(rate_eval, tf)
    He3_Be7__p_p_He4_He4(rate_eval, tf)
    t_Be7__n_p_He4_He4(rate_eval, tf)
    He4_Ca36__p_p_Ca38(rate_eval, tf)
    He4_O13__p_p_O15(rate_eval, tf)
    p_B11__He4_He4_He4(rate_eval, tf)
    n_B8__p_He4_He4(rate_eval, tf)
    p_Be9__d_He4_He4(rate_eval, tf)
    d_Li7__n_He4_He4(rate_eval, tf)
    He3_He3__p_p_He4(rate_eval, tf)
    He4_Fe76__n_Ni79(rate_eval, tf)
    p_Fe76__He4_Mn73(rate_eval, tf)
    He4_Fe75__n_Ni78(rate_eval, tf)
    p_Fe75__He4_Mn72(rate_eval, tf)
    p_Fe75__n_Co75(rate_eval, tf)
    He4_Fe74__n_Ni77(rate_eval, tf)
    p_Fe74__He4_Mn71(rate_eval, tf)
    p_Fe74__n_Co74(rate_eval, tf)
    Mg37__n_n_n_Al34__weak__mo03(rate_eval, tf)
    p_Fe73__He4_Mn70(rate_eval, tf)
    p_Fe73__n_Co73(rate_eval, tf)
    p_Fe72__He4_Mn69(rate_eval, tf)
    p_Fe72__n_Co72(rate_eval, tf)
    He4_Fe71__n_Ni74(rate_eval, tf)
    p_Fe71__He4_Mn68(rate_eval, tf)
    p_Fe71__n_Co71(rate_eval, tf)
    He4_Fe70__n_Ni73(rate_eval, tf)
    p_Fe70__He4_Mn67(rate_eval, tf)
    p_Fe70__n_Co70(rate_eval, tf)
    p_Fe69__He4_Mn66(rate_eval, tf)
    p_Fe69__n_Co69(rate_eval, tf)
    He4_Fe68__n_Ni71(rate_eval, tf)
    p_Fe68__He4_Mn65(rate_eval, tf)
    p_Fe67__He4_Mn64(rate_eval, tf)
    p_Fe65__He4_Mn62(rate_eval, tf)
    He4_Fe64__n_Ni67(rate_eval, tf)
    He4_Fe63__n_Ni66(rate_eval, tf)
    p_Fe63__He4_Mn60(rate_eval, tf)
    p_Fe62__He4_Mn59(rate_eval, tf)
    p_Fe61__He4_Mn58(rate_eval, tf)
    p_Fe61__n_Co61(rate_eval, tf)
    p_Fe60__He4_Mn57(rate_eval, tf)
    He4_Fe59__n_Ni62(rate_eval, tf)
    p_Fe59__He4_Mn56(rate_eval, tf)
    p_Fe59__n_Co59(rate_eval, tf)
    p_Fe57__He4_Mn54(rate_eval, tf)
    n_Fe56__He4_Cr53(rate_eval, tf)
    O28__n_O27(rate_eval, tf)
    p_Ar34__K35(rate_eval, tf)
    n_Fe55__p_Mn55(rate_eval, tf)
    n_Sc40__Sc41(rate_eval, tf)
    n_Fe54__p_Mn54(rate_eval, tf)
    He4_Sc59__V63(rate_eval, tf)
    n_Fe53__He4_Cr50(rate_eval, tf)
    Fe67__Co67__weak__wc12(rate_eval, tf)
    He4_S30__Ar34(rate_eval, tf)
    n_Fe53__p_Mn53(rate_eval, tf)
    He4_Fe52__p_Co55(rate_eval, tf)
    n_Al25__Al26(rate_eval, tf)
    p_Ca61__Sc62(rate_eval, tf)
    n_Fe52__He4_Cr49(rate_eval, tf)
    Mn58__Fe58__weak__wc12(rate_eval, tf)
    n_Fe51__He4_Cr48(rate_eval, tf)
    He4_Cr66__Fe70(rate_eval, tf)
    n_Fe50__He4_Cr47(rate_eval, tf)
    He4_Fe49__p_Co52(rate_eval, tf)
    n_Fe49__He4_Cr46(rate_eval, tf)
    n_Fe49__p_Mn49(rate_eval, tf)
    He4_Fe48__p_Co51(rate_eval, tf)
    p_Sc50__Ti51(rate_eval, tf)
    n_Fe47__He4_Cr44(rate_eval, tf)
    Al37__Si37__weak__wc17(rate_eval, tf)
    n_Fe46__He4_Cr43(rate_eval, tf)
    n_Fe46__p_Mn46(rate_eval, tf)
    He4_Mn73__n_Co76(rate_eval, tf)
    p_Mn73__He4_Cr70(rate_eval, tf)
    p_Mg34__Al35(rate_eval, tf)
    He4_Mn72__n_Co75(rate_eval, tf)
    p_Mn72__He4_Cr69(rate_eval, tf)
    p_Mn71__He4_Cr68(rate_eval, tf)
    Ca56__n_n_n_Sc53__weak__mo03(rate_eval, tf)
    He4_Mn69__n_Co72(rate_eval, tf)
    p_Mn69__He4_Cr66(rate_eval, tf)
    He4_Mn68__n_Co71(rate_eval, tf)
    p_Mn68__n_Fe68(rate_eval, tf)
    He4_Si33__n_S36(rate_eval, tf)
    p_Mn67__He4_Cr64(rate_eval, tf)
    p_Mn66__He4_Cr63(rate_eval, tf)
    p_Mn66__n_Fe66(rate_eval, tf)
    p_K48__Ca49(rate_eval, tf)
    p_P46__S47(rate_eval, tf)
    He4_Ca52__Ti56(rate_eval, tf)
    He4_Mn65__n_Co68(rate_eval, tf)
    p_Mn65__He4_Cr62(rate_eval, tf)
    p_Si44__n_P44(rate_eval, tf)
    He4_Mn68__Co72(rate_eval, tf)
    p_Mn64__He4_Cr61(rate_eval, tf)
    p_Mn62__He4_Cr59(rate_eval, tf)
    He4_Mn60__n_Co63(rate_eval, tf)
    p_Mn60__He4_Cr57(rate_eval, tf)
    p_Mn60__n_Fe60(rate_eval, tf)
    He4_Fe65__Ni69(rate_eval, tf)
    p_Mn59__He4_Cr56(rate_eval, tf)
    p_Mn57__n_Fe57(rate_eval, tf)
    p_Fe64__He4_Mn61(rate_eval, tf)
    p_Mn56__He4_Cr53(rate_eval, tf)
    p_Mn54__He4_Cr51(rate_eval, tf)
    S49__n_n_n_Cl46__weak__mo03(rate_eval, tf)
    He4_Mn53__p_Fe56(rate_eval, tf)
    p_Mn53__He4_Cr50(rate_eval, tf)
    n_Mn52__He4_V49(rate_eval, tf)
    Ar48__n_K47__weak__mp17(rate_eval, tf)
    n_Mn52__p_Cr52(rate_eval, tf)
    He4_Mn51__p_Fe54(rate_eval, tf)
    p_Ca53__n_Sc53(rate_eval, tf)
    n_Mn51__p_Cr51(rate_eval, tf)
    p_O22__n_F22(rate_eval, tf)
    n_Mn50__He4_V47(rate_eval, tf)
    He4_Mn49__p_Fe52(rate_eval, tf)
    n_Cl37__Cl38(rate_eval, tf)
    n_Mn48__He4_V45(rate_eval, tf)
    He4_Mn47__p_Fe50(rate_eval, tf)
    n_Ne20__Ne21(rate_eval, tf)
    n_Mn47__p_Cr47(rate_eval, tf)
    He4_Mn46__p_Fe49(rate_eval, tf)
    p_Ca44__Sc45(rate_eval, tf)
    n_Mn46__He4_V43(rate_eval, tf)
    n_Mn46__p_Cr46(rate_eval, tf)
    n_Mn45__p_Cr45(rate_eval, tf)
    He4_Mn44__p_Fe47(rate_eval, tf)
    He4_Cr70__n_Fe73(rate_eval, tf)
    n_F26__F27(rate_eval, tf)
    He4_Cr69__n_Fe72(rate_eval, tf)
    p_Cr68__He4_V65(rate_eval, tf)
    p_Cr68__n_Mn68(rate_eval, tf)
    p_Cr67__n_Mn67(rate_eval, tf)
    He4_Cr66__n_Fe69(rate_eval, tf)
    p_Cr66__He4_V63(rate_eval, tf)
    He4_Cr65__n_Fe68(rate_eval, tf)
    p_Cr65__He4_V62(rate_eval, tf)
    p_Mn72__n_Fe72(rate_eval, tf)
    He4_Cr64__n_Fe67(rate_eval, tf)
    p_O25__n_F25(rate_eval, tf)
    He4_Cr63__n_Fe66(rate_eval, tf)
    p_Cr63__n_Mn63(rate_eval, tf)
    He4_Cr62__n_Fe65(rate_eval, tf)
    p_Cr62__He4_V59(rate_eval, tf)
    N21__O21__weak__wc12(rate_eval, tf)
    He4_Mn48__Co52(rate_eval, tf)
    He4_Cr61__n_Fe64(rate_eval, tf)
    p_Cr60__He4_V57(rate_eval, tf)
    He4_Cr59__n_Fe62(rate_eval, tf)
    n_Ca50__Ca51(rate_eval, tf)
    p_Cr59__n_Mn59(rate_eval, tf)
    p_Fe62__n_Co62(rate_eval, tf)
    n_O18__O19(rate_eval, tf)
    p_Cr57__n_Mn57(rate_eval, tf)
    Mg22__Na22__weak__wc12(rate_eval, tf)
    He4_Cr55__n_Fe58(rate_eval, tf)
    Cr43__p_p_Sc41__weak__wc12(rate_eval, tf)
    n_Cr55__He4_Ti52(rate_eval, tf)
    p_Cr54__He4_V51(rate_eval, tf)
    p_Ne32__Na33(rate_eval, tf)
    p_Mg24__He4_Na21(rate_eval, tf)
    p_Si38__n_P38(rate_eval, tf)
    Mn54__Cr54__weak__wc12(rate_eval, tf)
    p_Mn55__He4_Cr52(rate_eval, tf)
    n_Cr51__He4_Ti48(rate_eval, tf)
    n_Cr50__He4_Ti47(rate_eval, tf)
    He4_Cr49__p_Mn52(rate_eval, tf)
    He4_Cr48__p_Mn51(rate_eval, tf)
    n_Cr48__p_V48(rate_eval, tf)
    p_Ti57__He4_Sc54(rate_eval, tf)
    n_Cr46__He4_Ti43(rate_eval, tf)
    He4_Cr45__p_Mn48(rate_eval, tf)
    n_B13__B14(rate_eval, tf)
    He4_Ne29__Mg33(rate_eval, tf)
    He4_Ti59__n_Cr62(rate_eval, tf)
    He4_P44__n_Cl47(rate_eval, tf)
    n_Cr45__He4_Ti42(rate_eval, tf)
    He4_Cr44__p_Mn47(rate_eval, tf)
    He4_Cr43__p_Mn46(rate_eval, tf)
    n_Cr43__p_V43(rate_eval, tf)
    He4_Cr42__p_Mn45(rate_eval, tf)
    n_Cr42__He4_Ti39(rate_eval, tf)
    n_Cr42__p_V42(rate_eval, tf)
    n_Cr41__He4_Ti38(rate_eval, tf)
    Ne26__n_Na25__weak__wc12(rate_eval, tf)
    He4_V67__n_Mn70(rate_eval, tf)
    He4_Sc37__p_Ti40(rate_eval, tf)
    p_V67__n_Cr67(rate_eval, tf)
    He4_V66__n_Mn69(rate_eval, tf)
    p_V66__n_Cr66(rate_eval, tf)
    He4_V50__p_Cr53(rate_eval, tf)
    p_K47__He4_Ar44(rate_eval, tf)
    p_V65__He4_Ti62(rate_eval, tf)
    He4_V64__n_Mn67(rate_eval, tf)
    n_Cr49__p_V49(rate_eval, tf)
    p_V64__He4_Ti61(rate_eval, tf)
    p_V63__n_Cr63(rate_eval, tf)
    He4_Mn60__Co64(rate_eval, tf)
    He4_V62__n_Mn65(rate_eval, tf)
    He4_V61__n_Mn64(rate_eval, tf)
    p_V61__n_Cr61(rate_eval, tf)
    p_P32__n_S32(rate_eval, tf)
    He4_Al32__n_P35(rate_eval, tf)
    He4_V63__Mn67(rate_eval, tf)
    p_V60__He4_Ti57(rate_eval, tf)
    t_He3__n_p_He4(rate_eval, tf)
    p_V60__n_Cr60(rate_eval, tf)
    p_O27__He4_N24(rate_eval, tf)
    p_Si43__n_P43(rate_eval, tf)
    He4_V59__n_Mn62(rate_eval, tf)
    He4_V58__n_Mn61(rate_eval, tf)
    p_V58__He4_Ti55(rate_eval, tf)
    p_V58__n_Cr58(rate_eval, tf)
    p_V57__He4_Ti54(rate_eval, tf)
    p_V57__n_Cr57(rate_eval, tf)
    n_Cr53__He4_Ti50(rate_eval, tf)
    He4_V56__n_Mn59(rate_eval, tf)
    Mn43__Cr43__weak__bqa_pos_(rate_eval, tf)
    He4_Al40__p_Si43(rate_eval, tf)
    He4_V55__n_Mn58(rate_eval, tf)
    Ne28__Na28__weak__wc17(rate_eval, tf)
    He4_Cr47__p_Mn50(rate_eval, tf)
    p_V55__n_Cr55(rate_eval, tf)
    He4_V54__n_Mn57(rate_eval, tf)
    He4_Ar52__Ca56(rate_eval, tf)
    p_V53__n_Cr53(rate_eval, tf)
    p_V52__He4_Ti49(rate_eval, tf)
    p_V52__n_Cr52(rate_eval, tf)
    He4_S45__n_Ar48(rate_eval, tf)
    He4_Ca43__Ti47(rate_eval, tf)
    p_V51__He4_Ti48(rate_eval, tf)
    p_F23__Ne24(rate_eval, tf)
    n_Mn69__Mn70(rate_eval, tf)
    p_V50__He4_Ti47(rate_eval, tf)
    p_V50__n_Cr50(rate_eval, tf)
    n_V50__p_Ti50(rate_eval, tf)
    p_F24__Ne25(rate_eval, tf)
    p_V49__He4_Ti46(rate_eval, tf)
    He4_N15__F19(rate_eval, tf)
    He4_V47__p_Cr50(rate_eval, tf)
    He4_V46__p_Cr49(rate_eval, tf)
    n_V46__He4_Sc43(rate_eval, tf)
    n_V46__p_Ti46(rate_eval, tf)
    He4_V58__Mn62(rate_eval, tf)
    p_Sc52__Ti53(rate_eval, tf)
    n_V44__He4_Sc41(rate_eval, tf)
    n_V44__p_Ti44(rate_eval, tf)
    Cl49__n_n_Ar47__weak__mp17(rate_eval, tf)
    He4_V43__p_Cr46(rate_eval, tf)
    n_V43__p_Ti43(rate_eval, tf)
    He4_V42__p_Cr45(rate_eval, tf)
    He4_Si43__n_S46(rate_eval, tf)
    Sc47__Ti47__weak__wc12(rate_eval, tf)
    He4_Ne33__n_Mg36(rate_eval, tf)
    n_V42__He4_Sc39(rate_eval, tf)
    n_V41__He4_Sc38(rate_eval, tf)
    n_V40__p_Ti40(rate_eval, tf)
    He4_V39__p_Cr42(rate_eval, tf)
    p_Sc53__n_Ti53(rate_eval, tf)
    He4_Ti65__n_Cr68(rate_eval, tf)
    p_Cr57__He4_V54(rate_eval, tf)
    p_Ne27__He4_F24(rate_eval, tf)
    He4_Ti64__n_Cr67(rate_eval, tf)
    p_Ti64__He4_Sc61(rate_eval, tf)
    He4_Ti63__n_Cr66(rate_eval, tf)
    p_Ti63__He4_Sc60(rate_eval, tf)
    p_Ti63__n_V63(rate_eval, tf)
    p_Ti61__n_V61(rate_eval, tf)
    He4_Ti60__n_Cr63(rate_eval, tf)
    n_O12__O13(rate_eval, tf)
    p_Ti60__n_V60(rate_eval, tf)
    p_Ti59__n_V59(rate_eval, tf)
    He4_Ti58__n_Cr61(rate_eval, tf)
    p_Ti58__n_V58(rate_eval, tf)
    K32__Ar32__weak__bqa_pos_(rate_eval, tf)
    He4_Ti55__n_Cr58(rate_eval, tf)
    p_Ti55__n_V55(rate_eval, tf)
    He4_Ti54__n_Cr57(rate_eval, tf)
    p_Ti54__He4_Sc51(rate_eval, tf)
    p_Ti54__n_V54(rate_eval, tf)
    p_F23__He4_O20(rate_eval, tf)
    He4_Ti53__n_Cr56(rate_eval, tf)
    p_Ti53__He4_Sc50(rate_eval, tf)
    n_Na33__Na34(rate_eval, tf)
    He4_Be10__C14(rate_eval, tf)
    p_Ti52__He4_Sc49(rate_eval, tf)
    p_Ti52__n_V52(rate_eval, tf)
    He4_Ti51__n_Cr54(rate_eval, tf)
    Ti43__Sc43__weak__wc12(rate_eval, tf)
    p_Ti51__n_V51(rate_eval, tf)
    n_Ti51__He4_Ca48(rate_eval, tf)
    He4_F26__Na30(rate_eval, tf)
    n_Ti49__He4_Ca46(rate_eval, tf)
    Sc61__n_n_Ti59__weak__mp17(rate_eval, tf)
    He4_Fe73__n_Ni76(rate_eval, tf)
    He4_K36__p_Ca39(rate_eval, tf)
    Sc56__n_Ti55__weak__mp17(rate_eval, tf)
    He4_Ar35__Ca39(rate_eval, tf)
    p_Ar51__He4_Cl48(rate_eval, tf)
    He4_Na19__Al23(rate_eval, tf)
    n_Na35__Na36(rate_eval, tf)
    n_Ti45__p_Sc45(rate_eval, tf)
    He4_Ti43__p_V46(rate_eval, tf)
    n_Ti43__He4_Ca40(rate_eval, tf)
    He4_F28__n_Na31(rate_eval, tf)
    He4_F31__n_Na34(rate_eval, tf)
    n_Ti41__He4_Ca38(rate_eval, tf)
    n_Ti41__p_Sc41(rate_eval, tf)
    He4_Ti40__p_V43(rate_eval, tf)
    n_K55__K56(rate_eval, tf)
    p_Cr55__n_Mn55(rate_eval, tf)
    p_F31__He4_O28(rate_eval, tf)
    He4_Ti39__p_V42(rate_eval, tf)
    n_Ti39__p_Sc39(rate_eval, tf)
    He4_Ti38__p_V41(rate_eval, tf)
    n_Ti38__He4_Ca35(rate_eval, tf)
    n_Ti38__p_Sc38(rate_eval, tf)
    He4_Ti37__p_V40(rate_eval, tf)
    Ti65__n_V64__weak__mp17(rate_eval, tf)
    He4_Sc62__n_V65(rate_eval, tf)
    He4_Sc61__n_V64(rate_eval, tf)
    p_Sc61__n_Ti61(rate_eval, tf)
    He4_Sc40__p_Ti43(rate_eval, tf)
    He4_Sc60__n_V63(rate_eval, tf)
    Ne34__n_n_n_Na31__weak__mo03(rate_eval, tf)
    p_Sc60__He4_Ca57(rate_eval, tf)
    p_Sc60__n_Ti60(rate_eval, tf)
    n_Fe48__p_Mn48(rate_eval, tf)
    He4_Sc59__n_V62(rate_eval, tf)
    n_Mn53__p_Cr53(rate_eval, tf)
    He4_Sc58__n_V61(rate_eval, tf)
    p_Sc58__He4_Ca55(rate_eval, tf)
    p_Sc58__n_Ti58(rate_eval, tf)
    He4_Sc57__n_V60(rate_eval, tf)
    Cr58__Mn58__weak__wc12(rate_eval, tf)
    He4_Sc56__n_V59(rate_eval, tf)
    He4_Sc55__n_V58(rate_eval, tf)
    p_Sc55__He4_Ca52(rate_eval, tf)
    n_Cr41__Cr42(rate_eval, tf)
    He4_Sc54__n_V57(rate_eval, tf)
    p_Sc54__n_Ti54(rate_eval, tf)
    n_Ar36__He4_S33(rate_eval, tf)
    He4_Sc52__n_V55(rate_eval, tf)
    p_Sc52__He4_Ca49(rate_eval, tf)
    p_S47__Cl48(rate_eval, tf)
    He4_C9__p_N12(rate_eval, tf)
    p_Sc52__n_Ti52(rate_eval, tf)
    He4_Sc51__n_V54(rate_eval, tf)
    p_Sc50__n_Ti50(rate_eval, tf)
    He4_Ar29__Ca33(rate_eval, tf)
    p_Sc49__He4_Ca46(rate_eval, tf)
    p_Sc48__He4_Ca45(rate_eval, tf)
    He4_Sc47__p_Ti50(rate_eval, tf)
    p_Sc47__He4_Ca44(rate_eval, tf)
    He4_Sc46__p_Ti49(rate_eval, tf)
    p_Sc46__He4_Ca43(rate_eval, tf)
    n_Sc46__p_Ca46(rate_eval, tf)
    n_V56__V57(rate_eval, tf)
    He4_Sc45__p_Ti48(rate_eval, tf)
    n_Si24__p_Al24(rate_eval, tf)
    n_Mg22__He4_Ne19(rate_eval, tf)
    p_Sc45__He4_Ca42(rate_eval, tf)
    n_Sc45__p_Ca45(rate_eval, tf)
    He4_Sc44__p_Ti47(rate_eval, tf)
    p_Sc44__He4_Ca41(rate_eval, tf)
    n_Sc44__p_Ca44(rate_eval, tf)
    He4_Sc43__p_Ti46(rate_eval, tf)
    n_Sc43__He4_K40(rate_eval, tf)
    n_Sc43__p_Ca43(rate_eval, tf)
    He4_Sc42__p_Ti45(rate_eval, tf)
    n_Sc42__He4_K39(rate_eval, tf)
    n_Sc42__p_Ca42(rate_eval, tf)
    p_Cr56__n_Mn56(rate_eval, tf)
    n_Sc41__He4_K38(rate_eval, tf)
    p_Si36__He4_Al33(rate_eval, tf)
    He4_Sc39__p_Ti42(rate_eval, tf)
    p_P31__S32(rate_eval, tf)
    n_Sc39__He4_K36(rate_eval, tf)
    p_Si45__P46(rate_eval, tf)
    He4_Sc38__p_Ti41(rate_eval, tf)
    n_Ti47__He4_Ca44(rate_eval, tf)
    p_Na36__n_Mg36(rate_eval, tf)
    n_Sc37__He4_K34(rate_eval, tf)
    He4_Sc36__p_Ti39(rate_eval, tf)
    Mg36__n_n_Al34__weak__mp17(rate_eval, tf)
    He4_Sc35__p_Ti38(rate_eval, tf)
    n_Sc35__He4_K32(rate_eval, tf)
    n_Sc35__p_Ca35(rate_eval, tf)
    p_Ca61__He4_K58(rate_eval, tf)
    p_Ca61__n_Sc61(rate_eval, tf)
    p_Ca60__n_Sc60(rate_eval, tf)
    n_Fe48__Fe49(rate_eval, tf)
    p_Ca59__n_Sc59(rate_eval, tf)
    He4_Ca58__n_Ti61(rate_eval, tf)
    p_Ca58__He4_K55(rate_eval, tf)
    n_Cr46__p_V46(rate_eval, tf)
    p_Ca58__n_Sc58(rate_eval, tf)
    He4_Al25__P29(rate_eval, tf)
    p_Ca56__He4_K53(rate_eval, tf)
    p_Ca55__He4_K52(rate_eval, tf)
    p_Ca55__n_Sc55(rate_eval, tf)
    He4_Ca53__n_Ti56(rate_eval, tf)
    He8__Li8__weak__wc12(rate_eval, tf)
    p_Ca52__n_Sc52(rate_eval, tf)
    p_P45__S46(rate_eval, tf)
    p_Cr56__He4_V53(rate_eval, tf)
    He4_Ca51__n_Ti54(rate_eval, tf)
    p_Ca51__He4_K48(rate_eval, tf)
    n_Si24__He4_Mg21(rate_eval, tf)
    p_Al39__He4_Mg36(rate_eval, tf)
    He4_Ca47__n_Ti50(rate_eval, tf)
    p_Ca47__n_Sc47(rate_eval, tf)
    S45__n_Cl44__weak__wc12(rate_eval, tf)
    C12_C12__He4_Ne20(rate_eval, tf)
    He4_Ca57__n_Ti60(rate_eval, tf)
    He4_Ca43__n_Ti46(rate_eval, tf)
    O24__F24__weak__wc12(rate_eval, tf)
    He4_Ti45__p_V48(rate_eval, tf)
    Na39__n_Mg38__weak__mp17(rate_eval, tf)
    p_Ca42__He4_K39(rate_eval, tf)
    n_Mn43__He4_V40(rate_eval, tf)
    He4_F16__Na20(rate_eval, tf)
    n_Ca40__He4_Ar37(rate_eval, tf)
    p_P42__n_S42(rate_eval, tf)
    He4_V63__n_Mn66(rate_eval, tf)
    n_Ca38__p_K38(rate_eval, tf)
    He4_Fe66__n_Ni69(rate_eval, tf)
    Ca53__n_Sc52__weak__wc12(rate_eval, tf)
    n_Ca37__He4_Ar34(rate_eval, tf)
    n_Ca37__p_K37(rate_eval, tf)
    n_Ca36__p_K36(rate_eval, tf)
    n_Cl35__p_S35(rate_eval, tf)
    He4_P39__n_Cl42(rate_eval, tf)
    n_Ca35__He4_Ar32(rate_eval, tf)
    n_Ca35__p_K35(rate_eval, tf)
    Cr67__Mn67__weak__mo03(rate_eval, tf)
    n_Ca34__He4_Ar31(rate_eval, tf)
    n_Ca34__p_K34(rate_eval, tf)
    He4_Ca48__Ti52(rate_eval, tf)
    He4_K57__n_Sc60(rate_eval, tf)
    p_K57__He4_Ar54(rate_eval, tf)
    He4_Si42__S46(rate_eval, tf)
    p_K57__n_Ca57(rate_eval, tf)
    He4_K56__n_Sc59(rate_eval, tf)
    p_K56__n_Ca56(rate_eval, tf)
    He4_K54__n_Sc57(rate_eval, tf)
    p_K54__n_Ca54(rate_eval, tf)
    Cl49__n_Ar48__weak__mp17(rate_eval, tf)
    He4_K53__n_Sc56(rate_eval, tf)
    n_O14__O15(rate_eval, tf)
    p_K53__n_Ca53(rate_eval, tf)
    n_K31__K32(rate_eval, tf)
    He4_K52__n_Sc55(rate_eval, tf)
    p_P29__S30(rate_eval, tf)
    He4_K51__n_Sc54(rate_eval, tf)
    p_K51__n_Ca51(rate_eval, tf)
    He4_Cr57__n_Fe60(rate_eval, tf)
    He4_K50__n_Sc53(rate_eval, tf)
    p_S42__Cl43(rate_eval, tf)
    He4_K48__n_Sc51(rate_eval, tf)
    n_Fe50__Fe51(rate_eval, tf)
    n_Cr44__He4_Ti41(rate_eval, tf)
    p_K48__He4_Ar45(rate_eval, tf)
    He4_Sc35__V39(rate_eval, tf)
    p_K45__He4_Ar42(rate_eval, tf)
    p_K45__n_Ca45(rate_eval, tf)
    p_K44__He4_Ar41(rate_eval, tf)
    Ne31__n_Na30__weak__mp17(rate_eval, tf)
    He4_K43__p_Ca46(rate_eval, tf)
    p_K43__n_Ca43(rate_eval, tf)
    n_V45__He4_Sc42(rate_eval, tf)
    He4_K42__p_Ca45(rate_eval, tf)
    He8__n_Li7__weak__wc12(rate_eval, tf)
    He4_K42__n_Sc45(rate_eval, tf)
    He4_K41__n_Sc44(rate_eval, tf)
    p_K41__He4_Ar38(rate_eval, tf)
    p_K41__n_Ca41(rate_eval, tf)
    He4_K46__p_Ca49(rate_eval, tf)
    p_K40__He4_Ar37(rate_eval, tf)
    p_K40__n_Ca40(rate_eval, tf)
    p_S37__Cl38(rate_eval, tf)
    n_K40__He4_Cl37(rate_eval, tf)
    n_K40__p_Ar40(rate_eval, tf)
    n_K39__p_Ar39(rate_eval, tf)
    p_O14__F15(rate_eval, tf)
    He4_Sc43__V47(rate_eval, tf)
    n_K38__p_Ar38(rate_eval, tf)
    n_Ar31__He4_S28(rate_eval, tf)
    He4_K37__p_Ca40(rate_eval, tf)
    He4_K44__p_Ca47(rate_eval, tf)
    n_K37__He4_Cl34(rate_eval, tf)
    n_K36__He4_Cl33(rate_eval, tf)
    n_K36__p_Ar36(rate_eval, tf)
    n_Sc46__He4_K43(rate_eval, tf)
    n_K35__p_Ar35(rate_eval, tf)
    He4_K34__p_Ca37(rate_eval, tf)
    p_Al39__n_Si39(rate_eval, tf)
    He4_Sc54__V58(rate_eval, tf)
    p_Cr61__He4_V58(rate_eval, tf)
    K52__Ca52__weak__wc17(rate_eval, tf)
    n_K33__p_Ar33(rate_eval, tf)
    p_Mn51__Fe52(rate_eval, tf)
    n_K32__He4_Cl29(rate_eval, tf)
    p_Mn56__Fe57(rate_eval, tf)
    n_K32__p_Ar32(rate_eval, tf)
    He4_K31__p_Ca34(rate_eval, tf)
    p_Ti38__V39(rate_eval, tf)
    n_K31__p_Ar31(rate_eval, tf)
    p_Ar54__n_K54(rate_eval, tf)
    p_Ar52__He4_Cl49(rate_eval, tf)
    p_Ar52__n_K52(rate_eval, tf)
    n_Ti39__He4_Ca36(rate_eval, tf)
    p_K59__n_Ca59(rate_eval, tf)
    p_Ar50__He4_Cl47(rate_eval, tf)
    n_Ca36__He4_Ar33(rate_eval, tf)
    V67__n_n_n_Cr64__weak__mo03(rate_eval, tf)
    He4_F20__n_Na23(rate_eval, tf)
    p_Ar48__He4_Cl45(rate_eval, tf)
    p_Ar48__n_K48(rate_eval, tf)
    He4_Ar46__n_Ca49(rate_eval, tf)
    p_F28__n_Ne28(rate_eval, tf)
    He4_Fe50__p_Co53(rate_eval, tf)
    n_d__t(rate_eval, tf)
    He4_Si35__n_S38(rate_eval, tf)
    p_Ar44__n_K44(rate_eval, tf)
    He4_Ar43__n_Ca46(rate_eval, tf)
    n_V39__V40(rate_eval, tf)
    p_Cr55__He4_V52(rate_eval, tf)
    p_Ar43__n_K43(rate_eval, tf)
    p_Fe47__Co48(rate_eval, tf)
    He4_Cl47__K51(rate_eval, tf)
    p_Ar41__n_K41(rate_eval, tf)
    n_Mn52__Mn53(rate_eval, tf)
    p_Ar40__He4_Cl37(rate_eval, tf)
    He4_Mn54__Co58(rate_eval, tf)
    He4_Fe68__Ni72(rate_eval, tf)
    p_Ar39__He4_Cl36(rate_eval, tf)
    p_Cr62__Mn63(rate_eval, tf)
    He4_Mn62__n_Co65(rate_eval, tf)
    n_Mn49__He4_V46(rate_eval, tf)
    n_Ar37__p_Cl37(rate_eval, tf)
    n_Ar35__He4_S32(rate_eval, tf)
    n_Ar35__p_Cl35(rate_eval, tf)
    He4_Ar34__p_K37(rate_eval, tf)
    n_Ar34__p_Cl34(rate_eval, tf)
    He4_Ar33__p_K36(rate_eval, tf)
    n_Ar33__p_Cl33(rate_eval, tf)
    n_Ar32__He4_S29(rate_eval, tf)
    n_Fe75__Fe76(rate_eval, tf)
    n_Ar32__p_Cl32(rate_eval, tf)
    He4_Ar31__p_K34(rate_eval, tf)
    n_Ar31__p_Cl31(rate_eval, tf)
    P27__p_Al26__weak__wc12(rate_eval, tf)
    n_Ar30__He4_S27(rate_eval, tf)
    n_Ar30__p_Cl30(rate_eval, tf)
    He4_Ar29__p_K32(rate_eval, tf)
    n_Ar29__He4_S26(rate_eval, tf)
    n_Ar29__p_Cl29(rate_eval, tf)
    p_Cl52__He4_S49(rate_eval, tf)
    p_Cl52__n_Ar52(rate_eval, tf)
    p_O16__F17(rate_eval, tf)
    He4_Cl51__n_K54(rate_eval, tf)
    n_Ti58__Ti59(rate_eval, tf)
    He4_Cl50__K54(rate_eval, tf)
    p_Cl51__He4_S48(rate_eval, tf)
    p_Cl50__He4_S47(rate_eval, tf)
    p_Cl50__n_Ar50(rate_eval, tf)
    n_Ar34__Ar35(rate_eval, tf)
    p_B12__n_C12(rate_eval, tf)
    He4_Cl49__n_K52(rate_eval, tf)
    He4_Ar36__Ca40(rate_eval, tf)
    p_Cl48__He4_S45(rate_eval, tf)
    He4_Ca50__n_Ti53(rate_eval, tf)
    p_Cl48__n_Ar48(rate_eval, tf)
    p_Ti62__n_V62(rate_eval, tf)
    He4_Cl47__n_K50(rate_eval, tf)
    p_Cl45__He4_S42(rate_eval, tf)
    p_Cl45__n_Ar45(rate_eval, tf)
    He4_Cl43__p_Ar46(rate_eval, tf)
    p_Cl43__He4_S40(rate_eval, tf)
    p_Mn61__n_Fe61(rate_eval, tf)
    He4_V49__Mn53(rate_eval, tf)
    p_V55__Cr56(rate_eval, tf)
    He4_Cl42__n_K45(rate_eval, tf)
    p_Cl42__He4_S39(rate_eval, tf)
    p_S47__n_Cl47(rate_eval, tf)
    n_Fe72__Fe73(rate_eval, tf)
    He4_Cl41__n_K44(rate_eval, tf)
    p_Cl41__He4_S38(rate_eval, tf)
    He4_Cl40__n_K43(rate_eval, tf)
    p_Cl40__n_Ar40(rate_eval, tf)
    p_O19__He4_N16(rate_eval, tf)
    n_Cl36__p_S36(rate_eval, tf)
    He4_F17__Na21(rate_eval, tf)
    n_Cl35__He4_P32(rate_eval, tf)
    He4_Cl34__p_Ar37(rate_eval, tf)
    n_C11__He4_He4_He4(rate_eval, tf)
    n_Cl34__He4_P31(rate_eval, tf)
    P42__n_n_S40__weak__mp17(rate_eval, tf)
    n_Cl34__p_S34(rate_eval, tf)
    n_Cl33__He4_P30(rate_eval, tf)
    p_Ti43__V44(rate_eval, tf)
    n_Cl33__p_S33(rate_eval, tf)
    p_Na34__Mg35(rate_eval, tf)
    He4_S48__n_Ar51(rate_eval, tf)
    n_Cl31__p_S31(rate_eval, tf)
    He4_Ar35__p_K38(rate_eval, tf)
    He4_Cl30__p_Ar33(rate_eval, tf)
    Ca35__K35__weak__wc17(rate_eval, tf)
    n_Cl29__He4_P26(rate_eval, tf)
    He4_Na25__Al29(rate_eval, tf)
    n_Cl29__p_S29(rate_eval, tf)
    He4_Cl28__p_Ar31(rate_eval, tf)
    n_V49__p_Ti49(rate_eval, tf)
    n_Cl28__He4_P25(rate_eval, tf)
    d_Li8__n_Be9(rate_eval, tf)
    Cr44__V44__weak__wc12(rate_eval, tf)
    n_Cr57__Cr58(rate_eval, tf)
    p_S49__n_Cl49(rate_eval, tf)
    He4_Mg38__n_Si41(rate_eval, tf)
    n_Ca52__Ca53(rate_eval, tf)
    p_S48__n_Cl48(rate_eval, tf)
    p_N15__O16(rate_eval, tf)
    p_S47__He4_P44(rate_eval, tf)
    p_K52__He4_Ar49(rate_eval, tf)
    p_S46__n_Cl46(rate_eval, tf)
    Na25__Mg25__weak__wc12(rate_eval, tf)
    d_Be7__p_He4_He4(rate_eval, tf)
    p_S45__He4_P42(rate_eval, tf)
    He4_S43__n_Ar46(rate_eval, tf)
    p_Mn64__n_Fe64(rate_eval, tf)
    p_S43__He4_P40(rate_eval, tf)
    He4_Mn67__n_Co70(rate_eval, tf)
    p_Cr60__Mn61(rate_eval, tf)
    p_Sc57__He4_Ca54(rate_eval, tf)
    He4_Fe56__Ni60(rate_eval, tf)
    He4_S42__n_Ar45(rate_eval, tf)
    He4_S41__n_Ar44(rate_eval, tf)
    He4_Sc63__n_V66(rate_eval, tf)
    p_S41__He4_P38(rate_eval, tf)
    p_Al30__He4_Mg27(rate_eval, tf)
    p_S40__n_Cl40(rate_eval, tf)
    p_Cl40__He4_S37(rate_eval, tf)
    He4_Fe47__Ni51(rate_eval, tf)
    d_Li8__t_Li7(rate_eval, tf)
    p_S39__He4_P36(rate_eval, tf)
    He4_S38__n_Ar41(rate_eval, tf)
    p_S38__He4_P35(rate_eval, tf)
    p_S38__n_Cl38(rate_eval, tf)
    He4_Mn47__Co51(rate_eval, tf)
    He4_S37__n_Ar40(rate_eval, tf)
    He4_K49__n_Sc52(rate_eval, tf)
    p_V56__He4_Ti53(rate_eval, tf)
    p_S37__n_Cl37(rate_eval, tf)
    p_K49__n_Ca49(rate_eval, tf)
    p_Cl45__Ar46(rate_eval, tf)
    p_Li6__Be7(rate_eval, tf)
    p_S36__He4_P33(rate_eval, tf)
    p_Cr69__He4_V66(rate_eval, tf)
    p_Sc51__He4_Ca48(rate_eval, tf)
    p_K51__He4_Ar48(rate_eval, tf)
    He4_P34__n_Cl37(rate_eval, tf)
    He4_S35__n_Ar38(rate_eval, tf)
    p_S35__He4_P32(rate_eval, tf)
    n_Si43__Si44(rate_eval, tf)
    p_Sc57__n_Ti57(rate_eval, tf)
    n_S35__He4_Si32(rate_eval, tf)
    He4_S34__p_Cl37(rate_eval, tf)
    n_Al36__Al37(rate_eval, tf)
    p_Cl35__He4_S32(rate_eval, tf)
    He4_Ti60__Cr64(rate_eval, tf)
    Cr68__Mn68__weak__mo03(rate_eval, tf)
    n_S33__He4_Si30(rate_eval, tf)
    He4_S31__p_Cl34(rate_eval, tf)
    He4_S30__p_Cl33(rate_eval, tf)
    n_S30__He4_Si27(rate_eval, tf)
    n_S30__p_P30(rate_eval, tf)
    Cl49__n_n_n_Ar46__weak__mo03(rate_eval, tf)
    He4_S28__p_Cl31(rate_eval, tf)
    n_Cr43__He4_Ti40(rate_eval, tf)
    n_S28__He4_Si25(rate_eval, tf)
    Ca53__Sc53__weak__wc12(rate_eval, tf)
    He4_S26__p_Cl29(rate_eval, tf)
    n_S26__He4_Si23(rate_eval, tf)
    p_V65__Cr66(rate_eval, tf)
    He4_P47__n_Cl50(rate_eval, tf)
    p_P47__n_S47(rate_eval, tf)
    p_P45__n_S45(rate_eval, tf)
    n_Si33__Si34(rate_eval, tf)
    He4_P43__n_Cl46(rate_eval, tf)
    p_P43__He4_Si40(rate_eval, tf)
    He4_Al38__n_P41(rate_eval, tf)
    p_P43__n_S43(rate_eval, tf)
    p_Sc55__n_Ti55(rate_eval, tf)
    p_P42__He4_Si39(rate_eval, tf)
    Ne27__n_Na26__weak__wc12(rate_eval, tf)
    He4_P41__p_S44(rate_eval, tf)
    He4_P41__n_Cl44(rate_eval, tf)
    p_O20__He4_N17(rate_eval, tf)
    p_Ar43__He4_Cl40(rate_eval, tf)
    p_P38__He4_Si35(rate_eval, tf)
    p_P38__n_S38(rate_eval, tf)
    n_S33__p_P33(rate_eval, tf)
    p_F18__He4_O15(rate_eval, tf)
    He4_P37__n_Cl40(rate_eval, tf)
    p_P37__He4_Si34(rate_eval, tf)
    p_P36__He4_Si33(rate_eval, tf)
    n_Ti54__Ti55(rate_eval, tf)
    p_P36__n_S36(rate_eval, tf)
    p_Mn69__n_Fe69(rate_eval, tf)
    p_P34__n_S34(rate_eval, tf)
    p_Ca56__n_Sc56(rate_eval, tf)
    He4_Cl44__p_Ar47(rate_eval, tf)
    p_Al25__Si26(rate_eval, tf)
    p_Sc45__Ti46(rate_eval, tf)
    p_P32__He4_Si29(rate_eval, tf)
    n_P32__p_Si32(rate_eval, tf)
    He4_P31__p_S34(rate_eval, tf)
    n_F25__F26(rate_eval, tf)
    He4_P30__p_S33(rate_eval, tf)
    Mg39__n_n_n_Al36__weak__mo03(rate_eval, tf)
    He4_K55__n_Sc58(rate_eval, tf)
    n_V47__He4_Sc44(rate_eval, tf)
    n_P28__p_Si28(rate_eval, tf)
    He4_P27__p_S30(rate_eval, tf)
    n_P27__He4_Al24(rate_eval, tf)
    n_P27__p_Si27(rate_eval, tf)
    He4_P26__p_S29(rate_eval, tf)
    n_Cr47__He4_Ti44(rate_eval, tf)
    n_P26__He4_Al23(rate_eval, tf)
    n_P26__p_Si26(rate_eval, tf)
    He4_P25__p_S28(rate_eval, tf)
    He4_P24__p_S27(rate_eval, tf)
    n_P24__He4_Al21(rate_eval, tf)
    n_P24__p_Si24(rate_eval, tf)
    p_Si45__He4_Al42(rate_eval, tf)
    p_Si45__n_P45(rate_eval, tf)
    He4_Si44__n_S47(rate_eval, tf)
    He4_P42__n_Cl45(rate_eval, tf)
    He4_Si42__n_S45(rate_eval, tf)
    Na26__Mg26__weak__wc12(rate_eval, tf)
    p_Si42__n_P42(rate_eval, tf)
    n_Mn54__p_Cr54(rate_eval, tf)
    Sc38__Ca38__weak__mo97(rate_eval, tf)
    He4_Si40__n_S43(rate_eval, tf)
    He4_Si39__n_S42(rate_eval, tf)
    Mn68__Fe68__weak__wc17(rate_eval, tf)
    p_S38__Cl39(rate_eval, tf)
    p_Si39__n_P39(rate_eval, tf)
    p_Sc62__n_Ti62(rate_eval, tf)
    n_Cr47__p_V47(rate_eval, tf)
    He4_Si38__n_S41(rate_eval, tf)
    p_Ti65__He4_Sc62(rate_eval, tf)
    He4_Si37__n_S40(rate_eval, tf)
    He4_Ca40__Ti44(rate_eval, tf)
    p_Si37__He4_Al34(rate_eval, tf)
    O14__N14__weak__wc12(rate_eval, tf)
    p_Si37__n_P37(rate_eval, tf)
    p_Si35__He4_Al32(rate_eval, tf)
    He3__t__weak__electron_capture(rate_eval, tf)
    p_Si33__n_P33(rate_eval, tf)
    He4_Mn45__p_Fe48(rate_eval, tf)
    He4_Cr41__p_Mn44(rate_eval, tf)
    He4_Mn43__Co47(rate_eval, tf)
    He4_V57__n_Mn60(rate_eval, tf)
    n_Mn51__He4_V48(rate_eval, tf)
    p_V49__Cr50(rate_eval, tf)
    B18__n_B17(rate_eval, tf)
    n_Ti37__He4_Ca34(rate_eval, tf)
    n_O24__O25(rate_eval, tf)
    He4_Ti61__n_Cr64(rate_eval, tf)
    Sc62__Ti62__weak__mo03(rate_eval, tf)
    He4_Si25__p_P28(rate_eval, tf)
    n_Ar35__Ar36(rate_eval, tf)
    p_Mn58__Fe59(rate_eval, tf)
    n_Si25__p_Al25(rate_eval, tf)
    He4_V40__p_Cr43(rate_eval, tf)
    He4_Si24__p_P27(rate_eval, tf)
    V64__n_n_Cr62__weak__mp17(rate_eval, tf)
    He4_Be7__C11(rate_eval, tf)
    He4_Ca54__Ti58(rate_eval, tf)
    He4_K40__p_Ca43(rate_eval, tf)
    He4_Si23__p_P26(rate_eval, tf)
    He4_Ar42__n_Ca45(rate_eval, tf)
    p_V61__He4_Ti58(rate_eval, tf)
    n_Si23__p_Al23(rate_eval, tf)
    He4_Si22__p_P25(rate_eval, tf)
    n_Si22__He4_Mg19(rate_eval, tf)
    n_Si22__p_Al22(rate_eval, tf)
    p_Al43__n_Si43(rate_eval, tf)
    Mg27__Al27__weak__wc12(rate_eval, tf)
    He4_Al42__n_P45(rate_eval, tf)
    p_Al41__He4_Mg38(rate_eval, tf)
    He4_Al40__n_P43(rate_eval, tf)
    p_Al40__He4_Mg37(rate_eval, tf)
    p_Al40__n_Si40(rate_eval, tf)
    He4_Al39__p_Si42(rate_eval, tf)
    He4_Al38__p_Si41(rate_eval, tf)
    He4_Mn49__Co53(rate_eval, tf)
    p_Al38__He4_Mg35(rate_eval, tf)
    p_V59__n_Cr59(rate_eval, tf)
    n_V48__p_Ti48(rate_eval, tf)
    p_Al37__He4_Mg34(rate_eval, tf)
    He4_Al36__p_Si39(rate_eval, tf)
    n_Si44__Si45(rate_eval, tf)
    He4_Al36__n_P39(rate_eval, tf)
    p_Al36__He4_Mg33(rate_eval, tf)
    C22__N22__weak__wc17(rate_eval, tf)
    He4_Mn59__Co63(rate_eval, tf)
    p_Al36__n_Si36(rate_eval, tf)
    p_Al41__n_Si41(rate_eval, tf)
    p_V64__n_Cr64(rate_eval, tf)
    He4_Al35__n_P38(rate_eval, tf)
    p_Al35__He4_Mg32(rate_eval, tf)
    He4_Al34__n_P37(rate_eval, tf)
    p_Al34__He4_Mg31(rate_eval, tf)
    p_Al34__n_Si34(rate_eval, tf)
    He4_K50__Sc54(rate_eval, tf)
    He4_Al33__n_P36(rate_eval, tf)
    p_Al33__He4_Mg30(rate_eval, tf)
    Si43__n_n_P41__weak__mp17(rate_eval, tf)
    He4_Si27__p_P30(rate_eval, tf)
    p_Cl46__He4_S43(rate_eval, tf)
    p_Al33__n_Si33(rate_eval, tf)
    p_Ne26__n_Na26(rate_eval, tf)
    p_Al32__He4_Mg29(rate_eval, tf)
    p_Al32__n_Si32(rate_eval, tf)
    n_Cr66__Cr67(rate_eval, tf)
    He4_Al31__p_Si34(rate_eval, tf)
    He4_Al31__n_P34(rate_eval, tf)
    p_Cl38__He4_S35(rate_eval, tf)
    p_Al31__He4_Mg28(rate_eval, tf)
    p_Al30__n_Si30(rate_eval, tf)
    He4_Al29__n_P32(rate_eval, tf)
    p_Al29__He4_Mg26(rate_eval, tf)
    p_Al29__n_Si29(rate_eval, tf)
    He4_Al37__n_P40(rate_eval, tf)
    p_Ne34__He4_F31(rate_eval, tf)
    n_Ti44__p_Sc44(rate_eval, tf)
    p_Al28__He4_Mg25(rate_eval, tf)
    n_Ti59__Ti60(rate_eval, tf)
    He4_K41__p_Ca44(rate_eval, tf)
    He4_Al27__p_Si30(rate_eval, tf)
    He4_Al27__n_P30(rate_eval, tf)
    p_Ca49__Sc50(rate_eval, tf)
    n_Al26__He4_Na23(rate_eval, tf)
    n_Al26__p_Mg26(rate_eval, tf)
    He4_Al32__P36(rate_eval, tf)
    n_Al25__p_Mg25(rate_eval, tf)
    He4_Al24__p_Si27(rate_eval, tf)
    p_S46__Cl47(rate_eval, tf)
    He4_Al25__p_Si28(rate_eval, tf)
    F31__n_n_Ne29__weak__mp17(rate_eval, tf)
    n_Al23__He4_Na20(rate_eval, tf)
    p_Na37__Mg38(rate_eval, tf)
    He4_Al22__p_Si25(rate_eval, tf)
    p_V67__He4_Ti64(rate_eval, tf)
    n_Al22__He4_Na19(rate_eval, tf)
    O28__n_n_n_F25__weak__mo03(rate_eval, tf)
    n_Al22__p_Mg22(rate_eval, tf)
    He4_Al21__p_Si24(rate_eval, tf)
    n_Sc48__p_Ca48(rate_eval, tf)
    He4_Mg40__n_Si43(rate_eval, tf)
    p_Mg40__n_Al40(rate_eval, tf)
    He4_Mg39__n_Si42(rate_eval, tf)
    p_Mg39__n_Al39(rate_eval, tf)
    Ca33__K33__weak__bqa_pos_(rate_eval, tf)
    p_Mg38__n_Al38(rate_eval, tf)
    p_Al27__He4_Mg24(rate_eval, tf)
    He4_Mg37__n_Si40(rate_eval, tf)
    p_Al38__n_Si38(rate_eval, tf)
    p_Na31__Mg32(rate_eval, tf)
    p_Ar45__He4_Cl42(rate_eval, tf)
    He4_Mg35__n_Si38(rate_eval, tf)
    He4_Mg34__n_Si37(rate_eval, tf)
    p_Mg34__He4_Na31(rate_eval, tf)
    p_Ti53__n_V53(rate_eval, tf)
    p_Mg33__He4_Na30(rate_eval, tf)
    Fe49__Mn49__weak__wc12(rate_eval, tf)
    p_Fe66__He4_Mn63(rate_eval, tf)
    He4_Mg32__n_Si35(rate_eval, tf)
    n_Mn47__He4_V44(rate_eval, tf)
    p_Mg32__He4_Na29(rate_eval, tf)
    n_Na19__p_Ne19(rate_eval, tf)
    p_Mn59__n_Fe59(rate_eval, tf)
    He4_Mg30__n_Si33(rate_eval, tf)
    p_Mg30__n_Al30(rate_eval, tf)
    n_P29__He4_Al26(rate_eval, tf)
    p_Ca45__Sc46(rate_eval, tf)
    He4_Cr46__p_Mn49(rate_eval, tf)
    p_Cl46__n_Ar46(rate_eval, tf)
    p_Mg29__He4_Na26(rate_eval, tf)
    p_Mg29__n_Al29(rate_eval, tf)
    p_Cr60__n_Mn60(rate_eval, tf)
    n_S29__He4_Si26(rate_eval, tf)
    n_K58__K59(rate_eval, tf)
    He4_K57__Sc61(rate_eval, tf)
    He4_Ne23__n_Mg26(rate_eval, tf)
    p_Ne31__He4_F28(rate_eval, tf)
    He4_Mg27__n_Si30(rate_eval, tf)
    He4_O23__n_Ne26(rate_eval, tf)
    He4_K35__p_Ca38(rate_eval, tf)
    He4_Mg26__n_Si29(rate_eval, tf)
    p_Ti59__V60(rate_eval, tf)
    n_Fe54__He4_Cr51(rate_eval, tf)
    n_Mn68__Mn69(rate_eval, tf)
    He4_Fe53__p_Co56(rate_eval, tf)
    n_Fe55__He4_Cr52(rate_eval, tf)
    He4_Mg25__n_Si28(rate_eval, tf)
    p_Fe69__Co70(rate_eval, tf)
    P40__S40__weak__wc12(rate_eval, tf)
    n_Cl43__Cl44(rate_eval, tf)
    n_Mg23__C12_C12(rate_eval, tf)
    n_Mg23__He4_Ne20(rate_eval, tf)
    n_Fe66__Fe67(rate_eval, tf)
    He4_Mg22__p_Al25(rate_eval, tf)
    n_Cl30__p_S30(rate_eval, tf)
    n_Mg21__He4_Ne18(rate_eval, tf)
    He4_Mg20__p_Al23(rate_eval, tf)
    Ca57__n_n_Sc55__weak__mp17(rate_eval, tf)
    He4_Na36__n_Al39(rate_eval, tf)
    n_Mg20__p_Na20(rate_eval, tf)
    p_Na39__n_Mg39(rate_eval, tf)
    Na27__n_Mg26__weak__wc12(rate_eval, tf)
    He4_Na38__n_Al41(rate_eval, tf)
    He4_Na37__p_Mg40(rate_eval, tf)
    He4_K33__Sc37(rate_eval, tf)
    p_Na37__He4_Ne34(rate_eval, tf)
    He4_Na35__n_Al38(rate_eval, tf)
    p_Na35__n_Mg35(rate_eval, tf)
    Mg37__n_Al36__weak__mp17(rate_eval, tf)
    n_V43__He4_Sc40(rate_eval, tf)
    He4_Na34__n_Al37(rate_eval, tf)
    He4_V60__n_Mn63(rate_eval, tf)
    He4_Na33__p_Mg36(rate_eval, tf)
    p_Na33__n_Mg33(rate_eval, tf)
    n_N18__N19(rate_eval, tf)
    S30__P30__weak__wc12(rate_eval, tf)
    n_Mn43__p_Cr43(rate_eval, tf)
    He4_Sc44__V48(rate_eval, tf)
    He4_Na31__n_Al34(rate_eval, tf)
    p_Na31__He4_Ne28(rate_eval, tf)
    p_Na31__n_Mg31(rate_eval, tf)
    p_Fe66__n_Co66(rate_eval, tf)
    p_Na30__He4_Ne27(rate_eval, tf)
    p_Cl40__Ar41(rate_eval, tf)
    n_S31__p_P31(rate_eval, tf)
    p_Na29__He4_Ne26(rate_eval, tf)
    He4_Na28__n_Al31(rate_eval, tf)
    p_Na28__n_Mg28(rate_eval, tf)
    Ar49__K49__weak__wc12(rate_eval, tf)
    p_Na27__n_Mg27(rate_eval, tf)
    n_Ar39__He4_S36(rate_eval, tf)
    He4_Na26__n_Al29(rate_eval, tf)
    p_Sc49__n_Ti49(rate_eval, tf)
    Ar52__n_n_K50__weak__mp17(rate_eval, tf)
    He4_Na24__p_Mg27(rate_eval, tf)
    p_Na24__He4_Ne21(rate_eval, tf)
    n_Ti42__p_Sc42(rate_eval, tf)
    p_K56__He4_Ar53(rate_eval, tf)
    p_K46__Ca47(rate_eval, tf)
    He4_Na23__p_Mg26(rate_eval, tf)
    p_Fe67__n_Co67(rate_eval, tf)
    n_Fe50__p_Mn50(rate_eval, tf)
    n_Sc43__Sc44(rate_eval, tf)
    n_S26__p_P26(rate_eval, tf)
    p_Na23__He4_Ne20(rate_eval, tf)
    p_Na23__n_Mg23(rate_eval, tf)
    He4_Na22__p_Mg25(rate_eval, tf)
    He4_S41__Ar45(rate_eval, tf)
    p_V56__Cr57(rate_eval, tf)
    n_Na21__He4_F18(rate_eval, tf)
    He4_S29__p_Cl32(rate_eval, tf)
    n_Na20__He4_F17(rate_eval, tf)
    n_V40__He4_Sc37(rate_eval, tf)
    He4_Cl35__p_Ar38(rate_eval, tf)
    p_Ne34__n_Na34(rate_eval, tf)
    n_Mn54__He4_V51(rate_eval, tf)
    n_Cl32__He4_P29(rate_eval, tf)
    p_Cl36__Ar37(rate_eval, tf)
    He4_S46__n_Ar49(rate_eval, tf)
    He4_Ne31__n_Mg34(rate_eval, tf)
    p_Al35__n_Si35(rate_eval, tf)
    He4_Ne30__n_Mg33(rate_eval, tf)
    p_Ne30__He4_F27(rate_eval, tf)
    n_Sc40__p_Ca40(rate_eval, tf)
    p_Ne29__He4_F26(rate_eval, tf)
    He4_Ar43__Ca47(rate_eval, tf)
    p_Ne29__n_Na29(rate_eval, tf)
    He4_Ne28__n_Mg31(rate_eval, tf)
    p_Ne28__n_Na28(rate_eval, tf)
    Si35__P35__weak__wc17(rate_eval, tf)
    He4_Ne27__n_Mg30(rate_eval, tf)
    p_Ne27__n_Na27(rate_eval, tf)
    He4_Ca39__Ti43(rate_eval, tf)
    N23__O23__weak__wc12(rate_eval, tf)
    He4_Ti54__Cr58(rate_eval, tf)
    He4_S39__n_Ar42(rate_eval, tf)
    p_Ne25__He4_F22(rate_eval, tf)
    p_Ne25__n_Na25(rate_eval, tf)
    K59__Ca59__weak__mo03(rate_eval, tf)
    He4_S27__p_Cl30(rate_eval, tf)
    He4_Ne24__n_Mg27(rate_eval, tf)
    p_Ne24__n_Na24(rate_eval, tf)
    Cl39__Ar39__weak__wc12(rate_eval, tf)
    p_S30__Cl31(rate_eval, tf)
    n_Ti45__He4_Ca42(rate_eval, tf)
    Cr69__Mn69__weak__mo03(rate_eval, tf)
    P33__S33__weak__wc12(rate_eval, tf)
    He4_Ca61__n_Ti64(rate_eval, tf)
    He4_K39__Sc43(rate_eval, tf)
    p_Ne23__n_Na23(rate_eval, tf)
    He4_Sc62__V66(rate_eval, tf)
    He4_Ne22__n_Mg25(rate_eval, tf)
    n_Cl38__He4_P35(rate_eval, tf)
    p_Al43__He4_Mg40(rate_eval, tf)
    He4_Ne21__n_Mg24(rate_eval, tf)
    n_Si27__Si28(rate_eval, tf)
    p_V42__Cr43(rate_eval, tf)
    C12_Ne20__He4_Si28(rate_eval, tf)
    C12_Ne20__p_P31(rate_eval, tf)
    n_Na30__Na31(rate_eval, tf)
    p_V54__n_Cr54(rate_eval, tf)
    p_Ne20__He4_F17(rate_eval, tf)
    p_Ne22__Na23(rate_eval, tf)
    He4_Al26__p_Si29(rate_eval, tf)
    p_K33__Ca34(rate_eval, tf)
    He4_Ne19__p_Na22(rate_eval, tf)
    He4_Ne18__p_Na21(rate_eval, tf)
    n_Si25__He4_Mg22(rate_eval, tf)
    n_Ne18__He4_O15(rate_eval, tf)
    n_Ne18__p_F18(rate_eval, tf)
    He4_Ne17__p_Na20(rate_eval, tf)
    n_Be7__He4_He4(rate_eval, tf)
    He4_Ne16__p_Na19(rate_eval, tf)
    He4_Cl49__K53(rate_eval, tf)
    n_Ne16__p_F16(rate_eval, tf)
    p_Cr67__He4_V64(rate_eval, tf)
    He4_Ar53__n_Ca56(rate_eval, tf)
    p_F31__n_Ne31(rate_eval, tf)
    He4_F30__p_Ne33(rate_eval, tf)
    p_Ar45__n_K45(rate_eval, tf)
    p_Mn47__Fe48(rate_eval, tf)
    p_F30__He4_O27(rate_eval, tf)
    He4_F29__n_Na32(rate_eval, tf)
    p_F29__He4_O26(rate_eval, tf)
    He4_F27__n_Na30(rate_eval, tf)
    p_F27__He4_O24(rate_eval, tf)
    p_F27__n_Ne27(rate_eval, tf)
    S27__p_Si26__weak__wc17(rate_eval, tf)
    He4_F26__n_Na29(rate_eval, tf)
    p_F26__n_Ne26(rate_eval, tf)
    p_Na34__He4_Ne31(rate_eval, tf)
    p_F25__He4_O22(rate_eval, tf)
    n_S30__S31(rate_eval, tf)
    p_F25__n_Ne25(rate_eval, tf)
    He4_Ca38__Ti42(rate_eval, tf)
    He4_F24__n_Na27(rate_eval, tf)
    p_F24__n_Ne24(rate_eval, tf)
    He4_Ti42__p_V45(rate_eval, tf)
    p_Na26__He4_Ne23(rate_eval, tf)
    p_F22__He4_O19(rate_eval, tf)
    p_F22__n_Ne22(rate_eval, tf)
    Cl48__n_Ar47__weak__mp17(rate_eval, tf)
    He4_F21__p_Ne24(rate_eval, tf)
    He4_F21__n_Na24(rate_eval, tf)
    p_Ne26__He4_F23(rate_eval, tf)
    He4_F20__p_Ne23(rate_eval, tf)
    n_Si26__p_Al26(rate_eval, tf)
    p_Al39__Si40(rate_eval, tf)
    p_F20__He4_O17(rate_eval, tf)
    He4_F19__p_Ne22(rate_eval, tf)
    p_F19__n_Ne19(rate_eval, tf)
    p_O21__n_F21(rate_eval, tf)
    He4_F18__p_Ne21(rate_eval, tf)
    p_O15__F16(rate_eval, tf)
    Al40__n_n_n_Si37__weak__mo03(rate_eval, tf)
    n_F18__He4_N15(rate_eval, tf)
    n_F15__He4_N12(rate_eval, tf)
    Fe76__n_n_n_Co73__weak__mo03(rate_eval, tf)
    n_Al41__Al42(rate_eval, tf)
    n_F14__He4_N11(rate_eval, tf)
    n_Ca33__p_K33(rate_eval, tf)
    S37__Cl37__weak__wc12(rate_eval, tf)
    He4_O28__n_Ne31(rate_eval, tf)
    He4_O26__n_Ne29(rate_eval, tf)
    p_O26__He4_N23(rate_eval, tf)
    He4_Ti44__p_V47(rate_eval, tf)
    Ne34__Na34__weak__mo03(rate_eval, tf)
    p_O26__n_F26(rate_eval, tf)
    He4_O24__n_Ne27(rate_eval, tf)
    p_O24__n_F24(rate_eval, tf)
    Na31__n_Mg30__weak__wc17(rate_eval, tf)
    He4_F30__n_Na33(rate_eval, tf)
    He4_O22__n_Ne25(rate_eval, tf)
    He4_Ar52__n_Ca55(rate_eval, tf)
    p_Ti57__n_V57(rate_eval, tf)
    p_O20__n_F20(rate_eval, tf)
    He4_O19__n_Ne22(rate_eval, tf)
    He4_Cl32__p_Ar35(rate_eval, tf)
    p_Cr62__n_Mn62(rate_eval, tf)
    p_O18__He4_N15(rate_eval, tf)
    He4_O17__n_Ne20(rate_eval, tf)
    p_S49__Cl50(rate_eval, tf)
    p_O17__He4_N14(rate_eval, tf)
    O16_O16__He4_Si28(rate_eval, tf)
    O16_O16__p_P31(rate_eval, tf)
    He4_Ne26__n_Mg29(rate_eval, tf)
    Cl32__S32__weak__wc12(rate_eval, tf)
    O16_O16__n_S31(rate_eval, tf)
    He4_Al28__n_P31(rate_eval, tf)
    C12_O16__He4_Mg24(rate_eval, tf)
    C12_O16__p_Al27(rate_eval, tf)
    p_K48__n_Ca48(rate_eval, tf)
    p_Ne28__He4_F25(rate_eval, tf)
    p_Al26__Si27(rate_eval, tf)
    p_Ca36__Sc37(rate_eval, tf)
    p_Na28__He4_Ne25(rate_eval, tf)
    n_K33__He4_Cl30(rate_eval, tf)
    He4_Cr45__Fe49(rate_eval, tf)
    p_Cr70__Mn71(rate_eval, tf)
    n_O14__He4_C11(rate_eval, tf)
    He4_O13__p_F16(rate_eval, tf)
    He4_Sc57__V61(rate_eval, tf)
    n_Ca33__He4_Ar30(rate_eval, tf)
    n_O13__He4_C10(rate_eval, tf)
    n_O13__p_N13(rate_eval, tf)
    n_O12__p_N12(rate_eval, tf)
    p_N15__He4_C12(rate_eval, tf)
    p_N15__n_O15(rate_eval, tf)
    n_Sc37__p_Ca37(rate_eval, tf)
    n_Mg19__He4_Ne16(rate_eval, tf)
    p_F28__He4_O25(rate_eval, tf)
    He4_Ar41__n_Ca44(rate_eval, tf)
    p_F29__Ne30(rate_eval, tf)
    n_N14__p_C14(rate_eval, tf)
    He4_N13__p_O16(rate_eval, tf)
    He4_C15__n_O18(rate_eval, tf)
    p_C15__n_N15(rate_eval, tf)
    He4_Cl50__n_K53(rate_eval, tf)
    He4_Si31__n_S34(rate_eval, tf)
    n_V39__p_Ti39(rate_eval, tf)
    He4_Cl45__n_K48(rate_eval, tf)
    Al36__Si36__weak__wc17(rate_eval, tf)
    He4_C13__n_O16(rate_eval, tf)
    Na38__Mg38__weak__mo03(rate_eval, tf)
    d_C13__n_N14(rate_eval, tf)
    p_C13__n_N13(rate_eval, tf)
    Sc53__Ti53__weak__wc12(rate_eval, tf)
    p_K44__n_Ca44(rate_eval, tf)
    n_Mn50__Mn51(rate_eval, tf)
    n_C11__p_B11(rate_eval, tf)
    He4_B13__n_N16(rate_eval, tf)
    n_K35__He4_Cl32(rate_eval, tf)
    p_Ar53__He4_Cl50(rate_eval, tf)
    He4_B12__n_N15(rate_eval, tf)
    p_B12__He4_Be9(rate_eval, tf)
    p_Ti56__He4_Sc53(rate_eval, tf)
    He4_B11__p_C14(rate_eval, tf)
    S44__n_Cl43__weak__wc12(rate_eval, tf)
    p_Ar41__K42(rate_eval, tf)
    He4_Fe46__p_Co49(rate_eval, tf)
    He4_B10__p_C13(rate_eval, tf)
    He4_B8__p_C11(rate_eval, tf)
    p_V63__He4_Ti60(rate_eval, tf)
    He4_Mn70__Co74(rate_eval, tf)
    He4_Li8__n_B11(rate_eval, tf)
    Si24__p_Mg23__weak__wc12(rate_eval, tf)
    n_Ti42__He4_Ca39(rate_eval, tf)
    n_Fe48__He4_Cr45(rate_eval, tf)
    He4_V49__p_Cr52(rate_eval, tf)
    n_Mn53__He4_V50(rate_eval, tf)
    d_Li7__p_Li8(rate_eval, tf)
    P45__n_n_n_S42__weak__mo03(rate_eval, tf)
    Be11__B11__weak__wc12(rate_eval, tf)
    n_Mn65__Mn66(rate_eval, tf)
    n_Li6__He4_t(rate_eval, tf)
    Na35__n_n_n_Mg32__weak__mo03(rate_eval, tf)
    p_Li6__He4_He3(rate_eval, tf)
    t_He3__d_He4(rate_eval, tf)
    d_He3__p_He4(rate_eval, tf)
    Cl51__Ar51__weak__mo03(rate_eval, tf)
    He4_V51__Mn55(rate_eval, tf)
    p_P34__S35(rate_eval, tf)
    n_He3__p_t(rate_eval, tf)
    d_t__n_He4(rate_eval, tf)
    d_d__p_t(rate_eval, tf)
    He4_Fe76__Ni80(rate_eval, tf)
    p_Fe76__Co77(rate_eval, tf)
    n_Cr61__Cr62(rate_eval, tf)
    n_V50__He4_Sc47(rate_eval, tf)
    He4_Fe73__Ni77(rate_eval, tf)
    p_Fe73__Co74(rate_eval, tf)
    p_Fe72__Co73(rate_eval, tf)
    p_Mg31__n_Al31(rate_eval, tf)
    n_Fe71__Fe72(rate_eval, tf)
    He4_Fe70__Ni74(rate_eval, tf)
    n_Cl28__Cl29(rate_eval, tf)
    He4_Ne18__Mg22(rate_eval, tf)
    p_Fe70__Co71(rate_eval, tf)
    Sc62__n_n_Ti60__weak__mp17(rate_eval, tf)
    n_Fe70__Fe71(rate_eval, tf)
    He4_Fe69__Ni73(rate_eval, tf)
    n_F16__p_O16(rate_eval, tf)
    n_Mn62__Mn63(rate_eval, tf)
    n_Fe69__Fe70(rate_eval, tf)
    p_P32__S33(rate_eval, tf)
    p_Fe68__Co69(rate_eval, tf)
    n_Fe68__Fe69(rate_eval, tf)
    He4_Fe67__Ni71(rate_eval, tf)
    C17__N17__weak__wc12(rate_eval, tf)
    n_Fe67__Fe68(rate_eval, tf)
    n_Na21__p_Ne21(rate_eval, tf)
    p_Fe66__Co67(rate_eval, tf)
    p_Fe65__Co66(rate_eval, tf)
    n_Fe65__Fe66(rate_eval, tf)
    Mg20__p_Ne19__weak__wc12(rate_eval, tf)
    He4_Fe64__Ni68(rate_eval, tf)
    p_Fe63__Co64(rate_eval, tf)
    He4_Sc48__n_V51(rate_eval, tf)
    n_Fe63__Fe64(rate_eval, tf)
    n_Fe62__Fe63(rate_eval, tf)
    n_S29__p_P29(rate_eval, tf)
    He4_P36__n_Cl39(rate_eval, tf)
    p_Fe61__Co62(rate_eval, tf)
    p_S46__He4_P43(rate_eval, tf)
    p_Fe60__Co61(rate_eval, tf)
    p_Al34__Si35(rate_eval, tf)
    He4_Fe59__Ni63(rate_eval, tf)
    p_Fe59__Co60(rate_eval, tf)
    He4_Fe58__Ni62(rate_eval, tf)
    n_Fe58__Fe59(rate_eval, tf)
    p_Fe57__Co58(rate_eval, tf)
    n_Fe57__Fe58(rate_eval, tf)
    p_Fe56__Co57(rate_eval, tf)
    Sc54__Ti54__weak__wc17(rate_eval, tf)
    n_Fe56__Fe57(rate_eval, tf)
    p_Fe55__Co56(rate_eval, tf)
    He4_Fe54__Ni58(rate_eval, tf)
    Ti38__Sc38__weak__mo97(rate_eval, tf)
    n_Fe54__Fe55(rate_eval, tf)
    He4_Fe52__Ni56(rate_eval, tf)
    p_Fe52__Co53(rate_eval, tf)
    He4_Fe51__Ni55(rate_eval, tf)
    p_Si36__n_P36(rate_eval, tf)
    p_Fe50__Co51(rate_eval, tf)
    p_Ne32__n_Na32(rate_eval, tf)
    n_Fe49__Fe50(rate_eval, tf)
    n_Ne30__Ne31(rate_eval, tf)
    p_Fe48__Co49(rate_eval, tf)
    He4_O25__n_Ne28(rate_eval, tf)
    n_Fe47__Fe48(rate_eval, tf)
    n_Cr55__Cr56(rate_eval, tf)
    He4_Fe46__Ni50(rate_eval, tf)
    He4_Fe57__Ni61(rate_eval, tf)
    He4_Fe45__Ni49(rate_eval, tf)
    p_Mn73__Fe74(rate_eval, tf)
    He4_Mn72__Co76(rate_eval, tf)
    n_Mn72__Mn73(rate_eval, tf)
    n_Mn71__Mn72(rate_eval, tf)
    n_Mn70__Mn71(rate_eval, tf)
    B12__C12__weak__wc17(rate_eval, tf)
    He4_Mn69__Co73(rate_eval, tf)
    p_Mn69__Fe70(rate_eval, tf)
    p_Mn68__Fe69(rate_eval, tf)
    Fe53__Mn53__weak__wc12(rate_eval, tf)
    p_Mn73__n_Fe73(rate_eval, tf)
    He4_Mn67__Co71(rate_eval, tf)
    He4_Cl30__K34(rate_eval, tf)
    p_Mn67__Fe68(rate_eval, tf)
    n_Mn67__Mn68(rate_eval, tf)
    He4_Mn66__Co70(rate_eval, tf)
    p_Mn66__Fe67(rate_eval, tf)
    He4_Mn64__Co68(rate_eval, tf)
    He4_Mn63__Co67(rate_eval, tf)
    n_Mn63__Mn64(rate_eval, tf)
    He4_Cl29__p_Ar32(rate_eval, tf)
    p_Ne33__n_Na33(rate_eval, tf)
    p_Mn62__Fe63(rate_eval, tf)
    He4_Mn61__Co65(rate_eval, tf)
    p_Mn61__Fe62(rate_eval, tf)
    Mg38__Al38__weak__mo03(rate_eval, tf)
    n_Fe51__p_Mn51(rate_eval, tf)
    P25__Si25__weak__bqa_pos_(rate_eval, tf)
    n_Mn60__Mn61(rate_eval, tf)
    p_Ca58__Sc59(rate_eval, tf)
    n_Mn59__Mn60(rate_eval, tf)
    n_Mn58__Mn59(rate_eval, tf)
    n_Mn56__Mn57(rate_eval, tf)
    p_K42__n_Ca42(rate_eval, tf)
    n_Mn55__Mn56(rate_eval, tf)
    p_Fe64__n_Co64(rate_eval, tf)
    He4_Mn53__Co57(rate_eval, tf)
    He4_Mn52__Co56(rate_eval, tf)
    He4_Mn50__Co54(rate_eval, tf)
    p_Mn50__Fe51(rate_eval, tf)
    p_Mn49__Fe50(rate_eval, tf)
    n_Mn49__Mn50(rate_eval, tf)
    He4_Si23__S27(rate_eval, tf)
    p_Mn48__Fe49(rate_eval, tf)
    He4_Mn46__Co50(rate_eval, tf)
    p_Mn46__Fe47(rate_eval, tf)
    He4_Mn45__Co49(rate_eval, tf)
    p_Mn45__Fe46(rate_eval, tf)
    n_Mn44__Mn45(rate_eval, tf)
    He4_Cr70__Fe74(rate_eval, tf)
    p_V53__He4_Ti50(rate_eval, tf)
    p_Cr69__Mn70(rate_eval, tf)
    n_Cr69__Cr70(rate_eval, tf)
    n_Cl40__Cl41(rate_eval, tf)
    He4_Cr67__Fe71(rate_eval, tf)
    K38__Ar38__weak__wc12(rate_eval, tf)
    p_Cr66__Mn67(rate_eval, tf)
    p_Cr65__Mn66(rate_eval, tf)
    He4_Cr63__Fe67(rate_eval, tf)
    p_Ca52__Sc53(rate_eval, tf)
    p_Cr63__Mn64(rate_eval, tf)
    O25__n_F24__weak__mp17(rate_eval, tf)
    He4_Cr62__Fe66(rate_eval, tf)
    n_Cr62__Cr63(rate_eval, tf)
    p_Sc48__n_Ti48(rate_eval, tf)
    p_Cr61__Mn62(rate_eval, tf)
    Al30__Si30__weak__wc12(rate_eval, tf)
    n_Ca43__He4_Ar40(rate_eval, tf)
    He4_Cr60__Fe64(rate_eval, tf)
    n_Fe51__Fe52(rate_eval, tf)
    Cr70__Mn70__weak__mo03(rate_eval, tf)
    n_Cr60__Cr61(rate_eval, tf)
    He4_Cr59__Fe63(rate_eval, tf)
    p_Cr59__Mn60(rate_eval, tf)
    He4_Mg19__p_Al22(rate_eval, tf)
    n_Cr59__Cr60(rate_eval, tf)
    He4_Cr58__Fe62(rate_eval, tf)
    p_Cr58__Mn59(rate_eval, tf)
    He4_Cr57__Fe61(rate_eval, tf)
    p_Cr57__Mn58(rate_eval, tf)
    p_Cr56__Mn57(rate_eval, tf)
    n_Cr56__Cr57(rate_eval, tf)
    He4_Cr54__Fe58(rate_eval, tf)
    p_Cr54__Mn55(rate_eval, tf)
    Cr47__V47__weak__wc12(rate_eval, tf)
    n_Mn49__p_Cr49(rate_eval, tf)
    He4_Cr53__Fe57(rate_eval, tf)
    p_Cr53__Mn54(rate_eval, tf)
    He4_Sc48__V52(rate_eval, tf)
    n_Cr53__Cr54(rate_eval, tf)
    p_Cl39__He4_S36(rate_eval, tf)
    p_Cr52__Mn53(rate_eval, tf)
    p_Cr51__Mn52(rate_eval, tf)
    p_Cr50__Mn51(rate_eval, tf)
    p_Cr49__Mn50(rate_eval, tf)
    n_O17__O18(rate_eval, tf)
    He4_Cr48__Fe52(rate_eval, tf)
    He4_Ar45__Ca49(rate_eval, tf)
    He4_K38__p_Ca41(rate_eval, tf)
    He4_P40__n_Cl43(rate_eval, tf)
    n_Cr48__Cr49(rate_eval, tf)
    Fe66__Co66__weak__wc12(rate_eval, tf)
    He4_Cr47__Fe51(rate_eval, tf)
    He4_Cr46__Fe50(rate_eval, tf)
    n_Ne19__He4_O16(rate_eval, tf)
    p_Cr46__Mn47(rate_eval, tf)
    n_Cr46__Cr47(rate_eval, tf)
    n_Cr45__Cr46(rate_eval, tf)
    He4_Cr44__Fe48(rate_eval, tf)
    n_Cr44__Cr45(rate_eval, tf)
    n_Sc55__Sc56(rate_eval, tf)
    He4_Cr43__Fe47(rate_eval, tf)
    n_Cr43__Cr44(rate_eval, tf)
    He4_Cr42__Fe46(rate_eval, tf)
    He4_Cr41__Fe45(rate_eval, tf)
    p_P44__He4_Si41(rate_eval, tf)
    He4_Mg22__Si26(rate_eval, tf)
    He4_V67__Mn71(rate_eval, tf)
    p_V67__Cr68(rate_eval, tf)
    He4_V66__Mn70(rate_eval, tf)
    p_V66__Cr67(rate_eval, tf)
    n_Mg27__Mg28(rate_eval, tf)
    He4_V64__Mn68(rate_eval, tf)
    n_Al37__Al38(rate_eval, tf)
    p_V64__Cr65(rate_eval, tf)
    He4_O14__p_F17(rate_eval, tf)
    p_K58__n_Ca58(rate_eval, tf)
    p_V63__Cr64(rate_eval, tf)
    n_V62__V63(rate_eval, tf)
    He4_V61__Mn65(rate_eval, tf)
    He4_V60__Mn64(rate_eval, tf)
    p_Ne32__He4_F29(rate_eval, tf)
    p_V60__Cr61(rate_eval, tf)
    p_V59__Cr60(rate_eval, tf)
    Na36__n_Mg35__weak__mp17(rate_eval, tf)
    n_V59__V60(rate_eval, tf)
    p_V58__Cr59(rate_eval, tf)
    He4_V57__Mn61(rate_eval, tf)
    p_V57__Cr58(rate_eval, tf)
    He4_V56__Mn60(rate_eval, tf)
    He4_Na37__n_Al40(rate_eval, tf)
    n_V55__V56(rate_eval, tf)
    He4_V54__Mn58(rate_eval, tf)
    p_V54__Cr55(rate_eval, tf)
    He4_V53__Mn57(rate_eval, tf)
    p_V53__Cr54(rate_eval, tf)
    n_V53__V54(rate_eval, tf)
    He4_V52__Mn56(rate_eval, tf)
    p_V62__n_Cr62(rate_eval, tf)
    He4_Ne25__Mg29(rate_eval, tf)
    p_V52__Cr53(rate_eval, tf)
    n_V51__V52(rate_eval, tf)
    He4_V50__Mn54(rate_eval, tf)
    He4_V65__Mn69(rate_eval, tf)
    p_V50__Cr51(rate_eval, tf)
    He4_Ne32__n_Mg35(rate_eval, tf)
    He4_F16__p_Ne19(rate_eval, tf)
    n_V49__V50(rate_eval, tf)
    p_V48__Cr49(rate_eval, tf)
    n_V48__V49(rate_eval, tf)
    n_S28__S29(rate_eval, tf)
    He4_V47__Mn51(rate_eval, tf)
    p_S42__n_Cl42(rate_eval, tf)
    p_Sc46__n_Ti46(rate_eval, tf)
    n_V47__V48(rate_eval, tf)
    He4_V46__Mn50(rate_eval, tf)
    p_V46__Cr47(rate_eval, tf)
    p_Si38__P39(rate_eval, tf)
    n_V46__V47(rate_eval, tf)
    He4_V45__Mn49(rate_eval, tf)
    p_Mn63__Fe64(rate_eval, tf)
    n_V45__V46(rate_eval, tf)
    He4_V43__Mn47(rate_eval, tf)
    p_V43__Cr44(rate_eval, tf)
    p_P40__n_S40(rate_eval, tf)
    p_Al42__He4_Mg39(rate_eval, tf)
    n_V42__V43(rate_eval, tf)
    He4_V41__Mn45(rate_eval, tf)
    n_Fe57__He4_Cr54(rate_eval, tf)
    p_V41__Cr42(rate_eval, tf)
    C16__n_N15__weak__wc12(rate_eval, tf)
    n_V41__V42(rate_eval, tf)
    He4_V39__Mn43(rate_eval, tf)
    n_Mn54__Mn55(rate_eval, tf)
    n_Ti64__Ti65(rate_eval, tf)
    He4_Ti63__Cr67(rate_eval, tf)
    p_Ti63__V64(rate_eval, tf)
    p_Ti62__V63(rate_eval, tf)
    He4_Ti61__Cr65(rate_eval, tf)
    Al39__n_Si38__weak__mp17(rate_eval, tf)
    n_Ne16__He4_O13(rate_eval, tf)
    p_N12__O13(rate_eval, tf)
    p_Ti61__V62(rate_eval, tf)
    p_Ti60__V61(rate_eval, tf)
    n_Ti60__Ti61(rate_eval, tf)
    p_Ti58__V59(rate_eval, tf)
    C21__n_C20(rate_eval, tf)
    p_Ti57__V58(rate_eval, tf)
    p_Ti56__V57(rate_eval, tf)
    p_Fe63__n_Co63(rate_eval, tf)
    p_Ti55__V56(rate_eval, tf)
    p_Cr58__n_Mn58(rate_eval, tf)
    p_Ar47__n_K47(rate_eval, tf)
    n_Ti55__Ti56(rate_eval, tf)
    p_Ar36__K37(rate_eval, tf)
    p_Ti54__V55(rate_eval, tf)
    He4_Ti53__Cr57(rate_eval, tf)
    p_Ti53__V54(rate_eval, tf)
    n_Ti57__Ti58(rate_eval, tf)
    He4_Ti52__Cr56(rate_eval, tf)
    C12_Ne20__n_S31(rate_eval, tf)
    p_Ti52__V53(rate_eval, tf)
    n_Ti52__Ti53(rate_eval, tf)
    n_V43__V44(rate_eval, tf)
    He4_Ti51__Cr55(rate_eval, tf)
    p_Ti49__V50(rate_eval, tf)
    t_Be9__n_B11(rate_eval, tf)
    n_Ti49__Ti50(rate_eval, tf)
    He4_Na39__n_Al42(rate_eval, tf)
    He4_Ti48__Cr52(rate_eval, tf)
    p_Ti47__V48(rate_eval, tf)
    He4_Ti57__n_Cr60(rate_eval, tf)
    n_Ti47__Ti48(rate_eval, tf)
    He4_Ti46__Cr50(rate_eval, tf)
    n_Ti46__Ti47(rate_eval, tf)
    He4_Ti45__Cr49(rate_eval, tf)
    n_Ti45__Ti46(rate_eval, tf)
    He4_Ti44__Cr48(rate_eval, tf)
    p_Ti44__V45(rate_eval, tf)
    n_Ti44__Ti45(rate_eval, tf)
    n_Mn44__p_Cr44(rate_eval, tf)
    He4_Al29__p_Si32(rate_eval, tf)
    He4_Ti43__Cr47(rate_eval, tf)
    n_Ti43__Ti44(rate_eval, tf)
    p_Ti42__V43(rate_eval, tf)
    He4_Ti41__Cr45(rate_eval, tf)
    He4_Na32__n_Al35(rate_eval, tf)
    p_Ti41__V42(rate_eval, tf)
    p_S28__Cl29(rate_eval, tf)
    n_Ti41__Ti42(rate_eval, tf)
    He4_Ti40__Cr44(rate_eval, tf)
    p_Ti40__V41(rate_eval, tf)
    p_Mn72__Fe73(rate_eval, tf)
    n_Ti40__Ti41(rate_eval, tf)
    He4_Ti38__Cr42(rate_eval, tf)
    p_Ar50__n_K50(rate_eval, tf)
    n_Ti38__Ti39(rate_eval, tf)
    n_Ti37__Ti38(rate_eval, tf)
    n_Ar34__He4_S31(rate_eval, tf)
    p_Sc63__Ti64(rate_eval, tf)
    n_Sc62__Sc63(rate_eval, tf)
    He4_Al35__P39(rate_eval, tf)
    p_Mn44__Fe45(rate_eval, tf)
    p_Sc61__Ti62(rate_eval, tf)
    He4_Sc60__V64(rate_eval, tf)
    n_Sc59__Sc60(rate_eval, tf)
    N16__O16__weak__wc12(rate_eval, tf)
    Si44__n_P43__weak__mp17(rate_eval, tf)
    He4_Sc58__V62(rate_eval, tf)
    p_Sc58__Ti59(rate_eval, tf)
    n_Sc58__Sc59(rate_eval, tf)
    He4_Ca60__n_Ti63(rate_eval, tf)
    p_Sc57__Ti58(rate_eval, tf)
    He4_Sc56__V60(rate_eval, tf)
    He4_Ti49__n_Cr52(rate_eval, tf)
    N17__n_O16__weak__wc12(rate_eval, tf)
    p_Sc56__Ti57(rate_eval, tf)
    n_Sc56__Sc57(rate_eval, tf)
    p_Sc37__Ti38(rate_eval, tf)
    He4_Sc55__V59(rate_eval, tf)
    p_Sc55__Ti56(rate_eval, tf)
    He4_K45__p_Ca48(rate_eval, tf)
    n_Sc54__Sc55(rate_eval, tf)
    p_Sc53__Ti54(rate_eval, tf)
    n_Sc53__Sc54(rate_eval, tf)
    n_Sc50__Sc51(rate_eval, tf)
    p_Mn57__He4_Cr54(rate_eval, tf)
    p_He3__He4__weak__bet_pos_(rate_eval, tf)
    He4_Sc49__V53(rate_eval, tf)
    He4_Mn44__Co48(rate_eval, tf)
    p_Mg31__Al32(rate_eval, tf)
    p_Sc49__Ti50(rate_eval, tf)
    n_Sc49__Sc50(rate_eval, tf)
    p_Sc48__Ti49(rate_eval, tf)
    n_Sc48__Sc49(rate_eval, tf)
    p_Ne21__Na22(rate_eval, tf)
    He4_Sc47__V51(rate_eval, tf)
    p_Sc46__Ti47(rate_eval, tf)
    n_Sc46__Sc47(rate_eval, tf)
    n_V47__p_Ti47(rate_eval, tf)
    He4_Sc45__V49(rate_eval, tf)
    He4_Mg20__Si24(rate_eval, tf)
    n_Sc45__Sc46(rate_eval, tf)
    p_Ca50__He4_K47(rate_eval, tf)
    p_Sc43__Ti44(rate_eval, tf)
    Cl52__n_n_n_Ar49__weak__mo03(rate_eval, tf)
    n_Cr63__Cr64(rate_eval, tf)
    F23__Ne23__weak__wc12(rate_eval, tf)
    He4_Sc42__V46(rate_eval, tf)
    p_Sc42__Ti43(rate_eval, tf)
    n_Sc42__Sc43(rate_eval, tf)
    He4_Sc41__V45(rate_eval, tf)
    p_Mn60__Fe61(rate_eval, tf)
    p_Sc41__Ti42(rate_eval, tf)
    n_Sc41__Sc42(rate_eval, tf)
    p_Sc40__Ti41(rate_eval, tf)
    He4_Sc39__V43(rate_eval, tf)
    n_Sc39__Sc40(rate_eval, tf)
    Mg36__Al36__weak__wc17(rate_eval, tf)
    He4_Sc38__V42(rate_eval, tf)
    p_Sc38__Ti39(rate_eval, tf)
    n_Sc38__Sc39(rate_eval, tf)
    p_Na33__He4_Ne30(rate_eval, tf)
    n_Sc37__Sc38(rate_eval, tf)
    He4_Cr55__Fe59(rate_eval, tf)
    p_Ca60__Sc61(rate_eval, tf)
    F27__n_n_Ne25__weak__mp17(rate_eval, tf)
    n_Ca60__Ca61(rate_eval, tf)
    He4_F25__n_Na28(rate_eval, tf)
    p_Ti51__V52(rate_eval, tf)
    He4_Ca59__Ti63(rate_eval, tf)
    n_Ar39__Ar40(rate_eval, tf)
    p_Ca59__Sc60(rate_eval, tf)
    He4_Cr64__Fe68(rate_eval, tf)
    p_Ca57__Sc58(rate_eval, tf)
    P47__n_n_n_S44__weak__mo03(rate_eval, tf)
    p_Na20__Mg21(rate_eval, tf)
    n_Ca57__Ca58(rate_eval, tf)
    Cl41__Ar41__weak__wc12(rate_eval, tf)
    C12_C12__p_Na23(rate_eval, tf)
    n_Ca56__Ca57(rate_eval, tf)
    n_Ca55__Ca56(rate_eval, tf)
    He4_Na27__n_Al30(rate_eval, tf)
    He4_Mn59__n_Co62(rate_eval, tf)
    He4_O27__Ne31(rate_eval, tf)
    Sc40__Ca40__weak__wc12(rate_eval, tf)
    p_Ca54__Sc55(rate_eval, tf)
    He4_V48__p_Cr51(rate_eval, tf)
    n_Ca54__Ca55(rate_eval, tf)
    Al39__n_n_Si37__weak__mp17(rate_eval, tf)
    n_Ca53__Ca54(rate_eval, tf)
    p_Fe58__Co59(rate_eval, tf)
    p_Mn71__Fe72(rate_eval, tf)
    P36__S36__weak__wc12(rate_eval, tf)
    He4_Ca51__Ti55(rate_eval, tf)
    S47__Cl47__weak__mo03(rate_eval, tf)
    p_Ca51__Sc52(rate_eval, tf)
    O27__F27__weak__mo03(rate_eval, tf)
    p_K42__He4_Ar39(rate_eval, tf)
    He4_Be11__n_C14(rate_eval, tf)
    n_Ca51__Ca52(rate_eval, tf)
    He4_Ca50__Ti54(rate_eval, tf)
    n_Ca49__Ca50(rate_eval, tf)
    He4_Ca47__Ti51(rate_eval, tf)
    B17__n_n_n_C14__weak__wc12(rate_eval, tf)
    He4_Na36__Al40(rate_eval, tf)
    He4_Ca46__Ti50(rate_eval, tf)
    Ca36__K36__weak__wc12(rate_eval, tf)
    Ca34__K34__weak__bqa_pos_(rate_eval, tf)
    C17__n_N16__weak__wc12(rate_eval, tf)
    n_Ca46__Ca47(rate_eval, tf)
    He4_Ca45__Ti49(rate_eval, tf)
    t_Li7__n_Be9(rate_eval, tf)
    He4_Li7__B11(rate_eval, tf)
    He4_Ca44__Ti48(rate_eval, tf)
    He4_Ca42__Ti46(rate_eval, tf)
    p_Ca42__Sc43(rate_eval, tf)
    p_Ca41__Sc42(rate_eval, tf)
    Si34__P34__weak__wc12(rate_eval, tf)
    n_Cr51__Cr52(rate_eval, tf)
    n_Ca41__Ca42(rate_eval, tf)
    p_Ca52__He4_K49(rate_eval, tf)
    n_F16__He4_N13(rate_eval, tf)
    p_Ca40__Sc41(rate_eval, tf)
    Al41__n_Si40__weak__mp17(rate_eval, tf)
    n_Ca40__Ca41(rate_eval, tf)
    He4_Ca37__Ti41(rate_eval, tf)
    n_Ca37__Ca38(rate_eval, tf)
    p_Fe64__Co65(rate_eval, tf)
    n_Na27__Na28(rate_eval, tf)
    n_Ca36__Ca37(rate_eval, tf)
    p_Si37__P38(rate_eval, tf)
    He4_Ca35__Ti39(rate_eval, tf)
    P37__S37__weak__wc12(rate_eval, tf)
    Ar54__n_K53__weak__mp17(rate_eval, tf)
    p_Ca35__Sc36(rate_eval, tf)
    He4_Ca34__Ti38(rate_eval, tf)
    He4_Cl46__n_K49(rate_eval, tf)
    p_Ca34__Sc35(rate_eval, tf)
    p_Be11__He4_Li8(rate_eval, tf)
    n_Fe47__p_Mn47(rate_eval, tf)
    He4_Ca33__Ti37(rate_eval, tf)
    He4_Na27__Al31(rate_eval, tf)
    p_K59__Ca60(rate_eval, tf)
    He4_K58__Sc62(rate_eval, tf)
    p_K50__n_Ca50(rate_eval, tf)
    Na27__Mg27__weak__wc12(rate_eval, tf)
    p_P30__S31(rate_eval, tf)
    p_K57__Ca58(rate_eval, tf)
    He4_Cl44__n_K47(rate_eval, tf)
    He4_Na29__Al33(rate_eval, tf)
    p_K56__Ca57(rate_eval, tf)
    He4_Si45__S49(rate_eval, tf)
    He4_K55__Sc59(rate_eval, tf)
    V60__Cr60__weak__wc17(rate_eval, tf)
    Fe60__Co60__weak__wc12(rate_eval, tf)
    p_Cl36__He4_S33(rate_eval, tf)
    n_K56__K57(rate_eval, tf)
    Sc55__n_Ti54__weak__wc12(rate_eval, tf)
    n_K53__K54(rate_eval, tf)
    He4_S27__Ar31(rate_eval, tf)
    p_K52__Ca53(rate_eval, tf)
    n_K52__K53(rate_eval, tf)
    He4_K51__Sc55(rate_eval, tf)
    p_F20__n_Ne20(rate_eval, tf)
    p_K51__Ca52(rate_eval, tf)
    n_K50__K51(rate_eval, tf)
    He4_K49__Sc53(rate_eval, tf)
    n_K46__K47(rate_eval, tf)
    p_Ti65__V66(rate_eval, tf)
    p_Ne26__Na27(rate_eval, tf)
    p_K45__Ca46(rate_eval, tf)
    He4_Ne17__Mg21(rate_eval, tf)
    Sc54__n_Ti53__weak__mp17(rate_eval, tf)
    n_K45__K46(rate_eval, tf)
    p_Ar38__K39(rate_eval, tf)
    He4_K44__Sc48(rate_eval, tf)
    n_K44__K45(rate_eval, tf)
    He4_K43__Sc47(rate_eval, tf)
    p_K43__Ca44(rate_eval, tf)
    n_K39__He4_Cl36(rate_eval, tf)
    p_Cr45__Mn46(rate_eval, tf)
    He4_Ti47__Cr51(rate_eval, tf)
    He4_Ne27__Mg31(rate_eval, tf)
    Mn70__n_Fe69__weak__mp17(rate_eval, tf)
    p_Sc62__Ti63(rate_eval, tf)
    n_K43__K44(rate_eval, tf)
    n_Al28__Al29(rate_eval, tf)
    p_K41__Ca42(rate_eval, tf)
    p_S34__Cl35(rate_eval, tf)
    n_K41__K42(rate_eval, tf)
    Ca35__p_p_Cl33__weak__wc12(rate_eval, tf)
    n_K40__K41(rate_eval, tf)
    p_K38__Ca39(rate_eval, tf)
    He4_Ca36__p_Sc39(rate_eval, tf)
    p_K37__Ca38(rate_eval, tf)
    He4_Sc48__p_Ti51(rate_eval, tf)
    n_Mn45__Mn46(rate_eval, tf)
    p_V56__n_Cr56(rate_eval, tf)
    n_K37__K38(rate_eval, tf)
    He4_P28__Cl32(rate_eval, tf)
    p_K36__Ca37(rate_eval, tf)
    n_K36__K37(rate_eval, tf)
    n_O15__He4_C12(rate_eval, tf)
    He4_K35__Sc39(rate_eval, tf)
    n_K34__K35(rate_eval, tf)
    n_K33__K34(rate_eval, tf)
    He4_K32__Sc36(rate_eval, tf)
    n_Si40__Si41(rate_eval, tf)
    n_K32__K33(rate_eval, tf)
    He4_Ar53__Ca57(rate_eval, tf)
    p_Ar51__K52(rate_eval, tf)
    Mn66__Fe66__weak__wc17(rate_eval, tf)
    p_Cl42__n_Ar42(rate_eval, tf)
    n_Ar51__Ar52(rate_eval, tf)
    n_Ar47__Ar48(rate_eval, tf)
    He4_Ar46__Ca50(rate_eval, tf)
    n_Ar46__Ar47(rate_eval, tf)
    n_F18__p_O18(rate_eval, tf)
    p_S41__Cl42(rate_eval, tf)
    p_Ar47__K48(rate_eval, tf)
    n_Ar45__Ar46(rate_eval, tf)
    Fe50__Mn50__weak__wc12(rate_eval, tf)
    p_Ar44__K45(rate_eval, tf)
    n_Ar44__Ar45(rate_eval, tf)
    p_Ar43__K44(rate_eval, tf)
    P46__n_n_n_S43__weak__mo03(rate_eval, tf)
    K53__n_Ca52__weak__wc17(rate_eval, tf)
    p_Ar42__K43(rate_eval, tf)
    n_Li7__Li8(rate_eval, tf)
    n_Ar42__Ar43(rate_eval, tf)
    n_Mg26__Mg27(rate_eval, tf)
    He4_Ar40__Ca44(rate_eval, tf)
    He4_Cr51__Fe55(rate_eval, tf)
    p_Ar40__K41(rate_eval, tf)
    n_Ar40__Ar41(rate_eval, tf)
    He4_Ar39__Ca43(rate_eval, tf)
    He4_Ar37__Ca41(rate_eval, tf)
    p_Ar37__K38(rate_eval, tf)
    He4_Ca36__Ti40(rate_eval, tf)
    Ne28__n_Na27__weak__wc12(rate_eval, tf)
    He4_Fe50__Ni54(rate_eval, tf)
    p_Ar35__K36(rate_eval, tf)
    Cl43__n_Ar42__weak__mp17(rate_eval, tf)
    p_F20__Ne21(rate_eval, tf)
    p_Si25__P26(rate_eval, tf)
    He4_Ar33__Ca37(rate_eval, tf)
    p_Ar33__K34(rate_eval, tf)
    He4_Ar32__Ca36(rate_eval, tf)
    p_Cl43__Ar44(rate_eval, tf)
    p_Ar32__K33(rate_eval, tf)
    Al41__Si41__weak__mo03(rate_eval, tf)
    n_Ar32__Ar33(rate_eval, tf)
    p_P33__He4_Si30(rate_eval, tf)
    p_Si44__He4_Al41(rate_eval, tf)
    Na32__n_n_Mg30__weak__wc12(rate_eval, tf)
    p_P28__S29(rate_eval, tf)
    He4_Ar31__Ca35(rate_eval, tf)
    p_Ar31__K32(rate_eval, tf)
    n_Ar31__Ar32(rate_eval, tf)
    He4_Ne20__Mg24(rate_eval, tf)
    Ne24__Na24__weak__wc12(rate_eval, tf)
    He4_Ar30__Ca34(rate_eval, tf)
    n_Ar29__Ar30(rate_eval, tf)
    He4_Cl51__K55(rate_eval, tf)
    He4_Mg34__Si38(rate_eval, tf)
    p_Cl51__Ar52(rate_eval, tf)
    n_Cl51__Cl52(rate_eval, tf)
    p_Mn57__Fe58(rate_eval, tf)
    He4_Cr60__n_Fe63(rate_eval, tf)
    p_Cl49__Ar50(rate_eval, tf)
    p_Ar53__n_K53(rate_eval, tf)
    Ca51__Sc51__weak__wc12(rate_eval, tf)
    n_Cl49__Cl50(rate_eval, tf)
    V46__Ti46__weak__wc12(rate_eval, tf)
    He4_Cl46__K50(rate_eval, tf)
    n_Cl46__Cl47(rate_eval, tf)
    Ti45__Sc45__weak__wc12(rate_eval, tf)
    n_Cl45__Cl46(rate_eval, tf)
    V62__n_Cr61__weak__mp17(rate_eval, tf)
    n_Cl44__Cl45(rate_eval, tf)
    He4_P26__Cl30(rate_eval, tf)
    He4_Cl42__K46(rate_eval, tf)
    n_Cl42__Cl43(rate_eval, tf)
    p_Cl41__Ar42(rate_eval, tf)
    He4_Cl39__K43(rate_eval, tf)
    Ne31__Na31__weak__wc17(rate_eval, tf)
    p_Cl46__Ar47(rate_eval, tf)
    p_Cl39__Ar40(rate_eval, tf)
    p_Cr64__n_Mn64(rate_eval, tf)
    Si45__n_P44__weak__mp17(rate_eval, tf)
    He4_Cl38__K42(rate_eval, tf)
    He4_Cl36__K40(rate_eval, tf)
    Na20__Ne20__weak__wc12(rate_eval, tf)
    He4_Cl35__K39(rate_eval, tf)
    p_Cl35__Ar36(rate_eval, tf)
    p_Ti39__V40(rate_eval, tf)
    p_Mg35__n_Al35(rate_eval, tf)
    He4_Cl33__K37(rate_eval, tf)
    n_Cl33__Cl34(rate_eval, tf)
    He4_Cl32__K36(rate_eval, tf)
    He4_O21__Ne25(rate_eval, tf)
    n_Mg32__Mg33(rate_eval, tf)
    p_Cl32__Ar33(rate_eval, tf)
    n_Ca44__Ca45(rate_eval, tf)
    p_Al42__Si43(rate_eval, tf)
    n_Cl32__Cl33(rate_eval, tf)
    He4_Cl31__K35(rate_eval, tf)
    He4_K45__Sc49(rate_eval, tf)
    p_Cl31__Ar32(rate_eval, tf)
    p_Cl30__Ar31(rate_eval, tf)
    p_Cl29__Ar30(rate_eval, tf)
    n_K47__K48(rate_eval, tf)
    K47__Ca47__weak__wc12(rate_eval, tf)
    He4_S49__Ar53(rate_eval, tf)
    He4_S48__Ar52(rate_eval, tf)
    p_Si34__P35(rate_eval, tf)
    He4_S47__Ar51(rate_eval, tf)
    Fe72__n_Co71__weak__mp17(rate_eval, tf)
    n_S47__S48(rate_eval, tf)
    He4_S44__Ar48(rate_eval, tf)
    p_S44__Cl45(rate_eval, tf)
    n_S44__S45(rate_eval, tf)
    n_Fe73__Fe74(rate_eval, tf)
    n_K49__K50(rate_eval, tf)
    n_Mg28__Mg29(rate_eval, tf)
    He4_S43__Ar47(rate_eval, tf)
    He4_S46__Ar50(rate_eval, tf)
    He4_S42__Ar46(rate_eval, tf)
    Mn61__Fe61__weak__wc12(rate_eval, tf)
    n_S42__S43(rate_eval, tf)
    Si33__P33__weak__wc12(rate_eval, tf)
    B17__n_n_C15__weak__wc12(rate_eval, tf)
    Al37__n_Si36__weak__mp17(rate_eval, tf)
    p_S40__Cl41(rate_eval, tf)
    n_S40__S41(rate_eval, tf)
    He4_F28__Na32(rate_eval, tf)
    p_Cl50__Ar51(rate_eval, tf)
    He4_S39__Ar43(rate_eval, tf)
    He4_Ar47__Ca51(rate_eval, tf)
    p_S39__Cl40(rate_eval, tf)
    n_S38__S39(rate_eval, tf)
    V47__Ti47__weak__wc12(rate_eval, tf)
    p_K34__Ca35(rate_eval, tf)
    He4_S36__Ar40(rate_eval, tf)
    He4_Mg36__Si40(rate_eval, tf)
    p_Na32__n_Mg32(rate_eval, tf)
    Cl47__n_n_Ar45__weak__mp17(rate_eval, tf)
    Ti51__V51__weak__wc12(rate_eval, tf)
    p_S36__Cl37(rate_eval, tf)
    He4_Ar54__n_Ca57(rate_eval, tf)
    p_S35__Cl36(rate_eval, tf)
    V45__Ti45__weak__wc12(rate_eval, tf)
    n_S34__S35(rate_eval, tf)
    He4_Ca45__n_Ti48(rate_eval, tf)
    n_S33__S34(rate_eval, tf)
    He4_S32__Ar36(rate_eval, tf)
    n_Ar52__Ar53(rate_eval, tf)
    p_S32__Cl33(rate_eval, tf)
    n_S32__S33(rate_eval, tf)
    p_S31__Cl32(rate_eval, tf)
    p_S29__Cl30(rate_eval, tf)
    He4_O22__Ne26(rate_eval, tf)
    He4_Ne24__Mg28(rate_eval, tf)
    He4_P37__Cl41(rate_eval, tf)
    Mg39__n_Al38__weak__mp17(rate_eval, tf)
    n_S27__S28(rate_eval, tf)
    p_Si33__P34(rate_eval, tf)
    n_S26__S27(rate_eval, tf)
    He4_Fe71__Ni75(rate_eval, tf)
    n_P45__P46(rate_eval, tf)
    n_P44__P45(rate_eval, tf)
    Al32__Si32__weak__wc12(rate_eval, tf)
    n_P42__P43(rate_eval, tf)
    n_P41__P42(rate_eval, tf)
    He4_O21__n_Ne24(rate_eval, tf)
    He4_P40__Cl44(rate_eval, tf)
    He4_K41__Sc45(rate_eval, tf)
    p_P40__S41(rate_eval, tf)
    C19__N19__weak__wc07(rate_eval, tf)
    He4_Cl37__K41(rate_eval, tf)
    He4_Mg33__n_Si36(rate_eval, tf)
    t__He3__weak__wc12(rate_eval, tf)
    p_P38__S39(rate_eval, tf)
    He4_Cl38__n_K41(rate_eval, tf)
    n_Na31__Na32(rate_eval, tf)
    n_P38__P39(rate_eval, tf)
    He4_P36__Cl40(rate_eval, tf)
    n_P36__P37(rate_eval, tf)
    He4_P35__Cl39(rate_eval, tf)
    C20__n_N19__weak__wc12(rate_eval, tf)
    He4_Cl44__K48(rate_eval, tf)
    p_P35__S36(rate_eval, tf)
    n_P35__P36(rate_eval, tf)
    n_P33__P34(rate_eval, tf)
    p_Fe58__He4_Mn55(rate_eval, tf)
    n_Ca38__Ca39(rate_eval, tf)
    He4_P32__Cl36(rate_eval, tf)
    n_P32__P33(rate_eval, tf)
    n_Mn45__He4_V42(rate_eval, tf)
    n_Cl32__p_S32(rate_eval, tf)
    n_Ar30__Ar31(rate_eval, tf)
    n_P28__P29(rate_eval, tf)
    He4_S26__Ar30(rate_eval, tf)
    B19__C19__weak__wc12(rate_eval, tf)
    He4_P27__Cl31(rate_eval, tf)
    n_P27__P28(rate_eval, tf)
    p_P26__S27(rate_eval, tf)
    n_P26__P27(rate_eval, tf)
    V55__Cr55__weak__wc12(rate_eval, tf)
    He4_Na31__Al35(rate_eval, tf)
    He4_P24__Cl28(rate_eval, tf)
    p_Mn70__Fe71(rate_eval, tf)
    He4_Cl33__p_Ar36(rate_eval, tf)
    S49__n_Cl48__weak__mp17(rate_eval, tf)
    p_Ca56__Sc57(rate_eval, tf)
    p_K55__n_Ca55(rate_eval, tf)
    p_Si42__P43(rate_eval, tf)
    K49__Ca49__weak__wc12(rate_eval, tf)
    Si31__P31__weak__wc12(rate_eval, tf)
    Mg37__Al37__weak__mo03(rate_eval, tf)
    n_Si42__Si43(rate_eval, tf)
    He4_Si41__S45(rate_eval, tf)
    He4_Si40__S44(rate_eval, tf)
    Ca59__n_n_Sc57__weak__mp17(rate_eval, tf)
    p_Si40__P41(rate_eval, tf)
    p_Si39__P40(rate_eval, tf)
    He4_Si38__S42(rate_eval, tf)
    p_Ar54__He4_Cl51(rate_eval, tf)
    F31__Ne31__weak__mo03(rate_eval, tf)
    S27__P27__weak__wc12(rate_eval, tf)
    Al34__n_Si33__weak__wc12(rate_eval, tf)
    n_Si38__Si39(rate_eval, tf)
    n_Si36__Si37(rate_eval, tf)
    n_Cr42__Cr43(rate_eval, tf)
    n_Al24__He4_Na21(rate_eval, tf)
    He4_Si34__S38(rate_eval, tf)
    He4_Si33__S37(rate_eval, tf)
    n_S45__S46(rate_eval, tf)
    He4_Cl29__K33(rate_eval, tf)
    p_Si32__P33(rate_eval, tf)
    p_Cl47__Ar48(rate_eval, tf)
    p_Mg37__n_Al37(rate_eval, tf)
    n_Si32__Si33(rate_eval, tf)
    n_Si22__Si23(rate_eval, tf)
    p_Si31__P32(rate_eval, tf)
    p_Si30__P31(rate_eval, tf)
    Cl29__S29__weak__bqa_pos_(rate_eval, tf)
    p_Si28__P29(rate_eval, tf)
    n_S41__S42(rate_eval, tf)
    p_Si26__P27(rate_eval, tf)
    n_Ne17__He4_O14(rate_eval, tf)
    n_Si26__Si27(rate_eval, tf)
    He4_Si24__S28(rate_eval, tf)
    Ca54__n_Sc53__weak__mp17(rate_eval, tf)
    p_Si24__P25(rate_eval, tf)
    p_Sc56__He4_Ca53(rate_eval, tf)
    p_Ca54__n_Sc54(rate_eval, tf)
    n_Si24__Si25(rate_eval, tf)
    Ca57__Sc57__weak__mo03(rate_eval, tf)
    He4_Al43__P47(rate_eval, tf)
    He4_Cl34__K38(rate_eval, tf)
    Mn62__Fe62__weak__mo03(rate_eval, tf)
    He4_Al42__P46(rate_eval, tf)
    He4_Ca38__p_Sc41(rate_eval, tf)
    p_O17__F18(rate_eval, tf)
    He4_Al40__P44(rate_eval, tf)
    p_Al40__Si41(rate_eval, tf)
    V65__Cr65__weak__mo03(rate_eval, tf)
    n_Al40__Al41(rate_eval, tf)
    p_Ti64__n_V64(rate_eval, tf)
    n_Al39__Al40(rate_eval, tf)
    He4_Al38__P42(rate_eval, tf)
    p_K40__Ca41(rate_eval, tf)
    n_Al38__Al39(rate_eval, tf)
    He4_Al37__P41(rate_eval, tf)
    p_Cl51__n_Ar51(rate_eval, tf)
    p_Al37__Si38(rate_eval, tf)
    P32__S32__weak__wc12(rate_eval, tf)
    Ne19__F19__weak__wc12(rate_eval, tf)
    n_Ar38__Ar39(rate_eval, tf)
    p_Sc59__He4_Ca56(rate_eval, tf)
    p_K44__Ca45(rate_eval, tf)
    S49__Cl49__weak__mo03(rate_eval, tf)
    He4_Al36__P40(rate_eval, tf)
    p_Si40__n_P40(rate_eval, tf)
    He4_Mg37__Si41(rate_eval, tf)
    p_Al36__Si37(rate_eval, tf)
    n_Al35__Al36(rate_eval, tf)
    He4_N14__n_F17(rate_eval, tf)
    n_V61__V62(rate_eval, tf)
    He4_Al34__P38(rate_eval, tf)
    n_Al34__Al35(rate_eval, tf)
    He4_Cr56__Fe60(rate_eval, tf)
    p_Al33__Si34(rate_eval, tf)
    p_Al31__Si32(rate_eval, tf)
    n_Al31__Al32(rate_eval, tf)
    Li11__n_n_Be9__weak__wc12(rate_eval, tf)
    He4_Al30__P34(rate_eval, tf)
    p_S49__He4_P46(rate_eval, tf)
    p_Al30__Si31(rate_eval, tf)
    n_V50__V51(rate_eval, tf)
    p_Al28__Si29(rate_eval, tf)
    He4_Ti62__n_Cr65(rate_eval, tf)
    p_Cr68__Mn69(rate_eval, tf)
    He4_Al27__P31(rate_eval, tf)
    Al25__Mg25__weak__wc12(rate_eval, tf)
    He4_Al26__P30(rate_eval, tf)
    n_Al26__Al27(rate_eval, tf)
    p_Al24__Si25(rate_eval, tf)
    n_Al24__Al25(rate_eval, tf)
    He4_Ti56__Cr60(rate_eval, tf)
    Fe69__Co69__weak__wc17(rate_eval, tf)
    He4_Mg41__Si45(rate_eval, tf)
    p_Cl39__n_Ar39(rate_eval, tf)
    He4_Mg39__Si43(rate_eval, tf)
    p_Mg39__Al40(rate_eval, tf)
    p_Mg37__Al38(rate_eval, tf)
    n_Sc44__Sc45(rate_eval, tf)
    n_Mg36__Mg37(rate_eval, tf)
    He4_Al41__P45(rate_eval, tf)
    d_Li6__n_Be7(rate_eval, tf)
    n_Mg35__Mg36(rate_eval, tf)
    p_Sc60__Ti61(rate_eval, tf)
    p_P46__He4_Si43(rate_eval, tf)
    n_Mg34__Mg35(rate_eval, tf)
    p_Cr47__Mn48(rate_eval, tf)
    He4_Si39__S43(rate_eval, tf)
    He4_Mg40__Si44(rate_eval, tf)
    p_Ca43__Sc44(rate_eval, tf)
    He4_Mg33__Si37(rate_eval, tf)
    He4_Mg31__Si35(rate_eval, tf)
    p_S48__He4_P45(rate_eval, tf)
    n_Si35__Si36(rate_eval, tf)
    He4_Al29__P33(rate_eval, tf)
    n_K37__p_Ar37(rate_eval, tf)
    n_Mg31__Mg32(rate_eval, tf)
    p_Fe49__Co50(rate_eval, tf)
    He4_K47__Sc51(rate_eval, tf)
    p_Mg30__Al31(rate_eval, tf)
    p_Si44__P45(rate_eval, tf)
    He4_Mg29__Si33(rate_eval, tf)
    p_Mg33__n_Al33(rate_eval, tf)
    n_Mg29__Mg30(rate_eval, tf)
    He4_Mg30__Si34(rate_eval, tf)
    n_Ca45__Ca46(rate_eval, tf)
    p_Mg32__Al33(rate_eval, tf)
    He4_Mg28__Si32(rate_eval, tf)
    p_Fe54__Co55(rate_eval, tf)
    p_Mg27__Al28(rate_eval, tf)
    He4_Mn65__Co69(rate_eval, tf)
    Mn70__Fe70__weak__mo03(rate_eval, tf)
    B17__C17__weak__wc17(rate_eval, tf)
    Ti64__n_n_V62__weak__mp17(rate_eval, tf)
    P44__S44__weak__wc17(rate_eval, tf)
    p_Fe46__Co47(rate_eval, tf)
    p_Mg26__Al27(rate_eval, tf)
    p_K49__Ca50(rate_eval, tf)
    Ne25__Na25__weak__wc12(rate_eval, tf)
    p_Mg24__Al25(rate_eval, tf)
    n_Mg24__Mg25(rate_eval, tf)
    n_Ca43__Ca44(rate_eval, tf)
    Fe68__n_Co67__weak__mp17(rate_eval, tf)
    He4_Mg23__Si27(rate_eval, tf)
    p_Mg23__Al24(rate_eval, tf)
    n_Mn44__He4_V41(rate_eval, tf)
    S45__n_n_Cl43__weak__mp17(rate_eval, tf)
    n_Mg23__Mg24(rate_eval, tf)
    He4_Mg31__n_Si34(rate_eval, tf)
    He4_Ca53__Ti57(rate_eval, tf)
    Cl28__S28__weak__bqa_pos_(rate_eval, tf)
    n_Cl34__Cl35(rate_eval, tf)
    p_Mg22__Al23(rate_eval, tf)
    n_Mg22__Mg23(rate_eval, tf)
    n_C14__C15(rate_eval, tf)
    He4_Mg21__Si25(rate_eval, tf)
    He4_Mn48__p_Fe51(rate_eval, tf)
    He4_He4_He4__C12(rate_eval, tf)
    He4_Cl43__K47(rate_eval, tf)
    He4_Mg19__Si23(rate_eval, tf)
    p_Na38__Mg39(rate_eval, tf)
    He4_Si31__S35(rate_eval, tf)
    p_Sc36__Ti37(rate_eval, tf)
    He4_Na37__Al41(rate_eval, tf)
    n_Na37__Na38(rate_eval, tf)
    n_Mn51__Mn52(rate_eval, tf)
    He4_S49__n_Ar52(rate_eval, tf)
    n_Na36__Na37(rate_eval, tf)
    p_Cl47__n_Ar47(rate_eval, tf)
    Ca38__K38__weak__wc12(rate_eval, tf)
    He4_Na34__Al38(rate_eval, tf)
    n_Na34__Na35(rate_eval, tf)
    He4_Na33__Al37(rate_eval, tf)
    n_He3__He4(rate_eval, tf)
    p_F21__n_Ne21(rate_eval, tf)
    He4_Na39__Al43(rate_eval, tf)
    Mg32__n_Al31__weak__wc12(rate_eval, tf)
    p_Na32__Mg33(rate_eval, tf)
    He4_Al28__p_Si31(rate_eval, tf)
    He4_Ne29__n_Mg32(rate_eval, tf)
    He4_P25__Cl29(rate_eval, tf)
    p_Na36__Mg37(rate_eval, tf)
    Cl50__Ar50__weak__mo03(rate_eval, tf)
    He4_Na28__Al32(rate_eval, tf)
    n_F15__F16(rate_eval, tf)
    p_Na26__Mg27(rate_eval, tf)
    He4_Ti56__n_Cr59(rate_eval, tf)
    Si45__P45__weak__mo03(rate_eval, tf)
    p_Na25__Mg26(rate_eval, tf)
    n_Na24__Na25(rate_eval, tf)
    Na36__Mg36__weak__mo03(rate_eval, tf)
    p_Ar52__K53(rate_eval, tf)
    Na28__Mg28__weak__wc12(rate_eval, tf)
    He4_F15__p_Ne18(rate_eval, tf)
    He4_Na23__Al27(rate_eval, tf)
    p_Ca51__n_Sc51(rate_eval, tf)
    p_Sc63__He4_Ca60(rate_eval, tf)
    p_Na23__Mg24(rate_eval, tf)
    Sc62__n_Ti61__weak__mp17(rate_eval, tf)
    p_Na22__Mg23(rate_eval, tf)
    n_Na22__Na23(rate_eval, tf)
    He4_V55__Mn59(rate_eval, tf)
    He4_Ar50__Ca54(rate_eval, tf)
    p_Na21__Mg22(rate_eval, tf)
    Ar53__n_n_K51__weak__mp17(rate_eval, tf)
    He4_Ti42__Cr46(rate_eval, tf)
    n_Na21__Na22(rate_eval, tf)
    p_Ti65__n_V65(rate_eval, tf)
    He4_Na20__Al24(rate_eval, tf)
    p_S33__Cl34(rate_eval, tf)
    n_Na20__Na21(rate_eval, tf)
    Sc63__Ti63__weak__mo03(rate_eval, tf)
    n_Na19__Na20(rate_eval, tf)
    p_Mg31__He4_Na28(rate_eval, tf)
    Al42__Si42__weak__mo03(rate_eval, tf)
    He4_K58__n_Sc61(rate_eval, tf)
    n_Mg40__Mg41(rate_eval, tf)
    He4_Ne34__Mg38(rate_eval, tf)
    p_Sc54__Ti55(rate_eval, tf)
    n_Ne32__Ne33(rate_eval, tf)
    p_Si29__P30(rate_eval, tf)
    Cr68__n_Mn67__weak__mp17(rate_eval, tf)
    He4_Ne31__Mg35(rate_eval, tf)
    p_Ne31__Na32(rate_eval, tf)
    He4_Ne30__Mg34(rate_eval, tf)
    He4_Ca58__Ti62(rate_eval, tf)
    Mg41__n_Al40__weak__mp17(rate_eval, tf)
    p_Ne30__Na31(rate_eval, tf)
    p_Mn71__n_Fe71(rate_eval, tf)
    Mn52__Cr52__weak__wc12(rate_eval, tf)
    Ti58__V58__weak__wc12(rate_eval, tf)
    Ne17__p_O16__weak__wc12(rate_eval, tf)
    p_Cl44__Ar45(rate_eval, tf)
    p_Ne28__Na29(rate_eval, tf)
    p_Na35__He4_Ne32(rate_eval, tf)
    n_Fe74__Fe75(rate_eval, tf)
    p_Ne27__Na28(rate_eval, tf)
    He4_Ne26__Mg30(rate_eval, tf)
    Ti41__p_Ca40__weak__wc12(rate_eval, tf)
    n_Ne26__Ne27(rate_eval, tf)
    S28__p_Si27__weak__wc12(rate_eval, tf)
    He4_Cl52__n_K55(rate_eval, tf)
    p_Ne25__Na26(rate_eval, tf)
    n_Mg19__Mg20(rate_eval, tf)
    n_Ne24__Ne25(rate_eval, tf)
    p_Ne23__Na24(rate_eval, tf)
    Sc42__Ca42__weak__wc12(rate_eval, tf)
    p_Al43__Si44(rate_eval, tf)
    p_Ne33__Na34(rate_eval, tf)
    p_F27__Ne28(rate_eval, tf)
    p_Ne20__Na21(rate_eval, tf)
    p_K53__Ca54(rate_eval, tf)
    p_Cr70__n_Mn70(rate_eval, tf)
    p_Ne19__Na20(rate_eval, tf)
    p_F24__He4_O21(rate_eval, tf)
    F24__Ne24__weak__wc12(rate_eval, tf)
    p_Mn52__Fe53(rate_eval, tf)
    n_Ne19__Ne20(rate_eval, tf)
    p_Ne18__Na19(rate_eval, tf)
    Ne32__n_Na31__weak__mp17(rate_eval, tf)
    p_Cr64__Mn65(rate_eval, tf)
    Sc61__n_Ti60__weak__mp17(rate_eval, tf)
    n_S46__S47(rate_eval, tf)
    Ca39__K39__weak__wc12(rate_eval, tf)
    n_Ne18__Ne19(rate_eval, tf)
    p_Cl48__Ar49(rate_eval, tf)
    n_Ne17__Ne18(rate_eval, tf)
    He4_Cr65__Fe69(rate_eval, tf)
    F25__Ne25__weak__wc12(rate_eval, tf)
    He4_Ne16__Mg20(rate_eval, tf)
    He4_Na30__Al34(rate_eval, tf)
    He4_O28__Ne32(rate_eval, tf)
    n_Ne16__Ne17(rate_eval, tf)
    He4_F31__Na35(rate_eval, tf)
    n_O13__O14(rate_eval, tf)
    p_F28__Ne29(rate_eval, tf)
    p_F19__He4_O16(rate_eval, tf)
    p_Mg38__Al39(rate_eval, tf)
    He4_Mg29__n_Si32(rate_eval, tf)
    He4_Ar41__Ca45(rate_eval, tf)
    n_V41__p_Ti41(rate_eval, tf)
    n_P39__P40(rate_eval, tf)
    n_Si34__Si35(rate_eval, tf)
    He4_F24__Na28(rate_eval, tf)
    He4_Al31__P35(rate_eval, tf)
    n_F23__F24(rate_eval, tf)
    He4_Mn51__Co55(rate_eval, tf)
    p_F22__Ne23(rate_eval, tf)
    n_F22__F23(rate_eval, tf)
    p_F21__Ne22(rate_eval, tf)
    n_Cr54__Cr55(rate_eval, tf)
    p_Fe51__Co52(rate_eval, tf)
    n_F21__F22(rate_eval, tf)
    Na30__n_Mg29__weak__wc17(rate_eval, tf)
    n_Al23__Al24(rate_eval, tf)
    n_F20__F21(rate_eval, tf)
    N22__O22__weak__wc12(rate_eval, tf)
    He4_F18__Na22(rate_eval, tf)
    n_F18__F19(rate_eval, tf)
    n_F17__F18(rate_eval, tf)
    He4_K59__Sc63(rate_eval, tf)
    n_F16__F17(rate_eval, tf)
    n_F14__F15(rate_eval, tf)
    p_O27__F28(rate_eval, tf)
    He4_Ar42__Ca46(rate_eval, tf)
    p_O26__F27(rate_eval, tf)
    p_Cl43__n_Ar43(rate_eval, tf)
    Cr67__n_Mn66__weak__mp17(rate_eval, tf)
    He4_O24__Ne28(rate_eval, tf)
    p_K35__Ca36(rate_eval, tf)
    n_Ne23__Ne24(rate_eval, tf)
    He4_O23__Ne27(rate_eval, tf)
    K36__He4_S32__weak__wc12(rate_eval, tf)
    n_O23__O24(rate_eval, tf)
    He4_F27__Na31(rate_eval, tf)
    n_K57__K58(rate_eval, tf)
    p_O22__F23(rate_eval, tf)
    n_O22__O23(rate_eval, tf)
    n_O21__O22(rate_eval, tf)
    n_Cl31__He4_P28(rate_eval, tf)
    He4_O20__Ne24(rate_eval, tf)
    p_O20__F21(rate_eval, tf)
    He4_O20__n_Ne23(rate_eval, tf)
    n_Ar48__Ar49(rate_eval, tf)
    He4_O19__Ne23(rate_eval, tf)
    He4_S28__Ar32(rate_eval, tf)
    K58__n_n_Ca56__weak__mp17(rate_eval, tf)
    He4_Ar44__n_Ca47(rate_eval, tf)
    He4_O17__Ne21(rate_eval, tf)
    n_O16__O17(rate_eval, tf)
    p_S44__n_Cl44(rate_eval, tf)
    n_O15__O16(rate_eval, tf)
    n_N19__N20(rate_eval, tf)
    n_Si27__He4_Mg24(rate_eval, tf)
    Sc63__n_Ti62__weak__mp17(rate_eval, tf)
    V58__n_Cr57__weak__mp17(rate_eval, tf)
    n_N17__N18(rate_eval, tf)
    Ar45__K45__weak__wc12(rate_eval, tf)
    He4_P33__Cl37(rate_eval, tf)
    n_N16__N17(rate_eval, tf)
    n_Cl29__Cl30(rate_eval, tf)
    n_Ti53__Ti54(rate_eval, tf)
    n_N15__N16(rate_eval, tf)
    Ti60__n_V59__weak__mp17(rate_eval, tf)
    p_N14__O15(rate_eval, tf)
    n_N13__N14(rate_eval, tf)
    Mg38__n_n_Al36__weak__mp17(rate_eval, tf)
    n_Fe53__Fe54(rate_eval, tf)
    p_C14__N15(rate_eval, tf)
    p_C13__N14(rate_eval, tf)
    p_C12__N13(rate_eval, tf)
    p_C11__N12(rate_eval, tf)
    n_V42__p_Ti42(rate_eval, tf)
    n_B12__B13(rate_eval, tf)
    n_p__d(rate_eval, tf)
    n_B11__B12(rate_eval, tf)
    p_B10__C11(rate_eval, tf)
    p_Na28__Mg29(rate_eval, tf)
    n_B10__B11(rate_eval, tf)
    n_Be11__Be12(rate_eval, tf)
    p_Be10__B11(rate_eval, tf)
    p_Sc39__Ti40(rate_eval, tf)
    He4_Ti64__Cr68(rate_eval, tf)
    n_Mg20__Mg21(rate_eval, tf)
    p_Be7__B8(rate_eval, tf)
    He4_Li9__B13(rate_eval, tf)
    He4_Mg26__Si30(rate_eval, tf)
    He4_Fe45__p_Co48(rate_eval, tf)
    p_P35__n_S35(rate_eval, tf)
    He4_Na24__Al28(rate_eval, tf)
    He4_Li8__B12(rate_eval, tf)
    He4_He3__Be7(rate_eval, tf)
    He4_Fe75__Ni79(rate_eval, tf)
    p_Ne24__Na25(rate_eval, tf)
    p_t__He4(rate_eval, tf)
    He4_d__Li6(rate_eval, tf)
    p_P27__S28(rate_eval, tf)
    He4_Cr49__Fe53(rate_eval, tf)
    He4_C12__O16(rate_eval, tf)
    Fe75__n_n_Co73__weak__mp17(rate_eval, tf)
    V61__n_Cr60__weak__wc12(rate_eval, tf)
    Fe73__n_n_Co71__weak__mp17(rate_eval, tf)
    Mn73__n_n_Fe71__weak__mp17(rate_eval, tf)
    He4_Fe62__n_Ni65(rate_eval, tf)
    F27__n_Ne26__weak__wc12(rate_eval, tf)
    Mn72__n_n_Fe70__weak__mp17(rate_eval, tf)
    Al22__Mg22__weak__wc12(rate_eval, tf)
    Mn71__n_n_Fe69__weak__mp17(rate_eval, tf)
    He4_Mg27__Si31(rate_eval, tf)
    Fe59__Co59__weak__wc12(rate_eval, tf)
    Mn70__n_n_Fe68__weak__mp17(rate_eval, tf)
    Ca61__n_n_n_Sc58__weak__mo03(rate_eval, tf)
    n_Ti47__p_Sc47(rate_eval, tf)
    p_Ca49__n_Sc49(rate_eval, tf)
    Mn68__n_n_Fe66__weak__mp17(rate_eval, tf)
    p_Si35__P36(rate_eval, tf)
    p_Ti46__V47(rate_eval, tf)
    He4_P34__Cl38(rate_eval, tf)
    p_Fe71__Co72(rate_eval, tf)
    Ti65__n_n_V63__weak__mp17(rate_eval, tf)
    Ar35__Cl35__weak__wc12(rate_eval, tf)
    Si42__P42__weak__wc17(rate_eval, tf)
    n_K51__K52(rate_eval, tf)
    Fe48__Mn48__weak__wc12(rate_eval, tf)
    He4_Ca49__n_Ti52(rate_eval, tf)
    Sc60__n_n_Ti58__weak__mp17(rate_eval, tf)
    n_V48__He4_Sc45(rate_eval, tf)
    p_F18__Ne19(rate_eval, tf)
    p_Mg36__Al37(rate_eval, tf)
    Ar49__n_K48__weak__wc12(rate_eval, tf)
    n_Ne28__Ne29(rate_eval, tf)
    n_Si25__Si26(rate_eval, tf)
    K59__n_n_Ca57__weak__mp17(rate_eval, tf)
    n_S31__He4_Si28(rate_eval, tf)
    K56__Ca56__weak__mo03(rate_eval, tf)
    n_P29__P30(rate_eval, tf)
    Mn67__Fe67__weak__wc17(rate_eval, tf)
    K53__n_n_Ca51__weak__mp17(rate_eval, tf)
    n_Cr58__Cr59(rate_eval, tf)
    He4_Mn73__Co77(rate_eval, tf)
    K52__n_n_Ca50__weak__mp17(rate_eval, tf)
    Ar54__n_n_K52__weak__mp17(rate_eval, tf)
    p_Ar42__He4_Cl39(rate_eval, tf)
    N21__n_O20__weak__wc12(rate_eval, tf)
    Cl52__n_n_Ar50__weak__mp17(rate_eval, tf)
    Cl50__n_n_Ar48__weak__mp17(rate_eval, tf)
    S49__n_n_Cl47__weak__mp17(rate_eval, tf)
    S47__n_n_Cl45__weak__mp17(rate_eval, tf)
    n_Cl30__He4_P27(rate_eval, tf)
    S27__p_p_Al25__weak__wc12(rate_eval, tf)
    P47__n_n_S45__weak__mp17(rate_eval, tf)
    O20__F20__weak__wc12(rate_eval, tf)
    He4_K42__Sc46(rate_eval, tf)
    P45__n_n_S43__weak__mp17(rate_eval, tf)
    He4_Na19__p_Mg22(rate_eval, tf)
    p_F25__Ne26(rate_eval, tf)
    P44__n_n_S42__weak__mp17(rate_eval, tf)
    P43__n_n_S41__weak__mp17(rate_eval, tf)
    Cr61__Mn61__weak__wc12(rate_eval, tf)
    Si44__n_n_P42__weak__mp17(rate_eval, tf)
    He4_Mn61__n_Co64(rate_eval, tf)
    Sc57__Ti57__weak__wc17(rate_eval, tf)
    He4_Si28__S32(rate_eval, tf)
    Si41__n_n_P39__weak__mp17(rate_eval, tf)
    p_K42__Ca43(rate_eval, tf)
    Si39__n_n_P37__weak__mp17(rate_eval, tf)
    Si23__p_p_Na21__weak__wc12(rate_eval, tf)
    He4_Sc41__p_Ti44(rate_eval, tf)
    He4_Sc36__V40(rate_eval, tf)
    p_S37__He4_P34(rate_eval, tf)
    Al43__n_n_Si41__weak__mp17(rate_eval, tf)
    Al41__n_n_Si39__weak__mp17(rate_eval, tf)
    He4_Mn43__p_Fe46(rate_eval, tf)
    n_K42__K43(rate_eval, tf)
    Al38__n_n_Si36__weak__mp17(rate_eval, tf)
    P41__n_S40__weak__wc12(rate_eval, tf)
    p_V40__Cr41(rate_eval, tf)
    Mg33__n_Al32__weak__wc12(rate_eval, tf)
    He4_K36__Sc40(rate_eval, tf)
    Mg37__n_n_Al35__weak__mp17(rate_eval, tf)
    p_K39__Ca40(rate_eval, tf)
    He4_Sc40__V44(rate_eval, tf)
    Cr43__p_Ti42__weak__wc17(rate_eval, tf)
    Al24__p_Na23__weak__wc12(rate_eval, tf)
    Mg33__n_n_Al31__weak__mp17(rate_eval, tf)
    Na35__n_n_Mg33__weak__mp17(rate_eval, tf)
    p_Sc51__n_Ti51(rate_eval, tf)
    Na31__n_n_Mg29__weak__wc12(rate_eval, tf)
    Sc59__n_n_Ti57__weak__mp17(rate_eval, tf)
    He4_K47__n_Sc50(rate_eval, tf)
    F24__n_Ne23__weak__wc12(rate_eval, tf)
    Na30__n_n_Mg28__weak__wc12(rate_eval, tf)
    Mn69__n_Fe68__weak__mp17(rate_eval, tf)
    Ne32__n_n_Na30__weak__mp17(rate_eval, tf)
    He4_O14__Ne18(rate_eval, tf)
    Al22__p_p_Ne20__weak__wc12(rate_eval, tf)
    p_Ti50__V51(rate_eval, tf)
    Ne29__n_n_Na27__weak__wc12(rate_eval, tf)
    F30__n_n_Ne28__weak__mp17(rate_eval, tf)
    O27__n_n_F25__weak__mp17(rate_eval, tf)
    n_Ar36__Ar37(rate_eval, tf)
    O26__n_n_F24__weak__mp17(rate_eval, tf)
    p_Mn53__Fe54(rate_eval, tf)
    C14__N14__weak__wc12(rate_eval, tf)
    He4_Mg38__Si42(rate_eval, tf)
    O25__n_n_F23__weak__mp17(rate_eval, tf)
    B15__n_n_C13__weak__wc12(rate_eval, tf)
    n_Ar43__Ar44(rate_eval, tf)
    He4_Si26__S30(rate_eval, tf)
    p_P33__S34(rate_eval, tf)
    Be16__n_n_Be14(rate_eval, tf)
    Be14__n_n_B12__weak__wc12(rate_eval, tf)
    He4_Na20__p_Mg23(rate_eval, tf)
    p_Al28__n_Si28(rate_eval, tf)
    Fe75__n_Co74__weak__mp17(rate_eval, tf)
    P43__n_S42__weak__wc12(rate_eval, tf)
    Fe73__n_Co72__weak__mp17(rate_eval, tf)
    Fe74__Co74__weak__mo03(rate_eval, tf)
    p_Cl41__n_Ar41(rate_eval, tf)
    n_Mg25__Mg26(rate_eval, tf)
    n_C11__C12(rate_eval, tf)
    Fe70__n_Co69__weak__mp17(rate_eval, tf)
    Mg35__n_Al34__weak__wc12(rate_eval, tf)
    n_Cl30__Cl31(rate_eval, tf)
    Fe69__n_Co68__weak__mp17(rate_eval, tf)
    He4_Fe74__Ni78(rate_eval, tf)
    p_K55__Ca56(rate_eval, tf)
    p_K47__n_Ca47(rate_eval, tf)
    p_Ca50__n_Sc50(rate_eval, tf)
    He4_V44__p_Cr47(rate_eval, tf)
    n_S35__S36(rate_eval, tf)
    He4_Mg36__n_Si39(rate_eval, tf)
    n_Ca48__Ca49(rate_eval, tf)
    He4_B11__n_N14(rate_eval, tf)
    He4_Mn58__Co62(rate_eval, tf)
    He4_Si32__S36(rate_eval, tf)
    p_V45__Cr46(rate_eval, tf)
    V60__n_Cr59__weak__mp17(rate_eval, tf)
    He4_S29__Ar33(rate_eval, tf)
    Sc44__Ca44__weak__wc12(rate_eval, tf)
    p_p__d__weak__bet_pos_(rate_eval, tf)
    p_p__d__weak__electron_capture(rate_eval, tf)
    Ti57__V57__weak__wc12(rate_eval, tf)
    p_Cl38__n_Ar38(rate_eval, tf)
    He4_F30__Na34(rate_eval, tf)
    He4_Fe63__Ni67(rate_eval, tf)
    n_Cl31__Cl32(rate_eval, tf)
    p_Al23__Si24(rate_eval, tf)
    n_Cl48__Cl49(rate_eval, tf)
    V65__n_Cr64__weak__mp17(rate_eval, tf)
    He4_F20__Na24(rate_eval, tf)
    He4_K59__n_Sc62(rate_eval, tf)
    He4_S47__n_Ar50(rate_eval, tf)
    p_Al41__Si42(rate_eval, tf)
    K48__n_Ca47__weak__wc12(rate_eval, tf)
    n_Mg19__p_Na19(rate_eval, tf)
    p_Cl38__Ar39(rate_eval, tf)
    p_Mg32__n_Al32(rate_eval, tf)
    He4_Cl28__K32(rate_eval, tf)
    Fe48__p_Cr47__weak__wc12(rate_eval, tf)
    p_Na27__Mg28(rate_eval, tf)
    p_P46__n_S46(rate_eval, tf)
    p_P41__n_S41(rate_eval, tf)
    Al43__n_Si42__weak__mp17(rate_eval, tf)
    Si23__Al23__weak__wc12(rate_eval, tf)
    Fe46__p_Cr45__weak__wc12(rate_eval, tf)
    p_P39__n_S39(rate_eval, tf)
    p_Cr55__Mn56(rate_eval, tf)
    n_Cl38__Cl39(rate_eval, tf)
    Ne18__F18__weak__wc12(rate_eval, tf)
    Fe45__p_Cr44__weak__wc17(rate_eval, tf)
    He4_Mg28__n_Si31(rate_eval, tf)
    Mn73__n_Fe72__weak__mp17(rate_eval, tf)
    Mn72__n_Fe71__weak__mp17(rate_eval, tf)
    p_Mn63__He4_Cr60(rate_eval, tf)
    n_Al23__p_Mg23(rate_eval, tf)
    Ar52__K52__weak__mo03(rate_eval, tf)
    Mn65__n_Fe64__weak__mp17(rate_eval, tf)
    Fe74__n_Co73__weak__mp17(rate_eval, tf)
    n_P40__P41(rate_eval, tf)
    S26__P26__weak__bqa_pos_(rate_eval, tf)
    n_Al24__p_Mg24(rate_eval, tf)
    He4_Cr68__n_Fe71(rate_eval, tf)
    He4_Fe66__Ni70(rate_eval, tf)
    p_Ca50__Sc51(rate_eval, tf)
    He4_Si29__S33(rate_eval, tf)
    p_Mn64__Fe65(rate_eval, tf)
    p_V44__Cr45(rate_eval, tf)
    Li11__Be11__weak__wc12(rate_eval, tf)
    Ca61__n_Sc60__weak__mp17(rate_eval, tf)
    n_Fe60__Fe61(rate_eval, tf)
    n_Si23__He4_Mg20(rate_eval, tf)
    Ti61__V61__weak__wc17(rate_eval, tf)
    n_Cl41__Cl42(rate_eval, tf)
    Al23__Mg23__weak__wc12(rate_eval, tf)
    p_N14__n_O14(rate_eval, tf)
    p_Na36__He4_Ne33(rate_eval, tf)
    He4_O18__n_Ne21(rate_eval, tf)
    He4_Be9__n_C12(rate_eval, tf)
    p_Cl34__Ar35(rate_eval, tf)
    K55__n_n_Ca53__weak__mp17(rate_eval, tf)
    He4_Fe61__Ni65(rate_eval, tf)
    p_Mg37__He4_Na34(rate_eval, tf)
    p_Na34__n_Mg34(rate_eval, tf)
    Mg39__n_n_Al37__weak__mp17(rate_eval, tf)
    n_Mg22__p_Na22(rate_eval, tf)
    He4_Ca35__p_Sc38(rate_eval, tf)
    Ne32__Na32__weak__wc17(rate_eval, tf)
    He4_Ar54__Ca58(rate_eval, tf)
    He4_V59__Mn63(rate_eval, tf)
    p_K58__Ca59(rate_eval, tf)
    Si32__P32__weak__wc12(rate_eval, tf)
    p_Fe53__Co54(rate_eval, tf)
    He4_P41__Cl45(rate_eval, tf)
    He4_P46__n_Cl49(rate_eval, tf)
    He4_K53__Sc57(rate_eval, tf)
    Mn46__p_V45__weak__wc12(rate_eval, tf)
    K57__n_n_Ca55__weak__mp17(rate_eval, tf)
    He4_S34__Ar38(rate_eval, tf)
    He4_Ca37__p_Sc40(rate_eval, tf)
    Be12__B12__weak__wc12(rate_eval, tf)
    N19__n_O18__weak__wc12(rate_eval, tf)
    p_P31__He4_Si28(rate_eval, tf)
    n_Ti37__p_Sc37(rate_eval, tf)
    Cr70__n_Mn69__weak__mp17(rate_eval, tf)
    O24__n_F23__weak__wc12(rate_eval, tf)
    Sc41__Ca41__weak__wc12(rate_eval, tf)
    Mn68__n_Fe67__weak__mp17(rate_eval, tf)
    p_P41__S42(rate_eval, tf)
    p_Cl44__n_Ar44(rate_eval, tf)
    Cr69__n_Mn68__weak__mp17(rate_eval, tf)
    n_Li8__Li9(rate_eval, tf)
    He4_N12__p_O15(rate_eval, tf)
    Cr66__n_Mn65__weak__mp17(rate_eval, tf)
    n_C13__C14(rate_eval, tf)
    n_Mg21__p_Na21(rate_eval, tf)
    Cr63__n_Mn62__weak__mp17(rate_eval, tf)
    He4_Mn71__Co75(rate_eval, tf)
    n_Ca59__Ca60(rate_eval, tf)
    N13__C13__weak__wc12(rate_eval, tf)
    p_Ca48__Sc49(rate_eval, tf)
    Sc37__Ca37__weak__bqa_pos_(rate_eval, tf)
    F29__Ne29__weak__wc17(rate_eval, tf)
    He4_V65__n_Mn68(rate_eval, tf)
    Cr62__n_Mn61__weak__mp17(rate_eval, tf)
    F30__n_Ne29__weak__mp17(rate_eval, tf)
    Cr61__n_Mn60__weak__mp17(rate_eval, tf)
    n_Si23__Si24(rate_eval, tf)
    p_Mg41__Al42(rate_eval, tf)
    He4_Be10__n_C13(rate_eval, tf)
    n_Be7__p_Li7(rate_eval, tf)
    n_Al21__Al22(rate_eval, tf)
    n_Si26__He4_Mg23(rate_eval, tf)
    n_Na32__Na33(rate_eval, tf)
    Mn44__Cr44__weak__bqa_pos_(rate_eval, tf)
    Fe73__Co73__weak__mo03(rate_eval, tf)
    He4_Ca55__n_Ti58(rate_eval, tf)
    He4_Ar44__Ca48(rate_eval, tf)
    Cr45__p_Ti44__weak__wc12(rate_eval, tf)
    n_P34__P35(rate_eval, tf)
    He4_P28__p_S31(rate_eval, tf)
    He4_Si25__S29(rate_eval, tf)
    n_Sc35__Sc36(rate_eval, tf)
    p_Sc47__Ti48(rate_eval, tf)
    He4_P38__Cl42(rate_eval, tf)
    n_Cl28__p_S28(rate_eval, tf)
    Ar51__n_K50__weak__mp17(rate_eval, tf)
    Cr42__p_Ti41__weak__wc12(rate_eval, tf)
    He4_Mg25__Si29(rate_eval, tf)
    He4_Mn52__p_Fe55(rate_eval, tf)
    n_Mn50__p_Cr50(rate_eval, tf)
    C15__N15__weak__wc12(rate_eval, tf)
    V63__n_Cr62__weak__wc12(rate_eval, tf)
    Ar52__n_K51__weak__mp17(rate_eval, tf)
    n_Cr41__p_V41(rate_eval, tf)
    p_Ar46__K47(rate_eval, tf)
    V59__n_Cr58__weak__wc12(rate_eval, tf)
    p_S42__He4_P39(rate_eval, tf)
    He4_N14__F18(rate_eval, tf)
    He4_Si36__n_S39(rate_eval, tf)
    p_Li8__n_He4_He4(rate_eval, tf)
    n_Ca47__Ca48(rate_eval, tf)
    p_Fe67__Co68(rate_eval, tf)
    Fe76__n_n_Co74__weak__mp17(rate_eval, tf)
    n_Cr47__Cr48(rate_eval, tf)
    He4_V48__Mn52(rate_eval, tf)
    He4_Ca61__Ti65(rate_eval, tf)
    He4_Fe62__Ni66(rate_eval, tf)
    He4_Ca55__Ti59(rate_eval, tf)
    n_S28__p_P28(rate_eval, tf)
    He4_P46__Cl50(rate_eval, tf)
    Ti56__V56__weak__wc12(rate_eval, tf)
    K55__n_Ca54__weak__mp17(rate_eval, tf)
    n_Mg20__He4_Ne17(rate_eval, tf)
    F22__Ne22__weak__wc17(rate_eval, tf)
    Sc39__Ca39__weak__mo97(rate_eval, tf)
    Fe75__Co75__weak__mo03(rate_eval, tf)
    He4_Al24__P28(rate_eval, tf)
    p_Si40__He4_Al37(rate_eval, tf)
    p_Mg41__n_Al41(rate_eval, tf)
    Mg39__Al39__weak__mo03(rate_eval, tf)
    p_Cl42__Ar43(rate_eval, tf)
    He4_Ti50__Cr54(rate_eval, tf)
    n_Sc52__Sc53(rate_eval, tf)
    p_Sc51__Ti52(rate_eval, tf)
    n_Ti40__p_Sc40(rate_eval, tf)
    He4_Al43__n_P46(rate_eval, tf)
    n_P30__p_Si30(rate_eval, tf)
    n_P46__P47(rate_eval, tf)
    O28__n_n_F26__weak__mp17(rate_eval, tf)
    He4_Fe51__p_Co54(rate_eval, tf)
    Cl31__p_P30__weak__wc12(rate_eval, tf)
    Mg40__n_n_Al38__weak__mp17(rate_eval, tf)
    p_F19__Ne20(rate_eval, tf)
    He4_Ne25__n_Mg28(rate_eval, tf)
    Cr70__n_n_Mn68__weak__mp17(rate_eval, tf)
    p_K50__He4_Ar47(rate_eval, tf)
    Ti64__n_V63__weak__mp17(rate_eval, tf)
    He4_O27__n_Ne30(rate_eval, tf)
    n_Mn57__Mn58(rate_eval, tf)
    He4_Ca60__Ti64(rate_eval, tf)
    n_P25__He4_Al22(rate_eval, tf)
    Ti63__n_V62__weak__mp17(rate_eval, tf)
    n_F19__F20(rate_eval, tf)
    V52__Cr52__weak__wc12(rate_eval, tf)
    Ti61__n_V60__weak__mp17(rate_eval, tf)
    He4_P39__Cl43(rate_eval, tf)
    V65__n_n_Cr63__weak__mp17(rate_eval, tf)
    n_Na22__p_Ne22(rate_eval, tf)
    p_S45__n_Cl45(rate_eval, tf)
    n_Cr52__Cr53(rate_eval, tf)
    n_P30__P31(rate_eval, tf)
    Ca55__n_Sc54__weak__mp17(rate_eval, tf)
    Sc57__n_Ti56__weak__mp17(rate_eval, tf)
    He4_S38__Ar42(rate_eval, tf)
    He4_Ar30__p_K33(rate_eval, tf)
    Ti58__n_V57__weak__mp17(rate_eval, tf)
    p_Ar30__K31(rate_eval, tf)
    Al37__n_n_Si35__weak__mp17(rate_eval, tf)
    Cr69__n_n_Mn67__weak__mp17(rate_eval, tf)
    He4_P31__Cl35(rate_eval, tf)
    p_Mn58__n_Fe58(rate_eval, tf)
    p_Ca57__He4_K54(rate_eval, tf)
    p_Cr65__n_Mn65(rate_eval, tf)
    p_F29__n_Ne29(rate_eval, tf)
    He4_Mg32__Si36(rate_eval, tf)
    Na21__Ne21__weak__wc12(rate_eval, tf)
    He4_Cl41__K45(rate_eval, tf)
    n_Ca39__He4_Ar36(rate_eval, tf)
    O26__n_O25(rate_eval, tf)
    d_d__He4(rate_eval, tf)
    Al40__n_Si39__weak__mp17(rate_eval, tf)
    p_N13__O14(rate_eval, tf)
    n_C12__C13(rate_eval, tf)
    Ar31__p_S30__weak__wc17(rate_eval, tf)
    p_Mn63__n_Fe63(rate_eval, tf)
    n_Al27__Al28(rate_eval, tf)
    Mn49__Cr49__weak__wc12(rate_eval, tf)
    He4_Cl43__n_K46(rate_eval, tf)
    Al42__n_n_Si40__weak__mo03(rate_eval, tf)
    He4_Na33__n_Al36(rate_eval, tf)
    Cl32__He4_Si28__weak__wc12(rate_eval, tf)
    S28__P28__weak__wc12(rate_eval, tf)
    n_K48__K49(rate_eval, tf)
    He4_Ti55__Cr59(rate_eval, tf)
    He4_V45__p_Cr48(rate_eval, tf)
    He4_Al39__P43(rate_eval, tf)
    p_Ne30__n_Na30(rate_eval, tf)
    p_F30__n_Ne30(rate_eval, tf)
    p_Na27__He4_Ne24(rate_eval, tf)
    n_Ti50__Ti51(rate_eval, tf)
    He4_Na25__n_Al28(rate_eval, tf)
    n_S27__He4_Si24(rate_eval, tf)
    Mn66__n_Fe65__weak__mp17(rate_eval, tf)
    C22__n_N21__weak__wc17(rate_eval, tf)
    p_Si33__He4_Al30(rate_eval, tf)
    p_B11__C12(rate_eval, tf)
    Ti39__p_Ca38__weak__wc12(rate_eval, tf)
    Ti44__Sc44__weak__wc12(rate_eval, tf)
    n_V64__V65(rate_eval, tf)
    Mg23__Na23__weak__wc12(rate_eval, tf)
    Ar39__K39__weak__wc12(rate_eval, tf)
    n_Sc36__p_Ca36(rate_eval, tf)
    p_K46__He4_Ar43(rate_eval, tf)
    p_S41__n_Cl41(rate_eval, tf)
    Sc59__n_Ti58__weak__mp17(rate_eval, tf)
    He4_t__Li7(rate_eval, tf)
    p_Mg36__n_Al36(rate_eval, tf)
    Sc58__n_Ti57__weak__mp17(rate_eval, tf)
    n_He4_He4__Be9(rate_eval, tf)
    He4_P47__Cl51(rate_eval, tf)
    K54__n_n_Ca52__weak__mp17(rate_eval, tf)
    p_Cr69__n_Mn69(rate_eval, tf)
    Sc59__Ti59__weak__mo03(rate_eval, tf)
    He4_Cl48__K52(rate_eval, tf)
    He4_Ar47__n_Ca50(rate_eval, tf)
    n_Al32__Al33(rate_eval, tf)
    n_Cr65__Cr66(rate_eval, tf)
    p_V51__Cr52(rate_eval, tf)
    Ca49__Sc49__weak__wc12(rate_eval, tf)
    p_Al38__Si39(rate_eval, tf)
    He4_S40__n_Ar43(rate_eval, tf)
    V54__Cr54__weak__wc12(rate_eval, tf)
    Na31__n_n_n_Mg28__weak__wc12(rate_eval, tf)
    He4_Si35__S39(rate_eval, tf)
    He4_P43__Cl47(rate_eval, tf)
    Ne17__F17__weak__wc17(rate_eval, tf)
    He4_Na29__n_Al32(rate_eval, tf)
    n_Ne21__Ne22(rate_eval, tf)
    n_Ca41__He4_Ar38(rate_eval, tf)
    P24__Si24__weak__bqa_pos_(rate_eval, tf)
    O26__n_F25__weak__mp17(rate_eval, tf)
    Sc40__He4_Ar36__weak__wc12(rate_eval, tf)
    He4_Mg35__Si39(rate_eval, tf)
    Na22__Ne22__weak__wc12(rate_eval, tf)
    He4_F23__Na27(rate_eval, tf)
    p_K49__He4_Ar46(rate_eval, tf)
    p_P25__S26(rate_eval, tf)
    p_Na24__Mg25(rate_eval, tf)
    Al34__Si34__weak__wc12(rate_eval, tf)
    S46__Cl46__weak__wc17(rate_eval, tf)
    n_Mg38__Mg39(rate_eval, tf)
    N20__n_O19__weak__wc12(rate_eval, tf)
    Ca59__n_Sc58__weak__mp17(rate_eval, tf)
    Mn73__Fe73__weak__mo03(rate_eval, tf)
    Al24__He4_Ne20__weak__wc12(rate_eval, tf)
    He4_Na21__Al25(rate_eval, tf)
    Ca55__Sc55__weak__wc12(rate_eval, tf)
    Ca58__n_Sc57__weak__mp17(rate_eval, tf)
    He4_P45__n_Cl48(rate_eval, tf)
    n_Ne31__Ne32(rate_eval, tf)
    He4_Sc52__V56(rate_eval, tf)
    Ar32__p_S31__weak__wc12(rate_eval, tf)
    Ca57__n_Sc56__weak__mp17(rate_eval, tf)
    He4_Mg41__n_Si44(rate_eval, tf)
    n_Cl39__Cl40(rate_eval, tf)
    He4_C14__O18(rate_eval, tf)
    Ca52__n_Sc51__weak__wc12(rate_eval, tf)
    He4_O18__Ne22(rate_eval, tf)
    Si24__Al24__weak__wc12(rate_eval, tf)
    n_V54__V55(rate_eval, tf)
    p_S39__n_Cl39(rate_eval, tf)
    Cl34__S34__weak__wc12(rate_eval, tf)
    He4_Mn62__Co66(rate_eval, tf)
    Al42__n_Si41__weak__mp17(rate_eval, tf)
    Si42__n_P41__weak__mp17(rate_eval, tf)
    He4_K44__n_Sc47(rate_eval, tf)
    n_Na19__He4_F16(rate_eval, tf)
    V62__Cr62__weak__wc17(rate_eval, tf)
    Cl46__n_Ar45__weak__wc12(rate_eval, tf)
    He4_Al28__P32(rate_eval, tf)
    He4_Mn70__n_Co73(rate_eval, tf)
    Cl51__n_Ar50__weak__mp17(rate_eval, tf)
    p_Cl33__Ar34(rate_eval, tf)
    Ca37__p_Ar36__weak__wc12(rate_eval, tf)
    n_Mg30__Mg31(rate_eval, tf)
    p_Ca46__Sc47(rate_eval, tf)
    Ca36__p_Ar35__weak__wc12(rate_eval, tf)
    p_Fe68__n_Co68(rate_eval, tf)
    n_Ti42__Ti43(rate_eval, tf)
    Ca35__p_Ar34__weak__wc17(rate_eval, tf)
    C18__N18__weak__wc12(rate_eval, tf)
    Si26__Al26__weak__wc12(rate_eval, tf)
    O26__F26__weak__mo03(rate_eval, tf)
    Cr48__V48__weak__wc12(rate_eval, tf)
    p_Na29__n_Mg29(rate_eval, tf)
    B14__C14__weak__wc12(rate_eval, tf)
    n_p_He4__Li6(rate_eval, tf)
    K58__n_Ca57__weak__mp17(rate_eval, tf)
    He4_Na25__p_Mg28(rate_eval, tf)
    He4_Cl52__K56(rate_eval, tf)
    n_Ar33__Ar34(rate_eval, tf)
    n_Ca33__Ca34(rate_eval, tf)
    K57__n_Ca56__weak__mp17(rate_eval, tf)
    He4_Sc53__n_V56(rate_eval, tf)
    p_V55__He4_Ti52(rate_eval, tf)
    p_Ca60__He4_K57(rate_eval, tf)
    p_Mn58__He4_Cr55(rate_eval, tf)
    n_Si39__Si40(rate_eval, tf)
    n_Fe46__Fe47(rate_eval, tf)
    n_Cr64__Cr65(rate_eval, tf)
    He4_K31__Sc35(rate_eval, tf)
    V39__Ti39__weak__bqa_pos_(rate_eval, tf)
    K59__n_Ca58__weak__mp17(rate_eval, tf)
    He4_S31__Ar35(rate_eval, tf)
    p_Al37__n_Si37(rate_eval, tf)
    S35__Cl35__weak__wc12(rate_eval, tf)
    K52__n_Ca51__weak__wc12(rate_eval, tf)
    He4_F15__Na19(rate_eval, tf)
    N18__O18__weak__wc12(rate_eval, tf)
    p_Ti48__V49(rate_eval, tf)
    K51__n_Ca50__weak__wc12(rate_eval, tf)
    Sc35__Ca35__weak__bqa_pos_(rate_eval, tf)
    Mg32__Al32__weak__wc12(rate_eval, tf)
    F20__Ne20__weak__wc12(rate_eval, tf)
    p_Ar41__He4_Cl38(rate_eval, tf)
    He4_Mg21__p_Al24(rate_eval, tf)
    K50__n_Ca49__weak__wc12(rate_eval, tf)
    He4_Ca41__Ti45(rate_eval, tf)
    He4_Cl40__K44(rate_eval, tf)
    p_Cl49__He4_S46(rate_eval, tf)
    Sc56__Ti56__weak__wc17(rate_eval, tf)
    He4_Ar45__n_Ca48(rate_eval, tf)
    He4_P29__Cl33(rate_eval, tf)
    K37__Ar37__weak__wc12(rate_eval, tf)
    n_Ca34__Ca35(rate_eval, tf)
    n_Sc38__p_Ca38(rate_eval, tf)
    p_Ar39__K40(rate_eval, tf)
    n_Ti51__Ti52(rate_eval, tf)
    He4_F25__Na29(rate_eval, tf)
    p_K47__Ca48(rate_eval, tf)
    p_O23__n_F23(rate_eval, tf)
    He4_Mn63__n_Co66(rate_eval, tf)
    He4_C11__p_N14(rate_eval, tf)
    He4_Fe61__n_Ni64(rate_eval, tf)
    K36__p_Cl35__weak__wc12(rate_eval, tf)
    He4_Si37__S41(rate_eval, tf)
    K35__p_Cl34__weak__wc12(rate_eval, tf)
    Ca58__n_n_Sc56__weak__mp17(rate_eval, tf)
    p_Ne34__Na35(rate_eval, tf)
    p_Ti61__He4_Sc58(rate_eval, tf)
    n_Si31__Si32(rate_eval, tf)
    n_Cl36__He4_P33(rate_eval, tf)
    n_S37__S38(rate_eval, tf)
    He4_Sc51__V55(rate_eval, tf)
    p_Ti60__He4_Sc57(rate_eval, tf)
    He4_Ti41__p_V44(rate_eval, tf)
    p_B10__He4_Be7(rate_eval, tf)
    n_Ar50__Ar51(rate_eval, tf)
    Ar31__Cl31__weak__wc12(rate_eval, tf)
    Ca59__Sc59__weak__mo03(rate_eval, tf)
    C9__He4_Li5__weak__wc12(rate_eval, tf)
    Mn67__n_Fe66__weak__mp17(rate_eval, tf)
    V66__Cr66__weak__mo03(rate_eval, tf)
    p_Cr42__Mn43(rate_eval, tf)
    n_Ca58__Ca59(rate_eval, tf)
    p_S40__He4_P37(rate_eval, tf)
    n_Ar41__Ar42(rate_eval, tf)
    He4_S35__Ar39(rate_eval, tf)
    p_K54__Ca55(rate_eval, tf)
    n_K42__He4_Cl39(rate_eval, tf)
    He4_S45__Ar49(rate_eval, tf)
    p_V61__Cr62(rate_eval, tf)
    p_Mg27__n_Al27(rate_eval, tf)
    P26__Si26__weak__wc12(rate_eval, tf)
    p_Mn70__He4_Cr67(rate_eval, tf)
    P38__S38__weak__wc12(rate_eval, tf)
    Ca41__K41__weak__wc12(rate_eval, tf)
    He4_K45__n_Sc48(rate_eval, tf)
    n_Ne29__Ne30(rate_eval, tf)
    Si22__p_Mg21__weak__wc12(rate_eval, tf)
    He4_P38__n_Cl41(rate_eval, tf)
    C18__n_N17__weak__wc12(rate_eval, tf)
    He4_Cl48__n_K51(rate_eval, tf)
    Sc63__n_n_Ti61__weak__mp17(rate_eval, tf)
    He4_Ne23__Mg27(rate_eval, tf)
    Si41__P41__weak__wc17(rate_eval, tf)
    n_F27__F28(rate_eval, tf)
    n_Cr51__p_V51(rate_eval, tf)
    n_V65__V66(rate_eval, tf)
    p_K46__n_Ca46(rate_eval, tf)
    V66__n_Cr65__weak__mp17(rate_eval, tf)
    Si38__P38__weak__mo03(rate_eval, tf)
    P47__n_S46__weak__mp17(rate_eval, tf)
    p_Sc59__Ti60(rate_eval, tf)
    p_Be9__B10(rate_eval, tf)
    He4_Ar50__n_Ca53(rate_eval, tf)
    Ne27__Na27__weak__wc12(rate_eval, tf)
    Si44__n_n_n_P41__weak__mo03(rate_eval, tf)
    p_P39__He4_Si36(rate_eval, tf)
    He4_Ti49__Cr53(rate_eval, tf)
    He4_K33__p_Ca36(rate_eval, tf)
    n_K31__He4_Cl28(rate_eval, tf)
    Ar50__n_K49__weak__wc12(rate_eval, tf)
    S39__Cl39__weak__wc12(rate_eval, tf)
    p_F26__Ne27(rate_eval, tf)
    Ar33__p_S32__weak__wc12(rate_eval, tf)
    Ca47__Sc47__weak__wc12(rate_eval, tf)
    He4_Li6__B10(rate_eval, tf)
    He4_S33__Ar37(rate_eval, tf)
    Mg34__n_Al33__weak__mp17(rate_eval, tf)
    S29__p_Si28__weak__wc12(rate_eval, tf)
    O28__n_F27__weak__mp17(rate_eval, tf)
    He4_Cr69__Fe73(rate_eval, tf)
    p_Li7__He4_He4(rate_eval, tf)
    Cl51__n_n_Ar49__weak__mp17(rate_eval, tf)
    n_O12__He4_C9(rate_eval, tf)
    He4_Ca56__Ti60(rate_eval, tf)
    p_Fe65__n_Co65(rate_eval, tf)
    p_Fe76__n_Co76(rate_eval, tf)
    n_O19__O20(rate_eval, tf)
    Ar47__K47__weak__wc12(rate_eval, tf)
    p_Na33__Mg34(rate_eval, tf)
    Cl52__n_Ar51__weak__mp17(rate_eval, tf)
    n_Cr45__p_V45(rate_eval, tf)
    Cl50__n_Ar49__weak__mp17(rate_eval, tf)
    S45__Cl45__weak__wc12(rate_eval, tf)
    n_Sc41__p_Ca41(rate_eval, tf)
    p_Mn67__n_Fe67(rate_eval, tf)
    n_Fe52__p_Mn52(rate_eval, tf)
    Ne34__n_n_Na32__weak__mp17(rate_eval, tf)
    Al33__Si33__weak__wc12(rate_eval, tf)
    n_S36__S37(rate_eval, tf)
    Cl47__n_Ar46__weak__wc12(rate_eval, tf)
    P46__n_S45__weak__mp17(rate_eval, tf)
    p_Ca57__n_Sc57(rate_eval, tf)
    Cl45__n_Ar44__weak__wc12(rate_eval, tf)
    Be11__He4_Li7__weak__wc12(rate_eval, tf)
    n_Ne27__Ne28(rate_eval, tf)
    He4_B10__n_N13(rate_eval, tf)
    p_Ca59__He4_K56(rate_eval, tf)
    n_Mn64__Mn65(rate_eval, tf)
    Sc48__Ti48__weak__wc12(rate_eval, tf)
    Cl44__n_Ar43__weak__mp17(rate_eval, tf)
    n_V44__V45(rate_eval, tf)
    Sc60__n_Ti59__weak__mp17(rate_eval, tf)
    Ti63__V63__weak__mo03(rate_eval, tf)
    He4_O15__Ne19(rate_eval, tf)
    d_d__n_He3(rate_eval, tf)
    Na32__Mg32__weak__wc12(rate_eval, tf)
    Si43__n_P42__weak__mp17(rate_eval, tf)
    Sc58__n_n_Ti56__weak__mp17(rate_eval, tf)
    Fe70__Co70__weak__wc17(rate_eval, tf)
    p_Ne31__n_Na31(rate_eval, tf)
    p_F21__He4_O18(rate_eval, tf)
    Mn64__Fe64__weak__wc12(rate_eval, tf)
    Ar48__K48__weak__wc17(rate_eval, tf)
    He4_Ne28__Mg32(rate_eval, tf)
    p_Sc61__He4_Ca58(rate_eval, tf)
    S48__n_n_Cl46__weak__mp17(rate_eval, tf)
    He4_Na35__Al39(rate_eval, tf)
    Al29__Si29__weak__wc12(rate_eval, tf)
    p_V65__n_Cr65(rate_eval, tf)
    p_Be9__He4_Li6(rate_eval, tf)
    He4_Cr61__Fe65(rate_eval, tf)
    Cl32__p_P31__weak__wc12(rate_eval, tf)
    p_Na26__n_Mg26(rate_eval, tf)
    He4_Ne32__Mg36(rate_eval, tf)
    p_Si27__P28(rate_eval, tf)
    Si36__P36__weak__wc12(rate_eval, tf)
    n_Si27__p_Al27(rate_eval, tf)
    n_Cl47__Cl48(rate_eval, tf)
    p_Ca54__He4_K51(rate_eval, tf)
    Sc40__p_K39__weak__wc12(rate_eval, tf)
    He4_Ne22__Mg26(rate_eval, tf)
    p_Fe74__Co75(rate_eval, tf)
    He4_Mn58__n_Co61(rate_eval, tf)
    S46__n_Cl45__weak__mp17(rate_eval, tf)
    Ti41__Sc41__weak__wc17(rate_eval, tf)
    p_O21__F22(rate_eval, tf)
    He4_Ti62__Cr66(rate_eval, tf)
    He4_Li9__n_B12(rate_eval, tf)
    Mg35__n_n_Al33__weak__mp17(rate_eval, tf)
    p_P42__S43(rate_eval, tf)
    p_Cr66__n_Mn66(rate_eval, tf)
    O13__N13__weak__wc17(rate_eval, tf)
    He4_Al23__p_Si26(rate_eval, tf)
    p_O27__n_F27(rate_eval, tf)
    n_Ti61__Ti62(rate_eval, tf)
    n_Mn46__Mn47(rate_eval, tf)
    p_Al31__n_Si31(rate_eval, tf)
    Cl48__n_n_Ar46__weak__mp17(rate_eval, tf)
    Na19__Ne19__weak__bqa_pos_(rate_eval, tf)
    F28__n_n_Ne26__weak__mp17(rate_eval, tf)
    n_Li6__Li7(rate_eval, tf)
    p_Ca53__He4_K50(rate_eval, tf)
    p_Ar45__K46(rate_eval, tf)
    Al23__p_Na22__weak__wc12(rate_eval, tf)
    O25__F25__weak__mo03(rate_eval, tf)
    p_Cr64__He4_V61(rate_eval, tf)
    He4_N16__n_F19(rate_eval, tf)
    Mg41__Al41__weak__mo03(rate_eval, tf)
    Mn48__Cr48__weak__wc12(rate_eval, tf)
    He4_Cl41__p_Ar44(rate_eval, tf)
    p_Si41__P42(rate_eval, tf)
    n_Mn48__p_Cr48(rate_eval, tf)
    He4_Si36__S40(rate_eval, tf)
    n_Cr49__He4_Ti46(rate_eval, tf)
    He4_Sc46__n_V49(rate_eval, tf)
    n_K38__He4_Cl35(rate_eval, tf)
    p_Mg30__He4_Na27(rate_eval, tf)
    N24__n_N23(rate_eval, tf)
    He4_Fe65__n_Ni68(rate_eval, tf)
    n_K34__He4_Cl31(rate_eval, tf)
    n_Ne17__p_F17(rate_eval, tf)
    p_Al35__Si36(rate_eval, tf)
    n_Ti43__p_Sc43(rate_eval, tf)
    Mg29__Al29__weak__wc12(rate_eval, tf)
    p_F17__Ne18(rate_eval, tf)
    p_Sc53__He4_Ca50(rate_eval, tf)
    P39__n_S38__weak__wc12(rate_eval, tf)
    P44__n_S43__weak__mp17(rate_eval, tf)
    Ca56__n_Sc55__weak__mp17(rate_eval, tf)
    K46__Ca46__weak__wc12(rate_eval, tf)
    P42__n_S41__weak__wc12(rate_eval, tf)
    Na35__n_Mg34__weak__mp17(rate_eval, tf)
    Na33__n_Mg32__weak__wc17(rate_eval, tf)
    Fe76__n_Co75__weak__mp17(rate_eval, tf)
    Mg38__n_n_n_Al35__weak__mo03(rate_eval, tf)
    Ar31__p_p_P29__weak__wc12(rate_eval, tf)
    He4_B13__N17(rate_eval, tf)
    p_Na25__n_Mg25(rate_eval, tf)
    n_Sc57__Sc58(rate_eval, tf)
    He4_P42__Cl46(rate_eval, tf)
    n_Na23__Na24(rate_eval, tf)
    p_N16__n_O16(rate_eval, tf)
    n_Cr44__p_V44(rate_eval, tf)
    p_Mn70__n_Fe70(rate_eval, tf)
    S44__Cl44__weak__wc12(rate_eval, tf)
    He4_Cl45__K49(rate_eval, tf)
    p_Mg41__He4_Na38(rate_eval, tf)
    Fe71__n_Co70__weak__mp17(rate_eval, tf)
    n_O17__He4_C14(rate_eval, tf)
    He4_F21__Na25(rate_eval, tf)
    P28__He4_Mg24__weak__wc12(rate_eval, tf)
    P43__S43__weak__wc17(rate_eval, tf)
    P28__p_Al27__weak__wc12(rate_eval, tf)
    Al31__Si31__weak__wc12(rate_eval, tf)
    p_P37__S38(rate_eval, tf)
    He4_Al39__n_P42(rate_eval, tf)
    He4_Ca49__Ti53(rate_eval, tf)
    Cr42__V42__weak__wc12(rate_eval, tf)
    t_Li7__n_n_He4_He4(rate_eval, tf)
    n_V66__V67(rate_eval, tf)
    He4_K48__Sc52(rate_eval, tf)
    Cl49__Ar49__weak__mo03(rate_eval, tf)
    n_Ar33__He4_S30(rate_eval, tf)
    p_Mn59__Fe60(rate_eval, tf)
    K54__n_Ca53__weak__mp17(rate_eval, tf)
    p_P44__n_S44(rate_eval, tf)
    p_Cl28__Ar29(rate_eval, tf)
    p_S27__Cl28(rate_eval, tf)
    He4_P45__Cl49(rate_eval, tf)
    p_B8__C9(rate_eval, tf)
    n_Sc61__Sc62(rate_eval, tf)
    p_K55__He4_Ar52(rate_eval, tf)
    Si41__n_P40__weak__mp17(rate_eval, tf)
    Mn57__Fe57__weak__wc12(rate_eval, tf)
    Si40__n_P39__weak__mp17(rate_eval, tf)
    Si38__n_P37__weak__mp17(rate_eval, tf)
    p_Mg29__Al30(rate_eval, tf)
    He4_Mn64__n_Co67(rate_eval, tf)
    He4_Cl31__p_Ar34(rate_eval, tf)
    He4_Na22__Al26(rate_eval, tf)
    Fe52__Mn52__weak__wc12(rate_eval, tf)
    K43__Ca43__weak__wc12(rate_eval, tf)
    Mg33__Al33__weak__wc12(rate_eval, tf)
    n_Sc36__He4_K33(rate_eval, tf)
    N11__C11__weak__btyk(rate_eval, tf)
    Ca60__n_Sc59__weak__mp17(rate_eval, tf)
    Al21__Mg21__weak__bqa_pos_(rate_eval, tf)
    O15__N15__weak__wc12(rate_eval, tf)
    V67__Cr67__weak__mo03(rate_eval, tf)
    n_K38__K39(rate_eval, tf)
    He4_Ti37__Cr41(rate_eval, tf)
    p_Si31__n_P31(rate_eval, tf)
    Ne33__n_n_n_Na30__weak__mo03(rate_eval, tf)
    He4_Na26__Al30(rate_eval, tf)
    He4_F22__Na26(rate_eval, tf)
    He4_Sc63__V67(rate_eval, tf)
    Cl46__Ar46__weak__wc12(rate_eval, tf)
    He4_Ti57__Cr61(rate_eval, tf)
    Ti62__n_V61__weak__mp17(rate_eval, tf)
    p_Mn68__He4_Cr65(rate_eval, tf)
    Cr64__n_Mn63__weak__mp17(rate_eval, tf)
    Mn60__Fe60__weak__wc12(rate_eval, tf)
    Si25__p_Mg24__weak__wc12(rate_eval, tf)
    n_Mg21__Mg22(rate_eval, tf)
    n_Fe61__Fe62(rate_eval, tf)
    P42__S42__weak__wc17(rate_eval, tf)
    He4_Fe67__n_Ni70(rate_eval, tf)
    O22__F22__weak__wc17(rate_eval, tf)
    He4_K40__Sc44(rate_eval, tf)
    K31__Ar31__weak__bqa_pos_(rate_eval, tf)
    He4_Ne34__n_Mg37(rate_eval, tf)
    n_V63__V64(rate_eval, tf)
    Na39__n_n_Mg37__weak__mp17(rate_eval, tf)
    Si23__p_Mg22__weak__wc17(rate_eval, tf)
    He4_Fe48__Ni52(rate_eval, tf)
    n_N14__N15(rate_eval, tf)
    n_F17__p_O17(rate_eval, tf)
    n_Fe45__p_Mn45(rate_eval, tf)
    He4_Na30__n_Al33(rate_eval, tf)
    p_Mg38__He4_Na35(rate_eval, tf)
    Fe47__p_Cr46__weak__wc12(rate_eval, tf)
    Al38__n_Si37__weak__mp17(rate_eval, tf)
    He4_Ar49__n_Ca52(rate_eval, tf)
    p_O24__F25(rate_eval, tf)
    p_Mg21__Al22(rate_eval, tf)
    n_Si30__Si31(rate_eval, tf)
    He4_Mn55__Co59(rate_eval, tf)
    Cr60__Mn60__weak__wc12(rate_eval, tf)
    p_Cr48__Mn49(rate_eval, tf)
    p_K52__n_Ca52(rate_eval, tf)
    He4_Si30__S34(rate_eval, tf)
    n_P31__P32(rate_eval, tf)
    He4_Si43__S47(rate_eval, tf)
    Al35__n_Si34__weak__wc12(rate_eval, tf)
    Cl52__Ar52__weak__mo03(rate_eval, tf)
    Mn69__Fe69__weak__wc17(rate_eval, tf)
    p_Mg35__He4_Na32(rate_eval, tf)
    Si39__n_P38__weak__mp17(rate_eval, tf)
    He4_Mn56__Co60(rate_eval, tf)
    Ne29__Na29__weak__wc12(rate_eval, tf)
    He4_P44__Cl48(rate_eval, tf)
    n_Fe45__Fe46(rate_eval, tf)
    He4_Sc37__V41(rate_eval, tf)
    N16__He4_C12__weak__wc12(rate_eval, tf)
    p_Cl37__Ar38(rate_eval, tf)
    P40__n_S39__weak__wc12(rate_eval, tf)
    Al32__n_Si31__weak__wc12(rate_eval, tf)
    p_K32__Ca33(rate_eval, tf)
    C10__B10__weak__wc12(rate_eval, tf)
    Cr57__Mn57__weak__wc12(rate_eval, tf)
    Cl36__Ar36__weak__wc12(rate_eval, tf)
    n_Fe59__Fe60(rate_eval, tf)
    He4_Na24__n_Al27(rate_eval, tf)
    B13__C13__weak__wc12(rate_eval, tf)
    p_Ar54__K55(rate_eval, tf)
    He4_O25__Ne29(rate_eval, tf)
    p_Sc50__He4_Ca47(rate_eval, tf)
    Fe61__Co61__weak__wc12(rate_eval, tf)
    p_P45__He4_Si42(rate_eval, tf)
    p_K43__He4_Ar40(rate_eval, tf)
    n_P37__P38(rate_eval, tf)
    He4_Si44__S48(rate_eval, tf)
    Na20__He4_O16__weak__wc12(rate_eval, tf)
    Si43__n_n_n_P40__weak__mo03(rate_eval, tf)
    P47__S47__weak__mo03(rate_eval, tf)
    Ti54__V54__weak__wc12(rate_eval, tf)
    K51__Ca51__weak__wc12(rate_eval, tf)
    Ti39__Sc39__weak__wc17(rate_eval, tf)
    Mg40__n_Al39__weak__mp17(rate_eval, tf)
    He4_K38__Sc42(rate_eval, tf)
    Mn72__n_n_n_Fe69__weak__mo03(rate_eval, tf)
    Mg38__n_Al37__weak__mp17(rate_eval, tf)
    p_S43__n_Cl43(rate_eval, tf)
    He4_Ti59__Cr63(rate_eval, tf)
    n_Ti62__Ti63(rate_eval, tf)
    Cr44__p_Ti43__weak__wc12(rate_eval, tf)
    O27__n_O26(rate_eval, tf)
    p_Mn54__Fe55(rate_eval, tf)
    Ca60__Sc60__weak__mo03(rate_eval, tf)
    p_P40__He4_Si37(rate_eval, tf)
    n_Mg33__Mg34(rate_eval, tf)
    p_P44__S45(rate_eval, tf)
    Ca58__Sc58__weak__mo03(rate_eval, tf)
    He4_V52__n_Mn55(rate_eval, tf)
    V61__Cr61__weak__wc12(rate_eval, tf)
    O21__F21__weak__wc12(rate_eval, tf)
    O13__p_C12__weak__wc12(rate_eval, tf)
    P45__S45__weak__mo03(rate_eval, tf)
    K56__n_Ca55__weak__mp17(rate_eval, tf)
    C20__N20__weak__wc12(rate_eval, tf)
    p_d__He3(rate_eval, tf)
    n_C15__C16(rate_eval, tf)
    Si25__Al25__weak__wc12(rate_eval, tf)
    K57__Ca57__weak__mo03(rate_eval, tf)
    S42__Cl42__weak__wc12(rate_eval, tf)
    p_V47__Cr48(rate_eval, tf)
    Mg21__p_Ne20__weak__wc12(rate_eval, tf)
    S31__P31__weak__wc12(rate_eval, tf)
    He4_Mn71__n_Co74(rate_eval, tf)
    K45__Ca45__weak__wc12(rate_eval, tf)
    Cr55__Mn55__weak__wc12(rate_eval, tf)
    n_Ca42__Ca43(rate_eval, tf)
    He4_Ar34__Ca38(rate_eval, tf)
    p_Na38__n_Mg38(rate_eval, tf)
    p_V54__He4_Ti51(rate_eval, tf)
    p_Ca53__Sc54(rate_eval, tf)
    n_Mn53__Mn54(rate_eval, tf)
    S43__Cl43__weak__wc12(rate_eval, tf)
    p_Na37__n_Mg37(rate_eval, tf)
    Ti62__V62__weak__mo03(rate_eval, tf)
    p_Mn62__n_Fe62(rate_eval, tf)
    n_Mn48__Mn49(rate_eval, tf)
    P27__Si27__weak__wc12(rate_eval, tf)
    n_Ti56__Ti57(rate_eval, tf)
    Mg28__Al28__weak__wc12(rate_eval, tf)
    Na38__n_Mg37__weak__mp17(rate_eval, tf)
    He4_Si22__S26(rate_eval, tf)
    Ar53__n_K52__weak__mp17(rate_eval, tf)
    n_S43__S44(rate_eval, tf)
    V67__n_Cr66__weak__mp17(rate_eval, tf)
    p_F23__n_Ne23(rate_eval, tf)
    Ti64__V64__weak__mo03(rate_eval, tf)
    S41__Cl41__weak__wc12(rate_eval, tf)
    Na34__n_Mg33__weak__wc12(rate_eval, tf)
    p_Ca38__Sc39(rate_eval, tf)
    n_Ti39__Ti40(rate_eval, tf)
    n_Ca39__p_K39(rate_eval, tf)
    He4_Ar51__Ca55(rate_eval, tf)
    n_Ti44__He4_Ca41(rate_eval, tf)
    Si37__n_P36__weak__wc12(rate_eval, tf)
    Mn64__n_Fe63__weak__wc12(rate_eval, tf)
    Ne33__n_Na32__weak__mp17(rate_eval, tf)
    He4_Mn66__n_Co69(rate_eval, tf)
    Na30__He4_Ne26__weak__wc12(rate_eval, tf)
    He4_Ca52__n_Ti55(rate_eval, tf)
    p_Cr43__Mn44(rate_eval, tf)
    He4_Ne19__Mg23(rate_eval, tf)
    Na29__n_Mg28__weak__wc12(rate_eval, tf)
    p_Sc56__n_Ti56(rate_eval, tf)
    n_Mg39__Mg40(rate_eval, tf)
    p_Si36__P37(rate_eval, tf)
    He4_Fe60__Ni64(rate_eval, tf)
    He4_Ar48__Ca52(rate_eval, tf)
    p_S43__Cl44(rate_eval, tf)
    Mg34__Al34__weak__wc17(rate_eval, tf)
    Ca48__Sc48__weak__mo03(rate_eval, tf)
    p_V62__He4_Ti59(rate_eval, tf)
    p_P47__He4_Si44(rate_eval, tf)
    He4_Ca54__n_Ti57(rate_eval, tf)
    n_S48__S49(rate_eval, tf)
    n_P43__P44(rate_eval, tf)
    n_P25__p_Si25(rate_eval, tf)
    Ar33__Cl33__weak__wc12(rate_eval, tf)
    p_Ar49__n_K49(rate_eval, tf)
    p_Cr44__Mn45(rate_eval, tf)
    V50__Ti50__weak__mo03(rate_eval, tf)
    p_Ti62__He4_Sc59(rate_eval, tf)
    Ca37__K37__weak__wc12(rate_eval, tf)
    O23__F23__weak__wc12(rate_eval, tf)
    He4_V42__Mn46(rate_eval, tf)
    p_Al22__Si23(rate_eval, tf)
    n_B10__He4_Li7(rate_eval, tf)
    Al26__Mg26__weak__wc12(rate_eval, tf)
    p_Ca55__Sc56(rate_eval, tf)
    n_Si27__C12_O16(rate_eval, tf)
    n_Si28__Si29(rate_eval, tf)
    He4_Fe55__Ni59(rate_eval, tf)
    Mn71__n_Fe70__weak__mp17(rate_eval, tf)
    Cl45__Ar45__weak__wc12(rate_eval, tf)
    Al24__Mg24__weak__wc12(rate_eval, tf)
    p_Na30__Mg31(rate_eval, tf)
    N18__n_O17__weak__wc12(rate_eval, tf)
    t_t__n_n_He4(rate_eval, tf)
    V67__n_n_Cr65__weak__mp17(rate_eval, tf)
    p_Cr59__He4_V56(rate_eval, tf)
    p_P35__He4_Si32(rate_eval, tf)
    p_Ar48__K49(rate_eval, tf)
    He6__Li6__weak__wc12(rate_eval, tf)
    p_Ne29__Na30(rate_eval, tf)
    p_Ar53__K54(rate_eval, tf)
    p_P34__He4_Si31(rate_eval, tf)
    n_Si41__Si42(rate_eval, tf)
    Ca61__Sc61__weak__mo03(rate_eval, tf)
    p_K39__He4_Ar36(rate_eval, tf)
    V40__Ti40__weak__bqa_pos_(rate_eval, tf)
    Cl43__Ar43__weak__wc12(rate_eval, tf)
    Fe71__Co71__weak__wc17(rate_eval, tf)
    He3_Li7__n_p_He4_He4(rate_eval, tf)
    P35__S35__weak__wc12(rate_eval, tf)
    n_K35__K36(rate_eval, tf)
    Fe45__p_p_V43__weak__wc12(rate_eval, tf)
    P46__S46__weak__mo03(rate_eval, tf)
    F18__O18__weak__wc12(rate_eval, tf)
    n_K39__K40(rate_eval, tf)
    Sc49__Ti49__weak__wc12(rate_eval, tf)
    He4_P29__p_S32(rate_eval, tf)
    p_Mn55__Fe56(rate_eval, tf)
    n_Al33__Al34(rate_eval, tf)
    p_Ar49__K50(rate_eval, tf)
    p_Mn65__n_Fe65(rate_eval, tf)
    d_C14__n_N15(rate_eval, tf)
    He4_Ti58__Cr62(rate_eval, tf)
    n_P29__p_Si29(rate_eval, tf)
    p_N16__He4_C13(rate_eval, tf)
    n_Na26__Na27(rate_eval, tf)
    n_K54__K55(rate_eval, tf)
    n_Ti63__Ti64(rate_eval, tf)
    Be12__n_B11__weak__wc12(rate_eval, tf)
    p_Ca39__Sc40(rate_eval, tf)
    p_Na32__He4_Ne29(rate_eval, tf)
    n_Cl50__Cl51(rate_eval, tf)
    Ti42__Sc42__weak__wc12(rate_eval, tf)
    p_Ti64__V65(rate_eval, tf)
    F31__n_Ne30__weak__mp17(rate_eval, tf)
    F26__n_Ne25__weak__wc12(rate_eval, tf)
    Ne29__n_Na28__weak__wc17(rate_eval, tf)
    He4_Cr52__Fe56(rate_eval, tf)
    K48__Ca48__weak__wc12(rate_eval, tf)
    V63__Cr63__weak__wc12(rate_eval, tf)
    n_V52__V53(rate_eval, tf)
    He4_Al21__P25(rate_eval, tf)
    n_Be10__Be11(rate_eval, tf)
    n_Al29__Al30(rate_eval, tf)
    Be7__Li7__weak__electron_capture(rate_eval, tf)
    Al38__Si38__weak__wc17(rate_eval, tf)
    n_Ar36__p_Cl36(rate_eval, tf)
    n_Ar53__Ar54(rate_eval, tf)
    Mg31__Al31__weak__wc12(rate_eval, tf)
    Ca60__n_n_Sc58__weak__mp17(rate_eval, tf)
    Ti40__p_Ca39__weak__wc12(rate_eval, tf)
    He4_Mg23__p_Al26(rate_eval, tf)
    He4_Ca34__p_Sc37(rate_eval, tf)
    n_Ne22__Ne23(rate_eval, tf)
    He4_Sc61__V65(rate_eval, tf)
    V48__Ti48__weak__wc12(rate_eval, tf)
    P34__S34__weak__wc12(rate_eval, tf)
    S29__P29__weak__wc12(rate_eval, tf)
    Ar43__K43__weak__wc12(rate_eval, tf)
    p_Cl49__n_Ar49(rate_eval, tf)
    p_Cl52__Ar53(rate_eval, tf)
    n_Sc36__Sc37(rate_eval, tf)
    P46__n_n_S44__weak__mp17(rate_eval, tf)
    n_Ca35__Ca36(rate_eval, tf)
    p_O25__F26(rate_eval, tf)
    V41__Ti41__weak__bqa_pos_(rate_eval, tf)
    He4_V44__Mn48(rate_eval, tf)
    O23__n_F22__weak__wc12(rate_eval, tf)
    V64__n_Cr63__weak__mp17(rate_eval, tf)
    Ti53__V53__weak__wc12(rate_eval, tf)
    p_K54__He4_Ar51(rate_eval, tf)
    He4_Fe53__Ni57(rate_eval, tf)
    p_Sc59__n_Ti59(rate_eval, tf)
    p_Ca37__Sc38(rate_eval, tf)
    Cr56__Mn56__weak__wc12(rate_eval, tf)
    p_P37__n_S37(rate_eval, tf)
    Fe72__Co72__weak__mo03(rate_eval, tf)
    He4_Al41__n_P44(rate_eval, tf)
    p_Mn61__He4_Cr58(rate_eval, tf)
    He4_F19__Na23(rate_eval, tf)
    He4_Si41__n_S44(rate_eval, tf)
    p_P43__S44(rate_eval, tf)
    p_Ti45__V46(rate_eval, tf)
    Fe47__Mn47__weak__wc12(rate_eval, tf)
    P28__Si28__weak__wc12(rate_eval, tf)
    Cr51__V51__weak__wc12(rate_eval, tf)
    Fe55__Mn55__weak__wc12(rate_eval, tf)
    p_Cl47__He4_S44(rate_eval, tf)
    n_Cl36__Cl37(rate_eval, tf)
    C19__n_N18__weak__wc12(rate_eval, tf)
    He4_Ti65__Cr69(rate_eval, tf)
    Ca52__Sc52__weak__wc12(rate_eval, tf)
    p_Al27__Si28(rate_eval, tf)
    He4_V62__Mn66(rate_eval, tf)
    Si43__P43__weak__mo03(rate_eval, tf)
    n_Na22__He4_F19(rate_eval, tf)
    Ne34__n_Na33__weak__mp17(rate_eval, tf)
    Sc52__Ti52__weak__wc12(rate_eval, tf)
    P45__n_S44__weak__mp17(rate_eval, tf)
    He4_V40__Mn44(rate_eval, tf)
    Ar51__K51__weak__mo03(rate_eval, tf)
    B19__n_C18__weak__wc17(rate_eval, tf)
    p_Ti56__n_V56(rate_eval, tf)
    B15__n_C14__weak__wc12(rate_eval, tf)
    He4_Ar51__n_Ca54(rate_eval, tf)
    n_S39__S40(rate_eval, tf)
    K40__Ar40__weak__wc12(rate_eval, tf)
    He4_K54__Sc58(rate_eval, tf)
    He4_Sc53__V57(rate_eval, tf)
    He4_Si27__S31(rate_eval, tf)
    F30__Ne30__weak__mo03(rate_eval, tf)
    p_Na29__Mg30(rate_eval, tf)
    Be15__n_Be14(rate_eval, tf)
    Ne30__Na30__weak__wc17(rate_eval, tf)
    Be14__n_B13__weak__wc17(rate_eval, tf)
    n_Mn56__He4_V53(rate_eval, tf)
    Li11__n_Be10__weak__wc17(rate_eval, tf)
    Al22__He4_Ne18__weak__wc12(rate_eval, tf)
    Ti37__Sc37__weak__bqa_pos_(rate_eval, tf)
    K33__Ar33__weak__bqa_pos_(rate_eval, tf)
    Cr64__Mn64__weak__wc12(rate_eval, tf)
    p_Ti59__He4_Sc56(rate_eval, tf)
    n_Ar37__Ar38(rate_eval, tf)
    He4_F29__Na33(rate_eval, tf)
    N17__O17__weak__wc12(rate_eval, tf)
    Fe63__Co63__weak__wc12(rate_eval, tf)
    Si27__Al27__weak__wc12(rate_eval, tf)
    B8__He4_He4__weak__wc12(rate_eval, tf)
    He4_Cr50__Fe54(rate_eval, tf)
    Fe68__Co68__weak__wc12(rate_eval, tf)
    n_Al22__Al23(rate_eval, tf)
    n_V57__V58(rate_eval, tf)
    He4_Ar38__Ca42(rate_eval, tf)
    Fe64__Co64__weak__wc12(rate_eval, tf)
    He4_Al23__P27(rate_eval, tf)
    He4_F22__n_Na25(rate_eval, tf)
    Cr62__Mn62__weak__wc12(rate_eval, tf)
    n_Al21__p_Mg21(rate_eval, tf)
    p_K50__Ca51(rate_eval, tf)
    Sc58__Ti58__weak__wc17(rate_eval, tf)
    O26__n_n_n_F23__weak__mo03(rate_eval, tf)
    Si36__n_P35__weak__wc12(rate_eval, tf)
    He4_Mg24__Si28(rate_eval, tf)
    He4_Si34__n_S37(rate_eval, tf)
    Ti59__V59__weak__wc12(rate_eval, tf)
    C11__B11__weak__wc12(rate_eval, tf)
    p_Si34__n_P34(rate_eval, tf)
    He4_Ne33__Mg37(rate_eval, tf)
    Fe46__Mn46__weak__wc12(rate_eval, tf)
    n_Na29__Na30(rate_eval, tf)
    Cr65__n_Mn64__weak__mp17(rate_eval, tf)
    p_O19__n_F19(rate_eval, tf)
    F21__Ne21__weak__wc12(rate_eval, tf)
    Mn65__Fe65__weak__wc17(rate_eval, tf)
    Mn63__Fe63__weak__wc12(rate_eval, tf)
    Mn59__Fe59__weak__wc12(rate_eval, tf)
    He4_Ca57__Ti61(rate_eval, tf)
    Mn56__Fe56__weak__wc12(rate_eval, tf)
    p_Mg25__Al26(rate_eval, tf)
    B17__n_C16__weak__wc17(rate_eval, tf)
    Mn50__Cr50__weak__wc12(rate_eval, tf)
    n_Cr67__Cr68(rate_eval, tf)
    Cr66__Mn66__weak__wc17(rate_eval, tf)
    P41__S41__weak__wc12(rate_eval, tf)
    Mn47__Cr47__weak__wc17(rate_eval, tf)
    Mn46__Cr46__weak__wc12(rate_eval, tf)
    Ar42__K42__weak__wc12(rate_eval, tf)
    He4_Ar48__n_Ca51(rate_eval, tf)
    Na30__Mg30__weak__wc12(rate_eval, tf)
    n_F14__p_O14(rate_eval, tf)
    n_Cr49__Cr50(rate_eval, tf)
    n_P25__P26(rate_eval, tf)
    Cr63__Mn63__weak__wc17(rate_eval, tf)
    Fe62__Co62__weak__wc12(rate_eval, tf)
    n_Al30__Al31(rate_eval, tf)
    Al36__n_n_Si34__weak__mp17(rate_eval, tf)
    C16__N16__weak__wc12(rate_eval, tf)
    Ar34__Cl34__weak__wc12(rate_eval, tf)
    Sc46__Ti46__weak__wc12(rate_eval, tf)
    p_Sc63__n_Ti63(rate_eval, tf)
    P38__n_S37__weak__wc12(rate_eval, tf)
    Cr59__Mn59__weak__wc12(rate_eval, tf)
    n_Ti48__Ti49(rate_eval, tf)
    n_Mn47__Mn48(rate_eval, tf)
    Cr49__V49__weak__wc12(rate_eval, tf)
    p_Al42__n_Si42(rate_eval, tf)
    Ca61__n_n_Sc59__weak__mp17(rate_eval, tf)
    n_Fe55__Fe56(rate_eval, tf)
    Mn48__p_V47__weak__wc12(rate_eval, tf)
    n_Cr68__Cr69(rate_eval, tf)
    He4_K32__p_Ca35(rate_eval, tf)
    Cr43__V43__weak__wc12(rate_eval, tf)
    He4_Mn57__Co61(rate_eval, tf)
    p_S45__Cl46(rate_eval, tf)
    n_Ne25__Ne26(rate_eval, tf)
    n_S31__S32(rate_eval, tf)
    He4_Cr58__n_Fe61(rate_eval, tf)
    He4_Si26__p_P29(rate_eval, tf)
    Mn71__Fe71__weak__mo03(rate_eval, tf)
    Mg36__n_Al35__weak__mp17(rate_eval, tf)
    Ne30__n_Na29__weak__wc12(rate_eval, tf)
    Be14__B14__weak__wc12(rate_eval, tf)
    Cr41__V41__weak__bqa_pos_(rate_eval, tf)
    Fe65__Co65__weak__wc12(rate_eval, tf)
    V58__Cr58__weak__wc17(rate_eval, tf)
    Cl51__n_n_n_Ar48__weak__mo03(rate_eval, tf)
    He4_Cr67__n_Fe70(rate_eval, tf)
    He4_Sc46__V50(rate_eval, tf)
    He4_Ca59__n_Ti62(rate_eval, tf)
    He4_S34__n_Ar37(rate_eval, tf)
    p_Ti58__He4_Sc55(rate_eval, tf)
    K44__Ca44__weak__wc12(rate_eval, tf)
    V43__Ti43__weak__wc12(rate_eval, tf)
    Sc50__Ti50__weak__wc12(rate_eval, tf)
    K53__Ca53__weak__wc17(rate_eval, tf)
    S47__n_Cl46__weak__mp17(rate_eval, tf)
    p_F31__Ne32(rate_eval, tf)
    p_Sc43__He4_Ca40(rate_eval, tf)
    S48__Cl48__weak__mo03(rate_eval, tf)
    n_K42__p_Ar42(rate_eval, tf)
    He4_V41__p_Cr44(rate_eval, tf)
    n_Fe45__He4_Cr42(rate_eval, tf)
    He4_Ti39__Cr43(rate_eval, tf)
    V66__n_n_Cr64__weak__mp17(rate_eval, tf)
    K54__Ca54__weak__wc17(rate_eval, tf)
    Cl48__Ar48__weak__mo03(rate_eval, tf)
    p_Sc62__He4_Ca59(rate_eval, tf)
    Ar46__K46__weak__wc12(rate_eval, tf)
    Li9__Be9__weak__wc12(rate_eval, tf)
    Ca50__Sc50__weak__wc12(rate_eval, tf)
    He4_Sc50__V54(rate_eval, tf)
    n_Fe52__Fe53(rate_eval, tf)
    n_Fe64__Fe65(rate_eval, tf)
    Al22__p_Na21__weak__wc17(rate_eval, tf)
    V64__Cr64__weak__wc17(rate_eval, tf)
    Cl40__Ar40__weak__wc12(rate_eval, tf)
    Na34__n_n_Mg32__weak__wc12(rate_eval, tf)
    Na34__Mg34__weak__wc12(rate_eval, tf)
    Ar53__K53__weak__mo03(rate_eval, tf)
    He4_F23__n_Na26(rate_eval, tf)
    Al28__Si28__weak__wc12(rate_eval, tf)
    K35__Ar35__weak__wc12(rate_eval, tf)
    Sc61__Ti61__weak__mo03(rate_eval, tf)
    Li8__He4_He4__weak__wc12(rate_eval, tf)
    K58__Ca58__weak__mo03(rate_eval, tf)
    Ti64__n_n_n_V61__weak__mo03(rate_eval, tf)
    n_Sc51__Sc52(rate_eval, tf)
    F29__n_Ne28__weak__wc12(rate_eval, tf)
    n_Fe59__He4_Cr56(rate_eval, tf)
    He4_S37__Ar41(rate_eval, tf)
    p_P47__S48(rate_eval, tf)
    Sc51__Ti51__weak__wc12(rate_eval, tf)
    K55__Ca55__weak__mo03(rate_eval, tf)
    Ti65__V65__weak__mo03(rate_eval, tf)
    d_Li6__p_Li7(rate_eval, tf)
    n_Si29__Si30(rate_eval, tf)
    N22__n_n_O20__weak__wc12(rate_eval, tf)
    n_Cl35__Cl36(rate_eval, tf)
    F25__n_Ne24__weak__wc12(rate_eval, tf)
    p_Mg28__Al29(rate_eval, tf)
    n_F15__p_O15(rate_eval, tf)
    Sc43__Ca43__weak__wc12(rate_eval, tf)
    n_Na20__p_Ne20(rate_eval, tf)
    n_Na38__Na39(rate_eval, tf)
    n_V52__He4_Sc49(rate_eval, tf)
    He4_Fe49__Ni53(rate_eval, tf)
    n_Cr50__Cr51(rate_eval, tf)
    N12__C12__weak__wc12(rate_eval, tf)
    Ne31__n_n_Na29__weak__mp17(rate_eval, tf)
    Fe51__Mn51__weak__wc12(rate_eval, tf)
    n_P24__P25(rate_eval, tf)
    p_O19__F20(rate_eval, tf)
    Ne32__n_n_n_Na29__weak__mo03(rate_eval, tf)
    p_Cr58__He4_V55(rate_eval, tf)
    V42__Ti42__weak__mo97(rate_eval, tf)
    Cl36__S36__weak__wc12(rate_eval, tf)
    p_Si41__n_P41(rate_eval, tf)
    Mn51__Cr51__weak__wc12(rate_eval, tf)
    He4_Fe47__p_Co50(rate_eval, tf)
    Ca54__Sc54__weak__wc17(rate_eval, tf)
    n_Ca42__He4_Ar39(rate_eval, tf)
    Ca45__Sc45__weak__wc12(rate_eval, tf)
    p_Na24__n_Mg24(rate_eval, tf)
    n_Na25__Na26(rate_eval, tf)
    p_Cr63__He4_V60(rate_eval, tf)
    Ne33__n_n_Na31__weak__mp17(rate_eval, tf)
    p_Si35__n_P35(rate_eval, tf)
    S40__Cl40__weak__wc12(rate_eval, tf)
    Na32__n_Mg31__weak__wc17(rate_eval, tf)
    n_V58__V59(rate_eval, tf)
    p_Si43__P44(rate_eval, tf)
    K50__Ca50__weak__wc12(rate_eval, tf)
    n_Mn61__Mn62(rate_eval, tf)
    Mg21__Na21__weak__wc12(rate_eval, tf)
    V57__Cr57__weak__wc12(rate_eval, tf)
    He4_Fe72__n_Ni75(rate_eval, tf)
    K57__n_n_n_Ca54__weak__mo03(rate_eval, tf)
    He4_Al33__P37(rate_eval, tf)
    Cl33__S33__weak__wc12(rate_eval, tf)
    S48__n_Cl47__weak__mp17(rate_eval, tf)
    n_Mn43__Mn44(rate_eval, tf)
    He4_Al22__P26(rate_eval, tf)
    Si40__P40__weak__wc17(rate_eval, tf)
    p_K53__He4_Ar50(rate_eval, tf)
    K36__Ar36__weak__wc12(rate_eval, tf)
    S43__n_Cl42__weak__wc12(rate_eval, tf)
    Mn53__Cr53__weak__wc12(rate_eval, tf)
    F27__Ne27__weak__wc17(rate_eval, tf)
    Ti55__V55__weak__wc12(rate_eval, tf)
    He4_O26__Ne30(rate_eval, tf)
    n_Ti40__He4_Ca37(rate_eval, tf)
    V56__Cr56__weak__wc12(rate_eval, tf)
    Ar50__K50__weak__wc12(rate_eval, tf)
    p_Na25__He4_Ne22(rate_eval, tf)
    He4_S44__n_Ar47(rate_eval, tf)
    p_Mg28__n_Al28(rate_eval, tf)
    n_V45__p_Ti45(rate_eval, tf)
    p_O18__F19(rate_eval, tf)
    p_P36__S37(rate_eval, tf)
    Na35__Mg35__weak__wc17(rate_eval, tf)
    He4_Fe72__Ni76(rate_eval, tf)
    Na24__Mg24__weak__wc12(rate_eval, tf)
    V59__Cr59__weak__wc12(rate_eval, tf)
    Ar41__K41__weak__wc12(rate_eval, tf)
    Cr65__Mn65__weak__wc17(rate_eval, tf)
    Cr46__V46__weak__wc12(rate_eval, tf)
    n_F24__F25(rate_eval, tf)
    Ar37__Cl37__weak__wc12(rate_eval, tf)
    Be10__B10__weak__wc12(rate_eval, tf)
    Ar32__Cl32__weak__wc12(rate_eval, tf)
    p_Mg39__He4_Na36(rate_eval, tf)
    n_S27__p_P27(rate_eval, tf)
    Ti63__n_n_V61__weak__mp17(rate_eval, tf)
    He4_Al30__n_P33(rate_eval, tf)
    Ar29__Cl29__weak__bqa_pos_(rate_eval, tf)
    Na31__Mg31__weak__wc12(rate_eval, tf)
    n_V60__V61(rate_eval, tf)
    p_Sc44__Ti45(rate_eval, tf)
    n_V40__V41(rate_eval, tf)
    B15__C15__weak__wc12(rate_eval, tf)
    Cl44__Ar44__weak__wc17(rate_eval, tf)
    He4_Ca33__p_Sc36(rate_eval, tf)
    Na33__Mg33__weak__wc12(rate_eval, tf)
    Ar44__K44__weak__wc12(rate_eval, tf)
    p_V66__He4_Ti63(rate_eval, tf)
    Sc60__n_n_n_Ti57__weak__mo03(rate_eval, tf)
    Cl31__S31__weak__wc12(rate_eval, tf)
    V53__Cr53__weak__wc12(rate_eval, tf)
    n_V39__He4_Sc36(rate_eval, tf)
    V44__Ti44__weak__wc12(rate_eval, tf)
    Fe49__p_Cr48__weak__wc12(rate_eval, tf)
    n_Sc60__Sc61(rate_eval, tf)
    Mn63__n_Fe62__weak__mp17(rate_eval, tf)
    Si37__P37__weak__wc12(rate_eval, tf)
    Al39__Si39__weak__wc17(rate_eval, tf)
    Fe76__Co76__weak__mo03(rate_eval, tf)
    He4_Na38__Al42(rate_eval, tf)
    Mg30__Al30__weak__wc12(rate_eval, tf)
    He4_Ar49__Ca53(rate_eval, tf)
    Al33__n_Si32__weak__wc12(rate_eval, tf)
    N19__O19__weak__wc12(rate_eval, tf)
    S38__Cl38__weak__wc12(rate_eval, tf)
    He4_K46__Sc50(rate_eval, tf)
    He4_Sc50__n_V53(rate_eval, tf)
    n_Sc39__p_Ca39(rate_eval, tf)
    Mg31__n_Al30__weak__wc12(rate_eval, tf)
    P39__S39__weak__wc12(rate_eval, tf)
    n_Sc40__He4_K37(rate_eval, tf)
    n_Ca39__Ca40(rate_eval, tf)
    n_Ne33__Ne34(rate_eval, tf)
    He4_O16__Ne20(rate_eval, tf)
    p_Ar51__n_K51(rate_eval, tf)
    p_Cr67__Mn68(rate_eval, tf)
    F30__n_n_n_Ne27__weak__mo03(rate_eval, tf)
    p_P41__He4_Si38(rate_eval, tf)
    p_Mg34__n_Al34(rate_eval, tf)
    p_Na39__Mg40(rate_eval, tf)
    Si22__Al22__weak__wc12(rate_eval, tf)
    Si39__P39__weak__wc17(rate_eval, tf)
    Al40__n_n_Si38__weak__mp17(rate_eval, tf)
    He4_Ca56__n_Ti59(rate_eval, tf)
    p_Be10__He4_Li7(rate_eval, tf)
    p_Mg35__Al36(rate_eval, tf)
    Cr45__V45__weak__wc12(rate_eval, tf)
    p_Ar50__K51(rate_eval, tf)
    K50__n_n_Ca48__weak__mp17(rate_eval, tf)
    Sc60__Ti60__weak__mo03(rate_eval, tf)
    p_Ca47__Sc48(rate_eval, tf)
    N18__He4_C14__weak__wc12(rate_eval, tf)
    He4_Cr68__Fe72(rate_eval, tf)
    N20__O20__weak__wc12(rate_eval, tf)
    p_Cl44__He4_S41(rate_eval, tf)
    Ar54__K54__weak__mo03(rate_eval, tf)
    n_Ca38__He4_Ar35(rate_eval, tf)
    p_Sc54__He4_Ca51(rate_eval, tf)
    n_Be9__Be10(rate_eval, tf)
    He4_Ne21__Mg25(rate_eval, tf)
    p_Cr70__He4_V67(rate_eval, tf)
    p_Mg40__Al41(rate_eval, tf)
    p_Ti55__He4_Sc52(rate_eval, tf)
    Ar51__n_n_K49__weak__mp17(rate_eval, tf)
    p_Mg33__Al34(rate_eval, tf)
    p_Al29__Si30(rate_eval, tf)
    p_Mn56__n_Fe56(rate_eval, tf)
    n_Sc47__Sc48(rate_eval, tf)
    p_V59__He4_Ti56(rate_eval, tf)
    Na37__n_n_Mg35__weak__mp17(rate_eval, tf)
    p_Ar49__He4_Cl46(rate_eval, tf)
    F28__Ne28__weak__mo03(rate_eval, tf)
    Mg35__Al35__weak__wc17(rate_eval, tf)
    He4_K52__Sc56(rate_eval, tf)
    p_Al32__Si33(rate_eval, tf)
    Ne23__Na23__weak__wc12(rate_eval, tf)
    Mn45__Cr45__weak__bqa_pos_(rate_eval, tf)
    Na33__n_n_Mg31__weak__wc12(rate_eval, tf)
    p_Na19__Mg20(rate_eval, tf)
    Mg20__Na20__weak__wc12(rate_eval, tf)
    Ne26__Na26__weak__wc12(rate_eval, tf)
    Ti60__V60__weak__wc17(rate_eval, tf)
    p_Fe62__Co63(rate_eval, tf)
    p_P39__S40(rate_eval, tf)
    K56__n_n_Ca54__weak__mp17(rate_eval, tf)
    Cl38__Ar38__weak__wc12(rate_eval, tf)
    He4_Na32__Al36(rate_eval, tf)
    Sc55__Ti55__weak__wc12(rate_eval, tf)
    He4_P30__Cl34(rate_eval, tf)
    p_F26__He4_O23(rate_eval, tf)
    F28__n_Ne27__weak__mp17(rate_eval, tf)
    n_S32__He4_Si29(rate_eval, tf)
    n_Si37__Si38(rate_eval, tf)
    Ca56__Sc56__weak__wc17(rate_eval, tf)
    p_S48__Cl49(rate_eval, tf)
    Cl42__Ar42__weak__wc12(rate_eval, tf)
    p_Sc42__He4_Ca39(rate_eval, tf)
    n_Sc38__He4_K35(rate_eval, tf)
    n_Al42__Al43(rate_eval, tf)
    O19__F19__weak__wc12(rate_eval, tf)
    n_Na28__Na29(rate_eval, tf)
    p_Si38__He4_Al35(rate_eval, tf)
    n_Al25__He4_Na22(rate_eval, tf)
    p_F30__Ne31(rate_eval, tf)
    N22__n_O21__weak__wc17(rate_eval, tf)
    Na29__Mg29__weak__wc12(rate_eval, tf)
    He4_K37__Sc41(rate_eval, tf)
    n_K34__p_Ar34(rate_eval, tf)
    He4_Si45__n_S48(rate_eval, tf)
    He4_Fe69__n_Ni72(rate_eval, tf)
    Mn72__Fe72__weak__mo03(rate_eval, tf)
    He4_S40__Ar44(rate_eval, tf)
    n_P28__He4_Al25(rate_eval, tf)
    p_O23__F24(rate_eval, tf)
    K49__n_Ca48__weak__wc12(rate_eval, tf)
    p_Fe75__Co76(rate_eval, tf)
    O27__n_F26__weak__mp17(rate_eval, tf)
    Ne33__Na33__weak__mo03(rate_eval, tf)
    p_Mn65__Fe66(rate_eval, tf)
    Na28__n_Mg27__weak__wc12(rate_eval, tf)
    Ti52__V52__weak__wc12(rate_eval, tf)
    He4_Mn50__p_Fe53(rate_eval, tf)
    Fe45__Mn45__weak__wc17(rate_eval, tf)
    Al35__Si35__weak__wc12(rate_eval, tf)
    F17__O17__weak__wc12(rate_eval, tf)
    n_Mn66__Mn67(rate_eval, tf)
    Al40__Si40__weak__mo03(rate_eval, tf)
    F26__Ne26__weak__wc12(rate_eval, tf)
    n_Ar49__Ar50(rate_eval, tf)
    Cl47__Ar47__weak__wc17(rate_eval, tf)
    p_Cr61__n_Mn61(rate_eval, tf)
    p_Na35__Mg36(rate_eval, tf)
    n_O20__O21(rate_eval, tf)
    He4_Ar32__p_K35(rate_eval, tf)
    Sc36__Ca36__weak__bqa_pos_(rate_eval, tf)
    n_Mg37__Mg38(rate_eval, tf)
    Al36__n_Si35__weak__mp17(rate_eval, tf)
    He4_K56__Sc60(rate_eval, tf)
    p_Na30__n_Mg30(rate_eval, tf)
    K34__Ar34__weak__bqa_pos_(rate_eval, tf)
    K42__Ca42__weak__wc12(rate_eval, tf)
    Na37__n_Mg36__weak__mp17(rate_eval, tf)
    n_S29__S30(rate_eval, tf)
    n_Cr48__He4_Ti45(rate_eval, tf)
    Cl30__S30__weak__bqa_pos_(rate_eval, tf)
    n_C16__C17(rate_eval, tf)
    K40__Ca40__weak__wc12(rate_eval, tf)
    P30__Si30__weak__wc12(rate_eval, tf)
    p_V62__Cr63(rate_eval, tf)
    p_Ar46__n_K46(rate_eval, tf)
    He4_K46__n_Sc49(rate_eval, tf)
    B19__n_n_C17__weak__wc12(rate_eval, tf)
    V49__Ti49__weak__wc12(rate_eval, tf)
    Ar30__Cl30__weak__bqa_pos_(rate_eval, tf)
    P29__Si29__weak__wc12(rate_eval, tf)
    He4_K34__Sc38(rate_eval, tf)

    if screen_func is not None:
        plasma_state = PlasmaState(T, rho, Y, Z)

        scn_fac = ScreenFactors(1, 1, 1, 1)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.n_p_p__p_d *= scor
        rate_eval.p_p__d__weak__bet_pos_ *= scor
        rate_eval.p_p__d__weak__electron_capture *= scor

        scn_fac = ScreenFactors(1, 1, 4, 9)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Be9__n_p_He4_He4 *= scor
        rate_eval.p_Be9__d_He4_He4 *= scor
        rate_eval.p_Be9__B10 *= scor
        rate_eval.p_Be9__He4_Li6 *= scor

        scn_fac = ScreenFactors(2, 3, 4, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He3_Be7__p_p_He4_He4 *= scor

        scn_fac = ScreenFactors(1, 3, 4, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.t_Be7__n_p_He4_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca36__p_p_Ca38 *= scor
        rate_eval.He4_Ca36__p_Sc39 *= scor
        rate_eval.He4_Ca36__Ti40 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O13__p_p_O15 *= scor
        rate_eval.He4_O13__p_F16 *= scor

        scn_fac = ScreenFactors(1, 1, 5, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_B11__He4_He4_He4 *= scor
        rate_eval.p_B11__C12 *= scor

        scn_fac = ScreenFactors(1, 2, 3, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_Li7__n_He4_He4 *= scor
        rate_eval.d_Li7__p_Li8 *= scor

        scn_fac = ScreenFactors(2, 3, 2, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He3_He3__p_p_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 76)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe76__n_Ni79 *= scor
        rate_eval.He4_Fe76__Ni80 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 76)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe76__He4_Mn73 *= scor
        rate_eval.p_Fe76__Co77 *= scor
        rate_eval.p_Fe76__n_Co76 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 75)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe75__n_Ni78 *= scor
        rate_eval.He4_Fe75__Ni79 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 75)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe75__He4_Mn72 *= scor
        rate_eval.p_Fe75__n_Co75 *= scor
        rate_eval.p_Fe75__Co76 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 74)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe74__n_Ni77 *= scor
        rate_eval.He4_Fe74__Ni78 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 74)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe74__He4_Mn71 *= scor
        rate_eval.p_Fe74__n_Co74 *= scor
        rate_eval.p_Fe74__Co75 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 73)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe73__He4_Mn70 *= scor
        rate_eval.p_Fe73__n_Co73 *= scor
        rate_eval.p_Fe73__Co74 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 72)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe72__He4_Mn69 *= scor
        rate_eval.p_Fe72__n_Co72 *= scor
        rate_eval.p_Fe72__Co73 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 71)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe71__n_Ni74 *= scor
        rate_eval.He4_Fe71__Ni75 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 71)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe71__He4_Mn68 *= scor
        rate_eval.p_Fe71__n_Co71 *= scor
        rate_eval.p_Fe71__Co72 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe70__n_Ni73 *= scor
        rate_eval.He4_Fe70__Ni74 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe70__He4_Mn67 *= scor
        rate_eval.p_Fe70__n_Co70 *= scor
        rate_eval.p_Fe70__Co71 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe69__He4_Mn66 *= scor
        rate_eval.p_Fe69__n_Co69 *= scor
        rate_eval.p_Fe69__Co70 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe68__n_Ni71 *= scor
        rate_eval.He4_Fe68__Ni72 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe68__He4_Mn65 *= scor
        rate_eval.p_Fe68__Co69 *= scor
        rate_eval.p_Fe68__n_Co68 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe67__He4_Mn64 *= scor
        rate_eval.p_Fe67__n_Co67 *= scor
        rate_eval.p_Fe67__Co68 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe65__He4_Mn62 *= scor
        rate_eval.p_Fe65__Co66 *= scor
        rate_eval.p_Fe65__n_Co65 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe64__n_Ni67 *= scor
        rate_eval.He4_Fe64__Ni68 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe63__n_Ni66 *= scor
        rate_eval.He4_Fe63__Ni67 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe63__He4_Mn60 *= scor
        rate_eval.p_Fe63__Co64 *= scor
        rate_eval.p_Fe63__n_Co63 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe62__He4_Mn59 *= scor
        rate_eval.p_Fe62__n_Co62 *= scor
        rate_eval.p_Fe62__Co63 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe61__He4_Mn58 *= scor
        rate_eval.p_Fe61__n_Co61 *= scor
        rate_eval.p_Fe61__Co62 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe60__He4_Mn57 *= scor
        rate_eval.p_Fe60__Co61 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe59__n_Ni62 *= scor
        rate_eval.He4_Fe59__Ni63 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe59__He4_Mn56 *= scor
        rate_eval.p_Fe59__n_Co59 *= scor
        rate_eval.p_Fe59__Co60 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe57__He4_Mn54 *= scor
        rate_eval.p_Fe57__Co58 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar34__K35 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc59__V63 *= scor
        rate_eval.He4_Sc59__n_V62 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S30__Ar34 *= scor
        rate_eval.He4_S30__p_Cl33 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe52__p_Co55 *= scor
        rate_eval.He4_Fe52__Ni56 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca61__Sc62 *= scor
        rate_eval.p_Ca61__He4_K58 *= scor
        rate_eval.p_Ca61__n_Sc61 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr66__Fe70 *= scor
        rate_eval.He4_Cr66__n_Fe69 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe49__p_Co52 *= scor
        rate_eval.He4_Fe49__Ni53 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe48__p_Co51 *= scor
        rate_eval.He4_Fe48__Ni52 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc50__Ti51 *= scor
        rate_eval.p_Sc50__n_Ti50 *= scor
        rate_eval.p_Sc50__He4_Ca47 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 73)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn73__n_Co76 *= scor
        rate_eval.He4_Mn73__Co77 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 73)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn73__He4_Cr70 *= scor
        rate_eval.p_Mn73__Fe74 *= scor
        rate_eval.p_Mn73__n_Fe73 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg34__Al35 *= scor
        rate_eval.p_Mg34__He4_Na31 *= scor
        rate_eval.p_Mg34__n_Al34 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 72)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn72__n_Co75 *= scor
        rate_eval.He4_Mn72__Co76 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 72)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn72__He4_Cr69 *= scor
        rate_eval.p_Mn72__n_Fe72 *= scor
        rate_eval.p_Mn72__Fe73 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 71)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn71__He4_Cr68 *= scor
        rate_eval.p_Mn71__Fe72 *= scor
        rate_eval.p_Mn71__n_Fe71 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn69__n_Co72 *= scor
        rate_eval.He4_Mn69__Co73 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn69__He4_Cr66 *= scor
        rate_eval.p_Mn69__n_Fe69 *= scor
        rate_eval.p_Mn69__Fe70 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn68__n_Co71 *= scor
        rate_eval.He4_Mn68__Co72 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn68__n_Fe68 *= scor
        rate_eval.p_Mn68__Fe69 *= scor
        rate_eval.p_Mn68__He4_Cr65 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si33__n_S36 *= scor
        rate_eval.He4_Si33__S37 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn67__He4_Cr64 *= scor
        rate_eval.p_Mn67__Fe68 *= scor
        rate_eval.p_Mn67__n_Fe67 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn66__He4_Cr63 *= scor
        rate_eval.p_Mn66__n_Fe66 *= scor
        rate_eval.p_Mn66__Fe67 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K48__Ca49 *= scor
        rate_eval.p_K48__He4_Ar45 *= scor
        rate_eval.p_K48__n_Ca48 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P46__S47 *= scor
        rate_eval.p_P46__He4_Si43 *= scor
        rate_eval.p_P46__n_S46 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca52__Ti56 *= scor
        rate_eval.He4_Ca52__n_Ti55 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn65__n_Co68 *= scor
        rate_eval.He4_Mn65__Co69 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn65__He4_Cr62 *= scor
        rate_eval.p_Mn65__n_Fe65 *= scor
        rate_eval.p_Mn65__Fe66 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si44__n_P44 *= scor
        rate_eval.p_Si44__He4_Al41 *= scor
        rate_eval.p_Si44__P45 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn64__He4_Cr61 *= scor
        rate_eval.p_Mn64__n_Fe64 *= scor
        rate_eval.p_Mn64__Fe65 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn62__He4_Cr59 *= scor
        rate_eval.p_Mn62__Fe63 *= scor
        rate_eval.p_Mn62__n_Fe62 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn60__n_Co63 *= scor
        rate_eval.He4_Mn60__Co64 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn60__He4_Cr57 *= scor
        rate_eval.p_Mn60__n_Fe60 *= scor
        rate_eval.p_Mn60__Fe61 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe65__Ni69 *= scor
        rate_eval.He4_Fe65__n_Ni68 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn59__He4_Cr56 *= scor
        rate_eval.p_Mn59__n_Fe59 *= scor
        rate_eval.p_Mn59__Fe60 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn57__n_Fe57 *= scor
        rate_eval.p_Mn57__He4_Cr54 *= scor
        rate_eval.p_Mn57__Fe58 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe64__He4_Mn61 *= scor
        rate_eval.p_Fe64__n_Co64 *= scor
        rate_eval.p_Fe64__Co65 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn56__He4_Cr53 *= scor
        rate_eval.p_Mn56__Fe57 *= scor
        rate_eval.p_Mn56__n_Fe56 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn54__He4_Cr51 *= scor
        rate_eval.p_Mn54__Fe55 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn53__p_Fe56 *= scor
        rate_eval.He4_Mn53__Co57 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn53__He4_Cr50 *= scor
        rate_eval.p_Mn53__Fe54 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn51__p_Fe54 *= scor
        rate_eval.He4_Mn51__Co55 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca53__n_Sc53 *= scor
        rate_eval.p_Ca53__He4_K50 *= scor
        rate_eval.p_Ca53__Sc54 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O22__n_F22 *= scor
        rate_eval.p_O22__F23 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn49__p_Fe52 *= scor
        rate_eval.He4_Mn49__Co53 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn47__p_Fe50 *= scor
        rate_eval.He4_Mn47__Co51 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn46__p_Fe49 *= scor
        rate_eval.He4_Mn46__Co50 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca44__Sc45 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn44__p_Fe47 *= scor
        rate_eval.He4_Mn44__Co48 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr70__n_Fe73 *= scor
        rate_eval.He4_Cr70__Fe74 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr69__n_Fe72 *= scor
        rate_eval.He4_Cr69__Fe73 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr68__He4_V65 *= scor
        rate_eval.p_Cr68__n_Mn68 *= scor
        rate_eval.p_Cr68__Mn69 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr67__n_Mn67 *= scor
        rate_eval.p_Cr67__He4_V64 *= scor
        rate_eval.p_Cr67__Mn68 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr66__He4_V63 *= scor
        rate_eval.p_Cr66__Mn67 *= scor
        rate_eval.p_Cr66__n_Mn66 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr65__n_Fe68 *= scor
        rate_eval.He4_Cr65__Fe69 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr65__He4_V62 *= scor
        rate_eval.p_Cr65__Mn66 *= scor
        rate_eval.p_Cr65__n_Mn65 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr64__n_Fe67 *= scor
        rate_eval.He4_Cr64__Fe68 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O25__n_F25 *= scor
        rate_eval.p_O25__F26 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr63__n_Fe66 *= scor
        rate_eval.He4_Cr63__Fe67 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr63__n_Mn63 *= scor
        rate_eval.p_Cr63__Mn64 *= scor
        rate_eval.p_Cr63__He4_V60 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr62__n_Fe65 *= scor
        rate_eval.He4_Cr62__Fe66 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr62__He4_V59 *= scor
        rate_eval.p_Cr62__Mn63 *= scor
        rate_eval.p_Cr62__n_Mn62 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn48__Co52 *= scor
        rate_eval.He4_Mn48__p_Fe51 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr61__n_Fe64 *= scor
        rate_eval.He4_Cr61__Fe65 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr60__He4_V57 *= scor
        rate_eval.p_Cr60__Mn61 *= scor
        rate_eval.p_Cr60__n_Mn60 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr59__n_Fe62 *= scor
        rate_eval.He4_Cr59__Fe63 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr59__n_Mn59 *= scor
        rate_eval.p_Cr59__Mn60 *= scor
        rate_eval.p_Cr59__He4_V56 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr57__n_Mn57 *= scor
        rate_eval.p_Cr57__He4_V54 *= scor
        rate_eval.p_Cr57__Mn58 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr55__n_Fe58 *= scor
        rate_eval.He4_Cr55__Fe59 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr54__He4_V51 *= scor
        rate_eval.p_Cr54__Mn55 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne32__Na33 *= scor
        rate_eval.p_Ne32__n_Na32 *= scor
        rate_eval.p_Ne32__He4_F29 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg24__He4_Na21 *= scor
        rate_eval.p_Mg24__Al25 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si38__n_P38 *= scor
        rate_eval.p_Si38__P39 *= scor
        rate_eval.p_Si38__He4_Al35 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn55__He4_Cr52 *= scor
        rate_eval.p_Mn55__Fe56 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr49__p_Mn52 *= scor
        rate_eval.He4_Cr49__Fe53 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr48__p_Mn51 *= scor
        rate_eval.He4_Cr48__Fe52 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti57__He4_Sc54 *= scor
        rate_eval.p_Ti57__n_V57 *= scor
        rate_eval.p_Ti57__V58 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr45__p_Mn48 *= scor
        rate_eval.He4_Cr45__Fe49 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne29__Mg33 *= scor
        rate_eval.He4_Ne29__n_Mg32 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti59__n_Cr62 *= scor
        rate_eval.He4_Ti59__Cr63 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P44__n_Cl47 *= scor
        rate_eval.He4_P44__Cl48 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr44__p_Mn47 *= scor
        rate_eval.He4_Cr44__Fe48 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr43__p_Mn46 *= scor
        rate_eval.He4_Cr43__Fe47 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr42__p_Mn45 *= scor
        rate_eval.He4_Cr42__Fe46 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V67__n_Mn70 *= scor
        rate_eval.He4_V67__Mn71 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc37__p_Ti40 *= scor
        rate_eval.He4_Sc37__V41 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V67__n_Cr67 *= scor
        rate_eval.p_V67__He4_Ti64 *= scor
        rate_eval.p_V67__Cr68 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V66__n_Mn69 *= scor
        rate_eval.He4_V66__Mn70 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V66__n_Cr66 *= scor
        rate_eval.p_V66__Cr67 *= scor
        rate_eval.p_V66__He4_Ti63 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V50__p_Cr53 *= scor
        rate_eval.He4_V50__Mn54 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K47__He4_Ar44 *= scor
        rate_eval.p_K47__n_Ca47 *= scor
        rate_eval.p_K47__Ca48 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V65__He4_Ti62 *= scor
        rate_eval.p_V65__Cr66 *= scor
        rate_eval.p_V65__n_Cr65 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V64__n_Mn67 *= scor
        rate_eval.He4_V64__Mn68 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V64__He4_Ti61 *= scor
        rate_eval.p_V64__n_Cr64 *= scor
        rate_eval.p_V64__Cr65 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V63__n_Cr63 *= scor
        rate_eval.p_V63__He4_Ti60 *= scor
        rate_eval.p_V63__Cr64 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V62__n_Mn65 *= scor
        rate_eval.He4_V62__Mn66 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V61__n_Mn64 *= scor
        rate_eval.He4_V61__Mn65 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V61__n_Cr61 *= scor
        rate_eval.p_V61__He4_Ti58 *= scor
        rate_eval.p_V61__Cr62 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P32__n_S32 *= scor
        rate_eval.p_P32__He4_Si29 *= scor
        rate_eval.p_P32__S33 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al32__n_P35 *= scor
        rate_eval.He4_Al32__P36 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V63__Mn67 *= scor
        rate_eval.He4_V63__n_Mn66 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V60__He4_Ti57 *= scor
        rate_eval.p_V60__n_Cr60 *= scor
        rate_eval.p_V60__Cr61 *= scor

        scn_fac = ScreenFactors(1, 3, 2, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.t_He3__n_p_He4 *= scor
        rate_eval.t_He3__d_He4 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O27__He4_N24 *= scor
        rate_eval.p_O27__F28 *= scor
        rate_eval.p_O27__n_F27 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si43__n_P43 *= scor
        rate_eval.p_Si43__P44 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V59__n_Mn62 *= scor
        rate_eval.He4_V59__Mn63 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V58__n_Mn61 *= scor
        rate_eval.He4_V58__Mn62 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V58__He4_Ti55 *= scor
        rate_eval.p_V58__n_Cr58 *= scor
        rate_eval.p_V58__Cr59 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V57__He4_Ti54 *= scor
        rate_eval.p_V57__n_Cr57 *= scor
        rate_eval.p_V57__Cr58 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V56__n_Mn59 *= scor
        rate_eval.He4_V56__Mn60 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al40__p_Si43 *= scor
        rate_eval.He4_Al40__n_P43 *= scor
        rate_eval.He4_Al40__P44 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V55__n_Mn58 *= scor
        rate_eval.He4_V55__Mn59 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr47__p_Mn50 *= scor
        rate_eval.He4_Cr47__Fe51 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V55__n_Cr55 *= scor
        rate_eval.p_V55__Cr56 *= scor
        rate_eval.p_V55__He4_Ti52 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V54__n_Mn57 *= scor
        rate_eval.He4_V54__Mn58 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar52__Ca56 *= scor
        rate_eval.He4_Ar52__n_Ca55 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V53__n_Cr53 *= scor
        rate_eval.p_V53__He4_Ti50 *= scor
        rate_eval.p_V53__Cr54 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V52__He4_Ti49 *= scor
        rate_eval.p_V52__n_Cr52 *= scor
        rate_eval.p_V52__Cr53 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S45__n_Ar48 *= scor
        rate_eval.He4_S45__Ar49 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca43__Ti47 *= scor
        rate_eval.He4_Ca43__n_Ti46 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V51__He4_Ti48 *= scor
        rate_eval.p_V51__Cr52 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F23__Ne24 *= scor
        rate_eval.p_F23__He4_O20 *= scor
        rate_eval.p_F23__n_Ne23 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V50__He4_Ti47 *= scor
        rate_eval.p_V50__n_Cr50 *= scor
        rate_eval.p_V50__Cr51 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F24__Ne25 *= scor
        rate_eval.p_F24__n_Ne24 *= scor
        rate_eval.p_F24__He4_O21 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V49__He4_Ti46 *= scor
        rate_eval.p_V49__Cr50 *= scor

        scn_fac = ScreenFactors(2, 4, 7, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_N15__F19 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V47__p_Cr50 *= scor
        rate_eval.He4_V47__Mn51 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V46__p_Cr49 *= scor
        rate_eval.He4_V46__Mn50 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc52__Ti53 *= scor
        rate_eval.p_Sc52__He4_Ca49 *= scor
        rate_eval.p_Sc52__n_Ti52 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V43__p_Cr46 *= scor
        rate_eval.He4_V43__Mn47 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V42__p_Cr45 *= scor
        rate_eval.He4_V42__Mn46 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si43__n_S46 *= scor
        rate_eval.He4_Si43__S47 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne33__n_Mg36 *= scor
        rate_eval.He4_Ne33__Mg37 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V39__p_Cr42 *= scor
        rate_eval.He4_V39__Mn43 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc53__n_Ti53 *= scor
        rate_eval.p_Sc53__Ti54 *= scor
        rate_eval.p_Sc53__He4_Ca50 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti65__n_Cr68 *= scor
        rate_eval.He4_Ti65__Cr69 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne27__He4_F24 *= scor
        rate_eval.p_Ne27__n_Na27 *= scor
        rate_eval.p_Ne27__Na28 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti64__n_Cr67 *= scor
        rate_eval.He4_Ti64__Cr68 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti64__He4_Sc61 *= scor
        rate_eval.p_Ti64__n_V64 *= scor
        rate_eval.p_Ti64__V65 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti63__n_Cr66 *= scor
        rate_eval.He4_Ti63__Cr67 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti63__He4_Sc60 *= scor
        rate_eval.p_Ti63__n_V63 *= scor
        rate_eval.p_Ti63__V64 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti61__n_V61 *= scor
        rate_eval.p_Ti61__V62 *= scor
        rate_eval.p_Ti61__He4_Sc58 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti60__n_Cr63 *= scor
        rate_eval.He4_Ti60__Cr64 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti60__n_V60 *= scor
        rate_eval.p_Ti60__V61 *= scor
        rate_eval.p_Ti60__He4_Sc57 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti59__n_V59 *= scor
        rate_eval.p_Ti59__V60 *= scor
        rate_eval.p_Ti59__He4_Sc56 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti58__n_Cr61 *= scor
        rate_eval.He4_Ti58__Cr62 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti58__n_V58 *= scor
        rate_eval.p_Ti58__V59 *= scor
        rate_eval.p_Ti58__He4_Sc55 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti55__n_Cr58 *= scor
        rate_eval.He4_Ti55__Cr59 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti55__n_V55 *= scor
        rate_eval.p_Ti55__V56 *= scor
        rate_eval.p_Ti55__He4_Sc52 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti54__n_Cr57 *= scor
        rate_eval.He4_Ti54__Cr58 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti54__He4_Sc51 *= scor
        rate_eval.p_Ti54__n_V54 *= scor
        rate_eval.p_Ti54__V55 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti53__n_Cr56 *= scor
        rate_eval.He4_Ti53__Cr57 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti53__He4_Sc50 *= scor
        rate_eval.p_Ti53__n_V53 *= scor
        rate_eval.p_Ti53__V54 *= scor

        scn_fac = ScreenFactors(2, 4, 4, 10)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Be10__C14 *= scor
        rate_eval.He4_Be10__n_C13 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti52__He4_Sc49 *= scor
        rate_eval.p_Ti52__n_V52 *= scor
        rate_eval.p_Ti52__V53 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti51__n_Cr54 *= scor
        rate_eval.He4_Ti51__Cr55 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti51__n_V51 *= scor
        rate_eval.p_Ti51__V52 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F26__Na30 *= scor
        rate_eval.He4_F26__n_Na29 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 73)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe73__n_Ni76 *= scor
        rate_eval.He4_Fe73__Ni77 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K36__p_Ca39 *= scor
        rate_eval.He4_K36__Sc40 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar35__Ca39 *= scor
        rate_eval.He4_Ar35__p_K38 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar51__He4_Cl48 *= scor
        rate_eval.p_Ar51__K52 *= scor
        rate_eval.p_Ar51__n_K51 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na19__Al23 *= scor
        rate_eval.He4_Na19__p_Mg22 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti43__p_V46 *= scor
        rate_eval.He4_Ti43__Cr47 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F28__n_Na31 *= scor
        rate_eval.He4_F28__Na32 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F31__n_Na34 *= scor
        rate_eval.He4_F31__Na35 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti40__p_V43 *= scor
        rate_eval.He4_Ti40__Cr44 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr55__n_Mn55 *= scor
        rate_eval.p_Cr55__He4_V52 *= scor
        rate_eval.p_Cr55__Mn56 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F31__He4_O28 *= scor
        rate_eval.p_F31__n_Ne31 *= scor
        rate_eval.p_F31__Ne32 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti39__p_V42 *= scor
        rate_eval.He4_Ti39__Cr43 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti38__p_V41 *= scor
        rate_eval.He4_Ti38__Cr42 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti37__p_V40 *= scor
        rate_eval.He4_Ti37__Cr41 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc62__n_V65 *= scor
        rate_eval.He4_Sc62__V66 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc61__n_V64 *= scor
        rate_eval.He4_Sc61__V65 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc61__n_Ti61 *= scor
        rate_eval.p_Sc61__Ti62 *= scor
        rate_eval.p_Sc61__He4_Ca58 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc40__p_Ti43 *= scor
        rate_eval.He4_Sc40__V44 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc60__n_V63 *= scor
        rate_eval.He4_Sc60__V64 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc60__He4_Ca57 *= scor
        rate_eval.p_Sc60__n_Ti60 *= scor
        rate_eval.p_Sc60__Ti61 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc58__n_V61 *= scor
        rate_eval.He4_Sc58__V62 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc58__He4_Ca55 *= scor
        rate_eval.p_Sc58__n_Ti58 *= scor
        rate_eval.p_Sc58__Ti59 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc57__n_V60 *= scor
        rate_eval.He4_Sc57__V61 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc56__n_V59 *= scor
        rate_eval.He4_Sc56__V60 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc55__n_V58 *= scor
        rate_eval.He4_Sc55__V59 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc55__He4_Ca52 *= scor
        rate_eval.p_Sc55__n_Ti55 *= scor
        rate_eval.p_Sc55__Ti56 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc54__n_V57 *= scor
        rate_eval.He4_Sc54__V58 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc54__n_Ti54 *= scor
        rate_eval.p_Sc54__Ti55 *= scor
        rate_eval.p_Sc54__He4_Ca51 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc52__n_V55 *= scor
        rate_eval.He4_Sc52__V56 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S47__Cl48 *= scor
        rate_eval.p_S47__n_Cl47 *= scor
        rate_eval.p_S47__He4_P44 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 9)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C9__p_N12 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc51__n_V54 *= scor
        rate_eval.He4_Sc51__V55 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar29__Ca33 *= scor
        rate_eval.He4_Ar29__p_K32 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc49__He4_Ca46 *= scor
        rate_eval.p_Sc49__n_Ti49 *= scor
        rate_eval.p_Sc49__Ti50 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc48__He4_Ca45 *= scor
        rate_eval.p_Sc48__n_Ti48 *= scor
        rate_eval.p_Sc48__Ti49 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc47__p_Ti50 *= scor
        rate_eval.He4_Sc47__V51 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc47__He4_Ca44 *= scor
        rate_eval.p_Sc47__Ti48 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc46__p_Ti49 *= scor
        rate_eval.He4_Sc46__n_V49 *= scor
        rate_eval.He4_Sc46__V50 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc46__He4_Ca43 *= scor
        rate_eval.p_Sc46__n_Ti46 *= scor
        rate_eval.p_Sc46__Ti47 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc45__p_Ti48 *= scor
        rate_eval.He4_Sc45__V49 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc45__He4_Ca42 *= scor
        rate_eval.p_Sc45__Ti46 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc44__p_Ti47 *= scor
        rate_eval.He4_Sc44__V48 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc44__He4_Ca41 *= scor
        rate_eval.p_Sc44__Ti45 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc43__p_Ti46 *= scor
        rate_eval.He4_Sc43__V47 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc42__p_Ti45 *= scor
        rate_eval.He4_Sc42__V46 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr56__n_Mn56 *= scor
        rate_eval.p_Cr56__He4_V53 *= scor
        rate_eval.p_Cr56__Mn57 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si36__He4_Al33 *= scor
        rate_eval.p_Si36__n_P36 *= scor
        rate_eval.p_Si36__P37 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc39__p_Ti42 *= scor
        rate_eval.He4_Sc39__V43 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P31__S32 *= scor
        rate_eval.p_P31__He4_Si28 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si45__P46 *= scor
        rate_eval.p_Si45__He4_Al42 *= scor
        rate_eval.p_Si45__n_P45 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc38__p_Ti41 *= scor
        rate_eval.He4_Sc38__V42 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na36__n_Mg36 *= scor
        rate_eval.p_Na36__Mg37 *= scor
        rate_eval.p_Na36__He4_Ne33 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc36__p_Ti39 *= scor
        rate_eval.He4_Sc36__V40 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc35__p_Ti38 *= scor
        rate_eval.He4_Sc35__V39 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca60__n_Sc60 *= scor
        rate_eval.p_Ca60__Sc61 *= scor
        rate_eval.p_Ca60__He4_K57 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca59__n_Sc59 *= scor
        rate_eval.p_Ca59__Sc60 *= scor
        rate_eval.p_Ca59__He4_K56 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca58__n_Ti61 *= scor
        rate_eval.He4_Ca58__Ti62 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca58__He4_K55 *= scor
        rate_eval.p_Ca58__n_Sc58 *= scor
        rate_eval.p_Ca58__Sc59 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al25__P29 *= scor
        rate_eval.He4_Al25__p_Si28 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca56__He4_K53 *= scor
        rate_eval.p_Ca56__n_Sc56 *= scor
        rate_eval.p_Ca56__Sc57 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca55__He4_K52 *= scor
        rate_eval.p_Ca55__n_Sc55 *= scor
        rate_eval.p_Ca55__Sc56 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca53__n_Ti56 *= scor
        rate_eval.He4_Ca53__Ti57 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca52__n_Sc52 *= scor
        rate_eval.p_Ca52__Sc53 *= scor
        rate_eval.p_Ca52__He4_K49 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P45__S46 *= scor
        rate_eval.p_P45__n_S45 *= scor
        rate_eval.p_P45__He4_Si42 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca51__n_Ti54 *= scor
        rate_eval.He4_Ca51__Ti55 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca51__He4_K48 *= scor
        rate_eval.p_Ca51__Sc52 *= scor
        rate_eval.p_Ca51__n_Sc51 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al39__He4_Mg36 *= scor
        rate_eval.p_Al39__n_Si39 *= scor
        rate_eval.p_Al39__Si40 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca47__n_Ti50 *= scor
        rate_eval.He4_Ca47__Ti51 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca47__n_Sc47 *= scor
        rate_eval.p_Ca47__Sc48 *= scor

        scn_fac = ScreenFactors(6, 12, 6, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.C12_C12__He4_Ne20 *= scor
        rate_eval.C12_C12__p_Na23 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca57__n_Ti60 *= scor
        rate_eval.He4_Ca57__Ti61 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti45__p_V48 *= scor
        rate_eval.He4_Ti45__Cr49 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca42__He4_K39 *= scor
        rate_eval.p_Ca42__Sc43 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F16__Na20 *= scor
        rate_eval.He4_F16__p_Ne19 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P42__n_S42 *= scor
        rate_eval.p_P42__He4_Si39 *= scor
        rate_eval.p_P42__S43 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe66__n_Ni69 *= scor
        rate_eval.He4_Fe66__Ni70 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P39__n_Cl42 *= scor
        rate_eval.He4_P39__Cl43 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca48__Ti52 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K57__n_Sc60 *= scor
        rate_eval.He4_K57__Sc61 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K57__He4_Ar54 *= scor
        rate_eval.p_K57__n_Ca57 *= scor
        rate_eval.p_K57__Ca58 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si42__S46 *= scor
        rate_eval.He4_Si42__n_S45 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K56__n_Sc59 *= scor
        rate_eval.He4_K56__Sc60 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K56__n_Ca56 *= scor
        rate_eval.p_K56__He4_Ar53 *= scor
        rate_eval.p_K56__Ca57 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K54__n_Sc57 *= scor
        rate_eval.He4_K54__Sc58 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K54__n_Ca54 *= scor
        rate_eval.p_K54__Ca55 *= scor
        rate_eval.p_K54__He4_Ar51 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K53__n_Sc56 *= scor
        rate_eval.He4_K53__Sc57 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K53__n_Ca53 *= scor
        rate_eval.p_K53__Ca54 *= scor
        rate_eval.p_K53__He4_Ar50 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K52__n_Sc55 *= scor
        rate_eval.He4_K52__Sc56 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P29__S30 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K51__n_Sc54 *= scor
        rate_eval.He4_K51__Sc55 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K51__n_Ca51 *= scor
        rate_eval.p_K51__He4_Ar48 *= scor
        rate_eval.p_K51__Ca52 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr57__n_Fe60 *= scor
        rate_eval.He4_Cr57__Fe61 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K50__n_Sc53 *= scor
        rate_eval.He4_K50__Sc54 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S42__Cl43 *= scor
        rate_eval.p_S42__n_Cl42 *= scor
        rate_eval.p_S42__He4_P39 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K48__n_Sc51 *= scor
        rate_eval.He4_K48__Sc52 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K45__He4_Ar42 *= scor
        rate_eval.p_K45__n_Ca45 *= scor
        rate_eval.p_K45__Ca46 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K44__He4_Ar41 *= scor
        rate_eval.p_K44__n_Ca44 *= scor
        rate_eval.p_K44__Ca45 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K43__p_Ca46 *= scor
        rate_eval.He4_K43__Sc47 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K43__n_Ca43 *= scor
        rate_eval.p_K43__Ca44 *= scor
        rate_eval.p_K43__He4_Ar40 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K42__p_Ca45 *= scor
        rate_eval.He4_K42__n_Sc45 *= scor
        rate_eval.He4_K42__Sc46 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K41__n_Sc44 *= scor
        rate_eval.He4_K41__p_Ca44 *= scor
        rate_eval.He4_K41__Sc45 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K41__He4_Ar38 *= scor
        rate_eval.p_K41__n_Ca41 *= scor
        rate_eval.p_K41__Ca42 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K46__p_Ca49 *= scor
        rate_eval.He4_K46__Sc50 *= scor
        rate_eval.He4_K46__n_Sc49 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K40__He4_Ar37 *= scor
        rate_eval.p_K40__n_Ca40 *= scor
        rate_eval.p_K40__Ca41 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S37__Cl38 *= scor
        rate_eval.p_S37__n_Cl37 *= scor
        rate_eval.p_S37__He4_P34 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O14__F15 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K37__p_Ca40 *= scor
        rate_eval.He4_K37__Sc41 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K44__p_Ca47 *= scor
        rate_eval.He4_K44__Sc48 *= scor
        rate_eval.He4_K44__n_Sc47 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K34__p_Ca37 *= scor
        rate_eval.He4_K34__Sc38 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr61__He4_V58 *= scor
        rate_eval.p_Cr61__Mn62 *= scor
        rate_eval.p_Cr61__n_Mn61 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn51__Fe52 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K31__p_Ca34 *= scor
        rate_eval.He4_K31__Sc35 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti38__V39 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar54__n_K54 *= scor
        rate_eval.p_Ar54__He4_Cl51 *= scor
        rate_eval.p_Ar54__K55 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar52__He4_Cl49 *= scor
        rate_eval.p_Ar52__n_K52 *= scor
        rate_eval.p_Ar52__K53 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K59__n_Ca59 *= scor
        rate_eval.p_K59__Ca60 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar50__He4_Cl47 *= scor
        rate_eval.p_Ar50__n_K50 *= scor
        rate_eval.p_Ar50__K51 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F20__n_Na23 *= scor
        rate_eval.He4_F20__p_Ne23 *= scor
        rate_eval.He4_F20__Na24 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar48__He4_Cl45 *= scor
        rate_eval.p_Ar48__n_K48 *= scor
        rate_eval.p_Ar48__K49 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar46__n_Ca49 *= scor
        rate_eval.He4_Ar46__Ca50 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F28__n_Ne28 *= scor
        rate_eval.p_F28__He4_O25 *= scor
        rate_eval.p_F28__Ne29 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe50__p_Co53 *= scor
        rate_eval.He4_Fe50__Ni54 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si35__n_S38 *= scor
        rate_eval.He4_Si35__S39 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar44__n_K44 *= scor
        rate_eval.p_Ar44__K45 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar43__n_Ca46 *= scor
        rate_eval.He4_Ar43__Ca47 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar43__n_K43 *= scor
        rate_eval.p_Ar43__He4_Cl40 *= scor
        rate_eval.p_Ar43__K44 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe47__Co48 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl47__K51 *= scor
        rate_eval.He4_Cl47__n_K50 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar41__n_K41 *= scor
        rate_eval.p_Ar41__K42 *= scor
        rate_eval.p_Ar41__He4_Cl38 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar40__He4_Cl37 *= scor
        rate_eval.p_Ar40__K41 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn54__Co58 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar39__He4_Cl36 *= scor
        rate_eval.p_Ar39__K40 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn62__n_Co65 *= scor
        rate_eval.He4_Mn62__Co66 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar34__p_K37 *= scor
        rate_eval.He4_Ar34__Ca38 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar33__p_K36 *= scor
        rate_eval.He4_Ar33__Ca37 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar31__p_K34 *= scor
        rate_eval.He4_Ar31__Ca35 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl52__He4_S49 *= scor
        rate_eval.p_Cl52__n_Ar52 *= scor
        rate_eval.p_Cl52__Ar53 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O16__F17 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl51__n_K54 *= scor
        rate_eval.He4_Cl51__K55 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl50__K54 *= scor
        rate_eval.He4_Cl50__n_K53 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl51__He4_S48 *= scor
        rate_eval.p_Cl51__Ar52 *= scor
        rate_eval.p_Cl51__n_Ar51 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl50__He4_S47 *= scor
        rate_eval.p_Cl50__n_Ar50 *= scor
        rate_eval.p_Cl50__Ar51 *= scor

        scn_fac = ScreenFactors(1, 1, 5, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_B12__n_C12 *= scor
        rate_eval.p_B12__He4_Be9 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl49__n_K52 *= scor
        rate_eval.He4_Cl49__K53 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar36__Ca40 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl48__He4_S45 *= scor
        rate_eval.p_Cl48__n_Ar48 *= scor
        rate_eval.p_Cl48__Ar49 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca50__n_Ti53 *= scor
        rate_eval.He4_Ca50__Ti54 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti62__n_V62 *= scor
        rate_eval.p_Ti62__V63 *= scor
        rate_eval.p_Ti62__He4_Sc59 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl45__He4_S42 *= scor
        rate_eval.p_Cl45__n_Ar45 *= scor
        rate_eval.p_Cl45__Ar46 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl43__p_Ar46 *= scor
        rate_eval.He4_Cl43__K47 *= scor
        rate_eval.He4_Cl43__n_K46 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl43__He4_S40 *= scor
        rate_eval.p_Cl43__Ar44 *= scor
        rate_eval.p_Cl43__n_Ar43 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn61__n_Fe61 *= scor
        rate_eval.p_Mn61__Fe62 *= scor
        rate_eval.p_Mn61__He4_Cr58 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V49__Mn53 *= scor
        rate_eval.He4_V49__p_Cr52 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl42__n_K45 *= scor
        rate_eval.He4_Cl42__K46 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl42__He4_S39 *= scor
        rate_eval.p_Cl42__n_Ar42 *= scor
        rate_eval.p_Cl42__Ar43 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl41__n_K44 *= scor
        rate_eval.He4_Cl41__K45 *= scor
        rate_eval.He4_Cl41__p_Ar44 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl41__He4_S38 *= scor
        rate_eval.p_Cl41__Ar42 *= scor
        rate_eval.p_Cl41__n_Ar41 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl40__n_K43 *= scor
        rate_eval.He4_Cl40__K44 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl40__n_Ar40 *= scor
        rate_eval.p_Cl40__He4_S37 *= scor
        rate_eval.p_Cl40__Ar41 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O19__He4_N16 *= scor
        rate_eval.p_O19__n_F19 *= scor
        rate_eval.p_O19__F20 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 17)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F17__Na21 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl34__p_Ar37 *= scor
        rate_eval.He4_Cl34__K38 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti43__V44 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na34__Mg35 *= scor
        rate_eval.p_Na34__He4_Ne31 *= scor
        rate_eval.p_Na34__n_Mg34 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S48__n_Ar51 *= scor
        rate_eval.He4_S48__Ar52 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl30__p_Ar33 *= scor
        rate_eval.He4_Cl30__K34 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na25__Al29 *= scor
        rate_eval.He4_Na25__n_Al28 *= scor
        rate_eval.He4_Na25__p_Mg28 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl28__p_Ar31 *= scor
        rate_eval.He4_Cl28__K32 *= scor

        scn_fac = ScreenFactors(1, 2, 3, 8)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_Li8__n_Be9 *= scor
        rate_eval.d_Li8__t_Li7 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S49__n_Cl49 *= scor
        rate_eval.p_S49__Cl50 *= scor
        rate_eval.p_S49__He4_P46 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg38__n_Si41 *= scor
        rate_eval.He4_Mg38__Si42 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S48__n_Cl48 *= scor
        rate_eval.p_S48__He4_P45 *= scor
        rate_eval.p_S48__Cl49 *= scor

        scn_fac = ScreenFactors(1, 1, 7, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_N15__O16 *= scor
        rate_eval.p_N15__He4_C12 *= scor
        rate_eval.p_N15__n_O15 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K52__He4_Ar49 *= scor
        rate_eval.p_K52__Ca53 *= scor
        rate_eval.p_K52__n_Ca52 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S46__n_Cl46 *= scor
        rate_eval.p_S46__Cl47 *= scor
        rate_eval.p_S46__He4_P43 *= scor

        scn_fac = ScreenFactors(1, 2, 4, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_Be7__p_He4_He4 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S45__He4_P42 *= scor
        rate_eval.p_S45__n_Cl45 *= scor
        rate_eval.p_S45__Cl46 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S43__n_Ar46 *= scor
        rate_eval.He4_S43__Ar47 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S43__He4_P40 *= scor
        rate_eval.p_S43__n_Cl43 *= scor
        rate_eval.p_S43__Cl44 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn67__n_Co70 *= scor
        rate_eval.He4_Mn67__Co71 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc57__He4_Ca54 *= scor
        rate_eval.p_Sc57__n_Ti57 *= scor
        rate_eval.p_Sc57__Ti58 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe56__Ni60 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S42__n_Ar45 *= scor
        rate_eval.He4_S42__Ar46 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S41__n_Ar44 *= scor
        rate_eval.He4_S41__Ar45 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc63__n_V66 *= scor
        rate_eval.He4_Sc63__V67 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S41__He4_P38 *= scor
        rate_eval.p_S41__Cl42 *= scor
        rate_eval.p_S41__n_Cl41 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al30__He4_Mg27 *= scor
        rate_eval.p_Al30__n_Si30 *= scor
        rate_eval.p_Al30__Si31 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S40__n_Cl40 *= scor
        rate_eval.p_S40__Cl41 *= scor
        rate_eval.p_S40__He4_P37 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe47__Ni51 *= scor
        rate_eval.He4_Fe47__p_Co50 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S39__He4_P36 *= scor
        rate_eval.p_S39__Cl40 *= scor
        rate_eval.p_S39__n_Cl39 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S38__n_Ar41 *= scor
        rate_eval.He4_S38__Ar42 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S38__He4_P35 *= scor
        rate_eval.p_S38__n_Cl38 *= scor
        rate_eval.p_S38__Cl39 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S37__n_Ar40 *= scor
        rate_eval.He4_S37__Ar41 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K49__n_Sc52 *= scor
        rate_eval.He4_K49__Sc53 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V56__He4_Ti53 *= scor
        rate_eval.p_V56__Cr57 *= scor
        rate_eval.p_V56__n_Cr56 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K49__n_Ca49 *= scor
        rate_eval.p_K49__Ca50 *= scor
        rate_eval.p_K49__He4_Ar46 *= scor

        scn_fac = ScreenFactors(1, 1, 3, 6)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Li6__Be7 *= scor
        rate_eval.p_Li6__He4_He3 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S36__He4_P33 *= scor
        rate_eval.p_S36__Cl37 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr69__He4_V66 *= scor
        rate_eval.p_Cr69__Mn70 *= scor
        rate_eval.p_Cr69__n_Mn69 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc51__He4_Ca48 *= scor
        rate_eval.p_Sc51__n_Ti51 *= scor
        rate_eval.p_Sc51__Ti52 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P34__n_Cl37 *= scor
        rate_eval.He4_P34__Cl38 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S35__n_Ar38 *= scor
        rate_eval.He4_S35__Ar39 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S35__He4_P32 *= scor
        rate_eval.p_S35__Cl36 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S34__p_Cl37 *= scor
        rate_eval.He4_S34__Ar38 *= scor
        rate_eval.He4_S34__n_Ar37 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl35__He4_S32 *= scor
        rate_eval.p_Cl35__Ar36 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S31__p_Cl34 *= scor
        rate_eval.He4_S31__Ar35 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S28__p_Cl31 *= scor
        rate_eval.He4_S28__Ar32 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S26__p_Cl29 *= scor
        rate_eval.He4_S26__Ar30 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P47__n_Cl50 *= scor
        rate_eval.He4_P47__Cl51 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P47__n_S47 *= scor
        rate_eval.p_P47__He4_Si44 *= scor
        rate_eval.p_P47__S48 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P43__n_Cl46 *= scor
        rate_eval.He4_P43__Cl47 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P43__He4_Si40 *= scor
        rate_eval.p_P43__n_S43 *= scor
        rate_eval.p_P43__S44 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al38__n_P41 *= scor
        rate_eval.He4_Al38__p_Si41 *= scor
        rate_eval.He4_Al38__P42 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P41__p_S44 *= scor
        rate_eval.He4_P41__n_Cl44 *= scor
        rate_eval.He4_P41__Cl45 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O20__He4_N17 *= scor
        rate_eval.p_O20__n_F20 *= scor
        rate_eval.p_O20__F21 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P38__He4_Si35 *= scor
        rate_eval.p_P38__n_S38 *= scor
        rate_eval.p_P38__S39 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F18__He4_O15 *= scor
        rate_eval.p_F18__Ne19 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P37__n_Cl40 *= scor
        rate_eval.He4_P37__Cl41 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P37__He4_Si34 *= scor
        rate_eval.p_P37__S38 *= scor
        rate_eval.p_P37__n_S37 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P36__He4_Si33 *= scor
        rate_eval.p_P36__n_S36 *= scor
        rate_eval.p_P36__S37 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P34__n_S34 *= scor
        rate_eval.p_P34__S35 *= scor
        rate_eval.p_P34__He4_Si31 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl44__p_Ar47 *= scor
        rate_eval.He4_Cl44__n_K47 *= scor
        rate_eval.He4_Cl44__K48 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al25__Si26 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P31__p_S34 *= scor
        rate_eval.He4_P31__Cl35 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P30__p_S33 *= scor
        rate_eval.He4_P30__Cl34 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K55__n_Sc58 *= scor
        rate_eval.He4_K55__Sc59 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P27__p_S30 *= scor
        rate_eval.He4_P27__Cl31 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P26__p_S29 *= scor
        rate_eval.He4_P26__Cl30 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P25__p_S28 *= scor
        rate_eval.He4_P25__Cl29 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P24__p_S27 *= scor
        rate_eval.He4_P24__Cl28 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si44__n_S47 *= scor
        rate_eval.He4_Si44__S48 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P42__n_Cl45 *= scor
        rate_eval.He4_P42__Cl46 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si42__n_P42 *= scor
        rate_eval.p_Si42__P43 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si40__n_S43 *= scor
        rate_eval.He4_Si40__S44 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si39__n_S42 *= scor
        rate_eval.He4_Si39__S43 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si39__n_P39 *= scor
        rate_eval.p_Si39__P40 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc62__n_Ti62 *= scor
        rate_eval.p_Sc62__Ti63 *= scor
        rate_eval.p_Sc62__He4_Ca59 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si38__n_S41 *= scor
        rate_eval.He4_Si38__S42 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti65__He4_Sc62 *= scor
        rate_eval.p_Ti65__V66 *= scor
        rate_eval.p_Ti65__n_V65 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si37__n_S40 *= scor
        rate_eval.He4_Si37__S41 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca40__Ti44 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si37__He4_Al34 *= scor
        rate_eval.p_Si37__n_P37 *= scor
        rate_eval.p_Si37__P38 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si35__He4_Al32 *= scor
        rate_eval.p_Si35__P36 *= scor
        rate_eval.p_Si35__n_P35 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si33__n_P33 *= scor
        rate_eval.p_Si33__P34 *= scor
        rate_eval.p_Si33__He4_Al30 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn45__p_Fe48 *= scor
        rate_eval.He4_Mn45__Co49 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr41__p_Mn44 *= scor
        rate_eval.He4_Cr41__Fe45 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn43__Co47 *= scor
        rate_eval.He4_Mn43__p_Fe46 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V57__n_Mn60 *= scor
        rate_eval.He4_V57__Mn61 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti61__n_Cr64 *= scor
        rate_eval.He4_Ti61__Cr65 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si25__p_P28 *= scor
        rate_eval.He4_Si25__S29 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn58__Fe59 *= scor
        rate_eval.p_Mn58__n_Fe58 *= scor
        rate_eval.p_Mn58__He4_Cr55 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V40__p_Cr43 *= scor
        rate_eval.He4_V40__Mn44 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si24__p_P27 *= scor
        rate_eval.He4_Si24__S28 *= scor

        scn_fac = ScreenFactors(2, 4, 4, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Be7__C11 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca54__Ti58 *= scor
        rate_eval.He4_Ca54__n_Ti57 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K40__p_Ca43 *= scor
        rate_eval.He4_K40__Sc44 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si23__p_P26 *= scor
        rate_eval.He4_Si23__S27 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar42__n_Ca45 *= scor
        rate_eval.He4_Ar42__Ca46 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si22__p_P25 *= scor
        rate_eval.He4_Si22__S26 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al43__n_Si43 *= scor
        rate_eval.p_Al43__He4_Mg40 *= scor
        rate_eval.p_Al43__Si44 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al42__n_P45 *= scor
        rate_eval.He4_Al42__P46 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al41__He4_Mg38 *= scor
        rate_eval.p_Al41__n_Si41 *= scor
        rate_eval.p_Al41__Si42 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al40__He4_Mg37 *= scor
        rate_eval.p_Al40__n_Si40 *= scor
        rate_eval.p_Al40__Si41 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al39__p_Si42 *= scor
        rate_eval.He4_Al39__P43 *= scor
        rate_eval.He4_Al39__n_P42 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al38__He4_Mg35 *= scor
        rate_eval.p_Al38__n_Si38 *= scor
        rate_eval.p_Al38__Si39 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V59__n_Cr59 *= scor
        rate_eval.p_V59__Cr60 *= scor
        rate_eval.p_V59__He4_Ti56 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al37__He4_Mg34 *= scor
        rate_eval.p_Al37__Si38 *= scor
        rate_eval.p_Al37__n_Si37 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al36__p_Si39 *= scor
        rate_eval.He4_Al36__n_P39 *= scor
        rate_eval.He4_Al36__P40 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al36__He4_Mg33 *= scor
        rate_eval.p_Al36__n_Si36 *= scor
        rate_eval.p_Al36__Si37 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn59__Co63 *= scor
        rate_eval.He4_Mn59__n_Co62 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al35__n_P38 *= scor
        rate_eval.He4_Al35__P39 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al35__He4_Mg32 *= scor
        rate_eval.p_Al35__n_Si35 *= scor
        rate_eval.p_Al35__Si36 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al34__n_P37 *= scor
        rate_eval.He4_Al34__P38 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al34__He4_Mg31 *= scor
        rate_eval.p_Al34__n_Si34 *= scor
        rate_eval.p_Al34__Si35 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al33__n_P36 *= scor
        rate_eval.He4_Al33__P37 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al33__He4_Mg30 *= scor
        rate_eval.p_Al33__n_Si33 *= scor
        rate_eval.p_Al33__Si34 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si27__p_P30 *= scor
        rate_eval.He4_Si27__S31 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl46__He4_S43 *= scor
        rate_eval.p_Cl46__n_Ar46 *= scor
        rate_eval.p_Cl46__Ar47 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne26__n_Na26 *= scor
        rate_eval.p_Ne26__He4_F23 *= scor
        rate_eval.p_Ne26__Na27 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al32__He4_Mg29 *= scor
        rate_eval.p_Al32__n_Si32 *= scor
        rate_eval.p_Al32__Si33 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al31__p_Si34 *= scor
        rate_eval.He4_Al31__n_P34 *= scor
        rate_eval.He4_Al31__P35 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl38__He4_S35 *= scor
        rate_eval.p_Cl38__n_Ar38 *= scor
        rate_eval.p_Cl38__Ar39 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al31__He4_Mg28 *= scor
        rate_eval.p_Al31__Si32 *= scor
        rate_eval.p_Al31__n_Si31 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al29__n_P32 *= scor
        rate_eval.He4_Al29__p_Si32 *= scor
        rate_eval.He4_Al29__P33 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al29__He4_Mg26 *= scor
        rate_eval.p_Al29__n_Si29 *= scor
        rate_eval.p_Al29__Si30 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al37__n_P40 *= scor
        rate_eval.He4_Al37__P41 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne34__He4_F31 *= scor
        rate_eval.p_Ne34__n_Na34 *= scor
        rate_eval.p_Ne34__Na35 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al28__He4_Mg25 *= scor
        rate_eval.p_Al28__Si29 *= scor
        rate_eval.p_Al28__n_Si28 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al27__p_Si30 *= scor
        rate_eval.He4_Al27__n_P30 *= scor
        rate_eval.He4_Al27__P31 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca49__Sc50 *= scor
        rate_eval.p_Ca49__n_Sc49 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al24__p_Si27 *= scor
        rate_eval.He4_Al24__P28 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na37__Mg38 *= scor
        rate_eval.p_Na37__He4_Ne34 *= scor
        rate_eval.p_Na37__n_Mg37 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al22__p_Si25 *= scor
        rate_eval.He4_Al22__P26 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al21__p_Si24 *= scor
        rate_eval.He4_Al21__P25 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg40__n_Si43 *= scor
        rate_eval.He4_Mg40__Si44 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg40__n_Al40 *= scor
        rate_eval.p_Mg40__Al41 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg39__n_Si42 *= scor
        rate_eval.He4_Mg39__Si43 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg39__n_Al39 *= scor
        rate_eval.p_Mg39__Al40 *= scor
        rate_eval.p_Mg39__He4_Na36 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg38__n_Al38 *= scor
        rate_eval.p_Mg38__Al39 *= scor
        rate_eval.p_Mg38__He4_Na35 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al27__He4_Mg24 *= scor
        rate_eval.p_Al27__Si28 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg37__n_Si40 *= scor
        rate_eval.He4_Mg37__Si41 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na31__Mg32 *= scor
        rate_eval.p_Na31__He4_Ne28 *= scor
        rate_eval.p_Na31__n_Mg31 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar45__He4_Cl42 *= scor
        rate_eval.p_Ar45__n_K45 *= scor
        rate_eval.p_Ar45__K46 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg35__n_Si38 *= scor
        rate_eval.He4_Mg35__Si39 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg34__n_Si37 *= scor
        rate_eval.He4_Mg34__Si38 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg33__He4_Na30 *= scor
        rate_eval.p_Mg33__n_Al33 *= scor
        rate_eval.p_Mg33__Al34 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe66__He4_Mn63 *= scor
        rate_eval.p_Fe66__n_Co66 *= scor
        rate_eval.p_Fe66__Co67 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg32__n_Si35 *= scor
        rate_eval.He4_Mg32__Si36 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg32__He4_Na29 *= scor
        rate_eval.p_Mg32__Al33 *= scor
        rate_eval.p_Mg32__n_Al32 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg30__n_Si33 *= scor
        rate_eval.He4_Mg30__Si34 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg30__n_Al30 *= scor
        rate_eval.p_Mg30__Al31 *= scor
        rate_eval.p_Mg30__He4_Na27 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca45__Sc46 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr46__p_Mn49 *= scor
        rate_eval.He4_Cr46__Fe50 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg29__He4_Na26 *= scor
        rate_eval.p_Mg29__n_Al29 *= scor
        rate_eval.p_Mg29__Al30 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne23__n_Mg26 *= scor
        rate_eval.He4_Ne23__Mg27 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne31__He4_F28 *= scor
        rate_eval.p_Ne31__Na32 *= scor
        rate_eval.p_Ne31__n_Na31 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg27__n_Si30 *= scor
        rate_eval.He4_Mg27__Si31 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O23__n_Ne26 *= scor
        rate_eval.He4_O23__Ne27 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K35__p_Ca38 *= scor
        rate_eval.He4_K35__Sc39 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg26__n_Si29 *= scor
        rate_eval.He4_Mg26__Si30 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe53__p_Co56 *= scor
        rate_eval.He4_Fe53__Ni57 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg25__n_Si28 *= scor
        rate_eval.He4_Mg25__Si29 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg22__p_Al25 *= scor
        rate_eval.He4_Mg22__Si26 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg20__p_Al23 *= scor
        rate_eval.He4_Mg20__Si24 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na36__n_Al39 *= scor
        rate_eval.He4_Na36__Al40 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na39__n_Mg39 *= scor
        rate_eval.p_Na39__Mg40 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na38__n_Al41 *= scor
        rate_eval.He4_Na38__Al42 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na37__p_Mg40 *= scor
        rate_eval.He4_Na37__n_Al40 *= scor
        rate_eval.He4_Na37__Al41 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K33__Sc37 *= scor
        rate_eval.He4_K33__p_Ca36 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na35__n_Al38 *= scor
        rate_eval.He4_Na35__Al39 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na35__n_Mg35 *= scor
        rate_eval.p_Na35__He4_Ne32 *= scor
        rate_eval.p_Na35__Mg36 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na34__n_Al37 *= scor
        rate_eval.He4_Na34__Al38 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V60__n_Mn63 *= scor
        rate_eval.He4_V60__Mn64 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na33__p_Mg36 *= scor
        rate_eval.He4_Na33__Al37 *= scor
        rate_eval.He4_Na33__n_Al36 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na33__n_Mg33 *= scor
        rate_eval.p_Na33__He4_Ne30 *= scor
        rate_eval.p_Na33__Mg34 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na31__n_Al34 *= scor
        rate_eval.He4_Na31__Al35 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na30__He4_Ne27 *= scor
        rate_eval.p_Na30__Mg31 *= scor
        rate_eval.p_Na30__n_Mg30 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na29__He4_Ne26 *= scor
        rate_eval.p_Na29__n_Mg29 *= scor
        rate_eval.p_Na29__Mg30 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na28__n_Al31 *= scor
        rate_eval.He4_Na28__Al32 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na28__n_Mg28 *= scor
        rate_eval.p_Na28__He4_Ne25 *= scor
        rate_eval.p_Na28__Mg29 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na27__n_Mg27 *= scor
        rate_eval.p_Na27__Mg28 *= scor
        rate_eval.p_Na27__He4_Ne24 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na26__n_Al29 *= scor
        rate_eval.He4_Na26__Al30 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na24__p_Mg27 *= scor
        rate_eval.He4_Na24__Al28 *= scor
        rate_eval.He4_Na24__n_Al27 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na24__He4_Ne21 *= scor
        rate_eval.p_Na24__Mg25 *= scor
        rate_eval.p_Na24__n_Mg24 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K46__Ca47 *= scor
        rate_eval.p_K46__He4_Ar43 *= scor
        rate_eval.p_K46__n_Ca46 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na23__p_Mg26 *= scor
        rate_eval.He4_Na23__Al27 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na23__He4_Ne20 *= scor
        rate_eval.p_Na23__n_Mg23 *= scor
        rate_eval.p_Na23__Mg24 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na22__p_Mg25 *= scor
        rate_eval.He4_Na22__Al26 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S29__p_Cl32 *= scor
        rate_eval.He4_S29__Ar33 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl35__p_Ar38 *= scor
        rate_eval.He4_Cl35__K39 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl36__Ar37 *= scor
        rate_eval.p_Cl36__He4_S33 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S46__n_Ar49 *= scor
        rate_eval.He4_S46__Ar50 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne31__n_Mg34 *= scor
        rate_eval.He4_Ne31__Mg35 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne30__n_Mg33 *= scor
        rate_eval.He4_Ne30__Mg34 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne30__He4_F27 *= scor
        rate_eval.p_Ne30__Na31 *= scor
        rate_eval.p_Ne30__n_Na30 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne29__He4_F26 *= scor
        rate_eval.p_Ne29__n_Na29 *= scor
        rate_eval.p_Ne29__Na30 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne28__n_Mg31 *= scor
        rate_eval.He4_Ne28__Mg32 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne28__n_Na28 *= scor
        rate_eval.p_Ne28__He4_F25 *= scor
        rate_eval.p_Ne28__Na29 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne27__n_Mg30 *= scor
        rate_eval.He4_Ne27__Mg31 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca39__Ti43 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S39__n_Ar42 *= scor
        rate_eval.He4_S39__Ar43 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne25__He4_F22 *= scor
        rate_eval.p_Ne25__n_Na25 *= scor
        rate_eval.p_Ne25__Na26 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S27__p_Cl30 *= scor
        rate_eval.He4_S27__Ar31 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne24__n_Mg27 *= scor
        rate_eval.He4_Ne24__Mg28 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne24__n_Na24 *= scor
        rate_eval.p_Ne24__Na25 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S30__Cl31 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca61__n_Ti64 *= scor
        rate_eval.He4_Ca61__Ti65 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K39__Sc43 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne23__n_Na23 *= scor
        rate_eval.p_Ne23__Na24 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne22__n_Mg25 *= scor
        rate_eval.He4_Ne22__Mg26 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne21__n_Mg24 *= scor
        rate_eval.He4_Ne21__Mg25 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V42__Cr43 *= scor

        scn_fac = ScreenFactors(6, 12, 10, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.C12_Ne20__He4_Si28 *= scor
        rate_eval.C12_Ne20__p_P31 *= scor
        rate_eval.C12_Ne20__n_S31 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V54__n_Cr54 *= scor
        rate_eval.p_V54__Cr55 *= scor
        rate_eval.p_V54__He4_Ti51 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne20__He4_F17 *= scor
        rate_eval.p_Ne20__Na21 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne22__Na23 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al26__p_Si29 *= scor
        rate_eval.He4_Al26__P30 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K33__Ca34 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne19__p_Na22 *= scor
        rate_eval.He4_Ne19__Mg23 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne18__p_Na21 *= scor
        rate_eval.He4_Ne18__Mg22 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 17)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne17__p_Na20 *= scor
        rate_eval.He4_Ne17__Mg21 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne16__p_Na19 *= scor
        rate_eval.He4_Ne16__Mg20 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar53__n_Ca56 *= scor
        rate_eval.He4_Ar53__Ca57 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F30__p_Ne33 *= scor
        rate_eval.He4_F30__n_Na33 *= scor
        rate_eval.He4_F30__Na34 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn47__Fe48 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F30__He4_O27 *= scor
        rate_eval.p_F30__n_Ne30 *= scor
        rate_eval.p_F30__Ne31 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F29__n_Na32 *= scor
        rate_eval.He4_F29__Na33 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F29__He4_O26 *= scor
        rate_eval.p_F29__Ne30 *= scor
        rate_eval.p_F29__n_Ne29 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F27__n_Na30 *= scor
        rate_eval.He4_F27__Na31 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F27__He4_O24 *= scor
        rate_eval.p_F27__n_Ne27 *= scor
        rate_eval.p_F27__Ne28 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F26__n_Ne26 *= scor
        rate_eval.p_F26__Ne27 *= scor
        rate_eval.p_F26__He4_O23 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F25__He4_O22 *= scor
        rate_eval.p_F25__n_Ne25 *= scor
        rate_eval.p_F25__Ne26 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca38__Ti42 *= scor
        rate_eval.He4_Ca38__p_Sc41 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F24__n_Na27 *= scor
        rate_eval.He4_F24__Na28 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti42__p_V45 *= scor
        rate_eval.He4_Ti42__Cr46 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na26__He4_Ne23 *= scor
        rate_eval.p_Na26__Mg27 *= scor
        rate_eval.p_Na26__n_Mg26 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F22__He4_O19 *= scor
        rate_eval.p_F22__n_Ne22 *= scor
        rate_eval.p_F22__Ne23 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F21__p_Ne24 *= scor
        rate_eval.He4_F21__n_Na24 *= scor
        rate_eval.He4_F21__Na25 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F20__He4_O17 *= scor
        rate_eval.p_F20__n_Ne20 *= scor
        rate_eval.p_F20__Ne21 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F19__p_Ne22 *= scor
        rate_eval.He4_F19__Na23 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F19__n_Ne19 *= scor
        rate_eval.p_F19__He4_O16 *= scor
        rate_eval.p_F19__Ne20 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O21__n_F21 *= scor
        rate_eval.p_O21__F22 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F18__p_Ne21 *= scor
        rate_eval.He4_F18__Na22 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O15__F16 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O28__n_Ne31 *= scor
        rate_eval.He4_O28__Ne32 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O26__n_Ne29 *= scor
        rate_eval.He4_O26__Ne30 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O26__He4_N23 *= scor
        rate_eval.p_O26__n_F26 *= scor
        rate_eval.p_O26__F27 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti44__p_V47 *= scor
        rate_eval.He4_Ti44__Cr48 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O24__n_Ne27 *= scor
        rate_eval.He4_O24__Ne28 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O24__n_F24 *= scor
        rate_eval.p_O24__F25 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O22__n_Ne25 *= scor
        rate_eval.He4_O22__Ne26 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O19__n_Ne22 *= scor
        rate_eval.He4_O19__Ne23 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl32__p_Ar35 *= scor
        rate_eval.He4_Cl32__K36 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O18__He4_N15 *= scor
        rate_eval.p_O18__F19 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 17)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O17__n_Ne20 *= scor
        rate_eval.He4_O17__Ne21 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 17)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O17__He4_N14 *= scor
        rate_eval.p_O17__F18 *= scor

        scn_fac = ScreenFactors(8, 16, 8, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.O16_O16__He4_Si28 *= scor
        rate_eval.O16_O16__p_P31 *= scor
        rate_eval.O16_O16__n_S31 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne26__n_Mg29 *= scor
        rate_eval.He4_Ne26__Mg30 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al28__n_P31 *= scor
        rate_eval.He4_Al28__p_Si31 *= scor
        rate_eval.He4_Al28__P32 *= scor

        scn_fac = ScreenFactors(6, 12, 8, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.C12_O16__He4_Mg24 *= scor
        rate_eval.C12_O16__p_Al27 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al26__Si27 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca36__Sc37 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr70__Mn71 *= scor
        rate_eval.p_Cr70__n_Mn70 *= scor
        rate_eval.p_Cr70__He4_V67 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar41__n_Ca44 *= scor
        rate_eval.He4_Ar41__Ca45 *= scor

        scn_fac = ScreenFactors(2, 4, 7, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_N13__p_O16 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C15__n_O18 *= scor

        scn_fac = ScreenFactors(1, 1, 6, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_C15__n_N15 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si31__n_S34 *= scor
        rate_eval.He4_Si31__S35 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl45__n_K48 *= scor
        rate_eval.He4_Cl45__K49 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C13__n_O16 *= scor

        scn_fac = ScreenFactors(1, 2, 6, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_C13__n_N14 *= scor

        scn_fac = ScreenFactors(1, 1, 6, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_C13__n_N13 *= scor
        rate_eval.p_C13__N14 *= scor

        scn_fac = ScreenFactors(2, 4, 5, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_B13__n_N16 *= scor
        rate_eval.He4_B13__N17 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar53__He4_Cl50 *= scor
        rate_eval.p_Ar53__n_K53 *= scor
        rate_eval.p_Ar53__K54 *= scor

        scn_fac = ScreenFactors(2, 4, 5, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_B12__n_N15 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti56__He4_Sc53 *= scor
        rate_eval.p_Ti56__V57 *= scor
        rate_eval.p_Ti56__n_V56 *= scor

        scn_fac = ScreenFactors(2, 4, 5, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_B11__p_C14 *= scor
        rate_eval.He4_B11__n_N14 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe46__p_Co49 *= scor
        rate_eval.He4_Fe46__Ni50 *= scor

        scn_fac = ScreenFactors(2, 4, 5, 10)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_B10__p_C13 *= scor
        rate_eval.He4_B10__n_N13 *= scor

        scn_fac = ScreenFactors(2, 4, 5, 8)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_B8__p_C11 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn70__Co74 *= scor
        rate_eval.He4_Mn70__n_Co73 *= scor

        scn_fac = ScreenFactors(2, 4, 3, 8)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Li8__n_B11 *= scor
        rate_eval.He4_Li8__B12 *= scor

        scn_fac = ScreenFactors(1, 2, 2, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_He3__p_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V51__Mn55 *= scor

        scn_fac = ScreenFactors(1, 2, 1, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_t__n_He4 *= scor

        scn_fac = ScreenFactors(1, 2, 1, 2)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_d__p_t *= scor
        rate_eval.d_d__He4 *= scor
        rate_eval.d_d__n_He3 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg31__n_Al31 *= scor
        rate_eval.p_Mg31__Al32 *= scor
        rate_eval.p_Mg31__He4_Na28 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe69__Ni73 *= scor
        rate_eval.He4_Fe69__n_Ni72 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe67__Ni71 *= scor
        rate_eval.He4_Fe67__n_Ni70 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc48__n_V51 *= scor
        rate_eval.He4_Sc48__V52 *= scor
        rate_eval.He4_Sc48__p_Ti51 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P36__n_Cl39 *= scor
        rate_eval.He4_P36__Cl40 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe58__Ni62 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe56__Co57 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe55__Co56 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe54__Ni58 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe52__Co53 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe51__Ni55 *= scor
        rate_eval.He4_Fe51__p_Co54 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe50__Co51 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe48__Co49 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O25__n_Ne28 *= scor
        rate_eval.He4_O25__Ne29 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe57__Ni61 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe45__Ni49 *= scor
        rate_eval.He4_Fe45__p_Co48 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn66__Co70 *= scor
        rate_eval.He4_Mn66__n_Co69 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn64__Co68 *= scor
        rate_eval.He4_Mn64__n_Co67 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn63__Co67 *= scor
        rate_eval.He4_Mn63__n_Co66 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl29__p_Ar32 *= scor
        rate_eval.He4_Cl29__K33 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne33__n_Na33 *= scor
        rate_eval.p_Ne33__Na34 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn61__Co65 *= scor
        rate_eval.He4_Mn61__n_Co64 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K42__n_Ca42 *= scor
        rate_eval.p_K42__He4_Ar39 *= scor
        rate_eval.p_K42__Ca43 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn52__Co56 *= scor
        rate_eval.He4_Mn52__p_Fe55 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn50__Co54 *= scor
        rate_eval.He4_Mn50__p_Fe53 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn50__Fe51 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn49__Fe50 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn48__Fe49 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn46__Fe47 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn45__Fe46 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr67__Fe71 *= scor
        rate_eval.He4_Cr67__n_Fe70 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr60__Fe64 *= scor
        rate_eval.He4_Cr60__n_Fe63 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg19__p_Al22 *= scor
        rate_eval.He4_Mg19__Si23 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr58__Fe62 *= scor
        rate_eval.He4_Cr58__n_Fe61 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr58__Mn59 *= scor
        rate_eval.p_Cr58__n_Mn58 *= scor
        rate_eval.p_Cr58__He4_V55 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr54__Fe58 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr53__Fe57 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr53__Mn54 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl39__He4_S36 *= scor
        rate_eval.p_Cl39__Ar40 *= scor
        rate_eval.p_Cl39__n_Ar39 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr52__Mn53 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr51__Mn52 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr50__Mn51 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr49__Mn50 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar45__Ca49 *= scor
        rate_eval.He4_Ar45__n_Ca48 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K38__p_Ca41 *= scor
        rate_eval.He4_K38__Sc42 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P40__n_Cl43 *= scor
        rate_eval.He4_P40__Cl44 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr46__Mn47 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P44__He4_Si41 *= scor
        rate_eval.p_P44__n_S44 *= scor
        rate_eval.p_P44__S45 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O14__p_F17 *= scor
        rate_eval.He4_O14__Ne18 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K58__n_Ca58 *= scor
        rate_eval.p_K58__Ca59 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V53__Mn57 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V52__Mn56 *= scor
        rate_eval.He4_V52__n_Mn55 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V62__n_Cr62 *= scor
        rate_eval.p_V62__He4_Ti59 *= scor
        rate_eval.p_V62__Cr63 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne25__Mg29 *= scor
        rate_eval.He4_Ne25__n_Mg28 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V65__Mn69 *= scor
        rate_eval.He4_V65__n_Mn68 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne32__n_Mg35 *= scor
        rate_eval.He4_Ne32__Mg36 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V48__Cr49 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V46__Cr47 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V45__Mn49 *= scor
        rate_eval.He4_V45__p_Cr48 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn63__Fe64 *= scor
        rate_eval.p_Mn63__He4_Cr60 *= scor
        rate_eval.p_Mn63__n_Fe63 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V43__Cr44 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P40__n_S40 *= scor
        rate_eval.p_P40__S41 *= scor
        rate_eval.p_P40__He4_Si37 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al42__He4_Mg39 *= scor
        rate_eval.p_Al42__Si43 *= scor
        rate_eval.p_Al42__n_Si42 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V41__Mn45 *= scor
        rate_eval.He4_V41__p_Cr44 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V41__Cr42 *= scor

        scn_fac = ScreenFactors(1, 1, 7, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_N12__O13 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar47__n_K47 *= scor
        rate_eval.p_Ar47__K48 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar36__K37 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti52__Cr56 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti49__V50 *= scor

        scn_fac = ScreenFactors(1, 3, 4, 9)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.t_Be9__n_B11 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na39__n_Al42 *= scor
        rate_eval.He4_Na39__Al43 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti48__Cr52 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti47__V48 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti57__n_Cr60 *= scor
        rate_eval.He4_Ti57__Cr61 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti46__Cr50 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti44__V45 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti42__V43 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti41__Cr45 *= scor
        rate_eval.He4_Ti41__p_V44 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na32__n_Al35 *= scor
        rate_eval.He4_Na32__Al36 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti41__V42 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S28__Cl29 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti40__V41 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc63__Ti64 *= scor
        rate_eval.p_Sc63__He4_Ca60 *= scor
        rate_eval.p_Sc63__n_Ti63 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn44__Fe45 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca60__n_Ti63 *= scor
        rate_eval.He4_Ca60__Ti64 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti49__n_Cr52 *= scor
        rate_eval.He4_Ti49__Cr53 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc56__Ti57 *= scor
        rate_eval.p_Sc56__He4_Ca53 *= scor
        rate_eval.p_Sc56__n_Ti56 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc37__Ti38 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K45__p_Ca48 *= scor
        rate_eval.He4_K45__Sc49 *= scor
        rate_eval.He4_K45__n_Sc48 *= scor

        scn_fac = ScreenFactors(1, 1, 2, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_He3__He4__weak__bet_pos_ *= scor

        scn_fac = ScreenFactors(2, 4, 21, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc49__V53 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne21__Na22 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca50__He4_K47 *= scor
        rate_eval.p_Ca50__n_Sc50 *= scor
        rate_eval.p_Ca50__Sc51 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc43__Ti44 *= scor
        rate_eval.p_Sc43__He4_Ca40 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc42__Ti43 *= scor
        rate_eval.p_Sc42__He4_Ca39 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc41__V45 *= scor
        rate_eval.He4_Sc41__p_Ti44 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc41__Ti42 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc40__Ti41 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc38__Ti39 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F25__n_Na28 *= scor
        rate_eval.He4_F25__Na29 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca59__Ti63 *= scor
        rate_eval.He4_Ca59__n_Ti62 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca57__Sc58 *= scor
        rate_eval.p_Ca57__He4_K54 *= scor
        rate_eval.p_Ca57__n_Sc57 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na20__Mg21 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na27__n_Al30 *= scor
        rate_eval.He4_Na27__Al31 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O27__Ne31 *= scor
        rate_eval.He4_O27__n_Ne30 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca54__Sc55 *= scor
        rate_eval.p_Ca54__n_Sc54 *= scor
        rate_eval.p_Ca54__He4_K51 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V48__p_Cr51 *= scor
        rate_eval.He4_V48__Mn52 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe58__Co59 *= scor
        rate_eval.p_Fe58__He4_Mn55 *= scor

        scn_fac = ScreenFactors(2, 4, 4, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Be11__n_C14 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca46__Ti50 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca45__Ti49 *= scor
        rate_eval.He4_Ca45__n_Ti48 *= scor

        scn_fac = ScreenFactors(1, 3, 3, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.t_Li7__n_Be9 *= scor
        rate_eval.t_Li7__n_n_He4_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 3, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Li7__B11 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca44__Ti48 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca42__Ti46 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca41__Sc42 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca40__Sc41 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca37__Ti41 *= scor
        rate_eval.He4_Ca37__p_Sc40 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca35__Ti39 *= scor
        rate_eval.He4_Ca35__p_Sc38 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca35__Sc36 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca34__Ti38 *= scor
        rate_eval.He4_Ca34__p_Sc37 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl46__n_K49 *= scor
        rate_eval.He4_Cl46__K50 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca34__Sc35 *= scor

        scn_fac = ScreenFactors(1, 1, 4, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Be11__He4_Li8 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca33__Ti37 *= scor
        rate_eval.He4_Ca33__p_Sc36 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K58__Sc62 *= scor
        rate_eval.He4_K58__n_Sc61 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K50__n_Ca50 *= scor
        rate_eval.p_K50__He4_Ar47 *= scor
        rate_eval.p_K50__Ca51 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P30__S31 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na29__Al33 *= scor
        rate_eval.He4_Na29__n_Al32 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si45__S49 *= scor
        rate_eval.He4_Si45__n_S48 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar38__K39 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr45__Mn46 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti47__Cr51 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S34__Cl35 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K38__Ca39 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K37__Ca38 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P28__Cl32 *= scor
        rate_eval.He4_P28__p_S31 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K36__Ca37 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K32__Sc36 *= scor
        rate_eval.He4_K32__p_Ca35 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar42__K43 *= scor
        rate_eval.p_Ar42__He4_Cl39 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar40__Ca44 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr51__Fe55 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar39__Ca43 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar37__Ca41 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar37__K38 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar35__K36 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si25__P26 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar33__K34 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar32__Ca36 *= scor
        rate_eval.He4_Ar32__p_K35 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar32__K33 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P33__He4_Si30 *= scor
        rate_eval.p_P33__S34 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P28__S29 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar31__K32 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne20__Mg24 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar30__Ca34 *= scor
        rate_eval.He4_Ar30__p_K33 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl49__Ar50 *= scor
        rate_eval.p_Cl49__He4_S46 *= scor
        rate_eval.p_Cl49__n_Ar49 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl39__K43 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr64__n_Mn64 *= scor
        rate_eval.p_Cr64__Mn65 *= scor
        rate_eval.p_Cr64__He4_V61 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl38__K42 *= scor
        rate_eval.He4_Cl38__n_K41 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl36__K40 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti39__V40 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg35__n_Al35 *= scor
        rate_eval.p_Mg35__He4_Na32 *= scor
        rate_eval.p_Mg35__Al36 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl33__K37 *= scor
        rate_eval.He4_Cl33__p_Ar36 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O21__Ne25 *= scor
        rate_eval.He4_O21__n_Ne24 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl32__Ar33 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl31__K35 *= scor
        rate_eval.He4_Cl31__p_Ar34 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl31__Ar32 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl30__Ar31 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl29__Ar30 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S49__Ar53 *= scor
        rate_eval.He4_S49__n_Ar52 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si34__P35 *= scor
        rate_eval.p_Si34__n_P34 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S47__Ar51 *= scor
        rate_eval.He4_S47__n_Ar50 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S44__Ar48 *= scor
        rate_eval.He4_S44__n_Ar47 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S44__Cl45 *= scor
        rate_eval.p_S44__n_Cl44 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar47__Ca51 *= scor
        rate_eval.He4_Ar47__n_Ca50 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K34__Ca35 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S36__Ar40 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg36__Si40 *= scor
        rate_eval.He4_Mg36__n_Si39 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na32__n_Mg32 *= scor
        rate_eval.p_Na32__Mg33 *= scor
        rate_eval.p_Na32__He4_Ne29 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar54__n_Ca57 *= scor
        rate_eval.He4_Ar54__Ca58 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S32__Ar36 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S32__Cl33 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S31__Cl32 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S29__Cl30 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl37__K41 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg33__n_Si36 *= scor
        rate_eval.He4_Mg33__Si37 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P35__Cl39 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P35__S36 *= scor
        rate_eval.p_P35__n_S35 *= scor
        rate_eval.p_P35__He4_Si32 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P32__Cl36 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P26__S27 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn70__Fe71 *= scor
        rate_eval.p_Mn70__He4_Cr67 *= scor
        rate_eval.p_Mn70__n_Fe70 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K55__n_Ca55 *= scor
        rate_eval.p_K55__Ca56 *= scor
        rate_eval.p_K55__He4_Ar52 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si41__S45 *= scor
        rate_eval.He4_Si41__n_S44 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si40__P41 *= scor
        rate_eval.p_Si40__n_P40 *= scor
        rate_eval.p_Si40__He4_Al37 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si34__S38 *= scor
        rate_eval.He4_Si34__n_S37 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si32__P33 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl47__Ar48 *= scor
        rate_eval.p_Cl47__n_Ar47 *= scor
        rate_eval.p_Cl47__He4_S44 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg37__n_Al37 *= scor
        rate_eval.p_Mg37__Al38 *= scor
        rate_eval.p_Mg37__He4_Na34 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si31__P32 *= scor
        rate_eval.p_Si31__n_P31 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si30__P31 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si28__P29 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si26__P27 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si24__P25 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al43__P47 *= scor
        rate_eval.He4_Al43__n_P46 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc59__He4_Ca56 *= scor
        rate_eval.p_Sc59__Ti60 *= scor
        rate_eval.p_Sc59__n_Ti59 *= scor

        scn_fac = ScreenFactors(2, 4, 7, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_N14__n_F17 *= scor
        rate_eval.He4_N14__F18 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr56__Fe60 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al30__P34 *= scor
        rate_eval.He4_Al30__n_P33 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti62__n_Cr65 *= scor
        rate_eval.He4_Ti62__Cr66 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al24__Si25 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti56__Cr60 *= scor
        rate_eval.He4_Ti56__n_Cr59 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg41__Si45 *= scor
        rate_eval.He4_Mg41__n_Si44 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al41__P45 *= scor
        rate_eval.He4_Al41__n_P44 *= scor

        scn_fac = ScreenFactors(1, 2, 3, 6)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_Li6__n_Be7 *= scor
        rate_eval.d_Li6__p_Li7 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr47__Mn48 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca43__Sc44 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg31__Si35 *= scor
        rate_eval.He4_Mg31__n_Si34 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe49__Co50 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K47__Sc51 *= scor
        rate_eval.He4_K47__n_Sc50 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg29__Si33 *= scor
        rate_eval.He4_Mg29__n_Si32 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg28__Si32 *= scor
        rate_eval.He4_Mg28__n_Si31 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe54__Co55 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg27__Al28 *= scor
        rate_eval.p_Mg27__n_Al27 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe46__Co47 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg26__Al27 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg23__Si27 *= scor
        rate_eval.He4_Mg23__p_Al26 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg23__Al24 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg22__Al23 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg21__Si25 *= scor
        rate_eval.He4_Mg21__p_Al24 *= scor

        scn_fac = ScreenFactors(2, 4, 2, 4)
        scor = screen_func(plasma_state, scn_fac)
        scn_fac2 = ScreenFactors(2, 4, 4, 8)
        scor2 = screen_func(plasma_state, scn_fac2)
        rate_eval.He4_He4_He4__C12 *= scor * scor2

        scn_fac = ScreenFactors(1, 1, 11, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na38__Mg39 *= scor
        rate_eval.p_Na38__n_Mg38 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc36__Ti37 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F21__n_Ne21 *= scor
        rate_eval.p_F21__Ne22 *= scor
        rate_eval.p_F21__He4_O18 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na25__Mg26 *= scor
        rate_eval.p_Na25__n_Mg25 *= scor
        rate_eval.p_Na25__He4_Ne22 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F15__p_Ne18 *= scor
        rate_eval.He4_F15__Na19 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na22__Mg23 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar50__Ca54 *= scor
        rate_eval.He4_Ar50__n_Ca53 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na21__Mg22 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na20__Al24 *= scor
        rate_eval.He4_Na20__p_Mg23 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S33__Cl34 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne34__Mg38 *= scor
        rate_eval.He4_Ne34__n_Mg37 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si29__P30 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl44__Ar45 *= scor
        rate_eval.p_Cl44__n_Ar44 *= scor
        rate_eval.p_Cl44__He4_S41 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl52__n_K55 *= scor
        rate_eval.He4_Cl52__K56 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne19__Na20 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn52__Fe53 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne18__Na19 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na30__Al34 *= scor
        rate_eval.He4_Na30__n_Al33 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe51__Co52 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K59__Sc63 *= scor
        rate_eval.He4_K59__n_Sc62 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K35__Ca36 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O20__Ne24 *= scor
        rate_eval.He4_O20__n_Ne23 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar44__n_Ca47 *= scor
        rate_eval.He4_Ar44__Ca48 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P33__Cl37 *= scor

        scn_fac = ScreenFactors(1, 1, 7, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_N14__O15 *= scor
        rate_eval.p_N14__n_O14 *= scor

        scn_fac = ScreenFactors(1, 1, 6, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_C14__N15 *= scor

        scn_fac = ScreenFactors(1, 1, 6, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_C12__N13 *= scor

        scn_fac = ScreenFactors(1, 1, 6, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_C11__N12 *= scor

        scn_fac = ScreenFactors(1, 1, 5, 10)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_B10__C11 *= scor
        rate_eval.p_B10__He4_Be7 *= scor

        scn_fac = ScreenFactors(1, 1, 4, 10)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Be10__B11 *= scor
        rate_eval.p_Be10__He4_Li7 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc39__Ti40 *= scor

        scn_fac = ScreenFactors(1, 1, 4, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Be7__B8 *= scor

        scn_fac = ScreenFactors(2, 4, 3, 9)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Li9__B13 *= scor
        rate_eval.He4_Li9__n_B12 *= scor

        scn_fac = ScreenFactors(2, 4, 2, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_He3__Be7 *= scor

        scn_fac = ScreenFactors(1, 1, 1, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_t__He4 *= scor

        scn_fac = ScreenFactors(1, 2, 2, 4)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_d__Li6 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P27__S28 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C12__O16 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe62__n_Ni65 *= scor
        rate_eval.He4_Fe62__Ni66 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti46__V47 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca49__n_Ti52 *= scor
        rate_eval.He4_Ca49__Ti53 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg36__Al37 *= scor
        rate_eval.p_Mg36__n_Al36 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si28__S32 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V40__Cr41 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K39__Ca40 *= scor
        rate_eval.p_K39__He4_Ar36 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti50__V51 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si26__S30 *= scor
        rate_eval.He4_Si26__p_P29 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V44__p_Cr47 *= scor
        rate_eval.He4_V44__Mn48 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn58__Co62 *= scor
        rate_eval.He4_Mn58__n_Co61 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si32__S36 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V45__Cr46 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al23__Si24 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P41__n_S41 *= scor
        rate_eval.p_P41__S42 *= scor
        rate_eval.p_P41__He4_Si38 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P39__n_S39 *= scor
        rate_eval.p_P39__He4_Si36 *= scor
        rate_eval.p_P39__S40 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr68__n_Fe71 *= scor
        rate_eval.He4_Cr68__Fe72 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si29__S33 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V44__Cr45 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O18__n_Ne21 *= scor
        rate_eval.He4_O18__Ne22 *= scor

        scn_fac = ScreenFactors(2, 4, 4, 9)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Be9__n_C12 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl34__Ar35 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe61__Ni65 *= scor
        rate_eval.He4_Fe61__n_Ni64 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe53__Co54 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P46__n_Cl49 *= scor
        rate_eval.He4_P46__Cl50 *= scor

        scn_fac = ScreenFactors(2, 4, 7, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_N12__p_O15 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 71)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn71__Co75 *= scor
        rate_eval.He4_Mn71__n_Co74 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca48__Sc49 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg41__Al42 *= scor
        rate_eval.p_Mg41__n_Al41 *= scor
        rate_eval.p_Mg41__He4_Na38 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca55__n_Ti58 *= scor
        rate_eval.He4_Ca55__Ti59 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P38__Cl42 *= scor
        rate_eval.He4_P38__n_Cl41 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar46__K47 *= scor
        rate_eval.p_Ar46__n_K46 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si36__n_S39 *= scor
        rate_eval.He4_Si36__S40 *= scor

        scn_fac = ScreenFactors(1, 1, 3, 8)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Li8__n_He4_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti50__Cr54 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar30__K31 *= scor

        scn_fac = ScreenFactors(1, 1, 7, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_N13__O14 *= scor

        scn_fac = ScreenFactors(1, 3, 2, 4)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_t__Li7 *= scor

        scn_fac = ScreenFactors(2, 4, 2, 4)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.n_He4_He4__Be9 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl48__K52 *= scor
        rate_eval.He4_Cl48__n_K51 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S40__n_Ar43 *= scor
        rate_eval.He4_S40__Ar44 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F23__Na27 *= scor
        rate_eval.He4_F23__n_Na26 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P25__S26 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na21__Al25 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P45__n_Cl48 *= scor
        rate_eval.He4_P45__Cl49 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C14__O18 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl33__Ar34 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca46__Sc47 *= scor

        scn_fac = ScreenFactors(1, 1, 2, 4)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.n_p_He4__Li6 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc53__n_V56 *= scor
        rate_eval.He4_Sc53__V57 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti48__V49 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca41__Ti45 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P29__Cl33 *= scor
        rate_eval.He4_P29__p_S32 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O23__n_F23 *= scor
        rate_eval.p_O23__F24 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C11__p_N14 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr42__Mn43 *= scor

        scn_fac = ScreenFactors(2, 4, 3, 6)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Li6__B10 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S33__Ar37 *= scor

        scn_fac = ScreenFactors(1, 1, 3, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Li7__He4_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca56__Ti60 *= scor
        rate_eval.He4_Ca56__n_Ti59 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O15__Ne19 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si27__P28 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al23__p_Si26 *= scor
        rate_eval.He4_Al23__P27 *= scor

        scn_fac = ScreenFactors(2, 4, 7, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_N16__n_F19 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si41__P42 *= scor
        rate_eval.p_Si41__n_P41 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 17)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F17__Ne18 *= scor

        scn_fac = ScreenFactors(1, 1, 7, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_N16__n_O16 *= scor
        rate_eval.p_N16__He4_C13 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl28__Ar29 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S27__Cl28 *= scor

        scn_fac = ScreenFactors(1, 1, 5, 8)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_B8__C9 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F22__Na26 *= scor
        rate_eval.He4_F22__n_Na25 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar49__n_Ca52 *= scor
        rate_eval.He4_Ar49__Ca53 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg21__Al22 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn55__Co59 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr48__Mn49 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si30__S34 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn56__Co60 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl37__Ar38 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K32__Ca33 *= scor

        scn_fac = ScreenFactors(1, 1, 1, 2)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_d__He3 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V47__Cr48 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca38__Sc39 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar51__Ca55 *= scor
        rate_eval.He4_Ar51__n_Ca54 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr43__Mn44 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe60__Ni64 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar48__Ca52 *= scor
        rate_eval.He4_Ar48__n_Ca51 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar49__n_K49 *= scor
        rate_eval.p_Ar49__K50 *= scor
        rate_eval.p_Ar49__He4_Cl46 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr44__Mn45 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al22__Si23 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe55__Ni59 *= scor

        scn_fac = ScreenFactors(1, 3, 1, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.t_t__n_n_He4 *= scor

        scn_fac = ScreenFactors(2, 3, 3, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He3_Li7__n_p_He4_He4 *= scor

        scn_fac = ScreenFactors(1, 2, 6, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_C14__n_N15 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca39__Sc40 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr52__Fe56 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca37__Sc38 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti45__V46 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr50__Fe54 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar38__Ca42 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg24__Si28 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg25__Al26 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn57__Co61 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc50__V54 *= scor
        rate_eval.He4_Sc50__n_V53 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg28__Al29 *= scor
        rate_eval.p_Mg28__n_Al28 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 72)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe72__n_Ni75 *= scor
        rate_eval.He4_Fe72__Ni76 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O16__Ne20 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na19__Mg20 *= scor

    dYdt = np.zeros((nnuc), dtype=np.float64)

    dYdt[jn] = (
          + 3*Y[jfe75]*rate_eval.Fe75__n_n_n_Co72__weak__mo03  +
          + 3*Y[jmn73]*rate_eval.Mn73__n_n_n_Fe70__weak__mo03  +
          + 3*Y[jmn71]*rate_eval.Mn71__n_n_n_Fe68__weak__mo03  +
          + 3*Y[jcr70]*rate_eval.Cr70__n_n_n_Mn67__weak__mo03  +
          + 3*Y[jv66]*rate_eval.V66__n_n_n_Cr63__weak__mo03  +
          + 3*Y[jv65]*rate_eval.V65__n_n_n_Cr62__weak__mo03  +
          + 3*Y[jti65]*rate_eval.Ti65__n_n_n_V62__weak__mo03  +
          + 3*Y[jsc63]*rate_eval.Sc63__n_n_n_Ti60__weak__mo03  +
          + 3*Y[jsc62]*rate_eval.Sc62__n_n_n_Ti59__weak__mo03  +
          + 3*Y[jsc61]*rate_eval.Sc61__n_n_n_Ti58__weak__mo03  +
          + 3*Y[jsc59]*rate_eval.Sc59__n_n_n_Ti56__weak__mo03  +
          + 3*Y[jsc58]*rate_eval.Sc58__n_n_n_Ti55__weak__mo03  +
          + 3*Y[jsc57]*rate_eval.Sc57__n_n_n_Ti54__weak__mo03  +
          + 3*Y[jca60]*rate_eval.Ca60__n_n_n_Sc57__weak__mo03  +
          + 3*Y[jca59]*rate_eval.Ca59__n_n_n_Sc56__weak__mo03  +
          + 3*Y[jca58]*rate_eval.Ca58__n_n_n_Sc55__weak__mo03  +
          + 3*Y[jca57]*rate_eval.Ca57__n_n_n_Sc54__weak__mo03  +
          + 3*Y[jk59]*rate_eval.K59__n_n_n_Ca56__weak__mo03  +
          + 3*Y[jk58]*rate_eval.K58__n_n_n_Ca55__weak__mo03  +
          + 3*Y[jk55]*rate_eval.K55__n_n_n_Ca52__weak__mo03  +
          + 3*Y[jk53]*rate_eval.K53__n_n_n_Ca50__weak__mo03  +
          + 3*Y[jar54]*rate_eval.Ar54__n_n_n_K51__weak__mo03  +
          + 3*Y[jar53]*rate_eval.Ar53__n_n_n_K50__weak__mo03  +
          + 3*Y[jar52]*rate_eval.Ar52__n_n_n_K49__weak__mo03  +
          + 3*Y[jcl50]*rate_eval.Cl50__n_n_n_Ar47__weak__mo03  +
          + 3*Y[js48]*rate_eval.S48__n_n_n_Cl45__weak__mo03  +
          + 3*Y[js47]*rate_eval.S47__n_n_n_Cl44__weak__mo03  +
          + 3*Y[jk56]*rate_eval.K56__n_n_n_Ca53__weak__mo03  +
          + 3*Y[jp44]*rate_eval.P44__n_n_n_S41__weak__mo03  +
          + 3*Y[jsi42]*rate_eval.Si42__n_n_n_P39__weak__mo03  +
          + 3*Y[jal43]*rate_eval.Al43__n_n_n_Si40__weak__mo03  +
          + 3*Y[jal42]*rate_eval.Al42__n_n_n_Si39__weak__mo03  +
          + 3*Y[jal41]*rate_eval.Al41__n_n_n_Si38__weak__mo03  +
          + 3*Y[jal39]*rate_eval.Al39__n_n_n_Si36__weak__mo03  +
          + 3*Y[jal38]*rate_eval.Al38__n_n_n_Si35__weak__mo03  +
          + 3*Y[jal37]*rate_eval.Al37__n_n_n_Si34__weak__mo03  +
          + 3*Y[jmg40]*rate_eval.Mg40__n_n_n_Al37__weak__mo03  +
          + 3*Y[jmg36]*rate_eval.Mg36__n_n_n_Al33__weak__mo03  +
          + 3*Y[jmg35]*rate_eval.Mg35__n_n_n_Al32__weak__mo03  +
          + 3*Y[jna34]*rate_eval.Na34__n_n_n_Mg31__weak__mo03  +
          + 3*Y[jna33]*rate_eval.Na33__n_n_n_Mg30__weak__mo03  +
          + 3*Y[jna32]*rate_eval.Na32__n_n_n_Mg29__weak__mo03  +
          + 3*Y[jne31]*rate_eval.Ne31__n_n_n_Na28__weak__mo03  +
          + 3*Y[jf31]*rate_eval.F31__n_n_n_Ne28__weak__mo03  +
          + 3*Y[jf29]*rate_eval.F29__n_n_n_Ne26__weak__mo03  +
          + 3*Y[jk54]*rate_eval.K54__n_n_n_Ca51__weak__mo03  +
          + 3*Y[jf28]*rate_eval.F28__n_n_n_Ne25__weak__mo03  +
          + 3*Y[jf27]*rate_eval.F27__n_n_n_Ne24__weak__mo03  +
          + 3*Y[jo27]*rate_eval.O27__n_n_n_F24__weak__mo03  +
          -5.00000000000000e-01*rho**2*Y[jn]*Y[jp]**2*rate_eval.n_p_p__p_d  +
          + -2*5.00000000000000e-01*rho**2*Y[jn]**2*Y[jhe4]*rate_eval.n_n_He4__He6  +
          +rho*Y[jt]*Y[jbe7]*rate_eval.t_Be7__n_p_He4_He4  +
          -rho*Y[jn]*Y[jb8]*rate_eval.n_B8__p_He4_He4  +
          +rho*Y[jd]*Y[jli7]*rate_eval.d_Li7__n_He4_He4  +
          +rho*Y[jhe4]*Y[jfe76]*rate_eval.He4_Fe76__n_Ni79  +
          +rho*Y[jhe4]*Y[jfe75]*rate_eval.He4_Fe75__n_Ni78  +
          +rho*Y[jp]*Y[jfe75]*rate_eval.p_Fe75__n_Co75  +
          +rho*Y[jhe4]*Y[jfe74]*rate_eval.He4_Fe74__n_Ni77  +
          +rho*Y[jp]*Y[jfe74]*rate_eval.p_Fe74__n_Co74  +
          + 3*Y[jmg37]*rate_eval.Mg37__n_n_n_Al34__weak__mo03  +
          +rho*Y[jp]*Y[jfe73]*rate_eval.p_Fe73__n_Co73  +
          +rho*Y[jp]*Y[jfe72]*rate_eval.p_Fe72__n_Co72  +
          +rho*Y[jhe4]*Y[jfe71]*rate_eval.He4_Fe71__n_Ni74  +
          +rho*Y[jp]*Y[jfe71]*rate_eval.p_Fe71__n_Co71  +
          +rho*Y[jhe4]*Y[jfe70]*rate_eval.He4_Fe70__n_Ni73  +
          +rho*Y[jp]*Y[jfe70]*rate_eval.p_Fe70__n_Co70  +
          +rho*Y[jp]*Y[jfe69]*rate_eval.p_Fe69__n_Co69  +
          +rho*Y[jhe4]*Y[jfe68]*rate_eval.He4_Fe68__n_Ni71  +
          +rho*Y[jhe4]*Y[jfe64]*rate_eval.He4_Fe64__n_Ni67  +
          +rho*Y[jhe4]*Y[jfe63]*rate_eval.He4_Fe63__n_Ni66  +
          +rho*Y[jp]*Y[jfe61]*rate_eval.p_Fe61__n_Co61  +
          +rho*Y[jhe4]*Y[jfe59]*rate_eval.He4_Fe59__n_Ni62  +
          +rho*Y[jp]*Y[jfe59]*rate_eval.p_Fe59__n_Co59  +
          -rho*Y[jn]*Y[jfe56]*rate_eval.n_Fe56__He4_Cr53  +
          +Y[jo28]*rate_eval.O28__n_O27  +
          -rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__p_Mn55  +
          -rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__Sc41  +
          -rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__p_Mn54  +
          -rho*Y[jn]*Y[jfe53]*rate_eval.n_Fe53__He4_Cr50  +
          -rho*Y[jn]*Y[jfe53]*rate_eval.n_Fe53__p_Mn53  +
          -rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__Al26  +
          -rho*Y[jn]*Y[jfe52]*rate_eval.n_Fe52__He4_Cr49  +
          -rho*Y[jn]*Y[jfe51]*rate_eval.n_Fe51__He4_Cr48  +
          -rho*Y[jn]*Y[jfe50]*rate_eval.n_Fe50__He4_Cr47  +
          -rho*Y[jn]*Y[jfe49]*rate_eval.n_Fe49__He4_Cr46  +
          -rho*Y[jn]*Y[jfe49]*rate_eval.n_Fe49__p_Mn49  +
          -rho*Y[jn]*Y[jfe47]*rate_eval.n_Fe47__He4_Cr44  +
          -rho*Y[jn]*Y[jfe46]*rate_eval.n_Fe46__He4_Cr43  +
          -rho*Y[jn]*Y[jfe46]*rate_eval.n_Fe46__p_Mn46  +
          +rho*Y[jhe4]*Y[jmn73]*rate_eval.He4_Mn73__n_Co76  +
          +rho*Y[jhe4]*Y[jmn72]*rate_eval.He4_Mn72__n_Co75  +
          + 3*Y[jca56]*rate_eval.Ca56__n_n_n_Sc53__weak__mo03  +
          +rho*Y[jhe4]*Y[jmn69]*rate_eval.He4_Mn69__n_Co72  +
          +rho*Y[jhe4]*Y[jmn68]*rate_eval.He4_Mn68__n_Co71  +
          +rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__n_Fe68  +
          +rho*Y[jhe4]*Y[jsi33]*rate_eval.He4_Si33__n_S36  +
          +rho*Y[jp]*Y[jmn66]*rate_eval.p_Mn66__n_Fe66  +
          +rho*Y[jhe4]*Y[jmn65]*rate_eval.He4_Mn65__n_Co68  +
          +rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__n_P44  +
          +rho*Y[jhe4]*Y[jmn60]*rate_eval.He4_Mn60__n_Co63  +
          +rho*Y[jp]*Y[jmn60]*rate_eval.p_Mn60__n_Fe60  +
          +rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__n_Fe57  +
          + 3*Y[js49]*rate_eval.S49__n_n_n_Cl46__weak__mo03  +
          -rho*Y[jn]*Y[jmn52]*rate_eval.n_Mn52__He4_V49  +
          +Y[jar48]*rate_eval.Ar48__n_K47__weak__mp17  +
          -rho*Y[jn]*Y[jmn52]*rate_eval.n_Mn52__p_Cr52  +
          +rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__n_Sc53  +
          -rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__p_Cr51  +
          +rho*Y[jp]*Y[jo22]*rate_eval.p_O22__n_F22  +
          -rho*Y[jn]*Y[jmn50]*rate_eval.n_Mn50__He4_V47  +
          -rho*Y[jn]*Y[jcl37]*rate_eval.n_Cl37__Cl38  +
          -rho*Y[jn]*Y[jmn48]*rate_eval.n_Mn48__He4_V45  +
          -rho*Y[jn]*Y[jne20]*rate_eval.n_Ne20__Ne21  +
          -rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__p_Cr47  +
          -rho*Y[jn]*Y[jmn46]*rate_eval.n_Mn46__He4_V43  +
          -rho*Y[jn]*Y[jmn46]*rate_eval.n_Mn46__p_Cr46  +
          -rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__p_Cr45  +
          +rho*Y[jhe4]*Y[jcr70]*rate_eval.He4_Cr70__n_Fe73  +
          -rho*Y[jn]*Y[jf26]*rate_eval.n_F26__F27  +
          +rho*Y[jhe4]*Y[jcr69]*rate_eval.He4_Cr69__n_Fe72  +
          +rho*Y[jp]*Y[jcr68]*rate_eval.p_Cr68__n_Mn68  +
          +rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__n_Mn67  +
          +rho*Y[jhe4]*Y[jcr66]*rate_eval.He4_Cr66__n_Fe69  +
          +rho*Y[jhe4]*Y[jcr65]*rate_eval.He4_Cr65__n_Fe68  +
          +rho*Y[jp]*Y[jmn72]*rate_eval.p_Mn72__n_Fe72  +
          +rho*Y[jhe4]*Y[jcr64]*rate_eval.He4_Cr64__n_Fe67  +
          +rho*Y[jp]*Y[jo25]*rate_eval.p_O25__n_F25  +
          +rho*Y[jhe4]*Y[jcr63]*rate_eval.He4_Cr63__n_Fe66  +
          +rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__n_Mn63  +
          +rho*Y[jhe4]*Y[jcr62]*rate_eval.He4_Cr62__n_Fe65  +
          +rho*Y[jhe4]*Y[jcr61]*rate_eval.He4_Cr61__n_Fe64  +
          +rho*Y[jhe4]*Y[jcr59]*rate_eval.He4_Cr59__n_Fe62  +
          -rho*Y[jn]*Y[jca50]*rate_eval.n_Ca50__Ca51  +
          +rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__n_Mn59  +
          +rho*Y[jp]*Y[jfe62]*rate_eval.p_Fe62__n_Co62  +
          -rho*Y[jn]*Y[jo18]*rate_eval.n_O18__O19  +
          +rho*Y[jp]*Y[jcr57]*rate_eval.p_Cr57__n_Mn57  +
          +rho*Y[jhe4]*Y[jcr55]*rate_eval.He4_Cr55__n_Fe58  +
          -rho*Y[jn]*Y[jcr55]*rate_eval.n_Cr55__He4_Ti52  +
          +rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__n_P38  +
          -rho*Y[jn]*Y[jcr51]*rate_eval.n_Cr51__He4_Ti48  +
          -rho*Y[jn]*Y[jcr50]*rate_eval.n_Cr50__He4_Ti47  +
          -rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__p_V48  +
          -rho*Y[jn]*Y[jcr46]*rate_eval.n_Cr46__He4_Ti43  +
          -rho*Y[jn]*Y[jb13]*rate_eval.n_B13__B14  +
          +rho*Y[jhe4]*Y[jti59]*rate_eval.He4_Ti59__n_Cr62  +
          +rho*Y[jhe4]*Y[jp44]*rate_eval.He4_P44__n_Cl47  +
          -rho*Y[jn]*Y[jcr45]*rate_eval.n_Cr45__He4_Ti42  +
          -rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__p_V43  +
          -rho*Y[jn]*Y[jcr42]*rate_eval.n_Cr42__He4_Ti39  +
          -rho*Y[jn]*Y[jcr42]*rate_eval.n_Cr42__p_V42  +
          -rho*Y[jn]*Y[jcr41]*rate_eval.n_Cr41__He4_Ti38  +
          +Y[jne26]*rate_eval.Ne26__n_Na25__weak__wc12  +
          +rho*Y[jhe4]*Y[jv67]*rate_eval.He4_V67__n_Mn70  +
          +rho*Y[jp]*Y[jv67]*rate_eval.p_V67__n_Cr67  +
          +rho*Y[jhe4]*Y[jv66]*rate_eval.He4_V66__n_Mn69  +
          +rho*Y[jp]*Y[jv66]*rate_eval.p_V66__n_Cr66  +
          +rho*Y[jhe4]*Y[jv64]*rate_eval.He4_V64__n_Mn67  +
          -rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__p_V49  +
          +rho*Y[jp]*Y[jv63]*rate_eval.p_V63__n_Cr63  +
          +rho*Y[jhe4]*Y[jv62]*rate_eval.He4_V62__n_Mn65  +
          +rho*Y[jhe4]*Y[jv61]*rate_eval.He4_V61__n_Mn64  +
          +rho*Y[jp]*Y[jv61]*rate_eval.p_V61__n_Cr61  +
          +rho*Y[jp]*Y[jp32]*rate_eval.p_P32__n_S32  +
          +rho*Y[jhe4]*Y[jal32]*rate_eval.He4_Al32__n_P35  +
          +rho*Y[jt]*Y[jhe3]*rate_eval.t_He3__n_p_He4  +
          +rho*Y[jp]*Y[jv60]*rate_eval.p_V60__n_Cr60  +
          +rho*Y[jp]*Y[jsi43]*rate_eval.p_Si43__n_P43  +
          +rho*Y[jhe4]*Y[jv59]*rate_eval.He4_V59__n_Mn62  +
          +rho*Y[jhe4]*Y[jv58]*rate_eval.He4_V58__n_Mn61  +
          +rho*Y[jp]*Y[jv58]*rate_eval.p_V58__n_Cr58  +
          +rho*Y[jp]*Y[jv57]*rate_eval.p_V57__n_Cr57  +
          -rho*Y[jn]*Y[jcr53]*rate_eval.n_Cr53__He4_Ti50  +
          +rho*Y[jhe4]*Y[jv56]*rate_eval.He4_V56__n_Mn59  +
          +rho*Y[jhe4]*Y[jv55]*rate_eval.He4_V55__n_Mn58  +
          +rho*Y[jp]*Y[jv55]*rate_eval.p_V55__n_Cr55  +
          +rho*Y[jhe4]*Y[jv54]*rate_eval.He4_V54__n_Mn57  +
          +rho*Y[jp]*Y[jv53]*rate_eval.p_V53__n_Cr53  +
          +rho*Y[jp]*Y[jv52]*rate_eval.p_V52__n_Cr52  +
          +rho*Y[jhe4]*Y[js45]*rate_eval.He4_S45__n_Ar48  +
          -rho*Y[jn]*Y[jmn69]*rate_eval.n_Mn69__Mn70  +
          +rho*Y[jp]*Y[jv50]*rate_eval.p_V50__n_Cr50  +
          -rho*Y[jn]*Y[jv50]*rate_eval.n_V50__p_Ti50  +
          -rho*Y[jn]*Y[jv46]*rate_eval.n_V46__He4_Sc43  +
          -rho*Y[jn]*Y[jv46]*rate_eval.n_V46__p_Ti46  +
          -rho*Y[jn]*Y[jv44]*rate_eval.n_V44__He4_Sc41  +
          -rho*Y[jn]*Y[jv44]*rate_eval.n_V44__p_Ti44  +
          + 2*Y[jcl49]*rate_eval.Cl49__n_n_Ar47__weak__mp17  +
          -rho*Y[jn]*Y[jv43]*rate_eval.n_V43__p_Ti43  +
          +rho*Y[jhe4]*Y[jsi43]*rate_eval.He4_Si43__n_S46  +
          +rho*Y[jhe4]*Y[jne33]*rate_eval.He4_Ne33__n_Mg36  +
          -rho*Y[jn]*Y[jv42]*rate_eval.n_V42__He4_Sc39  +
          -rho*Y[jn]*Y[jv41]*rate_eval.n_V41__He4_Sc38  +
          -rho*Y[jn]*Y[jv40]*rate_eval.n_V40__p_Ti40  +
          +rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__n_Ti53  +
          +rho*Y[jhe4]*Y[jti65]*rate_eval.He4_Ti65__n_Cr68  +
          +rho*Y[jhe4]*Y[jti64]*rate_eval.He4_Ti64__n_Cr67  +
          +rho*Y[jhe4]*Y[jti63]*rate_eval.He4_Ti63__n_Cr66  +
          +rho*Y[jp]*Y[jti63]*rate_eval.p_Ti63__n_V63  +
          +rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__n_V61  +
          +rho*Y[jhe4]*Y[jti60]*rate_eval.He4_Ti60__n_Cr63  +
          -rho*Y[jn]*Y[jo12]*rate_eval.n_O12__O13  +
          +rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__n_V60  +
          +rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__n_V59  +
          +rho*Y[jhe4]*Y[jti58]*rate_eval.He4_Ti58__n_Cr61  +
          +rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__n_V58  +
          +rho*Y[jhe4]*Y[jti55]*rate_eval.He4_Ti55__n_Cr58  +
          +rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__n_V55  +
          +rho*Y[jhe4]*Y[jti54]*rate_eval.He4_Ti54__n_Cr57  +
          +rho*Y[jp]*Y[jti54]*rate_eval.p_Ti54__n_V54  +
          +rho*Y[jhe4]*Y[jti53]*rate_eval.He4_Ti53__n_Cr56  +
          -rho*Y[jn]*Y[jna33]*rate_eval.n_Na33__Na34  +
          +rho*Y[jp]*Y[jti52]*rate_eval.p_Ti52__n_V52  +
          +rho*Y[jhe4]*Y[jti51]*rate_eval.He4_Ti51__n_Cr54  +
          +rho*Y[jp]*Y[jti51]*rate_eval.p_Ti51__n_V51  +
          -rho*Y[jn]*Y[jti51]*rate_eval.n_Ti51__He4_Ca48  +
          -rho*Y[jn]*Y[jti49]*rate_eval.n_Ti49__He4_Ca46  +
          + 2*Y[jsc61]*rate_eval.Sc61__n_n_Ti59__weak__mp17  +
          +rho*Y[jhe4]*Y[jfe73]*rate_eval.He4_Fe73__n_Ni76  +
          +Y[jsc56]*rate_eval.Sc56__n_Ti55__weak__mp17  +
          -rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__p_Sc45  +
          -rho*Y[jn]*Y[jti43]*rate_eval.n_Ti43__He4_Ca40  +
          +rho*Y[jhe4]*Y[jf28]*rate_eval.He4_F28__n_Na31  +
          +rho*Y[jhe4]*Y[jf31]*rate_eval.He4_F31__n_Na34  +
          -rho*Y[jn]*Y[jti41]*rate_eval.n_Ti41__He4_Ca38  +
          -rho*Y[jn]*Y[jti41]*rate_eval.n_Ti41__p_Sc41  +
          -rho*Y[jn]*Y[jk55]*rate_eval.n_K55__K56  +
          +rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__n_Mn55  +
          -rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__p_Sc39  +
          -rho*Y[jn]*Y[jti38]*rate_eval.n_Ti38__He4_Ca35  +
          -rho*Y[jn]*Y[jti38]*rate_eval.n_Ti38__p_Sc38  +
          +Y[jti65]*rate_eval.Ti65__n_V64__weak__mp17  +
          +rho*Y[jhe4]*Y[jsc62]*rate_eval.He4_Sc62__n_V65  +
          +rho*Y[jhe4]*Y[jsc61]*rate_eval.He4_Sc61__n_V64  +
          +rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__n_Ti61  +
          +rho*Y[jhe4]*Y[jsc60]*rate_eval.He4_Sc60__n_V63  +
          + 3*Y[jne34]*rate_eval.Ne34__n_n_n_Na31__weak__mo03  +
          +rho*Y[jp]*Y[jsc60]*rate_eval.p_Sc60__n_Ti60  +
          -rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__p_Mn48  +
          +rho*Y[jhe4]*Y[jsc59]*rate_eval.He4_Sc59__n_V62  +
          -rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__p_Cr53  +
          +rho*Y[jhe4]*Y[jsc58]*rate_eval.He4_Sc58__n_V61  +
          +rho*Y[jp]*Y[jsc58]*rate_eval.p_Sc58__n_Ti58  +
          +rho*Y[jhe4]*Y[jsc57]*rate_eval.He4_Sc57__n_V60  +
          +rho*Y[jhe4]*Y[jsc56]*rate_eval.He4_Sc56__n_V59  +
          +rho*Y[jhe4]*Y[jsc55]*rate_eval.He4_Sc55__n_V58  +
          -rho*Y[jn]*Y[jcr41]*rate_eval.n_Cr41__Cr42  +
          +rho*Y[jhe4]*Y[jsc54]*rate_eval.He4_Sc54__n_V57  +
          +rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__n_Ti54  +
          -rho*Y[jn]*Y[jar36]*rate_eval.n_Ar36__He4_S33  +
          +rho*Y[jhe4]*Y[jsc52]*rate_eval.He4_Sc52__n_V55  +
          +rho*Y[jp]*Y[jsc52]*rate_eval.p_Sc52__n_Ti52  +
          +rho*Y[jhe4]*Y[jsc51]*rate_eval.He4_Sc51__n_V54  +
          +rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__n_Ti50  +
          -rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__p_Ca46  +
          -rho*Y[jn]*Y[jv56]*rate_eval.n_V56__V57  +
          -rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__p_Al24  +
          -rho*Y[jn]*Y[jmg22]*rate_eval.n_Mg22__He4_Ne19  +
          -rho*Y[jn]*Y[jsc45]*rate_eval.n_Sc45__p_Ca45  +
          -rho*Y[jn]*Y[jsc44]*rate_eval.n_Sc44__p_Ca44  +
          -rho*Y[jn]*Y[jsc43]*rate_eval.n_Sc43__He4_K40  +
          -rho*Y[jn]*Y[jsc43]*rate_eval.n_Sc43__p_Ca43  +
          -rho*Y[jn]*Y[jsc42]*rate_eval.n_Sc42__He4_K39  +
          -rho*Y[jn]*Y[jsc42]*rate_eval.n_Sc42__p_Ca42  +
          +rho*Y[jp]*Y[jcr56]*rate_eval.p_Cr56__n_Mn56  +
          -rho*Y[jn]*Y[jsc41]*rate_eval.n_Sc41__He4_K38  +
          -rho*Y[jn]*Y[jsc39]*rate_eval.n_Sc39__He4_K36  +
          -rho*Y[jn]*Y[jti47]*rate_eval.n_Ti47__He4_Ca44  +
          +rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__n_Mg36  +
          -rho*Y[jn]*Y[jsc37]*rate_eval.n_Sc37__He4_K34  +
          + 2*Y[jmg36]*rate_eval.Mg36__n_n_Al34__weak__mp17  +
          -rho*Y[jn]*Y[jsc35]*rate_eval.n_Sc35__He4_K32  +
          -rho*Y[jn]*Y[jsc35]*rate_eval.n_Sc35__p_Ca35  +
          +rho*Y[jp]*Y[jca61]*rate_eval.p_Ca61__n_Sc61  +
          +rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__n_Sc60  +
          -rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__Fe49  +
          +rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__n_Sc59  +
          +rho*Y[jhe4]*Y[jca58]*rate_eval.He4_Ca58__n_Ti61  +
          -rho*Y[jn]*Y[jcr46]*rate_eval.n_Cr46__p_V46  +
          +rho*Y[jp]*Y[jca58]*rate_eval.p_Ca58__n_Sc58  +
          +rho*Y[jp]*Y[jca55]*rate_eval.p_Ca55__n_Sc55  +
          +rho*Y[jhe4]*Y[jca53]*rate_eval.He4_Ca53__n_Ti56  +
          +rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__n_Sc52  +
          +rho*Y[jhe4]*Y[jca51]*rate_eval.He4_Ca51__n_Ti54  +
          -rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__He4_Mg21  +
          +rho*Y[jhe4]*Y[jca47]*rate_eval.He4_Ca47__n_Ti50  +
          +rho*Y[jp]*Y[jca47]*rate_eval.p_Ca47__n_Sc47  +
          +Y[js45]*rate_eval.S45__n_Cl44__weak__wc12  +
          +rho*Y[jhe4]*Y[jca57]*rate_eval.He4_Ca57__n_Ti60  +
          +rho*Y[jhe4]*Y[jca43]*rate_eval.He4_Ca43__n_Ti46  +
          +Y[jna39]*rate_eval.Na39__n_Mg38__weak__mp17  +
          -rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__He4_V40  +
          -rho*Y[jn]*Y[jca40]*rate_eval.n_Ca40__He4_Ar37  +
          +rho*Y[jp]*Y[jp42]*rate_eval.p_P42__n_S42  +
          +rho*Y[jhe4]*Y[jv63]*rate_eval.He4_V63__n_Mn66  +
          -rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__p_K38  +
          +rho*Y[jhe4]*Y[jfe66]*rate_eval.He4_Fe66__n_Ni69  +
          +Y[jca53]*rate_eval.Ca53__n_Sc52__weak__wc12  +
          -rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__He4_Ar34  +
          -rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__p_K37  +
          -rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__p_K36  +
          -rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__p_S35  +
          +rho*Y[jhe4]*Y[jp39]*rate_eval.He4_P39__n_Cl42  +
          -rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__He4_Ar32  +
          -rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__p_K35  +
          -rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__He4_Ar31  +
          -rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__p_K34  +
          +rho*Y[jhe4]*Y[jk57]*rate_eval.He4_K57__n_Sc60  +
          +rho*Y[jp]*Y[jk57]*rate_eval.p_K57__n_Ca57  +
          +rho*Y[jhe4]*Y[jk56]*rate_eval.He4_K56__n_Sc59  +
          +rho*Y[jp]*Y[jk56]*rate_eval.p_K56__n_Ca56  +
          +rho*Y[jhe4]*Y[jk54]*rate_eval.He4_K54__n_Sc57  +
          +rho*Y[jp]*Y[jk54]*rate_eval.p_K54__n_Ca54  +
          +Y[jcl49]*rate_eval.Cl49__n_Ar48__weak__mp17  +
          +rho*Y[jhe4]*Y[jk53]*rate_eval.He4_K53__n_Sc56  +
          -rho*Y[jn]*Y[jo14]*rate_eval.n_O14__O15  +
          +rho*Y[jp]*Y[jk53]*rate_eval.p_K53__n_Ca53  +
          -rho*Y[jn]*Y[jk31]*rate_eval.n_K31__K32  +
          +rho*Y[jhe4]*Y[jk52]*rate_eval.He4_K52__n_Sc55  +
          +rho*Y[jhe4]*Y[jk51]*rate_eval.He4_K51__n_Sc54  +
          +rho*Y[jp]*Y[jk51]*rate_eval.p_K51__n_Ca51  +
          +rho*Y[jhe4]*Y[jcr57]*rate_eval.He4_Cr57__n_Fe60  +
          +rho*Y[jhe4]*Y[jk50]*rate_eval.He4_K50__n_Sc53  +
          +rho*Y[jhe4]*Y[jk48]*rate_eval.He4_K48__n_Sc51  +
          -rho*Y[jn]*Y[jfe50]*rate_eval.n_Fe50__Fe51  +
          -rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__He4_Ti41  +
          +rho*Y[jp]*Y[jk45]*rate_eval.p_K45__n_Ca45  +
          +Y[jne31]*rate_eval.Ne31__n_Na30__weak__mp17  +
          +rho*Y[jp]*Y[jk43]*rate_eval.p_K43__n_Ca43  +
          -rho*Y[jn]*Y[jv45]*rate_eval.n_V45__He4_Sc42  +
          +Y[jhe8]*rate_eval.He8__n_Li7__weak__wc12  +
          +rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__n_Sc45  +
          +rho*Y[jp]*Y[jk40]*rate_eval.p_K40__n_Ca40  +
          -rho*Y[jn]*Y[jk40]*rate_eval.n_K40__He4_Cl37  +
          -rho*Y[jn]*Y[jk40]*rate_eval.n_K40__p_Ar40  +
          -rho*Y[jn]*Y[jk39]*rate_eval.n_K39__p_Ar39  +
          -rho*Y[jn]*Y[jk38]*rate_eval.n_K38__p_Ar38  +
          -rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__He4_S28  +
          -rho*Y[jn]*Y[jk37]*rate_eval.n_K37__He4_Cl34  +
          -rho*Y[jn]*Y[jk36]*rate_eval.n_K36__He4_Cl33  +
          -rho*Y[jn]*Y[jk36]*rate_eval.n_K36__p_Ar36  +
          -rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__He4_K43  +
          -rho*Y[jn]*Y[jk35]*rate_eval.n_K35__p_Ar35  +
          +rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__n_Si39  +
          -rho*Y[jn]*Y[jk33]*rate_eval.n_K33__p_Ar33  +
          -rho*Y[jn]*Y[jk32]*rate_eval.n_K32__He4_Cl29  +
          -rho*Y[jn]*Y[jk32]*rate_eval.n_K32__p_Ar32  +
          -rho*Y[jn]*Y[jk31]*rate_eval.n_K31__p_Ar31  +
          +rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__n_K54  +
          +rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__n_K52  +
          -rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__He4_Ca36  +
          +rho*Y[jp]*Y[jk59]*rate_eval.p_K59__n_Ca59  +
          -rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__He4_Ar33  +
          + 3*Y[jv67]*rate_eval.V67__n_n_n_Cr64__weak__mo03  +
          +rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__n_Na23  +
          +rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__n_K48  +
          +rho*Y[jhe4]*Y[jar46]*rate_eval.He4_Ar46__n_Ca49  +
          +rho*Y[jp]*Y[jf28]*rate_eval.p_F28__n_Ne28  +
          -rho*Y[jn]*Y[jd]*rate_eval.n_d__t  +
          +rho*Y[jhe4]*Y[jsi35]*rate_eval.He4_Si35__n_S38  +
          +rho*Y[jp]*Y[jar44]*rate_eval.p_Ar44__n_K44  +
          +rho*Y[jhe4]*Y[jar43]*rate_eval.He4_Ar43__n_Ca46  +
          -rho*Y[jn]*Y[jv39]*rate_eval.n_V39__V40  +
          +rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__n_K43  +
          +rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__n_K41  +
          -rho*Y[jn]*Y[jmn52]*rate_eval.n_Mn52__Mn53  +
          +rho*Y[jhe4]*Y[jmn62]*rate_eval.He4_Mn62__n_Co65  +
          -rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__He4_V46  +
          -rho*Y[jn]*Y[jar37]*rate_eval.n_Ar37__p_Cl37  +
          -rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__He4_S32  +
          -rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__p_Cl35  +
          -rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__p_Cl34  +
          -rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__p_Cl33  +
          -rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__He4_S29  +
          -rho*Y[jn]*Y[jfe75]*rate_eval.n_Fe75__Fe76  +
          -rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__p_Cl32  +
          -rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__p_Cl31  +
          -rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__He4_S27  +
          -rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__p_Cl30  +
          -rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__He4_S26  +
          -rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__p_Cl29  +
          +rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__n_Ar52  +
          +rho*Y[jhe4]*Y[jcl51]*rate_eval.He4_Cl51__n_K54  +
          -rho*Y[jn]*Y[jti58]*rate_eval.n_Ti58__Ti59  +
          +rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__n_Ar50  +
          -rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__Ar35  +
          +rho*Y[jp]*Y[jb12]*rate_eval.p_B12__n_C12  +
          +rho*Y[jhe4]*Y[jcl49]*rate_eval.He4_Cl49__n_K52  +
          +rho*Y[jhe4]*Y[jca50]*rate_eval.He4_Ca50__n_Ti53  +
          +rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__n_Ar48  +
          +rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__n_V62  +
          +rho*Y[jhe4]*Y[jcl47]*rate_eval.He4_Cl47__n_K50  +
          +rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__n_Ar45  +
          +rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__n_Fe61  +
          +rho*Y[jhe4]*Y[jcl42]*rate_eval.He4_Cl42__n_K45  +
          +rho*Y[jp]*Y[js47]*rate_eval.p_S47__n_Cl47  +
          -rho*Y[jn]*Y[jfe72]*rate_eval.n_Fe72__Fe73  +
          +rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__n_K44  +
          +rho*Y[jhe4]*Y[jcl40]*rate_eval.He4_Cl40__n_K43  +
          +rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__n_Ar40  +
          -rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__p_S36  +
          -rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__He4_P32  +
          -rho*Y[jn]*Y[jc11]*rate_eval.n_C11__He4_He4_He4  +
          -rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__He4_P31  +
          + 2*Y[jp42]*rate_eval.P42__n_n_S40__weak__mp17  +
          -rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__p_S34  +
          -rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__He4_P30  +
          -rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__p_S33  +
          +rho*Y[jhe4]*Y[js48]*rate_eval.He4_S48__n_Ar51  +
          -rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__p_S31  +
          -rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__He4_P26  +
          -rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__p_S29  +
          -rho*Y[jn]*Y[jv49]*rate_eval.n_V49__p_Ti49  +
          -rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__He4_P25  +
          +rho*Y[jd]*Y[jli8]*rate_eval.d_Li8__n_Be9  +
          -rho*Y[jn]*Y[jcr57]*rate_eval.n_Cr57__Cr58  +
          +rho*Y[jp]*Y[js49]*rate_eval.p_S49__n_Cl49  +
          +rho*Y[jhe4]*Y[jmg38]*rate_eval.He4_Mg38__n_Si41  +
          -rho*Y[jn]*Y[jca52]*rate_eval.n_Ca52__Ca53  +
          +rho*Y[jp]*Y[js48]*rate_eval.p_S48__n_Cl48  +
          +rho*Y[jp]*Y[js46]*rate_eval.p_S46__n_Cl46  +
          +rho*Y[jhe4]*Y[js43]*rate_eval.He4_S43__n_Ar46  +
          +rho*Y[jp]*Y[jmn64]*rate_eval.p_Mn64__n_Fe64  +
          +rho*Y[jhe4]*Y[jmn67]*rate_eval.He4_Mn67__n_Co70  +
          +rho*Y[jhe4]*Y[js42]*rate_eval.He4_S42__n_Ar45  +
          +rho*Y[jhe4]*Y[js41]*rate_eval.He4_S41__n_Ar44  +
          +rho*Y[jhe4]*Y[jsc63]*rate_eval.He4_Sc63__n_V66  +
          +rho*Y[jp]*Y[js40]*rate_eval.p_S40__n_Cl40  +
          +rho*Y[jhe4]*Y[js38]*rate_eval.He4_S38__n_Ar41  +
          +rho*Y[jp]*Y[js38]*rate_eval.p_S38__n_Cl38  +
          +rho*Y[jhe4]*Y[js37]*rate_eval.He4_S37__n_Ar40  +
          +rho*Y[jhe4]*Y[jk49]*rate_eval.He4_K49__n_Sc52  +
          +rho*Y[jp]*Y[js37]*rate_eval.p_S37__n_Cl37  +
          +rho*Y[jp]*Y[jk49]*rate_eval.p_K49__n_Ca49  +
          +rho*Y[jhe4]*Y[jp34]*rate_eval.He4_P34__n_Cl37  +
          +rho*Y[jhe4]*Y[js35]*rate_eval.He4_S35__n_Ar38  +
          -rho*Y[jn]*Y[jsi43]*rate_eval.n_Si43__Si44  +
          +rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__n_Ti57  +
          -rho*Y[jn]*Y[js35]*rate_eval.n_S35__He4_Si32  +
          -rho*Y[jn]*Y[jal36]*rate_eval.n_Al36__Al37  +
          -rho*Y[jn]*Y[js33]*rate_eval.n_S33__He4_Si30  +
          -rho*Y[jn]*Y[js30]*rate_eval.n_S30__He4_Si27  +
          -rho*Y[jn]*Y[js30]*rate_eval.n_S30__p_P30  +
          + 3*Y[jcl49]*rate_eval.Cl49__n_n_n_Ar46__weak__mo03  +
          -rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__He4_Ti40  +
          -rho*Y[jn]*Y[js28]*rate_eval.n_S28__He4_Si25  +
          -rho*Y[jn]*Y[js26]*rate_eval.n_S26__He4_Si23  +
          +rho*Y[jhe4]*Y[jp47]*rate_eval.He4_P47__n_Cl50  +
          +rho*Y[jp]*Y[jp47]*rate_eval.p_P47__n_S47  +
          +rho*Y[jp]*Y[jp45]*rate_eval.p_P45__n_S45  +
          -rho*Y[jn]*Y[jsi33]*rate_eval.n_Si33__Si34  +
          +rho*Y[jhe4]*Y[jp43]*rate_eval.He4_P43__n_Cl46  +
          +rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__n_P41  +
          +rho*Y[jp]*Y[jp43]*rate_eval.p_P43__n_S43  +
          +rho*Y[jp]*Y[jsc55]*rate_eval.p_Sc55__n_Ti55  +
          +Y[jne27]*rate_eval.Ne27__n_Na26__weak__wc12  +
          +rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__n_Cl44  +
          +rho*Y[jp]*Y[jp38]*rate_eval.p_P38__n_S38  +
          -rho*Y[jn]*Y[js33]*rate_eval.n_S33__p_P33  +
          +rho*Y[jhe4]*Y[jp37]*rate_eval.He4_P37__n_Cl40  +
          -rho*Y[jn]*Y[jti54]*rate_eval.n_Ti54__Ti55  +
          +rho*Y[jp]*Y[jp36]*rate_eval.p_P36__n_S36  +
          +rho*Y[jp]*Y[jmn69]*rate_eval.p_Mn69__n_Fe69  +
          +rho*Y[jp]*Y[jp34]*rate_eval.p_P34__n_S34  +
          +rho*Y[jp]*Y[jca56]*rate_eval.p_Ca56__n_Sc56  +
          -rho*Y[jn]*Y[jp32]*rate_eval.n_P32__p_Si32  +
          -rho*Y[jn]*Y[jf25]*rate_eval.n_F25__F26  +
          + 3*Y[jmg39]*rate_eval.Mg39__n_n_n_Al36__weak__mo03  +
          +rho*Y[jhe4]*Y[jk55]*rate_eval.He4_K55__n_Sc58  +
          -rho*Y[jn]*Y[jv47]*rate_eval.n_V47__He4_Sc44  +
          -rho*Y[jn]*Y[jp28]*rate_eval.n_P28__p_Si28  +
          -rho*Y[jn]*Y[jp27]*rate_eval.n_P27__He4_Al24  +
          -rho*Y[jn]*Y[jp27]*rate_eval.n_P27__p_Si27  +
          -rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__He4_Ti44  +
          -rho*Y[jn]*Y[jp26]*rate_eval.n_P26__He4_Al23  +
          -rho*Y[jn]*Y[jp26]*rate_eval.n_P26__p_Si26  +
          -rho*Y[jn]*Y[jp24]*rate_eval.n_P24__He4_Al21  +
          -rho*Y[jn]*Y[jp24]*rate_eval.n_P24__p_Si24  +
          +rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__n_P45  +
          +rho*Y[jhe4]*Y[jsi44]*rate_eval.He4_Si44__n_S47  +
          +rho*Y[jhe4]*Y[jp42]*rate_eval.He4_P42__n_Cl45  +
          +rho*Y[jhe4]*Y[jsi42]*rate_eval.He4_Si42__n_S45  +
          +rho*Y[jp]*Y[jsi42]*rate_eval.p_Si42__n_P42  +
          -rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__p_Cr54  +
          +rho*Y[jhe4]*Y[jsi40]*rate_eval.He4_Si40__n_S43  +
          +rho*Y[jhe4]*Y[jsi39]*rate_eval.He4_Si39__n_S42  +
          +rho*Y[jp]*Y[jsi39]*rate_eval.p_Si39__n_P39  +
          +rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__n_Ti62  +
          -rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__p_V47  +
          +rho*Y[jhe4]*Y[jsi38]*rate_eval.He4_Si38__n_S41  +
          +rho*Y[jhe4]*Y[jsi37]*rate_eval.He4_Si37__n_S40  +
          +rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__n_P37  +
          +rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__n_P33  +
          +rho*Y[jhe4]*Y[jv57]*rate_eval.He4_V57__n_Mn60  +
          -rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__He4_V48  +
          +Y[jb18]*rate_eval.B18__n_B17  +
          -rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__He4_Ca34  +
          +rho*Y[jhe4]*Y[jti61]*rate_eval.He4_Ti61__n_Cr64  +
          -rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__Ar36  +
          -rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__p_Al25  +
          + 2*Y[jv64]*rate_eval.V64__n_n_Cr62__weak__mp17  +
          +rho*Y[jhe4]*Y[jar42]*rate_eval.He4_Ar42__n_Ca45  +
          -rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__p_Al23  +
          -rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__He4_Mg19  +
          -rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__p_Al22  +
          +rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__n_Si43  +
          +rho*Y[jhe4]*Y[jal42]*rate_eval.He4_Al42__n_P45  +
          +rho*Y[jhe4]*Y[jal40]*rate_eval.He4_Al40__n_P43  +
          +rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__n_Si40  +
          +rho*Y[jp]*Y[jv59]*rate_eval.p_V59__n_Cr59  +
          -rho*Y[jn]*Y[jv48]*rate_eval.n_V48__p_Ti48  +
          +rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__n_P39  +
          +rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__n_Si36  +
          +rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__n_Si41  +
          +rho*Y[jp]*Y[jv64]*rate_eval.p_V64__n_Cr64  +
          +rho*Y[jhe4]*Y[jal35]*rate_eval.He4_Al35__n_P38  +
          +rho*Y[jhe4]*Y[jal34]*rate_eval.He4_Al34__n_P37  +
          +rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__n_Si34  +
          +rho*Y[jhe4]*Y[jal33]*rate_eval.He4_Al33__n_P36  +
          + 2*Y[jsi43]*rate_eval.Si43__n_n_P41__weak__mp17  +
          +rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__n_Si33  +
          +rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__n_Na26  +
          +rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__n_Si32  +
          -rho*Y[jn]*Y[jcr66]*rate_eval.n_Cr66__Cr67  +
          +rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__n_P34  +
          +rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__n_Si30  +
          +rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__n_P32  +
          +rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__n_Si29  +
          +rho*Y[jhe4]*Y[jal37]*rate_eval.He4_Al37__n_P40  +
          -rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__p_Sc44  +
          -rho*Y[jn]*Y[jti59]*rate_eval.n_Ti59__Ti60  +
          -rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__He4_Na23  +
          -rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__p_Mg26  +
          -rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__p_Mg25  +
          + 2*Y[jf31]*rate_eval.F31__n_n_Ne29__weak__mp17  +
          -rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__He4_Na20  +
          -rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__He4_Na19  +
          + 3*Y[jo28]*rate_eval.O28__n_n_n_F25__weak__mo03  +
          -rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__p_Mg22  +
          -rho*Y[jn]*Y[jsc48]*rate_eval.n_Sc48__p_Ca48  +
          +rho*Y[jhe4]*Y[jmg40]*rate_eval.He4_Mg40__n_Si43  +
          +rho*Y[jp]*Y[jmg40]*rate_eval.p_Mg40__n_Al40  +
          +rho*Y[jhe4]*Y[jmg39]*rate_eval.He4_Mg39__n_Si42  +
          +rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__n_Al39  +
          +rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__n_Al38  +
          +rho*Y[jhe4]*Y[jmg37]*rate_eval.He4_Mg37__n_Si40  +
          +rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__n_Si38  +
          +rho*Y[jhe4]*Y[jmg35]*rate_eval.He4_Mg35__n_Si38  +
          +rho*Y[jhe4]*Y[jmg34]*rate_eval.He4_Mg34__n_Si37  +
          +rho*Y[jp]*Y[jti53]*rate_eval.p_Ti53__n_V53  +
          +rho*Y[jhe4]*Y[jmg32]*rate_eval.He4_Mg32__n_Si35  +
          -rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__He4_V44  +
          -rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__p_Ne19  +
          +rho*Y[jp]*Y[jmn59]*rate_eval.p_Mn59__n_Fe59  +
          +rho*Y[jhe4]*Y[jmg30]*rate_eval.He4_Mg30__n_Si33  +
          +rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__n_Al30  +
          -rho*Y[jn]*Y[jp29]*rate_eval.n_P29__He4_Al26  +
          +rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__n_Ar46  +
          +rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__n_Al29  +
          +rho*Y[jp]*Y[jcr60]*rate_eval.p_Cr60__n_Mn60  +
          -rho*Y[jn]*Y[js29]*rate_eval.n_S29__He4_Si26  +
          -rho*Y[jn]*Y[jk58]*rate_eval.n_K58__K59  +
          +rho*Y[jhe4]*Y[jne23]*rate_eval.He4_Ne23__n_Mg26  +
          +rho*Y[jhe4]*Y[jmg27]*rate_eval.He4_Mg27__n_Si30  +
          +rho*Y[jhe4]*Y[jo23]*rate_eval.He4_O23__n_Ne26  +
          +rho*Y[jhe4]*Y[jmg26]*rate_eval.He4_Mg26__n_Si29  +
          -rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__He4_Cr51  +
          -rho*Y[jn]*Y[jmn68]*rate_eval.n_Mn68__Mn69  +
          -rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__He4_Cr52  +
          +rho*Y[jhe4]*Y[jmg25]*rate_eval.He4_Mg25__n_Si28  +
          -rho*Y[jn]*Y[jcl43]*rate_eval.n_Cl43__Cl44  +
          -rho*Y[jn]*Y[jmg23]*rate_eval.n_Mg23__C12_C12  +
          -rho*Y[jn]*Y[jmg23]*rate_eval.n_Mg23__He4_Ne20  +
          -rho*Y[jn]*Y[jfe66]*rate_eval.n_Fe66__Fe67  +
          -rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__p_S30  +
          -rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__He4_Ne18  +
          + 2*Y[jca57]*rate_eval.Ca57__n_n_Sc55__weak__mp17  +
          +rho*Y[jhe4]*Y[jna36]*rate_eval.He4_Na36__n_Al39  +
          -rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__p_Na20  +
          +rho*Y[jp]*Y[jna39]*rate_eval.p_Na39__n_Mg39  +
          +Y[jna27]*rate_eval.Na27__n_Mg26__weak__wc12  +
          +rho*Y[jhe4]*Y[jna38]*rate_eval.He4_Na38__n_Al41  +
          +rho*Y[jhe4]*Y[jna35]*rate_eval.He4_Na35__n_Al38  +
          +rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__n_Mg35  +
          +Y[jmg37]*rate_eval.Mg37__n_Al36__weak__mp17  +
          -rho*Y[jn]*Y[jv43]*rate_eval.n_V43__He4_Sc40  +
          +rho*Y[jhe4]*Y[jna34]*rate_eval.He4_Na34__n_Al37  +
          +rho*Y[jhe4]*Y[jv60]*rate_eval.He4_V60__n_Mn63  +
          +rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__n_Mg33  +
          -rho*Y[jn]*Y[jn18]*rate_eval.n_N18__N19  +
          -rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__p_Cr43  +
          +rho*Y[jhe4]*Y[jna31]*rate_eval.He4_Na31__n_Al34  +
          +rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__n_Mg31  +
          +rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__n_Co66  +
          -rho*Y[jn]*Y[js31]*rate_eval.n_S31__p_P31  +
          +rho*Y[jhe4]*Y[jna28]*rate_eval.He4_Na28__n_Al31  +
          +rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__n_Mg28  +
          +rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__n_Mg27  +
          -rho*Y[jn]*Y[jar39]*rate_eval.n_Ar39__He4_S36  +
          +rho*Y[jhe4]*Y[jna26]*rate_eval.He4_Na26__n_Al29  +
          +rho*Y[jp]*Y[jsc49]*rate_eval.p_Sc49__n_Ti49  +
          + 2*Y[jar52]*rate_eval.Ar52__n_n_K50__weak__mp17  +
          -rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__p_Sc42  +
          +rho*Y[jp]*Y[jfe67]*rate_eval.p_Fe67__n_Co67  +
          -rho*Y[jn]*Y[jfe50]*rate_eval.n_Fe50__p_Mn50  +
          -rho*Y[jn]*Y[jsc43]*rate_eval.n_Sc43__Sc44  +
          -rho*Y[jn]*Y[js26]*rate_eval.n_S26__p_P26  +
          -rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__He4_F18  +
          -rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__He4_F17  +
          -rho*Y[jn]*Y[jv40]*rate_eval.n_V40__He4_Sc37  +
          +rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__n_Na34  +
          -rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__He4_V51  +
          -rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__He4_P29  +
          +rho*Y[jhe4]*Y[js46]*rate_eval.He4_S46__n_Ar49  +
          +rho*Y[jhe4]*Y[jne31]*rate_eval.He4_Ne31__n_Mg34  +
          +rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__n_Si35  +
          +rho*Y[jhe4]*Y[jne30]*rate_eval.He4_Ne30__n_Mg33  +
          -rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__p_Ca40  +
          +rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__n_Na29  +
          +rho*Y[jhe4]*Y[jne28]*rate_eval.He4_Ne28__n_Mg31  +
          +rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__n_Na28  +
          +rho*Y[jhe4]*Y[jne27]*rate_eval.He4_Ne27__n_Mg30  +
          +rho*Y[jp]*Y[jne27]*rate_eval.p_Ne27__n_Na27  +
          +rho*Y[jhe4]*Y[js39]*rate_eval.He4_S39__n_Ar42  +
          +rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__n_Na25  +
          +rho*Y[jhe4]*Y[jne24]*rate_eval.He4_Ne24__n_Mg27  +
          +rho*Y[jp]*Y[jne24]*rate_eval.p_Ne24__n_Na24  +
          -rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__He4_Ca42  +
          +rho*Y[jhe4]*Y[jca61]*rate_eval.He4_Ca61__n_Ti64  +
          +rho*Y[jp]*Y[jne23]*rate_eval.p_Ne23__n_Na23  +
          -rho*Y[jn]*Y[jcl38]*rate_eval.n_Cl38__He4_P35  +
          +rho*Y[jhe4]*Y[jne21]*rate_eval.He4_Ne21__n_Mg24  +
          -rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__Si28  +
          -rho*Y[jn]*Y[jna30]*rate_eval.n_Na30__Na31  +
          +rho*Y[jp]*Y[jv54]*rate_eval.p_V54__n_Cr54  +
          -rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__He4_Mg22  +
          -rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__He4_O15  +
          -rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__p_F18  +
          -rho*Y[jn]*Y[jbe7]*rate_eval.n_Be7__He4_He4  +
          -rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__p_F16  +
          +rho*Y[jhe4]*Y[jar53]*rate_eval.He4_Ar53__n_Ca56  +
          +rho*Y[jp]*Y[jf31]*rate_eval.p_F31__n_Ne31  +
          +rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__n_K45  +
          +rho*Y[jhe4]*Y[jf29]*rate_eval.He4_F29__n_Na32  +
          +rho*Y[jhe4]*Y[jf27]*rate_eval.He4_F27__n_Na30  +
          +rho*Y[jp]*Y[jf27]*rate_eval.p_F27__n_Ne27  +
          +rho*Y[jhe4]*Y[jf26]*rate_eval.He4_F26__n_Na29  +
          +rho*Y[jp]*Y[jf26]*rate_eval.p_F26__n_Ne26  +
          -rho*Y[jn]*Y[js30]*rate_eval.n_S30__S31  +
          +rho*Y[jp]*Y[jf25]*rate_eval.p_F25__n_Ne25  +
          +rho*Y[jhe4]*Y[jf24]*rate_eval.He4_F24__n_Na27  +
          +rho*Y[jp]*Y[jf24]*rate_eval.p_F24__n_Ne24  +
          +rho*Y[jp]*Y[jf22]*rate_eval.p_F22__n_Ne22  +
          +Y[jcl48]*rate_eval.Cl48__n_Ar47__weak__mp17  +
          +rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__n_Na24  +
          -rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__p_Al26  +
          +rho*Y[jp]*Y[jo21]*rate_eval.p_O21__n_F21  +
          + 3*Y[jal40]*rate_eval.Al40__n_n_n_Si37__weak__mo03  +
          -rho*Y[jn]*Y[jf18]*rate_eval.n_F18__He4_N15  +
          -rho*Y[jn]*Y[jf15]*rate_eval.n_F15__He4_N12  +
          + 3*Y[jfe76]*rate_eval.Fe76__n_n_n_Co73__weak__mo03  +
          -rho*Y[jn]*Y[jf14]*rate_eval.n_F14__He4_N11  +
          -rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__p_K33  +
          +rho*Y[jhe4]*Y[jo28]*rate_eval.He4_O28__n_Ne31  +
          +rho*Y[jhe4]*Y[jo26]*rate_eval.He4_O26__n_Ne29  +
          +rho*Y[jp]*Y[jo26]*rate_eval.p_O26__n_F26  +
          +rho*Y[jhe4]*Y[jo24]*rate_eval.He4_O24__n_Ne27  +
          +rho*Y[jp]*Y[jo24]*rate_eval.p_O24__n_F24  +
          +Y[jna31]*rate_eval.Na31__n_Mg30__weak__wc17  +
          +rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__n_Na33  +
          +rho*Y[jhe4]*Y[jo22]*rate_eval.He4_O22__n_Ne25  +
          +rho*Y[jhe4]*Y[jar52]*rate_eval.He4_Ar52__n_Ca55  +
          +rho*Y[jp]*Y[jti57]*rate_eval.p_Ti57__n_V57  +
          +rho*Y[jp]*Y[jo20]*rate_eval.p_O20__n_F20  +
          +rho*Y[jhe4]*Y[jo19]*rate_eval.He4_O19__n_Ne22  +
          +rho*Y[jp]*Y[jcr62]*rate_eval.p_Cr62__n_Mn62  +
          +rho*Y[jhe4]*Y[jo17]*rate_eval.He4_O17__n_Ne20  +
          +rho*Y[jhe4]*Y[jne26]*rate_eval.He4_Ne26__n_Mg29  +
          +5.00000000000000e-01*rho*Y[jo16]**2*rate_eval.O16_O16__n_S31  +
          +rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__n_P31  +
          +rho*Y[jp]*Y[jk48]*rate_eval.p_K48__n_Ca48  +
          -rho*Y[jn]*Y[jk33]*rate_eval.n_K33__He4_Cl30  +
          -rho*Y[jn]*Y[jo14]*rate_eval.n_O14__He4_C11  +
          -rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__He4_Ar30  +
          -rho*Y[jn]*Y[jo13]*rate_eval.n_O13__He4_C10  +
          -rho*Y[jn]*Y[jo13]*rate_eval.n_O13__p_N13  +
          -rho*Y[jn]*Y[jo12]*rate_eval.n_O12__p_N12  +
          -rho*Y[jn]*Y[jsc37]*rate_eval.n_Sc37__p_Ca37  +
          -rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__He4_Ne16  +
          +rho*Y[jhe4]*Y[jar41]*rate_eval.He4_Ar41__n_Ca44  +
          -rho*Y[jn]*Y[jn14]*rate_eval.n_N14__p_C14  +
          +rho*Y[jhe4]*Y[jc15]*rate_eval.He4_C15__n_O18  +
          +rho*Y[jp]*Y[jc15]*rate_eval.p_C15__n_N15  +
          +rho*Y[jhe4]*Y[jcl50]*rate_eval.He4_Cl50__n_K53  +
          +rho*Y[jhe4]*Y[jsi31]*rate_eval.He4_Si31__n_S34  +
          -rho*Y[jn]*Y[jv39]*rate_eval.n_V39__p_Ti39  +
          +rho*Y[jhe4]*Y[jcl45]*rate_eval.He4_Cl45__n_K48  +
          +rho*Y[jhe4]*Y[jc13]*rate_eval.He4_C13__n_O16  +
          +rho*Y[jd]*Y[jc13]*rate_eval.d_C13__n_N14  +
          +rho*Y[jp]*Y[jk44]*rate_eval.p_K44__n_Ca44  +
          -rho*Y[jn]*Y[jmn50]*rate_eval.n_Mn50__Mn51  +
          -rho*Y[jn]*Y[jc11]*rate_eval.n_C11__p_B11  +
          +rho*Y[jhe4]*Y[jb13]*rate_eval.He4_B13__n_N16  +
          -rho*Y[jn]*Y[jk35]*rate_eval.n_K35__He4_Cl32  +
          +rho*Y[jhe4]*Y[jb12]*rate_eval.He4_B12__n_N15  +
          +Y[js44]*rate_eval.S44__n_Cl43__weak__wc12  +
          +rho*Y[jhe4]*Y[jli8]*rate_eval.He4_Li8__n_B11  +
          -rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__He4_Ca39  +
          -rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__He4_Cr45  +
          -rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__He4_V50  +
          + 3*Y[jp45]*rate_eval.P45__n_n_n_S42__weak__mo03  +
          -rho*Y[jn]*Y[jmn65]*rate_eval.n_Mn65__Mn66  +
          -rho*Y[jn]*Y[jli6]*rate_eval.n_Li6__He4_t  +
          + 3*Y[jna35]*rate_eval.Na35__n_n_n_Mg32__weak__mo03  +
          -rho*Y[jn]*Y[jhe3]*rate_eval.n_He3__p_t  +
          +rho*Y[jd]*Y[jt]*rate_eval.d_t__n_He4  +
          -rho*Y[jn]*Y[jcr61]*rate_eval.n_Cr61__Cr62  +
          -rho*Y[jn]*Y[jv50]*rate_eval.n_V50__He4_Sc47  +
          +rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__n_Al31  +
          -rho*Y[jn]*Y[jfe71]*rate_eval.n_Fe71__Fe72  +
          -rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__Cl29  +
          + 2*Y[jsc62]*rate_eval.Sc62__n_n_Ti60__weak__mp17  +
          -rho*Y[jn]*Y[jfe70]*rate_eval.n_Fe70__Fe71  +
          -rho*Y[jn]*Y[jf16]*rate_eval.n_F16__p_O16  +
          -rho*Y[jn]*Y[jmn62]*rate_eval.n_Mn62__Mn63  +
          -rho*Y[jn]*Y[jfe69]*rate_eval.n_Fe69__Fe70  +
          -rho*Y[jn]*Y[jfe68]*rate_eval.n_Fe68__Fe69  +
          -rho*Y[jn]*Y[jfe67]*rate_eval.n_Fe67__Fe68  +
          -rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__p_Ne21  +
          -rho*Y[jn]*Y[jfe65]*rate_eval.n_Fe65__Fe66  +
          +rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__n_V51  +
          -rho*Y[jn]*Y[jfe63]*rate_eval.n_Fe63__Fe64  +
          -rho*Y[jn]*Y[jfe62]*rate_eval.n_Fe62__Fe63  +
          -rho*Y[jn]*Y[js29]*rate_eval.n_S29__p_P29  +
          +rho*Y[jhe4]*Y[jp36]*rate_eval.He4_P36__n_Cl39  +
          -rho*Y[jn]*Y[jfe58]*rate_eval.n_Fe58__Fe59  +
          -rho*Y[jn]*Y[jfe57]*rate_eval.n_Fe57__Fe58  +
          -rho*Y[jn]*Y[jfe56]*rate_eval.n_Fe56__Fe57  +
          -rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__Fe55  +
          +rho*Y[jp]*Y[jsi36]*rate_eval.p_Si36__n_P36  +
          +rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__n_Na32  +
          -rho*Y[jn]*Y[jfe49]*rate_eval.n_Fe49__Fe50  +
          -rho*Y[jn]*Y[jne30]*rate_eval.n_Ne30__Ne31  +
          +rho*Y[jhe4]*Y[jo25]*rate_eval.He4_O25__n_Ne28  +
          -rho*Y[jn]*Y[jfe47]*rate_eval.n_Fe47__Fe48  +
          -rho*Y[jn]*Y[jcr55]*rate_eval.n_Cr55__Cr56  +
          -rho*Y[jn]*Y[jmn72]*rate_eval.n_Mn72__Mn73  +
          -rho*Y[jn]*Y[jmn71]*rate_eval.n_Mn71__Mn72  +
          -rho*Y[jn]*Y[jmn70]*rate_eval.n_Mn70__Mn71  +
          +rho*Y[jp]*Y[jmn73]*rate_eval.p_Mn73__n_Fe73  +
          -rho*Y[jn]*Y[jmn67]*rate_eval.n_Mn67__Mn68  +
          -rho*Y[jn]*Y[jmn63]*rate_eval.n_Mn63__Mn64  +
          +rho*Y[jp]*Y[jne33]*rate_eval.p_Ne33__n_Na33  +
          -rho*Y[jn]*Y[jfe51]*rate_eval.n_Fe51__p_Mn51  +
          -rho*Y[jn]*Y[jmn60]*rate_eval.n_Mn60__Mn61  +
          -rho*Y[jn]*Y[jmn59]*rate_eval.n_Mn59__Mn60  +
          -rho*Y[jn]*Y[jmn58]*rate_eval.n_Mn58__Mn59  +
          -rho*Y[jn]*Y[jmn56]*rate_eval.n_Mn56__Mn57  +
          +rho*Y[jp]*Y[jk42]*rate_eval.p_K42__n_Ca42  +
          -rho*Y[jn]*Y[jmn55]*rate_eval.n_Mn55__Mn56  +
          +rho*Y[jp]*Y[jfe64]*rate_eval.p_Fe64__n_Co64  +
          -rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__Mn50  +
          -rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__Mn45  +
          -rho*Y[jn]*Y[jcr69]*rate_eval.n_Cr69__Cr70  +
          -rho*Y[jn]*Y[jcl40]*rate_eval.n_Cl40__Cl41  +
          +Y[jo25]*rate_eval.O25__n_F24__weak__mp17  +
          -rho*Y[jn]*Y[jcr62]*rate_eval.n_Cr62__Cr63  +
          +rho*Y[jp]*Y[jsc48]*rate_eval.p_Sc48__n_Ti48  +
          -rho*Y[jn]*Y[jca43]*rate_eval.n_Ca43__He4_Ar40  +
          -rho*Y[jn]*Y[jfe51]*rate_eval.n_Fe51__Fe52  +
          -rho*Y[jn]*Y[jcr60]*rate_eval.n_Cr60__Cr61  +
          -rho*Y[jn]*Y[jcr59]*rate_eval.n_Cr59__Cr60  +
          -rho*Y[jn]*Y[jcr56]*rate_eval.n_Cr56__Cr57  +
          -rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__p_Cr49  +
          -rho*Y[jn]*Y[jcr53]*rate_eval.n_Cr53__Cr54  +
          -rho*Y[jn]*Y[jo17]*rate_eval.n_O17__O18  +
          +rho*Y[jhe4]*Y[jp40]*rate_eval.He4_P40__n_Cl43  +
          -rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__Cr49  +
          -rho*Y[jn]*Y[jne19]*rate_eval.n_Ne19__He4_O16  +
          -rho*Y[jn]*Y[jcr46]*rate_eval.n_Cr46__Cr47  +
          -rho*Y[jn]*Y[jcr45]*rate_eval.n_Cr45__Cr46  +
          -rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__Cr45  +
          -rho*Y[jn]*Y[jsc55]*rate_eval.n_Sc55__Sc56  +
          -rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__Cr44  +
          -rho*Y[jn]*Y[jmg27]*rate_eval.n_Mg27__Mg28  +
          -rho*Y[jn]*Y[jal37]*rate_eval.n_Al37__Al38  +
          +rho*Y[jp]*Y[jk58]*rate_eval.p_K58__n_Ca58  +
          -rho*Y[jn]*Y[jv62]*rate_eval.n_V62__V63  +
          +Y[jna36]*rate_eval.Na36__n_Mg35__weak__mp17  +
          -rho*Y[jn]*Y[jv59]*rate_eval.n_V59__V60  +
          +rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__n_Al40  +
          -rho*Y[jn]*Y[jv55]*rate_eval.n_V55__V56  +
          -rho*Y[jn]*Y[jv53]*rate_eval.n_V53__V54  +
          +rho*Y[jp]*Y[jv62]*rate_eval.p_V62__n_Cr62  +
          -rho*Y[jn]*Y[jv51]*rate_eval.n_V51__V52  +
          +rho*Y[jhe4]*Y[jne32]*rate_eval.He4_Ne32__n_Mg35  +
          -rho*Y[jn]*Y[jv49]*rate_eval.n_V49__V50  +
          -rho*Y[jn]*Y[jv48]*rate_eval.n_V48__V49  +
          -rho*Y[jn]*Y[js28]*rate_eval.n_S28__S29  +
          +rho*Y[jp]*Y[js42]*rate_eval.p_S42__n_Cl42  +
          +rho*Y[jp]*Y[jsc46]*rate_eval.p_Sc46__n_Ti46  +
          -rho*Y[jn]*Y[jv47]*rate_eval.n_V47__V48  +
          -rho*Y[jn]*Y[jv46]*rate_eval.n_V46__V47  +
          -rho*Y[jn]*Y[jv45]*rate_eval.n_V45__V46  +
          +rho*Y[jp]*Y[jp40]*rate_eval.p_P40__n_S40  +
          -rho*Y[jn]*Y[jv42]*rate_eval.n_V42__V43  +
          -rho*Y[jn]*Y[jfe57]*rate_eval.n_Fe57__He4_Cr54  +
          +Y[jc16]*rate_eval.C16__n_N15__weak__wc12  +
          -rho*Y[jn]*Y[jv41]*rate_eval.n_V41__V42  +
          -rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__Mn55  +
          -rho*Y[jn]*Y[jti64]*rate_eval.n_Ti64__Ti65  +
          +Y[jal39]*rate_eval.Al39__n_Si38__weak__mp17  +
          -rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__He4_O13  +
          -rho*Y[jn]*Y[jti60]*rate_eval.n_Ti60__Ti61  +
          +Y[jc21]*rate_eval.C21__n_C20  +
          +rho*Y[jp]*Y[jfe63]*rate_eval.p_Fe63__n_Co63  +
          +rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__n_Mn58  +
          +rho*Y[jp]*Y[jar47]*rate_eval.p_Ar47__n_K47  +
          -rho*Y[jn]*Y[jti55]*rate_eval.n_Ti55__Ti56  +
          -rho*Y[jn]*Y[jti57]*rate_eval.n_Ti57__Ti58  +
          +rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__n_S31  +
          -rho*Y[jn]*Y[jti52]*rate_eval.n_Ti52__Ti53  +
          -rho*Y[jn]*Y[jv43]*rate_eval.n_V43__V44  +
          +rho*Y[jt]*Y[jbe9]*rate_eval.t_Be9__n_B11  +
          -rho*Y[jn]*Y[jti49]*rate_eval.n_Ti49__Ti50  +
          +rho*Y[jhe4]*Y[jna39]*rate_eval.He4_Na39__n_Al42  +
          +rho*Y[jhe4]*Y[jti57]*rate_eval.He4_Ti57__n_Cr60  +
          -rho*Y[jn]*Y[jti47]*rate_eval.n_Ti47__Ti48  +
          -rho*Y[jn]*Y[jti46]*rate_eval.n_Ti46__Ti47  +
          -rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__Ti46  +
          -rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__Ti45  +
          -rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__p_Cr44  +
          -rho*Y[jn]*Y[jti43]*rate_eval.n_Ti43__Ti44  +
          +rho*Y[jhe4]*Y[jna32]*rate_eval.He4_Na32__n_Al35  +
          -rho*Y[jn]*Y[jti41]*rate_eval.n_Ti41__Ti42  +
          -rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__Ti41  +
          +rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__n_K50  +
          -rho*Y[jn]*Y[jti38]*rate_eval.n_Ti38__Ti39  +
          -rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__Ti38  +
          -rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__He4_S31  +
          -rho*Y[jn]*Y[jsc62]*rate_eval.n_Sc62__Sc63  +
          -rho*Y[jn]*Y[jsc59]*rate_eval.n_Sc59__Sc60  +
          +Y[jsi44]*rate_eval.Si44__n_P43__weak__mp17  +
          -rho*Y[jn]*Y[jsc58]*rate_eval.n_Sc58__Sc59  +
          +rho*Y[jhe4]*Y[jca60]*rate_eval.He4_Ca60__n_Ti63  +
          +rho*Y[jhe4]*Y[jti49]*rate_eval.He4_Ti49__n_Cr52  +
          +Y[jn17]*rate_eval.N17__n_O16__weak__wc12  +
          -rho*Y[jn]*Y[jsc56]*rate_eval.n_Sc56__Sc57  +
          -rho*Y[jn]*Y[jsc54]*rate_eval.n_Sc54__Sc55  +
          -rho*Y[jn]*Y[jsc53]*rate_eval.n_Sc53__Sc54  +
          -rho*Y[jn]*Y[jsc50]*rate_eval.n_Sc50__Sc51  +
          -rho*Y[jn]*Y[jsc49]*rate_eval.n_Sc49__Sc50  +
          -rho*Y[jn]*Y[jsc48]*rate_eval.n_Sc48__Sc49  +
          -rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__Sc47  +
          -rho*Y[jn]*Y[jv47]*rate_eval.n_V47__p_Ti47  +
          -rho*Y[jn]*Y[jsc45]*rate_eval.n_Sc45__Sc46  +
          + 3*Y[jcl52]*rate_eval.Cl52__n_n_n_Ar49__weak__mo03  +
          -rho*Y[jn]*Y[jcr63]*rate_eval.n_Cr63__Cr64  +
          -rho*Y[jn]*Y[jsc42]*rate_eval.n_Sc42__Sc43  +
          -rho*Y[jn]*Y[jsc41]*rate_eval.n_Sc41__Sc42  +
          -rho*Y[jn]*Y[jsc39]*rate_eval.n_Sc39__Sc40  +
          -rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__Sc39  +
          -rho*Y[jn]*Y[jsc37]*rate_eval.n_Sc37__Sc38  +
          + 2*Y[jf27]*rate_eval.F27__n_n_Ne25__weak__mp17  +
          -rho*Y[jn]*Y[jca60]*rate_eval.n_Ca60__Ca61  +
          +rho*Y[jhe4]*Y[jf25]*rate_eval.He4_F25__n_Na28  +
          -rho*Y[jn]*Y[jar39]*rate_eval.n_Ar39__Ar40  +
          + 3*Y[jp47]*rate_eval.P47__n_n_n_S44__weak__mo03  +
          -rho*Y[jn]*Y[jca57]*rate_eval.n_Ca57__Ca58  +
          -rho*Y[jn]*Y[jca56]*rate_eval.n_Ca56__Ca57  +
          -rho*Y[jn]*Y[jca55]*rate_eval.n_Ca55__Ca56  +
          +rho*Y[jhe4]*Y[jna27]*rate_eval.He4_Na27__n_Al30  +
          +rho*Y[jhe4]*Y[jmn59]*rate_eval.He4_Mn59__n_Co62  +
          -rho*Y[jn]*Y[jca54]*rate_eval.n_Ca54__Ca55  +
          + 2*Y[jal39]*rate_eval.Al39__n_n_Si37__weak__mp17  +
          -rho*Y[jn]*Y[jca53]*rate_eval.n_Ca53__Ca54  +
          +rho*Y[jhe4]*Y[jbe11]*rate_eval.He4_Be11__n_C14  +
          -rho*Y[jn]*Y[jca51]*rate_eval.n_Ca51__Ca52  +
          -rho*Y[jn]*Y[jca49]*rate_eval.n_Ca49__Ca50  +
          + 3*Y[jb17]*rate_eval.B17__n_n_n_C14__weak__wc12  +
          +Y[jc17]*rate_eval.C17__n_N16__weak__wc12  +
          -rho*Y[jn]*Y[jca46]*rate_eval.n_Ca46__Ca47  +
          +rho*Y[jt]*Y[jli7]*rate_eval.t_Li7__n_Be9  +
          -rho*Y[jn]*Y[jcr51]*rate_eval.n_Cr51__Cr52  +
          -rho*Y[jn]*Y[jca41]*rate_eval.n_Ca41__Ca42  +
          -rho*Y[jn]*Y[jf16]*rate_eval.n_F16__He4_N13  +
          +Y[jal41]*rate_eval.Al41__n_Si40__weak__mp17  +
          -rho*Y[jn]*Y[jca40]*rate_eval.n_Ca40__Ca41  +
          -rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__Ca38  +
          -rho*Y[jn]*Y[jna27]*rate_eval.n_Na27__Na28  +
          -rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__Ca37  +
          +Y[jar54]*rate_eval.Ar54__n_K53__weak__mp17  +
          +rho*Y[jhe4]*Y[jcl46]*rate_eval.He4_Cl46__n_K49  +
          -rho*Y[jn]*Y[jfe47]*rate_eval.n_Fe47__p_Mn47  +
          +rho*Y[jp]*Y[jk50]*rate_eval.p_K50__n_Ca50  +
          +rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__n_K47  +
          -rho*Y[jn]*Y[jk56]*rate_eval.n_K56__K57  +
          +Y[jsc55]*rate_eval.Sc55__n_Ti54__weak__wc12  +
          -rho*Y[jn]*Y[jk53]*rate_eval.n_K53__K54  +
          -rho*Y[jn]*Y[jk52]*rate_eval.n_K52__K53  +
          +rho*Y[jp]*Y[jf20]*rate_eval.p_F20__n_Ne20  +
          -rho*Y[jn]*Y[jk50]*rate_eval.n_K50__K51  +
          -rho*Y[jn]*Y[jk46]*rate_eval.n_K46__K47  +
          +Y[jsc54]*rate_eval.Sc54__n_Ti53__weak__mp17  +
          -rho*Y[jn]*Y[jk45]*rate_eval.n_K45__K46  +
          -rho*Y[jn]*Y[jk44]*rate_eval.n_K44__K45  +
          -rho*Y[jn]*Y[jk39]*rate_eval.n_K39__He4_Cl36  +
          +Y[jmn70]*rate_eval.Mn70__n_Fe69__weak__mp17  +
          -rho*Y[jn]*Y[jk43]*rate_eval.n_K43__K44  +
          -rho*Y[jn]*Y[jal28]*rate_eval.n_Al28__Al29  +
          -rho*Y[jn]*Y[jk41]*rate_eval.n_K41__K42  +
          -rho*Y[jn]*Y[jk40]*rate_eval.n_K40__K41  +
          -rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__Mn46  +
          +rho*Y[jp]*Y[jv56]*rate_eval.p_V56__n_Cr56  +
          -rho*Y[jn]*Y[jk37]*rate_eval.n_K37__K38  +
          -rho*Y[jn]*Y[jk36]*rate_eval.n_K36__K37  +
          -rho*Y[jn]*Y[jo15]*rate_eval.n_O15__He4_C12  +
          -rho*Y[jn]*Y[jk34]*rate_eval.n_K34__K35  +
          -rho*Y[jn]*Y[jk33]*rate_eval.n_K33__K34  +
          -rho*Y[jn]*Y[jsi40]*rate_eval.n_Si40__Si41  +
          -rho*Y[jn]*Y[jk32]*rate_eval.n_K32__K33  +
          +rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__n_Ar42  +
          -rho*Y[jn]*Y[jar51]*rate_eval.n_Ar51__Ar52  +
          -rho*Y[jn]*Y[jar47]*rate_eval.n_Ar47__Ar48  +
          -rho*Y[jn]*Y[jar46]*rate_eval.n_Ar46__Ar47  +
          -rho*Y[jn]*Y[jf18]*rate_eval.n_F18__p_O18  +
          -rho*Y[jn]*Y[jar45]*rate_eval.n_Ar45__Ar46  +
          -rho*Y[jn]*Y[jar44]*rate_eval.n_Ar44__Ar45  +
          + 3*Y[jp46]*rate_eval.P46__n_n_n_S43__weak__mo03  +
          +Y[jk53]*rate_eval.K53__n_Ca52__weak__wc17  +
          -rho*Y[jn]*Y[jli7]*rate_eval.n_Li7__Li8  +
          -rho*Y[jn]*Y[jar42]*rate_eval.n_Ar42__Ar43  +
          -rho*Y[jn]*Y[jmg26]*rate_eval.n_Mg26__Mg27  +
          -rho*Y[jn]*Y[jar40]*rate_eval.n_Ar40__Ar41  +
          +Y[jne28]*rate_eval.Ne28__n_Na27__weak__wc12  +
          +Y[jcl43]*rate_eval.Cl43__n_Ar42__weak__mp17  +
          -rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__Ar33  +
          + 2*Y[jna32]*rate_eval.Na32__n_n_Mg30__weak__wc12  +
          -rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__Ar32  +
          -rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__Ar30  +
          +rho*Y[jhe4]*Y[jcr60]*rate_eval.He4_Cr60__n_Fe63  +
          +rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__n_K53  +
          -rho*Y[jn]*Y[jcl49]*rate_eval.n_Cl49__Cl50  +
          -rho*Y[jn]*Y[jcl46]*rate_eval.n_Cl46__Cl47  +
          -rho*Y[jn]*Y[jcl45]*rate_eval.n_Cl45__Cl46  +
          +Y[jv62]*rate_eval.V62__n_Cr61__weak__mp17  +
          -rho*Y[jn]*Y[jcl44]*rate_eval.n_Cl44__Cl45  +
          -rho*Y[jn]*Y[jcl42]*rate_eval.n_Cl42__Cl43  +
          +rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__n_Mn64  +
          +Y[jsi45]*rate_eval.Si45__n_P44__weak__mp17  +
          +rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__n_Al35  +
          -rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__Cl34  +
          -rho*Y[jn]*Y[jmg32]*rate_eval.n_Mg32__Mg33  +
          -rho*Y[jn]*Y[jca44]*rate_eval.n_Ca44__Ca45  +
          -rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__Cl33  +
          -rho*Y[jn]*Y[jk47]*rate_eval.n_K47__K48  +
          +Y[jfe72]*rate_eval.Fe72__n_Co71__weak__mp17  +
          -rho*Y[jn]*Y[js47]*rate_eval.n_S47__S48  +
          -rho*Y[jn]*Y[js44]*rate_eval.n_S44__S45  +
          -rho*Y[jn]*Y[jfe73]*rate_eval.n_Fe73__Fe74  +
          -rho*Y[jn]*Y[jk49]*rate_eval.n_K49__K50  +
          -rho*Y[jn]*Y[jmg28]*rate_eval.n_Mg28__Mg29  +
          -rho*Y[jn]*Y[js42]*rate_eval.n_S42__S43  +
          + 2*Y[jb17]*rate_eval.B17__n_n_C15__weak__wc12  +
          +Y[jal37]*rate_eval.Al37__n_Si36__weak__mp17  +
          -rho*Y[jn]*Y[js40]*rate_eval.n_S40__S41  +
          -rho*Y[jn]*Y[js38]*rate_eval.n_S38__S39  +
          +rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__n_Mg32  +
          + 2*Y[jcl47]*rate_eval.Cl47__n_n_Ar45__weak__mp17  +
          +rho*Y[jhe4]*Y[jar54]*rate_eval.He4_Ar54__n_Ca57  +
          -rho*Y[jn]*Y[js34]*rate_eval.n_S34__S35  +
          +rho*Y[jhe4]*Y[jca45]*rate_eval.He4_Ca45__n_Ti48  +
          -rho*Y[jn]*Y[js33]*rate_eval.n_S33__S34  +
          -rho*Y[jn]*Y[jar52]*rate_eval.n_Ar52__Ar53  +
          -rho*Y[jn]*Y[js32]*rate_eval.n_S32__S33  +
          +Y[jmg39]*rate_eval.Mg39__n_Al38__weak__mp17  +
          -rho*Y[jn]*Y[js27]*rate_eval.n_S27__S28  +
          -rho*Y[jn]*Y[js26]*rate_eval.n_S26__S27  +
          -rho*Y[jn]*Y[jp45]*rate_eval.n_P45__P46  +
          -rho*Y[jn]*Y[jp44]*rate_eval.n_P44__P45  +
          -rho*Y[jn]*Y[jp42]*rate_eval.n_P42__P43  +
          -rho*Y[jn]*Y[jp41]*rate_eval.n_P41__P42  +
          +rho*Y[jhe4]*Y[jo21]*rate_eval.He4_O21__n_Ne24  +
          +rho*Y[jhe4]*Y[jmg33]*rate_eval.He4_Mg33__n_Si36  +
          +rho*Y[jhe4]*Y[jcl38]*rate_eval.He4_Cl38__n_K41  +
          -rho*Y[jn]*Y[jna31]*rate_eval.n_Na31__Na32  +
          -rho*Y[jn]*Y[jp38]*rate_eval.n_P38__P39  +
          -rho*Y[jn]*Y[jp36]*rate_eval.n_P36__P37  +
          +Y[jc20]*rate_eval.C20__n_N19__weak__wc12  +
          -rho*Y[jn]*Y[jp35]*rate_eval.n_P35__P36  +
          -rho*Y[jn]*Y[jp33]*rate_eval.n_P33__P34  +
          -rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__Ca39  +
          -rho*Y[jn]*Y[jp32]*rate_eval.n_P32__P33  +
          -rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__He4_V42  +
          -rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__p_S32  +
          -rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__Ar31  +
          -rho*Y[jn]*Y[jp28]*rate_eval.n_P28__P29  +
          -rho*Y[jn]*Y[jp27]*rate_eval.n_P27__P28  +
          -rho*Y[jn]*Y[jp26]*rate_eval.n_P26__P27  +
          +Y[js49]*rate_eval.S49__n_Cl48__weak__mp17  +
          +rho*Y[jp]*Y[jk55]*rate_eval.p_K55__n_Ca55  +
          + 2*Y[jca59]*rate_eval.Ca59__n_n_Sc57__weak__mp17  +
          +Y[jal34]*rate_eval.Al34__n_Si33__weak__wc12  +
          -rho*Y[jn]*Y[jsi38]*rate_eval.n_Si38__Si39  +
          -rho*Y[jn]*Y[jsi36]*rate_eval.n_Si36__Si37  +
          -rho*Y[jn]*Y[jcr42]*rate_eval.n_Cr42__Cr43  +
          -rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__He4_Na21  +
          -rho*Y[jn]*Y[js45]*rate_eval.n_S45__S46  +
          +rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__n_Al37  +
          -rho*Y[jn]*Y[jsi32]*rate_eval.n_Si32__Si33  +
          -rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__Si23  +
          -rho*Y[jn]*Y[js41]*rate_eval.n_S41__S42  +
          -rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__He4_O14  +
          -rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__Si27  +
          +Y[jca54]*rate_eval.Ca54__n_Sc53__weak__mp17  +
          +rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__n_Sc54  +
          -rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__Si25  +
          -rho*Y[jn]*Y[jal40]*rate_eval.n_Al40__Al41  +
          +rho*Y[jp]*Y[jti64]*rate_eval.p_Ti64__n_V64  +
          -rho*Y[jn]*Y[jal38]*rate_eval.n_Al38__Al39  +
          +rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__n_Ar51  +
          -rho*Y[jn]*Y[jar38]*rate_eval.n_Ar38__Ar39  +
          +rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__n_P40  +
          -rho*Y[jn]*Y[jal35]*rate_eval.n_Al35__Al36  +
          -rho*Y[jn]*Y[jv61]*rate_eval.n_V61__V62  +
          -rho*Y[jn]*Y[jal34]*rate_eval.n_Al34__Al35  +
          -rho*Y[jn]*Y[jal31]*rate_eval.n_Al31__Al32  +
          + 2*Y[jli11]*rate_eval.Li11__n_n_Be9__weak__wc12  +
          -rho*Y[jn]*Y[jv50]*rate_eval.n_V50__V51  +
          +rho*Y[jhe4]*Y[jti62]*rate_eval.He4_Ti62__n_Cr65  +
          -rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__Al27  +
          -rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__Al25  +
          +rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__n_Ar39  +
          -rho*Y[jn]*Y[jsc44]*rate_eval.n_Sc44__Sc45  +
          +rho*Y[jd]*Y[jli6]*rate_eval.d_Li6__n_Be7  +
          -rho*Y[jn]*Y[jmg35]*rate_eval.n_Mg35__Mg36  +
          -rho*Y[jn]*Y[jsi35]*rate_eval.n_Si35__Si36  +
          -rho*Y[jn]*Y[jk37]*rate_eval.n_K37__p_Ar37  +
          -rho*Y[jn]*Y[jmg31]*rate_eval.n_Mg31__Mg32  +
          +rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__n_Al33  +
          -rho*Y[jn]*Y[jmg29]*rate_eval.n_Mg29__Mg30  +
          -rho*Y[jn]*Y[jca45]*rate_eval.n_Ca45__Ca46  +
          + 2*Y[jti64]*rate_eval.Ti64__n_n_V62__weak__mp17  +
          -rho*Y[jn]*Y[jmg24]*rate_eval.n_Mg24__Mg25  +
          -rho*Y[jn]*Y[jca43]*rate_eval.n_Ca43__Ca44  +
          +Y[jfe68]*rate_eval.Fe68__n_Co67__weak__mp17  +
          -rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__He4_V41  +
          + 2*Y[js45]*rate_eval.S45__n_n_Cl43__weak__mp17  +
          -rho*Y[jn]*Y[jmg23]*rate_eval.n_Mg23__Mg24  +
          +rho*Y[jhe4]*Y[jmg31]*rate_eval.He4_Mg31__n_Si34  +
          -rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__Cl35  +
          -rho*Y[jn]*Y[jmg22]*rate_eval.n_Mg22__Mg23  +
          -rho*Y[jn]*Y[jc14]*rate_eval.n_C14__C15  +
          -rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__Mn52  +
          +rho*Y[jhe4]*Y[js49]*rate_eval.He4_S49__n_Ar52  +
          -rho*Y[jn]*Y[jna36]*rate_eval.n_Na36__Na37  +
          +rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__n_Ar47  +
          -rho*Y[jn]*Y[jna34]*rate_eval.n_Na34__Na35  +
          -rho*Y[jn]*Y[jhe3]*rate_eval.n_He3__He4  +
          +rho*Y[jp]*Y[jf21]*rate_eval.p_F21__n_Ne21  +
          +Y[jmg32]*rate_eval.Mg32__n_Al31__weak__wc12  +
          +rho*Y[jhe4]*Y[jne29]*rate_eval.He4_Ne29__n_Mg32  +
          -rho*Y[jn]*Y[jf15]*rate_eval.n_F15__F16  +
          +rho*Y[jhe4]*Y[jti56]*rate_eval.He4_Ti56__n_Cr59  +
          -rho*Y[jn]*Y[jna24]*rate_eval.n_Na24__Na25  +
          +rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__n_Sc51  +
          +Y[jsc62]*rate_eval.Sc62__n_Ti61__weak__mp17  +
          -rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__Na23  +
          + 2*Y[jar53]*rate_eval.Ar53__n_n_K51__weak__mp17  +
          -rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__Na22  +
          +rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__n_V65  +
          -rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__Na21  +
          -rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__Na20  +
          +rho*Y[jhe4]*Y[jk58]*rate_eval.He4_K58__n_Sc61  +
          +Y[jcr68]*rate_eval.Cr68__n_Mn67__weak__mp17  +
          +Y[jmg41]*rate_eval.Mg41__n_Al40__weak__mp17  +
          +rho*Y[jp]*Y[jmn71]*rate_eval.p_Mn71__n_Fe71  +
          -rho*Y[jn]*Y[jfe74]*rate_eval.n_Fe74__Fe75  +
          -rho*Y[jn]*Y[jne26]*rate_eval.n_Ne26__Ne27  +
          +rho*Y[jhe4]*Y[jcl52]*rate_eval.He4_Cl52__n_K55  +
          -rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__Mg20  +
          -rho*Y[jn]*Y[jne24]*rate_eval.n_Ne24__Ne25  +
          +rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__n_Mn70  +
          -rho*Y[jn]*Y[jne19]*rate_eval.n_Ne19__Ne20  +
          +Y[jne32]*rate_eval.Ne32__n_Na31__weak__mp17  +
          +Y[jsc61]*rate_eval.Sc61__n_Ti60__weak__mp17  +
          -rho*Y[jn]*Y[js46]*rate_eval.n_S46__S47  +
          -rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__Ne19  +
          -rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__Ne18  +
          -rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__Ne17  +
          -rho*Y[jn]*Y[jo13]*rate_eval.n_O13__O14  +
          +rho*Y[jhe4]*Y[jmg29]*rate_eval.He4_Mg29__n_Si32  +
          -rho*Y[jn]*Y[jv41]*rate_eval.n_V41__p_Ti41  +
          -rho*Y[jn]*Y[jp39]*rate_eval.n_P39__P40  +
          -rho*Y[jn]*Y[jsi34]*rate_eval.n_Si34__Si35  +
          -rho*Y[jn]*Y[jf23]*rate_eval.n_F23__F24  +
          -rho*Y[jn]*Y[jf22]*rate_eval.n_F22__F23  +
          -rho*Y[jn]*Y[jcr54]*rate_eval.n_Cr54__Cr55  +
          -rho*Y[jn]*Y[jf21]*rate_eval.n_F21__F22  +
          +Y[jna30]*rate_eval.Na30__n_Mg29__weak__wc17  +
          -rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__Al24  +
          -rho*Y[jn]*Y[jf20]*rate_eval.n_F20__F21  +
          -rho*Y[jn]*Y[jf18]*rate_eval.n_F18__F19  +
          -rho*Y[jn]*Y[jf17]*rate_eval.n_F17__F18  +
          -rho*Y[jn]*Y[jf16]*rate_eval.n_F16__F17  +
          -rho*Y[jn]*Y[jf14]*rate_eval.n_F14__F15  +
          +rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__n_Ar43  +
          +Y[jcr67]*rate_eval.Cr67__n_Mn66__weak__mp17  +
          -rho*Y[jn]*Y[jne23]*rate_eval.n_Ne23__Ne24  +
          -rho*Y[jn]*Y[jo23]*rate_eval.n_O23__O24  +
          -rho*Y[jn]*Y[jk57]*rate_eval.n_K57__K58  +
          -rho*Y[jn]*Y[jo22]*rate_eval.n_O22__O23  +
          -rho*Y[jn]*Y[jo21]*rate_eval.n_O21__O22  +
          -rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__He4_P28  +
          +rho*Y[jhe4]*Y[jo20]*rate_eval.He4_O20__n_Ne23  +
          -rho*Y[jn]*Y[jar48]*rate_eval.n_Ar48__Ar49  +
          + 2*Y[jk58]*rate_eval.K58__n_n_Ca56__weak__mp17  +
          +rho*Y[jhe4]*Y[jar44]*rate_eval.He4_Ar44__n_Ca47  +
          -rho*Y[jn]*Y[jo16]*rate_eval.n_O16__O17  +
          +rho*Y[jp]*Y[js44]*rate_eval.p_S44__n_Cl44  +
          -rho*Y[jn]*Y[jo15]*rate_eval.n_O15__O16  +
          -rho*Y[jn]*Y[jn19]*rate_eval.n_N19__N20  +
          -rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__He4_Mg24  +
          +Y[jsc63]*rate_eval.Sc63__n_Ti62__weak__mp17  +
          +Y[jv58]*rate_eval.V58__n_Cr57__weak__mp17  +
          -rho*Y[jn]*Y[jn17]*rate_eval.n_N17__N18  +
          -rho*Y[jn]*Y[jn16]*rate_eval.n_N16__N17  +
          -rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__Cl30  +
          -rho*Y[jn]*Y[jti53]*rate_eval.n_Ti53__Ti54  +
          -rho*Y[jn]*Y[jn15]*rate_eval.n_N15__N16  +
          +Y[jti60]*rate_eval.Ti60__n_V59__weak__mp17  +
          -rho*Y[jn]*Y[jn13]*rate_eval.n_N13__N14  +
          + 2*Y[jmg38]*rate_eval.Mg38__n_n_Al36__weak__mp17  +
          -rho*Y[jn]*Y[jfe53]*rate_eval.n_Fe53__Fe54  +
          -rho*Y[jn]*Y[jv42]*rate_eval.n_V42__p_Ti42  +
          -rho*Y[jn]*Y[jb12]*rate_eval.n_B12__B13  +
          -rho*Y[jn]*Y[jp]*rate_eval.n_p__d  +
          -rho*Y[jn]*Y[jb11]*rate_eval.n_B11__B12  +
          -rho*Y[jn]*Y[jb10]*rate_eval.n_B10__B11  +
          -rho*Y[jn]*Y[jbe11]*rate_eval.n_Be11__Be12  +
          -rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__Mg21  +
          +rho*Y[jp]*Y[jp35]*rate_eval.p_P35__n_S35  +
          + 2*Y[jfe75]*rate_eval.Fe75__n_n_Co73__weak__mp17  +
          +Y[jv61]*rate_eval.V61__n_Cr60__weak__wc12  +
          + 2*Y[jfe73]*rate_eval.Fe73__n_n_Co71__weak__mp17  +
          + 2*Y[jmn73]*rate_eval.Mn73__n_n_Fe71__weak__mp17  +
          +rho*Y[jhe4]*Y[jfe62]*rate_eval.He4_Fe62__n_Ni65  +
          +Y[jf27]*rate_eval.F27__n_Ne26__weak__wc12  +
          + 2*Y[jmn72]*rate_eval.Mn72__n_n_Fe70__weak__mp17  +
          + 2*Y[jmn71]*rate_eval.Mn71__n_n_Fe69__weak__mp17  +
          + 2*Y[jmn70]*rate_eval.Mn70__n_n_Fe68__weak__mp17  +
          + 3*Y[jca61]*rate_eval.Ca61__n_n_n_Sc58__weak__mo03  +
          -rho*Y[jn]*Y[jti47]*rate_eval.n_Ti47__p_Sc47  +
          +rho*Y[jp]*Y[jca49]*rate_eval.p_Ca49__n_Sc49  +
          + 2*Y[jmn68]*rate_eval.Mn68__n_n_Fe66__weak__mp17  +
          + 2*Y[jti65]*rate_eval.Ti65__n_n_V63__weak__mp17  +
          -rho*Y[jn]*Y[jk51]*rate_eval.n_K51__K52  +
          +rho*Y[jhe4]*Y[jca49]*rate_eval.He4_Ca49__n_Ti52  +
          + 2*Y[jsc60]*rate_eval.Sc60__n_n_Ti58__weak__mp17  +
          -rho*Y[jn]*Y[jv48]*rate_eval.n_V48__He4_Sc45  +
          +Y[jar49]*rate_eval.Ar49__n_K48__weak__wc12  +
          -rho*Y[jn]*Y[jne28]*rate_eval.n_Ne28__Ne29  +
          -rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__Si26  +
          + 2*Y[jk59]*rate_eval.K59__n_n_Ca57__weak__mp17  +
          -rho*Y[jn]*Y[js31]*rate_eval.n_S31__He4_Si28  +
          -rho*Y[jn]*Y[jp29]*rate_eval.n_P29__P30  +
          + 2*Y[jk53]*rate_eval.K53__n_n_Ca51__weak__mp17  +
          -rho*Y[jn]*Y[jcr58]*rate_eval.n_Cr58__Cr59  +
          + 2*Y[jk52]*rate_eval.K52__n_n_Ca50__weak__mp17  +
          + 2*Y[jar54]*rate_eval.Ar54__n_n_K52__weak__mp17  +
          +Y[jn21]*rate_eval.N21__n_O20__weak__wc12  +
          + 2*Y[jcl52]*rate_eval.Cl52__n_n_Ar50__weak__mp17  +
          + 2*Y[jcl50]*rate_eval.Cl50__n_n_Ar48__weak__mp17  +
          + 2*Y[js49]*rate_eval.S49__n_n_Cl47__weak__mp17  +
          + 2*Y[js47]*rate_eval.S47__n_n_Cl45__weak__mp17  +
          -rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__He4_P27  +
          + 2*Y[jp47]*rate_eval.P47__n_n_S45__weak__mp17  +
          + 2*Y[jp45]*rate_eval.P45__n_n_S43__weak__mp17  +
          + 2*Y[jp44]*rate_eval.P44__n_n_S42__weak__mp17  +
          + 2*Y[jp43]*rate_eval.P43__n_n_S41__weak__mp17  +
          + 2*Y[jsi44]*rate_eval.Si44__n_n_P42__weak__mp17  +
          +rho*Y[jhe4]*Y[jmn61]*rate_eval.He4_Mn61__n_Co64  +
          + 2*Y[jsi41]*rate_eval.Si41__n_n_P39__weak__mp17  +
          + 2*Y[jsi39]*rate_eval.Si39__n_n_P37__weak__mp17  +
          + 2*Y[jal43]*rate_eval.Al43__n_n_Si41__weak__mp17  +
          + 2*Y[jal41]*rate_eval.Al41__n_n_Si39__weak__mp17  +
          -rho*Y[jn]*Y[jk42]*rate_eval.n_K42__K43  +
          + 2*Y[jal38]*rate_eval.Al38__n_n_Si36__weak__mp17  +
          +Y[jp41]*rate_eval.P41__n_S40__weak__wc12  +
          +Y[jmg33]*rate_eval.Mg33__n_Al32__weak__wc12  +
          + 2*Y[jmg37]*rate_eval.Mg37__n_n_Al35__weak__mp17  +
          + 2*Y[jmg33]*rate_eval.Mg33__n_n_Al31__weak__mp17  +
          + 2*Y[jna35]*rate_eval.Na35__n_n_Mg33__weak__mp17  +
          +rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__n_Ti51  +
          + 2*Y[jna31]*rate_eval.Na31__n_n_Mg29__weak__wc12  +
          + 2*Y[jsc59]*rate_eval.Sc59__n_n_Ti57__weak__mp17  +
          +rho*Y[jhe4]*Y[jk47]*rate_eval.He4_K47__n_Sc50  +
          +Y[jf24]*rate_eval.F24__n_Ne23__weak__wc12  +
          + 2*Y[jna30]*rate_eval.Na30__n_n_Mg28__weak__wc12  +
          +Y[jmn69]*rate_eval.Mn69__n_Fe68__weak__mp17  +
          + 2*Y[jne32]*rate_eval.Ne32__n_n_Na30__weak__mp17  +
          + 2*Y[jne29]*rate_eval.Ne29__n_n_Na27__weak__wc12  +
          + 2*Y[jf30]*rate_eval.F30__n_n_Ne28__weak__mp17  +
          + 2*Y[jo27]*rate_eval.O27__n_n_F25__weak__mp17  +
          -rho*Y[jn]*Y[jar36]*rate_eval.n_Ar36__Ar37  +
          + 2*Y[jo26]*rate_eval.O26__n_n_F24__weak__mp17  +
          + 2*Y[jo25]*rate_eval.O25__n_n_F23__weak__mp17  +
          + 2*Y[jb15]*rate_eval.B15__n_n_C13__weak__wc12  +
          -rho*Y[jn]*Y[jar43]*rate_eval.n_Ar43__Ar44  +
          + 2*Y[jbe16]*rate_eval.Be16__n_n_Be14  +
          + 2*Y[jbe14]*rate_eval.Be14__n_n_B12__weak__wc12  +
          +rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__n_Si28  +
          +Y[jfe75]*rate_eval.Fe75__n_Co74__weak__mp17  +
          +Y[jp43]*rate_eval.P43__n_S42__weak__wc12  +
          +Y[jfe73]*rate_eval.Fe73__n_Co72__weak__mp17  +
          +rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__n_Ar41  +
          -rho*Y[jn]*Y[jmg25]*rate_eval.n_Mg25__Mg26  +
          -rho*Y[jn]*Y[jc11]*rate_eval.n_C11__C12  +
          +Y[jfe70]*rate_eval.Fe70__n_Co69__weak__mp17  +
          +Y[jmg35]*rate_eval.Mg35__n_Al34__weak__wc12  +
          -rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__Cl31  +
          +Y[jfe69]*rate_eval.Fe69__n_Co68__weak__mp17  +
          +rho*Y[jp]*Y[jk47]*rate_eval.p_K47__n_Ca47  +
          +rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__n_Sc50  +
          -rho*Y[jn]*Y[js35]*rate_eval.n_S35__S36  +
          +rho*Y[jhe4]*Y[jmg36]*rate_eval.He4_Mg36__n_Si39  +
          -rho*Y[jn]*Y[jca48]*rate_eval.n_Ca48__Ca49  +
          +rho*Y[jhe4]*Y[jb11]*rate_eval.He4_B11__n_N14  +
          +Y[jv60]*rate_eval.V60__n_Cr59__weak__mp17  +
          +rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__n_Ar38  +
          -rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__Cl32  +
          -rho*Y[jn]*Y[jcl48]*rate_eval.n_Cl48__Cl49  +
          +Y[jv65]*rate_eval.V65__n_Cr64__weak__mp17  +
          +rho*Y[jhe4]*Y[jk59]*rate_eval.He4_K59__n_Sc62  +
          +rho*Y[jhe4]*Y[js47]*rate_eval.He4_S47__n_Ar50  +
          +Y[jk48]*rate_eval.K48__n_Ca47__weak__wc12  +
          -rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__p_Na19  +
          +rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__n_Al32  +
          +rho*Y[jp]*Y[jp46]*rate_eval.p_P46__n_S46  +
          +rho*Y[jp]*Y[jp41]*rate_eval.p_P41__n_S41  +
          +Y[jal43]*rate_eval.Al43__n_Si42__weak__mp17  +
          +rho*Y[jp]*Y[jp39]*rate_eval.p_P39__n_S39  +
          -rho*Y[jn]*Y[jcl38]*rate_eval.n_Cl38__Cl39  +
          +rho*Y[jhe4]*Y[jmg28]*rate_eval.He4_Mg28__n_Si31  +
          +Y[jmn73]*rate_eval.Mn73__n_Fe72__weak__mp17  +
          +Y[jmn72]*rate_eval.Mn72__n_Fe71__weak__mp17  +
          -rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__p_Mg23  +
          +Y[jmn65]*rate_eval.Mn65__n_Fe64__weak__mp17  +
          +Y[jfe74]*rate_eval.Fe74__n_Co73__weak__mp17  +
          -rho*Y[jn]*Y[jp40]*rate_eval.n_P40__P41  +
          -rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__p_Mg24  +
          +rho*Y[jhe4]*Y[jcr68]*rate_eval.He4_Cr68__n_Fe71  +
          +Y[jca61]*rate_eval.Ca61__n_Sc60__weak__mp17  +
          -rho*Y[jn]*Y[jfe60]*rate_eval.n_Fe60__Fe61  +
          -rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__He4_Mg20  +
          -rho*Y[jn]*Y[jcl41]*rate_eval.n_Cl41__Cl42  +
          +rho*Y[jhe4]*Y[jbe9]*rate_eval.He4_Be9__n_C12  +
          + 2*Y[jk55]*rate_eval.K55__n_n_Ca53__weak__mp17  +
          +rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__n_Mg34  +
          + 2*Y[jmg39]*rate_eval.Mg39__n_n_Al37__weak__mp17  +
          -rho*Y[jn]*Y[jmg22]*rate_eval.n_Mg22__p_Na22  +
          +rho*Y[jhe4]*Y[jp46]*rate_eval.He4_P46__n_Cl49  +
          + 2*Y[jk57]*rate_eval.K57__n_n_Ca55__weak__mp17  +
          +Y[jn19]*rate_eval.N19__n_O18__weak__wc12  +
          -rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__p_Sc37  +
          +Y[jcr70]*rate_eval.Cr70__n_Mn69__weak__mp17  +
          +Y[jo24]*rate_eval.O24__n_F23__weak__wc12  +
          +Y[jmn68]*rate_eval.Mn68__n_Fe67__weak__mp17  +
          +rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__n_Ar44  +
          +Y[jcr69]*rate_eval.Cr69__n_Mn68__weak__mp17  +
          -rho*Y[jn]*Y[jli8]*rate_eval.n_Li8__Li9  +
          +Y[jcr66]*rate_eval.Cr66__n_Mn65__weak__mp17  +
          -rho*Y[jn]*Y[jc13]*rate_eval.n_C13__C14  +
          -rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__p_Na21  +
          +Y[jcr63]*rate_eval.Cr63__n_Mn62__weak__mp17  +
          -rho*Y[jn]*Y[jca59]*rate_eval.n_Ca59__Ca60  +
          +rho*Y[jhe4]*Y[jv65]*rate_eval.He4_V65__n_Mn68  +
          +Y[jcr62]*rate_eval.Cr62__n_Mn61__weak__mp17  +
          +Y[jf30]*rate_eval.F30__n_Ne29__weak__mp17  +
          +Y[jcr61]*rate_eval.Cr61__n_Mn60__weak__mp17  +
          -rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__Si24  +
          +rho*Y[jhe4]*Y[jbe10]*rate_eval.He4_Be10__n_C13  +
          -rho*Y[jn]*Y[jbe7]*rate_eval.n_Be7__p_Li7  +
          -rho*Y[jn]*Y[jal21]*rate_eval.n_Al21__Al22  +
          -rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__He4_Mg23  +
          -rho*Y[jn]*Y[jna32]*rate_eval.n_Na32__Na33  +
          +rho*Y[jhe4]*Y[jca55]*rate_eval.He4_Ca55__n_Ti58  +
          -rho*Y[jn]*Y[jp34]*rate_eval.n_P34__P35  +
          -rho*Y[jn]*Y[jsc35]*rate_eval.n_Sc35__Sc36  +
          -rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__p_S28  +
          +Y[jar51]*rate_eval.Ar51__n_K50__weak__mp17  +
          -rho*Y[jn]*Y[jmn50]*rate_eval.n_Mn50__p_Cr50  +
          +Y[jv63]*rate_eval.V63__n_Cr62__weak__wc12  +
          +Y[jar52]*rate_eval.Ar52__n_K51__weak__mp17  +
          -rho*Y[jn]*Y[jcr41]*rate_eval.n_Cr41__p_V41  +
          +Y[jv59]*rate_eval.V59__n_Cr58__weak__wc12  +
          +rho*Y[jhe4]*Y[jsi36]*rate_eval.He4_Si36__n_S39  +
          +rho*Y[jp]*Y[jli8]*rate_eval.p_Li8__n_He4_He4  +
          -rho*Y[jn]*Y[jca47]*rate_eval.n_Ca47__Ca48  +
          + 2*Y[jfe76]*rate_eval.Fe76__n_n_Co74__weak__mp17  +
          -rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__Cr48  +
          -rho*Y[jn]*Y[js28]*rate_eval.n_S28__p_P28  +
          +Y[jk55]*rate_eval.K55__n_Ca54__weak__mp17  +
          -rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__He4_Ne17  +
          +rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__n_Al41  +
          -rho*Y[jn]*Y[jsc52]*rate_eval.n_Sc52__Sc53  +
          -rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__p_Sc40  +
          +rho*Y[jhe4]*Y[jal43]*rate_eval.He4_Al43__n_P46  +
          -rho*Y[jn]*Y[jp30]*rate_eval.n_P30__p_Si30  +
          -rho*Y[jn]*Y[jp46]*rate_eval.n_P46__P47  +
          + 2*Y[jo28]*rate_eval.O28__n_n_F26__weak__mp17  +
          + 2*Y[jmg40]*rate_eval.Mg40__n_n_Al38__weak__mp17  +
          +rho*Y[jhe4]*Y[jne25]*rate_eval.He4_Ne25__n_Mg28  +
          + 2*Y[jcr70]*rate_eval.Cr70__n_n_Mn68__weak__mp17  +
          +Y[jti64]*rate_eval.Ti64__n_V63__weak__mp17  +
          +rho*Y[jhe4]*Y[jo27]*rate_eval.He4_O27__n_Ne30  +
          -rho*Y[jn]*Y[jmn57]*rate_eval.n_Mn57__Mn58  +
          -rho*Y[jn]*Y[jp25]*rate_eval.n_P25__He4_Al22  +
          +Y[jti63]*rate_eval.Ti63__n_V62__weak__mp17  +
          -rho*Y[jn]*Y[jf19]*rate_eval.n_F19__F20  +
          +Y[jti61]*rate_eval.Ti61__n_V60__weak__mp17  +
          + 2*Y[jv65]*rate_eval.V65__n_n_Cr63__weak__mp17  +
          -rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__p_Ne22  +
          +rho*Y[jp]*Y[js45]*rate_eval.p_S45__n_Cl45  +
          -rho*Y[jn]*Y[jcr52]*rate_eval.n_Cr52__Cr53  +
          -rho*Y[jn]*Y[jp30]*rate_eval.n_P30__P31  +
          +Y[jca55]*rate_eval.Ca55__n_Sc54__weak__mp17  +
          +Y[jsc57]*rate_eval.Sc57__n_Ti56__weak__mp17  +
          +Y[jti58]*rate_eval.Ti58__n_V57__weak__mp17  +
          + 2*Y[jal37]*rate_eval.Al37__n_n_Si35__weak__mp17  +
          + 2*Y[jcr69]*rate_eval.Cr69__n_n_Mn67__weak__mp17  +
          +rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__n_Fe58  +
          +rho*Y[jp]*Y[jcr65]*rate_eval.p_Cr65__n_Mn65  +
          +rho*Y[jp]*Y[jf29]*rate_eval.p_F29__n_Ne29  +
          -rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__He4_Ar36  +
          +Y[jo26]*rate_eval.O26__n_O25  +
          +Y[jal40]*rate_eval.Al40__n_Si39__weak__mp17  +
          -rho*Y[jn]*Y[jc12]*rate_eval.n_C12__C13  +
          +rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__n_Fe63  +
          -rho*Y[jn]*Y[jal27]*rate_eval.n_Al27__Al28  +
          +rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__n_K46  +
          + 2*Y[jal42]*rate_eval.Al42__n_n_Si40__weak__mo03  +
          +rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__n_Al36  +
          -rho*Y[jn]*Y[jk48]*rate_eval.n_K48__K49  +
          +rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__n_Na30  +
          +rho*Y[jp]*Y[jf30]*rate_eval.p_F30__n_Ne30  +
          -rho*Y[jn]*Y[jti50]*rate_eval.n_Ti50__Ti51  +
          +rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__n_Al28  +
          -rho*Y[jn]*Y[js27]*rate_eval.n_S27__He4_Si24  +
          +Y[jmn66]*rate_eval.Mn66__n_Fe65__weak__mp17  +
          +Y[jc22]*rate_eval.C22__n_N21__weak__wc17  +
          -rho*Y[jn]*Y[jv64]*rate_eval.n_V64__V65  +
          -rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__p_Ca36  +
          +rho*Y[jp]*Y[js41]*rate_eval.p_S41__n_Cl41  +
          +Y[jsc59]*rate_eval.Sc59__n_Ti58__weak__mp17  +
          +rho*Y[jp]*Y[jmg36]*rate_eval.p_Mg36__n_Al36  +
          +Y[jsc58]*rate_eval.Sc58__n_Ti57__weak__mp17  +
          -5.00000000000000e-01*rho**2*Y[jn]*Y[jhe4]**2*rate_eval.n_He4_He4__Be9  +
          + 2*Y[jk54]*rate_eval.K54__n_n_Ca52__weak__mp17  +
          +rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__n_Mn69  +
          +rho*Y[jhe4]*Y[jar47]*rate_eval.He4_Ar47__n_Ca50  +
          -rho*Y[jn]*Y[jal32]*rate_eval.n_Al32__Al33  +
          -rho*Y[jn]*Y[jcr65]*rate_eval.n_Cr65__Cr66  +
          +rho*Y[jhe4]*Y[js40]*rate_eval.He4_S40__n_Ar43  +
          + 3*Y[jna31]*rate_eval.Na31__n_n_n_Mg28__weak__wc12  +
          +rho*Y[jhe4]*Y[jna29]*rate_eval.He4_Na29__n_Al32  +
          -rho*Y[jn]*Y[jne21]*rate_eval.n_Ne21__Ne22  +
          -rho*Y[jn]*Y[jca41]*rate_eval.n_Ca41__He4_Ar38  +
          +Y[jo26]*rate_eval.O26__n_F25__weak__mp17  +
          +Y[jn20]*rate_eval.N20__n_O19__weak__wc12  +
          +Y[jca59]*rate_eval.Ca59__n_Sc58__weak__mp17  +
          +Y[jca58]*rate_eval.Ca58__n_Sc57__weak__mp17  +
          +rho*Y[jhe4]*Y[jp45]*rate_eval.He4_P45__n_Cl48  +
          -rho*Y[jn]*Y[jne31]*rate_eval.n_Ne31__Ne32  +
          +Y[jca57]*rate_eval.Ca57__n_Sc56__weak__mp17  +
          +rho*Y[jhe4]*Y[jmg41]*rate_eval.He4_Mg41__n_Si44  +
          -rho*Y[jn]*Y[jcl39]*rate_eval.n_Cl39__Cl40  +
          +Y[jca52]*rate_eval.Ca52__n_Sc51__weak__wc12  +
          -rho*Y[jn]*Y[jv54]*rate_eval.n_V54__V55  +
          +rho*Y[jp]*Y[js39]*rate_eval.p_S39__n_Cl39  +
          +Y[jal42]*rate_eval.Al42__n_Si41__weak__mp17  +
          +Y[jsi42]*rate_eval.Si42__n_P41__weak__mp17  +
          +rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__n_Sc47  +
          -rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__He4_F16  +
          +Y[jcl46]*rate_eval.Cl46__n_Ar45__weak__wc12  +
          +rho*Y[jhe4]*Y[jmn70]*rate_eval.He4_Mn70__n_Co73  +
          +Y[jcl51]*rate_eval.Cl51__n_Ar50__weak__mp17  +
          -rho*Y[jn]*Y[jmg30]*rate_eval.n_Mg30__Mg31  +
          +rho*Y[jp]*Y[jfe68]*rate_eval.p_Fe68__n_Co68  +
          -rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__Ti43  +
          +rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__n_Mg29  +
          -rho**2*Y[jn]*Y[jp]*Y[jhe4]*rate_eval.n_p_He4__Li6  +
          +Y[jk58]*rate_eval.K58__n_Ca57__weak__mp17  +
          -rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__Ar34  +
          -rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__Ca34  +
          +Y[jk57]*rate_eval.K57__n_Ca56__weak__mp17  +
          +rho*Y[jhe4]*Y[jsc53]*rate_eval.He4_Sc53__n_V56  +
          -rho*Y[jn]*Y[jsi39]*rate_eval.n_Si39__Si40  +
          -rho*Y[jn]*Y[jfe46]*rate_eval.n_Fe46__Fe47  +
          -rho*Y[jn]*Y[jcr64]*rate_eval.n_Cr64__Cr65  +
          +Y[jk59]*rate_eval.K59__n_Ca58__weak__mp17  +
          +rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__n_Si37  +
          +Y[jk52]*rate_eval.K52__n_Ca51__weak__wc12  +
          +Y[jk51]*rate_eval.K51__n_Ca50__weak__wc12  +
          +Y[jk50]*rate_eval.K50__n_Ca49__weak__wc12  +
          +rho*Y[jhe4]*Y[jar45]*rate_eval.He4_Ar45__n_Ca48  +
          -rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__Ca35  +
          -rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__p_Ca38  +
          -rho*Y[jn]*Y[jti51]*rate_eval.n_Ti51__Ti52  +
          +rho*Y[jp]*Y[jo23]*rate_eval.p_O23__n_F23  +
          +rho*Y[jhe4]*Y[jmn63]*rate_eval.He4_Mn63__n_Co66  +
          +rho*Y[jhe4]*Y[jfe61]*rate_eval.He4_Fe61__n_Ni64  +
          + 2*Y[jca58]*rate_eval.Ca58__n_n_Sc56__weak__mp17  +
          -rho*Y[jn]*Y[jsi31]*rate_eval.n_Si31__Si32  +
          -rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__He4_P33  +
          -rho*Y[jn]*Y[js37]*rate_eval.n_S37__S38  +
          -rho*Y[jn]*Y[jar50]*rate_eval.n_Ar50__Ar51  +
          +Y[jmn67]*rate_eval.Mn67__n_Fe66__weak__mp17  +
          -rho*Y[jn]*Y[jca58]*rate_eval.n_Ca58__Ca59  +
          -rho*Y[jn]*Y[jar41]*rate_eval.n_Ar41__Ar42  +
          -rho*Y[jn]*Y[jk42]*rate_eval.n_K42__He4_Cl39  +
          +rho*Y[jp]*Y[jmg27]*rate_eval.p_Mg27__n_Al27  +
          +rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__n_Sc48  +
          -rho*Y[jn]*Y[jne29]*rate_eval.n_Ne29__Ne30  +
          +rho*Y[jhe4]*Y[jp38]*rate_eval.He4_P38__n_Cl41  +
          +Y[jc18]*rate_eval.C18__n_N17__weak__wc12  +
          +rho*Y[jhe4]*Y[jcl48]*rate_eval.He4_Cl48__n_K51  +
          + 2*Y[jsc63]*rate_eval.Sc63__n_n_Ti61__weak__mp17  +
          -rho*Y[jn]*Y[jcr51]*rate_eval.n_Cr51__p_V51  +
          -rho*Y[jn]*Y[jv65]*rate_eval.n_V65__V66  +
          +rho*Y[jp]*Y[jk46]*rate_eval.p_K46__n_Ca46  +
          +Y[jv66]*rate_eval.V66__n_Cr65__weak__mp17  +
          +Y[jp47]*rate_eval.P47__n_S46__weak__mp17  +
          +rho*Y[jhe4]*Y[jar50]*rate_eval.He4_Ar50__n_Ca53  +
          + 3*Y[jsi44]*rate_eval.Si44__n_n_n_P41__weak__mo03  +
          -rho*Y[jn]*Y[jk31]*rate_eval.n_K31__He4_Cl28  +
          +Y[jar50]*rate_eval.Ar50__n_K49__weak__wc12  +
          +Y[jmg34]*rate_eval.Mg34__n_Al33__weak__mp17  +
          +Y[jo28]*rate_eval.O28__n_F27__weak__mp17  +
          + 2*Y[jcl51]*rate_eval.Cl51__n_n_Ar49__weak__mp17  +
          -rho*Y[jn]*Y[jo12]*rate_eval.n_O12__He4_C9  +
          +rho*Y[jp]*Y[jfe65]*rate_eval.p_Fe65__n_Co65  +
          +rho*Y[jp]*Y[jfe76]*rate_eval.p_Fe76__n_Co76  +
          -rho*Y[jn]*Y[jo19]*rate_eval.n_O19__O20  +
          +Y[jcl52]*rate_eval.Cl52__n_Ar51__weak__mp17  +
          -rho*Y[jn]*Y[jcr45]*rate_eval.n_Cr45__p_V45  +
          +Y[jcl50]*rate_eval.Cl50__n_Ar49__weak__mp17  +
          -rho*Y[jn]*Y[jsc41]*rate_eval.n_Sc41__p_Ca41  +
          +rho*Y[jp]*Y[jmn67]*rate_eval.p_Mn67__n_Fe67  +
          -rho*Y[jn]*Y[jfe52]*rate_eval.n_Fe52__p_Mn52  +
          + 2*Y[jne34]*rate_eval.Ne34__n_n_Na32__weak__mp17  +
          -rho*Y[jn]*Y[js36]*rate_eval.n_S36__S37  +
          +Y[jcl47]*rate_eval.Cl47__n_Ar46__weak__wc12  +
          +Y[jp46]*rate_eval.P46__n_S45__weak__mp17  +
          +rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__n_Sc57  +
          +Y[jcl45]*rate_eval.Cl45__n_Ar44__weak__wc12  +
          -rho*Y[jn]*Y[jne27]*rate_eval.n_Ne27__Ne28  +
          +rho*Y[jhe4]*Y[jb10]*rate_eval.He4_B10__n_N13  +
          -rho*Y[jn]*Y[jmn64]*rate_eval.n_Mn64__Mn65  +
          +Y[jcl44]*rate_eval.Cl44__n_Ar43__weak__mp17  +
          -rho*Y[jn]*Y[jv44]*rate_eval.n_V44__V45  +
          +Y[jsc60]*rate_eval.Sc60__n_Ti59__weak__mp17  +
          +5.00000000000000e-01*rho*Y[jd]**2*rate_eval.d_d__n_He3  +
          +Y[jsi43]*rate_eval.Si43__n_P42__weak__mp17  +
          + 2*Y[jsc58]*rate_eval.Sc58__n_n_Ti56__weak__mp17  +
          +rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__n_Na31  +
          + 2*Y[js48]*rate_eval.S48__n_n_Cl46__weak__mp17  +
          +rho*Y[jp]*Y[jv65]*rate_eval.p_V65__n_Cr65  +
          +rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__n_Mg26  +
          -rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__p_Al27  +
          -rho*Y[jn]*Y[jcl47]*rate_eval.n_Cl47__Cl48  +
          +rho*Y[jhe4]*Y[jmn58]*rate_eval.He4_Mn58__n_Co61  +
          +Y[js46]*rate_eval.S46__n_Cl45__weak__mp17  +
          +rho*Y[jhe4]*Y[jli9]*rate_eval.He4_Li9__n_B12  +
          + 2*Y[jmg35]*rate_eval.Mg35__n_n_Al33__weak__mp17  +
          +rho*Y[jp]*Y[jcr66]*rate_eval.p_Cr66__n_Mn66  +
          +rho*Y[jp]*Y[jo27]*rate_eval.p_O27__n_F27  +
          -rho*Y[jn]*Y[jti61]*rate_eval.n_Ti61__Ti62  +
          -rho*Y[jn]*Y[jmn46]*rate_eval.n_Mn46__Mn47  +
          +rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__n_Si31  +
          + 2*Y[jcl48]*rate_eval.Cl48__n_n_Ar46__weak__mp17  +
          + 2*Y[jf28]*rate_eval.F28__n_n_Ne26__weak__mp17  +
          -rho*Y[jn]*Y[jli6]*rate_eval.n_Li6__Li7  +
          +rho*Y[jhe4]*Y[jn16]*rate_eval.He4_N16__n_F19  +
          -rho*Y[jn]*Y[jmn48]*rate_eval.n_Mn48__p_Cr48  +
          -rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__He4_Ti46  +
          +rho*Y[jhe4]*Y[jsc46]*rate_eval.He4_Sc46__n_V49  +
          -rho*Y[jn]*Y[jk38]*rate_eval.n_K38__He4_Cl35  +
          +Y[jn24]*rate_eval.N24__n_N23  +
          +rho*Y[jhe4]*Y[jfe65]*rate_eval.He4_Fe65__n_Ni68  +
          -rho*Y[jn]*Y[jk34]*rate_eval.n_K34__He4_Cl31  +
          -rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__p_F17  +
          -rho*Y[jn]*Y[jti43]*rate_eval.n_Ti43__p_Sc43  +
          +Y[jp39]*rate_eval.P39__n_S38__weak__wc12  +
          +Y[jp44]*rate_eval.P44__n_S43__weak__mp17  +
          +Y[jca56]*rate_eval.Ca56__n_Sc55__weak__mp17  +
          +Y[jp42]*rate_eval.P42__n_S41__weak__wc12  +
          +Y[jna35]*rate_eval.Na35__n_Mg34__weak__mp17  +
          +Y[jna33]*rate_eval.Na33__n_Mg32__weak__wc17  +
          +Y[jfe76]*rate_eval.Fe76__n_Co75__weak__mp17  +
          + 3*Y[jmg38]*rate_eval.Mg38__n_n_n_Al35__weak__mo03  +
          +rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__n_Mg25  +
          -rho*Y[jn]*Y[jsc57]*rate_eval.n_Sc57__Sc58  +
          -rho*Y[jn]*Y[jna23]*rate_eval.n_Na23__Na24  +
          +rho*Y[jp]*Y[jn16]*rate_eval.p_N16__n_O16  +
          -rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__p_V44  +
          +rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__n_Fe70  +
          +Y[jfe71]*rate_eval.Fe71__n_Co70__weak__mp17  +
          -rho*Y[jn]*Y[jo17]*rate_eval.n_O17__He4_C14  +
          +rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__n_P42  +
          + 2*rho*Y[jt]*Y[jli7]*rate_eval.t_Li7__n_n_He4_He4  +
          -rho*Y[jn]*Y[jv66]*rate_eval.n_V66__V67  +
          -rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__He4_S30  +
          +Y[jk54]*rate_eval.K54__n_Ca53__weak__mp17  +
          +rho*Y[jp]*Y[jp44]*rate_eval.p_P44__n_S44  +
          -rho*Y[jn]*Y[jsc61]*rate_eval.n_Sc61__Sc62  +
          +Y[jsi41]*rate_eval.Si41__n_P40__weak__mp17  +
          +Y[jsi40]*rate_eval.Si40__n_P39__weak__mp17  +
          +Y[jsi38]*rate_eval.Si38__n_P37__weak__mp17  +
          +rho*Y[jhe4]*Y[jmn64]*rate_eval.He4_Mn64__n_Co67  +
          -rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__He4_K33  +
          +Y[jca60]*rate_eval.Ca60__n_Sc59__weak__mp17  +
          -rho*Y[jn]*Y[jk38]*rate_eval.n_K38__K39  +
          +rho*Y[jp]*Y[jsi31]*rate_eval.p_Si31__n_P31  +
          + 3*Y[jne33]*rate_eval.Ne33__n_n_n_Na30__weak__mo03  +
          +Y[jti62]*rate_eval.Ti62__n_V61__weak__mp17  +
          +Y[jcr64]*rate_eval.Cr64__n_Mn63__weak__mp17  +
          -rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__Mg22  +
          -rho*Y[jn]*Y[jfe61]*rate_eval.n_Fe61__Fe62  +
          +rho*Y[jhe4]*Y[jfe67]*rate_eval.He4_Fe67__n_Ni70  +
          +rho*Y[jhe4]*Y[jne34]*rate_eval.He4_Ne34__n_Mg37  +
          -rho*Y[jn]*Y[jv63]*rate_eval.n_V63__V64  +
          + 2*Y[jna39]*rate_eval.Na39__n_n_Mg37__weak__mp17  +
          -rho*Y[jn]*Y[jn14]*rate_eval.n_N14__N15  +
          -rho*Y[jn]*Y[jf17]*rate_eval.n_F17__p_O17  +
          -rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__p_Mn45  +
          +rho*Y[jhe4]*Y[jna30]*rate_eval.He4_Na30__n_Al33  +
          +Y[jal38]*rate_eval.Al38__n_Si37__weak__mp17  +
          +rho*Y[jhe4]*Y[jar49]*rate_eval.He4_Ar49__n_Ca52  +
          -rho*Y[jn]*Y[jsi30]*rate_eval.n_Si30__Si31  +
          +rho*Y[jp]*Y[jk52]*rate_eval.p_K52__n_Ca52  +
          -rho*Y[jn]*Y[jp31]*rate_eval.n_P31__P32  +
          +Y[jal35]*rate_eval.Al35__n_Si34__weak__wc12  +
          +Y[jsi39]*rate_eval.Si39__n_P38__weak__mp17  +
          -rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__Fe46  +
          +Y[jp40]*rate_eval.P40__n_S39__weak__wc12  +
          +Y[jal32]*rate_eval.Al32__n_Si31__weak__wc12  +
          -rho*Y[jn]*Y[jfe59]*rate_eval.n_Fe59__Fe60  +
          +rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__n_Al27  +
          -rho*Y[jn]*Y[jp37]*rate_eval.n_P37__P38  +
          + 3*Y[jsi43]*rate_eval.Si43__n_n_n_P40__weak__mo03  +
          +Y[jmg40]*rate_eval.Mg40__n_Al39__weak__mp17  +
          + 3*Y[jmn72]*rate_eval.Mn72__n_n_n_Fe69__weak__mo03  +
          +Y[jmg38]*rate_eval.Mg38__n_Al37__weak__mp17  +
          +rho*Y[jp]*Y[js43]*rate_eval.p_S43__n_Cl43  +
          -rho*Y[jn]*Y[jti62]*rate_eval.n_Ti62__Ti63  +
          +Y[jo27]*rate_eval.O27__n_O26  +
          -rho*Y[jn]*Y[jmg33]*rate_eval.n_Mg33__Mg34  +
          +rho*Y[jhe4]*Y[jv52]*rate_eval.He4_V52__n_Mn55  +
          +Y[jk56]*rate_eval.K56__n_Ca55__weak__mp17  +
          -rho*Y[jn]*Y[jc15]*rate_eval.n_C15__C16  +
          +rho*Y[jhe4]*Y[jmn71]*rate_eval.He4_Mn71__n_Co74  +
          -rho*Y[jn]*Y[jca42]*rate_eval.n_Ca42__Ca43  +
          +rho*Y[jp]*Y[jna38]*rate_eval.p_Na38__n_Mg38  +
          -rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__Mn54  +
          +rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__n_Mg37  +
          +rho*Y[jp]*Y[jmn62]*rate_eval.p_Mn62__n_Fe62  +
          -rho*Y[jn]*Y[jmn48]*rate_eval.n_Mn48__Mn49  +
          -rho*Y[jn]*Y[jti56]*rate_eval.n_Ti56__Ti57  +
          +Y[jna38]*rate_eval.Na38__n_Mg37__weak__mp17  +
          +Y[jar53]*rate_eval.Ar53__n_K52__weak__mp17  +
          -rho*Y[jn]*Y[js43]*rate_eval.n_S43__S44  +
          +Y[jv67]*rate_eval.V67__n_Cr66__weak__mp17  +
          +rho*Y[jp]*Y[jf23]*rate_eval.p_F23__n_Ne23  +
          +Y[jna34]*rate_eval.Na34__n_Mg33__weak__wc12  +
          -rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__Ti40  +
          -rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__p_K39  +
          -rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__He4_Ca41  +
          +Y[jsi37]*rate_eval.Si37__n_P36__weak__wc12  +
          +Y[jmn64]*rate_eval.Mn64__n_Fe63__weak__wc12  +
          +Y[jne33]*rate_eval.Ne33__n_Na32__weak__mp17  +
          +rho*Y[jhe4]*Y[jmn66]*rate_eval.He4_Mn66__n_Co69  +
          +rho*Y[jhe4]*Y[jca52]*rate_eval.He4_Ca52__n_Ti55  +
          +Y[jna29]*rate_eval.Na29__n_Mg28__weak__wc12  +
          +rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__n_Ti56  +
          -rho*Y[jn]*Y[jmg39]*rate_eval.n_Mg39__Mg40  +
          +rho*Y[jhe4]*Y[jca54]*rate_eval.He4_Ca54__n_Ti57  +
          -rho*Y[jn]*Y[jp25]*rate_eval.n_P25__p_Si25  +
          +rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__n_K49  +
          -rho*Y[jn]*Y[jb10]*rate_eval.n_B10__He4_Li7  +
          -rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__C12_O16  +
          -rho*Y[jn]*Y[jsi28]*rate_eval.n_Si28__Si29  +
          +Y[jmn71]*rate_eval.Mn71__n_Fe70__weak__mp17  +
          +Y[jn18]*rate_eval.N18__n_O17__weak__wc12  +
          + 2*5.00000000000000e-01*rho*Y[jt]**2*rate_eval.t_t__n_n_He4  +
          + 2*Y[jv67]*rate_eval.V67__n_n_Cr65__weak__mp17  +
          -rho*Y[jn]*Y[jsi41]*rate_eval.n_Si41__Si42  +
          +rho*Y[jhe3]*Y[jli7]*rate_eval.He3_Li7__n_p_He4_He4  +
          -rho*Y[jn]*Y[jk35]*rate_eval.n_K35__K36  +
          -rho*Y[jn]*Y[jk39]*rate_eval.n_K39__K40  +
          -rho*Y[jn]*Y[jal33]*rate_eval.n_Al33__Al34  +
          +rho*Y[jp]*Y[jmn65]*rate_eval.p_Mn65__n_Fe65  +
          +rho*Y[jd]*Y[jc14]*rate_eval.d_C14__n_N15  +
          -rho*Y[jn]*Y[jp29]*rate_eval.n_P29__p_Si29  +
          -rho*Y[jn]*Y[jna26]*rate_eval.n_Na26__Na27  +
          -rho*Y[jn]*Y[jk54]*rate_eval.n_K54__K55  +
          -rho*Y[jn]*Y[jti63]*rate_eval.n_Ti63__Ti64  +
          +Y[jbe12]*rate_eval.Be12__n_B11__weak__wc12  +
          -rho*Y[jn]*Y[jcl50]*rate_eval.n_Cl50__Cl51  +
          +Y[jf31]*rate_eval.F31__n_Ne30__weak__mp17  +
          +Y[jf26]*rate_eval.F26__n_Ne25__weak__wc12  +
          +Y[jne29]*rate_eval.Ne29__n_Na28__weak__wc17  +
          -rho*Y[jn]*Y[jv52]*rate_eval.n_V52__V53  +
          -rho*Y[jn]*Y[jbe10]*rate_eval.n_Be10__Be11  +
          -rho*Y[jn]*Y[jal29]*rate_eval.n_Al29__Al30  +
          -rho*Y[jn]*Y[jar36]*rate_eval.n_Ar36__p_Cl36  +
          -rho*Y[jn]*Y[jar53]*rate_eval.n_Ar53__Ar54  +
          + 2*Y[jca60]*rate_eval.Ca60__n_n_Sc58__weak__mp17  +
          -rho*Y[jn]*Y[jne22]*rate_eval.n_Ne22__Ne23  +
          +rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__n_Ar49  +
          -rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__Sc37  +
          + 2*Y[jp46]*rate_eval.P46__n_n_S44__weak__mp17  +
          -rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__Ca36  +
          +Y[jo23]*rate_eval.O23__n_F22__weak__wc12  +
          +Y[jv64]*rate_eval.V64__n_Cr63__weak__mp17  +
          +rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__n_Ti59  +
          +rho*Y[jp]*Y[jp37]*rate_eval.p_P37__n_S37  +
          +rho*Y[jhe4]*Y[jal41]*rate_eval.He4_Al41__n_P44  +
          +rho*Y[jhe4]*Y[jsi41]*rate_eval.He4_Si41__n_S44  +
          -rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__Cl37  +
          +Y[jc19]*rate_eval.C19__n_N18__weak__wc12  +
          -rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__He4_F19  +
          +Y[jne34]*rate_eval.Ne34__n_Na33__weak__mp17  +
          +Y[jp45]*rate_eval.P45__n_S44__weak__mp17  +
          +Y[jb19]*rate_eval.B19__n_C18__weak__wc17  +
          +rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__n_V56  +
          +Y[jb15]*rate_eval.B15__n_C14__weak__wc12  +
          +rho*Y[jhe4]*Y[jar51]*rate_eval.He4_Ar51__n_Ca54  +
          -rho*Y[jn]*Y[js39]*rate_eval.n_S39__S40  +
          +Y[jbe15]*rate_eval.Be15__n_Be14  +
          +Y[jbe14]*rate_eval.Be14__n_B13__weak__wc17  +
          -rho*Y[jn]*Y[jmn56]*rate_eval.n_Mn56__He4_V53  +
          +Y[jli11]*rate_eval.Li11__n_Be10__weak__wc17  +
          -rho*Y[jn]*Y[jar37]*rate_eval.n_Ar37__Ar38  +
          -rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__Al23  +
          -rho*Y[jn]*Y[jv57]*rate_eval.n_V57__V58  +
          +rho*Y[jhe4]*Y[jf22]*rate_eval.He4_F22__n_Na25  +
          -rho*Y[jn]*Y[jal21]*rate_eval.n_Al21__p_Mg21  +
          + 3*Y[jo26]*rate_eval.O26__n_n_n_F23__weak__mo03  +
          +Y[jsi36]*rate_eval.Si36__n_P35__weak__wc12  +
          +rho*Y[jhe4]*Y[jsi34]*rate_eval.He4_Si34__n_S37  +
          +rho*Y[jp]*Y[jsi34]*rate_eval.p_Si34__n_P34  +
          -rho*Y[jn]*Y[jna29]*rate_eval.n_Na29__Na30  +
          +Y[jcr65]*rate_eval.Cr65__n_Mn64__weak__mp17  +
          +rho*Y[jp]*Y[jo19]*rate_eval.p_O19__n_F19  +
          +Y[jb17]*rate_eval.B17__n_C16__weak__wc17  +
          -rho*Y[jn]*Y[jcr67]*rate_eval.n_Cr67__Cr68  +
          +rho*Y[jhe4]*Y[jar48]*rate_eval.He4_Ar48__n_Ca51  +
          -rho*Y[jn]*Y[jf14]*rate_eval.n_F14__p_O14  +
          -rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__Cr50  +
          -rho*Y[jn]*Y[jp25]*rate_eval.n_P25__P26  +
          -rho*Y[jn]*Y[jal30]*rate_eval.n_Al30__Al31  +
          + 2*Y[jal36]*rate_eval.Al36__n_n_Si34__weak__mp17  +
          +rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__n_Ti63  +
          +Y[jp38]*rate_eval.P38__n_S37__weak__wc12  +
          -rho*Y[jn]*Y[jti48]*rate_eval.n_Ti48__Ti49  +
          -rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__Mn48  +
          +rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__n_Si42  +
          + 2*Y[jca61]*rate_eval.Ca61__n_n_Sc59__weak__mp17  +
          -rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__Fe56  +
          -rho*Y[jn]*Y[jcr68]*rate_eval.n_Cr68__Cr69  +
          -rho*Y[jn]*Y[jne25]*rate_eval.n_Ne25__Ne26  +
          -rho*Y[jn]*Y[js31]*rate_eval.n_S31__S32  +
          +rho*Y[jhe4]*Y[jcr58]*rate_eval.He4_Cr58__n_Fe61  +
          +Y[jmg36]*rate_eval.Mg36__n_Al35__weak__mp17  +
          +Y[jne30]*rate_eval.Ne30__n_Na29__weak__wc12  +
          + 3*Y[jcl51]*rate_eval.Cl51__n_n_n_Ar48__weak__mo03  +
          +rho*Y[jhe4]*Y[jcr67]*rate_eval.He4_Cr67__n_Fe70  +
          +rho*Y[jhe4]*Y[jca59]*rate_eval.He4_Ca59__n_Ti62  +
          +Y[js47]*rate_eval.S47__n_Cl46__weak__mp17  +
          -rho*Y[jn]*Y[jk42]*rate_eval.n_K42__p_Ar42  +
          -rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__He4_Cr42  +
          + 2*Y[jv66]*rate_eval.V66__n_n_Cr64__weak__mp17  +
          -rho*Y[jn]*Y[jfe52]*rate_eval.n_Fe52__Fe53  +
          -rho*Y[jn]*Y[jfe64]*rate_eval.n_Fe64__Fe65  +
          + 2*Y[jna34]*rate_eval.Na34__n_n_Mg32__weak__wc12  +
          +rho*Y[jhe4]*Y[jf23]*rate_eval.He4_F23__n_Na26  +
          + 3*Y[jti64]*rate_eval.Ti64__n_n_n_V61__weak__mo03  +
          -rho*Y[jn]*Y[jsc51]*rate_eval.n_Sc51__Sc52  +
          +Y[jf29]*rate_eval.F29__n_Ne28__weak__wc12  +
          -rho*Y[jn]*Y[jfe59]*rate_eval.n_Fe59__He4_Cr56  +
          -rho*Y[jn]*Y[jsi29]*rate_eval.n_Si29__Si30  +
          + 2*Y[jn22]*rate_eval.N22__n_n_O20__weak__wc12  +
          -rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__Cl36  +
          +Y[jf25]*rate_eval.F25__n_Ne24__weak__wc12  +
          -rho*Y[jn]*Y[jf15]*rate_eval.n_F15__p_O15  +
          -rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__p_Ne20  +
          -rho*Y[jn]*Y[jna38]*rate_eval.n_Na38__Na39  +
          -rho*Y[jn]*Y[jv52]*rate_eval.n_V52__He4_Sc49  +
          -rho*Y[jn]*Y[jcr50]*rate_eval.n_Cr50__Cr51  +
          + 2*Y[jne31]*rate_eval.Ne31__n_n_Na29__weak__mp17  +
          -rho*Y[jn]*Y[jp24]*rate_eval.n_P24__P25  +
          + 3*Y[jne32]*rate_eval.Ne32__n_n_n_Na29__weak__mo03  +
          +rho*Y[jp]*Y[jsi41]*rate_eval.p_Si41__n_P41  +
          -rho*Y[jn]*Y[jca42]*rate_eval.n_Ca42__He4_Ar39  +
          +rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__n_Mg24  +
          -rho*Y[jn]*Y[jna25]*rate_eval.n_Na25__Na26  +
          + 2*Y[jne33]*rate_eval.Ne33__n_n_Na31__weak__mp17  +
          +rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__n_P35  +
          +Y[jna32]*rate_eval.Na32__n_Mg31__weak__wc17  +
          -rho*Y[jn]*Y[jv58]*rate_eval.n_V58__V59  +
          -rho*Y[jn]*Y[jmn61]*rate_eval.n_Mn61__Mn62  +
          +rho*Y[jhe4]*Y[jfe72]*rate_eval.He4_Fe72__n_Ni75  +
          + 3*Y[jk57]*rate_eval.K57__n_n_n_Ca54__weak__mo03  +
          +Y[js48]*rate_eval.S48__n_Cl47__weak__mp17  +
          -rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__Mn44  +
          +Y[js43]*rate_eval.S43__n_Cl42__weak__wc12  +
          -rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__He4_Ca37  +
          +rho*Y[jhe4]*Y[js44]*rate_eval.He4_S44__n_Ar47  +
          +rho*Y[jp]*Y[jmg28]*rate_eval.p_Mg28__n_Al28  +
          -rho*Y[jn]*Y[jv45]*rate_eval.n_V45__p_Ti45  +
          -rho*Y[jn]*Y[jf24]*rate_eval.n_F24__F25  +
          -rho*Y[jn]*Y[js27]*rate_eval.n_S27__p_P27  +
          + 2*Y[jti63]*rate_eval.Ti63__n_n_V61__weak__mp17  +
          +rho*Y[jhe4]*Y[jal30]*rate_eval.He4_Al30__n_P33  +
          -rho*Y[jn]*Y[jv60]*rate_eval.n_V60__V61  +
          -rho*Y[jn]*Y[jv40]*rate_eval.n_V40__V41  +
          + 3*Y[jsc60]*rate_eval.Sc60__n_n_n_Ti57__weak__mo03  +
          -rho*Y[jn]*Y[jv39]*rate_eval.n_V39__He4_Sc36  +
          -rho*Y[jn]*Y[jsc60]*rate_eval.n_Sc60__Sc61  +
          +Y[jmn63]*rate_eval.Mn63__n_Fe62__weak__mp17  +
          +Y[jal33]*rate_eval.Al33__n_Si32__weak__wc12  +
          +rho*Y[jhe4]*Y[jsc50]*rate_eval.He4_Sc50__n_V53  +
          -rho*Y[jn]*Y[jsc39]*rate_eval.n_Sc39__p_Ca39  +
          +Y[jmg31]*rate_eval.Mg31__n_Al30__weak__wc12  +
          -rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__He4_K37  +
          -rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__Ca40  +
          -rho*Y[jn]*Y[jne33]*rate_eval.n_Ne33__Ne34  +
          +rho*Y[jp]*Y[jar51]*rate_eval.p_Ar51__n_K51  +
          + 3*Y[jf30]*rate_eval.F30__n_n_n_Ne27__weak__mo03  +
          +rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__n_Al34  +
          + 2*Y[jal40]*rate_eval.Al40__n_n_Si38__weak__mp17  +
          +rho*Y[jhe4]*Y[jca56]*rate_eval.He4_Ca56__n_Ti59  +
          + 2*Y[jk50]*rate_eval.K50__n_n_Ca48__weak__mp17  +
          -rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__He4_Ar35  +
          -rho*Y[jn]*Y[jbe9]*rate_eval.n_Be9__Be10  +
          + 2*Y[jar51]*rate_eval.Ar51__n_n_K49__weak__mp17  +
          +rho*Y[jp]*Y[jmn56]*rate_eval.p_Mn56__n_Fe56  +
          -rho*Y[jn]*Y[jsc47]*rate_eval.n_Sc47__Sc48  +
          + 2*Y[jna37]*rate_eval.Na37__n_n_Mg35__weak__mp17  +
          + 2*Y[jna33]*rate_eval.Na33__n_n_Mg31__weak__wc12  +
          + 2*Y[jk56]*rate_eval.K56__n_n_Ca54__weak__mp17  +
          +Y[jf28]*rate_eval.F28__n_Ne27__weak__mp17  +
          -rho*Y[jn]*Y[js32]*rate_eval.n_S32__He4_Si29  +
          -rho*Y[jn]*Y[jsi37]*rate_eval.n_Si37__Si38  +
          -rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__He4_K35  +
          -rho*Y[jn]*Y[jna28]*rate_eval.n_Na28__Na29  +
          -rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__He4_Na22  +
          +Y[jn22]*rate_eval.N22__n_O21__weak__wc17  +
          -rho*Y[jn]*Y[jk34]*rate_eval.n_K34__p_Ar34  +
          +rho*Y[jhe4]*Y[jsi45]*rate_eval.He4_Si45__n_S48  +
          +rho*Y[jhe4]*Y[jfe69]*rate_eval.He4_Fe69__n_Ni72  +
          -rho*Y[jn]*Y[jp28]*rate_eval.n_P28__He4_Al25  +
          +Y[jk49]*rate_eval.K49__n_Ca48__weak__wc12  +
          +Y[jo27]*rate_eval.O27__n_F26__weak__mp17  +
          +Y[jna28]*rate_eval.Na28__n_Mg27__weak__wc12  +
          -rho*Y[jn]*Y[jmn66]*rate_eval.n_Mn66__Mn67  +
          -rho*Y[jn]*Y[jar49]*rate_eval.n_Ar49__Ar50  +
          +rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__n_Mn61  +
          -rho*Y[jn]*Y[jo20]*rate_eval.n_O20__O21  +
          -rho*Y[jn]*Y[jmg37]*rate_eval.n_Mg37__Mg38  +
          +Y[jal36]*rate_eval.Al36__n_Si35__weak__mp17  +
          +rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__n_Mg30  +
          +Y[jna37]*rate_eval.Na37__n_Mg36__weak__mp17  +
          -rho*Y[jn]*Y[js29]*rate_eval.n_S29__S30  +
          -rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__He4_Ti45  +
          -rho*Y[jn]*Y[jc16]*rate_eval.n_C16__C17  +
          +rho*Y[jp]*Y[jar46]*rate_eval.p_Ar46__n_K46  +
          +rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__n_Sc49  +
          + 2*Y[jb19]*rate_eval.B19__n_n_C17__weak__wc12  +
          +rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__n_p_He4_He4  +
          -rho*Y[jn]*Y[jna35]*rate_eval.n_Na35__Na36  +
          +rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__n_Sc44  +
          +rho*Y[jp]*Y[jk41]*rate_eval.p_K41__n_Ca41  +
          -rho*Y[jn]*Y[jo24]*rate_eval.n_O24__O25  +
          -rho*Y[jn]*Y[jsi44]*rate_eval.n_Si44__Si45  +
          +rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__n_P30  +
          +rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__n_Mg23  +
          +rho*Y[jhe4]*Y[jne22]*rate_eval.He4_Ne22__n_Mg25  +
          +rho*Y[jp]*Y[jf19]*rate_eval.p_F19__n_Ne19  +
          -rho*Y[jn]*Y[jal41]*rate_eval.n_Al41__Al42  +
          +rho*Y[jp]*Y[jn15]*rate_eval.p_N15__n_O15  +
          +rho*Y[jp]*Y[jc13]*rate_eval.p_C13__n_N13  +
          -rho*Y[jn]*Y[jcl51]*rate_eval.n_Cl51__Cl52  +
          -rho*Y[jn]*Y[jsi42]*rate_eval.n_Si42__Si43  +
          -rho*Y[jn]*Y[jal39]*rate_eval.n_Al39__Al40  +
          +rho*Y[jhe4]*Y[jn14]*rate_eval.He4_N14__n_F17  +
          -rho*Y[jn]*Y[jmg36]*rate_eval.n_Mg36__Mg37  +
          -rho*Y[jn]*Y[jmg34]*rate_eval.n_Mg34__Mg35  +
          -rho*Y[jn]*Y[jna37]*rate_eval.n_Na37__Na38  +
          -rho*Y[jn]*Y[jmg40]*rate_eval.n_Mg40__Mg41  +
          -rho*Y[jn]*Y[jne32]*rate_eval.n_Ne32__Ne33  +
          +rho*Y[jp]*Y[jn14]*rate_eval.p_N14__n_O14  +
          +rho*Y[jhe4]*Y[jo18]*rate_eval.He4_O18__n_Ne21  +
          -rho*Y[jn]*Y[jmg38]*rate_eval.n_Mg38__Mg39  +
          -rho*Y[jn]*Y[jf27]*rate_eval.n_F27__F28  +
          -rho*Y[jn]*Y[js48]*rate_eval.n_S48__S49  +
          -rho*Y[jn]*Y[jp43]*rate_eval.n_P43__P44  +
          +rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__n_Ar37  +
          -rho*Y[jn]*Y[jal42]*rate_eval.n_Al42__Al43
       )

    dYdt[jp] = (
          + 3*Y[jfe45]*rate_eval.Fe45__p_p_p_Ti42__weak__wc12  +
          + 3*Y[jcr43]*rate_eval.Cr43__p_p_p_Ca40__weak__wc12  +
          -5.00000000000000e-01*rho**2*Y[jn]*Y[jp]**2*rate_eval.n_p_p__p_d  +
          + 2*rho*Y[jhe3]*Y[jbe7]*rate_eval.He3_Be7__p_p_He4_He4  +
          +rho*Y[jt]*Y[jbe7]*rate_eval.t_Be7__n_p_He4_He4  +
          + 2*rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__p_p_Ca38  +
          + 2*rho*Y[jhe4]*Y[jo13]*rate_eval.He4_O13__p_p_O15  +
          -rho*Y[jp]*Y[jb11]*rate_eval.p_B11__He4_He4_He4  +
          +rho*Y[jn]*Y[jb8]*rate_eval.n_B8__p_He4_He4  +
          -rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__d_He4_He4  +
          + 2*5.00000000000000e-01*rho*Y[jhe3]**2*rate_eval.He3_He3__p_p_He4  +
          -rho*Y[jp]*Y[jfe76]*rate_eval.p_Fe76__He4_Mn73  +
          -rho*Y[jp]*Y[jfe75]*rate_eval.p_Fe75__He4_Mn72  +
          -rho*Y[jp]*Y[jfe75]*rate_eval.p_Fe75__n_Co75  +
          -rho*Y[jp]*Y[jfe74]*rate_eval.p_Fe74__He4_Mn71  +
          -rho*Y[jp]*Y[jfe74]*rate_eval.p_Fe74__n_Co74  +
          -rho*Y[jp]*Y[jfe73]*rate_eval.p_Fe73__He4_Mn70  +
          -rho*Y[jp]*Y[jfe73]*rate_eval.p_Fe73__n_Co73  +
          -rho*Y[jp]*Y[jfe72]*rate_eval.p_Fe72__He4_Mn69  +
          -rho*Y[jp]*Y[jfe72]*rate_eval.p_Fe72__n_Co72  +
          -rho*Y[jp]*Y[jfe71]*rate_eval.p_Fe71__He4_Mn68  +
          -rho*Y[jp]*Y[jfe71]*rate_eval.p_Fe71__n_Co71  +
          -rho*Y[jp]*Y[jfe70]*rate_eval.p_Fe70__He4_Mn67  +
          -rho*Y[jp]*Y[jfe70]*rate_eval.p_Fe70__n_Co70  +
          -rho*Y[jp]*Y[jfe69]*rate_eval.p_Fe69__He4_Mn66  +
          -rho*Y[jp]*Y[jfe69]*rate_eval.p_Fe69__n_Co69  +
          -rho*Y[jp]*Y[jfe68]*rate_eval.p_Fe68__He4_Mn65  +
          -rho*Y[jp]*Y[jfe67]*rate_eval.p_Fe67__He4_Mn64  +
          -rho*Y[jp]*Y[jfe65]*rate_eval.p_Fe65__He4_Mn62  +
          -rho*Y[jp]*Y[jfe63]*rate_eval.p_Fe63__He4_Mn60  +
          -rho*Y[jp]*Y[jfe62]*rate_eval.p_Fe62__He4_Mn59  +
          -rho*Y[jp]*Y[jfe61]*rate_eval.p_Fe61__He4_Mn58  +
          -rho*Y[jp]*Y[jfe61]*rate_eval.p_Fe61__n_Co61  +
          -rho*Y[jp]*Y[jfe60]*rate_eval.p_Fe60__He4_Mn57  +
          -rho*Y[jp]*Y[jfe59]*rate_eval.p_Fe59__He4_Mn56  +
          -rho*Y[jp]*Y[jfe59]*rate_eval.p_Fe59__n_Co59  +
          -rho*Y[jp]*Y[jfe57]*rate_eval.p_Fe57__He4_Mn54  +
          -rho*Y[jp]*Y[jar34]*rate_eval.p_Ar34__K35  +
          +rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__p_Mn55  +
          +rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__p_Mn54  +
          +rho*Y[jn]*Y[jfe53]*rate_eval.n_Fe53__p_Mn53  +
          +rho*Y[jhe4]*Y[jfe52]*rate_eval.He4_Fe52__p_Co55  +
          -rho*Y[jp]*Y[jca61]*rate_eval.p_Ca61__Sc62  +
          +rho*Y[jhe4]*Y[jfe49]*rate_eval.He4_Fe49__p_Co52  +
          +rho*Y[jn]*Y[jfe49]*rate_eval.n_Fe49__p_Mn49  +
          +rho*Y[jhe4]*Y[jfe48]*rate_eval.He4_Fe48__p_Co51  +
          -rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__Ti51  +
          +rho*Y[jn]*Y[jfe46]*rate_eval.n_Fe46__p_Mn46  +
          -rho*Y[jp]*Y[jmn73]*rate_eval.p_Mn73__He4_Cr70  +
          -rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__Al35  +
          -rho*Y[jp]*Y[jmn72]*rate_eval.p_Mn72__He4_Cr69  +
          -rho*Y[jp]*Y[jmn71]*rate_eval.p_Mn71__He4_Cr68  +
          -rho*Y[jp]*Y[jmn69]*rate_eval.p_Mn69__He4_Cr66  +
          -rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__n_Fe68  +
          -rho*Y[jp]*Y[jmn67]*rate_eval.p_Mn67__He4_Cr64  +
          -rho*Y[jp]*Y[jmn66]*rate_eval.p_Mn66__He4_Cr63  +
          -rho*Y[jp]*Y[jmn66]*rate_eval.p_Mn66__n_Fe66  +
          -rho*Y[jp]*Y[jk48]*rate_eval.p_K48__Ca49  +
          -rho*Y[jp]*Y[jp46]*rate_eval.p_P46__S47  +
          -rho*Y[jp]*Y[jmn65]*rate_eval.p_Mn65__He4_Cr62  +
          -rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__n_P44  +
          -rho*Y[jp]*Y[jmn64]*rate_eval.p_Mn64__He4_Cr61  +
          -rho*Y[jp]*Y[jmn62]*rate_eval.p_Mn62__He4_Cr59  +
          -rho*Y[jp]*Y[jmn60]*rate_eval.p_Mn60__He4_Cr57  +
          -rho*Y[jp]*Y[jmn60]*rate_eval.p_Mn60__n_Fe60  +
          -rho*Y[jp]*Y[jmn59]*rate_eval.p_Mn59__He4_Cr56  +
          -rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__n_Fe57  +
          -rho*Y[jp]*Y[jfe64]*rate_eval.p_Fe64__He4_Mn61  +
          -rho*Y[jp]*Y[jmn56]*rate_eval.p_Mn56__He4_Cr53  +
          -rho*Y[jp]*Y[jmn54]*rate_eval.p_Mn54__He4_Cr51  +
          +rho*Y[jhe4]*Y[jmn53]*rate_eval.He4_Mn53__p_Fe56  +
          -rho*Y[jp]*Y[jmn53]*rate_eval.p_Mn53__He4_Cr50  +
          +rho*Y[jn]*Y[jmn52]*rate_eval.n_Mn52__p_Cr52  +
          +rho*Y[jhe4]*Y[jmn51]*rate_eval.He4_Mn51__p_Fe54  +
          -rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__n_Sc53  +
          +rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__p_Cr51  +
          -rho*Y[jp]*Y[jo22]*rate_eval.p_O22__n_F22  +
          +rho*Y[jhe4]*Y[jmn49]*rate_eval.He4_Mn49__p_Fe52  +
          +rho*Y[jhe4]*Y[jmn47]*rate_eval.He4_Mn47__p_Fe50  +
          +rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__p_Cr47  +
          +rho*Y[jhe4]*Y[jmn46]*rate_eval.He4_Mn46__p_Fe49  +
          -rho*Y[jp]*Y[jca44]*rate_eval.p_Ca44__Sc45  +
          +rho*Y[jn]*Y[jmn46]*rate_eval.n_Mn46__p_Cr46  +
          +rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__p_Cr45  +
          +rho*Y[jhe4]*Y[jmn44]*rate_eval.He4_Mn44__p_Fe47  +
          -rho*Y[jp]*Y[jcr68]*rate_eval.p_Cr68__He4_V65  +
          -rho*Y[jp]*Y[jcr68]*rate_eval.p_Cr68__n_Mn68  +
          -rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__n_Mn67  +
          -rho*Y[jp]*Y[jcr66]*rate_eval.p_Cr66__He4_V63  +
          -rho*Y[jp]*Y[jcr65]*rate_eval.p_Cr65__He4_V62  +
          -rho*Y[jp]*Y[jmn72]*rate_eval.p_Mn72__n_Fe72  +
          -rho*Y[jp]*Y[jo25]*rate_eval.p_O25__n_F25  +
          -rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__n_Mn63  +
          -rho*Y[jp]*Y[jcr62]*rate_eval.p_Cr62__He4_V59  +
          -rho*Y[jp]*Y[jcr60]*rate_eval.p_Cr60__He4_V57  +
          -rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__n_Mn59  +
          -rho*Y[jp]*Y[jfe62]*rate_eval.p_Fe62__n_Co62  +
          -rho*Y[jp]*Y[jcr57]*rate_eval.p_Cr57__n_Mn57  +
          + 2*Y[jcr43]*rate_eval.Cr43__p_p_Sc41__weak__wc12  +
          -rho*Y[jp]*Y[jcr54]*rate_eval.p_Cr54__He4_V51  +
          -rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__Na33  +
          -rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__n_P38  +
          -rho*Y[jp]*Y[jmn55]*rate_eval.p_Mn55__He4_Cr52  +
          +rho*Y[jhe4]*Y[jcr49]*rate_eval.He4_Cr49__p_Mn52  +
          +rho*Y[jhe4]*Y[jcr48]*rate_eval.He4_Cr48__p_Mn51  +
          +rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__p_V48  +
          -rho*Y[jp]*Y[jti57]*rate_eval.p_Ti57__He4_Sc54  +
          +rho*Y[jhe4]*Y[jcr45]*rate_eval.He4_Cr45__p_Mn48  +
          +rho*Y[jhe4]*Y[jcr44]*rate_eval.He4_Cr44__p_Mn47  +
          +rho*Y[jhe4]*Y[jcr43]*rate_eval.He4_Cr43__p_Mn46  +
          +rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__p_V43  +
          +rho*Y[jhe4]*Y[jcr42]*rate_eval.He4_Cr42__p_Mn45  +
          +rho*Y[jn]*Y[jcr42]*rate_eval.n_Cr42__p_V42  +
          +rho*Y[jhe4]*Y[jsc37]*rate_eval.He4_Sc37__p_Ti40  +
          -rho*Y[jp]*Y[jv67]*rate_eval.p_V67__n_Cr67  +
          -rho*Y[jp]*Y[jv66]*rate_eval.p_V66__n_Cr66  +
          +rho*Y[jhe4]*Y[jv50]*rate_eval.He4_V50__p_Cr53  +
          -rho*Y[jp]*Y[jk47]*rate_eval.p_K47__He4_Ar44  +
          -rho*Y[jp]*Y[jv65]*rate_eval.p_V65__He4_Ti62  +
          +rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__p_V49  +
          -rho*Y[jp]*Y[jv64]*rate_eval.p_V64__He4_Ti61  +
          -rho*Y[jp]*Y[jv63]*rate_eval.p_V63__n_Cr63  +
          -rho*Y[jp]*Y[jv61]*rate_eval.p_V61__n_Cr61  +
          -rho*Y[jp]*Y[jp32]*rate_eval.p_P32__n_S32  +
          -rho*Y[jp]*Y[jv60]*rate_eval.p_V60__He4_Ti57  +
          +rho*Y[jt]*Y[jhe3]*rate_eval.t_He3__n_p_He4  +
          -rho*Y[jp]*Y[jv60]*rate_eval.p_V60__n_Cr60  +
          -rho*Y[jp]*Y[jo27]*rate_eval.p_O27__He4_N24  +
          -rho*Y[jp]*Y[jsi43]*rate_eval.p_Si43__n_P43  +
          -rho*Y[jp]*Y[jv58]*rate_eval.p_V58__He4_Ti55  +
          -rho*Y[jp]*Y[jv58]*rate_eval.p_V58__n_Cr58  +
          -rho*Y[jp]*Y[jv57]*rate_eval.p_V57__He4_Ti54  +
          -rho*Y[jp]*Y[jv57]*rate_eval.p_V57__n_Cr57  +
          +rho*Y[jhe4]*Y[jal40]*rate_eval.He4_Al40__p_Si43  +
          +rho*Y[jhe4]*Y[jcr47]*rate_eval.He4_Cr47__p_Mn50  +
          -rho*Y[jp]*Y[jv55]*rate_eval.p_V55__n_Cr55  +
          -rho*Y[jp]*Y[jv53]*rate_eval.p_V53__n_Cr53  +
          -rho*Y[jp]*Y[jv52]*rate_eval.p_V52__He4_Ti49  +
          -rho*Y[jp]*Y[jv52]*rate_eval.p_V52__n_Cr52  +
          -rho*Y[jp]*Y[jv51]*rate_eval.p_V51__He4_Ti48  +
          -rho*Y[jp]*Y[jf23]*rate_eval.p_F23__Ne24  +
          -rho*Y[jp]*Y[jv50]*rate_eval.p_V50__He4_Ti47  +
          -rho*Y[jp]*Y[jv50]*rate_eval.p_V50__n_Cr50  +
          +rho*Y[jn]*Y[jv50]*rate_eval.n_V50__p_Ti50  +
          -rho*Y[jp]*Y[jf24]*rate_eval.p_F24__Ne25  +
          -rho*Y[jp]*Y[jv49]*rate_eval.p_V49__He4_Ti46  +
          +rho*Y[jhe4]*Y[jv47]*rate_eval.He4_V47__p_Cr50  +
          +rho*Y[jhe4]*Y[jv46]*rate_eval.He4_V46__p_Cr49  +
          +rho*Y[jn]*Y[jv46]*rate_eval.n_V46__p_Ti46  +
          -rho*Y[jp]*Y[jsc52]*rate_eval.p_Sc52__Ti53  +
          +rho*Y[jn]*Y[jv44]*rate_eval.n_V44__p_Ti44  +
          +rho*Y[jhe4]*Y[jv43]*rate_eval.He4_V43__p_Cr46  +
          +rho*Y[jn]*Y[jv43]*rate_eval.n_V43__p_Ti43  +
          +rho*Y[jhe4]*Y[jv42]*rate_eval.He4_V42__p_Cr45  +
          +rho*Y[jn]*Y[jv40]*rate_eval.n_V40__p_Ti40  +
          +rho*Y[jhe4]*Y[jv39]*rate_eval.He4_V39__p_Cr42  +
          -rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__n_Ti53  +
          -rho*Y[jp]*Y[jcr57]*rate_eval.p_Cr57__He4_V54  +
          -rho*Y[jp]*Y[jne27]*rate_eval.p_Ne27__He4_F24  +
          -rho*Y[jp]*Y[jti64]*rate_eval.p_Ti64__He4_Sc61  +
          -rho*Y[jp]*Y[jti63]*rate_eval.p_Ti63__He4_Sc60  +
          -rho*Y[jp]*Y[jti63]*rate_eval.p_Ti63__n_V63  +
          -rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__n_V61  +
          -rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__n_V60  +
          -rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__n_V59  +
          -rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__n_V58  +
          -rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__n_V55  +
          -rho*Y[jp]*Y[jti54]*rate_eval.p_Ti54__He4_Sc51  +
          -rho*Y[jp]*Y[jti54]*rate_eval.p_Ti54__n_V54  +
          -rho*Y[jp]*Y[jf23]*rate_eval.p_F23__He4_O20  +
          -rho*Y[jp]*Y[jti53]*rate_eval.p_Ti53__He4_Sc50  +
          -rho*Y[jp]*Y[jti52]*rate_eval.p_Ti52__He4_Sc49  +
          -rho*Y[jp]*Y[jti52]*rate_eval.p_Ti52__n_V52  +
          -rho*Y[jp]*Y[jti51]*rate_eval.p_Ti51__n_V51  +
          +rho*Y[jhe4]*Y[jk36]*rate_eval.He4_K36__p_Ca39  +
          -rho*Y[jp]*Y[jar51]*rate_eval.p_Ar51__He4_Cl48  +
          +rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__p_Sc45  +
          +rho*Y[jhe4]*Y[jti43]*rate_eval.He4_Ti43__p_V46  +
          +rho*Y[jn]*Y[jti41]*rate_eval.n_Ti41__p_Sc41  +
          +rho*Y[jhe4]*Y[jti40]*rate_eval.He4_Ti40__p_V43  +
          -rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__n_Mn55  +
          -rho*Y[jp]*Y[jf31]*rate_eval.p_F31__He4_O28  +
          +rho*Y[jhe4]*Y[jti39]*rate_eval.He4_Ti39__p_V42  +
          +rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__p_Sc39  +
          +rho*Y[jhe4]*Y[jti38]*rate_eval.He4_Ti38__p_V41  +
          +rho*Y[jn]*Y[jti38]*rate_eval.n_Ti38__p_Sc38  +
          +rho*Y[jhe4]*Y[jti37]*rate_eval.He4_Ti37__p_V40  +
          -rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__n_Ti61  +
          +rho*Y[jhe4]*Y[jsc40]*rate_eval.He4_Sc40__p_Ti43  +
          -rho*Y[jp]*Y[jsc60]*rate_eval.p_Sc60__He4_Ca57  +
          -rho*Y[jp]*Y[jsc60]*rate_eval.p_Sc60__n_Ti60  +
          +rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__p_Mn48  +
          +rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__p_Cr53  +
          -rho*Y[jp]*Y[jsc58]*rate_eval.p_Sc58__He4_Ca55  +
          -rho*Y[jp]*Y[jsc58]*rate_eval.p_Sc58__n_Ti58  +
          -rho*Y[jp]*Y[jsc55]*rate_eval.p_Sc55__He4_Ca52  +
          -rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__n_Ti54  +
          -rho*Y[jp]*Y[jsc52]*rate_eval.p_Sc52__He4_Ca49  +
          -rho*Y[jp]*Y[js47]*rate_eval.p_S47__Cl48  +
          +rho*Y[jhe4]*Y[jc9]*rate_eval.He4_C9__p_N12  +
          -rho*Y[jp]*Y[jsc52]*rate_eval.p_Sc52__n_Ti52  +
          -rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__n_Ti50  +
          -rho*Y[jp]*Y[jsc49]*rate_eval.p_Sc49__He4_Ca46  +
          -rho*Y[jp]*Y[jsc48]*rate_eval.p_Sc48__He4_Ca45  +
          +rho*Y[jhe4]*Y[jsc47]*rate_eval.He4_Sc47__p_Ti50  +
          -rho*Y[jp]*Y[jsc47]*rate_eval.p_Sc47__He4_Ca44  +
          +rho*Y[jhe4]*Y[jsc46]*rate_eval.He4_Sc46__p_Ti49  +
          -rho*Y[jp]*Y[jsc46]*rate_eval.p_Sc46__He4_Ca43  +
          +rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__p_Ca46  +
          +rho*Y[jhe4]*Y[jsc45]*rate_eval.He4_Sc45__p_Ti48  +
          +rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__p_Al24  +
          -rho*Y[jp]*Y[jsc45]*rate_eval.p_Sc45__He4_Ca42  +
          +rho*Y[jn]*Y[jsc45]*rate_eval.n_Sc45__p_Ca45  +
          +rho*Y[jhe4]*Y[jsc44]*rate_eval.He4_Sc44__p_Ti47  +
          -rho*Y[jp]*Y[jsc44]*rate_eval.p_Sc44__He4_Ca41  +
          +rho*Y[jn]*Y[jsc44]*rate_eval.n_Sc44__p_Ca44  +
          +rho*Y[jhe4]*Y[jsc43]*rate_eval.He4_Sc43__p_Ti46  +
          +rho*Y[jn]*Y[jsc43]*rate_eval.n_Sc43__p_Ca43  +
          +rho*Y[jhe4]*Y[jsc42]*rate_eval.He4_Sc42__p_Ti45  +
          +rho*Y[jn]*Y[jsc42]*rate_eval.n_Sc42__p_Ca42  +
          -rho*Y[jp]*Y[jcr56]*rate_eval.p_Cr56__n_Mn56  +
          -rho*Y[jp]*Y[jsi36]*rate_eval.p_Si36__He4_Al33  +
          +rho*Y[jhe4]*Y[jsc39]*rate_eval.He4_Sc39__p_Ti42  +
          -rho*Y[jp]*Y[jp31]*rate_eval.p_P31__S32  +
          -rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__P46  +
          +rho*Y[jhe4]*Y[jsc38]*rate_eval.He4_Sc38__p_Ti41  +
          -rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__n_Mg36  +
          +rho*Y[jhe4]*Y[jsc36]*rate_eval.He4_Sc36__p_Ti39  +
          +rho*Y[jhe4]*Y[jsc35]*rate_eval.He4_Sc35__p_Ti38  +
          +rho*Y[jn]*Y[jsc35]*rate_eval.n_Sc35__p_Ca35  +
          -rho*Y[jp]*Y[jca61]*rate_eval.p_Ca61__He4_K58  +
          -rho*Y[jp]*Y[jca61]*rate_eval.p_Ca61__n_Sc61  +
          -rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__n_Sc60  +
          -rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__n_Sc59  +
          -rho*Y[jp]*Y[jca58]*rate_eval.p_Ca58__He4_K55  +
          +rho*Y[jn]*Y[jcr46]*rate_eval.n_Cr46__p_V46  +
          -rho*Y[jp]*Y[jca58]*rate_eval.p_Ca58__n_Sc58  +
          -rho*Y[jp]*Y[jca56]*rate_eval.p_Ca56__He4_K53  +
          -rho*Y[jp]*Y[jca55]*rate_eval.p_Ca55__He4_K52  +
          -rho*Y[jp]*Y[jca55]*rate_eval.p_Ca55__n_Sc55  +
          -rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__n_Sc52  +
          -rho*Y[jp]*Y[jp45]*rate_eval.p_P45__S46  +
          -rho*Y[jp]*Y[jcr56]*rate_eval.p_Cr56__He4_V53  +
          -rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__He4_K48  +
          -rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__He4_Mg36  +
          -rho*Y[jp]*Y[jca47]*rate_eval.p_Ca47__n_Sc47  +
          +rho*Y[jhe4]*Y[jti45]*rate_eval.He4_Ti45__p_V48  +
          -rho*Y[jp]*Y[jca42]*rate_eval.p_Ca42__He4_K39  +
          -rho*Y[jp]*Y[jp42]*rate_eval.p_P42__n_S42  +
          +rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__p_K38  +
          +rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__p_K37  +
          +rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__p_K36  +
          +rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__p_S35  +
          +rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__p_K35  +
          +rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__p_K34  +
          -rho*Y[jp]*Y[jk57]*rate_eval.p_K57__He4_Ar54  +
          -rho*Y[jp]*Y[jk57]*rate_eval.p_K57__n_Ca57  +
          -rho*Y[jp]*Y[jk56]*rate_eval.p_K56__n_Ca56  +
          -rho*Y[jp]*Y[jk54]*rate_eval.p_K54__n_Ca54  +
          -rho*Y[jp]*Y[jk53]*rate_eval.p_K53__n_Ca53  +
          -rho*Y[jp]*Y[jp29]*rate_eval.p_P29__S30  +
          -rho*Y[jp]*Y[jk51]*rate_eval.p_K51__n_Ca51  +
          -rho*Y[jp]*Y[js42]*rate_eval.p_S42__Cl43  +
          -rho*Y[jp]*Y[jk48]*rate_eval.p_K48__He4_Ar45  +
          -rho*Y[jp]*Y[jk45]*rate_eval.p_K45__He4_Ar42  +
          -rho*Y[jp]*Y[jk45]*rate_eval.p_K45__n_Ca45  +
          -rho*Y[jp]*Y[jk44]*rate_eval.p_K44__He4_Ar41  +
          +rho*Y[jhe4]*Y[jk43]*rate_eval.He4_K43__p_Ca46  +
          -rho*Y[jp]*Y[jk43]*rate_eval.p_K43__n_Ca43  +
          +rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__p_Ca45  +
          -rho*Y[jp]*Y[jk41]*rate_eval.p_K41__He4_Ar38  +
          +rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__p_Ca49  +
          -rho*Y[jp]*Y[jk40]*rate_eval.p_K40__He4_Ar37  +
          -rho*Y[jp]*Y[jk40]*rate_eval.p_K40__n_Ca40  +
          -rho*Y[jp]*Y[js37]*rate_eval.p_S37__Cl38  +
          +rho*Y[jn]*Y[jk40]*rate_eval.n_K40__p_Ar40  +
          +rho*Y[jn]*Y[jk39]*rate_eval.n_K39__p_Ar39  +
          +rho*Y[jn]*Y[jk38]*rate_eval.n_K38__p_Ar38  +
          +rho*Y[jhe4]*Y[jk37]*rate_eval.He4_K37__p_Ca40  +
          +rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__p_Ca47  +
          +rho*Y[jn]*Y[jk36]*rate_eval.n_K36__p_Ar36  +
          +rho*Y[jn]*Y[jk35]*rate_eval.n_K35__p_Ar35  +
          +rho*Y[jhe4]*Y[jk34]*rate_eval.He4_K34__p_Ca37  +
          -rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__n_Si39  +
          -rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__He4_V58  +
          +rho*Y[jn]*Y[jk33]*rate_eval.n_K33__p_Ar33  +
          -rho*Y[jp]*Y[jmn51]*rate_eval.p_Mn51__Fe52  +
          -rho*Y[jp]*Y[jmn56]*rate_eval.p_Mn56__Fe57  +
          +rho*Y[jn]*Y[jk32]*rate_eval.n_K32__p_Ar32  +
          +rho*Y[jhe4]*Y[jk31]*rate_eval.He4_K31__p_Ca34  +
          +rho*Y[jn]*Y[jk31]*rate_eval.n_K31__p_Ar31  +
          -rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__n_K54  +
          -rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__He4_Cl49  +
          -rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__n_K52  +
          -rho*Y[jp]*Y[jk59]*rate_eval.p_K59__n_Ca59  +
          -rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__He4_Cl47  +
          -rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__He4_Cl45  +
          -rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__n_K48  +
          -rho*Y[jp]*Y[jf28]*rate_eval.p_F28__n_Ne28  +
          +rho*Y[jhe4]*Y[jfe50]*rate_eval.He4_Fe50__p_Co53  +
          -rho*Y[jp]*Y[jar44]*rate_eval.p_Ar44__n_K44  +
          -rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__He4_V52  +
          -rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__n_K43  +
          -rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__n_K41  +
          -rho*Y[jp]*Y[jar40]*rate_eval.p_Ar40__He4_Cl37  +
          -rho*Y[jp]*Y[jar39]*rate_eval.p_Ar39__He4_Cl36  +
          -rho*Y[jp]*Y[jcr62]*rate_eval.p_Cr62__Mn63  +
          +rho*Y[jn]*Y[jar37]*rate_eval.n_Ar37__p_Cl37  +
          +rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__p_Cl35  +
          +rho*Y[jhe4]*Y[jar34]*rate_eval.He4_Ar34__p_K37  +
          +rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__p_Cl34  +
          +rho*Y[jhe4]*Y[jar33]*rate_eval.He4_Ar33__p_K36  +
          +rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__p_Cl33  +
          +rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__p_Cl32  +
          +rho*Y[jhe4]*Y[jar31]*rate_eval.He4_Ar31__p_K34  +
          +rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__p_Cl31  +
          +Y[jp27]*rate_eval.P27__p_Al26__weak__wc12  +
          +rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__p_Cl30  +
          +rho*Y[jhe4]*Y[jar29]*rate_eval.He4_Ar29__p_K32  +
          +rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__p_Cl29  +
          -rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__He4_S49  +
          -rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__n_Ar52  +
          -rho*Y[jp]*Y[jo16]*rate_eval.p_O16__F17  +
          -rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__He4_S48  +
          -rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__He4_S47  +
          -rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__n_Ar50  +
          -rho*Y[jp]*Y[jb12]*rate_eval.p_B12__n_C12  +
          -rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__He4_S45  +
          -rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__n_Ar48  +
          -rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__n_V62  +
          -rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__He4_S42  +
          -rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__n_Ar45  +
          +rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__p_Ar46  +
          -rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__He4_S40  +
          -rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__n_Fe61  +
          -rho*Y[jp]*Y[jv55]*rate_eval.p_V55__Cr56  +
          -rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__He4_S39  +
          -rho*Y[jp]*Y[js47]*rate_eval.p_S47__n_Cl47  +
          -rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__He4_S38  +
          -rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__n_Ar40  +
          -rho*Y[jp]*Y[jo19]*rate_eval.p_O19__He4_N16  +
          +rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__p_S36  +
          +rho*Y[jhe4]*Y[jcl34]*rate_eval.He4_Cl34__p_Ar37  +
          +rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__p_S34  +
          -rho*Y[jp]*Y[jti43]*rate_eval.p_Ti43__V44  +
          +rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__p_S33  +
          -rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__Mg35  +
          +rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__p_S31  +
          +rho*Y[jhe4]*Y[jar35]*rate_eval.He4_Ar35__p_K38  +
          +rho*Y[jhe4]*Y[jcl30]*rate_eval.He4_Cl30__p_Ar33  +
          +rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__p_S29  +
          +rho*Y[jhe4]*Y[jcl28]*rate_eval.He4_Cl28__p_Ar31  +
          +rho*Y[jn]*Y[jv49]*rate_eval.n_V49__p_Ti49  +
          -rho*Y[jp]*Y[js49]*rate_eval.p_S49__n_Cl49  +
          -rho*Y[jp]*Y[js48]*rate_eval.p_S48__n_Cl48  +
          -rho*Y[jp]*Y[jn15]*rate_eval.p_N15__O16  +
          -rho*Y[jp]*Y[js47]*rate_eval.p_S47__He4_P44  +
          -rho*Y[jp]*Y[jk52]*rate_eval.p_K52__He4_Ar49  +
          -rho*Y[jp]*Y[js46]*rate_eval.p_S46__n_Cl46  +
          +rho*Y[jd]*Y[jbe7]*rate_eval.d_Be7__p_He4_He4  +
          -rho*Y[jp]*Y[js45]*rate_eval.p_S45__He4_P42  +
          -rho*Y[jp]*Y[jmn64]*rate_eval.p_Mn64__n_Fe64  +
          -rho*Y[jp]*Y[js43]*rate_eval.p_S43__He4_P40  +
          -rho*Y[jp]*Y[jcr60]*rate_eval.p_Cr60__Mn61  +
          -rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__He4_Ca54  +
          -rho*Y[jp]*Y[js41]*rate_eval.p_S41__He4_P38  +
          -rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__He4_Mg27  +
          -rho*Y[jp]*Y[js40]*rate_eval.p_S40__n_Cl40  +
          -rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__He4_S37  +
          -rho*Y[jp]*Y[js39]*rate_eval.p_S39__He4_P36  +
          -rho*Y[jp]*Y[js38]*rate_eval.p_S38__He4_P35  +
          -rho*Y[jp]*Y[js38]*rate_eval.p_S38__n_Cl38  +
          -rho*Y[jp]*Y[jv56]*rate_eval.p_V56__He4_Ti53  +
          -rho*Y[jp]*Y[js37]*rate_eval.p_S37__n_Cl37  +
          -rho*Y[jp]*Y[jk49]*rate_eval.p_K49__n_Ca49  +
          -rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__Ar46  +
          -rho*Y[jp]*Y[jli6]*rate_eval.p_Li6__Be7  +
          -rho*Y[jp]*Y[js36]*rate_eval.p_S36__He4_P33  +
          -rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__He4_V66  +
          -rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__He4_Ca48  +
          -rho*Y[jp]*Y[jk51]*rate_eval.p_K51__He4_Ar48  +
          -rho*Y[jp]*Y[js35]*rate_eval.p_S35__He4_P32  +
          -rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__n_Ti57  +
          -rho*Y[jp]*Y[jcl35]*rate_eval.p_Cl35__He4_S32  +
          +rho*Y[jhe4]*Y[js31]*rate_eval.He4_S31__p_Cl34  +
          +rho*Y[jhe4]*Y[js30]*rate_eval.He4_S30__p_Cl33  +
          +rho*Y[jn]*Y[js30]*rate_eval.n_S30__p_P30  +
          +rho*Y[jhe4]*Y[js28]*rate_eval.He4_S28__p_Cl31  +
          +rho*Y[jhe4]*Y[js26]*rate_eval.He4_S26__p_Cl29  +
          -rho*Y[jp]*Y[jv65]*rate_eval.p_V65__Cr66  +
          -rho*Y[jp]*Y[jp47]*rate_eval.p_P47__n_S47  +
          -rho*Y[jp]*Y[jp45]*rate_eval.p_P45__n_S45  +
          -rho*Y[jp]*Y[jp43]*rate_eval.p_P43__He4_Si40  +
          -rho*Y[jp]*Y[jp43]*rate_eval.p_P43__n_S43  +
          -rho*Y[jp]*Y[jsc55]*rate_eval.p_Sc55__n_Ti55  +
          -rho*Y[jp]*Y[jp42]*rate_eval.p_P42__He4_Si39  +
          +rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__p_S44  +
          -rho*Y[jp]*Y[jo20]*rate_eval.p_O20__He4_N17  +
          -rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__He4_Cl40  +
          -rho*Y[jp]*Y[jp38]*rate_eval.p_P38__He4_Si35  +
          -rho*Y[jp]*Y[jp38]*rate_eval.p_P38__n_S38  +
          +rho*Y[jn]*Y[js33]*rate_eval.n_S33__p_P33  +
          -rho*Y[jp]*Y[jf18]*rate_eval.p_F18__He4_O15  +
          -rho*Y[jp]*Y[jp37]*rate_eval.p_P37__He4_Si34  +
          -rho*Y[jp]*Y[jp36]*rate_eval.p_P36__He4_Si33  +
          -rho*Y[jp]*Y[jp36]*rate_eval.p_P36__n_S36  +
          -rho*Y[jp]*Y[jmn69]*rate_eval.p_Mn69__n_Fe69  +
          -rho*Y[jp]*Y[jp34]*rate_eval.p_P34__n_S34  +
          -rho*Y[jp]*Y[jca56]*rate_eval.p_Ca56__n_Sc56  +
          +rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__p_Ar47  +
          -rho*Y[jp]*Y[jal25]*rate_eval.p_Al25__Si26  +
          -rho*Y[jp]*Y[jsc45]*rate_eval.p_Sc45__Ti46  +
          -rho*Y[jp]*Y[jp32]*rate_eval.p_P32__He4_Si29  +
          +rho*Y[jn]*Y[jp32]*rate_eval.n_P32__p_Si32  +
          +rho*Y[jhe4]*Y[jp31]*rate_eval.He4_P31__p_S34  +
          +rho*Y[jhe4]*Y[jp30]*rate_eval.He4_P30__p_S33  +
          +rho*Y[jn]*Y[jp28]*rate_eval.n_P28__p_Si28  +
          +rho*Y[jhe4]*Y[jp27]*rate_eval.He4_P27__p_S30  +
          +rho*Y[jn]*Y[jp27]*rate_eval.n_P27__p_Si27  +
          +rho*Y[jhe4]*Y[jp26]*rate_eval.He4_P26__p_S29  +
          +rho*Y[jn]*Y[jp26]*rate_eval.n_P26__p_Si26  +
          +rho*Y[jhe4]*Y[jp25]*rate_eval.He4_P25__p_S28  +
          +rho*Y[jhe4]*Y[jp24]*rate_eval.He4_P24__p_S27  +
          +rho*Y[jn]*Y[jp24]*rate_eval.n_P24__p_Si24  +
          -rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__He4_Al42  +
          -rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__n_P45  +
          -rho*Y[jp]*Y[jsi42]*rate_eval.p_Si42__n_P42  +
          +rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__p_Cr54  +
          -rho*Y[jp]*Y[js38]*rate_eval.p_S38__Cl39  +
          -rho*Y[jp]*Y[jsi39]*rate_eval.p_Si39__n_P39  +
          -rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__n_Ti62  +
          +rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__p_V47  +
          -rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__He4_Sc62  +
          -rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__He4_Al34  +
          -rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__n_P37  +
          -rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__He4_Al32  +
          -rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__n_P33  +
          +rho*Y[jhe4]*Y[jmn45]*rate_eval.He4_Mn45__p_Fe48  +
          +rho*Y[jhe4]*Y[jcr41]*rate_eval.He4_Cr41__p_Mn44  +
          -rho*Y[jp]*Y[jv49]*rate_eval.p_V49__Cr50  +
          +rho*Y[jhe4]*Y[jsi25]*rate_eval.He4_Si25__p_P28  +
          -rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__Fe59  +
          +rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__p_Al25  +
          +rho*Y[jhe4]*Y[jv40]*rate_eval.He4_V40__p_Cr43  +
          +rho*Y[jhe4]*Y[jsi24]*rate_eval.He4_Si24__p_P27  +
          +rho*Y[jhe4]*Y[jk40]*rate_eval.He4_K40__p_Ca43  +
          +rho*Y[jhe4]*Y[jsi23]*rate_eval.He4_Si23__p_P26  +
          -rho*Y[jp]*Y[jv61]*rate_eval.p_V61__He4_Ti58  +
          +rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__p_Al23  +
          +rho*Y[jhe4]*Y[jsi22]*rate_eval.He4_Si22__p_P25  +
          +rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__p_Al22  +
          -rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__n_Si43  +
          -rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__He4_Mg38  +
          -rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__He4_Mg37  +
          -rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__n_Si40  +
          +rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__p_Si42  +
          +rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__p_Si41  +
          -rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__He4_Mg35  +
          -rho*Y[jp]*Y[jv59]*rate_eval.p_V59__n_Cr59  +
          +rho*Y[jn]*Y[jv48]*rate_eval.n_V48__p_Ti48  +
          -rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__He4_Mg34  +
          +rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__p_Si39  +
          -rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__He4_Mg33  +
          -rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__n_Si36  +
          -rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__n_Si41  +
          -rho*Y[jp]*Y[jv64]*rate_eval.p_V64__n_Cr64  +
          -rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__He4_Mg32  +
          -rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__He4_Mg31  +
          -rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__n_Si34  +
          -rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__He4_Mg30  +
          +rho*Y[jhe4]*Y[jsi27]*rate_eval.He4_Si27__p_P30  +
          -rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__He4_S43  +
          -rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__n_Si33  +
          -rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__n_Na26  +
          -rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__He4_Mg29  +
          -rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__n_Si32  +
          +rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__p_Si34  +
          -rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__He4_S35  +
          -rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__He4_Mg28  +
          -rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__n_Si30  +
          -rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__He4_Mg26  +
          -rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__n_Si29  +
          -rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__He4_F31  +
          +rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__p_Sc44  +
          -rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__He4_Mg25  +
          +rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__p_Ca44  +
          +rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__p_Si30  +
          -rho*Y[jp]*Y[jca49]*rate_eval.p_Ca49__Sc50  +
          +rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__p_Mg26  +
          +rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__p_Mg25  +
          +rho*Y[jhe4]*Y[jal24]*rate_eval.He4_Al24__p_Si27  +
          -rho*Y[jp]*Y[js46]*rate_eval.p_S46__Cl47  +
          +rho*Y[jhe4]*Y[jal25]*rate_eval.He4_Al25__p_Si28  +
          -rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__Mg38  +
          +rho*Y[jhe4]*Y[jal22]*rate_eval.He4_Al22__p_Si25  +
          -rho*Y[jp]*Y[jv67]*rate_eval.p_V67__He4_Ti64  +
          +rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__p_Mg22  +
          +rho*Y[jhe4]*Y[jal21]*rate_eval.He4_Al21__p_Si24  +
          +rho*Y[jn]*Y[jsc48]*rate_eval.n_Sc48__p_Ca48  +
          -rho*Y[jp]*Y[jmg40]*rate_eval.p_Mg40__n_Al40  +
          -rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__n_Al39  +
          -rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__n_Al38  +
          -rho*Y[jp]*Y[jal27]*rate_eval.p_Al27__He4_Mg24  +
          -rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__n_Si38  +
          -rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__Mg32  +
          -rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__He4_Cl42  +
          -rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__He4_Na31  +
          -rho*Y[jp]*Y[jti53]*rate_eval.p_Ti53__n_V53  +
          -rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__He4_Na30  +
          -rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__He4_Mn63  +
          -rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__He4_Na29  +
          +rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__p_Ne19  +
          -rho*Y[jp]*Y[jmn59]*rate_eval.p_Mn59__n_Fe59  +
          -rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__n_Al30  +
          -rho*Y[jp]*Y[jca45]*rate_eval.p_Ca45__Sc46  +
          +rho*Y[jhe4]*Y[jcr46]*rate_eval.He4_Cr46__p_Mn49  +
          -rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__n_Ar46  +
          -rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__He4_Na26  +
          -rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__n_Al29  +
          -rho*Y[jp]*Y[jcr60]*rate_eval.p_Cr60__n_Mn60  +
          -rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__He4_F28  +
          +rho*Y[jhe4]*Y[jk35]*rate_eval.He4_K35__p_Ca38  +
          -rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__V60  +
          +rho*Y[jhe4]*Y[jfe53]*rate_eval.He4_Fe53__p_Co56  +
          -rho*Y[jp]*Y[jfe69]*rate_eval.p_Fe69__Co70  +
          +rho*Y[jhe4]*Y[jmg22]*rate_eval.He4_Mg22__p_Al25  +
          +rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__p_S30  +
          +rho*Y[jhe4]*Y[jmg20]*rate_eval.He4_Mg20__p_Al23  +
          +rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__p_Na20  +
          -rho*Y[jp]*Y[jna39]*rate_eval.p_Na39__n_Mg39  +
          +rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__p_Mg40  +
          -rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__He4_Ne34  +
          -rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__n_Mg35  +
          +rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__p_Mg36  +
          -rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__n_Mg33  +
          +rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__p_Cr43  +
          -rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__He4_Ne28  +
          -rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__n_Mg31  +
          -rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__n_Co66  +
          -rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__He4_Ne27  +
          -rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__Ar41  +
          +rho*Y[jn]*Y[js31]*rate_eval.n_S31__p_P31  +
          -rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__He4_Ne26  +
          -rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__n_Mg28  +
          -rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__n_Mg27  +
          -rho*Y[jp]*Y[jsc49]*rate_eval.p_Sc49__n_Ti49  +
          +rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__p_Mg27  +
          -rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__He4_Ne21  +
          +rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__p_Sc42  +
          -rho*Y[jp]*Y[jk56]*rate_eval.p_K56__He4_Ar53  +
          -rho*Y[jp]*Y[jk46]*rate_eval.p_K46__Ca47  +
          +rho*Y[jhe4]*Y[jna23]*rate_eval.He4_Na23__p_Mg26  +
          -rho*Y[jp]*Y[jfe67]*rate_eval.p_Fe67__n_Co67  +
          +rho*Y[jn]*Y[jfe50]*rate_eval.n_Fe50__p_Mn50  +
          +rho*Y[jn]*Y[js26]*rate_eval.n_S26__p_P26  +
          -rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__He4_Ne20  +
          +rho*Y[jhe4]*Y[jna22]*rate_eval.He4_Na22__p_Mg25  +
          -rho*Y[jp]*Y[jv56]*rate_eval.p_V56__Cr57  +
          +rho*Y[jhe4]*Y[js29]*rate_eval.He4_S29__p_Cl32  +
          +rho*Y[jhe4]*Y[jcl35]*rate_eval.He4_Cl35__p_Ar38  +
          -rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__n_Na34  +
          -rho*Y[jp]*Y[jcl36]*rate_eval.p_Cl36__Ar37  +
          -rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__n_Si35  +
          -rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__He4_F27  +
          +rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__p_Ca40  +
          -rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__He4_F26  +
          -rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__n_Na29  +
          -rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__n_Na28  +
          -rho*Y[jp]*Y[jne27]*rate_eval.p_Ne27__n_Na27  +
          -rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__He4_F22  +
          -rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__n_Na25  +
          +rho*Y[jhe4]*Y[js27]*rate_eval.He4_S27__p_Cl30  +
          -rho*Y[jp]*Y[jne24]*rate_eval.p_Ne24__n_Na24  +
          -rho*Y[jp]*Y[js30]*rate_eval.p_S30__Cl31  +
          -rho*Y[jp]*Y[jne23]*rate_eval.p_Ne23__n_Na23  +
          -rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__He4_Mg40  +
          -rho*Y[jp]*Y[jv42]*rate_eval.p_V42__Cr43  +
          +rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__p_P31  +
          -rho*Y[jp]*Y[jv54]*rate_eval.p_V54__n_Cr54  +
          -rho*Y[jp]*Y[jne22]*rate_eval.p_Ne22__Na23  +
          +rho*Y[jhe4]*Y[jal26]*rate_eval.He4_Al26__p_Si29  +
          -rho*Y[jp]*Y[jk33]*rate_eval.p_K33__Ca34  +
          +rho*Y[jhe4]*Y[jne19]*rate_eval.He4_Ne19__p_Na22  +
          +rho*Y[jhe4]*Y[jne18]*rate_eval.He4_Ne18__p_Na21  +
          +rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__p_F18  +
          +rho*Y[jhe4]*Y[jne17]*rate_eval.He4_Ne17__p_Na20  +
          +rho*Y[jhe4]*Y[jne16]*rate_eval.He4_Ne16__p_Na19  +
          +rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__p_F16  +
          -rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__He4_V64  +
          -rho*Y[jp]*Y[jf31]*rate_eval.p_F31__n_Ne31  +
          +rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__p_Ne33  +
          -rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__n_K45  +
          -rho*Y[jp]*Y[jmn47]*rate_eval.p_Mn47__Fe48  +
          -rho*Y[jp]*Y[jf30]*rate_eval.p_F30__He4_O27  +
          -rho*Y[jp]*Y[jf29]*rate_eval.p_F29__He4_O26  +
          -rho*Y[jp]*Y[jf27]*rate_eval.p_F27__He4_O24  +
          -rho*Y[jp]*Y[jf27]*rate_eval.p_F27__n_Ne27  +
          +Y[js27]*rate_eval.S27__p_Si26__weak__wc17  +
          -rho*Y[jp]*Y[jf26]*rate_eval.p_F26__n_Ne26  +
          -rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__He4_Ne31  +
          -rho*Y[jp]*Y[jf25]*rate_eval.p_F25__He4_O22  +
          -rho*Y[jp]*Y[jf25]*rate_eval.p_F25__n_Ne25  +
          -rho*Y[jp]*Y[jf24]*rate_eval.p_F24__n_Ne24  +
          +rho*Y[jhe4]*Y[jti42]*rate_eval.He4_Ti42__p_V45  +
          -rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__He4_Ne23  +
          -rho*Y[jp]*Y[jf22]*rate_eval.p_F22__He4_O19  +
          -rho*Y[jp]*Y[jf22]*rate_eval.p_F22__n_Ne22  +
          +rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__p_Ne24  +
          -rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__He4_F23  +
          +rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__p_Ne23  +
          +rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__p_Al26  +
          -rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__Si40  +
          -rho*Y[jp]*Y[jf20]*rate_eval.p_F20__He4_O17  +
          +rho*Y[jhe4]*Y[jf19]*rate_eval.He4_F19__p_Ne22  +
          -rho*Y[jp]*Y[jo21]*rate_eval.p_O21__n_F21  +
          +rho*Y[jhe4]*Y[jf18]*rate_eval.He4_F18__p_Ne21  +
          +rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__p_K33  +
          -rho*Y[jp]*Y[jo26]*rate_eval.p_O26__He4_N23  +
          -rho*Y[jp]*Y[jo26]*rate_eval.p_O26__n_F26  +
          -rho*Y[jp]*Y[jo24]*rate_eval.p_O24__n_F24  +
          -rho*Y[jp]*Y[jti57]*rate_eval.p_Ti57__n_V57  +
          -rho*Y[jp]*Y[jo20]*rate_eval.p_O20__n_F20  +
          +rho*Y[jhe4]*Y[jcl32]*rate_eval.He4_Cl32__p_Ar35  +
          -rho*Y[jp]*Y[jcr62]*rate_eval.p_Cr62__n_Mn62  +
          -rho*Y[jp]*Y[jo18]*rate_eval.p_O18__He4_N15  +
          -rho*Y[jp]*Y[js49]*rate_eval.p_S49__Cl50  +
          -rho*Y[jp]*Y[jo17]*rate_eval.p_O17__He4_N14  +
          +5.00000000000000e-01*rho*Y[jo16]**2*rate_eval.O16_O16__p_P31  +
          +rho*Y[jc12]*Y[jo16]*rate_eval.C12_O16__p_Al27  +
          -rho*Y[jp]*Y[jk48]*rate_eval.p_K48__n_Ca48  +
          -rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__He4_F25  +
          -rho*Y[jp]*Y[jal26]*rate_eval.p_Al26__Si27  +
          -rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__He4_Ne25  +
          -rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__Mn71  +
          +rho*Y[jhe4]*Y[jo13]*rate_eval.He4_O13__p_F16  +
          +rho*Y[jn]*Y[jo13]*rate_eval.n_O13__p_N13  +
          +rho*Y[jn]*Y[jo12]*rate_eval.n_O12__p_N12  +
          -rho*Y[jp]*Y[jn15]*rate_eval.p_N15__He4_C12  +
          +rho*Y[jn]*Y[jsc37]*rate_eval.n_Sc37__p_Ca37  +
          -rho*Y[jp]*Y[jf28]*rate_eval.p_F28__He4_O25  +
          -rho*Y[jp]*Y[jf29]*rate_eval.p_F29__Ne30  +
          +rho*Y[jn]*Y[jn14]*rate_eval.n_N14__p_C14  +
          +rho*Y[jhe4]*Y[jn13]*rate_eval.He4_N13__p_O16  +
          -rho*Y[jp]*Y[jc15]*rate_eval.p_C15__n_N15  +
          +rho*Y[jn]*Y[jv39]*rate_eval.n_V39__p_Ti39  +
          -rho*Y[jp]*Y[jk44]*rate_eval.p_K44__n_Ca44  +
          +rho*Y[jn]*Y[jc11]*rate_eval.n_C11__p_B11  +
          -rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__He4_Cl50  +
          -rho*Y[jp]*Y[jb12]*rate_eval.p_B12__He4_Be9  +
          -rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__He4_Sc53  +
          +rho*Y[jhe4]*Y[jb11]*rate_eval.He4_B11__p_C14  +
          -rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__K42  +
          +rho*Y[jhe4]*Y[jfe46]*rate_eval.He4_Fe46__p_Co49  +
          +rho*Y[jhe4]*Y[jb10]*rate_eval.He4_B10__p_C13  +
          +rho*Y[jhe4]*Y[jb8]*rate_eval.He4_B8__p_C11  +
          -rho*Y[jp]*Y[jv63]*rate_eval.p_V63__He4_Ti60  +
          +Y[jsi24]*rate_eval.Si24__p_Mg23__weak__wc12  +
          +rho*Y[jhe4]*Y[jv49]*rate_eval.He4_V49__p_Cr52  +
          -rho*Y[jp]*Y[jli6]*rate_eval.p_Li6__He4_He3  +
          +rho*Y[jd]*Y[jhe3]*rate_eval.d_He3__p_He4  +
          -rho*Y[jp]*Y[jp34]*rate_eval.p_P34__S35  +
          +rho*Y[jn]*Y[jhe3]*rate_eval.n_He3__p_t  +
          +5.00000000000000e-01*rho*Y[jd]**2*rate_eval.d_d__p_t  +
          -rho*Y[jp]*Y[jfe76]*rate_eval.p_Fe76__Co77  +
          -rho*Y[jp]*Y[jfe73]*rate_eval.p_Fe73__Co74  +
          -rho*Y[jp]*Y[jfe72]*rate_eval.p_Fe72__Co73  +
          -rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__n_Al31  +
          -rho*Y[jp]*Y[jfe70]*rate_eval.p_Fe70__Co71  +
          +rho*Y[jn]*Y[jf16]*rate_eval.n_F16__p_O16  +
          -rho*Y[jp]*Y[jp32]*rate_eval.p_P32__S33  +
          -rho*Y[jp]*Y[jfe68]*rate_eval.p_Fe68__Co69  +
          +rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__p_Ne21  +
          -rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__Co67  +
          -rho*Y[jp]*Y[jfe65]*rate_eval.p_Fe65__Co66  +
          +Y[jmg20]*rate_eval.Mg20__p_Ne19__weak__wc12  +
          -rho*Y[jp]*Y[jfe63]*rate_eval.p_Fe63__Co64  +
          +rho*Y[jn]*Y[js29]*rate_eval.n_S29__p_P29  +
          -rho*Y[jp]*Y[jfe61]*rate_eval.p_Fe61__Co62  +
          -rho*Y[jp]*Y[js46]*rate_eval.p_S46__He4_P43  +
          -rho*Y[jp]*Y[jfe60]*rate_eval.p_Fe60__Co61  +
          -rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__Si35  +
          -rho*Y[jp]*Y[jfe59]*rate_eval.p_Fe59__Co60  +
          -rho*Y[jp]*Y[jfe57]*rate_eval.p_Fe57__Co58  +
          -rho*Y[jp]*Y[jfe56]*rate_eval.p_Fe56__Co57  +
          -rho*Y[jp]*Y[jfe55]*rate_eval.p_Fe55__Co56  +
          -rho*Y[jp]*Y[jfe52]*rate_eval.p_Fe52__Co53  +
          -rho*Y[jp]*Y[jsi36]*rate_eval.p_Si36__n_P36  +
          -rho*Y[jp]*Y[jfe50]*rate_eval.p_Fe50__Co51  +
          -rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__n_Na32  +
          -rho*Y[jp]*Y[jmn73]*rate_eval.p_Mn73__Fe74  +
          -rho*Y[jp]*Y[jmn69]*rate_eval.p_Mn69__Fe70  +
          -rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__Fe69  +
          -rho*Y[jp]*Y[jmn73]*rate_eval.p_Mn73__n_Fe73  +
          -rho*Y[jp]*Y[jmn67]*rate_eval.p_Mn67__Fe68  +
          -rho*Y[jp]*Y[jmn66]*rate_eval.p_Mn66__Fe67  +
          +rho*Y[jhe4]*Y[jcl29]*rate_eval.He4_Cl29__p_Ar32  +
          -rho*Y[jp]*Y[jne33]*rate_eval.p_Ne33__n_Na33  +
          -rho*Y[jp]*Y[jmn62]*rate_eval.p_Mn62__Fe63  +
          -rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__Fe62  +
          +rho*Y[jn]*Y[jfe51]*rate_eval.n_Fe51__p_Mn51  +
          -rho*Y[jp]*Y[jca58]*rate_eval.p_Ca58__Sc59  +
          -rho*Y[jp]*Y[jk42]*rate_eval.p_K42__n_Ca42  +
          -rho*Y[jp]*Y[jfe64]*rate_eval.p_Fe64__n_Co64  +
          -rho*Y[jp]*Y[jmn50]*rate_eval.p_Mn50__Fe51  +
          -rho*Y[jp]*Y[jmn49]*rate_eval.p_Mn49__Fe50  +
          -rho*Y[jp]*Y[jmn48]*rate_eval.p_Mn48__Fe49  +
          -rho*Y[jp]*Y[jmn46]*rate_eval.p_Mn46__Fe47  +
          -rho*Y[jp]*Y[jmn45]*rate_eval.p_Mn45__Fe46  +
          -rho*Y[jp]*Y[jv53]*rate_eval.p_V53__He4_Ti50  +
          -rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__Mn70  +
          -rho*Y[jp]*Y[jcr66]*rate_eval.p_Cr66__Mn67  +
          -rho*Y[jp]*Y[jcr65]*rate_eval.p_Cr65__Mn66  +
          -rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__Sc53  +
          -rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__Mn64  +
          -rho*Y[jp]*Y[jsc48]*rate_eval.p_Sc48__n_Ti48  +
          -rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__Mn62  +
          -rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__Mn60  +
          +rho*Y[jhe4]*Y[jmg19]*rate_eval.He4_Mg19__p_Al22  +
          -rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__Mn59  +
          -rho*Y[jp]*Y[jcr57]*rate_eval.p_Cr57__Mn58  +
          -rho*Y[jp]*Y[jcr56]*rate_eval.p_Cr56__Mn57  +
          -rho*Y[jp]*Y[jcr54]*rate_eval.p_Cr54__Mn55  +
          +rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__p_Cr49  +
          -rho*Y[jp]*Y[jcr53]*rate_eval.p_Cr53__Mn54  +
          -rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__He4_S36  +
          -rho*Y[jp]*Y[jcr52]*rate_eval.p_Cr52__Mn53  +
          -rho*Y[jp]*Y[jcr51]*rate_eval.p_Cr51__Mn52  +
          -rho*Y[jp]*Y[jcr50]*rate_eval.p_Cr50__Mn51  +
          -rho*Y[jp]*Y[jcr49]*rate_eval.p_Cr49__Mn50  +
          +rho*Y[jhe4]*Y[jk38]*rate_eval.He4_K38__p_Ca41  +
          -rho*Y[jp]*Y[jcr46]*rate_eval.p_Cr46__Mn47  +
          -rho*Y[jp]*Y[jp44]*rate_eval.p_P44__He4_Si41  +
          -rho*Y[jp]*Y[jv67]*rate_eval.p_V67__Cr68  +
          -rho*Y[jp]*Y[jv66]*rate_eval.p_V66__Cr67  +
          -rho*Y[jp]*Y[jv64]*rate_eval.p_V64__Cr65  +
          +rho*Y[jhe4]*Y[jo14]*rate_eval.He4_O14__p_F17  +
          -rho*Y[jp]*Y[jk58]*rate_eval.p_K58__n_Ca58  +
          -rho*Y[jp]*Y[jv63]*rate_eval.p_V63__Cr64  +
          -rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__He4_F29  +
          -rho*Y[jp]*Y[jv60]*rate_eval.p_V60__Cr61  +
          -rho*Y[jp]*Y[jv59]*rate_eval.p_V59__Cr60  +
          -rho*Y[jp]*Y[jv58]*rate_eval.p_V58__Cr59  +
          -rho*Y[jp]*Y[jv57]*rate_eval.p_V57__Cr58  +
          -rho*Y[jp]*Y[jv54]*rate_eval.p_V54__Cr55  +
          -rho*Y[jp]*Y[jv53]*rate_eval.p_V53__Cr54  +
          -rho*Y[jp]*Y[jv62]*rate_eval.p_V62__n_Cr62  +
          -rho*Y[jp]*Y[jv52]*rate_eval.p_V52__Cr53  +
          -rho*Y[jp]*Y[jv50]*rate_eval.p_V50__Cr51  +
          +rho*Y[jhe4]*Y[jf16]*rate_eval.He4_F16__p_Ne19  +
          -rho*Y[jp]*Y[jv48]*rate_eval.p_V48__Cr49  +
          -rho*Y[jp]*Y[js42]*rate_eval.p_S42__n_Cl42  +
          -rho*Y[jp]*Y[jsc46]*rate_eval.p_Sc46__n_Ti46  +
          -rho*Y[jp]*Y[jv46]*rate_eval.p_V46__Cr47  +
          -rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__P39  +
          -rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__Fe64  +
          -rho*Y[jp]*Y[jv43]*rate_eval.p_V43__Cr44  +
          -rho*Y[jp]*Y[jp40]*rate_eval.p_P40__n_S40  +
          -rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__He4_Mg39  +
          -rho*Y[jp]*Y[jv41]*rate_eval.p_V41__Cr42  +
          -rho*Y[jp]*Y[jti63]*rate_eval.p_Ti63__V64  +
          -rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__V63  +
          -rho*Y[jp]*Y[jn12]*rate_eval.p_N12__O13  +
          -rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__V62  +
          -rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__V61  +
          -rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__V59  +
          -rho*Y[jp]*Y[jti57]*rate_eval.p_Ti57__V58  +
          -rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__V57  +
          -rho*Y[jp]*Y[jfe63]*rate_eval.p_Fe63__n_Co63  +
          -rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__V56  +
          -rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__n_Mn58  +
          -rho*Y[jp]*Y[jar47]*rate_eval.p_Ar47__n_K47  +
          -rho*Y[jp]*Y[jar36]*rate_eval.p_Ar36__K37  +
          -rho*Y[jp]*Y[jti54]*rate_eval.p_Ti54__V55  +
          -rho*Y[jp]*Y[jti53]*rate_eval.p_Ti53__V54  +
          -rho*Y[jp]*Y[jti52]*rate_eval.p_Ti52__V53  +
          -rho*Y[jp]*Y[jti49]*rate_eval.p_Ti49__V50  +
          -rho*Y[jp]*Y[jti47]*rate_eval.p_Ti47__V48  +
          -rho*Y[jp]*Y[jti44]*rate_eval.p_Ti44__V45  +
          +rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__p_Cr44  +
          +rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__p_Si32  +
          -rho*Y[jp]*Y[jti42]*rate_eval.p_Ti42__V43  +
          -rho*Y[jp]*Y[jmn72]*rate_eval.p_Mn72__Fe73  +
          -rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__n_K50  +
          -rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__Ti64  +
          -rho*Y[jp]*Y[jmn44]*rate_eval.p_Mn44__Fe45  +
          -rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__Ti62  +
          -rho*Y[jp]*Y[jsc58]*rate_eval.p_Sc58__Ti59  +
          -rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__Ti58  +
          -rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__Ti57  +
          -rho*Y[jp]*Y[jsc37]*rate_eval.p_Sc37__Ti38  +
          -rho*Y[jp]*Y[jsc55]*rate_eval.p_Sc55__Ti56  +
          +rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__p_Ca48  +
          -rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__Ti54  +
          -rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__He4_Cr54  +
          -rho*Y[jp]*Y[jhe3]*rate_eval.p_He3__He4__weak__bet_pos_  +
          -rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__Al32  +
          -rho*Y[jp]*Y[jsc49]*rate_eval.p_Sc49__Ti50  +
          -rho*Y[jp]*Y[jsc48]*rate_eval.p_Sc48__Ti49  +
          -rho*Y[jp]*Y[jne21]*rate_eval.p_Ne21__Na22  +
          -rho*Y[jp]*Y[jsc46]*rate_eval.p_Sc46__Ti47  +
          +rho*Y[jn]*Y[jv47]*rate_eval.n_V47__p_Ti47  +
          -rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__He4_K47  +
          -rho*Y[jp]*Y[jsc43]*rate_eval.p_Sc43__Ti44  +
          -rho*Y[jp]*Y[jsc42]*rate_eval.p_Sc42__Ti43  +
          -rho*Y[jp]*Y[jmn60]*rate_eval.p_Mn60__Fe61  +
          -rho*Y[jp]*Y[jsc41]*rate_eval.p_Sc41__Ti42  +
          -rho*Y[jp]*Y[jsc40]*rate_eval.p_Sc40__Ti41  +
          -rho*Y[jp]*Y[jsc38]*rate_eval.p_Sc38__Ti39  +
          -rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__He4_Ne30  +
          -rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__Sc61  +
          -rho*Y[jp]*Y[jti51]*rate_eval.p_Ti51__V52  +
          -rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__Sc60  +
          -rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__Sc58  +
          -rho*Y[jp]*Y[jna20]*rate_eval.p_Na20__Mg21  +
          +5.00000000000000e-01*rho*Y[jc12]**2*rate_eval.C12_C12__p_Na23  +
          -rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__Sc55  +
          +rho*Y[jhe4]*Y[jv48]*rate_eval.He4_V48__p_Cr51  +
          -rho*Y[jp]*Y[jfe58]*rate_eval.p_Fe58__Co59  +
          -rho*Y[jp]*Y[jmn71]*rate_eval.p_Mn71__Fe72  +
          -rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__Sc52  +
          -rho*Y[jp]*Y[jk42]*rate_eval.p_K42__He4_Ar39  +
          -rho*Y[jp]*Y[jca42]*rate_eval.p_Ca42__Sc43  +
          -rho*Y[jp]*Y[jca41]*rate_eval.p_Ca41__Sc42  +
          -rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__He4_K49  +
          -rho*Y[jp]*Y[jca40]*rate_eval.p_Ca40__Sc41  +
          -rho*Y[jp]*Y[jfe64]*rate_eval.p_Fe64__Co65  +
          -rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__P38  +
          -rho*Y[jp]*Y[jbe11]*rate_eval.p_Be11__He4_Li8  +
          +rho*Y[jn]*Y[jfe47]*rate_eval.n_Fe47__p_Mn47  +
          -rho*Y[jp]*Y[jk59]*rate_eval.p_K59__Ca60  +
          -rho*Y[jp]*Y[jk50]*rate_eval.p_K50__n_Ca50  +
          -rho*Y[jp]*Y[jp30]*rate_eval.p_P30__S31  +
          -rho*Y[jp]*Y[jk57]*rate_eval.p_K57__Ca58  +
          -rho*Y[jp]*Y[jk56]*rate_eval.p_K56__Ca57  +
          -rho*Y[jp]*Y[jcl36]*rate_eval.p_Cl36__He4_S33  +
          -rho*Y[jp]*Y[jk52]*rate_eval.p_K52__Ca53  +
          -rho*Y[jp]*Y[jf20]*rate_eval.p_F20__n_Ne20  +
          -rho*Y[jp]*Y[jk51]*rate_eval.p_K51__Ca52  +
          -rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__V66  +
          -rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__Na27  +
          -rho*Y[jp]*Y[jk45]*rate_eval.p_K45__Ca46  +
          -rho*Y[jp]*Y[jar38]*rate_eval.p_Ar38__K39  +
          -rho*Y[jp]*Y[jk43]*rate_eval.p_K43__Ca44  +
          -rho*Y[jp]*Y[jcr45]*rate_eval.p_Cr45__Mn46  +
          -rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__Ti63  +
          -rho*Y[jp]*Y[jk41]*rate_eval.p_K41__Ca42  +
          -rho*Y[jp]*Y[js34]*rate_eval.p_S34__Cl35  +
          + 2*Y[jca35]*rate_eval.Ca35__p_p_Cl33__weak__wc12  +
          -rho*Y[jp]*Y[jk38]*rate_eval.p_K38__Ca39  +
          +rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__p_Sc39  +
          -rho*Y[jp]*Y[jk37]*rate_eval.p_K37__Ca38  +
          +rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__p_Ti51  +
          -rho*Y[jp]*Y[jv56]*rate_eval.p_V56__n_Cr56  +
          -rho*Y[jp]*Y[jk36]*rate_eval.p_K36__Ca37  +
          -rho*Y[jp]*Y[jar51]*rate_eval.p_Ar51__K52  +
          -rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__n_Ar42  +
          +rho*Y[jn]*Y[jf18]*rate_eval.n_F18__p_O18  +
          -rho*Y[jp]*Y[js41]*rate_eval.p_S41__Cl42  +
          -rho*Y[jp]*Y[jar47]*rate_eval.p_Ar47__K48  +
          -rho*Y[jp]*Y[jar44]*rate_eval.p_Ar44__K45  +
          -rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__K44  +
          -rho*Y[jp]*Y[jar42]*rate_eval.p_Ar42__K43  +
          -rho*Y[jp]*Y[jar40]*rate_eval.p_Ar40__K41  +
          -rho*Y[jp]*Y[jar37]*rate_eval.p_Ar37__K38  +
          -rho*Y[jp]*Y[jar35]*rate_eval.p_Ar35__K36  +
          -rho*Y[jp]*Y[jf20]*rate_eval.p_F20__Ne21  +
          -rho*Y[jp]*Y[jsi25]*rate_eval.p_Si25__P26  +
          -rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__Ar44  +
          -rho*Y[jp]*Y[jp33]*rate_eval.p_P33__He4_Si30  +
          -rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__He4_Al41  +
          -rho*Y[jp]*Y[jp28]*rate_eval.p_P28__S29  +
          -rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__Ar52  +
          -rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__Fe58  +
          -rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__Ar50  +
          -rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__n_K53  +
          -rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__Ar42  +
          -rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__Ar47  +
          -rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__Ar40  +
          -rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__n_Mn64  +
          -rho*Y[jp]*Y[jcl35]*rate_eval.p_Cl35__Ar36  +
          -rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__n_Al35  +
          -rho*Y[jp]*Y[jcl32]*rate_eval.p_Cl32__Ar33  +
          -rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__Si43  +
          -rho*Y[jp]*Y[jcl31]*rate_eval.p_Cl31__Ar32  +
          -rho*Y[jp]*Y[jcl30]*rate_eval.p_Cl30__Ar31  +
          -rho*Y[jp]*Y[jcl29]*rate_eval.p_Cl29__Ar30  +
          -rho*Y[jp]*Y[jsi34]*rate_eval.p_Si34__P35  +
          -rho*Y[jp]*Y[js44]*rate_eval.p_S44__Cl45  +
          -rho*Y[jp]*Y[js40]*rate_eval.p_S40__Cl41  +
          -rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__Ar51  +
          -rho*Y[jp]*Y[js39]*rate_eval.p_S39__Cl40  +
          -rho*Y[jp]*Y[jk34]*rate_eval.p_K34__Ca35  +
          -rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__n_Mg32  +
          -rho*Y[jp]*Y[js36]*rate_eval.p_S36__Cl37  +
          -rho*Y[jp]*Y[js35]*rate_eval.p_S35__Cl36  +
          -rho*Y[jp]*Y[js32]*rate_eval.p_S32__Cl33  +
          -rho*Y[jp]*Y[js31]*rate_eval.p_S31__Cl32  +
          -rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__P34  +
          -rho*Y[jp]*Y[jp40]*rate_eval.p_P40__S41  +
          -rho*Y[jp]*Y[jp38]*rate_eval.p_P38__S39  +
          -rho*Y[jp]*Y[jp35]*rate_eval.p_P35__S36  +
          -rho*Y[jp]*Y[jfe58]*rate_eval.p_Fe58__He4_Mn55  +
          +rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__p_S32  +
          -rho*Y[jp]*Y[jp26]*rate_eval.p_P26__S27  +
          -rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__Fe71  +
          +rho*Y[jhe4]*Y[jcl33]*rate_eval.He4_Cl33__p_Ar36  +
          -rho*Y[jp]*Y[jca56]*rate_eval.p_Ca56__Sc57  +
          -rho*Y[jp]*Y[jk55]*rate_eval.p_K55__n_Ca55  +
          -rho*Y[jp]*Y[jsi42]*rate_eval.p_Si42__P43  +
          -rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__P41  +
          -rho*Y[jp]*Y[jsi39]*rate_eval.p_Si39__P40  +
          -rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__He4_Cl51  +
          -rho*Y[jp]*Y[jsi32]*rate_eval.p_Si32__P33  +
          -rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__Ar48  +
          -rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__n_Al37  +
          -rho*Y[jp]*Y[jsi31]*rate_eval.p_Si31__P32  +
          -rho*Y[jp]*Y[jsi30]*rate_eval.p_Si30__P31  +
          -rho*Y[jp]*Y[jsi28]*rate_eval.p_Si28__P29  +
          -rho*Y[jp]*Y[jsi26]*rate_eval.p_Si26__P27  +
          -rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__He4_Ca53  +
          -rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__n_Sc54  +
          +rho*Y[jhe4]*Y[jca38]*rate_eval.He4_Ca38__p_Sc41  +
          -rho*Y[jp]*Y[jo17]*rate_eval.p_O17__F18  +
          -rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__Si41  +
          -rho*Y[jp]*Y[jti64]*rate_eval.p_Ti64__n_V64  +
          -rho*Y[jp]*Y[jk40]*rate_eval.p_K40__Ca41  +
          -rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__n_Ar51  +
          -rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__Si38  +
          -rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__He4_Ca56  +
          -rho*Y[jp]*Y[jk44]*rate_eval.p_K44__Ca45  +
          -rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__n_P40  +
          -rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__Si37  +
          -rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__Si34  +
          -rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__Si32  +
          -rho*Y[jp]*Y[js49]*rate_eval.p_S49__He4_P46  +
          -rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__Si31  +
          -rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__Si29  +
          -rho*Y[jp]*Y[jcr68]*rate_eval.p_Cr68__Mn69  +
          -rho*Y[jp]*Y[jal24]*rate_eval.p_Al24__Si25  +
          -rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__n_Ar39  +
          -rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__Al40  +
          -rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__Al38  +
          -rho*Y[jp]*Y[jsc60]*rate_eval.p_Sc60__Ti61  +
          -rho*Y[jp]*Y[jp46]*rate_eval.p_P46__He4_Si43  +
          -rho*Y[jp]*Y[jcr47]*rate_eval.p_Cr47__Mn48  +
          -rho*Y[jp]*Y[jca43]*rate_eval.p_Ca43__Sc44  +
          -rho*Y[jp]*Y[js48]*rate_eval.p_S48__He4_P45  +
          +rho*Y[jn]*Y[jk37]*rate_eval.n_K37__p_Ar37  +
          -rho*Y[jp]*Y[jfe49]*rate_eval.p_Fe49__Co50  +
          -rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__Al31  +
          -rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__P45  +
          -rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__n_Al33  +
          -rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__Al33  +
          -rho*Y[jp]*Y[jfe54]*rate_eval.p_Fe54__Co55  +
          -rho*Y[jp]*Y[jmg27]*rate_eval.p_Mg27__Al28  +
          -rho*Y[jp]*Y[jmg26]*rate_eval.p_Mg26__Al27  +
          -rho*Y[jp]*Y[jk49]*rate_eval.p_K49__Ca50  +
          -rho*Y[jp]*Y[jmg24]*rate_eval.p_Mg24__Al25  +
          -rho*Y[jp]*Y[jmg23]*rate_eval.p_Mg23__Al24  +
          -rho*Y[jp]*Y[jmg22]*rate_eval.p_Mg22__Al23  +
          +rho*Y[jhe4]*Y[jmn48]*rate_eval.He4_Mn48__p_Fe51  +
          -rho*Y[jp]*Y[jna38]*rate_eval.p_Na38__Mg39  +
          -rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__n_Ar47  +
          -rho*Y[jp]*Y[jf21]*rate_eval.p_F21__n_Ne21  +
          -rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__Mg33  +
          +rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__p_Si31  +
          -rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__Mg37  +
          -rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__Mg27  +
          -rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__Mg26  +
          -rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__K53  +
          +rho*Y[jhe4]*Y[jf15]*rate_eval.He4_F15__p_Ne18  +
          -rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__n_Sc51  +
          -rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__He4_Ca60  +
          -rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__Mg24  +
          -rho*Y[jp]*Y[jna22]*rate_eval.p_Na22__Mg23  +
          -rho*Y[jp]*Y[jna21]*rate_eval.p_Na21__Mg22  +
          -rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__n_V65  +
          -rho*Y[jp]*Y[js33]*rate_eval.p_S33__Cl34  +
          -rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__He4_Na28  +
          -rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__Ti55  +
          -rho*Y[jp]*Y[jsi29]*rate_eval.p_Si29__P30  +
          -rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__Na32  +
          -rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__Na31  +
          -rho*Y[jp]*Y[jmn71]*rate_eval.p_Mn71__n_Fe71  +
          +Y[jne17]*rate_eval.Ne17__p_O16__weak__wc12  +
          -rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__Ar45  +
          -rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__Na29  +
          -rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__He4_Ne32  +
          -rho*Y[jp]*Y[jne27]*rate_eval.p_Ne27__Na28  +
          +Y[jti41]*rate_eval.Ti41__p_Ca40__weak__wc12  +
          +Y[js28]*rate_eval.S28__p_Si27__weak__wc12  +
          -rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__Na26  +
          -rho*Y[jp]*Y[jne23]*rate_eval.p_Ne23__Na24  +
          -rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__Si44  +
          -rho*Y[jp]*Y[jne33]*rate_eval.p_Ne33__Na34  +
          -rho*Y[jp]*Y[jf27]*rate_eval.p_F27__Ne28  +
          -rho*Y[jp]*Y[jne20]*rate_eval.p_Ne20__Na21  +
          -rho*Y[jp]*Y[jk53]*rate_eval.p_K53__Ca54  +
          -rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__n_Mn70  +
          -rho*Y[jp]*Y[jne19]*rate_eval.p_Ne19__Na20  +
          -rho*Y[jp]*Y[jf24]*rate_eval.p_F24__He4_O21  +
          -rho*Y[jp]*Y[jmn52]*rate_eval.p_Mn52__Fe53  +
          -rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__Mn65  +
          -rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__Ar49  +
          -rho*Y[jp]*Y[jf28]*rate_eval.p_F28__Ne29  +
          -rho*Y[jp]*Y[jf19]*rate_eval.p_F19__He4_O16  +
          -rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__Al39  +
          +rho*Y[jn]*Y[jv41]*rate_eval.n_V41__p_Ti41  +
          -rho*Y[jp]*Y[jf22]*rate_eval.p_F22__Ne23  +
          -rho*Y[jp]*Y[jf21]*rate_eval.p_F21__Ne22  +
          -rho*Y[jp]*Y[jfe51]*rate_eval.p_Fe51__Co52  +
          -rho*Y[jp]*Y[jo27]*rate_eval.p_O27__F28  +
          -rho*Y[jp]*Y[jo26]*rate_eval.p_O26__F27  +
          -rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__n_Ar43  +
          -rho*Y[jp]*Y[jk35]*rate_eval.p_K35__Ca36  +
          -rho*Y[jp]*Y[jo22]*rate_eval.p_O22__F23  +
          -rho*Y[jp]*Y[jo20]*rate_eval.p_O20__F21  +
          -rho*Y[jp]*Y[js44]*rate_eval.p_S44__n_Cl44  +
          -rho*Y[jp]*Y[jn14]*rate_eval.p_N14__O15  +
          -rho*Y[jp]*Y[jc14]*rate_eval.p_C14__N15  +
          -rho*Y[jp]*Y[jc13]*rate_eval.p_C13__N14  +
          -rho*Y[jp]*Y[jc12]*rate_eval.p_C12__N13  +
          -rho*Y[jp]*Y[jc11]*rate_eval.p_C11__N12  +
          +rho*Y[jn]*Y[jv42]*rate_eval.n_V42__p_Ti42  +
          -rho*Y[jn]*Y[jp]*rate_eval.n_p__d  +
          -rho*Y[jp]*Y[jb10]*rate_eval.p_B10__C11  +
          -rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__Mg29  +
          -rho*Y[jp]*Y[jbe10]*rate_eval.p_Be10__B11  +
          -rho*Y[jp]*Y[jsc39]*rate_eval.p_Sc39__Ti40  +
          -rho*Y[jp]*Y[jbe7]*rate_eval.p_Be7__B8  +
          +rho*Y[jhe4]*Y[jfe45]*rate_eval.He4_Fe45__p_Co48  +
          -rho*Y[jp]*Y[jp35]*rate_eval.p_P35__n_S35  +
          -rho*Y[jp]*Y[jne24]*rate_eval.p_Ne24__Na25  +
          -rho*Y[jp]*Y[jt]*rate_eval.p_t__He4  +
          -rho*Y[jp]*Y[jp27]*rate_eval.p_P27__S28  +
          +rho*Y[jn]*Y[jti47]*rate_eval.n_Ti47__p_Sc47  +
          -rho*Y[jp]*Y[jca49]*rate_eval.p_Ca49__n_Sc49  +
          -rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__P36  +
          -rho*Y[jp]*Y[jti46]*rate_eval.p_Ti46__V47  +
          -rho*Y[jp]*Y[jfe71]*rate_eval.p_Fe71__Co72  +
          -rho*Y[jp]*Y[jf18]*rate_eval.p_F18__Ne19  +
          -rho*Y[jp]*Y[jmg36]*rate_eval.p_Mg36__Al37  +
          -rho*Y[jp]*Y[jar42]*rate_eval.p_Ar42__He4_Cl39  +
          + 2*Y[js27]*rate_eval.S27__p_p_Al25__weak__wc12  +
          +rho*Y[jhe4]*Y[jna19]*rate_eval.He4_Na19__p_Mg22  +
          -rho*Y[jp]*Y[jf25]*rate_eval.p_F25__Ne26  +
          -rho*Y[jp]*Y[jk42]*rate_eval.p_K42__Ca43  +
          + 2*Y[jsi23]*rate_eval.Si23__p_p_Na21__weak__wc12  +
          +rho*Y[jhe4]*Y[jsc41]*rate_eval.He4_Sc41__p_Ti44  +
          -rho*Y[jp]*Y[js37]*rate_eval.p_S37__He4_P34  +
          +rho*Y[jhe4]*Y[jmn43]*rate_eval.He4_Mn43__p_Fe46  +
          -rho*Y[jp]*Y[jk39]*rate_eval.p_K39__Ca40  +
          +Y[jcr43]*rate_eval.Cr43__p_Ti42__weak__wc17  +
          +Y[jal24]*rate_eval.Al24__p_Na23__weak__wc12  +
          -rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__n_Ti51  +
          + 2*Y[jal22]*rate_eval.Al22__p_p_Ne20__weak__wc12  +
          -rho*Y[jp]*Y[jti50]*rate_eval.p_Ti50__V51  +
          -rho*Y[jp]*Y[jmn53]*rate_eval.p_Mn53__Fe54  +
          -rho*Y[jp]*Y[jp33]*rate_eval.p_P33__S34  +
          +rho*Y[jhe4]*Y[jna20]*rate_eval.He4_Na20__p_Mg23  +
          -rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__n_Si28  +
          -rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__n_Ar41  +
          -rho*Y[jp]*Y[jk55]*rate_eval.p_K55__Ca56  +
          -rho*Y[jp]*Y[jk47]*rate_eval.p_K47__n_Ca47  +
          -rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__n_Sc50  +
          +rho*Y[jhe4]*Y[jv44]*rate_eval.He4_V44__p_Cr47  +
          -rho*Y[jp]*Y[jv45]*rate_eval.p_V45__Cr46  +
          + -2*5.00000000000000e-01*rho*Y[jp]**2*rate_eval.p_p__d__weak__bet_pos_  +
          + -2*5.00000000000000e-01*rho**2*ye(Y)*Y[jp]**2*rate_eval.p_p__d__weak__electron_capture  +
          -rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__n_Ar38  +
          -rho*Y[jp]*Y[jal23]*rate_eval.p_Al23__Si24  +
          -rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__Si42  +
          +rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__p_Na19  +
          -rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__Ar39  +
          -rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__n_Al32  +
          +Y[jfe48]*rate_eval.Fe48__p_Cr47__weak__wc12  +
          -rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__Mg28  +
          -rho*Y[jp]*Y[jp46]*rate_eval.p_P46__n_S46  +
          -rho*Y[jp]*Y[jp41]*rate_eval.p_P41__n_S41  +
          +Y[jfe46]*rate_eval.Fe46__p_Cr45__weak__wc12  +
          -rho*Y[jp]*Y[jp39]*rate_eval.p_P39__n_S39  +
          -rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__Mn56  +
          +Y[jfe45]*rate_eval.Fe45__p_Cr44__weak__wc17  +
          -rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__He4_Cr60  +
          +rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__p_Mg23  +
          +rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__p_Mg24  +
          -rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__Sc51  +
          -rho*Y[jp]*Y[jmn64]*rate_eval.p_Mn64__Fe65  +
          -rho*Y[jp]*Y[jv44]*rate_eval.p_V44__Cr45  +
          -rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__He4_Ne33  +
          -rho*Y[jp]*Y[jcl34]*rate_eval.p_Cl34__Ar35  +
          -rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__He4_Na34  +
          -rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__n_Mg34  +
          +rho*Y[jn]*Y[jmg22]*rate_eval.n_Mg22__p_Na22  +
          +rho*Y[jhe4]*Y[jca35]*rate_eval.He4_Ca35__p_Sc38  +
          -rho*Y[jp]*Y[jk58]*rate_eval.p_K58__Ca59  +
          -rho*Y[jp]*Y[jfe53]*rate_eval.p_Fe53__Co54  +
          +Y[jmn46]*rate_eval.Mn46__p_V45__weak__wc12  +
          +rho*Y[jhe4]*Y[jca37]*rate_eval.He4_Ca37__p_Sc40  +
          -rho*Y[jp]*Y[jp31]*rate_eval.p_P31__He4_Si28  +
          +rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__p_Sc37  +
          -rho*Y[jp]*Y[jp41]*rate_eval.p_P41__S42  +
          -rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__n_Ar44  +
          +rho*Y[jhe4]*Y[jn12]*rate_eval.He4_N12__p_O15  +
          +rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__p_Na21  +
          -rho*Y[jp]*Y[jca48]*rate_eval.p_Ca48__Sc49  +
          -rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__Al42  +
          +rho*Y[jn]*Y[jbe7]*rate_eval.n_Be7__p_Li7  +
          +Y[jcr45]*rate_eval.Cr45__p_Ti44__weak__wc12  +
          +rho*Y[jhe4]*Y[jp28]*rate_eval.He4_P28__p_S31  +
          -rho*Y[jp]*Y[jsc47]*rate_eval.p_Sc47__Ti48  +
          +rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__p_S28  +
          +Y[jcr42]*rate_eval.Cr42__p_Ti41__weak__wc12  +
          +rho*Y[jhe4]*Y[jmn52]*rate_eval.He4_Mn52__p_Fe55  +
          +rho*Y[jn]*Y[jmn50]*rate_eval.n_Mn50__p_Cr50  +
          +rho*Y[jn]*Y[jcr41]*rate_eval.n_Cr41__p_V41  +
          -rho*Y[jp]*Y[jar46]*rate_eval.p_Ar46__K47  +
          -rho*Y[jp]*Y[js42]*rate_eval.p_S42__He4_P39  +
          -rho*Y[jp]*Y[jli8]*rate_eval.p_Li8__n_He4_He4  +
          -rho*Y[jp]*Y[jfe67]*rate_eval.p_Fe67__Co68  +
          +rho*Y[jn]*Y[js28]*rate_eval.n_S28__p_P28  +
          -rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__He4_Al37  +
          -rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__n_Al41  +
          -rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__Ar43  +
          -rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__Ti52  +
          +rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__p_Sc40  +
          +rho*Y[jn]*Y[jp30]*rate_eval.n_P30__p_Si30  +
          +rho*Y[jhe4]*Y[jfe51]*rate_eval.He4_Fe51__p_Co54  +
          +Y[jcl31]*rate_eval.Cl31__p_P30__weak__wc12  +
          -rho*Y[jp]*Y[jf19]*rate_eval.p_F19__Ne20  +
          -rho*Y[jp]*Y[jk50]*rate_eval.p_K50__He4_Ar47  +
          +rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__p_Ne22  +
          -rho*Y[jp]*Y[js45]*rate_eval.p_S45__n_Cl45  +
          +rho*Y[jhe4]*Y[jar30]*rate_eval.He4_Ar30__p_K33  +
          -rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__n_Fe58  +
          -rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__He4_K54  +
          -rho*Y[jp]*Y[jcr65]*rate_eval.p_Cr65__n_Mn65  +
          -rho*Y[jp]*Y[jf29]*rate_eval.p_F29__n_Ne29  +
          -rho*Y[jp]*Y[jn13]*rate_eval.p_N13__O14  +
          +Y[jar31]*rate_eval.Ar31__p_S30__weak__wc17  +
          -rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__n_Fe63  +
          +rho*Y[jhe4]*Y[jv45]*rate_eval.He4_V45__p_Cr48  +
          -rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__n_Na30  +
          -rho*Y[jp]*Y[jf30]*rate_eval.p_F30__n_Ne30  +
          -rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__He4_Ne24  +
          -rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__He4_Al30  +
          -rho*Y[jp]*Y[jb11]*rate_eval.p_B11__C12  +
          +Y[jti39]*rate_eval.Ti39__p_Ca38__weak__wc12  +
          +rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__p_Ca36  +
          -rho*Y[jp]*Y[jk46]*rate_eval.p_K46__He4_Ar43  +
          -rho*Y[jp]*Y[js41]*rate_eval.p_S41__n_Cl41  +
          -rho*Y[jp]*Y[jmg36]*rate_eval.p_Mg36__n_Al36  +
          -rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__n_Mn69  +
          -rho*Y[jp]*Y[jv51]*rate_eval.p_V51__Cr52  +
          -rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__Si39  +
          -rho*Y[jp]*Y[jk49]*rate_eval.p_K49__He4_Ar46  +
          -rho*Y[jp]*Y[jp25]*rate_eval.p_P25__S26  +
          -rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__Mg25  +
          +Y[jar32]*rate_eval.Ar32__p_S31__weak__wc12  +
          -rho*Y[jp]*Y[js39]*rate_eval.p_S39__n_Cl39  +
          -rho*Y[jp]*Y[jcl33]*rate_eval.p_Cl33__Ar34  +
          +Y[jca37]*rate_eval.Ca37__p_Ar36__weak__wc12  +
          -rho*Y[jp]*Y[jca46]*rate_eval.p_Ca46__Sc47  +
          +Y[jca36]*rate_eval.Ca36__p_Ar35__weak__wc12  +
          -rho*Y[jp]*Y[jfe68]*rate_eval.p_Fe68__n_Co68  +
          +Y[jca35]*rate_eval.Ca35__p_Ar34__weak__wc17  +
          -rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__n_Mg29  +
          -rho**2*Y[jn]*Y[jp]*Y[jhe4]*rate_eval.n_p_He4__Li6  +
          +rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__p_Mg28  +
          -rho*Y[jp]*Y[jv55]*rate_eval.p_V55__He4_Ti52  +
          -rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__He4_K57  +
          -rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__He4_Cr55  +
          -rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__n_Si37  +
          -rho*Y[jp]*Y[jti48]*rate_eval.p_Ti48__V49  +
          -rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__He4_Cl38  +
          +rho*Y[jhe4]*Y[jmg21]*rate_eval.He4_Mg21__p_Al24  +
          -rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__He4_S46  +
          +rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__p_Ca38  +
          -rho*Y[jp]*Y[jar39]*rate_eval.p_Ar39__K40  +
          -rho*Y[jp]*Y[jk47]*rate_eval.p_K47__Ca48  +
          -rho*Y[jp]*Y[jo23]*rate_eval.p_O23__n_F23  +
          +rho*Y[jhe4]*Y[jc11]*rate_eval.He4_C11__p_N14  +
          +Y[jk36]*rate_eval.K36__p_Cl35__weak__wc12  +
          +Y[jk35]*rate_eval.K35__p_Cl34__weak__wc12  +
          -rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__Na35  +
          -rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__He4_Sc58  +
          -rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__He4_Sc57  +
          +rho*Y[jhe4]*Y[jti41]*rate_eval.He4_Ti41__p_V44  +
          -rho*Y[jp]*Y[jb10]*rate_eval.p_B10__He4_Be7  +
          -rho*Y[jp]*Y[js40]*rate_eval.p_S40__He4_P37  +
          -rho*Y[jp]*Y[jk54]*rate_eval.p_K54__Ca55  +
          -rho*Y[jp]*Y[jv61]*rate_eval.p_V61__Cr62  +
          -rho*Y[jp]*Y[jmg27]*rate_eval.p_Mg27__n_Al27  +
          -rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__He4_Cr67  +
          +Y[jsi22]*rate_eval.Si22__p_Mg21__weak__wc12  +
          +rho*Y[jn]*Y[jcr51]*rate_eval.n_Cr51__p_V51  +
          -rho*Y[jp]*Y[jk46]*rate_eval.p_K46__n_Ca46  +
          -rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__Ti60  +
          -rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__B10  +
          -rho*Y[jp]*Y[jp39]*rate_eval.p_P39__He4_Si36  +
          +rho*Y[jhe4]*Y[jk33]*rate_eval.He4_K33__p_Ca36  +
          -rho*Y[jp]*Y[jf26]*rate_eval.p_F26__Ne27  +
          +Y[jar33]*rate_eval.Ar33__p_S32__weak__wc12  +
          +Y[js29]*rate_eval.S29__p_Si28__weak__wc12  +
          -rho*Y[jp]*Y[jli7]*rate_eval.p_Li7__He4_He4  +
          -rho*Y[jp]*Y[jfe65]*rate_eval.p_Fe65__n_Co65  +
          -rho*Y[jp]*Y[jfe76]*rate_eval.p_Fe76__n_Co76  +
          -rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__Mg34  +
          +rho*Y[jn]*Y[jcr45]*rate_eval.n_Cr45__p_V45  +
          +rho*Y[jn]*Y[jsc41]*rate_eval.n_Sc41__p_Ca41  +
          -rho*Y[jp]*Y[jmn67]*rate_eval.p_Mn67__n_Fe67  +
          +rho*Y[jn]*Y[jfe52]*rate_eval.n_Fe52__p_Mn52  +
          -rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__n_Sc57  +
          -rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__He4_K56  +
          -rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__n_Na31  +
          -rho*Y[jp]*Y[jf21]*rate_eval.p_F21__He4_O18  +
          -rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__He4_Ca58  +
          -rho*Y[jp]*Y[jv65]*rate_eval.p_V65__n_Cr65  +
          -rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__He4_Li6  +
          +Y[jcl32]*rate_eval.Cl32__p_P31__weak__wc12  +
          -rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__n_Mg26  +
          -rho*Y[jp]*Y[jsi27]*rate_eval.p_Si27__P28  +
          +rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__p_Al27  +
          -rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__He4_K51  +
          +Y[jsc40]*rate_eval.Sc40__p_K39__weak__wc12  +
          -rho*Y[jp]*Y[jfe74]*rate_eval.p_Fe74__Co75  +
          -rho*Y[jp]*Y[jo21]*rate_eval.p_O21__F22  +
          -rho*Y[jp]*Y[jp42]*rate_eval.p_P42__S43  +
          -rho*Y[jp]*Y[jcr66]*rate_eval.p_Cr66__n_Mn66  +
          +rho*Y[jhe4]*Y[jal23]*rate_eval.He4_Al23__p_Si26  +
          -rho*Y[jp]*Y[jo27]*rate_eval.p_O27__n_F27  +
          -rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__n_Si31  +
          -rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__He4_K50  +
          -rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__K46  +
          +Y[jal23]*rate_eval.Al23__p_Na22__weak__wc12  +
          -rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__He4_V61  +
          +rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__p_Ar44  +
          -rho*Y[jp]*Y[jsi41]*rate_eval.p_Si41__P42  +
          +rho*Y[jn]*Y[jmn48]*rate_eval.n_Mn48__p_Cr48  +
          -rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__He4_Na27  +
          +rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__p_F17  +
          -rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__Si36  +
          +rho*Y[jn]*Y[jti43]*rate_eval.n_Ti43__p_Sc43  +
          -rho*Y[jp]*Y[jf17]*rate_eval.p_F17__Ne18  +
          -rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__He4_Ca50  +
          + 2*Y[jar31]*rate_eval.Ar31__p_p_P29__weak__wc12  +
          -rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__n_Mg25  +
          -rho*Y[jp]*Y[jn16]*rate_eval.p_N16__n_O16  +
          +rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__p_V44  +
          -rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__n_Fe70  +
          -rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__He4_Na38  +
          +Y[jp28]*rate_eval.P28__p_Al27__weak__wc12  +
          -rho*Y[jp]*Y[jp37]*rate_eval.p_P37__S38  +
          -rho*Y[jp]*Y[jmn59]*rate_eval.p_Mn59__Fe60  +
          -rho*Y[jp]*Y[jp44]*rate_eval.p_P44__n_S44  +
          -rho*Y[jp]*Y[jcl28]*rate_eval.p_Cl28__Ar29  +
          -rho*Y[jp]*Y[jb8]*rate_eval.p_B8__C9  +
          -rho*Y[jp]*Y[jk55]*rate_eval.p_K55__He4_Ar52  +
          -rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__Al30  +
          +rho*Y[jhe4]*Y[jcl31]*rate_eval.He4_Cl31__p_Ar34  +
          -rho*Y[jp]*Y[jsi31]*rate_eval.p_Si31__n_P31  +
          -rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__He4_Cr65  +
          +Y[jsi25]*rate_eval.Si25__p_Mg24__weak__wc12  +
          +Y[jsi23]*rate_eval.Si23__p_Mg22__weak__wc17  +
          +rho*Y[jn]*Y[jf17]*rate_eval.n_F17__p_O17  +
          +rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__p_Mn45  +
          -rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__He4_Na35  +
          +Y[jfe47]*rate_eval.Fe47__p_Cr46__weak__wc12  +
          -rho*Y[jp]*Y[jo24]*rate_eval.p_O24__F25  +
          -rho*Y[jp]*Y[jcr48]*rate_eval.p_Cr48__Mn49  +
          -rho*Y[jp]*Y[jk52]*rate_eval.p_K52__n_Ca52  +
          -rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__He4_Na32  +
          -rho*Y[jp]*Y[jcl37]*rate_eval.p_Cl37__Ar38  +
          -rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__K55  +
          -rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__He4_Ca47  +
          -rho*Y[jp]*Y[jp45]*rate_eval.p_P45__He4_Si42  +
          -rho*Y[jp]*Y[jk43]*rate_eval.p_K43__He4_Ar40  +
          -rho*Y[jp]*Y[js43]*rate_eval.p_S43__n_Cl43  +
          +Y[jcr44]*rate_eval.Cr44__p_Ti43__weak__wc12  +
          -rho*Y[jp]*Y[jmn54]*rate_eval.p_Mn54__Fe55  +
          -rho*Y[jp]*Y[jp40]*rate_eval.p_P40__He4_Si37  +
          -rho*Y[jp]*Y[jp44]*rate_eval.p_P44__S45  +
          +Y[jo13]*rate_eval.O13__p_C12__weak__wc12  +
          -rho*Y[jp]*Y[jd]*rate_eval.p_d__He3  +
          -rho*Y[jp]*Y[jv47]*rate_eval.p_V47__Cr48  +
          +Y[jmg21]*rate_eval.Mg21__p_Ne20__weak__wc12  +
          -rho*Y[jp]*Y[jna38]*rate_eval.p_Na38__n_Mg38  +
          -rho*Y[jp]*Y[jv54]*rate_eval.p_V54__He4_Ti51  +
          -rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__Sc54  +
          -rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__n_Mg37  +
          -rho*Y[jp]*Y[jmn62]*rate_eval.p_Mn62__n_Fe62  +
          -rho*Y[jp]*Y[jf23]*rate_eval.p_F23__n_Ne23  +
          +rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__p_K39  +
          -rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__n_Ti56  +
          -rho*Y[jp]*Y[jsi36]*rate_eval.p_Si36__P37  +
          -rho*Y[jp]*Y[js43]*rate_eval.p_S43__Cl44  +
          -rho*Y[jp]*Y[jv62]*rate_eval.p_V62__He4_Ti59  +
          -rho*Y[jp]*Y[jp47]*rate_eval.p_P47__He4_Si44  +
          +rho*Y[jn]*Y[jp25]*rate_eval.n_P25__p_Si25  +
          -rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__n_K49  +
          -rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__He4_Sc59  +
          -rho*Y[jp]*Y[jal22]*rate_eval.p_Al22__Si23  +
          -rho*Y[jp]*Y[jca55]*rate_eval.p_Ca55__Sc56  +
          -rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__Mg31  +
          -rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__He4_V56  +
          -rho*Y[jp]*Y[jp35]*rate_eval.p_P35__He4_Si32  +
          -rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__K49  +
          -rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__Na30  +
          -rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__K54  +
          -rho*Y[jp]*Y[jp34]*rate_eval.p_P34__He4_Si31  +
          -rho*Y[jp]*Y[jk39]*rate_eval.p_K39__He4_Ar36  +
          +rho*Y[jhe3]*Y[jli7]*rate_eval.He3_Li7__n_p_He4_He4  +
          + 2*Y[jfe45]*rate_eval.Fe45__p_p_V43__weak__wc12  +
          +rho*Y[jhe4]*Y[jp29]*rate_eval.He4_P29__p_S32  +
          -rho*Y[jp]*Y[jmn55]*rate_eval.p_Mn55__Fe56  +
          -rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__K50  +
          -rho*Y[jp]*Y[jmn65]*rate_eval.p_Mn65__n_Fe65  +
          +rho*Y[jn]*Y[jp29]*rate_eval.n_P29__p_Si29  +
          -rho*Y[jp]*Y[jn16]*rate_eval.p_N16__He4_C13  +
          -rho*Y[jp]*Y[jca39]*rate_eval.p_Ca39__Sc40  +
          -rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__He4_Ne29  +
          -rho*Y[jp]*Y[jti64]*rate_eval.p_Ti64__V65  +
          +rho*Y[jn]*Y[jar36]*rate_eval.n_Ar36__p_Cl36  +
          +Y[jti40]*rate_eval.Ti40__p_Ca39__weak__wc12  +
          +rho*Y[jhe4]*Y[jmg23]*rate_eval.He4_Mg23__p_Al26  +
          +rho*Y[jhe4]*Y[jca34]*rate_eval.He4_Ca34__p_Sc37  +
          -rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__n_Ar49  +
          -rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__Ar53  +
          -rho*Y[jp]*Y[jo25]*rate_eval.p_O25__F26  +
          -rho*Y[jp]*Y[jk54]*rate_eval.p_K54__He4_Ar51  +
          -rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__n_Ti59  +
          -rho*Y[jp]*Y[jp37]*rate_eval.p_P37__n_S37  +
          -rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__He4_Cr58  +
          -rho*Y[jp]*Y[jp43]*rate_eval.p_P43__S44  +
          -rho*Y[jp]*Y[jti45]*rate_eval.p_Ti45__V46  +
          -rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__He4_S44  +
          -rho*Y[jp]*Y[jal27]*rate_eval.p_Al27__Si28  +
          -rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__n_V56  +
          -rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__Mg30  +
          -rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__He4_Sc56  +
          +rho*Y[jn]*Y[jal21]*rate_eval.n_Al21__p_Mg21  +
          -rho*Y[jp]*Y[jk50]*rate_eval.p_K50__Ca51  +
          -rho*Y[jp]*Y[jsi34]*rate_eval.p_Si34__n_P34  +
          -rho*Y[jp]*Y[jo19]*rate_eval.p_O19__n_F19  +
          -rho*Y[jp]*Y[jmg25]*rate_eval.p_Mg25__Al26  +
          +rho*Y[jn]*Y[jf14]*rate_eval.n_F14__p_O14  +
          -rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__n_Ti63  +
          -rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__n_Si42  +
          +Y[jmn48]*rate_eval.Mn48__p_V47__weak__wc12  +
          +rho*Y[jhe4]*Y[jk32]*rate_eval.He4_K32__p_Ca35  +
          -rho*Y[jp]*Y[js45]*rate_eval.p_S45__Cl46  +
          +rho*Y[jhe4]*Y[jsi26]*rate_eval.He4_Si26__p_P29  +
          -rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__He4_Sc55  +
          -rho*Y[jp]*Y[jf31]*rate_eval.p_F31__Ne32  +
          -rho*Y[jp]*Y[jsc43]*rate_eval.p_Sc43__He4_Ca40  +
          +rho*Y[jn]*Y[jk42]*rate_eval.n_K42__p_Ar42  +
          +rho*Y[jhe4]*Y[jv41]*rate_eval.He4_V41__p_Cr44  +
          -rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__He4_Ca59  +
          +Y[jal22]*rate_eval.Al22__p_Na21__weak__wc17  +
          -rho*Y[jp]*Y[jp47]*rate_eval.p_P47__S48  +
          +rho*Y[jd]*Y[jli6]*rate_eval.d_Li6__p_Li7  +
          -rho*Y[jp]*Y[jmg28]*rate_eval.p_Mg28__Al29  +
          +rho*Y[jn]*Y[jf15]*rate_eval.n_F15__p_O15  +
          +rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__p_Ne20  +
          -rho*Y[jp]*Y[jo19]*rate_eval.p_O19__F20  +
          -rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__He4_V55  +
          -rho*Y[jp]*Y[jsi41]*rate_eval.p_Si41__n_P41  +
          +rho*Y[jhe4]*Y[jfe47]*rate_eval.He4_Fe47__p_Co50  +
          -rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__n_Mg24  +
          -rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__He4_V60  +
          -rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__n_P35  +
          -rho*Y[jp]*Y[jsi43]*rate_eval.p_Si43__P44  +
          -rho*Y[jp]*Y[jk53]*rate_eval.p_K53__He4_Ar50  +
          -rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__He4_Ne22  +
          -rho*Y[jp]*Y[jmg28]*rate_eval.p_Mg28__n_Al28  +
          +rho*Y[jn]*Y[jv45]*rate_eval.n_V45__p_Ti45  +
          -rho*Y[jp]*Y[jo18]*rate_eval.p_O18__F19  +
          -rho*Y[jp]*Y[jp36]*rate_eval.p_P36__S37  +
          -rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__He4_Na36  +
          +rho*Y[jn]*Y[js27]*rate_eval.n_S27__p_P27  +
          -rho*Y[jp]*Y[jsc44]*rate_eval.p_Sc44__Ti45  +
          +rho*Y[jhe4]*Y[jca33]*rate_eval.He4_Ca33__p_Sc36  +
          -rho*Y[jp]*Y[jv66]*rate_eval.p_V66__He4_Ti63  +
          +Y[jfe49]*rate_eval.Fe49__p_Cr48__weak__wc12  +
          +rho*Y[jn]*Y[jsc39]*rate_eval.n_Sc39__p_Ca39  +
          -rho*Y[jp]*Y[jar51]*rate_eval.p_Ar51__n_K51  +
          -rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__Mn68  +
          -rho*Y[jp]*Y[jp41]*rate_eval.p_P41__He4_Si38  +
          -rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__n_Al34  +
          -rho*Y[jp]*Y[jna39]*rate_eval.p_Na39__Mg40  +
          -rho*Y[jp]*Y[jbe10]*rate_eval.p_Be10__He4_Li7  +
          -rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__Al36  +
          -rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__K51  +
          -rho*Y[jp]*Y[jca47]*rate_eval.p_Ca47__Sc48  +
          -rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__He4_S41  +
          -rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__He4_Ca51  +
          -rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__He4_V67  +
          -rho*Y[jp]*Y[jmg40]*rate_eval.p_Mg40__Al41  +
          -rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__He4_Sc52  +
          -rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__Al34  +
          -rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__Si30  +
          -rho*Y[jp]*Y[jmn56]*rate_eval.p_Mn56__n_Fe56  +
          -rho*Y[jp]*Y[jv59]*rate_eval.p_V59__He4_Ti56  +
          -rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__He4_Cl46  +
          -rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__Si33  +
          -rho*Y[jp]*Y[jna19]*rate_eval.p_Na19__Mg20  +
          -rho*Y[jp]*Y[jfe62]*rate_eval.p_Fe62__Co63  +
          -rho*Y[jp]*Y[jp39]*rate_eval.p_P39__S40  +
          -rho*Y[jp]*Y[jf26]*rate_eval.p_F26__He4_O23  +
          -rho*Y[jp]*Y[js48]*rate_eval.p_S48__Cl49  +
          -rho*Y[jp]*Y[jsc42]*rate_eval.p_Sc42__He4_Ca39  +
          -rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__He4_Al35  +
          -rho*Y[jp]*Y[jf30]*rate_eval.p_F30__Ne31  +
          +rho*Y[jn]*Y[jk34]*rate_eval.n_K34__p_Ar34  +
          -rho*Y[jp]*Y[jo23]*rate_eval.p_O23__F24  +
          -rho*Y[jp]*Y[jfe75]*rate_eval.p_Fe75__Co76  +
          -rho*Y[jp]*Y[jmn65]*rate_eval.p_Mn65__Fe66  +
          +rho*Y[jhe4]*Y[jmn50]*rate_eval.He4_Mn50__p_Fe53  +
          -rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__n_Mn61  +
          -rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__Mg36  +
          +rho*Y[jhe4]*Y[jar32]*rate_eval.He4_Ar32__p_K35  +
          -rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__n_Mg30  +
          -rho*Y[jp]*Y[jv62]*rate_eval.p_V62__Cr63  +
          -rho*Y[jp]*Y[jar46]*rate_eval.p_Ar46__n_K46  +
          + 0*rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__n_p_He4_He4  +
          -rho*Y[jp]*Y[jmg24]*rate_eval.p_Mg24__He4_Na21  +
          -rho*Y[jp]*Y[jk41]*rate_eval.p_K41__n_Ca41  +
          -rho*Y[jp]*Y[jo14]*rate_eval.p_O14__F15  +
          -rho*Y[jp]*Y[jti38]*rate_eval.p_Ti38__V39  +
          -rho*Y[jp]*Y[jfe47]*rate_eval.p_Fe47__Co48  +
          +rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__p_Cl37  +
          -rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__n_Mg23  +
          -rho*Y[jp]*Y[jne20]*rate_eval.p_Ne20__He4_F17  +
          -rho*Y[jp]*Y[jf19]*rate_eval.p_F19__n_Ne19  +
          -rho*Y[jp]*Y[jo15]*rate_eval.p_O15__F16  +
          +rho*Y[jhe4]*Y[jti44]*rate_eval.He4_Ti44__p_V47  +
          -rho*Y[jp]*Y[jca36]*rate_eval.p_Ca36__Sc37  +
          -rho*Y[jp]*Y[jn15]*rate_eval.p_N15__n_O15  +
          -rho*Y[jp]*Y[jc13]*rate_eval.p_C13__n_N13  +
          +rho*Y[jd]*Y[jli7]*rate_eval.d_Li7__p_Li8  +
          -rho*Y[jp]*Y[jfe48]*rate_eval.p_Fe48__Co49  +
          -rho*Y[jp]*Y[jti41]*rate_eval.p_Ti41__V42  +
          -rho*Y[jp]*Y[js28]*rate_eval.p_S28__Cl29  +
          -rho*Y[jp]*Y[jti40]*rate_eval.p_Ti40__V41  +
          -rho*Y[jp]*Y[jca35]*rate_eval.p_Ca35__Sc36  +
          -rho*Y[jp]*Y[jca34]*rate_eval.p_Ca34__Sc35  +
          -rho*Y[jp]*Y[jar33]*rate_eval.p_Ar33__K34  +
          -rho*Y[jp]*Y[jar32]*rate_eval.p_Ar32__K33  +
          -rho*Y[jp]*Y[jar31]*rate_eval.p_Ar31__K32  +
          -rho*Y[jp]*Y[jti39]*rate_eval.p_Ti39__V40  +
          -rho*Y[jp]*Y[js29]*rate_eval.p_S29__Cl30  +
          -rho*Y[jp]*Y[jsi24]*rate_eval.p_Si24__P25  +
          -rho*Y[jp]*Y[jfe46]*rate_eval.p_Fe46__Co47  +
          -rho*Y[jp]*Y[jsc36]*rate_eval.p_Sc36__Ti37  +
          -rho*Y[jp]*Y[jne18]*rate_eval.p_Ne18__Na19  +
          -rho*Y[jp]*Y[jv40]*rate_eval.p_V40__Cr41  +
          -rho*Y[jp]*Y[jn14]*rate_eval.p_N14__n_O14  +
          -rho*Y[jp]*Y[jar30]*rate_eval.p_Ar30__K31  +
          -rho*Y[jp]*Y[jcr42]*rate_eval.p_Cr42__Mn43  +
          -rho*Y[jp]*Y[js27]*rate_eval.p_S27__Cl28  +
          -rho*Y[jp]*Y[jmg21]*rate_eval.p_Mg21__Al22  +
          -rho*Y[jp]*Y[jk32]*rate_eval.p_K32__Ca33  +
          -rho*Y[jp]*Y[jca38]*rate_eval.p_Ca38__Sc39  +
          -rho*Y[jp]*Y[jcr43]*rate_eval.p_Cr43__Mn44  +
          -rho*Y[jp]*Y[jcr44]*rate_eval.p_Cr44__Mn45  +
          -rho*Y[jp]*Y[jca37]*rate_eval.p_Ca37__Sc38
       )

    dYdt[jd] = (
          +5.00000000000000e-01*rho**2*Y[jn]*Y[jp]**2*rate_eval.n_p_p__p_d  +
          +rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__d_He4_He4  +
          -rho*Y[jd]*Y[jli7]*rate_eval.d_Li7__n_He4_He4  +
          -rho*Y[jn]*Y[jd]*rate_eval.n_d__t  +
          -rho*Y[jd]*Y[jli8]*rate_eval.d_Li8__n_Be9  +
          -rho*Y[jd]*Y[jbe7]*rate_eval.d_Be7__p_He4_He4  +
          -rho*Y[jd]*Y[jli8]*rate_eval.d_Li8__t_Li7  +
          -rho*Y[jd]*Y[jc13]*rate_eval.d_C13__n_N14  +
          +rho*Y[jt]*Y[jhe3]*rate_eval.t_He3__d_He4  +
          -rho*Y[jd]*Y[jhe3]*rate_eval.d_He3__p_He4  +
          -rho*Y[jd]*Y[jt]*rate_eval.d_t__n_He4  +
          + -2*5.00000000000000e-01*rho*Y[jd]**2*rate_eval.d_d__p_t  +
          -rho*Y[jd]*Y[jli6]*rate_eval.d_Li6__n_Be7  +
          +rho*Y[jn]*Y[jp]*rate_eval.n_p__d  +
          -rho*Y[jd]*Y[jhe4]*rate_eval.He4_d__Li6  +
          +5.00000000000000e-01*rho*Y[jp]**2*rate_eval.p_p__d__weak__bet_pos_  +
          +5.00000000000000e-01*rho**2*ye(Y)*Y[jp]**2*rate_eval.p_p__d__weak__electron_capture  +
          + -2*5.00000000000000e-01*rho*Y[jd]**2*rate_eval.d_d__He4  +
          + -2*5.00000000000000e-01*rho*Y[jd]**2*rate_eval.d_d__n_He3  +
          -rho*Y[jp]*Y[jd]*rate_eval.p_d__He3  +
          -rho*Y[jd]*Y[jc14]*rate_eval.d_C14__n_N15  +
          -rho*Y[jd]*Y[jli6]*rate_eval.d_Li6__p_Li7  +
          -rho*Y[jd]*Y[jli7]*rate_eval.d_Li7__p_Li8
       )

    dYdt[jt] = (
          -rho*Y[jt]*Y[jbe7]*rate_eval.t_Be7__n_p_He4_He4  +
          -rho*Y[jt]*Y[jhe3]*rate_eval.t_He3__n_p_He4  +
          +rho*Y[jn]*Y[jd]*rate_eval.n_d__t  +
          +rho*Y[jd]*Y[jli8]*rate_eval.d_Li8__t_Li7  +
          +rho*Y[jn]*Y[jli6]*rate_eval.n_Li6__He4_t  +
          -rho*Y[jt]*Y[jhe3]*rate_eval.t_He3__d_He4  +
          +rho*Y[jn]*Y[jhe3]*rate_eval.n_He3__p_t  +
          -rho*Y[jd]*Y[jt]*rate_eval.d_t__n_He4  +
          +5.00000000000000e-01*rho*Y[jd]**2*rate_eval.d_d__p_t  +
          -rho*Y[jt]*Y[jbe9]*rate_eval.t_Be9__n_B11  +
          -rho*Y[jt]*Y[jli7]*rate_eval.t_Li7__n_Be9  +
          ( -Y[jt]*rate_eval.t__He3__weak__wc12 +rho*ye(Y)*Y[jhe3]*rate_eval.He3__t__weak__electron_capture ) +
          -rho*Y[jp]*Y[jt]*rate_eval.p_t__He4  +
          -rho*Y[jt]*Y[jhe4]*rate_eval.He4_t__Li7  +
          -rho*Y[jt]*Y[jli7]*rate_eval.t_Li7__n_n_He4_He4  +
          + -2*5.00000000000000e-01*rho*Y[jt]**2*rate_eval.t_t__n_n_He4
       )

    dYdt[jhe3] = (
          -rho*Y[jhe3]*Y[jbe7]*rate_eval.He3_Be7__p_p_He4_He4  +
          + -2*5.00000000000000e-01*rho*Y[jhe3]**2*rate_eval.He3_He3__p_p_He4  +
          -rho*Y[jt]*Y[jhe3]*rate_eval.t_He3__n_p_He4  +
          +rho*Y[jp]*Y[jli6]*rate_eval.p_Li6__He4_He3  +
          -rho*Y[jt]*Y[jhe3]*rate_eval.t_He3__d_He4  +
          -rho*Y[jd]*Y[jhe3]*rate_eval.d_He3__p_He4  +
          -rho*Y[jn]*Y[jhe3]*rate_eval.n_He3__p_t  +
          -rho*Y[jp]*Y[jhe3]*rate_eval.p_He3__He4__weak__bet_pos_  +
          ( +Y[jt]*rate_eval.t__He3__weak__wc12 -rho*ye(Y)*Y[jhe3]*rate_eval.He3__t__weak__electron_capture ) +
          -rho*Y[jn]*Y[jhe3]*rate_eval.n_He3__He4  +
          -rho*Y[jhe3]*Y[jhe4]*rate_eval.He4_He3__Be7  +
          +5.00000000000000e-01*rho*Y[jd]**2*rate_eval.d_d__n_He3  +
          +rho*Y[jp]*Y[jd]*rate_eval.p_d__He3  +
          -rho*Y[jhe3]*Y[jli7]*rate_eval.He3_Li7__n_p_He4_He4
       )

    dYdt[jhe4] = (
          -5.00000000000000e-01*rho**2*Y[jn]**2*Y[jhe4]*rate_eval.n_n_He4__He6  +
          + 2*rho*Y[jhe3]*Y[jbe7]*rate_eval.He3_Be7__p_p_He4_He4  +
          + 2*rho*Y[jt]*Y[jbe7]*rate_eval.t_Be7__n_p_He4_He4  +
          -rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__p_p_Ca38  +
          -rho*Y[jhe4]*Y[jo13]*rate_eval.He4_O13__p_p_O15  +
          + 3*rho*Y[jp]*Y[jb11]*rate_eval.p_B11__He4_He4_He4  +
          + 2*rho*Y[jn]*Y[jb8]*rate_eval.n_B8__p_He4_He4  +
          + 2*rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__d_He4_He4  +
          + 2*rho*Y[jd]*Y[jli7]*rate_eval.d_Li7__n_He4_He4  +
          +5.00000000000000e-01*rho*Y[jhe3]**2*rate_eval.He3_He3__p_p_He4  +
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          -rho*Y[jhe4]*Y[jca51]*rate_eval.He4_Ca51__n_Ti54  +
          +rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__He4_K48  +
          +rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__He4_Mg21  +
          +rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__He4_Mg36  +
          -rho*Y[jhe4]*Y[jca47]*rate_eval.He4_Ca47__n_Ti50  +
          +5.00000000000000e-01*rho*Y[jc12]**2*rate_eval.C12_C12__He4_Ne20  +
          -rho*Y[jhe4]*Y[jca57]*rate_eval.He4_Ca57__n_Ti60  +
          -rho*Y[jhe4]*Y[jca43]*rate_eval.He4_Ca43__n_Ti46  +
          -rho*Y[jhe4]*Y[jti45]*rate_eval.He4_Ti45__p_V48  +
          +rho*Y[jp]*Y[jca42]*rate_eval.p_Ca42__He4_K39  +
          +rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__He4_V40  +
          -rho*Y[jhe4]*Y[jf16]*rate_eval.He4_F16__Na20  +
          +rho*Y[jn]*Y[jca40]*rate_eval.n_Ca40__He4_Ar37  +
          -rho*Y[jhe4]*Y[jv63]*rate_eval.He4_V63__n_Mn66  +
          -rho*Y[jhe4]*Y[jfe66]*rate_eval.He4_Fe66__n_Ni69  +
          +rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__He4_Ar34  +
          -rho*Y[jhe4]*Y[jp39]*rate_eval.He4_P39__n_Cl42  +
          +rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__He4_Ar32  +
          +rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__He4_Ar31  +
          -rho*Y[jhe4]*Y[jca48]*rate_eval.He4_Ca48__Ti52  +
          -rho*Y[jhe4]*Y[jk57]*rate_eval.He4_K57__n_Sc60  +
          +rho*Y[jp]*Y[jk57]*rate_eval.p_K57__He4_Ar54  +
          -rho*Y[jhe4]*Y[jsi42]*rate_eval.He4_Si42__S46  +
          -rho*Y[jhe4]*Y[jk56]*rate_eval.He4_K56__n_Sc59  +
          -rho*Y[jhe4]*Y[jk54]*rate_eval.He4_K54__n_Sc57  +
          -rho*Y[jhe4]*Y[jk53]*rate_eval.He4_K53__n_Sc56  +
          -rho*Y[jhe4]*Y[jk52]*rate_eval.He4_K52__n_Sc55  +
          -rho*Y[jhe4]*Y[jk51]*rate_eval.He4_K51__n_Sc54  +
          -rho*Y[jhe4]*Y[jcr57]*rate_eval.He4_Cr57__n_Fe60  +
          -rho*Y[jhe4]*Y[jk50]*rate_eval.He4_K50__n_Sc53  +
          -rho*Y[jhe4]*Y[jk48]*rate_eval.He4_K48__n_Sc51  +
          +rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__He4_Ti41  +
          +rho*Y[jp]*Y[jk48]*rate_eval.p_K48__He4_Ar45  +
          -rho*Y[jhe4]*Y[jsc35]*rate_eval.He4_Sc35__V39  +
          +rho*Y[jp]*Y[jk45]*rate_eval.p_K45__He4_Ar42  +
          +rho*Y[jp]*Y[jk44]*rate_eval.p_K44__He4_Ar41  +
          -rho*Y[jhe4]*Y[jk43]*rate_eval.He4_K43__p_Ca46  +
          +rho*Y[jn]*Y[jv45]*rate_eval.n_V45__He4_Sc42  +
          -rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__p_Ca45  +
          -rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__n_Sc45  +
          +rho*Y[jp]*Y[jk41]*rate_eval.p_K41__He4_Ar38  +
          -rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__p_Ca49  +
          +rho*Y[jp]*Y[jk40]*rate_eval.p_K40__He4_Ar37  +
          +rho*Y[jn]*Y[jk40]*rate_eval.n_K40__He4_Cl37  +
          -rho*Y[jhe4]*Y[jsc43]*rate_eval.He4_Sc43__V47  +
          +rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__He4_S28  +
          -rho*Y[jhe4]*Y[jk37]*rate_eval.He4_K37__p_Ca40  +
          -rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__p_Ca47  +
          +rho*Y[jn]*Y[jk37]*rate_eval.n_K37__He4_Cl34  +
          +rho*Y[jn]*Y[jk36]*rate_eval.n_K36__He4_Cl33  +
          +rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__He4_K43  +
          -rho*Y[jhe4]*Y[jk34]*rate_eval.He4_K34__p_Ca37  +
          -rho*Y[jhe4]*Y[jsc54]*rate_eval.He4_Sc54__V58  +
          +rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__He4_V58  +
          +rho*Y[jn]*Y[jk32]*rate_eval.n_K32__He4_Cl29  +
          -rho*Y[jhe4]*Y[jk31]*rate_eval.He4_K31__p_Ca34  +
          +rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__He4_Cl49  +
          +rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__He4_Ca36  +
          +rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__He4_Cl47  +
          +rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__He4_Ar33  +
          -rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__n_Na23  +
          +rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__He4_Cl45  +
          -rho*Y[jhe4]*Y[jar46]*rate_eval.He4_Ar46__n_Ca49  +
          -rho*Y[jhe4]*Y[jfe50]*rate_eval.He4_Fe50__p_Co53  +
          -rho*Y[jhe4]*Y[jsi35]*rate_eval.He4_Si35__n_S38  +
          -rho*Y[jhe4]*Y[jar43]*rate_eval.He4_Ar43__n_Ca46  +
          +rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__He4_V52  +
          -rho*Y[jhe4]*Y[jcl47]*rate_eval.He4_Cl47__K51  +
          +rho*Y[jp]*Y[jar40]*rate_eval.p_Ar40__He4_Cl37  +
          -rho*Y[jhe4]*Y[jmn54]*rate_eval.He4_Mn54__Co58  +
          -rho*Y[jhe4]*Y[jfe68]*rate_eval.He4_Fe68__Ni72  +
          +rho*Y[jp]*Y[jar39]*rate_eval.p_Ar39__He4_Cl36  +
          -rho*Y[jhe4]*Y[jmn62]*rate_eval.He4_Mn62__n_Co65  +
          +rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__He4_V46  +
          +rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__He4_S32  +
          -rho*Y[jhe4]*Y[jar34]*rate_eval.He4_Ar34__p_K37  +
          -rho*Y[jhe4]*Y[jar33]*rate_eval.He4_Ar33__p_K36  +
          +rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__He4_S29  +
          -rho*Y[jhe4]*Y[jar31]*rate_eval.He4_Ar31__p_K34  +
          +rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__He4_S27  +
          -rho*Y[jhe4]*Y[jar29]*rate_eval.He4_Ar29__p_K32  +
          +rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__He4_S26  +
          +rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__He4_S49  +
          -rho*Y[jhe4]*Y[jcl51]*rate_eval.He4_Cl51__n_K54  +
          -rho*Y[jhe4]*Y[jcl50]*rate_eval.He4_Cl50__K54  +
          +rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__He4_S48  +
          +rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__He4_S47  +
          -rho*Y[jhe4]*Y[jcl49]*rate_eval.He4_Cl49__n_K52  +
          -rho*Y[jhe4]*Y[jar36]*rate_eval.He4_Ar36__Ca40  +
          +rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__He4_S45  +
          -rho*Y[jhe4]*Y[jca50]*rate_eval.He4_Ca50__n_Ti53  +
          -rho*Y[jhe4]*Y[jcl47]*rate_eval.He4_Cl47__n_K50  +
          +rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__He4_S42  +
          -rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__p_Ar46  +
          +rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__He4_S40  +
          -rho*Y[jhe4]*Y[jv49]*rate_eval.He4_V49__Mn53  +
          -rho*Y[jhe4]*Y[jcl42]*rate_eval.He4_Cl42__n_K45  +
          +rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__He4_S39  +
          -rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__n_K44  +
          +rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__He4_S38  +
          -rho*Y[jhe4]*Y[jcl40]*rate_eval.He4_Cl40__n_K43  +
          +rho*Y[jp]*Y[jo19]*rate_eval.p_O19__He4_N16  +
          -rho*Y[jhe4]*Y[jf17]*rate_eval.He4_F17__Na21  +
          +rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__He4_P32  +
          -rho*Y[jhe4]*Y[jcl34]*rate_eval.He4_Cl34__p_Ar37  +
          + 3*rho*Y[jn]*Y[jc11]*rate_eval.n_C11__He4_He4_He4  +
          +rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__He4_P31  +
          +rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__He4_P30  +
          -rho*Y[jhe4]*Y[js48]*rate_eval.He4_S48__n_Ar51  +
          -rho*Y[jhe4]*Y[jar35]*rate_eval.He4_Ar35__p_K38  +
          -rho*Y[jhe4]*Y[jcl30]*rate_eval.He4_Cl30__p_Ar33  +
          +rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__He4_P26  +
          -rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__Al29  +
          -rho*Y[jhe4]*Y[jcl28]*rate_eval.He4_Cl28__p_Ar31  +
          +rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__He4_P25  +
          -rho*Y[jhe4]*Y[jmg38]*rate_eval.He4_Mg38__n_Si41  +
          +rho*Y[jp]*Y[js47]*rate_eval.p_S47__He4_P44  +
          +rho*Y[jp]*Y[jk52]*rate_eval.p_K52__He4_Ar49  +
          + 2*rho*Y[jd]*Y[jbe7]*rate_eval.d_Be7__p_He4_He4  +
          +rho*Y[jp]*Y[js45]*rate_eval.p_S45__He4_P42  +
          -rho*Y[jhe4]*Y[js43]*rate_eval.He4_S43__n_Ar46  +
          +rho*Y[jp]*Y[js43]*rate_eval.p_S43__He4_P40  +
          -rho*Y[jhe4]*Y[jmn67]*rate_eval.He4_Mn67__n_Co70  +
          +rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__He4_Ca54  +
          -rho*Y[jhe4]*Y[jfe56]*rate_eval.He4_Fe56__Ni60  +
          -rho*Y[jhe4]*Y[js42]*rate_eval.He4_S42__n_Ar45  +
          -rho*Y[jhe4]*Y[js41]*rate_eval.He4_S41__n_Ar44  +
          -rho*Y[jhe4]*Y[jsc63]*rate_eval.He4_Sc63__n_V66  +
          +rho*Y[jp]*Y[js41]*rate_eval.p_S41__He4_P38  +
          +rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__He4_Mg27  +
          +rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__He4_S37  +
          -rho*Y[jhe4]*Y[jfe47]*rate_eval.He4_Fe47__Ni51  +
          +rho*Y[jp]*Y[js39]*rate_eval.p_S39__He4_P36  +
          -rho*Y[jhe4]*Y[js38]*rate_eval.He4_S38__n_Ar41  +
          +rho*Y[jp]*Y[js38]*rate_eval.p_S38__He4_P35  +
          -rho*Y[jhe4]*Y[jmn47]*rate_eval.He4_Mn47__Co51  +
          -rho*Y[jhe4]*Y[js37]*rate_eval.He4_S37__n_Ar40  +
          -rho*Y[jhe4]*Y[jk49]*rate_eval.He4_K49__n_Sc52  +
          +rho*Y[jp]*Y[jv56]*rate_eval.p_V56__He4_Ti53  +
          +rho*Y[jp]*Y[js36]*rate_eval.p_S36__He4_P33  +
          +rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__He4_V66  +
          +rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__He4_Ca48  +
          +rho*Y[jp]*Y[jk51]*rate_eval.p_K51__He4_Ar48  +
          -rho*Y[jhe4]*Y[jp34]*rate_eval.He4_P34__n_Cl37  +
          -rho*Y[jhe4]*Y[js35]*rate_eval.He4_S35__n_Ar38  +
          +rho*Y[jp]*Y[js35]*rate_eval.p_S35__He4_P32  +
          +rho*Y[jn]*Y[js35]*rate_eval.n_S35__He4_Si32  +
          +rho*Y[jp]*Y[jcl35]*rate_eval.p_Cl35__He4_S32  +
          -rho*Y[jhe4]*Y[jti60]*rate_eval.He4_Ti60__Cr64  +
          +rho*Y[jn]*Y[js33]*rate_eval.n_S33__He4_Si30  +
          -rho*Y[jhe4]*Y[js31]*rate_eval.He4_S31__p_Cl34  +
          -rho*Y[jhe4]*Y[js30]*rate_eval.He4_S30__p_Cl33  +
          +rho*Y[jn]*Y[js30]*rate_eval.n_S30__He4_Si27  +
          -rho*Y[jhe4]*Y[js28]*rate_eval.He4_S28__p_Cl31  +
          +rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__He4_Ti40  +
          +rho*Y[jn]*Y[js28]*rate_eval.n_S28__He4_Si25  +
          -rho*Y[jhe4]*Y[js26]*rate_eval.He4_S26__p_Cl29  +
          +rho*Y[jn]*Y[js26]*rate_eval.n_S26__He4_Si23  +
          -rho*Y[jhe4]*Y[jp47]*rate_eval.He4_P47__n_Cl50  +
          -rho*Y[jhe4]*Y[jp43]*rate_eval.He4_P43__n_Cl46  +
          +rho*Y[jp]*Y[jp43]*rate_eval.p_P43__He4_Si40  +
          -rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__n_P41  +
          +rho*Y[jp]*Y[jp42]*rate_eval.p_P42__He4_Si39  +
          -rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__p_S44  +
          -rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__n_Cl44  +
          +rho*Y[jp]*Y[jo20]*rate_eval.p_O20__He4_N17  +
          +rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__He4_Cl40  +
          +rho*Y[jp]*Y[jp38]*rate_eval.p_P38__He4_Si35  +
          +rho*Y[jp]*Y[jf18]*rate_eval.p_F18__He4_O15  +
          -rho*Y[jhe4]*Y[jp37]*rate_eval.He4_P37__n_Cl40  +
          +rho*Y[jp]*Y[jp37]*rate_eval.p_P37__He4_Si34  +
          +rho*Y[jp]*Y[jp36]*rate_eval.p_P36__He4_Si33  +
          -rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__p_Ar47  +
          +rho*Y[jp]*Y[jp32]*rate_eval.p_P32__He4_Si29  +
          -rho*Y[jhe4]*Y[jp31]*rate_eval.He4_P31__p_S34  +
          -rho*Y[jhe4]*Y[jp30]*rate_eval.He4_P30__p_S33  +
          -rho*Y[jhe4]*Y[jk55]*rate_eval.He4_K55__n_Sc58  +
          +rho*Y[jn]*Y[jv47]*rate_eval.n_V47__He4_Sc44  +
          -rho*Y[jhe4]*Y[jp27]*rate_eval.He4_P27__p_S30  +
          +rho*Y[jn]*Y[jp27]*rate_eval.n_P27__He4_Al24  +
          -rho*Y[jhe4]*Y[jp26]*rate_eval.He4_P26__p_S29  +
          +rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__He4_Ti44  +
          +rho*Y[jn]*Y[jp26]*rate_eval.n_P26__He4_Al23  +
          -rho*Y[jhe4]*Y[jp25]*rate_eval.He4_P25__p_S28  +
          -rho*Y[jhe4]*Y[jp24]*rate_eval.He4_P24__p_S27  +
          +rho*Y[jn]*Y[jp24]*rate_eval.n_P24__He4_Al21  +
          +rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__He4_Al42  +
          -rho*Y[jhe4]*Y[jsi44]*rate_eval.He4_Si44__n_S47  +
          -rho*Y[jhe4]*Y[jp42]*rate_eval.He4_P42__n_Cl45  +
          -rho*Y[jhe4]*Y[jsi42]*rate_eval.He4_Si42__n_S45  +
          -rho*Y[jhe4]*Y[jsi40]*rate_eval.He4_Si40__n_S43  +
          -rho*Y[jhe4]*Y[jsi39]*rate_eval.He4_Si39__n_S42  +
          -rho*Y[jhe4]*Y[jsi38]*rate_eval.He4_Si38__n_S41  +
          +rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__He4_Sc62  +
          -rho*Y[jhe4]*Y[jsi37]*rate_eval.He4_Si37__n_S40  +
          -rho*Y[jhe4]*Y[jca40]*rate_eval.He4_Ca40__Ti44  +
          +rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__He4_Al34  +
          +rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__He4_Al32  +
          -rho*Y[jhe4]*Y[jmn45]*rate_eval.He4_Mn45__p_Fe48  +
          -rho*Y[jhe4]*Y[jcr41]*rate_eval.He4_Cr41__p_Mn44  +
          -rho*Y[jhe4]*Y[jmn43]*rate_eval.He4_Mn43__Co47  +
          -rho*Y[jhe4]*Y[jv57]*rate_eval.He4_V57__n_Mn60  +
          +rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__He4_V48  +
          +rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__He4_Ca34  +
          -rho*Y[jhe4]*Y[jti61]*rate_eval.He4_Ti61__n_Cr64  +
          -rho*Y[jhe4]*Y[jsi25]*rate_eval.He4_Si25__p_P28  +
          -rho*Y[jhe4]*Y[jv40]*rate_eval.He4_V40__p_Cr43  +
          -rho*Y[jhe4]*Y[jsi24]*rate_eval.He4_Si24__p_P27  +
          -rho*Y[jhe4]*Y[jbe7]*rate_eval.He4_Be7__C11  +
          -rho*Y[jhe4]*Y[jca54]*rate_eval.He4_Ca54__Ti58  +
          -rho*Y[jhe4]*Y[jk40]*rate_eval.He4_K40__p_Ca43  +
          -rho*Y[jhe4]*Y[jsi23]*rate_eval.He4_Si23__p_P26  +
          -rho*Y[jhe4]*Y[jar42]*rate_eval.He4_Ar42__n_Ca45  +
          +rho*Y[jp]*Y[jv61]*rate_eval.p_V61__He4_Ti58  +
          -rho*Y[jhe4]*Y[jsi22]*rate_eval.He4_Si22__p_P25  +
          +rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__He4_Mg19  +
          -rho*Y[jhe4]*Y[jal42]*rate_eval.He4_Al42__n_P45  +
          +rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__He4_Mg38  +
          -rho*Y[jhe4]*Y[jal40]*rate_eval.He4_Al40__n_P43  +
          +rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__He4_Mg37  +
          -rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__p_Si42  +
          -rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__p_Si41  +
          -rho*Y[jhe4]*Y[jmn49]*rate_eval.He4_Mn49__Co53  +
          +rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__He4_Mg35  +
          +rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__He4_Mg34  +
          -rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__p_Si39  +
          -rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__n_P39  +
          +rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__He4_Mg33  +
          -rho*Y[jhe4]*Y[jmn59]*rate_eval.He4_Mn59__Co63  +
          -rho*Y[jhe4]*Y[jal35]*rate_eval.He4_Al35__n_P38  +
          +rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__He4_Mg32  +
          -rho*Y[jhe4]*Y[jal34]*rate_eval.He4_Al34__n_P37  +
          +rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__He4_Mg31  +
          -rho*Y[jhe4]*Y[jk50]*rate_eval.He4_K50__Sc54  +
          -rho*Y[jhe4]*Y[jal33]*rate_eval.He4_Al33__n_P36  +
          +rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__He4_Mg30  +
          -rho*Y[jhe4]*Y[jsi27]*rate_eval.He4_Si27__p_P30  +
          +rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__He4_S43  +
          +rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__He4_Mg29  +
          -rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__p_Si34  +
          -rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__n_P34  +
          +rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__He4_S35  +
          +rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__He4_Mg28  +
          -rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__n_P32  +
          +rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__He4_Mg26  +
          -rho*Y[jhe4]*Y[jal37]*rate_eval.He4_Al37__n_P40  +
          +rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__He4_F31  +
          +rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__He4_Mg25  +
          -rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__p_Ca44  +
          -rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__p_Si30  +
          +rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__He4_Na23  +
          -rho*Y[jhe4]*Y[jal32]*rate_eval.He4_Al32__P36  +
          -rho*Y[jhe4]*Y[jal24]*rate_eval.He4_Al24__p_Si27  +
          -rho*Y[jhe4]*Y[jal25]*rate_eval.He4_Al25__p_Si28  +
          +rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__He4_Na20  +
          -rho*Y[jhe4]*Y[jal22]*rate_eval.He4_Al22__p_Si25  +
          +rho*Y[jp]*Y[jv67]*rate_eval.p_V67__He4_Ti64  +
          +rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__He4_Na19  +
          -rho*Y[jhe4]*Y[jal21]*rate_eval.He4_Al21__p_Si24  +
          -rho*Y[jhe4]*Y[jmg40]*rate_eval.He4_Mg40__n_Si43  +
          -rho*Y[jhe4]*Y[jmg39]*rate_eval.He4_Mg39__n_Si42  +
          +rho*Y[jp]*Y[jal27]*rate_eval.p_Al27__He4_Mg24  +
          -rho*Y[jhe4]*Y[jmg37]*rate_eval.He4_Mg37__n_Si40  +
          +rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__He4_Cl42  +
          -rho*Y[jhe4]*Y[jmg35]*rate_eval.He4_Mg35__n_Si38  +
          -rho*Y[jhe4]*Y[jmg34]*rate_eval.He4_Mg34__n_Si37  +
          +rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__He4_Na31  +
          +rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__He4_Na30  +
          +rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__He4_Mn63  +
          -rho*Y[jhe4]*Y[jmg32]*rate_eval.He4_Mg32__n_Si35  +
          +rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__He4_V44  +
          +rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__He4_Na29  +
          -rho*Y[jhe4]*Y[jmg30]*rate_eval.He4_Mg30__n_Si33  +
          +rho*Y[jn]*Y[jp29]*rate_eval.n_P29__He4_Al26  +
          -rho*Y[jhe4]*Y[jcr46]*rate_eval.He4_Cr46__p_Mn49  +
          +rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__He4_Na26  +
          +rho*Y[jn]*Y[js29]*rate_eval.n_S29__He4_Si26  +
          -rho*Y[jhe4]*Y[jk57]*rate_eval.He4_K57__Sc61  +
          -rho*Y[jhe4]*Y[jne23]*rate_eval.He4_Ne23__n_Mg26  +
          +rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__He4_F28  +
          -rho*Y[jhe4]*Y[jmg27]*rate_eval.He4_Mg27__n_Si30  +
          -rho*Y[jhe4]*Y[jo23]*rate_eval.He4_O23__n_Ne26  +
          -rho*Y[jhe4]*Y[jk35]*rate_eval.He4_K35__p_Ca38  +
          -rho*Y[jhe4]*Y[jmg26]*rate_eval.He4_Mg26__n_Si29  +
          +rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__He4_Cr51  +
          -rho*Y[jhe4]*Y[jfe53]*rate_eval.He4_Fe53__p_Co56  +
          +rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__He4_Cr52  +
          -rho*Y[jhe4]*Y[jmg25]*rate_eval.He4_Mg25__n_Si28  +
          +rho*Y[jn]*Y[jmg23]*rate_eval.n_Mg23__He4_Ne20  +
          -rho*Y[jhe4]*Y[jmg22]*rate_eval.He4_Mg22__p_Al25  +
          +rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__He4_Ne18  +
          -rho*Y[jhe4]*Y[jmg20]*rate_eval.He4_Mg20__p_Al23  +
          -rho*Y[jhe4]*Y[jna36]*rate_eval.He4_Na36__n_Al39  +
          -rho*Y[jhe4]*Y[jna38]*rate_eval.He4_Na38__n_Al41  +
          -rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__p_Mg40  +
          -rho*Y[jhe4]*Y[jk33]*rate_eval.He4_K33__Sc37  +
          +rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__He4_Ne34  +
          -rho*Y[jhe4]*Y[jna35]*rate_eval.He4_Na35__n_Al38  +
          +rho*Y[jn]*Y[jv43]*rate_eval.n_V43__He4_Sc40  +
          -rho*Y[jhe4]*Y[jna34]*rate_eval.He4_Na34__n_Al37  +
          -rho*Y[jhe4]*Y[jv60]*rate_eval.He4_V60__n_Mn63  +
          -rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__p_Mg36  +
          -rho*Y[jhe4]*Y[jsc44]*rate_eval.He4_Sc44__V48  +
          -rho*Y[jhe4]*Y[jna31]*rate_eval.He4_Na31__n_Al34  +
          +rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__He4_Ne28  +
          +rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__He4_Ne27  +
          +rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__He4_Ne26  +
          -rho*Y[jhe4]*Y[jna28]*rate_eval.He4_Na28__n_Al31  +
          +rho*Y[jn]*Y[jar39]*rate_eval.n_Ar39__He4_S36  +
          -rho*Y[jhe4]*Y[jna26]*rate_eval.He4_Na26__n_Al29  +
          -rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__p_Mg27  +
          +rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__He4_Ne21  +
          +rho*Y[jp]*Y[jk56]*rate_eval.p_K56__He4_Ar53  +
          -rho*Y[jhe4]*Y[jna23]*rate_eval.He4_Na23__p_Mg26  +
          +rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__He4_Ne20  +
          -rho*Y[jhe4]*Y[jna22]*rate_eval.He4_Na22__p_Mg25  +
          -rho*Y[jhe4]*Y[js41]*rate_eval.He4_S41__Ar45  +
          +rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__He4_F18  +
          -rho*Y[jhe4]*Y[js29]*rate_eval.He4_S29__p_Cl32  +
          +rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__He4_F17  +
          +rho*Y[jn]*Y[jv40]*rate_eval.n_V40__He4_Sc37  +
          -rho*Y[jhe4]*Y[jcl35]*rate_eval.He4_Cl35__p_Ar38  +
          +rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__He4_V51  +
          +rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__He4_P29  +
          -rho*Y[jhe4]*Y[js46]*rate_eval.He4_S46__n_Ar49  +
          -rho*Y[jhe4]*Y[jne31]*rate_eval.He4_Ne31__n_Mg34  +
          -rho*Y[jhe4]*Y[jne30]*rate_eval.He4_Ne30__n_Mg33  +
          +rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__He4_F27  +
          +rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__He4_F26  +
          -rho*Y[jhe4]*Y[jar43]*rate_eval.He4_Ar43__Ca47  +
          -rho*Y[jhe4]*Y[jne28]*rate_eval.He4_Ne28__n_Mg31  +
          -rho*Y[jhe4]*Y[jne27]*rate_eval.He4_Ne27__n_Mg30  +
          -rho*Y[jhe4]*Y[jca39]*rate_eval.He4_Ca39__Ti43  +
          -rho*Y[jhe4]*Y[jti54]*rate_eval.He4_Ti54__Cr58  +
          -rho*Y[jhe4]*Y[js39]*rate_eval.He4_S39__n_Ar42  +
          +rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__He4_F22  +
          -rho*Y[jhe4]*Y[js27]*rate_eval.He4_S27__p_Cl30  +
          -rho*Y[jhe4]*Y[jne24]*rate_eval.He4_Ne24__n_Mg27  +
          +rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__He4_Ca42  +
          -rho*Y[jhe4]*Y[jca61]*rate_eval.He4_Ca61__n_Ti64  +
          -rho*Y[jhe4]*Y[jk39]*rate_eval.He4_K39__Sc43  +
          -rho*Y[jhe4]*Y[jsc62]*rate_eval.He4_Sc62__V66  +
          +rho*Y[jn]*Y[jcl38]*rate_eval.n_Cl38__He4_P35  +
          +rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__He4_Mg40  +
          -rho*Y[jhe4]*Y[jne21]*rate_eval.He4_Ne21__n_Mg24  +
          +rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__He4_Si28  +
          -rho*Y[jhe4]*Y[jal26]*rate_eval.He4_Al26__p_Si29  +
          -rho*Y[jhe4]*Y[jne19]*rate_eval.He4_Ne19__p_Na22  +
          -rho*Y[jhe4]*Y[jne18]*rate_eval.He4_Ne18__p_Na21  +
          +rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__He4_Mg22  +
          +rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__He4_O15  +
          -rho*Y[jhe4]*Y[jne17]*rate_eval.He4_Ne17__p_Na20  +
          + 2*rho*Y[jn]*Y[jbe7]*rate_eval.n_Be7__He4_He4  +
          -rho*Y[jhe4]*Y[jne16]*rate_eval.He4_Ne16__p_Na19  +
          -rho*Y[jhe4]*Y[jcl49]*rate_eval.He4_Cl49__K53  +
          +rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__He4_V64  +
          -rho*Y[jhe4]*Y[jar53]*rate_eval.He4_Ar53__n_Ca56  +
          -rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__p_Ne33  +
          +rho*Y[jp]*Y[jf30]*rate_eval.p_F30__He4_O27  +
          -rho*Y[jhe4]*Y[jf29]*rate_eval.He4_F29__n_Na32  +
          +rho*Y[jp]*Y[jf29]*rate_eval.p_F29__He4_O26  +
          -rho*Y[jhe4]*Y[jf27]*rate_eval.He4_F27__n_Na30  +
          +rho*Y[jp]*Y[jf27]*rate_eval.p_F27__He4_O24  +
          -rho*Y[jhe4]*Y[jf26]*rate_eval.He4_F26__n_Na29  +
          +rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__He4_Ne31  +
          +rho*Y[jp]*Y[jf25]*rate_eval.p_F25__He4_O22  +
          -rho*Y[jhe4]*Y[jca38]*rate_eval.He4_Ca38__Ti42  +
          -rho*Y[jhe4]*Y[jf24]*rate_eval.He4_F24__n_Na27  +
          -rho*Y[jhe4]*Y[jti42]*rate_eval.He4_Ti42__p_V45  +
          +rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__He4_Ne23  +
          +rho*Y[jp]*Y[jf22]*rate_eval.p_F22__He4_O19  +
          -rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__p_Ne24  +
          -rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__n_Na24  +
          +rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__He4_F23  +
          -rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__p_Ne23  +
          +rho*Y[jp]*Y[jf20]*rate_eval.p_F20__He4_O17  +
          -rho*Y[jhe4]*Y[jf19]*rate_eval.He4_F19__p_Ne22  +
          -rho*Y[jhe4]*Y[jf18]*rate_eval.He4_F18__p_Ne21  +
          +rho*Y[jn]*Y[jf18]*rate_eval.n_F18__He4_N15  +
          +rho*Y[jn]*Y[jf15]*rate_eval.n_F15__He4_N12  +
          +rho*Y[jn]*Y[jf14]*rate_eval.n_F14__He4_N11  +
          -rho*Y[jhe4]*Y[jo28]*rate_eval.He4_O28__n_Ne31  +
          -rho*Y[jhe4]*Y[jo26]*rate_eval.He4_O26__n_Ne29  +
          +rho*Y[jp]*Y[jo26]*rate_eval.p_O26__He4_N23  +
          -rho*Y[jhe4]*Y[jo24]*rate_eval.He4_O24__n_Ne27  +
          -rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__n_Na33  +
          -rho*Y[jhe4]*Y[jo22]*rate_eval.He4_O22__n_Ne25  +
          -rho*Y[jhe4]*Y[jar52]*rate_eval.He4_Ar52__n_Ca55  +
          -rho*Y[jhe4]*Y[jo19]*rate_eval.He4_O19__n_Ne22  +
          -rho*Y[jhe4]*Y[jcl32]*rate_eval.He4_Cl32__p_Ar35  +
          +rho*Y[jp]*Y[jo18]*rate_eval.p_O18__He4_N15  +
          -rho*Y[jhe4]*Y[jo17]*rate_eval.He4_O17__n_Ne20  +
          +rho*Y[jp]*Y[jo17]*rate_eval.p_O17__He4_N14  +
          +5.00000000000000e-01*rho*Y[jo16]**2*rate_eval.O16_O16__He4_Si28  +
          -rho*Y[jhe4]*Y[jne26]*rate_eval.He4_Ne26__n_Mg29  +
          -rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__n_P31  +
          +rho*Y[jc12]*Y[jo16]*rate_eval.C12_O16__He4_Mg24  +
          +rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__He4_F25  +
          +rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__He4_Ne25  +
          +rho*Y[jn]*Y[jk33]*rate_eval.n_K33__He4_Cl30  +
          -rho*Y[jhe4]*Y[jcr45]*rate_eval.He4_Cr45__Fe49  +
          +rho*Y[jn]*Y[jo14]*rate_eval.n_O14__He4_C11  +
          -rho*Y[jhe4]*Y[jo13]*rate_eval.He4_O13__p_F16  +
          -rho*Y[jhe4]*Y[jsc57]*rate_eval.He4_Sc57__V61  +
          +rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__He4_Ar30  +
          +rho*Y[jn]*Y[jo13]*rate_eval.n_O13__He4_C10  +
          +rho*Y[jp]*Y[jn15]*rate_eval.p_N15__He4_C12  +
          +rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__He4_Ne16  +
          +rho*Y[jp]*Y[jf28]*rate_eval.p_F28__He4_O25  +
          -rho*Y[jhe4]*Y[jar41]*rate_eval.He4_Ar41__n_Ca44  +
          -rho*Y[jhe4]*Y[jn13]*rate_eval.He4_N13__p_O16  +
          -rho*Y[jhe4]*Y[jc15]*rate_eval.He4_C15__n_O18  +
          -rho*Y[jhe4]*Y[jcl50]*rate_eval.He4_Cl50__n_K53  +
          -rho*Y[jhe4]*Y[jsi31]*rate_eval.He4_Si31__n_S34  +
          -rho*Y[jhe4]*Y[jcl45]*rate_eval.He4_Cl45__n_K48  +
          -rho*Y[jhe4]*Y[jc13]*rate_eval.He4_C13__n_O16  +
          -rho*Y[jhe4]*Y[jb13]*rate_eval.He4_B13__n_N16  +
          +rho*Y[jn]*Y[jk35]*rate_eval.n_K35__He4_Cl32  +
          +rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__He4_Cl50  +
          -rho*Y[jhe4]*Y[jb12]*rate_eval.He4_B12__n_N15  +
          +rho*Y[jp]*Y[jb12]*rate_eval.p_B12__He4_Be9  +
          +rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__He4_Sc53  +
          -rho*Y[jhe4]*Y[jb11]*rate_eval.He4_B11__p_C14  +
          -rho*Y[jhe4]*Y[jfe46]*rate_eval.He4_Fe46__p_Co49  +
          -rho*Y[jhe4]*Y[jb10]*rate_eval.He4_B10__p_C13  +
          -rho*Y[jhe4]*Y[jb8]*rate_eval.He4_B8__p_C11  +
          +rho*Y[jp]*Y[jv63]*rate_eval.p_V63__He4_Ti60  +
          -rho*Y[jhe4]*Y[jmn70]*rate_eval.He4_Mn70__Co74  +
          -rho*Y[jhe4]*Y[jli8]*rate_eval.He4_Li8__n_B11  +
          +rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__He4_Ca39  +
          +rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__He4_Cr45  +
          -rho*Y[jhe4]*Y[jv49]*rate_eval.He4_V49__p_Cr52  +
          +rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__He4_V50  +
          +rho*Y[jn]*Y[jli6]*rate_eval.n_Li6__He4_t  +
          +rho*Y[jp]*Y[jli6]*rate_eval.p_Li6__He4_He3  +
          +rho*Y[jt]*Y[jhe3]*rate_eval.t_He3__d_He4  +
          +rho*Y[jd]*Y[jhe3]*rate_eval.d_He3__p_He4  +
          -rho*Y[jhe4]*Y[jv51]*rate_eval.He4_V51__Mn55  +
          +rho*Y[jd]*Y[jt]*rate_eval.d_t__n_He4  +
          -rho*Y[jhe4]*Y[jfe76]*rate_eval.He4_Fe76__Ni80  +
          +rho*Y[jn]*Y[jv50]*rate_eval.n_V50__He4_Sc47  +
          -rho*Y[jhe4]*Y[jfe73]*rate_eval.He4_Fe73__Ni77  +
          -rho*Y[jhe4]*Y[jfe70]*rate_eval.He4_Fe70__Ni74  +
          -rho*Y[jhe4]*Y[jne18]*rate_eval.He4_Ne18__Mg22  +
          -rho*Y[jhe4]*Y[jfe69]*rate_eval.He4_Fe69__Ni73  +
          -rho*Y[jhe4]*Y[jfe67]*rate_eval.He4_Fe67__Ni71  +
          -rho*Y[jhe4]*Y[jfe64]*rate_eval.He4_Fe64__Ni68  +
          -rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__n_V51  +
          -rho*Y[jhe4]*Y[jp36]*rate_eval.He4_P36__n_Cl39  +
          +rho*Y[jp]*Y[js46]*rate_eval.p_S46__He4_P43  +
          -rho*Y[jhe4]*Y[jfe59]*rate_eval.He4_Fe59__Ni63  +
          -rho*Y[jhe4]*Y[jfe58]*rate_eval.He4_Fe58__Ni62  +
          -rho*Y[jhe4]*Y[jfe54]*rate_eval.He4_Fe54__Ni58  +
          -rho*Y[jhe4]*Y[jfe52]*rate_eval.He4_Fe52__Ni56  +
          -rho*Y[jhe4]*Y[jfe51]*rate_eval.He4_Fe51__Ni55  +
          -rho*Y[jhe4]*Y[jo25]*rate_eval.He4_O25__n_Ne28  +
          -rho*Y[jhe4]*Y[jfe46]*rate_eval.He4_Fe46__Ni50  +
          -rho*Y[jhe4]*Y[jfe57]*rate_eval.He4_Fe57__Ni61  +
          -rho*Y[jhe4]*Y[jfe45]*rate_eval.He4_Fe45__Ni49  +
          -rho*Y[jhe4]*Y[jmn72]*rate_eval.He4_Mn72__Co76  +
          -rho*Y[jhe4]*Y[jmn69]*rate_eval.He4_Mn69__Co73  +
          -rho*Y[jhe4]*Y[jmn67]*rate_eval.He4_Mn67__Co71  +
          -rho*Y[jhe4]*Y[jcl30]*rate_eval.He4_Cl30__K34  +
          -rho*Y[jhe4]*Y[jmn66]*rate_eval.He4_Mn66__Co70  +
          -rho*Y[jhe4]*Y[jmn64]*rate_eval.He4_Mn64__Co68  +
          -rho*Y[jhe4]*Y[jmn63]*rate_eval.He4_Mn63__Co67  +
          -rho*Y[jhe4]*Y[jcl29]*rate_eval.He4_Cl29__p_Ar32  +
          -rho*Y[jhe4]*Y[jmn61]*rate_eval.He4_Mn61__Co65  +
          -rho*Y[jhe4]*Y[jmn53]*rate_eval.He4_Mn53__Co57  +
          -rho*Y[jhe4]*Y[jmn52]*rate_eval.He4_Mn52__Co56  +
          -rho*Y[jhe4]*Y[jmn50]*rate_eval.He4_Mn50__Co54  +
          -rho*Y[jhe4]*Y[jsi23]*rate_eval.He4_Si23__S27  +
          -rho*Y[jhe4]*Y[jmn46]*rate_eval.He4_Mn46__Co50  +
          -rho*Y[jhe4]*Y[jmn45]*rate_eval.He4_Mn45__Co49  +
          -rho*Y[jhe4]*Y[jcr70]*rate_eval.He4_Cr70__Fe74  +
          +rho*Y[jp]*Y[jv53]*rate_eval.p_V53__He4_Ti50  +
          -rho*Y[jhe4]*Y[jcr67]*rate_eval.He4_Cr67__Fe71  +
          -rho*Y[jhe4]*Y[jcr63]*rate_eval.He4_Cr63__Fe67  +
          -rho*Y[jhe4]*Y[jcr62]*rate_eval.He4_Cr62__Fe66  +
          +rho*Y[jn]*Y[jca43]*rate_eval.n_Ca43__He4_Ar40  +
          -rho*Y[jhe4]*Y[jcr60]*rate_eval.He4_Cr60__Fe64  +
          -rho*Y[jhe4]*Y[jcr59]*rate_eval.He4_Cr59__Fe63  +
          -rho*Y[jhe4]*Y[jmg19]*rate_eval.He4_Mg19__p_Al22  +
          -rho*Y[jhe4]*Y[jcr58]*rate_eval.He4_Cr58__Fe62  +
          -rho*Y[jhe4]*Y[jcr57]*rate_eval.He4_Cr57__Fe61  +
          -rho*Y[jhe4]*Y[jcr54]*rate_eval.He4_Cr54__Fe58  +
          -rho*Y[jhe4]*Y[jcr53]*rate_eval.He4_Cr53__Fe57  +
          -rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__V52  +
          +rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__He4_S36  +
          -rho*Y[jhe4]*Y[jcr48]*rate_eval.He4_Cr48__Fe52  +
          -rho*Y[jhe4]*Y[jar45]*rate_eval.He4_Ar45__Ca49  +
          -rho*Y[jhe4]*Y[jk38]*rate_eval.He4_K38__p_Ca41  +
          -rho*Y[jhe4]*Y[jp40]*rate_eval.He4_P40__n_Cl43  +
          -rho*Y[jhe4]*Y[jcr47]*rate_eval.He4_Cr47__Fe51  +
          -rho*Y[jhe4]*Y[jcr46]*rate_eval.He4_Cr46__Fe50  +
          +rho*Y[jn]*Y[jne19]*rate_eval.n_Ne19__He4_O16  +
          -rho*Y[jhe4]*Y[jcr44]*rate_eval.He4_Cr44__Fe48  +
          -rho*Y[jhe4]*Y[jcr43]*rate_eval.He4_Cr43__Fe47  +
          -rho*Y[jhe4]*Y[jcr42]*rate_eval.He4_Cr42__Fe46  +
          -rho*Y[jhe4]*Y[jcr41]*rate_eval.He4_Cr41__Fe45  +
          +rho*Y[jp]*Y[jp44]*rate_eval.p_P44__He4_Si41  +
          -rho*Y[jhe4]*Y[jmg22]*rate_eval.He4_Mg22__Si26  +
          -rho*Y[jhe4]*Y[jv67]*rate_eval.He4_V67__Mn71  +
          -rho*Y[jhe4]*Y[jv66]*rate_eval.He4_V66__Mn70  +
          -rho*Y[jhe4]*Y[jv64]*rate_eval.He4_V64__Mn68  +
          -rho*Y[jhe4]*Y[jo14]*rate_eval.He4_O14__p_F17  +
          -rho*Y[jhe4]*Y[jv61]*rate_eval.He4_V61__Mn65  +
          -rho*Y[jhe4]*Y[jv60]*rate_eval.He4_V60__Mn64  +
          +rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__He4_F29  +
          -rho*Y[jhe4]*Y[jv57]*rate_eval.He4_V57__Mn61  +
          -rho*Y[jhe4]*Y[jv56]*rate_eval.He4_V56__Mn60  +
          -rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__n_Al40  +
          -rho*Y[jhe4]*Y[jv54]*rate_eval.He4_V54__Mn58  +
          -rho*Y[jhe4]*Y[jv53]*rate_eval.He4_V53__Mn57  +
          -rho*Y[jhe4]*Y[jv52]*rate_eval.He4_V52__Mn56  +
          -rho*Y[jhe4]*Y[jne25]*rate_eval.He4_Ne25__Mg29  +
          -rho*Y[jhe4]*Y[jv50]*rate_eval.He4_V50__Mn54  +
          -rho*Y[jhe4]*Y[jv65]*rate_eval.He4_V65__Mn69  +
          -rho*Y[jhe4]*Y[jne32]*rate_eval.He4_Ne32__n_Mg35  +
          -rho*Y[jhe4]*Y[jf16]*rate_eval.He4_F16__p_Ne19  +
          -rho*Y[jhe4]*Y[jv47]*rate_eval.He4_V47__Mn51  +
          -rho*Y[jhe4]*Y[jv46]*rate_eval.He4_V46__Mn50  +
          -rho*Y[jhe4]*Y[jv45]*rate_eval.He4_V45__Mn49  +
          -rho*Y[jhe4]*Y[jv43]*rate_eval.He4_V43__Mn47  +
          +rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__He4_Mg39  +
          -rho*Y[jhe4]*Y[jv41]*rate_eval.He4_V41__Mn45  +
          +rho*Y[jn]*Y[jfe57]*rate_eval.n_Fe57__He4_Cr54  +
          -rho*Y[jhe4]*Y[jv39]*rate_eval.He4_V39__Mn43  +
          -rho*Y[jhe4]*Y[jti63]*rate_eval.He4_Ti63__Cr67  +
          -rho*Y[jhe4]*Y[jti61]*rate_eval.He4_Ti61__Cr65  +
          +rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__He4_O13  +
          -rho*Y[jhe4]*Y[jti53]*rate_eval.He4_Ti53__Cr57  +
          -rho*Y[jhe4]*Y[jti52]*rate_eval.He4_Ti52__Cr56  +
          -rho*Y[jhe4]*Y[jti51]*rate_eval.He4_Ti51__Cr55  +
          -rho*Y[jhe4]*Y[jna39]*rate_eval.He4_Na39__n_Al42  +
          -rho*Y[jhe4]*Y[jti48]*rate_eval.He4_Ti48__Cr52  +
          -rho*Y[jhe4]*Y[jti57]*rate_eval.He4_Ti57__n_Cr60  +
          -rho*Y[jhe4]*Y[jti46]*rate_eval.He4_Ti46__Cr50  +
          -rho*Y[jhe4]*Y[jti45]*rate_eval.He4_Ti45__Cr49  +
          -rho*Y[jhe4]*Y[jti44]*rate_eval.He4_Ti44__Cr48  +
          -rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__p_Si32  +
          -rho*Y[jhe4]*Y[jti43]*rate_eval.He4_Ti43__Cr47  +
          -rho*Y[jhe4]*Y[jti41]*rate_eval.He4_Ti41__Cr45  +
          -rho*Y[jhe4]*Y[jna32]*rate_eval.He4_Na32__n_Al35  +
          -rho*Y[jhe4]*Y[jti40]*rate_eval.He4_Ti40__Cr44  +
          -rho*Y[jhe4]*Y[jti38]*rate_eval.He4_Ti38__Cr42  +
          +rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__He4_S31  +
          -rho*Y[jhe4]*Y[jal35]*rate_eval.He4_Al35__P39  +
          -rho*Y[jhe4]*Y[jsc60]*rate_eval.He4_Sc60__V64  +
          -rho*Y[jhe4]*Y[jsc58]*rate_eval.He4_Sc58__V62  +
          -rho*Y[jhe4]*Y[jca60]*rate_eval.He4_Ca60__n_Ti63  +
          -rho*Y[jhe4]*Y[jsc56]*rate_eval.He4_Sc56__V60  +
          -rho*Y[jhe4]*Y[jti49]*rate_eval.He4_Ti49__n_Cr52  +
          -rho*Y[jhe4]*Y[jsc55]*rate_eval.He4_Sc55__V59  +
          -rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__p_Ca48  +
          +rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__He4_Cr54  +
          +rho*Y[jp]*Y[jhe3]*rate_eval.p_He3__He4__weak__bet_pos_  +
          -rho*Y[jhe4]*Y[jsc49]*rate_eval.He4_Sc49__V53  +
          -rho*Y[jhe4]*Y[jmn44]*rate_eval.He4_Mn44__Co48  +
          -rho*Y[jhe4]*Y[jsc47]*rate_eval.He4_Sc47__V51  +
          -rho*Y[jhe4]*Y[jsc45]*rate_eval.He4_Sc45__V49  +
          -rho*Y[jhe4]*Y[jmg20]*rate_eval.He4_Mg20__Si24  +
          +rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__He4_K47  +
          -rho*Y[jhe4]*Y[jsc42]*rate_eval.He4_Sc42__V46  +
          -rho*Y[jhe4]*Y[jsc41]*rate_eval.He4_Sc41__V45  +
          -rho*Y[jhe4]*Y[jsc39]*rate_eval.He4_Sc39__V43  +
          -rho*Y[jhe4]*Y[jsc38]*rate_eval.He4_Sc38__V42  +
          +rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__He4_Ne30  +
          -rho*Y[jhe4]*Y[jcr55]*rate_eval.He4_Cr55__Fe59  +
          -rho*Y[jhe4]*Y[jf25]*rate_eval.He4_F25__n_Na28  +
          -rho*Y[jhe4]*Y[jca59]*rate_eval.He4_Ca59__Ti63  +
          -rho*Y[jhe4]*Y[jcr64]*rate_eval.He4_Cr64__Fe68  +
          -rho*Y[jhe4]*Y[jna27]*rate_eval.He4_Na27__n_Al30  +
          -rho*Y[jhe4]*Y[jmn59]*rate_eval.He4_Mn59__n_Co62  +
          -rho*Y[jhe4]*Y[jo27]*rate_eval.He4_O27__Ne31  +
          -rho*Y[jhe4]*Y[jv48]*rate_eval.He4_V48__p_Cr51  +
          -rho*Y[jhe4]*Y[jca51]*rate_eval.He4_Ca51__Ti55  +
          +rho*Y[jp]*Y[jk42]*rate_eval.p_K42__He4_Ar39  +
          -rho*Y[jhe4]*Y[jbe11]*rate_eval.He4_Be11__n_C14  +
          -rho*Y[jhe4]*Y[jca50]*rate_eval.He4_Ca50__Ti54  +
          -rho*Y[jhe4]*Y[jca47]*rate_eval.He4_Ca47__Ti51  +
          -rho*Y[jhe4]*Y[jna36]*rate_eval.He4_Na36__Al40  +
          -rho*Y[jhe4]*Y[jca46]*rate_eval.He4_Ca46__Ti50  +
          -rho*Y[jhe4]*Y[jca45]*rate_eval.He4_Ca45__Ti49  +
          -rho*Y[jhe4]*Y[jli7]*rate_eval.He4_Li7__B11  +
          -rho*Y[jhe4]*Y[jca44]*rate_eval.He4_Ca44__Ti48  +
          -rho*Y[jhe4]*Y[jca42]*rate_eval.He4_Ca42__Ti46  +
          +rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__He4_K49  +
          +rho*Y[jn]*Y[jf16]*rate_eval.n_F16__He4_N13  +
          -rho*Y[jhe4]*Y[jca37]*rate_eval.He4_Ca37__Ti41  +
          -rho*Y[jhe4]*Y[jca35]*rate_eval.He4_Ca35__Ti39  +
          -rho*Y[jhe4]*Y[jca34]*rate_eval.He4_Ca34__Ti38  +
          -rho*Y[jhe4]*Y[jcl46]*rate_eval.He4_Cl46__n_K49  +
          +rho*Y[jp]*Y[jbe11]*rate_eval.p_Be11__He4_Li8  +
          -rho*Y[jhe4]*Y[jca33]*rate_eval.He4_Ca33__Ti37  +
          -rho*Y[jhe4]*Y[jna27]*rate_eval.He4_Na27__Al31  +
          -rho*Y[jhe4]*Y[jk58]*rate_eval.He4_K58__Sc62  +
          -rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__n_K47  +
          -rho*Y[jhe4]*Y[jna29]*rate_eval.He4_Na29__Al33  +
          -rho*Y[jhe4]*Y[jsi45]*rate_eval.He4_Si45__S49  +
          -rho*Y[jhe4]*Y[jk55]*rate_eval.He4_K55__Sc59  +
          +rho*Y[jp]*Y[jcl36]*rate_eval.p_Cl36__He4_S33  +
          -rho*Y[jhe4]*Y[js27]*rate_eval.He4_S27__Ar31  +
          -rho*Y[jhe4]*Y[jk51]*rate_eval.He4_K51__Sc55  +
          -rho*Y[jhe4]*Y[jk49]*rate_eval.He4_K49__Sc53  +
          -rho*Y[jhe4]*Y[jne17]*rate_eval.He4_Ne17__Mg21  +
          -rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__Sc48  +
          -rho*Y[jhe4]*Y[jk43]*rate_eval.He4_K43__Sc47  +
          +rho*Y[jn]*Y[jk39]*rate_eval.n_K39__He4_Cl36  +
          -rho*Y[jhe4]*Y[jti47]*rate_eval.He4_Ti47__Cr51  +
          -rho*Y[jhe4]*Y[jne27]*rate_eval.He4_Ne27__Mg31  +
          -rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__p_Sc39  +
          -rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__p_Ti51  +
          -rho*Y[jhe4]*Y[jp28]*rate_eval.He4_P28__Cl32  +
          +rho*Y[jn]*Y[jo15]*rate_eval.n_O15__He4_C12  +
          -rho*Y[jhe4]*Y[jk35]*rate_eval.He4_K35__Sc39  +
          -rho*Y[jhe4]*Y[jk32]*rate_eval.He4_K32__Sc36  +
          -rho*Y[jhe4]*Y[jar53]*rate_eval.He4_Ar53__Ca57  +
          -rho*Y[jhe4]*Y[jar46]*rate_eval.He4_Ar46__Ca50  +
          -rho*Y[jhe4]*Y[jar40]*rate_eval.He4_Ar40__Ca44  +
          -rho*Y[jhe4]*Y[jcr51]*rate_eval.He4_Cr51__Fe55  +
          -rho*Y[jhe4]*Y[jar39]*rate_eval.He4_Ar39__Ca43  +
          -rho*Y[jhe4]*Y[jar37]*rate_eval.He4_Ar37__Ca41  +
          -rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__Ti40  +
          -rho*Y[jhe4]*Y[jfe50]*rate_eval.He4_Fe50__Ni54  +
          -rho*Y[jhe4]*Y[jar33]*rate_eval.He4_Ar33__Ca37  +
          -rho*Y[jhe4]*Y[jar32]*rate_eval.He4_Ar32__Ca36  +
          +rho*Y[jp]*Y[jp33]*rate_eval.p_P33__He4_Si30  +
          +rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__He4_Al41  +
          -rho*Y[jhe4]*Y[jar31]*rate_eval.He4_Ar31__Ca35  +
          -rho*Y[jhe4]*Y[jne20]*rate_eval.He4_Ne20__Mg24  +
          -rho*Y[jhe4]*Y[jar30]*rate_eval.He4_Ar30__Ca34  +
          -rho*Y[jhe4]*Y[jcl51]*rate_eval.He4_Cl51__K55  +
          -rho*Y[jhe4]*Y[jmg34]*rate_eval.He4_Mg34__Si38  +
          -rho*Y[jhe4]*Y[jcr60]*rate_eval.He4_Cr60__n_Fe63  +
          -rho*Y[jhe4]*Y[jcl46]*rate_eval.He4_Cl46__K50  +
          -rho*Y[jhe4]*Y[jp26]*rate_eval.He4_P26__Cl30  +
          -rho*Y[jhe4]*Y[jcl42]*rate_eval.He4_Cl42__K46  +
          -rho*Y[jhe4]*Y[jcl39]*rate_eval.He4_Cl39__K43  +
          -rho*Y[jhe4]*Y[jcl38]*rate_eval.He4_Cl38__K42  +
          -rho*Y[jhe4]*Y[jcl36]*rate_eval.He4_Cl36__K40  +
          -rho*Y[jhe4]*Y[jcl35]*rate_eval.He4_Cl35__K39  +
          -rho*Y[jhe4]*Y[jcl33]*rate_eval.He4_Cl33__K37  +
          -rho*Y[jhe4]*Y[jcl32]*rate_eval.He4_Cl32__K36  +
          -rho*Y[jhe4]*Y[jo21]*rate_eval.He4_O21__Ne25  +
          -rho*Y[jhe4]*Y[jcl31]*rate_eval.He4_Cl31__K35  +
          -rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__Sc49  +
          -rho*Y[jhe4]*Y[js49]*rate_eval.He4_S49__Ar53  +
          -rho*Y[jhe4]*Y[js48]*rate_eval.He4_S48__Ar52  +
          -rho*Y[jhe4]*Y[js47]*rate_eval.He4_S47__Ar51  +
          -rho*Y[jhe4]*Y[js44]*rate_eval.He4_S44__Ar48  +
          -rho*Y[jhe4]*Y[js43]*rate_eval.He4_S43__Ar47  +
          -rho*Y[jhe4]*Y[js46]*rate_eval.He4_S46__Ar50  +
          -rho*Y[jhe4]*Y[js42]*rate_eval.He4_S42__Ar46  +
          -rho*Y[jhe4]*Y[jf28]*rate_eval.He4_F28__Na32  +
          -rho*Y[jhe4]*Y[js39]*rate_eval.He4_S39__Ar43  +
          -rho*Y[jhe4]*Y[jar47]*rate_eval.He4_Ar47__Ca51  +
          -rho*Y[jhe4]*Y[js36]*rate_eval.He4_S36__Ar40  +
          -rho*Y[jhe4]*Y[jmg36]*rate_eval.He4_Mg36__Si40  +
          -rho*Y[jhe4]*Y[jar54]*rate_eval.He4_Ar54__n_Ca57  +
          -rho*Y[jhe4]*Y[jca45]*rate_eval.He4_Ca45__n_Ti48  +
          -rho*Y[jhe4]*Y[js32]*rate_eval.He4_S32__Ar36  +
          -rho*Y[jhe4]*Y[jo22]*rate_eval.He4_O22__Ne26  +
          -rho*Y[jhe4]*Y[jne24]*rate_eval.He4_Ne24__Mg28  +
          -rho*Y[jhe4]*Y[jp37]*rate_eval.He4_P37__Cl41  +
          -rho*Y[jhe4]*Y[jfe71]*rate_eval.He4_Fe71__Ni75  +
          -rho*Y[jhe4]*Y[jo21]*rate_eval.He4_O21__n_Ne24  +
          -rho*Y[jhe4]*Y[jp40]*rate_eval.He4_P40__Cl44  +
          -rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__Sc45  +
          -rho*Y[jhe4]*Y[jcl37]*rate_eval.He4_Cl37__K41  +
          -rho*Y[jhe4]*Y[jmg33]*rate_eval.He4_Mg33__n_Si36  +
          -rho*Y[jhe4]*Y[jcl38]*rate_eval.He4_Cl38__n_K41  +
          -rho*Y[jhe4]*Y[jp36]*rate_eval.He4_P36__Cl40  +
          -rho*Y[jhe4]*Y[jp35]*rate_eval.He4_P35__Cl39  +
          -rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__K48  +
          +rho*Y[jp]*Y[jfe58]*rate_eval.p_Fe58__He4_Mn55  +
          -rho*Y[jhe4]*Y[jp32]*rate_eval.He4_P32__Cl36  +
          +rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__He4_V42  +
          -rho*Y[jhe4]*Y[js26]*rate_eval.He4_S26__Ar30  +
          -rho*Y[jhe4]*Y[jp27]*rate_eval.He4_P27__Cl31  +
          -rho*Y[jhe4]*Y[jna31]*rate_eval.He4_Na31__Al35  +
          -rho*Y[jhe4]*Y[jp24]*rate_eval.He4_P24__Cl28  +
          -rho*Y[jhe4]*Y[jcl33]*rate_eval.He4_Cl33__p_Ar36  +
          -rho*Y[jhe4]*Y[jsi41]*rate_eval.He4_Si41__S45  +
          -rho*Y[jhe4]*Y[jsi40]*rate_eval.He4_Si40__S44  +
          -rho*Y[jhe4]*Y[jsi38]*rate_eval.He4_Si38__S42  +
          +rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__He4_Cl51  +
          +rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__He4_Na21  +
          -rho*Y[jhe4]*Y[jsi34]*rate_eval.He4_Si34__S38  +
          -rho*Y[jhe4]*Y[jsi33]*rate_eval.He4_Si33__S37  +
          -rho*Y[jhe4]*Y[jcl29]*rate_eval.He4_Cl29__K33  +
          +rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__He4_O14  +
          -rho*Y[jhe4]*Y[jsi24]*rate_eval.He4_Si24__S28  +
          +rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__He4_Ca53  +
          -rho*Y[jhe4]*Y[jal43]*rate_eval.He4_Al43__P47  +
          -rho*Y[jhe4]*Y[jcl34]*rate_eval.He4_Cl34__K38  +
          -rho*Y[jhe4]*Y[jal42]*rate_eval.He4_Al42__P46  +
          -rho*Y[jhe4]*Y[jca38]*rate_eval.He4_Ca38__p_Sc41  +
          -rho*Y[jhe4]*Y[jal40]*rate_eval.He4_Al40__P44  +
          -rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__P42  +
          -rho*Y[jhe4]*Y[jal37]*rate_eval.He4_Al37__P41  +
          +rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__He4_Ca56  +
          -rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__P40  +
          -rho*Y[jhe4]*Y[jmg37]*rate_eval.He4_Mg37__Si41  +
          -rho*Y[jhe4]*Y[jal34]*rate_eval.He4_Al34__P38  +
          -rho*Y[jhe4]*Y[jcr56]*rate_eval.He4_Cr56__Fe60  +
          -rho*Y[jhe4]*Y[jal30]*rate_eval.He4_Al30__P34  +
          +rho*Y[jp]*Y[js49]*rate_eval.p_S49__He4_P46  +
          -rho*Y[jhe4]*Y[jti62]*rate_eval.He4_Ti62__n_Cr65  +
          -rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__P31  +
          -rho*Y[jhe4]*Y[jal26]*rate_eval.He4_Al26__P30  +
          -rho*Y[jhe4]*Y[jti56]*rate_eval.He4_Ti56__Cr60  +
          -rho*Y[jhe4]*Y[jmg41]*rate_eval.He4_Mg41__Si45  +
          -rho*Y[jhe4]*Y[jmg39]*rate_eval.He4_Mg39__Si43  +
          -rho*Y[jhe4]*Y[jal41]*rate_eval.He4_Al41__P45  +
          +rho*Y[jp]*Y[jp46]*rate_eval.p_P46__He4_Si43  +
          -rho*Y[jhe4]*Y[jsi39]*rate_eval.He4_Si39__S43  +
          -rho*Y[jhe4]*Y[jmg40]*rate_eval.He4_Mg40__Si44  +
          -rho*Y[jhe4]*Y[jmg33]*rate_eval.He4_Mg33__Si37  +
          -rho*Y[jhe4]*Y[jmg31]*rate_eval.He4_Mg31__Si35  +
          +rho*Y[jp]*Y[js48]*rate_eval.p_S48__He4_P45  +
          -rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__P33  +
          -rho*Y[jhe4]*Y[jk47]*rate_eval.He4_K47__Sc51  +
          -rho*Y[jhe4]*Y[jmg29]*rate_eval.He4_Mg29__Si33  +
          -rho*Y[jhe4]*Y[jmg30]*rate_eval.He4_Mg30__Si34  +
          -rho*Y[jhe4]*Y[jmg28]*rate_eval.He4_Mg28__Si32  +
          -rho*Y[jhe4]*Y[jmn65]*rate_eval.He4_Mn65__Co69  +
          -rho*Y[jhe4]*Y[jmg23]*rate_eval.He4_Mg23__Si27  +
          +rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__He4_V41  +
          -rho*Y[jhe4]*Y[jmg31]*rate_eval.He4_Mg31__n_Si34  +
          -rho*Y[jhe4]*Y[jca53]*rate_eval.He4_Ca53__Ti57  +
          -rho*Y[jhe4]*Y[jmg21]*rate_eval.He4_Mg21__Si25  +
          -rho*Y[jhe4]*Y[jmn48]*rate_eval.He4_Mn48__p_Fe51  +
          + -3*1.66666666666667e-01*rho**2*Y[jhe4]**3*rate_eval.He4_He4_He4__C12  +
          -rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__K47  +
          -rho*Y[jhe4]*Y[jmg19]*rate_eval.He4_Mg19__Si23  +
          -rho*Y[jhe4]*Y[jsi31]*rate_eval.He4_Si31__S35  +
          -rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__Al41  +
          -rho*Y[jhe4]*Y[js49]*rate_eval.He4_S49__n_Ar52  +
          -rho*Y[jhe4]*Y[jna34]*rate_eval.He4_Na34__Al38  +
          -rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__Al37  +
          +rho*Y[jn]*Y[jhe3]*rate_eval.n_He3__He4  +
          -rho*Y[jhe4]*Y[jna39]*rate_eval.He4_Na39__Al43  +
          -rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__p_Si31  +
          -rho*Y[jhe4]*Y[jne29]*rate_eval.He4_Ne29__n_Mg32  +
          -rho*Y[jhe4]*Y[jp25]*rate_eval.He4_P25__Cl29  +
          -rho*Y[jhe4]*Y[jna28]*rate_eval.He4_Na28__Al32  +
          -rho*Y[jhe4]*Y[jti56]*rate_eval.He4_Ti56__n_Cr59  +
          -rho*Y[jhe4]*Y[jf15]*rate_eval.He4_F15__p_Ne18  +
          -rho*Y[jhe4]*Y[jna23]*rate_eval.He4_Na23__Al27  +
          +rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__He4_Ca60  +
          -rho*Y[jhe4]*Y[jv55]*rate_eval.He4_V55__Mn59  +
          -rho*Y[jhe4]*Y[jar50]*rate_eval.He4_Ar50__Ca54  +
          -rho*Y[jhe4]*Y[jti42]*rate_eval.He4_Ti42__Cr46  +
          -rho*Y[jhe4]*Y[jna20]*rate_eval.He4_Na20__Al24  +
          +rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__He4_Na28  +
          -rho*Y[jhe4]*Y[jk58]*rate_eval.He4_K58__n_Sc61  +
          -rho*Y[jhe4]*Y[jne34]*rate_eval.He4_Ne34__Mg38  +
          -rho*Y[jhe4]*Y[jne31]*rate_eval.He4_Ne31__Mg35  +
          -rho*Y[jhe4]*Y[jne30]*rate_eval.He4_Ne30__Mg34  +
          -rho*Y[jhe4]*Y[jca58]*rate_eval.He4_Ca58__Ti62  +
          +rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__He4_Ne32  +
          -rho*Y[jhe4]*Y[jne26]*rate_eval.He4_Ne26__Mg30  +
          -rho*Y[jhe4]*Y[jcl52]*rate_eval.He4_Cl52__n_K55  +
          +rho*Y[jp]*Y[jf24]*rate_eval.p_F24__He4_O21  +
          -rho*Y[jhe4]*Y[jcr65]*rate_eval.He4_Cr65__Fe69  +
          -rho*Y[jhe4]*Y[jne16]*rate_eval.He4_Ne16__Mg20  +
          -rho*Y[jhe4]*Y[jna30]*rate_eval.He4_Na30__Al34  +
          -rho*Y[jhe4]*Y[jo28]*rate_eval.He4_O28__Ne32  +
          -rho*Y[jhe4]*Y[jf31]*rate_eval.He4_F31__Na35  +
          +rho*Y[jp]*Y[jf19]*rate_eval.p_F19__He4_O16  +
          -rho*Y[jhe4]*Y[jmg29]*rate_eval.He4_Mg29__n_Si32  +
          -rho*Y[jhe4]*Y[jar41]*rate_eval.He4_Ar41__Ca45  +
          -rho*Y[jhe4]*Y[jf24]*rate_eval.He4_F24__Na28  +
          -rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__P35  +
          -rho*Y[jhe4]*Y[jmn51]*rate_eval.He4_Mn51__Co55  +
          -rho*Y[jhe4]*Y[jf18]*rate_eval.He4_F18__Na22  +
          -rho*Y[jhe4]*Y[jk59]*rate_eval.He4_K59__Sc63  +
          -rho*Y[jhe4]*Y[jar42]*rate_eval.He4_Ar42__Ca46  +
          -rho*Y[jhe4]*Y[jo24]*rate_eval.He4_O24__Ne28  +
          -rho*Y[jhe4]*Y[jo23]*rate_eval.He4_O23__Ne27  +
          +Y[jk36]*rate_eval.K36__He4_S32__weak__wc12  +
          -rho*Y[jhe4]*Y[jf27]*rate_eval.He4_F27__Na31  +
          +rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__He4_P28  +
          -rho*Y[jhe4]*Y[jo20]*rate_eval.He4_O20__Ne24  +
          -rho*Y[jhe4]*Y[jo20]*rate_eval.He4_O20__n_Ne23  +
          -rho*Y[jhe4]*Y[jo19]*rate_eval.He4_O19__Ne23  +
          -rho*Y[jhe4]*Y[js28]*rate_eval.He4_S28__Ar32  +
          -rho*Y[jhe4]*Y[jar44]*rate_eval.He4_Ar44__n_Ca47  +
          -rho*Y[jhe4]*Y[jo17]*rate_eval.He4_O17__Ne21  +
          +rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__He4_Mg24  +
          -rho*Y[jhe4]*Y[jp33]*rate_eval.He4_P33__Cl37  +
          -rho*Y[jhe4]*Y[jti64]*rate_eval.He4_Ti64__Cr68  +
          -rho*Y[jhe4]*Y[jli9]*rate_eval.He4_Li9__B13  +
          -rho*Y[jhe4]*Y[jmg26]*rate_eval.He4_Mg26__Si30  +
          -rho*Y[jhe4]*Y[jfe45]*rate_eval.He4_Fe45__p_Co48  +
          -rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__Al28  +
          -rho*Y[jhe4]*Y[jli8]*rate_eval.He4_Li8__B12  +
          -rho*Y[jhe3]*Y[jhe4]*rate_eval.He4_He3__Be7  +
          -rho*Y[jhe4]*Y[jfe75]*rate_eval.He4_Fe75__Ni79  +
          +rho*Y[jp]*Y[jt]*rate_eval.p_t__He4  +
          -rho*Y[jd]*Y[jhe4]*rate_eval.He4_d__Li6  +
          -rho*Y[jhe4]*Y[jcr49]*rate_eval.He4_Cr49__Fe53  +
          -rho*Y[jhe4]*Y[jc12]*rate_eval.He4_C12__O16  +
          -rho*Y[jhe4]*Y[jfe62]*rate_eval.He4_Fe62__n_Ni65  +
          -rho*Y[jhe4]*Y[jmg27]*rate_eval.He4_Mg27__Si31  +
          -rho*Y[jhe4]*Y[jp34]*rate_eval.He4_P34__Cl38  +
          -rho*Y[jhe4]*Y[jca49]*rate_eval.He4_Ca49__n_Ti52  +
          +rho*Y[jn]*Y[jv48]*rate_eval.n_V48__He4_Sc45  +
          +rho*Y[jn]*Y[js31]*rate_eval.n_S31__He4_Si28  +
          -rho*Y[jhe4]*Y[jmn73]*rate_eval.He4_Mn73__Co77  +
          +rho*Y[jp]*Y[jar42]*rate_eval.p_Ar42__He4_Cl39  +
          +rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__He4_P27  +
          -rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__Sc46  +
          -rho*Y[jhe4]*Y[jna19]*rate_eval.He4_Na19__p_Mg22  +
          -rho*Y[jhe4]*Y[jmn61]*rate_eval.He4_Mn61__n_Co64  +
          -rho*Y[jhe4]*Y[jsi28]*rate_eval.He4_Si28__S32  +
          -rho*Y[jhe4]*Y[jsc41]*rate_eval.He4_Sc41__p_Ti44  +
          -rho*Y[jhe4]*Y[jsc36]*rate_eval.He4_Sc36__V40  +
          +rho*Y[jp]*Y[js37]*rate_eval.p_S37__He4_P34  +
          -rho*Y[jhe4]*Y[jmn43]*rate_eval.He4_Mn43__p_Fe46  +
          -rho*Y[jhe4]*Y[jk36]*rate_eval.He4_K36__Sc40  +
          -rho*Y[jhe4]*Y[jsc40]*rate_eval.He4_Sc40__V44  +
          -rho*Y[jhe4]*Y[jk47]*rate_eval.He4_K47__n_Sc50  +
          -rho*Y[jhe4]*Y[jo14]*rate_eval.He4_O14__Ne18  +
          -rho*Y[jhe4]*Y[jmg38]*rate_eval.He4_Mg38__Si42  +
          -rho*Y[jhe4]*Y[jsi26]*rate_eval.He4_Si26__S30  +
          -rho*Y[jhe4]*Y[jna20]*rate_eval.He4_Na20__p_Mg23  +
          -rho*Y[jhe4]*Y[jfe74]*rate_eval.He4_Fe74__Ni78  +
          -rho*Y[jhe4]*Y[jv44]*rate_eval.He4_V44__p_Cr47  +
          -rho*Y[jhe4]*Y[jmg36]*rate_eval.He4_Mg36__n_Si39  +
          -rho*Y[jhe4]*Y[jb11]*rate_eval.He4_B11__n_N14  +
          -rho*Y[jhe4]*Y[jmn58]*rate_eval.He4_Mn58__Co62  +
          -rho*Y[jhe4]*Y[jsi32]*rate_eval.He4_Si32__S36  +
          -rho*Y[jhe4]*Y[js29]*rate_eval.He4_S29__Ar33  +
          -rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__Na34  +
          -rho*Y[jhe4]*Y[jfe63]*rate_eval.He4_Fe63__Ni67  +
          -rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__Na24  +
          -rho*Y[jhe4]*Y[jk59]*rate_eval.He4_K59__n_Sc62  +
          -rho*Y[jhe4]*Y[js47]*rate_eval.He4_S47__n_Ar50  +
          -rho*Y[jhe4]*Y[jcl28]*rate_eval.He4_Cl28__K32  +
          -rho*Y[jhe4]*Y[jmg28]*rate_eval.He4_Mg28__n_Si31  +
          +rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__He4_Cr60  +
          -rho*Y[jhe4]*Y[jcr68]*rate_eval.He4_Cr68__n_Fe71  +
          -rho*Y[jhe4]*Y[jfe66]*rate_eval.He4_Fe66__Ni70  +
          -rho*Y[jhe4]*Y[jsi29]*rate_eval.He4_Si29__S33  +
          +rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__He4_Mg20  +
          +rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__He4_Ne33  +
          -rho*Y[jhe4]*Y[jbe9]*rate_eval.He4_Be9__n_C12  +
          -rho*Y[jhe4]*Y[jfe61]*rate_eval.He4_Fe61__Ni65  +
          +rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__He4_Na34  +
          -rho*Y[jhe4]*Y[jca35]*rate_eval.He4_Ca35__p_Sc38  +
          -rho*Y[jhe4]*Y[jar54]*rate_eval.He4_Ar54__Ca58  +
          -rho*Y[jhe4]*Y[jv59]*rate_eval.He4_V59__Mn63  +
          -rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__Cl45  +
          -rho*Y[jhe4]*Y[jp46]*rate_eval.He4_P46__n_Cl49  +
          -rho*Y[jhe4]*Y[jk53]*rate_eval.He4_K53__Sc57  +
          -rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__Ar38  +
          -rho*Y[jhe4]*Y[jca37]*rate_eval.He4_Ca37__p_Sc40  +
          +rho*Y[jp]*Y[jp31]*rate_eval.p_P31__He4_Si28  +
          -rho*Y[jhe4]*Y[jn12]*rate_eval.He4_N12__p_O15  +
          -rho*Y[jhe4]*Y[jmn71]*rate_eval.He4_Mn71__Co75  +
          -rho*Y[jhe4]*Y[jv65]*rate_eval.He4_V65__n_Mn68  +
          -rho*Y[jhe4]*Y[jbe10]*rate_eval.He4_Be10__n_C13  +
          +rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__He4_Mg23  +
          -rho*Y[jhe4]*Y[jca55]*rate_eval.He4_Ca55__n_Ti58  +
          -rho*Y[jhe4]*Y[jar44]*rate_eval.He4_Ar44__Ca48  +
          -rho*Y[jhe4]*Y[jp28]*rate_eval.He4_P28__p_S31  +
          -rho*Y[jhe4]*Y[jsi25]*rate_eval.He4_Si25__S29  +
          -rho*Y[jhe4]*Y[jp38]*rate_eval.He4_P38__Cl42  +
          -rho*Y[jhe4]*Y[jmg25]*rate_eval.He4_Mg25__Si29  +
          -rho*Y[jhe4]*Y[jmn52]*rate_eval.He4_Mn52__p_Fe55  +
          +rho*Y[jp]*Y[js42]*rate_eval.p_S42__He4_P39  +
          -rho*Y[jhe4]*Y[jn14]*rate_eval.He4_N14__F18  +
          -rho*Y[jhe4]*Y[jsi36]*rate_eval.He4_Si36__n_S39  +
          + 2*rho*Y[jp]*Y[jli8]*rate_eval.p_Li8__n_He4_He4  +
          -rho*Y[jhe4]*Y[jv48]*rate_eval.He4_V48__Mn52  +
          -rho*Y[jhe4]*Y[jca61]*rate_eval.He4_Ca61__Ti65  +
          -rho*Y[jhe4]*Y[jfe62]*rate_eval.He4_Fe62__Ni66  +
          -rho*Y[jhe4]*Y[jca55]*rate_eval.He4_Ca55__Ti59  +
          -rho*Y[jhe4]*Y[jp46]*rate_eval.He4_P46__Cl50  +
          +rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__He4_Ne17  +
          -rho*Y[jhe4]*Y[jal24]*rate_eval.He4_Al24__P28  +
          +rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__He4_Al37  +
          -rho*Y[jhe4]*Y[jti50]*rate_eval.He4_Ti50__Cr54  +
          -rho*Y[jhe4]*Y[jal43]*rate_eval.He4_Al43__n_P46  +
          -rho*Y[jhe4]*Y[jfe51]*rate_eval.He4_Fe51__p_Co54  +
          -rho*Y[jhe4]*Y[jne25]*rate_eval.He4_Ne25__n_Mg28  +
          +rho*Y[jp]*Y[jk50]*rate_eval.p_K50__He4_Ar47  +
          -rho*Y[jhe4]*Y[jo27]*rate_eval.He4_O27__n_Ne30  +
          -rho*Y[jhe4]*Y[jca60]*rate_eval.He4_Ca60__Ti64  +
          +rho*Y[jn]*Y[jp25]*rate_eval.n_P25__He4_Al22  +
          -rho*Y[jhe4]*Y[jp39]*rate_eval.He4_P39__Cl43  +
          -rho*Y[jhe4]*Y[js38]*rate_eval.He4_S38__Ar42  +
          -rho*Y[jhe4]*Y[jar30]*rate_eval.He4_Ar30__p_K33  +
          -rho*Y[jhe4]*Y[jp31]*rate_eval.He4_P31__Cl35  +
          +rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__He4_K54  +
          -rho*Y[jhe4]*Y[jmg32]*rate_eval.He4_Mg32__Si36  +
          -rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__K45  +
          +rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__He4_Ar36  +
          +5.00000000000000e-01*rho*Y[jd]**2*rate_eval.d_d__He4  +
          -rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__n_K46  +
          -rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__n_Al36  +
          +Y[jcl32]*rate_eval.Cl32__He4_Si28__weak__wc12  +
          -rho*Y[jhe4]*Y[jti55]*rate_eval.He4_Ti55__Cr59  +
          -rho*Y[jhe4]*Y[jv45]*rate_eval.He4_V45__p_Cr48  +
          -rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__P43  +
          +rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__He4_Ne24  +
          -rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__n_Al28  +
          +rho*Y[jn]*Y[js27]*rate_eval.n_S27__He4_Si24  +
          +rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__He4_Al30  +
          +rho*Y[jp]*Y[jk46]*rate_eval.p_K46__He4_Ar43  +
          -rho*Y[jt]*Y[jhe4]*rate_eval.He4_t__Li7  +
          + -2*5.00000000000000e-01*rho**2*Y[jn]*Y[jhe4]**2*rate_eval.n_He4_He4__Be9  +
          -rho*Y[jhe4]*Y[jp47]*rate_eval.He4_P47__Cl51  +
          -rho*Y[jhe4]*Y[jcl48]*rate_eval.He4_Cl48__K52  +
          -rho*Y[jhe4]*Y[jar47]*rate_eval.He4_Ar47__n_Ca50  +
          -rho*Y[jhe4]*Y[js40]*rate_eval.He4_S40__n_Ar43  +
          -rho*Y[jhe4]*Y[jsi35]*rate_eval.He4_Si35__S39  +
          -rho*Y[jhe4]*Y[jp43]*rate_eval.He4_P43__Cl47  +
          -rho*Y[jhe4]*Y[jna29]*rate_eval.He4_Na29__n_Al32  +
          +rho*Y[jn]*Y[jca41]*rate_eval.n_Ca41__He4_Ar38  +
          +Y[jsc40]*rate_eval.Sc40__He4_Ar36__weak__wc12  +
          -rho*Y[jhe4]*Y[jmg35]*rate_eval.He4_Mg35__Si39  +
          -rho*Y[jhe4]*Y[jf23]*rate_eval.He4_F23__Na27  +
          +rho*Y[jp]*Y[jk49]*rate_eval.p_K49__He4_Ar46  +
          +Y[jal24]*rate_eval.Al24__He4_Ne20__weak__wc12  +
          -rho*Y[jhe4]*Y[jna21]*rate_eval.He4_Na21__Al25  +
          -rho*Y[jhe4]*Y[jp45]*rate_eval.He4_P45__n_Cl48  +
          -rho*Y[jhe4]*Y[jsc52]*rate_eval.He4_Sc52__V56  +
          -rho*Y[jhe4]*Y[jmg41]*rate_eval.He4_Mg41__n_Si44  +
          -rho*Y[jhe4]*Y[jc14]*rate_eval.He4_C14__O18  +
          -rho*Y[jhe4]*Y[jo18]*rate_eval.He4_O18__Ne22  +
          -rho*Y[jhe4]*Y[jmn62]*rate_eval.He4_Mn62__Co66  +
          -rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__n_Sc47  +
          +rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__He4_F16  +
          -rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__P32  +
          -rho*Y[jhe4]*Y[jmn70]*rate_eval.He4_Mn70__n_Co73  +
          -rho**2*Y[jn]*Y[jp]*Y[jhe4]*rate_eval.n_p_He4__Li6  +
          -rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__p_Mg28  +
          -rho*Y[jhe4]*Y[jcl52]*rate_eval.He4_Cl52__K56  +
          -rho*Y[jhe4]*Y[jsc53]*rate_eval.He4_Sc53__n_V56  +
          +rho*Y[jp]*Y[jv55]*rate_eval.p_V55__He4_Ti52  +
          +rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__He4_K57  +
          +rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__He4_Cr55  +
          -rho*Y[jhe4]*Y[jk31]*rate_eval.He4_K31__Sc35  +
          -rho*Y[jhe4]*Y[js31]*rate_eval.He4_S31__Ar35  +
          -rho*Y[jhe4]*Y[jf15]*rate_eval.He4_F15__Na19  +
          +rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__He4_Cl38  +
          -rho*Y[jhe4]*Y[jmg21]*rate_eval.He4_Mg21__p_Al24  +
          -rho*Y[jhe4]*Y[jca41]*rate_eval.He4_Ca41__Ti45  +
          -rho*Y[jhe4]*Y[jcl40]*rate_eval.He4_Cl40__K44  +
          +rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__He4_S46  +
          -rho*Y[jhe4]*Y[jar45]*rate_eval.He4_Ar45__n_Ca48  +
          -rho*Y[jhe4]*Y[jp29]*rate_eval.He4_P29__Cl33  +
          -rho*Y[jhe4]*Y[jf25]*rate_eval.He4_F25__Na29  +
          -rho*Y[jhe4]*Y[jmn63]*rate_eval.He4_Mn63__n_Co66  +
          -rho*Y[jhe4]*Y[jc11]*rate_eval.He4_C11__p_N14  +
          -rho*Y[jhe4]*Y[jfe61]*rate_eval.He4_Fe61__n_Ni64  +
          -rho*Y[jhe4]*Y[jsi37]*rate_eval.He4_Si37__S41  +
          +rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__He4_Sc58  +
          +rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__He4_P33  +
          -rho*Y[jhe4]*Y[jsc51]*rate_eval.He4_Sc51__V55  +
          +rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__He4_Sc57  +
          -rho*Y[jhe4]*Y[jti41]*rate_eval.He4_Ti41__p_V44  +
          +rho*Y[jp]*Y[jb10]*rate_eval.p_B10__He4_Be7  +
          +Y[jc9]*rate_eval.C9__He4_Li5__weak__wc12  +
          +rho*Y[jp]*Y[js40]*rate_eval.p_S40__He4_P37  +
          -rho*Y[jhe4]*Y[js35]*rate_eval.He4_S35__Ar39  +
          +rho*Y[jn]*Y[jk42]*rate_eval.n_K42__He4_Cl39  +
          -rho*Y[jhe4]*Y[js45]*rate_eval.He4_S45__Ar49  +
          +rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__He4_Cr67  +
          -rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__n_Sc48  +
          -rho*Y[jhe4]*Y[jp38]*rate_eval.He4_P38__n_Cl41  +
          -rho*Y[jhe4]*Y[jcl48]*rate_eval.He4_Cl48__n_K51  +
          -rho*Y[jhe4]*Y[jne23]*rate_eval.He4_Ne23__Mg27  +
          -rho*Y[jhe4]*Y[jar50]*rate_eval.He4_Ar50__n_Ca53  +
          +rho*Y[jp]*Y[jp39]*rate_eval.p_P39__He4_Si36  +
          -rho*Y[jhe4]*Y[jti49]*rate_eval.He4_Ti49__Cr53  +
          -rho*Y[jhe4]*Y[jk33]*rate_eval.He4_K33__p_Ca36  +
          +rho*Y[jn]*Y[jk31]*rate_eval.n_K31__He4_Cl28  +
          -rho*Y[jhe4]*Y[jli6]*rate_eval.He4_Li6__B10  +
          -rho*Y[jhe4]*Y[js33]*rate_eval.He4_S33__Ar37  +
          -rho*Y[jhe4]*Y[jcr69]*rate_eval.He4_Cr69__Fe73  +
          + 2*rho*Y[jp]*Y[jli7]*rate_eval.p_Li7__He4_He4  +
          +rho*Y[jn]*Y[jo12]*rate_eval.n_O12__He4_C9  +
          -rho*Y[jhe4]*Y[jca56]*rate_eval.He4_Ca56__Ti60  +
          +Y[jbe11]*rate_eval.Be11__He4_Li7__weak__wc12  +
          -rho*Y[jhe4]*Y[jb10]*rate_eval.He4_B10__n_N13  +
          +rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__He4_K56  +
          -rho*Y[jhe4]*Y[jo15]*rate_eval.He4_O15__Ne19  +
          +rho*Y[jp]*Y[jf21]*rate_eval.p_F21__He4_O18  +
          -rho*Y[jhe4]*Y[jne28]*rate_eval.He4_Ne28__Mg32  +
          +rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__He4_Ca58  +
          -rho*Y[jhe4]*Y[jna35]*rate_eval.He4_Na35__Al39  +
          +rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__He4_Li6  +
          -rho*Y[jhe4]*Y[jcr61]*rate_eval.He4_Cr61__Fe65  +
          -rho*Y[jhe4]*Y[jne32]*rate_eval.He4_Ne32__Mg36  +
          +rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__He4_K51  +
          -rho*Y[jhe4]*Y[jne22]*rate_eval.He4_Ne22__Mg26  +
          -rho*Y[jhe4]*Y[jmn58]*rate_eval.He4_Mn58__n_Co61  +
          -rho*Y[jhe4]*Y[jti62]*rate_eval.He4_Ti62__Cr66  +
          -rho*Y[jhe4]*Y[jli9]*rate_eval.He4_Li9__n_B12  +
          -rho*Y[jhe4]*Y[jal23]*rate_eval.He4_Al23__p_Si26  +
          +rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__He4_K50  +
          +rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__He4_V61  +
          -rho*Y[jhe4]*Y[jn16]*rate_eval.He4_N16__n_F19  +
          -rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__p_Ar44  +
          -rho*Y[jhe4]*Y[jsi36]*rate_eval.He4_Si36__S40  +
          +rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__He4_Ti46  +
          -rho*Y[jhe4]*Y[jsc46]*rate_eval.He4_Sc46__n_V49  +
          +rho*Y[jn]*Y[jk38]*rate_eval.n_K38__He4_Cl35  +
          +rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__He4_Na27  +
          -rho*Y[jhe4]*Y[jfe65]*rate_eval.He4_Fe65__n_Ni68  +
          +rho*Y[jn]*Y[jk34]*rate_eval.n_K34__He4_Cl31  +
          +rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__He4_Ca50  +
          -rho*Y[jhe4]*Y[jb13]*rate_eval.He4_B13__N17  +
          -rho*Y[jhe4]*Y[jp42]*rate_eval.He4_P42__Cl46  +
          -rho*Y[jhe4]*Y[jcl45]*rate_eval.He4_Cl45__K49  +
          +rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__He4_Na38  +
          +rho*Y[jn]*Y[jo17]*rate_eval.n_O17__He4_C14  +
          -rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__Na25  +
          +Y[jp28]*rate_eval.P28__He4_Mg24__weak__wc12  +
          -rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__n_P42  +
          -rho*Y[jhe4]*Y[jca49]*rate_eval.He4_Ca49__Ti53  +
          + 2*rho*Y[jt]*Y[jli7]*rate_eval.t_Li7__n_n_He4_He4  +
          -rho*Y[jhe4]*Y[jk48]*rate_eval.He4_K48__Sc52  +
          +rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__He4_S30  +
          -rho*Y[jhe4]*Y[jp45]*rate_eval.He4_P45__Cl49  +
          +rho*Y[jp]*Y[jk55]*rate_eval.p_K55__He4_Ar52  +
          -rho*Y[jhe4]*Y[jmn64]*rate_eval.He4_Mn64__n_Co67  +
          -rho*Y[jhe4]*Y[jcl31]*rate_eval.He4_Cl31__p_Ar34  +
          -rho*Y[jhe4]*Y[jna22]*rate_eval.He4_Na22__Al26  +
          +rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__He4_K33  +
          -rho*Y[jhe4]*Y[jti37]*rate_eval.He4_Ti37__Cr41  +
          -rho*Y[jhe4]*Y[jna26]*rate_eval.He4_Na26__Al30  +
          -rho*Y[jhe4]*Y[jf22]*rate_eval.He4_F22__Na26  +
          -rho*Y[jhe4]*Y[jsc63]*rate_eval.He4_Sc63__V67  +
          -rho*Y[jhe4]*Y[jti57]*rate_eval.He4_Ti57__Cr61  +
          +rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__He4_Cr65  +
          -rho*Y[jhe4]*Y[jfe67]*rate_eval.He4_Fe67__n_Ni70  +
          -rho*Y[jhe4]*Y[jk40]*rate_eval.He4_K40__Sc44  +
          -rho*Y[jhe4]*Y[jne34]*rate_eval.He4_Ne34__n_Mg37  +
          -rho*Y[jhe4]*Y[jfe48]*rate_eval.He4_Fe48__Ni52  +
          -rho*Y[jhe4]*Y[jna30]*rate_eval.He4_Na30__n_Al33  +
          +rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__He4_Na35  +
          -rho*Y[jhe4]*Y[jar49]*rate_eval.He4_Ar49__n_Ca52  +
          -rho*Y[jhe4]*Y[jmn55]*rate_eval.He4_Mn55__Co59  +
          -rho*Y[jhe4]*Y[jsi30]*rate_eval.He4_Si30__S34  +
          -rho*Y[jhe4]*Y[jsi43]*rate_eval.He4_Si43__S47  +
          +rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__He4_Na32  +
          -rho*Y[jhe4]*Y[jmn56]*rate_eval.He4_Mn56__Co60  +
          -rho*Y[jhe4]*Y[jp44]*rate_eval.He4_P44__Cl48  +
          -rho*Y[jhe4]*Y[jsc37]*rate_eval.He4_Sc37__V41  +
          +Y[jn16]*rate_eval.N16__He4_C12__weak__wc12  +
          -rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__n_Al27  +
          -rho*Y[jhe4]*Y[jo25]*rate_eval.He4_O25__Ne29  +
          +rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__He4_Ca47  +
          +rho*Y[jp]*Y[jp45]*rate_eval.p_P45__He4_Si42  +
          +rho*Y[jp]*Y[jk43]*rate_eval.p_K43__He4_Ar40  +
          -rho*Y[jhe4]*Y[jsi44]*rate_eval.He4_Si44__S48  +
          +Y[jna20]*rate_eval.Na20__He4_O16__weak__wc12  +
          -rho*Y[jhe4]*Y[jk38]*rate_eval.He4_K38__Sc42  +
          -rho*Y[jhe4]*Y[jti59]*rate_eval.He4_Ti59__Cr63  +
          +rho*Y[jp]*Y[jp40]*rate_eval.p_P40__He4_Si37  +
          -rho*Y[jhe4]*Y[jv52]*rate_eval.He4_V52__n_Mn55  +
          -rho*Y[jhe4]*Y[jmn71]*rate_eval.He4_Mn71__n_Co74  +
          -rho*Y[jhe4]*Y[jar34]*rate_eval.He4_Ar34__Ca38  +
          +rho*Y[jp]*Y[jv54]*rate_eval.p_V54__He4_Ti51  +
          -rho*Y[jhe4]*Y[jsi22]*rate_eval.He4_Si22__S26  +
          -rho*Y[jhe4]*Y[jar51]*rate_eval.He4_Ar51__Ca55  +
          +rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__He4_Ca41  +
          -rho*Y[jhe4]*Y[jmn66]*rate_eval.He4_Mn66__n_Co69  +
          +Y[jna30]*rate_eval.Na30__He4_Ne26__weak__wc12  +
          -rho*Y[jhe4]*Y[jca52]*rate_eval.He4_Ca52__n_Ti55  +
          -rho*Y[jhe4]*Y[jne19]*rate_eval.He4_Ne19__Mg23  +
          -rho*Y[jhe4]*Y[jfe60]*rate_eval.He4_Fe60__Ni64  +
          -rho*Y[jhe4]*Y[jar48]*rate_eval.He4_Ar48__Ca52  +
          +rho*Y[jp]*Y[jv62]*rate_eval.p_V62__He4_Ti59  +
          +rho*Y[jp]*Y[jp47]*rate_eval.p_P47__He4_Si44  +
          -rho*Y[jhe4]*Y[jca54]*rate_eval.He4_Ca54__n_Ti57  +
          +rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__He4_Sc59  +
          -rho*Y[jhe4]*Y[jv42]*rate_eval.He4_V42__Mn46  +
          +rho*Y[jn]*Y[jb10]*rate_eval.n_B10__He4_Li7  +
          -rho*Y[jhe4]*Y[jfe55]*rate_eval.He4_Fe55__Ni59  +
          +5.00000000000000e-01*rho*Y[jt]**2*rate_eval.t_t__n_n_He4  +
          +rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__He4_V56  +
          +rho*Y[jp]*Y[jp35]*rate_eval.p_P35__He4_Si32  +
          +rho*Y[jp]*Y[jp34]*rate_eval.p_P34__He4_Si31  +
          +rho*Y[jp]*Y[jk39]*rate_eval.p_K39__He4_Ar36  +
          + 2*rho*Y[jhe3]*Y[jli7]*rate_eval.He3_Li7__n_p_He4_He4  +
          -rho*Y[jhe4]*Y[jp29]*rate_eval.He4_P29__p_S32  +
          -rho*Y[jhe4]*Y[jti58]*rate_eval.He4_Ti58__Cr62  +
          +rho*Y[jp]*Y[jn16]*rate_eval.p_N16__He4_C13  +
          +rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__He4_Ne29  +
          -rho*Y[jhe4]*Y[jcr52]*rate_eval.He4_Cr52__Fe56  +
          -rho*Y[jhe4]*Y[jal21]*rate_eval.He4_Al21__P25  +
          -rho*Y[jhe4]*Y[jmg23]*rate_eval.He4_Mg23__p_Al26  +
          -rho*Y[jhe4]*Y[jca34]*rate_eval.He4_Ca34__p_Sc37  +
          -rho*Y[jhe4]*Y[jsc61]*rate_eval.He4_Sc61__V65  +
          -rho*Y[jhe4]*Y[jv44]*rate_eval.He4_V44__Mn48  +
          +rho*Y[jp]*Y[jk54]*rate_eval.p_K54__He4_Ar51  +
          -rho*Y[jhe4]*Y[jfe53]*rate_eval.He4_Fe53__Ni57  +
          -rho*Y[jhe4]*Y[jal41]*rate_eval.He4_Al41__n_P44  +
          +rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__He4_Cr58  +
          -rho*Y[jhe4]*Y[jf19]*rate_eval.He4_F19__Na23  +
          -rho*Y[jhe4]*Y[jsi41]*rate_eval.He4_Si41__n_S44  +
          +rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__He4_S44  +
          -rho*Y[jhe4]*Y[jti65]*rate_eval.He4_Ti65__Cr69  +
          -rho*Y[jhe4]*Y[jv62]*rate_eval.He4_V62__Mn66  +
          +rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__He4_F19  +
          -rho*Y[jhe4]*Y[jv40]*rate_eval.He4_V40__Mn44  +
          -rho*Y[jhe4]*Y[jar51]*rate_eval.He4_Ar51__n_Ca54  +
          -rho*Y[jhe4]*Y[jk54]*rate_eval.He4_K54__Sc58  +
          -rho*Y[jhe4]*Y[jsc53]*rate_eval.He4_Sc53__V57  +
          -rho*Y[jhe4]*Y[jsi27]*rate_eval.He4_Si27__S31  +
          +rho*Y[jn]*Y[jmn56]*rate_eval.n_Mn56__He4_V53  +
          +Y[jal22]*rate_eval.Al22__He4_Ne18__weak__wc12  +
          +rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__He4_Sc56  +
          -rho*Y[jhe4]*Y[jf29]*rate_eval.He4_F29__Na33  +
          + 2*Y[jb8]*rate_eval.B8__He4_He4__weak__wc12  +
          -rho*Y[jhe4]*Y[jcr50]*rate_eval.He4_Cr50__Fe54  +
          -rho*Y[jhe4]*Y[jar38]*rate_eval.He4_Ar38__Ca42  +
          -rho*Y[jhe4]*Y[jal23]*rate_eval.He4_Al23__P27  +
          -rho*Y[jhe4]*Y[jf22]*rate_eval.He4_F22__n_Na25  +
          -rho*Y[jhe4]*Y[jmg24]*rate_eval.He4_Mg24__Si28  +
          -rho*Y[jhe4]*Y[jsi34]*rate_eval.He4_Si34__n_S37  +
          -rho*Y[jhe4]*Y[jne33]*rate_eval.He4_Ne33__Mg37  +
          -rho*Y[jhe4]*Y[jca57]*rate_eval.He4_Ca57__Ti61  +
          -rho*Y[jhe4]*Y[jar48]*rate_eval.He4_Ar48__n_Ca51  +
          -rho*Y[jhe4]*Y[jk32]*rate_eval.He4_K32__p_Ca35  +
          -rho*Y[jhe4]*Y[jmn57]*rate_eval.He4_Mn57__Co61  +
          -rho*Y[jhe4]*Y[jcr58]*rate_eval.He4_Cr58__n_Fe61  +
          -rho*Y[jhe4]*Y[jsi26]*rate_eval.He4_Si26__p_P29  +
          -rho*Y[jhe4]*Y[jcr67]*rate_eval.He4_Cr67__n_Fe70  +
          -rho*Y[jhe4]*Y[jsc46]*rate_eval.He4_Sc46__V50  +
          -rho*Y[jhe4]*Y[jca59]*rate_eval.He4_Ca59__n_Ti62  +
          +rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__He4_Sc55  +
          +rho*Y[jp]*Y[jsc43]*rate_eval.p_Sc43__He4_Ca40  +
          -rho*Y[jhe4]*Y[jv41]*rate_eval.He4_V41__p_Cr44  +
          +rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__He4_Cr42  +
          -rho*Y[jhe4]*Y[jti39]*rate_eval.He4_Ti39__Cr43  +
          +rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__He4_Ca59  +
          -rho*Y[jhe4]*Y[jsc50]*rate_eval.He4_Sc50__V54  +
          -rho*Y[jhe4]*Y[jf23]*rate_eval.He4_F23__n_Na26  +
          + 2*Y[jli8]*rate_eval.Li8__He4_He4__weak__wc12  +
          +rho*Y[jn]*Y[jfe59]*rate_eval.n_Fe59__He4_Cr56  +
          -rho*Y[jhe4]*Y[js37]*rate_eval.He4_S37__Ar41  +
          +rho*Y[jn]*Y[jv52]*rate_eval.n_V52__He4_Sc49  +
          -rho*Y[jhe4]*Y[jfe49]*rate_eval.He4_Fe49__Ni53  +
          +rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__He4_V55  +
          -rho*Y[jhe4]*Y[jfe47]*rate_eval.He4_Fe47__p_Co50  +
          +rho*Y[jn]*Y[jca42]*rate_eval.n_Ca42__He4_Ar39  +
          +rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__He4_V60  +
          -rho*Y[jhe4]*Y[jfe72]*rate_eval.He4_Fe72__n_Ni75  +
          -rho*Y[jhe4]*Y[jal33]*rate_eval.He4_Al33__P37  +
          -rho*Y[jhe4]*Y[jal22]*rate_eval.He4_Al22__P26  +
          +rho*Y[jp]*Y[jk53]*rate_eval.p_K53__He4_Ar50  +
          -rho*Y[jhe4]*Y[jo26]*rate_eval.He4_O26__Ne30  +
          +rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__He4_Ca37  +
          +rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__He4_Ne22  +
          -rho*Y[jhe4]*Y[js44]*rate_eval.He4_S44__n_Ar47  +
          -rho*Y[jhe4]*Y[jfe72]*rate_eval.He4_Fe72__Ni76  +
          +rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__He4_Na36  +
          -rho*Y[jhe4]*Y[jal30]*rate_eval.He4_Al30__n_P33  +
          -rho*Y[jhe4]*Y[jca33]*rate_eval.He4_Ca33__p_Sc36  +
          +rho*Y[jp]*Y[jv66]*rate_eval.p_V66__He4_Ti63  +
          +rho*Y[jn]*Y[jv39]*rate_eval.n_V39__He4_Sc36  +
          -rho*Y[jhe4]*Y[jna38]*rate_eval.He4_Na38__Al42  +
          -rho*Y[jhe4]*Y[jar49]*rate_eval.He4_Ar49__Ca53  +
          -rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__Sc50  +
          -rho*Y[jhe4]*Y[jsc50]*rate_eval.He4_Sc50__n_V53  +
          +rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__He4_K37  +
          -rho*Y[jhe4]*Y[jo16]*rate_eval.He4_O16__Ne20  +
          +rho*Y[jp]*Y[jp41]*rate_eval.p_P41__He4_Si38  +
          -rho*Y[jhe4]*Y[jca56]*rate_eval.He4_Ca56__n_Ti59  +
          +rho*Y[jp]*Y[jbe10]*rate_eval.p_Be10__He4_Li7  +
          +Y[jn18]*rate_eval.N18__He4_C14__weak__wc12  +
          -rho*Y[jhe4]*Y[jcr68]*rate_eval.He4_Cr68__Fe72  +
          +rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__He4_S41  +
          +rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__He4_Ar35  +
          +rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__He4_Ca51  +
          -rho*Y[jhe4]*Y[jne21]*rate_eval.He4_Ne21__Mg25  +
          +rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__He4_V67  +
          +rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__He4_Sc52  +
          +rho*Y[jp]*Y[jv59]*rate_eval.p_V59__He4_Ti56  +
          +rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__He4_Cl46  +
          -rho*Y[jhe4]*Y[jk52]*rate_eval.He4_K52__Sc56  +
          -rho*Y[jhe4]*Y[jna32]*rate_eval.He4_Na32__Al36  +
          -rho*Y[jhe4]*Y[jp30]*rate_eval.He4_P30__Cl34  +
          +rho*Y[jp]*Y[jf26]*rate_eval.p_F26__He4_O23  +
          +rho*Y[jn]*Y[js32]*rate_eval.n_S32__He4_Si29  +
          +rho*Y[jp]*Y[jsc42]*rate_eval.p_Sc42__He4_Ca39  +
          +rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__He4_K35  +
          +rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__He4_Al35  +
          +rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__He4_Na22  +
          -rho*Y[jhe4]*Y[jk37]*rate_eval.He4_K37__Sc41  +
          -rho*Y[jhe4]*Y[jsi45]*rate_eval.He4_Si45__n_S48  +
          -rho*Y[jhe4]*Y[jfe69]*rate_eval.He4_Fe69__n_Ni72  +
          -rho*Y[jhe4]*Y[js40]*rate_eval.He4_S40__Ar44  +
          +rho*Y[jn]*Y[jp28]*rate_eval.n_P28__He4_Al25  +
          -rho*Y[jhe4]*Y[jmn50]*rate_eval.He4_Mn50__p_Fe53  +
          -rho*Y[jhe4]*Y[jar32]*rate_eval.He4_Ar32__p_K35  +
          -rho*Y[jhe4]*Y[jk56]*rate_eval.He4_K56__Sc60  +
          +rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__He4_Ti45  +
          -rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__n_Sc49  +
          -rho*Y[jhe4]*Y[jk34]*rate_eval.He4_K34__Sc38  +
          + 2*rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__n_p_He4_He4  +
          +rho*Y[jp]*Y[jmg24]*rate_eval.p_Mg24__He4_Na21  +
          -rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__n_Sc44  +
          -rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__p_Cl37  +
          -rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__n_P30  +
          -rho*Y[jhe4]*Y[jne22]*rate_eval.He4_Ne22__n_Mg25  +
          +rho*Y[jp]*Y[jne20]*rate_eval.p_Ne20__He4_F17  +
          -rho*Y[jhe4]*Y[jti44]*rate_eval.He4_Ti44__p_V47  +
          -rho*Y[jhe4]*Y[jn14]*rate_eval.He4_N14__n_F17  +
          -rho*Y[jhe4]*Y[jo18]*rate_eval.He4_O18__n_Ne21  +
          -rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__n_Ar37
       )

    dYdt[jhe6] = (
          +5.00000000000000e-01*rho**2*Y[jn]**2*Y[jhe4]*rate_eval.n_n_He4__He6  +
          -Y[jhe6]*rate_eval.He6__Li6__weak__wc12
       )

    dYdt[jhe8] = (
          -Y[jhe8]*rate_eval.He8__Li8__weak__wc12  +
          -Y[jhe8]*rate_eval.He8__n_Li7__weak__wc12
       )

    dYdt[jli5] = (
          +Y[jc9]*rate_eval.C9__He4_Li5__weak__wc12
       )

    dYdt[jli6] = (
          -rho*Y[jp]*Y[jli6]*rate_eval.p_Li6__Be7  +
          -rho*Y[jn]*Y[jli6]*rate_eval.n_Li6__He4_t  +
          -rho*Y[jp]*Y[jli6]*rate_eval.p_Li6__He4_He3  +
          -rho*Y[jd]*Y[jli6]*rate_eval.d_Li6__n_Be7  +
          +rho*Y[jd]*Y[jhe4]*rate_eval.He4_d__Li6  +
          +rho**2*Y[jn]*Y[jp]*Y[jhe4]*rate_eval.n_p_He4__Li6  +
          -rho*Y[jhe4]*Y[jli6]*rate_eval.He4_Li6__B10  +
          +rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__He4_Li6  +
          -rho*Y[jn]*Y[jli6]*rate_eval.n_Li6__Li7  +
          +Y[jhe6]*rate_eval.He6__Li6__weak__wc12  +
          -rho*Y[jd]*Y[jli6]*rate_eval.d_Li6__p_Li7
       )

    dYdt[jli7] = (
          -rho*Y[jd]*Y[jli7]*rate_eval.d_Li7__n_He4_He4  +
          +Y[jhe8]*rate_eval.He8__n_Li7__weak__wc12  +
          +rho*Y[jd]*Y[jli8]*rate_eval.d_Li8__t_Li7  +
          -rho*Y[jt]*Y[jli7]*rate_eval.t_Li7__n_Be9  +
          -rho*Y[jhe4]*Y[jli7]*rate_eval.He4_Li7__B11  +
          -rho*Y[jn]*Y[jli7]*rate_eval.n_Li7__Li8  +
          +rho*Y[jn]*Y[jbe7]*rate_eval.n_Be7__p_Li7  +
          +rho*Y[jt]*Y[jhe4]*rate_eval.He4_t__Li7  +
          -rho*Y[jp]*Y[jli7]*rate_eval.p_Li7__He4_He4  +
          +Y[jbe11]*rate_eval.Be11__He4_Li7__weak__wc12  +
          +rho*Y[jn]*Y[jli6]*rate_eval.n_Li6__Li7  +
          -rho*Y[jt]*Y[jli7]*rate_eval.t_Li7__n_n_He4_He4  +
          +rho*Y[jn]*Y[jb10]*rate_eval.n_B10__He4_Li7  +
          -rho*Y[jhe3]*Y[jli7]*rate_eval.He3_Li7__n_p_He4_He4  +
          +rho*ye(Y)*Y[jbe7]*rate_eval.Be7__Li7__weak__electron_capture  +
          +rho*Y[jd]*Y[jli6]*rate_eval.d_Li6__p_Li7  +
          +rho*Y[jp]*Y[jbe10]*rate_eval.p_Be10__He4_Li7  +
          -rho*Y[jd]*Y[jli7]*rate_eval.d_Li7__p_Li8
       )

    dYdt[jli8] = (
          +Y[jhe8]*rate_eval.He8__Li8__weak__wc12  +
          -rho*Y[jd]*Y[jli8]*rate_eval.d_Li8__n_Be9  +
          -rho*Y[jd]*Y[jli8]*rate_eval.d_Li8__t_Li7  +
          -rho*Y[jhe4]*Y[jli8]*rate_eval.He4_Li8__n_B11  +
          +rho*Y[jp]*Y[jbe11]*rate_eval.p_Be11__He4_Li8  +
          +rho*Y[jn]*Y[jli7]*rate_eval.n_Li7__Li8  +
          -rho*Y[jhe4]*Y[jli8]*rate_eval.He4_Li8__B12  +
          -rho*Y[jn]*Y[jli8]*rate_eval.n_Li8__Li9  +
          -rho*Y[jp]*Y[jli8]*rate_eval.p_Li8__n_He4_He4  +
          -Y[jli8]*rate_eval.Li8__He4_He4__weak__wc12  +
          +rho*Y[jd]*Y[jli7]*rate_eval.d_Li7__p_Li8
       )

    dYdt[jli9] = (
          -rho*Y[jhe4]*Y[jli9]*rate_eval.He4_Li9__B13  +
          +rho*Y[jn]*Y[jli8]*rate_eval.n_Li8__Li9  +
          -rho*Y[jhe4]*Y[jli9]*rate_eval.He4_Li9__n_B12  +
          -Y[jli9]*rate_eval.Li9__Be9__weak__wc12
       )

    dYdt[jli11] = (
          -Y[jli11]*rate_eval.Li11__n_n_Be9__weak__wc12  +
          -Y[jli11]*rate_eval.Li11__Be11__weak__wc12  +
          -Y[jli11]*rate_eval.Li11__n_Be10__weak__wc17
       )

    dYdt[jbe7] = (
          -rho*Y[jhe3]*Y[jbe7]*rate_eval.He3_Be7__p_p_He4_He4  +
          -rho*Y[jt]*Y[jbe7]*rate_eval.t_Be7__n_p_He4_He4  +
          -rho*Y[jd]*Y[jbe7]*rate_eval.d_Be7__p_He4_He4  +
          +rho*Y[jp]*Y[jli6]*rate_eval.p_Li6__Be7  +
          -rho*Y[jhe4]*Y[jbe7]*rate_eval.He4_Be7__C11  +
          -rho*Y[jn]*Y[jbe7]*rate_eval.n_Be7__He4_He4  +
          +rho*Y[jd]*Y[jli6]*rate_eval.d_Li6__n_Be7  +
          -rho*Y[jp]*Y[jbe7]*rate_eval.p_Be7__B8  +
          +rho*Y[jhe3]*Y[jhe4]*rate_eval.He4_He3__Be7  +
          -rho*Y[jn]*Y[jbe7]*rate_eval.n_Be7__p_Li7  +
          +rho*Y[jp]*Y[jb10]*rate_eval.p_B10__He4_Be7  +
          -rho*ye(Y)*Y[jbe7]*rate_eval.Be7__Li7__weak__electron_capture
       )

    dYdt[jbe9] = (
          -rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__d_He4_He4  +
          +rho*Y[jd]*Y[jli8]*rate_eval.d_Li8__n_Be9  +
          +rho*Y[jp]*Y[jb12]*rate_eval.p_B12__He4_Be9  +
          -rho*Y[jt]*Y[jbe9]*rate_eval.t_Be9__n_B11  +
          +rho*Y[jt]*Y[jli7]*rate_eval.t_Li7__n_Be9  +
          +Y[jli11]*rate_eval.Li11__n_n_Be9__weak__wc12  +
          -rho*Y[jhe4]*Y[jbe9]*rate_eval.He4_Be9__n_C12  +
          +5.00000000000000e-01*rho**2*Y[jn]*Y[jhe4]**2*rate_eval.n_He4_He4__Be9  +
          -rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__B10  +
          -rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__He4_Li6  +
          +Y[jli9]*rate_eval.Li9__Be9__weak__wc12  +
          -rho*Y[jn]*Y[jbe9]*rate_eval.n_Be9__Be10  +
          -rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__n_p_He4_He4
       )

    dYdt[jbe10] = (
          -rho*Y[jhe4]*Y[jbe10]*rate_eval.He4_Be10__C14  +
          -rho*Y[jp]*Y[jbe10]*rate_eval.p_Be10__B11  +
          -rho*Y[jhe4]*Y[jbe10]*rate_eval.He4_Be10__n_C13  +
          -rho*Y[jn]*Y[jbe10]*rate_eval.n_Be10__Be11  +
          +Y[jli11]*rate_eval.Li11__n_Be10__weak__wc17  +
          -Y[jbe10]*rate_eval.Be10__B10__weak__wc12  +
          -rho*Y[jp]*Y[jbe10]*rate_eval.p_Be10__He4_Li7  +
          +rho*Y[jn]*Y[jbe9]*rate_eval.n_Be9__Be10
       )

    dYdt[jbe11] = (
          -Y[jbe11]*rate_eval.Be11__B11__weak__wc12  +
          -rho*Y[jhe4]*Y[jbe11]*rate_eval.He4_Be11__n_C14  +
          -rho*Y[jp]*Y[jbe11]*rate_eval.p_Be11__He4_Li8  +
          -rho*Y[jn]*Y[jbe11]*rate_eval.n_Be11__Be12  +
          +Y[jli11]*rate_eval.Li11__Be11__weak__wc12  +
          -Y[jbe11]*rate_eval.Be11__He4_Li7__weak__wc12  +
          +rho*Y[jn]*Y[jbe10]*rate_eval.n_Be10__Be11
       )

    dYdt[jbe12] = (
          +rho*Y[jn]*Y[jbe11]*rate_eval.n_Be11__Be12  +
          -Y[jbe12]*rate_eval.Be12__B12__weak__wc12  +
          -Y[jbe12]*rate_eval.Be12__n_B11__weak__wc12
       )

    dYdt[jbe14] = (
          +Y[jbe16]*rate_eval.Be16__n_n_Be14  +
          -Y[jbe14]*rate_eval.Be14__n_n_B12__weak__wc12  +
          +Y[jbe15]*rate_eval.Be15__n_Be14  +
          -Y[jbe14]*rate_eval.Be14__n_B13__weak__wc17  +
          -Y[jbe14]*rate_eval.Be14__B14__weak__wc12
       )

    dYdt[jbe15] = (
          -Y[jbe15]*rate_eval.Be15__n_Be14
       )

    dYdt[jbe16] = (
          -Y[jbe16]*rate_eval.Be16__n_n_Be14
       )

    dYdt[jb8] = (
          -rho*Y[jn]*Y[jb8]*rate_eval.n_B8__p_He4_He4  +
          -rho*Y[jhe4]*Y[jb8]*rate_eval.He4_B8__p_C11  +
          +rho*Y[jp]*Y[jbe7]*rate_eval.p_Be7__B8  +
          -rho*Y[jp]*Y[jb8]*rate_eval.p_B8__C9  +
          -Y[jb8]*rate_eval.B8__He4_He4__weak__wc12
       )

    dYdt[jb10] = (
          -rho*Y[jhe4]*Y[jb10]*rate_eval.He4_B10__p_C13  +
          -rho*Y[jp]*Y[jb10]*rate_eval.p_B10__C11  +
          -rho*Y[jn]*Y[jb10]*rate_eval.n_B10__B11  +
          -rho*Y[jp]*Y[jb10]*rate_eval.p_B10__He4_Be7  +
          +rho*Y[jp]*Y[jbe9]*rate_eval.p_Be9__B10  +
          +rho*Y[jhe4]*Y[jli6]*rate_eval.He4_Li6__B10  +
          -rho*Y[jhe4]*Y[jb10]*rate_eval.He4_B10__n_N13  +
          +Y[jc10]*rate_eval.C10__B10__weak__wc12  +
          -rho*Y[jn]*Y[jb10]*rate_eval.n_B10__He4_Li7  +
          +Y[jbe10]*rate_eval.Be10__B10__weak__wc12
       )

    dYdt[jb11] = (
          -rho*Y[jp]*Y[jb11]*rate_eval.p_B11__He4_He4_He4  +
          +rho*Y[jn]*Y[jc11]*rate_eval.n_C11__p_B11  +
          -rho*Y[jhe4]*Y[jb11]*rate_eval.He4_B11__p_C14  +
          +rho*Y[jhe4]*Y[jli8]*rate_eval.He4_Li8__n_B11  +
          +Y[jbe11]*rate_eval.Be11__B11__weak__wc12  +
          +rho*Y[jt]*Y[jbe9]*rate_eval.t_Be9__n_B11  +
          +rho*Y[jhe4]*Y[jli7]*rate_eval.He4_Li7__B11  +
          -rho*Y[jn]*Y[jb11]*rate_eval.n_B11__B12  +
          +rho*Y[jn]*Y[jb10]*rate_eval.n_B10__B11  +
          +rho*Y[jp]*Y[jbe10]*rate_eval.p_Be10__B11  +
          -rho*Y[jhe4]*Y[jb11]*rate_eval.He4_B11__n_N14  +
          -rho*Y[jp]*Y[jb11]*rate_eval.p_B11__C12  +
          +Y[jbe12]*rate_eval.Be12__n_B11__weak__wc12  +
          +Y[jc11]*rate_eval.C11__B11__weak__wc12
       )

    dYdt[jb12] = (
          -rho*Y[jp]*Y[jb12]*rate_eval.p_B12__n_C12  +
          -rho*Y[jhe4]*Y[jb12]*rate_eval.He4_B12__n_N15  +
          -rho*Y[jp]*Y[jb12]*rate_eval.p_B12__He4_Be9  +
          -Y[jb12]*rate_eval.B12__C12__weak__wc17  +
          -rho*Y[jn]*Y[jb12]*rate_eval.n_B12__B13  +
          +rho*Y[jn]*Y[jb11]*rate_eval.n_B11__B12  +
          +rho*Y[jhe4]*Y[jli8]*rate_eval.He4_Li8__B12  +
          +Y[jbe14]*rate_eval.Be14__n_n_B12__weak__wc12  +
          +Y[jbe12]*rate_eval.Be12__B12__weak__wc12  +
          +rho*Y[jhe4]*Y[jli9]*rate_eval.He4_Li9__n_B12
       )

    dYdt[jb13] = (
          -rho*Y[jn]*Y[jb13]*rate_eval.n_B13__B14  +
          -rho*Y[jhe4]*Y[jb13]*rate_eval.He4_B13__n_N16  +
          +rho*Y[jn]*Y[jb12]*rate_eval.n_B12__B13  +
          +rho*Y[jhe4]*Y[jli9]*rate_eval.He4_Li9__B13  +
          -rho*Y[jhe4]*Y[jb13]*rate_eval.He4_B13__N17  +
          -Y[jb13]*rate_eval.B13__C13__weak__wc12  +
          +Y[jbe14]*rate_eval.Be14__n_B13__weak__wc17
       )

    dYdt[jb14] = (
          +rho*Y[jn]*Y[jb13]*rate_eval.n_B13__B14  +
          -Y[jb14]*rate_eval.B14__C14__weak__wc12  +
          +Y[jbe14]*rate_eval.Be14__B14__weak__wc12
       )

    dYdt[jb15] = (
          -Y[jb15]*rate_eval.B15__n_n_C13__weak__wc12  +
          -Y[jb15]*rate_eval.B15__n_C14__weak__wc12  +
          -Y[jb15]*rate_eval.B15__C15__weak__wc12
       )

    dYdt[jb17] = (
          +Y[jb18]*rate_eval.B18__n_B17  +
          -Y[jb17]*rate_eval.B17__n_n_n_C14__weak__wc12  +
          -Y[jb17]*rate_eval.B17__n_n_C15__weak__wc12  +
          -Y[jb17]*rate_eval.B17__C17__weak__wc17  +
          -Y[jb17]*rate_eval.B17__n_C16__weak__wc17
       )

    dYdt[jb18] = (
          -Y[jb18]*rate_eval.B18__n_B17
       )

    dYdt[jb19] = (
          -Y[jb19]*rate_eval.B19__C19__weak__wc12  +
          -Y[jb19]*rate_eval.B19__n_C18__weak__wc17  +
          -Y[jb19]*rate_eval.B19__n_n_C17__weak__wc12
       )

    dYdt[jc9] = (
          -rho*Y[jhe4]*Y[jc9]*rate_eval.He4_C9__p_N12  +
          -Y[jc9]*rate_eval.C9__He4_Li5__weak__wc12  +
          +rho*Y[jn]*Y[jo12]*rate_eval.n_O12__He4_C9  +
          +rho*Y[jp]*Y[jb8]*rate_eval.p_B8__C9
       )

    dYdt[jc10] = (
          +rho*Y[jn]*Y[jo13]*rate_eval.n_O13__He4_C10  +
          -Y[jc10]*rate_eval.C10__B10__weak__wc12
       )

    dYdt[jc11] = (
          -rho*Y[jn]*Y[jc11]*rate_eval.n_C11__He4_He4_He4  +
          +rho*Y[jhe4]*Y[jbe7]*rate_eval.He4_Be7__C11  +
          +rho*Y[jn]*Y[jo14]*rate_eval.n_O14__He4_C11  +
          -rho*Y[jn]*Y[jc11]*rate_eval.n_C11__p_B11  +
          +rho*Y[jhe4]*Y[jb8]*rate_eval.He4_B8__p_C11  +
          -rho*Y[jp]*Y[jc11]*rate_eval.p_C11__N12  +
          +rho*Y[jp]*Y[jb10]*rate_eval.p_B10__C11  +
          -rho*Y[jn]*Y[jc11]*rate_eval.n_C11__C12  +
          -rho*Y[jhe4]*Y[jc11]*rate_eval.He4_C11__p_N14  +
          +Y[jn11]*rate_eval.N11__C11__weak__btyk  +
          -Y[jc11]*rate_eval.C11__B11__weak__wc12
       )

    dYdt[jc12] = (
          + -2*5.00000000000000e-01*rho*Y[jc12]**2*rate_eval.C12_C12__He4_Ne20  +
          +rho*Y[jp]*Y[jb12]*rate_eval.p_B12__n_C12  +
          + 2*rho*Y[jn]*Y[jmg23]*rate_eval.n_Mg23__C12_C12  +
          -rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__He4_Si28  +
          -rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__p_P31  +
          -rho*Y[jc12]*Y[jo16]*rate_eval.C12_O16__He4_Mg24  +
          -rho*Y[jc12]*Y[jo16]*rate_eval.C12_O16__p_Al27  +
          +rho*Y[jp]*Y[jn15]*rate_eval.p_N15__He4_C12  +
          +Y[jb12]*rate_eval.B12__C12__weak__wc17  +
          -rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__n_S31  +
          + -2*5.00000000000000e-01*rho*Y[jc12]**2*rate_eval.C12_C12__p_Na23  +
          +rho*Y[jn]*Y[jo15]*rate_eval.n_O15__He4_C12  +
          +1.66666666666667e-01*rho**2*Y[jhe4]**3*rate_eval.He4_He4_He4__C12  +
          -rho*Y[jp]*Y[jc12]*rate_eval.p_C12__N13  +
          -rho*Y[jhe4]*Y[jc12]*rate_eval.He4_C12__O16  +
          +rho*Y[jn]*Y[jc11]*rate_eval.n_C11__C12  +
          +rho*Y[jhe4]*Y[jbe9]*rate_eval.He4_Be9__n_C12  +
          -rho*Y[jn]*Y[jc12]*rate_eval.n_C12__C13  +
          +rho*Y[jp]*Y[jb11]*rate_eval.p_B11__C12  +
          +Y[jn16]*rate_eval.N16__He4_C12__weak__wc12  +
          +Y[jo13]*rate_eval.O13__p_C12__weak__wc12  +
          +rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__C12_O16  +
          +Y[jn12]*rate_eval.N12__C12__weak__wc12
       )

    dYdt[jc13] = (
          -rho*Y[jhe4]*Y[jc13]*rate_eval.He4_C13__n_O16  +
          -rho*Y[jd]*Y[jc13]*rate_eval.d_C13__n_N14  +
          +rho*Y[jhe4]*Y[jb10]*rate_eval.He4_B10__p_C13  +
          -rho*Y[jp]*Y[jc13]*rate_eval.p_C13__N14  +
          +Y[jb15]*rate_eval.B15__n_n_C13__weak__wc12  +
          -rho*Y[jn]*Y[jc13]*rate_eval.n_C13__C14  +
          +Y[jn13]*rate_eval.N13__C13__weak__wc12  +
          +rho*Y[jhe4]*Y[jbe10]*rate_eval.He4_Be10__n_C13  +
          +rho*Y[jn]*Y[jc12]*rate_eval.n_C12__C13  +
          +Y[jb13]*rate_eval.B13__C13__weak__wc12  +
          +rho*Y[jp]*Y[jn16]*rate_eval.p_N16__He4_C13  +
          -rho*Y[jp]*Y[jc13]*rate_eval.p_C13__n_N13
       )

    dYdt[jc14] = (
          +rho*Y[jhe4]*Y[jbe10]*rate_eval.He4_Be10__C14  +
          +rho*Y[jn]*Y[jn14]*rate_eval.n_N14__p_C14  +
          +rho*Y[jhe4]*Y[jb11]*rate_eval.He4_B11__p_C14  +
          +rho*Y[jhe4]*Y[jbe11]*rate_eval.He4_Be11__n_C14  +
          +Y[jb17]*rate_eval.B17__n_n_n_C14__weak__wc12  +
          -rho*Y[jn]*Y[jc14]*rate_eval.n_C14__C15  +
          -rho*Y[jp]*Y[jc14]*rate_eval.p_C14__N15  +
          -Y[jc14]*rate_eval.C14__N14__weak__wc12  +
          +rho*Y[jn]*Y[jc13]*rate_eval.n_C13__C14  +
          -rho*Y[jhe4]*Y[jc14]*rate_eval.He4_C14__O18  +
          +Y[jb14]*rate_eval.B14__C14__weak__wc12  +
          +rho*Y[jn]*Y[jo17]*rate_eval.n_O17__He4_C14  +
          -rho*Y[jd]*Y[jc14]*rate_eval.d_C14__n_N15  +
          +Y[jb15]*rate_eval.B15__n_C14__weak__wc12  +
          +Y[jn18]*rate_eval.N18__He4_C14__weak__wc12
       )

    dYdt[jc15] = (
          -rho*Y[jhe4]*Y[jc15]*rate_eval.He4_C15__n_O18  +
          -rho*Y[jp]*Y[jc15]*rate_eval.p_C15__n_N15  +
          +Y[jb17]*rate_eval.B17__n_n_C15__weak__wc12  +
          +rho*Y[jn]*Y[jc14]*rate_eval.n_C14__C15  +
          -Y[jc15]*rate_eval.C15__N15__weak__wc12  +
          -rho*Y[jn]*Y[jc15]*rate_eval.n_C15__C16  +
          +Y[jb15]*rate_eval.B15__C15__weak__wc12
       )

    dYdt[jc16] = (
          -Y[jc16]*rate_eval.C16__n_N15__weak__wc12  +
          +rho*Y[jn]*Y[jc15]*rate_eval.n_C15__C16  +
          +Y[jb17]*rate_eval.B17__n_C16__weak__wc17  +
          -Y[jc16]*rate_eval.C16__N16__weak__wc12  +
          -rho*Y[jn]*Y[jc16]*rate_eval.n_C16__C17
       )

    dYdt[jc17] = (
          -Y[jc17]*rate_eval.C17__N17__weak__wc12  +
          -Y[jc17]*rate_eval.C17__n_N16__weak__wc12  +
          +Y[jb17]*rate_eval.B17__C17__weak__wc17  +
          +rho*Y[jn]*Y[jc16]*rate_eval.n_C16__C17  +
          +Y[jb19]*rate_eval.B19__n_n_C17__weak__wc12
       )

    dYdt[jc18] = (
          -Y[jc18]*rate_eval.C18__N18__weak__wc12  +
          -Y[jc18]*rate_eval.C18__n_N17__weak__wc12  +
          +Y[jb19]*rate_eval.B19__n_C18__weak__wc17
       )

    dYdt[jc19] = (
          -Y[jc19]*rate_eval.C19__N19__weak__wc07  +
          +Y[jb19]*rate_eval.B19__C19__weak__wc12  +
          -Y[jc19]*rate_eval.C19__n_N18__weak__wc12
       )

    dYdt[jc20] = (
          +Y[jc21]*rate_eval.C21__n_C20  +
          -Y[jc20]*rate_eval.C20__n_N19__weak__wc12  +
          -Y[jc20]*rate_eval.C20__N20__weak__wc12
       )

    dYdt[jc21] = (
          -Y[jc21]*rate_eval.C21__n_C20
       )

    dYdt[jc22] = (
          -Y[jc22]*rate_eval.C22__N22__weak__wc17  +
          -Y[jc22]*rate_eval.C22__n_N21__weak__wc17
       )

    dYdt[jn11] = (
          +rho*Y[jn]*Y[jf14]*rate_eval.n_F14__He4_N11  +
          -Y[jn11]*rate_eval.N11__C11__weak__btyk
       )

    dYdt[jn12] = (
          +rho*Y[jhe4]*Y[jc9]*rate_eval.He4_C9__p_N12  +
          +rho*Y[jn]*Y[jf15]*rate_eval.n_F15__He4_N12  +
          +rho*Y[jn]*Y[jo12]*rate_eval.n_O12__p_N12  +
          -rho*Y[jp]*Y[jn12]*rate_eval.p_N12__O13  +
          +rho*Y[jp]*Y[jc11]*rate_eval.p_C11__N12  +
          -rho*Y[jhe4]*Y[jn12]*rate_eval.He4_N12__p_O15  +
          -Y[jn12]*rate_eval.N12__C12__weak__wc12
       )

    dYdt[jn13] = (
          +rho*Y[jn]*Y[jo13]*rate_eval.n_O13__p_N13  +
          -rho*Y[jhe4]*Y[jn13]*rate_eval.He4_N13__p_O16  +
          +rho*Y[jn]*Y[jf16]*rate_eval.n_F16__He4_N13  +
          -rho*Y[jn]*Y[jn13]*rate_eval.n_N13__N14  +
          +rho*Y[jp]*Y[jc12]*rate_eval.p_C12__N13  +
          -Y[jn13]*rate_eval.N13__C13__weak__wc12  +
          -rho*Y[jp]*Y[jn13]*rate_eval.p_N13__O14  +
          +rho*Y[jhe4]*Y[jb10]*rate_eval.He4_B10__n_N13  +
          +Y[jo13]*rate_eval.O13__N13__weak__wc17  +
          +rho*Y[jp]*Y[jc13]*rate_eval.p_C13__n_N13
       )

    dYdt[jn14] = (
          +Y[jo14]*rate_eval.O14__N14__weak__wc12  +
          +rho*Y[jp]*Y[jo17]*rate_eval.p_O17__He4_N14  +
          -rho*Y[jn]*Y[jn14]*rate_eval.n_N14__p_C14  +
          +rho*Y[jd]*Y[jc13]*rate_eval.d_C13__n_N14  +
          -rho*Y[jp]*Y[jn14]*rate_eval.p_N14__O15  +
          +rho*Y[jn]*Y[jn13]*rate_eval.n_N13__N14  +
          +rho*Y[jp]*Y[jc13]*rate_eval.p_C13__N14  +
          +Y[jc14]*rate_eval.C14__N14__weak__wc12  +
          +rho*Y[jhe4]*Y[jb11]*rate_eval.He4_B11__n_N14  +
          -rho*Y[jhe4]*Y[jn14]*rate_eval.He4_N14__F18  +
          +rho*Y[jhe4]*Y[jc11]*rate_eval.He4_C11__p_N14  +
          -rho*Y[jn]*Y[jn14]*rate_eval.n_N14__N15  +
          -rho*Y[jhe4]*Y[jn14]*rate_eval.He4_N14__n_F17  +
          -rho*Y[jp]*Y[jn14]*rate_eval.p_N14__n_O14
       )

    dYdt[jn15] = (
          -rho*Y[jhe4]*Y[jn15]*rate_eval.He4_N15__F19  +
          -rho*Y[jp]*Y[jn15]*rate_eval.p_N15__O16  +
          +rho*Y[jn]*Y[jf18]*rate_eval.n_F18__He4_N15  +
          +rho*Y[jp]*Y[jo18]*rate_eval.p_O18__He4_N15  +
          -rho*Y[jp]*Y[jn15]*rate_eval.p_N15__He4_C12  +
          +rho*Y[jp]*Y[jc15]*rate_eval.p_C15__n_N15  +
          +rho*Y[jhe4]*Y[jb12]*rate_eval.He4_B12__n_N15  +
          +Y[jc16]*rate_eval.C16__n_N15__weak__wc12  +
          -rho*Y[jn]*Y[jn15]*rate_eval.n_N15__N16  +
          +rho*Y[jp]*Y[jc14]*rate_eval.p_C14__N15  +
          +Y[jc15]*rate_eval.C15__N15__weak__wc12  +
          +Y[jo15]*rate_eval.O15__N15__weak__wc12  +
          +rho*Y[jn]*Y[jn14]*rate_eval.n_N14__N15  +
          +rho*Y[jd]*Y[jc14]*rate_eval.d_C14__n_N15  +
          -rho*Y[jp]*Y[jn15]*rate_eval.p_N15__n_O15
       )

    dYdt[jn16] = (
          +rho*Y[jp]*Y[jo19]*rate_eval.p_O19__He4_N16  +
          +rho*Y[jhe4]*Y[jb13]*rate_eval.He4_B13__n_N16  +
          -Y[jn16]*rate_eval.N16__O16__weak__wc12  +
          +Y[jc17]*rate_eval.C17__n_N16__weak__wc12  +
          -rho*Y[jn]*Y[jn16]*rate_eval.n_N16__N17  +
          +rho*Y[jn]*Y[jn15]*rate_eval.n_N15__N16  +
          -rho*Y[jhe4]*Y[jn16]*rate_eval.He4_N16__n_F19  +
          -rho*Y[jp]*Y[jn16]*rate_eval.p_N16__n_O16  +
          -Y[jn16]*rate_eval.N16__He4_C12__weak__wc12  +
          -rho*Y[jp]*Y[jn16]*rate_eval.p_N16__He4_C13  +
          +Y[jc16]*rate_eval.C16__N16__weak__wc12
       )

    dYdt[jn17] = (
          +rho*Y[jp]*Y[jo20]*rate_eval.p_O20__He4_N17  +
          +Y[jc17]*rate_eval.C17__N17__weak__wc12  +
          -Y[jn17]*rate_eval.N17__n_O16__weak__wc12  +
          -rho*Y[jn]*Y[jn17]*rate_eval.n_N17__N18  +
          +rho*Y[jn]*Y[jn16]*rate_eval.n_N16__N17  +
          +Y[jc18]*rate_eval.C18__n_N17__weak__wc12  +
          +rho*Y[jhe4]*Y[jb13]*rate_eval.He4_B13__N17  +
          -Y[jn17]*rate_eval.N17__O17__weak__wc12
       )

    dYdt[jn18] = (
          -rho*Y[jn]*Y[jn18]*rate_eval.n_N18__N19  +
          +rho*Y[jn]*Y[jn17]*rate_eval.n_N17__N18  +
          +Y[jc18]*rate_eval.C18__N18__weak__wc12  +
          -Y[jn18]*rate_eval.N18__O18__weak__wc12  +
          -Y[jn18]*rate_eval.N18__n_O17__weak__wc12  +
          +Y[jc19]*rate_eval.C19__n_N18__weak__wc12  +
          -Y[jn18]*rate_eval.N18__He4_C14__weak__wc12
       )

    dYdt[jn19] = (
          +rho*Y[jn]*Y[jn18]*rate_eval.n_N18__N19  +
          +Y[jc19]*rate_eval.C19__N19__weak__wc07  +
          +Y[jc20]*rate_eval.C20__n_N19__weak__wc12  +
          -rho*Y[jn]*Y[jn19]*rate_eval.n_N19__N20  +
          -Y[jn19]*rate_eval.N19__n_O18__weak__wc12  +
          -Y[jn19]*rate_eval.N19__O19__weak__wc12
       )

    dYdt[jn20] = (
          +rho*Y[jn]*Y[jn19]*rate_eval.n_N19__N20  +
          -Y[jn20]*rate_eval.N20__n_O19__weak__wc12  +
          +Y[jc20]*rate_eval.C20__N20__weak__wc12  +
          -Y[jn20]*rate_eval.N20__O20__weak__wc12
       )

    dYdt[jn21] = (
          -Y[jn21]*rate_eval.N21__O21__weak__wc12  +
          -Y[jn21]*rate_eval.N21__n_O20__weak__wc12  +
          +Y[jc22]*rate_eval.C22__n_N21__weak__wc17
       )

    dYdt[jn22] = (
          +Y[jc22]*rate_eval.C22__N22__weak__wc17  +
          -Y[jn22]*rate_eval.N22__O22__weak__wc12  +
          -Y[jn22]*rate_eval.N22__n_n_O20__weak__wc12  +
          -Y[jn22]*rate_eval.N22__n_O21__weak__wc17
       )

    dYdt[jn23] = (
          -Y[jn23]*rate_eval.N23__O23__weak__wc12  +
          +rho*Y[jp]*Y[jo26]*rate_eval.p_O26__He4_N23  +
          +Y[jn24]*rate_eval.N24__n_N23
       )

    dYdt[jn24] = (
          +rho*Y[jp]*Y[jo27]*rate_eval.p_O27__He4_N24  +
          -Y[jn24]*rate_eval.N24__n_N23
       )

    dYdt[jo12] = (
          -rho*Y[jn]*Y[jo12]*rate_eval.n_O12__O13  +
          -rho*Y[jn]*Y[jo12]*rate_eval.n_O12__p_N12  +
          -rho*Y[jn]*Y[jo12]*rate_eval.n_O12__He4_C9
       )

    dYdt[jo13] = (
          -rho*Y[jhe4]*Y[jo13]*rate_eval.He4_O13__p_p_O15  +
          +rho*Y[jn]*Y[jo12]*rate_eval.n_O12__O13  +
          -rho*Y[jhe4]*Y[jo13]*rate_eval.He4_O13__p_F16  +
          -rho*Y[jn]*Y[jo13]*rate_eval.n_O13__He4_C10  +
          -rho*Y[jn]*Y[jo13]*rate_eval.n_O13__p_N13  +
          +rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__He4_O13  +
          +rho*Y[jp]*Y[jn12]*rate_eval.p_N12__O13  +
          -rho*Y[jn]*Y[jo13]*rate_eval.n_O13__O14  +
          -Y[jo13]*rate_eval.O13__N13__weak__wc17  +
          -Y[jo13]*rate_eval.O13__p_C12__weak__wc12
       )

    dYdt[jo14] = (
          -rho*Y[jn]*Y[jo14]*rate_eval.n_O14__O15  +
          -Y[jo14]*rate_eval.O14__N14__weak__wc12  +
          -rho*Y[jn]*Y[jo14]*rate_eval.n_O14__He4_C11  +
          -rho*Y[jhe4]*Y[jo14]*rate_eval.He4_O14__p_F17  +
          +rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__He4_O14  +
          +rho*Y[jn]*Y[jo13]*rate_eval.n_O13__O14  +
          -rho*Y[jhe4]*Y[jo14]*rate_eval.He4_O14__Ne18  +
          +rho*Y[jp]*Y[jn13]*rate_eval.p_N13__O14  +
          +rho*Y[jn]*Y[jf14]*rate_eval.n_F14__p_O14  +
          -rho*Y[jp]*Y[jo14]*rate_eval.p_O14__F15  +
          +rho*Y[jp]*Y[jn14]*rate_eval.p_N14__n_O14
       )

    dYdt[jo15] = (
          +rho*Y[jhe4]*Y[jo13]*rate_eval.He4_O13__p_p_O15  +
          +rho*Y[jn]*Y[jo14]*rate_eval.n_O14__O15  +
          +rho*Y[jp]*Y[jf18]*rate_eval.p_F18__He4_O15  +
          +rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__He4_O15  +
          -rho*Y[jn]*Y[jo15]*rate_eval.n_O15__He4_C12  +
          -rho*Y[jn]*Y[jo15]*rate_eval.n_O15__O16  +
          +rho*Y[jp]*Y[jn14]*rate_eval.p_N14__O15  +
          +rho*Y[jhe4]*Y[jn12]*rate_eval.He4_N12__p_O15  +
          -rho*Y[jhe4]*Y[jo15]*rate_eval.He4_O15__Ne19  +
          -Y[jo15]*rate_eval.O15__N15__weak__wc12  +
          +rho*Y[jn]*Y[jf15]*rate_eval.n_F15__p_O15  +
          -rho*Y[jp]*Y[jo15]*rate_eval.p_O15__F16  +
          +rho*Y[jp]*Y[jn15]*rate_eval.p_N15__n_O15
       )

    dYdt[jo16] = (
          -rho*Y[jp]*Y[jo16]*rate_eval.p_O16__F17  +
          +rho*Y[jp]*Y[jn15]*rate_eval.p_N15__O16  +
          + -2*5.00000000000000e-01*rho*Y[jo16]**2*rate_eval.O16_O16__He4_Si28  +
          + -2*5.00000000000000e-01*rho*Y[jo16]**2*rate_eval.O16_O16__p_P31  +
          + -2*5.00000000000000e-01*rho*Y[jo16]**2*rate_eval.O16_O16__n_S31  +
          -rho*Y[jc12]*Y[jo16]*rate_eval.C12_O16__He4_Mg24  +
          -rho*Y[jc12]*Y[jo16]*rate_eval.C12_O16__p_Al27  +
          +rho*Y[jhe4]*Y[jn13]*rate_eval.He4_N13__p_O16  +
          +rho*Y[jhe4]*Y[jc13]*rate_eval.He4_C13__n_O16  +
          +rho*Y[jn]*Y[jf16]*rate_eval.n_F16__p_O16  +
          +rho*Y[jn]*Y[jne19]*rate_eval.n_Ne19__He4_O16  +
          +Y[jn16]*rate_eval.N16__O16__weak__wc12  +
          +Y[jn17]*rate_eval.N17__n_O16__weak__wc12  +
          +Y[jne17]*rate_eval.Ne17__p_O16__weak__wc12  +
          +rho*Y[jp]*Y[jf19]*rate_eval.p_F19__He4_O16  +
          -rho*Y[jn]*Y[jo16]*rate_eval.n_O16__O17  +
          +rho*Y[jn]*Y[jo15]*rate_eval.n_O15__O16  +
          +rho*Y[jhe4]*Y[jc12]*rate_eval.He4_C12__O16  +
          +rho*Y[jp]*Y[jn16]*rate_eval.p_N16__n_O16  +
          +Y[jna20]*rate_eval.Na20__He4_O16__weak__wc12  +
          +rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__C12_O16  +
          -rho*Y[jhe4]*Y[jo16]*rate_eval.He4_O16__Ne20
       )

    dYdt[jo17] = (
          +rho*Y[jp]*Y[jf20]*rate_eval.p_F20__He4_O17  +
          -rho*Y[jhe4]*Y[jo17]*rate_eval.He4_O17__n_Ne20  +
          -rho*Y[jp]*Y[jo17]*rate_eval.p_O17__He4_N14  +
          -rho*Y[jn]*Y[jo17]*rate_eval.n_O17__O18  +
          -rho*Y[jp]*Y[jo17]*rate_eval.p_O17__F18  +
          -rho*Y[jhe4]*Y[jo17]*rate_eval.He4_O17__Ne21  +
          +rho*Y[jn]*Y[jo16]*rate_eval.n_O16__O17  +
          -rho*Y[jn]*Y[jo17]*rate_eval.n_O17__He4_C14  +
          +rho*Y[jn]*Y[jf17]*rate_eval.n_F17__p_O17  +
          +Y[jn18]*rate_eval.N18__n_O17__weak__wc12  +
          +Y[jn17]*rate_eval.N17__O17__weak__wc12  +
          +Y[jf17]*rate_eval.F17__O17__weak__wc12
       )

    dYdt[jo18] = (
          -rho*Y[jn]*Y[jo18]*rate_eval.n_O18__O19  +
          -rho*Y[jp]*Y[jo18]*rate_eval.p_O18__He4_N15  +
          +rho*Y[jhe4]*Y[jc15]*rate_eval.He4_C15__n_O18  +
          +rho*Y[jn]*Y[jo17]*rate_eval.n_O17__O18  +
          +rho*Y[jn]*Y[jf18]*rate_eval.n_F18__p_O18  +
          +Y[jn19]*rate_eval.N19__n_O18__weak__wc12  +
          +rho*Y[jhe4]*Y[jc14]*rate_eval.He4_C14__O18  +
          -rho*Y[jhe4]*Y[jo18]*rate_eval.He4_O18__Ne22  +
          +Y[jn18]*rate_eval.N18__O18__weak__wc12  +
          +rho*Y[jp]*Y[jf21]*rate_eval.p_F21__He4_O18  +
          +Y[jf18]*rate_eval.F18__O18__weak__wc12  +
          -rho*Y[jp]*Y[jo18]*rate_eval.p_O18__F19  +
          -rho*Y[jhe4]*Y[jo18]*rate_eval.He4_O18__n_Ne21
       )

    dYdt[jo19] = (
          +rho*Y[jn]*Y[jo18]*rate_eval.n_O18__O19  +
          -rho*Y[jp]*Y[jo19]*rate_eval.p_O19__He4_N16  +
          +rho*Y[jp]*Y[jf22]*rate_eval.p_F22__He4_O19  +
          -rho*Y[jhe4]*Y[jo19]*rate_eval.He4_O19__n_Ne22  +
          -rho*Y[jhe4]*Y[jo19]*rate_eval.He4_O19__Ne23  +
          +Y[jn20]*rate_eval.N20__n_O19__weak__wc12  +
          -rho*Y[jn]*Y[jo19]*rate_eval.n_O19__O20  +
          -rho*Y[jp]*Y[jo19]*rate_eval.p_O19__n_F19  +
          -rho*Y[jp]*Y[jo19]*rate_eval.p_O19__F20  +
          +Y[jn19]*rate_eval.N19__O19__weak__wc12  +
          -Y[jo19]*rate_eval.O19__F19__weak__wc12
       )

    dYdt[jo20] = (
          +rho*Y[jp]*Y[jf23]*rate_eval.p_F23__He4_O20  +
          -rho*Y[jp]*Y[jo20]*rate_eval.p_O20__He4_N17  +
          -rho*Y[jp]*Y[jo20]*rate_eval.p_O20__n_F20  +
          -rho*Y[jhe4]*Y[jo20]*rate_eval.He4_O20__Ne24  +
          -rho*Y[jp]*Y[jo20]*rate_eval.p_O20__F21  +
          -rho*Y[jhe4]*Y[jo20]*rate_eval.He4_O20__n_Ne23  +
          +Y[jn21]*rate_eval.N21__n_O20__weak__wc12  +
          -Y[jo20]*rate_eval.O20__F20__weak__wc12  +
          +rho*Y[jn]*Y[jo19]*rate_eval.n_O19__O20  +
          +Y[jn22]*rate_eval.N22__n_n_O20__weak__wc12  +
          +Y[jn20]*rate_eval.N20__O20__weak__wc12  +
          -rho*Y[jn]*Y[jo20]*rate_eval.n_O20__O21
       )

    dYdt[jo21] = (
          +Y[jn21]*rate_eval.N21__O21__weak__wc12  +
          -rho*Y[jp]*Y[jo21]*rate_eval.p_O21__n_F21  +
          -rho*Y[jhe4]*Y[jo21]*rate_eval.He4_O21__Ne25  +
          -rho*Y[jhe4]*Y[jo21]*rate_eval.He4_O21__n_Ne24  +
          +rho*Y[jp]*Y[jf24]*rate_eval.p_F24__He4_O21  +
          -rho*Y[jn]*Y[jo21]*rate_eval.n_O21__O22  +
          -rho*Y[jp]*Y[jo21]*rate_eval.p_O21__F22  +
          -Y[jo21]*rate_eval.O21__F21__weak__wc12  +
          +Y[jn22]*rate_eval.N22__n_O21__weak__wc17  +
          +rho*Y[jn]*Y[jo20]*rate_eval.n_O20__O21
       )

    dYdt[jo22] = (
          -rho*Y[jp]*Y[jo22]*rate_eval.p_O22__n_F22  +
          +rho*Y[jp]*Y[jf25]*rate_eval.p_F25__He4_O22  +
          -rho*Y[jhe4]*Y[jo22]*rate_eval.He4_O22__n_Ne25  +
          -rho*Y[jhe4]*Y[jo22]*rate_eval.He4_O22__Ne26  +
          +Y[jn22]*rate_eval.N22__O22__weak__wc12  +
          -rho*Y[jp]*Y[jo22]*rate_eval.p_O22__F23  +
          -rho*Y[jn]*Y[jo22]*rate_eval.n_O22__O23  +
          +rho*Y[jn]*Y[jo21]*rate_eval.n_O21__O22  +
          -Y[jo22]*rate_eval.O22__F22__weak__wc17
       )

    dYdt[jo23] = (
          -rho*Y[jhe4]*Y[jo23]*rate_eval.He4_O23__n_Ne26  +
          +Y[jn23]*rate_eval.N23__O23__weak__wc12  +
          -rho*Y[jhe4]*Y[jo23]*rate_eval.He4_O23__Ne27  +
          -rho*Y[jn]*Y[jo23]*rate_eval.n_O23__O24  +
          +rho*Y[jn]*Y[jo22]*rate_eval.n_O22__O23  +
          -rho*Y[jp]*Y[jo23]*rate_eval.p_O23__n_F23  +
          -Y[jo23]*rate_eval.O23__F23__weak__wc12  +
          -Y[jo23]*rate_eval.O23__n_F22__weak__wc12  +
          +rho*Y[jp]*Y[jf26]*rate_eval.p_F26__He4_O23  +
          -rho*Y[jp]*Y[jo23]*rate_eval.p_O23__F24
       )

    dYdt[jo24] = (
          -Y[jo24]*rate_eval.O24__F24__weak__wc12  +
          +rho*Y[jp]*Y[jf27]*rate_eval.p_F27__He4_O24  +
          -rho*Y[jhe4]*Y[jo24]*rate_eval.He4_O24__n_Ne27  +
          -rho*Y[jp]*Y[jo24]*rate_eval.p_O24__n_F24  +
          -rho*Y[jhe4]*Y[jo24]*rate_eval.He4_O24__Ne28  +
          +rho*Y[jn]*Y[jo23]*rate_eval.n_O23__O24  +
          -Y[jo24]*rate_eval.O24__n_F23__weak__wc12  +
          -rho*Y[jp]*Y[jo24]*rate_eval.p_O24__F25  +
          -rho*Y[jn]*Y[jo24]*rate_eval.n_O24__O25
       )

    dYdt[jo25] = (
          -rho*Y[jp]*Y[jo25]*rate_eval.p_O25__n_F25  +
          +rho*Y[jp]*Y[jf28]*rate_eval.p_F28__He4_O25  +
          -rho*Y[jhe4]*Y[jo25]*rate_eval.He4_O25__n_Ne28  +
          -Y[jo25]*rate_eval.O25__n_F24__weak__mp17  +
          -Y[jo25]*rate_eval.O25__n_n_F23__weak__mp17  +
          +Y[jo26]*rate_eval.O26__n_O25  +
          -Y[jo25]*rate_eval.O25__F25__weak__mo03  +
          -rho*Y[jhe4]*Y[jo25]*rate_eval.He4_O25__Ne29  +
          -rho*Y[jp]*Y[jo25]*rate_eval.p_O25__F26  +
          +rho*Y[jn]*Y[jo24]*rate_eval.n_O24__O25
       )

    dYdt[jo26] = (
          +rho*Y[jp]*Y[jf29]*rate_eval.p_F29__He4_O26  +
          -rho*Y[jhe4]*Y[jo26]*rate_eval.He4_O26__n_Ne29  +
          -rho*Y[jp]*Y[jo26]*rate_eval.p_O26__He4_N23  +
          -rho*Y[jp]*Y[jo26]*rate_eval.p_O26__n_F26  +
          -rho*Y[jp]*Y[jo26]*rate_eval.p_O26__F27  +
          -Y[jo26]*rate_eval.O26__n_n_F24__weak__mp17  +
          -Y[jo26]*rate_eval.O26__n_O25  +
          -Y[jo26]*rate_eval.O26__n_F25__weak__mp17  +
          -Y[jo26]*rate_eval.O26__F26__weak__mo03  +
          +Y[jo27]*rate_eval.O27__n_O26  +
          -Y[jo26]*rate_eval.O26__n_n_n_F23__weak__mo03  +
          -rho*Y[jhe4]*Y[jo26]*rate_eval.He4_O26__Ne30
       )

    dYdt[jo27] = (
          -Y[jo27]*rate_eval.O27__n_n_n_F24__weak__mo03  +
          +Y[jo28]*rate_eval.O28__n_O27  +
          -rho*Y[jp]*Y[jo27]*rate_eval.p_O27__He4_N24  +
          +rho*Y[jp]*Y[jf30]*rate_eval.p_F30__He4_O27  +
          -rho*Y[jhe4]*Y[jo27]*rate_eval.He4_O27__Ne31  +
          -Y[jo27]*rate_eval.O27__F27__weak__mo03  +
          -rho*Y[jp]*Y[jo27]*rate_eval.p_O27__F28  +
          -Y[jo27]*rate_eval.O27__n_n_F25__weak__mp17  +
          -rho*Y[jhe4]*Y[jo27]*rate_eval.He4_O27__n_Ne30  +
          -rho*Y[jp]*Y[jo27]*rate_eval.p_O27__n_F27  +
          -Y[jo27]*rate_eval.O27__n_O26  +
          -Y[jo27]*rate_eval.O27__n_F26__weak__mp17
       )

    dYdt[jo28] = (
          -Y[jo28]*rate_eval.O28__n_O27  +
          +rho*Y[jp]*Y[jf31]*rate_eval.p_F31__He4_O28  +
          -Y[jo28]*rate_eval.O28__n_n_n_F25__weak__mo03  +
          -rho*Y[jhe4]*Y[jo28]*rate_eval.He4_O28__n_Ne31  +
          -rho*Y[jhe4]*Y[jo28]*rate_eval.He4_O28__Ne32  +
          -Y[jo28]*rate_eval.O28__n_n_F26__weak__mp17  +
          -Y[jo28]*rate_eval.O28__n_F27__weak__mp17
       )

    dYdt[jf14] = (
          -rho*Y[jn]*Y[jf14]*rate_eval.n_F14__He4_N11  +
          -rho*Y[jn]*Y[jf14]*rate_eval.n_F14__F15  +
          -rho*Y[jn]*Y[jf14]*rate_eval.n_F14__p_O14
       )

    dYdt[jf15] = (
          -rho*Y[jn]*Y[jf15]*rate_eval.n_F15__He4_N12  +
          -rho*Y[jn]*Y[jf15]*rate_eval.n_F15__F16  +
          -rho*Y[jhe4]*Y[jf15]*rate_eval.He4_F15__p_Ne18  +
          +rho*Y[jn]*Y[jf14]*rate_eval.n_F14__F15  +
          -rho*Y[jhe4]*Y[jf15]*rate_eval.He4_F15__Na19  +
          -rho*Y[jn]*Y[jf15]*rate_eval.n_F15__p_O15  +
          +rho*Y[jp]*Y[jo14]*rate_eval.p_O14__F15
       )

    dYdt[jf16] = (
          -rho*Y[jhe4]*Y[jf16]*rate_eval.He4_F16__Na20  +
          +rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__p_F16  +
          +rho*Y[jhe4]*Y[jo13]*rate_eval.He4_O13__p_F16  +
          -rho*Y[jn]*Y[jf16]*rate_eval.n_F16__p_O16  +
          -rho*Y[jhe4]*Y[jf16]*rate_eval.He4_F16__p_Ne19  +
          -rho*Y[jn]*Y[jf16]*rate_eval.n_F16__He4_N13  +
          +rho*Y[jn]*Y[jf15]*rate_eval.n_F15__F16  +
          -rho*Y[jn]*Y[jf16]*rate_eval.n_F16__F17  +
          +rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__He4_F16  +
          +rho*Y[jp]*Y[jo15]*rate_eval.p_O15__F16
       )

    dYdt[jf17] = (
          +rho*Y[jp]*Y[jo16]*rate_eval.p_O16__F17  +
          -rho*Y[jhe4]*Y[jf17]*rate_eval.He4_F17__Na21  +
          +rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__He4_F17  +
          +rho*Y[jhe4]*Y[jo14]*rate_eval.He4_O14__p_F17  +
          -rho*Y[jn]*Y[jf17]*rate_eval.n_F17__F18  +
          +rho*Y[jn]*Y[jf16]*rate_eval.n_F16__F17  +
          +Y[jne17]*rate_eval.Ne17__F17__weak__wc17  +
          +rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__p_F17  +
          -rho*Y[jp]*Y[jf17]*rate_eval.p_F17__Ne18  +
          -rho*Y[jn]*Y[jf17]*rate_eval.n_F17__p_O17  +
          -Y[jf17]*rate_eval.F17__O17__weak__wc12  +
          +rho*Y[jp]*Y[jne20]*rate_eval.p_Ne20__He4_F17  +
          +rho*Y[jhe4]*Y[jn14]*rate_eval.He4_N14__n_F17
       )

    dYdt[jf18] = (
          -rho*Y[jp]*Y[jf18]*rate_eval.p_F18__He4_O15  +
          +rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__He4_F18  +
          +rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__p_F18  +
          -rho*Y[jhe4]*Y[jf18]*rate_eval.He4_F18__p_Ne21  +
          -rho*Y[jn]*Y[jf18]*rate_eval.n_F18__He4_N15  +
          -rho*Y[jn]*Y[jf18]*rate_eval.n_F18__p_O18  +
          +rho*Y[jp]*Y[jo17]*rate_eval.p_O17__F18  +
          -rho*Y[jhe4]*Y[jf18]*rate_eval.He4_F18__Na22  +
          -rho*Y[jn]*Y[jf18]*rate_eval.n_F18__F19  +
          +rho*Y[jn]*Y[jf17]*rate_eval.n_F17__F18  +
          -rho*Y[jp]*Y[jf18]*rate_eval.p_F18__Ne19  +
          +Y[jne18]*rate_eval.Ne18__F18__weak__wc12  +
          +rho*Y[jhe4]*Y[jn14]*rate_eval.He4_N14__F18  +
          -Y[jf18]*rate_eval.F18__O18__weak__wc12
       )

    dYdt[jf19] = (
          +rho*Y[jhe4]*Y[jn15]*rate_eval.He4_N15__F19  +
          -rho*Y[jhe4]*Y[jf19]*rate_eval.He4_F19__p_Ne22  +
          +Y[jne19]*rate_eval.Ne19__F19__weak__wc12  +
          -rho*Y[jp]*Y[jf19]*rate_eval.p_F19__He4_O16  +
          +rho*Y[jn]*Y[jf18]*rate_eval.n_F18__F19  +
          -rho*Y[jp]*Y[jf19]*rate_eval.p_F19__Ne20  +
          -rho*Y[jn]*Y[jf19]*rate_eval.n_F19__F20  +
          +rho*Y[jhe4]*Y[jn16]*rate_eval.He4_N16__n_F19  +
          -rho*Y[jhe4]*Y[jf19]*rate_eval.He4_F19__Na23  +
          +rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__He4_F19  +
          +rho*Y[jp]*Y[jo19]*rate_eval.p_O19__n_F19  +
          +rho*Y[jp]*Y[jo18]*rate_eval.p_O18__F19  +
          +Y[jo19]*rate_eval.O19__F19__weak__wc12  +
          -rho*Y[jp]*Y[jf19]*rate_eval.p_F19__n_Ne19
       )

    dYdt[jf20] = (
          -rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__n_Na23  +
          -rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__p_Ne23  +
          -rho*Y[jp]*Y[jf20]*rate_eval.p_F20__He4_O17  +
          +rho*Y[jp]*Y[jo20]*rate_eval.p_O20__n_F20  +
          -rho*Y[jp]*Y[jf20]*rate_eval.p_F20__n_Ne20  +
          -rho*Y[jp]*Y[jf20]*rate_eval.p_F20__Ne21  +
          -rho*Y[jn]*Y[jf20]*rate_eval.n_F20__F21  +
          +Y[jo20]*rate_eval.O20__F20__weak__wc12  +
          -rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__Na24  +
          +rho*Y[jn]*Y[jf19]*rate_eval.n_F19__F20  +
          -Y[jf20]*rate_eval.F20__Ne20__weak__wc12  +
          +rho*Y[jp]*Y[jo19]*rate_eval.p_O19__F20
       )

    dYdt[jf21] = (
          -rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__p_Ne24  +
          -rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__n_Na24  +
          +rho*Y[jp]*Y[jo21]*rate_eval.p_O21__n_F21  +
          -rho*Y[jp]*Y[jf21]*rate_eval.p_F21__n_Ne21  +
          -rho*Y[jp]*Y[jf21]*rate_eval.p_F21__Ne22  +
          -rho*Y[jn]*Y[jf21]*rate_eval.n_F21__F22  +
          +rho*Y[jn]*Y[jf20]*rate_eval.n_F20__F21  +
          +rho*Y[jp]*Y[jo20]*rate_eval.p_O20__F21  +
          -rho*Y[jp]*Y[jf21]*rate_eval.p_F21__He4_O18  +
          -rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__Na25  +
          +Y[jo21]*rate_eval.O21__F21__weak__wc12  +
          -Y[jf21]*rate_eval.F21__Ne21__weak__wc12
       )

    dYdt[jf22] = (
          +rho*Y[jp]*Y[jo22]*rate_eval.p_O22__n_F22  +
          +rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__He4_F22  +
          -rho*Y[jp]*Y[jf22]*rate_eval.p_F22__He4_O19  +
          -rho*Y[jp]*Y[jf22]*rate_eval.p_F22__n_Ne22  +
          -rho*Y[jp]*Y[jf22]*rate_eval.p_F22__Ne23  +
          -rho*Y[jn]*Y[jf22]*rate_eval.n_F22__F23  +
          +rho*Y[jn]*Y[jf21]*rate_eval.n_F21__F22  +
          -Y[jf22]*rate_eval.F22__Ne22__weak__wc17  +
          +rho*Y[jp]*Y[jo21]*rate_eval.p_O21__F22  +
          -rho*Y[jhe4]*Y[jf22]*rate_eval.He4_F22__Na26  +
          +Y[jo22]*rate_eval.O22__F22__weak__wc17  +
          +Y[jo23]*rate_eval.O23__n_F22__weak__wc12  +
          -rho*Y[jhe4]*Y[jf22]*rate_eval.He4_F22__n_Na25
       )

    dYdt[jf23] = (
          -rho*Y[jp]*Y[jf23]*rate_eval.p_F23__Ne24  +
          -rho*Y[jp]*Y[jf23]*rate_eval.p_F23__He4_O20  +
          +rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__He4_F23  +
          -Y[jf23]*rate_eval.F23__Ne23__weak__wc12  +
          -rho*Y[jn]*Y[jf23]*rate_eval.n_F23__F24  +
          +rho*Y[jn]*Y[jf22]*rate_eval.n_F22__F23  +
          +rho*Y[jp]*Y[jo22]*rate_eval.p_O22__F23  +
          +Y[jo25]*rate_eval.O25__n_n_F23__weak__mp17  +
          +Y[jo24]*rate_eval.O24__n_F23__weak__wc12  +
          -rho*Y[jhe4]*Y[jf23]*rate_eval.He4_F23__Na27  +
          +rho*Y[jp]*Y[jo23]*rate_eval.p_O23__n_F23  +
          -rho*Y[jp]*Y[jf23]*rate_eval.p_F23__n_Ne23  +
          +Y[jo23]*rate_eval.O23__F23__weak__wc12  +
          +Y[jo26]*rate_eval.O26__n_n_n_F23__weak__mo03  +
          -rho*Y[jhe4]*Y[jf23]*rate_eval.He4_F23__n_Na26
       )

    dYdt[jf24] = (
          +Y[jo27]*rate_eval.O27__n_n_n_F24__weak__mo03  +
          -rho*Y[jp]*Y[jf24]*rate_eval.p_F24__Ne25  +
          +rho*Y[jp]*Y[jne27]*rate_eval.p_Ne27__He4_F24  +
          +Y[jo24]*rate_eval.O24__F24__weak__wc12  +
          -rho*Y[jhe4]*Y[jf24]*rate_eval.He4_F24__n_Na27  +
          -rho*Y[jp]*Y[jf24]*rate_eval.p_F24__n_Ne24  +
          +rho*Y[jp]*Y[jo24]*rate_eval.p_O24__n_F24  +
          +Y[jo25]*rate_eval.O25__n_F24__weak__mp17  +
          -rho*Y[jp]*Y[jf24]*rate_eval.p_F24__He4_O21  +
          -Y[jf24]*rate_eval.F24__Ne24__weak__wc12  +
          -rho*Y[jhe4]*Y[jf24]*rate_eval.He4_F24__Na28  +
          +rho*Y[jn]*Y[jf23]*rate_eval.n_F23__F24  +
          -Y[jf24]*rate_eval.F24__n_Ne23__weak__wc12  +
          +Y[jo26]*rate_eval.O26__n_n_F24__weak__mp17  +
          -rho*Y[jn]*Y[jf24]*rate_eval.n_F24__F25  +
          +rho*Y[jp]*Y[jo23]*rate_eval.p_O23__F24
       )

    dYdt[jf25] = (
          +rho*Y[jp]*Y[jo25]*rate_eval.p_O25__n_F25  +
          -rho*Y[jn]*Y[jf25]*rate_eval.n_F25__F26  +
          +Y[jo28]*rate_eval.O28__n_n_n_F25__weak__mo03  +
          -rho*Y[jp]*Y[jf25]*rate_eval.p_F25__He4_O22  +
          -rho*Y[jp]*Y[jf25]*rate_eval.p_F25__n_Ne25  +
          +rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__He4_F25  +
          -rho*Y[jhe4]*Y[jf25]*rate_eval.He4_F25__n_Na28  +
          -Y[jf25]*rate_eval.F25__Ne25__weak__wc12  +
          -rho*Y[jp]*Y[jf25]*rate_eval.p_F25__Ne26  +
          +Y[jo27]*rate_eval.O27__n_n_F25__weak__mp17  +
          +Y[jo26]*rate_eval.O26__n_F25__weak__mp17  +
          -rho*Y[jhe4]*Y[jf25]*rate_eval.He4_F25__Na29  +
          +Y[jo25]*rate_eval.O25__F25__weak__mo03  +
          +rho*Y[jp]*Y[jo24]*rate_eval.p_O24__F25  +
          -Y[jf25]*rate_eval.F25__n_Ne24__weak__wc12  +
          +rho*Y[jn]*Y[jf24]*rate_eval.n_F24__F25
       )

    dYdt[jf26] = (
          -rho*Y[jn]*Y[jf26]*rate_eval.n_F26__F27  +
          -rho*Y[jhe4]*Y[jf26]*rate_eval.He4_F26__Na30  +
          +rho*Y[jn]*Y[jf25]*rate_eval.n_F25__F26  +
          +rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__He4_F26  +
          -rho*Y[jhe4]*Y[jf26]*rate_eval.He4_F26__n_Na29  +
          -rho*Y[jp]*Y[jf26]*rate_eval.p_F26__n_Ne26  +
          +rho*Y[jp]*Y[jo26]*rate_eval.p_O26__n_F26  +
          +Y[jo28]*rate_eval.O28__n_n_F26__weak__mp17  +
          +Y[jo26]*rate_eval.O26__F26__weak__mo03  +
          -rho*Y[jp]*Y[jf26]*rate_eval.p_F26__Ne27  +
          -Y[jf26]*rate_eval.F26__n_Ne25__weak__wc12  +
          +rho*Y[jp]*Y[jo25]*rate_eval.p_O25__F26  +
          -rho*Y[jp]*Y[jf26]*rate_eval.p_F26__He4_O23  +
          +Y[jo27]*rate_eval.O27__n_F26__weak__mp17  +
          -Y[jf26]*rate_eval.F26__Ne26__weak__wc12
       )

    dYdt[jf27] = (
          -Y[jf27]*rate_eval.F27__n_n_n_Ne24__weak__mo03  +
          +rho*Y[jn]*Y[jf26]*rate_eval.n_F26__F27  +
          +rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__He4_F27  +
          -rho*Y[jhe4]*Y[jf27]*rate_eval.He4_F27__n_Na30  +
          -rho*Y[jp]*Y[jf27]*rate_eval.p_F27__He4_O24  +
          -rho*Y[jp]*Y[jf27]*rate_eval.p_F27__n_Ne27  +
          -Y[jf27]*rate_eval.F27__n_n_Ne25__weak__mp17  +
          +Y[jo27]*rate_eval.O27__F27__weak__mo03  +
          -rho*Y[jp]*Y[jf27]*rate_eval.p_F27__Ne28  +
          +rho*Y[jp]*Y[jo26]*rate_eval.p_O26__F27  +
          -rho*Y[jhe4]*Y[jf27]*rate_eval.He4_F27__Na31  +
          -Y[jf27]*rate_eval.F27__n_Ne26__weak__wc12  +
          +Y[jo28]*rate_eval.O28__n_F27__weak__mp17  +
          +rho*Y[jp]*Y[jo27]*rate_eval.p_O27__n_F27  +
          -Y[jf27]*rate_eval.F27__Ne27__weak__wc17  +
          -rho*Y[jn]*Y[jf27]*rate_eval.n_F27__F28
       )

    dYdt[jf28] = (
          -Y[jf28]*rate_eval.F28__n_n_n_Ne25__weak__mo03  +
          -rho*Y[jhe4]*Y[jf28]*rate_eval.He4_F28__n_Na31  +
          -rho*Y[jp]*Y[jf28]*rate_eval.p_F28__n_Ne28  +
          +rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__He4_F28  +
          -rho*Y[jp]*Y[jf28]*rate_eval.p_F28__He4_O25  +
          -rho*Y[jhe4]*Y[jf28]*rate_eval.He4_F28__Na32  +
          -rho*Y[jp]*Y[jf28]*rate_eval.p_F28__Ne29  +
          +rho*Y[jp]*Y[jo27]*rate_eval.p_O27__F28  +
          -Y[jf28]*rate_eval.F28__n_n_Ne26__weak__mp17  +
          -Y[jf28]*rate_eval.F28__Ne28__weak__mo03  +
          -Y[jf28]*rate_eval.F28__n_Ne27__weak__mp17  +
          +rho*Y[jn]*Y[jf27]*rate_eval.n_F27__F28
       )

    dYdt[jf29] = (
          -Y[jf29]*rate_eval.F29__n_n_n_Ne26__weak__mo03  +
          -rho*Y[jhe4]*Y[jf29]*rate_eval.He4_F29__n_Na32  +
          -rho*Y[jp]*Y[jf29]*rate_eval.p_F29__He4_O26  +
          -rho*Y[jp]*Y[jf29]*rate_eval.p_F29__Ne30  +
          +rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__He4_F29  +
          -Y[jf29]*rate_eval.F29__Ne29__weak__wc17  +
          -rho*Y[jp]*Y[jf29]*rate_eval.p_F29__n_Ne29  +
          -rho*Y[jhe4]*Y[jf29]*rate_eval.He4_F29__Na33  +
          -Y[jf29]*rate_eval.F29__n_Ne28__weak__wc12
       )

    dYdt[jf30] = (
          -rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__p_Ne33  +
          -rho*Y[jp]*Y[jf30]*rate_eval.p_F30__He4_O27  +
          -rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__n_Na33  +
          -Y[jf30]*rate_eval.F30__n_n_Ne28__weak__mp17  +
          -rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__Na34  +
          -Y[jf30]*rate_eval.F30__n_Ne29__weak__mp17  +
          -rho*Y[jp]*Y[jf30]*rate_eval.p_F30__n_Ne30  +
          -Y[jf30]*rate_eval.F30__Ne30__weak__mo03  +
          -Y[jf30]*rate_eval.F30__n_n_n_Ne27__weak__mo03  +
          -rho*Y[jp]*Y[jf30]*rate_eval.p_F30__Ne31
       )

    dYdt[jf31] = (
          -Y[jf31]*rate_eval.F31__n_n_n_Ne28__weak__mo03  +
          -rho*Y[jhe4]*Y[jf31]*rate_eval.He4_F31__n_Na34  +
          -rho*Y[jp]*Y[jf31]*rate_eval.p_F31__He4_O28  +
          +rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__He4_F31  +
          -Y[jf31]*rate_eval.F31__n_n_Ne29__weak__mp17  +
          -rho*Y[jp]*Y[jf31]*rate_eval.p_F31__n_Ne31  +
          -Y[jf31]*rate_eval.F31__Ne31__weak__mo03  +
          -rho*Y[jhe4]*Y[jf31]*rate_eval.He4_F31__Na35  +
          -Y[jf31]*rate_eval.F31__n_Ne30__weak__mp17  +
          -rho*Y[jp]*Y[jf31]*rate_eval.p_F31__Ne32
       )

    dYdt[jne16] = (
          -rho*Y[jhe4]*Y[jne16]*rate_eval.He4_Ne16__p_Na19  +
          -rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__p_F16  +
          +rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__He4_Ne16  +
          -rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__He4_O13  +
          -rho*Y[jhe4]*Y[jne16]*rate_eval.He4_Ne16__Mg20  +
          -rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__Ne17
       )

    dYdt[jne17] = (
          -rho*Y[jhe4]*Y[jne17]*rate_eval.He4_Ne17__p_Na20  +
          -rho*Y[jhe4]*Y[jne17]*rate_eval.He4_Ne17__Mg21  +
          -rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__He4_O14  +
          -Y[jne17]*rate_eval.Ne17__p_O16__weak__wc12  +
          -rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__Ne18  +
          +rho*Y[jn]*Y[jne16]*rate_eval.n_Ne16__Ne17  +
          +rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__He4_Ne17  +
          -Y[jne17]*rate_eval.Ne17__F17__weak__wc17  +
          -rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__p_F17
       )

    dYdt[jne18] = (
          +rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__He4_Ne18  +
          -rho*Y[jhe4]*Y[jne18]*rate_eval.He4_Ne18__p_Na21  +
          -rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__He4_O15  +
          -rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__p_F18  +
          -rho*Y[jhe4]*Y[jne18]*rate_eval.He4_Ne18__Mg22  +
          +rho*Y[jhe4]*Y[jf15]*rate_eval.He4_F15__p_Ne18  +
          -rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__Ne19  +
          +rho*Y[jn]*Y[jne17]*rate_eval.n_Ne17__Ne18  +
          +rho*Y[jhe4]*Y[jo14]*rate_eval.He4_O14__Ne18  +
          -Y[jne18]*rate_eval.Ne18__F18__weak__wc12  +
          +rho*Y[jp]*Y[jf17]*rate_eval.p_F17__Ne18  +
          +Y[jal22]*rate_eval.Al22__He4_Ne18__weak__wc12  +
          -rho*Y[jp]*Y[jne18]*rate_eval.p_Ne18__Na19
       )

    dYdt[jne19] = (
          +rho*Y[jn]*Y[jmg22]*rate_eval.n_Mg22__He4_Ne19  +
          +rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__p_Ne19  +
          -rho*Y[jhe4]*Y[jne19]*rate_eval.He4_Ne19__p_Na22  +
          +Y[jmg20]*rate_eval.Mg20__p_Ne19__weak__wc12  +
          -rho*Y[jn]*Y[jne19]*rate_eval.n_Ne19__He4_O16  +
          +rho*Y[jhe4]*Y[jf16]*rate_eval.He4_F16__p_Ne19  +
          -Y[jne19]*rate_eval.Ne19__F19__weak__wc12  +
          -rho*Y[jp]*Y[jne19]*rate_eval.p_Ne19__Na20  +
          -rho*Y[jn]*Y[jne19]*rate_eval.n_Ne19__Ne20  +
          +rho*Y[jn]*Y[jne18]*rate_eval.n_Ne18__Ne19  +
          +rho*Y[jp]*Y[jf18]*rate_eval.p_F18__Ne19  +
          +rho*Y[jhe4]*Y[jo15]*rate_eval.He4_O15__Ne19  +
          +Y[jna19]*rate_eval.Na19__Ne19__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[jne19]*rate_eval.He4_Ne19__Mg23  +
          +rho*Y[jp]*Y[jf19]*rate_eval.p_F19__n_Ne19
       )

    dYdt[jne20] = (
          -rho*Y[jn]*Y[jne20]*rate_eval.n_Ne20__Ne21  +
          +5.00000000000000e-01*rho*Y[jc12]**2*rate_eval.C12_C12__He4_Ne20  +
          +rho*Y[jn]*Y[jmg23]*rate_eval.n_Mg23__He4_Ne20  +
          +rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__He4_Ne20  +
          -rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__He4_Si28  +
          -rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__p_P31  +
          +rho*Y[jhe4]*Y[jo17]*rate_eval.He4_O17__n_Ne20  +
          -rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__n_S31  +
          +rho*Y[jp]*Y[jf20]*rate_eval.p_F20__n_Ne20  +
          -rho*Y[jhe4]*Y[jne20]*rate_eval.He4_Ne20__Mg24  +
          +Y[jna20]*rate_eval.Na20__Ne20__weak__wc12  +
          -rho*Y[jp]*Y[jne20]*rate_eval.p_Ne20__Na21  +
          +rho*Y[jn]*Y[jne19]*rate_eval.n_Ne19__Ne20  +
          +Y[jal22]*rate_eval.Al22__p_p_Ne20__weak__wc12  +
          +rho*Y[jp]*Y[jf19]*rate_eval.p_F19__Ne20  +
          +Y[jal24]*rate_eval.Al24__He4_Ne20__weak__wc12  +
          +Y[jf20]*rate_eval.F20__Ne20__weak__wc12  +
          +Y[jmg21]*rate_eval.Mg21__p_Ne20__weak__wc12  +
          +rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__p_Ne20  +
          +rho*Y[jhe4]*Y[jo16]*rate_eval.He4_O16__Ne20  +
          -rho*Y[jp]*Y[jne20]*rate_eval.p_Ne20__He4_F17
       )

    dYdt[jne21] = (
          +rho*Y[jn]*Y[jne20]*rate_eval.n_Ne20__Ne21  +
          +rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__He4_Ne21  +
          -rho*Y[jhe4]*Y[jne21]*rate_eval.He4_Ne21__n_Mg24  +
          +rho*Y[jhe4]*Y[jf18]*rate_eval.He4_F18__p_Ne21  +
          +rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__p_Ne21  +
          -rho*Y[jp]*Y[jne21]*rate_eval.p_Ne21__Na22  +
          +rho*Y[jp]*Y[jf20]*rate_eval.p_F20__Ne21  +
          +rho*Y[jp]*Y[jf21]*rate_eval.p_F21__n_Ne21  +
          +rho*Y[jhe4]*Y[jo17]*rate_eval.He4_O17__Ne21  +
          +Y[jna21]*rate_eval.Na21__Ne21__weak__wc12  +
          -rho*Y[jn]*Y[jne21]*rate_eval.n_Ne21__Ne22  +
          +Y[jf21]*rate_eval.F21__Ne21__weak__wc12  +
          -rho*Y[jhe4]*Y[jne21]*rate_eval.He4_Ne21__Mg25  +
          +rho*Y[jhe4]*Y[jo18]*rate_eval.He4_O18__n_Ne21
       )

    dYdt[jne22] = (
          -rho*Y[jp]*Y[jne22]*rate_eval.p_Ne22__Na23  +
          +rho*Y[jp]*Y[jf22]*rate_eval.p_F22__n_Ne22  +
          +rho*Y[jhe4]*Y[jf19]*rate_eval.He4_F19__p_Ne22  +
          +rho*Y[jhe4]*Y[jo19]*rate_eval.He4_O19__n_Ne22  +
          +rho*Y[jp]*Y[jf21]*rate_eval.p_F21__Ne22  +
          +Y[jf22]*rate_eval.F22__Ne22__weak__wc17  +
          +rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__p_Ne22  +
          +rho*Y[jn]*Y[jne21]*rate_eval.n_Ne21__Ne22  +
          +Y[jna22]*rate_eval.Na22__Ne22__weak__wc12  +
          +rho*Y[jhe4]*Y[jo18]*rate_eval.He4_O18__Ne22  +
          -rho*Y[jhe4]*Y[jne22]*rate_eval.He4_Ne22__Mg26  +
          -rho*Y[jn]*Y[jne22]*rate_eval.n_Ne22__Ne23  +
          +rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__He4_Ne22  +
          -rho*Y[jhe4]*Y[jne22]*rate_eval.He4_Ne22__n_Mg25
       )

    dYdt[jne23] = (
          -rho*Y[jhe4]*Y[jne23]*rate_eval.He4_Ne23__n_Mg26  +
          -rho*Y[jp]*Y[jne23]*rate_eval.p_Ne23__n_Na23  +
          +rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__He4_Ne23  +
          +rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__p_Ne23  +
          +Y[jf23]*rate_eval.F23__Ne23__weak__wc12  +
          -rho*Y[jp]*Y[jne23]*rate_eval.p_Ne23__Na24  +
          +rho*Y[jp]*Y[jf22]*rate_eval.p_F22__Ne23  +
          -rho*Y[jn]*Y[jne23]*rate_eval.n_Ne23__Ne24  +
          +rho*Y[jhe4]*Y[jo20]*rate_eval.He4_O20__n_Ne23  +
          +rho*Y[jhe4]*Y[jo19]*rate_eval.He4_O19__Ne23  +
          +Y[jf24]*rate_eval.F24__n_Ne23__weak__wc12  +
          -rho*Y[jhe4]*Y[jne23]*rate_eval.He4_Ne23__Mg27  +
          +rho*Y[jp]*Y[jf23]*rate_eval.p_F23__n_Ne23  +
          +rho*Y[jn]*Y[jne22]*rate_eval.n_Ne22__Ne23  +
          -Y[jne23]*rate_eval.Ne23__Na23__weak__wc12
       )

    dYdt[jne24] = (
          +Y[jf27]*rate_eval.F27__n_n_n_Ne24__weak__mo03  +
          +rho*Y[jp]*Y[jf23]*rate_eval.p_F23__Ne24  +
          -rho*Y[jhe4]*Y[jne24]*rate_eval.He4_Ne24__n_Mg27  +
          -rho*Y[jp]*Y[jne24]*rate_eval.p_Ne24__n_Na24  +
          +rho*Y[jp]*Y[jf24]*rate_eval.p_F24__n_Ne24  +
          +rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__p_Ne24  +
          -Y[jne24]*rate_eval.Ne24__Na24__weak__wc12  +
          -rho*Y[jhe4]*Y[jne24]*rate_eval.He4_Ne24__Mg28  +
          +rho*Y[jhe4]*Y[jo21]*rate_eval.He4_O21__n_Ne24  +
          -rho*Y[jn]*Y[jne24]*rate_eval.n_Ne24__Ne25  +
          +Y[jf24]*rate_eval.F24__Ne24__weak__wc12  +
          +rho*Y[jn]*Y[jne23]*rate_eval.n_Ne23__Ne24  +
          +rho*Y[jhe4]*Y[jo20]*rate_eval.He4_O20__Ne24  +
          -rho*Y[jp]*Y[jne24]*rate_eval.p_Ne24__Na25  +
          +rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__He4_Ne24  +
          +Y[jf25]*rate_eval.F25__n_Ne24__weak__wc12
       )

    dYdt[jne25] = (
          +Y[jf28]*rate_eval.F28__n_n_n_Ne25__weak__mo03  +
          +rho*Y[jp]*Y[jf24]*rate_eval.p_F24__Ne25  +
          -rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__He4_F22  +
          -rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__n_Na25  +
          +rho*Y[jp]*Y[jf25]*rate_eval.p_F25__n_Ne25  +
          +rho*Y[jhe4]*Y[jo22]*rate_eval.He4_O22__n_Ne25  +
          +rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__He4_Ne25  +
          -rho*Y[jhe4]*Y[jne25]*rate_eval.He4_Ne25__Mg29  +
          +Y[jf27]*rate_eval.F27__n_n_Ne25__weak__mp17  +
          +rho*Y[jhe4]*Y[jo21]*rate_eval.He4_O21__Ne25  +
          -Y[jne25]*rate_eval.Ne25__Na25__weak__wc12  +
          -rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__Na26  +
          +rho*Y[jn]*Y[jne24]*rate_eval.n_Ne24__Ne25  +
          +Y[jf25]*rate_eval.F25__Ne25__weak__wc12  +
          -rho*Y[jhe4]*Y[jne25]*rate_eval.He4_Ne25__n_Mg28  +
          +Y[jf26]*rate_eval.F26__n_Ne25__weak__wc12  +
          -rho*Y[jn]*Y[jne25]*rate_eval.n_Ne25__Ne26
       )

    dYdt[jne26] = (
          +Y[jf29]*rate_eval.F29__n_n_n_Ne26__weak__mo03  +
          -Y[jne26]*rate_eval.Ne26__n_Na25__weak__wc12  +
          -rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__n_Na26  +
          +rho*Y[jhe4]*Y[jo23]*rate_eval.He4_O23__n_Ne26  +
          +rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__He4_Ne26  +
          +rho*Y[jp]*Y[jf26]*rate_eval.p_F26__n_Ne26  +
          -rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__He4_F23  +
          -rho*Y[jhe4]*Y[jne26]*rate_eval.He4_Ne26__n_Mg29  +
          -rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__Na27  +
          +rho*Y[jhe4]*Y[jo22]*rate_eval.He4_O22__Ne26  +
          -rho*Y[jhe4]*Y[jne26]*rate_eval.He4_Ne26__Mg30  +
          -rho*Y[jn]*Y[jne26]*rate_eval.n_Ne26__Ne27  +
          +Y[jf27]*rate_eval.F27__n_Ne26__weak__wc12  +
          +rho*Y[jp]*Y[jf25]*rate_eval.p_F25__Ne26  +
          +Y[jf28]*rate_eval.F28__n_n_Ne26__weak__mp17  +
          +Y[jna30]*rate_eval.Na30__He4_Ne26__weak__wc12  +
          +rho*Y[jn]*Y[jne25]*rate_eval.n_Ne25__Ne26  +
          -Y[jne26]*rate_eval.Ne26__Na26__weak__wc12  +
          +Y[jf26]*rate_eval.F26__Ne26__weak__wc12
       )

    dYdt[jne27] = (
          -rho*Y[jp]*Y[jne27]*rate_eval.p_Ne27__He4_F24  +
          -Y[jne27]*rate_eval.Ne27__n_Na26__weak__wc12  +
          +rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__He4_Ne27  +
          -rho*Y[jhe4]*Y[jne27]*rate_eval.He4_Ne27__n_Mg30  +
          -rho*Y[jp]*Y[jne27]*rate_eval.p_Ne27__n_Na27  +
          +rho*Y[jp]*Y[jf27]*rate_eval.p_F27__n_Ne27  +
          +rho*Y[jhe4]*Y[jo24]*rate_eval.He4_O24__n_Ne27  +
          -rho*Y[jhe4]*Y[jne27]*rate_eval.He4_Ne27__Mg31  +
          -rho*Y[jp]*Y[jne27]*rate_eval.p_Ne27__Na28  +
          +rho*Y[jn]*Y[jne26]*rate_eval.n_Ne26__Ne27  +
          +rho*Y[jhe4]*Y[jo23]*rate_eval.He4_O23__Ne27  +
          -Y[jne27]*rate_eval.Ne27__Na27__weak__wc12  +
          +rho*Y[jp]*Y[jf26]*rate_eval.p_F26__Ne27  +
          -rho*Y[jn]*Y[jne27]*rate_eval.n_Ne27__Ne28  +
          +Y[jf27]*rate_eval.F27__Ne27__weak__wc17  +
          +Y[jf30]*rate_eval.F30__n_n_n_Ne27__weak__mo03  +
          +Y[jf28]*rate_eval.F28__n_Ne27__weak__mp17
       )

    dYdt[jne28] = (
          +Y[jf31]*rate_eval.F31__n_n_n_Ne28__weak__mo03  +
          -Y[jne28]*rate_eval.Ne28__Na28__weak__wc17  +
          +rho*Y[jp]*Y[jf28]*rate_eval.p_F28__n_Ne28  +
          +rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__He4_Ne28  +
          -rho*Y[jhe4]*Y[jne28]*rate_eval.He4_Ne28__n_Mg31  +
          -rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__n_Na28  +
          -rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__He4_F25  +
          +rho*Y[jhe4]*Y[jo25]*rate_eval.He4_O25__n_Ne28  +
          -Y[jne28]*rate_eval.Ne28__n_Na27__weak__wc12  +
          -rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__Na29  +
          +rho*Y[jp]*Y[jf27]*rate_eval.p_F27__Ne28  +
          +rho*Y[jhe4]*Y[jo24]*rate_eval.He4_O24__Ne28  +
          -rho*Y[jn]*Y[jne28]*rate_eval.n_Ne28__Ne29  +
          +Y[jf30]*rate_eval.F30__n_n_Ne28__weak__mp17  +
          +rho*Y[jn]*Y[jne27]*rate_eval.n_Ne27__Ne28  +
          -rho*Y[jhe4]*Y[jne28]*rate_eval.He4_Ne28__Mg32  +
          +Y[jf29]*rate_eval.F29__n_Ne28__weak__wc12  +
          +Y[jf28]*rate_eval.F28__Ne28__weak__mo03
       )

    dYdt[jne29] = (
          -rho*Y[jhe4]*Y[jne29]*rate_eval.He4_Ne29__Mg33  +
          +Y[jf31]*rate_eval.F31__n_n_Ne29__weak__mp17  +
          -rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__He4_F26  +
          -rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__n_Na29  +
          +rho*Y[jhe4]*Y[jo26]*rate_eval.He4_O26__n_Ne29  +
          -rho*Y[jhe4]*Y[jne29]*rate_eval.He4_Ne29__n_Mg32  +
          +rho*Y[jp]*Y[jf28]*rate_eval.p_F28__Ne29  +
          +rho*Y[jn]*Y[jne28]*rate_eval.n_Ne28__Ne29  +
          -Y[jne29]*rate_eval.Ne29__n_n_Na27__weak__wc12  +
          +Y[jf29]*rate_eval.F29__Ne29__weak__wc17  +
          +Y[jf30]*rate_eval.F30__n_Ne29__weak__mp17  +
          +rho*Y[jp]*Y[jf29]*rate_eval.p_F29__n_Ne29  +
          -rho*Y[jn]*Y[jne29]*rate_eval.n_Ne29__Ne30  +
          -Y[jne29]*rate_eval.Ne29__Na29__weak__wc12  +
          +rho*Y[jhe4]*Y[jo25]*rate_eval.He4_O25__Ne29  +
          -rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__Na30  +
          +rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__He4_Ne29  +
          -Y[jne29]*rate_eval.Ne29__n_Na28__weak__wc17
       )

    dYdt[jne30] = (
          -rho*Y[jhe4]*Y[jne30]*rate_eval.He4_Ne30__n_Mg33  +
          -rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__He4_F27  +
          +rho*Y[jp]*Y[jf29]*rate_eval.p_F29__Ne30  +
          -rho*Y[jn]*Y[jne30]*rate_eval.n_Ne30__Ne31  +
          +rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__He4_Ne30  +
          -rho*Y[jhe4]*Y[jne30]*rate_eval.He4_Ne30__Mg34  +
          -rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__Na31  +
          +rho*Y[jhe4]*Y[jo27]*rate_eval.He4_O27__n_Ne30  +
          -rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__n_Na30  +
          +rho*Y[jp]*Y[jf30]*rate_eval.p_F30__n_Ne30  +
          +rho*Y[jn]*Y[jne29]*rate_eval.n_Ne29__Ne30  +
          +Y[jf31]*rate_eval.F31__n_Ne30__weak__mp17  +
          +Y[jf30]*rate_eval.F30__Ne30__weak__mo03  +
          -Y[jne30]*rate_eval.Ne30__Na30__weak__wc17  +
          -Y[jne30]*rate_eval.Ne30__n_Na29__weak__wc12  +
          +rho*Y[jhe4]*Y[jo26]*rate_eval.He4_O26__Ne30
       )

    dYdt[jne31] = (
          -Y[jne31]*rate_eval.Ne31__n_n_n_Na28__weak__mo03  +
          -Y[jne31]*rate_eval.Ne31__n_Na30__weak__mp17  +
          -rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__He4_F28  +
          -rho*Y[jhe4]*Y[jne31]*rate_eval.He4_Ne31__n_Mg34  +
          +rho*Y[jp]*Y[jf31]*rate_eval.p_F31__n_Ne31  +
          +rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__He4_Ne31  +
          +rho*Y[jhe4]*Y[jo28]*rate_eval.He4_O28__n_Ne31  +
          +rho*Y[jn]*Y[jne30]*rate_eval.n_Ne30__Ne31  +
          +rho*Y[jhe4]*Y[jo27]*rate_eval.He4_O27__Ne31  +
          -Y[jne31]*rate_eval.Ne31__Na31__weak__wc17  +
          +Y[jf31]*rate_eval.F31__Ne31__weak__mo03  +
          -rho*Y[jhe4]*Y[jne31]*rate_eval.He4_Ne31__Mg35  +
          -rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__Na32  +
          -rho*Y[jn]*Y[jne31]*rate_eval.n_Ne31__Ne32  +
          -rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__n_Na31  +
          -Y[jne31]*rate_eval.Ne31__n_n_Na29__weak__mp17  +
          +rho*Y[jp]*Y[jf30]*rate_eval.p_F30__Ne31
       )

    dYdt[jne32] = (
          -rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__Na33  +
          -rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__n_Na32  +
          -rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__He4_F29  +
          -rho*Y[jhe4]*Y[jne32]*rate_eval.He4_Ne32__n_Mg35  +
          +rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__He4_Ne32  +
          -Y[jne32]*rate_eval.Ne32__n_Na31__weak__mp17  +
          +rho*Y[jhe4]*Y[jo28]*rate_eval.He4_O28__Ne32  +
          -Y[jne32]*rate_eval.Ne32__n_n_Na30__weak__mp17  +
          -Y[jne32]*rate_eval.Ne32__Na32__weak__wc17  +
          +rho*Y[jn]*Y[jne31]*rate_eval.n_Ne31__Ne32  +
          -rho*Y[jhe4]*Y[jne32]*rate_eval.He4_Ne32__Mg36  +
          +rho*Y[jp]*Y[jf31]*rate_eval.p_F31__Ne32  +
          -Y[jne32]*rate_eval.Ne32__n_n_n_Na29__weak__mo03  +
          -rho*Y[jn]*Y[jne32]*rate_eval.n_Ne32__Ne33
       )

    dYdt[jne33] = (
          -rho*Y[jhe4]*Y[jne33]*rate_eval.He4_Ne33__n_Mg36  +
          +rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__p_Ne33  +
          -rho*Y[jp]*Y[jne33]*rate_eval.p_Ne33__n_Na33  +
          -rho*Y[jp]*Y[jne33]*rate_eval.p_Ne33__Na34  +
          +rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__He4_Ne33  +
          -Y[jne33]*rate_eval.Ne33__n_n_n_Na30__weak__mo03  +
          -Y[jne33]*rate_eval.Ne33__n_Na32__weak__mp17  +
          -rho*Y[jhe4]*Y[jne33]*rate_eval.He4_Ne33__Mg37  +
          -Y[jne33]*rate_eval.Ne33__n_n_Na31__weak__mp17  +
          -rho*Y[jn]*Y[jne33]*rate_eval.n_Ne33__Ne34  +
          -Y[jne33]*rate_eval.Ne33__Na33__weak__mo03  +
          +rho*Y[jn]*Y[jne32]*rate_eval.n_Ne32__Ne33
       )

    dYdt[jne34] = (
          -Y[jne34]*rate_eval.Ne34__n_n_n_Na31__weak__mo03  +
          -rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__He4_F31  +
          +rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__He4_Ne34  +
          -rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__n_Na34  +
          -Y[jne34]*rate_eval.Ne34__Na34__weak__mo03  +
          -rho*Y[jhe4]*Y[jne34]*rate_eval.He4_Ne34__Mg38  +
          -rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__Na35  +
          -Y[jne34]*rate_eval.Ne34__n_n_Na32__weak__mp17  +
          -rho*Y[jhe4]*Y[jne34]*rate_eval.He4_Ne34__n_Mg37  +
          -Y[jne34]*rate_eval.Ne34__n_Na33__weak__mp17  +
          +rho*Y[jn]*Y[jne33]*rate_eval.n_Ne33__Ne34
       )

    dYdt[jna19] = (
          -rho*Y[jhe4]*Y[jna19]*rate_eval.He4_Na19__Al23  +
          +rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__He4_Na19  +
          -rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__p_Ne19  +
          +rho*Y[jhe4]*Y[jne16]*rate_eval.He4_Ne16__p_Na19  +
          -rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__Na20  +
          -rho*Y[jhe4]*Y[jna19]*rate_eval.He4_Na19__p_Mg22  +
          +rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__p_Na19  +
          -rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__He4_F16  +
          +rho*Y[jhe4]*Y[jf15]*rate_eval.He4_F15__Na19  +
          -Y[jna19]*rate_eval.Na19__Ne19__weak__bqa_pos_  +
          -rho*Y[jp]*Y[jna19]*rate_eval.p_Na19__Mg20  +
          +rho*Y[jp]*Y[jne18]*rate_eval.p_Ne18__Na19
       )

    dYdt[jna20] = (
          +rho*Y[jhe4]*Y[jf16]*rate_eval.He4_F16__Na20  +
          +rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__He4_Na20  +
          +rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__p_Na20  +
          -rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__He4_F17  +
          +rho*Y[jhe4]*Y[jne17]*rate_eval.He4_Ne17__p_Na20  +
          -rho*Y[jp]*Y[jna20]*rate_eval.p_Na20__Mg21  +
          -Y[jna20]*rate_eval.Na20__Ne20__weak__wc12  +
          -rho*Y[jhe4]*Y[jna20]*rate_eval.He4_Na20__Al24  +
          -rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__Na21  +
          +rho*Y[jn]*Y[jna19]*rate_eval.n_Na19__Na20  +
          +rho*Y[jp]*Y[jne19]*rate_eval.p_Ne19__Na20  +
          -rho*Y[jhe4]*Y[jna20]*rate_eval.He4_Na20__p_Mg23  +
          -Y[jna20]*rate_eval.Na20__He4_O16__weak__wc12  +
          -rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__p_Ne20  +
          +Y[jmg20]*rate_eval.Mg20__Na20__weak__wc12
       )

    dYdt[jna21] = (
          +rho*Y[jhe4]*Y[jf17]*rate_eval.He4_F17__Na21  +
          -rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__He4_F18  +
          +rho*Y[jhe4]*Y[jne18]*rate_eval.He4_Ne18__p_Na21  +
          -rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__p_Ne21  +
          +rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__He4_Na21  +
          -rho*Y[jp]*Y[jna21]*rate_eval.p_Na21__Mg22  +
          -rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__Na22  +
          +rho*Y[jn]*Y[jna20]*rate_eval.n_Na20__Na21  +
          +rho*Y[jp]*Y[jne20]*rate_eval.p_Ne20__Na21  +
          +Y[jsi23]*rate_eval.Si23__p_p_Na21__weak__wc12  +
          +rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__p_Na21  +
          -Y[jna21]*rate_eval.Na21__Ne21__weak__wc12  +
          -rho*Y[jhe4]*Y[jna21]*rate_eval.He4_Na21__Al25  +
          +Y[jal22]*rate_eval.Al22__p_Na21__weak__wc17  +
          +Y[jmg21]*rate_eval.Mg21__Na21__weak__wc12  +
          +rho*Y[jp]*Y[jmg24]*rate_eval.p_Mg24__He4_Na21
       )

    dYdt[jna22] = (
          +Y[jmg22]*rate_eval.Mg22__Na22__weak__wc12  +
          -rho*Y[jhe4]*Y[jna22]*rate_eval.He4_Na22__p_Mg25  +
          +rho*Y[jhe4]*Y[jne19]*rate_eval.He4_Ne19__p_Na22  +
          +rho*Y[jp]*Y[jne21]*rate_eval.p_Ne21__Na22  +
          -rho*Y[jp]*Y[jna22]*rate_eval.p_Na22__Mg23  +
          -rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__Na23  +
          +rho*Y[jn]*Y[jna21]*rate_eval.n_Na21__Na22  +
          +rho*Y[jhe4]*Y[jf18]*rate_eval.He4_F18__Na22  +
          +rho*Y[jn]*Y[jmg22]*rate_eval.n_Mg22__p_Na22  +
          -rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__p_Ne22  +
          -Y[jna22]*rate_eval.Na22__Ne22__weak__wc12  +
          +Y[jal23]*rate_eval.Al23__p_Na22__weak__wc12  +
          -rho*Y[jhe4]*Y[jna22]*rate_eval.He4_Na22__Al26  +
          -rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__He4_F19  +
          +rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__He4_Na22
       )

    dYdt[jna23] = (
          +rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__n_Na23  +
          +rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__He4_Na23  +
          -rho*Y[jhe4]*Y[jna23]*rate_eval.He4_Na23__p_Mg26  +
          -rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__He4_Ne20  +
          +rho*Y[jp]*Y[jne23]*rate_eval.p_Ne23__n_Na23  +
          +rho*Y[jp]*Y[jne22]*rate_eval.p_Ne22__Na23  +
          +5.00000000000000e-01*rho*Y[jc12]**2*rate_eval.C12_C12__p_Na23  +
          -rho*Y[jhe4]*Y[jna23]*rate_eval.He4_Na23__Al27  +
          -rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__Mg24  +
          +rho*Y[jn]*Y[jna22]*rate_eval.n_Na22__Na23  +
          +Y[jal24]*rate_eval.Al24__p_Na23__weak__wc12  +
          +Y[jmg23]*rate_eval.Mg23__Na23__weak__wc12  +
          -rho*Y[jn]*Y[jna23]*rate_eval.n_Na23__Na24  +
          +rho*Y[jhe4]*Y[jf19]*rate_eval.He4_F19__Na23  +
          +Y[jne23]*rate_eval.Ne23__Na23__weak__wc12  +
          -rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__n_Mg23
       )

    dYdt[jna24] = (
          -rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__p_Mg27  +
          -rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__He4_Ne21  +
          +rho*Y[jp]*Y[jne24]*rate_eval.p_Ne24__n_Na24  +
          +rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__n_Na24  +
          +Y[jne24]*rate_eval.Ne24__Na24__weak__wc12  +
          -rho*Y[jn]*Y[jna24]*rate_eval.n_Na24__Na25  +
          +rho*Y[jp]*Y[jne23]*rate_eval.p_Ne23__Na24  +
          -rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__Al28  +
          +rho*Y[jhe4]*Y[jf20]*rate_eval.He4_F20__Na24  +
          -rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__Mg25  +
          +rho*Y[jn]*Y[jna23]*rate_eval.n_Na23__Na24  +
          -rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__n_Al27  +
          -rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__n_Mg24  +
          -Y[jna24]*rate_eval.Na24__Mg24__weak__wc12
       )

    dYdt[jna25] = (
          +Y[jne26]*rate_eval.Ne26__n_Na25__weak__wc12  +
          -rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__Al29  +
          -Y[jna25]*rate_eval.Na25__Mg25__weak__wc12  +
          +rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__n_Na25  +
          +Y[jne25]*rate_eval.Ne25__Na25__weak__wc12  +
          -rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__Mg26  +
          +rho*Y[jn]*Y[jna24]*rate_eval.n_Na24__Na25  +
          +rho*Y[jp]*Y[jne24]*rate_eval.p_Ne24__Na25  +
          -rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__n_Al28  +
          -rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__p_Mg28  +
          -rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__n_Mg25  +
          +rho*Y[jhe4]*Y[jf21]*rate_eval.He4_F21__Na25  +
          +rho*Y[jhe4]*Y[jf22]*rate_eval.He4_F22__n_Na25  +
          -rho*Y[jn]*Y[jna25]*rate_eval.n_Na25__Na26  +
          -rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__He4_Ne22
       )

    dYdt[jna26] = (
          +Y[jne27]*rate_eval.Ne27__n_Na26__weak__wc12  +
          -Y[jna26]*rate_eval.Na26__Mg26__weak__wc12  +
          +rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__n_Na26  +
          +rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__He4_Na26  +
          -rho*Y[jhe4]*Y[jna26]*rate_eval.He4_Na26__n_Al29  +
          -rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__He4_Ne23  +
          -rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__Mg27  +
          +rho*Y[jp]*Y[jne25]*rate_eval.p_Ne25__Na26  +
          -rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__n_Mg26  +
          -rho*Y[jhe4]*Y[jna26]*rate_eval.He4_Na26__Al30  +
          +rho*Y[jhe4]*Y[jf22]*rate_eval.He4_F22__Na26  +
          -rho*Y[jn]*Y[jna26]*rate_eval.n_Na26__Na27  +
          +rho*Y[jhe4]*Y[jf23]*rate_eval.He4_F23__n_Na26  +
          +rho*Y[jn]*Y[jna25]*rate_eval.n_Na25__Na26  +
          +Y[jne26]*rate_eval.Ne26__Na26__weak__wc12
       )

    dYdt[jna27] = (
          -Y[jna27]*rate_eval.Na27__n_Mg26__weak__wc12  +
          -rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__n_Mg27  +
          +rho*Y[jp]*Y[jne27]*rate_eval.p_Ne27__n_Na27  +
          +rho*Y[jhe4]*Y[jf24]*rate_eval.He4_F24__n_Na27  +
          -rho*Y[jhe4]*Y[jna27]*rate_eval.He4_Na27__n_Al30  +
          -rho*Y[jn]*Y[jna27]*rate_eval.n_Na27__Na28  +
          -rho*Y[jhe4]*Y[jna27]*rate_eval.He4_Na27__Al31  +
          -Y[jna27]*rate_eval.Na27__Mg27__weak__wc12  +
          +rho*Y[jp]*Y[jne26]*rate_eval.p_Ne26__Na27  +
          +Y[jne28]*rate_eval.Ne28__n_Na27__weak__wc12  +
          +Y[jne29]*rate_eval.Ne29__n_n_Na27__weak__wc12  +
          -rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__Mg28  +
          -rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__He4_Ne24  +
          +rho*Y[jhe4]*Y[jf23]*rate_eval.He4_F23__Na27  +
          +Y[jne27]*rate_eval.Ne27__Na27__weak__wc12  +
          +rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__He4_Na27  +
          +rho*Y[jn]*Y[jna26]*rate_eval.n_Na26__Na27
       )

    dYdt[jna28] = (
          +Y[jne31]*rate_eval.Ne31__n_n_n_Na28__weak__mo03  +
          +Y[jne28]*rate_eval.Ne28__Na28__weak__wc17  +
          -rho*Y[jhe4]*Y[jna28]*rate_eval.He4_Na28__n_Al31  +
          -rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__n_Mg28  +
          +rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__n_Na28  +
          -rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__He4_Ne25  +
          +rho*Y[jhe4]*Y[jf25]*rate_eval.He4_F25__n_Na28  +
          +rho*Y[jn]*Y[jna27]*rate_eval.n_Na27__Na28  +
          -rho*Y[jhe4]*Y[jna28]*rate_eval.He4_Na28__Al32  +
          -Y[jna28]*rate_eval.Na28__Mg28__weak__wc12  +
          +rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__He4_Na28  +
          +rho*Y[jp]*Y[jne27]*rate_eval.p_Ne27__Na28  +
          +rho*Y[jhe4]*Y[jf24]*rate_eval.He4_F24__Na28  +
          -rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__Mg29  +
          +Y[jne29]*rate_eval.Ne29__n_Na28__weak__wc17  +
          -rho*Y[jn]*Y[jna28]*rate_eval.n_Na28__Na29  +
          -Y[jna28]*rate_eval.Na28__n_Mg27__weak__wc12
       )

    dYdt[jna29] = (
          +rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__He4_Na29  +
          -rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__He4_Ne26  +
          +rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__n_Na29  +
          +rho*Y[jhe4]*Y[jf26]*rate_eval.He4_F26__n_Na29  +
          -rho*Y[jhe4]*Y[jna29]*rate_eval.He4_Na29__Al33  +
          +rho*Y[jp]*Y[jne28]*rate_eval.p_Ne28__Na29  +
          -rho*Y[jhe4]*Y[jna29]*rate_eval.He4_Na29__n_Al32  +
          -rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__n_Mg29  +
          +rho*Y[jhe4]*Y[jf25]*rate_eval.He4_F25__Na29  +
          +Y[jne29]*rate_eval.Ne29__Na29__weak__wc12  +
          -Y[jna29]*rate_eval.Na29__n_Mg28__weak__wc12  +
          -rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__Mg30  +
          -rho*Y[jn]*Y[jna29]*rate_eval.n_Na29__Na30  +
          +Y[jne30]*rate_eval.Ne30__n_Na29__weak__wc12  +
          +Y[jne31]*rate_eval.Ne31__n_n_Na29__weak__mp17  +
          +Y[jne32]*rate_eval.Ne32__n_n_n_Na29__weak__mo03  +
          +rho*Y[jn]*Y[jna28]*rate_eval.n_Na28__Na29  +
          -Y[jna29]*rate_eval.Na29__Mg29__weak__wc12
       )

    dYdt[jna30] = (
          +rho*Y[jhe4]*Y[jf26]*rate_eval.He4_F26__Na30  +
          +Y[jne31]*rate_eval.Ne31__n_Na30__weak__mp17  +
          +rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__He4_Na30  +
          -rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__He4_Ne27  +
          -rho*Y[jn]*Y[jna30]*rate_eval.n_Na30__Na31  +
          +rho*Y[jhe4]*Y[jf27]*rate_eval.He4_F27__n_Na30  +
          -rho*Y[jhe4]*Y[jna30]*rate_eval.He4_Na30__Al34  +
          -Y[jna30]*rate_eval.Na30__n_Mg29__weak__wc17  +
          -Y[jna30]*rate_eval.Na30__n_n_Mg28__weak__wc12  +
          +Y[jne32]*rate_eval.Ne32__n_n_Na30__weak__mp17  +
          +rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__n_Na30  +
          +Y[jne33]*rate_eval.Ne33__n_n_n_Na30__weak__mo03  +
          -rho*Y[jhe4]*Y[jna30]*rate_eval.He4_Na30__n_Al33  +
          -Y[jna30]*rate_eval.Na30__He4_Ne26__weak__wc12  +
          -rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__Mg31  +
          +rho*Y[jp]*Y[jne29]*rate_eval.p_Ne29__Na30  +
          +Y[jne30]*rate_eval.Ne30__Na30__weak__wc17  +
          +rho*Y[jn]*Y[jna29]*rate_eval.n_Na29__Na30  +
          -Y[jna30]*rate_eval.Na30__Mg30__weak__wc12  +
          -rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__n_Mg30
       )

    dYdt[jna31] = (
          +rho*Y[jhe4]*Y[jf28]*rate_eval.He4_F28__n_Na31  +
          +Y[jne34]*rate_eval.Ne34__n_n_n_Na31__weak__mo03  +
          -rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__Mg32  +
          +rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__He4_Na31  +
          -rho*Y[jhe4]*Y[jna31]*rate_eval.He4_Na31__n_Al34  +
          -rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__He4_Ne28  +
          -rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__n_Mg31  +
          +rho*Y[jn]*Y[jna30]*rate_eval.n_Na30__Na31  +
          -Y[jna31]*rate_eval.Na31__n_Mg30__weak__wc17  +
          +Y[jne31]*rate_eval.Ne31__Na31__weak__wc17  +
          -rho*Y[jn]*Y[jna31]*rate_eval.n_Na31__Na32  +
          -rho*Y[jhe4]*Y[jna31]*rate_eval.He4_Na31__Al35  +
          +rho*Y[jp]*Y[jne30]*rate_eval.p_Ne30__Na31  +
          +Y[jne32]*rate_eval.Ne32__n_Na31__weak__mp17  +
          +rho*Y[jhe4]*Y[jf27]*rate_eval.He4_F27__Na31  +
          -Y[jna31]*rate_eval.Na31__n_n_Mg29__weak__wc12  +
          -Y[jna31]*rate_eval.Na31__n_n_n_Mg28__weak__wc12  +
          +rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__n_Na31  +
          +Y[jne33]*rate_eval.Ne33__n_n_Na31__weak__mp17  +
          -Y[jna31]*rate_eval.Na31__Mg31__weak__wc12
       )

    dYdt[jna32] = (
          -Y[jna32]*rate_eval.Na32__n_n_n_Mg29__weak__mo03  +
          +rho*Y[jhe4]*Y[jf29]*rate_eval.He4_F29__n_Na32  +
          +rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__n_Na32  +
          -rho*Y[jhe4]*Y[jna32]*rate_eval.He4_Na32__n_Al35  +
          -Y[jna32]*rate_eval.Na32__n_n_Mg30__weak__wc12  +
          +rho*Y[jhe4]*Y[jf28]*rate_eval.He4_F28__Na32  +
          -rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__n_Mg32  +
          +rho*Y[jn]*Y[jna31]*rate_eval.n_Na31__Na32  +
          -rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__Mg33  +
          +rho*Y[jp]*Y[jne31]*rate_eval.p_Ne31__Na32  +
          +Y[jne32]*rate_eval.Ne32__Na32__weak__wc17  +
          -rho*Y[jn]*Y[jna32]*rate_eval.n_Na32__Na33  +
          +Y[jne34]*rate_eval.Ne34__n_n_Na32__weak__mp17  +
          -Y[jna32]*rate_eval.Na32__Mg32__weak__wc12  +
          +rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__He4_Na32  +
          +Y[jne33]*rate_eval.Ne33__n_Na32__weak__mp17  +
          -rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__He4_Ne29  +
          -Y[jna32]*rate_eval.Na32__n_Mg31__weak__wc17  +
          -rho*Y[jhe4]*Y[jna32]*rate_eval.He4_Na32__Al36
       )

    dYdt[jna33] = (
          -Y[jna33]*rate_eval.Na33__n_n_n_Mg30__weak__mo03  +
          +rho*Y[jp]*Y[jne32]*rate_eval.p_Ne32__Na33  +
          -rho*Y[jn]*Y[jna33]*rate_eval.n_Na33__Na34  +
          -rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__p_Mg36  +
          -rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__n_Mg33  +
          +rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__n_Na33  +
          +rho*Y[jp]*Y[jne33]*rate_eval.p_Ne33__n_Na33  +
          -rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__He4_Ne30  +
          -rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__Al37  +
          +rho*Y[jn]*Y[jna32]*rate_eval.n_Na32__Na33  +
          -rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__n_Al36  +
          -rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__Mg34  +
          -Y[jna33]*rate_eval.Na33__n_Mg32__weak__wc17  +
          +Y[jne34]*rate_eval.Ne34__n_Na33__weak__mp17  +
          +rho*Y[jhe4]*Y[jf29]*rate_eval.He4_F29__Na33  +
          -Y[jna33]*rate_eval.Na33__Mg33__weak__wc12  +
          -Y[jna33]*rate_eval.Na33__n_n_Mg31__weak__wc12  +
          +Y[jne33]*rate_eval.Ne33__Na33__weak__mo03
       )

    dYdt[jna34] = (
          -Y[jna34]*rate_eval.Na34__n_n_n_Mg31__weak__mo03  +
          +rho*Y[jn]*Y[jna33]*rate_eval.n_Na33__Na34  +
          +rho*Y[jhe4]*Y[jf31]*rate_eval.He4_F31__n_Na34  +
          -rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__Mg35  +
          -rho*Y[jhe4]*Y[jna34]*rate_eval.He4_Na34__n_Al37  +
          +rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__n_Na34  +
          -rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__He4_Ne31  +
          +Y[jne34]*rate_eval.Ne34__Na34__weak__mo03  +
          -rho*Y[jhe4]*Y[jna34]*rate_eval.He4_Na34__Al38  +
          -rho*Y[jn]*Y[jna34]*rate_eval.n_Na34__Na35  +
          +rho*Y[jp]*Y[jne33]*rate_eval.p_Ne33__Na34  +
          +rho*Y[jhe4]*Y[jf30]*rate_eval.He4_F30__Na34  +
          +rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__He4_Na34  +
          -rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__n_Mg34  +
          -Y[jna34]*rate_eval.Na34__n_Mg33__weak__wc12  +
          -Y[jna34]*rate_eval.Na34__n_n_Mg32__weak__wc12  +
          -Y[jna34]*rate_eval.Na34__Mg34__weak__wc12
       )

    dYdt[jna35] = (
          -rho*Y[jhe4]*Y[jna35]*rate_eval.He4_Na35__n_Al38  +
          -rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__n_Mg35  +
          -Y[jna35]*rate_eval.Na35__n_n_n_Mg32__weak__mo03  +
          +rho*Y[jn]*Y[jna34]*rate_eval.n_Na34__Na35  +
          -rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__He4_Ne32  +
          +rho*Y[jhe4]*Y[jf31]*rate_eval.He4_F31__Na35  +
          -Y[jna35]*rate_eval.Na35__n_n_Mg33__weak__mp17  +
          +rho*Y[jp]*Y[jne34]*rate_eval.p_Ne34__Na35  +
          -rho*Y[jhe4]*Y[jna35]*rate_eval.He4_Na35__Al39  +
          -Y[jna35]*rate_eval.Na35__n_Mg34__weak__mp17  +
          +rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__He4_Na35  +
          -Y[jna35]*rate_eval.Na35__Mg35__weak__wc17  +
          -rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__Mg36  +
          -rho*Y[jn]*Y[jna35]*rate_eval.n_Na35__Na36
       )

    dYdt[jna36] = (
          -rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__n_Mg36  +
          -rho*Y[jhe4]*Y[jna36]*rate_eval.He4_Na36__n_Al39  +
          -Y[jna36]*rate_eval.Na36__n_Mg35__weak__mp17  +
          -rho*Y[jhe4]*Y[jna36]*rate_eval.He4_Na36__Al40  +
          -rho*Y[jn]*Y[jna36]*rate_eval.n_Na36__Na37  +
          -rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__Mg37  +
          -Y[jna36]*rate_eval.Na36__Mg36__weak__mo03  +
          -rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__He4_Ne33  +
          +rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__He4_Na36  +
          +rho*Y[jn]*Y[jna35]*rate_eval.n_Na35__Na36
       )

    dYdt[jna37] = (
          -rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__Mg38  +
          -rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__p_Mg40  +
          -rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__He4_Ne34  +
          -rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__n_Al40  +
          -rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__Al41  +
          +rho*Y[jn]*Y[jna36]*rate_eval.n_Na36__Na37  +
          -rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__n_Mg37  +
          -Y[jna37]*rate_eval.Na37__n_n_Mg35__weak__mp17  +
          -Y[jna37]*rate_eval.Na37__n_Mg36__weak__mp17  +
          -rho*Y[jn]*Y[jna37]*rate_eval.n_Na37__Na38
       )

    dYdt[jna38] = (
          -rho*Y[jhe4]*Y[jna38]*rate_eval.He4_Na38__n_Al41  +
          -Y[jna38]*rate_eval.Na38__Mg38__weak__mo03  +
          -rho*Y[jp]*Y[jna38]*rate_eval.p_Na38__Mg39  +
          +rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__He4_Na38  +
          -rho*Y[jp]*Y[jna38]*rate_eval.p_Na38__n_Mg38  +
          -Y[jna38]*rate_eval.Na38__n_Mg37__weak__mp17  +
          -rho*Y[jn]*Y[jna38]*rate_eval.n_Na38__Na39  +
          -rho*Y[jhe4]*Y[jna38]*rate_eval.He4_Na38__Al42  +
          +rho*Y[jn]*Y[jna37]*rate_eval.n_Na37__Na38
       )

    dYdt[jna39] = (
          -Y[jna39]*rate_eval.Na39__n_Mg38__weak__mp17  +
          -rho*Y[jp]*Y[jna39]*rate_eval.p_Na39__n_Mg39  +
          -rho*Y[jhe4]*Y[jna39]*rate_eval.He4_Na39__n_Al42  +
          -rho*Y[jhe4]*Y[jna39]*rate_eval.He4_Na39__Al43  +
          -Y[jna39]*rate_eval.Na39__n_n_Mg37__weak__mp17  +
          +rho*Y[jn]*Y[jna38]*rate_eval.n_Na38__Na39  +
          -rho*Y[jp]*Y[jna39]*rate_eval.p_Na39__Mg40
       )

    dYdt[jmg19] = (
          +rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__He4_Mg19  +
          -rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__He4_Ne16  +
          -rho*Y[jhe4]*Y[jmg19]*rate_eval.He4_Mg19__p_Al22  +
          -rho*Y[jhe4]*Y[jmg19]*rate_eval.He4_Mg19__Si23  +
          -rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__Mg20  +
          -rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__p_Na19
       )

    dYdt[jmg20] = (
          -rho*Y[jhe4]*Y[jmg20]*rate_eval.He4_Mg20__p_Al23  +
          -rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__p_Na20  +
          -Y[jmg20]*rate_eval.Mg20__p_Ne19__weak__wc12  +
          -rho*Y[jhe4]*Y[jmg20]*rate_eval.He4_Mg20__Si24  +
          +rho*Y[jn]*Y[jmg19]*rate_eval.n_Mg19__Mg20  +
          +rho*Y[jhe4]*Y[jne16]*rate_eval.He4_Ne16__Mg20  +
          -rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__Mg21  +
          +rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__He4_Mg20  +
          -rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__He4_Ne17  +
          +rho*Y[jp]*Y[jna19]*rate_eval.p_Na19__Mg20  +
          -Y[jmg20]*rate_eval.Mg20__Na20__weak__wc12
       )

    dYdt[jmg21] = (
          +rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__He4_Mg21  +
          -rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__He4_Ne18  +
          +rho*Y[jp]*Y[jna20]*rate_eval.p_Na20__Mg21  +
          +rho*Y[jhe4]*Y[jne17]*rate_eval.He4_Ne17__Mg21  +
          -rho*Y[jhe4]*Y[jmg21]*rate_eval.He4_Mg21__Si25  +
          +rho*Y[jn]*Y[jmg20]*rate_eval.n_Mg20__Mg21  +
          -rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__p_Na21  +
          -rho*Y[jhe4]*Y[jmg21]*rate_eval.He4_Mg21__p_Al24  +
          +Y[jsi22]*rate_eval.Si22__p_Mg21__weak__wc12  +
          +Y[jal21]*rate_eval.Al21__Mg21__weak__bqa_pos_  +
          -rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__Mg22  +
          -Y[jmg21]*rate_eval.Mg21__p_Ne20__weak__wc12  +
          +rho*Y[jn]*Y[jal21]*rate_eval.n_Al21__p_Mg21  +
          -Y[jmg21]*rate_eval.Mg21__Na21__weak__wc12  +
          -rho*Y[jp]*Y[jmg21]*rate_eval.p_Mg21__Al22
       )

    dYdt[jmg22] = (
          -Y[jmg22]*rate_eval.Mg22__Na22__weak__wc12  +
          -rho*Y[jn]*Y[jmg22]*rate_eval.n_Mg22__He4_Ne19  +
          +rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__p_Mg22  +
          -rho*Y[jhe4]*Y[jmg22]*rate_eval.He4_Mg22__p_Al25  +
          +rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__He4_Mg22  +
          +rho*Y[jhe4]*Y[jne18]*rate_eval.He4_Ne18__Mg22  +
          -rho*Y[jhe4]*Y[jmg22]*rate_eval.He4_Mg22__Si26  +
          -rho*Y[jp]*Y[jmg22]*rate_eval.p_Mg22__Al23  +
          -rho*Y[jn]*Y[jmg22]*rate_eval.n_Mg22__Mg23  +
          +rho*Y[jp]*Y[jna21]*rate_eval.p_Na21__Mg22  +
          +Y[jal22]*rate_eval.Al22__Mg22__weak__wc12  +
          +rho*Y[jhe4]*Y[jna19]*rate_eval.He4_Na19__p_Mg22  +
          -rho*Y[jn]*Y[jmg22]*rate_eval.n_Mg22__p_Na22  +
          +rho*Y[jn]*Y[jmg21]*rate_eval.n_Mg21__Mg22  +
          +Y[jsi23]*rate_eval.Si23__p_Mg22__weak__wc17
       )

    dYdt[jmg23] = (
          -rho*Y[jn]*Y[jmg23]*rate_eval.n_Mg23__C12_C12  +
          -rho*Y[jn]*Y[jmg23]*rate_eval.n_Mg23__He4_Ne20  +
          +Y[jsi24]*rate_eval.Si24__p_Mg23__weak__wc12  +
          -rho*Y[jhe4]*Y[jmg23]*rate_eval.He4_Mg23__Si27  +
          -rho*Y[jp]*Y[jmg23]*rate_eval.p_Mg23__Al24  +
          -rho*Y[jn]*Y[jmg23]*rate_eval.n_Mg23__Mg24  +
          +rho*Y[jn]*Y[jmg22]*rate_eval.n_Mg22__Mg23  +
          +rho*Y[jp]*Y[jna22]*rate_eval.p_Na22__Mg23  +
          +rho*Y[jhe4]*Y[jna20]*rate_eval.He4_Na20__p_Mg23  +
          +rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__p_Mg23  +
          +Y[jal23]*rate_eval.Al23__Mg23__weak__wc12  +
          +rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__He4_Mg23  +
          -Y[jmg23]*rate_eval.Mg23__Na23__weak__wc12  +
          +rho*Y[jhe4]*Y[jne19]*rate_eval.He4_Ne19__Mg23  +
          -rho*Y[jhe4]*Y[jmg23]*rate_eval.He4_Mg23__p_Al26  +
          +rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__n_Mg23
       )

    dYdt[jmg24] = (
          +rho*Y[jp]*Y[jal27]*rate_eval.p_Al27__He4_Mg24  +
          +rho*Y[jhe4]*Y[jne21]*rate_eval.He4_Ne21__n_Mg24  +
          +rho*Y[jc12]*Y[jo16]*rate_eval.C12_O16__He4_Mg24  +
          +rho*Y[jhe4]*Y[jne20]*rate_eval.He4_Ne20__Mg24  +
          -rho*Y[jp]*Y[jmg24]*rate_eval.p_Mg24__Al25  +
          -rho*Y[jn]*Y[jmg24]*rate_eval.n_Mg24__Mg25  +
          +rho*Y[jn]*Y[jmg23]*rate_eval.n_Mg23__Mg24  +
          +rho*Y[jp]*Y[jna23]*rate_eval.p_Na23__Mg24  +
          +rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__He4_Mg24  +
          +rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__p_Mg24  +
          +Y[jp28]*rate_eval.P28__He4_Mg24__weak__wc12  +
          +Y[jsi25]*rate_eval.Si25__p_Mg24__weak__wc12  +
          +Y[jal24]*rate_eval.Al24__Mg24__weak__wc12  +
          -rho*Y[jhe4]*Y[jmg24]*rate_eval.He4_Mg24__Si28  +
          +rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__n_Mg24  +
          +Y[jna24]*rate_eval.Na24__Mg24__weak__wc12  +
          -rho*Y[jp]*Y[jmg24]*rate_eval.p_Mg24__He4_Na21
       )

    dYdt[jmg25] = (
          +Y[jna25]*rate_eval.Na25__Mg25__weak__wc12  +
          +rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__He4_Mg25  +
          +rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__p_Mg25  +
          -rho*Y[jhe4]*Y[jmg25]*rate_eval.He4_Mg25__n_Si28  +
          +rho*Y[jhe4]*Y[jna22]*rate_eval.He4_Na22__p_Mg25  +
          +Y[jal25]*rate_eval.Al25__Mg25__weak__wc12  +
          +rho*Y[jn]*Y[jmg24]*rate_eval.n_Mg24__Mg25  +
          -rho*Y[jn]*Y[jmg25]*rate_eval.n_Mg25__Mg26  +
          -rho*Y[jhe4]*Y[jmg25]*rate_eval.He4_Mg25__Si29  +
          +rho*Y[jp]*Y[jna24]*rate_eval.p_Na24__Mg25  +
          +rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__n_Mg25  +
          -rho*Y[jp]*Y[jmg25]*rate_eval.p_Mg25__Al26  +
          +rho*Y[jhe4]*Y[jne21]*rate_eval.He4_Ne21__Mg25  +
          +rho*Y[jhe4]*Y[jne22]*rate_eval.He4_Ne22__n_Mg25
       )

    dYdt[jmg26] = (
          +Y[jna26]*rate_eval.Na26__Mg26__weak__wc12  +
          +rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__He4_Mg26  +
          +rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__p_Mg26  +
          +rho*Y[jhe4]*Y[jne23]*rate_eval.He4_Ne23__n_Mg26  +
          -rho*Y[jhe4]*Y[jmg26]*rate_eval.He4_Mg26__n_Si29  +
          +Y[jna27]*rate_eval.Na27__n_Mg26__weak__wc12  +
          +rho*Y[jhe4]*Y[jna23]*rate_eval.He4_Na23__p_Mg26  +
          -rho*Y[jn]*Y[jmg26]*rate_eval.n_Mg26__Mg27  +
          -rho*Y[jp]*Y[jmg26]*rate_eval.p_Mg26__Al27  +
          +rho*Y[jp]*Y[jna25]*rate_eval.p_Na25__Mg26  +
          -rho*Y[jhe4]*Y[jmg26]*rate_eval.He4_Mg26__Si30  +
          +rho*Y[jn]*Y[jmg25]*rate_eval.n_Mg25__Mg26  +
          +rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__n_Mg26  +
          +rho*Y[jhe4]*Y[jne22]*rate_eval.He4_Ne22__Mg26  +
          +Y[jal26]*rate_eval.Al26__Mg26__weak__wc12
       )

    dYdt[jmg27] = (
          +rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__He4_Mg27  +
          -Y[jmg27]*rate_eval.Mg27__Al27__weak__wc12  +
          -rho*Y[jhe4]*Y[jmg27]*rate_eval.He4_Mg27__n_Si30  +
          +rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__n_Mg27  +
          +rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__p_Mg27  +
          +rho*Y[jhe4]*Y[jne24]*rate_eval.He4_Ne24__n_Mg27  +
          -rho*Y[jn]*Y[jmg27]*rate_eval.n_Mg27__Mg28  +
          +Y[jna27]*rate_eval.Na27__Mg27__weak__wc12  +
          +rho*Y[jn]*Y[jmg26]*rate_eval.n_Mg26__Mg27  +
          -rho*Y[jp]*Y[jmg27]*rate_eval.p_Mg27__Al28  +
          +rho*Y[jp]*Y[jna26]*rate_eval.p_Na26__Mg27  +
          -rho*Y[jhe4]*Y[jmg27]*rate_eval.He4_Mg27__Si31  +
          -rho*Y[jp]*Y[jmg27]*rate_eval.p_Mg27__n_Al27  +
          +rho*Y[jhe4]*Y[jne23]*rate_eval.He4_Ne23__Mg27  +
          +Y[jna28]*rate_eval.Na28__n_Mg27__weak__wc12
       )

    dYdt[jmg28] = (
          +rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__He4_Mg28  +
          +rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__n_Mg28  +
          +rho*Y[jn]*Y[jmg27]*rate_eval.n_Mg27__Mg28  +
          -rho*Y[jn]*Y[jmg28]*rate_eval.n_Mg28__Mg29  +
          +rho*Y[jhe4]*Y[jne24]*rate_eval.He4_Ne24__Mg28  +
          -rho*Y[jhe4]*Y[jmg28]*rate_eval.He4_Mg28__Si32  +
          +Y[jna28]*rate_eval.Na28__Mg28__weak__wc12  +
          +Y[jna30]*rate_eval.Na30__n_n_Mg28__weak__wc12  +
          +rho*Y[jp]*Y[jna27]*rate_eval.p_Na27__Mg28  +
          -rho*Y[jhe4]*Y[jmg28]*rate_eval.He4_Mg28__n_Si31  +
          +rho*Y[jhe4]*Y[jne25]*rate_eval.He4_Ne25__n_Mg28  +
          +Y[jna31]*rate_eval.Na31__n_n_n_Mg28__weak__wc12  +
          +rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__p_Mg28  +
          -Y[jmg28]*rate_eval.Mg28__Al28__weak__wc12  +
          +Y[jna29]*rate_eval.Na29__n_Mg28__weak__wc12  +
          -rho*Y[jp]*Y[jmg28]*rate_eval.p_Mg28__Al29  +
          -rho*Y[jp]*Y[jmg28]*rate_eval.p_Mg28__n_Al28
       )

    dYdt[jmg29] = (
          +Y[jna32]*rate_eval.Na32__n_n_n_Mg29__weak__mo03  +
          +rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__He4_Mg29  +
          -rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__He4_Na26  +
          -rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__n_Al29  +
          +rho*Y[jhe4]*Y[jne26]*rate_eval.He4_Ne26__n_Mg29  +
          +rho*Y[jhe4]*Y[jne25]*rate_eval.He4_Ne25__Mg29  +
          +rho*Y[jn]*Y[jmg28]*rate_eval.n_Mg28__Mg29  +
          -rho*Y[jhe4]*Y[jmg29]*rate_eval.He4_Mg29__Si33  +
          -rho*Y[jn]*Y[jmg29]*rate_eval.n_Mg29__Mg30  +
          -rho*Y[jhe4]*Y[jmg29]*rate_eval.He4_Mg29__n_Si32  +
          +Y[jna30]*rate_eval.Na30__n_Mg29__weak__wc17  +
          +rho*Y[jp]*Y[jna28]*rate_eval.p_Na28__Mg29  +
          +Y[jna31]*rate_eval.Na31__n_n_Mg29__weak__wc12  +
          +rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__n_Mg29  +
          -Y[jmg29]*rate_eval.Mg29__Al29__weak__wc12  +
          -rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__Al30  +
          +Y[jna29]*rate_eval.Na29__Mg29__weak__wc12
       )

    dYdt[jmg30] = (
          +Y[jna33]*rate_eval.Na33__n_n_n_Mg30__weak__mo03  +
          +rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__He4_Mg30  +
          -rho*Y[jhe4]*Y[jmg30]*rate_eval.He4_Mg30__n_Si33  +
          -rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__n_Al30  +
          +rho*Y[jhe4]*Y[jne27]*rate_eval.He4_Ne27__n_Mg30  +
          +Y[jna31]*rate_eval.Na31__n_Mg30__weak__wc17  +
          +Y[jna32]*rate_eval.Na32__n_n_Mg30__weak__wc12  +
          -rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__Al31  +
          +rho*Y[jn]*Y[jmg29]*rate_eval.n_Mg29__Mg30  +
          -rho*Y[jhe4]*Y[jmg30]*rate_eval.He4_Mg30__Si34  +
          +rho*Y[jhe4]*Y[jne26]*rate_eval.He4_Ne26__Mg30  +
          -rho*Y[jn]*Y[jmg30]*rate_eval.n_Mg30__Mg31  +
          -rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__He4_Na27  +
          +rho*Y[jp]*Y[jna29]*rate_eval.p_Na29__Mg30  +
          +Y[jna30]*rate_eval.Na30__Mg30__weak__wc12  +
          -Y[jmg30]*rate_eval.Mg30__Al30__weak__wc12  +
          +rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__n_Mg30
       )

    dYdt[jmg31] = (
          +Y[jna34]*rate_eval.Na34__n_n_n_Mg31__weak__mo03  +
          +rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__He4_Mg31  +
          +rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__n_Mg31  +
          +rho*Y[jhe4]*Y[jne28]*rate_eval.He4_Ne28__n_Mg31  +
          -rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__n_Al31  +
          -rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__Al32  +
          +rho*Y[jhe4]*Y[jne27]*rate_eval.He4_Ne27__Mg31  +
          -rho*Y[jhe4]*Y[jmg31]*rate_eval.He4_Mg31__Si35  +
          -rho*Y[jn]*Y[jmg31]*rate_eval.n_Mg31__Mg32  +
          -rho*Y[jhe4]*Y[jmg31]*rate_eval.He4_Mg31__n_Si34  +
          -rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__He4_Na28  +
          +rho*Y[jn]*Y[jmg30]*rate_eval.n_Mg30__Mg31  +
          +rho*Y[jp]*Y[jna30]*rate_eval.p_Na30__Mg31  +
          -Y[jmg31]*rate_eval.Mg31__Al31__weak__wc12  +
          +Y[jna32]*rate_eval.Na32__n_Mg31__weak__wc17  +
          +Y[jna31]*rate_eval.Na31__Mg31__weak__wc12  +
          -Y[jmg31]*rate_eval.Mg31__n_Al30__weak__wc12  +
          +Y[jna33]*rate_eval.Na33__n_n_Mg31__weak__wc12
       )

    dYdt[jmg32] = (
          +rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__He4_Mg32  +
          +rho*Y[jp]*Y[jna31]*rate_eval.p_Na31__Mg32  +
          -rho*Y[jhe4]*Y[jmg32]*rate_eval.He4_Mg32__n_Si35  +
          -rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__He4_Na29  +
          +Y[jna35]*rate_eval.Na35__n_n_n_Mg32__weak__mo03  +
          -rho*Y[jn]*Y[jmg32]*rate_eval.n_Mg32__Mg33  +
          +rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__n_Mg32  +
          +rho*Y[jn]*Y[jmg31]*rate_eval.n_Mg31__Mg32  +
          -rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__Al33  +
          -Y[jmg32]*rate_eval.Mg32__n_Al31__weak__wc12  +
          +rho*Y[jhe4]*Y[jne29]*rate_eval.He4_Ne29__n_Mg32  +
          -rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__n_Al32  +
          -rho*Y[jhe4]*Y[jmg32]*rate_eval.He4_Mg32__Si36  +
          -Y[jmg32]*rate_eval.Mg32__Al32__weak__wc12  +
          +Y[jna32]*rate_eval.Na32__Mg32__weak__wc12  +
          +rho*Y[jhe4]*Y[jne28]*rate_eval.He4_Ne28__Mg32  +
          +Y[jna33]*rate_eval.Na33__n_Mg32__weak__wc17  +
          +Y[jna34]*rate_eval.Na34__n_n_Mg32__weak__wc12
       )

    dYdt[jmg33] = (
          +rho*Y[jhe4]*Y[jne29]*rate_eval.He4_Ne29__Mg33  +
          +rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__He4_Mg33  +
          -rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__He4_Na30  +
          +rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__n_Mg33  +
          +rho*Y[jhe4]*Y[jne30]*rate_eval.He4_Ne30__n_Mg33  +
          +rho*Y[jn]*Y[jmg32]*rate_eval.n_Mg32__Mg33  +
          -rho*Y[jhe4]*Y[jmg33]*rate_eval.He4_Mg33__n_Si36  +
          -rho*Y[jhe4]*Y[jmg33]*rate_eval.He4_Mg33__Si37  +
          -rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__n_Al33  +
          +rho*Y[jp]*Y[jna32]*rate_eval.p_Na32__Mg33  +
          -Y[jmg33]*rate_eval.Mg33__n_Al32__weak__wc12  +
          -Y[jmg33]*rate_eval.Mg33__n_n_Al31__weak__mp17  +
          +Y[jna35]*rate_eval.Na35__n_n_Mg33__weak__mp17  +
          -Y[jmg33]*rate_eval.Mg33__Al33__weak__wc12  +
          -rho*Y[jn]*Y[jmg33]*rate_eval.n_Mg33__Mg34  +
          +Y[jna34]*rate_eval.Na34__n_Mg33__weak__wc12  +
          +Y[jna33]*rate_eval.Na33__Mg33__weak__wc12  +
          -rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__Al34
       )

    dYdt[jmg34] = (
          -rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__Al35  +
          +rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__He4_Mg34  +
          -rho*Y[jhe4]*Y[jmg34]*rate_eval.He4_Mg34__n_Si37  +
          -rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__He4_Na31  +
          +rho*Y[jhe4]*Y[jne31]*rate_eval.He4_Ne31__n_Mg34  +
          -rho*Y[jhe4]*Y[jmg34]*rate_eval.He4_Mg34__Si38  +
          +rho*Y[jhe4]*Y[jne30]*rate_eval.He4_Ne30__Mg34  +
          +rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__n_Mg34  +
          -Y[jmg34]*rate_eval.Mg34__n_Al33__weak__mp17  +
          +rho*Y[jp]*Y[jna33]*rate_eval.p_Na33__Mg34  +
          +Y[jna35]*rate_eval.Na35__n_Mg34__weak__mp17  +
          +rho*Y[jn]*Y[jmg33]*rate_eval.n_Mg33__Mg34  +
          -Y[jmg34]*rate_eval.Mg34__Al34__weak__wc17  +
          +Y[jna34]*rate_eval.Na34__Mg34__weak__wc12  +
          -rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__n_Al34  +
          -rho*Y[jn]*Y[jmg34]*rate_eval.n_Mg34__Mg35
       )

    dYdt[jmg35] = (
          -Y[jmg35]*rate_eval.Mg35__n_n_n_Al32__weak__mo03  +
          +rho*Y[jp]*Y[jna34]*rate_eval.p_Na34__Mg35  +
          +rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__He4_Mg35  +
          -rho*Y[jhe4]*Y[jmg35]*rate_eval.He4_Mg35__n_Si38  +
          +rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__n_Mg35  +
          +Y[jna36]*rate_eval.Na36__n_Mg35__weak__mp17  +
          +rho*Y[jhe4]*Y[jne32]*rate_eval.He4_Ne32__n_Mg35  +
          -rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__n_Al35  +
          -rho*Y[jn]*Y[jmg35]*rate_eval.n_Mg35__Mg36  +
          +rho*Y[jhe4]*Y[jne31]*rate_eval.He4_Ne31__Mg35  +
          -Y[jmg35]*rate_eval.Mg35__n_Al34__weak__wc12  +
          -rho*Y[jhe4]*Y[jmg35]*rate_eval.He4_Mg35__Si39  +
          -Y[jmg35]*rate_eval.Mg35__n_n_Al33__weak__mp17  +
          -rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__He4_Na32  +
          +Y[jna35]*rate_eval.Na35__Mg35__weak__wc17  +
          -rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__Al36  +
          +Y[jna37]*rate_eval.Na37__n_n_Mg35__weak__mp17  +
          -Y[jmg35]*rate_eval.Mg35__Al35__weak__wc17  +
          +rho*Y[jn]*Y[jmg34]*rate_eval.n_Mg34__Mg35
       )

    dYdt[jmg36] = (
          -Y[jmg36]*rate_eval.Mg36__n_n_n_Al33__weak__mo03  +
          +rho*Y[jhe4]*Y[jne33]*rate_eval.He4_Ne33__n_Mg36  +
          +rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__n_Mg36  +
          -Y[jmg36]*rate_eval.Mg36__n_n_Al34__weak__mp17  +
          +rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__He4_Mg36  +
          +rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__p_Mg36  +
          -Y[jmg36]*rate_eval.Mg36__Al36__weak__wc17  +
          -rho*Y[jhe4]*Y[jmg36]*rate_eval.He4_Mg36__Si40  +
          +rho*Y[jn]*Y[jmg35]*rate_eval.n_Mg35__Mg36  +
          +Y[jna36]*rate_eval.Na36__Mg36__weak__mo03  +
          -rho*Y[jp]*Y[jmg36]*rate_eval.p_Mg36__Al37  +
          -rho*Y[jhe4]*Y[jmg36]*rate_eval.He4_Mg36__n_Si39  +
          -rho*Y[jp]*Y[jmg36]*rate_eval.p_Mg36__n_Al36  +
          +rho*Y[jhe4]*Y[jne32]*rate_eval.He4_Ne32__Mg36  +
          -Y[jmg36]*rate_eval.Mg36__n_Al35__weak__mp17  +
          +rho*Y[jp]*Y[jna35]*rate_eval.p_Na35__Mg36  +
          +Y[jna37]*rate_eval.Na37__n_Mg36__weak__mp17  +
          -rho*Y[jn]*Y[jmg36]*rate_eval.n_Mg36__Mg37
       )

    dYdt[jmg37] = (
          -Y[jmg37]*rate_eval.Mg37__n_n_n_Al34__weak__mo03  +
          +rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__He4_Mg37  +
          -rho*Y[jhe4]*Y[jmg37]*rate_eval.He4_Mg37__n_Si40  +
          -Y[jmg37]*rate_eval.Mg37__n_Al36__weak__mp17  +
          -Y[jmg37]*rate_eval.Mg37__Al37__weak__mo03  +
          -rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__n_Al37  +
          -rho*Y[jhe4]*Y[jmg37]*rate_eval.He4_Mg37__Si41  +
          -rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__Al38  +
          +rho*Y[jp]*Y[jna36]*rate_eval.p_Na36__Mg37  +
          -Y[jmg37]*rate_eval.Mg37__n_n_Al35__weak__mp17  +
          -rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__He4_Na34  +
          +rho*Y[jhe4]*Y[jne34]*rate_eval.He4_Ne34__n_Mg37  +
          +Y[jna39]*rate_eval.Na39__n_n_Mg37__weak__mp17  +
          +rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__n_Mg37  +
          +Y[jna38]*rate_eval.Na38__n_Mg37__weak__mp17  +
          +rho*Y[jhe4]*Y[jne33]*rate_eval.He4_Ne33__Mg37  +
          -rho*Y[jn]*Y[jmg37]*rate_eval.n_Mg37__Mg38  +
          +rho*Y[jn]*Y[jmg36]*rate_eval.n_Mg36__Mg37
       )

    dYdt[jmg38] = (
          +Y[jna39]*rate_eval.Na39__n_Mg38__weak__mp17  +
          -rho*Y[jhe4]*Y[jmg38]*rate_eval.He4_Mg38__n_Si41  +
          +rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__He4_Mg38  +
          +rho*Y[jp]*Y[jna37]*rate_eval.p_Na37__Mg38  +
          -rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__n_Al38  +
          +Y[jna38]*rate_eval.Na38__Mg38__weak__mo03  +
          -Y[jmg38]*rate_eval.Mg38__Al38__weak__mo03  +
          +rho*Y[jhe4]*Y[jne34]*rate_eval.He4_Ne34__Mg38  +
          -rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__Al39  +
          -Y[jmg38]*rate_eval.Mg38__n_n_Al36__weak__mp17  +
          -rho*Y[jhe4]*Y[jmg38]*rate_eval.He4_Mg38__Si42  +
          -Y[jmg38]*rate_eval.Mg38__n_n_n_Al35__weak__mo03  +
          -rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__He4_Na35  +
          -Y[jmg38]*rate_eval.Mg38__n_Al37__weak__mp17  +
          +rho*Y[jp]*Y[jna38]*rate_eval.p_Na38__n_Mg38  +
          +rho*Y[jn]*Y[jmg37]*rate_eval.n_Mg37__Mg38  +
          -rho*Y[jn]*Y[jmg38]*rate_eval.n_Mg38__Mg39
       )

    dYdt[jmg39] = (
          -Y[jmg39]*rate_eval.Mg39__n_n_n_Al36__weak__mo03  +
          -rho*Y[jhe4]*Y[jmg39]*rate_eval.He4_Mg39__n_Si42  +
          -rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__n_Al39  +
          +rho*Y[jp]*Y[jna39]*rate_eval.p_Na39__n_Mg39  +
          +rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__He4_Mg39  +
          -Y[jmg39]*rate_eval.Mg39__n_Al38__weak__mp17  +
          -rho*Y[jhe4]*Y[jmg39]*rate_eval.He4_Mg39__Si43  +
          -rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__Al40  +
          +rho*Y[jp]*Y[jna38]*rate_eval.p_Na38__Mg39  +
          -Y[jmg39]*rate_eval.Mg39__n_n_Al37__weak__mp17  +
          -Y[jmg39]*rate_eval.Mg39__Al39__weak__mo03  +
          -rho*Y[jn]*Y[jmg39]*rate_eval.n_Mg39__Mg40  +
          -rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__He4_Na36  +
          +rho*Y[jn]*Y[jmg38]*rate_eval.n_Mg38__Mg39
       )

    dYdt[jmg40] = (
          -Y[jmg40]*rate_eval.Mg40__n_n_n_Al37__weak__mo03  +
          -rho*Y[jhe4]*Y[jmg40]*rate_eval.He4_Mg40__n_Si43  +
          -rho*Y[jp]*Y[jmg40]*rate_eval.p_Mg40__n_Al40  +
          +rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__p_Mg40  +
          +rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__He4_Mg40  +
          -rho*Y[jhe4]*Y[jmg40]*rate_eval.He4_Mg40__Si44  +
          -Y[jmg40]*rate_eval.Mg40__n_n_Al38__weak__mp17  +
          -Y[jmg40]*rate_eval.Mg40__n_Al39__weak__mp17  +
          +rho*Y[jn]*Y[jmg39]*rate_eval.n_Mg39__Mg40  +
          +rho*Y[jp]*Y[jna39]*rate_eval.p_Na39__Mg40  +
          -rho*Y[jp]*Y[jmg40]*rate_eval.p_Mg40__Al41  +
          -rho*Y[jn]*Y[jmg40]*rate_eval.n_Mg40__Mg41
       )

    dYdt[jmg41] = (
          -rho*Y[jhe4]*Y[jmg41]*rate_eval.He4_Mg41__Si45  +
          -Y[jmg41]*rate_eval.Mg41__n_Al40__weak__mp17  +
          -rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__Al42  +
          -rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__n_Al41  +
          -rho*Y[jhe4]*Y[jmg41]*rate_eval.He4_Mg41__n_Si44  +
          -Y[jmg41]*rate_eval.Mg41__Al41__weak__mo03  +
          -rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__He4_Na38  +
          +rho*Y[jn]*Y[jmg40]*rate_eval.n_Mg40__Mg41
       )

    dYdt[jal21] = (
          +rho*Y[jn]*Y[jp24]*rate_eval.n_P24__He4_Al21  +
          -rho*Y[jhe4]*Y[jal21]*rate_eval.He4_Al21__p_Si24  +
          -rho*Y[jn]*Y[jal21]*rate_eval.n_Al21__Al22  +
          -Y[jal21]*rate_eval.Al21__Mg21__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[jal21]*rate_eval.He4_Al21__P25  +
          -rho*Y[jn]*Y[jal21]*rate_eval.n_Al21__p_Mg21
       )

    dYdt[jal22] = (
          +rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__p_Al22  +
          -rho*Y[jhe4]*Y[jal22]*rate_eval.He4_Al22__p_Si25  +
          -rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__He4_Na19  +
          -rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__p_Mg22  +
          +rho*Y[jhe4]*Y[jmg19]*rate_eval.He4_Mg19__p_Al22  +
          -Y[jal22]*rate_eval.Al22__Mg22__weak__wc12  +
          -Y[jal22]*rate_eval.Al22__p_p_Ne20__weak__wc12  +
          +rho*Y[jn]*Y[jal21]*rate_eval.n_Al21__Al22  +
          +rho*Y[jn]*Y[jp25]*rate_eval.n_P25__He4_Al22  +
          -rho*Y[jp]*Y[jal22]*rate_eval.p_Al22__Si23  +
          -Y[jal22]*rate_eval.Al22__He4_Ne18__weak__wc12  +
          -rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__Al23  +
          -Y[jal22]*rate_eval.Al22__p_Na21__weak__wc17  +
          -rho*Y[jhe4]*Y[jal22]*rate_eval.He4_Al22__P26  +
          +Y[jsi22]*rate_eval.Si22__Al22__weak__wc12  +
          +rho*Y[jp]*Y[jmg21]*rate_eval.p_Mg21__Al22
       )

    dYdt[jal23] = (
          +rho*Y[jhe4]*Y[jna19]*rate_eval.He4_Na19__Al23  +
          +rho*Y[jn]*Y[jp26]*rate_eval.n_P26__He4_Al23  +
          +rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__p_Al23  +
          -rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__He4_Na20  +
          +rho*Y[jhe4]*Y[jmg20]*rate_eval.He4_Mg20__p_Al23  +
          +rho*Y[jp]*Y[jmg22]*rate_eval.p_Mg22__Al23  +
          -rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__Al24  +
          -rho*Y[jp]*Y[jal23]*rate_eval.p_Al23__Si24  +
          +Y[jsi23]*rate_eval.Si23__Al23__weak__wc12  +
          -rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__p_Mg23  +
          -Y[jal23]*rate_eval.Al23__Mg23__weak__wc12  +
          -rho*Y[jhe4]*Y[jal23]*rate_eval.He4_Al23__p_Si26  +
          -Y[jal23]*rate_eval.Al23__p_Na22__weak__wc12  +
          +rho*Y[jn]*Y[jal22]*rate_eval.n_Al22__Al23  +
          -rho*Y[jhe4]*Y[jal23]*rate_eval.He4_Al23__P27
       )

    dYdt[jal24] = (
          +rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__p_Al24  +
          +rho*Y[jn]*Y[jp27]*rate_eval.n_P27__He4_Al24  +
          -rho*Y[jhe4]*Y[jal24]*rate_eval.He4_Al24__p_Si27  +
          -rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__He4_Na21  +
          -rho*Y[jp]*Y[jal24]*rate_eval.p_Al24__Si25  +
          -rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__Al25  +
          +rho*Y[jp]*Y[jmg23]*rate_eval.p_Mg23__Al24  +
          +rho*Y[jhe4]*Y[jna20]*rate_eval.He4_Na20__Al24  +
          +rho*Y[jn]*Y[jal23]*rate_eval.n_Al23__Al24  +
          -Y[jal24]*rate_eval.Al24__p_Na23__weak__wc12  +
          -rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__p_Mg24  +
          -rho*Y[jhe4]*Y[jal24]*rate_eval.He4_Al24__P28  +
          -Y[jal24]*rate_eval.Al24__He4_Ne20__weak__wc12  +
          +Y[jsi24]*rate_eval.Si24__Al24__weak__wc12  +
          +rho*Y[jhe4]*Y[jmg21]*rate_eval.He4_Mg21__p_Al24  +
          -Y[jal24]*rate_eval.Al24__Mg24__weak__wc12
       )

    dYdt[jal25] = (
          -rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__Al26  +
          -rho*Y[jhe4]*Y[jal25]*rate_eval.He4_Al25__P29  +
          -rho*Y[jp]*Y[jal25]*rate_eval.p_Al25__Si26  +
          +rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__p_Al25  +
          -rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__p_Mg25  +
          -rho*Y[jhe4]*Y[jal25]*rate_eval.He4_Al25__p_Si28  +
          +rho*Y[jhe4]*Y[jmg22]*rate_eval.He4_Mg22__p_Al25  +
          -Y[jal25]*rate_eval.Al25__Mg25__weak__wc12  +
          +rho*Y[jn]*Y[jal24]*rate_eval.n_Al24__Al25  +
          +rho*Y[jp]*Y[jmg24]*rate_eval.p_Mg24__Al25  +
          +Y[js27]*rate_eval.S27__p_p_Al25__weak__wc12  +
          +rho*Y[jhe4]*Y[jna21]*rate_eval.He4_Na21__Al25  +
          +Y[jsi25]*rate_eval.Si25__Al25__weak__wc12  +
          -rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__He4_Na22  +
          +rho*Y[jn]*Y[jp28]*rate_eval.n_P28__He4_Al25
       )

    dYdt[jal26] = (
          +rho*Y[jn]*Y[jal25]*rate_eval.n_Al25__Al26  +
          +Y[jp27]*rate_eval.P27__p_Al26__weak__wc12  +
          -rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__He4_Na23  +
          -rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__p_Mg26  +
          +rho*Y[jn]*Y[jp29]*rate_eval.n_P29__He4_Al26  +
          -rho*Y[jhe4]*Y[jal26]*rate_eval.He4_Al26__p_Si29  +
          +rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__p_Al26  +
          -rho*Y[jp]*Y[jal26]*rate_eval.p_Al26__Si27  +
          -rho*Y[jhe4]*Y[jal26]*rate_eval.He4_Al26__P30  +
          -rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__Al27  +
          +Y[jsi26]*rate_eval.Si26__Al26__weak__wc12  +
          +rho*Y[jhe4]*Y[jna22]*rate_eval.He4_Na22__Al26  +
          -Y[jal26]*rate_eval.Al26__Mg26__weak__wc12  +
          +rho*Y[jhe4]*Y[jmg23]*rate_eval.He4_Mg23__p_Al26  +
          +rho*Y[jp]*Y[jmg25]*rate_eval.p_Mg25__Al26
       )

    dYdt[jal27] = (
          +Y[jmg27]*rate_eval.Mg27__Al27__weak__wc12  +
          -rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__p_Si30  +
          -rho*Y[jp]*Y[jal27]*rate_eval.p_Al27__He4_Mg24  +
          +rho*Y[jc12]*Y[jo16]*rate_eval.C12_O16__p_Al27  +
          -rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__P31  +
          +rho*Y[jn]*Y[jal26]*rate_eval.n_Al26__Al27  +
          +rho*Y[jp]*Y[jmg26]*rate_eval.p_Mg26__Al27  +
          +rho*Y[jhe4]*Y[jna23]*rate_eval.He4_Na23__Al27  +
          -rho*Y[jn]*Y[jal27]*rate_eval.n_Al27__Al28  +
          +rho*Y[jp]*Y[jmg27]*rate_eval.p_Mg27__n_Al27  +
          +rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__p_Al27  +
          +Y[jp28]*rate_eval.P28__p_Al27__weak__wc12  +
          +rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__n_Al27  +
          -rho*Y[jp]*Y[jal27]*rate_eval.p_Al27__Si28  +
          +Y[jsi27]*rate_eval.Si27__Al27__weak__wc12  +
          -rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__n_P30
       )

    dYdt[jal28] = (
          -rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__He4_Mg25  +
          -rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__n_P31  +
          -rho*Y[jn]*Y[jal28]*rate_eval.n_Al28__Al29  +
          -rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__Si29  +
          +rho*Y[jp]*Y[jmg27]*rate_eval.p_Mg27__Al28  +
          -rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__p_Si31  +
          +rho*Y[jhe4]*Y[jna24]*rate_eval.He4_Na24__Al28  +
          -rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__n_Si28  +
          +rho*Y[jn]*Y[jal27]*rate_eval.n_Al27__Al28  +
          +rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__n_Al28  +
          -rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__P32  +
          +Y[jmg28]*rate_eval.Mg28__Al28__weak__wc12  +
          -Y[jal28]*rate_eval.Al28__Si28__weak__wc12  +
          +rho*Y[jp]*Y[jmg28]*rate_eval.p_Mg28__n_Al28
       )

    dYdt[jal29] = (
          +rho*Y[jhe4]*Y[jna25]*rate_eval.He4_Na25__Al29  +
          -rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__n_P32  +
          -rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__He4_Mg26  +
          -rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__n_Si29  +
          +rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__n_Al29  +
          +rho*Y[jhe4]*Y[jna26]*rate_eval.He4_Na26__n_Al29  +
          -rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__p_Si32  +
          +rho*Y[jn]*Y[jal28]*rate_eval.n_Al28__Al29  +
          -rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__P33  +
          -Y[jal29]*rate_eval.Al29__Si29__weak__wc12  +
          +Y[jmg29]*rate_eval.Mg29__Al29__weak__wc12  +
          -rho*Y[jn]*Y[jal29]*rate_eval.n_Al29__Al30  +
          +rho*Y[jp]*Y[jmg28]*rate_eval.p_Mg28__Al29  +
          -rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__Si30
       )

    dYdt[jal30] = (
          -rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__He4_Mg27  +
          -rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__n_Si30  +
          +rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__n_Al30  +
          -Y[jal30]*rate_eval.Al30__Si30__weak__wc12  +
          +rho*Y[jhe4]*Y[jna27]*rate_eval.He4_Na27__n_Al30  +
          -rho*Y[jhe4]*Y[jal30]*rate_eval.He4_Al30__P34  +
          -rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__Si31  +
          +rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__He4_Al30  +
          +rho*Y[jp]*Y[jmg29]*rate_eval.p_Mg29__Al30  +
          +rho*Y[jhe4]*Y[jna26]*rate_eval.He4_Na26__Al30  +
          +rho*Y[jn]*Y[jal29]*rate_eval.n_Al29__Al30  +
          -rho*Y[jn]*Y[jal30]*rate_eval.n_Al30__Al31  +
          -rho*Y[jhe4]*Y[jal30]*rate_eval.He4_Al30__n_P33  +
          +Y[jmg30]*rate_eval.Mg30__Al30__weak__wc12  +
          +Y[jmg31]*rate_eval.Mg31__n_Al30__weak__wc12
       )

    dYdt[jal31] = (
          -rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__p_Si34  +
          -rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__n_P34  +
          -rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__He4_Mg28  +
          +rho*Y[jhe4]*Y[jna28]*rate_eval.He4_Na28__n_Al31  +
          +rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__n_Al31  +
          +rho*Y[jhe4]*Y[jna27]*rate_eval.He4_Na27__Al31  +
          -rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__Si32  +
          -rho*Y[jn]*Y[jal31]*rate_eval.n_Al31__Al32  +
          +rho*Y[jp]*Y[jmg30]*rate_eval.p_Mg30__Al31  +
          +Y[jmg32]*rate_eval.Mg32__n_Al31__weak__wc12  +
          -rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__P35  +
          +Y[jmg33]*rate_eval.Mg33__n_n_Al31__weak__mp17  +
          -rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__n_Si31  +
          -Y[jal31]*rate_eval.Al31__Si31__weak__wc12  +
          +Y[jmg31]*rate_eval.Mg31__Al31__weak__wc12  +
          +rho*Y[jn]*Y[jal30]*rate_eval.n_Al30__Al31
       )

    dYdt[jal32] = (
          +Y[jmg35]*rate_eval.Mg35__n_n_n_Al32__weak__mo03  +
          -rho*Y[jhe4]*Y[jal32]*rate_eval.He4_Al32__n_P35  +
          +rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__He4_Al32  +
          -rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__He4_Mg29  +
          -rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__n_Si32  +
          -rho*Y[jhe4]*Y[jal32]*rate_eval.He4_Al32__P36  +
          +rho*Y[jp]*Y[jmg31]*rate_eval.p_Mg31__Al32  +
          -Y[jal32]*rate_eval.Al32__Si32__weak__wc12  +
          +rho*Y[jn]*Y[jal31]*rate_eval.n_Al31__Al32  +
          +rho*Y[jhe4]*Y[jna28]*rate_eval.He4_Na28__Al32  +
          +Y[jmg33]*rate_eval.Mg33__n_Al32__weak__wc12  +
          +rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__n_Al32  +
          -rho*Y[jn]*Y[jal32]*rate_eval.n_Al32__Al33  +
          +rho*Y[jhe4]*Y[jna29]*rate_eval.He4_Na29__n_Al32  +
          +Y[jmg32]*rate_eval.Mg32__Al32__weak__wc12  +
          -Y[jal32]*rate_eval.Al32__n_Si31__weak__wc12  +
          -rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__Si33
       )

    dYdt[jal33] = (
          +Y[jmg36]*rate_eval.Mg36__n_n_n_Al33__weak__mo03  +
          +rho*Y[jp]*Y[jsi36]*rate_eval.p_Si36__He4_Al33  +
          -rho*Y[jhe4]*Y[jal33]*rate_eval.He4_Al33__n_P36  +
          -rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__He4_Mg30  +
          -rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__n_Si33  +
          +rho*Y[jhe4]*Y[jna29]*rate_eval.He4_Na29__Al33  +
          -rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__Si34  +
          +rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__n_Al33  +
          +rho*Y[jp]*Y[jmg32]*rate_eval.p_Mg32__Al33  +
          +rho*Y[jn]*Y[jal32]*rate_eval.n_Al32__Al33  +
          +Y[jmg34]*rate_eval.Mg34__n_Al33__weak__mp17  +
          -Y[jal33]*rate_eval.Al33__Si33__weak__wc12  +
          +Y[jmg35]*rate_eval.Mg35__n_n_Al33__weak__mp17  +
          +Y[jmg33]*rate_eval.Mg33__Al33__weak__wc12  +
          +rho*Y[jhe4]*Y[jna30]*rate_eval.He4_Na30__n_Al33  +
          -rho*Y[jn]*Y[jal33]*rate_eval.n_Al33__Al34  +
          -rho*Y[jhe4]*Y[jal33]*rate_eval.He4_Al33__P37  +
          -Y[jal33]*rate_eval.Al33__n_Si32__weak__wc12
       )

    dYdt[jal34] = (
          +Y[jmg37]*rate_eval.Mg37__n_n_n_Al34__weak__mo03  +
          +Y[jmg36]*rate_eval.Mg36__n_n_Al34__weak__mp17  +
          +rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__He4_Al34  +
          -rho*Y[jhe4]*Y[jal34]*rate_eval.He4_Al34__n_P37  +
          -rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__He4_Mg31  +
          -rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__n_Si34  +
          +rho*Y[jhe4]*Y[jna31]*rate_eval.He4_Na31__n_Al34  +
          -rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__Si35  +
          -Y[jal34]*rate_eval.Al34__n_Si33__weak__wc12  +
          -rho*Y[jhe4]*Y[jal34]*rate_eval.He4_Al34__P38  +
          -rho*Y[jn]*Y[jal34]*rate_eval.n_Al34__Al35  +
          +rho*Y[jhe4]*Y[jna30]*rate_eval.He4_Na30__Al34  +
          +Y[jmg35]*rate_eval.Mg35__n_Al34__weak__wc12  +
          -Y[jal34]*rate_eval.Al34__Si34__weak__wc12  +
          +Y[jmg34]*rate_eval.Mg34__Al34__weak__wc17  +
          +rho*Y[jn]*Y[jal33]*rate_eval.n_Al33__Al34  +
          +rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__n_Al34  +
          +rho*Y[jp]*Y[jmg33]*rate_eval.p_Mg33__Al34
       )

    dYdt[jal35] = (
          +rho*Y[jp]*Y[jmg34]*rate_eval.p_Mg34__Al35  +
          -rho*Y[jhe4]*Y[jal35]*rate_eval.He4_Al35__n_P38  +
          -rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__He4_Mg32  +
          -rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__n_Si35  +
          +rho*Y[jhe4]*Y[jna32]*rate_eval.He4_Na32__n_Al35  +
          -rho*Y[jhe4]*Y[jal35]*rate_eval.He4_Al35__P39  +
          +rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__n_Al35  +
          +rho*Y[jhe4]*Y[jna31]*rate_eval.He4_Na31__Al35  +
          -rho*Y[jn]*Y[jal35]*rate_eval.n_Al35__Al36  +
          +rho*Y[jn]*Y[jal34]*rate_eval.n_Al34__Al35  +
          +Y[jmg37]*rate_eval.Mg37__n_n_Al35__weak__mp17  +
          -rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__Si36  +
          +Y[jmg38]*rate_eval.Mg38__n_n_n_Al35__weak__mo03  +
          -Y[jal35]*rate_eval.Al35__n_Si34__weak__wc12  +
          +Y[jmg36]*rate_eval.Mg36__n_Al35__weak__mp17  +
          +Y[jmg35]*rate_eval.Mg35__Al35__weak__wc17  +
          +rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__He4_Al35  +
          -Y[jal35]*rate_eval.Al35__Si35__weak__wc12
       )

    dYdt[jal36] = (
          -rho*Y[jn]*Y[jal36]*rate_eval.n_Al36__Al37  +
          +Y[jmg39]*rate_eval.Mg39__n_n_n_Al36__weak__mo03  +
          -rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__p_Si39  +
          -rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__n_P39  +
          -rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__He4_Mg33  +
          -rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__n_Si36  +
          +Y[jmg37]*rate_eval.Mg37__n_Al36__weak__mp17  +
          -Y[jal36]*rate_eval.Al36__Si36__weak__wc17  +
          +Y[jmg36]*rate_eval.Mg36__Al36__weak__wc17  +
          -rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__P40  +
          -rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__Si37  +
          +rho*Y[jn]*Y[jal35]*rate_eval.n_Al35__Al36  +
          +Y[jmg38]*rate_eval.Mg38__n_n_Al36__weak__mp17  +
          +rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__n_Al36  +
          +rho*Y[jp]*Y[jmg36]*rate_eval.p_Mg36__n_Al36  +
          -Y[jal36]*rate_eval.Al36__n_n_Si34__weak__mp17  +
          +rho*Y[jp]*Y[jmg35]*rate_eval.p_Mg35__Al36  +
          +rho*Y[jhe4]*Y[jna32]*rate_eval.He4_Na32__Al36  +
          -Y[jal36]*rate_eval.Al36__n_Si35__weak__mp17
       )

    dYdt[jal37] = (
          -Y[jal37]*rate_eval.Al37__n_n_n_Si34__weak__mo03  +
          +Y[jmg40]*rate_eval.Mg40__n_n_n_Al37__weak__mo03  +
          -Y[jal37]*rate_eval.Al37__Si37__weak__wc17  +
          +rho*Y[jn]*Y[jal36]*rate_eval.n_Al36__Al37  +
          -rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__He4_Mg34  +
          -rho*Y[jhe4]*Y[jal37]*rate_eval.He4_Al37__n_P40  +
          +rho*Y[jhe4]*Y[jna34]*rate_eval.He4_Na34__n_Al37  +
          -rho*Y[jn]*Y[jal37]*rate_eval.n_Al37__Al38  +
          -Y[jal37]*rate_eval.Al37__n_Si36__weak__mp17  +
          +Y[jmg37]*rate_eval.Mg37__Al37__weak__mo03  +
          +rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__n_Al37  +
          -rho*Y[jhe4]*Y[jal37]*rate_eval.He4_Al37__P41  +
          -rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__Si38  +
          +rho*Y[jhe4]*Y[jna33]*rate_eval.He4_Na33__Al37  +
          +rho*Y[jp]*Y[jmg36]*rate_eval.p_Mg36__Al37  +
          +Y[jmg39]*rate_eval.Mg39__n_n_Al37__weak__mp17  +
          +rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__He4_Al37  +
          -Y[jal37]*rate_eval.Al37__n_n_Si35__weak__mp17  +
          -rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__n_Si37  +
          +Y[jmg38]*rate_eval.Mg38__n_Al37__weak__mp17
       )

    dYdt[jal38] = (
          -Y[jal38]*rate_eval.Al38__n_n_n_Si35__weak__mo03  +
          -rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__n_P41  +
          -rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__p_Si41  +
          -rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__He4_Mg35  +
          +rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__n_Al38  +
          -rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__n_Si38  +
          +rho*Y[jhe4]*Y[jna35]*rate_eval.He4_Na35__n_Al38  +
          +Y[jmg38]*rate_eval.Mg38__Al38__weak__mo03  +
          +rho*Y[jn]*Y[jal37]*rate_eval.n_Al37__Al38  +
          +Y[jmg39]*rate_eval.Mg39__n_Al38__weak__mp17  +
          -rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__P42  +
          -rho*Y[jn]*Y[jal38]*rate_eval.n_Al38__Al39  +
          +rho*Y[jp]*Y[jmg37]*rate_eval.p_Mg37__Al38  +
          +rho*Y[jhe4]*Y[jna34]*rate_eval.He4_Na34__Al38  +
          -Y[jal38]*rate_eval.Al38__n_n_Si36__weak__mp17  +
          +Y[jmg40]*rate_eval.Mg40__n_n_Al38__weak__mp17  +
          -rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__Si39  +
          -Y[jal38]*rate_eval.Al38__n_Si37__weak__mp17  +
          -Y[jal38]*rate_eval.Al38__Si38__weak__wc17
       )

    dYdt[jal39] = (
          -Y[jal39]*rate_eval.Al39__n_n_n_Si36__weak__mo03  +
          -rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__He4_Mg36  +
          -rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__n_Si39  +
          -rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__p_Si42  +
          +rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__n_Al39  +
          +rho*Y[jhe4]*Y[jna36]*rate_eval.He4_Na36__n_Al39  +
          -rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__Si40  +
          -Y[jal39]*rate_eval.Al39__n_Si38__weak__mp17  +
          -Y[jal39]*rate_eval.Al39__n_n_Si37__weak__mp17  +
          +rho*Y[jn]*Y[jal38]*rate_eval.n_Al38__Al39  +
          +rho*Y[jp]*Y[jmg38]*rate_eval.p_Mg38__Al39  +
          +Y[jmg39]*rate_eval.Mg39__Al39__weak__mo03  +
          -rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__P43  +
          +rho*Y[jhe4]*Y[jna35]*rate_eval.He4_Na35__Al39  +
          -rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__n_P42  +
          +Y[jmg40]*rate_eval.Mg40__n_Al39__weak__mp17  +
          -Y[jal39]*rate_eval.Al39__Si39__weak__wc17  +
          -rho*Y[jn]*Y[jal39]*rate_eval.n_Al39__Al40
       )

    dYdt[jal40] = (
          -rho*Y[jhe4]*Y[jal40]*rate_eval.He4_Al40__p_Si43  +
          -rho*Y[jhe4]*Y[jal40]*rate_eval.He4_Al40__n_P43  +
          -rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__He4_Mg37  +
          -rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__n_Si40  +
          +rho*Y[jp]*Y[jmg40]*rate_eval.p_Mg40__n_Al40  +
          -Y[jal40]*rate_eval.Al40__n_n_n_Si37__weak__mo03  +
          +rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__n_Al40  +
          +rho*Y[jhe4]*Y[jna36]*rate_eval.He4_Na36__Al40  +
          -rho*Y[jhe4]*Y[jal40]*rate_eval.He4_Al40__P44  +
          -rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__Si41  +
          -rho*Y[jn]*Y[jal40]*rate_eval.n_Al40__Al41  +
          +rho*Y[jp]*Y[jmg39]*rate_eval.p_Mg39__Al40  +
          +Y[jmg41]*rate_eval.Mg41__n_Al40__weak__mp17  +
          -Y[jal40]*rate_eval.Al40__n_Si39__weak__mp17  +
          -Y[jal40]*rate_eval.Al40__n_n_Si38__weak__mp17  +
          -Y[jal40]*rate_eval.Al40__Si40__weak__mo03  +
          +rho*Y[jn]*Y[jal39]*rate_eval.n_Al39__Al40
       )

    dYdt[jal41] = (
          -Y[jal41]*rate_eval.Al41__n_n_n_Si38__weak__mo03  +
          -rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__He4_Mg38  +
          -rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__n_Si41  +
          +rho*Y[jhe4]*Y[jna38]*rate_eval.He4_Na38__n_Al41  +
          -Y[jal41]*rate_eval.Al41__n_Si40__weak__mp17  +
          -Y[jal41]*rate_eval.Al41__Si41__weak__mo03  +
          +rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__He4_Al41  +
          +rho*Y[jn]*Y[jal40]*rate_eval.n_Al40__Al41  +
          -rho*Y[jhe4]*Y[jal41]*rate_eval.He4_Al41__P45  +
          +rho*Y[jhe4]*Y[jna37]*rate_eval.He4_Na37__Al41  +
          -Y[jal41]*rate_eval.Al41__n_n_Si39__weak__mp17  +
          -rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__Si42  +
          +rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__n_Al41  +
          +Y[jmg41]*rate_eval.Mg41__Al41__weak__mo03  +
          -rho*Y[jhe4]*Y[jal41]*rate_eval.He4_Al41__n_P44  +
          +rho*Y[jp]*Y[jmg40]*rate_eval.p_Mg40__Al41  +
          -rho*Y[jn]*Y[jal41]*rate_eval.n_Al41__Al42
       )

    dYdt[jal42] = (
          -Y[jal42]*rate_eval.Al42__n_n_n_Si39__weak__mo03  +
          +rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__He4_Al42  +
          -rho*Y[jhe4]*Y[jal42]*rate_eval.He4_Al42__n_P45  +
          -rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__He4_Mg39  +
          +rho*Y[jhe4]*Y[jna39]*rate_eval.He4_Na39__n_Al42  +
          -rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__Si43  +
          -rho*Y[jhe4]*Y[jal42]*rate_eval.He4_Al42__P46  +
          -Y[jal42]*rate_eval.Al42__Si42__weak__mo03  +
          +rho*Y[jp]*Y[jmg41]*rate_eval.p_Mg41__Al42  +
          -Y[jal42]*rate_eval.Al42__n_n_Si40__weak__mo03  +
          -Y[jal42]*rate_eval.Al42__n_Si41__weak__mp17  +
          -rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__n_Si42  +
          +rho*Y[jhe4]*Y[jna38]*rate_eval.He4_Na38__Al42  +
          +rho*Y[jn]*Y[jal41]*rate_eval.n_Al41__Al42  +
          -rho*Y[jn]*Y[jal42]*rate_eval.n_Al42__Al43
       )

    dYdt[jal43] = (
          -Y[jal43]*rate_eval.Al43__n_n_n_Si40__weak__mo03  +
          -rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__n_Si43  +
          -rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__He4_Mg40  +
          -rho*Y[jhe4]*Y[jal43]*rate_eval.He4_Al43__P47  +
          +rho*Y[jhe4]*Y[jna39]*rate_eval.He4_Na39__Al43  +
          -rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__Si44  +
          -Y[jal43]*rate_eval.Al43__n_n_Si41__weak__mp17  +
          -Y[jal43]*rate_eval.Al43__n_Si42__weak__mp17  +
          -rho*Y[jhe4]*Y[jal43]*rate_eval.He4_Al43__n_P46  +
          +rho*Y[jn]*Y[jal42]*rate_eval.n_Al42__Al43
       )

    dYdt[jsi22] = (
          -rho*Y[jhe4]*Y[jsi22]*rate_eval.He4_Si22__p_P25  +
          -rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__He4_Mg19  +
          -rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__p_Al22  +
          -rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__Si23  +
          -Y[jsi22]*rate_eval.Si22__p_Mg21__weak__wc12  +
          -rho*Y[jhe4]*Y[jsi22]*rate_eval.He4_Si22__S26  +
          -Y[jsi22]*rate_eval.Si22__Al22__weak__wc12
       )

    dYdt[jsi23] = (
          +rho*Y[jn]*Y[js26]*rate_eval.n_S26__He4_Si23  +
          -rho*Y[jhe4]*Y[jsi23]*rate_eval.He4_Si23__p_P26  +
          -rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__p_Al23  +
          -rho*Y[jhe4]*Y[jsi23]*rate_eval.He4_Si23__S27  +
          +rho*Y[jn]*Y[jsi22]*rate_eval.n_Si22__Si23  +
          +rho*Y[jhe4]*Y[jmg19]*rate_eval.He4_Mg19__Si23  +
          -Y[jsi23]*rate_eval.Si23__p_p_Na21__weak__wc12  +
          -Y[jsi23]*rate_eval.Si23__Al23__weak__wc12  +
          -rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__He4_Mg20  +
          -rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__Si24  +
          -Y[jsi23]*rate_eval.Si23__p_Mg22__weak__wc17  +
          +rho*Y[jp]*Y[jal22]*rate_eval.p_Al22__Si23
       )

    dYdt[jsi24] = (
          -rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__p_Al24  +
          -rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__He4_Mg21  +
          +rho*Y[jn]*Y[jp24]*rate_eval.n_P24__p_Si24  +
          -rho*Y[jhe4]*Y[jsi24]*rate_eval.He4_Si24__p_P27  +
          +rho*Y[jhe4]*Y[jal21]*rate_eval.He4_Al21__p_Si24  +
          -Y[jsi24]*rate_eval.Si24__p_Mg23__weak__wc12  +
          +rho*Y[jhe4]*Y[jmg20]*rate_eval.He4_Mg20__Si24  +
          -rho*Y[jhe4]*Y[jsi24]*rate_eval.He4_Si24__S28  +
          -rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__Si25  +
          +rho*Y[jp]*Y[jal23]*rate_eval.p_Al23__Si24  +
          +rho*Y[jn]*Y[jsi23]*rate_eval.n_Si23__Si24  +
          +rho*Y[jn]*Y[js27]*rate_eval.n_S27__He4_Si24  +
          +Y[jp24]*rate_eval.P24__Si24__weak__bqa_pos_  +
          -Y[jsi24]*rate_eval.Si24__Al24__weak__wc12  +
          -rho*Y[jp]*Y[jsi24]*rate_eval.p_Si24__P25
       )

    dYdt[jsi25] = (
          +rho*Y[jn]*Y[js28]*rate_eval.n_S28__He4_Si25  +
          -rho*Y[jhe4]*Y[jsi25]*rate_eval.He4_Si25__p_P28  +
          -rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__p_Al25  +
          +rho*Y[jhe4]*Y[jal22]*rate_eval.He4_Al22__p_Si25  +
          -rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__He4_Mg22  +
          +Y[jp25]*rate_eval.P25__Si25__weak__bqa_pos_  +
          -rho*Y[jp]*Y[jsi25]*rate_eval.p_Si25__P26  +
          +rho*Y[jn]*Y[jsi24]*rate_eval.n_Si24__Si25  +
          +rho*Y[jp]*Y[jal24]*rate_eval.p_Al24__Si25  +
          +rho*Y[jhe4]*Y[jmg21]*rate_eval.He4_Mg21__Si25  +
          -rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__Si26  +
          -rho*Y[jhe4]*Y[jsi25]*rate_eval.He4_Si25__S29  +
          -Y[jsi25]*rate_eval.Si25__p_Mg24__weak__wc12  +
          -Y[jsi25]*rate_eval.Si25__Al25__weak__wc12  +
          +rho*Y[jn]*Y[jp25]*rate_eval.n_P25__p_Si25
       )

    dYdt[jsi26] = (
          +rho*Y[jp]*Y[jal25]*rate_eval.p_Al25__Si26  +
          +rho*Y[jn]*Y[jp26]*rate_eval.n_P26__p_Si26  +
          +rho*Y[jn]*Y[js29]*rate_eval.n_S29__He4_Si26  +
          +Y[js27]*rate_eval.S27__p_Si26__weak__wc17  +
          -rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__p_Al26  +
          +rho*Y[jhe4]*Y[jmg22]*rate_eval.He4_Mg22__Si26  +
          -rho*Y[jp]*Y[jsi26]*rate_eval.p_Si26__P27  +
          -rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__Si27  +
          +rho*Y[jn]*Y[jsi25]*rate_eval.n_Si25__Si26  +
          -rho*Y[jhe4]*Y[jsi26]*rate_eval.He4_Si26__S30  +
          -rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__He4_Mg23  +
          -Y[jsi26]*rate_eval.Si26__Al26__weak__wc12  +
          +Y[jp26]*rate_eval.P26__Si26__weak__wc12  +
          +rho*Y[jhe4]*Y[jal23]*rate_eval.He4_Al23__p_Si26  +
          -rho*Y[jhe4]*Y[jsi26]*rate_eval.He4_Si26__p_P29
       )

    dYdt[jsi27] = (
          +rho*Y[jn]*Y[js30]*rate_eval.n_S30__He4_Si27  +
          +rho*Y[jn]*Y[jp27]*rate_eval.n_P27__p_Si27  +
          -rho*Y[jhe4]*Y[jsi27]*rate_eval.He4_Si27__p_P30  +
          +rho*Y[jhe4]*Y[jal24]*rate_eval.He4_Al24__p_Si27  +
          -rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__Si28  +
          +rho*Y[jp]*Y[jal26]*rate_eval.p_Al26__Si27  +
          +rho*Y[jn]*Y[jsi26]*rate_eval.n_Si26__Si27  +
          +rho*Y[jhe4]*Y[jmg23]*rate_eval.He4_Mg23__Si27  +
          +Y[js28]*rate_eval.S28__p_Si27__weak__wc12  +
          -rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__He4_Mg24  +
          -rho*Y[jp]*Y[jsi27]*rate_eval.p_Si27__P28  +
          -rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__p_Al27  +
          +Y[jp27]*rate_eval.P27__Si27__weak__wc12  +
          -rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__C12_O16  +
          -rho*Y[jhe4]*Y[jsi27]*rate_eval.He4_Si27__S31  +
          -Y[jsi27]*rate_eval.Si27__Al27__weak__wc12
       )

    dYdt[jsi28] = (
          +rho*Y[jn]*Y[jp28]*rate_eval.n_P28__p_Si28  +
          +rho*Y[jhe4]*Y[jal25]*rate_eval.He4_Al25__p_Si28  +
          +rho*Y[jhe4]*Y[jmg25]*rate_eval.He4_Mg25__n_Si28  +
          +rho*Y[jn]*Y[jsi27]*rate_eval.n_Si27__Si28  +
          +rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__He4_Si28  +
          +5.00000000000000e-01*rho*Y[jo16]**2*rate_eval.O16_O16__He4_Si28  +
          -rho*Y[jp]*Y[jsi28]*rate_eval.p_Si28__P29  +
          +rho*Y[jn]*Y[js31]*rate_eval.n_S31__He4_Si28  +
          -rho*Y[jhe4]*Y[jsi28]*rate_eval.He4_Si28__S32  +
          +rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__n_Si28  +
          +rho*Y[jp]*Y[jp31]*rate_eval.p_P31__He4_Si28  +
          +Y[jcl32]*rate_eval.Cl32__He4_Si28__weak__wc12  +
          +Y[js29]*rate_eval.S29__p_Si28__weak__wc12  +
          -rho*Y[jn]*Y[jsi28]*rate_eval.n_Si28__Si29  +
          +Y[jp28]*rate_eval.P28__Si28__weak__wc12  +
          +rho*Y[jp]*Y[jal27]*rate_eval.p_Al27__Si28  +
          +rho*Y[jhe4]*Y[jmg24]*rate_eval.He4_Mg24__Si28  +
          +Y[jal28]*rate_eval.Al28__Si28__weak__wc12
       )

    dYdt[jsi29] = (
          +rho*Y[jp]*Y[jp32]*rate_eval.p_P32__He4_Si29  +
          +rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__n_Si29  +
          +rho*Y[jhe4]*Y[jmg26]*rate_eval.He4_Mg26__n_Si29  +
          +rho*Y[jhe4]*Y[jal26]*rate_eval.He4_Al26__p_Si29  +
          +rho*Y[jp]*Y[jal28]*rate_eval.p_Al28__Si29  +
          -rho*Y[jp]*Y[jsi29]*rate_eval.p_Si29__P30  +
          -rho*Y[jhe4]*Y[jsi29]*rate_eval.He4_Si29__S33  +
          +rho*Y[jhe4]*Y[jmg25]*rate_eval.He4_Mg25__Si29  +
          +Y[jal29]*rate_eval.Al29__Si29__weak__wc12  +
          +rho*Y[jn]*Y[jsi28]*rate_eval.n_Si28__Si29  +
          +rho*Y[jn]*Y[jp29]*rate_eval.n_P29__p_Si29  +
          -rho*Y[jn]*Y[jsi29]*rate_eval.n_Si29__Si30  +
          +rho*Y[jn]*Y[js32]*rate_eval.n_S32__He4_Si29  +
          +Y[jp29]*rate_eval.P29__Si29__weak__wc12
       )

    dYdt[jsi30] = (
          +rho*Y[jn]*Y[js33]*rate_eval.n_S33__He4_Si30  +
          +rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__n_Si30  +
          +rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__p_Si30  +
          +rho*Y[jhe4]*Y[jmg27]*rate_eval.He4_Mg27__n_Si30  +
          +Y[jal30]*rate_eval.Al30__Si30__weak__wc12  +
          +rho*Y[jp]*Y[jp33]*rate_eval.p_P33__He4_Si30  +
          -rho*Y[jp]*Y[jsi30]*rate_eval.p_Si30__P31  +
          +rho*Y[jhe4]*Y[jmg26]*rate_eval.He4_Mg26__Si30  +
          +rho*Y[jn]*Y[jp30]*rate_eval.n_P30__p_Si30  +
          -rho*Y[jn]*Y[jsi30]*rate_eval.n_Si30__Si31  +
          -rho*Y[jhe4]*Y[jsi30]*rate_eval.He4_Si30__S34  +
          +rho*Y[jn]*Y[jsi29]*rate_eval.n_Si29__Si30  +
          +rho*Y[jp]*Y[jal29]*rate_eval.p_Al29__Si30  +
          +Y[jp30]*rate_eval.P30__Si30__weak__wc12
       )

    dYdt[jsi31] = (
          -rho*Y[jhe4]*Y[jsi31]*rate_eval.He4_Si31__n_S34  +
          -Y[jsi31]*rate_eval.Si31__P31__weak__wc12  +
          -rho*Y[jp]*Y[jsi31]*rate_eval.p_Si31__P32  +
          +rho*Y[jp]*Y[jal30]*rate_eval.p_Al30__Si31  +
          -rho*Y[jhe4]*Y[jsi31]*rate_eval.He4_Si31__S35  +
          +rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__p_Si31  +
          +rho*Y[jhe4]*Y[jmg27]*rate_eval.He4_Mg27__Si31  +
          +rho*Y[jhe4]*Y[jmg28]*rate_eval.He4_Mg28__n_Si31  +
          -rho*Y[jn]*Y[jsi31]*rate_eval.n_Si31__Si32  +
          +rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__n_Si31  +
          +Y[jal31]*rate_eval.Al31__Si31__weak__wc12  +
          -rho*Y[jp]*Y[jsi31]*rate_eval.p_Si31__n_P31  +
          +rho*Y[jn]*Y[jsi30]*rate_eval.n_Si30__Si31  +
          +Y[jal32]*rate_eval.Al32__n_Si31__weak__wc12  +
          +rho*Y[jp]*Y[jp34]*rate_eval.p_P34__He4_Si31
       )

    dYdt[jsi32] = (
          +rho*Y[jn]*Y[js35]*rate_eval.n_S35__He4_Si32  +
          +rho*Y[jn]*Y[jp32]*rate_eval.n_P32__p_Si32  +
          +rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__n_Si32  +
          +rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__p_Si32  +
          +Y[jal32]*rate_eval.Al32__Si32__weak__wc12  +
          -rho*Y[jp]*Y[jsi32]*rate_eval.p_Si32__P33  +
          -rho*Y[jn]*Y[jsi32]*rate_eval.n_Si32__Si33  +
          +rho*Y[jp]*Y[jal31]*rate_eval.p_Al31__Si32  +
          +rho*Y[jhe4]*Y[jmg28]*rate_eval.He4_Mg28__Si32  +
          +rho*Y[jhe4]*Y[jmg29]*rate_eval.He4_Mg29__n_Si32  +
          -rho*Y[jhe4]*Y[jsi32]*rate_eval.He4_Si32__S36  +
          -Y[jsi32]*rate_eval.Si32__P32__weak__wc12  +
          +rho*Y[jn]*Y[jsi31]*rate_eval.n_Si31__Si32  +
          +rho*Y[jp]*Y[jp35]*rate_eval.p_P35__He4_Si32  +
          +Y[jal33]*rate_eval.Al33__n_Si32__weak__wc12
       )

    dYdt[jsi33] = (
          -rho*Y[jhe4]*Y[jsi33]*rate_eval.He4_Si33__n_S36  +
          -rho*Y[jn]*Y[jsi33]*rate_eval.n_Si33__Si34  +
          +rho*Y[jp]*Y[jp36]*rate_eval.p_P36__He4_Si33  +
          -rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__n_P33  +
          +rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__n_Si33  +
          +rho*Y[jhe4]*Y[jmg30]*rate_eval.He4_Mg30__n_Si33  +
          -Y[jsi33]*rate_eval.Si33__P33__weak__wc12  +
          -rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__P34  +
          +Y[jal34]*rate_eval.Al34__n_Si33__weak__wc12  +
          -rho*Y[jhe4]*Y[jsi33]*rate_eval.He4_Si33__S37  +
          +rho*Y[jn]*Y[jsi32]*rate_eval.n_Si32__Si33  +
          +rho*Y[jhe4]*Y[jmg29]*rate_eval.He4_Mg29__Si33  +
          -rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__He4_Al30  +
          +Y[jal33]*rate_eval.Al33__Si33__weak__wc12  +
          +rho*Y[jp]*Y[jal32]*rate_eval.p_Al32__Si33
       )

    dYdt[jsi34] = (
          +Y[jal37]*rate_eval.Al37__n_n_n_Si34__weak__mo03  +
          +rho*Y[jn]*Y[jsi33]*rate_eval.n_Si33__Si34  +
          +rho*Y[jp]*Y[jp37]*rate_eval.p_P37__He4_Si34  +
          +rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__n_Si34  +
          +rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__p_Si34  +
          -Y[jsi34]*rate_eval.Si34__P34__weak__wc12  +
          -rho*Y[jp]*Y[jsi34]*rate_eval.p_Si34__P35  +
          -rho*Y[jhe4]*Y[jsi34]*rate_eval.He4_Si34__S38  +
          +rho*Y[jp]*Y[jal33]*rate_eval.p_Al33__Si34  +
          +rho*Y[jhe4]*Y[jmg30]*rate_eval.He4_Mg30__Si34  +
          +rho*Y[jhe4]*Y[jmg31]*rate_eval.He4_Mg31__n_Si34  +
          -rho*Y[jn]*Y[jsi34]*rate_eval.n_Si34__Si35  +
          +Y[jal34]*rate_eval.Al34__Si34__weak__wc12  +
          +Y[jal35]*rate_eval.Al35__n_Si34__weak__wc12  +
          -rho*Y[jhe4]*Y[jsi34]*rate_eval.He4_Si34__n_S37  +
          -rho*Y[jp]*Y[jsi34]*rate_eval.p_Si34__n_P34  +
          +Y[jal36]*rate_eval.Al36__n_n_Si34__weak__mp17
       )

    dYdt[jsi35] = (
          +Y[jal38]*rate_eval.Al38__n_n_n_Si35__weak__mo03  +
          -rho*Y[jhe4]*Y[jsi35]*rate_eval.He4_Si35__n_S38  +
          +rho*Y[jp]*Y[jp38]*rate_eval.p_P38__He4_Si35  +
          -rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__He4_Al32  +
          +rho*Y[jhe4]*Y[jmg32]*rate_eval.He4_Mg32__n_Si35  +
          +rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__n_Si35  +
          -Y[jsi35]*rate_eval.Si35__P35__weak__wc17  +
          +rho*Y[jp]*Y[jal34]*rate_eval.p_Al34__Si35  +
          +rho*Y[jhe4]*Y[jmg31]*rate_eval.He4_Mg31__Si35  +
          -rho*Y[jn]*Y[jsi35]*rate_eval.n_Si35__Si36  +
          +rho*Y[jn]*Y[jsi34]*rate_eval.n_Si34__Si35  +
          -rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__P36  +
          +Y[jal37]*rate_eval.Al37__n_n_Si35__weak__mp17  +
          -rho*Y[jhe4]*Y[jsi35]*rate_eval.He4_Si35__S39  +
          -rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__n_P35  +
          +Y[jal35]*rate_eval.Al35__Si35__weak__wc12  +
          +Y[jal36]*rate_eval.Al36__n_Si35__weak__mp17
       )

    dYdt[jsi36] = (
          +Y[jal39]*rate_eval.Al39__n_n_n_Si36__weak__mo03  +
          -rho*Y[jp]*Y[jsi36]*rate_eval.p_Si36__He4_Al33  +
          +rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__n_Si36  +
          +Y[jal36]*rate_eval.Al36__Si36__weak__wc17  +
          -rho*Y[jp]*Y[jsi36]*rate_eval.p_Si36__n_P36  +
          +Y[jal37]*rate_eval.Al37__n_Si36__weak__mp17  +
          +rho*Y[jhe4]*Y[jmg33]*rate_eval.He4_Mg33__n_Si36  +
          -rho*Y[jn]*Y[jsi36]*rate_eval.n_Si36__Si37  +
          +rho*Y[jn]*Y[jsi35]*rate_eval.n_Si35__Si36  +
          +Y[jal38]*rate_eval.Al38__n_n_Si36__weak__mp17  +
          -rho*Y[jhe4]*Y[jsi36]*rate_eval.He4_Si36__n_S39  +
          +rho*Y[jhe4]*Y[jmg32]*rate_eval.He4_Mg32__Si36  +
          +rho*Y[jp]*Y[jp39]*rate_eval.p_P39__He4_Si36  +
          -Y[jsi36]*rate_eval.Si36__P36__weak__wc12  +
          -rho*Y[jhe4]*Y[jsi36]*rate_eval.He4_Si36__S40  +
          +rho*Y[jp]*Y[jal35]*rate_eval.p_Al35__Si36  +
          -rho*Y[jp]*Y[jsi36]*rate_eval.p_Si36__P37  +
          -Y[jsi36]*rate_eval.Si36__n_P35__weak__wc12
       )

    dYdt[jsi37] = (
          +Y[jal37]*rate_eval.Al37__Si37__weak__wc17  +
          -rho*Y[jhe4]*Y[jsi37]*rate_eval.He4_Si37__n_S40  +
          -rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__He4_Al34  +
          -rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__n_P37  +
          +rho*Y[jhe4]*Y[jmg34]*rate_eval.He4_Mg34__n_Si37  +
          +Y[jal40]*rate_eval.Al40__n_n_n_Si37__weak__mo03  +
          +Y[jal39]*rate_eval.Al39__n_n_Si37__weak__mp17  +
          -rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__P38  +
          +rho*Y[jn]*Y[jsi36]*rate_eval.n_Si36__Si37  +
          +rho*Y[jp]*Y[jal36]*rate_eval.p_Al36__Si37  +
          +rho*Y[jhe4]*Y[jmg33]*rate_eval.He4_Mg33__Si37  +
          +rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__n_Si37  +
          -rho*Y[jhe4]*Y[jsi37]*rate_eval.He4_Si37__S41  +
          +Y[jal38]*rate_eval.Al38__n_Si37__weak__mp17  +
          +rho*Y[jp]*Y[jp40]*rate_eval.p_P40__He4_Si37  +
          -Y[jsi37]*rate_eval.Si37__n_P36__weak__wc12  +
          -Y[jsi37]*rate_eval.Si37__P37__weak__wc12  +
          -rho*Y[jn]*Y[jsi37]*rate_eval.n_Si37__Si38
       )

    dYdt[jsi38] = (
          +Y[jal41]*rate_eval.Al41__n_n_n_Si38__weak__mo03  +
          -rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__n_P38  +
          -rho*Y[jhe4]*Y[jsi38]*rate_eval.He4_Si38__n_S41  +
          +rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__n_Si38  +
          +rho*Y[jhe4]*Y[jmg35]*rate_eval.He4_Mg35__n_Si38  +
          -rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__P39  +
          +Y[jal39]*rate_eval.Al39__n_Si38__weak__mp17  +
          +rho*Y[jhe4]*Y[jmg34]*rate_eval.He4_Mg34__Si38  +
          -rho*Y[jhe4]*Y[jsi38]*rate_eval.He4_Si38__S42  +
          -rho*Y[jn]*Y[jsi38]*rate_eval.n_Si38__Si39  +
          +rho*Y[jp]*Y[jal37]*rate_eval.p_Al37__Si38  +
          -Y[jsi38]*rate_eval.Si38__P38__weak__mo03  +
          -Y[jsi38]*rate_eval.Si38__n_P37__weak__mp17  +
          +Y[jal38]*rate_eval.Al38__Si38__weak__wc17  +
          +rho*Y[jp]*Y[jp41]*rate_eval.p_P41__He4_Si38  +
          +Y[jal40]*rate_eval.Al40__n_n_Si38__weak__mp17  +
          +rho*Y[jn]*Y[jsi37]*rate_eval.n_Si37__Si38  +
          -rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__He4_Al35
       )

    dYdt[jsi39] = (
          +Y[jal42]*rate_eval.Al42__n_n_n_Si39__weak__mo03  +
          +rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__n_Si39  +
          +rho*Y[jp]*Y[jp42]*rate_eval.p_P42__He4_Si39  +
          -rho*Y[jhe4]*Y[jsi39]*rate_eval.He4_Si39__n_S42  +
          -rho*Y[jp]*Y[jsi39]*rate_eval.p_Si39__n_P39  +
          +rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__p_Si39  +
          -rho*Y[jp]*Y[jsi39]*rate_eval.p_Si39__P40  +
          +rho*Y[jn]*Y[jsi38]*rate_eval.n_Si38__Si39  +
          -rho*Y[jhe4]*Y[jsi39]*rate_eval.He4_Si39__S43  +
          -Y[jsi39]*rate_eval.Si39__n_n_P37__weak__mp17  +
          +Y[jal41]*rate_eval.Al41__n_n_Si39__weak__mp17  +
          +rho*Y[jhe4]*Y[jmg36]*rate_eval.He4_Mg36__n_Si39  +
          +Y[jal40]*rate_eval.Al40__n_Si39__weak__mp17  +
          +rho*Y[jp]*Y[jal38]*rate_eval.p_Al38__Si39  +
          +rho*Y[jhe4]*Y[jmg35]*rate_eval.He4_Mg35__Si39  +
          -rho*Y[jn]*Y[jsi39]*rate_eval.n_Si39__Si40  +
          -Y[jsi39]*rate_eval.Si39__n_P38__weak__mp17  +
          +Y[jal39]*rate_eval.Al39__Si39__weak__wc17  +
          -Y[jsi39]*rate_eval.Si39__P39__weak__wc17
       )

    dYdt[jsi40] = (
          +Y[jal43]*rate_eval.Al43__n_n_n_Si40__weak__mo03  +
          +rho*Y[jp]*Y[jp43]*rate_eval.p_P43__He4_Si40  +
          -rho*Y[jhe4]*Y[jsi40]*rate_eval.He4_Si40__n_S43  +
          +rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__n_Si40  +
          +rho*Y[jhe4]*Y[jmg37]*rate_eval.He4_Mg37__n_Si40  +
          +rho*Y[jp]*Y[jal39]*rate_eval.p_Al39__Si40  +
          +Y[jal41]*rate_eval.Al41__n_Si40__weak__mp17  +
          -rho*Y[jn]*Y[jsi40]*rate_eval.n_Si40__Si41  +
          +rho*Y[jhe4]*Y[jmg36]*rate_eval.He4_Mg36__Si40  +
          -rho*Y[jhe4]*Y[jsi40]*rate_eval.He4_Si40__S44  +
          -rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__P41  +
          -rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__n_P40  +
          -rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__He4_Al37  +
          +Y[jal42]*rate_eval.Al42__n_n_Si40__weak__mo03  +
          +rho*Y[jn]*Y[jsi39]*rate_eval.n_Si39__Si40  +
          -Y[jsi40]*rate_eval.Si40__n_P39__weak__mp17  +
          -Y[jsi40]*rate_eval.Si40__P40__weak__wc17  +
          +Y[jal40]*rate_eval.Al40__Si40__weak__mo03
       )

    dYdt[jsi41] = (
          +rho*Y[jhe4]*Y[jmg38]*rate_eval.He4_Mg38__n_Si41  +
          +rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__p_Si41  +
          +rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__n_Si41  +
          +rho*Y[jp]*Y[jp44]*rate_eval.p_P44__He4_Si41  +
          +rho*Y[jn]*Y[jsi40]*rate_eval.n_Si40__Si41  +
          +Y[jal41]*rate_eval.Al41__Si41__weak__mo03  +
          -rho*Y[jhe4]*Y[jsi41]*rate_eval.He4_Si41__S45  +
          +rho*Y[jp]*Y[jal40]*rate_eval.p_Al40__Si41  +
          +rho*Y[jhe4]*Y[jmg37]*rate_eval.He4_Mg37__Si41  +
          -Y[jsi41]*rate_eval.Si41__n_n_P39__weak__mp17  +
          +Y[jal43]*rate_eval.Al43__n_n_Si41__weak__mp17  +
          +Y[jal42]*rate_eval.Al42__n_Si41__weak__mp17  +
          -Y[jsi41]*rate_eval.Si41__P41__weak__wc17  +
          -rho*Y[jp]*Y[jsi41]*rate_eval.p_Si41__P42  +
          -Y[jsi41]*rate_eval.Si41__n_P40__weak__mp17  +
          -rho*Y[jn]*Y[jsi41]*rate_eval.n_Si41__Si42  +
          -rho*Y[jhe4]*Y[jsi41]*rate_eval.He4_Si41__n_S44  +
          -rho*Y[jp]*Y[jsi41]*rate_eval.p_Si41__n_P41
       )

    dYdt[jsi42] = (
          -Y[jsi42]*rate_eval.Si42__n_n_n_P39__weak__mo03  +
          -rho*Y[jhe4]*Y[jsi42]*rate_eval.He4_Si42__S46  +
          -rho*Y[jhe4]*Y[jsi42]*rate_eval.He4_Si42__n_S45  +
          -rho*Y[jp]*Y[jsi42]*rate_eval.p_Si42__n_P42  +
          +rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__p_Si42  +
          +rho*Y[jhe4]*Y[jmg39]*rate_eval.He4_Mg39__n_Si42  +
          -rho*Y[jp]*Y[jsi42]*rate_eval.p_Si42__P43  +
          +Y[jal42]*rate_eval.Al42__Si42__weak__mo03  +
          -Y[jsi42]*rate_eval.Si42__P42__weak__wc17  +
          +rho*Y[jhe4]*Y[jmg38]*rate_eval.He4_Mg38__Si42  +
          +rho*Y[jp]*Y[jal41]*rate_eval.p_Al41__Si42  +
          +Y[jal43]*rate_eval.Al43__n_Si42__weak__mp17  +
          -Y[jsi42]*rate_eval.Si42__n_P41__weak__mp17  +
          +rho*Y[jp]*Y[jp45]*rate_eval.p_P45__He4_Si42  +
          +rho*Y[jn]*Y[jsi41]*rate_eval.n_Si41__Si42  +
          +rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__n_Si42  +
          -rho*Y[jn]*Y[jsi42]*rate_eval.n_Si42__Si43
       )

    dYdt[jsi43] = (
          -rho*Y[jp]*Y[jsi43]*rate_eval.p_Si43__n_P43  +
          +rho*Y[jhe4]*Y[jal40]*rate_eval.He4_Al40__p_Si43  +
          -rho*Y[jhe4]*Y[jsi43]*rate_eval.He4_Si43__n_S46  +
          -rho*Y[jn]*Y[jsi43]*rate_eval.n_Si43__Si44  +
          +rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__n_Si43  +
          -Y[jsi43]*rate_eval.Si43__n_n_P41__weak__mp17  +
          +rho*Y[jhe4]*Y[jmg40]*rate_eval.He4_Mg40__n_Si43  +
          +rho*Y[jp]*Y[jal42]*rate_eval.p_Al42__Si43  +
          +rho*Y[jhe4]*Y[jmg39]*rate_eval.He4_Mg39__Si43  +
          +rho*Y[jp]*Y[jp46]*rate_eval.p_P46__He4_Si43  +
          -Y[jsi43]*rate_eval.Si43__n_P42__weak__mp17  +
          -rho*Y[jhe4]*Y[jsi43]*rate_eval.He4_Si43__S47  +
          -Y[jsi43]*rate_eval.Si43__n_n_n_P40__weak__mo03  +
          -Y[jsi43]*rate_eval.Si43__P43__weak__mo03  +
          -rho*Y[jp]*Y[jsi43]*rate_eval.p_Si43__P44  +
          +rho*Y[jn]*Y[jsi42]*rate_eval.n_Si42__Si43
       )

    dYdt[jsi44] = (
          -rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__n_P44  +
          +rho*Y[jn]*Y[jsi43]*rate_eval.n_Si43__Si44  +
          -rho*Y[jhe4]*Y[jsi44]*rate_eval.He4_Si44__n_S47  +
          -Y[jsi44]*rate_eval.Si44__n_P43__weak__mp17  +
          -rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__He4_Al41  +
          +rho*Y[jhe4]*Y[jmg40]*rate_eval.He4_Mg40__Si44  +
          -rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__P45  +
          +rho*Y[jp]*Y[jal43]*rate_eval.p_Al43__Si44  +
          -Y[jsi44]*rate_eval.Si44__n_n_P42__weak__mp17  +
          +rho*Y[jhe4]*Y[jmg41]*rate_eval.He4_Mg41__n_Si44  +
          -Y[jsi44]*rate_eval.Si44__n_n_n_P41__weak__mo03  +
          -rho*Y[jhe4]*Y[jsi44]*rate_eval.He4_Si44__S48  +
          +rho*Y[jp]*Y[jp47]*rate_eval.p_P47__He4_Si44  +
          -rho*Y[jn]*Y[jsi44]*rate_eval.n_Si44__Si45
       )

    dYdt[jsi45] = (
          -rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__P46  +
          -rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__He4_Al42  +
          -rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__n_P45  +
          -rho*Y[jhe4]*Y[jsi45]*rate_eval.He4_Si45__S49  +
          -Y[jsi45]*rate_eval.Si45__n_P44__weak__mp17  +
          +rho*Y[jhe4]*Y[jmg41]*rate_eval.He4_Mg41__Si45  +
          -Y[jsi45]*rate_eval.Si45__P45__weak__mo03  +
          -rho*Y[jhe4]*Y[jsi45]*rate_eval.He4_Si45__n_S48  +
          +rho*Y[jn]*Y[jsi44]*rate_eval.n_Si44__Si45
       )

    dYdt[jp24] = (
          -rho*Y[jhe4]*Y[jp24]*rate_eval.He4_P24__p_S27  +
          -rho*Y[jn]*Y[jp24]*rate_eval.n_P24__He4_Al21  +
          -rho*Y[jn]*Y[jp24]*rate_eval.n_P24__p_Si24  +
          -rho*Y[jhe4]*Y[jp24]*rate_eval.He4_P24__Cl28  +
          -Y[jp24]*rate_eval.P24__Si24__weak__bqa_pos_  +
          -rho*Y[jn]*Y[jp24]*rate_eval.n_P24__P25
       )

    dYdt[jp25] = (
          +rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__He4_P25  +
          -rho*Y[jhe4]*Y[jp25]*rate_eval.He4_P25__p_S28  +
          +rho*Y[jhe4]*Y[jsi22]*rate_eval.He4_Si22__p_P25  +
          -Y[jp25]*rate_eval.P25__Si25__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[jp25]*rate_eval.He4_P25__Cl29  +
          -rho*Y[jn]*Y[jp25]*rate_eval.n_P25__He4_Al22  +
          -rho*Y[jp]*Y[jp25]*rate_eval.p_P25__S26  +
          -rho*Y[jn]*Y[jp25]*rate_eval.n_P25__p_Si25  +
          +rho*Y[jhe4]*Y[jal21]*rate_eval.He4_Al21__P25  +
          -rho*Y[jn]*Y[jp25]*rate_eval.n_P25__P26  +
          +rho*Y[jn]*Y[jp24]*rate_eval.n_P24__P25  +
          +rho*Y[jp]*Y[jsi24]*rate_eval.p_Si24__P25
       )

    dYdt[jp26] = (
          +rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__He4_P26  +
          -rho*Y[jhe4]*Y[jp26]*rate_eval.He4_P26__p_S29  +
          -rho*Y[jn]*Y[jp26]*rate_eval.n_P26__He4_Al23  +
          -rho*Y[jn]*Y[jp26]*rate_eval.n_P26__p_Si26  +
          +rho*Y[jhe4]*Y[jsi23]*rate_eval.He4_Si23__p_P26  +
          +rho*Y[jn]*Y[js26]*rate_eval.n_S26__p_P26  +
          +rho*Y[jp]*Y[jsi25]*rate_eval.p_Si25__P26  +
          -rho*Y[jhe4]*Y[jp26]*rate_eval.He4_P26__Cl30  +
          -rho*Y[jp]*Y[jp26]*rate_eval.p_P26__S27  +
          -rho*Y[jn]*Y[jp26]*rate_eval.n_P26__P27  +
          +Y[js26]*rate_eval.S26__P26__weak__bqa_pos_  +
          -Y[jp26]*rate_eval.P26__Si26__weak__wc12  +
          +rho*Y[jn]*Y[jp25]*rate_eval.n_P25__P26  +
          +rho*Y[jhe4]*Y[jal22]*rate_eval.He4_Al22__P26
       )

    dYdt[jp27] = (
          -Y[jp27]*rate_eval.P27__p_Al26__weak__wc12  +
          -rho*Y[jhe4]*Y[jp27]*rate_eval.He4_P27__p_S30  +
          -rho*Y[jn]*Y[jp27]*rate_eval.n_P27__He4_Al24  +
          -rho*Y[jn]*Y[jp27]*rate_eval.n_P27__p_Si27  +
          +rho*Y[jhe4]*Y[jsi24]*rate_eval.He4_Si24__p_P27  +
          -rho*Y[jhe4]*Y[jp27]*rate_eval.He4_P27__Cl31  +
          -rho*Y[jn]*Y[jp27]*rate_eval.n_P27__P28  +
          +rho*Y[jn]*Y[jp26]*rate_eval.n_P26__P27  +
          +Y[js27]*rate_eval.S27__P27__weak__wc12  +
          +rho*Y[jp]*Y[jsi26]*rate_eval.p_Si26__P27  +
          -rho*Y[jp]*Y[jp27]*rate_eval.p_P27__S28  +
          +rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__He4_P27  +
          -Y[jp27]*rate_eval.P27__Si27__weak__wc12  +
          +rho*Y[jhe4]*Y[jal23]*rate_eval.He4_Al23__P27  +
          +rho*Y[jn]*Y[js27]*rate_eval.n_S27__p_P27
       )

    dYdt[jp28] = (
          -rho*Y[jn]*Y[jp28]*rate_eval.n_P28__p_Si28  +
          +rho*Y[jhe4]*Y[jsi25]*rate_eval.He4_Si25__p_P28  +
          -rho*Y[jhe4]*Y[jp28]*rate_eval.He4_P28__Cl32  +
          -rho*Y[jp]*Y[jp28]*rate_eval.p_P28__S29  +
          -rho*Y[jn]*Y[jp28]*rate_eval.n_P28__P29  +
          +rho*Y[jn]*Y[jp27]*rate_eval.n_P27__P28  +
          +rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__He4_P28  +
          -rho*Y[jhe4]*Y[jp28]*rate_eval.He4_P28__p_S31  +
          +rho*Y[jn]*Y[js28]*rate_eval.n_S28__p_P28  +
          +rho*Y[jhe4]*Y[jal24]*rate_eval.He4_Al24__P28  +
          +Y[js28]*rate_eval.S28__P28__weak__wc12  +
          +rho*Y[jp]*Y[jsi27]*rate_eval.p_Si27__P28  +
          -Y[jp28]*rate_eval.P28__He4_Mg24__weak__wc12  +
          -Y[jp28]*rate_eval.P28__p_Al27__weak__wc12  +
          -Y[jp28]*rate_eval.P28__Si28__weak__wc12  +
          -rho*Y[jn]*Y[jp28]*rate_eval.n_P28__He4_Al25
       )

    dYdt[jp29] = (
          +rho*Y[jhe4]*Y[jal25]*rate_eval.He4_Al25__P29  +
          -rho*Y[jp]*Y[jp29]*rate_eval.p_P29__S30  +
          -rho*Y[jn]*Y[jp29]*rate_eval.n_P29__He4_Al26  +
          +rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__He4_P29  +
          +rho*Y[jn]*Y[js29]*rate_eval.n_S29__p_P29  +
          +rho*Y[jn]*Y[jp28]*rate_eval.n_P28__P29  +
          +rho*Y[jp]*Y[jsi28]*rate_eval.p_Si28__P29  +
          -rho*Y[jn]*Y[jp29]*rate_eval.n_P29__P30  +
          -rho*Y[jhe4]*Y[jp29]*rate_eval.He4_P29__Cl33  +
          +Y[jar31]*rate_eval.Ar31__p_p_P29__weak__wc12  +
          -rho*Y[jhe4]*Y[jp29]*rate_eval.He4_P29__p_S32  +
          -rho*Y[jn]*Y[jp29]*rate_eval.n_P29__p_Si29  +
          +Y[js29]*rate_eval.S29__P29__weak__wc12  +
          +rho*Y[jhe4]*Y[jsi26]*rate_eval.He4_Si26__p_P29  +
          -Y[jp29]*rate_eval.P29__Si29__weak__wc12
       )

    dYdt[jp30] = (
          +rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__He4_P30  +
          +rho*Y[jn]*Y[js30]*rate_eval.n_S30__p_P30  +
          -rho*Y[jhe4]*Y[jp30]*rate_eval.He4_P30__p_S33  +
          +rho*Y[jhe4]*Y[jsi27]*rate_eval.He4_Si27__p_P30  +
          +Y[js30]*rate_eval.S30__P30__weak__wc12  +
          -rho*Y[jp]*Y[jp30]*rate_eval.p_P30__S31  +
          +rho*Y[jhe4]*Y[jal26]*rate_eval.He4_Al26__P30  +
          +rho*Y[jp]*Y[jsi29]*rate_eval.p_Si29__P30  +
          +rho*Y[jn]*Y[jp29]*rate_eval.n_P29__P30  +
          -rho*Y[jn]*Y[jp30]*rate_eval.n_P30__p_Si30  +
          +Y[jcl31]*rate_eval.Cl31__p_P30__weak__wc12  +
          -rho*Y[jn]*Y[jp30]*rate_eval.n_P30__P31  +
          -rho*Y[jhe4]*Y[jp30]*rate_eval.He4_P30__Cl34  +
          -Y[jp30]*rate_eval.P30__Si30__weak__wc12  +
          +rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__n_P30
       )

    dYdt[jp31] = (
          -rho*Y[jp]*Y[jp31]*rate_eval.p_P31__S32  +
          +rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__He4_P31  +
          -rho*Y[jhe4]*Y[jp31]*rate_eval.He4_P31__p_S34  +
          +rho*Y[jn]*Y[js31]*rate_eval.n_S31__p_P31  +
          +rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__p_P31  +
          +5.00000000000000e-01*rho*Y[jo16]**2*rate_eval.O16_O16__p_P31  +
          +rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__n_P31  +
          +Y[jsi31]*rate_eval.Si31__P31__weak__wc12  +
          +rho*Y[jp]*Y[jsi30]*rate_eval.p_Si30__P31  +
          +rho*Y[jhe4]*Y[jal27]*rate_eval.He4_Al27__P31  +
          -rho*Y[jp]*Y[jp31]*rate_eval.p_P31__He4_Si28  +
          +rho*Y[jn]*Y[jp30]*rate_eval.n_P30__P31  +
          -rho*Y[jhe4]*Y[jp31]*rate_eval.He4_P31__Cl35  +
          +Y[jcl32]*rate_eval.Cl32__p_P31__weak__wc12  +
          +rho*Y[jp]*Y[jsi31]*rate_eval.p_Si31__n_P31  +
          -rho*Y[jn]*Y[jp31]*rate_eval.n_P31__P32  +
          +Y[js31]*rate_eval.S31__P31__weak__wc12
       )

    dYdt[jp32] = (
          -rho*Y[jp]*Y[jp32]*rate_eval.p_P32__n_S32  +
          +rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__He4_P32  +
          +rho*Y[jp]*Y[js35]*rate_eval.p_S35__He4_P32  +
          -rho*Y[jp]*Y[jp32]*rate_eval.p_P32__He4_Si29  +
          -rho*Y[jn]*Y[jp32]*rate_eval.n_P32__p_Si32  +
          +rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__n_P32  +
          -rho*Y[jp]*Y[jp32]*rate_eval.p_P32__S33  +
          -rho*Y[jhe4]*Y[jp32]*rate_eval.He4_P32__Cl36  +
          -rho*Y[jn]*Y[jp32]*rate_eval.n_P32__P33  +
          +rho*Y[jp]*Y[jsi31]*rate_eval.p_Si31__P32  +
          -Y[jp32]*rate_eval.P32__S32__weak__wc12  +
          +Y[jsi32]*rate_eval.Si32__P32__weak__wc12  +
          +rho*Y[jhe4]*Y[jal28]*rate_eval.He4_Al28__P32  +
          +rho*Y[jn]*Y[jp31]*rate_eval.n_P31__P32
       )

    dYdt[jp33] = (
          +rho*Y[jp]*Y[js36]*rate_eval.p_S36__He4_P33  +
          +rho*Y[jn]*Y[js33]*rate_eval.n_S33__p_P33  +
          +rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__n_P33  +
          -Y[jp33]*rate_eval.P33__S33__weak__wc12  +
          -rho*Y[jp]*Y[jp33]*rate_eval.p_P33__He4_Si30  +
          +Y[jsi33]*rate_eval.Si33__P33__weak__wc12  +
          -rho*Y[jn]*Y[jp33]*rate_eval.n_P33__P34  +
          +rho*Y[jn]*Y[jp32]*rate_eval.n_P32__P33  +
          +rho*Y[jp]*Y[jsi32]*rate_eval.p_Si32__P33  +
          +rho*Y[jhe4]*Y[jal29]*rate_eval.He4_Al29__P33  +
          -rho*Y[jhe4]*Y[jp33]*rate_eval.He4_P33__Cl37  +
          -rho*Y[jp]*Y[jp33]*rate_eval.p_P33__S34  +
          +rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__He4_P33  +
          +rho*Y[jhe4]*Y[jal30]*rate_eval.He4_Al30__n_P33
       )

    dYdt[jp34] = (
          -rho*Y[jhe4]*Y[jp34]*rate_eval.He4_P34__n_Cl37  +
          -rho*Y[jp]*Y[jp34]*rate_eval.p_P34__n_S34  +
          +rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__n_P34  +
          -rho*Y[jp]*Y[jp34]*rate_eval.p_P34__S35  +
          +Y[jsi34]*rate_eval.Si34__P34__weak__wc12  +
          +rho*Y[jp]*Y[jsi33]*rate_eval.p_Si33__P34  +
          +rho*Y[jn]*Y[jp33]*rate_eval.n_P33__P34  +
          +rho*Y[jhe4]*Y[jal30]*rate_eval.He4_Al30__P34  +
          -rho*Y[jhe4]*Y[jp34]*rate_eval.He4_P34__Cl38  +
          +rho*Y[jp]*Y[js37]*rate_eval.p_S37__He4_P34  +
          -rho*Y[jn]*Y[jp34]*rate_eval.n_P34__P35  +
          -rho*Y[jp]*Y[jp34]*rate_eval.p_P34__He4_Si31  +
          -Y[jp34]*rate_eval.P34__S34__weak__wc12  +
          +rho*Y[jp]*Y[jsi34]*rate_eval.p_Si34__n_P34
       )

    dYdt[jp35] = (
          +rho*Y[jhe4]*Y[jal32]*rate_eval.He4_Al32__n_P35  +
          +rho*Y[jp]*Y[js38]*rate_eval.p_S38__He4_P35  +
          +Y[jsi35]*rate_eval.Si35__P35__weak__wc17  +
          +rho*Y[jn]*Y[jcl38]*rate_eval.n_Cl38__He4_P35  +
          +rho*Y[jp]*Y[jsi34]*rate_eval.p_Si34__P35  +
          -rho*Y[jhe4]*Y[jp35]*rate_eval.He4_P35__Cl39  +
          -rho*Y[jp]*Y[jp35]*rate_eval.p_P35__S36  +
          -rho*Y[jn]*Y[jp35]*rate_eval.n_P35__P36  +
          +rho*Y[jhe4]*Y[jal31]*rate_eval.He4_Al31__P35  +
          -rho*Y[jp]*Y[jp35]*rate_eval.p_P35__n_S35  +
          +rho*Y[jn]*Y[jp34]*rate_eval.n_P34__P35  +
          -rho*Y[jp]*Y[jp35]*rate_eval.p_P35__He4_Si32  +
          -Y[jp35]*rate_eval.P35__S35__weak__wc12  +
          +Y[jsi36]*rate_eval.Si36__n_P35__weak__wc12  +
          +rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__n_P35
       )

    dYdt[jp36] = (
          +rho*Y[jp]*Y[js39]*rate_eval.p_S39__He4_P36  +
          -rho*Y[jp]*Y[jp36]*rate_eval.p_P36__He4_Si33  +
          -rho*Y[jp]*Y[jp36]*rate_eval.p_P36__n_S36  +
          +rho*Y[jhe4]*Y[jal33]*rate_eval.He4_Al33__n_P36  +
          +rho*Y[jhe4]*Y[jal32]*rate_eval.He4_Al32__P36  +
          -rho*Y[jhe4]*Y[jp36]*rate_eval.He4_P36__n_Cl39  +
          +rho*Y[jp]*Y[jsi36]*rate_eval.p_Si36__n_P36  +
          -Y[jp36]*rate_eval.P36__S36__weak__wc12  +
          -rho*Y[jhe4]*Y[jp36]*rate_eval.He4_P36__Cl40  +
          -rho*Y[jn]*Y[jp36]*rate_eval.n_P36__P37  +
          +rho*Y[jn]*Y[jp35]*rate_eval.n_P35__P36  +
          +rho*Y[jp]*Y[jsi35]*rate_eval.p_Si35__P36  +
          +Y[jsi36]*rate_eval.Si36__P36__weak__wc12  +
          +Y[jsi37]*rate_eval.Si37__n_P36__weak__wc12  +
          -rho*Y[jp]*Y[jp36]*rate_eval.p_P36__S37
       )

    dYdt[jp37] = (
          -rho*Y[jhe4]*Y[jp37]*rate_eval.He4_P37__n_Cl40  +
          -rho*Y[jp]*Y[jp37]*rate_eval.p_P37__He4_Si34  +
          +rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__n_P37  +
          +rho*Y[jhe4]*Y[jal34]*rate_eval.He4_Al34__n_P37  +
          -Y[jp37]*rate_eval.P37__S37__weak__wc12  +
          -rho*Y[jhe4]*Y[jp37]*rate_eval.He4_P37__Cl41  +
          +rho*Y[jn]*Y[jp36]*rate_eval.n_P36__P37  +
          +Y[jsi39]*rate_eval.Si39__n_n_P37__weak__mp17  +
          +rho*Y[jp]*Y[js40]*rate_eval.p_S40__He4_P37  +
          -rho*Y[jp]*Y[jp37]*rate_eval.p_P37__S38  +
          +Y[jsi38]*rate_eval.Si38__n_P37__weak__mp17  +
          -rho*Y[jn]*Y[jp37]*rate_eval.n_P37__P38  +
          +rho*Y[jp]*Y[jsi36]*rate_eval.p_Si36__P37  +
          -rho*Y[jp]*Y[jp37]*rate_eval.p_P37__n_S37  +
          +rho*Y[jhe4]*Y[jal33]*rate_eval.He4_Al33__P37  +
          +Y[jsi37]*rate_eval.Si37__P37__weak__wc12
       )

    dYdt[jp38] = (
          +rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__n_P38  +
          +rho*Y[jp]*Y[js41]*rate_eval.p_S41__He4_P38  +
          -rho*Y[jp]*Y[jp38]*rate_eval.p_P38__He4_Si35  +
          -rho*Y[jp]*Y[jp38]*rate_eval.p_P38__n_S38  +
          +rho*Y[jhe4]*Y[jal35]*rate_eval.He4_Al35__n_P38  +
          +rho*Y[jp]*Y[jsi37]*rate_eval.p_Si37__P38  +
          -rho*Y[jp]*Y[jp38]*rate_eval.p_P38__S39  +
          -rho*Y[jn]*Y[jp38]*rate_eval.n_P38__P39  +
          +rho*Y[jhe4]*Y[jal34]*rate_eval.He4_Al34__P38  +
          -rho*Y[jhe4]*Y[jp38]*rate_eval.He4_P38__Cl42  +
          -Y[jp38]*rate_eval.P38__S38__weak__wc12  +
          -rho*Y[jhe4]*Y[jp38]*rate_eval.He4_P38__n_Cl41  +
          +Y[jsi38]*rate_eval.Si38__P38__weak__mo03  +
          +Y[jsi39]*rate_eval.Si39__n_P38__weak__mp17  +
          +rho*Y[jn]*Y[jp37]*rate_eval.n_P37__P38  +
          -Y[jp38]*rate_eval.P38__n_S37__weak__wc12
       )

    dYdt[jp39] = (
          +Y[jsi42]*rate_eval.Si42__n_n_n_P39__weak__mo03  +
          -rho*Y[jhe4]*Y[jp39]*rate_eval.He4_P39__n_Cl42  +
          +rho*Y[jp]*Y[jsi39]*rate_eval.p_Si39__n_P39  +
          +rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__n_P39  +
          +rho*Y[jp]*Y[jsi38]*rate_eval.p_Si38__P39  +
          +rho*Y[jhe4]*Y[jal35]*rate_eval.He4_Al35__P39  +
          +rho*Y[jn]*Y[jp38]*rate_eval.n_P38__P39  +
          -rho*Y[jn]*Y[jp39]*rate_eval.n_P39__P40  +
          +Y[jsi41]*rate_eval.Si41__n_n_P39__weak__mp17  +
          -rho*Y[jp]*Y[jp39]*rate_eval.p_P39__n_S39  +
          +rho*Y[jp]*Y[js42]*rate_eval.p_S42__He4_P39  +
          -rho*Y[jhe4]*Y[jp39]*rate_eval.He4_P39__Cl43  +
          -rho*Y[jp]*Y[jp39]*rate_eval.p_P39__He4_Si36  +
          -Y[jp39]*rate_eval.P39__n_S38__weak__wc12  +
          +Y[jsi40]*rate_eval.Si40__n_P39__weak__mp17  +
          -Y[jp39]*rate_eval.P39__S39__weak__wc12  +
          +Y[jsi39]*rate_eval.Si39__P39__weak__wc17  +
          -rho*Y[jp]*Y[jp39]*rate_eval.p_P39__S40
       )

    dYdt[jp40] = (
          +rho*Y[jp]*Y[js43]*rate_eval.p_S43__He4_P40  +
          +rho*Y[jhe4]*Y[jal37]*rate_eval.He4_Al37__n_P40  +
          -Y[jp40]*rate_eval.P40__S40__weak__wc12  +
          -rho*Y[jhe4]*Y[jp40]*rate_eval.He4_P40__n_Cl43  +
          -rho*Y[jp]*Y[jp40]*rate_eval.p_P40__n_S40  +
          -rho*Y[jhe4]*Y[jp40]*rate_eval.He4_P40__Cl44  +
          -rho*Y[jp]*Y[jp40]*rate_eval.p_P40__S41  +
          +rho*Y[jp]*Y[jsi39]*rate_eval.p_Si39__P40  +
          +rho*Y[jhe4]*Y[jal36]*rate_eval.He4_Al36__P40  +
          +rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__n_P40  +
          +rho*Y[jn]*Y[jp39]*rate_eval.n_P39__P40  +
          -rho*Y[jn]*Y[jp40]*rate_eval.n_P40__P41  +
          +Y[jsi41]*rate_eval.Si41__n_P40__weak__mp17  +
          -Y[jp40]*rate_eval.P40__n_S39__weak__wc12  +
          +Y[jsi43]*rate_eval.Si43__n_n_n_P40__weak__mo03  +
          -rho*Y[jp]*Y[jp40]*rate_eval.p_P40__He4_Si37  +
          +Y[jsi40]*rate_eval.Si40__P40__weak__wc17
       )

    dYdt[jp41] = (
          +rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__n_P41  +
          -rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__p_S44  +
          -rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__n_Cl44  +
          +Y[jsi43]*rate_eval.Si43__n_n_P41__weak__mp17  +
          -rho*Y[jn]*Y[jp41]*rate_eval.n_P41__P42  +
          +rho*Y[jp]*Y[jsi40]*rate_eval.p_Si40__P41  +
          +rho*Y[jhe4]*Y[jal37]*rate_eval.He4_Al37__P41  +
          -Y[jp41]*rate_eval.P41__n_S40__weak__wc12  +
          -rho*Y[jp]*Y[jp41]*rate_eval.p_P41__n_S41  +
          +rho*Y[jn]*Y[jp40]*rate_eval.n_P40__P41  +
          -rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__Cl45  +
          -rho*Y[jp]*Y[jp41]*rate_eval.p_P41__S42  +
          +Y[jsi42]*rate_eval.Si42__n_P41__weak__mp17  +
          +Y[jsi41]*rate_eval.Si41__P41__weak__wc17  +
          +Y[jsi44]*rate_eval.Si44__n_n_n_P41__weak__mo03  +
          -Y[jp41]*rate_eval.P41__S41__weak__wc12  +
          +rho*Y[jp]*Y[jsi41]*rate_eval.p_Si41__n_P41  +
          -rho*Y[jp]*Y[jp41]*rate_eval.p_P41__He4_Si38
       )

    dYdt[jp42] = (
          -rho*Y[jp]*Y[jp42]*rate_eval.p_P42__n_S42  +
          -Y[jp42]*rate_eval.P42__n_n_S40__weak__mp17  +
          +rho*Y[jp]*Y[js45]*rate_eval.p_S45__He4_P42  +
          -rho*Y[jp]*Y[jp42]*rate_eval.p_P42__He4_Si39  +
          -rho*Y[jhe4]*Y[jp42]*rate_eval.He4_P42__n_Cl45  +
          +rho*Y[jp]*Y[jsi42]*rate_eval.p_Si42__n_P42  +
          -rho*Y[jn]*Y[jp42]*rate_eval.n_P42__P43  +
          +rho*Y[jn]*Y[jp41]*rate_eval.n_P41__P42  +
          +rho*Y[jhe4]*Y[jal38]*rate_eval.He4_Al38__P42  +
          +Y[jsi42]*rate_eval.Si42__P42__weak__wc17  +
          +Y[jsi44]*rate_eval.Si44__n_n_P42__weak__mp17  +
          +Y[jsi43]*rate_eval.Si43__n_P42__weak__mp17  +
          -rho*Y[jp]*Y[jp42]*rate_eval.p_P42__S43  +
          +rho*Y[jp]*Y[jsi41]*rate_eval.p_Si41__P42  +
          -Y[jp42]*rate_eval.P42__n_S41__weak__wc12  +
          -rho*Y[jhe4]*Y[jp42]*rate_eval.He4_P42__Cl46  +
          +rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__n_P42  +
          -Y[jp42]*rate_eval.P42__S42__weak__wc17
       )

    dYdt[jp43] = (
          +rho*Y[jp]*Y[jsi43]*rate_eval.p_Si43__n_P43  +
          -rho*Y[jhe4]*Y[jp43]*rate_eval.He4_P43__n_Cl46  +
          -rho*Y[jp]*Y[jp43]*rate_eval.p_P43__He4_Si40  +
          -rho*Y[jp]*Y[jp43]*rate_eval.p_P43__n_S43  +
          +rho*Y[jhe4]*Y[jal40]*rate_eval.He4_Al40__n_P43  +
          +rho*Y[jp]*Y[js46]*rate_eval.p_S46__He4_P43  +
          +Y[jsi44]*rate_eval.Si44__n_P43__weak__mp17  +
          +rho*Y[jn]*Y[jp42]*rate_eval.n_P42__P43  +
          +rho*Y[jp]*Y[jsi42]*rate_eval.p_Si42__P43  +
          -Y[jp43]*rate_eval.P43__n_n_S41__weak__mp17  +
          -Y[jp43]*rate_eval.P43__n_S42__weak__wc12  +
          +rho*Y[jhe4]*Y[jal39]*rate_eval.He4_Al39__P43  +
          -rho*Y[jhe4]*Y[jp43]*rate_eval.He4_P43__Cl47  +
          -Y[jp43]*rate_eval.P43__S43__weak__wc17  +
          -rho*Y[jp]*Y[jp43]*rate_eval.p_P43__S44  +
          +Y[jsi43]*rate_eval.Si43__P43__weak__mo03  +
          -rho*Y[jn]*Y[jp43]*rate_eval.n_P43__P44
       )

    dYdt[jp44] = (
          -Y[jp44]*rate_eval.P44__n_n_n_S41__weak__mo03  +
          +rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__n_P44  +
          -rho*Y[jhe4]*Y[jp44]*rate_eval.He4_P44__n_Cl47  +
          +rho*Y[jp]*Y[js47]*rate_eval.p_S47__He4_P44  +
          -rho*Y[jp]*Y[jp44]*rate_eval.p_P44__He4_Si41  +
          +Y[jsi45]*rate_eval.Si45__n_P44__weak__mp17  +
          -rho*Y[jn]*Y[jp44]*rate_eval.n_P44__P45  +
          +rho*Y[jhe4]*Y[jal40]*rate_eval.He4_Al40__P44  +
          -Y[jp44]*rate_eval.P44__S44__weak__wc17  +
          -Y[jp44]*rate_eval.P44__n_n_S42__weak__mp17  +
          -Y[jp44]*rate_eval.P44__n_S43__weak__mp17  +
          -rho*Y[jp]*Y[jp44]*rate_eval.p_P44__n_S44  +
          -rho*Y[jhe4]*Y[jp44]*rate_eval.He4_P44__Cl48  +
          -rho*Y[jp]*Y[jp44]*rate_eval.p_P44__S45  +
          +rho*Y[jhe4]*Y[jal41]*rate_eval.He4_Al41__n_P44  +
          +rho*Y[jp]*Y[jsi43]*rate_eval.p_Si43__P44  +
          +rho*Y[jn]*Y[jp43]*rate_eval.n_P43__P44
       )

    dYdt[jp45] = (
          -rho*Y[jp]*Y[jp45]*rate_eval.p_P45__S46  +
          -rho*Y[jp]*Y[jp45]*rate_eval.p_P45__n_S45  +
          +rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__n_P45  +
          +rho*Y[jhe4]*Y[jal42]*rate_eval.He4_Al42__n_P45  +
          -Y[jp45]*rate_eval.P45__n_n_n_S42__weak__mo03  +
          -rho*Y[jn]*Y[jp45]*rate_eval.n_P45__P46  +
          +rho*Y[jn]*Y[jp44]*rate_eval.n_P44__P45  +
          +rho*Y[jhe4]*Y[jal41]*rate_eval.He4_Al41__P45  +
          +rho*Y[jp]*Y[js48]*rate_eval.p_S48__He4_P45  +
          +rho*Y[jp]*Y[jsi44]*rate_eval.p_Si44__P45  +
          +Y[jsi45]*rate_eval.Si45__P45__weak__mo03  +
          -Y[jp45]*rate_eval.P45__n_n_S43__weak__mp17  +
          -rho*Y[jhe4]*Y[jp45]*rate_eval.He4_P45__n_Cl48  +
          -rho*Y[jhe4]*Y[jp45]*rate_eval.He4_P45__Cl49  +
          -rho*Y[jp]*Y[jp45]*rate_eval.p_P45__He4_Si42  +
          -Y[jp45]*rate_eval.P45__S45__weak__mo03  +
          -Y[jp45]*rate_eval.P45__n_S44__weak__mp17
       )

    dYdt[jp46] = (
          -rho*Y[jp]*Y[jp46]*rate_eval.p_P46__S47  +
          +rho*Y[jp]*Y[jsi45]*rate_eval.p_Si45__P46  +
          -Y[jp46]*rate_eval.P46__n_n_n_S43__weak__mo03  +
          +rho*Y[jn]*Y[jp45]*rate_eval.n_P45__P46  +
          +rho*Y[jhe4]*Y[jal42]*rate_eval.He4_Al42__P46  +
          +rho*Y[jp]*Y[js49]*rate_eval.p_S49__He4_P46  +
          -rho*Y[jp]*Y[jp46]*rate_eval.p_P46__He4_Si43  +
          -rho*Y[jp]*Y[jp46]*rate_eval.p_P46__n_S46  +
          -rho*Y[jhe4]*Y[jp46]*rate_eval.He4_P46__n_Cl49  +
          -rho*Y[jhe4]*Y[jp46]*rate_eval.He4_P46__Cl50  +
          +rho*Y[jhe4]*Y[jal43]*rate_eval.He4_Al43__n_P46  +
          -rho*Y[jn]*Y[jp46]*rate_eval.n_P46__P47  +
          -Y[jp46]*rate_eval.P46__n_S45__weak__mp17  +
          -Y[jp46]*rate_eval.P46__S46__weak__mo03  +
          -Y[jp46]*rate_eval.P46__n_n_S44__weak__mp17
       )

    dYdt[jp47] = (
          -rho*Y[jhe4]*Y[jp47]*rate_eval.He4_P47__n_Cl50  +
          -rho*Y[jp]*Y[jp47]*rate_eval.p_P47__n_S47  +
          -Y[jp47]*rate_eval.P47__n_n_n_S44__weak__mo03  +
          +rho*Y[jhe4]*Y[jal43]*rate_eval.He4_Al43__P47  +
          -Y[jp47]*rate_eval.P47__n_n_S45__weak__mp17  +
          +rho*Y[jn]*Y[jp46]*rate_eval.n_P46__P47  +
          -rho*Y[jhe4]*Y[jp47]*rate_eval.He4_P47__Cl51  +
          -Y[jp47]*rate_eval.P47__n_S46__weak__mp17  +
          -Y[jp47]*rate_eval.P47__S47__weak__mo03  +
          -rho*Y[jp]*Y[jp47]*rate_eval.p_P47__He4_Si44  +
          -rho*Y[jp]*Y[jp47]*rate_eval.p_P47__S48
       )

    dYdt[js26] = (
          +rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__He4_S26  +
          -rho*Y[jhe4]*Y[js26]*rate_eval.He4_S26__p_Cl29  +
          -rho*Y[jn]*Y[js26]*rate_eval.n_S26__He4_Si23  +
          -rho*Y[jn]*Y[js26]*rate_eval.n_S26__p_P26  +
          -rho*Y[jn]*Y[js26]*rate_eval.n_S26__S27  +
          -rho*Y[jhe4]*Y[js26]*rate_eval.He4_S26__Ar30  +
          -Y[js26]*rate_eval.S26__P26__weak__bqa_pos_  +
          +rho*Y[jp]*Y[jp25]*rate_eval.p_P25__S26  +
          +rho*Y[jhe4]*Y[jsi22]*rate_eval.He4_Si22__S26
       )

    dYdt[js27] = (
          +rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__He4_S27  +
          +rho*Y[jhe4]*Y[jp24]*rate_eval.He4_P24__p_S27  +
          -rho*Y[jhe4]*Y[js27]*rate_eval.He4_S27__p_Cl30  +
          -Y[js27]*rate_eval.S27__p_Si26__weak__wc17  +
          +rho*Y[jhe4]*Y[jsi23]*rate_eval.He4_Si23__S27  +
          -rho*Y[jhe4]*Y[js27]*rate_eval.He4_S27__Ar31  +
          -rho*Y[jn]*Y[js27]*rate_eval.n_S27__S28  +
          +rho*Y[jn]*Y[js26]*rate_eval.n_S26__S27  +
          +rho*Y[jp]*Y[jp26]*rate_eval.p_P26__S27  +
          -Y[js27]*rate_eval.S27__P27__weak__wc12  +
          -Y[js27]*rate_eval.S27__p_p_Al25__weak__wc12  +
          -rho*Y[jn]*Y[js27]*rate_eval.n_S27__He4_Si24  +
          -rho*Y[jn]*Y[js27]*rate_eval.n_S27__p_P27  +
          -rho*Y[jp]*Y[js27]*rate_eval.p_S27__Cl28
       )

    dYdt[js28] = (
          +rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__He4_S28  +
          -rho*Y[jhe4]*Y[js28]*rate_eval.He4_S28__p_Cl31  +
          -rho*Y[jn]*Y[js28]*rate_eval.n_S28__He4_Si25  +
          +rho*Y[jhe4]*Y[jp25]*rate_eval.He4_P25__p_S28  +
          -rho*Y[jn]*Y[js28]*rate_eval.n_S28__S29  +
          +rho*Y[jn]*Y[js27]*rate_eval.n_S27__S28  +
          +rho*Y[jhe4]*Y[jsi24]*rate_eval.He4_Si24__S28  +
          +Y[jcl28]*rate_eval.Cl28__S28__weak__bqa_pos_  +
          -Y[js28]*rate_eval.S28__p_Si27__weak__wc12  +
          -rho*Y[jhe4]*Y[js28]*rate_eval.He4_S28__Ar32  +
          +rho*Y[jp]*Y[jp27]*rate_eval.p_P27__S28  +
          +rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__p_S28  +
          -rho*Y[jn]*Y[js28]*rate_eval.n_S28__p_P28  +
          -Y[js28]*rate_eval.S28__P28__weak__wc12  +
          -rho*Y[jp]*Y[js28]*rate_eval.p_S28__Cl29
       )

    dYdt[js29] = (
          +rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__He4_S29  +
          +rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__p_S29  +
          +rho*Y[jhe4]*Y[jp26]*rate_eval.He4_P26__p_S29  +
          -rho*Y[jn]*Y[js29]*rate_eval.n_S29__He4_Si26  +
          -rho*Y[jhe4]*Y[js29]*rate_eval.He4_S29__p_Cl32  +
          -rho*Y[jn]*Y[js29]*rate_eval.n_S29__p_P29  +
          +rho*Y[jn]*Y[js28]*rate_eval.n_S28__S29  +
          +rho*Y[jp]*Y[jp28]*rate_eval.p_P28__S29  +
          +Y[jcl29]*rate_eval.Cl29__S29__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[js29]*rate_eval.He4_S29__Ar33  +
          +rho*Y[jhe4]*Y[jsi25]*rate_eval.He4_Si25__S29  +
          -Y[js29]*rate_eval.S29__p_Si28__weak__wc12  +
          -Y[js29]*rate_eval.S29__P29__weak__wc12  +
          -rho*Y[jn]*Y[js29]*rate_eval.n_S29__S30  +
          -rho*Y[jp]*Y[js29]*rate_eval.p_S29__Cl30
       )

    dYdt[js30] = (
          -rho*Y[jhe4]*Y[js30]*rate_eval.He4_S30__Ar34  +
          +rho*Y[jp]*Y[jp29]*rate_eval.p_P29__S30  +
          -rho*Y[jhe4]*Y[js30]*rate_eval.He4_S30__p_Cl33  +
          -rho*Y[jn]*Y[js30]*rate_eval.n_S30__He4_Si27  +
          -rho*Y[jn]*Y[js30]*rate_eval.n_S30__p_P30  +
          +rho*Y[jhe4]*Y[jp27]*rate_eval.He4_P27__p_S30  +
          +rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__p_S30  +
          -Y[js30]*rate_eval.S30__P30__weak__wc12  +
          -rho*Y[jp]*Y[js30]*rate_eval.p_S30__Cl31  +
          -rho*Y[jn]*Y[js30]*rate_eval.n_S30__S31  +
          +rho*Y[jhe4]*Y[jsi26]*rate_eval.He4_Si26__S30  +
          +Y[jar31]*rate_eval.Ar31__p_S30__weak__wc17  +
          +rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__He4_S30  +
          +rho*Y[jn]*Y[js29]*rate_eval.n_S29__S30  +
          +Y[jcl30]*rate_eval.Cl30__S30__weak__bqa_pos_
       )

    dYdt[js31] = (
          +rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__p_S31  +
          -rho*Y[jhe4]*Y[js31]*rate_eval.He4_S31__p_Cl34  +
          -rho*Y[jn]*Y[js31]*rate_eval.n_S31__p_P31  +
          +rho*Y[jn]*Y[js30]*rate_eval.n_S30__S31  +
          +5.00000000000000e-01*rho*Y[jo16]**2*rate_eval.O16_O16__n_S31  +
          +rho*Y[jc12]*Y[jne20]*rate_eval.C12_Ne20__n_S31  +
          +rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__He4_S31  +
          +rho*Y[jp]*Y[jp30]*rate_eval.p_P30__S31  +
          -rho*Y[jp]*Y[js31]*rate_eval.p_S31__Cl32  +
          -rho*Y[jn]*Y[js31]*rate_eval.n_S31__He4_Si28  +
          +rho*Y[jhe4]*Y[jp28]*rate_eval.He4_P28__p_S31  +
          +Y[jar32]*rate_eval.Ar32__p_S31__weak__wc12  +
          -rho*Y[jhe4]*Y[js31]*rate_eval.He4_S31__Ar35  +
          -Y[js31]*rate_eval.S31__P31__weak__wc12  +
          +rho*Y[jhe4]*Y[jsi27]*rate_eval.He4_Si27__S31  +
          -rho*Y[jn]*Y[js31]*rate_eval.n_S31__S32  +
          +Y[jcl31]*rate_eval.Cl31__S31__weak__wc12
       )

    dYdt[js32] = (
          +rho*Y[jp]*Y[jp32]*rate_eval.p_P32__n_S32  +
          +rho*Y[jp]*Y[jp31]*rate_eval.p_P31__S32  +
          +rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__He4_S32  +
          +rho*Y[jp]*Y[jcl35]*rate_eval.p_Cl35__He4_S32  +
          +Y[jcl32]*rate_eval.Cl32__S32__weak__wc12  +
          -rho*Y[jhe4]*Y[js32]*rate_eval.He4_S32__Ar36  +
          -rho*Y[jp]*Y[js32]*rate_eval.p_S32__Cl33  +
          -rho*Y[jn]*Y[js32]*rate_eval.n_S32__S33  +
          +rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__p_S32  +
          +Y[jp32]*rate_eval.P32__S32__weak__wc12  +
          +Y[jk36]*rate_eval.K36__He4_S32__weak__wc12  +
          +rho*Y[jhe4]*Y[jsi28]*rate_eval.He4_Si28__S32  +
          +Y[jar33]*rate_eval.Ar33__p_S32__weak__wc12  +
          +rho*Y[jhe4]*Y[jp29]*rate_eval.He4_P29__p_S32  +
          +rho*Y[jn]*Y[js31]*rate_eval.n_S31__S32  +
          -rho*Y[jn]*Y[js32]*rate_eval.n_S32__He4_Si29
       )

    dYdt[js33] = (
          +rho*Y[jn]*Y[jar36]*rate_eval.n_Ar36__He4_S33  +
          +rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__p_S33  +
          -rho*Y[jn]*Y[js33]*rate_eval.n_S33__He4_Si30  +
          -rho*Y[jn]*Y[js33]*rate_eval.n_S33__p_P33  +
          +rho*Y[jhe4]*Y[jp30]*rate_eval.He4_P30__p_S33  +
          +Y[jp33]*rate_eval.P33__S33__weak__wc12  +
          +rho*Y[jp]*Y[jp32]*rate_eval.p_P32__S33  +
          +rho*Y[jp]*Y[jcl36]*rate_eval.p_Cl36__He4_S33  +
          -rho*Y[jn]*Y[js33]*rate_eval.n_S33__S34  +
          +rho*Y[jn]*Y[js32]*rate_eval.n_S32__S33  +
          -rho*Y[jp]*Y[js33]*rate_eval.p_S33__Cl34  +
          +rho*Y[jhe4]*Y[jsi29]*rate_eval.He4_Si29__S33  +
          -rho*Y[jhe4]*Y[js33]*rate_eval.He4_S33__Ar37  +
          +Y[jcl33]*rate_eval.Cl33__S33__weak__wc12
       )

    dYdt[js34] = (
          +rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__p_S34  +
          +rho*Y[jp]*Y[jp34]*rate_eval.p_P34__n_S34  +
          +rho*Y[jhe4]*Y[jp31]*rate_eval.He4_P31__p_S34  +
          +rho*Y[jhe4]*Y[jsi31]*rate_eval.He4_Si31__n_S34  +
          -rho*Y[jp]*Y[js34]*rate_eval.p_S34__Cl35  +
          -rho*Y[jn]*Y[js34]*rate_eval.n_S34__S35  +
          +rho*Y[jn]*Y[js33]*rate_eval.n_S33__S34  +
          +rho*Y[jp]*Y[jp33]*rate_eval.p_P33__S34  +
          -rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__Ar38  +
          +Y[jcl34]*rate_eval.Cl34__S34__weak__wc12  +
          +rho*Y[jhe4]*Y[jsi30]*rate_eval.He4_Si30__S34  +
          +Y[jp34]*rate_eval.P34__S34__weak__wc12  +
          -rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__p_Cl37  +
          -rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__n_Ar37
       )

    dYdt[js35] = (
          +rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__p_S35  +
          -rho*Y[jhe4]*Y[js35]*rate_eval.He4_S35__n_Ar38  +
          -rho*Y[jp]*Y[js35]*rate_eval.p_S35__He4_P32  +
          -rho*Y[jn]*Y[js35]*rate_eval.n_S35__He4_Si32  +
          +rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__He4_S35  +
          +rho*Y[jp]*Y[jp34]*rate_eval.p_P34__S35  +
          -rho*Y[jp]*Y[js35]*rate_eval.p_S35__Cl36  +
          +rho*Y[jn]*Y[js34]*rate_eval.n_S34__S35  +
          +rho*Y[jhe4]*Y[jsi31]*rate_eval.He4_Si31__S35  +
          +rho*Y[jp]*Y[jp35]*rate_eval.p_P35__n_S35  +
          -rho*Y[jn]*Y[js35]*rate_eval.n_S35__S36  +
          -Y[js35]*rate_eval.S35__Cl35__weak__wc12  +
          -rho*Y[jhe4]*Y[js35]*rate_eval.He4_S35__Ar39  +
          +Y[jp35]*rate_eval.P35__S35__weak__wc12
       )

    dYdt[js36] = (
          +rho*Y[jhe4]*Y[jsi33]*rate_eval.He4_Si33__n_S36  +
          +rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__p_S36  +
          -rho*Y[jp]*Y[js36]*rate_eval.p_S36__He4_P33  +
          +rho*Y[jp]*Y[jp36]*rate_eval.p_P36__n_S36  +
          +rho*Y[jn]*Y[jar39]*rate_eval.n_Ar39__He4_S36  +
          +rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__He4_S36  +
          +Y[jp36]*rate_eval.P36__S36__weak__wc12  +
          -rho*Y[jhe4]*Y[js36]*rate_eval.He4_S36__Ar40  +
          -rho*Y[jp]*Y[js36]*rate_eval.p_S36__Cl37  +
          +rho*Y[jp]*Y[jp35]*rate_eval.p_P35__S36  +
          +rho*Y[jn]*Y[js35]*rate_eval.n_S35__S36  +
          +rho*Y[jhe4]*Y[jsi32]*rate_eval.He4_Si32__S36  +
          -rho*Y[jn]*Y[js36]*rate_eval.n_S36__S37  +
          +Y[jcl36]*rate_eval.Cl36__S36__weak__wc12
       )

    dYdt[js37] = (
          -rho*Y[jp]*Y[js37]*rate_eval.p_S37__Cl38  +
          +rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__He4_S37  +
          -rho*Y[jhe4]*Y[js37]*rate_eval.He4_S37__n_Ar40  +
          -rho*Y[jp]*Y[js37]*rate_eval.p_S37__n_Cl37  +
          -Y[js37]*rate_eval.S37__Cl37__weak__wc12  +
          +Y[jp37]*rate_eval.P37__S37__weak__wc12  +
          +rho*Y[jhe4]*Y[jsi33]*rate_eval.He4_Si33__S37  +
          -rho*Y[jp]*Y[js37]*rate_eval.p_S37__He4_P34  +
          -rho*Y[jn]*Y[js37]*rate_eval.n_S37__S38  +
          +rho*Y[jn]*Y[js36]*rate_eval.n_S36__S37  +
          +rho*Y[jp]*Y[jp37]*rate_eval.p_P37__n_S37  +
          +rho*Y[jhe4]*Y[jsi34]*rate_eval.He4_Si34__n_S37  +
          +Y[jp38]*rate_eval.P38__n_S37__weak__wc12  +
          -rho*Y[jhe4]*Y[js37]*rate_eval.He4_S37__Ar41  +
          +rho*Y[jp]*Y[jp36]*rate_eval.p_P36__S37
       )

    dYdt[js38] = (
          +rho*Y[jhe4]*Y[jsi35]*rate_eval.He4_Si35__n_S38  +
          +rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__He4_S38  +
          -rho*Y[jhe4]*Y[js38]*rate_eval.He4_S38__n_Ar41  +
          -rho*Y[jp]*Y[js38]*rate_eval.p_S38__He4_P35  +
          -rho*Y[jp]*Y[js38]*rate_eval.p_S38__n_Cl38  +
          +rho*Y[jp]*Y[jp38]*rate_eval.p_P38__n_S38  +
          -rho*Y[jp]*Y[js38]*rate_eval.p_S38__Cl39  +
          -rho*Y[jn]*Y[js38]*rate_eval.n_S38__S39  +
          +rho*Y[jhe4]*Y[jsi34]*rate_eval.He4_Si34__S38  +
          -rho*Y[jhe4]*Y[js38]*rate_eval.He4_S38__Ar42  +
          +rho*Y[jn]*Y[js37]*rate_eval.n_S37__S38  +
          +Y[jp38]*rate_eval.P38__S38__weak__wc12  +
          +Y[jp39]*rate_eval.P39__n_S38__weak__wc12  +
          +rho*Y[jp]*Y[jp37]*rate_eval.p_P37__S38  +
          -Y[js38]*rate_eval.S38__Cl38__weak__wc12
       )

    dYdt[js39] = (
          +rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__He4_S39  +
          -rho*Y[jp]*Y[js39]*rate_eval.p_S39__He4_P36  +
          -rho*Y[jhe4]*Y[js39]*rate_eval.He4_S39__n_Ar42  +
          -rho*Y[jhe4]*Y[js39]*rate_eval.He4_S39__Ar43  +
          -rho*Y[jp]*Y[js39]*rate_eval.p_S39__Cl40  +
          +rho*Y[jn]*Y[js38]*rate_eval.n_S38__S39  +
          +rho*Y[jp]*Y[jp38]*rate_eval.p_P38__S39  +
          +rho*Y[jp]*Y[jp39]*rate_eval.p_P39__n_S39  +
          +rho*Y[jhe4]*Y[jsi36]*rate_eval.He4_Si36__n_S39  +
          +rho*Y[jhe4]*Y[jsi35]*rate_eval.He4_Si35__S39  +
          -rho*Y[jp]*Y[js39]*rate_eval.p_S39__n_Cl39  +
          -Y[js39]*rate_eval.S39__Cl39__weak__wc12  +
          +Y[jp40]*rate_eval.P40__n_S39__weak__wc12  +
          -rho*Y[jn]*Y[js39]*rate_eval.n_S39__S40  +
          +Y[jp39]*rate_eval.P39__S39__weak__wc12
       )

    dYdt[js40] = (
          +rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__He4_S40  +
          +Y[jp42]*rate_eval.P42__n_n_S40__weak__mp17  +
          -rho*Y[jp]*Y[js40]*rate_eval.p_S40__n_Cl40  +
          +rho*Y[jhe4]*Y[jsi37]*rate_eval.He4_Si37__n_S40  +
          +Y[jp40]*rate_eval.P40__S40__weak__wc12  +
          +rho*Y[jp]*Y[jp40]*rate_eval.p_P40__n_S40  +
          -rho*Y[jp]*Y[js40]*rate_eval.p_S40__Cl41  +
          -rho*Y[jn]*Y[js40]*rate_eval.n_S40__S41  +
          +Y[jp41]*rate_eval.P41__n_S40__weak__wc12  +
          -rho*Y[jhe4]*Y[js40]*rate_eval.He4_S40__n_Ar43  +
          -rho*Y[jp]*Y[js40]*rate_eval.p_S40__He4_P37  +
          +rho*Y[jhe4]*Y[jsi36]*rate_eval.He4_Si36__S40  +
          +rho*Y[jn]*Y[js39]*rate_eval.n_S39__S40  +
          -Y[js40]*rate_eval.S40__Cl40__weak__wc12  +
          +rho*Y[jp]*Y[jp39]*rate_eval.p_P39__S40  +
          -rho*Y[jhe4]*Y[js40]*rate_eval.He4_S40__Ar44
       )

    dYdt[js41] = (
          +Y[jp44]*rate_eval.P44__n_n_n_S41__weak__mo03  +
          -rho*Y[jhe4]*Y[js41]*rate_eval.He4_S41__n_Ar44  +
          -rho*Y[jp]*Y[js41]*rate_eval.p_S41__He4_P38  +
          +rho*Y[jhe4]*Y[jsi38]*rate_eval.He4_Si38__n_S41  +
          -rho*Y[jhe4]*Y[js41]*rate_eval.He4_S41__Ar45  +
          -rho*Y[jp]*Y[js41]*rate_eval.p_S41__Cl42  +
          +rho*Y[jn]*Y[js40]*rate_eval.n_S40__S41  +
          +rho*Y[jp]*Y[jp40]*rate_eval.p_P40__S41  +
          -rho*Y[jn]*Y[js41]*rate_eval.n_S41__S42  +
          +Y[jp43]*rate_eval.P43__n_n_S41__weak__mp17  +
          +rho*Y[jp]*Y[jp41]*rate_eval.p_P41__n_S41  +
          -rho*Y[jp]*Y[js41]*rate_eval.p_S41__n_Cl41  +
          +rho*Y[jhe4]*Y[jsi37]*rate_eval.He4_Si37__S41  +
          +Y[jp42]*rate_eval.P42__n_S41__weak__wc12  +
          -Y[js41]*rate_eval.S41__Cl41__weak__wc12  +
          +Y[jp41]*rate_eval.P41__S41__weak__wc12  +
          +rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__He4_S41
       )

    dYdt[js42] = (
          +rho*Y[jp]*Y[jp42]*rate_eval.p_P42__n_S42  +
          -rho*Y[jp]*Y[js42]*rate_eval.p_S42__Cl43  +
          +rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__He4_S42  +
          -rho*Y[jhe4]*Y[js42]*rate_eval.He4_S42__n_Ar45  +
          +rho*Y[jhe4]*Y[jsi39]*rate_eval.He4_Si39__n_S42  +
          +Y[jp45]*rate_eval.P45__n_n_n_S42__weak__mo03  +
          -rho*Y[jp]*Y[js42]*rate_eval.p_S42__n_Cl42  +
          -rho*Y[jhe4]*Y[js42]*rate_eval.He4_S42__Ar46  +
          -rho*Y[jn]*Y[js42]*rate_eval.n_S42__S43  +
          +rho*Y[jhe4]*Y[jsi38]*rate_eval.He4_Si38__S42  +
          +rho*Y[jn]*Y[js41]*rate_eval.n_S41__S42  +
          +Y[jp44]*rate_eval.P44__n_n_S42__weak__mp17  +
          +Y[jp43]*rate_eval.P43__n_S42__weak__wc12  +
          +rho*Y[jp]*Y[jp41]*rate_eval.p_P41__S42  +
          -rho*Y[jp]*Y[js42]*rate_eval.p_S42__He4_P39  +
          +Y[jp42]*rate_eval.P42__S42__weak__wc17  +
          -Y[js42]*rate_eval.S42__Cl42__weak__wc12
       )

    dYdt[js43] = (
          -rho*Y[jhe4]*Y[js43]*rate_eval.He4_S43__n_Ar46  +
          -rho*Y[jp]*Y[js43]*rate_eval.p_S43__He4_P40  +
          +rho*Y[jp]*Y[jp43]*rate_eval.p_P43__n_S43  +
          +rho*Y[jhe4]*Y[jsi40]*rate_eval.He4_Si40__n_S43  +
          +rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__He4_S43  +
          +Y[jp46]*rate_eval.P46__n_n_n_S43__weak__mo03  +
          -rho*Y[jhe4]*Y[js43]*rate_eval.He4_S43__Ar47  +
          +rho*Y[jn]*Y[js42]*rate_eval.n_S42__S43  +
          +rho*Y[jhe4]*Y[jsi39]*rate_eval.He4_Si39__S43  +
          +Y[jp45]*rate_eval.P45__n_n_S43__weak__mp17  +
          +rho*Y[jp]*Y[jp42]*rate_eval.p_P42__S43  +
          +Y[jp44]*rate_eval.P44__n_S43__weak__mp17  +
          +Y[jp43]*rate_eval.P43__S43__weak__wc17  +
          -rho*Y[jp]*Y[js43]*rate_eval.p_S43__n_Cl43  +
          -Y[js43]*rate_eval.S43__Cl43__weak__wc12  +
          -rho*Y[jn]*Y[js43]*rate_eval.n_S43__S44  +
          -rho*Y[jp]*Y[js43]*rate_eval.p_S43__Cl44  +
          -Y[js43]*rate_eval.S43__n_Cl42__weak__wc12
       )

    dYdt[js44] = (
          +rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__p_S44  +
          -Y[js44]*rate_eval.S44__n_Cl43__weak__wc12  +
          +Y[jp47]*rate_eval.P47__n_n_n_S44__weak__mo03  +
          -rho*Y[jhe4]*Y[js44]*rate_eval.He4_S44__Ar48  +
          -rho*Y[jp]*Y[js44]*rate_eval.p_S44__Cl45  +
          -rho*Y[jn]*Y[js44]*rate_eval.n_S44__S45  +
          +rho*Y[jhe4]*Y[jsi40]*rate_eval.He4_Si40__S44  +
          +Y[jp44]*rate_eval.P44__S44__weak__wc17  +
          -rho*Y[jp]*Y[js44]*rate_eval.p_S44__n_Cl44  +
          -Y[js44]*rate_eval.S44__Cl44__weak__wc12  +
          +rho*Y[jp]*Y[jp44]*rate_eval.p_P44__n_S44  +
          +rho*Y[jn]*Y[js43]*rate_eval.n_S43__S44  +
          +Y[jp46]*rate_eval.P46__n_n_S44__weak__mp17  +
          +rho*Y[jhe4]*Y[jsi41]*rate_eval.He4_Si41__n_S44  +
          +rho*Y[jp]*Y[jp43]*rate_eval.p_P43__S44  +
          +rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__He4_S44  +
          +Y[jp45]*rate_eval.P45__n_S44__weak__mp17  +
          -rho*Y[jhe4]*Y[js44]*rate_eval.He4_S44__n_Ar47
       )

    dYdt[js45] = (
          -rho*Y[jhe4]*Y[js45]*rate_eval.He4_S45__n_Ar48  +
          -Y[js45]*rate_eval.S45__n_Cl44__weak__wc12  +
          +rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__He4_S45  +
          -rho*Y[jp]*Y[js45]*rate_eval.p_S45__He4_P42  +
          +rho*Y[jp]*Y[jp45]*rate_eval.p_P45__n_S45  +
          +rho*Y[jhe4]*Y[jsi42]*rate_eval.He4_Si42__n_S45  +
          +rho*Y[jn]*Y[js44]*rate_eval.n_S44__S45  +
          +rho*Y[jhe4]*Y[jsi41]*rate_eval.He4_Si41__S45  +
          -rho*Y[jn]*Y[js45]*rate_eval.n_S45__S46  +
          -Y[js45]*rate_eval.S45__n_n_Cl43__weak__mp17  +
          +Y[jp47]*rate_eval.P47__n_n_S45__weak__mp17  +
          -rho*Y[jp]*Y[js45]*rate_eval.p_S45__n_Cl45  +
          -rho*Y[jhe4]*Y[js45]*rate_eval.He4_S45__Ar49  +
          -Y[js45]*rate_eval.S45__Cl45__weak__wc12  +
          +Y[jp46]*rate_eval.P46__n_S45__weak__mp17  +
          +rho*Y[jp]*Y[jp44]*rate_eval.p_P44__S45  +
          +Y[jp45]*rate_eval.P45__S45__weak__mo03  +
          -rho*Y[jp]*Y[js45]*rate_eval.p_S45__Cl46
       )

    dYdt[js46] = (
          +rho*Y[jhe4]*Y[jsi43]*rate_eval.He4_Si43__n_S46  +
          +rho*Y[jp]*Y[jp45]*rate_eval.p_P45__S46  +
          +rho*Y[jhe4]*Y[jsi42]*rate_eval.He4_Si42__S46  +
          -rho*Y[jp]*Y[js46]*rate_eval.p_S46__n_Cl46  +
          -rho*Y[jp]*Y[js46]*rate_eval.p_S46__Cl47  +
          -rho*Y[jhe4]*Y[js46]*rate_eval.He4_S46__n_Ar49  +
          -rho*Y[jp]*Y[js46]*rate_eval.p_S46__He4_P43  +
          -rho*Y[jhe4]*Y[js46]*rate_eval.He4_S46__Ar50  +
          +rho*Y[jn]*Y[js45]*rate_eval.n_S45__S46  +
          -rho*Y[jn]*Y[js46]*rate_eval.n_S46__S47  +
          +rho*Y[jp]*Y[jp46]*rate_eval.p_P46__n_S46  +
          -Y[js46]*rate_eval.S46__Cl46__weak__wc17  +
          +rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__He4_S46  +
          +Y[jp47]*rate_eval.P47__n_S46__weak__mp17  +
          -Y[js46]*rate_eval.S46__n_Cl45__weak__mp17  +
          +Y[jp46]*rate_eval.P46__S46__weak__mo03
       )

    dYdt[js47] = (
          -Y[js47]*rate_eval.S47__n_n_n_Cl44__weak__mo03  +
          +rho*Y[jp]*Y[jp46]*rate_eval.p_P46__S47  +
          -rho*Y[jp]*Y[js47]*rate_eval.p_S47__Cl48  +
          +rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__He4_S47  +
          -rho*Y[jp]*Y[js47]*rate_eval.p_S47__n_Cl47  +
          -rho*Y[jp]*Y[js47]*rate_eval.p_S47__He4_P44  +
          +rho*Y[jp]*Y[jp47]*rate_eval.p_P47__n_S47  +
          +rho*Y[jhe4]*Y[jsi44]*rate_eval.He4_Si44__n_S47  +
          -Y[js47]*rate_eval.S47__Cl47__weak__mo03  +
          -rho*Y[jhe4]*Y[js47]*rate_eval.He4_S47__Ar51  +
          -rho*Y[jn]*Y[js47]*rate_eval.n_S47__S48  +
          +rho*Y[jn]*Y[js46]*rate_eval.n_S46__S47  +
          -Y[js47]*rate_eval.S47__n_n_Cl45__weak__mp17  +
          -rho*Y[jhe4]*Y[js47]*rate_eval.He4_S47__n_Ar50  +
          +rho*Y[jhe4]*Y[jsi43]*rate_eval.He4_Si43__S47  +
          +Y[jp47]*rate_eval.P47__S47__weak__mo03  +
          -Y[js47]*rate_eval.S47__n_Cl46__weak__mp17
       )

    dYdt[js48] = (
          -Y[js48]*rate_eval.S48__n_n_n_Cl45__weak__mo03  +
          +rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__He4_S48  +
          -rho*Y[jhe4]*Y[js48]*rate_eval.He4_S48__n_Ar51  +
          -rho*Y[jp]*Y[js48]*rate_eval.p_S48__n_Cl48  +
          -rho*Y[jhe4]*Y[js48]*rate_eval.He4_S48__Ar52  +
          +rho*Y[jn]*Y[js47]*rate_eval.n_S47__S48  +
          -rho*Y[jp]*Y[js48]*rate_eval.p_S48__He4_P45  +
          -Y[js48]*rate_eval.S48__n_n_Cl46__weak__mp17  +
          +rho*Y[jhe4]*Y[jsi44]*rate_eval.He4_Si44__S48  +
          -Y[js48]*rate_eval.S48__Cl48__weak__mo03  +
          +rho*Y[jp]*Y[jp47]*rate_eval.p_P47__S48  +
          -Y[js48]*rate_eval.S48__n_Cl47__weak__mp17  +
          -rho*Y[jp]*Y[js48]*rate_eval.p_S48__Cl49  +
          +rho*Y[jhe4]*Y[jsi45]*rate_eval.He4_Si45__n_S48  +
          -rho*Y[jn]*Y[js48]*rate_eval.n_S48__S49
       )

    dYdt[js49] = (
          -Y[js49]*rate_eval.S49__n_n_n_Cl46__weak__mo03  +
          +rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__He4_S49  +
          -rho*Y[jp]*Y[js49]*rate_eval.p_S49__n_Cl49  +
          -rho*Y[jp]*Y[js49]*rate_eval.p_S49__Cl50  +
          +rho*Y[jhe4]*Y[jsi45]*rate_eval.He4_Si45__S49  +
          -rho*Y[jhe4]*Y[js49]*rate_eval.He4_S49__Ar53  +
          -Y[js49]*rate_eval.S49__n_Cl48__weak__mp17  +
          -Y[js49]*rate_eval.S49__Cl49__weak__mo03  +
          -rho*Y[jp]*Y[js49]*rate_eval.p_S49__He4_P46  +
          -rho*Y[jhe4]*Y[js49]*rate_eval.He4_S49__n_Ar52  +
          -Y[js49]*rate_eval.S49__n_n_Cl47__weak__mp17  +
          +rho*Y[jn]*Y[js48]*rate_eval.n_S48__S49
       )

    dYdt[jcl28] = (
          -rho*Y[jhe4]*Y[jcl28]*rate_eval.He4_Cl28__p_Ar31  +
          -rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__He4_P25  +
          -rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__Cl29  +
          +rho*Y[jhe4]*Y[jp24]*rate_eval.He4_P24__Cl28  +
          -Y[jcl28]*rate_eval.Cl28__S28__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[jcl28]*rate_eval.He4_Cl28__K32  +
          -rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__p_S28  +
          +rho*Y[jn]*Y[jk31]*rate_eval.n_K31__He4_Cl28  +
          -rho*Y[jp]*Y[jcl28]*rate_eval.p_Cl28__Ar29  +
          +rho*Y[jp]*Y[js27]*rate_eval.p_S27__Cl28
       )

    dYdt[jcl29] = (
          +rho*Y[jn]*Y[jk32]*rate_eval.n_K32__He4_Cl29  +
          +rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__p_Cl29  +
          -rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__He4_P26  +
          -rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__p_S29  +
          +rho*Y[jhe4]*Y[js26]*rate_eval.He4_S26__p_Cl29  +
          +rho*Y[jn]*Y[jcl28]*rate_eval.n_Cl28__Cl29  +
          -rho*Y[jhe4]*Y[jcl29]*rate_eval.He4_Cl29__p_Ar32  +
          -rho*Y[jp]*Y[jcl29]*rate_eval.p_Cl29__Ar30  +
          -rho*Y[jhe4]*Y[jcl29]*rate_eval.He4_Cl29__K33  +
          -Y[jcl29]*rate_eval.Cl29__S29__weak__bqa_pos_  +
          +rho*Y[jhe4]*Y[jp25]*rate_eval.He4_P25__Cl29  +
          -rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__Cl30  +
          +Y[jar29]*rate_eval.Ar29__Cl29__weak__bqa_pos_  +
          +rho*Y[jp]*Y[js28]*rate_eval.p_S28__Cl29
       )

    dYdt[jcl30] = (
          +rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__p_Cl30  +
          -rho*Y[jhe4]*Y[jcl30]*rate_eval.He4_Cl30__p_Ar33  +
          -rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__p_S30  +
          +rho*Y[jhe4]*Y[js27]*rate_eval.He4_S27__p_Cl30  +
          +rho*Y[jn]*Y[jk33]*rate_eval.n_K33__He4_Cl30  +
          -rho*Y[jhe4]*Y[jcl30]*rate_eval.He4_Cl30__K34  +
          +rho*Y[jhe4]*Y[jp26]*rate_eval.He4_P26__Cl30  +
          -rho*Y[jp]*Y[jcl30]*rate_eval.p_Cl30__Ar31  +
          +rho*Y[jn]*Y[jcl29]*rate_eval.n_Cl29__Cl30  +
          -rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__He4_P27  +
          -rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__Cl31  +
          -Y[jcl30]*rate_eval.Cl30__S30__weak__bqa_pos_  +
          +Y[jar30]*rate_eval.Ar30__Cl30__weak__bqa_pos_  +
          +rho*Y[jp]*Y[js29]*rate_eval.p_S29__Cl30
       )

    dYdt[jcl31] = (
          +rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__p_Cl31  +
          -rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__p_S31  +
          +rho*Y[jhe4]*Y[js28]*rate_eval.He4_S28__p_Cl31  +
          +rho*Y[jp]*Y[js30]*rate_eval.p_S30__Cl31  +
          -rho*Y[jhe4]*Y[jcl31]*rate_eval.He4_Cl31__K35  +
          -rho*Y[jp]*Y[jcl31]*rate_eval.p_Cl31__Ar32  +
          +rho*Y[jhe4]*Y[jp27]*rate_eval.He4_P27__Cl31  +
          -rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__He4_P28  +
          +rho*Y[jn]*Y[jcl30]*rate_eval.n_Cl30__Cl31  +
          -rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__Cl32  +
          -Y[jcl31]*rate_eval.Cl31__p_P30__weak__wc12  +
          +Y[jar31]*rate_eval.Ar31__Cl31__weak__wc12  +
          +rho*Y[jn]*Y[jk34]*rate_eval.n_K34__He4_Cl31  +
          -rho*Y[jhe4]*Y[jcl31]*rate_eval.He4_Cl31__p_Ar34  +
          -Y[jcl31]*rate_eval.Cl31__S31__weak__wc12
       )

    dYdt[jcl32] = (
          +rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__p_Cl32  +
          +rho*Y[jhe4]*Y[js29]*rate_eval.He4_S29__p_Cl32  +
          -rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__He4_P29  +
          -rho*Y[jhe4]*Y[jcl32]*rate_eval.He4_Cl32__p_Ar35  +
          -Y[jcl32]*rate_eval.Cl32__S32__weak__wc12  +
          +rho*Y[jn]*Y[jk35]*rate_eval.n_K35__He4_Cl32  +
          +rho*Y[jhe4]*Y[jp28]*rate_eval.He4_P28__Cl32  +
          -rho*Y[jhe4]*Y[jcl32]*rate_eval.He4_Cl32__K36  +
          -rho*Y[jp]*Y[jcl32]*rate_eval.p_Cl32__Ar33  +
          -rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__Cl33  +
          +rho*Y[jp]*Y[js31]*rate_eval.p_S31__Cl32  +
          -rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__p_S32  +
          +rho*Y[jn]*Y[jcl31]*rate_eval.n_Cl31__Cl32  +
          -Y[jcl32]*rate_eval.Cl32__He4_Si28__weak__wc12  +
          -Y[jcl32]*rate_eval.Cl32__p_P31__weak__wc12  +
          +Y[jar32]*rate_eval.Ar32__Cl32__weak__wc12
       )

    dYdt[jcl33] = (
          +rho*Y[jn]*Y[jk36]*rate_eval.n_K36__He4_Cl33  +
          +rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__p_Cl33  +
          -rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__He4_P30  +
          -rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__p_S33  +
          +rho*Y[jhe4]*Y[js30]*rate_eval.He4_S30__p_Cl33  +
          +Y[jca35]*rate_eval.Ca35__p_p_Cl33__weak__wc12  +
          -rho*Y[jhe4]*Y[jcl33]*rate_eval.He4_Cl33__K37  +
          -rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__Cl34  +
          +rho*Y[jn]*Y[jcl32]*rate_eval.n_Cl32__Cl33  +
          +rho*Y[jp]*Y[js32]*rate_eval.p_S32__Cl33  +
          -rho*Y[jhe4]*Y[jcl33]*rate_eval.He4_Cl33__p_Ar36  +
          -rho*Y[jp]*Y[jcl33]*rate_eval.p_Cl33__Ar34  +
          +rho*Y[jhe4]*Y[jp29]*rate_eval.He4_P29__Cl33  +
          +Y[jar33]*rate_eval.Ar33__Cl33__weak__wc12  +
          -Y[jcl33]*rate_eval.Cl33__S33__weak__wc12
       )

    dYdt[jcl34] = (
          +rho*Y[jn]*Y[jk37]*rate_eval.n_K37__He4_Cl34  +
          +rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__p_Cl34  +
          -rho*Y[jhe4]*Y[jcl34]*rate_eval.He4_Cl34__p_Ar37  +
          -rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__He4_P31  +
          -rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__p_S34  +
          +rho*Y[jhe4]*Y[js31]*rate_eval.He4_S31__p_Cl34  +
          +rho*Y[jn]*Y[jcl33]*rate_eval.n_Cl33__Cl34  +
          -rho*Y[jhe4]*Y[jcl34]*rate_eval.He4_Cl34__K38  +
          -rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__Cl35  +
          +rho*Y[jp]*Y[js33]*rate_eval.p_S33__Cl34  +
          -rho*Y[jp]*Y[jcl34]*rate_eval.p_Cl34__Ar35  +
          -Y[jcl34]*rate_eval.Cl34__S34__weak__wc12  +
          +Y[jk35]*rate_eval.K35__p_Cl34__weak__wc12  +
          +Y[jar34]*rate_eval.Ar34__Cl34__weak__wc12  +
          +rho*Y[jhe4]*Y[jp30]*rate_eval.He4_P30__Cl34
       )

    dYdt[jcl35] = (
          -rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__p_S35  +
          +rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__p_Cl35  +
          -rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__He4_P32  +
          -rho*Y[jp]*Y[jcl35]*rate_eval.p_Cl35__He4_S32  +
          -rho*Y[jhe4]*Y[jcl35]*rate_eval.He4_Cl35__p_Ar38  +
          +rho*Y[jp]*Y[js34]*rate_eval.p_S34__Cl35  +
          -rho*Y[jhe4]*Y[jcl35]*rate_eval.He4_Cl35__K39  +
          -rho*Y[jp]*Y[jcl35]*rate_eval.p_Cl35__Ar36  +
          +rho*Y[jn]*Y[jcl34]*rate_eval.n_Cl34__Cl35  +
          +Y[jar35]*rate_eval.Ar35__Cl35__weak__wc12  +
          +rho*Y[jhe4]*Y[jp31]*rate_eval.He4_P31__Cl35  +
          +Y[js35]*rate_eval.S35__Cl35__weak__wc12  +
          +Y[jk36]*rate_eval.K36__p_Cl35__weak__wc12  +
          +rho*Y[jn]*Y[jk38]*rate_eval.n_K38__He4_Cl35  +
          -rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__Cl36
       )

    dYdt[jcl36] = (
          +rho*Y[jp]*Y[jar39]*rate_eval.p_Ar39__He4_Cl36  +
          -rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__p_S36  +
          -rho*Y[jp]*Y[jcl36]*rate_eval.p_Cl36__Ar37  +
          -rho*Y[jp]*Y[jcl36]*rate_eval.p_Cl36__He4_S33  +
          +rho*Y[jn]*Y[jk39]*rate_eval.n_K39__He4_Cl36  +
          -rho*Y[jhe4]*Y[jcl36]*rate_eval.He4_Cl36__K40  +
          +rho*Y[jp]*Y[js35]*rate_eval.p_S35__Cl36  +
          +rho*Y[jhe4]*Y[jp32]*rate_eval.He4_P32__Cl36  +
          -rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__He4_P33  +
          -Y[jcl36]*rate_eval.Cl36__Ar36__weak__wc12  +
          +rho*Y[jn]*Y[jar36]*rate_eval.n_Ar36__p_Cl36  +
          -rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__Cl37  +
          +rho*Y[jn]*Y[jcl35]*rate_eval.n_Cl35__Cl36  +
          -Y[jcl36]*rate_eval.Cl36__S36__weak__wc12
       )

    dYdt[jcl37] = (
          -rho*Y[jn]*Y[jcl37]*rate_eval.n_Cl37__Cl38  +
          +rho*Y[jn]*Y[jk40]*rate_eval.n_K40__He4_Cl37  +
          +rho*Y[jp]*Y[jar40]*rate_eval.p_Ar40__He4_Cl37  +
          +rho*Y[jn]*Y[jar37]*rate_eval.n_Ar37__p_Cl37  +
          +rho*Y[jp]*Y[js37]*rate_eval.p_S37__n_Cl37  +
          +rho*Y[jhe4]*Y[jp34]*rate_eval.He4_P34__n_Cl37  +
          +Y[js37]*rate_eval.S37__Cl37__weak__wc12  +
          +rho*Y[jp]*Y[js36]*rate_eval.p_S36__Cl37  +
          -rho*Y[jhe4]*Y[jcl37]*rate_eval.He4_Cl37__K41  +
          +rho*Y[jhe4]*Y[jp33]*rate_eval.He4_P33__Cl37  +
          -rho*Y[jp]*Y[jcl37]*rate_eval.p_Cl37__Ar38  +
          +rho*Y[jn]*Y[jcl36]*rate_eval.n_Cl36__Cl37  +
          +Y[jar37]*rate_eval.Ar37__Cl37__weak__wc12  +
          +rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__p_Cl37
       )

    dYdt[jcl38] = (
          +rho*Y[jn]*Y[jcl37]*rate_eval.n_Cl37__Cl38  +
          +rho*Y[jp]*Y[js37]*rate_eval.p_S37__Cl38  +
          +rho*Y[jp]*Y[js38]*rate_eval.p_S38__n_Cl38  +
          -rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__He4_S35  +
          -rho*Y[jn]*Y[jcl38]*rate_eval.n_Cl38__He4_P35  +
          -rho*Y[jhe4]*Y[jcl38]*rate_eval.He4_Cl38__K42  +
          -rho*Y[jhe4]*Y[jcl38]*rate_eval.He4_Cl38__n_K41  +
          +rho*Y[jhe4]*Y[jp34]*rate_eval.He4_P34__Cl38  +
          -rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__n_Ar38  +
          -rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__Ar39  +
          -rho*Y[jn]*Y[jcl38]*rate_eval.n_Cl38__Cl39  +
          +rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__He4_Cl38  +
          +Y[js38]*rate_eval.S38__Cl38__weak__wc12  +
          -Y[jcl38]*rate_eval.Cl38__Ar38__weak__wc12
       )

    dYdt[jcl39] = (
          +rho*Y[jp]*Y[js38]*rate_eval.p_S38__Cl39  +
          -Y[jcl39]*rate_eval.Cl39__Ar39__weak__wc12  +
          +rho*Y[jhe4]*Y[jp36]*rate_eval.He4_P36__n_Cl39  +
          -rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__He4_S36  +
          -rho*Y[jhe4]*Y[jcl39]*rate_eval.He4_Cl39__K43  +
          -rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__Ar40  +
          +rho*Y[jhe4]*Y[jp35]*rate_eval.He4_P35__Cl39  +
          -rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__n_Ar39  +
          +rho*Y[jp]*Y[jar42]*rate_eval.p_Ar42__He4_Cl39  +
          +rho*Y[jn]*Y[jcl38]*rate_eval.n_Cl38__Cl39  +
          -rho*Y[jn]*Y[jcl39]*rate_eval.n_Cl39__Cl40  +
          +rho*Y[jp]*Y[js39]*rate_eval.p_S39__n_Cl39  +
          +rho*Y[jn]*Y[jk42]*rate_eval.n_K42__He4_Cl39  +
          +Y[js39]*rate_eval.S39__Cl39__weak__wc12
       )

    dYdt[jcl40] = (
          -rho*Y[jhe4]*Y[jcl40]*rate_eval.He4_Cl40__n_K43  +
          -rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__n_Ar40  +
          +rho*Y[jp]*Y[js40]*rate_eval.p_S40__n_Cl40  +
          -rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__He4_S37  +
          +rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__He4_Cl40  +
          +rho*Y[jhe4]*Y[jp37]*rate_eval.He4_P37__n_Cl40  +
          -rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__Ar41  +
          -rho*Y[jn]*Y[jcl40]*rate_eval.n_Cl40__Cl41  +
          +rho*Y[jp]*Y[js39]*rate_eval.p_S39__Cl40  +
          +rho*Y[jhe4]*Y[jp36]*rate_eval.He4_P36__Cl40  +
          +rho*Y[jn]*Y[jcl39]*rate_eval.n_Cl39__Cl40  +
          -rho*Y[jhe4]*Y[jcl40]*rate_eval.He4_Cl40__K44  +
          -Y[jcl40]*rate_eval.Cl40__Ar40__weak__wc12  +
          +Y[js40]*rate_eval.S40__Cl40__weak__wc12
       )

    dYdt[jcl41] = (
          -rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__n_K44  +
          -rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__He4_S38  +
          +rho*Y[jn]*Y[jcl40]*rate_eval.n_Cl40__Cl41  +
          -Y[jcl41]*rate_eval.Cl41__Ar41__weak__wc12  +
          -rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__Ar42  +
          +rho*Y[jp]*Y[js40]*rate_eval.p_S40__Cl41  +
          +rho*Y[jhe4]*Y[jp37]*rate_eval.He4_P37__Cl41  +
          -rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__n_Ar41  +
          -rho*Y[jn]*Y[jcl41]*rate_eval.n_Cl41__Cl42  +
          -rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__K45  +
          +rho*Y[jp]*Y[js41]*rate_eval.p_S41__n_Cl41  +
          +rho*Y[jhe4]*Y[jp38]*rate_eval.He4_P38__n_Cl41  +
          -rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__p_Ar44  +
          +Y[js41]*rate_eval.S41__Cl41__weak__wc12
       )

    dYdt[jcl42] = (
          +rho*Y[jhe4]*Y[jp39]*rate_eval.He4_P39__n_Cl42  +
          -rho*Y[jhe4]*Y[jcl42]*rate_eval.He4_Cl42__n_K45  +
          -rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__He4_S39  +
          +rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__He4_Cl42  +
          +rho*Y[jp]*Y[js42]*rate_eval.p_S42__n_Cl42  +
          -rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__n_Ar42  +
          +rho*Y[jp]*Y[js41]*rate_eval.p_S41__Cl42  +
          -rho*Y[jhe4]*Y[jcl42]*rate_eval.He4_Cl42__K46  +
          -rho*Y[jn]*Y[jcl42]*rate_eval.n_Cl42__Cl43  +
          +rho*Y[jn]*Y[jcl41]*rate_eval.n_Cl41__Cl42  +
          +rho*Y[jhe4]*Y[jp38]*rate_eval.He4_P38__Cl42  +
          -rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__Ar43  +
          +Y[js42]*rate_eval.S42__Cl42__weak__wc12  +
          +Y[js43]*rate_eval.S43__n_Cl42__weak__wc12  +
          -Y[jcl42]*rate_eval.Cl42__Ar42__weak__wc12
       )

    dYdt[jcl43] = (
          +rho*Y[jp]*Y[js42]*rate_eval.p_S42__Cl43  +
          -rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__p_Ar46  +
          -rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__He4_S40  +
          -rho*Y[jn]*Y[jcl43]*rate_eval.n_Cl43__Cl44  +
          +Y[js44]*rate_eval.S44__n_Cl43__weak__wc12  +
          +rho*Y[jhe4]*Y[jp40]*rate_eval.He4_P40__n_Cl43  +
          -Y[jcl43]*rate_eval.Cl43__n_Ar42__weak__mp17  +
          -rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__Ar44  +
          +rho*Y[jn]*Y[jcl42]*rate_eval.n_Cl42__Cl43  +
          +Y[js45]*rate_eval.S45__n_n_Cl43__weak__mp17  +
          -rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__K47  +
          -rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__n_Ar43  +
          +rho*Y[jhe4]*Y[jp39]*rate_eval.He4_P39__Cl43  +
          -rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__n_K46  +
          +rho*Y[jp]*Y[js43]*rate_eval.p_S43__n_Cl43  +
          +Y[js43]*rate_eval.S43__Cl43__weak__wc12  +
          -Y[jcl43]*rate_eval.Cl43__Ar43__weak__wc12
       )

    dYdt[jcl44] = (
          +Y[js47]*rate_eval.S47__n_n_n_Cl44__weak__mo03  +
          +Y[js45]*rate_eval.S45__n_Cl44__weak__wc12  +
          +rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__n_Cl44  +
          -rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__p_Ar47  +
          +rho*Y[jn]*Y[jcl43]*rate_eval.n_Cl43__Cl44  +
          -rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__n_K47  +
          -rho*Y[jn]*Y[jcl44]*rate_eval.n_Cl44__Cl45  +
          +rho*Y[jhe4]*Y[jp40]*rate_eval.He4_P40__Cl44  +
          -rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__K48  +
          -rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__Ar45  +
          +rho*Y[jp]*Y[js44]*rate_eval.p_S44__n_Cl44  +
          -rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__n_Ar44  +
          -Y[jcl44]*rate_eval.Cl44__n_Ar43__weak__mp17  +
          +Y[js44]*rate_eval.S44__Cl44__weak__wc12  +
          +rho*Y[jp]*Y[js43]*rate_eval.p_S43__Cl44  +
          -Y[jcl44]*rate_eval.Cl44__Ar44__weak__wc17  +
          -rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__He4_S41
       )

    dYdt[jcl45] = (
          +Y[js48]*rate_eval.S48__n_n_n_Cl45__weak__mo03  +
          +rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__He4_Cl45  +
          -rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__He4_S42  +
          -rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__n_Ar45  +
          -rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__Ar46  +
          +rho*Y[jhe4]*Y[jp42]*rate_eval.He4_P42__n_Cl45  +
          -rho*Y[jhe4]*Y[jcl45]*rate_eval.He4_Cl45__n_K48  +
          -rho*Y[jn]*Y[jcl45]*rate_eval.n_Cl45__Cl46  +
          +rho*Y[jn]*Y[jcl44]*rate_eval.n_Cl44__Cl45  +
          +rho*Y[jp]*Y[js44]*rate_eval.p_S44__Cl45  +
          +Y[js47]*rate_eval.S47__n_n_Cl45__weak__mp17  +
          +rho*Y[jhe4]*Y[jp41]*rate_eval.He4_P41__Cl45  +
          +rho*Y[jp]*Y[js45]*rate_eval.p_S45__n_Cl45  +
          +Y[js45]*rate_eval.S45__Cl45__weak__wc12  +
          -Y[jcl45]*rate_eval.Cl45__n_Ar44__weak__wc12  +
          +Y[js46]*rate_eval.S46__n_Cl45__weak__mp17  +
          -rho*Y[jhe4]*Y[jcl45]*rate_eval.He4_Cl45__K49  +
          -Y[jcl45]*rate_eval.Cl45__Ar45__weak__wc12
       )

    dYdt[jcl46] = (
          +Y[js49]*rate_eval.S49__n_n_n_Cl46__weak__mo03  +
          +rho*Y[jp]*Y[js46]*rate_eval.p_S46__n_Cl46  +
          +rho*Y[jhe4]*Y[jp43]*rate_eval.He4_P43__n_Cl46  +
          -rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__He4_S43  +
          -rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__n_Ar46  +
          -rho*Y[jhe4]*Y[jcl46]*rate_eval.He4_Cl46__n_K49  +
          -rho*Y[jhe4]*Y[jcl46]*rate_eval.He4_Cl46__K50  +
          -rho*Y[jn]*Y[jcl46]*rate_eval.n_Cl46__Cl47  +
          +rho*Y[jn]*Y[jcl45]*rate_eval.n_Cl45__Cl46  +
          -rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__Ar47  +
          +Y[js46]*rate_eval.S46__Cl46__weak__wc17  +
          -Y[jcl46]*rate_eval.Cl46__n_Ar45__weak__wc12  +
          +Y[js48]*rate_eval.S48__n_n_Cl46__weak__mp17  +
          +rho*Y[jhe4]*Y[jp42]*rate_eval.He4_P42__Cl46  +
          -Y[jcl46]*rate_eval.Cl46__Ar46__weak__wc12  +
          +rho*Y[jp]*Y[js45]*rate_eval.p_S45__Cl46  +
          +Y[js47]*rate_eval.S47__n_Cl46__weak__mp17  +
          +rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__He4_Cl46
       )

    dYdt[jcl47] = (
          +rho*Y[jhe4]*Y[jp44]*rate_eval.He4_P44__n_Cl47  +
          +rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__He4_Cl47  +
          -rho*Y[jhe4]*Y[jcl47]*rate_eval.He4_Cl47__K51  +
          -rho*Y[jhe4]*Y[jcl47]*rate_eval.He4_Cl47__n_K50  +
          +rho*Y[jp]*Y[js47]*rate_eval.p_S47__n_Cl47  +
          +rho*Y[jp]*Y[js46]*rate_eval.p_S46__Cl47  +
          +Y[js47]*rate_eval.S47__Cl47__weak__mo03  +
          +rho*Y[jn]*Y[jcl46]*rate_eval.n_Cl46__Cl47  +
          -Y[jcl47]*rate_eval.Cl47__n_n_Ar45__weak__mp17  +
          -rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__Ar48  +
          -rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__n_Ar47  +
          +Y[js49]*rate_eval.S49__n_n_Cl47__weak__mp17  +
          +rho*Y[jhe4]*Y[jp43]*rate_eval.He4_P43__Cl47  +
          -Y[jcl47]*rate_eval.Cl47__n_Ar46__weak__wc12  +
          -rho*Y[jn]*Y[jcl47]*rate_eval.n_Cl47__Cl48  +
          -rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__He4_S44  +
          +Y[js48]*rate_eval.S48__n_Cl47__weak__mp17  +
          -Y[jcl47]*rate_eval.Cl47__Ar47__weak__wc17
       )

    dYdt[jcl48] = (
          +rho*Y[jp]*Y[jar51]*rate_eval.p_Ar51__He4_Cl48  +
          +rho*Y[jp]*Y[js47]*rate_eval.p_S47__Cl48  +
          -rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__He4_S45  +
          -rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__n_Ar48  +
          +rho*Y[jp]*Y[js48]*rate_eval.p_S48__n_Cl48  +
          -Y[jcl48]*rate_eval.Cl48__n_Ar47__weak__mp17  +
          +Y[js49]*rate_eval.S49__n_Cl48__weak__mp17  +
          -rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__Ar49  +
          -rho*Y[jn]*Y[jcl48]*rate_eval.n_Cl48__Cl49  +
          -rho*Y[jhe4]*Y[jcl48]*rate_eval.He4_Cl48__K52  +
          +rho*Y[jhe4]*Y[jp45]*rate_eval.He4_P45__n_Cl48  +
          -rho*Y[jhe4]*Y[jcl48]*rate_eval.He4_Cl48__n_K51  +
          +rho*Y[jn]*Y[jcl47]*rate_eval.n_Cl47__Cl48  +
          -Y[jcl48]*rate_eval.Cl48__n_n_Ar46__weak__mp17  +
          +rho*Y[jhe4]*Y[jp44]*rate_eval.He4_P44__Cl48  +
          +Y[js48]*rate_eval.S48__Cl48__weak__mo03  +
          -Y[jcl48]*rate_eval.Cl48__Ar48__weak__mo03
       )

    dYdt[jcl49] = (
          -Y[jcl49]*rate_eval.Cl49__n_n_Ar47__weak__mp17  +
          -Y[jcl49]*rate_eval.Cl49__n_Ar48__weak__mp17  +
          +rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__He4_Cl49  +
          -rho*Y[jhe4]*Y[jcl49]*rate_eval.He4_Cl49__n_K52  +
          +rho*Y[jp]*Y[js49]*rate_eval.p_S49__n_Cl49  +
          -Y[jcl49]*rate_eval.Cl49__n_n_n_Ar46__weak__mo03  +
          -rho*Y[jhe4]*Y[jcl49]*rate_eval.He4_Cl49__K53  +
          -rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__Ar50  +
          -rho*Y[jn]*Y[jcl49]*rate_eval.n_Cl49__Cl50  +
          +Y[js49]*rate_eval.S49__Cl49__weak__mo03  +
          +rho*Y[jn]*Y[jcl48]*rate_eval.n_Cl48__Cl49  +
          +rho*Y[jhe4]*Y[jp46]*rate_eval.He4_P46__n_Cl49  +
          -rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__He4_S46  +
          -Y[jcl49]*rate_eval.Cl49__Ar49__weak__mo03  +
          +rho*Y[jhe4]*Y[jp45]*rate_eval.He4_P45__Cl49  +
          -rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__n_Ar49  +
          +rho*Y[jp]*Y[js48]*rate_eval.p_S48__Cl49
       )

    dYdt[jcl50] = (
          -Y[jcl50]*rate_eval.Cl50__n_n_n_Ar47__weak__mo03  +
          -rho*Y[jhe4]*Y[jcl50]*rate_eval.He4_Cl50__K54  +
          -rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__He4_S47  +
          -rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__n_Ar50  +
          +rho*Y[jhe4]*Y[jp47]*rate_eval.He4_P47__n_Cl50  +
          +rho*Y[jp]*Y[js49]*rate_eval.p_S49__Cl50  +
          -rho*Y[jhe4]*Y[jcl50]*rate_eval.He4_Cl50__n_K53  +
          +rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__He4_Cl50  +
          +rho*Y[jn]*Y[jcl49]*rate_eval.n_Cl49__Cl50  +
          -rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__Ar51  +
          -Y[jcl50]*rate_eval.Cl50__Ar50__weak__mo03  +
          -Y[jcl50]*rate_eval.Cl50__n_n_Ar48__weak__mp17  +
          +rho*Y[jhe4]*Y[jp46]*rate_eval.He4_P46__Cl50  +
          -Y[jcl50]*rate_eval.Cl50__n_Ar49__weak__mp17  +
          -rho*Y[jn]*Y[jcl50]*rate_eval.n_Cl50__Cl51
       )

    dYdt[jcl51] = (
          -rho*Y[jhe4]*Y[jcl51]*rate_eval.He4_Cl51__n_K54  +
          -rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__He4_S48  +
          -Y[jcl51]*rate_eval.Cl51__Ar51__weak__mo03  +
          -rho*Y[jhe4]*Y[jcl51]*rate_eval.He4_Cl51__K55  +
          -rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__Ar52  +
          +rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__He4_Cl51  +
          -rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__n_Ar51  +
          +rho*Y[jhe4]*Y[jp47]*rate_eval.He4_P47__Cl51  +
          -Y[jcl51]*rate_eval.Cl51__n_Ar50__weak__mp17  +
          -Y[jcl51]*rate_eval.Cl51__n_n_Ar49__weak__mp17  +
          +rho*Y[jn]*Y[jcl50]*rate_eval.n_Cl50__Cl51  +
          -Y[jcl51]*rate_eval.Cl51__n_n_n_Ar48__weak__mo03  +
          -rho*Y[jn]*Y[jcl51]*rate_eval.n_Cl51__Cl52
       )

    dYdt[jcl52] = (
          -rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__He4_S49  +
          -rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__n_Ar52  +
          -Y[jcl52]*rate_eval.Cl52__n_n_n_Ar49__weak__mo03  +
          -rho*Y[jhe4]*Y[jcl52]*rate_eval.He4_Cl52__n_K55  +
          -Y[jcl52]*rate_eval.Cl52__n_n_Ar50__weak__mp17  +
          -rho*Y[jhe4]*Y[jcl52]*rate_eval.He4_Cl52__K56  +
          -Y[jcl52]*rate_eval.Cl52__n_Ar51__weak__mp17  +
          -Y[jcl52]*rate_eval.Cl52__Ar52__weak__mo03  +
          -rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__Ar53  +
          +rho*Y[jn]*Y[jcl51]*rate_eval.n_Cl51__Cl52
       )

    dYdt[jar29] = (
          -rho*Y[jhe4]*Y[jar29]*rate_eval.He4_Ar29__Ca33  +
          -rho*Y[jhe4]*Y[jar29]*rate_eval.He4_Ar29__p_K32  +
          -rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__He4_S26  +
          -rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__p_Cl29  +
          -rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__Ar30  +
          +rho*Y[jp]*Y[jcl28]*rate_eval.p_Cl28__Ar29  +
          -Y[jar29]*rate_eval.Ar29__Cl29__weak__bqa_pos_
       )

    dYdt[jar30] = (
          -rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__He4_S27  +
          -rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__p_Cl30  +
          +rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__He4_Ar30  +
          -rho*Y[jhe4]*Y[jar30]*rate_eval.He4_Ar30__Ca34  +
          +rho*Y[jn]*Y[jar29]*rate_eval.n_Ar29__Ar30  +
          +rho*Y[jp]*Y[jcl29]*rate_eval.p_Cl29__Ar30  +
          -rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__Ar31  +
          +rho*Y[jhe4]*Y[js26]*rate_eval.He4_S26__Ar30  +
          -rho*Y[jhe4]*Y[jar30]*rate_eval.He4_Ar30__p_K33  +
          -Y[jar30]*rate_eval.Ar30__Cl30__weak__bqa_pos_  +
          -rho*Y[jp]*Y[jar30]*rate_eval.p_Ar30__K31
       )

    dYdt[jar31] = (
          +rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__He4_Ar31  +
          -rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__He4_S28  +
          +rho*Y[jn]*Y[jk31]*rate_eval.n_K31__p_Ar31  +
          -rho*Y[jhe4]*Y[jar31]*rate_eval.He4_Ar31__p_K34  +
          -rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__p_Cl31  +
          +rho*Y[jhe4]*Y[jcl28]*rate_eval.He4_Cl28__p_Ar31  +
          +rho*Y[jhe4]*Y[js27]*rate_eval.He4_S27__Ar31  +
          -rho*Y[jhe4]*Y[jar31]*rate_eval.He4_Ar31__Ca35  +
          -rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__Ar32  +
          +rho*Y[jp]*Y[jcl30]*rate_eval.p_Cl30__Ar31  +
          +rho*Y[jn]*Y[jar30]*rate_eval.n_Ar30__Ar31  +
          -Y[jar31]*rate_eval.Ar31__p_S30__weak__wc17  +
          -Y[jar31]*rate_eval.Ar31__Cl31__weak__wc12  +
          -Y[jar31]*rate_eval.Ar31__p_p_P29__weak__wc12  +
          +Y[jk31]*rate_eval.K31__Ar31__weak__bqa_pos_  +
          -rho*Y[jp]*Y[jar31]*rate_eval.p_Ar31__K32
       )

    dYdt[jar32] = (
          +Y[jk32]*rate_eval.K32__Ar32__weak__bqa_pos_  +
          +rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__He4_Ar32  +
          +rho*Y[jn]*Y[jk32]*rate_eval.n_K32__p_Ar32  +
          -rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__He4_S29  +
          -rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__p_Cl32  +
          +rho*Y[jhe4]*Y[jcl29]*rate_eval.He4_Cl29__p_Ar32  +
          -rho*Y[jhe4]*Y[jar32]*rate_eval.He4_Ar32__Ca36  +
          -rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__Ar33  +
          +rho*Y[jn]*Y[jar31]*rate_eval.n_Ar31__Ar32  +
          +rho*Y[jp]*Y[jcl31]*rate_eval.p_Cl31__Ar32  +
          +rho*Y[jhe4]*Y[js28]*rate_eval.He4_S28__Ar32  +
          -Y[jar32]*rate_eval.Ar32__p_S31__weak__wc12  +
          -Y[jar32]*rate_eval.Ar32__Cl32__weak__wc12  +
          -rho*Y[jhe4]*Y[jar32]*rate_eval.He4_Ar32__p_K35  +
          -rho*Y[jp]*Y[jar32]*rate_eval.p_Ar32__K33
       )

    dYdt[jar33] = (
          +rho*Y[jn]*Y[jk33]*rate_eval.n_K33__p_Ar33  +
          +rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__He4_Ar33  +
          -rho*Y[jhe4]*Y[jar33]*rate_eval.He4_Ar33__p_K36  +
          -rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__p_Cl33  +
          +rho*Y[jhe4]*Y[jcl30]*rate_eval.He4_Cl30__p_Ar33  +
          -rho*Y[jhe4]*Y[jar33]*rate_eval.He4_Ar33__Ca37  +
          +rho*Y[jn]*Y[jar32]*rate_eval.n_Ar32__Ar33  +
          +rho*Y[jp]*Y[jcl32]*rate_eval.p_Cl32__Ar33  +
          +rho*Y[jhe4]*Y[js29]*rate_eval.He4_S29__Ar33  +
          -rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__Ar34  +
          -Y[jar33]*rate_eval.Ar33__p_S32__weak__wc12  +
          -rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__He4_S30  +
          -Y[jar33]*rate_eval.Ar33__Cl33__weak__wc12  +
          +Y[jk33]*rate_eval.K33__Ar33__weak__bqa_pos_  +
          -rho*Y[jp]*Y[jar33]*rate_eval.p_Ar33__K34
       )

    dYdt[jar34] = (
          -rho*Y[jp]*Y[jar34]*rate_eval.p_Ar34__K35  +
          +rho*Y[jhe4]*Y[js30]*rate_eval.He4_S30__Ar34  +
          +rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__He4_Ar34  +
          -rho*Y[jhe4]*Y[jar34]*rate_eval.He4_Ar34__p_K37  +
          -rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__p_Cl34  +
          -rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__Ar35  +
          -rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__He4_S31  +
          +rho*Y[jp]*Y[jcl33]*rate_eval.p_Cl33__Ar34  +
          +Y[jca35]*rate_eval.Ca35__p_Ar34__weak__wc17  +
          +rho*Y[jn]*Y[jar33]*rate_eval.n_Ar33__Ar34  +
          +rho*Y[jhe4]*Y[jcl31]*rate_eval.He4_Cl31__p_Ar34  +
          -rho*Y[jhe4]*Y[jar34]*rate_eval.He4_Ar34__Ca38  +
          -Y[jar34]*rate_eval.Ar34__Cl34__weak__wc12  +
          +rho*Y[jn]*Y[jk34]*rate_eval.n_K34__p_Ar34  +
          +Y[jk34]*rate_eval.K34__Ar34__weak__bqa_pos_
       )

    dYdt[jar35] = (
          -rho*Y[jhe4]*Y[jar35]*rate_eval.He4_Ar35__Ca39  +
          +rho*Y[jn]*Y[jk35]*rate_eval.n_K35__p_Ar35  +
          -rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__He4_S32  +
          -rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__p_Cl35  +
          +rho*Y[jn]*Y[jar34]*rate_eval.n_Ar34__Ar35  +
          -rho*Y[jhe4]*Y[jar35]*rate_eval.He4_Ar35__p_K38  +
          -rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__Ar36  +
          +rho*Y[jhe4]*Y[jcl32]*rate_eval.He4_Cl32__p_Ar35  +
          -rho*Y[jp]*Y[jar35]*rate_eval.p_Ar35__K36  +
          -Y[jar35]*rate_eval.Ar35__Cl35__weak__wc12  +
          +rho*Y[jp]*Y[jcl34]*rate_eval.p_Cl34__Ar35  +
          +Y[jca36]*rate_eval.Ca36__p_Ar35__weak__wc12  +
          +rho*Y[jhe4]*Y[js31]*rate_eval.He4_S31__Ar35  +
          +Y[jk35]*rate_eval.K35__Ar35__weak__wc12  +
          +rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__He4_Ar35
       )

    dYdt[jar36] = (
          -rho*Y[jn]*Y[jar36]*rate_eval.n_Ar36__He4_S33  +
          +rho*Y[jn]*Y[jk36]*rate_eval.n_K36__p_Ar36  +
          -rho*Y[jhe4]*Y[jar36]*rate_eval.He4_Ar36__Ca40  +
          +rho*Y[jn]*Y[jar35]*rate_eval.n_Ar35__Ar36  +
          -rho*Y[jp]*Y[jar36]*rate_eval.p_Ar36__K37  +
          +rho*Y[jp]*Y[jcl35]*rate_eval.p_Cl35__Ar36  +
          +rho*Y[jhe4]*Y[js32]*rate_eval.He4_S32__Ar36  +
          +rho*Y[jhe4]*Y[jcl33]*rate_eval.He4_Cl33__p_Ar36  +
          -rho*Y[jn]*Y[jar36]*rate_eval.n_Ar36__Ar37  +
          +rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__He4_Ar36  +
          +Y[jsc40]*rate_eval.Sc40__He4_Ar36__weak__wc12  +
          +Y[jca37]*rate_eval.Ca37__p_Ar36__weak__wc12  +
          +Y[jcl36]*rate_eval.Cl36__Ar36__weak__wc12  +
          +rho*Y[jp]*Y[jk39]*rate_eval.p_K39__He4_Ar36  +
          -rho*Y[jn]*Y[jar36]*rate_eval.n_Ar36__p_Cl36  +
          +Y[jk36]*rate_eval.K36__Ar36__weak__wc12
       )

    dYdt[jar37] = (
          +rho*Y[jn]*Y[jca40]*rate_eval.n_Ca40__He4_Ar37  +
          +rho*Y[jp]*Y[jk40]*rate_eval.p_K40__He4_Ar37  +
          -rho*Y[jn]*Y[jar37]*rate_eval.n_Ar37__p_Cl37  +
          +rho*Y[jhe4]*Y[jcl34]*rate_eval.He4_Cl34__p_Ar37  +
          +rho*Y[jp]*Y[jcl36]*rate_eval.p_Cl36__Ar37  +
          -rho*Y[jhe4]*Y[jar37]*rate_eval.He4_Ar37__Ca41  +
          -rho*Y[jp]*Y[jar37]*rate_eval.p_Ar37__K38  +
          +rho*Y[jn]*Y[jk37]*rate_eval.n_K37__p_Ar37  +
          +rho*Y[jn]*Y[jar36]*rate_eval.n_Ar36__Ar37  +
          +Y[jk37]*rate_eval.K37__Ar37__weak__wc12  +
          +rho*Y[jhe4]*Y[js33]*rate_eval.He4_S33__Ar37  +
          -rho*Y[jn]*Y[jar37]*rate_eval.n_Ar37__Ar38  +
          -Y[jar37]*rate_eval.Ar37__Cl37__weak__wc12  +
          +rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__n_Ar37
       )

    dYdt[jar38] = (
          +rho*Y[jp]*Y[jk41]*rate_eval.p_K41__He4_Ar38  +
          +rho*Y[jn]*Y[jk38]*rate_eval.n_K38__p_Ar38  +
          +rho*Y[jhe4]*Y[js35]*rate_eval.He4_S35__n_Ar38  +
          +rho*Y[jhe4]*Y[jcl35]*rate_eval.He4_Cl35__p_Ar38  +
          +Y[jk38]*rate_eval.K38__Ar38__weak__wc12  +
          -rho*Y[jp]*Y[jar38]*rate_eval.p_Ar38__K39  +
          -rho*Y[jn]*Y[jar38]*rate_eval.n_Ar38__Ar39  +
          +rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__n_Ar38  +
          +rho*Y[jhe4]*Y[js34]*rate_eval.He4_S34__Ar38  +
          +rho*Y[jn]*Y[jca41]*rate_eval.n_Ca41__He4_Ar38  +
          +rho*Y[jp]*Y[jcl37]*rate_eval.p_Cl37__Ar38  +
          +rho*Y[jn]*Y[jar37]*rate_eval.n_Ar37__Ar38  +
          -rho*Y[jhe4]*Y[jar38]*rate_eval.He4_Ar38__Ca42  +
          +Y[jcl38]*rate_eval.Cl38__Ar38__weak__wc12
       )

    dYdt[jar39] = (
          +rho*Y[jn]*Y[jk39]*rate_eval.n_K39__p_Ar39  +
          -rho*Y[jp]*Y[jar39]*rate_eval.p_Ar39__He4_Cl36  +
          -rho*Y[jn]*Y[jar39]*rate_eval.n_Ar39__He4_S36  +
          +Y[jcl39]*rate_eval.Cl39__Ar39__weak__wc12  +
          -rho*Y[jn]*Y[jar39]*rate_eval.n_Ar39__Ar40  +
          +rho*Y[jp]*Y[jk42]*rate_eval.p_K42__He4_Ar39  +
          -rho*Y[jhe4]*Y[jar39]*rate_eval.He4_Ar39__Ca43  +
          +rho*Y[jn]*Y[jar38]*rate_eval.n_Ar38__Ar39  +
          +rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__n_Ar39  +
          +rho*Y[jp]*Y[jcl38]*rate_eval.p_Cl38__Ar39  +
          -Y[jar39]*rate_eval.Ar39__K39__weak__wc12  +
          -rho*Y[jp]*Y[jar39]*rate_eval.p_Ar39__K40  +
          +rho*Y[jhe4]*Y[js35]*rate_eval.He4_S35__Ar39  +
          +rho*Y[jn]*Y[jca42]*rate_eval.n_Ca42__He4_Ar39
       )

    dYdt[jar40] = (
          +rho*Y[jn]*Y[jk40]*rate_eval.n_K40__p_Ar40  +
          -rho*Y[jp]*Y[jar40]*rate_eval.p_Ar40__He4_Cl37  +
          +rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__n_Ar40  +
          +rho*Y[jhe4]*Y[js37]*rate_eval.He4_S37__n_Ar40  +
          +rho*Y[jn]*Y[jca43]*rate_eval.n_Ca43__He4_Ar40  +
          +rho*Y[jn]*Y[jar39]*rate_eval.n_Ar39__Ar40  +
          -rho*Y[jhe4]*Y[jar40]*rate_eval.He4_Ar40__Ca44  +
          -rho*Y[jp]*Y[jar40]*rate_eval.p_Ar40__K41  +
          -rho*Y[jn]*Y[jar40]*rate_eval.n_Ar40__Ar41  +
          +rho*Y[jp]*Y[jcl39]*rate_eval.p_Cl39__Ar40  +
          +rho*Y[jhe4]*Y[js36]*rate_eval.He4_S36__Ar40  +
          +rho*Y[jp]*Y[jk43]*rate_eval.p_K43__He4_Ar40  +
          +Y[jk40]*rate_eval.K40__Ar40__weak__wc12  +
          +Y[jcl40]*rate_eval.Cl40__Ar40__weak__wc12
       )

    dYdt[jar41] = (
          +rho*Y[jp]*Y[jk44]*rate_eval.p_K44__He4_Ar41  +
          -rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__n_K41  +
          +rho*Y[jhe4]*Y[js38]*rate_eval.He4_S38__n_Ar41  +
          +rho*Y[jp]*Y[jcl40]*rate_eval.p_Cl40__Ar41  +
          -rho*Y[jhe4]*Y[jar41]*rate_eval.He4_Ar41__n_Ca44  +
          -rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__K42  +
          +Y[jcl41]*rate_eval.Cl41__Ar41__weak__wc12  +
          +rho*Y[jn]*Y[jar40]*rate_eval.n_Ar40__Ar41  +
          -rho*Y[jhe4]*Y[jar41]*rate_eval.He4_Ar41__Ca45  +
          +rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__n_Ar41  +
          -rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__He4_Cl38  +
          -rho*Y[jn]*Y[jar41]*rate_eval.n_Ar41__Ar42  +
          +rho*Y[jhe4]*Y[js37]*rate_eval.He4_S37__Ar41  +
          -Y[jar41]*rate_eval.Ar41__K41__weak__wc12
       )

    dYdt[jar42] = (
          +rho*Y[jp]*Y[jk45]*rate_eval.p_K45__He4_Ar42  +
          -rho*Y[jhe4]*Y[jar42]*rate_eval.He4_Ar42__n_Ca45  +
          +rho*Y[jhe4]*Y[js39]*rate_eval.He4_S39__n_Ar42  +
          +rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__n_Ar42  +
          -rho*Y[jp]*Y[jar42]*rate_eval.p_Ar42__K43  +
          -rho*Y[jn]*Y[jar42]*rate_eval.n_Ar42__Ar43  +
          +Y[jcl43]*rate_eval.Cl43__n_Ar42__weak__mp17  +
          +rho*Y[jp]*Y[jcl41]*rate_eval.p_Cl41__Ar42  +
          -rho*Y[jhe4]*Y[jar42]*rate_eval.He4_Ar42__Ca46  +
          -rho*Y[jp]*Y[jar42]*rate_eval.p_Ar42__He4_Cl39  +
          +rho*Y[jhe4]*Y[js38]*rate_eval.He4_S38__Ar42  +
          +rho*Y[jn]*Y[jar41]*rate_eval.n_Ar41__Ar42  +
          -Y[jar42]*rate_eval.Ar42__K42__weak__wc12  +
          +rho*Y[jn]*Y[jk42]*rate_eval.n_K42__p_Ar42  +
          +Y[jcl42]*rate_eval.Cl42__Ar42__weak__wc12
       )

    dYdt[jar43] = (
          -rho*Y[jhe4]*Y[jar43]*rate_eval.He4_Ar43__n_Ca46  +
          -rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__n_K43  +
          -rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__He4_Cl40  +
          -rho*Y[jhe4]*Y[jar43]*rate_eval.He4_Ar43__Ca47  +
          -rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__K44  +
          +rho*Y[jn]*Y[jar42]*rate_eval.n_Ar42__Ar43  +
          +rho*Y[jhe4]*Y[js39]*rate_eval.He4_S39__Ar43  +
          +rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__n_Ar43  +
          -rho*Y[jn]*Y[jar43]*rate_eval.n_Ar43__Ar44  +
          +rho*Y[jp]*Y[jcl42]*rate_eval.p_Cl42__Ar43  +
          +rho*Y[jp]*Y[jk46]*rate_eval.p_K46__He4_Ar43  +
          +rho*Y[jhe4]*Y[js40]*rate_eval.He4_S40__n_Ar43  +
          +Y[jcl44]*rate_eval.Cl44__n_Ar43__weak__mp17  +
          +Y[jcl43]*rate_eval.Cl43__Ar43__weak__wc12  +
          -Y[jar43]*rate_eval.Ar43__K43__weak__wc12
       )

    dYdt[jar44] = (
          +rho*Y[jp]*Y[jk47]*rate_eval.p_K47__He4_Ar44  +
          -rho*Y[jp]*Y[jar44]*rate_eval.p_Ar44__n_K44  +
          +rho*Y[jhe4]*Y[js41]*rate_eval.He4_S41__n_Ar44  +
          -rho*Y[jp]*Y[jar44]*rate_eval.p_Ar44__K45  +
          -rho*Y[jn]*Y[jar44]*rate_eval.n_Ar44__Ar45  +
          +rho*Y[jp]*Y[jcl43]*rate_eval.p_Cl43__Ar44  +
          -rho*Y[jhe4]*Y[jar44]*rate_eval.He4_Ar44__n_Ca47  +
          +rho*Y[jn]*Y[jar43]*rate_eval.n_Ar43__Ar44  +
          +rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__n_Ar44  +
          -rho*Y[jhe4]*Y[jar44]*rate_eval.He4_Ar44__Ca48  +
          +Y[jcl45]*rate_eval.Cl45__n_Ar44__weak__wc12  +
          +rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__p_Ar44  +
          +Y[jcl44]*rate_eval.Cl44__Ar44__weak__wc17  +
          -Y[jar44]*rate_eval.Ar44__K44__weak__wc12  +
          +rho*Y[jhe4]*Y[js40]*rate_eval.He4_S40__Ar44
       )

    dYdt[jar45] = (
          +rho*Y[jp]*Y[jk48]*rate_eval.p_K48__He4_Ar45  +
          +rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__n_Ar45  +
          +rho*Y[jhe4]*Y[js42]*rate_eval.He4_S42__n_Ar45  +
          -rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__He4_Cl42  +
          +rho*Y[jhe4]*Y[js41]*rate_eval.He4_S41__Ar45  +
          -rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__n_K45  +
          -rho*Y[jhe4]*Y[jar45]*rate_eval.He4_Ar45__Ca49  +
          -rho*Y[jn]*Y[jar45]*rate_eval.n_Ar45__Ar46  +
          +rho*Y[jn]*Y[jar44]*rate_eval.n_Ar44__Ar45  +
          +Y[jcl47]*rate_eval.Cl47__n_n_Ar45__weak__mp17  +
          +rho*Y[jp]*Y[jcl44]*rate_eval.p_Cl44__Ar45  +
          -Y[jar45]*rate_eval.Ar45__K45__weak__wc12  +
          +Y[jcl46]*rate_eval.Cl46__n_Ar45__weak__wc12  +
          -rho*Y[jhe4]*Y[jar45]*rate_eval.He4_Ar45__n_Ca48  +
          -rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__K46  +
          +Y[jcl45]*rate_eval.Cl45__Ar45__weak__wc12
       )

    dYdt[jar46] = (
          -rho*Y[jhe4]*Y[jar46]*rate_eval.He4_Ar46__n_Ca49  +
          +rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__p_Ar46  +
          +rho*Y[jhe4]*Y[js43]*rate_eval.He4_S43__n_Ar46  +
          +rho*Y[jp]*Y[jcl45]*rate_eval.p_Cl45__Ar46  +
          +Y[jcl49]*rate_eval.Cl49__n_n_n_Ar46__weak__mo03  +
          +rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__n_Ar46  +
          -rho*Y[jhe4]*Y[jar46]*rate_eval.He4_Ar46__Ca50  +
          -rho*Y[jn]*Y[jar46]*rate_eval.n_Ar46__Ar47  +
          +rho*Y[jn]*Y[jar45]*rate_eval.n_Ar45__Ar46  +
          +rho*Y[jhe4]*Y[js42]*rate_eval.He4_S42__Ar46  +
          -rho*Y[jp]*Y[jar46]*rate_eval.p_Ar46__K47  +
          +rho*Y[jp]*Y[jk49]*rate_eval.p_K49__He4_Ar46  +
          +Y[jcl47]*rate_eval.Cl47__n_Ar46__weak__wc12  +
          +Y[jcl48]*rate_eval.Cl48__n_n_Ar46__weak__mp17  +
          +Y[jcl46]*rate_eval.Cl46__Ar46__weak__wc12  +
          -Y[jar46]*rate_eval.Ar46__K46__weak__wc12  +
          -rho*Y[jp]*Y[jar46]*rate_eval.p_Ar46__n_K46
       )

    dYdt[jar47] = (
          +Y[jcl50]*rate_eval.Cl50__n_n_n_Ar47__weak__mo03  +
          +Y[jcl49]*rate_eval.Cl49__n_n_Ar47__weak__mp17  +
          +rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__p_Ar47  +
          +Y[jcl48]*rate_eval.Cl48__n_Ar47__weak__mp17  +
          -rho*Y[jp]*Y[jar47]*rate_eval.p_Ar47__n_K47  +
          -rho*Y[jn]*Y[jar47]*rate_eval.n_Ar47__Ar48  +
          +rho*Y[jn]*Y[jar46]*rate_eval.n_Ar46__Ar47  +
          -rho*Y[jp]*Y[jar47]*rate_eval.p_Ar47__K48  +
          +rho*Y[jp]*Y[jcl46]*rate_eval.p_Cl46__Ar47  +
          +rho*Y[jhe4]*Y[js43]*rate_eval.He4_S43__Ar47  +
          -rho*Y[jhe4]*Y[jar47]*rate_eval.He4_Ar47__Ca51  +
          +rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__n_Ar47  +
          +rho*Y[jp]*Y[jk50]*rate_eval.p_K50__He4_Ar47  +
          -rho*Y[jhe4]*Y[jar47]*rate_eval.He4_Ar47__n_Ca50  +
          -Y[jar47]*rate_eval.Ar47__K47__weak__wc12  +
          +rho*Y[jhe4]*Y[js44]*rate_eval.He4_S44__n_Ar47  +
          +Y[jcl47]*rate_eval.Cl47__Ar47__weak__wc17
       )

    dYdt[jar48] = (
          -Y[jar48]*rate_eval.Ar48__n_K47__weak__mp17  +
          +rho*Y[jhe4]*Y[js45]*rate_eval.He4_S45__n_Ar48  +
          +Y[jcl49]*rate_eval.Cl49__n_Ar48__weak__mp17  +
          -rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__He4_Cl45  +
          -rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__n_K48  +
          +rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__n_Ar48  +
          +rho*Y[jp]*Y[jk51]*rate_eval.p_K51__He4_Ar48  +
          +rho*Y[jn]*Y[jar47]*rate_eval.n_Ar47__Ar48  +
          +rho*Y[jhe4]*Y[js44]*rate_eval.He4_S44__Ar48  +
          +rho*Y[jp]*Y[jcl47]*rate_eval.p_Cl47__Ar48  +
          -rho*Y[jn]*Y[jar48]*rate_eval.n_Ar48__Ar49  +
          +Y[jcl50]*rate_eval.Cl50__n_n_Ar48__weak__mp17  +
          -Y[jar48]*rate_eval.Ar48__K48__weak__wc17  +
          -rho*Y[jhe4]*Y[jar48]*rate_eval.He4_Ar48__Ca52  +
          -rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__K49  +
          -rho*Y[jhe4]*Y[jar48]*rate_eval.He4_Ar48__n_Ca51  +
          +Y[jcl51]*rate_eval.Cl51__n_n_n_Ar48__weak__mo03  +
          +Y[jcl48]*rate_eval.Cl48__Ar48__weak__mo03
       )

    dYdt[jar49] = (
          +rho*Y[jp]*Y[jk52]*rate_eval.p_K52__He4_Ar49  +
          -Y[jar49]*rate_eval.Ar49__K49__weak__wc12  +
          +rho*Y[jhe4]*Y[js46]*rate_eval.He4_S46__n_Ar49  +
          +Y[jcl52]*rate_eval.Cl52__n_n_n_Ar49__weak__mo03  +
          +rho*Y[jp]*Y[jcl48]*rate_eval.p_Cl48__Ar49  +
          +rho*Y[jn]*Y[jar48]*rate_eval.n_Ar48__Ar49  +
          -Y[jar49]*rate_eval.Ar49__n_K48__weak__wc12  +
          +rho*Y[jhe4]*Y[js45]*rate_eval.He4_S45__Ar49  +
          +Y[jcl51]*rate_eval.Cl51__n_n_Ar49__weak__mp17  +
          +Y[jcl50]*rate_eval.Cl50__n_Ar49__weak__mp17  +
          +Y[jcl49]*rate_eval.Cl49__Ar49__weak__mo03  +
          -rho*Y[jhe4]*Y[jar49]*rate_eval.He4_Ar49__n_Ca52  +
          -rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__n_K49  +
          -rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__K50  +
          +rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__n_Ar49  +
          -rho*Y[jhe4]*Y[jar49]*rate_eval.He4_Ar49__Ca53  +
          -rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__He4_Cl46  +
          -rho*Y[jn]*Y[jar49]*rate_eval.n_Ar49__Ar50
       )

    dYdt[jar50] = (
          -rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__He4_Cl47  +
          +rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__n_Ar50  +
          -rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__n_K50  +
          +rho*Y[jp]*Y[jcl49]*rate_eval.p_Cl49__Ar50  +
          +rho*Y[jhe4]*Y[js46]*rate_eval.He4_S46__Ar50  +
          +Y[jcl50]*rate_eval.Cl50__Ar50__weak__mo03  +
          -rho*Y[jhe4]*Y[jar50]*rate_eval.He4_Ar50__Ca54  +
          +Y[jcl52]*rate_eval.Cl52__n_n_Ar50__weak__mp17  +
          +rho*Y[jhe4]*Y[js47]*rate_eval.He4_S47__n_Ar50  +
          +Y[jcl51]*rate_eval.Cl51__n_Ar50__weak__mp17  +
          -rho*Y[jn]*Y[jar50]*rate_eval.n_Ar50__Ar51  +
          -rho*Y[jhe4]*Y[jar50]*rate_eval.He4_Ar50__n_Ca53  +
          -Y[jar50]*rate_eval.Ar50__n_K49__weak__wc12  +
          +rho*Y[jp]*Y[jk53]*rate_eval.p_K53__He4_Ar50  +
          -Y[jar50]*rate_eval.Ar50__K50__weak__wc12  +
          -rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__K51  +
          +rho*Y[jn]*Y[jar49]*rate_eval.n_Ar49__Ar50
       )

    dYdt[jar51] = (
          -rho*Y[jp]*Y[jar51]*rate_eval.p_Ar51__He4_Cl48  +
          +rho*Y[jhe4]*Y[js48]*rate_eval.He4_S48__n_Ar51  +
          +Y[jcl51]*rate_eval.Cl51__Ar51__weak__mo03  +
          -rho*Y[jp]*Y[jar51]*rate_eval.p_Ar51__K52  +
          -rho*Y[jn]*Y[jar51]*rate_eval.n_Ar51__Ar52  +
          +rho*Y[jhe4]*Y[js47]*rate_eval.He4_S47__Ar51  +
          +rho*Y[jp]*Y[jcl50]*rate_eval.p_Cl50__Ar51  +
          +rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__n_Ar51  +
          -Y[jar51]*rate_eval.Ar51__n_K50__weak__mp17  +
          +rho*Y[jn]*Y[jar50]*rate_eval.n_Ar50__Ar51  +
          +Y[jcl52]*rate_eval.Cl52__n_Ar51__weak__mp17  +
          -rho*Y[jhe4]*Y[jar51]*rate_eval.He4_Ar51__Ca55  +
          +rho*Y[jp]*Y[jk54]*rate_eval.p_K54__He4_Ar51  +
          -Y[jar51]*rate_eval.Ar51__K51__weak__mo03  +
          -rho*Y[jhe4]*Y[jar51]*rate_eval.He4_Ar51__n_Ca54  +
          -rho*Y[jp]*Y[jar51]*rate_eval.p_Ar51__n_K51  +
          -Y[jar51]*rate_eval.Ar51__n_n_K49__weak__mp17
       )

    dYdt[jar52] = (
          -Y[jar52]*rate_eval.Ar52__n_n_n_K49__weak__mo03  +
          -rho*Y[jhe4]*Y[jar52]*rate_eval.He4_Ar52__Ca56  +
          -rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__He4_Cl49  +
          -rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__n_K52  +
          +rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__n_Ar52  +
          -Y[jar52]*rate_eval.Ar52__n_n_K50__weak__mp17  +
          -rho*Y[jhe4]*Y[jar52]*rate_eval.He4_Ar52__n_Ca55  +
          +rho*Y[jn]*Y[jar51]*rate_eval.n_Ar51__Ar52  +
          +rho*Y[jp]*Y[jcl51]*rate_eval.p_Cl51__Ar52  +
          +rho*Y[jhe4]*Y[js48]*rate_eval.He4_S48__Ar52  +
          -rho*Y[jn]*Y[jar52]*rate_eval.n_Ar52__Ar53  +
          +rho*Y[jhe4]*Y[js49]*rate_eval.He4_S49__n_Ar52  +
          -rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__K53  +
          -Y[jar52]*rate_eval.Ar52__K52__weak__mo03  +
          -Y[jar52]*rate_eval.Ar52__n_K51__weak__mp17  +
          +rho*Y[jp]*Y[jk55]*rate_eval.p_K55__He4_Ar52  +
          +Y[jcl52]*rate_eval.Cl52__Ar52__weak__mo03
       )

    dYdt[jar53] = (
          -Y[jar53]*rate_eval.Ar53__n_n_n_K50__weak__mo03  +
          +rho*Y[jp]*Y[jk56]*rate_eval.p_K56__He4_Ar53  +
          -rho*Y[jhe4]*Y[jar53]*rate_eval.He4_Ar53__n_Ca56  +
          -rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__He4_Cl50  +
          -rho*Y[jhe4]*Y[jar53]*rate_eval.He4_Ar53__Ca57  +
          -rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__n_K53  +
          +rho*Y[jhe4]*Y[js49]*rate_eval.He4_S49__Ar53  +
          +rho*Y[jn]*Y[jar52]*rate_eval.n_Ar52__Ar53  +
          -Y[jar53]*rate_eval.Ar53__n_n_K51__weak__mp17  +
          -Y[jar53]*rate_eval.Ar53__n_K52__weak__mp17  +
          -rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__K54  +
          -rho*Y[jn]*Y[jar53]*rate_eval.n_Ar53__Ar54  +
          +rho*Y[jp]*Y[jcl52]*rate_eval.p_Cl52__Ar53  +
          -Y[jar53]*rate_eval.Ar53__K53__weak__mo03
       )

    dYdt[jar54] = (
          -Y[jar54]*rate_eval.Ar54__n_n_n_K51__weak__mo03  +
          +rho*Y[jp]*Y[jk57]*rate_eval.p_K57__He4_Ar54  +
          -rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__n_K54  +
          -Y[jar54]*rate_eval.Ar54__n_K53__weak__mp17  +
          -rho*Y[jhe4]*Y[jar54]*rate_eval.He4_Ar54__n_Ca57  +
          -rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__He4_Cl51  +
          -Y[jar54]*rate_eval.Ar54__n_n_K52__weak__mp17  +
          -rho*Y[jhe4]*Y[jar54]*rate_eval.He4_Ar54__Ca58  +
          -rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__K55  +
          +rho*Y[jn]*Y[jar53]*rate_eval.n_Ar53__Ar54  +
          -Y[jar54]*rate_eval.Ar54__K54__weak__mo03
       )

    dYdt[jk31] = (
          -rho*Y[jn]*Y[jk31]*rate_eval.n_K31__K32  +
          -rho*Y[jhe4]*Y[jk31]*rate_eval.He4_K31__p_Ca34  +
          -rho*Y[jn]*Y[jk31]*rate_eval.n_K31__p_Ar31  +
          -rho*Y[jhe4]*Y[jk31]*rate_eval.He4_K31__Sc35  +
          -rho*Y[jn]*Y[jk31]*rate_eval.n_K31__He4_Cl28  +
          -Y[jk31]*rate_eval.K31__Ar31__weak__bqa_pos_  +
          +rho*Y[jp]*Y[jar30]*rate_eval.p_Ar30__K31
       )

    dYdt[jk32] = (
          -Y[jk32]*rate_eval.K32__Ar32__weak__bqa_pos_  +
          +rho*Y[jn]*Y[jsc35]*rate_eval.n_Sc35__He4_K32  +
          +rho*Y[jn]*Y[jk31]*rate_eval.n_K31__K32  +
          -rho*Y[jn]*Y[jk32]*rate_eval.n_K32__He4_Cl29  +
          -rho*Y[jn]*Y[jk32]*rate_eval.n_K32__p_Ar32  +
          +rho*Y[jhe4]*Y[jar29]*rate_eval.He4_Ar29__p_K32  +
          -rho*Y[jhe4]*Y[jk32]*rate_eval.He4_K32__Sc36  +
          -rho*Y[jn]*Y[jk32]*rate_eval.n_K32__K33  +
          +rho*Y[jhe4]*Y[jcl28]*rate_eval.He4_Cl28__K32  +
          -rho*Y[jhe4]*Y[jk32]*rate_eval.He4_K32__p_Ca35  +
          +rho*Y[jp]*Y[jar31]*rate_eval.p_Ar31__K32  +
          -rho*Y[jp]*Y[jk32]*rate_eval.p_K32__Ca33
       )

    dYdt[jk33] = (
          -rho*Y[jn]*Y[jk33]*rate_eval.n_K33__p_Ar33  +
          +Y[jca33]*rate_eval.Ca33__K33__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[jk33]*rate_eval.He4_K33__Sc37  +
          -rho*Y[jp]*Y[jk33]*rate_eval.p_K33__Ca34  +
          +rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__p_K33  +
          -rho*Y[jn]*Y[jk33]*rate_eval.n_K33__He4_Cl30  +
          -rho*Y[jn]*Y[jk33]*rate_eval.n_K33__K34  +
          +rho*Y[jn]*Y[jk32]*rate_eval.n_K32__K33  +
          +rho*Y[jhe4]*Y[jcl29]*rate_eval.He4_Cl29__K33  +
          +rho*Y[jhe4]*Y[jar30]*rate_eval.He4_Ar30__p_K33  +
          -rho*Y[jhe4]*Y[jk33]*rate_eval.He4_K33__p_Ca36  +
          +rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__He4_K33  +
          -Y[jk33]*rate_eval.K33__Ar33__weak__bqa_pos_  +
          +rho*Y[jp]*Y[jar32]*rate_eval.p_Ar32__K33
       )

    dYdt[jk34] = (
          +rho*Y[jn]*Y[jsc37]*rate_eval.n_Sc37__He4_K34  +
          +rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__p_K34  +
          -rho*Y[jhe4]*Y[jk34]*rate_eval.He4_K34__p_Ca37  +
          +rho*Y[jhe4]*Y[jar31]*rate_eval.He4_Ar31__p_K34  +
          +rho*Y[jhe4]*Y[jcl30]*rate_eval.He4_Cl30__K34  +
          +Y[jca34]*rate_eval.Ca34__K34__weak__bqa_pos_  +
          -rho*Y[jn]*Y[jk34]*rate_eval.n_K34__K35  +
          +rho*Y[jn]*Y[jk33]*rate_eval.n_K33__K34  +
          -rho*Y[jp]*Y[jk34]*rate_eval.p_K34__Ca35  +
          -rho*Y[jn]*Y[jk34]*rate_eval.n_K34__He4_Cl31  +
          -rho*Y[jn]*Y[jk34]*rate_eval.n_K34__p_Ar34  +
          -Y[jk34]*rate_eval.K34__Ar34__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[jk34]*rate_eval.He4_K34__Sc38  +
          +rho*Y[jp]*Y[jar33]*rate_eval.p_Ar33__K34
       )

    dYdt[jk35] = (
          +rho*Y[jp]*Y[jar34]*rate_eval.p_Ar34__K35  +
          +rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__p_K35  +
          -rho*Y[jn]*Y[jk35]*rate_eval.n_K35__p_Ar35  +
          +Y[jca35]*rate_eval.Ca35__K35__weak__wc17  +
          -rho*Y[jhe4]*Y[jk35]*rate_eval.He4_K35__p_Ca38  +
          -rho*Y[jn]*Y[jk35]*rate_eval.n_K35__He4_Cl32  +
          -rho*Y[jhe4]*Y[jk35]*rate_eval.He4_K35__Sc39  +
          +rho*Y[jn]*Y[jk34]*rate_eval.n_K34__K35  +
          +rho*Y[jhe4]*Y[jcl31]*rate_eval.He4_Cl31__K35  +
          -rho*Y[jp]*Y[jk35]*rate_eval.p_K35__Ca36  +
          -Y[jk35]*rate_eval.K35__p_Cl34__weak__wc12  +
          -rho*Y[jn]*Y[jk35]*rate_eval.n_K35__K36  +
          -Y[jk35]*rate_eval.K35__Ar35__weak__wc12  +
          +rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__He4_K35  +
          +rho*Y[jhe4]*Y[jar32]*rate_eval.He4_Ar32__p_K35
       )

    dYdt[jk36] = (
          -rho*Y[jhe4]*Y[jk36]*rate_eval.He4_K36__p_Ca39  +
          +rho*Y[jn]*Y[jsc39]*rate_eval.n_Sc39__He4_K36  +
          +rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__p_K36  +
          -rho*Y[jn]*Y[jk36]*rate_eval.n_K36__He4_Cl33  +
          -rho*Y[jn]*Y[jk36]*rate_eval.n_K36__p_Ar36  +
          +rho*Y[jhe4]*Y[jar33]*rate_eval.He4_Ar33__p_K36  +
          +Y[jca36]*rate_eval.Ca36__K36__weak__wc12  +
          -rho*Y[jp]*Y[jk36]*rate_eval.p_K36__Ca37  +
          -rho*Y[jn]*Y[jk36]*rate_eval.n_K36__K37  +
          +rho*Y[jp]*Y[jar35]*rate_eval.p_Ar35__K36  +
          +rho*Y[jhe4]*Y[jcl32]*rate_eval.He4_Cl32__K36  +
          -Y[jk36]*rate_eval.K36__He4_S32__weak__wc12  +
          -rho*Y[jhe4]*Y[jk36]*rate_eval.He4_K36__Sc40  +
          -Y[jk36]*rate_eval.K36__p_Cl35__weak__wc12  +
          +rho*Y[jn]*Y[jk35]*rate_eval.n_K35__K36  +
          -Y[jk36]*rate_eval.K36__Ar36__weak__wc12
       )

    dYdt[jk37] = (
          +rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__p_K37  +
          -rho*Y[jhe4]*Y[jk37]*rate_eval.He4_K37__p_Ca40  +
          -rho*Y[jn]*Y[jk37]*rate_eval.n_K37__He4_Cl34  +
          +rho*Y[jhe4]*Y[jar34]*rate_eval.He4_Ar34__p_K37  +
          +rho*Y[jp]*Y[jar36]*rate_eval.p_Ar36__K37  +
          -rho*Y[jp]*Y[jk37]*rate_eval.p_K37__Ca38  +
          -rho*Y[jn]*Y[jk37]*rate_eval.n_K37__K38  +
          +rho*Y[jn]*Y[jk36]*rate_eval.n_K36__K37  +
          +rho*Y[jhe4]*Y[jcl33]*rate_eval.He4_Cl33__K37  +
          -rho*Y[jn]*Y[jk37]*rate_eval.n_K37__p_Ar37  +
          -Y[jk37]*rate_eval.K37__Ar37__weak__wc12  +
          +Y[jca37]*rate_eval.Ca37__K37__weak__wc12  +
          +rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__He4_K37  +
          -rho*Y[jhe4]*Y[jk37]*rate_eval.He4_K37__Sc41
       )

    dYdt[jk38] = (
          +rho*Y[jn]*Y[jsc41]*rate_eval.n_Sc41__He4_K38  +
          +rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__p_K38  +
          -rho*Y[jn]*Y[jk38]*rate_eval.n_K38__p_Ar38  +
          +rho*Y[jhe4]*Y[jar35]*rate_eval.He4_Ar35__p_K38  +
          -Y[jk38]*rate_eval.K38__Ar38__weak__wc12  +
          -rho*Y[jhe4]*Y[jk38]*rate_eval.He4_K38__p_Ca41  +
          -rho*Y[jp]*Y[jk38]*rate_eval.p_K38__Ca39  +
          +rho*Y[jn]*Y[jk37]*rate_eval.n_K37__K38  +
          +rho*Y[jp]*Y[jar37]*rate_eval.p_Ar37__K38  +
          +rho*Y[jhe4]*Y[jcl34]*rate_eval.He4_Cl34__K38  +
          +Y[jca38]*rate_eval.Ca38__K38__weak__wc12  +
          -rho*Y[jn]*Y[jk38]*rate_eval.n_K38__He4_Cl35  +
          -rho*Y[jn]*Y[jk38]*rate_eval.n_K38__K39  +
          -rho*Y[jhe4]*Y[jk38]*rate_eval.He4_K38__Sc42
       )

    dYdt[jk39] = (
          +rho*Y[jn]*Y[jsc42]*rate_eval.n_Sc42__He4_K39  +
          +rho*Y[jp]*Y[jca42]*rate_eval.p_Ca42__He4_K39  +
          -rho*Y[jn]*Y[jk39]*rate_eval.n_K39__p_Ar39  +
          -rho*Y[jhe4]*Y[jk39]*rate_eval.He4_K39__Sc43  +
          +rho*Y[jp]*Y[jar38]*rate_eval.p_Ar38__K39  +
          -rho*Y[jn]*Y[jk39]*rate_eval.n_K39__He4_Cl36  +
          +rho*Y[jhe4]*Y[jcl35]*rate_eval.He4_Cl35__K39  +
          +Y[jca39]*rate_eval.Ca39__K39__weak__wc12  +
          -rho*Y[jp]*Y[jk39]*rate_eval.p_K39__Ca40  +
          +Y[jar39]*rate_eval.Ar39__K39__weak__wc12  +
          +Y[jsc40]*rate_eval.Sc40__p_K39__weak__wc12  +
          +rho*Y[jn]*Y[jk38]*rate_eval.n_K38__K39  +
          +rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__p_K39  +
          -rho*Y[jp]*Y[jk39]*rate_eval.p_K39__He4_Ar36  +
          -rho*Y[jn]*Y[jk39]*rate_eval.n_K39__K40
       )

    dYdt[jk40] = (
          +rho*Y[jn]*Y[jsc43]*rate_eval.n_Sc43__He4_K40  +
          -rho*Y[jp]*Y[jk40]*rate_eval.p_K40__He4_Ar37  +
          -rho*Y[jp]*Y[jk40]*rate_eval.p_K40__n_Ca40  +
          -rho*Y[jn]*Y[jk40]*rate_eval.n_K40__He4_Cl37  +
          -rho*Y[jn]*Y[jk40]*rate_eval.n_K40__p_Ar40  +
          -rho*Y[jhe4]*Y[jk40]*rate_eval.He4_K40__p_Ca43  +
          -rho*Y[jn]*Y[jk40]*rate_eval.n_K40__K41  +
          +rho*Y[jhe4]*Y[jcl36]*rate_eval.He4_Cl36__K40  +
          -rho*Y[jp]*Y[jk40]*rate_eval.p_K40__Ca41  +
          +rho*Y[jp]*Y[jar39]*rate_eval.p_Ar39__K40  +
          -rho*Y[jhe4]*Y[jk40]*rate_eval.He4_K40__Sc44  +
          +rho*Y[jn]*Y[jk39]*rate_eval.n_K39__K40  +
          -Y[jk40]*rate_eval.K40__Ar40__weak__wc12  +
          -Y[jk40]*rate_eval.K40__Ca40__weak__wc12
       )

    dYdt[jk41] = (
          -rho*Y[jp]*Y[jk41]*rate_eval.p_K41__He4_Ar38  +
          +rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__n_K41  +
          -rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__p_Ca44  +
          -rho*Y[jp]*Y[jk41]*rate_eval.p_K41__Ca42  +
          -rho*Y[jn]*Y[jk41]*rate_eval.n_K41__K42  +
          +rho*Y[jn]*Y[jk40]*rate_eval.n_K40__K41  +
          +rho*Y[jp]*Y[jar40]*rate_eval.p_Ar40__K41  +
          -rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__Sc45  +
          +rho*Y[jhe4]*Y[jcl37]*rate_eval.He4_Cl37__K41  +
          +rho*Y[jhe4]*Y[jcl38]*rate_eval.He4_Cl38__n_K41  +
          +Y[jca41]*rate_eval.Ca41__K41__weak__wc12  +
          +Y[jar41]*rate_eval.Ar41__K41__weak__wc12  +
          -rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__n_Sc44  +
          -rho*Y[jp]*Y[jk41]*rate_eval.p_K41__n_Ca41
       )

    dYdt[jk42] = (
          -rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__p_Ca45  +
          -rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__n_Sc45  +
          +rho*Y[jp]*Y[jar41]*rate_eval.p_Ar41__K42  +
          -rho*Y[jp]*Y[jk42]*rate_eval.p_K42__n_Ca42  +
          -rho*Y[jp]*Y[jk42]*rate_eval.p_K42__He4_Ar39  +
          +rho*Y[jn]*Y[jk41]*rate_eval.n_K41__K42  +
          +rho*Y[jhe4]*Y[jcl38]*rate_eval.He4_Cl38__K42  +
          -rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__Sc46  +
          -rho*Y[jp]*Y[jk42]*rate_eval.p_K42__Ca43  +
          -rho*Y[jn]*Y[jk42]*rate_eval.n_K42__K43  +
          -rho*Y[jn]*Y[jk42]*rate_eval.n_K42__He4_Cl39  +
          +Y[jar42]*rate_eval.Ar42__K42__weak__wc12  +
          -rho*Y[jn]*Y[jk42]*rate_eval.n_K42__p_Ar42  +
          -Y[jk42]*rate_eval.K42__Ca42__weak__wc12
       )

    dYdt[jk43] = (
          -rho*Y[jhe4]*Y[jk43]*rate_eval.He4_K43__p_Ca46  +
          -rho*Y[jp]*Y[jk43]*rate_eval.p_K43__n_Ca43  +
          +rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__He4_K43  +
          +rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__n_K43  +
          +rho*Y[jhe4]*Y[jcl40]*rate_eval.He4_Cl40__n_K43  +
          -rho*Y[jhe4]*Y[jk43]*rate_eval.He4_K43__Sc47  +
          -rho*Y[jp]*Y[jk43]*rate_eval.p_K43__Ca44  +
          -rho*Y[jn]*Y[jk43]*rate_eval.n_K43__K44  +
          +rho*Y[jp]*Y[jar42]*rate_eval.p_Ar42__K43  +
          +rho*Y[jhe4]*Y[jcl39]*rate_eval.He4_Cl39__K43  +
          +rho*Y[jn]*Y[jk42]*rate_eval.n_K42__K43  +
          -Y[jk43]*rate_eval.K43__Ca43__weak__wc12  +
          -rho*Y[jp]*Y[jk43]*rate_eval.p_K43__He4_Ar40  +
          +Y[jar43]*rate_eval.Ar43__K43__weak__wc12
       )

    dYdt[jk44] = (
          -rho*Y[jp]*Y[jk44]*rate_eval.p_K44__He4_Ar41  +
          -rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__p_Ca47  +
          +rho*Y[jp]*Y[jar44]*rate_eval.p_Ar44__n_K44  +
          +rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__n_K44  +
          -rho*Y[jp]*Y[jk44]*rate_eval.p_K44__n_Ca44  +
          -rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__Sc48  +
          -rho*Y[jn]*Y[jk44]*rate_eval.n_K44__K45  +
          +rho*Y[jn]*Y[jk43]*rate_eval.n_K43__K44  +
          +rho*Y[jp]*Y[jar43]*rate_eval.p_Ar43__K44  +
          -rho*Y[jp]*Y[jk44]*rate_eval.p_K44__Ca45  +
          -rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__n_Sc47  +
          +rho*Y[jhe4]*Y[jcl40]*rate_eval.He4_Cl40__K44  +
          -Y[jk44]*rate_eval.K44__Ca44__weak__wc12  +
          +Y[jar44]*rate_eval.Ar44__K44__weak__wc12
       )

    dYdt[jk45] = (
          -rho*Y[jp]*Y[jk45]*rate_eval.p_K45__He4_Ar42  +
          -rho*Y[jp]*Y[jk45]*rate_eval.p_K45__n_Ca45  +
          +rho*Y[jhe4]*Y[jcl42]*rate_eval.He4_Cl42__n_K45  +
          +rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__n_K45  +
          -rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__p_Ca48  +
          -rho*Y[jp]*Y[jk45]*rate_eval.p_K45__Ca46  +
          -rho*Y[jn]*Y[jk45]*rate_eval.n_K45__K46  +
          +rho*Y[jn]*Y[jk44]*rate_eval.n_K44__K45  +
          +rho*Y[jp]*Y[jar44]*rate_eval.p_Ar44__K45  +
          -rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__Sc49  +
          +Y[jar45]*rate_eval.Ar45__K45__weak__wc12  +
          +rho*Y[jhe4]*Y[jcl41]*rate_eval.He4_Cl41__K45  +
          -rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__n_Sc48  +
          -Y[jk45]*rate_eval.K45__Ca45__weak__wc12
       )

    dYdt[jk46] = (
          -rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__p_Ca49  +
          -rho*Y[jp]*Y[jk46]*rate_eval.p_K46__Ca47  +
          -rho*Y[jn]*Y[jk46]*rate_eval.n_K46__K47  +
          +rho*Y[jn]*Y[jk45]*rate_eval.n_K45__K46  +
          +rho*Y[jhe4]*Y[jcl42]*rate_eval.He4_Cl42__K46  +
          +rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__n_K46  +
          -rho*Y[jp]*Y[jk46]*rate_eval.p_K46__He4_Ar43  +
          -rho*Y[jp]*Y[jk46]*rate_eval.p_K46__n_Ca46  +
          +rho*Y[jp]*Y[jar45]*rate_eval.p_Ar45__K46  +
          -Y[jk46]*rate_eval.K46__Ca46__weak__wc12  +
          +Y[jar46]*rate_eval.Ar46__K46__weak__wc12  +
          -rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__Sc50  +
          +rho*Y[jp]*Y[jar46]*rate_eval.p_Ar46__n_K46  +
          -rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__n_Sc49
       )

    dYdt[jk47] = (
          +Y[jar48]*rate_eval.Ar48__n_K47__weak__mp17  +
          -rho*Y[jp]*Y[jk47]*rate_eval.p_K47__He4_Ar44  +
          +rho*Y[jp]*Y[jar47]*rate_eval.p_Ar47__n_K47  +
          +rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__He4_K47  +
          +rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__n_K47  +
          +rho*Y[jn]*Y[jk46]*rate_eval.n_K46__K47  +
          -rho*Y[jn]*Y[jk47]*rate_eval.n_K47__K48  +
          -Y[jk47]*rate_eval.K47__Ca47__weak__wc12  +
          -rho*Y[jhe4]*Y[jk47]*rate_eval.He4_K47__Sc51  +
          +rho*Y[jhe4]*Y[jcl43]*rate_eval.He4_Cl43__K47  +
          -rho*Y[jhe4]*Y[jk47]*rate_eval.He4_K47__n_Sc50  +
          -rho*Y[jp]*Y[jk47]*rate_eval.p_K47__n_Ca47  +
          +rho*Y[jp]*Y[jar46]*rate_eval.p_Ar46__K47  +
          -rho*Y[jp]*Y[jk47]*rate_eval.p_K47__Ca48  +
          +Y[jar47]*rate_eval.Ar47__K47__weak__wc12
       )

    dYdt[jk48] = (
          -rho*Y[jp]*Y[jk48]*rate_eval.p_K48__Ca49  +
          +rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__He4_K48  +
          -rho*Y[jhe4]*Y[jk48]*rate_eval.He4_K48__n_Sc51  +
          -rho*Y[jp]*Y[jk48]*rate_eval.p_K48__He4_Ar45  +
          +rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__n_K48  +
          -rho*Y[jp]*Y[jk48]*rate_eval.p_K48__n_Ca48  +
          +rho*Y[jhe4]*Y[jcl45]*rate_eval.He4_Cl45__n_K48  +
          +rho*Y[jp]*Y[jar47]*rate_eval.p_Ar47__K48  +
          +rho*Y[jn]*Y[jk47]*rate_eval.n_K47__K48  +
          +rho*Y[jhe4]*Y[jcl44]*rate_eval.He4_Cl44__K48  +
          +Y[jar49]*rate_eval.Ar49__n_K48__weak__wc12  +
          -Y[jk48]*rate_eval.K48__n_Ca47__weak__wc12  +
          -rho*Y[jn]*Y[jk48]*rate_eval.n_K48__K49  +
          +Y[jar48]*rate_eval.Ar48__K48__weak__wc17  +
          -rho*Y[jhe4]*Y[jk48]*rate_eval.He4_K48__Sc52  +
          -Y[jk48]*rate_eval.K48__Ca48__weak__wc12
       )

    dYdt[jk49] = (
          +Y[jar52]*rate_eval.Ar52__n_n_n_K49__weak__mo03  +
          -rho*Y[jhe4]*Y[jk49]*rate_eval.He4_K49__n_Sc52  +
          -rho*Y[jp]*Y[jk49]*rate_eval.p_K49__n_Ca49  +
          +Y[jar49]*rate_eval.Ar49__K49__weak__wc12  +
          +rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__He4_K49  +
          +rho*Y[jhe4]*Y[jcl46]*rate_eval.He4_Cl46__n_K49  +
          -rho*Y[jhe4]*Y[jk49]*rate_eval.He4_K49__Sc53  +
          -rho*Y[jn]*Y[jk49]*rate_eval.n_K49__K50  +
          -Y[jk49]*rate_eval.K49__Ca49__weak__wc12  +
          -rho*Y[jp]*Y[jk49]*rate_eval.p_K49__Ca50  +
          +rho*Y[jn]*Y[jk48]*rate_eval.n_K48__K49  +
          -rho*Y[jp]*Y[jk49]*rate_eval.p_K49__He4_Ar46  +
          +Y[jar50]*rate_eval.Ar50__n_K49__weak__wc12  +
          +rho*Y[jhe4]*Y[jcl45]*rate_eval.He4_Cl45__K49  +
          +rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__n_K49  +
          +rho*Y[jp]*Y[jar48]*rate_eval.p_Ar48__K49  +
          +Y[jar51]*rate_eval.Ar51__n_n_K49__weak__mp17  +
          -Y[jk49]*rate_eval.K49__n_Ca48__weak__wc12
       )

    dYdt[jk50] = (
          +Y[jar53]*rate_eval.Ar53__n_n_n_K50__weak__mo03  +
          -rho*Y[jhe4]*Y[jk50]*rate_eval.He4_K50__n_Sc53  +
          +rho*Y[jhe4]*Y[jcl47]*rate_eval.He4_Cl47__n_K50  +
          -rho*Y[jhe4]*Y[jk50]*rate_eval.He4_K50__Sc54  +
          +Y[jar52]*rate_eval.Ar52__n_n_K50__weak__mp17  +
          +rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__n_K50  +
          -rho*Y[jp]*Y[jk50]*rate_eval.p_K50__n_Ca50  +
          -rho*Y[jn]*Y[jk50]*rate_eval.n_K50__K51  +
          +rho*Y[jhe4]*Y[jcl46]*rate_eval.He4_Cl46__K50  +
          +rho*Y[jn]*Y[jk49]*rate_eval.n_K49__K50  +
          +Y[jar51]*rate_eval.Ar51__n_K50__weak__mp17  +
          -rho*Y[jp]*Y[jk50]*rate_eval.p_K50__He4_Ar47  +
          -Y[jk50]*rate_eval.K50__n_Ca49__weak__wc12  +
          +rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__He4_K50  +
          +rho*Y[jp]*Y[jar49]*rate_eval.p_Ar49__K50  +
          -rho*Y[jp]*Y[jk50]*rate_eval.p_K50__Ca51  +
          -Y[jk50]*rate_eval.K50__Ca50__weak__wc12  +
          +Y[jar50]*rate_eval.Ar50__K50__weak__wc12  +
          -Y[jk50]*rate_eval.K50__n_n_Ca48__weak__mp17
       )

    dYdt[jk51] = (
          +Y[jar54]*rate_eval.Ar54__n_n_n_K51__weak__mo03  +
          -rho*Y[jhe4]*Y[jk51]*rate_eval.He4_K51__n_Sc54  +
          -rho*Y[jp]*Y[jk51]*rate_eval.p_K51__n_Ca51  +
          +rho*Y[jhe4]*Y[jcl47]*rate_eval.He4_Cl47__K51  +
          -rho*Y[jp]*Y[jk51]*rate_eval.p_K51__He4_Ar48  +
          -rho*Y[jhe4]*Y[jk51]*rate_eval.He4_K51__Sc55  +
          -rho*Y[jp]*Y[jk51]*rate_eval.p_K51__Ca52  +
          +rho*Y[jn]*Y[jk50]*rate_eval.n_K50__K51  +
          +Y[jar53]*rate_eval.Ar53__n_n_K51__weak__mp17  +
          -rho*Y[jn]*Y[jk51]*rate_eval.n_K51__K52  +
          +Y[jar52]*rate_eval.Ar52__n_K51__weak__mp17  +
          -Y[jk51]*rate_eval.K51__n_Ca50__weak__wc12  +
          +rho*Y[jhe4]*Y[jcl48]*rate_eval.He4_Cl48__n_K51  +
          +rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__He4_K51  +
          -Y[jk51]*rate_eval.K51__Ca51__weak__wc12  +
          +Y[jar51]*rate_eval.Ar51__K51__weak__mo03  +
          +rho*Y[jp]*Y[jar51]*rate_eval.p_Ar51__n_K51  +
          +rho*Y[jp]*Y[jar50]*rate_eval.p_Ar50__K51
       )

    dYdt[jk52] = (
          +rho*Y[jp]*Y[jca55]*rate_eval.p_Ca55__He4_K52  +
          -rho*Y[jhe4]*Y[jk52]*rate_eval.He4_K52__n_Sc55  +
          -Y[jk52]*rate_eval.K52__Ca52__weak__wc17  +
          +rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__n_K52  +
          +rho*Y[jhe4]*Y[jcl49]*rate_eval.He4_Cl49__n_K52  +
          -rho*Y[jp]*Y[jk52]*rate_eval.p_K52__He4_Ar49  +
          -rho*Y[jp]*Y[jk52]*rate_eval.p_K52__Ca53  +
          -rho*Y[jn]*Y[jk52]*rate_eval.n_K52__K53  +
          +rho*Y[jp]*Y[jar51]*rate_eval.p_Ar51__K52  +
          +rho*Y[jn]*Y[jk51]*rate_eval.n_K51__K52  +
          -Y[jk52]*rate_eval.K52__n_n_Ca50__weak__mp17  +
          +Y[jar54]*rate_eval.Ar54__n_n_K52__weak__mp17  +
          +Y[jar52]*rate_eval.Ar52__K52__weak__mo03  +
          +rho*Y[jhe4]*Y[jcl48]*rate_eval.He4_Cl48__K52  +
          -Y[jk52]*rate_eval.K52__n_Ca51__weak__wc12  +
          -rho*Y[jp]*Y[jk52]*rate_eval.p_K52__n_Ca52  +
          +Y[jar53]*rate_eval.Ar53__n_K52__weak__mp17  +
          -rho*Y[jhe4]*Y[jk52]*rate_eval.He4_K52__Sc56
       )

    dYdt[jk53] = (
          -Y[jk53]*rate_eval.K53__n_n_n_Ca50__weak__mo03  +
          +rho*Y[jp]*Y[jca56]*rate_eval.p_Ca56__He4_K53  +
          -rho*Y[jhe4]*Y[jk53]*rate_eval.He4_K53__n_Sc56  +
          -rho*Y[jp]*Y[jk53]*rate_eval.p_K53__n_Ca53  +
          +rho*Y[jhe4]*Y[jcl49]*rate_eval.He4_Cl49__K53  +
          +rho*Y[jhe4]*Y[jcl50]*rate_eval.He4_Cl50__n_K53  +
          +Y[jar54]*rate_eval.Ar54__n_K53__weak__mp17  +
          -rho*Y[jn]*Y[jk53]*rate_eval.n_K53__K54  +
          +rho*Y[jn]*Y[jk52]*rate_eval.n_K52__K53  +
          -Y[jk53]*rate_eval.K53__n_Ca52__weak__wc17  +
          +rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__n_K53  +
          +rho*Y[jp]*Y[jar52]*rate_eval.p_Ar52__K53  +
          -rho*Y[jp]*Y[jk53]*rate_eval.p_K53__Ca54  +
          -Y[jk53]*rate_eval.K53__n_n_Ca51__weak__mp17  +
          -rho*Y[jhe4]*Y[jk53]*rate_eval.He4_K53__Sc57  +
          -Y[jk53]*rate_eval.K53__Ca53__weak__wc17  +
          +Y[jar53]*rate_eval.Ar53__K53__weak__mo03  +
          -rho*Y[jp]*Y[jk53]*rate_eval.p_K53__He4_Ar50
       )

    dYdt[jk54] = (
          -Y[jk54]*rate_eval.K54__n_n_n_Ca51__weak__mo03  +
          -rho*Y[jhe4]*Y[jk54]*rate_eval.He4_K54__n_Sc57  +
          -rho*Y[jp]*Y[jk54]*rate_eval.p_K54__n_Ca54  +
          +rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__n_K54  +
          +rho*Y[jhe4]*Y[jcl51]*rate_eval.He4_Cl51__n_K54  +
          +rho*Y[jhe4]*Y[jcl50]*rate_eval.He4_Cl50__K54  +
          +rho*Y[jn]*Y[jk53]*rate_eval.n_K53__K54  +
          +rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__He4_K54  +
          -Y[jk54]*rate_eval.K54__n_n_Ca52__weak__mp17  +
          -rho*Y[jp]*Y[jk54]*rate_eval.p_K54__Ca55  +
          -Y[jk54]*rate_eval.K54__n_Ca53__weak__mp17  +
          +rho*Y[jp]*Y[jar53]*rate_eval.p_Ar53__K54  +
          -rho*Y[jn]*Y[jk54]*rate_eval.n_K54__K55  +
          -rho*Y[jp]*Y[jk54]*rate_eval.p_K54__He4_Ar51  +
          -rho*Y[jhe4]*Y[jk54]*rate_eval.He4_K54__Sc58  +
          -Y[jk54]*rate_eval.K54__Ca54__weak__wc17  +
          +Y[jar54]*rate_eval.Ar54__K54__weak__mo03
       )

    dYdt[jk55] = (
          -Y[jk55]*rate_eval.K55__n_n_n_Ca52__weak__mo03  +
          -rho*Y[jn]*Y[jk55]*rate_eval.n_K55__K56  +
          +rho*Y[jp]*Y[jca58]*rate_eval.p_Ca58__He4_K55  +
          -rho*Y[jhe4]*Y[jk55]*rate_eval.He4_K55__n_Sc58  +
          -rho*Y[jhe4]*Y[jk55]*rate_eval.He4_K55__Sc59  +
          +rho*Y[jhe4]*Y[jcl51]*rate_eval.He4_Cl51__K55  +
          -rho*Y[jp]*Y[jk55]*rate_eval.p_K55__n_Ca55  +
          +rho*Y[jhe4]*Y[jcl52]*rate_eval.He4_Cl52__n_K55  +
          -rho*Y[jp]*Y[jk55]*rate_eval.p_K55__Ca56  +
          -Y[jk55]*rate_eval.K55__n_n_Ca53__weak__mp17  +
          -Y[jk55]*rate_eval.K55__n_Ca54__weak__mp17  +
          -rho*Y[jp]*Y[jk55]*rate_eval.p_K55__He4_Ar52  +
          +rho*Y[jp]*Y[jar54]*rate_eval.p_Ar54__K55  +
          +rho*Y[jn]*Y[jk54]*rate_eval.n_K54__K55  +
          -Y[jk55]*rate_eval.K55__Ca55__weak__mo03
       )

    dYdt[jk56] = (
          -Y[jk56]*rate_eval.K56__n_n_n_Ca53__weak__mo03  +
          +rho*Y[jn]*Y[jk55]*rate_eval.n_K55__K56  +
          -rho*Y[jhe4]*Y[jk56]*rate_eval.He4_K56__n_Sc59  +
          -rho*Y[jp]*Y[jk56]*rate_eval.p_K56__n_Ca56  +
          -rho*Y[jp]*Y[jk56]*rate_eval.p_K56__He4_Ar53  +
          -rho*Y[jp]*Y[jk56]*rate_eval.p_K56__Ca57  +
          -rho*Y[jn]*Y[jk56]*rate_eval.n_K56__K57  +
          -Y[jk56]*rate_eval.K56__Ca56__weak__mo03  +
          +rho*Y[jhe4]*Y[jcl52]*rate_eval.He4_Cl52__K56  +
          +rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__He4_K56  +
          -Y[jk56]*rate_eval.K56__n_Ca55__weak__mp17  +
          -Y[jk56]*rate_eval.K56__n_n_Ca54__weak__mp17  +
          -rho*Y[jhe4]*Y[jk56]*rate_eval.He4_K56__Sc60
       )

    dYdt[jk57] = (
          -rho*Y[jhe4]*Y[jk57]*rate_eval.He4_K57__n_Sc60  +
          -rho*Y[jp]*Y[jk57]*rate_eval.p_K57__He4_Ar54  +
          -rho*Y[jp]*Y[jk57]*rate_eval.p_K57__n_Ca57  +
          -rho*Y[jhe4]*Y[jk57]*rate_eval.He4_K57__Sc61  +
          -rho*Y[jp]*Y[jk57]*rate_eval.p_K57__Ca58  +
          +rho*Y[jn]*Y[jk56]*rate_eval.n_K56__K57  +
          -rho*Y[jn]*Y[jk57]*rate_eval.n_K57__K58  +
          -Y[jk57]*rate_eval.K57__n_n_Ca55__weak__mp17  +
          -Y[jk57]*rate_eval.K57__n_Ca56__weak__mp17  +
          +rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__He4_K57  +
          -Y[jk57]*rate_eval.K57__Ca57__weak__mo03  +
          -Y[jk57]*rate_eval.K57__n_n_n_Ca54__weak__mo03
       )

    dYdt[jk58] = (
          -Y[jk58]*rate_eval.K58__n_n_n_Ca55__weak__mo03  +
          +rho*Y[jp]*Y[jca61]*rate_eval.p_Ca61__He4_K58  +
          -rho*Y[jn]*Y[jk58]*rate_eval.n_K58__K59  +
          -rho*Y[jp]*Y[jk58]*rate_eval.p_K58__n_Ca58  +
          -rho*Y[jhe4]*Y[jk58]*rate_eval.He4_K58__Sc62  +
          -rho*Y[jhe4]*Y[jk58]*rate_eval.He4_K58__n_Sc61  +
          +rho*Y[jn]*Y[jk57]*rate_eval.n_K57__K58  +
          -Y[jk58]*rate_eval.K58__n_n_Ca56__weak__mp17  +
          -rho*Y[jp]*Y[jk58]*rate_eval.p_K58__Ca59  +
          -Y[jk58]*rate_eval.K58__n_Ca57__weak__mp17  +
          -Y[jk58]*rate_eval.K58__Ca58__weak__mo03
       )

    dYdt[jk59] = (
          -Y[jk59]*rate_eval.K59__n_n_n_Ca56__weak__mo03  +
          -rho*Y[jp]*Y[jk59]*rate_eval.p_K59__n_Ca59  +
          +rho*Y[jn]*Y[jk58]*rate_eval.n_K58__K59  +
          -Y[jk59]*rate_eval.K59__Ca59__weak__mo03  +
          -rho*Y[jp]*Y[jk59]*rate_eval.p_K59__Ca60  +
          -rho*Y[jhe4]*Y[jk59]*rate_eval.He4_K59__Sc63  +
          -Y[jk59]*rate_eval.K59__n_n_Ca57__weak__mp17  +
          -rho*Y[jhe4]*Y[jk59]*rate_eval.He4_K59__n_Sc62  +
          -Y[jk59]*rate_eval.K59__n_Ca58__weak__mp17
       )

    dYdt[jca33] = (
          +rho*Y[jhe4]*Y[jar29]*rate_eval.He4_Ar29__Ca33  +
          -Y[jca33]*rate_eval.Ca33__K33__weak__bqa_pos_  +
          -rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__p_K33  +
          -rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__He4_Ar30  +
          -rho*Y[jhe4]*Y[jca33]*rate_eval.He4_Ca33__Ti37  +
          -rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__Ca34  +
          -rho*Y[jhe4]*Y[jca33]*rate_eval.He4_Ca33__p_Sc36  +
          +rho*Y[jp]*Y[jk32]*rate_eval.p_K32__Ca33
       )

    dYdt[jca34] = (
          -rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__He4_Ar31  +
          -rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__p_K34  +
          +rho*Y[jhe4]*Y[jk31]*rate_eval.He4_K31__p_Ca34  +
          +rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__He4_Ca34  +
          +rho*Y[jp]*Y[jk33]*rate_eval.p_K33__Ca34  +
          -Y[jca34]*rate_eval.Ca34__K34__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[jca34]*rate_eval.He4_Ca34__Ti38  +
          +rho*Y[jhe4]*Y[jar30]*rate_eval.He4_Ar30__Ca34  +
          +rho*Y[jn]*Y[jca33]*rate_eval.n_Ca33__Ca34  +
          -rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__Ca35  +
          -rho*Y[jhe4]*Y[jca34]*rate_eval.He4_Ca34__p_Sc37  +
          -rho*Y[jp]*Y[jca34]*rate_eval.p_Ca34__Sc35
       )

    dYdt[jca35] = (
          +rho*Y[jn]*Y[jti38]*rate_eval.n_Ti38__He4_Ca35  +
          +rho*Y[jn]*Y[jsc35]*rate_eval.n_Sc35__p_Ca35  +
          -rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__He4_Ar32  +
          -rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__p_K35  +
          -Y[jca35]*rate_eval.Ca35__K35__weak__wc17  +
          -rho*Y[jhe4]*Y[jca35]*rate_eval.He4_Ca35__Ti39  +
          -Y[jca35]*rate_eval.Ca35__p_p_Cl33__weak__wc12  +
          +rho*Y[jhe4]*Y[jar31]*rate_eval.He4_Ar31__Ca35  +
          +rho*Y[jp]*Y[jk34]*rate_eval.p_K34__Ca35  +
          -rho*Y[jhe4]*Y[jca35]*rate_eval.He4_Ca35__p_Sc38  +
          -Y[jca35]*rate_eval.Ca35__p_Ar34__weak__wc17  +
          +Y[jsc35]*rate_eval.Sc35__Ca35__weak__bqa_pos_  +
          +rho*Y[jn]*Y[jca34]*rate_eval.n_Ca34__Ca35  +
          -rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__Ca36  +
          +rho*Y[jhe4]*Y[jk32]*rate_eval.He4_K32__p_Ca35  +
          -rho*Y[jp]*Y[jca35]*rate_eval.p_Ca35__Sc36
       )

    dYdt[jca36] = (
          -rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__p_p_Ca38  +
          -rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__p_K36  +
          +rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__He4_Ca36  +
          -rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__He4_Ar33  +
          -Y[jca36]*rate_eval.Ca36__K36__weak__wc12  +
          -rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__Ca37  +
          -rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__p_Sc39  +
          -rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__Ti40  +
          +rho*Y[jhe4]*Y[jar32]*rate_eval.He4_Ar32__Ca36  +
          +rho*Y[jp]*Y[jk35]*rate_eval.p_K35__Ca36  +
          +rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__p_Ca36  +
          -Y[jca36]*rate_eval.Ca36__p_Ar35__weak__wc12  +
          +rho*Y[jhe4]*Y[jk33]*rate_eval.He4_K33__p_Ca36  +
          +rho*Y[jn]*Y[jca35]*rate_eval.n_Ca35__Ca36  +
          +Y[jsc36]*rate_eval.Sc36__Ca36__weak__bqa_pos_  +
          -rho*Y[jp]*Y[jca36]*rate_eval.p_Ca36__Sc37
       )

    dYdt[jca37] = (
          -rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__He4_Ar34  +
          -rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__p_K37  +
          +rho*Y[jhe4]*Y[jk34]*rate_eval.He4_K34__p_Ca37  +
          +rho*Y[jn]*Y[jsc37]*rate_eval.n_Sc37__p_Ca37  +
          -rho*Y[jhe4]*Y[jca37]*rate_eval.He4_Ca37__Ti41  +
          -rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__Ca38  +
          +rho*Y[jn]*Y[jca36]*rate_eval.n_Ca36__Ca37  +
          +rho*Y[jp]*Y[jk36]*rate_eval.p_K36__Ca37  +
          +rho*Y[jhe4]*Y[jar33]*rate_eval.He4_Ar33__Ca37  +
          -rho*Y[jhe4]*Y[jca37]*rate_eval.He4_Ca37__p_Sc40  +
          +Y[jsc37]*rate_eval.Sc37__Ca37__weak__bqa_pos_  +
          -Y[jca37]*rate_eval.Ca37__p_Ar36__weak__wc12  +
          -Y[jca37]*rate_eval.Ca37__K37__weak__wc12  +
          +rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__He4_Ca37  +
          -rho*Y[jp]*Y[jca37]*rate_eval.p_Ca37__Sc38
       )

    dYdt[jca38] = (
          +rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__p_p_Ca38  +
          +rho*Y[jn]*Y[jti41]*rate_eval.n_Ti41__He4_Ca38  +
          -rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__p_K38  +
          +Y[jsc38]*rate_eval.Sc38__Ca38__weak__mo97  +
          +rho*Y[jhe4]*Y[jk35]*rate_eval.He4_K35__p_Ca38  +
          -rho*Y[jhe4]*Y[jca38]*rate_eval.He4_Ca38__Ti42  +
          +rho*Y[jn]*Y[jca37]*rate_eval.n_Ca37__Ca38  +
          +rho*Y[jp]*Y[jk37]*rate_eval.p_K37__Ca38  +
          -rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__Ca39  +
          -rho*Y[jhe4]*Y[jca38]*rate_eval.He4_Ca38__p_Sc41  +
          -Y[jca38]*rate_eval.Ca38__K38__weak__wc12  +
          +Y[jti39]*rate_eval.Ti39__p_Ca38__weak__wc12  +
          +rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__p_Ca38  +
          +rho*Y[jhe4]*Y[jar34]*rate_eval.He4_Ar34__Ca38  +
          -rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__He4_Ar35  +
          -rho*Y[jp]*Y[jca38]*rate_eval.p_Ca38__Sc39
       )

    dYdt[jca39] = (
          +rho*Y[jhe4]*Y[jk36]*rate_eval.He4_K36__p_Ca39  +
          +rho*Y[jhe4]*Y[jar35]*rate_eval.He4_Ar35__Ca39  +
          -rho*Y[jhe4]*Y[jca39]*rate_eval.He4_Ca39__Ti43  +
          +rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__He4_Ca39  +
          +rho*Y[jp]*Y[jk38]*rate_eval.p_K38__Ca39  +
          +rho*Y[jn]*Y[jca38]*rate_eval.n_Ca38__Ca39  +
          -Y[jca39]*rate_eval.Ca39__K39__weak__wc12  +
          +Y[jsc39]*rate_eval.Sc39__Ca39__weak__mo97  +
          -rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__He4_Ar36  +
          -rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__p_K39  +
          -rho*Y[jp]*Y[jca39]*rate_eval.p_Ca39__Sc40  +
          +Y[jti40]*rate_eval.Ti40__p_Ca39__weak__wc12  +
          +rho*Y[jn]*Y[jsc39]*rate_eval.n_Sc39__p_Ca39  +
          -rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__Ca40  +
          +rho*Y[jp]*Y[jsc42]*rate_eval.p_Sc42__He4_Ca39
       )

    dYdt[jca40] = (
          +Y[jcr43]*rate_eval.Cr43__p_p_p_Ca40__weak__wc12  +
          +rho*Y[jn]*Y[jti43]*rate_eval.n_Ti43__He4_Ca40  +
          -rho*Y[jn]*Y[jca40]*rate_eval.n_Ca40__He4_Ar37  +
          +rho*Y[jp]*Y[jk40]*rate_eval.p_K40__n_Ca40  +
          +rho*Y[jhe4]*Y[jk37]*rate_eval.He4_K37__p_Ca40  +
          +rho*Y[jhe4]*Y[jar36]*rate_eval.He4_Ar36__Ca40  +
          -rho*Y[jhe4]*Y[jca40]*rate_eval.He4_Ca40__Ti44  +
          +rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__p_Ca40  +
          +Y[jsc40]*rate_eval.Sc40__Ca40__weak__wc12  +
          -rho*Y[jp]*Y[jca40]*rate_eval.p_Ca40__Sc41  +
          -rho*Y[jn]*Y[jca40]*rate_eval.n_Ca40__Ca41  +
          +Y[jti41]*rate_eval.Ti41__p_Ca40__weak__wc12  +
          +rho*Y[jp]*Y[jk39]*rate_eval.p_K39__Ca40  +
          +rho*Y[jp]*Y[jsc43]*rate_eval.p_Sc43__He4_Ca40  +
          +rho*Y[jn]*Y[jca39]*rate_eval.n_Ca39__Ca40  +
          +Y[jk40]*rate_eval.K40__Ca40__weak__wc12
       )

    dYdt[jca41] = (
          +rho*Y[jp]*Y[jsc44]*rate_eval.p_Sc44__He4_Ca41  +
          +rho*Y[jhe4]*Y[jk38]*rate_eval.He4_K38__p_Ca41  +
          -rho*Y[jp]*Y[jca41]*rate_eval.p_Ca41__Sc42  +
          -rho*Y[jn]*Y[jca41]*rate_eval.n_Ca41__Ca42  +
          +rho*Y[jn]*Y[jca40]*rate_eval.n_Ca40__Ca41  +
          +rho*Y[jhe4]*Y[jar37]*rate_eval.He4_Ar37__Ca41  +
          +rho*Y[jp]*Y[jk40]*rate_eval.p_K40__Ca41  +
          +Y[jsc41]*rate_eval.Sc41__Ca41__weak__wc12  +
          -rho*Y[jn]*Y[jca41]*rate_eval.n_Ca41__He4_Ar38  +
          -rho*Y[jhe4]*Y[jca41]*rate_eval.He4_Ca41__Ti45  +
          -Y[jca41]*rate_eval.Ca41__K41__weak__wc12  +
          +rho*Y[jn]*Y[jsc41]*rate_eval.n_Sc41__p_Ca41  +
          +rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__He4_Ca41  +
          +rho*Y[jp]*Y[jk41]*rate_eval.p_K41__n_Ca41
       )

    dYdt[jca42] = (
          +rho*Y[jp]*Y[jsc45]*rate_eval.p_Sc45__He4_Ca42  +
          +rho*Y[jn]*Y[jsc42]*rate_eval.n_Sc42__p_Ca42  +
          -rho*Y[jp]*Y[jca42]*rate_eval.p_Ca42__He4_K39  +
          +rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__He4_Ca42  +
          +rho*Y[jp]*Y[jk42]*rate_eval.p_K42__n_Ca42  +
          -rho*Y[jhe4]*Y[jca42]*rate_eval.He4_Ca42__Ti46  +
          -rho*Y[jp]*Y[jca42]*rate_eval.p_Ca42__Sc43  +
          +rho*Y[jn]*Y[jca41]*rate_eval.n_Ca41__Ca42  +
          +rho*Y[jp]*Y[jk41]*rate_eval.p_K41__Ca42  +
          +Y[jsc42]*rate_eval.Sc42__Ca42__weak__wc12  +
          -rho*Y[jn]*Y[jca42]*rate_eval.n_Ca42__Ca43  +
          +rho*Y[jhe4]*Y[jar38]*rate_eval.He4_Ar38__Ca42  +
          -rho*Y[jn]*Y[jca42]*rate_eval.n_Ca42__He4_Ar39  +
          +Y[jk42]*rate_eval.K42__Ca42__weak__wc12
       )

    dYdt[jca43] = (
          -rho*Y[jhe4]*Y[jca43]*rate_eval.He4_Ca43__Ti47  +
          +rho*Y[jp]*Y[jsc46]*rate_eval.p_Sc46__He4_Ca43  +
          +rho*Y[jn]*Y[jsc43]*rate_eval.n_Sc43__p_Ca43  +
          -rho*Y[jhe4]*Y[jca43]*rate_eval.He4_Ca43__n_Ti46  +
          +rho*Y[jp]*Y[jk43]*rate_eval.p_K43__n_Ca43  +
          +rho*Y[jhe4]*Y[jk40]*rate_eval.He4_K40__p_Ca43  +
          -rho*Y[jn]*Y[jca43]*rate_eval.n_Ca43__He4_Ar40  +
          +rho*Y[jhe4]*Y[jar39]*rate_eval.He4_Ar39__Ca43  +
          -rho*Y[jp]*Y[jca43]*rate_eval.p_Ca43__Sc44  +
          -rho*Y[jn]*Y[jca43]*rate_eval.n_Ca43__Ca44  +
          +rho*Y[jp]*Y[jk42]*rate_eval.p_K42__Ca43  +
          +Y[jk43]*rate_eval.K43__Ca43__weak__wc12  +
          +rho*Y[jn]*Y[jca42]*rate_eval.n_Ca42__Ca43  +
          +Y[jsc43]*rate_eval.Sc43__Ca43__weak__wc12
       )

    dYdt[jca44] = (
          -rho*Y[jp]*Y[jca44]*rate_eval.p_Ca44__Sc45  +
          +rho*Y[jp]*Y[jsc47]*rate_eval.p_Sc47__He4_Ca44  +
          +rho*Y[jn]*Y[jsc44]*rate_eval.n_Sc44__p_Ca44  +
          +rho*Y[jn]*Y[jti47]*rate_eval.n_Ti47__He4_Ca44  +
          +rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__p_Ca44  +
          +rho*Y[jhe4]*Y[jar41]*rate_eval.He4_Ar41__n_Ca44  +
          +rho*Y[jp]*Y[jk44]*rate_eval.p_K44__n_Ca44  +
          -rho*Y[jhe4]*Y[jca44]*rate_eval.He4_Ca44__Ti48  +
          +rho*Y[jp]*Y[jk43]*rate_eval.p_K43__Ca44  +
          +rho*Y[jhe4]*Y[jar40]*rate_eval.He4_Ar40__Ca44  +
          -rho*Y[jn]*Y[jca44]*rate_eval.n_Ca44__Ca45  +
          +rho*Y[jn]*Y[jca43]*rate_eval.n_Ca43__Ca44  +
          +Y[jsc44]*rate_eval.Sc44__Ca44__weak__wc12  +
          +Y[jk44]*rate_eval.K44__Ca44__weak__wc12
       )

    dYdt[jca45] = (
          +rho*Y[jp]*Y[jsc48]*rate_eval.p_Sc48__He4_Ca45  +
          +rho*Y[jn]*Y[jsc45]*rate_eval.n_Sc45__p_Ca45  +
          +rho*Y[jp]*Y[jk45]*rate_eval.p_K45__n_Ca45  +
          +rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__p_Ca45  +
          +rho*Y[jhe4]*Y[jar42]*rate_eval.He4_Ar42__n_Ca45  +
          -rho*Y[jp]*Y[jca45]*rate_eval.p_Ca45__Sc46  +
          -rho*Y[jhe4]*Y[jca45]*rate_eval.He4_Ca45__Ti49  +
          +rho*Y[jn]*Y[jca44]*rate_eval.n_Ca44__Ca45  +
          -rho*Y[jhe4]*Y[jca45]*rate_eval.He4_Ca45__n_Ti48  +
          +rho*Y[jp]*Y[jk44]*rate_eval.p_K44__Ca45  +
          -rho*Y[jn]*Y[jca45]*rate_eval.n_Ca45__Ca46  +
          +rho*Y[jhe4]*Y[jar41]*rate_eval.He4_Ar41__Ca45  +
          +Y[jk45]*rate_eval.K45__Ca45__weak__wc12  +
          -Y[jca45]*rate_eval.Ca45__Sc45__weak__wc12
       )

    dYdt[jca46] = (
          +rho*Y[jn]*Y[jti49]*rate_eval.n_Ti49__He4_Ca46  +
          +rho*Y[jp]*Y[jsc49]*rate_eval.p_Sc49__He4_Ca46  +
          +rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__p_Ca46  +
          +rho*Y[jhe4]*Y[jk43]*rate_eval.He4_K43__p_Ca46  +
          +rho*Y[jhe4]*Y[jar43]*rate_eval.He4_Ar43__n_Ca46  +
          -rho*Y[jhe4]*Y[jca46]*rate_eval.He4_Ca46__Ti50  +
          -rho*Y[jn]*Y[jca46]*rate_eval.n_Ca46__Ca47  +
          +rho*Y[jp]*Y[jk45]*rate_eval.p_K45__Ca46  +
          +rho*Y[jn]*Y[jca45]*rate_eval.n_Ca45__Ca46  +
          +rho*Y[jhe4]*Y[jar42]*rate_eval.He4_Ar42__Ca46  +
          -rho*Y[jp]*Y[jca46]*rate_eval.p_Ca46__Sc47  +
          +rho*Y[jp]*Y[jk46]*rate_eval.p_K46__n_Ca46  +
          +Y[jk46]*rate_eval.K46__Ca46__weak__wc12
       )

    dYdt[jca47] = (
          -rho*Y[jhe4]*Y[jca47]*rate_eval.He4_Ca47__n_Ti50  +
          -rho*Y[jp]*Y[jca47]*rate_eval.p_Ca47__n_Sc47  +
          +rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__p_Ca47  +
          +rho*Y[jp]*Y[jk46]*rate_eval.p_K46__Ca47  +
          +rho*Y[jhe4]*Y[jar43]*rate_eval.He4_Ar43__Ca47  +
          -rho*Y[jhe4]*Y[jca47]*rate_eval.He4_Ca47__Ti51  +
          +rho*Y[jn]*Y[jca46]*rate_eval.n_Ca46__Ca47  +
          +Y[jk47]*rate_eval.K47__Ca47__weak__wc12  +
          +rho*Y[jhe4]*Y[jar44]*rate_eval.He4_Ar44__n_Ca47  +
          +rho*Y[jp]*Y[jk47]*rate_eval.p_K47__n_Ca47  +
          +Y[jk48]*rate_eval.K48__n_Ca47__weak__wc12  +
          -rho*Y[jn]*Y[jca47]*rate_eval.n_Ca47__Ca48  +
          -Y[jca47]*rate_eval.Ca47__Sc47__weak__wc12  +
          +rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__He4_Ca47  +
          -rho*Y[jp]*Y[jca47]*rate_eval.p_Ca47__Sc48
       )

    dYdt[jca48] = (
          +rho*Y[jn]*Y[jti51]*rate_eval.n_Ti51__He4_Ca48  +
          -rho*Y[jhe4]*Y[jca48]*rate_eval.He4_Ca48__Ti52  +
          +rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__He4_Ca48  +
          +rho*Y[jn]*Y[jsc48]*rate_eval.n_Sc48__p_Ca48  +
          +rho*Y[jp]*Y[jk48]*rate_eval.p_K48__n_Ca48  +
          +rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__p_Ca48  +
          -rho*Y[jn]*Y[jca48]*rate_eval.n_Ca48__Ca49  +
          -rho*Y[jp]*Y[jca48]*rate_eval.p_Ca48__Sc49  +
          +rho*Y[jhe4]*Y[jar44]*rate_eval.He4_Ar44__Ca48  +
          +rho*Y[jn]*Y[jca47]*rate_eval.n_Ca47__Ca48  +
          +rho*Y[jhe4]*Y[jar45]*rate_eval.He4_Ar45__n_Ca48  +
          +rho*Y[jp]*Y[jk47]*rate_eval.p_K47__Ca48  +
          -Y[jca48]*rate_eval.Ca48__Sc48__weak__mo03  +
          +Y[jk48]*rate_eval.K48__Ca48__weak__wc12  +
          +Y[jk50]*rate_eval.K50__n_n_Ca48__weak__mp17  +
          +Y[jk49]*rate_eval.K49__n_Ca48__weak__wc12
       )

    dYdt[jca49] = (
          +rho*Y[jp]*Y[jk48]*rate_eval.p_K48__Ca49  +
          +rho*Y[jp]*Y[jsc52]*rate_eval.p_Sc52__He4_Ca49  +
          +rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__p_Ca49  +
          +rho*Y[jhe4]*Y[jar46]*rate_eval.He4_Ar46__n_Ca49  +
          +rho*Y[jp]*Y[jk49]*rate_eval.p_K49__n_Ca49  +
          -rho*Y[jp]*Y[jca49]*rate_eval.p_Ca49__Sc50  +
          +rho*Y[jhe4]*Y[jar45]*rate_eval.He4_Ar45__Ca49  +
          -rho*Y[jn]*Y[jca49]*rate_eval.n_Ca49__Ca50  +
          +Y[jk49]*rate_eval.K49__Ca49__weak__wc12  +
          -rho*Y[jp]*Y[jca49]*rate_eval.p_Ca49__n_Sc49  +
          -rho*Y[jhe4]*Y[jca49]*rate_eval.He4_Ca49__n_Ti52  +
          +rho*Y[jn]*Y[jca48]*rate_eval.n_Ca48__Ca49  +
          -Y[jca49]*rate_eval.Ca49__Sc49__weak__wc12  +
          +Y[jk50]*rate_eval.K50__n_Ca49__weak__wc12  +
          -rho*Y[jhe4]*Y[jca49]*rate_eval.He4_Ca49__Ti53
       )

    dYdt[jca50] = (
          +Y[jk53]*rate_eval.K53__n_n_n_Ca50__weak__mo03  +
          -rho*Y[jn]*Y[jca50]*rate_eval.n_Ca50__Ca51  +
          -rho*Y[jhe4]*Y[jca50]*rate_eval.He4_Ca50__n_Ti53  +
          -rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__He4_K47  +
          -rho*Y[jhe4]*Y[jca50]*rate_eval.He4_Ca50__Ti54  +
          +rho*Y[jn]*Y[jca49]*rate_eval.n_Ca49__Ca50  +
          +rho*Y[jp]*Y[jk50]*rate_eval.p_K50__n_Ca50  +
          +rho*Y[jhe4]*Y[jar46]*rate_eval.He4_Ar46__Ca50  +
          +rho*Y[jp]*Y[jk49]*rate_eval.p_K49__Ca50  +
          +Y[jk52]*rate_eval.K52__n_n_Ca50__weak__mp17  +
          -rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__n_Sc50  +
          -rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__Sc51  +
          +rho*Y[jhe4]*Y[jar47]*rate_eval.He4_Ar47__n_Ca50  +
          +Y[jk51]*rate_eval.K51__n_Ca50__weak__wc12  +
          +rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__He4_Ca50  +
          -Y[jca50]*rate_eval.Ca50__Sc50__weak__wc12  +
          +Y[jk50]*rate_eval.K50__Ca50__weak__wc12
       )

    dYdt[jca51] = (
          +Y[jk54]*rate_eval.K54__n_n_n_Ca51__weak__mo03  +
          +rho*Y[jn]*Y[jca50]*rate_eval.n_Ca50__Ca51  +
          -rho*Y[jhe4]*Y[jca51]*rate_eval.He4_Ca51__n_Ti54  +
          -rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__He4_K48  +
          +rho*Y[jp]*Y[jk51]*rate_eval.p_K51__n_Ca51  +
          -rho*Y[jhe4]*Y[jca51]*rate_eval.He4_Ca51__Ti55  +
          -rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__Sc52  +
          -rho*Y[jn]*Y[jca51]*rate_eval.n_Ca51__Ca52  +
          -Y[jca51]*rate_eval.Ca51__Sc51__weak__wc12  +
          +rho*Y[jhe4]*Y[jar47]*rate_eval.He4_Ar47__Ca51  +
          -rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__n_Sc51  +
          +Y[jk53]*rate_eval.K53__n_n_Ca51__weak__mp17  +
          +Y[jk52]*rate_eval.K52__n_Ca51__weak__wc12  +
          +Y[jk51]*rate_eval.K51__Ca51__weak__wc12  +
          +rho*Y[jp]*Y[jk50]*rate_eval.p_K50__Ca51  +
          +rho*Y[jhe4]*Y[jar48]*rate_eval.He4_Ar48__n_Ca51  +
          +rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__He4_Ca51
       )

    dYdt[jca52] = (
          +Y[jk55]*rate_eval.K55__n_n_n_Ca52__weak__mo03  +
          -rho*Y[jhe4]*Y[jca52]*rate_eval.He4_Ca52__Ti56  +
          +rho*Y[jp]*Y[jsc55]*rate_eval.p_Sc55__He4_Ca52  +
          -rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__n_Sc52  +
          +Y[jk52]*rate_eval.K52__Ca52__weak__wc17  +
          -rho*Y[jn]*Y[jca52]*rate_eval.n_Ca52__Ca53  +
          -rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__Sc53  +
          +rho*Y[jn]*Y[jca51]*rate_eval.n_Ca51__Ca52  +
          -rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__He4_K49  +
          +rho*Y[jp]*Y[jk51]*rate_eval.p_K51__Ca52  +
          +Y[jk53]*rate_eval.K53__n_Ca52__weak__wc17  +
          +Y[jk54]*rate_eval.K54__n_n_Ca52__weak__mp17  +
          -Y[jca52]*rate_eval.Ca52__n_Sc51__weak__wc12  +
          +rho*Y[jhe4]*Y[jar49]*rate_eval.He4_Ar49__n_Ca52  +
          +rho*Y[jp]*Y[jk52]*rate_eval.p_K52__n_Ca52  +
          -rho*Y[jhe4]*Y[jca52]*rate_eval.He4_Ca52__n_Ti55  +
          +rho*Y[jhe4]*Y[jar48]*rate_eval.He4_Ar48__Ca52  +
          -Y[jca52]*rate_eval.Ca52__Sc52__weak__wc12
       )

    dYdt[jca53] = (
          +Y[jk56]*rate_eval.K56__n_n_n_Ca53__weak__mo03  +
          -rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__n_Sc53  +
          -rho*Y[jhe4]*Y[jca53]*rate_eval.He4_Ca53__n_Ti56  +
          -Y[jca53]*rate_eval.Ca53__n_Sc52__weak__wc12  +
          +rho*Y[jp]*Y[jk53]*rate_eval.p_K53__n_Ca53  +
          +rho*Y[jn]*Y[jca52]*rate_eval.n_Ca52__Ca53  +
          -Y[jca53]*rate_eval.Ca53__Sc53__weak__wc12  +
          -rho*Y[jn]*Y[jca53]*rate_eval.n_Ca53__Ca54  +
          +rho*Y[jp]*Y[jk52]*rate_eval.p_K52__Ca53  +
          +rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__He4_Ca53  +
          -rho*Y[jhe4]*Y[jca53]*rate_eval.He4_Ca53__Ti57  +
          +Y[jk55]*rate_eval.K55__n_n_Ca53__weak__mp17  +
          +rho*Y[jhe4]*Y[jar50]*rate_eval.He4_Ar50__n_Ca53  +
          -rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__He4_K50  +
          +Y[jk54]*rate_eval.K54__n_Ca53__weak__mp17  +
          -rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__Sc54  +
          +Y[jk53]*rate_eval.K53__Ca53__weak__wc17  +
          +rho*Y[jhe4]*Y[jar49]*rate_eval.He4_Ar49__Ca53
       )

    dYdt[jca54] = (
          +rho*Y[jp]*Y[jk54]*rate_eval.p_K54__n_Ca54  +
          +rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__He4_Ca54  +
          -rho*Y[jhe4]*Y[jca54]*rate_eval.He4_Ca54__Ti58  +
          -rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__Sc55  +
          -rho*Y[jn]*Y[jca54]*rate_eval.n_Ca54__Ca55  +
          +rho*Y[jn]*Y[jca53]*rate_eval.n_Ca53__Ca54  +
          -Y[jca54]*rate_eval.Ca54__n_Sc53__weak__mp17  +
          -rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__n_Sc54  +
          +rho*Y[jhe4]*Y[jar50]*rate_eval.He4_Ar50__Ca54  +
          +rho*Y[jp]*Y[jk53]*rate_eval.p_K53__Ca54  +
          +Y[jk55]*rate_eval.K55__n_Ca54__weak__mp17  +
          -rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__He4_K51  +
          -rho*Y[jhe4]*Y[jca54]*rate_eval.He4_Ca54__n_Ti57  +
          +rho*Y[jhe4]*Y[jar51]*rate_eval.He4_Ar51__n_Ca54  +
          +Y[jk54]*rate_eval.K54__Ca54__weak__wc17  +
          -Y[jca54]*rate_eval.Ca54__Sc54__weak__wc17  +
          +Y[jk57]*rate_eval.K57__n_n_n_Ca54__weak__mo03  +
          +Y[jk56]*rate_eval.K56__n_n_Ca54__weak__mp17
       )

    dYdt[jca55] = (
          +Y[jk58]*rate_eval.K58__n_n_n_Ca55__weak__mo03  +
          +rho*Y[jp]*Y[jsc58]*rate_eval.p_Sc58__He4_Ca55  +
          -rho*Y[jp]*Y[jca55]*rate_eval.p_Ca55__He4_K52  +
          -rho*Y[jp]*Y[jca55]*rate_eval.p_Ca55__n_Sc55  +
          +rho*Y[jhe4]*Y[jar52]*rate_eval.He4_Ar52__n_Ca55  +
          -rho*Y[jn]*Y[jca55]*rate_eval.n_Ca55__Ca56  +
          +rho*Y[jn]*Y[jca54]*rate_eval.n_Ca54__Ca55  +
          +rho*Y[jp]*Y[jk55]*rate_eval.p_K55__n_Ca55  +
          +Y[jk57]*rate_eval.K57__n_n_Ca55__weak__mp17  +
          -rho*Y[jhe4]*Y[jca55]*rate_eval.He4_Ca55__n_Ti58  +
          -rho*Y[jhe4]*Y[jca55]*rate_eval.He4_Ca55__Ti59  +
          -Y[jca55]*rate_eval.Ca55__n_Sc54__weak__mp17  +
          -Y[jca55]*rate_eval.Ca55__Sc55__weak__wc12  +
          +rho*Y[jp]*Y[jk54]*rate_eval.p_K54__Ca55  +
          +Y[jk56]*rate_eval.K56__n_Ca55__weak__mp17  +
          +rho*Y[jhe4]*Y[jar51]*rate_eval.He4_Ar51__Ca55  +
          -rho*Y[jp]*Y[jca55]*rate_eval.p_Ca55__Sc56  +
          +Y[jk55]*rate_eval.K55__Ca55__weak__mo03
       )

    dYdt[jca56] = (
          +Y[jk59]*rate_eval.K59__n_n_n_Ca56__weak__mo03  +
          -Y[jca56]*rate_eval.Ca56__n_n_n_Sc53__weak__mo03  +
          +rho*Y[jhe4]*Y[jar52]*rate_eval.He4_Ar52__Ca56  +
          -rho*Y[jp]*Y[jca56]*rate_eval.p_Ca56__He4_K53  +
          +rho*Y[jp]*Y[jk56]*rate_eval.p_K56__n_Ca56  +
          -rho*Y[jp]*Y[jca56]*rate_eval.p_Ca56__n_Sc56  +
          +rho*Y[jhe4]*Y[jar53]*rate_eval.He4_Ar53__n_Ca56  +
          -rho*Y[jn]*Y[jca56]*rate_eval.n_Ca56__Ca57  +
          +rho*Y[jn]*Y[jca55]*rate_eval.n_Ca55__Ca56  +
          -rho*Y[jp]*Y[jca56]*rate_eval.p_Ca56__Sc57  +
          +rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__He4_Ca56  +
          +Y[jk58]*rate_eval.K58__n_n_Ca56__weak__mp17  +
          +Y[jk56]*rate_eval.K56__Ca56__weak__mo03  +
          +rho*Y[jp]*Y[jk55]*rate_eval.p_K55__Ca56  +
          +Y[jk57]*rate_eval.K57__n_Ca56__weak__mp17  +
          -rho*Y[jhe4]*Y[jca56]*rate_eval.He4_Ca56__Ti60  +
          -Y[jca56]*rate_eval.Ca56__n_Sc55__weak__mp17  +
          -rho*Y[jhe4]*Y[jca56]*rate_eval.He4_Ca56__n_Ti59  +
          -Y[jca56]*rate_eval.Ca56__Sc56__weak__wc17
       )

    dYdt[jca57] = (
          -Y[jca57]*rate_eval.Ca57__n_n_n_Sc54__weak__mo03  +
          +rho*Y[jp]*Y[jsc60]*rate_eval.p_Sc60__He4_Ca57  +
          -rho*Y[jhe4]*Y[jca57]*rate_eval.He4_Ca57__n_Ti60  +
          +rho*Y[jp]*Y[jk57]*rate_eval.p_K57__n_Ca57  +
          -Y[jca57]*rate_eval.Ca57__n_n_Sc55__weak__mp17  +
          -rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__Sc58  +
          -rho*Y[jn]*Y[jca57]*rate_eval.n_Ca57__Ca58  +
          +rho*Y[jn]*Y[jca56]*rate_eval.n_Ca56__Ca57  +
          +rho*Y[jp]*Y[jk56]*rate_eval.p_K56__Ca57  +
          +rho*Y[jhe4]*Y[jar53]*rate_eval.He4_Ar53__Ca57  +
          +rho*Y[jhe4]*Y[jar54]*rate_eval.He4_Ar54__n_Ca57  +
          -Y[jca57]*rate_eval.Ca57__Sc57__weak__mo03  +
          +Y[jk59]*rate_eval.K59__n_n_Ca57__weak__mp17  +
          -rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__He4_K54  +
          -Y[jca57]*rate_eval.Ca57__n_Sc56__weak__mp17  +
          +Y[jk58]*rate_eval.K58__n_Ca57__weak__mp17  +
          -rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__n_Sc57  +
          +Y[jk57]*rate_eval.K57__Ca57__weak__mo03  +
          -rho*Y[jhe4]*Y[jca57]*rate_eval.He4_Ca57__Ti61
       )

    dYdt[jca58] = (
          -Y[jca58]*rate_eval.Ca58__n_n_n_Sc55__weak__mo03  +
          -rho*Y[jhe4]*Y[jca58]*rate_eval.He4_Ca58__n_Ti61  +
          -rho*Y[jp]*Y[jca58]*rate_eval.p_Ca58__He4_K55  +
          -rho*Y[jp]*Y[jca58]*rate_eval.p_Ca58__n_Sc58  +
          -rho*Y[jp]*Y[jca58]*rate_eval.p_Ca58__Sc59  +
          +rho*Y[jp]*Y[jk58]*rate_eval.p_K58__n_Ca58  +
          +rho*Y[jn]*Y[jca57]*rate_eval.n_Ca57__Ca58  +
          +rho*Y[jp]*Y[jk57]*rate_eval.p_K57__Ca58  +
          -rho*Y[jhe4]*Y[jca58]*rate_eval.He4_Ca58__Ti62  +
          +rho*Y[jhe4]*Y[jar54]*rate_eval.He4_Ar54__Ca58  +
          -Y[jca58]*rate_eval.Ca58__n_Sc57__weak__mp17  +
          +Y[jk59]*rate_eval.K59__n_Ca58__weak__mp17  +
          -Y[jca58]*rate_eval.Ca58__n_n_Sc56__weak__mp17  +
          -rho*Y[jn]*Y[jca58]*rate_eval.n_Ca58__Ca59  +
          +rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__He4_Ca58  +
          -Y[jca58]*rate_eval.Ca58__Sc58__weak__mo03  +
          +Y[jk58]*rate_eval.K58__Ca58__weak__mo03
       )

    dYdt[jca59] = (
          -Y[jca59]*rate_eval.Ca59__n_n_n_Sc56__weak__mo03  +
          -rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__n_Sc59  +
          +rho*Y[jp]*Y[jk59]*rate_eval.p_K59__n_Ca59  +
          +Y[jk59]*rate_eval.K59__Ca59__weak__mo03  +
          -rho*Y[jhe4]*Y[jca59]*rate_eval.He4_Ca59__Ti63  +
          -rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__Sc60  +
          -Y[jca59]*rate_eval.Ca59__n_n_Sc57__weak__mp17  +
          +rho*Y[jp]*Y[jk58]*rate_eval.p_K58__Ca59  +
          -rho*Y[jn]*Y[jca59]*rate_eval.n_Ca59__Ca60  +
          -Y[jca59]*rate_eval.Ca59__n_Sc58__weak__mp17  +
          -Y[jca59]*rate_eval.Ca59__Sc59__weak__mo03  +
          +rho*Y[jn]*Y[jca58]*rate_eval.n_Ca58__Ca59  +
          -rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__He4_K56  +
          -rho*Y[jhe4]*Y[jca59]*rate_eval.He4_Ca59__n_Ti62  +
          +rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__He4_Ca59
       )

    dYdt[jca60] = (
          -Y[jca60]*rate_eval.Ca60__n_n_n_Sc57__weak__mo03  +
          -rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__n_Sc60  +
          -rho*Y[jhe4]*Y[jca60]*rate_eval.He4_Ca60__n_Ti63  +
          -rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__Sc61  +
          -rho*Y[jn]*Y[jca60]*rate_eval.n_Ca60__Ca61  +
          +rho*Y[jp]*Y[jk59]*rate_eval.p_K59__Ca60  +
          +rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__He4_Ca60  +
          +rho*Y[jn]*Y[jca59]*rate_eval.n_Ca59__Ca60  +
          -rho*Y[jhe4]*Y[jca60]*rate_eval.He4_Ca60__Ti64  +
          -rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__He4_K57  +
          -Y[jca60]*rate_eval.Ca60__n_Sc59__weak__mp17  +
          -Y[jca60]*rate_eval.Ca60__Sc60__weak__mo03  +
          -Y[jca60]*rate_eval.Ca60__n_n_Sc58__weak__mp17
       )

    dYdt[jca61] = (
          -rho*Y[jp]*Y[jca61]*rate_eval.p_Ca61__Sc62  +
          -rho*Y[jp]*Y[jca61]*rate_eval.p_Ca61__He4_K58  +
          -rho*Y[jp]*Y[jca61]*rate_eval.p_Ca61__n_Sc61  +
          -rho*Y[jhe4]*Y[jca61]*rate_eval.He4_Ca61__n_Ti64  +
          +rho*Y[jn]*Y[jca60]*rate_eval.n_Ca60__Ca61  +
          -Y[jca61]*rate_eval.Ca61__n_n_n_Sc58__weak__mo03  +
          -Y[jca61]*rate_eval.Ca61__n_Sc60__weak__mp17  +
          -rho*Y[jhe4]*Y[jca61]*rate_eval.He4_Ca61__Ti65  +
          -Y[jca61]*rate_eval.Ca61__Sc61__weak__mo03  +
          -Y[jca61]*rate_eval.Ca61__n_n_Sc59__weak__mp17
       )

    dYdt[jsc35] = (
          -rho*Y[jhe4]*Y[jsc35]*rate_eval.He4_Sc35__p_Ti38  +
          -rho*Y[jn]*Y[jsc35]*rate_eval.n_Sc35__He4_K32  +
          -rho*Y[jn]*Y[jsc35]*rate_eval.n_Sc35__p_Ca35  +
          -rho*Y[jhe4]*Y[jsc35]*rate_eval.He4_Sc35__V39  +
          -rho*Y[jn]*Y[jsc35]*rate_eval.n_Sc35__Sc36  +
          +rho*Y[jhe4]*Y[jk31]*rate_eval.He4_K31__Sc35  +
          -Y[jsc35]*rate_eval.Sc35__Ca35__weak__bqa_pos_  +
          +rho*Y[jp]*Y[jca34]*rate_eval.p_Ca34__Sc35
       )

    dYdt[jsc36] = (
          -rho*Y[jhe4]*Y[jsc36]*rate_eval.He4_Sc36__p_Ti39  +
          +rho*Y[jhe4]*Y[jk32]*rate_eval.He4_K32__Sc36  +
          -rho*Y[jhe4]*Y[jsc36]*rate_eval.He4_Sc36__V40  +
          +rho*Y[jn]*Y[jsc35]*rate_eval.n_Sc35__Sc36  +
          -rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__p_Ca36  +
          -rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__He4_K33  +
          -rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__Sc37  +
          +rho*Y[jhe4]*Y[jca33]*rate_eval.He4_Ca33__p_Sc36  +
          +rho*Y[jn]*Y[jv39]*rate_eval.n_V39__He4_Sc36  +
          -Y[jsc36]*rate_eval.Sc36__Ca36__weak__bqa_pos_  +
          +rho*Y[jp]*Y[jca35]*rate_eval.p_Ca35__Sc36  +
          -rho*Y[jp]*Y[jsc36]*rate_eval.p_Sc36__Ti37
       )

    dYdt[jsc37] = (
          -rho*Y[jhe4]*Y[jsc37]*rate_eval.He4_Sc37__p_Ti40  +
          -rho*Y[jn]*Y[jsc37]*rate_eval.n_Sc37__He4_K34  +
          +rho*Y[jhe4]*Y[jk33]*rate_eval.He4_K33__Sc37  +
          +rho*Y[jn]*Y[jv40]*rate_eval.n_V40__He4_Sc37  +
          -rho*Y[jn]*Y[jsc37]*rate_eval.n_Sc37__p_Ca37  +
          -rho*Y[jp]*Y[jsc37]*rate_eval.p_Sc37__Ti38  +
          -rho*Y[jn]*Y[jsc37]*rate_eval.n_Sc37__Sc38  +
          +rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__p_Sc37  +
          -Y[jsc37]*rate_eval.Sc37__Ca37__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[jsc37]*rate_eval.He4_Sc37__V41  +
          +rho*Y[jhe4]*Y[jca34]*rate_eval.He4_Ca34__p_Sc37  +
          +rho*Y[jn]*Y[jsc36]*rate_eval.n_Sc36__Sc37  +
          +Y[jti37]*rate_eval.Ti37__Sc37__weak__bqa_pos_  +
          +rho*Y[jp]*Y[jca36]*rate_eval.p_Ca36__Sc37
       )

    dYdt[jsc38] = (
          +rho*Y[jn]*Y[jv41]*rate_eval.n_V41__He4_Sc38  +
          +rho*Y[jn]*Y[jti38]*rate_eval.n_Ti38__p_Sc38  +
          -rho*Y[jhe4]*Y[jsc38]*rate_eval.He4_Sc38__p_Ti41  +
          -Y[jsc38]*rate_eval.Sc38__Ca38__weak__mo97  +
          +Y[jti38]*rate_eval.Ti38__Sc38__weak__mo97  +
          -rho*Y[jhe4]*Y[jsc38]*rate_eval.He4_Sc38__V42  +
          -rho*Y[jp]*Y[jsc38]*rate_eval.p_Sc38__Ti39  +
          -rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__Sc39  +
          +rho*Y[jn]*Y[jsc37]*rate_eval.n_Sc37__Sc38  +
          +rho*Y[jhe4]*Y[jca35]*rate_eval.He4_Ca35__p_Sc38  +
          -rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__p_Ca38  +
          -rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__He4_K35  +
          +rho*Y[jhe4]*Y[jk34]*rate_eval.He4_K34__Sc38  +
          +rho*Y[jp]*Y[jca37]*rate_eval.p_Ca37__Sc38
       )

    dYdt[jsc39] = (
          +rho*Y[jn]*Y[jv42]*rate_eval.n_V42__He4_Sc39  +
          +rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__p_Sc39  +
          -rho*Y[jhe4]*Y[jsc39]*rate_eval.He4_Sc39__p_Ti42  +
          -rho*Y[jn]*Y[jsc39]*rate_eval.n_Sc39__He4_K36  +
          -rho*Y[jhe4]*Y[jsc39]*rate_eval.He4_Sc39__V43  +
          -rho*Y[jn]*Y[jsc39]*rate_eval.n_Sc39__Sc40  +
          +rho*Y[jn]*Y[jsc38]*rate_eval.n_Sc38__Sc39  +
          +rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__p_Sc39  +
          +rho*Y[jhe4]*Y[jk35]*rate_eval.He4_K35__Sc39  +
          -rho*Y[jp]*Y[jsc39]*rate_eval.p_Sc39__Ti40  +
          -Y[jsc39]*rate_eval.Sc39__Ca39__weak__mo97  +
          +Y[jti39]*rate_eval.Ti39__Sc39__weak__wc17  +
          -rho*Y[jn]*Y[jsc39]*rate_eval.n_Sc39__p_Ca39  +
          +rho*Y[jp]*Y[jca38]*rate_eval.p_Ca38__Sc39
       )

    dYdt[jsc40] = (
          -rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__Sc41  +
          -rho*Y[jhe4]*Y[jsc40]*rate_eval.He4_Sc40__p_Ti43  +
          +rho*Y[jn]*Y[jv43]*rate_eval.n_V43__He4_Sc40  +
          -rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__p_Ca40  +
          -rho*Y[jp]*Y[jsc40]*rate_eval.p_Sc40__Ti41  +
          +rho*Y[jn]*Y[jsc39]*rate_eval.n_Sc39__Sc40  +
          -Y[jsc40]*rate_eval.Sc40__Ca40__weak__wc12  +
          +rho*Y[jhe4]*Y[jk36]*rate_eval.He4_K36__Sc40  +
          -rho*Y[jhe4]*Y[jsc40]*rate_eval.He4_Sc40__V44  +
          +rho*Y[jhe4]*Y[jca37]*rate_eval.He4_Ca37__p_Sc40  +
          +rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__p_Sc40  +
          -Y[jsc40]*rate_eval.Sc40__He4_Ar36__weak__wc12  +
          -Y[jsc40]*rate_eval.Sc40__p_K39__weak__wc12  +
          +rho*Y[jp]*Y[jca39]*rate_eval.p_Ca39__Sc40  +
          -rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__He4_K37
       )

    dYdt[jsc41] = (
          +rho*Y[jn]*Y[jsc40]*rate_eval.n_Sc40__Sc41  +
          +Y[jcr43]*rate_eval.Cr43__p_p_Sc41__weak__wc12  +
          +rho*Y[jn]*Y[jv44]*rate_eval.n_V44__He4_Sc41  +
          +rho*Y[jn]*Y[jti41]*rate_eval.n_Ti41__p_Sc41  +
          -rho*Y[jn]*Y[jsc41]*rate_eval.n_Sc41__He4_K38  +
          -rho*Y[jhe4]*Y[jsc41]*rate_eval.He4_Sc41__V45  +
          -rho*Y[jp]*Y[jsc41]*rate_eval.p_Sc41__Ti42  +
          -rho*Y[jn]*Y[jsc41]*rate_eval.n_Sc41__Sc42  +
          +rho*Y[jp]*Y[jca40]*rate_eval.p_Ca40__Sc41  +
          +rho*Y[jhe4]*Y[jca38]*rate_eval.He4_Ca38__p_Sc41  +
          -rho*Y[jhe4]*Y[jsc41]*rate_eval.He4_Sc41__p_Ti44  +
          -Y[jsc41]*rate_eval.Sc41__Ca41__weak__wc12  +
          -rho*Y[jn]*Y[jsc41]*rate_eval.n_Sc41__p_Ca41  +
          +Y[jti41]*rate_eval.Ti41__Sc41__weak__wc17  +
          +rho*Y[jhe4]*Y[jk37]*rate_eval.He4_K37__Sc41
       )

    dYdt[jsc42] = (
          -rho*Y[jhe4]*Y[jsc42]*rate_eval.He4_Sc42__p_Ti45  +
          -rho*Y[jn]*Y[jsc42]*rate_eval.n_Sc42__He4_K39  +
          -rho*Y[jn]*Y[jsc42]*rate_eval.n_Sc42__p_Ca42  +
          +rho*Y[jn]*Y[jv45]*rate_eval.n_V45__He4_Sc42  +
          +rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__p_Sc42  +
          -rho*Y[jhe4]*Y[jsc42]*rate_eval.He4_Sc42__V46  +
          -rho*Y[jp]*Y[jsc42]*rate_eval.p_Sc42__Ti43  +
          -rho*Y[jn]*Y[jsc42]*rate_eval.n_Sc42__Sc43  +
          +rho*Y[jn]*Y[jsc41]*rate_eval.n_Sc41__Sc42  +
          +rho*Y[jp]*Y[jca41]*rate_eval.p_Ca41__Sc42  +
          -Y[jsc42]*rate_eval.Sc42__Ca42__weak__wc12  +
          +rho*Y[jhe4]*Y[jk38]*rate_eval.He4_K38__Sc42  +
          +Y[jti42]*rate_eval.Ti42__Sc42__weak__wc12  +
          -rho*Y[jp]*Y[jsc42]*rate_eval.p_Sc42__He4_Ca39
       )

    dYdt[jsc43] = (
          +rho*Y[jn]*Y[jv46]*rate_eval.n_V46__He4_Sc43  +
          +Y[jti43]*rate_eval.Ti43__Sc43__weak__wc12  +
          -rho*Y[jhe4]*Y[jsc43]*rate_eval.He4_Sc43__p_Ti46  +
          -rho*Y[jn]*Y[jsc43]*rate_eval.n_Sc43__He4_K40  +
          -rho*Y[jn]*Y[jsc43]*rate_eval.n_Sc43__p_Ca43  +
          -rho*Y[jhe4]*Y[jsc43]*rate_eval.He4_Sc43__V47  +
          -rho*Y[jn]*Y[jsc43]*rate_eval.n_Sc43__Sc44  +
          +rho*Y[jhe4]*Y[jk39]*rate_eval.He4_K39__Sc43  +
          -rho*Y[jp]*Y[jsc43]*rate_eval.p_Sc43__Ti44  +
          +rho*Y[jn]*Y[jsc42]*rate_eval.n_Sc42__Sc43  +
          +rho*Y[jp]*Y[jca42]*rate_eval.p_Ca42__Sc43  +
          +rho*Y[jn]*Y[jti43]*rate_eval.n_Ti43__p_Sc43  +
          -rho*Y[jp]*Y[jsc43]*rate_eval.p_Sc43__He4_Ca40  +
          -Y[jsc43]*rate_eval.Sc43__Ca43__weak__wc12
       )

    dYdt[jsc44] = (
          -rho*Y[jhe4]*Y[jsc44]*rate_eval.He4_Sc44__p_Ti47  +
          -rho*Y[jp]*Y[jsc44]*rate_eval.p_Sc44__He4_Ca41  +
          -rho*Y[jn]*Y[jsc44]*rate_eval.n_Sc44__p_Ca44  +
          +rho*Y[jn]*Y[jv47]*rate_eval.n_V47__He4_Sc44  +
          +rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__p_Sc44  +
          -rho*Y[jhe4]*Y[jsc44]*rate_eval.He4_Sc44__V48  +
          +rho*Y[jn]*Y[jsc43]*rate_eval.n_Sc43__Sc44  +
          -rho*Y[jn]*Y[jsc44]*rate_eval.n_Sc44__Sc45  +
          +rho*Y[jp]*Y[jca43]*rate_eval.p_Ca43__Sc44  +
          -Y[jsc44]*rate_eval.Sc44__Ca44__weak__wc12  +
          +Y[jti44]*rate_eval.Ti44__Sc44__weak__wc12  +
          +rho*Y[jhe4]*Y[jk40]*rate_eval.He4_K40__Sc44  +
          -rho*Y[jp]*Y[jsc44]*rate_eval.p_Sc44__Ti45  +
          +rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__n_Sc44
       )

    dYdt[jsc45] = (
          +rho*Y[jp]*Y[jca44]*rate_eval.p_Ca44__Sc45  +
          +rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__p_Sc45  +
          -rho*Y[jhe4]*Y[jsc45]*rate_eval.He4_Sc45__p_Ti48  +
          -rho*Y[jp]*Y[jsc45]*rate_eval.p_Sc45__He4_Ca42  +
          -rho*Y[jn]*Y[jsc45]*rate_eval.n_Sc45__p_Ca45  +
          +rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__n_Sc45  +
          -rho*Y[jp]*Y[jsc45]*rate_eval.p_Sc45__Ti46  +
          -rho*Y[jhe4]*Y[jsc45]*rate_eval.He4_Sc45__V49  +
          -rho*Y[jn]*Y[jsc45]*rate_eval.n_Sc45__Sc46  +
          +Y[jti45]*rate_eval.Ti45__Sc45__weak__wc12  +
          +rho*Y[jhe4]*Y[jk41]*rate_eval.He4_K41__Sc45  +
          +rho*Y[jn]*Y[jsc44]*rate_eval.n_Sc44__Sc45  +
          +rho*Y[jn]*Y[jv48]*rate_eval.n_V48__He4_Sc45  +
          +Y[jca45]*rate_eval.Ca45__Sc45__weak__wc12
       )

    dYdt[jsc46] = (
          -rho*Y[jhe4]*Y[jsc46]*rate_eval.He4_Sc46__p_Ti49  +
          -rho*Y[jp]*Y[jsc46]*rate_eval.p_Sc46__He4_Ca43  +
          -rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__p_Ca46  +
          -rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__He4_K43  +
          +rho*Y[jp]*Y[jca45]*rate_eval.p_Ca45__Sc46  +
          -rho*Y[jp]*Y[jsc46]*rate_eval.p_Sc46__n_Ti46  +
          -rho*Y[jp]*Y[jsc46]*rate_eval.p_Sc46__Ti47  +
          -rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__Sc47  +
          +rho*Y[jn]*Y[jsc45]*rate_eval.n_Sc45__Sc46  +
          +rho*Y[jhe4]*Y[jk42]*rate_eval.He4_K42__Sc46  +
          -rho*Y[jhe4]*Y[jsc46]*rate_eval.He4_Sc46__n_V49  +
          -Y[jsc46]*rate_eval.Sc46__Ti46__weak__wc12  +
          -rho*Y[jhe4]*Y[jsc46]*rate_eval.He4_Sc46__V50
       )

    dYdt[jsc47] = (
          -Y[jsc47]*rate_eval.Sc47__Ti47__weak__wc12  +
          -rho*Y[jhe4]*Y[jsc47]*rate_eval.He4_Sc47__p_Ti50  +
          -rho*Y[jp]*Y[jsc47]*rate_eval.p_Sc47__He4_Ca44  +
          +rho*Y[jp]*Y[jca47]*rate_eval.p_Ca47__n_Sc47  +
          +rho*Y[jn]*Y[jv50]*rate_eval.n_V50__He4_Sc47  +
          -rho*Y[jhe4]*Y[jsc47]*rate_eval.He4_Sc47__V51  +
          +rho*Y[jn]*Y[jsc46]*rate_eval.n_Sc46__Sc47  +
          +rho*Y[jhe4]*Y[jk43]*rate_eval.He4_K43__Sc47  +
          +rho*Y[jn]*Y[jti47]*rate_eval.n_Ti47__p_Sc47  +
          -rho*Y[jp]*Y[jsc47]*rate_eval.p_Sc47__Ti48  +
          +rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__n_Sc47  +
          +rho*Y[jp]*Y[jca46]*rate_eval.p_Ca46__Sc47  +
          +Y[jca47]*rate_eval.Ca47__Sc47__weak__wc12  +
          -rho*Y[jn]*Y[jsc47]*rate_eval.n_Sc47__Sc48
       )

    dYdt[jsc48] = (
          -rho*Y[jp]*Y[jsc48]*rate_eval.p_Sc48__He4_Ca45  +
          -rho*Y[jn]*Y[jsc48]*rate_eval.n_Sc48__p_Ca48  +
          -rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__n_V51  +
          -rho*Y[jp]*Y[jsc48]*rate_eval.p_Sc48__n_Ti48  +
          -rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__V52  +
          -rho*Y[jp]*Y[jsc48]*rate_eval.p_Sc48__Ti49  +
          -rho*Y[jn]*Y[jsc48]*rate_eval.n_Sc48__Sc49  +
          +rho*Y[jhe4]*Y[jk44]*rate_eval.He4_K44__Sc48  +
          -rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__p_Ti51  +
          +rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__n_Sc48  +
          -Y[jsc48]*rate_eval.Sc48__Ti48__weak__wc12  +
          +Y[jca48]*rate_eval.Ca48__Sc48__weak__mo03  +
          +rho*Y[jp]*Y[jca47]*rate_eval.p_Ca47__Sc48  +
          +rho*Y[jn]*Y[jsc47]*rate_eval.n_Sc47__Sc48
       )

    dYdt[jsc49] = (
          +rho*Y[jp]*Y[jti52]*rate_eval.p_Ti52__He4_Sc49  +
          -rho*Y[jp]*Y[jsc49]*rate_eval.p_Sc49__He4_Ca46  +
          -rho*Y[jp]*Y[jsc49]*rate_eval.p_Sc49__n_Ti49  +
          -rho*Y[jhe4]*Y[jsc49]*rate_eval.He4_Sc49__V53  +
          -rho*Y[jp]*Y[jsc49]*rate_eval.p_Sc49__Ti50  +
          -rho*Y[jn]*Y[jsc49]*rate_eval.n_Sc49__Sc50  +
          +rho*Y[jn]*Y[jsc48]*rate_eval.n_Sc48__Sc49  +
          +rho*Y[jhe4]*Y[jk45]*rate_eval.He4_K45__Sc49  +
          +rho*Y[jp]*Y[jca49]*rate_eval.p_Ca49__n_Sc49  +
          +rho*Y[jp]*Y[jca48]*rate_eval.p_Ca48__Sc49  +
          +Y[jca49]*rate_eval.Ca49__Sc49__weak__wc12  +
          -Y[jsc49]*rate_eval.Sc49__Ti49__weak__wc12  +
          +rho*Y[jn]*Y[jv52]*rate_eval.n_V52__He4_Sc49  +
          +rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__n_Sc49
       )

    dYdt[jsc50] = (
          -rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__Ti51  +
          +rho*Y[jp]*Y[jti53]*rate_eval.p_Ti53__He4_Sc50  +
          -rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__n_Ti50  +
          +rho*Y[jp]*Y[jca49]*rate_eval.p_Ca49__Sc50  +
          -rho*Y[jn]*Y[jsc50]*rate_eval.n_Sc50__Sc51  +
          +rho*Y[jn]*Y[jsc49]*rate_eval.n_Sc49__Sc50  +
          +rho*Y[jhe4]*Y[jk47]*rate_eval.He4_K47__n_Sc50  +
          +rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__n_Sc50  +
          -rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__He4_Ca47  +
          -Y[jsc50]*rate_eval.Sc50__Ti50__weak__wc12  +
          +Y[jca50]*rate_eval.Ca50__Sc50__weak__wc12  +
          -rho*Y[jhe4]*Y[jsc50]*rate_eval.He4_Sc50__V54  +
          +rho*Y[jhe4]*Y[jk46]*rate_eval.He4_K46__Sc50  +
          -rho*Y[jhe4]*Y[jsc50]*rate_eval.He4_Sc50__n_V53
       )

    dYdt[jsc51] = (
          +rho*Y[jp]*Y[jti54]*rate_eval.p_Ti54__He4_Sc51  +
          -rho*Y[jhe4]*Y[jsc51]*rate_eval.He4_Sc51__n_V54  +
          +rho*Y[jhe4]*Y[jk48]*rate_eval.He4_K48__n_Sc51  +
          -rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__He4_Ca48  +
          +rho*Y[jn]*Y[jsc50]*rate_eval.n_Sc50__Sc51  +
          +Y[jca51]*rate_eval.Ca51__Sc51__weak__wc12  +
          +rho*Y[jhe4]*Y[jk47]*rate_eval.He4_K47__Sc51  +
          +rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__n_Sc51  +
          -rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__n_Ti51  +
          +rho*Y[jp]*Y[jca50]*rate_eval.p_Ca50__Sc51  +
          -rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__Ti52  +
          +Y[jca52]*rate_eval.Ca52__n_Sc51__weak__wc12  +
          -rho*Y[jhe4]*Y[jsc51]*rate_eval.He4_Sc51__V55  +
          -rho*Y[jn]*Y[jsc51]*rate_eval.n_Sc51__Sc52  +
          -Y[jsc51]*rate_eval.Sc51__Ti51__weak__wc12
       )

    dYdt[jsc52] = (
          -rho*Y[jp]*Y[jsc52]*rate_eval.p_Sc52__Ti53  +
          -rho*Y[jhe4]*Y[jsc52]*rate_eval.He4_Sc52__n_V55  +
          -rho*Y[jp]*Y[jsc52]*rate_eval.p_Sc52__He4_Ca49  +
          -rho*Y[jp]*Y[jsc52]*rate_eval.p_Sc52__n_Ti52  +
          +rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__n_Sc52  +
          +Y[jca53]*rate_eval.Ca53__n_Sc52__weak__wc12  +
          +rho*Y[jhe4]*Y[jk49]*rate_eval.He4_K49__n_Sc52  +
          +rho*Y[jp]*Y[jca51]*rate_eval.p_Ca51__Sc52  +
          -rho*Y[jn]*Y[jsc52]*rate_eval.n_Sc52__Sc53  +
          -rho*Y[jhe4]*Y[jsc52]*rate_eval.He4_Sc52__V56  +
          +rho*Y[jhe4]*Y[jk48]*rate_eval.He4_K48__Sc52  +
          +Y[jca52]*rate_eval.Ca52__Sc52__weak__wc12  +
          -Y[jsc52]*rate_eval.Sc52__Ti52__weak__wc12  +
          +rho*Y[jn]*Y[jsc51]*rate_eval.n_Sc51__Sc52  +
          +rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__He4_Sc52
       )

    dYdt[jsc53] = (
          +Y[jca56]*rate_eval.Ca56__n_n_n_Sc53__weak__mo03  +
          +rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__n_Sc53  +
          -rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__n_Ti53  +
          +rho*Y[jhe4]*Y[jk50]*rate_eval.He4_K50__n_Sc53  +
          +Y[jca53]*rate_eval.Ca53__Sc53__weak__wc12  +
          -Y[jsc53]*rate_eval.Sc53__Ti53__weak__wc12  +
          +rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__He4_Sc53  +
          +rho*Y[jp]*Y[jca52]*rate_eval.p_Ca52__Sc53  +
          -rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__Ti54  +
          -rho*Y[jn]*Y[jsc53]*rate_eval.n_Sc53__Sc54  +
          +rho*Y[jhe4]*Y[jk49]*rate_eval.He4_K49__Sc53  +
          +Y[jca54]*rate_eval.Ca54__n_Sc53__weak__mp17  +
          +rho*Y[jn]*Y[jsc52]*rate_eval.n_Sc52__Sc53  +
          -rho*Y[jhe4]*Y[jsc53]*rate_eval.He4_Sc53__n_V56  +
          -rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__He4_Ca50  +
          -rho*Y[jhe4]*Y[jsc53]*rate_eval.He4_Sc53__V57
       )

    dYdt[jsc54] = (
          +Y[jca57]*rate_eval.Ca57__n_n_n_Sc54__weak__mo03  +
          +rho*Y[jp]*Y[jti57]*rate_eval.p_Ti57__He4_Sc54  +
          -rho*Y[jhe4]*Y[jsc54]*rate_eval.He4_Sc54__n_V57  +
          -rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__n_Ti54  +
          +rho*Y[jhe4]*Y[jk51]*rate_eval.He4_K51__n_Sc54  +
          -rho*Y[jhe4]*Y[jsc54]*rate_eval.He4_Sc54__V58  +
          +rho*Y[jhe4]*Y[jk50]*rate_eval.He4_K50__Sc54  +
          -Y[jsc54]*rate_eval.Sc54__Ti54__weak__wc17  +
          -rho*Y[jn]*Y[jsc54]*rate_eval.n_Sc54__Sc55  +
          +rho*Y[jn]*Y[jsc53]*rate_eval.n_Sc53__Sc54  +
          -Y[jsc54]*rate_eval.Sc54__n_Ti53__weak__mp17  +
          +rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__n_Sc54  +
          -rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__Ti55  +
          +Y[jca55]*rate_eval.Ca55__n_Sc54__weak__mp17  +
          +rho*Y[jp]*Y[jca53]*rate_eval.p_Ca53__Sc54  +
          +Y[jca54]*rate_eval.Ca54__Sc54__weak__wc17  +
          -rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__He4_Ca51
       )

    dYdt[jsc55] = (
          +Y[jca58]*rate_eval.Ca58__n_n_n_Sc55__weak__mo03  +
          -rho*Y[jhe4]*Y[jsc55]*rate_eval.He4_Sc55__n_V58  +
          -rho*Y[jp]*Y[jsc55]*rate_eval.p_Sc55__He4_Ca52  +
          +rho*Y[jp]*Y[jca55]*rate_eval.p_Ca55__n_Sc55  +
          +rho*Y[jhe4]*Y[jk52]*rate_eval.He4_K52__n_Sc55  +
          -rho*Y[jp]*Y[jsc55]*rate_eval.p_Sc55__n_Ti55  +
          +Y[jca57]*rate_eval.Ca57__n_n_Sc55__weak__mp17  +
          -rho*Y[jn]*Y[jsc55]*rate_eval.n_Sc55__Sc56  +
          -rho*Y[jhe4]*Y[jsc55]*rate_eval.He4_Sc55__V59  +
          -rho*Y[jp]*Y[jsc55]*rate_eval.p_Sc55__Ti56  +
          +rho*Y[jn]*Y[jsc54]*rate_eval.n_Sc54__Sc55  +
          +rho*Y[jp]*Y[jca54]*rate_eval.p_Ca54__Sc55  +
          -Y[jsc55]*rate_eval.Sc55__n_Ti54__weak__wc12  +
          +rho*Y[jhe4]*Y[jk51]*rate_eval.He4_K51__Sc55  +
          +Y[jca55]*rate_eval.Ca55__Sc55__weak__wc12  +
          +Y[jca56]*rate_eval.Ca56__n_Sc55__weak__mp17  +
          +rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__He4_Sc55  +
          -Y[jsc55]*rate_eval.Sc55__Ti55__weak__wc12
       )

    dYdt[jsc56] = (
          +Y[jca59]*rate_eval.Ca59__n_n_n_Sc56__weak__mo03  +
          -Y[jsc56]*rate_eval.Sc56__n_Ti55__weak__mp17  +
          -rho*Y[jhe4]*Y[jsc56]*rate_eval.He4_Sc56__n_V59  +
          +rho*Y[jhe4]*Y[jk53]*rate_eval.He4_K53__n_Sc56  +
          +rho*Y[jp]*Y[jca56]*rate_eval.p_Ca56__n_Sc56  +
          +rho*Y[jn]*Y[jsc55]*rate_eval.n_Sc55__Sc56  +
          -rho*Y[jhe4]*Y[jsc56]*rate_eval.He4_Sc56__V60  +
          -rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__Ti57  +
          -rho*Y[jn]*Y[jsc56]*rate_eval.n_Sc56__Sc57  +
          -rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__He4_Ca53  +
          +Y[jca57]*rate_eval.Ca57__n_Sc56__weak__mp17  +
          -Y[jsc56]*rate_eval.Sc56__Ti56__weak__wc17  +
          +Y[jca58]*rate_eval.Ca58__n_n_Sc56__weak__mp17  +
          -rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__n_Ti56  +
          +rho*Y[jp]*Y[jca55]*rate_eval.p_Ca55__Sc56  +
          +rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__He4_Sc56  +
          +rho*Y[jhe4]*Y[jk52]*rate_eval.He4_K52__Sc56  +
          +Y[jca56]*rate_eval.Ca56__Sc56__weak__wc17
       )

    dYdt[jsc57] = (
          -Y[jsc57]*rate_eval.Sc57__n_n_n_Ti54__weak__mo03  +
          +Y[jca60]*rate_eval.Ca60__n_n_n_Sc57__weak__mo03  +
          -rho*Y[jhe4]*Y[jsc57]*rate_eval.He4_Sc57__n_V60  +
          +rho*Y[jhe4]*Y[jk54]*rate_eval.He4_K54__n_Sc57  +
          -rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__He4_Ca54  +
          -rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__n_Ti57  +
          -rho*Y[jhe4]*Y[jsc57]*rate_eval.He4_Sc57__V61  +
          -rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__Ti58  +
          +rho*Y[jn]*Y[jsc56]*rate_eval.n_Sc56__Sc57  +
          +rho*Y[jp]*Y[jca56]*rate_eval.p_Ca56__Sc57  +
          +Y[jca59]*rate_eval.Ca59__n_n_Sc57__weak__mp17  +
          +Y[jca57]*rate_eval.Ca57__Sc57__weak__mo03  +
          -Y[jsc57]*rate_eval.Sc57__Ti57__weak__wc17  +
          +rho*Y[jhe4]*Y[jk53]*rate_eval.He4_K53__Sc57  +
          -Y[jsc57]*rate_eval.Sc57__n_Ti56__weak__mp17  +
          +Y[jca58]*rate_eval.Ca58__n_Sc57__weak__mp17  +
          +rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__He4_Sc57  +
          +rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__n_Sc57  +
          -rho*Y[jn]*Y[jsc57]*rate_eval.n_Sc57__Sc58
       )

    dYdt[jsc58] = (
          -Y[jsc58]*rate_eval.Sc58__n_n_n_Ti55__weak__mo03  +
          -rho*Y[jhe4]*Y[jsc58]*rate_eval.He4_Sc58__n_V61  +
          -rho*Y[jp]*Y[jsc58]*rate_eval.p_Sc58__He4_Ca55  +
          -rho*Y[jp]*Y[jsc58]*rate_eval.p_Sc58__n_Ti58  +
          +rho*Y[jp]*Y[jca58]*rate_eval.p_Ca58__n_Sc58  +
          +rho*Y[jhe4]*Y[jk55]*rate_eval.He4_K55__n_Sc58  +
          -rho*Y[jhe4]*Y[jsc58]*rate_eval.He4_Sc58__V62  +
          -rho*Y[jp]*Y[jsc58]*rate_eval.p_Sc58__Ti59  +
          -rho*Y[jn]*Y[jsc58]*rate_eval.n_Sc58__Sc59  +
          +rho*Y[jp]*Y[jca57]*rate_eval.p_Ca57__Sc58  +
          +Y[jca61]*rate_eval.Ca61__n_n_n_Sc58__weak__mo03  +
          -Y[jsc58]*rate_eval.Sc58__n_Ti57__weak__mp17  +
          +Y[jca59]*rate_eval.Ca59__n_Sc58__weak__mp17  +
          +rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__He4_Sc58  +
          -Y[jsc58]*rate_eval.Sc58__n_n_Ti56__weak__mp17  +
          +rho*Y[jn]*Y[jsc57]*rate_eval.n_Sc57__Sc58  +
          +Y[jca58]*rate_eval.Ca58__Sc58__weak__mo03  +
          +Y[jca60]*rate_eval.Ca60__n_n_Sc58__weak__mp17  +
          +rho*Y[jhe4]*Y[jk54]*rate_eval.He4_K54__Sc58  +
          -Y[jsc58]*rate_eval.Sc58__Ti58__weak__wc17
       )

    dYdt[jsc59] = (
          -Y[jsc59]*rate_eval.Sc59__n_n_n_Ti56__weak__mo03  +
          -rho*Y[jhe4]*Y[jsc59]*rate_eval.He4_Sc59__V63  +
          -rho*Y[jhe4]*Y[jsc59]*rate_eval.He4_Sc59__n_V62  +
          +rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__n_Sc59  +
          +rho*Y[jhe4]*Y[jk56]*rate_eval.He4_K56__n_Sc59  +
          +rho*Y[jp]*Y[jca58]*rate_eval.p_Ca58__Sc59  +
          -rho*Y[jn]*Y[jsc59]*rate_eval.n_Sc59__Sc60  +
          +rho*Y[jn]*Y[jsc58]*rate_eval.n_Sc58__Sc59  +
          +rho*Y[jhe4]*Y[jk55]*rate_eval.He4_K55__Sc59  +
          -rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__He4_Ca56  +
          -Y[jsc59]*rate_eval.Sc59__n_n_Ti57__weak__mp17  +
          -Y[jsc59]*rate_eval.Sc59__n_Ti58__weak__mp17  +
          -Y[jsc59]*rate_eval.Sc59__Ti59__weak__mo03  +
          +Y[jca59]*rate_eval.Ca59__Sc59__weak__mo03  +
          -rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__Ti60  +
          +Y[jca60]*rate_eval.Ca60__n_Sc59__weak__mp17  +
          +rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__He4_Sc59  +
          -rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__n_Ti59  +
          +Y[jca61]*rate_eval.Ca61__n_n_Sc59__weak__mp17
       )

    dYdt[jsc60] = (
          +rho*Y[jp]*Y[jti63]*rate_eval.p_Ti63__He4_Sc60  +
          -rho*Y[jhe4]*Y[jsc60]*rate_eval.He4_Sc60__n_V63  +
          -rho*Y[jp]*Y[jsc60]*rate_eval.p_Sc60__He4_Ca57  +
          -rho*Y[jp]*Y[jsc60]*rate_eval.p_Sc60__n_Ti60  +
          +rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__n_Sc60  +
          +rho*Y[jhe4]*Y[jk57]*rate_eval.He4_K57__n_Sc60  +
          -rho*Y[jhe4]*Y[jsc60]*rate_eval.He4_Sc60__V64  +
          +rho*Y[jn]*Y[jsc59]*rate_eval.n_Sc59__Sc60  +
          +rho*Y[jp]*Y[jca59]*rate_eval.p_Ca59__Sc60  +
          -rho*Y[jp]*Y[jsc60]*rate_eval.p_Sc60__Ti61  +
          -Y[jsc60]*rate_eval.Sc60__n_n_Ti58__weak__mp17  +
          +Y[jca61]*rate_eval.Ca61__n_Sc60__weak__mp17  +
          -Y[jsc60]*rate_eval.Sc60__n_Ti59__weak__mp17  +
          +Y[jca60]*rate_eval.Ca60__Sc60__weak__mo03  +
          -Y[jsc60]*rate_eval.Sc60__n_n_n_Ti57__weak__mo03  +
          -rho*Y[jn]*Y[jsc60]*rate_eval.n_Sc60__Sc61  +
          -Y[jsc60]*rate_eval.Sc60__Ti60__weak__mo03  +
          +rho*Y[jhe4]*Y[jk56]*rate_eval.He4_K56__Sc60
       )

    dYdt[jsc61] = (
          -Y[jsc61]*rate_eval.Sc61__n_n_n_Ti58__weak__mo03  +
          +rho*Y[jp]*Y[jti64]*rate_eval.p_Ti64__He4_Sc61  +
          -Y[jsc61]*rate_eval.Sc61__n_n_Ti59__weak__mp17  +
          -rho*Y[jhe4]*Y[jsc61]*rate_eval.He4_Sc61__n_V64  +
          -rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__n_Ti61  +
          +rho*Y[jp]*Y[jca61]*rate_eval.p_Ca61__n_Sc61  +
          +rho*Y[jhe4]*Y[jk57]*rate_eval.He4_K57__Sc61  +
          -rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__Ti62  +
          +rho*Y[jp]*Y[jca60]*rate_eval.p_Ca60__Sc61  +
          +rho*Y[jhe4]*Y[jk58]*rate_eval.He4_K58__n_Sc61  +
          -Y[jsc61]*rate_eval.Sc61__n_Ti60__weak__mp17  +
          -rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__He4_Ca58  +
          -rho*Y[jn]*Y[jsc61]*rate_eval.n_Sc61__Sc62  +
          +Y[jca61]*rate_eval.Ca61__Sc61__weak__mo03  +
          -rho*Y[jhe4]*Y[jsc61]*rate_eval.He4_Sc61__V65  +
          -Y[jsc61]*rate_eval.Sc61__Ti61__weak__mo03  +
          +rho*Y[jn]*Y[jsc60]*rate_eval.n_Sc60__Sc61
       )

    dYdt[jsc62] = (
          -Y[jsc62]*rate_eval.Sc62__n_n_n_Ti59__weak__mo03  +
          +rho*Y[jp]*Y[jca61]*rate_eval.p_Ca61__Sc62  +
          -rho*Y[jhe4]*Y[jsc62]*rate_eval.He4_Sc62__n_V65  +
          -rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__n_Ti62  +
          +rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__He4_Sc62  +
          -Y[jsc62]*rate_eval.Sc62__Ti62__weak__mo03  +
          -rho*Y[jhe4]*Y[jsc62]*rate_eval.He4_Sc62__V66  +
          -Y[jsc62]*rate_eval.Sc62__n_n_Ti60__weak__mp17  +
          -rho*Y[jn]*Y[jsc62]*rate_eval.n_Sc62__Sc63  +
          +rho*Y[jhe4]*Y[jk58]*rate_eval.He4_K58__Sc62  +
          -rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__Ti63  +
          -Y[jsc62]*rate_eval.Sc62__n_Ti61__weak__mp17  +
          +rho*Y[jhe4]*Y[jk59]*rate_eval.He4_K59__n_Sc62  +
          +rho*Y[jn]*Y[jsc61]*rate_eval.n_Sc61__Sc62  +
          -rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__He4_Ca59
       )

    dYdt[jsc63] = (
          -Y[jsc63]*rate_eval.Sc63__n_n_n_Ti60__weak__mo03  +
          -rho*Y[jhe4]*Y[jsc63]*rate_eval.He4_Sc63__n_V66  +
          -rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__Ti64  +
          +rho*Y[jn]*Y[jsc62]*rate_eval.n_Sc62__Sc63  +
          -rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__He4_Ca60  +
          -Y[jsc63]*rate_eval.Sc63__Ti63__weak__mo03  +
          +rho*Y[jhe4]*Y[jk59]*rate_eval.He4_K59__Sc63  +
          -Y[jsc63]*rate_eval.Sc63__n_Ti62__weak__mp17  +
          -Y[jsc63]*rate_eval.Sc63__n_n_Ti61__weak__mp17  +
          -rho*Y[jhe4]*Y[jsc63]*rate_eval.He4_Sc63__V67  +
          -rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__n_Ti63
       )

    dYdt[jti37] = (
          -rho*Y[jhe4]*Y[jti37]*rate_eval.He4_Ti37__p_V40  +
          -rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__He4_Ca34  +
          -rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__Ti38  +
          +rho*Y[jhe4]*Y[jca33]*rate_eval.He4_Ca33__Ti37  +
          -rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__p_Sc37  +
          -rho*Y[jhe4]*Y[jti37]*rate_eval.He4_Ti37__Cr41  +
          -Y[jti37]*rate_eval.Ti37__Sc37__weak__bqa_pos_  +
          +rho*Y[jp]*Y[jsc36]*rate_eval.p_Sc36__Ti37
       )

    dYdt[jti38] = (
          +rho*Y[jn]*Y[jcr41]*rate_eval.n_Cr41__He4_Ti38  +
          -rho*Y[jhe4]*Y[jti38]*rate_eval.He4_Ti38__p_V41  +
          -rho*Y[jn]*Y[jti38]*rate_eval.n_Ti38__He4_Ca35  +
          -rho*Y[jn]*Y[jti38]*rate_eval.n_Ti38__p_Sc38  +
          +rho*Y[jhe4]*Y[jsc35]*rate_eval.He4_Sc35__p_Ti38  +
          -Y[jti38]*rate_eval.Ti38__Sc38__weak__mo97  +
          -rho*Y[jhe4]*Y[jti38]*rate_eval.He4_Ti38__Cr42  +
          -rho*Y[jn]*Y[jti38]*rate_eval.n_Ti38__Ti39  +
          +rho*Y[jn]*Y[jti37]*rate_eval.n_Ti37__Ti38  +
          +rho*Y[jp]*Y[jsc37]*rate_eval.p_Sc37__Ti38  +
          +rho*Y[jhe4]*Y[jca34]*rate_eval.He4_Ca34__Ti38  +
          -rho*Y[jp]*Y[jti38]*rate_eval.p_Ti38__V39
       )

    dYdt[jti39] = (
          +rho*Y[jn]*Y[jcr42]*rate_eval.n_Cr42__He4_Ti39  +
          -rho*Y[jhe4]*Y[jti39]*rate_eval.He4_Ti39__p_V42  +
          -rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__p_Sc39  +
          +rho*Y[jhe4]*Y[jsc36]*rate_eval.He4_Sc36__p_Ti39  +
          -rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__He4_Ca36  +
          +rho*Y[jn]*Y[jv39]*rate_eval.n_V39__p_Ti39  +
          +rho*Y[jn]*Y[jti38]*rate_eval.n_Ti38__Ti39  +
          +rho*Y[jp]*Y[jsc38]*rate_eval.p_Sc38__Ti39  +
          +rho*Y[jhe4]*Y[jca35]*rate_eval.He4_Ca35__Ti39  +
          -Y[jti39]*rate_eval.Ti39__p_Ca38__weak__wc12  +
          +Y[jv39]*rate_eval.V39__Ti39__weak__bqa_pos_  +
          -Y[jti39]*rate_eval.Ti39__Sc39__weak__wc17  +
          -rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__Ti40  +
          -rho*Y[jhe4]*Y[jti39]*rate_eval.He4_Ti39__Cr43  +
          -rho*Y[jp]*Y[jti39]*rate_eval.p_Ti39__V40
       )

    dYdt[jti40] = (
          +rho*Y[jhe4]*Y[jsc37]*rate_eval.He4_Sc37__p_Ti40  +
          +rho*Y[jn]*Y[jv40]*rate_eval.n_V40__p_Ti40  +
          -rho*Y[jhe4]*Y[jti40]*rate_eval.He4_Ti40__p_V43  +
          +rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__He4_Ti40  +
          -rho*Y[jhe4]*Y[jti40]*rate_eval.He4_Ti40__Cr44  +
          -rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__Ti41  +
          +rho*Y[jhe4]*Y[jca36]*rate_eval.He4_Ca36__Ti40  +
          +rho*Y[jp]*Y[jsc39]*rate_eval.p_Sc39__Ti40  +
          -rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__p_Sc40  +
          +rho*Y[jn]*Y[jti39]*rate_eval.n_Ti39__Ti40  +
          +Y[jv40]*rate_eval.V40__Ti40__weak__bqa_pos_  +
          -Y[jti40]*rate_eval.Ti40__p_Ca39__weak__wc12  +
          -rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__He4_Ca37  +
          -rho*Y[jp]*Y[jti40]*rate_eval.p_Ti40__V41
       )

    dYdt[jti41] = (
          -rho*Y[jn]*Y[jti41]*rate_eval.n_Ti41__He4_Ca38  +
          -rho*Y[jn]*Y[jti41]*rate_eval.n_Ti41__p_Sc41  +
          +rho*Y[jhe4]*Y[jsc38]*rate_eval.He4_Sc38__p_Ti41  +
          +rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__He4_Ti41  +
          -rho*Y[jhe4]*Y[jti41]*rate_eval.He4_Ti41__Cr45  +
          -rho*Y[jn]*Y[jti41]*rate_eval.n_Ti41__Ti42  +
          +rho*Y[jn]*Y[jti40]*rate_eval.n_Ti40__Ti41  +
          +rho*Y[jp]*Y[jsc40]*rate_eval.p_Sc40__Ti41  +
          +rho*Y[jhe4]*Y[jca37]*rate_eval.He4_Ca37__Ti41  +
          -Y[jti41]*rate_eval.Ti41__p_Ca40__weak__wc12  +
          +rho*Y[jn]*Y[jv41]*rate_eval.n_V41__p_Ti41  +
          +Y[jcr42]*rate_eval.Cr42__p_Ti41__weak__wc12  +
          -rho*Y[jhe4]*Y[jti41]*rate_eval.He4_Ti41__p_V44  +
          -Y[jti41]*rate_eval.Ti41__Sc41__weak__wc17  +
          +Y[jv41]*rate_eval.V41__Ti41__weak__bqa_pos_  +
          -rho*Y[jp]*Y[jti41]*rate_eval.p_Ti41__V42
       )

    dYdt[jti42] = (
          +Y[jfe45]*rate_eval.Fe45__p_p_p_Ti42__weak__wc12  +
          +rho*Y[jn]*Y[jcr45]*rate_eval.n_Cr45__He4_Ti42  +
          +rho*Y[jhe4]*Y[jsc39]*rate_eval.He4_Sc39__p_Ti42  +
          -rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__p_Sc42  +
          +rho*Y[jhe4]*Y[jca38]*rate_eval.He4_Ca38__Ti42  +
          -rho*Y[jhe4]*Y[jti42]*rate_eval.He4_Ti42__p_V45  +
          -rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__He4_Ca39  +
          -rho*Y[jp]*Y[jti42]*rate_eval.p_Ti42__V43  +
          +rho*Y[jn]*Y[jti41]*rate_eval.n_Ti41__Ti42  +
          +rho*Y[jp]*Y[jsc41]*rate_eval.p_Sc41__Ti42  +
          -rho*Y[jhe4]*Y[jti42]*rate_eval.He4_Ti42__Cr46  +
          +rho*Y[jn]*Y[jv42]*rate_eval.n_V42__p_Ti42  +
          +Y[jcr43]*rate_eval.Cr43__p_Ti42__weak__wc17  +
          -rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__Ti43  +
          -Y[jti42]*rate_eval.Ti42__Sc42__weak__wc12  +
          +Y[jv42]*rate_eval.V42__Ti42__weak__mo97
       )

    dYdt[jti43] = (
          +rho*Y[jn]*Y[jcr46]*rate_eval.n_Cr46__He4_Ti43  +
          +rho*Y[jn]*Y[jv43]*rate_eval.n_V43__p_Ti43  +
          -Y[jti43]*rate_eval.Ti43__Sc43__weak__wc12  +
          -rho*Y[jhe4]*Y[jti43]*rate_eval.He4_Ti43__p_V46  +
          -rho*Y[jn]*Y[jti43]*rate_eval.n_Ti43__He4_Ca40  +
          +rho*Y[jhe4]*Y[jsc40]*rate_eval.He4_Sc40__p_Ti43  +
          -rho*Y[jp]*Y[jti43]*rate_eval.p_Ti43__V44  +
          +rho*Y[jhe4]*Y[jca39]*rate_eval.He4_Ca39__Ti43  +
          -rho*Y[jhe4]*Y[jti43]*rate_eval.He4_Ti43__Cr47  +
          -rho*Y[jn]*Y[jti43]*rate_eval.n_Ti43__Ti44  +
          +rho*Y[jp]*Y[jsc42]*rate_eval.p_Sc42__Ti43  +
          +rho*Y[jn]*Y[jti42]*rate_eval.n_Ti42__Ti43  +
          -rho*Y[jn]*Y[jti43]*rate_eval.n_Ti43__p_Sc43  +
          +Y[jcr44]*rate_eval.Cr44__p_Ti43__weak__wc12  +
          +Y[jv43]*rate_eval.V43__Ti43__weak__wc12
       )

    dYdt[jti44] = (
          +rho*Y[jn]*Y[jv44]*rate_eval.n_V44__p_Ti44  +
          +rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__He4_Ti44  +
          +rho*Y[jhe4]*Y[jca40]*rate_eval.He4_Ca40__Ti44  +
          -rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__p_Sc44  +
          -rho*Y[jhe4]*Y[jti44]*rate_eval.He4_Ti44__Cr48  +
          -rho*Y[jp]*Y[jti44]*rate_eval.p_Ti44__V45  +
          -rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__Ti45  +
          +rho*Y[jn]*Y[jti43]*rate_eval.n_Ti43__Ti44  +
          +rho*Y[jp]*Y[jsc43]*rate_eval.p_Sc43__Ti44  +
          +rho*Y[jhe4]*Y[jsc41]*rate_eval.He4_Sc41__p_Ti44  +
          +Y[jcr45]*rate_eval.Cr45__p_Ti44__weak__wc12  +
          -Y[jti44]*rate_eval.Ti44__Sc44__weak__wc12  +
          -rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__He4_Ca41  +
          +Y[jv44]*rate_eval.V44__Ti44__weak__wc12  +
          -rho*Y[jhe4]*Y[jti44]*rate_eval.He4_Ti44__p_V47
       )

    dYdt[jti45] = (
          -rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__p_Sc45  +
          +rho*Y[jhe4]*Y[jsc42]*rate_eval.He4_Sc42__p_Ti45  +
          -rho*Y[jhe4]*Y[jti45]*rate_eval.He4_Ti45__p_V48  +
          -rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__He4_Ca42  +
          -rho*Y[jhe4]*Y[jti45]*rate_eval.He4_Ti45__Cr49  +
          -rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__Ti46  +
          +rho*Y[jn]*Y[jti44]*rate_eval.n_Ti44__Ti45  +
          -Y[jti45]*rate_eval.Ti45__Sc45__weak__wc12  +
          +Y[jv45]*rate_eval.V45__Ti45__weak__wc12  +
          +rho*Y[jhe4]*Y[jca41]*rate_eval.He4_Ca41__Ti45  +
          -rho*Y[jp]*Y[jti45]*rate_eval.p_Ti45__V46  +
          +rho*Y[jn]*Y[jv45]*rate_eval.n_V45__p_Ti45  +
          +rho*Y[jp]*Y[jsc44]*rate_eval.p_Sc44__Ti45  +
          +rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__He4_Ti45
       )

    dYdt[jti46] = (
          +rho*Y[jp]*Y[jv49]*rate_eval.p_V49__He4_Ti46  +
          +rho*Y[jn]*Y[jv46]*rate_eval.n_V46__p_Ti46  +
          +rho*Y[jhe4]*Y[jsc43]*rate_eval.He4_Sc43__p_Ti46  +
          +rho*Y[jhe4]*Y[jca43]*rate_eval.He4_Ca43__n_Ti46  +
          +rho*Y[jp]*Y[jsc45]*rate_eval.p_Sc45__Ti46  +
          +rho*Y[jp]*Y[jsc46]*rate_eval.p_Sc46__n_Ti46  +
          -rho*Y[jhe4]*Y[jti46]*rate_eval.He4_Ti46__Cr50  +
          -rho*Y[jn]*Y[jti46]*rate_eval.n_Ti46__Ti47  +
          +rho*Y[jn]*Y[jti45]*rate_eval.n_Ti45__Ti46  +
          +rho*Y[jhe4]*Y[jca42]*rate_eval.He4_Ca42__Ti46  +
          +Y[jv46]*rate_eval.V46__Ti46__weak__wc12  +
          -rho*Y[jp]*Y[jti46]*rate_eval.p_Ti46__V47  +
          +rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__He4_Ti46  +
          +Y[jsc46]*rate_eval.Sc46__Ti46__weak__wc12
       )

    dYdt[jti47] = (
          +rho*Y[jn]*Y[jcr50]*rate_eval.n_Cr50__He4_Ti47  +
          +rho*Y[jhe4]*Y[jca43]*rate_eval.He4_Ca43__Ti47  +
          +rho*Y[jp]*Y[jv50]*rate_eval.p_V50__He4_Ti47  +
          +Y[jsc47]*rate_eval.Sc47__Ti47__weak__wc12  +
          +rho*Y[jhe4]*Y[jsc44]*rate_eval.He4_Sc44__p_Ti47  +
          -rho*Y[jn]*Y[jti47]*rate_eval.n_Ti47__He4_Ca44  +
          -rho*Y[jp]*Y[jti47]*rate_eval.p_Ti47__V48  +
          -rho*Y[jn]*Y[jti47]*rate_eval.n_Ti47__Ti48  +
          +rho*Y[jn]*Y[jti46]*rate_eval.n_Ti46__Ti47  +
          +rho*Y[jp]*Y[jsc46]*rate_eval.p_Sc46__Ti47  +
          +rho*Y[jn]*Y[jv47]*rate_eval.n_V47__p_Ti47  +
          -rho*Y[jhe4]*Y[jti47]*rate_eval.He4_Ti47__Cr51  +
          +Y[jv47]*rate_eval.V47__Ti47__weak__wc12  +
          -rho*Y[jn]*Y[jti47]*rate_eval.n_Ti47__p_Sc47
       )

    dYdt[jti48] = (
          +rho*Y[jn]*Y[jcr51]*rate_eval.n_Cr51__He4_Ti48  +
          +rho*Y[jp]*Y[jv51]*rate_eval.p_V51__He4_Ti48  +
          +rho*Y[jhe4]*Y[jsc45]*rate_eval.He4_Sc45__p_Ti48  +
          +rho*Y[jn]*Y[jv48]*rate_eval.n_V48__p_Ti48  +
          +rho*Y[jp]*Y[jsc48]*rate_eval.p_Sc48__n_Ti48  +
          -rho*Y[jhe4]*Y[jti48]*rate_eval.He4_Ti48__Cr52  +
          +rho*Y[jn]*Y[jti47]*rate_eval.n_Ti47__Ti48  +
          +rho*Y[jhe4]*Y[jca44]*rate_eval.He4_Ca44__Ti48  +
          +rho*Y[jhe4]*Y[jca45]*rate_eval.He4_Ca45__n_Ti48  +
          +rho*Y[jp]*Y[jsc47]*rate_eval.p_Sc47__Ti48  +
          -rho*Y[jp]*Y[jti48]*rate_eval.p_Ti48__V49  +
          +Y[jsc48]*rate_eval.Sc48__Ti48__weak__wc12  +
          +Y[jv48]*rate_eval.V48__Ti48__weak__wc12  +
          -rho*Y[jn]*Y[jti48]*rate_eval.n_Ti48__Ti49
       )

    dYdt[jti49] = (
          +rho*Y[jp]*Y[jv52]*rate_eval.p_V52__He4_Ti49  +
          -rho*Y[jn]*Y[jti49]*rate_eval.n_Ti49__He4_Ca46  +
          +rho*Y[jhe4]*Y[jsc46]*rate_eval.He4_Sc46__p_Ti49  +
          +rho*Y[jn]*Y[jv49]*rate_eval.n_V49__p_Ti49  +
          +rho*Y[jp]*Y[jsc49]*rate_eval.p_Sc49__n_Ti49  +
          -rho*Y[jp]*Y[jti49]*rate_eval.p_Ti49__V50  +
          -rho*Y[jn]*Y[jti49]*rate_eval.n_Ti49__Ti50  +
          -rho*Y[jhe4]*Y[jti49]*rate_eval.He4_Ti49__n_Cr52  +
          +rho*Y[jp]*Y[jsc48]*rate_eval.p_Sc48__Ti49  +
          +rho*Y[jhe4]*Y[jca45]*rate_eval.He4_Ca45__Ti49  +
          -rho*Y[jhe4]*Y[jti49]*rate_eval.He4_Ti49__Cr53  +
          +Y[jsc49]*rate_eval.Sc49__Ti49__weak__wc12  +
          +rho*Y[jn]*Y[jti48]*rate_eval.n_Ti48__Ti49  +
          +Y[jv49]*rate_eval.V49__Ti49__weak__wc12
       )

    dYdt[jti50] = (
          +rho*Y[jn]*Y[jcr53]*rate_eval.n_Cr53__He4_Ti50  +
          +rho*Y[jn]*Y[jv50]*rate_eval.n_V50__p_Ti50  +
          +rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__n_Ti50  +
          +rho*Y[jhe4]*Y[jsc47]*rate_eval.He4_Sc47__p_Ti50  +
          +rho*Y[jhe4]*Y[jca47]*rate_eval.He4_Ca47__n_Ti50  +
          +rho*Y[jp]*Y[jv53]*rate_eval.p_V53__He4_Ti50  +
          +rho*Y[jn]*Y[jti49]*rate_eval.n_Ti49__Ti50  +
          +rho*Y[jp]*Y[jsc49]*rate_eval.p_Sc49__Ti50  +
          +rho*Y[jhe4]*Y[jca46]*rate_eval.He4_Ca46__Ti50  +
          -rho*Y[jp]*Y[jti50]*rate_eval.p_Ti50__V51  +
          -rho*Y[jhe4]*Y[jti50]*rate_eval.He4_Ti50__Cr54  +
          -rho*Y[jn]*Y[jti50]*rate_eval.n_Ti50__Ti51  +
          +Y[jv50]*rate_eval.V50__Ti50__weak__mo03  +
          +Y[jsc50]*rate_eval.Sc50__Ti50__weak__wc12
       )

    dYdt[jti51] = (
          +rho*Y[jp]*Y[jsc50]*rate_eval.p_Sc50__Ti51  +
          -rho*Y[jhe4]*Y[jti51]*rate_eval.He4_Ti51__n_Cr54  +
          -rho*Y[jp]*Y[jti51]*rate_eval.p_Ti51__n_V51  +
          -rho*Y[jn]*Y[jti51]*rate_eval.n_Ti51__He4_Ca48  +
          -rho*Y[jhe4]*Y[jti51]*rate_eval.He4_Ti51__Cr55  +
          -rho*Y[jp]*Y[jti51]*rate_eval.p_Ti51__V52  +
          +rho*Y[jhe4]*Y[jca47]*rate_eval.He4_Ca47__Ti51  +
          +rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__p_Ti51  +
          -Y[jti51]*rate_eval.Ti51__V51__weak__wc12  +
          +rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__n_Ti51  +
          +rho*Y[jn]*Y[jti50]*rate_eval.n_Ti50__Ti51  +
          -rho*Y[jn]*Y[jti51]*rate_eval.n_Ti51__Ti52  +
          +rho*Y[jp]*Y[jv54]*rate_eval.p_V54__He4_Ti51  +
          +Y[jsc51]*rate_eval.Sc51__Ti51__weak__wc12
       )

    dYdt[jti52] = (
          +rho*Y[jn]*Y[jcr55]*rate_eval.n_Cr55__He4_Ti52  +
          -rho*Y[jp]*Y[jti52]*rate_eval.p_Ti52__He4_Sc49  +
          -rho*Y[jp]*Y[jti52]*rate_eval.p_Ti52__n_V52  +
          +rho*Y[jp]*Y[jsc52]*rate_eval.p_Sc52__n_Ti52  +
          +rho*Y[jhe4]*Y[jca48]*rate_eval.He4_Ca48__Ti52  +
          -rho*Y[jhe4]*Y[jti52]*rate_eval.He4_Ti52__Cr56  +
          -rho*Y[jp]*Y[jti52]*rate_eval.p_Ti52__V53  +
          -rho*Y[jn]*Y[jti52]*rate_eval.n_Ti52__Ti53  +
          +rho*Y[jhe4]*Y[jca49]*rate_eval.He4_Ca49__n_Ti52  +
          +rho*Y[jp]*Y[jsc51]*rate_eval.p_Sc51__Ti52  +
          +rho*Y[jp]*Y[jv55]*rate_eval.p_V55__He4_Ti52  +
          +rho*Y[jn]*Y[jti51]*rate_eval.n_Ti51__Ti52  +
          +Y[jsc52]*rate_eval.Sc52__Ti52__weak__wc12  +
          -Y[jti52]*rate_eval.Ti52__V52__weak__wc12
       )

    dYdt[jti53] = (
          +rho*Y[jp]*Y[jsc52]*rate_eval.p_Sc52__Ti53  +
          +rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__n_Ti53  +
          -rho*Y[jhe4]*Y[jti53]*rate_eval.He4_Ti53__n_Cr56  +
          -rho*Y[jp]*Y[jti53]*rate_eval.p_Ti53__He4_Sc50  +
          +rho*Y[jhe4]*Y[jca50]*rate_eval.He4_Ca50__n_Ti53  +
          +rho*Y[jp]*Y[jv56]*rate_eval.p_V56__He4_Ti53  +
          -rho*Y[jp]*Y[jti53]*rate_eval.p_Ti53__n_V53  +
          +Y[jsc53]*rate_eval.Sc53__Ti53__weak__wc12  +
          -rho*Y[jhe4]*Y[jti53]*rate_eval.He4_Ti53__Cr57  +
          -rho*Y[jp]*Y[jti53]*rate_eval.p_Ti53__V54  +
          +rho*Y[jn]*Y[jti52]*rate_eval.n_Ti52__Ti53  +
          +Y[jsc54]*rate_eval.Sc54__n_Ti53__weak__mp17  +
          -rho*Y[jn]*Y[jti53]*rate_eval.n_Ti53__Ti54  +
          +rho*Y[jhe4]*Y[jca49]*rate_eval.He4_Ca49__Ti53  +
          -Y[jti53]*rate_eval.Ti53__V53__weak__wc12
       )

    dYdt[jti54] = (
          +Y[jsc57]*rate_eval.Sc57__n_n_n_Ti54__weak__mo03  +
          +rho*Y[jp]*Y[jv57]*rate_eval.p_V57__He4_Ti54  +
          -rho*Y[jhe4]*Y[jti54]*rate_eval.He4_Ti54__n_Cr57  +
          -rho*Y[jp]*Y[jti54]*rate_eval.p_Ti54__He4_Sc51  +
          -rho*Y[jp]*Y[jti54]*rate_eval.p_Ti54__n_V54  +
          +rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__n_Ti54  +
          +rho*Y[jhe4]*Y[jca51]*rate_eval.He4_Ca51__n_Ti54  +
          -rho*Y[jn]*Y[jti54]*rate_eval.n_Ti54__Ti55  +
          -rho*Y[jhe4]*Y[jti54]*rate_eval.He4_Ti54__Cr58  +
          +Y[jsc54]*rate_eval.Sc54__Ti54__weak__wc17  +
          -rho*Y[jp]*Y[jti54]*rate_eval.p_Ti54__V55  +
          +rho*Y[jp]*Y[jsc53]*rate_eval.p_Sc53__Ti54  +
          +rho*Y[jhe4]*Y[jca50]*rate_eval.He4_Ca50__Ti54  +
          +Y[jsc55]*rate_eval.Sc55__n_Ti54__weak__wc12  +
          +rho*Y[jn]*Y[jti53]*rate_eval.n_Ti53__Ti54  +
          -Y[jti54]*rate_eval.Ti54__V54__weak__wc12
       )

    dYdt[jti55] = (
          +Y[jsc58]*rate_eval.Sc58__n_n_n_Ti55__weak__mo03  +
          +rho*Y[jp]*Y[jv58]*rate_eval.p_V58__He4_Ti55  +
          -rho*Y[jhe4]*Y[jti55]*rate_eval.He4_Ti55__n_Cr58  +
          -rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__n_V55  +
          +Y[jsc56]*rate_eval.Sc56__n_Ti55__weak__mp17  +
          +rho*Y[jp]*Y[jsc55]*rate_eval.p_Sc55__n_Ti55  +
          +rho*Y[jn]*Y[jti54]*rate_eval.n_Ti54__Ti55  +
          -rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__V56  +
          -rho*Y[jn]*Y[jti55]*rate_eval.n_Ti55__Ti56  +
          +rho*Y[jhe4]*Y[jca51]*rate_eval.He4_Ca51__Ti55  +
          +rho*Y[jp]*Y[jsc54]*rate_eval.p_Sc54__Ti55  +
          -rho*Y[jhe4]*Y[jti55]*rate_eval.He4_Ti55__Cr59  +
          +rho*Y[jhe4]*Y[jca52]*rate_eval.He4_Ca52__n_Ti55  +
          -Y[jti55]*rate_eval.Ti55__V55__weak__wc12  +
          -rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__He4_Sc52  +
          +Y[jsc55]*rate_eval.Sc55__Ti55__weak__wc12
       )

    dYdt[jti56] = (
          +Y[jsc59]*rate_eval.Sc59__n_n_n_Ti56__weak__mo03  +
          +rho*Y[jhe4]*Y[jca52]*rate_eval.He4_Ca52__Ti56  +
          +rho*Y[jhe4]*Y[jca53]*rate_eval.He4_Ca53__n_Ti56  +
          -rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__He4_Sc53  +
          -rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__V57  +
          +rho*Y[jn]*Y[jti55]*rate_eval.n_Ti55__Ti56  +
          +rho*Y[jp]*Y[jsc55]*rate_eval.p_Sc55__Ti56  +
          -rho*Y[jhe4]*Y[jti56]*rate_eval.He4_Ti56__Cr60  +
          -rho*Y[jhe4]*Y[jti56]*rate_eval.He4_Ti56__n_Cr59  +
          -Y[jti56]*rate_eval.Ti56__V56__weak__wc12  +
          +Y[jsc57]*rate_eval.Sc57__n_Ti56__weak__mp17  +
          +Y[jsc56]*rate_eval.Sc56__Ti56__weak__wc17  +
          +Y[jsc58]*rate_eval.Sc58__n_n_Ti56__weak__mp17  +
          -rho*Y[jn]*Y[jti56]*rate_eval.n_Ti56__Ti57  +
          +rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__n_Ti56  +
          -rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__n_V56  +
          +rho*Y[jp]*Y[jv59]*rate_eval.p_V59__He4_Ti56
       )

    dYdt[jti57] = (
          -rho*Y[jp]*Y[jti57]*rate_eval.p_Ti57__He4_Sc54  +
          +rho*Y[jp]*Y[jv60]*rate_eval.p_V60__He4_Ti57  +
          +rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__n_Ti57  +
          -rho*Y[jp]*Y[jti57]*rate_eval.p_Ti57__n_V57  +
          -rho*Y[jp]*Y[jti57]*rate_eval.p_Ti57__V58  +
          -rho*Y[jn]*Y[jti57]*rate_eval.n_Ti57__Ti58  +
          -rho*Y[jhe4]*Y[jti57]*rate_eval.He4_Ti57__n_Cr60  +
          +rho*Y[jp]*Y[jsc56]*rate_eval.p_Sc56__Ti57  +
          +rho*Y[jhe4]*Y[jca53]*rate_eval.He4_Ca53__Ti57  +
          +Y[jsc57]*rate_eval.Sc57__Ti57__weak__wc17  +
          +Y[jsc59]*rate_eval.Sc59__n_n_Ti57__weak__mp17  +
          -Y[jti57]*rate_eval.Ti57__V57__weak__wc12  +
          +Y[jsc58]*rate_eval.Sc58__n_Ti57__weak__mp17  +
          -rho*Y[jhe4]*Y[jti57]*rate_eval.He4_Ti57__Cr61  +
          +rho*Y[jn]*Y[jti56]*rate_eval.n_Ti56__Ti57  +
          +rho*Y[jhe4]*Y[jca54]*rate_eval.He4_Ca54__n_Ti57  +
          +Y[jsc60]*rate_eval.Sc60__n_n_n_Ti57__weak__mo03
       )

    dYdt[jti58] = (
          +Y[jsc61]*rate_eval.Sc61__n_n_n_Ti58__weak__mo03  +
          -rho*Y[jhe4]*Y[jti58]*rate_eval.He4_Ti58__n_Cr61  +
          -rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__n_V58  +
          +rho*Y[jp]*Y[jsc58]*rate_eval.p_Sc58__n_Ti58  +
          -rho*Y[jn]*Y[jti58]*rate_eval.n_Ti58__Ti59  +
          +rho*Y[jhe4]*Y[jca54]*rate_eval.He4_Ca54__Ti58  +
          +rho*Y[jp]*Y[jv61]*rate_eval.p_V61__He4_Ti58  +
          -rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__V59  +
          +rho*Y[jn]*Y[jti57]*rate_eval.n_Ti57__Ti58  +
          +rho*Y[jp]*Y[jsc57]*rate_eval.p_Sc57__Ti58  +
          -Y[jti58]*rate_eval.Ti58__V58__weak__wc12  +
          +Y[jsc60]*rate_eval.Sc60__n_n_Ti58__weak__mp17  +
          +rho*Y[jhe4]*Y[jca55]*rate_eval.He4_Ca55__n_Ti58  +
          -Y[jti58]*rate_eval.Ti58__n_V57__weak__mp17  +
          +Y[jsc59]*rate_eval.Sc59__n_Ti58__weak__mp17  +
          -rho*Y[jhe4]*Y[jti58]*rate_eval.He4_Ti58__Cr62  +
          +Y[jsc58]*rate_eval.Sc58__Ti58__weak__wc17  +
          -rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__He4_Sc55
       )

    dYdt[jti59] = (
          +Y[jsc62]*rate_eval.Sc62__n_n_n_Ti59__weak__mo03  +
          -rho*Y[jhe4]*Y[jti59]*rate_eval.He4_Ti59__n_Cr62  +
          -rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__n_V59  +
          +Y[jsc61]*rate_eval.Sc61__n_n_Ti59__weak__mp17  +
          +rho*Y[jn]*Y[jti58]*rate_eval.n_Ti58__Ti59  +
          -rho*Y[jn]*Y[jti59]*rate_eval.n_Ti59__Ti60  +
          -rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__V60  +
          +rho*Y[jp]*Y[jsc58]*rate_eval.p_Sc58__Ti59  +
          +rho*Y[jhe4]*Y[jca55]*rate_eval.He4_Ca55__Ti59  +
          +Y[jsc59]*rate_eval.Sc59__Ti59__weak__mo03  +
          +Y[jsc60]*rate_eval.Sc60__n_Ti59__weak__mp17  +
          -rho*Y[jhe4]*Y[jti59]*rate_eval.He4_Ti59__Cr63  +
          +rho*Y[jp]*Y[jv62]*rate_eval.p_V62__He4_Ti59  +
          +rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__n_Ti59  +
          -rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__He4_Sc56  +
          -Y[jti59]*rate_eval.Ti59__V59__weak__wc12  +
          +rho*Y[jhe4]*Y[jca56]*rate_eval.He4_Ca56__n_Ti59
       )

    dYdt[jti60] = (
          +Y[jsc63]*rate_eval.Sc63__n_n_n_Ti60__weak__mo03  +
          -rho*Y[jhe4]*Y[jti60]*rate_eval.He4_Ti60__n_Cr63  +
          -rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__n_V60  +
          +rho*Y[jp]*Y[jsc60]*rate_eval.p_Sc60__n_Ti60  +
          +rho*Y[jhe4]*Y[jca57]*rate_eval.He4_Ca57__n_Ti60  +
          -rho*Y[jhe4]*Y[jti60]*rate_eval.He4_Ti60__Cr64  +
          +rho*Y[jn]*Y[jti59]*rate_eval.n_Ti59__Ti60  +
          +rho*Y[jp]*Y[jv63]*rate_eval.p_V63__He4_Ti60  +
          +Y[jsc62]*rate_eval.Sc62__n_n_Ti60__weak__mp17  +
          -rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__V61  +
          -rho*Y[jn]*Y[jti60]*rate_eval.n_Ti60__Ti61  +
          +Y[jsc61]*rate_eval.Sc61__n_Ti60__weak__mp17  +
          -Y[jti60]*rate_eval.Ti60__n_V59__weak__mp17  +
          -rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__He4_Sc57  +
          +rho*Y[jp]*Y[jsc59]*rate_eval.p_Sc59__Ti60  +
          +rho*Y[jhe4]*Y[jca56]*rate_eval.He4_Ca56__Ti60  +
          +Y[jsc60]*rate_eval.Sc60__Ti60__weak__mo03  +
          -Y[jti60]*rate_eval.Ti60__V60__weak__wc17
       )

    dYdt[jti61] = (
          +rho*Y[jp]*Y[jv64]*rate_eval.p_V64__He4_Ti61  +
          -rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__n_V61  +
          +rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__n_Ti61  +
          +rho*Y[jhe4]*Y[jca58]*rate_eval.He4_Ca58__n_Ti61  +
          -rho*Y[jhe4]*Y[jti61]*rate_eval.He4_Ti61__n_Cr64  +
          -rho*Y[jhe4]*Y[jti61]*rate_eval.He4_Ti61__Cr65  +
          -rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__V62  +
          +rho*Y[jn]*Y[jti60]*rate_eval.n_Ti60__Ti61  +
          +rho*Y[jp]*Y[jsc60]*rate_eval.p_Sc60__Ti61  +
          +Y[jsc62]*rate_eval.Sc62__n_Ti61__weak__mp17  +
          -Y[jti61]*rate_eval.Ti61__V61__weak__wc17  +
          -Y[jti61]*rate_eval.Ti61__n_V60__weak__mp17  +
          -rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__He4_Sc58  +
          +Y[jsc63]*rate_eval.Sc63__n_n_Ti61__weak__mp17  +
          -rho*Y[jn]*Y[jti61]*rate_eval.n_Ti61__Ti62  +
          +rho*Y[jhe4]*Y[jca57]*rate_eval.He4_Ca57__Ti61  +
          +Y[jsc61]*rate_eval.Sc61__Ti61__weak__mo03
       )

    dYdt[jti62] = (
          +rho*Y[jp]*Y[jv65]*rate_eval.p_V65__He4_Ti62  +
          -rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__n_V62  +
          +rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__n_Ti62  +
          +Y[jsc62]*rate_eval.Sc62__Ti62__weak__mo03  +
          -rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__V63  +
          +rho*Y[jp]*Y[jsc61]*rate_eval.p_Sc61__Ti62  +
          -rho*Y[jhe4]*Y[jti62]*rate_eval.He4_Ti62__n_Cr65  +
          +rho*Y[jhe4]*Y[jca58]*rate_eval.He4_Ca58__Ti62  +
          +Y[jsc63]*rate_eval.Sc63__n_Ti62__weak__mp17  +
          -rho*Y[jhe4]*Y[jti62]*rate_eval.He4_Ti62__Cr66  +
          +rho*Y[jn]*Y[jti61]*rate_eval.n_Ti61__Ti62  +
          -Y[jti62]*rate_eval.Ti62__n_V61__weak__mp17  +
          -rho*Y[jn]*Y[jti62]*rate_eval.n_Ti62__Ti63  +
          -Y[jti62]*rate_eval.Ti62__V62__weak__mo03  +
          -rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__He4_Sc59  +
          +rho*Y[jhe4]*Y[jca59]*rate_eval.He4_Ca59__n_Ti62
       )

    dYdt[jti63] = (
          -rho*Y[jhe4]*Y[jti63]*rate_eval.He4_Ti63__n_Cr66  +
          -rho*Y[jp]*Y[jti63]*rate_eval.p_Ti63__He4_Sc60  +
          -rho*Y[jp]*Y[jti63]*rate_eval.p_Ti63__n_V63  +
          -rho*Y[jhe4]*Y[jti63]*rate_eval.He4_Ti63__Cr67  +
          -rho*Y[jp]*Y[jti63]*rate_eval.p_Ti63__V64  +
          +rho*Y[jhe4]*Y[jca60]*rate_eval.He4_Ca60__n_Ti63  +
          +rho*Y[jhe4]*Y[jca59]*rate_eval.He4_Ca59__Ti63  +
          +rho*Y[jp]*Y[jsc62]*rate_eval.p_Sc62__Ti63  +
          +Y[jsc63]*rate_eval.Sc63__Ti63__weak__mo03  +
          -Y[jti63]*rate_eval.Ti63__n_V62__weak__mp17  +
          -Y[jti63]*rate_eval.Ti63__V63__weak__mo03  +
          +rho*Y[jn]*Y[jti62]*rate_eval.n_Ti62__Ti63  +
          -rho*Y[jn]*Y[jti63]*rate_eval.n_Ti63__Ti64  +
          +rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__n_Ti63  +
          -Y[jti63]*rate_eval.Ti63__n_n_V61__weak__mp17  +
          +rho*Y[jp]*Y[jv66]*rate_eval.p_V66__He4_Ti63
       )

    dYdt[jti64] = (
          -rho*Y[jhe4]*Y[jti64]*rate_eval.He4_Ti64__n_Cr67  +
          -rho*Y[jp]*Y[jti64]*rate_eval.p_Ti64__He4_Sc61  +
          +rho*Y[jp]*Y[jv67]*rate_eval.p_V67__He4_Ti64  +
          +rho*Y[jhe4]*Y[jca61]*rate_eval.He4_Ca61__n_Ti64  +
          -rho*Y[jn]*Y[jti64]*rate_eval.n_Ti64__Ti65  +
          +rho*Y[jp]*Y[jsc63]*rate_eval.p_Sc63__Ti64  +
          -rho*Y[jp]*Y[jti64]*rate_eval.p_Ti64__n_V64  +
          -Y[jti64]*rate_eval.Ti64__n_n_V62__weak__mp17  +
          -rho*Y[jhe4]*Y[jti64]*rate_eval.He4_Ti64__Cr68  +
          -Y[jti64]*rate_eval.Ti64__n_V63__weak__mp17  +
          +rho*Y[jhe4]*Y[jca60]*rate_eval.He4_Ca60__Ti64  +
          -Y[jti64]*rate_eval.Ti64__V64__weak__mo03  +
          +rho*Y[jn]*Y[jti63]*rate_eval.n_Ti63__Ti64  +
          -rho*Y[jp]*Y[jti64]*rate_eval.p_Ti64__V65  +
          -Y[jti64]*rate_eval.Ti64__n_n_n_V61__weak__mo03
       )

    dYdt[jti65] = (
          -Y[jti65]*rate_eval.Ti65__n_n_n_V62__weak__mo03  +
          -rho*Y[jhe4]*Y[jti65]*rate_eval.He4_Ti65__n_Cr68  +
          -Y[jti65]*rate_eval.Ti65__n_V64__weak__mp17  +
          -rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__He4_Sc62  +
          +rho*Y[jn]*Y[jti64]*rate_eval.n_Ti64__Ti65  +
          -rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__V66  +
          -rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__n_V65  +
          -Y[jti65]*rate_eval.Ti65__n_n_V63__weak__mp17  +
          +rho*Y[jhe4]*Y[jca61]*rate_eval.He4_Ca61__Ti65  +
          -rho*Y[jhe4]*Y[jti65]*rate_eval.He4_Ti65__Cr69  +
          -Y[jti65]*rate_eval.Ti65__V65__weak__mo03
       )

    dYdt[jv39] = (
          -rho*Y[jhe4]*Y[jv39]*rate_eval.He4_V39__p_Cr42  +
          +rho*Y[jhe4]*Y[jsc35]*rate_eval.He4_Sc35__V39  +
          -rho*Y[jn]*Y[jv39]*rate_eval.n_V39__V40  +
          -rho*Y[jn]*Y[jv39]*rate_eval.n_V39__p_Ti39  +
          -rho*Y[jhe4]*Y[jv39]*rate_eval.He4_V39__Mn43  +
          -Y[jv39]*rate_eval.V39__Ti39__weak__bqa_pos_  +
          -rho*Y[jn]*Y[jv39]*rate_eval.n_V39__He4_Sc36  +
          +rho*Y[jp]*Y[jti38]*rate_eval.p_Ti38__V39
       )

    dYdt[jv40] = (
          -rho*Y[jn]*Y[jv40]*rate_eval.n_V40__p_Ti40  +
          +rho*Y[jhe4]*Y[jti37]*rate_eval.He4_Ti37__p_V40  +
          +rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__He4_V40  +
          +rho*Y[jn]*Y[jv39]*rate_eval.n_V39__V40  +
          -rho*Y[jhe4]*Y[jv40]*rate_eval.He4_V40__p_Cr43  +
          -rho*Y[jn]*Y[jv40]*rate_eval.n_V40__He4_Sc37  +
          +rho*Y[jhe4]*Y[jsc36]*rate_eval.He4_Sc36__V40  +
          -Y[jv40]*rate_eval.V40__Ti40__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[jv40]*rate_eval.He4_V40__Mn44  +
          -rho*Y[jn]*Y[jv40]*rate_eval.n_V40__V41  +
          +rho*Y[jp]*Y[jti39]*rate_eval.p_Ti39__V40  +
          -rho*Y[jp]*Y[jv40]*rate_eval.p_V40__Cr41
       )

    dYdt[jv41] = (
          -rho*Y[jn]*Y[jv41]*rate_eval.n_V41__He4_Sc38  +
          +rho*Y[jhe4]*Y[jti38]*rate_eval.He4_Ti38__p_V41  +
          -rho*Y[jhe4]*Y[jv41]*rate_eval.He4_V41__Mn45  +
          -rho*Y[jp]*Y[jv41]*rate_eval.p_V41__Cr42  +
          -rho*Y[jn]*Y[jv41]*rate_eval.n_V41__V42  +
          +rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__He4_V41  +
          -rho*Y[jn]*Y[jv41]*rate_eval.n_V41__p_Ti41  +
          +rho*Y[jn]*Y[jcr41]*rate_eval.n_Cr41__p_V41  +
          +rho*Y[jhe4]*Y[jsc37]*rate_eval.He4_Sc37__V41  +
          -Y[jv41]*rate_eval.V41__Ti41__weak__bqa_pos_  +
          +Y[jcr41]*rate_eval.Cr41__V41__weak__bqa_pos_  +
          -rho*Y[jhe4]*Y[jv41]*rate_eval.He4_V41__p_Cr44  +
          +rho*Y[jn]*Y[jv40]*rate_eval.n_V40__V41  +
          +rho*Y[jp]*Y[jti40]*rate_eval.p_Ti40__V41
       )

    dYdt[jv42] = (
          +rho*Y[jn]*Y[jcr42]*rate_eval.n_Cr42__p_V42  +
          -rho*Y[jhe4]*Y[jv42]*rate_eval.He4_V42__p_Cr45  +
          -rho*Y[jn]*Y[jv42]*rate_eval.n_V42__He4_Sc39  +
          +rho*Y[jhe4]*Y[jti39]*rate_eval.He4_Ti39__p_V42  +
          -rho*Y[jp]*Y[jv42]*rate_eval.p_V42__Cr43  +
          -rho*Y[jn]*Y[jv42]*rate_eval.n_V42__V43  +
          +rho*Y[jn]*Y[jv41]*rate_eval.n_V41__V42  +
          +rho*Y[jhe4]*Y[jsc38]*rate_eval.He4_Sc38__V42  +
          +rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__He4_V42  +
          -rho*Y[jn]*Y[jv42]*rate_eval.n_V42__p_Ti42  +
          +Y[jcr42]*rate_eval.Cr42__V42__weak__wc12  +
          -rho*Y[jhe4]*Y[jv42]*rate_eval.He4_V42__Mn46  +
          -Y[jv42]*rate_eval.V42__Ti42__weak__mo97  +
          +rho*Y[jp]*Y[jti41]*rate_eval.p_Ti41__V42
       )

    dYdt[jv43] = (
          +rho*Y[jn]*Y[jmn46]*rate_eval.n_Mn46__He4_V43  +
          +rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__p_V43  +
          -rho*Y[jhe4]*Y[jv43]*rate_eval.He4_V43__p_Cr46  +
          -rho*Y[jn]*Y[jv43]*rate_eval.n_V43__p_Ti43  +
          +rho*Y[jhe4]*Y[jti40]*rate_eval.He4_Ti40__p_V43  +
          -rho*Y[jn]*Y[jv43]*rate_eval.n_V43__He4_Sc40  +
          -rho*Y[jhe4]*Y[jv43]*rate_eval.He4_V43__Mn47  +
          -rho*Y[jp]*Y[jv43]*rate_eval.p_V43__Cr44  +
          +rho*Y[jn]*Y[jv42]*rate_eval.n_V42__V43  +
          -rho*Y[jn]*Y[jv43]*rate_eval.n_V43__V44  +
          +rho*Y[jp]*Y[jti42]*rate_eval.p_Ti42__V43  +
          +rho*Y[jhe4]*Y[jsc39]*rate_eval.He4_Sc39__V43  +
          +Y[jfe45]*rate_eval.Fe45__p_p_V43__weak__wc12  +
          +Y[jcr43]*rate_eval.Cr43__V43__weak__wc12  +
          -Y[jv43]*rate_eval.V43__Ti43__weak__wc12
       )

    dYdt[jv44] = (
          -rho*Y[jn]*Y[jv44]*rate_eval.n_V44__He4_Sc41  +
          -rho*Y[jn]*Y[jv44]*rate_eval.n_V44__p_Ti44  +
          +rho*Y[jp]*Y[jti43]*rate_eval.p_Ti43__V44  +
          +Y[jcr44]*rate_eval.Cr44__V44__weak__wc12  +
          +rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__He4_V44  +
          +rho*Y[jn]*Y[jv43]*rate_eval.n_V43__V44  +
          +rho*Y[jhe4]*Y[jsc40]*rate_eval.He4_Sc40__V44  +
          -rho*Y[jhe4]*Y[jv44]*rate_eval.He4_V44__p_Cr47  +
          -rho*Y[jp]*Y[jv44]*rate_eval.p_V44__Cr45  +
          +rho*Y[jhe4]*Y[jti41]*rate_eval.He4_Ti41__p_V44  +
          -rho*Y[jn]*Y[jv44]*rate_eval.n_V44__V45  +
          +rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__p_V44  +
          -rho*Y[jhe4]*Y[jv44]*rate_eval.He4_V44__Mn48  +
          -Y[jv44]*rate_eval.V44__Ti44__weak__wc12
       )

    dYdt[jv45] = (
          +rho*Y[jn]*Y[jmn48]*rate_eval.n_Mn48__He4_V45  +
          -rho*Y[jn]*Y[jv45]*rate_eval.n_V45__He4_Sc42  +
          +rho*Y[jhe4]*Y[jti42]*rate_eval.He4_Ti42__p_V45  +
          -rho*Y[jhe4]*Y[jv45]*rate_eval.He4_V45__Mn49  +
          -rho*Y[jn]*Y[jv45]*rate_eval.n_V45__V46  +
          +rho*Y[jp]*Y[jti44]*rate_eval.p_Ti44__V45  +
          +rho*Y[jhe4]*Y[jsc41]*rate_eval.He4_Sc41__V45  +
          -Y[jv45]*rate_eval.V45__Ti45__weak__wc12  +
          -rho*Y[jp]*Y[jv45]*rate_eval.p_V45__Cr46  +
          +Y[jmn46]*rate_eval.Mn46__p_V45__weak__wc12  +
          -rho*Y[jhe4]*Y[jv45]*rate_eval.He4_V45__p_Cr48  +
          +rho*Y[jn]*Y[jcr45]*rate_eval.n_Cr45__p_V45  +
          +rho*Y[jn]*Y[jv44]*rate_eval.n_V44__V45  +
          -rho*Y[jn]*Y[jv45]*rate_eval.n_V45__p_Ti45  +
          +Y[jcr45]*rate_eval.Cr45__V45__weak__wc12
       )

    dYdt[jv46] = (
          -rho*Y[jhe4]*Y[jv46]*rate_eval.He4_V46__p_Cr49  +
          -rho*Y[jn]*Y[jv46]*rate_eval.n_V46__He4_Sc43  +
          -rho*Y[jn]*Y[jv46]*rate_eval.n_V46__p_Ti46  +
          +rho*Y[jhe4]*Y[jti43]*rate_eval.He4_Ti43__p_V46  +
          +rho*Y[jn]*Y[jcr46]*rate_eval.n_Cr46__p_V46  +
          +rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__He4_V46  +
          -rho*Y[jhe4]*Y[jv46]*rate_eval.He4_V46__Mn50  +
          -rho*Y[jp]*Y[jv46]*rate_eval.p_V46__Cr47  +
          -rho*Y[jn]*Y[jv46]*rate_eval.n_V46__V47  +
          +rho*Y[jn]*Y[jv45]*rate_eval.n_V45__V46  +
          +rho*Y[jhe4]*Y[jsc42]*rate_eval.He4_Sc42__V46  +
          -Y[jv46]*rate_eval.V46__Ti46__weak__wc12  +
          +rho*Y[jp]*Y[jti45]*rate_eval.p_Ti45__V46  +
          +Y[jcr46]*rate_eval.Cr46__V46__weak__wc12
       )

    dYdt[jv47] = (
          +rho*Y[jn]*Y[jmn50]*rate_eval.n_Mn50__He4_V47  +
          -rho*Y[jhe4]*Y[jv47]*rate_eval.He4_V47__p_Cr50  +
          +rho*Y[jhe4]*Y[jsc43]*rate_eval.He4_Sc43__V47  +
          -rho*Y[jn]*Y[jv47]*rate_eval.n_V47__He4_Sc44  +
          +rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__p_V47  +
          +Y[jcr47]*rate_eval.Cr47__V47__weak__wc12  +
          -rho*Y[jhe4]*Y[jv47]*rate_eval.He4_V47__Mn51  +
          -rho*Y[jn]*Y[jv47]*rate_eval.n_V47__V48  +
          +rho*Y[jn]*Y[jv46]*rate_eval.n_V46__V47  +
          -rho*Y[jn]*Y[jv47]*rate_eval.n_V47__p_Ti47  +
          -Y[jv47]*rate_eval.V47__Ti47__weak__wc12  +
          +rho*Y[jp]*Y[jti46]*rate_eval.p_Ti46__V47  +
          -rho*Y[jp]*Y[jv47]*rate_eval.p_V47__Cr48  +
          +Y[jmn48]*rate_eval.Mn48__p_V47__weak__wc12  +
          +rho*Y[jhe4]*Y[jti44]*rate_eval.He4_Ti44__p_V47
       )

    dYdt[jv48] = (
          +rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__p_V48  +
          +rho*Y[jhe4]*Y[jti45]*rate_eval.He4_Ti45__p_V48  +
          +rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__He4_V48  +
          -rho*Y[jn]*Y[jv48]*rate_eval.n_V48__p_Ti48  +
          +rho*Y[jhe4]*Y[jsc44]*rate_eval.He4_Sc44__V48  +
          -rho*Y[jp]*Y[jv48]*rate_eval.p_V48__Cr49  +
          -rho*Y[jn]*Y[jv48]*rate_eval.n_V48__V49  +
          +rho*Y[jn]*Y[jv47]*rate_eval.n_V47__V48  +
          +rho*Y[jp]*Y[jti47]*rate_eval.p_Ti47__V48  +
          -rho*Y[jhe4]*Y[jv48]*rate_eval.He4_V48__p_Cr51  +
          -rho*Y[jn]*Y[jv48]*rate_eval.n_V48__He4_Sc45  +
          -rho*Y[jhe4]*Y[jv48]*rate_eval.He4_V48__Mn52  +
          +Y[jcr48]*rate_eval.Cr48__V48__weak__wc12  +
          -Y[jv48]*rate_eval.V48__Ti48__weak__wc12
       )

    dYdt[jv49] = (
          +rho*Y[jn]*Y[jmn52]*rate_eval.n_Mn52__He4_V49  +
          +rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__p_V49  +
          -rho*Y[jp]*Y[jv49]*rate_eval.p_V49__He4_Ti46  +
          -rho*Y[jhe4]*Y[jv49]*rate_eval.He4_V49__Mn53  +
          -rho*Y[jn]*Y[jv49]*rate_eval.n_V49__p_Ti49  +
          -rho*Y[jp]*Y[jv49]*rate_eval.p_V49__Cr50  +
          -rho*Y[jhe4]*Y[jv49]*rate_eval.He4_V49__p_Cr52  +
          -rho*Y[jn]*Y[jv49]*rate_eval.n_V49__V50  +
          +rho*Y[jn]*Y[jv48]*rate_eval.n_V48__V49  +
          +rho*Y[jhe4]*Y[jsc45]*rate_eval.He4_Sc45__V49  +
          +rho*Y[jp]*Y[jti48]*rate_eval.p_Ti48__V49  +
          +rho*Y[jhe4]*Y[jsc46]*rate_eval.He4_Sc46__n_V49  +
          +Y[jcr49]*rate_eval.Cr49__V49__weak__wc12  +
          -Y[jv49]*rate_eval.V49__Ti49__weak__wc12
       )

    dYdt[jv50] = (
          -rho*Y[jhe4]*Y[jv50]*rate_eval.He4_V50__p_Cr53  +
          -rho*Y[jp]*Y[jv50]*rate_eval.p_V50__He4_Ti47  +
          -rho*Y[jp]*Y[jv50]*rate_eval.p_V50__n_Cr50  +
          -rho*Y[jn]*Y[jv50]*rate_eval.n_V50__p_Ti50  +
          +rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__He4_V50  +
          -rho*Y[jn]*Y[jv50]*rate_eval.n_V50__He4_Sc47  +
          -rho*Y[jhe4]*Y[jv50]*rate_eval.He4_V50__Mn54  +
          -rho*Y[jp]*Y[jv50]*rate_eval.p_V50__Cr51  +
          +rho*Y[jn]*Y[jv49]*rate_eval.n_V49__V50  +
          +rho*Y[jp]*Y[jti49]*rate_eval.p_Ti49__V50  +
          -rho*Y[jn]*Y[jv50]*rate_eval.n_V50__V51  +
          -Y[jv50]*rate_eval.V50__Ti50__weak__mo03  +
          +rho*Y[jhe4]*Y[jsc46]*rate_eval.He4_Sc46__V50
       )

    dYdt[jv51] = (
          +rho*Y[jp]*Y[jcr54]*rate_eval.p_Cr54__He4_V51  +
          -rho*Y[jp]*Y[jv51]*rate_eval.p_V51__He4_Ti48  +
          +rho*Y[jp]*Y[jti51]*rate_eval.p_Ti51__n_V51  +
          +rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__He4_V51  +
          -rho*Y[jhe4]*Y[jv51]*rate_eval.He4_V51__Mn55  +
          +rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__n_V51  +
          -rho*Y[jn]*Y[jv51]*rate_eval.n_V51__V52  +
          +rho*Y[jhe4]*Y[jsc47]*rate_eval.He4_Sc47__V51  +
          +Y[jti51]*rate_eval.Ti51__V51__weak__wc12  +
          +rho*Y[jn]*Y[jv50]*rate_eval.n_V50__V51  +
          +rho*Y[jp]*Y[jti50]*rate_eval.p_Ti50__V51  +
          -rho*Y[jp]*Y[jv51]*rate_eval.p_V51__Cr52  +
          +rho*Y[jn]*Y[jcr51]*rate_eval.n_Cr51__p_V51  +
          +Y[jcr51]*rate_eval.Cr51__V51__weak__wc12
       )

    dYdt[jv52] = (
          -rho*Y[jp]*Y[jv52]*rate_eval.p_V52__He4_Ti49  +
          -rho*Y[jp]*Y[jv52]*rate_eval.p_V52__n_Cr52  +
          +rho*Y[jp]*Y[jti52]*rate_eval.p_Ti52__n_V52  +
          +rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__He4_V52  +
          +rho*Y[jhe4]*Y[jsc48]*rate_eval.He4_Sc48__V52  +
          -rho*Y[jhe4]*Y[jv52]*rate_eval.He4_V52__Mn56  +
          -rho*Y[jp]*Y[jv52]*rate_eval.p_V52__Cr53  +
          +rho*Y[jn]*Y[jv51]*rate_eval.n_V51__V52  +
          +rho*Y[jp]*Y[jti51]*rate_eval.p_Ti51__V52  +
          -Y[jv52]*rate_eval.V52__Cr52__weak__wc12  +
          -rho*Y[jhe4]*Y[jv52]*rate_eval.He4_V52__n_Mn55  +
          -rho*Y[jn]*Y[jv52]*rate_eval.n_V52__V53  +
          -rho*Y[jn]*Y[jv52]*rate_eval.n_V52__He4_Sc49  +
          +Y[jti52]*rate_eval.Ti52__V52__weak__wc12
       )

    dYdt[jv53] = (
          -rho*Y[jp]*Y[jv53]*rate_eval.p_V53__n_Cr53  +
          +rho*Y[jp]*Y[jcr56]*rate_eval.p_Cr56__He4_V53  +
          +rho*Y[jp]*Y[jti53]*rate_eval.p_Ti53__n_V53  +
          -rho*Y[jp]*Y[jv53]*rate_eval.p_V53__He4_Ti50  +
          -rho*Y[jhe4]*Y[jv53]*rate_eval.He4_V53__Mn57  +
          -rho*Y[jp]*Y[jv53]*rate_eval.p_V53__Cr54  +
          -rho*Y[jn]*Y[jv53]*rate_eval.n_V53__V54  +
          +rho*Y[jp]*Y[jti52]*rate_eval.p_Ti52__V53  +
          +rho*Y[jhe4]*Y[jsc49]*rate_eval.He4_Sc49__V53  +
          +rho*Y[jn]*Y[jv52]*rate_eval.n_V52__V53  +
          +Y[jti53]*rate_eval.Ti53__V53__weak__wc12  +
          +rho*Y[jn]*Y[jmn56]*rate_eval.n_Mn56__He4_V53  +
          -Y[jv53]*rate_eval.V53__Cr53__weak__wc12  +
          +rho*Y[jhe4]*Y[jsc50]*rate_eval.He4_Sc50__n_V53
       )

    dYdt[jv54] = (
          -rho*Y[jhe4]*Y[jv54]*rate_eval.He4_V54__n_Mn57  +
          +rho*Y[jp]*Y[jcr57]*rate_eval.p_Cr57__He4_V54  +
          +rho*Y[jp]*Y[jti54]*rate_eval.p_Ti54__n_V54  +
          +rho*Y[jhe4]*Y[jsc51]*rate_eval.He4_Sc51__n_V54  +
          -rho*Y[jp]*Y[jv54]*rate_eval.p_V54__n_Cr54  +
          -rho*Y[jhe4]*Y[jv54]*rate_eval.He4_V54__Mn58  +
          -rho*Y[jp]*Y[jv54]*rate_eval.p_V54__Cr55  +
          +rho*Y[jn]*Y[jv53]*rate_eval.n_V53__V54  +
          +rho*Y[jp]*Y[jti53]*rate_eval.p_Ti53__V54  +
          -Y[jv54]*rate_eval.V54__Cr54__weak__wc12  +
          -rho*Y[jn]*Y[jv54]*rate_eval.n_V54__V55  +
          +Y[jti54]*rate_eval.Ti54__V54__weak__wc12  +
          -rho*Y[jp]*Y[jv54]*rate_eval.p_V54__He4_Ti51  +
          +rho*Y[jhe4]*Y[jsc50]*rate_eval.He4_Sc50__V54
       )

    dYdt[jv55] = (
          -rho*Y[jhe4]*Y[jv55]*rate_eval.He4_V55__n_Mn58  +
          -rho*Y[jp]*Y[jv55]*rate_eval.p_V55__n_Cr55  +
          +rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__n_V55  +
          +rho*Y[jhe4]*Y[jsc52]*rate_eval.He4_Sc52__n_V55  +
          -rho*Y[jp]*Y[jv55]*rate_eval.p_V55__Cr56  +
          -rho*Y[jn]*Y[jv55]*rate_eval.n_V55__V56  +
          +rho*Y[jp]*Y[jti54]*rate_eval.p_Ti54__V55  +
          -Y[jv55]*rate_eval.V55__Cr55__weak__wc12  +
          -rho*Y[jhe4]*Y[jv55]*rate_eval.He4_V55__Mn59  +
          +rho*Y[jn]*Y[jv54]*rate_eval.n_V54__V55  +
          -rho*Y[jp]*Y[jv55]*rate_eval.p_V55__He4_Ti52  +
          +rho*Y[jhe4]*Y[jsc51]*rate_eval.He4_Sc51__V55  +
          +rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__He4_V55  +
          +Y[jti55]*rate_eval.Ti55__V55__weak__wc12
       )

    dYdt[jv56] = (
          -rho*Y[jhe4]*Y[jv56]*rate_eval.He4_V56__n_Mn59  +
          -rho*Y[jn]*Y[jv56]*rate_eval.n_V56__V57  +
          -rho*Y[jp]*Y[jv56]*rate_eval.p_V56__He4_Ti53  +
          -rho*Y[jp]*Y[jv56]*rate_eval.p_V56__Cr57  +
          -rho*Y[jhe4]*Y[jv56]*rate_eval.He4_V56__Mn60  +
          +rho*Y[jn]*Y[jv55]*rate_eval.n_V55__V56  +
          +rho*Y[jp]*Y[jti55]*rate_eval.p_Ti55__V56  +
          -rho*Y[jp]*Y[jv56]*rate_eval.p_V56__n_Cr56  +
          +Y[jti56]*rate_eval.Ti56__V56__weak__wc12  +
          +rho*Y[jhe4]*Y[jsc52]*rate_eval.He4_Sc52__V56  +
          +rho*Y[jhe4]*Y[jsc53]*rate_eval.He4_Sc53__n_V56  +
          +rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__He4_V56  +
          +rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__n_V56  +
          -Y[jv56]*rate_eval.V56__Cr56__weak__wc12
       )

    dYdt[jv57] = (
          +rho*Y[jp]*Y[jcr60]*rate_eval.p_Cr60__He4_V57  +
          -rho*Y[jp]*Y[jv57]*rate_eval.p_V57__He4_Ti54  +
          -rho*Y[jp]*Y[jv57]*rate_eval.p_V57__n_Cr57  +
          +rho*Y[jhe4]*Y[jsc54]*rate_eval.He4_Sc54__n_V57  +
          +rho*Y[jn]*Y[jv56]*rate_eval.n_V56__V57  +
          -rho*Y[jhe4]*Y[jv57]*rate_eval.He4_V57__n_Mn60  +
          +rho*Y[jp]*Y[jti57]*rate_eval.p_Ti57__n_V57  +
          -rho*Y[jhe4]*Y[jv57]*rate_eval.He4_V57__Mn61  +
          -rho*Y[jp]*Y[jv57]*rate_eval.p_V57__Cr58  +
          +rho*Y[jp]*Y[jti56]*rate_eval.p_Ti56__V57  +
          +Y[jti57]*rate_eval.Ti57__V57__weak__wc12  +
          +Y[jti58]*rate_eval.Ti58__n_V57__weak__mp17  +
          +rho*Y[jhe4]*Y[jsc53]*rate_eval.He4_Sc53__V57  +
          -rho*Y[jn]*Y[jv57]*rate_eval.n_V57__V58  +
          -Y[jv57]*rate_eval.V57__Cr57__weak__wc12
       )

    dYdt[jv58] = (
          -rho*Y[jhe4]*Y[jv58]*rate_eval.He4_V58__n_Mn61  +
          -rho*Y[jp]*Y[jv58]*rate_eval.p_V58__He4_Ti55  +
          -rho*Y[jp]*Y[jv58]*rate_eval.p_V58__n_Cr58  +
          -rho*Y[jhe4]*Y[jv58]*rate_eval.He4_V58__Mn62  +
          +rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__n_V58  +
          +rho*Y[jhe4]*Y[jsc55]*rate_eval.He4_Sc55__n_V58  +
          +rho*Y[jhe4]*Y[jsc54]*rate_eval.He4_Sc54__V58  +
          +rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__He4_V58  +
          -rho*Y[jp]*Y[jv58]*rate_eval.p_V58__Cr59  +
          +rho*Y[jp]*Y[jti57]*rate_eval.p_Ti57__V58  +
          +Y[jti58]*rate_eval.Ti58__V58__weak__wc12  +
          -Y[jv58]*rate_eval.V58__n_Cr57__weak__mp17  +
          +rho*Y[jn]*Y[jv57]*rate_eval.n_V57__V58  +
          -Y[jv58]*rate_eval.V58__Cr58__weak__wc17  +
          -rho*Y[jn]*Y[jv58]*rate_eval.n_V58__V59
       )

    dYdt[jv59] = (
          +rho*Y[jp]*Y[jcr62]*rate_eval.p_Cr62__He4_V59  +
          -rho*Y[jhe4]*Y[jv59]*rate_eval.He4_V59__n_Mn62  +
          +rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__n_V59  +
          +rho*Y[jhe4]*Y[jsc56]*rate_eval.He4_Sc56__n_V59  +
          -rho*Y[jp]*Y[jv59]*rate_eval.p_V59__n_Cr59  +
          -rho*Y[jp]*Y[jv59]*rate_eval.p_V59__Cr60  +
          -rho*Y[jn]*Y[jv59]*rate_eval.n_V59__V60  +
          +rho*Y[jp]*Y[jti58]*rate_eval.p_Ti58__V59  +
          +rho*Y[jhe4]*Y[jsc55]*rate_eval.He4_Sc55__V59  +
          +Y[jti60]*rate_eval.Ti60__n_V59__weak__mp17  +
          -rho*Y[jhe4]*Y[jv59]*rate_eval.He4_V59__Mn63  +
          -Y[jv59]*rate_eval.V59__n_Cr58__weak__wc12  +
          +Y[jti59]*rate_eval.Ti59__V59__weak__wc12  +
          +rho*Y[jn]*Y[jv58]*rate_eval.n_V58__V59  +
          -Y[jv59]*rate_eval.V59__Cr59__weak__wc12  +
          -rho*Y[jp]*Y[jv59]*rate_eval.p_V59__He4_Ti56
       )

    dYdt[jv60] = (
          -rho*Y[jp]*Y[jv60]*rate_eval.p_V60__He4_Ti57  +
          -rho*Y[jp]*Y[jv60]*rate_eval.p_V60__n_Cr60  +
          +rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__n_V60  +
          +rho*Y[jhe4]*Y[jsc57]*rate_eval.He4_Sc57__n_V60  +
          +rho*Y[jp]*Y[jti59]*rate_eval.p_Ti59__V60  +
          -rho*Y[jhe4]*Y[jv60]*rate_eval.He4_V60__n_Mn63  +
          -rho*Y[jhe4]*Y[jv60]*rate_eval.He4_V60__Mn64  +
          -rho*Y[jp]*Y[jv60]*rate_eval.p_V60__Cr61  +
          +rho*Y[jn]*Y[jv59]*rate_eval.n_V59__V60  +
          +rho*Y[jhe4]*Y[jsc56]*rate_eval.He4_Sc56__V60  +
          -Y[jv60]*rate_eval.V60__Cr60__weak__wc17  +
          -Y[jv60]*rate_eval.V60__n_Cr59__weak__mp17  +
          +Y[jti61]*rate_eval.Ti61__n_V60__weak__mp17  +
          +rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__He4_V60  +
          -rho*Y[jn]*Y[jv60]*rate_eval.n_V60__V61  +
          +Y[jti60]*rate_eval.Ti60__V60__weak__wc17
       )

    dYdt[jv61] = (
          -rho*Y[jhe4]*Y[jv61]*rate_eval.He4_V61__n_Mn64  +
          -rho*Y[jp]*Y[jv61]*rate_eval.p_V61__n_Cr61  +
          +rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__n_V61  +
          +rho*Y[jhe4]*Y[jsc58]*rate_eval.He4_Sc58__n_V61  +
          -rho*Y[jp]*Y[jv61]*rate_eval.p_V61__He4_Ti58  +
          +rho*Y[jhe4]*Y[jsc57]*rate_eval.He4_Sc57__V61  +
          -rho*Y[jhe4]*Y[jv61]*rate_eval.He4_V61__Mn65  +
          +rho*Y[jp]*Y[jti60]*rate_eval.p_Ti60__V61  +
          -rho*Y[jn]*Y[jv61]*rate_eval.n_V61__V62  +
          -Y[jv61]*rate_eval.V61__n_Cr60__weak__wc12  +
          +Y[jti61]*rate_eval.Ti61__V61__weak__wc17  +
          -rho*Y[jp]*Y[jv61]*rate_eval.p_V61__Cr62  +
          +rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__He4_V61  +
          +Y[jti62]*rate_eval.Ti62__n_V61__weak__mp17  +
          -Y[jv61]*rate_eval.V61__Cr61__weak__wc12  +
          +Y[jti64]*rate_eval.Ti64__n_n_n_V61__weak__mo03  +
          +Y[jti63]*rate_eval.Ti63__n_n_V61__weak__mp17  +
          +rho*Y[jn]*Y[jv60]*rate_eval.n_V60__V61
       )

    dYdt[jv62] = (
          +Y[jti65]*rate_eval.Ti65__n_n_n_V62__weak__mo03  +
          +rho*Y[jp]*Y[jcr65]*rate_eval.p_Cr65__He4_V62  +
          -rho*Y[jhe4]*Y[jv62]*rate_eval.He4_V62__n_Mn65  +
          +rho*Y[jhe4]*Y[jsc59]*rate_eval.He4_Sc59__n_V62  +
          +rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__n_V62  +
          -rho*Y[jn]*Y[jv62]*rate_eval.n_V62__V63  +
          -rho*Y[jp]*Y[jv62]*rate_eval.p_V62__n_Cr62  +
          +rho*Y[jp]*Y[jti61]*rate_eval.p_Ti61__V62  +
          +rho*Y[jhe4]*Y[jsc58]*rate_eval.He4_Sc58__V62  +
          -Y[jv62]*rate_eval.V62__n_Cr61__weak__mp17  +
          +rho*Y[jn]*Y[jv61]*rate_eval.n_V61__V62  +
          +Y[jti64]*rate_eval.Ti64__n_n_V62__weak__mp17  +
          +Y[jti63]*rate_eval.Ti63__n_V62__weak__mp17  +
          -Y[jv62]*rate_eval.V62__Cr62__weak__wc17  +
          +Y[jti62]*rate_eval.Ti62__V62__weak__mo03  +
          -rho*Y[jp]*Y[jv62]*rate_eval.p_V62__He4_Ti59  +
          -rho*Y[jhe4]*Y[jv62]*rate_eval.He4_V62__Mn66  +
          -rho*Y[jp]*Y[jv62]*rate_eval.p_V62__Cr63
       )

    dYdt[jv63] = (
          +rho*Y[jhe4]*Y[jsc59]*rate_eval.He4_Sc59__V63  +
          +rho*Y[jp]*Y[jcr66]*rate_eval.p_Cr66__He4_V63  +
          -rho*Y[jp]*Y[jv63]*rate_eval.p_V63__n_Cr63  +
          -rho*Y[jhe4]*Y[jv63]*rate_eval.He4_V63__Mn67  +
          +rho*Y[jp]*Y[jti63]*rate_eval.p_Ti63__n_V63  +
          +rho*Y[jhe4]*Y[jsc60]*rate_eval.He4_Sc60__n_V63  +
          -rho*Y[jhe4]*Y[jv63]*rate_eval.He4_V63__n_Mn66  +
          -rho*Y[jp]*Y[jv63]*rate_eval.p_V63__He4_Ti60  +
          -rho*Y[jp]*Y[jv63]*rate_eval.p_V63__Cr64  +
          +rho*Y[jn]*Y[jv62]*rate_eval.n_V62__V63  +
          +rho*Y[jp]*Y[jti62]*rate_eval.p_Ti62__V63  +
          +Y[jti65]*rate_eval.Ti65__n_n_V63__weak__mp17  +
          -Y[jv63]*rate_eval.V63__n_Cr62__weak__wc12  +
          +Y[jti64]*rate_eval.Ti64__n_V63__weak__mp17  +
          +Y[jti63]*rate_eval.Ti63__V63__weak__mo03  +
          -rho*Y[jn]*Y[jv63]*rate_eval.n_V63__V64  +
          -Y[jv63]*rate_eval.V63__Cr63__weak__wc12
       )

    dYdt[jv64] = (
          -rho*Y[jhe4]*Y[jv64]*rate_eval.He4_V64__n_Mn67  +
          -rho*Y[jp]*Y[jv64]*rate_eval.p_V64__He4_Ti61  +
          +Y[jti65]*rate_eval.Ti65__n_V64__weak__mp17  +
          +rho*Y[jhe4]*Y[jsc61]*rate_eval.He4_Sc61__n_V64  +
          -Y[jv64]*rate_eval.V64__n_n_Cr62__weak__mp17  +
          -rho*Y[jp]*Y[jv64]*rate_eval.p_V64__n_Cr64  +
          +rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__He4_V64  +
          -rho*Y[jhe4]*Y[jv64]*rate_eval.He4_V64__Mn68  +
          -rho*Y[jp]*Y[jv64]*rate_eval.p_V64__Cr65  +
          +rho*Y[jp]*Y[jti63]*rate_eval.p_Ti63__V64  +
          +rho*Y[jhe4]*Y[jsc60]*rate_eval.He4_Sc60__V64  +
          +rho*Y[jp]*Y[jti64]*rate_eval.p_Ti64__n_V64  +
          -rho*Y[jn]*Y[jv64]*rate_eval.n_V64__V65  +
          +rho*Y[jn]*Y[jv63]*rate_eval.n_V63__V64  +
          +Y[jti64]*rate_eval.Ti64__V64__weak__mo03  +
          -Y[jv64]*rate_eval.V64__n_Cr63__weak__mp17  +
          -Y[jv64]*rate_eval.V64__Cr64__weak__wc17
       )

    dYdt[jv65] = (
          -Y[jv65]*rate_eval.V65__n_n_n_Cr62__weak__mo03  +
          +rho*Y[jp]*Y[jcr68]*rate_eval.p_Cr68__He4_V65  +
          -rho*Y[jp]*Y[jv65]*rate_eval.p_V65__He4_Ti62  +
          +rho*Y[jhe4]*Y[jsc62]*rate_eval.He4_Sc62__n_V65  +
          -rho*Y[jp]*Y[jv65]*rate_eval.p_V65__Cr66  +
          -rho*Y[jhe4]*Y[jv65]*rate_eval.He4_V65__Mn69  +
          -Y[jv65]*rate_eval.V65__Cr65__weak__mo03  +
          +rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__n_V65  +
          -Y[jv65]*rate_eval.V65__n_Cr64__weak__mp17  +
          -rho*Y[jhe4]*Y[jv65]*rate_eval.He4_V65__n_Mn68  +
          -Y[jv65]*rate_eval.V65__n_n_Cr63__weak__mp17  +
          +rho*Y[jn]*Y[jv64]*rate_eval.n_V64__V65  +
          -rho*Y[jn]*Y[jv65]*rate_eval.n_V65__V66  +
          -rho*Y[jp]*Y[jv65]*rate_eval.p_V65__n_Cr65  +
          +rho*Y[jp]*Y[jti64]*rate_eval.p_Ti64__V65  +
          +rho*Y[jhe4]*Y[jsc61]*rate_eval.He4_Sc61__V65  +
          +Y[jti65]*rate_eval.Ti65__V65__weak__mo03
       )

    dYdt[jv66] = (
          -Y[jv66]*rate_eval.V66__n_n_n_Cr63__weak__mo03  +
          -rho*Y[jhe4]*Y[jv66]*rate_eval.He4_V66__n_Mn69  +
          -rho*Y[jp]*Y[jv66]*rate_eval.p_V66__n_Cr66  +
          +rho*Y[jhe4]*Y[jsc63]*rate_eval.He4_Sc63__n_V66  +
          +rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__He4_V66  +
          +rho*Y[jhe4]*Y[jsc62]*rate_eval.He4_Sc62__V66  +
          -rho*Y[jhe4]*Y[jv66]*rate_eval.He4_V66__Mn70  +
          -rho*Y[jp]*Y[jv66]*rate_eval.p_V66__Cr67  +
          +rho*Y[jp]*Y[jti65]*rate_eval.p_Ti65__V66  +
          -Y[jv66]*rate_eval.V66__Cr66__weak__mo03  +
          +rho*Y[jn]*Y[jv65]*rate_eval.n_V65__V66  +
          -Y[jv66]*rate_eval.V66__n_Cr65__weak__mp17  +
          -rho*Y[jn]*Y[jv66]*rate_eval.n_V66__V67  +
          -Y[jv66]*rate_eval.V66__n_n_Cr64__weak__mp17  +
          -rho*Y[jp]*Y[jv66]*rate_eval.p_V66__He4_Ti63
       )

    dYdt[jv67] = (
          -rho*Y[jhe4]*Y[jv67]*rate_eval.He4_V67__n_Mn70  +
          -rho*Y[jp]*Y[jv67]*rate_eval.p_V67__n_Cr67  +
          -Y[jv67]*rate_eval.V67__n_n_n_Cr64__weak__mo03  +
          -rho*Y[jp]*Y[jv67]*rate_eval.p_V67__He4_Ti64  +
          -rho*Y[jhe4]*Y[jv67]*rate_eval.He4_V67__Mn71  +
          -rho*Y[jp]*Y[jv67]*rate_eval.p_V67__Cr68  +
          +rho*Y[jn]*Y[jv66]*rate_eval.n_V66__V67  +
          -Y[jv67]*rate_eval.V67__Cr67__weak__mo03  +
          +rho*Y[jhe4]*Y[jsc63]*rate_eval.He4_Sc63__V67  +
          -Y[jv67]*rate_eval.V67__n_Cr66__weak__mp17  +
          -Y[jv67]*rate_eval.V67__n_n_Cr65__weak__mp17  +
          +rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__He4_V67
       )

    dYdt[jcr41] = (
          -rho*Y[jn]*Y[jcr41]*rate_eval.n_Cr41__He4_Ti38  +
          -rho*Y[jn]*Y[jcr41]*rate_eval.n_Cr41__Cr42  +
          -rho*Y[jhe4]*Y[jcr41]*rate_eval.He4_Cr41__p_Mn44  +
          -rho*Y[jhe4]*Y[jcr41]*rate_eval.He4_Cr41__Fe45  +
          -rho*Y[jn]*Y[jcr41]*rate_eval.n_Cr41__p_V41  +
          +rho*Y[jhe4]*Y[jti37]*rate_eval.He4_Ti37__Cr41  +
          -Y[jcr41]*rate_eval.Cr41__V41__weak__bqa_pos_  +
          +rho*Y[jp]*Y[jv40]*rate_eval.p_V40__Cr41
       )

    dYdt[jcr42] = (
          -rho*Y[jhe4]*Y[jcr42]*rate_eval.He4_Cr42__p_Mn45  +
          -rho*Y[jn]*Y[jcr42]*rate_eval.n_Cr42__He4_Ti39  +
          -rho*Y[jn]*Y[jcr42]*rate_eval.n_Cr42__p_V42  +
          +rho*Y[jhe4]*Y[jv39]*rate_eval.He4_V39__p_Cr42  +
          +rho*Y[jn]*Y[jcr41]*rate_eval.n_Cr41__Cr42  +
          -rho*Y[jhe4]*Y[jcr42]*rate_eval.He4_Cr42__Fe46  +
          +rho*Y[jp]*Y[jv41]*rate_eval.p_V41__Cr42  +
          +rho*Y[jhe4]*Y[jti38]*rate_eval.He4_Ti38__Cr42  +
          -rho*Y[jn]*Y[jcr42]*rate_eval.n_Cr42__Cr43  +
          -Y[jcr42]*rate_eval.Cr42__p_Ti41__weak__wc12  +
          -Y[jcr42]*rate_eval.Cr42__V42__weak__wc12  +
          +rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__He4_Cr42  +
          -rho*Y[jp]*Y[jcr42]*rate_eval.p_Cr42__Mn43
       )

    dYdt[jcr43] = (
          -Y[jcr43]*rate_eval.Cr43__p_p_p_Ca40__weak__wc12  +
          +rho*Y[jn]*Y[jfe46]*rate_eval.n_Fe46__He4_Cr43  +
          -Y[jcr43]*rate_eval.Cr43__p_p_Sc41__weak__wc12  +
          -rho*Y[jhe4]*Y[jcr43]*rate_eval.He4_Cr43__p_Mn46  +
          -rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__p_V43  +
          +Y[jmn43]*rate_eval.Mn43__Cr43__weak__bqa_pos_  +
          -rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__He4_Ti40  +
          +rho*Y[jhe4]*Y[jv40]*rate_eval.He4_V40__p_Cr43  +
          +rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__p_Cr43  +
          +rho*Y[jp]*Y[jv42]*rate_eval.p_V42__Cr43  +
          -rho*Y[jhe4]*Y[jcr43]*rate_eval.He4_Cr43__Fe47  +
          -rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__Cr44  +
          +rho*Y[jn]*Y[jcr42]*rate_eval.n_Cr42__Cr43  +
          -Y[jcr43]*rate_eval.Cr43__p_Ti42__weak__wc17  +
          -Y[jcr43]*rate_eval.Cr43__V43__weak__wc12  +
          +rho*Y[jhe4]*Y[jti39]*rate_eval.He4_Ti39__Cr43  +
          -rho*Y[jp]*Y[jcr43]*rate_eval.p_Cr43__Mn44
       )

    dYdt[jcr44] = (
          +rho*Y[jn]*Y[jfe47]*rate_eval.n_Fe47__He4_Cr44  +
          -rho*Y[jhe4]*Y[jcr44]*rate_eval.He4_Cr44__p_Mn47  +
          -rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__He4_Ti41  +
          -Y[jcr44]*rate_eval.Cr44__V44__weak__wc12  +
          -rho*Y[jhe4]*Y[jcr44]*rate_eval.He4_Cr44__Fe48  +
          -rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__Cr45  +
          +rho*Y[jn]*Y[jcr43]*rate_eval.n_Cr43__Cr44  +
          +rho*Y[jp]*Y[jv43]*rate_eval.p_V43__Cr44  +
          +rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__p_Cr44  +
          +rho*Y[jhe4]*Y[jti40]*rate_eval.He4_Ti40__Cr44  +
          +Y[jfe45]*rate_eval.Fe45__p_Cr44__weak__wc17  +
          +Y[jmn44]*rate_eval.Mn44__Cr44__weak__bqa_pos_  +
          -rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__p_V44  +
          -Y[jcr44]*rate_eval.Cr44__p_Ti43__weak__wc12  +
          +rho*Y[jhe4]*Y[jv41]*rate_eval.He4_V41__p_Cr44  +
          -rho*Y[jp]*Y[jcr44]*rate_eval.p_Cr44__Mn45
       )

    dYdt[jcr45] = (
          +rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__p_Cr45  +
          -rho*Y[jhe4]*Y[jcr45]*rate_eval.He4_Cr45__p_Mn48  +
          -rho*Y[jn]*Y[jcr45]*rate_eval.n_Cr45__He4_Ti42  +
          +rho*Y[jhe4]*Y[jv42]*rate_eval.He4_V42__p_Cr45  +
          -rho*Y[jhe4]*Y[jcr45]*rate_eval.He4_Cr45__Fe49  +
          +rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__He4_Cr45  +
          -rho*Y[jn]*Y[jcr45]*rate_eval.n_Cr45__Cr46  +
          +rho*Y[jn]*Y[jcr44]*rate_eval.n_Cr44__Cr45  +
          +rho*Y[jhe4]*Y[jti41]*rate_eval.He4_Ti41__Cr45  +
          -rho*Y[jp]*Y[jcr45]*rate_eval.p_Cr45__Mn46  +
          +Y[jfe46]*rate_eval.Fe46__p_Cr45__weak__wc12  +
          +rho*Y[jp]*Y[jv44]*rate_eval.p_V44__Cr45  +
          -Y[jcr45]*rate_eval.Cr45__p_Ti44__weak__wc12  +
          -rho*Y[jn]*Y[jcr45]*rate_eval.n_Cr45__p_V45  +
          -Y[jcr45]*rate_eval.Cr45__V45__weak__wc12  +
          +Y[jmn45]*rate_eval.Mn45__Cr45__weak__bqa_pos_
       )

    dYdt[jcr46] = (
          +rho*Y[jn]*Y[jfe49]*rate_eval.n_Fe49__He4_Cr46  +
          +rho*Y[jn]*Y[jmn46]*rate_eval.n_Mn46__p_Cr46  +
          -rho*Y[jn]*Y[jcr46]*rate_eval.n_Cr46__He4_Ti43  +
          +rho*Y[jhe4]*Y[jv43]*rate_eval.He4_V43__p_Cr46  +
          -rho*Y[jn]*Y[jcr46]*rate_eval.n_Cr46__p_V46  +
          -rho*Y[jhe4]*Y[jcr46]*rate_eval.He4_Cr46__p_Mn49  +
          -rho*Y[jhe4]*Y[jcr46]*rate_eval.He4_Cr46__Fe50  +
          -rho*Y[jp]*Y[jcr46]*rate_eval.p_Cr46__Mn47  +
          -rho*Y[jn]*Y[jcr46]*rate_eval.n_Cr46__Cr47  +
          +rho*Y[jn]*Y[jcr45]*rate_eval.n_Cr45__Cr46  +
          +rho*Y[jhe4]*Y[jti42]*rate_eval.He4_Ti42__Cr46  +
          +rho*Y[jp]*Y[jv45]*rate_eval.p_V45__Cr46  +
          +Y[jfe47]*rate_eval.Fe47__p_Cr46__weak__wc12  +
          +Y[jmn46]*rate_eval.Mn46__Cr46__weak__wc12  +
          -Y[jcr46]*rate_eval.Cr46__V46__weak__wc12
       )

    dYdt[jcr47] = (
          +rho*Y[jn]*Y[jfe50]*rate_eval.n_Fe50__He4_Cr47  +
          +rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__p_Cr47  +
          -rho*Y[jhe4]*Y[jcr47]*rate_eval.He4_Cr47__p_Mn50  +
          -rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__He4_Ti44  +
          -rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__p_V47  +
          -Y[jcr47]*rate_eval.Cr47__V47__weak__wc12  +
          -rho*Y[jhe4]*Y[jcr47]*rate_eval.He4_Cr47__Fe51  +
          +rho*Y[jn]*Y[jcr46]*rate_eval.n_Cr46__Cr47  +
          +rho*Y[jp]*Y[jv46]*rate_eval.p_V46__Cr47  +
          +rho*Y[jhe4]*Y[jti43]*rate_eval.He4_Ti43__Cr47  +
          -rho*Y[jp]*Y[jcr47]*rate_eval.p_Cr47__Mn48  +
          +rho*Y[jhe4]*Y[jv44]*rate_eval.He4_V44__p_Cr47  +
          +Y[jfe48]*rate_eval.Fe48__p_Cr47__weak__wc12  +
          -rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__Cr48  +
          +Y[jmn47]*rate_eval.Mn47__Cr47__weak__wc17
       )

    dYdt[jcr48] = (
          +rho*Y[jn]*Y[jfe51]*rate_eval.n_Fe51__He4_Cr48  +
          -rho*Y[jhe4]*Y[jcr48]*rate_eval.He4_Cr48__p_Mn51  +
          -rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__p_V48  +
          -rho*Y[jhe4]*Y[jcr48]*rate_eval.He4_Cr48__Fe52  +
          -rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__Cr49  +
          +rho*Y[jhe4]*Y[jti44]*rate_eval.He4_Ti44__Cr48  +
          +rho*Y[jn]*Y[jcr47]*rate_eval.n_Cr47__Cr48  +
          +rho*Y[jhe4]*Y[jv45]*rate_eval.He4_V45__p_Cr48  +
          -Y[jcr48]*rate_eval.Cr48__V48__weak__wc12  +
          +Y[jmn48]*rate_eval.Mn48__Cr48__weak__wc12  +
          +rho*Y[jn]*Y[jmn48]*rate_eval.n_Mn48__p_Cr48  +
          -rho*Y[jp]*Y[jcr48]*rate_eval.p_Cr48__Mn49  +
          +rho*Y[jp]*Y[jv47]*rate_eval.p_V47__Cr48  +
          +Y[jfe49]*rate_eval.Fe49__p_Cr48__weak__wc12  +
          -rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__He4_Ti45
       )

    dYdt[jcr49] = (
          +rho*Y[jn]*Y[jfe52]*rate_eval.n_Fe52__He4_Cr49  +
          -rho*Y[jhe4]*Y[jcr49]*rate_eval.He4_Cr49__p_Mn52  +
          -rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__p_V49  +
          +rho*Y[jhe4]*Y[jv46]*rate_eval.He4_V46__p_Cr49  +
          +rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__p_Cr49  +
          -rho*Y[jp]*Y[jcr49]*rate_eval.p_Cr49__Mn50  +
          +rho*Y[jn]*Y[jcr48]*rate_eval.n_Cr48__Cr49  +
          +rho*Y[jp]*Y[jv48]*rate_eval.p_V48__Cr49  +
          +rho*Y[jhe4]*Y[jti45]*rate_eval.He4_Ti45__Cr49  +
          -rho*Y[jhe4]*Y[jcr49]*rate_eval.He4_Cr49__Fe53  +
          +Y[jmn49]*rate_eval.Mn49__Cr49__weak__wc12  +
          -rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__He4_Ti46  +
          -rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__Cr50  +
          -Y[jcr49]*rate_eval.Cr49__V49__weak__wc12
       )

    dYdt[jcr50] = (
          +rho*Y[jn]*Y[jfe53]*rate_eval.n_Fe53__He4_Cr50  +
          +rho*Y[jp]*Y[jmn53]*rate_eval.p_Mn53__He4_Cr50  +
          -rho*Y[jn]*Y[jcr50]*rate_eval.n_Cr50__He4_Ti47  +
          +rho*Y[jp]*Y[jv50]*rate_eval.p_V50__n_Cr50  +
          +rho*Y[jhe4]*Y[jv47]*rate_eval.He4_V47__p_Cr50  +
          +rho*Y[jp]*Y[jv49]*rate_eval.p_V49__Cr50  +
          -rho*Y[jp]*Y[jcr50]*rate_eval.p_Cr50__Mn51  +
          +rho*Y[jhe4]*Y[jti46]*rate_eval.He4_Ti46__Cr50  +
          +rho*Y[jn]*Y[jmn50]*rate_eval.n_Mn50__p_Cr50  +
          -rho*Y[jhe4]*Y[jcr50]*rate_eval.He4_Cr50__Fe54  +
          +Y[jmn50]*rate_eval.Mn50__Cr50__weak__wc12  +
          +rho*Y[jn]*Y[jcr49]*rate_eval.n_Cr49__Cr50  +
          -rho*Y[jn]*Y[jcr50]*rate_eval.n_Cr50__Cr51
       )

    dYdt[jcr51] = (
          +rho*Y[jp]*Y[jmn54]*rate_eval.p_Mn54__He4_Cr51  +
          +rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__p_Cr51  +
          -rho*Y[jn]*Y[jcr51]*rate_eval.n_Cr51__He4_Ti48  +
          +rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__He4_Cr51  +
          -rho*Y[jp]*Y[jcr51]*rate_eval.p_Cr51__Mn52  +
          +rho*Y[jp]*Y[jv50]*rate_eval.p_V50__Cr51  +
          +rho*Y[jhe4]*Y[jv48]*rate_eval.He4_V48__p_Cr51  +
          -rho*Y[jn]*Y[jcr51]*rate_eval.n_Cr51__Cr52  +
          +rho*Y[jhe4]*Y[jti47]*rate_eval.He4_Ti47__Cr51  +
          -rho*Y[jhe4]*Y[jcr51]*rate_eval.He4_Cr51__Fe55  +
          -rho*Y[jn]*Y[jcr51]*rate_eval.n_Cr51__p_V51  +
          -Y[jcr51]*rate_eval.Cr51__V51__weak__wc12  +
          +rho*Y[jn]*Y[jcr50]*rate_eval.n_Cr50__Cr51  +
          +Y[jmn51]*rate_eval.Mn51__Cr51__weak__wc12
       )

    dYdt[jcr52] = (
          +rho*Y[jn]*Y[jmn52]*rate_eval.n_Mn52__p_Cr52  +
          +rho*Y[jp]*Y[jmn55]*rate_eval.p_Mn55__He4_Cr52  +
          +rho*Y[jp]*Y[jv52]*rate_eval.p_V52__n_Cr52  +
          +rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__He4_Cr52  +
          +rho*Y[jhe4]*Y[jv49]*rate_eval.He4_V49__p_Cr52  +
          -rho*Y[jp]*Y[jcr52]*rate_eval.p_Cr52__Mn53  +
          +rho*Y[jhe4]*Y[jti48]*rate_eval.He4_Ti48__Cr52  +
          +rho*Y[jhe4]*Y[jti49]*rate_eval.He4_Ti49__n_Cr52  +
          +rho*Y[jn]*Y[jcr51]*rate_eval.n_Cr51__Cr52  +
          +Y[jmn52]*rate_eval.Mn52__Cr52__weak__wc12  +
          +Y[jv52]*rate_eval.V52__Cr52__weak__wc12  +
          -rho*Y[jn]*Y[jcr52]*rate_eval.n_Cr52__Cr53  +
          +rho*Y[jp]*Y[jv51]*rate_eval.p_V51__Cr52  +
          -rho*Y[jhe4]*Y[jcr52]*rate_eval.He4_Cr52__Fe56
       )

    dYdt[jcr53] = (
          +rho*Y[jn]*Y[jfe56]*rate_eval.n_Fe56__He4_Cr53  +
          +rho*Y[jp]*Y[jmn56]*rate_eval.p_Mn56__He4_Cr53  +
          +rho*Y[jhe4]*Y[jv50]*rate_eval.He4_V50__p_Cr53  +
          -rho*Y[jn]*Y[jcr53]*rate_eval.n_Cr53__He4_Ti50  +
          +rho*Y[jp]*Y[jv53]*rate_eval.p_V53__n_Cr53  +
          +rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__p_Cr53  +
          -rho*Y[jhe4]*Y[jcr53]*rate_eval.He4_Cr53__Fe57  +
          -rho*Y[jp]*Y[jcr53]*rate_eval.p_Cr53__Mn54  +
          -rho*Y[jn]*Y[jcr53]*rate_eval.n_Cr53__Cr54  +
          +rho*Y[jp]*Y[jv52]*rate_eval.p_V52__Cr53  +
          +rho*Y[jn]*Y[jcr52]*rate_eval.n_Cr52__Cr53  +
          +rho*Y[jhe4]*Y[jti49]*rate_eval.He4_Ti49__Cr53  +
          +Y[jmn53]*rate_eval.Mn53__Cr53__weak__wc12  +
          +Y[jv53]*rate_eval.V53__Cr53__weak__wc12
       )

    dYdt[jcr54] = (
          -rho*Y[jp]*Y[jcr54]*rate_eval.p_Cr54__He4_V51  +
          +Y[jmn54]*rate_eval.Mn54__Cr54__weak__wc12  +
          +rho*Y[jhe4]*Y[jti51]*rate_eval.He4_Ti51__n_Cr54  +
          +rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__p_Cr54  +
          +rho*Y[jp]*Y[jv54]*rate_eval.p_V54__n_Cr54  +
          -rho*Y[jhe4]*Y[jcr54]*rate_eval.He4_Cr54__Fe58  +
          -rho*Y[jp]*Y[jcr54]*rate_eval.p_Cr54__Mn55  +
          +rho*Y[jn]*Y[jcr53]*rate_eval.n_Cr53__Cr54  +
          +rho*Y[jp]*Y[jv53]*rate_eval.p_V53__Cr54  +
          +rho*Y[jn]*Y[jfe57]*rate_eval.n_Fe57__He4_Cr54  +
          +rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__He4_Cr54  +
          -rho*Y[jn]*Y[jcr54]*rate_eval.n_Cr54__Cr55  +
          +rho*Y[jhe4]*Y[jti50]*rate_eval.He4_Ti50__Cr54  +
          +Y[jv54]*rate_eval.V54__Cr54__weak__wc12
       )

    dYdt[jcr55] = (
          -rho*Y[jhe4]*Y[jcr55]*rate_eval.He4_Cr55__n_Fe58  +
          -rho*Y[jn]*Y[jcr55]*rate_eval.n_Cr55__He4_Ti52  +
          +rho*Y[jp]*Y[jv55]*rate_eval.p_V55__n_Cr55  +
          -rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__n_Mn55  +
          -rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__He4_V52  +
          -rho*Y[jn]*Y[jcr55]*rate_eval.n_Cr55__Cr56  +
          +rho*Y[jp]*Y[jv54]*rate_eval.p_V54__Cr55  +
          +rho*Y[jhe4]*Y[jti51]*rate_eval.He4_Ti51__Cr55  +
          -rho*Y[jhe4]*Y[jcr55]*rate_eval.He4_Cr55__Fe59  +
          +Y[jv55]*rate_eval.V55__Cr55__weak__wc12  +
          +rho*Y[jn]*Y[jcr54]*rate_eval.n_Cr54__Cr55  +
          -rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__Mn56  +
          +rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__He4_Cr55  +
          -Y[jcr55]*rate_eval.Cr55__Mn55__weak__wc12
       )

    dYdt[jcr56] = (
          +rho*Y[jp]*Y[jmn59]*rate_eval.p_Mn59__He4_Cr56  +
          +rho*Y[jhe4]*Y[jti53]*rate_eval.He4_Ti53__n_Cr56  +
          -rho*Y[jp]*Y[jcr56]*rate_eval.p_Cr56__n_Mn56  +
          -rho*Y[jp]*Y[jcr56]*rate_eval.p_Cr56__He4_V53  +
          +rho*Y[jp]*Y[jv55]*rate_eval.p_V55__Cr56  +
          +rho*Y[jn]*Y[jcr55]*rate_eval.n_Cr55__Cr56  +
          -rho*Y[jp]*Y[jcr56]*rate_eval.p_Cr56__Mn57  +
          -rho*Y[jn]*Y[jcr56]*rate_eval.n_Cr56__Cr57  +
          +rho*Y[jhe4]*Y[jti52]*rate_eval.He4_Ti52__Cr56  +
          +rho*Y[jp]*Y[jv56]*rate_eval.p_V56__n_Cr56  +
          -rho*Y[jhe4]*Y[jcr56]*rate_eval.He4_Cr56__Fe60  +
          -Y[jcr56]*rate_eval.Cr56__Mn56__weak__wc12  +
          +rho*Y[jn]*Y[jfe59]*rate_eval.n_Fe59__He4_Cr56  +
          +Y[jv56]*rate_eval.V56__Cr56__weak__wc12
       )

    dYdt[jcr57] = (
          +rho*Y[jp]*Y[jmn60]*rate_eval.p_Mn60__He4_Cr57  +
          -rho*Y[jp]*Y[jcr57]*rate_eval.p_Cr57__n_Mn57  +
          +rho*Y[jp]*Y[jv57]*rate_eval.p_V57__n_Cr57  +
          -rho*Y[jp]*Y[jcr57]*rate_eval.p_Cr57__He4_V54  +
          +rho*Y[jhe4]*Y[jti54]*rate_eval.He4_Ti54__n_Cr57  +
          -rho*Y[jhe4]*Y[jcr57]*rate_eval.He4_Cr57__n_Fe60  +
          -rho*Y[jn]*Y[jcr57]*rate_eval.n_Cr57__Cr58  +
          +rho*Y[jp]*Y[jv56]*rate_eval.p_V56__Cr57  +
          -rho*Y[jhe4]*Y[jcr57]*rate_eval.He4_Cr57__Fe61  +
          -rho*Y[jp]*Y[jcr57]*rate_eval.p_Cr57__Mn58  +
          +rho*Y[jn]*Y[jcr56]*rate_eval.n_Cr56__Cr57  +
          +rho*Y[jhe4]*Y[jti53]*rate_eval.He4_Ti53__Cr57  +
          +Y[jv58]*rate_eval.V58__n_Cr57__weak__mp17  +
          -Y[jcr57]*rate_eval.Cr57__Mn57__weak__wc12  +
          +Y[jv57]*rate_eval.V57__Cr57__weak__wc12
       )

    dYdt[jcr58] = (
          +rho*Y[jp]*Y[jv58]*rate_eval.p_V58__n_Cr58  +
          +rho*Y[jhe4]*Y[jti55]*rate_eval.He4_Ti55__n_Cr58  +
          -Y[jcr58]*rate_eval.Cr58__Mn58__weak__wc12  +
          +rho*Y[jn]*Y[jcr57]*rate_eval.n_Cr57__Cr58  +
          +rho*Y[jhe4]*Y[jti54]*rate_eval.He4_Ti54__Cr58  +
          -rho*Y[jhe4]*Y[jcr58]*rate_eval.He4_Cr58__Fe62  +
          -rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__Mn59  +
          +rho*Y[jp]*Y[jv57]*rate_eval.p_V57__Cr58  +
          -rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__n_Mn58  +
          -rho*Y[jn]*Y[jcr58]*rate_eval.n_Cr58__Cr59  +
          +Y[jv59]*rate_eval.V59__n_Cr58__weak__wc12  +
          +rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__He4_Cr58  +
          -rho*Y[jhe4]*Y[jcr58]*rate_eval.He4_Cr58__n_Fe61  +
          +Y[jv58]*rate_eval.V58__Cr58__weak__wc17  +
          -rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__He4_V55
       )

    dYdt[jcr59] = (
          +rho*Y[jp]*Y[jmn62]*rate_eval.p_Mn62__He4_Cr59  +
          -rho*Y[jhe4]*Y[jcr59]*rate_eval.He4_Cr59__n_Fe62  +
          -rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__n_Mn59  +
          +rho*Y[jp]*Y[jv59]*rate_eval.p_V59__n_Cr59  +
          -rho*Y[jhe4]*Y[jcr59]*rate_eval.He4_Cr59__Fe63  +
          -rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__Mn60  +
          -rho*Y[jn]*Y[jcr59]*rate_eval.n_Cr59__Cr60  +
          +rho*Y[jp]*Y[jv58]*rate_eval.p_V58__Cr59  +
          +rho*Y[jhe4]*Y[jti56]*rate_eval.He4_Ti56__n_Cr59  +
          +rho*Y[jn]*Y[jcr58]*rate_eval.n_Cr58__Cr59  +
          +Y[jv60]*rate_eval.V60__n_Cr59__weak__mp17  +
          +rho*Y[jhe4]*Y[jti55]*rate_eval.He4_Ti55__Cr59  +
          -rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__He4_V56  +
          -Y[jcr59]*rate_eval.Cr59__Mn59__weak__wc12  +
          +Y[jv59]*rate_eval.V59__Cr59__weak__wc12
       )

    dYdt[jcr60] = (
          -rho*Y[jp]*Y[jcr60]*rate_eval.p_Cr60__He4_V57  +
          +rho*Y[jp]*Y[jv60]*rate_eval.p_V60__n_Cr60  +
          -rho*Y[jp]*Y[jcr60]*rate_eval.p_Cr60__Mn61  +
          -rho*Y[jp]*Y[jcr60]*rate_eval.p_Cr60__n_Mn60  +
          -rho*Y[jhe4]*Y[jcr60]*rate_eval.He4_Cr60__Fe64  +
          -rho*Y[jn]*Y[jcr60]*rate_eval.n_Cr60__Cr61  +
          +rho*Y[jn]*Y[jcr59]*rate_eval.n_Cr59__Cr60  +
          +rho*Y[jp]*Y[jv59]*rate_eval.p_V59__Cr60  +
          +rho*Y[jhe4]*Y[jti57]*rate_eval.He4_Ti57__n_Cr60  +
          +Y[jv60]*rate_eval.V60__Cr60__weak__wc17  +
          -rho*Y[jhe4]*Y[jcr60]*rate_eval.He4_Cr60__n_Fe63  +
          +rho*Y[jhe4]*Y[jti56]*rate_eval.He4_Ti56__Cr60  +
          +Y[jv61]*rate_eval.V61__n_Cr60__weak__wc12  +
          +rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__He4_Cr60  +
          -Y[jcr60]*rate_eval.Cr60__Mn60__weak__wc12
       )

    dYdt[jcr61] = (
          +rho*Y[jp]*Y[jmn64]*rate_eval.p_Mn64__He4_Cr61  +
          -rho*Y[jhe4]*Y[jcr61]*rate_eval.He4_Cr61__n_Fe64  +
          +rho*Y[jp]*Y[jv61]*rate_eval.p_V61__n_Cr61  +
          +rho*Y[jhe4]*Y[jti58]*rate_eval.He4_Ti58__n_Cr61  +
          -rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__He4_V58  +
          -rho*Y[jn]*Y[jcr61]*rate_eval.n_Cr61__Cr62  +
          -rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__Mn62  +
          +rho*Y[jn]*Y[jcr60]*rate_eval.n_Cr60__Cr61  +
          +rho*Y[jp]*Y[jv60]*rate_eval.p_V60__Cr61  +
          +Y[jv62]*rate_eval.V62__n_Cr61__weak__mp17  +
          -Y[jcr61]*rate_eval.Cr61__Mn61__weak__wc12  +
          -Y[jcr61]*rate_eval.Cr61__n_Mn60__weak__mp17  +
          -rho*Y[jhe4]*Y[jcr61]*rate_eval.He4_Cr61__Fe65  +
          +rho*Y[jhe4]*Y[jti57]*rate_eval.He4_Ti57__Cr61  +
          +Y[jv61]*rate_eval.V61__Cr61__weak__wc12  +
          -rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__n_Mn61
       )

    dYdt[jcr62] = (
          +Y[jv65]*rate_eval.V65__n_n_n_Cr62__weak__mo03  +
          +rho*Y[jp]*Y[jmn65]*rate_eval.p_Mn65__He4_Cr62  +
          -rho*Y[jhe4]*Y[jcr62]*rate_eval.He4_Cr62__n_Fe65  +
          -rho*Y[jp]*Y[jcr62]*rate_eval.p_Cr62__He4_V59  +
          +rho*Y[jhe4]*Y[jti59]*rate_eval.He4_Ti59__n_Cr62  +
          -rho*Y[jp]*Y[jcr62]*rate_eval.p_Cr62__Mn63  +
          +Y[jv64]*rate_eval.V64__n_n_Cr62__weak__mp17  +
          -rho*Y[jp]*Y[jcr62]*rate_eval.p_Cr62__n_Mn62  +
          +rho*Y[jn]*Y[jcr61]*rate_eval.n_Cr61__Cr62  +
          -rho*Y[jhe4]*Y[jcr62]*rate_eval.He4_Cr62__Fe66  +
          -rho*Y[jn]*Y[jcr62]*rate_eval.n_Cr62__Cr63  +
          +rho*Y[jp]*Y[jv62]*rate_eval.p_V62__n_Cr62  +
          -Y[jcr62]*rate_eval.Cr62__n_Mn61__weak__mp17  +
          +Y[jv63]*rate_eval.V63__n_Cr62__weak__wc12  +
          +Y[jv62]*rate_eval.V62__Cr62__weak__wc17  +
          +rho*Y[jp]*Y[jv61]*rate_eval.p_V61__Cr62  +
          +rho*Y[jhe4]*Y[jti58]*rate_eval.He4_Ti58__Cr62  +
          -Y[jcr62]*rate_eval.Cr62__Mn62__weak__wc12
       )

    dYdt[jcr63] = (
          +Y[jv66]*rate_eval.V66__n_n_n_Cr63__weak__mo03  +
          +rho*Y[jp]*Y[jmn66]*rate_eval.p_Mn66__He4_Cr63  +
          -rho*Y[jhe4]*Y[jcr63]*rate_eval.He4_Cr63__n_Fe66  +
          -rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__n_Mn63  +
          +rho*Y[jp]*Y[jv63]*rate_eval.p_V63__n_Cr63  +
          +rho*Y[jhe4]*Y[jti60]*rate_eval.He4_Ti60__n_Cr63  +
          -rho*Y[jhe4]*Y[jcr63]*rate_eval.He4_Cr63__Fe67  +
          -rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__Mn64  +
          +rho*Y[jn]*Y[jcr62]*rate_eval.n_Cr62__Cr63  +
          -rho*Y[jn]*Y[jcr63]*rate_eval.n_Cr63__Cr64  +
          -Y[jcr63]*rate_eval.Cr63__n_Mn62__weak__mp17  +
          +Y[jv65]*rate_eval.V65__n_n_Cr63__weak__mp17  +
          +rho*Y[jhe4]*Y[jti59]*rate_eval.He4_Ti59__Cr63  +
          +Y[jv63]*rate_eval.V63__Cr63__weak__wc12  +
          +Y[jv64]*rate_eval.V64__n_Cr63__weak__mp17  +
          -Y[jcr63]*rate_eval.Cr63__Mn63__weak__wc17  +
          -rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__He4_V60  +
          +rho*Y[jp]*Y[jv62]*rate_eval.p_V62__Cr63
       )

    dYdt[jcr64] = (
          +rho*Y[jp]*Y[jmn67]*rate_eval.p_Mn67__He4_Cr64  +
          -rho*Y[jhe4]*Y[jcr64]*rate_eval.He4_Cr64__n_Fe67  +
          +Y[jv67]*rate_eval.V67__n_n_n_Cr64__weak__mo03  +
          +rho*Y[jhe4]*Y[jti60]*rate_eval.He4_Ti60__Cr64  +
          +rho*Y[jhe4]*Y[jti61]*rate_eval.He4_Ti61__n_Cr64  +
          +rho*Y[jp]*Y[jv64]*rate_eval.p_V64__n_Cr64  +
          +rho*Y[jp]*Y[jv63]*rate_eval.p_V63__Cr64  +
          +rho*Y[jn]*Y[jcr63]*rate_eval.n_Cr63__Cr64  +
          -rho*Y[jhe4]*Y[jcr64]*rate_eval.He4_Cr64__Fe68  +
          -rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__n_Mn64  +
          -rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__Mn65  +
          +Y[jv65]*rate_eval.V65__n_Cr64__weak__mp17  +
          -rho*Y[jn]*Y[jcr64]*rate_eval.n_Cr64__Cr65  +
          -rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__He4_V61  +
          -Y[jcr64]*rate_eval.Cr64__n_Mn63__weak__mp17  +
          -Y[jcr64]*rate_eval.Cr64__Mn64__weak__wc12  +
          +Y[jv66]*rate_eval.V66__n_n_Cr64__weak__mp17  +
          +Y[jv64]*rate_eval.V64__Cr64__weak__wc17
       )

    dYdt[jcr65] = (
          -rho*Y[jhe4]*Y[jcr65]*rate_eval.He4_Cr65__n_Fe68  +
          -rho*Y[jp]*Y[jcr65]*rate_eval.p_Cr65__He4_V62  +
          -rho*Y[jp]*Y[jcr65]*rate_eval.p_Cr65__Mn66  +
          +rho*Y[jp]*Y[jv64]*rate_eval.p_V64__Cr65  +
          +rho*Y[jhe4]*Y[jti61]*rate_eval.He4_Ti61__Cr65  +
          +Y[jv65]*rate_eval.V65__Cr65__weak__mo03  +
          +rho*Y[jhe4]*Y[jti62]*rate_eval.He4_Ti62__n_Cr65  +
          -rho*Y[jhe4]*Y[jcr65]*rate_eval.He4_Cr65__Fe69  +
          -rho*Y[jp]*Y[jcr65]*rate_eval.p_Cr65__n_Mn65  +
          -rho*Y[jn]*Y[jcr65]*rate_eval.n_Cr65__Cr66  +
          +rho*Y[jn]*Y[jcr64]*rate_eval.n_Cr64__Cr65  +
          +Y[jv66]*rate_eval.V66__n_Cr65__weak__mp17  +
          +rho*Y[jp]*Y[jv65]*rate_eval.p_V65__n_Cr65  +
          +rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__He4_Cr65  +
          +Y[jv67]*rate_eval.V67__n_n_Cr65__weak__mp17  +
          -Y[jcr65]*rate_eval.Cr65__n_Mn64__weak__mp17  +
          -Y[jcr65]*rate_eval.Cr65__Mn65__weak__wc17
       )

    dYdt[jcr66] = (
          -rho*Y[jhe4]*Y[jcr66]*rate_eval.He4_Cr66__Fe70  +
          +rho*Y[jp]*Y[jmn69]*rate_eval.p_Mn69__He4_Cr66  +
          -rho*Y[jhe4]*Y[jcr66]*rate_eval.He4_Cr66__n_Fe69  +
          -rho*Y[jp]*Y[jcr66]*rate_eval.p_Cr66__He4_V63  +
          +rho*Y[jp]*Y[jv66]*rate_eval.p_V66__n_Cr66  +
          +rho*Y[jhe4]*Y[jti63]*rate_eval.He4_Ti63__n_Cr66  +
          +rho*Y[jp]*Y[jv65]*rate_eval.p_V65__Cr66  +
          -rho*Y[jn]*Y[jcr66]*rate_eval.n_Cr66__Cr67  +
          -rho*Y[jp]*Y[jcr66]*rate_eval.p_Cr66__Mn67  +
          -Y[jcr66]*rate_eval.Cr66__n_Mn65__weak__mp17  +
          +rho*Y[jn]*Y[jcr65]*rate_eval.n_Cr65__Cr66  +
          +Y[jv66]*rate_eval.V66__Cr66__weak__mo03  +
          +rho*Y[jhe4]*Y[jti62]*rate_eval.He4_Ti62__Cr66  +
          -rho*Y[jp]*Y[jcr66]*rate_eval.p_Cr66__n_Mn66  +
          +Y[jv67]*rate_eval.V67__n_Cr66__weak__mp17  +
          -Y[jcr66]*rate_eval.Cr66__Mn66__weak__wc17
       )

    dYdt[jcr67] = (
          -rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__n_Mn67  +
          +rho*Y[jp]*Y[jv67]*rate_eval.p_V67__n_Cr67  +
          +rho*Y[jhe4]*Y[jti64]*rate_eval.He4_Ti64__n_Cr67  +
          -Y[jcr67]*rate_eval.Cr67__Mn67__weak__mo03  +
          +rho*Y[jn]*Y[jcr66]*rate_eval.n_Cr66__Cr67  +
          -rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__He4_V64  +
          -rho*Y[jhe4]*Y[jcr67]*rate_eval.He4_Cr67__Fe71  +
          +rho*Y[jp]*Y[jv66]*rate_eval.p_V66__Cr67  +
          +rho*Y[jhe4]*Y[jti63]*rate_eval.He4_Ti63__Cr67  +
          -Y[jcr67]*rate_eval.Cr67__n_Mn66__weak__mp17  +
          +rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__He4_Cr67  +
          +Y[jv67]*rate_eval.V67__Cr67__weak__mo03  +
          -rho*Y[jn]*Y[jcr67]*rate_eval.n_Cr67__Cr68  +
          -rho*Y[jhe4]*Y[jcr67]*rate_eval.He4_Cr67__n_Fe70  +
          -rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__Mn68
       )

    dYdt[jcr68] = (
          +rho*Y[jp]*Y[jmn71]*rate_eval.p_Mn71__He4_Cr68  +
          -rho*Y[jp]*Y[jcr68]*rate_eval.p_Cr68__He4_V65  +
          -rho*Y[jp]*Y[jcr68]*rate_eval.p_Cr68__n_Mn68  +
          +rho*Y[jhe4]*Y[jti65]*rate_eval.He4_Ti65__n_Cr68  +
          -Y[jcr68]*rate_eval.Cr68__Mn68__weak__mo03  +
          +rho*Y[jp]*Y[jv67]*rate_eval.p_V67__Cr68  +
          -rho*Y[jp]*Y[jcr68]*rate_eval.p_Cr68__Mn69  +
          -Y[jcr68]*rate_eval.Cr68__n_Mn67__weak__mp17  +
          +rho*Y[jhe4]*Y[jti64]*rate_eval.He4_Ti64__Cr68  +
          -rho*Y[jhe4]*Y[jcr68]*rate_eval.He4_Cr68__n_Fe71  +
          +rho*Y[jn]*Y[jcr67]*rate_eval.n_Cr67__Cr68  +
          -rho*Y[jn]*Y[jcr68]*rate_eval.n_Cr68__Cr69  +
          -rho*Y[jhe4]*Y[jcr68]*rate_eval.He4_Cr68__Fe72
       )

    dYdt[jcr69] = (
          +rho*Y[jp]*Y[jmn72]*rate_eval.p_Mn72__He4_Cr69  +
          -rho*Y[jhe4]*Y[jcr69]*rate_eval.He4_Cr69__n_Fe72  +
          -rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__He4_V66  +
          -Y[jcr69]*rate_eval.Cr69__Mn69__weak__mo03  +
          -rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__Mn70  +
          -rho*Y[jn]*Y[jcr69]*rate_eval.n_Cr69__Cr70  +
          -Y[jcr69]*rate_eval.Cr69__n_Mn68__weak__mp17  +
          -Y[jcr69]*rate_eval.Cr69__n_n_Mn67__weak__mp17  +
          -rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__n_Mn69  +
          -rho*Y[jhe4]*Y[jcr69]*rate_eval.He4_Cr69__Fe73  +
          +rho*Y[jhe4]*Y[jti65]*rate_eval.He4_Ti65__Cr69  +
          +rho*Y[jn]*Y[jcr68]*rate_eval.n_Cr68__Cr69
       )

    dYdt[jcr70] = (
          -Y[jcr70]*rate_eval.Cr70__n_n_n_Mn67__weak__mo03  +
          +rho*Y[jp]*Y[jmn73]*rate_eval.p_Mn73__He4_Cr70  +
          -rho*Y[jhe4]*Y[jcr70]*rate_eval.He4_Cr70__n_Fe73  +
          -rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__Mn71  +
          -rho*Y[jhe4]*Y[jcr70]*rate_eval.He4_Cr70__Fe74  +
          +rho*Y[jn]*Y[jcr69]*rate_eval.n_Cr69__Cr70  +
          -Y[jcr70]*rate_eval.Cr70__Mn70__weak__mo03  +
          -rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__n_Mn70  +
          -Y[jcr70]*rate_eval.Cr70__n_Mn69__weak__mp17  +
          -Y[jcr70]*rate_eval.Cr70__n_n_Mn68__weak__mp17  +
          -rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__He4_V67
       )

    dYdt[jmn43] = (
          -Y[jmn43]*rate_eval.Mn43__Cr43__weak__bqa_pos_  +
          -rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__He4_V40  +
          -rho*Y[jhe4]*Y[jmn43]*rate_eval.He4_Mn43__Co47  +
          -rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__p_Cr43  +
          +rho*Y[jhe4]*Y[jv39]*rate_eval.He4_V39__Mn43  +
          -rho*Y[jhe4]*Y[jmn43]*rate_eval.He4_Mn43__p_Fe46  +
          -rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__Mn44  +
          +rho*Y[jp]*Y[jcr42]*rate_eval.p_Cr42__Mn43
       )

    dYdt[jmn44] = (
          -rho*Y[jhe4]*Y[jmn44]*rate_eval.He4_Mn44__p_Fe47  +
          +rho*Y[jhe4]*Y[jcr41]*rate_eval.He4_Cr41__p_Mn44  +
          -rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__Mn45  +
          -rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__p_Cr44  +
          -rho*Y[jp]*Y[jmn44]*rate_eval.p_Mn44__Fe45  +
          -rho*Y[jhe4]*Y[jmn44]*rate_eval.He4_Mn44__Co48  +
          -rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__He4_V41  +
          -Y[jmn44]*rate_eval.Mn44__Cr44__weak__bqa_pos_  +
          +rho*Y[jhe4]*Y[jv40]*rate_eval.He4_V40__Mn44  +
          +rho*Y[jn]*Y[jmn43]*rate_eval.n_Mn43__Mn44  +
          +rho*Y[jp]*Y[jcr43]*rate_eval.p_Cr43__Mn44
       )

    dYdt[jmn45] = (
          -rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__p_Cr45  +
          +rho*Y[jhe4]*Y[jcr42]*rate_eval.He4_Cr42__p_Mn45  +
          -rho*Y[jhe4]*Y[jmn45]*rate_eval.He4_Mn45__p_Fe48  +
          -rho*Y[jhe4]*Y[jmn45]*rate_eval.He4_Mn45__Co49  +
          -rho*Y[jp]*Y[jmn45]*rate_eval.p_Mn45__Fe46  +
          +rho*Y[jn]*Y[jmn44]*rate_eval.n_Mn44__Mn45  +
          +rho*Y[jhe4]*Y[jv41]*rate_eval.He4_V41__Mn45  +
          -rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__Mn46  +
          -rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__He4_V42  +
          +rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__p_Mn45  +
          -Y[jmn45]*rate_eval.Mn45__Cr45__weak__bqa_pos_  +
          +Y[jfe45]*rate_eval.Fe45__Mn45__weak__wc17  +
          +rho*Y[jp]*Y[jcr44]*rate_eval.p_Cr44__Mn45
       )

    dYdt[jmn46] = (
          +rho*Y[jn]*Y[jfe46]*rate_eval.n_Fe46__p_Mn46  +
          -rho*Y[jhe4]*Y[jmn46]*rate_eval.He4_Mn46__p_Fe49  +
          -rho*Y[jn]*Y[jmn46]*rate_eval.n_Mn46__He4_V43  +
          -rho*Y[jn]*Y[jmn46]*rate_eval.n_Mn46__p_Cr46  +
          +rho*Y[jhe4]*Y[jcr43]*rate_eval.He4_Cr43__p_Mn46  +
          -rho*Y[jhe4]*Y[jmn46]*rate_eval.He4_Mn46__Co50  +
          -rho*Y[jp]*Y[jmn46]*rate_eval.p_Mn46__Fe47  +
          +rho*Y[jp]*Y[jcr45]*rate_eval.p_Cr45__Mn46  +
          +rho*Y[jn]*Y[jmn45]*rate_eval.n_Mn45__Mn46  +
          -Y[jmn46]*rate_eval.Mn46__p_V45__weak__wc12  +
          -rho*Y[jn]*Y[jmn46]*rate_eval.n_Mn46__Mn47  +
          +rho*Y[jhe4]*Y[jv42]*rate_eval.He4_V42__Mn46  +
          +Y[jfe46]*rate_eval.Fe46__Mn46__weak__wc12  +
          -Y[jmn46]*rate_eval.Mn46__Cr46__weak__wc12
       )

    dYdt[jmn47] = (
          -rho*Y[jhe4]*Y[jmn47]*rate_eval.He4_Mn47__p_Fe50  +
          -rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__p_Cr47  +
          +rho*Y[jhe4]*Y[jcr44]*rate_eval.He4_Cr44__p_Mn47  +
          -rho*Y[jhe4]*Y[jmn47]*rate_eval.He4_Mn47__Co51  +
          -rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__He4_V44  +
          -rho*Y[jp]*Y[jmn47]*rate_eval.p_Mn47__Fe48  +
          +rho*Y[jp]*Y[jcr46]*rate_eval.p_Cr46__Mn47  +
          +rho*Y[jhe4]*Y[jv43]*rate_eval.He4_V43__Mn47  +
          +rho*Y[jn]*Y[jfe47]*rate_eval.n_Fe47__p_Mn47  +
          +rho*Y[jn]*Y[jmn46]*rate_eval.n_Mn46__Mn47  +
          +Y[jfe47]*rate_eval.Fe47__Mn47__weak__wc12  +
          -Y[jmn47]*rate_eval.Mn47__Cr47__weak__wc17  +
          -rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__Mn48
       )

    dYdt[jmn48] = (
          -rho*Y[jn]*Y[jmn48]*rate_eval.n_Mn48__He4_V45  +
          -rho*Y[jhe4]*Y[jmn48]*rate_eval.He4_Mn48__Co52  +
          +rho*Y[jhe4]*Y[jcr45]*rate_eval.He4_Cr45__p_Mn48  +
          +rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__p_Mn48  +
          -rho*Y[jp]*Y[jmn48]*rate_eval.p_Mn48__Fe49  +
          +rho*Y[jp]*Y[jcr47]*rate_eval.p_Cr47__Mn48  +
          -rho*Y[jhe4]*Y[jmn48]*rate_eval.He4_Mn48__p_Fe51  +
          +Y[jfe48]*rate_eval.Fe48__Mn48__weak__wc12  +
          -Y[jmn48]*rate_eval.Mn48__Cr48__weak__wc12  +
          -rho*Y[jn]*Y[jmn48]*rate_eval.n_Mn48__p_Cr48  +
          -rho*Y[jn]*Y[jmn48]*rate_eval.n_Mn48__Mn49  +
          +rho*Y[jhe4]*Y[jv44]*rate_eval.He4_V44__Mn48  +
          +rho*Y[jn]*Y[jmn47]*rate_eval.n_Mn47__Mn48  +
          -Y[jmn48]*rate_eval.Mn48__p_V47__weak__wc12
       )

    dYdt[jmn49] = (
          +rho*Y[jn]*Y[jfe49]*rate_eval.n_Fe49__p_Mn49  +
          -rho*Y[jhe4]*Y[jmn49]*rate_eval.He4_Mn49__p_Fe52  +
          -rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__He4_V46  +
          -rho*Y[jhe4]*Y[jmn49]*rate_eval.He4_Mn49__Co53  +
          +Y[jfe49]*rate_eval.Fe49__Mn49__weak__wc12  +
          +rho*Y[jhe4]*Y[jcr46]*rate_eval.He4_Cr46__p_Mn49  +
          -rho*Y[jp]*Y[jmn49]*rate_eval.p_Mn49__Fe50  +
          -rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__Mn50  +
          -rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__p_Cr49  +
          +rho*Y[jhe4]*Y[jv45]*rate_eval.He4_V45__Mn49  +
          -Y[jmn49]*rate_eval.Mn49__Cr49__weak__wc12  +
          +rho*Y[jp]*Y[jcr48]*rate_eval.p_Cr48__Mn49  +
          +rho*Y[jn]*Y[jmn48]*rate_eval.n_Mn48__Mn49
       )

    dYdt[jmn50] = (
          -rho*Y[jn]*Y[jmn50]*rate_eval.n_Mn50__He4_V47  +
          +rho*Y[jhe4]*Y[jcr47]*rate_eval.He4_Cr47__p_Mn50  +
          +rho*Y[jn]*Y[jfe50]*rate_eval.n_Fe50__p_Mn50  +
          -rho*Y[jn]*Y[jmn50]*rate_eval.n_Mn50__Mn51  +
          -rho*Y[jhe4]*Y[jmn50]*rate_eval.He4_Mn50__Co54  +
          -rho*Y[jp]*Y[jmn50]*rate_eval.p_Mn50__Fe51  +
          +rho*Y[jn]*Y[jmn49]*rate_eval.n_Mn49__Mn50  +
          +rho*Y[jp]*Y[jcr49]*rate_eval.p_Cr49__Mn50  +
          +rho*Y[jhe4]*Y[jv46]*rate_eval.He4_V46__Mn50  +
          +Y[jfe50]*rate_eval.Fe50__Mn50__weak__wc12  +
          -rho*Y[jn]*Y[jmn50]*rate_eval.n_Mn50__p_Cr50  +
          -Y[jmn50]*rate_eval.Mn50__Cr50__weak__wc12  +
          -rho*Y[jhe4]*Y[jmn50]*rate_eval.He4_Mn50__p_Fe53
       )

    dYdt[jmn51] = (
          -rho*Y[jhe4]*Y[jmn51]*rate_eval.He4_Mn51__p_Fe54  +
          -rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__p_Cr51  +
          +rho*Y[jhe4]*Y[jcr48]*rate_eval.He4_Cr48__p_Mn51  +
          -rho*Y[jp]*Y[jmn51]*rate_eval.p_Mn51__Fe52  +
          -rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__He4_V48  +
          +rho*Y[jn]*Y[jmn50]*rate_eval.n_Mn50__Mn51  +
          +rho*Y[jn]*Y[jfe51]*rate_eval.n_Fe51__p_Mn51  +
          +rho*Y[jp]*Y[jcr50]*rate_eval.p_Cr50__Mn51  +
          +rho*Y[jhe4]*Y[jv47]*rate_eval.He4_V47__Mn51  +
          -rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__Mn52  +
          -rho*Y[jhe4]*Y[jmn51]*rate_eval.He4_Mn51__Co55  +
          +Y[jfe51]*rate_eval.Fe51__Mn51__weak__wc12  +
          -Y[jmn51]*rate_eval.Mn51__Cr51__weak__wc12
       )

    dYdt[jmn52] = (
          -rho*Y[jn]*Y[jmn52]*rate_eval.n_Mn52__He4_V49  +
          -rho*Y[jn]*Y[jmn52]*rate_eval.n_Mn52__p_Cr52  +
          +rho*Y[jhe4]*Y[jcr49]*rate_eval.He4_Cr49__p_Mn52  +
          -rho*Y[jn]*Y[jmn52]*rate_eval.n_Mn52__Mn53  +
          -rho*Y[jhe4]*Y[jmn52]*rate_eval.He4_Mn52__Co56  +
          +rho*Y[jp]*Y[jcr51]*rate_eval.p_Cr51__Mn52  +
          +rho*Y[jn]*Y[jmn51]*rate_eval.n_Mn51__Mn52  +
          -Y[jmn52]*rate_eval.Mn52__Cr52__weak__wc12  +
          -rho*Y[jp]*Y[jmn52]*rate_eval.p_Mn52__Fe53  +
          -rho*Y[jhe4]*Y[jmn52]*rate_eval.He4_Mn52__p_Fe55  +
          +rho*Y[jhe4]*Y[jv48]*rate_eval.He4_V48__Mn52  +
          +rho*Y[jn]*Y[jfe52]*rate_eval.n_Fe52__p_Mn52  +
          +Y[jfe52]*rate_eval.Fe52__Mn52__weak__wc12
       )

    dYdt[jmn53] = (
          +rho*Y[jn]*Y[jfe53]*rate_eval.n_Fe53__p_Mn53  +
          -rho*Y[jhe4]*Y[jmn53]*rate_eval.He4_Mn53__p_Fe56  +
          -rho*Y[jp]*Y[jmn53]*rate_eval.p_Mn53__He4_Cr50  +
          -rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__p_Cr53  +
          +rho*Y[jn]*Y[jmn52]*rate_eval.n_Mn52__Mn53  +
          +rho*Y[jhe4]*Y[jv49]*rate_eval.He4_V49__Mn53  +
          -rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__He4_V50  +
          +Y[jfe53]*rate_eval.Fe53__Mn53__weak__wc12  +
          -rho*Y[jhe4]*Y[jmn53]*rate_eval.He4_Mn53__Co57  +
          +rho*Y[jp]*Y[jcr52]*rate_eval.p_Cr52__Mn53  +
          -rho*Y[jp]*Y[jmn53]*rate_eval.p_Mn53__Fe54  +
          -rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__Mn54  +
          -Y[jmn53]*rate_eval.Mn53__Cr53__weak__wc12
       )

    dYdt[jmn54] = (
          +rho*Y[jp]*Y[jfe57]*rate_eval.p_Fe57__He4_Mn54  +
          +rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__p_Mn54  +
          -rho*Y[jp]*Y[jmn54]*rate_eval.p_Mn54__He4_Cr51  +
          -Y[jmn54]*rate_eval.Mn54__Cr54__weak__wc12  +
          -rho*Y[jhe4]*Y[jmn54]*rate_eval.He4_Mn54__Co58  +
          -rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__p_Cr54  +
          -rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__He4_V51  +
          +rho*Y[jp]*Y[jcr53]*rate_eval.p_Cr53__Mn54  +
          +rho*Y[jhe4]*Y[jv50]*rate_eval.He4_V50__Mn54  +
          -rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__Mn55  +
          -rho*Y[jp]*Y[jmn54]*rate_eval.p_Mn54__Fe55  +
          +rho*Y[jn]*Y[jmn53]*rate_eval.n_Mn53__Mn54
       )

    dYdt[jmn55] = (
          +rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__p_Mn55  +
          -rho*Y[jp]*Y[jmn55]*rate_eval.p_Mn55__He4_Cr52  +
          +rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__n_Mn55  +
          +rho*Y[jhe4]*Y[jv51]*rate_eval.He4_V51__Mn55  +
          -rho*Y[jn]*Y[jmn55]*rate_eval.n_Mn55__Mn56  +
          +rho*Y[jp]*Y[jcr54]*rate_eval.p_Cr54__Mn55  +
          +rho*Y[jn]*Y[jmn54]*rate_eval.n_Mn54__Mn55  +
          +rho*Y[jp]*Y[jfe58]*rate_eval.p_Fe58__He4_Mn55  +
          -rho*Y[jhe4]*Y[jmn55]*rate_eval.He4_Mn55__Co59  +
          +rho*Y[jhe4]*Y[jv52]*rate_eval.He4_V52__n_Mn55  +
          +Y[jcr55]*rate_eval.Cr55__Mn55__weak__wc12  +
          -rho*Y[jp]*Y[jmn55]*rate_eval.p_Mn55__Fe56  +
          +Y[jfe55]*rate_eval.Fe55__Mn55__weak__wc12
       )

    dYdt[jmn56] = (
          +rho*Y[jp]*Y[jfe59]*rate_eval.p_Fe59__He4_Mn56  +
          -rho*Y[jp]*Y[jmn56]*rate_eval.p_Mn56__He4_Cr53  +
          +rho*Y[jp]*Y[jcr56]*rate_eval.p_Cr56__n_Mn56  +
          -rho*Y[jp]*Y[jmn56]*rate_eval.p_Mn56__Fe57  +
          -rho*Y[jn]*Y[jmn56]*rate_eval.n_Mn56__Mn57  +
          +rho*Y[jn]*Y[jmn55]*rate_eval.n_Mn55__Mn56  +
          +rho*Y[jhe4]*Y[jv52]*rate_eval.He4_V52__Mn56  +
          +rho*Y[jp]*Y[jcr55]*rate_eval.p_Cr55__Mn56  +
          -rho*Y[jhe4]*Y[jmn56]*rate_eval.He4_Mn56__Co60  +
          +Y[jcr56]*rate_eval.Cr56__Mn56__weak__wc12  +
          -rho*Y[jn]*Y[jmn56]*rate_eval.n_Mn56__He4_V53  +
          -Y[jmn56]*rate_eval.Mn56__Fe56__weak__wc12  +
          -rho*Y[jp]*Y[jmn56]*rate_eval.p_Mn56__n_Fe56
       )

    dYdt[jmn57] = (
          +rho*Y[jp]*Y[jfe60]*rate_eval.p_Fe60__He4_Mn57  +
          -rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__n_Fe57  +
          +rho*Y[jp]*Y[jcr57]*rate_eval.p_Cr57__n_Mn57  +
          +rho*Y[jhe4]*Y[jv54]*rate_eval.He4_V54__n_Mn57  +
          +rho*Y[jn]*Y[jmn56]*rate_eval.n_Mn56__Mn57  +
          +rho*Y[jp]*Y[jcr56]*rate_eval.p_Cr56__Mn57  +
          +rho*Y[jhe4]*Y[jv53]*rate_eval.He4_V53__Mn57  +
          -rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__He4_Cr54  +
          -rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__Fe58  +
          -rho*Y[jn]*Y[jmn57]*rate_eval.n_Mn57__Mn58  +
          -Y[jmn57]*rate_eval.Mn57__Fe57__weak__wc12  +
          +Y[jcr57]*rate_eval.Cr57__Mn57__weak__wc12  +
          -rho*Y[jhe4]*Y[jmn57]*rate_eval.He4_Mn57__Co61
       )

    dYdt[jmn58] = (
          +rho*Y[jp]*Y[jfe61]*rate_eval.p_Fe61__He4_Mn58  +
          -Y[jmn58]*rate_eval.Mn58__Fe58__weak__wc12  +
          +rho*Y[jhe4]*Y[jv55]*rate_eval.He4_V55__n_Mn58  +
          +Y[jcr58]*rate_eval.Cr58__Mn58__weak__wc12  +
          -rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__Fe59  +
          -rho*Y[jn]*Y[jmn58]*rate_eval.n_Mn58__Mn59  +
          +rho*Y[jp]*Y[jcr57]*rate_eval.p_Cr57__Mn58  +
          +rho*Y[jhe4]*Y[jv54]*rate_eval.He4_V54__Mn58  +
          +rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__n_Mn58  +
          -rho*Y[jhe4]*Y[jmn58]*rate_eval.He4_Mn58__Co62  +
          +rho*Y[jn]*Y[jmn57]*rate_eval.n_Mn57__Mn58  +
          -rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__n_Fe58  +
          -rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__He4_Cr55  +
          -rho*Y[jhe4]*Y[jmn58]*rate_eval.He4_Mn58__n_Co61
       )

    dYdt[jmn59] = (
          +rho*Y[jp]*Y[jfe62]*rate_eval.p_Fe62__He4_Mn59  +
          -rho*Y[jp]*Y[jmn59]*rate_eval.p_Mn59__He4_Cr56  +
          +rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__n_Mn59  +
          +rho*Y[jhe4]*Y[jv56]*rate_eval.He4_V56__n_Mn59  +
          -rho*Y[jhe4]*Y[jmn59]*rate_eval.He4_Mn59__Co63  +
          -rho*Y[jp]*Y[jmn59]*rate_eval.p_Mn59__n_Fe59  +
          -rho*Y[jn]*Y[jmn59]*rate_eval.n_Mn59__Mn60  +
          +rho*Y[jn]*Y[jmn58]*rate_eval.n_Mn58__Mn59  +
          +rho*Y[jp]*Y[jcr58]*rate_eval.p_Cr58__Mn59  +
          -rho*Y[jhe4]*Y[jmn59]*rate_eval.He4_Mn59__n_Co62  +
          +rho*Y[jhe4]*Y[jv55]*rate_eval.He4_V55__Mn59  +
          -rho*Y[jp]*Y[jmn59]*rate_eval.p_Mn59__Fe60  +
          -Y[jmn59]*rate_eval.Mn59__Fe59__weak__wc12  +
          +Y[jcr59]*rate_eval.Cr59__Mn59__weak__wc12
       )

    dYdt[jmn60] = (
          +rho*Y[jp]*Y[jfe63]*rate_eval.p_Fe63__He4_Mn60  +
          -rho*Y[jhe4]*Y[jmn60]*rate_eval.He4_Mn60__n_Co63  +
          -rho*Y[jp]*Y[jmn60]*rate_eval.p_Mn60__He4_Cr57  +
          -rho*Y[jp]*Y[jmn60]*rate_eval.p_Mn60__n_Fe60  +
          -rho*Y[jhe4]*Y[jmn60]*rate_eval.He4_Mn60__Co64  +
          +rho*Y[jhe4]*Y[jv57]*rate_eval.He4_V57__n_Mn60  +
          +rho*Y[jp]*Y[jcr60]*rate_eval.p_Cr60__n_Mn60  +
          -rho*Y[jn]*Y[jmn60]*rate_eval.n_Mn60__Mn61  +
          +rho*Y[jn]*Y[jmn59]*rate_eval.n_Mn59__Mn60  +
          +rho*Y[jp]*Y[jcr59]*rate_eval.p_Cr59__Mn60  +
          +rho*Y[jhe4]*Y[jv56]*rate_eval.He4_V56__Mn60  +
          -rho*Y[jp]*Y[jmn60]*rate_eval.p_Mn60__Fe61  +
          +Y[jcr61]*rate_eval.Cr61__n_Mn60__weak__mp17  +
          -Y[jmn60]*rate_eval.Mn60__Fe60__weak__wc12  +
          +Y[jcr60]*rate_eval.Cr60__Mn60__weak__wc12
       )

    dYdt[jmn61] = (
          +rho*Y[jp]*Y[jfe64]*rate_eval.p_Fe64__He4_Mn61  +
          +rho*Y[jhe4]*Y[jv58]*rate_eval.He4_V58__n_Mn61  +
          -rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__n_Fe61  +
          +rho*Y[jp]*Y[jcr60]*rate_eval.p_Cr60__Mn61  +
          -rho*Y[jhe4]*Y[jmn61]*rate_eval.He4_Mn61__Co65  +
          -rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__Fe62  +
          +rho*Y[jn]*Y[jmn60]*rate_eval.n_Mn60__Mn61  +
          +rho*Y[jhe4]*Y[jv57]*rate_eval.He4_V57__Mn61  +
          -Y[jmn61]*rate_eval.Mn61__Fe61__weak__wc12  +
          +Y[jcr61]*rate_eval.Cr61__Mn61__weak__wc12  +
          -rho*Y[jhe4]*Y[jmn61]*rate_eval.He4_Mn61__n_Co64  +
          +Y[jcr62]*rate_eval.Cr62__n_Mn61__weak__mp17  +
          -rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__He4_Cr58  +
          -rho*Y[jn]*Y[jmn61]*rate_eval.n_Mn61__Mn62  +
          +rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__n_Mn61
       )

    dYdt[jmn62] = (
          +rho*Y[jp]*Y[jfe65]*rate_eval.p_Fe65__He4_Mn62  +
          -rho*Y[jp]*Y[jmn62]*rate_eval.p_Mn62__He4_Cr59  +
          +rho*Y[jhe4]*Y[jv59]*rate_eval.He4_V59__n_Mn62  +
          +rho*Y[jhe4]*Y[jv58]*rate_eval.He4_V58__Mn62  +
          -rho*Y[jhe4]*Y[jmn62]*rate_eval.He4_Mn62__n_Co65  +
          +rho*Y[jp]*Y[jcr62]*rate_eval.p_Cr62__n_Mn62  +
          -rho*Y[jn]*Y[jmn62]*rate_eval.n_Mn62__Mn63  +
          -rho*Y[jp]*Y[jmn62]*rate_eval.p_Mn62__Fe63  +
          +rho*Y[jp]*Y[jcr61]*rate_eval.p_Cr61__Mn62  +
          -Y[jmn62]*rate_eval.Mn62__Fe62__weak__mo03  +
          +Y[jcr63]*rate_eval.Cr63__n_Mn62__weak__mp17  +
          -rho*Y[jhe4]*Y[jmn62]*rate_eval.He4_Mn62__Co66  +
          -rho*Y[jp]*Y[jmn62]*rate_eval.p_Mn62__n_Fe62  +
          +Y[jcr62]*rate_eval.Cr62__Mn62__weak__wc12  +
          +rho*Y[jn]*Y[jmn61]*rate_eval.n_Mn61__Mn62
       )

    dYdt[jmn63] = (
          +rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__n_Mn63  +
          +rho*Y[jp]*Y[jcr62]*rate_eval.p_Cr62__Mn63  +
          +rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__He4_Mn63  +
          +rho*Y[jhe4]*Y[jv60]*rate_eval.He4_V60__n_Mn63  +
          +rho*Y[jn]*Y[jmn62]*rate_eval.n_Mn62__Mn63  +
          -rho*Y[jhe4]*Y[jmn63]*rate_eval.He4_Mn63__Co67  +
          -rho*Y[jn]*Y[jmn63]*rate_eval.n_Mn63__Mn64  +
          -rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__Fe64  +
          -rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__He4_Cr60  +
          +rho*Y[jhe4]*Y[jv59]*rate_eval.He4_V59__Mn63  +
          -rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__n_Fe63  +
          -rho*Y[jhe4]*Y[jmn63]*rate_eval.He4_Mn63__n_Co66  +
          +Y[jcr64]*rate_eval.Cr64__n_Mn63__weak__mp17  +
          -Y[jmn63]*rate_eval.Mn63__Fe63__weak__wc12  +
          +Y[jcr63]*rate_eval.Cr63__Mn63__weak__wc17  +
          -Y[jmn63]*rate_eval.Mn63__n_Fe62__weak__mp17
       )

    dYdt[jmn64] = (
          +rho*Y[jp]*Y[jfe67]*rate_eval.p_Fe67__He4_Mn64  +
          -rho*Y[jp]*Y[jmn64]*rate_eval.p_Mn64__He4_Cr61  +
          +rho*Y[jhe4]*Y[jv61]*rate_eval.He4_V61__n_Mn64  +
          -rho*Y[jp]*Y[jmn64]*rate_eval.p_Mn64__n_Fe64  +
          -rho*Y[jhe4]*Y[jmn64]*rate_eval.He4_Mn64__Co68  +
          +rho*Y[jn]*Y[jmn63]*rate_eval.n_Mn63__Mn64  +
          +rho*Y[jp]*Y[jcr63]*rate_eval.p_Cr63__Mn64  +
          +rho*Y[jhe4]*Y[jv60]*rate_eval.He4_V60__Mn64  +
          +rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__n_Mn64  +
          -rho*Y[jp]*Y[jmn64]*rate_eval.p_Mn64__Fe65  +
          -rho*Y[jn]*Y[jmn64]*rate_eval.n_Mn64__Mn65  +
          -Y[jmn64]*rate_eval.Mn64__Fe64__weak__wc12  +
          -rho*Y[jhe4]*Y[jmn64]*rate_eval.He4_Mn64__n_Co67  +
          -Y[jmn64]*rate_eval.Mn64__n_Fe63__weak__wc12  +
          +Y[jcr64]*rate_eval.Cr64__Mn64__weak__wc12  +
          +Y[jcr65]*rate_eval.Cr65__n_Mn64__weak__mp17
       )

    dYdt[jmn65] = (
          +rho*Y[jp]*Y[jfe68]*rate_eval.p_Fe68__He4_Mn65  +
          -rho*Y[jhe4]*Y[jmn65]*rate_eval.He4_Mn65__n_Co68  +
          -rho*Y[jp]*Y[jmn65]*rate_eval.p_Mn65__He4_Cr62  +
          +rho*Y[jhe4]*Y[jv62]*rate_eval.He4_V62__n_Mn65  +
          -rho*Y[jn]*Y[jmn65]*rate_eval.n_Mn65__Mn66  +
          +rho*Y[jhe4]*Y[jv61]*rate_eval.He4_V61__Mn65  +
          -rho*Y[jhe4]*Y[jmn65]*rate_eval.He4_Mn65__Co69  +
          +rho*Y[jp]*Y[jcr64]*rate_eval.p_Cr64__Mn65  +
          -Y[jmn65]*rate_eval.Mn65__n_Fe64__weak__mp17  +
          +Y[jcr66]*rate_eval.Cr66__n_Mn65__weak__mp17  +
          +rho*Y[jp]*Y[jcr65]*rate_eval.p_Cr65__n_Mn65  +
          +rho*Y[jn]*Y[jmn64]*rate_eval.n_Mn64__Mn65  +
          -rho*Y[jp]*Y[jmn65]*rate_eval.p_Mn65__n_Fe65  +
          -Y[jmn65]*rate_eval.Mn65__Fe65__weak__wc17  +
          +Y[jcr65]*rate_eval.Cr65__Mn65__weak__wc17  +
          -rho*Y[jp]*Y[jmn65]*rate_eval.p_Mn65__Fe66
       )

    dYdt[jmn66] = (
          +rho*Y[jp]*Y[jfe69]*rate_eval.p_Fe69__He4_Mn66  +
          -rho*Y[jp]*Y[jmn66]*rate_eval.p_Mn66__He4_Cr63  +
          -rho*Y[jp]*Y[jmn66]*rate_eval.p_Mn66__n_Fe66  +
          +rho*Y[jhe4]*Y[jv63]*rate_eval.He4_V63__n_Mn66  +
          +rho*Y[jn]*Y[jmn65]*rate_eval.n_Mn65__Mn66  +
          -rho*Y[jhe4]*Y[jmn66]*rate_eval.He4_Mn66__Co70  +
          -rho*Y[jp]*Y[jmn66]*rate_eval.p_Mn66__Fe67  +
          +rho*Y[jp]*Y[jcr65]*rate_eval.p_Cr65__Mn66  +
          -Y[jmn66]*rate_eval.Mn66__Fe66__weak__wc17  +
          +Y[jcr67]*rate_eval.Cr67__n_Mn66__weak__mp17  +
          -Y[jmn66]*rate_eval.Mn66__n_Fe65__weak__mp17  +
          +rho*Y[jp]*Y[jcr66]*rate_eval.p_Cr66__n_Mn66  +
          -rho*Y[jhe4]*Y[jmn66]*rate_eval.He4_Mn66__n_Co69  +
          +rho*Y[jhe4]*Y[jv62]*rate_eval.He4_V62__Mn66  +
          +Y[jcr66]*rate_eval.Cr66__Mn66__weak__wc17  +
          -rho*Y[jn]*Y[jmn66]*rate_eval.n_Mn66__Mn67
       )

    dYdt[jmn67] = (
          +Y[jcr70]*rate_eval.Cr70__n_n_n_Mn67__weak__mo03  +
          +rho*Y[jp]*Y[jfe70]*rate_eval.p_Fe70__He4_Mn67  +
          -rho*Y[jp]*Y[jmn67]*rate_eval.p_Mn67__He4_Cr64  +
          +rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__n_Mn67  +
          +rho*Y[jhe4]*Y[jv64]*rate_eval.He4_V64__n_Mn67  +
          +rho*Y[jhe4]*Y[jv63]*rate_eval.He4_V63__Mn67  +
          +Y[jcr67]*rate_eval.Cr67__Mn67__weak__mo03  +
          -rho*Y[jhe4]*Y[jmn67]*rate_eval.He4_Mn67__n_Co70  +
          -rho*Y[jhe4]*Y[jmn67]*rate_eval.He4_Mn67__Co71  +
          -rho*Y[jp]*Y[jmn67]*rate_eval.p_Mn67__Fe68  +
          -rho*Y[jn]*Y[jmn67]*rate_eval.n_Mn67__Mn68  +
          +rho*Y[jp]*Y[jcr66]*rate_eval.p_Cr66__Mn67  +
          +Y[jcr68]*rate_eval.Cr68__n_Mn67__weak__mp17  +
          -Y[jmn67]*rate_eval.Mn67__Fe67__weak__wc17  +
          +Y[jcr69]*rate_eval.Cr69__n_n_Mn67__weak__mp17  +
          -Y[jmn67]*rate_eval.Mn67__n_Fe66__weak__mp17  +
          -rho*Y[jp]*Y[jmn67]*rate_eval.p_Mn67__n_Fe67  +
          +rho*Y[jn]*Y[jmn66]*rate_eval.n_Mn66__Mn67
       )

    dYdt[jmn68] = (
          +rho*Y[jp]*Y[jfe71]*rate_eval.p_Fe71__He4_Mn68  +
          -rho*Y[jhe4]*Y[jmn68]*rate_eval.He4_Mn68__n_Co71  +
          -rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__n_Fe68  +
          -rho*Y[jhe4]*Y[jmn68]*rate_eval.He4_Mn68__Co72  +
          +rho*Y[jp]*Y[jcr68]*rate_eval.p_Cr68__n_Mn68  +
          +Y[jcr68]*rate_eval.Cr68__Mn68__weak__mo03  +
          -Y[jmn68]*rate_eval.Mn68__Fe68__weak__wc17  +
          -rho*Y[jn]*Y[jmn68]*rate_eval.n_Mn68__Mn69  +
          -rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__Fe69  +
          +rho*Y[jn]*Y[jmn67]*rate_eval.n_Mn67__Mn68  +
          +rho*Y[jhe4]*Y[jv64]*rate_eval.He4_V64__Mn68  +
          -Y[jmn68]*rate_eval.Mn68__n_n_Fe66__weak__mp17  +
          -Y[jmn68]*rate_eval.Mn68__n_Fe67__weak__mp17  +
          +Y[jcr69]*rate_eval.Cr69__n_Mn68__weak__mp17  +
          +rho*Y[jhe4]*Y[jv65]*rate_eval.He4_V65__n_Mn68  +
          +Y[jcr70]*rate_eval.Cr70__n_n_Mn68__weak__mp17  +
          -rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__He4_Cr65  +
          +rho*Y[jp]*Y[jcr67]*rate_eval.p_Cr67__Mn68
       )

    dYdt[jmn69] = (
          +rho*Y[jp]*Y[jfe72]*rate_eval.p_Fe72__He4_Mn69  +
          -rho*Y[jhe4]*Y[jmn69]*rate_eval.He4_Mn69__n_Co72  +
          -rho*Y[jp]*Y[jmn69]*rate_eval.p_Mn69__He4_Cr66  +
          +rho*Y[jhe4]*Y[jv66]*rate_eval.He4_V66__n_Mn69  +
          -rho*Y[jn]*Y[jmn69]*rate_eval.n_Mn69__Mn70  +
          -rho*Y[jp]*Y[jmn69]*rate_eval.p_Mn69__n_Fe69  +
          +rho*Y[jn]*Y[jmn68]*rate_eval.n_Mn68__Mn69  +
          +Y[jcr69]*rate_eval.Cr69__Mn69__weak__mo03  +
          -rho*Y[jhe4]*Y[jmn69]*rate_eval.He4_Mn69__Co73  +
          -rho*Y[jp]*Y[jmn69]*rate_eval.p_Mn69__Fe70  +
          +rho*Y[jhe4]*Y[jv65]*rate_eval.He4_V65__Mn69  +
          +rho*Y[jp]*Y[jcr68]*rate_eval.p_Cr68__Mn69  +
          -Y[jmn69]*rate_eval.Mn69__n_Fe68__weak__mp17  +
          +Y[jcr70]*rate_eval.Cr70__n_Mn69__weak__mp17  +
          +rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__n_Mn69  +
          -Y[jmn69]*rate_eval.Mn69__Fe69__weak__wc17
       )

    dYdt[jmn70] = (
          +rho*Y[jp]*Y[jfe73]*rate_eval.p_Fe73__He4_Mn70  +
          +rho*Y[jhe4]*Y[jv67]*rate_eval.He4_V67__n_Mn70  +
          +rho*Y[jn]*Y[jmn69]*rate_eval.n_Mn69__Mn70  +
          -rho*Y[jhe4]*Y[jmn70]*rate_eval.He4_Mn70__Co74  +
          -rho*Y[jn]*Y[jmn70]*rate_eval.n_Mn70__Mn71  +
          +rho*Y[jp]*Y[jcr69]*rate_eval.p_Cr69__Mn70  +
          +Y[jcr70]*rate_eval.Cr70__Mn70__weak__mo03  +
          +rho*Y[jhe4]*Y[jv66]*rate_eval.He4_V66__Mn70  +
          -Y[jmn70]*rate_eval.Mn70__n_Fe69__weak__mp17  +
          -rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__Fe71  +
          -Y[jmn70]*rate_eval.Mn70__Fe70__weak__mo03  +
          +rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__n_Mn70  +
          -Y[jmn70]*rate_eval.Mn70__n_n_Fe68__weak__mp17  +
          -rho*Y[jhe4]*Y[jmn70]*rate_eval.He4_Mn70__n_Co73  +
          -rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__He4_Cr67  +
          -rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__n_Fe70
       )

    dYdt[jmn71] = (
          -Y[jmn71]*rate_eval.Mn71__n_n_n_Fe68__weak__mo03  +
          +rho*Y[jp]*Y[jfe74]*rate_eval.p_Fe74__He4_Mn71  +
          -rho*Y[jp]*Y[jmn71]*rate_eval.p_Mn71__He4_Cr68  +
          +rho*Y[jp]*Y[jcr70]*rate_eval.p_Cr70__Mn71  +
          -rho*Y[jn]*Y[jmn71]*rate_eval.n_Mn71__Mn72  +
          +rho*Y[jn]*Y[jmn70]*rate_eval.n_Mn70__Mn71  +
          +rho*Y[jhe4]*Y[jv67]*rate_eval.He4_V67__Mn71  +
          -rho*Y[jp]*Y[jmn71]*rate_eval.p_Mn71__Fe72  +
          -rho*Y[jp]*Y[jmn71]*rate_eval.p_Mn71__n_Fe71  +
          -Y[jmn71]*rate_eval.Mn71__n_n_Fe69__weak__mp17  +
          -rho*Y[jhe4]*Y[jmn71]*rate_eval.He4_Mn71__Co75  +
          -rho*Y[jhe4]*Y[jmn71]*rate_eval.He4_Mn71__n_Co74  +
          -Y[jmn71]*rate_eval.Mn71__n_Fe70__weak__mp17  +
          -Y[jmn71]*rate_eval.Mn71__Fe71__weak__mo03
       )

    dYdt[jmn72] = (
          +rho*Y[jp]*Y[jfe75]*rate_eval.p_Fe75__He4_Mn72  +
          -rho*Y[jhe4]*Y[jmn72]*rate_eval.He4_Mn72__n_Co75  +
          -rho*Y[jp]*Y[jmn72]*rate_eval.p_Mn72__He4_Cr69  +
          -rho*Y[jp]*Y[jmn72]*rate_eval.p_Mn72__n_Fe72  +
          -rho*Y[jhe4]*Y[jmn72]*rate_eval.He4_Mn72__Co76  +
          -rho*Y[jn]*Y[jmn72]*rate_eval.n_Mn72__Mn73  +
          +rho*Y[jn]*Y[jmn71]*rate_eval.n_Mn71__Mn72  +
          -rho*Y[jp]*Y[jmn72]*rate_eval.p_Mn72__Fe73  +
          -Y[jmn72]*rate_eval.Mn72__n_n_Fe70__weak__mp17  +
          -Y[jmn72]*rate_eval.Mn72__n_Fe71__weak__mp17  +
          -Y[jmn72]*rate_eval.Mn72__n_n_n_Fe69__weak__mo03  +
          -Y[jmn72]*rate_eval.Mn72__Fe72__weak__mo03
       )

    dYdt[jmn73] = (
          -Y[jmn73]*rate_eval.Mn73__n_n_n_Fe70__weak__mo03  +
          +rho*Y[jp]*Y[jfe76]*rate_eval.p_Fe76__He4_Mn73  +
          -rho*Y[jhe4]*Y[jmn73]*rate_eval.He4_Mn73__n_Co76  +
          -rho*Y[jp]*Y[jmn73]*rate_eval.p_Mn73__He4_Cr70  +
          -rho*Y[jp]*Y[jmn73]*rate_eval.p_Mn73__Fe74  +
          +rho*Y[jn]*Y[jmn72]*rate_eval.n_Mn72__Mn73  +
          -rho*Y[jp]*Y[jmn73]*rate_eval.p_Mn73__n_Fe73  +
          -Y[jmn73]*rate_eval.Mn73__n_n_Fe71__weak__mp17  +
          -rho*Y[jhe4]*Y[jmn73]*rate_eval.He4_Mn73__Co77  +
          -Y[jmn73]*rate_eval.Mn73__n_Fe72__weak__mp17  +
          -Y[jmn73]*rate_eval.Mn73__Fe73__weak__mo03
       )

    dYdt[jfe45] = (
          -Y[jfe45]*rate_eval.Fe45__p_p_p_Ti42__weak__wc12  +
          -rho*Y[jhe4]*Y[jfe45]*rate_eval.He4_Fe45__Ni49  +
          +rho*Y[jhe4]*Y[jcr41]*rate_eval.He4_Cr41__Fe45  +
          +rho*Y[jp]*Y[jmn44]*rate_eval.p_Mn44__Fe45  +
          -rho*Y[jhe4]*Y[jfe45]*rate_eval.He4_Fe45__p_Co48  +
          -Y[jfe45]*rate_eval.Fe45__p_Cr44__weak__wc17  +
          -rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__p_Mn45  +
          -rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__Fe46  +
          -Y[jfe45]*rate_eval.Fe45__p_p_V43__weak__wc12  +
          -rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__He4_Cr42  +
          -Y[jfe45]*rate_eval.Fe45__Mn45__weak__wc17
       )

    dYdt[jfe46] = (
          -rho*Y[jn]*Y[jfe46]*rate_eval.n_Fe46__He4_Cr43  +
          -rho*Y[jn]*Y[jfe46]*rate_eval.n_Fe46__p_Mn46  +
          -rho*Y[jhe4]*Y[jfe46]*rate_eval.He4_Fe46__p_Co49  +
          -rho*Y[jhe4]*Y[jfe46]*rate_eval.He4_Fe46__Ni50  +
          +rho*Y[jp]*Y[jmn45]*rate_eval.p_Mn45__Fe46  +
          +rho*Y[jhe4]*Y[jcr42]*rate_eval.He4_Cr42__Fe46  +
          +rho*Y[jhe4]*Y[jmn43]*rate_eval.He4_Mn43__p_Fe46  +
          -Y[jfe46]*rate_eval.Fe46__p_Cr45__weak__wc12  +
          -rho*Y[jn]*Y[jfe46]*rate_eval.n_Fe46__Fe47  +
          +rho*Y[jn]*Y[jfe45]*rate_eval.n_Fe45__Fe46  +
          -Y[jfe46]*rate_eval.Fe46__Mn46__weak__wc12  +
          -rho*Y[jp]*Y[jfe46]*rate_eval.p_Fe46__Co47
       )

    dYdt[jfe47] = (
          -rho*Y[jn]*Y[jfe47]*rate_eval.n_Fe47__He4_Cr44  +
          +rho*Y[jhe4]*Y[jmn44]*rate_eval.He4_Mn44__p_Fe47  +
          -rho*Y[jhe4]*Y[jfe47]*rate_eval.He4_Fe47__Ni51  +
          -rho*Y[jn]*Y[jfe47]*rate_eval.n_Fe47__Fe48  +
          +rho*Y[jp]*Y[jmn46]*rate_eval.p_Mn46__Fe47  +
          +rho*Y[jhe4]*Y[jcr43]*rate_eval.He4_Cr43__Fe47  +
          -rho*Y[jn]*Y[jfe47]*rate_eval.n_Fe47__p_Mn47  +
          +rho*Y[jn]*Y[jfe46]*rate_eval.n_Fe46__Fe47  +
          -Y[jfe47]*rate_eval.Fe47__p_Cr46__weak__wc12  +
          -Y[jfe47]*rate_eval.Fe47__Mn47__weak__wc12  +
          -rho*Y[jhe4]*Y[jfe47]*rate_eval.He4_Fe47__p_Co50  +
          -rho*Y[jp]*Y[jfe47]*rate_eval.p_Fe47__Co48
       )

    dYdt[jfe48] = (
          -rho*Y[jhe4]*Y[jfe48]*rate_eval.He4_Fe48__p_Co51  +
          -rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__p_Mn48  +
          -rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__Fe49  +
          +rho*Y[jhe4]*Y[jmn45]*rate_eval.He4_Mn45__p_Fe48  +
          +rho*Y[jp]*Y[jmn47]*rate_eval.p_Mn47__Fe48  +
          -rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__He4_Cr45  +
          +rho*Y[jn]*Y[jfe47]*rate_eval.n_Fe47__Fe48  +
          +rho*Y[jhe4]*Y[jcr44]*rate_eval.He4_Cr44__Fe48  +
          -Y[jfe48]*rate_eval.Fe48__Mn48__weak__wc12  +
          -Y[jfe48]*rate_eval.Fe48__p_Cr47__weak__wc12  +
          -rho*Y[jhe4]*Y[jfe48]*rate_eval.He4_Fe48__Ni52  +
          -rho*Y[jp]*Y[jfe48]*rate_eval.p_Fe48__Co49
       )

    dYdt[jfe49] = (
          -rho*Y[jhe4]*Y[jfe49]*rate_eval.He4_Fe49__p_Co52  +
          -rho*Y[jn]*Y[jfe49]*rate_eval.n_Fe49__He4_Cr46  +
          -rho*Y[jn]*Y[jfe49]*rate_eval.n_Fe49__p_Mn49  +
          +rho*Y[jhe4]*Y[jmn46]*rate_eval.He4_Mn46__p_Fe49  +
          +rho*Y[jn]*Y[jfe48]*rate_eval.n_Fe48__Fe49  +
          -Y[jfe49]*rate_eval.Fe49__Mn49__weak__wc12  +
          +rho*Y[jhe4]*Y[jcr45]*rate_eval.He4_Cr45__Fe49  +
          -rho*Y[jn]*Y[jfe49]*rate_eval.n_Fe49__Fe50  +
          +rho*Y[jp]*Y[jmn48]*rate_eval.p_Mn48__Fe49  +
          -rho*Y[jp]*Y[jfe49]*rate_eval.p_Fe49__Co50  +
          -rho*Y[jhe4]*Y[jfe49]*rate_eval.He4_Fe49__Ni53  +
          -Y[jfe49]*rate_eval.Fe49__p_Cr48__weak__wc12
       )

    dYdt[jfe50] = (
          -rho*Y[jn]*Y[jfe50]*rate_eval.n_Fe50__He4_Cr47  +
          +rho*Y[jhe4]*Y[jmn47]*rate_eval.He4_Mn47__p_Fe50  +
          -rho*Y[jn]*Y[jfe50]*rate_eval.n_Fe50__Fe51  +
          -rho*Y[jhe4]*Y[jfe50]*rate_eval.He4_Fe50__p_Co53  +
          -rho*Y[jn]*Y[jfe50]*rate_eval.n_Fe50__p_Mn50  +
          -rho*Y[jp]*Y[jfe50]*rate_eval.p_Fe50__Co51  +
          +rho*Y[jn]*Y[jfe49]*rate_eval.n_Fe49__Fe50  +
          +rho*Y[jp]*Y[jmn49]*rate_eval.p_Mn49__Fe50  +
          +rho*Y[jhe4]*Y[jcr46]*rate_eval.He4_Cr46__Fe50  +
          -Y[jfe50]*rate_eval.Fe50__Mn50__weak__wc12  +
          -rho*Y[jhe4]*Y[jfe50]*rate_eval.He4_Fe50__Ni54
       )

    dYdt[jfe51] = (
          -rho*Y[jn]*Y[jfe51]*rate_eval.n_Fe51__He4_Cr48  +
          +rho*Y[jn]*Y[jfe50]*rate_eval.n_Fe50__Fe51  +
          -rho*Y[jhe4]*Y[jfe51]*rate_eval.He4_Fe51__Ni55  +
          -rho*Y[jn]*Y[jfe51]*rate_eval.n_Fe51__p_Mn51  +
          +rho*Y[jp]*Y[jmn50]*rate_eval.p_Mn50__Fe51  +
          -rho*Y[jn]*Y[jfe51]*rate_eval.n_Fe51__Fe52  +
          +rho*Y[jhe4]*Y[jcr47]*rate_eval.He4_Cr47__Fe51  +
          +rho*Y[jhe4]*Y[jmn48]*rate_eval.He4_Mn48__p_Fe51  +
          -rho*Y[jp]*Y[jfe51]*rate_eval.p_Fe51__Co52  +
          -rho*Y[jhe4]*Y[jfe51]*rate_eval.He4_Fe51__p_Co54  +
          -Y[jfe51]*rate_eval.Fe51__Mn51__weak__wc12
       )

    dYdt[jfe52] = (
          -rho*Y[jhe4]*Y[jfe52]*rate_eval.He4_Fe52__p_Co55  +
          -rho*Y[jn]*Y[jfe52]*rate_eval.n_Fe52__He4_Cr49  +
          +rho*Y[jhe4]*Y[jmn49]*rate_eval.He4_Mn49__p_Fe52  +
          +rho*Y[jp]*Y[jmn51]*rate_eval.p_Mn51__Fe52  +
          -rho*Y[jhe4]*Y[jfe52]*rate_eval.He4_Fe52__Ni56  +
          -rho*Y[jp]*Y[jfe52]*rate_eval.p_Fe52__Co53  +
          +rho*Y[jn]*Y[jfe51]*rate_eval.n_Fe51__Fe52  +
          +rho*Y[jhe4]*Y[jcr48]*rate_eval.He4_Cr48__Fe52  +
          -rho*Y[jn]*Y[jfe52]*rate_eval.n_Fe52__p_Mn52  +
          -Y[jfe52]*rate_eval.Fe52__Mn52__weak__wc12  +
          -rho*Y[jn]*Y[jfe52]*rate_eval.n_Fe52__Fe53
       )

    dYdt[jfe53] = (
          -rho*Y[jn]*Y[jfe53]*rate_eval.n_Fe53__He4_Cr50  +
          -rho*Y[jn]*Y[jfe53]*rate_eval.n_Fe53__p_Mn53  +
          -rho*Y[jhe4]*Y[jfe53]*rate_eval.He4_Fe53__p_Co56  +
          -Y[jfe53]*rate_eval.Fe53__Mn53__weak__wc12  +
          +rho*Y[jp]*Y[jmn52]*rate_eval.p_Mn52__Fe53  +
          -rho*Y[jn]*Y[jfe53]*rate_eval.n_Fe53__Fe54  +
          +rho*Y[jhe4]*Y[jcr49]*rate_eval.He4_Cr49__Fe53  +
          -rho*Y[jp]*Y[jfe53]*rate_eval.p_Fe53__Co54  +
          -rho*Y[jhe4]*Y[jfe53]*rate_eval.He4_Fe53__Ni57  +
          +rho*Y[jn]*Y[jfe52]*rate_eval.n_Fe52__Fe53  +
          +rho*Y[jhe4]*Y[jmn50]*rate_eval.He4_Mn50__p_Fe53
       )

    dYdt[jfe54] = (
          -rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__p_Mn54  +
          +rho*Y[jhe4]*Y[jmn51]*rate_eval.He4_Mn51__p_Fe54  +
          -rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__He4_Cr51  +
          -rho*Y[jhe4]*Y[jfe54]*rate_eval.He4_Fe54__Ni58  +
          -rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__Fe55  +
          -rho*Y[jp]*Y[jfe54]*rate_eval.p_Fe54__Co55  +
          +rho*Y[jn]*Y[jfe53]*rate_eval.n_Fe53__Fe54  +
          +rho*Y[jp]*Y[jmn53]*rate_eval.p_Mn53__Fe54  +
          +rho*Y[jhe4]*Y[jcr50]*rate_eval.He4_Cr50__Fe54
       )

    dYdt[jfe55] = (
          -rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__p_Mn55  +
          -rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__He4_Cr52  +
          -rho*Y[jp]*Y[jfe55]*rate_eval.p_Fe55__Co56  +
          +rho*Y[jn]*Y[jfe54]*rate_eval.n_Fe54__Fe55  +
          +rho*Y[jhe4]*Y[jcr51]*rate_eval.He4_Cr51__Fe55  +
          +rho*Y[jhe4]*Y[jmn52]*rate_eval.He4_Mn52__p_Fe55  +
          +rho*Y[jp]*Y[jmn54]*rate_eval.p_Mn54__Fe55  +
          -rho*Y[jhe4]*Y[jfe55]*rate_eval.He4_Fe55__Ni59  +
          -Y[jfe55]*rate_eval.Fe55__Mn55__weak__wc12  +
          -rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__Fe56
       )

    dYdt[jfe56] = (
          -rho*Y[jn]*Y[jfe56]*rate_eval.n_Fe56__He4_Cr53  +
          +rho*Y[jhe4]*Y[jmn53]*rate_eval.He4_Mn53__p_Fe56  +
          -rho*Y[jhe4]*Y[jfe56]*rate_eval.He4_Fe56__Ni60  +
          -rho*Y[jp]*Y[jfe56]*rate_eval.p_Fe56__Co57  +
          -rho*Y[jn]*Y[jfe56]*rate_eval.n_Fe56__Fe57  +
          +rho*Y[jp]*Y[jmn55]*rate_eval.p_Mn55__Fe56  +
          +rho*Y[jhe4]*Y[jcr52]*rate_eval.He4_Cr52__Fe56  +
          +Y[jmn56]*rate_eval.Mn56__Fe56__weak__wc12  +
          +rho*Y[jn]*Y[jfe55]*rate_eval.n_Fe55__Fe56  +
          +rho*Y[jp]*Y[jmn56]*rate_eval.p_Mn56__n_Fe56
       )

    dYdt[jfe57] = (
          -rho*Y[jp]*Y[jfe57]*rate_eval.p_Fe57__He4_Mn54  +
          +rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__n_Fe57  +
          +rho*Y[jp]*Y[jmn56]*rate_eval.p_Mn56__Fe57  +
          -rho*Y[jp]*Y[jfe57]*rate_eval.p_Fe57__Co58  +
          -rho*Y[jn]*Y[jfe57]*rate_eval.n_Fe57__Fe58  +
          +rho*Y[jn]*Y[jfe56]*rate_eval.n_Fe56__Fe57  +
          -rho*Y[jhe4]*Y[jfe57]*rate_eval.He4_Fe57__Ni61  +
          +rho*Y[jhe4]*Y[jcr53]*rate_eval.He4_Cr53__Fe57  +
          -rho*Y[jn]*Y[jfe57]*rate_eval.n_Fe57__He4_Cr54  +
          +Y[jmn57]*rate_eval.Mn57__Fe57__weak__wc12
       )

    dYdt[jfe58] = (
          +Y[jmn58]*rate_eval.Mn58__Fe58__weak__wc12  +
          +rho*Y[jhe4]*Y[jcr55]*rate_eval.He4_Cr55__n_Fe58  +
          -rho*Y[jhe4]*Y[jfe58]*rate_eval.He4_Fe58__Ni62  +
          -rho*Y[jn]*Y[jfe58]*rate_eval.n_Fe58__Fe59  +
          +rho*Y[jn]*Y[jfe57]*rate_eval.n_Fe57__Fe58  +
          +rho*Y[jhe4]*Y[jcr54]*rate_eval.He4_Cr54__Fe58  +
          -rho*Y[jp]*Y[jfe58]*rate_eval.p_Fe58__Co59  +
          +rho*Y[jp]*Y[jmn57]*rate_eval.p_Mn57__Fe58  +
          -rho*Y[jp]*Y[jfe58]*rate_eval.p_Fe58__He4_Mn55  +
          +rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__n_Fe58
       )

    dYdt[jfe59] = (
          -rho*Y[jhe4]*Y[jfe59]*rate_eval.He4_Fe59__n_Ni62  +
          -rho*Y[jp]*Y[jfe59]*rate_eval.p_Fe59__He4_Mn56  +
          -rho*Y[jp]*Y[jfe59]*rate_eval.p_Fe59__n_Co59  +
          +rho*Y[jp]*Y[jmn58]*rate_eval.p_Mn58__Fe59  +
          +rho*Y[jp]*Y[jmn59]*rate_eval.p_Mn59__n_Fe59  +
          -rho*Y[jhe4]*Y[jfe59]*rate_eval.He4_Fe59__Ni63  +
          -rho*Y[jp]*Y[jfe59]*rate_eval.p_Fe59__Co60  +
          +rho*Y[jn]*Y[jfe58]*rate_eval.n_Fe58__Fe59  +
          +rho*Y[jhe4]*Y[jcr55]*rate_eval.He4_Cr55__Fe59  +
          -Y[jfe59]*rate_eval.Fe59__Co59__weak__wc12  +
          -rho*Y[jn]*Y[jfe59]*rate_eval.n_Fe59__Fe60  +
          +Y[jmn59]*rate_eval.Mn59__Fe59__weak__wc12  +
          -rho*Y[jn]*Y[jfe59]*rate_eval.n_Fe59__He4_Cr56
       )

    dYdt[jfe60] = (
          -rho*Y[jp]*Y[jfe60]*rate_eval.p_Fe60__He4_Mn57  +
          +rho*Y[jp]*Y[jmn60]*rate_eval.p_Mn60__n_Fe60  +
          +rho*Y[jhe4]*Y[jcr57]*rate_eval.He4_Cr57__n_Fe60  +
          -rho*Y[jp]*Y[jfe60]*rate_eval.p_Fe60__Co61  +
          -Y[jfe60]*rate_eval.Fe60__Co60__weak__wc12  +
          +rho*Y[jhe4]*Y[jcr56]*rate_eval.He4_Cr56__Fe60  +
          -rho*Y[jn]*Y[jfe60]*rate_eval.n_Fe60__Fe61  +
          +rho*Y[jp]*Y[jmn59]*rate_eval.p_Mn59__Fe60  +
          +Y[jmn60]*rate_eval.Mn60__Fe60__weak__wc12  +
          +rho*Y[jn]*Y[jfe59]*rate_eval.n_Fe59__Fe60  +
          -rho*Y[jhe4]*Y[jfe60]*rate_eval.He4_Fe60__Ni64
       )

    dYdt[jfe61] = (
          -rho*Y[jp]*Y[jfe61]*rate_eval.p_Fe61__He4_Mn58  +
          -rho*Y[jp]*Y[jfe61]*rate_eval.p_Fe61__n_Co61  +
          +rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__n_Fe61  +
          -rho*Y[jp]*Y[jfe61]*rate_eval.p_Fe61__Co62  +
          +rho*Y[jhe4]*Y[jcr57]*rate_eval.He4_Cr57__Fe61  +
          +rho*Y[jp]*Y[jmn60]*rate_eval.p_Mn60__Fe61  +
          +Y[jmn61]*rate_eval.Mn61__Fe61__weak__wc12  +
          +rho*Y[jn]*Y[jfe60]*rate_eval.n_Fe60__Fe61  +
          -rho*Y[jhe4]*Y[jfe61]*rate_eval.He4_Fe61__Ni65  +
          -rho*Y[jhe4]*Y[jfe61]*rate_eval.He4_Fe61__n_Ni64  +
          -rho*Y[jn]*Y[jfe61]*rate_eval.n_Fe61__Fe62  +
          -Y[jfe61]*rate_eval.Fe61__Co61__weak__wc12  +
          +rho*Y[jhe4]*Y[jcr58]*rate_eval.He4_Cr58__n_Fe61
       )

    dYdt[jfe62] = (
          -rho*Y[jp]*Y[jfe62]*rate_eval.p_Fe62__He4_Mn59  +
          +rho*Y[jhe4]*Y[jcr59]*rate_eval.He4_Cr59__n_Fe62  +
          -rho*Y[jp]*Y[jfe62]*rate_eval.p_Fe62__n_Co62  +
          -rho*Y[jn]*Y[jfe62]*rate_eval.n_Fe62__Fe63  +
          +rho*Y[jp]*Y[jmn61]*rate_eval.p_Mn61__Fe62  +
          +rho*Y[jhe4]*Y[jcr58]*rate_eval.He4_Cr58__Fe62  +
          +Y[jmn62]*rate_eval.Mn62__Fe62__weak__mo03  +
          -rho*Y[jhe4]*Y[jfe62]*rate_eval.He4_Fe62__n_Ni65  +
          -rho*Y[jhe4]*Y[jfe62]*rate_eval.He4_Fe62__Ni66  +
          +rho*Y[jn]*Y[jfe61]*rate_eval.n_Fe61__Fe62  +
          +rho*Y[jp]*Y[jmn62]*rate_eval.p_Mn62__n_Fe62  +
          -Y[jfe62]*rate_eval.Fe62__Co62__weak__wc12  +
          +Y[jmn63]*rate_eval.Mn63__n_Fe62__weak__mp17  +
          -rho*Y[jp]*Y[jfe62]*rate_eval.p_Fe62__Co63
       )

    dYdt[jfe63] = (
          -rho*Y[jhe4]*Y[jfe63]*rate_eval.He4_Fe63__n_Ni66  +
          -rho*Y[jp]*Y[jfe63]*rate_eval.p_Fe63__He4_Mn60  +
          -rho*Y[jp]*Y[jfe63]*rate_eval.p_Fe63__Co64  +
          -rho*Y[jn]*Y[jfe63]*rate_eval.n_Fe63__Fe64  +
          +rho*Y[jn]*Y[jfe62]*rate_eval.n_Fe62__Fe63  +
          +rho*Y[jp]*Y[jmn62]*rate_eval.p_Mn62__Fe63  +
          +rho*Y[jhe4]*Y[jcr59]*rate_eval.He4_Cr59__Fe63  +
          -rho*Y[jp]*Y[jfe63]*rate_eval.p_Fe63__n_Co63  +
          +rho*Y[jhe4]*Y[jcr60]*rate_eval.He4_Cr60__n_Fe63  +
          -rho*Y[jhe4]*Y[jfe63]*rate_eval.He4_Fe63__Ni67  +
          +rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__n_Fe63  +
          +Y[jmn64]*rate_eval.Mn64__n_Fe63__weak__wc12  +
          -Y[jfe63]*rate_eval.Fe63__Co63__weak__wc12  +
          +Y[jmn63]*rate_eval.Mn63__Fe63__weak__wc12
       )

    dYdt[jfe64] = (
          -rho*Y[jhe4]*Y[jfe64]*rate_eval.He4_Fe64__n_Ni67  +
          -rho*Y[jp]*Y[jfe64]*rate_eval.p_Fe64__He4_Mn61  +
          +rho*Y[jhe4]*Y[jcr61]*rate_eval.He4_Cr61__n_Fe64  +
          +rho*Y[jp]*Y[jmn64]*rate_eval.p_Mn64__n_Fe64  +
          -rho*Y[jhe4]*Y[jfe64]*rate_eval.He4_Fe64__Ni68  +
          +rho*Y[jn]*Y[jfe63]*rate_eval.n_Fe63__Fe64  +
          -rho*Y[jp]*Y[jfe64]*rate_eval.p_Fe64__n_Co64  +
          +rho*Y[jhe4]*Y[jcr60]*rate_eval.He4_Cr60__Fe64  +
          +rho*Y[jp]*Y[jmn63]*rate_eval.p_Mn63__Fe64  +
          -rho*Y[jp]*Y[jfe64]*rate_eval.p_Fe64__Co65  +
          +Y[jmn65]*rate_eval.Mn65__n_Fe64__weak__mp17  +
          +Y[jmn64]*rate_eval.Mn64__Fe64__weak__wc12  +
          -Y[jfe64]*rate_eval.Fe64__Co64__weak__wc12  +
          -rho*Y[jn]*Y[jfe64]*rate_eval.n_Fe64__Fe65
       )

    dYdt[jfe65] = (
          -rho*Y[jp]*Y[jfe65]*rate_eval.p_Fe65__He4_Mn62  +
          -rho*Y[jhe4]*Y[jfe65]*rate_eval.He4_Fe65__Ni69  +
          +rho*Y[jhe4]*Y[jcr62]*rate_eval.He4_Cr62__n_Fe65  +
          -rho*Y[jp]*Y[jfe65]*rate_eval.p_Fe65__Co66  +
          -rho*Y[jn]*Y[jfe65]*rate_eval.n_Fe65__Fe66  +
          +rho*Y[jp]*Y[jmn64]*rate_eval.p_Mn64__Fe65  +
          +Y[jmn66]*rate_eval.Mn66__n_Fe65__weak__mp17  +
          -rho*Y[jp]*Y[jfe65]*rate_eval.p_Fe65__n_Co65  +
          +rho*Y[jhe4]*Y[jcr61]*rate_eval.He4_Cr61__Fe65  +
          -rho*Y[jhe4]*Y[jfe65]*rate_eval.He4_Fe65__n_Ni68  +
          +rho*Y[jp]*Y[jmn65]*rate_eval.p_Mn65__n_Fe65  +
          +Y[jmn65]*rate_eval.Mn65__Fe65__weak__wc17  +
          -Y[jfe65]*rate_eval.Fe65__Co65__weak__wc12  +
          +rho*Y[jn]*Y[jfe64]*rate_eval.n_Fe64__Fe65
       )

    dYdt[jfe66] = (
          +rho*Y[jp]*Y[jmn66]*rate_eval.p_Mn66__n_Fe66  +
          +rho*Y[jhe4]*Y[jcr63]*rate_eval.He4_Cr63__n_Fe66  +
          -rho*Y[jhe4]*Y[jfe66]*rate_eval.He4_Fe66__n_Ni69  +
          -rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__He4_Mn63  +
          -rho*Y[jn]*Y[jfe66]*rate_eval.n_Fe66__Fe67  +
          -rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__n_Co66  +
          -rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__Co67  +
          +rho*Y[jn]*Y[jfe65]*rate_eval.n_Fe65__Fe66  +
          +rho*Y[jhe4]*Y[jcr62]*rate_eval.He4_Cr62__Fe66  +
          -Y[jfe66]*rate_eval.Fe66__Co66__weak__wc12  +
          +Y[jmn66]*rate_eval.Mn66__Fe66__weak__wc17  +
          +Y[jmn68]*rate_eval.Mn68__n_n_Fe66__weak__mp17  +
          -rho*Y[jhe4]*Y[jfe66]*rate_eval.He4_Fe66__Ni70  +
          +Y[jmn67]*rate_eval.Mn67__n_Fe66__weak__mp17  +
          +rho*Y[jp]*Y[jmn65]*rate_eval.p_Mn65__Fe66
       )

    dYdt[jfe67] = (
          -rho*Y[jp]*Y[jfe67]*rate_eval.p_Fe67__He4_Mn64  +
          -Y[jfe67]*rate_eval.Fe67__Co67__weak__wc12  +
          +rho*Y[jhe4]*Y[jcr64]*rate_eval.He4_Cr64__n_Fe67  +
          +rho*Y[jn]*Y[jfe66]*rate_eval.n_Fe66__Fe67  +
          -rho*Y[jp]*Y[jfe67]*rate_eval.p_Fe67__n_Co67  +
          -rho*Y[jhe4]*Y[jfe67]*rate_eval.He4_Fe67__Ni71  +
          -rho*Y[jn]*Y[jfe67]*rate_eval.n_Fe67__Fe68  +
          +rho*Y[jp]*Y[jmn66]*rate_eval.p_Mn66__Fe67  +
          +rho*Y[jhe4]*Y[jcr63]*rate_eval.He4_Cr63__Fe67  +
          +Y[jmn67]*rate_eval.Mn67__Fe67__weak__wc17  +
          +Y[jmn68]*rate_eval.Mn68__n_Fe67__weak__mp17  +
          -rho*Y[jp]*Y[jfe67]*rate_eval.p_Fe67__Co68  +
          +rho*Y[jp]*Y[jmn67]*rate_eval.p_Mn67__n_Fe67  +
          -rho*Y[jhe4]*Y[jfe67]*rate_eval.He4_Fe67__n_Ni70
       )

    dYdt[jfe68] = (
          +Y[jmn71]*rate_eval.Mn71__n_n_n_Fe68__weak__mo03  +
          -rho*Y[jhe4]*Y[jfe68]*rate_eval.He4_Fe68__n_Ni71  +
          -rho*Y[jp]*Y[jfe68]*rate_eval.p_Fe68__He4_Mn65  +
          +rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__n_Fe68  +
          +rho*Y[jhe4]*Y[jcr65]*rate_eval.He4_Cr65__n_Fe68  +
          -rho*Y[jhe4]*Y[jfe68]*rate_eval.He4_Fe68__Ni72  +
          +Y[jmn68]*rate_eval.Mn68__Fe68__weak__wc17  +
          -rho*Y[jp]*Y[jfe68]*rate_eval.p_Fe68__Co69  +
          -rho*Y[jn]*Y[jfe68]*rate_eval.n_Fe68__Fe69  +
          +rho*Y[jn]*Y[jfe67]*rate_eval.n_Fe67__Fe68  +
          +rho*Y[jp]*Y[jmn67]*rate_eval.p_Mn67__Fe68  +
          +rho*Y[jhe4]*Y[jcr64]*rate_eval.He4_Cr64__Fe68  +
          -Y[jfe68]*rate_eval.Fe68__n_Co67__weak__mp17  +
          +Y[jmn70]*rate_eval.Mn70__n_n_Fe68__weak__mp17  +
          +Y[jmn69]*rate_eval.Mn69__n_Fe68__weak__mp17  +
          -rho*Y[jp]*Y[jfe68]*rate_eval.p_Fe68__n_Co68  +
          -Y[jfe68]*rate_eval.Fe68__Co68__weak__wc12
       )

    dYdt[jfe69] = (
          -rho*Y[jp]*Y[jfe69]*rate_eval.p_Fe69__He4_Mn66  +
          -rho*Y[jp]*Y[jfe69]*rate_eval.p_Fe69__n_Co69  +
          +rho*Y[jhe4]*Y[jcr66]*rate_eval.He4_Cr66__n_Fe69  +
          +rho*Y[jp]*Y[jmn69]*rate_eval.p_Mn69__n_Fe69  +
          -rho*Y[jp]*Y[jfe69]*rate_eval.p_Fe69__Co70  +
          -rho*Y[jhe4]*Y[jfe69]*rate_eval.He4_Fe69__Ni73  +
          -rho*Y[jn]*Y[jfe69]*rate_eval.n_Fe69__Fe70  +
          +rho*Y[jn]*Y[jfe68]*rate_eval.n_Fe68__Fe69  +
          +rho*Y[jp]*Y[jmn68]*rate_eval.p_Mn68__Fe69  +
          +Y[jmn70]*rate_eval.Mn70__n_Fe69__weak__mp17  +
          -Y[jfe69]*rate_eval.Fe69__Co69__weak__wc17  +
          +rho*Y[jhe4]*Y[jcr65]*rate_eval.He4_Cr65__Fe69  +
          +Y[jmn71]*rate_eval.Mn71__n_n_Fe69__weak__mp17  +
          -Y[jfe69]*rate_eval.Fe69__n_Co68__weak__mp17  +
          +Y[jmn69]*rate_eval.Mn69__Fe69__weak__wc17  +
          +Y[jmn72]*rate_eval.Mn72__n_n_n_Fe69__weak__mo03  +
          -rho*Y[jhe4]*Y[jfe69]*rate_eval.He4_Fe69__n_Ni72
       )

    dYdt[jfe70] = (
          +Y[jmn73]*rate_eval.Mn73__n_n_n_Fe70__weak__mo03  +
          -rho*Y[jhe4]*Y[jfe70]*rate_eval.He4_Fe70__n_Ni73  +
          -rho*Y[jp]*Y[jfe70]*rate_eval.p_Fe70__He4_Mn67  +
          -rho*Y[jp]*Y[jfe70]*rate_eval.p_Fe70__n_Co70  +
          +rho*Y[jhe4]*Y[jcr66]*rate_eval.He4_Cr66__Fe70  +
          -rho*Y[jhe4]*Y[jfe70]*rate_eval.He4_Fe70__Ni74  +
          -rho*Y[jp]*Y[jfe70]*rate_eval.p_Fe70__Co71  +
          -rho*Y[jn]*Y[jfe70]*rate_eval.n_Fe70__Fe71  +
          +rho*Y[jn]*Y[jfe69]*rate_eval.n_Fe69__Fe70  +
          +rho*Y[jp]*Y[jmn69]*rate_eval.p_Mn69__Fe70  +
          +Y[jmn70]*rate_eval.Mn70__Fe70__weak__mo03  +
          +Y[jmn72]*rate_eval.Mn72__n_n_Fe70__weak__mp17  +
          -Y[jfe70]*rate_eval.Fe70__n_Co69__weak__mp17  +
          -Y[jfe70]*rate_eval.Fe70__Co70__weak__wc17  +
          +rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__n_Fe70  +
          +Y[jmn71]*rate_eval.Mn71__n_Fe70__weak__mp17  +
          +rho*Y[jhe4]*Y[jcr67]*rate_eval.He4_Cr67__n_Fe70
       )

    dYdt[jfe71] = (
          -rho*Y[jhe4]*Y[jfe71]*rate_eval.He4_Fe71__n_Ni74  +
          -rho*Y[jp]*Y[jfe71]*rate_eval.p_Fe71__He4_Mn68  +
          -rho*Y[jp]*Y[jfe71]*rate_eval.p_Fe71__n_Co71  +
          -rho*Y[jn]*Y[jfe71]*rate_eval.n_Fe71__Fe72  +
          +rho*Y[jn]*Y[jfe70]*rate_eval.n_Fe70__Fe71  +
          +rho*Y[jhe4]*Y[jcr67]*rate_eval.He4_Cr67__Fe71  +
          -rho*Y[jhe4]*Y[jfe71]*rate_eval.He4_Fe71__Ni75  +
          +rho*Y[jp]*Y[jmn70]*rate_eval.p_Mn70__Fe71  +
          +rho*Y[jp]*Y[jmn71]*rate_eval.p_Mn71__n_Fe71  +
          +Y[jmn73]*rate_eval.Mn73__n_n_Fe71__weak__mp17  +
          -rho*Y[jp]*Y[jfe71]*rate_eval.p_Fe71__Co72  +
          +Y[jmn72]*rate_eval.Mn72__n_Fe71__weak__mp17  +
          +rho*Y[jhe4]*Y[jcr68]*rate_eval.He4_Cr68__n_Fe71  +
          -Y[jfe71]*rate_eval.Fe71__n_Co70__weak__mp17  +
          -Y[jfe71]*rate_eval.Fe71__Co71__weak__wc17  +
          +Y[jmn71]*rate_eval.Mn71__Fe71__weak__mo03
       )

    dYdt[jfe72] = (
          -rho*Y[jp]*Y[jfe72]*rate_eval.p_Fe72__He4_Mn69  +
          -rho*Y[jp]*Y[jfe72]*rate_eval.p_Fe72__n_Co72  +
          +rho*Y[jhe4]*Y[jcr69]*rate_eval.He4_Cr69__n_Fe72  +
          +rho*Y[jp]*Y[jmn72]*rate_eval.p_Mn72__n_Fe72  +
          -rho*Y[jn]*Y[jfe72]*rate_eval.n_Fe72__Fe73  +
          -rho*Y[jp]*Y[jfe72]*rate_eval.p_Fe72__Co73  +
          +rho*Y[jn]*Y[jfe71]*rate_eval.n_Fe71__Fe72  +
          +rho*Y[jp]*Y[jmn71]*rate_eval.p_Mn71__Fe72  +
          -Y[jfe72]*rate_eval.Fe72__n_Co71__weak__mp17  +
          +Y[jmn73]*rate_eval.Mn73__n_Fe72__weak__mp17  +
          -Y[jfe72]*rate_eval.Fe72__Co72__weak__mo03  +
          -rho*Y[jhe4]*Y[jfe72]*rate_eval.He4_Fe72__n_Ni75  +
          -rho*Y[jhe4]*Y[jfe72]*rate_eval.He4_Fe72__Ni76  +
          +rho*Y[jhe4]*Y[jcr68]*rate_eval.He4_Cr68__Fe72  +
          +Y[jmn72]*rate_eval.Mn72__Fe72__weak__mo03
       )

    dYdt[jfe73] = (
          -rho*Y[jp]*Y[jfe73]*rate_eval.p_Fe73__He4_Mn70  +
          -rho*Y[jp]*Y[jfe73]*rate_eval.p_Fe73__n_Co73  +
          +rho*Y[jhe4]*Y[jcr70]*rate_eval.He4_Cr70__n_Fe73  +
          -rho*Y[jhe4]*Y[jfe73]*rate_eval.He4_Fe73__n_Ni76  +
          +rho*Y[jn]*Y[jfe72]*rate_eval.n_Fe72__Fe73  +
          -rho*Y[jhe4]*Y[jfe73]*rate_eval.He4_Fe73__Ni77  +
          -rho*Y[jp]*Y[jfe73]*rate_eval.p_Fe73__Co74  +
          +rho*Y[jp]*Y[jmn73]*rate_eval.p_Mn73__n_Fe73  +
          +rho*Y[jp]*Y[jmn72]*rate_eval.p_Mn72__Fe73  +
          -rho*Y[jn]*Y[jfe73]*rate_eval.n_Fe73__Fe74  +
          -Y[jfe73]*rate_eval.Fe73__n_n_Co71__weak__mp17  +
          -Y[jfe73]*rate_eval.Fe73__n_Co72__weak__mp17  +
          -Y[jfe73]*rate_eval.Fe73__Co73__weak__mo03  +
          +Y[jmn73]*rate_eval.Mn73__Fe73__weak__mo03  +
          +rho*Y[jhe4]*Y[jcr69]*rate_eval.He4_Cr69__Fe73
       )

    dYdt[jfe74] = (
          -rho*Y[jhe4]*Y[jfe74]*rate_eval.He4_Fe74__n_Ni77  +
          -rho*Y[jp]*Y[jfe74]*rate_eval.p_Fe74__He4_Mn71  +
          -rho*Y[jp]*Y[jfe74]*rate_eval.p_Fe74__n_Co74  +
          +rho*Y[jp]*Y[jmn73]*rate_eval.p_Mn73__Fe74  +
          +rho*Y[jhe4]*Y[jcr70]*rate_eval.He4_Cr70__Fe74  +
          +rho*Y[jn]*Y[jfe73]*rate_eval.n_Fe73__Fe74  +
          -rho*Y[jn]*Y[jfe74]*rate_eval.n_Fe74__Fe75  +
          -Y[jfe74]*rate_eval.Fe74__Co74__weak__mo03  +
          -rho*Y[jhe4]*Y[jfe74]*rate_eval.He4_Fe74__Ni78  +
          -Y[jfe74]*rate_eval.Fe74__n_Co73__weak__mp17  +
          -rho*Y[jp]*Y[jfe74]*rate_eval.p_Fe74__Co75
       )

    dYdt[jfe75] = (
          -Y[jfe75]*rate_eval.Fe75__n_n_n_Co72__weak__mo03  +
          -rho*Y[jhe4]*Y[jfe75]*rate_eval.He4_Fe75__n_Ni78  +
          -rho*Y[jp]*Y[jfe75]*rate_eval.p_Fe75__He4_Mn72  +
          -rho*Y[jp]*Y[jfe75]*rate_eval.p_Fe75__n_Co75  +
          -rho*Y[jn]*Y[jfe75]*rate_eval.n_Fe75__Fe76  +
          +rho*Y[jn]*Y[jfe74]*rate_eval.n_Fe74__Fe75  +
          -rho*Y[jhe4]*Y[jfe75]*rate_eval.He4_Fe75__Ni79  +
          -Y[jfe75]*rate_eval.Fe75__n_n_Co73__weak__mp17  +
          -Y[jfe75]*rate_eval.Fe75__n_Co74__weak__mp17  +
          -Y[jfe75]*rate_eval.Fe75__Co75__weak__mo03  +
          -rho*Y[jp]*Y[jfe75]*rate_eval.p_Fe75__Co76
       )

    dYdt[jfe76] = (
          -rho*Y[jhe4]*Y[jfe76]*rate_eval.He4_Fe76__n_Ni79  +
          -rho*Y[jp]*Y[jfe76]*rate_eval.p_Fe76__He4_Mn73  +
          +rho*Y[jn]*Y[jfe75]*rate_eval.n_Fe75__Fe76  +
          -Y[jfe76]*rate_eval.Fe76__n_n_n_Co73__weak__mo03  +
          -rho*Y[jhe4]*Y[jfe76]*rate_eval.He4_Fe76__Ni80  +
          -rho*Y[jp]*Y[jfe76]*rate_eval.p_Fe76__Co77  +
          -Y[jfe76]*rate_eval.Fe76__n_n_Co74__weak__mp17  +
          -rho*Y[jp]*Y[jfe76]*rate_eval.p_Fe76__n_Co76  +
          -Y[jfe76]*rate_eval.Fe76__n_Co75__weak__mp17  +
          -Y[jfe76]*rate_eval.Fe76__Co76__weak__mo03
       )

    dYdt[jco47] = (
          +rho*Y[jhe4]*Y[jmn43]*rate_eval.He4_Mn43__Co47  +
          +rho*Y[jp]*Y[jfe46]*rate_eval.p_Fe46__Co47
       )

    dYdt[jco48] = (
          +rho*Y[jhe4]*Y[jmn44]*rate_eval.He4_Mn44__Co48  +
          +rho*Y[jhe4]*Y[jfe45]*rate_eval.He4_Fe45__p_Co48  +
          +rho*Y[jp]*Y[jfe47]*rate_eval.p_Fe47__Co48
       )

    dYdt[jco49] = (
          +rho*Y[jhe4]*Y[jfe46]*rate_eval.He4_Fe46__p_Co49  +
          +rho*Y[jhe4]*Y[jmn45]*rate_eval.He4_Mn45__Co49  +
          +rho*Y[jp]*Y[jfe48]*rate_eval.p_Fe48__Co49
       )

    dYdt[jco50] = (
          +rho*Y[jhe4]*Y[jmn46]*rate_eval.He4_Mn46__Co50  +
          +rho*Y[jp]*Y[jfe49]*rate_eval.p_Fe49__Co50  +
          +rho*Y[jhe4]*Y[jfe47]*rate_eval.He4_Fe47__p_Co50
       )

    dYdt[jco51] = (
          +rho*Y[jhe4]*Y[jfe48]*rate_eval.He4_Fe48__p_Co51  +
          +rho*Y[jhe4]*Y[jmn47]*rate_eval.He4_Mn47__Co51  +
          +rho*Y[jp]*Y[jfe50]*rate_eval.p_Fe50__Co51
       )

    dYdt[jco52] = (
          +rho*Y[jhe4]*Y[jfe49]*rate_eval.He4_Fe49__p_Co52  +
          +rho*Y[jhe4]*Y[jmn48]*rate_eval.He4_Mn48__Co52  +
          +rho*Y[jp]*Y[jfe51]*rate_eval.p_Fe51__Co52
       )

    dYdt[jco53] = (
          +rho*Y[jhe4]*Y[jfe50]*rate_eval.He4_Fe50__p_Co53  +
          +rho*Y[jhe4]*Y[jmn49]*rate_eval.He4_Mn49__Co53  +
          +rho*Y[jp]*Y[jfe52]*rate_eval.p_Fe52__Co53
       )

    dYdt[jco54] = (
          +rho*Y[jhe4]*Y[jmn50]*rate_eval.He4_Mn50__Co54  +
          +rho*Y[jp]*Y[jfe53]*rate_eval.p_Fe53__Co54  +
          +rho*Y[jhe4]*Y[jfe51]*rate_eval.He4_Fe51__p_Co54
       )

    dYdt[jco55] = (
          +rho*Y[jhe4]*Y[jfe52]*rate_eval.He4_Fe52__p_Co55  +
          +rho*Y[jp]*Y[jfe54]*rate_eval.p_Fe54__Co55  +
          +rho*Y[jhe4]*Y[jmn51]*rate_eval.He4_Mn51__Co55
       )

    dYdt[jco56] = (
          +rho*Y[jhe4]*Y[jfe53]*rate_eval.He4_Fe53__p_Co56  +
          +rho*Y[jp]*Y[jfe55]*rate_eval.p_Fe55__Co56  +
          +rho*Y[jhe4]*Y[jmn52]*rate_eval.He4_Mn52__Co56
       )

    dYdt[jco57] = (
          +rho*Y[jp]*Y[jfe56]*rate_eval.p_Fe56__Co57  +
          +rho*Y[jhe4]*Y[jmn53]*rate_eval.He4_Mn53__Co57
       )

    dYdt[jco58] = (
          +rho*Y[jhe4]*Y[jmn54]*rate_eval.He4_Mn54__Co58  +
          +rho*Y[jp]*Y[jfe57]*rate_eval.p_Fe57__Co58
       )

    dYdt[jco59] = (
          +rho*Y[jp]*Y[jfe59]*rate_eval.p_Fe59__n_Co59  +
          +rho*Y[jp]*Y[jfe58]*rate_eval.p_Fe58__Co59  +
          +Y[jfe59]*rate_eval.Fe59__Co59__weak__wc12  +
          +rho*Y[jhe4]*Y[jmn55]*rate_eval.He4_Mn55__Co59
       )

    dYdt[jco60] = (
          +rho*Y[jp]*Y[jfe59]*rate_eval.p_Fe59__Co60  +
          +Y[jfe60]*rate_eval.Fe60__Co60__weak__wc12  +
          +rho*Y[jhe4]*Y[jmn56]*rate_eval.He4_Mn56__Co60
       )

    dYdt[jco61] = (
          +rho*Y[jp]*Y[jfe61]*rate_eval.p_Fe61__n_Co61  +
          +rho*Y[jp]*Y[jfe60]*rate_eval.p_Fe60__Co61  +
          +rho*Y[jhe4]*Y[jmn58]*rate_eval.He4_Mn58__n_Co61  +
          +Y[jfe61]*rate_eval.Fe61__Co61__weak__wc12  +
          +rho*Y[jhe4]*Y[jmn57]*rate_eval.He4_Mn57__Co61
       )

    dYdt[jco62] = (
          +rho*Y[jp]*Y[jfe62]*rate_eval.p_Fe62__n_Co62  +
          +rho*Y[jp]*Y[jfe61]*rate_eval.p_Fe61__Co62  +
          +rho*Y[jhe4]*Y[jmn59]*rate_eval.He4_Mn59__n_Co62  +
          +rho*Y[jhe4]*Y[jmn58]*rate_eval.He4_Mn58__Co62  +
          +Y[jfe62]*rate_eval.Fe62__Co62__weak__wc12
       )

    dYdt[jco63] = (
          +rho*Y[jhe4]*Y[jmn60]*rate_eval.He4_Mn60__n_Co63  +
          +rho*Y[jhe4]*Y[jmn59]*rate_eval.He4_Mn59__Co63  +
          +rho*Y[jp]*Y[jfe63]*rate_eval.p_Fe63__n_Co63  +
          +Y[jfe63]*rate_eval.Fe63__Co63__weak__wc12  +
          +rho*Y[jp]*Y[jfe62]*rate_eval.p_Fe62__Co63
       )

    dYdt[jco64] = (
          +rho*Y[jhe4]*Y[jmn60]*rate_eval.He4_Mn60__Co64  +
          +rho*Y[jp]*Y[jfe63]*rate_eval.p_Fe63__Co64  +
          +rho*Y[jp]*Y[jfe64]*rate_eval.p_Fe64__n_Co64  +
          +rho*Y[jhe4]*Y[jmn61]*rate_eval.He4_Mn61__n_Co64  +
          +Y[jfe64]*rate_eval.Fe64__Co64__weak__wc12
       )

    dYdt[jco65] = (
          +rho*Y[jhe4]*Y[jmn62]*rate_eval.He4_Mn62__n_Co65  +
          +rho*Y[jhe4]*Y[jmn61]*rate_eval.He4_Mn61__Co65  +
          +rho*Y[jp]*Y[jfe64]*rate_eval.p_Fe64__Co65  +
          +rho*Y[jp]*Y[jfe65]*rate_eval.p_Fe65__n_Co65  +
          +Y[jfe65]*rate_eval.Fe65__Co65__weak__wc12
       )

    dYdt[jco66] = (
          +rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__n_Co66  +
          +rho*Y[jp]*Y[jfe65]*rate_eval.p_Fe65__Co66  +
          +Y[jfe66]*rate_eval.Fe66__Co66__weak__wc12  +
          +rho*Y[jhe4]*Y[jmn62]*rate_eval.He4_Mn62__Co66  +
          +rho*Y[jhe4]*Y[jmn63]*rate_eval.He4_Mn63__n_Co66
       )

    dYdt[jco67] = (
          +Y[jfe67]*rate_eval.Fe67__Co67__weak__wc12  +
          +rho*Y[jp]*Y[jfe67]*rate_eval.p_Fe67__n_Co67  +
          +rho*Y[jp]*Y[jfe66]*rate_eval.p_Fe66__Co67  +
          +rho*Y[jhe4]*Y[jmn63]*rate_eval.He4_Mn63__Co67  +
          +Y[jfe68]*rate_eval.Fe68__n_Co67__weak__mp17  +
          +rho*Y[jhe4]*Y[jmn64]*rate_eval.He4_Mn64__n_Co67
       )

    dYdt[jco68] = (
          +rho*Y[jhe4]*Y[jmn65]*rate_eval.He4_Mn65__n_Co68  +
          +rho*Y[jhe4]*Y[jmn64]*rate_eval.He4_Mn64__Co68  +
          +Y[jfe69]*rate_eval.Fe69__n_Co68__weak__mp17  +
          +rho*Y[jp]*Y[jfe67]*rate_eval.p_Fe67__Co68  +
          +rho*Y[jp]*Y[jfe68]*rate_eval.p_Fe68__n_Co68  +
          +Y[jfe68]*rate_eval.Fe68__Co68__weak__wc12
       )

    dYdt[jco69] = (
          +rho*Y[jp]*Y[jfe69]*rate_eval.p_Fe69__n_Co69  +
          +rho*Y[jp]*Y[jfe68]*rate_eval.p_Fe68__Co69  +
          +Y[jfe69]*rate_eval.Fe69__Co69__weak__wc17  +
          +rho*Y[jhe4]*Y[jmn65]*rate_eval.He4_Mn65__Co69  +
          +Y[jfe70]*rate_eval.Fe70__n_Co69__weak__mp17  +
          +rho*Y[jhe4]*Y[jmn66]*rate_eval.He4_Mn66__n_Co69
       )

    dYdt[jco70] = (
          +rho*Y[jp]*Y[jfe70]*rate_eval.p_Fe70__n_Co70  +
          +rho*Y[jhe4]*Y[jmn67]*rate_eval.He4_Mn67__n_Co70  +
          +rho*Y[jp]*Y[jfe69]*rate_eval.p_Fe69__Co70  +
          +rho*Y[jhe4]*Y[jmn66]*rate_eval.He4_Mn66__Co70  +
          +Y[jfe70]*rate_eval.Fe70__Co70__weak__wc17  +
          +Y[jfe71]*rate_eval.Fe71__n_Co70__weak__mp17
       )

    dYdt[jco71] = (
          +rho*Y[jp]*Y[jfe71]*rate_eval.p_Fe71__n_Co71  +
          +rho*Y[jhe4]*Y[jmn68]*rate_eval.He4_Mn68__n_Co71  +
          +rho*Y[jp]*Y[jfe70]*rate_eval.p_Fe70__Co71  +
          +rho*Y[jhe4]*Y[jmn67]*rate_eval.He4_Mn67__Co71  +
          +Y[jfe72]*rate_eval.Fe72__n_Co71__weak__mp17  +
          +Y[jfe73]*rate_eval.Fe73__n_n_Co71__weak__mp17  +
          +Y[jfe71]*rate_eval.Fe71__Co71__weak__wc17
       )

    dYdt[jco72] = (
          +Y[jfe75]*rate_eval.Fe75__n_n_n_Co72__weak__mo03  +
          +rho*Y[jp]*Y[jfe72]*rate_eval.p_Fe72__n_Co72  +
          +rho*Y[jhe4]*Y[jmn69]*rate_eval.He4_Mn69__n_Co72  +
          +rho*Y[jhe4]*Y[jmn68]*rate_eval.He4_Mn68__Co72  +
          +rho*Y[jp]*Y[jfe71]*rate_eval.p_Fe71__Co72  +
          +Y[jfe73]*rate_eval.Fe73__n_Co72__weak__mp17  +
          +Y[jfe72]*rate_eval.Fe72__Co72__weak__mo03
       )

    dYdt[jco73] = (
          +rho*Y[jp]*Y[jfe73]*rate_eval.p_Fe73__n_Co73  +
          +Y[jfe76]*rate_eval.Fe76__n_n_n_Co73__weak__mo03  +
          +rho*Y[jp]*Y[jfe72]*rate_eval.p_Fe72__Co73  +
          +rho*Y[jhe4]*Y[jmn69]*rate_eval.He4_Mn69__Co73  +
          +Y[jfe75]*rate_eval.Fe75__n_n_Co73__weak__mp17  +
          +Y[jfe74]*rate_eval.Fe74__n_Co73__weak__mp17  +
          +Y[jfe73]*rate_eval.Fe73__Co73__weak__mo03  +
          +rho*Y[jhe4]*Y[jmn70]*rate_eval.He4_Mn70__n_Co73
       )

    dYdt[jco74] = (
          +rho*Y[jp]*Y[jfe74]*rate_eval.p_Fe74__n_Co74  +
          +rho*Y[jhe4]*Y[jmn70]*rate_eval.He4_Mn70__Co74  +
          +rho*Y[jp]*Y[jfe73]*rate_eval.p_Fe73__Co74  +
          +Y[jfe75]*rate_eval.Fe75__n_Co74__weak__mp17  +
          +Y[jfe74]*rate_eval.Fe74__Co74__weak__mo03  +
          +Y[jfe76]*rate_eval.Fe76__n_n_Co74__weak__mp17  +
          +rho*Y[jhe4]*Y[jmn71]*rate_eval.He4_Mn71__n_Co74
       )

    dYdt[jco75] = (
          +rho*Y[jp]*Y[jfe75]*rate_eval.p_Fe75__n_Co75  +
          +rho*Y[jhe4]*Y[jmn72]*rate_eval.He4_Mn72__n_Co75  +
          +rho*Y[jhe4]*Y[jmn71]*rate_eval.He4_Mn71__Co75  +
          +Y[jfe75]*rate_eval.Fe75__Co75__weak__mo03  +
          +rho*Y[jp]*Y[jfe74]*rate_eval.p_Fe74__Co75  +
          +Y[jfe76]*rate_eval.Fe76__n_Co75__weak__mp17
       )

    dYdt[jco76] = (
          +rho*Y[jhe4]*Y[jmn73]*rate_eval.He4_Mn73__n_Co76  +
          +rho*Y[jhe4]*Y[jmn72]*rate_eval.He4_Mn72__Co76  +
          +rho*Y[jp]*Y[jfe76]*rate_eval.p_Fe76__n_Co76  +
          +Y[jfe76]*rate_eval.Fe76__Co76__weak__mo03  +
          +rho*Y[jp]*Y[jfe75]*rate_eval.p_Fe75__Co76
       )

    dYdt[jco77] = (
          +rho*Y[jp]*Y[jfe76]*rate_eval.p_Fe76__Co77  +
          +rho*Y[jhe4]*Y[jmn73]*rate_eval.He4_Mn73__Co77
       )

    dYdt[jni49] = (
          +rho*Y[jhe4]*Y[jfe45]*rate_eval.He4_Fe45__Ni49
       )

    dYdt[jni50] = (
          +rho*Y[jhe4]*Y[jfe46]*rate_eval.He4_Fe46__Ni50
       )

    dYdt[jni51] = (
          +rho*Y[jhe4]*Y[jfe47]*rate_eval.He4_Fe47__Ni51
       )

    dYdt[jni52] = (
          +rho*Y[jhe4]*Y[jfe48]*rate_eval.He4_Fe48__Ni52
       )

    dYdt[jni53] = (
          +rho*Y[jhe4]*Y[jfe49]*rate_eval.He4_Fe49__Ni53
       )

    dYdt[jni54] = (
          +rho*Y[jhe4]*Y[jfe50]*rate_eval.He4_Fe50__Ni54
       )

    dYdt[jni55] = (
          +rho*Y[jhe4]*Y[jfe51]*rate_eval.He4_Fe51__Ni55
       )

    dYdt[jni56] = (
          +rho*Y[jhe4]*Y[jfe52]*rate_eval.He4_Fe52__Ni56
       )

    dYdt[jni57] = (
          +rho*Y[jhe4]*Y[jfe53]*rate_eval.He4_Fe53__Ni57
       )

    dYdt[jni58] = (
          +rho*Y[jhe4]*Y[jfe54]*rate_eval.He4_Fe54__Ni58
       )

    dYdt[jni59] = (
          +rho*Y[jhe4]*Y[jfe55]*rate_eval.He4_Fe55__Ni59
       )

    dYdt[jni60] = (
          +rho*Y[jhe4]*Y[jfe56]*rate_eval.He4_Fe56__Ni60
       )

    dYdt[jni61] = (
          +rho*Y[jhe4]*Y[jfe57]*rate_eval.He4_Fe57__Ni61
       )

    dYdt[jni62] = (
          +rho*Y[jhe4]*Y[jfe59]*rate_eval.He4_Fe59__n_Ni62  +
          +rho*Y[jhe4]*Y[jfe58]*rate_eval.He4_Fe58__Ni62
       )

    dYdt[jni63] = (
          +rho*Y[jhe4]*Y[jfe59]*rate_eval.He4_Fe59__Ni63
       )

    dYdt[jni64] = (
          +rho*Y[jhe4]*Y[jfe61]*rate_eval.He4_Fe61__n_Ni64  +
          +rho*Y[jhe4]*Y[jfe60]*rate_eval.He4_Fe60__Ni64
       )

    dYdt[jni65] = (
          +rho*Y[jhe4]*Y[jfe62]*rate_eval.He4_Fe62__n_Ni65  +
          +rho*Y[jhe4]*Y[jfe61]*rate_eval.He4_Fe61__Ni65
       )

    dYdt[jni66] = (
          +rho*Y[jhe4]*Y[jfe63]*rate_eval.He4_Fe63__n_Ni66  +
          +rho*Y[jhe4]*Y[jfe62]*rate_eval.He4_Fe62__Ni66
       )

    dYdt[jni67] = (
          +rho*Y[jhe4]*Y[jfe64]*rate_eval.He4_Fe64__n_Ni67  +
          +rho*Y[jhe4]*Y[jfe63]*rate_eval.He4_Fe63__Ni67
       )

    dYdt[jni68] = (
          +rho*Y[jhe4]*Y[jfe64]*rate_eval.He4_Fe64__Ni68  +
          +rho*Y[jhe4]*Y[jfe65]*rate_eval.He4_Fe65__n_Ni68
       )

    dYdt[jni69] = (
          +rho*Y[jhe4]*Y[jfe65]*rate_eval.He4_Fe65__Ni69  +
          +rho*Y[jhe4]*Y[jfe66]*rate_eval.He4_Fe66__n_Ni69
       )

    dYdt[jni70] = (
          +rho*Y[jhe4]*Y[jfe66]*rate_eval.He4_Fe66__Ni70  +
          +rho*Y[jhe4]*Y[jfe67]*rate_eval.He4_Fe67__n_Ni70
       )

    dYdt[jni71] = (
          +rho*Y[jhe4]*Y[jfe68]*rate_eval.He4_Fe68__n_Ni71  +
          +rho*Y[jhe4]*Y[jfe67]*rate_eval.He4_Fe67__Ni71
       )

    dYdt[jni72] = (
          +rho*Y[jhe4]*Y[jfe68]*rate_eval.He4_Fe68__Ni72  +
          +rho*Y[jhe4]*Y[jfe69]*rate_eval.He4_Fe69__n_Ni72
       )

    dYdt[jni73] = (
          +rho*Y[jhe4]*Y[jfe70]*rate_eval.He4_Fe70__n_Ni73  +
          +rho*Y[jhe4]*Y[jfe69]*rate_eval.He4_Fe69__Ni73
       )

    dYdt[jni74] = (
          +rho*Y[jhe4]*Y[jfe71]*rate_eval.He4_Fe71__n_Ni74  +
          +rho*Y[jhe4]*Y[jfe70]*rate_eval.He4_Fe70__Ni74
       )

    dYdt[jni75] = (
          +rho*Y[jhe4]*Y[jfe71]*rate_eval.He4_Fe71__Ni75  +
          +rho*Y[jhe4]*Y[jfe72]*rate_eval.He4_Fe72__n_Ni75
       )

    dYdt[jni76] = (
          +rho*Y[jhe4]*Y[jfe73]*rate_eval.He4_Fe73__n_Ni76  +
          +rho*Y[jhe4]*Y[jfe72]*rate_eval.He4_Fe72__Ni76
       )

    dYdt[jni77] = (
          +rho*Y[jhe4]*Y[jfe74]*rate_eval.He4_Fe74__n_Ni77  +
          +rho*Y[jhe4]*Y[jfe73]*rate_eval.He4_Fe73__Ni77
       )

    dYdt[jni78] = (
          +rho*Y[jhe4]*Y[jfe75]*rate_eval.He4_Fe75__n_Ni78  +
          +rho*Y[jhe4]*Y[jfe74]*rate_eval.He4_Fe74__Ni78
       )

    dYdt[jni79] = (
          +rho*Y[jhe4]*Y[jfe76]*rate_eval.He4_Fe76__n_Ni79  +
          +rho*Y[jhe4]*Y[jfe75]*rate_eval.He4_Fe75__Ni79
       )

    dYdt[jni80] = (
          +rho*Y[jhe4]*Y[jfe76]*rate_eval.He4_Fe76__Ni80
       )

    return dYdt

def jacobian(t, Y, rho, T, screen_func=None):
    return jacobian_eq(t, Y, rho, T, screen_func)

@numba.njit()
def jacobian_eq(t, Y, rho, T, screen_func):

    tf = Tfactors(T)
    rate_eval = RateEval()

    # reaclib rates
    Fe45__p_p_p_Ti42__weak__wc12(rate_eval, tf)
    Cr43__p_p_p_Ca40__weak__wc12(rate_eval, tf)
    Fe75__n_n_n_Co72__weak__mo03(rate_eval, tf)
    Mn73__n_n_n_Fe70__weak__mo03(rate_eval, tf)
    Mn71__n_n_n_Fe68__weak__mo03(rate_eval, tf)
    Cr70__n_n_n_Mn67__weak__mo03(rate_eval, tf)
    V66__n_n_n_Cr63__weak__mo03(rate_eval, tf)
    V65__n_n_n_Cr62__weak__mo03(rate_eval, tf)
    Ti65__n_n_n_V62__weak__mo03(rate_eval, tf)
    Sc63__n_n_n_Ti60__weak__mo03(rate_eval, tf)
    Sc62__n_n_n_Ti59__weak__mo03(rate_eval, tf)
    Sc61__n_n_n_Ti58__weak__mo03(rate_eval, tf)
    Sc59__n_n_n_Ti56__weak__mo03(rate_eval, tf)
    Sc58__n_n_n_Ti55__weak__mo03(rate_eval, tf)
    Sc57__n_n_n_Ti54__weak__mo03(rate_eval, tf)
    Ca60__n_n_n_Sc57__weak__mo03(rate_eval, tf)
    Ca59__n_n_n_Sc56__weak__mo03(rate_eval, tf)
    Ca58__n_n_n_Sc55__weak__mo03(rate_eval, tf)
    Ca57__n_n_n_Sc54__weak__mo03(rate_eval, tf)
    K59__n_n_n_Ca56__weak__mo03(rate_eval, tf)
    K58__n_n_n_Ca55__weak__mo03(rate_eval, tf)
    K55__n_n_n_Ca52__weak__mo03(rate_eval, tf)
    K53__n_n_n_Ca50__weak__mo03(rate_eval, tf)
    Ar54__n_n_n_K51__weak__mo03(rate_eval, tf)
    Ar53__n_n_n_K50__weak__mo03(rate_eval, tf)
    Ar52__n_n_n_K49__weak__mo03(rate_eval, tf)
    Cl50__n_n_n_Ar47__weak__mo03(rate_eval, tf)
    S48__n_n_n_Cl45__weak__mo03(rate_eval, tf)
    S47__n_n_n_Cl44__weak__mo03(rate_eval, tf)
    K56__n_n_n_Ca53__weak__mo03(rate_eval, tf)
    P44__n_n_n_S41__weak__mo03(rate_eval, tf)
    Si42__n_n_n_P39__weak__mo03(rate_eval, tf)
    Al43__n_n_n_Si40__weak__mo03(rate_eval, tf)
    Al42__n_n_n_Si39__weak__mo03(rate_eval, tf)
    Al41__n_n_n_Si38__weak__mo03(rate_eval, tf)
    Al39__n_n_n_Si36__weak__mo03(rate_eval, tf)
    Al38__n_n_n_Si35__weak__mo03(rate_eval, tf)
    Al37__n_n_n_Si34__weak__mo03(rate_eval, tf)
    Mg40__n_n_n_Al37__weak__mo03(rate_eval, tf)
    Mg36__n_n_n_Al33__weak__mo03(rate_eval, tf)
    Mg35__n_n_n_Al32__weak__mo03(rate_eval, tf)
    Na34__n_n_n_Mg31__weak__mo03(rate_eval, tf)
    Na33__n_n_n_Mg30__weak__mo03(rate_eval, tf)
    Na32__n_n_n_Mg29__weak__mo03(rate_eval, tf)
    Ne31__n_n_n_Na28__weak__mo03(rate_eval, tf)
    F31__n_n_n_Ne28__weak__mo03(rate_eval, tf)
    F29__n_n_n_Ne26__weak__mo03(rate_eval, tf)
    K54__n_n_n_Ca51__weak__mo03(rate_eval, tf)
    F28__n_n_n_Ne25__weak__mo03(rate_eval, tf)
    F27__n_n_n_Ne24__weak__mo03(rate_eval, tf)
    O27__n_n_n_F24__weak__mo03(rate_eval, tf)
    n_p_p__p_d(rate_eval, tf)
    n_n_He4__He6(rate_eval, tf)
    p_Be9__n_p_He4_He4(rate_eval, tf)
    He3_Be7__p_p_He4_He4(rate_eval, tf)
    t_Be7__n_p_He4_He4(rate_eval, tf)
    He4_Ca36__p_p_Ca38(rate_eval, tf)
    He4_O13__p_p_O15(rate_eval, tf)
    p_B11__He4_He4_He4(rate_eval, tf)
    n_B8__p_He4_He4(rate_eval, tf)
    p_Be9__d_He4_He4(rate_eval, tf)
    d_Li7__n_He4_He4(rate_eval, tf)
    He3_He3__p_p_He4(rate_eval, tf)
    He4_Fe76__n_Ni79(rate_eval, tf)
    p_Fe76__He4_Mn73(rate_eval, tf)
    He4_Fe75__n_Ni78(rate_eval, tf)
    p_Fe75__He4_Mn72(rate_eval, tf)
    p_Fe75__n_Co75(rate_eval, tf)
    He4_Fe74__n_Ni77(rate_eval, tf)
    p_Fe74__He4_Mn71(rate_eval, tf)
    p_Fe74__n_Co74(rate_eval, tf)
    Mg37__n_n_n_Al34__weak__mo03(rate_eval, tf)
    p_Fe73__He4_Mn70(rate_eval, tf)
    p_Fe73__n_Co73(rate_eval, tf)
    p_Fe72__He4_Mn69(rate_eval, tf)
    p_Fe72__n_Co72(rate_eval, tf)
    He4_Fe71__n_Ni74(rate_eval, tf)
    p_Fe71__He4_Mn68(rate_eval, tf)
    p_Fe71__n_Co71(rate_eval, tf)
    He4_Fe70__n_Ni73(rate_eval, tf)
    p_Fe70__He4_Mn67(rate_eval, tf)
    p_Fe70__n_Co70(rate_eval, tf)
    p_Fe69__He4_Mn66(rate_eval, tf)
    p_Fe69__n_Co69(rate_eval, tf)
    He4_Fe68__n_Ni71(rate_eval, tf)
    p_Fe68__He4_Mn65(rate_eval, tf)
    p_Fe67__He4_Mn64(rate_eval, tf)
    p_Fe65__He4_Mn62(rate_eval, tf)
    He4_Fe64__n_Ni67(rate_eval, tf)
    He4_Fe63__n_Ni66(rate_eval, tf)
    p_Fe63__He4_Mn60(rate_eval, tf)
    p_Fe62__He4_Mn59(rate_eval, tf)
    p_Fe61__He4_Mn58(rate_eval, tf)
    p_Fe61__n_Co61(rate_eval, tf)
    p_Fe60__He4_Mn57(rate_eval, tf)
    He4_Fe59__n_Ni62(rate_eval, tf)
    p_Fe59__He4_Mn56(rate_eval, tf)
    p_Fe59__n_Co59(rate_eval, tf)
    p_Fe57__He4_Mn54(rate_eval, tf)
    n_Fe56__He4_Cr53(rate_eval, tf)
    O28__n_O27(rate_eval, tf)
    p_Ar34__K35(rate_eval, tf)
    n_Fe55__p_Mn55(rate_eval, tf)
    n_Sc40__Sc41(rate_eval, tf)
    n_Fe54__p_Mn54(rate_eval, tf)
    He4_Sc59__V63(rate_eval, tf)
    n_Fe53__He4_Cr50(rate_eval, tf)
    Fe67__Co67__weak__wc12(rate_eval, tf)
    He4_S30__Ar34(rate_eval, tf)
    n_Fe53__p_Mn53(rate_eval, tf)
    He4_Fe52__p_Co55(rate_eval, tf)
    n_Al25__Al26(rate_eval, tf)
    p_Ca61__Sc62(rate_eval, tf)
    n_Fe52__He4_Cr49(rate_eval, tf)
    Mn58__Fe58__weak__wc12(rate_eval, tf)
    n_Fe51__He4_Cr48(rate_eval, tf)
    He4_Cr66__Fe70(rate_eval, tf)
    n_Fe50__He4_Cr47(rate_eval, tf)
    He4_Fe49__p_Co52(rate_eval, tf)
    n_Fe49__He4_Cr46(rate_eval, tf)
    n_Fe49__p_Mn49(rate_eval, tf)
    He4_Fe48__p_Co51(rate_eval, tf)
    p_Sc50__Ti51(rate_eval, tf)
    n_Fe47__He4_Cr44(rate_eval, tf)
    Al37__Si37__weak__wc17(rate_eval, tf)
    n_Fe46__He4_Cr43(rate_eval, tf)
    n_Fe46__p_Mn46(rate_eval, tf)
    He4_Mn73__n_Co76(rate_eval, tf)
    p_Mn73__He4_Cr70(rate_eval, tf)
    p_Mg34__Al35(rate_eval, tf)
    He4_Mn72__n_Co75(rate_eval, tf)
    p_Mn72__He4_Cr69(rate_eval, tf)
    p_Mn71__He4_Cr68(rate_eval, tf)
    Ca56__n_n_n_Sc53__weak__mo03(rate_eval, tf)
    He4_Mn69__n_Co72(rate_eval, tf)
    p_Mn69__He4_Cr66(rate_eval, tf)
    He4_Mn68__n_Co71(rate_eval, tf)
    p_Mn68__n_Fe68(rate_eval, tf)
    He4_Si33__n_S36(rate_eval, tf)
    p_Mn67__He4_Cr64(rate_eval, tf)
    p_Mn66__He4_Cr63(rate_eval, tf)
    p_Mn66__n_Fe66(rate_eval, tf)
    p_K48__Ca49(rate_eval, tf)
    p_P46__S47(rate_eval, tf)
    He4_Ca52__Ti56(rate_eval, tf)
    He4_Mn65__n_Co68(rate_eval, tf)
    p_Mn65__He4_Cr62(rate_eval, tf)
    p_Si44__n_P44(rate_eval, tf)
    He4_Mn68__Co72(rate_eval, tf)
    p_Mn64__He4_Cr61(rate_eval, tf)
    p_Mn62__He4_Cr59(rate_eval, tf)
    He4_Mn60__n_Co63(rate_eval, tf)
    p_Mn60__He4_Cr57(rate_eval, tf)
    p_Mn60__n_Fe60(rate_eval, tf)
    He4_Fe65__Ni69(rate_eval, tf)
    p_Mn59__He4_Cr56(rate_eval, tf)
    p_Mn57__n_Fe57(rate_eval, tf)
    p_Fe64__He4_Mn61(rate_eval, tf)
    p_Mn56__He4_Cr53(rate_eval, tf)
    p_Mn54__He4_Cr51(rate_eval, tf)
    S49__n_n_n_Cl46__weak__mo03(rate_eval, tf)
    He4_Mn53__p_Fe56(rate_eval, tf)
    p_Mn53__He4_Cr50(rate_eval, tf)
    n_Mn52__He4_V49(rate_eval, tf)
    Ar48__n_K47__weak__mp17(rate_eval, tf)
    n_Mn52__p_Cr52(rate_eval, tf)
    He4_Mn51__p_Fe54(rate_eval, tf)
    p_Ca53__n_Sc53(rate_eval, tf)
    n_Mn51__p_Cr51(rate_eval, tf)
    p_O22__n_F22(rate_eval, tf)
    n_Mn50__He4_V47(rate_eval, tf)
    He4_Mn49__p_Fe52(rate_eval, tf)
    n_Cl37__Cl38(rate_eval, tf)
    n_Mn48__He4_V45(rate_eval, tf)
    He4_Mn47__p_Fe50(rate_eval, tf)
    n_Ne20__Ne21(rate_eval, tf)
    n_Mn47__p_Cr47(rate_eval, tf)
    He4_Mn46__p_Fe49(rate_eval, tf)
    p_Ca44__Sc45(rate_eval, tf)
    n_Mn46__He4_V43(rate_eval, tf)
    n_Mn46__p_Cr46(rate_eval, tf)
    n_Mn45__p_Cr45(rate_eval, tf)
    He4_Mn44__p_Fe47(rate_eval, tf)
    He4_Cr70__n_Fe73(rate_eval, tf)
    n_F26__F27(rate_eval, tf)
    He4_Cr69__n_Fe72(rate_eval, tf)
    p_Cr68__He4_V65(rate_eval, tf)
    p_Cr68__n_Mn68(rate_eval, tf)
    p_Cr67__n_Mn67(rate_eval, tf)
    He4_Cr66__n_Fe69(rate_eval, tf)
    p_Cr66__He4_V63(rate_eval, tf)
    He4_Cr65__n_Fe68(rate_eval, tf)
    p_Cr65__He4_V62(rate_eval, tf)
    p_Mn72__n_Fe72(rate_eval, tf)
    He4_Cr64__n_Fe67(rate_eval, tf)
    p_O25__n_F25(rate_eval, tf)
    He4_Cr63__n_Fe66(rate_eval, tf)
    p_Cr63__n_Mn63(rate_eval, tf)
    He4_Cr62__n_Fe65(rate_eval, tf)
    p_Cr62__He4_V59(rate_eval, tf)
    N21__O21__weak__wc12(rate_eval, tf)
    He4_Mn48__Co52(rate_eval, tf)
    He4_Cr61__n_Fe64(rate_eval, tf)
    p_Cr60__He4_V57(rate_eval, tf)
    He4_Cr59__n_Fe62(rate_eval, tf)
    n_Ca50__Ca51(rate_eval, tf)
    p_Cr59__n_Mn59(rate_eval, tf)
    p_Fe62__n_Co62(rate_eval, tf)
    n_O18__O19(rate_eval, tf)
    p_Cr57__n_Mn57(rate_eval, tf)
    Mg22__Na22__weak__wc12(rate_eval, tf)
    He4_Cr55__n_Fe58(rate_eval, tf)
    Cr43__p_p_Sc41__weak__wc12(rate_eval, tf)
    n_Cr55__He4_Ti52(rate_eval, tf)
    p_Cr54__He4_V51(rate_eval, tf)
    p_Ne32__Na33(rate_eval, tf)
    p_Mg24__He4_Na21(rate_eval, tf)
    p_Si38__n_P38(rate_eval, tf)
    Mn54__Cr54__weak__wc12(rate_eval, tf)
    p_Mn55__He4_Cr52(rate_eval, tf)
    n_Cr51__He4_Ti48(rate_eval, tf)
    n_Cr50__He4_Ti47(rate_eval, tf)
    He4_Cr49__p_Mn52(rate_eval, tf)
    He4_Cr48__p_Mn51(rate_eval, tf)
    n_Cr48__p_V48(rate_eval, tf)
    p_Ti57__He4_Sc54(rate_eval, tf)
    n_Cr46__He4_Ti43(rate_eval, tf)
    He4_Cr45__p_Mn48(rate_eval, tf)
    n_B13__B14(rate_eval, tf)
    He4_Ne29__Mg33(rate_eval, tf)
    He4_Ti59__n_Cr62(rate_eval, tf)
    He4_P44__n_Cl47(rate_eval, tf)
    n_Cr45__He4_Ti42(rate_eval, tf)
    He4_Cr44__p_Mn47(rate_eval, tf)
    He4_Cr43__p_Mn46(rate_eval, tf)
    n_Cr43__p_V43(rate_eval, tf)
    He4_Cr42__p_Mn45(rate_eval, tf)
    n_Cr42__He4_Ti39(rate_eval, tf)
    n_Cr42__p_V42(rate_eval, tf)
    n_Cr41__He4_Ti38(rate_eval, tf)
    Ne26__n_Na25__weak__wc12(rate_eval, tf)
    He4_V67__n_Mn70(rate_eval, tf)
    He4_Sc37__p_Ti40(rate_eval, tf)
    p_V67__n_Cr67(rate_eval, tf)
    He4_V66__n_Mn69(rate_eval, tf)
    p_V66__n_Cr66(rate_eval, tf)
    He4_V50__p_Cr53(rate_eval, tf)
    p_K47__He4_Ar44(rate_eval, tf)
    p_V65__He4_Ti62(rate_eval, tf)
    He4_V64__n_Mn67(rate_eval, tf)
    n_Cr49__p_V49(rate_eval, tf)
    p_V64__He4_Ti61(rate_eval, tf)
    p_V63__n_Cr63(rate_eval, tf)
    He4_Mn60__Co64(rate_eval, tf)
    He4_V62__n_Mn65(rate_eval, tf)
    He4_V61__n_Mn64(rate_eval, tf)
    p_V61__n_Cr61(rate_eval, tf)
    p_P32__n_S32(rate_eval, tf)
    He4_Al32__n_P35(rate_eval, tf)
    He4_V63__Mn67(rate_eval, tf)
    p_V60__He4_Ti57(rate_eval, tf)
    t_He3__n_p_He4(rate_eval, tf)
    p_V60__n_Cr60(rate_eval, tf)
    p_O27__He4_N24(rate_eval, tf)
    p_Si43__n_P43(rate_eval, tf)
    He4_V59__n_Mn62(rate_eval, tf)
    He4_V58__n_Mn61(rate_eval, tf)
    p_V58__He4_Ti55(rate_eval, tf)
    p_V58__n_Cr58(rate_eval, tf)
    p_V57__He4_Ti54(rate_eval, tf)
    p_V57__n_Cr57(rate_eval, tf)
    n_Cr53__He4_Ti50(rate_eval, tf)
    He4_V56__n_Mn59(rate_eval, tf)
    Mn43__Cr43__weak__bqa_pos_(rate_eval, tf)
    He4_Al40__p_Si43(rate_eval, tf)
    He4_V55__n_Mn58(rate_eval, tf)
    Ne28__Na28__weak__wc17(rate_eval, tf)
    He4_Cr47__p_Mn50(rate_eval, tf)
    p_V55__n_Cr55(rate_eval, tf)
    He4_V54__n_Mn57(rate_eval, tf)
    He4_Ar52__Ca56(rate_eval, tf)
    p_V53__n_Cr53(rate_eval, tf)
    p_V52__He4_Ti49(rate_eval, tf)
    p_V52__n_Cr52(rate_eval, tf)
    He4_S45__n_Ar48(rate_eval, tf)
    He4_Ca43__Ti47(rate_eval, tf)
    p_V51__He4_Ti48(rate_eval, tf)
    p_F23__Ne24(rate_eval, tf)
    n_Mn69__Mn70(rate_eval, tf)
    p_V50__He4_Ti47(rate_eval, tf)
    p_V50__n_Cr50(rate_eval, tf)
    n_V50__p_Ti50(rate_eval, tf)
    p_F24__Ne25(rate_eval, tf)
    p_V49__He4_Ti46(rate_eval, tf)
    He4_N15__F19(rate_eval, tf)
    He4_V47__p_Cr50(rate_eval, tf)
    He4_V46__p_Cr49(rate_eval, tf)
    n_V46__He4_Sc43(rate_eval, tf)
    n_V46__p_Ti46(rate_eval, tf)
    He4_V58__Mn62(rate_eval, tf)
    p_Sc52__Ti53(rate_eval, tf)
    n_V44__He4_Sc41(rate_eval, tf)
    n_V44__p_Ti44(rate_eval, tf)
    Cl49__n_n_Ar47__weak__mp17(rate_eval, tf)
    He4_V43__p_Cr46(rate_eval, tf)
    n_V43__p_Ti43(rate_eval, tf)
    He4_V42__p_Cr45(rate_eval, tf)
    He4_Si43__n_S46(rate_eval, tf)
    Sc47__Ti47__weak__wc12(rate_eval, tf)
    He4_Ne33__n_Mg36(rate_eval, tf)
    n_V42__He4_Sc39(rate_eval, tf)
    n_V41__He4_Sc38(rate_eval, tf)
    n_V40__p_Ti40(rate_eval, tf)
    He4_V39__p_Cr42(rate_eval, tf)
    p_Sc53__n_Ti53(rate_eval, tf)
    He4_Ti65__n_Cr68(rate_eval, tf)
    p_Cr57__He4_V54(rate_eval, tf)
    p_Ne27__He4_F24(rate_eval, tf)
    He4_Ti64__n_Cr67(rate_eval, tf)
    p_Ti64__He4_Sc61(rate_eval, tf)
    He4_Ti63__n_Cr66(rate_eval, tf)
    p_Ti63__He4_Sc60(rate_eval, tf)
    p_Ti63__n_V63(rate_eval, tf)
    p_Ti61__n_V61(rate_eval, tf)
    He4_Ti60__n_Cr63(rate_eval, tf)
    n_O12__O13(rate_eval, tf)
    p_Ti60__n_V60(rate_eval, tf)
    p_Ti59__n_V59(rate_eval, tf)
    He4_Ti58__n_Cr61(rate_eval, tf)
    p_Ti58__n_V58(rate_eval, tf)
    K32__Ar32__weak__bqa_pos_(rate_eval, tf)
    He4_Ti55__n_Cr58(rate_eval, tf)
    p_Ti55__n_V55(rate_eval, tf)
    He4_Ti54__n_Cr57(rate_eval, tf)
    p_Ti54__He4_Sc51(rate_eval, tf)
    p_Ti54__n_V54(rate_eval, tf)
    p_F23__He4_O20(rate_eval, tf)
    He4_Ti53__n_Cr56(rate_eval, tf)
    p_Ti53__He4_Sc50(rate_eval, tf)
    n_Na33__Na34(rate_eval, tf)
    He4_Be10__C14(rate_eval, tf)
    p_Ti52__He4_Sc49(rate_eval, tf)
    p_Ti52__n_V52(rate_eval, tf)
    He4_Ti51__n_Cr54(rate_eval, tf)
    Ti43__Sc43__weak__wc12(rate_eval, tf)
    p_Ti51__n_V51(rate_eval, tf)
    n_Ti51__He4_Ca48(rate_eval, tf)
    He4_F26__Na30(rate_eval, tf)
    n_Ti49__He4_Ca46(rate_eval, tf)
    Sc61__n_n_Ti59__weak__mp17(rate_eval, tf)
    He4_Fe73__n_Ni76(rate_eval, tf)
    He4_K36__p_Ca39(rate_eval, tf)
    Sc56__n_Ti55__weak__mp17(rate_eval, tf)
    He4_Ar35__Ca39(rate_eval, tf)
    p_Ar51__He4_Cl48(rate_eval, tf)
    He4_Na19__Al23(rate_eval, tf)
    n_Na35__Na36(rate_eval, tf)
    n_Ti45__p_Sc45(rate_eval, tf)
    He4_Ti43__p_V46(rate_eval, tf)
    n_Ti43__He4_Ca40(rate_eval, tf)
    He4_F28__n_Na31(rate_eval, tf)
    He4_F31__n_Na34(rate_eval, tf)
    n_Ti41__He4_Ca38(rate_eval, tf)
    n_Ti41__p_Sc41(rate_eval, tf)
    He4_Ti40__p_V43(rate_eval, tf)
    n_K55__K56(rate_eval, tf)
    p_Cr55__n_Mn55(rate_eval, tf)
    p_F31__He4_O28(rate_eval, tf)
    He4_Ti39__p_V42(rate_eval, tf)
    n_Ti39__p_Sc39(rate_eval, tf)
    He4_Ti38__p_V41(rate_eval, tf)
    n_Ti38__He4_Ca35(rate_eval, tf)
    n_Ti38__p_Sc38(rate_eval, tf)
    He4_Ti37__p_V40(rate_eval, tf)
    Ti65__n_V64__weak__mp17(rate_eval, tf)
    He4_Sc62__n_V65(rate_eval, tf)
    He4_Sc61__n_V64(rate_eval, tf)
    p_Sc61__n_Ti61(rate_eval, tf)
    He4_Sc40__p_Ti43(rate_eval, tf)
    He4_Sc60__n_V63(rate_eval, tf)
    Ne34__n_n_n_Na31__weak__mo03(rate_eval, tf)
    p_Sc60__He4_Ca57(rate_eval, tf)
    p_Sc60__n_Ti60(rate_eval, tf)
    n_Fe48__p_Mn48(rate_eval, tf)
    He4_Sc59__n_V62(rate_eval, tf)
    n_Mn53__p_Cr53(rate_eval, tf)
    He4_Sc58__n_V61(rate_eval, tf)
    p_Sc58__He4_Ca55(rate_eval, tf)
    p_Sc58__n_Ti58(rate_eval, tf)
    He4_Sc57__n_V60(rate_eval, tf)
    Cr58__Mn58__weak__wc12(rate_eval, tf)
    He4_Sc56__n_V59(rate_eval, tf)
    He4_Sc55__n_V58(rate_eval, tf)
    p_Sc55__He4_Ca52(rate_eval, tf)
    n_Cr41__Cr42(rate_eval, tf)
    He4_Sc54__n_V57(rate_eval, tf)
    p_Sc54__n_Ti54(rate_eval, tf)
    n_Ar36__He4_S33(rate_eval, tf)
    He4_Sc52__n_V55(rate_eval, tf)
    p_Sc52__He4_Ca49(rate_eval, tf)
    p_S47__Cl48(rate_eval, tf)
    He4_C9__p_N12(rate_eval, tf)
    p_Sc52__n_Ti52(rate_eval, tf)
    He4_Sc51__n_V54(rate_eval, tf)
    p_Sc50__n_Ti50(rate_eval, tf)
    He4_Ar29__Ca33(rate_eval, tf)
    p_Sc49__He4_Ca46(rate_eval, tf)
    p_Sc48__He4_Ca45(rate_eval, tf)
    He4_Sc47__p_Ti50(rate_eval, tf)
    p_Sc47__He4_Ca44(rate_eval, tf)
    He4_Sc46__p_Ti49(rate_eval, tf)
    p_Sc46__He4_Ca43(rate_eval, tf)
    n_Sc46__p_Ca46(rate_eval, tf)
    n_V56__V57(rate_eval, tf)
    He4_Sc45__p_Ti48(rate_eval, tf)
    n_Si24__p_Al24(rate_eval, tf)
    n_Mg22__He4_Ne19(rate_eval, tf)
    p_Sc45__He4_Ca42(rate_eval, tf)
    n_Sc45__p_Ca45(rate_eval, tf)
    He4_Sc44__p_Ti47(rate_eval, tf)
    p_Sc44__He4_Ca41(rate_eval, tf)
    n_Sc44__p_Ca44(rate_eval, tf)
    He4_Sc43__p_Ti46(rate_eval, tf)
    n_Sc43__He4_K40(rate_eval, tf)
    n_Sc43__p_Ca43(rate_eval, tf)
    He4_Sc42__p_Ti45(rate_eval, tf)
    n_Sc42__He4_K39(rate_eval, tf)
    n_Sc42__p_Ca42(rate_eval, tf)
    p_Cr56__n_Mn56(rate_eval, tf)
    n_Sc41__He4_K38(rate_eval, tf)
    p_Si36__He4_Al33(rate_eval, tf)
    He4_Sc39__p_Ti42(rate_eval, tf)
    p_P31__S32(rate_eval, tf)
    n_Sc39__He4_K36(rate_eval, tf)
    p_Si45__P46(rate_eval, tf)
    He4_Sc38__p_Ti41(rate_eval, tf)
    n_Ti47__He4_Ca44(rate_eval, tf)
    p_Na36__n_Mg36(rate_eval, tf)
    n_Sc37__He4_K34(rate_eval, tf)
    He4_Sc36__p_Ti39(rate_eval, tf)
    Mg36__n_n_Al34__weak__mp17(rate_eval, tf)
    He4_Sc35__p_Ti38(rate_eval, tf)
    n_Sc35__He4_K32(rate_eval, tf)
    n_Sc35__p_Ca35(rate_eval, tf)
    p_Ca61__He4_K58(rate_eval, tf)
    p_Ca61__n_Sc61(rate_eval, tf)
    p_Ca60__n_Sc60(rate_eval, tf)
    n_Fe48__Fe49(rate_eval, tf)
    p_Ca59__n_Sc59(rate_eval, tf)
    He4_Ca58__n_Ti61(rate_eval, tf)
    p_Ca58__He4_K55(rate_eval, tf)
    n_Cr46__p_V46(rate_eval, tf)
    p_Ca58__n_Sc58(rate_eval, tf)
    He4_Al25__P29(rate_eval, tf)
    p_Ca56__He4_K53(rate_eval, tf)
    p_Ca55__He4_K52(rate_eval, tf)
    p_Ca55__n_Sc55(rate_eval, tf)
    He4_Ca53__n_Ti56(rate_eval, tf)
    He8__Li8__weak__wc12(rate_eval, tf)
    p_Ca52__n_Sc52(rate_eval, tf)
    p_P45__S46(rate_eval, tf)
    p_Cr56__He4_V53(rate_eval, tf)
    He4_Ca51__n_Ti54(rate_eval, tf)
    p_Ca51__He4_K48(rate_eval, tf)
    n_Si24__He4_Mg21(rate_eval, tf)
    p_Al39__He4_Mg36(rate_eval, tf)
    He4_Ca47__n_Ti50(rate_eval, tf)
    p_Ca47__n_Sc47(rate_eval, tf)
    S45__n_Cl44__weak__wc12(rate_eval, tf)
    C12_C12__He4_Ne20(rate_eval, tf)
    He4_Ca57__n_Ti60(rate_eval, tf)
    He4_Ca43__n_Ti46(rate_eval, tf)
    O24__F24__weak__wc12(rate_eval, tf)
    He4_Ti45__p_V48(rate_eval, tf)
    Na39__n_Mg38__weak__mp17(rate_eval, tf)
    p_Ca42__He4_K39(rate_eval, tf)
    n_Mn43__He4_V40(rate_eval, tf)
    He4_F16__Na20(rate_eval, tf)
    n_Ca40__He4_Ar37(rate_eval, tf)
    p_P42__n_S42(rate_eval, tf)
    He4_V63__n_Mn66(rate_eval, tf)
    n_Ca38__p_K38(rate_eval, tf)
    He4_Fe66__n_Ni69(rate_eval, tf)
    Ca53__n_Sc52__weak__wc12(rate_eval, tf)
    n_Ca37__He4_Ar34(rate_eval, tf)
    n_Ca37__p_K37(rate_eval, tf)
    n_Ca36__p_K36(rate_eval, tf)
    n_Cl35__p_S35(rate_eval, tf)
    He4_P39__n_Cl42(rate_eval, tf)
    n_Ca35__He4_Ar32(rate_eval, tf)
    n_Ca35__p_K35(rate_eval, tf)
    Cr67__Mn67__weak__mo03(rate_eval, tf)
    n_Ca34__He4_Ar31(rate_eval, tf)
    n_Ca34__p_K34(rate_eval, tf)
    He4_Ca48__Ti52(rate_eval, tf)
    He4_K57__n_Sc60(rate_eval, tf)
    p_K57__He4_Ar54(rate_eval, tf)
    He4_Si42__S46(rate_eval, tf)
    p_K57__n_Ca57(rate_eval, tf)
    He4_K56__n_Sc59(rate_eval, tf)
    p_K56__n_Ca56(rate_eval, tf)
    He4_K54__n_Sc57(rate_eval, tf)
    p_K54__n_Ca54(rate_eval, tf)
    Cl49__n_Ar48__weak__mp17(rate_eval, tf)
    He4_K53__n_Sc56(rate_eval, tf)
    n_O14__O15(rate_eval, tf)
    p_K53__n_Ca53(rate_eval, tf)
    n_K31__K32(rate_eval, tf)
    He4_K52__n_Sc55(rate_eval, tf)
    p_P29__S30(rate_eval, tf)
    He4_K51__n_Sc54(rate_eval, tf)
    p_K51__n_Ca51(rate_eval, tf)
    He4_Cr57__n_Fe60(rate_eval, tf)
    He4_K50__n_Sc53(rate_eval, tf)
    p_S42__Cl43(rate_eval, tf)
    He4_K48__n_Sc51(rate_eval, tf)
    n_Fe50__Fe51(rate_eval, tf)
    n_Cr44__He4_Ti41(rate_eval, tf)
    p_K48__He4_Ar45(rate_eval, tf)
    He4_Sc35__V39(rate_eval, tf)
    p_K45__He4_Ar42(rate_eval, tf)
    p_K45__n_Ca45(rate_eval, tf)
    p_K44__He4_Ar41(rate_eval, tf)
    Ne31__n_Na30__weak__mp17(rate_eval, tf)
    He4_K43__p_Ca46(rate_eval, tf)
    p_K43__n_Ca43(rate_eval, tf)
    n_V45__He4_Sc42(rate_eval, tf)
    He4_K42__p_Ca45(rate_eval, tf)
    He8__n_Li7__weak__wc12(rate_eval, tf)
    He4_K42__n_Sc45(rate_eval, tf)
    He4_K41__n_Sc44(rate_eval, tf)
    p_K41__He4_Ar38(rate_eval, tf)
    p_K41__n_Ca41(rate_eval, tf)
    He4_K46__p_Ca49(rate_eval, tf)
    p_K40__He4_Ar37(rate_eval, tf)
    p_K40__n_Ca40(rate_eval, tf)
    p_S37__Cl38(rate_eval, tf)
    n_K40__He4_Cl37(rate_eval, tf)
    n_K40__p_Ar40(rate_eval, tf)
    n_K39__p_Ar39(rate_eval, tf)
    p_O14__F15(rate_eval, tf)
    He4_Sc43__V47(rate_eval, tf)
    n_K38__p_Ar38(rate_eval, tf)
    n_Ar31__He4_S28(rate_eval, tf)
    He4_K37__p_Ca40(rate_eval, tf)
    He4_K44__p_Ca47(rate_eval, tf)
    n_K37__He4_Cl34(rate_eval, tf)
    n_K36__He4_Cl33(rate_eval, tf)
    n_K36__p_Ar36(rate_eval, tf)
    n_Sc46__He4_K43(rate_eval, tf)
    n_K35__p_Ar35(rate_eval, tf)
    He4_K34__p_Ca37(rate_eval, tf)
    p_Al39__n_Si39(rate_eval, tf)
    He4_Sc54__V58(rate_eval, tf)
    p_Cr61__He4_V58(rate_eval, tf)
    K52__Ca52__weak__wc17(rate_eval, tf)
    n_K33__p_Ar33(rate_eval, tf)
    p_Mn51__Fe52(rate_eval, tf)
    n_K32__He4_Cl29(rate_eval, tf)
    p_Mn56__Fe57(rate_eval, tf)
    n_K32__p_Ar32(rate_eval, tf)
    He4_K31__p_Ca34(rate_eval, tf)
    p_Ti38__V39(rate_eval, tf)
    n_K31__p_Ar31(rate_eval, tf)
    p_Ar54__n_K54(rate_eval, tf)
    p_Ar52__He4_Cl49(rate_eval, tf)
    p_Ar52__n_K52(rate_eval, tf)
    n_Ti39__He4_Ca36(rate_eval, tf)
    p_K59__n_Ca59(rate_eval, tf)
    p_Ar50__He4_Cl47(rate_eval, tf)
    n_Ca36__He4_Ar33(rate_eval, tf)
    V67__n_n_n_Cr64__weak__mo03(rate_eval, tf)
    He4_F20__n_Na23(rate_eval, tf)
    p_Ar48__He4_Cl45(rate_eval, tf)
    p_Ar48__n_K48(rate_eval, tf)
    He4_Ar46__n_Ca49(rate_eval, tf)
    p_F28__n_Ne28(rate_eval, tf)
    He4_Fe50__p_Co53(rate_eval, tf)
    n_d__t(rate_eval, tf)
    He4_Si35__n_S38(rate_eval, tf)
    p_Ar44__n_K44(rate_eval, tf)
    He4_Ar43__n_Ca46(rate_eval, tf)
    n_V39__V40(rate_eval, tf)
    p_Cr55__He4_V52(rate_eval, tf)
    p_Ar43__n_K43(rate_eval, tf)
    p_Fe47__Co48(rate_eval, tf)
    He4_Cl47__K51(rate_eval, tf)
    p_Ar41__n_K41(rate_eval, tf)
    n_Mn52__Mn53(rate_eval, tf)
    p_Ar40__He4_Cl37(rate_eval, tf)
    He4_Mn54__Co58(rate_eval, tf)
    He4_Fe68__Ni72(rate_eval, tf)
    p_Ar39__He4_Cl36(rate_eval, tf)
    p_Cr62__Mn63(rate_eval, tf)
    He4_Mn62__n_Co65(rate_eval, tf)
    n_Mn49__He4_V46(rate_eval, tf)
    n_Ar37__p_Cl37(rate_eval, tf)
    n_Ar35__He4_S32(rate_eval, tf)
    n_Ar35__p_Cl35(rate_eval, tf)
    He4_Ar34__p_K37(rate_eval, tf)
    n_Ar34__p_Cl34(rate_eval, tf)
    He4_Ar33__p_K36(rate_eval, tf)
    n_Ar33__p_Cl33(rate_eval, tf)
    n_Ar32__He4_S29(rate_eval, tf)
    n_Fe75__Fe76(rate_eval, tf)
    n_Ar32__p_Cl32(rate_eval, tf)
    He4_Ar31__p_K34(rate_eval, tf)
    n_Ar31__p_Cl31(rate_eval, tf)
    P27__p_Al26__weak__wc12(rate_eval, tf)
    n_Ar30__He4_S27(rate_eval, tf)
    n_Ar30__p_Cl30(rate_eval, tf)
    He4_Ar29__p_K32(rate_eval, tf)
    n_Ar29__He4_S26(rate_eval, tf)
    n_Ar29__p_Cl29(rate_eval, tf)
    p_Cl52__He4_S49(rate_eval, tf)
    p_Cl52__n_Ar52(rate_eval, tf)
    p_O16__F17(rate_eval, tf)
    He4_Cl51__n_K54(rate_eval, tf)
    n_Ti58__Ti59(rate_eval, tf)
    He4_Cl50__K54(rate_eval, tf)
    p_Cl51__He4_S48(rate_eval, tf)
    p_Cl50__He4_S47(rate_eval, tf)
    p_Cl50__n_Ar50(rate_eval, tf)
    n_Ar34__Ar35(rate_eval, tf)
    p_B12__n_C12(rate_eval, tf)
    He4_Cl49__n_K52(rate_eval, tf)
    He4_Ar36__Ca40(rate_eval, tf)
    p_Cl48__He4_S45(rate_eval, tf)
    He4_Ca50__n_Ti53(rate_eval, tf)
    p_Cl48__n_Ar48(rate_eval, tf)
    p_Ti62__n_V62(rate_eval, tf)
    He4_Cl47__n_K50(rate_eval, tf)
    p_Cl45__He4_S42(rate_eval, tf)
    p_Cl45__n_Ar45(rate_eval, tf)
    He4_Cl43__p_Ar46(rate_eval, tf)
    p_Cl43__He4_S40(rate_eval, tf)
    p_Mn61__n_Fe61(rate_eval, tf)
    He4_V49__Mn53(rate_eval, tf)
    p_V55__Cr56(rate_eval, tf)
    He4_Cl42__n_K45(rate_eval, tf)
    p_Cl42__He4_S39(rate_eval, tf)
    p_S47__n_Cl47(rate_eval, tf)
    n_Fe72__Fe73(rate_eval, tf)
    He4_Cl41__n_K44(rate_eval, tf)
    p_Cl41__He4_S38(rate_eval, tf)
    He4_Cl40__n_K43(rate_eval, tf)
    p_Cl40__n_Ar40(rate_eval, tf)
    p_O19__He4_N16(rate_eval, tf)
    n_Cl36__p_S36(rate_eval, tf)
    He4_F17__Na21(rate_eval, tf)
    n_Cl35__He4_P32(rate_eval, tf)
    He4_Cl34__p_Ar37(rate_eval, tf)
    n_C11__He4_He4_He4(rate_eval, tf)
    n_Cl34__He4_P31(rate_eval, tf)
    P42__n_n_S40__weak__mp17(rate_eval, tf)
    n_Cl34__p_S34(rate_eval, tf)
    n_Cl33__He4_P30(rate_eval, tf)
    p_Ti43__V44(rate_eval, tf)
    n_Cl33__p_S33(rate_eval, tf)
    p_Na34__Mg35(rate_eval, tf)
    He4_S48__n_Ar51(rate_eval, tf)
    n_Cl31__p_S31(rate_eval, tf)
    He4_Ar35__p_K38(rate_eval, tf)
    He4_Cl30__p_Ar33(rate_eval, tf)
    Ca35__K35__weak__wc17(rate_eval, tf)
    n_Cl29__He4_P26(rate_eval, tf)
    He4_Na25__Al29(rate_eval, tf)
    n_Cl29__p_S29(rate_eval, tf)
    He4_Cl28__p_Ar31(rate_eval, tf)
    n_V49__p_Ti49(rate_eval, tf)
    n_Cl28__He4_P25(rate_eval, tf)
    d_Li8__n_Be9(rate_eval, tf)
    Cr44__V44__weak__wc12(rate_eval, tf)
    n_Cr57__Cr58(rate_eval, tf)
    p_S49__n_Cl49(rate_eval, tf)
    He4_Mg38__n_Si41(rate_eval, tf)
    n_Ca52__Ca53(rate_eval, tf)
    p_S48__n_Cl48(rate_eval, tf)
    p_N15__O16(rate_eval, tf)
    p_S47__He4_P44(rate_eval, tf)
    p_K52__He4_Ar49(rate_eval, tf)
    p_S46__n_Cl46(rate_eval, tf)
    Na25__Mg25__weak__wc12(rate_eval, tf)
    d_Be7__p_He4_He4(rate_eval, tf)
    p_S45__He4_P42(rate_eval, tf)
    He4_S43__n_Ar46(rate_eval, tf)
    p_Mn64__n_Fe64(rate_eval, tf)
    p_S43__He4_P40(rate_eval, tf)
    He4_Mn67__n_Co70(rate_eval, tf)
    p_Cr60__Mn61(rate_eval, tf)
    p_Sc57__He4_Ca54(rate_eval, tf)
    He4_Fe56__Ni60(rate_eval, tf)
    He4_S42__n_Ar45(rate_eval, tf)
    He4_S41__n_Ar44(rate_eval, tf)
    He4_Sc63__n_V66(rate_eval, tf)
    p_S41__He4_P38(rate_eval, tf)
    p_Al30__He4_Mg27(rate_eval, tf)
    p_S40__n_Cl40(rate_eval, tf)
    p_Cl40__He4_S37(rate_eval, tf)
    He4_Fe47__Ni51(rate_eval, tf)
    d_Li8__t_Li7(rate_eval, tf)
    p_S39__He4_P36(rate_eval, tf)
    He4_S38__n_Ar41(rate_eval, tf)
    p_S38__He4_P35(rate_eval, tf)
    p_S38__n_Cl38(rate_eval, tf)
    He4_Mn47__Co51(rate_eval, tf)
    He4_S37__n_Ar40(rate_eval, tf)
    He4_K49__n_Sc52(rate_eval, tf)
    p_V56__He4_Ti53(rate_eval, tf)
    p_S37__n_Cl37(rate_eval, tf)
    p_K49__n_Ca49(rate_eval, tf)
    p_Cl45__Ar46(rate_eval, tf)
    p_Li6__Be7(rate_eval, tf)
    p_S36__He4_P33(rate_eval, tf)
    p_Cr69__He4_V66(rate_eval, tf)
    p_Sc51__He4_Ca48(rate_eval, tf)
    p_K51__He4_Ar48(rate_eval, tf)
    He4_P34__n_Cl37(rate_eval, tf)
    He4_S35__n_Ar38(rate_eval, tf)
    p_S35__He4_P32(rate_eval, tf)
    n_Si43__Si44(rate_eval, tf)
    p_Sc57__n_Ti57(rate_eval, tf)
    n_S35__He4_Si32(rate_eval, tf)
    He4_S34__p_Cl37(rate_eval, tf)
    n_Al36__Al37(rate_eval, tf)
    p_Cl35__He4_S32(rate_eval, tf)
    He4_Ti60__Cr64(rate_eval, tf)
    Cr68__Mn68__weak__mo03(rate_eval, tf)
    n_S33__He4_Si30(rate_eval, tf)
    He4_S31__p_Cl34(rate_eval, tf)
    He4_S30__p_Cl33(rate_eval, tf)
    n_S30__He4_Si27(rate_eval, tf)
    n_S30__p_P30(rate_eval, tf)
    Cl49__n_n_n_Ar46__weak__mo03(rate_eval, tf)
    He4_S28__p_Cl31(rate_eval, tf)
    n_Cr43__He4_Ti40(rate_eval, tf)
    n_S28__He4_Si25(rate_eval, tf)
    Ca53__Sc53__weak__wc12(rate_eval, tf)
    He4_S26__p_Cl29(rate_eval, tf)
    n_S26__He4_Si23(rate_eval, tf)
    p_V65__Cr66(rate_eval, tf)
    He4_P47__n_Cl50(rate_eval, tf)
    p_P47__n_S47(rate_eval, tf)
    p_P45__n_S45(rate_eval, tf)
    n_Si33__Si34(rate_eval, tf)
    He4_P43__n_Cl46(rate_eval, tf)
    p_P43__He4_Si40(rate_eval, tf)
    He4_Al38__n_P41(rate_eval, tf)
    p_P43__n_S43(rate_eval, tf)
    p_Sc55__n_Ti55(rate_eval, tf)
    p_P42__He4_Si39(rate_eval, tf)
    Ne27__n_Na26__weak__wc12(rate_eval, tf)
    He4_P41__p_S44(rate_eval, tf)
    He4_P41__n_Cl44(rate_eval, tf)
    p_O20__He4_N17(rate_eval, tf)
    p_Ar43__He4_Cl40(rate_eval, tf)
    p_P38__He4_Si35(rate_eval, tf)
    p_P38__n_S38(rate_eval, tf)
    n_S33__p_P33(rate_eval, tf)
    p_F18__He4_O15(rate_eval, tf)
    He4_P37__n_Cl40(rate_eval, tf)
    p_P37__He4_Si34(rate_eval, tf)
    p_P36__He4_Si33(rate_eval, tf)
    n_Ti54__Ti55(rate_eval, tf)
    p_P36__n_S36(rate_eval, tf)
    p_Mn69__n_Fe69(rate_eval, tf)
    p_P34__n_S34(rate_eval, tf)
    p_Ca56__n_Sc56(rate_eval, tf)
    He4_Cl44__p_Ar47(rate_eval, tf)
    p_Al25__Si26(rate_eval, tf)
    p_Sc45__Ti46(rate_eval, tf)
    p_P32__He4_Si29(rate_eval, tf)
    n_P32__p_Si32(rate_eval, tf)
    He4_P31__p_S34(rate_eval, tf)
    n_F25__F26(rate_eval, tf)
    He4_P30__p_S33(rate_eval, tf)
    Mg39__n_n_n_Al36__weak__mo03(rate_eval, tf)
    He4_K55__n_Sc58(rate_eval, tf)
    n_V47__He4_Sc44(rate_eval, tf)
    n_P28__p_Si28(rate_eval, tf)
    He4_P27__p_S30(rate_eval, tf)
    n_P27__He4_Al24(rate_eval, tf)
    n_P27__p_Si27(rate_eval, tf)
    He4_P26__p_S29(rate_eval, tf)
    n_Cr47__He4_Ti44(rate_eval, tf)
    n_P26__He4_Al23(rate_eval, tf)
    n_P26__p_Si26(rate_eval, tf)
    He4_P25__p_S28(rate_eval, tf)
    He4_P24__p_S27(rate_eval, tf)
    n_P24__He4_Al21(rate_eval, tf)
    n_P24__p_Si24(rate_eval, tf)
    p_Si45__He4_Al42(rate_eval, tf)
    p_Si45__n_P45(rate_eval, tf)
    He4_Si44__n_S47(rate_eval, tf)
    He4_P42__n_Cl45(rate_eval, tf)
    He4_Si42__n_S45(rate_eval, tf)
    Na26__Mg26__weak__wc12(rate_eval, tf)
    p_Si42__n_P42(rate_eval, tf)
    n_Mn54__p_Cr54(rate_eval, tf)
    Sc38__Ca38__weak__mo97(rate_eval, tf)
    He4_Si40__n_S43(rate_eval, tf)
    He4_Si39__n_S42(rate_eval, tf)
    Mn68__Fe68__weak__wc17(rate_eval, tf)
    p_S38__Cl39(rate_eval, tf)
    p_Si39__n_P39(rate_eval, tf)
    p_Sc62__n_Ti62(rate_eval, tf)
    n_Cr47__p_V47(rate_eval, tf)
    He4_Si38__n_S41(rate_eval, tf)
    p_Ti65__He4_Sc62(rate_eval, tf)
    He4_Si37__n_S40(rate_eval, tf)
    He4_Ca40__Ti44(rate_eval, tf)
    p_Si37__He4_Al34(rate_eval, tf)
    O14__N14__weak__wc12(rate_eval, tf)
    p_Si37__n_P37(rate_eval, tf)
    p_Si35__He4_Al32(rate_eval, tf)
    He3__t__weak__electron_capture(rate_eval, tf)
    p_Si33__n_P33(rate_eval, tf)
    He4_Mn45__p_Fe48(rate_eval, tf)
    He4_Cr41__p_Mn44(rate_eval, tf)
    He4_Mn43__Co47(rate_eval, tf)
    He4_V57__n_Mn60(rate_eval, tf)
    n_Mn51__He4_V48(rate_eval, tf)
    p_V49__Cr50(rate_eval, tf)
    B18__n_B17(rate_eval, tf)
    n_Ti37__He4_Ca34(rate_eval, tf)
    n_O24__O25(rate_eval, tf)
    He4_Ti61__n_Cr64(rate_eval, tf)
    Sc62__Ti62__weak__mo03(rate_eval, tf)
    He4_Si25__p_P28(rate_eval, tf)
    n_Ar35__Ar36(rate_eval, tf)
    p_Mn58__Fe59(rate_eval, tf)
    n_Si25__p_Al25(rate_eval, tf)
    He4_V40__p_Cr43(rate_eval, tf)
    He4_Si24__p_P27(rate_eval, tf)
    V64__n_n_Cr62__weak__mp17(rate_eval, tf)
    He4_Be7__C11(rate_eval, tf)
    He4_Ca54__Ti58(rate_eval, tf)
    He4_K40__p_Ca43(rate_eval, tf)
    He4_Si23__p_P26(rate_eval, tf)
    He4_Ar42__n_Ca45(rate_eval, tf)
    p_V61__He4_Ti58(rate_eval, tf)
    n_Si23__p_Al23(rate_eval, tf)
    He4_Si22__p_P25(rate_eval, tf)
    n_Si22__He4_Mg19(rate_eval, tf)
    n_Si22__p_Al22(rate_eval, tf)
    p_Al43__n_Si43(rate_eval, tf)
    Mg27__Al27__weak__wc12(rate_eval, tf)
    He4_Al42__n_P45(rate_eval, tf)
    p_Al41__He4_Mg38(rate_eval, tf)
    He4_Al40__n_P43(rate_eval, tf)
    p_Al40__He4_Mg37(rate_eval, tf)
    p_Al40__n_Si40(rate_eval, tf)
    He4_Al39__p_Si42(rate_eval, tf)
    He4_Al38__p_Si41(rate_eval, tf)
    He4_Mn49__Co53(rate_eval, tf)
    p_Al38__He4_Mg35(rate_eval, tf)
    p_V59__n_Cr59(rate_eval, tf)
    n_V48__p_Ti48(rate_eval, tf)
    p_Al37__He4_Mg34(rate_eval, tf)
    He4_Al36__p_Si39(rate_eval, tf)
    n_Si44__Si45(rate_eval, tf)
    He4_Al36__n_P39(rate_eval, tf)
    p_Al36__He4_Mg33(rate_eval, tf)
    C22__N22__weak__wc17(rate_eval, tf)
    He4_Mn59__Co63(rate_eval, tf)
    p_Al36__n_Si36(rate_eval, tf)
    p_Al41__n_Si41(rate_eval, tf)
    p_V64__n_Cr64(rate_eval, tf)
    He4_Al35__n_P38(rate_eval, tf)
    p_Al35__He4_Mg32(rate_eval, tf)
    He4_Al34__n_P37(rate_eval, tf)
    p_Al34__He4_Mg31(rate_eval, tf)
    p_Al34__n_Si34(rate_eval, tf)
    He4_K50__Sc54(rate_eval, tf)
    He4_Al33__n_P36(rate_eval, tf)
    p_Al33__He4_Mg30(rate_eval, tf)
    Si43__n_n_P41__weak__mp17(rate_eval, tf)
    He4_Si27__p_P30(rate_eval, tf)
    p_Cl46__He4_S43(rate_eval, tf)
    p_Al33__n_Si33(rate_eval, tf)
    p_Ne26__n_Na26(rate_eval, tf)
    p_Al32__He4_Mg29(rate_eval, tf)
    p_Al32__n_Si32(rate_eval, tf)
    n_Cr66__Cr67(rate_eval, tf)
    He4_Al31__p_Si34(rate_eval, tf)
    He4_Al31__n_P34(rate_eval, tf)
    p_Cl38__He4_S35(rate_eval, tf)
    p_Al31__He4_Mg28(rate_eval, tf)
    p_Al30__n_Si30(rate_eval, tf)
    He4_Al29__n_P32(rate_eval, tf)
    p_Al29__He4_Mg26(rate_eval, tf)
    p_Al29__n_Si29(rate_eval, tf)
    He4_Al37__n_P40(rate_eval, tf)
    p_Ne34__He4_F31(rate_eval, tf)
    n_Ti44__p_Sc44(rate_eval, tf)
    p_Al28__He4_Mg25(rate_eval, tf)
    n_Ti59__Ti60(rate_eval, tf)
    He4_K41__p_Ca44(rate_eval, tf)
    He4_Al27__p_Si30(rate_eval, tf)
    He4_Al27__n_P30(rate_eval, tf)
    p_Ca49__Sc50(rate_eval, tf)
    n_Al26__He4_Na23(rate_eval, tf)
    n_Al26__p_Mg26(rate_eval, tf)
    He4_Al32__P36(rate_eval, tf)
    n_Al25__p_Mg25(rate_eval, tf)
    He4_Al24__p_Si27(rate_eval, tf)
    p_S46__Cl47(rate_eval, tf)
    He4_Al25__p_Si28(rate_eval, tf)
    F31__n_n_Ne29__weak__mp17(rate_eval, tf)
    n_Al23__He4_Na20(rate_eval, tf)
    p_Na37__Mg38(rate_eval, tf)
    He4_Al22__p_Si25(rate_eval, tf)
    p_V67__He4_Ti64(rate_eval, tf)
    n_Al22__He4_Na19(rate_eval, tf)
    O28__n_n_n_F25__weak__mo03(rate_eval, tf)
    n_Al22__p_Mg22(rate_eval, tf)
    He4_Al21__p_Si24(rate_eval, tf)
    n_Sc48__p_Ca48(rate_eval, tf)
    He4_Mg40__n_Si43(rate_eval, tf)
    p_Mg40__n_Al40(rate_eval, tf)
    He4_Mg39__n_Si42(rate_eval, tf)
    p_Mg39__n_Al39(rate_eval, tf)
    Ca33__K33__weak__bqa_pos_(rate_eval, tf)
    p_Mg38__n_Al38(rate_eval, tf)
    p_Al27__He4_Mg24(rate_eval, tf)
    He4_Mg37__n_Si40(rate_eval, tf)
    p_Al38__n_Si38(rate_eval, tf)
    p_Na31__Mg32(rate_eval, tf)
    p_Ar45__He4_Cl42(rate_eval, tf)
    He4_Mg35__n_Si38(rate_eval, tf)
    He4_Mg34__n_Si37(rate_eval, tf)
    p_Mg34__He4_Na31(rate_eval, tf)
    p_Ti53__n_V53(rate_eval, tf)
    p_Mg33__He4_Na30(rate_eval, tf)
    Fe49__Mn49__weak__wc12(rate_eval, tf)
    p_Fe66__He4_Mn63(rate_eval, tf)
    He4_Mg32__n_Si35(rate_eval, tf)
    n_Mn47__He4_V44(rate_eval, tf)
    p_Mg32__He4_Na29(rate_eval, tf)
    n_Na19__p_Ne19(rate_eval, tf)
    p_Mn59__n_Fe59(rate_eval, tf)
    He4_Mg30__n_Si33(rate_eval, tf)
    p_Mg30__n_Al30(rate_eval, tf)
    n_P29__He4_Al26(rate_eval, tf)
    p_Ca45__Sc46(rate_eval, tf)
    He4_Cr46__p_Mn49(rate_eval, tf)
    p_Cl46__n_Ar46(rate_eval, tf)
    p_Mg29__He4_Na26(rate_eval, tf)
    p_Mg29__n_Al29(rate_eval, tf)
    p_Cr60__n_Mn60(rate_eval, tf)
    n_S29__He4_Si26(rate_eval, tf)
    n_K58__K59(rate_eval, tf)
    He4_K57__Sc61(rate_eval, tf)
    He4_Ne23__n_Mg26(rate_eval, tf)
    p_Ne31__He4_F28(rate_eval, tf)
    He4_Mg27__n_Si30(rate_eval, tf)
    He4_O23__n_Ne26(rate_eval, tf)
    He4_K35__p_Ca38(rate_eval, tf)
    He4_Mg26__n_Si29(rate_eval, tf)
    p_Ti59__V60(rate_eval, tf)
    n_Fe54__He4_Cr51(rate_eval, tf)
    n_Mn68__Mn69(rate_eval, tf)
    He4_Fe53__p_Co56(rate_eval, tf)
    n_Fe55__He4_Cr52(rate_eval, tf)
    He4_Mg25__n_Si28(rate_eval, tf)
    p_Fe69__Co70(rate_eval, tf)
    P40__S40__weak__wc12(rate_eval, tf)
    n_Cl43__Cl44(rate_eval, tf)
    n_Mg23__C12_C12(rate_eval, tf)
    n_Mg23__He4_Ne20(rate_eval, tf)
    n_Fe66__Fe67(rate_eval, tf)
    He4_Mg22__p_Al25(rate_eval, tf)
    n_Cl30__p_S30(rate_eval, tf)
    n_Mg21__He4_Ne18(rate_eval, tf)
    He4_Mg20__p_Al23(rate_eval, tf)
    Ca57__n_n_Sc55__weak__mp17(rate_eval, tf)
    He4_Na36__n_Al39(rate_eval, tf)
    n_Mg20__p_Na20(rate_eval, tf)
    p_Na39__n_Mg39(rate_eval, tf)
    Na27__n_Mg26__weak__wc12(rate_eval, tf)
    He4_Na38__n_Al41(rate_eval, tf)
    He4_Na37__p_Mg40(rate_eval, tf)
    He4_K33__Sc37(rate_eval, tf)
    p_Na37__He4_Ne34(rate_eval, tf)
    He4_Na35__n_Al38(rate_eval, tf)
    p_Na35__n_Mg35(rate_eval, tf)
    Mg37__n_Al36__weak__mp17(rate_eval, tf)
    n_V43__He4_Sc40(rate_eval, tf)
    He4_Na34__n_Al37(rate_eval, tf)
    He4_V60__n_Mn63(rate_eval, tf)
    He4_Na33__p_Mg36(rate_eval, tf)
    p_Na33__n_Mg33(rate_eval, tf)
    n_N18__N19(rate_eval, tf)
    S30__P30__weak__wc12(rate_eval, tf)
    n_Mn43__p_Cr43(rate_eval, tf)
    He4_Sc44__V48(rate_eval, tf)
    He4_Na31__n_Al34(rate_eval, tf)
    p_Na31__He4_Ne28(rate_eval, tf)
    p_Na31__n_Mg31(rate_eval, tf)
    p_Fe66__n_Co66(rate_eval, tf)
    p_Na30__He4_Ne27(rate_eval, tf)
    p_Cl40__Ar41(rate_eval, tf)
    n_S31__p_P31(rate_eval, tf)
    p_Na29__He4_Ne26(rate_eval, tf)
    He4_Na28__n_Al31(rate_eval, tf)
    p_Na28__n_Mg28(rate_eval, tf)
    Ar49__K49__weak__wc12(rate_eval, tf)
    p_Na27__n_Mg27(rate_eval, tf)
    n_Ar39__He4_S36(rate_eval, tf)
    He4_Na26__n_Al29(rate_eval, tf)
    p_Sc49__n_Ti49(rate_eval, tf)
    Ar52__n_n_K50__weak__mp17(rate_eval, tf)
    He4_Na24__p_Mg27(rate_eval, tf)
    p_Na24__He4_Ne21(rate_eval, tf)
    n_Ti42__p_Sc42(rate_eval, tf)
    p_K56__He4_Ar53(rate_eval, tf)
    p_K46__Ca47(rate_eval, tf)
    He4_Na23__p_Mg26(rate_eval, tf)
    p_Fe67__n_Co67(rate_eval, tf)
    n_Fe50__p_Mn50(rate_eval, tf)
    n_Sc43__Sc44(rate_eval, tf)
    n_S26__p_P26(rate_eval, tf)
    p_Na23__He4_Ne20(rate_eval, tf)
    p_Na23__n_Mg23(rate_eval, tf)
    He4_Na22__p_Mg25(rate_eval, tf)
    He4_S41__Ar45(rate_eval, tf)
    p_V56__Cr57(rate_eval, tf)
    n_Na21__He4_F18(rate_eval, tf)
    He4_S29__p_Cl32(rate_eval, tf)
    n_Na20__He4_F17(rate_eval, tf)
    n_V40__He4_Sc37(rate_eval, tf)
    He4_Cl35__p_Ar38(rate_eval, tf)
    p_Ne34__n_Na34(rate_eval, tf)
    n_Mn54__He4_V51(rate_eval, tf)
    n_Cl32__He4_P29(rate_eval, tf)
    p_Cl36__Ar37(rate_eval, tf)
    He4_S46__n_Ar49(rate_eval, tf)
    He4_Ne31__n_Mg34(rate_eval, tf)
    p_Al35__n_Si35(rate_eval, tf)
    He4_Ne30__n_Mg33(rate_eval, tf)
    p_Ne30__He4_F27(rate_eval, tf)
    n_Sc40__p_Ca40(rate_eval, tf)
    p_Ne29__He4_F26(rate_eval, tf)
    He4_Ar43__Ca47(rate_eval, tf)
    p_Ne29__n_Na29(rate_eval, tf)
    He4_Ne28__n_Mg31(rate_eval, tf)
    p_Ne28__n_Na28(rate_eval, tf)
    Si35__P35__weak__wc17(rate_eval, tf)
    He4_Ne27__n_Mg30(rate_eval, tf)
    p_Ne27__n_Na27(rate_eval, tf)
    He4_Ca39__Ti43(rate_eval, tf)
    N23__O23__weak__wc12(rate_eval, tf)
    He4_Ti54__Cr58(rate_eval, tf)
    He4_S39__n_Ar42(rate_eval, tf)
    p_Ne25__He4_F22(rate_eval, tf)
    p_Ne25__n_Na25(rate_eval, tf)
    K59__Ca59__weak__mo03(rate_eval, tf)
    He4_S27__p_Cl30(rate_eval, tf)
    He4_Ne24__n_Mg27(rate_eval, tf)
    p_Ne24__n_Na24(rate_eval, tf)
    Cl39__Ar39__weak__wc12(rate_eval, tf)
    p_S30__Cl31(rate_eval, tf)
    n_Ti45__He4_Ca42(rate_eval, tf)
    Cr69__Mn69__weak__mo03(rate_eval, tf)
    P33__S33__weak__wc12(rate_eval, tf)
    He4_Ca61__n_Ti64(rate_eval, tf)
    He4_K39__Sc43(rate_eval, tf)
    p_Ne23__n_Na23(rate_eval, tf)
    He4_Sc62__V66(rate_eval, tf)
    He4_Ne22__n_Mg25(rate_eval, tf)
    n_Cl38__He4_P35(rate_eval, tf)
    p_Al43__He4_Mg40(rate_eval, tf)
    He4_Ne21__n_Mg24(rate_eval, tf)
    n_Si27__Si28(rate_eval, tf)
    p_V42__Cr43(rate_eval, tf)
    C12_Ne20__He4_Si28(rate_eval, tf)
    C12_Ne20__p_P31(rate_eval, tf)
    n_Na30__Na31(rate_eval, tf)
    p_V54__n_Cr54(rate_eval, tf)
    p_Ne20__He4_F17(rate_eval, tf)
    p_Ne22__Na23(rate_eval, tf)
    He4_Al26__p_Si29(rate_eval, tf)
    p_K33__Ca34(rate_eval, tf)
    He4_Ne19__p_Na22(rate_eval, tf)
    He4_Ne18__p_Na21(rate_eval, tf)
    n_Si25__He4_Mg22(rate_eval, tf)
    n_Ne18__He4_O15(rate_eval, tf)
    n_Ne18__p_F18(rate_eval, tf)
    He4_Ne17__p_Na20(rate_eval, tf)
    n_Be7__He4_He4(rate_eval, tf)
    He4_Ne16__p_Na19(rate_eval, tf)
    He4_Cl49__K53(rate_eval, tf)
    n_Ne16__p_F16(rate_eval, tf)
    p_Cr67__He4_V64(rate_eval, tf)
    He4_Ar53__n_Ca56(rate_eval, tf)
    p_F31__n_Ne31(rate_eval, tf)
    He4_F30__p_Ne33(rate_eval, tf)
    p_Ar45__n_K45(rate_eval, tf)
    p_Mn47__Fe48(rate_eval, tf)
    p_F30__He4_O27(rate_eval, tf)
    He4_F29__n_Na32(rate_eval, tf)
    p_F29__He4_O26(rate_eval, tf)
    He4_F27__n_Na30(rate_eval, tf)
    p_F27__He4_O24(rate_eval, tf)
    p_F27__n_Ne27(rate_eval, tf)
    S27__p_Si26__weak__wc17(rate_eval, tf)
    He4_F26__n_Na29(rate_eval, tf)
    p_F26__n_Ne26(rate_eval, tf)
    p_Na34__He4_Ne31(rate_eval, tf)
    p_F25__He4_O22(rate_eval, tf)
    n_S30__S31(rate_eval, tf)
    p_F25__n_Ne25(rate_eval, tf)
    He4_Ca38__Ti42(rate_eval, tf)
    He4_F24__n_Na27(rate_eval, tf)
    p_F24__n_Ne24(rate_eval, tf)
    He4_Ti42__p_V45(rate_eval, tf)
    p_Na26__He4_Ne23(rate_eval, tf)
    p_F22__He4_O19(rate_eval, tf)
    p_F22__n_Ne22(rate_eval, tf)
    Cl48__n_Ar47__weak__mp17(rate_eval, tf)
    He4_F21__p_Ne24(rate_eval, tf)
    He4_F21__n_Na24(rate_eval, tf)
    p_Ne26__He4_F23(rate_eval, tf)
    He4_F20__p_Ne23(rate_eval, tf)
    n_Si26__p_Al26(rate_eval, tf)
    p_Al39__Si40(rate_eval, tf)
    p_F20__He4_O17(rate_eval, tf)
    He4_F19__p_Ne22(rate_eval, tf)
    p_F19__n_Ne19(rate_eval, tf)
    p_O21__n_F21(rate_eval, tf)
    He4_F18__p_Ne21(rate_eval, tf)
    p_O15__F16(rate_eval, tf)
    Al40__n_n_n_Si37__weak__mo03(rate_eval, tf)
    n_F18__He4_N15(rate_eval, tf)
    n_F15__He4_N12(rate_eval, tf)
    Fe76__n_n_n_Co73__weak__mo03(rate_eval, tf)
    n_Al41__Al42(rate_eval, tf)
    n_F14__He4_N11(rate_eval, tf)
    n_Ca33__p_K33(rate_eval, tf)
    S37__Cl37__weak__wc12(rate_eval, tf)
    He4_O28__n_Ne31(rate_eval, tf)
    He4_O26__n_Ne29(rate_eval, tf)
    p_O26__He4_N23(rate_eval, tf)
    He4_Ti44__p_V47(rate_eval, tf)
    Ne34__Na34__weak__mo03(rate_eval, tf)
    p_O26__n_F26(rate_eval, tf)
    He4_O24__n_Ne27(rate_eval, tf)
    p_O24__n_F24(rate_eval, tf)
    Na31__n_Mg30__weak__wc17(rate_eval, tf)
    He4_F30__n_Na33(rate_eval, tf)
    He4_O22__n_Ne25(rate_eval, tf)
    He4_Ar52__n_Ca55(rate_eval, tf)
    p_Ti57__n_V57(rate_eval, tf)
    p_O20__n_F20(rate_eval, tf)
    He4_O19__n_Ne22(rate_eval, tf)
    He4_Cl32__p_Ar35(rate_eval, tf)
    p_Cr62__n_Mn62(rate_eval, tf)
    p_O18__He4_N15(rate_eval, tf)
    He4_O17__n_Ne20(rate_eval, tf)
    p_S49__Cl50(rate_eval, tf)
    p_O17__He4_N14(rate_eval, tf)
    O16_O16__He4_Si28(rate_eval, tf)
    O16_O16__p_P31(rate_eval, tf)
    He4_Ne26__n_Mg29(rate_eval, tf)
    Cl32__S32__weak__wc12(rate_eval, tf)
    O16_O16__n_S31(rate_eval, tf)
    He4_Al28__n_P31(rate_eval, tf)
    C12_O16__He4_Mg24(rate_eval, tf)
    C12_O16__p_Al27(rate_eval, tf)
    p_K48__n_Ca48(rate_eval, tf)
    p_Ne28__He4_F25(rate_eval, tf)
    p_Al26__Si27(rate_eval, tf)
    p_Ca36__Sc37(rate_eval, tf)
    p_Na28__He4_Ne25(rate_eval, tf)
    n_K33__He4_Cl30(rate_eval, tf)
    He4_Cr45__Fe49(rate_eval, tf)
    p_Cr70__Mn71(rate_eval, tf)
    n_O14__He4_C11(rate_eval, tf)
    He4_O13__p_F16(rate_eval, tf)
    He4_Sc57__V61(rate_eval, tf)
    n_Ca33__He4_Ar30(rate_eval, tf)
    n_O13__He4_C10(rate_eval, tf)
    n_O13__p_N13(rate_eval, tf)
    n_O12__p_N12(rate_eval, tf)
    p_N15__He4_C12(rate_eval, tf)
    p_N15__n_O15(rate_eval, tf)
    n_Sc37__p_Ca37(rate_eval, tf)
    n_Mg19__He4_Ne16(rate_eval, tf)
    p_F28__He4_O25(rate_eval, tf)
    He4_Ar41__n_Ca44(rate_eval, tf)
    p_F29__Ne30(rate_eval, tf)
    n_N14__p_C14(rate_eval, tf)
    He4_N13__p_O16(rate_eval, tf)
    He4_C15__n_O18(rate_eval, tf)
    p_C15__n_N15(rate_eval, tf)
    He4_Cl50__n_K53(rate_eval, tf)
    He4_Si31__n_S34(rate_eval, tf)
    n_V39__p_Ti39(rate_eval, tf)
    He4_Cl45__n_K48(rate_eval, tf)
    Al36__Si36__weak__wc17(rate_eval, tf)
    He4_C13__n_O16(rate_eval, tf)
    Na38__Mg38__weak__mo03(rate_eval, tf)
    d_C13__n_N14(rate_eval, tf)
    p_C13__n_N13(rate_eval, tf)
    Sc53__Ti53__weak__wc12(rate_eval, tf)
    p_K44__n_Ca44(rate_eval, tf)
    n_Mn50__Mn51(rate_eval, tf)
    n_C11__p_B11(rate_eval, tf)
    He4_B13__n_N16(rate_eval, tf)
    n_K35__He4_Cl32(rate_eval, tf)
    p_Ar53__He4_Cl50(rate_eval, tf)
    He4_B12__n_N15(rate_eval, tf)
    p_B12__He4_Be9(rate_eval, tf)
    p_Ti56__He4_Sc53(rate_eval, tf)
    He4_B11__p_C14(rate_eval, tf)
    S44__n_Cl43__weak__wc12(rate_eval, tf)
    p_Ar41__K42(rate_eval, tf)
    He4_Fe46__p_Co49(rate_eval, tf)
    He4_B10__p_C13(rate_eval, tf)
    He4_B8__p_C11(rate_eval, tf)
    p_V63__He4_Ti60(rate_eval, tf)
    He4_Mn70__Co74(rate_eval, tf)
    He4_Li8__n_B11(rate_eval, tf)
    Si24__p_Mg23__weak__wc12(rate_eval, tf)
    n_Ti42__He4_Ca39(rate_eval, tf)
    n_Fe48__He4_Cr45(rate_eval, tf)
    He4_V49__p_Cr52(rate_eval, tf)
    n_Mn53__He4_V50(rate_eval, tf)
    d_Li7__p_Li8(rate_eval, tf)
    P45__n_n_n_S42__weak__mo03(rate_eval, tf)
    Be11__B11__weak__wc12(rate_eval, tf)
    n_Mn65__Mn66(rate_eval, tf)
    n_Li6__He4_t(rate_eval, tf)
    Na35__n_n_n_Mg32__weak__mo03(rate_eval, tf)
    p_Li6__He4_He3(rate_eval, tf)
    t_He3__d_He4(rate_eval, tf)
    d_He3__p_He4(rate_eval, tf)
    Cl51__Ar51__weak__mo03(rate_eval, tf)
    He4_V51__Mn55(rate_eval, tf)
    p_P34__S35(rate_eval, tf)
    n_He3__p_t(rate_eval, tf)
    d_t__n_He4(rate_eval, tf)
    d_d__p_t(rate_eval, tf)
    He4_Fe76__Ni80(rate_eval, tf)
    p_Fe76__Co77(rate_eval, tf)
    n_Cr61__Cr62(rate_eval, tf)
    n_V50__He4_Sc47(rate_eval, tf)
    He4_Fe73__Ni77(rate_eval, tf)
    p_Fe73__Co74(rate_eval, tf)
    p_Fe72__Co73(rate_eval, tf)
    p_Mg31__n_Al31(rate_eval, tf)
    n_Fe71__Fe72(rate_eval, tf)
    He4_Fe70__Ni74(rate_eval, tf)
    n_Cl28__Cl29(rate_eval, tf)
    He4_Ne18__Mg22(rate_eval, tf)
    p_Fe70__Co71(rate_eval, tf)
    Sc62__n_n_Ti60__weak__mp17(rate_eval, tf)
    n_Fe70__Fe71(rate_eval, tf)
    He4_Fe69__Ni73(rate_eval, tf)
    n_F16__p_O16(rate_eval, tf)
    n_Mn62__Mn63(rate_eval, tf)
    n_Fe69__Fe70(rate_eval, tf)
    p_P32__S33(rate_eval, tf)
    p_Fe68__Co69(rate_eval, tf)
    n_Fe68__Fe69(rate_eval, tf)
    He4_Fe67__Ni71(rate_eval, tf)
    C17__N17__weak__wc12(rate_eval, tf)
    n_Fe67__Fe68(rate_eval, tf)
    n_Na21__p_Ne21(rate_eval, tf)
    p_Fe66__Co67(rate_eval, tf)
    p_Fe65__Co66(rate_eval, tf)
    n_Fe65__Fe66(rate_eval, tf)
    Mg20__p_Ne19__weak__wc12(rate_eval, tf)
    He4_Fe64__Ni68(rate_eval, tf)
    p_Fe63__Co64(rate_eval, tf)
    He4_Sc48__n_V51(rate_eval, tf)
    n_Fe63__Fe64(rate_eval, tf)
    n_Fe62__Fe63(rate_eval, tf)
    n_S29__p_P29(rate_eval, tf)
    He4_P36__n_Cl39(rate_eval, tf)
    p_Fe61__Co62(rate_eval, tf)
    p_S46__He4_P43(rate_eval, tf)
    p_Fe60__Co61(rate_eval, tf)
    p_Al34__Si35(rate_eval, tf)
    He4_Fe59__Ni63(rate_eval, tf)
    p_Fe59__Co60(rate_eval, tf)
    He4_Fe58__Ni62(rate_eval, tf)
    n_Fe58__Fe59(rate_eval, tf)
    p_Fe57__Co58(rate_eval, tf)
    n_Fe57__Fe58(rate_eval, tf)
    p_Fe56__Co57(rate_eval, tf)
    Sc54__Ti54__weak__wc17(rate_eval, tf)
    n_Fe56__Fe57(rate_eval, tf)
    p_Fe55__Co56(rate_eval, tf)
    He4_Fe54__Ni58(rate_eval, tf)
    Ti38__Sc38__weak__mo97(rate_eval, tf)
    n_Fe54__Fe55(rate_eval, tf)
    He4_Fe52__Ni56(rate_eval, tf)
    p_Fe52__Co53(rate_eval, tf)
    He4_Fe51__Ni55(rate_eval, tf)
    p_Si36__n_P36(rate_eval, tf)
    p_Fe50__Co51(rate_eval, tf)
    p_Ne32__n_Na32(rate_eval, tf)
    n_Fe49__Fe50(rate_eval, tf)
    n_Ne30__Ne31(rate_eval, tf)
    p_Fe48__Co49(rate_eval, tf)
    He4_O25__n_Ne28(rate_eval, tf)
    n_Fe47__Fe48(rate_eval, tf)
    n_Cr55__Cr56(rate_eval, tf)
    He4_Fe46__Ni50(rate_eval, tf)
    He4_Fe57__Ni61(rate_eval, tf)
    He4_Fe45__Ni49(rate_eval, tf)
    p_Mn73__Fe74(rate_eval, tf)
    He4_Mn72__Co76(rate_eval, tf)
    n_Mn72__Mn73(rate_eval, tf)
    n_Mn71__Mn72(rate_eval, tf)
    n_Mn70__Mn71(rate_eval, tf)
    B12__C12__weak__wc17(rate_eval, tf)
    He4_Mn69__Co73(rate_eval, tf)
    p_Mn69__Fe70(rate_eval, tf)
    p_Mn68__Fe69(rate_eval, tf)
    Fe53__Mn53__weak__wc12(rate_eval, tf)
    p_Mn73__n_Fe73(rate_eval, tf)
    He4_Mn67__Co71(rate_eval, tf)
    He4_Cl30__K34(rate_eval, tf)
    p_Mn67__Fe68(rate_eval, tf)
    n_Mn67__Mn68(rate_eval, tf)
    He4_Mn66__Co70(rate_eval, tf)
    p_Mn66__Fe67(rate_eval, tf)
    He4_Mn64__Co68(rate_eval, tf)
    He4_Mn63__Co67(rate_eval, tf)
    n_Mn63__Mn64(rate_eval, tf)
    He4_Cl29__p_Ar32(rate_eval, tf)
    p_Ne33__n_Na33(rate_eval, tf)
    p_Mn62__Fe63(rate_eval, tf)
    He4_Mn61__Co65(rate_eval, tf)
    p_Mn61__Fe62(rate_eval, tf)
    Mg38__Al38__weak__mo03(rate_eval, tf)
    n_Fe51__p_Mn51(rate_eval, tf)
    P25__Si25__weak__bqa_pos_(rate_eval, tf)
    n_Mn60__Mn61(rate_eval, tf)
    p_Ca58__Sc59(rate_eval, tf)
    n_Mn59__Mn60(rate_eval, tf)
    n_Mn58__Mn59(rate_eval, tf)
    n_Mn56__Mn57(rate_eval, tf)
    p_K42__n_Ca42(rate_eval, tf)
    n_Mn55__Mn56(rate_eval, tf)
    p_Fe64__n_Co64(rate_eval, tf)
    He4_Mn53__Co57(rate_eval, tf)
    He4_Mn52__Co56(rate_eval, tf)
    He4_Mn50__Co54(rate_eval, tf)
    p_Mn50__Fe51(rate_eval, tf)
    p_Mn49__Fe50(rate_eval, tf)
    n_Mn49__Mn50(rate_eval, tf)
    He4_Si23__S27(rate_eval, tf)
    p_Mn48__Fe49(rate_eval, tf)
    He4_Mn46__Co50(rate_eval, tf)
    p_Mn46__Fe47(rate_eval, tf)
    He4_Mn45__Co49(rate_eval, tf)
    p_Mn45__Fe46(rate_eval, tf)
    n_Mn44__Mn45(rate_eval, tf)
    He4_Cr70__Fe74(rate_eval, tf)
    p_V53__He4_Ti50(rate_eval, tf)
    p_Cr69__Mn70(rate_eval, tf)
    n_Cr69__Cr70(rate_eval, tf)
    n_Cl40__Cl41(rate_eval, tf)
    He4_Cr67__Fe71(rate_eval, tf)
    K38__Ar38__weak__wc12(rate_eval, tf)
    p_Cr66__Mn67(rate_eval, tf)
    p_Cr65__Mn66(rate_eval, tf)
    He4_Cr63__Fe67(rate_eval, tf)
    p_Ca52__Sc53(rate_eval, tf)
    p_Cr63__Mn64(rate_eval, tf)
    O25__n_F24__weak__mp17(rate_eval, tf)
    He4_Cr62__Fe66(rate_eval, tf)
    n_Cr62__Cr63(rate_eval, tf)
    p_Sc48__n_Ti48(rate_eval, tf)
    p_Cr61__Mn62(rate_eval, tf)
    Al30__Si30__weak__wc12(rate_eval, tf)
    n_Ca43__He4_Ar40(rate_eval, tf)
    He4_Cr60__Fe64(rate_eval, tf)
    n_Fe51__Fe52(rate_eval, tf)
    Cr70__Mn70__weak__mo03(rate_eval, tf)
    n_Cr60__Cr61(rate_eval, tf)
    He4_Cr59__Fe63(rate_eval, tf)
    p_Cr59__Mn60(rate_eval, tf)
    He4_Mg19__p_Al22(rate_eval, tf)
    n_Cr59__Cr60(rate_eval, tf)
    He4_Cr58__Fe62(rate_eval, tf)
    p_Cr58__Mn59(rate_eval, tf)
    He4_Cr57__Fe61(rate_eval, tf)
    p_Cr57__Mn58(rate_eval, tf)
    p_Cr56__Mn57(rate_eval, tf)
    n_Cr56__Cr57(rate_eval, tf)
    He4_Cr54__Fe58(rate_eval, tf)
    p_Cr54__Mn55(rate_eval, tf)
    Cr47__V47__weak__wc12(rate_eval, tf)
    n_Mn49__p_Cr49(rate_eval, tf)
    He4_Cr53__Fe57(rate_eval, tf)
    p_Cr53__Mn54(rate_eval, tf)
    He4_Sc48__V52(rate_eval, tf)
    n_Cr53__Cr54(rate_eval, tf)
    p_Cl39__He4_S36(rate_eval, tf)
    p_Cr52__Mn53(rate_eval, tf)
    p_Cr51__Mn52(rate_eval, tf)
    p_Cr50__Mn51(rate_eval, tf)
    p_Cr49__Mn50(rate_eval, tf)
    n_O17__O18(rate_eval, tf)
    He4_Cr48__Fe52(rate_eval, tf)
    He4_Ar45__Ca49(rate_eval, tf)
    He4_K38__p_Ca41(rate_eval, tf)
    He4_P40__n_Cl43(rate_eval, tf)
    n_Cr48__Cr49(rate_eval, tf)
    Fe66__Co66__weak__wc12(rate_eval, tf)
    He4_Cr47__Fe51(rate_eval, tf)
    He4_Cr46__Fe50(rate_eval, tf)
    n_Ne19__He4_O16(rate_eval, tf)
    p_Cr46__Mn47(rate_eval, tf)
    n_Cr46__Cr47(rate_eval, tf)
    n_Cr45__Cr46(rate_eval, tf)
    He4_Cr44__Fe48(rate_eval, tf)
    n_Cr44__Cr45(rate_eval, tf)
    n_Sc55__Sc56(rate_eval, tf)
    He4_Cr43__Fe47(rate_eval, tf)
    n_Cr43__Cr44(rate_eval, tf)
    He4_Cr42__Fe46(rate_eval, tf)
    He4_Cr41__Fe45(rate_eval, tf)
    p_P44__He4_Si41(rate_eval, tf)
    He4_Mg22__Si26(rate_eval, tf)
    He4_V67__Mn71(rate_eval, tf)
    p_V67__Cr68(rate_eval, tf)
    He4_V66__Mn70(rate_eval, tf)
    p_V66__Cr67(rate_eval, tf)
    n_Mg27__Mg28(rate_eval, tf)
    He4_V64__Mn68(rate_eval, tf)
    n_Al37__Al38(rate_eval, tf)
    p_V64__Cr65(rate_eval, tf)
    He4_O14__p_F17(rate_eval, tf)
    p_K58__n_Ca58(rate_eval, tf)
    p_V63__Cr64(rate_eval, tf)
    n_V62__V63(rate_eval, tf)
    He4_V61__Mn65(rate_eval, tf)
    He4_V60__Mn64(rate_eval, tf)
    p_Ne32__He4_F29(rate_eval, tf)
    p_V60__Cr61(rate_eval, tf)
    p_V59__Cr60(rate_eval, tf)
    Na36__n_Mg35__weak__mp17(rate_eval, tf)
    n_V59__V60(rate_eval, tf)
    p_V58__Cr59(rate_eval, tf)
    He4_V57__Mn61(rate_eval, tf)
    p_V57__Cr58(rate_eval, tf)
    He4_V56__Mn60(rate_eval, tf)
    He4_Na37__n_Al40(rate_eval, tf)
    n_V55__V56(rate_eval, tf)
    He4_V54__Mn58(rate_eval, tf)
    p_V54__Cr55(rate_eval, tf)
    He4_V53__Mn57(rate_eval, tf)
    p_V53__Cr54(rate_eval, tf)
    n_V53__V54(rate_eval, tf)
    He4_V52__Mn56(rate_eval, tf)
    p_V62__n_Cr62(rate_eval, tf)
    He4_Ne25__Mg29(rate_eval, tf)
    p_V52__Cr53(rate_eval, tf)
    n_V51__V52(rate_eval, tf)
    He4_V50__Mn54(rate_eval, tf)
    He4_V65__Mn69(rate_eval, tf)
    p_V50__Cr51(rate_eval, tf)
    He4_Ne32__n_Mg35(rate_eval, tf)
    He4_F16__p_Ne19(rate_eval, tf)
    n_V49__V50(rate_eval, tf)
    p_V48__Cr49(rate_eval, tf)
    n_V48__V49(rate_eval, tf)
    n_S28__S29(rate_eval, tf)
    He4_V47__Mn51(rate_eval, tf)
    p_S42__n_Cl42(rate_eval, tf)
    p_Sc46__n_Ti46(rate_eval, tf)
    n_V47__V48(rate_eval, tf)
    He4_V46__Mn50(rate_eval, tf)
    p_V46__Cr47(rate_eval, tf)
    p_Si38__P39(rate_eval, tf)
    n_V46__V47(rate_eval, tf)
    He4_V45__Mn49(rate_eval, tf)
    p_Mn63__Fe64(rate_eval, tf)
    n_V45__V46(rate_eval, tf)
    He4_V43__Mn47(rate_eval, tf)
    p_V43__Cr44(rate_eval, tf)
    p_P40__n_S40(rate_eval, tf)
    p_Al42__He4_Mg39(rate_eval, tf)
    n_V42__V43(rate_eval, tf)
    He4_V41__Mn45(rate_eval, tf)
    n_Fe57__He4_Cr54(rate_eval, tf)
    p_V41__Cr42(rate_eval, tf)
    C16__n_N15__weak__wc12(rate_eval, tf)
    n_V41__V42(rate_eval, tf)
    He4_V39__Mn43(rate_eval, tf)
    n_Mn54__Mn55(rate_eval, tf)
    n_Ti64__Ti65(rate_eval, tf)
    He4_Ti63__Cr67(rate_eval, tf)
    p_Ti63__V64(rate_eval, tf)
    p_Ti62__V63(rate_eval, tf)
    He4_Ti61__Cr65(rate_eval, tf)
    Al39__n_Si38__weak__mp17(rate_eval, tf)
    n_Ne16__He4_O13(rate_eval, tf)
    p_N12__O13(rate_eval, tf)
    p_Ti61__V62(rate_eval, tf)
    p_Ti60__V61(rate_eval, tf)
    n_Ti60__Ti61(rate_eval, tf)
    p_Ti58__V59(rate_eval, tf)
    C21__n_C20(rate_eval, tf)
    p_Ti57__V58(rate_eval, tf)
    p_Ti56__V57(rate_eval, tf)
    p_Fe63__n_Co63(rate_eval, tf)
    p_Ti55__V56(rate_eval, tf)
    p_Cr58__n_Mn58(rate_eval, tf)
    p_Ar47__n_K47(rate_eval, tf)
    n_Ti55__Ti56(rate_eval, tf)
    p_Ar36__K37(rate_eval, tf)
    p_Ti54__V55(rate_eval, tf)
    He4_Ti53__Cr57(rate_eval, tf)
    p_Ti53__V54(rate_eval, tf)
    n_Ti57__Ti58(rate_eval, tf)
    He4_Ti52__Cr56(rate_eval, tf)
    C12_Ne20__n_S31(rate_eval, tf)
    p_Ti52__V53(rate_eval, tf)
    n_Ti52__Ti53(rate_eval, tf)
    n_V43__V44(rate_eval, tf)
    He4_Ti51__Cr55(rate_eval, tf)
    p_Ti49__V50(rate_eval, tf)
    t_Be9__n_B11(rate_eval, tf)
    n_Ti49__Ti50(rate_eval, tf)
    He4_Na39__n_Al42(rate_eval, tf)
    He4_Ti48__Cr52(rate_eval, tf)
    p_Ti47__V48(rate_eval, tf)
    He4_Ti57__n_Cr60(rate_eval, tf)
    n_Ti47__Ti48(rate_eval, tf)
    He4_Ti46__Cr50(rate_eval, tf)
    n_Ti46__Ti47(rate_eval, tf)
    He4_Ti45__Cr49(rate_eval, tf)
    n_Ti45__Ti46(rate_eval, tf)
    He4_Ti44__Cr48(rate_eval, tf)
    p_Ti44__V45(rate_eval, tf)
    n_Ti44__Ti45(rate_eval, tf)
    n_Mn44__p_Cr44(rate_eval, tf)
    He4_Al29__p_Si32(rate_eval, tf)
    He4_Ti43__Cr47(rate_eval, tf)
    n_Ti43__Ti44(rate_eval, tf)
    p_Ti42__V43(rate_eval, tf)
    He4_Ti41__Cr45(rate_eval, tf)
    He4_Na32__n_Al35(rate_eval, tf)
    p_Ti41__V42(rate_eval, tf)
    p_S28__Cl29(rate_eval, tf)
    n_Ti41__Ti42(rate_eval, tf)
    He4_Ti40__Cr44(rate_eval, tf)
    p_Ti40__V41(rate_eval, tf)
    p_Mn72__Fe73(rate_eval, tf)
    n_Ti40__Ti41(rate_eval, tf)
    He4_Ti38__Cr42(rate_eval, tf)
    p_Ar50__n_K50(rate_eval, tf)
    n_Ti38__Ti39(rate_eval, tf)
    n_Ti37__Ti38(rate_eval, tf)
    n_Ar34__He4_S31(rate_eval, tf)
    p_Sc63__Ti64(rate_eval, tf)
    n_Sc62__Sc63(rate_eval, tf)
    He4_Al35__P39(rate_eval, tf)
    p_Mn44__Fe45(rate_eval, tf)
    p_Sc61__Ti62(rate_eval, tf)
    He4_Sc60__V64(rate_eval, tf)
    n_Sc59__Sc60(rate_eval, tf)
    N16__O16__weak__wc12(rate_eval, tf)
    Si44__n_P43__weak__mp17(rate_eval, tf)
    He4_Sc58__V62(rate_eval, tf)
    p_Sc58__Ti59(rate_eval, tf)
    n_Sc58__Sc59(rate_eval, tf)
    He4_Ca60__n_Ti63(rate_eval, tf)
    p_Sc57__Ti58(rate_eval, tf)
    He4_Sc56__V60(rate_eval, tf)
    He4_Ti49__n_Cr52(rate_eval, tf)
    N17__n_O16__weak__wc12(rate_eval, tf)
    p_Sc56__Ti57(rate_eval, tf)
    n_Sc56__Sc57(rate_eval, tf)
    p_Sc37__Ti38(rate_eval, tf)
    He4_Sc55__V59(rate_eval, tf)
    p_Sc55__Ti56(rate_eval, tf)
    He4_K45__p_Ca48(rate_eval, tf)
    n_Sc54__Sc55(rate_eval, tf)
    p_Sc53__Ti54(rate_eval, tf)
    n_Sc53__Sc54(rate_eval, tf)
    n_Sc50__Sc51(rate_eval, tf)
    p_Mn57__He4_Cr54(rate_eval, tf)
    p_He3__He4__weak__bet_pos_(rate_eval, tf)
    He4_Sc49__V53(rate_eval, tf)
    He4_Mn44__Co48(rate_eval, tf)
    p_Mg31__Al32(rate_eval, tf)
    p_Sc49__Ti50(rate_eval, tf)
    n_Sc49__Sc50(rate_eval, tf)
    p_Sc48__Ti49(rate_eval, tf)
    n_Sc48__Sc49(rate_eval, tf)
    p_Ne21__Na22(rate_eval, tf)
    He4_Sc47__V51(rate_eval, tf)
    p_Sc46__Ti47(rate_eval, tf)
    n_Sc46__Sc47(rate_eval, tf)
    n_V47__p_Ti47(rate_eval, tf)
    He4_Sc45__V49(rate_eval, tf)
    He4_Mg20__Si24(rate_eval, tf)
    n_Sc45__Sc46(rate_eval, tf)
    p_Ca50__He4_K47(rate_eval, tf)
    p_Sc43__Ti44(rate_eval, tf)
    Cl52__n_n_n_Ar49__weak__mo03(rate_eval, tf)
    n_Cr63__Cr64(rate_eval, tf)
    F23__Ne23__weak__wc12(rate_eval, tf)
    He4_Sc42__V46(rate_eval, tf)
    p_Sc42__Ti43(rate_eval, tf)
    n_Sc42__Sc43(rate_eval, tf)
    He4_Sc41__V45(rate_eval, tf)
    p_Mn60__Fe61(rate_eval, tf)
    p_Sc41__Ti42(rate_eval, tf)
    n_Sc41__Sc42(rate_eval, tf)
    p_Sc40__Ti41(rate_eval, tf)
    He4_Sc39__V43(rate_eval, tf)
    n_Sc39__Sc40(rate_eval, tf)
    Mg36__Al36__weak__wc17(rate_eval, tf)
    He4_Sc38__V42(rate_eval, tf)
    p_Sc38__Ti39(rate_eval, tf)
    n_Sc38__Sc39(rate_eval, tf)
    p_Na33__He4_Ne30(rate_eval, tf)
    n_Sc37__Sc38(rate_eval, tf)
    He4_Cr55__Fe59(rate_eval, tf)
    p_Ca60__Sc61(rate_eval, tf)
    F27__n_n_Ne25__weak__mp17(rate_eval, tf)
    n_Ca60__Ca61(rate_eval, tf)
    He4_F25__n_Na28(rate_eval, tf)
    p_Ti51__V52(rate_eval, tf)
    He4_Ca59__Ti63(rate_eval, tf)
    n_Ar39__Ar40(rate_eval, tf)
    p_Ca59__Sc60(rate_eval, tf)
    He4_Cr64__Fe68(rate_eval, tf)
    p_Ca57__Sc58(rate_eval, tf)
    P47__n_n_n_S44__weak__mo03(rate_eval, tf)
    p_Na20__Mg21(rate_eval, tf)
    n_Ca57__Ca58(rate_eval, tf)
    Cl41__Ar41__weak__wc12(rate_eval, tf)
    C12_C12__p_Na23(rate_eval, tf)
    n_Ca56__Ca57(rate_eval, tf)
    n_Ca55__Ca56(rate_eval, tf)
    He4_Na27__n_Al30(rate_eval, tf)
    He4_Mn59__n_Co62(rate_eval, tf)
    He4_O27__Ne31(rate_eval, tf)
    Sc40__Ca40__weak__wc12(rate_eval, tf)
    p_Ca54__Sc55(rate_eval, tf)
    He4_V48__p_Cr51(rate_eval, tf)
    n_Ca54__Ca55(rate_eval, tf)
    Al39__n_n_Si37__weak__mp17(rate_eval, tf)
    n_Ca53__Ca54(rate_eval, tf)
    p_Fe58__Co59(rate_eval, tf)
    p_Mn71__Fe72(rate_eval, tf)
    P36__S36__weak__wc12(rate_eval, tf)
    He4_Ca51__Ti55(rate_eval, tf)
    S47__Cl47__weak__mo03(rate_eval, tf)
    p_Ca51__Sc52(rate_eval, tf)
    O27__F27__weak__mo03(rate_eval, tf)
    p_K42__He4_Ar39(rate_eval, tf)
    He4_Be11__n_C14(rate_eval, tf)
    n_Ca51__Ca52(rate_eval, tf)
    He4_Ca50__Ti54(rate_eval, tf)
    n_Ca49__Ca50(rate_eval, tf)
    He4_Ca47__Ti51(rate_eval, tf)
    B17__n_n_n_C14__weak__wc12(rate_eval, tf)
    He4_Na36__Al40(rate_eval, tf)
    He4_Ca46__Ti50(rate_eval, tf)
    Ca36__K36__weak__wc12(rate_eval, tf)
    Ca34__K34__weak__bqa_pos_(rate_eval, tf)
    C17__n_N16__weak__wc12(rate_eval, tf)
    n_Ca46__Ca47(rate_eval, tf)
    He4_Ca45__Ti49(rate_eval, tf)
    t_Li7__n_Be9(rate_eval, tf)
    He4_Li7__B11(rate_eval, tf)
    He4_Ca44__Ti48(rate_eval, tf)
    He4_Ca42__Ti46(rate_eval, tf)
    p_Ca42__Sc43(rate_eval, tf)
    p_Ca41__Sc42(rate_eval, tf)
    Si34__P34__weak__wc12(rate_eval, tf)
    n_Cr51__Cr52(rate_eval, tf)
    n_Ca41__Ca42(rate_eval, tf)
    p_Ca52__He4_K49(rate_eval, tf)
    n_F16__He4_N13(rate_eval, tf)
    p_Ca40__Sc41(rate_eval, tf)
    Al41__n_Si40__weak__mp17(rate_eval, tf)
    n_Ca40__Ca41(rate_eval, tf)
    He4_Ca37__Ti41(rate_eval, tf)
    n_Ca37__Ca38(rate_eval, tf)
    p_Fe64__Co65(rate_eval, tf)
    n_Na27__Na28(rate_eval, tf)
    n_Ca36__Ca37(rate_eval, tf)
    p_Si37__P38(rate_eval, tf)
    He4_Ca35__Ti39(rate_eval, tf)
    P37__S37__weak__wc12(rate_eval, tf)
    Ar54__n_K53__weak__mp17(rate_eval, tf)
    p_Ca35__Sc36(rate_eval, tf)
    He4_Ca34__Ti38(rate_eval, tf)
    He4_Cl46__n_K49(rate_eval, tf)
    p_Ca34__Sc35(rate_eval, tf)
    p_Be11__He4_Li8(rate_eval, tf)
    n_Fe47__p_Mn47(rate_eval, tf)
    He4_Ca33__Ti37(rate_eval, tf)
    He4_Na27__Al31(rate_eval, tf)
    p_K59__Ca60(rate_eval, tf)
    He4_K58__Sc62(rate_eval, tf)
    p_K50__n_Ca50(rate_eval, tf)
    Na27__Mg27__weak__wc12(rate_eval, tf)
    p_P30__S31(rate_eval, tf)
    p_K57__Ca58(rate_eval, tf)
    He4_Cl44__n_K47(rate_eval, tf)
    He4_Na29__Al33(rate_eval, tf)
    p_K56__Ca57(rate_eval, tf)
    He4_Si45__S49(rate_eval, tf)
    He4_K55__Sc59(rate_eval, tf)
    V60__Cr60__weak__wc17(rate_eval, tf)
    Fe60__Co60__weak__wc12(rate_eval, tf)
    p_Cl36__He4_S33(rate_eval, tf)
    n_K56__K57(rate_eval, tf)
    Sc55__n_Ti54__weak__wc12(rate_eval, tf)
    n_K53__K54(rate_eval, tf)
    He4_S27__Ar31(rate_eval, tf)
    p_K52__Ca53(rate_eval, tf)
    n_K52__K53(rate_eval, tf)
    He4_K51__Sc55(rate_eval, tf)
    p_F20__n_Ne20(rate_eval, tf)
    p_K51__Ca52(rate_eval, tf)
    n_K50__K51(rate_eval, tf)
    He4_K49__Sc53(rate_eval, tf)
    n_K46__K47(rate_eval, tf)
    p_Ti65__V66(rate_eval, tf)
    p_Ne26__Na27(rate_eval, tf)
    p_K45__Ca46(rate_eval, tf)
    He4_Ne17__Mg21(rate_eval, tf)
    Sc54__n_Ti53__weak__mp17(rate_eval, tf)
    n_K45__K46(rate_eval, tf)
    p_Ar38__K39(rate_eval, tf)
    He4_K44__Sc48(rate_eval, tf)
    n_K44__K45(rate_eval, tf)
    He4_K43__Sc47(rate_eval, tf)
    p_K43__Ca44(rate_eval, tf)
    n_K39__He4_Cl36(rate_eval, tf)
    p_Cr45__Mn46(rate_eval, tf)
    He4_Ti47__Cr51(rate_eval, tf)
    He4_Ne27__Mg31(rate_eval, tf)
    Mn70__n_Fe69__weak__mp17(rate_eval, tf)
    p_Sc62__Ti63(rate_eval, tf)
    n_K43__K44(rate_eval, tf)
    n_Al28__Al29(rate_eval, tf)
    p_K41__Ca42(rate_eval, tf)
    p_S34__Cl35(rate_eval, tf)
    n_K41__K42(rate_eval, tf)
    Ca35__p_p_Cl33__weak__wc12(rate_eval, tf)
    n_K40__K41(rate_eval, tf)
    p_K38__Ca39(rate_eval, tf)
    He4_Ca36__p_Sc39(rate_eval, tf)
    p_K37__Ca38(rate_eval, tf)
    He4_Sc48__p_Ti51(rate_eval, tf)
    n_Mn45__Mn46(rate_eval, tf)
    p_V56__n_Cr56(rate_eval, tf)
    n_K37__K38(rate_eval, tf)
    He4_P28__Cl32(rate_eval, tf)
    p_K36__Ca37(rate_eval, tf)
    n_K36__K37(rate_eval, tf)
    n_O15__He4_C12(rate_eval, tf)
    He4_K35__Sc39(rate_eval, tf)
    n_K34__K35(rate_eval, tf)
    n_K33__K34(rate_eval, tf)
    He4_K32__Sc36(rate_eval, tf)
    n_Si40__Si41(rate_eval, tf)
    n_K32__K33(rate_eval, tf)
    He4_Ar53__Ca57(rate_eval, tf)
    p_Ar51__K52(rate_eval, tf)
    Mn66__Fe66__weak__wc17(rate_eval, tf)
    p_Cl42__n_Ar42(rate_eval, tf)
    n_Ar51__Ar52(rate_eval, tf)
    n_Ar47__Ar48(rate_eval, tf)
    He4_Ar46__Ca50(rate_eval, tf)
    n_Ar46__Ar47(rate_eval, tf)
    n_F18__p_O18(rate_eval, tf)
    p_S41__Cl42(rate_eval, tf)
    p_Ar47__K48(rate_eval, tf)
    n_Ar45__Ar46(rate_eval, tf)
    Fe50__Mn50__weak__wc12(rate_eval, tf)
    p_Ar44__K45(rate_eval, tf)
    n_Ar44__Ar45(rate_eval, tf)
    p_Ar43__K44(rate_eval, tf)
    P46__n_n_n_S43__weak__mo03(rate_eval, tf)
    K53__n_Ca52__weak__wc17(rate_eval, tf)
    p_Ar42__K43(rate_eval, tf)
    n_Li7__Li8(rate_eval, tf)
    n_Ar42__Ar43(rate_eval, tf)
    n_Mg26__Mg27(rate_eval, tf)
    He4_Ar40__Ca44(rate_eval, tf)
    He4_Cr51__Fe55(rate_eval, tf)
    p_Ar40__K41(rate_eval, tf)
    n_Ar40__Ar41(rate_eval, tf)
    He4_Ar39__Ca43(rate_eval, tf)
    He4_Ar37__Ca41(rate_eval, tf)
    p_Ar37__K38(rate_eval, tf)
    He4_Ca36__Ti40(rate_eval, tf)
    Ne28__n_Na27__weak__wc12(rate_eval, tf)
    He4_Fe50__Ni54(rate_eval, tf)
    p_Ar35__K36(rate_eval, tf)
    Cl43__n_Ar42__weak__mp17(rate_eval, tf)
    p_F20__Ne21(rate_eval, tf)
    p_Si25__P26(rate_eval, tf)
    He4_Ar33__Ca37(rate_eval, tf)
    p_Ar33__K34(rate_eval, tf)
    He4_Ar32__Ca36(rate_eval, tf)
    p_Cl43__Ar44(rate_eval, tf)
    p_Ar32__K33(rate_eval, tf)
    Al41__Si41__weak__mo03(rate_eval, tf)
    n_Ar32__Ar33(rate_eval, tf)
    p_P33__He4_Si30(rate_eval, tf)
    p_Si44__He4_Al41(rate_eval, tf)
    Na32__n_n_Mg30__weak__wc12(rate_eval, tf)
    p_P28__S29(rate_eval, tf)
    He4_Ar31__Ca35(rate_eval, tf)
    p_Ar31__K32(rate_eval, tf)
    n_Ar31__Ar32(rate_eval, tf)
    He4_Ne20__Mg24(rate_eval, tf)
    Ne24__Na24__weak__wc12(rate_eval, tf)
    He4_Ar30__Ca34(rate_eval, tf)
    n_Ar29__Ar30(rate_eval, tf)
    He4_Cl51__K55(rate_eval, tf)
    He4_Mg34__Si38(rate_eval, tf)
    p_Cl51__Ar52(rate_eval, tf)
    n_Cl51__Cl52(rate_eval, tf)
    p_Mn57__Fe58(rate_eval, tf)
    He4_Cr60__n_Fe63(rate_eval, tf)
    p_Cl49__Ar50(rate_eval, tf)
    p_Ar53__n_K53(rate_eval, tf)
    Ca51__Sc51__weak__wc12(rate_eval, tf)
    n_Cl49__Cl50(rate_eval, tf)
    V46__Ti46__weak__wc12(rate_eval, tf)
    He4_Cl46__K50(rate_eval, tf)
    n_Cl46__Cl47(rate_eval, tf)
    Ti45__Sc45__weak__wc12(rate_eval, tf)
    n_Cl45__Cl46(rate_eval, tf)
    V62__n_Cr61__weak__mp17(rate_eval, tf)
    n_Cl44__Cl45(rate_eval, tf)
    He4_P26__Cl30(rate_eval, tf)
    He4_Cl42__K46(rate_eval, tf)
    n_Cl42__Cl43(rate_eval, tf)
    p_Cl41__Ar42(rate_eval, tf)
    He4_Cl39__K43(rate_eval, tf)
    Ne31__Na31__weak__wc17(rate_eval, tf)
    p_Cl46__Ar47(rate_eval, tf)
    p_Cl39__Ar40(rate_eval, tf)
    p_Cr64__n_Mn64(rate_eval, tf)
    Si45__n_P44__weak__mp17(rate_eval, tf)
    He4_Cl38__K42(rate_eval, tf)
    He4_Cl36__K40(rate_eval, tf)
    Na20__Ne20__weak__wc12(rate_eval, tf)
    He4_Cl35__K39(rate_eval, tf)
    p_Cl35__Ar36(rate_eval, tf)
    p_Ti39__V40(rate_eval, tf)
    p_Mg35__n_Al35(rate_eval, tf)
    He4_Cl33__K37(rate_eval, tf)
    n_Cl33__Cl34(rate_eval, tf)
    He4_Cl32__K36(rate_eval, tf)
    He4_O21__Ne25(rate_eval, tf)
    n_Mg32__Mg33(rate_eval, tf)
    p_Cl32__Ar33(rate_eval, tf)
    n_Ca44__Ca45(rate_eval, tf)
    p_Al42__Si43(rate_eval, tf)
    n_Cl32__Cl33(rate_eval, tf)
    He4_Cl31__K35(rate_eval, tf)
    He4_K45__Sc49(rate_eval, tf)
    p_Cl31__Ar32(rate_eval, tf)
    p_Cl30__Ar31(rate_eval, tf)
    p_Cl29__Ar30(rate_eval, tf)
    n_K47__K48(rate_eval, tf)
    K47__Ca47__weak__wc12(rate_eval, tf)
    He4_S49__Ar53(rate_eval, tf)
    He4_S48__Ar52(rate_eval, tf)
    p_Si34__P35(rate_eval, tf)
    He4_S47__Ar51(rate_eval, tf)
    Fe72__n_Co71__weak__mp17(rate_eval, tf)
    n_S47__S48(rate_eval, tf)
    He4_S44__Ar48(rate_eval, tf)
    p_S44__Cl45(rate_eval, tf)
    n_S44__S45(rate_eval, tf)
    n_Fe73__Fe74(rate_eval, tf)
    n_K49__K50(rate_eval, tf)
    n_Mg28__Mg29(rate_eval, tf)
    He4_S43__Ar47(rate_eval, tf)
    He4_S46__Ar50(rate_eval, tf)
    He4_S42__Ar46(rate_eval, tf)
    Mn61__Fe61__weak__wc12(rate_eval, tf)
    n_S42__S43(rate_eval, tf)
    Si33__P33__weak__wc12(rate_eval, tf)
    B17__n_n_C15__weak__wc12(rate_eval, tf)
    Al37__n_Si36__weak__mp17(rate_eval, tf)
    p_S40__Cl41(rate_eval, tf)
    n_S40__S41(rate_eval, tf)
    He4_F28__Na32(rate_eval, tf)
    p_Cl50__Ar51(rate_eval, tf)
    He4_S39__Ar43(rate_eval, tf)
    He4_Ar47__Ca51(rate_eval, tf)
    p_S39__Cl40(rate_eval, tf)
    n_S38__S39(rate_eval, tf)
    V47__Ti47__weak__wc12(rate_eval, tf)
    p_K34__Ca35(rate_eval, tf)
    He4_S36__Ar40(rate_eval, tf)
    He4_Mg36__Si40(rate_eval, tf)
    p_Na32__n_Mg32(rate_eval, tf)
    Cl47__n_n_Ar45__weak__mp17(rate_eval, tf)
    Ti51__V51__weak__wc12(rate_eval, tf)
    p_S36__Cl37(rate_eval, tf)
    He4_Ar54__n_Ca57(rate_eval, tf)
    p_S35__Cl36(rate_eval, tf)
    V45__Ti45__weak__wc12(rate_eval, tf)
    n_S34__S35(rate_eval, tf)
    He4_Ca45__n_Ti48(rate_eval, tf)
    n_S33__S34(rate_eval, tf)
    He4_S32__Ar36(rate_eval, tf)
    n_Ar52__Ar53(rate_eval, tf)
    p_S32__Cl33(rate_eval, tf)
    n_S32__S33(rate_eval, tf)
    p_S31__Cl32(rate_eval, tf)
    p_S29__Cl30(rate_eval, tf)
    He4_O22__Ne26(rate_eval, tf)
    He4_Ne24__Mg28(rate_eval, tf)
    He4_P37__Cl41(rate_eval, tf)
    Mg39__n_Al38__weak__mp17(rate_eval, tf)
    n_S27__S28(rate_eval, tf)
    p_Si33__P34(rate_eval, tf)
    n_S26__S27(rate_eval, tf)
    He4_Fe71__Ni75(rate_eval, tf)
    n_P45__P46(rate_eval, tf)
    n_P44__P45(rate_eval, tf)
    Al32__Si32__weak__wc12(rate_eval, tf)
    n_P42__P43(rate_eval, tf)
    n_P41__P42(rate_eval, tf)
    He4_O21__n_Ne24(rate_eval, tf)
    He4_P40__Cl44(rate_eval, tf)
    He4_K41__Sc45(rate_eval, tf)
    p_P40__S41(rate_eval, tf)
    C19__N19__weak__wc07(rate_eval, tf)
    He4_Cl37__K41(rate_eval, tf)
    He4_Mg33__n_Si36(rate_eval, tf)
    t__He3__weak__wc12(rate_eval, tf)
    p_P38__S39(rate_eval, tf)
    He4_Cl38__n_K41(rate_eval, tf)
    n_Na31__Na32(rate_eval, tf)
    n_P38__P39(rate_eval, tf)
    He4_P36__Cl40(rate_eval, tf)
    n_P36__P37(rate_eval, tf)
    He4_P35__Cl39(rate_eval, tf)
    C20__n_N19__weak__wc12(rate_eval, tf)
    He4_Cl44__K48(rate_eval, tf)
    p_P35__S36(rate_eval, tf)
    n_P35__P36(rate_eval, tf)
    n_P33__P34(rate_eval, tf)
    p_Fe58__He4_Mn55(rate_eval, tf)
    n_Ca38__Ca39(rate_eval, tf)
    He4_P32__Cl36(rate_eval, tf)
    n_P32__P33(rate_eval, tf)
    n_Mn45__He4_V42(rate_eval, tf)
    n_Cl32__p_S32(rate_eval, tf)
    n_Ar30__Ar31(rate_eval, tf)
    n_P28__P29(rate_eval, tf)
    He4_S26__Ar30(rate_eval, tf)
    B19__C19__weak__wc12(rate_eval, tf)
    He4_P27__Cl31(rate_eval, tf)
    n_P27__P28(rate_eval, tf)
    p_P26__S27(rate_eval, tf)
    n_P26__P27(rate_eval, tf)
    V55__Cr55__weak__wc12(rate_eval, tf)
    He4_Na31__Al35(rate_eval, tf)
    He4_P24__Cl28(rate_eval, tf)
    p_Mn70__Fe71(rate_eval, tf)
    He4_Cl33__p_Ar36(rate_eval, tf)
    S49__n_Cl48__weak__mp17(rate_eval, tf)
    p_Ca56__Sc57(rate_eval, tf)
    p_K55__n_Ca55(rate_eval, tf)
    p_Si42__P43(rate_eval, tf)
    K49__Ca49__weak__wc12(rate_eval, tf)
    Si31__P31__weak__wc12(rate_eval, tf)
    Mg37__Al37__weak__mo03(rate_eval, tf)
    n_Si42__Si43(rate_eval, tf)
    He4_Si41__S45(rate_eval, tf)
    He4_Si40__S44(rate_eval, tf)
    Ca59__n_n_Sc57__weak__mp17(rate_eval, tf)
    p_Si40__P41(rate_eval, tf)
    p_Si39__P40(rate_eval, tf)
    He4_Si38__S42(rate_eval, tf)
    p_Ar54__He4_Cl51(rate_eval, tf)
    F31__Ne31__weak__mo03(rate_eval, tf)
    S27__P27__weak__wc12(rate_eval, tf)
    Al34__n_Si33__weak__wc12(rate_eval, tf)
    n_Si38__Si39(rate_eval, tf)
    n_Si36__Si37(rate_eval, tf)
    n_Cr42__Cr43(rate_eval, tf)
    n_Al24__He4_Na21(rate_eval, tf)
    He4_Si34__S38(rate_eval, tf)
    He4_Si33__S37(rate_eval, tf)
    n_S45__S46(rate_eval, tf)
    He4_Cl29__K33(rate_eval, tf)
    p_Si32__P33(rate_eval, tf)
    p_Cl47__Ar48(rate_eval, tf)
    p_Mg37__n_Al37(rate_eval, tf)
    n_Si32__Si33(rate_eval, tf)
    n_Si22__Si23(rate_eval, tf)
    p_Si31__P32(rate_eval, tf)
    p_Si30__P31(rate_eval, tf)
    Cl29__S29__weak__bqa_pos_(rate_eval, tf)
    p_Si28__P29(rate_eval, tf)
    n_S41__S42(rate_eval, tf)
    p_Si26__P27(rate_eval, tf)
    n_Ne17__He4_O14(rate_eval, tf)
    n_Si26__Si27(rate_eval, tf)
    He4_Si24__S28(rate_eval, tf)
    Ca54__n_Sc53__weak__mp17(rate_eval, tf)
    p_Si24__P25(rate_eval, tf)
    p_Sc56__He4_Ca53(rate_eval, tf)
    p_Ca54__n_Sc54(rate_eval, tf)
    n_Si24__Si25(rate_eval, tf)
    Ca57__Sc57__weak__mo03(rate_eval, tf)
    He4_Al43__P47(rate_eval, tf)
    He4_Cl34__K38(rate_eval, tf)
    Mn62__Fe62__weak__mo03(rate_eval, tf)
    He4_Al42__P46(rate_eval, tf)
    He4_Ca38__p_Sc41(rate_eval, tf)
    p_O17__F18(rate_eval, tf)
    He4_Al40__P44(rate_eval, tf)
    p_Al40__Si41(rate_eval, tf)
    V65__Cr65__weak__mo03(rate_eval, tf)
    n_Al40__Al41(rate_eval, tf)
    p_Ti64__n_V64(rate_eval, tf)
    n_Al39__Al40(rate_eval, tf)
    He4_Al38__P42(rate_eval, tf)
    p_K40__Ca41(rate_eval, tf)
    n_Al38__Al39(rate_eval, tf)
    He4_Al37__P41(rate_eval, tf)
    p_Cl51__n_Ar51(rate_eval, tf)
    p_Al37__Si38(rate_eval, tf)
    P32__S32__weak__wc12(rate_eval, tf)
    Ne19__F19__weak__wc12(rate_eval, tf)
    n_Ar38__Ar39(rate_eval, tf)
    p_Sc59__He4_Ca56(rate_eval, tf)
    p_K44__Ca45(rate_eval, tf)
    S49__Cl49__weak__mo03(rate_eval, tf)
    He4_Al36__P40(rate_eval, tf)
    p_Si40__n_P40(rate_eval, tf)
    He4_Mg37__Si41(rate_eval, tf)
    p_Al36__Si37(rate_eval, tf)
    n_Al35__Al36(rate_eval, tf)
    He4_N14__n_F17(rate_eval, tf)
    n_V61__V62(rate_eval, tf)
    He4_Al34__P38(rate_eval, tf)
    n_Al34__Al35(rate_eval, tf)
    He4_Cr56__Fe60(rate_eval, tf)
    p_Al33__Si34(rate_eval, tf)
    p_Al31__Si32(rate_eval, tf)
    n_Al31__Al32(rate_eval, tf)
    Li11__n_n_Be9__weak__wc12(rate_eval, tf)
    He4_Al30__P34(rate_eval, tf)
    p_S49__He4_P46(rate_eval, tf)
    p_Al30__Si31(rate_eval, tf)
    n_V50__V51(rate_eval, tf)
    p_Al28__Si29(rate_eval, tf)
    He4_Ti62__n_Cr65(rate_eval, tf)
    p_Cr68__Mn69(rate_eval, tf)
    He4_Al27__P31(rate_eval, tf)
    Al25__Mg25__weak__wc12(rate_eval, tf)
    He4_Al26__P30(rate_eval, tf)
    n_Al26__Al27(rate_eval, tf)
    p_Al24__Si25(rate_eval, tf)
    n_Al24__Al25(rate_eval, tf)
    He4_Ti56__Cr60(rate_eval, tf)
    Fe69__Co69__weak__wc17(rate_eval, tf)
    He4_Mg41__Si45(rate_eval, tf)
    p_Cl39__n_Ar39(rate_eval, tf)
    He4_Mg39__Si43(rate_eval, tf)
    p_Mg39__Al40(rate_eval, tf)
    p_Mg37__Al38(rate_eval, tf)
    n_Sc44__Sc45(rate_eval, tf)
    n_Mg36__Mg37(rate_eval, tf)
    He4_Al41__P45(rate_eval, tf)
    d_Li6__n_Be7(rate_eval, tf)
    n_Mg35__Mg36(rate_eval, tf)
    p_Sc60__Ti61(rate_eval, tf)
    p_P46__He4_Si43(rate_eval, tf)
    n_Mg34__Mg35(rate_eval, tf)
    p_Cr47__Mn48(rate_eval, tf)
    He4_Si39__S43(rate_eval, tf)
    He4_Mg40__Si44(rate_eval, tf)
    p_Ca43__Sc44(rate_eval, tf)
    He4_Mg33__Si37(rate_eval, tf)
    He4_Mg31__Si35(rate_eval, tf)
    p_S48__He4_P45(rate_eval, tf)
    n_Si35__Si36(rate_eval, tf)
    He4_Al29__P33(rate_eval, tf)
    n_K37__p_Ar37(rate_eval, tf)
    n_Mg31__Mg32(rate_eval, tf)
    p_Fe49__Co50(rate_eval, tf)
    He4_K47__Sc51(rate_eval, tf)
    p_Mg30__Al31(rate_eval, tf)
    p_Si44__P45(rate_eval, tf)
    He4_Mg29__Si33(rate_eval, tf)
    p_Mg33__n_Al33(rate_eval, tf)
    n_Mg29__Mg30(rate_eval, tf)
    He4_Mg30__Si34(rate_eval, tf)
    n_Ca45__Ca46(rate_eval, tf)
    p_Mg32__Al33(rate_eval, tf)
    He4_Mg28__Si32(rate_eval, tf)
    p_Fe54__Co55(rate_eval, tf)
    p_Mg27__Al28(rate_eval, tf)
    He4_Mn65__Co69(rate_eval, tf)
    Mn70__Fe70__weak__mo03(rate_eval, tf)
    B17__C17__weak__wc17(rate_eval, tf)
    Ti64__n_n_V62__weak__mp17(rate_eval, tf)
    P44__S44__weak__wc17(rate_eval, tf)
    p_Fe46__Co47(rate_eval, tf)
    p_Mg26__Al27(rate_eval, tf)
    p_K49__Ca50(rate_eval, tf)
    Ne25__Na25__weak__wc12(rate_eval, tf)
    p_Mg24__Al25(rate_eval, tf)
    n_Mg24__Mg25(rate_eval, tf)
    n_Ca43__Ca44(rate_eval, tf)
    Fe68__n_Co67__weak__mp17(rate_eval, tf)
    He4_Mg23__Si27(rate_eval, tf)
    p_Mg23__Al24(rate_eval, tf)
    n_Mn44__He4_V41(rate_eval, tf)
    S45__n_n_Cl43__weak__mp17(rate_eval, tf)
    n_Mg23__Mg24(rate_eval, tf)
    He4_Mg31__n_Si34(rate_eval, tf)
    He4_Ca53__Ti57(rate_eval, tf)
    Cl28__S28__weak__bqa_pos_(rate_eval, tf)
    n_Cl34__Cl35(rate_eval, tf)
    p_Mg22__Al23(rate_eval, tf)
    n_Mg22__Mg23(rate_eval, tf)
    n_C14__C15(rate_eval, tf)
    He4_Mg21__Si25(rate_eval, tf)
    He4_Mn48__p_Fe51(rate_eval, tf)
    He4_He4_He4__C12(rate_eval, tf)
    He4_Cl43__K47(rate_eval, tf)
    He4_Mg19__Si23(rate_eval, tf)
    p_Na38__Mg39(rate_eval, tf)
    He4_Si31__S35(rate_eval, tf)
    p_Sc36__Ti37(rate_eval, tf)
    He4_Na37__Al41(rate_eval, tf)
    n_Na37__Na38(rate_eval, tf)
    n_Mn51__Mn52(rate_eval, tf)
    He4_S49__n_Ar52(rate_eval, tf)
    n_Na36__Na37(rate_eval, tf)
    p_Cl47__n_Ar47(rate_eval, tf)
    Ca38__K38__weak__wc12(rate_eval, tf)
    He4_Na34__Al38(rate_eval, tf)
    n_Na34__Na35(rate_eval, tf)
    He4_Na33__Al37(rate_eval, tf)
    n_He3__He4(rate_eval, tf)
    p_F21__n_Ne21(rate_eval, tf)
    He4_Na39__Al43(rate_eval, tf)
    Mg32__n_Al31__weak__wc12(rate_eval, tf)
    p_Na32__Mg33(rate_eval, tf)
    He4_Al28__p_Si31(rate_eval, tf)
    He4_Ne29__n_Mg32(rate_eval, tf)
    He4_P25__Cl29(rate_eval, tf)
    p_Na36__Mg37(rate_eval, tf)
    Cl50__Ar50__weak__mo03(rate_eval, tf)
    He4_Na28__Al32(rate_eval, tf)
    n_F15__F16(rate_eval, tf)
    p_Na26__Mg27(rate_eval, tf)
    He4_Ti56__n_Cr59(rate_eval, tf)
    Si45__P45__weak__mo03(rate_eval, tf)
    p_Na25__Mg26(rate_eval, tf)
    n_Na24__Na25(rate_eval, tf)
    Na36__Mg36__weak__mo03(rate_eval, tf)
    p_Ar52__K53(rate_eval, tf)
    Na28__Mg28__weak__wc12(rate_eval, tf)
    He4_F15__p_Ne18(rate_eval, tf)
    He4_Na23__Al27(rate_eval, tf)
    p_Ca51__n_Sc51(rate_eval, tf)
    p_Sc63__He4_Ca60(rate_eval, tf)
    p_Na23__Mg24(rate_eval, tf)
    Sc62__n_Ti61__weak__mp17(rate_eval, tf)
    p_Na22__Mg23(rate_eval, tf)
    n_Na22__Na23(rate_eval, tf)
    He4_V55__Mn59(rate_eval, tf)
    He4_Ar50__Ca54(rate_eval, tf)
    p_Na21__Mg22(rate_eval, tf)
    Ar53__n_n_K51__weak__mp17(rate_eval, tf)
    He4_Ti42__Cr46(rate_eval, tf)
    n_Na21__Na22(rate_eval, tf)
    p_Ti65__n_V65(rate_eval, tf)
    He4_Na20__Al24(rate_eval, tf)
    p_S33__Cl34(rate_eval, tf)
    n_Na20__Na21(rate_eval, tf)
    Sc63__Ti63__weak__mo03(rate_eval, tf)
    n_Na19__Na20(rate_eval, tf)
    p_Mg31__He4_Na28(rate_eval, tf)
    Al42__Si42__weak__mo03(rate_eval, tf)
    He4_K58__n_Sc61(rate_eval, tf)
    n_Mg40__Mg41(rate_eval, tf)
    He4_Ne34__Mg38(rate_eval, tf)
    p_Sc54__Ti55(rate_eval, tf)
    n_Ne32__Ne33(rate_eval, tf)
    p_Si29__P30(rate_eval, tf)
    Cr68__n_Mn67__weak__mp17(rate_eval, tf)
    He4_Ne31__Mg35(rate_eval, tf)
    p_Ne31__Na32(rate_eval, tf)
    He4_Ne30__Mg34(rate_eval, tf)
    He4_Ca58__Ti62(rate_eval, tf)
    Mg41__n_Al40__weak__mp17(rate_eval, tf)
    p_Ne30__Na31(rate_eval, tf)
    p_Mn71__n_Fe71(rate_eval, tf)
    Mn52__Cr52__weak__wc12(rate_eval, tf)
    Ti58__V58__weak__wc12(rate_eval, tf)
    Ne17__p_O16__weak__wc12(rate_eval, tf)
    p_Cl44__Ar45(rate_eval, tf)
    p_Ne28__Na29(rate_eval, tf)
    p_Na35__He4_Ne32(rate_eval, tf)
    n_Fe74__Fe75(rate_eval, tf)
    p_Ne27__Na28(rate_eval, tf)
    He4_Ne26__Mg30(rate_eval, tf)
    Ti41__p_Ca40__weak__wc12(rate_eval, tf)
    n_Ne26__Ne27(rate_eval, tf)
    S28__p_Si27__weak__wc12(rate_eval, tf)
    He4_Cl52__n_K55(rate_eval, tf)
    p_Ne25__Na26(rate_eval, tf)
    n_Mg19__Mg20(rate_eval, tf)
    n_Ne24__Ne25(rate_eval, tf)
    p_Ne23__Na24(rate_eval, tf)
    Sc42__Ca42__weak__wc12(rate_eval, tf)
    p_Al43__Si44(rate_eval, tf)
    p_Ne33__Na34(rate_eval, tf)
    p_F27__Ne28(rate_eval, tf)
    p_Ne20__Na21(rate_eval, tf)
    p_K53__Ca54(rate_eval, tf)
    p_Cr70__n_Mn70(rate_eval, tf)
    p_Ne19__Na20(rate_eval, tf)
    p_F24__He4_O21(rate_eval, tf)
    F24__Ne24__weak__wc12(rate_eval, tf)
    p_Mn52__Fe53(rate_eval, tf)
    n_Ne19__Ne20(rate_eval, tf)
    p_Ne18__Na19(rate_eval, tf)
    Ne32__n_Na31__weak__mp17(rate_eval, tf)
    p_Cr64__Mn65(rate_eval, tf)
    Sc61__n_Ti60__weak__mp17(rate_eval, tf)
    n_S46__S47(rate_eval, tf)
    Ca39__K39__weak__wc12(rate_eval, tf)
    n_Ne18__Ne19(rate_eval, tf)
    p_Cl48__Ar49(rate_eval, tf)
    n_Ne17__Ne18(rate_eval, tf)
    He4_Cr65__Fe69(rate_eval, tf)
    F25__Ne25__weak__wc12(rate_eval, tf)
    He4_Ne16__Mg20(rate_eval, tf)
    He4_Na30__Al34(rate_eval, tf)
    He4_O28__Ne32(rate_eval, tf)
    n_Ne16__Ne17(rate_eval, tf)
    He4_F31__Na35(rate_eval, tf)
    n_O13__O14(rate_eval, tf)
    p_F28__Ne29(rate_eval, tf)
    p_F19__He4_O16(rate_eval, tf)
    p_Mg38__Al39(rate_eval, tf)
    He4_Mg29__n_Si32(rate_eval, tf)
    He4_Ar41__Ca45(rate_eval, tf)
    n_V41__p_Ti41(rate_eval, tf)
    n_P39__P40(rate_eval, tf)
    n_Si34__Si35(rate_eval, tf)
    He4_F24__Na28(rate_eval, tf)
    He4_Al31__P35(rate_eval, tf)
    n_F23__F24(rate_eval, tf)
    He4_Mn51__Co55(rate_eval, tf)
    p_F22__Ne23(rate_eval, tf)
    n_F22__F23(rate_eval, tf)
    p_F21__Ne22(rate_eval, tf)
    n_Cr54__Cr55(rate_eval, tf)
    p_Fe51__Co52(rate_eval, tf)
    n_F21__F22(rate_eval, tf)
    Na30__n_Mg29__weak__wc17(rate_eval, tf)
    n_Al23__Al24(rate_eval, tf)
    n_F20__F21(rate_eval, tf)
    N22__O22__weak__wc12(rate_eval, tf)
    He4_F18__Na22(rate_eval, tf)
    n_F18__F19(rate_eval, tf)
    n_F17__F18(rate_eval, tf)
    He4_K59__Sc63(rate_eval, tf)
    n_F16__F17(rate_eval, tf)
    n_F14__F15(rate_eval, tf)
    p_O27__F28(rate_eval, tf)
    He4_Ar42__Ca46(rate_eval, tf)
    p_O26__F27(rate_eval, tf)
    p_Cl43__n_Ar43(rate_eval, tf)
    Cr67__n_Mn66__weak__mp17(rate_eval, tf)
    He4_O24__Ne28(rate_eval, tf)
    p_K35__Ca36(rate_eval, tf)
    n_Ne23__Ne24(rate_eval, tf)
    He4_O23__Ne27(rate_eval, tf)
    K36__He4_S32__weak__wc12(rate_eval, tf)
    n_O23__O24(rate_eval, tf)
    He4_F27__Na31(rate_eval, tf)
    n_K57__K58(rate_eval, tf)
    p_O22__F23(rate_eval, tf)
    n_O22__O23(rate_eval, tf)
    n_O21__O22(rate_eval, tf)
    n_Cl31__He4_P28(rate_eval, tf)
    He4_O20__Ne24(rate_eval, tf)
    p_O20__F21(rate_eval, tf)
    He4_O20__n_Ne23(rate_eval, tf)
    n_Ar48__Ar49(rate_eval, tf)
    He4_O19__Ne23(rate_eval, tf)
    He4_S28__Ar32(rate_eval, tf)
    K58__n_n_Ca56__weak__mp17(rate_eval, tf)
    He4_Ar44__n_Ca47(rate_eval, tf)
    He4_O17__Ne21(rate_eval, tf)
    n_O16__O17(rate_eval, tf)
    p_S44__n_Cl44(rate_eval, tf)
    n_O15__O16(rate_eval, tf)
    n_N19__N20(rate_eval, tf)
    n_Si27__He4_Mg24(rate_eval, tf)
    Sc63__n_Ti62__weak__mp17(rate_eval, tf)
    V58__n_Cr57__weak__mp17(rate_eval, tf)
    n_N17__N18(rate_eval, tf)
    Ar45__K45__weak__wc12(rate_eval, tf)
    He4_P33__Cl37(rate_eval, tf)
    n_N16__N17(rate_eval, tf)
    n_Cl29__Cl30(rate_eval, tf)
    n_Ti53__Ti54(rate_eval, tf)
    n_N15__N16(rate_eval, tf)
    Ti60__n_V59__weak__mp17(rate_eval, tf)
    p_N14__O15(rate_eval, tf)
    n_N13__N14(rate_eval, tf)
    Mg38__n_n_Al36__weak__mp17(rate_eval, tf)
    n_Fe53__Fe54(rate_eval, tf)
    p_C14__N15(rate_eval, tf)
    p_C13__N14(rate_eval, tf)
    p_C12__N13(rate_eval, tf)
    p_C11__N12(rate_eval, tf)
    n_V42__p_Ti42(rate_eval, tf)
    n_B12__B13(rate_eval, tf)
    n_p__d(rate_eval, tf)
    n_B11__B12(rate_eval, tf)
    p_B10__C11(rate_eval, tf)
    p_Na28__Mg29(rate_eval, tf)
    n_B10__B11(rate_eval, tf)
    n_Be11__Be12(rate_eval, tf)
    p_Be10__B11(rate_eval, tf)
    p_Sc39__Ti40(rate_eval, tf)
    He4_Ti64__Cr68(rate_eval, tf)
    n_Mg20__Mg21(rate_eval, tf)
    p_Be7__B8(rate_eval, tf)
    He4_Li9__B13(rate_eval, tf)
    He4_Mg26__Si30(rate_eval, tf)
    He4_Fe45__p_Co48(rate_eval, tf)
    p_P35__n_S35(rate_eval, tf)
    He4_Na24__Al28(rate_eval, tf)
    He4_Li8__B12(rate_eval, tf)
    He4_He3__Be7(rate_eval, tf)
    He4_Fe75__Ni79(rate_eval, tf)
    p_Ne24__Na25(rate_eval, tf)
    p_t__He4(rate_eval, tf)
    He4_d__Li6(rate_eval, tf)
    p_P27__S28(rate_eval, tf)
    He4_Cr49__Fe53(rate_eval, tf)
    He4_C12__O16(rate_eval, tf)
    Fe75__n_n_Co73__weak__mp17(rate_eval, tf)
    V61__n_Cr60__weak__wc12(rate_eval, tf)
    Fe73__n_n_Co71__weak__mp17(rate_eval, tf)
    Mn73__n_n_Fe71__weak__mp17(rate_eval, tf)
    He4_Fe62__n_Ni65(rate_eval, tf)
    F27__n_Ne26__weak__wc12(rate_eval, tf)
    Mn72__n_n_Fe70__weak__mp17(rate_eval, tf)
    Al22__Mg22__weak__wc12(rate_eval, tf)
    Mn71__n_n_Fe69__weak__mp17(rate_eval, tf)
    He4_Mg27__Si31(rate_eval, tf)
    Fe59__Co59__weak__wc12(rate_eval, tf)
    Mn70__n_n_Fe68__weak__mp17(rate_eval, tf)
    Ca61__n_n_n_Sc58__weak__mo03(rate_eval, tf)
    n_Ti47__p_Sc47(rate_eval, tf)
    p_Ca49__n_Sc49(rate_eval, tf)
    Mn68__n_n_Fe66__weak__mp17(rate_eval, tf)
    p_Si35__P36(rate_eval, tf)
    p_Ti46__V47(rate_eval, tf)
    He4_P34__Cl38(rate_eval, tf)
    p_Fe71__Co72(rate_eval, tf)
    Ti65__n_n_V63__weak__mp17(rate_eval, tf)
    Ar35__Cl35__weak__wc12(rate_eval, tf)
    Si42__P42__weak__wc17(rate_eval, tf)
    n_K51__K52(rate_eval, tf)
    Fe48__Mn48__weak__wc12(rate_eval, tf)
    He4_Ca49__n_Ti52(rate_eval, tf)
    Sc60__n_n_Ti58__weak__mp17(rate_eval, tf)
    n_V48__He4_Sc45(rate_eval, tf)
    p_F18__Ne19(rate_eval, tf)
    p_Mg36__Al37(rate_eval, tf)
    Ar49__n_K48__weak__wc12(rate_eval, tf)
    n_Ne28__Ne29(rate_eval, tf)
    n_Si25__Si26(rate_eval, tf)
    K59__n_n_Ca57__weak__mp17(rate_eval, tf)
    n_S31__He4_Si28(rate_eval, tf)
    K56__Ca56__weak__mo03(rate_eval, tf)
    n_P29__P30(rate_eval, tf)
    Mn67__Fe67__weak__wc17(rate_eval, tf)
    K53__n_n_Ca51__weak__mp17(rate_eval, tf)
    n_Cr58__Cr59(rate_eval, tf)
    He4_Mn73__Co77(rate_eval, tf)
    K52__n_n_Ca50__weak__mp17(rate_eval, tf)
    Ar54__n_n_K52__weak__mp17(rate_eval, tf)
    p_Ar42__He4_Cl39(rate_eval, tf)
    N21__n_O20__weak__wc12(rate_eval, tf)
    Cl52__n_n_Ar50__weak__mp17(rate_eval, tf)
    Cl50__n_n_Ar48__weak__mp17(rate_eval, tf)
    S49__n_n_Cl47__weak__mp17(rate_eval, tf)
    S47__n_n_Cl45__weak__mp17(rate_eval, tf)
    n_Cl30__He4_P27(rate_eval, tf)
    S27__p_p_Al25__weak__wc12(rate_eval, tf)
    P47__n_n_S45__weak__mp17(rate_eval, tf)
    O20__F20__weak__wc12(rate_eval, tf)
    He4_K42__Sc46(rate_eval, tf)
    P45__n_n_S43__weak__mp17(rate_eval, tf)
    He4_Na19__p_Mg22(rate_eval, tf)
    p_F25__Ne26(rate_eval, tf)
    P44__n_n_S42__weak__mp17(rate_eval, tf)
    P43__n_n_S41__weak__mp17(rate_eval, tf)
    Cr61__Mn61__weak__wc12(rate_eval, tf)
    Si44__n_n_P42__weak__mp17(rate_eval, tf)
    He4_Mn61__n_Co64(rate_eval, tf)
    Sc57__Ti57__weak__wc17(rate_eval, tf)
    He4_Si28__S32(rate_eval, tf)
    Si41__n_n_P39__weak__mp17(rate_eval, tf)
    p_K42__Ca43(rate_eval, tf)
    Si39__n_n_P37__weak__mp17(rate_eval, tf)
    Si23__p_p_Na21__weak__wc12(rate_eval, tf)
    He4_Sc41__p_Ti44(rate_eval, tf)
    He4_Sc36__V40(rate_eval, tf)
    p_S37__He4_P34(rate_eval, tf)
    Al43__n_n_Si41__weak__mp17(rate_eval, tf)
    Al41__n_n_Si39__weak__mp17(rate_eval, tf)
    He4_Mn43__p_Fe46(rate_eval, tf)
    n_K42__K43(rate_eval, tf)
    Al38__n_n_Si36__weak__mp17(rate_eval, tf)
    P41__n_S40__weak__wc12(rate_eval, tf)
    p_V40__Cr41(rate_eval, tf)
    Mg33__n_Al32__weak__wc12(rate_eval, tf)
    He4_K36__Sc40(rate_eval, tf)
    Mg37__n_n_Al35__weak__mp17(rate_eval, tf)
    p_K39__Ca40(rate_eval, tf)
    He4_Sc40__V44(rate_eval, tf)
    Cr43__p_Ti42__weak__wc17(rate_eval, tf)
    Al24__p_Na23__weak__wc12(rate_eval, tf)
    Mg33__n_n_Al31__weak__mp17(rate_eval, tf)
    Na35__n_n_Mg33__weak__mp17(rate_eval, tf)
    p_Sc51__n_Ti51(rate_eval, tf)
    Na31__n_n_Mg29__weak__wc12(rate_eval, tf)
    Sc59__n_n_Ti57__weak__mp17(rate_eval, tf)
    He4_K47__n_Sc50(rate_eval, tf)
    F24__n_Ne23__weak__wc12(rate_eval, tf)
    Na30__n_n_Mg28__weak__wc12(rate_eval, tf)
    Mn69__n_Fe68__weak__mp17(rate_eval, tf)
    Ne32__n_n_Na30__weak__mp17(rate_eval, tf)
    He4_O14__Ne18(rate_eval, tf)
    Al22__p_p_Ne20__weak__wc12(rate_eval, tf)
    p_Ti50__V51(rate_eval, tf)
    Ne29__n_n_Na27__weak__wc12(rate_eval, tf)
    F30__n_n_Ne28__weak__mp17(rate_eval, tf)
    O27__n_n_F25__weak__mp17(rate_eval, tf)
    n_Ar36__Ar37(rate_eval, tf)
    O26__n_n_F24__weak__mp17(rate_eval, tf)
    p_Mn53__Fe54(rate_eval, tf)
    C14__N14__weak__wc12(rate_eval, tf)
    He4_Mg38__Si42(rate_eval, tf)
    O25__n_n_F23__weak__mp17(rate_eval, tf)
    B15__n_n_C13__weak__wc12(rate_eval, tf)
    n_Ar43__Ar44(rate_eval, tf)
    He4_Si26__S30(rate_eval, tf)
    p_P33__S34(rate_eval, tf)
    Be16__n_n_Be14(rate_eval, tf)
    Be14__n_n_B12__weak__wc12(rate_eval, tf)
    He4_Na20__p_Mg23(rate_eval, tf)
    p_Al28__n_Si28(rate_eval, tf)
    Fe75__n_Co74__weak__mp17(rate_eval, tf)
    P43__n_S42__weak__wc12(rate_eval, tf)
    Fe73__n_Co72__weak__mp17(rate_eval, tf)
    Fe74__Co74__weak__mo03(rate_eval, tf)
    p_Cl41__n_Ar41(rate_eval, tf)
    n_Mg25__Mg26(rate_eval, tf)
    n_C11__C12(rate_eval, tf)
    Fe70__n_Co69__weak__mp17(rate_eval, tf)
    Mg35__n_Al34__weak__wc12(rate_eval, tf)
    n_Cl30__Cl31(rate_eval, tf)
    Fe69__n_Co68__weak__mp17(rate_eval, tf)
    He4_Fe74__Ni78(rate_eval, tf)
    p_K55__Ca56(rate_eval, tf)
    p_K47__n_Ca47(rate_eval, tf)
    p_Ca50__n_Sc50(rate_eval, tf)
    He4_V44__p_Cr47(rate_eval, tf)
    n_S35__S36(rate_eval, tf)
    He4_Mg36__n_Si39(rate_eval, tf)
    n_Ca48__Ca49(rate_eval, tf)
    He4_B11__n_N14(rate_eval, tf)
    He4_Mn58__Co62(rate_eval, tf)
    He4_Si32__S36(rate_eval, tf)
    p_V45__Cr46(rate_eval, tf)
    V60__n_Cr59__weak__mp17(rate_eval, tf)
    He4_S29__Ar33(rate_eval, tf)
    Sc44__Ca44__weak__wc12(rate_eval, tf)
    p_p__d__weak__bet_pos_(rate_eval, tf)
    p_p__d__weak__electron_capture(rate_eval, tf)
    Ti57__V57__weak__wc12(rate_eval, tf)
    p_Cl38__n_Ar38(rate_eval, tf)
    He4_F30__Na34(rate_eval, tf)
    He4_Fe63__Ni67(rate_eval, tf)
    n_Cl31__Cl32(rate_eval, tf)
    p_Al23__Si24(rate_eval, tf)
    n_Cl48__Cl49(rate_eval, tf)
    V65__n_Cr64__weak__mp17(rate_eval, tf)
    He4_F20__Na24(rate_eval, tf)
    He4_K59__n_Sc62(rate_eval, tf)
    He4_S47__n_Ar50(rate_eval, tf)
    p_Al41__Si42(rate_eval, tf)
    K48__n_Ca47__weak__wc12(rate_eval, tf)
    n_Mg19__p_Na19(rate_eval, tf)
    p_Cl38__Ar39(rate_eval, tf)
    p_Mg32__n_Al32(rate_eval, tf)
    He4_Cl28__K32(rate_eval, tf)
    Fe48__p_Cr47__weak__wc12(rate_eval, tf)
    p_Na27__Mg28(rate_eval, tf)
    p_P46__n_S46(rate_eval, tf)
    p_P41__n_S41(rate_eval, tf)
    Al43__n_Si42__weak__mp17(rate_eval, tf)
    Si23__Al23__weak__wc12(rate_eval, tf)
    Fe46__p_Cr45__weak__wc12(rate_eval, tf)
    p_P39__n_S39(rate_eval, tf)
    p_Cr55__Mn56(rate_eval, tf)
    n_Cl38__Cl39(rate_eval, tf)
    Ne18__F18__weak__wc12(rate_eval, tf)
    Fe45__p_Cr44__weak__wc17(rate_eval, tf)
    He4_Mg28__n_Si31(rate_eval, tf)
    Mn73__n_Fe72__weak__mp17(rate_eval, tf)
    Mn72__n_Fe71__weak__mp17(rate_eval, tf)
    p_Mn63__He4_Cr60(rate_eval, tf)
    n_Al23__p_Mg23(rate_eval, tf)
    Ar52__K52__weak__mo03(rate_eval, tf)
    Mn65__n_Fe64__weak__mp17(rate_eval, tf)
    Fe74__n_Co73__weak__mp17(rate_eval, tf)
    n_P40__P41(rate_eval, tf)
    S26__P26__weak__bqa_pos_(rate_eval, tf)
    n_Al24__p_Mg24(rate_eval, tf)
    He4_Cr68__n_Fe71(rate_eval, tf)
    He4_Fe66__Ni70(rate_eval, tf)
    p_Ca50__Sc51(rate_eval, tf)
    He4_Si29__S33(rate_eval, tf)
    p_Mn64__Fe65(rate_eval, tf)
    p_V44__Cr45(rate_eval, tf)
    Li11__Be11__weak__wc12(rate_eval, tf)
    Ca61__n_Sc60__weak__mp17(rate_eval, tf)
    n_Fe60__Fe61(rate_eval, tf)
    n_Si23__He4_Mg20(rate_eval, tf)
    Ti61__V61__weak__wc17(rate_eval, tf)
    n_Cl41__Cl42(rate_eval, tf)
    Al23__Mg23__weak__wc12(rate_eval, tf)
    p_N14__n_O14(rate_eval, tf)
    p_Na36__He4_Ne33(rate_eval, tf)
    He4_O18__n_Ne21(rate_eval, tf)
    He4_Be9__n_C12(rate_eval, tf)
    p_Cl34__Ar35(rate_eval, tf)
    K55__n_n_Ca53__weak__mp17(rate_eval, tf)
    He4_Fe61__Ni65(rate_eval, tf)
    p_Mg37__He4_Na34(rate_eval, tf)
    p_Na34__n_Mg34(rate_eval, tf)
    Mg39__n_n_Al37__weak__mp17(rate_eval, tf)
    n_Mg22__p_Na22(rate_eval, tf)
    He4_Ca35__p_Sc38(rate_eval, tf)
    Ne32__Na32__weak__wc17(rate_eval, tf)
    He4_Ar54__Ca58(rate_eval, tf)
    He4_V59__Mn63(rate_eval, tf)
    p_K58__Ca59(rate_eval, tf)
    Si32__P32__weak__wc12(rate_eval, tf)
    p_Fe53__Co54(rate_eval, tf)
    He4_P41__Cl45(rate_eval, tf)
    He4_P46__n_Cl49(rate_eval, tf)
    He4_K53__Sc57(rate_eval, tf)
    Mn46__p_V45__weak__wc12(rate_eval, tf)
    K57__n_n_Ca55__weak__mp17(rate_eval, tf)
    He4_S34__Ar38(rate_eval, tf)
    He4_Ca37__p_Sc40(rate_eval, tf)
    Be12__B12__weak__wc12(rate_eval, tf)
    N19__n_O18__weak__wc12(rate_eval, tf)
    p_P31__He4_Si28(rate_eval, tf)
    n_Ti37__p_Sc37(rate_eval, tf)
    Cr70__n_Mn69__weak__mp17(rate_eval, tf)
    O24__n_F23__weak__wc12(rate_eval, tf)
    Sc41__Ca41__weak__wc12(rate_eval, tf)
    Mn68__n_Fe67__weak__mp17(rate_eval, tf)
    p_P41__S42(rate_eval, tf)
    p_Cl44__n_Ar44(rate_eval, tf)
    Cr69__n_Mn68__weak__mp17(rate_eval, tf)
    n_Li8__Li9(rate_eval, tf)
    He4_N12__p_O15(rate_eval, tf)
    Cr66__n_Mn65__weak__mp17(rate_eval, tf)
    n_C13__C14(rate_eval, tf)
    n_Mg21__p_Na21(rate_eval, tf)
    Cr63__n_Mn62__weak__mp17(rate_eval, tf)
    He4_Mn71__Co75(rate_eval, tf)
    n_Ca59__Ca60(rate_eval, tf)
    N13__C13__weak__wc12(rate_eval, tf)
    p_Ca48__Sc49(rate_eval, tf)
    Sc37__Ca37__weak__bqa_pos_(rate_eval, tf)
    F29__Ne29__weak__wc17(rate_eval, tf)
    He4_V65__n_Mn68(rate_eval, tf)
    Cr62__n_Mn61__weak__mp17(rate_eval, tf)
    F30__n_Ne29__weak__mp17(rate_eval, tf)
    Cr61__n_Mn60__weak__mp17(rate_eval, tf)
    n_Si23__Si24(rate_eval, tf)
    p_Mg41__Al42(rate_eval, tf)
    He4_Be10__n_C13(rate_eval, tf)
    n_Be7__p_Li7(rate_eval, tf)
    n_Al21__Al22(rate_eval, tf)
    n_Si26__He4_Mg23(rate_eval, tf)
    n_Na32__Na33(rate_eval, tf)
    Mn44__Cr44__weak__bqa_pos_(rate_eval, tf)
    Fe73__Co73__weak__mo03(rate_eval, tf)
    He4_Ca55__n_Ti58(rate_eval, tf)
    He4_Ar44__Ca48(rate_eval, tf)
    Cr45__p_Ti44__weak__wc12(rate_eval, tf)
    n_P34__P35(rate_eval, tf)
    He4_P28__p_S31(rate_eval, tf)
    He4_Si25__S29(rate_eval, tf)
    n_Sc35__Sc36(rate_eval, tf)
    p_Sc47__Ti48(rate_eval, tf)
    He4_P38__Cl42(rate_eval, tf)
    n_Cl28__p_S28(rate_eval, tf)
    Ar51__n_K50__weak__mp17(rate_eval, tf)
    Cr42__p_Ti41__weak__wc12(rate_eval, tf)
    He4_Mg25__Si29(rate_eval, tf)
    He4_Mn52__p_Fe55(rate_eval, tf)
    n_Mn50__p_Cr50(rate_eval, tf)
    C15__N15__weak__wc12(rate_eval, tf)
    V63__n_Cr62__weak__wc12(rate_eval, tf)
    Ar52__n_K51__weak__mp17(rate_eval, tf)
    n_Cr41__p_V41(rate_eval, tf)
    p_Ar46__K47(rate_eval, tf)
    V59__n_Cr58__weak__wc12(rate_eval, tf)
    p_S42__He4_P39(rate_eval, tf)
    He4_N14__F18(rate_eval, tf)
    He4_Si36__n_S39(rate_eval, tf)
    p_Li8__n_He4_He4(rate_eval, tf)
    n_Ca47__Ca48(rate_eval, tf)
    p_Fe67__Co68(rate_eval, tf)
    Fe76__n_n_Co74__weak__mp17(rate_eval, tf)
    n_Cr47__Cr48(rate_eval, tf)
    He4_V48__Mn52(rate_eval, tf)
    He4_Ca61__Ti65(rate_eval, tf)
    He4_Fe62__Ni66(rate_eval, tf)
    He4_Ca55__Ti59(rate_eval, tf)
    n_S28__p_P28(rate_eval, tf)
    He4_P46__Cl50(rate_eval, tf)
    Ti56__V56__weak__wc12(rate_eval, tf)
    K55__n_Ca54__weak__mp17(rate_eval, tf)
    n_Mg20__He4_Ne17(rate_eval, tf)
    F22__Ne22__weak__wc17(rate_eval, tf)
    Sc39__Ca39__weak__mo97(rate_eval, tf)
    Fe75__Co75__weak__mo03(rate_eval, tf)
    He4_Al24__P28(rate_eval, tf)
    p_Si40__He4_Al37(rate_eval, tf)
    p_Mg41__n_Al41(rate_eval, tf)
    Mg39__Al39__weak__mo03(rate_eval, tf)
    p_Cl42__Ar43(rate_eval, tf)
    He4_Ti50__Cr54(rate_eval, tf)
    n_Sc52__Sc53(rate_eval, tf)
    p_Sc51__Ti52(rate_eval, tf)
    n_Ti40__p_Sc40(rate_eval, tf)
    He4_Al43__n_P46(rate_eval, tf)
    n_P30__p_Si30(rate_eval, tf)
    n_P46__P47(rate_eval, tf)
    O28__n_n_F26__weak__mp17(rate_eval, tf)
    He4_Fe51__p_Co54(rate_eval, tf)
    Cl31__p_P30__weak__wc12(rate_eval, tf)
    Mg40__n_n_Al38__weak__mp17(rate_eval, tf)
    p_F19__Ne20(rate_eval, tf)
    He4_Ne25__n_Mg28(rate_eval, tf)
    Cr70__n_n_Mn68__weak__mp17(rate_eval, tf)
    p_K50__He4_Ar47(rate_eval, tf)
    Ti64__n_V63__weak__mp17(rate_eval, tf)
    He4_O27__n_Ne30(rate_eval, tf)
    n_Mn57__Mn58(rate_eval, tf)
    He4_Ca60__Ti64(rate_eval, tf)
    n_P25__He4_Al22(rate_eval, tf)
    Ti63__n_V62__weak__mp17(rate_eval, tf)
    n_F19__F20(rate_eval, tf)
    V52__Cr52__weak__wc12(rate_eval, tf)
    Ti61__n_V60__weak__mp17(rate_eval, tf)
    He4_P39__Cl43(rate_eval, tf)
    V65__n_n_Cr63__weak__mp17(rate_eval, tf)
    n_Na22__p_Ne22(rate_eval, tf)
    p_S45__n_Cl45(rate_eval, tf)
    n_Cr52__Cr53(rate_eval, tf)
    n_P30__P31(rate_eval, tf)
    Ca55__n_Sc54__weak__mp17(rate_eval, tf)
    Sc57__n_Ti56__weak__mp17(rate_eval, tf)
    He4_S38__Ar42(rate_eval, tf)
    He4_Ar30__p_K33(rate_eval, tf)
    Ti58__n_V57__weak__mp17(rate_eval, tf)
    p_Ar30__K31(rate_eval, tf)
    Al37__n_n_Si35__weak__mp17(rate_eval, tf)
    Cr69__n_n_Mn67__weak__mp17(rate_eval, tf)
    He4_P31__Cl35(rate_eval, tf)
    p_Mn58__n_Fe58(rate_eval, tf)
    p_Ca57__He4_K54(rate_eval, tf)
    p_Cr65__n_Mn65(rate_eval, tf)
    p_F29__n_Ne29(rate_eval, tf)
    He4_Mg32__Si36(rate_eval, tf)
    Na21__Ne21__weak__wc12(rate_eval, tf)
    He4_Cl41__K45(rate_eval, tf)
    n_Ca39__He4_Ar36(rate_eval, tf)
    O26__n_O25(rate_eval, tf)
    d_d__He4(rate_eval, tf)
    Al40__n_Si39__weak__mp17(rate_eval, tf)
    p_N13__O14(rate_eval, tf)
    n_C12__C13(rate_eval, tf)
    Ar31__p_S30__weak__wc17(rate_eval, tf)
    p_Mn63__n_Fe63(rate_eval, tf)
    n_Al27__Al28(rate_eval, tf)
    Mn49__Cr49__weak__wc12(rate_eval, tf)
    He4_Cl43__n_K46(rate_eval, tf)
    Al42__n_n_Si40__weak__mo03(rate_eval, tf)
    He4_Na33__n_Al36(rate_eval, tf)
    Cl32__He4_Si28__weak__wc12(rate_eval, tf)
    S28__P28__weak__wc12(rate_eval, tf)
    n_K48__K49(rate_eval, tf)
    He4_Ti55__Cr59(rate_eval, tf)
    He4_V45__p_Cr48(rate_eval, tf)
    He4_Al39__P43(rate_eval, tf)
    p_Ne30__n_Na30(rate_eval, tf)
    p_F30__n_Ne30(rate_eval, tf)
    p_Na27__He4_Ne24(rate_eval, tf)
    n_Ti50__Ti51(rate_eval, tf)
    He4_Na25__n_Al28(rate_eval, tf)
    n_S27__He4_Si24(rate_eval, tf)
    Mn66__n_Fe65__weak__mp17(rate_eval, tf)
    C22__n_N21__weak__wc17(rate_eval, tf)
    p_Si33__He4_Al30(rate_eval, tf)
    p_B11__C12(rate_eval, tf)
    Ti39__p_Ca38__weak__wc12(rate_eval, tf)
    Ti44__Sc44__weak__wc12(rate_eval, tf)
    n_V64__V65(rate_eval, tf)
    Mg23__Na23__weak__wc12(rate_eval, tf)
    Ar39__K39__weak__wc12(rate_eval, tf)
    n_Sc36__p_Ca36(rate_eval, tf)
    p_K46__He4_Ar43(rate_eval, tf)
    p_S41__n_Cl41(rate_eval, tf)
    Sc59__n_Ti58__weak__mp17(rate_eval, tf)
    He4_t__Li7(rate_eval, tf)
    p_Mg36__n_Al36(rate_eval, tf)
    Sc58__n_Ti57__weak__mp17(rate_eval, tf)
    n_He4_He4__Be9(rate_eval, tf)
    He4_P47__Cl51(rate_eval, tf)
    K54__n_n_Ca52__weak__mp17(rate_eval, tf)
    p_Cr69__n_Mn69(rate_eval, tf)
    Sc59__Ti59__weak__mo03(rate_eval, tf)
    He4_Cl48__K52(rate_eval, tf)
    He4_Ar47__n_Ca50(rate_eval, tf)
    n_Al32__Al33(rate_eval, tf)
    n_Cr65__Cr66(rate_eval, tf)
    p_V51__Cr52(rate_eval, tf)
    Ca49__Sc49__weak__wc12(rate_eval, tf)
    p_Al38__Si39(rate_eval, tf)
    He4_S40__n_Ar43(rate_eval, tf)
    V54__Cr54__weak__wc12(rate_eval, tf)
    Na31__n_n_n_Mg28__weak__wc12(rate_eval, tf)
    He4_Si35__S39(rate_eval, tf)
    He4_P43__Cl47(rate_eval, tf)
    Ne17__F17__weak__wc17(rate_eval, tf)
    He4_Na29__n_Al32(rate_eval, tf)
    n_Ne21__Ne22(rate_eval, tf)
    n_Ca41__He4_Ar38(rate_eval, tf)
    P24__Si24__weak__bqa_pos_(rate_eval, tf)
    O26__n_F25__weak__mp17(rate_eval, tf)
    Sc40__He4_Ar36__weak__wc12(rate_eval, tf)
    He4_Mg35__Si39(rate_eval, tf)
    Na22__Ne22__weak__wc12(rate_eval, tf)
    He4_F23__Na27(rate_eval, tf)
    p_K49__He4_Ar46(rate_eval, tf)
    p_P25__S26(rate_eval, tf)
    p_Na24__Mg25(rate_eval, tf)
    Al34__Si34__weak__wc12(rate_eval, tf)
    S46__Cl46__weak__wc17(rate_eval, tf)
    n_Mg38__Mg39(rate_eval, tf)
    N20__n_O19__weak__wc12(rate_eval, tf)
    Ca59__n_Sc58__weak__mp17(rate_eval, tf)
    Mn73__Fe73__weak__mo03(rate_eval, tf)
    Al24__He4_Ne20__weak__wc12(rate_eval, tf)
    He4_Na21__Al25(rate_eval, tf)
    Ca55__Sc55__weak__wc12(rate_eval, tf)
    Ca58__n_Sc57__weak__mp17(rate_eval, tf)
    He4_P45__n_Cl48(rate_eval, tf)
    n_Ne31__Ne32(rate_eval, tf)
    He4_Sc52__V56(rate_eval, tf)
    Ar32__p_S31__weak__wc12(rate_eval, tf)
    Ca57__n_Sc56__weak__mp17(rate_eval, tf)
    He4_Mg41__n_Si44(rate_eval, tf)
    n_Cl39__Cl40(rate_eval, tf)
    He4_C14__O18(rate_eval, tf)
    Ca52__n_Sc51__weak__wc12(rate_eval, tf)
    He4_O18__Ne22(rate_eval, tf)
    Si24__Al24__weak__wc12(rate_eval, tf)
    n_V54__V55(rate_eval, tf)
    p_S39__n_Cl39(rate_eval, tf)
    Cl34__S34__weak__wc12(rate_eval, tf)
    He4_Mn62__Co66(rate_eval, tf)
    Al42__n_Si41__weak__mp17(rate_eval, tf)
    Si42__n_P41__weak__mp17(rate_eval, tf)
    He4_K44__n_Sc47(rate_eval, tf)
    n_Na19__He4_F16(rate_eval, tf)
    V62__Cr62__weak__wc17(rate_eval, tf)
    Cl46__n_Ar45__weak__wc12(rate_eval, tf)
    He4_Al28__P32(rate_eval, tf)
    He4_Mn70__n_Co73(rate_eval, tf)
    Cl51__n_Ar50__weak__mp17(rate_eval, tf)
    p_Cl33__Ar34(rate_eval, tf)
    Ca37__p_Ar36__weak__wc12(rate_eval, tf)
    n_Mg30__Mg31(rate_eval, tf)
    p_Ca46__Sc47(rate_eval, tf)
    Ca36__p_Ar35__weak__wc12(rate_eval, tf)
    p_Fe68__n_Co68(rate_eval, tf)
    n_Ti42__Ti43(rate_eval, tf)
    Ca35__p_Ar34__weak__wc17(rate_eval, tf)
    C18__N18__weak__wc12(rate_eval, tf)
    Si26__Al26__weak__wc12(rate_eval, tf)
    O26__F26__weak__mo03(rate_eval, tf)
    Cr48__V48__weak__wc12(rate_eval, tf)
    p_Na29__n_Mg29(rate_eval, tf)
    B14__C14__weak__wc12(rate_eval, tf)
    n_p_He4__Li6(rate_eval, tf)
    K58__n_Ca57__weak__mp17(rate_eval, tf)
    He4_Na25__p_Mg28(rate_eval, tf)
    He4_Cl52__K56(rate_eval, tf)
    n_Ar33__Ar34(rate_eval, tf)
    n_Ca33__Ca34(rate_eval, tf)
    K57__n_Ca56__weak__mp17(rate_eval, tf)
    He4_Sc53__n_V56(rate_eval, tf)
    p_V55__He4_Ti52(rate_eval, tf)
    p_Ca60__He4_K57(rate_eval, tf)
    p_Mn58__He4_Cr55(rate_eval, tf)
    n_Si39__Si40(rate_eval, tf)
    n_Fe46__Fe47(rate_eval, tf)
    n_Cr64__Cr65(rate_eval, tf)
    He4_K31__Sc35(rate_eval, tf)
    V39__Ti39__weak__bqa_pos_(rate_eval, tf)
    K59__n_Ca58__weak__mp17(rate_eval, tf)
    He4_S31__Ar35(rate_eval, tf)
    p_Al37__n_Si37(rate_eval, tf)
    S35__Cl35__weak__wc12(rate_eval, tf)
    K52__n_Ca51__weak__wc12(rate_eval, tf)
    He4_F15__Na19(rate_eval, tf)
    N18__O18__weak__wc12(rate_eval, tf)
    p_Ti48__V49(rate_eval, tf)
    K51__n_Ca50__weak__wc12(rate_eval, tf)
    Sc35__Ca35__weak__bqa_pos_(rate_eval, tf)
    Mg32__Al32__weak__wc12(rate_eval, tf)
    F20__Ne20__weak__wc12(rate_eval, tf)
    p_Ar41__He4_Cl38(rate_eval, tf)
    He4_Mg21__p_Al24(rate_eval, tf)
    K50__n_Ca49__weak__wc12(rate_eval, tf)
    He4_Ca41__Ti45(rate_eval, tf)
    He4_Cl40__K44(rate_eval, tf)
    p_Cl49__He4_S46(rate_eval, tf)
    Sc56__Ti56__weak__wc17(rate_eval, tf)
    He4_Ar45__n_Ca48(rate_eval, tf)
    He4_P29__Cl33(rate_eval, tf)
    K37__Ar37__weak__wc12(rate_eval, tf)
    n_Ca34__Ca35(rate_eval, tf)
    n_Sc38__p_Ca38(rate_eval, tf)
    p_Ar39__K40(rate_eval, tf)
    n_Ti51__Ti52(rate_eval, tf)
    He4_F25__Na29(rate_eval, tf)
    p_K47__Ca48(rate_eval, tf)
    p_O23__n_F23(rate_eval, tf)
    He4_Mn63__n_Co66(rate_eval, tf)
    He4_C11__p_N14(rate_eval, tf)
    He4_Fe61__n_Ni64(rate_eval, tf)
    K36__p_Cl35__weak__wc12(rate_eval, tf)
    He4_Si37__S41(rate_eval, tf)
    K35__p_Cl34__weak__wc12(rate_eval, tf)
    Ca58__n_n_Sc56__weak__mp17(rate_eval, tf)
    p_Ne34__Na35(rate_eval, tf)
    p_Ti61__He4_Sc58(rate_eval, tf)
    n_Si31__Si32(rate_eval, tf)
    n_Cl36__He4_P33(rate_eval, tf)
    n_S37__S38(rate_eval, tf)
    He4_Sc51__V55(rate_eval, tf)
    p_Ti60__He4_Sc57(rate_eval, tf)
    He4_Ti41__p_V44(rate_eval, tf)
    p_B10__He4_Be7(rate_eval, tf)
    n_Ar50__Ar51(rate_eval, tf)
    Ar31__Cl31__weak__wc12(rate_eval, tf)
    Ca59__Sc59__weak__mo03(rate_eval, tf)
    C9__He4_Li5__weak__wc12(rate_eval, tf)
    Mn67__n_Fe66__weak__mp17(rate_eval, tf)
    V66__Cr66__weak__mo03(rate_eval, tf)
    p_Cr42__Mn43(rate_eval, tf)
    n_Ca58__Ca59(rate_eval, tf)
    p_S40__He4_P37(rate_eval, tf)
    n_Ar41__Ar42(rate_eval, tf)
    He4_S35__Ar39(rate_eval, tf)
    p_K54__Ca55(rate_eval, tf)
    n_K42__He4_Cl39(rate_eval, tf)
    He4_S45__Ar49(rate_eval, tf)
    p_V61__Cr62(rate_eval, tf)
    p_Mg27__n_Al27(rate_eval, tf)
    P26__Si26__weak__wc12(rate_eval, tf)
    p_Mn70__He4_Cr67(rate_eval, tf)
    P38__S38__weak__wc12(rate_eval, tf)
    Ca41__K41__weak__wc12(rate_eval, tf)
    He4_K45__n_Sc48(rate_eval, tf)
    n_Ne29__Ne30(rate_eval, tf)
    Si22__p_Mg21__weak__wc12(rate_eval, tf)
    He4_P38__n_Cl41(rate_eval, tf)
    C18__n_N17__weak__wc12(rate_eval, tf)
    He4_Cl48__n_K51(rate_eval, tf)
    Sc63__n_n_Ti61__weak__mp17(rate_eval, tf)
    He4_Ne23__Mg27(rate_eval, tf)
    Si41__P41__weak__wc17(rate_eval, tf)
    n_F27__F28(rate_eval, tf)
    n_Cr51__p_V51(rate_eval, tf)
    n_V65__V66(rate_eval, tf)
    p_K46__n_Ca46(rate_eval, tf)
    V66__n_Cr65__weak__mp17(rate_eval, tf)
    Si38__P38__weak__mo03(rate_eval, tf)
    P47__n_S46__weak__mp17(rate_eval, tf)
    p_Sc59__Ti60(rate_eval, tf)
    p_Be9__B10(rate_eval, tf)
    He4_Ar50__n_Ca53(rate_eval, tf)
    Ne27__Na27__weak__wc12(rate_eval, tf)
    Si44__n_n_n_P41__weak__mo03(rate_eval, tf)
    p_P39__He4_Si36(rate_eval, tf)
    He4_Ti49__Cr53(rate_eval, tf)
    He4_K33__p_Ca36(rate_eval, tf)
    n_K31__He4_Cl28(rate_eval, tf)
    Ar50__n_K49__weak__wc12(rate_eval, tf)
    S39__Cl39__weak__wc12(rate_eval, tf)
    p_F26__Ne27(rate_eval, tf)
    Ar33__p_S32__weak__wc12(rate_eval, tf)
    Ca47__Sc47__weak__wc12(rate_eval, tf)
    He4_Li6__B10(rate_eval, tf)
    He4_S33__Ar37(rate_eval, tf)
    Mg34__n_Al33__weak__mp17(rate_eval, tf)
    S29__p_Si28__weak__wc12(rate_eval, tf)
    O28__n_F27__weak__mp17(rate_eval, tf)
    He4_Cr69__Fe73(rate_eval, tf)
    p_Li7__He4_He4(rate_eval, tf)
    Cl51__n_n_Ar49__weak__mp17(rate_eval, tf)
    n_O12__He4_C9(rate_eval, tf)
    He4_Ca56__Ti60(rate_eval, tf)
    p_Fe65__n_Co65(rate_eval, tf)
    p_Fe76__n_Co76(rate_eval, tf)
    n_O19__O20(rate_eval, tf)
    Ar47__K47__weak__wc12(rate_eval, tf)
    p_Na33__Mg34(rate_eval, tf)
    Cl52__n_Ar51__weak__mp17(rate_eval, tf)
    n_Cr45__p_V45(rate_eval, tf)
    Cl50__n_Ar49__weak__mp17(rate_eval, tf)
    S45__Cl45__weak__wc12(rate_eval, tf)
    n_Sc41__p_Ca41(rate_eval, tf)
    p_Mn67__n_Fe67(rate_eval, tf)
    n_Fe52__p_Mn52(rate_eval, tf)
    Ne34__n_n_Na32__weak__mp17(rate_eval, tf)
    Al33__Si33__weak__wc12(rate_eval, tf)
    n_S36__S37(rate_eval, tf)
    Cl47__n_Ar46__weak__wc12(rate_eval, tf)
    P46__n_S45__weak__mp17(rate_eval, tf)
    p_Ca57__n_Sc57(rate_eval, tf)
    Cl45__n_Ar44__weak__wc12(rate_eval, tf)
    Be11__He4_Li7__weak__wc12(rate_eval, tf)
    n_Ne27__Ne28(rate_eval, tf)
    He4_B10__n_N13(rate_eval, tf)
    p_Ca59__He4_K56(rate_eval, tf)
    n_Mn64__Mn65(rate_eval, tf)
    Sc48__Ti48__weak__wc12(rate_eval, tf)
    Cl44__n_Ar43__weak__mp17(rate_eval, tf)
    n_V44__V45(rate_eval, tf)
    Sc60__n_Ti59__weak__mp17(rate_eval, tf)
    Ti63__V63__weak__mo03(rate_eval, tf)
    He4_O15__Ne19(rate_eval, tf)
    d_d__n_He3(rate_eval, tf)
    Na32__Mg32__weak__wc12(rate_eval, tf)
    Si43__n_P42__weak__mp17(rate_eval, tf)
    Sc58__n_n_Ti56__weak__mp17(rate_eval, tf)
    Fe70__Co70__weak__wc17(rate_eval, tf)
    p_Ne31__n_Na31(rate_eval, tf)
    p_F21__He4_O18(rate_eval, tf)
    Mn64__Fe64__weak__wc12(rate_eval, tf)
    Ar48__K48__weak__wc17(rate_eval, tf)
    He4_Ne28__Mg32(rate_eval, tf)
    p_Sc61__He4_Ca58(rate_eval, tf)
    S48__n_n_Cl46__weak__mp17(rate_eval, tf)
    He4_Na35__Al39(rate_eval, tf)
    Al29__Si29__weak__wc12(rate_eval, tf)
    p_V65__n_Cr65(rate_eval, tf)
    p_Be9__He4_Li6(rate_eval, tf)
    He4_Cr61__Fe65(rate_eval, tf)
    Cl32__p_P31__weak__wc12(rate_eval, tf)
    p_Na26__n_Mg26(rate_eval, tf)
    He4_Ne32__Mg36(rate_eval, tf)
    p_Si27__P28(rate_eval, tf)
    Si36__P36__weak__wc12(rate_eval, tf)
    n_Si27__p_Al27(rate_eval, tf)
    n_Cl47__Cl48(rate_eval, tf)
    p_Ca54__He4_K51(rate_eval, tf)
    Sc40__p_K39__weak__wc12(rate_eval, tf)
    He4_Ne22__Mg26(rate_eval, tf)
    p_Fe74__Co75(rate_eval, tf)
    He4_Mn58__n_Co61(rate_eval, tf)
    S46__n_Cl45__weak__mp17(rate_eval, tf)
    Ti41__Sc41__weak__wc17(rate_eval, tf)
    p_O21__F22(rate_eval, tf)
    He4_Ti62__Cr66(rate_eval, tf)
    He4_Li9__n_B12(rate_eval, tf)
    Mg35__n_n_Al33__weak__mp17(rate_eval, tf)
    p_P42__S43(rate_eval, tf)
    p_Cr66__n_Mn66(rate_eval, tf)
    O13__N13__weak__wc17(rate_eval, tf)
    He4_Al23__p_Si26(rate_eval, tf)
    p_O27__n_F27(rate_eval, tf)
    n_Ti61__Ti62(rate_eval, tf)
    n_Mn46__Mn47(rate_eval, tf)
    p_Al31__n_Si31(rate_eval, tf)
    Cl48__n_n_Ar46__weak__mp17(rate_eval, tf)
    Na19__Ne19__weak__bqa_pos_(rate_eval, tf)
    F28__n_n_Ne26__weak__mp17(rate_eval, tf)
    n_Li6__Li7(rate_eval, tf)
    p_Ca53__He4_K50(rate_eval, tf)
    p_Ar45__K46(rate_eval, tf)
    Al23__p_Na22__weak__wc12(rate_eval, tf)
    O25__F25__weak__mo03(rate_eval, tf)
    p_Cr64__He4_V61(rate_eval, tf)
    He4_N16__n_F19(rate_eval, tf)
    Mg41__Al41__weak__mo03(rate_eval, tf)
    Mn48__Cr48__weak__wc12(rate_eval, tf)
    He4_Cl41__p_Ar44(rate_eval, tf)
    p_Si41__P42(rate_eval, tf)
    n_Mn48__p_Cr48(rate_eval, tf)
    He4_Si36__S40(rate_eval, tf)
    n_Cr49__He4_Ti46(rate_eval, tf)
    He4_Sc46__n_V49(rate_eval, tf)
    n_K38__He4_Cl35(rate_eval, tf)
    p_Mg30__He4_Na27(rate_eval, tf)
    N24__n_N23(rate_eval, tf)
    He4_Fe65__n_Ni68(rate_eval, tf)
    n_K34__He4_Cl31(rate_eval, tf)
    n_Ne17__p_F17(rate_eval, tf)
    p_Al35__Si36(rate_eval, tf)
    n_Ti43__p_Sc43(rate_eval, tf)
    Mg29__Al29__weak__wc12(rate_eval, tf)
    p_F17__Ne18(rate_eval, tf)
    p_Sc53__He4_Ca50(rate_eval, tf)
    P39__n_S38__weak__wc12(rate_eval, tf)
    P44__n_S43__weak__mp17(rate_eval, tf)
    Ca56__n_Sc55__weak__mp17(rate_eval, tf)
    K46__Ca46__weak__wc12(rate_eval, tf)
    P42__n_S41__weak__wc12(rate_eval, tf)
    Na35__n_Mg34__weak__mp17(rate_eval, tf)
    Na33__n_Mg32__weak__wc17(rate_eval, tf)
    Fe76__n_Co75__weak__mp17(rate_eval, tf)
    Mg38__n_n_n_Al35__weak__mo03(rate_eval, tf)
    Ar31__p_p_P29__weak__wc12(rate_eval, tf)
    He4_B13__N17(rate_eval, tf)
    p_Na25__n_Mg25(rate_eval, tf)
    n_Sc57__Sc58(rate_eval, tf)
    He4_P42__Cl46(rate_eval, tf)
    n_Na23__Na24(rate_eval, tf)
    p_N16__n_O16(rate_eval, tf)
    n_Cr44__p_V44(rate_eval, tf)
    p_Mn70__n_Fe70(rate_eval, tf)
    S44__Cl44__weak__wc12(rate_eval, tf)
    He4_Cl45__K49(rate_eval, tf)
    p_Mg41__He4_Na38(rate_eval, tf)
    Fe71__n_Co70__weak__mp17(rate_eval, tf)
    n_O17__He4_C14(rate_eval, tf)
    He4_F21__Na25(rate_eval, tf)
    P28__He4_Mg24__weak__wc12(rate_eval, tf)
    P43__S43__weak__wc17(rate_eval, tf)
    P28__p_Al27__weak__wc12(rate_eval, tf)
    Al31__Si31__weak__wc12(rate_eval, tf)
    p_P37__S38(rate_eval, tf)
    He4_Al39__n_P42(rate_eval, tf)
    He4_Ca49__Ti53(rate_eval, tf)
    Cr42__V42__weak__wc12(rate_eval, tf)
    t_Li7__n_n_He4_He4(rate_eval, tf)
    n_V66__V67(rate_eval, tf)
    He4_K48__Sc52(rate_eval, tf)
    Cl49__Ar49__weak__mo03(rate_eval, tf)
    n_Ar33__He4_S30(rate_eval, tf)
    p_Mn59__Fe60(rate_eval, tf)
    K54__n_Ca53__weak__mp17(rate_eval, tf)
    p_P44__n_S44(rate_eval, tf)
    p_Cl28__Ar29(rate_eval, tf)
    p_S27__Cl28(rate_eval, tf)
    He4_P45__Cl49(rate_eval, tf)
    p_B8__C9(rate_eval, tf)
    n_Sc61__Sc62(rate_eval, tf)
    p_K55__He4_Ar52(rate_eval, tf)
    Si41__n_P40__weak__mp17(rate_eval, tf)
    Mn57__Fe57__weak__wc12(rate_eval, tf)
    Si40__n_P39__weak__mp17(rate_eval, tf)
    Si38__n_P37__weak__mp17(rate_eval, tf)
    p_Mg29__Al30(rate_eval, tf)
    He4_Mn64__n_Co67(rate_eval, tf)
    He4_Cl31__p_Ar34(rate_eval, tf)
    He4_Na22__Al26(rate_eval, tf)
    Fe52__Mn52__weak__wc12(rate_eval, tf)
    K43__Ca43__weak__wc12(rate_eval, tf)
    Mg33__Al33__weak__wc12(rate_eval, tf)
    n_Sc36__He4_K33(rate_eval, tf)
    N11__C11__weak__btyk(rate_eval, tf)
    Ca60__n_Sc59__weak__mp17(rate_eval, tf)
    Al21__Mg21__weak__bqa_pos_(rate_eval, tf)
    O15__N15__weak__wc12(rate_eval, tf)
    V67__Cr67__weak__mo03(rate_eval, tf)
    n_K38__K39(rate_eval, tf)
    He4_Ti37__Cr41(rate_eval, tf)
    p_Si31__n_P31(rate_eval, tf)
    Ne33__n_n_n_Na30__weak__mo03(rate_eval, tf)
    He4_Na26__Al30(rate_eval, tf)
    He4_F22__Na26(rate_eval, tf)
    He4_Sc63__V67(rate_eval, tf)
    Cl46__Ar46__weak__wc12(rate_eval, tf)
    He4_Ti57__Cr61(rate_eval, tf)
    Ti62__n_V61__weak__mp17(rate_eval, tf)
    p_Mn68__He4_Cr65(rate_eval, tf)
    Cr64__n_Mn63__weak__mp17(rate_eval, tf)
    Mn60__Fe60__weak__wc12(rate_eval, tf)
    Si25__p_Mg24__weak__wc12(rate_eval, tf)
    n_Mg21__Mg22(rate_eval, tf)
    n_Fe61__Fe62(rate_eval, tf)
    P42__S42__weak__wc17(rate_eval, tf)
    He4_Fe67__n_Ni70(rate_eval, tf)
    O22__F22__weak__wc17(rate_eval, tf)
    He4_K40__Sc44(rate_eval, tf)
    K31__Ar31__weak__bqa_pos_(rate_eval, tf)
    He4_Ne34__n_Mg37(rate_eval, tf)
    n_V63__V64(rate_eval, tf)
    Na39__n_n_Mg37__weak__mp17(rate_eval, tf)
    Si23__p_Mg22__weak__wc17(rate_eval, tf)
    He4_Fe48__Ni52(rate_eval, tf)
    n_N14__N15(rate_eval, tf)
    n_F17__p_O17(rate_eval, tf)
    n_Fe45__p_Mn45(rate_eval, tf)
    He4_Na30__n_Al33(rate_eval, tf)
    p_Mg38__He4_Na35(rate_eval, tf)
    Fe47__p_Cr46__weak__wc12(rate_eval, tf)
    Al38__n_Si37__weak__mp17(rate_eval, tf)
    He4_Ar49__n_Ca52(rate_eval, tf)
    p_O24__F25(rate_eval, tf)
    p_Mg21__Al22(rate_eval, tf)
    n_Si30__Si31(rate_eval, tf)
    He4_Mn55__Co59(rate_eval, tf)
    Cr60__Mn60__weak__wc12(rate_eval, tf)
    p_Cr48__Mn49(rate_eval, tf)
    p_K52__n_Ca52(rate_eval, tf)
    He4_Si30__S34(rate_eval, tf)
    n_P31__P32(rate_eval, tf)
    He4_Si43__S47(rate_eval, tf)
    Al35__n_Si34__weak__wc12(rate_eval, tf)
    Cl52__Ar52__weak__mo03(rate_eval, tf)
    Mn69__Fe69__weak__wc17(rate_eval, tf)
    p_Mg35__He4_Na32(rate_eval, tf)
    Si39__n_P38__weak__mp17(rate_eval, tf)
    He4_Mn56__Co60(rate_eval, tf)
    Ne29__Na29__weak__wc12(rate_eval, tf)
    He4_P44__Cl48(rate_eval, tf)
    n_Fe45__Fe46(rate_eval, tf)
    He4_Sc37__V41(rate_eval, tf)
    N16__He4_C12__weak__wc12(rate_eval, tf)
    p_Cl37__Ar38(rate_eval, tf)
    P40__n_S39__weak__wc12(rate_eval, tf)
    Al32__n_Si31__weak__wc12(rate_eval, tf)
    p_K32__Ca33(rate_eval, tf)
    C10__B10__weak__wc12(rate_eval, tf)
    Cr57__Mn57__weak__wc12(rate_eval, tf)
    Cl36__Ar36__weak__wc12(rate_eval, tf)
    n_Fe59__Fe60(rate_eval, tf)
    He4_Na24__n_Al27(rate_eval, tf)
    B13__C13__weak__wc12(rate_eval, tf)
    p_Ar54__K55(rate_eval, tf)
    He4_O25__Ne29(rate_eval, tf)
    p_Sc50__He4_Ca47(rate_eval, tf)
    Fe61__Co61__weak__wc12(rate_eval, tf)
    p_P45__He4_Si42(rate_eval, tf)
    p_K43__He4_Ar40(rate_eval, tf)
    n_P37__P38(rate_eval, tf)
    He4_Si44__S48(rate_eval, tf)
    Na20__He4_O16__weak__wc12(rate_eval, tf)
    Si43__n_n_n_P40__weak__mo03(rate_eval, tf)
    P47__S47__weak__mo03(rate_eval, tf)
    Ti54__V54__weak__wc12(rate_eval, tf)
    K51__Ca51__weak__wc12(rate_eval, tf)
    Ti39__Sc39__weak__wc17(rate_eval, tf)
    Mg40__n_Al39__weak__mp17(rate_eval, tf)
    He4_K38__Sc42(rate_eval, tf)
    Mn72__n_n_n_Fe69__weak__mo03(rate_eval, tf)
    Mg38__n_Al37__weak__mp17(rate_eval, tf)
    p_S43__n_Cl43(rate_eval, tf)
    He4_Ti59__Cr63(rate_eval, tf)
    n_Ti62__Ti63(rate_eval, tf)
    Cr44__p_Ti43__weak__wc12(rate_eval, tf)
    O27__n_O26(rate_eval, tf)
    p_Mn54__Fe55(rate_eval, tf)
    Ca60__Sc60__weak__mo03(rate_eval, tf)
    p_P40__He4_Si37(rate_eval, tf)
    n_Mg33__Mg34(rate_eval, tf)
    p_P44__S45(rate_eval, tf)
    Ca58__Sc58__weak__mo03(rate_eval, tf)
    He4_V52__n_Mn55(rate_eval, tf)
    V61__Cr61__weak__wc12(rate_eval, tf)
    O21__F21__weak__wc12(rate_eval, tf)
    O13__p_C12__weak__wc12(rate_eval, tf)
    P45__S45__weak__mo03(rate_eval, tf)
    K56__n_Ca55__weak__mp17(rate_eval, tf)
    C20__N20__weak__wc12(rate_eval, tf)
    p_d__He3(rate_eval, tf)
    n_C15__C16(rate_eval, tf)
    Si25__Al25__weak__wc12(rate_eval, tf)
    K57__Ca57__weak__mo03(rate_eval, tf)
    S42__Cl42__weak__wc12(rate_eval, tf)
    p_V47__Cr48(rate_eval, tf)
    Mg21__p_Ne20__weak__wc12(rate_eval, tf)
    S31__P31__weak__wc12(rate_eval, tf)
    He4_Mn71__n_Co74(rate_eval, tf)
    K45__Ca45__weak__wc12(rate_eval, tf)
    Cr55__Mn55__weak__wc12(rate_eval, tf)
    n_Ca42__Ca43(rate_eval, tf)
    He4_Ar34__Ca38(rate_eval, tf)
    p_Na38__n_Mg38(rate_eval, tf)
    p_V54__He4_Ti51(rate_eval, tf)
    p_Ca53__Sc54(rate_eval, tf)
    n_Mn53__Mn54(rate_eval, tf)
    S43__Cl43__weak__wc12(rate_eval, tf)
    p_Na37__n_Mg37(rate_eval, tf)
    Ti62__V62__weak__mo03(rate_eval, tf)
    p_Mn62__n_Fe62(rate_eval, tf)
    n_Mn48__Mn49(rate_eval, tf)
    P27__Si27__weak__wc12(rate_eval, tf)
    n_Ti56__Ti57(rate_eval, tf)
    Mg28__Al28__weak__wc12(rate_eval, tf)
    Na38__n_Mg37__weak__mp17(rate_eval, tf)
    He4_Si22__S26(rate_eval, tf)
    Ar53__n_K52__weak__mp17(rate_eval, tf)
    n_S43__S44(rate_eval, tf)
    V67__n_Cr66__weak__mp17(rate_eval, tf)
    p_F23__n_Ne23(rate_eval, tf)
    Ti64__V64__weak__mo03(rate_eval, tf)
    S41__Cl41__weak__wc12(rate_eval, tf)
    Na34__n_Mg33__weak__wc12(rate_eval, tf)
    p_Ca38__Sc39(rate_eval, tf)
    n_Ti39__Ti40(rate_eval, tf)
    n_Ca39__p_K39(rate_eval, tf)
    He4_Ar51__Ca55(rate_eval, tf)
    n_Ti44__He4_Ca41(rate_eval, tf)
    Si37__n_P36__weak__wc12(rate_eval, tf)
    Mn64__n_Fe63__weak__wc12(rate_eval, tf)
    Ne33__n_Na32__weak__mp17(rate_eval, tf)
    He4_Mn66__n_Co69(rate_eval, tf)
    Na30__He4_Ne26__weak__wc12(rate_eval, tf)
    He4_Ca52__n_Ti55(rate_eval, tf)
    p_Cr43__Mn44(rate_eval, tf)
    He4_Ne19__Mg23(rate_eval, tf)
    Na29__n_Mg28__weak__wc12(rate_eval, tf)
    p_Sc56__n_Ti56(rate_eval, tf)
    n_Mg39__Mg40(rate_eval, tf)
    p_Si36__P37(rate_eval, tf)
    He4_Fe60__Ni64(rate_eval, tf)
    He4_Ar48__Ca52(rate_eval, tf)
    p_S43__Cl44(rate_eval, tf)
    Mg34__Al34__weak__wc17(rate_eval, tf)
    Ca48__Sc48__weak__mo03(rate_eval, tf)
    p_V62__He4_Ti59(rate_eval, tf)
    p_P47__He4_Si44(rate_eval, tf)
    He4_Ca54__n_Ti57(rate_eval, tf)
    n_S48__S49(rate_eval, tf)
    n_P43__P44(rate_eval, tf)
    n_P25__p_Si25(rate_eval, tf)
    Ar33__Cl33__weak__wc12(rate_eval, tf)
    p_Ar49__n_K49(rate_eval, tf)
    p_Cr44__Mn45(rate_eval, tf)
    V50__Ti50__weak__mo03(rate_eval, tf)
    p_Ti62__He4_Sc59(rate_eval, tf)
    Ca37__K37__weak__wc12(rate_eval, tf)
    O23__F23__weak__wc12(rate_eval, tf)
    He4_V42__Mn46(rate_eval, tf)
    p_Al22__Si23(rate_eval, tf)
    n_B10__He4_Li7(rate_eval, tf)
    Al26__Mg26__weak__wc12(rate_eval, tf)
    p_Ca55__Sc56(rate_eval, tf)
    n_Si27__C12_O16(rate_eval, tf)
    n_Si28__Si29(rate_eval, tf)
    He4_Fe55__Ni59(rate_eval, tf)
    Mn71__n_Fe70__weak__mp17(rate_eval, tf)
    Cl45__Ar45__weak__wc12(rate_eval, tf)
    Al24__Mg24__weak__wc12(rate_eval, tf)
    p_Na30__Mg31(rate_eval, tf)
    N18__n_O17__weak__wc12(rate_eval, tf)
    t_t__n_n_He4(rate_eval, tf)
    V67__n_n_Cr65__weak__mp17(rate_eval, tf)
    p_Cr59__He4_V56(rate_eval, tf)
    p_P35__He4_Si32(rate_eval, tf)
    p_Ar48__K49(rate_eval, tf)
    He6__Li6__weak__wc12(rate_eval, tf)
    p_Ne29__Na30(rate_eval, tf)
    p_Ar53__K54(rate_eval, tf)
    p_P34__He4_Si31(rate_eval, tf)
    n_Si41__Si42(rate_eval, tf)
    Ca61__Sc61__weak__mo03(rate_eval, tf)
    p_K39__He4_Ar36(rate_eval, tf)
    V40__Ti40__weak__bqa_pos_(rate_eval, tf)
    Cl43__Ar43__weak__wc12(rate_eval, tf)
    Fe71__Co71__weak__wc17(rate_eval, tf)
    He3_Li7__n_p_He4_He4(rate_eval, tf)
    P35__S35__weak__wc12(rate_eval, tf)
    n_K35__K36(rate_eval, tf)
    Fe45__p_p_V43__weak__wc12(rate_eval, tf)
    P46__S46__weak__mo03(rate_eval, tf)
    F18__O18__weak__wc12(rate_eval, tf)
    n_K39__K40(rate_eval, tf)
    Sc49__Ti49__weak__wc12(rate_eval, tf)
    He4_P29__p_S32(rate_eval, tf)
    p_Mn55__Fe56(rate_eval, tf)
    n_Al33__Al34(rate_eval, tf)
    p_Ar49__K50(rate_eval, tf)
    p_Mn65__n_Fe65(rate_eval, tf)
    d_C14__n_N15(rate_eval, tf)
    He4_Ti58__Cr62(rate_eval, tf)
    n_P29__p_Si29(rate_eval, tf)
    p_N16__He4_C13(rate_eval, tf)
    n_Na26__Na27(rate_eval, tf)
    n_K54__K55(rate_eval, tf)
    n_Ti63__Ti64(rate_eval, tf)
    Be12__n_B11__weak__wc12(rate_eval, tf)
    p_Ca39__Sc40(rate_eval, tf)
    p_Na32__He4_Ne29(rate_eval, tf)
    n_Cl50__Cl51(rate_eval, tf)
    Ti42__Sc42__weak__wc12(rate_eval, tf)
    p_Ti64__V65(rate_eval, tf)
    F31__n_Ne30__weak__mp17(rate_eval, tf)
    F26__n_Ne25__weak__wc12(rate_eval, tf)
    Ne29__n_Na28__weak__wc17(rate_eval, tf)
    He4_Cr52__Fe56(rate_eval, tf)
    K48__Ca48__weak__wc12(rate_eval, tf)
    V63__Cr63__weak__wc12(rate_eval, tf)
    n_V52__V53(rate_eval, tf)
    He4_Al21__P25(rate_eval, tf)
    n_Be10__Be11(rate_eval, tf)
    n_Al29__Al30(rate_eval, tf)
    Be7__Li7__weak__electron_capture(rate_eval, tf)
    Al38__Si38__weak__wc17(rate_eval, tf)
    n_Ar36__p_Cl36(rate_eval, tf)
    n_Ar53__Ar54(rate_eval, tf)
    Mg31__Al31__weak__wc12(rate_eval, tf)
    Ca60__n_n_Sc58__weak__mp17(rate_eval, tf)
    Ti40__p_Ca39__weak__wc12(rate_eval, tf)
    He4_Mg23__p_Al26(rate_eval, tf)
    He4_Ca34__p_Sc37(rate_eval, tf)
    n_Ne22__Ne23(rate_eval, tf)
    He4_Sc61__V65(rate_eval, tf)
    V48__Ti48__weak__wc12(rate_eval, tf)
    P34__S34__weak__wc12(rate_eval, tf)
    S29__P29__weak__wc12(rate_eval, tf)
    Ar43__K43__weak__wc12(rate_eval, tf)
    p_Cl49__n_Ar49(rate_eval, tf)
    p_Cl52__Ar53(rate_eval, tf)
    n_Sc36__Sc37(rate_eval, tf)
    P46__n_n_S44__weak__mp17(rate_eval, tf)
    n_Ca35__Ca36(rate_eval, tf)
    p_O25__F26(rate_eval, tf)
    V41__Ti41__weak__bqa_pos_(rate_eval, tf)
    He4_V44__Mn48(rate_eval, tf)
    O23__n_F22__weak__wc12(rate_eval, tf)
    V64__n_Cr63__weak__mp17(rate_eval, tf)
    Ti53__V53__weak__wc12(rate_eval, tf)
    p_K54__He4_Ar51(rate_eval, tf)
    He4_Fe53__Ni57(rate_eval, tf)
    p_Sc59__n_Ti59(rate_eval, tf)
    p_Ca37__Sc38(rate_eval, tf)
    Cr56__Mn56__weak__wc12(rate_eval, tf)
    p_P37__n_S37(rate_eval, tf)
    Fe72__Co72__weak__mo03(rate_eval, tf)
    He4_Al41__n_P44(rate_eval, tf)
    p_Mn61__He4_Cr58(rate_eval, tf)
    He4_F19__Na23(rate_eval, tf)
    He4_Si41__n_S44(rate_eval, tf)
    p_P43__S44(rate_eval, tf)
    p_Ti45__V46(rate_eval, tf)
    Fe47__Mn47__weak__wc12(rate_eval, tf)
    P28__Si28__weak__wc12(rate_eval, tf)
    Cr51__V51__weak__wc12(rate_eval, tf)
    Fe55__Mn55__weak__wc12(rate_eval, tf)
    p_Cl47__He4_S44(rate_eval, tf)
    n_Cl36__Cl37(rate_eval, tf)
    C19__n_N18__weak__wc12(rate_eval, tf)
    He4_Ti65__Cr69(rate_eval, tf)
    Ca52__Sc52__weak__wc12(rate_eval, tf)
    p_Al27__Si28(rate_eval, tf)
    He4_V62__Mn66(rate_eval, tf)
    Si43__P43__weak__mo03(rate_eval, tf)
    n_Na22__He4_F19(rate_eval, tf)
    Ne34__n_Na33__weak__mp17(rate_eval, tf)
    Sc52__Ti52__weak__wc12(rate_eval, tf)
    P45__n_S44__weak__mp17(rate_eval, tf)
    He4_V40__Mn44(rate_eval, tf)
    Ar51__K51__weak__mo03(rate_eval, tf)
    B19__n_C18__weak__wc17(rate_eval, tf)
    p_Ti56__n_V56(rate_eval, tf)
    B15__n_C14__weak__wc12(rate_eval, tf)
    He4_Ar51__n_Ca54(rate_eval, tf)
    n_S39__S40(rate_eval, tf)
    K40__Ar40__weak__wc12(rate_eval, tf)
    He4_K54__Sc58(rate_eval, tf)
    He4_Sc53__V57(rate_eval, tf)
    He4_Si27__S31(rate_eval, tf)
    F30__Ne30__weak__mo03(rate_eval, tf)
    p_Na29__Mg30(rate_eval, tf)
    Be15__n_Be14(rate_eval, tf)
    Ne30__Na30__weak__wc17(rate_eval, tf)
    Be14__n_B13__weak__wc17(rate_eval, tf)
    n_Mn56__He4_V53(rate_eval, tf)
    Li11__n_Be10__weak__wc17(rate_eval, tf)
    Al22__He4_Ne18__weak__wc12(rate_eval, tf)
    Ti37__Sc37__weak__bqa_pos_(rate_eval, tf)
    K33__Ar33__weak__bqa_pos_(rate_eval, tf)
    Cr64__Mn64__weak__wc12(rate_eval, tf)
    p_Ti59__He4_Sc56(rate_eval, tf)
    n_Ar37__Ar38(rate_eval, tf)
    He4_F29__Na33(rate_eval, tf)
    N17__O17__weak__wc12(rate_eval, tf)
    Fe63__Co63__weak__wc12(rate_eval, tf)
    Si27__Al27__weak__wc12(rate_eval, tf)
    B8__He4_He4__weak__wc12(rate_eval, tf)
    He4_Cr50__Fe54(rate_eval, tf)
    Fe68__Co68__weak__wc12(rate_eval, tf)
    n_Al22__Al23(rate_eval, tf)
    n_V57__V58(rate_eval, tf)
    He4_Ar38__Ca42(rate_eval, tf)
    Fe64__Co64__weak__wc12(rate_eval, tf)
    He4_Al23__P27(rate_eval, tf)
    He4_F22__n_Na25(rate_eval, tf)
    Cr62__Mn62__weak__wc12(rate_eval, tf)
    n_Al21__p_Mg21(rate_eval, tf)
    p_K50__Ca51(rate_eval, tf)
    Sc58__Ti58__weak__wc17(rate_eval, tf)
    O26__n_n_n_F23__weak__mo03(rate_eval, tf)
    Si36__n_P35__weak__wc12(rate_eval, tf)
    He4_Mg24__Si28(rate_eval, tf)
    He4_Si34__n_S37(rate_eval, tf)
    Ti59__V59__weak__wc12(rate_eval, tf)
    C11__B11__weak__wc12(rate_eval, tf)
    p_Si34__n_P34(rate_eval, tf)
    He4_Ne33__Mg37(rate_eval, tf)
    Fe46__Mn46__weak__wc12(rate_eval, tf)
    n_Na29__Na30(rate_eval, tf)
    Cr65__n_Mn64__weak__mp17(rate_eval, tf)
    p_O19__n_F19(rate_eval, tf)
    F21__Ne21__weak__wc12(rate_eval, tf)
    Mn65__Fe65__weak__wc17(rate_eval, tf)
    Mn63__Fe63__weak__wc12(rate_eval, tf)
    Mn59__Fe59__weak__wc12(rate_eval, tf)
    He4_Ca57__Ti61(rate_eval, tf)
    Mn56__Fe56__weak__wc12(rate_eval, tf)
    p_Mg25__Al26(rate_eval, tf)
    B17__n_C16__weak__wc17(rate_eval, tf)
    Mn50__Cr50__weak__wc12(rate_eval, tf)
    n_Cr67__Cr68(rate_eval, tf)
    Cr66__Mn66__weak__wc17(rate_eval, tf)
    P41__S41__weak__wc12(rate_eval, tf)
    Mn47__Cr47__weak__wc17(rate_eval, tf)
    Mn46__Cr46__weak__wc12(rate_eval, tf)
    Ar42__K42__weak__wc12(rate_eval, tf)
    He4_Ar48__n_Ca51(rate_eval, tf)
    Na30__Mg30__weak__wc12(rate_eval, tf)
    n_F14__p_O14(rate_eval, tf)
    n_Cr49__Cr50(rate_eval, tf)
    n_P25__P26(rate_eval, tf)
    Cr63__Mn63__weak__wc17(rate_eval, tf)
    Fe62__Co62__weak__wc12(rate_eval, tf)
    n_Al30__Al31(rate_eval, tf)
    Al36__n_n_Si34__weak__mp17(rate_eval, tf)
    C16__N16__weak__wc12(rate_eval, tf)
    Ar34__Cl34__weak__wc12(rate_eval, tf)
    Sc46__Ti46__weak__wc12(rate_eval, tf)
    p_Sc63__n_Ti63(rate_eval, tf)
    P38__n_S37__weak__wc12(rate_eval, tf)
    Cr59__Mn59__weak__wc12(rate_eval, tf)
    n_Ti48__Ti49(rate_eval, tf)
    n_Mn47__Mn48(rate_eval, tf)
    Cr49__V49__weak__wc12(rate_eval, tf)
    p_Al42__n_Si42(rate_eval, tf)
    Ca61__n_n_Sc59__weak__mp17(rate_eval, tf)
    n_Fe55__Fe56(rate_eval, tf)
    Mn48__p_V47__weak__wc12(rate_eval, tf)
    n_Cr68__Cr69(rate_eval, tf)
    He4_K32__p_Ca35(rate_eval, tf)
    Cr43__V43__weak__wc12(rate_eval, tf)
    He4_Mn57__Co61(rate_eval, tf)
    p_S45__Cl46(rate_eval, tf)
    n_Ne25__Ne26(rate_eval, tf)
    n_S31__S32(rate_eval, tf)
    He4_Cr58__n_Fe61(rate_eval, tf)
    He4_Si26__p_P29(rate_eval, tf)
    Mn71__Fe71__weak__mo03(rate_eval, tf)
    Mg36__n_Al35__weak__mp17(rate_eval, tf)
    Ne30__n_Na29__weak__wc12(rate_eval, tf)
    Be14__B14__weak__wc12(rate_eval, tf)
    Cr41__V41__weak__bqa_pos_(rate_eval, tf)
    Fe65__Co65__weak__wc12(rate_eval, tf)
    V58__Cr58__weak__wc17(rate_eval, tf)
    Cl51__n_n_n_Ar48__weak__mo03(rate_eval, tf)
    He4_Cr67__n_Fe70(rate_eval, tf)
    He4_Sc46__V50(rate_eval, tf)
    He4_Ca59__n_Ti62(rate_eval, tf)
    He4_S34__n_Ar37(rate_eval, tf)
    p_Ti58__He4_Sc55(rate_eval, tf)
    K44__Ca44__weak__wc12(rate_eval, tf)
    V43__Ti43__weak__wc12(rate_eval, tf)
    Sc50__Ti50__weak__wc12(rate_eval, tf)
    K53__Ca53__weak__wc17(rate_eval, tf)
    S47__n_Cl46__weak__mp17(rate_eval, tf)
    p_F31__Ne32(rate_eval, tf)
    p_Sc43__He4_Ca40(rate_eval, tf)
    S48__Cl48__weak__mo03(rate_eval, tf)
    n_K42__p_Ar42(rate_eval, tf)
    He4_V41__p_Cr44(rate_eval, tf)
    n_Fe45__He4_Cr42(rate_eval, tf)
    He4_Ti39__Cr43(rate_eval, tf)
    V66__n_n_Cr64__weak__mp17(rate_eval, tf)
    K54__Ca54__weak__wc17(rate_eval, tf)
    Cl48__Ar48__weak__mo03(rate_eval, tf)
    p_Sc62__He4_Ca59(rate_eval, tf)
    Ar46__K46__weak__wc12(rate_eval, tf)
    Li9__Be9__weak__wc12(rate_eval, tf)
    Ca50__Sc50__weak__wc12(rate_eval, tf)
    He4_Sc50__V54(rate_eval, tf)
    n_Fe52__Fe53(rate_eval, tf)
    n_Fe64__Fe65(rate_eval, tf)
    Al22__p_Na21__weak__wc17(rate_eval, tf)
    V64__Cr64__weak__wc17(rate_eval, tf)
    Cl40__Ar40__weak__wc12(rate_eval, tf)
    Na34__n_n_Mg32__weak__wc12(rate_eval, tf)
    Na34__Mg34__weak__wc12(rate_eval, tf)
    Ar53__K53__weak__mo03(rate_eval, tf)
    He4_F23__n_Na26(rate_eval, tf)
    Al28__Si28__weak__wc12(rate_eval, tf)
    K35__Ar35__weak__wc12(rate_eval, tf)
    Sc61__Ti61__weak__mo03(rate_eval, tf)
    Li8__He4_He4__weak__wc12(rate_eval, tf)
    K58__Ca58__weak__mo03(rate_eval, tf)
    Ti64__n_n_n_V61__weak__mo03(rate_eval, tf)
    n_Sc51__Sc52(rate_eval, tf)
    F29__n_Ne28__weak__wc12(rate_eval, tf)
    n_Fe59__He4_Cr56(rate_eval, tf)
    He4_S37__Ar41(rate_eval, tf)
    p_P47__S48(rate_eval, tf)
    Sc51__Ti51__weak__wc12(rate_eval, tf)
    K55__Ca55__weak__mo03(rate_eval, tf)
    Ti65__V65__weak__mo03(rate_eval, tf)
    d_Li6__p_Li7(rate_eval, tf)
    n_Si29__Si30(rate_eval, tf)
    N22__n_n_O20__weak__wc12(rate_eval, tf)
    n_Cl35__Cl36(rate_eval, tf)
    F25__n_Ne24__weak__wc12(rate_eval, tf)
    p_Mg28__Al29(rate_eval, tf)
    n_F15__p_O15(rate_eval, tf)
    Sc43__Ca43__weak__wc12(rate_eval, tf)
    n_Na20__p_Ne20(rate_eval, tf)
    n_Na38__Na39(rate_eval, tf)
    n_V52__He4_Sc49(rate_eval, tf)
    He4_Fe49__Ni53(rate_eval, tf)
    n_Cr50__Cr51(rate_eval, tf)
    N12__C12__weak__wc12(rate_eval, tf)
    Ne31__n_n_Na29__weak__mp17(rate_eval, tf)
    Fe51__Mn51__weak__wc12(rate_eval, tf)
    n_P24__P25(rate_eval, tf)
    p_O19__F20(rate_eval, tf)
    Ne32__n_n_n_Na29__weak__mo03(rate_eval, tf)
    p_Cr58__He4_V55(rate_eval, tf)
    V42__Ti42__weak__mo97(rate_eval, tf)
    Cl36__S36__weak__wc12(rate_eval, tf)
    p_Si41__n_P41(rate_eval, tf)
    Mn51__Cr51__weak__wc12(rate_eval, tf)
    He4_Fe47__p_Co50(rate_eval, tf)
    Ca54__Sc54__weak__wc17(rate_eval, tf)
    n_Ca42__He4_Ar39(rate_eval, tf)
    Ca45__Sc45__weak__wc12(rate_eval, tf)
    p_Na24__n_Mg24(rate_eval, tf)
    n_Na25__Na26(rate_eval, tf)
    p_Cr63__He4_V60(rate_eval, tf)
    Ne33__n_n_Na31__weak__mp17(rate_eval, tf)
    p_Si35__n_P35(rate_eval, tf)
    S40__Cl40__weak__wc12(rate_eval, tf)
    Na32__n_Mg31__weak__wc17(rate_eval, tf)
    n_V58__V59(rate_eval, tf)
    p_Si43__P44(rate_eval, tf)
    K50__Ca50__weak__wc12(rate_eval, tf)
    n_Mn61__Mn62(rate_eval, tf)
    Mg21__Na21__weak__wc12(rate_eval, tf)
    V57__Cr57__weak__wc12(rate_eval, tf)
    He4_Fe72__n_Ni75(rate_eval, tf)
    K57__n_n_n_Ca54__weak__mo03(rate_eval, tf)
    He4_Al33__P37(rate_eval, tf)
    Cl33__S33__weak__wc12(rate_eval, tf)
    S48__n_Cl47__weak__mp17(rate_eval, tf)
    n_Mn43__Mn44(rate_eval, tf)
    He4_Al22__P26(rate_eval, tf)
    Si40__P40__weak__wc17(rate_eval, tf)
    p_K53__He4_Ar50(rate_eval, tf)
    K36__Ar36__weak__wc12(rate_eval, tf)
    S43__n_Cl42__weak__wc12(rate_eval, tf)
    Mn53__Cr53__weak__wc12(rate_eval, tf)
    F27__Ne27__weak__wc17(rate_eval, tf)
    Ti55__V55__weak__wc12(rate_eval, tf)
    He4_O26__Ne30(rate_eval, tf)
    n_Ti40__He4_Ca37(rate_eval, tf)
    V56__Cr56__weak__wc12(rate_eval, tf)
    Ar50__K50__weak__wc12(rate_eval, tf)
    p_Na25__He4_Ne22(rate_eval, tf)
    He4_S44__n_Ar47(rate_eval, tf)
    p_Mg28__n_Al28(rate_eval, tf)
    n_V45__p_Ti45(rate_eval, tf)
    p_O18__F19(rate_eval, tf)
    p_P36__S37(rate_eval, tf)
    Na35__Mg35__weak__wc17(rate_eval, tf)
    He4_Fe72__Ni76(rate_eval, tf)
    Na24__Mg24__weak__wc12(rate_eval, tf)
    V59__Cr59__weak__wc12(rate_eval, tf)
    Ar41__K41__weak__wc12(rate_eval, tf)
    Cr65__Mn65__weak__wc17(rate_eval, tf)
    Cr46__V46__weak__wc12(rate_eval, tf)
    n_F24__F25(rate_eval, tf)
    Ar37__Cl37__weak__wc12(rate_eval, tf)
    Be10__B10__weak__wc12(rate_eval, tf)
    Ar32__Cl32__weak__wc12(rate_eval, tf)
    p_Mg39__He4_Na36(rate_eval, tf)
    n_S27__p_P27(rate_eval, tf)
    Ti63__n_n_V61__weak__mp17(rate_eval, tf)
    He4_Al30__n_P33(rate_eval, tf)
    Ar29__Cl29__weak__bqa_pos_(rate_eval, tf)
    Na31__Mg31__weak__wc12(rate_eval, tf)
    n_V60__V61(rate_eval, tf)
    p_Sc44__Ti45(rate_eval, tf)
    n_V40__V41(rate_eval, tf)
    B15__C15__weak__wc12(rate_eval, tf)
    Cl44__Ar44__weak__wc17(rate_eval, tf)
    He4_Ca33__p_Sc36(rate_eval, tf)
    Na33__Mg33__weak__wc12(rate_eval, tf)
    Ar44__K44__weak__wc12(rate_eval, tf)
    p_V66__He4_Ti63(rate_eval, tf)
    Sc60__n_n_n_Ti57__weak__mo03(rate_eval, tf)
    Cl31__S31__weak__wc12(rate_eval, tf)
    V53__Cr53__weak__wc12(rate_eval, tf)
    n_V39__He4_Sc36(rate_eval, tf)
    V44__Ti44__weak__wc12(rate_eval, tf)
    Fe49__p_Cr48__weak__wc12(rate_eval, tf)
    n_Sc60__Sc61(rate_eval, tf)
    Mn63__n_Fe62__weak__mp17(rate_eval, tf)
    Si37__P37__weak__wc12(rate_eval, tf)
    Al39__Si39__weak__wc17(rate_eval, tf)
    Fe76__Co76__weak__mo03(rate_eval, tf)
    He4_Na38__Al42(rate_eval, tf)
    Mg30__Al30__weak__wc12(rate_eval, tf)
    He4_Ar49__Ca53(rate_eval, tf)
    Al33__n_Si32__weak__wc12(rate_eval, tf)
    N19__O19__weak__wc12(rate_eval, tf)
    S38__Cl38__weak__wc12(rate_eval, tf)
    He4_K46__Sc50(rate_eval, tf)
    He4_Sc50__n_V53(rate_eval, tf)
    n_Sc39__p_Ca39(rate_eval, tf)
    Mg31__n_Al30__weak__wc12(rate_eval, tf)
    P39__S39__weak__wc12(rate_eval, tf)
    n_Sc40__He4_K37(rate_eval, tf)
    n_Ca39__Ca40(rate_eval, tf)
    n_Ne33__Ne34(rate_eval, tf)
    He4_O16__Ne20(rate_eval, tf)
    p_Ar51__n_K51(rate_eval, tf)
    p_Cr67__Mn68(rate_eval, tf)
    F30__n_n_n_Ne27__weak__mo03(rate_eval, tf)
    p_P41__He4_Si38(rate_eval, tf)
    p_Mg34__n_Al34(rate_eval, tf)
    p_Na39__Mg40(rate_eval, tf)
    Si22__Al22__weak__wc12(rate_eval, tf)
    Si39__P39__weak__wc17(rate_eval, tf)
    Al40__n_n_Si38__weak__mp17(rate_eval, tf)
    He4_Ca56__n_Ti59(rate_eval, tf)
    p_Be10__He4_Li7(rate_eval, tf)
    p_Mg35__Al36(rate_eval, tf)
    Cr45__V45__weak__wc12(rate_eval, tf)
    p_Ar50__K51(rate_eval, tf)
    K50__n_n_Ca48__weak__mp17(rate_eval, tf)
    Sc60__Ti60__weak__mo03(rate_eval, tf)
    p_Ca47__Sc48(rate_eval, tf)
    N18__He4_C14__weak__wc12(rate_eval, tf)
    He4_Cr68__Fe72(rate_eval, tf)
    N20__O20__weak__wc12(rate_eval, tf)
    p_Cl44__He4_S41(rate_eval, tf)
    Ar54__K54__weak__mo03(rate_eval, tf)
    n_Ca38__He4_Ar35(rate_eval, tf)
    p_Sc54__He4_Ca51(rate_eval, tf)
    n_Be9__Be10(rate_eval, tf)
    He4_Ne21__Mg25(rate_eval, tf)
    p_Cr70__He4_V67(rate_eval, tf)
    p_Mg40__Al41(rate_eval, tf)
    p_Ti55__He4_Sc52(rate_eval, tf)
    Ar51__n_n_K49__weak__mp17(rate_eval, tf)
    p_Mg33__Al34(rate_eval, tf)
    p_Al29__Si30(rate_eval, tf)
    p_Mn56__n_Fe56(rate_eval, tf)
    n_Sc47__Sc48(rate_eval, tf)
    p_V59__He4_Ti56(rate_eval, tf)
    Na37__n_n_Mg35__weak__mp17(rate_eval, tf)
    p_Ar49__He4_Cl46(rate_eval, tf)
    F28__Ne28__weak__mo03(rate_eval, tf)
    Mg35__Al35__weak__wc17(rate_eval, tf)
    He4_K52__Sc56(rate_eval, tf)
    p_Al32__Si33(rate_eval, tf)
    Ne23__Na23__weak__wc12(rate_eval, tf)
    Mn45__Cr45__weak__bqa_pos_(rate_eval, tf)
    Na33__n_n_Mg31__weak__wc12(rate_eval, tf)
    p_Na19__Mg20(rate_eval, tf)
    Mg20__Na20__weak__wc12(rate_eval, tf)
    Ne26__Na26__weak__wc12(rate_eval, tf)
    Ti60__V60__weak__wc17(rate_eval, tf)
    p_Fe62__Co63(rate_eval, tf)
    p_P39__S40(rate_eval, tf)
    K56__n_n_Ca54__weak__mp17(rate_eval, tf)
    Cl38__Ar38__weak__wc12(rate_eval, tf)
    He4_Na32__Al36(rate_eval, tf)
    Sc55__Ti55__weak__wc12(rate_eval, tf)
    He4_P30__Cl34(rate_eval, tf)
    p_F26__He4_O23(rate_eval, tf)
    F28__n_Ne27__weak__mp17(rate_eval, tf)
    n_S32__He4_Si29(rate_eval, tf)
    n_Si37__Si38(rate_eval, tf)
    Ca56__Sc56__weak__wc17(rate_eval, tf)
    p_S48__Cl49(rate_eval, tf)
    Cl42__Ar42__weak__wc12(rate_eval, tf)
    p_Sc42__He4_Ca39(rate_eval, tf)
    n_Sc38__He4_K35(rate_eval, tf)
    n_Al42__Al43(rate_eval, tf)
    O19__F19__weak__wc12(rate_eval, tf)
    n_Na28__Na29(rate_eval, tf)
    p_Si38__He4_Al35(rate_eval, tf)
    n_Al25__He4_Na22(rate_eval, tf)
    p_F30__Ne31(rate_eval, tf)
    N22__n_O21__weak__wc17(rate_eval, tf)
    Na29__Mg29__weak__wc12(rate_eval, tf)
    He4_K37__Sc41(rate_eval, tf)
    n_K34__p_Ar34(rate_eval, tf)
    He4_Si45__n_S48(rate_eval, tf)
    He4_Fe69__n_Ni72(rate_eval, tf)
    Mn72__Fe72__weak__mo03(rate_eval, tf)
    He4_S40__Ar44(rate_eval, tf)
    n_P28__He4_Al25(rate_eval, tf)
    p_O23__F24(rate_eval, tf)
    K49__n_Ca48__weak__wc12(rate_eval, tf)
    p_Fe75__Co76(rate_eval, tf)
    O27__n_F26__weak__mp17(rate_eval, tf)
    Ne33__Na33__weak__mo03(rate_eval, tf)
    p_Mn65__Fe66(rate_eval, tf)
    Na28__n_Mg27__weak__wc12(rate_eval, tf)
    Ti52__V52__weak__wc12(rate_eval, tf)
    He4_Mn50__p_Fe53(rate_eval, tf)
    Fe45__Mn45__weak__wc17(rate_eval, tf)
    Al35__Si35__weak__wc12(rate_eval, tf)
    F17__O17__weak__wc12(rate_eval, tf)
    n_Mn66__Mn67(rate_eval, tf)
    Al40__Si40__weak__mo03(rate_eval, tf)
    F26__Ne26__weak__wc12(rate_eval, tf)
    n_Ar49__Ar50(rate_eval, tf)
    Cl47__Ar47__weak__wc17(rate_eval, tf)
    p_Cr61__n_Mn61(rate_eval, tf)
    p_Na35__Mg36(rate_eval, tf)
    n_O20__O21(rate_eval, tf)
    He4_Ar32__p_K35(rate_eval, tf)
    Sc36__Ca36__weak__bqa_pos_(rate_eval, tf)
    n_Mg37__Mg38(rate_eval, tf)
    Al36__n_Si35__weak__mp17(rate_eval, tf)
    He4_K56__Sc60(rate_eval, tf)
    p_Na30__n_Mg30(rate_eval, tf)
    K34__Ar34__weak__bqa_pos_(rate_eval, tf)
    K42__Ca42__weak__wc12(rate_eval, tf)
    Na37__n_Mg36__weak__mp17(rate_eval, tf)
    n_S29__S30(rate_eval, tf)
    n_Cr48__He4_Ti45(rate_eval, tf)
    Cl30__S30__weak__bqa_pos_(rate_eval, tf)
    n_C16__C17(rate_eval, tf)
    K40__Ca40__weak__wc12(rate_eval, tf)
    P30__Si30__weak__wc12(rate_eval, tf)
    p_V62__Cr63(rate_eval, tf)
    p_Ar46__n_K46(rate_eval, tf)
    He4_K46__n_Sc49(rate_eval, tf)
    B19__n_n_C17__weak__wc12(rate_eval, tf)
    V49__Ti49__weak__wc12(rate_eval, tf)
    Ar30__Cl30__weak__bqa_pos_(rate_eval, tf)
    P29__Si29__weak__wc12(rate_eval, tf)
    He4_K34__Sc38(rate_eval, tf)

    if screen_func is not None:
        plasma_state = PlasmaState(T, rho, Y, Z)

        scn_fac = ScreenFactors(1, 1, 1, 1)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.n_p_p__p_d *= scor
        rate_eval.p_p__d__weak__bet_pos_ *= scor
        rate_eval.p_p__d__weak__electron_capture *= scor

        scn_fac = ScreenFactors(1, 1, 4, 9)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Be9__n_p_He4_He4 *= scor
        rate_eval.p_Be9__d_He4_He4 *= scor
        rate_eval.p_Be9__B10 *= scor
        rate_eval.p_Be9__He4_Li6 *= scor

        scn_fac = ScreenFactors(2, 3, 4, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He3_Be7__p_p_He4_He4 *= scor

        scn_fac = ScreenFactors(1, 3, 4, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.t_Be7__n_p_He4_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca36__p_p_Ca38 *= scor
        rate_eval.He4_Ca36__p_Sc39 *= scor
        rate_eval.He4_Ca36__Ti40 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O13__p_p_O15 *= scor
        rate_eval.He4_O13__p_F16 *= scor

        scn_fac = ScreenFactors(1, 1, 5, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_B11__He4_He4_He4 *= scor
        rate_eval.p_B11__C12 *= scor

        scn_fac = ScreenFactors(1, 2, 3, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_Li7__n_He4_He4 *= scor
        rate_eval.d_Li7__p_Li8 *= scor

        scn_fac = ScreenFactors(2, 3, 2, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He3_He3__p_p_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 76)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe76__n_Ni79 *= scor
        rate_eval.He4_Fe76__Ni80 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 76)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe76__He4_Mn73 *= scor
        rate_eval.p_Fe76__Co77 *= scor
        rate_eval.p_Fe76__n_Co76 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 75)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe75__n_Ni78 *= scor
        rate_eval.He4_Fe75__Ni79 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 75)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe75__He4_Mn72 *= scor
        rate_eval.p_Fe75__n_Co75 *= scor
        rate_eval.p_Fe75__Co76 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 74)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe74__n_Ni77 *= scor
        rate_eval.He4_Fe74__Ni78 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 74)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe74__He4_Mn71 *= scor
        rate_eval.p_Fe74__n_Co74 *= scor
        rate_eval.p_Fe74__Co75 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 73)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe73__He4_Mn70 *= scor
        rate_eval.p_Fe73__n_Co73 *= scor
        rate_eval.p_Fe73__Co74 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 72)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe72__He4_Mn69 *= scor
        rate_eval.p_Fe72__n_Co72 *= scor
        rate_eval.p_Fe72__Co73 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 71)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe71__n_Ni74 *= scor
        rate_eval.He4_Fe71__Ni75 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 71)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe71__He4_Mn68 *= scor
        rate_eval.p_Fe71__n_Co71 *= scor
        rate_eval.p_Fe71__Co72 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe70__n_Ni73 *= scor
        rate_eval.He4_Fe70__Ni74 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe70__He4_Mn67 *= scor
        rate_eval.p_Fe70__n_Co70 *= scor
        rate_eval.p_Fe70__Co71 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe69__He4_Mn66 *= scor
        rate_eval.p_Fe69__n_Co69 *= scor
        rate_eval.p_Fe69__Co70 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe68__n_Ni71 *= scor
        rate_eval.He4_Fe68__Ni72 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe68__He4_Mn65 *= scor
        rate_eval.p_Fe68__Co69 *= scor
        rate_eval.p_Fe68__n_Co68 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe67__He4_Mn64 *= scor
        rate_eval.p_Fe67__n_Co67 *= scor
        rate_eval.p_Fe67__Co68 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe65__He4_Mn62 *= scor
        rate_eval.p_Fe65__Co66 *= scor
        rate_eval.p_Fe65__n_Co65 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe64__n_Ni67 *= scor
        rate_eval.He4_Fe64__Ni68 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe63__n_Ni66 *= scor
        rate_eval.He4_Fe63__Ni67 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe63__He4_Mn60 *= scor
        rate_eval.p_Fe63__Co64 *= scor
        rate_eval.p_Fe63__n_Co63 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe62__He4_Mn59 *= scor
        rate_eval.p_Fe62__n_Co62 *= scor
        rate_eval.p_Fe62__Co63 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe61__He4_Mn58 *= scor
        rate_eval.p_Fe61__n_Co61 *= scor
        rate_eval.p_Fe61__Co62 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe60__He4_Mn57 *= scor
        rate_eval.p_Fe60__Co61 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe59__n_Ni62 *= scor
        rate_eval.He4_Fe59__Ni63 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe59__He4_Mn56 *= scor
        rate_eval.p_Fe59__n_Co59 *= scor
        rate_eval.p_Fe59__Co60 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe57__He4_Mn54 *= scor
        rate_eval.p_Fe57__Co58 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar34__K35 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc59__V63 *= scor
        rate_eval.He4_Sc59__n_V62 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S30__Ar34 *= scor
        rate_eval.He4_S30__p_Cl33 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe52__p_Co55 *= scor
        rate_eval.He4_Fe52__Ni56 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca61__Sc62 *= scor
        rate_eval.p_Ca61__He4_K58 *= scor
        rate_eval.p_Ca61__n_Sc61 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr66__Fe70 *= scor
        rate_eval.He4_Cr66__n_Fe69 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe49__p_Co52 *= scor
        rate_eval.He4_Fe49__Ni53 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe48__p_Co51 *= scor
        rate_eval.He4_Fe48__Ni52 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc50__Ti51 *= scor
        rate_eval.p_Sc50__n_Ti50 *= scor
        rate_eval.p_Sc50__He4_Ca47 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 73)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn73__n_Co76 *= scor
        rate_eval.He4_Mn73__Co77 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 73)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn73__He4_Cr70 *= scor
        rate_eval.p_Mn73__Fe74 *= scor
        rate_eval.p_Mn73__n_Fe73 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg34__Al35 *= scor
        rate_eval.p_Mg34__He4_Na31 *= scor
        rate_eval.p_Mg34__n_Al34 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 72)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn72__n_Co75 *= scor
        rate_eval.He4_Mn72__Co76 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 72)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn72__He4_Cr69 *= scor
        rate_eval.p_Mn72__n_Fe72 *= scor
        rate_eval.p_Mn72__Fe73 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 71)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn71__He4_Cr68 *= scor
        rate_eval.p_Mn71__Fe72 *= scor
        rate_eval.p_Mn71__n_Fe71 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn69__n_Co72 *= scor
        rate_eval.He4_Mn69__Co73 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn69__He4_Cr66 *= scor
        rate_eval.p_Mn69__n_Fe69 *= scor
        rate_eval.p_Mn69__Fe70 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn68__n_Co71 *= scor
        rate_eval.He4_Mn68__Co72 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn68__n_Fe68 *= scor
        rate_eval.p_Mn68__Fe69 *= scor
        rate_eval.p_Mn68__He4_Cr65 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si33__n_S36 *= scor
        rate_eval.He4_Si33__S37 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn67__He4_Cr64 *= scor
        rate_eval.p_Mn67__Fe68 *= scor
        rate_eval.p_Mn67__n_Fe67 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn66__He4_Cr63 *= scor
        rate_eval.p_Mn66__n_Fe66 *= scor
        rate_eval.p_Mn66__Fe67 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K48__Ca49 *= scor
        rate_eval.p_K48__He4_Ar45 *= scor
        rate_eval.p_K48__n_Ca48 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P46__S47 *= scor
        rate_eval.p_P46__He4_Si43 *= scor
        rate_eval.p_P46__n_S46 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca52__Ti56 *= scor
        rate_eval.He4_Ca52__n_Ti55 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn65__n_Co68 *= scor
        rate_eval.He4_Mn65__Co69 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn65__He4_Cr62 *= scor
        rate_eval.p_Mn65__n_Fe65 *= scor
        rate_eval.p_Mn65__Fe66 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si44__n_P44 *= scor
        rate_eval.p_Si44__He4_Al41 *= scor
        rate_eval.p_Si44__P45 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn64__He4_Cr61 *= scor
        rate_eval.p_Mn64__n_Fe64 *= scor
        rate_eval.p_Mn64__Fe65 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn62__He4_Cr59 *= scor
        rate_eval.p_Mn62__Fe63 *= scor
        rate_eval.p_Mn62__n_Fe62 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn60__n_Co63 *= scor
        rate_eval.He4_Mn60__Co64 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn60__He4_Cr57 *= scor
        rate_eval.p_Mn60__n_Fe60 *= scor
        rate_eval.p_Mn60__Fe61 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe65__Ni69 *= scor
        rate_eval.He4_Fe65__n_Ni68 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn59__He4_Cr56 *= scor
        rate_eval.p_Mn59__n_Fe59 *= scor
        rate_eval.p_Mn59__Fe60 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn57__n_Fe57 *= scor
        rate_eval.p_Mn57__He4_Cr54 *= scor
        rate_eval.p_Mn57__Fe58 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe64__He4_Mn61 *= scor
        rate_eval.p_Fe64__n_Co64 *= scor
        rate_eval.p_Fe64__Co65 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn56__He4_Cr53 *= scor
        rate_eval.p_Mn56__Fe57 *= scor
        rate_eval.p_Mn56__n_Fe56 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn54__He4_Cr51 *= scor
        rate_eval.p_Mn54__Fe55 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn53__p_Fe56 *= scor
        rate_eval.He4_Mn53__Co57 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn53__He4_Cr50 *= scor
        rate_eval.p_Mn53__Fe54 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn51__p_Fe54 *= scor
        rate_eval.He4_Mn51__Co55 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca53__n_Sc53 *= scor
        rate_eval.p_Ca53__He4_K50 *= scor
        rate_eval.p_Ca53__Sc54 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O22__n_F22 *= scor
        rate_eval.p_O22__F23 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn49__p_Fe52 *= scor
        rate_eval.He4_Mn49__Co53 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn47__p_Fe50 *= scor
        rate_eval.He4_Mn47__Co51 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn46__p_Fe49 *= scor
        rate_eval.He4_Mn46__Co50 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca44__Sc45 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn44__p_Fe47 *= scor
        rate_eval.He4_Mn44__Co48 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr70__n_Fe73 *= scor
        rate_eval.He4_Cr70__Fe74 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr69__n_Fe72 *= scor
        rate_eval.He4_Cr69__Fe73 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr68__He4_V65 *= scor
        rate_eval.p_Cr68__n_Mn68 *= scor
        rate_eval.p_Cr68__Mn69 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr67__n_Mn67 *= scor
        rate_eval.p_Cr67__He4_V64 *= scor
        rate_eval.p_Cr67__Mn68 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr66__He4_V63 *= scor
        rate_eval.p_Cr66__Mn67 *= scor
        rate_eval.p_Cr66__n_Mn66 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr65__n_Fe68 *= scor
        rate_eval.He4_Cr65__Fe69 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr65__He4_V62 *= scor
        rate_eval.p_Cr65__Mn66 *= scor
        rate_eval.p_Cr65__n_Mn65 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr64__n_Fe67 *= scor
        rate_eval.He4_Cr64__Fe68 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O25__n_F25 *= scor
        rate_eval.p_O25__F26 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr63__n_Fe66 *= scor
        rate_eval.He4_Cr63__Fe67 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr63__n_Mn63 *= scor
        rate_eval.p_Cr63__Mn64 *= scor
        rate_eval.p_Cr63__He4_V60 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr62__n_Fe65 *= scor
        rate_eval.He4_Cr62__Fe66 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr62__He4_V59 *= scor
        rate_eval.p_Cr62__Mn63 *= scor
        rate_eval.p_Cr62__n_Mn62 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn48__Co52 *= scor
        rate_eval.He4_Mn48__p_Fe51 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr61__n_Fe64 *= scor
        rate_eval.He4_Cr61__Fe65 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr60__He4_V57 *= scor
        rate_eval.p_Cr60__Mn61 *= scor
        rate_eval.p_Cr60__n_Mn60 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr59__n_Fe62 *= scor
        rate_eval.He4_Cr59__Fe63 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr59__n_Mn59 *= scor
        rate_eval.p_Cr59__Mn60 *= scor
        rate_eval.p_Cr59__He4_V56 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr57__n_Mn57 *= scor
        rate_eval.p_Cr57__He4_V54 *= scor
        rate_eval.p_Cr57__Mn58 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr55__n_Fe58 *= scor
        rate_eval.He4_Cr55__Fe59 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr54__He4_V51 *= scor
        rate_eval.p_Cr54__Mn55 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne32__Na33 *= scor
        rate_eval.p_Ne32__n_Na32 *= scor
        rate_eval.p_Ne32__He4_F29 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg24__He4_Na21 *= scor
        rate_eval.p_Mg24__Al25 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si38__n_P38 *= scor
        rate_eval.p_Si38__P39 *= scor
        rate_eval.p_Si38__He4_Al35 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn55__He4_Cr52 *= scor
        rate_eval.p_Mn55__Fe56 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr49__p_Mn52 *= scor
        rate_eval.He4_Cr49__Fe53 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr48__p_Mn51 *= scor
        rate_eval.He4_Cr48__Fe52 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti57__He4_Sc54 *= scor
        rate_eval.p_Ti57__n_V57 *= scor
        rate_eval.p_Ti57__V58 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr45__p_Mn48 *= scor
        rate_eval.He4_Cr45__Fe49 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne29__Mg33 *= scor
        rate_eval.He4_Ne29__n_Mg32 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti59__n_Cr62 *= scor
        rate_eval.He4_Ti59__Cr63 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P44__n_Cl47 *= scor
        rate_eval.He4_P44__Cl48 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr44__p_Mn47 *= scor
        rate_eval.He4_Cr44__Fe48 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr43__p_Mn46 *= scor
        rate_eval.He4_Cr43__Fe47 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr42__p_Mn45 *= scor
        rate_eval.He4_Cr42__Fe46 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V67__n_Mn70 *= scor
        rate_eval.He4_V67__Mn71 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc37__p_Ti40 *= scor
        rate_eval.He4_Sc37__V41 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V67__n_Cr67 *= scor
        rate_eval.p_V67__He4_Ti64 *= scor
        rate_eval.p_V67__Cr68 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V66__n_Mn69 *= scor
        rate_eval.He4_V66__Mn70 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V66__n_Cr66 *= scor
        rate_eval.p_V66__Cr67 *= scor
        rate_eval.p_V66__He4_Ti63 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V50__p_Cr53 *= scor
        rate_eval.He4_V50__Mn54 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K47__He4_Ar44 *= scor
        rate_eval.p_K47__n_Ca47 *= scor
        rate_eval.p_K47__Ca48 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V65__He4_Ti62 *= scor
        rate_eval.p_V65__Cr66 *= scor
        rate_eval.p_V65__n_Cr65 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V64__n_Mn67 *= scor
        rate_eval.He4_V64__Mn68 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V64__He4_Ti61 *= scor
        rate_eval.p_V64__n_Cr64 *= scor
        rate_eval.p_V64__Cr65 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V63__n_Cr63 *= scor
        rate_eval.p_V63__He4_Ti60 *= scor
        rate_eval.p_V63__Cr64 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V62__n_Mn65 *= scor
        rate_eval.He4_V62__Mn66 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V61__n_Mn64 *= scor
        rate_eval.He4_V61__Mn65 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V61__n_Cr61 *= scor
        rate_eval.p_V61__He4_Ti58 *= scor
        rate_eval.p_V61__Cr62 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P32__n_S32 *= scor
        rate_eval.p_P32__He4_Si29 *= scor
        rate_eval.p_P32__S33 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al32__n_P35 *= scor
        rate_eval.He4_Al32__P36 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V63__Mn67 *= scor
        rate_eval.He4_V63__n_Mn66 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V60__He4_Ti57 *= scor
        rate_eval.p_V60__n_Cr60 *= scor
        rate_eval.p_V60__Cr61 *= scor

        scn_fac = ScreenFactors(1, 3, 2, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.t_He3__n_p_He4 *= scor
        rate_eval.t_He3__d_He4 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O27__He4_N24 *= scor
        rate_eval.p_O27__F28 *= scor
        rate_eval.p_O27__n_F27 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si43__n_P43 *= scor
        rate_eval.p_Si43__P44 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V59__n_Mn62 *= scor
        rate_eval.He4_V59__Mn63 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V58__n_Mn61 *= scor
        rate_eval.He4_V58__Mn62 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V58__He4_Ti55 *= scor
        rate_eval.p_V58__n_Cr58 *= scor
        rate_eval.p_V58__Cr59 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V57__He4_Ti54 *= scor
        rate_eval.p_V57__n_Cr57 *= scor
        rate_eval.p_V57__Cr58 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V56__n_Mn59 *= scor
        rate_eval.He4_V56__Mn60 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al40__p_Si43 *= scor
        rate_eval.He4_Al40__n_P43 *= scor
        rate_eval.He4_Al40__P44 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V55__n_Mn58 *= scor
        rate_eval.He4_V55__Mn59 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr47__p_Mn50 *= scor
        rate_eval.He4_Cr47__Fe51 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V55__n_Cr55 *= scor
        rate_eval.p_V55__Cr56 *= scor
        rate_eval.p_V55__He4_Ti52 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V54__n_Mn57 *= scor
        rate_eval.He4_V54__Mn58 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar52__Ca56 *= scor
        rate_eval.He4_Ar52__n_Ca55 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V53__n_Cr53 *= scor
        rate_eval.p_V53__He4_Ti50 *= scor
        rate_eval.p_V53__Cr54 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V52__He4_Ti49 *= scor
        rate_eval.p_V52__n_Cr52 *= scor
        rate_eval.p_V52__Cr53 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S45__n_Ar48 *= scor
        rate_eval.He4_S45__Ar49 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca43__Ti47 *= scor
        rate_eval.He4_Ca43__n_Ti46 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V51__He4_Ti48 *= scor
        rate_eval.p_V51__Cr52 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F23__Ne24 *= scor
        rate_eval.p_F23__He4_O20 *= scor
        rate_eval.p_F23__n_Ne23 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V50__He4_Ti47 *= scor
        rate_eval.p_V50__n_Cr50 *= scor
        rate_eval.p_V50__Cr51 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F24__Ne25 *= scor
        rate_eval.p_F24__n_Ne24 *= scor
        rate_eval.p_F24__He4_O21 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V49__He4_Ti46 *= scor
        rate_eval.p_V49__Cr50 *= scor

        scn_fac = ScreenFactors(2, 4, 7, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_N15__F19 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V47__p_Cr50 *= scor
        rate_eval.He4_V47__Mn51 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V46__p_Cr49 *= scor
        rate_eval.He4_V46__Mn50 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc52__Ti53 *= scor
        rate_eval.p_Sc52__He4_Ca49 *= scor
        rate_eval.p_Sc52__n_Ti52 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V43__p_Cr46 *= scor
        rate_eval.He4_V43__Mn47 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V42__p_Cr45 *= scor
        rate_eval.He4_V42__Mn46 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si43__n_S46 *= scor
        rate_eval.He4_Si43__S47 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne33__n_Mg36 *= scor
        rate_eval.He4_Ne33__Mg37 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V39__p_Cr42 *= scor
        rate_eval.He4_V39__Mn43 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc53__n_Ti53 *= scor
        rate_eval.p_Sc53__Ti54 *= scor
        rate_eval.p_Sc53__He4_Ca50 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti65__n_Cr68 *= scor
        rate_eval.He4_Ti65__Cr69 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne27__He4_F24 *= scor
        rate_eval.p_Ne27__n_Na27 *= scor
        rate_eval.p_Ne27__Na28 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti64__n_Cr67 *= scor
        rate_eval.He4_Ti64__Cr68 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti64__He4_Sc61 *= scor
        rate_eval.p_Ti64__n_V64 *= scor
        rate_eval.p_Ti64__V65 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti63__n_Cr66 *= scor
        rate_eval.He4_Ti63__Cr67 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti63__He4_Sc60 *= scor
        rate_eval.p_Ti63__n_V63 *= scor
        rate_eval.p_Ti63__V64 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti61__n_V61 *= scor
        rate_eval.p_Ti61__V62 *= scor
        rate_eval.p_Ti61__He4_Sc58 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti60__n_Cr63 *= scor
        rate_eval.He4_Ti60__Cr64 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti60__n_V60 *= scor
        rate_eval.p_Ti60__V61 *= scor
        rate_eval.p_Ti60__He4_Sc57 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti59__n_V59 *= scor
        rate_eval.p_Ti59__V60 *= scor
        rate_eval.p_Ti59__He4_Sc56 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti58__n_Cr61 *= scor
        rate_eval.He4_Ti58__Cr62 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti58__n_V58 *= scor
        rate_eval.p_Ti58__V59 *= scor
        rate_eval.p_Ti58__He4_Sc55 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti55__n_Cr58 *= scor
        rate_eval.He4_Ti55__Cr59 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti55__n_V55 *= scor
        rate_eval.p_Ti55__V56 *= scor
        rate_eval.p_Ti55__He4_Sc52 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti54__n_Cr57 *= scor
        rate_eval.He4_Ti54__Cr58 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti54__He4_Sc51 *= scor
        rate_eval.p_Ti54__n_V54 *= scor
        rate_eval.p_Ti54__V55 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti53__n_Cr56 *= scor
        rate_eval.He4_Ti53__Cr57 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti53__He4_Sc50 *= scor
        rate_eval.p_Ti53__n_V53 *= scor
        rate_eval.p_Ti53__V54 *= scor

        scn_fac = ScreenFactors(2, 4, 4, 10)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Be10__C14 *= scor
        rate_eval.He4_Be10__n_C13 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti52__He4_Sc49 *= scor
        rate_eval.p_Ti52__n_V52 *= scor
        rate_eval.p_Ti52__V53 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti51__n_Cr54 *= scor
        rate_eval.He4_Ti51__Cr55 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti51__n_V51 *= scor
        rate_eval.p_Ti51__V52 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F26__Na30 *= scor
        rate_eval.He4_F26__n_Na29 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 73)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe73__n_Ni76 *= scor
        rate_eval.He4_Fe73__Ni77 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K36__p_Ca39 *= scor
        rate_eval.He4_K36__Sc40 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar35__Ca39 *= scor
        rate_eval.He4_Ar35__p_K38 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar51__He4_Cl48 *= scor
        rate_eval.p_Ar51__K52 *= scor
        rate_eval.p_Ar51__n_K51 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na19__Al23 *= scor
        rate_eval.He4_Na19__p_Mg22 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti43__p_V46 *= scor
        rate_eval.He4_Ti43__Cr47 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F28__n_Na31 *= scor
        rate_eval.He4_F28__Na32 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F31__n_Na34 *= scor
        rate_eval.He4_F31__Na35 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti40__p_V43 *= scor
        rate_eval.He4_Ti40__Cr44 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr55__n_Mn55 *= scor
        rate_eval.p_Cr55__He4_V52 *= scor
        rate_eval.p_Cr55__Mn56 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F31__He4_O28 *= scor
        rate_eval.p_F31__n_Ne31 *= scor
        rate_eval.p_F31__Ne32 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti39__p_V42 *= scor
        rate_eval.He4_Ti39__Cr43 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti38__p_V41 *= scor
        rate_eval.He4_Ti38__Cr42 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti37__p_V40 *= scor
        rate_eval.He4_Ti37__Cr41 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc62__n_V65 *= scor
        rate_eval.He4_Sc62__V66 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc61__n_V64 *= scor
        rate_eval.He4_Sc61__V65 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc61__n_Ti61 *= scor
        rate_eval.p_Sc61__Ti62 *= scor
        rate_eval.p_Sc61__He4_Ca58 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc40__p_Ti43 *= scor
        rate_eval.He4_Sc40__V44 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc60__n_V63 *= scor
        rate_eval.He4_Sc60__V64 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc60__He4_Ca57 *= scor
        rate_eval.p_Sc60__n_Ti60 *= scor
        rate_eval.p_Sc60__Ti61 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc58__n_V61 *= scor
        rate_eval.He4_Sc58__V62 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc58__He4_Ca55 *= scor
        rate_eval.p_Sc58__n_Ti58 *= scor
        rate_eval.p_Sc58__Ti59 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc57__n_V60 *= scor
        rate_eval.He4_Sc57__V61 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc56__n_V59 *= scor
        rate_eval.He4_Sc56__V60 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc55__n_V58 *= scor
        rate_eval.He4_Sc55__V59 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc55__He4_Ca52 *= scor
        rate_eval.p_Sc55__n_Ti55 *= scor
        rate_eval.p_Sc55__Ti56 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc54__n_V57 *= scor
        rate_eval.He4_Sc54__V58 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc54__n_Ti54 *= scor
        rate_eval.p_Sc54__Ti55 *= scor
        rate_eval.p_Sc54__He4_Ca51 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc52__n_V55 *= scor
        rate_eval.He4_Sc52__V56 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S47__Cl48 *= scor
        rate_eval.p_S47__n_Cl47 *= scor
        rate_eval.p_S47__He4_P44 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 9)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C9__p_N12 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc51__n_V54 *= scor
        rate_eval.He4_Sc51__V55 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar29__Ca33 *= scor
        rate_eval.He4_Ar29__p_K32 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc49__He4_Ca46 *= scor
        rate_eval.p_Sc49__n_Ti49 *= scor
        rate_eval.p_Sc49__Ti50 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc48__He4_Ca45 *= scor
        rate_eval.p_Sc48__n_Ti48 *= scor
        rate_eval.p_Sc48__Ti49 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc47__p_Ti50 *= scor
        rate_eval.He4_Sc47__V51 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc47__He4_Ca44 *= scor
        rate_eval.p_Sc47__Ti48 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc46__p_Ti49 *= scor
        rate_eval.He4_Sc46__n_V49 *= scor
        rate_eval.He4_Sc46__V50 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc46__He4_Ca43 *= scor
        rate_eval.p_Sc46__n_Ti46 *= scor
        rate_eval.p_Sc46__Ti47 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc45__p_Ti48 *= scor
        rate_eval.He4_Sc45__V49 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc45__He4_Ca42 *= scor
        rate_eval.p_Sc45__Ti46 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc44__p_Ti47 *= scor
        rate_eval.He4_Sc44__V48 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc44__He4_Ca41 *= scor
        rate_eval.p_Sc44__Ti45 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc43__p_Ti46 *= scor
        rate_eval.He4_Sc43__V47 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc42__p_Ti45 *= scor
        rate_eval.He4_Sc42__V46 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr56__n_Mn56 *= scor
        rate_eval.p_Cr56__He4_V53 *= scor
        rate_eval.p_Cr56__Mn57 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si36__He4_Al33 *= scor
        rate_eval.p_Si36__n_P36 *= scor
        rate_eval.p_Si36__P37 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc39__p_Ti42 *= scor
        rate_eval.He4_Sc39__V43 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P31__S32 *= scor
        rate_eval.p_P31__He4_Si28 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si45__P46 *= scor
        rate_eval.p_Si45__He4_Al42 *= scor
        rate_eval.p_Si45__n_P45 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc38__p_Ti41 *= scor
        rate_eval.He4_Sc38__V42 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na36__n_Mg36 *= scor
        rate_eval.p_Na36__Mg37 *= scor
        rate_eval.p_Na36__He4_Ne33 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc36__p_Ti39 *= scor
        rate_eval.He4_Sc36__V40 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc35__p_Ti38 *= scor
        rate_eval.He4_Sc35__V39 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca60__n_Sc60 *= scor
        rate_eval.p_Ca60__Sc61 *= scor
        rate_eval.p_Ca60__He4_K57 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca59__n_Sc59 *= scor
        rate_eval.p_Ca59__Sc60 *= scor
        rate_eval.p_Ca59__He4_K56 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca58__n_Ti61 *= scor
        rate_eval.He4_Ca58__Ti62 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca58__He4_K55 *= scor
        rate_eval.p_Ca58__n_Sc58 *= scor
        rate_eval.p_Ca58__Sc59 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al25__P29 *= scor
        rate_eval.He4_Al25__p_Si28 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca56__He4_K53 *= scor
        rate_eval.p_Ca56__n_Sc56 *= scor
        rate_eval.p_Ca56__Sc57 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca55__He4_K52 *= scor
        rate_eval.p_Ca55__n_Sc55 *= scor
        rate_eval.p_Ca55__Sc56 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca53__n_Ti56 *= scor
        rate_eval.He4_Ca53__Ti57 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca52__n_Sc52 *= scor
        rate_eval.p_Ca52__Sc53 *= scor
        rate_eval.p_Ca52__He4_K49 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P45__S46 *= scor
        rate_eval.p_P45__n_S45 *= scor
        rate_eval.p_P45__He4_Si42 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca51__n_Ti54 *= scor
        rate_eval.He4_Ca51__Ti55 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca51__He4_K48 *= scor
        rate_eval.p_Ca51__Sc52 *= scor
        rate_eval.p_Ca51__n_Sc51 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al39__He4_Mg36 *= scor
        rate_eval.p_Al39__n_Si39 *= scor
        rate_eval.p_Al39__Si40 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca47__n_Ti50 *= scor
        rate_eval.He4_Ca47__Ti51 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca47__n_Sc47 *= scor
        rate_eval.p_Ca47__Sc48 *= scor

        scn_fac = ScreenFactors(6, 12, 6, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.C12_C12__He4_Ne20 *= scor
        rate_eval.C12_C12__p_Na23 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca57__n_Ti60 *= scor
        rate_eval.He4_Ca57__Ti61 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti45__p_V48 *= scor
        rate_eval.He4_Ti45__Cr49 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca42__He4_K39 *= scor
        rate_eval.p_Ca42__Sc43 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F16__Na20 *= scor
        rate_eval.He4_F16__p_Ne19 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P42__n_S42 *= scor
        rate_eval.p_P42__He4_Si39 *= scor
        rate_eval.p_P42__S43 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe66__n_Ni69 *= scor
        rate_eval.He4_Fe66__Ni70 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P39__n_Cl42 *= scor
        rate_eval.He4_P39__Cl43 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca48__Ti52 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K57__n_Sc60 *= scor
        rate_eval.He4_K57__Sc61 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K57__He4_Ar54 *= scor
        rate_eval.p_K57__n_Ca57 *= scor
        rate_eval.p_K57__Ca58 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si42__S46 *= scor
        rate_eval.He4_Si42__n_S45 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K56__n_Sc59 *= scor
        rate_eval.He4_K56__Sc60 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K56__n_Ca56 *= scor
        rate_eval.p_K56__He4_Ar53 *= scor
        rate_eval.p_K56__Ca57 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K54__n_Sc57 *= scor
        rate_eval.He4_K54__Sc58 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K54__n_Ca54 *= scor
        rate_eval.p_K54__Ca55 *= scor
        rate_eval.p_K54__He4_Ar51 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K53__n_Sc56 *= scor
        rate_eval.He4_K53__Sc57 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K53__n_Ca53 *= scor
        rate_eval.p_K53__Ca54 *= scor
        rate_eval.p_K53__He4_Ar50 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K52__n_Sc55 *= scor
        rate_eval.He4_K52__Sc56 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P29__S30 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K51__n_Sc54 *= scor
        rate_eval.He4_K51__Sc55 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K51__n_Ca51 *= scor
        rate_eval.p_K51__He4_Ar48 *= scor
        rate_eval.p_K51__Ca52 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr57__n_Fe60 *= scor
        rate_eval.He4_Cr57__Fe61 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K50__n_Sc53 *= scor
        rate_eval.He4_K50__Sc54 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S42__Cl43 *= scor
        rate_eval.p_S42__n_Cl42 *= scor
        rate_eval.p_S42__He4_P39 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K48__n_Sc51 *= scor
        rate_eval.He4_K48__Sc52 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K45__He4_Ar42 *= scor
        rate_eval.p_K45__n_Ca45 *= scor
        rate_eval.p_K45__Ca46 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K44__He4_Ar41 *= scor
        rate_eval.p_K44__n_Ca44 *= scor
        rate_eval.p_K44__Ca45 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K43__p_Ca46 *= scor
        rate_eval.He4_K43__Sc47 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K43__n_Ca43 *= scor
        rate_eval.p_K43__Ca44 *= scor
        rate_eval.p_K43__He4_Ar40 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K42__p_Ca45 *= scor
        rate_eval.He4_K42__n_Sc45 *= scor
        rate_eval.He4_K42__Sc46 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K41__n_Sc44 *= scor
        rate_eval.He4_K41__p_Ca44 *= scor
        rate_eval.He4_K41__Sc45 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K41__He4_Ar38 *= scor
        rate_eval.p_K41__n_Ca41 *= scor
        rate_eval.p_K41__Ca42 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K46__p_Ca49 *= scor
        rate_eval.He4_K46__Sc50 *= scor
        rate_eval.He4_K46__n_Sc49 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K40__He4_Ar37 *= scor
        rate_eval.p_K40__n_Ca40 *= scor
        rate_eval.p_K40__Ca41 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S37__Cl38 *= scor
        rate_eval.p_S37__n_Cl37 *= scor
        rate_eval.p_S37__He4_P34 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O14__F15 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K37__p_Ca40 *= scor
        rate_eval.He4_K37__Sc41 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K44__p_Ca47 *= scor
        rate_eval.He4_K44__Sc48 *= scor
        rate_eval.He4_K44__n_Sc47 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K34__p_Ca37 *= scor
        rate_eval.He4_K34__Sc38 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr61__He4_V58 *= scor
        rate_eval.p_Cr61__Mn62 *= scor
        rate_eval.p_Cr61__n_Mn61 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn51__Fe52 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K31__p_Ca34 *= scor
        rate_eval.He4_K31__Sc35 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti38__V39 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar54__n_K54 *= scor
        rate_eval.p_Ar54__He4_Cl51 *= scor
        rate_eval.p_Ar54__K55 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar52__He4_Cl49 *= scor
        rate_eval.p_Ar52__n_K52 *= scor
        rate_eval.p_Ar52__K53 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K59__n_Ca59 *= scor
        rate_eval.p_K59__Ca60 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar50__He4_Cl47 *= scor
        rate_eval.p_Ar50__n_K50 *= scor
        rate_eval.p_Ar50__K51 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F20__n_Na23 *= scor
        rate_eval.He4_F20__p_Ne23 *= scor
        rate_eval.He4_F20__Na24 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar48__He4_Cl45 *= scor
        rate_eval.p_Ar48__n_K48 *= scor
        rate_eval.p_Ar48__K49 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar46__n_Ca49 *= scor
        rate_eval.He4_Ar46__Ca50 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F28__n_Ne28 *= scor
        rate_eval.p_F28__He4_O25 *= scor
        rate_eval.p_F28__Ne29 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe50__p_Co53 *= scor
        rate_eval.He4_Fe50__Ni54 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si35__n_S38 *= scor
        rate_eval.He4_Si35__S39 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar44__n_K44 *= scor
        rate_eval.p_Ar44__K45 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar43__n_Ca46 *= scor
        rate_eval.He4_Ar43__Ca47 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar43__n_K43 *= scor
        rate_eval.p_Ar43__He4_Cl40 *= scor
        rate_eval.p_Ar43__K44 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe47__Co48 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl47__K51 *= scor
        rate_eval.He4_Cl47__n_K50 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar41__n_K41 *= scor
        rate_eval.p_Ar41__K42 *= scor
        rate_eval.p_Ar41__He4_Cl38 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar40__He4_Cl37 *= scor
        rate_eval.p_Ar40__K41 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn54__Co58 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar39__He4_Cl36 *= scor
        rate_eval.p_Ar39__K40 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn62__n_Co65 *= scor
        rate_eval.He4_Mn62__Co66 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar34__p_K37 *= scor
        rate_eval.He4_Ar34__Ca38 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar33__p_K36 *= scor
        rate_eval.He4_Ar33__Ca37 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar31__p_K34 *= scor
        rate_eval.He4_Ar31__Ca35 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl52__He4_S49 *= scor
        rate_eval.p_Cl52__n_Ar52 *= scor
        rate_eval.p_Cl52__Ar53 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O16__F17 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl51__n_K54 *= scor
        rate_eval.He4_Cl51__K55 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl50__K54 *= scor
        rate_eval.He4_Cl50__n_K53 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl51__He4_S48 *= scor
        rate_eval.p_Cl51__Ar52 *= scor
        rate_eval.p_Cl51__n_Ar51 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl50__He4_S47 *= scor
        rate_eval.p_Cl50__n_Ar50 *= scor
        rate_eval.p_Cl50__Ar51 *= scor

        scn_fac = ScreenFactors(1, 1, 5, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_B12__n_C12 *= scor
        rate_eval.p_B12__He4_Be9 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl49__n_K52 *= scor
        rate_eval.He4_Cl49__K53 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar36__Ca40 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl48__He4_S45 *= scor
        rate_eval.p_Cl48__n_Ar48 *= scor
        rate_eval.p_Cl48__Ar49 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca50__n_Ti53 *= scor
        rate_eval.He4_Ca50__Ti54 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti62__n_V62 *= scor
        rate_eval.p_Ti62__V63 *= scor
        rate_eval.p_Ti62__He4_Sc59 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl45__He4_S42 *= scor
        rate_eval.p_Cl45__n_Ar45 *= scor
        rate_eval.p_Cl45__Ar46 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl43__p_Ar46 *= scor
        rate_eval.He4_Cl43__K47 *= scor
        rate_eval.He4_Cl43__n_K46 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl43__He4_S40 *= scor
        rate_eval.p_Cl43__Ar44 *= scor
        rate_eval.p_Cl43__n_Ar43 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn61__n_Fe61 *= scor
        rate_eval.p_Mn61__Fe62 *= scor
        rate_eval.p_Mn61__He4_Cr58 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V49__Mn53 *= scor
        rate_eval.He4_V49__p_Cr52 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl42__n_K45 *= scor
        rate_eval.He4_Cl42__K46 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl42__He4_S39 *= scor
        rate_eval.p_Cl42__n_Ar42 *= scor
        rate_eval.p_Cl42__Ar43 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl41__n_K44 *= scor
        rate_eval.He4_Cl41__K45 *= scor
        rate_eval.He4_Cl41__p_Ar44 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl41__He4_S38 *= scor
        rate_eval.p_Cl41__Ar42 *= scor
        rate_eval.p_Cl41__n_Ar41 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl40__n_K43 *= scor
        rate_eval.He4_Cl40__K44 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl40__n_Ar40 *= scor
        rate_eval.p_Cl40__He4_S37 *= scor
        rate_eval.p_Cl40__Ar41 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O19__He4_N16 *= scor
        rate_eval.p_O19__n_F19 *= scor
        rate_eval.p_O19__F20 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 17)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F17__Na21 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl34__p_Ar37 *= scor
        rate_eval.He4_Cl34__K38 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti43__V44 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na34__Mg35 *= scor
        rate_eval.p_Na34__He4_Ne31 *= scor
        rate_eval.p_Na34__n_Mg34 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S48__n_Ar51 *= scor
        rate_eval.He4_S48__Ar52 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl30__p_Ar33 *= scor
        rate_eval.He4_Cl30__K34 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na25__Al29 *= scor
        rate_eval.He4_Na25__n_Al28 *= scor
        rate_eval.He4_Na25__p_Mg28 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl28__p_Ar31 *= scor
        rate_eval.He4_Cl28__K32 *= scor

        scn_fac = ScreenFactors(1, 2, 3, 8)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_Li8__n_Be9 *= scor
        rate_eval.d_Li8__t_Li7 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S49__n_Cl49 *= scor
        rate_eval.p_S49__Cl50 *= scor
        rate_eval.p_S49__He4_P46 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg38__n_Si41 *= scor
        rate_eval.He4_Mg38__Si42 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S48__n_Cl48 *= scor
        rate_eval.p_S48__He4_P45 *= scor
        rate_eval.p_S48__Cl49 *= scor

        scn_fac = ScreenFactors(1, 1, 7, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_N15__O16 *= scor
        rate_eval.p_N15__He4_C12 *= scor
        rate_eval.p_N15__n_O15 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K52__He4_Ar49 *= scor
        rate_eval.p_K52__Ca53 *= scor
        rate_eval.p_K52__n_Ca52 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S46__n_Cl46 *= scor
        rate_eval.p_S46__Cl47 *= scor
        rate_eval.p_S46__He4_P43 *= scor

        scn_fac = ScreenFactors(1, 2, 4, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_Be7__p_He4_He4 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S45__He4_P42 *= scor
        rate_eval.p_S45__n_Cl45 *= scor
        rate_eval.p_S45__Cl46 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S43__n_Ar46 *= scor
        rate_eval.He4_S43__Ar47 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S43__He4_P40 *= scor
        rate_eval.p_S43__n_Cl43 *= scor
        rate_eval.p_S43__Cl44 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn67__n_Co70 *= scor
        rate_eval.He4_Mn67__Co71 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc57__He4_Ca54 *= scor
        rate_eval.p_Sc57__n_Ti57 *= scor
        rate_eval.p_Sc57__Ti58 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe56__Ni60 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S42__n_Ar45 *= scor
        rate_eval.He4_S42__Ar46 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S41__n_Ar44 *= scor
        rate_eval.He4_S41__Ar45 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc63__n_V66 *= scor
        rate_eval.He4_Sc63__V67 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S41__He4_P38 *= scor
        rate_eval.p_S41__Cl42 *= scor
        rate_eval.p_S41__n_Cl41 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al30__He4_Mg27 *= scor
        rate_eval.p_Al30__n_Si30 *= scor
        rate_eval.p_Al30__Si31 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S40__n_Cl40 *= scor
        rate_eval.p_S40__Cl41 *= scor
        rate_eval.p_S40__He4_P37 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe47__Ni51 *= scor
        rate_eval.He4_Fe47__p_Co50 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S39__He4_P36 *= scor
        rate_eval.p_S39__Cl40 *= scor
        rate_eval.p_S39__n_Cl39 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S38__n_Ar41 *= scor
        rate_eval.He4_S38__Ar42 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S38__He4_P35 *= scor
        rate_eval.p_S38__n_Cl38 *= scor
        rate_eval.p_S38__Cl39 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S37__n_Ar40 *= scor
        rate_eval.He4_S37__Ar41 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K49__n_Sc52 *= scor
        rate_eval.He4_K49__Sc53 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V56__He4_Ti53 *= scor
        rate_eval.p_V56__Cr57 *= scor
        rate_eval.p_V56__n_Cr56 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K49__n_Ca49 *= scor
        rate_eval.p_K49__Ca50 *= scor
        rate_eval.p_K49__He4_Ar46 *= scor

        scn_fac = ScreenFactors(1, 1, 3, 6)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Li6__Be7 *= scor
        rate_eval.p_Li6__He4_He3 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S36__He4_P33 *= scor
        rate_eval.p_S36__Cl37 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr69__He4_V66 *= scor
        rate_eval.p_Cr69__Mn70 *= scor
        rate_eval.p_Cr69__n_Mn69 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc51__He4_Ca48 *= scor
        rate_eval.p_Sc51__n_Ti51 *= scor
        rate_eval.p_Sc51__Ti52 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P34__n_Cl37 *= scor
        rate_eval.He4_P34__Cl38 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S35__n_Ar38 *= scor
        rate_eval.He4_S35__Ar39 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S35__He4_P32 *= scor
        rate_eval.p_S35__Cl36 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S34__p_Cl37 *= scor
        rate_eval.He4_S34__Ar38 *= scor
        rate_eval.He4_S34__n_Ar37 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl35__He4_S32 *= scor
        rate_eval.p_Cl35__Ar36 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S31__p_Cl34 *= scor
        rate_eval.He4_S31__Ar35 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S28__p_Cl31 *= scor
        rate_eval.He4_S28__Ar32 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S26__p_Cl29 *= scor
        rate_eval.He4_S26__Ar30 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P47__n_Cl50 *= scor
        rate_eval.He4_P47__Cl51 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P47__n_S47 *= scor
        rate_eval.p_P47__He4_Si44 *= scor
        rate_eval.p_P47__S48 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P43__n_Cl46 *= scor
        rate_eval.He4_P43__Cl47 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P43__He4_Si40 *= scor
        rate_eval.p_P43__n_S43 *= scor
        rate_eval.p_P43__S44 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al38__n_P41 *= scor
        rate_eval.He4_Al38__p_Si41 *= scor
        rate_eval.He4_Al38__P42 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P41__p_S44 *= scor
        rate_eval.He4_P41__n_Cl44 *= scor
        rate_eval.He4_P41__Cl45 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O20__He4_N17 *= scor
        rate_eval.p_O20__n_F20 *= scor
        rate_eval.p_O20__F21 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P38__He4_Si35 *= scor
        rate_eval.p_P38__n_S38 *= scor
        rate_eval.p_P38__S39 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F18__He4_O15 *= scor
        rate_eval.p_F18__Ne19 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P37__n_Cl40 *= scor
        rate_eval.He4_P37__Cl41 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P37__He4_Si34 *= scor
        rate_eval.p_P37__S38 *= scor
        rate_eval.p_P37__n_S37 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P36__He4_Si33 *= scor
        rate_eval.p_P36__n_S36 *= scor
        rate_eval.p_P36__S37 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P34__n_S34 *= scor
        rate_eval.p_P34__S35 *= scor
        rate_eval.p_P34__He4_Si31 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl44__p_Ar47 *= scor
        rate_eval.He4_Cl44__n_K47 *= scor
        rate_eval.He4_Cl44__K48 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al25__Si26 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P31__p_S34 *= scor
        rate_eval.He4_P31__Cl35 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P30__p_S33 *= scor
        rate_eval.He4_P30__Cl34 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K55__n_Sc58 *= scor
        rate_eval.He4_K55__Sc59 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P27__p_S30 *= scor
        rate_eval.He4_P27__Cl31 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P26__p_S29 *= scor
        rate_eval.He4_P26__Cl30 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P25__p_S28 *= scor
        rate_eval.He4_P25__Cl29 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P24__p_S27 *= scor
        rate_eval.He4_P24__Cl28 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si44__n_S47 *= scor
        rate_eval.He4_Si44__S48 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P42__n_Cl45 *= scor
        rate_eval.He4_P42__Cl46 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si42__n_P42 *= scor
        rate_eval.p_Si42__P43 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si40__n_S43 *= scor
        rate_eval.He4_Si40__S44 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si39__n_S42 *= scor
        rate_eval.He4_Si39__S43 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si39__n_P39 *= scor
        rate_eval.p_Si39__P40 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc62__n_Ti62 *= scor
        rate_eval.p_Sc62__Ti63 *= scor
        rate_eval.p_Sc62__He4_Ca59 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si38__n_S41 *= scor
        rate_eval.He4_Si38__S42 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti65__He4_Sc62 *= scor
        rate_eval.p_Ti65__V66 *= scor
        rate_eval.p_Ti65__n_V65 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si37__n_S40 *= scor
        rate_eval.He4_Si37__S41 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca40__Ti44 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si37__He4_Al34 *= scor
        rate_eval.p_Si37__n_P37 *= scor
        rate_eval.p_Si37__P38 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si35__He4_Al32 *= scor
        rate_eval.p_Si35__P36 *= scor
        rate_eval.p_Si35__n_P35 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si33__n_P33 *= scor
        rate_eval.p_Si33__P34 *= scor
        rate_eval.p_Si33__He4_Al30 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn45__p_Fe48 *= scor
        rate_eval.He4_Mn45__Co49 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr41__p_Mn44 *= scor
        rate_eval.He4_Cr41__Fe45 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn43__Co47 *= scor
        rate_eval.He4_Mn43__p_Fe46 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V57__n_Mn60 *= scor
        rate_eval.He4_V57__Mn61 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti61__n_Cr64 *= scor
        rate_eval.He4_Ti61__Cr65 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si25__p_P28 *= scor
        rate_eval.He4_Si25__S29 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn58__Fe59 *= scor
        rate_eval.p_Mn58__n_Fe58 *= scor
        rate_eval.p_Mn58__He4_Cr55 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V40__p_Cr43 *= scor
        rate_eval.He4_V40__Mn44 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si24__p_P27 *= scor
        rate_eval.He4_Si24__S28 *= scor

        scn_fac = ScreenFactors(2, 4, 4, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Be7__C11 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca54__Ti58 *= scor
        rate_eval.He4_Ca54__n_Ti57 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K40__p_Ca43 *= scor
        rate_eval.He4_K40__Sc44 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si23__p_P26 *= scor
        rate_eval.He4_Si23__S27 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar42__n_Ca45 *= scor
        rate_eval.He4_Ar42__Ca46 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si22__p_P25 *= scor
        rate_eval.He4_Si22__S26 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al43__n_Si43 *= scor
        rate_eval.p_Al43__He4_Mg40 *= scor
        rate_eval.p_Al43__Si44 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al42__n_P45 *= scor
        rate_eval.He4_Al42__P46 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al41__He4_Mg38 *= scor
        rate_eval.p_Al41__n_Si41 *= scor
        rate_eval.p_Al41__Si42 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al40__He4_Mg37 *= scor
        rate_eval.p_Al40__n_Si40 *= scor
        rate_eval.p_Al40__Si41 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al39__p_Si42 *= scor
        rate_eval.He4_Al39__P43 *= scor
        rate_eval.He4_Al39__n_P42 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al38__He4_Mg35 *= scor
        rate_eval.p_Al38__n_Si38 *= scor
        rate_eval.p_Al38__Si39 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V59__n_Cr59 *= scor
        rate_eval.p_V59__Cr60 *= scor
        rate_eval.p_V59__He4_Ti56 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al37__He4_Mg34 *= scor
        rate_eval.p_Al37__Si38 *= scor
        rate_eval.p_Al37__n_Si37 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al36__p_Si39 *= scor
        rate_eval.He4_Al36__n_P39 *= scor
        rate_eval.He4_Al36__P40 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al36__He4_Mg33 *= scor
        rate_eval.p_Al36__n_Si36 *= scor
        rate_eval.p_Al36__Si37 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn59__Co63 *= scor
        rate_eval.He4_Mn59__n_Co62 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al35__n_P38 *= scor
        rate_eval.He4_Al35__P39 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al35__He4_Mg32 *= scor
        rate_eval.p_Al35__n_Si35 *= scor
        rate_eval.p_Al35__Si36 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al34__n_P37 *= scor
        rate_eval.He4_Al34__P38 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al34__He4_Mg31 *= scor
        rate_eval.p_Al34__n_Si34 *= scor
        rate_eval.p_Al34__Si35 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al33__n_P36 *= scor
        rate_eval.He4_Al33__P37 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al33__He4_Mg30 *= scor
        rate_eval.p_Al33__n_Si33 *= scor
        rate_eval.p_Al33__Si34 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si27__p_P30 *= scor
        rate_eval.He4_Si27__S31 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl46__He4_S43 *= scor
        rate_eval.p_Cl46__n_Ar46 *= scor
        rate_eval.p_Cl46__Ar47 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne26__n_Na26 *= scor
        rate_eval.p_Ne26__He4_F23 *= scor
        rate_eval.p_Ne26__Na27 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al32__He4_Mg29 *= scor
        rate_eval.p_Al32__n_Si32 *= scor
        rate_eval.p_Al32__Si33 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al31__p_Si34 *= scor
        rate_eval.He4_Al31__n_P34 *= scor
        rate_eval.He4_Al31__P35 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl38__He4_S35 *= scor
        rate_eval.p_Cl38__n_Ar38 *= scor
        rate_eval.p_Cl38__Ar39 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al31__He4_Mg28 *= scor
        rate_eval.p_Al31__Si32 *= scor
        rate_eval.p_Al31__n_Si31 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al29__n_P32 *= scor
        rate_eval.He4_Al29__p_Si32 *= scor
        rate_eval.He4_Al29__P33 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al29__He4_Mg26 *= scor
        rate_eval.p_Al29__n_Si29 *= scor
        rate_eval.p_Al29__Si30 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al37__n_P40 *= scor
        rate_eval.He4_Al37__P41 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne34__He4_F31 *= scor
        rate_eval.p_Ne34__n_Na34 *= scor
        rate_eval.p_Ne34__Na35 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al28__He4_Mg25 *= scor
        rate_eval.p_Al28__Si29 *= scor
        rate_eval.p_Al28__n_Si28 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al27__p_Si30 *= scor
        rate_eval.He4_Al27__n_P30 *= scor
        rate_eval.He4_Al27__P31 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca49__Sc50 *= scor
        rate_eval.p_Ca49__n_Sc49 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al24__p_Si27 *= scor
        rate_eval.He4_Al24__P28 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na37__Mg38 *= scor
        rate_eval.p_Na37__He4_Ne34 *= scor
        rate_eval.p_Na37__n_Mg37 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al22__p_Si25 *= scor
        rate_eval.He4_Al22__P26 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al21__p_Si24 *= scor
        rate_eval.He4_Al21__P25 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg40__n_Si43 *= scor
        rate_eval.He4_Mg40__Si44 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg40__n_Al40 *= scor
        rate_eval.p_Mg40__Al41 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg39__n_Si42 *= scor
        rate_eval.He4_Mg39__Si43 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg39__n_Al39 *= scor
        rate_eval.p_Mg39__Al40 *= scor
        rate_eval.p_Mg39__He4_Na36 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg38__n_Al38 *= scor
        rate_eval.p_Mg38__Al39 *= scor
        rate_eval.p_Mg38__He4_Na35 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al27__He4_Mg24 *= scor
        rate_eval.p_Al27__Si28 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg37__n_Si40 *= scor
        rate_eval.He4_Mg37__Si41 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na31__Mg32 *= scor
        rate_eval.p_Na31__He4_Ne28 *= scor
        rate_eval.p_Na31__n_Mg31 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar45__He4_Cl42 *= scor
        rate_eval.p_Ar45__n_K45 *= scor
        rate_eval.p_Ar45__K46 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg35__n_Si38 *= scor
        rate_eval.He4_Mg35__Si39 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg34__n_Si37 *= scor
        rate_eval.He4_Mg34__Si38 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg33__He4_Na30 *= scor
        rate_eval.p_Mg33__n_Al33 *= scor
        rate_eval.p_Mg33__Al34 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe66__He4_Mn63 *= scor
        rate_eval.p_Fe66__n_Co66 *= scor
        rate_eval.p_Fe66__Co67 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg32__n_Si35 *= scor
        rate_eval.He4_Mg32__Si36 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg32__He4_Na29 *= scor
        rate_eval.p_Mg32__Al33 *= scor
        rate_eval.p_Mg32__n_Al32 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg30__n_Si33 *= scor
        rate_eval.He4_Mg30__Si34 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg30__n_Al30 *= scor
        rate_eval.p_Mg30__Al31 *= scor
        rate_eval.p_Mg30__He4_Na27 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca45__Sc46 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr46__p_Mn49 *= scor
        rate_eval.He4_Cr46__Fe50 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg29__He4_Na26 *= scor
        rate_eval.p_Mg29__n_Al29 *= scor
        rate_eval.p_Mg29__Al30 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne23__n_Mg26 *= scor
        rate_eval.He4_Ne23__Mg27 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne31__He4_F28 *= scor
        rate_eval.p_Ne31__Na32 *= scor
        rate_eval.p_Ne31__n_Na31 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg27__n_Si30 *= scor
        rate_eval.He4_Mg27__Si31 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O23__n_Ne26 *= scor
        rate_eval.He4_O23__Ne27 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K35__p_Ca38 *= scor
        rate_eval.He4_K35__Sc39 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg26__n_Si29 *= scor
        rate_eval.He4_Mg26__Si30 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe53__p_Co56 *= scor
        rate_eval.He4_Fe53__Ni57 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg25__n_Si28 *= scor
        rate_eval.He4_Mg25__Si29 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg22__p_Al25 *= scor
        rate_eval.He4_Mg22__Si26 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg20__p_Al23 *= scor
        rate_eval.He4_Mg20__Si24 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na36__n_Al39 *= scor
        rate_eval.He4_Na36__Al40 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na39__n_Mg39 *= scor
        rate_eval.p_Na39__Mg40 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na38__n_Al41 *= scor
        rate_eval.He4_Na38__Al42 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na37__p_Mg40 *= scor
        rate_eval.He4_Na37__n_Al40 *= scor
        rate_eval.He4_Na37__Al41 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K33__Sc37 *= scor
        rate_eval.He4_K33__p_Ca36 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na35__n_Al38 *= scor
        rate_eval.He4_Na35__Al39 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na35__n_Mg35 *= scor
        rate_eval.p_Na35__He4_Ne32 *= scor
        rate_eval.p_Na35__Mg36 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na34__n_Al37 *= scor
        rate_eval.He4_Na34__Al38 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V60__n_Mn63 *= scor
        rate_eval.He4_V60__Mn64 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na33__p_Mg36 *= scor
        rate_eval.He4_Na33__Al37 *= scor
        rate_eval.He4_Na33__n_Al36 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na33__n_Mg33 *= scor
        rate_eval.p_Na33__He4_Ne30 *= scor
        rate_eval.p_Na33__Mg34 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na31__n_Al34 *= scor
        rate_eval.He4_Na31__Al35 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na30__He4_Ne27 *= scor
        rate_eval.p_Na30__Mg31 *= scor
        rate_eval.p_Na30__n_Mg30 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na29__He4_Ne26 *= scor
        rate_eval.p_Na29__n_Mg29 *= scor
        rate_eval.p_Na29__Mg30 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na28__n_Al31 *= scor
        rate_eval.He4_Na28__Al32 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na28__n_Mg28 *= scor
        rate_eval.p_Na28__He4_Ne25 *= scor
        rate_eval.p_Na28__Mg29 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na27__n_Mg27 *= scor
        rate_eval.p_Na27__Mg28 *= scor
        rate_eval.p_Na27__He4_Ne24 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na26__n_Al29 *= scor
        rate_eval.He4_Na26__Al30 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na24__p_Mg27 *= scor
        rate_eval.He4_Na24__Al28 *= scor
        rate_eval.He4_Na24__n_Al27 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na24__He4_Ne21 *= scor
        rate_eval.p_Na24__Mg25 *= scor
        rate_eval.p_Na24__n_Mg24 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K46__Ca47 *= scor
        rate_eval.p_K46__He4_Ar43 *= scor
        rate_eval.p_K46__n_Ca46 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na23__p_Mg26 *= scor
        rate_eval.He4_Na23__Al27 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na23__He4_Ne20 *= scor
        rate_eval.p_Na23__n_Mg23 *= scor
        rate_eval.p_Na23__Mg24 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na22__p_Mg25 *= scor
        rate_eval.He4_Na22__Al26 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S29__p_Cl32 *= scor
        rate_eval.He4_S29__Ar33 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl35__p_Ar38 *= scor
        rate_eval.He4_Cl35__K39 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl36__Ar37 *= scor
        rate_eval.p_Cl36__He4_S33 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S46__n_Ar49 *= scor
        rate_eval.He4_S46__Ar50 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne31__n_Mg34 *= scor
        rate_eval.He4_Ne31__Mg35 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne30__n_Mg33 *= scor
        rate_eval.He4_Ne30__Mg34 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne30__He4_F27 *= scor
        rate_eval.p_Ne30__Na31 *= scor
        rate_eval.p_Ne30__n_Na30 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne29__He4_F26 *= scor
        rate_eval.p_Ne29__n_Na29 *= scor
        rate_eval.p_Ne29__Na30 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne28__n_Mg31 *= scor
        rate_eval.He4_Ne28__Mg32 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne28__n_Na28 *= scor
        rate_eval.p_Ne28__He4_F25 *= scor
        rate_eval.p_Ne28__Na29 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne27__n_Mg30 *= scor
        rate_eval.He4_Ne27__Mg31 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca39__Ti43 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S39__n_Ar42 *= scor
        rate_eval.He4_S39__Ar43 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne25__He4_F22 *= scor
        rate_eval.p_Ne25__n_Na25 *= scor
        rate_eval.p_Ne25__Na26 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S27__p_Cl30 *= scor
        rate_eval.He4_S27__Ar31 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne24__n_Mg27 *= scor
        rate_eval.He4_Ne24__Mg28 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne24__n_Na24 *= scor
        rate_eval.p_Ne24__Na25 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S30__Cl31 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca61__n_Ti64 *= scor
        rate_eval.He4_Ca61__Ti65 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K39__Sc43 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne23__n_Na23 *= scor
        rate_eval.p_Ne23__Na24 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne22__n_Mg25 *= scor
        rate_eval.He4_Ne22__Mg26 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne21__n_Mg24 *= scor
        rate_eval.He4_Ne21__Mg25 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V42__Cr43 *= scor

        scn_fac = ScreenFactors(6, 12, 10, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.C12_Ne20__He4_Si28 *= scor
        rate_eval.C12_Ne20__p_P31 *= scor
        rate_eval.C12_Ne20__n_S31 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V54__n_Cr54 *= scor
        rate_eval.p_V54__Cr55 *= scor
        rate_eval.p_V54__He4_Ti51 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne20__He4_F17 *= scor
        rate_eval.p_Ne20__Na21 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne22__Na23 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al26__p_Si29 *= scor
        rate_eval.He4_Al26__P30 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K33__Ca34 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne19__p_Na22 *= scor
        rate_eval.He4_Ne19__Mg23 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne18__p_Na21 *= scor
        rate_eval.He4_Ne18__Mg22 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 17)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne17__p_Na20 *= scor
        rate_eval.He4_Ne17__Mg21 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne16__p_Na19 *= scor
        rate_eval.He4_Ne16__Mg20 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar53__n_Ca56 *= scor
        rate_eval.He4_Ar53__Ca57 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F30__p_Ne33 *= scor
        rate_eval.He4_F30__n_Na33 *= scor
        rate_eval.He4_F30__Na34 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn47__Fe48 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F30__He4_O27 *= scor
        rate_eval.p_F30__n_Ne30 *= scor
        rate_eval.p_F30__Ne31 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F29__n_Na32 *= scor
        rate_eval.He4_F29__Na33 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F29__He4_O26 *= scor
        rate_eval.p_F29__Ne30 *= scor
        rate_eval.p_F29__n_Ne29 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F27__n_Na30 *= scor
        rate_eval.He4_F27__Na31 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F27__He4_O24 *= scor
        rate_eval.p_F27__n_Ne27 *= scor
        rate_eval.p_F27__Ne28 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F26__n_Ne26 *= scor
        rate_eval.p_F26__Ne27 *= scor
        rate_eval.p_F26__He4_O23 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F25__He4_O22 *= scor
        rate_eval.p_F25__n_Ne25 *= scor
        rate_eval.p_F25__Ne26 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca38__Ti42 *= scor
        rate_eval.He4_Ca38__p_Sc41 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F24__n_Na27 *= scor
        rate_eval.He4_F24__Na28 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti42__p_V45 *= scor
        rate_eval.He4_Ti42__Cr46 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na26__He4_Ne23 *= scor
        rate_eval.p_Na26__Mg27 *= scor
        rate_eval.p_Na26__n_Mg26 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F22__He4_O19 *= scor
        rate_eval.p_F22__n_Ne22 *= scor
        rate_eval.p_F22__Ne23 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F21__p_Ne24 *= scor
        rate_eval.He4_F21__n_Na24 *= scor
        rate_eval.He4_F21__Na25 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F20__He4_O17 *= scor
        rate_eval.p_F20__n_Ne20 *= scor
        rate_eval.p_F20__Ne21 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F19__p_Ne22 *= scor
        rate_eval.He4_F19__Na23 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F19__n_Ne19 *= scor
        rate_eval.p_F19__He4_O16 *= scor
        rate_eval.p_F19__Ne20 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O21__n_F21 *= scor
        rate_eval.p_O21__F22 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F18__p_Ne21 *= scor
        rate_eval.He4_F18__Na22 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O15__F16 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O28__n_Ne31 *= scor
        rate_eval.He4_O28__Ne32 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O26__n_Ne29 *= scor
        rate_eval.He4_O26__Ne30 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O26__He4_N23 *= scor
        rate_eval.p_O26__n_F26 *= scor
        rate_eval.p_O26__F27 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti44__p_V47 *= scor
        rate_eval.He4_Ti44__Cr48 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O24__n_Ne27 *= scor
        rate_eval.He4_O24__Ne28 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O24__n_F24 *= scor
        rate_eval.p_O24__F25 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O22__n_Ne25 *= scor
        rate_eval.He4_O22__Ne26 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O19__n_Ne22 *= scor
        rate_eval.He4_O19__Ne23 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl32__p_Ar35 *= scor
        rate_eval.He4_Cl32__K36 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O18__He4_N15 *= scor
        rate_eval.p_O18__F19 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 17)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O17__n_Ne20 *= scor
        rate_eval.He4_O17__Ne21 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 17)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O17__He4_N14 *= scor
        rate_eval.p_O17__F18 *= scor

        scn_fac = ScreenFactors(8, 16, 8, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.O16_O16__He4_Si28 *= scor
        rate_eval.O16_O16__p_P31 *= scor
        rate_eval.O16_O16__n_S31 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne26__n_Mg29 *= scor
        rate_eval.He4_Ne26__Mg30 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al28__n_P31 *= scor
        rate_eval.He4_Al28__p_Si31 *= scor
        rate_eval.He4_Al28__P32 *= scor

        scn_fac = ScreenFactors(6, 12, 8, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.C12_O16__He4_Mg24 *= scor
        rate_eval.C12_O16__p_Al27 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al26__Si27 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca36__Sc37 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr70__Mn71 *= scor
        rate_eval.p_Cr70__n_Mn70 *= scor
        rate_eval.p_Cr70__He4_V67 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar41__n_Ca44 *= scor
        rate_eval.He4_Ar41__Ca45 *= scor

        scn_fac = ScreenFactors(2, 4, 7, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_N13__p_O16 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C15__n_O18 *= scor

        scn_fac = ScreenFactors(1, 1, 6, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_C15__n_N15 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si31__n_S34 *= scor
        rate_eval.He4_Si31__S35 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl45__n_K48 *= scor
        rate_eval.He4_Cl45__K49 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C13__n_O16 *= scor

        scn_fac = ScreenFactors(1, 2, 6, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_C13__n_N14 *= scor

        scn_fac = ScreenFactors(1, 1, 6, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_C13__n_N13 *= scor
        rate_eval.p_C13__N14 *= scor

        scn_fac = ScreenFactors(2, 4, 5, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_B13__n_N16 *= scor
        rate_eval.He4_B13__N17 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar53__He4_Cl50 *= scor
        rate_eval.p_Ar53__n_K53 *= scor
        rate_eval.p_Ar53__K54 *= scor

        scn_fac = ScreenFactors(2, 4, 5, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_B12__n_N15 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti56__He4_Sc53 *= scor
        rate_eval.p_Ti56__V57 *= scor
        rate_eval.p_Ti56__n_V56 *= scor

        scn_fac = ScreenFactors(2, 4, 5, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_B11__p_C14 *= scor
        rate_eval.He4_B11__n_N14 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe46__p_Co49 *= scor
        rate_eval.He4_Fe46__Ni50 *= scor

        scn_fac = ScreenFactors(2, 4, 5, 10)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_B10__p_C13 *= scor
        rate_eval.He4_B10__n_N13 *= scor

        scn_fac = ScreenFactors(2, 4, 5, 8)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_B8__p_C11 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn70__Co74 *= scor
        rate_eval.He4_Mn70__n_Co73 *= scor

        scn_fac = ScreenFactors(2, 4, 3, 8)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Li8__n_B11 *= scor
        rate_eval.He4_Li8__B12 *= scor

        scn_fac = ScreenFactors(1, 2, 2, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_He3__p_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V51__Mn55 *= scor

        scn_fac = ScreenFactors(1, 2, 1, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_t__n_He4 *= scor

        scn_fac = ScreenFactors(1, 2, 1, 2)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_d__p_t *= scor
        rate_eval.d_d__He4 *= scor
        rate_eval.d_d__n_He3 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg31__n_Al31 *= scor
        rate_eval.p_Mg31__Al32 *= scor
        rate_eval.p_Mg31__He4_Na28 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 69)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe69__Ni73 *= scor
        rate_eval.He4_Fe69__n_Ni72 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe67__Ni71 *= scor
        rate_eval.He4_Fe67__n_Ni70 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc48__n_V51 *= scor
        rate_eval.He4_Sc48__V52 *= scor
        rate_eval.He4_Sc48__p_Ti51 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P36__n_Cl39 *= scor
        rate_eval.He4_P36__Cl40 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe58__Ni62 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe56__Co57 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe55__Co56 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe54__Ni58 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe52__Co53 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe51__Ni55 *= scor
        rate_eval.He4_Fe51__p_Co54 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe50__Co51 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe48__Co49 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O25__n_Ne28 *= scor
        rate_eval.He4_O25__Ne29 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe57__Ni61 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe45__Ni49 *= scor
        rate_eval.He4_Fe45__p_Co48 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 66)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn66__Co70 *= scor
        rate_eval.He4_Mn66__n_Co69 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn64__Co68 *= scor
        rate_eval.He4_Mn64__n_Co67 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn63__Co67 *= scor
        rate_eval.He4_Mn63__n_Co66 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl29__p_Ar32 *= scor
        rate_eval.He4_Cl29__K33 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne33__n_Na33 *= scor
        rate_eval.p_Ne33__Na34 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn61__Co65 *= scor
        rate_eval.He4_Mn61__n_Co64 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K42__n_Ca42 *= scor
        rate_eval.p_K42__He4_Ar39 *= scor
        rate_eval.p_K42__Ca43 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn52__Co56 *= scor
        rate_eval.He4_Mn52__p_Fe55 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn50__Co54 *= scor
        rate_eval.He4_Mn50__p_Fe53 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn50__Fe51 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn49__Fe50 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn48__Fe49 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn46__Fe47 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn45__Fe46 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 67)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr67__Fe71 *= scor
        rate_eval.He4_Cr67__n_Fe70 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr60__Fe64 *= scor
        rate_eval.He4_Cr60__n_Fe63 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg19__p_Al22 *= scor
        rate_eval.He4_Mg19__Si23 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr58__Fe62 *= scor
        rate_eval.He4_Cr58__n_Fe61 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr58__Mn59 *= scor
        rate_eval.p_Cr58__n_Mn58 *= scor
        rate_eval.p_Cr58__He4_V55 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr54__Fe58 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr53__Fe57 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr53__Mn54 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl39__He4_S36 *= scor
        rate_eval.p_Cl39__Ar40 *= scor
        rate_eval.p_Cl39__n_Ar39 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr52__Mn53 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr51__Mn52 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr50__Mn51 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr49__Mn50 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar45__Ca49 *= scor
        rate_eval.He4_Ar45__n_Ca48 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K38__p_Ca41 *= scor
        rate_eval.He4_K38__Sc42 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P40__n_Cl43 *= scor
        rate_eval.He4_P40__Cl44 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr46__Mn47 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P44__He4_Si41 *= scor
        rate_eval.p_P44__n_S44 *= scor
        rate_eval.p_P44__S45 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O14__p_F17 *= scor
        rate_eval.He4_O14__Ne18 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K58__n_Ca58 *= scor
        rate_eval.p_K58__Ca59 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V53__Mn57 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V52__Mn56 *= scor
        rate_eval.He4_V52__n_Mn55 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V62__n_Cr62 *= scor
        rate_eval.p_V62__He4_Ti59 *= scor
        rate_eval.p_V62__Cr63 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne25__Mg29 *= scor
        rate_eval.He4_Ne25__n_Mg28 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 65)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V65__Mn69 *= scor
        rate_eval.He4_V65__n_Mn68 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne32__n_Mg35 *= scor
        rate_eval.He4_Ne32__Mg36 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V48__Cr49 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V46__Cr47 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V45__Mn49 *= scor
        rate_eval.He4_V45__p_Cr48 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn63__Fe64 *= scor
        rate_eval.p_Mn63__He4_Cr60 *= scor
        rate_eval.p_Mn63__n_Fe63 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V43__Cr44 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P40__n_S40 *= scor
        rate_eval.p_P40__S41 *= scor
        rate_eval.p_P40__He4_Si37 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al42__He4_Mg39 *= scor
        rate_eval.p_Al42__Si43 *= scor
        rate_eval.p_Al42__n_Si42 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V41__Mn45 *= scor
        rate_eval.He4_V41__p_Cr44 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V41__Cr42 *= scor

        scn_fac = ScreenFactors(1, 1, 7, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_N12__O13 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar47__n_K47 *= scor
        rate_eval.p_Ar47__K48 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar36__K37 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti52__Cr56 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti49__V50 *= scor

        scn_fac = ScreenFactors(1, 3, 4, 9)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.t_Be9__n_B11 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na39__n_Al42 *= scor
        rate_eval.He4_Na39__Al43 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti48__Cr52 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti47__V48 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti57__n_Cr60 *= scor
        rate_eval.He4_Ti57__Cr61 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti46__Cr50 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti44__V45 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti42__V43 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti41__Cr45 *= scor
        rate_eval.He4_Ti41__p_V44 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na32__n_Al35 *= scor
        rate_eval.He4_Na32__Al36 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti41__V42 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S28__Cl29 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti40__V41 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 63)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc63__Ti64 *= scor
        rate_eval.p_Sc63__He4_Ca60 *= scor
        rate_eval.p_Sc63__n_Ti63 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn44__Fe45 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca60__n_Ti63 *= scor
        rate_eval.He4_Ca60__Ti64 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti49__n_Cr52 *= scor
        rate_eval.He4_Ti49__Cr53 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc56__Ti57 *= scor
        rate_eval.p_Sc56__He4_Ca53 *= scor
        rate_eval.p_Sc56__n_Ti56 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc37__Ti38 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K45__p_Ca48 *= scor
        rate_eval.He4_K45__Sc49 *= scor
        rate_eval.He4_K45__n_Sc48 *= scor

        scn_fac = ScreenFactors(1, 1, 2, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_He3__He4__weak__bet_pos_ *= scor

        scn_fac = ScreenFactors(2, 4, 21, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc49__V53 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne21__Na22 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca50__He4_K47 *= scor
        rate_eval.p_Ca50__n_Sc50 *= scor
        rate_eval.p_Ca50__Sc51 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc43__Ti44 *= scor
        rate_eval.p_Sc43__He4_Ca40 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc42__Ti43 *= scor
        rate_eval.p_Sc42__He4_Ca39 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc41__V45 *= scor
        rate_eval.He4_Sc41__p_Ti44 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc41__Ti42 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc40__Ti41 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc38__Ti39 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F25__n_Na28 *= scor
        rate_eval.He4_F25__Na29 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca59__Ti63 *= scor
        rate_eval.He4_Ca59__n_Ti62 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca57__Sc58 *= scor
        rate_eval.p_Ca57__He4_K54 *= scor
        rate_eval.p_Ca57__n_Sc57 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na20__Mg21 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na27__n_Al30 *= scor
        rate_eval.He4_Na27__Al31 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O27__Ne31 *= scor
        rate_eval.He4_O27__n_Ne30 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca54__Sc55 *= scor
        rate_eval.p_Ca54__n_Sc54 *= scor
        rate_eval.p_Ca54__He4_K51 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V48__p_Cr51 *= scor
        rate_eval.He4_V48__Mn52 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe58__Co59 *= scor
        rate_eval.p_Fe58__He4_Mn55 *= scor

        scn_fac = ScreenFactors(2, 4, 4, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Be11__n_C14 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca46__Ti50 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca45__Ti49 *= scor
        rate_eval.He4_Ca45__n_Ti48 *= scor

        scn_fac = ScreenFactors(1, 3, 3, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.t_Li7__n_Be9 *= scor
        rate_eval.t_Li7__n_n_He4_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 3, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Li7__B11 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca44__Ti48 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca42__Ti46 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca41__Sc42 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca40__Sc41 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca37__Ti41 *= scor
        rate_eval.He4_Ca37__p_Sc40 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca35__Ti39 *= scor
        rate_eval.He4_Ca35__p_Sc38 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca35__Sc36 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca34__Ti38 *= scor
        rate_eval.He4_Ca34__p_Sc37 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl46__n_K49 *= scor
        rate_eval.He4_Cl46__K50 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca34__Sc35 *= scor

        scn_fac = ScreenFactors(1, 1, 4, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Be11__He4_Li8 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca33__Ti37 *= scor
        rate_eval.He4_Ca33__p_Sc36 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K58__Sc62 *= scor
        rate_eval.He4_K58__n_Sc61 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K50__n_Ca50 *= scor
        rate_eval.p_K50__He4_Ar47 *= scor
        rate_eval.p_K50__Ca51 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P30__S31 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na29__Al33 *= scor
        rate_eval.He4_Na29__n_Al32 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si45__S49 *= scor
        rate_eval.He4_Si45__n_S48 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar38__K39 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr45__Mn46 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti47__Cr51 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S34__Cl35 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K38__Ca39 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K37__Ca38 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P28__Cl32 *= scor
        rate_eval.He4_P28__p_S31 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K36__Ca37 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K32__Sc36 *= scor
        rate_eval.He4_K32__p_Ca35 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar42__K43 *= scor
        rate_eval.p_Ar42__He4_Cl39 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar40__Ca44 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr51__Fe55 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar39__Ca43 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar37__Ca41 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar37__K38 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar35__K36 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si25__P26 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar33__K34 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar32__Ca36 *= scor
        rate_eval.He4_Ar32__p_K35 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar32__K33 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P33__He4_Si30 *= scor
        rate_eval.p_P33__S34 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P28__S29 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar31__K32 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne20__Mg24 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar30__Ca34 *= scor
        rate_eval.He4_Ar30__p_K33 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl49__Ar50 *= scor
        rate_eval.p_Cl49__He4_S46 *= scor
        rate_eval.p_Cl49__n_Ar49 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl39__K43 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 64)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr64__n_Mn64 *= scor
        rate_eval.p_Cr64__Mn65 *= scor
        rate_eval.p_Cr64__He4_V61 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl38__K42 *= scor
        rate_eval.He4_Cl38__n_K41 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl36__K40 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti39__V40 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg35__n_Al35 *= scor
        rate_eval.p_Mg35__He4_Na32 *= scor
        rate_eval.p_Mg35__Al36 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl33__K37 *= scor
        rate_eval.He4_Cl33__p_Ar36 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O21__Ne25 *= scor
        rate_eval.He4_O21__n_Ne24 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl32__Ar33 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl31__K35 *= scor
        rate_eval.He4_Cl31__p_Ar34 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl31__Ar32 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl30__Ar31 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl29__Ar30 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S49__Ar53 *= scor
        rate_eval.He4_S49__n_Ar52 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si34__P35 *= scor
        rate_eval.p_Si34__n_P34 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S47__Ar51 *= scor
        rate_eval.He4_S47__n_Ar50 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S44__Ar48 *= scor
        rate_eval.He4_S44__n_Ar47 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S44__Cl45 *= scor
        rate_eval.p_S44__n_Cl44 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar47__Ca51 *= scor
        rate_eval.He4_Ar47__n_Ca50 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K34__Ca35 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S36__Ar40 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg36__Si40 *= scor
        rate_eval.He4_Mg36__n_Si39 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na32__n_Mg32 *= scor
        rate_eval.p_Na32__Mg33 *= scor
        rate_eval.p_Na32__He4_Ne29 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar54__n_Ca57 *= scor
        rate_eval.He4_Ar54__Ca58 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S32__Ar36 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S32__Cl33 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S31__Cl32 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S29__Cl30 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl37__K41 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg33__n_Si36 *= scor
        rate_eval.He4_Mg33__Si37 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P35__Cl39 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P35__S36 *= scor
        rate_eval.p_P35__n_S35 *= scor
        rate_eval.p_P35__He4_Si32 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P32__Cl36 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P26__S27 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 70)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn70__Fe71 *= scor
        rate_eval.p_Mn70__He4_Cr67 *= scor
        rate_eval.p_Mn70__n_Fe70 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K55__n_Ca55 *= scor
        rate_eval.p_K55__Ca56 *= scor
        rate_eval.p_K55__He4_Ar52 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si41__S45 *= scor
        rate_eval.He4_Si41__n_S44 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si40__P41 *= scor
        rate_eval.p_Si40__n_P40 *= scor
        rate_eval.p_Si40__He4_Al37 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si34__S38 *= scor
        rate_eval.He4_Si34__n_S37 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si32__P33 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl47__Ar48 *= scor
        rate_eval.p_Cl47__n_Ar47 *= scor
        rate_eval.p_Cl47__He4_S44 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg37__n_Al37 *= scor
        rate_eval.p_Mg37__Al38 *= scor
        rate_eval.p_Mg37__He4_Na34 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si31__P32 *= scor
        rate_eval.p_Si31__n_P31 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si30__P31 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si28__P29 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si26__P27 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si24__P25 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al43__P47 *= scor
        rate_eval.He4_Al43__n_P46 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc59__He4_Ca56 *= scor
        rate_eval.p_Sc59__Ti60 *= scor
        rate_eval.p_Sc59__n_Ti59 *= scor

        scn_fac = ScreenFactors(2, 4, 7, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_N14__n_F17 *= scor
        rate_eval.He4_N14__F18 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr56__Fe60 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al30__P34 *= scor
        rate_eval.He4_Al30__n_P33 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti62__n_Cr65 *= scor
        rate_eval.He4_Ti62__Cr66 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al24__Si25 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti56__Cr60 *= scor
        rate_eval.He4_Ti56__n_Cr59 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg41__Si45 *= scor
        rate_eval.He4_Mg41__n_Si44 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al41__P45 *= scor
        rate_eval.He4_Al41__n_P44 *= scor

        scn_fac = ScreenFactors(1, 2, 3, 6)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_Li6__n_Be7 *= scor
        rate_eval.d_Li6__p_Li7 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr47__Mn48 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca43__Sc44 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 31)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg31__Si35 *= scor
        rate_eval.He4_Mg31__n_Si34 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe49__Co50 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K47__Sc51 *= scor
        rate_eval.He4_K47__n_Sc50 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg29__Si33 *= scor
        rate_eval.He4_Mg29__n_Si32 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg28__Si32 *= scor
        rate_eval.He4_Mg28__n_Si31 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 54)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe54__Co55 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg27__Al28 *= scor
        rate_eval.p_Mg27__n_Al27 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe46__Co47 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg26__Al27 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg23__Si27 *= scor
        rate_eval.He4_Mg23__p_Al26 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg23__Al24 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg22__Al23 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg21__Si25 *= scor
        rate_eval.He4_Mg21__p_Al24 *= scor

        scn_fac = ScreenFactors(2, 4, 2, 4)
        scor = screen_func(plasma_state, scn_fac)
        scn_fac2 = ScreenFactors(2, 4, 4, 8)
        scor2 = screen_func(plasma_state, scn_fac2)
        rate_eval.He4_He4_He4__C12 *= scor * scor2

        scn_fac = ScreenFactors(1, 1, 11, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na38__Mg39 *= scor
        rate_eval.p_Na38__n_Mg38 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc36__Ti37 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F21__n_Ne21 *= scor
        rate_eval.p_F21__Ne22 *= scor
        rate_eval.p_F21__He4_O18 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na25__Mg26 *= scor
        rate_eval.p_Na25__n_Mg25 *= scor
        rate_eval.p_Na25__He4_Ne22 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F15__p_Ne18 *= scor
        rate_eval.He4_F15__Na19 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na22__Mg23 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar50__Ca54 *= scor
        rate_eval.He4_Ar50__n_Ca53 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na21__Mg22 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na20__Al24 *= scor
        rate_eval.He4_Na20__p_Mg23 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S33__Cl34 *= scor

        scn_fac = ScreenFactors(2, 4, 10, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ne34__Mg38 *= scor
        rate_eval.He4_Ne34__n_Mg37 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si29__P30 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl44__Ar45 *= scor
        rate_eval.p_Cl44__n_Ar44 *= scor
        rate_eval.p_Cl44__He4_S41 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl52__n_K55 *= scor
        rate_eval.He4_Cl52__K56 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne19__Na20 *= scor

        scn_fac = ScreenFactors(1, 1, 25, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mn52__Fe53 *= scor

        scn_fac = ScreenFactors(1, 1, 10, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ne18__Na19 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na30__Al34 *= scor
        rate_eval.He4_Na30__n_Al33 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe51__Co52 *= scor

        scn_fac = ScreenFactors(2, 4, 19, 59)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_K59__Sc63 *= scor
        rate_eval.He4_K59__n_Sc62 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 35)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K35__Ca36 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 20)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O20__Ne24 *= scor
        rate_eval.He4_O20__n_Ne23 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar44__n_Ca47 *= scor
        rate_eval.He4_Ar44__Ca48 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P33__Cl37 *= scor

        scn_fac = ScreenFactors(1, 1, 7, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_N14__O15 *= scor
        rate_eval.p_N14__n_O14 *= scor

        scn_fac = ScreenFactors(1, 1, 6, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_C14__N15 *= scor

        scn_fac = ScreenFactors(1, 1, 6, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_C12__N13 *= scor

        scn_fac = ScreenFactors(1, 1, 6, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_C11__N12 *= scor

        scn_fac = ScreenFactors(1, 1, 5, 10)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_B10__C11 *= scor
        rate_eval.p_B10__He4_Be7 *= scor

        scn_fac = ScreenFactors(1, 1, 4, 10)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Be10__B11 *= scor
        rate_eval.p_Be10__He4_Li7 *= scor

        scn_fac = ScreenFactors(1, 1, 21, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Sc39__Ti40 *= scor

        scn_fac = ScreenFactors(1, 1, 4, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Be7__B8 *= scor

        scn_fac = ScreenFactors(2, 4, 3, 9)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Li9__B13 *= scor
        rate_eval.He4_Li9__n_B12 *= scor

        scn_fac = ScreenFactors(2, 4, 2, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_He3__Be7 *= scor

        scn_fac = ScreenFactors(1, 1, 1, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_t__He4 *= scor

        scn_fac = ScreenFactors(1, 2, 2, 4)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_d__Li6 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P27__S28 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C12__O16 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 62)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe62__n_Ni65 *= scor
        rate_eval.He4_Fe62__Ni66 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti46__V47 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca49__n_Ti52 *= scor
        rate_eval.He4_Ca49__Ti53 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg36__Al37 *= scor
        rate_eval.p_Mg36__n_Al36 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si28__S32 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V40__Cr41 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K39__Ca40 *= scor
        rate_eval.p_K39__He4_Ar36 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti50__V51 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 26)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si26__S30 *= scor
        rate_eval.He4_Si26__p_P29 *= scor

        scn_fac = ScreenFactors(2, 4, 23, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_V44__p_Cr47 *= scor
        rate_eval.He4_V44__Mn48 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 58)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn58__Co62 *= scor
        rate_eval.He4_Mn58__n_Co61 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si32__S36 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V45__Cr46 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al23__Si24 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P41__n_S41 *= scor
        rate_eval.p_P41__S42 *= scor
        rate_eval.p_P41__He4_Si38 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P39__n_S39 *= scor
        rate_eval.p_P39__He4_Si36 *= scor
        rate_eval.p_P39__S40 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 68)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr68__n_Fe71 *= scor
        rate_eval.He4_Cr68__Fe72 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si29__S33 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V44__Cr45 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 18)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O18__n_Ne21 *= scor
        rate_eval.He4_O18__Ne22 *= scor

        scn_fac = ScreenFactors(2, 4, 4, 9)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Be9__n_C12 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 34)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl34__Ar35 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 61)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe61__Ni65 *= scor
        rate_eval.He4_Fe61__n_Ni64 *= scor

        scn_fac = ScreenFactors(1, 1, 26, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Fe53__Co54 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P46__n_Cl49 *= scor
        rate_eval.He4_P46__Cl50 *= scor

        scn_fac = ScreenFactors(2, 4, 7, 12)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_N12__p_O15 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 71)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn71__Co75 *= scor
        rate_eval.He4_Mn71__n_Co74 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca48__Sc49 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg41__Al42 *= scor
        rate_eval.p_Mg41__n_Al41 *= scor
        rate_eval.p_Mg41__He4_Na38 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca55__n_Ti58 *= scor
        rate_eval.He4_Ca55__Ti59 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P38__Cl42 *= scor
        rate_eval.He4_P38__n_Cl41 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar46__K47 *= scor
        rate_eval.p_Ar46__n_K46 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 36)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si36__n_S39 *= scor
        rate_eval.He4_Si36__S40 *= scor

        scn_fac = ScreenFactors(1, 1, 3, 8)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Li8__n_He4_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 22, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ti50__Cr54 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar30__K31 *= scor

        scn_fac = ScreenFactors(1, 1, 7, 13)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_N13__O14 *= scor

        scn_fac = ScreenFactors(1, 3, 2, 4)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_t__Li7 *= scor

        scn_fac = ScreenFactors(2, 4, 2, 4)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.n_He4_He4__Be9 *= scor

        scn_fac = ScreenFactors(2, 4, 17, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cl48__K52 *= scor
        rate_eval.He4_Cl48__n_K51 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 40)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S40__n_Ar43 *= scor
        rate_eval.He4_S40__Ar44 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F23__Na27 *= scor
        rate_eval.He4_F23__n_Na26 *= scor

        scn_fac = ScreenFactors(1, 1, 15, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_P25__S26 *= scor

        scn_fac = ScreenFactors(2, 4, 11, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Na21__Al25 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P45__n_Cl48 *= scor
        rate_eval.He4_P45__Cl49 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C14__O18 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl33__Ar34 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 46)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca46__Sc47 *= scor

        scn_fac = ScreenFactors(1, 1, 2, 4)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.n_p_He4__Li6 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 53)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc53__n_V56 *= scor
        rate_eval.He4_Sc53__V57 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti48__V49 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca41__Ti45 *= scor

        scn_fac = ScreenFactors(2, 4, 15, 29)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_P29__Cl33 *= scor
        rate_eval.He4_P29__p_S32 *= scor

        scn_fac = ScreenFactors(1, 1, 8, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_O23__n_F23 *= scor
        rate_eval.p_O23__F24 *= scor

        scn_fac = ScreenFactors(2, 4, 6, 11)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_C11__p_N14 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 42)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr42__Mn43 *= scor

        scn_fac = ScreenFactors(2, 4, 3, 6)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Li6__B10 *= scor

        scn_fac = ScreenFactors(2, 4, 16, 33)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_S33__Ar37 *= scor

        scn_fac = ScreenFactors(1, 1, 3, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Li7__He4_He4 *= scor

        scn_fac = ScreenFactors(2, 4, 20, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ca56__Ti60 *= scor
        rate_eval.He4_Ca56__n_Ti59 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 15)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O15__Ne19 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si27__P28 *= scor

        scn_fac = ScreenFactors(2, 4, 13, 23)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Al23__p_Si26 *= scor
        rate_eval.He4_Al23__P27 *= scor

        scn_fac = ScreenFactors(2, 4, 7, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_N16__n_F19 *= scor

        scn_fac = ScreenFactors(1, 1, 14, 41)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Si41__P42 *= scor
        rate_eval.p_Si41__n_P41 *= scor

        scn_fac = ScreenFactors(1, 1, 9, 17)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_F17__Ne18 *= scor

        scn_fac = ScreenFactors(1, 1, 7, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_N16__n_O16 *= scor
        rate_eval.p_N16__He4_C13 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl28__Ar29 *= scor

        scn_fac = ScreenFactors(1, 1, 16, 27)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_S27__Cl28 *= scor

        scn_fac = ScreenFactors(1, 1, 5, 8)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_B8__C9 *= scor

        scn_fac = ScreenFactors(2, 4, 9, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_F22__Na26 *= scor
        rate_eval.He4_F22__n_Na25 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar49__n_Ca52 *= scor
        rate_eval.He4_Ar49__Ca53 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 21)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg21__Al22 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn55__Co59 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr48__Mn49 *= scor

        scn_fac = ScreenFactors(2, 4, 14, 30)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Si30__S34 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 56)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn56__Co60 *= scor

        scn_fac = ScreenFactors(1, 1, 17, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cl37__Ar38 *= scor

        scn_fac = ScreenFactors(1, 1, 19, 32)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_K32__Ca33 *= scor

        scn_fac = ScreenFactors(1, 1, 1, 2)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_d__He3 *= scor

        scn_fac = ScreenFactors(1, 1, 23, 47)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_V47__Cr48 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca38__Sc39 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 51)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar51__Ca55 *= scor
        rate_eval.He4_Ar51__n_Ca54 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 43)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr43__Mn44 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 60)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe60__Ni64 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 48)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar48__Ca52 *= scor
        rate_eval.He4_Ar48__n_Ca51 *= scor

        scn_fac = ScreenFactors(1, 1, 18, 49)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ar49__n_K49 *= scor
        rate_eval.p_Ar49__K50 *= scor
        rate_eval.p_Ar49__He4_Cl46 *= scor

        scn_fac = ScreenFactors(1, 1, 24, 44)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Cr44__Mn45 *= scor

        scn_fac = ScreenFactors(1, 1, 13, 22)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Al22__Si23 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 55)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe55__Ni59 *= scor

        scn_fac = ScreenFactors(1, 3, 1, 3)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.t_t__n_n_He4 *= scor

        scn_fac = ScreenFactors(2, 3, 3, 7)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He3_Li7__n_p_He4_He4 *= scor

        scn_fac = ScreenFactors(1, 2, 6, 14)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.d_C14__n_N15 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 39)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca39__Sc40 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 52)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr52__Fe56 *= scor

        scn_fac = ScreenFactors(1, 1, 20, 37)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ca37__Sc38 *= scor

        scn_fac = ScreenFactors(1, 1, 22, 45)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Ti45__V46 *= scor

        scn_fac = ScreenFactors(2, 4, 24, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Cr50__Fe54 *= scor

        scn_fac = ScreenFactors(2, 4, 18, 38)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Ar38__Ca42 *= scor

        scn_fac = ScreenFactors(2, 4, 12, 24)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mg24__Si28 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 25)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg25__Al26 *= scor

        scn_fac = ScreenFactors(2, 4, 25, 57)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Mn57__Co61 *= scor

        scn_fac = ScreenFactors(2, 4, 21, 50)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Sc50__V54 *= scor
        rate_eval.He4_Sc50__n_V53 *= scor

        scn_fac = ScreenFactors(1, 1, 12, 28)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Mg28__Al29 *= scor
        rate_eval.p_Mg28__n_Al28 *= scor

        scn_fac = ScreenFactors(2, 4, 26, 72)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_Fe72__n_Ni75 *= scor
        rate_eval.He4_Fe72__Ni76 *= scor

        scn_fac = ScreenFactors(2, 4, 8, 16)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.He4_O16__Ne20 *= scor

        scn_fac = ScreenFactors(1, 1, 11, 19)
        scor = screen_func(plasma_state, scn_fac)
        rate_eval.p_Na19__Mg20 *= scor

    jac = np.zeros((nnuc, nnuc), dtype=np.float64)

    jac[jn, jn] = (
       -5.00000000000000e-01*rho**2*Y[jp]**2*rate_eval.n_p_p__p_d
       -2*5.00000000000000e-01*rho**2*2*Y[jn]*Y[jhe4]*rate_eval.n_n_He4__He6
       -rho*Y[jb8]*rate_eval.n_B8__p_He4_He4
       -rho*Y[jfe56]*rate_eval.n_Fe56__He4_Cr53
       -rho*Y[jfe55]*rate_eval.n_Fe55__p_Mn55
       -rho*Y[jsc40]*rate_eval.n_Sc40__Sc41
       -rho*Y[jfe54]*rate_eval.n_Fe54__p_Mn54
       -rho*Y[jfe53]*rate_eval.n_Fe53__He4_Cr50
       -rho*Y[jfe53]*rate_eval.n_Fe53__p_Mn53
       -rho*Y[jal25]*rate_eval.n_Al25__Al26
       -rho*Y[jfe52]*rate_eval.n_Fe52__He4_Cr49
       -rho*Y[jfe51]*rate_eval.n_Fe51__He4_Cr48
       -rho*Y[jfe50]*rate_eval.n_Fe50__He4_Cr47
       -rho*Y[jfe49]*rate_eval.n_Fe49__He4_Cr46
       -rho*Y[jfe49]*rate_eval.n_Fe49__p_Mn49
       -rho*Y[jfe47]*rate_eval.n_Fe47__He4_Cr44
       -rho*Y[jfe46]*rate_eval.n_Fe46__He4_Cr43
       -rho*Y[jfe46]*rate_eval.n_Fe46__p_Mn46
       -rho*Y[jmn52]*rate_eval.n_Mn52__He4_V49
       -rho*Y[jmn52]*rate_eval.n_Mn52__p_Cr52
       -rho*Y[jmn51]*rate_eval.n_Mn51__p_Cr51
       -rho*Y[jmn50]*rate_eval.n_Mn50__He4_V47
       -rho*Y[jcl37]*rate_eval.n_Cl37__Cl38
       -rho*Y[jmn48]*rate_eval.n_Mn48__He4_V45
       -rho*Y[jne20]*rate_eval.n_Ne20__Ne21
       -rho*Y[jmn47]*rate_eval.n_Mn47__p_Cr47
       -rho*Y[jmn46]*rate_eval.n_Mn46__He4_V43
       -rho*Y[jmn46]*rate_eval.n_Mn46__p_Cr46
       -rho*Y[jmn45]*rate_eval.n_Mn45__p_Cr45
       -rho*Y[jf26]*rate_eval.n_F26__F27
       -rho*Y[jca50]*rate_eval.n_Ca50__Ca51
       -rho*Y[jo18]*rate_eval.n_O18__O19
       -rho*Y[jcr55]*rate_eval.n_Cr55__He4_Ti52
       -rho*Y[jcr51]*rate_eval.n_Cr51__He4_Ti48
       -rho*Y[jcr50]*rate_eval.n_Cr50__He4_Ti47
       -rho*Y[jcr48]*rate_eval.n_Cr48__p_V48
       -rho*Y[jcr46]*rate_eval.n_Cr46__He4_Ti43
       -rho*Y[jb13]*rate_eval.n_B13__B14
       -rho*Y[jcr45]*rate_eval.n_Cr45__He4_Ti42
       -rho*Y[jcr43]*rate_eval.n_Cr43__p_V43
       -rho*Y[jcr42]*rate_eval.n_Cr42__He4_Ti39
       -rho*Y[jcr42]*rate_eval.n_Cr42__p_V42
       -rho*Y[jcr41]*rate_eval.n_Cr41__He4_Ti38
       -rho*Y[jcr49]*rate_eval.n_Cr49__p_V49
       -rho*Y[jcr53]*rate_eval.n_Cr53__He4_Ti50
       -rho*Y[jmn69]*rate_eval.n_Mn69__Mn70
       -rho*Y[jv50]*rate_eval.n_V50__p_Ti50
       -rho*Y[jv46]*rate_eval.n_V46__He4_Sc43
       -rho*Y[jv46]*rate_eval.n_V46__p_Ti46
       -rho*Y[jv44]*rate_eval.n_V44__He4_Sc41
       -rho*Y[jv44]*rate_eval.n_V44__p_Ti44
       -rho*Y[jv43]*rate_eval.n_V43__p_Ti43
       -rho*Y[jv42]*rate_eval.n_V42__He4_Sc39
       -rho*Y[jv41]*rate_eval.n_V41__He4_Sc38
       -rho*Y[jv40]*rate_eval.n_V40__p_Ti40
       -rho*Y[jo12]*rate_eval.n_O12__O13
       -rho*Y[jna33]*rate_eval.n_Na33__Na34
       -rho*Y[jti51]*rate_eval.n_Ti51__He4_Ca48
       -rho*Y[jti49]*rate_eval.n_Ti49__He4_Ca46
       -rho*Y[jna35]*rate_eval.n_Na35__Na36
       -rho*Y[jti45]*rate_eval.n_Ti45__p_Sc45
       -rho*Y[jti43]*rate_eval.n_Ti43__He4_Ca40
       -rho*Y[jti41]*rate_eval.n_Ti41__He4_Ca38
       -rho*Y[jti41]*rate_eval.n_Ti41__p_Sc41
       -rho*Y[jk55]*rate_eval.n_K55__K56
       -rho*Y[jti39]*rate_eval.n_Ti39__p_Sc39
       -rho*Y[jti38]*rate_eval.n_Ti38__He4_Ca35
       -rho*Y[jti38]*rate_eval.n_Ti38__p_Sc38
       -rho*Y[jfe48]*rate_eval.n_Fe48__p_Mn48
       -rho*Y[jmn53]*rate_eval.n_Mn53__p_Cr53
       -rho*Y[jcr41]*rate_eval.n_Cr41__Cr42
       -rho*Y[jar36]*rate_eval.n_Ar36__He4_S33
       -rho*Y[jsc46]*rate_eval.n_Sc46__p_Ca46
       -rho*Y[jv56]*rate_eval.n_V56__V57
       -rho*Y[jsi24]*rate_eval.n_Si24__p_Al24
       -rho*Y[jmg22]*rate_eval.n_Mg22__He4_Ne19
       -rho*Y[jsc45]*rate_eval.n_Sc45__p_Ca45
       -rho*Y[jsc44]*rate_eval.n_Sc44__p_Ca44
       -rho*Y[jsc43]*rate_eval.n_Sc43__He4_K40
       -rho*Y[jsc43]*rate_eval.n_Sc43__p_Ca43
       -rho*Y[jsc42]*rate_eval.n_Sc42__He4_K39
       -rho*Y[jsc42]*rate_eval.n_Sc42__p_Ca42
       -rho*Y[jsc41]*rate_eval.n_Sc41__He4_K38
       -rho*Y[jsc39]*rate_eval.n_Sc39__He4_K36
       -rho*Y[jti47]*rate_eval.n_Ti47__He4_Ca44
       -rho*Y[jsc37]*rate_eval.n_Sc37__He4_K34
       -rho*Y[jsc35]*rate_eval.n_Sc35__He4_K32
       -rho*Y[jsc35]*rate_eval.n_Sc35__p_Ca35
       -rho*Y[jfe48]*rate_eval.n_Fe48__Fe49
       -rho*Y[jcr46]*rate_eval.n_Cr46__p_V46
       -rho*Y[jsi24]*rate_eval.n_Si24__He4_Mg21
       -rho*Y[jmn43]*rate_eval.n_Mn43__He4_V40
       -rho*Y[jca40]*rate_eval.n_Ca40__He4_Ar37
       -rho*Y[jca38]*rate_eval.n_Ca38__p_K38
       -rho*Y[jca37]*rate_eval.n_Ca37__He4_Ar34
       -rho*Y[jca37]*rate_eval.n_Ca37__p_K37
       -rho*Y[jca36]*rate_eval.n_Ca36__p_K36
       -rho*Y[jcl35]*rate_eval.n_Cl35__p_S35
       -rho*Y[jca35]*rate_eval.n_Ca35__He4_Ar32
       -rho*Y[jca35]*rate_eval.n_Ca35__p_K35
       -rho*Y[jca34]*rate_eval.n_Ca34__He4_Ar31
       -rho*Y[jca34]*rate_eval.n_Ca34__p_K34
       -rho*Y[jo14]*rate_eval.n_O14__O15
       -rho*Y[jk31]*rate_eval.n_K31__K32
       -rho*Y[jfe50]*rate_eval.n_Fe50__Fe51
       -rho*Y[jcr44]*rate_eval.n_Cr44__He4_Ti41
       -rho*Y[jv45]*rate_eval.n_V45__He4_Sc42
       -rho*Y[jk40]*rate_eval.n_K40__He4_Cl37
       -rho*Y[jk40]*rate_eval.n_K40__p_Ar40
       -rho*Y[jk39]*rate_eval.n_K39__p_Ar39
       -rho*Y[jk38]*rate_eval.n_K38__p_Ar38
       -rho*Y[jar31]*rate_eval.n_Ar31__He4_S28
       -rho*Y[jk37]*rate_eval.n_K37__He4_Cl34
       -rho*Y[jk36]*rate_eval.n_K36__He4_Cl33
       -rho*Y[jk36]*rate_eval.n_K36__p_Ar36
       -rho*Y[jsc46]*rate_eval.n_Sc46__He4_K43
       -rho*Y[jk35]*rate_eval.n_K35__p_Ar35
       -rho*Y[jk33]*rate_eval.n_K33__p_Ar33
       -rho*Y[jk32]*rate_eval.n_K32__He4_Cl29
       -rho*Y[jk32]*rate_eval.n_K32__p_Ar32
       -rho*Y[jk31]*rate_eval.n_K31__p_Ar31
       -rho*Y[jti39]*rate_eval.n_Ti39__He4_Ca36
       -rho*Y[jca36]*rate_eval.n_Ca36__He4_Ar33
       -rho*Y[jd]*rate_eval.n_d__t
       -rho*Y[jv39]*rate_eval.n_V39__V40
       -rho*Y[jmn52]*rate_eval.n_Mn52__Mn53
       -rho*Y[jmn49]*rate_eval.n_Mn49__He4_V46
       -rho*Y[jar37]*rate_eval.n_Ar37__p_Cl37
       -rho*Y[jar35]*rate_eval.n_Ar35__He4_S32
       -rho*Y[jar35]*rate_eval.n_Ar35__p_Cl35
       -rho*Y[jar34]*rate_eval.n_Ar34__p_Cl34
       -rho*Y[jar33]*rate_eval.n_Ar33__p_Cl33
       -rho*Y[jar32]*rate_eval.n_Ar32__He4_S29
       -rho*Y[jfe75]*rate_eval.n_Fe75__Fe76
       -rho*Y[jar32]*rate_eval.n_Ar32__p_Cl32
       -rho*Y[jar31]*rate_eval.n_Ar31__p_Cl31
       -rho*Y[jar30]*rate_eval.n_Ar30__He4_S27
       -rho*Y[jar30]*rate_eval.n_Ar30__p_Cl30
       -rho*Y[jar29]*rate_eval.n_Ar29__He4_S26
       -rho*Y[jar29]*rate_eval.n_Ar29__p_Cl29
       -rho*Y[jti58]*rate_eval.n_Ti58__Ti59
       -rho*Y[jar34]*rate_eval.n_Ar34__Ar35
       -rho*Y[jfe72]*rate_eval.n_Fe72__Fe73
       -rho*Y[jcl36]*rate_eval.n_Cl36__p_S36
       -rho*Y[jcl35]*rate_eval.n_Cl35__He4_P32
       -rho*Y[jc11]*rate_eval.n_C11__He4_He4_He4
       -rho*Y[jcl34]*rate_eval.n_Cl34__He4_P31
       -rho*Y[jcl34]*rate_eval.n_Cl34__p_S34
       -rho*Y[jcl33]*rate_eval.n_Cl33__He4_P30
       -rho*Y[jcl33]*rate_eval.n_Cl33__p_S33
       -rho*Y[jcl31]*rate_eval.n_Cl31__p_S31
       -rho*Y[jcl29]*rate_eval.n_Cl29__He4_P26
       -rho*Y[jcl29]*rate_eval.n_Cl29__p_S29
       -rho*Y[jv49]*rate_eval.n_V49__p_Ti49
       -rho*Y[jcl28]*rate_eval.n_Cl28__He4_P25
       -rho*Y[jcr57]*rate_eval.n_Cr57__Cr58
       -rho*Y[jca52]*rate_eval.n_Ca52__Ca53
       -rho*Y[jsi43]*rate_eval.n_Si43__Si44
       -rho*Y[js35]*rate_eval.n_S35__He4_Si32
       -rho*Y[jal36]*rate_eval.n_Al36__Al37
       -rho*Y[js33]*rate_eval.n_S33__He4_Si30
       -rho*Y[js30]*rate_eval.n_S30__He4_Si27
       -rho*Y[js30]*rate_eval.n_S30__p_P30
       -rho*Y[jcr43]*rate_eval.n_Cr43__He4_Ti40
       -rho*Y[js28]*rate_eval.n_S28__He4_Si25
       -rho*Y[js26]*rate_eval.n_S26__He4_Si23
       -rho*Y[jsi33]*rate_eval.n_Si33__Si34
       -rho*Y[js33]*rate_eval.n_S33__p_P33
       -rho*Y[jti54]*rate_eval.n_Ti54__Ti55
       -rho*Y[jp32]*rate_eval.n_P32__p_Si32
       -rho*Y[jf25]*rate_eval.n_F25__F26
       -rho*Y[jv47]*rate_eval.n_V47__He4_Sc44
       -rho*Y[jp28]*rate_eval.n_P28__p_Si28
       -rho*Y[jp27]*rate_eval.n_P27__He4_Al24
       -rho*Y[jp27]*rate_eval.n_P27__p_Si27
       -rho*Y[jcr47]*rate_eval.n_Cr47__He4_Ti44
       -rho*Y[jp26]*rate_eval.n_P26__He4_Al23
       -rho*Y[jp26]*rate_eval.n_P26__p_Si26
       -rho*Y[jp24]*rate_eval.n_P24__He4_Al21
       -rho*Y[jp24]*rate_eval.n_P24__p_Si24
       -rho*Y[jmn54]*rate_eval.n_Mn54__p_Cr54
       -rho*Y[jcr47]*rate_eval.n_Cr47__p_V47
       -rho*Y[jmn51]*rate_eval.n_Mn51__He4_V48
       -rho*Y[jti37]*rate_eval.n_Ti37__He4_Ca34
       -rho*Y[jo24]*rate_eval.n_O24__O25
       -rho*Y[jar35]*rate_eval.n_Ar35__Ar36
       -rho*Y[jsi25]*rate_eval.n_Si25__p_Al25
       -rho*Y[jsi23]*rate_eval.n_Si23__p_Al23
       -rho*Y[jsi22]*rate_eval.n_Si22__He4_Mg19
       -rho*Y[jsi22]*rate_eval.n_Si22__p_Al22
       -rho*Y[jv48]*rate_eval.n_V48__p_Ti48
       -rho*Y[jsi44]*rate_eval.n_Si44__Si45
       -rho*Y[jcr66]*rate_eval.n_Cr66__Cr67
       -rho*Y[jti44]*rate_eval.n_Ti44__p_Sc44
       -rho*Y[jti59]*rate_eval.n_Ti59__Ti60
       -rho*Y[jal26]*rate_eval.n_Al26__He4_Na23
       -rho*Y[jal26]*rate_eval.n_Al26__p_Mg26
       -rho*Y[jal25]*rate_eval.n_Al25__p_Mg25
       -rho*Y[jal23]*rate_eval.n_Al23__He4_Na20
       -rho*Y[jal22]*rate_eval.n_Al22__He4_Na19
       -rho*Y[jal22]*rate_eval.n_Al22__p_Mg22
       -rho*Y[jsc48]*rate_eval.n_Sc48__p_Ca48
       -rho*Y[jmn47]*rate_eval.n_Mn47__He4_V44
       -rho*Y[jna19]*rate_eval.n_Na19__p_Ne19
       -rho*Y[jp29]*rate_eval.n_P29__He4_Al26
       -rho*Y[js29]*rate_eval.n_S29__He4_Si26
       -rho*Y[jk58]*rate_eval.n_K58__K59
       -rho*Y[jfe54]*rate_eval.n_Fe54__He4_Cr51
       -rho*Y[jmn68]*rate_eval.n_Mn68__Mn69
       -rho*Y[jfe55]*rate_eval.n_Fe55__He4_Cr52
       -rho*Y[jcl43]*rate_eval.n_Cl43__Cl44
       -rho*Y[jmg23]*rate_eval.n_Mg23__C12_C12
       -rho*Y[jmg23]*rate_eval.n_Mg23__He4_Ne20
       -rho*Y[jfe66]*rate_eval.n_Fe66__Fe67
       -rho*Y[jcl30]*rate_eval.n_Cl30__p_S30
       -rho*Y[jmg21]*rate_eval.n_Mg21__He4_Ne18
       -rho*Y[jmg20]*rate_eval.n_Mg20__p_Na20
       -rho*Y[jv43]*rate_eval.n_V43__He4_Sc40
       -rho*Y[jn18]*rate_eval.n_N18__N19
       -rho*Y[jmn43]*rate_eval.n_Mn43__p_Cr43
       -rho*Y[js31]*rate_eval.n_S31__p_P31
       -rho*Y[jar39]*rate_eval.n_Ar39__He4_S36
       -rho*Y[jti42]*rate_eval.n_Ti42__p_Sc42
       -rho*Y[jfe50]*rate_eval.n_Fe50__p_Mn50
       -rho*Y[jsc43]*rate_eval.n_Sc43__Sc44
       -rho*Y[js26]*rate_eval.n_S26__p_P26
       -rho*Y[jna21]*rate_eval.n_Na21__He4_F18
       -rho*Y[jna20]*rate_eval.n_Na20__He4_F17
       -rho*Y[jv40]*rate_eval.n_V40__He4_Sc37
       -rho*Y[jmn54]*rate_eval.n_Mn54__He4_V51
       -rho*Y[jcl32]*rate_eval.n_Cl32__He4_P29
       -rho*Y[jsc40]*rate_eval.n_Sc40__p_Ca40
       -rho*Y[jti45]*rate_eval.n_Ti45__He4_Ca42
       -rho*Y[jcl38]*rate_eval.n_Cl38__He4_P35
       -rho*Y[jsi27]*rate_eval.n_Si27__Si28
       -rho*Y[jna30]*rate_eval.n_Na30__Na31
       -rho*Y[jsi25]*rate_eval.n_Si25__He4_Mg22
       -rho*Y[jne18]*rate_eval.n_Ne18__He4_O15
       -rho*Y[jne18]*rate_eval.n_Ne18__p_F18
       -rho*Y[jbe7]*rate_eval.n_Be7__He4_He4
       -rho*Y[jne16]*rate_eval.n_Ne16__p_F16
       -rho*Y[js30]*rate_eval.n_S30__S31
       -rho*Y[jsi26]*rate_eval.n_Si26__p_Al26
       -rho*Y[jf18]*rate_eval.n_F18__He4_N15
       -rho*Y[jf15]*rate_eval.n_F15__He4_N12
       -rho*Y[jal41]*rate_eval.n_Al41__Al42
       -rho*Y[jf14]*rate_eval.n_F14__He4_N11
       -rho*Y[jca33]*rate_eval.n_Ca33__p_K33
       -rho*Y[jk33]*rate_eval.n_K33__He4_Cl30
       -rho*Y[jo14]*rate_eval.n_O14__He4_C11
       -rho*Y[jca33]*rate_eval.n_Ca33__He4_Ar30
       -rho*Y[jo13]*rate_eval.n_O13__He4_C10
       -rho*Y[jo13]*rate_eval.n_O13__p_N13
       -rho*Y[jo12]*rate_eval.n_O12__p_N12
       -rho*Y[jsc37]*rate_eval.n_Sc37__p_Ca37
       -rho*Y[jmg19]*rate_eval.n_Mg19__He4_Ne16
       -rho*Y[jn14]*rate_eval.n_N14__p_C14
       -rho*Y[jv39]*rate_eval.n_V39__p_Ti39
       -rho*Y[jmn50]*rate_eval.n_Mn50__Mn51
       -rho*Y[jc11]*rate_eval.n_C11__p_B11
       -rho*Y[jk35]*rate_eval.n_K35__He4_Cl32
       -rho*Y[jti42]*rate_eval.n_Ti42__He4_Ca39
       -rho*Y[jfe48]*rate_eval.n_Fe48__He4_Cr45
       -rho*Y[jmn53]*rate_eval.n_Mn53__He4_V50
       -rho*Y[jmn65]*rate_eval.n_Mn65__Mn66
       -rho*Y[jli6]*rate_eval.n_Li6__He4_t
       -rho*Y[jhe3]*rate_eval.n_He3__p_t
       -rho*Y[jcr61]*rate_eval.n_Cr61__Cr62
       -rho*Y[jv50]*rate_eval.n_V50__He4_Sc47
       -rho*Y[jfe71]*rate_eval.n_Fe71__Fe72
       -rho*Y[jcl28]*rate_eval.n_Cl28__Cl29
       -rho*Y[jfe70]*rate_eval.n_Fe70__Fe71
       -rho*Y[jf16]*rate_eval.n_F16__p_O16
       -rho*Y[jmn62]*rate_eval.n_Mn62__Mn63
       -rho*Y[jfe69]*rate_eval.n_Fe69__Fe70
       -rho*Y[jfe68]*rate_eval.n_Fe68__Fe69
       -rho*Y[jfe67]*rate_eval.n_Fe67__Fe68
       -rho*Y[jna21]*rate_eval.n_Na21__p_Ne21
       -rho*Y[jfe65]*rate_eval.n_Fe65__Fe66
       -rho*Y[jfe63]*rate_eval.n_Fe63__Fe64
       -rho*Y[jfe62]*rate_eval.n_Fe62__Fe63
       -rho*Y[js29]*rate_eval.n_S29__p_P29
       -rho*Y[jfe58]*rate_eval.n_Fe58__Fe59
       -rho*Y[jfe57]*rate_eval.n_Fe57__Fe58
       -rho*Y[jfe56]*rate_eval.n_Fe56__Fe57
       -rho*Y[jfe54]*rate_eval.n_Fe54__Fe55
       -rho*Y[jfe49]*rate_eval.n_Fe49__Fe50
       -rho*Y[jne30]*rate_eval.n_Ne30__Ne31
       -rho*Y[jfe47]*rate_eval.n_Fe47__Fe48
       -rho*Y[jcr55]*rate_eval.n_Cr55__Cr56
       -rho*Y[jmn72]*rate_eval.n_Mn72__Mn73
       -rho*Y[jmn71]*rate_eval.n_Mn71__Mn72
       -rho*Y[jmn70]*rate_eval.n_Mn70__Mn71
       -rho*Y[jmn67]*rate_eval.n_Mn67__Mn68
       -rho*Y[jmn63]*rate_eval.n_Mn63__Mn64
       -rho*Y[jfe51]*rate_eval.n_Fe51__p_Mn51
       -rho*Y[jmn60]*rate_eval.n_Mn60__Mn61
       -rho*Y[jmn59]*rate_eval.n_Mn59__Mn60
       -rho*Y[jmn58]*rate_eval.n_Mn58__Mn59
       -rho*Y[jmn56]*rate_eval.n_Mn56__Mn57
       -rho*Y[jmn55]*rate_eval.n_Mn55__Mn56
       -rho*Y[jmn49]*rate_eval.n_Mn49__Mn50
       -rho*Y[jmn44]*rate_eval.n_Mn44__Mn45
       -rho*Y[jcr69]*rate_eval.n_Cr69__Cr70
       -rho*Y[jcl40]*rate_eval.n_Cl40__Cl41
       -rho*Y[jcr62]*rate_eval.n_Cr62__Cr63
       -rho*Y[jca43]*rate_eval.n_Ca43__He4_Ar40
       -rho*Y[jfe51]*rate_eval.n_Fe51__Fe52
       -rho*Y[jcr60]*rate_eval.n_Cr60__Cr61
       -rho*Y[jcr59]*rate_eval.n_Cr59__Cr60
       -rho*Y[jcr56]*rate_eval.n_Cr56__Cr57
       -rho*Y[jmn49]*rate_eval.n_Mn49__p_Cr49
       -rho*Y[jcr53]*rate_eval.n_Cr53__Cr54
       -rho*Y[jo17]*rate_eval.n_O17__O18
       -rho*Y[jcr48]*rate_eval.n_Cr48__Cr49
       -rho*Y[jne19]*rate_eval.n_Ne19__He4_O16
       -rho*Y[jcr46]*rate_eval.n_Cr46__Cr47
       -rho*Y[jcr45]*rate_eval.n_Cr45__Cr46
       -rho*Y[jcr44]*rate_eval.n_Cr44__Cr45
       -rho*Y[jsc55]*rate_eval.n_Sc55__Sc56
       -rho*Y[jcr43]*rate_eval.n_Cr43__Cr44
       -rho*Y[jmg27]*rate_eval.n_Mg27__Mg28
       -rho*Y[jal37]*rate_eval.n_Al37__Al38
       -rho*Y[jv62]*rate_eval.n_V62__V63
       -rho*Y[jv59]*rate_eval.n_V59__V60
       -rho*Y[jv55]*rate_eval.n_V55__V56
       -rho*Y[jv53]*rate_eval.n_V53__V54
       -rho*Y[jv51]*rate_eval.n_V51__V52
       -rho*Y[jv49]*rate_eval.n_V49__V50
       -rho*Y[jv48]*rate_eval.n_V48__V49
       -rho*Y[js28]*rate_eval.n_S28__S29
       -rho*Y[jv47]*rate_eval.n_V47__V48
       -rho*Y[jv46]*rate_eval.n_V46__V47
       -rho*Y[jv45]*rate_eval.n_V45__V46
       -rho*Y[jv42]*rate_eval.n_V42__V43
       -rho*Y[jfe57]*rate_eval.n_Fe57__He4_Cr54
       -rho*Y[jv41]*rate_eval.n_V41__V42
       -rho*Y[jmn54]*rate_eval.n_Mn54__Mn55
       -rho*Y[jti64]*rate_eval.n_Ti64__Ti65
       -rho*Y[jne16]*rate_eval.n_Ne16__He4_O13
       -rho*Y[jti60]*rate_eval.n_Ti60__Ti61
       -rho*Y[jti55]*rate_eval.n_Ti55__Ti56
       -rho*Y[jti57]*rate_eval.n_Ti57__Ti58
       -rho*Y[jti52]*rate_eval.n_Ti52__Ti53
       -rho*Y[jv43]*rate_eval.n_V43__V44
       -rho*Y[jti49]*rate_eval.n_Ti49__Ti50
       -rho*Y[jti47]*rate_eval.n_Ti47__Ti48
       -rho*Y[jti46]*rate_eval.n_Ti46__Ti47
       -rho*Y[jti45]*rate_eval.n_Ti45__Ti46
       -rho*Y[jti44]*rate_eval.n_Ti44__Ti45
       -rho*Y[jmn44]*rate_eval.n_Mn44__p_Cr44
       -rho*Y[jti43]*rate_eval.n_Ti43__Ti44
       -rho*Y[jti41]*rate_eval.n_Ti41__Ti42
       -rho*Y[jti40]*rate_eval.n_Ti40__Ti41
       -rho*Y[jti38]*rate_eval.n_Ti38__Ti39
       -rho*Y[jti37]*rate_eval.n_Ti37__Ti38
       -rho*Y[jar34]*rate_eval.n_Ar34__He4_S31
       -rho*Y[jsc62]*rate_eval.n_Sc62__Sc63
       -rho*Y[jsc59]*rate_eval.n_Sc59__Sc60
       -rho*Y[jsc58]*rate_eval.n_Sc58__Sc59
       -rho*Y[jsc56]*rate_eval.n_Sc56__Sc57
       -rho*Y[jsc54]*rate_eval.n_Sc54__Sc55
       -rho*Y[jsc53]*rate_eval.n_Sc53__Sc54
       -rho*Y[jsc50]*rate_eval.n_Sc50__Sc51
       -rho*Y[jsc49]*rate_eval.n_Sc49__Sc50
       -rho*Y[jsc48]*rate_eval.n_Sc48__Sc49
       -rho*Y[jsc46]*rate_eval.n_Sc46__Sc47
       -rho*Y[jv47]*rate_eval.n_V47__p_Ti47
       -rho*Y[jsc45]*rate_eval.n_Sc45__Sc46
       -rho*Y[jcr63]*rate_eval.n_Cr63__Cr64
       -rho*Y[jsc42]*rate_eval.n_Sc42__Sc43
       -rho*Y[jsc41]*rate_eval.n_Sc41__Sc42
       -rho*Y[jsc39]*rate_eval.n_Sc39__Sc40
       -rho*Y[jsc38]*rate_eval.n_Sc38__Sc39
       -rho*Y[jsc37]*rate_eval.n_Sc37__Sc38
       -rho*Y[jca60]*rate_eval.n_Ca60__Ca61
       -rho*Y[jar39]*rate_eval.n_Ar39__Ar40
       -rho*Y[jca57]*rate_eval.n_Ca57__Ca58
       -rho*Y[jca56]*rate_eval.n_Ca56__Ca57
       -rho*Y[jca55]*rate_eval.n_Ca55__Ca56
       -rho*Y[jca54]*rate_eval.n_Ca54__Ca55
       -rho*Y[jca53]*rate_eval.n_Ca53__Ca54
       -rho*Y[jca51]*rate_eval.n_Ca51__Ca52
       -rho*Y[jca49]*rate_eval.n_Ca49__Ca50
       -rho*Y[jca46]*rate_eval.n_Ca46__Ca47
       -rho*Y[jcr51]*rate_eval.n_Cr51__Cr52
       -rho*Y[jca41]*rate_eval.n_Ca41__Ca42
       -rho*Y[jf16]*rate_eval.n_F16__He4_N13
       -rho*Y[jca40]*rate_eval.n_Ca40__Ca41
       -rho*Y[jca37]*rate_eval.n_Ca37__Ca38
       -rho*Y[jna27]*rate_eval.n_Na27__Na28
       -rho*Y[jca36]*rate_eval.n_Ca36__Ca37
       -rho*Y[jfe47]*rate_eval.n_Fe47__p_Mn47
       -rho*Y[jk56]*rate_eval.n_K56__K57
       -rho*Y[jk53]*rate_eval.n_K53__K54
       -rho*Y[jk52]*rate_eval.n_K52__K53
       -rho*Y[jk50]*rate_eval.n_K50__K51
       -rho*Y[jk46]*rate_eval.n_K46__K47
       -rho*Y[jk45]*rate_eval.n_K45__K46
       -rho*Y[jk44]*rate_eval.n_K44__K45
       -rho*Y[jk39]*rate_eval.n_K39__He4_Cl36
       -rho*Y[jk43]*rate_eval.n_K43__K44
       -rho*Y[jal28]*rate_eval.n_Al28__Al29
       -rho*Y[jk41]*rate_eval.n_K41__K42
       -rho*Y[jk40]*rate_eval.n_K40__K41
       -rho*Y[jmn45]*rate_eval.n_Mn45__Mn46
       -rho*Y[jk37]*rate_eval.n_K37__K38
       -rho*Y[jk36]*rate_eval.n_K36__K37
       -rho*Y[jo15]*rate_eval.n_O15__He4_C12
       -rho*Y[jk34]*rate_eval.n_K34__K35
       -rho*Y[jk33]*rate_eval.n_K33__K34
       -rho*Y[jsi40]*rate_eval.n_Si40__Si41
       -rho*Y[jk32]*rate_eval.n_K32__K33
       -rho*Y[jar51]*rate_eval.n_Ar51__Ar52
       -rho*Y[jar47]*rate_eval.n_Ar47__Ar48
       -rho*Y[jar46]*rate_eval.n_Ar46__Ar47
       -rho*Y[jf18]*rate_eval.n_F18__p_O18
       -rho*Y[jar45]*rate_eval.n_Ar45__Ar46
       -rho*Y[jar44]*rate_eval.n_Ar44__Ar45
       -rho*Y[jli7]*rate_eval.n_Li7__Li8
       -rho*Y[jar42]*rate_eval.n_Ar42__Ar43
       -rho*Y[jmg26]*rate_eval.n_Mg26__Mg27
       -rho*Y[jar40]*rate_eval.n_Ar40__Ar41
       -rho*Y[jar32]*rate_eval.n_Ar32__Ar33
       -rho*Y[jar31]*rate_eval.n_Ar31__Ar32
       -rho*Y[jar29]*rate_eval.n_Ar29__Ar30
       -rho*Y[jcl51]*rate_eval.n_Cl51__Cl52
       -rho*Y[jcl49]*rate_eval.n_Cl49__Cl50
       -rho*Y[jcl46]*rate_eval.n_Cl46__Cl47
       -rho*Y[jcl45]*rate_eval.n_Cl45__Cl46
       -rho*Y[jcl44]*rate_eval.n_Cl44__Cl45
       -rho*Y[jcl42]*rate_eval.n_Cl42__Cl43
       -rho*Y[jcl33]*rate_eval.n_Cl33__Cl34
       -rho*Y[jmg32]*rate_eval.n_Mg32__Mg33
       -rho*Y[jca44]*rate_eval.n_Ca44__Ca45
       -rho*Y[jcl32]*rate_eval.n_Cl32__Cl33
       -rho*Y[jk47]*rate_eval.n_K47__K48
       -rho*Y[js47]*rate_eval.n_S47__S48
       -rho*Y[js44]*rate_eval.n_S44__S45
       -rho*Y[jfe73]*rate_eval.n_Fe73__Fe74
       -rho*Y[jk49]*rate_eval.n_K49__K50
       -rho*Y[jmg28]*rate_eval.n_Mg28__Mg29
       -rho*Y[js42]*rate_eval.n_S42__S43
       -rho*Y[js40]*rate_eval.n_S40__S41
       -rho*Y[js38]*rate_eval.n_S38__S39
       -rho*Y[js34]*rate_eval.n_S34__S35
       -rho*Y[js33]*rate_eval.n_S33__S34
       -rho*Y[jar52]*rate_eval.n_Ar52__Ar53
       -rho*Y[js32]*rate_eval.n_S32__S33
       -rho*Y[js27]*rate_eval.n_S27__S28
       -rho*Y[js26]*rate_eval.n_S26__S27
       -rho*Y[jp45]*rate_eval.n_P45__P46
       -rho*Y[jp44]*rate_eval.n_P44__P45
       -rho*Y[jp42]*rate_eval.n_P42__P43
       -rho*Y[jp41]*rate_eval.n_P41__P42
       -rho*Y[jna31]*rate_eval.n_Na31__Na32
       -rho*Y[jp38]*rate_eval.n_P38__P39
       -rho*Y[jp36]*rate_eval.n_P36__P37
       -rho*Y[jp35]*rate_eval.n_P35__P36
       -rho*Y[jp33]*rate_eval.n_P33__P34
       -rho*Y[jca38]*rate_eval.n_Ca38__Ca39
       -rho*Y[jp32]*rate_eval.n_P32__P33
       -rho*Y[jmn45]*rate_eval.n_Mn45__He4_V42
       -rho*Y[jcl32]*rate_eval.n_Cl32__p_S32
       -rho*Y[jar30]*rate_eval.n_Ar30__Ar31
       -rho*Y[jp28]*rate_eval.n_P28__P29
       -rho*Y[jp27]*rate_eval.n_P27__P28
       -rho*Y[jp26]*rate_eval.n_P26__P27
       -rho*Y[jsi42]*rate_eval.n_Si42__Si43
       -rho*Y[jsi38]*rate_eval.n_Si38__Si39
       -rho*Y[jsi36]*rate_eval.n_Si36__Si37
       -rho*Y[jcr42]*rate_eval.n_Cr42__Cr43
       -rho*Y[jal24]*rate_eval.n_Al24__He4_Na21
       -rho*Y[js45]*rate_eval.n_S45__S46
       -rho*Y[jsi32]*rate_eval.n_Si32__Si33
       -rho*Y[jsi22]*rate_eval.n_Si22__Si23
       -rho*Y[js41]*rate_eval.n_S41__S42
       -rho*Y[jne17]*rate_eval.n_Ne17__He4_O14
       -rho*Y[jsi26]*rate_eval.n_Si26__Si27
       -rho*Y[jsi24]*rate_eval.n_Si24__Si25
       -rho*Y[jal40]*rate_eval.n_Al40__Al41
       -rho*Y[jal39]*rate_eval.n_Al39__Al40
       -rho*Y[jal38]*rate_eval.n_Al38__Al39
       -rho*Y[jar38]*rate_eval.n_Ar38__Ar39
       -rho*Y[jal35]*rate_eval.n_Al35__Al36
       -rho*Y[jv61]*rate_eval.n_V61__V62
       -rho*Y[jal34]*rate_eval.n_Al34__Al35
       -rho*Y[jal31]*rate_eval.n_Al31__Al32
       -rho*Y[jv50]*rate_eval.n_V50__V51
       -rho*Y[jal26]*rate_eval.n_Al26__Al27
       -rho*Y[jal24]*rate_eval.n_Al24__Al25
       -rho*Y[jsc44]*rate_eval.n_Sc44__Sc45
       -rho*Y[jmg36]*rate_eval.n_Mg36__Mg37
       -rho*Y[jmg35]*rate_eval.n_Mg35__Mg36
       -rho*Y[jmg34]*rate_eval.n_Mg34__Mg35
       -rho*Y[jsi35]*rate_eval.n_Si35__Si36
       -rho*Y[jk37]*rate_eval.n_K37__p_Ar37
       -rho*Y[jmg31]*rate_eval.n_Mg31__Mg32
       -rho*Y[jmg29]*rate_eval.n_Mg29__Mg30
       -rho*Y[jca45]*rate_eval.n_Ca45__Ca46
       -rho*Y[jmg24]*rate_eval.n_Mg24__Mg25
       -rho*Y[jca43]*rate_eval.n_Ca43__Ca44
       -rho*Y[jmn44]*rate_eval.n_Mn44__He4_V41
       -rho*Y[jmg23]*rate_eval.n_Mg23__Mg24
       -rho*Y[jcl34]*rate_eval.n_Cl34__Cl35
       -rho*Y[jmg22]*rate_eval.n_Mg22__Mg23
       -rho*Y[jc14]*rate_eval.n_C14__C15
       -rho*Y[jna37]*rate_eval.n_Na37__Na38
       -rho*Y[jmn51]*rate_eval.n_Mn51__Mn52
       -rho*Y[jna36]*rate_eval.n_Na36__Na37
       -rho*Y[jna34]*rate_eval.n_Na34__Na35
       -rho*Y[jhe3]*rate_eval.n_He3__He4
       -rho*Y[jf15]*rate_eval.n_F15__F16
       -rho*Y[jna24]*rate_eval.n_Na24__Na25
       -rho*Y[jna22]*rate_eval.n_Na22__Na23
       -rho*Y[jna21]*rate_eval.n_Na21__Na22
       -rho*Y[jna20]*rate_eval.n_Na20__Na21
       -rho*Y[jna19]*rate_eval.n_Na19__Na20
       -rho*Y[jmg40]*rate_eval.n_Mg40__Mg41
       -rho*Y[jne32]*rate_eval.n_Ne32__Ne33
       -rho*Y[jfe74]*rate_eval.n_Fe74__Fe75
       -rho*Y[jne26]*rate_eval.n_Ne26__Ne27
       -rho*Y[jmg19]*rate_eval.n_Mg19__Mg20
       -rho*Y[jne24]*rate_eval.n_Ne24__Ne25
       -rho*Y[jne19]*rate_eval.n_Ne19__Ne20
       -rho*Y[js46]*rate_eval.n_S46__S47
       -rho*Y[jne18]*rate_eval.n_Ne18__Ne19
       -rho*Y[jne17]*rate_eval.n_Ne17__Ne18
       -rho*Y[jne16]*rate_eval.n_Ne16__Ne17
       -rho*Y[jo13]*rate_eval.n_O13__O14
       -rho*Y[jv41]*rate_eval.n_V41__p_Ti41
       -rho*Y[jp39]*rate_eval.n_P39__P40
       -rho*Y[jsi34]*rate_eval.n_Si34__Si35
       -rho*Y[jf23]*rate_eval.n_F23__F24
       -rho*Y[jf22]*rate_eval.n_F22__F23
       -rho*Y[jcr54]*rate_eval.n_Cr54__Cr55
       -rho*Y[jf21]*rate_eval.n_F21__F22
       -rho*Y[jal23]*rate_eval.n_Al23__Al24
       -rho*Y[jf20]*rate_eval.n_F20__F21
       -rho*Y[jf18]*rate_eval.n_F18__F19
       -rho*Y[jf17]*rate_eval.n_F17__F18
       -rho*Y[jf16]*rate_eval.n_F16__F17
       -rho*Y[jf14]*rate_eval.n_F14__F15
       -rho*Y[jne23]*rate_eval.n_Ne23__Ne24
       -rho*Y[jo23]*rate_eval.n_O23__O24
       -rho*Y[jk57]*rate_eval.n_K57__K58
       -rho*Y[jo22]*rate_eval.n_O22__O23
       -rho*Y[jo21]*rate_eval.n_O21__O22
       -rho*Y[jcl31]*rate_eval.n_Cl31__He4_P28
       -rho*Y[jar48]*rate_eval.n_Ar48__Ar49
       -rho*Y[jo16]*rate_eval.n_O16__O17
       -rho*Y[jo15]*rate_eval.n_O15__O16
       -rho*Y[jn19]*rate_eval.n_N19__N20
       -rho*Y[jsi27]*rate_eval.n_Si27__He4_Mg24
       -rho*Y[jn17]*rate_eval.n_N17__N18
       -rho*Y[jn16]*rate_eval.n_N16__N17
       -rho*Y[jcl29]*rate_eval.n_Cl29__Cl30
       -rho*Y[jti53]*rate_eval.n_Ti53__Ti54
       -rho*Y[jn15]*rate_eval.n_N15__N16
       -rho*Y[jn13]*rate_eval.n_N13__N14
       -rho*Y[jfe53]*rate_eval.n_Fe53__Fe54
       -rho*Y[jv42]*rate_eval.n_V42__p_Ti42
       -rho*Y[jb12]*rate_eval.n_B12__B13
       -rho*Y[jp]*rate_eval.n_p__d
       -rho*Y[jb11]*rate_eval.n_B11__B12
       -rho*Y[jb10]*rate_eval.n_B10__B11
       -rho*Y[jbe11]*rate_eval.n_Be11__Be12
       -rho*Y[jmg20]*rate_eval.n_Mg20__Mg21
       -rho*Y[jti47]*rate_eval.n_Ti47__p_Sc47
       -rho*Y[jk51]*rate_eval.n_K51__K52
       -rho*Y[jv48]*rate_eval.n_V48__He4_Sc45
       -rho*Y[jne28]*rate_eval.n_Ne28__Ne29
       -rho*Y[jsi25]*rate_eval.n_Si25__Si26
       -rho*Y[js31]*rate_eval.n_S31__He4_Si28
       -rho*Y[jp29]*rate_eval.n_P29__P30
       -rho*Y[jcr58]*rate_eval.n_Cr58__Cr59
       -rho*Y[jcl30]*rate_eval.n_Cl30__He4_P27
       -rho*Y[jk42]*rate_eval.n_K42__K43
       -rho*Y[jar36]*rate_eval.n_Ar36__Ar37
       -rho*Y[jar43]*rate_eval.n_Ar43__Ar44
       -rho*Y[jmg25]*rate_eval.n_Mg25__Mg26
       -rho*Y[jc11]*rate_eval.n_C11__C12
       -rho*Y[jcl30]*rate_eval.n_Cl30__Cl31
       -rho*Y[js35]*rate_eval.n_S35__S36
       -rho*Y[jca48]*rate_eval.n_Ca48__Ca49
       -rho*Y[jcl31]*rate_eval.n_Cl31__Cl32
       -rho*Y[jcl48]*rate_eval.n_Cl48__Cl49
       -rho*Y[jmg19]*rate_eval.n_Mg19__p_Na19
       -rho*Y[jcl38]*rate_eval.n_Cl38__Cl39
       -rho*Y[jal23]*rate_eval.n_Al23__p_Mg23
       -rho*Y[jp40]*rate_eval.n_P40__P41
       -rho*Y[jal24]*rate_eval.n_Al24__p_Mg24
       -rho*Y[jfe60]*rate_eval.n_Fe60__Fe61
       -rho*Y[jsi23]*rate_eval.n_Si23__He4_Mg20
       -rho*Y[jcl41]*rate_eval.n_Cl41__Cl42
       -rho*Y[jmg22]*rate_eval.n_Mg22__p_Na22
       -rho*Y[jti37]*rate_eval.n_Ti37__p_Sc37
       -rho*Y[jli8]*rate_eval.n_Li8__Li9
       -rho*Y[jc13]*rate_eval.n_C13__C14
       -rho*Y[jmg21]*rate_eval.n_Mg21__p_Na21
       -rho*Y[jca59]*rate_eval.n_Ca59__Ca60
       -rho*Y[jsi23]*rate_eval.n_Si23__Si24
       -rho*Y[jbe7]*rate_eval.n_Be7__p_Li7
       -rho*Y[jal21]*rate_eval.n_Al21__Al22
       -rho*Y[jsi26]*rate_eval.n_Si26__He4_Mg23
       -rho*Y[jna32]*rate_eval.n_Na32__Na33
       -rho*Y[jp34]*rate_eval.n_P34__P35
       -rho*Y[jsc35]*rate_eval.n_Sc35__Sc36
       -rho*Y[jcl28]*rate_eval.n_Cl28__p_S28
       -rho*Y[jmn50]*rate_eval.n_Mn50__p_Cr50
       -rho*Y[jcr41]*rate_eval.n_Cr41__p_V41
       -rho*Y[jca47]*rate_eval.n_Ca47__Ca48
       -rho*Y[jcr47]*rate_eval.n_Cr47__Cr48
       -rho*Y[js28]*rate_eval.n_S28__p_P28
       -rho*Y[jmg20]*rate_eval.n_Mg20__He4_Ne17
       -rho*Y[jsc52]*rate_eval.n_Sc52__Sc53
       -rho*Y[jti40]*rate_eval.n_Ti40__p_Sc40
       -rho*Y[jp30]*rate_eval.n_P30__p_Si30
       -rho*Y[jp46]*rate_eval.n_P46__P47
       -rho*Y[jmn57]*rate_eval.n_Mn57__Mn58
       -rho*Y[jp25]*rate_eval.n_P25__He4_Al22
       -rho*Y[jf19]*rate_eval.n_F19__F20
       -rho*Y[jna22]*rate_eval.n_Na22__p_Ne22
       -rho*Y[jcr52]*rate_eval.n_Cr52__Cr53
       -rho*Y[jp30]*rate_eval.n_P30__P31
       -rho*Y[jca39]*rate_eval.n_Ca39__He4_Ar36
       -rho*Y[jc12]*rate_eval.n_C12__C13
       -rho*Y[jal27]*rate_eval.n_Al27__Al28
       -rho*Y[jk48]*rate_eval.n_K48__K49
       -rho*Y[jti50]*rate_eval.n_Ti50__Ti51
       -rho*Y[js27]*rate_eval.n_S27__He4_Si24
       -rho*Y[jv64]*rate_eval.n_V64__V65
       -rho*Y[jsc36]*rate_eval.n_Sc36__p_Ca36
       -5.00000000000000e-01*rho**2*Y[jhe4]**2*rate_eval.n_He4_He4__Be9
       -rho*Y[jal32]*rate_eval.n_Al32__Al33
       -rho*Y[jcr65]*rate_eval.n_Cr65__Cr66
       -rho*Y[jne21]*rate_eval.n_Ne21__Ne22
       -rho*Y[jca41]*rate_eval.n_Ca41__He4_Ar38
       -rho*Y[jmg38]*rate_eval.n_Mg38__Mg39
       -rho*Y[jne31]*rate_eval.n_Ne31__Ne32
       -rho*Y[jcl39]*rate_eval.n_Cl39__Cl40
       -rho*Y[jv54]*rate_eval.n_V54__V55
       -rho*Y[jna19]*rate_eval.n_Na19__He4_F16
       -rho*Y[jmg30]*rate_eval.n_Mg30__Mg31
       -rho*Y[jti42]*rate_eval.n_Ti42__Ti43
       -rho**2*Y[jp]*Y[jhe4]*rate_eval.n_p_He4__Li6
       -rho*Y[jar33]*rate_eval.n_Ar33__Ar34
       -rho*Y[jca33]*rate_eval.n_Ca33__Ca34
       -rho*Y[jsi39]*rate_eval.n_Si39__Si40
       -rho*Y[jfe46]*rate_eval.n_Fe46__Fe47
       -rho*Y[jcr64]*rate_eval.n_Cr64__Cr65
       -rho*Y[jca34]*rate_eval.n_Ca34__Ca35
       -rho*Y[jsc38]*rate_eval.n_Sc38__p_Ca38
       -rho*Y[jti51]*rate_eval.n_Ti51__Ti52
       -rho*Y[jsi31]*rate_eval.n_Si31__Si32
       -rho*Y[jcl36]*rate_eval.n_Cl36__He4_P33
       -rho*Y[js37]*rate_eval.n_S37__S38
       -rho*Y[jar50]*rate_eval.n_Ar50__Ar51
       -rho*Y[jca58]*rate_eval.n_Ca58__Ca59
       -rho*Y[jar41]*rate_eval.n_Ar41__Ar42
       -rho*Y[jk42]*rate_eval.n_K42__He4_Cl39
       -rho*Y[jne29]*rate_eval.n_Ne29__Ne30
       -rho*Y[jf27]*rate_eval.n_F27__F28
       -rho*Y[jcr51]*rate_eval.n_Cr51__p_V51
       -rho*Y[jv65]*rate_eval.n_V65__V66
       -rho*Y[jk31]*rate_eval.n_K31__He4_Cl28
       -rho*Y[jo12]*rate_eval.n_O12__He4_C9
       -rho*Y[jo19]*rate_eval.n_O19__O20
       -rho*Y[jcr45]*rate_eval.n_Cr45__p_V45
       -rho*Y[jsc41]*rate_eval.n_Sc41__p_Ca41
       -rho*Y[jfe52]*rate_eval.n_Fe52__p_Mn52
       -rho*Y[js36]*rate_eval.n_S36__S37
       -rho*Y[jne27]*rate_eval.n_Ne27__Ne28
       -rho*Y[jmn64]*rate_eval.n_Mn64__Mn65
       -rho*Y[jv44]*rate_eval.n_V44__V45
       -rho*Y[jsi27]*rate_eval.n_Si27__p_Al27
       -rho*Y[jcl47]*rate_eval.n_Cl47__Cl48
       -rho*Y[jti61]*rate_eval.n_Ti61__Ti62
       -rho*Y[jmn46]*rate_eval.n_Mn46__Mn47
       -rho*Y[jli6]*rate_eval.n_Li6__Li7
       -rho*Y[jmn48]*rate_eval.n_Mn48__p_Cr48
       -rho*Y[jcr49]*rate_eval.n_Cr49__He4_Ti46
       -rho*Y[jk38]*rate_eval.n_K38__He4_Cl35
       -rho*Y[jk34]*rate_eval.n_K34__He4_Cl31
       -rho*Y[jne17]*rate_eval.n_Ne17__p_F17
       -rho*Y[jti43]*rate_eval.n_Ti43__p_Sc43
       -rho*Y[jsc57]*rate_eval.n_Sc57__Sc58
       -rho*Y[jna23]*rate_eval.n_Na23__Na24
       -rho*Y[jcr44]*rate_eval.n_Cr44__p_V44
       -rho*Y[jo17]*rate_eval.n_O17__He4_C14
       -rho*Y[jv66]*rate_eval.n_V66__V67
       -rho*Y[jar33]*rate_eval.n_Ar33__He4_S30
       -rho*Y[jsc61]*rate_eval.n_Sc61__Sc62
       -rho*Y[jsc36]*rate_eval.n_Sc36__He4_K33
       -rho*Y[jk38]*rate_eval.n_K38__K39
       -rho*Y[jmg21]*rate_eval.n_Mg21__Mg22
       -rho*Y[jfe61]*rate_eval.n_Fe61__Fe62
       -rho*Y[jv63]*rate_eval.n_V63__V64
       -rho*Y[jn14]*rate_eval.n_N14__N15
       -rho*Y[jf17]*rate_eval.n_F17__p_O17
       -rho*Y[jfe45]*rate_eval.n_Fe45__p_Mn45
       -rho*Y[jsi30]*rate_eval.n_Si30__Si31
       -rho*Y[jp31]*rate_eval.n_P31__P32
       -rho*Y[jfe45]*rate_eval.n_Fe45__Fe46
       -rho*Y[jfe59]*rate_eval.n_Fe59__Fe60
       -rho*Y[jp37]*rate_eval.n_P37__P38
       -rho*Y[jti62]*rate_eval.n_Ti62__Ti63
       -rho*Y[jmg33]*rate_eval.n_Mg33__Mg34
       -rho*Y[jc15]*rate_eval.n_C15__C16
       -rho*Y[jca42]*rate_eval.n_Ca42__Ca43
       -rho*Y[jmn53]*rate_eval.n_Mn53__Mn54
       -rho*Y[jmn48]*rate_eval.n_Mn48__Mn49
       -rho*Y[jti56]*rate_eval.n_Ti56__Ti57
       -rho*Y[js43]*rate_eval.n_S43__S44
       -rho*Y[jti39]*rate_eval.n_Ti39__Ti40
       -rho*Y[jca39]*rate_eval.n_Ca39__p_K39
       -rho*Y[jti44]*rate_eval.n_Ti44__He4_Ca41
       -rho*Y[jmg39]*rate_eval.n_Mg39__Mg40
       -rho*Y[js48]*rate_eval.n_S48__S49
       -rho*Y[jp43]*rate_eval.n_P43__P44
       -rho*Y[jp25]*rate_eval.n_P25__p_Si25
       -rho*Y[jb10]*rate_eval.n_B10__He4_Li7
       -rho*Y[jsi27]*rate_eval.n_Si27__C12_O16
       -rho*Y[jsi28]*rate_eval.n_Si28__Si29
       -rho*Y[jsi41]*rate_eval.n_Si41__Si42
       -rho*Y[jk35]*rate_eval.n_K35__K36
       -rho*Y[jk39]*rate_eval.n_K39__K40
       -rho*Y[jal33]*rate_eval.n_Al33__Al34
       -rho*Y[jp29]*rate_eval.n_P29__p_Si29
       -rho*Y[jna26]*rate_eval.n_Na26__Na27
       -rho*Y[jk54]*rate_eval.n_K54__K55
       -rho*Y[jti63]*rate_eval.n_Ti63__Ti64
       -rho*Y[jcl50]*rate_eval.n_Cl50__Cl51
       -rho*Y[jv52]*rate_eval.n_V52__V53
       -rho*Y[jbe10]*rate_eval.n_Be10__Be11
       -rho*Y[jal29]*rate_eval.n_Al29__Al30
       -rho*Y[jar36]*rate_eval.n_Ar36__p_Cl36
       -rho*Y[jar53]*rate_eval.n_Ar53__Ar54
       -rho*Y[jne22]*rate_eval.n_Ne22__Ne23
       -rho*Y[jsc36]*rate_eval.n_Sc36__Sc37
       -rho*Y[jca35]*rate_eval.n_Ca35__Ca36
       -rho*Y[jcl36]*rate_eval.n_Cl36__Cl37
       -rho*Y[jna22]*rate_eval.n_Na22__He4_F19
       -rho*Y[js39]*rate_eval.n_S39__S40
       -rho*Y[jmn56]*rate_eval.n_Mn56__He4_V53
       -rho*Y[jar37]*rate_eval.n_Ar37__Ar38
       -rho*Y[jal22]*rate_eval.n_Al22__Al23
       -rho*Y[jv57]*rate_eval.n_V57__V58
       -rho*Y[jal21]*rate_eval.n_Al21__p_Mg21
       -rho*Y[jna29]*rate_eval.n_Na29__Na30
       -rho*Y[jcr67]*rate_eval.n_Cr67__Cr68
       -rho*Y[jf14]*rate_eval.n_F14__p_O14
       -rho*Y[jcr49]*rate_eval.n_Cr49__Cr50
       -rho*Y[jp25]*rate_eval.n_P25__P26
       -rho*Y[jal30]*rate_eval.n_Al30__Al31
       -rho*Y[jti48]*rate_eval.n_Ti48__Ti49
       -rho*Y[jmn47]*rate_eval.n_Mn47__Mn48
       -rho*Y[jfe55]*rate_eval.n_Fe55__Fe56
       -rho*Y[jcr68]*rate_eval.n_Cr68__Cr69
       -rho*Y[jne25]*rate_eval.n_Ne25__Ne26
       -rho*Y[js31]*rate_eval.n_S31__S32
       -rho*Y[jk42]*rate_eval.n_K42__p_Ar42
       -rho*Y[jfe45]*rate_eval.n_Fe45__He4_Cr42
       -rho*Y[jfe52]*rate_eval.n_Fe52__Fe53
       -rho*Y[jfe64]*rate_eval.n_Fe64__Fe65
       -rho*Y[jsc51]*rate_eval.n_Sc51__Sc52
       -rho*Y[jfe59]*rate_eval.n_Fe59__He4_Cr56
       -rho*Y[jsi29]*rate_eval.n_Si29__Si30
       -rho*Y[jcl35]*rate_eval.n_Cl35__Cl36
       -rho*Y[jf15]*rate_eval.n_F15__p_O15
       -rho*Y[jna20]*rate_eval.n_Na20__p_Ne20
       -rho*Y[jna38]*rate_eval.n_Na38__Na39
       -rho*Y[jv52]*rate_eval.n_V52__He4_Sc49
       -rho*Y[jcr50]*rate_eval.n_Cr50__Cr51
       -rho*Y[jp24]*rate_eval.n_P24__P25
       -rho*Y[jca42]*rate_eval.n_Ca42__He4_Ar39
       -rho*Y[jna25]*rate_eval.n_Na25__Na26
       -rho*Y[jv58]*rate_eval.n_V58__V59
       -rho*Y[jmn61]*rate_eval.n_Mn61__Mn62
       -rho*Y[jmn43]*rate_eval.n_Mn43__Mn44
       -rho*Y[jti40]*rate_eval.n_Ti40__He4_Ca37
       -rho*Y[jv45]*rate_eval.n_V45__p_Ti45
       -rho*Y[jf24]*rate_eval.n_F24__F25
       -rho*Y[js27]*rate_eval.n_S27__p_P27
       -rho*Y[jv60]*rate_eval.n_V60__V61
       -rho*Y[jv40]*rate_eval.n_V40__V41
       -rho*Y[jv39]*rate_eval.n_V39__He4_Sc36
       -rho*Y[jsc60]*rate_eval.n_Sc60__Sc61
       -rho*Y[jsc39]*rate_eval.n_Sc39__p_Ca39
       -rho*Y[jsc40]*rate_eval.n_Sc40__He4_K37
       -rho*Y[jca39]*rate_eval.n_Ca39__Ca40
       -rho*Y[jne33]*rate_eval.n_Ne33__Ne34
       -rho*Y[jca38]*rate_eval.n_Ca38__He4_Ar35
       -rho*Y[jbe9]*rate_eval.n_Be9__Be10
       -rho*Y[jsc47]*rate_eval.n_Sc47__Sc48
       -rho*Y[js32]*rate_eval.n_S32__He4_Si29
       -rho*Y[jsi37]*rate_eval.n_Si37__Si38
       -rho*Y[jsc38]*rate_eval.n_Sc38__He4_K35
       -rho*Y[jal42]*rate_eval.n_Al42__Al43
       -rho*Y[jna28]*rate_eval.n_Na28__Na29
       -rho*Y[jal25]*rate_eval.n_Al25__He4_Na22
       -rho*Y[jk34]*rate_eval.n_K34__p_Ar34
       -rho*Y[jp28]*rate_eval.n_P28__He4_Al25
       -rho*Y[jmn66]*rate_eval.n_Mn66__Mn67
       -rho*Y[jar49]*rate_eval.n_Ar49__Ar50
       -rho*Y[jo20]*rate_eval.n_O20__O21
       -rho*Y[jmg37]*rate_eval.n_Mg37__Mg38
       -rho*Y[js29]*rate_eval.n_S29__S30
       -rho*Y[jcr48]*rate_eval.n_Cr48__He4_Ti45
       -rho*Y[jc16]*rate_eval.n_C16__C17
       )

    jac[jn, jp] = (
       -5.00000000000000e-01*rho**2*Y[jn]*2*Y[jp]*rate_eval.n_p_p__p_d
       -rho*Y[jn]*rate_eval.n_p__d
       -rho**2*Y[jn]*Y[jhe4]*rate_eval.n_p_He4__Li6
       +rho*Y[jbe9]*rate_eval.p_Be9__n_p_He4_He4
       +rho*Y[jfe75]*rate_eval.p_Fe75__n_Co75
       +rho*Y[jfe74]*rate_eval.p_Fe74__n_Co74
       +rho*Y[jfe73]*rate_eval.p_Fe73__n_Co73
       +rho*Y[jfe72]*rate_eval.p_Fe72__n_Co72
       +rho*Y[jfe71]*rate_eval.p_Fe71__n_Co71
       +rho*Y[jfe70]*rate_eval.p_Fe70__n_Co70
       +rho*Y[jfe69]*rate_eval.p_Fe69__n_Co69
       +rho*Y[jfe61]*rate_eval.p_Fe61__n_Co61
       +rho*Y[jfe59]*rate_eval.p_Fe59__n_Co59
       +rho*Y[jmn68]*rate_eval.p_Mn68__n_Fe68
       +rho*Y[jmn66]*rate_eval.p_Mn66__n_Fe66
       +rho*Y[jsi44]*rate_eval.p_Si44__n_P44
       +rho*Y[jmn60]*rate_eval.p_Mn60__n_Fe60
       +rho*Y[jmn57]*rate_eval.p_Mn57__n_Fe57
       +rho*Y[jca53]*rate_eval.p_Ca53__n_Sc53
       +rho*Y[jo22]*rate_eval.p_O22__n_F22
       +rho*Y[jcr68]*rate_eval.p_Cr68__n_Mn68
       +rho*Y[jcr67]*rate_eval.p_Cr67__n_Mn67
       +rho*Y[jmn72]*rate_eval.p_Mn72__n_Fe72
       +rho*Y[jo25]*rate_eval.p_O25__n_F25
       +rho*Y[jcr63]*rate_eval.p_Cr63__n_Mn63
       +rho*Y[jcr59]*rate_eval.p_Cr59__n_Mn59
       +rho*Y[jfe62]*rate_eval.p_Fe62__n_Co62
       +rho*Y[jcr57]*rate_eval.p_Cr57__n_Mn57
       +rho*Y[jsi38]*rate_eval.p_Si38__n_P38
       +rho*Y[jv67]*rate_eval.p_V67__n_Cr67
       +rho*Y[jv66]*rate_eval.p_V66__n_Cr66
       +rho*Y[jv63]*rate_eval.p_V63__n_Cr63
       +rho*Y[jv61]*rate_eval.p_V61__n_Cr61
       +rho*Y[jp32]*rate_eval.p_P32__n_S32
       +rho*Y[jv60]*rate_eval.p_V60__n_Cr60
       +rho*Y[jsi43]*rate_eval.p_Si43__n_P43
       +rho*Y[jv58]*rate_eval.p_V58__n_Cr58
       +rho*Y[jv57]*rate_eval.p_V57__n_Cr57
       +rho*Y[jv55]*rate_eval.p_V55__n_Cr55
       +rho*Y[jv53]*rate_eval.p_V53__n_Cr53
       +rho*Y[jv52]*rate_eval.p_V52__n_Cr52
       +rho*Y[jv50]*rate_eval.p_V50__n_Cr50
       +rho*Y[jsc53]*rate_eval.p_Sc53__n_Ti53
       +rho*Y[jti63]*rate_eval.p_Ti63__n_V63
       +rho*Y[jti61]*rate_eval.p_Ti61__n_V61
       +rho*Y[jti60]*rate_eval.p_Ti60__n_V60
       +rho*Y[jti59]*rate_eval.p_Ti59__n_V59
       +rho*Y[jti58]*rate_eval.p_Ti58__n_V58
       +rho*Y[jti55]*rate_eval.p_Ti55__n_V55
       +rho*Y[jti54]*rate_eval.p_Ti54__n_V54
       +rho*Y[jti52]*rate_eval.p_Ti52__n_V52
       +rho*Y[jti51]*rate_eval.p_Ti51__n_V51
       +rho*Y[jcr55]*rate_eval.p_Cr55__n_Mn55
       +rho*Y[jsc61]*rate_eval.p_Sc61__n_Ti61
       +rho*Y[jsc60]*rate_eval.p_Sc60__n_Ti60
       +rho*Y[jsc58]*rate_eval.p_Sc58__n_Ti58
       +rho*Y[jsc54]*rate_eval.p_Sc54__n_Ti54
       +rho*Y[jsc52]*rate_eval.p_Sc52__n_Ti52
       +rho*Y[jsc50]*rate_eval.p_Sc50__n_Ti50
       +rho*Y[jcr56]*rate_eval.p_Cr56__n_Mn56
       +rho*Y[jna36]*rate_eval.p_Na36__n_Mg36
       +rho*Y[jca61]*rate_eval.p_Ca61__n_Sc61
       +rho*Y[jca60]*rate_eval.p_Ca60__n_Sc60
       +rho*Y[jca59]*rate_eval.p_Ca59__n_Sc59
       +rho*Y[jca58]*rate_eval.p_Ca58__n_Sc58
       +rho*Y[jca55]*rate_eval.p_Ca55__n_Sc55
       +rho*Y[jca52]*rate_eval.p_Ca52__n_Sc52
       +rho*Y[jca47]*rate_eval.p_Ca47__n_Sc47
       +rho*Y[jp42]*rate_eval.p_P42__n_S42
       +rho*Y[jk57]*rate_eval.p_K57__n_Ca57
       +rho*Y[jk56]*rate_eval.p_K56__n_Ca56
       +rho*Y[jk54]*rate_eval.p_K54__n_Ca54
       +rho*Y[jk53]*rate_eval.p_K53__n_Ca53
       +rho*Y[jk51]*rate_eval.p_K51__n_Ca51
       +rho*Y[jk45]*rate_eval.p_K45__n_Ca45
       +rho*Y[jk43]*rate_eval.p_K43__n_Ca43
       +rho*Y[jk41]*rate_eval.p_K41__n_Ca41
       +rho*Y[jk40]*rate_eval.p_K40__n_Ca40
       +rho*Y[jal39]*rate_eval.p_Al39__n_Si39
       +rho*Y[jar54]*rate_eval.p_Ar54__n_K54
       +rho*Y[jar52]*rate_eval.p_Ar52__n_K52
       +rho*Y[jk59]*rate_eval.p_K59__n_Ca59
       +rho*Y[jar48]*rate_eval.p_Ar48__n_K48
       +rho*Y[jf28]*rate_eval.p_F28__n_Ne28
       +rho*Y[jar44]*rate_eval.p_Ar44__n_K44
       +rho*Y[jar43]*rate_eval.p_Ar43__n_K43
       +rho*Y[jar41]*rate_eval.p_Ar41__n_K41
       +rho*Y[jcl52]*rate_eval.p_Cl52__n_Ar52
       +rho*Y[jcl50]*rate_eval.p_Cl50__n_Ar50
       +rho*Y[jb12]*rate_eval.p_B12__n_C12
       +rho*Y[jcl48]*rate_eval.p_Cl48__n_Ar48
       +rho*Y[jti62]*rate_eval.p_Ti62__n_V62
       +rho*Y[jcl45]*rate_eval.p_Cl45__n_Ar45
       +rho*Y[jmn61]*rate_eval.p_Mn61__n_Fe61
       +rho*Y[js47]*rate_eval.p_S47__n_Cl47
       +rho*Y[jcl40]*rate_eval.p_Cl40__n_Ar40
       +rho*Y[js49]*rate_eval.p_S49__n_Cl49
       +rho*Y[js48]*rate_eval.p_S48__n_Cl48
       +rho*Y[js46]*rate_eval.p_S46__n_Cl46
       +rho*Y[jmn64]*rate_eval.p_Mn64__n_Fe64
       +rho*Y[js40]*rate_eval.p_S40__n_Cl40
       +rho*Y[js38]*rate_eval.p_S38__n_Cl38
       +rho*Y[js37]*rate_eval.p_S37__n_Cl37
       +rho*Y[jk49]*rate_eval.p_K49__n_Ca49
       +rho*Y[jsc57]*rate_eval.p_Sc57__n_Ti57
       +rho*Y[jp47]*rate_eval.p_P47__n_S47
       +rho*Y[jp45]*rate_eval.p_P45__n_S45
       +rho*Y[jp43]*rate_eval.p_P43__n_S43
       +rho*Y[jsc55]*rate_eval.p_Sc55__n_Ti55
       +rho*Y[jp38]*rate_eval.p_P38__n_S38
       +rho*Y[jp36]*rate_eval.p_P36__n_S36
       +rho*Y[jmn69]*rate_eval.p_Mn69__n_Fe69
       +rho*Y[jp34]*rate_eval.p_P34__n_S34
       +rho*Y[jca56]*rate_eval.p_Ca56__n_Sc56
       +rho*Y[jsi45]*rate_eval.p_Si45__n_P45
       +rho*Y[jsi42]*rate_eval.p_Si42__n_P42
       +rho*Y[jsi39]*rate_eval.p_Si39__n_P39
       +rho*Y[jsc62]*rate_eval.p_Sc62__n_Ti62
       +rho*Y[jsi37]*rate_eval.p_Si37__n_P37
       +rho*Y[jsi33]*rate_eval.p_Si33__n_P33
       +rho*Y[jal43]*rate_eval.p_Al43__n_Si43
       +rho*Y[jal40]*rate_eval.p_Al40__n_Si40
       +rho*Y[jv59]*rate_eval.p_V59__n_Cr59
       +rho*Y[jal36]*rate_eval.p_Al36__n_Si36
       +rho*Y[jal41]*rate_eval.p_Al41__n_Si41
       +rho*Y[jv64]*rate_eval.p_V64__n_Cr64
       +rho*Y[jal34]*rate_eval.p_Al34__n_Si34
       +rho*Y[jal33]*rate_eval.p_Al33__n_Si33
       +rho*Y[jne26]*rate_eval.p_Ne26__n_Na26
       +rho*Y[jal32]*rate_eval.p_Al32__n_Si32
       +rho*Y[jal30]*rate_eval.p_Al30__n_Si30
       +rho*Y[jal29]*rate_eval.p_Al29__n_Si29
       +rho*Y[jmg40]*rate_eval.p_Mg40__n_Al40
       +rho*Y[jmg39]*rate_eval.p_Mg39__n_Al39
       +rho*Y[jmg38]*rate_eval.p_Mg38__n_Al38
       +rho*Y[jal38]*rate_eval.p_Al38__n_Si38
       +rho*Y[jti53]*rate_eval.p_Ti53__n_V53
       +rho*Y[jmn59]*rate_eval.p_Mn59__n_Fe59
       +rho*Y[jmg30]*rate_eval.p_Mg30__n_Al30
       +rho*Y[jcl46]*rate_eval.p_Cl46__n_Ar46
       +rho*Y[jmg29]*rate_eval.p_Mg29__n_Al29
       +rho*Y[jcr60]*rate_eval.p_Cr60__n_Mn60
       +rho*Y[jna39]*rate_eval.p_Na39__n_Mg39
       +rho*Y[jna35]*rate_eval.p_Na35__n_Mg35
       +rho*Y[jna33]*rate_eval.p_Na33__n_Mg33
       +rho*Y[jna31]*rate_eval.p_Na31__n_Mg31
       +rho*Y[jfe66]*rate_eval.p_Fe66__n_Co66
       +rho*Y[jna28]*rate_eval.p_Na28__n_Mg28
       +rho*Y[jna27]*rate_eval.p_Na27__n_Mg27
       +rho*Y[jsc49]*rate_eval.p_Sc49__n_Ti49
       +rho*Y[jfe67]*rate_eval.p_Fe67__n_Co67
       +rho*Y[jna23]*rate_eval.p_Na23__n_Mg23
       +rho*Y[jne34]*rate_eval.p_Ne34__n_Na34
       +rho*Y[jal35]*rate_eval.p_Al35__n_Si35
       +rho*Y[jne29]*rate_eval.p_Ne29__n_Na29
       +rho*Y[jne28]*rate_eval.p_Ne28__n_Na28
       +rho*Y[jne27]*rate_eval.p_Ne27__n_Na27
       +rho*Y[jne25]*rate_eval.p_Ne25__n_Na25
       +rho*Y[jne24]*rate_eval.p_Ne24__n_Na24
       +rho*Y[jne23]*rate_eval.p_Ne23__n_Na23
       +rho*Y[jv54]*rate_eval.p_V54__n_Cr54
       +rho*Y[jf31]*rate_eval.p_F31__n_Ne31
       +rho*Y[jar45]*rate_eval.p_Ar45__n_K45
       +rho*Y[jf27]*rate_eval.p_F27__n_Ne27
       +rho*Y[jf26]*rate_eval.p_F26__n_Ne26
       +rho*Y[jf25]*rate_eval.p_F25__n_Ne25
       +rho*Y[jf24]*rate_eval.p_F24__n_Ne24
       +rho*Y[jf22]*rate_eval.p_F22__n_Ne22
       +rho*Y[jf19]*rate_eval.p_F19__n_Ne19
       +rho*Y[jo21]*rate_eval.p_O21__n_F21
       +rho*Y[jo26]*rate_eval.p_O26__n_F26
       +rho*Y[jo24]*rate_eval.p_O24__n_F24
       +rho*Y[jti57]*rate_eval.p_Ti57__n_V57
       +rho*Y[jo20]*rate_eval.p_O20__n_F20
       +rho*Y[jcr62]*rate_eval.p_Cr62__n_Mn62
       +rho*Y[jk48]*rate_eval.p_K48__n_Ca48
       +rho*Y[jn15]*rate_eval.p_N15__n_O15
       +rho*Y[jc15]*rate_eval.p_C15__n_N15
       +rho*Y[jc13]*rate_eval.p_C13__n_N13
       +rho*Y[jk44]*rate_eval.p_K44__n_Ca44
       +rho*Y[jmg31]*rate_eval.p_Mg31__n_Al31
       +rho*Y[jsi36]*rate_eval.p_Si36__n_P36
       +rho*Y[jne32]*rate_eval.p_Ne32__n_Na32
       +rho*Y[jmn73]*rate_eval.p_Mn73__n_Fe73
       +rho*Y[jne33]*rate_eval.p_Ne33__n_Na33
       +rho*Y[jk42]*rate_eval.p_K42__n_Ca42
       +rho*Y[jfe64]*rate_eval.p_Fe64__n_Co64
       +rho*Y[jsc48]*rate_eval.p_Sc48__n_Ti48
       +rho*Y[jk58]*rate_eval.p_K58__n_Ca58
       +rho*Y[jv62]*rate_eval.p_V62__n_Cr62
       +rho*Y[js42]*rate_eval.p_S42__n_Cl42
       +rho*Y[jsc46]*rate_eval.p_Sc46__n_Ti46
       +rho*Y[jp40]*rate_eval.p_P40__n_S40
       +rho*Y[jfe63]*rate_eval.p_Fe63__n_Co63
       +rho*Y[jcr58]*rate_eval.p_Cr58__n_Mn58
       +rho*Y[jar47]*rate_eval.p_Ar47__n_K47
       +rho*Y[jar50]*rate_eval.p_Ar50__n_K50
       +rho*Y[jk50]*rate_eval.p_K50__n_Ca50
       +rho*Y[jf20]*rate_eval.p_F20__n_Ne20
       +rho*Y[jv56]*rate_eval.p_V56__n_Cr56
       +rho*Y[jcl42]*rate_eval.p_Cl42__n_Ar42
       +rho*Y[jar53]*rate_eval.p_Ar53__n_K53
       +rho*Y[jcr64]*rate_eval.p_Cr64__n_Mn64
       +rho*Y[jmg35]*rate_eval.p_Mg35__n_Al35
       +rho*Y[jna32]*rate_eval.p_Na32__n_Mg32
       +rho*Y[jk55]*rate_eval.p_K55__n_Ca55
       +rho*Y[jmg37]*rate_eval.p_Mg37__n_Al37
       +rho*Y[jca54]*rate_eval.p_Ca54__n_Sc54
       +rho*Y[jti64]*rate_eval.p_Ti64__n_V64
       +rho*Y[jcl51]*rate_eval.p_Cl51__n_Ar51
       +rho*Y[jsi40]*rate_eval.p_Si40__n_P40
       +rho*Y[jcl39]*rate_eval.p_Cl39__n_Ar39
       +rho*Y[jmg33]*rate_eval.p_Mg33__n_Al33
       +rho*Y[jcl47]*rate_eval.p_Cl47__n_Ar47
       +rho*Y[jf21]*rate_eval.p_F21__n_Ne21
       +rho*Y[jca51]*rate_eval.p_Ca51__n_Sc51
       +rho*Y[jti65]*rate_eval.p_Ti65__n_V65
       +rho*Y[jmn71]*rate_eval.p_Mn71__n_Fe71
       +rho*Y[jcr70]*rate_eval.p_Cr70__n_Mn70
       +rho*Y[jcl43]*rate_eval.p_Cl43__n_Ar43
       +rho*Y[js44]*rate_eval.p_S44__n_Cl44
       +rho*Y[jp35]*rate_eval.p_P35__n_S35
       +rho*Y[jca49]*rate_eval.p_Ca49__n_Sc49
       +rho*Y[jsc51]*rate_eval.p_Sc51__n_Ti51
       +rho*Y[jal28]*rate_eval.p_Al28__n_Si28
       +rho*Y[jcl41]*rate_eval.p_Cl41__n_Ar41
       +rho*Y[jk47]*rate_eval.p_K47__n_Ca47
       +rho*Y[jca50]*rate_eval.p_Ca50__n_Sc50
       +rho*Y[jcl38]*rate_eval.p_Cl38__n_Ar38
       +rho*Y[jmg32]*rate_eval.p_Mg32__n_Al32
       +rho*Y[jp46]*rate_eval.p_P46__n_S46
       +rho*Y[jp41]*rate_eval.p_P41__n_S41
       +rho*Y[jp39]*rate_eval.p_P39__n_S39
       +rho*Y[jn14]*rate_eval.p_N14__n_O14
       +rho*Y[jna34]*rate_eval.p_Na34__n_Mg34
       +rho*Y[jcl44]*rate_eval.p_Cl44__n_Ar44
       +rho*Y[jli8]*rate_eval.p_Li8__n_He4_He4
       +rho*Y[jmg41]*rate_eval.p_Mg41__n_Al41
       +rho*Y[js45]*rate_eval.p_S45__n_Cl45
       +rho*Y[jmn58]*rate_eval.p_Mn58__n_Fe58
       +rho*Y[jcr65]*rate_eval.p_Cr65__n_Mn65
       +rho*Y[jf29]*rate_eval.p_F29__n_Ne29
       +rho*Y[jmn63]*rate_eval.p_Mn63__n_Fe63
       +rho*Y[jne30]*rate_eval.p_Ne30__n_Na30
       +rho*Y[jf30]*rate_eval.p_F30__n_Ne30
       +rho*Y[js41]*rate_eval.p_S41__n_Cl41
       +rho*Y[jmg36]*rate_eval.p_Mg36__n_Al36
       +rho*Y[jcr69]*rate_eval.p_Cr69__n_Mn69
       +rho*Y[js39]*rate_eval.p_S39__n_Cl39
       +rho*Y[jfe68]*rate_eval.p_Fe68__n_Co68
       +rho*Y[jna29]*rate_eval.p_Na29__n_Mg29
       +rho*Y[jal37]*rate_eval.p_Al37__n_Si37
       +rho*Y[jo23]*rate_eval.p_O23__n_F23
       +rho*Y[jmg27]*rate_eval.p_Mg27__n_Al27
       +rho*Y[jk46]*rate_eval.p_K46__n_Ca46
       +rho*Y[jfe65]*rate_eval.p_Fe65__n_Co65
       +rho*Y[jfe76]*rate_eval.p_Fe76__n_Co76
       +rho*Y[jmn67]*rate_eval.p_Mn67__n_Fe67
       +rho*Y[jca57]*rate_eval.p_Ca57__n_Sc57
       +rho*Y[jne31]*rate_eval.p_Ne31__n_Na31
       +rho*Y[jv65]*rate_eval.p_V65__n_Cr65
       +rho*Y[jna26]*rate_eval.p_Na26__n_Mg26
       +rho*Y[jcr66]*rate_eval.p_Cr66__n_Mn66
       +rho*Y[jo27]*rate_eval.p_O27__n_F27
       +rho*Y[jal31]*rate_eval.p_Al31__n_Si31
       +rho*Y[jna25]*rate_eval.p_Na25__n_Mg25
       +rho*Y[jn16]*rate_eval.p_N16__n_O16
       +rho*Y[jmn70]*rate_eval.p_Mn70__n_Fe70
       +rho*Y[jp44]*rate_eval.p_P44__n_S44
       +rho*Y[jsi31]*rate_eval.p_Si31__n_P31
       +rho*Y[jk52]*rate_eval.p_K52__n_Ca52
       +rho*Y[js43]*rate_eval.p_S43__n_Cl43
       +rho*Y[jna38]*rate_eval.p_Na38__n_Mg38
       +rho*Y[jna37]*rate_eval.p_Na37__n_Mg37
       +rho*Y[jmn62]*rate_eval.p_Mn62__n_Fe62
       +rho*Y[jf23]*rate_eval.p_F23__n_Ne23
       +rho*Y[jsc56]*rate_eval.p_Sc56__n_Ti56
       +rho*Y[jar49]*rate_eval.p_Ar49__n_K49
       +rho*Y[jmn65]*rate_eval.p_Mn65__n_Fe65
       +rho*Y[jcl49]*rate_eval.p_Cl49__n_Ar49
       +rho*Y[jsc59]*rate_eval.p_Sc59__n_Ti59
       +rho*Y[jp37]*rate_eval.p_P37__n_S37
       +rho*Y[jti56]*rate_eval.p_Ti56__n_V56
       +rho*Y[jsi34]*rate_eval.p_Si34__n_P34
       +rho*Y[jo19]*rate_eval.p_O19__n_F19
       +rho*Y[jsc63]*rate_eval.p_Sc63__n_Ti63
       +rho*Y[jal42]*rate_eval.p_Al42__n_Si42
       +rho*Y[jsi41]*rate_eval.p_Si41__n_P41
       +rho*Y[jna24]*rate_eval.p_Na24__n_Mg24
       +rho*Y[jsi35]*rate_eval.p_Si35__n_P35
       +rho*Y[jmg28]*rate_eval.p_Mg28__n_Al28
       +rho*Y[jar51]*rate_eval.p_Ar51__n_K51
       +rho*Y[jmg34]*rate_eval.p_Mg34__n_Al34
       +rho*Y[jmn56]*rate_eval.p_Mn56__n_Fe56
       +rho*Y[jcr61]*rate_eval.p_Cr61__n_Mn61
       +rho*Y[jna30]*rate_eval.p_Na30__n_Mg30
       +rho*Y[jar46]*rate_eval.p_Ar46__n_K46
       )

    jac[jn, jd] = (
       -rho*Y[jn]*rate_eval.n_d__t
       +rho*Y[jli7]*rate_eval.d_Li7__n_He4_He4
       +rho*Y[jli8]*rate_eval.d_Li8__n_Be9
       +rho*Y[jc13]*rate_eval.d_C13__n_N14
       +rho*Y[jt]*rate_eval.d_t__n_He4
       +rho*Y[jli6]*rate_eval.d_Li6__n_Be7
       +5.00000000000000e-01*rho*2*Y[jd]*rate_eval.d_d__n_He3
       +rho*Y[jc14]*rate_eval.d_C14__n_N15
       )

    jac[jn, jt] = (
       +rho*Y[jbe7]*rate_eval.t_Be7__n_p_He4_He4
       +rho*Y[jhe3]*rate_eval.t_He3__n_p_He4
       +rho*Y[jd]*rate_eval.d_t__n_He4
       +rho*Y[jbe9]*rate_eval.t_Be9__n_B11
       +rho*Y[jli7]*rate_eval.t_Li7__n_Be9
       +2*rho*Y[jli7]*rate_eval.t_Li7__n_n_He4_He4
       +2*5.00000000000000e-01*rho*2*Y[jt]*rate_eval.t_t__n_n_He4
       )

    jac[jn, jhe3] = (
       -rho*Y[jn]*rate_eval.n_He3__p_t
       -rho*Y[jn]*rate_eval.n_He3__He4
       +rho*Y[jt]*rate_eval.t_He3__n_p_He4
       +rho*Y[jli7]*rate_eval.He3_Li7__n_p_He4_He4
       )

    jac[jn, jhe4] = (
       -2*5.00000000000000e-01*rho**2*Y[jn]**2*rate_eval.n_n_He4__He6
       -5.00000000000000e-01*rho**2*Y[jn]*2*Y[jhe4]*rate_eval.n_He4_He4__Be9
       -rho**2*Y[jn]*Y[jp]*rate_eval.n_p_He4__Li6
       +rho*Y[jfe76]*rate_eval.He4_Fe76__n_Ni79
       +rho*Y[jfe75]*rate_eval.He4_Fe75__n_Ni78
       +rho*Y[jfe74]*rate_eval.He4_Fe74__n_Ni77
       +rho*Y[jfe71]*rate_eval.He4_Fe71__n_Ni74
       +rho*Y[jfe70]*rate_eval.He4_Fe70__n_Ni73
       +rho*Y[jfe68]*rate_eval.He4_Fe68__n_Ni71
       +rho*Y[jfe64]*rate_eval.He4_Fe64__n_Ni67
       +rho*Y[jfe63]*rate_eval.He4_Fe63__n_Ni66
       +rho*Y[jfe59]*rate_eval.He4_Fe59__n_Ni62
       +rho*Y[jmn73]*rate_eval.He4_Mn73__n_Co76
       +rho*Y[jmn72]*rate_eval.He4_Mn72__n_Co75
       +rho*Y[jmn69]*rate_eval.He4_Mn69__n_Co72
       +rho*Y[jmn68]*rate_eval.He4_Mn68__n_Co71
       +rho*Y[jsi33]*rate_eval.He4_Si33__n_S36
       +rho*Y[jmn65]*rate_eval.He4_Mn65__n_Co68
       +rho*Y[jmn60]*rate_eval.He4_Mn60__n_Co63
       +rho*Y[jcr70]*rate_eval.He4_Cr70__n_Fe73
       +rho*Y[jcr69]*rate_eval.He4_Cr69__n_Fe72
       +rho*Y[jcr66]*rate_eval.He4_Cr66__n_Fe69
       +rho*Y[jcr65]*rate_eval.He4_Cr65__n_Fe68
       +rho*Y[jcr64]*rate_eval.He4_Cr64__n_Fe67
       +rho*Y[jcr63]*rate_eval.He4_Cr63__n_Fe66
       +rho*Y[jcr62]*rate_eval.He4_Cr62__n_Fe65
       +rho*Y[jcr61]*rate_eval.He4_Cr61__n_Fe64
       +rho*Y[jcr59]*rate_eval.He4_Cr59__n_Fe62
       +rho*Y[jcr55]*rate_eval.He4_Cr55__n_Fe58
       +rho*Y[jti59]*rate_eval.He4_Ti59__n_Cr62
       +rho*Y[jp44]*rate_eval.He4_P44__n_Cl47
       +rho*Y[jv67]*rate_eval.He4_V67__n_Mn70
       +rho*Y[jv66]*rate_eval.He4_V66__n_Mn69
       +rho*Y[jv64]*rate_eval.He4_V64__n_Mn67
       +rho*Y[jv62]*rate_eval.He4_V62__n_Mn65
       +rho*Y[jv61]*rate_eval.He4_V61__n_Mn64
       +rho*Y[jal32]*rate_eval.He4_Al32__n_P35
       +rho*Y[jv59]*rate_eval.He4_V59__n_Mn62
       +rho*Y[jv58]*rate_eval.He4_V58__n_Mn61
       +rho*Y[jv56]*rate_eval.He4_V56__n_Mn59
       +rho*Y[jv55]*rate_eval.He4_V55__n_Mn58
       +rho*Y[jv54]*rate_eval.He4_V54__n_Mn57
       +rho*Y[js45]*rate_eval.He4_S45__n_Ar48
       +rho*Y[jsi43]*rate_eval.He4_Si43__n_S46
       +rho*Y[jne33]*rate_eval.He4_Ne33__n_Mg36
       +rho*Y[jti65]*rate_eval.He4_Ti65__n_Cr68
       +rho*Y[jti64]*rate_eval.He4_Ti64__n_Cr67
       +rho*Y[jti63]*rate_eval.He4_Ti63__n_Cr66
       +rho*Y[jti60]*rate_eval.He4_Ti60__n_Cr63
       +rho*Y[jti58]*rate_eval.He4_Ti58__n_Cr61
       +rho*Y[jti55]*rate_eval.He4_Ti55__n_Cr58
       +rho*Y[jti54]*rate_eval.He4_Ti54__n_Cr57
       +rho*Y[jti53]*rate_eval.He4_Ti53__n_Cr56
       +rho*Y[jti51]*rate_eval.He4_Ti51__n_Cr54
       +rho*Y[jfe73]*rate_eval.He4_Fe73__n_Ni76
       +rho*Y[jf28]*rate_eval.He4_F28__n_Na31
       +rho*Y[jf31]*rate_eval.He4_F31__n_Na34
       +rho*Y[jsc62]*rate_eval.He4_Sc62__n_V65
       +rho*Y[jsc61]*rate_eval.He4_Sc61__n_V64
       +rho*Y[jsc60]*rate_eval.He4_Sc60__n_V63
       +rho*Y[jsc59]*rate_eval.He4_Sc59__n_V62
       +rho*Y[jsc58]*rate_eval.He4_Sc58__n_V61
       +rho*Y[jsc57]*rate_eval.He4_Sc57__n_V60
       +rho*Y[jsc56]*rate_eval.He4_Sc56__n_V59
       +rho*Y[jsc55]*rate_eval.He4_Sc55__n_V58
       +rho*Y[jsc54]*rate_eval.He4_Sc54__n_V57
       +rho*Y[jsc52]*rate_eval.He4_Sc52__n_V55
       +rho*Y[jsc51]*rate_eval.He4_Sc51__n_V54
       +rho*Y[jca58]*rate_eval.He4_Ca58__n_Ti61
       +rho*Y[jca53]*rate_eval.He4_Ca53__n_Ti56
       +rho*Y[jca51]*rate_eval.He4_Ca51__n_Ti54
       +rho*Y[jca47]*rate_eval.He4_Ca47__n_Ti50
       +rho*Y[jca57]*rate_eval.He4_Ca57__n_Ti60
       +rho*Y[jca43]*rate_eval.He4_Ca43__n_Ti46
       +rho*Y[jv63]*rate_eval.He4_V63__n_Mn66
       +rho*Y[jfe66]*rate_eval.He4_Fe66__n_Ni69
       +rho*Y[jp39]*rate_eval.He4_P39__n_Cl42
       +rho*Y[jk57]*rate_eval.He4_K57__n_Sc60
       +rho*Y[jk56]*rate_eval.He4_K56__n_Sc59
       +rho*Y[jk54]*rate_eval.He4_K54__n_Sc57
       +rho*Y[jk53]*rate_eval.He4_K53__n_Sc56
       +rho*Y[jk52]*rate_eval.He4_K52__n_Sc55
       +rho*Y[jk51]*rate_eval.He4_K51__n_Sc54
       +rho*Y[jcr57]*rate_eval.He4_Cr57__n_Fe60
       +rho*Y[jk50]*rate_eval.He4_K50__n_Sc53
       +rho*Y[jk48]*rate_eval.He4_K48__n_Sc51
       +rho*Y[jk42]*rate_eval.He4_K42__n_Sc45
       +rho*Y[jk41]*rate_eval.He4_K41__n_Sc44
       +rho*Y[jf20]*rate_eval.He4_F20__n_Na23
       +rho*Y[jar46]*rate_eval.He4_Ar46__n_Ca49
       +rho*Y[jsi35]*rate_eval.He4_Si35__n_S38
       +rho*Y[jar43]*rate_eval.He4_Ar43__n_Ca46
       +rho*Y[jmn62]*rate_eval.He4_Mn62__n_Co65
       +rho*Y[jcl51]*rate_eval.He4_Cl51__n_K54
       +rho*Y[jcl49]*rate_eval.He4_Cl49__n_K52
       +rho*Y[jca50]*rate_eval.He4_Ca50__n_Ti53
       +rho*Y[jcl47]*rate_eval.He4_Cl47__n_K50
       +rho*Y[jcl42]*rate_eval.He4_Cl42__n_K45
       +rho*Y[jcl41]*rate_eval.He4_Cl41__n_K44
       +rho*Y[jcl40]*rate_eval.He4_Cl40__n_K43
       +rho*Y[js48]*rate_eval.He4_S48__n_Ar51
       +rho*Y[jmg38]*rate_eval.He4_Mg38__n_Si41
       +rho*Y[js43]*rate_eval.He4_S43__n_Ar46
       +rho*Y[jmn67]*rate_eval.He4_Mn67__n_Co70
       +rho*Y[js42]*rate_eval.He4_S42__n_Ar45
       +rho*Y[js41]*rate_eval.He4_S41__n_Ar44
       +rho*Y[jsc63]*rate_eval.He4_Sc63__n_V66
       +rho*Y[js38]*rate_eval.He4_S38__n_Ar41
       +rho*Y[js37]*rate_eval.He4_S37__n_Ar40
       +rho*Y[jk49]*rate_eval.He4_K49__n_Sc52
       +rho*Y[jp34]*rate_eval.He4_P34__n_Cl37
       +rho*Y[js35]*rate_eval.He4_S35__n_Ar38
       +rho*Y[jp47]*rate_eval.He4_P47__n_Cl50
       +rho*Y[jp43]*rate_eval.He4_P43__n_Cl46
       +rho*Y[jal38]*rate_eval.He4_Al38__n_P41
       +rho*Y[jp41]*rate_eval.He4_P41__n_Cl44
       +rho*Y[jp37]*rate_eval.He4_P37__n_Cl40
       +rho*Y[jk55]*rate_eval.He4_K55__n_Sc58
       +rho*Y[jsi44]*rate_eval.He4_Si44__n_S47
       +rho*Y[jp42]*rate_eval.He4_P42__n_Cl45
       +rho*Y[jsi42]*rate_eval.He4_Si42__n_S45
       +rho*Y[jsi40]*rate_eval.He4_Si40__n_S43
       +rho*Y[jsi39]*rate_eval.He4_Si39__n_S42
       +rho*Y[jsi38]*rate_eval.He4_Si38__n_S41
       +rho*Y[jsi37]*rate_eval.He4_Si37__n_S40
       +rho*Y[jv57]*rate_eval.He4_V57__n_Mn60
       +rho*Y[jti61]*rate_eval.He4_Ti61__n_Cr64
       +rho*Y[jar42]*rate_eval.He4_Ar42__n_Ca45
       +rho*Y[jal42]*rate_eval.He4_Al42__n_P45
       +rho*Y[jal40]*rate_eval.He4_Al40__n_P43
       +rho*Y[jal36]*rate_eval.He4_Al36__n_P39
       +rho*Y[jal35]*rate_eval.He4_Al35__n_P38
       +rho*Y[jal34]*rate_eval.He4_Al34__n_P37
       +rho*Y[jal33]*rate_eval.He4_Al33__n_P36
       +rho*Y[jal31]*rate_eval.He4_Al31__n_P34
       +rho*Y[jal29]*rate_eval.He4_Al29__n_P32
       +rho*Y[jal37]*rate_eval.He4_Al37__n_P40
       +rho*Y[jal27]*rate_eval.He4_Al27__n_P30
       +rho*Y[jmg40]*rate_eval.He4_Mg40__n_Si43
       +rho*Y[jmg39]*rate_eval.He4_Mg39__n_Si42
       +rho*Y[jmg37]*rate_eval.He4_Mg37__n_Si40
       +rho*Y[jmg35]*rate_eval.He4_Mg35__n_Si38
       +rho*Y[jmg34]*rate_eval.He4_Mg34__n_Si37
       +rho*Y[jmg32]*rate_eval.He4_Mg32__n_Si35
       +rho*Y[jmg30]*rate_eval.He4_Mg30__n_Si33
       +rho*Y[jne23]*rate_eval.He4_Ne23__n_Mg26
       +rho*Y[jmg27]*rate_eval.He4_Mg27__n_Si30
       +rho*Y[jo23]*rate_eval.He4_O23__n_Ne26
       +rho*Y[jmg26]*rate_eval.He4_Mg26__n_Si29
       +rho*Y[jmg25]*rate_eval.He4_Mg25__n_Si28
       +rho*Y[jna36]*rate_eval.He4_Na36__n_Al39
       +rho*Y[jna38]*rate_eval.He4_Na38__n_Al41
       +rho*Y[jna35]*rate_eval.He4_Na35__n_Al38
       +rho*Y[jna34]*rate_eval.He4_Na34__n_Al37
       +rho*Y[jv60]*rate_eval.He4_V60__n_Mn63
       +rho*Y[jna31]*rate_eval.He4_Na31__n_Al34
       +rho*Y[jna28]*rate_eval.He4_Na28__n_Al31
       +rho*Y[jna26]*rate_eval.He4_Na26__n_Al29
       +rho*Y[js46]*rate_eval.He4_S46__n_Ar49
       +rho*Y[jne31]*rate_eval.He4_Ne31__n_Mg34
       +rho*Y[jne30]*rate_eval.He4_Ne30__n_Mg33
       +rho*Y[jne28]*rate_eval.He4_Ne28__n_Mg31
       +rho*Y[jne27]*rate_eval.He4_Ne27__n_Mg30
       +rho*Y[js39]*rate_eval.He4_S39__n_Ar42
       +rho*Y[jne24]*rate_eval.He4_Ne24__n_Mg27
       +rho*Y[jca61]*rate_eval.He4_Ca61__n_Ti64
       +rho*Y[jne22]*rate_eval.He4_Ne22__n_Mg25
       +rho*Y[jne21]*rate_eval.He4_Ne21__n_Mg24
       +rho*Y[jar53]*rate_eval.He4_Ar53__n_Ca56
       +rho*Y[jf29]*rate_eval.He4_F29__n_Na32
       +rho*Y[jf27]*rate_eval.He4_F27__n_Na30
       +rho*Y[jf26]*rate_eval.He4_F26__n_Na29
       +rho*Y[jf24]*rate_eval.He4_F24__n_Na27
       +rho*Y[jf21]*rate_eval.He4_F21__n_Na24
       +rho*Y[jo28]*rate_eval.He4_O28__n_Ne31
       +rho*Y[jo26]*rate_eval.He4_O26__n_Ne29
       +rho*Y[jo24]*rate_eval.He4_O24__n_Ne27
       +rho*Y[jf30]*rate_eval.He4_F30__n_Na33
       +rho*Y[jo22]*rate_eval.He4_O22__n_Ne25
       +rho*Y[jar52]*rate_eval.He4_Ar52__n_Ca55
       +rho*Y[jo19]*rate_eval.He4_O19__n_Ne22
       +rho*Y[jo17]*rate_eval.He4_O17__n_Ne20
       +rho*Y[jne26]*rate_eval.He4_Ne26__n_Mg29
       +rho*Y[jal28]*rate_eval.He4_Al28__n_P31
       +rho*Y[jar41]*rate_eval.He4_Ar41__n_Ca44
       +rho*Y[jc15]*rate_eval.He4_C15__n_O18
       +rho*Y[jcl50]*rate_eval.He4_Cl50__n_K53
       +rho*Y[jsi31]*rate_eval.He4_Si31__n_S34
       +rho*Y[jcl45]*rate_eval.He4_Cl45__n_K48
       +rho*Y[jc13]*rate_eval.He4_C13__n_O16
       +rho*Y[jb13]*rate_eval.He4_B13__n_N16
       +rho*Y[jb12]*rate_eval.He4_B12__n_N15
       +rho*Y[jli8]*rate_eval.He4_Li8__n_B11
       +rho*Y[jsc48]*rate_eval.He4_Sc48__n_V51
       +rho*Y[jp36]*rate_eval.He4_P36__n_Cl39
       +rho*Y[jo25]*rate_eval.He4_O25__n_Ne28
       +rho*Y[jp40]*rate_eval.He4_P40__n_Cl43
       +rho*Y[jna37]*rate_eval.He4_Na37__n_Al40
       +rho*Y[jne32]*rate_eval.He4_Ne32__n_Mg35
       +rho*Y[jna39]*rate_eval.He4_Na39__n_Al42
       +rho*Y[jti57]*rate_eval.He4_Ti57__n_Cr60
       +rho*Y[jna32]*rate_eval.He4_Na32__n_Al35
       +rho*Y[jca60]*rate_eval.He4_Ca60__n_Ti63
       +rho*Y[jti49]*rate_eval.He4_Ti49__n_Cr52
       +rho*Y[jf25]*rate_eval.He4_F25__n_Na28
       +rho*Y[jna27]*rate_eval.He4_Na27__n_Al30
       +rho*Y[jmn59]*rate_eval.He4_Mn59__n_Co62
       +rho*Y[jbe11]*rate_eval.He4_Be11__n_C14
       +rho*Y[jcl46]*rate_eval.He4_Cl46__n_K49
       +rho*Y[jcl44]*rate_eval.He4_Cl44__n_K47
       +rho*Y[jcr60]*rate_eval.He4_Cr60__n_Fe63
       +rho*Y[jar54]*rate_eval.He4_Ar54__n_Ca57
       +rho*Y[jca45]*rate_eval.He4_Ca45__n_Ti48
       +rho*Y[jo21]*rate_eval.He4_O21__n_Ne24
       +rho*Y[jmg33]*rate_eval.He4_Mg33__n_Si36
       +rho*Y[jcl38]*rate_eval.He4_Cl38__n_K41
       +rho*Y[jn14]*rate_eval.He4_N14__n_F17
       +rho*Y[jti62]*rate_eval.He4_Ti62__n_Cr65
       +rho*Y[jmg31]*rate_eval.He4_Mg31__n_Si34
       +rho*Y[js49]*rate_eval.He4_S49__n_Ar52
       +rho*Y[jne29]*rate_eval.He4_Ne29__n_Mg32
       +rho*Y[jti56]*rate_eval.He4_Ti56__n_Cr59
       +rho*Y[jk58]*rate_eval.He4_K58__n_Sc61
       +rho*Y[jcl52]*rate_eval.He4_Cl52__n_K55
       +rho*Y[jmg29]*rate_eval.He4_Mg29__n_Si32
       +rho*Y[jo20]*rate_eval.He4_O20__n_Ne23
       +rho*Y[jar44]*rate_eval.He4_Ar44__n_Ca47
       +rho*Y[jfe62]*rate_eval.He4_Fe62__n_Ni65
       +rho*Y[jca49]*rate_eval.He4_Ca49__n_Ti52
       +rho*Y[jmn61]*rate_eval.He4_Mn61__n_Co64
       +rho*Y[jk47]*rate_eval.He4_K47__n_Sc50
       +rho*Y[jmg36]*rate_eval.He4_Mg36__n_Si39
       +rho*Y[jb11]*rate_eval.He4_B11__n_N14
       +rho*Y[jk59]*rate_eval.He4_K59__n_Sc62
       +rho*Y[js47]*rate_eval.He4_S47__n_Ar50
       +rho*Y[jmg28]*rate_eval.He4_Mg28__n_Si31
       +rho*Y[jcr68]*rate_eval.He4_Cr68__n_Fe71
       +rho*Y[jo18]*rate_eval.He4_O18__n_Ne21
       +rho*Y[jbe9]*rate_eval.He4_Be9__n_C12
       +rho*Y[jp46]*rate_eval.He4_P46__n_Cl49
       +rho*Y[jv65]*rate_eval.He4_V65__n_Mn68
       +rho*Y[jbe10]*rate_eval.He4_Be10__n_C13
       +rho*Y[jca55]*rate_eval.He4_Ca55__n_Ti58
       +rho*Y[jsi36]*rate_eval.He4_Si36__n_S39
       +rho*Y[jal43]*rate_eval.He4_Al43__n_P46
       +rho*Y[jne25]*rate_eval.He4_Ne25__n_Mg28
       +rho*Y[jo27]*rate_eval.He4_O27__n_Ne30
       +rho*Y[jcl43]*rate_eval.He4_Cl43__n_K46
       +rho*Y[jna33]*rate_eval.He4_Na33__n_Al36
       +rho*Y[jna25]*rate_eval.He4_Na25__n_Al28
       +rho*Y[jar47]*rate_eval.He4_Ar47__n_Ca50
       +rho*Y[js40]*rate_eval.He4_S40__n_Ar43
       +rho*Y[jna29]*rate_eval.He4_Na29__n_Al32
       +rho*Y[jp45]*rate_eval.He4_P45__n_Cl48
       +rho*Y[jmg41]*rate_eval.He4_Mg41__n_Si44
       +rho*Y[jk44]*rate_eval.He4_K44__n_Sc47
       +rho*Y[jmn70]*rate_eval.He4_Mn70__n_Co73
       +rho*Y[jsc53]*rate_eval.He4_Sc53__n_V56
       +rho*Y[jar45]*rate_eval.He4_Ar45__n_Ca48
       +rho*Y[jmn63]*rate_eval.He4_Mn63__n_Co66
       +rho*Y[jfe61]*rate_eval.He4_Fe61__n_Ni64
       +rho*Y[jk45]*rate_eval.He4_K45__n_Sc48
       +rho*Y[jp38]*rate_eval.He4_P38__n_Cl41
       +rho*Y[jcl48]*rate_eval.He4_Cl48__n_K51
       +rho*Y[jar50]*rate_eval.He4_Ar50__n_Ca53
       +rho*Y[jb10]*rate_eval.He4_B10__n_N13
       +rho*Y[jmn58]*rate_eval.He4_Mn58__n_Co61
       +rho*Y[jli9]*rate_eval.He4_Li9__n_B12
       +rho*Y[jn16]*rate_eval.He4_N16__n_F19
       +rho*Y[jsc46]*rate_eval.He4_Sc46__n_V49
       +rho*Y[jfe65]*rate_eval.He4_Fe65__n_Ni68
       +rho*Y[jal39]*rate_eval.He4_Al39__n_P42
       +rho*Y[jmn64]*rate_eval.He4_Mn64__n_Co67
       +rho*Y[jfe67]*rate_eval.He4_Fe67__n_Ni70
       +rho*Y[jne34]*rate_eval.He4_Ne34__n_Mg37
       +rho*Y[jna30]*rate_eval.He4_Na30__n_Al33
       +rho*Y[jar49]*rate_eval.He4_Ar49__n_Ca52
       +rho*Y[jna24]*rate_eval.He4_Na24__n_Al27
       +rho*Y[jv52]*rate_eval.He4_V52__n_Mn55
       +rho*Y[jmn71]*rate_eval.He4_Mn71__n_Co74
       +rho*Y[jmn66]*rate_eval.He4_Mn66__n_Co69
       +rho*Y[jca52]*rate_eval.He4_Ca52__n_Ti55
       +rho*Y[jca54]*rate_eval.He4_Ca54__n_Ti57
       +rho*Y[jal41]*rate_eval.He4_Al41__n_P44
       +rho*Y[jsi41]*rate_eval.He4_Si41__n_S44
       +rho*Y[jar51]*rate_eval.He4_Ar51__n_Ca54
       +rho*Y[jf22]*rate_eval.He4_F22__n_Na25
       +rho*Y[jsi34]*rate_eval.He4_Si34__n_S37
       +rho*Y[jar48]*rate_eval.He4_Ar48__n_Ca51
       +rho*Y[jcr58]*rate_eval.He4_Cr58__n_Fe61
       +rho*Y[jcr67]*rate_eval.He4_Cr67__n_Fe70
       +rho*Y[jca59]*rate_eval.He4_Ca59__n_Ti62
       +rho*Y[js34]*rate_eval.He4_S34__n_Ar37
       +rho*Y[jf23]*rate_eval.He4_F23__n_Na26
       +rho*Y[jfe72]*rate_eval.He4_Fe72__n_Ni75
       +rho*Y[js44]*rate_eval.He4_S44__n_Ar47
       +rho*Y[jal30]*rate_eval.He4_Al30__n_P33
       +rho*Y[jsc50]*rate_eval.He4_Sc50__n_V53
       +rho*Y[jca56]*rate_eval.He4_Ca56__n_Ti59
       +rho*Y[jsi45]*rate_eval.He4_Si45__n_S48
       +rho*Y[jfe69]*rate_eval.He4_Fe69__n_Ni72
       +rho*Y[jk46]*rate_eval.He4_K46__n_Sc49
       )

    jac[jn, jhe8] = (
       +rate_eval.He8__n_Li7__weak__wc12
       )

    jac[jn, jli6] = (
       -rho*Y[jn]*rate_eval.n_Li6__He4_t
       -rho*Y[jn]*rate_eval.n_Li6__Li7
       +rho*Y[jd]*rate_eval.d_Li6__n_Be7
       )

    jac[jn, jli7] = (
       -rho*Y[jn]*rate_eval.n_Li7__Li8
       +rho*Y[jd]*rate_eval.d_Li7__n_He4_He4
       +rho*Y[jt]*rate_eval.t_Li7__n_Be9
       +2*rho*Y[jt]*rate_eval.t_Li7__n_n_He4_He4
       +rho*Y[jhe3]*rate_eval.He3_Li7__n_p_He4_He4
       )

    jac[jn, jli8] = (
       -rho*Y[jn]*rate_eval.n_Li8__Li9
       +rho*Y[jd]*rate_eval.d_Li8__n_Be9
       +rho*Y[jhe4]*rate_eval.He4_Li8__n_B11
       +rho*Y[jp]*rate_eval.p_Li8__n_He4_He4
       )

    jac[jn, jli9] = (
       +rho*Y[jhe4]*rate_eval.He4_Li9__n_B12
       )

    jac[jn, jli11] = (
       +2*rate_eval.Li11__n_n_Be9__weak__wc12
       +rate_eval.Li11__n_Be10__weak__wc17
       )

    jac[jn, jbe7] = (
       -rho*Y[jn]*rate_eval.n_Be7__He4_He4
       -rho*Y[jn]*rate_eval.n_Be7__p_Li7
       +rho*Y[jt]*rate_eval.t_Be7__n_p_He4_He4
       )

    jac[jn, jbe9] = (
       -rho*Y[jn]*rate_eval.n_Be9__Be10
       +rho*Y[jp]*rate_eval.p_Be9__n_p_He4_He4
       +rho*Y[jt]*rate_eval.t_Be9__n_B11
       +rho*Y[jhe4]*rate_eval.He4_Be9__n_C12
       )

    jac[jn, jbe10] = (
       -rho*Y[jn]*rate_eval.n_Be10__Be11
       +rho*Y[jhe4]*rate_eval.He4_Be10__n_C13
       )

    jac[jn, jbe11] = (
       -rho*Y[jn]*rate_eval.n_Be11__Be12
       +rho*Y[jhe4]*rate_eval.He4_Be11__n_C14
       )

    jac[jn, jbe12] = (
       +rate_eval.Be12__n_B11__weak__wc12
       )

    jac[jn, jbe14] = (
       +2*rate_eval.Be14__n_n_B12__weak__wc12
       +rate_eval.Be14__n_B13__weak__wc17
       )

    jac[jn, jbe15] = (
       +rate_eval.Be15__n_Be14
       )

    jac[jn, jbe16] = (
       +2*rate_eval.Be16__n_n_Be14
       )

    jac[jn, jb8] = (
       -rho*Y[jn]*rate_eval.n_B8__p_He4_He4
       )

    jac[jn, jb10] = (
       -rho*Y[jn]*rate_eval.n_B10__B11
       -rho*Y[jn]*rate_eval.n_B10__He4_Li7
       +rho*Y[jhe4]*rate_eval.He4_B10__n_N13
       )

    jac[jn, jb11] = (
       -rho*Y[jn]*rate_eval.n_B11__B12
       +rho*Y[jhe4]*rate_eval.He4_B11__n_N14
       )

    jac[jn, jb12] = (
       -rho*Y[jn]*rate_eval.n_B12__B13
       +rho*Y[jp]*rate_eval.p_B12__n_C12
       +rho*Y[jhe4]*rate_eval.He4_B12__n_N15
       )

    jac[jn, jb13] = (
       -rho*Y[jn]*rate_eval.n_B13__B14
       +rho*Y[jhe4]*rate_eval.He4_B13__n_N16
       )

    jac[jn, jb15] = (
       +2*rate_eval.B15__n_n_C13__weak__wc12
       +rate_eval.B15__n_C14__weak__wc12
       )

    jac[jn, jb17] = (
       +3*rate_eval.B17__n_n_n_C14__weak__wc12
       +2*rate_eval.B17__n_n_C15__weak__wc12
       +rate_eval.B17__n_C16__weak__wc17
       )

    jac[jn, jb18] = (
       +rate_eval.B18__n_B17
       )

    jac[jn, jb19] = (
       +rate_eval.B19__n_C18__weak__wc17
       +2*rate_eval.B19__n_n_C17__weak__wc12
       )

    jac[jn, jc11] = (
       -rho*Y[jn]*rate_eval.n_C11__He4_He4_He4
       -rho*Y[jn]*rate_eval.n_C11__p_B11
       -rho*Y[jn]*rate_eval.n_C11__C12
       )

    jac[jn, jc12] = (
       -rho*Y[jn]*rate_eval.n_C12__C13
       +rho*Y[jne20]*rate_eval.C12_Ne20__n_S31
       )

    jac[jn, jc13] = (
       -rho*Y[jn]*rate_eval.n_C13__C14
       +rho*Y[jhe4]*rate_eval.He4_C13__n_O16
       +rho*Y[jd]*rate_eval.d_C13__n_N14
       +rho*Y[jp]*rate_eval.p_C13__n_N13
       )

    jac[jn, jc14] = (
       -rho*Y[jn]*rate_eval.n_C14__C15
       +rho*Y[jd]*rate_eval.d_C14__n_N15
       )

    jac[jn, jc15] = (
       -rho*Y[jn]*rate_eval.n_C15__C16
       +rho*Y[jhe4]*rate_eval.He4_C15__n_O18
       +rho*Y[jp]*rate_eval.p_C15__n_N15
       )

    jac[jn, jc16] = (
       -rho*Y[jn]*rate_eval.n_C16__C17
       +rate_eval.C16__n_N15__weak__wc12
       )

    jac[jn, jc17] = (
       +rate_eval.C17__n_N16__weak__wc12
       )

    jac[jn, jc18] = (
       +rate_eval.C18__n_N17__weak__wc12
       )

    jac[jn, jc19] = (
       +rate_eval.C19__n_N18__weak__wc12
       )

    jac[jn, jc20] = (
       +rate_eval.C20__n_N19__weak__wc12
       )

    jac[jn, jc21] = (
       +rate_eval.C21__n_C20
       )

    jac[jn, jc22] = (
       +rate_eval.C22__n_N21__weak__wc17
       )

    jac[jn, jn13] = (
       -rho*Y[jn]*rate_eval.n_N13__N14
       )

    jac[jn, jn14] = (
       -rho*Y[jn]*rate_eval.n_N14__p_C14
       -rho*Y[jn]*rate_eval.n_N14__N15
       +rho*Y[jhe4]*rate_eval.He4_N14__n_F17
       +rho*Y[jp]*rate_eval.p_N14__n_O14
       )

    jac[jn, jn15] = (
       -rho*Y[jn]*rate_eval.n_N15__N16
       +rho*Y[jp]*rate_eval.p_N15__n_O15
       )

    jac[jn, jn16] = (
       -rho*Y[jn]*rate_eval.n_N16__N17
       +rho*Y[jhe4]*rate_eval.He4_N16__n_F19
       +rho*Y[jp]*rate_eval.p_N16__n_O16
       )

    jac[jn, jn17] = (
       -rho*Y[jn]*rate_eval.n_N17__N18
       +rate_eval.N17__n_O16__weak__wc12
       )

    jac[jn, jn18] = (
       -rho*Y[jn]*rate_eval.n_N18__N19
       +rate_eval.N18__n_O17__weak__wc12
       )

    jac[jn, jn19] = (
       -rho*Y[jn]*rate_eval.n_N19__N20
       +rate_eval.N19__n_O18__weak__wc12
       )

    jac[jn, jn20] = (
       +rate_eval.N20__n_O19__weak__wc12
       )

    jac[jn, jn21] = (
       +rate_eval.N21__n_O20__weak__wc12
       )

    jac[jn, jn22] = (
       +2*rate_eval.N22__n_n_O20__weak__wc12
       +rate_eval.N22__n_O21__weak__wc17
       )

    jac[jn, jn24] = (
       +rate_eval.N24__n_N23
       )

    jac[jn, jo12] = (
       -rho*Y[jn]*rate_eval.n_O12__O13
       -rho*Y[jn]*rate_eval.n_O12__p_N12
       -rho*Y[jn]*rate_eval.n_O12__He4_C9
       )

    jac[jn, jo13] = (
       -rho*Y[jn]*rate_eval.n_O13__He4_C10
       -rho*Y[jn]*rate_eval.n_O13__p_N13
       -rho*Y[jn]*rate_eval.n_O13__O14
       )

    jac[jn, jo14] = (
       -rho*Y[jn]*rate_eval.n_O14__O15
       -rho*Y[jn]*rate_eval.n_O14__He4_C11
       )

    jac[jn, jo15] = (
       -rho*Y[jn]*rate_eval.n_O15__He4_C12
       -rho*Y[jn]*rate_eval.n_O15__O16
       )

    jac[jn, jo16] = (
       -rho*Y[jn]*rate_eval.n_O16__O17
       +5.00000000000000e-01*rho*2*Y[jo16]*rate_eval.O16_O16__n_S31
       )

    jac[jn, jo17] = (
       -rho*Y[jn]*rate_eval.n_O17__O18
       -rho*Y[jn]*rate_eval.n_O17__He4_C14
       +rho*Y[jhe4]*rate_eval.He4_O17__n_Ne20
       )

    jac[jn, jo18] = (
       -rho*Y[jn]*rate_eval.n_O18__O19
       +rho*Y[jhe4]*rate_eval.He4_O18__n_Ne21
       )

    jac[jn, jo19] = (
       -rho*Y[jn]*rate_eval.n_O19__O20
       +rho*Y[jhe4]*rate_eval.He4_O19__n_Ne22
       +rho*Y[jp]*rate_eval.p_O19__n_F19
       )

    jac[jn, jo20] = (
       -rho*Y[jn]*rate_eval.n_O20__O21
       +rho*Y[jp]*rate_eval.p_O20__n_F20
       +rho*Y[jhe4]*rate_eval.He4_O20__n_Ne23
       )

    jac[jn, jo21] = (
       -rho*Y[jn]*rate_eval.n_O21__O22
       +rho*Y[jp]*rate_eval.p_O21__n_F21
       +rho*Y[jhe4]*rate_eval.He4_O21__n_Ne24
       )

    jac[jn, jo22] = (
       -rho*Y[jn]*rate_eval.n_O22__O23
       +rho*Y[jp]*rate_eval.p_O22__n_F22
       +rho*Y[jhe4]*rate_eval.He4_O22__n_Ne25
       )

    jac[jn, jo23] = (
       -rho*Y[jn]*rate_eval.n_O23__O24
       +rho*Y[jhe4]*rate_eval.He4_O23__n_Ne26
       +rho*Y[jp]*rate_eval.p_O23__n_F23
       +rate_eval.O23__n_F22__weak__wc12
       )

    jac[jn, jo24] = (
       -rho*Y[jn]*rate_eval.n_O24__O25
       +rho*Y[jhe4]*rate_eval.He4_O24__n_Ne27
       +rho*Y[jp]*rate_eval.p_O24__n_F24
       +rate_eval.O24__n_F23__weak__wc12
       )

    jac[jn, jo25] = (
       +rho*Y[jp]*rate_eval.p_O25__n_F25
       +rho*Y[jhe4]*rate_eval.He4_O25__n_Ne28
       +rate_eval.O25__n_F24__weak__mp17
       +2*rate_eval.O25__n_n_F23__weak__mp17
       )

    jac[jn, jo26] = (
       +rho*Y[jhe4]*rate_eval.He4_O26__n_Ne29
       +rho*Y[jp]*rate_eval.p_O26__n_F26
       +2*rate_eval.O26__n_n_F24__weak__mp17
       +rate_eval.O26__n_O25
       +rate_eval.O26__n_F25__weak__mp17
       +3*rate_eval.O26__n_n_n_F23__weak__mo03
       )

    jac[jn, jo27] = (
       +3*rate_eval.O27__n_n_n_F24__weak__mo03
       +2*rate_eval.O27__n_n_F25__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_O27__n_Ne30
       +rho*Y[jp]*rate_eval.p_O27__n_F27
       +rate_eval.O27__n_O26
       +rate_eval.O27__n_F26__weak__mp17
       )

    jac[jn, jo28] = (
       +rate_eval.O28__n_O27
       +3*rate_eval.O28__n_n_n_F25__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_O28__n_Ne31
       +2*rate_eval.O28__n_n_F26__weak__mp17
       +rate_eval.O28__n_F27__weak__mp17
       )

    jac[jn, jf14] = (
       -rho*Y[jn]*rate_eval.n_F14__He4_N11
       -rho*Y[jn]*rate_eval.n_F14__F15
       -rho*Y[jn]*rate_eval.n_F14__p_O14
       )

    jac[jn, jf15] = (
       -rho*Y[jn]*rate_eval.n_F15__He4_N12
       -rho*Y[jn]*rate_eval.n_F15__F16
       -rho*Y[jn]*rate_eval.n_F15__p_O15
       )

    jac[jn, jf16] = (
       -rho*Y[jn]*rate_eval.n_F16__p_O16
       -rho*Y[jn]*rate_eval.n_F16__He4_N13
       -rho*Y[jn]*rate_eval.n_F16__F17
       )

    jac[jn, jf17] = (
       -rho*Y[jn]*rate_eval.n_F17__F18
       -rho*Y[jn]*rate_eval.n_F17__p_O17
       )

    jac[jn, jf18] = (
       -rho*Y[jn]*rate_eval.n_F18__He4_N15
       -rho*Y[jn]*rate_eval.n_F18__p_O18
       -rho*Y[jn]*rate_eval.n_F18__F19
       )

    jac[jn, jf19] = (
       -rho*Y[jn]*rate_eval.n_F19__F20
       +rho*Y[jp]*rate_eval.p_F19__n_Ne19
       )

    jac[jn, jf20] = (
       -rho*Y[jn]*rate_eval.n_F20__F21
       +rho*Y[jhe4]*rate_eval.He4_F20__n_Na23
       +rho*Y[jp]*rate_eval.p_F20__n_Ne20
       )

    jac[jn, jf21] = (
       -rho*Y[jn]*rate_eval.n_F21__F22
       +rho*Y[jhe4]*rate_eval.He4_F21__n_Na24
       +rho*Y[jp]*rate_eval.p_F21__n_Ne21
       )

    jac[jn, jf22] = (
       -rho*Y[jn]*rate_eval.n_F22__F23
       +rho*Y[jp]*rate_eval.p_F22__n_Ne22
       +rho*Y[jhe4]*rate_eval.He4_F22__n_Na25
       )

    jac[jn, jf23] = (
       -rho*Y[jn]*rate_eval.n_F23__F24
       +rho*Y[jp]*rate_eval.p_F23__n_Ne23
       +rho*Y[jhe4]*rate_eval.He4_F23__n_Na26
       )

    jac[jn, jf24] = (
       -rho*Y[jn]*rate_eval.n_F24__F25
       +rho*Y[jhe4]*rate_eval.He4_F24__n_Na27
       +rho*Y[jp]*rate_eval.p_F24__n_Ne24
       +rate_eval.F24__n_Ne23__weak__wc12
       )

    jac[jn, jf25] = (
       -rho*Y[jn]*rate_eval.n_F25__F26
       +rho*Y[jp]*rate_eval.p_F25__n_Ne25
       +rho*Y[jhe4]*rate_eval.He4_F25__n_Na28
       +rate_eval.F25__n_Ne24__weak__wc12
       )

    jac[jn, jf26] = (
       -rho*Y[jn]*rate_eval.n_F26__F27
       +rho*Y[jhe4]*rate_eval.He4_F26__n_Na29
       +rho*Y[jp]*rate_eval.p_F26__n_Ne26
       +rate_eval.F26__n_Ne25__weak__wc12
       )

    jac[jn, jf27] = (
       -rho*Y[jn]*rate_eval.n_F27__F28
       +3*rate_eval.F27__n_n_n_Ne24__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_F27__n_Na30
       +rho*Y[jp]*rate_eval.p_F27__n_Ne27
       +2*rate_eval.F27__n_n_Ne25__weak__mp17
       +rate_eval.F27__n_Ne26__weak__wc12
       )

    jac[jn, jf28] = (
       +3*rate_eval.F28__n_n_n_Ne25__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_F28__n_Na31
       +rho*Y[jp]*rate_eval.p_F28__n_Ne28
       +2*rate_eval.F28__n_n_Ne26__weak__mp17
       +rate_eval.F28__n_Ne27__weak__mp17
       )

    jac[jn, jf29] = (
       +3*rate_eval.F29__n_n_n_Ne26__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_F29__n_Na32
       +rho*Y[jp]*rate_eval.p_F29__n_Ne29
       +rate_eval.F29__n_Ne28__weak__wc12
       )

    jac[jn, jf30] = (
       +rho*Y[jhe4]*rate_eval.He4_F30__n_Na33
       +2*rate_eval.F30__n_n_Ne28__weak__mp17
       +rate_eval.F30__n_Ne29__weak__mp17
       +rho*Y[jp]*rate_eval.p_F30__n_Ne30
       +3*rate_eval.F30__n_n_n_Ne27__weak__mo03
       )

    jac[jn, jf31] = (
       +3*rate_eval.F31__n_n_n_Ne28__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_F31__n_Na34
       +2*rate_eval.F31__n_n_Ne29__weak__mp17
       +rho*Y[jp]*rate_eval.p_F31__n_Ne31
       +rate_eval.F31__n_Ne30__weak__mp17
       )

    jac[jn, jne16] = (
       -rho*Y[jn]*rate_eval.n_Ne16__p_F16
       -rho*Y[jn]*rate_eval.n_Ne16__He4_O13
       -rho*Y[jn]*rate_eval.n_Ne16__Ne17
       )

    jac[jn, jne17] = (
       -rho*Y[jn]*rate_eval.n_Ne17__He4_O14
       -rho*Y[jn]*rate_eval.n_Ne17__Ne18
       -rho*Y[jn]*rate_eval.n_Ne17__p_F17
       )

    jac[jn, jne18] = (
       -rho*Y[jn]*rate_eval.n_Ne18__He4_O15
       -rho*Y[jn]*rate_eval.n_Ne18__p_F18
       -rho*Y[jn]*rate_eval.n_Ne18__Ne19
       )

    jac[jn, jne19] = (
       -rho*Y[jn]*rate_eval.n_Ne19__He4_O16
       -rho*Y[jn]*rate_eval.n_Ne19__Ne20
       )

    jac[jn, jne20] = (
       -rho*Y[jn]*rate_eval.n_Ne20__Ne21
       +rho*Y[jc12]*rate_eval.C12_Ne20__n_S31
       )

    jac[jn, jne21] = (
       -rho*Y[jn]*rate_eval.n_Ne21__Ne22
       +rho*Y[jhe4]*rate_eval.He4_Ne21__n_Mg24
       )

    jac[jn, jne22] = (
       -rho*Y[jn]*rate_eval.n_Ne22__Ne23
       +rho*Y[jhe4]*rate_eval.He4_Ne22__n_Mg25
       )

    jac[jn, jne23] = (
       -rho*Y[jn]*rate_eval.n_Ne23__Ne24
       +rho*Y[jhe4]*rate_eval.He4_Ne23__n_Mg26
       +rho*Y[jp]*rate_eval.p_Ne23__n_Na23
       )

    jac[jn, jne24] = (
       -rho*Y[jn]*rate_eval.n_Ne24__Ne25
       +rho*Y[jhe4]*rate_eval.He4_Ne24__n_Mg27
       +rho*Y[jp]*rate_eval.p_Ne24__n_Na24
       )

    jac[jn, jne25] = (
       -rho*Y[jn]*rate_eval.n_Ne25__Ne26
       +rho*Y[jp]*rate_eval.p_Ne25__n_Na25
       +rho*Y[jhe4]*rate_eval.He4_Ne25__n_Mg28
       )

    jac[jn, jne26] = (
       -rho*Y[jn]*rate_eval.n_Ne26__Ne27
       +rate_eval.Ne26__n_Na25__weak__wc12
       +rho*Y[jp]*rate_eval.p_Ne26__n_Na26
       +rho*Y[jhe4]*rate_eval.He4_Ne26__n_Mg29
       )

    jac[jn, jne27] = (
       -rho*Y[jn]*rate_eval.n_Ne27__Ne28
       +rate_eval.Ne27__n_Na26__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Ne27__n_Mg30
       +rho*Y[jp]*rate_eval.p_Ne27__n_Na27
       )

    jac[jn, jne28] = (
       -rho*Y[jn]*rate_eval.n_Ne28__Ne29
       +rho*Y[jhe4]*rate_eval.He4_Ne28__n_Mg31
       +rho*Y[jp]*rate_eval.p_Ne28__n_Na28
       +rate_eval.Ne28__n_Na27__weak__wc12
       )

    jac[jn, jne29] = (
       -rho*Y[jn]*rate_eval.n_Ne29__Ne30
       +rho*Y[jp]*rate_eval.p_Ne29__n_Na29
       +rho*Y[jhe4]*rate_eval.He4_Ne29__n_Mg32
       +2*rate_eval.Ne29__n_n_Na27__weak__wc12
       +rate_eval.Ne29__n_Na28__weak__wc17
       )

    jac[jn, jne30] = (
       -rho*Y[jn]*rate_eval.n_Ne30__Ne31
       +rho*Y[jhe4]*rate_eval.He4_Ne30__n_Mg33
       +rho*Y[jp]*rate_eval.p_Ne30__n_Na30
       +rate_eval.Ne30__n_Na29__weak__wc12
       )

    jac[jn, jne31] = (
       -rho*Y[jn]*rate_eval.n_Ne31__Ne32
       +3*rate_eval.Ne31__n_n_n_Na28__weak__mo03
       +rate_eval.Ne31__n_Na30__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Ne31__n_Mg34
       +rho*Y[jp]*rate_eval.p_Ne31__n_Na31
       +2*rate_eval.Ne31__n_n_Na29__weak__mp17
       )

    jac[jn, jne32] = (
       -rho*Y[jn]*rate_eval.n_Ne32__Ne33
       +rho*Y[jp]*rate_eval.p_Ne32__n_Na32
       +rho*Y[jhe4]*rate_eval.He4_Ne32__n_Mg35
       +rate_eval.Ne32__n_Na31__weak__mp17
       +2*rate_eval.Ne32__n_n_Na30__weak__mp17
       +3*rate_eval.Ne32__n_n_n_Na29__weak__mo03
       )

    jac[jn, jne33] = (
       -rho*Y[jn]*rate_eval.n_Ne33__Ne34
       +rho*Y[jhe4]*rate_eval.He4_Ne33__n_Mg36
       +rho*Y[jp]*rate_eval.p_Ne33__n_Na33
       +3*rate_eval.Ne33__n_n_n_Na30__weak__mo03
       +rate_eval.Ne33__n_Na32__weak__mp17
       +2*rate_eval.Ne33__n_n_Na31__weak__mp17
       )

    jac[jn, jne34] = (
       +3*rate_eval.Ne34__n_n_n_Na31__weak__mo03
       +rho*Y[jp]*rate_eval.p_Ne34__n_Na34
       +2*rate_eval.Ne34__n_n_Na32__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Ne34__n_Mg37
       +rate_eval.Ne34__n_Na33__weak__mp17
       )

    jac[jn, jna19] = (
       -rho*Y[jn]*rate_eval.n_Na19__p_Ne19
       -rho*Y[jn]*rate_eval.n_Na19__Na20
       -rho*Y[jn]*rate_eval.n_Na19__He4_F16
       )

    jac[jn, jna20] = (
       -rho*Y[jn]*rate_eval.n_Na20__He4_F17
       -rho*Y[jn]*rate_eval.n_Na20__Na21
       -rho*Y[jn]*rate_eval.n_Na20__p_Ne20
       )

    jac[jn, jna21] = (
       -rho*Y[jn]*rate_eval.n_Na21__He4_F18
       -rho*Y[jn]*rate_eval.n_Na21__p_Ne21
       -rho*Y[jn]*rate_eval.n_Na21__Na22
       )

    jac[jn, jna22] = (
       -rho*Y[jn]*rate_eval.n_Na22__Na23
       -rho*Y[jn]*rate_eval.n_Na22__p_Ne22
       -rho*Y[jn]*rate_eval.n_Na22__He4_F19
       )

    jac[jn, jna23] = (
       -rho*Y[jn]*rate_eval.n_Na23__Na24
       +rho*Y[jp]*rate_eval.p_Na23__n_Mg23
       )

    jac[jn, jna24] = (
       -rho*Y[jn]*rate_eval.n_Na24__Na25
       +rho*Y[jhe4]*rate_eval.He4_Na24__n_Al27
       +rho*Y[jp]*rate_eval.p_Na24__n_Mg24
       )

    jac[jn, jna25] = (
       -rho*Y[jn]*rate_eval.n_Na25__Na26
       +rho*Y[jhe4]*rate_eval.He4_Na25__n_Al28
       +rho*Y[jp]*rate_eval.p_Na25__n_Mg25
       )

    jac[jn, jna26] = (
       -rho*Y[jn]*rate_eval.n_Na26__Na27
       +rho*Y[jhe4]*rate_eval.He4_Na26__n_Al29
       +rho*Y[jp]*rate_eval.p_Na26__n_Mg26
       )

    jac[jn, jna27] = (
       -rho*Y[jn]*rate_eval.n_Na27__Na28
       +rate_eval.Na27__n_Mg26__weak__wc12
       +rho*Y[jp]*rate_eval.p_Na27__n_Mg27
       +rho*Y[jhe4]*rate_eval.He4_Na27__n_Al30
       )

    jac[jn, jna28] = (
       -rho*Y[jn]*rate_eval.n_Na28__Na29
       +rho*Y[jhe4]*rate_eval.He4_Na28__n_Al31
       +rho*Y[jp]*rate_eval.p_Na28__n_Mg28
       +rate_eval.Na28__n_Mg27__weak__wc12
       )

    jac[jn, jna29] = (
       -rho*Y[jn]*rate_eval.n_Na29__Na30
       +rho*Y[jhe4]*rate_eval.He4_Na29__n_Al32
       +rho*Y[jp]*rate_eval.p_Na29__n_Mg29
       +rate_eval.Na29__n_Mg28__weak__wc12
       )

    jac[jn, jna30] = (
       -rho*Y[jn]*rate_eval.n_Na30__Na31
       +rate_eval.Na30__n_Mg29__weak__wc17
       +2*rate_eval.Na30__n_n_Mg28__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Na30__n_Al33
       +rho*Y[jp]*rate_eval.p_Na30__n_Mg30
       )

    jac[jn, jna31] = (
       -rho*Y[jn]*rate_eval.n_Na31__Na32
       +rho*Y[jhe4]*rate_eval.He4_Na31__n_Al34
       +rho*Y[jp]*rate_eval.p_Na31__n_Mg31
       +rate_eval.Na31__n_Mg30__weak__wc17
       +2*rate_eval.Na31__n_n_Mg29__weak__wc12
       +3*rate_eval.Na31__n_n_n_Mg28__weak__wc12
       )

    jac[jn, jna32] = (
       -rho*Y[jn]*rate_eval.n_Na32__Na33
       +3*rate_eval.Na32__n_n_n_Mg29__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Na32__n_Al35
       +2*rate_eval.Na32__n_n_Mg30__weak__wc12
       +rho*Y[jp]*rate_eval.p_Na32__n_Mg32
       +rate_eval.Na32__n_Mg31__weak__wc17
       )

    jac[jn, jna33] = (
       -rho*Y[jn]*rate_eval.n_Na33__Na34
       +3*rate_eval.Na33__n_n_n_Mg30__weak__mo03
       +rho*Y[jp]*rate_eval.p_Na33__n_Mg33
       +rho*Y[jhe4]*rate_eval.He4_Na33__n_Al36
       +rate_eval.Na33__n_Mg32__weak__wc17
       +2*rate_eval.Na33__n_n_Mg31__weak__wc12
       )

    jac[jn, jna34] = (
       -rho*Y[jn]*rate_eval.n_Na34__Na35
       +3*rate_eval.Na34__n_n_n_Mg31__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Na34__n_Al37
       +rho*Y[jp]*rate_eval.p_Na34__n_Mg34
       +rate_eval.Na34__n_Mg33__weak__wc12
       +2*rate_eval.Na34__n_n_Mg32__weak__wc12
       )

    jac[jn, jna35] = (
       -rho*Y[jn]*rate_eval.n_Na35__Na36
       +rho*Y[jhe4]*rate_eval.He4_Na35__n_Al38
       +rho*Y[jp]*rate_eval.p_Na35__n_Mg35
       +3*rate_eval.Na35__n_n_n_Mg32__weak__mo03
       +2*rate_eval.Na35__n_n_Mg33__weak__mp17
       +rate_eval.Na35__n_Mg34__weak__mp17
       )

    jac[jn, jna36] = (
       -rho*Y[jn]*rate_eval.n_Na36__Na37
       +rho*Y[jp]*rate_eval.p_Na36__n_Mg36
       +rho*Y[jhe4]*rate_eval.He4_Na36__n_Al39
       +rate_eval.Na36__n_Mg35__weak__mp17
       )

    jac[jn, jna37] = (
       -rho*Y[jn]*rate_eval.n_Na37__Na38
       +rho*Y[jhe4]*rate_eval.He4_Na37__n_Al40
       +rho*Y[jp]*rate_eval.p_Na37__n_Mg37
       +2*rate_eval.Na37__n_n_Mg35__weak__mp17
       +rate_eval.Na37__n_Mg36__weak__mp17
       )

    jac[jn, jna38] = (
       -rho*Y[jn]*rate_eval.n_Na38__Na39
       +rho*Y[jhe4]*rate_eval.He4_Na38__n_Al41
       +rho*Y[jp]*rate_eval.p_Na38__n_Mg38
       +rate_eval.Na38__n_Mg37__weak__mp17
       )

    jac[jn, jna39] = (
       +rate_eval.Na39__n_Mg38__weak__mp17
       +rho*Y[jp]*rate_eval.p_Na39__n_Mg39
       +rho*Y[jhe4]*rate_eval.He4_Na39__n_Al42
       +2*rate_eval.Na39__n_n_Mg37__weak__mp17
       )

    jac[jn, jmg19] = (
       -rho*Y[jn]*rate_eval.n_Mg19__He4_Ne16
       -rho*Y[jn]*rate_eval.n_Mg19__Mg20
       -rho*Y[jn]*rate_eval.n_Mg19__p_Na19
       )

    jac[jn, jmg20] = (
       -rho*Y[jn]*rate_eval.n_Mg20__p_Na20
       -rho*Y[jn]*rate_eval.n_Mg20__Mg21
       -rho*Y[jn]*rate_eval.n_Mg20__He4_Ne17
       )

    jac[jn, jmg21] = (
       -rho*Y[jn]*rate_eval.n_Mg21__He4_Ne18
       -rho*Y[jn]*rate_eval.n_Mg21__p_Na21
       -rho*Y[jn]*rate_eval.n_Mg21__Mg22
       )

    jac[jn, jmg22] = (
       -rho*Y[jn]*rate_eval.n_Mg22__He4_Ne19
       -rho*Y[jn]*rate_eval.n_Mg22__Mg23
       -rho*Y[jn]*rate_eval.n_Mg22__p_Na22
       )

    jac[jn, jmg23] = (
       -rho*Y[jn]*rate_eval.n_Mg23__C12_C12
       -rho*Y[jn]*rate_eval.n_Mg23__He4_Ne20
       -rho*Y[jn]*rate_eval.n_Mg23__Mg24
       )

    jac[jn, jmg24] = (
       -rho*Y[jn]*rate_eval.n_Mg24__Mg25
       )

    jac[jn, jmg25] = (
       -rho*Y[jn]*rate_eval.n_Mg25__Mg26
       +rho*Y[jhe4]*rate_eval.He4_Mg25__n_Si28
       )

    jac[jn, jmg26] = (
       -rho*Y[jn]*rate_eval.n_Mg26__Mg27
       +rho*Y[jhe4]*rate_eval.He4_Mg26__n_Si29
       )

    jac[jn, jmg27] = (
       -rho*Y[jn]*rate_eval.n_Mg27__Mg28
       +rho*Y[jhe4]*rate_eval.He4_Mg27__n_Si30
       +rho*Y[jp]*rate_eval.p_Mg27__n_Al27
       )

    jac[jn, jmg28] = (
       -rho*Y[jn]*rate_eval.n_Mg28__Mg29
       +rho*Y[jhe4]*rate_eval.He4_Mg28__n_Si31
       +rho*Y[jp]*rate_eval.p_Mg28__n_Al28
       )

    jac[jn, jmg29] = (
       -rho*Y[jn]*rate_eval.n_Mg29__Mg30
       +rho*Y[jp]*rate_eval.p_Mg29__n_Al29
       +rho*Y[jhe4]*rate_eval.He4_Mg29__n_Si32
       )

    jac[jn, jmg30] = (
       -rho*Y[jn]*rate_eval.n_Mg30__Mg31
       +rho*Y[jhe4]*rate_eval.He4_Mg30__n_Si33
       +rho*Y[jp]*rate_eval.p_Mg30__n_Al30
       )

    jac[jn, jmg31] = (
       -rho*Y[jn]*rate_eval.n_Mg31__Mg32
       +rho*Y[jp]*rate_eval.p_Mg31__n_Al31
       +rho*Y[jhe4]*rate_eval.He4_Mg31__n_Si34
       +rate_eval.Mg31__n_Al30__weak__wc12
       )

    jac[jn, jmg32] = (
       -rho*Y[jn]*rate_eval.n_Mg32__Mg33
       +rho*Y[jhe4]*rate_eval.He4_Mg32__n_Si35
       +rate_eval.Mg32__n_Al31__weak__wc12
       +rho*Y[jp]*rate_eval.p_Mg32__n_Al32
       )

    jac[jn, jmg33] = (
       -rho*Y[jn]*rate_eval.n_Mg33__Mg34
       +rho*Y[jhe4]*rate_eval.He4_Mg33__n_Si36
       +rho*Y[jp]*rate_eval.p_Mg33__n_Al33
       +rate_eval.Mg33__n_Al32__weak__wc12
       +2*rate_eval.Mg33__n_n_Al31__weak__mp17
       )

    jac[jn, jmg34] = (
       -rho*Y[jn]*rate_eval.n_Mg34__Mg35
       +rho*Y[jhe4]*rate_eval.He4_Mg34__n_Si37
       +rate_eval.Mg34__n_Al33__weak__mp17
       +rho*Y[jp]*rate_eval.p_Mg34__n_Al34
       )

    jac[jn, jmg35] = (
       -rho*Y[jn]*rate_eval.n_Mg35__Mg36
       +3*rate_eval.Mg35__n_n_n_Al32__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Mg35__n_Si38
       +rho*Y[jp]*rate_eval.p_Mg35__n_Al35
       +rate_eval.Mg35__n_Al34__weak__wc12
       +2*rate_eval.Mg35__n_n_Al33__weak__mp17
       )

    jac[jn, jmg36] = (
       -rho*Y[jn]*rate_eval.n_Mg36__Mg37
       +3*rate_eval.Mg36__n_n_n_Al33__weak__mo03
       +2*rate_eval.Mg36__n_n_Al34__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Mg36__n_Si39
       +rho*Y[jp]*rate_eval.p_Mg36__n_Al36
       +rate_eval.Mg36__n_Al35__weak__mp17
       )

    jac[jn, jmg37] = (
       -rho*Y[jn]*rate_eval.n_Mg37__Mg38
       +3*rate_eval.Mg37__n_n_n_Al34__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Mg37__n_Si40
       +rate_eval.Mg37__n_Al36__weak__mp17
       +rho*Y[jp]*rate_eval.p_Mg37__n_Al37
       +2*rate_eval.Mg37__n_n_Al35__weak__mp17
       )

    jac[jn, jmg38] = (
       -rho*Y[jn]*rate_eval.n_Mg38__Mg39
       +rho*Y[jhe4]*rate_eval.He4_Mg38__n_Si41
       +rho*Y[jp]*rate_eval.p_Mg38__n_Al38
       +2*rate_eval.Mg38__n_n_Al36__weak__mp17
       +3*rate_eval.Mg38__n_n_n_Al35__weak__mo03
       +rate_eval.Mg38__n_Al37__weak__mp17
       )

    jac[jn, jmg39] = (
       -rho*Y[jn]*rate_eval.n_Mg39__Mg40
       +3*rate_eval.Mg39__n_n_n_Al36__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Mg39__n_Si42
       +rho*Y[jp]*rate_eval.p_Mg39__n_Al39
       +rate_eval.Mg39__n_Al38__weak__mp17
       +2*rate_eval.Mg39__n_n_Al37__weak__mp17
       )

    jac[jn, jmg40] = (
       -rho*Y[jn]*rate_eval.n_Mg40__Mg41
       +3*rate_eval.Mg40__n_n_n_Al37__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Mg40__n_Si43
       +rho*Y[jp]*rate_eval.p_Mg40__n_Al40
       +2*rate_eval.Mg40__n_n_Al38__weak__mp17
       +rate_eval.Mg40__n_Al39__weak__mp17
       )

    jac[jn, jmg41] = (
       +rate_eval.Mg41__n_Al40__weak__mp17
       +rho*Y[jp]*rate_eval.p_Mg41__n_Al41
       +rho*Y[jhe4]*rate_eval.He4_Mg41__n_Si44
       )

    jac[jn, jal21] = (
       -rho*Y[jn]*rate_eval.n_Al21__Al22
       -rho*Y[jn]*rate_eval.n_Al21__p_Mg21
       )

    jac[jn, jal22] = (
       -rho*Y[jn]*rate_eval.n_Al22__He4_Na19
       -rho*Y[jn]*rate_eval.n_Al22__p_Mg22
       -rho*Y[jn]*rate_eval.n_Al22__Al23
       )

    jac[jn, jal23] = (
       -rho*Y[jn]*rate_eval.n_Al23__He4_Na20
       -rho*Y[jn]*rate_eval.n_Al23__Al24
       -rho*Y[jn]*rate_eval.n_Al23__p_Mg23
       )

    jac[jn, jal24] = (
       -rho*Y[jn]*rate_eval.n_Al24__He4_Na21
       -rho*Y[jn]*rate_eval.n_Al24__Al25
       -rho*Y[jn]*rate_eval.n_Al24__p_Mg24
       )

    jac[jn, jal25] = (
       -rho*Y[jn]*rate_eval.n_Al25__Al26
       -rho*Y[jn]*rate_eval.n_Al25__p_Mg25
       -rho*Y[jn]*rate_eval.n_Al25__He4_Na22
       )

    jac[jn, jal26] = (
       -rho*Y[jn]*rate_eval.n_Al26__He4_Na23
       -rho*Y[jn]*rate_eval.n_Al26__p_Mg26
       -rho*Y[jn]*rate_eval.n_Al26__Al27
       )

    jac[jn, jal27] = (
       -rho*Y[jn]*rate_eval.n_Al27__Al28
       +rho*Y[jhe4]*rate_eval.He4_Al27__n_P30
       )

    jac[jn, jal28] = (
       -rho*Y[jn]*rate_eval.n_Al28__Al29
       +rho*Y[jhe4]*rate_eval.He4_Al28__n_P31
       +rho*Y[jp]*rate_eval.p_Al28__n_Si28
       )

    jac[jn, jal29] = (
       -rho*Y[jn]*rate_eval.n_Al29__Al30
       +rho*Y[jhe4]*rate_eval.He4_Al29__n_P32
       +rho*Y[jp]*rate_eval.p_Al29__n_Si29
       )

    jac[jn, jal30] = (
       -rho*Y[jn]*rate_eval.n_Al30__Al31
       +rho*Y[jp]*rate_eval.p_Al30__n_Si30
       +rho*Y[jhe4]*rate_eval.He4_Al30__n_P33
       )

    jac[jn, jal31] = (
       -rho*Y[jn]*rate_eval.n_Al31__Al32
       +rho*Y[jhe4]*rate_eval.He4_Al31__n_P34
       +rho*Y[jp]*rate_eval.p_Al31__n_Si31
       )

    jac[jn, jal32] = (
       -rho*Y[jn]*rate_eval.n_Al32__Al33
       +rho*Y[jhe4]*rate_eval.He4_Al32__n_P35
       +rho*Y[jp]*rate_eval.p_Al32__n_Si32
       +rate_eval.Al32__n_Si31__weak__wc12
       )

    jac[jn, jal33] = (
       -rho*Y[jn]*rate_eval.n_Al33__Al34
       +rho*Y[jhe4]*rate_eval.He4_Al33__n_P36
       +rho*Y[jp]*rate_eval.p_Al33__n_Si33
       +rate_eval.Al33__n_Si32__weak__wc12
       )

    jac[jn, jal34] = (
       -rho*Y[jn]*rate_eval.n_Al34__Al35
       +rho*Y[jhe4]*rate_eval.He4_Al34__n_P37
       +rho*Y[jp]*rate_eval.p_Al34__n_Si34
       +rate_eval.Al34__n_Si33__weak__wc12
       )

    jac[jn, jal35] = (
       -rho*Y[jn]*rate_eval.n_Al35__Al36
       +rho*Y[jhe4]*rate_eval.He4_Al35__n_P38
       +rho*Y[jp]*rate_eval.p_Al35__n_Si35
       +rate_eval.Al35__n_Si34__weak__wc12
       )

    jac[jn, jal36] = (
       -rho*Y[jn]*rate_eval.n_Al36__Al37
       +rho*Y[jhe4]*rate_eval.He4_Al36__n_P39
       +rho*Y[jp]*rate_eval.p_Al36__n_Si36
       +2*rate_eval.Al36__n_n_Si34__weak__mp17
       +rate_eval.Al36__n_Si35__weak__mp17
       )

    jac[jn, jal37] = (
       -rho*Y[jn]*rate_eval.n_Al37__Al38
       +3*rate_eval.Al37__n_n_n_Si34__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Al37__n_P40
       +rate_eval.Al37__n_Si36__weak__mp17
       +2*rate_eval.Al37__n_n_Si35__weak__mp17
       +rho*Y[jp]*rate_eval.p_Al37__n_Si37
       )

    jac[jn, jal38] = (
       -rho*Y[jn]*rate_eval.n_Al38__Al39
       +3*rate_eval.Al38__n_n_n_Si35__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Al38__n_P41
       +rho*Y[jp]*rate_eval.p_Al38__n_Si38
       +2*rate_eval.Al38__n_n_Si36__weak__mp17
       +rate_eval.Al38__n_Si37__weak__mp17
       )

    jac[jn, jal39] = (
       -rho*Y[jn]*rate_eval.n_Al39__Al40
       +3*rate_eval.Al39__n_n_n_Si36__weak__mo03
       +rho*Y[jp]*rate_eval.p_Al39__n_Si39
       +rate_eval.Al39__n_Si38__weak__mp17
       +2*rate_eval.Al39__n_n_Si37__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Al39__n_P42
       )

    jac[jn, jal40] = (
       -rho*Y[jn]*rate_eval.n_Al40__Al41
       +rho*Y[jhe4]*rate_eval.He4_Al40__n_P43
       +rho*Y[jp]*rate_eval.p_Al40__n_Si40
       +3*rate_eval.Al40__n_n_n_Si37__weak__mo03
       +rate_eval.Al40__n_Si39__weak__mp17
       +2*rate_eval.Al40__n_n_Si38__weak__mp17
       )

    jac[jn, jal41] = (
       -rho*Y[jn]*rate_eval.n_Al41__Al42
       +3*rate_eval.Al41__n_n_n_Si38__weak__mo03
       +rho*Y[jp]*rate_eval.p_Al41__n_Si41
       +rate_eval.Al41__n_Si40__weak__mp17
       +2*rate_eval.Al41__n_n_Si39__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Al41__n_P44
       )

    jac[jn, jal42] = (
       -rho*Y[jn]*rate_eval.n_Al42__Al43
       +3*rate_eval.Al42__n_n_n_Si39__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Al42__n_P45
       +2*rate_eval.Al42__n_n_Si40__weak__mo03
       +rate_eval.Al42__n_Si41__weak__mp17
       +rho*Y[jp]*rate_eval.p_Al42__n_Si42
       )

    jac[jn, jal43] = (
       +3*rate_eval.Al43__n_n_n_Si40__weak__mo03
       +rho*Y[jp]*rate_eval.p_Al43__n_Si43
       +2*rate_eval.Al43__n_n_Si41__weak__mp17
       +rate_eval.Al43__n_Si42__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Al43__n_P46
       )

    jac[jn, jsi22] = (
       -rho*Y[jn]*rate_eval.n_Si22__He4_Mg19
       -rho*Y[jn]*rate_eval.n_Si22__p_Al22
       -rho*Y[jn]*rate_eval.n_Si22__Si23
       )

    jac[jn, jsi23] = (
       -rho*Y[jn]*rate_eval.n_Si23__p_Al23
       -rho*Y[jn]*rate_eval.n_Si23__He4_Mg20
       -rho*Y[jn]*rate_eval.n_Si23__Si24
       )

    jac[jn, jsi24] = (
       -rho*Y[jn]*rate_eval.n_Si24__p_Al24
       -rho*Y[jn]*rate_eval.n_Si24__He4_Mg21
       -rho*Y[jn]*rate_eval.n_Si24__Si25
       )

    jac[jn, jsi25] = (
       -rho*Y[jn]*rate_eval.n_Si25__p_Al25
       -rho*Y[jn]*rate_eval.n_Si25__He4_Mg22
       -rho*Y[jn]*rate_eval.n_Si25__Si26
       )

    jac[jn, jsi26] = (
       -rho*Y[jn]*rate_eval.n_Si26__p_Al26
       -rho*Y[jn]*rate_eval.n_Si26__Si27
       -rho*Y[jn]*rate_eval.n_Si26__He4_Mg23
       )

    jac[jn, jsi27] = (
       -rho*Y[jn]*rate_eval.n_Si27__Si28
       -rho*Y[jn]*rate_eval.n_Si27__He4_Mg24
       -rho*Y[jn]*rate_eval.n_Si27__p_Al27
       -rho*Y[jn]*rate_eval.n_Si27__C12_O16
       )

    jac[jn, jsi28] = (
       -rho*Y[jn]*rate_eval.n_Si28__Si29
       )

    jac[jn, jsi29] = (
       -rho*Y[jn]*rate_eval.n_Si29__Si30
       )

    jac[jn, jsi30] = (
       -rho*Y[jn]*rate_eval.n_Si30__Si31
       )

    jac[jn, jsi31] = (
       -rho*Y[jn]*rate_eval.n_Si31__Si32
       +rho*Y[jhe4]*rate_eval.He4_Si31__n_S34
       +rho*Y[jp]*rate_eval.p_Si31__n_P31
       )

    jac[jn, jsi32] = (
       -rho*Y[jn]*rate_eval.n_Si32__Si33
       )

    jac[jn, jsi33] = (
       -rho*Y[jn]*rate_eval.n_Si33__Si34
       +rho*Y[jhe4]*rate_eval.He4_Si33__n_S36
       +rho*Y[jp]*rate_eval.p_Si33__n_P33
       )

    jac[jn, jsi34] = (
       -rho*Y[jn]*rate_eval.n_Si34__Si35
       +rho*Y[jhe4]*rate_eval.He4_Si34__n_S37
       +rho*Y[jp]*rate_eval.p_Si34__n_P34
       )

    jac[jn, jsi35] = (
       -rho*Y[jn]*rate_eval.n_Si35__Si36
       +rho*Y[jhe4]*rate_eval.He4_Si35__n_S38
       +rho*Y[jp]*rate_eval.p_Si35__n_P35
       )

    jac[jn, jsi36] = (
       -rho*Y[jn]*rate_eval.n_Si36__Si37
       +rho*Y[jp]*rate_eval.p_Si36__n_P36
       +rho*Y[jhe4]*rate_eval.He4_Si36__n_S39
       +rate_eval.Si36__n_P35__weak__wc12
       )

    jac[jn, jsi37] = (
       -rho*Y[jn]*rate_eval.n_Si37__Si38
       +rho*Y[jhe4]*rate_eval.He4_Si37__n_S40
       +rho*Y[jp]*rate_eval.p_Si37__n_P37
       +rate_eval.Si37__n_P36__weak__wc12
       )

    jac[jn, jsi38] = (
       -rho*Y[jn]*rate_eval.n_Si38__Si39
       +rho*Y[jp]*rate_eval.p_Si38__n_P38
       +rho*Y[jhe4]*rate_eval.He4_Si38__n_S41
       +rate_eval.Si38__n_P37__weak__mp17
       )

    jac[jn, jsi39] = (
       -rho*Y[jn]*rate_eval.n_Si39__Si40
       +rho*Y[jhe4]*rate_eval.He4_Si39__n_S42
       +rho*Y[jp]*rate_eval.p_Si39__n_P39
       +2*rate_eval.Si39__n_n_P37__weak__mp17
       +rate_eval.Si39__n_P38__weak__mp17
       )

    jac[jn, jsi40] = (
       -rho*Y[jn]*rate_eval.n_Si40__Si41
       +rho*Y[jhe4]*rate_eval.He4_Si40__n_S43
       +rho*Y[jp]*rate_eval.p_Si40__n_P40
       +rate_eval.Si40__n_P39__weak__mp17
       )

    jac[jn, jsi41] = (
       -rho*Y[jn]*rate_eval.n_Si41__Si42
       +2*rate_eval.Si41__n_n_P39__weak__mp17
       +rate_eval.Si41__n_P40__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Si41__n_S44
       +rho*Y[jp]*rate_eval.p_Si41__n_P41
       )

    jac[jn, jsi42] = (
       -rho*Y[jn]*rate_eval.n_Si42__Si43
       +3*rate_eval.Si42__n_n_n_P39__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Si42__n_S45
       +rho*Y[jp]*rate_eval.p_Si42__n_P42
       +rate_eval.Si42__n_P41__weak__mp17
       )

    jac[jn, jsi43] = (
       -rho*Y[jn]*rate_eval.n_Si43__Si44
       +rho*Y[jp]*rate_eval.p_Si43__n_P43
       +rho*Y[jhe4]*rate_eval.He4_Si43__n_S46
       +2*rate_eval.Si43__n_n_P41__weak__mp17
       +rate_eval.Si43__n_P42__weak__mp17
       +3*rate_eval.Si43__n_n_n_P40__weak__mo03
       )

    jac[jn, jsi44] = (
       -rho*Y[jn]*rate_eval.n_Si44__Si45
       +rho*Y[jp]*rate_eval.p_Si44__n_P44
       +rho*Y[jhe4]*rate_eval.He4_Si44__n_S47
       +rate_eval.Si44__n_P43__weak__mp17
       +2*rate_eval.Si44__n_n_P42__weak__mp17
       +3*rate_eval.Si44__n_n_n_P41__weak__mo03
       )

    jac[jn, jsi45] = (
       +rho*Y[jp]*rate_eval.p_Si45__n_P45
       +rate_eval.Si45__n_P44__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Si45__n_S48
       )

    jac[jn, jp24] = (
       -rho*Y[jn]*rate_eval.n_P24__He4_Al21
       -rho*Y[jn]*rate_eval.n_P24__p_Si24
       -rho*Y[jn]*rate_eval.n_P24__P25
       )

    jac[jn, jp25] = (
       -rho*Y[jn]*rate_eval.n_P25__He4_Al22
       -rho*Y[jn]*rate_eval.n_P25__p_Si25
       -rho*Y[jn]*rate_eval.n_P25__P26
       )

    jac[jn, jp26] = (
       -rho*Y[jn]*rate_eval.n_P26__He4_Al23
       -rho*Y[jn]*rate_eval.n_P26__p_Si26
       -rho*Y[jn]*rate_eval.n_P26__P27
       )

    jac[jn, jp27] = (
       -rho*Y[jn]*rate_eval.n_P27__He4_Al24
       -rho*Y[jn]*rate_eval.n_P27__p_Si27
       -rho*Y[jn]*rate_eval.n_P27__P28
       )

    jac[jn, jp28] = (
       -rho*Y[jn]*rate_eval.n_P28__p_Si28
       -rho*Y[jn]*rate_eval.n_P28__P29
       -rho*Y[jn]*rate_eval.n_P28__He4_Al25
       )

    jac[jn, jp29] = (
       -rho*Y[jn]*rate_eval.n_P29__He4_Al26
       -rho*Y[jn]*rate_eval.n_P29__P30
       -rho*Y[jn]*rate_eval.n_P29__p_Si29
       )

    jac[jn, jp30] = (
       -rho*Y[jn]*rate_eval.n_P30__p_Si30
       -rho*Y[jn]*rate_eval.n_P30__P31
       )

    jac[jn, jp31] = (
       -rho*Y[jn]*rate_eval.n_P31__P32
       )

    jac[jn, jp32] = (
       -rho*Y[jn]*rate_eval.n_P32__p_Si32
       -rho*Y[jn]*rate_eval.n_P32__P33
       +rho*Y[jp]*rate_eval.p_P32__n_S32
       )

    jac[jn, jp33] = (
       -rho*Y[jn]*rate_eval.n_P33__P34
       )

    jac[jn, jp34] = (
       -rho*Y[jn]*rate_eval.n_P34__P35
       +rho*Y[jhe4]*rate_eval.He4_P34__n_Cl37
       +rho*Y[jp]*rate_eval.p_P34__n_S34
       )

    jac[jn, jp35] = (
       -rho*Y[jn]*rate_eval.n_P35__P36
       +rho*Y[jp]*rate_eval.p_P35__n_S35
       )

    jac[jn, jp36] = (
       -rho*Y[jn]*rate_eval.n_P36__P37
       +rho*Y[jp]*rate_eval.p_P36__n_S36
       +rho*Y[jhe4]*rate_eval.He4_P36__n_Cl39
       )

    jac[jn, jp37] = (
       -rho*Y[jn]*rate_eval.n_P37__P38
       +rho*Y[jhe4]*rate_eval.He4_P37__n_Cl40
       +rho*Y[jp]*rate_eval.p_P37__n_S37
       )

    jac[jn, jp38] = (
       -rho*Y[jn]*rate_eval.n_P38__P39
       +rho*Y[jp]*rate_eval.p_P38__n_S38
       +rho*Y[jhe4]*rate_eval.He4_P38__n_Cl41
       +rate_eval.P38__n_S37__weak__wc12
       )

    jac[jn, jp39] = (
       -rho*Y[jn]*rate_eval.n_P39__P40
       +rho*Y[jhe4]*rate_eval.He4_P39__n_Cl42
       +rho*Y[jp]*rate_eval.p_P39__n_S39
       +rate_eval.P39__n_S38__weak__wc12
       )

    jac[jn, jp40] = (
       -rho*Y[jn]*rate_eval.n_P40__P41
       +rho*Y[jhe4]*rate_eval.He4_P40__n_Cl43
       +rho*Y[jp]*rate_eval.p_P40__n_S40
       +rate_eval.P40__n_S39__weak__wc12
       )

    jac[jn, jp41] = (
       -rho*Y[jn]*rate_eval.n_P41__P42
       +rho*Y[jhe4]*rate_eval.He4_P41__n_Cl44
       +rate_eval.P41__n_S40__weak__wc12
       +rho*Y[jp]*rate_eval.p_P41__n_S41
       )

    jac[jn, jp42] = (
       -rho*Y[jn]*rate_eval.n_P42__P43
       +rho*Y[jp]*rate_eval.p_P42__n_S42
       +2*rate_eval.P42__n_n_S40__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_P42__n_Cl45
       +rate_eval.P42__n_S41__weak__wc12
       )

    jac[jn, jp43] = (
       -rho*Y[jn]*rate_eval.n_P43__P44
       +rho*Y[jhe4]*rate_eval.He4_P43__n_Cl46
       +rho*Y[jp]*rate_eval.p_P43__n_S43
       +2*rate_eval.P43__n_n_S41__weak__mp17
       +rate_eval.P43__n_S42__weak__wc12
       )

    jac[jn, jp44] = (
       -rho*Y[jn]*rate_eval.n_P44__P45
       +3*rate_eval.P44__n_n_n_S41__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_P44__n_Cl47
       +2*rate_eval.P44__n_n_S42__weak__mp17
       +rate_eval.P44__n_S43__weak__mp17
       +rho*Y[jp]*rate_eval.p_P44__n_S44
       )

    jac[jn, jp45] = (
       -rho*Y[jn]*rate_eval.n_P45__P46
       +rho*Y[jp]*rate_eval.p_P45__n_S45
       +3*rate_eval.P45__n_n_n_S42__weak__mo03
       +2*rate_eval.P45__n_n_S43__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_P45__n_Cl48
       +rate_eval.P45__n_S44__weak__mp17
       )

    jac[jn, jp46] = (
       -rho*Y[jn]*rate_eval.n_P46__P47
       +3*rate_eval.P46__n_n_n_S43__weak__mo03
       +rho*Y[jp]*rate_eval.p_P46__n_S46
       +rho*Y[jhe4]*rate_eval.He4_P46__n_Cl49
       +rate_eval.P46__n_S45__weak__mp17
       +2*rate_eval.P46__n_n_S44__weak__mp17
       )

    jac[jn, jp47] = (
       +rho*Y[jhe4]*rate_eval.He4_P47__n_Cl50
       +rho*Y[jp]*rate_eval.p_P47__n_S47
       +3*rate_eval.P47__n_n_n_S44__weak__mo03
       +2*rate_eval.P47__n_n_S45__weak__mp17
       +rate_eval.P47__n_S46__weak__mp17
       )

    jac[jn, js26] = (
       -rho*Y[jn]*rate_eval.n_S26__He4_Si23
       -rho*Y[jn]*rate_eval.n_S26__p_P26
       -rho*Y[jn]*rate_eval.n_S26__S27
       )

    jac[jn, js27] = (
       -rho*Y[jn]*rate_eval.n_S27__S28
       -rho*Y[jn]*rate_eval.n_S27__He4_Si24
       -rho*Y[jn]*rate_eval.n_S27__p_P27
       )

    jac[jn, js28] = (
       -rho*Y[jn]*rate_eval.n_S28__He4_Si25
       -rho*Y[jn]*rate_eval.n_S28__S29
       -rho*Y[jn]*rate_eval.n_S28__p_P28
       )

    jac[jn, js29] = (
       -rho*Y[jn]*rate_eval.n_S29__He4_Si26
       -rho*Y[jn]*rate_eval.n_S29__p_P29
       -rho*Y[jn]*rate_eval.n_S29__S30
       )

    jac[jn, js30] = (
       -rho*Y[jn]*rate_eval.n_S30__He4_Si27
       -rho*Y[jn]*rate_eval.n_S30__p_P30
       -rho*Y[jn]*rate_eval.n_S30__S31
       )

    jac[jn, js31] = (
       -rho*Y[jn]*rate_eval.n_S31__p_P31
       -rho*Y[jn]*rate_eval.n_S31__He4_Si28
       -rho*Y[jn]*rate_eval.n_S31__S32
       )

    jac[jn, js32] = (
       -rho*Y[jn]*rate_eval.n_S32__S33
       -rho*Y[jn]*rate_eval.n_S32__He4_Si29
       )

    jac[jn, js33] = (
       -rho*Y[jn]*rate_eval.n_S33__He4_Si30
       -rho*Y[jn]*rate_eval.n_S33__p_P33
       -rho*Y[jn]*rate_eval.n_S33__S34
       )

    jac[jn, js34] = (
       -rho*Y[jn]*rate_eval.n_S34__S35
       +rho*Y[jhe4]*rate_eval.He4_S34__n_Ar37
       )

    jac[jn, js35] = (
       -rho*Y[jn]*rate_eval.n_S35__He4_Si32
       -rho*Y[jn]*rate_eval.n_S35__S36
       +rho*Y[jhe4]*rate_eval.He4_S35__n_Ar38
       )

    jac[jn, js36] = (
       -rho*Y[jn]*rate_eval.n_S36__S37
       )

    jac[jn, js37] = (
       -rho*Y[jn]*rate_eval.n_S37__S38
       +rho*Y[jhe4]*rate_eval.He4_S37__n_Ar40
       +rho*Y[jp]*rate_eval.p_S37__n_Cl37
       )

    jac[jn, js38] = (
       -rho*Y[jn]*rate_eval.n_S38__S39
       +rho*Y[jhe4]*rate_eval.He4_S38__n_Ar41
       +rho*Y[jp]*rate_eval.p_S38__n_Cl38
       )

    jac[jn, js39] = (
       -rho*Y[jn]*rate_eval.n_S39__S40
       +rho*Y[jhe4]*rate_eval.He4_S39__n_Ar42
       +rho*Y[jp]*rate_eval.p_S39__n_Cl39
       )

    jac[jn, js40] = (
       -rho*Y[jn]*rate_eval.n_S40__S41
       +rho*Y[jp]*rate_eval.p_S40__n_Cl40
       +rho*Y[jhe4]*rate_eval.He4_S40__n_Ar43
       )

    jac[jn, js41] = (
       -rho*Y[jn]*rate_eval.n_S41__S42
       +rho*Y[jhe4]*rate_eval.He4_S41__n_Ar44
       +rho*Y[jp]*rate_eval.p_S41__n_Cl41
       )

    jac[jn, js42] = (
       -rho*Y[jn]*rate_eval.n_S42__S43
       +rho*Y[jhe4]*rate_eval.He4_S42__n_Ar45
       +rho*Y[jp]*rate_eval.p_S42__n_Cl42
       )

    jac[jn, js43] = (
       -rho*Y[jn]*rate_eval.n_S43__S44
       +rho*Y[jhe4]*rate_eval.He4_S43__n_Ar46
       +rho*Y[jp]*rate_eval.p_S43__n_Cl43
       +rate_eval.S43__n_Cl42__weak__wc12
       )

    jac[jn, js44] = (
       -rho*Y[jn]*rate_eval.n_S44__S45
       +rate_eval.S44__n_Cl43__weak__wc12
       +rho*Y[jp]*rate_eval.p_S44__n_Cl44
       +rho*Y[jhe4]*rate_eval.He4_S44__n_Ar47
       )

    jac[jn, js45] = (
       -rho*Y[jn]*rate_eval.n_S45__S46
       +rho*Y[jhe4]*rate_eval.He4_S45__n_Ar48
       +rate_eval.S45__n_Cl44__weak__wc12
       +2*rate_eval.S45__n_n_Cl43__weak__mp17
       +rho*Y[jp]*rate_eval.p_S45__n_Cl45
       )

    jac[jn, js46] = (
       -rho*Y[jn]*rate_eval.n_S46__S47
       +rho*Y[jp]*rate_eval.p_S46__n_Cl46
       +rho*Y[jhe4]*rate_eval.He4_S46__n_Ar49
       +rate_eval.S46__n_Cl45__weak__mp17
       )

    jac[jn, js47] = (
       -rho*Y[jn]*rate_eval.n_S47__S48
       +3*rate_eval.S47__n_n_n_Cl44__weak__mo03
       +rho*Y[jp]*rate_eval.p_S47__n_Cl47
       +2*rate_eval.S47__n_n_Cl45__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_S47__n_Ar50
       +rate_eval.S47__n_Cl46__weak__mp17
       )

    jac[jn, js48] = (
       -rho*Y[jn]*rate_eval.n_S48__S49
       +3*rate_eval.S48__n_n_n_Cl45__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_S48__n_Ar51
       +rho*Y[jp]*rate_eval.p_S48__n_Cl48
       +2*rate_eval.S48__n_n_Cl46__weak__mp17
       +rate_eval.S48__n_Cl47__weak__mp17
       )

    jac[jn, js49] = (
       +3*rate_eval.S49__n_n_n_Cl46__weak__mo03
       +rho*Y[jp]*rate_eval.p_S49__n_Cl49
       +rate_eval.S49__n_Cl48__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_S49__n_Ar52
       +2*rate_eval.S49__n_n_Cl47__weak__mp17
       )

    jac[jn, jcl28] = (
       -rho*Y[jn]*rate_eval.n_Cl28__He4_P25
       -rho*Y[jn]*rate_eval.n_Cl28__Cl29
       -rho*Y[jn]*rate_eval.n_Cl28__p_S28
       )

    jac[jn, jcl29] = (
       -rho*Y[jn]*rate_eval.n_Cl29__He4_P26
       -rho*Y[jn]*rate_eval.n_Cl29__p_S29
       -rho*Y[jn]*rate_eval.n_Cl29__Cl30
       )

    jac[jn, jcl30] = (
       -rho*Y[jn]*rate_eval.n_Cl30__p_S30
       -rho*Y[jn]*rate_eval.n_Cl30__He4_P27
       -rho*Y[jn]*rate_eval.n_Cl30__Cl31
       )

    jac[jn, jcl31] = (
       -rho*Y[jn]*rate_eval.n_Cl31__p_S31
       -rho*Y[jn]*rate_eval.n_Cl31__He4_P28
       -rho*Y[jn]*rate_eval.n_Cl31__Cl32
       )

    jac[jn, jcl32] = (
       -rho*Y[jn]*rate_eval.n_Cl32__He4_P29
       -rho*Y[jn]*rate_eval.n_Cl32__Cl33
       -rho*Y[jn]*rate_eval.n_Cl32__p_S32
       )

    jac[jn, jcl33] = (
       -rho*Y[jn]*rate_eval.n_Cl33__He4_P30
       -rho*Y[jn]*rate_eval.n_Cl33__p_S33
       -rho*Y[jn]*rate_eval.n_Cl33__Cl34
       )

    jac[jn, jcl34] = (
       -rho*Y[jn]*rate_eval.n_Cl34__He4_P31
       -rho*Y[jn]*rate_eval.n_Cl34__p_S34
       -rho*Y[jn]*rate_eval.n_Cl34__Cl35
       )

    jac[jn, jcl35] = (
       -rho*Y[jn]*rate_eval.n_Cl35__p_S35
       -rho*Y[jn]*rate_eval.n_Cl35__He4_P32
       -rho*Y[jn]*rate_eval.n_Cl35__Cl36
       )

    jac[jn, jcl36] = (
       -rho*Y[jn]*rate_eval.n_Cl36__p_S36
       -rho*Y[jn]*rate_eval.n_Cl36__He4_P33
       -rho*Y[jn]*rate_eval.n_Cl36__Cl37
       )

    jac[jn, jcl37] = (
       -rho*Y[jn]*rate_eval.n_Cl37__Cl38
       )

    jac[jn, jcl38] = (
       -rho*Y[jn]*rate_eval.n_Cl38__He4_P35
       -rho*Y[jn]*rate_eval.n_Cl38__Cl39
       +rho*Y[jhe4]*rate_eval.He4_Cl38__n_K41
       +rho*Y[jp]*rate_eval.p_Cl38__n_Ar38
       )

    jac[jn, jcl39] = (
       -rho*Y[jn]*rate_eval.n_Cl39__Cl40
       +rho*Y[jp]*rate_eval.p_Cl39__n_Ar39
       )

    jac[jn, jcl40] = (
       -rho*Y[jn]*rate_eval.n_Cl40__Cl41
       +rho*Y[jhe4]*rate_eval.He4_Cl40__n_K43
       +rho*Y[jp]*rate_eval.p_Cl40__n_Ar40
       )

    jac[jn, jcl41] = (
       -rho*Y[jn]*rate_eval.n_Cl41__Cl42
       +rho*Y[jhe4]*rate_eval.He4_Cl41__n_K44
       +rho*Y[jp]*rate_eval.p_Cl41__n_Ar41
       )

    jac[jn, jcl42] = (
       -rho*Y[jn]*rate_eval.n_Cl42__Cl43
       +rho*Y[jhe4]*rate_eval.He4_Cl42__n_K45
       +rho*Y[jp]*rate_eval.p_Cl42__n_Ar42
       )

    jac[jn, jcl43] = (
       -rho*Y[jn]*rate_eval.n_Cl43__Cl44
       +rate_eval.Cl43__n_Ar42__weak__mp17
       +rho*Y[jp]*rate_eval.p_Cl43__n_Ar43
       +rho*Y[jhe4]*rate_eval.He4_Cl43__n_K46
       )

    jac[jn, jcl44] = (
       -rho*Y[jn]*rate_eval.n_Cl44__Cl45
       +rho*Y[jhe4]*rate_eval.He4_Cl44__n_K47
       +rho*Y[jp]*rate_eval.p_Cl44__n_Ar44
       +rate_eval.Cl44__n_Ar43__weak__mp17
       )

    jac[jn, jcl45] = (
       -rho*Y[jn]*rate_eval.n_Cl45__Cl46
       +rho*Y[jp]*rate_eval.p_Cl45__n_Ar45
       +rho*Y[jhe4]*rate_eval.He4_Cl45__n_K48
       +rate_eval.Cl45__n_Ar44__weak__wc12
       )

    jac[jn, jcl46] = (
       -rho*Y[jn]*rate_eval.n_Cl46__Cl47
       +rho*Y[jp]*rate_eval.p_Cl46__n_Ar46
       +rho*Y[jhe4]*rate_eval.He4_Cl46__n_K49
       +rate_eval.Cl46__n_Ar45__weak__wc12
       )

    jac[jn, jcl47] = (
       -rho*Y[jn]*rate_eval.n_Cl47__Cl48
       +rho*Y[jhe4]*rate_eval.He4_Cl47__n_K50
       +2*rate_eval.Cl47__n_n_Ar45__weak__mp17
       +rho*Y[jp]*rate_eval.p_Cl47__n_Ar47
       +rate_eval.Cl47__n_Ar46__weak__wc12
       )

    jac[jn, jcl48] = (
       -rho*Y[jn]*rate_eval.n_Cl48__Cl49
       +rho*Y[jp]*rate_eval.p_Cl48__n_Ar48
       +rate_eval.Cl48__n_Ar47__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Cl48__n_K51
       +2*rate_eval.Cl48__n_n_Ar46__weak__mp17
       )

    jac[jn, jcl49] = (
       -rho*Y[jn]*rate_eval.n_Cl49__Cl50
       +2*rate_eval.Cl49__n_n_Ar47__weak__mp17
       +rate_eval.Cl49__n_Ar48__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Cl49__n_K52
       +3*rate_eval.Cl49__n_n_n_Ar46__weak__mo03
       +rho*Y[jp]*rate_eval.p_Cl49__n_Ar49
       )

    jac[jn, jcl50] = (
       -rho*Y[jn]*rate_eval.n_Cl50__Cl51
       +3*rate_eval.Cl50__n_n_n_Ar47__weak__mo03
       +rho*Y[jp]*rate_eval.p_Cl50__n_Ar50
       +rho*Y[jhe4]*rate_eval.He4_Cl50__n_K53
       +2*rate_eval.Cl50__n_n_Ar48__weak__mp17
       +rate_eval.Cl50__n_Ar49__weak__mp17
       )

    jac[jn, jcl51] = (
       -rho*Y[jn]*rate_eval.n_Cl51__Cl52
       +rho*Y[jhe4]*rate_eval.He4_Cl51__n_K54
       +rho*Y[jp]*rate_eval.p_Cl51__n_Ar51
       +rate_eval.Cl51__n_Ar50__weak__mp17
       +2*rate_eval.Cl51__n_n_Ar49__weak__mp17
       +3*rate_eval.Cl51__n_n_n_Ar48__weak__mo03
       )

    jac[jn, jcl52] = (
       +rho*Y[jp]*rate_eval.p_Cl52__n_Ar52
       +3*rate_eval.Cl52__n_n_n_Ar49__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Cl52__n_K55
       +2*rate_eval.Cl52__n_n_Ar50__weak__mp17
       +rate_eval.Cl52__n_Ar51__weak__mp17
       )

    jac[jn, jar29] = (
       -rho*Y[jn]*rate_eval.n_Ar29__He4_S26
       -rho*Y[jn]*rate_eval.n_Ar29__p_Cl29
       -rho*Y[jn]*rate_eval.n_Ar29__Ar30
       )

    jac[jn, jar30] = (
       -rho*Y[jn]*rate_eval.n_Ar30__He4_S27
       -rho*Y[jn]*rate_eval.n_Ar30__p_Cl30
       -rho*Y[jn]*rate_eval.n_Ar30__Ar31
       )

    jac[jn, jar31] = (
       -rho*Y[jn]*rate_eval.n_Ar31__He4_S28
       -rho*Y[jn]*rate_eval.n_Ar31__p_Cl31
       -rho*Y[jn]*rate_eval.n_Ar31__Ar32
       )

    jac[jn, jar32] = (
       -rho*Y[jn]*rate_eval.n_Ar32__He4_S29
       -rho*Y[jn]*rate_eval.n_Ar32__p_Cl32
       -rho*Y[jn]*rate_eval.n_Ar32__Ar33
       )

    jac[jn, jar33] = (
       -rho*Y[jn]*rate_eval.n_Ar33__p_Cl33
       -rho*Y[jn]*rate_eval.n_Ar33__Ar34
       -rho*Y[jn]*rate_eval.n_Ar33__He4_S30
       )

    jac[jn, jar34] = (
       -rho*Y[jn]*rate_eval.n_Ar34__p_Cl34
       -rho*Y[jn]*rate_eval.n_Ar34__Ar35
       -rho*Y[jn]*rate_eval.n_Ar34__He4_S31
       )

    jac[jn, jar35] = (
       -rho*Y[jn]*rate_eval.n_Ar35__He4_S32
       -rho*Y[jn]*rate_eval.n_Ar35__p_Cl35
       -rho*Y[jn]*rate_eval.n_Ar35__Ar36
       )

    jac[jn, jar36] = (
       -rho*Y[jn]*rate_eval.n_Ar36__He4_S33
       -rho*Y[jn]*rate_eval.n_Ar36__Ar37
       -rho*Y[jn]*rate_eval.n_Ar36__p_Cl36
       )

    jac[jn, jar37] = (
       -rho*Y[jn]*rate_eval.n_Ar37__p_Cl37
       -rho*Y[jn]*rate_eval.n_Ar37__Ar38
       )

    jac[jn, jar38] = (
       -rho*Y[jn]*rate_eval.n_Ar38__Ar39
       )

    jac[jn, jar39] = (
       -rho*Y[jn]*rate_eval.n_Ar39__He4_S36
       -rho*Y[jn]*rate_eval.n_Ar39__Ar40
       )

    jac[jn, jar40] = (
       -rho*Y[jn]*rate_eval.n_Ar40__Ar41
       )

    jac[jn, jar41] = (
       -rho*Y[jn]*rate_eval.n_Ar41__Ar42
       +rho*Y[jp]*rate_eval.p_Ar41__n_K41
       +rho*Y[jhe4]*rate_eval.He4_Ar41__n_Ca44
       )

    jac[jn, jar42] = (
       -rho*Y[jn]*rate_eval.n_Ar42__Ar43
       +rho*Y[jhe4]*rate_eval.He4_Ar42__n_Ca45
       )

    jac[jn, jar43] = (
       -rho*Y[jn]*rate_eval.n_Ar43__Ar44
       +rho*Y[jhe4]*rate_eval.He4_Ar43__n_Ca46
       +rho*Y[jp]*rate_eval.p_Ar43__n_K43
       )

    jac[jn, jar44] = (
       -rho*Y[jn]*rate_eval.n_Ar44__Ar45
       +rho*Y[jp]*rate_eval.p_Ar44__n_K44
       +rho*Y[jhe4]*rate_eval.He4_Ar44__n_Ca47
       )

    jac[jn, jar45] = (
       -rho*Y[jn]*rate_eval.n_Ar45__Ar46
       +rho*Y[jp]*rate_eval.p_Ar45__n_K45
       +rho*Y[jhe4]*rate_eval.He4_Ar45__n_Ca48
       )

    jac[jn, jar46] = (
       -rho*Y[jn]*rate_eval.n_Ar46__Ar47
       +rho*Y[jhe4]*rate_eval.He4_Ar46__n_Ca49
       +rho*Y[jp]*rate_eval.p_Ar46__n_K46
       )

    jac[jn, jar47] = (
       -rho*Y[jn]*rate_eval.n_Ar47__Ar48
       +rho*Y[jp]*rate_eval.p_Ar47__n_K47
       +rho*Y[jhe4]*rate_eval.He4_Ar47__n_Ca50
       )

    jac[jn, jar48] = (
       -rho*Y[jn]*rate_eval.n_Ar48__Ar49
       +rate_eval.Ar48__n_K47__weak__mp17
       +rho*Y[jp]*rate_eval.p_Ar48__n_K48
       +rho*Y[jhe4]*rate_eval.He4_Ar48__n_Ca51
       )

    jac[jn, jar49] = (
       -rho*Y[jn]*rate_eval.n_Ar49__Ar50
       +rate_eval.Ar49__n_K48__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Ar49__n_Ca52
       +rho*Y[jp]*rate_eval.p_Ar49__n_K49
       )

    jac[jn, jar50] = (
       -rho*Y[jn]*rate_eval.n_Ar50__Ar51
       +rho*Y[jp]*rate_eval.p_Ar50__n_K50
       +rho*Y[jhe4]*rate_eval.He4_Ar50__n_Ca53
       +rate_eval.Ar50__n_K49__weak__wc12
       )

    jac[jn, jar51] = (
       -rho*Y[jn]*rate_eval.n_Ar51__Ar52
       +rate_eval.Ar51__n_K50__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Ar51__n_Ca54
       +rho*Y[jp]*rate_eval.p_Ar51__n_K51
       +2*rate_eval.Ar51__n_n_K49__weak__mp17
       )

    jac[jn, jar52] = (
       -rho*Y[jn]*rate_eval.n_Ar52__Ar53
       +3*rate_eval.Ar52__n_n_n_K49__weak__mo03
       +rho*Y[jp]*rate_eval.p_Ar52__n_K52
       +2*rate_eval.Ar52__n_n_K50__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Ar52__n_Ca55
       +rate_eval.Ar52__n_K51__weak__mp17
       )

    jac[jn, jar53] = (
       -rho*Y[jn]*rate_eval.n_Ar53__Ar54
       +3*rate_eval.Ar53__n_n_n_K50__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Ar53__n_Ca56
       +rho*Y[jp]*rate_eval.p_Ar53__n_K53
       +2*rate_eval.Ar53__n_n_K51__weak__mp17
       +rate_eval.Ar53__n_K52__weak__mp17
       )

    jac[jn, jar54] = (
       +3*rate_eval.Ar54__n_n_n_K51__weak__mo03
       +rho*Y[jp]*rate_eval.p_Ar54__n_K54
       +rate_eval.Ar54__n_K53__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Ar54__n_Ca57
       +2*rate_eval.Ar54__n_n_K52__weak__mp17
       )

    jac[jn, jk31] = (
       -rho*Y[jn]*rate_eval.n_K31__K32
       -rho*Y[jn]*rate_eval.n_K31__p_Ar31
       -rho*Y[jn]*rate_eval.n_K31__He4_Cl28
       )

    jac[jn, jk32] = (
       -rho*Y[jn]*rate_eval.n_K32__He4_Cl29
       -rho*Y[jn]*rate_eval.n_K32__p_Ar32
       -rho*Y[jn]*rate_eval.n_K32__K33
       )

    jac[jn, jk33] = (
       -rho*Y[jn]*rate_eval.n_K33__p_Ar33
       -rho*Y[jn]*rate_eval.n_K33__He4_Cl30
       -rho*Y[jn]*rate_eval.n_K33__K34
       )

    jac[jn, jk34] = (
       -rho*Y[jn]*rate_eval.n_K34__K35
       -rho*Y[jn]*rate_eval.n_K34__He4_Cl31
       -rho*Y[jn]*rate_eval.n_K34__p_Ar34
       )

    jac[jn, jk35] = (
       -rho*Y[jn]*rate_eval.n_K35__p_Ar35
       -rho*Y[jn]*rate_eval.n_K35__He4_Cl32
       -rho*Y[jn]*rate_eval.n_K35__K36
       )

    jac[jn, jk36] = (
       -rho*Y[jn]*rate_eval.n_K36__He4_Cl33
       -rho*Y[jn]*rate_eval.n_K36__p_Ar36
       -rho*Y[jn]*rate_eval.n_K36__K37
       )

    jac[jn, jk37] = (
       -rho*Y[jn]*rate_eval.n_K37__He4_Cl34
       -rho*Y[jn]*rate_eval.n_K37__K38
       -rho*Y[jn]*rate_eval.n_K37__p_Ar37
       )

    jac[jn, jk38] = (
       -rho*Y[jn]*rate_eval.n_K38__p_Ar38
       -rho*Y[jn]*rate_eval.n_K38__He4_Cl35
       -rho*Y[jn]*rate_eval.n_K38__K39
       )

    jac[jn, jk39] = (
       -rho*Y[jn]*rate_eval.n_K39__p_Ar39
       -rho*Y[jn]*rate_eval.n_K39__He4_Cl36
       -rho*Y[jn]*rate_eval.n_K39__K40
       )

    jac[jn, jk40] = (
       -rho*Y[jn]*rate_eval.n_K40__He4_Cl37
       -rho*Y[jn]*rate_eval.n_K40__p_Ar40
       -rho*Y[jn]*rate_eval.n_K40__K41
       +rho*Y[jp]*rate_eval.p_K40__n_Ca40
       )

    jac[jn, jk41] = (
       -rho*Y[jn]*rate_eval.n_K41__K42
       +rho*Y[jhe4]*rate_eval.He4_K41__n_Sc44
       +rho*Y[jp]*rate_eval.p_K41__n_Ca41
       )

    jac[jn, jk42] = (
       -rho*Y[jn]*rate_eval.n_K42__K43
       -rho*Y[jn]*rate_eval.n_K42__He4_Cl39
       -rho*Y[jn]*rate_eval.n_K42__p_Ar42
       +rho*Y[jhe4]*rate_eval.He4_K42__n_Sc45
       +rho*Y[jp]*rate_eval.p_K42__n_Ca42
       )

    jac[jn, jk43] = (
       -rho*Y[jn]*rate_eval.n_K43__K44
       +rho*Y[jp]*rate_eval.p_K43__n_Ca43
       )

    jac[jn, jk44] = (
       -rho*Y[jn]*rate_eval.n_K44__K45
       +rho*Y[jp]*rate_eval.p_K44__n_Ca44
       +rho*Y[jhe4]*rate_eval.He4_K44__n_Sc47
       )

    jac[jn, jk45] = (
       -rho*Y[jn]*rate_eval.n_K45__K46
       +rho*Y[jp]*rate_eval.p_K45__n_Ca45
       +rho*Y[jhe4]*rate_eval.He4_K45__n_Sc48
       )

    jac[jn, jk46] = (
       -rho*Y[jn]*rate_eval.n_K46__K47
       +rho*Y[jp]*rate_eval.p_K46__n_Ca46
       +rho*Y[jhe4]*rate_eval.He4_K46__n_Sc49
       )

    jac[jn, jk47] = (
       -rho*Y[jn]*rate_eval.n_K47__K48
       +rho*Y[jhe4]*rate_eval.He4_K47__n_Sc50
       +rho*Y[jp]*rate_eval.p_K47__n_Ca47
       )

    jac[jn, jk48] = (
       -rho*Y[jn]*rate_eval.n_K48__K49
       +rho*Y[jhe4]*rate_eval.He4_K48__n_Sc51
       +rho*Y[jp]*rate_eval.p_K48__n_Ca48
       +rate_eval.K48__n_Ca47__weak__wc12
       )

    jac[jn, jk49] = (
       -rho*Y[jn]*rate_eval.n_K49__K50
       +rho*Y[jhe4]*rate_eval.He4_K49__n_Sc52
       +rho*Y[jp]*rate_eval.p_K49__n_Ca49
       +rate_eval.K49__n_Ca48__weak__wc12
       )

    jac[jn, jk50] = (
       -rho*Y[jn]*rate_eval.n_K50__K51
       +rho*Y[jhe4]*rate_eval.He4_K50__n_Sc53
       +rho*Y[jp]*rate_eval.p_K50__n_Ca50
       +rate_eval.K50__n_Ca49__weak__wc12
       +2*rate_eval.K50__n_n_Ca48__weak__mp17
       )

    jac[jn, jk51] = (
       -rho*Y[jn]*rate_eval.n_K51__K52
       +rho*Y[jhe4]*rate_eval.He4_K51__n_Sc54
       +rho*Y[jp]*rate_eval.p_K51__n_Ca51
       +rate_eval.K51__n_Ca50__weak__wc12
       )

    jac[jn, jk52] = (
       -rho*Y[jn]*rate_eval.n_K52__K53
       +rho*Y[jhe4]*rate_eval.He4_K52__n_Sc55
       +2*rate_eval.K52__n_n_Ca50__weak__mp17
       +rate_eval.K52__n_Ca51__weak__wc12
       +rho*Y[jp]*rate_eval.p_K52__n_Ca52
       )

    jac[jn, jk53] = (
       -rho*Y[jn]*rate_eval.n_K53__K54
       +3*rate_eval.K53__n_n_n_Ca50__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_K53__n_Sc56
       +rho*Y[jp]*rate_eval.p_K53__n_Ca53
       +rate_eval.K53__n_Ca52__weak__wc17
       +2*rate_eval.K53__n_n_Ca51__weak__mp17
       )

    jac[jn, jk54] = (
       -rho*Y[jn]*rate_eval.n_K54__K55
       +3*rate_eval.K54__n_n_n_Ca51__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_K54__n_Sc57
       +rho*Y[jp]*rate_eval.p_K54__n_Ca54
       +2*rate_eval.K54__n_n_Ca52__weak__mp17
       +rate_eval.K54__n_Ca53__weak__mp17
       )

    jac[jn, jk55] = (
       -rho*Y[jn]*rate_eval.n_K55__K56
       +3*rate_eval.K55__n_n_n_Ca52__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_K55__n_Sc58
       +rho*Y[jp]*rate_eval.p_K55__n_Ca55
       +2*rate_eval.K55__n_n_Ca53__weak__mp17
       +rate_eval.K55__n_Ca54__weak__mp17
       )

    jac[jn, jk56] = (
       -rho*Y[jn]*rate_eval.n_K56__K57
       +3*rate_eval.K56__n_n_n_Ca53__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_K56__n_Sc59
       +rho*Y[jp]*rate_eval.p_K56__n_Ca56
       +rate_eval.K56__n_Ca55__weak__mp17
       +2*rate_eval.K56__n_n_Ca54__weak__mp17
       )

    jac[jn, jk57] = (
       -rho*Y[jn]*rate_eval.n_K57__K58
       +rho*Y[jhe4]*rate_eval.He4_K57__n_Sc60
       +rho*Y[jp]*rate_eval.p_K57__n_Ca57
       +2*rate_eval.K57__n_n_Ca55__weak__mp17
       +rate_eval.K57__n_Ca56__weak__mp17
       +3*rate_eval.K57__n_n_n_Ca54__weak__mo03
       )

    jac[jn, jk58] = (
       -rho*Y[jn]*rate_eval.n_K58__K59
       +3*rate_eval.K58__n_n_n_Ca55__weak__mo03
       +rho*Y[jp]*rate_eval.p_K58__n_Ca58
       +rho*Y[jhe4]*rate_eval.He4_K58__n_Sc61
       +2*rate_eval.K58__n_n_Ca56__weak__mp17
       +rate_eval.K58__n_Ca57__weak__mp17
       )

    jac[jn, jk59] = (
       +3*rate_eval.K59__n_n_n_Ca56__weak__mo03
       +rho*Y[jp]*rate_eval.p_K59__n_Ca59
       +2*rate_eval.K59__n_n_Ca57__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_K59__n_Sc62
       +rate_eval.K59__n_Ca58__weak__mp17
       )

    jac[jn, jca33] = (
       -rho*Y[jn]*rate_eval.n_Ca33__p_K33
       -rho*Y[jn]*rate_eval.n_Ca33__He4_Ar30
       -rho*Y[jn]*rate_eval.n_Ca33__Ca34
       )

    jac[jn, jca34] = (
       -rho*Y[jn]*rate_eval.n_Ca34__He4_Ar31
       -rho*Y[jn]*rate_eval.n_Ca34__p_K34
       -rho*Y[jn]*rate_eval.n_Ca34__Ca35
       )

    jac[jn, jca35] = (
       -rho*Y[jn]*rate_eval.n_Ca35__He4_Ar32
       -rho*Y[jn]*rate_eval.n_Ca35__p_K35
       -rho*Y[jn]*rate_eval.n_Ca35__Ca36
       )

    jac[jn, jca36] = (
       -rho*Y[jn]*rate_eval.n_Ca36__p_K36
       -rho*Y[jn]*rate_eval.n_Ca36__He4_Ar33
       -rho*Y[jn]*rate_eval.n_Ca36__Ca37
       )

    jac[jn, jca37] = (
       -rho*Y[jn]*rate_eval.n_Ca37__He4_Ar34
       -rho*Y[jn]*rate_eval.n_Ca37__p_K37
       -rho*Y[jn]*rate_eval.n_Ca37__Ca38
       )

    jac[jn, jca38] = (
       -rho*Y[jn]*rate_eval.n_Ca38__p_K38
       -rho*Y[jn]*rate_eval.n_Ca38__Ca39
       -rho*Y[jn]*rate_eval.n_Ca38__He4_Ar35
       )

    jac[jn, jca39] = (
       -rho*Y[jn]*rate_eval.n_Ca39__He4_Ar36
       -rho*Y[jn]*rate_eval.n_Ca39__p_K39
       -rho*Y[jn]*rate_eval.n_Ca39__Ca40
       )

    jac[jn, jca40] = (
       -rho*Y[jn]*rate_eval.n_Ca40__He4_Ar37
       -rho*Y[jn]*rate_eval.n_Ca40__Ca41
       )

    jac[jn, jca41] = (
       -rho*Y[jn]*rate_eval.n_Ca41__Ca42
       -rho*Y[jn]*rate_eval.n_Ca41__He4_Ar38
       )

    jac[jn, jca42] = (
       -rho*Y[jn]*rate_eval.n_Ca42__Ca43
       -rho*Y[jn]*rate_eval.n_Ca42__He4_Ar39
       )

    jac[jn, jca43] = (
       -rho*Y[jn]*rate_eval.n_Ca43__He4_Ar40
       -rho*Y[jn]*rate_eval.n_Ca43__Ca44
       +rho*Y[jhe4]*rate_eval.He4_Ca43__n_Ti46
       )

    jac[jn, jca44] = (
       -rho*Y[jn]*rate_eval.n_Ca44__Ca45
       )

    jac[jn, jca45] = (
       -rho*Y[jn]*rate_eval.n_Ca45__Ca46
       +rho*Y[jhe4]*rate_eval.He4_Ca45__n_Ti48
       )

    jac[jn, jca46] = (
       -rho*Y[jn]*rate_eval.n_Ca46__Ca47
       )

    jac[jn, jca47] = (
       -rho*Y[jn]*rate_eval.n_Ca47__Ca48
       +rho*Y[jhe4]*rate_eval.He4_Ca47__n_Ti50
       +rho*Y[jp]*rate_eval.p_Ca47__n_Sc47
       )

    jac[jn, jca48] = (
       -rho*Y[jn]*rate_eval.n_Ca48__Ca49
       )

    jac[jn, jca49] = (
       -rho*Y[jn]*rate_eval.n_Ca49__Ca50
       +rho*Y[jp]*rate_eval.p_Ca49__n_Sc49
       +rho*Y[jhe4]*rate_eval.He4_Ca49__n_Ti52
       )

    jac[jn, jca50] = (
       -rho*Y[jn]*rate_eval.n_Ca50__Ca51
       +rho*Y[jhe4]*rate_eval.He4_Ca50__n_Ti53
       +rho*Y[jp]*rate_eval.p_Ca50__n_Sc50
       )

    jac[jn, jca51] = (
       -rho*Y[jn]*rate_eval.n_Ca51__Ca52
       +rho*Y[jhe4]*rate_eval.He4_Ca51__n_Ti54
       +rho*Y[jp]*rate_eval.p_Ca51__n_Sc51
       )

    jac[jn, jca52] = (
       -rho*Y[jn]*rate_eval.n_Ca52__Ca53
       +rho*Y[jp]*rate_eval.p_Ca52__n_Sc52
       +rate_eval.Ca52__n_Sc51__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Ca52__n_Ti55
       )

    jac[jn, jca53] = (
       -rho*Y[jn]*rate_eval.n_Ca53__Ca54
       +rho*Y[jp]*rate_eval.p_Ca53__n_Sc53
       +rho*Y[jhe4]*rate_eval.He4_Ca53__n_Ti56
       +rate_eval.Ca53__n_Sc52__weak__wc12
       )

    jac[jn, jca54] = (
       -rho*Y[jn]*rate_eval.n_Ca54__Ca55
       +rate_eval.Ca54__n_Sc53__weak__mp17
       +rho*Y[jp]*rate_eval.p_Ca54__n_Sc54
       +rho*Y[jhe4]*rate_eval.He4_Ca54__n_Ti57
       )

    jac[jn, jca55] = (
       -rho*Y[jn]*rate_eval.n_Ca55__Ca56
       +rho*Y[jp]*rate_eval.p_Ca55__n_Sc55
       +rho*Y[jhe4]*rate_eval.He4_Ca55__n_Ti58
       +rate_eval.Ca55__n_Sc54__weak__mp17
       )

    jac[jn, jca56] = (
       -rho*Y[jn]*rate_eval.n_Ca56__Ca57
       +3*rate_eval.Ca56__n_n_n_Sc53__weak__mo03
       +rho*Y[jp]*rate_eval.p_Ca56__n_Sc56
       +rate_eval.Ca56__n_Sc55__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Ca56__n_Ti59
       )

    jac[jn, jca57] = (
       -rho*Y[jn]*rate_eval.n_Ca57__Ca58
       +3*rate_eval.Ca57__n_n_n_Sc54__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Ca57__n_Ti60
       +2*rate_eval.Ca57__n_n_Sc55__weak__mp17
       +rate_eval.Ca57__n_Sc56__weak__mp17
       +rho*Y[jp]*rate_eval.p_Ca57__n_Sc57
       )

    jac[jn, jca58] = (
       -rho*Y[jn]*rate_eval.n_Ca58__Ca59
       +3*rate_eval.Ca58__n_n_n_Sc55__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Ca58__n_Ti61
       +rho*Y[jp]*rate_eval.p_Ca58__n_Sc58
       +rate_eval.Ca58__n_Sc57__weak__mp17
       +2*rate_eval.Ca58__n_n_Sc56__weak__mp17
       )

    jac[jn, jca59] = (
       -rho*Y[jn]*rate_eval.n_Ca59__Ca60
       +3*rate_eval.Ca59__n_n_n_Sc56__weak__mo03
       +rho*Y[jp]*rate_eval.p_Ca59__n_Sc59
       +2*rate_eval.Ca59__n_n_Sc57__weak__mp17
       +rate_eval.Ca59__n_Sc58__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Ca59__n_Ti62
       )

    jac[jn, jca60] = (
       -rho*Y[jn]*rate_eval.n_Ca60__Ca61
       +3*rate_eval.Ca60__n_n_n_Sc57__weak__mo03
       +rho*Y[jp]*rate_eval.p_Ca60__n_Sc60
       +rho*Y[jhe4]*rate_eval.He4_Ca60__n_Ti63
       +rate_eval.Ca60__n_Sc59__weak__mp17
       +2*rate_eval.Ca60__n_n_Sc58__weak__mp17
       )

    jac[jn, jca61] = (
       +rho*Y[jp]*rate_eval.p_Ca61__n_Sc61
       +rho*Y[jhe4]*rate_eval.He4_Ca61__n_Ti64
       +3*rate_eval.Ca61__n_n_n_Sc58__weak__mo03
       +rate_eval.Ca61__n_Sc60__weak__mp17
       +2*rate_eval.Ca61__n_n_Sc59__weak__mp17
       )

    jac[jn, jsc35] = (
       -rho*Y[jn]*rate_eval.n_Sc35__He4_K32
       -rho*Y[jn]*rate_eval.n_Sc35__p_Ca35
       -rho*Y[jn]*rate_eval.n_Sc35__Sc36
       )

    jac[jn, jsc36] = (
       -rho*Y[jn]*rate_eval.n_Sc36__p_Ca36
       -rho*Y[jn]*rate_eval.n_Sc36__He4_K33
       -rho*Y[jn]*rate_eval.n_Sc36__Sc37
       )

    jac[jn, jsc37] = (
       -rho*Y[jn]*rate_eval.n_Sc37__He4_K34
       -rho*Y[jn]*rate_eval.n_Sc37__p_Ca37
       -rho*Y[jn]*rate_eval.n_Sc37__Sc38
       )

    jac[jn, jsc38] = (
       -rho*Y[jn]*rate_eval.n_Sc38__Sc39
       -rho*Y[jn]*rate_eval.n_Sc38__p_Ca38
       -rho*Y[jn]*rate_eval.n_Sc38__He4_K35
       )

    jac[jn, jsc39] = (
       -rho*Y[jn]*rate_eval.n_Sc39__He4_K36
       -rho*Y[jn]*rate_eval.n_Sc39__Sc40
       -rho*Y[jn]*rate_eval.n_Sc39__p_Ca39
       )

    jac[jn, jsc40] = (
       -rho*Y[jn]*rate_eval.n_Sc40__Sc41
       -rho*Y[jn]*rate_eval.n_Sc40__p_Ca40
       -rho*Y[jn]*rate_eval.n_Sc40__He4_K37
       )

    jac[jn, jsc41] = (
       -rho*Y[jn]*rate_eval.n_Sc41__He4_K38
       -rho*Y[jn]*rate_eval.n_Sc41__Sc42
       -rho*Y[jn]*rate_eval.n_Sc41__p_Ca41
       )

    jac[jn, jsc42] = (
       -rho*Y[jn]*rate_eval.n_Sc42__He4_K39
       -rho*Y[jn]*rate_eval.n_Sc42__p_Ca42
       -rho*Y[jn]*rate_eval.n_Sc42__Sc43
       )

    jac[jn, jsc43] = (
       -rho*Y[jn]*rate_eval.n_Sc43__He4_K40
       -rho*Y[jn]*rate_eval.n_Sc43__p_Ca43
       -rho*Y[jn]*rate_eval.n_Sc43__Sc44
       )

    jac[jn, jsc44] = (
       -rho*Y[jn]*rate_eval.n_Sc44__p_Ca44
       -rho*Y[jn]*rate_eval.n_Sc44__Sc45
       )

    jac[jn, jsc45] = (
       -rho*Y[jn]*rate_eval.n_Sc45__p_Ca45
       -rho*Y[jn]*rate_eval.n_Sc45__Sc46
       )

    jac[jn, jsc46] = (
       -rho*Y[jn]*rate_eval.n_Sc46__p_Ca46
       -rho*Y[jn]*rate_eval.n_Sc46__He4_K43
       -rho*Y[jn]*rate_eval.n_Sc46__Sc47
       +rho*Y[jp]*rate_eval.p_Sc46__n_Ti46
       +rho*Y[jhe4]*rate_eval.He4_Sc46__n_V49
       )

    jac[jn, jsc47] = (
       -rho*Y[jn]*rate_eval.n_Sc47__Sc48
       )

    jac[jn, jsc48] = (
       -rho*Y[jn]*rate_eval.n_Sc48__p_Ca48
       -rho*Y[jn]*rate_eval.n_Sc48__Sc49
       +rho*Y[jhe4]*rate_eval.He4_Sc48__n_V51
       +rho*Y[jp]*rate_eval.p_Sc48__n_Ti48
       )

    jac[jn, jsc49] = (
       -rho*Y[jn]*rate_eval.n_Sc49__Sc50
       +rho*Y[jp]*rate_eval.p_Sc49__n_Ti49
       )

    jac[jn, jsc50] = (
       -rho*Y[jn]*rate_eval.n_Sc50__Sc51
       +rho*Y[jp]*rate_eval.p_Sc50__n_Ti50
       +rho*Y[jhe4]*rate_eval.He4_Sc50__n_V53
       )

    jac[jn, jsc51] = (
       -rho*Y[jn]*rate_eval.n_Sc51__Sc52
       +rho*Y[jhe4]*rate_eval.He4_Sc51__n_V54
       +rho*Y[jp]*rate_eval.p_Sc51__n_Ti51
       )

    jac[jn, jsc52] = (
       -rho*Y[jn]*rate_eval.n_Sc52__Sc53
       +rho*Y[jhe4]*rate_eval.He4_Sc52__n_V55
       +rho*Y[jp]*rate_eval.p_Sc52__n_Ti52
       )

    jac[jn, jsc53] = (
       -rho*Y[jn]*rate_eval.n_Sc53__Sc54
       +rho*Y[jp]*rate_eval.p_Sc53__n_Ti53
       +rho*Y[jhe4]*rate_eval.He4_Sc53__n_V56
       )

    jac[jn, jsc54] = (
       -rho*Y[jn]*rate_eval.n_Sc54__Sc55
       +rho*Y[jhe4]*rate_eval.He4_Sc54__n_V57
       +rho*Y[jp]*rate_eval.p_Sc54__n_Ti54
       +rate_eval.Sc54__n_Ti53__weak__mp17
       )

    jac[jn, jsc55] = (
       -rho*Y[jn]*rate_eval.n_Sc55__Sc56
       +rho*Y[jhe4]*rate_eval.He4_Sc55__n_V58
       +rho*Y[jp]*rate_eval.p_Sc55__n_Ti55
       +rate_eval.Sc55__n_Ti54__weak__wc12
       )

    jac[jn, jsc56] = (
       -rho*Y[jn]*rate_eval.n_Sc56__Sc57
       +rate_eval.Sc56__n_Ti55__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Sc56__n_V59
       +rho*Y[jp]*rate_eval.p_Sc56__n_Ti56
       )

    jac[jn, jsc57] = (
       -rho*Y[jn]*rate_eval.n_Sc57__Sc58
       +3*rate_eval.Sc57__n_n_n_Ti54__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Sc57__n_V60
       +rho*Y[jp]*rate_eval.p_Sc57__n_Ti57
       +rate_eval.Sc57__n_Ti56__weak__mp17
       )

    jac[jn, jsc58] = (
       -rho*Y[jn]*rate_eval.n_Sc58__Sc59
       +3*rate_eval.Sc58__n_n_n_Ti55__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Sc58__n_V61
       +rho*Y[jp]*rate_eval.p_Sc58__n_Ti58
       +rate_eval.Sc58__n_Ti57__weak__mp17
       +2*rate_eval.Sc58__n_n_Ti56__weak__mp17
       )

    jac[jn, jsc59] = (
       -rho*Y[jn]*rate_eval.n_Sc59__Sc60
       +3*rate_eval.Sc59__n_n_n_Ti56__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Sc59__n_V62
       +2*rate_eval.Sc59__n_n_Ti57__weak__mp17
       +rate_eval.Sc59__n_Ti58__weak__mp17
       +rho*Y[jp]*rate_eval.p_Sc59__n_Ti59
       )

    jac[jn, jsc60] = (
       -rho*Y[jn]*rate_eval.n_Sc60__Sc61
       +rho*Y[jhe4]*rate_eval.He4_Sc60__n_V63
       +rho*Y[jp]*rate_eval.p_Sc60__n_Ti60
       +2*rate_eval.Sc60__n_n_Ti58__weak__mp17
       +rate_eval.Sc60__n_Ti59__weak__mp17
       +3*rate_eval.Sc60__n_n_n_Ti57__weak__mo03
       )

    jac[jn, jsc61] = (
       -rho*Y[jn]*rate_eval.n_Sc61__Sc62
       +3*rate_eval.Sc61__n_n_n_Ti58__weak__mo03
       +2*rate_eval.Sc61__n_n_Ti59__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Sc61__n_V64
       +rho*Y[jp]*rate_eval.p_Sc61__n_Ti61
       +rate_eval.Sc61__n_Ti60__weak__mp17
       )

    jac[jn, jsc62] = (
       -rho*Y[jn]*rate_eval.n_Sc62__Sc63
       +3*rate_eval.Sc62__n_n_n_Ti59__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Sc62__n_V65
       +rho*Y[jp]*rate_eval.p_Sc62__n_Ti62
       +2*rate_eval.Sc62__n_n_Ti60__weak__mp17
       +rate_eval.Sc62__n_Ti61__weak__mp17
       )

    jac[jn, jsc63] = (
       +3*rate_eval.Sc63__n_n_n_Ti60__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Sc63__n_V66
       +rate_eval.Sc63__n_Ti62__weak__mp17
       +2*rate_eval.Sc63__n_n_Ti61__weak__mp17
       +rho*Y[jp]*rate_eval.p_Sc63__n_Ti63
       )

    jac[jn, jti37] = (
       -rho*Y[jn]*rate_eval.n_Ti37__He4_Ca34
       -rho*Y[jn]*rate_eval.n_Ti37__Ti38
       -rho*Y[jn]*rate_eval.n_Ti37__p_Sc37
       )

    jac[jn, jti38] = (
       -rho*Y[jn]*rate_eval.n_Ti38__He4_Ca35
       -rho*Y[jn]*rate_eval.n_Ti38__p_Sc38
       -rho*Y[jn]*rate_eval.n_Ti38__Ti39
       )

    jac[jn, jti39] = (
       -rho*Y[jn]*rate_eval.n_Ti39__p_Sc39
       -rho*Y[jn]*rate_eval.n_Ti39__He4_Ca36
       -rho*Y[jn]*rate_eval.n_Ti39__Ti40
       )

    jac[jn, jti40] = (
       -rho*Y[jn]*rate_eval.n_Ti40__Ti41
       -rho*Y[jn]*rate_eval.n_Ti40__p_Sc40
       -rho*Y[jn]*rate_eval.n_Ti40__He4_Ca37
       )

    jac[jn, jti41] = (
       -rho*Y[jn]*rate_eval.n_Ti41__He4_Ca38
       -rho*Y[jn]*rate_eval.n_Ti41__p_Sc41
       -rho*Y[jn]*rate_eval.n_Ti41__Ti42
       )

    jac[jn, jti42] = (
       -rho*Y[jn]*rate_eval.n_Ti42__p_Sc42
       -rho*Y[jn]*rate_eval.n_Ti42__He4_Ca39
       -rho*Y[jn]*rate_eval.n_Ti42__Ti43
       )

    jac[jn, jti43] = (
       -rho*Y[jn]*rate_eval.n_Ti43__He4_Ca40
       -rho*Y[jn]*rate_eval.n_Ti43__Ti44
       -rho*Y[jn]*rate_eval.n_Ti43__p_Sc43
       )

    jac[jn, jti44] = (
       -rho*Y[jn]*rate_eval.n_Ti44__p_Sc44
       -rho*Y[jn]*rate_eval.n_Ti44__Ti45
       -rho*Y[jn]*rate_eval.n_Ti44__He4_Ca41
       )

    jac[jn, jti45] = (
       -rho*Y[jn]*rate_eval.n_Ti45__p_Sc45
       -rho*Y[jn]*rate_eval.n_Ti45__He4_Ca42
       -rho*Y[jn]*rate_eval.n_Ti45__Ti46
       )

    jac[jn, jti46] = (
       -rho*Y[jn]*rate_eval.n_Ti46__Ti47
       )

    jac[jn, jti47] = (
       -rho*Y[jn]*rate_eval.n_Ti47__He4_Ca44
       -rho*Y[jn]*rate_eval.n_Ti47__Ti48
       -rho*Y[jn]*rate_eval.n_Ti47__p_Sc47
       )

    jac[jn, jti48] = (
       -rho*Y[jn]*rate_eval.n_Ti48__Ti49
       )

    jac[jn, jti49] = (
       -rho*Y[jn]*rate_eval.n_Ti49__He4_Ca46
       -rho*Y[jn]*rate_eval.n_Ti49__Ti50
       +rho*Y[jhe4]*rate_eval.He4_Ti49__n_Cr52
       )

    jac[jn, jti50] = (
       -rho*Y[jn]*rate_eval.n_Ti50__Ti51
       )

    jac[jn, jti51] = (
       -rho*Y[jn]*rate_eval.n_Ti51__He4_Ca48
       -rho*Y[jn]*rate_eval.n_Ti51__Ti52
       +rho*Y[jhe4]*rate_eval.He4_Ti51__n_Cr54
       +rho*Y[jp]*rate_eval.p_Ti51__n_V51
       )

    jac[jn, jti52] = (
       -rho*Y[jn]*rate_eval.n_Ti52__Ti53
       +rho*Y[jp]*rate_eval.p_Ti52__n_V52
       )

    jac[jn, jti53] = (
       -rho*Y[jn]*rate_eval.n_Ti53__Ti54
       +rho*Y[jhe4]*rate_eval.He4_Ti53__n_Cr56
       +rho*Y[jp]*rate_eval.p_Ti53__n_V53
       )

    jac[jn, jti54] = (
       -rho*Y[jn]*rate_eval.n_Ti54__Ti55
       +rho*Y[jhe4]*rate_eval.He4_Ti54__n_Cr57
       +rho*Y[jp]*rate_eval.p_Ti54__n_V54
       )

    jac[jn, jti55] = (
       -rho*Y[jn]*rate_eval.n_Ti55__Ti56
       +rho*Y[jhe4]*rate_eval.He4_Ti55__n_Cr58
       +rho*Y[jp]*rate_eval.p_Ti55__n_V55
       )

    jac[jn, jti56] = (
       -rho*Y[jn]*rate_eval.n_Ti56__Ti57
       +rho*Y[jhe4]*rate_eval.He4_Ti56__n_Cr59
       +rho*Y[jp]*rate_eval.p_Ti56__n_V56
       )

    jac[jn, jti57] = (
       -rho*Y[jn]*rate_eval.n_Ti57__Ti58
       +rho*Y[jp]*rate_eval.p_Ti57__n_V57
       +rho*Y[jhe4]*rate_eval.He4_Ti57__n_Cr60
       )

    jac[jn, jti58] = (
       -rho*Y[jn]*rate_eval.n_Ti58__Ti59
       +rho*Y[jhe4]*rate_eval.He4_Ti58__n_Cr61
       +rho*Y[jp]*rate_eval.p_Ti58__n_V58
       +rate_eval.Ti58__n_V57__weak__mp17
       )

    jac[jn, jti59] = (
       -rho*Y[jn]*rate_eval.n_Ti59__Ti60
       +rho*Y[jhe4]*rate_eval.He4_Ti59__n_Cr62
       +rho*Y[jp]*rate_eval.p_Ti59__n_V59
       )

    jac[jn, jti60] = (
       -rho*Y[jn]*rate_eval.n_Ti60__Ti61
       +rho*Y[jhe4]*rate_eval.He4_Ti60__n_Cr63
       +rho*Y[jp]*rate_eval.p_Ti60__n_V60
       +rate_eval.Ti60__n_V59__weak__mp17
       )

    jac[jn, jti61] = (
       -rho*Y[jn]*rate_eval.n_Ti61__Ti62
       +rho*Y[jp]*rate_eval.p_Ti61__n_V61
       +rho*Y[jhe4]*rate_eval.He4_Ti61__n_Cr64
       +rate_eval.Ti61__n_V60__weak__mp17
       )

    jac[jn, jti62] = (
       -rho*Y[jn]*rate_eval.n_Ti62__Ti63
       +rho*Y[jp]*rate_eval.p_Ti62__n_V62
       +rho*Y[jhe4]*rate_eval.He4_Ti62__n_Cr65
       +rate_eval.Ti62__n_V61__weak__mp17
       )

    jac[jn, jti63] = (
       -rho*Y[jn]*rate_eval.n_Ti63__Ti64
       +rho*Y[jhe4]*rate_eval.He4_Ti63__n_Cr66
       +rho*Y[jp]*rate_eval.p_Ti63__n_V63
       +rate_eval.Ti63__n_V62__weak__mp17
       +2*rate_eval.Ti63__n_n_V61__weak__mp17
       )

    jac[jn, jti64] = (
       -rho*Y[jn]*rate_eval.n_Ti64__Ti65
       +rho*Y[jhe4]*rate_eval.He4_Ti64__n_Cr67
       +rho*Y[jp]*rate_eval.p_Ti64__n_V64
       +2*rate_eval.Ti64__n_n_V62__weak__mp17
       +rate_eval.Ti64__n_V63__weak__mp17
       +3*rate_eval.Ti64__n_n_n_V61__weak__mo03
       )

    jac[jn, jti65] = (
       +3*rate_eval.Ti65__n_n_n_V62__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Ti65__n_Cr68
       +rate_eval.Ti65__n_V64__weak__mp17
       +rho*Y[jp]*rate_eval.p_Ti65__n_V65
       +2*rate_eval.Ti65__n_n_V63__weak__mp17
       )

    jac[jn, jv39] = (
       -rho*Y[jn]*rate_eval.n_V39__V40
       -rho*Y[jn]*rate_eval.n_V39__p_Ti39
       -rho*Y[jn]*rate_eval.n_V39__He4_Sc36
       )

    jac[jn, jv40] = (
       -rho*Y[jn]*rate_eval.n_V40__p_Ti40
       -rho*Y[jn]*rate_eval.n_V40__He4_Sc37
       -rho*Y[jn]*rate_eval.n_V40__V41
       )

    jac[jn, jv41] = (
       -rho*Y[jn]*rate_eval.n_V41__He4_Sc38
       -rho*Y[jn]*rate_eval.n_V41__V42
       -rho*Y[jn]*rate_eval.n_V41__p_Ti41
       )

    jac[jn, jv42] = (
       -rho*Y[jn]*rate_eval.n_V42__He4_Sc39
       -rho*Y[jn]*rate_eval.n_V42__V43
       -rho*Y[jn]*rate_eval.n_V42__p_Ti42
       )

    jac[jn, jv43] = (
       -rho*Y[jn]*rate_eval.n_V43__p_Ti43
       -rho*Y[jn]*rate_eval.n_V43__He4_Sc40
       -rho*Y[jn]*rate_eval.n_V43__V44
       )

    jac[jn, jv44] = (
       -rho*Y[jn]*rate_eval.n_V44__He4_Sc41
       -rho*Y[jn]*rate_eval.n_V44__p_Ti44
       -rho*Y[jn]*rate_eval.n_V44__V45
       )

    jac[jn, jv45] = (
       -rho*Y[jn]*rate_eval.n_V45__He4_Sc42
       -rho*Y[jn]*rate_eval.n_V45__V46
       -rho*Y[jn]*rate_eval.n_V45__p_Ti45
       )

    jac[jn, jv46] = (
       -rho*Y[jn]*rate_eval.n_V46__He4_Sc43
       -rho*Y[jn]*rate_eval.n_V46__p_Ti46
       -rho*Y[jn]*rate_eval.n_V46__V47
       )

    jac[jn, jv47] = (
       -rho*Y[jn]*rate_eval.n_V47__He4_Sc44
       -rho*Y[jn]*rate_eval.n_V47__V48
       -rho*Y[jn]*rate_eval.n_V47__p_Ti47
       )

    jac[jn, jv48] = (
       -rho*Y[jn]*rate_eval.n_V48__p_Ti48
       -rho*Y[jn]*rate_eval.n_V48__V49
       -rho*Y[jn]*rate_eval.n_V48__He4_Sc45
       )

    jac[jn, jv49] = (
       -rho*Y[jn]*rate_eval.n_V49__p_Ti49
       -rho*Y[jn]*rate_eval.n_V49__V50
       )

    jac[jn, jv50] = (
       -rho*Y[jn]*rate_eval.n_V50__p_Ti50
       -rho*Y[jn]*rate_eval.n_V50__He4_Sc47
       -rho*Y[jn]*rate_eval.n_V50__V51
       +rho*Y[jp]*rate_eval.p_V50__n_Cr50
       )

    jac[jn, jv51] = (
       -rho*Y[jn]*rate_eval.n_V51__V52
       )

    jac[jn, jv52] = (
       -rho*Y[jn]*rate_eval.n_V52__V53
       -rho*Y[jn]*rate_eval.n_V52__He4_Sc49
       +rho*Y[jp]*rate_eval.p_V52__n_Cr52
       +rho*Y[jhe4]*rate_eval.He4_V52__n_Mn55
       )

    jac[jn, jv53] = (
       -rho*Y[jn]*rate_eval.n_V53__V54
       +rho*Y[jp]*rate_eval.p_V53__n_Cr53
       )

    jac[jn, jv54] = (
       -rho*Y[jn]*rate_eval.n_V54__V55
       +rho*Y[jhe4]*rate_eval.He4_V54__n_Mn57
       +rho*Y[jp]*rate_eval.p_V54__n_Cr54
       )

    jac[jn, jv55] = (
       -rho*Y[jn]*rate_eval.n_V55__V56
       +rho*Y[jhe4]*rate_eval.He4_V55__n_Mn58
       +rho*Y[jp]*rate_eval.p_V55__n_Cr55
       )

    jac[jn, jv56] = (
       -rho*Y[jn]*rate_eval.n_V56__V57
       +rho*Y[jhe4]*rate_eval.He4_V56__n_Mn59
       +rho*Y[jp]*rate_eval.p_V56__n_Cr56
       )

    jac[jn, jv57] = (
       -rho*Y[jn]*rate_eval.n_V57__V58
       +rho*Y[jp]*rate_eval.p_V57__n_Cr57
       +rho*Y[jhe4]*rate_eval.He4_V57__n_Mn60
       )

    jac[jn, jv58] = (
       -rho*Y[jn]*rate_eval.n_V58__V59
       +rho*Y[jhe4]*rate_eval.He4_V58__n_Mn61
       +rho*Y[jp]*rate_eval.p_V58__n_Cr58
       +rate_eval.V58__n_Cr57__weak__mp17
       )

    jac[jn, jv59] = (
       -rho*Y[jn]*rate_eval.n_V59__V60
       +rho*Y[jhe4]*rate_eval.He4_V59__n_Mn62
       +rho*Y[jp]*rate_eval.p_V59__n_Cr59
       +rate_eval.V59__n_Cr58__weak__wc12
       )

    jac[jn, jv60] = (
       -rho*Y[jn]*rate_eval.n_V60__V61
       +rho*Y[jp]*rate_eval.p_V60__n_Cr60
       +rho*Y[jhe4]*rate_eval.He4_V60__n_Mn63
       +rate_eval.V60__n_Cr59__weak__mp17
       )

    jac[jn, jv61] = (
       -rho*Y[jn]*rate_eval.n_V61__V62
       +rho*Y[jhe4]*rate_eval.He4_V61__n_Mn64
       +rho*Y[jp]*rate_eval.p_V61__n_Cr61
       +rate_eval.V61__n_Cr60__weak__wc12
       )

    jac[jn, jv62] = (
       -rho*Y[jn]*rate_eval.n_V62__V63
       +rho*Y[jhe4]*rate_eval.He4_V62__n_Mn65
       +rho*Y[jp]*rate_eval.p_V62__n_Cr62
       +rate_eval.V62__n_Cr61__weak__mp17
       )

    jac[jn, jv63] = (
       -rho*Y[jn]*rate_eval.n_V63__V64
       +rho*Y[jp]*rate_eval.p_V63__n_Cr63
       +rho*Y[jhe4]*rate_eval.He4_V63__n_Mn66
       +rate_eval.V63__n_Cr62__weak__wc12
       )

    jac[jn, jv64] = (
       -rho*Y[jn]*rate_eval.n_V64__V65
       +rho*Y[jhe4]*rate_eval.He4_V64__n_Mn67
       +2*rate_eval.V64__n_n_Cr62__weak__mp17
       +rho*Y[jp]*rate_eval.p_V64__n_Cr64
       +rate_eval.V64__n_Cr63__weak__mp17
       )

    jac[jn, jv65] = (
       -rho*Y[jn]*rate_eval.n_V65__V66
       +3*rate_eval.V65__n_n_n_Cr62__weak__mo03
       +rate_eval.V65__n_Cr64__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_V65__n_Mn68
       +2*rate_eval.V65__n_n_Cr63__weak__mp17
       +rho*Y[jp]*rate_eval.p_V65__n_Cr65
       )

    jac[jn, jv66] = (
       -rho*Y[jn]*rate_eval.n_V66__V67
       +3*rate_eval.V66__n_n_n_Cr63__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_V66__n_Mn69
       +rho*Y[jp]*rate_eval.p_V66__n_Cr66
       +rate_eval.V66__n_Cr65__weak__mp17
       +2*rate_eval.V66__n_n_Cr64__weak__mp17
       )

    jac[jn, jv67] = (
       +rho*Y[jhe4]*rate_eval.He4_V67__n_Mn70
       +rho*Y[jp]*rate_eval.p_V67__n_Cr67
       +3*rate_eval.V67__n_n_n_Cr64__weak__mo03
       +rate_eval.V67__n_Cr66__weak__mp17
       +2*rate_eval.V67__n_n_Cr65__weak__mp17
       )

    jac[jn, jcr41] = (
       -rho*Y[jn]*rate_eval.n_Cr41__He4_Ti38
       -rho*Y[jn]*rate_eval.n_Cr41__Cr42
       -rho*Y[jn]*rate_eval.n_Cr41__p_V41
       )

    jac[jn, jcr42] = (
       -rho*Y[jn]*rate_eval.n_Cr42__He4_Ti39
       -rho*Y[jn]*rate_eval.n_Cr42__p_V42
       -rho*Y[jn]*rate_eval.n_Cr42__Cr43
       )

    jac[jn, jcr43] = (
       -rho*Y[jn]*rate_eval.n_Cr43__p_V43
       -rho*Y[jn]*rate_eval.n_Cr43__He4_Ti40
       -rho*Y[jn]*rate_eval.n_Cr43__Cr44
       )

    jac[jn, jcr44] = (
       -rho*Y[jn]*rate_eval.n_Cr44__He4_Ti41
       -rho*Y[jn]*rate_eval.n_Cr44__Cr45
       -rho*Y[jn]*rate_eval.n_Cr44__p_V44
       )

    jac[jn, jcr45] = (
       -rho*Y[jn]*rate_eval.n_Cr45__He4_Ti42
       -rho*Y[jn]*rate_eval.n_Cr45__Cr46
       -rho*Y[jn]*rate_eval.n_Cr45__p_V45
       )

    jac[jn, jcr46] = (
       -rho*Y[jn]*rate_eval.n_Cr46__He4_Ti43
       -rho*Y[jn]*rate_eval.n_Cr46__p_V46
       -rho*Y[jn]*rate_eval.n_Cr46__Cr47
       )

    jac[jn, jcr47] = (
       -rho*Y[jn]*rate_eval.n_Cr47__He4_Ti44
       -rho*Y[jn]*rate_eval.n_Cr47__p_V47
       -rho*Y[jn]*rate_eval.n_Cr47__Cr48
       )

    jac[jn, jcr48] = (
       -rho*Y[jn]*rate_eval.n_Cr48__p_V48
       -rho*Y[jn]*rate_eval.n_Cr48__Cr49
       -rho*Y[jn]*rate_eval.n_Cr48__He4_Ti45
       )

    jac[jn, jcr49] = (
       -rho*Y[jn]*rate_eval.n_Cr49__p_V49
       -rho*Y[jn]*rate_eval.n_Cr49__He4_Ti46
       -rho*Y[jn]*rate_eval.n_Cr49__Cr50
       )

    jac[jn, jcr50] = (
       -rho*Y[jn]*rate_eval.n_Cr50__He4_Ti47
       -rho*Y[jn]*rate_eval.n_Cr50__Cr51
       )

    jac[jn, jcr51] = (
       -rho*Y[jn]*rate_eval.n_Cr51__He4_Ti48
       -rho*Y[jn]*rate_eval.n_Cr51__Cr52
       -rho*Y[jn]*rate_eval.n_Cr51__p_V51
       )

    jac[jn, jcr52] = (
       -rho*Y[jn]*rate_eval.n_Cr52__Cr53
       )

    jac[jn, jcr53] = (
       -rho*Y[jn]*rate_eval.n_Cr53__He4_Ti50
       -rho*Y[jn]*rate_eval.n_Cr53__Cr54
       )

    jac[jn, jcr54] = (
       -rho*Y[jn]*rate_eval.n_Cr54__Cr55
       )

    jac[jn, jcr55] = (
       -rho*Y[jn]*rate_eval.n_Cr55__He4_Ti52
       -rho*Y[jn]*rate_eval.n_Cr55__Cr56
       +rho*Y[jhe4]*rate_eval.He4_Cr55__n_Fe58
       +rho*Y[jp]*rate_eval.p_Cr55__n_Mn55
       )

    jac[jn, jcr56] = (
       -rho*Y[jn]*rate_eval.n_Cr56__Cr57
       +rho*Y[jp]*rate_eval.p_Cr56__n_Mn56
       )

    jac[jn, jcr57] = (
       -rho*Y[jn]*rate_eval.n_Cr57__Cr58
       +rho*Y[jp]*rate_eval.p_Cr57__n_Mn57
       +rho*Y[jhe4]*rate_eval.He4_Cr57__n_Fe60
       )

    jac[jn, jcr58] = (
       -rho*Y[jn]*rate_eval.n_Cr58__Cr59
       +rho*Y[jp]*rate_eval.p_Cr58__n_Mn58
       +rho*Y[jhe4]*rate_eval.He4_Cr58__n_Fe61
       )

    jac[jn, jcr59] = (
       -rho*Y[jn]*rate_eval.n_Cr59__Cr60
       +rho*Y[jhe4]*rate_eval.He4_Cr59__n_Fe62
       +rho*Y[jp]*rate_eval.p_Cr59__n_Mn59
       )

    jac[jn, jcr60] = (
       -rho*Y[jn]*rate_eval.n_Cr60__Cr61
       +rho*Y[jp]*rate_eval.p_Cr60__n_Mn60
       +rho*Y[jhe4]*rate_eval.He4_Cr60__n_Fe63
       )

    jac[jn, jcr61] = (
       -rho*Y[jn]*rate_eval.n_Cr61__Cr62
       +rho*Y[jhe4]*rate_eval.He4_Cr61__n_Fe64
       +rate_eval.Cr61__n_Mn60__weak__mp17
       +rho*Y[jp]*rate_eval.p_Cr61__n_Mn61
       )

    jac[jn, jcr62] = (
       -rho*Y[jn]*rate_eval.n_Cr62__Cr63
       +rho*Y[jhe4]*rate_eval.He4_Cr62__n_Fe65
       +rho*Y[jp]*rate_eval.p_Cr62__n_Mn62
       +rate_eval.Cr62__n_Mn61__weak__mp17
       )

    jac[jn, jcr63] = (
       -rho*Y[jn]*rate_eval.n_Cr63__Cr64
       +rho*Y[jhe4]*rate_eval.He4_Cr63__n_Fe66
       +rho*Y[jp]*rate_eval.p_Cr63__n_Mn63
       +rate_eval.Cr63__n_Mn62__weak__mp17
       )

    jac[jn, jcr64] = (
       -rho*Y[jn]*rate_eval.n_Cr64__Cr65
       +rho*Y[jhe4]*rate_eval.He4_Cr64__n_Fe67
       +rho*Y[jp]*rate_eval.p_Cr64__n_Mn64
       +rate_eval.Cr64__n_Mn63__weak__mp17
       )

    jac[jn, jcr65] = (
       -rho*Y[jn]*rate_eval.n_Cr65__Cr66
       +rho*Y[jhe4]*rate_eval.He4_Cr65__n_Fe68
       +rho*Y[jp]*rate_eval.p_Cr65__n_Mn65
       +rate_eval.Cr65__n_Mn64__weak__mp17
       )

    jac[jn, jcr66] = (
       -rho*Y[jn]*rate_eval.n_Cr66__Cr67
       +rho*Y[jhe4]*rate_eval.He4_Cr66__n_Fe69
       +rate_eval.Cr66__n_Mn65__weak__mp17
       +rho*Y[jp]*rate_eval.p_Cr66__n_Mn66
       )

    jac[jn, jcr67] = (
       -rho*Y[jn]*rate_eval.n_Cr67__Cr68
       +rho*Y[jp]*rate_eval.p_Cr67__n_Mn67
       +rate_eval.Cr67__n_Mn66__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Cr67__n_Fe70
       )

    jac[jn, jcr68] = (
       -rho*Y[jn]*rate_eval.n_Cr68__Cr69
       +rho*Y[jp]*rate_eval.p_Cr68__n_Mn68
       +rate_eval.Cr68__n_Mn67__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Cr68__n_Fe71
       )

    jac[jn, jcr69] = (
       -rho*Y[jn]*rate_eval.n_Cr69__Cr70
       +rho*Y[jhe4]*rate_eval.He4_Cr69__n_Fe72
       +rate_eval.Cr69__n_Mn68__weak__mp17
       +2*rate_eval.Cr69__n_n_Mn67__weak__mp17
       +rho*Y[jp]*rate_eval.p_Cr69__n_Mn69
       )

    jac[jn, jcr70] = (
       +3*rate_eval.Cr70__n_n_n_Mn67__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Cr70__n_Fe73
       +rho*Y[jp]*rate_eval.p_Cr70__n_Mn70
       +rate_eval.Cr70__n_Mn69__weak__mp17
       +2*rate_eval.Cr70__n_n_Mn68__weak__mp17
       )

    jac[jn, jmn43] = (
       -rho*Y[jn]*rate_eval.n_Mn43__He4_V40
       -rho*Y[jn]*rate_eval.n_Mn43__p_Cr43
       -rho*Y[jn]*rate_eval.n_Mn43__Mn44
       )

    jac[jn, jmn44] = (
       -rho*Y[jn]*rate_eval.n_Mn44__Mn45
       -rho*Y[jn]*rate_eval.n_Mn44__p_Cr44
       -rho*Y[jn]*rate_eval.n_Mn44__He4_V41
       )

    jac[jn, jmn45] = (
       -rho*Y[jn]*rate_eval.n_Mn45__p_Cr45
       -rho*Y[jn]*rate_eval.n_Mn45__Mn46
       -rho*Y[jn]*rate_eval.n_Mn45__He4_V42
       )

    jac[jn, jmn46] = (
       -rho*Y[jn]*rate_eval.n_Mn46__He4_V43
       -rho*Y[jn]*rate_eval.n_Mn46__p_Cr46
       -rho*Y[jn]*rate_eval.n_Mn46__Mn47
       )

    jac[jn, jmn47] = (
       -rho*Y[jn]*rate_eval.n_Mn47__p_Cr47
       -rho*Y[jn]*rate_eval.n_Mn47__He4_V44
       -rho*Y[jn]*rate_eval.n_Mn47__Mn48
       )

    jac[jn, jmn48] = (
       -rho*Y[jn]*rate_eval.n_Mn48__He4_V45
       -rho*Y[jn]*rate_eval.n_Mn48__p_Cr48
       -rho*Y[jn]*rate_eval.n_Mn48__Mn49
       )

    jac[jn, jmn49] = (
       -rho*Y[jn]*rate_eval.n_Mn49__He4_V46
       -rho*Y[jn]*rate_eval.n_Mn49__Mn50
       -rho*Y[jn]*rate_eval.n_Mn49__p_Cr49
       )

    jac[jn, jmn50] = (
       -rho*Y[jn]*rate_eval.n_Mn50__He4_V47
       -rho*Y[jn]*rate_eval.n_Mn50__Mn51
       -rho*Y[jn]*rate_eval.n_Mn50__p_Cr50
       )

    jac[jn, jmn51] = (
       -rho*Y[jn]*rate_eval.n_Mn51__p_Cr51
       -rho*Y[jn]*rate_eval.n_Mn51__He4_V48
       -rho*Y[jn]*rate_eval.n_Mn51__Mn52
       )

    jac[jn, jmn52] = (
       -rho*Y[jn]*rate_eval.n_Mn52__He4_V49
       -rho*Y[jn]*rate_eval.n_Mn52__p_Cr52
       -rho*Y[jn]*rate_eval.n_Mn52__Mn53
       )

    jac[jn, jmn53] = (
       -rho*Y[jn]*rate_eval.n_Mn53__p_Cr53
       -rho*Y[jn]*rate_eval.n_Mn53__He4_V50
       -rho*Y[jn]*rate_eval.n_Mn53__Mn54
       )

    jac[jn, jmn54] = (
       -rho*Y[jn]*rate_eval.n_Mn54__p_Cr54
       -rho*Y[jn]*rate_eval.n_Mn54__He4_V51
       -rho*Y[jn]*rate_eval.n_Mn54__Mn55
       )

    jac[jn, jmn55] = (
       -rho*Y[jn]*rate_eval.n_Mn55__Mn56
       )

    jac[jn, jmn56] = (
       -rho*Y[jn]*rate_eval.n_Mn56__Mn57
       -rho*Y[jn]*rate_eval.n_Mn56__He4_V53
       +rho*Y[jp]*rate_eval.p_Mn56__n_Fe56
       )

    jac[jn, jmn57] = (
       -rho*Y[jn]*rate_eval.n_Mn57__Mn58
       +rho*Y[jp]*rate_eval.p_Mn57__n_Fe57
       )

    jac[jn, jmn58] = (
       -rho*Y[jn]*rate_eval.n_Mn58__Mn59
       +rho*Y[jp]*rate_eval.p_Mn58__n_Fe58
       +rho*Y[jhe4]*rate_eval.He4_Mn58__n_Co61
       )

    jac[jn, jmn59] = (
       -rho*Y[jn]*rate_eval.n_Mn59__Mn60
       +rho*Y[jp]*rate_eval.p_Mn59__n_Fe59
       +rho*Y[jhe4]*rate_eval.He4_Mn59__n_Co62
       )

    jac[jn, jmn60] = (
       -rho*Y[jn]*rate_eval.n_Mn60__Mn61
       +rho*Y[jhe4]*rate_eval.He4_Mn60__n_Co63
       +rho*Y[jp]*rate_eval.p_Mn60__n_Fe60
       )

    jac[jn, jmn61] = (
       -rho*Y[jn]*rate_eval.n_Mn61__Mn62
       +rho*Y[jp]*rate_eval.p_Mn61__n_Fe61
       +rho*Y[jhe4]*rate_eval.He4_Mn61__n_Co64
       )

    jac[jn, jmn62] = (
       -rho*Y[jn]*rate_eval.n_Mn62__Mn63
       +rho*Y[jhe4]*rate_eval.He4_Mn62__n_Co65
       +rho*Y[jp]*rate_eval.p_Mn62__n_Fe62
       )

    jac[jn, jmn63] = (
       -rho*Y[jn]*rate_eval.n_Mn63__Mn64
       +rho*Y[jp]*rate_eval.p_Mn63__n_Fe63
       +rho*Y[jhe4]*rate_eval.He4_Mn63__n_Co66
       +rate_eval.Mn63__n_Fe62__weak__mp17
       )

    jac[jn, jmn64] = (
       -rho*Y[jn]*rate_eval.n_Mn64__Mn65
       +rho*Y[jp]*rate_eval.p_Mn64__n_Fe64
       +rho*Y[jhe4]*rate_eval.He4_Mn64__n_Co67
       +rate_eval.Mn64__n_Fe63__weak__wc12
       )

    jac[jn, jmn65] = (
       -rho*Y[jn]*rate_eval.n_Mn65__Mn66
       +rho*Y[jhe4]*rate_eval.He4_Mn65__n_Co68
       +rate_eval.Mn65__n_Fe64__weak__mp17
       +rho*Y[jp]*rate_eval.p_Mn65__n_Fe65
       )

    jac[jn, jmn66] = (
       -rho*Y[jn]*rate_eval.n_Mn66__Mn67
       +rho*Y[jp]*rate_eval.p_Mn66__n_Fe66
       +rate_eval.Mn66__n_Fe65__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Mn66__n_Co69
       )

    jac[jn, jmn67] = (
       -rho*Y[jn]*rate_eval.n_Mn67__Mn68
       +rho*Y[jhe4]*rate_eval.He4_Mn67__n_Co70
       +rate_eval.Mn67__n_Fe66__weak__mp17
       +rho*Y[jp]*rate_eval.p_Mn67__n_Fe67
       )

    jac[jn, jmn68] = (
       -rho*Y[jn]*rate_eval.n_Mn68__Mn69
       +rho*Y[jhe4]*rate_eval.He4_Mn68__n_Co71
       +rho*Y[jp]*rate_eval.p_Mn68__n_Fe68
       +2*rate_eval.Mn68__n_n_Fe66__weak__mp17
       +rate_eval.Mn68__n_Fe67__weak__mp17
       )

    jac[jn, jmn69] = (
       -rho*Y[jn]*rate_eval.n_Mn69__Mn70
       +rho*Y[jhe4]*rate_eval.He4_Mn69__n_Co72
       +rho*Y[jp]*rate_eval.p_Mn69__n_Fe69
       +rate_eval.Mn69__n_Fe68__weak__mp17
       )

    jac[jn, jmn70] = (
       -rho*Y[jn]*rate_eval.n_Mn70__Mn71
       +rate_eval.Mn70__n_Fe69__weak__mp17
       +2*rate_eval.Mn70__n_n_Fe68__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Mn70__n_Co73
       +rho*Y[jp]*rate_eval.p_Mn70__n_Fe70
       )

    jac[jn, jmn71] = (
       -rho*Y[jn]*rate_eval.n_Mn71__Mn72
       +3*rate_eval.Mn71__n_n_n_Fe68__weak__mo03
       +rho*Y[jp]*rate_eval.p_Mn71__n_Fe71
       +2*rate_eval.Mn71__n_n_Fe69__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Mn71__n_Co74
       +rate_eval.Mn71__n_Fe70__weak__mp17
       )

    jac[jn, jmn72] = (
       -rho*Y[jn]*rate_eval.n_Mn72__Mn73
       +rho*Y[jhe4]*rate_eval.He4_Mn72__n_Co75
       +rho*Y[jp]*rate_eval.p_Mn72__n_Fe72
       +2*rate_eval.Mn72__n_n_Fe70__weak__mp17
       +rate_eval.Mn72__n_Fe71__weak__mp17
       +3*rate_eval.Mn72__n_n_n_Fe69__weak__mo03
       )

    jac[jn, jmn73] = (
       +3*rate_eval.Mn73__n_n_n_Fe70__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Mn73__n_Co76
       +rho*Y[jp]*rate_eval.p_Mn73__n_Fe73
       +2*rate_eval.Mn73__n_n_Fe71__weak__mp17
       +rate_eval.Mn73__n_Fe72__weak__mp17
       )

    jac[jn, jfe45] = (
       -rho*Y[jn]*rate_eval.n_Fe45__p_Mn45
       -rho*Y[jn]*rate_eval.n_Fe45__Fe46
       -rho*Y[jn]*rate_eval.n_Fe45__He4_Cr42
       )

    jac[jn, jfe46] = (
       -rho*Y[jn]*rate_eval.n_Fe46__He4_Cr43
       -rho*Y[jn]*rate_eval.n_Fe46__p_Mn46
       -rho*Y[jn]*rate_eval.n_Fe46__Fe47
       )

    jac[jn, jfe47] = (
       -rho*Y[jn]*rate_eval.n_Fe47__He4_Cr44
       -rho*Y[jn]*rate_eval.n_Fe47__Fe48
       -rho*Y[jn]*rate_eval.n_Fe47__p_Mn47
       )

    jac[jn, jfe48] = (
       -rho*Y[jn]*rate_eval.n_Fe48__p_Mn48
       -rho*Y[jn]*rate_eval.n_Fe48__Fe49
       -rho*Y[jn]*rate_eval.n_Fe48__He4_Cr45
       )

    jac[jn, jfe49] = (
       -rho*Y[jn]*rate_eval.n_Fe49__He4_Cr46
       -rho*Y[jn]*rate_eval.n_Fe49__p_Mn49
       -rho*Y[jn]*rate_eval.n_Fe49__Fe50
       )

    jac[jn, jfe50] = (
       -rho*Y[jn]*rate_eval.n_Fe50__He4_Cr47
       -rho*Y[jn]*rate_eval.n_Fe50__Fe51
       -rho*Y[jn]*rate_eval.n_Fe50__p_Mn50
       )

    jac[jn, jfe51] = (
       -rho*Y[jn]*rate_eval.n_Fe51__He4_Cr48
       -rho*Y[jn]*rate_eval.n_Fe51__p_Mn51
       -rho*Y[jn]*rate_eval.n_Fe51__Fe52
       )

    jac[jn, jfe52] = (
       -rho*Y[jn]*rate_eval.n_Fe52__He4_Cr49
       -rho*Y[jn]*rate_eval.n_Fe52__p_Mn52
       -rho*Y[jn]*rate_eval.n_Fe52__Fe53
       )

    jac[jn, jfe53] = (
       -rho*Y[jn]*rate_eval.n_Fe53__He4_Cr50
       -rho*Y[jn]*rate_eval.n_Fe53__p_Mn53
       -rho*Y[jn]*rate_eval.n_Fe53__Fe54
       )

    jac[jn, jfe54] = (
       -rho*Y[jn]*rate_eval.n_Fe54__p_Mn54
       -rho*Y[jn]*rate_eval.n_Fe54__He4_Cr51
       -rho*Y[jn]*rate_eval.n_Fe54__Fe55
       )

    jac[jn, jfe55] = (
       -rho*Y[jn]*rate_eval.n_Fe55__p_Mn55
       -rho*Y[jn]*rate_eval.n_Fe55__He4_Cr52
       -rho*Y[jn]*rate_eval.n_Fe55__Fe56
       )

    jac[jn, jfe56] = (
       -rho*Y[jn]*rate_eval.n_Fe56__He4_Cr53
       -rho*Y[jn]*rate_eval.n_Fe56__Fe57
       )

    jac[jn, jfe57] = (
       -rho*Y[jn]*rate_eval.n_Fe57__Fe58
       -rho*Y[jn]*rate_eval.n_Fe57__He4_Cr54
       )

    jac[jn, jfe58] = (
       -rho*Y[jn]*rate_eval.n_Fe58__Fe59
       )

    jac[jn, jfe59] = (
       -rho*Y[jn]*rate_eval.n_Fe59__Fe60
       -rho*Y[jn]*rate_eval.n_Fe59__He4_Cr56
       +rho*Y[jhe4]*rate_eval.He4_Fe59__n_Ni62
       +rho*Y[jp]*rate_eval.p_Fe59__n_Co59
       )

    jac[jn, jfe60] = (
       -rho*Y[jn]*rate_eval.n_Fe60__Fe61
       )

    jac[jn, jfe61] = (
       -rho*Y[jn]*rate_eval.n_Fe61__Fe62
       +rho*Y[jp]*rate_eval.p_Fe61__n_Co61
       +rho*Y[jhe4]*rate_eval.He4_Fe61__n_Ni64
       )

    jac[jn, jfe62] = (
       -rho*Y[jn]*rate_eval.n_Fe62__Fe63
       +rho*Y[jp]*rate_eval.p_Fe62__n_Co62
       +rho*Y[jhe4]*rate_eval.He4_Fe62__n_Ni65
       )

    jac[jn, jfe63] = (
       -rho*Y[jn]*rate_eval.n_Fe63__Fe64
       +rho*Y[jhe4]*rate_eval.He4_Fe63__n_Ni66
       +rho*Y[jp]*rate_eval.p_Fe63__n_Co63
       )

    jac[jn, jfe64] = (
       -rho*Y[jn]*rate_eval.n_Fe64__Fe65
       +rho*Y[jhe4]*rate_eval.He4_Fe64__n_Ni67
       +rho*Y[jp]*rate_eval.p_Fe64__n_Co64
       )

    jac[jn, jfe65] = (
       -rho*Y[jn]*rate_eval.n_Fe65__Fe66
       +rho*Y[jp]*rate_eval.p_Fe65__n_Co65
       +rho*Y[jhe4]*rate_eval.He4_Fe65__n_Ni68
       )

    jac[jn, jfe66] = (
       -rho*Y[jn]*rate_eval.n_Fe66__Fe67
       +rho*Y[jhe4]*rate_eval.He4_Fe66__n_Ni69
       +rho*Y[jp]*rate_eval.p_Fe66__n_Co66
       )

    jac[jn, jfe67] = (
       -rho*Y[jn]*rate_eval.n_Fe67__Fe68
       +rho*Y[jp]*rate_eval.p_Fe67__n_Co67
       +rho*Y[jhe4]*rate_eval.He4_Fe67__n_Ni70
       )

    jac[jn, jfe68] = (
       -rho*Y[jn]*rate_eval.n_Fe68__Fe69
       +rho*Y[jhe4]*rate_eval.He4_Fe68__n_Ni71
       +rate_eval.Fe68__n_Co67__weak__mp17
       +rho*Y[jp]*rate_eval.p_Fe68__n_Co68
       )

    jac[jn, jfe69] = (
       -rho*Y[jn]*rate_eval.n_Fe69__Fe70
       +rho*Y[jp]*rate_eval.p_Fe69__n_Co69
       +rate_eval.Fe69__n_Co68__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Fe69__n_Ni72
       )

    jac[jn, jfe70] = (
       -rho*Y[jn]*rate_eval.n_Fe70__Fe71
       +rho*Y[jhe4]*rate_eval.He4_Fe70__n_Ni73
       +rho*Y[jp]*rate_eval.p_Fe70__n_Co70
       +rate_eval.Fe70__n_Co69__weak__mp17
       )

    jac[jn, jfe71] = (
       -rho*Y[jn]*rate_eval.n_Fe71__Fe72
       +rho*Y[jhe4]*rate_eval.He4_Fe71__n_Ni74
       +rho*Y[jp]*rate_eval.p_Fe71__n_Co71
       +rate_eval.Fe71__n_Co70__weak__mp17
       )

    jac[jn, jfe72] = (
       -rho*Y[jn]*rate_eval.n_Fe72__Fe73
       +rho*Y[jp]*rate_eval.p_Fe72__n_Co72
       +rate_eval.Fe72__n_Co71__weak__mp17
       +rho*Y[jhe4]*rate_eval.He4_Fe72__n_Ni75
       )

    jac[jn, jfe73] = (
       -rho*Y[jn]*rate_eval.n_Fe73__Fe74
       +rho*Y[jp]*rate_eval.p_Fe73__n_Co73
       +rho*Y[jhe4]*rate_eval.He4_Fe73__n_Ni76
       +2*rate_eval.Fe73__n_n_Co71__weak__mp17
       +rate_eval.Fe73__n_Co72__weak__mp17
       )

    jac[jn, jfe74] = (
       -rho*Y[jn]*rate_eval.n_Fe74__Fe75
       +rho*Y[jhe4]*rate_eval.He4_Fe74__n_Ni77
       +rho*Y[jp]*rate_eval.p_Fe74__n_Co74
       +rate_eval.Fe74__n_Co73__weak__mp17
       )

    jac[jn, jfe75] = (
       -rho*Y[jn]*rate_eval.n_Fe75__Fe76
       +3*rate_eval.Fe75__n_n_n_Co72__weak__mo03
       +rho*Y[jhe4]*rate_eval.He4_Fe75__n_Ni78
       +rho*Y[jp]*rate_eval.p_Fe75__n_Co75
       +2*rate_eval.Fe75__n_n_Co73__weak__mp17
       +rate_eval.Fe75__n_Co74__weak__mp17
       )

    jac[jn, jfe76] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe76__n_Ni79
       +3*rate_eval.Fe76__n_n_n_Co73__weak__mo03
       +2*rate_eval.Fe76__n_n_Co74__weak__mp17
       +rho*Y[jp]*rate_eval.p_Fe76__n_Co76
       +rate_eval.Fe76__n_Co75__weak__mp17
       )

    jac[jp, jn] = (
       -2*5.00000000000000e-01*rho**2*Y[jp]**2*rate_eval.n_p_p__p_d
       -rho*Y[jp]*rate_eval.n_p__d
       -rho**2*Y[jp]*Y[jhe4]*rate_eval.n_p_He4__Li6
       +5.00000000000000e-01*rho**2*Y[jp]**2*rate_eval.n_p_p__p_d
       +rho*Y[jb8]*rate_eval.n_B8__p_He4_He4
       +rho*Y[jfe55]*rate_eval.n_Fe55__p_Mn55
       +rho*Y[jfe54]*rate_eval.n_Fe54__p_Mn54
       +rho*Y[jfe53]*rate_eval.n_Fe53__p_Mn53
       +rho*Y[jfe49]*rate_eval.n_Fe49__p_Mn49
       +rho*Y[jfe46]*rate_eval.n_Fe46__p_Mn46
       +rho*Y[jmn52]*rate_eval.n_Mn52__p_Cr52
       +rho*Y[jmn51]*rate_eval.n_Mn51__p_Cr51
       +rho*Y[jmn47]*rate_eval.n_Mn47__p_Cr47
       +rho*Y[jmn46]*rate_eval.n_Mn46__p_Cr46
       +rho*Y[jmn45]*rate_eval.n_Mn45__p_Cr45
       +rho*Y[jcr48]*rate_eval.n_Cr48__p_V48
       +rho*Y[jcr43]*rate_eval.n_Cr43__p_V43
       +rho*Y[jcr42]*rate_eval.n_Cr42__p_V42
       +rho*Y[jcr49]*rate_eval.n_Cr49__p_V49
       +rho*Y[jv50]*rate_eval.n_V50__p_Ti50
       +rho*Y[jv46]*rate_eval.n_V46__p_Ti46
       +rho*Y[jv44]*rate_eval.n_V44__p_Ti44
       +rho*Y[jv43]*rate_eval.n_V43__p_Ti43
       +rho*Y[jv40]*rate_eval.n_V40__p_Ti40
       +rho*Y[jti45]*rate_eval.n_Ti45__p_Sc45
       +rho*Y[jti41]*rate_eval.n_Ti41__p_Sc41
       +rho*Y[jti39]*rate_eval.n_Ti39__p_Sc39
       +rho*Y[jti38]*rate_eval.n_Ti38__p_Sc38
       +rho*Y[jfe48]*rate_eval.n_Fe48__p_Mn48
       +rho*Y[jmn53]*rate_eval.n_Mn53__p_Cr53
       +rho*Y[jsc46]*rate_eval.n_Sc46__p_Ca46
       +rho*Y[jsi24]*rate_eval.n_Si24__p_Al24
       +rho*Y[jsc45]*rate_eval.n_Sc45__p_Ca45
       +rho*Y[jsc44]*rate_eval.n_Sc44__p_Ca44
       +rho*Y[jsc43]*rate_eval.n_Sc43__p_Ca43
       +rho*Y[jsc42]*rate_eval.n_Sc42__p_Ca42
       +rho*Y[jsc35]*rate_eval.n_Sc35__p_Ca35
       +rho*Y[jcr46]*rate_eval.n_Cr46__p_V46
       +rho*Y[jca38]*rate_eval.n_Ca38__p_K38
       +rho*Y[jca37]*rate_eval.n_Ca37__p_K37
       +rho*Y[jca36]*rate_eval.n_Ca36__p_K36
       +rho*Y[jcl35]*rate_eval.n_Cl35__p_S35
       +rho*Y[jca35]*rate_eval.n_Ca35__p_K35
       +rho*Y[jca34]*rate_eval.n_Ca34__p_K34
       +rho*Y[jk40]*rate_eval.n_K40__p_Ar40
       +rho*Y[jk39]*rate_eval.n_K39__p_Ar39
       +rho*Y[jk38]*rate_eval.n_K38__p_Ar38
       +rho*Y[jk36]*rate_eval.n_K36__p_Ar36
       +rho*Y[jk35]*rate_eval.n_K35__p_Ar35
       +rho*Y[jk33]*rate_eval.n_K33__p_Ar33
       +rho*Y[jk32]*rate_eval.n_K32__p_Ar32
       +rho*Y[jk31]*rate_eval.n_K31__p_Ar31
       +rho*Y[jar37]*rate_eval.n_Ar37__p_Cl37
       +rho*Y[jar35]*rate_eval.n_Ar35__p_Cl35
       +rho*Y[jar34]*rate_eval.n_Ar34__p_Cl34
       +rho*Y[jar33]*rate_eval.n_Ar33__p_Cl33
       +rho*Y[jar32]*rate_eval.n_Ar32__p_Cl32
       +rho*Y[jar31]*rate_eval.n_Ar31__p_Cl31
       +rho*Y[jar30]*rate_eval.n_Ar30__p_Cl30
       +rho*Y[jar29]*rate_eval.n_Ar29__p_Cl29
       +rho*Y[jcl36]*rate_eval.n_Cl36__p_S36
       +rho*Y[jcl34]*rate_eval.n_Cl34__p_S34
       +rho*Y[jcl33]*rate_eval.n_Cl33__p_S33
       +rho*Y[jcl31]*rate_eval.n_Cl31__p_S31
       +rho*Y[jcl29]*rate_eval.n_Cl29__p_S29
       +rho*Y[jv49]*rate_eval.n_V49__p_Ti49
       +rho*Y[js30]*rate_eval.n_S30__p_P30
       +rho*Y[js33]*rate_eval.n_S33__p_P33
       +rho*Y[jp32]*rate_eval.n_P32__p_Si32
       +rho*Y[jp28]*rate_eval.n_P28__p_Si28
       +rho*Y[jp27]*rate_eval.n_P27__p_Si27
       +rho*Y[jp26]*rate_eval.n_P26__p_Si26
       +rho*Y[jp24]*rate_eval.n_P24__p_Si24
       +rho*Y[jmn54]*rate_eval.n_Mn54__p_Cr54
       +rho*Y[jcr47]*rate_eval.n_Cr47__p_V47
       +rho*Y[jsi25]*rate_eval.n_Si25__p_Al25
       +rho*Y[jsi23]*rate_eval.n_Si23__p_Al23
       +rho*Y[jsi22]*rate_eval.n_Si22__p_Al22
       +rho*Y[jv48]*rate_eval.n_V48__p_Ti48
       +rho*Y[jti44]*rate_eval.n_Ti44__p_Sc44
       +rho*Y[jal26]*rate_eval.n_Al26__p_Mg26
       +rho*Y[jal25]*rate_eval.n_Al25__p_Mg25
       +rho*Y[jal22]*rate_eval.n_Al22__p_Mg22
       +rho*Y[jsc48]*rate_eval.n_Sc48__p_Ca48
       +rho*Y[jna19]*rate_eval.n_Na19__p_Ne19
       +rho*Y[jcl30]*rate_eval.n_Cl30__p_S30
       +rho*Y[jmg20]*rate_eval.n_Mg20__p_Na20
       +rho*Y[jmn43]*rate_eval.n_Mn43__p_Cr43
       +rho*Y[js31]*rate_eval.n_S31__p_P31
       +rho*Y[jti42]*rate_eval.n_Ti42__p_Sc42
       +rho*Y[jfe50]*rate_eval.n_Fe50__p_Mn50
       +rho*Y[js26]*rate_eval.n_S26__p_P26
       +rho*Y[jsc40]*rate_eval.n_Sc40__p_Ca40
       +rho*Y[jne18]*rate_eval.n_Ne18__p_F18
       +rho*Y[jne16]*rate_eval.n_Ne16__p_F16
       +rho*Y[jsi26]*rate_eval.n_Si26__p_Al26
       +rho*Y[jca33]*rate_eval.n_Ca33__p_K33
       +rho*Y[jo13]*rate_eval.n_O13__p_N13
       +rho*Y[jo12]*rate_eval.n_O12__p_N12
       +rho*Y[jsc37]*rate_eval.n_Sc37__p_Ca37
       +rho*Y[jn14]*rate_eval.n_N14__p_C14
       +rho*Y[jv39]*rate_eval.n_V39__p_Ti39
       +rho*Y[jc11]*rate_eval.n_C11__p_B11
       +rho*Y[jhe3]*rate_eval.n_He3__p_t
       +rho*Y[jf16]*rate_eval.n_F16__p_O16
       +rho*Y[jna21]*rate_eval.n_Na21__p_Ne21
       +rho*Y[js29]*rate_eval.n_S29__p_P29
       +rho*Y[jfe51]*rate_eval.n_Fe51__p_Mn51
       +rho*Y[jmn49]*rate_eval.n_Mn49__p_Cr49
       +rho*Y[jmn44]*rate_eval.n_Mn44__p_Cr44
       +rho*Y[jv47]*rate_eval.n_V47__p_Ti47
       +rho*Y[jfe47]*rate_eval.n_Fe47__p_Mn47
       +rho*Y[jf18]*rate_eval.n_F18__p_O18
       +rho*Y[jcl32]*rate_eval.n_Cl32__p_S32
       +rho*Y[jk37]*rate_eval.n_K37__p_Ar37
       +rho*Y[jv41]*rate_eval.n_V41__p_Ti41
       +rho*Y[jv42]*rate_eval.n_V42__p_Ti42
       +rho*Y[jti47]*rate_eval.n_Ti47__p_Sc47
       +rho*Y[jmg19]*rate_eval.n_Mg19__p_Na19
       +rho*Y[jal23]*rate_eval.n_Al23__p_Mg23
       +rho*Y[jal24]*rate_eval.n_Al24__p_Mg24
       +rho*Y[jmg22]*rate_eval.n_Mg22__p_Na22
       +rho*Y[jti37]*rate_eval.n_Ti37__p_Sc37
       +rho*Y[jmg21]*rate_eval.n_Mg21__p_Na21
       +rho*Y[jbe7]*rate_eval.n_Be7__p_Li7
       +rho*Y[jcl28]*rate_eval.n_Cl28__p_S28
       +rho*Y[jmn50]*rate_eval.n_Mn50__p_Cr50
       +rho*Y[jcr41]*rate_eval.n_Cr41__p_V41
       +rho*Y[js28]*rate_eval.n_S28__p_P28
       +rho*Y[jti40]*rate_eval.n_Ti40__p_Sc40
       +rho*Y[jp30]*rate_eval.n_P30__p_Si30
       +rho*Y[jna22]*rate_eval.n_Na22__p_Ne22
       +rho*Y[jsc36]*rate_eval.n_Sc36__p_Ca36
       +rho*Y[jsc38]*rate_eval.n_Sc38__p_Ca38
       +rho*Y[jcr51]*rate_eval.n_Cr51__p_V51
       +rho*Y[jcr45]*rate_eval.n_Cr45__p_V45
       +rho*Y[jsc41]*rate_eval.n_Sc41__p_Ca41
       +rho*Y[jfe52]*rate_eval.n_Fe52__p_Mn52
       +rho*Y[jsi27]*rate_eval.n_Si27__p_Al27
       +rho*Y[jmn48]*rate_eval.n_Mn48__p_Cr48
       +rho*Y[jne17]*rate_eval.n_Ne17__p_F17
       +rho*Y[jti43]*rate_eval.n_Ti43__p_Sc43
       +rho*Y[jcr44]*rate_eval.n_Cr44__p_V44
       +rho*Y[jf17]*rate_eval.n_F17__p_O17
       +rho*Y[jfe45]*rate_eval.n_Fe45__p_Mn45
       +rho*Y[jca39]*rate_eval.n_Ca39__p_K39
       +rho*Y[jp25]*rate_eval.n_P25__p_Si25
       +rho*Y[jp29]*rate_eval.n_P29__p_Si29
       +rho*Y[jar36]*rate_eval.n_Ar36__p_Cl36
       +rho*Y[jal21]*rate_eval.n_Al21__p_Mg21
       +rho*Y[jf14]*rate_eval.n_F14__p_O14
       +rho*Y[jk42]*rate_eval.n_K42__p_Ar42
       +rho*Y[jf15]*rate_eval.n_F15__p_O15
       +rho*Y[jna20]*rate_eval.n_Na20__p_Ne20
       +rho*Y[jv45]*rate_eval.n_V45__p_Ti45
       +rho*Y[js27]*rate_eval.n_S27__p_P27
       +rho*Y[jsc39]*rate_eval.n_Sc39__p_Ca39
       +rho*Y[jk34]*rate_eval.n_K34__p_Ar34
       )

    jac[jp, jp] = (
       -2*5.00000000000000e-01*rho**2*Y[jn]*2*Y[jp]*rate_eval.n_p_p__p_d
       -rho*Y[jbe9]*rate_eval.p_Be9__n_p_He4_He4
       -rho*Y[jb11]*rate_eval.p_B11__He4_He4_He4
       -rho*Y[jbe9]*rate_eval.p_Be9__d_He4_He4
       -rho*Y[jfe76]*rate_eval.p_Fe76__He4_Mn73
       -rho*Y[jfe75]*rate_eval.p_Fe75__He4_Mn72
       -rho*Y[jfe75]*rate_eval.p_Fe75__n_Co75
       -rho*Y[jfe74]*rate_eval.p_Fe74__He4_Mn71
       -rho*Y[jfe74]*rate_eval.p_Fe74__n_Co74
       -rho*Y[jfe73]*rate_eval.p_Fe73__He4_Mn70
       -rho*Y[jfe73]*rate_eval.p_Fe73__n_Co73
       -rho*Y[jfe72]*rate_eval.p_Fe72__He4_Mn69
       -rho*Y[jfe72]*rate_eval.p_Fe72__n_Co72
       -rho*Y[jfe71]*rate_eval.p_Fe71__He4_Mn68
       -rho*Y[jfe71]*rate_eval.p_Fe71__n_Co71
       -rho*Y[jfe70]*rate_eval.p_Fe70__He4_Mn67
       -rho*Y[jfe70]*rate_eval.p_Fe70__n_Co70
       -rho*Y[jfe69]*rate_eval.p_Fe69__He4_Mn66
       -rho*Y[jfe69]*rate_eval.p_Fe69__n_Co69
       -rho*Y[jfe68]*rate_eval.p_Fe68__He4_Mn65
       -rho*Y[jfe67]*rate_eval.p_Fe67__He4_Mn64
       -rho*Y[jfe65]*rate_eval.p_Fe65__He4_Mn62
       -rho*Y[jfe63]*rate_eval.p_Fe63__He4_Mn60
       -rho*Y[jfe62]*rate_eval.p_Fe62__He4_Mn59
       -rho*Y[jfe61]*rate_eval.p_Fe61__He4_Mn58
       -rho*Y[jfe61]*rate_eval.p_Fe61__n_Co61
       -rho*Y[jfe60]*rate_eval.p_Fe60__He4_Mn57
       -rho*Y[jfe59]*rate_eval.p_Fe59__He4_Mn56
       -rho*Y[jfe59]*rate_eval.p_Fe59__n_Co59
       -rho*Y[jfe57]*rate_eval.p_Fe57__He4_Mn54
       -rho*Y[jar34]*rate_eval.p_Ar34__K35
       -rho*Y[jca61]*rate_eval.p_Ca61__Sc62
       -rho*Y[jsc50]*rate_eval.p_Sc50__Ti51
       -rho*Y[jmn73]*rate_eval.p_Mn73__He4_Cr70
       -rho*Y[jmg34]*rate_eval.p_Mg34__Al35
       -rho*Y[jmn72]*rate_eval.p_Mn72__He4_Cr69
       -rho*Y[jmn71]*rate_eval.p_Mn71__He4_Cr68
       -rho*Y[jmn69]*rate_eval.p_Mn69__He4_Cr66
       -rho*Y[jmn68]*rate_eval.p_Mn68__n_Fe68
       -rho*Y[jmn67]*rate_eval.p_Mn67__He4_Cr64
       -rho*Y[jmn66]*rate_eval.p_Mn66__He4_Cr63
       -rho*Y[jmn66]*rate_eval.p_Mn66__n_Fe66
       -rho*Y[jk48]*rate_eval.p_K48__Ca49
       -rho*Y[jp46]*rate_eval.p_P46__S47
       -rho*Y[jmn65]*rate_eval.p_Mn65__He4_Cr62
       -rho*Y[jsi44]*rate_eval.p_Si44__n_P44
       -rho*Y[jmn64]*rate_eval.p_Mn64__He4_Cr61
       -rho*Y[jmn62]*rate_eval.p_Mn62__He4_Cr59
       -rho*Y[jmn60]*rate_eval.p_Mn60__He4_Cr57
       -rho*Y[jmn60]*rate_eval.p_Mn60__n_Fe60
       -rho*Y[jmn59]*rate_eval.p_Mn59__He4_Cr56
       -rho*Y[jmn57]*rate_eval.p_Mn57__n_Fe57
       -rho*Y[jfe64]*rate_eval.p_Fe64__He4_Mn61
       -rho*Y[jmn56]*rate_eval.p_Mn56__He4_Cr53
       -rho*Y[jmn54]*rate_eval.p_Mn54__He4_Cr51
       -rho*Y[jmn53]*rate_eval.p_Mn53__He4_Cr50
       -rho*Y[jca53]*rate_eval.p_Ca53__n_Sc53
       -rho*Y[jo22]*rate_eval.p_O22__n_F22
       -rho*Y[jca44]*rate_eval.p_Ca44__Sc45
       -rho*Y[jcr68]*rate_eval.p_Cr68__He4_V65
       -rho*Y[jcr68]*rate_eval.p_Cr68__n_Mn68
       -rho*Y[jcr67]*rate_eval.p_Cr67__n_Mn67
       -rho*Y[jcr66]*rate_eval.p_Cr66__He4_V63
       -rho*Y[jcr65]*rate_eval.p_Cr65__He4_V62
       -rho*Y[jmn72]*rate_eval.p_Mn72__n_Fe72
       -rho*Y[jo25]*rate_eval.p_O25__n_F25
       -rho*Y[jcr63]*rate_eval.p_Cr63__n_Mn63
       -rho*Y[jcr62]*rate_eval.p_Cr62__He4_V59
       -rho*Y[jcr60]*rate_eval.p_Cr60__He4_V57
       -rho*Y[jcr59]*rate_eval.p_Cr59__n_Mn59
       -rho*Y[jfe62]*rate_eval.p_Fe62__n_Co62
       -rho*Y[jcr57]*rate_eval.p_Cr57__n_Mn57
       -rho*Y[jcr54]*rate_eval.p_Cr54__He4_V51
       -rho*Y[jne32]*rate_eval.p_Ne32__Na33
       -rho*Y[jmg24]*rate_eval.p_Mg24__He4_Na21
       -rho*Y[jsi38]*rate_eval.p_Si38__n_P38
       -rho*Y[jmn55]*rate_eval.p_Mn55__He4_Cr52
       -rho*Y[jti57]*rate_eval.p_Ti57__He4_Sc54
       -rho*Y[jv67]*rate_eval.p_V67__n_Cr67
       -rho*Y[jv66]*rate_eval.p_V66__n_Cr66
       -rho*Y[jk47]*rate_eval.p_K47__He4_Ar44
       -rho*Y[jv65]*rate_eval.p_V65__He4_Ti62
       -rho*Y[jv64]*rate_eval.p_V64__He4_Ti61
       -rho*Y[jv63]*rate_eval.p_V63__n_Cr63
       -rho*Y[jv61]*rate_eval.p_V61__n_Cr61
       -rho*Y[jp32]*rate_eval.p_P32__n_S32
       -rho*Y[jv60]*rate_eval.p_V60__He4_Ti57
       -rho*Y[jv60]*rate_eval.p_V60__n_Cr60
       -rho*Y[jo27]*rate_eval.p_O27__He4_N24
       -rho*Y[jsi43]*rate_eval.p_Si43__n_P43
       -rho*Y[jv58]*rate_eval.p_V58__He4_Ti55
       -rho*Y[jv58]*rate_eval.p_V58__n_Cr58
       -rho*Y[jv57]*rate_eval.p_V57__He4_Ti54
       -rho*Y[jv57]*rate_eval.p_V57__n_Cr57
       -rho*Y[jv55]*rate_eval.p_V55__n_Cr55
       -rho*Y[jv53]*rate_eval.p_V53__n_Cr53
       -rho*Y[jv52]*rate_eval.p_V52__He4_Ti49
       -rho*Y[jv52]*rate_eval.p_V52__n_Cr52
       -rho*Y[jv51]*rate_eval.p_V51__He4_Ti48
       -rho*Y[jf23]*rate_eval.p_F23__Ne24
       -rho*Y[jv50]*rate_eval.p_V50__He4_Ti47
       -rho*Y[jv50]*rate_eval.p_V50__n_Cr50
       -rho*Y[jf24]*rate_eval.p_F24__Ne25
       -rho*Y[jv49]*rate_eval.p_V49__He4_Ti46
       -rho*Y[jsc52]*rate_eval.p_Sc52__Ti53
       -rho*Y[jsc53]*rate_eval.p_Sc53__n_Ti53
       -rho*Y[jcr57]*rate_eval.p_Cr57__He4_V54
       -rho*Y[jne27]*rate_eval.p_Ne27__He4_F24
       -rho*Y[jti64]*rate_eval.p_Ti64__He4_Sc61
       -rho*Y[jti63]*rate_eval.p_Ti63__He4_Sc60
       -rho*Y[jti63]*rate_eval.p_Ti63__n_V63
       -rho*Y[jti61]*rate_eval.p_Ti61__n_V61
       -rho*Y[jti60]*rate_eval.p_Ti60__n_V60
       -rho*Y[jti59]*rate_eval.p_Ti59__n_V59
       -rho*Y[jti58]*rate_eval.p_Ti58__n_V58
       -rho*Y[jti55]*rate_eval.p_Ti55__n_V55
       -rho*Y[jti54]*rate_eval.p_Ti54__He4_Sc51
       -rho*Y[jti54]*rate_eval.p_Ti54__n_V54
       -rho*Y[jf23]*rate_eval.p_F23__He4_O20
       -rho*Y[jti53]*rate_eval.p_Ti53__He4_Sc50
       -rho*Y[jti52]*rate_eval.p_Ti52__He4_Sc49
       -rho*Y[jti52]*rate_eval.p_Ti52__n_V52
       -rho*Y[jti51]*rate_eval.p_Ti51__n_V51
       -rho*Y[jar51]*rate_eval.p_Ar51__He4_Cl48
       -rho*Y[jcr55]*rate_eval.p_Cr55__n_Mn55
       -rho*Y[jf31]*rate_eval.p_F31__He4_O28
       -rho*Y[jsc61]*rate_eval.p_Sc61__n_Ti61
       -rho*Y[jsc60]*rate_eval.p_Sc60__He4_Ca57
       -rho*Y[jsc60]*rate_eval.p_Sc60__n_Ti60
       -rho*Y[jsc58]*rate_eval.p_Sc58__He4_Ca55
       -rho*Y[jsc58]*rate_eval.p_Sc58__n_Ti58
       -rho*Y[jsc55]*rate_eval.p_Sc55__He4_Ca52
       -rho*Y[jsc54]*rate_eval.p_Sc54__n_Ti54
       -rho*Y[jsc52]*rate_eval.p_Sc52__He4_Ca49
       -rho*Y[js47]*rate_eval.p_S47__Cl48
       -rho*Y[jsc52]*rate_eval.p_Sc52__n_Ti52
       -rho*Y[jsc50]*rate_eval.p_Sc50__n_Ti50
       -rho*Y[jsc49]*rate_eval.p_Sc49__He4_Ca46
       -rho*Y[jsc48]*rate_eval.p_Sc48__He4_Ca45
       -rho*Y[jsc47]*rate_eval.p_Sc47__He4_Ca44
       -rho*Y[jsc46]*rate_eval.p_Sc46__He4_Ca43
       -rho*Y[jsc45]*rate_eval.p_Sc45__He4_Ca42
       -rho*Y[jsc44]*rate_eval.p_Sc44__He4_Ca41
       -rho*Y[jcr56]*rate_eval.p_Cr56__n_Mn56
       -rho*Y[jsi36]*rate_eval.p_Si36__He4_Al33
       -rho*Y[jp31]*rate_eval.p_P31__S32
       -rho*Y[jsi45]*rate_eval.p_Si45__P46
       -rho*Y[jna36]*rate_eval.p_Na36__n_Mg36
       -rho*Y[jca61]*rate_eval.p_Ca61__He4_K58
       -rho*Y[jca61]*rate_eval.p_Ca61__n_Sc61
       -rho*Y[jca60]*rate_eval.p_Ca60__n_Sc60
       -rho*Y[jca59]*rate_eval.p_Ca59__n_Sc59
       -rho*Y[jca58]*rate_eval.p_Ca58__He4_K55
       -rho*Y[jca58]*rate_eval.p_Ca58__n_Sc58
       -rho*Y[jca56]*rate_eval.p_Ca56__He4_K53
       -rho*Y[jca55]*rate_eval.p_Ca55__He4_K52
       -rho*Y[jca55]*rate_eval.p_Ca55__n_Sc55
       -rho*Y[jca52]*rate_eval.p_Ca52__n_Sc52
       -rho*Y[jp45]*rate_eval.p_P45__S46
       -rho*Y[jcr56]*rate_eval.p_Cr56__He4_V53
       -rho*Y[jca51]*rate_eval.p_Ca51__He4_K48
       -rho*Y[jal39]*rate_eval.p_Al39__He4_Mg36
       -rho*Y[jca47]*rate_eval.p_Ca47__n_Sc47
       -rho*Y[jca42]*rate_eval.p_Ca42__He4_K39
       -rho*Y[jp42]*rate_eval.p_P42__n_S42
       -rho*Y[jk57]*rate_eval.p_K57__He4_Ar54
       -rho*Y[jk57]*rate_eval.p_K57__n_Ca57
       -rho*Y[jk56]*rate_eval.p_K56__n_Ca56
       -rho*Y[jk54]*rate_eval.p_K54__n_Ca54
       -rho*Y[jk53]*rate_eval.p_K53__n_Ca53
       -rho*Y[jp29]*rate_eval.p_P29__S30
       -rho*Y[jk51]*rate_eval.p_K51__n_Ca51
       -rho*Y[js42]*rate_eval.p_S42__Cl43
       -rho*Y[jk48]*rate_eval.p_K48__He4_Ar45
       -rho*Y[jk45]*rate_eval.p_K45__He4_Ar42
       -rho*Y[jk45]*rate_eval.p_K45__n_Ca45
       -rho*Y[jk44]*rate_eval.p_K44__He4_Ar41
       -rho*Y[jk43]*rate_eval.p_K43__n_Ca43
       -rho*Y[jk41]*rate_eval.p_K41__He4_Ar38
       -rho*Y[jk41]*rate_eval.p_K41__n_Ca41
       -rho*Y[jk40]*rate_eval.p_K40__He4_Ar37
       -rho*Y[jk40]*rate_eval.p_K40__n_Ca40
       -rho*Y[js37]*rate_eval.p_S37__Cl38
       -rho*Y[jo14]*rate_eval.p_O14__F15
       -rho*Y[jal39]*rate_eval.p_Al39__n_Si39
       -rho*Y[jcr61]*rate_eval.p_Cr61__He4_V58
       -rho*Y[jmn51]*rate_eval.p_Mn51__Fe52
       -rho*Y[jmn56]*rate_eval.p_Mn56__Fe57
       -rho*Y[jti38]*rate_eval.p_Ti38__V39
       -rho*Y[jar54]*rate_eval.p_Ar54__n_K54
       -rho*Y[jar52]*rate_eval.p_Ar52__He4_Cl49
       -rho*Y[jar52]*rate_eval.p_Ar52__n_K52
       -rho*Y[jk59]*rate_eval.p_K59__n_Ca59
       -rho*Y[jar50]*rate_eval.p_Ar50__He4_Cl47
       -rho*Y[jar48]*rate_eval.p_Ar48__He4_Cl45
       -rho*Y[jar48]*rate_eval.p_Ar48__n_K48
       -rho*Y[jf28]*rate_eval.p_F28__n_Ne28
       -rho*Y[jar44]*rate_eval.p_Ar44__n_K44
       -rho*Y[jcr55]*rate_eval.p_Cr55__He4_V52
       -rho*Y[jar43]*rate_eval.p_Ar43__n_K43
       -rho*Y[jfe47]*rate_eval.p_Fe47__Co48
       -rho*Y[jar41]*rate_eval.p_Ar41__n_K41
       -rho*Y[jar40]*rate_eval.p_Ar40__He4_Cl37
       -rho*Y[jar39]*rate_eval.p_Ar39__He4_Cl36
       -rho*Y[jcr62]*rate_eval.p_Cr62__Mn63
       -rho*Y[jcl52]*rate_eval.p_Cl52__He4_S49
       -rho*Y[jcl52]*rate_eval.p_Cl52__n_Ar52
       -rho*Y[jo16]*rate_eval.p_O16__F17
       -rho*Y[jcl51]*rate_eval.p_Cl51__He4_S48
       -rho*Y[jcl50]*rate_eval.p_Cl50__He4_S47
       -rho*Y[jcl50]*rate_eval.p_Cl50__n_Ar50
       -rho*Y[jb12]*rate_eval.p_B12__n_C12
       -rho*Y[jcl48]*rate_eval.p_Cl48__He4_S45
       -rho*Y[jcl48]*rate_eval.p_Cl48__n_Ar48
       -rho*Y[jti62]*rate_eval.p_Ti62__n_V62
       -rho*Y[jcl45]*rate_eval.p_Cl45__He4_S42
       -rho*Y[jcl45]*rate_eval.p_Cl45__n_Ar45
       -rho*Y[jcl43]*rate_eval.p_Cl43__He4_S40
       -rho*Y[jmn61]*rate_eval.p_Mn61__n_Fe61
       -rho*Y[jv55]*rate_eval.p_V55__Cr56
       -rho*Y[jcl42]*rate_eval.p_Cl42__He4_S39
       -rho*Y[js47]*rate_eval.p_S47__n_Cl47
       -rho*Y[jcl41]*rate_eval.p_Cl41__He4_S38
       -rho*Y[jcl40]*rate_eval.p_Cl40__n_Ar40
       -rho*Y[jo19]*rate_eval.p_O19__He4_N16
       -rho*Y[jti43]*rate_eval.p_Ti43__V44
       -rho*Y[jna34]*rate_eval.p_Na34__Mg35
       -rho*Y[js49]*rate_eval.p_S49__n_Cl49
       -rho*Y[js48]*rate_eval.p_S48__n_Cl48
       -rho*Y[jn15]*rate_eval.p_N15__O16
       -rho*Y[js47]*rate_eval.p_S47__He4_P44
       -rho*Y[jk52]*rate_eval.p_K52__He4_Ar49
       -rho*Y[js46]*rate_eval.p_S46__n_Cl46
       -rho*Y[js45]*rate_eval.p_S45__He4_P42
       -rho*Y[jmn64]*rate_eval.p_Mn64__n_Fe64
       -rho*Y[js43]*rate_eval.p_S43__He4_P40
       -rho*Y[jcr60]*rate_eval.p_Cr60__Mn61
       -rho*Y[jsc57]*rate_eval.p_Sc57__He4_Ca54
       -rho*Y[js41]*rate_eval.p_S41__He4_P38
       -rho*Y[jal30]*rate_eval.p_Al30__He4_Mg27
       -rho*Y[js40]*rate_eval.p_S40__n_Cl40
       -rho*Y[jcl40]*rate_eval.p_Cl40__He4_S37
       -rho*Y[js39]*rate_eval.p_S39__He4_P36
       -rho*Y[js38]*rate_eval.p_S38__He4_P35
       -rho*Y[js38]*rate_eval.p_S38__n_Cl38
       -rho*Y[jv56]*rate_eval.p_V56__He4_Ti53
       -rho*Y[js37]*rate_eval.p_S37__n_Cl37
       -rho*Y[jk49]*rate_eval.p_K49__n_Ca49
       -rho*Y[jcl45]*rate_eval.p_Cl45__Ar46
       -rho*Y[jli6]*rate_eval.p_Li6__Be7
       -rho*Y[js36]*rate_eval.p_S36__He4_P33
       -rho*Y[jcr69]*rate_eval.p_Cr69__He4_V66
       -rho*Y[jsc51]*rate_eval.p_Sc51__He4_Ca48
       -rho*Y[jk51]*rate_eval.p_K51__He4_Ar48
       -rho*Y[js35]*rate_eval.p_S35__He4_P32
       -rho*Y[jsc57]*rate_eval.p_Sc57__n_Ti57
       -rho*Y[jcl35]*rate_eval.p_Cl35__He4_S32
       -rho*Y[jv65]*rate_eval.p_V65__Cr66
       -rho*Y[jp47]*rate_eval.p_P47__n_S47
       -rho*Y[jp45]*rate_eval.p_P45__n_S45
       -rho*Y[jp43]*rate_eval.p_P43__He4_Si40
       -rho*Y[jp43]*rate_eval.p_P43__n_S43
       -rho*Y[jsc55]*rate_eval.p_Sc55__n_Ti55
       -rho*Y[jp42]*rate_eval.p_P42__He4_Si39
       -rho*Y[jo20]*rate_eval.p_O20__He4_N17
       -rho*Y[jar43]*rate_eval.p_Ar43__He4_Cl40
       -rho*Y[jp38]*rate_eval.p_P38__He4_Si35
       -rho*Y[jp38]*rate_eval.p_P38__n_S38
       -rho*Y[jf18]*rate_eval.p_F18__He4_O15
       -rho*Y[jp37]*rate_eval.p_P37__He4_Si34
       -rho*Y[jp36]*rate_eval.p_P36__He4_Si33
       -rho*Y[jp36]*rate_eval.p_P36__n_S36
       -rho*Y[jmn69]*rate_eval.p_Mn69__n_Fe69
       -rho*Y[jp34]*rate_eval.p_P34__n_S34
       -rho*Y[jca56]*rate_eval.p_Ca56__n_Sc56
       -rho*Y[jal25]*rate_eval.p_Al25__Si26
       -rho*Y[jsc45]*rate_eval.p_Sc45__Ti46
       -rho*Y[jp32]*rate_eval.p_P32__He4_Si29
       -rho*Y[jsi45]*rate_eval.p_Si45__He4_Al42
       -rho*Y[jsi45]*rate_eval.p_Si45__n_P45
       -rho*Y[jsi42]*rate_eval.p_Si42__n_P42
       -rho*Y[js38]*rate_eval.p_S38__Cl39
       -rho*Y[jsi39]*rate_eval.p_Si39__n_P39
       -rho*Y[jsc62]*rate_eval.p_Sc62__n_Ti62
       -rho*Y[jti65]*rate_eval.p_Ti65__He4_Sc62
       -rho*Y[jsi37]*rate_eval.p_Si37__He4_Al34
       -rho*Y[jsi37]*rate_eval.p_Si37__n_P37
       -rho*Y[jsi35]*rate_eval.p_Si35__He4_Al32
       -rho*Y[jsi33]*rate_eval.p_Si33__n_P33
       -rho*Y[jv49]*rate_eval.p_V49__Cr50
       -rho*Y[jmn58]*rate_eval.p_Mn58__Fe59
       -rho*Y[jv61]*rate_eval.p_V61__He4_Ti58
       -rho*Y[jal43]*rate_eval.p_Al43__n_Si43
       -rho*Y[jal41]*rate_eval.p_Al41__He4_Mg38
       -rho*Y[jal40]*rate_eval.p_Al40__He4_Mg37
       -rho*Y[jal40]*rate_eval.p_Al40__n_Si40
       -rho*Y[jal38]*rate_eval.p_Al38__He4_Mg35
       -rho*Y[jv59]*rate_eval.p_V59__n_Cr59
       -rho*Y[jal37]*rate_eval.p_Al37__He4_Mg34
       -rho*Y[jal36]*rate_eval.p_Al36__He4_Mg33
       -rho*Y[jal36]*rate_eval.p_Al36__n_Si36
       -rho*Y[jal41]*rate_eval.p_Al41__n_Si41
       -rho*Y[jv64]*rate_eval.p_V64__n_Cr64
       -rho*Y[jal35]*rate_eval.p_Al35__He4_Mg32
       -rho*Y[jal34]*rate_eval.p_Al34__He4_Mg31
       -rho*Y[jal34]*rate_eval.p_Al34__n_Si34
       -rho*Y[jal33]*rate_eval.p_Al33__He4_Mg30
       -rho*Y[jcl46]*rate_eval.p_Cl46__He4_S43
       -rho*Y[jal33]*rate_eval.p_Al33__n_Si33
       -rho*Y[jne26]*rate_eval.p_Ne26__n_Na26
       -rho*Y[jal32]*rate_eval.p_Al32__He4_Mg29
       -rho*Y[jal32]*rate_eval.p_Al32__n_Si32
       -rho*Y[jcl38]*rate_eval.p_Cl38__He4_S35
       -rho*Y[jal31]*rate_eval.p_Al31__He4_Mg28
       -rho*Y[jal30]*rate_eval.p_Al30__n_Si30
       -rho*Y[jal29]*rate_eval.p_Al29__He4_Mg26
       -rho*Y[jal29]*rate_eval.p_Al29__n_Si29
       -rho*Y[jne34]*rate_eval.p_Ne34__He4_F31
       -rho*Y[jal28]*rate_eval.p_Al28__He4_Mg25
       -rho*Y[jca49]*rate_eval.p_Ca49__Sc50
       -rho*Y[js46]*rate_eval.p_S46__Cl47
       -rho*Y[jna37]*rate_eval.p_Na37__Mg38
       -rho*Y[jv67]*rate_eval.p_V67__He4_Ti64
       -rho*Y[jmg40]*rate_eval.p_Mg40__n_Al40
       -rho*Y[jmg39]*rate_eval.p_Mg39__n_Al39
       -rho*Y[jmg38]*rate_eval.p_Mg38__n_Al38
       -rho*Y[jal27]*rate_eval.p_Al27__He4_Mg24
       -rho*Y[jal38]*rate_eval.p_Al38__n_Si38
       -rho*Y[jna31]*rate_eval.p_Na31__Mg32
       -rho*Y[jar45]*rate_eval.p_Ar45__He4_Cl42
       -rho*Y[jmg34]*rate_eval.p_Mg34__He4_Na31
       -rho*Y[jti53]*rate_eval.p_Ti53__n_V53
       -rho*Y[jmg33]*rate_eval.p_Mg33__He4_Na30
       -rho*Y[jfe66]*rate_eval.p_Fe66__He4_Mn63
       -rho*Y[jmg32]*rate_eval.p_Mg32__He4_Na29
       -rho*Y[jmn59]*rate_eval.p_Mn59__n_Fe59
       -rho*Y[jmg30]*rate_eval.p_Mg30__n_Al30
       -rho*Y[jca45]*rate_eval.p_Ca45__Sc46
       -rho*Y[jcl46]*rate_eval.p_Cl46__n_Ar46
       -rho*Y[jmg29]*rate_eval.p_Mg29__He4_Na26
       -rho*Y[jmg29]*rate_eval.p_Mg29__n_Al29
       -rho*Y[jcr60]*rate_eval.p_Cr60__n_Mn60
       -rho*Y[jne31]*rate_eval.p_Ne31__He4_F28
       -rho*Y[jti59]*rate_eval.p_Ti59__V60
       -rho*Y[jfe69]*rate_eval.p_Fe69__Co70
       -rho*Y[jna39]*rate_eval.p_Na39__n_Mg39
       -rho*Y[jna37]*rate_eval.p_Na37__He4_Ne34
       -rho*Y[jna35]*rate_eval.p_Na35__n_Mg35
       -rho*Y[jna33]*rate_eval.p_Na33__n_Mg33
       -rho*Y[jna31]*rate_eval.p_Na31__He4_Ne28
       -rho*Y[jna31]*rate_eval.p_Na31__n_Mg31
       -rho*Y[jfe66]*rate_eval.p_Fe66__n_Co66
       -rho*Y[jna30]*rate_eval.p_Na30__He4_Ne27
       -rho*Y[jcl40]*rate_eval.p_Cl40__Ar41
       -rho*Y[jna29]*rate_eval.p_Na29__He4_Ne26
       -rho*Y[jna28]*rate_eval.p_Na28__n_Mg28
       -rho*Y[jna27]*rate_eval.p_Na27__n_Mg27
       -rho*Y[jsc49]*rate_eval.p_Sc49__n_Ti49
       -rho*Y[jna24]*rate_eval.p_Na24__He4_Ne21
       -rho*Y[jk56]*rate_eval.p_K56__He4_Ar53
       -rho*Y[jk46]*rate_eval.p_K46__Ca47
       -rho*Y[jfe67]*rate_eval.p_Fe67__n_Co67
       -rho*Y[jna23]*rate_eval.p_Na23__He4_Ne20
       -rho*Y[jna23]*rate_eval.p_Na23__n_Mg23
       -rho*Y[jv56]*rate_eval.p_V56__Cr57
       -rho*Y[jne34]*rate_eval.p_Ne34__n_Na34
       -rho*Y[jcl36]*rate_eval.p_Cl36__Ar37
       -rho*Y[jal35]*rate_eval.p_Al35__n_Si35
       -rho*Y[jne30]*rate_eval.p_Ne30__He4_F27
       -rho*Y[jne29]*rate_eval.p_Ne29__He4_F26
       -rho*Y[jne29]*rate_eval.p_Ne29__n_Na29
       -rho*Y[jne28]*rate_eval.p_Ne28__n_Na28
       -rho*Y[jne27]*rate_eval.p_Ne27__n_Na27
       -rho*Y[jne25]*rate_eval.p_Ne25__He4_F22
       -rho*Y[jne25]*rate_eval.p_Ne25__n_Na25
       -rho*Y[jne24]*rate_eval.p_Ne24__n_Na24
       -rho*Y[js30]*rate_eval.p_S30__Cl31
       -rho*Y[jne23]*rate_eval.p_Ne23__n_Na23
       -rho*Y[jal43]*rate_eval.p_Al43__He4_Mg40
       -rho*Y[jv42]*rate_eval.p_V42__Cr43
       -rho*Y[jv54]*rate_eval.p_V54__n_Cr54
       -rho*Y[jne20]*rate_eval.p_Ne20__He4_F17
       -rho*Y[jne22]*rate_eval.p_Ne22__Na23
       -rho*Y[jk33]*rate_eval.p_K33__Ca34
       -rho*Y[jcr67]*rate_eval.p_Cr67__He4_V64
       -rho*Y[jf31]*rate_eval.p_F31__n_Ne31
       -rho*Y[jar45]*rate_eval.p_Ar45__n_K45
       -rho*Y[jmn47]*rate_eval.p_Mn47__Fe48
       -rho*Y[jf30]*rate_eval.p_F30__He4_O27
       -rho*Y[jf29]*rate_eval.p_F29__He4_O26
       -rho*Y[jf27]*rate_eval.p_F27__He4_O24
       -rho*Y[jf27]*rate_eval.p_F27__n_Ne27
       -rho*Y[jf26]*rate_eval.p_F26__n_Ne26
       -rho*Y[jna34]*rate_eval.p_Na34__He4_Ne31
       -rho*Y[jf25]*rate_eval.p_F25__He4_O22
       -rho*Y[jf25]*rate_eval.p_F25__n_Ne25
       -rho*Y[jf24]*rate_eval.p_F24__n_Ne24
       -rho*Y[jna26]*rate_eval.p_Na26__He4_Ne23
       -rho*Y[jf22]*rate_eval.p_F22__He4_O19
       -rho*Y[jf22]*rate_eval.p_F22__n_Ne22
       -rho*Y[jne26]*rate_eval.p_Ne26__He4_F23
       -rho*Y[jal39]*rate_eval.p_Al39__Si40
       -rho*Y[jf20]*rate_eval.p_F20__He4_O17
       -rho*Y[jf19]*rate_eval.p_F19__n_Ne19
       -rho*Y[jo21]*rate_eval.p_O21__n_F21
       -rho*Y[jo15]*rate_eval.p_O15__F16
       -rho*Y[jo26]*rate_eval.p_O26__He4_N23
       -rho*Y[jo26]*rate_eval.p_O26__n_F26
       -rho*Y[jo24]*rate_eval.p_O24__n_F24
       -rho*Y[jti57]*rate_eval.p_Ti57__n_V57
       -rho*Y[jo20]*rate_eval.p_O20__n_F20
       -rho*Y[jcr62]*rate_eval.p_Cr62__n_Mn62
       -rho*Y[jo18]*rate_eval.p_O18__He4_N15
       -rho*Y[js49]*rate_eval.p_S49__Cl50
       -rho*Y[jo17]*rate_eval.p_O17__He4_N14
       -rho*Y[jk48]*rate_eval.p_K48__n_Ca48
       -rho*Y[jne28]*rate_eval.p_Ne28__He4_F25
       -rho*Y[jal26]*rate_eval.p_Al26__Si27
       -rho*Y[jca36]*rate_eval.p_Ca36__Sc37
       -rho*Y[jna28]*rate_eval.p_Na28__He4_Ne25
       -rho*Y[jcr70]*rate_eval.p_Cr70__Mn71
       -rho*Y[jn15]*rate_eval.p_N15__He4_C12
       -rho*Y[jn15]*rate_eval.p_N15__n_O15
       -rho*Y[jf28]*rate_eval.p_F28__He4_O25
       -rho*Y[jf29]*rate_eval.p_F29__Ne30
       -rho*Y[jc15]*rate_eval.p_C15__n_N15
       -rho*Y[jc13]*rate_eval.p_C13__n_N13
       -rho*Y[jk44]*rate_eval.p_K44__n_Ca44
       -rho*Y[jar53]*rate_eval.p_Ar53__He4_Cl50
       -rho*Y[jb12]*rate_eval.p_B12__He4_Be9
       -rho*Y[jti56]*rate_eval.p_Ti56__He4_Sc53
       -rho*Y[jar41]*rate_eval.p_Ar41__K42
       -rho*Y[jv63]*rate_eval.p_V63__He4_Ti60
       -rho*Y[jli6]*rate_eval.p_Li6__He4_He3
       -rho*Y[jp34]*rate_eval.p_P34__S35
       -rho*Y[jfe76]*rate_eval.p_Fe76__Co77
       -rho*Y[jfe73]*rate_eval.p_Fe73__Co74
       -rho*Y[jfe72]*rate_eval.p_Fe72__Co73
       -rho*Y[jmg31]*rate_eval.p_Mg31__n_Al31
       -rho*Y[jfe70]*rate_eval.p_Fe70__Co71
       -rho*Y[jp32]*rate_eval.p_P32__S33
       -rho*Y[jfe68]*rate_eval.p_Fe68__Co69
       -rho*Y[jfe66]*rate_eval.p_Fe66__Co67
       -rho*Y[jfe65]*rate_eval.p_Fe65__Co66
       -rho*Y[jfe63]*rate_eval.p_Fe63__Co64
       -rho*Y[jfe61]*rate_eval.p_Fe61__Co62
       -rho*Y[js46]*rate_eval.p_S46__He4_P43
       -rho*Y[jfe60]*rate_eval.p_Fe60__Co61
       -rho*Y[jal34]*rate_eval.p_Al34__Si35
       -rho*Y[jfe59]*rate_eval.p_Fe59__Co60
       -rho*Y[jfe57]*rate_eval.p_Fe57__Co58
       -rho*Y[jfe56]*rate_eval.p_Fe56__Co57
       -rho*Y[jfe55]*rate_eval.p_Fe55__Co56
       -rho*Y[jfe52]*rate_eval.p_Fe52__Co53
       -rho*Y[jsi36]*rate_eval.p_Si36__n_P36
       -rho*Y[jfe50]*rate_eval.p_Fe50__Co51
       -rho*Y[jne32]*rate_eval.p_Ne32__n_Na32
       -rho*Y[jfe48]*rate_eval.p_Fe48__Co49
       -rho*Y[jmn73]*rate_eval.p_Mn73__Fe74
       -rho*Y[jmn69]*rate_eval.p_Mn69__Fe70
       -rho*Y[jmn68]*rate_eval.p_Mn68__Fe69
       -rho*Y[jmn73]*rate_eval.p_Mn73__n_Fe73
       -rho*Y[jmn67]*rate_eval.p_Mn67__Fe68
       -rho*Y[jmn66]*rate_eval.p_Mn66__Fe67
       -rho*Y[jne33]*rate_eval.p_Ne33__n_Na33
       -rho*Y[jmn62]*rate_eval.p_Mn62__Fe63
       -rho*Y[jmn61]*rate_eval.p_Mn61__Fe62
       -rho*Y[jca58]*rate_eval.p_Ca58__Sc59
       -rho*Y[jk42]*rate_eval.p_K42__n_Ca42
       -rho*Y[jfe64]*rate_eval.p_Fe64__n_Co64
       -rho*Y[jmn50]*rate_eval.p_Mn50__Fe51
       -rho*Y[jmn49]*rate_eval.p_Mn49__Fe50
       -rho*Y[jmn48]*rate_eval.p_Mn48__Fe49
       -rho*Y[jmn46]*rate_eval.p_Mn46__Fe47
       -rho*Y[jmn45]*rate_eval.p_Mn45__Fe46
       -rho*Y[jv53]*rate_eval.p_V53__He4_Ti50
       -rho*Y[jcr69]*rate_eval.p_Cr69__Mn70
       -rho*Y[jcr66]*rate_eval.p_Cr66__Mn67
       -rho*Y[jcr65]*rate_eval.p_Cr65__Mn66
       -rho*Y[jca52]*rate_eval.p_Ca52__Sc53
       -rho*Y[jcr63]*rate_eval.p_Cr63__Mn64
       -rho*Y[jsc48]*rate_eval.p_Sc48__n_Ti48
       -rho*Y[jcr61]*rate_eval.p_Cr61__Mn62
       -rho*Y[jcr59]*rate_eval.p_Cr59__Mn60
       -rho*Y[jcr58]*rate_eval.p_Cr58__Mn59
       -rho*Y[jcr57]*rate_eval.p_Cr57__Mn58
       -rho*Y[jcr56]*rate_eval.p_Cr56__Mn57
       -rho*Y[jcr54]*rate_eval.p_Cr54__Mn55
       -rho*Y[jcr53]*rate_eval.p_Cr53__Mn54
       -rho*Y[jcl39]*rate_eval.p_Cl39__He4_S36
       -rho*Y[jcr52]*rate_eval.p_Cr52__Mn53
       -rho*Y[jcr51]*rate_eval.p_Cr51__Mn52
       -rho*Y[jcr50]*rate_eval.p_Cr50__Mn51
       -rho*Y[jcr49]*rate_eval.p_Cr49__Mn50
       -rho*Y[jcr46]*rate_eval.p_Cr46__Mn47
       -rho*Y[jp44]*rate_eval.p_P44__He4_Si41
       -rho*Y[jv67]*rate_eval.p_V67__Cr68
       -rho*Y[jv66]*rate_eval.p_V66__Cr67
       -rho*Y[jv64]*rate_eval.p_V64__Cr65
       -rho*Y[jk58]*rate_eval.p_K58__n_Ca58
       -rho*Y[jv63]*rate_eval.p_V63__Cr64
       -rho*Y[jne32]*rate_eval.p_Ne32__He4_F29
       -rho*Y[jv60]*rate_eval.p_V60__Cr61
       -rho*Y[jv59]*rate_eval.p_V59__Cr60
       -rho*Y[jv58]*rate_eval.p_V58__Cr59
       -rho*Y[jv57]*rate_eval.p_V57__Cr58
       -rho*Y[jv54]*rate_eval.p_V54__Cr55
       -rho*Y[jv53]*rate_eval.p_V53__Cr54
       -rho*Y[jv62]*rate_eval.p_V62__n_Cr62
       -rho*Y[jv52]*rate_eval.p_V52__Cr53
       -rho*Y[jv50]*rate_eval.p_V50__Cr51
       -rho*Y[jv48]*rate_eval.p_V48__Cr49
       -rho*Y[js42]*rate_eval.p_S42__n_Cl42
       -rho*Y[jsc46]*rate_eval.p_Sc46__n_Ti46
       -rho*Y[jv46]*rate_eval.p_V46__Cr47
       -rho*Y[jsi38]*rate_eval.p_Si38__P39
       -rho*Y[jmn63]*rate_eval.p_Mn63__Fe64
       -rho*Y[jv43]*rate_eval.p_V43__Cr44
       -rho*Y[jp40]*rate_eval.p_P40__n_S40
       -rho*Y[jal42]*rate_eval.p_Al42__He4_Mg39
       -rho*Y[jv41]*rate_eval.p_V41__Cr42
       -rho*Y[jti63]*rate_eval.p_Ti63__V64
       -rho*Y[jti62]*rate_eval.p_Ti62__V63
       -rho*Y[jn12]*rate_eval.p_N12__O13
       -rho*Y[jti61]*rate_eval.p_Ti61__V62
       -rho*Y[jti60]*rate_eval.p_Ti60__V61
       -rho*Y[jti58]*rate_eval.p_Ti58__V59
       -rho*Y[jti57]*rate_eval.p_Ti57__V58
       -rho*Y[jti56]*rate_eval.p_Ti56__V57
       -rho*Y[jfe63]*rate_eval.p_Fe63__n_Co63
       -rho*Y[jti55]*rate_eval.p_Ti55__V56
       -rho*Y[jcr58]*rate_eval.p_Cr58__n_Mn58
       -rho*Y[jar47]*rate_eval.p_Ar47__n_K47
       -rho*Y[jar36]*rate_eval.p_Ar36__K37
       -rho*Y[jti54]*rate_eval.p_Ti54__V55
       -rho*Y[jti53]*rate_eval.p_Ti53__V54
       -rho*Y[jti52]*rate_eval.p_Ti52__V53
       -rho*Y[jti49]*rate_eval.p_Ti49__V50
       -rho*Y[jti47]*rate_eval.p_Ti47__V48
       -rho*Y[jti44]*rate_eval.p_Ti44__V45
       -rho*Y[jti42]*rate_eval.p_Ti42__V43
       -rho*Y[jti41]*rate_eval.p_Ti41__V42
       -rho*Y[js28]*rate_eval.p_S28__Cl29
       -rho*Y[jti40]*rate_eval.p_Ti40__V41
       -rho*Y[jmn72]*rate_eval.p_Mn72__Fe73
       -rho*Y[jar50]*rate_eval.p_Ar50__n_K50
       -rho*Y[jsc63]*rate_eval.p_Sc63__Ti64
       -rho*Y[jmn44]*rate_eval.p_Mn44__Fe45
       -rho*Y[jsc61]*rate_eval.p_Sc61__Ti62
       -rho*Y[jsc58]*rate_eval.p_Sc58__Ti59
       -rho*Y[jsc57]*rate_eval.p_Sc57__Ti58
       -rho*Y[jsc56]*rate_eval.p_Sc56__Ti57
       -rho*Y[jsc37]*rate_eval.p_Sc37__Ti38
       -rho*Y[jsc55]*rate_eval.p_Sc55__Ti56
       -rho*Y[jsc53]*rate_eval.p_Sc53__Ti54
       -rho*Y[jmn57]*rate_eval.p_Mn57__He4_Cr54
       -rho*Y[jhe3]*rate_eval.p_He3__He4__weak__bet_pos_
       -rho*Y[jmg31]*rate_eval.p_Mg31__Al32
       -rho*Y[jsc49]*rate_eval.p_Sc49__Ti50
       -rho*Y[jsc48]*rate_eval.p_Sc48__Ti49
       -rho*Y[jne21]*rate_eval.p_Ne21__Na22
       -rho*Y[jsc46]*rate_eval.p_Sc46__Ti47
       -rho*Y[jca50]*rate_eval.p_Ca50__He4_K47
       -rho*Y[jsc43]*rate_eval.p_Sc43__Ti44
       -rho*Y[jsc42]*rate_eval.p_Sc42__Ti43
       -rho*Y[jmn60]*rate_eval.p_Mn60__Fe61
       -rho*Y[jsc41]*rate_eval.p_Sc41__Ti42
       -rho*Y[jsc40]*rate_eval.p_Sc40__Ti41
       -rho*Y[jsc38]*rate_eval.p_Sc38__Ti39
       -rho*Y[jna33]*rate_eval.p_Na33__He4_Ne30
       -rho*Y[jca60]*rate_eval.p_Ca60__Sc61
       -rho*Y[jti51]*rate_eval.p_Ti51__V52
       -rho*Y[jca59]*rate_eval.p_Ca59__Sc60
       -rho*Y[jca57]*rate_eval.p_Ca57__Sc58
       -rho*Y[jna20]*rate_eval.p_Na20__Mg21
       -rho*Y[jca54]*rate_eval.p_Ca54__Sc55
       -rho*Y[jfe58]*rate_eval.p_Fe58__Co59
       -rho*Y[jmn71]*rate_eval.p_Mn71__Fe72
       -rho*Y[jca51]*rate_eval.p_Ca51__Sc52
       -rho*Y[jk42]*rate_eval.p_K42__He4_Ar39
       -rho*Y[jca42]*rate_eval.p_Ca42__Sc43
       -rho*Y[jca41]*rate_eval.p_Ca41__Sc42
       -rho*Y[jca52]*rate_eval.p_Ca52__He4_K49
       -rho*Y[jca40]*rate_eval.p_Ca40__Sc41
       -rho*Y[jfe64]*rate_eval.p_Fe64__Co65
       -rho*Y[jsi37]*rate_eval.p_Si37__P38
       -rho*Y[jca35]*rate_eval.p_Ca35__Sc36
       -rho*Y[jca34]*rate_eval.p_Ca34__Sc35
       -rho*Y[jbe11]*rate_eval.p_Be11__He4_Li8
       -rho*Y[jk59]*rate_eval.p_K59__Ca60
       -rho*Y[jk50]*rate_eval.p_K50__n_Ca50
       -rho*Y[jp30]*rate_eval.p_P30__S31
       -rho*Y[jk57]*rate_eval.p_K57__Ca58
       -rho*Y[jk56]*rate_eval.p_K56__Ca57
       -rho*Y[jcl36]*rate_eval.p_Cl36__He4_S33
       -rho*Y[jk52]*rate_eval.p_K52__Ca53
       -rho*Y[jf20]*rate_eval.p_F20__n_Ne20
       -rho*Y[jk51]*rate_eval.p_K51__Ca52
       -rho*Y[jti65]*rate_eval.p_Ti65__V66
       -rho*Y[jne26]*rate_eval.p_Ne26__Na27
       -rho*Y[jk45]*rate_eval.p_K45__Ca46
       -rho*Y[jar38]*rate_eval.p_Ar38__K39
       -rho*Y[jk43]*rate_eval.p_K43__Ca44
       -rho*Y[jcr45]*rate_eval.p_Cr45__Mn46
       -rho*Y[jsc62]*rate_eval.p_Sc62__Ti63
       -rho*Y[jk41]*rate_eval.p_K41__Ca42
       -rho*Y[js34]*rate_eval.p_S34__Cl35
       -rho*Y[jk38]*rate_eval.p_K38__Ca39
       -rho*Y[jk37]*rate_eval.p_K37__Ca38
       -rho*Y[jv56]*rate_eval.p_V56__n_Cr56
       -rho*Y[jk36]*rate_eval.p_K36__Ca37
       -rho*Y[jar51]*rate_eval.p_Ar51__K52
       -rho*Y[jcl42]*rate_eval.p_Cl42__n_Ar42
       -rho*Y[js41]*rate_eval.p_S41__Cl42
       -rho*Y[jar47]*rate_eval.p_Ar47__K48
       -rho*Y[jar44]*rate_eval.p_Ar44__K45
       -rho*Y[jar43]*rate_eval.p_Ar43__K44
       -rho*Y[jar42]*rate_eval.p_Ar42__K43
       -rho*Y[jar40]*rate_eval.p_Ar40__K41
       -rho*Y[jar37]*rate_eval.p_Ar37__K38
       -rho*Y[jar35]*rate_eval.p_Ar35__K36
       -rho*Y[jf20]*rate_eval.p_F20__Ne21
       -rho*Y[jsi25]*rate_eval.p_Si25__P26
       -rho*Y[jar33]*rate_eval.p_Ar33__K34
       -rho*Y[jcl43]*rate_eval.p_Cl43__Ar44
       -rho*Y[jar32]*rate_eval.p_Ar32__K33
       -rho*Y[jp33]*rate_eval.p_P33__He4_Si30
       -rho*Y[jsi44]*rate_eval.p_Si44__He4_Al41
       -rho*Y[jp28]*rate_eval.p_P28__S29
       -rho*Y[jar31]*rate_eval.p_Ar31__K32
       -rho*Y[jcl51]*rate_eval.p_Cl51__Ar52
       -rho*Y[jmn57]*rate_eval.p_Mn57__Fe58
       -rho*Y[jcl49]*rate_eval.p_Cl49__Ar50
       -rho*Y[jar53]*rate_eval.p_Ar53__n_K53
       -rho*Y[jcl41]*rate_eval.p_Cl41__Ar42
       -rho*Y[jcl46]*rate_eval.p_Cl46__Ar47
       -rho*Y[jcl39]*rate_eval.p_Cl39__Ar40
       -rho*Y[jcr64]*rate_eval.p_Cr64__n_Mn64
       -rho*Y[jcl35]*rate_eval.p_Cl35__Ar36
       -rho*Y[jti39]*rate_eval.p_Ti39__V40
       -rho*Y[jmg35]*rate_eval.p_Mg35__n_Al35
       -rho*Y[jcl32]*rate_eval.p_Cl32__Ar33
       -rho*Y[jal42]*rate_eval.p_Al42__Si43
       -rho*Y[jcl31]*rate_eval.p_Cl31__Ar32
       -rho*Y[jcl30]*rate_eval.p_Cl30__Ar31
       -rho*Y[jcl29]*rate_eval.p_Cl29__Ar30
       -rho*Y[jsi34]*rate_eval.p_Si34__P35
       -rho*Y[js44]*rate_eval.p_S44__Cl45
       -rho*Y[js40]*rate_eval.p_S40__Cl41
       -rho*Y[jcl50]*rate_eval.p_Cl50__Ar51
       -rho*Y[js39]*rate_eval.p_S39__Cl40
       -rho*Y[jk34]*rate_eval.p_K34__Ca35
       -rho*Y[jna32]*rate_eval.p_Na32__n_Mg32
       -rho*Y[js36]*rate_eval.p_S36__Cl37
       -rho*Y[js35]*rate_eval.p_S35__Cl36
       -rho*Y[js32]*rate_eval.p_S32__Cl33
       -rho*Y[js31]*rate_eval.p_S31__Cl32
       -rho*Y[js29]*rate_eval.p_S29__Cl30
       -rho*Y[jsi33]*rate_eval.p_Si33__P34
       -rho*Y[jp40]*rate_eval.p_P40__S41
       -rho*Y[jp38]*rate_eval.p_P38__S39
       -rho*Y[jp35]*rate_eval.p_P35__S36
       -rho*Y[jfe58]*rate_eval.p_Fe58__He4_Mn55
       -rho*Y[jp26]*rate_eval.p_P26__S27
       -rho*Y[jmn70]*rate_eval.p_Mn70__Fe71
       -rho*Y[jca56]*rate_eval.p_Ca56__Sc57
       -rho*Y[jk55]*rate_eval.p_K55__n_Ca55
       -rho*Y[jsi42]*rate_eval.p_Si42__P43
       -rho*Y[jsi40]*rate_eval.p_Si40__P41
       -rho*Y[jsi39]*rate_eval.p_Si39__P40
       -rho*Y[jar54]*rate_eval.p_Ar54__He4_Cl51
       -rho*Y[jsi32]*rate_eval.p_Si32__P33
       -rho*Y[jcl47]*rate_eval.p_Cl47__Ar48
       -rho*Y[jmg37]*rate_eval.p_Mg37__n_Al37
       -rho*Y[jsi31]*rate_eval.p_Si31__P32
       -rho*Y[jsi30]*rate_eval.p_Si30__P31
       -rho*Y[jsi28]*rate_eval.p_Si28__P29
       -rho*Y[jsi26]*rate_eval.p_Si26__P27
       -rho*Y[jsi24]*rate_eval.p_Si24__P25
       -rho*Y[jsc56]*rate_eval.p_Sc56__He4_Ca53
       -rho*Y[jca54]*rate_eval.p_Ca54__n_Sc54
       -rho*Y[jo17]*rate_eval.p_O17__F18
       -rho*Y[jal40]*rate_eval.p_Al40__Si41
       -rho*Y[jti64]*rate_eval.p_Ti64__n_V64
       -rho*Y[jk40]*rate_eval.p_K40__Ca41
       -rho*Y[jcl51]*rate_eval.p_Cl51__n_Ar51
       -rho*Y[jal37]*rate_eval.p_Al37__Si38
       -rho*Y[jsc59]*rate_eval.p_Sc59__He4_Ca56
       -rho*Y[jk44]*rate_eval.p_K44__Ca45
       -rho*Y[jsi40]*rate_eval.p_Si40__n_P40
       -rho*Y[jal36]*rate_eval.p_Al36__Si37
       -rho*Y[jal33]*rate_eval.p_Al33__Si34
       -rho*Y[jal31]*rate_eval.p_Al31__Si32
       -rho*Y[js49]*rate_eval.p_S49__He4_P46
       -rho*Y[jal30]*rate_eval.p_Al30__Si31
       -rho*Y[jal28]*rate_eval.p_Al28__Si29
       -rho*Y[jcr68]*rate_eval.p_Cr68__Mn69
       -rho*Y[jal24]*rate_eval.p_Al24__Si25
       -rho*Y[jcl39]*rate_eval.p_Cl39__n_Ar39
       -rho*Y[jmg39]*rate_eval.p_Mg39__Al40
       -rho*Y[jmg37]*rate_eval.p_Mg37__Al38
       -rho*Y[jsc60]*rate_eval.p_Sc60__Ti61
       -rho*Y[jp46]*rate_eval.p_P46__He4_Si43
       -rho*Y[jcr47]*rate_eval.p_Cr47__Mn48
       -rho*Y[jca43]*rate_eval.p_Ca43__Sc44
       -rho*Y[js48]*rate_eval.p_S48__He4_P45
       -rho*Y[jfe49]*rate_eval.p_Fe49__Co50
       -rho*Y[jmg30]*rate_eval.p_Mg30__Al31
       -rho*Y[jsi44]*rate_eval.p_Si44__P45
       -rho*Y[jmg33]*rate_eval.p_Mg33__n_Al33
       -rho*Y[jmg32]*rate_eval.p_Mg32__Al33
       -rho*Y[jfe54]*rate_eval.p_Fe54__Co55
       -rho*Y[jmg27]*rate_eval.p_Mg27__Al28
       -rho*Y[jfe46]*rate_eval.p_Fe46__Co47
       -rho*Y[jmg26]*rate_eval.p_Mg26__Al27
       -rho*Y[jk49]*rate_eval.p_K49__Ca50
       -rho*Y[jmg24]*rate_eval.p_Mg24__Al25
       -rho*Y[jmg23]*rate_eval.p_Mg23__Al24
       -rho*Y[jmg22]*rate_eval.p_Mg22__Al23
       -rho*Y[jna38]*rate_eval.p_Na38__Mg39
       -rho*Y[jsc36]*rate_eval.p_Sc36__Ti37
       -rho*Y[jcl47]*rate_eval.p_Cl47__n_Ar47
       -rho*Y[jf21]*rate_eval.p_F21__n_Ne21
       -rho*Y[jna32]*rate_eval.p_Na32__Mg33
       -rho*Y[jna36]*rate_eval.p_Na36__Mg37
       -rho*Y[jna26]*rate_eval.p_Na26__Mg27
       -rho*Y[jna25]*rate_eval.p_Na25__Mg26
       -rho*Y[jar52]*rate_eval.p_Ar52__K53
       -rho*Y[jca51]*rate_eval.p_Ca51__n_Sc51
       -rho*Y[jsc63]*rate_eval.p_Sc63__He4_Ca60
       -rho*Y[jna23]*rate_eval.p_Na23__Mg24
       -rho*Y[jna22]*rate_eval.p_Na22__Mg23
       -rho*Y[jna21]*rate_eval.p_Na21__Mg22
       -rho*Y[jti65]*rate_eval.p_Ti65__n_V65
       -rho*Y[js33]*rate_eval.p_S33__Cl34
       -rho*Y[jmg31]*rate_eval.p_Mg31__He4_Na28
       -rho*Y[jsc54]*rate_eval.p_Sc54__Ti55
       -rho*Y[jsi29]*rate_eval.p_Si29__P30
       -rho*Y[jne31]*rate_eval.p_Ne31__Na32
       -rho*Y[jne30]*rate_eval.p_Ne30__Na31
       -rho*Y[jmn71]*rate_eval.p_Mn71__n_Fe71
       -rho*Y[jcl44]*rate_eval.p_Cl44__Ar45
       -rho*Y[jne28]*rate_eval.p_Ne28__Na29
       -rho*Y[jna35]*rate_eval.p_Na35__He4_Ne32
       -rho*Y[jne27]*rate_eval.p_Ne27__Na28
       -rho*Y[jne25]*rate_eval.p_Ne25__Na26
       -rho*Y[jne23]*rate_eval.p_Ne23__Na24
       -rho*Y[jal43]*rate_eval.p_Al43__Si44
       -rho*Y[jne33]*rate_eval.p_Ne33__Na34
       -rho*Y[jf27]*rate_eval.p_F27__Ne28
       -rho*Y[jne20]*rate_eval.p_Ne20__Na21
       -rho*Y[jk53]*rate_eval.p_K53__Ca54
       -rho*Y[jcr70]*rate_eval.p_Cr70__n_Mn70
       -rho*Y[jne19]*rate_eval.p_Ne19__Na20
       -rho*Y[jf24]*rate_eval.p_F24__He4_O21
       -rho*Y[jmn52]*rate_eval.p_Mn52__Fe53
       -rho*Y[jne18]*rate_eval.p_Ne18__Na19
       -rho*Y[jcr64]*rate_eval.p_Cr64__Mn65
       -rho*Y[jcl48]*rate_eval.p_Cl48__Ar49
       -rho*Y[jf28]*rate_eval.p_F28__Ne29
       -rho*Y[jf19]*rate_eval.p_F19__He4_O16
       -rho*Y[jmg38]*rate_eval.p_Mg38__Al39
       -rho*Y[jf22]*rate_eval.p_F22__Ne23
       -rho*Y[jf21]*rate_eval.p_F21__Ne22
       -rho*Y[jfe51]*rate_eval.p_Fe51__Co52
       -rho*Y[jo27]*rate_eval.p_O27__F28
       -rho*Y[jo26]*rate_eval.p_O26__F27
       -rho*Y[jcl43]*rate_eval.p_Cl43__n_Ar43
       -rho*Y[jk35]*rate_eval.p_K35__Ca36
       -rho*Y[jo22]*rate_eval.p_O22__F23
       -rho*Y[jo20]*rate_eval.p_O20__F21
       -rho*Y[js44]*rate_eval.p_S44__n_Cl44
       -rho*Y[jn14]*rate_eval.p_N14__O15
       -rho*Y[jc14]*rate_eval.p_C14__N15
       -rho*Y[jc13]*rate_eval.p_C13__N14
       -rho*Y[jc12]*rate_eval.p_C12__N13
       -rho*Y[jc11]*rate_eval.p_C11__N12
       -rho*Y[jn]*rate_eval.n_p__d
       -rho*Y[jb10]*rate_eval.p_B10__C11
       -rho*Y[jna28]*rate_eval.p_Na28__Mg29
       -rho*Y[jbe10]*rate_eval.p_Be10__B11
       -rho*Y[jsc39]*rate_eval.p_Sc39__Ti40
       -rho*Y[jbe7]*rate_eval.p_Be7__B8
       -rho*Y[jp35]*rate_eval.p_P35__n_S35
       -rho*Y[jne24]*rate_eval.p_Ne24__Na25
       -rho*Y[jt]*rate_eval.p_t__He4
       -rho*Y[jp27]*rate_eval.p_P27__S28
       -rho*Y[jca49]*rate_eval.p_Ca49__n_Sc49
       -rho*Y[jsi35]*rate_eval.p_Si35__P36
       -rho*Y[jti46]*rate_eval.p_Ti46__V47
       -rho*Y[jfe71]*rate_eval.p_Fe71__Co72
       -rho*Y[jf18]*rate_eval.p_F18__Ne19
       -rho*Y[jmg36]*rate_eval.p_Mg36__Al37
       -rho*Y[jar42]*rate_eval.p_Ar42__He4_Cl39
       -rho*Y[jf25]*rate_eval.p_F25__Ne26
       -rho*Y[jk42]*rate_eval.p_K42__Ca43
       -rho*Y[js37]*rate_eval.p_S37__He4_P34
       -rho*Y[jv40]*rate_eval.p_V40__Cr41
       -rho*Y[jk39]*rate_eval.p_K39__Ca40
       -rho*Y[jsc51]*rate_eval.p_Sc51__n_Ti51
       -rho*Y[jti50]*rate_eval.p_Ti50__V51
       -rho*Y[jmn53]*rate_eval.p_Mn53__Fe54
       -rho*Y[jp33]*rate_eval.p_P33__S34
       -rho*Y[jal28]*rate_eval.p_Al28__n_Si28
       -rho*Y[jcl41]*rate_eval.p_Cl41__n_Ar41
       -rho*Y[jk55]*rate_eval.p_K55__Ca56
       -rho*Y[jk47]*rate_eval.p_K47__n_Ca47
       -rho*Y[jca50]*rate_eval.p_Ca50__n_Sc50
       -rho*Y[jv45]*rate_eval.p_V45__Cr46
       -2*5.00000000000000e-01*rho*2*Y[jp]*rate_eval.p_p__d__weak__bet_pos_
       -2*5.00000000000000e-01*rho**2*ye(Y)*2*Y[jp]*rate_eval.p_p__d__weak__electron_capture
       -rho*Y[jcl38]*rate_eval.p_Cl38__n_Ar38
       -rho*Y[jal23]*rate_eval.p_Al23__Si24
       -rho*Y[jal41]*rate_eval.p_Al41__Si42
       -rho*Y[jcl38]*rate_eval.p_Cl38__Ar39
       -rho*Y[jmg32]*rate_eval.p_Mg32__n_Al32
       -rho*Y[jna27]*rate_eval.p_Na27__Mg28
       -rho*Y[jp46]*rate_eval.p_P46__n_S46
       -rho*Y[jp41]*rate_eval.p_P41__n_S41
       -rho*Y[jp39]*rate_eval.p_P39__n_S39
       -rho*Y[jcr55]*rate_eval.p_Cr55__Mn56
       -rho*Y[jmn63]*rate_eval.p_Mn63__He4_Cr60
       -rho*Y[jca50]*rate_eval.p_Ca50__Sc51
       -rho*Y[jmn64]*rate_eval.p_Mn64__Fe65
       -rho*Y[jv44]*rate_eval.p_V44__Cr45
       -rho*Y[jn14]*rate_eval.p_N14__n_O14
       -rho*Y[jna36]*rate_eval.p_Na36__He4_Ne33
       -rho*Y[jcl34]*rate_eval.p_Cl34__Ar35
       -rho*Y[jmg37]*rate_eval.p_Mg37__He4_Na34
       -rho*Y[jna34]*rate_eval.p_Na34__n_Mg34
       -rho*Y[jk58]*rate_eval.p_K58__Ca59
       -rho*Y[jfe53]*rate_eval.p_Fe53__Co54
       -rho*Y[jp31]*rate_eval.p_P31__He4_Si28
       -rho*Y[jp41]*rate_eval.p_P41__S42
       -rho*Y[jcl44]*rate_eval.p_Cl44__n_Ar44
       -rho*Y[jca48]*rate_eval.p_Ca48__Sc49
       -rho*Y[jmg41]*rate_eval.p_Mg41__Al42
       -rho*Y[jsc47]*rate_eval.p_Sc47__Ti48
       -rho*Y[jar46]*rate_eval.p_Ar46__K47
       -rho*Y[js42]*rate_eval.p_S42__He4_P39
       -rho*Y[jli8]*rate_eval.p_Li8__n_He4_He4
       -rho*Y[jfe67]*rate_eval.p_Fe67__Co68
       -rho*Y[jsi40]*rate_eval.p_Si40__He4_Al37
       -rho*Y[jmg41]*rate_eval.p_Mg41__n_Al41
       -rho*Y[jcl42]*rate_eval.p_Cl42__Ar43
       -rho*Y[jsc51]*rate_eval.p_Sc51__Ti52
       -rho*Y[jf19]*rate_eval.p_F19__Ne20
       -rho*Y[jk50]*rate_eval.p_K50__He4_Ar47
       -rho*Y[js45]*rate_eval.p_S45__n_Cl45
       -rho*Y[jar30]*rate_eval.p_Ar30__K31
       -rho*Y[jmn58]*rate_eval.p_Mn58__n_Fe58
       -rho*Y[jca57]*rate_eval.p_Ca57__He4_K54
       -rho*Y[jcr65]*rate_eval.p_Cr65__n_Mn65
       -rho*Y[jf29]*rate_eval.p_F29__n_Ne29
       -rho*Y[jn13]*rate_eval.p_N13__O14
       -rho*Y[jmn63]*rate_eval.p_Mn63__n_Fe63
       -rho*Y[jne30]*rate_eval.p_Ne30__n_Na30
       -rho*Y[jf30]*rate_eval.p_F30__n_Ne30
       -rho*Y[jna27]*rate_eval.p_Na27__He4_Ne24
       -rho*Y[jsi33]*rate_eval.p_Si33__He4_Al30
       -rho*Y[jb11]*rate_eval.p_B11__C12
       -rho*Y[jk46]*rate_eval.p_K46__He4_Ar43
       -rho*Y[js41]*rate_eval.p_S41__n_Cl41
       -rho*Y[jmg36]*rate_eval.p_Mg36__n_Al36
       -rho*Y[jcr69]*rate_eval.p_Cr69__n_Mn69
       -rho*Y[jv51]*rate_eval.p_V51__Cr52
       -rho*Y[jal38]*rate_eval.p_Al38__Si39
       -rho*Y[jk49]*rate_eval.p_K49__He4_Ar46
       -rho*Y[jp25]*rate_eval.p_P25__S26
       -rho*Y[jna24]*rate_eval.p_Na24__Mg25
       -rho*Y[js39]*rate_eval.p_S39__n_Cl39
       -rho*Y[jcl33]*rate_eval.p_Cl33__Ar34
       -rho*Y[jca46]*rate_eval.p_Ca46__Sc47
       -rho*Y[jfe68]*rate_eval.p_Fe68__n_Co68
       -rho*Y[jna29]*rate_eval.p_Na29__n_Mg29
       -rho**2*Y[jn]*Y[jhe4]*rate_eval.n_p_He4__Li6
       -rho*Y[jv55]*rate_eval.p_V55__He4_Ti52
       -rho*Y[jca60]*rate_eval.p_Ca60__He4_K57
       -rho*Y[jmn58]*rate_eval.p_Mn58__He4_Cr55
       -rho*Y[jal37]*rate_eval.p_Al37__n_Si37
       -rho*Y[jti48]*rate_eval.p_Ti48__V49
       -rho*Y[jar41]*rate_eval.p_Ar41__He4_Cl38
       -rho*Y[jcl49]*rate_eval.p_Cl49__He4_S46
       -rho*Y[jar39]*rate_eval.p_Ar39__K40
       -rho*Y[jk47]*rate_eval.p_K47__Ca48
       -rho*Y[jo23]*rate_eval.p_O23__n_F23
       -rho*Y[jne34]*rate_eval.p_Ne34__Na35
       -rho*Y[jti61]*rate_eval.p_Ti61__He4_Sc58
       -rho*Y[jti60]*rate_eval.p_Ti60__He4_Sc57
       -rho*Y[jb10]*rate_eval.p_B10__He4_Be7
       -rho*Y[jcr42]*rate_eval.p_Cr42__Mn43
       -rho*Y[js40]*rate_eval.p_S40__He4_P37
       -rho*Y[jk54]*rate_eval.p_K54__Ca55
       -rho*Y[jv61]*rate_eval.p_V61__Cr62
       -rho*Y[jmg27]*rate_eval.p_Mg27__n_Al27
       -rho*Y[jmn70]*rate_eval.p_Mn70__He4_Cr67
       -rho*Y[jk46]*rate_eval.p_K46__n_Ca46
       -rho*Y[jsc59]*rate_eval.p_Sc59__Ti60
       -rho*Y[jbe9]*rate_eval.p_Be9__B10
       -rho*Y[jp39]*rate_eval.p_P39__He4_Si36
       -rho*Y[jf26]*rate_eval.p_F26__Ne27
       -rho*Y[jli7]*rate_eval.p_Li7__He4_He4
       -rho*Y[jfe65]*rate_eval.p_Fe65__n_Co65
       -rho*Y[jfe76]*rate_eval.p_Fe76__n_Co76
       -rho*Y[jna33]*rate_eval.p_Na33__Mg34
       -rho*Y[jmn67]*rate_eval.p_Mn67__n_Fe67
       -rho*Y[jca57]*rate_eval.p_Ca57__n_Sc57
       -rho*Y[jca59]*rate_eval.p_Ca59__He4_K56
       -rho*Y[jne31]*rate_eval.p_Ne31__n_Na31
       -rho*Y[jf21]*rate_eval.p_F21__He4_O18
       -rho*Y[jsc61]*rate_eval.p_Sc61__He4_Ca58
       -rho*Y[jv65]*rate_eval.p_V65__n_Cr65
       -rho*Y[jbe9]*rate_eval.p_Be9__He4_Li6
       -rho*Y[jna26]*rate_eval.p_Na26__n_Mg26
       -rho*Y[jsi27]*rate_eval.p_Si27__P28
       -rho*Y[jca54]*rate_eval.p_Ca54__He4_K51
       -rho*Y[jfe74]*rate_eval.p_Fe74__Co75
       -rho*Y[jo21]*rate_eval.p_O21__F22
       -rho*Y[jp42]*rate_eval.p_P42__S43
       -rho*Y[jcr66]*rate_eval.p_Cr66__n_Mn66
       -rho*Y[jo27]*rate_eval.p_O27__n_F27
       -rho*Y[jal31]*rate_eval.p_Al31__n_Si31
       -rho*Y[jca53]*rate_eval.p_Ca53__He4_K50
       -rho*Y[jar45]*rate_eval.p_Ar45__K46
       -rho*Y[jcr64]*rate_eval.p_Cr64__He4_V61
       -rho*Y[jsi41]*rate_eval.p_Si41__P42
       -rho*Y[jmg30]*rate_eval.p_Mg30__He4_Na27
       -rho*Y[jal35]*rate_eval.p_Al35__Si36
       -rho*Y[jf17]*rate_eval.p_F17__Ne18
       -rho*Y[jsc53]*rate_eval.p_Sc53__He4_Ca50
       -rho*Y[jna25]*rate_eval.p_Na25__n_Mg25
       -rho*Y[jn16]*rate_eval.p_N16__n_O16
       -rho*Y[jmn70]*rate_eval.p_Mn70__n_Fe70
       -rho*Y[jmg41]*rate_eval.p_Mg41__He4_Na38
       -rho*Y[jp37]*rate_eval.p_P37__S38
       -rho*Y[jmn59]*rate_eval.p_Mn59__Fe60
       -rho*Y[jp44]*rate_eval.p_P44__n_S44
       -rho*Y[jcl28]*rate_eval.p_Cl28__Ar29
       -rho*Y[js27]*rate_eval.p_S27__Cl28
       -rho*Y[jb8]*rate_eval.p_B8__C9
       -rho*Y[jk55]*rate_eval.p_K55__He4_Ar52
       -rho*Y[jmg29]*rate_eval.p_Mg29__Al30
       -rho*Y[jsi31]*rate_eval.p_Si31__n_P31
       -rho*Y[jmn68]*rate_eval.p_Mn68__He4_Cr65
       -rho*Y[jmg38]*rate_eval.p_Mg38__He4_Na35
       -rho*Y[jo24]*rate_eval.p_O24__F25
       -rho*Y[jmg21]*rate_eval.p_Mg21__Al22
       -rho*Y[jcr48]*rate_eval.p_Cr48__Mn49
       -rho*Y[jk52]*rate_eval.p_K52__n_Ca52
       -rho*Y[jmg35]*rate_eval.p_Mg35__He4_Na32
       -rho*Y[jcl37]*rate_eval.p_Cl37__Ar38
       -rho*Y[jk32]*rate_eval.p_K32__Ca33
       -rho*Y[jar54]*rate_eval.p_Ar54__K55
       -rho*Y[jsc50]*rate_eval.p_Sc50__He4_Ca47
       -rho*Y[jp45]*rate_eval.p_P45__He4_Si42
       -rho*Y[jk43]*rate_eval.p_K43__He4_Ar40
       -rho*Y[js43]*rate_eval.p_S43__n_Cl43
       -rho*Y[jmn54]*rate_eval.p_Mn54__Fe55
       -rho*Y[jp40]*rate_eval.p_P40__He4_Si37
       -rho*Y[jp44]*rate_eval.p_P44__S45
       -rho*Y[jd]*rate_eval.p_d__He3
       -rho*Y[jv47]*rate_eval.p_V47__Cr48
       -rho*Y[jna38]*rate_eval.p_Na38__n_Mg38
       -rho*Y[jv54]*rate_eval.p_V54__He4_Ti51
       -rho*Y[jca53]*rate_eval.p_Ca53__Sc54
       -rho*Y[jna37]*rate_eval.p_Na37__n_Mg37
       -rho*Y[jmn62]*rate_eval.p_Mn62__n_Fe62
       -rho*Y[jf23]*rate_eval.p_F23__n_Ne23
       -rho*Y[jca38]*rate_eval.p_Ca38__Sc39
       -rho*Y[jcr43]*rate_eval.p_Cr43__Mn44
       -rho*Y[jsc56]*rate_eval.p_Sc56__n_Ti56
       -rho*Y[jsi36]*rate_eval.p_Si36__P37
       -rho*Y[js43]*rate_eval.p_S43__Cl44
       -rho*Y[jv62]*rate_eval.p_V62__He4_Ti59
       -rho*Y[jp47]*rate_eval.p_P47__He4_Si44
       -rho*Y[jar49]*rate_eval.p_Ar49__n_K49
       -rho*Y[jcr44]*rate_eval.p_Cr44__Mn45
       -rho*Y[jti62]*rate_eval.p_Ti62__He4_Sc59
       -rho*Y[jal22]*rate_eval.p_Al22__Si23
       -rho*Y[jca55]*rate_eval.p_Ca55__Sc56
       -rho*Y[jna30]*rate_eval.p_Na30__Mg31
       -rho*Y[jcr59]*rate_eval.p_Cr59__He4_V56
       -rho*Y[jp35]*rate_eval.p_P35__He4_Si32
       -rho*Y[jar48]*rate_eval.p_Ar48__K49
       -rho*Y[jne29]*rate_eval.p_Ne29__Na30
       -rho*Y[jar53]*rate_eval.p_Ar53__K54
       -rho*Y[jp34]*rate_eval.p_P34__He4_Si31
       -rho*Y[jk39]*rate_eval.p_K39__He4_Ar36
       -rho*Y[jmn55]*rate_eval.p_Mn55__Fe56
       -rho*Y[jar49]*rate_eval.p_Ar49__K50
       -rho*Y[jmn65]*rate_eval.p_Mn65__n_Fe65
       -rho*Y[jn16]*rate_eval.p_N16__He4_C13
       -rho*Y[jca39]*rate_eval.p_Ca39__Sc40
       -rho*Y[jna32]*rate_eval.p_Na32__He4_Ne29
       -rho*Y[jti64]*rate_eval.p_Ti64__V65
       -rho*Y[jcl49]*rate_eval.p_Cl49__n_Ar49
       -rho*Y[jcl52]*rate_eval.p_Cl52__Ar53
       -rho*Y[jo25]*rate_eval.p_O25__F26
       -rho*Y[jk54]*rate_eval.p_K54__He4_Ar51
       -rho*Y[jsc59]*rate_eval.p_Sc59__n_Ti59
       -rho*Y[jca37]*rate_eval.p_Ca37__Sc38
       -rho*Y[jp37]*rate_eval.p_P37__n_S37
       -rho*Y[jmn61]*rate_eval.p_Mn61__He4_Cr58
       -rho*Y[jp43]*rate_eval.p_P43__S44
       -rho*Y[jti45]*rate_eval.p_Ti45__V46
       -rho*Y[jcl47]*rate_eval.p_Cl47__He4_S44
       -rho*Y[jal27]*rate_eval.p_Al27__Si28
       -rho*Y[jti56]*rate_eval.p_Ti56__n_V56
       -rho*Y[jna29]*rate_eval.p_Na29__Mg30
       -rho*Y[jti59]*rate_eval.p_Ti59__He4_Sc56
       -rho*Y[jk50]*rate_eval.p_K50__Ca51
       -rho*Y[jsi34]*rate_eval.p_Si34__n_P34
       -rho*Y[jo19]*rate_eval.p_O19__n_F19
       -rho*Y[jmg25]*rate_eval.p_Mg25__Al26
       -rho*Y[jsc63]*rate_eval.p_Sc63__n_Ti63
       -rho*Y[jal42]*rate_eval.p_Al42__n_Si42
       -rho*Y[js45]*rate_eval.p_S45__Cl46
       -rho*Y[jti58]*rate_eval.p_Ti58__He4_Sc55
       -rho*Y[jf31]*rate_eval.p_F31__Ne32
       -rho*Y[jsc43]*rate_eval.p_Sc43__He4_Ca40
       -rho*Y[jsc62]*rate_eval.p_Sc62__He4_Ca59
       -rho*Y[jp47]*rate_eval.p_P47__S48
       -rho*Y[jmg28]*rate_eval.p_Mg28__Al29
       -rho*Y[jo19]*rate_eval.p_O19__F20
       -rho*Y[jcr58]*rate_eval.p_Cr58__He4_V55
       -rho*Y[jsi41]*rate_eval.p_Si41__n_P41
       -rho*Y[jna24]*rate_eval.p_Na24__n_Mg24
       -rho*Y[jcr63]*rate_eval.p_Cr63__He4_V60
       -rho*Y[jsi35]*rate_eval.p_Si35__n_P35
       -rho*Y[jsi43]*rate_eval.p_Si43__P44
       -rho*Y[jk53]*rate_eval.p_K53__He4_Ar50
       -rho*Y[jna25]*rate_eval.p_Na25__He4_Ne22
       -rho*Y[jmg28]*rate_eval.p_Mg28__n_Al28
       -rho*Y[jo18]*rate_eval.p_O18__F19
       -rho*Y[jp36]*rate_eval.p_P36__S37
       -rho*Y[jmg39]*rate_eval.p_Mg39__He4_Na36
       -rho*Y[jsc44]*rate_eval.p_Sc44__Ti45
       -rho*Y[jv66]*rate_eval.p_V66__He4_Ti63
       -rho*Y[jar51]*rate_eval.p_Ar51__n_K51
       -rho*Y[jcr67]*rate_eval.p_Cr67__Mn68
       -rho*Y[jp41]*rate_eval.p_P41__He4_Si38
       -rho*Y[jmg34]*rate_eval.p_Mg34__n_Al34
       -rho*Y[jna39]*rate_eval.p_Na39__Mg40
       -rho*Y[jbe10]*rate_eval.p_Be10__He4_Li7
       -rho*Y[jmg35]*rate_eval.p_Mg35__Al36
       -rho*Y[jar50]*rate_eval.p_Ar50__K51
       -rho*Y[jca47]*rate_eval.p_Ca47__Sc48
       -rho*Y[jcl44]*rate_eval.p_Cl44__He4_S41
       -rho*Y[jsc54]*rate_eval.p_Sc54__He4_Ca51
       -rho*Y[jcr70]*rate_eval.p_Cr70__He4_V67
       -rho*Y[jmg40]*rate_eval.p_Mg40__Al41
       -rho*Y[jti55]*rate_eval.p_Ti55__He4_Sc52
       -rho*Y[jmg33]*rate_eval.p_Mg33__Al34
       -rho*Y[jal29]*rate_eval.p_Al29__Si30
       -rho*Y[jmn56]*rate_eval.p_Mn56__n_Fe56
       -rho*Y[jv59]*rate_eval.p_V59__He4_Ti56
       -rho*Y[jar49]*rate_eval.p_Ar49__He4_Cl46
       -rho*Y[jal32]*rate_eval.p_Al32__Si33
       -rho*Y[jna19]*rate_eval.p_Na19__Mg20
       -rho*Y[jfe62]*rate_eval.p_Fe62__Co63
       -rho*Y[jp39]*rate_eval.p_P39__S40
       -rho*Y[jf26]*rate_eval.p_F26__He4_O23
       -rho*Y[js48]*rate_eval.p_S48__Cl49
       -rho*Y[jsc42]*rate_eval.p_Sc42__He4_Ca39
       -rho*Y[jsi38]*rate_eval.p_Si38__He4_Al35
       -rho*Y[jf30]*rate_eval.p_F30__Ne31
       -rho*Y[jo23]*rate_eval.p_O23__F24
       -rho*Y[jfe75]*rate_eval.p_Fe75__Co76
       -rho*Y[jmn65]*rate_eval.p_Mn65__Fe66
       -rho*Y[jcr61]*rate_eval.p_Cr61__n_Mn61
       -rho*Y[jna35]*rate_eval.p_Na35__Mg36
       -rho*Y[jna30]*rate_eval.p_Na30__n_Mg30
       -rho*Y[jv62]*rate_eval.p_V62__Cr63
       -rho*Y[jar46]*rate_eval.p_Ar46__n_K46
       +5.00000000000000e-01*rho**2*Y[jn]*2*Y[jp]*rate_eval.n_p_p__p_d
       +rho*Y[jbe9]*rate_eval.p_Be9__n_p_He4_He4
       )

    jac[jp, jd] = (
       -rho*Y[jp]*rate_eval.p_d__He3
       +rho*Y[jbe7]*rate_eval.d_Be7__p_He4_He4
       +rho*Y[jli7]*rate_eval.d_Li7__p_Li8
       +rho*Y[jhe3]*rate_eval.d_He3__p_He4
       +5.00000000000000e-01*rho*2*Y[jd]*rate_eval.d_d__p_t
       +rho*Y[jli6]*rate_eval.d_Li6__p_Li7
       )

    jac[jp, jt] = (
       -rho*Y[jp]*rate_eval.p_t__He4
       +rho*Y[jbe7]*rate_eval.t_Be7__n_p_He4_He4
       +rho*Y[jhe3]*rate_eval.t_He3__n_p_He4
       )

    jac[jp, jhe3] = (
       -rho*Y[jp]*rate_eval.p_He3__He4__weak__bet_pos_
       +2*rho*Y[jbe7]*rate_eval.He3_Be7__p_p_He4_He4
       +2*5.00000000000000e-01*rho*2*Y[jhe3]*rate_eval.He3_He3__p_p_He4
       +rho*Y[jt]*rate_eval.t_He3__n_p_He4
       +rho*Y[jd]*rate_eval.d_He3__p_He4
       +rho*Y[jn]*rate_eval.n_He3__p_t
       +rho*Y[jli7]*rate_eval.He3_Li7__n_p_He4_He4
       )

    jac[jp, jhe4] = (
       -rho**2*Y[jn]*Y[jp]*rate_eval.n_p_He4__Li6
       +2*rho*Y[jca36]*rate_eval.He4_Ca36__p_p_Ca38
       +2*rho*Y[jo13]*rate_eval.He4_O13__p_p_O15
       +rho*Y[jfe52]*rate_eval.He4_Fe52__p_Co55
       +rho*Y[jfe49]*rate_eval.He4_Fe49__p_Co52
       +rho*Y[jfe48]*rate_eval.He4_Fe48__p_Co51
       +rho*Y[jmn53]*rate_eval.He4_Mn53__p_Fe56
       +rho*Y[jmn51]*rate_eval.He4_Mn51__p_Fe54
       +rho*Y[jmn49]*rate_eval.He4_Mn49__p_Fe52
       +rho*Y[jmn47]*rate_eval.He4_Mn47__p_Fe50
       +rho*Y[jmn46]*rate_eval.He4_Mn46__p_Fe49
       +rho*Y[jmn44]*rate_eval.He4_Mn44__p_Fe47
       +rho*Y[jcr49]*rate_eval.He4_Cr49__p_Mn52
       +rho*Y[jcr48]*rate_eval.He4_Cr48__p_Mn51
       +rho*Y[jcr45]*rate_eval.He4_Cr45__p_Mn48
       +rho*Y[jcr44]*rate_eval.He4_Cr44__p_Mn47
       +rho*Y[jcr43]*rate_eval.He4_Cr43__p_Mn46
       +rho*Y[jcr42]*rate_eval.He4_Cr42__p_Mn45
       +rho*Y[jsc37]*rate_eval.He4_Sc37__p_Ti40
       +rho*Y[jv50]*rate_eval.He4_V50__p_Cr53
       +rho*Y[jal40]*rate_eval.He4_Al40__p_Si43
       +rho*Y[jcr47]*rate_eval.He4_Cr47__p_Mn50
       +rho*Y[jv47]*rate_eval.He4_V47__p_Cr50
       +rho*Y[jv46]*rate_eval.He4_V46__p_Cr49
       +rho*Y[jv43]*rate_eval.He4_V43__p_Cr46
       +rho*Y[jv42]*rate_eval.He4_V42__p_Cr45
       +rho*Y[jv39]*rate_eval.He4_V39__p_Cr42
       +rho*Y[jk36]*rate_eval.He4_K36__p_Ca39
       +rho*Y[jti43]*rate_eval.He4_Ti43__p_V46
       +rho*Y[jti40]*rate_eval.He4_Ti40__p_V43
       +rho*Y[jti39]*rate_eval.He4_Ti39__p_V42
       +rho*Y[jti38]*rate_eval.He4_Ti38__p_V41
       +rho*Y[jti37]*rate_eval.He4_Ti37__p_V40
       +rho*Y[jsc40]*rate_eval.He4_Sc40__p_Ti43
       +rho*Y[jc9]*rate_eval.He4_C9__p_N12
       +rho*Y[jsc47]*rate_eval.He4_Sc47__p_Ti50
       +rho*Y[jsc46]*rate_eval.He4_Sc46__p_Ti49
       +rho*Y[jsc45]*rate_eval.He4_Sc45__p_Ti48
       +rho*Y[jsc44]*rate_eval.He4_Sc44__p_Ti47
       +rho*Y[jsc43]*rate_eval.He4_Sc43__p_Ti46
       +rho*Y[jsc42]*rate_eval.He4_Sc42__p_Ti45
       +rho*Y[jsc39]*rate_eval.He4_Sc39__p_Ti42
       +rho*Y[jsc38]*rate_eval.He4_Sc38__p_Ti41
       +rho*Y[jsc36]*rate_eval.He4_Sc36__p_Ti39
       +rho*Y[jsc35]*rate_eval.He4_Sc35__p_Ti38
       +rho*Y[jti45]*rate_eval.He4_Ti45__p_V48
       +rho*Y[jk43]*rate_eval.He4_K43__p_Ca46
       +rho*Y[jk42]*rate_eval.He4_K42__p_Ca45
       +rho*Y[jk46]*rate_eval.He4_K46__p_Ca49
       +rho*Y[jk37]*rate_eval.He4_K37__p_Ca40
       +rho*Y[jk44]*rate_eval.He4_K44__p_Ca47
       +rho*Y[jk34]*rate_eval.He4_K34__p_Ca37
       +rho*Y[jk31]*rate_eval.He4_K31__p_Ca34
       +rho*Y[jfe50]*rate_eval.He4_Fe50__p_Co53
       +rho*Y[jar34]*rate_eval.He4_Ar34__p_K37
       +rho*Y[jar33]*rate_eval.He4_Ar33__p_K36
       +rho*Y[jar31]*rate_eval.He4_Ar31__p_K34
       +rho*Y[jar29]*rate_eval.He4_Ar29__p_K32
       +rho*Y[jcl43]*rate_eval.He4_Cl43__p_Ar46
       +rho*Y[jcl34]*rate_eval.He4_Cl34__p_Ar37
       +rho*Y[jar35]*rate_eval.He4_Ar35__p_K38
       +rho*Y[jcl30]*rate_eval.He4_Cl30__p_Ar33
       +rho*Y[jcl28]*rate_eval.He4_Cl28__p_Ar31
       +rho*Y[js34]*rate_eval.He4_S34__p_Cl37
       +rho*Y[js31]*rate_eval.He4_S31__p_Cl34
       +rho*Y[js30]*rate_eval.He4_S30__p_Cl33
       +rho*Y[js28]*rate_eval.He4_S28__p_Cl31
       +rho*Y[js26]*rate_eval.He4_S26__p_Cl29
       +rho*Y[jp41]*rate_eval.He4_P41__p_S44
       +rho*Y[jcl44]*rate_eval.He4_Cl44__p_Ar47
       +rho*Y[jp31]*rate_eval.He4_P31__p_S34
       +rho*Y[jp30]*rate_eval.He4_P30__p_S33
       +rho*Y[jp27]*rate_eval.He4_P27__p_S30
       +rho*Y[jp26]*rate_eval.He4_P26__p_S29
       +rho*Y[jp25]*rate_eval.He4_P25__p_S28
       +rho*Y[jp24]*rate_eval.He4_P24__p_S27
       +rho*Y[jmn45]*rate_eval.He4_Mn45__p_Fe48
       +rho*Y[jcr41]*rate_eval.He4_Cr41__p_Mn44
       +rho*Y[jsi25]*rate_eval.He4_Si25__p_P28
       +rho*Y[jv40]*rate_eval.He4_V40__p_Cr43
       +rho*Y[jsi24]*rate_eval.He4_Si24__p_P27
       +rho*Y[jk40]*rate_eval.He4_K40__p_Ca43
       +rho*Y[jsi23]*rate_eval.He4_Si23__p_P26
       +rho*Y[jsi22]*rate_eval.He4_Si22__p_P25
       +rho*Y[jal39]*rate_eval.He4_Al39__p_Si42
       +rho*Y[jal38]*rate_eval.He4_Al38__p_Si41
       +rho*Y[jal36]*rate_eval.He4_Al36__p_Si39
       +rho*Y[jsi27]*rate_eval.He4_Si27__p_P30
       +rho*Y[jal31]*rate_eval.He4_Al31__p_Si34
       +rho*Y[jk41]*rate_eval.He4_K41__p_Ca44
       +rho*Y[jal27]*rate_eval.He4_Al27__p_Si30
       +rho*Y[jal24]*rate_eval.He4_Al24__p_Si27
       +rho*Y[jal25]*rate_eval.He4_Al25__p_Si28
       +rho*Y[jal22]*rate_eval.He4_Al22__p_Si25
       +rho*Y[jal21]*rate_eval.He4_Al21__p_Si24
       +rho*Y[jcr46]*rate_eval.He4_Cr46__p_Mn49
       +rho*Y[jk35]*rate_eval.He4_K35__p_Ca38
       +rho*Y[jfe53]*rate_eval.He4_Fe53__p_Co56
       +rho*Y[jmg22]*rate_eval.He4_Mg22__p_Al25
       +rho*Y[jmg20]*rate_eval.He4_Mg20__p_Al23
       +rho*Y[jna37]*rate_eval.He4_Na37__p_Mg40
       +rho*Y[jna33]*rate_eval.He4_Na33__p_Mg36
       +rho*Y[jna24]*rate_eval.He4_Na24__p_Mg27
       +rho*Y[jna23]*rate_eval.He4_Na23__p_Mg26
       +rho*Y[jna22]*rate_eval.He4_Na22__p_Mg25
       +rho*Y[js29]*rate_eval.He4_S29__p_Cl32
       +rho*Y[jcl35]*rate_eval.He4_Cl35__p_Ar38
       +rho*Y[js27]*rate_eval.He4_S27__p_Cl30
       +rho*Y[jal26]*rate_eval.He4_Al26__p_Si29
       +rho*Y[jne19]*rate_eval.He4_Ne19__p_Na22
       +rho*Y[jne18]*rate_eval.He4_Ne18__p_Na21
       +rho*Y[jne17]*rate_eval.He4_Ne17__p_Na20
       +rho*Y[jne16]*rate_eval.He4_Ne16__p_Na19
       +rho*Y[jf30]*rate_eval.He4_F30__p_Ne33
       +rho*Y[jti42]*rate_eval.He4_Ti42__p_V45
       +rho*Y[jf21]*rate_eval.He4_F21__p_Ne24
       +rho*Y[jf20]*rate_eval.He4_F20__p_Ne23
       +rho*Y[jf19]*rate_eval.He4_F19__p_Ne22
       +rho*Y[jf18]*rate_eval.He4_F18__p_Ne21
       +rho*Y[jti44]*rate_eval.He4_Ti44__p_V47
       +rho*Y[jcl32]*rate_eval.He4_Cl32__p_Ar35
       +rho*Y[jo13]*rate_eval.He4_O13__p_F16
       +rho*Y[jn13]*rate_eval.He4_N13__p_O16
       +rho*Y[jb11]*rate_eval.He4_B11__p_C14
       +rho*Y[jfe46]*rate_eval.He4_Fe46__p_Co49
       +rho*Y[jb10]*rate_eval.He4_B10__p_C13
       +rho*Y[jb8]*rate_eval.He4_B8__p_C11
       +rho*Y[jv49]*rate_eval.He4_V49__p_Cr52
       +rho*Y[jcl29]*rate_eval.He4_Cl29__p_Ar32
       +rho*Y[jmg19]*rate_eval.He4_Mg19__p_Al22
       +rho*Y[jk38]*rate_eval.He4_K38__p_Ca41
       +rho*Y[jo14]*rate_eval.He4_O14__p_F17
       +rho*Y[jf16]*rate_eval.He4_F16__p_Ne19
       +rho*Y[jal29]*rate_eval.He4_Al29__p_Si32
       +rho*Y[jk45]*rate_eval.He4_K45__p_Ca48
       +rho*Y[jv48]*rate_eval.He4_V48__p_Cr51
       +rho*Y[jca36]*rate_eval.He4_Ca36__p_Sc39
       +rho*Y[jsc48]*rate_eval.He4_Sc48__p_Ti51
       +rho*Y[jcl33]*rate_eval.He4_Cl33__p_Ar36
       +rho*Y[jca38]*rate_eval.He4_Ca38__p_Sc41
       +rho*Y[jmn48]*rate_eval.He4_Mn48__p_Fe51
       +rho*Y[jal28]*rate_eval.He4_Al28__p_Si31
       +rho*Y[jf15]*rate_eval.He4_F15__p_Ne18
       +rho*Y[jfe45]*rate_eval.He4_Fe45__p_Co48
       +rho*Y[jna19]*rate_eval.He4_Na19__p_Mg22
       +rho*Y[jsc41]*rate_eval.He4_Sc41__p_Ti44
       +rho*Y[jmn43]*rate_eval.He4_Mn43__p_Fe46
       +rho*Y[jna20]*rate_eval.He4_Na20__p_Mg23
       +rho*Y[jv44]*rate_eval.He4_V44__p_Cr47
       +rho*Y[jca35]*rate_eval.He4_Ca35__p_Sc38
       +rho*Y[jca37]*rate_eval.He4_Ca37__p_Sc40
       +rho*Y[jn12]*rate_eval.He4_N12__p_O15
       +rho*Y[jp28]*rate_eval.He4_P28__p_S31
       +rho*Y[jmn52]*rate_eval.He4_Mn52__p_Fe55
       +rho*Y[jfe51]*rate_eval.He4_Fe51__p_Co54
       +rho*Y[jar30]*rate_eval.He4_Ar30__p_K33
       +rho*Y[jv45]*rate_eval.He4_V45__p_Cr48
       +rho*Y[jna25]*rate_eval.He4_Na25__p_Mg28
       +rho*Y[jmg21]*rate_eval.He4_Mg21__p_Al24
       +rho*Y[jc11]*rate_eval.He4_C11__p_N14
       +rho*Y[jti41]*rate_eval.He4_Ti41__p_V44
       +rho*Y[jk33]*rate_eval.He4_K33__p_Ca36
       +rho*Y[jal23]*rate_eval.He4_Al23__p_Si26
       +rho*Y[jcl41]*rate_eval.He4_Cl41__p_Ar44
       +rho*Y[jcl31]*rate_eval.He4_Cl31__p_Ar34
       +rho*Y[jp29]*rate_eval.He4_P29__p_S32
       +rho*Y[jmg23]*rate_eval.He4_Mg23__p_Al26
       +rho*Y[jca34]*rate_eval.He4_Ca34__p_Sc37
       +rho*Y[jk32]*rate_eval.He4_K32__p_Ca35
       +rho*Y[jsi26]*rate_eval.He4_Si26__p_P29
       +rho*Y[jv41]*rate_eval.He4_V41__p_Cr44
       +rho*Y[jfe47]*rate_eval.He4_Fe47__p_Co50
       +rho*Y[jca33]*rate_eval.He4_Ca33__p_Sc36
       +rho*Y[jmn50]*rate_eval.He4_Mn50__p_Fe53
       +rho*Y[jar32]*rate_eval.He4_Ar32__p_K35
       )

    jac[jp, jli6] = (
       -rho*Y[jp]*rate_eval.p_Li6__Be7
       -rho*Y[jp]*rate_eval.p_Li6__He4_He3
       +rho*Y[jd]*rate_eval.d_Li6__p_Li7
       )

    jac[jp, jli7] = (
       -rho*Y[jp]*rate_eval.p_Li7__He4_He4
       +rho*Y[jd]*rate_eval.d_Li7__p_Li8
       +rho*Y[jhe3]*rate_eval.He3_Li7__n_p_He4_He4
       )

    jac[jp, jli8] = (
       -rho*Y[jp]*rate_eval.p_Li8__n_He4_He4
       )

    jac[jp, jbe7] = (
       -rho*Y[jp]*rate_eval.p_Be7__B8
       +2*rho*Y[jhe3]*rate_eval.He3_Be7__p_p_He4_He4
       +rho*Y[jt]*rate_eval.t_Be7__n_p_He4_He4
       +rho*Y[jd]*rate_eval.d_Be7__p_He4_He4
       +rho*Y[jn]*rate_eval.n_Be7__p_Li7
       )

    jac[jp, jbe9] = (
       -rho*Y[jp]*rate_eval.p_Be9__n_p_He4_He4
       -rho*Y[jp]*rate_eval.p_Be9__d_He4_He4
       -rho*Y[jp]*rate_eval.p_Be9__B10
       -rho*Y[jp]*rate_eval.p_Be9__He4_Li6
       +rho*Y[jp]*rate_eval.p_Be9__n_p_He4_He4
       )

    jac[jp, jbe10] = (
       -rho*Y[jp]*rate_eval.p_Be10__B11
       -rho*Y[jp]*rate_eval.p_Be10__He4_Li7
       )

    jac[jp, jbe11] = (
       -rho*Y[jp]*rate_eval.p_Be11__He4_Li8
       )

    jac[jp, jb8] = (
       -rho*Y[jp]*rate_eval.p_B8__C9
       +rho*Y[jn]*rate_eval.n_B8__p_He4_He4
       +rho*Y[jhe4]*rate_eval.He4_B8__p_C11
       )

    jac[jp, jb10] = (
       -rho*Y[jp]*rate_eval.p_B10__C11
       -rho*Y[jp]*rate_eval.p_B10__He4_Be7
       +rho*Y[jhe4]*rate_eval.He4_B10__p_C13
       )

    jac[jp, jb11] = (
       -rho*Y[jp]*rate_eval.p_B11__He4_He4_He4
       -rho*Y[jp]*rate_eval.p_B11__C12
       +rho*Y[jhe4]*rate_eval.He4_B11__p_C14
       )

    jac[jp, jb12] = (
       -rho*Y[jp]*rate_eval.p_B12__n_C12
       -rho*Y[jp]*rate_eval.p_B12__He4_Be9
       )

    jac[jp, jc9] = (
       +rho*Y[jhe4]*rate_eval.He4_C9__p_N12
       )

    jac[jp, jc11] = (
       -rho*Y[jp]*rate_eval.p_C11__N12
       +rho*Y[jn]*rate_eval.n_C11__p_B11
       +rho*Y[jhe4]*rate_eval.He4_C11__p_N14
       )

    jac[jp, jc12] = (
       -rho*Y[jp]*rate_eval.p_C12__N13
       +rho*Y[jne20]*rate_eval.C12_Ne20__p_P31
       +rho*Y[jo16]*rate_eval.C12_O16__p_Al27
       +5.00000000000000e-01*rho*2*Y[jc12]*rate_eval.C12_C12__p_Na23
       )

    jac[jp, jc13] = (
       -rho*Y[jp]*rate_eval.p_C13__n_N13
       -rho*Y[jp]*rate_eval.p_C13__N14
       )

    jac[jp, jc14] = (
       -rho*Y[jp]*rate_eval.p_C14__N15
       )

    jac[jp, jc15] = (
       -rho*Y[jp]*rate_eval.p_C15__n_N15
       )

    jac[jp, jn12] = (
       -rho*Y[jp]*rate_eval.p_N12__O13
       +rho*Y[jhe4]*rate_eval.He4_N12__p_O15
       )

    jac[jp, jn13] = (
       -rho*Y[jp]*rate_eval.p_N13__O14
       +rho*Y[jhe4]*rate_eval.He4_N13__p_O16
       )

    jac[jp, jn14] = (
       -rho*Y[jp]*rate_eval.p_N14__O15
       -rho*Y[jp]*rate_eval.p_N14__n_O14
       +rho*Y[jn]*rate_eval.n_N14__p_C14
       )

    jac[jp, jn15] = (
       -rho*Y[jp]*rate_eval.p_N15__O16
       -rho*Y[jp]*rate_eval.p_N15__He4_C12
       -rho*Y[jp]*rate_eval.p_N15__n_O15
       )

    jac[jp, jn16] = (
       -rho*Y[jp]*rate_eval.p_N16__n_O16
       -rho*Y[jp]*rate_eval.p_N16__He4_C13
       )

    jac[jp, jo12] = (
       +rho*Y[jn]*rate_eval.n_O12__p_N12
       )

    jac[jp, jo13] = (
       +2*rho*Y[jhe4]*rate_eval.He4_O13__p_p_O15
       +rho*Y[jhe4]*rate_eval.He4_O13__p_F16
       +rho*Y[jn]*rate_eval.n_O13__p_N13
       +rate_eval.O13__p_C12__weak__wc12
       )

    jac[jp, jo14] = (
       -rho*Y[jp]*rate_eval.p_O14__F15
       +rho*Y[jhe4]*rate_eval.He4_O14__p_F17
       )

    jac[jp, jo15] = (
       -rho*Y[jp]*rate_eval.p_O15__F16
       )

    jac[jp, jo16] = (
       -rho*Y[jp]*rate_eval.p_O16__F17
       +5.00000000000000e-01*rho*2*Y[jo16]*rate_eval.O16_O16__p_P31
       +rho*Y[jc12]*rate_eval.C12_O16__p_Al27
       )

    jac[jp, jo17] = (
       -rho*Y[jp]*rate_eval.p_O17__He4_N14
       -rho*Y[jp]*rate_eval.p_O17__F18
       )

    jac[jp, jo18] = (
       -rho*Y[jp]*rate_eval.p_O18__He4_N15
       -rho*Y[jp]*rate_eval.p_O18__F19
       )

    jac[jp, jo19] = (
       -rho*Y[jp]*rate_eval.p_O19__He4_N16
       -rho*Y[jp]*rate_eval.p_O19__n_F19
       -rho*Y[jp]*rate_eval.p_O19__F20
       )

    jac[jp, jo20] = (
       -rho*Y[jp]*rate_eval.p_O20__He4_N17
       -rho*Y[jp]*rate_eval.p_O20__n_F20
       -rho*Y[jp]*rate_eval.p_O20__F21
       )

    jac[jp, jo21] = (
       -rho*Y[jp]*rate_eval.p_O21__n_F21
       -rho*Y[jp]*rate_eval.p_O21__F22
       )

    jac[jp, jo22] = (
       -rho*Y[jp]*rate_eval.p_O22__n_F22
       -rho*Y[jp]*rate_eval.p_O22__F23
       )

    jac[jp, jo23] = (
       -rho*Y[jp]*rate_eval.p_O23__n_F23
       -rho*Y[jp]*rate_eval.p_O23__F24
       )

    jac[jp, jo24] = (
       -rho*Y[jp]*rate_eval.p_O24__n_F24
       -rho*Y[jp]*rate_eval.p_O24__F25
       )

    jac[jp, jo25] = (
       -rho*Y[jp]*rate_eval.p_O25__n_F25
       -rho*Y[jp]*rate_eval.p_O25__F26
       )

    jac[jp, jo26] = (
       -rho*Y[jp]*rate_eval.p_O26__He4_N23
       -rho*Y[jp]*rate_eval.p_O26__n_F26
       -rho*Y[jp]*rate_eval.p_O26__F27
       )

    jac[jp, jo27] = (
       -rho*Y[jp]*rate_eval.p_O27__He4_N24
       -rho*Y[jp]*rate_eval.p_O27__F28
       -rho*Y[jp]*rate_eval.p_O27__n_F27
       )

    jac[jp, jf14] = (
       +rho*Y[jn]*rate_eval.n_F14__p_O14
       )

    jac[jp, jf15] = (
       +rho*Y[jhe4]*rate_eval.He4_F15__p_Ne18
       +rho*Y[jn]*rate_eval.n_F15__p_O15
       )

    jac[jp, jf16] = (
       +rho*Y[jn]*rate_eval.n_F16__p_O16
       +rho*Y[jhe4]*rate_eval.He4_F16__p_Ne19
       )

    jac[jp, jf17] = (
       -rho*Y[jp]*rate_eval.p_F17__Ne18
       +rho*Y[jn]*rate_eval.n_F17__p_O17
       )

    jac[jp, jf18] = (
       -rho*Y[jp]*rate_eval.p_F18__He4_O15
       -rho*Y[jp]*rate_eval.p_F18__Ne19
       +rho*Y[jhe4]*rate_eval.He4_F18__p_Ne21
       +rho*Y[jn]*rate_eval.n_F18__p_O18
       )

    jac[jp, jf19] = (
       -rho*Y[jp]*rate_eval.p_F19__n_Ne19
       -rho*Y[jp]*rate_eval.p_F19__He4_O16
       -rho*Y[jp]*rate_eval.p_F19__Ne20
       +rho*Y[jhe4]*rate_eval.He4_F19__p_Ne22
       )

    jac[jp, jf20] = (
       -rho*Y[jp]*rate_eval.p_F20__He4_O17
       -rho*Y[jp]*rate_eval.p_F20__n_Ne20
       -rho*Y[jp]*rate_eval.p_F20__Ne21
       +rho*Y[jhe4]*rate_eval.He4_F20__p_Ne23
       )

    jac[jp, jf21] = (
       -rho*Y[jp]*rate_eval.p_F21__n_Ne21
       -rho*Y[jp]*rate_eval.p_F21__Ne22
       -rho*Y[jp]*rate_eval.p_F21__He4_O18
       +rho*Y[jhe4]*rate_eval.He4_F21__p_Ne24
       )

    jac[jp, jf22] = (
       -rho*Y[jp]*rate_eval.p_F22__He4_O19
       -rho*Y[jp]*rate_eval.p_F22__n_Ne22
       -rho*Y[jp]*rate_eval.p_F22__Ne23
       )

    jac[jp, jf23] = (
       -rho*Y[jp]*rate_eval.p_F23__Ne24
       -rho*Y[jp]*rate_eval.p_F23__He4_O20
       -rho*Y[jp]*rate_eval.p_F23__n_Ne23
       )

    jac[jp, jf24] = (
       -rho*Y[jp]*rate_eval.p_F24__Ne25
       -rho*Y[jp]*rate_eval.p_F24__n_Ne24
       -rho*Y[jp]*rate_eval.p_F24__He4_O21
       )

    jac[jp, jf25] = (
       -rho*Y[jp]*rate_eval.p_F25__He4_O22
       -rho*Y[jp]*rate_eval.p_F25__n_Ne25
       -rho*Y[jp]*rate_eval.p_F25__Ne26
       )

    jac[jp, jf26] = (
       -rho*Y[jp]*rate_eval.p_F26__n_Ne26
       -rho*Y[jp]*rate_eval.p_F26__Ne27
       -rho*Y[jp]*rate_eval.p_F26__He4_O23
       )

    jac[jp, jf27] = (
       -rho*Y[jp]*rate_eval.p_F27__He4_O24
       -rho*Y[jp]*rate_eval.p_F27__n_Ne27
       -rho*Y[jp]*rate_eval.p_F27__Ne28
       )

    jac[jp, jf28] = (
       -rho*Y[jp]*rate_eval.p_F28__n_Ne28
       -rho*Y[jp]*rate_eval.p_F28__He4_O25
       -rho*Y[jp]*rate_eval.p_F28__Ne29
       )

    jac[jp, jf29] = (
       -rho*Y[jp]*rate_eval.p_F29__He4_O26
       -rho*Y[jp]*rate_eval.p_F29__Ne30
       -rho*Y[jp]*rate_eval.p_F29__n_Ne29
       )

    jac[jp, jf30] = (
       -rho*Y[jp]*rate_eval.p_F30__He4_O27
       -rho*Y[jp]*rate_eval.p_F30__n_Ne30
       -rho*Y[jp]*rate_eval.p_F30__Ne31
       +rho*Y[jhe4]*rate_eval.He4_F30__p_Ne33
       )

    jac[jp, jf31] = (
       -rho*Y[jp]*rate_eval.p_F31__He4_O28
       -rho*Y[jp]*rate_eval.p_F31__n_Ne31
       -rho*Y[jp]*rate_eval.p_F31__Ne32
       )

    jac[jp, jne16] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne16__p_Na19
       +rho*Y[jn]*rate_eval.n_Ne16__p_F16
       )

    jac[jp, jne17] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne17__p_Na20
       +rate_eval.Ne17__p_O16__weak__wc12
       +rho*Y[jn]*rate_eval.n_Ne17__p_F17
       )

    jac[jp, jne18] = (
       -rho*Y[jp]*rate_eval.p_Ne18__Na19
       +rho*Y[jhe4]*rate_eval.He4_Ne18__p_Na21
       +rho*Y[jn]*rate_eval.n_Ne18__p_F18
       )

    jac[jp, jne19] = (
       -rho*Y[jp]*rate_eval.p_Ne19__Na20
       +rho*Y[jhe4]*rate_eval.He4_Ne19__p_Na22
       )

    jac[jp, jne20] = (
       -rho*Y[jp]*rate_eval.p_Ne20__He4_F17
       -rho*Y[jp]*rate_eval.p_Ne20__Na21
       +rho*Y[jc12]*rate_eval.C12_Ne20__p_P31
       )

    jac[jp, jne21] = (
       -rho*Y[jp]*rate_eval.p_Ne21__Na22
       )

    jac[jp, jne22] = (
       -rho*Y[jp]*rate_eval.p_Ne22__Na23
       )

    jac[jp, jne23] = (
       -rho*Y[jp]*rate_eval.p_Ne23__n_Na23
       -rho*Y[jp]*rate_eval.p_Ne23__Na24
       )

    jac[jp, jne24] = (
       -rho*Y[jp]*rate_eval.p_Ne24__n_Na24
       -rho*Y[jp]*rate_eval.p_Ne24__Na25
       )

    jac[jp, jne25] = (
       -rho*Y[jp]*rate_eval.p_Ne25__He4_F22
       -rho*Y[jp]*rate_eval.p_Ne25__n_Na25
       -rho*Y[jp]*rate_eval.p_Ne25__Na26
       )

    jac[jp, jne26] = (
       -rho*Y[jp]*rate_eval.p_Ne26__n_Na26
       -rho*Y[jp]*rate_eval.p_Ne26__He4_F23
       -rho*Y[jp]*rate_eval.p_Ne26__Na27
       )

    jac[jp, jne27] = (
       -rho*Y[jp]*rate_eval.p_Ne27__He4_F24
       -rho*Y[jp]*rate_eval.p_Ne27__n_Na27
       -rho*Y[jp]*rate_eval.p_Ne27__Na28
       )

    jac[jp, jne28] = (
       -rho*Y[jp]*rate_eval.p_Ne28__n_Na28
       -rho*Y[jp]*rate_eval.p_Ne28__He4_F25
       -rho*Y[jp]*rate_eval.p_Ne28__Na29
       )

    jac[jp, jne29] = (
       -rho*Y[jp]*rate_eval.p_Ne29__He4_F26
       -rho*Y[jp]*rate_eval.p_Ne29__n_Na29
       -rho*Y[jp]*rate_eval.p_Ne29__Na30
       )

    jac[jp, jne30] = (
       -rho*Y[jp]*rate_eval.p_Ne30__He4_F27
       -rho*Y[jp]*rate_eval.p_Ne30__Na31
       -rho*Y[jp]*rate_eval.p_Ne30__n_Na30
       )

    jac[jp, jne31] = (
       -rho*Y[jp]*rate_eval.p_Ne31__He4_F28
       -rho*Y[jp]*rate_eval.p_Ne31__Na32
       -rho*Y[jp]*rate_eval.p_Ne31__n_Na31
       )

    jac[jp, jne32] = (
       -rho*Y[jp]*rate_eval.p_Ne32__Na33
       -rho*Y[jp]*rate_eval.p_Ne32__n_Na32
       -rho*Y[jp]*rate_eval.p_Ne32__He4_F29
       )

    jac[jp, jne33] = (
       -rho*Y[jp]*rate_eval.p_Ne33__n_Na33
       -rho*Y[jp]*rate_eval.p_Ne33__Na34
       )

    jac[jp, jne34] = (
       -rho*Y[jp]*rate_eval.p_Ne34__He4_F31
       -rho*Y[jp]*rate_eval.p_Ne34__n_Na34
       -rho*Y[jp]*rate_eval.p_Ne34__Na35
       )

    jac[jp, jna19] = (
       -rho*Y[jp]*rate_eval.p_Na19__Mg20
       +rho*Y[jn]*rate_eval.n_Na19__p_Ne19
       +rho*Y[jhe4]*rate_eval.He4_Na19__p_Mg22
       )

    jac[jp, jna20] = (
       -rho*Y[jp]*rate_eval.p_Na20__Mg21
       +rho*Y[jhe4]*rate_eval.He4_Na20__p_Mg23
       +rho*Y[jn]*rate_eval.n_Na20__p_Ne20
       )

    jac[jp, jna21] = (
       -rho*Y[jp]*rate_eval.p_Na21__Mg22
       +rho*Y[jn]*rate_eval.n_Na21__p_Ne21
       )

    jac[jp, jna22] = (
       -rho*Y[jp]*rate_eval.p_Na22__Mg23
       +rho*Y[jhe4]*rate_eval.He4_Na22__p_Mg25
       +rho*Y[jn]*rate_eval.n_Na22__p_Ne22
       )

    jac[jp, jna23] = (
       -rho*Y[jp]*rate_eval.p_Na23__He4_Ne20
       -rho*Y[jp]*rate_eval.p_Na23__n_Mg23
       -rho*Y[jp]*rate_eval.p_Na23__Mg24
       +rho*Y[jhe4]*rate_eval.He4_Na23__p_Mg26
       )

    jac[jp, jna24] = (
       -rho*Y[jp]*rate_eval.p_Na24__He4_Ne21
       -rho*Y[jp]*rate_eval.p_Na24__Mg25
       -rho*Y[jp]*rate_eval.p_Na24__n_Mg24
       +rho*Y[jhe4]*rate_eval.He4_Na24__p_Mg27
       )

    jac[jp, jna25] = (
       -rho*Y[jp]*rate_eval.p_Na25__Mg26
       -rho*Y[jp]*rate_eval.p_Na25__n_Mg25
       -rho*Y[jp]*rate_eval.p_Na25__He4_Ne22
       +rho*Y[jhe4]*rate_eval.He4_Na25__p_Mg28
       )

    jac[jp, jna26] = (
       -rho*Y[jp]*rate_eval.p_Na26__He4_Ne23
       -rho*Y[jp]*rate_eval.p_Na26__Mg27
       -rho*Y[jp]*rate_eval.p_Na26__n_Mg26
       )

    jac[jp, jna27] = (
       -rho*Y[jp]*rate_eval.p_Na27__n_Mg27
       -rho*Y[jp]*rate_eval.p_Na27__Mg28
       -rho*Y[jp]*rate_eval.p_Na27__He4_Ne24
       )

    jac[jp, jna28] = (
       -rho*Y[jp]*rate_eval.p_Na28__n_Mg28
       -rho*Y[jp]*rate_eval.p_Na28__He4_Ne25
       -rho*Y[jp]*rate_eval.p_Na28__Mg29
       )

    jac[jp, jna29] = (
       -rho*Y[jp]*rate_eval.p_Na29__He4_Ne26
       -rho*Y[jp]*rate_eval.p_Na29__n_Mg29
       -rho*Y[jp]*rate_eval.p_Na29__Mg30
       )

    jac[jp, jna30] = (
       -rho*Y[jp]*rate_eval.p_Na30__He4_Ne27
       -rho*Y[jp]*rate_eval.p_Na30__Mg31
       -rho*Y[jp]*rate_eval.p_Na30__n_Mg30
       )

    jac[jp, jna31] = (
       -rho*Y[jp]*rate_eval.p_Na31__Mg32
       -rho*Y[jp]*rate_eval.p_Na31__He4_Ne28
       -rho*Y[jp]*rate_eval.p_Na31__n_Mg31
       )

    jac[jp, jna32] = (
       -rho*Y[jp]*rate_eval.p_Na32__n_Mg32
       -rho*Y[jp]*rate_eval.p_Na32__Mg33
       -rho*Y[jp]*rate_eval.p_Na32__He4_Ne29
       )

    jac[jp, jna33] = (
       -rho*Y[jp]*rate_eval.p_Na33__n_Mg33
       -rho*Y[jp]*rate_eval.p_Na33__He4_Ne30
       -rho*Y[jp]*rate_eval.p_Na33__Mg34
       +rho*Y[jhe4]*rate_eval.He4_Na33__p_Mg36
       )

    jac[jp, jna34] = (
       -rho*Y[jp]*rate_eval.p_Na34__Mg35
       -rho*Y[jp]*rate_eval.p_Na34__He4_Ne31
       -rho*Y[jp]*rate_eval.p_Na34__n_Mg34
       )

    jac[jp, jna35] = (
       -rho*Y[jp]*rate_eval.p_Na35__n_Mg35
       -rho*Y[jp]*rate_eval.p_Na35__He4_Ne32
       -rho*Y[jp]*rate_eval.p_Na35__Mg36
       )

    jac[jp, jna36] = (
       -rho*Y[jp]*rate_eval.p_Na36__n_Mg36
       -rho*Y[jp]*rate_eval.p_Na36__Mg37
       -rho*Y[jp]*rate_eval.p_Na36__He4_Ne33
       )

    jac[jp, jna37] = (
       -rho*Y[jp]*rate_eval.p_Na37__Mg38
       -rho*Y[jp]*rate_eval.p_Na37__He4_Ne34
       -rho*Y[jp]*rate_eval.p_Na37__n_Mg37
       +rho*Y[jhe4]*rate_eval.He4_Na37__p_Mg40
       )

    jac[jp, jna38] = (
       -rho*Y[jp]*rate_eval.p_Na38__Mg39
       -rho*Y[jp]*rate_eval.p_Na38__n_Mg38
       )

    jac[jp, jna39] = (
       -rho*Y[jp]*rate_eval.p_Na39__n_Mg39
       -rho*Y[jp]*rate_eval.p_Na39__Mg40
       )

    jac[jp, jmg19] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg19__p_Al22
       +rho*Y[jn]*rate_eval.n_Mg19__p_Na19
       )

    jac[jp, jmg20] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg20__p_Al23
       +rho*Y[jn]*rate_eval.n_Mg20__p_Na20
       +rate_eval.Mg20__p_Ne19__weak__wc12
       )

    jac[jp, jmg21] = (
       -rho*Y[jp]*rate_eval.p_Mg21__Al22
       +rho*Y[jn]*rate_eval.n_Mg21__p_Na21
       +rho*Y[jhe4]*rate_eval.He4_Mg21__p_Al24
       +rate_eval.Mg21__p_Ne20__weak__wc12
       )

    jac[jp, jmg22] = (
       -rho*Y[jp]*rate_eval.p_Mg22__Al23
       +rho*Y[jhe4]*rate_eval.He4_Mg22__p_Al25
       +rho*Y[jn]*rate_eval.n_Mg22__p_Na22
       )

    jac[jp, jmg23] = (
       -rho*Y[jp]*rate_eval.p_Mg23__Al24
       +rho*Y[jhe4]*rate_eval.He4_Mg23__p_Al26
       )

    jac[jp, jmg24] = (
       -rho*Y[jp]*rate_eval.p_Mg24__He4_Na21
       -rho*Y[jp]*rate_eval.p_Mg24__Al25
       )

    jac[jp, jmg25] = (
       -rho*Y[jp]*rate_eval.p_Mg25__Al26
       )

    jac[jp, jmg26] = (
       -rho*Y[jp]*rate_eval.p_Mg26__Al27
       )

    jac[jp, jmg27] = (
       -rho*Y[jp]*rate_eval.p_Mg27__Al28
       -rho*Y[jp]*rate_eval.p_Mg27__n_Al27
       )

    jac[jp, jmg28] = (
       -rho*Y[jp]*rate_eval.p_Mg28__Al29
       -rho*Y[jp]*rate_eval.p_Mg28__n_Al28
       )

    jac[jp, jmg29] = (
       -rho*Y[jp]*rate_eval.p_Mg29__He4_Na26
       -rho*Y[jp]*rate_eval.p_Mg29__n_Al29
       -rho*Y[jp]*rate_eval.p_Mg29__Al30
       )

    jac[jp, jmg30] = (
       -rho*Y[jp]*rate_eval.p_Mg30__n_Al30
       -rho*Y[jp]*rate_eval.p_Mg30__Al31
       -rho*Y[jp]*rate_eval.p_Mg30__He4_Na27
       )

    jac[jp, jmg31] = (
       -rho*Y[jp]*rate_eval.p_Mg31__n_Al31
       -rho*Y[jp]*rate_eval.p_Mg31__Al32
       -rho*Y[jp]*rate_eval.p_Mg31__He4_Na28
       )

    jac[jp, jmg32] = (
       -rho*Y[jp]*rate_eval.p_Mg32__He4_Na29
       -rho*Y[jp]*rate_eval.p_Mg32__Al33
       -rho*Y[jp]*rate_eval.p_Mg32__n_Al32
       )

    jac[jp, jmg33] = (
       -rho*Y[jp]*rate_eval.p_Mg33__He4_Na30
       -rho*Y[jp]*rate_eval.p_Mg33__n_Al33
       -rho*Y[jp]*rate_eval.p_Mg33__Al34
       )

    jac[jp, jmg34] = (
       -rho*Y[jp]*rate_eval.p_Mg34__Al35
       -rho*Y[jp]*rate_eval.p_Mg34__He4_Na31
       -rho*Y[jp]*rate_eval.p_Mg34__n_Al34
       )

    jac[jp, jmg35] = (
       -rho*Y[jp]*rate_eval.p_Mg35__n_Al35
       -rho*Y[jp]*rate_eval.p_Mg35__He4_Na32
       -rho*Y[jp]*rate_eval.p_Mg35__Al36
       )

    jac[jp, jmg36] = (
       -rho*Y[jp]*rate_eval.p_Mg36__Al37
       -rho*Y[jp]*rate_eval.p_Mg36__n_Al36
       )

    jac[jp, jmg37] = (
       -rho*Y[jp]*rate_eval.p_Mg37__n_Al37
       -rho*Y[jp]*rate_eval.p_Mg37__Al38
       -rho*Y[jp]*rate_eval.p_Mg37__He4_Na34
       )

    jac[jp, jmg38] = (
       -rho*Y[jp]*rate_eval.p_Mg38__n_Al38
       -rho*Y[jp]*rate_eval.p_Mg38__Al39
       -rho*Y[jp]*rate_eval.p_Mg38__He4_Na35
       )

    jac[jp, jmg39] = (
       -rho*Y[jp]*rate_eval.p_Mg39__n_Al39
       -rho*Y[jp]*rate_eval.p_Mg39__Al40
       -rho*Y[jp]*rate_eval.p_Mg39__He4_Na36
       )

    jac[jp, jmg40] = (
       -rho*Y[jp]*rate_eval.p_Mg40__n_Al40
       -rho*Y[jp]*rate_eval.p_Mg40__Al41
       )

    jac[jp, jmg41] = (
       -rho*Y[jp]*rate_eval.p_Mg41__Al42
       -rho*Y[jp]*rate_eval.p_Mg41__n_Al41
       -rho*Y[jp]*rate_eval.p_Mg41__He4_Na38
       )

    jac[jp, jal21] = (
       +rho*Y[jhe4]*rate_eval.He4_Al21__p_Si24
       +rho*Y[jn]*rate_eval.n_Al21__p_Mg21
       )

    jac[jp, jal22] = (
       -rho*Y[jp]*rate_eval.p_Al22__Si23
       +rho*Y[jhe4]*rate_eval.He4_Al22__p_Si25
       +rho*Y[jn]*rate_eval.n_Al22__p_Mg22
       +2*rate_eval.Al22__p_p_Ne20__weak__wc12
       +rate_eval.Al22__p_Na21__weak__wc17
       )

    jac[jp, jal23] = (
       -rho*Y[jp]*rate_eval.p_Al23__Si24
       +rho*Y[jn]*rate_eval.n_Al23__p_Mg23
       +rho*Y[jhe4]*rate_eval.He4_Al23__p_Si26
       +rate_eval.Al23__p_Na22__weak__wc12
       )

    jac[jp, jal24] = (
       -rho*Y[jp]*rate_eval.p_Al24__Si25
       +rho*Y[jhe4]*rate_eval.He4_Al24__p_Si27
       +rate_eval.Al24__p_Na23__weak__wc12
       +rho*Y[jn]*rate_eval.n_Al24__p_Mg24
       )

    jac[jp, jal25] = (
       -rho*Y[jp]*rate_eval.p_Al25__Si26
       +rho*Y[jn]*rate_eval.n_Al25__p_Mg25
       +rho*Y[jhe4]*rate_eval.He4_Al25__p_Si28
       )

    jac[jp, jal26] = (
       -rho*Y[jp]*rate_eval.p_Al26__Si27
       +rho*Y[jn]*rate_eval.n_Al26__p_Mg26
       +rho*Y[jhe4]*rate_eval.He4_Al26__p_Si29
       )

    jac[jp, jal27] = (
       -rho*Y[jp]*rate_eval.p_Al27__He4_Mg24
       -rho*Y[jp]*rate_eval.p_Al27__Si28
       +rho*Y[jhe4]*rate_eval.He4_Al27__p_Si30
       )

    jac[jp, jal28] = (
       -rho*Y[jp]*rate_eval.p_Al28__He4_Mg25
       -rho*Y[jp]*rate_eval.p_Al28__Si29
       -rho*Y[jp]*rate_eval.p_Al28__n_Si28
       +rho*Y[jhe4]*rate_eval.He4_Al28__p_Si31
       )

    jac[jp, jal29] = (
       -rho*Y[jp]*rate_eval.p_Al29__He4_Mg26
       -rho*Y[jp]*rate_eval.p_Al29__n_Si29
       -rho*Y[jp]*rate_eval.p_Al29__Si30
       +rho*Y[jhe4]*rate_eval.He4_Al29__p_Si32
       )

    jac[jp, jal30] = (
       -rho*Y[jp]*rate_eval.p_Al30__He4_Mg27
       -rho*Y[jp]*rate_eval.p_Al30__n_Si30
       -rho*Y[jp]*rate_eval.p_Al30__Si31
       )

    jac[jp, jal31] = (
       -rho*Y[jp]*rate_eval.p_Al31__He4_Mg28
       -rho*Y[jp]*rate_eval.p_Al31__Si32
       -rho*Y[jp]*rate_eval.p_Al31__n_Si31
       +rho*Y[jhe4]*rate_eval.He4_Al31__p_Si34
       )

    jac[jp, jal32] = (
       -rho*Y[jp]*rate_eval.p_Al32__He4_Mg29
       -rho*Y[jp]*rate_eval.p_Al32__n_Si32
       -rho*Y[jp]*rate_eval.p_Al32__Si33
       )

    jac[jp, jal33] = (
       -rho*Y[jp]*rate_eval.p_Al33__He4_Mg30
       -rho*Y[jp]*rate_eval.p_Al33__n_Si33
       -rho*Y[jp]*rate_eval.p_Al33__Si34
       )

    jac[jp, jal34] = (
       -rho*Y[jp]*rate_eval.p_Al34__He4_Mg31
       -rho*Y[jp]*rate_eval.p_Al34__n_Si34
       -rho*Y[jp]*rate_eval.p_Al34__Si35
       )

    jac[jp, jal35] = (
       -rho*Y[jp]*rate_eval.p_Al35__He4_Mg32
       -rho*Y[jp]*rate_eval.p_Al35__n_Si35
       -rho*Y[jp]*rate_eval.p_Al35__Si36
       )

    jac[jp, jal36] = (
       -rho*Y[jp]*rate_eval.p_Al36__He4_Mg33
       -rho*Y[jp]*rate_eval.p_Al36__n_Si36
       -rho*Y[jp]*rate_eval.p_Al36__Si37
       +rho*Y[jhe4]*rate_eval.He4_Al36__p_Si39
       )

    jac[jp, jal37] = (
       -rho*Y[jp]*rate_eval.p_Al37__He4_Mg34
       -rho*Y[jp]*rate_eval.p_Al37__Si38
       -rho*Y[jp]*rate_eval.p_Al37__n_Si37
       )

    jac[jp, jal38] = (
       -rho*Y[jp]*rate_eval.p_Al38__He4_Mg35
       -rho*Y[jp]*rate_eval.p_Al38__n_Si38
       -rho*Y[jp]*rate_eval.p_Al38__Si39
       +rho*Y[jhe4]*rate_eval.He4_Al38__p_Si41
       )

    jac[jp, jal39] = (
       -rho*Y[jp]*rate_eval.p_Al39__He4_Mg36
       -rho*Y[jp]*rate_eval.p_Al39__n_Si39
       -rho*Y[jp]*rate_eval.p_Al39__Si40
       +rho*Y[jhe4]*rate_eval.He4_Al39__p_Si42
       )

    jac[jp, jal40] = (
       -rho*Y[jp]*rate_eval.p_Al40__He4_Mg37
       -rho*Y[jp]*rate_eval.p_Al40__n_Si40
       -rho*Y[jp]*rate_eval.p_Al40__Si41
       +rho*Y[jhe4]*rate_eval.He4_Al40__p_Si43
       )

    jac[jp, jal41] = (
       -rho*Y[jp]*rate_eval.p_Al41__He4_Mg38
       -rho*Y[jp]*rate_eval.p_Al41__n_Si41
       -rho*Y[jp]*rate_eval.p_Al41__Si42
       )

    jac[jp, jal42] = (
       -rho*Y[jp]*rate_eval.p_Al42__He4_Mg39
       -rho*Y[jp]*rate_eval.p_Al42__Si43
       -rho*Y[jp]*rate_eval.p_Al42__n_Si42
       )

    jac[jp, jal43] = (
       -rho*Y[jp]*rate_eval.p_Al43__n_Si43
       -rho*Y[jp]*rate_eval.p_Al43__He4_Mg40
       -rho*Y[jp]*rate_eval.p_Al43__Si44
       )

    jac[jp, jsi22] = (
       +rho*Y[jhe4]*rate_eval.He4_Si22__p_P25
       +rho*Y[jn]*rate_eval.n_Si22__p_Al22
       +rate_eval.Si22__p_Mg21__weak__wc12
       )

    jac[jp, jsi23] = (
       +rho*Y[jhe4]*rate_eval.He4_Si23__p_P26
       +rho*Y[jn]*rate_eval.n_Si23__p_Al23
       +2*rate_eval.Si23__p_p_Na21__weak__wc12
       +rate_eval.Si23__p_Mg22__weak__wc17
       )

    jac[jp, jsi24] = (
       -rho*Y[jp]*rate_eval.p_Si24__P25
       +rho*Y[jn]*rate_eval.n_Si24__p_Al24
       +rho*Y[jhe4]*rate_eval.He4_Si24__p_P27
       +rate_eval.Si24__p_Mg23__weak__wc12
       )

    jac[jp, jsi25] = (
       -rho*Y[jp]*rate_eval.p_Si25__P26
       +rho*Y[jhe4]*rate_eval.He4_Si25__p_P28
       +rho*Y[jn]*rate_eval.n_Si25__p_Al25
       +rate_eval.Si25__p_Mg24__weak__wc12
       )

    jac[jp, jsi26] = (
       -rho*Y[jp]*rate_eval.p_Si26__P27
       +rho*Y[jn]*rate_eval.n_Si26__p_Al26
       +rho*Y[jhe4]*rate_eval.He4_Si26__p_P29
       )

    jac[jp, jsi27] = (
       -rho*Y[jp]*rate_eval.p_Si27__P28
       +rho*Y[jhe4]*rate_eval.He4_Si27__p_P30
       +rho*Y[jn]*rate_eval.n_Si27__p_Al27
       )

    jac[jp, jsi28] = (
       -rho*Y[jp]*rate_eval.p_Si28__P29
       )

    jac[jp, jsi29] = (
       -rho*Y[jp]*rate_eval.p_Si29__P30
       )

    jac[jp, jsi30] = (
       -rho*Y[jp]*rate_eval.p_Si30__P31
       )

    jac[jp, jsi31] = (
       -rho*Y[jp]*rate_eval.p_Si31__P32
       -rho*Y[jp]*rate_eval.p_Si31__n_P31
       )

    jac[jp, jsi32] = (
       -rho*Y[jp]*rate_eval.p_Si32__P33
       )

    jac[jp, jsi33] = (
       -rho*Y[jp]*rate_eval.p_Si33__n_P33
       -rho*Y[jp]*rate_eval.p_Si33__P34
       -rho*Y[jp]*rate_eval.p_Si33__He4_Al30
       )

    jac[jp, jsi34] = (
       -rho*Y[jp]*rate_eval.p_Si34__P35
       -rho*Y[jp]*rate_eval.p_Si34__n_P34
       )

    jac[jp, jsi35] = (
       -rho*Y[jp]*rate_eval.p_Si35__He4_Al32
       -rho*Y[jp]*rate_eval.p_Si35__P36
       -rho*Y[jp]*rate_eval.p_Si35__n_P35
       )

    jac[jp, jsi36] = (
       -rho*Y[jp]*rate_eval.p_Si36__He4_Al33
       -rho*Y[jp]*rate_eval.p_Si36__n_P36
       -rho*Y[jp]*rate_eval.p_Si36__P37
       )

    jac[jp, jsi37] = (
       -rho*Y[jp]*rate_eval.p_Si37__He4_Al34
       -rho*Y[jp]*rate_eval.p_Si37__n_P37
       -rho*Y[jp]*rate_eval.p_Si37__P38
       )

    jac[jp, jsi38] = (
       -rho*Y[jp]*rate_eval.p_Si38__n_P38
       -rho*Y[jp]*rate_eval.p_Si38__P39
       -rho*Y[jp]*rate_eval.p_Si38__He4_Al35
       )

    jac[jp, jsi39] = (
       -rho*Y[jp]*rate_eval.p_Si39__n_P39
       -rho*Y[jp]*rate_eval.p_Si39__P40
       )

    jac[jp, jsi40] = (
       -rho*Y[jp]*rate_eval.p_Si40__P41
       -rho*Y[jp]*rate_eval.p_Si40__n_P40
       -rho*Y[jp]*rate_eval.p_Si40__He4_Al37
       )

    jac[jp, jsi41] = (
       -rho*Y[jp]*rate_eval.p_Si41__P42
       -rho*Y[jp]*rate_eval.p_Si41__n_P41
       )

    jac[jp, jsi42] = (
       -rho*Y[jp]*rate_eval.p_Si42__n_P42
       -rho*Y[jp]*rate_eval.p_Si42__P43
       )

    jac[jp, jsi43] = (
       -rho*Y[jp]*rate_eval.p_Si43__n_P43
       -rho*Y[jp]*rate_eval.p_Si43__P44
       )

    jac[jp, jsi44] = (
       -rho*Y[jp]*rate_eval.p_Si44__n_P44
       -rho*Y[jp]*rate_eval.p_Si44__He4_Al41
       -rho*Y[jp]*rate_eval.p_Si44__P45
       )

    jac[jp, jsi45] = (
       -rho*Y[jp]*rate_eval.p_Si45__P46
       -rho*Y[jp]*rate_eval.p_Si45__He4_Al42
       -rho*Y[jp]*rate_eval.p_Si45__n_P45
       )

    jac[jp, jp24] = (
       +rho*Y[jhe4]*rate_eval.He4_P24__p_S27
       +rho*Y[jn]*rate_eval.n_P24__p_Si24
       )

    jac[jp, jp25] = (
       -rho*Y[jp]*rate_eval.p_P25__S26
       +rho*Y[jhe4]*rate_eval.He4_P25__p_S28
       +rho*Y[jn]*rate_eval.n_P25__p_Si25
       )

    jac[jp, jp26] = (
       -rho*Y[jp]*rate_eval.p_P26__S27
       +rho*Y[jhe4]*rate_eval.He4_P26__p_S29
       +rho*Y[jn]*rate_eval.n_P26__p_Si26
       )

    jac[jp, jp27] = (
       -rho*Y[jp]*rate_eval.p_P27__S28
       +rate_eval.P27__p_Al26__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_P27__p_S30
       +rho*Y[jn]*rate_eval.n_P27__p_Si27
       )

    jac[jp, jp28] = (
       -rho*Y[jp]*rate_eval.p_P28__S29
       +rho*Y[jn]*rate_eval.n_P28__p_Si28
       +rho*Y[jhe4]*rate_eval.He4_P28__p_S31
       +rate_eval.P28__p_Al27__weak__wc12
       )

    jac[jp, jp29] = (
       -rho*Y[jp]*rate_eval.p_P29__S30
       +rho*Y[jhe4]*rate_eval.He4_P29__p_S32
       +rho*Y[jn]*rate_eval.n_P29__p_Si29
       )

    jac[jp, jp30] = (
       -rho*Y[jp]*rate_eval.p_P30__S31
       +rho*Y[jhe4]*rate_eval.He4_P30__p_S33
       +rho*Y[jn]*rate_eval.n_P30__p_Si30
       )

    jac[jp, jp31] = (
       -rho*Y[jp]*rate_eval.p_P31__S32
       -rho*Y[jp]*rate_eval.p_P31__He4_Si28
       +rho*Y[jhe4]*rate_eval.He4_P31__p_S34
       )

    jac[jp, jp32] = (
       -rho*Y[jp]*rate_eval.p_P32__n_S32
       -rho*Y[jp]*rate_eval.p_P32__He4_Si29
       -rho*Y[jp]*rate_eval.p_P32__S33
       +rho*Y[jn]*rate_eval.n_P32__p_Si32
       )

    jac[jp, jp33] = (
       -rho*Y[jp]*rate_eval.p_P33__He4_Si30
       -rho*Y[jp]*rate_eval.p_P33__S34
       )

    jac[jp, jp34] = (
       -rho*Y[jp]*rate_eval.p_P34__n_S34
       -rho*Y[jp]*rate_eval.p_P34__S35
       -rho*Y[jp]*rate_eval.p_P34__He4_Si31
       )

    jac[jp, jp35] = (
       -rho*Y[jp]*rate_eval.p_P35__S36
       -rho*Y[jp]*rate_eval.p_P35__n_S35
       -rho*Y[jp]*rate_eval.p_P35__He4_Si32
       )

    jac[jp, jp36] = (
       -rho*Y[jp]*rate_eval.p_P36__He4_Si33
       -rho*Y[jp]*rate_eval.p_P36__n_S36
       -rho*Y[jp]*rate_eval.p_P36__S37
       )

    jac[jp, jp37] = (
       -rho*Y[jp]*rate_eval.p_P37__He4_Si34
       -rho*Y[jp]*rate_eval.p_P37__S38
       -rho*Y[jp]*rate_eval.p_P37__n_S37
       )

    jac[jp, jp38] = (
       -rho*Y[jp]*rate_eval.p_P38__He4_Si35
       -rho*Y[jp]*rate_eval.p_P38__n_S38
       -rho*Y[jp]*rate_eval.p_P38__S39
       )

    jac[jp, jp39] = (
       -rho*Y[jp]*rate_eval.p_P39__n_S39
       -rho*Y[jp]*rate_eval.p_P39__He4_Si36
       -rho*Y[jp]*rate_eval.p_P39__S40
       )

    jac[jp, jp40] = (
       -rho*Y[jp]*rate_eval.p_P40__n_S40
       -rho*Y[jp]*rate_eval.p_P40__S41
       -rho*Y[jp]*rate_eval.p_P40__He4_Si37
       )

    jac[jp, jp41] = (
       -rho*Y[jp]*rate_eval.p_P41__n_S41
       -rho*Y[jp]*rate_eval.p_P41__S42
       -rho*Y[jp]*rate_eval.p_P41__He4_Si38
       +rho*Y[jhe4]*rate_eval.He4_P41__p_S44
       )

    jac[jp, jp42] = (
       -rho*Y[jp]*rate_eval.p_P42__n_S42
       -rho*Y[jp]*rate_eval.p_P42__He4_Si39
       -rho*Y[jp]*rate_eval.p_P42__S43
       )

    jac[jp, jp43] = (
       -rho*Y[jp]*rate_eval.p_P43__He4_Si40
       -rho*Y[jp]*rate_eval.p_P43__n_S43
       -rho*Y[jp]*rate_eval.p_P43__S44
       )

    jac[jp, jp44] = (
       -rho*Y[jp]*rate_eval.p_P44__He4_Si41
       -rho*Y[jp]*rate_eval.p_P44__n_S44
       -rho*Y[jp]*rate_eval.p_P44__S45
       )

    jac[jp, jp45] = (
       -rho*Y[jp]*rate_eval.p_P45__S46
       -rho*Y[jp]*rate_eval.p_P45__n_S45
       -rho*Y[jp]*rate_eval.p_P45__He4_Si42
       )

    jac[jp, jp46] = (
       -rho*Y[jp]*rate_eval.p_P46__S47
       -rho*Y[jp]*rate_eval.p_P46__He4_Si43
       -rho*Y[jp]*rate_eval.p_P46__n_S46
       )

    jac[jp, jp47] = (
       -rho*Y[jp]*rate_eval.p_P47__n_S47
       -rho*Y[jp]*rate_eval.p_P47__He4_Si44
       -rho*Y[jp]*rate_eval.p_P47__S48
       )

    jac[jp, js26] = (
       +rho*Y[jhe4]*rate_eval.He4_S26__p_Cl29
       +rho*Y[jn]*rate_eval.n_S26__p_P26
       )

    jac[jp, js27] = (
       -rho*Y[jp]*rate_eval.p_S27__Cl28
       +rho*Y[jhe4]*rate_eval.He4_S27__p_Cl30
       +rate_eval.S27__p_Si26__weak__wc17
       +2*rate_eval.S27__p_p_Al25__weak__wc12
       +rho*Y[jn]*rate_eval.n_S27__p_P27
       )

    jac[jp, js28] = (
       -rho*Y[jp]*rate_eval.p_S28__Cl29
       +rho*Y[jhe4]*rate_eval.He4_S28__p_Cl31
       +rate_eval.S28__p_Si27__weak__wc12
       +rho*Y[jn]*rate_eval.n_S28__p_P28
       )

    jac[jp, js29] = (
       -rho*Y[jp]*rate_eval.p_S29__Cl30
       +rho*Y[jhe4]*rate_eval.He4_S29__p_Cl32
       +rho*Y[jn]*rate_eval.n_S29__p_P29
       +rate_eval.S29__p_Si28__weak__wc12
       )

    jac[jp, js30] = (
       -rho*Y[jp]*rate_eval.p_S30__Cl31
       +rho*Y[jhe4]*rate_eval.He4_S30__p_Cl33
       +rho*Y[jn]*rate_eval.n_S30__p_P30
       )

    jac[jp, js31] = (
       -rho*Y[jp]*rate_eval.p_S31__Cl32
       +rho*Y[jhe4]*rate_eval.He4_S31__p_Cl34
       +rho*Y[jn]*rate_eval.n_S31__p_P31
       )

    jac[jp, js32] = (
       -rho*Y[jp]*rate_eval.p_S32__Cl33
       )

    jac[jp, js33] = (
       -rho*Y[jp]*rate_eval.p_S33__Cl34
       +rho*Y[jn]*rate_eval.n_S33__p_P33
       )

    jac[jp, js34] = (
       -rho*Y[jp]*rate_eval.p_S34__Cl35
       +rho*Y[jhe4]*rate_eval.He4_S34__p_Cl37
       )

    jac[jp, js35] = (
       -rho*Y[jp]*rate_eval.p_S35__He4_P32
       -rho*Y[jp]*rate_eval.p_S35__Cl36
       )

    jac[jp, js36] = (
       -rho*Y[jp]*rate_eval.p_S36__He4_P33
       -rho*Y[jp]*rate_eval.p_S36__Cl37
       )

    jac[jp, js37] = (
       -rho*Y[jp]*rate_eval.p_S37__Cl38
       -rho*Y[jp]*rate_eval.p_S37__n_Cl37
       -rho*Y[jp]*rate_eval.p_S37__He4_P34
       )

    jac[jp, js38] = (
       -rho*Y[jp]*rate_eval.p_S38__He4_P35
       -rho*Y[jp]*rate_eval.p_S38__n_Cl38
       -rho*Y[jp]*rate_eval.p_S38__Cl39
       )

    jac[jp, js39] = (
       -rho*Y[jp]*rate_eval.p_S39__He4_P36
       -rho*Y[jp]*rate_eval.p_S39__Cl40
       -rho*Y[jp]*rate_eval.p_S39__n_Cl39
       )

    jac[jp, js40] = (
       -rho*Y[jp]*rate_eval.p_S40__n_Cl40
       -rho*Y[jp]*rate_eval.p_S40__Cl41
       -rho*Y[jp]*rate_eval.p_S40__He4_P37
       )

    jac[jp, js41] = (
       -rho*Y[jp]*rate_eval.p_S41__He4_P38
       -rho*Y[jp]*rate_eval.p_S41__Cl42
       -rho*Y[jp]*rate_eval.p_S41__n_Cl41
       )

    jac[jp, js42] = (
       -rho*Y[jp]*rate_eval.p_S42__Cl43
       -rho*Y[jp]*rate_eval.p_S42__n_Cl42
       -rho*Y[jp]*rate_eval.p_S42__He4_P39
       )

    jac[jp, js43] = (
       -rho*Y[jp]*rate_eval.p_S43__He4_P40
       -rho*Y[jp]*rate_eval.p_S43__n_Cl43
       -rho*Y[jp]*rate_eval.p_S43__Cl44
       )

    jac[jp, js44] = (
       -rho*Y[jp]*rate_eval.p_S44__Cl45
       -rho*Y[jp]*rate_eval.p_S44__n_Cl44
       )

    jac[jp, js45] = (
       -rho*Y[jp]*rate_eval.p_S45__He4_P42
       -rho*Y[jp]*rate_eval.p_S45__n_Cl45
       -rho*Y[jp]*rate_eval.p_S45__Cl46
       )

    jac[jp, js46] = (
       -rho*Y[jp]*rate_eval.p_S46__n_Cl46
       -rho*Y[jp]*rate_eval.p_S46__Cl47
       -rho*Y[jp]*rate_eval.p_S46__He4_P43
       )

    jac[jp, js47] = (
       -rho*Y[jp]*rate_eval.p_S47__Cl48
       -rho*Y[jp]*rate_eval.p_S47__n_Cl47
       -rho*Y[jp]*rate_eval.p_S47__He4_P44
       )

    jac[jp, js48] = (
       -rho*Y[jp]*rate_eval.p_S48__n_Cl48
       -rho*Y[jp]*rate_eval.p_S48__He4_P45
       -rho*Y[jp]*rate_eval.p_S48__Cl49
       )

    jac[jp, js49] = (
       -rho*Y[jp]*rate_eval.p_S49__n_Cl49
       -rho*Y[jp]*rate_eval.p_S49__Cl50
       -rho*Y[jp]*rate_eval.p_S49__He4_P46
       )

    jac[jp, jcl28] = (
       -rho*Y[jp]*rate_eval.p_Cl28__Ar29
       +rho*Y[jhe4]*rate_eval.He4_Cl28__p_Ar31
       +rho*Y[jn]*rate_eval.n_Cl28__p_S28
       )

    jac[jp, jcl29] = (
       -rho*Y[jp]*rate_eval.p_Cl29__Ar30
       +rho*Y[jn]*rate_eval.n_Cl29__p_S29
       +rho*Y[jhe4]*rate_eval.He4_Cl29__p_Ar32
       )

    jac[jp, jcl30] = (
       -rho*Y[jp]*rate_eval.p_Cl30__Ar31
       +rho*Y[jhe4]*rate_eval.He4_Cl30__p_Ar33
       +rho*Y[jn]*rate_eval.n_Cl30__p_S30
       )

    jac[jp, jcl31] = (
       -rho*Y[jp]*rate_eval.p_Cl31__Ar32
       +rho*Y[jn]*rate_eval.n_Cl31__p_S31
       +rate_eval.Cl31__p_P30__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Cl31__p_Ar34
       )

    jac[jp, jcl32] = (
       -rho*Y[jp]*rate_eval.p_Cl32__Ar33
       +rho*Y[jhe4]*rate_eval.He4_Cl32__p_Ar35
       +rho*Y[jn]*rate_eval.n_Cl32__p_S32
       +rate_eval.Cl32__p_P31__weak__wc12
       )

    jac[jp, jcl33] = (
       -rho*Y[jp]*rate_eval.p_Cl33__Ar34
       +rho*Y[jn]*rate_eval.n_Cl33__p_S33
       +rho*Y[jhe4]*rate_eval.He4_Cl33__p_Ar36
       )

    jac[jp, jcl34] = (
       -rho*Y[jp]*rate_eval.p_Cl34__Ar35
       +rho*Y[jhe4]*rate_eval.He4_Cl34__p_Ar37
       +rho*Y[jn]*rate_eval.n_Cl34__p_S34
       )

    jac[jp, jcl35] = (
       -rho*Y[jp]*rate_eval.p_Cl35__He4_S32
       -rho*Y[jp]*rate_eval.p_Cl35__Ar36
       +rho*Y[jn]*rate_eval.n_Cl35__p_S35
       +rho*Y[jhe4]*rate_eval.He4_Cl35__p_Ar38
       )

    jac[jp, jcl36] = (
       -rho*Y[jp]*rate_eval.p_Cl36__Ar37
       -rho*Y[jp]*rate_eval.p_Cl36__He4_S33
       +rho*Y[jn]*rate_eval.n_Cl36__p_S36
       )

    jac[jp, jcl37] = (
       -rho*Y[jp]*rate_eval.p_Cl37__Ar38
       )

    jac[jp, jcl38] = (
       -rho*Y[jp]*rate_eval.p_Cl38__He4_S35
       -rho*Y[jp]*rate_eval.p_Cl38__n_Ar38
       -rho*Y[jp]*rate_eval.p_Cl38__Ar39
       )

    jac[jp, jcl39] = (
       -rho*Y[jp]*rate_eval.p_Cl39__He4_S36
       -rho*Y[jp]*rate_eval.p_Cl39__Ar40
       -rho*Y[jp]*rate_eval.p_Cl39__n_Ar39
       )

    jac[jp, jcl40] = (
       -rho*Y[jp]*rate_eval.p_Cl40__n_Ar40
       -rho*Y[jp]*rate_eval.p_Cl40__He4_S37
       -rho*Y[jp]*rate_eval.p_Cl40__Ar41
       )

    jac[jp, jcl41] = (
       -rho*Y[jp]*rate_eval.p_Cl41__He4_S38
       -rho*Y[jp]*rate_eval.p_Cl41__Ar42
       -rho*Y[jp]*rate_eval.p_Cl41__n_Ar41
       +rho*Y[jhe4]*rate_eval.He4_Cl41__p_Ar44
       )

    jac[jp, jcl42] = (
       -rho*Y[jp]*rate_eval.p_Cl42__He4_S39
       -rho*Y[jp]*rate_eval.p_Cl42__n_Ar42
       -rho*Y[jp]*rate_eval.p_Cl42__Ar43
       )

    jac[jp, jcl43] = (
       -rho*Y[jp]*rate_eval.p_Cl43__He4_S40
       -rho*Y[jp]*rate_eval.p_Cl43__Ar44
       -rho*Y[jp]*rate_eval.p_Cl43__n_Ar43
       +rho*Y[jhe4]*rate_eval.He4_Cl43__p_Ar46
       )

    jac[jp, jcl44] = (
       -rho*Y[jp]*rate_eval.p_Cl44__Ar45
       -rho*Y[jp]*rate_eval.p_Cl44__n_Ar44
       -rho*Y[jp]*rate_eval.p_Cl44__He4_S41
       +rho*Y[jhe4]*rate_eval.He4_Cl44__p_Ar47
       )

    jac[jp, jcl45] = (
       -rho*Y[jp]*rate_eval.p_Cl45__He4_S42
       -rho*Y[jp]*rate_eval.p_Cl45__n_Ar45
       -rho*Y[jp]*rate_eval.p_Cl45__Ar46
       )

    jac[jp, jcl46] = (
       -rho*Y[jp]*rate_eval.p_Cl46__He4_S43
       -rho*Y[jp]*rate_eval.p_Cl46__n_Ar46
       -rho*Y[jp]*rate_eval.p_Cl46__Ar47
       )

    jac[jp, jcl47] = (
       -rho*Y[jp]*rate_eval.p_Cl47__Ar48
       -rho*Y[jp]*rate_eval.p_Cl47__n_Ar47
       -rho*Y[jp]*rate_eval.p_Cl47__He4_S44
       )

    jac[jp, jcl48] = (
       -rho*Y[jp]*rate_eval.p_Cl48__He4_S45
       -rho*Y[jp]*rate_eval.p_Cl48__n_Ar48
       -rho*Y[jp]*rate_eval.p_Cl48__Ar49
       )

    jac[jp, jcl49] = (
       -rho*Y[jp]*rate_eval.p_Cl49__Ar50
       -rho*Y[jp]*rate_eval.p_Cl49__He4_S46
       -rho*Y[jp]*rate_eval.p_Cl49__n_Ar49
       )

    jac[jp, jcl50] = (
       -rho*Y[jp]*rate_eval.p_Cl50__He4_S47
       -rho*Y[jp]*rate_eval.p_Cl50__n_Ar50
       -rho*Y[jp]*rate_eval.p_Cl50__Ar51
       )

    jac[jp, jcl51] = (
       -rho*Y[jp]*rate_eval.p_Cl51__He4_S48
       -rho*Y[jp]*rate_eval.p_Cl51__Ar52
       -rho*Y[jp]*rate_eval.p_Cl51__n_Ar51
       )

    jac[jp, jcl52] = (
       -rho*Y[jp]*rate_eval.p_Cl52__He4_S49
       -rho*Y[jp]*rate_eval.p_Cl52__n_Ar52
       -rho*Y[jp]*rate_eval.p_Cl52__Ar53
       )

    jac[jp, jar29] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar29__p_K32
       +rho*Y[jn]*rate_eval.n_Ar29__p_Cl29
       )

    jac[jp, jar30] = (
       -rho*Y[jp]*rate_eval.p_Ar30__K31
       +rho*Y[jn]*rate_eval.n_Ar30__p_Cl30
       +rho*Y[jhe4]*rate_eval.He4_Ar30__p_K33
       )

    jac[jp, jar31] = (
       -rho*Y[jp]*rate_eval.p_Ar31__K32
       +rho*Y[jhe4]*rate_eval.He4_Ar31__p_K34
       +rho*Y[jn]*rate_eval.n_Ar31__p_Cl31
       +rate_eval.Ar31__p_S30__weak__wc17
       +2*rate_eval.Ar31__p_p_P29__weak__wc12
       )

    jac[jp, jar32] = (
       -rho*Y[jp]*rate_eval.p_Ar32__K33
       +rho*Y[jn]*rate_eval.n_Ar32__p_Cl32
       +rate_eval.Ar32__p_S31__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Ar32__p_K35
       )

    jac[jp, jar33] = (
       -rho*Y[jp]*rate_eval.p_Ar33__K34
       +rho*Y[jhe4]*rate_eval.He4_Ar33__p_K36
       +rho*Y[jn]*rate_eval.n_Ar33__p_Cl33
       +rate_eval.Ar33__p_S32__weak__wc12
       )

    jac[jp, jar34] = (
       -rho*Y[jp]*rate_eval.p_Ar34__K35
       +rho*Y[jhe4]*rate_eval.He4_Ar34__p_K37
       +rho*Y[jn]*rate_eval.n_Ar34__p_Cl34
       )

    jac[jp, jar35] = (
       -rho*Y[jp]*rate_eval.p_Ar35__K36
       +rho*Y[jn]*rate_eval.n_Ar35__p_Cl35
       +rho*Y[jhe4]*rate_eval.He4_Ar35__p_K38
       )

    jac[jp, jar36] = (
       -rho*Y[jp]*rate_eval.p_Ar36__K37
       +rho*Y[jn]*rate_eval.n_Ar36__p_Cl36
       )

    jac[jp, jar37] = (
       -rho*Y[jp]*rate_eval.p_Ar37__K38
       +rho*Y[jn]*rate_eval.n_Ar37__p_Cl37
       )

    jac[jp, jar38] = (
       -rho*Y[jp]*rate_eval.p_Ar38__K39
       )

    jac[jp, jar39] = (
       -rho*Y[jp]*rate_eval.p_Ar39__He4_Cl36
       -rho*Y[jp]*rate_eval.p_Ar39__K40
       )

    jac[jp, jar40] = (
       -rho*Y[jp]*rate_eval.p_Ar40__He4_Cl37
       -rho*Y[jp]*rate_eval.p_Ar40__K41
       )

    jac[jp, jar41] = (
       -rho*Y[jp]*rate_eval.p_Ar41__n_K41
       -rho*Y[jp]*rate_eval.p_Ar41__K42
       -rho*Y[jp]*rate_eval.p_Ar41__He4_Cl38
       )

    jac[jp, jar42] = (
       -rho*Y[jp]*rate_eval.p_Ar42__K43
       -rho*Y[jp]*rate_eval.p_Ar42__He4_Cl39
       )

    jac[jp, jar43] = (
       -rho*Y[jp]*rate_eval.p_Ar43__n_K43
       -rho*Y[jp]*rate_eval.p_Ar43__He4_Cl40
       -rho*Y[jp]*rate_eval.p_Ar43__K44
       )

    jac[jp, jar44] = (
       -rho*Y[jp]*rate_eval.p_Ar44__n_K44
       -rho*Y[jp]*rate_eval.p_Ar44__K45
       )

    jac[jp, jar45] = (
       -rho*Y[jp]*rate_eval.p_Ar45__He4_Cl42
       -rho*Y[jp]*rate_eval.p_Ar45__n_K45
       -rho*Y[jp]*rate_eval.p_Ar45__K46
       )

    jac[jp, jar46] = (
       -rho*Y[jp]*rate_eval.p_Ar46__K47
       -rho*Y[jp]*rate_eval.p_Ar46__n_K46
       )

    jac[jp, jar47] = (
       -rho*Y[jp]*rate_eval.p_Ar47__n_K47
       -rho*Y[jp]*rate_eval.p_Ar47__K48
       )

    jac[jp, jar48] = (
       -rho*Y[jp]*rate_eval.p_Ar48__He4_Cl45
       -rho*Y[jp]*rate_eval.p_Ar48__n_K48
       -rho*Y[jp]*rate_eval.p_Ar48__K49
       )

    jac[jp, jar49] = (
       -rho*Y[jp]*rate_eval.p_Ar49__n_K49
       -rho*Y[jp]*rate_eval.p_Ar49__K50
       -rho*Y[jp]*rate_eval.p_Ar49__He4_Cl46
       )

    jac[jp, jar50] = (
       -rho*Y[jp]*rate_eval.p_Ar50__He4_Cl47
       -rho*Y[jp]*rate_eval.p_Ar50__n_K50
       -rho*Y[jp]*rate_eval.p_Ar50__K51
       )

    jac[jp, jar51] = (
       -rho*Y[jp]*rate_eval.p_Ar51__He4_Cl48
       -rho*Y[jp]*rate_eval.p_Ar51__K52
       -rho*Y[jp]*rate_eval.p_Ar51__n_K51
       )

    jac[jp, jar52] = (
       -rho*Y[jp]*rate_eval.p_Ar52__He4_Cl49
       -rho*Y[jp]*rate_eval.p_Ar52__n_K52
       -rho*Y[jp]*rate_eval.p_Ar52__K53
       )

    jac[jp, jar53] = (
       -rho*Y[jp]*rate_eval.p_Ar53__He4_Cl50
       -rho*Y[jp]*rate_eval.p_Ar53__n_K53
       -rho*Y[jp]*rate_eval.p_Ar53__K54
       )

    jac[jp, jar54] = (
       -rho*Y[jp]*rate_eval.p_Ar54__n_K54
       -rho*Y[jp]*rate_eval.p_Ar54__He4_Cl51
       -rho*Y[jp]*rate_eval.p_Ar54__K55
       )

    jac[jp, jk31] = (
       +rho*Y[jhe4]*rate_eval.He4_K31__p_Ca34
       +rho*Y[jn]*rate_eval.n_K31__p_Ar31
       )

    jac[jp, jk32] = (
       -rho*Y[jp]*rate_eval.p_K32__Ca33
       +rho*Y[jn]*rate_eval.n_K32__p_Ar32
       +rho*Y[jhe4]*rate_eval.He4_K32__p_Ca35
       )

    jac[jp, jk33] = (
       -rho*Y[jp]*rate_eval.p_K33__Ca34
       +rho*Y[jn]*rate_eval.n_K33__p_Ar33
       +rho*Y[jhe4]*rate_eval.He4_K33__p_Ca36
       )

    jac[jp, jk34] = (
       -rho*Y[jp]*rate_eval.p_K34__Ca35
       +rho*Y[jhe4]*rate_eval.He4_K34__p_Ca37
       +rho*Y[jn]*rate_eval.n_K34__p_Ar34
       )

    jac[jp, jk35] = (
       -rho*Y[jp]*rate_eval.p_K35__Ca36
       +rho*Y[jn]*rate_eval.n_K35__p_Ar35
       +rho*Y[jhe4]*rate_eval.He4_K35__p_Ca38
       +rate_eval.K35__p_Cl34__weak__wc12
       )

    jac[jp, jk36] = (
       -rho*Y[jp]*rate_eval.p_K36__Ca37
       +rho*Y[jhe4]*rate_eval.He4_K36__p_Ca39
       +rho*Y[jn]*rate_eval.n_K36__p_Ar36
       +rate_eval.K36__p_Cl35__weak__wc12
       )

    jac[jp, jk37] = (
       -rho*Y[jp]*rate_eval.p_K37__Ca38
       +rho*Y[jhe4]*rate_eval.He4_K37__p_Ca40
       +rho*Y[jn]*rate_eval.n_K37__p_Ar37
       )

    jac[jp, jk38] = (
       -rho*Y[jp]*rate_eval.p_K38__Ca39
       +rho*Y[jn]*rate_eval.n_K38__p_Ar38
       +rho*Y[jhe4]*rate_eval.He4_K38__p_Ca41
       )

    jac[jp, jk39] = (
       -rho*Y[jp]*rate_eval.p_K39__Ca40
       -rho*Y[jp]*rate_eval.p_K39__He4_Ar36
       +rho*Y[jn]*rate_eval.n_K39__p_Ar39
       )

    jac[jp, jk40] = (
       -rho*Y[jp]*rate_eval.p_K40__He4_Ar37
       -rho*Y[jp]*rate_eval.p_K40__n_Ca40
       -rho*Y[jp]*rate_eval.p_K40__Ca41
       +rho*Y[jn]*rate_eval.n_K40__p_Ar40
       +rho*Y[jhe4]*rate_eval.He4_K40__p_Ca43
       )

    jac[jp, jk41] = (
       -rho*Y[jp]*rate_eval.p_K41__He4_Ar38
       -rho*Y[jp]*rate_eval.p_K41__n_Ca41
       -rho*Y[jp]*rate_eval.p_K41__Ca42
       +rho*Y[jhe4]*rate_eval.He4_K41__p_Ca44
       )

    jac[jp, jk42] = (
       -rho*Y[jp]*rate_eval.p_K42__n_Ca42
       -rho*Y[jp]*rate_eval.p_K42__He4_Ar39
       -rho*Y[jp]*rate_eval.p_K42__Ca43
       +rho*Y[jhe4]*rate_eval.He4_K42__p_Ca45
       +rho*Y[jn]*rate_eval.n_K42__p_Ar42
       )

    jac[jp, jk43] = (
       -rho*Y[jp]*rate_eval.p_K43__n_Ca43
       -rho*Y[jp]*rate_eval.p_K43__Ca44
       -rho*Y[jp]*rate_eval.p_K43__He4_Ar40
       +rho*Y[jhe4]*rate_eval.He4_K43__p_Ca46
       )

    jac[jp, jk44] = (
       -rho*Y[jp]*rate_eval.p_K44__He4_Ar41
       -rho*Y[jp]*rate_eval.p_K44__n_Ca44
       -rho*Y[jp]*rate_eval.p_K44__Ca45
       +rho*Y[jhe4]*rate_eval.He4_K44__p_Ca47
       )

    jac[jp, jk45] = (
       -rho*Y[jp]*rate_eval.p_K45__He4_Ar42
       -rho*Y[jp]*rate_eval.p_K45__n_Ca45
       -rho*Y[jp]*rate_eval.p_K45__Ca46
       +rho*Y[jhe4]*rate_eval.He4_K45__p_Ca48
       )

    jac[jp, jk46] = (
       -rho*Y[jp]*rate_eval.p_K46__Ca47
       -rho*Y[jp]*rate_eval.p_K46__He4_Ar43
       -rho*Y[jp]*rate_eval.p_K46__n_Ca46
       +rho*Y[jhe4]*rate_eval.He4_K46__p_Ca49
       )

    jac[jp, jk47] = (
       -rho*Y[jp]*rate_eval.p_K47__He4_Ar44
       -rho*Y[jp]*rate_eval.p_K47__n_Ca47
       -rho*Y[jp]*rate_eval.p_K47__Ca48
       )

    jac[jp, jk48] = (
       -rho*Y[jp]*rate_eval.p_K48__Ca49
       -rho*Y[jp]*rate_eval.p_K48__He4_Ar45
       -rho*Y[jp]*rate_eval.p_K48__n_Ca48
       )

    jac[jp, jk49] = (
       -rho*Y[jp]*rate_eval.p_K49__n_Ca49
       -rho*Y[jp]*rate_eval.p_K49__Ca50
       -rho*Y[jp]*rate_eval.p_K49__He4_Ar46
       )

    jac[jp, jk50] = (
       -rho*Y[jp]*rate_eval.p_K50__n_Ca50
       -rho*Y[jp]*rate_eval.p_K50__He4_Ar47
       -rho*Y[jp]*rate_eval.p_K50__Ca51
       )

    jac[jp, jk51] = (
       -rho*Y[jp]*rate_eval.p_K51__n_Ca51
       -rho*Y[jp]*rate_eval.p_K51__He4_Ar48
       -rho*Y[jp]*rate_eval.p_K51__Ca52
       )

    jac[jp, jk52] = (
       -rho*Y[jp]*rate_eval.p_K52__He4_Ar49
       -rho*Y[jp]*rate_eval.p_K52__Ca53
       -rho*Y[jp]*rate_eval.p_K52__n_Ca52
       )

    jac[jp, jk53] = (
       -rho*Y[jp]*rate_eval.p_K53__n_Ca53
       -rho*Y[jp]*rate_eval.p_K53__Ca54
       -rho*Y[jp]*rate_eval.p_K53__He4_Ar50
       )

    jac[jp, jk54] = (
       -rho*Y[jp]*rate_eval.p_K54__n_Ca54
       -rho*Y[jp]*rate_eval.p_K54__Ca55
       -rho*Y[jp]*rate_eval.p_K54__He4_Ar51
       )

    jac[jp, jk55] = (
       -rho*Y[jp]*rate_eval.p_K55__n_Ca55
       -rho*Y[jp]*rate_eval.p_K55__Ca56
       -rho*Y[jp]*rate_eval.p_K55__He4_Ar52
       )

    jac[jp, jk56] = (
       -rho*Y[jp]*rate_eval.p_K56__n_Ca56
       -rho*Y[jp]*rate_eval.p_K56__He4_Ar53
       -rho*Y[jp]*rate_eval.p_K56__Ca57
       )

    jac[jp, jk57] = (
       -rho*Y[jp]*rate_eval.p_K57__He4_Ar54
       -rho*Y[jp]*rate_eval.p_K57__n_Ca57
       -rho*Y[jp]*rate_eval.p_K57__Ca58
       )

    jac[jp, jk58] = (
       -rho*Y[jp]*rate_eval.p_K58__n_Ca58
       -rho*Y[jp]*rate_eval.p_K58__Ca59
       )

    jac[jp, jk59] = (
       -rho*Y[jp]*rate_eval.p_K59__n_Ca59
       -rho*Y[jp]*rate_eval.p_K59__Ca60
       )

    jac[jp, jca33] = (
       +rho*Y[jn]*rate_eval.n_Ca33__p_K33
       +rho*Y[jhe4]*rate_eval.He4_Ca33__p_Sc36
       )

    jac[jp, jca34] = (
       -rho*Y[jp]*rate_eval.p_Ca34__Sc35
       +rho*Y[jn]*rate_eval.n_Ca34__p_K34
       +rho*Y[jhe4]*rate_eval.He4_Ca34__p_Sc37
       )

    jac[jp, jca35] = (
       -rho*Y[jp]*rate_eval.p_Ca35__Sc36
       +rho*Y[jn]*rate_eval.n_Ca35__p_K35
       +2*rate_eval.Ca35__p_p_Cl33__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Ca35__p_Sc38
       +rate_eval.Ca35__p_Ar34__weak__wc17
       )

    jac[jp, jca36] = (
       -rho*Y[jp]*rate_eval.p_Ca36__Sc37
       +2*rho*Y[jhe4]*rate_eval.He4_Ca36__p_p_Ca38
       +rho*Y[jn]*rate_eval.n_Ca36__p_K36
       +rho*Y[jhe4]*rate_eval.He4_Ca36__p_Sc39
       +rate_eval.Ca36__p_Ar35__weak__wc12
       )

    jac[jp, jca37] = (
       -rho*Y[jp]*rate_eval.p_Ca37__Sc38
       +rho*Y[jn]*rate_eval.n_Ca37__p_K37
       +rho*Y[jhe4]*rate_eval.He4_Ca37__p_Sc40
       +rate_eval.Ca37__p_Ar36__weak__wc12
       )

    jac[jp, jca38] = (
       -rho*Y[jp]*rate_eval.p_Ca38__Sc39
       +rho*Y[jn]*rate_eval.n_Ca38__p_K38
       +rho*Y[jhe4]*rate_eval.He4_Ca38__p_Sc41
       )

    jac[jp, jca39] = (
       -rho*Y[jp]*rate_eval.p_Ca39__Sc40
       +rho*Y[jn]*rate_eval.n_Ca39__p_K39
       )

    jac[jp, jca40] = (
       -rho*Y[jp]*rate_eval.p_Ca40__Sc41
       )

    jac[jp, jca41] = (
       -rho*Y[jp]*rate_eval.p_Ca41__Sc42
       )

    jac[jp, jca42] = (
       -rho*Y[jp]*rate_eval.p_Ca42__He4_K39
       -rho*Y[jp]*rate_eval.p_Ca42__Sc43
       )

    jac[jp, jca43] = (
       -rho*Y[jp]*rate_eval.p_Ca43__Sc44
       )

    jac[jp, jca44] = (
       -rho*Y[jp]*rate_eval.p_Ca44__Sc45
       )

    jac[jp, jca45] = (
       -rho*Y[jp]*rate_eval.p_Ca45__Sc46
       )

    jac[jp, jca46] = (
       -rho*Y[jp]*rate_eval.p_Ca46__Sc47
       )

    jac[jp, jca47] = (
       -rho*Y[jp]*rate_eval.p_Ca47__n_Sc47
       -rho*Y[jp]*rate_eval.p_Ca47__Sc48
       )

    jac[jp, jca48] = (
       -rho*Y[jp]*rate_eval.p_Ca48__Sc49
       )

    jac[jp, jca49] = (
       -rho*Y[jp]*rate_eval.p_Ca49__Sc50
       -rho*Y[jp]*rate_eval.p_Ca49__n_Sc49
       )

    jac[jp, jca50] = (
       -rho*Y[jp]*rate_eval.p_Ca50__He4_K47
       -rho*Y[jp]*rate_eval.p_Ca50__n_Sc50
       -rho*Y[jp]*rate_eval.p_Ca50__Sc51
       )

    jac[jp, jca51] = (
       -rho*Y[jp]*rate_eval.p_Ca51__He4_K48
       -rho*Y[jp]*rate_eval.p_Ca51__Sc52
       -rho*Y[jp]*rate_eval.p_Ca51__n_Sc51
       )

    jac[jp, jca52] = (
       -rho*Y[jp]*rate_eval.p_Ca52__n_Sc52
       -rho*Y[jp]*rate_eval.p_Ca52__Sc53
       -rho*Y[jp]*rate_eval.p_Ca52__He4_K49
       )

    jac[jp, jca53] = (
       -rho*Y[jp]*rate_eval.p_Ca53__n_Sc53
       -rho*Y[jp]*rate_eval.p_Ca53__He4_K50
       -rho*Y[jp]*rate_eval.p_Ca53__Sc54
       )

    jac[jp, jca54] = (
       -rho*Y[jp]*rate_eval.p_Ca54__Sc55
       -rho*Y[jp]*rate_eval.p_Ca54__n_Sc54
       -rho*Y[jp]*rate_eval.p_Ca54__He4_K51
       )

    jac[jp, jca55] = (
       -rho*Y[jp]*rate_eval.p_Ca55__He4_K52
       -rho*Y[jp]*rate_eval.p_Ca55__n_Sc55
       -rho*Y[jp]*rate_eval.p_Ca55__Sc56
       )

    jac[jp, jca56] = (
       -rho*Y[jp]*rate_eval.p_Ca56__He4_K53
       -rho*Y[jp]*rate_eval.p_Ca56__n_Sc56
       -rho*Y[jp]*rate_eval.p_Ca56__Sc57
       )

    jac[jp, jca57] = (
       -rho*Y[jp]*rate_eval.p_Ca57__Sc58
       -rho*Y[jp]*rate_eval.p_Ca57__He4_K54
       -rho*Y[jp]*rate_eval.p_Ca57__n_Sc57
       )

    jac[jp, jca58] = (
       -rho*Y[jp]*rate_eval.p_Ca58__He4_K55
       -rho*Y[jp]*rate_eval.p_Ca58__n_Sc58
       -rho*Y[jp]*rate_eval.p_Ca58__Sc59
       )

    jac[jp, jca59] = (
       -rho*Y[jp]*rate_eval.p_Ca59__n_Sc59
       -rho*Y[jp]*rate_eval.p_Ca59__Sc60
       -rho*Y[jp]*rate_eval.p_Ca59__He4_K56
       )

    jac[jp, jca60] = (
       -rho*Y[jp]*rate_eval.p_Ca60__n_Sc60
       -rho*Y[jp]*rate_eval.p_Ca60__Sc61
       -rho*Y[jp]*rate_eval.p_Ca60__He4_K57
       )

    jac[jp, jca61] = (
       -rho*Y[jp]*rate_eval.p_Ca61__Sc62
       -rho*Y[jp]*rate_eval.p_Ca61__He4_K58
       -rho*Y[jp]*rate_eval.p_Ca61__n_Sc61
       )

    jac[jp, jsc35] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc35__p_Ti38
       +rho*Y[jn]*rate_eval.n_Sc35__p_Ca35
       )

    jac[jp, jsc36] = (
       -rho*Y[jp]*rate_eval.p_Sc36__Ti37
       +rho*Y[jhe4]*rate_eval.He4_Sc36__p_Ti39
       +rho*Y[jn]*rate_eval.n_Sc36__p_Ca36
       )

    jac[jp, jsc37] = (
       -rho*Y[jp]*rate_eval.p_Sc37__Ti38
       +rho*Y[jhe4]*rate_eval.He4_Sc37__p_Ti40
       +rho*Y[jn]*rate_eval.n_Sc37__p_Ca37
       )

    jac[jp, jsc38] = (
       -rho*Y[jp]*rate_eval.p_Sc38__Ti39
       +rho*Y[jhe4]*rate_eval.He4_Sc38__p_Ti41
       +rho*Y[jn]*rate_eval.n_Sc38__p_Ca38
       )

    jac[jp, jsc39] = (
       -rho*Y[jp]*rate_eval.p_Sc39__Ti40
       +rho*Y[jhe4]*rate_eval.He4_Sc39__p_Ti42
       +rho*Y[jn]*rate_eval.n_Sc39__p_Ca39
       )

    jac[jp, jsc40] = (
       -rho*Y[jp]*rate_eval.p_Sc40__Ti41
       +rho*Y[jhe4]*rate_eval.He4_Sc40__p_Ti43
       +rho*Y[jn]*rate_eval.n_Sc40__p_Ca40
       +rate_eval.Sc40__p_K39__weak__wc12
       )

    jac[jp, jsc41] = (
       -rho*Y[jp]*rate_eval.p_Sc41__Ti42
       +rho*Y[jhe4]*rate_eval.He4_Sc41__p_Ti44
       +rho*Y[jn]*rate_eval.n_Sc41__p_Ca41
       )

    jac[jp, jsc42] = (
       -rho*Y[jp]*rate_eval.p_Sc42__Ti43
       -rho*Y[jp]*rate_eval.p_Sc42__He4_Ca39
       +rho*Y[jhe4]*rate_eval.He4_Sc42__p_Ti45
       +rho*Y[jn]*rate_eval.n_Sc42__p_Ca42
       )

    jac[jp, jsc43] = (
       -rho*Y[jp]*rate_eval.p_Sc43__Ti44
       -rho*Y[jp]*rate_eval.p_Sc43__He4_Ca40
       +rho*Y[jhe4]*rate_eval.He4_Sc43__p_Ti46
       +rho*Y[jn]*rate_eval.n_Sc43__p_Ca43
       )

    jac[jp, jsc44] = (
       -rho*Y[jp]*rate_eval.p_Sc44__He4_Ca41
       -rho*Y[jp]*rate_eval.p_Sc44__Ti45
       +rho*Y[jhe4]*rate_eval.He4_Sc44__p_Ti47
       +rho*Y[jn]*rate_eval.n_Sc44__p_Ca44
       )

    jac[jp, jsc45] = (
       -rho*Y[jp]*rate_eval.p_Sc45__He4_Ca42
       -rho*Y[jp]*rate_eval.p_Sc45__Ti46
       +rho*Y[jhe4]*rate_eval.He4_Sc45__p_Ti48
       +rho*Y[jn]*rate_eval.n_Sc45__p_Ca45
       )

    jac[jp, jsc46] = (
       -rho*Y[jp]*rate_eval.p_Sc46__He4_Ca43
       -rho*Y[jp]*rate_eval.p_Sc46__n_Ti46
       -rho*Y[jp]*rate_eval.p_Sc46__Ti47
       +rho*Y[jhe4]*rate_eval.He4_Sc46__p_Ti49
       +rho*Y[jn]*rate_eval.n_Sc46__p_Ca46
       )

    jac[jp, jsc47] = (
       -rho*Y[jp]*rate_eval.p_Sc47__He4_Ca44
       -rho*Y[jp]*rate_eval.p_Sc47__Ti48
       +rho*Y[jhe4]*rate_eval.He4_Sc47__p_Ti50
       )

    jac[jp, jsc48] = (
       -rho*Y[jp]*rate_eval.p_Sc48__He4_Ca45
       -rho*Y[jp]*rate_eval.p_Sc48__n_Ti48
       -rho*Y[jp]*rate_eval.p_Sc48__Ti49
       +rho*Y[jn]*rate_eval.n_Sc48__p_Ca48
       +rho*Y[jhe4]*rate_eval.He4_Sc48__p_Ti51
       )

    jac[jp, jsc49] = (
       -rho*Y[jp]*rate_eval.p_Sc49__He4_Ca46
       -rho*Y[jp]*rate_eval.p_Sc49__n_Ti49
       -rho*Y[jp]*rate_eval.p_Sc49__Ti50
       )

    jac[jp, jsc50] = (
       -rho*Y[jp]*rate_eval.p_Sc50__Ti51
       -rho*Y[jp]*rate_eval.p_Sc50__n_Ti50
       -rho*Y[jp]*rate_eval.p_Sc50__He4_Ca47
       )

    jac[jp, jsc51] = (
       -rho*Y[jp]*rate_eval.p_Sc51__He4_Ca48
       -rho*Y[jp]*rate_eval.p_Sc51__n_Ti51
       -rho*Y[jp]*rate_eval.p_Sc51__Ti52
       )

    jac[jp, jsc52] = (
       -rho*Y[jp]*rate_eval.p_Sc52__Ti53
       -rho*Y[jp]*rate_eval.p_Sc52__He4_Ca49
       -rho*Y[jp]*rate_eval.p_Sc52__n_Ti52
       )

    jac[jp, jsc53] = (
       -rho*Y[jp]*rate_eval.p_Sc53__n_Ti53
       -rho*Y[jp]*rate_eval.p_Sc53__Ti54
       -rho*Y[jp]*rate_eval.p_Sc53__He4_Ca50
       )

    jac[jp, jsc54] = (
       -rho*Y[jp]*rate_eval.p_Sc54__n_Ti54
       -rho*Y[jp]*rate_eval.p_Sc54__Ti55
       -rho*Y[jp]*rate_eval.p_Sc54__He4_Ca51
       )

    jac[jp, jsc55] = (
       -rho*Y[jp]*rate_eval.p_Sc55__He4_Ca52
       -rho*Y[jp]*rate_eval.p_Sc55__n_Ti55
       -rho*Y[jp]*rate_eval.p_Sc55__Ti56
       )

    jac[jp, jsc56] = (
       -rho*Y[jp]*rate_eval.p_Sc56__Ti57
       -rho*Y[jp]*rate_eval.p_Sc56__He4_Ca53
       -rho*Y[jp]*rate_eval.p_Sc56__n_Ti56
       )

    jac[jp, jsc57] = (
       -rho*Y[jp]*rate_eval.p_Sc57__He4_Ca54
       -rho*Y[jp]*rate_eval.p_Sc57__n_Ti57
       -rho*Y[jp]*rate_eval.p_Sc57__Ti58
       )

    jac[jp, jsc58] = (
       -rho*Y[jp]*rate_eval.p_Sc58__He4_Ca55
       -rho*Y[jp]*rate_eval.p_Sc58__n_Ti58
       -rho*Y[jp]*rate_eval.p_Sc58__Ti59
       )

    jac[jp, jsc59] = (
       -rho*Y[jp]*rate_eval.p_Sc59__He4_Ca56
       -rho*Y[jp]*rate_eval.p_Sc59__Ti60
       -rho*Y[jp]*rate_eval.p_Sc59__n_Ti59
       )

    jac[jp, jsc60] = (
       -rho*Y[jp]*rate_eval.p_Sc60__He4_Ca57
       -rho*Y[jp]*rate_eval.p_Sc60__n_Ti60
       -rho*Y[jp]*rate_eval.p_Sc60__Ti61
       )

    jac[jp, jsc61] = (
       -rho*Y[jp]*rate_eval.p_Sc61__n_Ti61
       -rho*Y[jp]*rate_eval.p_Sc61__Ti62
       -rho*Y[jp]*rate_eval.p_Sc61__He4_Ca58
       )

    jac[jp, jsc62] = (
       -rho*Y[jp]*rate_eval.p_Sc62__n_Ti62
       -rho*Y[jp]*rate_eval.p_Sc62__Ti63
       -rho*Y[jp]*rate_eval.p_Sc62__He4_Ca59
       )

    jac[jp, jsc63] = (
       -rho*Y[jp]*rate_eval.p_Sc63__Ti64
       -rho*Y[jp]*rate_eval.p_Sc63__He4_Ca60
       -rho*Y[jp]*rate_eval.p_Sc63__n_Ti63
       )

    jac[jp, jti37] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti37__p_V40
       +rho*Y[jn]*rate_eval.n_Ti37__p_Sc37
       )

    jac[jp, jti38] = (
       -rho*Y[jp]*rate_eval.p_Ti38__V39
       +rho*Y[jhe4]*rate_eval.He4_Ti38__p_V41
       +rho*Y[jn]*rate_eval.n_Ti38__p_Sc38
       )

    jac[jp, jti39] = (
       -rho*Y[jp]*rate_eval.p_Ti39__V40
       +rho*Y[jhe4]*rate_eval.He4_Ti39__p_V42
       +rho*Y[jn]*rate_eval.n_Ti39__p_Sc39
       +rate_eval.Ti39__p_Ca38__weak__wc12
       )

    jac[jp, jti40] = (
       -rho*Y[jp]*rate_eval.p_Ti40__V41
       +rho*Y[jhe4]*rate_eval.He4_Ti40__p_V43
       +rho*Y[jn]*rate_eval.n_Ti40__p_Sc40
       +rate_eval.Ti40__p_Ca39__weak__wc12
       )

    jac[jp, jti41] = (
       -rho*Y[jp]*rate_eval.p_Ti41__V42
       +rho*Y[jn]*rate_eval.n_Ti41__p_Sc41
       +rate_eval.Ti41__p_Ca40__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Ti41__p_V44
       )

    jac[jp, jti42] = (
       -rho*Y[jp]*rate_eval.p_Ti42__V43
       +rho*Y[jn]*rate_eval.n_Ti42__p_Sc42
       +rho*Y[jhe4]*rate_eval.He4_Ti42__p_V45
       )

    jac[jp, jti43] = (
       -rho*Y[jp]*rate_eval.p_Ti43__V44
       +rho*Y[jhe4]*rate_eval.He4_Ti43__p_V46
       +rho*Y[jn]*rate_eval.n_Ti43__p_Sc43
       )

    jac[jp, jti44] = (
       -rho*Y[jp]*rate_eval.p_Ti44__V45
       +rho*Y[jn]*rate_eval.n_Ti44__p_Sc44
       +rho*Y[jhe4]*rate_eval.He4_Ti44__p_V47
       )

    jac[jp, jti45] = (
       -rho*Y[jp]*rate_eval.p_Ti45__V46
       +rho*Y[jn]*rate_eval.n_Ti45__p_Sc45
       +rho*Y[jhe4]*rate_eval.He4_Ti45__p_V48
       )

    jac[jp, jti46] = (
       -rho*Y[jp]*rate_eval.p_Ti46__V47
       )

    jac[jp, jti47] = (
       -rho*Y[jp]*rate_eval.p_Ti47__V48
       +rho*Y[jn]*rate_eval.n_Ti47__p_Sc47
       )

    jac[jp, jti48] = (
       -rho*Y[jp]*rate_eval.p_Ti48__V49
       )

    jac[jp, jti49] = (
       -rho*Y[jp]*rate_eval.p_Ti49__V50
       )

    jac[jp, jti50] = (
       -rho*Y[jp]*rate_eval.p_Ti50__V51
       )

    jac[jp, jti51] = (
       -rho*Y[jp]*rate_eval.p_Ti51__n_V51
       -rho*Y[jp]*rate_eval.p_Ti51__V52
       )

    jac[jp, jti52] = (
       -rho*Y[jp]*rate_eval.p_Ti52__He4_Sc49
       -rho*Y[jp]*rate_eval.p_Ti52__n_V52
       -rho*Y[jp]*rate_eval.p_Ti52__V53
       )

    jac[jp, jti53] = (
       -rho*Y[jp]*rate_eval.p_Ti53__He4_Sc50
       -rho*Y[jp]*rate_eval.p_Ti53__n_V53
       -rho*Y[jp]*rate_eval.p_Ti53__V54
       )

    jac[jp, jti54] = (
       -rho*Y[jp]*rate_eval.p_Ti54__He4_Sc51
       -rho*Y[jp]*rate_eval.p_Ti54__n_V54
       -rho*Y[jp]*rate_eval.p_Ti54__V55
       )

    jac[jp, jti55] = (
       -rho*Y[jp]*rate_eval.p_Ti55__n_V55
       -rho*Y[jp]*rate_eval.p_Ti55__V56
       -rho*Y[jp]*rate_eval.p_Ti55__He4_Sc52
       )

    jac[jp, jti56] = (
       -rho*Y[jp]*rate_eval.p_Ti56__He4_Sc53
       -rho*Y[jp]*rate_eval.p_Ti56__V57
       -rho*Y[jp]*rate_eval.p_Ti56__n_V56
       )

    jac[jp, jti57] = (
       -rho*Y[jp]*rate_eval.p_Ti57__He4_Sc54
       -rho*Y[jp]*rate_eval.p_Ti57__n_V57
       -rho*Y[jp]*rate_eval.p_Ti57__V58
       )

    jac[jp, jti58] = (
       -rho*Y[jp]*rate_eval.p_Ti58__n_V58
       -rho*Y[jp]*rate_eval.p_Ti58__V59
       -rho*Y[jp]*rate_eval.p_Ti58__He4_Sc55
       )

    jac[jp, jti59] = (
       -rho*Y[jp]*rate_eval.p_Ti59__n_V59
       -rho*Y[jp]*rate_eval.p_Ti59__V60
       -rho*Y[jp]*rate_eval.p_Ti59__He4_Sc56
       )

    jac[jp, jti60] = (
       -rho*Y[jp]*rate_eval.p_Ti60__n_V60
       -rho*Y[jp]*rate_eval.p_Ti60__V61
       -rho*Y[jp]*rate_eval.p_Ti60__He4_Sc57
       )

    jac[jp, jti61] = (
       -rho*Y[jp]*rate_eval.p_Ti61__n_V61
       -rho*Y[jp]*rate_eval.p_Ti61__V62
       -rho*Y[jp]*rate_eval.p_Ti61__He4_Sc58
       )

    jac[jp, jti62] = (
       -rho*Y[jp]*rate_eval.p_Ti62__n_V62
       -rho*Y[jp]*rate_eval.p_Ti62__V63
       -rho*Y[jp]*rate_eval.p_Ti62__He4_Sc59
       )

    jac[jp, jti63] = (
       -rho*Y[jp]*rate_eval.p_Ti63__He4_Sc60
       -rho*Y[jp]*rate_eval.p_Ti63__n_V63
       -rho*Y[jp]*rate_eval.p_Ti63__V64
       )

    jac[jp, jti64] = (
       -rho*Y[jp]*rate_eval.p_Ti64__He4_Sc61
       -rho*Y[jp]*rate_eval.p_Ti64__n_V64
       -rho*Y[jp]*rate_eval.p_Ti64__V65
       )

    jac[jp, jti65] = (
       -rho*Y[jp]*rate_eval.p_Ti65__He4_Sc62
       -rho*Y[jp]*rate_eval.p_Ti65__V66
       -rho*Y[jp]*rate_eval.p_Ti65__n_V65
       )

    jac[jp, jv39] = (
       +rho*Y[jhe4]*rate_eval.He4_V39__p_Cr42
       +rho*Y[jn]*rate_eval.n_V39__p_Ti39
       )

    jac[jp, jv40] = (
       -rho*Y[jp]*rate_eval.p_V40__Cr41
       +rho*Y[jn]*rate_eval.n_V40__p_Ti40
       +rho*Y[jhe4]*rate_eval.He4_V40__p_Cr43
       )

    jac[jp, jv41] = (
       -rho*Y[jp]*rate_eval.p_V41__Cr42
       +rho*Y[jn]*rate_eval.n_V41__p_Ti41
       +rho*Y[jhe4]*rate_eval.He4_V41__p_Cr44
       )

    jac[jp, jv42] = (
       -rho*Y[jp]*rate_eval.p_V42__Cr43
       +rho*Y[jhe4]*rate_eval.He4_V42__p_Cr45
       +rho*Y[jn]*rate_eval.n_V42__p_Ti42
       )

    jac[jp, jv43] = (
       -rho*Y[jp]*rate_eval.p_V43__Cr44
       +rho*Y[jhe4]*rate_eval.He4_V43__p_Cr46
       +rho*Y[jn]*rate_eval.n_V43__p_Ti43
       )

    jac[jp, jv44] = (
       -rho*Y[jp]*rate_eval.p_V44__Cr45
       +rho*Y[jn]*rate_eval.n_V44__p_Ti44
       +rho*Y[jhe4]*rate_eval.He4_V44__p_Cr47
       )

    jac[jp, jv45] = (
       -rho*Y[jp]*rate_eval.p_V45__Cr46
       +rho*Y[jhe4]*rate_eval.He4_V45__p_Cr48
       +rho*Y[jn]*rate_eval.n_V45__p_Ti45
       )

    jac[jp, jv46] = (
       -rho*Y[jp]*rate_eval.p_V46__Cr47
       +rho*Y[jhe4]*rate_eval.He4_V46__p_Cr49
       +rho*Y[jn]*rate_eval.n_V46__p_Ti46
       )

    jac[jp, jv47] = (
       -rho*Y[jp]*rate_eval.p_V47__Cr48
       +rho*Y[jhe4]*rate_eval.He4_V47__p_Cr50
       +rho*Y[jn]*rate_eval.n_V47__p_Ti47
       )

    jac[jp, jv48] = (
       -rho*Y[jp]*rate_eval.p_V48__Cr49
       +rho*Y[jn]*rate_eval.n_V48__p_Ti48
       +rho*Y[jhe4]*rate_eval.He4_V48__p_Cr51
       )

    jac[jp, jv49] = (
       -rho*Y[jp]*rate_eval.p_V49__He4_Ti46
       -rho*Y[jp]*rate_eval.p_V49__Cr50
       +rho*Y[jn]*rate_eval.n_V49__p_Ti49
       +rho*Y[jhe4]*rate_eval.He4_V49__p_Cr52
       )

    jac[jp, jv50] = (
       -rho*Y[jp]*rate_eval.p_V50__He4_Ti47
       -rho*Y[jp]*rate_eval.p_V50__n_Cr50
       -rho*Y[jp]*rate_eval.p_V50__Cr51
       +rho*Y[jhe4]*rate_eval.He4_V50__p_Cr53
       +rho*Y[jn]*rate_eval.n_V50__p_Ti50
       )

    jac[jp, jv51] = (
       -rho*Y[jp]*rate_eval.p_V51__He4_Ti48
       -rho*Y[jp]*rate_eval.p_V51__Cr52
       )

    jac[jp, jv52] = (
       -rho*Y[jp]*rate_eval.p_V52__He4_Ti49
       -rho*Y[jp]*rate_eval.p_V52__n_Cr52
       -rho*Y[jp]*rate_eval.p_V52__Cr53
       )

    jac[jp, jv53] = (
       -rho*Y[jp]*rate_eval.p_V53__n_Cr53
       -rho*Y[jp]*rate_eval.p_V53__He4_Ti50
       -rho*Y[jp]*rate_eval.p_V53__Cr54
       )

    jac[jp, jv54] = (
       -rho*Y[jp]*rate_eval.p_V54__n_Cr54
       -rho*Y[jp]*rate_eval.p_V54__Cr55
       -rho*Y[jp]*rate_eval.p_V54__He4_Ti51
       )

    jac[jp, jv55] = (
       -rho*Y[jp]*rate_eval.p_V55__n_Cr55
       -rho*Y[jp]*rate_eval.p_V55__Cr56
       -rho*Y[jp]*rate_eval.p_V55__He4_Ti52
       )

    jac[jp, jv56] = (
       -rho*Y[jp]*rate_eval.p_V56__He4_Ti53
       -rho*Y[jp]*rate_eval.p_V56__Cr57
       -rho*Y[jp]*rate_eval.p_V56__n_Cr56
       )

    jac[jp, jv57] = (
       -rho*Y[jp]*rate_eval.p_V57__He4_Ti54
       -rho*Y[jp]*rate_eval.p_V57__n_Cr57
       -rho*Y[jp]*rate_eval.p_V57__Cr58
       )

    jac[jp, jv58] = (
       -rho*Y[jp]*rate_eval.p_V58__He4_Ti55
       -rho*Y[jp]*rate_eval.p_V58__n_Cr58
       -rho*Y[jp]*rate_eval.p_V58__Cr59
       )

    jac[jp, jv59] = (
       -rho*Y[jp]*rate_eval.p_V59__n_Cr59
       -rho*Y[jp]*rate_eval.p_V59__Cr60
       -rho*Y[jp]*rate_eval.p_V59__He4_Ti56
       )

    jac[jp, jv60] = (
       -rho*Y[jp]*rate_eval.p_V60__He4_Ti57
       -rho*Y[jp]*rate_eval.p_V60__n_Cr60
       -rho*Y[jp]*rate_eval.p_V60__Cr61
       )

    jac[jp, jv61] = (
       -rho*Y[jp]*rate_eval.p_V61__n_Cr61
       -rho*Y[jp]*rate_eval.p_V61__He4_Ti58
       -rho*Y[jp]*rate_eval.p_V61__Cr62
       )

    jac[jp, jv62] = (
       -rho*Y[jp]*rate_eval.p_V62__n_Cr62
       -rho*Y[jp]*rate_eval.p_V62__He4_Ti59
       -rho*Y[jp]*rate_eval.p_V62__Cr63
       )

    jac[jp, jv63] = (
       -rho*Y[jp]*rate_eval.p_V63__n_Cr63
       -rho*Y[jp]*rate_eval.p_V63__He4_Ti60
       -rho*Y[jp]*rate_eval.p_V63__Cr64
       )

    jac[jp, jv64] = (
       -rho*Y[jp]*rate_eval.p_V64__He4_Ti61
       -rho*Y[jp]*rate_eval.p_V64__n_Cr64
       -rho*Y[jp]*rate_eval.p_V64__Cr65
       )

    jac[jp, jv65] = (
       -rho*Y[jp]*rate_eval.p_V65__He4_Ti62
       -rho*Y[jp]*rate_eval.p_V65__Cr66
       -rho*Y[jp]*rate_eval.p_V65__n_Cr65
       )

    jac[jp, jv66] = (
       -rho*Y[jp]*rate_eval.p_V66__n_Cr66
       -rho*Y[jp]*rate_eval.p_V66__Cr67
       -rho*Y[jp]*rate_eval.p_V66__He4_Ti63
       )

    jac[jp, jv67] = (
       -rho*Y[jp]*rate_eval.p_V67__n_Cr67
       -rho*Y[jp]*rate_eval.p_V67__He4_Ti64
       -rho*Y[jp]*rate_eval.p_V67__Cr68
       )

    jac[jp, jcr41] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr41__p_Mn44
       +rho*Y[jn]*rate_eval.n_Cr41__p_V41
       )

    jac[jp, jcr42] = (
       -rho*Y[jp]*rate_eval.p_Cr42__Mn43
       +rho*Y[jhe4]*rate_eval.He4_Cr42__p_Mn45
       +rho*Y[jn]*rate_eval.n_Cr42__p_V42
       +rate_eval.Cr42__p_Ti41__weak__wc12
       )

    jac[jp, jcr43] = (
       -rho*Y[jp]*rate_eval.p_Cr43__Mn44
       +3*rate_eval.Cr43__p_p_p_Ca40__weak__wc12
       +2*rate_eval.Cr43__p_p_Sc41__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Cr43__p_Mn46
       +rho*Y[jn]*rate_eval.n_Cr43__p_V43
       +rate_eval.Cr43__p_Ti42__weak__wc17
       )

    jac[jp, jcr44] = (
       -rho*Y[jp]*rate_eval.p_Cr44__Mn45
       +rho*Y[jhe4]*rate_eval.He4_Cr44__p_Mn47
       +rho*Y[jn]*rate_eval.n_Cr44__p_V44
       +rate_eval.Cr44__p_Ti43__weak__wc12
       )

    jac[jp, jcr45] = (
       -rho*Y[jp]*rate_eval.p_Cr45__Mn46
       +rho*Y[jhe4]*rate_eval.He4_Cr45__p_Mn48
       +rate_eval.Cr45__p_Ti44__weak__wc12
       +rho*Y[jn]*rate_eval.n_Cr45__p_V45
       )

    jac[jp, jcr46] = (
       -rho*Y[jp]*rate_eval.p_Cr46__Mn47
       +rho*Y[jn]*rate_eval.n_Cr46__p_V46
       +rho*Y[jhe4]*rate_eval.He4_Cr46__p_Mn49
       )

    jac[jp, jcr47] = (
       -rho*Y[jp]*rate_eval.p_Cr47__Mn48
       +rho*Y[jhe4]*rate_eval.He4_Cr47__p_Mn50
       +rho*Y[jn]*rate_eval.n_Cr47__p_V47
       )

    jac[jp, jcr48] = (
       -rho*Y[jp]*rate_eval.p_Cr48__Mn49
       +rho*Y[jhe4]*rate_eval.He4_Cr48__p_Mn51
       +rho*Y[jn]*rate_eval.n_Cr48__p_V48
       )

    jac[jp, jcr49] = (
       -rho*Y[jp]*rate_eval.p_Cr49__Mn50
       +rho*Y[jhe4]*rate_eval.He4_Cr49__p_Mn52
       +rho*Y[jn]*rate_eval.n_Cr49__p_V49
       )

    jac[jp, jcr50] = (
       -rho*Y[jp]*rate_eval.p_Cr50__Mn51
       )

    jac[jp, jcr51] = (
       -rho*Y[jp]*rate_eval.p_Cr51__Mn52
       +rho*Y[jn]*rate_eval.n_Cr51__p_V51
       )

    jac[jp, jcr52] = (
       -rho*Y[jp]*rate_eval.p_Cr52__Mn53
       )

    jac[jp, jcr53] = (
       -rho*Y[jp]*rate_eval.p_Cr53__Mn54
       )

    jac[jp, jcr54] = (
       -rho*Y[jp]*rate_eval.p_Cr54__He4_V51
       -rho*Y[jp]*rate_eval.p_Cr54__Mn55
       )

    jac[jp, jcr55] = (
       -rho*Y[jp]*rate_eval.p_Cr55__n_Mn55
       -rho*Y[jp]*rate_eval.p_Cr55__He4_V52
       -rho*Y[jp]*rate_eval.p_Cr55__Mn56
       )

    jac[jp, jcr56] = (
       -rho*Y[jp]*rate_eval.p_Cr56__n_Mn56
       -rho*Y[jp]*rate_eval.p_Cr56__He4_V53
       -rho*Y[jp]*rate_eval.p_Cr56__Mn57
       )

    jac[jp, jcr57] = (
       -rho*Y[jp]*rate_eval.p_Cr57__n_Mn57
       -rho*Y[jp]*rate_eval.p_Cr57__He4_V54
       -rho*Y[jp]*rate_eval.p_Cr57__Mn58
       )

    jac[jp, jcr58] = (
       -rho*Y[jp]*rate_eval.p_Cr58__Mn59
       -rho*Y[jp]*rate_eval.p_Cr58__n_Mn58
       -rho*Y[jp]*rate_eval.p_Cr58__He4_V55
       )

    jac[jp, jcr59] = (
       -rho*Y[jp]*rate_eval.p_Cr59__n_Mn59
       -rho*Y[jp]*rate_eval.p_Cr59__Mn60
       -rho*Y[jp]*rate_eval.p_Cr59__He4_V56
       )

    jac[jp, jcr60] = (
       -rho*Y[jp]*rate_eval.p_Cr60__He4_V57
       -rho*Y[jp]*rate_eval.p_Cr60__Mn61
       -rho*Y[jp]*rate_eval.p_Cr60__n_Mn60
       )

    jac[jp, jcr61] = (
       -rho*Y[jp]*rate_eval.p_Cr61__He4_V58
       -rho*Y[jp]*rate_eval.p_Cr61__Mn62
       -rho*Y[jp]*rate_eval.p_Cr61__n_Mn61
       )

    jac[jp, jcr62] = (
       -rho*Y[jp]*rate_eval.p_Cr62__He4_V59
       -rho*Y[jp]*rate_eval.p_Cr62__Mn63
       -rho*Y[jp]*rate_eval.p_Cr62__n_Mn62
       )

    jac[jp, jcr63] = (
       -rho*Y[jp]*rate_eval.p_Cr63__n_Mn63
       -rho*Y[jp]*rate_eval.p_Cr63__Mn64
       -rho*Y[jp]*rate_eval.p_Cr63__He4_V60
       )

    jac[jp, jcr64] = (
       -rho*Y[jp]*rate_eval.p_Cr64__n_Mn64
       -rho*Y[jp]*rate_eval.p_Cr64__Mn65
       -rho*Y[jp]*rate_eval.p_Cr64__He4_V61
       )

    jac[jp, jcr65] = (
       -rho*Y[jp]*rate_eval.p_Cr65__He4_V62
       -rho*Y[jp]*rate_eval.p_Cr65__Mn66
       -rho*Y[jp]*rate_eval.p_Cr65__n_Mn65
       )

    jac[jp, jcr66] = (
       -rho*Y[jp]*rate_eval.p_Cr66__He4_V63
       -rho*Y[jp]*rate_eval.p_Cr66__Mn67
       -rho*Y[jp]*rate_eval.p_Cr66__n_Mn66
       )

    jac[jp, jcr67] = (
       -rho*Y[jp]*rate_eval.p_Cr67__n_Mn67
       -rho*Y[jp]*rate_eval.p_Cr67__He4_V64
       -rho*Y[jp]*rate_eval.p_Cr67__Mn68
       )

    jac[jp, jcr68] = (
       -rho*Y[jp]*rate_eval.p_Cr68__He4_V65
       -rho*Y[jp]*rate_eval.p_Cr68__n_Mn68
       -rho*Y[jp]*rate_eval.p_Cr68__Mn69
       )

    jac[jp, jcr69] = (
       -rho*Y[jp]*rate_eval.p_Cr69__He4_V66
       -rho*Y[jp]*rate_eval.p_Cr69__Mn70
       -rho*Y[jp]*rate_eval.p_Cr69__n_Mn69
       )

    jac[jp, jcr70] = (
       -rho*Y[jp]*rate_eval.p_Cr70__Mn71
       -rho*Y[jp]*rate_eval.p_Cr70__n_Mn70
       -rho*Y[jp]*rate_eval.p_Cr70__He4_V67
       )

    jac[jp, jmn43] = (
       +rho*Y[jn]*rate_eval.n_Mn43__p_Cr43
       +rho*Y[jhe4]*rate_eval.He4_Mn43__p_Fe46
       )

    jac[jp, jmn44] = (
       -rho*Y[jp]*rate_eval.p_Mn44__Fe45
       +rho*Y[jhe4]*rate_eval.He4_Mn44__p_Fe47
       +rho*Y[jn]*rate_eval.n_Mn44__p_Cr44
       )

    jac[jp, jmn45] = (
       -rho*Y[jp]*rate_eval.p_Mn45__Fe46
       +rho*Y[jn]*rate_eval.n_Mn45__p_Cr45
       +rho*Y[jhe4]*rate_eval.He4_Mn45__p_Fe48
       )

    jac[jp, jmn46] = (
       -rho*Y[jp]*rate_eval.p_Mn46__Fe47
       +rho*Y[jhe4]*rate_eval.He4_Mn46__p_Fe49
       +rho*Y[jn]*rate_eval.n_Mn46__p_Cr46
       +rate_eval.Mn46__p_V45__weak__wc12
       )

    jac[jp, jmn47] = (
       -rho*Y[jp]*rate_eval.p_Mn47__Fe48
       +rho*Y[jhe4]*rate_eval.He4_Mn47__p_Fe50
       +rho*Y[jn]*rate_eval.n_Mn47__p_Cr47
       )

    jac[jp, jmn48] = (
       -rho*Y[jp]*rate_eval.p_Mn48__Fe49
       +rho*Y[jhe4]*rate_eval.He4_Mn48__p_Fe51
       +rho*Y[jn]*rate_eval.n_Mn48__p_Cr48
       +rate_eval.Mn48__p_V47__weak__wc12
       )

    jac[jp, jmn49] = (
       -rho*Y[jp]*rate_eval.p_Mn49__Fe50
       +rho*Y[jhe4]*rate_eval.He4_Mn49__p_Fe52
       +rho*Y[jn]*rate_eval.n_Mn49__p_Cr49
       )

    jac[jp, jmn50] = (
       -rho*Y[jp]*rate_eval.p_Mn50__Fe51
       +rho*Y[jn]*rate_eval.n_Mn50__p_Cr50
       +rho*Y[jhe4]*rate_eval.He4_Mn50__p_Fe53
       )

    jac[jp, jmn51] = (
       -rho*Y[jp]*rate_eval.p_Mn51__Fe52
       +rho*Y[jhe4]*rate_eval.He4_Mn51__p_Fe54
       +rho*Y[jn]*rate_eval.n_Mn51__p_Cr51
       )

    jac[jp, jmn52] = (
       -rho*Y[jp]*rate_eval.p_Mn52__Fe53
       +rho*Y[jn]*rate_eval.n_Mn52__p_Cr52
       +rho*Y[jhe4]*rate_eval.He4_Mn52__p_Fe55
       )

    jac[jp, jmn53] = (
       -rho*Y[jp]*rate_eval.p_Mn53__He4_Cr50
       -rho*Y[jp]*rate_eval.p_Mn53__Fe54
       +rho*Y[jhe4]*rate_eval.He4_Mn53__p_Fe56
       +rho*Y[jn]*rate_eval.n_Mn53__p_Cr53
       )

    jac[jp, jmn54] = (
       -rho*Y[jp]*rate_eval.p_Mn54__He4_Cr51
       -rho*Y[jp]*rate_eval.p_Mn54__Fe55
       +rho*Y[jn]*rate_eval.n_Mn54__p_Cr54
       )

    jac[jp, jmn55] = (
       -rho*Y[jp]*rate_eval.p_Mn55__He4_Cr52
       -rho*Y[jp]*rate_eval.p_Mn55__Fe56
       )

    jac[jp, jmn56] = (
       -rho*Y[jp]*rate_eval.p_Mn56__He4_Cr53
       -rho*Y[jp]*rate_eval.p_Mn56__Fe57
       -rho*Y[jp]*rate_eval.p_Mn56__n_Fe56
       )

    jac[jp, jmn57] = (
       -rho*Y[jp]*rate_eval.p_Mn57__n_Fe57
       -rho*Y[jp]*rate_eval.p_Mn57__He4_Cr54
       -rho*Y[jp]*rate_eval.p_Mn57__Fe58
       )

    jac[jp, jmn58] = (
       -rho*Y[jp]*rate_eval.p_Mn58__Fe59
       -rho*Y[jp]*rate_eval.p_Mn58__n_Fe58
       -rho*Y[jp]*rate_eval.p_Mn58__He4_Cr55
       )

    jac[jp, jmn59] = (
       -rho*Y[jp]*rate_eval.p_Mn59__He4_Cr56
       -rho*Y[jp]*rate_eval.p_Mn59__n_Fe59
       -rho*Y[jp]*rate_eval.p_Mn59__Fe60
       )

    jac[jp, jmn60] = (
       -rho*Y[jp]*rate_eval.p_Mn60__He4_Cr57
       -rho*Y[jp]*rate_eval.p_Mn60__n_Fe60
       -rho*Y[jp]*rate_eval.p_Mn60__Fe61
       )

    jac[jp, jmn61] = (
       -rho*Y[jp]*rate_eval.p_Mn61__n_Fe61
       -rho*Y[jp]*rate_eval.p_Mn61__Fe62
       -rho*Y[jp]*rate_eval.p_Mn61__He4_Cr58
       )

    jac[jp, jmn62] = (
       -rho*Y[jp]*rate_eval.p_Mn62__He4_Cr59
       -rho*Y[jp]*rate_eval.p_Mn62__Fe63
       -rho*Y[jp]*rate_eval.p_Mn62__n_Fe62
       )

    jac[jp, jmn63] = (
       -rho*Y[jp]*rate_eval.p_Mn63__Fe64
       -rho*Y[jp]*rate_eval.p_Mn63__He4_Cr60
       -rho*Y[jp]*rate_eval.p_Mn63__n_Fe63
       )

    jac[jp, jmn64] = (
       -rho*Y[jp]*rate_eval.p_Mn64__He4_Cr61
       -rho*Y[jp]*rate_eval.p_Mn64__n_Fe64
       -rho*Y[jp]*rate_eval.p_Mn64__Fe65
       )

    jac[jp, jmn65] = (
       -rho*Y[jp]*rate_eval.p_Mn65__He4_Cr62
       -rho*Y[jp]*rate_eval.p_Mn65__n_Fe65
       -rho*Y[jp]*rate_eval.p_Mn65__Fe66
       )

    jac[jp, jmn66] = (
       -rho*Y[jp]*rate_eval.p_Mn66__He4_Cr63
       -rho*Y[jp]*rate_eval.p_Mn66__n_Fe66
       -rho*Y[jp]*rate_eval.p_Mn66__Fe67
       )

    jac[jp, jmn67] = (
       -rho*Y[jp]*rate_eval.p_Mn67__He4_Cr64
       -rho*Y[jp]*rate_eval.p_Mn67__Fe68
       -rho*Y[jp]*rate_eval.p_Mn67__n_Fe67
       )

    jac[jp, jmn68] = (
       -rho*Y[jp]*rate_eval.p_Mn68__n_Fe68
       -rho*Y[jp]*rate_eval.p_Mn68__Fe69
       -rho*Y[jp]*rate_eval.p_Mn68__He4_Cr65
       )

    jac[jp, jmn69] = (
       -rho*Y[jp]*rate_eval.p_Mn69__He4_Cr66
       -rho*Y[jp]*rate_eval.p_Mn69__n_Fe69
       -rho*Y[jp]*rate_eval.p_Mn69__Fe70
       )

    jac[jp, jmn70] = (
       -rho*Y[jp]*rate_eval.p_Mn70__Fe71
       -rho*Y[jp]*rate_eval.p_Mn70__He4_Cr67
       -rho*Y[jp]*rate_eval.p_Mn70__n_Fe70
       )

    jac[jp, jmn71] = (
       -rho*Y[jp]*rate_eval.p_Mn71__He4_Cr68
       -rho*Y[jp]*rate_eval.p_Mn71__Fe72
       -rho*Y[jp]*rate_eval.p_Mn71__n_Fe71
       )

    jac[jp, jmn72] = (
       -rho*Y[jp]*rate_eval.p_Mn72__He4_Cr69
       -rho*Y[jp]*rate_eval.p_Mn72__n_Fe72
       -rho*Y[jp]*rate_eval.p_Mn72__Fe73
       )

    jac[jp, jmn73] = (
       -rho*Y[jp]*rate_eval.p_Mn73__He4_Cr70
       -rho*Y[jp]*rate_eval.p_Mn73__Fe74
       -rho*Y[jp]*rate_eval.p_Mn73__n_Fe73
       )

    jac[jp, jfe45] = (
       +3*rate_eval.Fe45__p_p_p_Ti42__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Fe45__p_Co48
       +rate_eval.Fe45__p_Cr44__weak__wc17
       +rho*Y[jn]*rate_eval.n_Fe45__p_Mn45
       +2*rate_eval.Fe45__p_p_V43__weak__wc12
       )

    jac[jp, jfe46] = (
       -rho*Y[jp]*rate_eval.p_Fe46__Co47
       +rho*Y[jn]*rate_eval.n_Fe46__p_Mn46
       +rho*Y[jhe4]*rate_eval.He4_Fe46__p_Co49
       +rate_eval.Fe46__p_Cr45__weak__wc12
       )

    jac[jp, jfe47] = (
       -rho*Y[jp]*rate_eval.p_Fe47__Co48
       +rho*Y[jn]*rate_eval.n_Fe47__p_Mn47
       +rate_eval.Fe47__p_Cr46__weak__wc12
       +rho*Y[jhe4]*rate_eval.He4_Fe47__p_Co50
       )

    jac[jp, jfe48] = (
       -rho*Y[jp]*rate_eval.p_Fe48__Co49
       +rho*Y[jhe4]*rate_eval.He4_Fe48__p_Co51
       +rho*Y[jn]*rate_eval.n_Fe48__p_Mn48
       +rate_eval.Fe48__p_Cr47__weak__wc12
       )

    jac[jp, jfe49] = (
       -rho*Y[jp]*rate_eval.p_Fe49__Co50
       +rho*Y[jhe4]*rate_eval.He4_Fe49__p_Co52
       +rho*Y[jn]*rate_eval.n_Fe49__p_Mn49
       +rate_eval.Fe49__p_Cr48__weak__wc12
       )

    jac[jp, jfe50] = (
       -rho*Y[jp]*rate_eval.p_Fe50__Co51
       +rho*Y[jhe4]*rate_eval.He4_Fe50__p_Co53
       +rho*Y[jn]*rate_eval.n_Fe50__p_Mn50
       )

    jac[jp, jfe51] = (
       -rho*Y[jp]*rate_eval.p_Fe51__Co52
       +rho*Y[jn]*rate_eval.n_Fe51__p_Mn51
       +rho*Y[jhe4]*rate_eval.He4_Fe51__p_Co54
       )

    jac[jp, jfe52] = (
       -rho*Y[jp]*rate_eval.p_Fe52__Co53
       +rho*Y[jhe4]*rate_eval.He4_Fe52__p_Co55
       +rho*Y[jn]*rate_eval.n_Fe52__p_Mn52
       )

    jac[jp, jfe53] = (
       -rho*Y[jp]*rate_eval.p_Fe53__Co54
       +rho*Y[jn]*rate_eval.n_Fe53__p_Mn53
       +rho*Y[jhe4]*rate_eval.He4_Fe53__p_Co56
       )

    jac[jp, jfe54] = (
       -rho*Y[jp]*rate_eval.p_Fe54__Co55
       +rho*Y[jn]*rate_eval.n_Fe54__p_Mn54
       )

    jac[jp, jfe55] = (
       -rho*Y[jp]*rate_eval.p_Fe55__Co56
       +rho*Y[jn]*rate_eval.n_Fe55__p_Mn55
       )

    jac[jp, jfe56] = (
       -rho*Y[jp]*rate_eval.p_Fe56__Co57
       )

    jac[jp, jfe57] = (
       -rho*Y[jp]*rate_eval.p_Fe57__He4_Mn54
       -rho*Y[jp]*rate_eval.p_Fe57__Co58
       )

    jac[jp, jfe58] = (
       -rho*Y[jp]*rate_eval.p_Fe58__Co59
       -rho*Y[jp]*rate_eval.p_Fe58__He4_Mn55
       )

    jac[jp, jfe59] = (
       -rho*Y[jp]*rate_eval.p_Fe59__He4_Mn56
       -rho*Y[jp]*rate_eval.p_Fe59__n_Co59
       -rho*Y[jp]*rate_eval.p_Fe59__Co60
       )

    jac[jp, jfe60] = (
       -rho*Y[jp]*rate_eval.p_Fe60__He4_Mn57
       -rho*Y[jp]*rate_eval.p_Fe60__Co61
       )

    jac[jp, jfe61] = (
       -rho*Y[jp]*rate_eval.p_Fe61__He4_Mn58
       -rho*Y[jp]*rate_eval.p_Fe61__n_Co61
       -rho*Y[jp]*rate_eval.p_Fe61__Co62
       )

    jac[jp, jfe62] = (
       -rho*Y[jp]*rate_eval.p_Fe62__He4_Mn59
       -rho*Y[jp]*rate_eval.p_Fe62__n_Co62
       -rho*Y[jp]*rate_eval.p_Fe62__Co63
       )

    jac[jp, jfe63] = (
       -rho*Y[jp]*rate_eval.p_Fe63__He4_Mn60
       -rho*Y[jp]*rate_eval.p_Fe63__Co64
       -rho*Y[jp]*rate_eval.p_Fe63__n_Co63
       )

    jac[jp, jfe64] = (
       -rho*Y[jp]*rate_eval.p_Fe64__He4_Mn61
       -rho*Y[jp]*rate_eval.p_Fe64__n_Co64
       -rho*Y[jp]*rate_eval.p_Fe64__Co65
       )

    jac[jp, jfe65] = (
       -rho*Y[jp]*rate_eval.p_Fe65__He4_Mn62
       -rho*Y[jp]*rate_eval.p_Fe65__Co66
       -rho*Y[jp]*rate_eval.p_Fe65__n_Co65
       )

    jac[jp, jfe66] = (
       -rho*Y[jp]*rate_eval.p_Fe66__He4_Mn63
       -rho*Y[jp]*rate_eval.p_Fe66__n_Co66
       -rho*Y[jp]*rate_eval.p_Fe66__Co67
       )

    jac[jp, jfe67] = (
       -rho*Y[jp]*rate_eval.p_Fe67__He4_Mn64
       -rho*Y[jp]*rate_eval.p_Fe67__n_Co67
       -rho*Y[jp]*rate_eval.p_Fe67__Co68
       )

    jac[jp, jfe68] = (
       -rho*Y[jp]*rate_eval.p_Fe68__He4_Mn65
       -rho*Y[jp]*rate_eval.p_Fe68__Co69
       -rho*Y[jp]*rate_eval.p_Fe68__n_Co68
       )

    jac[jp, jfe69] = (
       -rho*Y[jp]*rate_eval.p_Fe69__He4_Mn66
       -rho*Y[jp]*rate_eval.p_Fe69__n_Co69
       -rho*Y[jp]*rate_eval.p_Fe69__Co70
       )

    jac[jp, jfe70] = (
       -rho*Y[jp]*rate_eval.p_Fe70__He4_Mn67
       -rho*Y[jp]*rate_eval.p_Fe70__n_Co70
       -rho*Y[jp]*rate_eval.p_Fe70__Co71
       )

    jac[jp, jfe71] = (
       -rho*Y[jp]*rate_eval.p_Fe71__He4_Mn68
       -rho*Y[jp]*rate_eval.p_Fe71__n_Co71
       -rho*Y[jp]*rate_eval.p_Fe71__Co72
       )

    jac[jp, jfe72] = (
       -rho*Y[jp]*rate_eval.p_Fe72__He4_Mn69
       -rho*Y[jp]*rate_eval.p_Fe72__n_Co72
       -rho*Y[jp]*rate_eval.p_Fe72__Co73
       )

    jac[jp, jfe73] = (
       -rho*Y[jp]*rate_eval.p_Fe73__He4_Mn70
       -rho*Y[jp]*rate_eval.p_Fe73__n_Co73
       -rho*Y[jp]*rate_eval.p_Fe73__Co74
       )

    jac[jp, jfe74] = (
       -rho*Y[jp]*rate_eval.p_Fe74__He4_Mn71
       -rho*Y[jp]*rate_eval.p_Fe74__n_Co74
       -rho*Y[jp]*rate_eval.p_Fe74__Co75
       )

    jac[jp, jfe75] = (
       -rho*Y[jp]*rate_eval.p_Fe75__He4_Mn72
       -rho*Y[jp]*rate_eval.p_Fe75__n_Co75
       -rho*Y[jp]*rate_eval.p_Fe75__Co76
       )

    jac[jp, jfe76] = (
       -rho*Y[jp]*rate_eval.p_Fe76__He4_Mn73
       -rho*Y[jp]*rate_eval.p_Fe76__Co77
       -rho*Y[jp]*rate_eval.p_Fe76__n_Co76
       )

    jac[jd, jn] = (
       -rho*Y[jd]*rate_eval.n_d__t
       +5.00000000000000e-01*rho**2*Y[jp]**2*rate_eval.n_p_p__p_d
       +rho*Y[jp]*rate_eval.n_p__d
       )

    jac[jd, jp] = (
       -rho*Y[jd]*rate_eval.p_d__He3
       +5.00000000000000e-01*rho**2*Y[jn]*2*Y[jp]*rate_eval.n_p_p__p_d
       +rho*Y[jbe9]*rate_eval.p_Be9__d_He4_He4
       +rho*Y[jn]*rate_eval.n_p__d
       +5.00000000000000e-01*rho*2*Y[jp]*rate_eval.p_p__d__weak__bet_pos_
       +5.00000000000000e-01*rho**2*ye(Y)*2*Y[jp]*rate_eval.p_p__d__weak__electron_capture
       )

    jac[jd, jd] = (
       -rho*Y[jli7]*rate_eval.d_Li7__n_He4_He4
       -rho*Y[jn]*rate_eval.n_d__t
       -rho*Y[jli8]*rate_eval.d_Li8__n_Be9
       -rho*Y[jbe7]*rate_eval.d_Be7__p_He4_He4
       -rho*Y[jli8]*rate_eval.d_Li8__t_Li7
       -rho*Y[jc13]*rate_eval.d_C13__n_N14
       -rho*Y[jli7]*rate_eval.d_Li7__p_Li8
       -rho*Y[jhe3]*rate_eval.d_He3__p_He4
       -rho*Y[jt]*rate_eval.d_t__n_He4
       -2*5.00000000000000e-01*rho*2*Y[jd]*rate_eval.d_d__p_t
       -rho*Y[jli6]*rate_eval.d_Li6__n_Be7
       -rho*Y[jhe4]*rate_eval.He4_d__Li6
       -2*5.00000000000000e-01*rho*2*Y[jd]*rate_eval.d_d__He4
       -2*5.00000000000000e-01*rho*2*Y[jd]*rate_eval.d_d__n_He3
       -rho*Y[jp]*rate_eval.p_d__He3
       -rho*Y[jc14]*rate_eval.d_C14__n_N15
       -rho*Y[jli6]*rate_eval.d_Li6__p_Li7
       )

    jac[jd, jt] = (
       -rho*Y[jd]*rate_eval.d_t__n_He4
       +rho*Y[jhe3]*rate_eval.t_He3__d_He4
       )

    jac[jd, jhe3] = (
       -rho*Y[jd]*rate_eval.d_He3__p_He4
       +rho*Y[jt]*rate_eval.t_He3__d_He4
       )

    jac[jd, jhe4] = (
       -rho*Y[jd]*rate_eval.He4_d__Li6
       )

    jac[jd, jli6] = (
       -rho*Y[jd]*rate_eval.d_Li6__n_Be7
       -rho*Y[jd]*rate_eval.d_Li6__p_Li7
       )

    jac[jd, jli7] = (
       -rho*Y[jd]*rate_eval.d_Li7__n_He4_He4
       -rho*Y[jd]*rate_eval.d_Li7__p_Li8
       )

    jac[jd, jli8] = (
       -rho*Y[jd]*rate_eval.d_Li8__n_Be9
       -rho*Y[jd]*rate_eval.d_Li8__t_Li7
       )

    jac[jd, jbe7] = (
       -rho*Y[jd]*rate_eval.d_Be7__p_He4_He4
       )

    jac[jd, jbe9] = (
       +rho*Y[jp]*rate_eval.p_Be9__d_He4_He4
       )

    jac[jd, jc13] = (
       -rho*Y[jd]*rate_eval.d_C13__n_N14
       )

    jac[jd, jc14] = (
       -rho*Y[jd]*rate_eval.d_C14__n_N15
       )

    jac[jt, jn] = (
       +rho*Y[jd]*rate_eval.n_d__t
       +rho*Y[jli6]*rate_eval.n_Li6__He4_t
       +rho*Y[jhe3]*rate_eval.n_He3__p_t
       )

    jac[jt, jp] = (
       -rho*Y[jt]*rate_eval.p_t__He4
       )

    jac[jt, jd] = (
       -rho*Y[jt]*rate_eval.d_t__n_He4
       +rho*Y[jn]*rate_eval.n_d__t
       +rho*Y[jli8]*rate_eval.d_Li8__t_Li7
       +5.00000000000000e-01*rho*2*Y[jd]*rate_eval.d_d__p_t
       )

    jac[jt, jt] = (
       -rho*Y[jbe7]*rate_eval.t_Be7__n_p_He4_He4
       -rho*Y[jhe3]*rate_eval.t_He3__n_p_He4
       -rho*Y[jhe3]*rate_eval.t_He3__d_He4
       -rho*Y[jd]*rate_eval.d_t__n_He4
       -rho*Y[jbe9]*rate_eval.t_Be9__n_B11
       -rho*Y[jli7]*rate_eval.t_Li7__n_Be9
       -rate_eval.t__He3__weak__wc12
       -rho*Y[jp]*rate_eval.p_t__He4
       -rho*Y[jhe4]*rate_eval.He4_t__Li7
       -rho*Y[jli7]*rate_eval.t_Li7__n_n_He4_He4
       -2*5.00000000000000e-01*rho*2*Y[jt]*rate_eval.t_t__n_n_He4
       )

    jac[jt, jhe3] = (
       -rho*Y[jt]*rate_eval.t_He3__n_p_He4
       -rho*Y[jt]*rate_eval.t_He3__d_He4
       +rho*ye(Y)*rate_eval.He3__t__weak__electron_capture
       +rho*Y[jn]*rate_eval.n_He3__p_t
       )

    jac[jt, jhe4] = (
       -rho*Y[jt]*rate_eval.He4_t__Li7
       )

    jac[jt, jli6] = (
       +rho*Y[jn]*rate_eval.n_Li6__He4_t
       )

    jac[jt, jli7] = (
       -rho*Y[jt]*rate_eval.t_Li7__n_Be9
       -rho*Y[jt]*rate_eval.t_Li7__n_n_He4_He4
       )

    jac[jt, jli8] = (
       +rho*Y[jd]*rate_eval.d_Li8__t_Li7
       )

    jac[jt, jbe7] = (
       -rho*Y[jt]*rate_eval.t_Be7__n_p_He4_He4
       )

    jac[jt, jbe9] = (
       -rho*Y[jt]*rate_eval.t_Be9__n_B11
       )

    jac[jhe3, jn] = (
       -rho*Y[jhe3]*rate_eval.n_He3__p_t
       -rho*Y[jhe3]*rate_eval.n_He3__He4
       )

    jac[jhe3, jp] = (
       -rho*Y[jhe3]*rate_eval.p_He3__He4__weak__bet_pos_
       +rho*Y[jli6]*rate_eval.p_Li6__He4_He3
       +rho*Y[jd]*rate_eval.p_d__He3
       )

    jac[jhe3, jd] = (
       -rho*Y[jhe3]*rate_eval.d_He3__p_He4
       +5.00000000000000e-01*rho*2*Y[jd]*rate_eval.d_d__n_He3
       +rho*Y[jp]*rate_eval.p_d__He3
       )

    jac[jhe3, jt] = (
       -rho*Y[jhe3]*rate_eval.t_He3__n_p_He4
       -rho*Y[jhe3]*rate_eval.t_He3__d_He4
       +rate_eval.t__He3__weak__wc12
       )

    jac[jhe3, jhe3] = (
       -rho*Y[jbe7]*rate_eval.He3_Be7__p_p_He4_He4
       -2*5.00000000000000e-01*rho*2*Y[jhe3]*rate_eval.He3_He3__p_p_He4
       -rho*Y[jt]*rate_eval.t_He3__n_p_He4
       -rho*ye(Y)*rate_eval.He3__t__weak__electron_capture
       -rho*Y[jt]*rate_eval.t_He3__d_He4
       -rho*Y[jd]*rate_eval.d_He3__p_He4
       -rho*Y[jn]*rate_eval.n_He3__p_t
       -rho*Y[jp]*rate_eval.p_He3__He4__weak__bet_pos_
       -rho*Y[jn]*rate_eval.n_He3__He4
       -rho*Y[jhe4]*rate_eval.He4_He3__Be7
       -rho*Y[jli7]*rate_eval.He3_Li7__n_p_He4_He4
       )

    jac[jhe3, jhe4] = (
       -rho*Y[jhe3]*rate_eval.He4_He3__Be7
       )

    jac[jhe3, jli6] = (
       +rho*Y[jp]*rate_eval.p_Li6__He4_He3
       )

    jac[jhe3, jli7] = (
       -rho*Y[jhe3]*rate_eval.He3_Li7__n_p_He4_He4
       )

    jac[jhe3, jbe7] = (
       -rho*Y[jhe3]*rate_eval.He3_Be7__p_p_He4_He4
       )

    jac[jhe4, jn] = (
       -5.00000000000000e-01*rho**2*2*Y[jn]*Y[jhe4]*rate_eval.n_n_He4__He6
       -2*5.00000000000000e-01*rho**2*Y[jhe4]**2*rate_eval.n_He4_He4__Be9
       -rho**2*Y[jp]*Y[jhe4]*rate_eval.n_p_He4__Li6
       +2*rho*Y[jb8]*rate_eval.n_B8__p_He4_He4
       +rho*Y[jfe56]*rate_eval.n_Fe56__He4_Cr53
       +rho*Y[jfe53]*rate_eval.n_Fe53__He4_Cr50
       +rho*Y[jfe52]*rate_eval.n_Fe52__He4_Cr49
       +rho*Y[jfe51]*rate_eval.n_Fe51__He4_Cr48
       +rho*Y[jfe50]*rate_eval.n_Fe50__He4_Cr47
       +rho*Y[jfe49]*rate_eval.n_Fe49__He4_Cr46
       +rho*Y[jfe47]*rate_eval.n_Fe47__He4_Cr44
       +rho*Y[jfe46]*rate_eval.n_Fe46__He4_Cr43
       +rho*Y[jmn52]*rate_eval.n_Mn52__He4_V49
       +rho*Y[jmn50]*rate_eval.n_Mn50__He4_V47
       +rho*Y[jmn48]*rate_eval.n_Mn48__He4_V45
       +rho*Y[jmn46]*rate_eval.n_Mn46__He4_V43
       +rho*Y[jcr55]*rate_eval.n_Cr55__He4_Ti52
       +rho*Y[jcr51]*rate_eval.n_Cr51__He4_Ti48
       +rho*Y[jcr50]*rate_eval.n_Cr50__He4_Ti47
       +rho*Y[jcr46]*rate_eval.n_Cr46__He4_Ti43
       +rho*Y[jcr45]*rate_eval.n_Cr45__He4_Ti42
       +rho*Y[jcr42]*rate_eval.n_Cr42__He4_Ti39
       +rho*Y[jcr41]*rate_eval.n_Cr41__He4_Ti38
       +rho*Y[jcr53]*rate_eval.n_Cr53__He4_Ti50
       +rho*Y[jv46]*rate_eval.n_V46__He4_Sc43
       +rho*Y[jv44]*rate_eval.n_V44__He4_Sc41
       +rho*Y[jv42]*rate_eval.n_V42__He4_Sc39
       +rho*Y[jv41]*rate_eval.n_V41__He4_Sc38
       +rho*Y[jti51]*rate_eval.n_Ti51__He4_Ca48
       +rho*Y[jti49]*rate_eval.n_Ti49__He4_Ca46
       +rho*Y[jti43]*rate_eval.n_Ti43__He4_Ca40
       +rho*Y[jti41]*rate_eval.n_Ti41__He4_Ca38
       +rho*Y[jti38]*rate_eval.n_Ti38__He4_Ca35
       +rho*Y[jar36]*rate_eval.n_Ar36__He4_S33
       +rho*Y[jmg22]*rate_eval.n_Mg22__He4_Ne19
       +rho*Y[jsc43]*rate_eval.n_Sc43__He4_K40
       +rho*Y[jsc42]*rate_eval.n_Sc42__He4_K39
       +rho*Y[jsc41]*rate_eval.n_Sc41__He4_K38
       +rho*Y[jsc39]*rate_eval.n_Sc39__He4_K36
       +rho*Y[jti47]*rate_eval.n_Ti47__He4_Ca44
       +rho*Y[jsc37]*rate_eval.n_Sc37__He4_K34
       +rho*Y[jsc35]*rate_eval.n_Sc35__He4_K32
       +rho*Y[jsi24]*rate_eval.n_Si24__He4_Mg21
       +rho*Y[jmn43]*rate_eval.n_Mn43__He4_V40
       +rho*Y[jca40]*rate_eval.n_Ca40__He4_Ar37
       +rho*Y[jca37]*rate_eval.n_Ca37__He4_Ar34
       +rho*Y[jca35]*rate_eval.n_Ca35__He4_Ar32
       +rho*Y[jca34]*rate_eval.n_Ca34__He4_Ar31
       +rho*Y[jcr44]*rate_eval.n_Cr44__He4_Ti41
       +rho*Y[jv45]*rate_eval.n_V45__He4_Sc42
       +rho*Y[jk40]*rate_eval.n_K40__He4_Cl37
       +rho*Y[jar31]*rate_eval.n_Ar31__He4_S28
       +rho*Y[jk37]*rate_eval.n_K37__He4_Cl34
       +rho*Y[jk36]*rate_eval.n_K36__He4_Cl33
       +rho*Y[jsc46]*rate_eval.n_Sc46__He4_K43
       +rho*Y[jk32]*rate_eval.n_K32__He4_Cl29
       +rho*Y[jti39]*rate_eval.n_Ti39__He4_Ca36
       +rho*Y[jca36]*rate_eval.n_Ca36__He4_Ar33
       +rho*Y[jmn49]*rate_eval.n_Mn49__He4_V46
       +rho*Y[jar35]*rate_eval.n_Ar35__He4_S32
       +rho*Y[jar32]*rate_eval.n_Ar32__He4_S29
       +rho*Y[jar30]*rate_eval.n_Ar30__He4_S27
       +rho*Y[jar29]*rate_eval.n_Ar29__He4_S26
       +rho*Y[jcl35]*rate_eval.n_Cl35__He4_P32
       +3*rho*Y[jc11]*rate_eval.n_C11__He4_He4_He4
       +rho*Y[jcl34]*rate_eval.n_Cl34__He4_P31
       +rho*Y[jcl33]*rate_eval.n_Cl33__He4_P30
       +rho*Y[jcl29]*rate_eval.n_Cl29__He4_P26
       +rho*Y[jcl28]*rate_eval.n_Cl28__He4_P25
       +rho*Y[js35]*rate_eval.n_S35__He4_Si32
       +rho*Y[js33]*rate_eval.n_S33__He4_Si30
       +rho*Y[js30]*rate_eval.n_S30__He4_Si27
       +rho*Y[jcr43]*rate_eval.n_Cr43__He4_Ti40
       +rho*Y[js28]*rate_eval.n_S28__He4_Si25
       +rho*Y[js26]*rate_eval.n_S26__He4_Si23
       +rho*Y[jv47]*rate_eval.n_V47__He4_Sc44
       +rho*Y[jp27]*rate_eval.n_P27__He4_Al24
       +rho*Y[jcr47]*rate_eval.n_Cr47__He4_Ti44
       +rho*Y[jp26]*rate_eval.n_P26__He4_Al23
       +rho*Y[jp24]*rate_eval.n_P24__He4_Al21
       +rho*Y[jmn51]*rate_eval.n_Mn51__He4_V48
       +rho*Y[jti37]*rate_eval.n_Ti37__He4_Ca34
       +rho*Y[jsi22]*rate_eval.n_Si22__He4_Mg19
       +rho*Y[jal26]*rate_eval.n_Al26__He4_Na23
       +rho*Y[jal23]*rate_eval.n_Al23__He4_Na20
       +rho*Y[jal22]*rate_eval.n_Al22__He4_Na19
       +rho*Y[jmn47]*rate_eval.n_Mn47__He4_V44
       +rho*Y[jp29]*rate_eval.n_P29__He4_Al26
       +rho*Y[js29]*rate_eval.n_S29__He4_Si26
       +rho*Y[jfe54]*rate_eval.n_Fe54__He4_Cr51
       +rho*Y[jfe55]*rate_eval.n_Fe55__He4_Cr52
       +rho*Y[jmg23]*rate_eval.n_Mg23__He4_Ne20
       +rho*Y[jmg21]*rate_eval.n_Mg21__He4_Ne18
       +rho*Y[jv43]*rate_eval.n_V43__He4_Sc40
       +rho*Y[jar39]*rate_eval.n_Ar39__He4_S36
       +rho*Y[jna21]*rate_eval.n_Na21__He4_F18
       +rho*Y[jna20]*rate_eval.n_Na20__He4_F17
       +rho*Y[jv40]*rate_eval.n_V40__He4_Sc37
       +rho*Y[jmn54]*rate_eval.n_Mn54__He4_V51
       +rho*Y[jcl32]*rate_eval.n_Cl32__He4_P29
       +rho*Y[jti45]*rate_eval.n_Ti45__He4_Ca42
       +rho*Y[jcl38]*rate_eval.n_Cl38__He4_P35
       +rho*Y[jsi25]*rate_eval.n_Si25__He4_Mg22
       +rho*Y[jne18]*rate_eval.n_Ne18__He4_O15
       +2*rho*Y[jbe7]*rate_eval.n_Be7__He4_He4
       +rho*Y[jf18]*rate_eval.n_F18__He4_N15
       +rho*Y[jf15]*rate_eval.n_F15__He4_N12
       +rho*Y[jf14]*rate_eval.n_F14__He4_N11
       +rho*Y[jk33]*rate_eval.n_K33__He4_Cl30
       +rho*Y[jo14]*rate_eval.n_O14__He4_C11
       +rho*Y[jca33]*rate_eval.n_Ca33__He4_Ar30
       +rho*Y[jo13]*rate_eval.n_O13__He4_C10
       +rho*Y[jmg19]*rate_eval.n_Mg19__He4_Ne16
       +rho*Y[jk35]*rate_eval.n_K35__He4_Cl32
       +rho*Y[jti42]*rate_eval.n_Ti42__He4_Ca39
       +rho*Y[jfe48]*rate_eval.n_Fe48__He4_Cr45
       +rho*Y[jmn53]*rate_eval.n_Mn53__He4_V50
       +rho*Y[jli6]*rate_eval.n_Li6__He4_t
       +rho*Y[jv50]*rate_eval.n_V50__He4_Sc47
       +rho*Y[jca43]*rate_eval.n_Ca43__He4_Ar40
       +rho*Y[jne19]*rate_eval.n_Ne19__He4_O16
       +rho*Y[jfe57]*rate_eval.n_Fe57__He4_Cr54
       +rho*Y[jne16]*rate_eval.n_Ne16__He4_O13
       +rho*Y[jar34]*rate_eval.n_Ar34__He4_S31
       +rho*Y[jf16]*rate_eval.n_F16__He4_N13
       +rho*Y[jk39]*rate_eval.n_K39__He4_Cl36
       +rho*Y[jo15]*rate_eval.n_O15__He4_C12
       +rho*Y[jmn45]*rate_eval.n_Mn45__He4_V42
       +rho*Y[jal24]*rate_eval.n_Al24__He4_Na21
       +rho*Y[jne17]*rate_eval.n_Ne17__He4_O14
       +rho*Y[jmn44]*rate_eval.n_Mn44__He4_V41
       +rho*Y[jhe3]*rate_eval.n_He3__He4
       +rho*Y[jcl31]*rate_eval.n_Cl31__He4_P28
       +rho*Y[jsi27]*rate_eval.n_Si27__He4_Mg24
       +rho*Y[jv48]*rate_eval.n_V48__He4_Sc45
       +rho*Y[js31]*rate_eval.n_S31__He4_Si28
       +rho*Y[jcl30]*rate_eval.n_Cl30__He4_P27
       +rho*Y[jsi23]*rate_eval.n_Si23__He4_Mg20
       +rho*Y[jsi26]*rate_eval.n_Si26__He4_Mg23
       +rho*Y[jmg20]*rate_eval.n_Mg20__He4_Ne17
       +rho*Y[jp25]*rate_eval.n_P25__He4_Al22
       +rho*Y[jca39]*rate_eval.n_Ca39__He4_Ar36
       +rho*Y[js27]*rate_eval.n_S27__He4_Si24
       +rho*Y[jca41]*rate_eval.n_Ca41__He4_Ar38
       +rho*Y[jna19]*rate_eval.n_Na19__He4_F16
       +rho*Y[jcl36]*rate_eval.n_Cl36__He4_P33
       +rho*Y[jk42]*rate_eval.n_K42__He4_Cl39
       +rho*Y[jk31]*rate_eval.n_K31__He4_Cl28
       +rho*Y[jo12]*rate_eval.n_O12__He4_C9
       +rho*Y[jcr49]*rate_eval.n_Cr49__He4_Ti46
       +rho*Y[jk38]*rate_eval.n_K38__He4_Cl35
       +rho*Y[jk34]*rate_eval.n_K34__He4_Cl31
       +rho*Y[jo17]*rate_eval.n_O17__He4_C14
       +rho*Y[jar33]*rate_eval.n_Ar33__He4_S30
       +rho*Y[jsc36]*rate_eval.n_Sc36__He4_K33
       +rho*Y[jti44]*rate_eval.n_Ti44__He4_Ca41
       +rho*Y[jb10]*rate_eval.n_B10__He4_Li7
       +rho*Y[jna22]*rate_eval.n_Na22__He4_F19
       +rho*Y[jmn56]*rate_eval.n_Mn56__He4_V53
       +rho*Y[jfe45]*rate_eval.n_Fe45__He4_Cr42
       +rho*Y[jfe59]*rate_eval.n_Fe59__He4_Cr56
       +rho*Y[jv52]*rate_eval.n_V52__He4_Sc49
       +rho*Y[jca42]*rate_eval.n_Ca42__He4_Ar39
       +rho*Y[jti40]*rate_eval.n_Ti40__He4_Ca37
       +rho*Y[jv39]*rate_eval.n_V39__He4_Sc36
       +rho*Y[jsc40]*rate_eval.n_Sc40__He4_K37
       +rho*Y[jca38]*rate_eval.n_Ca38__He4_Ar35
       +rho*Y[js32]*rate_eval.n_S32__He4_Si29
       +rho*Y[jsc38]*rate_eval.n_Sc38__He4_K35
       +rho*Y[jal25]*rate_eval.n_Al25__He4_Na22
       +rho*Y[jp28]*rate_eval.n_P28__He4_Al25
       +rho*Y[jcr48]*rate_eval.n_Cr48__He4_Ti45
       )

    jac[jhe4, jp] = (
       -rho**2*Y[jn]*Y[jhe4]*rate_eval.n_p_He4__Li6
       +2*rho*Y[jbe9]*rate_eval.p_Be9__n_p_He4_He4
       +3*rho*Y[jb11]*rate_eval.p_B11__He4_He4_He4
       +2*rho*Y[jbe9]*rate_eval.p_Be9__d_He4_He4
       +rho*Y[jfe76]*rate_eval.p_Fe76__He4_Mn73
       +rho*Y[jfe75]*rate_eval.p_Fe75__He4_Mn72
       +rho*Y[jfe74]*rate_eval.p_Fe74__He4_Mn71
       +rho*Y[jfe73]*rate_eval.p_Fe73__He4_Mn70
       +rho*Y[jfe72]*rate_eval.p_Fe72__He4_Mn69
       +rho*Y[jfe71]*rate_eval.p_Fe71__He4_Mn68
       +rho*Y[jfe70]*rate_eval.p_Fe70__He4_Mn67
       +rho*Y[jfe69]*rate_eval.p_Fe69__He4_Mn66
       +rho*Y[jfe68]*rate_eval.p_Fe68__He4_Mn65
       +rho*Y[jfe67]*rate_eval.p_Fe67__He4_Mn64
       +rho*Y[jfe65]*rate_eval.p_Fe65__He4_Mn62
       +rho*Y[jfe63]*rate_eval.p_Fe63__He4_Mn60
       +rho*Y[jfe62]*rate_eval.p_Fe62__He4_Mn59
       +rho*Y[jfe61]*rate_eval.p_Fe61__He4_Mn58
       +rho*Y[jfe60]*rate_eval.p_Fe60__He4_Mn57
       +rho*Y[jfe59]*rate_eval.p_Fe59__He4_Mn56
       +rho*Y[jfe57]*rate_eval.p_Fe57__He4_Mn54
       +rho*Y[jmn73]*rate_eval.p_Mn73__He4_Cr70
       +rho*Y[jmn72]*rate_eval.p_Mn72__He4_Cr69
       +rho*Y[jmn71]*rate_eval.p_Mn71__He4_Cr68
       +rho*Y[jmn69]*rate_eval.p_Mn69__He4_Cr66
       +rho*Y[jmn67]*rate_eval.p_Mn67__He4_Cr64
       +rho*Y[jmn66]*rate_eval.p_Mn66__He4_Cr63
       +rho*Y[jmn65]*rate_eval.p_Mn65__He4_Cr62
       +rho*Y[jmn64]*rate_eval.p_Mn64__He4_Cr61
       +rho*Y[jmn62]*rate_eval.p_Mn62__He4_Cr59
       +rho*Y[jmn60]*rate_eval.p_Mn60__He4_Cr57
       +rho*Y[jmn59]*rate_eval.p_Mn59__He4_Cr56
       +rho*Y[jfe64]*rate_eval.p_Fe64__He4_Mn61
       +rho*Y[jmn56]*rate_eval.p_Mn56__He4_Cr53
       +rho*Y[jmn54]*rate_eval.p_Mn54__He4_Cr51
       +rho*Y[jmn53]*rate_eval.p_Mn53__He4_Cr50
       +rho*Y[jcr68]*rate_eval.p_Cr68__He4_V65
       +rho*Y[jcr66]*rate_eval.p_Cr66__He4_V63
       +rho*Y[jcr65]*rate_eval.p_Cr65__He4_V62
       +rho*Y[jcr62]*rate_eval.p_Cr62__He4_V59
       +rho*Y[jcr60]*rate_eval.p_Cr60__He4_V57
       +rho*Y[jcr54]*rate_eval.p_Cr54__He4_V51
       +rho*Y[jmg24]*rate_eval.p_Mg24__He4_Na21
       +rho*Y[jmn55]*rate_eval.p_Mn55__He4_Cr52
       +rho*Y[jti57]*rate_eval.p_Ti57__He4_Sc54
       +rho*Y[jk47]*rate_eval.p_K47__He4_Ar44
       +rho*Y[jv65]*rate_eval.p_V65__He4_Ti62
       +rho*Y[jv64]*rate_eval.p_V64__He4_Ti61
       +rho*Y[jv60]*rate_eval.p_V60__He4_Ti57
       +rho*Y[jo27]*rate_eval.p_O27__He4_N24
       +rho*Y[jv58]*rate_eval.p_V58__He4_Ti55
       +rho*Y[jv57]*rate_eval.p_V57__He4_Ti54
       +rho*Y[jv52]*rate_eval.p_V52__He4_Ti49
       +rho*Y[jv51]*rate_eval.p_V51__He4_Ti48
       +rho*Y[jv50]*rate_eval.p_V50__He4_Ti47
       +rho*Y[jv49]*rate_eval.p_V49__He4_Ti46
       +rho*Y[jcr57]*rate_eval.p_Cr57__He4_V54
       +rho*Y[jne27]*rate_eval.p_Ne27__He4_F24
       +rho*Y[jti64]*rate_eval.p_Ti64__He4_Sc61
       +rho*Y[jti63]*rate_eval.p_Ti63__He4_Sc60
       +rho*Y[jti54]*rate_eval.p_Ti54__He4_Sc51
       +rho*Y[jf23]*rate_eval.p_F23__He4_O20
       +rho*Y[jti53]*rate_eval.p_Ti53__He4_Sc50
       +rho*Y[jti52]*rate_eval.p_Ti52__He4_Sc49
       +rho*Y[jar51]*rate_eval.p_Ar51__He4_Cl48
       +rho*Y[jf31]*rate_eval.p_F31__He4_O28
       +rho*Y[jsc60]*rate_eval.p_Sc60__He4_Ca57
       +rho*Y[jsc58]*rate_eval.p_Sc58__He4_Ca55
       +rho*Y[jsc55]*rate_eval.p_Sc55__He4_Ca52
       +rho*Y[jsc52]*rate_eval.p_Sc52__He4_Ca49
       +rho*Y[jsc49]*rate_eval.p_Sc49__He4_Ca46
       +rho*Y[jsc48]*rate_eval.p_Sc48__He4_Ca45
       +rho*Y[jsc47]*rate_eval.p_Sc47__He4_Ca44
       +rho*Y[jsc46]*rate_eval.p_Sc46__He4_Ca43
       +rho*Y[jsc45]*rate_eval.p_Sc45__He4_Ca42
       +rho*Y[jsc44]*rate_eval.p_Sc44__He4_Ca41
       +rho*Y[jsi36]*rate_eval.p_Si36__He4_Al33
       +rho*Y[jca61]*rate_eval.p_Ca61__He4_K58
       +rho*Y[jca58]*rate_eval.p_Ca58__He4_K55
       +rho*Y[jca56]*rate_eval.p_Ca56__He4_K53
       +rho*Y[jca55]*rate_eval.p_Ca55__He4_K52
       +rho*Y[jcr56]*rate_eval.p_Cr56__He4_V53
       +rho*Y[jca51]*rate_eval.p_Ca51__He4_K48
       +rho*Y[jal39]*rate_eval.p_Al39__He4_Mg36
       +rho*Y[jca42]*rate_eval.p_Ca42__He4_K39
       +rho*Y[jk57]*rate_eval.p_K57__He4_Ar54
       +rho*Y[jk48]*rate_eval.p_K48__He4_Ar45
       +rho*Y[jk45]*rate_eval.p_K45__He4_Ar42
       +rho*Y[jk44]*rate_eval.p_K44__He4_Ar41
       +rho*Y[jk41]*rate_eval.p_K41__He4_Ar38
       +rho*Y[jk40]*rate_eval.p_K40__He4_Ar37
       +rho*Y[jcr61]*rate_eval.p_Cr61__He4_V58
       +rho*Y[jar52]*rate_eval.p_Ar52__He4_Cl49
       +rho*Y[jar50]*rate_eval.p_Ar50__He4_Cl47
       +rho*Y[jar48]*rate_eval.p_Ar48__He4_Cl45
       +rho*Y[jcr55]*rate_eval.p_Cr55__He4_V52
       +rho*Y[jar40]*rate_eval.p_Ar40__He4_Cl37
       +rho*Y[jar39]*rate_eval.p_Ar39__He4_Cl36
       +rho*Y[jcl52]*rate_eval.p_Cl52__He4_S49
       +rho*Y[jcl51]*rate_eval.p_Cl51__He4_S48
       +rho*Y[jcl50]*rate_eval.p_Cl50__He4_S47
       +rho*Y[jcl48]*rate_eval.p_Cl48__He4_S45
       +rho*Y[jcl45]*rate_eval.p_Cl45__He4_S42
       +rho*Y[jcl43]*rate_eval.p_Cl43__He4_S40
       +rho*Y[jcl42]*rate_eval.p_Cl42__He4_S39
       +rho*Y[jcl41]*rate_eval.p_Cl41__He4_S38
       +rho*Y[jo19]*rate_eval.p_O19__He4_N16
       +rho*Y[js47]*rate_eval.p_S47__He4_P44
       +rho*Y[jk52]*rate_eval.p_K52__He4_Ar49
       +rho*Y[js45]*rate_eval.p_S45__He4_P42
       +rho*Y[js43]*rate_eval.p_S43__He4_P40
       +rho*Y[jsc57]*rate_eval.p_Sc57__He4_Ca54
       +rho*Y[js41]*rate_eval.p_S41__He4_P38
       +rho*Y[jal30]*rate_eval.p_Al30__He4_Mg27
       +rho*Y[jcl40]*rate_eval.p_Cl40__He4_S37
       +rho*Y[js39]*rate_eval.p_S39__He4_P36
       +rho*Y[js38]*rate_eval.p_S38__He4_P35
       +rho*Y[jv56]*rate_eval.p_V56__He4_Ti53
       +rho*Y[js36]*rate_eval.p_S36__He4_P33
       +rho*Y[jcr69]*rate_eval.p_Cr69__He4_V66
       +rho*Y[jsc51]*rate_eval.p_Sc51__He4_Ca48
       +rho*Y[jk51]*rate_eval.p_K51__He4_Ar48
       +rho*Y[js35]*rate_eval.p_S35__He4_P32
       +rho*Y[jcl35]*rate_eval.p_Cl35__He4_S32
       +rho*Y[jp43]*rate_eval.p_P43__He4_Si40
       +rho*Y[jp42]*rate_eval.p_P42__He4_Si39
       +rho*Y[jo20]*rate_eval.p_O20__He4_N17
       +rho*Y[jar43]*rate_eval.p_Ar43__He4_Cl40
       +rho*Y[jp38]*rate_eval.p_P38__He4_Si35
       +rho*Y[jf18]*rate_eval.p_F18__He4_O15
       +rho*Y[jp37]*rate_eval.p_P37__He4_Si34
       +rho*Y[jp36]*rate_eval.p_P36__He4_Si33
       +rho*Y[jp32]*rate_eval.p_P32__He4_Si29
       +rho*Y[jsi45]*rate_eval.p_Si45__He4_Al42
       +rho*Y[jti65]*rate_eval.p_Ti65__He4_Sc62
       +rho*Y[jsi37]*rate_eval.p_Si37__He4_Al34
       +rho*Y[jsi35]*rate_eval.p_Si35__He4_Al32
       +rho*Y[jv61]*rate_eval.p_V61__He4_Ti58
       +rho*Y[jal41]*rate_eval.p_Al41__He4_Mg38
       +rho*Y[jal40]*rate_eval.p_Al40__He4_Mg37
       +rho*Y[jal38]*rate_eval.p_Al38__He4_Mg35
       +rho*Y[jal37]*rate_eval.p_Al37__He4_Mg34
       +rho*Y[jal36]*rate_eval.p_Al36__He4_Mg33
       +rho*Y[jal35]*rate_eval.p_Al35__He4_Mg32
       +rho*Y[jal34]*rate_eval.p_Al34__He4_Mg31
       +rho*Y[jal33]*rate_eval.p_Al33__He4_Mg30
       +rho*Y[jcl46]*rate_eval.p_Cl46__He4_S43
       +rho*Y[jal32]*rate_eval.p_Al32__He4_Mg29
       +rho*Y[jcl38]*rate_eval.p_Cl38__He4_S35
       +rho*Y[jal31]*rate_eval.p_Al31__He4_Mg28
       +rho*Y[jal29]*rate_eval.p_Al29__He4_Mg26
       +rho*Y[jne34]*rate_eval.p_Ne34__He4_F31
       +rho*Y[jal28]*rate_eval.p_Al28__He4_Mg25
       +rho*Y[jv67]*rate_eval.p_V67__He4_Ti64
       +rho*Y[jal27]*rate_eval.p_Al27__He4_Mg24
       +rho*Y[jar45]*rate_eval.p_Ar45__He4_Cl42
       +rho*Y[jmg34]*rate_eval.p_Mg34__He4_Na31
       +rho*Y[jmg33]*rate_eval.p_Mg33__He4_Na30
       +rho*Y[jfe66]*rate_eval.p_Fe66__He4_Mn63
       +rho*Y[jmg32]*rate_eval.p_Mg32__He4_Na29
       +rho*Y[jmg29]*rate_eval.p_Mg29__He4_Na26
       +rho*Y[jne31]*rate_eval.p_Ne31__He4_F28
       +rho*Y[jna37]*rate_eval.p_Na37__He4_Ne34
       +rho*Y[jna31]*rate_eval.p_Na31__He4_Ne28
       +rho*Y[jna30]*rate_eval.p_Na30__He4_Ne27
       +rho*Y[jna29]*rate_eval.p_Na29__He4_Ne26
       +rho*Y[jna24]*rate_eval.p_Na24__He4_Ne21
       +rho*Y[jk56]*rate_eval.p_K56__He4_Ar53
       +rho*Y[jna23]*rate_eval.p_Na23__He4_Ne20
       +rho*Y[jne30]*rate_eval.p_Ne30__He4_F27
       +rho*Y[jne29]*rate_eval.p_Ne29__He4_F26
       +rho*Y[jne25]*rate_eval.p_Ne25__He4_F22
       +rho*Y[jal43]*rate_eval.p_Al43__He4_Mg40
       +rho*Y[jne20]*rate_eval.p_Ne20__He4_F17
       +rho*Y[jcr67]*rate_eval.p_Cr67__He4_V64
       +rho*Y[jf30]*rate_eval.p_F30__He4_O27
       +rho*Y[jf29]*rate_eval.p_F29__He4_O26
       +rho*Y[jf27]*rate_eval.p_F27__He4_O24
       +rho*Y[jna34]*rate_eval.p_Na34__He4_Ne31
       +rho*Y[jf25]*rate_eval.p_F25__He4_O22
       +rho*Y[jna26]*rate_eval.p_Na26__He4_Ne23
       +rho*Y[jf22]*rate_eval.p_F22__He4_O19
       +rho*Y[jne26]*rate_eval.p_Ne26__He4_F23
       +rho*Y[jf20]*rate_eval.p_F20__He4_O17
       +rho*Y[jo26]*rate_eval.p_O26__He4_N23
       +rho*Y[jo18]*rate_eval.p_O18__He4_N15
       +rho*Y[jo17]*rate_eval.p_O17__He4_N14
       +rho*Y[jne28]*rate_eval.p_Ne28__He4_F25
       +rho*Y[jna28]*rate_eval.p_Na28__He4_Ne25
       +rho*Y[jn15]*rate_eval.p_N15__He4_C12
       +rho*Y[jf28]*rate_eval.p_F28__He4_O25
       +rho*Y[jar53]*rate_eval.p_Ar53__He4_Cl50
       +rho*Y[jb12]*rate_eval.p_B12__He4_Be9
       +rho*Y[jti56]*rate_eval.p_Ti56__He4_Sc53
       +rho*Y[jv63]*rate_eval.p_V63__He4_Ti60
       +rho*Y[jli6]*rate_eval.p_Li6__He4_He3
       +rho*Y[js46]*rate_eval.p_S46__He4_P43
       +rho*Y[jv53]*rate_eval.p_V53__He4_Ti50
       +rho*Y[jcl39]*rate_eval.p_Cl39__He4_S36
       +rho*Y[jp44]*rate_eval.p_P44__He4_Si41
       +rho*Y[jne32]*rate_eval.p_Ne32__He4_F29
       +rho*Y[jal42]*rate_eval.p_Al42__He4_Mg39
       +rho*Y[jmn57]*rate_eval.p_Mn57__He4_Cr54
       +rho*Y[jhe3]*rate_eval.p_He3__He4__weak__bet_pos_
       +rho*Y[jca50]*rate_eval.p_Ca50__He4_K47
       +rho*Y[jna33]*rate_eval.p_Na33__He4_Ne30
       +rho*Y[jk42]*rate_eval.p_K42__He4_Ar39
       +rho*Y[jca52]*rate_eval.p_Ca52__He4_K49
       +rho*Y[jbe11]*rate_eval.p_Be11__He4_Li8
       +rho*Y[jcl36]*rate_eval.p_Cl36__He4_S33
       +rho*Y[jp33]*rate_eval.p_P33__He4_Si30
       +rho*Y[jsi44]*rate_eval.p_Si44__He4_Al41
       +rho*Y[jfe58]*rate_eval.p_Fe58__He4_Mn55
       +rho*Y[jar54]*rate_eval.p_Ar54__He4_Cl51
       +rho*Y[jsc56]*rate_eval.p_Sc56__He4_Ca53
       +rho*Y[jsc59]*rate_eval.p_Sc59__He4_Ca56
       +rho*Y[js49]*rate_eval.p_S49__He4_P46
       +rho*Y[jp46]*rate_eval.p_P46__He4_Si43
       +rho*Y[js48]*rate_eval.p_S48__He4_P45
       +rho*Y[jsc63]*rate_eval.p_Sc63__He4_Ca60
       +rho*Y[jmg31]*rate_eval.p_Mg31__He4_Na28
       +rho*Y[jna35]*rate_eval.p_Na35__He4_Ne32
       +rho*Y[jf24]*rate_eval.p_F24__He4_O21
       +rho*Y[jf19]*rate_eval.p_F19__He4_O16
       +rho*Y[jt]*rate_eval.p_t__He4
       +rho*Y[jar42]*rate_eval.p_Ar42__He4_Cl39
       +rho*Y[js37]*rate_eval.p_S37__He4_P34
       +rho*Y[jmn63]*rate_eval.p_Mn63__He4_Cr60
       +rho*Y[jna36]*rate_eval.p_Na36__He4_Ne33
       +rho*Y[jmg37]*rate_eval.p_Mg37__He4_Na34
       +rho*Y[jp31]*rate_eval.p_P31__He4_Si28
       +rho*Y[js42]*rate_eval.p_S42__He4_P39
       +2*rho*Y[jli8]*rate_eval.p_Li8__n_He4_He4
       +rho*Y[jsi40]*rate_eval.p_Si40__He4_Al37
       +rho*Y[jk50]*rate_eval.p_K50__He4_Ar47
       +rho*Y[jca57]*rate_eval.p_Ca57__He4_K54
       +rho*Y[jna27]*rate_eval.p_Na27__He4_Ne24
       +rho*Y[jsi33]*rate_eval.p_Si33__He4_Al30
       +rho*Y[jk46]*rate_eval.p_K46__He4_Ar43
       +rho*Y[jk49]*rate_eval.p_K49__He4_Ar46
       +rho*Y[jv55]*rate_eval.p_V55__He4_Ti52
       +rho*Y[jca60]*rate_eval.p_Ca60__He4_K57
       +rho*Y[jmn58]*rate_eval.p_Mn58__He4_Cr55
       +rho*Y[jar41]*rate_eval.p_Ar41__He4_Cl38
       +rho*Y[jcl49]*rate_eval.p_Cl49__He4_S46
       +rho*Y[jti61]*rate_eval.p_Ti61__He4_Sc58
       +rho*Y[jti60]*rate_eval.p_Ti60__He4_Sc57
       +rho*Y[jb10]*rate_eval.p_B10__He4_Be7
       +rho*Y[js40]*rate_eval.p_S40__He4_P37
       +rho*Y[jmn70]*rate_eval.p_Mn70__He4_Cr67
       +rho*Y[jp39]*rate_eval.p_P39__He4_Si36
       +2*rho*Y[jli7]*rate_eval.p_Li7__He4_He4
       +rho*Y[jca59]*rate_eval.p_Ca59__He4_K56
       +rho*Y[jf21]*rate_eval.p_F21__He4_O18
       +rho*Y[jsc61]*rate_eval.p_Sc61__He4_Ca58
       +rho*Y[jbe9]*rate_eval.p_Be9__He4_Li6
       +rho*Y[jca54]*rate_eval.p_Ca54__He4_K51
       +rho*Y[jca53]*rate_eval.p_Ca53__He4_K50
       +rho*Y[jcr64]*rate_eval.p_Cr64__He4_V61
       +rho*Y[jmg30]*rate_eval.p_Mg30__He4_Na27
       +rho*Y[jsc53]*rate_eval.p_Sc53__He4_Ca50
       +rho*Y[jmg41]*rate_eval.p_Mg41__He4_Na38
       +rho*Y[jk55]*rate_eval.p_K55__He4_Ar52
       +rho*Y[jmn68]*rate_eval.p_Mn68__He4_Cr65
       +rho*Y[jmg38]*rate_eval.p_Mg38__He4_Na35
       +rho*Y[jmg35]*rate_eval.p_Mg35__He4_Na32
       +rho*Y[jsc50]*rate_eval.p_Sc50__He4_Ca47
       +rho*Y[jp45]*rate_eval.p_P45__He4_Si42
       +rho*Y[jk43]*rate_eval.p_K43__He4_Ar40
       +rho*Y[jp40]*rate_eval.p_P40__He4_Si37
       +rho*Y[jv54]*rate_eval.p_V54__He4_Ti51
       +rho*Y[jv62]*rate_eval.p_V62__He4_Ti59
       +rho*Y[jp47]*rate_eval.p_P47__He4_Si44
       +rho*Y[jti62]*rate_eval.p_Ti62__He4_Sc59
       +rho*Y[jcr59]*rate_eval.p_Cr59__He4_V56
       +rho*Y[jp35]*rate_eval.p_P35__He4_Si32
       +rho*Y[jp34]*rate_eval.p_P34__He4_Si31
       +rho*Y[jk39]*rate_eval.p_K39__He4_Ar36
       +rho*Y[jn16]*rate_eval.p_N16__He4_C13
       +rho*Y[jna32]*rate_eval.p_Na32__He4_Ne29
       +rho*Y[jk54]*rate_eval.p_K54__He4_Ar51
       +rho*Y[jmn61]*rate_eval.p_Mn61__He4_Cr58
       +rho*Y[jcl47]*rate_eval.p_Cl47__He4_S44
       +rho*Y[jti59]*rate_eval.p_Ti59__He4_Sc56
       +rho*Y[jti58]*rate_eval.p_Ti58__He4_Sc55
       +rho*Y[jsc43]*rate_eval.p_Sc43__He4_Ca40
       +rho*Y[jsc62]*rate_eval.p_Sc62__He4_Ca59
       +rho*Y[jcr58]*rate_eval.p_Cr58__He4_V55
       +rho*Y[jcr63]*rate_eval.p_Cr63__He4_V60
       +rho*Y[jk53]*rate_eval.p_K53__He4_Ar50
       +rho*Y[jna25]*rate_eval.p_Na25__He4_Ne22
       +rho*Y[jmg39]*rate_eval.p_Mg39__He4_Na36
       +rho*Y[jv66]*rate_eval.p_V66__He4_Ti63
       +rho*Y[jp41]*rate_eval.p_P41__He4_Si38
       +rho*Y[jbe10]*rate_eval.p_Be10__He4_Li7
       +rho*Y[jcl44]*rate_eval.p_Cl44__He4_S41
       +rho*Y[jsc54]*rate_eval.p_Sc54__He4_Ca51
       +rho*Y[jcr70]*rate_eval.p_Cr70__He4_V67
       +rho*Y[jti55]*rate_eval.p_Ti55__He4_Sc52
       +rho*Y[jv59]*rate_eval.p_V59__He4_Ti56
       +rho*Y[jar49]*rate_eval.p_Ar49__He4_Cl46
       +rho*Y[jf26]*rate_eval.p_F26__He4_O23
       +rho*Y[jsc42]*rate_eval.p_Sc42__He4_Ca39
       +rho*Y[jsi38]*rate_eval.p_Si38__He4_Al35
       )

    jac[jhe4, jd] = (
       -rho*Y[jhe4]*rate_eval.He4_d__Li6
       +2*rho*Y[jli7]*rate_eval.d_Li7__n_He4_He4
       +2*rho*Y[jbe7]*rate_eval.d_Be7__p_He4_He4
       +rho*Y[jhe3]*rate_eval.d_He3__p_He4
       +rho*Y[jt]*rate_eval.d_t__n_He4
       +5.00000000000000e-01*rho*2*Y[jd]*rate_eval.d_d__He4
       )

    jac[jhe4, jt] = (
       -rho*Y[jhe4]*rate_eval.He4_t__Li7
       +2*rho*Y[jbe7]*rate_eval.t_Be7__n_p_He4_He4
       +rho*Y[jhe3]*rate_eval.t_He3__n_p_He4
       +rho*Y[jhe3]*rate_eval.t_He3__d_He4
       +rho*Y[jd]*rate_eval.d_t__n_He4
       +rho*Y[jp]*rate_eval.p_t__He4
       +2*rho*Y[jli7]*rate_eval.t_Li7__n_n_He4_He4
       +5.00000000000000e-01*rho*2*Y[jt]*rate_eval.t_t__n_n_He4
       )

    jac[jhe4, jhe3] = (
       -rho*Y[jhe4]*rate_eval.He4_He3__Be7
       +2*rho*Y[jbe7]*rate_eval.He3_Be7__p_p_He4_He4
       +5.00000000000000e-01*rho*2*Y[jhe3]*rate_eval.He3_He3__p_p_He4
       +rho*Y[jt]*rate_eval.t_He3__n_p_He4
       +rho*Y[jt]*rate_eval.t_He3__d_He4
       +rho*Y[jd]*rate_eval.d_He3__p_He4
       +rho*Y[jp]*rate_eval.p_He3__He4__weak__bet_pos_
       +rho*Y[jn]*rate_eval.n_He3__He4
       +2*rho*Y[jli7]*rate_eval.He3_Li7__n_p_He4_He4
       )

    jac[jhe4, jhe4] = (
       -5.00000000000000e-01*rho**2*Y[jn]**2*rate_eval.n_n_He4__He6
       -rho*Y[jca36]*rate_eval.He4_Ca36__p_p_Ca38
       -rho*Y[jo13]*rate_eval.He4_O13__p_p_O15
       -rho*Y[jfe76]*rate_eval.He4_Fe76__n_Ni79
       -rho*Y[jfe75]*rate_eval.He4_Fe75__n_Ni78
       -rho*Y[jfe74]*rate_eval.He4_Fe74__n_Ni77
       -rho*Y[jfe71]*rate_eval.He4_Fe71__n_Ni74
       -rho*Y[jfe70]*rate_eval.He4_Fe70__n_Ni73
       -rho*Y[jfe68]*rate_eval.He4_Fe68__n_Ni71
       -rho*Y[jfe64]*rate_eval.He4_Fe64__n_Ni67
       -rho*Y[jfe63]*rate_eval.He4_Fe63__n_Ni66
       -rho*Y[jfe59]*rate_eval.He4_Fe59__n_Ni62
       -rho*Y[jsc59]*rate_eval.He4_Sc59__V63
       -rho*Y[js30]*rate_eval.He4_S30__Ar34
       -rho*Y[jfe52]*rate_eval.He4_Fe52__p_Co55
       -rho*Y[jcr66]*rate_eval.He4_Cr66__Fe70
       -rho*Y[jfe49]*rate_eval.He4_Fe49__p_Co52
       -rho*Y[jfe48]*rate_eval.He4_Fe48__p_Co51
       -rho*Y[jmn73]*rate_eval.He4_Mn73__n_Co76
       -rho*Y[jmn72]*rate_eval.He4_Mn72__n_Co75
       -rho*Y[jmn69]*rate_eval.He4_Mn69__n_Co72
       -rho*Y[jmn68]*rate_eval.He4_Mn68__n_Co71
       -rho*Y[jsi33]*rate_eval.He4_Si33__n_S36
       -rho*Y[jca52]*rate_eval.He4_Ca52__Ti56
       -rho*Y[jmn65]*rate_eval.He4_Mn65__n_Co68
       -rho*Y[jmn68]*rate_eval.He4_Mn68__Co72
       -rho*Y[jmn60]*rate_eval.He4_Mn60__n_Co63
       -rho*Y[jfe65]*rate_eval.He4_Fe65__Ni69
       -rho*Y[jmn53]*rate_eval.He4_Mn53__p_Fe56
       -rho*Y[jmn51]*rate_eval.He4_Mn51__p_Fe54
       -rho*Y[jmn49]*rate_eval.He4_Mn49__p_Fe52
       -rho*Y[jmn47]*rate_eval.He4_Mn47__p_Fe50
       -rho*Y[jmn46]*rate_eval.He4_Mn46__p_Fe49
       -rho*Y[jmn44]*rate_eval.He4_Mn44__p_Fe47
       -rho*Y[jcr70]*rate_eval.He4_Cr70__n_Fe73
       -rho*Y[jcr69]*rate_eval.He4_Cr69__n_Fe72
       -rho*Y[jcr66]*rate_eval.He4_Cr66__n_Fe69
       -rho*Y[jcr65]*rate_eval.He4_Cr65__n_Fe68
       -rho*Y[jcr64]*rate_eval.He4_Cr64__n_Fe67
       -rho*Y[jcr63]*rate_eval.He4_Cr63__n_Fe66
       -rho*Y[jcr62]*rate_eval.He4_Cr62__n_Fe65
       -rho*Y[jmn48]*rate_eval.He4_Mn48__Co52
       -rho*Y[jcr61]*rate_eval.He4_Cr61__n_Fe64
       -rho*Y[jcr59]*rate_eval.He4_Cr59__n_Fe62
       -rho*Y[jcr55]*rate_eval.He4_Cr55__n_Fe58
       -rho*Y[jcr49]*rate_eval.He4_Cr49__p_Mn52
       -rho*Y[jcr48]*rate_eval.He4_Cr48__p_Mn51
       -rho*Y[jcr45]*rate_eval.He4_Cr45__p_Mn48
       -rho*Y[jne29]*rate_eval.He4_Ne29__Mg33
       -rho*Y[jti59]*rate_eval.He4_Ti59__n_Cr62
       -rho*Y[jp44]*rate_eval.He4_P44__n_Cl47
       -rho*Y[jcr44]*rate_eval.He4_Cr44__p_Mn47
       -rho*Y[jcr43]*rate_eval.He4_Cr43__p_Mn46
       -rho*Y[jcr42]*rate_eval.He4_Cr42__p_Mn45
       -rho*Y[jv67]*rate_eval.He4_V67__n_Mn70
       -rho*Y[jsc37]*rate_eval.He4_Sc37__p_Ti40
       -rho*Y[jv66]*rate_eval.He4_V66__n_Mn69
       -rho*Y[jv50]*rate_eval.He4_V50__p_Cr53
       -rho*Y[jv64]*rate_eval.He4_V64__n_Mn67
       -rho*Y[jmn60]*rate_eval.He4_Mn60__Co64
       -rho*Y[jv62]*rate_eval.He4_V62__n_Mn65
       -rho*Y[jv61]*rate_eval.He4_V61__n_Mn64
       -rho*Y[jal32]*rate_eval.He4_Al32__n_P35
       -rho*Y[jv63]*rate_eval.He4_V63__Mn67
       -rho*Y[jv59]*rate_eval.He4_V59__n_Mn62
       -rho*Y[jv58]*rate_eval.He4_V58__n_Mn61
       -rho*Y[jv56]*rate_eval.He4_V56__n_Mn59
       -rho*Y[jal40]*rate_eval.He4_Al40__p_Si43
       -rho*Y[jv55]*rate_eval.He4_V55__n_Mn58
       -rho*Y[jcr47]*rate_eval.He4_Cr47__p_Mn50
       -rho*Y[jv54]*rate_eval.He4_V54__n_Mn57
       -rho*Y[jar52]*rate_eval.He4_Ar52__Ca56
       -rho*Y[js45]*rate_eval.He4_S45__n_Ar48
       -rho*Y[jca43]*rate_eval.He4_Ca43__Ti47
       -rho*Y[jn15]*rate_eval.He4_N15__F19
       -rho*Y[jv47]*rate_eval.He4_V47__p_Cr50
       -rho*Y[jv46]*rate_eval.He4_V46__p_Cr49
       -rho*Y[jv58]*rate_eval.He4_V58__Mn62
       -rho*Y[jv43]*rate_eval.He4_V43__p_Cr46
       -rho*Y[jv42]*rate_eval.He4_V42__p_Cr45
       -rho*Y[jsi43]*rate_eval.He4_Si43__n_S46
       -rho*Y[jne33]*rate_eval.He4_Ne33__n_Mg36
       -rho*Y[jv39]*rate_eval.He4_V39__p_Cr42
       -rho*Y[jti65]*rate_eval.He4_Ti65__n_Cr68
       -rho*Y[jti64]*rate_eval.He4_Ti64__n_Cr67
       -rho*Y[jti63]*rate_eval.He4_Ti63__n_Cr66
       -rho*Y[jti60]*rate_eval.He4_Ti60__n_Cr63
       -rho*Y[jti58]*rate_eval.He4_Ti58__n_Cr61
       -rho*Y[jti55]*rate_eval.He4_Ti55__n_Cr58
       -rho*Y[jti54]*rate_eval.He4_Ti54__n_Cr57
       -rho*Y[jti53]*rate_eval.He4_Ti53__n_Cr56
       -rho*Y[jbe10]*rate_eval.He4_Be10__C14
       -rho*Y[jti51]*rate_eval.He4_Ti51__n_Cr54
       -rho*Y[jf26]*rate_eval.He4_F26__Na30
       -rho*Y[jfe73]*rate_eval.He4_Fe73__n_Ni76
       -rho*Y[jk36]*rate_eval.He4_K36__p_Ca39
       -rho*Y[jar35]*rate_eval.He4_Ar35__Ca39
       -rho*Y[jna19]*rate_eval.He4_Na19__Al23
       -rho*Y[jti43]*rate_eval.He4_Ti43__p_V46
       -rho*Y[jf28]*rate_eval.He4_F28__n_Na31
       -rho*Y[jf31]*rate_eval.He4_F31__n_Na34
       -rho*Y[jti40]*rate_eval.He4_Ti40__p_V43
       -rho*Y[jti39]*rate_eval.He4_Ti39__p_V42
       -rho*Y[jti38]*rate_eval.He4_Ti38__p_V41
       -rho*Y[jti37]*rate_eval.He4_Ti37__p_V40
       -rho*Y[jsc62]*rate_eval.He4_Sc62__n_V65
       -rho*Y[jsc61]*rate_eval.He4_Sc61__n_V64
       -rho*Y[jsc40]*rate_eval.He4_Sc40__p_Ti43
       -rho*Y[jsc60]*rate_eval.He4_Sc60__n_V63
       -rho*Y[jsc59]*rate_eval.He4_Sc59__n_V62
       -rho*Y[jsc58]*rate_eval.He4_Sc58__n_V61
       -rho*Y[jsc57]*rate_eval.He4_Sc57__n_V60
       -rho*Y[jsc56]*rate_eval.He4_Sc56__n_V59
       -rho*Y[jsc55]*rate_eval.He4_Sc55__n_V58
       -rho*Y[jsc54]*rate_eval.He4_Sc54__n_V57
       -rho*Y[jsc52]*rate_eval.He4_Sc52__n_V55
       -rho*Y[jc9]*rate_eval.He4_C9__p_N12
       -rho*Y[jsc51]*rate_eval.He4_Sc51__n_V54
       -rho*Y[jar29]*rate_eval.He4_Ar29__Ca33
       -rho*Y[jsc47]*rate_eval.He4_Sc47__p_Ti50
       -rho*Y[jsc46]*rate_eval.He4_Sc46__p_Ti49
       -rho*Y[jsc45]*rate_eval.He4_Sc45__p_Ti48
       -rho*Y[jsc44]*rate_eval.He4_Sc44__p_Ti47
       -rho*Y[jsc43]*rate_eval.He4_Sc43__p_Ti46
       -rho*Y[jsc42]*rate_eval.He4_Sc42__p_Ti45
       -rho*Y[jsc39]*rate_eval.He4_Sc39__p_Ti42
       -rho*Y[jsc38]*rate_eval.He4_Sc38__p_Ti41
       -rho*Y[jsc36]*rate_eval.He4_Sc36__p_Ti39
       -rho*Y[jsc35]*rate_eval.He4_Sc35__p_Ti38
       -rho*Y[jca58]*rate_eval.He4_Ca58__n_Ti61
       -rho*Y[jal25]*rate_eval.He4_Al25__P29
       -rho*Y[jca53]*rate_eval.He4_Ca53__n_Ti56
       -rho*Y[jca51]*rate_eval.He4_Ca51__n_Ti54
       -rho*Y[jca47]*rate_eval.He4_Ca47__n_Ti50
       -rho*Y[jca57]*rate_eval.He4_Ca57__n_Ti60
       -rho*Y[jca43]*rate_eval.He4_Ca43__n_Ti46
       -rho*Y[jti45]*rate_eval.He4_Ti45__p_V48
       -rho*Y[jf16]*rate_eval.He4_F16__Na20
       -rho*Y[jv63]*rate_eval.He4_V63__n_Mn66
       -rho*Y[jfe66]*rate_eval.He4_Fe66__n_Ni69
       -rho*Y[jp39]*rate_eval.He4_P39__n_Cl42
       -rho*Y[jca48]*rate_eval.He4_Ca48__Ti52
       -rho*Y[jk57]*rate_eval.He4_K57__n_Sc60
       -rho*Y[jsi42]*rate_eval.He4_Si42__S46
       -rho*Y[jk56]*rate_eval.He4_K56__n_Sc59
       -rho*Y[jk54]*rate_eval.He4_K54__n_Sc57
       -rho*Y[jk53]*rate_eval.He4_K53__n_Sc56
       -rho*Y[jk52]*rate_eval.He4_K52__n_Sc55
       -rho*Y[jk51]*rate_eval.He4_K51__n_Sc54
       -rho*Y[jcr57]*rate_eval.He4_Cr57__n_Fe60
       -rho*Y[jk50]*rate_eval.He4_K50__n_Sc53
       -rho*Y[jk48]*rate_eval.He4_K48__n_Sc51
       -rho*Y[jsc35]*rate_eval.He4_Sc35__V39
       -rho*Y[jk43]*rate_eval.He4_K43__p_Ca46
       -rho*Y[jk42]*rate_eval.He4_K42__p_Ca45
       -rho*Y[jk42]*rate_eval.He4_K42__n_Sc45
       -rho*Y[jk41]*rate_eval.He4_K41__n_Sc44
       -rho*Y[jk46]*rate_eval.He4_K46__p_Ca49
       -rho*Y[jsc43]*rate_eval.He4_Sc43__V47
       -rho*Y[jk37]*rate_eval.He4_K37__p_Ca40
       -rho*Y[jk44]*rate_eval.He4_K44__p_Ca47
       -rho*Y[jk34]*rate_eval.He4_K34__p_Ca37
       -rho*Y[jsc54]*rate_eval.He4_Sc54__V58
       -rho*Y[jk31]*rate_eval.He4_K31__p_Ca34
       -rho*Y[jf20]*rate_eval.He4_F20__n_Na23
       -rho*Y[jar46]*rate_eval.He4_Ar46__n_Ca49
       -rho*Y[jfe50]*rate_eval.He4_Fe50__p_Co53
       -rho*Y[jsi35]*rate_eval.He4_Si35__n_S38
       -rho*Y[jar43]*rate_eval.He4_Ar43__n_Ca46
       -rho*Y[jcl47]*rate_eval.He4_Cl47__K51
       -rho*Y[jmn54]*rate_eval.He4_Mn54__Co58
       -rho*Y[jfe68]*rate_eval.He4_Fe68__Ni72
       -rho*Y[jmn62]*rate_eval.He4_Mn62__n_Co65
       -rho*Y[jar34]*rate_eval.He4_Ar34__p_K37
       -rho*Y[jar33]*rate_eval.He4_Ar33__p_K36
       -rho*Y[jar31]*rate_eval.He4_Ar31__p_K34
       -rho*Y[jar29]*rate_eval.He4_Ar29__p_K32
       -rho*Y[jcl51]*rate_eval.He4_Cl51__n_K54
       -rho*Y[jcl50]*rate_eval.He4_Cl50__K54
       -rho*Y[jcl49]*rate_eval.He4_Cl49__n_K52
       -rho*Y[jar36]*rate_eval.He4_Ar36__Ca40
       -rho*Y[jca50]*rate_eval.He4_Ca50__n_Ti53
       -rho*Y[jcl47]*rate_eval.He4_Cl47__n_K50
       -rho*Y[jcl43]*rate_eval.He4_Cl43__p_Ar46
       -rho*Y[jv49]*rate_eval.He4_V49__Mn53
       -rho*Y[jcl42]*rate_eval.He4_Cl42__n_K45
       -rho*Y[jcl41]*rate_eval.He4_Cl41__n_K44
       -rho*Y[jcl40]*rate_eval.He4_Cl40__n_K43
       -rho*Y[jf17]*rate_eval.He4_F17__Na21
       -rho*Y[jcl34]*rate_eval.He4_Cl34__p_Ar37
       -rho*Y[js48]*rate_eval.He4_S48__n_Ar51
       -rho*Y[jar35]*rate_eval.He4_Ar35__p_K38
       -rho*Y[jcl30]*rate_eval.He4_Cl30__p_Ar33
       -rho*Y[jna25]*rate_eval.He4_Na25__Al29
       -rho*Y[jcl28]*rate_eval.He4_Cl28__p_Ar31
       -rho*Y[jmg38]*rate_eval.He4_Mg38__n_Si41
       -rho*Y[js43]*rate_eval.He4_S43__n_Ar46
       -rho*Y[jmn67]*rate_eval.He4_Mn67__n_Co70
       -rho*Y[jfe56]*rate_eval.He4_Fe56__Ni60
       -rho*Y[js42]*rate_eval.He4_S42__n_Ar45
       -rho*Y[js41]*rate_eval.He4_S41__n_Ar44
       -rho*Y[jsc63]*rate_eval.He4_Sc63__n_V66
       -rho*Y[jfe47]*rate_eval.He4_Fe47__Ni51
       -rho*Y[js38]*rate_eval.He4_S38__n_Ar41
       -rho*Y[jmn47]*rate_eval.He4_Mn47__Co51
       -rho*Y[js37]*rate_eval.He4_S37__n_Ar40
       -rho*Y[jk49]*rate_eval.He4_K49__n_Sc52
       -rho*Y[jp34]*rate_eval.He4_P34__n_Cl37
       -rho*Y[js35]*rate_eval.He4_S35__n_Ar38
       -rho*Y[js34]*rate_eval.He4_S34__p_Cl37
       -rho*Y[jti60]*rate_eval.He4_Ti60__Cr64
       -rho*Y[js31]*rate_eval.He4_S31__p_Cl34
       -rho*Y[js30]*rate_eval.He4_S30__p_Cl33
       -rho*Y[js28]*rate_eval.He4_S28__p_Cl31
       -rho*Y[js26]*rate_eval.He4_S26__p_Cl29
       -rho*Y[jp47]*rate_eval.He4_P47__n_Cl50
       -rho*Y[jp43]*rate_eval.He4_P43__n_Cl46
       -rho*Y[jal38]*rate_eval.He4_Al38__n_P41
       -rho*Y[jp41]*rate_eval.He4_P41__p_S44
       -rho*Y[jp41]*rate_eval.He4_P41__n_Cl44
       -rho*Y[jp37]*rate_eval.He4_P37__n_Cl40
       -rho*Y[jcl44]*rate_eval.He4_Cl44__p_Ar47
       -rho*Y[jp31]*rate_eval.He4_P31__p_S34
       -rho*Y[jp30]*rate_eval.He4_P30__p_S33
       -rho*Y[jk55]*rate_eval.He4_K55__n_Sc58
       -rho*Y[jp27]*rate_eval.He4_P27__p_S30
       -rho*Y[jp26]*rate_eval.He4_P26__p_S29
       -rho*Y[jp25]*rate_eval.He4_P25__p_S28
       -rho*Y[jp24]*rate_eval.He4_P24__p_S27
       -rho*Y[jsi44]*rate_eval.He4_Si44__n_S47
       -rho*Y[jp42]*rate_eval.He4_P42__n_Cl45
       -rho*Y[jsi42]*rate_eval.He4_Si42__n_S45
       -rho*Y[jsi40]*rate_eval.He4_Si40__n_S43
       -rho*Y[jsi39]*rate_eval.He4_Si39__n_S42
       -rho*Y[jsi38]*rate_eval.He4_Si38__n_S41
       -rho*Y[jsi37]*rate_eval.He4_Si37__n_S40
       -rho*Y[jca40]*rate_eval.He4_Ca40__Ti44
       -rho*Y[jmn45]*rate_eval.He4_Mn45__p_Fe48
       -rho*Y[jcr41]*rate_eval.He4_Cr41__p_Mn44
       -rho*Y[jmn43]*rate_eval.He4_Mn43__Co47
       -rho*Y[jv57]*rate_eval.He4_V57__n_Mn60
       -rho*Y[jti61]*rate_eval.He4_Ti61__n_Cr64
       -rho*Y[jsi25]*rate_eval.He4_Si25__p_P28
       -rho*Y[jv40]*rate_eval.He4_V40__p_Cr43
       -rho*Y[jsi24]*rate_eval.He4_Si24__p_P27
       -rho*Y[jbe7]*rate_eval.He4_Be7__C11
       -rho*Y[jca54]*rate_eval.He4_Ca54__Ti58
       -rho*Y[jk40]*rate_eval.He4_K40__p_Ca43
       -rho*Y[jsi23]*rate_eval.He4_Si23__p_P26
       -rho*Y[jar42]*rate_eval.He4_Ar42__n_Ca45
       -rho*Y[jsi22]*rate_eval.He4_Si22__p_P25
       -rho*Y[jal42]*rate_eval.He4_Al42__n_P45
       -rho*Y[jal40]*rate_eval.He4_Al40__n_P43
       -rho*Y[jal39]*rate_eval.He4_Al39__p_Si42
       -rho*Y[jal38]*rate_eval.He4_Al38__p_Si41
       -rho*Y[jmn49]*rate_eval.He4_Mn49__Co53
       -rho*Y[jal36]*rate_eval.He4_Al36__p_Si39
       -rho*Y[jal36]*rate_eval.He4_Al36__n_P39
       -rho*Y[jmn59]*rate_eval.He4_Mn59__Co63
       -rho*Y[jal35]*rate_eval.He4_Al35__n_P38
       -rho*Y[jal34]*rate_eval.He4_Al34__n_P37
       -rho*Y[jk50]*rate_eval.He4_K50__Sc54
       -rho*Y[jal33]*rate_eval.He4_Al33__n_P36
       -rho*Y[jsi27]*rate_eval.He4_Si27__p_P30
       -rho*Y[jal31]*rate_eval.He4_Al31__p_Si34
       -rho*Y[jal31]*rate_eval.He4_Al31__n_P34
       -rho*Y[jal29]*rate_eval.He4_Al29__n_P32
       -rho*Y[jal37]*rate_eval.He4_Al37__n_P40
       -rho*Y[jk41]*rate_eval.He4_K41__p_Ca44
       -rho*Y[jal27]*rate_eval.He4_Al27__p_Si30
       -rho*Y[jal27]*rate_eval.He4_Al27__n_P30
       -rho*Y[jal32]*rate_eval.He4_Al32__P36
       -rho*Y[jal24]*rate_eval.He4_Al24__p_Si27
       -rho*Y[jal25]*rate_eval.He4_Al25__p_Si28
       -rho*Y[jal22]*rate_eval.He4_Al22__p_Si25
       -rho*Y[jal21]*rate_eval.He4_Al21__p_Si24
       -rho*Y[jmg40]*rate_eval.He4_Mg40__n_Si43
       -rho*Y[jmg39]*rate_eval.He4_Mg39__n_Si42
       -rho*Y[jmg37]*rate_eval.He4_Mg37__n_Si40
       -rho*Y[jmg35]*rate_eval.He4_Mg35__n_Si38
       -rho*Y[jmg34]*rate_eval.He4_Mg34__n_Si37
       -rho*Y[jmg32]*rate_eval.He4_Mg32__n_Si35
       -rho*Y[jmg30]*rate_eval.He4_Mg30__n_Si33
       -rho*Y[jcr46]*rate_eval.He4_Cr46__p_Mn49
       -rho*Y[jk57]*rate_eval.He4_K57__Sc61
       -rho*Y[jne23]*rate_eval.He4_Ne23__n_Mg26
       -rho*Y[jmg27]*rate_eval.He4_Mg27__n_Si30
       -rho*Y[jo23]*rate_eval.He4_O23__n_Ne26
       -rho*Y[jk35]*rate_eval.He4_K35__p_Ca38
       -rho*Y[jmg26]*rate_eval.He4_Mg26__n_Si29
       -rho*Y[jfe53]*rate_eval.He4_Fe53__p_Co56
       -rho*Y[jmg25]*rate_eval.He4_Mg25__n_Si28
       -rho*Y[jmg22]*rate_eval.He4_Mg22__p_Al25
       -rho*Y[jmg20]*rate_eval.He4_Mg20__p_Al23
       -rho*Y[jna36]*rate_eval.He4_Na36__n_Al39
       -rho*Y[jna38]*rate_eval.He4_Na38__n_Al41
       -rho*Y[jna37]*rate_eval.He4_Na37__p_Mg40
       -rho*Y[jk33]*rate_eval.He4_K33__Sc37
       -rho*Y[jna35]*rate_eval.He4_Na35__n_Al38
       -rho*Y[jna34]*rate_eval.He4_Na34__n_Al37
       -rho*Y[jv60]*rate_eval.He4_V60__n_Mn63
       -rho*Y[jna33]*rate_eval.He4_Na33__p_Mg36
       -rho*Y[jsc44]*rate_eval.He4_Sc44__V48
       -rho*Y[jna31]*rate_eval.He4_Na31__n_Al34
       -rho*Y[jna28]*rate_eval.He4_Na28__n_Al31
       -rho*Y[jna26]*rate_eval.He4_Na26__n_Al29
       -rho*Y[jna24]*rate_eval.He4_Na24__p_Mg27
       -rho*Y[jna23]*rate_eval.He4_Na23__p_Mg26
       -rho*Y[jna22]*rate_eval.He4_Na22__p_Mg25
       -rho*Y[js41]*rate_eval.He4_S41__Ar45
       -rho*Y[js29]*rate_eval.He4_S29__p_Cl32
       -rho*Y[jcl35]*rate_eval.He4_Cl35__p_Ar38
       -rho*Y[js46]*rate_eval.He4_S46__n_Ar49
       -rho*Y[jne31]*rate_eval.He4_Ne31__n_Mg34
       -rho*Y[jne30]*rate_eval.He4_Ne30__n_Mg33
       -rho*Y[jar43]*rate_eval.He4_Ar43__Ca47
       -rho*Y[jne28]*rate_eval.He4_Ne28__n_Mg31
       -rho*Y[jne27]*rate_eval.He4_Ne27__n_Mg30
       -rho*Y[jca39]*rate_eval.He4_Ca39__Ti43
       -rho*Y[jti54]*rate_eval.He4_Ti54__Cr58
       -rho*Y[js39]*rate_eval.He4_S39__n_Ar42
       -rho*Y[js27]*rate_eval.He4_S27__p_Cl30
       -rho*Y[jne24]*rate_eval.He4_Ne24__n_Mg27
       -rho*Y[jca61]*rate_eval.He4_Ca61__n_Ti64
       -rho*Y[jk39]*rate_eval.He4_K39__Sc43
       -rho*Y[jsc62]*rate_eval.He4_Sc62__V66
       -rho*Y[jne22]*rate_eval.He4_Ne22__n_Mg25
       -rho*Y[jne21]*rate_eval.He4_Ne21__n_Mg24
       -rho*Y[jal26]*rate_eval.He4_Al26__p_Si29
       -rho*Y[jne19]*rate_eval.He4_Ne19__p_Na22
       -rho*Y[jne18]*rate_eval.He4_Ne18__p_Na21
       -rho*Y[jne17]*rate_eval.He4_Ne17__p_Na20
       -rho*Y[jne16]*rate_eval.He4_Ne16__p_Na19
       -rho*Y[jcl49]*rate_eval.He4_Cl49__K53
       -rho*Y[jar53]*rate_eval.He4_Ar53__n_Ca56
       -rho*Y[jf30]*rate_eval.He4_F30__p_Ne33
       -rho*Y[jf29]*rate_eval.He4_F29__n_Na32
       -rho*Y[jf27]*rate_eval.He4_F27__n_Na30
       -rho*Y[jf26]*rate_eval.He4_F26__n_Na29
       -rho*Y[jca38]*rate_eval.He4_Ca38__Ti42
       -rho*Y[jf24]*rate_eval.He4_F24__n_Na27
       -rho*Y[jti42]*rate_eval.He4_Ti42__p_V45
       -rho*Y[jf21]*rate_eval.He4_F21__p_Ne24
       -rho*Y[jf21]*rate_eval.He4_F21__n_Na24
       -rho*Y[jf20]*rate_eval.He4_F20__p_Ne23
       -rho*Y[jf19]*rate_eval.He4_F19__p_Ne22
       -rho*Y[jf18]*rate_eval.He4_F18__p_Ne21
       -rho*Y[jo28]*rate_eval.He4_O28__n_Ne31
       -rho*Y[jo26]*rate_eval.He4_O26__n_Ne29
       -rho*Y[jti44]*rate_eval.He4_Ti44__p_V47
       -rho*Y[jo24]*rate_eval.He4_O24__n_Ne27
       -rho*Y[jf30]*rate_eval.He4_F30__n_Na33
       -rho*Y[jo22]*rate_eval.He4_O22__n_Ne25
       -rho*Y[jar52]*rate_eval.He4_Ar52__n_Ca55
       -rho*Y[jo19]*rate_eval.He4_O19__n_Ne22
       -rho*Y[jcl32]*rate_eval.He4_Cl32__p_Ar35
       -rho*Y[jo17]*rate_eval.He4_O17__n_Ne20
       -rho*Y[jne26]*rate_eval.He4_Ne26__n_Mg29
       -rho*Y[jal28]*rate_eval.He4_Al28__n_P31
       -rho*Y[jcr45]*rate_eval.He4_Cr45__Fe49
       -rho*Y[jo13]*rate_eval.He4_O13__p_F16
       -rho*Y[jsc57]*rate_eval.He4_Sc57__V61
       -rho*Y[jar41]*rate_eval.He4_Ar41__n_Ca44
       -rho*Y[jn13]*rate_eval.He4_N13__p_O16
       -rho*Y[jc15]*rate_eval.He4_C15__n_O18
       -rho*Y[jcl50]*rate_eval.He4_Cl50__n_K53
       -rho*Y[jsi31]*rate_eval.He4_Si31__n_S34
       -rho*Y[jcl45]*rate_eval.He4_Cl45__n_K48
       -rho*Y[jc13]*rate_eval.He4_C13__n_O16
       -rho*Y[jb13]*rate_eval.He4_B13__n_N16
       -rho*Y[jb12]*rate_eval.He4_B12__n_N15
       -rho*Y[jb11]*rate_eval.He4_B11__p_C14
       -rho*Y[jfe46]*rate_eval.He4_Fe46__p_Co49
       -rho*Y[jb10]*rate_eval.He4_B10__p_C13
       -rho*Y[jb8]*rate_eval.He4_B8__p_C11
       -rho*Y[jmn70]*rate_eval.He4_Mn70__Co74
       -rho*Y[jli8]*rate_eval.He4_Li8__n_B11
       -rho*Y[jv49]*rate_eval.He4_V49__p_Cr52
       -rho*Y[jv51]*rate_eval.He4_V51__Mn55
       -rho*Y[jfe76]*rate_eval.He4_Fe76__Ni80
       -rho*Y[jfe73]*rate_eval.He4_Fe73__Ni77
       -rho*Y[jfe70]*rate_eval.He4_Fe70__Ni74
       -rho*Y[jne18]*rate_eval.He4_Ne18__Mg22
       -rho*Y[jfe69]*rate_eval.He4_Fe69__Ni73
       -rho*Y[jfe67]*rate_eval.He4_Fe67__Ni71
       -rho*Y[jfe64]*rate_eval.He4_Fe64__Ni68
       -rho*Y[jsc48]*rate_eval.He4_Sc48__n_V51
       -rho*Y[jp36]*rate_eval.He4_P36__n_Cl39
       -rho*Y[jfe59]*rate_eval.He4_Fe59__Ni63
       -rho*Y[jfe58]*rate_eval.He4_Fe58__Ni62
       -rho*Y[jfe54]*rate_eval.He4_Fe54__Ni58
       -rho*Y[jfe52]*rate_eval.He4_Fe52__Ni56
       -rho*Y[jfe51]*rate_eval.He4_Fe51__Ni55
       -rho*Y[jo25]*rate_eval.He4_O25__n_Ne28
       -rho*Y[jfe46]*rate_eval.He4_Fe46__Ni50
       -rho*Y[jfe57]*rate_eval.He4_Fe57__Ni61
       -rho*Y[jfe45]*rate_eval.He4_Fe45__Ni49
       -rho*Y[jmn72]*rate_eval.He4_Mn72__Co76
       -rho*Y[jmn69]*rate_eval.He4_Mn69__Co73
       -rho*Y[jmn67]*rate_eval.He4_Mn67__Co71
       -rho*Y[jcl30]*rate_eval.He4_Cl30__K34
       -rho*Y[jmn66]*rate_eval.He4_Mn66__Co70
       -rho*Y[jmn64]*rate_eval.He4_Mn64__Co68
       -rho*Y[jmn63]*rate_eval.He4_Mn63__Co67
       -rho*Y[jcl29]*rate_eval.He4_Cl29__p_Ar32
       -rho*Y[jmn61]*rate_eval.He4_Mn61__Co65
       -rho*Y[jmn53]*rate_eval.He4_Mn53__Co57
       -rho*Y[jmn52]*rate_eval.He4_Mn52__Co56
       -rho*Y[jmn50]*rate_eval.He4_Mn50__Co54
       -rho*Y[jsi23]*rate_eval.He4_Si23__S27
       -rho*Y[jmn46]*rate_eval.He4_Mn46__Co50
       -rho*Y[jmn45]*rate_eval.He4_Mn45__Co49
       -rho*Y[jcr70]*rate_eval.He4_Cr70__Fe74
       -rho*Y[jcr67]*rate_eval.He4_Cr67__Fe71
       -rho*Y[jcr63]*rate_eval.He4_Cr63__Fe67
       -rho*Y[jcr62]*rate_eval.He4_Cr62__Fe66
       -rho*Y[jcr60]*rate_eval.He4_Cr60__Fe64
       -rho*Y[jcr59]*rate_eval.He4_Cr59__Fe63
       -rho*Y[jmg19]*rate_eval.He4_Mg19__p_Al22
       -rho*Y[jcr58]*rate_eval.He4_Cr58__Fe62
       -rho*Y[jcr57]*rate_eval.He4_Cr57__Fe61
       -rho*Y[jcr54]*rate_eval.He4_Cr54__Fe58
       -rho*Y[jcr53]*rate_eval.He4_Cr53__Fe57
       -rho*Y[jsc48]*rate_eval.He4_Sc48__V52
       -rho*Y[jcr48]*rate_eval.He4_Cr48__Fe52
       -rho*Y[jar45]*rate_eval.He4_Ar45__Ca49
       -rho*Y[jk38]*rate_eval.He4_K38__p_Ca41
       -rho*Y[jp40]*rate_eval.He4_P40__n_Cl43
       -rho*Y[jcr47]*rate_eval.He4_Cr47__Fe51
       -rho*Y[jcr46]*rate_eval.He4_Cr46__Fe50
       -rho*Y[jcr44]*rate_eval.He4_Cr44__Fe48
       -rho*Y[jcr43]*rate_eval.He4_Cr43__Fe47
       -rho*Y[jcr42]*rate_eval.He4_Cr42__Fe46
       -rho*Y[jcr41]*rate_eval.He4_Cr41__Fe45
       -rho*Y[jmg22]*rate_eval.He4_Mg22__Si26
       -rho*Y[jv67]*rate_eval.He4_V67__Mn71
       -rho*Y[jv66]*rate_eval.He4_V66__Mn70
       -rho*Y[jv64]*rate_eval.He4_V64__Mn68
       -rho*Y[jo14]*rate_eval.He4_O14__p_F17
       -rho*Y[jv61]*rate_eval.He4_V61__Mn65
       -rho*Y[jv60]*rate_eval.He4_V60__Mn64
       -rho*Y[jv57]*rate_eval.He4_V57__Mn61
       -rho*Y[jv56]*rate_eval.He4_V56__Mn60
       -rho*Y[jna37]*rate_eval.He4_Na37__n_Al40
       -rho*Y[jv54]*rate_eval.He4_V54__Mn58
       -rho*Y[jv53]*rate_eval.He4_V53__Mn57
       -rho*Y[jv52]*rate_eval.He4_V52__Mn56
       -rho*Y[jne25]*rate_eval.He4_Ne25__Mg29
       -rho*Y[jv50]*rate_eval.He4_V50__Mn54
       -rho*Y[jv65]*rate_eval.He4_V65__Mn69
       -rho*Y[jne32]*rate_eval.He4_Ne32__n_Mg35
       -rho*Y[jf16]*rate_eval.He4_F16__p_Ne19
       -rho*Y[jv47]*rate_eval.He4_V47__Mn51
       -rho*Y[jv46]*rate_eval.He4_V46__Mn50
       -rho*Y[jv45]*rate_eval.He4_V45__Mn49
       -rho*Y[jv43]*rate_eval.He4_V43__Mn47
       -rho*Y[jv41]*rate_eval.He4_V41__Mn45
       -rho*Y[jv39]*rate_eval.He4_V39__Mn43
       -rho*Y[jti63]*rate_eval.He4_Ti63__Cr67
       -rho*Y[jti61]*rate_eval.He4_Ti61__Cr65
       -rho*Y[jti53]*rate_eval.He4_Ti53__Cr57
       -rho*Y[jti52]*rate_eval.He4_Ti52__Cr56
       -rho*Y[jti51]*rate_eval.He4_Ti51__Cr55
       -rho*Y[jna39]*rate_eval.He4_Na39__n_Al42
       -rho*Y[jti48]*rate_eval.He4_Ti48__Cr52
       -rho*Y[jti57]*rate_eval.He4_Ti57__n_Cr60
       -rho*Y[jti46]*rate_eval.He4_Ti46__Cr50
       -rho*Y[jti45]*rate_eval.He4_Ti45__Cr49
       -rho*Y[jti44]*rate_eval.He4_Ti44__Cr48
       -rho*Y[jal29]*rate_eval.He4_Al29__p_Si32
       -rho*Y[jti43]*rate_eval.He4_Ti43__Cr47
       -rho*Y[jti41]*rate_eval.He4_Ti41__Cr45
       -rho*Y[jna32]*rate_eval.He4_Na32__n_Al35
       -rho*Y[jti40]*rate_eval.He4_Ti40__Cr44
       -rho*Y[jti38]*rate_eval.He4_Ti38__Cr42
       -rho*Y[jal35]*rate_eval.He4_Al35__P39
       -rho*Y[jsc60]*rate_eval.He4_Sc60__V64
       -rho*Y[jsc58]*rate_eval.He4_Sc58__V62
       -rho*Y[jca60]*rate_eval.He4_Ca60__n_Ti63
       -rho*Y[jsc56]*rate_eval.He4_Sc56__V60
       -rho*Y[jti49]*rate_eval.He4_Ti49__n_Cr52
       -rho*Y[jsc55]*rate_eval.He4_Sc55__V59
       -rho*Y[jk45]*rate_eval.He4_K45__p_Ca48
       -rho*Y[jsc49]*rate_eval.He4_Sc49__V53
       -rho*Y[jmn44]*rate_eval.He4_Mn44__Co48
       -rho*Y[jsc47]*rate_eval.He4_Sc47__V51
       -rho*Y[jsc45]*rate_eval.He4_Sc45__V49
       -rho*Y[jmg20]*rate_eval.He4_Mg20__Si24
       -rho*Y[jsc42]*rate_eval.He4_Sc42__V46
       -rho*Y[jsc41]*rate_eval.He4_Sc41__V45
       -rho*Y[jsc39]*rate_eval.He4_Sc39__V43
       -rho*Y[jsc38]*rate_eval.He4_Sc38__V42
       -rho*Y[jcr55]*rate_eval.He4_Cr55__Fe59
       -rho*Y[jf25]*rate_eval.He4_F25__n_Na28
       -rho*Y[jca59]*rate_eval.He4_Ca59__Ti63
       -rho*Y[jcr64]*rate_eval.He4_Cr64__Fe68
       -rho*Y[jna27]*rate_eval.He4_Na27__n_Al30
       -rho*Y[jmn59]*rate_eval.He4_Mn59__n_Co62
       -rho*Y[jo27]*rate_eval.He4_O27__Ne31
       -rho*Y[jv48]*rate_eval.He4_V48__p_Cr51
       -rho*Y[jca51]*rate_eval.He4_Ca51__Ti55
       -rho*Y[jbe11]*rate_eval.He4_Be11__n_C14
       -rho*Y[jca50]*rate_eval.He4_Ca50__Ti54
       -rho*Y[jca47]*rate_eval.He4_Ca47__Ti51
       -rho*Y[jna36]*rate_eval.He4_Na36__Al40
       -rho*Y[jca46]*rate_eval.He4_Ca46__Ti50
       -rho*Y[jca45]*rate_eval.He4_Ca45__Ti49
       -rho*Y[jli7]*rate_eval.He4_Li7__B11
       -rho*Y[jca44]*rate_eval.He4_Ca44__Ti48
       -rho*Y[jca42]*rate_eval.He4_Ca42__Ti46
       -rho*Y[jca37]*rate_eval.He4_Ca37__Ti41
       -rho*Y[jca35]*rate_eval.He4_Ca35__Ti39
       -rho*Y[jca34]*rate_eval.He4_Ca34__Ti38
       -rho*Y[jcl46]*rate_eval.He4_Cl46__n_K49
       -rho*Y[jca33]*rate_eval.He4_Ca33__Ti37
       -rho*Y[jna27]*rate_eval.He4_Na27__Al31
       -rho*Y[jk58]*rate_eval.He4_K58__Sc62
       -rho*Y[jcl44]*rate_eval.He4_Cl44__n_K47
       -rho*Y[jna29]*rate_eval.He4_Na29__Al33
       -rho*Y[jsi45]*rate_eval.He4_Si45__S49
       -rho*Y[jk55]*rate_eval.He4_K55__Sc59
       -rho*Y[js27]*rate_eval.He4_S27__Ar31
       -rho*Y[jk51]*rate_eval.He4_K51__Sc55
       -rho*Y[jk49]*rate_eval.He4_K49__Sc53
       -rho*Y[jne17]*rate_eval.He4_Ne17__Mg21
       -rho*Y[jk44]*rate_eval.He4_K44__Sc48
       -rho*Y[jk43]*rate_eval.He4_K43__Sc47
       -rho*Y[jti47]*rate_eval.He4_Ti47__Cr51
       -rho*Y[jne27]*rate_eval.He4_Ne27__Mg31
       -rho*Y[jca36]*rate_eval.He4_Ca36__p_Sc39
       -rho*Y[jsc48]*rate_eval.He4_Sc48__p_Ti51
       -rho*Y[jp28]*rate_eval.He4_P28__Cl32
       -rho*Y[jk35]*rate_eval.He4_K35__Sc39
       -rho*Y[jk32]*rate_eval.He4_K32__Sc36
       -rho*Y[jar53]*rate_eval.He4_Ar53__Ca57
       -rho*Y[jar46]*rate_eval.He4_Ar46__Ca50
       -rho*Y[jar40]*rate_eval.He4_Ar40__Ca44
       -rho*Y[jcr51]*rate_eval.He4_Cr51__Fe55
       -rho*Y[jar39]*rate_eval.He4_Ar39__Ca43
       -rho*Y[jar37]*rate_eval.He4_Ar37__Ca41
       -rho*Y[jca36]*rate_eval.He4_Ca36__Ti40
       -rho*Y[jfe50]*rate_eval.He4_Fe50__Ni54
       -rho*Y[jar33]*rate_eval.He4_Ar33__Ca37
       -rho*Y[jar32]*rate_eval.He4_Ar32__Ca36
       -rho*Y[jar31]*rate_eval.He4_Ar31__Ca35
       -rho*Y[jne20]*rate_eval.He4_Ne20__Mg24
       -rho*Y[jar30]*rate_eval.He4_Ar30__Ca34
       -rho*Y[jcl51]*rate_eval.He4_Cl51__K55
       -rho*Y[jmg34]*rate_eval.He4_Mg34__Si38
       -rho*Y[jcr60]*rate_eval.He4_Cr60__n_Fe63
       -rho*Y[jcl46]*rate_eval.He4_Cl46__K50
       -rho*Y[jp26]*rate_eval.He4_P26__Cl30
       -rho*Y[jcl42]*rate_eval.He4_Cl42__K46
       -rho*Y[jcl39]*rate_eval.He4_Cl39__K43
       -rho*Y[jcl38]*rate_eval.He4_Cl38__K42
       -rho*Y[jcl36]*rate_eval.He4_Cl36__K40
       -rho*Y[jcl35]*rate_eval.He4_Cl35__K39
       -rho*Y[jcl33]*rate_eval.He4_Cl33__K37
       -rho*Y[jcl32]*rate_eval.He4_Cl32__K36
       -rho*Y[jo21]*rate_eval.He4_O21__Ne25
       -rho*Y[jcl31]*rate_eval.He4_Cl31__K35
       -rho*Y[jk45]*rate_eval.He4_K45__Sc49
       -rho*Y[js49]*rate_eval.He4_S49__Ar53
       -rho*Y[js48]*rate_eval.He4_S48__Ar52
       -rho*Y[js47]*rate_eval.He4_S47__Ar51
       -rho*Y[js44]*rate_eval.He4_S44__Ar48
       -rho*Y[js43]*rate_eval.He4_S43__Ar47
       -rho*Y[js46]*rate_eval.He4_S46__Ar50
       -rho*Y[js42]*rate_eval.He4_S42__Ar46
       -rho*Y[jf28]*rate_eval.He4_F28__Na32
       -rho*Y[js39]*rate_eval.He4_S39__Ar43
       -rho*Y[jar47]*rate_eval.He4_Ar47__Ca51
       -rho*Y[js36]*rate_eval.He4_S36__Ar40
       -rho*Y[jmg36]*rate_eval.He4_Mg36__Si40
       -rho*Y[jar54]*rate_eval.He4_Ar54__n_Ca57
       -rho*Y[jca45]*rate_eval.He4_Ca45__n_Ti48
       -rho*Y[js32]*rate_eval.He4_S32__Ar36
       -rho*Y[jo22]*rate_eval.He4_O22__Ne26
       -rho*Y[jne24]*rate_eval.He4_Ne24__Mg28
       -rho*Y[jp37]*rate_eval.He4_P37__Cl41
       -rho*Y[jfe71]*rate_eval.He4_Fe71__Ni75
       -rho*Y[jo21]*rate_eval.He4_O21__n_Ne24
       -rho*Y[jp40]*rate_eval.He4_P40__Cl44
       -rho*Y[jk41]*rate_eval.He4_K41__Sc45
       -rho*Y[jcl37]*rate_eval.He4_Cl37__K41
       -rho*Y[jmg33]*rate_eval.He4_Mg33__n_Si36
       -rho*Y[jcl38]*rate_eval.He4_Cl38__n_K41
       -rho*Y[jp36]*rate_eval.He4_P36__Cl40
       -rho*Y[jp35]*rate_eval.He4_P35__Cl39
       -rho*Y[jcl44]*rate_eval.He4_Cl44__K48
       -rho*Y[jp32]*rate_eval.He4_P32__Cl36
       -rho*Y[js26]*rate_eval.He4_S26__Ar30
       -rho*Y[jp27]*rate_eval.He4_P27__Cl31
       -rho*Y[jna31]*rate_eval.He4_Na31__Al35
       -rho*Y[jp24]*rate_eval.He4_P24__Cl28
       -rho*Y[jcl33]*rate_eval.He4_Cl33__p_Ar36
       -rho*Y[jsi41]*rate_eval.He4_Si41__S45
       -rho*Y[jsi40]*rate_eval.He4_Si40__S44
       -rho*Y[jsi38]*rate_eval.He4_Si38__S42
       -rho*Y[jsi34]*rate_eval.He4_Si34__S38
       -rho*Y[jsi33]*rate_eval.He4_Si33__S37
       -rho*Y[jcl29]*rate_eval.He4_Cl29__K33
       -rho*Y[jsi24]*rate_eval.He4_Si24__S28
       -rho*Y[jal43]*rate_eval.He4_Al43__P47
       -rho*Y[jcl34]*rate_eval.He4_Cl34__K38
       -rho*Y[jal42]*rate_eval.He4_Al42__P46
       -rho*Y[jca38]*rate_eval.He4_Ca38__p_Sc41
       -rho*Y[jal40]*rate_eval.He4_Al40__P44
       -rho*Y[jal38]*rate_eval.He4_Al38__P42
       -rho*Y[jal37]*rate_eval.He4_Al37__P41
       -rho*Y[jal36]*rate_eval.He4_Al36__P40
       -rho*Y[jmg37]*rate_eval.He4_Mg37__Si41
       -rho*Y[jn14]*rate_eval.He4_N14__n_F17
       -rho*Y[jal34]*rate_eval.He4_Al34__P38
       -rho*Y[jcr56]*rate_eval.He4_Cr56__Fe60
       -rho*Y[jal30]*rate_eval.He4_Al30__P34
       -rho*Y[jti62]*rate_eval.He4_Ti62__n_Cr65
       -rho*Y[jal27]*rate_eval.He4_Al27__P31
       -rho*Y[jal26]*rate_eval.He4_Al26__P30
       -rho*Y[jti56]*rate_eval.He4_Ti56__Cr60
       -rho*Y[jmg41]*rate_eval.He4_Mg41__Si45
       -rho*Y[jmg39]*rate_eval.He4_Mg39__Si43
       -rho*Y[jal41]*rate_eval.He4_Al41__P45
       -rho*Y[jsi39]*rate_eval.He4_Si39__S43
       -rho*Y[jmg40]*rate_eval.He4_Mg40__Si44
       -rho*Y[jmg33]*rate_eval.He4_Mg33__Si37
       -rho*Y[jmg31]*rate_eval.He4_Mg31__Si35
       -rho*Y[jal29]*rate_eval.He4_Al29__P33
       -rho*Y[jk47]*rate_eval.He4_K47__Sc51
       -rho*Y[jmg29]*rate_eval.He4_Mg29__Si33
       -rho*Y[jmg30]*rate_eval.He4_Mg30__Si34
       -rho*Y[jmg28]*rate_eval.He4_Mg28__Si32
       -rho*Y[jmn65]*rate_eval.He4_Mn65__Co69
       -rho*Y[jmg23]*rate_eval.He4_Mg23__Si27
       -rho*Y[jmg31]*rate_eval.He4_Mg31__n_Si34
       -rho*Y[jca53]*rate_eval.He4_Ca53__Ti57
       -rho*Y[jmg21]*rate_eval.He4_Mg21__Si25
       -rho*Y[jmn48]*rate_eval.He4_Mn48__p_Fe51
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       -rho*Y[jcl43]*rate_eval.He4_Cl43__K47
       -rho*Y[jmg19]*rate_eval.He4_Mg19__Si23
       -rho*Y[jsi31]*rate_eval.He4_Si31__S35
       -rho*Y[jna37]*rate_eval.He4_Na37__Al41
       -rho*Y[js49]*rate_eval.He4_S49__n_Ar52
       -rho*Y[jna34]*rate_eval.He4_Na34__Al38
       -rho*Y[jna33]*rate_eval.He4_Na33__Al37
       -rho*Y[jna39]*rate_eval.He4_Na39__Al43
       -rho*Y[jal28]*rate_eval.He4_Al28__p_Si31
       -rho*Y[jne29]*rate_eval.He4_Ne29__n_Mg32
       -rho*Y[jp25]*rate_eval.He4_P25__Cl29
       -rho*Y[jna28]*rate_eval.He4_Na28__Al32
       -rho*Y[jti56]*rate_eval.He4_Ti56__n_Cr59
       -rho*Y[jf15]*rate_eval.He4_F15__p_Ne18
       -rho*Y[jna23]*rate_eval.He4_Na23__Al27
       -rho*Y[jv55]*rate_eval.He4_V55__Mn59
       -rho*Y[jar50]*rate_eval.He4_Ar50__Ca54
       -rho*Y[jti42]*rate_eval.He4_Ti42__Cr46
       -rho*Y[jna20]*rate_eval.He4_Na20__Al24
       -rho*Y[jk58]*rate_eval.He4_K58__n_Sc61
       -rho*Y[jne34]*rate_eval.He4_Ne34__Mg38
       -rho*Y[jne31]*rate_eval.He4_Ne31__Mg35
       -rho*Y[jne30]*rate_eval.He4_Ne30__Mg34
       -rho*Y[jca58]*rate_eval.He4_Ca58__Ti62
       -rho*Y[jne26]*rate_eval.He4_Ne26__Mg30
       -rho*Y[jcl52]*rate_eval.He4_Cl52__n_K55
       -rho*Y[jcr65]*rate_eval.He4_Cr65__Fe69
       -rho*Y[jne16]*rate_eval.He4_Ne16__Mg20
       -rho*Y[jna30]*rate_eval.He4_Na30__Al34
       -rho*Y[jo28]*rate_eval.He4_O28__Ne32
       -rho*Y[jf31]*rate_eval.He4_F31__Na35
       -rho*Y[jmg29]*rate_eval.He4_Mg29__n_Si32
       -rho*Y[jar41]*rate_eval.He4_Ar41__Ca45
       -rho*Y[jf24]*rate_eval.He4_F24__Na28
       -rho*Y[jal31]*rate_eval.He4_Al31__P35
       -rho*Y[jmn51]*rate_eval.He4_Mn51__Co55
       -rho*Y[jf18]*rate_eval.He4_F18__Na22
       -rho*Y[jk59]*rate_eval.He4_K59__Sc63
       -rho*Y[jar42]*rate_eval.He4_Ar42__Ca46
       -rho*Y[jo24]*rate_eval.He4_O24__Ne28
       -rho*Y[jo23]*rate_eval.He4_O23__Ne27
       -rho*Y[jf27]*rate_eval.He4_F27__Na31
       -rho*Y[jo20]*rate_eval.He4_O20__Ne24
       -rho*Y[jo20]*rate_eval.He4_O20__n_Ne23
       -rho*Y[jo19]*rate_eval.He4_O19__Ne23
       -rho*Y[js28]*rate_eval.He4_S28__Ar32
       -rho*Y[jar44]*rate_eval.He4_Ar44__n_Ca47
       -rho*Y[jo17]*rate_eval.He4_O17__Ne21
       -rho*Y[jp33]*rate_eval.He4_P33__Cl37
       -rho*Y[jti64]*rate_eval.He4_Ti64__Cr68
       -rho*Y[jli9]*rate_eval.He4_Li9__B13
       -rho*Y[jmg26]*rate_eval.He4_Mg26__Si30
       -rho*Y[jfe45]*rate_eval.He4_Fe45__p_Co48
       -rho*Y[jna24]*rate_eval.He4_Na24__Al28
       -rho*Y[jli8]*rate_eval.He4_Li8__B12
       -rho*Y[jhe3]*rate_eval.He4_He3__Be7
       -rho*Y[jfe75]*rate_eval.He4_Fe75__Ni79
       -rho*Y[jd]*rate_eval.He4_d__Li6
       -rho*Y[jcr49]*rate_eval.He4_Cr49__Fe53
       -rho*Y[jc12]*rate_eval.He4_C12__O16
       -rho*Y[jfe62]*rate_eval.He4_Fe62__n_Ni65
       -rho*Y[jmg27]*rate_eval.He4_Mg27__Si31
       -rho*Y[jp34]*rate_eval.He4_P34__Cl38
       -rho*Y[jca49]*rate_eval.He4_Ca49__n_Ti52
       -rho*Y[jmn73]*rate_eval.He4_Mn73__Co77
       -rho*Y[jk42]*rate_eval.He4_K42__Sc46
       -rho*Y[jna19]*rate_eval.He4_Na19__p_Mg22
       -rho*Y[jmn61]*rate_eval.He4_Mn61__n_Co64
       -rho*Y[jsi28]*rate_eval.He4_Si28__S32
       -rho*Y[jsc41]*rate_eval.He4_Sc41__p_Ti44
       -rho*Y[jsc36]*rate_eval.He4_Sc36__V40
       -rho*Y[jmn43]*rate_eval.He4_Mn43__p_Fe46
       -rho*Y[jk36]*rate_eval.He4_K36__Sc40
       -rho*Y[jsc40]*rate_eval.He4_Sc40__V44
       -rho*Y[jk47]*rate_eval.He4_K47__n_Sc50
       -rho*Y[jo14]*rate_eval.He4_O14__Ne18
       -rho*Y[jmg38]*rate_eval.He4_Mg38__Si42
       -rho*Y[jsi26]*rate_eval.He4_Si26__S30
       -rho*Y[jna20]*rate_eval.He4_Na20__p_Mg23
       -rho*Y[jfe74]*rate_eval.He4_Fe74__Ni78
       -rho*Y[jv44]*rate_eval.He4_V44__p_Cr47
       -rho*Y[jmg36]*rate_eval.He4_Mg36__n_Si39
       -rho*Y[jb11]*rate_eval.He4_B11__n_N14
       -rho*Y[jmn58]*rate_eval.He4_Mn58__Co62
       -rho*Y[jsi32]*rate_eval.He4_Si32__S36
       -rho*Y[js29]*rate_eval.He4_S29__Ar33
       -rho*Y[jf30]*rate_eval.He4_F30__Na34
       -rho*Y[jfe63]*rate_eval.He4_Fe63__Ni67
       -rho*Y[jf20]*rate_eval.He4_F20__Na24
       -rho*Y[jk59]*rate_eval.He4_K59__n_Sc62
       -rho*Y[js47]*rate_eval.He4_S47__n_Ar50
       -rho*Y[jcl28]*rate_eval.He4_Cl28__K32
       -rho*Y[jmg28]*rate_eval.He4_Mg28__n_Si31
       -rho*Y[jcr68]*rate_eval.He4_Cr68__n_Fe71
       -rho*Y[jfe66]*rate_eval.He4_Fe66__Ni70
       -rho*Y[jsi29]*rate_eval.He4_Si29__S33
       -rho*Y[jo18]*rate_eval.He4_O18__n_Ne21
       -rho*Y[jbe9]*rate_eval.He4_Be9__n_C12
       -rho*Y[jfe61]*rate_eval.He4_Fe61__Ni65
       -rho*Y[jca35]*rate_eval.He4_Ca35__p_Sc38
       -rho*Y[jar54]*rate_eval.He4_Ar54__Ca58
       -rho*Y[jv59]*rate_eval.He4_V59__Mn63
       -rho*Y[jp41]*rate_eval.He4_P41__Cl45
       -rho*Y[jp46]*rate_eval.He4_P46__n_Cl49
       -rho*Y[jk53]*rate_eval.He4_K53__Sc57
       -rho*Y[js34]*rate_eval.He4_S34__Ar38
       -rho*Y[jca37]*rate_eval.He4_Ca37__p_Sc40
       -rho*Y[jn12]*rate_eval.He4_N12__p_O15
       -rho*Y[jmn71]*rate_eval.He4_Mn71__Co75
       -rho*Y[jv65]*rate_eval.He4_V65__n_Mn68
       -rho*Y[jbe10]*rate_eval.He4_Be10__n_C13
       -rho*Y[jca55]*rate_eval.He4_Ca55__n_Ti58
       -rho*Y[jar44]*rate_eval.He4_Ar44__Ca48
       -rho*Y[jp28]*rate_eval.He4_P28__p_S31
       -rho*Y[jsi25]*rate_eval.He4_Si25__S29
       -rho*Y[jp38]*rate_eval.He4_P38__Cl42
       -rho*Y[jmg25]*rate_eval.He4_Mg25__Si29
       -rho*Y[jmn52]*rate_eval.He4_Mn52__p_Fe55
       -rho*Y[jn14]*rate_eval.He4_N14__F18
       -rho*Y[jsi36]*rate_eval.He4_Si36__n_S39
       -rho*Y[jv48]*rate_eval.He4_V48__Mn52
       -rho*Y[jca61]*rate_eval.He4_Ca61__Ti65
       -rho*Y[jfe62]*rate_eval.He4_Fe62__Ni66
       -rho*Y[jca55]*rate_eval.He4_Ca55__Ti59
       -rho*Y[jp46]*rate_eval.He4_P46__Cl50
       -rho*Y[jal24]*rate_eval.He4_Al24__P28
       -rho*Y[jti50]*rate_eval.He4_Ti50__Cr54
       -rho*Y[jal43]*rate_eval.He4_Al43__n_P46
       -rho*Y[jfe51]*rate_eval.He4_Fe51__p_Co54
       -rho*Y[jne25]*rate_eval.He4_Ne25__n_Mg28
       -rho*Y[jo27]*rate_eval.He4_O27__n_Ne30
       -rho*Y[jca60]*rate_eval.He4_Ca60__Ti64
       -rho*Y[jp39]*rate_eval.He4_P39__Cl43
       -rho*Y[js38]*rate_eval.He4_S38__Ar42
       -rho*Y[jar30]*rate_eval.He4_Ar30__p_K33
       -rho*Y[jp31]*rate_eval.He4_P31__Cl35
       -rho*Y[jmg32]*rate_eval.He4_Mg32__Si36
       -rho*Y[jcl41]*rate_eval.He4_Cl41__K45
       -rho*Y[jcl43]*rate_eval.He4_Cl43__n_K46
       -rho*Y[jna33]*rate_eval.He4_Na33__n_Al36
       -rho*Y[jti55]*rate_eval.He4_Ti55__Cr59
       -rho*Y[jv45]*rate_eval.He4_V45__p_Cr48
       -rho*Y[jal39]*rate_eval.He4_Al39__P43
       -rho*Y[jna25]*rate_eval.He4_Na25__n_Al28
       -rho*Y[jt]*rate_eval.He4_t__Li7
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       -rho*Y[jp47]*rate_eval.He4_P47__Cl51
       -rho*Y[jcl48]*rate_eval.He4_Cl48__K52
       -rho*Y[jar47]*rate_eval.He4_Ar47__n_Ca50
       -rho*Y[js40]*rate_eval.He4_S40__n_Ar43
       -rho*Y[jsi35]*rate_eval.He4_Si35__S39
       -rho*Y[jp43]*rate_eval.He4_P43__Cl47
       -rho*Y[jna29]*rate_eval.He4_Na29__n_Al32
       -rho*Y[jmg35]*rate_eval.He4_Mg35__Si39
       -rho*Y[jf23]*rate_eval.He4_F23__Na27
       -rho*Y[jna21]*rate_eval.He4_Na21__Al25
       -rho*Y[jp45]*rate_eval.He4_P45__n_Cl48
       -rho*Y[jsc52]*rate_eval.He4_Sc52__V56
       -rho*Y[jmg41]*rate_eval.He4_Mg41__n_Si44
       -rho*Y[jc14]*rate_eval.He4_C14__O18
       -rho*Y[jo18]*rate_eval.He4_O18__Ne22
       -rho*Y[jmn62]*rate_eval.He4_Mn62__Co66
       -rho*Y[jk44]*rate_eval.He4_K44__n_Sc47
       -rho*Y[jal28]*rate_eval.He4_Al28__P32
       -rho*Y[jmn70]*rate_eval.He4_Mn70__n_Co73
       -rho**2*Y[jn]*Y[jp]*rate_eval.n_p_He4__Li6
       -rho*Y[jna25]*rate_eval.He4_Na25__p_Mg28
       -rho*Y[jcl52]*rate_eval.He4_Cl52__K56
       -rho*Y[jsc53]*rate_eval.He4_Sc53__n_V56
       -rho*Y[jk31]*rate_eval.He4_K31__Sc35
       -rho*Y[js31]*rate_eval.He4_S31__Ar35
       -rho*Y[jf15]*rate_eval.He4_F15__Na19
       -rho*Y[jmg21]*rate_eval.He4_Mg21__p_Al24
       -rho*Y[jca41]*rate_eval.He4_Ca41__Ti45
       -rho*Y[jcl40]*rate_eval.He4_Cl40__K44
       -rho*Y[jar45]*rate_eval.He4_Ar45__n_Ca48
       -rho*Y[jp29]*rate_eval.He4_P29__Cl33
       -rho*Y[jf25]*rate_eval.He4_F25__Na29
       -rho*Y[jmn63]*rate_eval.He4_Mn63__n_Co66
       -rho*Y[jc11]*rate_eval.He4_C11__p_N14
       -rho*Y[jfe61]*rate_eval.He4_Fe61__n_Ni64
       -rho*Y[jsi37]*rate_eval.He4_Si37__S41
       -rho*Y[jsc51]*rate_eval.He4_Sc51__V55
       -rho*Y[jti41]*rate_eval.He4_Ti41__p_V44
       -rho*Y[js35]*rate_eval.He4_S35__Ar39
       -rho*Y[js45]*rate_eval.He4_S45__Ar49
       -rho*Y[jk45]*rate_eval.He4_K45__n_Sc48
       -rho*Y[jp38]*rate_eval.He4_P38__n_Cl41
       -rho*Y[jcl48]*rate_eval.He4_Cl48__n_K51
       -rho*Y[jne23]*rate_eval.He4_Ne23__Mg27
       -rho*Y[jar50]*rate_eval.He4_Ar50__n_Ca53
       -rho*Y[jti49]*rate_eval.He4_Ti49__Cr53
       -rho*Y[jk33]*rate_eval.He4_K33__p_Ca36
       -rho*Y[jli6]*rate_eval.He4_Li6__B10
       -rho*Y[js33]*rate_eval.He4_S33__Ar37
       -rho*Y[jcr69]*rate_eval.He4_Cr69__Fe73
       -rho*Y[jca56]*rate_eval.He4_Ca56__Ti60
       -rho*Y[jb10]*rate_eval.He4_B10__n_N13
       -rho*Y[jo15]*rate_eval.He4_O15__Ne19
       -rho*Y[jne28]*rate_eval.He4_Ne28__Mg32
       -rho*Y[jna35]*rate_eval.He4_Na35__Al39
       -rho*Y[jcr61]*rate_eval.He4_Cr61__Fe65
       -rho*Y[jne32]*rate_eval.He4_Ne32__Mg36
       -rho*Y[jne22]*rate_eval.He4_Ne22__Mg26
       -rho*Y[jmn58]*rate_eval.He4_Mn58__n_Co61
       -rho*Y[jti62]*rate_eval.He4_Ti62__Cr66
       -rho*Y[jli9]*rate_eval.He4_Li9__n_B12
       -rho*Y[jal23]*rate_eval.He4_Al23__p_Si26
       -rho*Y[jn16]*rate_eval.He4_N16__n_F19
       -rho*Y[jcl41]*rate_eval.He4_Cl41__p_Ar44
       -rho*Y[jsi36]*rate_eval.He4_Si36__S40
       -rho*Y[jsc46]*rate_eval.He4_Sc46__n_V49
       -rho*Y[jfe65]*rate_eval.He4_Fe65__n_Ni68
       -rho*Y[jb13]*rate_eval.He4_B13__N17
       -rho*Y[jp42]*rate_eval.He4_P42__Cl46
       -rho*Y[jcl45]*rate_eval.He4_Cl45__K49
       -rho*Y[jf21]*rate_eval.He4_F21__Na25
       -rho*Y[jal39]*rate_eval.He4_Al39__n_P42
       -rho*Y[jca49]*rate_eval.He4_Ca49__Ti53
       -rho*Y[jk48]*rate_eval.He4_K48__Sc52
       -rho*Y[jp45]*rate_eval.He4_P45__Cl49
       -rho*Y[jmn64]*rate_eval.He4_Mn64__n_Co67
       -rho*Y[jcl31]*rate_eval.He4_Cl31__p_Ar34
       -rho*Y[jna22]*rate_eval.He4_Na22__Al26
       -rho*Y[jti37]*rate_eval.He4_Ti37__Cr41
       -rho*Y[jna26]*rate_eval.He4_Na26__Al30
       -rho*Y[jf22]*rate_eval.He4_F22__Na26
       -rho*Y[jsc63]*rate_eval.He4_Sc63__V67
       -rho*Y[jti57]*rate_eval.He4_Ti57__Cr61
       -rho*Y[jfe67]*rate_eval.He4_Fe67__n_Ni70
       -rho*Y[jk40]*rate_eval.He4_K40__Sc44
       -rho*Y[jne34]*rate_eval.He4_Ne34__n_Mg37
       -rho*Y[jfe48]*rate_eval.He4_Fe48__Ni52
       -rho*Y[jna30]*rate_eval.He4_Na30__n_Al33
       -rho*Y[jar49]*rate_eval.He4_Ar49__n_Ca52
       -rho*Y[jmn55]*rate_eval.He4_Mn55__Co59
       -rho*Y[jsi30]*rate_eval.He4_Si30__S34
       -rho*Y[jsi43]*rate_eval.He4_Si43__S47
       -rho*Y[jmn56]*rate_eval.He4_Mn56__Co60
       -rho*Y[jp44]*rate_eval.He4_P44__Cl48
       -rho*Y[jsc37]*rate_eval.He4_Sc37__V41
       -rho*Y[jna24]*rate_eval.He4_Na24__n_Al27
       -rho*Y[jo25]*rate_eval.He4_O25__Ne29
       -rho*Y[jsi44]*rate_eval.He4_Si44__S48
       -rho*Y[jk38]*rate_eval.He4_K38__Sc42
       -rho*Y[jti59]*rate_eval.He4_Ti59__Cr63
       -rho*Y[jv52]*rate_eval.He4_V52__n_Mn55
       -rho*Y[jmn71]*rate_eval.He4_Mn71__n_Co74
       -rho*Y[jar34]*rate_eval.He4_Ar34__Ca38
       -rho*Y[jsi22]*rate_eval.He4_Si22__S26
       -rho*Y[jar51]*rate_eval.He4_Ar51__Ca55
       -rho*Y[jmn66]*rate_eval.He4_Mn66__n_Co69
       -rho*Y[jca52]*rate_eval.He4_Ca52__n_Ti55
       -rho*Y[jne19]*rate_eval.He4_Ne19__Mg23
       -rho*Y[jfe60]*rate_eval.He4_Fe60__Ni64
       -rho*Y[jar48]*rate_eval.He4_Ar48__Ca52
       -rho*Y[jca54]*rate_eval.He4_Ca54__n_Ti57
       -rho*Y[jv42]*rate_eval.He4_V42__Mn46
       -rho*Y[jfe55]*rate_eval.He4_Fe55__Ni59
       -rho*Y[jp29]*rate_eval.He4_P29__p_S32
       -rho*Y[jti58]*rate_eval.He4_Ti58__Cr62
       -rho*Y[jcr52]*rate_eval.He4_Cr52__Fe56
       -rho*Y[jal21]*rate_eval.He4_Al21__P25
       -rho*Y[jmg23]*rate_eval.He4_Mg23__p_Al26
       -rho*Y[jca34]*rate_eval.He4_Ca34__p_Sc37
       -rho*Y[jsc61]*rate_eval.He4_Sc61__V65
       -rho*Y[jv44]*rate_eval.He4_V44__Mn48
       -rho*Y[jfe53]*rate_eval.He4_Fe53__Ni57
       -rho*Y[jal41]*rate_eval.He4_Al41__n_P44
       -rho*Y[jf19]*rate_eval.He4_F19__Na23
       -rho*Y[jsi41]*rate_eval.He4_Si41__n_S44
       -rho*Y[jti65]*rate_eval.He4_Ti65__Cr69
       -rho*Y[jv62]*rate_eval.He4_V62__Mn66
       -rho*Y[jv40]*rate_eval.He4_V40__Mn44
       -rho*Y[jar51]*rate_eval.He4_Ar51__n_Ca54
       -rho*Y[jk54]*rate_eval.He4_K54__Sc58
       -rho*Y[jsc53]*rate_eval.He4_Sc53__V57
       -rho*Y[jsi27]*rate_eval.He4_Si27__S31
       -rho*Y[jf29]*rate_eval.He4_F29__Na33
       -rho*Y[jcr50]*rate_eval.He4_Cr50__Fe54
       -rho*Y[jar38]*rate_eval.He4_Ar38__Ca42
       -rho*Y[jal23]*rate_eval.He4_Al23__P27
       -rho*Y[jf22]*rate_eval.He4_F22__n_Na25
       -rho*Y[jmg24]*rate_eval.He4_Mg24__Si28
       -rho*Y[jsi34]*rate_eval.He4_Si34__n_S37
       -rho*Y[jne33]*rate_eval.He4_Ne33__Mg37
       -rho*Y[jca57]*rate_eval.He4_Ca57__Ti61
       -rho*Y[jar48]*rate_eval.He4_Ar48__n_Ca51
       -rho*Y[jk32]*rate_eval.He4_K32__p_Ca35
       -rho*Y[jmn57]*rate_eval.He4_Mn57__Co61
       -rho*Y[jcr58]*rate_eval.He4_Cr58__n_Fe61
       -rho*Y[jsi26]*rate_eval.He4_Si26__p_P29
       -rho*Y[jcr67]*rate_eval.He4_Cr67__n_Fe70
       -rho*Y[jsc46]*rate_eval.He4_Sc46__V50
       -rho*Y[jca59]*rate_eval.He4_Ca59__n_Ti62
       -rho*Y[js34]*rate_eval.He4_S34__n_Ar37
       -rho*Y[jv41]*rate_eval.He4_V41__p_Cr44
       -rho*Y[jti39]*rate_eval.He4_Ti39__Cr43
       -rho*Y[jsc50]*rate_eval.He4_Sc50__V54
       -rho*Y[jf23]*rate_eval.He4_F23__n_Na26
       -rho*Y[js37]*rate_eval.He4_S37__Ar41
       -rho*Y[jfe49]*rate_eval.He4_Fe49__Ni53
       -rho*Y[jfe47]*rate_eval.He4_Fe47__p_Co50
       -rho*Y[jfe72]*rate_eval.He4_Fe72__n_Ni75
       -rho*Y[jal33]*rate_eval.He4_Al33__P37
       -rho*Y[jal22]*rate_eval.He4_Al22__P26
       -rho*Y[jo26]*rate_eval.He4_O26__Ne30
       -rho*Y[js44]*rate_eval.He4_S44__n_Ar47
       -rho*Y[jfe72]*rate_eval.He4_Fe72__Ni76
       -rho*Y[jal30]*rate_eval.He4_Al30__n_P33
       -rho*Y[jca33]*rate_eval.He4_Ca33__p_Sc36
       -rho*Y[jna38]*rate_eval.He4_Na38__Al42
       -rho*Y[jar49]*rate_eval.He4_Ar49__Ca53
       -rho*Y[jk46]*rate_eval.He4_K46__Sc50
       -rho*Y[jsc50]*rate_eval.He4_Sc50__n_V53
       -rho*Y[jo16]*rate_eval.He4_O16__Ne20
       -rho*Y[jca56]*rate_eval.He4_Ca56__n_Ti59
       -rho*Y[jcr68]*rate_eval.He4_Cr68__Fe72
       -rho*Y[jne21]*rate_eval.He4_Ne21__Mg25
       -rho*Y[jk52]*rate_eval.He4_K52__Sc56
       -rho*Y[jna32]*rate_eval.He4_Na32__Al36
       -rho*Y[jp30]*rate_eval.He4_P30__Cl34
       -rho*Y[jk37]*rate_eval.He4_K37__Sc41
       -rho*Y[jsi45]*rate_eval.He4_Si45__n_S48
       -rho*Y[jfe69]*rate_eval.He4_Fe69__n_Ni72
       -rho*Y[js40]*rate_eval.He4_S40__Ar44
       -rho*Y[jmn50]*rate_eval.He4_Mn50__p_Fe53
       -rho*Y[jar32]*rate_eval.He4_Ar32__p_K35
       -rho*Y[jk56]*rate_eval.He4_K56__Sc60
       -rho*Y[jk46]*rate_eval.He4_K46__n_Sc49
       -rho*Y[jk34]*rate_eval.He4_K34__Sc38
       )

    jac[jhe4, jli6] = (
       -rho*Y[jhe4]*rate_eval.He4_Li6__B10
       +rho*Y[jn]*rate_eval.n_Li6__He4_t
       +rho*Y[jp]*rate_eval.p_Li6__He4_He3
       )

    jac[jhe4, jli7] = (
       -rho*Y[jhe4]*rate_eval.He4_Li7__B11
       +2*rho*Y[jd]*rate_eval.d_Li7__n_He4_He4
       +2*rho*Y[jp]*rate_eval.p_Li7__He4_He4
       +2*rho*Y[jt]*rate_eval.t_Li7__n_n_He4_He4
       +2*rho*Y[jhe3]*rate_eval.He3_Li7__n_p_He4_He4
       )

    jac[jhe4, jli8] = (
       -rho*Y[jhe4]*rate_eval.He4_Li8__n_B11
       -rho*Y[jhe4]*rate_eval.He4_Li8__B12
       +2*rho*Y[jp]*rate_eval.p_Li8__n_He4_He4
       +2*rate_eval.Li8__He4_He4__weak__wc12
       )

    jac[jhe4, jli9] = (
       -rho*Y[jhe4]*rate_eval.He4_Li9__B13
       -rho*Y[jhe4]*rate_eval.He4_Li9__n_B12
       )

    jac[jhe4, jbe7] = (
       -rho*Y[jhe4]*rate_eval.He4_Be7__C11
       +2*rho*Y[jhe3]*rate_eval.He3_Be7__p_p_He4_He4
       +2*rho*Y[jt]*rate_eval.t_Be7__n_p_He4_He4
       +2*rho*Y[jd]*rate_eval.d_Be7__p_He4_He4
       +2*rho*Y[jn]*rate_eval.n_Be7__He4_He4
       )

    jac[jhe4, jbe9] = (
       -rho*Y[jhe4]*rate_eval.He4_Be9__n_C12
       +2*rho*Y[jp]*rate_eval.p_Be9__n_p_He4_He4
       +2*rho*Y[jp]*rate_eval.p_Be9__d_He4_He4
       +rho*Y[jp]*rate_eval.p_Be9__He4_Li6
       )

    jac[jhe4, jbe10] = (
       -rho*Y[jhe4]*rate_eval.He4_Be10__C14
       -rho*Y[jhe4]*rate_eval.He4_Be10__n_C13
       +rho*Y[jp]*rate_eval.p_Be10__He4_Li7
       )

    jac[jhe4, jbe11] = (
       -rho*Y[jhe4]*rate_eval.He4_Be11__n_C14
       +rho*Y[jp]*rate_eval.p_Be11__He4_Li8
       +rate_eval.Be11__He4_Li7__weak__wc12
       )

    jac[jhe4, jb8] = (
       -rho*Y[jhe4]*rate_eval.He4_B8__p_C11
       +2*rho*Y[jn]*rate_eval.n_B8__p_He4_He4
       +2*rate_eval.B8__He4_He4__weak__wc12
       )

    jac[jhe4, jb10] = (
       -rho*Y[jhe4]*rate_eval.He4_B10__p_C13
       -rho*Y[jhe4]*rate_eval.He4_B10__n_N13
       +rho*Y[jp]*rate_eval.p_B10__He4_Be7
       +rho*Y[jn]*rate_eval.n_B10__He4_Li7
       )

    jac[jhe4, jb11] = (
       -rho*Y[jhe4]*rate_eval.He4_B11__p_C14
       -rho*Y[jhe4]*rate_eval.He4_B11__n_N14
       +3*rho*Y[jp]*rate_eval.p_B11__He4_He4_He4
       )

    jac[jhe4, jb12] = (
       -rho*Y[jhe4]*rate_eval.He4_B12__n_N15
       +rho*Y[jp]*rate_eval.p_B12__He4_Be9
       )

    jac[jhe4, jb13] = (
       -rho*Y[jhe4]*rate_eval.He4_B13__n_N16
       -rho*Y[jhe4]*rate_eval.He4_B13__N17
       )

    jac[jhe4, jc9] = (
       -rho*Y[jhe4]*rate_eval.He4_C9__p_N12
       +rate_eval.C9__He4_Li5__weak__wc12
       )

    jac[jhe4, jc11] = (
       -rho*Y[jhe4]*rate_eval.He4_C11__p_N14
       +3*rho*Y[jn]*rate_eval.n_C11__He4_He4_He4
       )

    jac[jhe4, jc12] = (
       -rho*Y[jhe4]*rate_eval.He4_C12__O16
       +5.00000000000000e-01*rho*2*Y[jc12]*rate_eval.C12_C12__He4_Ne20
       +rho*Y[jne20]*rate_eval.C12_Ne20__He4_Si28
       +rho*Y[jo16]*rate_eval.C12_O16__He4_Mg24
       )

    jac[jhe4, jc13] = (
       -rho*Y[jhe4]*rate_eval.He4_C13__n_O16
       )

    jac[jhe4, jc14] = (
       -rho*Y[jhe4]*rate_eval.He4_C14__O18
       )

    jac[jhe4, jc15] = (
       -rho*Y[jhe4]*rate_eval.He4_C15__n_O18
       )

    jac[jhe4, jn12] = (
       -rho*Y[jhe4]*rate_eval.He4_N12__p_O15
       )

    jac[jhe4, jn13] = (
       -rho*Y[jhe4]*rate_eval.He4_N13__p_O16
       )

    jac[jhe4, jn14] = (
       -rho*Y[jhe4]*rate_eval.He4_N14__n_F17
       -rho*Y[jhe4]*rate_eval.He4_N14__F18
       )

    jac[jhe4, jn15] = (
       -rho*Y[jhe4]*rate_eval.He4_N15__F19
       +rho*Y[jp]*rate_eval.p_N15__He4_C12
       )

    jac[jhe4, jn16] = (
       -rho*Y[jhe4]*rate_eval.He4_N16__n_F19
       +rate_eval.N16__He4_C12__weak__wc12
       +rho*Y[jp]*rate_eval.p_N16__He4_C13
       )

    jac[jhe4, jn18] = (
       +rate_eval.N18__He4_C14__weak__wc12
       )

    jac[jhe4, jo12] = (
       +rho*Y[jn]*rate_eval.n_O12__He4_C9
       )

    jac[jhe4, jo13] = (
       -rho*Y[jhe4]*rate_eval.He4_O13__p_p_O15
       -rho*Y[jhe4]*rate_eval.He4_O13__p_F16
       +rho*Y[jn]*rate_eval.n_O13__He4_C10
       )

    jac[jhe4, jo14] = (
       -rho*Y[jhe4]*rate_eval.He4_O14__p_F17
       -rho*Y[jhe4]*rate_eval.He4_O14__Ne18
       +rho*Y[jn]*rate_eval.n_O14__He4_C11
       )

    jac[jhe4, jo15] = (
       -rho*Y[jhe4]*rate_eval.He4_O15__Ne19
       +rho*Y[jn]*rate_eval.n_O15__He4_C12
       )

    jac[jhe4, jo16] = (
       -rho*Y[jhe4]*rate_eval.He4_O16__Ne20
       +5.00000000000000e-01*rho*2*Y[jo16]*rate_eval.O16_O16__He4_Si28
       +rho*Y[jc12]*rate_eval.C12_O16__He4_Mg24
       )

    jac[jhe4, jo17] = (
       -rho*Y[jhe4]*rate_eval.He4_O17__n_Ne20
       -rho*Y[jhe4]*rate_eval.He4_O17__Ne21
       +rho*Y[jp]*rate_eval.p_O17__He4_N14
       +rho*Y[jn]*rate_eval.n_O17__He4_C14
       )

    jac[jhe4, jo18] = (
       -rho*Y[jhe4]*rate_eval.He4_O18__n_Ne21
       -rho*Y[jhe4]*rate_eval.He4_O18__Ne22
       +rho*Y[jp]*rate_eval.p_O18__He4_N15
       )

    jac[jhe4, jo19] = (
       -rho*Y[jhe4]*rate_eval.He4_O19__n_Ne22
       -rho*Y[jhe4]*rate_eval.He4_O19__Ne23
       +rho*Y[jp]*rate_eval.p_O19__He4_N16
       )

    jac[jhe4, jo20] = (
       -rho*Y[jhe4]*rate_eval.He4_O20__Ne24
       -rho*Y[jhe4]*rate_eval.He4_O20__n_Ne23
       +rho*Y[jp]*rate_eval.p_O20__He4_N17
       )

    jac[jhe4, jo21] = (
       -rho*Y[jhe4]*rate_eval.He4_O21__Ne25
       -rho*Y[jhe4]*rate_eval.He4_O21__n_Ne24
       )

    jac[jhe4, jo22] = (
       -rho*Y[jhe4]*rate_eval.He4_O22__n_Ne25
       -rho*Y[jhe4]*rate_eval.He4_O22__Ne26
       )

    jac[jhe4, jo23] = (
       -rho*Y[jhe4]*rate_eval.He4_O23__n_Ne26
       -rho*Y[jhe4]*rate_eval.He4_O23__Ne27
       )

    jac[jhe4, jo24] = (
       -rho*Y[jhe4]*rate_eval.He4_O24__n_Ne27
       -rho*Y[jhe4]*rate_eval.He4_O24__Ne28
       )

    jac[jhe4, jo25] = (
       -rho*Y[jhe4]*rate_eval.He4_O25__n_Ne28
       -rho*Y[jhe4]*rate_eval.He4_O25__Ne29
       )

    jac[jhe4, jo26] = (
       -rho*Y[jhe4]*rate_eval.He4_O26__n_Ne29
       -rho*Y[jhe4]*rate_eval.He4_O26__Ne30
       +rho*Y[jp]*rate_eval.p_O26__He4_N23
       )

    jac[jhe4, jo27] = (
       -rho*Y[jhe4]*rate_eval.He4_O27__Ne31
       -rho*Y[jhe4]*rate_eval.He4_O27__n_Ne30
       +rho*Y[jp]*rate_eval.p_O27__He4_N24
       )

    jac[jhe4, jo28] = (
       -rho*Y[jhe4]*rate_eval.He4_O28__n_Ne31
       -rho*Y[jhe4]*rate_eval.He4_O28__Ne32
       )

    jac[jhe4, jf14] = (
       +rho*Y[jn]*rate_eval.n_F14__He4_N11
       )

    jac[jhe4, jf15] = (
       -rho*Y[jhe4]*rate_eval.He4_F15__p_Ne18
       -rho*Y[jhe4]*rate_eval.He4_F15__Na19
       +rho*Y[jn]*rate_eval.n_F15__He4_N12
       )

    jac[jhe4, jf16] = (
       -rho*Y[jhe4]*rate_eval.He4_F16__Na20
       -rho*Y[jhe4]*rate_eval.He4_F16__p_Ne19
       +rho*Y[jn]*rate_eval.n_F16__He4_N13
       )

    jac[jhe4, jf17] = (
       -rho*Y[jhe4]*rate_eval.He4_F17__Na21
       )

    jac[jhe4, jf18] = (
       -rho*Y[jhe4]*rate_eval.He4_F18__p_Ne21
       -rho*Y[jhe4]*rate_eval.He4_F18__Na22
       +rho*Y[jp]*rate_eval.p_F18__He4_O15
       +rho*Y[jn]*rate_eval.n_F18__He4_N15
       )

    jac[jhe4, jf19] = (
       -rho*Y[jhe4]*rate_eval.He4_F19__p_Ne22
       -rho*Y[jhe4]*rate_eval.He4_F19__Na23
       +rho*Y[jp]*rate_eval.p_F19__He4_O16
       )

    jac[jhe4, jf20] = (
       -rho*Y[jhe4]*rate_eval.He4_F20__n_Na23
       -rho*Y[jhe4]*rate_eval.He4_F20__p_Ne23
       -rho*Y[jhe4]*rate_eval.He4_F20__Na24
       +rho*Y[jp]*rate_eval.p_F20__He4_O17
       )

    jac[jhe4, jf21] = (
       -rho*Y[jhe4]*rate_eval.He4_F21__p_Ne24
       -rho*Y[jhe4]*rate_eval.He4_F21__n_Na24
       -rho*Y[jhe4]*rate_eval.He4_F21__Na25
       +rho*Y[jp]*rate_eval.p_F21__He4_O18
       )

    jac[jhe4, jf22] = (
       -rho*Y[jhe4]*rate_eval.He4_F22__Na26
       -rho*Y[jhe4]*rate_eval.He4_F22__n_Na25
       +rho*Y[jp]*rate_eval.p_F22__He4_O19
       )

    jac[jhe4, jf23] = (
       -rho*Y[jhe4]*rate_eval.He4_F23__Na27
       -rho*Y[jhe4]*rate_eval.He4_F23__n_Na26
       +rho*Y[jp]*rate_eval.p_F23__He4_O20
       )

    jac[jhe4, jf24] = (
       -rho*Y[jhe4]*rate_eval.He4_F24__n_Na27
       -rho*Y[jhe4]*rate_eval.He4_F24__Na28
       +rho*Y[jp]*rate_eval.p_F24__He4_O21
       )

    jac[jhe4, jf25] = (
       -rho*Y[jhe4]*rate_eval.He4_F25__n_Na28
       -rho*Y[jhe4]*rate_eval.He4_F25__Na29
       +rho*Y[jp]*rate_eval.p_F25__He4_O22
       )

    jac[jhe4, jf26] = (
       -rho*Y[jhe4]*rate_eval.He4_F26__Na30
       -rho*Y[jhe4]*rate_eval.He4_F26__n_Na29
       +rho*Y[jp]*rate_eval.p_F26__He4_O23
       )

    jac[jhe4, jf27] = (
       -rho*Y[jhe4]*rate_eval.He4_F27__n_Na30
       -rho*Y[jhe4]*rate_eval.He4_F27__Na31
       +rho*Y[jp]*rate_eval.p_F27__He4_O24
       )

    jac[jhe4, jf28] = (
       -rho*Y[jhe4]*rate_eval.He4_F28__n_Na31
       -rho*Y[jhe4]*rate_eval.He4_F28__Na32
       +rho*Y[jp]*rate_eval.p_F28__He4_O25
       )

    jac[jhe4, jf29] = (
       -rho*Y[jhe4]*rate_eval.He4_F29__n_Na32
       -rho*Y[jhe4]*rate_eval.He4_F29__Na33
       +rho*Y[jp]*rate_eval.p_F29__He4_O26
       )

    jac[jhe4, jf30] = (
       -rho*Y[jhe4]*rate_eval.He4_F30__p_Ne33
       -rho*Y[jhe4]*rate_eval.He4_F30__n_Na33
       -rho*Y[jhe4]*rate_eval.He4_F30__Na34
       +rho*Y[jp]*rate_eval.p_F30__He4_O27
       )

    jac[jhe4, jf31] = (
       -rho*Y[jhe4]*rate_eval.He4_F31__n_Na34
       -rho*Y[jhe4]*rate_eval.He4_F31__Na35
       +rho*Y[jp]*rate_eval.p_F31__He4_O28
       )

    jac[jhe4, jne16] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne16__p_Na19
       -rho*Y[jhe4]*rate_eval.He4_Ne16__Mg20
       +rho*Y[jn]*rate_eval.n_Ne16__He4_O13
       )

    jac[jhe4, jne17] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne17__p_Na20
       -rho*Y[jhe4]*rate_eval.He4_Ne17__Mg21
       +rho*Y[jn]*rate_eval.n_Ne17__He4_O14
       )

    jac[jhe4, jne18] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne18__p_Na21
       -rho*Y[jhe4]*rate_eval.He4_Ne18__Mg22
       +rho*Y[jn]*rate_eval.n_Ne18__He4_O15
       )

    jac[jhe4, jne19] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne19__p_Na22
       -rho*Y[jhe4]*rate_eval.He4_Ne19__Mg23
       +rho*Y[jn]*rate_eval.n_Ne19__He4_O16
       )

    jac[jhe4, jne20] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne20__Mg24
       +rho*Y[jc12]*rate_eval.C12_Ne20__He4_Si28
       +rho*Y[jp]*rate_eval.p_Ne20__He4_F17
       )

    jac[jhe4, jne21] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne21__n_Mg24
       -rho*Y[jhe4]*rate_eval.He4_Ne21__Mg25
       )

    jac[jhe4, jne22] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne22__n_Mg25
       -rho*Y[jhe4]*rate_eval.He4_Ne22__Mg26
       )

    jac[jhe4, jne23] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne23__n_Mg26
       -rho*Y[jhe4]*rate_eval.He4_Ne23__Mg27
       )

    jac[jhe4, jne24] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne24__n_Mg27
       -rho*Y[jhe4]*rate_eval.He4_Ne24__Mg28
       )

    jac[jhe4, jne25] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne25__Mg29
       -rho*Y[jhe4]*rate_eval.He4_Ne25__n_Mg28
       +rho*Y[jp]*rate_eval.p_Ne25__He4_F22
       )

    jac[jhe4, jne26] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne26__n_Mg29
       -rho*Y[jhe4]*rate_eval.He4_Ne26__Mg30
       +rho*Y[jp]*rate_eval.p_Ne26__He4_F23
       )

    jac[jhe4, jne27] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne27__n_Mg30
       -rho*Y[jhe4]*rate_eval.He4_Ne27__Mg31
       +rho*Y[jp]*rate_eval.p_Ne27__He4_F24
       )

    jac[jhe4, jne28] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne28__n_Mg31
       -rho*Y[jhe4]*rate_eval.He4_Ne28__Mg32
       +rho*Y[jp]*rate_eval.p_Ne28__He4_F25
       )

    jac[jhe4, jne29] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne29__Mg33
       -rho*Y[jhe4]*rate_eval.He4_Ne29__n_Mg32
       +rho*Y[jp]*rate_eval.p_Ne29__He4_F26
       )

    jac[jhe4, jne30] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne30__n_Mg33
       -rho*Y[jhe4]*rate_eval.He4_Ne30__Mg34
       +rho*Y[jp]*rate_eval.p_Ne30__He4_F27
       )

    jac[jhe4, jne31] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne31__n_Mg34
       -rho*Y[jhe4]*rate_eval.He4_Ne31__Mg35
       +rho*Y[jp]*rate_eval.p_Ne31__He4_F28
       )

    jac[jhe4, jne32] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne32__n_Mg35
       -rho*Y[jhe4]*rate_eval.He4_Ne32__Mg36
       +rho*Y[jp]*rate_eval.p_Ne32__He4_F29
       )

    jac[jhe4, jne33] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne33__n_Mg36
       -rho*Y[jhe4]*rate_eval.He4_Ne33__Mg37
       )

    jac[jhe4, jne34] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne34__Mg38
       -rho*Y[jhe4]*rate_eval.He4_Ne34__n_Mg37
       +rho*Y[jp]*rate_eval.p_Ne34__He4_F31
       )

    jac[jhe4, jna19] = (
       -rho*Y[jhe4]*rate_eval.He4_Na19__Al23
       -rho*Y[jhe4]*rate_eval.He4_Na19__p_Mg22
       +rho*Y[jn]*rate_eval.n_Na19__He4_F16
       )

    jac[jhe4, jna20] = (
       -rho*Y[jhe4]*rate_eval.He4_Na20__Al24
       -rho*Y[jhe4]*rate_eval.He4_Na20__p_Mg23
       +rho*Y[jn]*rate_eval.n_Na20__He4_F17
       +rate_eval.Na20__He4_O16__weak__wc12
       )

    jac[jhe4, jna21] = (
       -rho*Y[jhe4]*rate_eval.He4_Na21__Al25
       +rho*Y[jn]*rate_eval.n_Na21__He4_F18
       )

    jac[jhe4, jna22] = (
       -rho*Y[jhe4]*rate_eval.He4_Na22__p_Mg25
       -rho*Y[jhe4]*rate_eval.He4_Na22__Al26
       +rho*Y[jn]*rate_eval.n_Na22__He4_F19
       )

    jac[jhe4, jna23] = (
       -rho*Y[jhe4]*rate_eval.He4_Na23__p_Mg26
       -rho*Y[jhe4]*rate_eval.He4_Na23__Al27
       +rho*Y[jp]*rate_eval.p_Na23__He4_Ne20
       )

    jac[jhe4, jna24] = (
       -rho*Y[jhe4]*rate_eval.He4_Na24__p_Mg27
       -rho*Y[jhe4]*rate_eval.He4_Na24__Al28
       -rho*Y[jhe4]*rate_eval.He4_Na24__n_Al27
       +rho*Y[jp]*rate_eval.p_Na24__He4_Ne21
       )

    jac[jhe4, jna25] = (
       -rho*Y[jhe4]*rate_eval.He4_Na25__Al29
       -rho*Y[jhe4]*rate_eval.He4_Na25__n_Al28
       -rho*Y[jhe4]*rate_eval.He4_Na25__p_Mg28
       +rho*Y[jp]*rate_eval.p_Na25__He4_Ne22
       )

    jac[jhe4, jna26] = (
       -rho*Y[jhe4]*rate_eval.He4_Na26__n_Al29
       -rho*Y[jhe4]*rate_eval.He4_Na26__Al30
       +rho*Y[jp]*rate_eval.p_Na26__He4_Ne23
       )

    jac[jhe4, jna27] = (
       -rho*Y[jhe4]*rate_eval.He4_Na27__n_Al30
       -rho*Y[jhe4]*rate_eval.He4_Na27__Al31
       +rho*Y[jp]*rate_eval.p_Na27__He4_Ne24
       )

    jac[jhe4, jna28] = (
       -rho*Y[jhe4]*rate_eval.He4_Na28__n_Al31
       -rho*Y[jhe4]*rate_eval.He4_Na28__Al32
       +rho*Y[jp]*rate_eval.p_Na28__He4_Ne25
       )

    jac[jhe4, jna29] = (
       -rho*Y[jhe4]*rate_eval.He4_Na29__Al33
       -rho*Y[jhe4]*rate_eval.He4_Na29__n_Al32
       +rho*Y[jp]*rate_eval.p_Na29__He4_Ne26
       )

    jac[jhe4, jna30] = (
       -rho*Y[jhe4]*rate_eval.He4_Na30__Al34
       -rho*Y[jhe4]*rate_eval.He4_Na30__n_Al33
       +rho*Y[jp]*rate_eval.p_Na30__He4_Ne27
       +rate_eval.Na30__He4_Ne26__weak__wc12
       )

    jac[jhe4, jna31] = (
       -rho*Y[jhe4]*rate_eval.He4_Na31__n_Al34
       -rho*Y[jhe4]*rate_eval.He4_Na31__Al35
       +rho*Y[jp]*rate_eval.p_Na31__He4_Ne28
       )

    jac[jhe4, jna32] = (
       -rho*Y[jhe4]*rate_eval.He4_Na32__n_Al35
       -rho*Y[jhe4]*rate_eval.He4_Na32__Al36
       +rho*Y[jp]*rate_eval.p_Na32__He4_Ne29
       )

    jac[jhe4, jna33] = (
       -rho*Y[jhe4]*rate_eval.He4_Na33__p_Mg36
       -rho*Y[jhe4]*rate_eval.He4_Na33__Al37
       -rho*Y[jhe4]*rate_eval.He4_Na33__n_Al36
       +rho*Y[jp]*rate_eval.p_Na33__He4_Ne30
       )

    jac[jhe4, jna34] = (
       -rho*Y[jhe4]*rate_eval.He4_Na34__n_Al37
       -rho*Y[jhe4]*rate_eval.He4_Na34__Al38
       +rho*Y[jp]*rate_eval.p_Na34__He4_Ne31
       )

    jac[jhe4, jna35] = (
       -rho*Y[jhe4]*rate_eval.He4_Na35__n_Al38
       -rho*Y[jhe4]*rate_eval.He4_Na35__Al39
       +rho*Y[jp]*rate_eval.p_Na35__He4_Ne32
       )

    jac[jhe4, jna36] = (
       -rho*Y[jhe4]*rate_eval.He4_Na36__n_Al39
       -rho*Y[jhe4]*rate_eval.He4_Na36__Al40
       +rho*Y[jp]*rate_eval.p_Na36__He4_Ne33
       )

    jac[jhe4, jna37] = (
       -rho*Y[jhe4]*rate_eval.He4_Na37__p_Mg40
       -rho*Y[jhe4]*rate_eval.He4_Na37__n_Al40
       -rho*Y[jhe4]*rate_eval.He4_Na37__Al41
       +rho*Y[jp]*rate_eval.p_Na37__He4_Ne34
       )

    jac[jhe4, jna38] = (
       -rho*Y[jhe4]*rate_eval.He4_Na38__n_Al41
       -rho*Y[jhe4]*rate_eval.He4_Na38__Al42
       )

    jac[jhe4, jna39] = (
       -rho*Y[jhe4]*rate_eval.He4_Na39__n_Al42
       -rho*Y[jhe4]*rate_eval.He4_Na39__Al43
       )

    jac[jhe4, jmg19] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg19__p_Al22
       -rho*Y[jhe4]*rate_eval.He4_Mg19__Si23
       +rho*Y[jn]*rate_eval.n_Mg19__He4_Ne16
       )

    jac[jhe4, jmg20] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg20__p_Al23
       -rho*Y[jhe4]*rate_eval.He4_Mg20__Si24
       +rho*Y[jn]*rate_eval.n_Mg20__He4_Ne17
       )

    jac[jhe4, jmg21] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg21__Si25
       -rho*Y[jhe4]*rate_eval.He4_Mg21__p_Al24
       +rho*Y[jn]*rate_eval.n_Mg21__He4_Ne18
       )

    jac[jhe4, jmg22] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg22__p_Al25
       -rho*Y[jhe4]*rate_eval.He4_Mg22__Si26
       +rho*Y[jn]*rate_eval.n_Mg22__He4_Ne19
       )

    jac[jhe4, jmg23] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg23__Si27
       -rho*Y[jhe4]*rate_eval.He4_Mg23__p_Al26
       +rho*Y[jn]*rate_eval.n_Mg23__He4_Ne20
       )

    jac[jhe4, jmg24] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg24__Si28
       +rho*Y[jp]*rate_eval.p_Mg24__He4_Na21
       )

    jac[jhe4, jmg25] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg25__n_Si28
       -rho*Y[jhe4]*rate_eval.He4_Mg25__Si29
       )

    jac[jhe4, jmg26] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg26__n_Si29
       -rho*Y[jhe4]*rate_eval.He4_Mg26__Si30
       )

    jac[jhe4, jmg27] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg27__n_Si30
       -rho*Y[jhe4]*rate_eval.He4_Mg27__Si31
       )

    jac[jhe4, jmg28] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg28__Si32
       -rho*Y[jhe4]*rate_eval.He4_Mg28__n_Si31
       )

    jac[jhe4, jmg29] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg29__Si33
       -rho*Y[jhe4]*rate_eval.He4_Mg29__n_Si32
       +rho*Y[jp]*rate_eval.p_Mg29__He4_Na26
       )

    jac[jhe4, jmg30] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg30__n_Si33
       -rho*Y[jhe4]*rate_eval.He4_Mg30__Si34
       +rho*Y[jp]*rate_eval.p_Mg30__He4_Na27
       )

    jac[jhe4, jmg31] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg31__Si35
       -rho*Y[jhe4]*rate_eval.He4_Mg31__n_Si34
       +rho*Y[jp]*rate_eval.p_Mg31__He4_Na28
       )

    jac[jhe4, jmg32] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg32__n_Si35
       -rho*Y[jhe4]*rate_eval.He4_Mg32__Si36
       +rho*Y[jp]*rate_eval.p_Mg32__He4_Na29
       )

    jac[jhe4, jmg33] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg33__n_Si36
       -rho*Y[jhe4]*rate_eval.He4_Mg33__Si37
       +rho*Y[jp]*rate_eval.p_Mg33__He4_Na30
       )

    jac[jhe4, jmg34] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg34__n_Si37
       -rho*Y[jhe4]*rate_eval.He4_Mg34__Si38
       +rho*Y[jp]*rate_eval.p_Mg34__He4_Na31
       )

    jac[jhe4, jmg35] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg35__n_Si38
       -rho*Y[jhe4]*rate_eval.He4_Mg35__Si39
       +rho*Y[jp]*rate_eval.p_Mg35__He4_Na32
       )

    jac[jhe4, jmg36] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg36__Si40
       -rho*Y[jhe4]*rate_eval.He4_Mg36__n_Si39
       )

    jac[jhe4, jmg37] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg37__n_Si40
       -rho*Y[jhe4]*rate_eval.He4_Mg37__Si41
       +rho*Y[jp]*rate_eval.p_Mg37__He4_Na34
       )

    jac[jhe4, jmg38] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg38__n_Si41
       -rho*Y[jhe4]*rate_eval.He4_Mg38__Si42
       +rho*Y[jp]*rate_eval.p_Mg38__He4_Na35
       )

    jac[jhe4, jmg39] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg39__n_Si42
       -rho*Y[jhe4]*rate_eval.He4_Mg39__Si43
       +rho*Y[jp]*rate_eval.p_Mg39__He4_Na36
       )

    jac[jhe4, jmg40] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg40__n_Si43
       -rho*Y[jhe4]*rate_eval.He4_Mg40__Si44
       )

    jac[jhe4, jmg41] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg41__Si45
       -rho*Y[jhe4]*rate_eval.He4_Mg41__n_Si44
       +rho*Y[jp]*rate_eval.p_Mg41__He4_Na38
       )

    jac[jhe4, jal21] = (
       -rho*Y[jhe4]*rate_eval.He4_Al21__p_Si24
       -rho*Y[jhe4]*rate_eval.He4_Al21__P25
       )

    jac[jhe4, jal22] = (
       -rho*Y[jhe4]*rate_eval.He4_Al22__p_Si25
       -rho*Y[jhe4]*rate_eval.He4_Al22__P26
       +rho*Y[jn]*rate_eval.n_Al22__He4_Na19
       +rate_eval.Al22__He4_Ne18__weak__wc12
       )

    jac[jhe4, jal23] = (
       -rho*Y[jhe4]*rate_eval.He4_Al23__p_Si26
       -rho*Y[jhe4]*rate_eval.He4_Al23__P27
       +rho*Y[jn]*rate_eval.n_Al23__He4_Na20
       )

    jac[jhe4, jal24] = (
       -rho*Y[jhe4]*rate_eval.He4_Al24__p_Si27
       -rho*Y[jhe4]*rate_eval.He4_Al24__P28
       +rho*Y[jn]*rate_eval.n_Al24__He4_Na21
       +rate_eval.Al24__He4_Ne20__weak__wc12
       )

    jac[jhe4, jal25] = (
       -rho*Y[jhe4]*rate_eval.He4_Al25__P29
       -rho*Y[jhe4]*rate_eval.He4_Al25__p_Si28
       +rho*Y[jn]*rate_eval.n_Al25__He4_Na22
       )

    jac[jhe4, jal26] = (
       -rho*Y[jhe4]*rate_eval.He4_Al26__p_Si29
       -rho*Y[jhe4]*rate_eval.He4_Al26__P30
       +rho*Y[jn]*rate_eval.n_Al26__He4_Na23
       )

    jac[jhe4, jal27] = (
       -rho*Y[jhe4]*rate_eval.He4_Al27__p_Si30
       -rho*Y[jhe4]*rate_eval.He4_Al27__n_P30
       -rho*Y[jhe4]*rate_eval.He4_Al27__P31
       +rho*Y[jp]*rate_eval.p_Al27__He4_Mg24
       )

    jac[jhe4, jal28] = (
       -rho*Y[jhe4]*rate_eval.He4_Al28__n_P31
       -rho*Y[jhe4]*rate_eval.He4_Al28__p_Si31
       -rho*Y[jhe4]*rate_eval.He4_Al28__P32
       +rho*Y[jp]*rate_eval.p_Al28__He4_Mg25
       )

    jac[jhe4, jal29] = (
       -rho*Y[jhe4]*rate_eval.He4_Al29__n_P32
       -rho*Y[jhe4]*rate_eval.He4_Al29__p_Si32
       -rho*Y[jhe4]*rate_eval.He4_Al29__P33
       +rho*Y[jp]*rate_eval.p_Al29__He4_Mg26
       )

    jac[jhe4, jal30] = (
       -rho*Y[jhe4]*rate_eval.He4_Al30__P34
       -rho*Y[jhe4]*rate_eval.He4_Al30__n_P33
       +rho*Y[jp]*rate_eval.p_Al30__He4_Mg27
       )

    jac[jhe4, jal31] = (
       -rho*Y[jhe4]*rate_eval.He4_Al31__p_Si34
       -rho*Y[jhe4]*rate_eval.He4_Al31__n_P34
       -rho*Y[jhe4]*rate_eval.He4_Al31__P35
       +rho*Y[jp]*rate_eval.p_Al31__He4_Mg28
       )

    jac[jhe4, jal32] = (
       -rho*Y[jhe4]*rate_eval.He4_Al32__n_P35
       -rho*Y[jhe4]*rate_eval.He4_Al32__P36
       +rho*Y[jp]*rate_eval.p_Al32__He4_Mg29
       )

    jac[jhe4, jal33] = (
       -rho*Y[jhe4]*rate_eval.He4_Al33__n_P36
       -rho*Y[jhe4]*rate_eval.He4_Al33__P37
       +rho*Y[jp]*rate_eval.p_Al33__He4_Mg30
       )

    jac[jhe4, jal34] = (
       -rho*Y[jhe4]*rate_eval.He4_Al34__n_P37
       -rho*Y[jhe4]*rate_eval.He4_Al34__P38
       +rho*Y[jp]*rate_eval.p_Al34__He4_Mg31
       )

    jac[jhe4, jal35] = (
       -rho*Y[jhe4]*rate_eval.He4_Al35__n_P38
       -rho*Y[jhe4]*rate_eval.He4_Al35__P39
       +rho*Y[jp]*rate_eval.p_Al35__He4_Mg32
       )

    jac[jhe4, jal36] = (
       -rho*Y[jhe4]*rate_eval.He4_Al36__p_Si39
       -rho*Y[jhe4]*rate_eval.He4_Al36__n_P39
       -rho*Y[jhe4]*rate_eval.He4_Al36__P40
       +rho*Y[jp]*rate_eval.p_Al36__He4_Mg33
       )

    jac[jhe4, jal37] = (
       -rho*Y[jhe4]*rate_eval.He4_Al37__n_P40
       -rho*Y[jhe4]*rate_eval.He4_Al37__P41
       +rho*Y[jp]*rate_eval.p_Al37__He4_Mg34
       )

    jac[jhe4, jal38] = (
       -rho*Y[jhe4]*rate_eval.He4_Al38__n_P41
       -rho*Y[jhe4]*rate_eval.He4_Al38__p_Si41
       -rho*Y[jhe4]*rate_eval.He4_Al38__P42
       +rho*Y[jp]*rate_eval.p_Al38__He4_Mg35
       )

    jac[jhe4, jal39] = (
       -rho*Y[jhe4]*rate_eval.He4_Al39__p_Si42
       -rho*Y[jhe4]*rate_eval.He4_Al39__P43
       -rho*Y[jhe4]*rate_eval.He4_Al39__n_P42
       +rho*Y[jp]*rate_eval.p_Al39__He4_Mg36
       )

    jac[jhe4, jal40] = (
       -rho*Y[jhe4]*rate_eval.He4_Al40__p_Si43
       -rho*Y[jhe4]*rate_eval.He4_Al40__n_P43
       -rho*Y[jhe4]*rate_eval.He4_Al40__P44
       +rho*Y[jp]*rate_eval.p_Al40__He4_Mg37
       )

    jac[jhe4, jal41] = (
       -rho*Y[jhe4]*rate_eval.He4_Al41__P45
       -rho*Y[jhe4]*rate_eval.He4_Al41__n_P44
       +rho*Y[jp]*rate_eval.p_Al41__He4_Mg38
       )

    jac[jhe4, jal42] = (
       -rho*Y[jhe4]*rate_eval.He4_Al42__n_P45
       -rho*Y[jhe4]*rate_eval.He4_Al42__P46
       +rho*Y[jp]*rate_eval.p_Al42__He4_Mg39
       )

    jac[jhe4, jal43] = (
       -rho*Y[jhe4]*rate_eval.He4_Al43__P47
       -rho*Y[jhe4]*rate_eval.He4_Al43__n_P46
       +rho*Y[jp]*rate_eval.p_Al43__He4_Mg40
       )

    jac[jhe4, jsi22] = (
       -rho*Y[jhe4]*rate_eval.He4_Si22__p_P25
       -rho*Y[jhe4]*rate_eval.He4_Si22__S26
       +rho*Y[jn]*rate_eval.n_Si22__He4_Mg19
       )

    jac[jhe4, jsi23] = (
       -rho*Y[jhe4]*rate_eval.He4_Si23__p_P26
       -rho*Y[jhe4]*rate_eval.He4_Si23__S27
       +rho*Y[jn]*rate_eval.n_Si23__He4_Mg20
       )

    jac[jhe4, jsi24] = (
       -rho*Y[jhe4]*rate_eval.He4_Si24__p_P27
       -rho*Y[jhe4]*rate_eval.He4_Si24__S28
       +rho*Y[jn]*rate_eval.n_Si24__He4_Mg21
       )

    jac[jhe4, jsi25] = (
       -rho*Y[jhe4]*rate_eval.He4_Si25__p_P28
       -rho*Y[jhe4]*rate_eval.He4_Si25__S29
       +rho*Y[jn]*rate_eval.n_Si25__He4_Mg22
       )

    jac[jhe4, jsi26] = (
       -rho*Y[jhe4]*rate_eval.He4_Si26__S30
       -rho*Y[jhe4]*rate_eval.He4_Si26__p_P29
       +rho*Y[jn]*rate_eval.n_Si26__He4_Mg23
       )

    jac[jhe4, jsi27] = (
       -rho*Y[jhe4]*rate_eval.He4_Si27__p_P30
       -rho*Y[jhe4]*rate_eval.He4_Si27__S31
       +rho*Y[jn]*rate_eval.n_Si27__He4_Mg24
       )

    jac[jhe4, jsi28] = (
       -rho*Y[jhe4]*rate_eval.He4_Si28__S32
       )

    jac[jhe4, jsi29] = (
       -rho*Y[jhe4]*rate_eval.He4_Si29__S33
       )

    jac[jhe4, jsi30] = (
       -rho*Y[jhe4]*rate_eval.He4_Si30__S34
       )

    jac[jhe4, jsi31] = (
       -rho*Y[jhe4]*rate_eval.He4_Si31__n_S34
       -rho*Y[jhe4]*rate_eval.He4_Si31__S35
       )

    jac[jhe4, jsi32] = (
       -rho*Y[jhe4]*rate_eval.He4_Si32__S36
       )

    jac[jhe4, jsi33] = (
       -rho*Y[jhe4]*rate_eval.He4_Si33__n_S36
       -rho*Y[jhe4]*rate_eval.He4_Si33__S37
       +rho*Y[jp]*rate_eval.p_Si33__He4_Al30
       )

    jac[jhe4, jsi34] = (
       -rho*Y[jhe4]*rate_eval.He4_Si34__S38
       -rho*Y[jhe4]*rate_eval.He4_Si34__n_S37
       )

    jac[jhe4, jsi35] = (
       -rho*Y[jhe4]*rate_eval.He4_Si35__n_S38
       -rho*Y[jhe4]*rate_eval.He4_Si35__S39
       +rho*Y[jp]*rate_eval.p_Si35__He4_Al32
       )

    jac[jhe4, jsi36] = (
       -rho*Y[jhe4]*rate_eval.He4_Si36__n_S39
       -rho*Y[jhe4]*rate_eval.He4_Si36__S40
       +rho*Y[jp]*rate_eval.p_Si36__He4_Al33
       )

    jac[jhe4, jsi37] = (
       -rho*Y[jhe4]*rate_eval.He4_Si37__n_S40
       -rho*Y[jhe4]*rate_eval.He4_Si37__S41
       +rho*Y[jp]*rate_eval.p_Si37__He4_Al34
       )

    jac[jhe4, jsi38] = (
       -rho*Y[jhe4]*rate_eval.He4_Si38__n_S41
       -rho*Y[jhe4]*rate_eval.He4_Si38__S42
       +rho*Y[jp]*rate_eval.p_Si38__He4_Al35
       )

    jac[jhe4, jsi39] = (
       -rho*Y[jhe4]*rate_eval.He4_Si39__n_S42
       -rho*Y[jhe4]*rate_eval.He4_Si39__S43
       )

    jac[jhe4, jsi40] = (
       -rho*Y[jhe4]*rate_eval.He4_Si40__n_S43
       -rho*Y[jhe4]*rate_eval.He4_Si40__S44
       +rho*Y[jp]*rate_eval.p_Si40__He4_Al37
       )

    jac[jhe4, jsi41] = (
       -rho*Y[jhe4]*rate_eval.He4_Si41__S45
       -rho*Y[jhe4]*rate_eval.He4_Si41__n_S44
       )

    jac[jhe4, jsi42] = (
       -rho*Y[jhe4]*rate_eval.He4_Si42__S46
       -rho*Y[jhe4]*rate_eval.He4_Si42__n_S45
       )

    jac[jhe4, jsi43] = (
       -rho*Y[jhe4]*rate_eval.He4_Si43__n_S46
       -rho*Y[jhe4]*rate_eval.He4_Si43__S47
       )

    jac[jhe4, jsi44] = (
       -rho*Y[jhe4]*rate_eval.He4_Si44__n_S47
       -rho*Y[jhe4]*rate_eval.He4_Si44__S48
       +rho*Y[jp]*rate_eval.p_Si44__He4_Al41
       )

    jac[jhe4, jsi45] = (
       -rho*Y[jhe4]*rate_eval.He4_Si45__S49
       -rho*Y[jhe4]*rate_eval.He4_Si45__n_S48
       +rho*Y[jp]*rate_eval.p_Si45__He4_Al42
       )

    jac[jhe4, jp24] = (
       -rho*Y[jhe4]*rate_eval.He4_P24__p_S27
       -rho*Y[jhe4]*rate_eval.He4_P24__Cl28
       +rho*Y[jn]*rate_eval.n_P24__He4_Al21
       )

    jac[jhe4, jp25] = (
       -rho*Y[jhe4]*rate_eval.He4_P25__p_S28
       -rho*Y[jhe4]*rate_eval.He4_P25__Cl29
       +rho*Y[jn]*rate_eval.n_P25__He4_Al22
       )

    jac[jhe4, jp26] = (
       -rho*Y[jhe4]*rate_eval.He4_P26__p_S29
       -rho*Y[jhe4]*rate_eval.He4_P26__Cl30
       +rho*Y[jn]*rate_eval.n_P26__He4_Al23
       )

    jac[jhe4, jp27] = (
       -rho*Y[jhe4]*rate_eval.He4_P27__p_S30
       -rho*Y[jhe4]*rate_eval.He4_P27__Cl31
       +rho*Y[jn]*rate_eval.n_P27__He4_Al24
       )

    jac[jhe4, jp28] = (
       -rho*Y[jhe4]*rate_eval.He4_P28__Cl32
       -rho*Y[jhe4]*rate_eval.He4_P28__p_S31
       +rate_eval.P28__He4_Mg24__weak__wc12
       +rho*Y[jn]*rate_eval.n_P28__He4_Al25
       )

    jac[jhe4, jp29] = (
       -rho*Y[jhe4]*rate_eval.He4_P29__Cl33
       -rho*Y[jhe4]*rate_eval.He4_P29__p_S32
       +rho*Y[jn]*rate_eval.n_P29__He4_Al26
       )

    jac[jhe4, jp30] = (
       -rho*Y[jhe4]*rate_eval.He4_P30__p_S33
       -rho*Y[jhe4]*rate_eval.He4_P30__Cl34
       )

    jac[jhe4, jp31] = (
       -rho*Y[jhe4]*rate_eval.He4_P31__p_S34
       -rho*Y[jhe4]*rate_eval.He4_P31__Cl35
       +rho*Y[jp]*rate_eval.p_P31__He4_Si28
       )

    jac[jhe4, jp32] = (
       -rho*Y[jhe4]*rate_eval.He4_P32__Cl36
       +rho*Y[jp]*rate_eval.p_P32__He4_Si29
       )

    jac[jhe4, jp33] = (
       -rho*Y[jhe4]*rate_eval.He4_P33__Cl37
       +rho*Y[jp]*rate_eval.p_P33__He4_Si30
       )

    jac[jhe4, jp34] = (
       -rho*Y[jhe4]*rate_eval.He4_P34__n_Cl37
       -rho*Y[jhe4]*rate_eval.He4_P34__Cl38
       +rho*Y[jp]*rate_eval.p_P34__He4_Si31
       )

    jac[jhe4, jp35] = (
       -rho*Y[jhe4]*rate_eval.He4_P35__Cl39
       +rho*Y[jp]*rate_eval.p_P35__He4_Si32
       )

    jac[jhe4, jp36] = (
       -rho*Y[jhe4]*rate_eval.He4_P36__n_Cl39
       -rho*Y[jhe4]*rate_eval.He4_P36__Cl40
       +rho*Y[jp]*rate_eval.p_P36__He4_Si33
       )

    jac[jhe4, jp37] = (
       -rho*Y[jhe4]*rate_eval.He4_P37__n_Cl40
       -rho*Y[jhe4]*rate_eval.He4_P37__Cl41
       +rho*Y[jp]*rate_eval.p_P37__He4_Si34
       )

    jac[jhe4, jp38] = (
       -rho*Y[jhe4]*rate_eval.He4_P38__Cl42
       -rho*Y[jhe4]*rate_eval.He4_P38__n_Cl41
       +rho*Y[jp]*rate_eval.p_P38__He4_Si35
       )

    jac[jhe4, jp39] = (
       -rho*Y[jhe4]*rate_eval.He4_P39__n_Cl42
       -rho*Y[jhe4]*rate_eval.He4_P39__Cl43
       +rho*Y[jp]*rate_eval.p_P39__He4_Si36
       )

    jac[jhe4, jp40] = (
       -rho*Y[jhe4]*rate_eval.He4_P40__n_Cl43
       -rho*Y[jhe4]*rate_eval.He4_P40__Cl44
       +rho*Y[jp]*rate_eval.p_P40__He4_Si37
       )

    jac[jhe4, jp41] = (
       -rho*Y[jhe4]*rate_eval.He4_P41__p_S44
       -rho*Y[jhe4]*rate_eval.He4_P41__n_Cl44
       -rho*Y[jhe4]*rate_eval.He4_P41__Cl45
       +rho*Y[jp]*rate_eval.p_P41__He4_Si38
       )

    jac[jhe4, jp42] = (
       -rho*Y[jhe4]*rate_eval.He4_P42__n_Cl45
       -rho*Y[jhe4]*rate_eval.He4_P42__Cl46
       +rho*Y[jp]*rate_eval.p_P42__He4_Si39
       )

    jac[jhe4, jp43] = (
       -rho*Y[jhe4]*rate_eval.He4_P43__n_Cl46
       -rho*Y[jhe4]*rate_eval.He4_P43__Cl47
       +rho*Y[jp]*rate_eval.p_P43__He4_Si40
       )

    jac[jhe4, jp44] = (
       -rho*Y[jhe4]*rate_eval.He4_P44__n_Cl47
       -rho*Y[jhe4]*rate_eval.He4_P44__Cl48
       +rho*Y[jp]*rate_eval.p_P44__He4_Si41
       )

    jac[jhe4, jp45] = (
       -rho*Y[jhe4]*rate_eval.He4_P45__n_Cl48
       -rho*Y[jhe4]*rate_eval.He4_P45__Cl49
       +rho*Y[jp]*rate_eval.p_P45__He4_Si42
       )

    jac[jhe4, jp46] = (
       -rho*Y[jhe4]*rate_eval.He4_P46__n_Cl49
       -rho*Y[jhe4]*rate_eval.He4_P46__Cl50
       +rho*Y[jp]*rate_eval.p_P46__He4_Si43
       )

    jac[jhe4, jp47] = (
       -rho*Y[jhe4]*rate_eval.He4_P47__n_Cl50
       -rho*Y[jhe4]*rate_eval.He4_P47__Cl51
       +rho*Y[jp]*rate_eval.p_P47__He4_Si44
       )

    jac[jhe4, js26] = (
       -rho*Y[jhe4]*rate_eval.He4_S26__p_Cl29
       -rho*Y[jhe4]*rate_eval.He4_S26__Ar30
       +rho*Y[jn]*rate_eval.n_S26__He4_Si23
       )

    jac[jhe4, js27] = (
       -rho*Y[jhe4]*rate_eval.He4_S27__p_Cl30
       -rho*Y[jhe4]*rate_eval.He4_S27__Ar31
       +rho*Y[jn]*rate_eval.n_S27__He4_Si24
       )

    jac[jhe4, js28] = (
       -rho*Y[jhe4]*rate_eval.He4_S28__p_Cl31
       -rho*Y[jhe4]*rate_eval.He4_S28__Ar32
       +rho*Y[jn]*rate_eval.n_S28__He4_Si25
       )

    jac[jhe4, js29] = (
       -rho*Y[jhe4]*rate_eval.He4_S29__p_Cl32
       -rho*Y[jhe4]*rate_eval.He4_S29__Ar33
       +rho*Y[jn]*rate_eval.n_S29__He4_Si26
       )

    jac[jhe4, js30] = (
       -rho*Y[jhe4]*rate_eval.He4_S30__Ar34
       -rho*Y[jhe4]*rate_eval.He4_S30__p_Cl33
       +rho*Y[jn]*rate_eval.n_S30__He4_Si27
       )

    jac[jhe4, js31] = (
       -rho*Y[jhe4]*rate_eval.He4_S31__p_Cl34
       -rho*Y[jhe4]*rate_eval.He4_S31__Ar35
       +rho*Y[jn]*rate_eval.n_S31__He4_Si28
       )

    jac[jhe4, js32] = (
       -rho*Y[jhe4]*rate_eval.He4_S32__Ar36
       +rho*Y[jn]*rate_eval.n_S32__He4_Si29
       )

    jac[jhe4, js33] = (
       -rho*Y[jhe4]*rate_eval.He4_S33__Ar37
       +rho*Y[jn]*rate_eval.n_S33__He4_Si30
       )

    jac[jhe4, js34] = (
       -rho*Y[jhe4]*rate_eval.He4_S34__p_Cl37
       -rho*Y[jhe4]*rate_eval.He4_S34__Ar38
       -rho*Y[jhe4]*rate_eval.He4_S34__n_Ar37
       )

    jac[jhe4, js35] = (
       -rho*Y[jhe4]*rate_eval.He4_S35__n_Ar38
       -rho*Y[jhe4]*rate_eval.He4_S35__Ar39
       +rho*Y[jp]*rate_eval.p_S35__He4_P32
       +rho*Y[jn]*rate_eval.n_S35__He4_Si32
       )

    jac[jhe4, js36] = (
       -rho*Y[jhe4]*rate_eval.He4_S36__Ar40
       +rho*Y[jp]*rate_eval.p_S36__He4_P33
       )

    jac[jhe4, js37] = (
       -rho*Y[jhe4]*rate_eval.He4_S37__n_Ar40
       -rho*Y[jhe4]*rate_eval.He4_S37__Ar41
       +rho*Y[jp]*rate_eval.p_S37__He4_P34
       )

    jac[jhe4, js38] = (
       -rho*Y[jhe4]*rate_eval.He4_S38__n_Ar41
       -rho*Y[jhe4]*rate_eval.He4_S38__Ar42
       +rho*Y[jp]*rate_eval.p_S38__He4_P35
       )

    jac[jhe4, js39] = (
       -rho*Y[jhe4]*rate_eval.He4_S39__n_Ar42
       -rho*Y[jhe4]*rate_eval.He4_S39__Ar43
       +rho*Y[jp]*rate_eval.p_S39__He4_P36
       )

    jac[jhe4, js40] = (
       -rho*Y[jhe4]*rate_eval.He4_S40__n_Ar43
       -rho*Y[jhe4]*rate_eval.He4_S40__Ar44
       +rho*Y[jp]*rate_eval.p_S40__He4_P37
       )

    jac[jhe4, js41] = (
       -rho*Y[jhe4]*rate_eval.He4_S41__n_Ar44
       -rho*Y[jhe4]*rate_eval.He4_S41__Ar45
       +rho*Y[jp]*rate_eval.p_S41__He4_P38
       )

    jac[jhe4, js42] = (
       -rho*Y[jhe4]*rate_eval.He4_S42__n_Ar45
       -rho*Y[jhe4]*rate_eval.He4_S42__Ar46
       +rho*Y[jp]*rate_eval.p_S42__He4_P39
       )

    jac[jhe4, js43] = (
       -rho*Y[jhe4]*rate_eval.He4_S43__n_Ar46
       -rho*Y[jhe4]*rate_eval.He4_S43__Ar47
       +rho*Y[jp]*rate_eval.p_S43__He4_P40
       )

    jac[jhe4, js44] = (
       -rho*Y[jhe4]*rate_eval.He4_S44__Ar48
       -rho*Y[jhe4]*rate_eval.He4_S44__n_Ar47
       )

    jac[jhe4, js45] = (
       -rho*Y[jhe4]*rate_eval.He4_S45__n_Ar48
       -rho*Y[jhe4]*rate_eval.He4_S45__Ar49
       +rho*Y[jp]*rate_eval.p_S45__He4_P42
       )

    jac[jhe4, js46] = (
       -rho*Y[jhe4]*rate_eval.He4_S46__n_Ar49
       -rho*Y[jhe4]*rate_eval.He4_S46__Ar50
       +rho*Y[jp]*rate_eval.p_S46__He4_P43
       )

    jac[jhe4, js47] = (
       -rho*Y[jhe4]*rate_eval.He4_S47__Ar51
       -rho*Y[jhe4]*rate_eval.He4_S47__n_Ar50
       +rho*Y[jp]*rate_eval.p_S47__He4_P44
       )

    jac[jhe4, js48] = (
       -rho*Y[jhe4]*rate_eval.He4_S48__n_Ar51
       -rho*Y[jhe4]*rate_eval.He4_S48__Ar52
       +rho*Y[jp]*rate_eval.p_S48__He4_P45
       )

    jac[jhe4, js49] = (
       -rho*Y[jhe4]*rate_eval.He4_S49__Ar53
       -rho*Y[jhe4]*rate_eval.He4_S49__n_Ar52
       +rho*Y[jp]*rate_eval.p_S49__He4_P46
       )

    jac[jhe4, jcl28] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl28__p_Ar31
       -rho*Y[jhe4]*rate_eval.He4_Cl28__K32
       +rho*Y[jn]*rate_eval.n_Cl28__He4_P25
       )

    jac[jhe4, jcl29] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl29__p_Ar32
       -rho*Y[jhe4]*rate_eval.He4_Cl29__K33
       +rho*Y[jn]*rate_eval.n_Cl29__He4_P26
       )

    jac[jhe4, jcl30] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl30__p_Ar33
       -rho*Y[jhe4]*rate_eval.He4_Cl30__K34
       +rho*Y[jn]*rate_eval.n_Cl30__He4_P27
       )

    jac[jhe4, jcl31] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl31__K35
       -rho*Y[jhe4]*rate_eval.He4_Cl31__p_Ar34
       +rho*Y[jn]*rate_eval.n_Cl31__He4_P28
       )

    jac[jhe4, jcl32] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl32__p_Ar35
       -rho*Y[jhe4]*rate_eval.He4_Cl32__K36
       +rho*Y[jn]*rate_eval.n_Cl32__He4_P29
       +rate_eval.Cl32__He4_Si28__weak__wc12
       )

    jac[jhe4, jcl33] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl33__K37
       -rho*Y[jhe4]*rate_eval.He4_Cl33__p_Ar36
       +rho*Y[jn]*rate_eval.n_Cl33__He4_P30
       )

    jac[jhe4, jcl34] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl34__p_Ar37
       -rho*Y[jhe4]*rate_eval.He4_Cl34__K38
       +rho*Y[jn]*rate_eval.n_Cl34__He4_P31
       )

    jac[jhe4, jcl35] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl35__p_Ar38
       -rho*Y[jhe4]*rate_eval.He4_Cl35__K39
       +rho*Y[jn]*rate_eval.n_Cl35__He4_P32
       +rho*Y[jp]*rate_eval.p_Cl35__He4_S32
       )

    jac[jhe4, jcl36] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl36__K40
       +rho*Y[jp]*rate_eval.p_Cl36__He4_S33
       +rho*Y[jn]*rate_eval.n_Cl36__He4_P33
       )

    jac[jhe4, jcl37] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl37__K41
       )

    jac[jhe4, jcl38] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl38__K42
       -rho*Y[jhe4]*rate_eval.He4_Cl38__n_K41
       +rho*Y[jp]*rate_eval.p_Cl38__He4_S35
       +rho*Y[jn]*rate_eval.n_Cl38__He4_P35
       )

    jac[jhe4, jcl39] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl39__K43
       +rho*Y[jp]*rate_eval.p_Cl39__He4_S36
       )

    jac[jhe4, jcl40] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl40__n_K43
       -rho*Y[jhe4]*rate_eval.He4_Cl40__K44
       +rho*Y[jp]*rate_eval.p_Cl40__He4_S37
       )

    jac[jhe4, jcl41] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl41__n_K44
       -rho*Y[jhe4]*rate_eval.He4_Cl41__K45
       -rho*Y[jhe4]*rate_eval.He4_Cl41__p_Ar44
       +rho*Y[jp]*rate_eval.p_Cl41__He4_S38
       )

    jac[jhe4, jcl42] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl42__n_K45
       -rho*Y[jhe4]*rate_eval.He4_Cl42__K46
       +rho*Y[jp]*rate_eval.p_Cl42__He4_S39
       )

    jac[jhe4, jcl43] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl43__p_Ar46
       -rho*Y[jhe4]*rate_eval.He4_Cl43__K47
       -rho*Y[jhe4]*rate_eval.He4_Cl43__n_K46
       +rho*Y[jp]*rate_eval.p_Cl43__He4_S40
       )

    jac[jhe4, jcl44] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl44__p_Ar47
       -rho*Y[jhe4]*rate_eval.He4_Cl44__n_K47
       -rho*Y[jhe4]*rate_eval.He4_Cl44__K48
       +rho*Y[jp]*rate_eval.p_Cl44__He4_S41
       )

    jac[jhe4, jcl45] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl45__n_K48
       -rho*Y[jhe4]*rate_eval.He4_Cl45__K49
       +rho*Y[jp]*rate_eval.p_Cl45__He4_S42
       )

    jac[jhe4, jcl46] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl46__n_K49
       -rho*Y[jhe4]*rate_eval.He4_Cl46__K50
       +rho*Y[jp]*rate_eval.p_Cl46__He4_S43
       )

    jac[jhe4, jcl47] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl47__K51
       -rho*Y[jhe4]*rate_eval.He4_Cl47__n_K50
       +rho*Y[jp]*rate_eval.p_Cl47__He4_S44
       )

    jac[jhe4, jcl48] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl48__K52
       -rho*Y[jhe4]*rate_eval.He4_Cl48__n_K51
       +rho*Y[jp]*rate_eval.p_Cl48__He4_S45
       )

    jac[jhe4, jcl49] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl49__n_K52
       -rho*Y[jhe4]*rate_eval.He4_Cl49__K53
       +rho*Y[jp]*rate_eval.p_Cl49__He4_S46
       )

    jac[jhe4, jcl50] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl50__K54
       -rho*Y[jhe4]*rate_eval.He4_Cl50__n_K53
       +rho*Y[jp]*rate_eval.p_Cl50__He4_S47
       )

    jac[jhe4, jcl51] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl51__n_K54
       -rho*Y[jhe4]*rate_eval.He4_Cl51__K55
       +rho*Y[jp]*rate_eval.p_Cl51__He4_S48
       )

    jac[jhe4, jcl52] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl52__n_K55
       -rho*Y[jhe4]*rate_eval.He4_Cl52__K56
       +rho*Y[jp]*rate_eval.p_Cl52__He4_S49
       )

    jac[jhe4, jar29] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar29__Ca33
       -rho*Y[jhe4]*rate_eval.He4_Ar29__p_K32
       +rho*Y[jn]*rate_eval.n_Ar29__He4_S26
       )

    jac[jhe4, jar30] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar30__Ca34
       -rho*Y[jhe4]*rate_eval.He4_Ar30__p_K33
       +rho*Y[jn]*rate_eval.n_Ar30__He4_S27
       )

    jac[jhe4, jar31] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar31__p_K34
       -rho*Y[jhe4]*rate_eval.He4_Ar31__Ca35
       +rho*Y[jn]*rate_eval.n_Ar31__He4_S28
       )

    jac[jhe4, jar32] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar32__Ca36
       -rho*Y[jhe4]*rate_eval.He4_Ar32__p_K35
       +rho*Y[jn]*rate_eval.n_Ar32__He4_S29
       )

    jac[jhe4, jar33] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar33__p_K36
       -rho*Y[jhe4]*rate_eval.He4_Ar33__Ca37
       +rho*Y[jn]*rate_eval.n_Ar33__He4_S30
       )

    jac[jhe4, jar34] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar34__p_K37
       -rho*Y[jhe4]*rate_eval.He4_Ar34__Ca38
       +rho*Y[jn]*rate_eval.n_Ar34__He4_S31
       )

    jac[jhe4, jar35] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar35__Ca39
       -rho*Y[jhe4]*rate_eval.He4_Ar35__p_K38
       +rho*Y[jn]*rate_eval.n_Ar35__He4_S32
       )

    jac[jhe4, jar36] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar36__Ca40
       +rho*Y[jn]*rate_eval.n_Ar36__He4_S33
       )

    jac[jhe4, jar37] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar37__Ca41
       )

    jac[jhe4, jar38] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar38__Ca42
       )

    jac[jhe4, jar39] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar39__Ca43
       +rho*Y[jp]*rate_eval.p_Ar39__He4_Cl36
       +rho*Y[jn]*rate_eval.n_Ar39__He4_S36
       )

    jac[jhe4, jar40] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar40__Ca44
       +rho*Y[jp]*rate_eval.p_Ar40__He4_Cl37
       )

    jac[jhe4, jar41] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar41__n_Ca44
       -rho*Y[jhe4]*rate_eval.He4_Ar41__Ca45
       +rho*Y[jp]*rate_eval.p_Ar41__He4_Cl38
       )

    jac[jhe4, jar42] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar42__n_Ca45
       -rho*Y[jhe4]*rate_eval.He4_Ar42__Ca46
       +rho*Y[jp]*rate_eval.p_Ar42__He4_Cl39
       )

    jac[jhe4, jar43] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar43__n_Ca46
       -rho*Y[jhe4]*rate_eval.He4_Ar43__Ca47
       +rho*Y[jp]*rate_eval.p_Ar43__He4_Cl40
       )

    jac[jhe4, jar44] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar44__n_Ca47
       -rho*Y[jhe4]*rate_eval.He4_Ar44__Ca48
       )

    jac[jhe4, jar45] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar45__Ca49
       -rho*Y[jhe4]*rate_eval.He4_Ar45__n_Ca48
       +rho*Y[jp]*rate_eval.p_Ar45__He4_Cl42
       )

    jac[jhe4, jar46] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar46__n_Ca49
       -rho*Y[jhe4]*rate_eval.He4_Ar46__Ca50
       )

    jac[jhe4, jar47] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar47__Ca51
       -rho*Y[jhe4]*rate_eval.He4_Ar47__n_Ca50
       )

    jac[jhe4, jar48] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar48__Ca52
       -rho*Y[jhe4]*rate_eval.He4_Ar48__n_Ca51
       +rho*Y[jp]*rate_eval.p_Ar48__He4_Cl45
       )

    jac[jhe4, jar49] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar49__n_Ca52
       -rho*Y[jhe4]*rate_eval.He4_Ar49__Ca53
       +rho*Y[jp]*rate_eval.p_Ar49__He4_Cl46
       )

    jac[jhe4, jar50] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar50__Ca54
       -rho*Y[jhe4]*rate_eval.He4_Ar50__n_Ca53
       +rho*Y[jp]*rate_eval.p_Ar50__He4_Cl47
       )

    jac[jhe4, jar51] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar51__Ca55
       -rho*Y[jhe4]*rate_eval.He4_Ar51__n_Ca54
       +rho*Y[jp]*rate_eval.p_Ar51__He4_Cl48
       )

    jac[jhe4, jar52] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar52__Ca56
       -rho*Y[jhe4]*rate_eval.He4_Ar52__n_Ca55
       +rho*Y[jp]*rate_eval.p_Ar52__He4_Cl49
       )

    jac[jhe4, jar53] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar53__n_Ca56
       -rho*Y[jhe4]*rate_eval.He4_Ar53__Ca57
       +rho*Y[jp]*rate_eval.p_Ar53__He4_Cl50
       )

    jac[jhe4, jar54] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar54__n_Ca57
       -rho*Y[jhe4]*rate_eval.He4_Ar54__Ca58
       +rho*Y[jp]*rate_eval.p_Ar54__He4_Cl51
       )

    jac[jhe4, jk31] = (
       -rho*Y[jhe4]*rate_eval.He4_K31__p_Ca34
       -rho*Y[jhe4]*rate_eval.He4_K31__Sc35
       +rho*Y[jn]*rate_eval.n_K31__He4_Cl28
       )

    jac[jhe4, jk32] = (
       -rho*Y[jhe4]*rate_eval.He4_K32__Sc36
       -rho*Y[jhe4]*rate_eval.He4_K32__p_Ca35
       +rho*Y[jn]*rate_eval.n_K32__He4_Cl29
       )

    jac[jhe4, jk33] = (
       -rho*Y[jhe4]*rate_eval.He4_K33__Sc37
       -rho*Y[jhe4]*rate_eval.He4_K33__p_Ca36
       +rho*Y[jn]*rate_eval.n_K33__He4_Cl30
       )

    jac[jhe4, jk34] = (
       -rho*Y[jhe4]*rate_eval.He4_K34__p_Ca37
       -rho*Y[jhe4]*rate_eval.He4_K34__Sc38
       +rho*Y[jn]*rate_eval.n_K34__He4_Cl31
       )

    jac[jhe4, jk35] = (
       -rho*Y[jhe4]*rate_eval.He4_K35__p_Ca38
       -rho*Y[jhe4]*rate_eval.He4_K35__Sc39
       +rho*Y[jn]*rate_eval.n_K35__He4_Cl32
       )

    jac[jhe4, jk36] = (
       -rho*Y[jhe4]*rate_eval.He4_K36__p_Ca39
       -rho*Y[jhe4]*rate_eval.He4_K36__Sc40
       +rho*Y[jn]*rate_eval.n_K36__He4_Cl33
       +rate_eval.K36__He4_S32__weak__wc12
       )

    jac[jhe4, jk37] = (
       -rho*Y[jhe4]*rate_eval.He4_K37__p_Ca40
       -rho*Y[jhe4]*rate_eval.He4_K37__Sc41
       +rho*Y[jn]*rate_eval.n_K37__He4_Cl34
       )

    jac[jhe4, jk38] = (
       -rho*Y[jhe4]*rate_eval.He4_K38__p_Ca41
       -rho*Y[jhe4]*rate_eval.He4_K38__Sc42
       +rho*Y[jn]*rate_eval.n_K38__He4_Cl35
       )

    jac[jhe4, jk39] = (
       -rho*Y[jhe4]*rate_eval.He4_K39__Sc43
       +rho*Y[jn]*rate_eval.n_K39__He4_Cl36
       +rho*Y[jp]*rate_eval.p_K39__He4_Ar36
       )

    jac[jhe4, jk40] = (
       -rho*Y[jhe4]*rate_eval.He4_K40__p_Ca43
       -rho*Y[jhe4]*rate_eval.He4_K40__Sc44
       +rho*Y[jp]*rate_eval.p_K40__He4_Ar37
       +rho*Y[jn]*rate_eval.n_K40__He4_Cl37
       )

    jac[jhe4, jk41] = (
       -rho*Y[jhe4]*rate_eval.He4_K41__n_Sc44
       -rho*Y[jhe4]*rate_eval.He4_K41__p_Ca44
       -rho*Y[jhe4]*rate_eval.He4_K41__Sc45
       +rho*Y[jp]*rate_eval.p_K41__He4_Ar38
       )

    jac[jhe4, jk42] = (
       -rho*Y[jhe4]*rate_eval.He4_K42__p_Ca45
       -rho*Y[jhe4]*rate_eval.He4_K42__n_Sc45
       -rho*Y[jhe4]*rate_eval.He4_K42__Sc46
       +rho*Y[jp]*rate_eval.p_K42__He4_Ar39
       +rho*Y[jn]*rate_eval.n_K42__He4_Cl39
       )

    jac[jhe4, jk43] = (
       -rho*Y[jhe4]*rate_eval.He4_K43__p_Ca46
       -rho*Y[jhe4]*rate_eval.He4_K43__Sc47
       +rho*Y[jp]*rate_eval.p_K43__He4_Ar40
       )

    jac[jhe4, jk44] = (
       -rho*Y[jhe4]*rate_eval.He4_K44__p_Ca47
       -rho*Y[jhe4]*rate_eval.He4_K44__Sc48
       -rho*Y[jhe4]*rate_eval.He4_K44__n_Sc47
       +rho*Y[jp]*rate_eval.p_K44__He4_Ar41
       )

    jac[jhe4, jk45] = (
       -rho*Y[jhe4]*rate_eval.He4_K45__p_Ca48
       -rho*Y[jhe4]*rate_eval.He4_K45__Sc49
       -rho*Y[jhe4]*rate_eval.He4_K45__n_Sc48
       +rho*Y[jp]*rate_eval.p_K45__He4_Ar42
       )

    jac[jhe4, jk46] = (
       -rho*Y[jhe4]*rate_eval.He4_K46__p_Ca49
       -rho*Y[jhe4]*rate_eval.He4_K46__Sc50
       -rho*Y[jhe4]*rate_eval.He4_K46__n_Sc49
       +rho*Y[jp]*rate_eval.p_K46__He4_Ar43
       )

    jac[jhe4, jk47] = (
       -rho*Y[jhe4]*rate_eval.He4_K47__Sc51
       -rho*Y[jhe4]*rate_eval.He4_K47__n_Sc50
       +rho*Y[jp]*rate_eval.p_K47__He4_Ar44
       )

    jac[jhe4, jk48] = (
       -rho*Y[jhe4]*rate_eval.He4_K48__n_Sc51
       -rho*Y[jhe4]*rate_eval.He4_K48__Sc52
       +rho*Y[jp]*rate_eval.p_K48__He4_Ar45
       )

    jac[jhe4, jk49] = (
       -rho*Y[jhe4]*rate_eval.He4_K49__n_Sc52
       -rho*Y[jhe4]*rate_eval.He4_K49__Sc53
       +rho*Y[jp]*rate_eval.p_K49__He4_Ar46
       )

    jac[jhe4, jk50] = (
       -rho*Y[jhe4]*rate_eval.He4_K50__n_Sc53
       -rho*Y[jhe4]*rate_eval.He4_K50__Sc54
       +rho*Y[jp]*rate_eval.p_K50__He4_Ar47
       )

    jac[jhe4, jk51] = (
       -rho*Y[jhe4]*rate_eval.He4_K51__n_Sc54
       -rho*Y[jhe4]*rate_eval.He4_K51__Sc55
       +rho*Y[jp]*rate_eval.p_K51__He4_Ar48
       )

    jac[jhe4, jk52] = (
       -rho*Y[jhe4]*rate_eval.He4_K52__n_Sc55
       -rho*Y[jhe4]*rate_eval.He4_K52__Sc56
       +rho*Y[jp]*rate_eval.p_K52__He4_Ar49
       )

    jac[jhe4, jk53] = (
       -rho*Y[jhe4]*rate_eval.He4_K53__n_Sc56
       -rho*Y[jhe4]*rate_eval.He4_K53__Sc57
       +rho*Y[jp]*rate_eval.p_K53__He4_Ar50
       )

    jac[jhe4, jk54] = (
       -rho*Y[jhe4]*rate_eval.He4_K54__n_Sc57
       -rho*Y[jhe4]*rate_eval.He4_K54__Sc58
       +rho*Y[jp]*rate_eval.p_K54__He4_Ar51
       )

    jac[jhe4, jk55] = (
       -rho*Y[jhe4]*rate_eval.He4_K55__n_Sc58
       -rho*Y[jhe4]*rate_eval.He4_K55__Sc59
       +rho*Y[jp]*rate_eval.p_K55__He4_Ar52
       )

    jac[jhe4, jk56] = (
       -rho*Y[jhe4]*rate_eval.He4_K56__n_Sc59
       -rho*Y[jhe4]*rate_eval.He4_K56__Sc60
       +rho*Y[jp]*rate_eval.p_K56__He4_Ar53
       )

    jac[jhe4, jk57] = (
       -rho*Y[jhe4]*rate_eval.He4_K57__n_Sc60
       -rho*Y[jhe4]*rate_eval.He4_K57__Sc61
       +rho*Y[jp]*rate_eval.p_K57__He4_Ar54
       )

    jac[jhe4, jk58] = (
       -rho*Y[jhe4]*rate_eval.He4_K58__Sc62
       -rho*Y[jhe4]*rate_eval.He4_K58__n_Sc61
       )

    jac[jhe4, jk59] = (
       -rho*Y[jhe4]*rate_eval.He4_K59__Sc63
       -rho*Y[jhe4]*rate_eval.He4_K59__n_Sc62
       )

    jac[jhe4, jca33] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca33__Ti37
       -rho*Y[jhe4]*rate_eval.He4_Ca33__p_Sc36
       +rho*Y[jn]*rate_eval.n_Ca33__He4_Ar30
       )

    jac[jhe4, jca34] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca34__Ti38
       -rho*Y[jhe4]*rate_eval.He4_Ca34__p_Sc37
       +rho*Y[jn]*rate_eval.n_Ca34__He4_Ar31
       )

    jac[jhe4, jca35] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca35__Ti39
       -rho*Y[jhe4]*rate_eval.He4_Ca35__p_Sc38
       +rho*Y[jn]*rate_eval.n_Ca35__He4_Ar32
       )

    jac[jhe4, jca36] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca36__p_p_Ca38
       -rho*Y[jhe4]*rate_eval.He4_Ca36__p_Sc39
       -rho*Y[jhe4]*rate_eval.He4_Ca36__Ti40
       +rho*Y[jn]*rate_eval.n_Ca36__He4_Ar33
       )

    jac[jhe4, jca37] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca37__Ti41
       -rho*Y[jhe4]*rate_eval.He4_Ca37__p_Sc40
       +rho*Y[jn]*rate_eval.n_Ca37__He4_Ar34
       )

    jac[jhe4, jca38] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca38__Ti42
       -rho*Y[jhe4]*rate_eval.He4_Ca38__p_Sc41
       +rho*Y[jn]*rate_eval.n_Ca38__He4_Ar35
       )

    jac[jhe4, jca39] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca39__Ti43
       +rho*Y[jn]*rate_eval.n_Ca39__He4_Ar36
       )

    jac[jhe4, jca40] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca40__Ti44
       +rho*Y[jn]*rate_eval.n_Ca40__He4_Ar37
       )

    jac[jhe4, jca41] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca41__Ti45
       +rho*Y[jn]*rate_eval.n_Ca41__He4_Ar38
       )

    jac[jhe4, jca42] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca42__Ti46
       +rho*Y[jp]*rate_eval.p_Ca42__He4_K39
       +rho*Y[jn]*rate_eval.n_Ca42__He4_Ar39
       )

    jac[jhe4, jca43] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca43__Ti47
       -rho*Y[jhe4]*rate_eval.He4_Ca43__n_Ti46
       +rho*Y[jn]*rate_eval.n_Ca43__He4_Ar40
       )

    jac[jhe4, jca44] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca44__Ti48
       )

    jac[jhe4, jca45] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca45__Ti49
       -rho*Y[jhe4]*rate_eval.He4_Ca45__n_Ti48
       )

    jac[jhe4, jca46] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca46__Ti50
       )

    jac[jhe4, jca47] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca47__n_Ti50
       -rho*Y[jhe4]*rate_eval.He4_Ca47__Ti51
       )

    jac[jhe4, jca48] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca48__Ti52
       )

    jac[jhe4, jca49] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca49__n_Ti52
       -rho*Y[jhe4]*rate_eval.He4_Ca49__Ti53
       )

    jac[jhe4, jca50] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca50__n_Ti53
       -rho*Y[jhe4]*rate_eval.He4_Ca50__Ti54
       +rho*Y[jp]*rate_eval.p_Ca50__He4_K47
       )

    jac[jhe4, jca51] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca51__n_Ti54
       -rho*Y[jhe4]*rate_eval.He4_Ca51__Ti55
       +rho*Y[jp]*rate_eval.p_Ca51__He4_K48
       )

    jac[jhe4, jca52] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca52__Ti56
       -rho*Y[jhe4]*rate_eval.He4_Ca52__n_Ti55
       +rho*Y[jp]*rate_eval.p_Ca52__He4_K49
       )

    jac[jhe4, jca53] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca53__n_Ti56
       -rho*Y[jhe4]*rate_eval.He4_Ca53__Ti57
       +rho*Y[jp]*rate_eval.p_Ca53__He4_K50
       )

    jac[jhe4, jca54] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca54__Ti58
       -rho*Y[jhe4]*rate_eval.He4_Ca54__n_Ti57
       +rho*Y[jp]*rate_eval.p_Ca54__He4_K51
       )

    jac[jhe4, jca55] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca55__n_Ti58
       -rho*Y[jhe4]*rate_eval.He4_Ca55__Ti59
       +rho*Y[jp]*rate_eval.p_Ca55__He4_K52
       )

    jac[jhe4, jca56] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca56__Ti60
       -rho*Y[jhe4]*rate_eval.He4_Ca56__n_Ti59
       +rho*Y[jp]*rate_eval.p_Ca56__He4_K53
       )

    jac[jhe4, jca57] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca57__n_Ti60
       -rho*Y[jhe4]*rate_eval.He4_Ca57__Ti61
       +rho*Y[jp]*rate_eval.p_Ca57__He4_K54
       )

    jac[jhe4, jca58] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca58__n_Ti61
       -rho*Y[jhe4]*rate_eval.He4_Ca58__Ti62
       +rho*Y[jp]*rate_eval.p_Ca58__He4_K55
       )

    jac[jhe4, jca59] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca59__Ti63
       -rho*Y[jhe4]*rate_eval.He4_Ca59__n_Ti62
       +rho*Y[jp]*rate_eval.p_Ca59__He4_K56
       )

    jac[jhe4, jca60] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca60__n_Ti63
       -rho*Y[jhe4]*rate_eval.He4_Ca60__Ti64
       +rho*Y[jp]*rate_eval.p_Ca60__He4_K57
       )

    jac[jhe4, jca61] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca61__n_Ti64
       -rho*Y[jhe4]*rate_eval.He4_Ca61__Ti65
       +rho*Y[jp]*rate_eval.p_Ca61__He4_K58
       )

    jac[jhe4, jsc35] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc35__p_Ti38
       -rho*Y[jhe4]*rate_eval.He4_Sc35__V39
       +rho*Y[jn]*rate_eval.n_Sc35__He4_K32
       )

    jac[jhe4, jsc36] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc36__p_Ti39
       -rho*Y[jhe4]*rate_eval.He4_Sc36__V40
       +rho*Y[jn]*rate_eval.n_Sc36__He4_K33
       )

    jac[jhe4, jsc37] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc37__p_Ti40
       -rho*Y[jhe4]*rate_eval.He4_Sc37__V41
       +rho*Y[jn]*rate_eval.n_Sc37__He4_K34
       )

    jac[jhe4, jsc38] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc38__p_Ti41
       -rho*Y[jhe4]*rate_eval.He4_Sc38__V42
       +rho*Y[jn]*rate_eval.n_Sc38__He4_K35
       )

    jac[jhe4, jsc39] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc39__p_Ti42
       -rho*Y[jhe4]*rate_eval.He4_Sc39__V43
       +rho*Y[jn]*rate_eval.n_Sc39__He4_K36
       )

    jac[jhe4, jsc40] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc40__p_Ti43
       -rho*Y[jhe4]*rate_eval.He4_Sc40__V44
       +rate_eval.Sc40__He4_Ar36__weak__wc12
       +rho*Y[jn]*rate_eval.n_Sc40__He4_K37
       )

    jac[jhe4, jsc41] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc41__V45
       -rho*Y[jhe4]*rate_eval.He4_Sc41__p_Ti44
       +rho*Y[jn]*rate_eval.n_Sc41__He4_K38
       )

    jac[jhe4, jsc42] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc42__p_Ti45
       -rho*Y[jhe4]*rate_eval.He4_Sc42__V46
       +rho*Y[jn]*rate_eval.n_Sc42__He4_K39
       +rho*Y[jp]*rate_eval.p_Sc42__He4_Ca39
       )

    jac[jhe4, jsc43] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc43__p_Ti46
       -rho*Y[jhe4]*rate_eval.He4_Sc43__V47
       +rho*Y[jn]*rate_eval.n_Sc43__He4_K40
       +rho*Y[jp]*rate_eval.p_Sc43__He4_Ca40
       )

    jac[jhe4, jsc44] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc44__p_Ti47
       -rho*Y[jhe4]*rate_eval.He4_Sc44__V48
       +rho*Y[jp]*rate_eval.p_Sc44__He4_Ca41
       )

    jac[jhe4, jsc45] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc45__p_Ti48
       -rho*Y[jhe4]*rate_eval.He4_Sc45__V49
       +rho*Y[jp]*rate_eval.p_Sc45__He4_Ca42
       )

    jac[jhe4, jsc46] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc46__p_Ti49
       -rho*Y[jhe4]*rate_eval.He4_Sc46__n_V49
       -rho*Y[jhe4]*rate_eval.He4_Sc46__V50
       +rho*Y[jp]*rate_eval.p_Sc46__He4_Ca43
       +rho*Y[jn]*rate_eval.n_Sc46__He4_K43
       )

    jac[jhe4, jsc47] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc47__p_Ti50
       -rho*Y[jhe4]*rate_eval.He4_Sc47__V51
       +rho*Y[jp]*rate_eval.p_Sc47__He4_Ca44
       )

    jac[jhe4, jsc48] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc48__n_V51
       -rho*Y[jhe4]*rate_eval.He4_Sc48__V52
       -rho*Y[jhe4]*rate_eval.He4_Sc48__p_Ti51
       +rho*Y[jp]*rate_eval.p_Sc48__He4_Ca45
       )

    jac[jhe4, jsc49] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc49__V53
       +rho*Y[jp]*rate_eval.p_Sc49__He4_Ca46
       )

    jac[jhe4, jsc50] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc50__V54
       -rho*Y[jhe4]*rate_eval.He4_Sc50__n_V53
       +rho*Y[jp]*rate_eval.p_Sc50__He4_Ca47
       )

    jac[jhe4, jsc51] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc51__n_V54
       -rho*Y[jhe4]*rate_eval.He4_Sc51__V55
       +rho*Y[jp]*rate_eval.p_Sc51__He4_Ca48
       )

    jac[jhe4, jsc52] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc52__n_V55
       -rho*Y[jhe4]*rate_eval.He4_Sc52__V56
       +rho*Y[jp]*rate_eval.p_Sc52__He4_Ca49
       )

    jac[jhe4, jsc53] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc53__n_V56
       -rho*Y[jhe4]*rate_eval.He4_Sc53__V57
       +rho*Y[jp]*rate_eval.p_Sc53__He4_Ca50
       )

    jac[jhe4, jsc54] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc54__n_V57
       -rho*Y[jhe4]*rate_eval.He4_Sc54__V58
       +rho*Y[jp]*rate_eval.p_Sc54__He4_Ca51
       )

    jac[jhe4, jsc55] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc55__n_V58
       -rho*Y[jhe4]*rate_eval.He4_Sc55__V59
       +rho*Y[jp]*rate_eval.p_Sc55__He4_Ca52
       )

    jac[jhe4, jsc56] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc56__n_V59
       -rho*Y[jhe4]*rate_eval.He4_Sc56__V60
       +rho*Y[jp]*rate_eval.p_Sc56__He4_Ca53
       )

    jac[jhe4, jsc57] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc57__n_V60
       -rho*Y[jhe4]*rate_eval.He4_Sc57__V61
       +rho*Y[jp]*rate_eval.p_Sc57__He4_Ca54
       )

    jac[jhe4, jsc58] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc58__n_V61
       -rho*Y[jhe4]*rate_eval.He4_Sc58__V62
       +rho*Y[jp]*rate_eval.p_Sc58__He4_Ca55
       )

    jac[jhe4, jsc59] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc59__V63
       -rho*Y[jhe4]*rate_eval.He4_Sc59__n_V62
       +rho*Y[jp]*rate_eval.p_Sc59__He4_Ca56
       )

    jac[jhe4, jsc60] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc60__n_V63
       -rho*Y[jhe4]*rate_eval.He4_Sc60__V64
       +rho*Y[jp]*rate_eval.p_Sc60__He4_Ca57
       )

    jac[jhe4, jsc61] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc61__n_V64
       -rho*Y[jhe4]*rate_eval.He4_Sc61__V65
       +rho*Y[jp]*rate_eval.p_Sc61__He4_Ca58
       )

    jac[jhe4, jsc62] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc62__n_V65
       -rho*Y[jhe4]*rate_eval.He4_Sc62__V66
       +rho*Y[jp]*rate_eval.p_Sc62__He4_Ca59
       )

    jac[jhe4, jsc63] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc63__n_V66
       -rho*Y[jhe4]*rate_eval.He4_Sc63__V67
       +rho*Y[jp]*rate_eval.p_Sc63__He4_Ca60
       )

    jac[jhe4, jti37] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti37__p_V40
       -rho*Y[jhe4]*rate_eval.He4_Ti37__Cr41
       +rho*Y[jn]*rate_eval.n_Ti37__He4_Ca34
       )

    jac[jhe4, jti38] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti38__p_V41
       -rho*Y[jhe4]*rate_eval.He4_Ti38__Cr42
       +rho*Y[jn]*rate_eval.n_Ti38__He4_Ca35
       )

    jac[jhe4, jti39] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti39__p_V42
       -rho*Y[jhe4]*rate_eval.He4_Ti39__Cr43
       +rho*Y[jn]*rate_eval.n_Ti39__He4_Ca36
       )

    jac[jhe4, jti40] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti40__p_V43
       -rho*Y[jhe4]*rate_eval.He4_Ti40__Cr44
       +rho*Y[jn]*rate_eval.n_Ti40__He4_Ca37
       )

    jac[jhe4, jti41] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti41__Cr45
       -rho*Y[jhe4]*rate_eval.He4_Ti41__p_V44
       +rho*Y[jn]*rate_eval.n_Ti41__He4_Ca38
       )

    jac[jhe4, jti42] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti42__p_V45
       -rho*Y[jhe4]*rate_eval.He4_Ti42__Cr46
       +rho*Y[jn]*rate_eval.n_Ti42__He4_Ca39
       )

    jac[jhe4, jti43] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti43__p_V46
       -rho*Y[jhe4]*rate_eval.He4_Ti43__Cr47
       +rho*Y[jn]*rate_eval.n_Ti43__He4_Ca40
       )

    jac[jhe4, jti44] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti44__p_V47
       -rho*Y[jhe4]*rate_eval.He4_Ti44__Cr48
       +rho*Y[jn]*rate_eval.n_Ti44__He4_Ca41
       )

    jac[jhe4, jti45] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti45__p_V48
       -rho*Y[jhe4]*rate_eval.He4_Ti45__Cr49
       +rho*Y[jn]*rate_eval.n_Ti45__He4_Ca42
       )

    jac[jhe4, jti46] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti46__Cr50
       )

    jac[jhe4, jti47] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti47__Cr51
       +rho*Y[jn]*rate_eval.n_Ti47__He4_Ca44
       )

    jac[jhe4, jti48] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti48__Cr52
       )

    jac[jhe4, jti49] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti49__n_Cr52
       -rho*Y[jhe4]*rate_eval.He4_Ti49__Cr53
       +rho*Y[jn]*rate_eval.n_Ti49__He4_Ca46
       )

    jac[jhe4, jti50] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti50__Cr54
       )

    jac[jhe4, jti51] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti51__n_Cr54
       -rho*Y[jhe4]*rate_eval.He4_Ti51__Cr55
       +rho*Y[jn]*rate_eval.n_Ti51__He4_Ca48
       )

    jac[jhe4, jti52] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti52__Cr56
       +rho*Y[jp]*rate_eval.p_Ti52__He4_Sc49
       )

    jac[jhe4, jti53] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti53__n_Cr56
       -rho*Y[jhe4]*rate_eval.He4_Ti53__Cr57
       +rho*Y[jp]*rate_eval.p_Ti53__He4_Sc50
       )

    jac[jhe4, jti54] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti54__n_Cr57
       -rho*Y[jhe4]*rate_eval.He4_Ti54__Cr58
       +rho*Y[jp]*rate_eval.p_Ti54__He4_Sc51
       )

    jac[jhe4, jti55] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti55__n_Cr58
       -rho*Y[jhe4]*rate_eval.He4_Ti55__Cr59
       +rho*Y[jp]*rate_eval.p_Ti55__He4_Sc52
       )

    jac[jhe4, jti56] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti56__Cr60
       -rho*Y[jhe4]*rate_eval.He4_Ti56__n_Cr59
       +rho*Y[jp]*rate_eval.p_Ti56__He4_Sc53
       )

    jac[jhe4, jti57] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti57__n_Cr60
       -rho*Y[jhe4]*rate_eval.He4_Ti57__Cr61
       +rho*Y[jp]*rate_eval.p_Ti57__He4_Sc54
       )

    jac[jhe4, jti58] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti58__n_Cr61
       -rho*Y[jhe4]*rate_eval.He4_Ti58__Cr62
       +rho*Y[jp]*rate_eval.p_Ti58__He4_Sc55
       )

    jac[jhe4, jti59] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti59__n_Cr62
       -rho*Y[jhe4]*rate_eval.He4_Ti59__Cr63
       +rho*Y[jp]*rate_eval.p_Ti59__He4_Sc56
       )

    jac[jhe4, jti60] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti60__n_Cr63
       -rho*Y[jhe4]*rate_eval.He4_Ti60__Cr64
       +rho*Y[jp]*rate_eval.p_Ti60__He4_Sc57
       )

    jac[jhe4, jti61] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti61__n_Cr64
       -rho*Y[jhe4]*rate_eval.He4_Ti61__Cr65
       +rho*Y[jp]*rate_eval.p_Ti61__He4_Sc58
       )

    jac[jhe4, jti62] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti62__n_Cr65
       -rho*Y[jhe4]*rate_eval.He4_Ti62__Cr66
       +rho*Y[jp]*rate_eval.p_Ti62__He4_Sc59
       )

    jac[jhe4, jti63] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti63__n_Cr66
       -rho*Y[jhe4]*rate_eval.He4_Ti63__Cr67
       +rho*Y[jp]*rate_eval.p_Ti63__He4_Sc60
       )

    jac[jhe4, jti64] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti64__n_Cr67
       -rho*Y[jhe4]*rate_eval.He4_Ti64__Cr68
       +rho*Y[jp]*rate_eval.p_Ti64__He4_Sc61
       )

    jac[jhe4, jti65] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti65__n_Cr68
       -rho*Y[jhe4]*rate_eval.He4_Ti65__Cr69
       +rho*Y[jp]*rate_eval.p_Ti65__He4_Sc62
       )

    jac[jhe4, jv39] = (
       -rho*Y[jhe4]*rate_eval.He4_V39__p_Cr42
       -rho*Y[jhe4]*rate_eval.He4_V39__Mn43
       +rho*Y[jn]*rate_eval.n_V39__He4_Sc36
       )

    jac[jhe4, jv40] = (
       -rho*Y[jhe4]*rate_eval.He4_V40__p_Cr43
       -rho*Y[jhe4]*rate_eval.He4_V40__Mn44
       +rho*Y[jn]*rate_eval.n_V40__He4_Sc37
       )

    jac[jhe4, jv41] = (
       -rho*Y[jhe4]*rate_eval.He4_V41__Mn45
       -rho*Y[jhe4]*rate_eval.He4_V41__p_Cr44
       +rho*Y[jn]*rate_eval.n_V41__He4_Sc38
       )

    jac[jhe4, jv42] = (
       -rho*Y[jhe4]*rate_eval.He4_V42__p_Cr45
       -rho*Y[jhe4]*rate_eval.He4_V42__Mn46
       +rho*Y[jn]*rate_eval.n_V42__He4_Sc39
       )

    jac[jhe4, jv43] = (
       -rho*Y[jhe4]*rate_eval.He4_V43__p_Cr46
       -rho*Y[jhe4]*rate_eval.He4_V43__Mn47
       +rho*Y[jn]*rate_eval.n_V43__He4_Sc40
       )

    jac[jhe4, jv44] = (
       -rho*Y[jhe4]*rate_eval.He4_V44__p_Cr47
       -rho*Y[jhe4]*rate_eval.He4_V44__Mn48
       +rho*Y[jn]*rate_eval.n_V44__He4_Sc41
       )

    jac[jhe4, jv45] = (
       -rho*Y[jhe4]*rate_eval.He4_V45__Mn49
       -rho*Y[jhe4]*rate_eval.He4_V45__p_Cr48
       +rho*Y[jn]*rate_eval.n_V45__He4_Sc42
       )

    jac[jhe4, jv46] = (
       -rho*Y[jhe4]*rate_eval.He4_V46__p_Cr49
       -rho*Y[jhe4]*rate_eval.He4_V46__Mn50
       +rho*Y[jn]*rate_eval.n_V46__He4_Sc43
       )

    jac[jhe4, jv47] = (
       -rho*Y[jhe4]*rate_eval.He4_V47__p_Cr50
       -rho*Y[jhe4]*rate_eval.He4_V47__Mn51
       +rho*Y[jn]*rate_eval.n_V47__He4_Sc44
       )

    jac[jhe4, jv48] = (
       -rho*Y[jhe4]*rate_eval.He4_V48__p_Cr51
       -rho*Y[jhe4]*rate_eval.He4_V48__Mn52
       +rho*Y[jn]*rate_eval.n_V48__He4_Sc45
       )

    jac[jhe4, jv49] = (
       -rho*Y[jhe4]*rate_eval.He4_V49__Mn53
       -rho*Y[jhe4]*rate_eval.He4_V49__p_Cr52
       +rho*Y[jp]*rate_eval.p_V49__He4_Ti46
       )

    jac[jhe4, jv50] = (
       -rho*Y[jhe4]*rate_eval.He4_V50__p_Cr53
       -rho*Y[jhe4]*rate_eval.He4_V50__Mn54
       +rho*Y[jp]*rate_eval.p_V50__He4_Ti47
       +rho*Y[jn]*rate_eval.n_V50__He4_Sc47
       )

    jac[jhe4, jv51] = (
       -rho*Y[jhe4]*rate_eval.He4_V51__Mn55
       +rho*Y[jp]*rate_eval.p_V51__He4_Ti48
       )

    jac[jhe4, jv52] = (
       -rho*Y[jhe4]*rate_eval.He4_V52__Mn56
       -rho*Y[jhe4]*rate_eval.He4_V52__n_Mn55
       +rho*Y[jp]*rate_eval.p_V52__He4_Ti49
       +rho*Y[jn]*rate_eval.n_V52__He4_Sc49
       )

    jac[jhe4, jv53] = (
       -rho*Y[jhe4]*rate_eval.He4_V53__Mn57
       +rho*Y[jp]*rate_eval.p_V53__He4_Ti50
       )

    jac[jhe4, jv54] = (
       -rho*Y[jhe4]*rate_eval.He4_V54__n_Mn57
       -rho*Y[jhe4]*rate_eval.He4_V54__Mn58
       +rho*Y[jp]*rate_eval.p_V54__He4_Ti51
       )

    jac[jhe4, jv55] = (
       -rho*Y[jhe4]*rate_eval.He4_V55__n_Mn58
       -rho*Y[jhe4]*rate_eval.He4_V55__Mn59
       +rho*Y[jp]*rate_eval.p_V55__He4_Ti52
       )

    jac[jhe4, jv56] = (
       -rho*Y[jhe4]*rate_eval.He4_V56__n_Mn59
       -rho*Y[jhe4]*rate_eval.He4_V56__Mn60
       +rho*Y[jp]*rate_eval.p_V56__He4_Ti53
       )

    jac[jhe4, jv57] = (
       -rho*Y[jhe4]*rate_eval.He4_V57__n_Mn60
       -rho*Y[jhe4]*rate_eval.He4_V57__Mn61
       +rho*Y[jp]*rate_eval.p_V57__He4_Ti54
       )

    jac[jhe4, jv58] = (
       -rho*Y[jhe4]*rate_eval.He4_V58__n_Mn61
       -rho*Y[jhe4]*rate_eval.He4_V58__Mn62
       +rho*Y[jp]*rate_eval.p_V58__He4_Ti55
       )

    jac[jhe4, jv59] = (
       -rho*Y[jhe4]*rate_eval.He4_V59__n_Mn62
       -rho*Y[jhe4]*rate_eval.He4_V59__Mn63
       +rho*Y[jp]*rate_eval.p_V59__He4_Ti56
       )

    jac[jhe4, jv60] = (
       -rho*Y[jhe4]*rate_eval.He4_V60__n_Mn63
       -rho*Y[jhe4]*rate_eval.He4_V60__Mn64
       +rho*Y[jp]*rate_eval.p_V60__He4_Ti57
       )

    jac[jhe4, jv61] = (
       -rho*Y[jhe4]*rate_eval.He4_V61__n_Mn64
       -rho*Y[jhe4]*rate_eval.He4_V61__Mn65
       +rho*Y[jp]*rate_eval.p_V61__He4_Ti58
       )

    jac[jhe4, jv62] = (
       -rho*Y[jhe4]*rate_eval.He4_V62__n_Mn65
       -rho*Y[jhe4]*rate_eval.He4_V62__Mn66
       +rho*Y[jp]*rate_eval.p_V62__He4_Ti59
       )

    jac[jhe4, jv63] = (
       -rho*Y[jhe4]*rate_eval.He4_V63__Mn67
       -rho*Y[jhe4]*rate_eval.He4_V63__n_Mn66
       +rho*Y[jp]*rate_eval.p_V63__He4_Ti60
       )

    jac[jhe4, jv64] = (
       -rho*Y[jhe4]*rate_eval.He4_V64__n_Mn67
       -rho*Y[jhe4]*rate_eval.He4_V64__Mn68
       +rho*Y[jp]*rate_eval.p_V64__He4_Ti61
       )

    jac[jhe4, jv65] = (
       -rho*Y[jhe4]*rate_eval.He4_V65__Mn69
       -rho*Y[jhe4]*rate_eval.He4_V65__n_Mn68
       +rho*Y[jp]*rate_eval.p_V65__He4_Ti62
       )

    jac[jhe4, jv66] = (
       -rho*Y[jhe4]*rate_eval.He4_V66__n_Mn69
       -rho*Y[jhe4]*rate_eval.He4_V66__Mn70
       +rho*Y[jp]*rate_eval.p_V66__He4_Ti63
       )

    jac[jhe4, jv67] = (
       -rho*Y[jhe4]*rate_eval.He4_V67__n_Mn70
       -rho*Y[jhe4]*rate_eval.He4_V67__Mn71
       +rho*Y[jp]*rate_eval.p_V67__He4_Ti64
       )

    jac[jhe4, jcr41] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr41__p_Mn44
       -rho*Y[jhe4]*rate_eval.He4_Cr41__Fe45
       +rho*Y[jn]*rate_eval.n_Cr41__He4_Ti38
       )

    jac[jhe4, jcr42] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr42__p_Mn45
       -rho*Y[jhe4]*rate_eval.He4_Cr42__Fe46
       +rho*Y[jn]*rate_eval.n_Cr42__He4_Ti39
       )

    jac[jhe4, jcr43] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr43__p_Mn46
       -rho*Y[jhe4]*rate_eval.He4_Cr43__Fe47
       +rho*Y[jn]*rate_eval.n_Cr43__He4_Ti40
       )

    jac[jhe4, jcr44] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr44__p_Mn47
       -rho*Y[jhe4]*rate_eval.He4_Cr44__Fe48
       +rho*Y[jn]*rate_eval.n_Cr44__He4_Ti41
       )

    jac[jhe4, jcr45] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr45__p_Mn48
       -rho*Y[jhe4]*rate_eval.He4_Cr45__Fe49
       +rho*Y[jn]*rate_eval.n_Cr45__He4_Ti42
       )

    jac[jhe4, jcr46] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr46__p_Mn49
       -rho*Y[jhe4]*rate_eval.He4_Cr46__Fe50
       +rho*Y[jn]*rate_eval.n_Cr46__He4_Ti43
       )

    jac[jhe4, jcr47] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr47__p_Mn50
       -rho*Y[jhe4]*rate_eval.He4_Cr47__Fe51
       +rho*Y[jn]*rate_eval.n_Cr47__He4_Ti44
       )

    jac[jhe4, jcr48] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr48__p_Mn51
       -rho*Y[jhe4]*rate_eval.He4_Cr48__Fe52
       +rho*Y[jn]*rate_eval.n_Cr48__He4_Ti45
       )

    jac[jhe4, jcr49] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr49__p_Mn52
       -rho*Y[jhe4]*rate_eval.He4_Cr49__Fe53
       +rho*Y[jn]*rate_eval.n_Cr49__He4_Ti46
       )

    jac[jhe4, jcr50] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr50__Fe54
       +rho*Y[jn]*rate_eval.n_Cr50__He4_Ti47
       )

    jac[jhe4, jcr51] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr51__Fe55
       +rho*Y[jn]*rate_eval.n_Cr51__He4_Ti48
       )

    jac[jhe4, jcr52] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr52__Fe56
       )

    jac[jhe4, jcr53] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr53__Fe57
       +rho*Y[jn]*rate_eval.n_Cr53__He4_Ti50
       )

    jac[jhe4, jcr54] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr54__Fe58
       +rho*Y[jp]*rate_eval.p_Cr54__He4_V51
       )

    jac[jhe4, jcr55] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr55__n_Fe58
       -rho*Y[jhe4]*rate_eval.He4_Cr55__Fe59
       +rho*Y[jn]*rate_eval.n_Cr55__He4_Ti52
       +rho*Y[jp]*rate_eval.p_Cr55__He4_V52
       )

    jac[jhe4, jcr56] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr56__Fe60
       +rho*Y[jp]*rate_eval.p_Cr56__He4_V53
       )

    jac[jhe4, jcr57] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr57__n_Fe60
       -rho*Y[jhe4]*rate_eval.He4_Cr57__Fe61
       +rho*Y[jp]*rate_eval.p_Cr57__He4_V54
       )

    jac[jhe4, jcr58] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr58__Fe62
       -rho*Y[jhe4]*rate_eval.He4_Cr58__n_Fe61
       +rho*Y[jp]*rate_eval.p_Cr58__He4_V55
       )

    jac[jhe4, jcr59] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr59__n_Fe62
       -rho*Y[jhe4]*rate_eval.He4_Cr59__Fe63
       +rho*Y[jp]*rate_eval.p_Cr59__He4_V56
       )

    jac[jhe4, jcr60] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr60__Fe64
       -rho*Y[jhe4]*rate_eval.He4_Cr60__n_Fe63
       +rho*Y[jp]*rate_eval.p_Cr60__He4_V57
       )

    jac[jhe4, jcr61] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr61__n_Fe64
       -rho*Y[jhe4]*rate_eval.He4_Cr61__Fe65
       +rho*Y[jp]*rate_eval.p_Cr61__He4_V58
       )

    jac[jhe4, jcr62] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr62__n_Fe65
       -rho*Y[jhe4]*rate_eval.He4_Cr62__Fe66
       +rho*Y[jp]*rate_eval.p_Cr62__He4_V59
       )

    jac[jhe4, jcr63] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr63__n_Fe66
       -rho*Y[jhe4]*rate_eval.He4_Cr63__Fe67
       +rho*Y[jp]*rate_eval.p_Cr63__He4_V60
       )

    jac[jhe4, jcr64] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr64__n_Fe67
       -rho*Y[jhe4]*rate_eval.He4_Cr64__Fe68
       +rho*Y[jp]*rate_eval.p_Cr64__He4_V61
       )

    jac[jhe4, jcr65] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr65__n_Fe68
       -rho*Y[jhe4]*rate_eval.He4_Cr65__Fe69
       +rho*Y[jp]*rate_eval.p_Cr65__He4_V62
       )

    jac[jhe4, jcr66] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr66__Fe70
       -rho*Y[jhe4]*rate_eval.He4_Cr66__n_Fe69
       +rho*Y[jp]*rate_eval.p_Cr66__He4_V63
       )

    jac[jhe4, jcr67] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr67__Fe71
       -rho*Y[jhe4]*rate_eval.He4_Cr67__n_Fe70
       +rho*Y[jp]*rate_eval.p_Cr67__He4_V64
       )

    jac[jhe4, jcr68] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr68__n_Fe71
       -rho*Y[jhe4]*rate_eval.He4_Cr68__Fe72
       +rho*Y[jp]*rate_eval.p_Cr68__He4_V65
       )

    jac[jhe4, jcr69] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr69__n_Fe72
       -rho*Y[jhe4]*rate_eval.He4_Cr69__Fe73
       +rho*Y[jp]*rate_eval.p_Cr69__He4_V66
       )

    jac[jhe4, jcr70] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr70__n_Fe73
       -rho*Y[jhe4]*rate_eval.He4_Cr70__Fe74
       +rho*Y[jp]*rate_eval.p_Cr70__He4_V67
       )

    jac[jhe4, jmn43] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn43__Co47
       -rho*Y[jhe4]*rate_eval.He4_Mn43__p_Fe46
       +rho*Y[jn]*rate_eval.n_Mn43__He4_V40
       )

    jac[jhe4, jmn44] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn44__p_Fe47
       -rho*Y[jhe4]*rate_eval.He4_Mn44__Co48
       +rho*Y[jn]*rate_eval.n_Mn44__He4_V41
       )

    jac[jhe4, jmn45] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn45__p_Fe48
       -rho*Y[jhe4]*rate_eval.He4_Mn45__Co49
       +rho*Y[jn]*rate_eval.n_Mn45__He4_V42
       )

    jac[jhe4, jmn46] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn46__p_Fe49
       -rho*Y[jhe4]*rate_eval.He4_Mn46__Co50
       +rho*Y[jn]*rate_eval.n_Mn46__He4_V43
       )

    jac[jhe4, jmn47] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn47__p_Fe50
       -rho*Y[jhe4]*rate_eval.He4_Mn47__Co51
       +rho*Y[jn]*rate_eval.n_Mn47__He4_V44
       )

    jac[jhe4, jmn48] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn48__Co52
       -rho*Y[jhe4]*rate_eval.He4_Mn48__p_Fe51
       +rho*Y[jn]*rate_eval.n_Mn48__He4_V45
       )

    jac[jhe4, jmn49] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn49__p_Fe52
       -rho*Y[jhe4]*rate_eval.He4_Mn49__Co53
       +rho*Y[jn]*rate_eval.n_Mn49__He4_V46
       )

    jac[jhe4, jmn50] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn50__Co54
       -rho*Y[jhe4]*rate_eval.He4_Mn50__p_Fe53
       +rho*Y[jn]*rate_eval.n_Mn50__He4_V47
       )

    jac[jhe4, jmn51] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn51__p_Fe54
       -rho*Y[jhe4]*rate_eval.He4_Mn51__Co55
       +rho*Y[jn]*rate_eval.n_Mn51__He4_V48
       )

    jac[jhe4, jmn52] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn52__Co56
       -rho*Y[jhe4]*rate_eval.He4_Mn52__p_Fe55
       +rho*Y[jn]*rate_eval.n_Mn52__He4_V49
       )

    jac[jhe4, jmn53] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn53__p_Fe56
       -rho*Y[jhe4]*rate_eval.He4_Mn53__Co57
       +rho*Y[jp]*rate_eval.p_Mn53__He4_Cr50
       +rho*Y[jn]*rate_eval.n_Mn53__He4_V50
       )

    jac[jhe4, jmn54] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn54__Co58
       +rho*Y[jp]*rate_eval.p_Mn54__He4_Cr51
       +rho*Y[jn]*rate_eval.n_Mn54__He4_V51
       )

    jac[jhe4, jmn55] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn55__Co59
       +rho*Y[jp]*rate_eval.p_Mn55__He4_Cr52
       )

    jac[jhe4, jmn56] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn56__Co60
       +rho*Y[jp]*rate_eval.p_Mn56__He4_Cr53
       +rho*Y[jn]*rate_eval.n_Mn56__He4_V53
       )

    jac[jhe4, jmn57] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn57__Co61
       +rho*Y[jp]*rate_eval.p_Mn57__He4_Cr54
       )

    jac[jhe4, jmn58] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn58__Co62
       -rho*Y[jhe4]*rate_eval.He4_Mn58__n_Co61
       +rho*Y[jp]*rate_eval.p_Mn58__He4_Cr55
       )

    jac[jhe4, jmn59] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn59__Co63
       -rho*Y[jhe4]*rate_eval.He4_Mn59__n_Co62
       +rho*Y[jp]*rate_eval.p_Mn59__He4_Cr56
       )

    jac[jhe4, jmn60] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn60__n_Co63
       -rho*Y[jhe4]*rate_eval.He4_Mn60__Co64
       +rho*Y[jp]*rate_eval.p_Mn60__He4_Cr57
       )

    jac[jhe4, jmn61] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn61__Co65
       -rho*Y[jhe4]*rate_eval.He4_Mn61__n_Co64
       +rho*Y[jp]*rate_eval.p_Mn61__He4_Cr58
       )

    jac[jhe4, jmn62] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn62__n_Co65
       -rho*Y[jhe4]*rate_eval.He4_Mn62__Co66
       +rho*Y[jp]*rate_eval.p_Mn62__He4_Cr59
       )

    jac[jhe4, jmn63] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn63__Co67
       -rho*Y[jhe4]*rate_eval.He4_Mn63__n_Co66
       +rho*Y[jp]*rate_eval.p_Mn63__He4_Cr60
       )

    jac[jhe4, jmn64] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn64__Co68
       -rho*Y[jhe4]*rate_eval.He4_Mn64__n_Co67
       +rho*Y[jp]*rate_eval.p_Mn64__He4_Cr61
       )

    jac[jhe4, jmn65] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn65__n_Co68
       -rho*Y[jhe4]*rate_eval.He4_Mn65__Co69
       +rho*Y[jp]*rate_eval.p_Mn65__He4_Cr62
       )

    jac[jhe4, jmn66] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn66__Co70
       -rho*Y[jhe4]*rate_eval.He4_Mn66__n_Co69
       +rho*Y[jp]*rate_eval.p_Mn66__He4_Cr63
       )

    jac[jhe4, jmn67] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn67__n_Co70
       -rho*Y[jhe4]*rate_eval.He4_Mn67__Co71
       +rho*Y[jp]*rate_eval.p_Mn67__He4_Cr64
       )

    jac[jhe4, jmn68] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn68__n_Co71
       -rho*Y[jhe4]*rate_eval.He4_Mn68__Co72
       +rho*Y[jp]*rate_eval.p_Mn68__He4_Cr65
       )

    jac[jhe4, jmn69] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn69__n_Co72
       -rho*Y[jhe4]*rate_eval.He4_Mn69__Co73
       +rho*Y[jp]*rate_eval.p_Mn69__He4_Cr66
       )

    jac[jhe4, jmn70] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn70__Co74
       -rho*Y[jhe4]*rate_eval.He4_Mn70__n_Co73
       +rho*Y[jp]*rate_eval.p_Mn70__He4_Cr67
       )

    jac[jhe4, jmn71] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn71__Co75
       -rho*Y[jhe4]*rate_eval.He4_Mn71__n_Co74
       +rho*Y[jp]*rate_eval.p_Mn71__He4_Cr68
       )

    jac[jhe4, jmn72] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn72__n_Co75
       -rho*Y[jhe4]*rate_eval.He4_Mn72__Co76
       +rho*Y[jp]*rate_eval.p_Mn72__He4_Cr69
       )

    jac[jhe4, jmn73] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn73__n_Co76
       -rho*Y[jhe4]*rate_eval.He4_Mn73__Co77
       +rho*Y[jp]*rate_eval.p_Mn73__He4_Cr70
       )

    jac[jhe4, jfe45] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe45__Ni49
       -rho*Y[jhe4]*rate_eval.He4_Fe45__p_Co48
       +rho*Y[jn]*rate_eval.n_Fe45__He4_Cr42
       )

    jac[jhe4, jfe46] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe46__p_Co49
       -rho*Y[jhe4]*rate_eval.He4_Fe46__Ni50
       +rho*Y[jn]*rate_eval.n_Fe46__He4_Cr43
       )

    jac[jhe4, jfe47] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe47__Ni51
       -rho*Y[jhe4]*rate_eval.He4_Fe47__p_Co50
       +rho*Y[jn]*rate_eval.n_Fe47__He4_Cr44
       )

    jac[jhe4, jfe48] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe48__p_Co51
       -rho*Y[jhe4]*rate_eval.He4_Fe48__Ni52
       +rho*Y[jn]*rate_eval.n_Fe48__He4_Cr45
       )

    jac[jhe4, jfe49] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe49__p_Co52
       -rho*Y[jhe4]*rate_eval.He4_Fe49__Ni53
       +rho*Y[jn]*rate_eval.n_Fe49__He4_Cr46
       )

    jac[jhe4, jfe50] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe50__p_Co53
       -rho*Y[jhe4]*rate_eval.He4_Fe50__Ni54
       +rho*Y[jn]*rate_eval.n_Fe50__He4_Cr47
       )

    jac[jhe4, jfe51] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe51__Ni55
       -rho*Y[jhe4]*rate_eval.He4_Fe51__p_Co54
       +rho*Y[jn]*rate_eval.n_Fe51__He4_Cr48
       )

    jac[jhe4, jfe52] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe52__p_Co55
       -rho*Y[jhe4]*rate_eval.He4_Fe52__Ni56
       +rho*Y[jn]*rate_eval.n_Fe52__He4_Cr49
       )

    jac[jhe4, jfe53] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe53__p_Co56
       -rho*Y[jhe4]*rate_eval.He4_Fe53__Ni57
       +rho*Y[jn]*rate_eval.n_Fe53__He4_Cr50
       )

    jac[jhe4, jfe54] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe54__Ni58
       +rho*Y[jn]*rate_eval.n_Fe54__He4_Cr51
       )

    jac[jhe4, jfe55] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe55__Ni59
       +rho*Y[jn]*rate_eval.n_Fe55__He4_Cr52
       )

    jac[jhe4, jfe56] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe56__Ni60
       +rho*Y[jn]*rate_eval.n_Fe56__He4_Cr53
       )

    jac[jhe4, jfe57] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe57__Ni61
       +rho*Y[jp]*rate_eval.p_Fe57__He4_Mn54
       +rho*Y[jn]*rate_eval.n_Fe57__He4_Cr54
       )

    jac[jhe4, jfe58] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe58__Ni62
       +rho*Y[jp]*rate_eval.p_Fe58__He4_Mn55
       )

    jac[jhe4, jfe59] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe59__n_Ni62
       -rho*Y[jhe4]*rate_eval.He4_Fe59__Ni63
       +rho*Y[jp]*rate_eval.p_Fe59__He4_Mn56
       +rho*Y[jn]*rate_eval.n_Fe59__He4_Cr56
       )

    jac[jhe4, jfe60] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe60__Ni64
       +rho*Y[jp]*rate_eval.p_Fe60__He4_Mn57
       )

    jac[jhe4, jfe61] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe61__Ni65
       -rho*Y[jhe4]*rate_eval.He4_Fe61__n_Ni64
       +rho*Y[jp]*rate_eval.p_Fe61__He4_Mn58
       )

    jac[jhe4, jfe62] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe62__n_Ni65
       -rho*Y[jhe4]*rate_eval.He4_Fe62__Ni66
       +rho*Y[jp]*rate_eval.p_Fe62__He4_Mn59
       )

    jac[jhe4, jfe63] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe63__n_Ni66
       -rho*Y[jhe4]*rate_eval.He4_Fe63__Ni67
       +rho*Y[jp]*rate_eval.p_Fe63__He4_Mn60
       )

    jac[jhe4, jfe64] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe64__n_Ni67
       -rho*Y[jhe4]*rate_eval.He4_Fe64__Ni68
       +rho*Y[jp]*rate_eval.p_Fe64__He4_Mn61
       )

    jac[jhe4, jfe65] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe65__Ni69
       -rho*Y[jhe4]*rate_eval.He4_Fe65__n_Ni68
       +rho*Y[jp]*rate_eval.p_Fe65__He4_Mn62
       )

    jac[jhe4, jfe66] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe66__n_Ni69
       -rho*Y[jhe4]*rate_eval.He4_Fe66__Ni70
       +rho*Y[jp]*rate_eval.p_Fe66__He4_Mn63
       )

    jac[jhe4, jfe67] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe67__Ni71
       -rho*Y[jhe4]*rate_eval.He4_Fe67__n_Ni70
       +rho*Y[jp]*rate_eval.p_Fe67__He4_Mn64
       )

    jac[jhe4, jfe68] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe68__n_Ni71
       -rho*Y[jhe4]*rate_eval.He4_Fe68__Ni72
       +rho*Y[jp]*rate_eval.p_Fe68__He4_Mn65
       )

    jac[jhe4, jfe69] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe69__Ni73
       -rho*Y[jhe4]*rate_eval.He4_Fe69__n_Ni72
       +rho*Y[jp]*rate_eval.p_Fe69__He4_Mn66
       )

    jac[jhe4, jfe70] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe70__n_Ni73
       -rho*Y[jhe4]*rate_eval.He4_Fe70__Ni74
       +rho*Y[jp]*rate_eval.p_Fe70__He4_Mn67
       )

    jac[jhe4, jfe71] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe71__n_Ni74
       -rho*Y[jhe4]*rate_eval.He4_Fe71__Ni75
       +rho*Y[jp]*rate_eval.p_Fe71__He4_Mn68
       )

    jac[jhe4, jfe72] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe72__n_Ni75
       -rho*Y[jhe4]*rate_eval.He4_Fe72__Ni76
       +rho*Y[jp]*rate_eval.p_Fe72__He4_Mn69
       )

    jac[jhe4, jfe73] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe73__n_Ni76
       -rho*Y[jhe4]*rate_eval.He4_Fe73__Ni77
       +rho*Y[jp]*rate_eval.p_Fe73__He4_Mn70
       )

    jac[jhe4, jfe74] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe74__n_Ni77
       -rho*Y[jhe4]*rate_eval.He4_Fe74__Ni78
       +rho*Y[jp]*rate_eval.p_Fe74__He4_Mn71
       )

    jac[jhe4, jfe75] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe75__n_Ni78
       -rho*Y[jhe4]*rate_eval.He4_Fe75__Ni79
       +rho*Y[jp]*rate_eval.p_Fe75__He4_Mn72
       )

    jac[jhe4, jfe76] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe76__n_Ni79
       -rho*Y[jhe4]*rate_eval.He4_Fe76__Ni80
       +rho*Y[jp]*rate_eval.p_Fe76__He4_Mn73
       )

    jac[jhe6, jn] = (
       +5.00000000000000e-01*rho**2*2*Y[jn]*Y[jhe4]*rate_eval.n_n_He4__He6
       )

    jac[jhe6, jhe4] = (
       +5.00000000000000e-01*rho**2*Y[jn]**2*rate_eval.n_n_He4__He6
       )

    jac[jhe6, jhe6] = (
       -rate_eval.He6__Li6__weak__wc12
       )

    jac[jhe8, jhe8] = (
       -rate_eval.He8__Li8__weak__wc12
       -rate_eval.He8__n_Li7__weak__wc12
       )

    jac[jli5, jc9] = (
       +rate_eval.C9__He4_Li5__weak__wc12
       )

    jac[jli6, jn] = (
       -rho*Y[jli6]*rate_eval.n_Li6__He4_t
       -rho*Y[jli6]*rate_eval.n_Li6__Li7
       +rho**2*Y[jp]*Y[jhe4]*rate_eval.n_p_He4__Li6
       )

    jac[jli6, jp] = (
       -rho*Y[jli6]*rate_eval.p_Li6__Be7
       -rho*Y[jli6]*rate_eval.p_Li6__He4_He3
       +rho**2*Y[jn]*Y[jhe4]*rate_eval.n_p_He4__Li6
       +rho*Y[jbe9]*rate_eval.p_Be9__He4_Li6
       )

    jac[jli6, jd] = (
       -rho*Y[jli6]*rate_eval.d_Li6__n_Be7
       -rho*Y[jli6]*rate_eval.d_Li6__p_Li7
       +rho*Y[jhe4]*rate_eval.He4_d__Li6
       )

    jac[jli6, jhe4] = (
       -rho*Y[jli6]*rate_eval.He4_Li6__B10
       +rho*Y[jd]*rate_eval.He4_d__Li6
       +rho**2*Y[jn]*Y[jp]*rate_eval.n_p_He4__Li6
       )

    jac[jli6, jhe6] = (
       +rate_eval.He6__Li6__weak__wc12
       )

    jac[jli6, jli6] = (
       -rho*Y[jp]*rate_eval.p_Li6__Be7
       -rho*Y[jn]*rate_eval.n_Li6__He4_t
       -rho*Y[jp]*rate_eval.p_Li6__He4_He3
       -rho*Y[jd]*rate_eval.d_Li6__n_Be7
       -rho*Y[jhe4]*rate_eval.He4_Li6__B10
       -rho*Y[jn]*rate_eval.n_Li6__Li7
       -rho*Y[jd]*rate_eval.d_Li6__p_Li7
       )

    jac[jli6, jbe9] = (
       +rho*Y[jp]*rate_eval.p_Be9__He4_Li6
       )

    jac[jli7, jn] = (
       -rho*Y[jli7]*rate_eval.n_Li7__Li8
       +rho*Y[jbe7]*rate_eval.n_Be7__p_Li7
       +rho*Y[jli6]*rate_eval.n_Li6__Li7
       +rho*Y[jb10]*rate_eval.n_B10__He4_Li7
       )

    jac[jli7, jp] = (
       -rho*Y[jli7]*rate_eval.p_Li7__He4_He4
       +rho*Y[jbe10]*rate_eval.p_Be10__He4_Li7
       )

    jac[jli7, jd] = (
       -rho*Y[jli7]*rate_eval.d_Li7__n_He4_He4
       -rho*Y[jli7]*rate_eval.d_Li7__p_Li8
       +rho*Y[jli8]*rate_eval.d_Li8__t_Li7
       +rho*Y[jli6]*rate_eval.d_Li6__p_Li7
       )

    jac[jli7, jt] = (
       -rho*Y[jli7]*rate_eval.t_Li7__n_Be9
       -rho*Y[jli7]*rate_eval.t_Li7__n_n_He4_He4
       +rho*Y[jhe4]*rate_eval.He4_t__Li7
       )

    jac[jli7, jhe3] = (
       -rho*Y[jli7]*rate_eval.He3_Li7__n_p_He4_He4
       )

    jac[jli7, jhe4] = (
       -rho*Y[jli7]*rate_eval.He4_Li7__B11
       +rho*Y[jt]*rate_eval.He4_t__Li7
       )

    jac[jli7, jhe8] = (
       +rate_eval.He8__n_Li7__weak__wc12
       )

    jac[jli7, jli6] = (
       +rho*Y[jn]*rate_eval.n_Li6__Li7
       +rho*Y[jd]*rate_eval.d_Li6__p_Li7
       )

    jac[jli7, jli7] = (
       -rho*Y[jd]*rate_eval.d_Li7__n_He4_He4
       -rho*Y[jd]*rate_eval.d_Li7__p_Li8
       -rho*Y[jt]*rate_eval.t_Li7__n_Be9
       -rho*Y[jhe4]*rate_eval.He4_Li7__B11
       -rho*Y[jn]*rate_eval.n_Li7__Li8
       -rho*Y[jp]*rate_eval.p_Li7__He4_He4
       -rho*Y[jt]*rate_eval.t_Li7__n_n_He4_He4
       -rho*Y[jhe3]*rate_eval.He3_Li7__n_p_He4_He4
       )

    jac[jli7, jli8] = (
       +rho*Y[jd]*rate_eval.d_Li8__t_Li7
       )

    jac[jli7, jbe7] = (
       +rho*Y[jn]*rate_eval.n_Be7__p_Li7
       +rho*ye(Y)*rate_eval.Be7__Li7__weak__electron_capture
       )

    jac[jli7, jbe10] = (
       +rho*Y[jp]*rate_eval.p_Be10__He4_Li7
       )

    jac[jli7, jbe11] = (
       +rate_eval.Be11__He4_Li7__weak__wc12
       )

    jac[jli7, jb10] = (
       +rho*Y[jn]*rate_eval.n_B10__He4_Li7
       )

    jac[jli8, jn] = (
       -rho*Y[jli8]*rate_eval.n_Li8__Li9
       +rho*Y[jli7]*rate_eval.n_Li7__Li8
       )

    jac[jli8, jp] = (
       -rho*Y[jli8]*rate_eval.p_Li8__n_He4_He4
       +rho*Y[jbe11]*rate_eval.p_Be11__He4_Li8
       )

    jac[jli8, jd] = (
       -rho*Y[jli8]*rate_eval.d_Li8__n_Be9
       -rho*Y[jli8]*rate_eval.d_Li8__t_Li7
       +rho*Y[jli7]*rate_eval.d_Li7__p_Li8
       )

    jac[jli8, jhe4] = (
       -rho*Y[jli8]*rate_eval.He4_Li8__n_B11
       -rho*Y[jli8]*rate_eval.He4_Li8__B12
       )

    jac[jli8, jhe8] = (
       +rate_eval.He8__Li8__weak__wc12
       )

    jac[jli8, jli7] = (
       +rho*Y[jd]*rate_eval.d_Li7__p_Li8
       +rho*Y[jn]*rate_eval.n_Li7__Li8
       )

    jac[jli8, jli8] = (
       -rho*Y[jd]*rate_eval.d_Li8__n_Be9
       -rho*Y[jd]*rate_eval.d_Li8__t_Li7
       -rho*Y[jhe4]*rate_eval.He4_Li8__n_B11
       -rho*Y[jhe4]*rate_eval.He4_Li8__B12
       -rho*Y[jn]*rate_eval.n_Li8__Li9
       -rho*Y[jp]*rate_eval.p_Li8__n_He4_He4
       -rate_eval.Li8__He4_He4__weak__wc12
       )

    jac[jli8, jbe11] = (
       +rho*Y[jp]*rate_eval.p_Be11__He4_Li8
       )

    jac[jli9, jn] = (
       +rho*Y[jli8]*rate_eval.n_Li8__Li9
       )

    jac[jli9, jhe4] = (
       -rho*Y[jli9]*rate_eval.He4_Li9__B13
       -rho*Y[jli9]*rate_eval.He4_Li9__n_B12
       )

    jac[jli9, jli8] = (
       +rho*Y[jn]*rate_eval.n_Li8__Li9
       )

    jac[jli9, jli9] = (
       -rho*Y[jhe4]*rate_eval.He4_Li9__B13
       -rho*Y[jhe4]*rate_eval.He4_Li9__n_B12
       -rate_eval.Li9__Be9__weak__wc12
       )

    jac[jli11, jli11] = (
       -rate_eval.Li11__n_n_Be9__weak__wc12
       -rate_eval.Li11__Be11__weak__wc12
       -rate_eval.Li11__n_Be10__weak__wc17
       )

    jac[jbe7, jn] = (
       -rho*Y[jbe7]*rate_eval.n_Be7__He4_He4
       -rho*Y[jbe7]*rate_eval.n_Be7__p_Li7
       )

    jac[jbe7, jp] = (
       -rho*Y[jbe7]*rate_eval.p_Be7__B8
       +rho*Y[jli6]*rate_eval.p_Li6__Be7
       +rho*Y[jb10]*rate_eval.p_B10__He4_Be7
       )

    jac[jbe7, jd] = (
       -rho*Y[jbe7]*rate_eval.d_Be7__p_He4_He4
       +rho*Y[jli6]*rate_eval.d_Li6__n_Be7
       )

    jac[jbe7, jt] = (
       -rho*Y[jbe7]*rate_eval.t_Be7__n_p_He4_He4
       )

    jac[jbe7, jhe3] = (
       -rho*Y[jbe7]*rate_eval.He3_Be7__p_p_He4_He4
       +rho*Y[jhe4]*rate_eval.He4_He3__Be7
       )

    jac[jbe7, jhe4] = (
       -rho*Y[jbe7]*rate_eval.He4_Be7__C11
       +rho*Y[jhe3]*rate_eval.He4_He3__Be7
       )

    jac[jbe7, jli6] = (
       +rho*Y[jp]*rate_eval.p_Li6__Be7
       +rho*Y[jd]*rate_eval.d_Li6__n_Be7
       )

    jac[jbe7, jbe7] = (
       -rho*Y[jhe3]*rate_eval.He3_Be7__p_p_He4_He4
       -rho*Y[jt]*rate_eval.t_Be7__n_p_He4_He4
       -rho*Y[jd]*rate_eval.d_Be7__p_He4_He4
       -rho*Y[jhe4]*rate_eval.He4_Be7__C11
       -rho*Y[jn]*rate_eval.n_Be7__He4_He4
       -rho*Y[jp]*rate_eval.p_Be7__B8
       -rho*Y[jn]*rate_eval.n_Be7__p_Li7
       -rho*ye(Y)*rate_eval.Be7__Li7__weak__electron_capture
       )

    jac[jbe7, jb10] = (
       +rho*Y[jp]*rate_eval.p_B10__He4_Be7
       )

    jac[jbe9, jn] = (
       -rho*Y[jbe9]*rate_eval.n_Be9__Be10
       +5.00000000000000e-01*rho**2*Y[jhe4]**2*rate_eval.n_He4_He4__Be9
       )

    jac[jbe9, jp] = (
       -rho*Y[jbe9]*rate_eval.p_Be9__n_p_He4_He4
       -rho*Y[jbe9]*rate_eval.p_Be9__d_He4_He4
       -rho*Y[jbe9]*rate_eval.p_Be9__B10
       -rho*Y[jbe9]*rate_eval.p_Be9__He4_Li6
       +rho*Y[jb12]*rate_eval.p_B12__He4_Be9
       )

    jac[jbe9, jd] = (
       +rho*Y[jli8]*rate_eval.d_Li8__n_Be9
       )

    jac[jbe9, jt] = (
       -rho*Y[jbe9]*rate_eval.t_Be9__n_B11
       +rho*Y[jli7]*rate_eval.t_Li7__n_Be9
       )

    jac[jbe9, jhe4] = (
       -rho*Y[jbe9]*rate_eval.He4_Be9__n_C12
       +5.00000000000000e-01*rho**2*Y[jn]*2*Y[jhe4]*rate_eval.n_He4_He4__Be9
       )

    jac[jbe9, jli7] = (
       +rho*Y[jt]*rate_eval.t_Li7__n_Be9
       )

    jac[jbe9, jli8] = (
       +rho*Y[jd]*rate_eval.d_Li8__n_Be9
       )

    jac[jbe9, jli9] = (
       +rate_eval.Li9__Be9__weak__wc12
       )

    jac[jbe9, jli11] = (
       +rate_eval.Li11__n_n_Be9__weak__wc12
       )

    jac[jbe9, jbe9] = (
       -rho*Y[jp]*rate_eval.p_Be9__n_p_He4_He4
       -rho*Y[jp]*rate_eval.p_Be9__d_He4_He4
       -rho*Y[jt]*rate_eval.t_Be9__n_B11
       -rho*Y[jhe4]*rate_eval.He4_Be9__n_C12
       -rho*Y[jp]*rate_eval.p_Be9__B10
       -rho*Y[jp]*rate_eval.p_Be9__He4_Li6
       -rho*Y[jn]*rate_eval.n_Be9__Be10
       )

    jac[jbe9, jb12] = (
       +rho*Y[jp]*rate_eval.p_B12__He4_Be9
       )

    jac[jbe10, jn] = (
       -rho*Y[jbe10]*rate_eval.n_Be10__Be11
       +rho*Y[jbe9]*rate_eval.n_Be9__Be10
       )

    jac[jbe10, jp] = (
       -rho*Y[jbe10]*rate_eval.p_Be10__B11
       -rho*Y[jbe10]*rate_eval.p_Be10__He4_Li7
       )

    jac[jbe10, jhe4] = (
       -rho*Y[jbe10]*rate_eval.He4_Be10__C14
       -rho*Y[jbe10]*rate_eval.He4_Be10__n_C13
       )

    jac[jbe10, jli11] = (
       +rate_eval.Li11__n_Be10__weak__wc17
       )

    jac[jbe10, jbe9] = (
       +rho*Y[jn]*rate_eval.n_Be9__Be10
       )

    jac[jbe10, jbe10] = (
       -rho*Y[jhe4]*rate_eval.He4_Be10__C14
       -rho*Y[jp]*rate_eval.p_Be10__B11
       -rho*Y[jhe4]*rate_eval.He4_Be10__n_C13
       -rho*Y[jn]*rate_eval.n_Be10__Be11
       -rate_eval.Be10__B10__weak__wc12
       -rho*Y[jp]*rate_eval.p_Be10__He4_Li7
       )

    jac[jbe11, jn] = (
       -rho*Y[jbe11]*rate_eval.n_Be11__Be12
       +rho*Y[jbe10]*rate_eval.n_Be10__Be11
       )

    jac[jbe11, jp] = (
       -rho*Y[jbe11]*rate_eval.p_Be11__He4_Li8
       )

    jac[jbe11, jhe4] = (
       -rho*Y[jbe11]*rate_eval.He4_Be11__n_C14
       )

    jac[jbe11, jli11] = (
       +rate_eval.Li11__Be11__weak__wc12
       )

    jac[jbe11, jbe10] = (
       +rho*Y[jn]*rate_eval.n_Be10__Be11
       )

    jac[jbe11, jbe11] = (
       -rate_eval.Be11__B11__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Be11__n_C14
       -rho*Y[jp]*rate_eval.p_Be11__He4_Li8
       -rho*Y[jn]*rate_eval.n_Be11__Be12
       -rate_eval.Be11__He4_Li7__weak__wc12
       )

    jac[jbe12, jn] = (
       +rho*Y[jbe11]*rate_eval.n_Be11__Be12
       )

    jac[jbe12, jbe11] = (
       +rho*Y[jn]*rate_eval.n_Be11__Be12
       )

    jac[jbe12, jbe12] = (
       -rate_eval.Be12__B12__weak__wc12
       -rate_eval.Be12__n_B11__weak__wc12
       )

    jac[jbe14, jbe14] = (
       -rate_eval.Be14__n_n_B12__weak__wc12
       -rate_eval.Be14__n_B13__weak__wc17
       -rate_eval.Be14__B14__weak__wc12
       )

    jac[jbe14, jbe15] = (
       +rate_eval.Be15__n_Be14
       )

    jac[jbe14, jbe16] = (
       +rate_eval.Be16__n_n_Be14
       )

    jac[jbe15, jbe15] = (
       -rate_eval.Be15__n_Be14
       )

    jac[jbe16, jbe16] = (
       -rate_eval.Be16__n_n_Be14
       )

    jac[jb8, jn] = (
       -rho*Y[jb8]*rate_eval.n_B8__p_He4_He4
       )

    jac[jb8, jp] = (
       -rho*Y[jb8]*rate_eval.p_B8__C9
       +rho*Y[jbe7]*rate_eval.p_Be7__B8
       )

    jac[jb8, jhe4] = (
       -rho*Y[jb8]*rate_eval.He4_B8__p_C11
       )

    jac[jb8, jbe7] = (
       +rho*Y[jp]*rate_eval.p_Be7__B8
       )

    jac[jb8, jb8] = (
       -rho*Y[jn]*rate_eval.n_B8__p_He4_He4
       -rho*Y[jhe4]*rate_eval.He4_B8__p_C11
       -rho*Y[jp]*rate_eval.p_B8__C9
       -rate_eval.B8__He4_He4__weak__wc12
       )

    jac[jb10, jn] = (
       -rho*Y[jb10]*rate_eval.n_B10__B11
       -rho*Y[jb10]*rate_eval.n_B10__He4_Li7
       )

    jac[jb10, jp] = (
       -rho*Y[jb10]*rate_eval.p_B10__C11
       -rho*Y[jb10]*rate_eval.p_B10__He4_Be7
       +rho*Y[jbe9]*rate_eval.p_Be9__B10
       )

    jac[jb10, jhe4] = (
       -rho*Y[jb10]*rate_eval.He4_B10__p_C13
       -rho*Y[jb10]*rate_eval.He4_B10__n_N13
       +rho*Y[jli6]*rate_eval.He4_Li6__B10
       )

    jac[jb10, jli6] = (
       +rho*Y[jhe4]*rate_eval.He4_Li6__B10
       )

    jac[jb10, jbe9] = (
       +rho*Y[jp]*rate_eval.p_Be9__B10
       )

    jac[jb10, jbe10] = (
       +rate_eval.Be10__B10__weak__wc12
       )

    jac[jb10, jb10] = (
       -rho*Y[jhe4]*rate_eval.He4_B10__p_C13
       -rho*Y[jp]*rate_eval.p_B10__C11
       -rho*Y[jn]*rate_eval.n_B10__B11
       -rho*Y[jp]*rate_eval.p_B10__He4_Be7
       -rho*Y[jhe4]*rate_eval.He4_B10__n_N13
       -rho*Y[jn]*rate_eval.n_B10__He4_Li7
       )

    jac[jb10, jc10] = (
       +rate_eval.C10__B10__weak__wc12
       )

    jac[jb11, jn] = (
       -rho*Y[jb11]*rate_eval.n_B11__B12
       +rho*Y[jc11]*rate_eval.n_C11__p_B11
       +rho*Y[jb10]*rate_eval.n_B10__B11
       )

    jac[jb11, jp] = (
       -rho*Y[jb11]*rate_eval.p_B11__He4_He4_He4
       -rho*Y[jb11]*rate_eval.p_B11__C12
       +rho*Y[jbe10]*rate_eval.p_Be10__B11
       )

    jac[jb11, jt] = (
       +rho*Y[jbe9]*rate_eval.t_Be9__n_B11
       )

    jac[jb11, jhe4] = (
       -rho*Y[jb11]*rate_eval.He4_B11__p_C14
       -rho*Y[jb11]*rate_eval.He4_B11__n_N14
       +rho*Y[jli8]*rate_eval.He4_Li8__n_B11
       +rho*Y[jli7]*rate_eval.He4_Li7__B11
       )

    jac[jb11, jli7] = (
       +rho*Y[jhe4]*rate_eval.He4_Li7__B11
       )

    jac[jb11, jli8] = (
       +rho*Y[jhe4]*rate_eval.He4_Li8__n_B11
       )

    jac[jb11, jbe9] = (
       +rho*Y[jt]*rate_eval.t_Be9__n_B11
       )

    jac[jb11, jbe10] = (
       +rho*Y[jp]*rate_eval.p_Be10__B11
       )

    jac[jb11, jbe11] = (
       +rate_eval.Be11__B11__weak__wc12
       )

    jac[jb11, jbe12] = (
       +rate_eval.Be12__n_B11__weak__wc12
       )

    jac[jb11, jb10] = (
       +rho*Y[jn]*rate_eval.n_B10__B11
       )

    jac[jb11, jb11] = (
       -rho*Y[jp]*rate_eval.p_B11__He4_He4_He4
       -rho*Y[jhe4]*rate_eval.He4_B11__p_C14
       -rho*Y[jn]*rate_eval.n_B11__B12
       -rho*Y[jhe4]*rate_eval.He4_B11__n_N14
       -rho*Y[jp]*rate_eval.p_B11__C12
       )

    jac[jb11, jc11] = (
       +rho*Y[jn]*rate_eval.n_C11__p_B11
       +rate_eval.C11__B11__weak__wc12
       )

    jac[jb12, jn] = (
       -rho*Y[jb12]*rate_eval.n_B12__B13
       +rho*Y[jb11]*rate_eval.n_B11__B12
       )

    jac[jb12, jp] = (
       -rho*Y[jb12]*rate_eval.p_B12__n_C12
       -rho*Y[jb12]*rate_eval.p_B12__He4_Be9
       )

    jac[jb12, jhe4] = (
       -rho*Y[jb12]*rate_eval.He4_B12__n_N15
       +rho*Y[jli8]*rate_eval.He4_Li8__B12
       +rho*Y[jli9]*rate_eval.He4_Li9__n_B12
       )

    jac[jb12, jli8] = (
       +rho*Y[jhe4]*rate_eval.He4_Li8__B12
       )

    jac[jb12, jli9] = (
       +rho*Y[jhe4]*rate_eval.He4_Li9__n_B12
       )

    jac[jb12, jbe12] = (
       +rate_eval.Be12__B12__weak__wc12
       )

    jac[jb12, jbe14] = (
       +rate_eval.Be14__n_n_B12__weak__wc12
       )

    jac[jb12, jb11] = (
       +rho*Y[jn]*rate_eval.n_B11__B12
       )

    jac[jb12, jb12] = (
       -rho*Y[jp]*rate_eval.p_B12__n_C12
       -rho*Y[jhe4]*rate_eval.He4_B12__n_N15
       -rho*Y[jp]*rate_eval.p_B12__He4_Be9
       -rate_eval.B12__C12__weak__wc17
       -rho*Y[jn]*rate_eval.n_B12__B13
       )

    jac[jb13, jn] = (
       -rho*Y[jb13]*rate_eval.n_B13__B14
       +rho*Y[jb12]*rate_eval.n_B12__B13
       )

    jac[jb13, jhe4] = (
       -rho*Y[jb13]*rate_eval.He4_B13__n_N16
       -rho*Y[jb13]*rate_eval.He4_B13__N17
       +rho*Y[jli9]*rate_eval.He4_Li9__B13
       )

    jac[jb13, jli9] = (
       +rho*Y[jhe4]*rate_eval.He4_Li9__B13
       )

    jac[jb13, jbe14] = (
       +rate_eval.Be14__n_B13__weak__wc17
       )

    jac[jb13, jb12] = (
       +rho*Y[jn]*rate_eval.n_B12__B13
       )

    jac[jb13, jb13] = (
       -rho*Y[jn]*rate_eval.n_B13__B14
       -rho*Y[jhe4]*rate_eval.He4_B13__n_N16
       -rho*Y[jhe4]*rate_eval.He4_B13__N17
       -rate_eval.B13__C13__weak__wc12
       )

    jac[jb14, jn] = (
       +rho*Y[jb13]*rate_eval.n_B13__B14
       )

    jac[jb14, jbe14] = (
       +rate_eval.Be14__B14__weak__wc12
       )

    jac[jb14, jb13] = (
       +rho*Y[jn]*rate_eval.n_B13__B14
       )

    jac[jb14, jb14] = (
       -rate_eval.B14__C14__weak__wc12
       )

    jac[jb15, jb15] = (
       -rate_eval.B15__n_n_C13__weak__wc12
       -rate_eval.B15__n_C14__weak__wc12
       -rate_eval.B15__C15__weak__wc12
       )

    jac[jb17, jb17] = (
       -rate_eval.B17__n_n_n_C14__weak__wc12
       -rate_eval.B17__n_n_C15__weak__wc12
       -rate_eval.B17__C17__weak__wc17
       -rate_eval.B17__n_C16__weak__wc17
       )

    jac[jb17, jb18] = (
       +rate_eval.B18__n_B17
       )

    jac[jb18, jb18] = (
       -rate_eval.B18__n_B17
       )

    jac[jb19, jb19] = (
       -rate_eval.B19__C19__weak__wc12
       -rate_eval.B19__n_C18__weak__wc17
       -rate_eval.B19__n_n_C17__weak__wc12
       )

    jac[jc9, jn] = (
       +rho*Y[jo12]*rate_eval.n_O12__He4_C9
       )

    jac[jc9, jp] = (
       +rho*Y[jb8]*rate_eval.p_B8__C9
       )

    jac[jc9, jhe4] = (
       -rho*Y[jc9]*rate_eval.He4_C9__p_N12
       )

    jac[jc9, jb8] = (
       +rho*Y[jp]*rate_eval.p_B8__C9
       )

    jac[jc9, jc9] = (
       -rho*Y[jhe4]*rate_eval.He4_C9__p_N12
       -rate_eval.C9__He4_Li5__weak__wc12
       )

    jac[jc9, jo12] = (
       +rho*Y[jn]*rate_eval.n_O12__He4_C9
       )

    jac[jc10, jn] = (
       +rho*Y[jo13]*rate_eval.n_O13__He4_C10
       )

    jac[jc10, jc10] = (
       -rate_eval.C10__B10__weak__wc12
       )

    jac[jc10, jo13] = (
       +rho*Y[jn]*rate_eval.n_O13__He4_C10
       )

    jac[jc11, jn] = (
       -rho*Y[jc11]*rate_eval.n_C11__He4_He4_He4
       -rho*Y[jc11]*rate_eval.n_C11__p_B11
       -rho*Y[jc11]*rate_eval.n_C11__C12
       +rho*Y[jo14]*rate_eval.n_O14__He4_C11
       )

    jac[jc11, jp] = (
       -rho*Y[jc11]*rate_eval.p_C11__N12
       +rho*Y[jb10]*rate_eval.p_B10__C11
       )

    jac[jc11, jhe4] = (
       -rho*Y[jc11]*rate_eval.He4_C11__p_N14
       +rho*Y[jbe7]*rate_eval.He4_Be7__C11
       +rho*Y[jb8]*rate_eval.He4_B8__p_C11
       )

    jac[jc11, jbe7] = (
       +rho*Y[jhe4]*rate_eval.He4_Be7__C11
       )

    jac[jc11, jb8] = (
       +rho*Y[jhe4]*rate_eval.He4_B8__p_C11
       )

    jac[jc11, jb10] = (
       +rho*Y[jp]*rate_eval.p_B10__C11
       )

    jac[jc11, jc11] = (
       -rho*Y[jn]*rate_eval.n_C11__He4_He4_He4
       -rho*Y[jn]*rate_eval.n_C11__p_B11
       -rho*Y[jp]*rate_eval.p_C11__N12
       -rho*Y[jn]*rate_eval.n_C11__C12
       -rho*Y[jhe4]*rate_eval.He4_C11__p_N14
       -rate_eval.C11__B11__weak__wc12
       )

    jac[jc11, jn11] = (
       +rate_eval.N11__C11__weak__btyk
       )

    jac[jc11, jo14] = (
       +rho*Y[jn]*rate_eval.n_O14__He4_C11
       )

    jac[jc12, jn] = (
       -rho*Y[jc12]*rate_eval.n_C12__C13
       +2*rho*Y[jmg23]*rate_eval.n_Mg23__C12_C12
       +rho*Y[jo15]*rate_eval.n_O15__He4_C12
       +rho*Y[jc11]*rate_eval.n_C11__C12
       +rho*Y[jsi27]*rate_eval.n_Si27__C12_O16
       )

    jac[jc12, jp] = (
       -rho*Y[jc12]*rate_eval.p_C12__N13
       +rho*Y[jb12]*rate_eval.p_B12__n_C12
       +rho*Y[jn15]*rate_eval.p_N15__He4_C12
       +rho*Y[jb11]*rate_eval.p_B11__C12
       )

    jac[jc12, jhe4] = (
       -rho*Y[jc12]*rate_eval.He4_C12__O16
       +1.66666666666667e-01*rho**2*3*Y[jhe4]**2*rate_eval.He4_He4_He4__C12
       +rho*Y[jbe9]*rate_eval.He4_Be9__n_C12
       )

    jac[jc12, jbe9] = (
       +rho*Y[jhe4]*rate_eval.He4_Be9__n_C12
       )

    jac[jc12, jb11] = (
       +rho*Y[jp]*rate_eval.p_B11__C12
       )

    jac[jc12, jb12] = (
       +rho*Y[jp]*rate_eval.p_B12__n_C12
       +rate_eval.B12__C12__weak__wc17
       )

    jac[jc12, jc11] = (
       +rho*Y[jn]*rate_eval.n_C11__C12
       )

    jac[jc12, jc12] = (
       -2*5.00000000000000e-01*rho*2*Y[jc12]*rate_eval.C12_C12__He4_Ne20
       -rho*Y[jne20]*rate_eval.C12_Ne20__He4_Si28
       -rho*Y[jne20]*rate_eval.C12_Ne20__p_P31
       -rho*Y[jo16]*rate_eval.C12_O16__He4_Mg24
       -rho*Y[jo16]*rate_eval.C12_O16__p_Al27
       -rho*Y[jne20]*rate_eval.C12_Ne20__n_S31
       -2*5.00000000000000e-01*rho*2*Y[jc12]*rate_eval.C12_C12__p_Na23
       -rho*Y[jp]*rate_eval.p_C12__N13
       -rho*Y[jhe4]*rate_eval.He4_C12__O16
       -rho*Y[jn]*rate_eval.n_C12__C13
       )

    jac[jc12, jn12] = (
       +rate_eval.N12__C12__weak__wc12
       )

    jac[jc12, jn15] = (
       +rho*Y[jp]*rate_eval.p_N15__He4_C12
       )

    jac[jc12, jn16] = (
       +rate_eval.N16__He4_C12__weak__wc12
       )

    jac[jc12, jo13] = (
       +rate_eval.O13__p_C12__weak__wc12
       )

    jac[jc12, jo15] = (
       +rho*Y[jn]*rate_eval.n_O15__He4_C12
       )

    jac[jc12, jo16] = (
       -rho*Y[jc12]*rate_eval.C12_O16__He4_Mg24
       -rho*Y[jc12]*rate_eval.C12_O16__p_Al27
       )

    jac[jc12, jne20] = (
       -rho*Y[jc12]*rate_eval.C12_Ne20__He4_Si28
       -rho*Y[jc12]*rate_eval.C12_Ne20__p_P31
       -rho*Y[jc12]*rate_eval.C12_Ne20__n_S31
       )

    jac[jc12, jmg23] = (
       +2*rho*Y[jn]*rate_eval.n_Mg23__C12_C12
       )

    jac[jc12, jsi27] = (
       +rho*Y[jn]*rate_eval.n_Si27__C12_O16
       )

    jac[jc13, jn] = (
       -rho*Y[jc13]*rate_eval.n_C13__C14
       +rho*Y[jc12]*rate_eval.n_C12__C13
       )

    jac[jc13, jp] = (
       -rho*Y[jc13]*rate_eval.p_C13__n_N13
       -rho*Y[jc13]*rate_eval.p_C13__N14
       +rho*Y[jn16]*rate_eval.p_N16__He4_C13
       )

    jac[jc13, jd] = (
       -rho*Y[jc13]*rate_eval.d_C13__n_N14
       )

    jac[jc13, jhe4] = (
       -rho*Y[jc13]*rate_eval.He4_C13__n_O16
       +rho*Y[jb10]*rate_eval.He4_B10__p_C13
       +rho*Y[jbe10]*rate_eval.He4_Be10__n_C13
       )

    jac[jc13, jbe10] = (
       +rho*Y[jhe4]*rate_eval.He4_Be10__n_C13
       )

    jac[jc13, jb10] = (
       +rho*Y[jhe4]*rate_eval.He4_B10__p_C13
       )

    jac[jc13, jb13] = (
       +rate_eval.B13__C13__weak__wc12
       )

    jac[jc13, jb15] = (
       +rate_eval.B15__n_n_C13__weak__wc12
       )

    jac[jc13, jc12] = (
       +rho*Y[jn]*rate_eval.n_C12__C13
       )

    jac[jc13, jc13] = (
       -rho*Y[jhe4]*rate_eval.He4_C13__n_O16
       -rho*Y[jd]*rate_eval.d_C13__n_N14
       -rho*Y[jp]*rate_eval.p_C13__n_N13
       -rho*Y[jp]*rate_eval.p_C13__N14
       -rho*Y[jn]*rate_eval.n_C13__C14
       )

    jac[jc13, jn13] = (
       +rate_eval.N13__C13__weak__wc12
       )

    jac[jc13, jn16] = (
       +rho*Y[jp]*rate_eval.p_N16__He4_C13
       )

    jac[jc14, jn] = (
       -rho*Y[jc14]*rate_eval.n_C14__C15
       +rho*Y[jn14]*rate_eval.n_N14__p_C14
       +rho*Y[jc13]*rate_eval.n_C13__C14
       +rho*Y[jo17]*rate_eval.n_O17__He4_C14
       )

    jac[jc14, jp] = (
       -rho*Y[jc14]*rate_eval.p_C14__N15
       )

    jac[jc14, jd] = (
       -rho*Y[jc14]*rate_eval.d_C14__n_N15
       )

    jac[jc14, jhe4] = (
       -rho*Y[jc14]*rate_eval.He4_C14__O18
       +rho*Y[jbe10]*rate_eval.He4_Be10__C14
       +rho*Y[jb11]*rate_eval.He4_B11__p_C14
       +rho*Y[jbe11]*rate_eval.He4_Be11__n_C14
       )

    jac[jc14, jbe10] = (
       +rho*Y[jhe4]*rate_eval.He4_Be10__C14
       )

    jac[jc14, jbe11] = (
       +rho*Y[jhe4]*rate_eval.He4_Be11__n_C14
       )

    jac[jc14, jb11] = (
       +rho*Y[jhe4]*rate_eval.He4_B11__p_C14
       )

    jac[jc14, jb14] = (
       +rate_eval.B14__C14__weak__wc12
       )

    jac[jc14, jb15] = (
       +rate_eval.B15__n_C14__weak__wc12
       )

    jac[jc14, jb17] = (
       +rate_eval.B17__n_n_n_C14__weak__wc12
       )

    jac[jc14, jc13] = (
       +rho*Y[jn]*rate_eval.n_C13__C14
       )

    jac[jc14, jc14] = (
       -rho*Y[jn]*rate_eval.n_C14__C15
       -rho*Y[jp]*rate_eval.p_C14__N15
       -rate_eval.C14__N14__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_C14__O18
       -rho*Y[jd]*rate_eval.d_C14__n_N15
       )

    jac[jc14, jn14] = (
       +rho*Y[jn]*rate_eval.n_N14__p_C14
       )

    jac[jc14, jn18] = (
       +rate_eval.N18__He4_C14__weak__wc12
       )

    jac[jc14, jo17] = (
       +rho*Y[jn]*rate_eval.n_O17__He4_C14
       )

    jac[jc15, jn] = (
       -rho*Y[jc15]*rate_eval.n_C15__C16
       +rho*Y[jc14]*rate_eval.n_C14__C15
       )

    jac[jc15, jp] = (
       -rho*Y[jc15]*rate_eval.p_C15__n_N15
       )

    jac[jc15, jhe4] = (
       -rho*Y[jc15]*rate_eval.He4_C15__n_O18
       )

    jac[jc15, jb15] = (
       +rate_eval.B15__C15__weak__wc12
       )

    jac[jc15, jb17] = (
       +rate_eval.B17__n_n_C15__weak__wc12
       )

    jac[jc15, jc14] = (
       +rho*Y[jn]*rate_eval.n_C14__C15
       )

    jac[jc15, jc15] = (
       -rho*Y[jhe4]*rate_eval.He4_C15__n_O18
       -rho*Y[jp]*rate_eval.p_C15__n_N15
       -rate_eval.C15__N15__weak__wc12
       -rho*Y[jn]*rate_eval.n_C15__C16
       )

    jac[jc16, jn] = (
       -rho*Y[jc16]*rate_eval.n_C16__C17
       +rho*Y[jc15]*rate_eval.n_C15__C16
       )

    jac[jc16, jb17] = (
       +rate_eval.B17__n_C16__weak__wc17
       )

    jac[jc16, jc15] = (
       +rho*Y[jn]*rate_eval.n_C15__C16
       )

    jac[jc16, jc16] = (
       -rate_eval.C16__n_N15__weak__wc12
       -rate_eval.C16__N16__weak__wc12
       -rho*Y[jn]*rate_eval.n_C16__C17
       )

    jac[jc17, jn] = (
       +rho*Y[jc16]*rate_eval.n_C16__C17
       )

    jac[jc17, jb17] = (
       +rate_eval.B17__C17__weak__wc17
       )

    jac[jc17, jb19] = (
       +rate_eval.B19__n_n_C17__weak__wc12
       )

    jac[jc17, jc16] = (
       +rho*Y[jn]*rate_eval.n_C16__C17
       )

    jac[jc17, jc17] = (
       -rate_eval.C17__N17__weak__wc12
       -rate_eval.C17__n_N16__weak__wc12
       )

    jac[jc18, jb19] = (
       +rate_eval.B19__n_C18__weak__wc17
       )

    jac[jc18, jc18] = (
       -rate_eval.C18__N18__weak__wc12
       -rate_eval.C18__n_N17__weak__wc12
       )

    jac[jc19, jb19] = (
       +rate_eval.B19__C19__weak__wc12
       )

    jac[jc19, jc19] = (
       -rate_eval.C19__N19__weak__wc07
       -rate_eval.C19__n_N18__weak__wc12
       )

    jac[jc20, jc20] = (
       -rate_eval.C20__n_N19__weak__wc12
       -rate_eval.C20__N20__weak__wc12
       )

    jac[jc20, jc21] = (
       +rate_eval.C21__n_C20
       )

    jac[jc21, jc21] = (
       -rate_eval.C21__n_C20
       )

    jac[jc22, jc22] = (
       -rate_eval.C22__N22__weak__wc17
       -rate_eval.C22__n_N21__weak__wc17
       )

    jac[jn11, jn] = (
       +rho*Y[jf14]*rate_eval.n_F14__He4_N11
       )

    jac[jn11, jn11] = (
       -rate_eval.N11__C11__weak__btyk
       )

    jac[jn11, jf14] = (
       +rho*Y[jn]*rate_eval.n_F14__He4_N11
       )

    jac[jn12, jn] = (
       +rho*Y[jf15]*rate_eval.n_F15__He4_N12
       +rho*Y[jo12]*rate_eval.n_O12__p_N12
       )

    jac[jn12, jp] = (
       -rho*Y[jn12]*rate_eval.p_N12__O13
       +rho*Y[jc11]*rate_eval.p_C11__N12
       )

    jac[jn12, jhe4] = (
       -rho*Y[jn12]*rate_eval.He4_N12__p_O15
       +rho*Y[jc9]*rate_eval.He4_C9__p_N12
       )

    jac[jn12, jc9] = (
       +rho*Y[jhe4]*rate_eval.He4_C9__p_N12
       )

    jac[jn12, jc11] = (
       +rho*Y[jp]*rate_eval.p_C11__N12
       )

    jac[jn12, jn12] = (
       -rho*Y[jp]*rate_eval.p_N12__O13
       -rho*Y[jhe4]*rate_eval.He4_N12__p_O15
       -rate_eval.N12__C12__weak__wc12
       )

    jac[jn12, jo12] = (
       +rho*Y[jn]*rate_eval.n_O12__p_N12
       )

    jac[jn12, jf15] = (
       +rho*Y[jn]*rate_eval.n_F15__He4_N12
       )

    jac[jn13, jn] = (
       -rho*Y[jn13]*rate_eval.n_N13__N14
       +rho*Y[jo13]*rate_eval.n_O13__p_N13
       +rho*Y[jf16]*rate_eval.n_F16__He4_N13
       )

    jac[jn13, jp] = (
       -rho*Y[jn13]*rate_eval.p_N13__O14
       +rho*Y[jc13]*rate_eval.p_C13__n_N13
       +rho*Y[jc12]*rate_eval.p_C12__N13
       )

    jac[jn13, jhe4] = (
       -rho*Y[jn13]*rate_eval.He4_N13__p_O16
       +rho*Y[jb10]*rate_eval.He4_B10__n_N13
       )

    jac[jn13, jb10] = (
       +rho*Y[jhe4]*rate_eval.He4_B10__n_N13
       )

    jac[jn13, jc12] = (
       +rho*Y[jp]*rate_eval.p_C12__N13
       )

    jac[jn13, jc13] = (
       +rho*Y[jp]*rate_eval.p_C13__n_N13
       )

    jac[jn13, jn13] = (
       -rho*Y[jhe4]*rate_eval.He4_N13__p_O16
       -rho*Y[jn]*rate_eval.n_N13__N14
       -rate_eval.N13__C13__weak__wc12
       -rho*Y[jp]*rate_eval.p_N13__O14
       )

    jac[jn13, jo13] = (
       +rho*Y[jn]*rate_eval.n_O13__p_N13
       +rate_eval.O13__N13__weak__wc17
       )

    jac[jn13, jf16] = (
       +rho*Y[jn]*rate_eval.n_F16__He4_N13
       )

    jac[jn14, jn] = (
       -rho*Y[jn14]*rate_eval.n_N14__p_C14
       -rho*Y[jn14]*rate_eval.n_N14__N15
       +rho*Y[jn13]*rate_eval.n_N13__N14
       )

    jac[jn14, jp] = (
       -rho*Y[jn14]*rate_eval.p_N14__O15
       -rho*Y[jn14]*rate_eval.p_N14__n_O14
       +rho*Y[jo17]*rate_eval.p_O17__He4_N14
       +rho*Y[jc13]*rate_eval.p_C13__N14
       )

    jac[jn14, jd] = (
       +rho*Y[jc13]*rate_eval.d_C13__n_N14
       )

    jac[jn14, jhe4] = (
       -rho*Y[jn14]*rate_eval.He4_N14__n_F17
       -rho*Y[jn14]*rate_eval.He4_N14__F18
       +rho*Y[jb11]*rate_eval.He4_B11__n_N14
       +rho*Y[jc11]*rate_eval.He4_C11__p_N14
       )

    jac[jn14, jb11] = (
       +rho*Y[jhe4]*rate_eval.He4_B11__n_N14
       )

    jac[jn14, jc11] = (
       +rho*Y[jhe4]*rate_eval.He4_C11__p_N14
       )

    jac[jn14, jc13] = (
       +rho*Y[jd]*rate_eval.d_C13__n_N14
       +rho*Y[jp]*rate_eval.p_C13__N14
       )

    jac[jn14, jc14] = (
       +rate_eval.C14__N14__weak__wc12
       )

    jac[jn14, jn13] = (
       +rho*Y[jn]*rate_eval.n_N13__N14
       )

    jac[jn14, jn14] = (
       -rho*Y[jn]*rate_eval.n_N14__p_C14
       -rho*Y[jhe4]*rate_eval.He4_N14__n_F17
       -rho*Y[jp]*rate_eval.p_N14__O15
       -rho*Y[jp]*rate_eval.p_N14__n_O14
       -rho*Y[jhe4]*rate_eval.He4_N14__F18
       -rho*Y[jn]*rate_eval.n_N14__N15
       )

    jac[jn14, jo14] = (
       +rate_eval.O14__N14__weak__wc12
       )

    jac[jn14, jo17] = (
       +rho*Y[jp]*rate_eval.p_O17__He4_N14
       )

    jac[jn15, jn] = (
       -rho*Y[jn15]*rate_eval.n_N15__N16
       +rho*Y[jf18]*rate_eval.n_F18__He4_N15
       +rho*Y[jn14]*rate_eval.n_N14__N15
       )

    jac[jn15, jp] = (
       -rho*Y[jn15]*rate_eval.p_N15__O16
       -rho*Y[jn15]*rate_eval.p_N15__He4_C12
       -rho*Y[jn15]*rate_eval.p_N15__n_O15
       +rho*Y[jo18]*rate_eval.p_O18__He4_N15
       +rho*Y[jc15]*rate_eval.p_C15__n_N15
       +rho*Y[jc14]*rate_eval.p_C14__N15
       )

    jac[jn15, jd] = (
       +rho*Y[jc14]*rate_eval.d_C14__n_N15
       )

    jac[jn15, jhe4] = (
       -rho*Y[jn15]*rate_eval.He4_N15__F19
       +rho*Y[jb12]*rate_eval.He4_B12__n_N15
       )

    jac[jn15, jb12] = (
       +rho*Y[jhe4]*rate_eval.He4_B12__n_N15
       )

    jac[jn15, jc14] = (
       +rho*Y[jp]*rate_eval.p_C14__N15
       +rho*Y[jd]*rate_eval.d_C14__n_N15
       )

    jac[jn15, jc15] = (
       +rho*Y[jp]*rate_eval.p_C15__n_N15
       +rate_eval.C15__N15__weak__wc12
       )

    jac[jn15, jc16] = (
       +rate_eval.C16__n_N15__weak__wc12
       )

    jac[jn15, jn14] = (
       +rho*Y[jn]*rate_eval.n_N14__N15
       )

    jac[jn15, jn15] = (
       -rho*Y[jhe4]*rate_eval.He4_N15__F19
       -rho*Y[jp]*rate_eval.p_N15__O16
       -rho*Y[jp]*rate_eval.p_N15__He4_C12
       -rho*Y[jp]*rate_eval.p_N15__n_O15
       -rho*Y[jn]*rate_eval.n_N15__N16
       )

    jac[jn15, jo15] = (
       +rate_eval.O15__N15__weak__wc12
       )

    jac[jn15, jo18] = (
       +rho*Y[jp]*rate_eval.p_O18__He4_N15
       )

    jac[jn15, jf18] = (
       +rho*Y[jn]*rate_eval.n_F18__He4_N15
       )

    jac[jn16, jn] = (
       -rho*Y[jn16]*rate_eval.n_N16__N17
       +rho*Y[jn15]*rate_eval.n_N15__N16
       )

    jac[jn16, jp] = (
       -rho*Y[jn16]*rate_eval.p_N16__n_O16
       -rho*Y[jn16]*rate_eval.p_N16__He4_C13
       +rho*Y[jo19]*rate_eval.p_O19__He4_N16
       )

    jac[jn16, jhe4] = (
       -rho*Y[jn16]*rate_eval.He4_N16__n_F19
       +rho*Y[jb13]*rate_eval.He4_B13__n_N16
       )

    jac[jn16, jb13] = (
       +rho*Y[jhe4]*rate_eval.He4_B13__n_N16
       )

    jac[jn16, jc16] = (
       +rate_eval.C16__N16__weak__wc12
       )

    jac[jn16, jc17] = (
       +rate_eval.C17__n_N16__weak__wc12
       )

    jac[jn16, jn15] = (
       +rho*Y[jn]*rate_eval.n_N15__N16
       )

    jac[jn16, jn16] = (
       -rate_eval.N16__O16__weak__wc12
       -rho*Y[jn]*rate_eval.n_N16__N17
       -rho*Y[jhe4]*rate_eval.He4_N16__n_F19
       -rho*Y[jp]*rate_eval.p_N16__n_O16
       -rate_eval.N16__He4_C12__weak__wc12
       -rho*Y[jp]*rate_eval.p_N16__He4_C13
       )

    jac[jn16, jo19] = (
       +rho*Y[jp]*rate_eval.p_O19__He4_N16
       )

    jac[jn17, jn] = (
       -rho*Y[jn17]*rate_eval.n_N17__N18
       +rho*Y[jn16]*rate_eval.n_N16__N17
       )

    jac[jn17, jp] = (
       +rho*Y[jo20]*rate_eval.p_O20__He4_N17
       )

    jac[jn17, jhe4] = (
       +rho*Y[jb13]*rate_eval.He4_B13__N17
       )

    jac[jn17, jb13] = (
       +rho*Y[jhe4]*rate_eval.He4_B13__N17
       )

    jac[jn17, jc17] = (
       +rate_eval.C17__N17__weak__wc12
       )

    jac[jn17, jc18] = (
       +rate_eval.C18__n_N17__weak__wc12
       )

    jac[jn17, jn16] = (
       +rho*Y[jn]*rate_eval.n_N16__N17
       )

    jac[jn17, jn17] = (
       -rate_eval.N17__n_O16__weak__wc12
       -rho*Y[jn]*rate_eval.n_N17__N18
       -rate_eval.N17__O17__weak__wc12
       )

    jac[jn17, jo20] = (
       +rho*Y[jp]*rate_eval.p_O20__He4_N17
       )

    jac[jn18, jn] = (
       -rho*Y[jn18]*rate_eval.n_N18__N19
       +rho*Y[jn17]*rate_eval.n_N17__N18
       )

    jac[jn18, jc18] = (
       +rate_eval.C18__N18__weak__wc12
       )

    jac[jn18, jc19] = (
       +rate_eval.C19__n_N18__weak__wc12
       )

    jac[jn18, jn17] = (
       +rho*Y[jn]*rate_eval.n_N17__N18
       )

    jac[jn18, jn18] = (
       -rho*Y[jn]*rate_eval.n_N18__N19
       -rate_eval.N18__O18__weak__wc12
       -rate_eval.N18__n_O17__weak__wc12
       -rate_eval.N18__He4_C14__weak__wc12
       )

    jac[jn19, jn] = (
       -rho*Y[jn19]*rate_eval.n_N19__N20
       +rho*Y[jn18]*rate_eval.n_N18__N19
       )

    jac[jn19, jc19] = (
       +rate_eval.C19__N19__weak__wc07
       )

    jac[jn19, jc20] = (
       +rate_eval.C20__n_N19__weak__wc12
       )

    jac[jn19, jn18] = (
       +rho*Y[jn]*rate_eval.n_N18__N19
       )

    jac[jn19, jn19] = (
       -rho*Y[jn]*rate_eval.n_N19__N20
       -rate_eval.N19__n_O18__weak__wc12
       -rate_eval.N19__O19__weak__wc12
       )

    jac[jn20, jn] = (
       +rho*Y[jn19]*rate_eval.n_N19__N20
       )

    jac[jn20, jc20] = (
       +rate_eval.C20__N20__weak__wc12
       )

    jac[jn20, jn19] = (
       +rho*Y[jn]*rate_eval.n_N19__N20
       )

    jac[jn20, jn20] = (
       -rate_eval.N20__n_O19__weak__wc12
       -rate_eval.N20__O20__weak__wc12
       )

    jac[jn21, jc22] = (
       +rate_eval.C22__n_N21__weak__wc17
       )

    jac[jn21, jn21] = (
       -rate_eval.N21__O21__weak__wc12
       -rate_eval.N21__n_O20__weak__wc12
       )

    jac[jn22, jc22] = (
       +rate_eval.C22__N22__weak__wc17
       )

    jac[jn22, jn22] = (
       -rate_eval.N22__O22__weak__wc12
       -rate_eval.N22__n_n_O20__weak__wc12
       -rate_eval.N22__n_O21__weak__wc17
       )

    jac[jn23, jp] = (
       +rho*Y[jo26]*rate_eval.p_O26__He4_N23
       )

    jac[jn23, jn23] = (
       -rate_eval.N23__O23__weak__wc12
       )

    jac[jn23, jn24] = (
       +rate_eval.N24__n_N23
       )

    jac[jn23, jo26] = (
       +rho*Y[jp]*rate_eval.p_O26__He4_N23
       )

    jac[jn24, jp] = (
       +rho*Y[jo27]*rate_eval.p_O27__He4_N24
       )

    jac[jn24, jn24] = (
       -rate_eval.N24__n_N23
       )

    jac[jn24, jo27] = (
       +rho*Y[jp]*rate_eval.p_O27__He4_N24
       )

    jac[jo12, jn] = (
       -rho*Y[jo12]*rate_eval.n_O12__O13
       -rho*Y[jo12]*rate_eval.n_O12__p_N12
       -rho*Y[jo12]*rate_eval.n_O12__He4_C9
       )

    jac[jo12, jo12] = (
       -rho*Y[jn]*rate_eval.n_O12__O13
       -rho*Y[jn]*rate_eval.n_O12__p_N12
       -rho*Y[jn]*rate_eval.n_O12__He4_C9
       )

    jac[jo13, jn] = (
       -rho*Y[jo13]*rate_eval.n_O13__He4_C10
       -rho*Y[jo13]*rate_eval.n_O13__p_N13
       -rho*Y[jo13]*rate_eval.n_O13__O14
       +rho*Y[jo12]*rate_eval.n_O12__O13
       +rho*Y[jne16]*rate_eval.n_Ne16__He4_O13
       )

    jac[jo13, jp] = (
       +rho*Y[jn12]*rate_eval.p_N12__O13
       )

    jac[jo13, jhe4] = (
       -rho*Y[jo13]*rate_eval.He4_O13__p_p_O15
       -rho*Y[jo13]*rate_eval.He4_O13__p_F16
       )

    jac[jo13, jn12] = (
       +rho*Y[jp]*rate_eval.p_N12__O13
       )

    jac[jo13, jo12] = (
       +rho*Y[jn]*rate_eval.n_O12__O13
       )

    jac[jo13, jo13] = (
       -rho*Y[jhe4]*rate_eval.He4_O13__p_p_O15
       -rho*Y[jhe4]*rate_eval.He4_O13__p_F16
       -rho*Y[jn]*rate_eval.n_O13__He4_C10
       -rho*Y[jn]*rate_eval.n_O13__p_N13
       -rho*Y[jn]*rate_eval.n_O13__O14
       -rate_eval.O13__N13__weak__wc17
       -rate_eval.O13__p_C12__weak__wc12
       )

    jac[jo13, jne16] = (
       +rho*Y[jn]*rate_eval.n_Ne16__He4_O13
       )

    jac[jo14, jn] = (
       -rho*Y[jo14]*rate_eval.n_O14__O15
       -rho*Y[jo14]*rate_eval.n_O14__He4_C11
       +rho*Y[jne17]*rate_eval.n_Ne17__He4_O14
       +rho*Y[jo13]*rate_eval.n_O13__O14
       +rho*Y[jf14]*rate_eval.n_F14__p_O14
       )

    jac[jo14, jp] = (
       -rho*Y[jo14]*rate_eval.p_O14__F15
       +rho*Y[jn14]*rate_eval.p_N14__n_O14
       +rho*Y[jn13]*rate_eval.p_N13__O14
       )

    jac[jo14, jhe4] = (
       -rho*Y[jo14]*rate_eval.He4_O14__p_F17
       -rho*Y[jo14]*rate_eval.He4_O14__Ne18
       )

    jac[jo14, jn13] = (
       +rho*Y[jp]*rate_eval.p_N13__O14
       )

    jac[jo14, jn14] = (
       +rho*Y[jp]*rate_eval.p_N14__n_O14
       )

    jac[jo14, jo13] = (
       +rho*Y[jn]*rate_eval.n_O13__O14
       )

    jac[jo14, jo14] = (
       -rho*Y[jn]*rate_eval.n_O14__O15
       -rho*Y[jp]*rate_eval.p_O14__F15
       -rate_eval.O14__N14__weak__wc12
       -rho*Y[jn]*rate_eval.n_O14__He4_C11
       -rho*Y[jhe4]*rate_eval.He4_O14__p_F17
       -rho*Y[jhe4]*rate_eval.He4_O14__Ne18
       )

    jac[jo14, jf14] = (
       +rho*Y[jn]*rate_eval.n_F14__p_O14
       )

    jac[jo14, jne17] = (
       +rho*Y[jn]*rate_eval.n_Ne17__He4_O14
       )

    jac[jo15, jn] = (
       -rho*Y[jo15]*rate_eval.n_O15__He4_C12
       -rho*Y[jo15]*rate_eval.n_O15__O16
       +rho*Y[jo14]*rate_eval.n_O14__O15
       +rho*Y[jne18]*rate_eval.n_Ne18__He4_O15
       +rho*Y[jf15]*rate_eval.n_F15__p_O15
       )

    jac[jo15, jp] = (
       -rho*Y[jo15]*rate_eval.p_O15__F16
       +rho*Y[jf18]*rate_eval.p_F18__He4_O15
       +rho*Y[jn15]*rate_eval.p_N15__n_O15
       +rho*Y[jn14]*rate_eval.p_N14__O15
       )

    jac[jo15, jhe4] = (
       -rho*Y[jo15]*rate_eval.He4_O15__Ne19
       +rho*Y[jo13]*rate_eval.He4_O13__p_p_O15
       +rho*Y[jn12]*rate_eval.He4_N12__p_O15
       )

    jac[jo15, jn12] = (
       +rho*Y[jhe4]*rate_eval.He4_N12__p_O15
       )

    jac[jo15, jn14] = (
       +rho*Y[jp]*rate_eval.p_N14__O15
       )

    jac[jo15, jn15] = (
       +rho*Y[jp]*rate_eval.p_N15__n_O15
       )

    jac[jo15, jo13] = (
       +rho*Y[jhe4]*rate_eval.He4_O13__p_p_O15
       )

    jac[jo15, jo14] = (
       +rho*Y[jn]*rate_eval.n_O14__O15
       )

    jac[jo15, jo15] = (
       -rho*Y[jp]*rate_eval.p_O15__F16
       -rho*Y[jn]*rate_eval.n_O15__He4_C12
       -rho*Y[jn]*rate_eval.n_O15__O16
       -rho*Y[jhe4]*rate_eval.He4_O15__Ne19
       -rate_eval.O15__N15__weak__wc12
       )

    jac[jo15, jf15] = (
       +rho*Y[jn]*rate_eval.n_F15__p_O15
       )

    jac[jo15, jf18] = (
       +rho*Y[jp]*rate_eval.p_F18__He4_O15
       )

    jac[jo15, jne18] = (
       +rho*Y[jn]*rate_eval.n_Ne18__He4_O15
       )

    jac[jo16, jn] = (
       -rho*Y[jo16]*rate_eval.n_O16__O17
       +rho*Y[jf16]*rate_eval.n_F16__p_O16
       +rho*Y[jne19]*rate_eval.n_Ne19__He4_O16
       +rho*Y[jo15]*rate_eval.n_O15__O16
       +rho*Y[jsi27]*rate_eval.n_Si27__C12_O16
       )

    jac[jo16, jp] = (
       -rho*Y[jo16]*rate_eval.p_O16__F17
       +rho*Y[jn15]*rate_eval.p_N15__O16
       +rho*Y[jf19]*rate_eval.p_F19__He4_O16
       +rho*Y[jn16]*rate_eval.p_N16__n_O16
       )

    jac[jo16, jhe4] = (
       -rho*Y[jo16]*rate_eval.He4_O16__Ne20
       +rho*Y[jn13]*rate_eval.He4_N13__p_O16
       +rho*Y[jc13]*rate_eval.He4_C13__n_O16
       +rho*Y[jc12]*rate_eval.He4_C12__O16
       )

    jac[jo16, jc12] = (
       -rho*Y[jo16]*rate_eval.C12_O16__He4_Mg24
       -rho*Y[jo16]*rate_eval.C12_O16__p_Al27
       +rho*Y[jhe4]*rate_eval.He4_C12__O16
       )

    jac[jo16, jc13] = (
       +rho*Y[jhe4]*rate_eval.He4_C13__n_O16
       )

    jac[jo16, jn13] = (
       +rho*Y[jhe4]*rate_eval.He4_N13__p_O16
       )

    jac[jo16, jn15] = (
       +rho*Y[jp]*rate_eval.p_N15__O16
       )

    jac[jo16, jn16] = (
       +rate_eval.N16__O16__weak__wc12
       +rho*Y[jp]*rate_eval.p_N16__n_O16
       )

    jac[jo16, jn17] = (
       +rate_eval.N17__n_O16__weak__wc12
       )

    jac[jo16, jo15] = (
       +rho*Y[jn]*rate_eval.n_O15__O16
       )

    jac[jo16, jo16] = (
       -rho*Y[jp]*rate_eval.p_O16__F17
       -2*5.00000000000000e-01*rho*2*Y[jo16]*rate_eval.O16_O16__He4_Si28
       -2*5.00000000000000e-01*rho*2*Y[jo16]*rate_eval.O16_O16__p_P31
       -2*5.00000000000000e-01*rho*2*Y[jo16]*rate_eval.O16_O16__n_S31
       -rho*Y[jc12]*rate_eval.C12_O16__He4_Mg24
       -rho*Y[jc12]*rate_eval.C12_O16__p_Al27
       -rho*Y[jn]*rate_eval.n_O16__O17
       -rho*Y[jhe4]*rate_eval.He4_O16__Ne20
       )

    jac[jo16, jf16] = (
       +rho*Y[jn]*rate_eval.n_F16__p_O16
       )

    jac[jo16, jf19] = (
       +rho*Y[jp]*rate_eval.p_F19__He4_O16
       )

    jac[jo16, jne17] = (
       +rate_eval.Ne17__p_O16__weak__wc12
       )

    jac[jo16, jne19] = (
       +rho*Y[jn]*rate_eval.n_Ne19__He4_O16
       )

    jac[jo16, jna20] = (
       +rate_eval.Na20__He4_O16__weak__wc12
       )

    jac[jo16, jsi27] = (
       +rho*Y[jn]*rate_eval.n_Si27__C12_O16
       )

    jac[jo17, jn] = (
       -rho*Y[jo17]*rate_eval.n_O17__O18
       -rho*Y[jo17]*rate_eval.n_O17__He4_C14
       +rho*Y[jo16]*rate_eval.n_O16__O17
       +rho*Y[jf17]*rate_eval.n_F17__p_O17
       )

    jac[jo17, jp] = (
       -rho*Y[jo17]*rate_eval.p_O17__He4_N14
       -rho*Y[jo17]*rate_eval.p_O17__F18
       +rho*Y[jf20]*rate_eval.p_F20__He4_O17
       )

    jac[jo17, jhe4] = (
       -rho*Y[jo17]*rate_eval.He4_O17__n_Ne20
       -rho*Y[jo17]*rate_eval.He4_O17__Ne21
       )

    jac[jo17, jn17] = (
       +rate_eval.N17__O17__weak__wc12
       )

    jac[jo17, jn18] = (
       +rate_eval.N18__n_O17__weak__wc12
       )

    jac[jo17, jo16] = (
       +rho*Y[jn]*rate_eval.n_O16__O17
       )

    jac[jo17, jo17] = (
       -rho*Y[jhe4]*rate_eval.He4_O17__n_Ne20
       -rho*Y[jp]*rate_eval.p_O17__He4_N14
       -rho*Y[jn]*rate_eval.n_O17__O18
       -rho*Y[jp]*rate_eval.p_O17__F18
       -rho*Y[jhe4]*rate_eval.He4_O17__Ne21
       -rho*Y[jn]*rate_eval.n_O17__He4_C14
       )

    jac[jo17, jf17] = (
       +rho*Y[jn]*rate_eval.n_F17__p_O17
       +rate_eval.F17__O17__weak__wc12
       )

    jac[jo17, jf20] = (
       +rho*Y[jp]*rate_eval.p_F20__He4_O17
       )

    jac[jo18, jn] = (
       -rho*Y[jo18]*rate_eval.n_O18__O19
       +rho*Y[jo17]*rate_eval.n_O17__O18
       +rho*Y[jf18]*rate_eval.n_F18__p_O18
       )

    jac[jo18, jp] = (
       -rho*Y[jo18]*rate_eval.p_O18__He4_N15
       -rho*Y[jo18]*rate_eval.p_O18__F19
       +rho*Y[jf21]*rate_eval.p_F21__He4_O18
       )

    jac[jo18, jhe4] = (
       -rho*Y[jo18]*rate_eval.He4_O18__n_Ne21
       -rho*Y[jo18]*rate_eval.He4_O18__Ne22
       +rho*Y[jc15]*rate_eval.He4_C15__n_O18
       +rho*Y[jc14]*rate_eval.He4_C14__O18
       )

    jac[jo18, jc14] = (
       +rho*Y[jhe4]*rate_eval.He4_C14__O18
       )

    jac[jo18, jc15] = (
       +rho*Y[jhe4]*rate_eval.He4_C15__n_O18
       )

    jac[jo18, jn18] = (
       +rate_eval.N18__O18__weak__wc12
       )

    jac[jo18, jn19] = (
       +rate_eval.N19__n_O18__weak__wc12
       )

    jac[jo18, jo17] = (
       +rho*Y[jn]*rate_eval.n_O17__O18
       )

    jac[jo18, jo18] = (
       -rho*Y[jn]*rate_eval.n_O18__O19
       -rho*Y[jp]*rate_eval.p_O18__He4_N15
       -rho*Y[jhe4]*rate_eval.He4_O18__n_Ne21
       -rho*Y[jhe4]*rate_eval.He4_O18__Ne22
       -rho*Y[jp]*rate_eval.p_O18__F19
       )

    jac[jo18, jf18] = (
       +rho*Y[jn]*rate_eval.n_F18__p_O18
       +rate_eval.F18__O18__weak__wc12
       )

    jac[jo18, jf21] = (
       +rho*Y[jp]*rate_eval.p_F21__He4_O18
       )

    jac[jo19, jn] = (
       -rho*Y[jo19]*rate_eval.n_O19__O20
       +rho*Y[jo18]*rate_eval.n_O18__O19
       )

    jac[jo19, jp] = (
       -rho*Y[jo19]*rate_eval.p_O19__He4_N16
       -rho*Y[jo19]*rate_eval.p_O19__n_F19
       -rho*Y[jo19]*rate_eval.p_O19__F20
       +rho*Y[jf22]*rate_eval.p_F22__He4_O19
       )

    jac[jo19, jhe4] = (
       -rho*Y[jo19]*rate_eval.He4_O19__n_Ne22
       -rho*Y[jo19]*rate_eval.He4_O19__Ne23
       )

    jac[jo19, jn19] = (
       +rate_eval.N19__O19__weak__wc12
       )

    jac[jo19, jn20] = (
       +rate_eval.N20__n_O19__weak__wc12
       )

    jac[jo19, jo18] = (
       +rho*Y[jn]*rate_eval.n_O18__O19
       )

    jac[jo19, jo19] = (
       -rho*Y[jp]*rate_eval.p_O19__He4_N16
       -rho*Y[jhe4]*rate_eval.He4_O19__n_Ne22
       -rho*Y[jhe4]*rate_eval.He4_O19__Ne23
       -rho*Y[jn]*rate_eval.n_O19__O20
       -rho*Y[jp]*rate_eval.p_O19__n_F19
       -rho*Y[jp]*rate_eval.p_O19__F20
       -rate_eval.O19__F19__weak__wc12
       )

    jac[jo19, jf22] = (
       +rho*Y[jp]*rate_eval.p_F22__He4_O19
       )

    jac[jo20, jn] = (
       -rho*Y[jo20]*rate_eval.n_O20__O21
       +rho*Y[jo19]*rate_eval.n_O19__O20
       )

    jac[jo20, jp] = (
       -rho*Y[jo20]*rate_eval.p_O20__He4_N17
       -rho*Y[jo20]*rate_eval.p_O20__n_F20
       -rho*Y[jo20]*rate_eval.p_O20__F21
       +rho*Y[jf23]*rate_eval.p_F23__He4_O20
       )

    jac[jo20, jhe4] = (
       -rho*Y[jo20]*rate_eval.He4_O20__Ne24
       -rho*Y[jo20]*rate_eval.He4_O20__n_Ne23
       )

    jac[jo20, jn20] = (
       +rate_eval.N20__O20__weak__wc12
       )

    jac[jo20, jn21] = (
       +rate_eval.N21__n_O20__weak__wc12
       )

    jac[jo20, jn22] = (
       +rate_eval.N22__n_n_O20__weak__wc12
       )

    jac[jo20, jo19] = (
       +rho*Y[jn]*rate_eval.n_O19__O20
       )

    jac[jo20, jo20] = (
       -rho*Y[jp]*rate_eval.p_O20__He4_N17
       -rho*Y[jp]*rate_eval.p_O20__n_F20
       -rho*Y[jhe4]*rate_eval.He4_O20__Ne24
       -rho*Y[jp]*rate_eval.p_O20__F21
       -rho*Y[jhe4]*rate_eval.He4_O20__n_Ne23
       -rate_eval.O20__F20__weak__wc12
       -rho*Y[jn]*rate_eval.n_O20__O21
       )

    jac[jo20, jf23] = (
       +rho*Y[jp]*rate_eval.p_F23__He4_O20
       )

    jac[jo21, jn] = (
       -rho*Y[jo21]*rate_eval.n_O21__O22
       +rho*Y[jo20]*rate_eval.n_O20__O21
       )

    jac[jo21, jp] = (
       -rho*Y[jo21]*rate_eval.p_O21__n_F21
       -rho*Y[jo21]*rate_eval.p_O21__F22
       +rho*Y[jf24]*rate_eval.p_F24__He4_O21
       )

    jac[jo21, jhe4] = (
       -rho*Y[jo21]*rate_eval.He4_O21__Ne25
       -rho*Y[jo21]*rate_eval.He4_O21__n_Ne24
       )

    jac[jo21, jn21] = (
       +rate_eval.N21__O21__weak__wc12
       )

    jac[jo21, jn22] = (
       +rate_eval.N22__n_O21__weak__wc17
       )

    jac[jo21, jo20] = (
       +rho*Y[jn]*rate_eval.n_O20__O21
       )

    jac[jo21, jo21] = (
       -rho*Y[jp]*rate_eval.p_O21__n_F21
       -rho*Y[jhe4]*rate_eval.He4_O21__Ne25
       -rho*Y[jhe4]*rate_eval.He4_O21__n_Ne24
       -rho*Y[jn]*rate_eval.n_O21__O22
       -rho*Y[jp]*rate_eval.p_O21__F22
       -rate_eval.O21__F21__weak__wc12
       )

    jac[jo21, jf24] = (
       +rho*Y[jp]*rate_eval.p_F24__He4_O21
       )

    jac[jo22, jn] = (
       -rho*Y[jo22]*rate_eval.n_O22__O23
       +rho*Y[jo21]*rate_eval.n_O21__O22
       )

    jac[jo22, jp] = (
       -rho*Y[jo22]*rate_eval.p_O22__n_F22
       -rho*Y[jo22]*rate_eval.p_O22__F23
       +rho*Y[jf25]*rate_eval.p_F25__He4_O22
       )

    jac[jo22, jhe4] = (
       -rho*Y[jo22]*rate_eval.He4_O22__n_Ne25
       -rho*Y[jo22]*rate_eval.He4_O22__Ne26
       )

    jac[jo22, jn22] = (
       +rate_eval.N22__O22__weak__wc12
       )

    jac[jo22, jo21] = (
       +rho*Y[jn]*rate_eval.n_O21__O22
       )

    jac[jo22, jo22] = (
       -rho*Y[jp]*rate_eval.p_O22__n_F22
       -rho*Y[jhe4]*rate_eval.He4_O22__n_Ne25
       -rho*Y[jhe4]*rate_eval.He4_O22__Ne26
       -rho*Y[jp]*rate_eval.p_O22__F23
       -rho*Y[jn]*rate_eval.n_O22__O23
       -rate_eval.O22__F22__weak__wc17
       )

    jac[jo22, jf25] = (
       +rho*Y[jp]*rate_eval.p_F25__He4_O22
       )

    jac[jo23, jn] = (
       -rho*Y[jo23]*rate_eval.n_O23__O24
       +rho*Y[jo22]*rate_eval.n_O22__O23
       )

    jac[jo23, jp] = (
       -rho*Y[jo23]*rate_eval.p_O23__n_F23
       -rho*Y[jo23]*rate_eval.p_O23__F24
       +rho*Y[jf26]*rate_eval.p_F26__He4_O23
       )

    jac[jo23, jhe4] = (
       -rho*Y[jo23]*rate_eval.He4_O23__n_Ne26
       -rho*Y[jo23]*rate_eval.He4_O23__Ne27
       )

    jac[jo23, jn23] = (
       +rate_eval.N23__O23__weak__wc12
       )

    jac[jo23, jo22] = (
       +rho*Y[jn]*rate_eval.n_O22__O23
       )

    jac[jo23, jo23] = (
       -rho*Y[jhe4]*rate_eval.He4_O23__n_Ne26
       -rho*Y[jhe4]*rate_eval.He4_O23__Ne27
       -rho*Y[jn]*rate_eval.n_O23__O24
       -rho*Y[jp]*rate_eval.p_O23__n_F23
       -rate_eval.O23__F23__weak__wc12
       -rate_eval.O23__n_F22__weak__wc12
       -rho*Y[jp]*rate_eval.p_O23__F24
       )

    jac[jo23, jf26] = (
       +rho*Y[jp]*rate_eval.p_F26__He4_O23
       )

    jac[jo24, jn] = (
       -rho*Y[jo24]*rate_eval.n_O24__O25
       +rho*Y[jo23]*rate_eval.n_O23__O24
       )

    jac[jo24, jp] = (
       -rho*Y[jo24]*rate_eval.p_O24__n_F24
       -rho*Y[jo24]*rate_eval.p_O24__F25
       +rho*Y[jf27]*rate_eval.p_F27__He4_O24
       )

    jac[jo24, jhe4] = (
       -rho*Y[jo24]*rate_eval.He4_O24__n_Ne27
       -rho*Y[jo24]*rate_eval.He4_O24__Ne28
       )

    jac[jo24, jo23] = (
       +rho*Y[jn]*rate_eval.n_O23__O24
       )

    jac[jo24, jo24] = (
       -rate_eval.O24__F24__weak__wc12
       -rho*Y[jn]*rate_eval.n_O24__O25
       -rho*Y[jhe4]*rate_eval.He4_O24__n_Ne27
       -rho*Y[jp]*rate_eval.p_O24__n_F24
       -rho*Y[jhe4]*rate_eval.He4_O24__Ne28
       -rate_eval.O24__n_F23__weak__wc12
       -rho*Y[jp]*rate_eval.p_O24__F25
       )

    jac[jo24, jf27] = (
       +rho*Y[jp]*rate_eval.p_F27__He4_O24
       )

    jac[jo25, jn] = (
       +rho*Y[jo24]*rate_eval.n_O24__O25
       )

    jac[jo25, jp] = (
       -rho*Y[jo25]*rate_eval.p_O25__n_F25
       -rho*Y[jo25]*rate_eval.p_O25__F26
       +rho*Y[jf28]*rate_eval.p_F28__He4_O25
       )

    jac[jo25, jhe4] = (
       -rho*Y[jo25]*rate_eval.He4_O25__n_Ne28
       -rho*Y[jo25]*rate_eval.He4_O25__Ne29
       )

    jac[jo25, jo24] = (
       +rho*Y[jn]*rate_eval.n_O24__O25
       )

    jac[jo25, jo25] = (
       -rho*Y[jp]*rate_eval.p_O25__n_F25
       -rho*Y[jhe4]*rate_eval.He4_O25__n_Ne28
       -rate_eval.O25__n_F24__weak__mp17
       -rate_eval.O25__n_n_F23__weak__mp17
       -rate_eval.O25__F25__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_O25__Ne29
       -rho*Y[jp]*rate_eval.p_O25__F26
       )

    jac[jo25, jo26] = (
       +rate_eval.O26__n_O25
       )

    jac[jo25, jf28] = (
       +rho*Y[jp]*rate_eval.p_F28__He4_O25
       )

    jac[jo26, jp] = (
       -rho*Y[jo26]*rate_eval.p_O26__He4_N23
       -rho*Y[jo26]*rate_eval.p_O26__n_F26
       -rho*Y[jo26]*rate_eval.p_O26__F27
       +rho*Y[jf29]*rate_eval.p_F29__He4_O26
       )

    jac[jo26, jhe4] = (
       -rho*Y[jo26]*rate_eval.He4_O26__n_Ne29
       -rho*Y[jo26]*rate_eval.He4_O26__Ne30
       )

    jac[jo26, jo26] = (
       -rho*Y[jhe4]*rate_eval.He4_O26__n_Ne29
       -rho*Y[jp]*rate_eval.p_O26__He4_N23
       -rho*Y[jp]*rate_eval.p_O26__n_F26
       -rho*Y[jp]*rate_eval.p_O26__F27
       -rate_eval.O26__n_n_F24__weak__mp17
       -rate_eval.O26__n_O25
       -rate_eval.O26__n_F25__weak__mp17
       -rate_eval.O26__F26__weak__mo03
       -rate_eval.O26__n_n_n_F23__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_O26__Ne30
       )

    jac[jo26, jo27] = (
       +rate_eval.O27__n_O26
       )

    jac[jo26, jf29] = (
       +rho*Y[jp]*rate_eval.p_F29__He4_O26
       )

    jac[jo27, jp] = (
       -rho*Y[jo27]*rate_eval.p_O27__He4_N24
       -rho*Y[jo27]*rate_eval.p_O27__F28
       -rho*Y[jo27]*rate_eval.p_O27__n_F27
       +rho*Y[jf30]*rate_eval.p_F30__He4_O27
       )

    jac[jo27, jhe4] = (
       -rho*Y[jo27]*rate_eval.He4_O27__Ne31
       -rho*Y[jo27]*rate_eval.He4_O27__n_Ne30
       )

    jac[jo27, jo27] = (
       -rate_eval.O27__n_n_n_F24__weak__mo03
       -rho*Y[jp]*rate_eval.p_O27__He4_N24
       -rho*Y[jhe4]*rate_eval.He4_O27__Ne31
       -rate_eval.O27__F27__weak__mo03
       -rho*Y[jp]*rate_eval.p_O27__F28
       -rate_eval.O27__n_n_F25__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_O27__n_Ne30
       -rho*Y[jp]*rate_eval.p_O27__n_F27
       -rate_eval.O27__n_O26
       -rate_eval.O27__n_F26__weak__mp17
       )

    jac[jo27, jo28] = (
       +rate_eval.O28__n_O27
       )

    jac[jo27, jf30] = (
       +rho*Y[jp]*rate_eval.p_F30__He4_O27
       )

    jac[jo28, jp] = (
       +rho*Y[jf31]*rate_eval.p_F31__He4_O28
       )

    jac[jo28, jhe4] = (
       -rho*Y[jo28]*rate_eval.He4_O28__n_Ne31
       -rho*Y[jo28]*rate_eval.He4_O28__Ne32
       )

    jac[jo28, jo28] = (
       -rate_eval.O28__n_O27
       -rate_eval.O28__n_n_n_F25__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_O28__n_Ne31
       -rho*Y[jhe4]*rate_eval.He4_O28__Ne32
       -rate_eval.O28__n_n_F26__weak__mp17
       -rate_eval.O28__n_F27__weak__mp17
       )

    jac[jo28, jf31] = (
       +rho*Y[jp]*rate_eval.p_F31__He4_O28
       )

    jac[jf14, jn] = (
       -rho*Y[jf14]*rate_eval.n_F14__He4_N11
       -rho*Y[jf14]*rate_eval.n_F14__F15
       -rho*Y[jf14]*rate_eval.n_F14__p_O14
       )

    jac[jf14, jf14] = (
       -rho*Y[jn]*rate_eval.n_F14__He4_N11
       -rho*Y[jn]*rate_eval.n_F14__F15
       -rho*Y[jn]*rate_eval.n_F14__p_O14
       )

    jac[jf15, jn] = (
       -rho*Y[jf15]*rate_eval.n_F15__He4_N12
       -rho*Y[jf15]*rate_eval.n_F15__F16
       -rho*Y[jf15]*rate_eval.n_F15__p_O15
       +rho*Y[jf14]*rate_eval.n_F14__F15
       )

    jac[jf15, jp] = (
       +rho*Y[jo14]*rate_eval.p_O14__F15
       )

    jac[jf15, jhe4] = (
       -rho*Y[jf15]*rate_eval.He4_F15__p_Ne18
       -rho*Y[jf15]*rate_eval.He4_F15__Na19
       )

    jac[jf15, jo14] = (
       +rho*Y[jp]*rate_eval.p_O14__F15
       )

    jac[jf15, jf14] = (
       +rho*Y[jn]*rate_eval.n_F14__F15
       )

    jac[jf15, jf15] = (
       -rho*Y[jn]*rate_eval.n_F15__He4_N12
       -rho*Y[jn]*rate_eval.n_F15__F16
       -rho*Y[jhe4]*rate_eval.He4_F15__p_Ne18
       -rho*Y[jhe4]*rate_eval.He4_F15__Na19
       -rho*Y[jn]*rate_eval.n_F15__p_O15
       )

    jac[jf16, jn] = (
       -rho*Y[jf16]*rate_eval.n_F16__p_O16
       -rho*Y[jf16]*rate_eval.n_F16__He4_N13
       -rho*Y[jf16]*rate_eval.n_F16__F17
       +rho*Y[jne16]*rate_eval.n_Ne16__p_F16
       +rho*Y[jf15]*rate_eval.n_F15__F16
       +rho*Y[jna19]*rate_eval.n_Na19__He4_F16
       )

    jac[jf16, jp] = (
       +rho*Y[jo15]*rate_eval.p_O15__F16
       )

    jac[jf16, jhe4] = (
       -rho*Y[jf16]*rate_eval.He4_F16__Na20
       -rho*Y[jf16]*rate_eval.He4_F16__p_Ne19
       +rho*Y[jo13]*rate_eval.He4_O13__p_F16
       )

    jac[jf16, jo13] = (
       +rho*Y[jhe4]*rate_eval.He4_O13__p_F16
       )

    jac[jf16, jo15] = (
       +rho*Y[jp]*rate_eval.p_O15__F16
       )

    jac[jf16, jf15] = (
       +rho*Y[jn]*rate_eval.n_F15__F16
       )

    jac[jf16, jf16] = (
       -rho*Y[jhe4]*rate_eval.He4_F16__Na20
       -rho*Y[jn]*rate_eval.n_F16__p_O16
       -rho*Y[jhe4]*rate_eval.He4_F16__p_Ne19
       -rho*Y[jn]*rate_eval.n_F16__He4_N13
       -rho*Y[jn]*rate_eval.n_F16__F17
       )

    jac[jf16, jne16] = (
       +rho*Y[jn]*rate_eval.n_Ne16__p_F16
       )

    jac[jf16, jna19] = (
       +rho*Y[jn]*rate_eval.n_Na19__He4_F16
       )

    jac[jf17, jn] = (
       -rho*Y[jf17]*rate_eval.n_F17__F18
       -rho*Y[jf17]*rate_eval.n_F17__p_O17
       +rho*Y[jna20]*rate_eval.n_Na20__He4_F17
       +rho*Y[jf16]*rate_eval.n_F16__F17
       +rho*Y[jne17]*rate_eval.n_Ne17__p_F17
       )

    jac[jf17, jp] = (
       -rho*Y[jf17]*rate_eval.p_F17__Ne18
       +rho*Y[jo16]*rate_eval.p_O16__F17
       +rho*Y[jne20]*rate_eval.p_Ne20__He4_F17
       )

    jac[jf17, jhe4] = (
       -rho*Y[jf17]*rate_eval.He4_F17__Na21
       +rho*Y[jo14]*rate_eval.He4_O14__p_F17
       +rho*Y[jn14]*rate_eval.He4_N14__n_F17
       )

    jac[jf17, jn14] = (
       +rho*Y[jhe4]*rate_eval.He4_N14__n_F17
       )

    jac[jf17, jo14] = (
       +rho*Y[jhe4]*rate_eval.He4_O14__p_F17
       )

    jac[jf17, jo16] = (
       +rho*Y[jp]*rate_eval.p_O16__F17
       )

    jac[jf17, jf16] = (
       +rho*Y[jn]*rate_eval.n_F16__F17
       )

    jac[jf17, jf17] = (
       -rho*Y[jhe4]*rate_eval.He4_F17__Na21
       -rho*Y[jn]*rate_eval.n_F17__F18
       -rho*Y[jp]*rate_eval.p_F17__Ne18
       -rho*Y[jn]*rate_eval.n_F17__p_O17
       -rate_eval.F17__O17__weak__wc12
       )

    jac[jf17, jne17] = (
       +rate_eval.Ne17__F17__weak__wc17
       +rho*Y[jn]*rate_eval.n_Ne17__p_F17
       )

    jac[jf17, jne20] = (
       +rho*Y[jp]*rate_eval.p_Ne20__He4_F17
       )

    jac[jf17, jna20] = (
       +rho*Y[jn]*rate_eval.n_Na20__He4_F17
       )

    jac[jf18, jn] = (
       -rho*Y[jf18]*rate_eval.n_F18__He4_N15
       -rho*Y[jf18]*rate_eval.n_F18__p_O18
       -rho*Y[jf18]*rate_eval.n_F18__F19
       +rho*Y[jna21]*rate_eval.n_Na21__He4_F18
       +rho*Y[jne18]*rate_eval.n_Ne18__p_F18
       +rho*Y[jf17]*rate_eval.n_F17__F18
       )

    jac[jf18, jp] = (
       -rho*Y[jf18]*rate_eval.p_F18__He4_O15
       -rho*Y[jf18]*rate_eval.p_F18__Ne19
       +rho*Y[jo17]*rate_eval.p_O17__F18
       )

    jac[jf18, jhe4] = (
       -rho*Y[jf18]*rate_eval.He4_F18__p_Ne21
       -rho*Y[jf18]*rate_eval.He4_F18__Na22
       +rho*Y[jn14]*rate_eval.He4_N14__F18
       )

    jac[jf18, jn14] = (
       +rho*Y[jhe4]*rate_eval.He4_N14__F18
       )

    jac[jf18, jo17] = (
       +rho*Y[jp]*rate_eval.p_O17__F18
       )

    jac[jf18, jf17] = (
       +rho*Y[jn]*rate_eval.n_F17__F18
       )

    jac[jf18, jf18] = (
       -rho*Y[jp]*rate_eval.p_F18__He4_O15
       -rho*Y[jhe4]*rate_eval.He4_F18__p_Ne21
       -rho*Y[jn]*rate_eval.n_F18__He4_N15
       -rho*Y[jn]*rate_eval.n_F18__p_O18
       -rho*Y[jhe4]*rate_eval.He4_F18__Na22
       -rho*Y[jn]*rate_eval.n_F18__F19
       -rho*Y[jp]*rate_eval.p_F18__Ne19
       -rate_eval.F18__O18__weak__wc12
       )

    jac[jf18, jne18] = (
       +rho*Y[jn]*rate_eval.n_Ne18__p_F18
       +rate_eval.Ne18__F18__weak__wc12
       )

    jac[jf18, jna21] = (
       +rho*Y[jn]*rate_eval.n_Na21__He4_F18
       )

    jac[jf19, jn] = (
       -rho*Y[jf19]*rate_eval.n_F19__F20
       +rho*Y[jf18]*rate_eval.n_F18__F19
       +rho*Y[jna22]*rate_eval.n_Na22__He4_F19
       )

    jac[jf19, jp] = (
       -rho*Y[jf19]*rate_eval.p_F19__n_Ne19
       -rho*Y[jf19]*rate_eval.p_F19__He4_O16
       -rho*Y[jf19]*rate_eval.p_F19__Ne20
       +rho*Y[jo19]*rate_eval.p_O19__n_F19
       +rho*Y[jo18]*rate_eval.p_O18__F19
       )

    jac[jf19, jhe4] = (
       -rho*Y[jf19]*rate_eval.He4_F19__p_Ne22
       -rho*Y[jf19]*rate_eval.He4_F19__Na23
       +rho*Y[jn15]*rate_eval.He4_N15__F19
       +rho*Y[jn16]*rate_eval.He4_N16__n_F19
       )

    jac[jf19, jn15] = (
       +rho*Y[jhe4]*rate_eval.He4_N15__F19
       )

    jac[jf19, jn16] = (
       +rho*Y[jhe4]*rate_eval.He4_N16__n_F19
       )

    jac[jf19, jo18] = (
       +rho*Y[jp]*rate_eval.p_O18__F19
       )

    jac[jf19, jo19] = (
       +rho*Y[jp]*rate_eval.p_O19__n_F19
       +rate_eval.O19__F19__weak__wc12
       )

    jac[jf19, jf18] = (
       +rho*Y[jn]*rate_eval.n_F18__F19
       )

    jac[jf19, jf19] = (
       -rho*Y[jhe4]*rate_eval.He4_F19__p_Ne22
       -rho*Y[jp]*rate_eval.p_F19__n_Ne19
       -rho*Y[jp]*rate_eval.p_F19__He4_O16
       -rho*Y[jp]*rate_eval.p_F19__Ne20
       -rho*Y[jn]*rate_eval.n_F19__F20
       -rho*Y[jhe4]*rate_eval.He4_F19__Na23
       )

    jac[jf19, jne19] = (
       +rate_eval.Ne19__F19__weak__wc12
       )

    jac[jf19, jna22] = (
       +rho*Y[jn]*rate_eval.n_Na22__He4_F19
       )

    jac[jf20, jn] = (
       -rho*Y[jf20]*rate_eval.n_F20__F21
       +rho*Y[jf19]*rate_eval.n_F19__F20
       )

    jac[jf20, jp] = (
       -rho*Y[jf20]*rate_eval.p_F20__He4_O17
       -rho*Y[jf20]*rate_eval.p_F20__n_Ne20
       -rho*Y[jf20]*rate_eval.p_F20__Ne21
       +rho*Y[jo20]*rate_eval.p_O20__n_F20
       +rho*Y[jo19]*rate_eval.p_O19__F20
       )

    jac[jf20, jhe4] = (
       -rho*Y[jf20]*rate_eval.He4_F20__n_Na23
       -rho*Y[jf20]*rate_eval.He4_F20__p_Ne23
       -rho*Y[jf20]*rate_eval.He4_F20__Na24
       )

    jac[jf20, jo19] = (
       +rho*Y[jp]*rate_eval.p_O19__F20
       )

    jac[jf20, jo20] = (
       +rho*Y[jp]*rate_eval.p_O20__n_F20
       +rate_eval.O20__F20__weak__wc12
       )

    jac[jf20, jf19] = (
       +rho*Y[jn]*rate_eval.n_F19__F20
       )

    jac[jf20, jf20] = (
       -rho*Y[jhe4]*rate_eval.He4_F20__n_Na23
       -rho*Y[jhe4]*rate_eval.He4_F20__p_Ne23
       -rho*Y[jp]*rate_eval.p_F20__He4_O17
       -rho*Y[jp]*rate_eval.p_F20__n_Ne20
       -rho*Y[jp]*rate_eval.p_F20__Ne21
       -rho*Y[jn]*rate_eval.n_F20__F21
       -rho*Y[jhe4]*rate_eval.He4_F20__Na24
       -rate_eval.F20__Ne20__weak__wc12
       )

    jac[jf21, jn] = (
       -rho*Y[jf21]*rate_eval.n_F21__F22
       +rho*Y[jf20]*rate_eval.n_F20__F21
       )

    jac[jf21, jp] = (
       -rho*Y[jf21]*rate_eval.p_F21__n_Ne21
       -rho*Y[jf21]*rate_eval.p_F21__Ne22
       -rho*Y[jf21]*rate_eval.p_F21__He4_O18
       +rho*Y[jo21]*rate_eval.p_O21__n_F21
       +rho*Y[jo20]*rate_eval.p_O20__F21
       )

    jac[jf21, jhe4] = (
       -rho*Y[jf21]*rate_eval.He4_F21__p_Ne24
       -rho*Y[jf21]*rate_eval.He4_F21__n_Na24
       -rho*Y[jf21]*rate_eval.He4_F21__Na25
       )

    jac[jf21, jo20] = (
       +rho*Y[jp]*rate_eval.p_O20__F21
       )

    jac[jf21, jo21] = (
       +rho*Y[jp]*rate_eval.p_O21__n_F21
       +rate_eval.O21__F21__weak__wc12
       )

    jac[jf21, jf20] = (
       +rho*Y[jn]*rate_eval.n_F20__F21
       )

    jac[jf21, jf21] = (
       -rho*Y[jhe4]*rate_eval.He4_F21__p_Ne24
       -rho*Y[jhe4]*rate_eval.He4_F21__n_Na24
       -rho*Y[jp]*rate_eval.p_F21__n_Ne21
       -rho*Y[jp]*rate_eval.p_F21__Ne22
       -rho*Y[jn]*rate_eval.n_F21__F22
       -rho*Y[jp]*rate_eval.p_F21__He4_O18
       -rho*Y[jhe4]*rate_eval.He4_F21__Na25
       -rate_eval.F21__Ne21__weak__wc12
       )

    jac[jf22, jn] = (
       -rho*Y[jf22]*rate_eval.n_F22__F23
       +rho*Y[jf21]*rate_eval.n_F21__F22
       )

    jac[jf22, jp] = (
       -rho*Y[jf22]*rate_eval.p_F22__He4_O19
       -rho*Y[jf22]*rate_eval.p_F22__n_Ne22
       -rho*Y[jf22]*rate_eval.p_F22__Ne23
       +rho*Y[jo22]*rate_eval.p_O22__n_F22
       +rho*Y[jne25]*rate_eval.p_Ne25__He4_F22
       +rho*Y[jo21]*rate_eval.p_O21__F22
       )

    jac[jf22, jhe4] = (
       -rho*Y[jf22]*rate_eval.He4_F22__Na26
       -rho*Y[jf22]*rate_eval.He4_F22__n_Na25
       )

    jac[jf22, jo21] = (
       +rho*Y[jp]*rate_eval.p_O21__F22
       )

    jac[jf22, jo22] = (
       +rho*Y[jp]*rate_eval.p_O22__n_F22
       +rate_eval.O22__F22__weak__wc17
       )

    jac[jf22, jo23] = (
       +rate_eval.O23__n_F22__weak__wc12
       )

    jac[jf22, jf21] = (
       +rho*Y[jn]*rate_eval.n_F21__F22
       )

    jac[jf22, jf22] = (
       -rho*Y[jp]*rate_eval.p_F22__He4_O19
       -rho*Y[jp]*rate_eval.p_F22__n_Ne22
       -rho*Y[jp]*rate_eval.p_F22__Ne23
       -rho*Y[jn]*rate_eval.n_F22__F23
       -rate_eval.F22__Ne22__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_F22__Na26
       -rho*Y[jhe4]*rate_eval.He4_F22__n_Na25
       )

    jac[jf22, jne25] = (
       +rho*Y[jp]*rate_eval.p_Ne25__He4_F22
       )

    jac[jf23, jn] = (
       -rho*Y[jf23]*rate_eval.n_F23__F24
       +rho*Y[jf22]*rate_eval.n_F22__F23
       )

    jac[jf23, jp] = (
       -rho*Y[jf23]*rate_eval.p_F23__Ne24
       -rho*Y[jf23]*rate_eval.p_F23__He4_O20
       -rho*Y[jf23]*rate_eval.p_F23__n_Ne23
       +rho*Y[jne26]*rate_eval.p_Ne26__He4_F23
       +rho*Y[jo22]*rate_eval.p_O22__F23
       +rho*Y[jo23]*rate_eval.p_O23__n_F23
       )

    jac[jf23, jhe4] = (
       -rho*Y[jf23]*rate_eval.He4_F23__Na27
       -rho*Y[jf23]*rate_eval.He4_F23__n_Na26
       )

    jac[jf23, jo22] = (
       +rho*Y[jp]*rate_eval.p_O22__F23
       )

    jac[jf23, jo23] = (
       +rho*Y[jp]*rate_eval.p_O23__n_F23
       +rate_eval.O23__F23__weak__wc12
       )

    jac[jf23, jo24] = (
       +rate_eval.O24__n_F23__weak__wc12
       )

    jac[jf23, jo25] = (
       +rate_eval.O25__n_n_F23__weak__mp17
       )

    jac[jf23, jo26] = (
       +rate_eval.O26__n_n_n_F23__weak__mo03
       )

    jac[jf23, jf22] = (
       +rho*Y[jn]*rate_eval.n_F22__F23
       )

    jac[jf23, jf23] = (
       -rho*Y[jp]*rate_eval.p_F23__Ne24
       -rho*Y[jp]*rate_eval.p_F23__He4_O20
       -rate_eval.F23__Ne23__weak__wc12
       -rho*Y[jn]*rate_eval.n_F23__F24
       -rho*Y[jhe4]*rate_eval.He4_F23__Na27
       -rho*Y[jp]*rate_eval.p_F23__n_Ne23
       -rho*Y[jhe4]*rate_eval.He4_F23__n_Na26
       )

    jac[jf23, jne26] = (
       +rho*Y[jp]*rate_eval.p_Ne26__He4_F23
       )

    jac[jf24, jn] = (
       -rho*Y[jf24]*rate_eval.n_F24__F25
       +rho*Y[jf23]*rate_eval.n_F23__F24
       )

    jac[jf24, jp] = (
       -rho*Y[jf24]*rate_eval.p_F24__Ne25
       -rho*Y[jf24]*rate_eval.p_F24__n_Ne24
       -rho*Y[jf24]*rate_eval.p_F24__He4_O21
       +rho*Y[jne27]*rate_eval.p_Ne27__He4_F24
       +rho*Y[jo24]*rate_eval.p_O24__n_F24
       +rho*Y[jo23]*rate_eval.p_O23__F24
       )

    jac[jf24, jhe4] = (
       -rho*Y[jf24]*rate_eval.He4_F24__n_Na27
       -rho*Y[jf24]*rate_eval.He4_F24__Na28
       )

    jac[jf24, jo23] = (
       +rho*Y[jp]*rate_eval.p_O23__F24
       )

    jac[jf24, jo24] = (
       +rate_eval.O24__F24__weak__wc12
       +rho*Y[jp]*rate_eval.p_O24__n_F24
       )

    jac[jf24, jo25] = (
       +rate_eval.O25__n_F24__weak__mp17
       )

    jac[jf24, jo26] = (
       +rate_eval.O26__n_n_F24__weak__mp17
       )

    jac[jf24, jo27] = (
       +rate_eval.O27__n_n_n_F24__weak__mo03
       )

    jac[jf24, jf23] = (
       +rho*Y[jn]*rate_eval.n_F23__F24
       )

    jac[jf24, jf24] = (
       -rho*Y[jp]*rate_eval.p_F24__Ne25
       -rho*Y[jhe4]*rate_eval.He4_F24__n_Na27
       -rho*Y[jp]*rate_eval.p_F24__n_Ne24
       -rho*Y[jp]*rate_eval.p_F24__He4_O21
       -rate_eval.F24__Ne24__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_F24__Na28
       -rate_eval.F24__n_Ne23__weak__wc12
       -rho*Y[jn]*rate_eval.n_F24__F25
       )

    jac[jf24, jne27] = (
       +rho*Y[jp]*rate_eval.p_Ne27__He4_F24
       )

    jac[jf25, jn] = (
       -rho*Y[jf25]*rate_eval.n_F25__F26
       +rho*Y[jf24]*rate_eval.n_F24__F25
       )

    jac[jf25, jp] = (
       -rho*Y[jf25]*rate_eval.p_F25__He4_O22
       -rho*Y[jf25]*rate_eval.p_F25__n_Ne25
       -rho*Y[jf25]*rate_eval.p_F25__Ne26
       +rho*Y[jo25]*rate_eval.p_O25__n_F25
       +rho*Y[jne28]*rate_eval.p_Ne28__He4_F25
       +rho*Y[jo24]*rate_eval.p_O24__F25
       )

    jac[jf25, jhe4] = (
       -rho*Y[jf25]*rate_eval.He4_F25__n_Na28
       -rho*Y[jf25]*rate_eval.He4_F25__Na29
       )

    jac[jf25, jo24] = (
       +rho*Y[jp]*rate_eval.p_O24__F25
       )

    jac[jf25, jo25] = (
       +rho*Y[jp]*rate_eval.p_O25__n_F25
       +rate_eval.O25__F25__weak__mo03
       )

    jac[jf25, jo26] = (
       +rate_eval.O26__n_F25__weak__mp17
       )

    jac[jf25, jo27] = (
       +rate_eval.O27__n_n_F25__weak__mp17
       )

    jac[jf25, jo28] = (
       +rate_eval.O28__n_n_n_F25__weak__mo03
       )

    jac[jf25, jf24] = (
       +rho*Y[jn]*rate_eval.n_F24__F25
       )

    jac[jf25, jf25] = (
       -rho*Y[jn]*rate_eval.n_F25__F26
       -rho*Y[jp]*rate_eval.p_F25__He4_O22
       -rho*Y[jp]*rate_eval.p_F25__n_Ne25
       -rho*Y[jhe4]*rate_eval.He4_F25__n_Na28
       -rate_eval.F25__Ne25__weak__wc12
       -rho*Y[jp]*rate_eval.p_F25__Ne26
       -rho*Y[jhe4]*rate_eval.He4_F25__Na29
       -rate_eval.F25__n_Ne24__weak__wc12
       )

    jac[jf25, jne28] = (
       +rho*Y[jp]*rate_eval.p_Ne28__He4_F25
       )

    jac[jf26, jn] = (
       -rho*Y[jf26]*rate_eval.n_F26__F27
       +rho*Y[jf25]*rate_eval.n_F25__F26
       )

    jac[jf26, jp] = (
       -rho*Y[jf26]*rate_eval.p_F26__n_Ne26
       -rho*Y[jf26]*rate_eval.p_F26__Ne27
       -rho*Y[jf26]*rate_eval.p_F26__He4_O23
       +rho*Y[jne29]*rate_eval.p_Ne29__He4_F26
       +rho*Y[jo26]*rate_eval.p_O26__n_F26
       +rho*Y[jo25]*rate_eval.p_O25__F26
       )

    jac[jf26, jhe4] = (
       -rho*Y[jf26]*rate_eval.He4_F26__Na30
       -rho*Y[jf26]*rate_eval.He4_F26__n_Na29
       )

    jac[jf26, jo25] = (
       +rho*Y[jp]*rate_eval.p_O25__F26
       )

    jac[jf26, jo26] = (
       +rho*Y[jp]*rate_eval.p_O26__n_F26
       +rate_eval.O26__F26__weak__mo03
       )

    jac[jf26, jo27] = (
       +rate_eval.O27__n_F26__weak__mp17
       )

    jac[jf26, jo28] = (
       +rate_eval.O28__n_n_F26__weak__mp17
       )

    jac[jf26, jf25] = (
       +rho*Y[jn]*rate_eval.n_F25__F26
       )

    jac[jf26, jf26] = (
       -rho*Y[jn]*rate_eval.n_F26__F27
       -rho*Y[jhe4]*rate_eval.He4_F26__Na30
       -rho*Y[jhe4]*rate_eval.He4_F26__n_Na29
       -rho*Y[jp]*rate_eval.p_F26__n_Ne26
       -rho*Y[jp]*rate_eval.p_F26__Ne27
       -rate_eval.F26__n_Ne25__weak__wc12
       -rho*Y[jp]*rate_eval.p_F26__He4_O23
       -rate_eval.F26__Ne26__weak__wc12
       )

    jac[jf26, jne29] = (
       +rho*Y[jp]*rate_eval.p_Ne29__He4_F26
       )

    jac[jf27, jn] = (
       -rho*Y[jf27]*rate_eval.n_F27__F28
       +rho*Y[jf26]*rate_eval.n_F26__F27
       )

    jac[jf27, jp] = (
       -rho*Y[jf27]*rate_eval.p_F27__He4_O24
       -rho*Y[jf27]*rate_eval.p_F27__n_Ne27
       -rho*Y[jf27]*rate_eval.p_F27__Ne28
       +rho*Y[jne30]*rate_eval.p_Ne30__He4_F27
       +rho*Y[jo26]*rate_eval.p_O26__F27
       +rho*Y[jo27]*rate_eval.p_O27__n_F27
       )

    jac[jf27, jhe4] = (
       -rho*Y[jf27]*rate_eval.He4_F27__n_Na30
       -rho*Y[jf27]*rate_eval.He4_F27__Na31
       )

    jac[jf27, jo26] = (
       +rho*Y[jp]*rate_eval.p_O26__F27
       )

    jac[jf27, jo27] = (
       +rate_eval.O27__F27__weak__mo03
       +rho*Y[jp]*rate_eval.p_O27__n_F27
       )

    jac[jf27, jo28] = (
       +rate_eval.O28__n_F27__weak__mp17
       )

    jac[jf27, jf26] = (
       +rho*Y[jn]*rate_eval.n_F26__F27
       )

    jac[jf27, jf27] = (
       -rate_eval.F27__n_n_n_Ne24__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_F27__n_Na30
       -rho*Y[jp]*rate_eval.p_F27__He4_O24
       -rho*Y[jp]*rate_eval.p_F27__n_Ne27
       -rate_eval.F27__n_n_Ne25__weak__mp17
       -rho*Y[jp]*rate_eval.p_F27__Ne28
       -rho*Y[jhe4]*rate_eval.He4_F27__Na31
       -rate_eval.F27__n_Ne26__weak__wc12
       -rho*Y[jn]*rate_eval.n_F27__F28
       -rate_eval.F27__Ne27__weak__wc17
       )

    jac[jf27, jne30] = (
       +rho*Y[jp]*rate_eval.p_Ne30__He4_F27
       )

    jac[jf28, jn] = (
       +rho*Y[jf27]*rate_eval.n_F27__F28
       )

    jac[jf28, jp] = (
       -rho*Y[jf28]*rate_eval.p_F28__n_Ne28
       -rho*Y[jf28]*rate_eval.p_F28__He4_O25
       -rho*Y[jf28]*rate_eval.p_F28__Ne29
       +rho*Y[jne31]*rate_eval.p_Ne31__He4_F28
       +rho*Y[jo27]*rate_eval.p_O27__F28
       )

    jac[jf28, jhe4] = (
       -rho*Y[jf28]*rate_eval.He4_F28__n_Na31
       -rho*Y[jf28]*rate_eval.He4_F28__Na32
       )

    jac[jf28, jo27] = (
       +rho*Y[jp]*rate_eval.p_O27__F28
       )

    jac[jf28, jf27] = (
       +rho*Y[jn]*rate_eval.n_F27__F28
       )

    jac[jf28, jf28] = (
       -rate_eval.F28__n_n_n_Ne25__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_F28__n_Na31
       -rho*Y[jp]*rate_eval.p_F28__n_Ne28
       -rho*Y[jp]*rate_eval.p_F28__He4_O25
       -rho*Y[jhe4]*rate_eval.He4_F28__Na32
       -rho*Y[jp]*rate_eval.p_F28__Ne29
       -rate_eval.F28__n_n_Ne26__weak__mp17
       -rate_eval.F28__Ne28__weak__mo03
       -rate_eval.F28__n_Ne27__weak__mp17
       )

    jac[jf28, jne31] = (
       +rho*Y[jp]*rate_eval.p_Ne31__He4_F28
       )

    jac[jf29, jp] = (
       -rho*Y[jf29]*rate_eval.p_F29__He4_O26
       -rho*Y[jf29]*rate_eval.p_F29__Ne30
       -rho*Y[jf29]*rate_eval.p_F29__n_Ne29
       +rho*Y[jne32]*rate_eval.p_Ne32__He4_F29
       )

    jac[jf29, jhe4] = (
       -rho*Y[jf29]*rate_eval.He4_F29__n_Na32
       -rho*Y[jf29]*rate_eval.He4_F29__Na33
       )

    jac[jf29, jf29] = (
       -rate_eval.F29__n_n_n_Ne26__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_F29__n_Na32
       -rho*Y[jp]*rate_eval.p_F29__He4_O26
       -rho*Y[jp]*rate_eval.p_F29__Ne30
       -rate_eval.F29__Ne29__weak__wc17
       -rho*Y[jp]*rate_eval.p_F29__n_Ne29
       -rho*Y[jhe4]*rate_eval.He4_F29__Na33
       -rate_eval.F29__n_Ne28__weak__wc12
       )

    jac[jf29, jne32] = (
       +rho*Y[jp]*rate_eval.p_Ne32__He4_F29
       )

    jac[jf30, jp] = (
       -rho*Y[jf30]*rate_eval.p_F30__He4_O27
       -rho*Y[jf30]*rate_eval.p_F30__n_Ne30
       -rho*Y[jf30]*rate_eval.p_F30__Ne31
       )

    jac[jf30, jhe4] = (
       -rho*Y[jf30]*rate_eval.He4_F30__p_Ne33
       -rho*Y[jf30]*rate_eval.He4_F30__n_Na33
       -rho*Y[jf30]*rate_eval.He4_F30__Na34
       )

    jac[jf30, jf30] = (
       -rho*Y[jhe4]*rate_eval.He4_F30__p_Ne33
       -rho*Y[jp]*rate_eval.p_F30__He4_O27
       -rho*Y[jhe4]*rate_eval.He4_F30__n_Na33
       -rate_eval.F30__n_n_Ne28__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_F30__Na34
       -rate_eval.F30__n_Ne29__weak__mp17
       -rho*Y[jp]*rate_eval.p_F30__n_Ne30
       -rate_eval.F30__Ne30__weak__mo03
       -rate_eval.F30__n_n_n_Ne27__weak__mo03
       -rho*Y[jp]*rate_eval.p_F30__Ne31
       )

    jac[jf31, jp] = (
       -rho*Y[jf31]*rate_eval.p_F31__He4_O28
       -rho*Y[jf31]*rate_eval.p_F31__n_Ne31
       -rho*Y[jf31]*rate_eval.p_F31__Ne32
       +rho*Y[jne34]*rate_eval.p_Ne34__He4_F31
       )

    jac[jf31, jhe4] = (
       -rho*Y[jf31]*rate_eval.He4_F31__n_Na34
       -rho*Y[jf31]*rate_eval.He4_F31__Na35
       )

    jac[jf31, jf31] = (
       -rate_eval.F31__n_n_n_Ne28__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_F31__n_Na34
       -rho*Y[jp]*rate_eval.p_F31__He4_O28
       -rate_eval.F31__n_n_Ne29__weak__mp17
       -rho*Y[jp]*rate_eval.p_F31__n_Ne31
       -rate_eval.F31__Ne31__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_F31__Na35
       -rate_eval.F31__n_Ne30__weak__mp17
       -rho*Y[jp]*rate_eval.p_F31__Ne32
       )

    jac[jf31, jne34] = (
       +rho*Y[jp]*rate_eval.p_Ne34__He4_F31
       )

    jac[jne16, jn] = (
       -rho*Y[jne16]*rate_eval.n_Ne16__p_F16
       -rho*Y[jne16]*rate_eval.n_Ne16__He4_O13
       -rho*Y[jne16]*rate_eval.n_Ne16__Ne17
       +rho*Y[jmg19]*rate_eval.n_Mg19__He4_Ne16
       )

    jac[jne16, jhe4] = (
       -rho*Y[jne16]*rate_eval.He4_Ne16__p_Na19
       -rho*Y[jne16]*rate_eval.He4_Ne16__Mg20
       )

    jac[jne16, jne16] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne16__p_Na19
       -rho*Y[jn]*rate_eval.n_Ne16__p_F16
       -rho*Y[jn]*rate_eval.n_Ne16__He4_O13
       -rho*Y[jhe4]*rate_eval.He4_Ne16__Mg20
       -rho*Y[jn]*rate_eval.n_Ne16__Ne17
       )

    jac[jne16, jmg19] = (
       +rho*Y[jn]*rate_eval.n_Mg19__He4_Ne16
       )

    jac[jne17, jn] = (
       -rho*Y[jne17]*rate_eval.n_Ne17__He4_O14
       -rho*Y[jne17]*rate_eval.n_Ne17__Ne18
       -rho*Y[jne17]*rate_eval.n_Ne17__p_F17
       +rho*Y[jne16]*rate_eval.n_Ne16__Ne17
       +rho*Y[jmg20]*rate_eval.n_Mg20__He4_Ne17
       )

    jac[jne17, jhe4] = (
       -rho*Y[jne17]*rate_eval.He4_Ne17__p_Na20
       -rho*Y[jne17]*rate_eval.He4_Ne17__Mg21
       )

    jac[jne17, jne16] = (
       +rho*Y[jn]*rate_eval.n_Ne16__Ne17
       )

    jac[jne17, jne17] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne17__p_Na20
       -rho*Y[jhe4]*rate_eval.He4_Ne17__Mg21
       -rho*Y[jn]*rate_eval.n_Ne17__He4_O14
       -rate_eval.Ne17__p_O16__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ne17__Ne18
       -rate_eval.Ne17__F17__weak__wc17
       -rho*Y[jn]*rate_eval.n_Ne17__p_F17
       )

    jac[jne17, jmg20] = (
       +rho*Y[jn]*rate_eval.n_Mg20__He4_Ne17
       )

    jac[jne18, jn] = (
       -rho*Y[jne18]*rate_eval.n_Ne18__He4_O15
       -rho*Y[jne18]*rate_eval.n_Ne18__p_F18
       -rho*Y[jne18]*rate_eval.n_Ne18__Ne19
       +rho*Y[jmg21]*rate_eval.n_Mg21__He4_Ne18
       +rho*Y[jne17]*rate_eval.n_Ne17__Ne18
       )

    jac[jne18, jp] = (
       -rho*Y[jne18]*rate_eval.p_Ne18__Na19
       +rho*Y[jf17]*rate_eval.p_F17__Ne18
       )

    jac[jne18, jhe4] = (
       -rho*Y[jne18]*rate_eval.He4_Ne18__p_Na21
       -rho*Y[jne18]*rate_eval.He4_Ne18__Mg22
       +rho*Y[jf15]*rate_eval.He4_F15__p_Ne18
       +rho*Y[jo14]*rate_eval.He4_O14__Ne18
       )

    jac[jne18, jo14] = (
       +rho*Y[jhe4]*rate_eval.He4_O14__Ne18
       )

    jac[jne18, jf15] = (
       +rho*Y[jhe4]*rate_eval.He4_F15__p_Ne18
       )

    jac[jne18, jf17] = (
       +rho*Y[jp]*rate_eval.p_F17__Ne18
       )

    jac[jne18, jne17] = (
       +rho*Y[jn]*rate_eval.n_Ne17__Ne18
       )

    jac[jne18, jne18] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne18__p_Na21
       -rho*Y[jn]*rate_eval.n_Ne18__He4_O15
       -rho*Y[jn]*rate_eval.n_Ne18__p_F18
       -rho*Y[jhe4]*rate_eval.He4_Ne18__Mg22
       -rho*Y[jp]*rate_eval.p_Ne18__Na19
       -rho*Y[jn]*rate_eval.n_Ne18__Ne19
       -rate_eval.Ne18__F18__weak__wc12
       )

    jac[jne18, jmg21] = (
       +rho*Y[jn]*rate_eval.n_Mg21__He4_Ne18
       )

    jac[jne18, jal22] = (
       +rate_eval.Al22__He4_Ne18__weak__wc12
       )

    jac[jne19, jn] = (
       -rho*Y[jne19]*rate_eval.n_Ne19__He4_O16
       -rho*Y[jne19]*rate_eval.n_Ne19__Ne20
       +rho*Y[jmg22]*rate_eval.n_Mg22__He4_Ne19
       +rho*Y[jna19]*rate_eval.n_Na19__p_Ne19
       +rho*Y[jne18]*rate_eval.n_Ne18__Ne19
       )

    jac[jne19, jp] = (
       -rho*Y[jne19]*rate_eval.p_Ne19__Na20
       +rho*Y[jf19]*rate_eval.p_F19__n_Ne19
       +rho*Y[jf18]*rate_eval.p_F18__Ne19
       )

    jac[jne19, jhe4] = (
       -rho*Y[jne19]*rate_eval.He4_Ne19__p_Na22
       -rho*Y[jne19]*rate_eval.He4_Ne19__Mg23
       +rho*Y[jf16]*rate_eval.He4_F16__p_Ne19
       +rho*Y[jo15]*rate_eval.He4_O15__Ne19
       )

    jac[jne19, jo15] = (
       +rho*Y[jhe4]*rate_eval.He4_O15__Ne19
       )

    jac[jne19, jf16] = (
       +rho*Y[jhe4]*rate_eval.He4_F16__p_Ne19
       )

    jac[jne19, jf18] = (
       +rho*Y[jp]*rate_eval.p_F18__Ne19
       )

    jac[jne19, jf19] = (
       +rho*Y[jp]*rate_eval.p_F19__n_Ne19
       )

    jac[jne19, jne18] = (
       +rho*Y[jn]*rate_eval.n_Ne18__Ne19
       )

    jac[jne19, jne19] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne19__p_Na22
       -rho*Y[jn]*rate_eval.n_Ne19__He4_O16
       -rate_eval.Ne19__F19__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ne19__Na20
       -rho*Y[jn]*rate_eval.n_Ne19__Ne20
       -rho*Y[jhe4]*rate_eval.He4_Ne19__Mg23
       )

    jac[jne19, jna19] = (
       +rho*Y[jn]*rate_eval.n_Na19__p_Ne19
       +rate_eval.Na19__Ne19__weak__bqa_pos_
       )

    jac[jne19, jmg20] = (
       +rate_eval.Mg20__p_Ne19__weak__wc12
       )

    jac[jne19, jmg22] = (
       +rho*Y[jn]*rate_eval.n_Mg22__He4_Ne19
       )

    jac[jne20, jn] = (
       -rho*Y[jne20]*rate_eval.n_Ne20__Ne21
       +rho*Y[jmg23]*rate_eval.n_Mg23__He4_Ne20
       +rho*Y[jne19]*rate_eval.n_Ne19__Ne20
       +rho*Y[jna20]*rate_eval.n_Na20__p_Ne20
       )

    jac[jne20, jp] = (
       -rho*Y[jne20]*rate_eval.p_Ne20__He4_F17
       -rho*Y[jne20]*rate_eval.p_Ne20__Na21
       +rho*Y[jna23]*rate_eval.p_Na23__He4_Ne20
       +rho*Y[jf20]*rate_eval.p_F20__n_Ne20
       +rho*Y[jf19]*rate_eval.p_F19__Ne20
       )

    jac[jne20, jhe4] = (
       -rho*Y[jne20]*rate_eval.He4_Ne20__Mg24
       +rho*Y[jo17]*rate_eval.He4_O17__n_Ne20
       +rho*Y[jo16]*rate_eval.He4_O16__Ne20
       )

    jac[jne20, jc12] = (
       -rho*Y[jne20]*rate_eval.C12_Ne20__He4_Si28
       -rho*Y[jne20]*rate_eval.C12_Ne20__p_P31
       -rho*Y[jne20]*rate_eval.C12_Ne20__n_S31
       +5.00000000000000e-01*rho*2*Y[jc12]*rate_eval.C12_C12__He4_Ne20
       )

    jac[jne20, jo16] = (
       +rho*Y[jhe4]*rate_eval.He4_O16__Ne20
       )

    jac[jne20, jo17] = (
       +rho*Y[jhe4]*rate_eval.He4_O17__n_Ne20
       )

    jac[jne20, jf19] = (
       +rho*Y[jp]*rate_eval.p_F19__Ne20
       )

    jac[jne20, jf20] = (
       +rho*Y[jp]*rate_eval.p_F20__n_Ne20
       +rate_eval.F20__Ne20__weak__wc12
       )

    jac[jne20, jne19] = (
       +rho*Y[jn]*rate_eval.n_Ne19__Ne20
       )

    jac[jne20, jne20] = (
       -rho*Y[jn]*rate_eval.n_Ne20__Ne21
       -rho*Y[jc12]*rate_eval.C12_Ne20__He4_Si28
       -rho*Y[jc12]*rate_eval.C12_Ne20__p_P31
       -rho*Y[jp]*rate_eval.p_Ne20__He4_F17
       -rho*Y[jc12]*rate_eval.C12_Ne20__n_S31
       -rho*Y[jhe4]*rate_eval.He4_Ne20__Mg24
       -rho*Y[jp]*rate_eval.p_Ne20__Na21
       )

    jac[jne20, jna20] = (
       +rate_eval.Na20__Ne20__weak__wc12
       +rho*Y[jn]*rate_eval.n_Na20__p_Ne20
       )

    jac[jne20, jna23] = (
       +rho*Y[jp]*rate_eval.p_Na23__He4_Ne20
       )

    jac[jne20, jmg21] = (
       +rate_eval.Mg21__p_Ne20__weak__wc12
       )

    jac[jne20, jmg23] = (
       +rho*Y[jn]*rate_eval.n_Mg23__He4_Ne20
       )

    jac[jne20, jal22] = (
       +rate_eval.Al22__p_p_Ne20__weak__wc12
       )

    jac[jne20, jal24] = (
       +rate_eval.Al24__He4_Ne20__weak__wc12
       )

    jac[jne21, jn] = (
       -rho*Y[jne21]*rate_eval.n_Ne21__Ne22
       +rho*Y[jne20]*rate_eval.n_Ne20__Ne21
       +rho*Y[jna21]*rate_eval.n_Na21__p_Ne21
       )

    jac[jne21, jp] = (
       -rho*Y[jne21]*rate_eval.p_Ne21__Na22
       +rho*Y[jna24]*rate_eval.p_Na24__He4_Ne21
       +rho*Y[jf20]*rate_eval.p_F20__Ne21
       +rho*Y[jf21]*rate_eval.p_F21__n_Ne21
       )

    jac[jne21, jhe4] = (
       -rho*Y[jne21]*rate_eval.He4_Ne21__n_Mg24
       -rho*Y[jne21]*rate_eval.He4_Ne21__Mg25
       +rho*Y[jf18]*rate_eval.He4_F18__p_Ne21
       +rho*Y[jo17]*rate_eval.He4_O17__Ne21
       +rho*Y[jo18]*rate_eval.He4_O18__n_Ne21
       )

    jac[jne21, jo17] = (
       +rho*Y[jhe4]*rate_eval.He4_O17__Ne21
       )

    jac[jne21, jo18] = (
       +rho*Y[jhe4]*rate_eval.He4_O18__n_Ne21
       )

    jac[jne21, jf18] = (
       +rho*Y[jhe4]*rate_eval.He4_F18__p_Ne21
       )

    jac[jne21, jf20] = (
       +rho*Y[jp]*rate_eval.p_F20__Ne21
       )

    jac[jne21, jf21] = (
       +rho*Y[jp]*rate_eval.p_F21__n_Ne21
       +rate_eval.F21__Ne21__weak__wc12
       )

    jac[jne21, jne20] = (
       +rho*Y[jn]*rate_eval.n_Ne20__Ne21
       )

    jac[jne21, jne21] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne21__n_Mg24
       -rho*Y[jp]*rate_eval.p_Ne21__Na22
       -rho*Y[jn]*rate_eval.n_Ne21__Ne22
       -rho*Y[jhe4]*rate_eval.He4_Ne21__Mg25
       )

    jac[jne21, jna21] = (
       +rho*Y[jn]*rate_eval.n_Na21__p_Ne21
       +rate_eval.Na21__Ne21__weak__wc12
       )

    jac[jne21, jna24] = (
       +rho*Y[jp]*rate_eval.p_Na24__He4_Ne21
       )

    jac[jne22, jn] = (
       -rho*Y[jne22]*rate_eval.n_Ne22__Ne23
       +rho*Y[jna22]*rate_eval.n_Na22__p_Ne22
       +rho*Y[jne21]*rate_eval.n_Ne21__Ne22
       )

    jac[jne22, jp] = (
       -rho*Y[jne22]*rate_eval.p_Ne22__Na23
       +rho*Y[jf22]*rate_eval.p_F22__n_Ne22
       +rho*Y[jf21]*rate_eval.p_F21__Ne22
       +rho*Y[jna25]*rate_eval.p_Na25__He4_Ne22
       )

    jac[jne22, jhe4] = (
       -rho*Y[jne22]*rate_eval.He4_Ne22__n_Mg25
       -rho*Y[jne22]*rate_eval.He4_Ne22__Mg26
       +rho*Y[jf19]*rate_eval.He4_F19__p_Ne22
       +rho*Y[jo19]*rate_eval.He4_O19__n_Ne22
       +rho*Y[jo18]*rate_eval.He4_O18__Ne22
       )

    jac[jne22, jo18] = (
       +rho*Y[jhe4]*rate_eval.He4_O18__Ne22
       )

    jac[jne22, jo19] = (
       +rho*Y[jhe4]*rate_eval.He4_O19__n_Ne22
       )

    jac[jne22, jf19] = (
       +rho*Y[jhe4]*rate_eval.He4_F19__p_Ne22
       )

    jac[jne22, jf21] = (
       +rho*Y[jp]*rate_eval.p_F21__Ne22
       )

    jac[jne22, jf22] = (
       +rho*Y[jp]*rate_eval.p_F22__n_Ne22
       +rate_eval.F22__Ne22__weak__wc17
       )

    jac[jne22, jne21] = (
       +rho*Y[jn]*rate_eval.n_Ne21__Ne22
       )

    jac[jne22, jne22] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne22__n_Mg25
       -rho*Y[jp]*rate_eval.p_Ne22__Na23
       -rho*Y[jhe4]*rate_eval.He4_Ne22__Mg26
       -rho*Y[jn]*rate_eval.n_Ne22__Ne23
       )

    jac[jne22, jna22] = (
       +rho*Y[jn]*rate_eval.n_Na22__p_Ne22
       +rate_eval.Na22__Ne22__weak__wc12
       )

    jac[jne22, jna25] = (
       +rho*Y[jp]*rate_eval.p_Na25__He4_Ne22
       )

    jac[jne23, jn] = (
       -rho*Y[jne23]*rate_eval.n_Ne23__Ne24
       +rho*Y[jne22]*rate_eval.n_Ne22__Ne23
       )

    jac[jne23, jp] = (
       -rho*Y[jne23]*rate_eval.p_Ne23__n_Na23
       -rho*Y[jne23]*rate_eval.p_Ne23__Na24
       +rho*Y[jna26]*rate_eval.p_Na26__He4_Ne23
       +rho*Y[jf22]*rate_eval.p_F22__Ne23
       +rho*Y[jf23]*rate_eval.p_F23__n_Ne23
       )

    jac[jne23, jhe4] = (
       -rho*Y[jne23]*rate_eval.He4_Ne23__n_Mg26
       -rho*Y[jne23]*rate_eval.He4_Ne23__Mg27
       +rho*Y[jf20]*rate_eval.He4_F20__p_Ne23
       +rho*Y[jo20]*rate_eval.He4_O20__n_Ne23
       +rho*Y[jo19]*rate_eval.He4_O19__Ne23
       )

    jac[jne23, jo19] = (
       +rho*Y[jhe4]*rate_eval.He4_O19__Ne23
       )

    jac[jne23, jo20] = (
       +rho*Y[jhe4]*rate_eval.He4_O20__n_Ne23
       )

    jac[jne23, jf20] = (
       +rho*Y[jhe4]*rate_eval.He4_F20__p_Ne23
       )

    jac[jne23, jf22] = (
       +rho*Y[jp]*rate_eval.p_F22__Ne23
       )

    jac[jne23, jf23] = (
       +rate_eval.F23__Ne23__weak__wc12
       +rho*Y[jp]*rate_eval.p_F23__n_Ne23
       )

    jac[jne23, jf24] = (
       +rate_eval.F24__n_Ne23__weak__wc12
       )

    jac[jne23, jne22] = (
       +rho*Y[jn]*rate_eval.n_Ne22__Ne23
       )

    jac[jne23, jne23] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne23__n_Mg26
       -rho*Y[jp]*rate_eval.p_Ne23__n_Na23
       -rho*Y[jp]*rate_eval.p_Ne23__Na24
       -rho*Y[jn]*rate_eval.n_Ne23__Ne24
       -rho*Y[jhe4]*rate_eval.He4_Ne23__Mg27
       -rate_eval.Ne23__Na23__weak__wc12
       )

    jac[jne23, jna26] = (
       +rho*Y[jp]*rate_eval.p_Na26__He4_Ne23
       )

    jac[jne24, jn] = (
       -rho*Y[jne24]*rate_eval.n_Ne24__Ne25
       +rho*Y[jne23]*rate_eval.n_Ne23__Ne24
       )

    jac[jne24, jp] = (
       -rho*Y[jne24]*rate_eval.p_Ne24__n_Na24
       -rho*Y[jne24]*rate_eval.p_Ne24__Na25
       +rho*Y[jf23]*rate_eval.p_F23__Ne24
       +rho*Y[jf24]*rate_eval.p_F24__n_Ne24
       +rho*Y[jna27]*rate_eval.p_Na27__He4_Ne24
       )

    jac[jne24, jhe4] = (
       -rho*Y[jne24]*rate_eval.He4_Ne24__n_Mg27
       -rho*Y[jne24]*rate_eval.He4_Ne24__Mg28
       +rho*Y[jf21]*rate_eval.He4_F21__p_Ne24
       +rho*Y[jo21]*rate_eval.He4_O21__n_Ne24
       +rho*Y[jo20]*rate_eval.He4_O20__Ne24
       )

    jac[jne24, jo20] = (
       +rho*Y[jhe4]*rate_eval.He4_O20__Ne24
       )

    jac[jne24, jo21] = (
       +rho*Y[jhe4]*rate_eval.He4_O21__n_Ne24
       )

    jac[jne24, jf21] = (
       +rho*Y[jhe4]*rate_eval.He4_F21__p_Ne24
       )

    jac[jne24, jf23] = (
       +rho*Y[jp]*rate_eval.p_F23__Ne24
       )

    jac[jne24, jf24] = (
       +rho*Y[jp]*rate_eval.p_F24__n_Ne24
       +rate_eval.F24__Ne24__weak__wc12
       )

    jac[jne24, jf25] = (
       +rate_eval.F25__n_Ne24__weak__wc12
       )

    jac[jne24, jf27] = (
       +rate_eval.F27__n_n_n_Ne24__weak__mo03
       )

    jac[jne24, jne23] = (
       +rho*Y[jn]*rate_eval.n_Ne23__Ne24
       )

    jac[jne24, jne24] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne24__n_Mg27
       -rho*Y[jp]*rate_eval.p_Ne24__n_Na24
       -rate_eval.Ne24__Na24__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ne24__Mg28
       -rho*Y[jn]*rate_eval.n_Ne24__Ne25
       -rho*Y[jp]*rate_eval.p_Ne24__Na25
       )

    jac[jne24, jna27] = (
       +rho*Y[jp]*rate_eval.p_Na27__He4_Ne24
       )

    jac[jne25, jn] = (
       -rho*Y[jne25]*rate_eval.n_Ne25__Ne26
       +rho*Y[jne24]*rate_eval.n_Ne24__Ne25
       )

    jac[jne25, jp] = (
       -rho*Y[jne25]*rate_eval.p_Ne25__He4_F22
       -rho*Y[jne25]*rate_eval.p_Ne25__n_Na25
       -rho*Y[jne25]*rate_eval.p_Ne25__Na26
       +rho*Y[jf24]*rate_eval.p_F24__Ne25
       +rho*Y[jf25]*rate_eval.p_F25__n_Ne25
       +rho*Y[jna28]*rate_eval.p_Na28__He4_Ne25
       )

    jac[jne25, jhe4] = (
       -rho*Y[jne25]*rate_eval.He4_Ne25__Mg29
       -rho*Y[jne25]*rate_eval.He4_Ne25__n_Mg28
       +rho*Y[jo22]*rate_eval.He4_O22__n_Ne25
       +rho*Y[jo21]*rate_eval.He4_O21__Ne25
       )

    jac[jne25, jo21] = (
       +rho*Y[jhe4]*rate_eval.He4_O21__Ne25
       )

    jac[jne25, jo22] = (
       +rho*Y[jhe4]*rate_eval.He4_O22__n_Ne25
       )

    jac[jne25, jf24] = (
       +rho*Y[jp]*rate_eval.p_F24__Ne25
       )

    jac[jne25, jf25] = (
       +rho*Y[jp]*rate_eval.p_F25__n_Ne25
       +rate_eval.F25__Ne25__weak__wc12
       )

    jac[jne25, jf26] = (
       +rate_eval.F26__n_Ne25__weak__wc12
       )

    jac[jne25, jf27] = (
       +rate_eval.F27__n_n_Ne25__weak__mp17
       )

    jac[jne25, jf28] = (
       +rate_eval.F28__n_n_n_Ne25__weak__mo03
       )

    jac[jne25, jne24] = (
       +rho*Y[jn]*rate_eval.n_Ne24__Ne25
       )

    jac[jne25, jne25] = (
       -rho*Y[jp]*rate_eval.p_Ne25__He4_F22
       -rho*Y[jp]*rate_eval.p_Ne25__n_Na25
       -rho*Y[jhe4]*rate_eval.He4_Ne25__Mg29
       -rate_eval.Ne25__Na25__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ne25__Na26
       -rho*Y[jhe4]*rate_eval.He4_Ne25__n_Mg28
       -rho*Y[jn]*rate_eval.n_Ne25__Ne26
       )

    jac[jne25, jna28] = (
       +rho*Y[jp]*rate_eval.p_Na28__He4_Ne25
       )

    jac[jne26, jn] = (
       -rho*Y[jne26]*rate_eval.n_Ne26__Ne27
       +rho*Y[jne25]*rate_eval.n_Ne25__Ne26
       )

    jac[jne26, jp] = (
       -rho*Y[jne26]*rate_eval.p_Ne26__n_Na26
       -rho*Y[jne26]*rate_eval.p_Ne26__He4_F23
       -rho*Y[jne26]*rate_eval.p_Ne26__Na27
       +rho*Y[jna29]*rate_eval.p_Na29__He4_Ne26
       +rho*Y[jf26]*rate_eval.p_F26__n_Ne26
       +rho*Y[jf25]*rate_eval.p_F25__Ne26
       )

    jac[jne26, jhe4] = (
       -rho*Y[jne26]*rate_eval.He4_Ne26__n_Mg29
       -rho*Y[jne26]*rate_eval.He4_Ne26__Mg30
       +rho*Y[jo23]*rate_eval.He4_O23__n_Ne26
       +rho*Y[jo22]*rate_eval.He4_O22__Ne26
       )

    jac[jne26, jo22] = (
       +rho*Y[jhe4]*rate_eval.He4_O22__Ne26
       )

    jac[jne26, jo23] = (
       +rho*Y[jhe4]*rate_eval.He4_O23__n_Ne26
       )

    jac[jne26, jf25] = (
       +rho*Y[jp]*rate_eval.p_F25__Ne26
       )

    jac[jne26, jf26] = (
       +rho*Y[jp]*rate_eval.p_F26__n_Ne26
       +rate_eval.F26__Ne26__weak__wc12
       )

    jac[jne26, jf27] = (
       +rate_eval.F27__n_Ne26__weak__wc12
       )

    jac[jne26, jf28] = (
       +rate_eval.F28__n_n_Ne26__weak__mp17
       )

    jac[jne26, jf29] = (
       +rate_eval.F29__n_n_n_Ne26__weak__mo03
       )

    jac[jne26, jne25] = (
       +rho*Y[jn]*rate_eval.n_Ne25__Ne26
       )

    jac[jne26, jne26] = (
       -rate_eval.Ne26__n_Na25__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ne26__n_Na26
       -rho*Y[jp]*rate_eval.p_Ne26__He4_F23
       -rho*Y[jhe4]*rate_eval.He4_Ne26__n_Mg29
       -rho*Y[jp]*rate_eval.p_Ne26__Na27
       -rho*Y[jhe4]*rate_eval.He4_Ne26__Mg30
       -rho*Y[jn]*rate_eval.n_Ne26__Ne27
       -rate_eval.Ne26__Na26__weak__wc12
       )

    jac[jne26, jna29] = (
       +rho*Y[jp]*rate_eval.p_Na29__He4_Ne26
       )

    jac[jne26, jna30] = (
       +rate_eval.Na30__He4_Ne26__weak__wc12
       )

    jac[jne27, jn] = (
       -rho*Y[jne27]*rate_eval.n_Ne27__Ne28
       +rho*Y[jne26]*rate_eval.n_Ne26__Ne27
       )

    jac[jne27, jp] = (
       -rho*Y[jne27]*rate_eval.p_Ne27__He4_F24
       -rho*Y[jne27]*rate_eval.p_Ne27__n_Na27
       -rho*Y[jne27]*rate_eval.p_Ne27__Na28
       +rho*Y[jna30]*rate_eval.p_Na30__He4_Ne27
       +rho*Y[jf27]*rate_eval.p_F27__n_Ne27
       +rho*Y[jf26]*rate_eval.p_F26__Ne27
       )

    jac[jne27, jhe4] = (
       -rho*Y[jne27]*rate_eval.He4_Ne27__n_Mg30
       -rho*Y[jne27]*rate_eval.He4_Ne27__Mg31
       +rho*Y[jo24]*rate_eval.He4_O24__n_Ne27
       +rho*Y[jo23]*rate_eval.He4_O23__Ne27
       )

    jac[jne27, jo23] = (
       +rho*Y[jhe4]*rate_eval.He4_O23__Ne27
       )

    jac[jne27, jo24] = (
       +rho*Y[jhe4]*rate_eval.He4_O24__n_Ne27
       )

    jac[jne27, jf26] = (
       +rho*Y[jp]*rate_eval.p_F26__Ne27
       )

    jac[jne27, jf27] = (
       +rho*Y[jp]*rate_eval.p_F27__n_Ne27
       +rate_eval.F27__Ne27__weak__wc17
       )

    jac[jne27, jf28] = (
       +rate_eval.F28__n_Ne27__weak__mp17
       )

    jac[jne27, jf30] = (
       +rate_eval.F30__n_n_n_Ne27__weak__mo03
       )

    jac[jne27, jne26] = (
       +rho*Y[jn]*rate_eval.n_Ne26__Ne27
       )

    jac[jne27, jne27] = (
       -rho*Y[jp]*rate_eval.p_Ne27__He4_F24
       -rate_eval.Ne27__n_Na26__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ne27__n_Mg30
       -rho*Y[jp]*rate_eval.p_Ne27__n_Na27
       -rho*Y[jhe4]*rate_eval.He4_Ne27__Mg31
       -rho*Y[jp]*rate_eval.p_Ne27__Na28
       -rate_eval.Ne27__Na27__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ne27__Ne28
       )

    jac[jne27, jna30] = (
       +rho*Y[jp]*rate_eval.p_Na30__He4_Ne27
       )

    jac[jne28, jn] = (
       -rho*Y[jne28]*rate_eval.n_Ne28__Ne29
       +rho*Y[jne27]*rate_eval.n_Ne27__Ne28
       )

    jac[jne28, jp] = (
       -rho*Y[jne28]*rate_eval.p_Ne28__n_Na28
       -rho*Y[jne28]*rate_eval.p_Ne28__He4_F25
       -rho*Y[jne28]*rate_eval.p_Ne28__Na29
       +rho*Y[jf28]*rate_eval.p_F28__n_Ne28
       +rho*Y[jna31]*rate_eval.p_Na31__He4_Ne28
       +rho*Y[jf27]*rate_eval.p_F27__Ne28
       )

    jac[jne28, jhe4] = (
       -rho*Y[jne28]*rate_eval.He4_Ne28__n_Mg31
       -rho*Y[jne28]*rate_eval.He4_Ne28__Mg32
       +rho*Y[jo25]*rate_eval.He4_O25__n_Ne28
       +rho*Y[jo24]*rate_eval.He4_O24__Ne28
       )

    jac[jne28, jo24] = (
       +rho*Y[jhe4]*rate_eval.He4_O24__Ne28
       )

    jac[jne28, jo25] = (
       +rho*Y[jhe4]*rate_eval.He4_O25__n_Ne28
       )

    jac[jne28, jf27] = (
       +rho*Y[jp]*rate_eval.p_F27__Ne28
       )

    jac[jne28, jf28] = (
       +rho*Y[jp]*rate_eval.p_F28__n_Ne28
       +rate_eval.F28__Ne28__weak__mo03
       )

    jac[jne28, jf29] = (
       +rate_eval.F29__n_Ne28__weak__wc12
       )

    jac[jne28, jf30] = (
       +rate_eval.F30__n_n_Ne28__weak__mp17
       )

    jac[jne28, jf31] = (
       +rate_eval.F31__n_n_n_Ne28__weak__mo03
       )

    jac[jne28, jne27] = (
       +rho*Y[jn]*rate_eval.n_Ne27__Ne28
       )

    jac[jne28, jne28] = (
       -rate_eval.Ne28__Na28__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_Ne28__n_Mg31
       -rho*Y[jp]*rate_eval.p_Ne28__n_Na28
       -rho*Y[jp]*rate_eval.p_Ne28__He4_F25
       -rate_eval.Ne28__n_Na27__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ne28__Na29
       -rho*Y[jn]*rate_eval.n_Ne28__Ne29
       -rho*Y[jhe4]*rate_eval.He4_Ne28__Mg32
       )

    jac[jne28, jna31] = (
       +rho*Y[jp]*rate_eval.p_Na31__He4_Ne28
       )

    jac[jne29, jn] = (
       -rho*Y[jne29]*rate_eval.n_Ne29__Ne30
       +rho*Y[jne28]*rate_eval.n_Ne28__Ne29
       )

    jac[jne29, jp] = (
       -rho*Y[jne29]*rate_eval.p_Ne29__He4_F26
       -rho*Y[jne29]*rate_eval.p_Ne29__n_Na29
       -rho*Y[jne29]*rate_eval.p_Ne29__Na30
       +rho*Y[jf28]*rate_eval.p_F28__Ne29
       +rho*Y[jf29]*rate_eval.p_F29__n_Ne29
       +rho*Y[jna32]*rate_eval.p_Na32__He4_Ne29
       )

    jac[jne29, jhe4] = (
       -rho*Y[jne29]*rate_eval.He4_Ne29__Mg33
       -rho*Y[jne29]*rate_eval.He4_Ne29__n_Mg32
       +rho*Y[jo26]*rate_eval.He4_O26__n_Ne29
       +rho*Y[jo25]*rate_eval.He4_O25__Ne29
       )

    jac[jne29, jo25] = (
       +rho*Y[jhe4]*rate_eval.He4_O25__Ne29
       )

    jac[jne29, jo26] = (
       +rho*Y[jhe4]*rate_eval.He4_O26__n_Ne29
       )

    jac[jne29, jf28] = (
       +rho*Y[jp]*rate_eval.p_F28__Ne29
       )

    jac[jne29, jf29] = (
       +rate_eval.F29__Ne29__weak__wc17
       +rho*Y[jp]*rate_eval.p_F29__n_Ne29
       )

    jac[jne29, jf30] = (
       +rate_eval.F30__n_Ne29__weak__mp17
       )

    jac[jne29, jf31] = (
       +rate_eval.F31__n_n_Ne29__weak__mp17
       )

    jac[jne29, jne28] = (
       +rho*Y[jn]*rate_eval.n_Ne28__Ne29
       )

    jac[jne29, jne29] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne29__Mg33
       -rho*Y[jp]*rate_eval.p_Ne29__He4_F26
       -rho*Y[jp]*rate_eval.p_Ne29__n_Na29
       -rho*Y[jhe4]*rate_eval.He4_Ne29__n_Mg32
       -rate_eval.Ne29__n_n_Na27__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ne29__Ne30
       -rate_eval.Ne29__Na29__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ne29__Na30
       -rate_eval.Ne29__n_Na28__weak__wc17
       )

    jac[jne29, jna32] = (
       +rho*Y[jp]*rate_eval.p_Na32__He4_Ne29
       )

    jac[jne30, jn] = (
       -rho*Y[jne30]*rate_eval.n_Ne30__Ne31
       +rho*Y[jne29]*rate_eval.n_Ne29__Ne30
       )

    jac[jne30, jp] = (
       -rho*Y[jne30]*rate_eval.p_Ne30__He4_F27
       -rho*Y[jne30]*rate_eval.p_Ne30__Na31
       -rho*Y[jne30]*rate_eval.p_Ne30__n_Na30
       +rho*Y[jf29]*rate_eval.p_F29__Ne30
       +rho*Y[jna33]*rate_eval.p_Na33__He4_Ne30
       +rho*Y[jf30]*rate_eval.p_F30__n_Ne30
       )

    jac[jne30, jhe4] = (
       -rho*Y[jne30]*rate_eval.He4_Ne30__n_Mg33
       -rho*Y[jne30]*rate_eval.He4_Ne30__Mg34
       +rho*Y[jo27]*rate_eval.He4_O27__n_Ne30
       +rho*Y[jo26]*rate_eval.He4_O26__Ne30
       )

    jac[jne30, jo26] = (
       +rho*Y[jhe4]*rate_eval.He4_O26__Ne30
       )

    jac[jne30, jo27] = (
       +rho*Y[jhe4]*rate_eval.He4_O27__n_Ne30
       )

    jac[jne30, jf29] = (
       +rho*Y[jp]*rate_eval.p_F29__Ne30
       )

    jac[jne30, jf30] = (
       +rho*Y[jp]*rate_eval.p_F30__n_Ne30
       +rate_eval.F30__Ne30__weak__mo03
       )

    jac[jne30, jf31] = (
       +rate_eval.F31__n_Ne30__weak__mp17
       )

    jac[jne30, jne29] = (
       +rho*Y[jn]*rate_eval.n_Ne29__Ne30
       )

    jac[jne30, jne30] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne30__n_Mg33
       -rho*Y[jp]*rate_eval.p_Ne30__He4_F27
       -rho*Y[jn]*rate_eval.n_Ne30__Ne31
       -rho*Y[jhe4]*rate_eval.He4_Ne30__Mg34
       -rho*Y[jp]*rate_eval.p_Ne30__Na31
       -rho*Y[jp]*rate_eval.p_Ne30__n_Na30
       -rate_eval.Ne30__Na30__weak__wc17
       -rate_eval.Ne30__n_Na29__weak__wc12
       )

    jac[jne30, jna33] = (
       +rho*Y[jp]*rate_eval.p_Na33__He4_Ne30
       )

    jac[jne31, jn] = (
       -rho*Y[jne31]*rate_eval.n_Ne31__Ne32
       +rho*Y[jne30]*rate_eval.n_Ne30__Ne31
       )

    jac[jne31, jp] = (
       -rho*Y[jne31]*rate_eval.p_Ne31__He4_F28
       -rho*Y[jne31]*rate_eval.p_Ne31__Na32
       -rho*Y[jne31]*rate_eval.p_Ne31__n_Na31
       +rho*Y[jf31]*rate_eval.p_F31__n_Ne31
       +rho*Y[jna34]*rate_eval.p_Na34__He4_Ne31
       +rho*Y[jf30]*rate_eval.p_F30__Ne31
       )

    jac[jne31, jhe4] = (
       -rho*Y[jne31]*rate_eval.He4_Ne31__n_Mg34
       -rho*Y[jne31]*rate_eval.He4_Ne31__Mg35
       +rho*Y[jo28]*rate_eval.He4_O28__n_Ne31
       +rho*Y[jo27]*rate_eval.He4_O27__Ne31
       )

    jac[jne31, jo27] = (
       +rho*Y[jhe4]*rate_eval.He4_O27__Ne31
       )

    jac[jne31, jo28] = (
       +rho*Y[jhe4]*rate_eval.He4_O28__n_Ne31
       )

    jac[jne31, jf30] = (
       +rho*Y[jp]*rate_eval.p_F30__Ne31
       )

    jac[jne31, jf31] = (
       +rho*Y[jp]*rate_eval.p_F31__n_Ne31
       +rate_eval.F31__Ne31__weak__mo03
       )

    jac[jne31, jne30] = (
       +rho*Y[jn]*rate_eval.n_Ne30__Ne31
       )

    jac[jne31, jne31] = (
       -rate_eval.Ne31__n_n_n_Na28__weak__mo03
       -rate_eval.Ne31__n_Na30__weak__mp17
       -rho*Y[jp]*rate_eval.p_Ne31__He4_F28
       -rho*Y[jhe4]*rate_eval.He4_Ne31__n_Mg34
       -rate_eval.Ne31__Na31__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_Ne31__Mg35
       -rho*Y[jp]*rate_eval.p_Ne31__Na32
       -rho*Y[jn]*rate_eval.n_Ne31__Ne32
       -rho*Y[jp]*rate_eval.p_Ne31__n_Na31
       -rate_eval.Ne31__n_n_Na29__weak__mp17
       )

    jac[jne31, jna34] = (
       +rho*Y[jp]*rate_eval.p_Na34__He4_Ne31
       )

    jac[jne32, jn] = (
       -rho*Y[jne32]*rate_eval.n_Ne32__Ne33
       +rho*Y[jne31]*rate_eval.n_Ne31__Ne32
       )

    jac[jne32, jp] = (
       -rho*Y[jne32]*rate_eval.p_Ne32__Na33
       -rho*Y[jne32]*rate_eval.p_Ne32__n_Na32
       -rho*Y[jne32]*rate_eval.p_Ne32__He4_F29
       +rho*Y[jna35]*rate_eval.p_Na35__He4_Ne32
       +rho*Y[jf31]*rate_eval.p_F31__Ne32
       )

    jac[jne32, jhe4] = (
       -rho*Y[jne32]*rate_eval.He4_Ne32__n_Mg35
       -rho*Y[jne32]*rate_eval.He4_Ne32__Mg36
       +rho*Y[jo28]*rate_eval.He4_O28__Ne32
       )

    jac[jne32, jo28] = (
       +rho*Y[jhe4]*rate_eval.He4_O28__Ne32
       )

    jac[jne32, jf31] = (
       +rho*Y[jp]*rate_eval.p_F31__Ne32
       )

    jac[jne32, jne31] = (
       +rho*Y[jn]*rate_eval.n_Ne31__Ne32
       )

    jac[jne32, jne32] = (
       -rho*Y[jp]*rate_eval.p_Ne32__Na33
       -rho*Y[jp]*rate_eval.p_Ne32__n_Na32
       -rho*Y[jp]*rate_eval.p_Ne32__He4_F29
       -rho*Y[jhe4]*rate_eval.He4_Ne32__n_Mg35
       -rho*Y[jn]*rate_eval.n_Ne32__Ne33
       -rate_eval.Ne32__n_Na31__weak__mp17
       -rate_eval.Ne32__n_n_Na30__weak__mp17
       -rate_eval.Ne32__Na32__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_Ne32__Mg36
       -rate_eval.Ne32__n_n_n_Na29__weak__mo03
       )

    jac[jne32, jna35] = (
       +rho*Y[jp]*rate_eval.p_Na35__He4_Ne32
       )

    jac[jne33, jn] = (
       -rho*Y[jne33]*rate_eval.n_Ne33__Ne34
       +rho*Y[jne32]*rate_eval.n_Ne32__Ne33
       )

    jac[jne33, jp] = (
       -rho*Y[jne33]*rate_eval.p_Ne33__n_Na33
       -rho*Y[jne33]*rate_eval.p_Ne33__Na34
       +rho*Y[jna36]*rate_eval.p_Na36__He4_Ne33
       )

    jac[jne33, jhe4] = (
       -rho*Y[jne33]*rate_eval.He4_Ne33__n_Mg36
       -rho*Y[jne33]*rate_eval.He4_Ne33__Mg37
       +rho*Y[jf30]*rate_eval.He4_F30__p_Ne33
       )

    jac[jne33, jf30] = (
       +rho*Y[jhe4]*rate_eval.He4_F30__p_Ne33
       )

    jac[jne33, jne32] = (
       +rho*Y[jn]*rate_eval.n_Ne32__Ne33
       )

    jac[jne33, jne33] = (
       -rho*Y[jhe4]*rate_eval.He4_Ne33__n_Mg36
       -rho*Y[jp]*rate_eval.p_Ne33__n_Na33
       -rho*Y[jp]*rate_eval.p_Ne33__Na34
       -rate_eval.Ne33__n_n_n_Na30__weak__mo03
       -rate_eval.Ne33__n_Na32__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ne33__Mg37
       -rate_eval.Ne33__n_n_Na31__weak__mp17
       -rho*Y[jn]*rate_eval.n_Ne33__Ne34
       -rate_eval.Ne33__Na33__weak__mo03
       )

    jac[jne33, jna36] = (
       +rho*Y[jp]*rate_eval.p_Na36__He4_Ne33
       )

    jac[jne34, jn] = (
       +rho*Y[jne33]*rate_eval.n_Ne33__Ne34
       )

    jac[jne34, jp] = (
       -rho*Y[jne34]*rate_eval.p_Ne34__He4_F31
       -rho*Y[jne34]*rate_eval.p_Ne34__n_Na34
       -rho*Y[jne34]*rate_eval.p_Ne34__Na35
       +rho*Y[jna37]*rate_eval.p_Na37__He4_Ne34
       )

    jac[jne34, jhe4] = (
       -rho*Y[jne34]*rate_eval.He4_Ne34__Mg38
       -rho*Y[jne34]*rate_eval.He4_Ne34__n_Mg37
       )

    jac[jne34, jne33] = (
       +rho*Y[jn]*rate_eval.n_Ne33__Ne34
       )

    jac[jne34, jne34] = (
       -rate_eval.Ne34__n_n_n_Na31__weak__mo03
       -rho*Y[jp]*rate_eval.p_Ne34__He4_F31
       -rho*Y[jp]*rate_eval.p_Ne34__n_Na34
       -rate_eval.Ne34__Na34__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Ne34__Mg38
       -rho*Y[jp]*rate_eval.p_Ne34__Na35
       -rate_eval.Ne34__n_n_Na32__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ne34__n_Mg37
       -rate_eval.Ne34__n_Na33__weak__mp17
       )

    jac[jne34, jna37] = (
       +rho*Y[jp]*rate_eval.p_Na37__He4_Ne34
       )

    jac[jna19, jn] = (
       -rho*Y[jna19]*rate_eval.n_Na19__p_Ne19
       -rho*Y[jna19]*rate_eval.n_Na19__Na20
       -rho*Y[jna19]*rate_eval.n_Na19__He4_F16
       +rho*Y[jal22]*rate_eval.n_Al22__He4_Na19
       +rho*Y[jmg19]*rate_eval.n_Mg19__p_Na19
       )

    jac[jna19, jp] = (
       -rho*Y[jna19]*rate_eval.p_Na19__Mg20
       +rho*Y[jne18]*rate_eval.p_Ne18__Na19
       )

    jac[jna19, jhe4] = (
       -rho*Y[jna19]*rate_eval.He4_Na19__Al23
       -rho*Y[jna19]*rate_eval.He4_Na19__p_Mg22
       +rho*Y[jne16]*rate_eval.He4_Ne16__p_Na19
       +rho*Y[jf15]*rate_eval.He4_F15__Na19
       )

    jac[jna19, jf15] = (
       +rho*Y[jhe4]*rate_eval.He4_F15__Na19
       )

    jac[jna19, jne16] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne16__p_Na19
       )

    jac[jna19, jne18] = (
       +rho*Y[jp]*rate_eval.p_Ne18__Na19
       )

    jac[jna19, jna19] = (
       -rho*Y[jhe4]*rate_eval.He4_Na19__Al23
       -rho*Y[jn]*rate_eval.n_Na19__p_Ne19
       -rho*Y[jn]*rate_eval.n_Na19__Na20
       -rho*Y[jhe4]*rate_eval.He4_Na19__p_Mg22
       -rho*Y[jn]*rate_eval.n_Na19__He4_F16
       -rate_eval.Na19__Ne19__weak__bqa_pos_
       -rho*Y[jp]*rate_eval.p_Na19__Mg20
       )

    jac[jna19, jmg19] = (
       +rho*Y[jn]*rate_eval.n_Mg19__p_Na19
       )

    jac[jna19, jal22] = (
       +rho*Y[jn]*rate_eval.n_Al22__He4_Na19
       )

    jac[jna20, jn] = (
       -rho*Y[jna20]*rate_eval.n_Na20__He4_F17
       -rho*Y[jna20]*rate_eval.n_Na20__Na21
       -rho*Y[jna20]*rate_eval.n_Na20__p_Ne20
       +rho*Y[jal23]*rate_eval.n_Al23__He4_Na20
       +rho*Y[jmg20]*rate_eval.n_Mg20__p_Na20
       +rho*Y[jna19]*rate_eval.n_Na19__Na20
       )

    jac[jna20, jp] = (
       -rho*Y[jna20]*rate_eval.p_Na20__Mg21
       +rho*Y[jne19]*rate_eval.p_Ne19__Na20
       )

    jac[jna20, jhe4] = (
       -rho*Y[jna20]*rate_eval.He4_Na20__Al24
       -rho*Y[jna20]*rate_eval.He4_Na20__p_Mg23
       +rho*Y[jf16]*rate_eval.He4_F16__Na20
       +rho*Y[jne17]*rate_eval.He4_Ne17__p_Na20
       )

    jac[jna20, jf16] = (
       +rho*Y[jhe4]*rate_eval.He4_F16__Na20
       )

    jac[jna20, jne17] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne17__p_Na20
       )

    jac[jna20, jne19] = (
       +rho*Y[jp]*rate_eval.p_Ne19__Na20
       )

    jac[jna20, jna19] = (
       +rho*Y[jn]*rate_eval.n_Na19__Na20
       )

    jac[jna20, jna20] = (
       -rho*Y[jn]*rate_eval.n_Na20__He4_F17
       -rho*Y[jp]*rate_eval.p_Na20__Mg21
       -rate_eval.Na20__Ne20__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Na20__Al24
       -rho*Y[jn]*rate_eval.n_Na20__Na21
       -rho*Y[jhe4]*rate_eval.He4_Na20__p_Mg23
       -rate_eval.Na20__He4_O16__weak__wc12
       -rho*Y[jn]*rate_eval.n_Na20__p_Ne20
       )

    jac[jna20, jmg20] = (
       +rho*Y[jn]*rate_eval.n_Mg20__p_Na20
       +rate_eval.Mg20__Na20__weak__wc12
       )

    jac[jna20, jal23] = (
       +rho*Y[jn]*rate_eval.n_Al23__He4_Na20
       )

    jac[jna21, jn] = (
       -rho*Y[jna21]*rate_eval.n_Na21__He4_F18
       -rho*Y[jna21]*rate_eval.n_Na21__p_Ne21
       -rho*Y[jna21]*rate_eval.n_Na21__Na22
       +rho*Y[jal24]*rate_eval.n_Al24__He4_Na21
       +rho*Y[jna20]*rate_eval.n_Na20__Na21
       +rho*Y[jmg21]*rate_eval.n_Mg21__p_Na21
       )

    jac[jna21, jp] = (
       -rho*Y[jna21]*rate_eval.p_Na21__Mg22
       +rho*Y[jmg24]*rate_eval.p_Mg24__He4_Na21
       +rho*Y[jne20]*rate_eval.p_Ne20__Na21
       )

    jac[jna21, jhe4] = (
       -rho*Y[jna21]*rate_eval.He4_Na21__Al25
       +rho*Y[jf17]*rate_eval.He4_F17__Na21
       +rho*Y[jne18]*rate_eval.He4_Ne18__p_Na21
       )

    jac[jna21, jf17] = (
       +rho*Y[jhe4]*rate_eval.He4_F17__Na21
       )

    jac[jna21, jne18] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne18__p_Na21
       )

    jac[jna21, jne20] = (
       +rho*Y[jp]*rate_eval.p_Ne20__Na21
       )

    jac[jna21, jna20] = (
       +rho*Y[jn]*rate_eval.n_Na20__Na21
       )

    jac[jna21, jna21] = (
       -rho*Y[jn]*rate_eval.n_Na21__He4_F18
       -rho*Y[jn]*rate_eval.n_Na21__p_Ne21
       -rho*Y[jp]*rate_eval.p_Na21__Mg22
       -rho*Y[jn]*rate_eval.n_Na21__Na22
       -rate_eval.Na21__Ne21__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Na21__Al25
       )

    jac[jna21, jmg21] = (
       +rho*Y[jn]*rate_eval.n_Mg21__p_Na21
       +rate_eval.Mg21__Na21__weak__wc12
       )

    jac[jna21, jmg24] = (
       +rho*Y[jp]*rate_eval.p_Mg24__He4_Na21
       )

    jac[jna21, jal22] = (
       +rate_eval.Al22__p_Na21__weak__wc17
       )

    jac[jna21, jal24] = (
       +rho*Y[jn]*rate_eval.n_Al24__He4_Na21
       )

    jac[jna21, jsi23] = (
       +rate_eval.Si23__p_p_Na21__weak__wc12
       )

    jac[jna22, jn] = (
       -rho*Y[jna22]*rate_eval.n_Na22__Na23
       -rho*Y[jna22]*rate_eval.n_Na22__p_Ne22
       -rho*Y[jna22]*rate_eval.n_Na22__He4_F19
       +rho*Y[jna21]*rate_eval.n_Na21__Na22
       +rho*Y[jmg22]*rate_eval.n_Mg22__p_Na22
       +rho*Y[jal25]*rate_eval.n_Al25__He4_Na22
       )

    jac[jna22, jp] = (
       -rho*Y[jna22]*rate_eval.p_Na22__Mg23
       +rho*Y[jne21]*rate_eval.p_Ne21__Na22
       )

    jac[jna22, jhe4] = (
       -rho*Y[jna22]*rate_eval.He4_Na22__p_Mg25
       -rho*Y[jna22]*rate_eval.He4_Na22__Al26
       +rho*Y[jne19]*rate_eval.He4_Ne19__p_Na22
       +rho*Y[jf18]*rate_eval.He4_F18__Na22
       )

    jac[jna22, jf18] = (
       +rho*Y[jhe4]*rate_eval.He4_F18__Na22
       )

    jac[jna22, jne19] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne19__p_Na22
       )

    jac[jna22, jne21] = (
       +rho*Y[jp]*rate_eval.p_Ne21__Na22
       )

    jac[jna22, jna21] = (
       +rho*Y[jn]*rate_eval.n_Na21__Na22
       )

    jac[jna22, jna22] = (
       -rho*Y[jhe4]*rate_eval.He4_Na22__p_Mg25
       -rho*Y[jp]*rate_eval.p_Na22__Mg23
       -rho*Y[jn]*rate_eval.n_Na22__Na23
       -rho*Y[jn]*rate_eval.n_Na22__p_Ne22
       -rate_eval.Na22__Ne22__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Na22__Al26
       -rho*Y[jn]*rate_eval.n_Na22__He4_F19
       )

    jac[jna22, jmg22] = (
       +rate_eval.Mg22__Na22__weak__wc12
       +rho*Y[jn]*rate_eval.n_Mg22__p_Na22
       )

    jac[jna22, jal23] = (
       +rate_eval.Al23__p_Na22__weak__wc12
       )

    jac[jna22, jal25] = (
       +rho*Y[jn]*rate_eval.n_Al25__He4_Na22
       )

    jac[jna23, jn] = (
       -rho*Y[jna23]*rate_eval.n_Na23__Na24
       +rho*Y[jal26]*rate_eval.n_Al26__He4_Na23
       +rho*Y[jna22]*rate_eval.n_Na22__Na23
       )

    jac[jna23, jp] = (
       -rho*Y[jna23]*rate_eval.p_Na23__He4_Ne20
       -rho*Y[jna23]*rate_eval.p_Na23__n_Mg23
       -rho*Y[jna23]*rate_eval.p_Na23__Mg24
       +rho*Y[jne23]*rate_eval.p_Ne23__n_Na23
       +rho*Y[jne22]*rate_eval.p_Ne22__Na23
       )

    jac[jna23, jhe4] = (
       -rho*Y[jna23]*rate_eval.He4_Na23__p_Mg26
       -rho*Y[jna23]*rate_eval.He4_Na23__Al27
       +rho*Y[jf20]*rate_eval.He4_F20__n_Na23
       +rho*Y[jf19]*rate_eval.He4_F19__Na23
       )

    jac[jna23, jc12] = (
       +5.00000000000000e-01*rho*2*Y[jc12]*rate_eval.C12_C12__p_Na23
       )

    jac[jna23, jf19] = (
       +rho*Y[jhe4]*rate_eval.He4_F19__Na23
       )

    jac[jna23, jf20] = (
       +rho*Y[jhe4]*rate_eval.He4_F20__n_Na23
       )

    jac[jna23, jne22] = (
       +rho*Y[jp]*rate_eval.p_Ne22__Na23
       )

    jac[jna23, jne23] = (
       +rho*Y[jp]*rate_eval.p_Ne23__n_Na23
       +rate_eval.Ne23__Na23__weak__wc12
       )

    jac[jna23, jna22] = (
       +rho*Y[jn]*rate_eval.n_Na22__Na23
       )

    jac[jna23, jna23] = (
       -rho*Y[jhe4]*rate_eval.He4_Na23__p_Mg26
       -rho*Y[jp]*rate_eval.p_Na23__He4_Ne20
       -rho*Y[jp]*rate_eval.p_Na23__n_Mg23
       -rho*Y[jhe4]*rate_eval.He4_Na23__Al27
       -rho*Y[jp]*rate_eval.p_Na23__Mg24
       -rho*Y[jn]*rate_eval.n_Na23__Na24
       )

    jac[jna23, jmg23] = (
       +rate_eval.Mg23__Na23__weak__wc12
       )

    jac[jna23, jal24] = (
       +rate_eval.Al24__p_Na23__weak__wc12
       )

    jac[jna23, jal26] = (
       +rho*Y[jn]*rate_eval.n_Al26__He4_Na23
       )

    jac[jna24, jn] = (
       -rho*Y[jna24]*rate_eval.n_Na24__Na25
       +rho*Y[jna23]*rate_eval.n_Na23__Na24
       )

    jac[jna24, jp] = (
       -rho*Y[jna24]*rate_eval.p_Na24__He4_Ne21
       -rho*Y[jna24]*rate_eval.p_Na24__Mg25
       -rho*Y[jna24]*rate_eval.p_Na24__n_Mg24
       +rho*Y[jne24]*rate_eval.p_Ne24__n_Na24
       +rho*Y[jne23]*rate_eval.p_Ne23__Na24
       )

    jac[jna24, jhe4] = (
       -rho*Y[jna24]*rate_eval.He4_Na24__p_Mg27
       -rho*Y[jna24]*rate_eval.He4_Na24__Al28
       -rho*Y[jna24]*rate_eval.He4_Na24__n_Al27
       +rho*Y[jf21]*rate_eval.He4_F21__n_Na24
       +rho*Y[jf20]*rate_eval.He4_F20__Na24
       )

    jac[jna24, jf20] = (
       +rho*Y[jhe4]*rate_eval.He4_F20__Na24
       )

    jac[jna24, jf21] = (
       +rho*Y[jhe4]*rate_eval.He4_F21__n_Na24
       )

    jac[jna24, jne23] = (
       +rho*Y[jp]*rate_eval.p_Ne23__Na24
       )

    jac[jna24, jne24] = (
       +rho*Y[jp]*rate_eval.p_Ne24__n_Na24
       +rate_eval.Ne24__Na24__weak__wc12
       )

    jac[jna24, jna23] = (
       +rho*Y[jn]*rate_eval.n_Na23__Na24
       )

    jac[jna24, jna24] = (
       -rho*Y[jhe4]*rate_eval.He4_Na24__p_Mg27
       -rho*Y[jp]*rate_eval.p_Na24__He4_Ne21
       -rho*Y[jn]*rate_eval.n_Na24__Na25
       -rho*Y[jhe4]*rate_eval.He4_Na24__Al28
       -rho*Y[jp]*rate_eval.p_Na24__Mg25
       -rho*Y[jhe4]*rate_eval.He4_Na24__n_Al27
       -rho*Y[jp]*rate_eval.p_Na24__n_Mg24
       -rate_eval.Na24__Mg24__weak__wc12
       )

    jac[jna25, jn] = (
       -rho*Y[jna25]*rate_eval.n_Na25__Na26
       +rho*Y[jna24]*rate_eval.n_Na24__Na25
       )

    jac[jna25, jp] = (
       -rho*Y[jna25]*rate_eval.p_Na25__Mg26
       -rho*Y[jna25]*rate_eval.p_Na25__n_Mg25
       -rho*Y[jna25]*rate_eval.p_Na25__He4_Ne22
       +rho*Y[jne25]*rate_eval.p_Ne25__n_Na25
       +rho*Y[jne24]*rate_eval.p_Ne24__Na25
       )

    jac[jna25, jhe4] = (
       -rho*Y[jna25]*rate_eval.He4_Na25__Al29
       -rho*Y[jna25]*rate_eval.He4_Na25__n_Al28
       -rho*Y[jna25]*rate_eval.He4_Na25__p_Mg28
       +rho*Y[jf21]*rate_eval.He4_F21__Na25
       +rho*Y[jf22]*rate_eval.He4_F22__n_Na25
       )

    jac[jna25, jf21] = (
       +rho*Y[jhe4]*rate_eval.He4_F21__Na25
       )

    jac[jna25, jf22] = (
       +rho*Y[jhe4]*rate_eval.He4_F22__n_Na25
       )

    jac[jna25, jne24] = (
       +rho*Y[jp]*rate_eval.p_Ne24__Na25
       )

    jac[jna25, jne25] = (
       +rho*Y[jp]*rate_eval.p_Ne25__n_Na25
       +rate_eval.Ne25__Na25__weak__wc12
       )

    jac[jna25, jne26] = (
       +rate_eval.Ne26__n_Na25__weak__wc12
       )

    jac[jna25, jna24] = (
       +rho*Y[jn]*rate_eval.n_Na24__Na25
       )

    jac[jna25, jna25] = (
       -rho*Y[jhe4]*rate_eval.He4_Na25__Al29
       -rate_eval.Na25__Mg25__weak__wc12
       -rho*Y[jp]*rate_eval.p_Na25__Mg26
       -rho*Y[jhe4]*rate_eval.He4_Na25__n_Al28
       -rho*Y[jhe4]*rate_eval.He4_Na25__p_Mg28
       -rho*Y[jp]*rate_eval.p_Na25__n_Mg25
       -rho*Y[jn]*rate_eval.n_Na25__Na26
       -rho*Y[jp]*rate_eval.p_Na25__He4_Ne22
       )

    jac[jna26, jn] = (
       -rho*Y[jna26]*rate_eval.n_Na26__Na27
       +rho*Y[jna25]*rate_eval.n_Na25__Na26
       )

    jac[jna26, jp] = (
       -rho*Y[jna26]*rate_eval.p_Na26__He4_Ne23
       -rho*Y[jna26]*rate_eval.p_Na26__Mg27
       -rho*Y[jna26]*rate_eval.p_Na26__n_Mg26
       +rho*Y[jne26]*rate_eval.p_Ne26__n_Na26
       +rho*Y[jmg29]*rate_eval.p_Mg29__He4_Na26
       +rho*Y[jne25]*rate_eval.p_Ne25__Na26
       )

    jac[jna26, jhe4] = (
       -rho*Y[jna26]*rate_eval.He4_Na26__n_Al29
       -rho*Y[jna26]*rate_eval.He4_Na26__Al30
       +rho*Y[jf22]*rate_eval.He4_F22__Na26
       +rho*Y[jf23]*rate_eval.He4_F23__n_Na26
       )

    jac[jna26, jf22] = (
       +rho*Y[jhe4]*rate_eval.He4_F22__Na26
       )

    jac[jna26, jf23] = (
       +rho*Y[jhe4]*rate_eval.He4_F23__n_Na26
       )

    jac[jna26, jne25] = (
       +rho*Y[jp]*rate_eval.p_Ne25__Na26
       )

    jac[jna26, jne26] = (
       +rho*Y[jp]*rate_eval.p_Ne26__n_Na26
       +rate_eval.Ne26__Na26__weak__wc12
       )

    jac[jna26, jne27] = (
       +rate_eval.Ne27__n_Na26__weak__wc12
       )

    jac[jna26, jna25] = (
       +rho*Y[jn]*rate_eval.n_Na25__Na26
       )

    jac[jna26, jna26] = (
       -rate_eval.Na26__Mg26__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Na26__n_Al29
       -rho*Y[jp]*rate_eval.p_Na26__He4_Ne23
       -rho*Y[jp]*rate_eval.p_Na26__Mg27
       -rho*Y[jp]*rate_eval.p_Na26__n_Mg26
       -rho*Y[jhe4]*rate_eval.He4_Na26__Al30
       -rho*Y[jn]*rate_eval.n_Na26__Na27
       )

    jac[jna26, jmg29] = (
       +rho*Y[jp]*rate_eval.p_Mg29__He4_Na26
       )

    jac[jna27, jn] = (
       -rho*Y[jna27]*rate_eval.n_Na27__Na28
       +rho*Y[jna26]*rate_eval.n_Na26__Na27
       )

    jac[jna27, jp] = (
       -rho*Y[jna27]*rate_eval.p_Na27__n_Mg27
       -rho*Y[jna27]*rate_eval.p_Na27__Mg28
       -rho*Y[jna27]*rate_eval.p_Na27__He4_Ne24
       +rho*Y[jne27]*rate_eval.p_Ne27__n_Na27
       +rho*Y[jne26]*rate_eval.p_Ne26__Na27
       +rho*Y[jmg30]*rate_eval.p_Mg30__He4_Na27
       )

    jac[jna27, jhe4] = (
       -rho*Y[jna27]*rate_eval.He4_Na27__n_Al30
       -rho*Y[jna27]*rate_eval.He4_Na27__Al31
       +rho*Y[jf24]*rate_eval.He4_F24__n_Na27
       +rho*Y[jf23]*rate_eval.He4_F23__Na27
       )

    jac[jna27, jf23] = (
       +rho*Y[jhe4]*rate_eval.He4_F23__Na27
       )

    jac[jna27, jf24] = (
       +rho*Y[jhe4]*rate_eval.He4_F24__n_Na27
       )

    jac[jna27, jne26] = (
       +rho*Y[jp]*rate_eval.p_Ne26__Na27
       )

    jac[jna27, jne27] = (
       +rho*Y[jp]*rate_eval.p_Ne27__n_Na27
       +rate_eval.Ne27__Na27__weak__wc12
       )

    jac[jna27, jne28] = (
       +rate_eval.Ne28__n_Na27__weak__wc12
       )

    jac[jna27, jne29] = (
       +rate_eval.Ne29__n_n_Na27__weak__wc12
       )

    jac[jna27, jna26] = (
       +rho*Y[jn]*rate_eval.n_Na26__Na27
       )

    jac[jna27, jna27] = (
       -rate_eval.Na27__n_Mg26__weak__wc12
       -rho*Y[jp]*rate_eval.p_Na27__n_Mg27
       -rho*Y[jhe4]*rate_eval.He4_Na27__n_Al30
       -rho*Y[jn]*rate_eval.n_Na27__Na28
       -rho*Y[jhe4]*rate_eval.He4_Na27__Al31
       -rate_eval.Na27__Mg27__weak__wc12
       -rho*Y[jp]*rate_eval.p_Na27__Mg28
       -rho*Y[jp]*rate_eval.p_Na27__He4_Ne24
       )

    jac[jna27, jmg30] = (
       +rho*Y[jp]*rate_eval.p_Mg30__He4_Na27
       )

    jac[jna28, jn] = (
       -rho*Y[jna28]*rate_eval.n_Na28__Na29
       +rho*Y[jna27]*rate_eval.n_Na27__Na28
       )

    jac[jna28, jp] = (
       -rho*Y[jna28]*rate_eval.p_Na28__n_Mg28
       -rho*Y[jna28]*rate_eval.p_Na28__He4_Ne25
       -rho*Y[jna28]*rate_eval.p_Na28__Mg29
       +rho*Y[jne28]*rate_eval.p_Ne28__n_Na28
       +rho*Y[jmg31]*rate_eval.p_Mg31__He4_Na28
       +rho*Y[jne27]*rate_eval.p_Ne27__Na28
       )

    jac[jna28, jhe4] = (
       -rho*Y[jna28]*rate_eval.He4_Na28__n_Al31
       -rho*Y[jna28]*rate_eval.He4_Na28__Al32
       +rho*Y[jf25]*rate_eval.He4_F25__n_Na28
       +rho*Y[jf24]*rate_eval.He4_F24__Na28
       )

    jac[jna28, jf24] = (
       +rho*Y[jhe4]*rate_eval.He4_F24__Na28
       )

    jac[jna28, jf25] = (
       +rho*Y[jhe4]*rate_eval.He4_F25__n_Na28
       )

    jac[jna28, jne27] = (
       +rho*Y[jp]*rate_eval.p_Ne27__Na28
       )

    jac[jna28, jne28] = (
       +rate_eval.Ne28__Na28__weak__wc17
       +rho*Y[jp]*rate_eval.p_Ne28__n_Na28
       )

    jac[jna28, jne29] = (
       +rate_eval.Ne29__n_Na28__weak__wc17
       )

    jac[jna28, jne31] = (
       +rate_eval.Ne31__n_n_n_Na28__weak__mo03
       )

    jac[jna28, jna27] = (
       +rho*Y[jn]*rate_eval.n_Na27__Na28
       )

    jac[jna28, jna28] = (
       -rho*Y[jhe4]*rate_eval.He4_Na28__n_Al31
       -rho*Y[jp]*rate_eval.p_Na28__n_Mg28
       -rho*Y[jp]*rate_eval.p_Na28__He4_Ne25
       -rho*Y[jhe4]*rate_eval.He4_Na28__Al32
       -rate_eval.Na28__Mg28__weak__wc12
       -rho*Y[jp]*rate_eval.p_Na28__Mg29
       -rho*Y[jn]*rate_eval.n_Na28__Na29
       -rate_eval.Na28__n_Mg27__weak__wc12
       )

    jac[jna28, jmg31] = (
       +rho*Y[jp]*rate_eval.p_Mg31__He4_Na28
       )

    jac[jna29, jn] = (
       -rho*Y[jna29]*rate_eval.n_Na29__Na30
       +rho*Y[jna28]*rate_eval.n_Na28__Na29
       )

    jac[jna29, jp] = (
       -rho*Y[jna29]*rate_eval.p_Na29__He4_Ne26
       -rho*Y[jna29]*rate_eval.p_Na29__n_Mg29
       -rho*Y[jna29]*rate_eval.p_Na29__Mg30
       +rho*Y[jmg32]*rate_eval.p_Mg32__He4_Na29
       +rho*Y[jne29]*rate_eval.p_Ne29__n_Na29
       +rho*Y[jne28]*rate_eval.p_Ne28__Na29
       )

    jac[jna29, jhe4] = (
       -rho*Y[jna29]*rate_eval.He4_Na29__Al33
       -rho*Y[jna29]*rate_eval.He4_Na29__n_Al32
       +rho*Y[jf26]*rate_eval.He4_F26__n_Na29
       +rho*Y[jf25]*rate_eval.He4_F25__Na29
       )

    jac[jna29, jf25] = (
       +rho*Y[jhe4]*rate_eval.He4_F25__Na29
       )

    jac[jna29, jf26] = (
       +rho*Y[jhe4]*rate_eval.He4_F26__n_Na29
       )

    jac[jna29, jne28] = (
       +rho*Y[jp]*rate_eval.p_Ne28__Na29
       )

    jac[jna29, jne29] = (
       +rho*Y[jp]*rate_eval.p_Ne29__n_Na29
       +rate_eval.Ne29__Na29__weak__wc12
       )

    jac[jna29, jne30] = (
       +rate_eval.Ne30__n_Na29__weak__wc12
       )

    jac[jna29, jne31] = (
       +rate_eval.Ne31__n_n_Na29__weak__mp17
       )

    jac[jna29, jne32] = (
       +rate_eval.Ne32__n_n_n_Na29__weak__mo03
       )

    jac[jna29, jna28] = (
       +rho*Y[jn]*rate_eval.n_Na28__Na29
       )

    jac[jna29, jna29] = (
       -rho*Y[jp]*rate_eval.p_Na29__He4_Ne26
       -rho*Y[jhe4]*rate_eval.He4_Na29__Al33
       -rho*Y[jhe4]*rate_eval.He4_Na29__n_Al32
       -rho*Y[jp]*rate_eval.p_Na29__n_Mg29
       -rate_eval.Na29__n_Mg28__weak__wc12
       -rho*Y[jp]*rate_eval.p_Na29__Mg30
       -rho*Y[jn]*rate_eval.n_Na29__Na30
       -rate_eval.Na29__Mg29__weak__wc12
       )

    jac[jna29, jmg32] = (
       +rho*Y[jp]*rate_eval.p_Mg32__He4_Na29
       )

    jac[jna30, jn] = (
       -rho*Y[jna30]*rate_eval.n_Na30__Na31
       +rho*Y[jna29]*rate_eval.n_Na29__Na30
       )

    jac[jna30, jp] = (
       -rho*Y[jna30]*rate_eval.p_Na30__He4_Ne27
       -rho*Y[jna30]*rate_eval.p_Na30__Mg31
       -rho*Y[jna30]*rate_eval.p_Na30__n_Mg30
       +rho*Y[jmg33]*rate_eval.p_Mg33__He4_Na30
       +rho*Y[jne30]*rate_eval.p_Ne30__n_Na30
       +rho*Y[jne29]*rate_eval.p_Ne29__Na30
       )

    jac[jna30, jhe4] = (
       -rho*Y[jna30]*rate_eval.He4_Na30__Al34
       -rho*Y[jna30]*rate_eval.He4_Na30__n_Al33
       +rho*Y[jf26]*rate_eval.He4_F26__Na30
       +rho*Y[jf27]*rate_eval.He4_F27__n_Na30
       )

    jac[jna30, jf26] = (
       +rho*Y[jhe4]*rate_eval.He4_F26__Na30
       )

    jac[jna30, jf27] = (
       +rho*Y[jhe4]*rate_eval.He4_F27__n_Na30
       )

    jac[jna30, jne29] = (
       +rho*Y[jp]*rate_eval.p_Ne29__Na30
       )

    jac[jna30, jne30] = (
       +rho*Y[jp]*rate_eval.p_Ne30__n_Na30
       +rate_eval.Ne30__Na30__weak__wc17
       )

    jac[jna30, jne31] = (
       +rate_eval.Ne31__n_Na30__weak__mp17
       )

    jac[jna30, jne32] = (
       +rate_eval.Ne32__n_n_Na30__weak__mp17
       )

    jac[jna30, jne33] = (
       +rate_eval.Ne33__n_n_n_Na30__weak__mo03
       )

    jac[jna30, jna29] = (
       +rho*Y[jn]*rate_eval.n_Na29__Na30
       )

    jac[jna30, jna30] = (
       -rho*Y[jp]*rate_eval.p_Na30__He4_Ne27
       -rho*Y[jn]*rate_eval.n_Na30__Na31
       -rho*Y[jhe4]*rate_eval.He4_Na30__Al34
       -rate_eval.Na30__n_Mg29__weak__wc17
       -rate_eval.Na30__n_n_Mg28__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Na30__n_Al33
       -rate_eval.Na30__He4_Ne26__weak__wc12
       -rho*Y[jp]*rate_eval.p_Na30__Mg31
       -rate_eval.Na30__Mg30__weak__wc12
       -rho*Y[jp]*rate_eval.p_Na30__n_Mg30
       )

    jac[jna30, jmg33] = (
       +rho*Y[jp]*rate_eval.p_Mg33__He4_Na30
       )

    jac[jna31, jn] = (
       -rho*Y[jna31]*rate_eval.n_Na31__Na32
       +rho*Y[jna30]*rate_eval.n_Na30__Na31
       )

    jac[jna31, jp] = (
       -rho*Y[jna31]*rate_eval.p_Na31__Mg32
       -rho*Y[jna31]*rate_eval.p_Na31__He4_Ne28
       -rho*Y[jna31]*rate_eval.p_Na31__n_Mg31
       +rho*Y[jmg34]*rate_eval.p_Mg34__He4_Na31
       +rho*Y[jne30]*rate_eval.p_Ne30__Na31
       +rho*Y[jne31]*rate_eval.p_Ne31__n_Na31
       )

    jac[jna31, jhe4] = (
       -rho*Y[jna31]*rate_eval.He4_Na31__n_Al34
       -rho*Y[jna31]*rate_eval.He4_Na31__Al35
       +rho*Y[jf28]*rate_eval.He4_F28__n_Na31
       +rho*Y[jf27]*rate_eval.He4_F27__Na31
       )

    jac[jna31, jf27] = (
       +rho*Y[jhe4]*rate_eval.He4_F27__Na31
       )

    jac[jna31, jf28] = (
       +rho*Y[jhe4]*rate_eval.He4_F28__n_Na31
       )

    jac[jna31, jne30] = (
       +rho*Y[jp]*rate_eval.p_Ne30__Na31
       )

    jac[jna31, jne31] = (
       +rate_eval.Ne31__Na31__weak__wc17
       +rho*Y[jp]*rate_eval.p_Ne31__n_Na31
       )

    jac[jna31, jne32] = (
       +rate_eval.Ne32__n_Na31__weak__mp17
       )

    jac[jna31, jne33] = (
       +rate_eval.Ne33__n_n_Na31__weak__mp17
       )

    jac[jna31, jne34] = (
       +rate_eval.Ne34__n_n_n_Na31__weak__mo03
       )

    jac[jna31, jna30] = (
       +rho*Y[jn]*rate_eval.n_Na30__Na31
       )

    jac[jna31, jna31] = (
       -rho*Y[jp]*rate_eval.p_Na31__Mg32
       -rho*Y[jhe4]*rate_eval.He4_Na31__n_Al34
       -rho*Y[jp]*rate_eval.p_Na31__He4_Ne28
       -rho*Y[jp]*rate_eval.p_Na31__n_Mg31
       -rate_eval.Na31__n_Mg30__weak__wc17
       -rho*Y[jn]*rate_eval.n_Na31__Na32
       -rho*Y[jhe4]*rate_eval.He4_Na31__Al35
       -rate_eval.Na31__n_n_Mg29__weak__wc12
       -rate_eval.Na31__n_n_n_Mg28__weak__wc12
       -rate_eval.Na31__Mg31__weak__wc12
       )

    jac[jna31, jmg34] = (
       +rho*Y[jp]*rate_eval.p_Mg34__He4_Na31
       )

    jac[jna32, jn] = (
       -rho*Y[jna32]*rate_eval.n_Na32__Na33
       +rho*Y[jna31]*rate_eval.n_Na31__Na32
       )

    jac[jna32, jp] = (
       -rho*Y[jna32]*rate_eval.p_Na32__n_Mg32
       -rho*Y[jna32]*rate_eval.p_Na32__Mg33
       -rho*Y[jna32]*rate_eval.p_Na32__He4_Ne29
       +rho*Y[jne32]*rate_eval.p_Ne32__n_Na32
       +rho*Y[jne31]*rate_eval.p_Ne31__Na32
       +rho*Y[jmg35]*rate_eval.p_Mg35__He4_Na32
       )

    jac[jna32, jhe4] = (
       -rho*Y[jna32]*rate_eval.He4_Na32__n_Al35
       -rho*Y[jna32]*rate_eval.He4_Na32__Al36
       +rho*Y[jf29]*rate_eval.He4_F29__n_Na32
       +rho*Y[jf28]*rate_eval.He4_F28__Na32
       )

    jac[jna32, jf28] = (
       +rho*Y[jhe4]*rate_eval.He4_F28__Na32
       )

    jac[jna32, jf29] = (
       +rho*Y[jhe4]*rate_eval.He4_F29__n_Na32
       )

    jac[jna32, jne31] = (
       +rho*Y[jp]*rate_eval.p_Ne31__Na32
       )

    jac[jna32, jne32] = (
       +rho*Y[jp]*rate_eval.p_Ne32__n_Na32
       +rate_eval.Ne32__Na32__weak__wc17
       )

    jac[jna32, jne33] = (
       +rate_eval.Ne33__n_Na32__weak__mp17
       )

    jac[jna32, jne34] = (
       +rate_eval.Ne34__n_n_Na32__weak__mp17
       )

    jac[jna32, jna31] = (
       +rho*Y[jn]*rate_eval.n_Na31__Na32
       )

    jac[jna32, jna32] = (
       -rate_eval.Na32__n_n_n_Mg29__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Na32__n_Al35
       -rate_eval.Na32__n_n_Mg30__weak__wc12
       -rho*Y[jp]*rate_eval.p_Na32__n_Mg32
       -rho*Y[jp]*rate_eval.p_Na32__Mg33
       -rho*Y[jn]*rate_eval.n_Na32__Na33
       -rate_eval.Na32__Mg32__weak__wc12
       -rho*Y[jp]*rate_eval.p_Na32__He4_Ne29
       -rate_eval.Na32__n_Mg31__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_Na32__Al36
       )

    jac[jna32, jmg35] = (
       +rho*Y[jp]*rate_eval.p_Mg35__He4_Na32
       )

    jac[jna33, jn] = (
       -rho*Y[jna33]*rate_eval.n_Na33__Na34
       +rho*Y[jna32]*rate_eval.n_Na32__Na33
       )

    jac[jna33, jp] = (
       -rho*Y[jna33]*rate_eval.p_Na33__n_Mg33
       -rho*Y[jna33]*rate_eval.p_Na33__He4_Ne30
       -rho*Y[jna33]*rate_eval.p_Na33__Mg34
       +rho*Y[jne32]*rate_eval.p_Ne32__Na33
       +rho*Y[jne33]*rate_eval.p_Ne33__n_Na33
       )

    jac[jna33, jhe4] = (
       -rho*Y[jna33]*rate_eval.He4_Na33__p_Mg36
       -rho*Y[jna33]*rate_eval.He4_Na33__Al37
       -rho*Y[jna33]*rate_eval.He4_Na33__n_Al36
       +rho*Y[jf30]*rate_eval.He4_F30__n_Na33
       +rho*Y[jf29]*rate_eval.He4_F29__Na33
       )

    jac[jna33, jf29] = (
       +rho*Y[jhe4]*rate_eval.He4_F29__Na33
       )

    jac[jna33, jf30] = (
       +rho*Y[jhe4]*rate_eval.He4_F30__n_Na33
       )

    jac[jna33, jne32] = (
       +rho*Y[jp]*rate_eval.p_Ne32__Na33
       )

    jac[jna33, jne33] = (
       +rho*Y[jp]*rate_eval.p_Ne33__n_Na33
       +rate_eval.Ne33__Na33__weak__mo03
       )

    jac[jna33, jne34] = (
       +rate_eval.Ne34__n_Na33__weak__mp17
       )

    jac[jna33, jna32] = (
       +rho*Y[jn]*rate_eval.n_Na32__Na33
       )

    jac[jna33, jna33] = (
       -rate_eval.Na33__n_n_n_Mg30__weak__mo03
       -rho*Y[jn]*rate_eval.n_Na33__Na34
       -rho*Y[jhe4]*rate_eval.He4_Na33__p_Mg36
       -rho*Y[jp]*rate_eval.p_Na33__n_Mg33
       -rho*Y[jp]*rate_eval.p_Na33__He4_Ne30
       -rho*Y[jhe4]*rate_eval.He4_Na33__Al37
       -rho*Y[jhe4]*rate_eval.He4_Na33__n_Al36
       -rho*Y[jp]*rate_eval.p_Na33__Mg34
       -rate_eval.Na33__n_Mg32__weak__wc17
       -rate_eval.Na33__Mg33__weak__wc12
       -rate_eval.Na33__n_n_Mg31__weak__wc12
       )

    jac[jna34, jn] = (
       -rho*Y[jna34]*rate_eval.n_Na34__Na35
       +rho*Y[jna33]*rate_eval.n_Na33__Na34
       )

    jac[jna34, jp] = (
       -rho*Y[jna34]*rate_eval.p_Na34__Mg35
       -rho*Y[jna34]*rate_eval.p_Na34__He4_Ne31
       -rho*Y[jna34]*rate_eval.p_Na34__n_Mg34
       +rho*Y[jne34]*rate_eval.p_Ne34__n_Na34
       +rho*Y[jne33]*rate_eval.p_Ne33__Na34
       +rho*Y[jmg37]*rate_eval.p_Mg37__He4_Na34
       )

    jac[jna34, jhe4] = (
       -rho*Y[jna34]*rate_eval.He4_Na34__n_Al37
       -rho*Y[jna34]*rate_eval.He4_Na34__Al38
       +rho*Y[jf31]*rate_eval.He4_F31__n_Na34
       +rho*Y[jf30]*rate_eval.He4_F30__Na34
       )

    jac[jna34, jf30] = (
       +rho*Y[jhe4]*rate_eval.He4_F30__Na34
       )

    jac[jna34, jf31] = (
       +rho*Y[jhe4]*rate_eval.He4_F31__n_Na34
       )

    jac[jna34, jne33] = (
       +rho*Y[jp]*rate_eval.p_Ne33__Na34
       )

    jac[jna34, jne34] = (
       +rho*Y[jp]*rate_eval.p_Ne34__n_Na34
       +rate_eval.Ne34__Na34__weak__mo03
       )

    jac[jna34, jna33] = (
       +rho*Y[jn]*rate_eval.n_Na33__Na34
       )

    jac[jna34, jna34] = (
       -rate_eval.Na34__n_n_n_Mg31__weak__mo03
       -rho*Y[jp]*rate_eval.p_Na34__Mg35
       -rho*Y[jhe4]*rate_eval.He4_Na34__n_Al37
       -rho*Y[jp]*rate_eval.p_Na34__He4_Ne31
       -rho*Y[jhe4]*rate_eval.He4_Na34__Al38
       -rho*Y[jn]*rate_eval.n_Na34__Na35
       -rho*Y[jp]*rate_eval.p_Na34__n_Mg34
       -rate_eval.Na34__n_Mg33__weak__wc12
       -rate_eval.Na34__n_n_Mg32__weak__wc12
       -rate_eval.Na34__Mg34__weak__wc12
       )

    jac[jna34, jmg37] = (
       +rho*Y[jp]*rate_eval.p_Mg37__He4_Na34
       )

    jac[jna35, jn] = (
       -rho*Y[jna35]*rate_eval.n_Na35__Na36
       +rho*Y[jna34]*rate_eval.n_Na34__Na35
       )

    jac[jna35, jp] = (
       -rho*Y[jna35]*rate_eval.p_Na35__n_Mg35
       -rho*Y[jna35]*rate_eval.p_Na35__He4_Ne32
       -rho*Y[jna35]*rate_eval.p_Na35__Mg36
       +rho*Y[jne34]*rate_eval.p_Ne34__Na35
       +rho*Y[jmg38]*rate_eval.p_Mg38__He4_Na35
       )

    jac[jna35, jhe4] = (
       -rho*Y[jna35]*rate_eval.He4_Na35__n_Al38
       -rho*Y[jna35]*rate_eval.He4_Na35__Al39
       +rho*Y[jf31]*rate_eval.He4_F31__Na35
       )

    jac[jna35, jf31] = (
       +rho*Y[jhe4]*rate_eval.He4_F31__Na35
       )

    jac[jna35, jne34] = (
       +rho*Y[jp]*rate_eval.p_Ne34__Na35
       )

    jac[jna35, jna34] = (
       +rho*Y[jn]*rate_eval.n_Na34__Na35
       )

    jac[jna35, jna35] = (
       -rho*Y[jn]*rate_eval.n_Na35__Na36
       -rho*Y[jhe4]*rate_eval.He4_Na35__n_Al38
       -rho*Y[jp]*rate_eval.p_Na35__n_Mg35
       -rate_eval.Na35__n_n_n_Mg32__weak__mo03
       -rho*Y[jp]*rate_eval.p_Na35__He4_Ne32
       -rate_eval.Na35__n_n_Mg33__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Na35__Al39
       -rate_eval.Na35__n_Mg34__weak__mp17
       -rate_eval.Na35__Mg35__weak__wc17
       -rho*Y[jp]*rate_eval.p_Na35__Mg36
       )

    jac[jna35, jmg38] = (
       +rho*Y[jp]*rate_eval.p_Mg38__He4_Na35
       )

    jac[jna36, jn] = (
       -rho*Y[jna36]*rate_eval.n_Na36__Na37
       +rho*Y[jna35]*rate_eval.n_Na35__Na36
       )

    jac[jna36, jp] = (
       -rho*Y[jna36]*rate_eval.p_Na36__n_Mg36
       -rho*Y[jna36]*rate_eval.p_Na36__Mg37
       -rho*Y[jna36]*rate_eval.p_Na36__He4_Ne33
       +rho*Y[jmg39]*rate_eval.p_Mg39__He4_Na36
       )

    jac[jna36, jhe4] = (
       -rho*Y[jna36]*rate_eval.He4_Na36__n_Al39
       -rho*Y[jna36]*rate_eval.He4_Na36__Al40
       )

    jac[jna36, jna35] = (
       +rho*Y[jn]*rate_eval.n_Na35__Na36
       )

    jac[jna36, jna36] = (
       -rho*Y[jp]*rate_eval.p_Na36__n_Mg36
       -rho*Y[jhe4]*rate_eval.He4_Na36__n_Al39
       -rate_eval.Na36__n_Mg35__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Na36__Al40
       -rho*Y[jn]*rate_eval.n_Na36__Na37
       -rho*Y[jp]*rate_eval.p_Na36__Mg37
       -rate_eval.Na36__Mg36__weak__mo03
       -rho*Y[jp]*rate_eval.p_Na36__He4_Ne33
       )

    jac[jna36, jmg39] = (
       +rho*Y[jp]*rate_eval.p_Mg39__He4_Na36
       )

    jac[jna37, jn] = (
       -rho*Y[jna37]*rate_eval.n_Na37__Na38
       +rho*Y[jna36]*rate_eval.n_Na36__Na37
       )

    jac[jna37, jp] = (
       -rho*Y[jna37]*rate_eval.p_Na37__Mg38
       -rho*Y[jna37]*rate_eval.p_Na37__He4_Ne34
       -rho*Y[jna37]*rate_eval.p_Na37__n_Mg37
       )

    jac[jna37, jhe4] = (
       -rho*Y[jna37]*rate_eval.He4_Na37__p_Mg40
       -rho*Y[jna37]*rate_eval.He4_Na37__n_Al40
       -rho*Y[jna37]*rate_eval.He4_Na37__Al41
       )

    jac[jna37, jna36] = (
       +rho*Y[jn]*rate_eval.n_Na36__Na37
       )

    jac[jna37, jna37] = (
       -rho*Y[jp]*rate_eval.p_Na37__Mg38
       -rho*Y[jhe4]*rate_eval.He4_Na37__p_Mg40
       -rho*Y[jp]*rate_eval.p_Na37__He4_Ne34
       -rho*Y[jhe4]*rate_eval.He4_Na37__n_Al40
       -rho*Y[jhe4]*rate_eval.He4_Na37__Al41
       -rho*Y[jn]*rate_eval.n_Na37__Na38
       -rho*Y[jp]*rate_eval.p_Na37__n_Mg37
       -rate_eval.Na37__n_n_Mg35__weak__mp17
       -rate_eval.Na37__n_Mg36__weak__mp17
       )

    jac[jna38, jn] = (
       -rho*Y[jna38]*rate_eval.n_Na38__Na39
       +rho*Y[jna37]*rate_eval.n_Na37__Na38
       )

    jac[jna38, jp] = (
       -rho*Y[jna38]*rate_eval.p_Na38__Mg39
       -rho*Y[jna38]*rate_eval.p_Na38__n_Mg38
       +rho*Y[jmg41]*rate_eval.p_Mg41__He4_Na38
       )

    jac[jna38, jhe4] = (
       -rho*Y[jna38]*rate_eval.He4_Na38__n_Al41
       -rho*Y[jna38]*rate_eval.He4_Na38__Al42
       )

    jac[jna38, jna37] = (
       +rho*Y[jn]*rate_eval.n_Na37__Na38
       )

    jac[jna38, jna38] = (
       -rho*Y[jhe4]*rate_eval.He4_Na38__n_Al41
       -rate_eval.Na38__Mg38__weak__mo03
       -rho*Y[jp]*rate_eval.p_Na38__Mg39
       -rho*Y[jp]*rate_eval.p_Na38__n_Mg38
       -rate_eval.Na38__n_Mg37__weak__mp17
       -rho*Y[jn]*rate_eval.n_Na38__Na39
       -rho*Y[jhe4]*rate_eval.He4_Na38__Al42
       )

    jac[jna38, jmg41] = (
       +rho*Y[jp]*rate_eval.p_Mg41__He4_Na38
       )

    jac[jna39, jn] = (
       +rho*Y[jna38]*rate_eval.n_Na38__Na39
       )

    jac[jna39, jp] = (
       -rho*Y[jna39]*rate_eval.p_Na39__n_Mg39
       -rho*Y[jna39]*rate_eval.p_Na39__Mg40
       )

    jac[jna39, jhe4] = (
       -rho*Y[jna39]*rate_eval.He4_Na39__n_Al42
       -rho*Y[jna39]*rate_eval.He4_Na39__Al43
       )

    jac[jna39, jna38] = (
       +rho*Y[jn]*rate_eval.n_Na38__Na39
       )

    jac[jna39, jna39] = (
       -rate_eval.Na39__n_Mg38__weak__mp17
       -rho*Y[jp]*rate_eval.p_Na39__n_Mg39
       -rho*Y[jhe4]*rate_eval.He4_Na39__n_Al42
       -rho*Y[jhe4]*rate_eval.He4_Na39__Al43
       -rate_eval.Na39__n_n_Mg37__weak__mp17
       -rho*Y[jp]*rate_eval.p_Na39__Mg40
       )

    jac[jmg19, jn] = (
       -rho*Y[jmg19]*rate_eval.n_Mg19__He4_Ne16
       -rho*Y[jmg19]*rate_eval.n_Mg19__Mg20
       -rho*Y[jmg19]*rate_eval.n_Mg19__p_Na19
       +rho*Y[jsi22]*rate_eval.n_Si22__He4_Mg19
       )

    jac[jmg19, jhe4] = (
       -rho*Y[jmg19]*rate_eval.He4_Mg19__p_Al22
       -rho*Y[jmg19]*rate_eval.He4_Mg19__Si23
       )

    jac[jmg19, jmg19] = (
       -rho*Y[jn]*rate_eval.n_Mg19__He4_Ne16
       -rho*Y[jhe4]*rate_eval.He4_Mg19__p_Al22
       -rho*Y[jhe4]*rate_eval.He4_Mg19__Si23
       -rho*Y[jn]*rate_eval.n_Mg19__Mg20
       -rho*Y[jn]*rate_eval.n_Mg19__p_Na19
       )

    jac[jmg19, jsi22] = (
       +rho*Y[jn]*rate_eval.n_Si22__He4_Mg19
       )

    jac[jmg20, jn] = (
       -rho*Y[jmg20]*rate_eval.n_Mg20__p_Na20
       -rho*Y[jmg20]*rate_eval.n_Mg20__Mg21
       -rho*Y[jmg20]*rate_eval.n_Mg20__He4_Ne17
       +rho*Y[jmg19]*rate_eval.n_Mg19__Mg20
       +rho*Y[jsi23]*rate_eval.n_Si23__He4_Mg20
       )

    jac[jmg20, jp] = (
       +rho*Y[jna19]*rate_eval.p_Na19__Mg20
       )

    jac[jmg20, jhe4] = (
       -rho*Y[jmg20]*rate_eval.He4_Mg20__p_Al23
       -rho*Y[jmg20]*rate_eval.He4_Mg20__Si24
       +rho*Y[jne16]*rate_eval.He4_Ne16__Mg20
       )

    jac[jmg20, jne16] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne16__Mg20
       )

    jac[jmg20, jna19] = (
       +rho*Y[jp]*rate_eval.p_Na19__Mg20
       )

    jac[jmg20, jmg19] = (
       +rho*Y[jn]*rate_eval.n_Mg19__Mg20
       )

    jac[jmg20, jmg20] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg20__p_Al23
       -rho*Y[jn]*rate_eval.n_Mg20__p_Na20
       -rate_eval.Mg20__p_Ne19__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Mg20__Si24
       -rho*Y[jn]*rate_eval.n_Mg20__Mg21
       -rho*Y[jn]*rate_eval.n_Mg20__He4_Ne17
       -rate_eval.Mg20__Na20__weak__wc12
       )

    jac[jmg20, jsi23] = (
       +rho*Y[jn]*rate_eval.n_Si23__He4_Mg20
       )

    jac[jmg21, jn] = (
       -rho*Y[jmg21]*rate_eval.n_Mg21__He4_Ne18
       -rho*Y[jmg21]*rate_eval.n_Mg21__p_Na21
       -rho*Y[jmg21]*rate_eval.n_Mg21__Mg22
       +rho*Y[jsi24]*rate_eval.n_Si24__He4_Mg21
       +rho*Y[jmg20]*rate_eval.n_Mg20__Mg21
       +rho*Y[jal21]*rate_eval.n_Al21__p_Mg21
       )

    jac[jmg21, jp] = (
       -rho*Y[jmg21]*rate_eval.p_Mg21__Al22
       +rho*Y[jna20]*rate_eval.p_Na20__Mg21
       )

    jac[jmg21, jhe4] = (
       -rho*Y[jmg21]*rate_eval.He4_Mg21__Si25
       -rho*Y[jmg21]*rate_eval.He4_Mg21__p_Al24
       +rho*Y[jne17]*rate_eval.He4_Ne17__Mg21
       )

    jac[jmg21, jne17] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne17__Mg21
       )

    jac[jmg21, jna20] = (
       +rho*Y[jp]*rate_eval.p_Na20__Mg21
       )

    jac[jmg21, jmg20] = (
       +rho*Y[jn]*rate_eval.n_Mg20__Mg21
       )

    jac[jmg21, jmg21] = (
       -rho*Y[jn]*rate_eval.n_Mg21__He4_Ne18
       -rho*Y[jhe4]*rate_eval.He4_Mg21__Si25
       -rho*Y[jn]*rate_eval.n_Mg21__p_Na21
       -rho*Y[jhe4]*rate_eval.He4_Mg21__p_Al24
       -rho*Y[jn]*rate_eval.n_Mg21__Mg22
       -rho*Y[jp]*rate_eval.p_Mg21__Al22
       -rate_eval.Mg21__p_Ne20__weak__wc12
       -rate_eval.Mg21__Na21__weak__wc12
       )

    jac[jmg21, jal21] = (
       +rate_eval.Al21__Mg21__weak__bqa_pos_
       +rho*Y[jn]*rate_eval.n_Al21__p_Mg21
       )

    jac[jmg21, jsi22] = (
       +rate_eval.Si22__p_Mg21__weak__wc12
       )

    jac[jmg21, jsi24] = (
       +rho*Y[jn]*rate_eval.n_Si24__He4_Mg21
       )

    jac[jmg22, jn] = (
       -rho*Y[jmg22]*rate_eval.n_Mg22__He4_Ne19
       -rho*Y[jmg22]*rate_eval.n_Mg22__Mg23
       -rho*Y[jmg22]*rate_eval.n_Mg22__p_Na22
       +rho*Y[jal22]*rate_eval.n_Al22__p_Mg22
       +rho*Y[jsi25]*rate_eval.n_Si25__He4_Mg22
       +rho*Y[jmg21]*rate_eval.n_Mg21__Mg22
       )

    jac[jmg22, jp] = (
       -rho*Y[jmg22]*rate_eval.p_Mg22__Al23
       +rho*Y[jna21]*rate_eval.p_Na21__Mg22
       )

    jac[jmg22, jhe4] = (
       -rho*Y[jmg22]*rate_eval.He4_Mg22__p_Al25
       -rho*Y[jmg22]*rate_eval.He4_Mg22__Si26
       +rho*Y[jne18]*rate_eval.He4_Ne18__Mg22
       +rho*Y[jna19]*rate_eval.He4_Na19__p_Mg22
       )

    jac[jmg22, jne18] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne18__Mg22
       )

    jac[jmg22, jna19] = (
       +rho*Y[jhe4]*rate_eval.He4_Na19__p_Mg22
       )

    jac[jmg22, jna21] = (
       +rho*Y[jp]*rate_eval.p_Na21__Mg22
       )

    jac[jmg22, jmg21] = (
       +rho*Y[jn]*rate_eval.n_Mg21__Mg22
       )

    jac[jmg22, jmg22] = (
       -rate_eval.Mg22__Na22__weak__wc12
       -rho*Y[jn]*rate_eval.n_Mg22__He4_Ne19
       -rho*Y[jhe4]*rate_eval.He4_Mg22__p_Al25
       -rho*Y[jhe4]*rate_eval.He4_Mg22__Si26
       -rho*Y[jp]*rate_eval.p_Mg22__Al23
       -rho*Y[jn]*rate_eval.n_Mg22__Mg23
       -rho*Y[jn]*rate_eval.n_Mg22__p_Na22
       )

    jac[jmg22, jal22] = (
       +rho*Y[jn]*rate_eval.n_Al22__p_Mg22
       +rate_eval.Al22__Mg22__weak__wc12
       )

    jac[jmg22, jsi23] = (
       +rate_eval.Si23__p_Mg22__weak__wc17
       )

    jac[jmg22, jsi25] = (
       +rho*Y[jn]*rate_eval.n_Si25__He4_Mg22
       )

    jac[jmg23, jn] = (
       -rho*Y[jmg23]*rate_eval.n_Mg23__C12_C12
       -rho*Y[jmg23]*rate_eval.n_Mg23__He4_Ne20
       -rho*Y[jmg23]*rate_eval.n_Mg23__Mg24
       +rho*Y[jmg22]*rate_eval.n_Mg22__Mg23
       +rho*Y[jal23]*rate_eval.n_Al23__p_Mg23
       +rho*Y[jsi26]*rate_eval.n_Si26__He4_Mg23
       )

    jac[jmg23, jp] = (
       -rho*Y[jmg23]*rate_eval.p_Mg23__Al24
       +rho*Y[jna23]*rate_eval.p_Na23__n_Mg23
       +rho*Y[jna22]*rate_eval.p_Na22__Mg23
       )

    jac[jmg23, jhe4] = (
       -rho*Y[jmg23]*rate_eval.He4_Mg23__Si27
       -rho*Y[jmg23]*rate_eval.He4_Mg23__p_Al26
       +rho*Y[jna20]*rate_eval.He4_Na20__p_Mg23
       +rho*Y[jne19]*rate_eval.He4_Ne19__Mg23
       )

    jac[jmg23, jne19] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne19__Mg23
       )

    jac[jmg23, jna20] = (
       +rho*Y[jhe4]*rate_eval.He4_Na20__p_Mg23
       )

    jac[jmg23, jna22] = (
       +rho*Y[jp]*rate_eval.p_Na22__Mg23
       )

    jac[jmg23, jna23] = (
       +rho*Y[jp]*rate_eval.p_Na23__n_Mg23
       )

    jac[jmg23, jmg22] = (
       +rho*Y[jn]*rate_eval.n_Mg22__Mg23
       )

    jac[jmg23, jmg23] = (
       -rho*Y[jn]*rate_eval.n_Mg23__C12_C12
       -rho*Y[jn]*rate_eval.n_Mg23__He4_Ne20
       -rho*Y[jhe4]*rate_eval.He4_Mg23__Si27
       -rho*Y[jp]*rate_eval.p_Mg23__Al24
       -rho*Y[jn]*rate_eval.n_Mg23__Mg24
       -rate_eval.Mg23__Na23__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Mg23__p_Al26
       )

    jac[jmg23, jal23] = (
       +rho*Y[jn]*rate_eval.n_Al23__p_Mg23
       +rate_eval.Al23__Mg23__weak__wc12
       )

    jac[jmg23, jsi24] = (
       +rate_eval.Si24__p_Mg23__weak__wc12
       )

    jac[jmg23, jsi26] = (
       +rho*Y[jn]*rate_eval.n_Si26__He4_Mg23
       )

    jac[jmg24, jn] = (
       -rho*Y[jmg24]*rate_eval.n_Mg24__Mg25
       +rho*Y[jmg23]*rate_eval.n_Mg23__Mg24
       +rho*Y[jsi27]*rate_eval.n_Si27__He4_Mg24
       +rho*Y[jal24]*rate_eval.n_Al24__p_Mg24
       )

    jac[jmg24, jp] = (
       -rho*Y[jmg24]*rate_eval.p_Mg24__He4_Na21
       -rho*Y[jmg24]*rate_eval.p_Mg24__Al25
       +rho*Y[jal27]*rate_eval.p_Al27__He4_Mg24
       +rho*Y[jna23]*rate_eval.p_Na23__Mg24
       +rho*Y[jna24]*rate_eval.p_Na24__n_Mg24
       )

    jac[jmg24, jhe4] = (
       -rho*Y[jmg24]*rate_eval.He4_Mg24__Si28
       +rho*Y[jne21]*rate_eval.He4_Ne21__n_Mg24
       +rho*Y[jne20]*rate_eval.He4_Ne20__Mg24
       )

    jac[jmg24, jc12] = (
       +rho*Y[jo16]*rate_eval.C12_O16__He4_Mg24
       )

    jac[jmg24, jo16] = (
       +rho*Y[jc12]*rate_eval.C12_O16__He4_Mg24
       )

    jac[jmg24, jne20] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne20__Mg24
       )

    jac[jmg24, jne21] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne21__n_Mg24
       )

    jac[jmg24, jna23] = (
       +rho*Y[jp]*rate_eval.p_Na23__Mg24
       )

    jac[jmg24, jna24] = (
       +rho*Y[jp]*rate_eval.p_Na24__n_Mg24
       +rate_eval.Na24__Mg24__weak__wc12
       )

    jac[jmg24, jmg23] = (
       +rho*Y[jn]*rate_eval.n_Mg23__Mg24
       )

    jac[jmg24, jmg24] = (
       -rho*Y[jp]*rate_eval.p_Mg24__He4_Na21
       -rho*Y[jp]*rate_eval.p_Mg24__Al25
       -rho*Y[jn]*rate_eval.n_Mg24__Mg25
       -rho*Y[jhe4]*rate_eval.He4_Mg24__Si28
       )

    jac[jmg24, jal24] = (
       +rho*Y[jn]*rate_eval.n_Al24__p_Mg24
       +rate_eval.Al24__Mg24__weak__wc12
       )

    jac[jmg24, jal27] = (
       +rho*Y[jp]*rate_eval.p_Al27__He4_Mg24
       )

    jac[jmg24, jsi25] = (
       +rate_eval.Si25__p_Mg24__weak__wc12
       )

    jac[jmg24, jsi27] = (
       +rho*Y[jn]*rate_eval.n_Si27__He4_Mg24
       )

    jac[jmg24, jp28] = (
       +rate_eval.P28__He4_Mg24__weak__wc12
       )

    jac[jmg25, jn] = (
       -rho*Y[jmg25]*rate_eval.n_Mg25__Mg26
       +rho*Y[jal25]*rate_eval.n_Al25__p_Mg25
       +rho*Y[jmg24]*rate_eval.n_Mg24__Mg25
       )

    jac[jmg25, jp] = (
       -rho*Y[jmg25]*rate_eval.p_Mg25__Al26
       +rho*Y[jal28]*rate_eval.p_Al28__He4_Mg25
       +rho*Y[jna24]*rate_eval.p_Na24__Mg25
       +rho*Y[jna25]*rate_eval.p_Na25__n_Mg25
       )

    jac[jmg25, jhe4] = (
       -rho*Y[jmg25]*rate_eval.He4_Mg25__n_Si28
       -rho*Y[jmg25]*rate_eval.He4_Mg25__Si29
       +rho*Y[jna22]*rate_eval.He4_Na22__p_Mg25
       +rho*Y[jne22]*rate_eval.He4_Ne22__n_Mg25
       +rho*Y[jne21]*rate_eval.He4_Ne21__Mg25
       )

    jac[jmg25, jne21] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne21__Mg25
       )

    jac[jmg25, jne22] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne22__n_Mg25
       )

    jac[jmg25, jna22] = (
       +rho*Y[jhe4]*rate_eval.He4_Na22__p_Mg25
       )

    jac[jmg25, jna24] = (
       +rho*Y[jp]*rate_eval.p_Na24__Mg25
       )

    jac[jmg25, jna25] = (
       +rate_eval.Na25__Mg25__weak__wc12
       +rho*Y[jp]*rate_eval.p_Na25__n_Mg25
       )

    jac[jmg25, jmg24] = (
       +rho*Y[jn]*rate_eval.n_Mg24__Mg25
       )

    jac[jmg25, jmg25] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg25__n_Si28
       -rho*Y[jn]*rate_eval.n_Mg25__Mg26
       -rho*Y[jhe4]*rate_eval.He4_Mg25__Si29
       -rho*Y[jp]*rate_eval.p_Mg25__Al26
       )

    jac[jmg25, jal25] = (
       +rho*Y[jn]*rate_eval.n_Al25__p_Mg25
       +rate_eval.Al25__Mg25__weak__wc12
       )

    jac[jmg25, jal28] = (
       +rho*Y[jp]*rate_eval.p_Al28__He4_Mg25
       )

    jac[jmg26, jn] = (
       -rho*Y[jmg26]*rate_eval.n_Mg26__Mg27
       +rho*Y[jal26]*rate_eval.n_Al26__p_Mg26
       +rho*Y[jmg25]*rate_eval.n_Mg25__Mg26
       )

    jac[jmg26, jp] = (
       -rho*Y[jmg26]*rate_eval.p_Mg26__Al27
       +rho*Y[jal29]*rate_eval.p_Al29__He4_Mg26
       +rho*Y[jna25]*rate_eval.p_Na25__Mg26
       +rho*Y[jna26]*rate_eval.p_Na26__n_Mg26
       )

    jac[jmg26, jhe4] = (
       -rho*Y[jmg26]*rate_eval.He4_Mg26__n_Si29
       -rho*Y[jmg26]*rate_eval.He4_Mg26__Si30
       +rho*Y[jne23]*rate_eval.He4_Ne23__n_Mg26
       +rho*Y[jna23]*rate_eval.He4_Na23__p_Mg26
       +rho*Y[jne22]*rate_eval.He4_Ne22__Mg26
       )

    jac[jmg26, jne22] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne22__Mg26
       )

    jac[jmg26, jne23] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne23__n_Mg26
       )

    jac[jmg26, jna23] = (
       +rho*Y[jhe4]*rate_eval.He4_Na23__p_Mg26
       )

    jac[jmg26, jna25] = (
       +rho*Y[jp]*rate_eval.p_Na25__Mg26
       )

    jac[jmg26, jna26] = (
       +rate_eval.Na26__Mg26__weak__wc12
       +rho*Y[jp]*rate_eval.p_Na26__n_Mg26
       )

    jac[jmg26, jna27] = (
       +rate_eval.Na27__n_Mg26__weak__wc12
       )

    jac[jmg26, jmg25] = (
       +rho*Y[jn]*rate_eval.n_Mg25__Mg26
       )

    jac[jmg26, jmg26] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg26__n_Si29
       -rho*Y[jn]*rate_eval.n_Mg26__Mg27
       -rho*Y[jp]*rate_eval.p_Mg26__Al27
       -rho*Y[jhe4]*rate_eval.He4_Mg26__Si30
       )

    jac[jmg26, jal26] = (
       +rho*Y[jn]*rate_eval.n_Al26__p_Mg26
       +rate_eval.Al26__Mg26__weak__wc12
       )

    jac[jmg26, jal29] = (
       +rho*Y[jp]*rate_eval.p_Al29__He4_Mg26
       )

    jac[jmg27, jn] = (
       -rho*Y[jmg27]*rate_eval.n_Mg27__Mg28
       +rho*Y[jmg26]*rate_eval.n_Mg26__Mg27
       )

    jac[jmg27, jp] = (
       -rho*Y[jmg27]*rate_eval.p_Mg27__Al28
       -rho*Y[jmg27]*rate_eval.p_Mg27__n_Al27
       +rho*Y[jal30]*rate_eval.p_Al30__He4_Mg27
       +rho*Y[jna27]*rate_eval.p_Na27__n_Mg27
       +rho*Y[jna26]*rate_eval.p_Na26__Mg27
       )

    jac[jmg27, jhe4] = (
       -rho*Y[jmg27]*rate_eval.He4_Mg27__n_Si30
       -rho*Y[jmg27]*rate_eval.He4_Mg27__Si31
       +rho*Y[jna24]*rate_eval.He4_Na24__p_Mg27
       +rho*Y[jne24]*rate_eval.He4_Ne24__n_Mg27
       +rho*Y[jne23]*rate_eval.He4_Ne23__Mg27
       )

    jac[jmg27, jne23] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne23__Mg27
       )

    jac[jmg27, jne24] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne24__n_Mg27
       )

    jac[jmg27, jna24] = (
       +rho*Y[jhe4]*rate_eval.He4_Na24__p_Mg27
       )

    jac[jmg27, jna26] = (
       +rho*Y[jp]*rate_eval.p_Na26__Mg27
       )

    jac[jmg27, jna27] = (
       +rho*Y[jp]*rate_eval.p_Na27__n_Mg27
       +rate_eval.Na27__Mg27__weak__wc12
       )

    jac[jmg27, jna28] = (
       +rate_eval.Na28__n_Mg27__weak__wc12
       )

    jac[jmg27, jmg26] = (
       +rho*Y[jn]*rate_eval.n_Mg26__Mg27
       )

    jac[jmg27, jmg27] = (
       -rate_eval.Mg27__Al27__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Mg27__n_Si30
       -rho*Y[jn]*rate_eval.n_Mg27__Mg28
       -rho*Y[jp]*rate_eval.p_Mg27__Al28
       -rho*Y[jhe4]*rate_eval.He4_Mg27__Si31
       -rho*Y[jp]*rate_eval.p_Mg27__n_Al27
       )

    jac[jmg27, jal30] = (
       +rho*Y[jp]*rate_eval.p_Al30__He4_Mg27
       )

    jac[jmg28, jn] = (
       -rho*Y[jmg28]*rate_eval.n_Mg28__Mg29
       +rho*Y[jmg27]*rate_eval.n_Mg27__Mg28
       )

    jac[jmg28, jp] = (
       -rho*Y[jmg28]*rate_eval.p_Mg28__Al29
       -rho*Y[jmg28]*rate_eval.p_Mg28__n_Al28
       +rho*Y[jal31]*rate_eval.p_Al31__He4_Mg28
       +rho*Y[jna28]*rate_eval.p_Na28__n_Mg28
       +rho*Y[jna27]*rate_eval.p_Na27__Mg28
       )

    jac[jmg28, jhe4] = (
       -rho*Y[jmg28]*rate_eval.He4_Mg28__Si32
       -rho*Y[jmg28]*rate_eval.He4_Mg28__n_Si31
       +rho*Y[jne24]*rate_eval.He4_Ne24__Mg28
       +rho*Y[jne25]*rate_eval.He4_Ne25__n_Mg28
       +rho*Y[jna25]*rate_eval.He4_Na25__p_Mg28
       )

    jac[jmg28, jne24] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne24__Mg28
       )

    jac[jmg28, jne25] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne25__n_Mg28
       )

    jac[jmg28, jna25] = (
       +rho*Y[jhe4]*rate_eval.He4_Na25__p_Mg28
       )

    jac[jmg28, jna27] = (
       +rho*Y[jp]*rate_eval.p_Na27__Mg28
       )

    jac[jmg28, jna28] = (
       +rho*Y[jp]*rate_eval.p_Na28__n_Mg28
       +rate_eval.Na28__Mg28__weak__wc12
       )

    jac[jmg28, jna29] = (
       +rate_eval.Na29__n_Mg28__weak__wc12
       )

    jac[jmg28, jna30] = (
       +rate_eval.Na30__n_n_Mg28__weak__wc12
       )

    jac[jmg28, jna31] = (
       +rate_eval.Na31__n_n_n_Mg28__weak__wc12
       )

    jac[jmg28, jmg27] = (
       +rho*Y[jn]*rate_eval.n_Mg27__Mg28
       )

    jac[jmg28, jmg28] = (
       -rho*Y[jn]*rate_eval.n_Mg28__Mg29
       -rho*Y[jhe4]*rate_eval.He4_Mg28__Si32
       -rho*Y[jhe4]*rate_eval.He4_Mg28__n_Si31
       -rate_eval.Mg28__Al28__weak__wc12
       -rho*Y[jp]*rate_eval.p_Mg28__Al29
       -rho*Y[jp]*rate_eval.p_Mg28__n_Al28
       )

    jac[jmg28, jal31] = (
       +rho*Y[jp]*rate_eval.p_Al31__He4_Mg28
       )

    jac[jmg29, jn] = (
       -rho*Y[jmg29]*rate_eval.n_Mg29__Mg30
       +rho*Y[jmg28]*rate_eval.n_Mg28__Mg29
       )

    jac[jmg29, jp] = (
       -rho*Y[jmg29]*rate_eval.p_Mg29__He4_Na26
       -rho*Y[jmg29]*rate_eval.p_Mg29__n_Al29
       -rho*Y[jmg29]*rate_eval.p_Mg29__Al30
       +rho*Y[jal32]*rate_eval.p_Al32__He4_Mg29
       +rho*Y[jna28]*rate_eval.p_Na28__Mg29
       +rho*Y[jna29]*rate_eval.p_Na29__n_Mg29
       )

    jac[jmg29, jhe4] = (
       -rho*Y[jmg29]*rate_eval.He4_Mg29__Si33
       -rho*Y[jmg29]*rate_eval.He4_Mg29__n_Si32
       +rho*Y[jne26]*rate_eval.He4_Ne26__n_Mg29
       +rho*Y[jne25]*rate_eval.He4_Ne25__Mg29
       )

    jac[jmg29, jne25] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne25__Mg29
       )

    jac[jmg29, jne26] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne26__n_Mg29
       )

    jac[jmg29, jna28] = (
       +rho*Y[jp]*rate_eval.p_Na28__Mg29
       )

    jac[jmg29, jna29] = (
       +rho*Y[jp]*rate_eval.p_Na29__n_Mg29
       +rate_eval.Na29__Mg29__weak__wc12
       )

    jac[jmg29, jna30] = (
       +rate_eval.Na30__n_Mg29__weak__wc17
       )

    jac[jmg29, jna31] = (
       +rate_eval.Na31__n_n_Mg29__weak__wc12
       )

    jac[jmg29, jna32] = (
       +rate_eval.Na32__n_n_n_Mg29__weak__mo03
       )

    jac[jmg29, jmg28] = (
       +rho*Y[jn]*rate_eval.n_Mg28__Mg29
       )

    jac[jmg29, jmg29] = (
       -rho*Y[jp]*rate_eval.p_Mg29__He4_Na26
       -rho*Y[jp]*rate_eval.p_Mg29__n_Al29
       -rho*Y[jhe4]*rate_eval.He4_Mg29__Si33
       -rho*Y[jn]*rate_eval.n_Mg29__Mg30
       -rho*Y[jhe4]*rate_eval.He4_Mg29__n_Si32
       -rate_eval.Mg29__Al29__weak__wc12
       -rho*Y[jp]*rate_eval.p_Mg29__Al30
       )

    jac[jmg29, jal32] = (
       +rho*Y[jp]*rate_eval.p_Al32__He4_Mg29
       )

    jac[jmg30, jn] = (
       -rho*Y[jmg30]*rate_eval.n_Mg30__Mg31
       +rho*Y[jmg29]*rate_eval.n_Mg29__Mg30
       )

    jac[jmg30, jp] = (
       -rho*Y[jmg30]*rate_eval.p_Mg30__n_Al30
       -rho*Y[jmg30]*rate_eval.p_Mg30__Al31
       -rho*Y[jmg30]*rate_eval.p_Mg30__He4_Na27
       +rho*Y[jal33]*rate_eval.p_Al33__He4_Mg30
       +rho*Y[jna29]*rate_eval.p_Na29__Mg30
       +rho*Y[jna30]*rate_eval.p_Na30__n_Mg30
       )

    jac[jmg30, jhe4] = (
       -rho*Y[jmg30]*rate_eval.He4_Mg30__n_Si33
       -rho*Y[jmg30]*rate_eval.He4_Mg30__Si34
       +rho*Y[jne27]*rate_eval.He4_Ne27__n_Mg30
       +rho*Y[jne26]*rate_eval.He4_Ne26__Mg30
       )

    jac[jmg30, jne26] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne26__Mg30
       )

    jac[jmg30, jne27] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne27__n_Mg30
       )

    jac[jmg30, jna29] = (
       +rho*Y[jp]*rate_eval.p_Na29__Mg30
       )

    jac[jmg30, jna30] = (
       +rate_eval.Na30__Mg30__weak__wc12
       +rho*Y[jp]*rate_eval.p_Na30__n_Mg30
       )

    jac[jmg30, jna31] = (
       +rate_eval.Na31__n_Mg30__weak__wc17
       )

    jac[jmg30, jna32] = (
       +rate_eval.Na32__n_n_Mg30__weak__wc12
       )

    jac[jmg30, jna33] = (
       +rate_eval.Na33__n_n_n_Mg30__weak__mo03
       )

    jac[jmg30, jmg29] = (
       +rho*Y[jn]*rate_eval.n_Mg29__Mg30
       )

    jac[jmg30, jmg30] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg30__n_Si33
       -rho*Y[jp]*rate_eval.p_Mg30__n_Al30
       -rho*Y[jp]*rate_eval.p_Mg30__Al31
       -rho*Y[jhe4]*rate_eval.He4_Mg30__Si34
       -rho*Y[jn]*rate_eval.n_Mg30__Mg31
       -rho*Y[jp]*rate_eval.p_Mg30__He4_Na27
       -rate_eval.Mg30__Al30__weak__wc12
       )

    jac[jmg30, jal33] = (
       +rho*Y[jp]*rate_eval.p_Al33__He4_Mg30
       )

    jac[jmg31, jn] = (
       -rho*Y[jmg31]*rate_eval.n_Mg31__Mg32
       +rho*Y[jmg30]*rate_eval.n_Mg30__Mg31
       )

    jac[jmg31, jp] = (
       -rho*Y[jmg31]*rate_eval.p_Mg31__n_Al31
       -rho*Y[jmg31]*rate_eval.p_Mg31__Al32
       -rho*Y[jmg31]*rate_eval.p_Mg31__He4_Na28
       +rho*Y[jal34]*rate_eval.p_Al34__He4_Mg31
       +rho*Y[jna31]*rate_eval.p_Na31__n_Mg31
       +rho*Y[jna30]*rate_eval.p_Na30__Mg31
       )

    jac[jmg31, jhe4] = (
       -rho*Y[jmg31]*rate_eval.He4_Mg31__Si35
       -rho*Y[jmg31]*rate_eval.He4_Mg31__n_Si34
       +rho*Y[jne28]*rate_eval.He4_Ne28__n_Mg31
       +rho*Y[jne27]*rate_eval.He4_Ne27__Mg31
       )

    jac[jmg31, jne27] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne27__Mg31
       )

    jac[jmg31, jne28] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne28__n_Mg31
       )

    jac[jmg31, jna30] = (
       +rho*Y[jp]*rate_eval.p_Na30__Mg31
       )

    jac[jmg31, jna31] = (
       +rho*Y[jp]*rate_eval.p_Na31__n_Mg31
       +rate_eval.Na31__Mg31__weak__wc12
       )

    jac[jmg31, jna32] = (
       +rate_eval.Na32__n_Mg31__weak__wc17
       )

    jac[jmg31, jna33] = (
       +rate_eval.Na33__n_n_Mg31__weak__wc12
       )

    jac[jmg31, jna34] = (
       +rate_eval.Na34__n_n_n_Mg31__weak__mo03
       )

    jac[jmg31, jmg30] = (
       +rho*Y[jn]*rate_eval.n_Mg30__Mg31
       )

    jac[jmg31, jmg31] = (
       -rho*Y[jp]*rate_eval.p_Mg31__n_Al31
       -rho*Y[jp]*rate_eval.p_Mg31__Al32
       -rho*Y[jhe4]*rate_eval.He4_Mg31__Si35
       -rho*Y[jn]*rate_eval.n_Mg31__Mg32
       -rho*Y[jhe4]*rate_eval.He4_Mg31__n_Si34
       -rho*Y[jp]*rate_eval.p_Mg31__He4_Na28
       -rate_eval.Mg31__Al31__weak__wc12
       -rate_eval.Mg31__n_Al30__weak__wc12
       )

    jac[jmg31, jal34] = (
       +rho*Y[jp]*rate_eval.p_Al34__He4_Mg31
       )

    jac[jmg32, jn] = (
       -rho*Y[jmg32]*rate_eval.n_Mg32__Mg33
       +rho*Y[jmg31]*rate_eval.n_Mg31__Mg32
       )

    jac[jmg32, jp] = (
       -rho*Y[jmg32]*rate_eval.p_Mg32__He4_Na29
       -rho*Y[jmg32]*rate_eval.p_Mg32__Al33
       -rho*Y[jmg32]*rate_eval.p_Mg32__n_Al32
       +rho*Y[jal35]*rate_eval.p_Al35__He4_Mg32
       +rho*Y[jna31]*rate_eval.p_Na31__Mg32
       +rho*Y[jna32]*rate_eval.p_Na32__n_Mg32
       )

    jac[jmg32, jhe4] = (
       -rho*Y[jmg32]*rate_eval.He4_Mg32__n_Si35
       -rho*Y[jmg32]*rate_eval.He4_Mg32__Si36
       +rho*Y[jne29]*rate_eval.He4_Ne29__n_Mg32
       +rho*Y[jne28]*rate_eval.He4_Ne28__Mg32
       )

    jac[jmg32, jne28] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne28__Mg32
       )

    jac[jmg32, jne29] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne29__n_Mg32
       )

    jac[jmg32, jna31] = (
       +rho*Y[jp]*rate_eval.p_Na31__Mg32
       )

    jac[jmg32, jna32] = (
       +rho*Y[jp]*rate_eval.p_Na32__n_Mg32
       +rate_eval.Na32__Mg32__weak__wc12
       )

    jac[jmg32, jna33] = (
       +rate_eval.Na33__n_Mg32__weak__wc17
       )

    jac[jmg32, jna34] = (
       +rate_eval.Na34__n_n_Mg32__weak__wc12
       )

    jac[jmg32, jna35] = (
       +rate_eval.Na35__n_n_n_Mg32__weak__mo03
       )

    jac[jmg32, jmg31] = (
       +rho*Y[jn]*rate_eval.n_Mg31__Mg32
       )

    jac[jmg32, jmg32] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg32__n_Si35
       -rho*Y[jp]*rate_eval.p_Mg32__He4_Na29
       -rho*Y[jn]*rate_eval.n_Mg32__Mg33
       -rho*Y[jp]*rate_eval.p_Mg32__Al33
       -rate_eval.Mg32__n_Al31__weak__wc12
       -rho*Y[jp]*rate_eval.p_Mg32__n_Al32
       -rho*Y[jhe4]*rate_eval.He4_Mg32__Si36
       -rate_eval.Mg32__Al32__weak__wc12
       )

    jac[jmg32, jal35] = (
       +rho*Y[jp]*rate_eval.p_Al35__He4_Mg32
       )

    jac[jmg33, jn] = (
       -rho*Y[jmg33]*rate_eval.n_Mg33__Mg34
       +rho*Y[jmg32]*rate_eval.n_Mg32__Mg33
       )

    jac[jmg33, jp] = (
       -rho*Y[jmg33]*rate_eval.p_Mg33__He4_Na30
       -rho*Y[jmg33]*rate_eval.p_Mg33__n_Al33
       -rho*Y[jmg33]*rate_eval.p_Mg33__Al34
       +rho*Y[jal36]*rate_eval.p_Al36__He4_Mg33
       +rho*Y[jna33]*rate_eval.p_Na33__n_Mg33
       +rho*Y[jna32]*rate_eval.p_Na32__Mg33
       )

    jac[jmg33, jhe4] = (
       -rho*Y[jmg33]*rate_eval.He4_Mg33__n_Si36
       -rho*Y[jmg33]*rate_eval.He4_Mg33__Si37
       +rho*Y[jne29]*rate_eval.He4_Ne29__Mg33
       +rho*Y[jne30]*rate_eval.He4_Ne30__n_Mg33
       )

    jac[jmg33, jne29] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne29__Mg33
       )

    jac[jmg33, jne30] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne30__n_Mg33
       )

    jac[jmg33, jna32] = (
       +rho*Y[jp]*rate_eval.p_Na32__Mg33
       )

    jac[jmg33, jna33] = (
       +rho*Y[jp]*rate_eval.p_Na33__n_Mg33
       +rate_eval.Na33__Mg33__weak__wc12
       )

    jac[jmg33, jna34] = (
       +rate_eval.Na34__n_Mg33__weak__wc12
       )

    jac[jmg33, jna35] = (
       +rate_eval.Na35__n_n_Mg33__weak__mp17
       )

    jac[jmg33, jmg32] = (
       +rho*Y[jn]*rate_eval.n_Mg32__Mg33
       )

    jac[jmg33, jmg33] = (
       -rho*Y[jp]*rate_eval.p_Mg33__He4_Na30
       -rho*Y[jhe4]*rate_eval.He4_Mg33__n_Si36
       -rho*Y[jhe4]*rate_eval.He4_Mg33__Si37
       -rho*Y[jp]*rate_eval.p_Mg33__n_Al33
       -rate_eval.Mg33__n_Al32__weak__wc12
       -rate_eval.Mg33__n_n_Al31__weak__mp17
       -rate_eval.Mg33__Al33__weak__wc12
       -rho*Y[jn]*rate_eval.n_Mg33__Mg34
       -rho*Y[jp]*rate_eval.p_Mg33__Al34
       )

    jac[jmg33, jal36] = (
       +rho*Y[jp]*rate_eval.p_Al36__He4_Mg33
       )

    jac[jmg34, jn] = (
       -rho*Y[jmg34]*rate_eval.n_Mg34__Mg35
       +rho*Y[jmg33]*rate_eval.n_Mg33__Mg34
       )

    jac[jmg34, jp] = (
       -rho*Y[jmg34]*rate_eval.p_Mg34__Al35
       -rho*Y[jmg34]*rate_eval.p_Mg34__He4_Na31
       -rho*Y[jmg34]*rate_eval.p_Mg34__n_Al34
       +rho*Y[jal37]*rate_eval.p_Al37__He4_Mg34
       +rho*Y[jna34]*rate_eval.p_Na34__n_Mg34
       +rho*Y[jna33]*rate_eval.p_Na33__Mg34
       )

    jac[jmg34, jhe4] = (
       -rho*Y[jmg34]*rate_eval.He4_Mg34__n_Si37
       -rho*Y[jmg34]*rate_eval.He4_Mg34__Si38
       +rho*Y[jne31]*rate_eval.He4_Ne31__n_Mg34
       +rho*Y[jne30]*rate_eval.He4_Ne30__Mg34
       )

    jac[jmg34, jne30] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne30__Mg34
       )

    jac[jmg34, jne31] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne31__n_Mg34
       )

    jac[jmg34, jna33] = (
       +rho*Y[jp]*rate_eval.p_Na33__Mg34
       )

    jac[jmg34, jna34] = (
       +rho*Y[jp]*rate_eval.p_Na34__n_Mg34
       +rate_eval.Na34__Mg34__weak__wc12
       )

    jac[jmg34, jna35] = (
       +rate_eval.Na35__n_Mg34__weak__mp17
       )

    jac[jmg34, jmg33] = (
       +rho*Y[jn]*rate_eval.n_Mg33__Mg34
       )

    jac[jmg34, jmg34] = (
       -rho*Y[jp]*rate_eval.p_Mg34__Al35
       -rho*Y[jhe4]*rate_eval.He4_Mg34__n_Si37
       -rho*Y[jp]*rate_eval.p_Mg34__He4_Na31
       -rho*Y[jhe4]*rate_eval.He4_Mg34__Si38
       -rho*Y[jn]*rate_eval.n_Mg34__Mg35
       -rate_eval.Mg34__n_Al33__weak__mp17
       -rate_eval.Mg34__Al34__weak__wc17
       -rho*Y[jp]*rate_eval.p_Mg34__n_Al34
       )

    jac[jmg34, jal37] = (
       +rho*Y[jp]*rate_eval.p_Al37__He4_Mg34
       )

    jac[jmg35, jn] = (
       -rho*Y[jmg35]*rate_eval.n_Mg35__Mg36
       +rho*Y[jmg34]*rate_eval.n_Mg34__Mg35
       )

    jac[jmg35, jp] = (
       -rho*Y[jmg35]*rate_eval.p_Mg35__n_Al35
       -rho*Y[jmg35]*rate_eval.p_Mg35__He4_Na32
       -rho*Y[jmg35]*rate_eval.p_Mg35__Al36
       +rho*Y[jna34]*rate_eval.p_Na34__Mg35
       +rho*Y[jal38]*rate_eval.p_Al38__He4_Mg35
       +rho*Y[jna35]*rate_eval.p_Na35__n_Mg35
       )

    jac[jmg35, jhe4] = (
       -rho*Y[jmg35]*rate_eval.He4_Mg35__n_Si38
       -rho*Y[jmg35]*rate_eval.He4_Mg35__Si39
       +rho*Y[jne32]*rate_eval.He4_Ne32__n_Mg35
       +rho*Y[jne31]*rate_eval.He4_Ne31__Mg35
       )

    jac[jmg35, jne31] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne31__Mg35
       )

    jac[jmg35, jne32] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne32__n_Mg35
       )

    jac[jmg35, jna34] = (
       +rho*Y[jp]*rate_eval.p_Na34__Mg35
       )

    jac[jmg35, jna35] = (
       +rho*Y[jp]*rate_eval.p_Na35__n_Mg35
       +rate_eval.Na35__Mg35__weak__wc17
       )

    jac[jmg35, jna36] = (
       +rate_eval.Na36__n_Mg35__weak__mp17
       )

    jac[jmg35, jna37] = (
       +rate_eval.Na37__n_n_Mg35__weak__mp17
       )

    jac[jmg35, jmg34] = (
       +rho*Y[jn]*rate_eval.n_Mg34__Mg35
       )

    jac[jmg35, jmg35] = (
       -rate_eval.Mg35__n_n_n_Al32__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Mg35__n_Si38
       -rho*Y[jp]*rate_eval.p_Mg35__n_Al35
       -rho*Y[jn]*rate_eval.n_Mg35__Mg36
       -rate_eval.Mg35__n_Al34__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Mg35__Si39
       -rate_eval.Mg35__n_n_Al33__weak__mp17
       -rho*Y[jp]*rate_eval.p_Mg35__He4_Na32
       -rho*Y[jp]*rate_eval.p_Mg35__Al36
       -rate_eval.Mg35__Al35__weak__wc17
       )

    jac[jmg35, jal38] = (
       +rho*Y[jp]*rate_eval.p_Al38__He4_Mg35
       )

    jac[jmg36, jn] = (
       -rho*Y[jmg36]*rate_eval.n_Mg36__Mg37
       +rho*Y[jmg35]*rate_eval.n_Mg35__Mg36
       )

    jac[jmg36, jp] = (
       -rho*Y[jmg36]*rate_eval.p_Mg36__Al37
       -rho*Y[jmg36]*rate_eval.p_Mg36__n_Al36
       +rho*Y[jna36]*rate_eval.p_Na36__n_Mg36
       +rho*Y[jal39]*rate_eval.p_Al39__He4_Mg36
       +rho*Y[jna35]*rate_eval.p_Na35__Mg36
       )

    jac[jmg36, jhe4] = (
       -rho*Y[jmg36]*rate_eval.He4_Mg36__Si40
       -rho*Y[jmg36]*rate_eval.He4_Mg36__n_Si39
       +rho*Y[jne33]*rate_eval.He4_Ne33__n_Mg36
       +rho*Y[jna33]*rate_eval.He4_Na33__p_Mg36
       +rho*Y[jne32]*rate_eval.He4_Ne32__Mg36
       )

    jac[jmg36, jne32] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne32__Mg36
       )

    jac[jmg36, jne33] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne33__n_Mg36
       )

    jac[jmg36, jna33] = (
       +rho*Y[jhe4]*rate_eval.He4_Na33__p_Mg36
       )

    jac[jmg36, jna35] = (
       +rho*Y[jp]*rate_eval.p_Na35__Mg36
       )

    jac[jmg36, jna36] = (
       +rho*Y[jp]*rate_eval.p_Na36__n_Mg36
       +rate_eval.Na36__Mg36__weak__mo03
       )

    jac[jmg36, jna37] = (
       +rate_eval.Na37__n_Mg36__weak__mp17
       )

    jac[jmg36, jmg35] = (
       +rho*Y[jn]*rate_eval.n_Mg35__Mg36
       )

    jac[jmg36, jmg36] = (
       -rate_eval.Mg36__n_n_n_Al33__weak__mo03
       -rate_eval.Mg36__n_n_Al34__weak__mp17
       -rate_eval.Mg36__Al36__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_Mg36__Si40
       -rho*Y[jn]*rate_eval.n_Mg36__Mg37
       -rho*Y[jp]*rate_eval.p_Mg36__Al37
       -rho*Y[jhe4]*rate_eval.He4_Mg36__n_Si39
       -rho*Y[jp]*rate_eval.p_Mg36__n_Al36
       -rate_eval.Mg36__n_Al35__weak__mp17
       )

    jac[jmg36, jal39] = (
       +rho*Y[jp]*rate_eval.p_Al39__He4_Mg36
       )

    jac[jmg37, jn] = (
       -rho*Y[jmg37]*rate_eval.n_Mg37__Mg38
       +rho*Y[jmg36]*rate_eval.n_Mg36__Mg37
       )

    jac[jmg37, jp] = (
       -rho*Y[jmg37]*rate_eval.p_Mg37__n_Al37
       -rho*Y[jmg37]*rate_eval.p_Mg37__Al38
       -rho*Y[jmg37]*rate_eval.p_Mg37__He4_Na34
       +rho*Y[jal40]*rate_eval.p_Al40__He4_Mg37
       +rho*Y[jna36]*rate_eval.p_Na36__Mg37
       +rho*Y[jna37]*rate_eval.p_Na37__n_Mg37
       )

    jac[jmg37, jhe4] = (
       -rho*Y[jmg37]*rate_eval.He4_Mg37__n_Si40
       -rho*Y[jmg37]*rate_eval.He4_Mg37__Si41
       +rho*Y[jne34]*rate_eval.He4_Ne34__n_Mg37
       +rho*Y[jne33]*rate_eval.He4_Ne33__Mg37
       )

    jac[jmg37, jne33] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne33__Mg37
       )

    jac[jmg37, jne34] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne34__n_Mg37
       )

    jac[jmg37, jna36] = (
       +rho*Y[jp]*rate_eval.p_Na36__Mg37
       )

    jac[jmg37, jna37] = (
       +rho*Y[jp]*rate_eval.p_Na37__n_Mg37
       )

    jac[jmg37, jna38] = (
       +rate_eval.Na38__n_Mg37__weak__mp17
       )

    jac[jmg37, jna39] = (
       +rate_eval.Na39__n_n_Mg37__weak__mp17
       )

    jac[jmg37, jmg36] = (
       +rho*Y[jn]*rate_eval.n_Mg36__Mg37
       )

    jac[jmg37, jmg37] = (
       -rate_eval.Mg37__n_n_n_Al34__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Mg37__n_Si40
       -rate_eval.Mg37__n_Al36__weak__mp17
       -rate_eval.Mg37__Al37__weak__mo03
       -rho*Y[jp]*rate_eval.p_Mg37__n_Al37
       -rho*Y[jhe4]*rate_eval.He4_Mg37__Si41
       -rho*Y[jp]*rate_eval.p_Mg37__Al38
       -rate_eval.Mg37__n_n_Al35__weak__mp17
       -rho*Y[jp]*rate_eval.p_Mg37__He4_Na34
       -rho*Y[jn]*rate_eval.n_Mg37__Mg38
       )

    jac[jmg37, jal40] = (
       +rho*Y[jp]*rate_eval.p_Al40__He4_Mg37
       )

    jac[jmg38, jn] = (
       -rho*Y[jmg38]*rate_eval.n_Mg38__Mg39
       +rho*Y[jmg37]*rate_eval.n_Mg37__Mg38
       )

    jac[jmg38, jp] = (
       -rho*Y[jmg38]*rate_eval.p_Mg38__n_Al38
       -rho*Y[jmg38]*rate_eval.p_Mg38__Al39
       -rho*Y[jmg38]*rate_eval.p_Mg38__He4_Na35
       +rho*Y[jal41]*rate_eval.p_Al41__He4_Mg38
       +rho*Y[jna37]*rate_eval.p_Na37__Mg38
       +rho*Y[jna38]*rate_eval.p_Na38__n_Mg38
       )

    jac[jmg38, jhe4] = (
       -rho*Y[jmg38]*rate_eval.He4_Mg38__n_Si41
       -rho*Y[jmg38]*rate_eval.He4_Mg38__Si42
       +rho*Y[jne34]*rate_eval.He4_Ne34__Mg38
       )

    jac[jmg38, jne34] = (
       +rho*Y[jhe4]*rate_eval.He4_Ne34__Mg38
       )

    jac[jmg38, jna37] = (
       +rho*Y[jp]*rate_eval.p_Na37__Mg38
       )

    jac[jmg38, jna38] = (
       +rate_eval.Na38__Mg38__weak__mo03
       +rho*Y[jp]*rate_eval.p_Na38__n_Mg38
       )

    jac[jmg38, jna39] = (
       +rate_eval.Na39__n_Mg38__weak__mp17
       )

    jac[jmg38, jmg37] = (
       +rho*Y[jn]*rate_eval.n_Mg37__Mg38
       )

    jac[jmg38, jmg38] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg38__n_Si41
       -rho*Y[jp]*rate_eval.p_Mg38__n_Al38
       -rate_eval.Mg38__Al38__weak__mo03
       -rho*Y[jp]*rate_eval.p_Mg38__Al39
       -rate_eval.Mg38__n_n_Al36__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Mg38__Si42
       -rho*Y[jn]*rate_eval.n_Mg38__Mg39
       -rate_eval.Mg38__n_n_n_Al35__weak__mo03
       -rho*Y[jp]*rate_eval.p_Mg38__He4_Na35
       -rate_eval.Mg38__n_Al37__weak__mp17
       )

    jac[jmg38, jal41] = (
       +rho*Y[jp]*rate_eval.p_Al41__He4_Mg38
       )

    jac[jmg39, jn] = (
       -rho*Y[jmg39]*rate_eval.n_Mg39__Mg40
       +rho*Y[jmg38]*rate_eval.n_Mg38__Mg39
       )

    jac[jmg39, jp] = (
       -rho*Y[jmg39]*rate_eval.p_Mg39__n_Al39
       -rho*Y[jmg39]*rate_eval.p_Mg39__Al40
       -rho*Y[jmg39]*rate_eval.p_Mg39__He4_Na36
       +rho*Y[jna39]*rate_eval.p_Na39__n_Mg39
       +rho*Y[jal42]*rate_eval.p_Al42__He4_Mg39
       +rho*Y[jna38]*rate_eval.p_Na38__Mg39
       )

    jac[jmg39, jhe4] = (
       -rho*Y[jmg39]*rate_eval.He4_Mg39__n_Si42
       -rho*Y[jmg39]*rate_eval.He4_Mg39__Si43
       )

    jac[jmg39, jna38] = (
       +rho*Y[jp]*rate_eval.p_Na38__Mg39
       )

    jac[jmg39, jna39] = (
       +rho*Y[jp]*rate_eval.p_Na39__n_Mg39
       )

    jac[jmg39, jmg38] = (
       +rho*Y[jn]*rate_eval.n_Mg38__Mg39
       )

    jac[jmg39, jmg39] = (
       -rate_eval.Mg39__n_n_n_Al36__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Mg39__n_Si42
       -rho*Y[jp]*rate_eval.p_Mg39__n_Al39
       -rate_eval.Mg39__n_Al38__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Mg39__Si43
       -rho*Y[jp]*rate_eval.p_Mg39__Al40
       -rate_eval.Mg39__n_n_Al37__weak__mp17
       -rate_eval.Mg39__Al39__weak__mo03
       -rho*Y[jn]*rate_eval.n_Mg39__Mg40
       -rho*Y[jp]*rate_eval.p_Mg39__He4_Na36
       )

    jac[jmg39, jal42] = (
       +rho*Y[jp]*rate_eval.p_Al42__He4_Mg39
       )

    jac[jmg40, jn] = (
       -rho*Y[jmg40]*rate_eval.n_Mg40__Mg41
       +rho*Y[jmg39]*rate_eval.n_Mg39__Mg40
       )

    jac[jmg40, jp] = (
       -rho*Y[jmg40]*rate_eval.p_Mg40__n_Al40
       -rho*Y[jmg40]*rate_eval.p_Mg40__Al41
       +rho*Y[jal43]*rate_eval.p_Al43__He4_Mg40
       +rho*Y[jna39]*rate_eval.p_Na39__Mg40
       )

    jac[jmg40, jhe4] = (
       -rho*Y[jmg40]*rate_eval.He4_Mg40__n_Si43
       -rho*Y[jmg40]*rate_eval.He4_Mg40__Si44
       +rho*Y[jna37]*rate_eval.He4_Na37__p_Mg40
       )

    jac[jmg40, jna37] = (
       +rho*Y[jhe4]*rate_eval.He4_Na37__p_Mg40
       )

    jac[jmg40, jna39] = (
       +rho*Y[jp]*rate_eval.p_Na39__Mg40
       )

    jac[jmg40, jmg39] = (
       +rho*Y[jn]*rate_eval.n_Mg39__Mg40
       )

    jac[jmg40, jmg40] = (
       -rate_eval.Mg40__n_n_n_Al37__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Mg40__n_Si43
       -rho*Y[jp]*rate_eval.p_Mg40__n_Al40
       -rho*Y[jhe4]*rate_eval.He4_Mg40__Si44
       -rho*Y[jn]*rate_eval.n_Mg40__Mg41
       -rate_eval.Mg40__n_n_Al38__weak__mp17
       -rate_eval.Mg40__n_Al39__weak__mp17
       -rho*Y[jp]*rate_eval.p_Mg40__Al41
       )

    jac[jmg40, jal43] = (
       +rho*Y[jp]*rate_eval.p_Al43__He4_Mg40
       )

    jac[jmg41, jn] = (
       +rho*Y[jmg40]*rate_eval.n_Mg40__Mg41
       )

    jac[jmg41, jp] = (
       -rho*Y[jmg41]*rate_eval.p_Mg41__Al42
       -rho*Y[jmg41]*rate_eval.p_Mg41__n_Al41
       -rho*Y[jmg41]*rate_eval.p_Mg41__He4_Na38
       )

    jac[jmg41, jhe4] = (
       -rho*Y[jmg41]*rate_eval.He4_Mg41__Si45
       -rho*Y[jmg41]*rate_eval.He4_Mg41__n_Si44
       )

    jac[jmg41, jmg40] = (
       +rho*Y[jn]*rate_eval.n_Mg40__Mg41
       )

    jac[jmg41, jmg41] = (
       -rho*Y[jhe4]*rate_eval.He4_Mg41__Si45
       -rate_eval.Mg41__n_Al40__weak__mp17
       -rho*Y[jp]*rate_eval.p_Mg41__Al42
       -rho*Y[jp]*rate_eval.p_Mg41__n_Al41
       -rho*Y[jhe4]*rate_eval.He4_Mg41__n_Si44
       -rate_eval.Mg41__Al41__weak__mo03
       -rho*Y[jp]*rate_eval.p_Mg41__He4_Na38
       )

    jac[jal21, jn] = (
       -rho*Y[jal21]*rate_eval.n_Al21__Al22
       -rho*Y[jal21]*rate_eval.n_Al21__p_Mg21
       +rho*Y[jp24]*rate_eval.n_P24__He4_Al21
       )

    jac[jal21, jhe4] = (
       -rho*Y[jal21]*rate_eval.He4_Al21__p_Si24
       -rho*Y[jal21]*rate_eval.He4_Al21__P25
       )

    jac[jal21, jal21] = (
       -rho*Y[jhe4]*rate_eval.He4_Al21__p_Si24
       -rho*Y[jn]*rate_eval.n_Al21__Al22
       -rate_eval.Al21__Mg21__weak__bqa_pos_
       -rho*Y[jhe4]*rate_eval.He4_Al21__P25
       -rho*Y[jn]*rate_eval.n_Al21__p_Mg21
       )

    jac[jal21, jp24] = (
       +rho*Y[jn]*rate_eval.n_P24__He4_Al21
       )

    jac[jal22, jn] = (
       -rho*Y[jal22]*rate_eval.n_Al22__He4_Na19
       -rho*Y[jal22]*rate_eval.n_Al22__p_Mg22
       -rho*Y[jal22]*rate_eval.n_Al22__Al23
       +rho*Y[jsi22]*rate_eval.n_Si22__p_Al22
       +rho*Y[jal21]*rate_eval.n_Al21__Al22
       +rho*Y[jp25]*rate_eval.n_P25__He4_Al22
       )

    jac[jal22, jp] = (
       -rho*Y[jal22]*rate_eval.p_Al22__Si23
       +rho*Y[jmg21]*rate_eval.p_Mg21__Al22
       )

    jac[jal22, jhe4] = (
       -rho*Y[jal22]*rate_eval.He4_Al22__p_Si25
       -rho*Y[jal22]*rate_eval.He4_Al22__P26
       +rho*Y[jmg19]*rate_eval.He4_Mg19__p_Al22
       )

    jac[jal22, jmg19] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg19__p_Al22
       )

    jac[jal22, jmg21] = (
       +rho*Y[jp]*rate_eval.p_Mg21__Al22
       )

    jac[jal22, jal21] = (
       +rho*Y[jn]*rate_eval.n_Al21__Al22
       )

    jac[jal22, jal22] = (
       -rho*Y[jhe4]*rate_eval.He4_Al22__p_Si25
       -rho*Y[jn]*rate_eval.n_Al22__He4_Na19
       -rho*Y[jn]*rate_eval.n_Al22__p_Mg22
       -rate_eval.Al22__Mg22__weak__wc12
       -rate_eval.Al22__p_p_Ne20__weak__wc12
       -rho*Y[jp]*rate_eval.p_Al22__Si23
       -rate_eval.Al22__He4_Ne18__weak__wc12
       -rho*Y[jn]*rate_eval.n_Al22__Al23
       -rate_eval.Al22__p_Na21__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_Al22__P26
       )

    jac[jal22, jsi22] = (
       +rho*Y[jn]*rate_eval.n_Si22__p_Al22
       +rate_eval.Si22__Al22__weak__wc12
       )

    jac[jal22, jp25] = (
       +rho*Y[jn]*rate_eval.n_P25__He4_Al22
       )

    jac[jal23, jn] = (
       -rho*Y[jal23]*rate_eval.n_Al23__He4_Na20
       -rho*Y[jal23]*rate_eval.n_Al23__Al24
       -rho*Y[jal23]*rate_eval.n_Al23__p_Mg23
       +rho*Y[jp26]*rate_eval.n_P26__He4_Al23
       +rho*Y[jsi23]*rate_eval.n_Si23__p_Al23
       +rho*Y[jal22]*rate_eval.n_Al22__Al23
       )

    jac[jal23, jp] = (
       -rho*Y[jal23]*rate_eval.p_Al23__Si24
       +rho*Y[jmg22]*rate_eval.p_Mg22__Al23
       )

    jac[jal23, jhe4] = (
       -rho*Y[jal23]*rate_eval.He4_Al23__p_Si26
       -rho*Y[jal23]*rate_eval.He4_Al23__P27
       +rho*Y[jna19]*rate_eval.He4_Na19__Al23
       +rho*Y[jmg20]*rate_eval.He4_Mg20__p_Al23
       )

    jac[jal23, jna19] = (
       +rho*Y[jhe4]*rate_eval.He4_Na19__Al23
       )

    jac[jal23, jmg20] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg20__p_Al23
       )

    jac[jal23, jmg22] = (
       +rho*Y[jp]*rate_eval.p_Mg22__Al23
       )

    jac[jal23, jal22] = (
       +rho*Y[jn]*rate_eval.n_Al22__Al23
       )

    jac[jal23, jal23] = (
       -rho*Y[jn]*rate_eval.n_Al23__He4_Na20
       -rho*Y[jn]*rate_eval.n_Al23__Al24
       -rho*Y[jp]*rate_eval.p_Al23__Si24
       -rho*Y[jn]*rate_eval.n_Al23__p_Mg23
       -rate_eval.Al23__Mg23__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Al23__p_Si26
       -rate_eval.Al23__p_Na22__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Al23__P27
       )

    jac[jal23, jsi23] = (
       +rho*Y[jn]*rate_eval.n_Si23__p_Al23
       +rate_eval.Si23__Al23__weak__wc12
       )

    jac[jal23, jp26] = (
       +rho*Y[jn]*rate_eval.n_P26__He4_Al23
       )

    jac[jal24, jn] = (
       -rho*Y[jal24]*rate_eval.n_Al24__He4_Na21
       -rho*Y[jal24]*rate_eval.n_Al24__Al25
       -rho*Y[jal24]*rate_eval.n_Al24__p_Mg24
       +rho*Y[jsi24]*rate_eval.n_Si24__p_Al24
       +rho*Y[jp27]*rate_eval.n_P27__He4_Al24
       +rho*Y[jal23]*rate_eval.n_Al23__Al24
       )

    jac[jal24, jp] = (
       -rho*Y[jal24]*rate_eval.p_Al24__Si25
       +rho*Y[jmg23]*rate_eval.p_Mg23__Al24
       )

    jac[jal24, jhe4] = (
       -rho*Y[jal24]*rate_eval.He4_Al24__p_Si27
       -rho*Y[jal24]*rate_eval.He4_Al24__P28
       +rho*Y[jna20]*rate_eval.He4_Na20__Al24
       +rho*Y[jmg21]*rate_eval.He4_Mg21__p_Al24
       )

    jac[jal24, jna20] = (
       +rho*Y[jhe4]*rate_eval.He4_Na20__Al24
       )

    jac[jal24, jmg21] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg21__p_Al24
       )

    jac[jal24, jmg23] = (
       +rho*Y[jp]*rate_eval.p_Mg23__Al24
       )

    jac[jal24, jal23] = (
       +rho*Y[jn]*rate_eval.n_Al23__Al24
       )

    jac[jal24, jal24] = (
       -rho*Y[jhe4]*rate_eval.He4_Al24__p_Si27
       -rho*Y[jn]*rate_eval.n_Al24__He4_Na21
       -rho*Y[jp]*rate_eval.p_Al24__Si25
       -rho*Y[jn]*rate_eval.n_Al24__Al25
       -rate_eval.Al24__p_Na23__weak__wc12
       -rho*Y[jn]*rate_eval.n_Al24__p_Mg24
       -rho*Y[jhe4]*rate_eval.He4_Al24__P28
       -rate_eval.Al24__He4_Ne20__weak__wc12
       -rate_eval.Al24__Mg24__weak__wc12
       )

    jac[jal24, jsi24] = (
       +rho*Y[jn]*rate_eval.n_Si24__p_Al24
       +rate_eval.Si24__Al24__weak__wc12
       )

    jac[jal24, jp27] = (
       +rho*Y[jn]*rate_eval.n_P27__He4_Al24
       )

    jac[jal25, jn] = (
       -rho*Y[jal25]*rate_eval.n_Al25__Al26
       -rho*Y[jal25]*rate_eval.n_Al25__p_Mg25
       -rho*Y[jal25]*rate_eval.n_Al25__He4_Na22
       +rho*Y[jsi25]*rate_eval.n_Si25__p_Al25
       +rho*Y[jal24]*rate_eval.n_Al24__Al25
       +rho*Y[jp28]*rate_eval.n_P28__He4_Al25
       )

    jac[jal25, jp] = (
       -rho*Y[jal25]*rate_eval.p_Al25__Si26
       +rho*Y[jmg24]*rate_eval.p_Mg24__Al25
       )

    jac[jal25, jhe4] = (
       -rho*Y[jal25]*rate_eval.He4_Al25__P29
       -rho*Y[jal25]*rate_eval.He4_Al25__p_Si28
       +rho*Y[jmg22]*rate_eval.He4_Mg22__p_Al25
       +rho*Y[jna21]*rate_eval.He4_Na21__Al25
       )

    jac[jal25, jna21] = (
       +rho*Y[jhe4]*rate_eval.He4_Na21__Al25
       )

    jac[jal25, jmg22] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg22__p_Al25
       )

    jac[jal25, jmg24] = (
       +rho*Y[jp]*rate_eval.p_Mg24__Al25
       )

    jac[jal25, jal24] = (
       +rho*Y[jn]*rate_eval.n_Al24__Al25
       )

    jac[jal25, jal25] = (
       -rho*Y[jn]*rate_eval.n_Al25__Al26
       -rho*Y[jhe4]*rate_eval.He4_Al25__P29
       -rho*Y[jp]*rate_eval.p_Al25__Si26
       -rho*Y[jn]*rate_eval.n_Al25__p_Mg25
       -rho*Y[jhe4]*rate_eval.He4_Al25__p_Si28
       -rate_eval.Al25__Mg25__weak__wc12
       -rho*Y[jn]*rate_eval.n_Al25__He4_Na22
       )

    jac[jal25, jsi25] = (
       +rho*Y[jn]*rate_eval.n_Si25__p_Al25
       +rate_eval.Si25__Al25__weak__wc12
       )

    jac[jal25, jp28] = (
       +rho*Y[jn]*rate_eval.n_P28__He4_Al25
       )

    jac[jal25, js27] = (
       +rate_eval.S27__p_p_Al25__weak__wc12
       )

    jac[jal26, jn] = (
       -rho*Y[jal26]*rate_eval.n_Al26__He4_Na23
       -rho*Y[jal26]*rate_eval.n_Al26__p_Mg26
       -rho*Y[jal26]*rate_eval.n_Al26__Al27
       +rho*Y[jal25]*rate_eval.n_Al25__Al26
       +rho*Y[jp29]*rate_eval.n_P29__He4_Al26
       +rho*Y[jsi26]*rate_eval.n_Si26__p_Al26
       )

    jac[jal26, jp] = (
       -rho*Y[jal26]*rate_eval.p_Al26__Si27
       +rho*Y[jmg25]*rate_eval.p_Mg25__Al26
       )

    jac[jal26, jhe4] = (
       -rho*Y[jal26]*rate_eval.He4_Al26__p_Si29
       -rho*Y[jal26]*rate_eval.He4_Al26__P30
       +rho*Y[jna22]*rate_eval.He4_Na22__Al26
       +rho*Y[jmg23]*rate_eval.He4_Mg23__p_Al26
       )

    jac[jal26, jna22] = (
       +rho*Y[jhe4]*rate_eval.He4_Na22__Al26
       )

    jac[jal26, jmg23] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg23__p_Al26
       )

    jac[jal26, jmg25] = (
       +rho*Y[jp]*rate_eval.p_Mg25__Al26
       )

    jac[jal26, jal25] = (
       +rho*Y[jn]*rate_eval.n_Al25__Al26
       )

    jac[jal26, jal26] = (
       -rho*Y[jn]*rate_eval.n_Al26__He4_Na23
       -rho*Y[jn]*rate_eval.n_Al26__p_Mg26
       -rho*Y[jhe4]*rate_eval.He4_Al26__p_Si29
       -rho*Y[jp]*rate_eval.p_Al26__Si27
       -rho*Y[jhe4]*rate_eval.He4_Al26__P30
       -rho*Y[jn]*rate_eval.n_Al26__Al27
       -rate_eval.Al26__Mg26__weak__wc12
       )

    jac[jal26, jsi26] = (
       +rho*Y[jn]*rate_eval.n_Si26__p_Al26
       +rate_eval.Si26__Al26__weak__wc12
       )

    jac[jal26, jp27] = (
       +rate_eval.P27__p_Al26__weak__wc12
       )

    jac[jal26, jp29] = (
       +rho*Y[jn]*rate_eval.n_P29__He4_Al26
       )

    jac[jal27, jn] = (
       -rho*Y[jal27]*rate_eval.n_Al27__Al28
       +rho*Y[jal26]*rate_eval.n_Al26__Al27
       +rho*Y[jsi27]*rate_eval.n_Si27__p_Al27
       )

    jac[jal27, jp] = (
       -rho*Y[jal27]*rate_eval.p_Al27__He4_Mg24
       -rho*Y[jal27]*rate_eval.p_Al27__Si28
       +rho*Y[jmg26]*rate_eval.p_Mg26__Al27
       +rho*Y[jmg27]*rate_eval.p_Mg27__n_Al27
       )

    jac[jal27, jhe4] = (
       -rho*Y[jal27]*rate_eval.He4_Al27__p_Si30
       -rho*Y[jal27]*rate_eval.He4_Al27__n_P30
       -rho*Y[jal27]*rate_eval.He4_Al27__P31
       +rho*Y[jna23]*rate_eval.He4_Na23__Al27
       +rho*Y[jna24]*rate_eval.He4_Na24__n_Al27
       )

    jac[jal27, jc12] = (
       +rho*Y[jo16]*rate_eval.C12_O16__p_Al27
       )

    jac[jal27, jo16] = (
       +rho*Y[jc12]*rate_eval.C12_O16__p_Al27
       )

    jac[jal27, jna23] = (
       +rho*Y[jhe4]*rate_eval.He4_Na23__Al27
       )

    jac[jal27, jna24] = (
       +rho*Y[jhe4]*rate_eval.He4_Na24__n_Al27
       )

    jac[jal27, jmg26] = (
       +rho*Y[jp]*rate_eval.p_Mg26__Al27
       )

    jac[jal27, jmg27] = (
       +rate_eval.Mg27__Al27__weak__wc12
       +rho*Y[jp]*rate_eval.p_Mg27__n_Al27
       )

    jac[jal27, jal26] = (
       +rho*Y[jn]*rate_eval.n_Al26__Al27
       )

    jac[jal27, jal27] = (
       -rho*Y[jhe4]*rate_eval.He4_Al27__p_Si30
       -rho*Y[jhe4]*rate_eval.He4_Al27__n_P30
       -rho*Y[jp]*rate_eval.p_Al27__He4_Mg24
       -rho*Y[jhe4]*rate_eval.He4_Al27__P31
       -rho*Y[jn]*rate_eval.n_Al27__Al28
       -rho*Y[jp]*rate_eval.p_Al27__Si28
       )

    jac[jal27, jsi27] = (
       +rho*Y[jn]*rate_eval.n_Si27__p_Al27
       +rate_eval.Si27__Al27__weak__wc12
       )

    jac[jal27, jp28] = (
       +rate_eval.P28__p_Al27__weak__wc12
       )

    jac[jal28, jn] = (
       -rho*Y[jal28]*rate_eval.n_Al28__Al29
       +rho*Y[jal27]*rate_eval.n_Al27__Al28
       )

    jac[jal28, jp] = (
       -rho*Y[jal28]*rate_eval.p_Al28__He4_Mg25
       -rho*Y[jal28]*rate_eval.p_Al28__Si29
       -rho*Y[jal28]*rate_eval.p_Al28__n_Si28
       +rho*Y[jmg27]*rate_eval.p_Mg27__Al28
       +rho*Y[jmg28]*rate_eval.p_Mg28__n_Al28
       )

    jac[jal28, jhe4] = (
       -rho*Y[jal28]*rate_eval.He4_Al28__n_P31
       -rho*Y[jal28]*rate_eval.He4_Al28__p_Si31
       -rho*Y[jal28]*rate_eval.He4_Al28__P32
       +rho*Y[jna24]*rate_eval.He4_Na24__Al28
       +rho*Y[jna25]*rate_eval.He4_Na25__n_Al28
       )

    jac[jal28, jna24] = (
       +rho*Y[jhe4]*rate_eval.He4_Na24__Al28
       )

    jac[jal28, jna25] = (
       +rho*Y[jhe4]*rate_eval.He4_Na25__n_Al28
       )

    jac[jal28, jmg27] = (
       +rho*Y[jp]*rate_eval.p_Mg27__Al28
       )

    jac[jal28, jmg28] = (
       +rate_eval.Mg28__Al28__weak__wc12
       +rho*Y[jp]*rate_eval.p_Mg28__n_Al28
       )

    jac[jal28, jal27] = (
       +rho*Y[jn]*rate_eval.n_Al27__Al28
       )

    jac[jal28, jal28] = (
       -rho*Y[jp]*rate_eval.p_Al28__He4_Mg25
       -rho*Y[jhe4]*rate_eval.He4_Al28__n_P31
       -rho*Y[jn]*rate_eval.n_Al28__Al29
       -rho*Y[jp]*rate_eval.p_Al28__Si29
       -rho*Y[jhe4]*rate_eval.He4_Al28__p_Si31
       -rho*Y[jp]*rate_eval.p_Al28__n_Si28
       -rho*Y[jhe4]*rate_eval.He4_Al28__P32
       -rate_eval.Al28__Si28__weak__wc12
       )

    jac[jal29, jn] = (
       -rho*Y[jal29]*rate_eval.n_Al29__Al30
       +rho*Y[jal28]*rate_eval.n_Al28__Al29
       )

    jac[jal29, jp] = (
       -rho*Y[jal29]*rate_eval.p_Al29__He4_Mg26
       -rho*Y[jal29]*rate_eval.p_Al29__n_Si29
       -rho*Y[jal29]*rate_eval.p_Al29__Si30
       +rho*Y[jmg29]*rate_eval.p_Mg29__n_Al29
       +rho*Y[jmg28]*rate_eval.p_Mg28__Al29
       )

    jac[jal29, jhe4] = (
       -rho*Y[jal29]*rate_eval.He4_Al29__n_P32
       -rho*Y[jal29]*rate_eval.He4_Al29__p_Si32
       -rho*Y[jal29]*rate_eval.He4_Al29__P33
       +rho*Y[jna25]*rate_eval.He4_Na25__Al29
       +rho*Y[jna26]*rate_eval.He4_Na26__n_Al29
       )

    jac[jal29, jna25] = (
       +rho*Y[jhe4]*rate_eval.He4_Na25__Al29
       )

    jac[jal29, jna26] = (
       +rho*Y[jhe4]*rate_eval.He4_Na26__n_Al29
       )

    jac[jal29, jmg28] = (
       +rho*Y[jp]*rate_eval.p_Mg28__Al29
       )

    jac[jal29, jmg29] = (
       +rho*Y[jp]*rate_eval.p_Mg29__n_Al29
       +rate_eval.Mg29__Al29__weak__wc12
       )

    jac[jal29, jal28] = (
       +rho*Y[jn]*rate_eval.n_Al28__Al29
       )

    jac[jal29, jal29] = (
       -rho*Y[jhe4]*rate_eval.He4_Al29__n_P32
       -rho*Y[jp]*rate_eval.p_Al29__He4_Mg26
       -rho*Y[jp]*rate_eval.p_Al29__n_Si29
       -rho*Y[jhe4]*rate_eval.He4_Al29__p_Si32
       -rho*Y[jhe4]*rate_eval.He4_Al29__P33
       -rate_eval.Al29__Si29__weak__wc12
       -rho*Y[jn]*rate_eval.n_Al29__Al30
       -rho*Y[jp]*rate_eval.p_Al29__Si30
       )

    jac[jal30, jn] = (
       -rho*Y[jal30]*rate_eval.n_Al30__Al31
       +rho*Y[jal29]*rate_eval.n_Al29__Al30
       )

    jac[jal30, jp] = (
       -rho*Y[jal30]*rate_eval.p_Al30__He4_Mg27
       -rho*Y[jal30]*rate_eval.p_Al30__n_Si30
       -rho*Y[jal30]*rate_eval.p_Al30__Si31
       +rho*Y[jmg30]*rate_eval.p_Mg30__n_Al30
       +rho*Y[jsi33]*rate_eval.p_Si33__He4_Al30
       +rho*Y[jmg29]*rate_eval.p_Mg29__Al30
       )

    jac[jal30, jhe4] = (
       -rho*Y[jal30]*rate_eval.He4_Al30__P34
       -rho*Y[jal30]*rate_eval.He4_Al30__n_P33
       +rho*Y[jna27]*rate_eval.He4_Na27__n_Al30
       +rho*Y[jna26]*rate_eval.He4_Na26__Al30
       )

    jac[jal30, jna26] = (
       +rho*Y[jhe4]*rate_eval.He4_Na26__Al30
       )

    jac[jal30, jna27] = (
       +rho*Y[jhe4]*rate_eval.He4_Na27__n_Al30
       )

    jac[jal30, jmg29] = (
       +rho*Y[jp]*rate_eval.p_Mg29__Al30
       )

    jac[jal30, jmg30] = (
       +rho*Y[jp]*rate_eval.p_Mg30__n_Al30
       +rate_eval.Mg30__Al30__weak__wc12
       )

    jac[jal30, jmg31] = (
       +rate_eval.Mg31__n_Al30__weak__wc12
       )

    jac[jal30, jal29] = (
       +rho*Y[jn]*rate_eval.n_Al29__Al30
       )

    jac[jal30, jal30] = (
       -rho*Y[jp]*rate_eval.p_Al30__He4_Mg27
       -rho*Y[jp]*rate_eval.p_Al30__n_Si30
       -rate_eval.Al30__Si30__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Al30__P34
       -rho*Y[jp]*rate_eval.p_Al30__Si31
       -rho*Y[jn]*rate_eval.n_Al30__Al31
       -rho*Y[jhe4]*rate_eval.He4_Al30__n_P33
       )

    jac[jal30, jsi33] = (
       +rho*Y[jp]*rate_eval.p_Si33__He4_Al30
       )

    jac[jal31, jn] = (
       -rho*Y[jal31]*rate_eval.n_Al31__Al32
       +rho*Y[jal30]*rate_eval.n_Al30__Al31
       )

    jac[jal31, jp] = (
       -rho*Y[jal31]*rate_eval.p_Al31__He4_Mg28
       -rho*Y[jal31]*rate_eval.p_Al31__Si32
       -rho*Y[jal31]*rate_eval.p_Al31__n_Si31
       +rho*Y[jmg31]*rate_eval.p_Mg31__n_Al31
       +rho*Y[jmg30]*rate_eval.p_Mg30__Al31
       )

    jac[jal31, jhe4] = (
       -rho*Y[jal31]*rate_eval.He4_Al31__p_Si34
       -rho*Y[jal31]*rate_eval.He4_Al31__n_P34
       -rho*Y[jal31]*rate_eval.He4_Al31__P35
       +rho*Y[jna28]*rate_eval.He4_Na28__n_Al31
       +rho*Y[jna27]*rate_eval.He4_Na27__Al31
       )

    jac[jal31, jna27] = (
       +rho*Y[jhe4]*rate_eval.He4_Na27__Al31
       )

    jac[jal31, jna28] = (
       +rho*Y[jhe4]*rate_eval.He4_Na28__n_Al31
       )

    jac[jal31, jmg30] = (
       +rho*Y[jp]*rate_eval.p_Mg30__Al31
       )

    jac[jal31, jmg31] = (
       +rho*Y[jp]*rate_eval.p_Mg31__n_Al31
       +rate_eval.Mg31__Al31__weak__wc12
       )

    jac[jal31, jmg32] = (
       +rate_eval.Mg32__n_Al31__weak__wc12
       )

    jac[jal31, jmg33] = (
       +rate_eval.Mg33__n_n_Al31__weak__mp17
       )

    jac[jal31, jal30] = (
       +rho*Y[jn]*rate_eval.n_Al30__Al31
       )

    jac[jal31, jal31] = (
       -rho*Y[jhe4]*rate_eval.He4_Al31__p_Si34
       -rho*Y[jhe4]*rate_eval.He4_Al31__n_P34
       -rho*Y[jp]*rate_eval.p_Al31__He4_Mg28
       -rho*Y[jp]*rate_eval.p_Al31__Si32
       -rho*Y[jn]*rate_eval.n_Al31__Al32
       -rho*Y[jhe4]*rate_eval.He4_Al31__P35
       -rho*Y[jp]*rate_eval.p_Al31__n_Si31
       -rate_eval.Al31__Si31__weak__wc12
       )

    jac[jal32, jn] = (
       -rho*Y[jal32]*rate_eval.n_Al32__Al33
       +rho*Y[jal31]*rate_eval.n_Al31__Al32
       )

    jac[jal32, jp] = (
       -rho*Y[jal32]*rate_eval.p_Al32__He4_Mg29
       -rho*Y[jal32]*rate_eval.p_Al32__n_Si32
       -rho*Y[jal32]*rate_eval.p_Al32__Si33
       +rho*Y[jsi35]*rate_eval.p_Si35__He4_Al32
       +rho*Y[jmg31]*rate_eval.p_Mg31__Al32
       +rho*Y[jmg32]*rate_eval.p_Mg32__n_Al32
       )

    jac[jal32, jhe4] = (
       -rho*Y[jal32]*rate_eval.He4_Al32__n_P35
       -rho*Y[jal32]*rate_eval.He4_Al32__P36
       +rho*Y[jna28]*rate_eval.He4_Na28__Al32
       +rho*Y[jna29]*rate_eval.He4_Na29__n_Al32
       )

    jac[jal32, jna28] = (
       +rho*Y[jhe4]*rate_eval.He4_Na28__Al32
       )

    jac[jal32, jna29] = (
       +rho*Y[jhe4]*rate_eval.He4_Na29__n_Al32
       )

    jac[jal32, jmg31] = (
       +rho*Y[jp]*rate_eval.p_Mg31__Al32
       )

    jac[jal32, jmg32] = (
       +rho*Y[jp]*rate_eval.p_Mg32__n_Al32
       +rate_eval.Mg32__Al32__weak__wc12
       )

    jac[jal32, jmg33] = (
       +rate_eval.Mg33__n_Al32__weak__wc12
       )

    jac[jal32, jmg35] = (
       +rate_eval.Mg35__n_n_n_Al32__weak__mo03
       )

    jac[jal32, jal31] = (
       +rho*Y[jn]*rate_eval.n_Al31__Al32
       )

    jac[jal32, jal32] = (
       -rho*Y[jhe4]*rate_eval.He4_Al32__n_P35
       -rho*Y[jp]*rate_eval.p_Al32__He4_Mg29
       -rho*Y[jp]*rate_eval.p_Al32__n_Si32
       -rho*Y[jhe4]*rate_eval.He4_Al32__P36
       -rate_eval.Al32__Si32__weak__wc12
       -rho*Y[jn]*rate_eval.n_Al32__Al33
       -rate_eval.Al32__n_Si31__weak__wc12
       -rho*Y[jp]*rate_eval.p_Al32__Si33
       )

    jac[jal32, jsi35] = (
       +rho*Y[jp]*rate_eval.p_Si35__He4_Al32
       )

    jac[jal33, jn] = (
       -rho*Y[jal33]*rate_eval.n_Al33__Al34
       +rho*Y[jal32]*rate_eval.n_Al32__Al33
       )

    jac[jal33, jp] = (
       -rho*Y[jal33]*rate_eval.p_Al33__He4_Mg30
       -rho*Y[jal33]*rate_eval.p_Al33__n_Si33
       -rho*Y[jal33]*rate_eval.p_Al33__Si34
       +rho*Y[jsi36]*rate_eval.p_Si36__He4_Al33
       +rho*Y[jmg33]*rate_eval.p_Mg33__n_Al33
       +rho*Y[jmg32]*rate_eval.p_Mg32__Al33
       )

    jac[jal33, jhe4] = (
       -rho*Y[jal33]*rate_eval.He4_Al33__n_P36
       -rho*Y[jal33]*rate_eval.He4_Al33__P37
       +rho*Y[jna29]*rate_eval.He4_Na29__Al33
       +rho*Y[jna30]*rate_eval.He4_Na30__n_Al33
       )

    jac[jal33, jna29] = (
       +rho*Y[jhe4]*rate_eval.He4_Na29__Al33
       )

    jac[jal33, jna30] = (
       +rho*Y[jhe4]*rate_eval.He4_Na30__n_Al33
       )

    jac[jal33, jmg32] = (
       +rho*Y[jp]*rate_eval.p_Mg32__Al33
       )

    jac[jal33, jmg33] = (
       +rho*Y[jp]*rate_eval.p_Mg33__n_Al33
       +rate_eval.Mg33__Al33__weak__wc12
       )

    jac[jal33, jmg34] = (
       +rate_eval.Mg34__n_Al33__weak__mp17
       )

    jac[jal33, jmg35] = (
       +rate_eval.Mg35__n_n_Al33__weak__mp17
       )

    jac[jal33, jmg36] = (
       +rate_eval.Mg36__n_n_n_Al33__weak__mo03
       )

    jac[jal33, jal32] = (
       +rho*Y[jn]*rate_eval.n_Al32__Al33
       )

    jac[jal33, jal33] = (
       -rho*Y[jhe4]*rate_eval.He4_Al33__n_P36
       -rho*Y[jp]*rate_eval.p_Al33__He4_Mg30
       -rho*Y[jp]*rate_eval.p_Al33__n_Si33
       -rho*Y[jp]*rate_eval.p_Al33__Si34
       -rate_eval.Al33__Si33__weak__wc12
       -rho*Y[jn]*rate_eval.n_Al33__Al34
       -rho*Y[jhe4]*rate_eval.He4_Al33__P37
       -rate_eval.Al33__n_Si32__weak__wc12
       )

    jac[jal33, jsi36] = (
       +rho*Y[jp]*rate_eval.p_Si36__He4_Al33
       )

    jac[jal34, jn] = (
       -rho*Y[jal34]*rate_eval.n_Al34__Al35
       +rho*Y[jal33]*rate_eval.n_Al33__Al34
       )

    jac[jal34, jp] = (
       -rho*Y[jal34]*rate_eval.p_Al34__He4_Mg31
       -rho*Y[jal34]*rate_eval.p_Al34__n_Si34
       -rho*Y[jal34]*rate_eval.p_Al34__Si35
       +rho*Y[jsi37]*rate_eval.p_Si37__He4_Al34
       +rho*Y[jmg34]*rate_eval.p_Mg34__n_Al34
       +rho*Y[jmg33]*rate_eval.p_Mg33__Al34
       )

    jac[jal34, jhe4] = (
       -rho*Y[jal34]*rate_eval.He4_Al34__n_P37
       -rho*Y[jal34]*rate_eval.He4_Al34__P38
       +rho*Y[jna31]*rate_eval.He4_Na31__n_Al34
       +rho*Y[jna30]*rate_eval.He4_Na30__Al34
       )

    jac[jal34, jna30] = (
       +rho*Y[jhe4]*rate_eval.He4_Na30__Al34
       )

    jac[jal34, jna31] = (
       +rho*Y[jhe4]*rate_eval.He4_Na31__n_Al34
       )

    jac[jal34, jmg33] = (
       +rho*Y[jp]*rate_eval.p_Mg33__Al34
       )

    jac[jal34, jmg34] = (
       +rate_eval.Mg34__Al34__weak__wc17
       +rho*Y[jp]*rate_eval.p_Mg34__n_Al34
       )

    jac[jal34, jmg35] = (
       +rate_eval.Mg35__n_Al34__weak__wc12
       )

    jac[jal34, jmg36] = (
       +rate_eval.Mg36__n_n_Al34__weak__mp17
       )

    jac[jal34, jmg37] = (
       +rate_eval.Mg37__n_n_n_Al34__weak__mo03
       )

    jac[jal34, jal33] = (
       +rho*Y[jn]*rate_eval.n_Al33__Al34
       )

    jac[jal34, jal34] = (
       -rho*Y[jhe4]*rate_eval.He4_Al34__n_P37
       -rho*Y[jp]*rate_eval.p_Al34__He4_Mg31
       -rho*Y[jp]*rate_eval.p_Al34__n_Si34
       -rho*Y[jp]*rate_eval.p_Al34__Si35
       -rate_eval.Al34__n_Si33__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Al34__P38
       -rho*Y[jn]*rate_eval.n_Al34__Al35
       -rate_eval.Al34__Si34__weak__wc12
       )

    jac[jal34, jsi37] = (
       +rho*Y[jp]*rate_eval.p_Si37__He4_Al34
       )

    jac[jal35, jn] = (
       -rho*Y[jal35]*rate_eval.n_Al35__Al36
       +rho*Y[jal34]*rate_eval.n_Al34__Al35
       )

    jac[jal35, jp] = (
       -rho*Y[jal35]*rate_eval.p_Al35__He4_Mg32
       -rho*Y[jal35]*rate_eval.p_Al35__n_Si35
       -rho*Y[jal35]*rate_eval.p_Al35__Si36
       +rho*Y[jmg34]*rate_eval.p_Mg34__Al35
       +rho*Y[jmg35]*rate_eval.p_Mg35__n_Al35
       +rho*Y[jsi38]*rate_eval.p_Si38__He4_Al35
       )

    jac[jal35, jhe4] = (
       -rho*Y[jal35]*rate_eval.He4_Al35__n_P38
       -rho*Y[jal35]*rate_eval.He4_Al35__P39
       +rho*Y[jna32]*rate_eval.He4_Na32__n_Al35
       +rho*Y[jna31]*rate_eval.He4_Na31__Al35
       )

    jac[jal35, jna31] = (
       +rho*Y[jhe4]*rate_eval.He4_Na31__Al35
       )

    jac[jal35, jna32] = (
       +rho*Y[jhe4]*rate_eval.He4_Na32__n_Al35
       )

    jac[jal35, jmg34] = (
       +rho*Y[jp]*rate_eval.p_Mg34__Al35
       )

    jac[jal35, jmg35] = (
       +rho*Y[jp]*rate_eval.p_Mg35__n_Al35
       +rate_eval.Mg35__Al35__weak__wc17
       )

    jac[jal35, jmg36] = (
       +rate_eval.Mg36__n_Al35__weak__mp17
       )

    jac[jal35, jmg37] = (
       +rate_eval.Mg37__n_n_Al35__weak__mp17
       )

    jac[jal35, jmg38] = (
       +rate_eval.Mg38__n_n_n_Al35__weak__mo03
       )

    jac[jal35, jal34] = (
       +rho*Y[jn]*rate_eval.n_Al34__Al35
       )

    jac[jal35, jal35] = (
       -rho*Y[jhe4]*rate_eval.He4_Al35__n_P38
       -rho*Y[jp]*rate_eval.p_Al35__He4_Mg32
       -rho*Y[jp]*rate_eval.p_Al35__n_Si35
       -rho*Y[jhe4]*rate_eval.He4_Al35__P39
       -rho*Y[jn]*rate_eval.n_Al35__Al36
       -rho*Y[jp]*rate_eval.p_Al35__Si36
       -rate_eval.Al35__n_Si34__weak__wc12
       -rate_eval.Al35__Si35__weak__wc12
       )

    jac[jal35, jsi38] = (
       +rho*Y[jp]*rate_eval.p_Si38__He4_Al35
       )

    jac[jal36, jn] = (
       -rho*Y[jal36]*rate_eval.n_Al36__Al37
       +rho*Y[jal35]*rate_eval.n_Al35__Al36
       )

    jac[jal36, jp] = (
       -rho*Y[jal36]*rate_eval.p_Al36__He4_Mg33
       -rho*Y[jal36]*rate_eval.p_Al36__n_Si36
       -rho*Y[jal36]*rate_eval.p_Al36__Si37
       +rho*Y[jmg36]*rate_eval.p_Mg36__n_Al36
       +rho*Y[jmg35]*rate_eval.p_Mg35__Al36
       )

    jac[jal36, jhe4] = (
       -rho*Y[jal36]*rate_eval.He4_Al36__p_Si39
       -rho*Y[jal36]*rate_eval.He4_Al36__n_P39
       -rho*Y[jal36]*rate_eval.He4_Al36__P40
       +rho*Y[jna33]*rate_eval.He4_Na33__n_Al36
       +rho*Y[jna32]*rate_eval.He4_Na32__Al36
       )

    jac[jal36, jna32] = (
       +rho*Y[jhe4]*rate_eval.He4_Na32__Al36
       )

    jac[jal36, jna33] = (
       +rho*Y[jhe4]*rate_eval.He4_Na33__n_Al36
       )

    jac[jal36, jmg35] = (
       +rho*Y[jp]*rate_eval.p_Mg35__Al36
       )

    jac[jal36, jmg36] = (
       +rate_eval.Mg36__Al36__weak__wc17
       +rho*Y[jp]*rate_eval.p_Mg36__n_Al36
       )

    jac[jal36, jmg37] = (
       +rate_eval.Mg37__n_Al36__weak__mp17
       )

    jac[jal36, jmg38] = (
       +rate_eval.Mg38__n_n_Al36__weak__mp17
       )

    jac[jal36, jmg39] = (
       +rate_eval.Mg39__n_n_n_Al36__weak__mo03
       )

    jac[jal36, jal35] = (
       +rho*Y[jn]*rate_eval.n_Al35__Al36
       )

    jac[jal36, jal36] = (
       -rho*Y[jn]*rate_eval.n_Al36__Al37
       -rho*Y[jhe4]*rate_eval.He4_Al36__p_Si39
       -rho*Y[jhe4]*rate_eval.He4_Al36__n_P39
       -rho*Y[jp]*rate_eval.p_Al36__He4_Mg33
       -rho*Y[jp]*rate_eval.p_Al36__n_Si36
       -rate_eval.Al36__Si36__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_Al36__P40
       -rho*Y[jp]*rate_eval.p_Al36__Si37
       -rate_eval.Al36__n_n_Si34__weak__mp17
       -rate_eval.Al36__n_Si35__weak__mp17
       )

    jac[jal37, jn] = (
       -rho*Y[jal37]*rate_eval.n_Al37__Al38
       +rho*Y[jal36]*rate_eval.n_Al36__Al37
       )

    jac[jal37, jp] = (
       -rho*Y[jal37]*rate_eval.p_Al37__He4_Mg34
       -rho*Y[jal37]*rate_eval.p_Al37__Si38
       -rho*Y[jal37]*rate_eval.p_Al37__n_Si37
       +rho*Y[jmg37]*rate_eval.p_Mg37__n_Al37
       +rho*Y[jmg36]*rate_eval.p_Mg36__Al37
       +rho*Y[jsi40]*rate_eval.p_Si40__He4_Al37
       )

    jac[jal37, jhe4] = (
       -rho*Y[jal37]*rate_eval.He4_Al37__n_P40
       -rho*Y[jal37]*rate_eval.He4_Al37__P41
       +rho*Y[jna34]*rate_eval.He4_Na34__n_Al37
       +rho*Y[jna33]*rate_eval.He4_Na33__Al37
       )

    jac[jal37, jna33] = (
       +rho*Y[jhe4]*rate_eval.He4_Na33__Al37
       )

    jac[jal37, jna34] = (
       +rho*Y[jhe4]*rate_eval.He4_Na34__n_Al37
       )

    jac[jal37, jmg36] = (
       +rho*Y[jp]*rate_eval.p_Mg36__Al37
       )

    jac[jal37, jmg37] = (
       +rate_eval.Mg37__Al37__weak__mo03
       +rho*Y[jp]*rate_eval.p_Mg37__n_Al37
       )

    jac[jal37, jmg38] = (
       +rate_eval.Mg38__n_Al37__weak__mp17
       )

    jac[jal37, jmg39] = (
       +rate_eval.Mg39__n_n_Al37__weak__mp17
       )

    jac[jal37, jmg40] = (
       +rate_eval.Mg40__n_n_n_Al37__weak__mo03
       )

    jac[jal37, jal36] = (
       +rho*Y[jn]*rate_eval.n_Al36__Al37
       )

    jac[jal37, jal37] = (
       -rate_eval.Al37__n_n_n_Si34__weak__mo03
       -rate_eval.Al37__Si37__weak__wc17
       -rho*Y[jp]*rate_eval.p_Al37__He4_Mg34
       -rho*Y[jhe4]*rate_eval.He4_Al37__n_P40
       -rho*Y[jn]*rate_eval.n_Al37__Al38
       -rate_eval.Al37__n_Si36__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Al37__P41
       -rho*Y[jp]*rate_eval.p_Al37__Si38
       -rate_eval.Al37__n_n_Si35__weak__mp17
       -rho*Y[jp]*rate_eval.p_Al37__n_Si37
       )

    jac[jal37, jsi40] = (
       +rho*Y[jp]*rate_eval.p_Si40__He4_Al37
       )

    jac[jal38, jn] = (
       -rho*Y[jal38]*rate_eval.n_Al38__Al39
       +rho*Y[jal37]*rate_eval.n_Al37__Al38
       )

    jac[jal38, jp] = (
       -rho*Y[jal38]*rate_eval.p_Al38__He4_Mg35
       -rho*Y[jal38]*rate_eval.p_Al38__n_Si38
       -rho*Y[jal38]*rate_eval.p_Al38__Si39
       +rho*Y[jmg38]*rate_eval.p_Mg38__n_Al38
       +rho*Y[jmg37]*rate_eval.p_Mg37__Al38
       )

    jac[jal38, jhe4] = (
       -rho*Y[jal38]*rate_eval.He4_Al38__n_P41
       -rho*Y[jal38]*rate_eval.He4_Al38__p_Si41
       -rho*Y[jal38]*rate_eval.He4_Al38__P42
       +rho*Y[jna35]*rate_eval.He4_Na35__n_Al38
       +rho*Y[jna34]*rate_eval.He4_Na34__Al38
       )

    jac[jal38, jna34] = (
       +rho*Y[jhe4]*rate_eval.He4_Na34__Al38
       )

    jac[jal38, jna35] = (
       +rho*Y[jhe4]*rate_eval.He4_Na35__n_Al38
       )

    jac[jal38, jmg37] = (
       +rho*Y[jp]*rate_eval.p_Mg37__Al38
       )

    jac[jal38, jmg38] = (
       +rho*Y[jp]*rate_eval.p_Mg38__n_Al38
       +rate_eval.Mg38__Al38__weak__mo03
       )

    jac[jal38, jmg39] = (
       +rate_eval.Mg39__n_Al38__weak__mp17
       )

    jac[jal38, jmg40] = (
       +rate_eval.Mg40__n_n_Al38__weak__mp17
       )

    jac[jal38, jal37] = (
       +rho*Y[jn]*rate_eval.n_Al37__Al38
       )

    jac[jal38, jal38] = (
       -rate_eval.Al38__n_n_n_Si35__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Al38__n_P41
       -rho*Y[jhe4]*rate_eval.He4_Al38__p_Si41
       -rho*Y[jp]*rate_eval.p_Al38__He4_Mg35
       -rho*Y[jp]*rate_eval.p_Al38__n_Si38
       -rho*Y[jhe4]*rate_eval.He4_Al38__P42
       -rho*Y[jn]*rate_eval.n_Al38__Al39
       -rate_eval.Al38__n_n_Si36__weak__mp17
       -rho*Y[jp]*rate_eval.p_Al38__Si39
       -rate_eval.Al38__n_Si37__weak__mp17
       -rate_eval.Al38__Si38__weak__wc17
       )

    jac[jal39, jn] = (
       -rho*Y[jal39]*rate_eval.n_Al39__Al40
       +rho*Y[jal38]*rate_eval.n_Al38__Al39
       )

    jac[jal39, jp] = (
       -rho*Y[jal39]*rate_eval.p_Al39__He4_Mg36
       -rho*Y[jal39]*rate_eval.p_Al39__n_Si39
       -rho*Y[jal39]*rate_eval.p_Al39__Si40
       +rho*Y[jmg39]*rate_eval.p_Mg39__n_Al39
       +rho*Y[jmg38]*rate_eval.p_Mg38__Al39
       )

    jac[jal39, jhe4] = (
       -rho*Y[jal39]*rate_eval.He4_Al39__p_Si42
       -rho*Y[jal39]*rate_eval.He4_Al39__P43
       -rho*Y[jal39]*rate_eval.He4_Al39__n_P42
       +rho*Y[jna36]*rate_eval.He4_Na36__n_Al39
       +rho*Y[jna35]*rate_eval.He4_Na35__Al39
       )

    jac[jal39, jna35] = (
       +rho*Y[jhe4]*rate_eval.He4_Na35__Al39
       )

    jac[jal39, jna36] = (
       +rho*Y[jhe4]*rate_eval.He4_Na36__n_Al39
       )

    jac[jal39, jmg38] = (
       +rho*Y[jp]*rate_eval.p_Mg38__Al39
       )

    jac[jal39, jmg39] = (
       +rho*Y[jp]*rate_eval.p_Mg39__n_Al39
       +rate_eval.Mg39__Al39__weak__mo03
       )

    jac[jal39, jmg40] = (
       +rate_eval.Mg40__n_Al39__weak__mp17
       )

    jac[jal39, jal38] = (
       +rho*Y[jn]*rate_eval.n_Al38__Al39
       )

    jac[jal39, jal39] = (
       -rate_eval.Al39__n_n_n_Si36__weak__mo03
       -rho*Y[jp]*rate_eval.p_Al39__He4_Mg36
       -rho*Y[jp]*rate_eval.p_Al39__n_Si39
       -rho*Y[jhe4]*rate_eval.He4_Al39__p_Si42
       -rho*Y[jp]*rate_eval.p_Al39__Si40
       -rate_eval.Al39__n_Si38__weak__mp17
       -rate_eval.Al39__n_n_Si37__weak__mp17
       -rho*Y[jn]*rate_eval.n_Al39__Al40
       -rho*Y[jhe4]*rate_eval.He4_Al39__P43
       -rho*Y[jhe4]*rate_eval.He4_Al39__n_P42
       -rate_eval.Al39__Si39__weak__wc17
       )

    jac[jal40, jn] = (
       -rho*Y[jal40]*rate_eval.n_Al40__Al41
       +rho*Y[jal39]*rate_eval.n_Al39__Al40
       )

    jac[jal40, jp] = (
       -rho*Y[jal40]*rate_eval.p_Al40__He4_Mg37
       -rho*Y[jal40]*rate_eval.p_Al40__n_Si40
       -rho*Y[jal40]*rate_eval.p_Al40__Si41
       +rho*Y[jmg40]*rate_eval.p_Mg40__n_Al40
       +rho*Y[jmg39]*rate_eval.p_Mg39__Al40
       )

    jac[jal40, jhe4] = (
       -rho*Y[jal40]*rate_eval.He4_Al40__p_Si43
       -rho*Y[jal40]*rate_eval.He4_Al40__n_P43
       -rho*Y[jal40]*rate_eval.He4_Al40__P44
       +rho*Y[jna37]*rate_eval.He4_Na37__n_Al40
       +rho*Y[jna36]*rate_eval.He4_Na36__Al40
       )

    jac[jal40, jna36] = (
       +rho*Y[jhe4]*rate_eval.He4_Na36__Al40
       )

    jac[jal40, jna37] = (
       +rho*Y[jhe4]*rate_eval.He4_Na37__n_Al40
       )

    jac[jal40, jmg39] = (
       +rho*Y[jp]*rate_eval.p_Mg39__Al40
       )

    jac[jal40, jmg40] = (
       +rho*Y[jp]*rate_eval.p_Mg40__n_Al40
       )

    jac[jal40, jmg41] = (
       +rate_eval.Mg41__n_Al40__weak__mp17
       )

    jac[jal40, jal39] = (
       +rho*Y[jn]*rate_eval.n_Al39__Al40
       )

    jac[jal40, jal40] = (
       -rho*Y[jhe4]*rate_eval.He4_Al40__p_Si43
       -rho*Y[jhe4]*rate_eval.He4_Al40__n_P43
       -rho*Y[jp]*rate_eval.p_Al40__He4_Mg37
       -rho*Y[jp]*rate_eval.p_Al40__n_Si40
       -rate_eval.Al40__n_n_n_Si37__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Al40__P44
       -rho*Y[jp]*rate_eval.p_Al40__Si41
       -rho*Y[jn]*rate_eval.n_Al40__Al41
       -rate_eval.Al40__n_Si39__weak__mp17
       -rate_eval.Al40__n_n_Si38__weak__mp17
       -rate_eval.Al40__Si40__weak__mo03
       )

    jac[jal41, jn] = (
       -rho*Y[jal41]*rate_eval.n_Al41__Al42
       +rho*Y[jal40]*rate_eval.n_Al40__Al41
       )

    jac[jal41, jp] = (
       -rho*Y[jal41]*rate_eval.p_Al41__He4_Mg38
       -rho*Y[jal41]*rate_eval.p_Al41__n_Si41
       -rho*Y[jal41]*rate_eval.p_Al41__Si42
       +rho*Y[jsi44]*rate_eval.p_Si44__He4_Al41
       +rho*Y[jmg41]*rate_eval.p_Mg41__n_Al41
       +rho*Y[jmg40]*rate_eval.p_Mg40__Al41
       )

    jac[jal41, jhe4] = (
       -rho*Y[jal41]*rate_eval.He4_Al41__P45
       -rho*Y[jal41]*rate_eval.He4_Al41__n_P44
       +rho*Y[jna38]*rate_eval.He4_Na38__n_Al41
       +rho*Y[jna37]*rate_eval.He4_Na37__Al41
       )

    jac[jal41, jna37] = (
       +rho*Y[jhe4]*rate_eval.He4_Na37__Al41
       )

    jac[jal41, jna38] = (
       +rho*Y[jhe4]*rate_eval.He4_Na38__n_Al41
       )

    jac[jal41, jmg40] = (
       +rho*Y[jp]*rate_eval.p_Mg40__Al41
       )

    jac[jal41, jmg41] = (
       +rho*Y[jp]*rate_eval.p_Mg41__n_Al41
       +rate_eval.Mg41__Al41__weak__mo03
       )

    jac[jal41, jal40] = (
       +rho*Y[jn]*rate_eval.n_Al40__Al41
       )

    jac[jal41, jal41] = (
       -rate_eval.Al41__n_n_n_Si38__weak__mo03
       -rho*Y[jp]*rate_eval.p_Al41__He4_Mg38
       -rho*Y[jp]*rate_eval.p_Al41__n_Si41
       -rho*Y[jn]*rate_eval.n_Al41__Al42
       -rate_eval.Al41__n_Si40__weak__mp17
       -rate_eval.Al41__Si41__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Al41__P45
       -rate_eval.Al41__n_n_Si39__weak__mp17
       -rho*Y[jp]*rate_eval.p_Al41__Si42
       -rho*Y[jhe4]*rate_eval.He4_Al41__n_P44
       )

    jac[jal41, jsi44] = (
       +rho*Y[jp]*rate_eval.p_Si44__He4_Al41
       )

    jac[jal42, jn] = (
       -rho*Y[jal42]*rate_eval.n_Al42__Al43
       +rho*Y[jal41]*rate_eval.n_Al41__Al42
       )

    jac[jal42, jp] = (
       -rho*Y[jal42]*rate_eval.p_Al42__He4_Mg39
       -rho*Y[jal42]*rate_eval.p_Al42__Si43
       -rho*Y[jal42]*rate_eval.p_Al42__n_Si42
       +rho*Y[jsi45]*rate_eval.p_Si45__He4_Al42
       +rho*Y[jmg41]*rate_eval.p_Mg41__Al42
       )

    jac[jal42, jhe4] = (
       -rho*Y[jal42]*rate_eval.He4_Al42__n_P45
       -rho*Y[jal42]*rate_eval.He4_Al42__P46
       +rho*Y[jna39]*rate_eval.He4_Na39__n_Al42
       +rho*Y[jna38]*rate_eval.He4_Na38__Al42
       )

    jac[jal42, jna38] = (
       +rho*Y[jhe4]*rate_eval.He4_Na38__Al42
       )

    jac[jal42, jna39] = (
       +rho*Y[jhe4]*rate_eval.He4_Na39__n_Al42
       )

    jac[jal42, jmg41] = (
       +rho*Y[jp]*rate_eval.p_Mg41__Al42
       )

    jac[jal42, jal41] = (
       +rho*Y[jn]*rate_eval.n_Al41__Al42
       )

    jac[jal42, jal42] = (
       -rate_eval.Al42__n_n_n_Si39__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Al42__n_P45
       -rho*Y[jp]*rate_eval.p_Al42__He4_Mg39
       -rho*Y[jp]*rate_eval.p_Al42__Si43
       -rho*Y[jhe4]*rate_eval.He4_Al42__P46
       -rate_eval.Al42__Si42__weak__mo03
       -rate_eval.Al42__n_n_Si40__weak__mo03
       -rate_eval.Al42__n_Si41__weak__mp17
       -rho*Y[jp]*rate_eval.p_Al42__n_Si42
       -rho*Y[jn]*rate_eval.n_Al42__Al43
       )

    jac[jal42, jsi45] = (
       +rho*Y[jp]*rate_eval.p_Si45__He4_Al42
       )

    jac[jal43, jn] = (
       +rho*Y[jal42]*rate_eval.n_Al42__Al43
       )

    jac[jal43, jp] = (
       -rho*Y[jal43]*rate_eval.p_Al43__n_Si43
       -rho*Y[jal43]*rate_eval.p_Al43__He4_Mg40
       -rho*Y[jal43]*rate_eval.p_Al43__Si44
       )

    jac[jal43, jhe4] = (
       -rho*Y[jal43]*rate_eval.He4_Al43__P47
       -rho*Y[jal43]*rate_eval.He4_Al43__n_P46
       +rho*Y[jna39]*rate_eval.He4_Na39__Al43
       )

    jac[jal43, jna39] = (
       +rho*Y[jhe4]*rate_eval.He4_Na39__Al43
       )

    jac[jal43, jal42] = (
       +rho*Y[jn]*rate_eval.n_Al42__Al43
       )

    jac[jal43, jal43] = (
       -rate_eval.Al43__n_n_n_Si40__weak__mo03
       -rho*Y[jp]*rate_eval.p_Al43__n_Si43
       -rho*Y[jp]*rate_eval.p_Al43__He4_Mg40
       -rho*Y[jhe4]*rate_eval.He4_Al43__P47
       -rho*Y[jp]*rate_eval.p_Al43__Si44
       -rate_eval.Al43__n_n_Si41__weak__mp17
       -rate_eval.Al43__n_Si42__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Al43__n_P46
       )

    jac[jsi22, jn] = (
       -rho*Y[jsi22]*rate_eval.n_Si22__He4_Mg19
       -rho*Y[jsi22]*rate_eval.n_Si22__p_Al22
       -rho*Y[jsi22]*rate_eval.n_Si22__Si23
       )

    jac[jsi22, jhe4] = (
       -rho*Y[jsi22]*rate_eval.He4_Si22__p_P25
       -rho*Y[jsi22]*rate_eval.He4_Si22__S26
       )

    jac[jsi22, jsi22] = (
       -rho*Y[jhe4]*rate_eval.He4_Si22__p_P25
       -rho*Y[jn]*rate_eval.n_Si22__He4_Mg19
       -rho*Y[jn]*rate_eval.n_Si22__p_Al22
       -rho*Y[jn]*rate_eval.n_Si22__Si23
       -rate_eval.Si22__p_Mg21__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Si22__S26
       -rate_eval.Si22__Al22__weak__wc12
       )

    jac[jsi23, jn] = (
       -rho*Y[jsi23]*rate_eval.n_Si23__p_Al23
       -rho*Y[jsi23]*rate_eval.n_Si23__He4_Mg20
       -rho*Y[jsi23]*rate_eval.n_Si23__Si24
       +rho*Y[js26]*rate_eval.n_S26__He4_Si23
       +rho*Y[jsi22]*rate_eval.n_Si22__Si23
       )

    jac[jsi23, jp] = (
       +rho*Y[jal22]*rate_eval.p_Al22__Si23
       )

    jac[jsi23, jhe4] = (
       -rho*Y[jsi23]*rate_eval.He4_Si23__p_P26
       -rho*Y[jsi23]*rate_eval.He4_Si23__S27
       +rho*Y[jmg19]*rate_eval.He4_Mg19__Si23
       )

    jac[jsi23, jmg19] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg19__Si23
       )

    jac[jsi23, jal22] = (
       +rho*Y[jp]*rate_eval.p_Al22__Si23
       )

    jac[jsi23, jsi22] = (
       +rho*Y[jn]*rate_eval.n_Si22__Si23
       )

    jac[jsi23, jsi23] = (
       -rho*Y[jhe4]*rate_eval.He4_Si23__p_P26
       -rho*Y[jn]*rate_eval.n_Si23__p_Al23
       -rho*Y[jhe4]*rate_eval.He4_Si23__S27
       -rate_eval.Si23__p_p_Na21__weak__wc12
       -rate_eval.Si23__Al23__weak__wc12
       -rho*Y[jn]*rate_eval.n_Si23__He4_Mg20
       -rho*Y[jn]*rate_eval.n_Si23__Si24
       -rate_eval.Si23__p_Mg22__weak__wc17
       )

    jac[jsi23, js26] = (
       +rho*Y[jn]*rate_eval.n_S26__He4_Si23
       )

    jac[jsi24, jn] = (
       -rho*Y[jsi24]*rate_eval.n_Si24__p_Al24
       -rho*Y[jsi24]*rate_eval.n_Si24__He4_Mg21
       -rho*Y[jsi24]*rate_eval.n_Si24__Si25
       +rho*Y[jp24]*rate_eval.n_P24__p_Si24
       +rho*Y[jsi23]*rate_eval.n_Si23__Si24
       +rho*Y[js27]*rate_eval.n_S27__He4_Si24
       )

    jac[jsi24, jp] = (
       -rho*Y[jsi24]*rate_eval.p_Si24__P25
       +rho*Y[jal23]*rate_eval.p_Al23__Si24
       )

    jac[jsi24, jhe4] = (
       -rho*Y[jsi24]*rate_eval.He4_Si24__p_P27
       -rho*Y[jsi24]*rate_eval.He4_Si24__S28
       +rho*Y[jal21]*rate_eval.He4_Al21__p_Si24
       +rho*Y[jmg20]*rate_eval.He4_Mg20__Si24
       )

    jac[jsi24, jmg20] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg20__Si24
       )

    jac[jsi24, jal21] = (
       +rho*Y[jhe4]*rate_eval.He4_Al21__p_Si24
       )

    jac[jsi24, jal23] = (
       +rho*Y[jp]*rate_eval.p_Al23__Si24
       )

    jac[jsi24, jsi23] = (
       +rho*Y[jn]*rate_eval.n_Si23__Si24
       )

    jac[jsi24, jsi24] = (
       -rho*Y[jn]*rate_eval.n_Si24__p_Al24
       -rho*Y[jn]*rate_eval.n_Si24__He4_Mg21
       -rho*Y[jhe4]*rate_eval.He4_Si24__p_P27
       -rate_eval.Si24__p_Mg23__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Si24__S28
       -rho*Y[jp]*rate_eval.p_Si24__P25
       -rho*Y[jn]*rate_eval.n_Si24__Si25
       -rate_eval.Si24__Al24__weak__wc12
       )

    jac[jsi24, jp24] = (
       +rho*Y[jn]*rate_eval.n_P24__p_Si24
       +rate_eval.P24__Si24__weak__bqa_pos_
       )

    jac[jsi24, js27] = (
       +rho*Y[jn]*rate_eval.n_S27__He4_Si24
       )

    jac[jsi25, jn] = (
       -rho*Y[jsi25]*rate_eval.n_Si25__p_Al25
       -rho*Y[jsi25]*rate_eval.n_Si25__He4_Mg22
       -rho*Y[jsi25]*rate_eval.n_Si25__Si26
       +rho*Y[js28]*rate_eval.n_S28__He4_Si25
       +rho*Y[jsi24]*rate_eval.n_Si24__Si25
       +rho*Y[jp25]*rate_eval.n_P25__p_Si25
       )

    jac[jsi25, jp] = (
       -rho*Y[jsi25]*rate_eval.p_Si25__P26
       +rho*Y[jal24]*rate_eval.p_Al24__Si25
       )

    jac[jsi25, jhe4] = (
       -rho*Y[jsi25]*rate_eval.He4_Si25__p_P28
       -rho*Y[jsi25]*rate_eval.He4_Si25__S29
       +rho*Y[jal22]*rate_eval.He4_Al22__p_Si25
       +rho*Y[jmg21]*rate_eval.He4_Mg21__Si25
       )

    jac[jsi25, jmg21] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg21__Si25
       )

    jac[jsi25, jal22] = (
       +rho*Y[jhe4]*rate_eval.He4_Al22__p_Si25
       )

    jac[jsi25, jal24] = (
       +rho*Y[jp]*rate_eval.p_Al24__Si25
       )

    jac[jsi25, jsi24] = (
       +rho*Y[jn]*rate_eval.n_Si24__Si25
       )

    jac[jsi25, jsi25] = (
       -rho*Y[jhe4]*rate_eval.He4_Si25__p_P28
       -rho*Y[jn]*rate_eval.n_Si25__p_Al25
       -rho*Y[jn]*rate_eval.n_Si25__He4_Mg22
       -rho*Y[jp]*rate_eval.p_Si25__P26
       -rho*Y[jn]*rate_eval.n_Si25__Si26
       -rho*Y[jhe4]*rate_eval.He4_Si25__S29
       -rate_eval.Si25__p_Mg24__weak__wc12
       -rate_eval.Si25__Al25__weak__wc12
       )

    jac[jsi25, jp25] = (
       +rate_eval.P25__Si25__weak__bqa_pos_
       +rho*Y[jn]*rate_eval.n_P25__p_Si25
       )

    jac[jsi25, js28] = (
       +rho*Y[jn]*rate_eval.n_S28__He4_Si25
       )

    jac[jsi26, jn] = (
       -rho*Y[jsi26]*rate_eval.n_Si26__p_Al26
       -rho*Y[jsi26]*rate_eval.n_Si26__Si27
       -rho*Y[jsi26]*rate_eval.n_Si26__He4_Mg23
       +rho*Y[jp26]*rate_eval.n_P26__p_Si26
       +rho*Y[js29]*rate_eval.n_S29__He4_Si26
       +rho*Y[jsi25]*rate_eval.n_Si25__Si26
       )

    jac[jsi26, jp] = (
       -rho*Y[jsi26]*rate_eval.p_Si26__P27
       +rho*Y[jal25]*rate_eval.p_Al25__Si26
       )

    jac[jsi26, jhe4] = (
       -rho*Y[jsi26]*rate_eval.He4_Si26__S30
       -rho*Y[jsi26]*rate_eval.He4_Si26__p_P29
       +rho*Y[jmg22]*rate_eval.He4_Mg22__Si26
       +rho*Y[jal23]*rate_eval.He4_Al23__p_Si26
       )

    jac[jsi26, jmg22] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg22__Si26
       )

    jac[jsi26, jal23] = (
       +rho*Y[jhe4]*rate_eval.He4_Al23__p_Si26
       )

    jac[jsi26, jal25] = (
       +rho*Y[jp]*rate_eval.p_Al25__Si26
       )

    jac[jsi26, jsi25] = (
       +rho*Y[jn]*rate_eval.n_Si25__Si26
       )

    jac[jsi26, jsi26] = (
       -rho*Y[jn]*rate_eval.n_Si26__p_Al26
       -rho*Y[jp]*rate_eval.p_Si26__P27
       -rho*Y[jn]*rate_eval.n_Si26__Si27
       -rho*Y[jhe4]*rate_eval.He4_Si26__S30
       -rho*Y[jn]*rate_eval.n_Si26__He4_Mg23
       -rate_eval.Si26__Al26__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Si26__p_P29
       )

    jac[jsi26, jp26] = (
       +rho*Y[jn]*rate_eval.n_P26__p_Si26
       +rate_eval.P26__Si26__weak__wc12
       )

    jac[jsi26, js27] = (
       +rate_eval.S27__p_Si26__weak__wc17
       )

    jac[jsi26, js29] = (
       +rho*Y[jn]*rate_eval.n_S29__He4_Si26
       )

    jac[jsi27, jn] = (
       -rho*Y[jsi27]*rate_eval.n_Si27__Si28
       -rho*Y[jsi27]*rate_eval.n_Si27__He4_Mg24
       -rho*Y[jsi27]*rate_eval.n_Si27__p_Al27
       -rho*Y[jsi27]*rate_eval.n_Si27__C12_O16
       +rho*Y[js30]*rate_eval.n_S30__He4_Si27
       +rho*Y[jp27]*rate_eval.n_P27__p_Si27
       +rho*Y[jsi26]*rate_eval.n_Si26__Si27
       )

    jac[jsi27, jp] = (
       -rho*Y[jsi27]*rate_eval.p_Si27__P28
       +rho*Y[jal26]*rate_eval.p_Al26__Si27
       )

    jac[jsi27, jhe4] = (
       -rho*Y[jsi27]*rate_eval.He4_Si27__p_P30
       -rho*Y[jsi27]*rate_eval.He4_Si27__S31
       +rho*Y[jal24]*rate_eval.He4_Al24__p_Si27
       +rho*Y[jmg23]*rate_eval.He4_Mg23__Si27
       )

    jac[jsi27, jmg23] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg23__Si27
       )

    jac[jsi27, jal24] = (
       +rho*Y[jhe4]*rate_eval.He4_Al24__p_Si27
       )

    jac[jsi27, jal26] = (
       +rho*Y[jp]*rate_eval.p_Al26__Si27
       )

    jac[jsi27, jsi26] = (
       +rho*Y[jn]*rate_eval.n_Si26__Si27
       )

    jac[jsi27, jsi27] = (
       -rho*Y[jhe4]*rate_eval.He4_Si27__p_P30
       -rho*Y[jn]*rate_eval.n_Si27__Si28
       -rho*Y[jn]*rate_eval.n_Si27__He4_Mg24
       -rho*Y[jp]*rate_eval.p_Si27__P28
       -rho*Y[jn]*rate_eval.n_Si27__p_Al27
       -rho*Y[jn]*rate_eval.n_Si27__C12_O16
       -rho*Y[jhe4]*rate_eval.He4_Si27__S31
       -rate_eval.Si27__Al27__weak__wc12
       )

    jac[jsi27, jp27] = (
       +rho*Y[jn]*rate_eval.n_P27__p_Si27
       +rate_eval.P27__Si27__weak__wc12
       )

    jac[jsi27, js28] = (
       +rate_eval.S28__p_Si27__weak__wc12
       )

    jac[jsi27, js30] = (
       +rho*Y[jn]*rate_eval.n_S30__He4_Si27
       )

    jac[jsi28, jn] = (
       -rho*Y[jsi28]*rate_eval.n_Si28__Si29
       +rho*Y[jp28]*rate_eval.n_P28__p_Si28
       +rho*Y[jsi27]*rate_eval.n_Si27__Si28
       +rho*Y[js31]*rate_eval.n_S31__He4_Si28
       )

    jac[jsi28, jp] = (
       -rho*Y[jsi28]*rate_eval.p_Si28__P29
       +rho*Y[jal28]*rate_eval.p_Al28__n_Si28
       +rho*Y[jp31]*rate_eval.p_P31__He4_Si28
       +rho*Y[jal27]*rate_eval.p_Al27__Si28
       )

    jac[jsi28, jhe4] = (
       -rho*Y[jsi28]*rate_eval.He4_Si28__S32
       +rho*Y[jal25]*rate_eval.He4_Al25__p_Si28
       +rho*Y[jmg25]*rate_eval.He4_Mg25__n_Si28
       +rho*Y[jmg24]*rate_eval.He4_Mg24__Si28
       )

    jac[jsi28, jc12] = (
       +rho*Y[jne20]*rate_eval.C12_Ne20__He4_Si28
       )

    jac[jsi28, jo16] = (
       +5.00000000000000e-01*rho*2*Y[jo16]*rate_eval.O16_O16__He4_Si28
       )

    jac[jsi28, jne20] = (
       +rho*Y[jc12]*rate_eval.C12_Ne20__He4_Si28
       )

    jac[jsi28, jmg24] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg24__Si28
       )

    jac[jsi28, jmg25] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg25__n_Si28
       )

    jac[jsi28, jal25] = (
       +rho*Y[jhe4]*rate_eval.He4_Al25__p_Si28
       )

    jac[jsi28, jal27] = (
       +rho*Y[jp]*rate_eval.p_Al27__Si28
       )

    jac[jsi28, jal28] = (
       +rho*Y[jp]*rate_eval.p_Al28__n_Si28
       +rate_eval.Al28__Si28__weak__wc12
       )

    jac[jsi28, jsi27] = (
       +rho*Y[jn]*rate_eval.n_Si27__Si28
       )

    jac[jsi28, jsi28] = (
       -rho*Y[jp]*rate_eval.p_Si28__P29
       -rho*Y[jhe4]*rate_eval.He4_Si28__S32
       -rho*Y[jn]*rate_eval.n_Si28__Si29
       )

    jac[jsi28, jp28] = (
       +rho*Y[jn]*rate_eval.n_P28__p_Si28
       +rate_eval.P28__Si28__weak__wc12
       )

    jac[jsi28, jp31] = (
       +rho*Y[jp]*rate_eval.p_P31__He4_Si28
       )

    jac[jsi28, js29] = (
       +rate_eval.S29__p_Si28__weak__wc12
       )

    jac[jsi28, js31] = (
       +rho*Y[jn]*rate_eval.n_S31__He4_Si28
       )

    jac[jsi28, jcl32] = (
       +rate_eval.Cl32__He4_Si28__weak__wc12
       )

    jac[jsi29, jn] = (
       -rho*Y[jsi29]*rate_eval.n_Si29__Si30
       +rho*Y[jsi28]*rate_eval.n_Si28__Si29
       +rho*Y[jp29]*rate_eval.n_P29__p_Si29
       +rho*Y[js32]*rate_eval.n_S32__He4_Si29
       )

    jac[jsi29, jp] = (
       -rho*Y[jsi29]*rate_eval.p_Si29__P30
       +rho*Y[jp32]*rate_eval.p_P32__He4_Si29
       +rho*Y[jal29]*rate_eval.p_Al29__n_Si29
       +rho*Y[jal28]*rate_eval.p_Al28__Si29
       )

    jac[jsi29, jhe4] = (
       -rho*Y[jsi29]*rate_eval.He4_Si29__S33
       +rho*Y[jmg26]*rate_eval.He4_Mg26__n_Si29
       +rho*Y[jal26]*rate_eval.He4_Al26__p_Si29
       +rho*Y[jmg25]*rate_eval.He4_Mg25__Si29
       )

    jac[jsi29, jmg25] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg25__Si29
       )

    jac[jsi29, jmg26] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg26__n_Si29
       )

    jac[jsi29, jal26] = (
       +rho*Y[jhe4]*rate_eval.He4_Al26__p_Si29
       )

    jac[jsi29, jal28] = (
       +rho*Y[jp]*rate_eval.p_Al28__Si29
       )

    jac[jsi29, jal29] = (
       +rho*Y[jp]*rate_eval.p_Al29__n_Si29
       +rate_eval.Al29__Si29__weak__wc12
       )

    jac[jsi29, jsi28] = (
       +rho*Y[jn]*rate_eval.n_Si28__Si29
       )

    jac[jsi29, jsi29] = (
       -rho*Y[jp]*rate_eval.p_Si29__P30
       -rho*Y[jhe4]*rate_eval.He4_Si29__S33
       -rho*Y[jn]*rate_eval.n_Si29__Si30
       )

    jac[jsi29, jp29] = (
       +rho*Y[jn]*rate_eval.n_P29__p_Si29
       +rate_eval.P29__Si29__weak__wc12
       )

    jac[jsi29, jp32] = (
       +rho*Y[jp]*rate_eval.p_P32__He4_Si29
       )

    jac[jsi29, js32] = (
       +rho*Y[jn]*rate_eval.n_S32__He4_Si29
       )

    jac[jsi30, jn] = (
       -rho*Y[jsi30]*rate_eval.n_Si30__Si31
       +rho*Y[js33]*rate_eval.n_S33__He4_Si30
       +rho*Y[jp30]*rate_eval.n_P30__p_Si30
       +rho*Y[jsi29]*rate_eval.n_Si29__Si30
       )

    jac[jsi30, jp] = (
       -rho*Y[jsi30]*rate_eval.p_Si30__P31
       +rho*Y[jal30]*rate_eval.p_Al30__n_Si30
       +rho*Y[jp33]*rate_eval.p_P33__He4_Si30
       +rho*Y[jal29]*rate_eval.p_Al29__Si30
       )

    jac[jsi30, jhe4] = (
       -rho*Y[jsi30]*rate_eval.He4_Si30__S34
       +rho*Y[jal27]*rate_eval.He4_Al27__p_Si30
       +rho*Y[jmg27]*rate_eval.He4_Mg27__n_Si30
       +rho*Y[jmg26]*rate_eval.He4_Mg26__Si30
       )

    jac[jsi30, jmg26] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg26__Si30
       )

    jac[jsi30, jmg27] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg27__n_Si30
       )

    jac[jsi30, jal27] = (
       +rho*Y[jhe4]*rate_eval.He4_Al27__p_Si30
       )

    jac[jsi30, jal29] = (
       +rho*Y[jp]*rate_eval.p_Al29__Si30
       )

    jac[jsi30, jal30] = (
       +rho*Y[jp]*rate_eval.p_Al30__n_Si30
       +rate_eval.Al30__Si30__weak__wc12
       )

    jac[jsi30, jsi29] = (
       +rho*Y[jn]*rate_eval.n_Si29__Si30
       )

    jac[jsi30, jsi30] = (
       -rho*Y[jp]*rate_eval.p_Si30__P31
       -rho*Y[jn]*rate_eval.n_Si30__Si31
       -rho*Y[jhe4]*rate_eval.He4_Si30__S34
       )

    jac[jsi30, jp30] = (
       +rho*Y[jn]*rate_eval.n_P30__p_Si30
       +rate_eval.P30__Si30__weak__wc12
       )

    jac[jsi30, jp33] = (
       +rho*Y[jp]*rate_eval.p_P33__He4_Si30
       )

    jac[jsi30, js33] = (
       +rho*Y[jn]*rate_eval.n_S33__He4_Si30
       )

    jac[jsi31, jn] = (
       -rho*Y[jsi31]*rate_eval.n_Si31__Si32
       +rho*Y[jsi30]*rate_eval.n_Si30__Si31
       )

    jac[jsi31, jp] = (
       -rho*Y[jsi31]*rate_eval.p_Si31__P32
       -rho*Y[jsi31]*rate_eval.p_Si31__n_P31
       +rho*Y[jal30]*rate_eval.p_Al30__Si31
       +rho*Y[jal31]*rate_eval.p_Al31__n_Si31
       +rho*Y[jp34]*rate_eval.p_P34__He4_Si31
       )

    jac[jsi31, jhe4] = (
       -rho*Y[jsi31]*rate_eval.He4_Si31__n_S34
       -rho*Y[jsi31]*rate_eval.He4_Si31__S35
       +rho*Y[jal28]*rate_eval.He4_Al28__p_Si31
       +rho*Y[jmg27]*rate_eval.He4_Mg27__Si31
       +rho*Y[jmg28]*rate_eval.He4_Mg28__n_Si31
       )

    jac[jsi31, jmg27] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg27__Si31
       )

    jac[jsi31, jmg28] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg28__n_Si31
       )

    jac[jsi31, jal28] = (
       +rho*Y[jhe4]*rate_eval.He4_Al28__p_Si31
       )

    jac[jsi31, jal30] = (
       +rho*Y[jp]*rate_eval.p_Al30__Si31
       )

    jac[jsi31, jal31] = (
       +rho*Y[jp]*rate_eval.p_Al31__n_Si31
       +rate_eval.Al31__Si31__weak__wc12
       )

    jac[jsi31, jal32] = (
       +rate_eval.Al32__n_Si31__weak__wc12
       )

    jac[jsi31, jsi30] = (
       +rho*Y[jn]*rate_eval.n_Si30__Si31
       )

    jac[jsi31, jsi31] = (
       -rho*Y[jhe4]*rate_eval.He4_Si31__n_S34
       -rate_eval.Si31__P31__weak__wc12
       -rho*Y[jp]*rate_eval.p_Si31__P32
       -rho*Y[jhe4]*rate_eval.He4_Si31__S35
       -rho*Y[jn]*rate_eval.n_Si31__Si32
       -rho*Y[jp]*rate_eval.p_Si31__n_P31
       )

    jac[jsi31, jp34] = (
       +rho*Y[jp]*rate_eval.p_P34__He4_Si31
       )

    jac[jsi32, jn] = (
       -rho*Y[jsi32]*rate_eval.n_Si32__Si33
       +rho*Y[js35]*rate_eval.n_S35__He4_Si32
       +rho*Y[jp32]*rate_eval.n_P32__p_Si32
       +rho*Y[jsi31]*rate_eval.n_Si31__Si32
       )

    jac[jsi32, jp] = (
       -rho*Y[jsi32]*rate_eval.p_Si32__P33
       +rho*Y[jal32]*rate_eval.p_Al32__n_Si32
       +rho*Y[jal31]*rate_eval.p_Al31__Si32
       +rho*Y[jp35]*rate_eval.p_P35__He4_Si32
       )

    jac[jsi32, jhe4] = (
       -rho*Y[jsi32]*rate_eval.He4_Si32__S36
       +rho*Y[jal29]*rate_eval.He4_Al29__p_Si32
       +rho*Y[jmg28]*rate_eval.He4_Mg28__Si32
       +rho*Y[jmg29]*rate_eval.He4_Mg29__n_Si32
       )

    jac[jsi32, jmg28] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg28__Si32
       )

    jac[jsi32, jmg29] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg29__n_Si32
       )

    jac[jsi32, jal29] = (
       +rho*Y[jhe4]*rate_eval.He4_Al29__p_Si32
       )

    jac[jsi32, jal31] = (
       +rho*Y[jp]*rate_eval.p_Al31__Si32
       )

    jac[jsi32, jal32] = (
       +rho*Y[jp]*rate_eval.p_Al32__n_Si32
       +rate_eval.Al32__Si32__weak__wc12
       )

    jac[jsi32, jal33] = (
       +rate_eval.Al33__n_Si32__weak__wc12
       )

    jac[jsi32, jsi31] = (
       +rho*Y[jn]*rate_eval.n_Si31__Si32
       )

    jac[jsi32, jsi32] = (
       -rho*Y[jp]*rate_eval.p_Si32__P33
       -rho*Y[jn]*rate_eval.n_Si32__Si33
       -rho*Y[jhe4]*rate_eval.He4_Si32__S36
       -rate_eval.Si32__P32__weak__wc12
       )

    jac[jsi32, jp32] = (
       +rho*Y[jn]*rate_eval.n_P32__p_Si32
       )

    jac[jsi32, jp35] = (
       +rho*Y[jp]*rate_eval.p_P35__He4_Si32
       )

    jac[jsi32, js35] = (
       +rho*Y[jn]*rate_eval.n_S35__He4_Si32
       )

    jac[jsi33, jn] = (
       -rho*Y[jsi33]*rate_eval.n_Si33__Si34
       +rho*Y[jsi32]*rate_eval.n_Si32__Si33
       )

    jac[jsi33, jp] = (
       -rho*Y[jsi33]*rate_eval.p_Si33__n_P33
       -rho*Y[jsi33]*rate_eval.p_Si33__P34
       -rho*Y[jsi33]*rate_eval.p_Si33__He4_Al30
       +rho*Y[jp36]*rate_eval.p_P36__He4_Si33
       +rho*Y[jal33]*rate_eval.p_Al33__n_Si33
       +rho*Y[jal32]*rate_eval.p_Al32__Si33
       )

    jac[jsi33, jhe4] = (
       -rho*Y[jsi33]*rate_eval.He4_Si33__n_S36
       -rho*Y[jsi33]*rate_eval.He4_Si33__S37
       +rho*Y[jmg30]*rate_eval.He4_Mg30__n_Si33
       +rho*Y[jmg29]*rate_eval.He4_Mg29__Si33
       )

    jac[jsi33, jmg29] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg29__Si33
       )

    jac[jsi33, jmg30] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg30__n_Si33
       )

    jac[jsi33, jal32] = (
       +rho*Y[jp]*rate_eval.p_Al32__Si33
       )

    jac[jsi33, jal33] = (
       +rho*Y[jp]*rate_eval.p_Al33__n_Si33
       +rate_eval.Al33__Si33__weak__wc12
       )

    jac[jsi33, jal34] = (
       +rate_eval.Al34__n_Si33__weak__wc12
       )

    jac[jsi33, jsi32] = (
       +rho*Y[jn]*rate_eval.n_Si32__Si33
       )

    jac[jsi33, jsi33] = (
       -rho*Y[jhe4]*rate_eval.He4_Si33__n_S36
       -rho*Y[jn]*rate_eval.n_Si33__Si34
       -rho*Y[jp]*rate_eval.p_Si33__n_P33
       -rate_eval.Si33__P33__weak__wc12
       -rho*Y[jp]*rate_eval.p_Si33__P34
       -rho*Y[jhe4]*rate_eval.He4_Si33__S37
       -rho*Y[jp]*rate_eval.p_Si33__He4_Al30
       )

    jac[jsi33, jp36] = (
       +rho*Y[jp]*rate_eval.p_P36__He4_Si33
       )

    jac[jsi34, jn] = (
       -rho*Y[jsi34]*rate_eval.n_Si34__Si35
       +rho*Y[jsi33]*rate_eval.n_Si33__Si34
       )

    jac[jsi34, jp] = (
       -rho*Y[jsi34]*rate_eval.p_Si34__P35
       -rho*Y[jsi34]*rate_eval.p_Si34__n_P34
       +rho*Y[jp37]*rate_eval.p_P37__He4_Si34
       +rho*Y[jal34]*rate_eval.p_Al34__n_Si34
       +rho*Y[jal33]*rate_eval.p_Al33__Si34
       )

    jac[jsi34, jhe4] = (
       -rho*Y[jsi34]*rate_eval.He4_Si34__S38
       -rho*Y[jsi34]*rate_eval.He4_Si34__n_S37
       +rho*Y[jal31]*rate_eval.He4_Al31__p_Si34
       +rho*Y[jmg30]*rate_eval.He4_Mg30__Si34
       +rho*Y[jmg31]*rate_eval.He4_Mg31__n_Si34
       )

    jac[jsi34, jmg30] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg30__Si34
       )

    jac[jsi34, jmg31] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg31__n_Si34
       )

    jac[jsi34, jal31] = (
       +rho*Y[jhe4]*rate_eval.He4_Al31__p_Si34
       )

    jac[jsi34, jal33] = (
       +rho*Y[jp]*rate_eval.p_Al33__Si34
       )

    jac[jsi34, jal34] = (
       +rho*Y[jp]*rate_eval.p_Al34__n_Si34
       +rate_eval.Al34__Si34__weak__wc12
       )

    jac[jsi34, jal35] = (
       +rate_eval.Al35__n_Si34__weak__wc12
       )

    jac[jsi34, jal36] = (
       +rate_eval.Al36__n_n_Si34__weak__mp17
       )

    jac[jsi34, jal37] = (
       +rate_eval.Al37__n_n_n_Si34__weak__mo03
       )

    jac[jsi34, jsi33] = (
       +rho*Y[jn]*rate_eval.n_Si33__Si34
       )

    jac[jsi34, jsi34] = (
       -rate_eval.Si34__P34__weak__wc12
       -rho*Y[jp]*rate_eval.p_Si34__P35
       -rho*Y[jhe4]*rate_eval.He4_Si34__S38
       -rho*Y[jn]*rate_eval.n_Si34__Si35
       -rho*Y[jhe4]*rate_eval.He4_Si34__n_S37
       -rho*Y[jp]*rate_eval.p_Si34__n_P34
       )

    jac[jsi34, jp37] = (
       +rho*Y[jp]*rate_eval.p_P37__He4_Si34
       )

    jac[jsi35, jn] = (
       -rho*Y[jsi35]*rate_eval.n_Si35__Si36
       +rho*Y[jsi34]*rate_eval.n_Si34__Si35
       )

    jac[jsi35, jp] = (
       -rho*Y[jsi35]*rate_eval.p_Si35__He4_Al32
       -rho*Y[jsi35]*rate_eval.p_Si35__P36
       -rho*Y[jsi35]*rate_eval.p_Si35__n_P35
       +rho*Y[jp38]*rate_eval.p_P38__He4_Si35
       +rho*Y[jal35]*rate_eval.p_Al35__n_Si35
       +rho*Y[jal34]*rate_eval.p_Al34__Si35
       )

    jac[jsi35, jhe4] = (
       -rho*Y[jsi35]*rate_eval.He4_Si35__n_S38
       -rho*Y[jsi35]*rate_eval.He4_Si35__S39
       +rho*Y[jmg32]*rate_eval.He4_Mg32__n_Si35
       +rho*Y[jmg31]*rate_eval.He4_Mg31__Si35
       )

    jac[jsi35, jmg31] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg31__Si35
       )

    jac[jsi35, jmg32] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg32__n_Si35
       )

    jac[jsi35, jal34] = (
       +rho*Y[jp]*rate_eval.p_Al34__Si35
       )

    jac[jsi35, jal35] = (
       +rho*Y[jp]*rate_eval.p_Al35__n_Si35
       +rate_eval.Al35__Si35__weak__wc12
       )

    jac[jsi35, jal36] = (
       +rate_eval.Al36__n_Si35__weak__mp17
       )

    jac[jsi35, jal37] = (
       +rate_eval.Al37__n_n_Si35__weak__mp17
       )

    jac[jsi35, jal38] = (
       +rate_eval.Al38__n_n_n_Si35__weak__mo03
       )

    jac[jsi35, jsi34] = (
       +rho*Y[jn]*rate_eval.n_Si34__Si35
       )

    jac[jsi35, jsi35] = (
       -rho*Y[jhe4]*rate_eval.He4_Si35__n_S38
       -rho*Y[jp]*rate_eval.p_Si35__He4_Al32
       -rate_eval.Si35__P35__weak__wc17
       -rho*Y[jn]*rate_eval.n_Si35__Si36
       -rho*Y[jp]*rate_eval.p_Si35__P36
       -rho*Y[jhe4]*rate_eval.He4_Si35__S39
       -rho*Y[jp]*rate_eval.p_Si35__n_P35
       )

    jac[jsi35, jp38] = (
       +rho*Y[jp]*rate_eval.p_P38__He4_Si35
       )

    jac[jsi36, jn] = (
       -rho*Y[jsi36]*rate_eval.n_Si36__Si37
       +rho*Y[jsi35]*rate_eval.n_Si35__Si36
       )

    jac[jsi36, jp] = (
       -rho*Y[jsi36]*rate_eval.p_Si36__He4_Al33
       -rho*Y[jsi36]*rate_eval.p_Si36__n_P36
       -rho*Y[jsi36]*rate_eval.p_Si36__P37
       +rho*Y[jal36]*rate_eval.p_Al36__n_Si36
       +rho*Y[jp39]*rate_eval.p_P39__He4_Si36
       +rho*Y[jal35]*rate_eval.p_Al35__Si36
       )

    jac[jsi36, jhe4] = (
       -rho*Y[jsi36]*rate_eval.He4_Si36__n_S39
       -rho*Y[jsi36]*rate_eval.He4_Si36__S40
       +rho*Y[jmg33]*rate_eval.He4_Mg33__n_Si36
       +rho*Y[jmg32]*rate_eval.He4_Mg32__Si36
       )

    jac[jsi36, jmg32] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg32__Si36
       )

    jac[jsi36, jmg33] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg33__n_Si36
       )

    jac[jsi36, jal35] = (
       +rho*Y[jp]*rate_eval.p_Al35__Si36
       )

    jac[jsi36, jal36] = (
       +rho*Y[jp]*rate_eval.p_Al36__n_Si36
       +rate_eval.Al36__Si36__weak__wc17
       )

    jac[jsi36, jal37] = (
       +rate_eval.Al37__n_Si36__weak__mp17
       )

    jac[jsi36, jal38] = (
       +rate_eval.Al38__n_n_Si36__weak__mp17
       )

    jac[jsi36, jal39] = (
       +rate_eval.Al39__n_n_n_Si36__weak__mo03
       )

    jac[jsi36, jsi35] = (
       +rho*Y[jn]*rate_eval.n_Si35__Si36
       )

    jac[jsi36, jsi36] = (
       -rho*Y[jp]*rate_eval.p_Si36__He4_Al33
       -rho*Y[jp]*rate_eval.p_Si36__n_P36
       -rho*Y[jn]*rate_eval.n_Si36__Si37
       -rho*Y[jhe4]*rate_eval.He4_Si36__n_S39
       -rate_eval.Si36__P36__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Si36__S40
       -rho*Y[jp]*rate_eval.p_Si36__P37
       -rate_eval.Si36__n_P35__weak__wc12
       )

    jac[jsi36, jp39] = (
       +rho*Y[jp]*rate_eval.p_P39__He4_Si36
       )

    jac[jsi37, jn] = (
       -rho*Y[jsi37]*rate_eval.n_Si37__Si38
       +rho*Y[jsi36]*rate_eval.n_Si36__Si37
       )

    jac[jsi37, jp] = (
       -rho*Y[jsi37]*rate_eval.p_Si37__He4_Al34
       -rho*Y[jsi37]*rate_eval.p_Si37__n_P37
       -rho*Y[jsi37]*rate_eval.p_Si37__P38
       +rho*Y[jal36]*rate_eval.p_Al36__Si37
       +rho*Y[jal37]*rate_eval.p_Al37__n_Si37
       +rho*Y[jp40]*rate_eval.p_P40__He4_Si37
       )

    jac[jsi37, jhe4] = (
       -rho*Y[jsi37]*rate_eval.He4_Si37__n_S40
       -rho*Y[jsi37]*rate_eval.He4_Si37__S41
       +rho*Y[jmg34]*rate_eval.He4_Mg34__n_Si37
       +rho*Y[jmg33]*rate_eval.He4_Mg33__Si37
       )

    jac[jsi37, jmg33] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg33__Si37
       )

    jac[jsi37, jmg34] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg34__n_Si37
       )

    jac[jsi37, jal36] = (
       +rho*Y[jp]*rate_eval.p_Al36__Si37
       )

    jac[jsi37, jal37] = (
       +rate_eval.Al37__Si37__weak__wc17
       +rho*Y[jp]*rate_eval.p_Al37__n_Si37
       )

    jac[jsi37, jal38] = (
       +rate_eval.Al38__n_Si37__weak__mp17
       )

    jac[jsi37, jal39] = (
       +rate_eval.Al39__n_n_Si37__weak__mp17
       )

    jac[jsi37, jal40] = (
       +rate_eval.Al40__n_n_n_Si37__weak__mo03
       )

    jac[jsi37, jsi36] = (
       +rho*Y[jn]*rate_eval.n_Si36__Si37
       )

    jac[jsi37, jsi37] = (
       -rho*Y[jhe4]*rate_eval.He4_Si37__n_S40
       -rho*Y[jp]*rate_eval.p_Si37__He4_Al34
       -rho*Y[jp]*rate_eval.p_Si37__n_P37
       -rho*Y[jp]*rate_eval.p_Si37__P38
       -rho*Y[jhe4]*rate_eval.He4_Si37__S41
       -rate_eval.Si37__n_P36__weak__wc12
       -rate_eval.Si37__P37__weak__wc12
       -rho*Y[jn]*rate_eval.n_Si37__Si38
       )

    jac[jsi37, jp40] = (
       +rho*Y[jp]*rate_eval.p_P40__He4_Si37
       )

    jac[jsi38, jn] = (
       -rho*Y[jsi38]*rate_eval.n_Si38__Si39
       +rho*Y[jsi37]*rate_eval.n_Si37__Si38
       )

    jac[jsi38, jp] = (
       -rho*Y[jsi38]*rate_eval.p_Si38__n_P38
       -rho*Y[jsi38]*rate_eval.p_Si38__P39
       -rho*Y[jsi38]*rate_eval.p_Si38__He4_Al35
       +rho*Y[jal38]*rate_eval.p_Al38__n_Si38
       +rho*Y[jal37]*rate_eval.p_Al37__Si38
       +rho*Y[jp41]*rate_eval.p_P41__He4_Si38
       )

    jac[jsi38, jhe4] = (
       -rho*Y[jsi38]*rate_eval.He4_Si38__n_S41
       -rho*Y[jsi38]*rate_eval.He4_Si38__S42
       +rho*Y[jmg35]*rate_eval.He4_Mg35__n_Si38
       +rho*Y[jmg34]*rate_eval.He4_Mg34__Si38
       )

    jac[jsi38, jmg34] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg34__Si38
       )

    jac[jsi38, jmg35] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg35__n_Si38
       )

    jac[jsi38, jal37] = (
       +rho*Y[jp]*rate_eval.p_Al37__Si38
       )

    jac[jsi38, jal38] = (
       +rho*Y[jp]*rate_eval.p_Al38__n_Si38
       +rate_eval.Al38__Si38__weak__wc17
       )

    jac[jsi38, jal39] = (
       +rate_eval.Al39__n_Si38__weak__mp17
       )

    jac[jsi38, jal40] = (
       +rate_eval.Al40__n_n_Si38__weak__mp17
       )

    jac[jsi38, jal41] = (
       +rate_eval.Al41__n_n_n_Si38__weak__mo03
       )

    jac[jsi38, jsi37] = (
       +rho*Y[jn]*rate_eval.n_Si37__Si38
       )

    jac[jsi38, jsi38] = (
       -rho*Y[jp]*rate_eval.p_Si38__n_P38
       -rho*Y[jhe4]*rate_eval.He4_Si38__n_S41
       -rho*Y[jp]*rate_eval.p_Si38__P39
       -rho*Y[jhe4]*rate_eval.He4_Si38__S42
       -rho*Y[jn]*rate_eval.n_Si38__Si39
       -rate_eval.Si38__P38__weak__mo03
       -rate_eval.Si38__n_P37__weak__mp17
       -rho*Y[jp]*rate_eval.p_Si38__He4_Al35
       )

    jac[jsi38, jp41] = (
       +rho*Y[jp]*rate_eval.p_P41__He4_Si38
       )

    jac[jsi39, jn] = (
       -rho*Y[jsi39]*rate_eval.n_Si39__Si40
       +rho*Y[jsi38]*rate_eval.n_Si38__Si39
       )

    jac[jsi39, jp] = (
       -rho*Y[jsi39]*rate_eval.p_Si39__n_P39
       -rho*Y[jsi39]*rate_eval.p_Si39__P40
       +rho*Y[jal39]*rate_eval.p_Al39__n_Si39
       +rho*Y[jp42]*rate_eval.p_P42__He4_Si39
       +rho*Y[jal38]*rate_eval.p_Al38__Si39
       )

    jac[jsi39, jhe4] = (
       -rho*Y[jsi39]*rate_eval.He4_Si39__n_S42
       -rho*Y[jsi39]*rate_eval.He4_Si39__S43
       +rho*Y[jal36]*rate_eval.He4_Al36__p_Si39
       +rho*Y[jmg36]*rate_eval.He4_Mg36__n_Si39
       +rho*Y[jmg35]*rate_eval.He4_Mg35__Si39
       )

    jac[jsi39, jmg35] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg35__Si39
       )

    jac[jsi39, jmg36] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg36__n_Si39
       )

    jac[jsi39, jal36] = (
       +rho*Y[jhe4]*rate_eval.He4_Al36__p_Si39
       )

    jac[jsi39, jal38] = (
       +rho*Y[jp]*rate_eval.p_Al38__Si39
       )

    jac[jsi39, jal39] = (
       +rho*Y[jp]*rate_eval.p_Al39__n_Si39
       +rate_eval.Al39__Si39__weak__wc17
       )

    jac[jsi39, jal40] = (
       +rate_eval.Al40__n_Si39__weak__mp17
       )

    jac[jsi39, jal41] = (
       +rate_eval.Al41__n_n_Si39__weak__mp17
       )

    jac[jsi39, jal42] = (
       +rate_eval.Al42__n_n_n_Si39__weak__mo03
       )

    jac[jsi39, jsi38] = (
       +rho*Y[jn]*rate_eval.n_Si38__Si39
       )

    jac[jsi39, jsi39] = (
       -rho*Y[jhe4]*rate_eval.He4_Si39__n_S42
       -rho*Y[jp]*rate_eval.p_Si39__n_P39
       -rho*Y[jp]*rate_eval.p_Si39__P40
       -rho*Y[jhe4]*rate_eval.He4_Si39__S43
       -rate_eval.Si39__n_n_P37__weak__mp17
       -rho*Y[jn]*rate_eval.n_Si39__Si40
       -rate_eval.Si39__n_P38__weak__mp17
       -rate_eval.Si39__P39__weak__wc17
       )

    jac[jsi39, jp42] = (
       +rho*Y[jp]*rate_eval.p_P42__He4_Si39
       )

    jac[jsi40, jn] = (
       -rho*Y[jsi40]*rate_eval.n_Si40__Si41
       +rho*Y[jsi39]*rate_eval.n_Si39__Si40
       )

    jac[jsi40, jp] = (
       -rho*Y[jsi40]*rate_eval.p_Si40__P41
       -rho*Y[jsi40]*rate_eval.p_Si40__n_P40
       -rho*Y[jsi40]*rate_eval.p_Si40__He4_Al37
       +rho*Y[jp43]*rate_eval.p_P43__He4_Si40
       +rho*Y[jal40]*rate_eval.p_Al40__n_Si40
       +rho*Y[jal39]*rate_eval.p_Al39__Si40
       )

    jac[jsi40, jhe4] = (
       -rho*Y[jsi40]*rate_eval.He4_Si40__n_S43
       -rho*Y[jsi40]*rate_eval.He4_Si40__S44
       +rho*Y[jmg37]*rate_eval.He4_Mg37__n_Si40
       +rho*Y[jmg36]*rate_eval.He4_Mg36__Si40
       )

    jac[jsi40, jmg36] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg36__Si40
       )

    jac[jsi40, jmg37] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg37__n_Si40
       )

    jac[jsi40, jal39] = (
       +rho*Y[jp]*rate_eval.p_Al39__Si40
       )

    jac[jsi40, jal40] = (
       +rho*Y[jp]*rate_eval.p_Al40__n_Si40
       +rate_eval.Al40__Si40__weak__mo03
       )

    jac[jsi40, jal41] = (
       +rate_eval.Al41__n_Si40__weak__mp17
       )

    jac[jsi40, jal42] = (
       +rate_eval.Al42__n_n_Si40__weak__mo03
       )

    jac[jsi40, jal43] = (
       +rate_eval.Al43__n_n_n_Si40__weak__mo03
       )

    jac[jsi40, jsi39] = (
       +rho*Y[jn]*rate_eval.n_Si39__Si40
       )

    jac[jsi40, jsi40] = (
       -rho*Y[jhe4]*rate_eval.He4_Si40__n_S43
       -rho*Y[jn]*rate_eval.n_Si40__Si41
       -rho*Y[jhe4]*rate_eval.He4_Si40__S44
       -rho*Y[jp]*rate_eval.p_Si40__P41
       -rho*Y[jp]*rate_eval.p_Si40__n_P40
       -rho*Y[jp]*rate_eval.p_Si40__He4_Al37
       -rate_eval.Si40__n_P39__weak__mp17
       -rate_eval.Si40__P40__weak__wc17
       )

    jac[jsi40, jp43] = (
       +rho*Y[jp]*rate_eval.p_P43__He4_Si40
       )

    jac[jsi41, jn] = (
       -rho*Y[jsi41]*rate_eval.n_Si41__Si42
       +rho*Y[jsi40]*rate_eval.n_Si40__Si41
       )

    jac[jsi41, jp] = (
       -rho*Y[jsi41]*rate_eval.p_Si41__P42
       -rho*Y[jsi41]*rate_eval.p_Si41__n_P41
       +rho*Y[jal41]*rate_eval.p_Al41__n_Si41
       +rho*Y[jp44]*rate_eval.p_P44__He4_Si41
       +rho*Y[jal40]*rate_eval.p_Al40__Si41
       )

    jac[jsi41, jhe4] = (
       -rho*Y[jsi41]*rate_eval.He4_Si41__S45
       -rho*Y[jsi41]*rate_eval.He4_Si41__n_S44
       +rho*Y[jmg38]*rate_eval.He4_Mg38__n_Si41
       +rho*Y[jal38]*rate_eval.He4_Al38__p_Si41
       +rho*Y[jmg37]*rate_eval.He4_Mg37__Si41
       )

    jac[jsi41, jmg37] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg37__Si41
       )

    jac[jsi41, jmg38] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg38__n_Si41
       )

    jac[jsi41, jal38] = (
       +rho*Y[jhe4]*rate_eval.He4_Al38__p_Si41
       )

    jac[jsi41, jal40] = (
       +rho*Y[jp]*rate_eval.p_Al40__Si41
       )

    jac[jsi41, jal41] = (
       +rho*Y[jp]*rate_eval.p_Al41__n_Si41
       +rate_eval.Al41__Si41__weak__mo03
       )

    jac[jsi41, jal42] = (
       +rate_eval.Al42__n_Si41__weak__mp17
       )

    jac[jsi41, jal43] = (
       +rate_eval.Al43__n_n_Si41__weak__mp17
       )

    jac[jsi41, jsi40] = (
       +rho*Y[jn]*rate_eval.n_Si40__Si41
       )

    jac[jsi41, jsi41] = (
       -rho*Y[jhe4]*rate_eval.He4_Si41__S45
       -rate_eval.Si41__n_n_P39__weak__mp17
       -rate_eval.Si41__P41__weak__wc17
       -rho*Y[jp]*rate_eval.p_Si41__P42
       -rate_eval.Si41__n_P40__weak__mp17
       -rho*Y[jn]*rate_eval.n_Si41__Si42
       -rho*Y[jhe4]*rate_eval.He4_Si41__n_S44
       -rho*Y[jp]*rate_eval.p_Si41__n_P41
       )

    jac[jsi41, jp44] = (
       +rho*Y[jp]*rate_eval.p_P44__He4_Si41
       )

    jac[jsi42, jn] = (
       -rho*Y[jsi42]*rate_eval.n_Si42__Si43
       +rho*Y[jsi41]*rate_eval.n_Si41__Si42
       )

    jac[jsi42, jp] = (
       -rho*Y[jsi42]*rate_eval.p_Si42__n_P42
       -rho*Y[jsi42]*rate_eval.p_Si42__P43
       +rho*Y[jal41]*rate_eval.p_Al41__Si42
       +rho*Y[jp45]*rate_eval.p_P45__He4_Si42
       +rho*Y[jal42]*rate_eval.p_Al42__n_Si42
       )

    jac[jsi42, jhe4] = (
       -rho*Y[jsi42]*rate_eval.He4_Si42__S46
       -rho*Y[jsi42]*rate_eval.He4_Si42__n_S45
       +rho*Y[jal39]*rate_eval.He4_Al39__p_Si42
       +rho*Y[jmg39]*rate_eval.He4_Mg39__n_Si42
       +rho*Y[jmg38]*rate_eval.He4_Mg38__Si42
       )

    jac[jsi42, jmg38] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg38__Si42
       )

    jac[jsi42, jmg39] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg39__n_Si42
       )

    jac[jsi42, jal39] = (
       +rho*Y[jhe4]*rate_eval.He4_Al39__p_Si42
       )

    jac[jsi42, jal41] = (
       +rho*Y[jp]*rate_eval.p_Al41__Si42
       )

    jac[jsi42, jal42] = (
       +rate_eval.Al42__Si42__weak__mo03
       +rho*Y[jp]*rate_eval.p_Al42__n_Si42
       )

    jac[jsi42, jal43] = (
       +rate_eval.Al43__n_Si42__weak__mp17
       )

    jac[jsi42, jsi41] = (
       +rho*Y[jn]*rate_eval.n_Si41__Si42
       )

    jac[jsi42, jsi42] = (
       -rate_eval.Si42__n_n_n_P39__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Si42__S46
       -rho*Y[jhe4]*rate_eval.He4_Si42__n_S45
       -rho*Y[jp]*rate_eval.p_Si42__n_P42
       -rho*Y[jp]*rate_eval.p_Si42__P43
       -rho*Y[jn]*rate_eval.n_Si42__Si43
       -rate_eval.Si42__P42__weak__wc17
       -rate_eval.Si42__n_P41__weak__mp17
       )

    jac[jsi42, jp45] = (
       +rho*Y[jp]*rate_eval.p_P45__He4_Si42
       )

    jac[jsi43, jn] = (
       -rho*Y[jsi43]*rate_eval.n_Si43__Si44
       +rho*Y[jsi42]*rate_eval.n_Si42__Si43
       )

    jac[jsi43, jp] = (
       -rho*Y[jsi43]*rate_eval.p_Si43__n_P43
       -rho*Y[jsi43]*rate_eval.p_Si43__P44
       +rho*Y[jal43]*rate_eval.p_Al43__n_Si43
       +rho*Y[jal42]*rate_eval.p_Al42__Si43
       +rho*Y[jp46]*rate_eval.p_P46__He4_Si43
       )

    jac[jsi43, jhe4] = (
       -rho*Y[jsi43]*rate_eval.He4_Si43__n_S46
       -rho*Y[jsi43]*rate_eval.He4_Si43__S47
       +rho*Y[jal40]*rate_eval.He4_Al40__p_Si43
       +rho*Y[jmg40]*rate_eval.He4_Mg40__n_Si43
       +rho*Y[jmg39]*rate_eval.He4_Mg39__Si43
       )

    jac[jsi43, jmg39] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg39__Si43
       )

    jac[jsi43, jmg40] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg40__n_Si43
       )

    jac[jsi43, jal40] = (
       +rho*Y[jhe4]*rate_eval.He4_Al40__p_Si43
       )

    jac[jsi43, jal42] = (
       +rho*Y[jp]*rate_eval.p_Al42__Si43
       )

    jac[jsi43, jal43] = (
       +rho*Y[jp]*rate_eval.p_Al43__n_Si43
       )

    jac[jsi43, jsi42] = (
       +rho*Y[jn]*rate_eval.n_Si42__Si43
       )

    jac[jsi43, jsi43] = (
       -rho*Y[jp]*rate_eval.p_Si43__n_P43
       -rho*Y[jhe4]*rate_eval.He4_Si43__n_S46
       -rho*Y[jn]*rate_eval.n_Si43__Si44
       -rate_eval.Si43__n_n_P41__weak__mp17
       -rate_eval.Si43__n_P42__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Si43__S47
       -rate_eval.Si43__n_n_n_P40__weak__mo03
       -rate_eval.Si43__P43__weak__mo03
       -rho*Y[jp]*rate_eval.p_Si43__P44
       )

    jac[jsi43, jp46] = (
       +rho*Y[jp]*rate_eval.p_P46__He4_Si43
       )

    jac[jsi44, jn] = (
       -rho*Y[jsi44]*rate_eval.n_Si44__Si45
       +rho*Y[jsi43]*rate_eval.n_Si43__Si44
       )

    jac[jsi44, jp] = (
       -rho*Y[jsi44]*rate_eval.p_Si44__n_P44
       -rho*Y[jsi44]*rate_eval.p_Si44__He4_Al41
       -rho*Y[jsi44]*rate_eval.p_Si44__P45
       +rho*Y[jal43]*rate_eval.p_Al43__Si44
       +rho*Y[jp47]*rate_eval.p_P47__He4_Si44
       )

    jac[jsi44, jhe4] = (
       -rho*Y[jsi44]*rate_eval.He4_Si44__n_S47
       -rho*Y[jsi44]*rate_eval.He4_Si44__S48
       +rho*Y[jmg40]*rate_eval.He4_Mg40__Si44
       +rho*Y[jmg41]*rate_eval.He4_Mg41__n_Si44
       )

    jac[jsi44, jmg40] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg40__Si44
       )

    jac[jsi44, jmg41] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg41__n_Si44
       )

    jac[jsi44, jal43] = (
       +rho*Y[jp]*rate_eval.p_Al43__Si44
       )

    jac[jsi44, jsi43] = (
       +rho*Y[jn]*rate_eval.n_Si43__Si44
       )

    jac[jsi44, jsi44] = (
       -rho*Y[jp]*rate_eval.p_Si44__n_P44
       -rho*Y[jhe4]*rate_eval.He4_Si44__n_S47
       -rho*Y[jn]*rate_eval.n_Si44__Si45
       -rate_eval.Si44__n_P43__weak__mp17
       -rho*Y[jp]*rate_eval.p_Si44__He4_Al41
       -rho*Y[jp]*rate_eval.p_Si44__P45
       -rate_eval.Si44__n_n_P42__weak__mp17
       -rate_eval.Si44__n_n_n_P41__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Si44__S48
       )

    jac[jsi44, jp47] = (
       +rho*Y[jp]*rate_eval.p_P47__He4_Si44
       )

    jac[jsi45, jn] = (
       +rho*Y[jsi44]*rate_eval.n_Si44__Si45
       )

    jac[jsi45, jp] = (
       -rho*Y[jsi45]*rate_eval.p_Si45__P46
       -rho*Y[jsi45]*rate_eval.p_Si45__He4_Al42
       -rho*Y[jsi45]*rate_eval.p_Si45__n_P45
       )

    jac[jsi45, jhe4] = (
       -rho*Y[jsi45]*rate_eval.He4_Si45__S49
       -rho*Y[jsi45]*rate_eval.He4_Si45__n_S48
       +rho*Y[jmg41]*rate_eval.He4_Mg41__Si45
       )

    jac[jsi45, jmg41] = (
       +rho*Y[jhe4]*rate_eval.He4_Mg41__Si45
       )

    jac[jsi45, jsi44] = (
       +rho*Y[jn]*rate_eval.n_Si44__Si45
       )

    jac[jsi45, jsi45] = (
       -rho*Y[jp]*rate_eval.p_Si45__P46
       -rho*Y[jp]*rate_eval.p_Si45__He4_Al42
       -rho*Y[jp]*rate_eval.p_Si45__n_P45
       -rho*Y[jhe4]*rate_eval.He4_Si45__S49
       -rate_eval.Si45__n_P44__weak__mp17
       -rate_eval.Si45__P45__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Si45__n_S48
       )

    jac[jp24, jn] = (
       -rho*Y[jp24]*rate_eval.n_P24__He4_Al21
       -rho*Y[jp24]*rate_eval.n_P24__p_Si24
       -rho*Y[jp24]*rate_eval.n_P24__P25
       )

    jac[jp24, jhe4] = (
       -rho*Y[jp24]*rate_eval.He4_P24__p_S27
       -rho*Y[jp24]*rate_eval.He4_P24__Cl28
       )

    jac[jp24, jp24] = (
       -rho*Y[jhe4]*rate_eval.He4_P24__p_S27
       -rho*Y[jn]*rate_eval.n_P24__He4_Al21
       -rho*Y[jn]*rate_eval.n_P24__p_Si24
       -rho*Y[jhe4]*rate_eval.He4_P24__Cl28
       -rate_eval.P24__Si24__weak__bqa_pos_
       -rho*Y[jn]*rate_eval.n_P24__P25
       )

    jac[jp25, jn] = (
       -rho*Y[jp25]*rate_eval.n_P25__He4_Al22
       -rho*Y[jp25]*rate_eval.n_P25__p_Si25
       -rho*Y[jp25]*rate_eval.n_P25__P26
       +rho*Y[jcl28]*rate_eval.n_Cl28__He4_P25
       +rho*Y[jp24]*rate_eval.n_P24__P25
       )

    jac[jp25, jp] = (
       -rho*Y[jp25]*rate_eval.p_P25__S26
       +rho*Y[jsi24]*rate_eval.p_Si24__P25
       )

    jac[jp25, jhe4] = (
       -rho*Y[jp25]*rate_eval.He4_P25__p_S28
       -rho*Y[jp25]*rate_eval.He4_P25__Cl29
       +rho*Y[jsi22]*rate_eval.He4_Si22__p_P25
       +rho*Y[jal21]*rate_eval.He4_Al21__P25
       )

    jac[jp25, jal21] = (
       +rho*Y[jhe4]*rate_eval.He4_Al21__P25
       )

    jac[jp25, jsi22] = (
       +rho*Y[jhe4]*rate_eval.He4_Si22__p_P25
       )

    jac[jp25, jsi24] = (
       +rho*Y[jp]*rate_eval.p_Si24__P25
       )

    jac[jp25, jp24] = (
       +rho*Y[jn]*rate_eval.n_P24__P25
       )

    jac[jp25, jp25] = (
       -rho*Y[jhe4]*rate_eval.He4_P25__p_S28
       -rate_eval.P25__Si25__weak__bqa_pos_
       -rho*Y[jhe4]*rate_eval.He4_P25__Cl29
       -rho*Y[jn]*rate_eval.n_P25__He4_Al22
       -rho*Y[jp]*rate_eval.p_P25__S26
       -rho*Y[jn]*rate_eval.n_P25__p_Si25
       -rho*Y[jn]*rate_eval.n_P25__P26
       )

    jac[jp25, jcl28] = (
       +rho*Y[jn]*rate_eval.n_Cl28__He4_P25
       )

    jac[jp26, jn] = (
       -rho*Y[jp26]*rate_eval.n_P26__He4_Al23
       -rho*Y[jp26]*rate_eval.n_P26__p_Si26
       -rho*Y[jp26]*rate_eval.n_P26__P27
       +rho*Y[jcl29]*rate_eval.n_Cl29__He4_P26
       +rho*Y[js26]*rate_eval.n_S26__p_P26
       +rho*Y[jp25]*rate_eval.n_P25__P26
       )

    jac[jp26, jp] = (
       -rho*Y[jp26]*rate_eval.p_P26__S27
       +rho*Y[jsi25]*rate_eval.p_Si25__P26
       )

    jac[jp26, jhe4] = (
       -rho*Y[jp26]*rate_eval.He4_P26__p_S29
       -rho*Y[jp26]*rate_eval.He4_P26__Cl30
       +rho*Y[jsi23]*rate_eval.He4_Si23__p_P26
       +rho*Y[jal22]*rate_eval.He4_Al22__P26
       )

    jac[jp26, jal22] = (
       +rho*Y[jhe4]*rate_eval.He4_Al22__P26
       )

    jac[jp26, jsi23] = (
       +rho*Y[jhe4]*rate_eval.He4_Si23__p_P26
       )

    jac[jp26, jsi25] = (
       +rho*Y[jp]*rate_eval.p_Si25__P26
       )

    jac[jp26, jp25] = (
       +rho*Y[jn]*rate_eval.n_P25__P26
       )

    jac[jp26, jp26] = (
       -rho*Y[jhe4]*rate_eval.He4_P26__p_S29
       -rho*Y[jn]*rate_eval.n_P26__He4_Al23
       -rho*Y[jn]*rate_eval.n_P26__p_Si26
       -rho*Y[jhe4]*rate_eval.He4_P26__Cl30
       -rho*Y[jp]*rate_eval.p_P26__S27
       -rho*Y[jn]*rate_eval.n_P26__P27
       -rate_eval.P26__Si26__weak__wc12
       )

    jac[jp26, js26] = (
       +rho*Y[jn]*rate_eval.n_S26__p_P26
       +rate_eval.S26__P26__weak__bqa_pos_
       )

    jac[jp26, jcl29] = (
       +rho*Y[jn]*rate_eval.n_Cl29__He4_P26
       )

    jac[jp27, jn] = (
       -rho*Y[jp27]*rate_eval.n_P27__He4_Al24
       -rho*Y[jp27]*rate_eval.n_P27__p_Si27
       -rho*Y[jp27]*rate_eval.n_P27__P28
       +rho*Y[jp26]*rate_eval.n_P26__P27
       +rho*Y[jcl30]*rate_eval.n_Cl30__He4_P27
       +rho*Y[js27]*rate_eval.n_S27__p_P27
       )

    jac[jp27, jp] = (
       -rho*Y[jp27]*rate_eval.p_P27__S28
       +rho*Y[jsi26]*rate_eval.p_Si26__P27
       )

    jac[jp27, jhe4] = (
       -rho*Y[jp27]*rate_eval.He4_P27__p_S30
       -rho*Y[jp27]*rate_eval.He4_P27__Cl31
       +rho*Y[jsi24]*rate_eval.He4_Si24__p_P27
       +rho*Y[jal23]*rate_eval.He4_Al23__P27
       )

    jac[jp27, jal23] = (
       +rho*Y[jhe4]*rate_eval.He4_Al23__P27
       )

    jac[jp27, jsi24] = (
       +rho*Y[jhe4]*rate_eval.He4_Si24__p_P27
       )

    jac[jp27, jsi26] = (
       +rho*Y[jp]*rate_eval.p_Si26__P27
       )

    jac[jp27, jp26] = (
       +rho*Y[jn]*rate_eval.n_P26__P27
       )

    jac[jp27, jp27] = (
       -rate_eval.P27__p_Al26__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_P27__p_S30
       -rho*Y[jn]*rate_eval.n_P27__He4_Al24
       -rho*Y[jn]*rate_eval.n_P27__p_Si27
       -rho*Y[jhe4]*rate_eval.He4_P27__Cl31
       -rho*Y[jn]*rate_eval.n_P27__P28
       -rho*Y[jp]*rate_eval.p_P27__S28
       -rate_eval.P27__Si27__weak__wc12
       )

    jac[jp27, js27] = (
       +rate_eval.S27__P27__weak__wc12
       +rho*Y[jn]*rate_eval.n_S27__p_P27
       )

    jac[jp27, jcl30] = (
       +rho*Y[jn]*rate_eval.n_Cl30__He4_P27
       )

    jac[jp28, jn] = (
       -rho*Y[jp28]*rate_eval.n_P28__p_Si28
       -rho*Y[jp28]*rate_eval.n_P28__P29
       -rho*Y[jp28]*rate_eval.n_P28__He4_Al25
       +rho*Y[jp27]*rate_eval.n_P27__P28
       +rho*Y[jcl31]*rate_eval.n_Cl31__He4_P28
       +rho*Y[js28]*rate_eval.n_S28__p_P28
       )

    jac[jp28, jp] = (
       -rho*Y[jp28]*rate_eval.p_P28__S29
       +rho*Y[jsi27]*rate_eval.p_Si27__P28
       )

    jac[jp28, jhe4] = (
       -rho*Y[jp28]*rate_eval.He4_P28__Cl32
       -rho*Y[jp28]*rate_eval.He4_P28__p_S31
       +rho*Y[jsi25]*rate_eval.He4_Si25__p_P28
       +rho*Y[jal24]*rate_eval.He4_Al24__P28
       )

    jac[jp28, jal24] = (
       +rho*Y[jhe4]*rate_eval.He4_Al24__P28
       )

    jac[jp28, jsi25] = (
       +rho*Y[jhe4]*rate_eval.He4_Si25__p_P28
       )

    jac[jp28, jsi27] = (
       +rho*Y[jp]*rate_eval.p_Si27__P28
       )

    jac[jp28, jp27] = (
       +rho*Y[jn]*rate_eval.n_P27__P28
       )

    jac[jp28, jp28] = (
       -rho*Y[jn]*rate_eval.n_P28__p_Si28
       -rho*Y[jhe4]*rate_eval.He4_P28__Cl32
       -rho*Y[jp]*rate_eval.p_P28__S29
       -rho*Y[jn]*rate_eval.n_P28__P29
       -rho*Y[jhe4]*rate_eval.He4_P28__p_S31
       -rate_eval.P28__He4_Mg24__weak__wc12
       -rate_eval.P28__p_Al27__weak__wc12
       -rate_eval.P28__Si28__weak__wc12
       -rho*Y[jn]*rate_eval.n_P28__He4_Al25
       )

    jac[jp28, js28] = (
       +rho*Y[jn]*rate_eval.n_S28__p_P28
       +rate_eval.S28__P28__weak__wc12
       )

    jac[jp28, jcl31] = (
       +rho*Y[jn]*rate_eval.n_Cl31__He4_P28
       )

    jac[jp29, jn] = (
       -rho*Y[jp29]*rate_eval.n_P29__He4_Al26
       -rho*Y[jp29]*rate_eval.n_P29__P30
       -rho*Y[jp29]*rate_eval.n_P29__p_Si29
       +rho*Y[jcl32]*rate_eval.n_Cl32__He4_P29
       +rho*Y[js29]*rate_eval.n_S29__p_P29
       +rho*Y[jp28]*rate_eval.n_P28__P29
       )

    jac[jp29, jp] = (
       -rho*Y[jp29]*rate_eval.p_P29__S30
       +rho*Y[jsi28]*rate_eval.p_Si28__P29
       )

    jac[jp29, jhe4] = (
       -rho*Y[jp29]*rate_eval.He4_P29__Cl33
       -rho*Y[jp29]*rate_eval.He4_P29__p_S32
       +rho*Y[jal25]*rate_eval.He4_Al25__P29
       +rho*Y[jsi26]*rate_eval.He4_Si26__p_P29
       )

    jac[jp29, jal25] = (
       +rho*Y[jhe4]*rate_eval.He4_Al25__P29
       )

    jac[jp29, jsi26] = (
       +rho*Y[jhe4]*rate_eval.He4_Si26__p_P29
       )

    jac[jp29, jsi28] = (
       +rho*Y[jp]*rate_eval.p_Si28__P29
       )

    jac[jp29, jp28] = (
       +rho*Y[jn]*rate_eval.n_P28__P29
       )

    jac[jp29, jp29] = (
       -rho*Y[jp]*rate_eval.p_P29__S30
       -rho*Y[jn]*rate_eval.n_P29__He4_Al26
       -rho*Y[jn]*rate_eval.n_P29__P30
       -rho*Y[jhe4]*rate_eval.He4_P29__Cl33
       -rho*Y[jhe4]*rate_eval.He4_P29__p_S32
       -rho*Y[jn]*rate_eval.n_P29__p_Si29
       -rate_eval.P29__Si29__weak__wc12
       )

    jac[jp29, js29] = (
       +rho*Y[jn]*rate_eval.n_S29__p_P29
       +rate_eval.S29__P29__weak__wc12
       )

    jac[jp29, jcl32] = (
       +rho*Y[jn]*rate_eval.n_Cl32__He4_P29
       )

    jac[jp29, jar31] = (
       +rate_eval.Ar31__p_p_P29__weak__wc12
       )

    jac[jp30, jn] = (
       -rho*Y[jp30]*rate_eval.n_P30__p_Si30
       -rho*Y[jp30]*rate_eval.n_P30__P31
       +rho*Y[jcl33]*rate_eval.n_Cl33__He4_P30
       +rho*Y[js30]*rate_eval.n_S30__p_P30
       +rho*Y[jp29]*rate_eval.n_P29__P30
       )

    jac[jp30, jp] = (
       -rho*Y[jp30]*rate_eval.p_P30__S31
       +rho*Y[jsi29]*rate_eval.p_Si29__P30
       )

    jac[jp30, jhe4] = (
       -rho*Y[jp30]*rate_eval.He4_P30__p_S33
       -rho*Y[jp30]*rate_eval.He4_P30__Cl34
       +rho*Y[jsi27]*rate_eval.He4_Si27__p_P30
       +rho*Y[jal27]*rate_eval.He4_Al27__n_P30
       +rho*Y[jal26]*rate_eval.He4_Al26__P30
       )

    jac[jp30, jal26] = (
       +rho*Y[jhe4]*rate_eval.He4_Al26__P30
       )

    jac[jp30, jal27] = (
       +rho*Y[jhe4]*rate_eval.He4_Al27__n_P30
       )

    jac[jp30, jsi27] = (
       +rho*Y[jhe4]*rate_eval.He4_Si27__p_P30
       )

    jac[jp30, jsi29] = (
       +rho*Y[jp]*rate_eval.p_Si29__P30
       )

    jac[jp30, jp29] = (
       +rho*Y[jn]*rate_eval.n_P29__P30
       )

    jac[jp30, jp30] = (
       -rho*Y[jhe4]*rate_eval.He4_P30__p_S33
       -rho*Y[jp]*rate_eval.p_P30__S31
       -rho*Y[jn]*rate_eval.n_P30__p_Si30
       -rho*Y[jn]*rate_eval.n_P30__P31
       -rho*Y[jhe4]*rate_eval.He4_P30__Cl34
       -rate_eval.P30__Si30__weak__wc12
       )

    jac[jp30, js30] = (
       +rho*Y[jn]*rate_eval.n_S30__p_P30
       +rate_eval.S30__P30__weak__wc12
       )

    jac[jp30, jcl31] = (
       +rate_eval.Cl31__p_P30__weak__wc12
       )

    jac[jp30, jcl33] = (
       +rho*Y[jn]*rate_eval.n_Cl33__He4_P30
       )

    jac[jp31, jn] = (
       -rho*Y[jp31]*rate_eval.n_P31__P32
       +rho*Y[jcl34]*rate_eval.n_Cl34__He4_P31
       +rho*Y[js31]*rate_eval.n_S31__p_P31
       +rho*Y[jp30]*rate_eval.n_P30__P31
       )

    jac[jp31, jp] = (
       -rho*Y[jp31]*rate_eval.p_P31__S32
       -rho*Y[jp31]*rate_eval.p_P31__He4_Si28
       +rho*Y[jsi30]*rate_eval.p_Si30__P31
       +rho*Y[jsi31]*rate_eval.p_Si31__n_P31
       )

    jac[jp31, jhe4] = (
       -rho*Y[jp31]*rate_eval.He4_P31__p_S34
       -rho*Y[jp31]*rate_eval.He4_P31__Cl35
       +rho*Y[jal28]*rate_eval.He4_Al28__n_P31
       +rho*Y[jal27]*rate_eval.He4_Al27__P31
       )

    jac[jp31, jc12] = (
       +rho*Y[jne20]*rate_eval.C12_Ne20__p_P31
       )

    jac[jp31, jo16] = (
       +5.00000000000000e-01*rho*2*Y[jo16]*rate_eval.O16_O16__p_P31
       )

    jac[jp31, jne20] = (
       +rho*Y[jc12]*rate_eval.C12_Ne20__p_P31
       )

    jac[jp31, jal27] = (
       +rho*Y[jhe4]*rate_eval.He4_Al27__P31
       )

    jac[jp31, jal28] = (
       +rho*Y[jhe4]*rate_eval.He4_Al28__n_P31
       )

    jac[jp31, jsi30] = (
       +rho*Y[jp]*rate_eval.p_Si30__P31
       )

    jac[jp31, jsi31] = (
       +rate_eval.Si31__P31__weak__wc12
       +rho*Y[jp]*rate_eval.p_Si31__n_P31
       )

    jac[jp31, jp30] = (
       +rho*Y[jn]*rate_eval.n_P30__P31
       )

    jac[jp31, jp31] = (
       -rho*Y[jp]*rate_eval.p_P31__S32
       -rho*Y[jhe4]*rate_eval.He4_P31__p_S34
       -rho*Y[jp]*rate_eval.p_P31__He4_Si28
       -rho*Y[jhe4]*rate_eval.He4_P31__Cl35
       -rho*Y[jn]*rate_eval.n_P31__P32
       )

    jac[jp31, js31] = (
       +rho*Y[jn]*rate_eval.n_S31__p_P31
       +rate_eval.S31__P31__weak__wc12
       )

    jac[jp31, jcl32] = (
       +rate_eval.Cl32__p_P31__weak__wc12
       )

    jac[jp31, jcl34] = (
       +rho*Y[jn]*rate_eval.n_Cl34__He4_P31
       )

    jac[jp32, jn] = (
       -rho*Y[jp32]*rate_eval.n_P32__p_Si32
       -rho*Y[jp32]*rate_eval.n_P32__P33
       +rho*Y[jcl35]*rate_eval.n_Cl35__He4_P32
       +rho*Y[jp31]*rate_eval.n_P31__P32
       )

    jac[jp32, jp] = (
       -rho*Y[jp32]*rate_eval.p_P32__n_S32
       -rho*Y[jp32]*rate_eval.p_P32__He4_Si29
       -rho*Y[jp32]*rate_eval.p_P32__S33
       +rho*Y[js35]*rate_eval.p_S35__He4_P32
       +rho*Y[jsi31]*rate_eval.p_Si31__P32
       )

    jac[jp32, jhe4] = (
       -rho*Y[jp32]*rate_eval.He4_P32__Cl36
       +rho*Y[jal29]*rate_eval.He4_Al29__n_P32
       +rho*Y[jal28]*rate_eval.He4_Al28__P32
       )

    jac[jp32, jal28] = (
       +rho*Y[jhe4]*rate_eval.He4_Al28__P32
       )

    jac[jp32, jal29] = (
       +rho*Y[jhe4]*rate_eval.He4_Al29__n_P32
       )

    jac[jp32, jsi31] = (
       +rho*Y[jp]*rate_eval.p_Si31__P32
       )

    jac[jp32, jsi32] = (
       +rate_eval.Si32__P32__weak__wc12
       )

    jac[jp32, jp31] = (
       +rho*Y[jn]*rate_eval.n_P31__P32
       )

    jac[jp32, jp32] = (
       -rho*Y[jp]*rate_eval.p_P32__n_S32
       -rho*Y[jp]*rate_eval.p_P32__He4_Si29
       -rho*Y[jn]*rate_eval.n_P32__p_Si32
       -rho*Y[jp]*rate_eval.p_P32__S33
       -rho*Y[jhe4]*rate_eval.He4_P32__Cl36
       -rho*Y[jn]*rate_eval.n_P32__P33
       -rate_eval.P32__S32__weak__wc12
       )

    jac[jp32, js35] = (
       +rho*Y[jp]*rate_eval.p_S35__He4_P32
       )

    jac[jp32, jcl35] = (
       +rho*Y[jn]*rate_eval.n_Cl35__He4_P32
       )

    jac[jp33, jn] = (
       -rho*Y[jp33]*rate_eval.n_P33__P34
       +rho*Y[js33]*rate_eval.n_S33__p_P33
       +rho*Y[jp32]*rate_eval.n_P32__P33
       +rho*Y[jcl36]*rate_eval.n_Cl36__He4_P33
       )

    jac[jp33, jp] = (
       -rho*Y[jp33]*rate_eval.p_P33__He4_Si30
       -rho*Y[jp33]*rate_eval.p_P33__S34
       +rho*Y[js36]*rate_eval.p_S36__He4_P33
       +rho*Y[jsi33]*rate_eval.p_Si33__n_P33
       +rho*Y[jsi32]*rate_eval.p_Si32__P33
       )

    jac[jp33, jhe4] = (
       -rho*Y[jp33]*rate_eval.He4_P33__Cl37
       +rho*Y[jal29]*rate_eval.He4_Al29__P33
       +rho*Y[jal30]*rate_eval.He4_Al30__n_P33
       )

    jac[jp33, jal29] = (
       +rho*Y[jhe4]*rate_eval.He4_Al29__P33
       )

    jac[jp33, jal30] = (
       +rho*Y[jhe4]*rate_eval.He4_Al30__n_P33
       )

    jac[jp33, jsi32] = (
       +rho*Y[jp]*rate_eval.p_Si32__P33
       )

    jac[jp33, jsi33] = (
       +rho*Y[jp]*rate_eval.p_Si33__n_P33
       +rate_eval.Si33__P33__weak__wc12
       )

    jac[jp33, jp32] = (
       +rho*Y[jn]*rate_eval.n_P32__P33
       )

    jac[jp33, jp33] = (
       -rate_eval.P33__S33__weak__wc12
       -rho*Y[jp]*rate_eval.p_P33__He4_Si30
       -rho*Y[jn]*rate_eval.n_P33__P34
       -rho*Y[jhe4]*rate_eval.He4_P33__Cl37
       -rho*Y[jp]*rate_eval.p_P33__S34
       )

    jac[jp33, js33] = (
       +rho*Y[jn]*rate_eval.n_S33__p_P33
       )

    jac[jp33, js36] = (
       +rho*Y[jp]*rate_eval.p_S36__He4_P33
       )

    jac[jp33, jcl36] = (
       +rho*Y[jn]*rate_eval.n_Cl36__He4_P33
       )

    jac[jp34, jn] = (
       -rho*Y[jp34]*rate_eval.n_P34__P35
       +rho*Y[jp33]*rate_eval.n_P33__P34
       )

    jac[jp34, jp] = (
       -rho*Y[jp34]*rate_eval.p_P34__n_S34
       -rho*Y[jp34]*rate_eval.p_P34__S35
       -rho*Y[jp34]*rate_eval.p_P34__He4_Si31
       +rho*Y[jsi33]*rate_eval.p_Si33__P34
       +rho*Y[js37]*rate_eval.p_S37__He4_P34
       +rho*Y[jsi34]*rate_eval.p_Si34__n_P34
       )

    jac[jp34, jhe4] = (
       -rho*Y[jp34]*rate_eval.He4_P34__n_Cl37
       -rho*Y[jp34]*rate_eval.He4_P34__Cl38
       +rho*Y[jal31]*rate_eval.He4_Al31__n_P34
       +rho*Y[jal30]*rate_eval.He4_Al30__P34
       )

    jac[jp34, jal30] = (
       +rho*Y[jhe4]*rate_eval.He4_Al30__P34
       )

    jac[jp34, jal31] = (
       +rho*Y[jhe4]*rate_eval.He4_Al31__n_P34
       )

    jac[jp34, jsi33] = (
       +rho*Y[jp]*rate_eval.p_Si33__P34
       )

    jac[jp34, jsi34] = (
       +rate_eval.Si34__P34__weak__wc12
       +rho*Y[jp]*rate_eval.p_Si34__n_P34
       )

    jac[jp34, jp33] = (
       +rho*Y[jn]*rate_eval.n_P33__P34
       )

    jac[jp34, jp34] = (
       -rho*Y[jhe4]*rate_eval.He4_P34__n_Cl37
       -rho*Y[jp]*rate_eval.p_P34__n_S34
       -rho*Y[jp]*rate_eval.p_P34__S35
       -rho*Y[jhe4]*rate_eval.He4_P34__Cl38
       -rho*Y[jn]*rate_eval.n_P34__P35
       -rho*Y[jp]*rate_eval.p_P34__He4_Si31
       -rate_eval.P34__S34__weak__wc12
       )

    jac[jp34, js37] = (
       +rho*Y[jp]*rate_eval.p_S37__He4_P34
       )

    jac[jp35, jn] = (
       -rho*Y[jp35]*rate_eval.n_P35__P36
       +rho*Y[jcl38]*rate_eval.n_Cl38__He4_P35
       +rho*Y[jp34]*rate_eval.n_P34__P35
       )

    jac[jp35, jp] = (
       -rho*Y[jp35]*rate_eval.p_P35__S36
       -rho*Y[jp35]*rate_eval.p_P35__n_S35
       -rho*Y[jp35]*rate_eval.p_P35__He4_Si32
       +rho*Y[js38]*rate_eval.p_S38__He4_P35
       +rho*Y[jsi34]*rate_eval.p_Si34__P35
       +rho*Y[jsi35]*rate_eval.p_Si35__n_P35
       )

    jac[jp35, jhe4] = (
       -rho*Y[jp35]*rate_eval.He4_P35__Cl39
       +rho*Y[jal32]*rate_eval.He4_Al32__n_P35
       +rho*Y[jal31]*rate_eval.He4_Al31__P35
       )

    jac[jp35, jal31] = (
       +rho*Y[jhe4]*rate_eval.He4_Al31__P35
       )

    jac[jp35, jal32] = (
       +rho*Y[jhe4]*rate_eval.He4_Al32__n_P35
       )

    jac[jp35, jsi34] = (
       +rho*Y[jp]*rate_eval.p_Si34__P35
       )

    jac[jp35, jsi35] = (
       +rate_eval.Si35__P35__weak__wc17
       +rho*Y[jp]*rate_eval.p_Si35__n_P35
       )

    jac[jp35, jsi36] = (
       +rate_eval.Si36__n_P35__weak__wc12
       )

    jac[jp35, jp34] = (
       +rho*Y[jn]*rate_eval.n_P34__P35
       )

    jac[jp35, jp35] = (
       -rho*Y[jhe4]*rate_eval.He4_P35__Cl39
       -rho*Y[jp]*rate_eval.p_P35__S36
       -rho*Y[jn]*rate_eval.n_P35__P36
       -rho*Y[jp]*rate_eval.p_P35__n_S35
       -rho*Y[jp]*rate_eval.p_P35__He4_Si32
       -rate_eval.P35__S35__weak__wc12
       )

    jac[jp35, js38] = (
       +rho*Y[jp]*rate_eval.p_S38__He4_P35
       )

    jac[jp35, jcl38] = (
       +rho*Y[jn]*rate_eval.n_Cl38__He4_P35
       )

    jac[jp36, jn] = (
       -rho*Y[jp36]*rate_eval.n_P36__P37
       +rho*Y[jp35]*rate_eval.n_P35__P36
       )

    jac[jp36, jp] = (
       -rho*Y[jp36]*rate_eval.p_P36__He4_Si33
       -rho*Y[jp36]*rate_eval.p_P36__n_S36
       -rho*Y[jp36]*rate_eval.p_P36__S37
       +rho*Y[js39]*rate_eval.p_S39__He4_P36
       +rho*Y[jsi36]*rate_eval.p_Si36__n_P36
       +rho*Y[jsi35]*rate_eval.p_Si35__P36
       )

    jac[jp36, jhe4] = (
       -rho*Y[jp36]*rate_eval.He4_P36__n_Cl39
       -rho*Y[jp36]*rate_eval.He4_P36__Cl40
       +rho*Y[jal33]*rate_eval.He4_Al33__n_P36
       +rho*Y[jal32]*rate_eval.He4_Al32__P36
       )

    jac[jp36, jal32] = (
       +rho*Y[jhe4]*rate_eval.He4_Al32__P36
       )

    jac[jp36, jal33] = (
       +rho*Y[jhe4]*rate_eval.He4_Al33__n_P36
       )

    jac[jp36, jsi35] = (
       +rho*Y[jp]*rate_eval.p_Si35__P36
       )

    jac[jp36, jsi36] = (
       +rho*Y[jp]*rate_eval.p_Si36__n_P36
       +rate_eval.Si36__P36__weak__wc12
       )

    jac[jp36, jsi37] = (
       +rate_eval.Si37__n_P36__weak__wc12
       )

    jac[jp36, jp35] = (
       +rho*Y[jn]*rate_eval.n_P35__P36
       )

    jac[jp36, jp36] = (
       -rho*Y[jp]*rate_eval.p_P36__He4_Si33
       -rho*Y[jp]*rate_eval.p_P36__n_S36
       -rho*Y[jhe4]*rate_eval.He4_P36__n_Cl39
       -rate_eval.P36__S36__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_P36__Cl40
       -rho*Y[jn]*rate_eval.n_P36__P37
       -rho*Y[jp]*rate_eval.p_P36__S37
       )

    jac[jp36, js39] = (
       +rho*Y[jp]*rate_eval.p_S39__He4_P36
       )

    jac[jp37, jn] = (
       -rho*Y[jp37]*rate_eval.n_P37__P38
       +rho*Y[jp36]*rate_eval.n_P36__P37
       )

    jac[jp37, jp] = (
       -rho*Y[jp37]*rate_eval.p_P37__He4_Si34
       -rho*Y[jp37]*rate_eval.p_P37__S38
       -rho*Y[jp37]*rate_eval.p_P37__n_S37
       +rho*Y[jsi37]*rate_eval.p_Si37__n_P37
       +rho*Y[js40]*rate_eval.p_S40__He4_P37
       +rho*Y[jsi36]*rate_eval.p_Si36__P37
       )

    jac[jp37, jhe4] = (
       -rho*Y[jp37]*rate_eval.He4_P37__n_Cl40
       -rho*Y[jp37]*rate_eval.He4_P37__Cl41
       +rho*Y[jal34]*rate_eval.He4_Al34__n_P37
       +rho*Y[jal33]*rate_eval.He4_Al33__P37
       )

    jac[jp37, jal33] = (
       +rho*Y[jhe4]*rate_eval.He4_Al33__P37
       )

    jac[jp37, jal34] = (
       +rho*Y[jhe4]*rate_eval.He4_Al34__n_P37
       )

    jac[jp37, jsi36] = (
       +rho*Y[jp]*rate_eval.p_Si36__P37
       )

    jac[jp37, jsi37] = (
       +rho*Y[jp]*rate_eval.p_Si37__n_P37
       +rate_eval.Si37__P37__weak__wc12
       )

    jac[jp37, jsi38] = (
       +rate_eval.Si38__n_P37__weak__mp17
       )

    jac[jp37, jsi39] = (
       +rate_eval.Si39__n_n_P37__weak__mp17
       )

    jac[jp37, jp36] = (
       +rho*Y[jn]*rate_eval.n_P36__P37
       )

    jac[jp37, jp37] = (
       -rho*Y[jhe4]*rate_eval.He4_P37__n_Cl40
       -rho*Y[jp]*rate_eval.p_P37__He4_Si34
       -rate_eval.P37__S37__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_P37__Cl41
       -rho*Y[jp]*rate_eval.p_P37__S38
       -rho*Y[jn]*rate_eval.n_P37__P38
       -rho*Y[jp]*rate_eval.p_P37__n_S37
       )

    jac[jp37, js40] = (
       +rho*Y[jp]*rate_eval.p_S40__He4_P37
       )

    jac[jp38, jn] = (
       -rho*Y[jp38]*rate_eval.n_P38__P39
       +rho*Y[jp37]*rate_eval.n_P37__P38
       )

    jac[jp38, jp] = (
       -rho*Y[jp38]*rate_eval.p_P38__He4_Si35
       -rho*Y[jp38]*rate_eval.p_P38__n_S38
       -rho*Y[jp38]*rate_eval.p_P38__S39
       +rho*Y[jsi38]*rate_eval.p_Si38__n_P38
       +rho*Y[js41]*rate_eval.p_S41__He4_P38
       +rho*Y[jsi37]*rate_eval.p_Si37__P38
       )

    jac[jp38, jhe4] = (
       -rho*Y[jp38]*rate_eval.He4_P38__Cl42
       -rho*Y[jp38]*rate_eval.He4_P38__n_Cl41
       +rho*Y[jal35]*rate_eval.He4_Al35__n_P38
       +rho*Y[jal34]*rate_eval.He4_Al34__P38
       )

    jac[jp38, jal34] = (
       +rho*Y[jhe4]*rate_eval.He4_Al34__P38
       )

    jac[jp38, jal35] = (
       +rho*Y[jhe4]*rate_eval.He4_Al35__n_P38
       )

    jac[jp38, jsi37] = (
       +rho*Y[jp]*rate_eval.p_Si37__P38
       )

    jac[jp38, jsi38] = (
       +rho*Y[jp]*rate_eval.p_Si38__n_P38
       +rate_eval.Si38__P38__weak__mo03
       )

    jac[jp38, jsi39] = (
       +rate_eval.Si39__n_P38__weak__mp17
       )

    jac[jp38, jp37] = (
       +rho*Y[jn]*rate_eval.n_P37__P38
       )

    jac[jp38, jp38] = (
       -rho*Y[jp]*rate_eval.p_P38__He4_Si35
       -rho*Y[jp]*rate_eval.p_P38__n_S38
       -rho*Y[jp]*rate_eval.p_P38__S39
       -rho*Y[jn]*rate_eval.n_P38__P39
       -rho*Y[jhe4]*rate_eval.He4_P38__Cl42
       -rate_eval.P38__S38__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_P38__n_Cl41
       -rate_eval.P38__n_S37__weak__wc12
       )

    jac[jp38, js41] = (
       +rho*Y[jp]*rate_eval.p_S41__He4_P38
       )

    jac[jp39, jn] = (
       -rho*Y[jp39]*rate_eval.n_P39__P40
       +rho*Y[jp38]*rate_eval.n_P38__P39
       )

    jac[jp39, jp] = (
       -rho*Y[jp39]*rate_eval.p_P39__n_S39
       -rho*Y[jp39]*rate_eval.p_P39__He4_Si36
       -rho*Y[jp39]*rate_eval.p_P39__S40
       +rho*Y[jsi39]*rate_eval.p_Si39__n_P39
       +rho*Y[jsi38]*rate_eval.p_Si38__P39
       +rho*Y[js42]*rate_eval.p_S42__He4_P39
       )

    jac[jp39, jhe4] = (
       -rho*Y[jp39]*rate_eval.He4_P39__n_Cl42
       -rho*Y[jp39]*rate_eval.He4_P39__Cl43
       +rho*Y[jal36]*rate_eval.He4_Al36__n_P39
       +rho*Y[jal35]*rate_eval.He4_Al35__P39
       )

    jac[jp39, jal35] = (
       +rho*Y[jhe4]*rate_eval.He4_Al35__P39
       )

    jac[jp39, jal36] = (
       +rho*Y[jhe4]*rate_eval.He4_Al36__n_P39
       )

    jac[jp39, jsi38] = (
       +rho*Y[jp]*rate_eval.p_Si38__P39
       )

    jac[jp39, jsi39] = (
       +rho*Y[jp]*rate_eval.p_Si39__n_P39
       +rate_eval.Si39__P39__weak__wc17
       )

    jac[jp39, jsi40] = (
       +rate_eval.Si40__n_P39__weak__mp17
       )

    jac[jp39, jsi41] = (
       +rate_eval.Si41__n_n_P39__weak__mp17
       )

    jac[jp39, jsi42] = (
       +rate_eval.Si42__n_n_n_P39__weak__mo03
       )

    jac[jp39, jp38] = (
       +rho*Y[jn]*rate_eval.n_P38__P39
       )

    jac[jp39, jp39] = (
       -rho*Y[jhe4]*rate_eval.He4_P39__n_Cl42
       -rho*Y[jn]*rate_eval.n_P39__P40
       -rho*Y[jp]*rate_eval.p_P39__n_S39
       -rho*Y[jhe4]*rate_eval.He4_P39__Cl43
       -rho*Y[jp]*rate_eval.p_P39__He4_Si36
       -rate_eval.P39__n_S38__weak__wc12
       -rate_eval.P39__S39__weak__wc12
       -rho*Y[jp]*rate_eval.p_P39__S40
       )

    jac[jp39, js42] = (
       +rho*Y[jp]*rate_eval.p_S42__He4_P39
       )

    jac[jp40, jn] = (
       -rho*Y[jp40]*rate_eval.n_P40__P41
       +rho*Y[jp39]*rate_eval.n_P39__P40
       )

    jac[jp40, jp] = (
       -rho*Y[jp40]*rate_eval.p_P40__n_S40
       -rho*Y[jp40]*rate_eval.p_P40__S41
       -rho*Y[jp40]*rate_eval.p_P40__He4_Si37
       +rho*Y[js43]*rate_eval.p_S43__He4_P40
       +rho*Y[jsi39]*rate_eval.p_Si39__P40
       +rho*Y[jsi40]*rate_eval.p_Si40__n_P40
       )

    jac[jp40, jhe4] = (
       -rho*Y[jp40]*rate_eval.He4_P40__n_Cl43
       -rho*Y[jp40]*rate_eval.He4_P40__Cl44
       +rho*Y[jal37]*rate_eval.He4_Al37__n_P40
       +rho*Y[jal36]*rate_eval.He4_Al36__P40
       )

    jac[jp40, jal36] = (
       +rho*Y[jhe4]*rate_eval.He4_Al36__P40
       )

    jac[jp40, jal37] = (
       +rho*Y[jhe4]*rate_eval.He4_Al37__n_P40
       )

    jac[jp40, jsi39] = (
       +rho*Y[jp]*rate_eval.p_Si39__P40
       )

    jac[jp40, jsi40] = (
       +rho*Y[jp]*rate_eval.p_Si40__n_P40
       +rate_eval.Si40__P40__weak__wc17
       )

    jac[jp40, jsi41] = (
       +rate_eval.Si41__n_P40__weak__mp17
       )

    jac[jp40, jsi43] = (
       +rate_eval.Si43__n_n_n_P40__weak__mo03
       )

    jac[jp40, jp39] = (
       +rho*Y[jn]*rate_eval.n_P39__P40
       )

    jac[jp40, jp40] = (
       -rate_eval.P40__S40__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_P40__n_Cl43
       -rho*Y[jp]*rate_eval.p_P40__n_S40
       -rho*Y[jhe4]*rate_eval.He4_P40__Cl44
       -rho*Y[jp]*rate_eval.p_P40__S41
       -rho*Y[jn]*rate_eval.n_P40__P41
       -rate_eval.P40__n_S39__weak__wc12
       -rho*Y[jp]*rate_eval.p_P40__He4_Si37
       )

    jac[jp40, js43] = (
       +rho*Y[jp]*rate_eval.p_S43__He4_P40
       )

    jac[jp41, jn] = (
       -rho*Y[jp41]*rate_eval.n_P41__P42
       +rho*Y[jp40]*rate_eval.n_P40__P41
       )

    jac[jp41, jp] = (
       -rho*Y[jp41]*rate_eval.p_P41__n_S41
       -rho*Y[jp41]*rate_eval.p_P41__S42
       -rho*Y[jp41]*rate_eval.p_P41__He4_Si38
       +rho*Y[jsi40]*rate_eval.p_Si40__P41
       +rho*Y[jsi41]*rate_eval.p_Si41__n_P41
       )

    jac[jp41, jhe4] = (
       -rho*Y[jp41]*rate_eval.He4_P41__p_S44
       -rho*Y[jp41]*rate_eval.He4_P41__n_Cl44
       -rho*Y[jp41]*rate_eval.He4_P41__Cl45
       +rho*Y[jal38]*rate_eval.He4_Al38__n_P41
       +rho*Y[jal37]*rate_eval.He4_Al37__P41
       )

    jac[jp41, jal37] = (
       +rho*Y[jhe4]*rate_eval.He4_Al37__P41
       )

    jac[jp41, jal38] = (
       +rho*Y[jhe4]*rate_eval.He4_Al38__n_P41
       )

    jac[jp41, jsi40] = (
       +rho*Y[jp]*rate_eval.p_Si40__P41
       )

    jac[jp41, jsi41] = (
       +rate_eval.Si41__P41__weak__wc17
       +rho*Y[jp]*rate_eval.p_Si41__n_P41
       )

    jac[jp41, jsi42] = (
       +rate_eval.Si42__n_P41__weak__mp17
       )

    jac[jp41, jsi43] = (
       +rate_eval.Si43__n_n_P41__weak__mp17
       )

    jac[jp41, jsi44] = (
       +rate_eval.Si44__n_n_n_P41__weak__mo03
       )

    jac[jp41, jp40] = (
       +rho*Y[jn]*rate_eval.n_P40__P41
       )

    jac[jp41, jp41] = (
       -rho*Y[jhe4]*rate_eval.He4_P41__p_S44
       -rho*Y[jhe4]*rate_eval.He4_P41__n_Cl44
       -rho*Y[jn]*rate_eval.n_P41__P42
       -rate_eval.P41__n_S40__weak__wc12
       -rho*Y[jp]*rate_eval.p_P41__n_S41
       -rho*Y[jhe4]*rate_eval.He4_P41__Cl45
       -rho*Y[jp]*rate_eval.p_P41__S42
       -rate_eval.P41__S41__weak__wc12
       -rho*Y[jp]*rate_eval.p_P41__He4_Si38
       )

    jac[jp42, jn] = (
       -rho*Y[jp42]*rate_eval.n_P42__P43
       +rho*Y[jp41]*rate_eval.n_P41__P42
       )

    jac[jp42, jp] = (
       -rho*Y[jp42]*rate_eval.p_P42__n_S42
       -rho*Y[jp42]*rate_eval.p_P42__He4_Si39
       -rho*Y[jp42]*rate_eval.p_P42__S43
       +rho*Y[js45]*rate_eval.p_S45__He4_P42
       +rho*Y[jsi42]*rate_eval.p_Si42__n_P42
       +rho*Y[jsi41]*rate_eval.p_Si41__P42
       )

    jac[jp42, jhe4] = (
       -rho*Y[jp42]*rate_eval.He4_P42__n_Cl45
       -rho*Y[jp42]*rate_eval.He4_P42__Cl46
       +rho*Y[jal38]*rate_eval.He4_Al38__P42
       +rho*Y[jal39]*rate_eval.He4_Al39__n_P42
       )

    jac[jp42, jal38] = (
       +rho*Y[jhe4]*rate_eval.He4_Al38__P42
       )

    jac[jp42, jal39] = (
       +rho*Y[jhe4]*rate_eval.He4_Al39__n_P42
       )

    jac[jp42, jsi41] = (
       +rho*Y[jp]*rate_eval.p_Si41__P42
       )

    jac[jp42, jsi42] = (
       +rho*Y[jp]*rate_eval.p_Si42__n_P42
       +rate_eval.Si42__P42__weak__wc17
       )

    jac[jp42, jsi43] = (
       +rate_eval.Si43__n_P42__weak__mp17
       )

    jac[jp42, jsi44] = (
       +rate_eval.Si44__n_n_P42__weak__mp17
       )

    jac[jp42, jp41] = (
       +rho*Y[jn]*rate_eval.n_P41__P42
       )

    jac[jp42, jp42] = (
       -rho*Y[jp]*rate_eval.p_P42__n_S42
       -rate_eval.P42__n_n_S40__weak__mp17
       -rho*Y[jp]*rate_eval.p_P42__He4_Si39
       -rho*Y[jhe4]*rate_eval.He4_P42__n_Cl45
       -rho*Y[jn]*rate_eval.n_P42__P43
       -rho*Y[jp]*rate_eval.p_P42__S43
       -rate_eval.P42__n_S41__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_P42__Cl46
       -rate_eval.P42__S42__weak__wc17
       )

    jac[jp42, js45] = (
       +rho*Y[jp]*rate_eval.p_S45__He4_P42
       )

    jac[jp43, jn] = (
       -rho*Y[jp43]*rate_eval.n_P43__P44
       +rho*Y[jp42]*rate_eval.n_P42__P43
       )

    jac[jp43, jp] = (
       -rho*Y[jp43]*rate_eval.p_P43__He4_Si40
       -rho*Y[jp43]*rate_eval.p_P43__n_S43
       -rho*Y[jp43]*rate_eval.p_P43__S44
       +rho*Y[jsi43]*rate_eval.p_Si43__n_P43
       +rho*Y[js46]*rate_eval.p_S46__He4_P43
       +rho*Y[jsi42]*rate_eval.p_Si42__P43
       )

    jac[jp43, jhe4] = (
       -rho*Y[jp43]*rate_eval.He4_P43__n_Cl46
       -rho*Y[jp43]*rate_eval.He4_P43__Cl47
       +rho*Y[jal40]*rate_eval.He4_Al40__n_P43
       +rho*Y[jal39]*rate_eval.He4_Al39__P43
       )

    jac[jp43, jal39] = (
       +rho*Y[jhe4]*rate_eval.He4_Al39__P43
       )

    jac[jp43, jal40] = (
       +rho*Y[jhe4]*rate_eval.He4_Al40__n_P43
       )

    jac[jp43, jsi42] = (
       +rho*Y[jp]*rate_eval.p_Si42__P43
       )

    jac[jp43, jsi43] = (
       +rho*Y[jp]*rate_eval.p_Si43__n_P43
       +rate_eval.Si43__P43__weak__mo03
       )

    jac[jp43, jsi44] = (
       +rate_eval.Si44__n_P43__weak__mp17
       )

    jac[jp43, jp42] = (
       +rho*Y[jn]*rate_eval.n_P42__P43
       )

    jac[jp43, jp43] = (
       -rho*Y[jhe4]*rate_eval.He4_P43__n_Cl46
       -rho*Y[jp]*rate_eval.p_P43__He4_Si40
       -rho*Y[jp]*rate_eval.p_P43__n_S43
       -rate_eval.P43__n_n_S41__weak__mp17
       -rate_eval.P43__n_S42__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_P43__Cl47
       -rate_eval.P43__S43__weak__wc17
       -rho*Y[jn]*rate_eval.n_P43__P44
       -rho*Y[jp]*rate_eval.p_P43__S44
       )

    jac[jp43, js46] = (
       +rho*Y[jp]*rate_eval.p_S46__He4_P43
       )

    jac[jp44, jn] = (
       -rho*Y[jp44]*rate_eval.n_P44__P45
       +rho*Y[jp43]*rate_eval.n_P43__P44
       )

    jac[jp44, jp] = (
       -rho*Y[jp44]*rate_eval.p_P44__He4_Si41
       -rho*Y[jp44]*rate_eval.p_P44__n_S44
       -rho*Y[jp44]*rate_eval.p_P44__S45
       +rho*Y[jsi44]*rate_eval.p_Si44__n_P44
       +rho*Y[js47]*rate_eval.p_S47__He4_P44
       +rho*Y[jsi43]*rate_eval.p_Si43__P44
       )

    jac[jp44, jhe4] = (
       -rho*Y[jp44]*rate_eval.He4_P44__n_Cl47
       -rho*Y[jp44]*rate_eval.He4_P44__Cl48
       +rho*Y[jal40]*rate_eval.He4_Al40__P44
       +rho*Y[jal41]*rate_eval.He4_Al41__n_P44
       )

    jac[jp44, jal40] = (
       +rho*Y[jhe4]*rate_eval.He4_Al40__P44
       )

    jac[jp44, jal41] = (
       +rho*Y[jhe4]*rate_eval.He4_Al41__n_P44
       )

    jac[jp44, jsi43] = (
       +rho*Y[jp]*rate_eval.p_Si43__P44
       )

    jac[jp44, jsi44] = (
       +rho*Y[jp]*rate_eval.p_Si44__n_P44
       )

    jac[jp44, jsi45] = (
       +rate_eval.Si45__n_P44__weak__mp17
       )

    jac[jp44, jp43] = (
       +rho*Y[jn]*rate_eval.n_P43__P44
       )

    jac[jp44, jp44] = (
       -rate_eval.P44__n_n_n_S41__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_P44__n_Cl47
       -rho*Y[jp]*rate_eval.p_P44__He4_Si41
       -rho*Y[jn]*rate_eval.n_P44__P45
       -rate_eval.P44__S44__weak__wc17
       -rate_eval.P44__n_n_S42__weak__mp17
       -rate_eval.P44__n_S43__weak__mp17
       -rho*Y[jp]*rate_eval.p_P44__n_S44
       -rho*Y[jhe4]*rate_eval.He4_P44__Cl48
       -rho*Y[jp]*rate_eval.p_P44__S45
       )

    jac[jp44, js47] = (
       +rho*Y[jp]*rate_eval.p_S47__He4_P44
       )

    jac[jp45, jn] = (
       -rho*Y[jp45]*rate_eval.n_P45__P46
       +rho*Y[jp44]*rate_eval.n_P44__P45
       )

    jac[jp45, jp] = (
       -rho*Y[jp45]*rate_eval.p_P45__S46
       -rho*Y[jp45]*rate_eval.p_P45__n_S45
       -rho*Y[jp45]*rate_eval.p_P45__He4_Si42
       +rho*Y[jsi45]*rate_eval.p_Si45__n_P45
       +rho*Y[js48]*rate_eval.p_S48__He4_P45
       +rho*Y[jsi44]*rate_eval.p_Si44__P45
       )

    jac[jp45, jhe4] = (
       -rho*Y[jp45]*rate_eval.He4_P45__n_Cl48
       -rho*Y[jp45]*rate_eval.He4_P45__Cl49
       +rho*Y[jal42]*rate_eval.He4_Al42__n_P45
       +rho*Y[jal41]*rate_eval.He4_Al41__P45
       )

    jac[jp45, jal41] = (
       +rho*Y[jhe4]*rate_eval.He4_Al41__P45
       )

    jac[jp45, jal42] = (
       +rho*Y[jhe4]*rate_eval.He4_Al42__n_P45
       )

    jac[jp45, jsi44] = (
       +rho*Y[jp]*rate_eval.p_Si44__P45
       )

    jac[jp45, jsi45] = (
       +rho*Y[jp]*rate_eval.p_Si45__n_P45
       +rate_eval.Si45__P45__weak__mo03
       )

    jac[jp45, jp44] = (
       +rho*Y[jn]*rate_eval.n_P44__P45
       )

    jac[jp45, jp45] = (
       -rho*Y[jp]*rate_eval.p_P45__S46
       -rho*Y[jp]*rate_eval.p_P45__n_S45
       -rate_eval.P45__n_n_n_S42__weak__mo03
       -rho*Y[jn]*rate_eval.n_P45__P46
       -rate_eval.P45__n_n_S43__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_P45__n_Cl48
       -rho*Y[jhe4]*rate_eval.He4_P45__Cl49
       -rho*Y[jp]*rate_eval.p_P45__He4_Si42
       -rate_eval.P45__S45__weak__mo03
       -rate_eval.P45__n_S44__weak__mp17
       )

    jac[jp45, js48] = (
       +rho*Y[jp]*rate_eval.p_S48__He4_P45
       )

    jac[jp46, jn] = (
       -rho*Y[jp46]*rate_eval.n_P46__P47
       +rho*Y[jp45]*rate_eval.n_P45__P46
       )

    jac[jp46, jp] = (
       -rho*Y[jp46]*rate_eval.p_P46__S47
       -rho*Y[jp46]*rate_eval.p_P46__He4_Si43
       -rho*Y[jp46]*rate_eval.p_P46__n_S46
       +rho*Y[jsi45]*rate_eval.p_Si45__P46
       +rho*Y[js49]*rate_eval.p_S49__He4_P46
       )

    jac[jp46, jhe4] = (
       -rho*Y[jp46]*rate_eval.He4_P46__n_Cl49
       -rho*Y[jp46]*rate_eval.He4_P46__Cl50
       +rho*Y[jal42]*rate_eval.He4_Al42__P46
       +rho*Y[jal43]*rate_eval.He4_Al43__n_P46
       )

    jac[jp46, jal42] = (
       +rho*Y[jhe4]*rate_eval.He4_Al42__P46
       )

    jac[jp46, jal43] = (
       +rho*Y[jhe4]*rate_eval.He4_Al43__n_P46
       )

    jac[jp46, jsi45] = (
       +rho*Y[jp]*rate_eval.p_Si45__P46
       )

    jac[jp46, jp45] = (
       +rho*Y[jn]*rate_eval.n_P45__P46
       )

    jac[jp46, jp46] = (
       -rho*Y[jp]*rate_eval.p_P46__S47
       -rate_eval.P46__n_n_n_S43__weak__mo03
       -rho*Y[jp]*rate_eval.p_P46__He4_Si43
       -rho*Y[jp]*rate_eval.p_P46__n_S46
       -rho*Y[jhe4]*rate_eval.He4_P46__n_Cl49
       -rho*Y[jhe4]*rate_eval.He4_P46__Cl50
       -rho*Y[jn]*rate_eval.n_P46__P47
       -rate_eval.P46__n_S45__weak__mp17
       -rate_eval.P46__S46__weak__mo03
       -rate_eval.P46__n_n_S44__weak__mp17
       )

    jac[jp46, js49] = (
       +rho*Y[jp]*rate_eval.p_S49__He4_P46
       )

    jac[jp47, jn] = (
       +rho*Y[jp46]*rate_eval.n_P46__P47
       )

    jac[jp47, jp] = (
       -rho*Y[jp47]*rate_eval.p_P47__n_S47
       -rho*Y[jp47]*rate_eval.p_P47__He4_Si44
       -rho*Y[jp47]*rate_eval.p_P47__S48
       )

    jac[jp47, jhe4] = (
       -rho*Y[jp47]*rate_eval.He4_P47__n_Cl50
       -rho*Y[jp47]*rate_eval.He4_P47__Cl51
       +rho*Y[jal43]*rate_eval.He4_Al43__P47
       )

    jac[jp47, jal43] = (
       +rho*Y[jhe4]*rate_eval.He4_Al43__P47
       )

    jac[jp47, jp46] = (
       +rho*Y[jn]*rate_eval.n_P46__P47
       )

    jac[jp47, jp47] = (
       -rho*Y[jhe4]*rate_eval.He4_P47__n_Cl50
       -rho*Y[jp]*rate_eval.p_P47__n_S47
       -rate_eval.P47__n_n_n_S44__weak__mo03
       -rate_eval.P47__n_n_S45__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_P47__Cl51
       -rate_eval.P47__n_S46__weak__mp17
       -rate_eval.P47__S47__weak__mo03
       -rho*Y[jp]*rate_eval.p_P47__He4_Si44
       -rho*Y[jp]*rate_eval.p_P47__S48
       )

    jac[js26, jn] = (
       -rho*Y[js26]*rate_eval.n_S26__He4_Si23
       -rho*Y[js26]*rate_eval.n_S26__p_P26
       -rho*Y[js26]*rate_eval.n_S26__S27
       +rho*Y[jar29]*rate_eval.n_Ar29__He4_S26
       )

    jac[js26, jp] = (
       +rho*Y[jp25]*rate_eval.p_P25__S26
       )

    jac[js26, jhe4] = (
       -rho*Y[js26]*rate_eval.He4_S26__p_Cl29
       -rho*Y[js26]*rate_eval.He4_S26__Ar30
       +rho*Y[jsi22]*rate_eval.He4_Si22__S26
       )

    jac[js26, jsi22] = (
       +rho*Y[jhe4]*rate_eval.He4_Si22__S26
       )

    jac[js26, jp25] = (
       +rho*Y[jp]*rate_eval.p_P25__S26
       )

    jac[js26, js26] = (
       -rho*Y[jhe4]*rate_eval.He4_S26__p_Cl29
       -rho*Y[jn]*rate_eval.n_S26__He4_Si23
       -rho*Y[jn]*rate_eval.n_S26__p_P26
       -rho*Y[jn]*rate_eval.n_S26__S27
       -rho*Y[jhe4]*rate_eval.He4_S26__Ar30
       -rate_eval.S26__P26__weak__bqa_pos_
       )

    jac[js26, jar29] = (
       +rho*Y[jn]*rate_eval.n_Ar29__He4_S26
       )

    jac[js27, jn] = (
       -rho*Y[js27]*rate_eval.n_S27__S28
       -rho*Y[js27]*rate_eval.n_S27__He4_Si24
       -rho*Y[js27]*rate_eval.n_S27__p_P27
       +rho*Y[jar30]*rate_eval.n_Ar30__He4_S27
       +rho*Y[js26]*rate_eval.n_S26__S27
       )

    jac[js27, jp] = (
       -rho*Y[js27]*rate_eval.p_S27__Cl28
       +rho*Y[jp26]*rate_eval.p_P26__S27
       )

    jac[js27, jhe4] = (
       -rho*Y[js27]*rate_eval.He4_S27__p_Cl30
       -rho*Y[js27]*rate_eval.He4_S27__Ar31
       +rho*Y[jp24]*rate_eval.He4_P24__p_S27
       +rho*Y[jsi23]*rate_eval.He4_Si23__S27
       )

    jac[js27, jsi23] = (
       +rho*Y[jhe4]*rate_eval.He4_Si23__S27
       )

    jac[js27, jp24] = (
       +rho*Y[jhe4]*rate_eval.He4_P24__p_S27
       )

    jac[js27, jp26] = (
       +rho*Y[jp]*rate_eval.p_P26__S27
       )

    jac[js27, js26] = (
       +rho*Y[jn]*rate_eval.n_S26__S27
       )

    jac[js27, js27] = (
       -rho*Y[jhe4]*rate_eval.He4_S27__p_Cl30
       -rate_eval.S27__p_Si26__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_S27__Ar31
       -rho*Y[jn]*rate_eval.n_S27__S28
       -rate_eval.S27__P27__weak__wc12
       -rate_eval.S27__p_p_Al25__weak__wc12
       -rho*Y[jn]*rate_eval.n_S27__He4_Si24
       -rho*Y[jp]*rate_eval.p_S27__Cl28
       -rho*Y[jn]*rate_eval.n_S27__p_P27
       )

    jac[js27, jar30] = (
       +rho*Y[jn]*rate_eval.n_Ar30__He4_S27
       )

    jac[js28, jn] = (
       -rho*Y[js28]*rate_eval.n_S28__He4_Si25
       -rho*Y[js28]*rate_eval.n_S28__S29
       -rho*Y[js28]*rate_eval.n_S28__p_P28
       +rho*Y[jar31]*rate_eval.n_Ar31__He4_S28
       +rho*Y[js27]*rate_eval.n_S27__S28
       +rho*Y[jcl28]*rate_eval.n_Cl28__p_S28
       )

    jac[js28, jp] = (
       -rho*Y[js28]*rate_eval.p_S28__Cl29
       +rho*Y[jp27]*rate_eval.p_P27__S28
       )

    jac[js28, jhe4] = (
       -rho*Y[js28]*rate_eval.He4_S28__p_Cl31
       -rho*Y[js28]*rate_eval.He4_S28__Ar32
       +rho*Y[jp25]*rate_eval.He4_P25__p_S28
       +rho*Y[jsi24]*rate_eval.He4_Si24__S28
       )

    jac[js28, jsi24] = (
       +rho*Y[jhe4]*rate_eval.He4_Si24__S28
       )

    jac[js28, jp25] = (
       +rho*Y[jhe4]*rate_eval.He4_P25__p_S28
       )

    jac[js28, jp27] = (
       +rho*Y[jp]*rate_eval.p_P27__S28
       )

    jac[js28, js27] = (
       +rho*Y[jn]*rate_eval.n_S27__S28
       )

    jac[js28, js28] = (
       -rho*Y[jhe4]*rate_eval.He4_S28__p_Cl31
       -rho*Y[jn]*rate_eval.n_S28__He4_Si25
       -rho*Y[jn]*rate_eval.n_S28__S29
       -rho*Y[jp]*rate_eval.p_S28__Cl29
       -rate_eval.S28__p_Si27__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_S28__Ar32
       -rho*Y[jn]*rate_eval.n_S28__p_P28
       -rate_eval.S28__P28__weak__wc12
       )

    jac[js28, jcl28] = (
       +rate_eval.Cl28__S28__weak__bqa_pos_
       +rho*Y[jn]*rate_eval.n_Cl28__p_S28
       )

    jac[js28, jar31] = (
       +rho*Y[jn]*rate_eval.n_Ar31__He4_S28
       )

    jac[js29, jn] = (
       -rho*Y[js29]*rate_eval.n_S29__He4_Si26
       -rho*Y[js29]*rate_eval.n_S29__p_P29
       -rho*Y[js29]*rate_eval.n_S29__S30
       +rho*Y[jar32]*rate_eval.n_Ar32__He4_S29
       +rho*Y[jcl29]*rate_eval.n_Cl29__p_S29
       +rho*Y[js28]*rate_eval.n_S28__S29
       )

    jac[js29, jp] = (
       -rho*Y[js29]*rate_eval.p_S29__Cl30
       +rho*Y[jp28]*rate_eval.p_P28__S29
       )

    jac[js29, jhe4] = (
       -rho*Y[js29]*rate_eval.He4_S29__p_Cl32
       -rho*Y[js29]*rate_eval.He4_S29__Ar33
       +rho*Y[jp26]*rate_eval.He4_P26__p_S29
       +rho*Y[jsi25]*rate_eval.He4_Si25__S29
       )

    jac[js29, jsi25] = (
       +rho*Y[jhe4]*rate_eval.He4_Si25__S29
       )

    jac[js29, jp26] = (
       +rho*Y[jhe4]*rate_eval.He4_P26__p_S29
       )

    jac[js29, jp28] = (
       +rho*Y[jp]*rate_eval.p_P28__S29
       )

    jac[js29, js28] = (
       +rho*Y[jn]*rate_eval.n_S28__S29
       )

    jac[js29, js29] = (
       -rho*Y[jn]*rate_eval.n_S29__He4_Si26
       -rho*Y[jhe4]*rate_eval.He4_S29__p_Cl32
       -rho*Y[jn]*rate_eval.n_S29__p_P29
       -rho*Y[jp]*rate_eval.p_S29__Cl30
       -rho*Y[jhe4]*rate_eval.He4_S29__Ar33
       -rate_eval.S29__p_Si28__weak__wc12
       -rate_eval.S29__P29__weak__wc12
       -rho*Y[jn]*rate_eval.n_S29__S30
       )

    jac[js29, jcl29] = (
       +rho*Y[jn]*rate_eval.n_Cl29__p_S29
       +rate_eval.Cl29__S29__weak__bqa_pos_
       )

    jac[js29, jar32] = (
       +rho*Y[jn]*rate_eval.n_Ar32__He4_S29
       )

    jac[js30, jn] = (
       -rho*Y[js30]*rate_eval.n_S30__He4_Si27
       -rho*Y[js30]*rate_eval.n_S30__p_P30
       -rho*Y[js30]*rate_eval.n_S30__S31
       +rho*Y[jcl30]*rate_eval.n_Cl30__p_S30
       +rho*Y[jar33]*rate_eval.n_Ar33__He4_S30
       +rho*Y[js29]*rate_eval.n_S29__S30
       )

    jac[js30, jp] = (
       -rho*Y[js30]*rate_eval.p_S30__Cl31
       +rho*Y[jp29]*rate_eval.p_P29__S30
       )

    jac[js30, jhe4] = (
       -rho*Y[js30]*rate_eval.He4_S30__Ar34
       -rho*Y[js30]*rate_eval.He4_S30__p_Cl33
       +rho*Y[jp27]*rate_eval.He4_P27__p_S30
       +rho*Y[jsi26]*rate_eval.He4_Si26__S30
       )

    jac[js30, jsi26] = (
       +rho*Y[jhe4]*rate_eval.He4_Si26__S30
       )

    jac[js30, jp27] = (
       +rho*Y[jhe4]*rate_eval.He4_P27__p_S30
       )

    jac[js30, jp29] = (
       +rho*Y[jp]*rate_eval.p_P29__S30
       )

    jac[js30, js29] = (
       +rho*Y[jn]*rate_eval.n_S29__S30
       )

    jac[js30, js30] = (
       -rho*Y[jhe4]*rate_eval.He4_S30__Ar34
       -rho*Y[jhe4]*rate_eval.He4_S30__p_Cl33
       -rho*Y[jn]*rate_eval.n_S30__He4_Si27
       -rho*Y[jn]*rate_eval.n_S30__p_P30
       -rate_eval.S30__P30__weak__wc12
       -rho*Y[jp]*rate_eval.p_S30__Cl31
       -rho*Y[jn]*rate_eval.n_S30__S31
       )

    jac[js30, jcl30] = (
       +rho*Y[jn]*rate_eval.n_Cl30__p_S30
       +rate_eval.Cl30__S30__weak__bqa_pos_
       )

    jac[js30, jar31] = (
       +rate_eval.Ar31__p_S30__weak__wc17
       )

    jac[js30, jar33] = (
       +rho*Y[jn]*rate_eval.n_Ar33__He4_S30
       )

    jac[js31, jn] = (
       -rho*Y[js31]*rate_eval.n_S31__p_P31
       -rho*Y[js31]*rate_eval.n_S31__He4_Si28
       -rho*Y[js31]*rate_eval.n_S31__S32
       +rho*Y[jcl31]*rate_eval.n_Cl31__p_S31
       +rho*Y[js30]*rate_eval.n_S30__S31
       +rho*Y[jar34]*rate_eval.n_Ar34__He4_S31
       )

    jac[js31, jp] = (
       -rho*Y[js31]*rate_eval.p_S31__Cl32
       +rho*Y[jp30]*rate_eval.p_P30__S31
       )

    jac[js31, jhe4] = (
       -rho*Y[js31]*rate_eval.He4_S31__p_Cl34
       -rho*Y[js31]*rate_eval.He4_S31__Ar35
       +rho*Y[jp28]*rate_eval.He4_P28__p_S31
       +rho*Y[jsi27]*rate_eval.He4_Si27__S31
       )

    jac[js31, jc12] = (
       +rho*Y[jne20]*rate_eval.C12_Ne20__n_S31
       )

    jac[js31, jo16] = (
       +5.00000000000000e-01*rho*2*Y[jo16]*rate_eval.O16_O16__n_S31
       )

    jac[js31, jne20] = (
       +rho*Y[jc12]*rate_eval.C12_Ne20__n_S31
       )

    jac[js31, jsi27] = (
       +rho*Y[jhe4]*rate_eval.He4_Si27__S31
       )

    jac[js31, jp28] = (
       +rho*Y[jhe4]*rate_eval.He4_P28__p_S31
       )

    jac[js31, jp30] = (
       +rho*Y[jp]*rate_eval.p_P30__S31
       )

    jac[js31, js30] = (
       +rho*Y[jn]*rate_eval.n_S30__S31
       )

    jac[js31, js31] = (
       -rho*Y[jhe4]*rate_eval.He4_S31__p_Cl34
       -rho*Y[jn]*rate_eval.n_S31__p_P31
       -rho*Y[jp]*rate_eval.p_S31__Cl32
       -rho*Y[jn]*rate_eval.n_S31__He4_Si28
       -rho*Y[jhe4]*rate_eval.He4_S31__Ar35
       -rate_eval.S31__P31__weak__wc12
       -rho*Y[jn]*rate_eval.n_S31__S32
       )

    jac[js31, jcl31] = (
       +rho*Y[jn]*rate_eval.n_Cl31__p_S31
       +rate_eval.Cl31__S31__weak__wc12
       )

    jac[js31, jar32] = (
       +rate_eval.Ar32__p_S31__weak__wc12
       )

    jac[js31, jar34] = (
       +rho*Y[jn]*rate_eval.n_Ar34__He4_S31
       )

    jac[js32, jn] = (
       -rho*Y[js32]*rate_eval.n_S32__S33
       -rho*Y[js32]*rate_eval.n_S32__He4_Si29
       +rho*Y[jar35]*rate_eval.n_Ar35__He4_S32
       +rho*Y[jcl32]*rate_eval.n_Cl32__p_S32
       +rho*Y[js31]*rate_eval.n_S31__S32
       )

    jac[js32, jp] = (
       -rho*Y[js32]*rate_eval.p_S32__Cl33
       +rho*Y[jp32]*rate_eval.p_P32__n_S32
       +rho*Y[jp31]*rate_eval.p_P31__S32
       +rho*Y[jcl35]*rate_eval.p_Cl35__He4_S32
       )

    jac[js32, jhe4] = (
       -rho*Y[js32]*rate_eval.He4_S32__Ar36
       +rho*Y[jsi28]*rate_eval.He4_Si28__S32
       +rho*Y[jp29]*rate_eval.He4_P29__p_S32
       )

    jac[js32, jsi28] = (
       +rho*Y[jhe4]*rate_eval.He4_Si28__S32
       )

    jac[js32, jp29] = (
       +rho*Y[jhe4]*rate_eval.He4_P29__p_S32
       )

    jac[js32, jp31] = (
       +rho*Y[jp]*rate_eval.p_P31__S32
       )

    jac[js32, jp32] = (
       +rho*Y[jp]*rate_eval.p_P32__n_S32
       +rate_eval.P32__S32__weak__wc12
       )

    jac[js32, js31] = (
       +rho*Y[jn]*rate_eval.n_S31__S32
       )

    jac[js32, js32] = (
       -rho*Y[jhe4]*rate_eval.He4_S32__Ar36
       -rho*Y[jp]*rate_eval.p_S32__Cl33
       -rho*Y[jn]*rate_eval.n_S32__S33
       -rho*Y[jn]*rate_eval.n_S32__He4_Si29
       )

    jac[js32, jcl32] = (
       +rate_eval.Cl32__S32__weak__wc12
       +rho*Y[jn]*rate_eval.n_Cl32__p_S32
       )

    jac[js32, jcl35] = (
       +rho*Y[jp]*rate_eval.p_Cl35__He4_S32
       )

    jac[js32, jar33] = (
       +rate_eval.Ar33__p_S32__weak__wc12
       )

    jac[js32, jar35] = (
       +rho*Y[jn]*rate_eval.n_Ar35__He4_S32
       )

    jac[js32, jk36] = (
       +rate_eval.K36__He4_S32__weak__wc12
       )

    jac[js33, jn] = (
       -rho*Y[js33]*rate_eval.n_S33__He4_Si30
       -rho*Y[js33]*rate_eval.n_S33__p_P33
       -rho*Y[js33]*rate_eval.n_S33__S34
       +rho*Y[jar36]*rate_eval.n_Ar36__He4_S33
       +rho*Y[jcl33]*rate_eval.n_Cl33__p_S33
       +rho*Y[js32]*rate_eval.n_S32__S33
       )

    jac[js33, jp] = (
       -rho*Y[js33]*rate_eval.p_S33__Cl34
       +rho*Y[jp32]*rate_eval.p_P32__S33
       +rho*Y[jcl36]*rate_eval.p_Cl36__He4_S33
       )

    jac[js33, jhe4] = (
       -rho*Y[js33]*rate_eval.He4_S33__Ar37
       +rho*Y[jp30]*rate_eval.He4_P30__p_S33
       +rho*Y[jsi29]*rate_eval.He4_Si29__S33
       )

    jac[js33, jsi29] = (
       +rho*Y[jhe4]*rate_eval.He4_Si29__S33
       )

    jac[js33, jp30] = (
       +rho*Y[jhe4]*rate_eval.He4_P30__p_S33
       )

    jac[js33, jp32] = (
       +rho*Y[jp]*rate_eval.p_P32__S33
       )

    jac[js33, jp33] = (
       +rate_eval.P33__S33__weak__wc12
       )

    jac[js33, js32] = (
       +rho*Y[jn]*rate_eval.n_S32__S33
       )

    jac[js33, js33] = (
       -rho*Y[jn]*rate_eval.n_S33__He4_Si30
       -rho*Y[jn]*rate_eval.n_S33__p_P33
       -rho*Y[jn]*rate_eval.n_S33__S34
       -rho*Y[jp]*rate_eval.p_S33__Cl34
       -rho*Y[jhe4]*rate_eval.He4_S33__Ar37
       )

    jac[js33, jcl33] = (
       +rho*Y[jn]*rate_eval.n_Cl33__p_S33
       +rate_eval.Cl33__S33__weak__wc12
       )

    jac[js33, jcl36] = (
       +rho*Y[jp]*rate_eval.p_Cl36__He4_S33
       )

    jac[js33, jar36] = (
       +rho*Y[jn]*rate_eval.n_Ar36__He4_S33
       )

    jac[js34, jn] = (
       -rho*Y[js34]*rate_eval.n_S34__S35
       +rho*Y[jcl34]*rate_eval.n_Cl34__p_S34
       +rho*Y[js33]*rate_eval.n_S33__S34
       )

    jac[js34, jp] = (
       -rho*Y[js34]*rate_eval.p_S34__Cl35
       +rho*Y[jp34]*rate_eval.p_P34__n_S34
       +rho*Y[jp33]*rate_eval.p_P33__S34
       )

    jac[js34, jhe4] = (
       -rho*Y[js34]*rate_eval.He4_S34__p_Cl37
       -rho*Y[js34]*rate_eval.He4_S34__Ar38
       -rho*Y[js34]*rate_eval.He4_S34__n_Ar37
       +rho*Y[jp31]*rate_eval.He4_P31__p_S34
       +rho*Y[jsi31]*rate_eval.He4_Si31__n_S34
       +rho*Y[jsi30]*rate_eval.He4_Si30__S34
       )

    jac[js34, jsi30] = (
       +rho*Y[jhe4]*rate_eval.He4_Si30__S34
       )

    jac[js34, jsi31] = (
       +rho*Y[jhe4]*rate_eval.He4_Si31__n_S34
       )

    jac[js34, jp31] = (
       +rho*Y[jhe4]*rate_eval.He4_P31__p_S34
       )

    jac[js34, jp33] = (
       +rho*Y[jp]*rate_eval.p_P33__S34
       )

    jac[js34, jp34] = (
       +rho*Y[jp]*rate_eval.p_P34__n_S34
       +rate_eval.P34__S34__weak__wc12
       )

    jac[js34, js33] = (
       +rho*Y[jn]*rate_eval.n_S33__S34
       )

    jac[js34, js34] = (
       -rho*Y[jhe4]*rate_eval.He4_S34__p_Cl37
       -rho*Y[jp]*rate_eval.p_S34__Cl35
       -rho*Y[jn]*rate_eval.n_S34__S35
       -rho*Y[jhe4]*rate_eval.He4_S34__Ar38
       -rho*Y[jhe4]*rate_eval.He4_S34__n_Ar37
       )

    jac[js34, jcl34] = (
       +rho*Y[jn]*rate_eval.n_Cl34__p_S34
       +rate_eval.Cl34__S34__weak__wc12
       )

    jac[js35, jn] = (
       -rho*Y[js35]*rate_eval.n_S35__He4_Si32
       -rho*Y[js35]*rate_eval.n_S35__S36
       +rho*Y[jcl35]*rate_eval.n_Cl35__p_S35
       +rho*Y[js34]*rate_eval.n_S34__S35
       )

    jac[js35, jp] = (
       -rho*Y[js35]*rate_eval.p_S35__He4_P32
       -rho*Y[js35]*rate_eval.p_S35__Cl36
       +rho*Y[jcl38]*rate_eval.p_Cl38__He4_S35
       +rho*Y[jp34]*rate_eval.p_P34__S35
       +rho*Y[jp35]*rate_eval.p_P35__n_S35
       )

    jac[js35, jhe4] = (
       -rho*Y[js35]*rate_eval.He4_S35__n_Ar38
       -rho*Y[js35]*rate_eval.He4_S35__Ar39
       +rho*Y[jsi31]*rate_eval.He4_Si31__S35
       )

    jac[js35, jsi31] = (
       +rho*Y[jhe4]*rate_eval.He4_Si31__S35
       )

    jac[js35, jp34] = (
       +rho*Y[jp]*rate_eval.p_P34__S35
       )

    jac[js35, jp35] = (
       +rho*Y[jp]*rate_eval.p_P35__n_S35
       +rate_eval.P35__S35__weak__wc12
       )

    jac[js35, js34] = (
       +rho*Y[jn]*rate_eval.n_S34__S35
       )

    jac[js35, js35] = (
       -rho*Y[jhe4]*rate_eval.He4_S35__n_Ar38
       -rho*Y[jp]*rate_eval.p_S35__He4_P32
       -rho*Y[jn]*rate_eval.n_S35__He4_Si32
       -rho*Y[jp]*rate_eval.p_S35__Cl36
       -rho*Y[jn]*rate_eval.n_S35__S36
       -rate_eval.S35__Cl35__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_S35__Ar39
       )

    jac[js35, jcl35] = (
       +rho*Y[jn]*rate_eval.n_Cl35__p_S35
       )

    jac[js35, jcl38] = (
       +rho*Y[jp]*rate_eval.p_Cl38__He4_S35
       )

    jac[js36, jn] = (
       -rho*Y[js36]*rate_eval.n_S36__S37
       +rho*Y[jcl36]*rate_eval.n_Cl36__p_S36
       +rho*Y[jar39]*rate_eval.n_Ar39__He4_S36
       +rho*Y[js35]*rate_eval.n_S35__S36
       )

    jac[js36, jp] = (
       -rho*Y[js36]*rate_eval.p_S36__He4_P33
       -rho*Y[js36]*rate_eval.p_S36__Cl37
       +rho*Y[jp36]*rate_eval.p_P36__n_S36
       +rho*Y[jcl39]*rate_eval.p_Cl39__He4_S36
       +rho*Y[jp35]*rate_eval.p_P35__S36
       )

    jac[js36, jhe4] = (
       -rho*Y[js36]*rate_eval.He4_S36__Ar40
       +rho*Y[jsi33]*rate_eval.He4_Si33__n_S36
       +rho*Y[jsi32]*rate_eval.He4_Si32__S36
       )

    jac[js36, jsi32] = (
       +rho*Y[jhe4]*rate_eval.He4_Si32__S36
       )

    jac[js36, jsi33] = (
       +rho*Y[jhe4]*rate_eval.He4_Si33__n_S36
       )

    jac[js36, jp35] = (
       +rho*Y[jp]*rate_eval.p_P35__S36
       )

    jac[js36, jp36] = (
       +rho*Y[jp]*rate_eval.p_P36__n_S36
       +rate_eval.P36__S36__weak__wc12
       )

    jac[js36, js35] = (
       +rho*Y[jn]*rate_eval.n_S35__S36
       )

    jac[js36, js36] = (
       -rho*Y[jp]*rate_eval.p_S36__He4_P33
       -rho*Y[jhe4]*rate_eval.He4_S36__Ar40
       -rho*Y[jp]*rate_eval.p_S36__Cl37
       -rho*Y[jn]*rate_eval.n_S36__S37
       )

    jac[js36, jcl36] = (
       +rho*Y[jn]*rate_eval.n_Cl36__p_S36
       +rate_eval.Cl36__S36__weak__wc12
       )

    jac[js36, jcl39] = (
       +rho*Y[jp]*rate_eval.p_Cl39__He4_S36
       )

    jac[js36, jar39] = (
       +rho*Y[jn]*rate_eval.n_Ar39__He4_S36
       )

    jac[js37, jn] = (
       -rho*Y[js37]*rate_eval.n_S37__S38
       +rho*Y[js36]*rate_eval.n_S36__S37
       )

    jac[js37, jp] = (
       -rho*Y[js37]*rate_eval.p_S37__Cl38
       -rho*Y[js37]*rate_eval.p_S37__n_Cl37
       -rho*Y[js37]*rate_eval.p_S37__He4_P34
       +rho*Y[jcl40]*rate_eval.p_Cl40__He4_S37
       +rho*Y[jp37]*rate_eval.p_P37__n_S37
       +rho*Y[jp36]*rate_eval.p_P36__S37
       )

    jac[js37, jhe4] = (
       -rho*Y[js37]*rate_eval.He4_S37__n_Ar40
       -rho*Y[js37]*rate_eval.He4_S37__Ar41
       +rho*Y[jsi33]*rate_eval.He4_Si33__S37
       +rho*Y[jsi34]*rate_eval.He4_Si34__n_S37
       )

    jac[js37, jsi33] = (
       +rho*Y[jhe4]*rate_eval.He4_Si33__S37
       )

    jac[js37, jsi34] = (
       +rho*Y[jhe4]*rate_eval.He4_Si34__n_S37
       )

    jac[js37, jp36] = (
       +rho*Y[jp]*rate_eval.p_P36__S37
       )

    jac[js37, jp37] = (
       +rate_eval.P37__S37__weak__wc12
       +rho*Y[jp]*rate_eval.p_P37__n_S37
       )

    jac[js37, jp38] = (
       +rate_eval.P38__n_S37__weak__wc12
       )

    jac[js37, js36] = (
       +rho*Y[jn]*rate_eval.n_S36__S37
       )

    jac[js37, js37] = (
       -rho*Y[jp]*rate_eval.p_S37__Cl38
       -rho*Y[jhe4]*rate_eval.He4_S37__n_Ar40
       -rho*Y[jp]*rate_eval.p_S37__n_Cl37
       -rate_eval.S37__Cl37__weak__wc12
       -rho*Y[jp]*rate_eval.p_S37__He4_P34
       -rho*Y[jn]*rate_eval.n_S37__S38
       -rho*Y[jhe4]*rate_eval.He4_S37__Ar41
       )

    jac[js37, jcl40] = (
       +rho*Y[jp]*rate_eval.p_Cl40__He4_S37
       )

    jac[js38, jn] = (
       -rho*Y[js38]*rate_eval.n_S38__S39
       +rho*Y[js37]*rate_eval.n_S37__S38
       )

    jac[js38, jp] = (
       -rho*Y[js38]*rate_eval.p_S38__He4_P35
       -rho*Y[js38]*rate_eval.p_S38__n_Cl38
       -rho*Y[js38]*rate_eval.p_S38__Cl39
       +rho*Y[jcl41]*rate_eval.p_Cl41__He4_S38
       +rho*Y[jp38]*rate_eval.p_P38__n_S38
       +rho*Y[jp37]*rate_eval.p_P37__S38
       )

    jac[js38, jhe4] = (
       -rho*Y[js38]*rate_eval.He4_S38__n_Ar41
       -rho*Y[js38]*rate_eval.He4_S38__Ar42
       +rho*Y[jsi35]*rate_eval.He4_Si35__n_S38
       +rho*Y[jsi34]*rate_eval.He4_Si34__S38
       )

    jac[js38, jsi34] = (
       +rho*Y[jhe4]*rate_eval.He4_Si34__S38
       )

    jac[js38, jsi35] = (
       +rho*Y[jhe4]*rate_eval.He4_Si35__n_S38
       )

    jac[js38, jp37] = (
       +rho*Y[jp]*rate_eval.p_P37__S38
       )

    jac[js38, jp38] = (
       +rho*Y[jp]*rate_eval.p_P38__n_S38
       +rate_eval.P38__S38__weak__wc12
       )

    jac[js38, jp39] = (
       +rate_eval.P39__n_S38__weak__wc12
       )

    jac[js38, js37] = (
       +rho*Y[jn]*rate_eval.n_S37__S38
       )

    jac[js38, js38] = (
       -rho*Y[jhe4]*rate_eval.He4_S38__n_Ar41
       -rho*Y[jp]*rate_eval.p_S38__He4_P35
       -rho*Y[jp]*rate_eval.p_S38__n_Cl38
       -rho*Y[jp]*rate_eval.p_S38__Cl39
       -rho*Y[jn]*rate_eval.n_S38__S39
       -rho*Y[jhe4]*rate_eval.He4_S38__Ar42
       -rate_eval.S38__Cl38__weak__wc12
       )

    jac[js38, jcl41] = (
       +rho*Y[jp]*rate_eval.p_Cl41__He4_S38
       )

    jac[js39, jn] = (
       -rho*Y[js39]*rate_eval.n_S39__S40
       +rho*Y[js38]*rate_eval.n_S38__S39
       )

    jac[js39, jp] = (
       -rho*Y[js39]*rate_eval.p_S39__He4_P36
       -rho*Y[js39]*rate_eval.p_S39__Cl40
       -rho*Y[js39]*rate_eval.p_S39__n_Cl39
       +rho*Y[jcl42]*rate_eval.p_Cl42__He4_S39
       +rho*Y[jp38]*rate_eval.p_P38__S39
       +rho*Y[jp39]*rate_eval.p_P39__n_S39
       )

    jac[js39, jhe4] = (
       -rho*Y[js39]*rate_eval.He4_S39__n_Ar42
       -rho*Y[js39]*rate_eval.He4_S39__Ar43
       +rho*Y[jsi36]*rate_eval.He4_Si36__n_S39
       +rho*Y[jsi35]*rate_eval.He4_Si35__S39
       )

    jac[js39, jsi35] = (
       +rho*Y[jhe4]*rate_eval.He4_Si35__S39
       )

    jac[js39, jsi36] = (
       +rho*Y[jhe4]*rate_eval.He4_Si36__n_S39
       )

    jac[js39, jp38] = (
       +rho*Y[jp]*rate_eval.p_P38__S39
       )

    jac[js39, jp39] = (
       +rho*Y[jp]*rate_eval.p_P39__n_S39
       +rate_eval.P39__S39__weak__wc12
       )

    jac[js39, jp40] = (
       +rate_eval.P40__n_S39__weak__wc12
       )

    jac[js39, js38] = (
       +rho*Y[jn]*rate_eval.n_S38__S39
       )

    jac[js39, js39] = (
       -rho*Y[jp]*rate_eval.p_S39__He4_P36
       -rho*Y[jhe4]*rate_eval.He4_S39__n_Ar42
       -rho*Y[jhe4]*rate_eval.He4_S39__Ar43
       -rho*Y[jp]*rate_eval.p_S39__Cl40
       -rho*Y[jp]*rate_eval.p_S39__n_Cl39
       -rate_eval.S39__Cl39__weak__wc12
       -rho*Y[jn]*rate_eval.n_S39__S40
       )

    jac[js39, jcl42] = (
       +rho*Y[jp]*rate_eval.p_Cl42__He4_S39
       )

    jac[js40, jn] = (
       -rho*Y[js40]*rate_eval.n_S40__S41
       +rho*Y[js39]*rate_eval.n_S39__S40
       )

    jac[js40, jp] = (
       -rho*Y[js40]*rate_eval.p_S40__n_Cl40
       -rho*Y[js40]*rate_eval.p_S40__Cl41
       -rho*Y[js40]*rate_eval.p_S40__He4_P37
       +rho*Y[jcl43]*rate_eval.p_Cl43__He4_S40
       +rho*Y[jp40]*rate_eval.p_P40__n_S40
       +rho*Y[jp39]*rate_eval.p_P39__S40
       )

    jac[js40, jhe4] = (
       -rho*Y[js40]*rate_eval.He4_S40__n_Ar43
       -rho*Y[js40]*rate_eval.He4_S40__Ar44
       +rho*Y[jsi37]*rate_eval.He4_Si37__n_S40
       +rho*Y[jsi36]*rate_eval.He4_Si36__S40
       )

    jac[js40, jsi36] = (
       +rho*Y[jhe4]*rate_eval.He4_Si36__S40
       )

    jac[js40, jsi37] = (
       +rho*Y[jhe4]*rate_eval.He4_Si37__n_S40
       )

    jac[js40, jp39] = (
       +rho*Y[jp]*rate_eval.p_P39__S40
       )

    jac[js40, jp40] = (
       +rate_eval.P40__S40__weak__wc12
       +rho*Y[jp]*rate_eval.p_P40__n_S40
       )

    jac[js40, jp41] = (
       +rate_eval.P41__n_S40__weak__wc12
       )

    jac[js40, jp42] = (
       +rate_eval.P42__n_n_S40__weak__mp17
       )

    jac[js40, js39] = (
       +rho*Y[jn]*rate_eval.n_S39__S40
       )

    jac[js40, js40] = (
       -rho*Y[jp]*rate_eval.p_S40__n_Cl40
       -rho*Y[jp]*rate_eval.p_S40__Cl41
       -rho*Y[jn]*rate_eval.n_S40__S41
       -rho*Y[jhe4]*rate_eval.He4_S40__n_Ar43
       -rho*Y[jp]*rate_eval.p_S40__He4_P37
       -rate_eval.S40__Cl40__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_S40__Ar44
       )

    jac[js40, jcl43] = (
       +rho*Y[jp]*rate_eval.p_Cl43__He4_S40
       )

    jac[js41, jn] = (
       -rho*Y[js41]*rate_eval.n_S41__S42
       +rho*Y[js40]*rate_eval.n_S40__S41
       )

    jac[js41, jp] = (
       -rho*Y[js41]*rate_eval.p_S41__He4_P38
       -rho*Y[js41]*rate_eval.p_S41__Cl42
       -rho*Y[js41]*rate_eval.p_S41__n_Cl41
       +rho*Y[jp40]*rate_eval.p_P40__S41
       +rho*Y[jp41]*rate_eval.p_P41__n_S41
       +rho*Y[jcl44]*rate_eval.p_Cl44__He4_S41
       )

    jac[js41, jhe4] = (
       -rho*Y[js41]*rate_eval.He4_S41__n_Ar44
       -rho*Y[js41]*rate_eval.He4_S41__Ar45
       +rho*Y[jsi38]*rate_eval.He4_Si38__n_S41
       +rho*Y[jsi37]*rate_eval.He4_Si37__S41
       )

    jac[js41, jsi37] = (
       +rho*Y[jhe4]*rate_eval.He4_Si37__S41
       )

    jac[js41, jsi38] = (
       +rho*Y[jhe4]*rate_eval.He4_Si38__n_S41
       )

    jac[js41, jp40] = (
       +rho*Y[jp]*rate_eval.p_P40__S41
       )

    jac[js41, jp41] = (
       +rho*Y[jp]*rate_eval.p_P41__n_S41
       +rate_eval.P41__S41__weak__wc12
       )

    jac[js41, jp42] = (
       +rate_eval.P42__n_S41__weak__wc12
       )

    jac[js41, jp43] = (
       +rate_eval.P43__n_n_S41__weak__mp17
       )

    jac[js41, jp44] = (
       +rate_eval.P44__n_n_n_S41__weak__mo03
       )

    jac[js41, js40] = (
       +rho*Y[jn]*rate_eval.n_S40__S41
       )

    jac[js41, js41] = (
       -rho*Y[jhe4]*rate_eval.He4_S41__n_Ar44
       -rho*Y[jp]*rate_eval.p_S41__He4_P38
       -rho*Y[jhe4]*rate_eval.He4_S41__Ar45
       -rho*Y[jp]*rate_eval.p_S41__Cl42
       -rho*Y[jn]*rate_eval.n_S41__S42
       -rho*Y[jp]*rate_eval.p_S41__n_Cl41
       -rate_eval.S41__Cl41__weak__wc12
       )

    jac[js41, jcl44] = (
       +rho*Y[jp]*rate_eval.p_Cl44__He4_S41
       )

    jac[js42, jn] = (
       -rho*Y[js42]*rate_eval.n_S42__S43
       +rho*Y[js41]*rate_eval.n_S41__S42
       )

    jac[js42, jp] = (
       -rho*Y[js42]*rate_eval.p_S42__Cl43
       -rho*Y[js42]*rate_eval.p_S42__n_Cl42
       -rho*Y[js42]*rate_eval.p_S42__He4_P39
       +rho*Y[jp42]*rate_eval.p_P42__n_S42
       +rho*Y[jcl45]*rate_eval.p_Cl45__He4_S42
       +rho*Y[jp41]*rate_eval.p_P41__S42
       )

    jac[js42, jhe4] = (
       -rho*Y[js42]*rate_eval.He4_S42__n_Ar45
       -rho*Y[js42]*rate_eval.He4_S42__Ar46
       +rho*Y[jsi39]*rate_eval.He4_Si39__n_S42
       +rho*Y[jsi38]*rate_eval.He4_Si38__S42
       )

    jac[js42, jsi38] = (
       +rho*Y[jhe4]*rate_eval.He4_Si38__S42
       )

    jac[js42, jsi39] = (
       +rho*Y[jhe4]*rate_eval.He4_Si39__n_S42
       )

    jac[js42, jp41] = (
       +rho*Y[jp]*rate_eval.p_P41__S42
       )

    jac[js42, jp42] = (
       +rho*Y[jp]*rate_eval.p_P42__n_S42
       +rate_eval.P42__S42__weak__wc17
       )

    jac[js42, jp43] = (
       +rate_eval.P43__n_S42__weak__wc12
       )

    jac[js42, jp44] = (
       +rate_eval.P44__n_n_S42__weak__mp17
       )

    jac[js42, jp45] = (
       +rate_eval.P45__n_n_n_S42__weak__mo03
       )

    jac[js42, js41] = (
       +rho*Y[jn]*rate_eval.n_S41__S42
       )

    jac[js42, js42] = (
       -rho*Y[jp]*rate_eval.p_S42__Cl43
       -rho*Y[jhe4]*rate_eval.He4_S42__n_Ar45
       -rho*Y[jp]*rate_eval.p_S42__n_Cl42
       -rho*Y[jhe4]*rate_eval.He4_S42__Ar46
       -rho*Y[jn]*rate_eval.n_S42__S43
       -rho*Y[jp]*rate_eval.p_S42__He4_P39
       -rate_eval.S42__Cl42__weak__wc12
       )

    jac[js42, jcl45] = (
       +rho*Y[jp]*rate_eval.p_Cl45__He4_S42
       )

    jac[js43, jn] = (
       -rho*Y[js43]*rate_eval.n_S43__S44
       +rho*Y[js42]*rate_eval.n_S42__S43
       )

    jac[js43, jp] = (
       -rho*Y[js43]*rate_eval.p_S43__He4_P40
       -rho*Y[js43]*rate_eval.p_S43__n_Cl43
       -rho*Y[js43]*rate_eval.p_S43__Cl44
       +rho*Y[jp43]*rate_eval.p_P43__n_S43
       +rho*Y[jcl46]*rate_eval.p_Cl46__He4_S43
       +rho*Y[jp42]*rate_eval.p_P42__S43
       )

    jac[js43, jhe4] = (
       -rho*Y[js43]*rate_eval.He4_S43__n_Ar46
       -rho*Y[js43]*rate_eval.He4_S43__Ar47
       +rho*Y[jsi40]*rate_eval.He4_Si40__n_S43
       +rho*Y[jsi39]*rate_eval.He4_Si39__S43
       )

    jac[js43, jsi39] = (
       +rho*Y[jhe4]*rate_eval.He4_Si39__S43
       )

    jac[js43, jsi40] = (
       +rho*Y[jhe4]*rate_eval.He4_Si40__n_S43
       )

    jac[js43, jp42] = (
       +rho*Y[jp]*rate_eval.p_P42__S43
       )

    jac[js43, jp43] = (
       +rho*Y[jp]*rate_eval.p_P43__n_S43
       +rate_eval.P43__S43__weak__wc17
       )

    jac[js43, jp44] = (
       +rate_eval.P44__n_S43__weak__mp17
       )

    jac[js43, jp45] = (
       +rate_eval.P45__n_n_S43__weak__mp17
       )

    jac[js43, jp46] = (
       +rate_eval.P46__n_n_n_S43__weak__mo03
       )

    jac[js43, js42] = (
       +rho*Y[jn]*rate_eval.n_S42__S43
       )

    jac[js43, js43] = (
       -rho*Y[jhe4]*rate_eval.He4_S43__n_Ar46
       -rho*Y[jp]*rate_eval.p_S43__He4_P40
       -rho*Y[jhe4]*rate_eval.He4_S43__Ar47
       -rho*Y[jp]*rate_eval.p_S43__n_Cl43
       -rate_eval.S43__Cl43__weak__wc12
       -rho*Y[jn]*rate_eval.n_S43__S44
       -rho*Y[jp]*rate_eval.p_S43__Cl44
       -rate_eval.S43__n_Cl42__weak__wc12
       )

    jac[js43, jcl46] = (
       +rho*Y[jp]*rate_eval.p_Cl46__He4_S43
       )

    jac[js44, jn] = (
       -rho*Y[js44]*rate_eval.n_S44__S45
       +rho*Y[js43]*rate_eval.n_S43__S44
       )

    jac[js44, jp] = (
       -rho*Y[js44]*rate_eval.p_S44__Cl45
       -rho*Y[js44]*rate_eval.p_S44__n_Cl44
       +rho*Y[jp44]*rate_eval.p_P44__n_S44
       +rho*Y[jp43]*rate_eval.p_P43__S44
       +rho*Y[jcl47]*rate_eval.p_Cl47__He4_S44
       )

    jac[js44, jhe4] = (
       -rho*Y[js44]*rate_eval.He4_S44__Ar48
       -rho*Y[js44]*rate_eval.He4_S44__n_Ar47
       +rho*Y[jp41]*rate_eval.He4_P41__p_S44
       +rho*Y[jsi40]*rate_eval.He4_Si40__S44
       +rho*Y[jsi41]*rate_eval.He4_Si41__n_S44
       )

    jac[js44, jsi40] = (
       +rho*Y[jhe4]*rate_eval.He4_Si40__S44
       )

    jac[js44, jsi41] = (
       +rho*Y[jhe4]*rate_eval.He4_Si41__n_S44
       )

    jac[js44, jp41] = (
       +rho*Y[jhe4]*rate_eval.He4_P41__p_S44
       )

    jac[js44, jp43] = (
       +rho*Y[jp]*rate_eval.p_P43__S44
       )

    jac[js44, jp44] = (
       +rate_eval.P44__S44__weak__wc17
       +rho*Y[jp]*rate_eval.p_P44__n_S44
       )

    jac[js44, jp45] = (
       +rate_eval.P45__n_S44__weak__mp17
       )

    jac[js44, jp46] = (
       +rate_eval.P46__n_n_S44__weak__mp17
       )

    jac[js44, jp47] = (
       +rate_eval.P47__n_n_n_S44__weak__mo03
       )

    jac[js44, js43] = (
       +rho*Y[jn]*rate_eval.n_S43__S44
       )

    jac[js44, js44] = (
       -rate_eval.S44__n_Cl43__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_S44__Ar48
       -rho*Y[jp]*rate_eval.p_S44__Cl45
       -rho*Y[jn]*rate_eval.n_S44__S45
       -rho*Y[jp]*rate_eval.p_S44__n_Cl44
       -rate_eval.S44__Cl44__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_S44__n_Ar47
       )

    jac[js44, jcl47] = (
       +rho*Y[jp]*rate_eval.p_Cl47__He4_S44
       )

    jac[js45, jn] = (
       -rho*Y[js45]*rate_eval.n_S45__S46
       +rho*Y[js44]*rate_eval.n_S44__S45
       )

    jac[js45, jp] = (
       -rho*Y[js45]*rate_eval.p_S45__He4_P42
       -rho*Y[js45]*rate_eval.p_S45__n_Cl45
       -rho*Y[js45]*rate_eval.p_S45__Cl46
       +rho*Y[jcl48]*rate_eval.p_Cl48__He4_S45
       +rho*Y[jp45]*rate_eval.p_P45__n_S45
       +rho*Y[jp44]*rate_eval.p_P44__S45
       )

    jac[js45, jhe4] = (
       -rho*Y[js45]*rate_eval.He4_S45__n_Ar48
       -rho*Y[js45]*rate_eval.He4_S45__Ar49
       +rho*Y[jsi42]*rate_eval.He4_Si42__n_S45
       +rho*Y[jsi41]*rate_eval.He4_Si41__S45
       )

    jac[js45, jsi41] = (
       +rho*Y[jhe4]*rate_eval.He4_Si41__S45
       )

    jac[js45, jsi42] = (
       +rho*Y[jhe4]*rate_eval.He4_Si42__n_S45
       )

    jac[js45, jp44] = (
       +rho*Y[jp]*rate_eval.p_P44__S45
       )

    jac[js45, jp45] = (
       +rho*Y[jp]*rate_eval.p_P45__n_S45
       +rate_eval.P45__S45__weak__mo03
       )

    jac[js45, jp46] = (
       +rate_eval.P46__n_S45__weak__mp17
       )

    jac[js45, jp47] = (
       +rate_eval.P47__n_n_S45__weak__mp17
       )

    jac[js45, js44] = (
       +rho*Y[jn]*rate_eval.n_S44__S45
       )

    jac[js45, js45] = (
       -rho*Y[jhe4]*rate_eval.He4_S45__n_Ar48
       -rate_eval.S45__n_Cl44__weak__wc12
       -rho*Y[jp]*rate_eval.p_S45__He4_P42
       -rho*Y[jn]*rate_eval.n_S45__S46
       -rate_eval.S45__n_n_Cl43__weak__mp17
       -rho*Y[jp]*rate_eval.p_S45__n_Cl45
       -rho*Y[jhe4]*rate_eval.He4_S45__Ar49
       -rate_eval.S45__Cl45__weak__wc12
       -rho*Y[jp]*rate_eval.p_S45__Cl46
       )

    jac[js45, jcl48] = (
       +rho*Y[jp]*rate_eval.p_Cl48__He4_S45
       )

    jac[js46, jn] = (
       -rho*Y[js46]*rate_eval.n_S46__S47
       +rho*Y[js45]*rate_eval.n_S45__S46
       )

    jac[js46, jp] = (
       -rho*Y[js46]*rate_eval.p_S46__n_Cl46
       -rho*Y[js46]*rate_eval.p_S46__Cl47
       -rho*Y[js46]*rate_eval.p_S46__He4_P43
       +rho*Y[jp45]*rate_eval.p_P45__S46
       +rho*Y[jp46]*rate_eval.p_P46__n_S46
       +rho*Y[jcl49]*rate_eval.p_Cl49__He4_S46
       )

    jac[js46, jhe4] = (
       -rho*Y[js46]*rate_eval.He4_S46__n_Ar49
       -rho*Y[js46]*rate_eval.He4_S46__Ar50
       +rho*Y[jsi43]*rate_eval.He4_Si43__n_S46
       +rho*Y[jsi42]*rate_eval.He4_Si42__S46
       )

    jac[js46, jsi42] = (
       +rho*Y[jhe4]*rate_eval.He4_Si42__S46
       )

    jac[js46, jsi43] = (
       +rho*Y[jhe4]*rate_eval.He4_Si43__n_S46
       )

    jac[js46, jp45] = (
       +rho*Y[jp]*rate_eval.p_P45__S46
       )

    jac[js46, jp46] = (
       +rho*Y[jp]*rate_eval.p_P46__n_S46
       +rate_eval.P46__S46__weak__mo03
       )

    jac[js46, jp47] = (
       +rate_eval.P47__n_S46__weak__mp17
       )

    jac[js46, js45] = (
       +rho*Y[jn]*rate_eval.n_S45__S46
       )

    jac[js46, js46] = (
       -rho*Y[jp]*rate_eval.p_S46__n_Cl46
       -rho*Y[jp]*rate_eval.p_S46__Cl47
       -rho*Y[jhe4]*rate_eval.He4_S46__n_Ar49
       -rho*Y[jp]*rate_eval.p_S46__He4_P43
       -rho*Y[jhe4]*rate_eval.He4_S46__Ar50
       -rho*Y[jn]*rate_eval.n_S46__S47
       -rate_eval.S46__Cl46__weak__wc17
       -rate_eval.S46__n_Cl45__weak__mp17
       )

    jac[js46, jcl49] = (
       +rho*Y[jp]*rate_eval.p_Cl49__He4_S46
       )

    jac[js47, jn] = (
       -rho*Y[js47]*rate_eval.n_S47__S48
       +rho*Y[js46]*rate_eval.n_S46__S47
       )

    jac[js47, jp] = (
       -rho*Y[js47]*rate_eval.p_S47__Cl48
       -rho*Y[js47]*rate_eval.p_S47__n_Cl47
       -rho*Y[js47]*rate_eval.p_S47__He4_P44
       +rho*Y[jp46]*rate_eval.p_P46__S47
       +rho*Y[jcl50]*rate_eval.p_Cl50__He4_S47
       +rho*Y[jp47]*rate_eval.p_P47__n_S47
       )

    jac[js47, jhe4] = (
       -rho*Y[js47]*rate_eval.He4_S47__Ar51
       -rho*Y[js47]*rate_eval.He4_S47__n_Ar50
       +rho*Y[jsi44]*rate_eval.He4_Si44__n_S47
       +rho*Y[jsi43]*rate_eval.He4_Si43__S47
       )

    jac[js47, jsi43] = (
       +rho*Y[jhe4]*rate_eval.He4_Si43__S47
       )

    jac[js47, jsi44] = (
       +rho*Y[jhe4]*rate_eval.He4_Si44__n_S47
       )

    jac[js47, jp46] = (
       +rho*Y[jp]*rate_eval.p_P46__S47
       )

    jac[js47, jp47] = (
       +rho*Y[jp]*rate_eval.p_P47__n_S47
       +rate_eval.P47__S47__weak__mo03
       )

    jac[js47, js46] = (
       +rho*Y[jn]*rate_eval.n_S46__S47
       )

    jac[js47, js47] = (
       -rate_eval.S47__n_n_n_Cl44__weak__mo03
       -rho*Y[jp]*rate_eval.p_S47__Cl48
       -rho*Y[jp]*rate_eval.p_S47__n_Cl47
       -rho*Y[jp]*rate_eval.p_S47__He4_P44
       -rate_eval.S47__Cl47__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_S47__Ar51
       -rho*Y[jn]*rate_eval.n_S47__S48
       -rate_eval.S47__n_n_Cl45__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_S47__n_Ar50
       -rate_eval.S47__n_Cl46__weak__mp17
       )

    jac[js47, jcl50] = (
       +rho*Y[jp]*rate_eval.p_Cl50__He4_S47
       )

    jac[js48, jn] = (
       -rho*Y[js48]*rate_eval.n_S48__S49
       +rho*Y[js47]*rate_eval.n_S47__S48
       )

    jac[js48, jp] = (
       -rho*Y[js48]*rate_eval.p_S48__n_Cl48
       -rho*Y[js48]*rate_eval.p_S48__He4_P45
       -rho*Y[js48]*rate_eval.p_S48__Cl49
       +rho*Y[jcl51]*rate_eval.p_Cl51__He4_S48
       +rho*Y[jp47]*rate_eval.p_P47__S48
       )

    jac[js48, jhe4] = (
       -rho*Y[js48]*rate_eval.He4_S48__n_Ar51
       -rho*Y[js48]*rate_eval.He4_S48__Ar52
       +rho*Y[jsi44]*rate_eval.He4_Si44__S48
       +rho*Y[jsi45]*rate_eval.He4_Si45__n_S48
       )

    jac[js48, jsi44] = (
       +rho*Y[jhe4]*rate_eval.He4_Si44__S48
       )

    jac[js48, jsi45] = (
       +rho*Y[jhe4]*rate_eval.He4_Si45__n_S48
       )

    jac[js48, jp47] = (
       +rho*Y[jp]*rate_eval.p_P47__S48
       )

    jac[js48, js47] = (
       +rho*Y[jn]*rate_eval.n_S47__S48
       )

    jac[js48, js48] = (
       -rate_eval.S48__n_n_n_Cl45__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_S48__n_Ar51
       -rho*Y[jp]*rate_eval.p_S48__n_Cl48
       -rho*Y[jhe4]*rate_eval.He4_S48__Ar52
       -rho*Y[jp]*rate_eval.p_S48__He4_P45
       -rate_eval.S48__n_n_Cl46__weak__mp17
       -rho*Y[jn]*rate_eval.n_S48__S49
       -rate_eval.S48__Cl48__weak__mo03
       -rate_eval.S48__n_Cl47__weak__mp17
       -rho*Y[jp]*rate_eval.p_S48__Cl49
       )

    jac[js48, jcl51] = (
       +rho*Y[jp]*rate_eval.p_Cl51__He4_S48
       )

    jac[js49, jn] = (
       +rho*Y[js48]*rate_eval.n_S48__S49
       )

    jac[js49, jp] = (
       -rho*Y[js49]*rate_eval.p_S49__n_Cl49
       -rho*Y[js49]*rate_eval.p_S49__Cl50
       -rho*Y[js49]*rate_eval.p_S49__He4_P46
       +rho*Y[jcl52]*rate_eval.p_Cl52__He4_S49
       )

    jac[js49, jhe4] = (
       -rho*Y[js49]*rate_eval.He4_S49__Ar53
       -rho*Y[js49]*rate_eval.He4_S49__n_Ar52
       +rho*Y[jsi45]*rate_eval.He4_Si45__S49
       )

    jac[js49, jsi45] = (
       +rho*Y[jhe4]*rate_eval.He4_Si45__S49
       )

    jac[js49, js48] = (
       +rho*Y[jn]*rate_eval.n_S48__S49
       )

    jac[js49, js49] = (
       -rate_eval.S49__n_n_n_Cl46__weak__mo03
       -rho*Y[jp]*rate_eval.p_S49__n_Cl49
       -rho*Y[jp]*rate_eval.p_S49__Cl50
       -rho*Y[jhe4]*rate_eval.He4_S49__Ar53
       -rate_eval.S49__n_Cl48__weak__mp17
       -rate_eval.S49__Cl49__weak__mo03
       -rho*Y[jp]*rate_eval.p_S49__He4_P46
       -rho*Y[jhe4]*rate_eval.He4_S49__n_Ar52
       -rate_eval.S49__n_n_Cl47__weak__mp17
       )

    jac[js49, jcl52] = (
       +rho*Y[jp]*rate_eval.p_Cl52__He4_S49
       )

    jac[jcl28, jn] = (
       -rho*Y[jcl28]*rate_eval.n_Cl28__He4_P25
       -rho*Y[jcl28]*rate_eval.n_Cl28__Cl29
       -rho*Y[jcl28]*rate_eval.n_Cl28__p_S28
       +rho*Y[jk31]*rate_eval.n_K31__He4_Cl28
       )

    jac[jcl28, jp] = (
       -rho*Y[jcl28]*rate_eval.p_Cl28__Ar29
       +rho*Y[js27]*rate_eval.p_S27__Cl28
       )

    jac[jcl28, jhe4] = (
       -rho*Y[jcl28]*rate_eval.He4_Cl28__p_Ar31
       -rho*Y[jcl28]*rate_eval.He4_Cl28__K32
       +rho*Y[jp24]*rate_eval.He4_P24__Cl28
       )

    jac[jcl28, jp24] = (
       +rho*Y[jhe4]*rate_eval.He4_P24__Cl28
       )

    jac[jcl28, js27] = (
       +rho*Y[jp]*rate_eval.p_S27__Cl28
       )

    jac[jcl28, jcl28] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl28__p_Ar31
       -rho*Y[jn]*rate_eval.n_Cl28__He4_P25
       -rho*Y[jn]*rate_eval.n_Cl28__Cl29
       -rate_eval.Cl28__S28__weak__bqa_pos_
       -rho*Y[jhe4]*rate_eval.He4_Cl28__K32
       -rho*Y[jn]*rate_eval.n_Cl28__p_S28
       -rho*Y[jp]*rate_eval.p_Cl28__Ar29
       )

    jac[jcl28, jk31] = (
       +rho*Y[jn]*rate_eval.n_K31__He4_Cl28
       )

    jac[jcl29, jn] = (
       -rho*Y[jcl29]*rate_eval.n_Cl29__He4_P26
       -rho*Y[jcl29]*rate_eval.n_Cl29__p_S29
       -rho*Y[jcl29]*rate_eval.n_Cl29__Cl30
       +rho*Y[jk32]*rate_eval.n_K32__He4_Cl29
       +rho*Y[jar29]*rate_eval.n_Ar29__p_Cl29
       +rho*Y[jcl28]*rate_eval.n_Cl28__Cl29
       )

    jac[jcl29, jp] = (
       -rho*Y[jcl29]*rate_eval.p_Cl29__Ar30
       +rho*Y[js28]*rate_eval.p_S28__Cl29
       )

    jac[jcl29, jhe4] = (
       -rho*Y[jcl29]*rate_eval.He4_Cl29__p_Ar32
       -rho*Y[jcl29]*rate_eval.He4_Cl29__K33
       +rho*Y[js26]*rate_eval.He4_S26__p_Cl29
       +rho*Y[jp25]*rate_eval.He4_P25__Cl29
       )

    jac[jcl29, jp25] = (
       +rho*Y[jhe4]*rate_eval.He4_P25__Cl29
       )

    jac[jcl29, js26] = (
       +rho*Y[jhe4]*rate_eval.He4_S26__p_Cl29
       )

    jac[jcl29, js28] = (
       +rho*Y[jp]*rate_eval.p_S28__Cl29
       )

    jac[jcl29, jcl28] = (
       +rho*Y[jn]*rate_eval.n_Cl28__Cl29
       )

    jac[jcl29, jcl29] = (
       -rho*Y[jn]*rate_eval.n_Cl29__He4_P26
       -rho*Y[jn]*rate_eval.n_Cl29__p_S29
       -rho*Y[jhe4]*rate_eval.He4_Cl29__p_Ar32
       -rho*Y[jp]*rate_eval.p_Cl29__Ar30
       -rho*Y[jhe4]*rate_eval.He4_Cl29__K33
       -rate_eval.Cl29__S29__weak__bqa_pos_
       -rho*Y[jn]*rate_eval.n_Cl29__Cl30
       )

    jac[jcl29, jar29] = (
       +rho*Y[jn]*rate_eval.n_Ar29__p_Cl29
       +rate_eval.Ar29__Cl29__weak__bqa_pos_
       )

    jac[jcl29, jk32] = (
       +rho*Y[jn]*rate_eval.n_K32__He4_Cl29
       )

    jac[jcl30, jn] = (
       -rho*Y[jcl30]*rate_eval.n_Cl30__p_S30
       -rho*Y[jcl30]*rate_eval.n_Cl30__He4_P27
       -rho*Y[jcl30]*rate_eval.n_Cl30__Cl31
       +rho*Y[jar30]*rate_eval.n_Ar30__p_Cl30
       +rho*Y[jk33]*rate_eval.n_K33__He4_Cl30
       +rho*Y[jcl29]*rate_eval.n_Cl29__Cl30
       )

    jac[jcl30, jp] = (
       -rho*Y[jcl30]*rate_eval.p_Cl30__Ar31
       +rho*Y[js29]*rate_eval.p_S29__Cl30
       )

    jac[jcl30, jhe4] = (
       -rho*Y[jcl30]*rate_eval.He4_Cl30__p_Ar33
       -rho*Y[jcl30]*rate_eval.He4_Cl30__K34
       +rho*Y[js27]*rate_eval.He4_S27__p_Cl30
       +rho*Y[jp26]*rate_eval.He4_P26__Cl30
       )

    jac[jcl30, jp26] = (
       +rho*Y[jhe4]*rate_eval.He4_P26__Cl30
       )

    jac[jcl30, js27] = (
       +rho*Y[jhe4]*rate_eval.He4_S27__p_Cl30
       )

    jac[jcl30, js29] = (
       +rho*Y[jp]*rate_eval.p_S29__Cl30
       )

    jac[jcl30, jcl29] = (
       +rho*Y[jn]*rate_eval.n_Cl29__Cl30
       )

    jac[jcl30, jcl30] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl30__p_Ar33
       -rho*Y[jn]*rate_eval.n_Cl30__p_S30
       -rho*Y[jhe4]*rate_eval.He4_Cl30__K34
       -rho*Y[jp]*rate_eval.p_Cl30__Ar31
       -rho*Y[jn]*rate_eval.n_Cl30__He4_P27
       -rho*Y[jn]*rate_eval.n_Cl30__Cl31
       -rate_eval.Cl30__S30__weak__bqa_pos_
       )

    jac[jcl30, jar30] = (
       +rho*Y[jn]*rate_eval.n_Ar30__p_Cl30
       +rate_eval.Ar30__Cl30__weak__bqa_pos_
       )

    jac[jcl30, jk33] = (
       +rho*Y[jn]*rate_eval.n_K33__He4_Cl30
       )

    jac[jcl31, jn] = (
       -rho*Y[jcl31]*rate_eval.n_Cl31__p_S31
       -rho*Y[jcl31]*rate_eval.n_Cl31__He4_P28
       -rho*Y[jcl31]*rate_eval.n_Cl31__Cl32
       +rho*Y[jar31]*rate_eval.n_Ar31__p_Cl31
       +rho*Y[jcl30]*rate_eval.n_Cl30__Cl31
       +rho*Y[jk34]*rate_eval.n_K34__He4_Cl31
       )

    jac[jcl31, jp] = (
       -rho*Y[jcl31]*rate_eval.p_Cl31__Ar32
       +rho*Y[js30]*rate_eval.p_S30__Cl31
       )

    jac[jcl31, jhe4] = (
       -rho*Y[jcl31]*rate_eval.He4_Cl31__K35
       -rho*Y[jcl31]*rate_eval.He4_Cl31__p_Ar34
       +rho*Y[js28]*rate_eval.He4_S28__p_Cl31
       +rho*Y[jp27]*rate_eval.He4_P27__Cl31
       )

    jac[jcl31, jp27] = (
       +rho*Y[jhe4]*rate_eval.He4_P27__Cl31
       )

    jac[jcl31, js28] = (
       +rho*Y[jhe4]*rate_eval.He4_S28__p_Cl31
       )

    jac[jcl31, js30] = (
       +rho*Y[jp]*rate_eval.p_S30__Cl31
       )

    jac[jcl31, jcl30] = (
       +rho*Y[jn]*rate_eval.n_Cl30__Cl31
       )

    jac[jcl31, jcl31] = (
       -rho*Y[jn]*rate_eval.n_Cl31__p_S31
       -rho*Y[jhe4]*rate_eval.He4_Cl31__K35
       -rho*Y[jp]*rate_eval.p_Cl31__Ar32
       -rho*Y[jn]*rate_eval.n_Cl31__He4_P28
       -rho*Y[jn]*rate_eval.n_Cl31__Cl32
       -rate_eval.Cl31__p_P30__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Cl31__p_Ar34
       -rate_eval.Cl31__S31__weak__wc12
       )

    jac[jcl31, jar31] = (
       +rho*Y[jn]*rate_eval.n_Ar31__p_Cl31
       +rate_eval.Ar31__Cl31__weak__wc12
       )

    jac[jcl31, jk34] = (
       +rho*Y[jn]*rate_eval.n_K34__He4_Cl31
       )

    jac[jcl32, jn] = (
       -rho*Y[jcl32]*rate_eval.n_Cl32__He4_P29
       -rho*Y[jcl32]*rate_eval.n_Cl32__Cl33
       -rho*Y[jcl32]*rate_eval.n_Cl32__p_S32
       +rho*Y[jar32]*rate_eval.n_Ar32__p_Cl32
       +rho*Y[jk35]*rate_eval.n_K35__He4_Cl32
       +rho*Y[jcl31]*rate_eval.n_Cl31__Cl32
       )

    jac[jcl32, jp] = (
       -rho*Y[jcl32]*rate_eval.p_Cl32__Ar33
       +rho*Y[js31]*rate_eval.p_S31__Cl32
       )

    jac[jcl32, jhe4] = (
       -rho*Y[jcl32]*rate_eval.He4_Cl32__p_Ar35
       -rho*Y[jcl32]*rate_eval.He4_Cl32__K36
       +rho*Y[js29]*rate_eval.He4_S29__p_Cl32
       +rho*Y[jp28]*rate_eval.He4_P28__Cl32
       )

    jac[jcl32, jp28] = (
       +rho*Y[jhe4]*rate_eval.He4_P28__Cl32
       )

    jac[jcl32, js29] = (
       +rho*Y[jhe4]*rate_eval.He4_S29__p_Cl32
       )

    jac[jcl32, js31] = (
       +rho*Y[jp]*rate_eval.p_S31__Cl32
       )

    jac[jcl32, jcl31] = (
       +rho*Y[jn]*rate_eval.n_Cl31__Cl32
       )

    jac[jcl32, jcl32] = (
       -rho*Y[jn]*rate_eval.n_Cl32__He4_P29
       -rho*Y[jhe4]*rate_eval.He4_Cl32__p_Ar35
       -rate_eval.Cl32__S32__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Cl32__K36
       -rho*Y[jp]*rate_eval.p_Cl32__Ar33
       -rho*Y[jn]*rate_eval.n_Cl32__Cl33
       -rho*Y[jn]*rate_eval.n_Cl32__p_S32
       -rate_eval.Cl32__He4_Si28__weak__wc12
       -rate_eval.Cl32__p_P31__weak__wc12
       )

    jac[jcl32, jar32] = (
       +rho*Y[jn]*rate_eval.n_Ar32__p_Cl32
       +rate_eval.Ar32__Cl32__weak__wc12
       )

    jac[jcl32, jk35] = (
       +rho*Y[jn]*rate_eval.n_K35__He4_Cl32
       )

    jac[jcl33, jn] = (
       -rho*Y[jcl33]*rate_eval.n_Cl33__He4_P30
       -rho*Y[jcl33]*rate_eval.n_Cl33__p_S33
       -rho*Y[jcl33]*rate_eval.n_Cl33__Cl34
       +rho*Y[jk36]*rate_eval.n_K36__He4_Cl33
       +rho*Y[jar33]*rate_eval.n_Ar33__p_Cl33
       +rho*Y[jcl32]*rate_eval.n_Cl32__Cl33
       )

    jac[jcl33, jp] = (
       -rho*Y[jcl33]*rate_eval.p_Cl33__Ar34
       +rho*Y[js32]*rate_eval.p_S32__Cl33
       )

    jac[jcl33, jhe4] = (
       -rho*Y[jcl33]*rate_eval.He4_Cl33__K37
       -rho*Y[jcl33]*rate_eval.He4_Cl33__p_Ar36
       +rho*Y[js30]*rate_eval.He4_S30__p_Cl33
       +rho*Y[jp29]*rate_eval.He4_P29__Cl33
       )

    jac[jcl33, jp29] = (
       +rho*Y[jhe4]*rate_eval.He4_P29__Cl33
       )

    jac[jcl33, js30] = (
       +rho*Y[jhe4]*rate_eval.He4_S30__p_Cl33
       )

    jac[jcl33, js32] = (
       +rho*Y[jp]*rate_eval.p_S32__Cl33
       )

    jac[jcl33, jcl32] = (
       +rho*Y[jn]*rate_eval.n_Cl32__Cl33
       )

    jac[jcl33, jcl33] = (
       -rho*Y[jn]*rate_eval.n_Cl33__He4_P30
       -rho*Y[jn]*rate_eval.n_Cl33__p_S33
       -rho*Y[jhe4]*rate_eval.He4_Cl33__K37
       -rho*Y[jn]*rate_eval.n_Cl33__Cl34
       -rho*Y[jhe4]*rate_eval.He4_Cl33__p_Ar36
       -rho*Y[jp]*rate_eval.p_Cl33__Ar34
       -rate_eval.Cl33__S33__weak__wc12
       )

    jac[jcl33, jar33] = (
       +rho*Y[jn]*rate_eval.n_Ar33__p_Cl33
       +rate_eval.Ar33__Cl33__weak__wc12
       )

    jac[jcl33, jk36] = (
       +rho*Y[jn]*rate_eval.n_K36__He4_Cl33
       )

    jac[jcl33, jca35] = (
       +rate_eval.Ca35__p_p_Cl33__weak__wc12
       )

    jac[jcl34, jn] = (
       -rho*Y[jcl34]*rate_eval.n_Cl34__He4_P31
       -rho*Y[jcl34]*rate_eval.n_Cl34__p_S34
       -rho*Y[jcl34]*rate_eval.n_Cl34__Cl35
       +rho*Y[jk37]*rate_eval.n_K37__He4_Cl34
       +rho*Y[jar34]*rate_eval.n_Ar34__p_Cl34
       +rho*Y[jcl33]*rate_eval.n_Cl33__Cl34
       )

    jac[jcl34, jp] = (
       -rho*Y[jcl34]*rate_eval.p_Cl34__Ar35
       +rho*Y[js33]*rate_eval.p_S33__Cl34
       )

    jac[jcl34, jhe4] = (
       -rho*Y[jcl34]*rate_eval.He4_Cl34__p_Ar37
       -rho*Y[jcl34]*rate_eval.He4_Cl34__K38
       +rho*Y[js31]*rate_eval.He4_S31__p_Cl34
       +rho*Y[jp30]*rate_eval.He4_P30__Cl34
       )

    jac[jcl34, jp30] = (
       +rho*Y[jhe4]*rate_eval.He4_P30__Cl34
       )

    jac[jcl34, js31] = (
       +rho*Y[jhe4]*rate_eval.He4_S31__p_Cl34
       )

    jac[jcl34, js33] = (
       +rho*Y[jp]*rate_eval.p_S33__Cl34
       )

    jac[jcl34, jcl33] = (
       +rho*Y[jn]*rate_eval.n_Cl33__Cl34
       )

    jac[jcl34, jcl34] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl34__p_Ar37
       -rho*Y[jn]*rate_eval.n_Cl34__He4_P31
       -rho*Y[jn]*rate_eval.n_Cl34__p_S34
       -rho*Y[jhe4]*rate_eval.He4_Cl34__K38
       -rho*Y[jn]*rate_eval.n_Cl34__Cl35
       -rho*Y[jp]*rate_eval.p_Cl34__Ar35
       -rate_eval.Cl34__S34__weak__wc12
       )

    jac[jcl34, jar34] = (
       +rho*Y[jn]*rate_eval.n_Ar34__p_Cl34
       +rate_eval.Ar34__Cl34__weak__wc12
       )

    jac[jcl34, jk35] = (
       +rate_eval.K35__p_Cl34__weak__wc12
       )

    jac[jcl34, jk37] = (
       +rho*Y[jn]*rate_eval.n_K37__He4_Cl34
       )

    jac[jcl35, jn] = (
       -rho*Y[jcl35]*rate_eval.n_Cl35__p_S35
       -rho*Y[jcl35]*rate_eval.n_Cl35__He4_P32
       -rho*Y[jcl35]*rate_eval.n_Cl35__Cl36
       +rho*Y[jar35]*rate_eval.n_Ar35__p_Cl35
       +rho*Y[jcl34]*rate_eval.n_Cl34__Cl35
       +rho*Y[jk38]*rate_eval.n_K38__He4_Cl35
       )

    jac[jcl35, jp] = (
       -rho*Y[jcl35]*rate_eval.p_Cl35__He4_S32
       -rho*Y[jcl35]*rate_eval.p_Cl35__Ar36
       +rho*Y[js34]*rate_eval.p_S34__Cl35
       )

    jac[jcl35, jhe4] = (
       -rho*Y[jcl35]*rate_eval.He4_Cl35__p_Ar38
       -rho*Y[jcl35]*rate_eval.He4_Cl35__K39
       +rho*Y[jp31]*rate_eval.He4_P31__Cl35
       )

    jac[jcl35, jp31] = (
       +rho*Y[jhe4]*rate_eval.He4_P31__Cl35
       )

    jac[jcl35, js34] = (
       +rho*Y[jp]*rate_eval.p_S34__Cl35
       )

    jac[jcl35, js35] = (
       +rate_eval.S35__Cl35__weak__wc12
       )

    jac[jcl35, jcl34] = (
       +rho*Y[jn]*rate_eval.n_Cl34__Cl35
       )

    jac[jcl35, jcl35] = (
       -rho*Y[jn]*rate_eval.n_Cl35__p_S35
       -rho*Y[jn]*rate_eval.n_Cl35__He4_P32
       -rho*Y[jp]*rate_eval.p_Cl35__He4_S32
       -rho*Y[jhe4]*rate_eval.He4_Cl35__p_Ar38
       -rho*Y[jhe4]*rate_eval.He4_Cl35__K39
       -rho*Y[jp]*rate_eval.p_Cl35__Ar36
       -rho*Y[jn]*rate_eval.n_Cl35__Cl36
       )

    jac[jcl35, jar35] = (
       +rho*Y[jn]*rate_eval.n_Ar35__p_Cl35
       +rate_eval.Ar35__Cl35__weak__wc12
       )

    jac[jcl35, jk36] = (
       +rate_eval.K36__p_Cl35__weak__wc12
       )

    jac[jcl35, jk38] = (
       +rho*Y[jn]*rate_eval.n_K38__He4_Cl35
       )

    jac[jcl36, jn] = (
       -rho*Y[jcl36]*rate_eval.n_Cl36__p_S36
       -rho*Y[jcl36]*rate_eval.n_Cl36__He4_P33
       -rho*Y[jcl36]*rate_eval.n_Cl36__Cl37
       +rho*Y[jk39]*rate_eval.n_K39__He4_Cl36
       +rho*Y[jar36]*rate_eval.n_Ar36__p_Cl36
       +rho*Y[jcl35]*rate_eval.n_Cl35__Cl36
       )

    jac[jcl36, jp] = (
       -rho*Y[jcl36]*rate_eval.p_Cl36__Ar37
       -rho*Y[jcl36]*rate_eval.p_Cl36__He4_S33
       +rho*Y[jar39]*rate_eval.p_Ar39__He4_Cl36
       +rho*Y[js35]*rate_eval.p_S35__Cl36
       )

    jac[jcl36, jhe4] = (
       -rho*Y[jcl36]*rate_eval.He4_Cl36__K40
       +rho*Y[jp32]*rate_eval.He4_P32__Cl36
       )

    jac[jcl36, jp32] = (
       +rho*Y[jhe4]*rate_eval.He4_P32__Cl36
       )

    jac[jcl36, js35] = (
       +rho*Y[jp]*rate_eval.p_S35__Cl36
       )

    jac[jcl36, jcl35] = (
       +rho*Y[jn]*rate_eval.n_Cl35__Cl36
       )

    jac[jcl36, jcl36] = (
       -rho*Y[jn]*rate_eval.n_Cl36__p_S36
       -rho*Y[jp]*rate_eval.p_Cl36__Ar37
       -rho*Y[jp]*rate_eval.p_Cl36__He4_S33
       -rho*Y[jhe4]*rate_eval.He4_Cl36__K40
       -rho*Y[jn]*rate_eval.n_Cl36__He4_P33
       -rate_eval.Cl36__Ar36__weak__wc12
       -rho*Y[jn]*rate_eval.n_Cl36__Cl37
       -rate_eval.Cl36__S36__weak__wc12
       )

    jac[jcl36, jar36] = (
       +rho*Y[jn]*rate_eval.n_Ar36__p_Cl36
       )

    jac[jcl36, jar39] = (
       +rho*Y[jp]*rate_eval.p_Ar39__He4_Cl36
       )

    jac[jcl36, jk39] = (
       +rho*Y[jn]*rate_eval.n_K39__He4_Cl36
       )

    jac[jcl37, jn] = (
       -rho*Y[jcl37]*rate_eval.n_Cl37__Cl38
       +rho*Y[jk40]*rate_eval.n_K40__He4_Cl37
       +rho*Y[jar37]*rate_eval.n_Ar37__p_Cl37
       +rho*Y[jcl36]*rate_eval.n_Cl36__Cl37
       )

    jac[jcl37, jp] = (
       -rho*Y[jcl37]*rate_eval.p_Cl37__Ar38
       +rho*Y[jar40]*rate_eval.p_Ar40__He4_Cl37
       +rho*Y[js37]*rate_eval.p_S37__n_Cl37
       +rho*Y[js36]*rate_eval.p_S36__Cl37
       )

    jac[jcl37, jhe4] = (
       -rho*Y[jcl37]*rate_eval.He4_Cl37__K41
       +rho*Y[jp34]*rate_eval.He4_P34__n_Cl37
       +rho*Y[js34]*rate_eval.He4_S34__p_Cl37
       +rho*Y[jp33]*rate_eval.He4_P33__Cl37
       )

    jac[jcl37, jp33] = (
       +rho*Y[jhe4]*rate_eval.He4_P33__Cl37
       )

    jac[jcl37, jp34] = (
       +rho*Y[jhe4]*rate_eval.He4_P34__n_Cl37
       )

    jac[jcl37, js34] = (
       +rho*Y[jhe4]*rate_eval.He4_S34__p_Cl37
       )

    jac[jcl37, js36] = (
       +rho*Y[jp]*rate_eval.p_S36__Cl37
       )

    jac[jcl37, js37] = (
       +rho*Y[jp]*rate_eval.p_S37__n_Cl37
       +rate_eval.S37__Cl37__weak__wc12
       )

    jac[jcl37, jcl36] = (
       +rho*Y[jn]*rate_eval.n_Cl36__Cl37
       )

    jac[jcl37, jcl37] = (
       -rho*Y[jn]*rate_eval.n_Cl37__Cl38
       -rho*Y[jhe4]*rate_eval.He4_Cl37__K41
       -rho*Y[jp]*rate_eval.p_Cl37__Ar38
       )

    jac[jcl37, jar37] = (
       +rho*Y[jn]*rate_eval.n_Ar37__p_Cl37
       +rate_eval.Ar37__Cl37__weak__wc12
       )

    jac[jcl37, jar40] = (
       +rho*Y[jp]*rate_eval.p_Ar40__He4_Cl37
       )

    jac[jcl37, jk40] = (
       +rho*Y[jn]*rate_eval.n_K40__He4_Cl37
       )

    jac[jcl38, jn] = (
       -rho*Y[jcl38]*rate_eval.n_Cl38__He4_P35
       -rho*Y[jcl38]*rate_eval.n_Cl38__Cl39
       +rho*Y[jcl37]*rate_eval.n_Cl37__Cl38
       )

    jac[jcl38, jp] = (
       -rho*Y[jcl38]*rate_eval.p_Cl38__He4_S35
       -rho*Y[jcl38]*rate_eval.p_Cl38__n_Ar38
       -rho*Y[jcl38]*rate_eval.p_Cl38__Ar39
       +rho*Y[js37]*rate_eval.p_S37__Cl38
       +rho*Y[js38]*rate_eval.p_S38__n_Cl38
       +rho*Y[jar41]*rate_eval.p_Ar41__He4_Cl38
       )

    jac[jcl38, jhe4] = (
       -rho*Y[jcl38]*rate_eval.He4_Cl38__K42
       -rho*Y[jcl38]*rate_eval.He4_Cl38__n_K41
       +rho*Y[jp34]*rate_eval.He4_P34__Cl38
       )

    jac[jcl38, jp34] = (
       +rho*Y[jhe4]*rate_eval.He4_P34__Cl38
       )

    jac[jcl38, js37] = (
       +rho*Y[jp]*rate_eval.p_S37__Cl38
       )

    jac[jcl38, js38] = (
       +rho*Y[jp]*rate_eval.p_S38__n_Cl38
       +rate_eval.S38__Cl38__weak__wc12
       )

    jac[jcl38, jcl37] = (
       +rho*Y[jn]*rate_eval.n_Cl37__Cl38
       )

    jac[jcl38, jcl38] = (
       -rho*Y[jp]*rate_eval.p_Cl38__He4_S35
       -rho*Y[jn]*rate_eval.n_Cl38__He4_P35
       -rho*Y[jhe4]*rate_eval.He4_Cl38__K42
       -rho*Y[jhe4]*rate_eval.He4_Cl38__n_K41
       -rho*Y[jp]*rate_eval.p_Cl38__n_Ar38
       -rho*Y[jp]*rate_eval.p_Cl38__Ar39
       -rho*Y[jn]*rate_eval.n_Cl38__Cl39
       -rate_eval.Cl38__Ar38__weak__wc12
       )

    jac[jcl38, jar41] = (
       +rho*Y[jp]*rate_eval.p_Ar41__He4_Cl38
       )

    jac[jcl39, jn] = (
       -rho*Y[jcl39]*rate_eval.n_Cl39__Cl40
       +rho*Y[jcl38]*rate_eval.n_Cl38__Cl39
       +rho*Y[jk42]*rate_eval.n_K42__He4_Cl39
       )

    jac[jcl39, jp] = (
       -rho*Y[jcl39]*rate_eval.p_Cl39__He4_S36
       -rho*Y[jcl39]*rate_eval.p_Cl39__Ar40
       -rho*Y[jcl39]*rate_eval.p_Cl39__n_Ar39
       +rho*Y[js38]*rate_eval.p_S38__Cl39
       +rho*Y[jar42]*rate_eval.p_Ar42__He4_Cl39
       +rho*Y[js39]*rate_eval.p_S39__n_Cl39
       )

    jac[jcl39, jhe4] = (
       -rho*Y[jcl39]*rate_eval.He4_Cl39__K43
       +rho*Y[jp36]*rate_eval.He4_P36__n_Cl39
       +rho*Y[jp35]*rate_eval.He4_P35__Cl39
       )

    jac[jcl39, jp35] = (
       +rho*Y[jhe4]*rate_eval.He4_P35__Cl39
       )

    jac[jcl39, jp36] = (
       +rho*Y[jhe4]*rate_eval.He4_P36__n_Cl39
       )

    jac[jcl39, js38] = (
       +rho*Y[jp]*rate_eval.p_S38__Cl39
       )

    jac[jcl39, js39] = (
       +rho*Y[jp]*rate_eval.p_S39__n_Cl39
       +rate_eval.S39__Cl39__weak__wc12
       )

    jac[jcl39, jcl38] = (
       +rho*Y[jn]*rate_eval.n_Cl38__Cl39
       )

    jac[jcl39, jcl39] = (
       -rate_eval.Cl39__Ar39__weak__wc12
       -rho*Y[jp]*rate_eval.p_Cl39__He4_S36
       -rho*Y[jhe4]*rate_eval.He4_Cl39__K43
       -rho*Y[jp]*rate_eval.p_Cl39__Ar40
       -rho*Y[jp]*rate_eval.p_Cl39__n_Ar39
       -rho*Y[jn]*rate_eval.n_Cl39__Cl40
       )

    jac[jcl39, jar42] = (
       +rho*Y[jp]*rate_eval.p_Ar42__He4_Cl39
       )

    jac[jcl39, jk42] = (
       +rho*Y[jn]*rate_eval.n_K42__He4_Cl39
       )

    jac[jcl40, jn] = (
       -rho*Y[jcl40]*rate_eval.n_Cl40__Cl41
       +rho*Y[jcl39]*rate_eval.n_Cl39__Cl40
       )

    jac[jcl40, jp] = (
       -rho*Y[jcl40]*rate_eval.p_Cl40__n_Ar40
       -rho*Y[jcl40]*rate_eval.p_Cl40__He4_S37
       -rho*Y[jcl40]*rate_eval.p_Cl40__Ar41
       +rho*Y[js40]*rate_eval.p_S40__n_Cl40
       +rho*Y[jar43]*rate_eval.p_Ar43__He4_Cl40
       +rho*Y[js39]*rate_eval.p_S39__Cl40
       )

    jac[jcl40, jhe4] = (
       -rho*Y[jcl40]*rate_eval.He4_Cl40__n_K43
       -rho*Y[jcl40]*rate_eval.He4_Cl40__K44
       +rho*Y[jp37]*rate_eval.He4_P37__n_Cl40
       +rho*Y[jp36]*rate_eval.He4_P36__Cl40
       )

    jac[jcl40, jp36] = (
       +rho*Y[jhe4]*rate_eval.He4_P36__Cl40
       )

    jac[jcl40, jp37] = (
       +rho*Y[jhe4]*rate_eval.He4_P37__n_Cl40
       )

    jac[jcl40, js39] = (
       +rho*Y[jp]*rate_eval.p_S39__Cl40
       )

    jac[jcl40, js40] = (
       +rho*Y[jp]*rate_eval.p_S40__n_Cl40
       +rate_eval.S40__Cl40__weak__wc12
       )

    jac[jcl40, jcl39] = (
       +rho*Y[jn]*rate_eval.n_Cl39__Cl40
       )

    jac[jcl40, jcl40] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl40__n_K43
       -rho*Y[jp]*rate_eval.p_Cl40__n_Ar40
       -rho*Y[jp]*rate_eval.p_Cl40__He4_S37
       -rho*Y[jp]*rate_eval.p_Cl40__Ar41
       -rho*Y[jn]*rate_eval.n_Cl40__Cl41
       -rho*Y[jhe4]*rate_eval.He4_Cl40__K44
       -rate_eval.Cl40__Ar40__weak__wc12
       )

    jac[jcl40, jar43] = (
       +rho*Y[jp]*rate_eval.p_Ar43__He4_Cl40
       )

    jac[jcl41, jn] = (
       -rho*Y[jcl41]*rate_eval.n_Cl41__Cl42
       +rho*Y[jcl40]*rate_eval.n_Cl40__Cl41
       )

    jac[jcl41, jp] = (
       -rho*Y[jcl41]*rate_eval.p_Cl41__He4_S38
       -rho*Y[jcl41]*rate_eval.p_Cl41__Ar42
       -rho*Y[jcl41]*rate_eval.p_Cl41__n_Ar41
       +rho*Y[js40]*rate_eval.p_S40__Cl41
       +rho*Y[js41]*rate_eval.p_S41__n_Cl41
       )

    jac[jcl41, jhe4] = (
       -rho*Y[jcl41]*rate_eval.He4_Cl41__n_K44
       -rho*Y[jcl41]*rate_eval.He4_Cl41__K45
       -rho*Y[jcl41]*rate_eval.He4_Cl41__p_Ar44
       +rho*Y[jp37]*rate_eval.He4_P37__Cl41
       +rho*Y[jp38]*rate_eval.He4_P38__n_Cl41
       )

    jac[jcl41, jp37] = (
       +rho*Y[jhe4]*rate_eval.He4_P37__Cl41
       )

    jac[jcl41, jp38] = (
       +rho*Y[jhe4]*rate_eval.He4_P38__n_Cl41
       )

    jac[jcl41, js40] = (
       +rho*Y[jp]*rate_eval.p_S40__Cl41
       )

    jac[jcl41, js41] = (
       +rho*Y[jp]*rate_eval.p_S41__n_Cl41
       +rate_eval.S41__Cl41__weak__wc12
       )

    jac[jcl41, jcl40] = (
       +rho*Y[jn]*rate_eval.n_Cl40__Cl41
       )

    jac[jcl41, jcl41] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl41__n_K44
       -rho*Y[jp]*rate_eval.p_Cl41__He4_S38
       -rate_eval.Cl41__Ar41__weak__wc12
       -rho*Y[jp]*rate_eval.p_Cl41__Ar42
       -rho*Y[jp]*rate_eval.p_Cl41__n_Ar41
       -rho*Y[jn]*rate_eval.n_Cl41__Cl42
       -rho*Y[jhe4]*rate_eval.He4_Cl41__K45
       -rho*Y[jhe4]*rate_eval.He4_Cl41__p_Ar44
       )

    jac[jcl42, jn] = (
       -rho*Y[jcl42]*rate_eval.n_Cl42__Cl43
       +rho*Y[jcl41]*rate_eval.n_Cl41__Cl42
       )

    jac[jcl42, jp] = (
       -rho*Y[jcl42]*rate_eval.p_Cl42__He4_S39
       -rho*Y[jcl42]*rate_eval.p_Cl42__n_Ar42
       -rho*Y[jcl42]*rate_eval.p_Cl42__Ar43
       +rho*Y[jar45]*rate_eval.p_Ar45__He4_Cl42
       +rho*Y[js42]*rate_eval.p_S42__n_Cl42
       +rho*Y[js41]*rate_eval.p_S41__Cl42
       )

    jac[jcl42, jhe4] = (
       -rho*Y[jcl42]*rate_eval.He4_Cl42__n_K45
       -rho*Y[jcl42]*rate_eval.He4_Cl42__K46
       +rho*Y[jp39]*rate_eval.He4_P39__n_Cl42
       +rho*Y[jp38]*rate_eval.He4_P38__Cl42
       )

    jac[jcl42, jp38] = (
       +rho*Y[jhe4]*rate_eval.He4_P38__Cl42
       )

    jac[jcl42, jp39] = (
       +rho*Y[jhe4]*rate_eval.He4_P39__n_Cl42
       )

    jac[jcl42, js41] = (
       +rho*Y[jp]*rate_eval.p_S41__Cl42
       )

    jac[jcl42, js42] = (
       +rho*Y[jp]*rate_eval.p_S42__n_Cl42
       +rate_eval.S42__Cl42__weak__wc12
       )

    jac[jcl42, js43] = (
       +rate_eval.S43__n_Cl42__weak__wc12
       )

    jac[jcl42, jcl41] = (
       +rho*Y[jn]*rate_eval.n_Cl41__Cl42
       )

    jac[jcl42, jcl42] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl42__n_K45
       -rho*Y[jp]*rate_eval.p_Cl42__He4_S39
       -rho*Y[jp]*rate_eval.p_Cl42__n_Ar42
       -rho*Y[jhe4]*rate_eval.He4_Cl42__K46
       -rho*Y[jn]*rate_eval.n_Cl42__Cl43
       -rho*Y[jp]*rate_eval.p_Cl42__Ar43
       -rate_eval.Cl42__Ar42__weak__wc12
       )

    jac[jcl42, jar45] = (
       +rho*Y[jp]*rate_eval.p_Ar45__He4_Cl42
       )

    jac[jcl43, jn] = (
       -rho*Y[jcl43]*rate_eval.n_Cl43__Cl44
       +rho*Y[jcl42]*rate_eval.n_Cl42__Cl43
       )

    jac[jcl43, jp] = (
       -rho*Y[jcl43]*rate_eval.p_Cl43__He4_S40
       -rho*Y[jcl43]*rate_eval.p_Cl43__Ar44
       -rho*Y[jcl43]*rate_eval.p_Cl43__n_Ar43
       +rho*Y[js42]*rate_eval.p_S42__Cl43
       +rho*Y[js43]*rate_eval.p_S43__n_Cl43
       )

    jac[jcl43, jhe4] = (
       -rho*Y[jcl43]*rate_eval.He4_Cl43__p_Ar46
       -rho*Y[jcl43]*rate_eval.He4_Cl43__K47
       -rho*Y[jcl43]*rate_eval.He4_Cl43__n_K46
       +rho*Y[jp40]*rate_eval.He4_P40__n_Cl43
       +rho*Y[jp39]*rate_eval.He4_P39__Cl43
       )

    jac[jcl43, jp39] = (
       +rho*Y[jhe4]*rate_eval.He4_P39__Cl43
       )

    jac[jcl43, jp40] = (
       +rho*Y[jhe4]*rate_eval.He4_P40__n_Cl43
       )

    jac[jcl43, js42] = (
       +rho*Y[jp]*rate_eval.p_S42__Cl43
       )

    jac[jcl43, js43] = (
       +rho*Y[jp]*rate_eval.p_S43__n_Cl43
       +rate_eval.S43__Cl43__weak__wc12
       )

    jac[jcl43, js44] = (
       +rate_eval.S44__n_Cl43__weak__wc12
       )

    jac[jcl43, js45] = (
       +rate_eval.S45__n_n_Cl43__weak__mp17
       )

    jac[jcl43, jcl42] = (
       +rho*Y[jn]*rate_eval.n_Cl42__Cl43
       )

    jac[jcl43, jcl43] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl43__p_Ar46
       -rho*Y[jp]*rate_eval.p_Cl43__He4_S40
       -rho*Y[jn]*rate_eval.n_Cl43__Cl44
       -rate_eval.Cl43__n_Ar42__weak__mp17
       -rho*Y[jp]*rate_eval.p_Cl43__Ar44
       -rho*Y[jhe4]*rate_eval.He4_Cl43__K47
       -rho*Y[jp]*rate_eval.p_Cl43__n_Ar43
       -rho*Y[jhe4]*rate_eval.He4_Cl43__n_K46
       -rate_eval.Cl43__Ar43__weak__wc12
       )

    jac[jcl44, jn] = (
       -rho*Y[jcl44]*rate_eval.n_Cl44__Cl45
       +rho*Y[jcl43]*rate_eval.n_Cl43__Cl44
       )

    jac[jcl44, jp] = (
       -rho*Y[jcl44]*rate_eval.p_Cl44__Ar45
       -rho*Y[jcl44]*rate_eval.p_Cl44__n_Ar44
       -rho*Y[jcl44]*rate_eval.p_Cl44__He4_S41
       +rho*Y[js44]*rate_eval.p_S44__n_Cl44
       +rho*Y[js43]*rate_eval.p_S43__Cl44
       )

    jac[jcl44, jhe4] = (
       -rho*Y[jcl44]*rate_eval.He4_Cl44__p_Ar47
       -rho*Y[jcl44]*rate_eval.He4_Cl44__n_K47
       -rho*Y[jcl44]*rate_eval.He4_Cl44__K48
       +rho*Y[jp41]*rate_eval.He4_P41__n_Cl44
       +rho*Y[jp40]*rate_eval.He4_P40__Cl44
       )

    jac[jcl44, jp40] = (
       +rho*Y[jhe4]*rate_eval.He4_P40__Cl44
       )

    jac[jcl44, jp41] = (
       +rho*Y[jhe4]*rate_eval.He4_P41__n_Cl44
       )

    jac[jcl44, js43] = (
       +rho*Y[jp]*rate_eval.p_S43__Cl44
       )

    jac[jcl44, js44] = (
       +rho*Y[jp]*rate_eval.p_S44__n_Cl44
       +rate_eval.S44__Cl44__weak__wc12
       )

    jac[jcl44, js45] = (
       +rate_eval.S45__n_Cl44__weak__wc12
       )

    jac[jcl44, js47] = (
       +rate_eval.S47__n_n_n_Cl44__weak__mo03
       )

    jac[jcl44, jcl43] = (
       +rho*Y[jn]*rate_eval.n_Cl43__Cl44
       )

    jac[jcl44, jcl44] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl44__p_Ar47
       -rho*Y[jhe4]*rate_eval.He4_Cl44__n_K47
       -rho*Y[jn]*rate_eval.n_Cl44__Cl45
       -rho*Y[jhe4]*rate_eval.He4_Cl44__K48
       -rho*Y[jp]*rate_eval.p_Cl44__Ar45
       -rho*Y[jp]*rate_eval.p_Cl44__n_Ar44
       -rate_eval.Cl44__n_Ar43__weak__mp17
       -rate_eval.Cl44__Ar44__weak__wc17
       -rho*Y[jp]*rate_eval.p_Cl44__He4_S41
       )

    jac[jcl45, jn] = (
       -rho*Y[jcl45]*rate_eval.n_Cl45__Cl46
       +rho*Y[jcl44]*rate_eval.n_Cl44__Cl45
       )

    jac[jcl45, jp] = (
       -rho*Y[jcl45]*rate_eval.p_Cl45__He4_S42
       -rho*Y[jcl45]*rate_eval.p_Cl45__n_Ar45
       -rho*Y[jcl45]*rate_eval.p_Cl45__Ar46
       +rho*Y[jar48]*rate_eval.p_Ar48__He4_Cl45
       +rho*Y[js44]*rate_eval.p_S44__Cl45
       +rho*Y[js45]*rate_eval.p_S45__n_Cl45
       )

    jac[jcl45, jhe4] = (
       -rho*Y[jcl45]*rate_eval.He4_Cl45__n_K48
       -rho*Y[jcl45]*rate_eval.He4_Cl45__K49
       +rho*Y[jp42]*rate_eval.He4_P42__n_Cl45
       +rho*Y[jp41]*rate_eval.He4_P41__Cl45
       )

    jac[jcl45, jp41] = (
       +rho*Y[jhe4]*rate_eval.He4_P41__Cl45
       )

    jac[jcl45, jp42] = (
       +rho*Y[jhe4]*rate_eval.He4_P42__n_Cl45
       )

    jac[jcl45, js44] = (
       +rho*Y[jp]*rate_eval.p_S44__Cl45
       )

    jac[jcl45, js45] = (
       +rho*Y[jp]*rate_eval.p_S45__n_Cl45
       +rate_eval.S45__Cl45__weak__wc12
       )

    jac[jcl45, js46] = (
       +rate_eval.S46__n_Cl45__weak__mp17
       )

    jac[jcl45, js47] = (
       +rate_eval.S47__n_n_Cl45__weak__mp17
       )

    jac[jcl45, js48] = (
       +rate_eval.S48__n_n_n_Cl45__weak__mo03
       )

    jac[jcl45, jcl44] = (
       +rho*Y[jn]*rate_eval.n_Cl44__Cl45
       )

    jac[jcl45, jcl45] = (
       -rho*Y[jp]*rate_eval.p_Cl45__He4_S42
       -rho*Y[jp]*rate_eval.p_Cl45__n_Ar45
       -rho*Y[jp]*rate_eval.p_Cl45__Ar46
       -rho*Y[jhe4]*rate_eval.He4_Cl45__n_K48
       -rho*Y[jn]*rate_eval.n_Cl45__Cl46
       -rate_eval.Cl45__n_Ar44__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Cl45__K49
       -rate_eval.Cl45__Ar45__weak__wc12
       )

    jac[jcl45, jar48] = (
       +rho*Y[jp]*rate_eval.p_Ar48__He4_Cl45
       )

    jac[jcl46, jn] = (
       -rho*Y[jcl46]*rate_eval.n_Cl46__Cl47
       +rho*Y[jcl45]*rate_eval.n_Cl45__Cl46
       )

    jac[jcl46, jp] = (
       -rho*Y[jcl46]*rate_eval.p_Cl46__He4_S43
       -rho*Y[jcl46]*rate_eval.p_Cl46__n_Ar46
       -rho*Y[jcl46]*rate_eval.p_Cl46__Ar47
       +rho*Y[js46]*rate_eval.p_S46__n_Cl46
       +rho*Y[js45]*rate_eval.p_S45__Cl46
       +rho*Y[jar49]*rate_eval.p_Ar49__He4_Cl46
       )

    jac[jcl46, jhe4] = (
       -rho*Y[jcl46]*rate_eval.He4_Cl46__n_K49
       -rho*Y[jcl46]*rate_eval.He4_Cl46__K50
       +rho*Y[jp43]*rate_eval.He4_P43__n_Cl46
       +rho*Y[jp42]*rate_eval.He4_P42__Cl46
       )

    jac[jcl46, jp42] = (
       +rho*Y[jhe4]*rate_eval.He4_P42__Cl46
       )

    jac[jcl46, jp43] = (
       +rho*Y[jhe4]*rate_eval.He4_P43__n_Cl46
       )

    jac[jcl46, js45] = (
       +rho*Y[jp]*rate_eval.p_S45__Cl46
       )

    jac[jcl46, js46] = (
       +rho*Y[jp]*rate_eval.p_S46__n_Cl46
       +rate_eval.S46__Cl46__weak__wc17
       )

    jac[jcl46, js47] = (
       +rate_eval.S47__n_Cl46__weak__mp17
       )

    jac[jcl46, js48] = (
       +rate_eval.S48__n_n_Cl46__weak__mp17
       )

    jac[jcl46, js49] = (
       +rate_eval.S49__n_n_n_Cl46__weak__mo03
       )

    jac[jcl46, jcl45] = (
       +rho*Y[jn]*rate_eval.n_Cl45__Cl46
       )

    jac[jcl46, jcl46] = (
       -rho*Y[jp]*rate_eval.p_Cl46__He4_S43
       -rho*Y[jp]*rate_eval.p_Cl46__n_Ar46
       -rho*Y[jhe4]*rate_eval.He4_Cl46__n_K49
       -rho*Y[jhe4]*rate_eval.He4_Cl46__K50
       -rho*Y[jn]*rate_eval.n_Cl46__Cl47
       -rho*Y[jp]*rate_eval.p_Cl46__Ar47
       -rate_eval.Cl46__n_Ar45__weak__wc12
       -rate_eval.Cl46__Ar46__weak__wc12
       )

    jac[jcl46, jar49] = (
       +rho*Y[jp]*rate_eval.p_Ar49__He4_Cl46
       )

    jac[jcl47, jn] = (
       -rho*Y[jcl47]*rate_eval.n_Cl47__Cl48
       +rho*Y[jcl46]*rate_eval.n_Cl46__Cl47
       )

    jac[jcl47, jp] = (
       -rho*Y[jcl47]*rate_eval.p_Cl47__Ar48
       -rho*Y[jcl47]*rate_eval.p_Cl47__n_Ar47
       -rho*Y[jcl47]*rate_eval.p_Cl47__He4_S44
       +rho*Y[jar50]*rate_eval.p_Ar50__He4_Cl47
       +rho*Y[js47]*rate_eval.p_S47__n_Cl47
       +rho*Y[js46]*rate_eval.p_S46__Cl47
       )

    jac[jcl47, jhe4] = (
       -rho*Y[jcl47]*rate_eval.He4_Cl47__K51
       -rho*Y[jcl47]*rate_eval.He4_Cl47__n_K50
       +rho*Y[jp44]*rate_eval.He4_P44__n_Cl47
       +rho*Y[jp43]*rate_eval.He4_P43__Cl47
       )

    jac[jcl47, jp43] = (
       +rho*Y[jhe4]*rate_eval.He4_P43__Cl47
       )

    jac[jcl47, jp44] = (
       +rho*Y[jhe4]*rate_eval.He4_P44__n_Cl47
       )

    jac[jcl47, js46] = (
       +rho*Y[jp]*rate_eval.p_S46__Cl47
       )

    jac[jcl47, js47] = (
       +rho*Y[jp]*rate_eval.p_S47__n_Cl47
       +rate_eval.S47__Cl47__weak__mo03
       )

    jac[jcl47, js48] = (
       +rate_eval.S48__n_Cl47__weak__mp17
       )

    jac[jcl47, js49] = (
       +rate_eval.S49__n_n_Cl47__weak__mp17
       )

    jac[jcl47, jcl46] = (
       +rho*Y[jn]*rate_eval.n_Cl46__Cl47
       )

    jac[jcl47, jcl47] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl47__K51
       -rho*Y[jhe4]*rate_eval.He4_Cl47__n_K50
       -rate_eval.Cl47__n_n_Ar45__weak__mp17
       -rho*Y[jp]*rate_eval.p_Cl47__Ar48
       -rho*Y[jp]*rate_eval.p_Cl47__n_Ar47
       -rate_eval.Cl47__n_Ar46__weak__wc12
       -rho*Y[jn]*rate_eval.n_Cl47__Cl48
       -rho*Y[jp]*rate_eval.p_Cl47__He4_S44
       -rate_eval.Cl47__Ar47__weak__wc17
       )

    jac[jcl47, jar50] = (
       +rho*Y[jp]*rate_eval.p_Ar50__He4_Cl47
       )

    jac[jcl48, jn] = (
       -rho*Y[jcl48]*rate_eval.n_Cl48__Cl49
       +rho*Y[jcl47]*rate_eval.n_Cl47__Cl48
       )

    jac[jcl48, jp] = (
       -rho*Y[jcl48]*rate_eval.p_Cl48__He4_S45
       -rho*Y[jcl48]*rate_eval.p_Cl48__n_Ar48
       -rho*Y[jcl48]*rate_eval.p_Cl48__Ar49
       +rho*Y[jar51]*rate_eval.p_Ar51__He4_Cl48
       +rho*Y[js47]*rate_eval.p_S47__Cl48
       +rho*Y[js48]*rate_eval.p_S48__n_Cl48
       )

    jac[jcl48, jhe4] = (
       -rho*Y[jcl48]*rate_eval.He4_Cl48__K52
       -rho*Y[jcl48]*rate_eval.He4_Cl48__n_K51
       +rho*Y[jp45]*rate_eval.He4_P45__n_Cl48
       +rho*Y[jp44]*rate_eval.He4_P44__Cl48
       )

    jac[jcl48, jp44] = (
       +rho*Y[jhe4]*rate_eval.He4_P44__Cl48
       )

    jac[jcl48, jp45] = (
       +rho*Y[jhe4]*rate_eval.He4_P45__n_Cl48
       )

    jac[jcl48, js47] = (
       +rho*Y[jp]*rate_eval.p_S47__Cl48
       )

    jac[jcl48, js48] = (
       +rho*Y[jp]*rate_eval.p_S48__n_Cl48
       +rate_eval.S48__Cl48__weak__mo03
       )

    jac[jcl48, js49] = (
       +rate_eval.S49__n_Cl48__weak__mp17
       )

    jac[jcl48, jcl47] = (
       +rho*Y[jn]*rate_eval.n_Cl47__Cl48
       )

    jac[jcl48, jcl48] = (
       -rho*Y[jp]*rate_eval.p_Cl48__He4_S45
       -rho*Y[jp]*rate_eval.p_Cl48__n_Ar48
       -rate_eval.Cl48__n_Ar47__weak__mp17
       -rho*Y[jp]*rate_eval.p_Cl48__Ar49
       -rho*Y[jn]*rate_eval.n_Cl48__Cl49
       -rho*Y[jhe4]*rate_eval.He4_Cl48__K52
       -rho*Y[jhe4]*rate_eval.He4_Cl48__n_K51
       -rate_eval.Cl48__n_n_Ar46__weak__mp17
       -rate_eval.Cl48__Ar48__weak__mo03
       )

    jac[jcl48, jar51] = (
       +rho*Y[jp]*rate_eval.p_Ar51__He4_Cl48
       )

    jac[jcl49, jn] = (
       -rho*Y[jcl49]*rate_eval.n_Cl49__Cl50
       +rho*Y[jcl48]*rate_eval.n_Cl48__Cl49
       )

    jac[jcl49, jp] = (
       -rho*Y[jcl49]*rate_eval.p_Cl49__Ar50
       -rho*Y[jcl49]*rate_eval.p_Cl49__He4_S46
       -rho*Y[jcl49]*rate_eval.p_Cl49__n_Ar49
       +rho*Y[jar52]*rate_eval.p_Ar52__He4_Cl49
       +rho*Y[js49]*rate_eval.p_S49__n_Cl49
       +rho*Y[js48]*rate_eval.p_S48__Cl49
       )

    jac[jcl49, jhe4] = (
       -rho*Y[jcl49]*rate_eval.He4_Cl49__n_K52
       -rho*Y[jcl49]*rate_eval.He4_Cl49__K53
       +rho*Y[jp46]*rate_eval.He4_P46__n_Cl49
       +rho*Y[jp45]*rate_eval.He4_P45__Cl49
       )

    jac[jcl49, jp45] = (
       +rho*Y[jhe4]*rate_eval.He4_P45__Cl49
       )

    jac[jcl49, jp46] = (
       +rho*Y[jhe4]*rate_eval.He4_P46__n_Cl49
       )

    jac[jcl49, js48] = (
       +rho*Y[jp]*rate_eval.p_S48__Cl49
       )

    jac[jcl49, js49] = (
       +rho*Y[jp]*rate_eval.p_S49__n_Cl49
       +rate_eval.S49__Cl49__weak__mo03
       )

    jac[jcl49, jcl48] = (
       +rho*Y[jn]*rate_eval.n_Cl48__Cl49
       )

    jac[jcl49, jcl49] = (
       -rate_eval.Cl49__n_n_Ar47__weak__mp17
       -rate_eval.Cl49__n_Ar48__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Cl49__n_K52
       -rate_eval.Cl49__n_n_n_Ar46__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Cl49__K53
       -rho*Y[jp]*rate_eval.p_Cl49__Ar50
       -rho*Y[jn]*rate_eval.n_Cl49__Cl50
       -rho*Y[jp]*rate_eval.p_Cl49__He4_S46
       -rate_eval.Cl49__Ar49__weak__mo03
       -rho*Y[jp]*rate_eval.p_Cl49__n_Ar49
       )

    jac[jcl49, jar52] = (
       +rho*Y[jp]*rate_eval.p_Ar52__He4_Cl49
       )

    jac[jcl50, jn] = (
       -rho*Y[jcl50]*rate_eval.n_Cl50__Cl51
       +rho*Y[jcl49]*rate_eval.n_Cl49__Cl50
       )

    jac[jcl50, jp] = (
       -rho*Y[jcl50]*rate_eval.p_Cl50__He4_S47
       -rho*Y[jcl50]*rate_eval.p_Cl50__n_Ar50
       -rho*Y[jcl50]*rate_eval.p_Cl50__Ar51
       +rho*Y[js49]*rate_eval.p_S49__Cl50
       +rho*Y[jar53]*rate_eval.p_Ar53__He4_Cl50
       )

    jac[jcl50, jhe4] = (
       -rho*Y[jcl50]*rate_eval.He4_Cl50__K54
       -rho*Y[jcl50]*rate_eval.He4_Cl50__n_K53
       +rho*Y[jp47]*rate_eval.He4_P47__n_Cl50
       +rho*Y[jp46]*rate_eval.He4_P46__Cl50
       )

    jac[jcl50, jp46] = (
       +rho*Y[jhe4]*rate_eval.He4_P46__Cl50
       )

    jac[jcl50, jp47] = (
       +rho*Y[jhe4]*rate_eval.He4_P47__n_Cl50
       )

    jac[jcl50, js49] = (
       +rho*Y[jp]*rate_eval.p_S49__Cl50
       )

    jac[jcl50, jcl49] = (
       +rho*Y[jn]*rate_eval.n_Cl49__Cl50
       )

    jac[jcl50, jcl50] = (
       -rate_eval.Cl50__n_n_n_Ar47__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Cl50__K54
       -rho*Y[jp]*rate_eval.p_Cl50__He4_S47
       -rho*Y[jp]*rate_eval.p_Cl50__n_Ar50
       -rho*Y[jhe4]*rate_eval.He4_Cl50__n_K53
       -rho*Y[jp]*rate_eval.p_Cl50__Ar51
       -rate_eval.Cl50__Ar50__weak__mo03
       -rate_eval.Cl50__n_n_Ar48__weak__mp17
       -rate_eval.Cl50__n_Ar49__weak__mp17
       -rho*Y[jn]*rate_eval.n_Cl50__Cl51
       )

    jac[jcl50, jar53] = (
       +rho*Y[jp]*rate_eval.p_Ar53__He4_Cl50
       )

    jac[jcl51, jn] = (
       -rho*Y[jcl51]*rate_eval.n_Cl51__Cl52
       +rho*Y[jcl50]*rate_eval.n_Cl50__Cl51
       )

    jac[jcl51, jp] = (
       -rho*Y[jcl51]*rate_eval.p_Cl51__He4_S48
       -rho*Y[jcl51]*rate_eval.p_Cl51__Ar52
       -rho*Y[jcl51]*rate_eval.p_Cl51__n_Ar51
       +rho*Y[jar54]*rate_eval.p_Ar54__He4_Cl51
       )

    jac[jcl51, jhe4] = (
       -rho*Y[jcl51]*rate_eval.He4_Cl51__n_K54
       -rho*Y[jcl51]*rate_eval.He4_Cl51__K55
       +rho*Y[jp47]*rate_eval.He4_P47__Cl51
       )

    jac[jcl51, jp47] = (
       +rho*Y[jhe4]*rate_eval.He4_P47__Cl51
       )

    jac[jcl51, jcl50] = (
       +rho*Y[jn]*rate_eval.n_Cl50__Cl51
       )

    jac[jcl51, jcl51] = (
       -rho*Y[jhe4]*rate_eval.He4_Cl51__n_K54
       -rho*Y[jp]*rate_eval.p_Cl51__He4_S48
       -rate_eval.Cl51__Ar51__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Cl51__K55
       -rho*Y[jp]*rate_eval.p_Cl51__Ar52
       -rho*Y[jn]*rate_eval.n_Cl51__Cl52
       -rho*Y[jp]*rate_eval.p_Cl51__n_Ar51
       -rate_eval.Cl51__n_Ar50__weak__mp17
       -rate_eval.Cl51__n_n_Ar49__weak__mp17
       -rate_eval.Cl51__n_n_n_Ar48__weak__mo03
       )

    jac[jcl51, jar54] = (
       +rho*Y[jp]*rate_eval.p_Ar54__He4_Cl51
       )

    jac[jcl52, jn] = (
       +rho*Y[jcl51]*rate_eval.n_Cl51__Cl52
       )

    jac[jcl52, jp] = (
       -rho*Y[jcl52]*rate_eval.p_Cl52__He4_S49
       -rho*Y[jcl52]*rate_eval.p_Cl52__n_Ar52
       -rho*Y[jcl52]*rate_eval.p_Cl52__Ar53
       )

    jac[jcl52, jhe4] = (
       -rho*Y[jcl52]*rate_eval.He4_Cl52__n_K55
       -rho*Y[jcl52]*rate_eval.He4_Cl52__K56
       )

    jac[jcl52, jcl51] = (
       +rho*Y[jn]*rate_eval.n_Cl51__Cl52
       )

    jac[jcl52, jcl52] = (
       -rho*Y[jp]*rate_eval.p_Cl52__He4_S49
       -rho*Y[jp]*rate_eval.p_Cl52__n_Ar52
       -rate_eval.Cl52__n_n_n_Ar49__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Cl52__n_K55
       -rate_eval.Cl52__n_n_Ar50__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Cl52__K56
       -rate_eval.Cl52__n_Ar51__weak__mp17
       -rate_eval.Cl52__Ar52__weak__mo03
       -rho*Y[jp]*rate_eval.p_Cl52__Ar53
       )

    jac[jar29, jn] = (
       -rho*Y[jar29]*rate_eval.n_Ar29__He4_S26
       -rho*Y[jar29]*rate_eval.n_Ar29__p_Cl29
       -rho*Y[jar29]*rate_eval.n_Ar29__Ar30
       )

    jac[jar29, jp] = (
       +rho*Y[jcl28]*rate_eval.p_Cl28__Ar29
       )

    jac[jar29, jhe4] = (
       -rho*Y[jar29]*rate_eval.He4_Ar29__Ca33
       -rho*Y[jar29]*rate_eval.He4_Ar29__p_K32
       )

    jac[jar29, jcl28] = (
       +rho*Y[jp]*rate_eval.p_Cl28__Ar29
       )

    jac[jar29, jar29] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar29__Ca33
       -rho*Y[jhe4]*rate_eval.He4_Ar29__p_K32
       -rho*Y[jn]*rate_eval.n_Ar29__He4_S26
       -rho*Y[jn]*rate_eval.n_Ar29__p_Cl29
       -rho*Y[jn]*rate_eval.n_Ar29__Ar30
       -rate_eval.Ar29__Cl29__weak__bqa_pos_
       )

    jac[jar30, jn] = (
       -rho*Y[jar30]*rate_eval.n_Ar30__He4_S27
       -rho*Y[jar30]*rate_eval.n_Ar30__p_Cl30
       -rho*Y[jar30]*rate_eval.n_Ar30__Ar31
       +rho*Y[jca33]*rate_eval.n_Ca33__He4_Ar30
       +rho*Y[jar29]*rate_eval.n_Ar29__Ar30
       )

    jac[jar30, jp] = (
       -rho*Y[jar30]*rate_eval.p_Ar30__K31
       +rho*Y[jcl29]*rate_eval.p_Cl29__Ar30
       )

    jac[jar30, jhe4] = (
       -rho*Y[jar30]*rate_eval.He4_Ar30__Ca34
       -rho*Y[jar30]*rate_eval.He4_Ar30__p_K33
       +rho*Y[js26]*rate_eval.He4_S26__Ar30
       )

    jac[jar30, js26] = (
       +rho*Y[jhe4]*rate_eval.He4_S26__Ar30
       )

    jac[jar30, jcl29] = (
       +rho*Y[jp]*rate_eval.p_Cl29__Ar30
       )

    jac[jar30, jar29] = (
       +rho*Y[jn]*rate_eval.n_Ar29__Ar30
       )

    jac[jar30, jar30] = (
       -rho*Y[jn]*rate_eval.n_Ar30__He4_S27
       -rho*Y[jn]*rate_eval.n_Ar30__p_Cl30
       -rho*Y[jhe4]*rate_eval.He4_Ar30__Ca34
       -rho*Y[jn]*rate_eval.n_Ar30__Ar31
       -rho*Y[jhe4]*rate_eval.He4_Ar30__p_K33
       -rho*Y[jp]*rate_eval.p_Ar30__K31
       -rate_eval.Ar30__Cl30__weak__bqa_pos_
       )

    jac[jar30, jca33] = (
       +rho*Y[jn]*rate_eval.n_Ca33__He4_Ar30
       )

    jac[jar31, jn] = (
       -rho*Y[jar31]*rate_eval.n_Ar31__He4_S28
       -rho*Y[jar31]*rate_eval.n_Ar31__p_Cl31
       -rho*Y[jar31]*rate_eval.n_Ar31__Ar32
       +rho*Y[jca34]*rate_eval.n_Ca34__He4_Ar31
       +rho*Y[jk31]*rate_eval.n_K31__p_Ar31
       +rho*Y[jar30]*rate_eval.n_Ar30__Ar31
       )

    jac[jar31, jp] = (
       -rho*Y[jar31]*rate_eval.p_Ar31__K32
       +rho*Y[jcl30]*rate_eval.p_Cl30__Ar31
       )

    jac[jar31, jhe4] = (
       -rho*Y[jar31]*rate_eval.He4_Ar31__p_K34
       -rho*Y[jar31]*rate_eval.He4_Ar31__Ca35
       +rho*Y[jcl28]*rate_eval.He4_Cl28__p_Ar31
       +rho*Y[js27]*rate_eval.He4_S27__Ar31
       )

    jac[jar31, js27] = (
       +rho*Y[jhe4]*rate_eval.He4_S27__Ar31
       )

    jac[jar31, jcl28] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl28__p_Ar31
       )

    jac[jar31, jcl30] = (
       +rho*Y[jp]*rate_eval.p_Cl30__Ar31
       )

    jac[jar31, jar30] = (
       +rho*Y[jn]*rate_eval.n_Ar30__Ar31
       )

    jac[jar31, jar31] = (
       -rho*Y[jn]*rate_eval.n_Ar31__He4_S28
       -rho*Y[jhe4]*rate_eval.He4_Ar31__p_K34
       -rho*Y[jn]*rate_eval.n_Ar31__p_Cl31
       -rho*Y[jhe4]*rate_eval.He4_Ar31__Ca35
       -rho*Y[jp]*rate_eval.p_Ar31__K32
       -rho*Y[jn]*rate_eval.n_Ar31__Ar32
       -rate_eval.Ar31__p_S30__weak__wc17
       -rate_eval.Ar31__Cl31__weak__wc12
       -rate_eval.Ar31__p_p_P29__weak__wc12
       )

    jac[jar31, jk31] = (
       +rho*Y[jn]*rate_eval.n_K31__p_Ar31
       +rate_eval.K31__Ar31__weak__bqa_pos_
       )

    jac[jar31, jca34] = (
       +rho*Y[jn]*rate_eval.n_Ca34__He4_Ar31
       )

    jac[jar32, jn] = (
       -rho*Y[jar32]*rate_eval.n_Ar32__He4_S29
       -rho*Y[jar32]*rate_eval.n_Ar32__p_Cl32
       -rho*Y[jar32]*rate_eval.n_Ar32__Ar33
       +rho*Y[jca35]*rate_eval.n_Ca35__He4_Ar32
       +rho*Y[jk32]*rate_eval.n_K32__p_Ar32
       +rho*Y[jar31]*rate_eval.n_Ar31__Ar32
       )

    jac[jar32, jp] = (
       -rho*Y[jar32]*rate_eval.p_Ar32__K33
       +rho*Y[jcl31]*rate_eval.p_Cl31__Ar32
       )

    jac[jar32, jhe4] = (
       -rho*Y[jar32]*rate_eval.He4_Ar32__Ca36
       -rho*Y[jar32]*rate_eval.He4_Ar32__p_K35
       +rho*Y[jcl29]*rate_eval.He4_Cl29__p_Ar32
       +rho*Y[js28]*rate_eval.He4_S28__Ar32
       )

    jac[jar32, js28] = (
       +rho*Y[jhe4]*rate_eval.He4_S28__Ar32
       )

    jac[jar32, jcl29] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl29__p_Ar32
       )

    jac[jar32, jcl31] = (
       +rho*Y[jp]*rate_eval.p_Cl31__Ar32
       )

    jac[jar32, jar31] = (
       +rho*Y[jn]*rate_eval.n_Ar31__Ar32
       )

    jac[jar32, jar32] = (
       -rho*Y[jn]*rate_eval.n_Ar32__He4_S29
       -rho*Y[jn]*rate_eval.n_Ar32__p_Cl32
       -rho*Y[jhe4]*rate_eval.He4_Ar32__Ca36
       -rho*Y[jp]*rate_eval.p_Ar32__K33
       -rho*Y[jn]*rate_eval.n_Ar32__Ar33
       -rate_eval.Ar32__p_S31__weak__wc12
       -rate_eval.Ar32__Cl32__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ar32__p_K35
       )

    jac[jar32, jk32] = (
       +rate_eval.K32__Ar32__weak__bqa_pos_
       +rho*Y[jn]*rate_eval.n_K32__p_Ar32
       )

    jac[jar32, jca35] = (
       +rho*Y[jn]*rate_eval.n_Ca35__He4_Ar32
       )

    jac[jar33, jn] = (
       -rho*Y[jar33]*rate_eval.n_Ar33__p_Cl33
       -rho*Y[jar33]*rate_eval.n_Ar33__Ar34
       -rho*Y[jar33]*rate_eval.n_Ar33__He4_S30
       +rho*Y[jk33]*rate_eval.n_K33__p_Ar33
       +rho*Y[jca36]*rate_eval.n_Ca36__He4_Ar33
       +rho*Y[jar32]*rate_eval.n_Ar32__Ar33
       )

    jac[jar33, jp] = (
       -rho*Y[jar33]*rate_eval.p_Ar33__K34
       +rho*Y[jcl32]*rate_eval.p_Cl32__Ar33
       )

    jac[jar33, jhe4] = (
       -rho*Y[jar33]*rate_eval.He4_Ar33__p_K36
       -rho*Y[jar33]*rate_eval.He4_Ar33__Ca37
       +rho*Y[jcl30]*rate_eval.He4_Cl30__p_Ar33
       +rho*Y[js29]*rate_eval.He4_S29__Ar33
       )

    jac[jar33, js29] = (
       +rho*Y[jhe4]*rate_eval.He4_S29__Ar33
       )

    jac[jar33, jcl30] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl30__p_Ar33
       )

    jac[jar33, jcl32] = (
       +rho*Y[jp]*rate_eval.p_Cl32__Ar33
       )

    jac[jar33, jar32] = (
       +rho*Y[jn]*rate_eval.n_Ar32__Ar33
       )

    jac[jar33, jar33] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar33__p_K36
       -rho*Y[jn]*rate_eval.n_Ar33__p_Cl33
       -rho*Y[jhe4]*rate_eval.He4_Ar33__Ca37
       -rho*Y[jp]*rate_eval.p_Ar33__K34
       -rho*Y[jn]*rate_eval.n_Ar33__Ar34
       -rate_eval.Ar33__p_S32__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ar33__He4_S30
       -rate_eval.Ar33__Cl33__weak__wc12
       )

    jac[jar33, jk33] = (
       +rho*Y[jn]*rate_eval.n_K33__p_Ar33
       +rate_eval.K33__Ar33__weak__bqa_pos_
       )

    jac[jar33, jca36] = (
       +rho*Y[jn]*rate_eval.n_Ca36__He4_Ar33
       )

    jac[jar34, jn] = (
       -rho*Y[jar34]*rate_eval.n_Ar34__p_Cl34
       -rho*Y[jar34]*rate_eval.n_Ar34__Ar35
       -rho*Y[jar34]*rate_eval.n_Ar34__He4_S31
       +rho*Y[jca37]*rate_eval.n_Ca37__He4_Ar34
       +rho*Y[jar33]*rate_eval.n_Ar33__Ar34
       +rho*Y[jk34]*rate_eval.n_K34__p_Ar34
       )

    jac[jar34, jp] = (
       -rho*Y[jar34]*rate_eval.p_Ar34__K35
       +rho*Y[jcl33]*rate_eval.p_Cl33__Ar34
       )

    jac[jar34, jhe4] = (
       -rho*Y[jar34]*rate_eval.He4_Ar34__p_K37
       -rho*Y[jar34]*rate_eval.He4_Ar34__Ca38
       +rho*Y[js30]*rate_eval.He4_S30__Ar34
       +rho*Y[jcl31]*rate_eval.He4_Cl31__p_Ar34
       )

    jac[jar34, js30] = (
       +rho*Y[jhe4]*rate_eval.He4_S30__Ar34
       )

    jac[jar34, jcl31] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl31__p_Ar34
       )

    jac[jar34, jcl33] = (
       +rho*Y[jp]*rate_eval.p_Cl33__Ar34
       )

    jac[jar34, jar33] = (
       +rho*Y[jn]*rate_eval.n_Ar33__Ar34
       )

    jac[jar34, jar34] = (
       -rho*Y[jp]*rate_eval.p_Ar34__K35
       -rho*Y[jhe4]*rate_eval.He4_Ar34__p_K37
       -rho*Y[jn]*rate_eval.n_Ar34__p_Cl34
       -rho*Y[jn]*rate_eval.n_Ar34__Ar35
       -rho*Y[jn]*rate_eval.n_Ar34__He4_S31
       -rho*Y[jhe4]*rate_eval.He4_Ar34__Ca38
       -rate_eval.Ar34__Cl34__weak__wc12
       )

    jac[jar34, jk34] = (
       +rho*Y[jn]*rate_eval.n_K34__p_Ar34
       +rate_eval.K34__Ar34__weak__bqa_pos_
       )

    jac[jar34, jca35] = (
       +rate_eval.Ca35__p_Ar34__weak__wc17
       )

    jac[jar34, jca37] = (
       +rho*Y[jn]*rate_eval.n_Ca37__He4_Ar34
       )

    jac[jar35, jn] = (
       -rho*Y[jar35]*rate_eval.n_Ar35__He4_S32
       -rho*Y[jar35]*rate_eval.n_Ar35__p_Cl35
       -rho*Y[jar35]*rate_eval.n_Ar35__Ar36
       +rho*Y[jk35]*rate_eval.n_K35__p_Ar35
       +rho*Y[jar34]*rate_eval.n_Ar34__Ar35
       +rho*Y[jca38]*rate_eval.n_Ca38__He4_Ar35
       )

    jac[jar35, jp] = (
       -rho*Y[jar35]*rate_eval.p_Ar35__K36
       +rho*Y[jcl34]*rate_eval.p_Cl34__Ar35
       )

    jac[jar35, jhe4] = (
       -rho*Y[jar35]*rate_eval.He4_Ar35__Ca39
       -rho*Y[jar35]*rate_eval.He4_Ar35__p_K38
       +rho*Y[jcl32]*rate_eval.He4_Cl32__p_Ar35
       +rho*Y[js31]*rate_eval.He4_S31__Ar35
       )

    jac[jar35, js31] = (
       +rho*Y[jhe4]*rate_eval.He4_S31__Ar35
       )

    jac[jar35, jcl32] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl32__p_Ar35
       )

    jac[jar35, jcl34] = (
       +rho*Y[jp]*rate_eval.p_Cl34__Ar35
       )

    jac[jar35, jar34] = (
       +rho*Y[jn]*rate_eval.n_Ar34__Ar35
       )

    jac[jar35, jar35] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar35__Ca39
       -rho*Y[jn]*rate_eval.n_Ar35__He4_S32
       -rho*Y[jn]*rate_eval.n_Ar35__p_Cl35
       -rho*Y[jhe4]*rate_eval.He4_Ar35__p_K38
       -rho*Y[jn]*rate_eval.n_Ar35__Ar36
       -rho*Y[jp]*rate_eval.p_Ar35__K36
       -rate_eval.Ar35__Cl35__weak__wc12
       )

    jac[jar35, jk35] = (
       +rho*Y[jn]*rate_eval.n_K35__p_Ar35
       +rate_eval.K35__Ar35__weak__wc12
       )

    jac[jar35, jca36] = (
       +rate_eval.Ca36__p_Ar35__weak__wc12
       )

    jac[jar35, jca38] = (
       +rho*Y[jn]*rate_eval.n_Ca38__He4_Ar35
       )

    jac[jar36, jn] = (
       -rho*Y[jar36]*rate_eval.n_Ar36__He4_S33
       -rho*Y[jar36]*rate_eval.n_Ar36__Ar37
       -rho*Y[jar36]*rate_eval.n_Ar36__p_Cl36
       +rho*Y[jk36]*rate_eval.n_K36__p_Ar36
       +rho*Y[jar35]*rate_eval.n_Ar35__Ar36
       +rho*Y[jca39]*rate_eval.n_Ca39__He4_Ar36
       )

    jac[jar36, jp] = (
       -rho*Y[jar36]*rate_eval.p_Ar36__K37
       +rho*Y[jcl35]*rate_eval.p_Cl35__Ar36
       +rho*Y[jk39]*rate_eval.p_K39__He4_Ar36
       )

    jac[jar36, jhe4] = (
       -rho*Y[jar36]*rate_eval.He4_Ar36__Ca40
       +rho*Y[js32]*rate_eval.He4_S32__Ar36
       +rho*Y[jcl33]*rate_eval.He4_Cl33__p_Ar36
       )

    jac[jar36, js32] = (
       +rho*Y[jhe4]*rate_eval.He4_S32__Ar36
       )

    jac[jar36, jcl33] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl33__p_Ar36
       )

    jac[jar36, jcl35] = (
       +rho*Y[jp]*rate_eval.p_Cl35__Ar36
       )

    jac[jar36, jcl36] = (
       +rate_eval.Cl36__Ar36__weak__wc12
       )

    jac[jar36, jar35] = (
       +rho*Y[jn]*rate_eval.n_Ar35__Ar36
       )

    jac[jar36, jar36] = (
       -rho*Y[jn]*rate_eval.n_Ar36__He4_S33
       -rho*Y[jhe4]*rate_eval.He4_Ar36__Ca40
       -rho*Y[jp]*rate_eval.p_Ar36__K37
       -rho*Y[jn]*rate_eval.n_Ar36__Ar37
       -rho*Y[jn]*rate_eval.n_Ar36__p_Cl36
       )

    jac[jar36, jk36] = (
       +rho*Y[jn]*rate_eval.n_K36__p_Ar36
       +rate_eval.K36__Ar36__weak__wc12
       )

    jac[jar36, jk39] = (
       +rho*Y[jp]*rate_eval.p_K39__He4_Ar36
       )

    jac[jar36, jca37] = (
       +rate_eval.Ca37__p_Ar36__weak__wc12
       )

    jac[jar36, jca39] = (
       +rho*Y[jn]*rate_eval.n_Ca39__He4_Ar36
       )

    jac[jar36, jsc40] = (
       +rate_eval.Sc40__He4_Ar36__weak__wc12
       )

    jac[jar37, jn] = (
       -rho*Y[jar37]*rate_eval.n_Ar37__p_Cl37
       -rho*Y[jar37]*rate_eval.n_Ar37__Ar38
       +rho*Y[jca40]*rate_eval.n_Ca40__He4_Ar37
       +rho*Y[jk37]*rate_eval.n_K37__p_Ar37
       +rho*Y[jar36]*rate_eval.n_Ar36__Ar37
       )

    jac[jar37, jp] = (
       -rho*Y[jar37]*rate_eval.p_Ar37__K38
       +rho*Y[jk40]*rate_eval.p_K40__He4_Ar37
       +rho*Y[jcl36]*rate_eval.p_Cl36__Ar37
       )

    jac[jar37, jhe4] = (
       -rho*Y[jar37]*rate_eval.He4_Ar37__Ca41
       +rho*Y[jcl34]*rate_eval.He4_Cl34__p_Ar37
       +rho*Y[js33]*rate_eval.He4_S33__Ar37
       +rho*Y[js34]*rate_eval.He4_S34__n_Ar37
       )

    jac[jar37, js33] = (
       +rho*Y[jhe4]*rate_eval.He4_S33__Ar37
       )

    jac[jar37, js34] = (
       +rho*Y[jhe4]*rate_eval.He4_S34__n_Ar37
       )

    jac[jar37, jcl34] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl34__p_Ar37
       )

    jac[jar37, jcl36] = (
       +rho*Y[jp]*rate_eval.p_Cl36__Ar37
       )

    jac[jar37, jar36] = (
       +rho*Y[jn]*rate_eval.n_Ar36__Ar37
       )

    jac[jar37, jar37] = (
       -rho*Y[jn]*rate_eval.n_Ar37__p_Cl37
       -rho*Y[jhe4]*rate_eval.He4_Ar37__Ca41
       -rho*Y[jp]*rate_eval.p_Ar37__K38
       -rho*Y[jn]*rate_eval.n_Ar37__Ar38
       -rate_eval.Ar37__Cl37__weak__wc12
       )

    jac[jar37, jk37] = (
       +rho*Y[jn]*rate_eval.n_K37__p_Ar37
       +rate_eval.K37__Ar37__weak__wc12
       )

    jac[jar37, jk40] = (
       +rho*Y[jp]*rate_eval.p_K40__He4_Ar37
       )

    jac[jar37, jca40] = (
       +rho*Y[jn]*rate_eval.n_Ca40__He4_Ar37
       )

    jac[jar38, jn] = (
       -rho*Y[jar38]*rate_eval.n_Ar38__Ar39
       +rho*Y[jk38]*rate_eval.n_K38__p_Ar38
       +rho*Y[jca41]*rate_eval.n_Ca41__He4_Ar38
       +rho*Y[jar37]*rate_eval.n_Ar37__Ar38
       )

    jac[jar38, jp] = (
       -rho*Y[jar38]*rate_eval.p_Ar38__K39
       +rho*Y[jk41]*rate_eval.p_K41__He4_Ar38
       +rho*Y[jcl38]*rate_eval.p_Cl38__n_Ar38
       +rho*Y[jcl37]*rate_eval.p_Cl37__Ar38
       )

    jac[jar38, jhe4] = (
       -rho*Y[jar38]*rate_eval.He4_Ar38__Ca42
       +rho*Y[js35]*rate_eval.He4_S35__n_Ar38
       +rho*Y[jcl35]*rate_eval.He4_Cl35__p_Ar38
       +rho*Y[js34]*rate_eval.He4_S34__Ar38
       )

    jac[jar38, js34] = (
       +rho*Y[jhe4]*rate_eval.He4_S34__Ar38
       )

    jac[jar38, js35] = (
       +rho*Y[jhe4]*rate_eval.He4_S35__n_Ar38
       )

    jac[jar38, jcl35] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl35__p_Ar38
       )

    jac[jar38, jcl37] = (
       +rho*Y[jp]*rate_eval.p_Cl37__Ar38
       )

    jac[jar38, jcl38] = (
       +rho*Y[jp]*rate_eval.p_Cl38__n_Ar38
       +rate_eval.Cl38__Ar38__weak__wc12
       )

    jac[jar38, jar37] = (
       +rho*Y[jn]*rate_eval.n_Ar37__Ar38
       )

    jac[jar38, jar38] = (
       -rho*Y[jp]*rate_eval.p_Ar38__K39
       -rho*Y[jn]*rate_eval.n_Ar38__Ar39
       -rho*Y[jhe4]*rate_eval.He4_Ar38__Ca42
       )

    jac[jar38, jk38] = (
       +rho*Y[jn]*rate_eval.n_K38__p_Ar38
       +rate_eval.K38__Ar38__weak__wc12
       )

    jac[jar38, jk41] = (
       +rho*Y[jp]*rate_eval.p_K41__He4_Ar38
       )

    jac[jar38, jca41] = (
       +rho*Y[jn]*rate_eval.n_Ca41__He4_Ar38
       )

    jac[jar39, jn] = (
       -rho*Y[jar39]*rate_eval.n_Ar39__He4_S36
       -rho*Y[jar39]*rate_eval.n_Ar39__Ar40
       +rho*Y[jk39]*rate_eval.n_K39__p_Ar39
       +rho*Y[jar38]*rate_eval.n_Ar38__Ar39
       +rho*Y[jca42]*rate_eval.n_Ca42__He4_Ar39
       )

    jac[jar39, jp] = (
       -rho*Y[jar39]*rate_eval.p_Ar39__He4_Cl36
       -rho*Y[jar39]*rate_eval.p_Ar39__K40
       +rho*Y[jk42]*rate_eval.p_K42__He4_Ar39
       +rho*Y[jcl39]*rate_eval.p_Cl39__n_Ar39
       +rho*Y[jcl38]*rate_eval.p_Cl38__Ar39
       )

    jac[jar39, jhe4] = (
       -rho*Y[jar39]*rate_eval.He4_Ar39__Ca43
       +rho*Y[js35]*rate_eval.He4_S35__Ar39
       )

    jac[jar39, js35] = (
       +rho*Y[jhe4]*rate_eval.He4_S35__Ar39
       )

    jac[jar39, jcl38] = (
       +rho*Y[jp]*rate_eval.p_Cl38__Ar39
       )

    jac[jar39, jcl39] = (
       +rate_eval.Cl39__Ar39__weak__wc12
       +rho*Y[jp]*rate_eval.p_Cl39__n_Ar39
       )

    jac[jar39, jar38] = (
       +rho*Y[jn]*rate_eval.n_Ar38__Ar39
       )

    jac[jar39, jar39] = (
       -rho*Y[jp]*rate_eval.p_Ar39__He4_Cl36
       -rho*Y[jn]*rate_eval.n_Ar39__He4_S36
       -rho*Y[jn]*rate_eval.n_Ar39__Ar40
       -rho*Y[jhe4]*rate_eval.He4_Ar39__Ca43
       -rate_eval.Ar39__K39__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ar39__K40
       )

    jac[jar39, jk39] = (
       +rho*Y[jn]*rate_eval.n_K39__p_Ar39
       )

    jac[jar39, jk42] = (
       +rho*Y[jp]*rate_eval.p_K42__He4_Ar39
       )

    jac[jar39, jca42] = (
       +rho*Y[jn]*rate_eval.n_Ca42__He4_Ar39
       )

    jac[jar40, jn] = (
       -rho*Y[jar40]*rate_eval.n_Ar40__Ar41
       +rho*Y[jk40]*rate_eval.n_K40__p_Ar40
       +rho*Y[jca43]*rate_eval.n_Ca43__He4_Ar40
       +rho*Y[jar39]*rate_eval.n_Ar39__Ar40
       )

    jac[jar40, jp] = (
       -rho*Y[jar40]*rate_eval.p_Ar40__He4_Cl37
       -rho*Y[jar40]*rate_eval.p_Ar40__K41
       +rho*Y[jcl40]*rate_eval.p_Cl40__n_Ar40
       +rho*Y[jcl39]*rate_eval.p_Cl39__Ar40
       +rho*Y[jk43]*rate_eval.p_K43__He4_Ar40
       )

    jac[jar40, jhe4] = (
       -rho*Y[jar40]*rate_eval.He4_Ar40__Ca44
       +rho*Y[js37]*rate_eval.He4_S37__n_Ar40
       +rho*Y[js36]*rate_eval.He4_S36__Ar40
       )

    jac[jar40, js36] = (
       +rho*Y[jhe4]*rate_eval.He4_S36__Ar40
       )

    jac[jar40, js37] = (
       +rho*Y[jhe4]*rate_eval.He4_S37__n_Ar40
       )

    jac[jar40, jcl39] = (
       +rho*Y[jp]*rate_eval.p_Cl39__Ar40
       )

    jac[jar40, jcl40] = (
       +rho*Y[jp]*rate_eval.p_Cl40__n_Ar40
       +rate_eval.Cl40__Ar40__weak__wc12
       )

    jac[jar40, jar39] = (
       +rho*Y[jn]*rate_eval.n_Ar39__Ar40
       )

    jac[jar40, jar40] = (
       -rho*Y[jp]*rate_eval.p_Ar40__He4_Cl37
       -rho*Y[jhe4]*rate_eval.He4_Ar40__Ca44
       -rho*Y[jp]*rate_eval.p_Ar40__K41
       -rho*Y[jn]*rate_eval.n_Ar40__Ar41
       )

    jac[jar40, jk40] = (
       +rho*Y[jn]*rate_eval.n_K40__p_Ar40
       +rate_eval.K40__Ar40__weak__wc12
       )

    jac[jar40, jk43] = (
       +rho*Y[jp]*rate_eval.p_K43__He4_Ar40
       )

    jac[jar40, jca43] = (
       +rho*Y[jn]*rate_eval.n_Ca43__He4_Ar40
       )

    jac[jar41, jn] = (
       -rho*Y[jar41]*rate_eval.n_Ar41__Ar42
       +rho*Y[jar40]*rate_eval.n_Ar40__Ar41
       )

    jac[jar41, jp] = (
       -rho*Y[jar41]*rate_eval.p_Ar41__n_K41
       -rho*Y[jar41]*rate_eval.p_Ar41__K42
       -rho*Y[jar41]*rate_eval.p_Ar41__He4_Cl38
       +rho*Y[jk44]*rate_eval.p_K44__He4_Ar41
       +rho*Y[jcl40]*rate_eval.p_Cl40__Ar41
       +rho*Y[jcl41]*rate_eval.p_Cl41__n_Ar41
       )

    jac[jar41, jhe4] = (
       -rho*Y[jar41]*rate_eval.He4_Ar41__n_Ca44
       -rho*Y[jar41]*rate_eval.He4_Ar41__Ca45
       +rho*Y[js38]*rate_eval.He4_S38__n_Ar41
       +rho*Y[js37]*rate_eval.He4_S37__Ar41
       )

    jac[jar41, js37] = (
       +rho*Y[jhe4]*rate_eval.He4_S37__Ar41
       )

    jac[jar41, js38] = (
       +rho*Y[jhe4]*rate_eval.He4_S38__n_Ar41
       )

    jac[jar41, jcl40] = (
       +rho*Y[jp]*rate_eval.p_Cl40__Ar41
       )

    jac[jar41, jcl41] = (
       +rate_eval.Cl41__Ar41__weak__wc12
       +rho*Y[jp]*rate_eval.p_Cl41__n_Ar41
       )

    jac[jar41, jar40] = (
       +rho*Y[jn]*rate_eval.n_Ar40__Ar41
       )

    jac[jar41, jar41] = (
       -rho*Y[jp]*rate_eval.p_Ar41__n_K41
       -rho*Y[jhe4]*rate_eval.He4_Ar41__n_Ca44
       -rho*Y[jp]*rate_eval.p_Ar41__K42
       -rho*Y[jhe4]*rate_eval.He4_Ar41__Ca45
       -rho*Y[jp]*rate_eval.p_Ar41__He4_Cl38
       -rho*Y[jn]*rate_eval.n_Ar41__Ar42
       -rate_eval.Ar41__K41__weak__wc12
       )

    jac[jar41, jk44] = (
       +rho*Y[jp]*rate_eval.p_K44__He4_Ar41
       )

    jac[jar42, jn] = (
       -rho*Y[jar42]*rate_eval.n_Ar42__Ar43
       +rho*Y[jar41]*rate_eval.n_Ar41__Ar42
       +rho*Y[jk42]*rate_eval.n_K42__p_Ar42
       )

    jac[jar42, jp] = (
       -rho*Y[jar42]*rate_eval.p_Ar42__K43
       -rho*Y[jar42]*rate_eval.p_Ar42__He4_Cl39
       +rho*Y[jk45]*rate_eval.p_K45__He4_Ar42
       +rho*Y[jcl42]*rate_eval.p_Cl42__n_Ar42
       +rho*Y[jcl41]*rate_eval.p_Cl41__Ar42
       )

    jac[jar42, jhe4] = (
       -rho*Y[jar42]*rate_eval.He4_Ar42__n_Ca45
       -rho*Y[jar42]*rate_eval.He4_Ar42__Ca46
       +rho*Y[js39]*rate_eval.He4_S39__n_Ar42
       +rho*Y[js38]*rate_eval.He4_S38__Ar42
       )

    jac[jar42, js38] = (
       +rho*Y[jhe4]*rate_eval.He4_S38__Ar42
       )

    jac[jar42, js39] = (
       +rho*Y[jhe4]*rate_eval.He4_S39__n_Ar42
       )

    jac[jar42, jcl41] = (
       +rho*Y[jp]*rate_eval.p_Cl41__Ar42
       )

    jac[jar42, jcl42] = (
       +rho*Y[jp]*rate_eval.p_Cl42__n_Ar42
       +rate_eval.Cl42__Ar42__weak__wc12
       )

    jac[jar42, jcl43] = (
       +rate_eval.Cl43__n_Ar42__weak__mp17
       )

    jac[jar42, jar41] = (
       +rho*Y[jn]*rate_eval.n_Ar41__Ar42
       )

    jac[jar42, jar42] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar42__n_Ca45
       -rho*Y[jp]*rate_eval.p_Ar42__K43
       -rho*Y[jn]*rate_eval.n_Ar42__Ar43
       -rho*Y[jhe4]*rate_eval.He4_Ar42__Ca46
       -rho*Y[jp]*rate_eval.p_Ar42__He4_Cl39
       -rate_eval.Ar42__K42__weak__wc12
       )

    jac[jar42, jk42] = (
       +rho*Y[jn]*rate_eval.n_K42__p_Ar42
       )

    jac[jar42, jk45] = (
       +rho*Y[jp]*rate_eval.p_K45__He4_Ar42
       )

    jac[jar43, jn] = (
       -rho*Y[jar43]*rate_eval.n_Ar43__Ar44
       +rho*Y[jar42]*rate_eval.n_Ar42__Ar43
       )

    jac[jar43, jp] = (
       -rho*Y[jar43]*rate_eval.p_Ar43__n_K43
       -rho*Y[jar43]*rate_eval.p_Ar43__He4_Cl40
       -rho*Y[jar43]*rate_eval.p_Ar43__K44
       +rho*Y[jcl43]*rate_eval.p_Cl43__n_Ar43
       +rho*Y[jcl42]*rate_eval.p_Cl42__Ar43
       +rho*Y[jk46]*rate_eval.p_K46__He4_Ar43
       )

    jac[jar43, jhe4] = (
       -rho*Y[jar43]*rate_eval.He4_Ar43__n_Ca46
       -rho*Y[jar43]*rate_eval.He4_Ar43__Ca47
       +rho*Y[js39]*rate_eval.He4_S39__Ar43
       +rho*Y[js40]*rate_eval.He4_S40__n_Ar43
       )

    jac[jar43, js39] = (
       +rho*Y[jhe4]*rate_eval.He4_S39__Ar43
       )

    jac[jar43, js40] = (
       +rho*Y[jhe4]*rate_eval.He4_S40__n_Ar43
       )

    jac[jar43, jcl42] = (
       +rho*Y[jp]*rate_eval.p_Cl42__Ar43
       )

    jac[jar43, jcl43] = (
       +rho*Y[jp]*rate_eval.p_Cl43__n_Ar43
       +rate_eval.Cl43__Ar43__weak__wc12
       )

    jac[jar43, jcl44] = (
       +rate_eval.Cl44__n_Ar43__weak__mp17
       )

    jac[jar43, jar42] = (
       +rho*Y[jn]*rate_eval.n_Ar42__Ar43
       )

    jac[jar43, jar43] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar43__n_Ca46
       -rho*Y[jp]*rate_eval.p_Ar43__n_K43
       -rho*Y[jp]*rate_eval.p_Ar43__He4_Cl40
       -rho*Y[jhe4]*rate_eval.He4_Ar43__Ca47
       -rho*Y[jp]*rate_eval.p_Ar43__K44
       -rho*Y[jn]*rate_eval.n_Ar43__Ar44
       -rate_eval.Ar43__K43__weak__wc12
       )

    jac[jar43, jk46] = (
       +rho*Y[jp]*rate_eval.p_K46__He4_Ar43
       )

    jac[jar44, jn] = (
       -rho*Y[jar44]*rate_eval.n_Ar44__Ar45
       +rho*Y[jar43]*rate_eval.n_Ar43__Ar44
       )

    jac[jar44, jp] = (
       -rho*Y[jar44]*rate_eval.p_Ar44__n_K44
       -rho*Y[jar44]*rate_eval.p_Ar44__K45
       +rho*Y[jk47]*rate_eval.p_K47__He4_Ar44
       +rho*Y[jcl43]*rate_eval.p_Cl43__Ar44
       +rho*Y[jcl44]*rate_eval.p_Cl44__n_Ar44
       )

    jac[jar44, jhe4] = (
       -rho*Y[jar44]*rate_eval.He4_Ar44__n_Ca47
       -rho*Y[jar44]*rate_eval.He4_Ar44__Ca48
       +rho*Y[js41]*rate_eval.He4_S41__n_Ar44
       +rho*Y[jcl41]*rate_eval.He4_Cl41__p_Ar44
       +rho*Y[js40]*rate_eval.He4_S40__Ar44
       )

    jac[jar44, js40] = (
       +rho*Y[jhe4]*rate_eval.He4_S40__Ar44
       )

    jac[jar44, js41] = (
       +rho*Y[jhe4]*rate_eval.He4_S41__n_Ar44
       )

    jac[jar44, jcl41] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl41__p_Ar44
       )

    jac[jar44, jcl43] = (
       +rho*Y[jp]*rate_eval.p_Cl43__Ar44
       )

    jac[jar44, jcl44] = (
       +rho*Y[jp]*rate_eval.p_Cl44__n_Ar44
       +rate_eval.Cl44__Ar44__weak__wc17
       )

    jac[jar44, jcl45] = (
       +rate_eval.Cl45__n_Ar44__weak__wc12
       )

    jac[jar44, jar43] = (
       +rho*Y[jn]*rate_eval.n_Ar43__Ar44
       )

    jac[jar44, jar44] = (
       -rho*Y[jp]*rate_eval.p_Ar44__n_K44
       -rho*Y[jp]*rate_eval.p_Ar44__K45
       -rho*Y[jn]*rate_eval.n_Ar44__Ar45
       -rho*Y[jhe4]*rate_eval.He4_Ar44__n_Ca47
       -rho*Y[jhe4]*rate_eval.He4_Ar44__Ca48
       -rate_eval.Ar44__K44__weak__wc12
       )

    jac[jar44, jk47] = (
       +rho*Y[jp]*rate_eval.p_K47__He4_Ar44
       )

    jac[jar45, jn] = (
       -rho*Y[jar45]*rate_eval.n_Ar45__Ar46
       +rho*Y[jar44]*rate_eval.n_Ar44__Ar45
       )

    jac[jar45, jp] = (
       -rho*Y[jar45]*rate_eval.p_Ar45__He4_Cl42
       -rho*Y[jar45]*rate_eval.p_Ar45__n_K45
       -rho*Y[jar45]*rate_eval.p_Ar45__K46
       +rho*Y[jk48]*rate_eval.p_K48__He4_Ar45
       +rho*Y[jcl45]*rate_eval.p_Cl45__n_Ar45
       +rho*Y[jcl44]*rate_eval.p_Cl44__Ar45
       )

    jac[jar45, jhe4] = (
       -rho*Y[jar45]*rate_eval.He4_Ar45__Ca49
       -rho*Y[jar45]*rate_eval.He4_Ar45__n_Ca48
       +rho*Y[js42]*rate_eval.He4_S42__n_Ar45
       +rho*Y[js41]*rate_eval.He4_S41__Ar45
       )

    jac[jar45, js41] = (
       +rho*Y[jhe4]*rate_eval.He4_S41__Ar45
       )

    jac[jar45, js42] = (
       +rho*Y[jhe4]*rate_eval.He4_S42__n_Ar45
       )

    jac[jar45, jcl44] = (
       +rho*Y[jp]*rate_eval.p_Cl44__Ar45
       )

    jac[jar45, jcl45] = (
       +rho*Y[jp]*rate_eval.p_Cl45__n_Ar45
       +rate_eval.Cl45__Ar45__weak__wc12
       )

    jac[jar45, jcl46] = (
       +rate_eval.Cl46__n_Ar45__weak__wc12
       )

    jac[jar45, jcl47] = (
       +rate_eval.Cl47__n_n_Ar45__weak__mp17
       )

    jac[jar45, jar44] = (
       +rho*Y[jn]*rate_eval.n_Ar44__Ar45
       )

    jac[jar45, jar45] = (
       -rho*Y[jp]*rate_eval.p_Ar45__He4_Cl42
       -rho*Y[jp]*rate_eval.p_Ar45__n_K45
       -rho*Y[jhe4]*rate_eval.He4_Ar45__Ca49
       -rho*Y[jn]*rate_eval.n_Ar45__Ar46
       -rate_eval.Ar45__K45__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ar45__n_Ca48
       -rho*Y[jp]*rate_eval.p_Ar45__K46
       )

    jac[jar45, jk48] = (
       +rho*Y[jp]*rate_eval.p_K48__He4_Ar45
       )

    jac[jar46, jn] = (
       -rho*Y[jar46]*rate_eval.n_Ar46__Ar47
       +rho*Y[jar45]*rate_eval.n_Ar45__Ar46
       )

    jac[jar46, jp] = (
       -rho*Y[jar46]*rate_eval.p_Ar46__K47
       -rho*Y[jar46]*rate_eval.p_Ar46__n_K46
       +rho*Y[jcl45]*rate_eval.p_Cl45__Ar46
       +rho*Y[jcl46]*rate_eval.p_Cl46__n_Ar46
       +rho*Y[jk49]*rate_eval.p_K49__He4_Ar46
       )

    jac[jar46, jhe4] = (
       -rho*Y[jar46]*rate_eval.He4_Ar46__n_Ca49
       -rho*Y[jar46]*rate_eval.He4_Ar46__Ca50
       +rho*Y[jcl43]*rate_eval.He4_Cl43__p_Ar46
       +rho*Y[js43]*rate_eval.He4_S43__n_Ar46
       +rho*Y[js42]*rate_eval.He4_S42__Ar46
       )

    jac[jar46, js42] = (
       +rho*Y[jhe4]*rate_eval.He4_S42__Ar46
       )

    jac[jar46, js43] = (
       +rho*Y[jhe4]*rate_eval.He4_S43__n_Ar46
       )

    jac[jar46, jcl43] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl43__p_Ar46
       )

    jac[jar46, jcl45] = (
       +rho*Y[jp]*rate_eval.p_Cl45__Ar46
       )

    jac[jar46, jcl46] = (
       +rho*Y[jp]*rate_eval.p_Cl46__n_Ar46
       +rate_eval.Cl46__Ar46__weak__wc12
       )

    jac[jar46, jcl47] = (
       +rate_eval.Cl47__n_Ar46__weak__wc12
       )

    jac[jar46, jcl48] = (
       +rate_eval.Cl48__n_n_Ar46__weak__mp17
       )

    jac[jar46, jcl49] = (
       +rate_eval.Cl49__n_n_n_Ar46__weak__mo03
       )

    jac[jar46, jar45] = (
       +rho*Y[jn]*rate_eval.n_Ar45__Ar46
       )

    jac[jar46, jar46] = (
       -rho*Y[jhe4]*rate_eval.He4_Ar46__n_Ca49
       -rho*Y[jhe4]*rate_eval.He4_Ar46__Ca50
       -rho*Y[jn]*rate_eval.n_Ar46__Ar47
       -rho*Y[jp]*rate_eval.p_Ar46__K47
       -rate_eval.Ar46__K46__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ar46__n_K46
       )

    jac[jar46, jk49] = (
       +rho*Y[jp]*rate_eval.p_K49__He4_Ar46
       )

    jac[jar47, jn] = (
       -rho*Y[jar47]*rate_eval.n_Ar47__Ar48
       +rho*Y[jar46]*rate_eval.n_Ar46__Ar47
       )

    jac[jar47, jp] = (
       -rho*Y[jar47]*rate_eval.p_Ar47__n_K47
       -rho*Y[jar47]*rate_eval.p_Ar47__K48
       +rho*Y[jcl46]*rate_eval.p_Cl46__Ar47
       +rho*Y[jcl47]*rate_eval.p_Cl47__n_Ar47
       +rho*Y[jk50]*rate_eval.p_K50__He4_Ar47
       )

    jac[jar47, jhe4] = (
       -rho*Y[jar47]*rate_eval.He4_Ar47__Ca51
       -rho*Y[jar47]*rate_eval.He4_Ar47__n_Ca50
       +rho*Y[jcl44]*rate_eval.He4_Cl44__p_Ar47
       +rho*Y[js43]*rate_eval.He4_S43__Ar47
       +rho*Y[js44]*rate_eval.He4_S44__n_Ar47
       )

    jac[jar47, js43] = (
       +rho*Y[jhe4]*rate_eval.He4_S43__Ar47
       )

    jac[jar47, js44] = (
       +rho*Y[jhe4]*rate_eval.He4_S44__n_Ar47
       )

    jac[jar47, jcl44] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl44__p_Ar47
       )

    jac[jar47, jcl46] = (
       +rho*Y[jp]*rate_eval.p_Cl46__Ar47
       )

    jac[jar47, jcl47] = (
       +rho*Y[jp]*rate_eval.p_Cl47__n_Ar47
       +rate_eval.Cl47__Ar47__weak__wc17
       )

    jac[jar47, jcl48] = (
       +rate_eval.Cl48__n_Ar47__weak__mp17
       )

    jac[jar47, jcl49] = (
       +rate_eval.Cl49__n_n_Ar47__weak__mp17
       )

    jac[jar47, jcl50] = (
       +rate_eval.Cl50__n_n_n_Ar47__weak__mo03
       )

    jac[jar47, jar46] = (
       +rho*Y[jn]*rate_eval.n_Ar46__Ar47
       )

    jac[jar47, jar47] = (
       -rho*Y[jp]*rate_eval.p_Ar47__n_K47
       -rho*Y[jn]*rate_eval.n_Ar47__Ar48
       -rho*Y[jp]*rate_eval.p_Ar47__K48
       -rho*Y[jhe4]*rate_eval.He4_Ar47__Ca51
       -rho*Y[jhe4]*rate_eval.He4_Ar47__n_Ca50
       -rate_eval.Ar47__K47__weak__wc12
       )

    jac[jar47, jk50] = (
       +rho*Y[jp]*rate_eval.p_K50__He4_Ar47
       )

    jac[jar48, jn] = (
       -rho*Y[jar48]*rate_eval.n_Ar48__Ar49
       +rho*Y[jar47]*rate_eval.n_Ar47__Ar48
       )

    jac[jar48, jp] = (
       -rho*Y[jar48]*rate_eval.p_Ar48__He4_Cl45
       -rho*Y[jar48]*rate_eval.p_Ar48__n_K48
       -rho*Y[jar48]*rate_eval.p_Ar48__K49
       +rho*Y[jcl48]*rate_eval.p_Cl48__n_Ar48
       +rho*Y[jk51]*rate_eval.p_K51__He4_Ar48
       +rho*Y[jcl47]*rate_eval.p_Cl47__Ar48
       )

    jac[jar48, jhe4] = (
       -rho*Y[jar48]*rate_eval.He4_Ar48__Ca52
       -rho*Y[jar48]*rate_eval.He4_Ar48__n_Ca51
       +rho*Y[js45]*rate_eval.He4_S45__n_Ar48
       +rho*Y[js44]*rate_eval.He4_S44__Ar48
       )

    jac[jar48, js44] = (
       +rho*Y[jhe4]*rate_eval.He4_S44__Ar48
       )

    jac[jar48, js45] = (
       +rho*Y[jhe4]*rate_eval.He4_S45__n_Ar48
       )

    jac[jar48, jcl47] = (
       +rho*Y[jp]*rate_eval.p_Cl47__Ar48
       )

    jac[jar48, jcl48] = (
       +rho*Y[jp]*rate_eval.p_Cl48__n_Ar48
       +rate_eval.Cl48__Ar48__weak__mo03
       )

    jac[jar48, jcl49] = (
       +rate_eval.Cl49__n_Ar48__weak__mp17
       )

    jac[jar48, jcl50] = (
       +rate_eval.Cl50__n_n_Ar48__weak__mp17
       )

    jac[jar48, jcl51] = (
       +rate_eval.Cl51__n_n_n_Ar48__weak__mo03
       )

    jac[jar48, jar47] = (
       +rho*Y[jn]*rate_eval.n_Ar47__Ar48
       )

    jac[jar48, jar48] = (
       -rate_eval.Ar48__n_K47__weak__mp17
       -rho*Y[jp]*rate_eval.p_Ar48__He4_Cl45
       -rho*Y[jp]*rate_eval.p_Ar48__n_K48
       -rho*Y[jn]*rate_eval.n_Ar48__Ar49
       -rate_eval.Ar48__K48__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_Ar48__Ca52
       -rho*Y[jp]*rate_eval.p_Ar48__K49
       -rho*Y[jhe4]*rate_eval.He4_Ar48__n_Ca51
       )

    jac[jar48, jk51] = (
       +rho*Y[jp]*rate_eval.p_K51__He4_Ar48
       )

    jac[jar49, jn] = (
       -rho*Y[jar49]*rate_eval.n_Ar49__Ar50
       +rho*Y[jar48]*rate_eval.n_Ar48__Ar49
       )

    jac[jar49, jp] = (
       -rho*Y[jar49]*rate_eval.p_Ar49__n_K49
       -rho*Y[jar49]*rate_eval.p_Ar49__K50
       -rho*Y[jar49]*rate_eval.p_Ar49__He4_Cl46
       +rho*Y[jk52]*rate_eval.p_K52__He4_Ar49
       +rho*Y[jcl48]*rate_eval.p_Cl48__Ar49
       +rho*Y[jcl49]*rate_eval.p_Cl49__n_Ar49
       )

    jac[jar49, jhe4] = (
       -rho*Y[jar49]*rate_eval.He4_Ar49__n_Ca52
       -rho*Y[jar49]*rate_eval.He4_Ar49__Ca53
       +rho*Y[js46]*rate_eval.He4_S46__n_Ar49
       +rho*Y[js45]*rate_eval.He4_S45__Ar49
       )

    jac[jar49, js45] = (
       +rho*Y[jhe4]*rate_eval.He4_S45__Ar49
       )

    jac[jar49, js46] = (
       +rho*Y[jhe4]*rate_eval.He4_S46__n_Ar49
       )

    jac[jar49, jcl48] = (
       +rho*Y[jp]*rate_eval.p_Cl48__Ar49
       )

    jac[jar49, jcl49] = (
       +rate_eval.Cl49__Ar49__weak__mo03
       +rho*Y[jp]*rate_eval.p_Cl49__n_Ar49
       )

    jac[jar49, jcl50] = (
       +rate_eval.Cl50__n_Ar49__weak__mp17
       )

    jac[jar49, jcl51] = (
       +rate_eval.Cl51__n_n_Ar49__weak__mp17
       )

    jac[jar49, jcl52] = (
       +rate_eval.Cl52__n_n_n_Ar49__weak__mo03
       )

    jac[jar49, jar48] = (
       +rho*Y[jn]*rate_eval.n_Ar48__Ar49
       )

    jac[jar49, jar49] = (
       -rate_eval.Ar49__K49__weak__wc12
       -rate_eval.Ar49__n_K48__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ar49__n_Ca52
       -rho*Y[jp]*rate_eval.p_Ar49__n_K49
       -rho*Y[jp]*rate_eval.p_Ar49__K50
       -rho*Y[jhe4]*rate_eval.He4_Ar49__Ca53
       -rho*Y[jp]*rate_eval.p_Ar49__He4_Cl46
       -rho*Y[jn]*rate_eval.n_Ar49__Ar50
       )

    jac[jar49, jk52] = (
       +rho*Y[jp]*rate_eval.p_K52__He4_Ar49
       )

    jac[jar50, jn] = (
       -rho*Y[jar50]*rate_eval.n_Ar50__Ar51
       +rho*Y[jar49]*rate_eval.n_Ar49__Ar50
       )

    jac[jar50, jp] = (
       -rho*Y[jar50]*rate_eval.p_Ar50__He4_Cl47
       -rho*Y[jar50]*rate_eval.p_Ar50__n_K50
       -rho*Y[jar50]*rate_eval.p_Ar50__K51
       +rho*Y[jcl50]*rate_eval.p_Cl50__n_Ar50
       +rho*Y[jcl49]*rate_eval.p_Cl49__Ar50
       +rho*Y[jk53]*rate_eval.p_K53__He4_Ar50
       )

    jac[jar50, jhe4] = (
       -rho*Y[jar50]*rate_eval.He4_Ar50__Ca54
       -rho*Y[jar50]*rate_eval.He4_Ar50__n_Ca53
       +rho*Y[js46]*rate_eval.He4_S46__Ar50
       +rho*Y[js47]*rate_eval.He4_S47__n_Ar50
       )

    jac[jar50, js46] = (
       +rho*Y[jhe4]*rate_eval.He4_S46__Ar50
       )

    jac[jar50, js47] = (
       +rho*Y[jhe4]*rate_eval.He4_S47__n_Ar50
       )

    jac[jar50, jcl49] = (
       +rho*Y[jp]*rate_eval.p_Cl49__Ar50
       )

    jac[jar50, jcl50] = (
       +rho*Y[jp]*rate_eval.p_Cl50__n_Ar50
       +rate_eval.Cl50__Ar50__weak__mo03
       )

    jac[jar50, jcl51] = (
       +rate_eval.Cl51__n_Ar50__weak__mp17
       )

    jac[jar50, jcl52] = (
       +rate_eval.Cl52__n_n_Ar50__weak__mp17
       )

    jac[jar50, jar49] = (
       +rho*Y[jn]*rate_eval.n_Ar49__Ar50
       )

    jac[jar50, jar50] = (
       -rho*Y[jp]*rate_eval.p_Ar50__He4_Cl47
       -rho*Y[jp]*rate_eval.p_Ar50__n_K50
       -rho*Y[jhe4]*rate_eval.He4_Ar50__Ca54
       -rho*Y[jn]*rate_eval.n_Ar50__Ar51
       -rho*Y[jhe4]*rate_eval.He4_Ar50__n_Ca53
       -rate_eval.Ar50__n_K49__weak__wc12
       -rate_eval.Ar50__K50__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ar50__K51
       )

    jac[jar50, jk53] = (
       +rho*Y[jp]*rate_eval.p_K53__He4_Ar50
       )

    jac[jar51, jn] = (
       -rho*Y[jar51]*rate_eval.n_Ar51__Ar52
       +rho*Y[jar50]*rate_eval.n_Ar50__Ar51
       )

    jac[jar51, jp] = (
       -rho*Y[jar51]*rate_eval.p_Ar51__He4_Cl48
       -rho*Y[jar51]*rate_eval.p_Ar51__K52
       -rho*Y[jar51]*rate_eval.p_Ar51__n_K51
       +rho*Y[jcl50]*rate_eval.p_Cl50__Ar51
       +rho*Y[jcl51]*rate_eval.p_Cl51__n_Ar51
       +rho*Y[jk54]*rate_eval.p_K54__He4_Ar51
       )

    jac[jar51, jhe4] = (
       -rho*Y[jar51]*rate_eval.He4_Ar51__Ca55
       -rho*Y[jar51]*rate_eval.He4_Ar51__n_Ca54
       +rho*Y[js48]*rate_eval.He4_S48__n_Ar51
       +rho*Y[js47]*rate_eval.He4_S47__Ar51
       )

    jac[jar51, js47] = (
       +rho*Y[jhe4]*rate_eval.He4_S47__Ar51
       )

    jac[jar51, js48] = (
       +rho*Y[jhe4]*rate_eval.He4_S48__n_Ar51
       )

    jac[jar51, jcl50] = (
       +rho*Y[jp]*rate_eval.p_Cl50__Ar51
       )

    jac[jar51, jcl51] = (
       +rate_eval.Cl51__Ar51__weak__mo03
       +rho*Y[jp]*rate_eval.p_Cl51__n_Ar51
       )

    jac[jar51, jcl52] = (
       +rate_eval.Cl52__n_Ar51__weak__mp17
       )

    jac[jar51, jar50] = (
       +rho*Y[jn]*rate_eval.n_Ar50__Ar51
       )

    jac[jar51, jar51] = (
       -rho*Y[jp]*rate_eval.p_Ar51__He4_Cl48
       -rho*Y[jp]*rate_eval.p_Ar51__K52
       -rho*Y[jn]*rate_eval.n_Ar51__Ar52
       -rate_eval.Ar51__n_K50__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ar51__Ca55
       -rate_eval.Ar51__K51__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Ar51__n_Ca54
       -rho*Y[jp]*rate_eval.p_Ar51__n_K51
       -rate_eval.Ar51__n_n_K49__weak__mp17
       )

    jac[jar51, jk54] = (
       +rho*Y[jp]*rate_eval.p_K54__He4_Ar51
       )

    jac[jar52, jn] = (
       -rho*Y[jar52]*rate_eval.n_Ar52__Ar53
       +rho*Y[jar51]*rate_eval.n_Ar51__Ar52
       )

    jac[jar52, jp] = (
       -rho*Y[jar52]*rate_eval.p_Ar52__He4_Cl49
       -rho*Y[jar52]*rate_eval.p_Ar52__n_K52
       -rho*Y[jar52]*rate_eval.p_Ar52__K53
       +rho*Y[jcl52]*rate_eval.p_Cl52__n_Ar52
       +rho*Y[jcl51]*rate_eval.p_Cl51__Ar52
       +rho*Y[jk55]*rate_eval.p_K55__He4_Ar52
       )

    jac[jar52, jhe4] = (
       -rho*Y[jar52]*rate_eval.He4_Ar52__Ca56
       -rho*Y[jar52]*rate_eval.He4_Ar52__n_Ca55
       +rho*Y[js48]*rate_eval.He4_S48__Ar52
       +rho*Y[js49]*rate_eval.He4_S49__n_Ar52
       )

    jac[jar52, js48] = (
       +rho*Y[jhe4]*rate_eval.He4_S48__Ar52
       )

    jac[jar52, js49] = (
       +rho*Y[jhe4]*rate_eval.He4_S49__n_Ar52
       )

    jac[jar52, jcl51] = (
       +rho*Y[jp]*rate_eval.p_Cl51__Ar52
       )

    jac[jar52, jcl52] = (
       +rho*Y[jp]*rate_eval.p_Cl52__n_Ar52
       +rate_eval.Cl52__Ar52__weak__mo03
       )

    jac[jar52, jar51] = (
       +rho*Y[jn]*rate_eval.n_Ar51__Ar52
       )

    jac[jar52, jar52] = (
       -rate_eval.Ar52__n_n_n_K49__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Ar52__Ca56
       -rho*Y[jp]*rate_eval.p_Ar52__He4_Cl49
       -rho*Y[jp]*rate_eval.p_Ar52__n_K52
       -rate_eval.Ar52__n_n_K50__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ar52__n_Ca55
       -rho*Y[jn]*rate_eval.n_Ar52__Ar53
       -rho*Y[jp]*rate_eval.p_Ar52__K53
       -rate_eval.Ar52__K52__weak__mo03
       -rate_eval.Ar52__n_K51__weak__mp17
       )

    jac[jar52, jk55] = (
       +rho*Y[jp]*rate_eval.p_K55__He4_Ar52
       )

    jac[jar53, jn] = (
       -rho*Y[jar53]*rate_eval.n_Ar53__Ar54
       +rho*Y[jar52]*rate_eval.n_Ar52__Ar53
       )

    jac[jar53, jp] = (
       -rho*Y[jar53]*rate_eval.p_Ar53__He4_Cl50
       -rho*Y[jar53]*rate_eval.p_Ar53__n_K53
       -rho*Y[jar53]*rate_eval.p_Ar53__K54
       +rho*Y[jk56]*rate_eval.p_K56__He4_Ar53
       +rho*Y[jcl52]*rate_eval.p_Cl52__Ar53
       )

    jac[jar53, jhe4] = (
       -rho*Y[jar53]*rate_eval.He4_Ar53__n_Ca56
       -rho*Y[jar53]*rate_eval.He4_Ar53__Ca57
       +rho*Y[js49]*rate_eval.He4_S49__Ar53
       )

    jac[jar53, js49] = (
       +rho*Y[jhe4]*rate_eval.He4_S49__Ar53
       )

    jac[jar53, jcl52] = (
       +rho*Y[jp]*rate_eval.p_Cl52__Ar53
       )

    jac[jar53, jar52] = (
       +rho*Y[jn]*rate_eval.n_Ar52__Ar53
       )

    jac[jar53, jar53] = (
       -rate_eval.Ar53__n_n_n_K50__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Ar53__n_Ca56
       -rho*Y[jp]*rate_eval.p_Ar53__He4_Cl50
       -rho*Y[jhe4]*rate_eval.He4_Ar53__Ca57
       -rho*Y[jp]*rate_eval.p_Ar53__n_K53
       -rate_eval.Ar53__n_n_K51__weak__mp17
       -rate_eval.Ar53__n_K52__weak__mp17
       -rho*Y[jp]*rate_eval.p_Ar53__K54
       -rho*Y[jn]*rate_eval.n_Ar53__Ar54
       -rate_eval.Ar53__K53__weak__mo03
       )

    jac[jar53, jk56] = (
       +rho*Y[jp]*rate_eval.p_K56__He4_Ar53
       )

    jac[jar54, jn] = (
       +rho*Y[jar53]*rate_eval.n_Ar53__Ar54
       )

    jac[jar54, jp] = (
       -rho*Y[jar54]*rate_eval.p_Ar54__n_K54
       -rho*Y[jar54]*rate_eval.p_Ar54__He4_Cl51
       -rho*Y[jar54]*rate_eval.p_Ar54__K55
       +rho*Y[jk57]*rate_eval.p_K57__He4_Ar54
       )

    jac[jar54, jhe4] = (
       -rho*Y[jar54]*rate_eval.He4_Ar54__n_Ca57
       -rho*Y[jar54]*rate_eval.He4_Ar54__Ca58
       )

    jac[jar54, jar53] = (
       +rho*Y[jn]*rate_eval.n_Ar53__Ar54
       )

    jac[jar54, jar54] = (
       -rate_eval.Ar54__n_n_n_K51__weak__mo03
       -rho*Y[jp]*rate_eval.p_Ar54__n_K54
       -rate_eval.Ar54__n_K53__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ar54__n_Ca57
       -rho*Y[jp]*rate_eval.p_Ar54__He4_Cl51
       -rate_eval.Ar54__n_n_K52__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ar54__Ca58
       -rho*Y[jp]*rate_eval.p_Ar54__K55
       -rate_eval.Ar54__K54__weak__mo03
       )

    jac[jar54, jk57] = (
       +rho*Y[jp]*rate_eval.p_K57__He4_Ar54
       )

    jac[jk31, jn] = (
       -rho*Y[jk31]*rate_eval.n_K31__K32
       -rho*Y[jk31]*rate_eval.n_K31__p_Ar31
       -rho*Y[jk31]*rate_eval.n_K31__He4_Cl28
       )

    jac[jk31, jp] = (
       +rho*Y[jar30]*rate_eval.p_Ar30__K31
       )

    jac[jk31, jhe4] = (
       -rho*Y[jk31]*rate_eval.He4_K31__p_Ca34
       -rho*Y[jk31]*rate_eval.He4_K31__Sc35
       )

    jac[jk31, jar30] = (
       +rho*Y[jp]*rate_eval.p_Ar30__K31
       )

    jac[jk31, jk31] = (
       -rho*Y[jn]*rate_eval.n_K31__K32
       -rho*Y[jhe4]*rate_eval.He4_K31__p_Ca34
       -rho*Y[jn]*rate_eval.n_K31__p_Ar31
       -rho*Y[jhe4]*rate_eval.He4_K31__Sc35
       -rho*Y[jn]*rate_eval.n_K31__He4_Cl28
       -rate_eval.K31__Ar31__weak__bqa_pos_
       )

    jac[jk32, jn] = (
       -rho*Y[jk32]*rate_eval.n_K32__He4_Cl29
       -rho*Y[jk32]*rate_eval.n_K32__p_Ar32
       -rho*Y[jk32]*rate_eval.n_K32__K33
       +rho*Y[jsc35]*rate_eval.n_Sc35__He4_K32
       +rho*Y[jk31]*rate_eval.n_K31__K32
       )

    jac[jk32, jp] = (
       -rho*Y[jk32]*rate_eval.p_K32__Ca33
       +rho*Y[jar31]*rate_eval.p_Ar31__K32
       )

    jac[jk32, jhe4] = (
       -rho*Y[jk32]*rate_eval.He4_K32__Sc36
       -rho*Y[jk32]*rate_eval.He4_K32__p_Ca35
       +rho*Y[jar29]*rate_eval.He4_Ar29__p_K32
       +rho*Y[jcl28]*rate_eval.He4_Cl28__K32
       )

    jac[jk32, jcl28] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl28__K32
       )

    jac[jk32, jar29] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar29__p_K32
       )

    jac[jk32, jar31] = (
       +rho*Y[jp]*rate_eval.p_Ar31__K32
       )

    jac[jk32, jk31] = (
       +rho*Y[jn]*rate_eval.n_K31__K32
       )

    jac[jk32, jk32] = (
       -rate_eval.K32__Ar32__weak__bqa_pos_
       -rho*Y[jn]*rate_eval.n_K32__He4_Cl29
       -rho*Y[jn]*rate_eval.n_K32__p_Ar32
       -rho*Y[jhe4]*rate_eval.He4_K32__Sc36
       -rho*Y[jn]*rate_eval.n_K32__K33
       -rho*Y[jp]*rate_eval.p_K32__Ca33
       -rho*Y[jhe4]*rate_eval.He4_K32__p_Ca35
       )

    jac[jk32, jsc35] = (
       +rho*Y[jn]*rate_eval.n_Sc35__He4_K32
       )

    jac[jk33, jn] = (
       -rho*Y[jk33]*rate_eval.n_K33__p_Ar33
       -rho*Y[jk33]*rate_eval.n_K33__He4_Cl30
       -rho*Y[jk33]*rate_eval.n_K33__K34
       +rho*Y[jca33]*rate_eval.n_Ca33__p_K33
       +rho*Y[jk32]*rate_eval.n_K32__K33
       +rho*Y[jsc36]*rate_eval.n_Sc36__He4_K33
       )

    jac[jk33, jp] = (
       -rho*Y[jk33]*rate_eval.p_K33__Ca34
       +rho*Y[jar32]*rate_eval.p_Ar32__K33
       )

    jac[jk33, jhe4] = (
       -rho*Y[jk33]*rate_eval.He4_K33__Sc37
       -rho*Y[jk33]*rate_eval.He4_K33__p_Ca36
       +rho*Y[jcl29]*rate_eval.He4_Cl29__K33
       +rho*Y[jar30]*rate_eval.He4_Ar30__p_K33
       )

    jac[jk33, jcl29] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl29__K33
       )

    jac[jk33, jar30] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar30__p_K33
       )

    jac[jk33, jar32] = (
       +rho*Y[jp]*rate_eval.p_Ar32__K33
       )

    jac[jk33, jk32] = (
       +rho*Y[jn]*rate_eval.n_K32__K33
       )

    jac[jk33, jk33] = (
       -rho*Y[jn]*rate_eval.n_K33__p_Ar33
       -rho*Y[jhe4]*rate_eval.He4_K33__Sc37
       -rho*Y[jp]*rate_eval.p_K33__Ca34
       -rho*Y[jn]*rate_eval.n_K33__He4_Cl30
       -rho*Y[jn]*rate_eval.n_K33__K34
       -rho*Y[jhe4]*rate_eval.He4_K33__p_Ca36
       -rate_eval.K33__Ar33__weak__bqa_pos_
       )

    jac[jk33, jca33] = (
       +rate_eval.Ca33__K33__weak__bqa_pos_
       +rho*Y[jn]*rate_eval.n_Ca33__p_K33
       )

    jac[jk33, jsc36] = (
       +rho*Y[jn]*rate_eval.n_Sc36__He4_K33
       )

    jac[jk34, jn] = (
       -rho*Y[jk34]*rate_eval.n_K34__K35
       -rho*Y[jk34]*rate_eval.n_K34__He4_Cl31
       -rho*Y[jk34]*rate_eval.n_K34__p_Ar34
       +rho*Y[jsc37]*rate_eval.n_Sc37__He4_K34
       +rho*Y[jca34]*rate_eval.n_Ca34__p_K34
       +rho*Y[jk33]*rate_eval.n_K33__K34
       )

    jac[jk34, jp] = (
       -rho*Y[jk34]*rate_eval.p_K34__Ca35
       +rho*Y[jar33]*rate_eval.p_Ar33__K34
       )

    jac[jk34, jhe4] = (
       -rho*Y[jk34]*rate_eval.He4_K34__p_Ca37
       -rho*Y[jk34]*rate_eval.He4_K34__Sc38
       +rho*Y[jar31]*rate_eval.He4_Ar31__p_K34
       +rho*Y[jcl30]*rate_eval.He4_Cl30__K34
       )

    jac[jk34, jcl30] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl30__K34
       )

    jac[jk34, jar31] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar31__p_K34
       )

    jac[jk34, jar33] = (
       +rho*Y[jp]*rate_eval.p_Ar33__K34
       )

    jac[jk34, jk33] = (
       +rho*Y[jn]*rate_eval.n_K33__K34
       )

    jac[jk34, jk34] = (
       -rho*Y[jhe4]*rate_eval.He4_K34__p_Ca37
       -rho*Y[jn]*rate_eval.n_K34__K35
       -rho*Y[jp]*rate_eval.p_K34__Ca35
       -rho*Y[jn]*rate_eval.n_K34__He4_Cl31
       -rho*Y[jn]*rate_eval.n_K34__p_Ar34
       -rate_eval.K34__Ar34__weak__bqa_pos_
       -rho*Y[jhe4]*rate_eval.He4_K34__Sc38
       )

    jac[jk34, jca34] = (
       +rho*Y[jn]*rate_eval.n_Ca34__p_K34
       +rate_eval.Ca34__K34__weak__bqa_pos_
       )

    jac[jk34, jsc37] = (
       +rho*Y[jn]*rate_eval.n_Sc37__He4_K34
       )

    jac[jk35, jn] = (
       -rho*Y[jk35]*rate_eval.n_K35__p_Ar35
       -rho*Y[jk35]*rate_eval.n_K35__He4_Cl32
       -rho*Y[jk35]*rate_eval.n_K35__K36
       +rho*Y[jca35]*rate_eval.n_Ca35__p_K35
       +rho*Y[jk34]*rate_eval.n_K34__K35
       +rho*Y[jsc38]*rate_eval.n_Sc38__He4_K35
       )

    jac[jk35, jp] = (
       -rho*Y[jk35]*rate_eval.p_K35__Ca36
       +rho*Y[jar34]*rate_eval.p_Ar34__K35
       )

    jac[jk35, jhe4] = (
       -rho*Y[jk35]*rate_eval.He4_K35__p_Ca38
       -rho*Y[jk35]*rate_eval.He4_K35__Sc39
       +rho*Y[jcl31]*rate_eval.He4_Cl31__K35
       +rho*Y[jar32]*rate_eval.He4_Ar32__p_K35
       )

    jac[jk35, jcl31] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl31__K35
       )

    jac[jk35, jar32] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar32__p_K35
       )

    jac[jk35, jar34] = (
       +rho*Y[jp]*rate_eval.p_Ar34__K35
       )

    jac[jk35, jk34] = (
       +rho*Y[jn]*rate_eval.n_K34__K35
       )

    jac[jk35, jk35] = (
       -rho*Y[jn]*rate_eval.n_K35__p_Ar35
       -rho*Y[jhe4]*rate_eval.He4_K35__p_Ca38
       -rho*Y[jn]*rate_eval.n_K35__He4_Cl32
       -rho*Y[jhe4]*rate_eval.He4_K35__Sc39
       -rho*Y[jp]*rate_eval.p_K35__Ca36
       -rate_eval.K35__p_Cl34__weak__wc12
       -rho*Y[jn]*rate_eval.n_K35__K36
       -rate_eval.K35__Ar35__weak__wc12
       )

    jac[jk35, jca35] = (
       +rho*Y[jn]*rate_eval.n_Ca35__p_K35
       +rate_eval.Ca35__K35__weak__wc17
       )

    jac[jk35, jsc38] = (
       +rho*Y[jn]*rate_eval.n_Sc38__He4_K35
       )

    jac[jk36, jn] = (
       -rho*Y[jk36]*rate_eval.n_K36__He4_Cl33
       -rho*Y[jk36]*rate_eval.n_K36__p_Ar36
       -rho*Y[jk36]*rate_eval.n_K36__K37
       +rho*Y[jsc39]*rate_eval.n_Sc39__He4_K36
       +rho*Y[jca36]*rate_eval.n_Ca36__p_K36
       +rho*Y[jk35]*rate_eval.n_K35__K36
       )

    jac[jk36, jp] = (
       -rho*Y[jk36]*rate_eval.p_K36__Ca37
       +rho*Y[jar35]*rate_eval.p_Ar35__K36
       )

    jac[jk36, jhe4] = (
       -rho*Y[jk36]*rate_eval.He4_K36__p_Ca39
       -rho*Y[jk36]*rate_eval.He4_K36__Sc40
       +rho*Y[jar33]*rate_eval.He4_Ar33__p_K36
       +rho*Y[jcl32]*rate_eval.He4_Cl32__K36
       )

    jac[jk36, jcl32] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl32__K36
       )

    jac[jk36, jar33] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar33__p_K36
       )

    jac[jk36, jar35] = (
       +rho*Y[jp]*rate_eval.p_Ar35__K36
       )

    jac[jk36, jk35] = (
       +rho*Y[jn]*rate_eval.n_K35__K36
       )

    jac[jk36, jk36] = (
       -rho*Y[jhe4]*rate_eval.He4_K36__p_Ca39
       -rho*Y[jn]*rate_eval.n_K36__He4_Cl33
       -rho*Y[jn]*rate_eval.n_K36__p_Ar36
       -rho*Y[jp]*rate_eval.p_K36__Ca37
       -rho*Y[jn]*rate_eval.n_K36__K37
       -rate_eval.K36__He4_S32__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_K36__Sc40
       -rate_eval.K36__p_Cl35__weak__wc12
       -rate_eval.K36__Ar36__weak__wc12
       )

    jac[jk36, jca36] = (
       +rho*Y[jn]*rate_eval.n_Ca36__p_K36
       +rate_eval.Ca36__K36__weak__wc12
       )

    jac[jk36, jsc39] = (
       +rho*Y[jn]*rate_eval.n_Sc39__He4_K36
       )

    jac[jk37, jn] = (
       -rho*Y[jk37]*rate_eval.n_K37__He4_Cl34
       -rho*Y[jk37]*rate_eval.n_K37__K38
       -rho*Y[jk37]*rate_eval.n_K37__p_Ar37
       +rho*Y[jca37]*rate_eval.n_Ca37__p_K37
       +rho*Y[jk36]*rate_eval.n_K36__K37
       +rho*Y[jsc40]*rate_eval.n_Sc40__He4_K37
       )

    jac[jk37, jp] = (
       -rho*Y[jk37]*rate_eval.p_K37__Ca38
       +rho*Y[jar36]*rate_eval.p_Ar36__K37
       )

    jac[jk37, jhe4] = (
       -rho*Y[jk37]*rate_eval.He4_K37__p_Ca40
       -rho*Y[jk37]*rate_eval.He4_K37__Sc41
       +rho*Y[jar34]*rate_eval.He4_Ar34__p_K37
       +rho*Y[jcl33]*rate_eval.He4_Cl33__K37
       )

    jac[jk37, jcl33] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl33__K37
       )

    jac[jk37, jar34] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar34__p_K37
       )

    jac[jk37, jar36] = (
       +rho*Y[jp]*rate_eval.p_Ar36__K37
       )

    jac[jk37, jk36] = (
       +rho*Y[jn]*rate_eval.n_K36__K37
       )

    jac[jk37, jk37] = (
       -rho*Y[jhe4]*rate_eval.He4_K37__p_Ca40
       -rho*Y[jn]*rate_eval.n_K37__He4_Cl34
       -rho*Y[jp]*rate_eval.p_K37__Ca38
       -rho*Y[jn]*rate_eval.n_K37__K38
       -rho*Y[jn]*rate_eval.n_K37__p_Ar37
       -rate_eval.K37__Ar37__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_K37__Sc41
       )

    jac[jk37, jca37] = (
       +rho*Y[jn]*rate_eval.n_Ca37__p_K37
       +rate_eval.Ca37__K37__weak__wc12
       )

    jac[jk37, jsc40] = (
       +rho*Y[jn]*rate_eval.n_Sc40__He4_K37
       )

    jac[jk38, jn] = (
       -rho*Y[jk38]*rate_eval.n_K38__p_Ar38
       -rho*Y[jk38]*rate_eval.n_K38__He4_Cl35
       -rho*Y[jk38]*rate_eval.n_K38__K39
       +rho*Y[jsc41]*rate_eval.n_Sc41__He4_K38
       +rho*Y[jca38]*rate_eval.n_Ca38__p_K38
       +rho*Y[jk37]*rate_eval.n_K37__K38
       )

    jac[jk38, jp] = (
       -rho*Y[jk38]*rate_eval.p_K38__Ca39
       +rho*Y[jar37]*rate_eval.p_Ar37__K38
       )

    jac[jk38, jhe4] = (
       -rho*Y[jk38]*rate_eval.He4_K38__p_Ca41
       -rho*Y[jk38]*rate_eval.He4_K38__Sc42
       +rho*Y[jar35]*rate_eval.He4_Ar35__p_K38
       +rho*Y[jcl34]*rate_eval.He4_Cl34__K38
       )

    jac[jk38, jcl34] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl34__K38
       )

    jac[jk38, jar35] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar35__p_K38
       )

    jac[jk38, jar37] = (
       +rho*Y[jp]*rate_eval.p_Ar37__K38
       )

    jac[jk38, jk37] = (
       +rho*Y[jn]*rate_eval.n_K37__K38
       )

    jac[jk38, jk38] = (
       -rho*Y[jn]*rate_eval.n_K38__p_Ar38
       -rate_eval.K38__Ar38__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_K38__p_Ca41
       -rho*Y[jp]*rate_eval.p_K38__Ca39
       -rho*Y[jn]*rate_eval.n_K38__He4_Cl35
       -rho*Y[jn]*rate_eval.n_K38__K39
       -rho*Y[jhe4]*rate_eval.He4_K38__Sc42
       )

    jac[jk38, jca38] = (
       +rho*Y[jn]*rate_eval.n_Ca38__p_K38
       +rate_eval.Ca38__K38__weak__wc12
       )

    jac[jk38, jsc41] = (
       +rho*Y[jn]*rate_eval.n_Sc41__He4_K38
       )

    jac[jk39, jn] = (
       -rho*Y[jk39]*rate_eval.n_K39__p_Ar39
       -rho*Y[jk39]*rate_eval.n_K39__He4_Cl36
       -rho*Y[jk39]*rate_eval.n_K39__K40
       +rho*Y[jsc42]*rate_eval.n_Sc42__He4_K39
       +rho*Y[jk38]*rate_eval.n_K38__K39
       +rho*Y[jca39]*rate_eval.n_Ca39__p_K39
       )

    jac[jk39, jp] = (
       -rho*Y[jk39]*rate_eval.p_K39__Ca40
       -rho*Y[jk39]*rate_eval.p_K39__He4_Ar36
       +rho*Y[jca42]*rate_eval.p_Ca42__He4_K39
       +rho*Y[jar38]*rate_eval.p_Ar38__K39
       )

    jac[jk39, jhe4] = (
       -rho*Y[jk39]*rate_eval.He4_K39__Sc43
       +rho*Y[jcl35]*rate_eval.He4_Cl35__K39
       )

    jac[jk39, jcl35] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl35__K39
       )

    jac[jk39, jar38] = (
       +rho*Y[jp]*rate_eval.p_Ar38__K39
       )

    jac[jk39, jar39] = (
       +rate_eval.Ar39__K39__weak__wc12
       )

    jac[jk39, jk38] = (
       +rho*Y[jn]*rate_eval.n_K38__K39
       )

    jac[jk39, jk39] = (
       -rho*Y[jn]*rate_eval.n_K39__p_Ar39
       -rho*Y[jhe4]*rate_eval.He4_K39__Sc43
       -rho*Y[jn]*rate_eval.n_K39__He4_Cl36
       -rho*Y[jp]*rate_eval.p_K39__Ca40
       -rho*Y[jp]*rate_eval.p_K39__He4_Ar36
       -rho*Y[jn]*rate_eval.n_K39__K40
       )

    jac[jk39, jca39] = (
       +rate_eval.Ca39__K39__weak__wc12
       +rho*Y[jn]*rate_eval.n_Ca39__p_K39
       )

    jac[jk39, jca42] = (
       +rho*Y[jp]*rate_eval.p_Ca42__He4_K39
       )

    jac[jk39, jsc40] = (
       +rate_eval.Sc40__p_K39__weak__wc12
       )

    jac[jk39, jsc42] = (
       +rho*Y[jn]*rate_eval.n_Sc42__He4_K39
       )

    jac[jk40, jn] = (
       -rho*Y[jk40]*rate_eval.n_K40__He4_Cl37
       -rho*Y[jk40]*rate_eval.n_K40__p_Ar40
       -rho*Y[jk40]*rate_eval.n_K40__K41
       +rho*Y[jsc43]*rate_eval.n_Sc43__He4_K40
       +rho*Y[jk39]*rate_eval.n_K39__K40
       )

    jac[jk40, jp] = (
       -rho*Y[jk40]*rate_eval.p_K40__He4_Ar37
       -rho*Y[jk40]*rate_eval.p_K40__n_Ca40
       -rho*Y[jk40]*rate_eval.p_K40__Ca41
       +rho*Y[jar39]*rate_eval.p_Ar39__K40
       )

    jac[jk40, jhe4] = (
       -rho*Y[jk40]*rate_eval.He4_K40__p_Ca43
       -rho*Y[jk40]*rate_eval.He4_K40__Sc44
       +rho*Y[jcl36]*rate_eval.He4_Cl36__K40
       )

    jac[jk40, jcl36] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl36__K40
       )

    jac[jk40, jar39] = (
       +rho*Y[jp]*rate_eval.p_Ar39__K40
       )

    jac[jk40, jk39] = (
       +rho*Y[jn]*rate_eval.n_K39__K40
       )

    jac[jk40, jk40] = (
       -rho*Y[jp]*rate_eval.p_K40__He4_Ar37
       -rho*Y[jp]*rate_eval.p_K40__n_Ca40
       -rho*Y[jn]*rate_eval.n_K40__He4_Cl37
       -rho*Y[jn]*rate_eval.n_K40__p_Ar40
       -rho*Y[jhe4]*rate_eval.He4_K40__p_Ca43
       -rho*Y[jn]*rate_eval.n_K40__K41
       -rho*Y[jp]*rate_eval.p_K40__Ca41
       -rho*Y[jhe4]*rate_eval.He4_K40__Sc44
       -rate_eval.K40__Ar40__weak__wc12
       -rate_eval.K40__Ca40__weak__wc12
       )

    jac[jk40, jsc43] = (
       +rho*Y[jn]*rate_eval.n_Sc43__He4_K40
       )

    jac[jk41, jn] = (
       -rho*Y[jk41]*rate_eval.n_K41__K42
       +rho*Y[jk40]*rate_eval.n_K40__K41
       )

    jac[jk41, jp] = (
       -rho*Y[jk41]*rate_eval.p_K41__He4_Ar38
       -rho*Y[jk41]*rate_eval.p_K41__n_Ca41
       -rho*Y[jk41]*rate_eval.p_K41__Ca42
       +rho*Y[jar41]*rate_eval.p_Ar41__n_K41
       +rho*Y[jar40]*rate_eval.p_Ar40__K41
       )

    jac[jk41, jhe4] = (
       -rho*Y[jk41]*rate_eval.He4_K41__n_Sc44
       -rho*Y[jk41]*rate_eval.He4_K41__p_Ca44
       -rho*Y[jk41]*rate_eval.He4_K41__Sc45
       +rho*Y[jcl37]*rate_eval.He4_Cl37__K41
       +rho*Y[jcl38]*rate_eval.He4_Cl38__n_K41
       )

    jac[jk41, jcl37] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl37__K41
       )

    jac[jk41, jcl38] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl38__n_K41
       )

    jac[jk41, jar40] = (
       +rho*Y[jp]*rate_eval.p_Ar40__K41
       )

    jac[jk41, jar41] = (
       +rho*Y[jp]*rate_eval.p_Ar41__n_K41
       +rate_eval.Ar41__K41__weak__wc12
       )

    jac[jk41, jk40] = (
       +rho*Y[jn]*rate_eval.n_K40__K41
       )

    jac[jk41, jk41] = (
       -rho*Y[jhe4]*rate_eval.He4_K41__n_Sc44
       -rho*Y[jp]*rate_eval.p_K41__He4_Ar38
       -rho*Y[jp]*rate_eval.p_K41__n_Ca41
       -rho*Y[jhe4]*rate_eval.He4_K41__p_Ca44
       -rho*Y[jp]*rate_eval.p_K41__Ca42
       -rho*Y[jn]*rate_eval.n_K41__K42
       -rho*Y[jhe4]*rate_eval.He4_K41__Sc45
       )

    jac[jk41, jca41] = (
       +rate_eval.Ca41__K41__weak__wc12
       )

    jac[jk42, jn] = (
       -rho*Y[jk42]*rate_eval.n_K42__K43
       -rho*Y[jk42]*rate_eval.n_K42__He4_Cl39
       -rho*Y[jk42]*rate_eval.n_K42__p_Ar42
       +rho*Y[jk41]*rate_eval.n_K41__K42
       )

    jac[jk42, jp] = (
       -rho*Y[jk42]*rate_eval.p_K42__n_Ca42
       -rho*Y[jk42]*rate_eval.p_K42__He4_Ar39
       -rho*Y[jk42]*rate_eval.p_K42__Ca43
       +rho*Y[jar41]*rate_eval.p_Ar41__K42
       )

    jac[jk42, jhe4] = (
       -rho*Y[jk42]*rate_eval.He4_K42__p_Ca45
       -rho*Y[jk42]*rate_eval.He4_K42__n_Sc45
       -rho*Y[jk42]*rate_eval.He4_K42__Sc46
       +rho*Y[jcl38]*rate_eval.He4_Cl38__K42
       )

    jac[jk42, jcl38] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl38__K42
       )

    jac[jk42, jar41] = (
       +rho*Y[jp]*rate_eval.p_Ar41__K42
       )

    jac[jk42, jar42] = (
       +rate_eval.Ar42__K42__weak__wc12
       )

    jac[jk42, jk41] = (
       +rho*Y[jn]*rate_eval.n_K41__K42
       )

    jac[jk42, jk42] = (
       -rho*Y[jhe4]*rate_eval.He4_K42__p_Ca45
       -rho*Y[jhe4]*rate_eval.He4_K42__n_Sc45
       -rho*Y[jp]*rate_eval.p_K42__n_Ca42
       -rho*Y[jp]*rate_eval.p_K42__He4_Ar39
       -rho*Y[jhe4]*rate_eval.He4_K42__Sc46
       -rho*Y[jp]*rate_eval.p_K42__Ca43
       -rho*Y[jn]*rate_eval.n_K42__K43
       -rho*Y[jn]*rate_eval.n_K42__He4_Cl39
       -rho*Y[jn]*rate_eval.n_K42__p_Ar42
       -rate_eval.K42__Ca42__weak__wc12
       )

    jac[jk43, jn] = (
       -rho*Y[jk43]*rate_eval.n_K43__K44
       +rho*Y[jsc46]*rate_eval.n_Sc46__He4_K43
       +rho*Y[jk42]*rate_eval.n_K42__K43
       )

    jac[jk43, jp] = (
       -rho*Y[jk43]*rate_eval.p_K43__n_Ca43
       -rho*Y[jk43]*rate_eval.p_K43__Ca44
       -rho*Y[jk43]*rate_eval.p_K43__He4_Ar40
       +rho*Y[jar43]*rate_eval.p_Ar43__n_K43
       +rho*Y[jar42]*rate_eval.p_Ar42__K43
       )

    jac[jk43, jhe4] = (
       -rho*Y[jk43]*rate_eval.He4_K43__p_Ca46
       -rho*Y[jk43]*rate_eval.He4_K43__Sc47
       +rho*Y[jcl40]*rate_eval.He4_Cl40__n_K43
       +rho*Y[jcl39]*rate_eval.He4_Cl39__K43
       )

    jac[jk43, jcl39] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl39__K43
       )

    jac[jk43, jcl40] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl40__n_K43
       )

    jac[jk43, jar42] = (
       +rho*Y[jp]*rate_eval.p_Ar42__K43
       )

    jac[jk43, jar43] = (
       +rho*Y[jp]*rate_eval.p_Ar43__n_K43
       +rate_eval.Ar43__K43__weak__wc12
       )

    jac[jk43, jk42] = (
       +rho*Y[jn]*rate_eval.n_K42__K43
       )

    jac[jk43, jk43] = (
       -rho*Y[jhe4]*rate_eval.He4_K43__p_Ca46
       -rho*Y[jp]*rate_eval.p_K43__n_Ca43
       -rho*Y[jhe4]*rate_eval.He4_K43__Sc47
       -rho*Y[jp]*rate_eval.p_K43__Ca44
       -rho*Y[jn]*rate_eval.n_K43__K44
       -rate_eval.K43__Ca43__weak__wc12
       -rho*Y[jp]*rate_eval.p_K43__He4_Ar40
       )

    jac[jk43, jsc46] = (
       +rho*Y[jn]*rate_eval.n_Sc46__He4_K43
       )

    jac[jk44, jn] = (
       -rho*Y[jk44]*rate_eval.n_K44__K45
       +rho*Y[jk43]*rate_eval.n_K43__K44
       )

    jac[jk44, jp] = (
       -rho*Y[jk44]*rate_eval.p_K44__He4_Ar41
       -rho*Y[jk44]*rate_eval.p_K44__n_Ca44
       -rho*Y[jk44]*rate_eval.p_K44__Ca45
       +rho*Y[jar44]*rate_eval.p_Ar44__n_K44
       +rho*Y[jar43]*rate_eval.p_Ar43__K44
       )

    jac[jk44, jhe4] = (
       -rho*Y[jk44]*rate_eval.He4_K44__p_Ca47
       -rho*Y[jk44]*rate_eval.He4_K44__Sc48
       -rho*Y[jk44]*rate_eval.He4_K44__n_Sc47
       +rho*Y[jcl41]*rate_eval.He4_Cl41__n_K44
       +rho*Y[jcl40]*rate_eval.He4_Cl40__K44
       )

    jac[jk44, jcl40] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl40__K44
       )

    jac[jk44, jcl41] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl41__n_K44
       )

    jac[jk44, jar43] = (
       +rho*Y[jp]*rate_eval.p_Ar43__K44
       )

    jac[jk44, jar44] = (
       +rho*Y[jp]*rate_eval.p_Ar44__n_K44
       +rate_eval.Ar44__K44__weak__wc12
       )

    jac[jk44, jk43] = (
       +rho*Y[jn]*rate_eval.n_K43__K44
       )

    jac[jk44, jk44] = (
       -rho*Y[jp]*rate_eval.p_K44__He4_Ar41
       -rho*Y[jhe4]*rate_eval.He4_K44__p_Ca47
       -rho*Y[jp]*rate_eval.p_K44__n_Ca44
       -rho*Y[jhe4]*rate_eval.He4_K44__Sc48
       -rho*Y[jn]*rate_eval.n_K44__K45
       -rho*Y[jp]*rate_eval.p_K44__Ca45
       -rho*Y[jhe4]*rate_eval.He4_K44__n_Sc47
       -rate_eval.K44__Ca44__weak__wc12
       )

    jac[jk45, jn] = (
       -rho*Y[jk45]*rate_eval.n_K45__K46
       +rho*Y[jk44]*rate_eval.n_K44__K45
       )

    jac[jk45, jp] = (
       -rho*Y[jk45]*rate_eval.p_K45__He4_Ar42
       -rho*Y[jk45]*rate_eval.p_K45__n_Ca45
       -rho*Y[jk45]*rate_eval.p_K45__Ca46
       +rho*Y[jar45]*rate_eval.p_Ar45__n_K45
       +rho*Y[jar44]*rate_eval.p_Ar44__K45
       )

    jac[jk45, jhe4] = (
       -rho*Y[jk45]*rate_eval.He4_K45__p_Ca48
       -rho*Y[jk45]*rate_eval.He4_K45__Sc49
       -rho*Y[jk45]*rate_eval.He4_K45__n_Sc48
       +rho*Y[jcl42]*rate_eval.He4_Cl42__n_K45
       +rho*Y[jcl41]*rate_eval.He4_Cl41__K45
       )

    jac[jk45, jcl41] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl41__K45
       )

    jac[jk45, jcl42] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl42__n_K45
       )

    jac[jk45, jar44] = (
       +rho*Y[jp]*rate_eval.p_Ar44__K45
       )

    jac[jk45, jar45] = (
       +rho*Y[jp]*rate_eval.p_Ar45__n_K45
       +rate_eval.Ar45__K45__weak__wc12
       )

    jac[jk45, jk44] = (
       +rho*Y[jn]*rate_eval.n_K44__K45
       )

    jac[jk45, jk45] = (
       -rho*Y[jp]*rate_eval.p_K45__He4_Ar42
       -rho*Y[jp]*rate_eval.p_K45__n_Ca45
       -rho*Y[jhe4]*rate_eval.He4_K45__p_Ca48
       -rho*Y[jp]*rate_eval.p_K45__Ca46
       -rho*Y[jn]*rate_eval.n_K45__K46
       -rho*Y[jhe4]*rate_eval.He4_K45__Sc49
       -rho*Y[jhe4]*rate_eval.He4_K45__n_Sc48
       -rate_eval.K45__Ca45__weak__wc12
       )

    jac[jk46, jn] = (
       -rho*Y[jk46]*rate_eval.n_K46__K47
       +rho*Y[jk45]*rate_eval.n_K45__K46
       )

    jac[jk46, jp] = (
       -rho*Y[jk46]*rate_eval.p_K46__Ca47
       -rho*Y[jk46]*rate_eval.p_K46__He4_Ar43
       -rho*Y[jk46]*rate_eval.p_K46__n_Ca46
       +rho*Y[jar45]*rate_eval.p_Ar45__K46
       +rho*Y[jar46]*rate_eval.p_Ar46__n_K46
       )

    jac[jk46, jhe4] = (
       -rho*Y[jk46]*rate_eval.He4_K46__p_Ca49
       -rho*Y[jk46]*rate_eval.He4_K46__Sc50
       -rho*Y[jk46]*rate_eval.He4_K46__n_Sc49
       +rho*Y[jcl42]*rate_eval.He4_Cl42__K46
       +rho*Y[jcl43]*rate_eval.He4_Cl43__n_K46
       )

    jac[jk46, jcl42] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl42__K46
       )

    jac[jk46, jcl43] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl43__n_K46
       )

    jac[jk46, jar45] = (
       +rho*Y[jp]*rate_eval.p_Ar45__K46
       )

    jac[jk46, jar46] = (
       +rate_eval.Ar46__K46__weak__wc12
       +rho*Y[jp]*rate_eval.p_Ar46__n_K46
       )

    jac[jk46, jk45] = (
       +rho*Y[jn]*rate_eval.n_K45__K46
       )

    jac[jk46, jk46] = (
       -rho*Y[jhe4]*rate_eval.He4_K46__p_Ca49
       -rho*Y[jp]*rate_eval.p_K46__Ca47
       -rho*Y[jn]*rate_eval.n_K46__K47
       -rho*Y[jp]*rate_eval.p_K46__He4_Ar43
       -rho*Y[jp]*rate_eval.p_K46__n_Ca46
       -rate_eval.K46__Ca46__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_K46__Sc50
       -rho*Y[jhe4]*rate_eval.He4_K46__n_Sc49
       )

    jac[jk47, jn] = (
       -rho*Y[jk47]*rate_eval.n_K47__K48
       +rho*Y[jk46]*rate_eval.n_K46__K47
       )

    jac[jk47, jp] = (
       -rho*Y[jk47]*rate_eval.p_K47__He4_Ar44
       -rho*Y[jk47]*rate_eval.p_K47__n_Ca47
       -rho*Y[jk47]*rate_eval.p_K47__Ca48
       +rho*Y[jar47]*rate_eval.p_Ar47__n_K47
       +rho*Y[jca50]*rate_eval.p_Ca50__He4_K47
       +rho*Y[jar46]*rate_eval.p_Ar46__K47
       )

    jac[jk47, jhe4] = (
       -rho*Y[jk47]*rate_eval.He4_K47__Sc51
       -rho*Y[jk47]*rate_eval.He4_K47__n_Sc50
       +rho*Y[jcl44]*rate_eval.He4_Cl44__n_K47
       +rho*Y[jcl43]*rate_eval.He4_Cl43__K47
       )

    jac[jk47, jcl43] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl43__K47
       )

    jac[jk47, jcl44] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl44__n_K47
       )

    jac[jk47, jar46] = (
       +rho*Y[jp]*rate_eval.p_Ar46__K47
       )

    jac[jk47, jar47] = (
       +rho*Y[jp]*rate_eval.p_Ar47__n_K47
       +rate_eval.Ar47__K47__weak__wc12
       )

    jac[jk47, jar48] = (
       +rate_eval.Ar48__n_K47__weak__mp17
       )

    jac[jk47, jk46] = (
       +rho*Y[jn]*rate_eval.n_K46__K47
       )

    jac[jk47, jk47] = (
       -rho*Y[jp]*rate_eval.p_K47__He4_Ar44
       -rho*Y[jn]*rate_eval.n_K47__K48
       -rate_eval.K47__Ca47__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_K47__Sc51
       -rho*Y[jhe4]*rate_eval.He4_K47__n_Sc50
       -rho*Y[jp]*rate_eval.p_K47__n_Ca47
       -rho*Y[jp]*rate_eval.p_K47__Ca48
       )

    jac[jk47, jca50] = (
       +rho*Y[jp]*rate_eval.p_Ca50__He4_K47
       )

    jac[jk48, jn] = (
       -rho*Y[jk48]*rate_eval.n_K48__K49
       +rho*Y[jk47]*rate_eval.n_K47__K48
       )

    jac[jk48, jp] = (
       -rho*Y[jk48]*rate_eval.p_K48__Ca49
       -rho*Y[jk48]*rate_eval.p_K48__He4_Ar45
       -rho*Y[jk48]*rate_eval.p_K48__n_Ca48
       +rho*Y[jca51]*rate_eval.p_Ca51__He4_K48
       +rho*Y[jar48]*rate_eval.p_Ar48__n_K48
       +rho*Y[jar47]*rate_eval.p_Ar47__K48
       )

    jac[jk48, jhe4] = (
       -rho*Y[jk48]*rate_eval.He4_K48__n_Sc51
       -rho*Y[jk48]*rate_eval.He4_K48__Sc52
       +rho*Y[jcl45]*rate_eval.He4_Cl45__n_K48
       +rho*Y[jcl44]*rate_eval.He4_Cl44__K48
       )

    jac[jk48, jcl44] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl44__K48
       )

    jac[jk48, jcl45] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl45__n_K48
       )

    jac[jk48, jar47] = (
       +rho*Y[jp]*rate_eval.p_Ar47__K48
       )

    jac[jk48, jar48] = (
       +rho*Y[jp]*rate_eval.p_Ar48__n_K48
       +rate_eval.Ar48__K48__weak__wc17
       )

    jac[jk48, jar49] = (
       +rate_eval.Ar49__n_K48__weak__wc12
       )

    jac[jk48, jk47] = (
       +rho*Y[jn]*rate_eval.n_K47__K48
       )

    jac[jk48, jk48] = (
       -rho*Y[jp]*rate_eval.p_K48__Ca49
       -rho*Y[jhe4]*rate_eval.He4_K48__n_Sc51
       -rho*Y[jp]*rate_eval.p_K48__He4_Ar45
       -rho*Y[jp]*rate_eval.p_K48__n_Ca48
       -rate_eval.K48__n_Ca47__weak__wc12
       -rho*Y[jn]*rate_eval.n_K48__K49
       -rho*Y[jhe4]*rate_eval.He4_K48__Sc52
       -rate_eval.K48__Ca48__weak__wc12
       )

    jac[jk48, jca51] = (
       +rho*Y[jp]*rate_eval.p_Ca51__He4_K48
       )

    jac[jk49, jn] = (
       -rho*Y[jk49]*rate_eval.n_K49__K50
       +rho*Y[jk48]*rate_eval.n_K48__K49
       )

    jac[jk49, jp] = (
       -rho*Y[jk49]*rate_eval.p_K49__n_Ca49
       -rho*Y[jk49]*rate_eval.p_K49__Ca50
       -rho*Y[jk49]*rate_eval.p_K49__He4_Ar46
       +rho*Y[jca52]*rate_eval.p_Ca52__He4_K49
       +rho*Y[jar49]*rate_eval.p_Ar49__n_K49
       +rho*Y[jar48]*rate_eval.p_Ar48__K49
       )

    jac[jk49, jhe4] = (
       -rho*Y[jk49]*rate_eval.He4_K49__n_Sc52
       -rho*Y[jk49]*rate_eval.He4_K49__Sc53
       +rho*Y[jcl46]*rate_eval.He4_Cl46__n_K49
       +rho*Y[jcl45]*rate_eval.He4_Cl45__K49
       )

    jac[jk49, jcl45] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl45__K49
       )

    jac[jk49, jcl46] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl46__n_K49
       )

    jac[jk49, jar48] = (
       +rho*Y[jp]*rate_eval.p_Ar48__K49
       )

    jac[jk49, jar49] = (
       +rate_eval.Ar49__K49__weak__wc12
       +rho*Y[jp]*rate_eval.p_Ar49__n_K49
       )

    jac[jk49, jar50] = (
       +rate_eval.Ar50__n_K49__weak__wc12
       )

    jac[jk49, jar51] = (
       +rate_eval.Ar51__n_n_K49__weak__mp17
       )

    jac[jk49, jar52] = (
       +rate_eval.Ar52__n_n_n_K49__weak__mo03
       )

    jac[jk49, jk48] = (
       +rho*Y[jn]*rate_eval.n_K48__K49
       )

    jac[jk49, jk49] = (
       -rho*Y[jhe4]*rate_eval.He4_K49__n_Sc52
       -rho*Y[jp]*rate_eval.p_K49__n_Ca49
       -rho*Y[jhe4]*rate_eval.He4_K49__Sc53
       -rho*Y[jn]*rate_eval.n_K49__K50
       -rate_eval.K49__Ca49__weak__wc12
       -rho*Y[jp]*rate_eval.p_K49__Ca50
       -rho*Y[jp]*rate_eval.p_K49__He4_Ar46
       -rate_eval.K49__n_Ca48__weak__wc12
       )

    jac[jk49, jca52] = (
       +rho*Y[jp]*rate_eval.p_Ca52__He4_K49
       )

    jac[jk50, jn] = (
       -rho*Y[jk50]*rate_eval.n_K50__K51
       +rho*Y[jk49]*rate_eval.n_K49__K50
       )

    jac[jk50, jp] = (
       -rho*Y[jk50]*rate_eval.p_K50__n_Ca50
       -rho*Y[jk50]*rate_eval.p_K50__He4_Ar47
       -rho*Y[jk50]*rate_eval.p_K50__Ca51
       +rho*Y[jar50]*rate_eval.p_Ar50__n_K50
       +rho*Y[jca53]*rate_eval.p_Ca53__He4_K50
       +rho*Y[jar49]*rate_eval.p_Ar49__K50
       )

    jac[jk50, jhe4] = (
       -rho*Y[jk50]*rate_eval.He4_K50__n_Sc53
       -rho*Y[jk50]*rate_eval.He4_K50__Sc54
       +rho*Y[jcl47]*rate_eval.He4_Cl47__n_K50
       +rho*Y[jcl46]*rate_eval.He4_Cl46__K50
       )

    jac[jk50, jcl46] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl46__K50
       )

    jac[jk50, jcl47] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl47__n_K50
       )

    jac[jk50, jar49] = (
       +rho*Y[jp]*rate_eval.p_Ar49__K50
       )

    jac[jk50, jar50] = (
       +rho*Y[jp]*rate_eval.p_Ar50__n_K50
       +rate_eval.Ar50__K50__weak__wc12
       )

    jac[jk50, jar51] = (
       +rate_eval.Ar51__n_K50__weak__mp17
       )

    jac[jk50, jar52] = (
       +rate_eval.Ar52__n_n_K50__weak__mp17
       )

    jac[jk50, jar53] = (
       +rate_eval.Ar53__n_n_n_K50__weak__mo03
       )

    jac[jk50, jk49] = (
       +rho*Y[jn]*rate_eval.n_K49__K50
       )

    jac[jk50, jk50] = (
       -rho*Y[jhe4]*rate_eval.He4_K50__n_Sc53
       -rho*Y[jhe4]*rate_eval.He4_K50__Sc54
       -rho*Y[jp]*rate_eval.p_K50__n_Ca50
       -rho*Y[jn]*rate_eval.n_K50__K51
       -rho*Y[jp]*rate_eval.p_K50__He4_Ar47
       -rate_eval.K50__n_Ca49__weak__wc12
       -rho*Y[jp]*rate_eval.p_K50__Ca51
       -rate_eval.K50__Ca50__weak__wc12
       -rate_eval.K50__n_n_Ca48__weak__mp17
       )

    jac[jk50, jca53] = (
       +rho*Y[jp]*rate_eval.p_Ca53__He4_K50
       )

    jac[jk51, jn] = (
       -rho*Y[jk51]*rate_eval.n_K51__K52
       +rho*Y[jk50]*rate_eval.n_K50__K51
       )

    jac[jk51, jp] = (
       -rho*Y[jk51]*rate_eval.p_K51__n_Ca51
       -rho*Y[jk51]*rate_eval.p_K51__He4_Ar48
       -rho*Y[jk51]*rate_eval.p_K51__Ca52
       +rho*Y[jca54]*rate_eval.p_Ca54__He4_K51
       +rho*Y[jar51]*rate_eval.p_Ar51__n_K51
       +rho*Y[jar50]*rate_eval.p_Ar50__K51
       )

    jac[jk51, jhe4] = (
       -rho*Y[jk51]*rate_eval.He4_K51__n_Sc54
       -rho*Y[jk51]*rate_eval.He4_K51__Sc55
       +rho*Y[jcl47]*rate_eval.He4_Cl47__K51
       +rho*Y[jcl48]*rate_eval.He4_Cl48__n_K51
       )

    jac[jk51, jcl47] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl47__K51
       )

    jac[jk51, jcl48] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl48__n_K51
       )

    jac[jk51, jar50] = (
       +rho*Y[jp]*rate_eval.p_Ar50__K51
       )

    jac[jk51, jar51] = (
       +rate_eval.Ar51__K51__weak__mo03
       +rho*Y[jp]*rate_eval.p_Ar51__n_K51
       )

    jac[jk51, jar52] = (
       +rate_eval.Ar52__n_K51__weak__mp17
       )

    jac[jk51, jar53] = (
       +rate_eval.Ar53__n_n_K51__weak__mp17
       )

    jac[jk51, jar54] = (
       +rate_eval.Ar54__n_n_n_K51__weak__mo03
       )

    jac[jk51, jk50] = (
       +rho*Y[jn]*rate_eval.n_K50__K51
       )

    jac[jk51, jk51] = (
       -rho*Y[jhe4]*rate_eval.He4_K51__n_Sc54
       -rho*Y[jp]*rate_eval.p_K51__n_Ca51
       -rho*Y[jp]*rate_eval.p_K51__He4_Ar48
       -rho*Y[jhe4]*rate_eval.He4_K51__Sc55
       -rho*Y[jp]*rate_eval.p_K51__Ca52
       -rho*Y[jn]*rate_eval.n_K51__K52
       -rate_eval.K51__n_Ca50__weak__wc12
       -rate_eval.K51__Ca51__weak__wc12
       )

    jac[jk51, jca54] = (
       +rho*Y[jp]*rate_eval.p_Ca54__He4_K51
       )

    jac[jk52, jn] = (
       -rho*Y[jk52]*rate_eval.n_K52__K53
       +rho*Y[jk51]*rate_eval.n_K51__K52
       )

    jac[jk52, jp] = (
       -rho*Y[jk52]*rate_eval.p_K52__He4_Ar49
       -rho*Y[jk52]*rate_eval.p_K52__Ca53
       -rho*Y[jk52]*rate_eval.p_K52__n_Ca52
       +rho*Y[jca55]*rate_eval.p_Ca55__He4_K52
       +rho*Y[jar52]*rate_eval.p_Ar52__n_K52
       +rho*Y[jar51]*rate_eval.p_Ar51__K52
       )

    jac[jk52, jhe4] = (
       -rho*Y[jk52]*rate_eval.He4_K52__n_Sc55
       -rho*Y[jk52]*rate_eval.He4_K52__Sc56
       +rho*Y[jcl49]*rate_eval.He4_Cl49__n_K52
       +rho*Y[jcl48]*rate_eval.He4_Cl48__K52
       )

    jac[jk52, jcl48] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl48__K52
       )

    jac[jk52, jcl49] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl49__n_K52
       )

    jac[jk52, jar51] = (
       +rho*Y[jp]*rate_eval.p_Ar51__K52
       )

    jac[jk52, jar52] = (
       +rho*Y[jp]*rate_eval.p_Ar52__n_K52
       +rate_eval.Ar52__K52__weak__mo03
       )

    jac[jk52, jar53] = (
       +rate_eval.Ar53__n_K52__weak__mp17
       )

    jac[jk52, jar54] = (
       +rate_eval.Ar54__n_n_K52__weak__mp17
       )

    jac[jk52, jk51] = (
       +rho*Y[jn]*rate_eval.n_K51__K52
       )

    jac[jk52, jk52] = (
       -rho*Y[jhe4]*rate_eval.He4_K52__n_Sc55
       -rate_eval.K52__Ca52__weak__wc17
       -rho*Y[jp]*rate_eval.p_K52__He4_Ar49
       -rho*Y[jp]*rate_eval.p_K52__Ca53
       -rho*Y[jn]*rate_eval.n_K52__K53
       -rate_eval.K52__n_n_Ca50__weak__mp17
       -rate_eval.K52__n_Ca51__weak__wc12
       -rho*Y[jp]*rate_eval.p_K52__n_Ca52
       -rho*Y[jhe4]*rate_eval.He4_K52__Sc56
       )

    jac[jk52, jca55] = (
       +rho*Y[jp]*rate_eval.p_Ca55__He4_K52
       )

    jac[jk53, jn] = (
       -rho*Y[jk53]*rate_eval.n_K53__K54
       +rho*Y[jk52]*rate_eval.n_K52__K53
       )

    jac[jk53, jp] = (
       -rho*Y[jk53]*rate_eval.p_K53__n_Ca53
       -rho*Y[jk53]*rate_eval.p_K53__Ca54
       -rho*Y[jk53]*rate_eval.p_K53__He4_Ar50
       +rho*Y[jca56]*rate_eval.p_Ca56__He4_K53
       +rho*Y[jar53]*rate_eval.p_Ar53__n_K53
       +rho*Y[jar52]*rate_eval.p_Ar52__K53
       )

    jac[jk53, jhe4] = (
       -rho*Y[jk53]*rate_eval.He4_K53__n_Sc56
       -rho*Y[jk53]*rate_eval.He4_K53__Sc57
       +rho*Y[jcl49]*rate_eval.He4_Cl49__K53
       +rho*Y[jcl50]*rate_eval.He4_Cl50__n_K53
       )

    jac[jk53, jcl49] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl49__K53
       )

    jac[jk53, jcl50] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl50__n_K53
       )

    jac[jk53, jar52] = (
       +rho*Y[jp]*rate_eval.p_Ar52__K53
       )

    jac[jk53, jar53] = (
       +rho*Y[jp]*rate_eval.p_Ar53__n_K53
       +rate_eval.Ar53__K53__weak__mo03
       )

    jac[jk53, jar54] = (
       +rate_eval.Ar54__n_K53__weak__mp17
       )

    jac[jk53, jk52] = (
       +rho*Y[jn]*rate_eval.n_K52__K53
       )

    jac[jk53, jk53] = (
       -rate_eval.K53__n_n_n_Ca50__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_K53__n_Sc56
       -rho*Y[jp]*rate_eval.p_K53__n_Ca53
       -rho*Y[jn]*rate_eval.n_K53__K54
       -rate_eval.K53__n_Ca52__weak__wc17
       -rho*Y[jp]*rate_eval.p_K53__Ca54
       -rate_eval.K53__n_n_Ca51__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_K53__Sc57
       -rate_eval.K53__Ca53__weak__wc17
       -rho*Y[jp]*rate_eval.p_K53__He4_Ar50
       )

    jac[jk53, jca56] = (
       +rho*Y[jp]*rate_eval.p_Ca56__He4_K53
       )

    jac[jk54, jn] = (
       -rho*Y[jk54]*rate_eval.n_K54__K55
       +rho*Y[jk53]*rate_eval.n_K53__K54
       )

    jac[jk54, jp] = (
       -rho*Y[jk54]*rate_eval.p_K54__n_Ca54
       -rho*Y[jk54]*rate_eval.p_K54__Ca55
       -rho*Y[jk54]*rate_eval.p_K54__He4_Ar51
       +rho*Y[jar54]*rate_eval.p_Ar54__n_K54
       +rho*Y[jca57]*rate_eval.p_Ca57__He4_K54
       +rho*Y[jar53]*rate_eval.p_Ar53__K54
       )

    jac[jk54, jhe4] = (
       -rho*Y[jk54]*rate_eval.He4_K54__n_Sc57
       -rho*Y[jk54]*rate_eval.He4_K54__Sc58
       +rho*Y[jcl51]*rate_eval.He4_Cl51__n_K54
       +rho*Y[jcl50]*rate_eval.He4_Cl50__K54
       )

    jac[jk54, jcl50] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl50__K54
       )

    jac[jk54, jcl51] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl51__n_K54
       )

    jac[jk54, jar53] = (
       +rho*Y[jp]*rate_eval.p_Ar53__K54
       )

    jac[jk54, jar54] = (
       +rho*Y[jp]*rate_eval.p_Ar54__n_K54
       +rate_eval.Ar54__K54__weak__mo03
       )

    jac[jk54, jk53] = (
       +rho*Y[jn]*rate_eval.n_K53__K54
       )

    jac[jk54, jk54] = (
       -rate_eval.K54__n_n_n_Ca51__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_K54__n_Sc57
       -rho*Y[jp]*rate_eval.p_K54__n_Ca54
       -rate_eval.K54__n_n_Ca52__weak__mp17
       -rho*Y[jp]*rate_eval.p_K54__Ca55
       -rate_eval.K54__n_Ca53__weak__mp17
       -rho*Y[jn]*rate_eval.n_K54__K55
       -rho*Y[jp]*rate_eval.p_K54__He4_Ar51
       -rho*Y[jhe4]*rate_eval.He4_K54__Sc58
       -rate_eval.K54__Ca54__weak__wc17
       )

    jac[jk54, jca57] = (
       +rho*Y[jp]*rate_eval.p_Ca57__He4_K54
       )

    jac[jk55, jn] = (
       -rho*Y[jk55]*rate_eval.n_K55__K56
       +rho*Y[jk54]*rate_eval.n_K54__K55
       )

    jac[jk55, jp] = (
       -rho*Y[jk55]*rate_eval.p_K55__n_Ca55
       -rho*Y[jk55]*rate_eval.p_K55__Ca56
       -rho*Y[jk55]*rate_eval.p_K55__He4_Ar52
       +rho*Y[jca58]*rate_eval.p_Ca58__He4_K55
       +rho*Y[jar54]*rate_eval.p_Ar54__K55
       )

    jac[jk55, jhe4] = (
       -rho*Y[jk55]*rate_eval.He4_K55__n_Sc58
       -rho*Y[jk55]*rate_eval.He4_K55__Sc59
       +rho*Y[jcl51]*rate_eval.He4_Cl51__K55
       +rho*Y[jcl52]*rate_eval.He4_Cl52__n_K55
       )

    jac[jk55, jcl51] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl51__K55
       )

    jac[jk55, jcl52] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl52__n_K55
       )

    jac[jk55, jar54] = (
       +rho*Y[jp]*rate_eval.p_Ar54__K55
       )

    jac[jk55, jk54] = (
       +rho*Y[jn]*rate_eval.n_K54__K55
       )

    jac[jk55, jk55] = (
       -rate_eval.K55__n_n_n_Ca52__weak__mo03
       -rho*Y[jn]*rate_eval.n_K55__K56
       -rho*Y[jhe4]*rate_eval.He4_K55__n_Sc58
       -rho*Y[jhe4]*rate_eval.He4_K55__Sc59
       -rho*Y[jp]*rate_eval.p_K55__n_Ca55
       -rho*Y[jp]*rate_eval.p_K55__Ca56
       -rate_eval.K55__n_n_Ca53__weak__mp17
       -rate_eval.K55__n_Ca54__weak__mp17
       -rho*Y[jp]*rate_eval.p_K55__He4_Ar52
       -rate_eval.K55__Ca55__weak__mo03
       )

    jac[jk55, jca58] = (
       +rho*Y[jp]*rate_eval.p_Ca58__He4_K55
       )

    jac[jk56, jn] = (
       -rho*Y[jk56]*rate_eval.n_K56__K57
       +rho*Y[jk55]*rate_eval.n_K55__K56
       )

    jac[jk56, jp] = (
       -rho*Y[jk56]*rate_eval.p_K56__n_Ca56
       -rho*Y[jk56]*rate_eval.p_K56__He4_Ar53
       -rho*Y[jk56]*rate_eval.p_K56__Ca57
       +rho*Y[jca59]*rate_eval.p_Ca59__He4_K56
       )

    jac[jk56, jhe4] = (
       -rho*Y[jk56]*rate_eval.He4_K56__n_Sc59
       -rho*Y[jk56]*rate_eval.He4_K56__Sc60
       +rho*Y[jcl52]*rate_eval.He4_Cl52__K56
       )

    jac[jk56, jcl52] = (
       +rho*Y[jhe4]*rate_eval.He4_Cl52__K56
       )

    jac[jk56, jk55] = (
       +rho*Y[jn]*rate_eval.n_K55__K56
       )

    jac[jk56, jk56] = (
       -rate_eval.K56__n_n_n_Ca53__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_K56__n_Sc59
       -rho*Y[jp]*rate_eval.p_K56__n_Ca56
       -rho*Y[jp]*rate_eval.p_K56__He4_Ar53
       -rho*Y[jp]*rate_eval.p_K56__Ca57
       -rho*Y[jn]*rate_eval.n_K56__K57
       -rate_eval.K56__Ca56__weak__mo03
       -rate_eval.K56__n_Ca55__weak__mp17
       -rate_eval.K56__n_n_Ca54__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_K56__Sc60
       )

    jac[jk56, jca59] = (
       +rho*Y[jp]*rate_eval.p_Ca59__He4_K56
       )

    jac[jk57, jn] = (
       -rho*Y[jk57]*rate_eval.n_K57__K58
       +rho*Y[jk56]*rate_eval.n_K56__K57
       )

    jac[jk57, jp] = (
       -rho*Y[jk57]*rate_eval.p_K57__He4_Ar54
       -rho*Y[jk57]*rate_eval.p_K57__n_Ca57
       -rho*Y[jk57]*rate_eval.p_K57__Ca58
       +rho*Y[jca60]*rate_eval.p_Ca60__He4_K57
       )

    jac[jk57, jhe4] = (
       -rho*Y[jk57]*rate_eval.He4_K57__n_Sc60
       -rho*Y[jk57]*rate_eval.He4_K57__Sc61
       )

    jac[jk57, jk56] = (
       +rho*Y[jn]*rate_eval.n_K56__K57
       )

    jac[jk57, jk57] = (
       -rho*Y[jhe4]*rate_eval.He4_K57__n_Sc60
       -rho*Y[jp]*rate_eval.p_K57__He4_Ar54
       -rho*Y[jp]*rate_eval.p_K57__n_Ca57
       -rho*Y[jhe4]*rate_eval.He4_K57__Sc61
       -rho*Y[jp]*rate_eval.p_K57__Ca58
       -rho*Y[jn]*rate_eval.n_K57__K58
       -rate_eval.K57__n_n_Ca55__weak__mp17
       -rate_eval.K57__n_Ca56__weak__mp17
       -rate_eval.K57__Ca57__weak__mo03
       -rate_eval.K57__n_n_n_Ca54__weak__mo03
       )

    jac[jk57, jca60] = (
       +rho*Y[jp]*rate_eval.p_Ca60__He4_K57
       )

    jac[jk58, jn] = (
       -rho*Y[jk58]*rate_eval.n_K58__K59
       +rho*Y[jk57]*rate_eval.n_K57__K58
       )

    jac[jk58, jp] = (
       -rho*Y[jk58]*rate_eval.p_K58__n_Ca58
       -rho*Y[jk58]*rate_eval.p_K58__Ca59
       +rho*Y[jca61]*rate_eval.p_Ca61__He4_K58
       )

    jac[jk58, jhe4] = (
       -rho*Y[jk58]*rate_eval.He4_K58__Sc62
       -rho*Y[jk58]*rate_eval.He4_K58__n_Sc61
       )

    jac[jk58, jk57] = (
       +rho*Y[jn]*rate_eval.n_K57__K58
       )

    jac[jk58, jk58] = (
       -rate_eval.K58__n_n_n_Ca55__weak__mo03
       -rho*Y[jn]*rate_eval.n_K58__K59
       -rho*Y[jp]*rate_eval.p_K58__n_Ca58
       -rho*Y[jhe4]*rate_eval.He4_K58__Sc62
       -rho*Y[jhe4]*rate_eval.He4_K58__n_Sc61
       -rate_eval.K58__n_n_Ca56__weak__mp17
       -rho*Y[jp]*rate_eval.p_K58__Ca59
       -rate_eval.K58__n_Ca57__weak__mp17
       -rate_eval.K58__Ca58__weak__mo03
       )

    jac[jk58, jca61] = (
       +rho*Y[jp]*rate_eval.p_Ca61__He4_K58
       )

    jac[jk59, jn] = (
       +rho*Y[jk58]*rate_eval.n_K58__K59
       )

    jac[jk59, jp] = (
       -rho*Y[jk59]*rate_eval.p_K59__n_Ca59
       -rho*Y[jk59]*rate_eval.p_K59__Ca60
       )

    jac[jk59, jhe4] = (
       -rho*Y[jk59]*rate_eval.He4_K59__Sc63
       -rho*Y[jk59]*rate_eval.He4_K59__n_Sc62
       )

    jac[jk59, jk58] = (
       +rho*Y[jn]*rate_eval.n_K58__K59
       )

    jac[jk59, jk59] = (
       -rate_eval.K59__n_n_n_Ca56__weak__mo03
       -rho*Y[jp]*rate_eval.p_K59__n_Ca59
       -rate_eval.K59__Ca59__weak__mo03
       -rho*Y[jp]*rate_eval.p_K59__Ca60
       -rho*Y[jhe4]*rate_eval.He4_K59__Sc63
       -rate_eval.K59__n_n_Ca57__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_K59__n_Sc62
       -rate_eval.K59__n_Ca58__weak__mp17
       )

    jac[jca33, jn] = (
       -rho*Y[jca33]*rate_eval.n_Ca33__p_K33
       -rho*Y[jca33]*rate_eval.n_Ca33__He4_Ar30
       -rho*Y[jca33]*rate_eval.n_Ca33__Ca34
       )

    jac[jca33, jp] = (
       +rho*Y[jk32]*rate_eval.p_K32__Ca33
       )

    jac[jca33, jhe4] = (
       -rho*Y[jca33]*rate_eval.He4_Ca33__Ti37
       -rho*Y[jca33]*rate_eval.He4_Ca33__p_Sc36
       +rho*Y[jar29]*rate_eval.He4_Ar29__Ca33
       )

    jac[jca33, jar29] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar29__Ca33
       )

    jac[jca33, jk32] = (
       +rho*Y[jp]*rate_eval.p_K32__Ca33
       )

    jac[jca33, jca33] = (
       -rate_eval.Ca33__K33__weak__bqa_pos_
       -rho*Y[jn]*rate_eval.n_Ca33__p_K33
       -rho*Y[jn]*rate_eval.n_Ca33__He4_Ar30
       -rho*Y[jhe4]*rate_eval.He4_Ca33__Ti37
       -rho*Y[jn]*rate_eval.n_Ca33__Ca34
       -rho*Y[jhe4]*rate_eval.He4_Ca33__p_Sc36
       )

    jac[jca34, jn] = (
       -rho*Y[jca34]*rate_eval.n_Ca34__He4_Ar31
       -rho*Y[jca34]*rate_eval.n_Ca34__p_K34
       -rho*Y[jca34]*rate_eval.n_Ca34__Ca35
       +rho*Y[jti37]*rate_eval.n_Ti37__He4_Ca34
       +rho*Y[jca33]*rate_eval.n_Ca33__Ca34
       )

    jac[jca34, jp] = (
       -rho*Y[jca34]*rate_eval.p_Ca34__Sc35
       +rho*Y[jk33]*rate_eval.p_K33__Ca34
       )

    jac[jca34, jhe4] = (
       -rho*Y[jca34]*rate_eval.He4_Ca34__Ti38
       -rho*Y[jca34]*rate_eval.He4_Ca34__p_Sc37
       +rho*Y[jk31]*rate_eval.He4_K31__p_Ca34
       +rho*Y[jar30]*rate_eval.He4_Ar30__Ca34
       )

    jac[jca34, jar30] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar30__Ca34
       )

    jac[jca34, jk31] = (
       +rho*Y[jhe4]*rate_eval.He4_K31__p_Ca34
       )

    jac[jca34, jk33] = (
       +rho*Y[jp]*rate_eval.p_K33__Ca34
       )

    jac[jca34, jca33] = (
       +rho*Y[jn]*rate_eval.n_Ca33__Ca34
       )

    jac[jca34, jca34] = (
       -rho*Y[jn]*rate_eval.n_Ca34__He4_Ar31
       -rho*Y[jn]*rate_eval.n_Ca34__p_K34
       -rate_eval.Ca34__K34__weak__bqa_pos_
       -rho*Y[jhe4]*rate_eval.He4_Ca34__Ti38
       -rho*Y[jp]*rate_eval.p_Ca34__Sc35
       -rho*Y[jn]*rate_eval.n_Ca34__Ca35
       -rho*Y[jhe4]*rate_eval.He4_Ca34__p_Sc37
       )

    jac[jca34, jti37] = (
       +rho*Y[jn]*rate_eval.n_Ti37__He4_Ca34
       )

    jac[jca35, jn] = (
       -rho*Y[jca35]*rate_eval.n_Ca35__He4_Ar32
       -rho*Y[jca35]*rate_eval.n_Ca35__p_K35
       -rho*Y[jca35]*rate_eval.n_Ca35__Ca36
       +rho*Y[jti38]*rate_eval.n_Ti38__He4_Ca35
       +rho*Y[jsc35]*rate_eval.n_Sc35__p_Ca35
       +rho*Y[jca34]*rate_eval.n_Ca34__Ca35
       )

    jac[jca35, jp] = (
       -rho*Y[jca35]*rate_eval.p_Ca35__Sc36
       +rho*Y[jk34]*rate_eval.p_K34__Ca35
       )

    jac[jca35, jhe4] = (
       -rho*Y[jca35]*rate_eval.He4_Ca35__Ti39
       -rho*Y[jca35]*rate_eval.He4_Ca35__p_Sc38
       +rho*Y[jar31]*rate_eval.He4_Ar31__Ca35
       +rho*Y[jk32]*rate_eval.He4_K32__p_Ca35
       )

    jac[jca35, jar31] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar31__Ca35
       )

    jac[jca35, jk32] = (
       +rho*Y[jhe4]*rate_eval.He4_K32__p_Ca35
       )

    jac[jca35, jk34] = (
       +rho*Y[jp]*rate_eval.p_K34__Ca35
       )

    jac[jca35, jca34] = (
       +rho*Y[jn]*rate_eval.n_Ca34__Ca35
       )

    jac[jca35, jca35] = (
       -rho*Y[jn]*rate_eval.n_Ca35__He4_Ar32
       -rho*Y[jn]*rate_eval.n_Ca35__p_K35
       -rate_eval.Ca35__K35__weak__wc17
       -rho*Y[jhe4]*rate_eval.He4_Ca35__Ti39
       -rho*Y[jp]*rate_eval.p_Ca35__Sc36
       -rate_eval.Ca35__p_p_Cl33__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ca35__p_Sc38
       -rate_eval.Ca35__p_Ar34__weak__wc17
       -rho*Y[jn]*rate_eval.n_Ca35__Ca36
       )

    jac[jca35, jsc35] = (
       +rho*Y[jn]*rate_eval.n_Sc35__p_Ca35
       +rate_eval.Sc35__Ca35__weak__bqa_pos_
       )

    jac[jca35, jti38] = (
       +rho*Y[jn]*rate_eval.n_Ti38__He4_Ca35
       )

    jac[jca36, jn] = (
       -rho*Y[jca36]*rate_eval.n_Ca36__p_K36
       -rho*Y[jca36]*rate_eval.n_Ca36__He4_Ar33
       -rho*Y[jca36]*rate_eval.n_Ca36__Ca37
       +rho*Y[jti39]*rate_eval.n_Ti39__He4_Ca36
       +rho*Y[jsc36]*rate_eval.n_Sc36__p_Ca36
       +rho*Y[jca35]*rate_eval.n_Ca35__Ca36
       )

    jac[jca36, jp] = (
       -rho*Y[jca36]*rate_eval.p_Ca36__Sc37
       +rho*Y[jk35]*rate_eval.p_K35__Ca36
       )

    jac[jca36, jhe4] = (
       -rho*Y[jca36]*rate_eval.He4_Ca36__p_p_Ca38
       -rho*Y[jca36]*rate_eval.He4_Ca36__p_Sc39
       -rho*Y[jca36]*rate_eval.He4_Ca36__Ti40
       +rho*Y[jar32]*rate_eval.He4_Ar32__Ca36
       +rho*Y[jk33]*rate_eval.He4_K33__p_Ca36
       )

    jac[jca36, jar32] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar32__Ca36
       )

    jac[jca36, jk33] = (
       +rho*Y[jhe4]*rate_eval.He4_K33__p_Ca36
       )

    jac[jca36, jk35] = (
       +rho*Y[jp]*rate_eval.p_K35__Ca36
       )

    jac[jca36, jca35] = (
       +rho*Y[jn]*rate_eval.n_Ca35__Ca36
       )

    jac[jca36, jca36] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca36__p_p_Ca38
       -rho*Y[jn]*rate_eval.n_Ca36__p_K36
       -rho*Y[jn]*rate_eval.n_Ca36__He4_Ar33
       -rho*Y[jp]*rate_eval.p_Ca36__Sc37
       -rate_eval.Ca36__K36__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ca36__Ca37
       -rho*Y[jhe4]*rate_eval.He4_Ca36__p_Sc39
       -rho*Y[jhe4]*rate_eval.He4_Ca36__Ti40
       -rate_eval.Ca36__p_Ar35__weak__wc12
       )

    jac[jca36, jsc36] = (
       +rho*Y[jn]*rate_eval.n_Sc36__p_Ca36
       +rate_eval.Sc36__Ca36__weak__bqa_pos_
       )

    jac[jca36, jti39] = (
       +rho*Y[jn]*rate_eval.n_Ti39__He4_Ca36
       )

    jac[jca37, jn] = (
       -rho*Y[jca37]*rate_eval.n_Ca37__He4_Ar34
       -rho*Y[jca37]*rate_eval.n_Ca37__p_K37
       -rho*Y[jca37]*rate_eval.n_Ca37__Ca38
       +rho*Y[jsc37]*rate_eval.n_Sc37__p_Ca37
       +rho*Y[jca36]*rate_eval.n_Ca36__Ca37
       +rho*Y[jti40]*rate_eval.n_Ti40__He4_Ca37
       )

    jac[jca37, jp] = (
       -rho*Y[jca37]*rate_eval.p_Ca37__Sc38
       +rho*Y[jk36]*rate_eval.p_K36__Ca37
       )

    jac[jca37, jhe4] = (
       -rho*Y[jca37]*rate_eval.He4_Ca37__Ti41
       -rho*Y[jca37]*rate_eval.He4_Ca37__p_Sc40
       +rho*Y[jk34]*rate_eval.He4_K34__p_Ca37
       +rho*Y[jar33]*rate_eval.He4_Ar33__Ca37
       )

    jac[jca37, jar33] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar33__Ca37
       )

    jac[jca37, jk34] = (
       +rho*Y[jhe4]*rate_eval.He4_K34__p_Ca37
       )

    jac[jca37, jk36] = (
       +rho*Y[jp]*rate_eval.p_K36__Ca37
       )

    jac[jca37, jca36] = (
       +rho*Y[jn]*rate_eval.n_Ca36__Ca37
       )

    jac[jca37, jca37] = (
       -rho*Y[jn]*rate_eval.n_Ca37__He4_Ar34
       -rho*Y[jn]*rate_eval.n_Ca37__p_K37
       -rho*Y[jhe4]*rate_eval.He4_Ca37__Ti41
       -rho*Y[jn]*rate_eval.n_Ca37__Ca38
       -rho*Y[jhe4]*rate_eval.He4_Ca37__p_Sc40
       -rate_eval.Ca37__p_Ar36__weak__wc12
       -rate_eval.Ca37__K37__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ca37__Sc38
       )

    jac[jca37, jsc37] = (
       +rho*Y[jn]*rate_eval.n_Sc37__p_Ca37
       +rate_eval.Sc37__Ca37__weak__bqa_pos_
       )

    jac[jca37, jti40] = (
       +rho*Y[jn]*rate_eval.n_Ti40__He4_Ca37
       )

    jac[jca38, jn] = (
       -rho*Y[jca38]*rate_eval.n_Ca38__p_K38
       -rho*Y[jca38]*rate_eval.n_Ca38__Ca39
       -rho*Y[jca38]*rate_eval.n_Ca38__He4_Ar35
       +rho*Y[jti41]*rate_eval.n_Ti41__He4_Ca38
       +rho*Y[jca37]*rate_eval.n_Ca37__Ca38
       +rho*Y[jsc38]*rate_eval.n_Sc38__p_Ca38
       )

    jac[jca38, jp] = (
       -rho*Y[jca38]*rate_eval.p_Ca38__Sc39
       +rho*Y[jk37]*rate_eval.p_K37__Ca38
       )

    jac[jca38, jhe4] = (
       -rho*Y[jca38]*rate_eval.He4_Ca38__Ti42
       -rho*Y[jca38]*rate_eval.He4_Ca38__p_Sc41
       +rho*Y[jca36]*rate_eval.He4_Ca36__p_p_Ca38
       +rho*Y[jk35]*rate_eval.He4_K35__p_Ca38
       +rho*Y[jar34]*rate_eval.He4_Ar34__Ca38
       )

    jac[jca38, jar34] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar34__Ca38
       )

    jac[jca38, jk35] = (
       +rho*Y[jhe4]*rate_eval.He4_K35__p_Ca38
       )

    jac[jca38, jk37] = (
       +rho*Y[jp]*rate_eval.p_K37__Ca38
       )

    jac[jca38, jca36] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca36__p_p_Ca38
       )

    jac[jca38, jca37] = (
       +rho*Y[jn]*rate_eval.n_Ca37__Ca38
       )

    jac[jca38, jca38] = (
       -rho*Y[jn]*rate_eval.n_Ca38__p_K38
       -rho*Y[jhe4]*rate_eval.He4_Ca38__Ti42
       -rho*Y[jn]*rate_eval.n_Ca38__Ca39
       -rho*Y[jhe4]*rate_eval.He4_Ca38__p_Sc41
       -rate_eval.Ca38__K38__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ca38__Sc39
       -rho*Y[jn]*rate_eval.n_Ca38__He4_Ar35
       )

    jac[jca38, jsc38] = (
       +rate_eval.Sc38__Ca38__weak__mo97
       +rho*Y[jn]*rate_eval.n_Sc38__p_Ca38
       )

    jac[jca38, jti39] = (
       +rate_eval.Ti39__p_Ca38__weak__wc12
       )

    jac[jca38, jti41] = (
       +rho*Y[jn]*rate_eval.n_Ti41__He4_Ca38
       )

    jac[jca39, jn] = (
       -rho*Y[jca39]*rate_eval.n_Ca39__He4_Ar36
       -rho*Y[jca39]*rate_eval.n_Ca39__p_K39
       -rho*Y[jca39]*rate_eval.n_Ca39__Ca40
       +rho*Y[jti42]*rate_eval.n_Ti42__He4_Ca39
       +rho*Y[jca38]*rate_eval.n_Ca38__Ca39
       +rho*Y[jsc39]*rate_eval.n_Sc39__p_Ca39
       )

    jac[jca39, jp] = (
       -rho*Y[jca39]*rate_eval.p_Ca39__Sc40
       +rho*Y[jk38]*rate_eval.p_K38__Ca39
       +rho*Y[jsc42]*rate_eval.p_Sc42__He4_Ca39
       )

    jac[jca39, jhe4] = (
       -rho*Y[jca39]*rate_eval.He4_Ca39__Ti43
       +rho*Y[jk36]*rate_eval.He4_K36__p_Ca39
       +rho*Y[jar35]*rate_eval.He4_Ar35__Ca39
       )

    jac[jca39, jar35] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar35__Ca39
       )

    jac[jca39, jk36] = (
       +rho*Y[jhe4]*rate_eval.He4_K36__p_Ca39
       )

    jac[jca39, jk38] = (
       +rho*Y[jp]*rate_eval.p_K38__Ca39
       )

    jac[jca39, jca38] = (
       +rho*Y[jn]*rate_eval.n_Ca38__Ca39
       )

    jac[jca39, jca39] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca39__Ti43
       -rate_eval.Ca39__K39__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ca39__He4_Ar36
       -rho*Y[jn]*rate_eval.n_Ca39__p_K39
       -rho*Y[jp]*rate_eval.p_Ca39__Sc40
       -rho*Y[jn]*rate_eval.n_Ca39__Ca40
       )

    jac[jca39, jsc39] = (
       +rate_eval.Sc39__Ca39__weak__mo97
       +rho*Y[jn]*rate_eval.n_Sc39__p_Ca39
       )

    jac[jca39, jsc42] = (
       +rho*Y[jp]*rate_eval.p_Sc42__He4_Ca39
       )

    jac[jca39, jti40] = (
       +rate_eval.Ti40__p_Ca39__weak__wc12
       )

    jac[jca39, jti42] = (
       +rho*Y[jn]*rate_eval.n_Ti42__He4_Ca39
       )

    jac[jca40, jn] = (
       -rho*Y[jca40]*rate_eval.n_Ca40__He4_Ar37
       -rho*Y[jca40]*rate_eval.n_Ca40__Ca41
       +rho*Y[jti43]*rate_eval.n_Ti43__He4_Ca40
       +rho*Y[jsc40]*rate_eval.n_Sc40__p_Ca40
       +rho*Y[jca39]*rate_eval.n_Ca39__Ca40
       )

    jac[jca40, jp] = (
       -rho*Y[jca40]*rate_eval.p_Ca40__Sc41
       +rho*Y[jk40]*rate_eval.p_K40__n_Ca40
       +rho*Y[jk39]*rate_eval.p_K39__Ca40
       +rho*Y[jsc43]*rate_eval.p_Sc43__He4_Ca40
       )

    jac[jca40, jhe4] = (
       -rho*Y[jca40]*rate_eval.He4_Ca40__Ti44
       +rho*Y[jk37]*rate_eval.He4_K37__p_Ca40
       +rho*Y[jar36]*rate_eval.He4_Ar36__Ca40
       )

    jac[jca40, jar36] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar36__Ca40
       )

    jac[jca40, jk37] = (
       +rho*Y[jhe4]*rate_eval.He4_K37__p_Ca40
       )

    jac[jca40, jk39] = (
       +rho*Y[jp]*rate_eval.p_K39__Ca40
       )

    jac[jca40, jk40] = (
       +rho*Y[jp]*rate_eval.p_K40__n_Ca40
       +rate_eval.K40__Ca40__weak__wc12
       )

    jac[jca40, jca39] = (
       +rho*Y[jn]*rate_eval.n_Ca39__Ca40
       )

    jac[jca40, jca40] = (
       -rho*Y[jn]*rate_eval.n_Ca40__He4_Ar37
       -rho*Y[jhe4]*rate_eval.He4_Ca40__Ti44
       -rho*Y[jp]*rate_eval.p_Ca40__Sc41
       -rho*Y[jn]*rate_eval.n_Ca40__Ca41
       )

    jac[jca40, jsc40] = (
       +rho*Y[jn]*rate_eval.n_Sc40__p_Ca40
       +rate_eval.Sc40__Ca40__weak__wc12
       )

    jac[jca40, jsc43] = (
       +rho*Y[jp]*rate_eval.p_Sc43__He4_Ca40
       )

    jac[jca40, jti41] = (
       +rate_eval.Ti41__p_Ca40__weak__wc12
       )

    jac[jca40, jti43] = (
       +rho*Y[jn]*rate_eval.n_Ti43__He4_Ca40
       )

    jac[jca40, jcr43] = (
       +rate_eval.Cr43__p_p_p_Ca40__weak__wc12
       )

    jac[jca41, jn] = (
       -rho*Y[jca41]*rate_eval.n_Ca41__Ca42
       -rho*Y[jca41]*rate_eval.n_Ca41__He4_Ar38
       +rho*Y[jca40]*rate_eval.n_Ca40__Ca41
       +rho*Y[jsc41]*rate_eval.n_Sc41__p_Ca41
       +rho*Y[jti44]*rate_eval.n_Ti44__He4_Ca41
       )

    jac[jca41, jp] = (
       -rho*Y[jca41]*rate_eval.p_Ca41__Sc42
       +rho*Y[jsc44]*rate_eval.p_Sc44__He4_Ca41
       +rho*Y[jk41]*rate_eval.p_K41__n_Ca41
       +rho*Y[jk40]*rate_eval.p_K40__Ca41
       )

    jac[jca41, jhe4] = (
       -rho*Y[jca41]*rate_eval.He4_Ca41__Ti45
       +rho*Y[jk38]*rate_eval.He4_K38__p_Ca41
       +rho*Y[jar37]*rate_eval.He4_Ar37__Ca41
       )

    jac[jca41, jar37] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar37__Ca41
       )

    jac[jca41, jk38] = (
       +rho*Y[jhe4]*rate_eval.He4_K38__p_Ca41
       )

    jac[jca41, jk40] = (
       +rho*Y[jp]*rate_eval.p_K40__Ca41
       )

    jac[jca41, jk41] = (
       +rho*Y[jp]*rate_eval.p_K41__n_Ca41
       )

    jac[jca41, jca40] = (
       +rho*Y[jn]*rate_eval.n_Ca40__Ca41
       )

    jac[jca41, jca41] = (
       -rho*Y[jp]*rate_eval.p_Ca41__Sc42
       -rho*Y[jn]*rate_eval.n_Ca41__Ca42
       -rho*Y[jn]*rate_eval.n_Ca41__He4_Ar38
       -rho*Y[jhe4]*rate_eval.He4_Ca41__Ti45
       -rate_eval.Ca41__K41__weak__wc12
       )

    jac[jca41, jsc41] = (
       +rate_eval.Sc41__Ca41__weak__wc12
       +rho*Y[jn]*rate_eval.n_Sc41__p_Ca41
       )

    jac[jca41, jsc44] = (
       +rho*Y[jp]*rate_eval.p_Sc44__He4_Ca41
       )

    jac[jca41, jti44] = (
       +rho*Y[jn]*rate_eval.n_Ti44__He4_Ca41
       )

    jac[jca42, jn] = (
       -rho*Y[jca42]*rate_eval.n_Ca42__Ca43
       -rho*Y[jca42]*rate_eval.n_Ca42__He4_Ar39
       +rho*Y[jsc42]*rate_eval.n_Sc42__p_Ca42
       +rho*Y[jti45]*rate_eval.n_Ti45__He4_Ca42
       +rho*Y[jca41]*rate_eval.n_Ca41__Ca42
       )

    jac[jca42, jp] = (
       -rho*Y[jca42]*rate_eval.p_Ca42__He4_K39
       -rho*Y[jca42]*rate_eval.p_Ca42__Sc43
       +rho*Y[jsc45]*rate_eval.p_Sc45__He4_Ca42
       +rho*Y[jk42]*rate_eval.p_K42__n_Ca42
       +rho*Y[jk41]*rate_eval.p_K41__Ca42
       )

    jac[jca42, jhe4] = (
       -rho*Y[jca42]*rate_eval.He4_Ca42__Ti46
       +rho*Y[jar38]*rate_eval.He4_Ar38__Ca42
       )

    jac[jca42, jar38] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar38__Ca42
       )

    jac[jca42, jk41] = (
       +rho*Y[jp]*rate_eval.p_K41__Ca42
       )

    jac[jca42, jk42] = (
       +rho*Y[jp]*rate_eval.p_K42__n_Ca42
       +rate_eval.K42__Ca42__weak__wc12
       )

    jac[jca42, jca41] = (
       +rho*Y[jn]*rate_eval.n_Ca41__Ca42
       )

    jac[jca42, jca42] = (
       -rho*Y[jp]*rate_eval.p_Ca42__He4_K39
       -rho*Y[jhe4]*rate_eval.He4_Ca42__Ti46
       -rho*Y[jp]*rate_eval.p_Ca42__Sc43
       -rho*Y[jn]*rate_eval.n_Ca42__Ca43
       -rho*Y[jn]*rate_eval.n_Ca42__He4_Ar39
       )

    jac[jca42, jsc42] = (
       +rho*Y[jn]*rate_eval.n_Sc42__p_Ca42
       +rate_eval.Sc42__Ca42__weak__wc12
       )

    jac[jca42, jsc45] = (
       +rho*Y[jp]*rate_eval.p_Sc45__He4_Ca42
       )

    jac[jca42, jti45] = (
       +rho*Y[jn]*rate_eval.n_Ti45__He4_Ca42
       )

    jac[jca43, jn] = (
       -rho*Y[jca43]*rate_eval.n_Ca43__He4_Ar40
       -rho*Y[jca43]*rate_eval.n_Ca43__Ca44
       +rho*Y[jsc43]*rate_eval.n_Sc43__p_Ca43
       +rho*Y[jca42]*rate_eval.n_Ca42__Ca43
       )

    jac[jca43, jp] = (
       -rho*Y[jca43]*rate_eval.p_Ca43__Sc44
       +rho*Y[jsc46]*rate_eval.p_Sc46__He4_Ca43
       +rho*Y[jk43]*rate_eval.p_K43__n_Ca43
       +rho*Y[jk42]*rate_eval.p_K42__Ca43
       )

    jac[jca43, jhe4] = (
       -rho*Y[jca43]*rate_eval.He4_Ca43__Ti47
       -rho*Y[jca43]*rate_eval.He4_Ca43__n_Ti46
       +rho*Y[jk40]*rate_eval.He4_K40__p_Ca43
       +rho*Y[jar39]*rate_eval.He4_Ar39__Ca43
       )

    jac[jca43, jar39] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar39__Ca43
       )

    jac[jca43, jk40] = (
       +rho*Y[jhe4]*rate_eval.He4_K40__p_Ca43
       )

    jac[jca43, jk42] = (
       +rho*Y[jp]*rate_eval.p_K42__Ca43
       )

    jac[jca43, jk43] = (
       +rho*Y[jp]*rate_eval.p_K43__n_Ca43
       +rate_eval.K43__Ca43__weak__wc12
       )

    jac[jca43, jca42] = (
       +rho*Y[jn]*rate_eval.n_Ca42__Ca43
       )

    jac[jca43, jca43] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca43__Ti47
       -rho*Y[jhe4]*rate_eval.He4_Ca43__n_Ti46
       -rho*Y[jn]*rate_eval.n_Ca43__He4_Ar40
       -rho*Y[jp]*rate_eval.p_Ca43__Sc44
       -rho*Y[jn]*rate_eval.n_Ca43__Ca44
       )

    jac[jca43, jsc43] = (
       +rho*Y[jn]*rate_eval.n_Sc43__p_Ca43
       +rate_eval.Sc43__Ca43__weak__wc12
       )

    jac[jca43, jsc46] = (
       +rho*Y[jp]*rate_eval.p_Sc46__He4_Ca43
       )

    jac[jca44, jn] = (
       -rho*Y[jca44]*rate_eval.n_Ca44__Ca45
       +rho*Y[jsc44]*rate_eval.n_Sc44__p_Ca44
       +rho*Y[jti47]*rate_eval.n_Ti47__He4_Ca44
       +rho*Y[jca43]*rate_eval.n_Ca43__Ca44
       )

    jac[jca44, jp] = (
       -rho*Y[jca44]*rate_eval.p_Ca44__Sc45
       +rho*Y[jsc47]*rate_eval.p_Sc47__He4_Ca44
       +rho*Y[jk44]*rate_eval.p_K44__n_Ca44
       +rho*Y[jk43]*rate_eval.p_K43__Ca44
       )

    jac[jca44, jhe4] = (
       -rho*Y[jca44]*rate_eval.He4_Ca44__Ti48
       +rho*Y[jk41]*rate_eval.He4_K41__p_Ca44
       +rho*Y[jar41]*rate_eval.He4_Ar41__n_Ca44
       +rho*Y[jar40]*rate_eval.He4_Ar40__Ca44
       )

    jac[jca44, jar40] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar40__Ca44
       )

    jac[jca44, jar41] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar41__n_Ca44
       )

    jac[jca44, jk41] = (
       +rho*Y[jhe4]*rate_eval.He4_K41__p_Ca44
       )

    jac[jca44, jk43] = (
       +rho*Y[jp]*rate_eval.p_K43__Ca44
       )

    jac[jca44, jk44] = (
       +rho*Y[jp]*rate_eval.p_K44__n_Ca44
       +rate_eval.K44__Ca44__weak__wc12
       )

    jac[jca44, jca43] = (
       +rho*Y[jn]*rate_eval.n_Ca43__Ca44
       )

    jac[jca44, jca44] = (
       -rho*Y[jp]*rate_eval.p_Ca44__Sc45
       -rho*Y[jhe4]*rate_eval.He4_Ca44__Ti48
       -rho*Y[jn]*rate_eval.n_Ca44__Ca45
       )

    jac[jca44, jsc44] = (
       +rho*Y[jn]*rate_eval.n_Sc44__p_Ca44
       +rate_eval.Sc44__Ca44__weak__wc12
       )

    jac[jca44, jsc47] = (
       +rho*Y[jp]*rate_eval.p_Sc47__He4_Ca44
       )

    jac[jca44, jti47] = (
       +rho*Y[jn]*rate_eval.n_Ti47__He4_Ca44
       )

    jac[jca45, jn] = (
       -rho*Y[jca45]*rate_eval.n_Ca45__Ca46
       +rho*Y[jsc45]*rate_eval.n_Sc45__p_Ca45
       +rho*Y[jca44]*rate_eval.n_Ca44__Ca45
       )

    jac[jca45, jp] = (
       -rho*Y[jca45]*rate_eval.p_Ca45__Sc46
       +rho*Y[jsc48]*rate_eval.p_Sc48__He4_Ca45
       +rho*Y[jk45]*rate_eval.p_K45__n_Ca45
       +rho*Y[jk44]*rate_eval.p_K44__Ca45
       )

    jac[jca45, jhe4] = (
       -rho*Y[jca45]*rate_eval.He4_Ca45__Ti49
       -rho*Y[jca45]*rate_eval.He4_Ca45__n_Ti48
       +rho*Y[jk42]*rate_eval.He4_K42__p_Ca45
       +rho*Y[jar42]*rate_eval.He4_Ar42__n_Ca45
       +rho*Y[jar41]*rate_eval.He4_Ar41__Ca45
       )

    jac[jca45, jar41] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar41__Ca45
       )

    jac[jca45, jar42] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar42__n_Ca45
       )

    jac[jca45, jk42] = (
       +rho*Y[jhe4]*rate_eval.He4_K42__p_Ca45
       )

    jac[jca45, jk44] = (
       +rho*Y[jp]*rate_eval.p_K44__Ca45
       )

    jac[jca45, jk45] = (
       +rho*Y[jp]*rate_eval.p_K45__n_Ca45
       +rate_eval.K45__Ca45__weak__wc12
       )

    jac[jca45, jca44] = (
       +rho*Y[jn]*rate_eval.n_Ca44__Ca45
       )

    jac[jca45, jca45] = (
       -rho*Y[jp]*rate_eval.p_Ca45__Sc46
       -rho*Y[jhe4]*rate_eval.He4_Ca45__Ti49
       -rho*Y[jhe4]*rate_eval.He4_Ca45__n_Ti48
       -rho*Y[jn]*rate_eval.n_Ca45__Ca46
       -rate_eval.Ca45__Sc45__weak__wc12
       )

    jac[jca45, jsc45] = (
       +rho*Y[jn]*rate_eval.n_Sc45__p_Ca45
       )

    jac[jca45, jsc48] = (
       +rho*Y[jp]*rate_eval.p_Sc48__He4_Ca45
       )

    jac[jca46, jn] = (
       -rho*Y[jca46]*rate_eval.n_Ca46__Ca47
       +rho*Y[jti49]*rate_eval.n_Ti49__He4_Ca46
       +rho*Y[jsc46]*rate_eval.n_Sc46__p_Ca46
       +rho*Y[jca45]*rate_eval.n_Ca45__Ca46
       )

    jac[jca46, jp] = (
       -rho*Y[jca46]*rate_eval.p_Ca46__Sc47
       +rho*Y[jsc49]*rate_eval.p_Sc49__He4_Ca46
       +rho*Y[jk45]*rate_eval.p_K45__Ca46
       +rho*Y[jk46]*rate_eval.p_K46__n_Ca46
       )

    jac[jca46, jhe4] = (
       -rho*Y[jca46]*rate_eval.He4_Ca46__Ti50
       +rho*Y[jk43]*rate_eval.He4_K43__p_Ca46
       +rho*Y[jar43]*rate_eval.He4_Ar43__n_Ca46
       +rho*Y[jar42]*rate_eval.He4_Ar42__Ca46
       )

    jac[jca46, jar42] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar42__Ca46
       )

    jac[jca46, jar43] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar43__n_Ca46
       )

    jac[jca46, jk43] = (
       +rho*Y[jhe4]*rate_eval.He4_K43__p_Ca46
       )

    jac[jca46, jk45] = (
       +rho*Y[jp]*rate_eval.p_K45__Ca46
       )

    jac[jca46, jk46] = (
       +rho*Y[jp]*rate_eval.p_K46__n_Ca46
       +rate_eval.K46__Ca46__weak__wc12
       )

    jac[jca46, jca45] = (
       +rho*Y[jn]*rate_eval.n_Ca45__Ca46
       )

    jac[jca46, jca46] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca46__Ti50
       -rho*Y[jn]*rate_eval.n_Ca46__Ca47
       -rho*Y[jp]*rate_eval.p_Ca46__Sc47
       )

    jac[jca46, jsc46] = (
       +rho*Y[jn]*rate_eval.n_Sc46__p_Ca46
       )

    jac[jca46, jsc49] = (
       +rho*Y[jp]*rate_eval.p_Sc49__He4_Ca46
       )

    jac[jca46, jti49] = (
       +rho*Y[jn]*rate_eval.n_Ti49__He4_Ca46
       )

    jac[jca47, jn] = (
       -rho*Y[jca47]*rate_eval.n_Ca47__Ca48
       +rho*Y[jca46]*rate_eval.n_Ca46__Ca47
       )

    jac[jca47, jp] = (
       -rho*Y[jca47]*rate_eval.p_Ca47__n_Sc47
       -rho*Y[jca47]*rate_eval.p_Ca47__Sc48
       +rho*Y[jk46]*rate_eval.p_K46__Ca47
       +rho*Y[jk47]*rate_eval.p_K47__n_Ca47
       +rho*Y[jsc50]*rate_eval.p_Sc50__He4_Ca47
       )

    jac[jca47, jhe4] = (
       -rho*Y[jca47]*rate_eval.He4_Ca47__n_Ti50
       -rho*Y[jca47]*rate_eval.He4_Ca47__Ti51
       +rho*Y[jk44]*rate_eval.He4_K44__p_Ca47
       +rho*Y[jar43]*rate_eval.He4_Ar43__Ca47
       +rho*Y[jar44]*rate_eval.He4_Ar44__n_Ca47
       )

    jac[jca47, jar43] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar43__Ca47
       )

    jac[jca47, jar44] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar44__n_Ca47
       )

    jac[jca47, jk44] = (
       +rho*Y[jhe4]*rate_eval.He4_K44__p_Ca47
       )

    jac[jca47, jk46] = (
       +rho*Y[jp]*rate_eval.p_K46__Ca47
       )

    jac[jca47, jk47] = (
       +rate_eval.K47__Ca47__weak__wc12
       +rho*Y[jp]*rate_eval.p_K47__n_Ca47
       )

    jac[jca47, jk48] = (
       +rate_eval.K48__n_Ca47__weak__wc12
       )

    jac[jca47, jca46] = (
       +rho*Y[jn]*rate_eval.n_Ca46__Ca47
       )

    jac[jca47, jca47] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca47__n_Ti50
       -rho*Y[jp]*rate_eval.p_Ca47__n_Sc47
       -rho*Y[jhe4]*rate_eval.He4_Ca47__Ti51
       -rho*Y[jn]*rate_eval.n_Ca47__Ca48
       -rate_eval.Ca47__Sc47__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ca47__Sc48
       )

    jac[jca47, jsc50] = (
       +rho*Y[jp]*rate_eval.p_Sc50__He4_Ca47
       )

    jac[jca48, jn] = (
       -rho*Y[jca48]*rate_eval.n_Ca48__Ca49
       +rho*Y[jti51]*rate_eval.n_Ti51__He4_Ca48
       +rho*Y[jsc48]*rate_eval.n_Sc48__p_Ca48
       +rho*Y[jca47]*rate_eval.n_Ca47__Ca48
       )

    jac[jca48, jp] = (
       -rho*Y[jca48]*rate_eval.p_Ca48__Sc49
       +rho*Y[jsc51]*rate_eval.p_Sc51__He4_Ca48
       +rho*Y[jk48]*rate_eval.p_K48__n_Ca48
       +rho*Y[jk47]*rate_eval.p_K47__Ca48
       )

    jac[jca48, jhe4] = (
       -rho*Y[jca48]*rate_eval.He4_Ca48__Ti52
       +rho*Y[jk45]*rate_eval.He4_K45__p_Ca48
       +rho*Y[jar44]*rate_eval.He4_Ar44__Ca48
       +rho*Y[jar45]*rate_eval.He4_Ar45__n_Ca48
       )

    jac[jca48, jar44] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar44__Ca48
       )

    jac[jca48, jar45] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar45__n_Ca48
       )

    jac[jca48, jk45] = (
       +rho*Y[jhe4]*rate_eval.He4_K45__p_Ca48
       )

    jac[jca48, jk47] = (
       +rho*Y[jp]*rate_eval.p_K47__Ca48
       )

    jac[jca48, jk48] = (
       +rho*Y[jp]*rate_eval.p_K48__n_Ca48
       +rate_eval.K48__Ca48__weak__wc12
       )

    jac[jca48, jk49] = (
       +rate_eval.K49__n_Ca48__weak__wc12
       )

    jac[jca48, jk50] = (
       +rate_eval.K50__n_n_Ca48__weak__mp17
       )

    jac[jca48, jca47] = (
       +rho*Y[jn]*rate_eval.n_Ca47__Ca48
       )

    jac[jca48, jca48] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca48__Ti52
       -rho*Y[jn]*rate_eval.n_Ca48__Ca49
       -rho*Y[jp]*rate_eval.p_Ca48__Sc49
       -rate_eval.Ca48__Sc48__weak__mo03
       )

    jac[jca48, jsc48] = (
       +rho*Y[jn]*rate_eval.n_Sc48__p_Ca48
       )

    jac[jca48, jsc51] = (
       +rho*Y[jp]*rate_eval.p_Sc51__He4_Ca48
       )

    jac[jca48, jti51] = (
       +rho*Y[jn]*rate_eval.n_Ti51__He4_Ca48
       )

    jac[jca49, jn] = (
       -rho*Y[jca49]*rate_eval.n_Ca49__Ca50
       +rho*Y[jca48]*rate_eval.n_Ca48__Ca49
       )

    jac[jca49, jp] = (
       -rho*Y[jca49]*rate_eval.p_Ca49__Sc50
       -rho*Y[jca49]*rate_eval.p_Ca49__n_Sc49
       +rho*Y[jk48]*rate_eval.p_K48__Ca49
       +rho*Y[jsc52]*rate_eval.p_Sc52__He4_Ca49
       +rho*Y[jk49]*rate_eval.p_K49__n_Ca49
       )

    jac[jca49, jhe4] = (
       -rho*Y[jca49]*rate_eval.He4_Ca49__n_Ti52
       -rho*Y[jca49]*rate_eval.He4_Ca49__Ti53
       +rho*Y[jk46]*rate_eval.He4_K46__p_Ca49
       +rho*Y[jar46]*rate_eval.He4_Ar46__n_Ca49
       +rho*Y[jar45]*rate_eval.He4_Ar45__Ca49
       )

    jac[jca49, jar45] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar45__Ca49
       )

    jac[jca49, jar46] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar46__n_Ca49
       )

    jac[jca49, jk46] = (
       +rho*Y[jhe4]*rate_eval.He4_K46__p_Ca49
       )

    jac[jca49, jk48] = (
       +rho*Y[jp]*rate_eval.p_K48__Ca49
       )

    jac[jca49, jk49] = (
       +rho*Y[jp]*rate_eval.p_K49__n_Ca49
       +rate_eval.K49__Ca49__weak__wc12
       )

    jac[jca49, jk50] = (
       +rate_eval.K50__n_Ca49__weak__wc12
       )

    jac[jca49, jca48] = (
       +rho*Y[jn]*rate_eval.n_Ca48__Ca49
       )

    jac[jca49, jca49] = (
       -rho*Y[jp]*rate_eval.p_Ca49__Sc50
       -rho*Y[jn]*rate_eval.n_Ca49__Ca50
       -rho*Y[jp]*rate_eval.p_Ca49__n_Sc49
       -rho*Y[jhe4]*rate_eval.He4_Ca49__n_Ti52
       -rate_eval.Ca49__Sc49__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ca49__Ti53
       )

    jac[jca49, jsc52] = (
       +rho*Y[jp]*rate_eval.p_Sc52__He4_Ca49
       )

    jac[jca50, jn] = (
       -rho*Y[jca50]*rate_eval.n_Ca50__Ca51
       +rho*Y[jca49]*rate_eval.n_Ca49__Ca50
       )

    jac[jca50, jp] = (
       -rho*Y[jca50]*rate_eval.p_Ca50__He4_K47
       -rho*Y[jca50]*rate_eval.p_Ca50__n_Sc50
       -rho*Y[jca50]*rate_eval.p_Ca50__Sc51
       +rho*Y[jk50]*rate_eval.p_K50__n_Ca50
       +rho*Y[jk49]*rate_eval.p_K49__Ca50
       +rho*Y[jsc53]*rate_eval.p_Sc53__He4_Ca50
       )

    jac[jca50, jhe4] = (
       -rho*Y[jca50]*rate_eval.He4_Ca50__n_Ti53
       -rho*Y[jca50]*rate_eval.He4_Ca50__Ti54
       +rho*Y[jar46]*rate_eval.He4_Ar46__Ca50
       +rho*Y[jar47]*rate_eval.He4_Ar47__n_Ca50
       )

    jac[jca50, jar46] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar46__Ca50
       )

    jac[jca50, jar47] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar47__n_Ca50
       )

    jac[jca50, jk49] = (
       +rho*Y[jp]*rate_eval.p_K49__Ca50
       )

    jac[jca50, jk50] = (
       +rho*Y[jp]*rate_eval.p_K50__n_Ca50
       +rate_eval.K50__Ca50__weak__wc12
       )

    jac[jca50, jk51] = (
       +rate_eval.K51__n_Ca50__weak__wc12
       )

    jac[jca50, jk52] = (
       +rate_eval.K52__n_n_Ca50__weak__mp17
       )

    jac[jca50, jk53] = (
       +rate_eval.K53__n_n_n_Ca50__weak__mo03
       )

    jac[jca50, jca49] = (
       +rho*Y[jn]*rate_eval.n_Ca49__Ca50
       )

    jac[jca50, jca50] = (
       -rho*Y[jn]*rate_eval.n_Ca50__Ca51
       -rho*Y[jhe4]*rate_eval.He4_Ca50__n_Ti53
       -rho*Y[jp]*rate_eval.p_Ca50__He4_K47
       -rho*Y[jhe4]*rate_eval.He4_Ca50__Ti54
       -rho*Y[jp]*rate_eval.p_Ca50__n_Sc50
       -rho*Y[jp]*rate_eval.p_Ca50__Sc51
       -rate_eval.Ca50__Sc50__weak__wc12
       )

    jac[jca50, jsc53] = (
       +rho*Y[jp]*rate_eval.p_Sc53__He4_Ca50
       )

    jac[jca51, jn] = (
       -rho*Y[jca51]*rate_eval.n_Ca51__Ca52
       +rho*Y[jca50]*rate_eval.n_Ca50__Ca51
       )

    jac[jca51, jp] = (
       -rho*Y[jca51]*rate_eval.p_Ca51__He4_K48
       -rho*Y[jca51]*rate_eval.p_Ca51__Sc52
       -rho*Y[jca51]*rate_eval.p_Ca51__n_Sc51
       +rho*Y[jk51]*rate_eval.p_K51__n_Ca51
       +rho*Y[jk50]*rate_eval.p_K50__Ca51
       +rho*Y[jsc54]*rate_eval.p_Sc54__He4_Ca51
       )

    jac[jca51, jhe4] = (
       -rho*Y[jca51]*rate_eval.He4_Ca51__n_Ti54
       -rho*Y[jca51]*rate_eval.He4_Ca51__Ti55
       +rho*Y[jar47]*rate_eval.He4_Ar47__Ca51
       +rho*Y[jar48]*rate_eval.He4_Ar48__n_Ca51
       )

    jac[jca51, jar47] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar47__Ca51
       )

    jac[jca51, jar48] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar48__n_Ca51
       )

    jac[jca51, jk50] = (
       +rho*Y[jp]*rate_eval.p_K50__Ca51
       )

    jac[jca51, jk51] = (
       +rho*Y[jp]*rate_eval.p_K51__n_Ca51
       +rate_eval.K51__Ca51__weak__wc12
       )

    jac[jca51, jk52] = (
       +rate_eval.K52__n_Ca51__weak__wc12
       )

    jac[jca51, jk53] = (
       +rate_eval.K53__n_n_Ca51__weak__mp17
       )

    jac[jca51, jk54] = (
       +rate_eval.K54__n_n_n_Ca51__weak__mo03
       )

    jac[jca51, jca50] = (
       +rho*Y[jn]*rate_eval.n_Ca50__Ca51
       )

    jac[jca51, jca51] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca51__n_Ti54
       -rho*Y[jp]*rate_eval.p_Ca51__He4_K48
       -rho*Y[jhe4]*rate_eval.He4_Ca51__Ti55
       -rho*Y[jp]*rate_eval.p_Ca51__Sc52
       -rho*Y[jn]*rate_eval.n_Ca51__Ca52
       -rate_eval.Ca51__Sc51__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ca51__n_Sc51
       )

    jac[jca51, jsc54] = (
       +rho*Y[jp]*rate_eval.p_Sc54__He4_Ca51
       )

    jac[jca52, jn] = (
       -rho*Y[jca52]*rate_eval.n_Ca52__Ca53
       +rho*Y[jca51]*rate_eval.n_Ca51__Ca52
       )

    jac[jca52, jp] = (
       -rho*Y[jca52]*rate_eval.p_Ca52__n_Sc52
       -rho*Y[jca52]*rate_eval.p_Ca52__Sc53
       -rho*Y[jca52]*rate_eval.p_Ca52__He4_K49
       +rho*Y[jsc55]*rate_eval.p_Sc55__He4_Ca52
       +rho*Y[jk51]*rate_eval.p_K51__Ca52
       +rho*Y[jk52]*rate_eval.p_K52__n_Ca52
       )

    jac[jca52, jhe4] = (
       -rho*Y[jca52]*rate_eval.He4_Ca52__Ti56
       -rho*Y[jca52]*rate_eval.He4_Ca52__n_Ti55
       +rho*Y[jar49]*rate_eval.He4_Ar49__n_Ca52
       +rho*Y[jar48]*rate_eval.He4_Ar48__Ca52
       )

    jac[jca52, jar48] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar48__Ca52
       )

    jac[jca52, jar49] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar49__n_Ca52
       )

    jac[jca52, jk51] = (
       +rho*Y[jp]*rate_eval.p_K51__Ca52
       )

    jac[jca52, jk52] = (
       +rate_eval.K52__Ca52__weak__wc17
       +rho*Y[jp]*rate_eval.p_K52__n_Ca52
       )

    jac[jca52, jk53] = (
       +rate_eval.K53__n_Ca52__weak__wc17
       )

    jac[jca52, jk54] = (
       +rate_eval.K54__n_n_Ca52__weak__mp17
       )

    jac[jca52, jk55] = (
       +rate_eval.K55__n_n_n_Ca52__weak__mo03
       )

    jac[jca52, jca51] = (
       +rho*Y[jn]*rate_eval.n_Ca51__Ca52
       )

    jac[jca52, jca52] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca52__Ti56
       -rho*Y[jp]*rate_eval.p_Ca52__n_Sc52
       -rho*Y[jn]*rate_eval.n_Ca52__Ca53
       -rho*Y[jp]*rate_eval.p_Ca52__Sc53
       -rho*Y[jp]*rate_eval.p_Ca52__He4_K49
       -rate_eval.Ca52__n_Sc51__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ca52__n_Ti55
       -rate_eval.Ca52__Sc52__weak__wc12
       )

    jac[jca52, jsc55] = (
       +rho*Y[jp]*rate_eval.p_Sc55__He4_Ca52
       )

    jac[jca53, jn] = (
       -rho*Y[jca53]*rate_eval.n_Ca53__Ca54
       +rho*Y[jca52]*rate_eval.n_Ca52__Ca53
       )

    jac[jca53, jp] = (
       -rho*Y[jca53]*rate_eval.p_Ca53__n_Sc53
       -rho*Y[jca53]*rate_eval.p_Ca53__He4_K50
       -rho*Y[jca53]*rate_eval.p_Ca53__Sc54
       +rho*Y[jk53]*rate_eval.p_K53__n_Ca53
       +rho*Y[jk52]*rate_eval.p_K52__Ca53
       +rho*Y[jsc56]*rate_eval.p_Sc56__He4_Ca53
       )

    jac[jca53, jhe4] = (
       -rho*Y[jca53]*rate_eval.He4_Ca53__n_Ti56
       -rho*Y[jca53]*rate_eval.He4_Ca53__Ti57
       +rho*Y[jar50]*rate_eval.He4_Ar50__n_Ca53
       +rho*Y[jar49]*rate_eval.He4_Ar49__Ca53
       )

    jac[jca53, jar49] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar49__Ca53
       )

    jac[jca53, jar50] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar50__n_Ca53
       )

    jac[jca53, jk52] = (
       +rho*Y[jp]*rate_eval.p_K52__Ca53
       )

    jac[jca53, jk53] = (
       +rho*Y[jp]*rate_eval.p_K53__n_Ca53
       +rate_eval.K53__Ca53__weak__wc17
       )

    jac[jca53, jk54] = (
       +rate_eval.K54__n_Ca53__weak__mp17
       )

    jac[jca53, jk55] = (
       +rate_eval.K55__n_n_Ca53__weak__mp17
       )

    jac[jca53, jk56] = (
       +rate_eval.K56__n_n_n_Ca53__weak__mo03
       )

    jac[jca53, jca52] = (
       +rho*Y[jn]*rate_eval.n_Ca52__Ca53
       )

    jac[jca53, jca53] = (
       -rho*Y[jp]*rate_eval.p_Ca53__n_Sc53
       -rho*Y[jhe4]*rate_eval.He4_Ca53__n_Ti56
       -rate_eval.Ca53__n_Sc52__weak__wc12
       -rate_eval.Ca53__Sc53__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ca53__Ca54
       -rho*Y[jhe4]*rate_eval.He4_Ca53__Ti57
       -rho*Y[jp]*rate_eval.p_Ca53__He4_K50
       -rho*Y[jp]*rate_eval.p_Ca53__Sc54
       )

    jac[jca53, jsc56] = (
       +rho*Y[jp]*rate_eval.p_Sc56__He4_Ca53
       )

    jac[jca54, jn] = (
       -rho*Y[jca54]*rate_eval.n_Ca54__Ca55
       +rho*Y[jca53]*rate_eval.n_Ca53__Ca54
       )

    jac[jca54, jp] = (
       -rho*Y[jca54]*rate_eval.p_Ca54__Sc55
       -rho*Y[jca54]*rate_eval.p_Ca54__n_Sc54
       -rho*Y[jca54]*rate_eval.p_Ca54__He4_K51
       +rho*Y[jk54]*rate_eval.p_K54__n_Ca54
       +rho*Y[jsc57]*rate_eval.p_Sc57__He4_Ca54
       +rho*Y[jk53]*rate_eval.p_K53__Ca54
       )

    jac[jca54, jhe4] = (
       -rho*Y[jca54]*rate_eval.He4_Ca54__Ti58
       -rho*Y[jca54]*rate_eval.He4_Ca54__n_Ti57
       +rho*Y[jar50]*rate_eval.He4_Ar50__Ca54
       +rho*Y[jar51]*rate_eval.He4_Ar51__n_Ca54
       )

    jac[jca54, jar50] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar50__Ca54
       )

    jac[jca54, jar51] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar51__n_Ca54
       )

    jac[jca54, jk53] = (
       +rho*Y[jp]*rate_eval.p_K53__Ca54
       )

    jac[jca54, jk54] = (
       +rho*Y[jp]*rate_eval.p_K54__n_Ca54
       +rate_eval.K54__Ca54__weak__wc17
       )

    jac[jca54, jk55] = (
       +rate_eval.K55__n_Ca54__weak__mp17
       )

    jac[jca54, jk56] = (
       +rate_eval.K56__n_n_Ca54__weak__mp17
       )

    jac[jca54, jk57] = (
       +rate_eval.K57__n_n_n_Ca54__weak__mo03
       )

    jac[jca54, jca53] = (
       +rho*Y[jn]*rate_eval.n_Ca53__Ca54
       )

    jac[jca54, jca54] = (
       -rho*Y[jhe4]*rate_eval.He4_Ca54__Ti58
       -rho*Y[jp]*rate_eval.p_Ca54__Sc55
       -rho*Y[jn]*rate_eval.n_Ca54__Ca55
       -rate_eval.Ca54__n_Sc53__weak__mp17
       -rho*Y[jp]*rate_eval.p_Ca54__n_Sc54
       -rho*Y[jp]*rate_eval.p_Ca54__He4_K51
       -rho*Y[jhe4]*rate_eval.He4_Ca54__n_Ti57
       -rate_eval.Ca54__Sc54__weak__wc17
       )

    jac[jca54, jsc57] = (
       +rho*Y[jp]*rate_eval.p_Sc57__He4_Ca54
       )

    jac[jca55, jn] = (
       -rho*Y[jca55]*rate_eval.n_Ca55__Ca56
       +rho*Y[jca54]*rate_eval.n_Ca54__Ca55
       )

    jac[jca55, jp] = (
       -rho*Y[jca55]*rate_eval.p_Ca55__He4_K52
       -rho*Y[jca55]*rate_eval.p_Ca55__n_Sc55
       -rho*Y[jca55]*rate_eval.p_Ca55__Sc56
       +rho*Y[jsc58]*rate_eval.p_Sc58__He4_Ca55
       +rho*Y[jk55]*rate_eval.p_K55__n_Ca55
       +rho*Y[jk54]*rate_eval.p_K54__Ca55
       )

    jac[jca55, jhe4] = (
       -rho*Y[jca55]*rate_eval.He4_Ca55__n_Ti58
       -rho*Y[jca55]*rate_eval.He4_Ca55__Ti59
       +rho*Y[jar52]*rate_eval.He4_Ar52__n_Ca55
       +rho*Y[jar51]*rate_eval.He4_Ar51__Ca55
       )

    jac[jca55, jar51] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar51__Ca55
       )

    jac[jca55, jar52] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar52__n_Ca55
       )

    jac[jca55, jk54] = (
       +rho*Y[jp]*rate_eval.p_K54__Ca55
       )

    jac[jca55, jk55] = (
       +rho*Y[jp]*rate_eval.p_K55__n_Ca55
       +rate_eval.K55__Ca55__weak__mo03
       )

    jac[jca55, jk56] = (
       +rate_eval.K56__n_Ca55__weak__mp17
       )

    jac[jca55, jk57] = (
       +rate_eval.K57__n_n_Ca55__weak__mp17
       )

    jac[jca55, jk58] = (
       +rate_eval.K58__n_n_n_Ca55__weak__mo03
       )

    jac[jca55, jca54] = (
       +rho*Y[jn]*rate_eval.n_Ca54__Ca55
       )

    jac[jca55, jca55] = (
       -rho*Y[jp]*rate_eval.p_Ca55__He4_K52
       -rho*Y[jp]*rate_eval.p_Ca55__n_Sc55
       -rho*Y[jn]*rate_eval.n_Ca55__Ca56
       -rho*Y[jhe4]*rate_eval.He4_Ca55__n_Ti58
       -rho*Y[jhe4]*rate_eval.He4_Ca55__Ti59
       -rate_eval.Ca55__n_Sc54__weak__mp17
       -rate_eval.Ca55__Sc55__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ca55__Sc56
       )

    jac[jca55, jsc58] = (
       +rho*Y[jp]*rate_eval.p_Sc58__He4_Ca55
       )

    jac[jca56, jn] = (
       -rho*Y[jca56]*rate_eval.n_Ca56__Ca57
       +rho*Y[jca55]*rate_eval.n_Ca55__Ca56
       )

    jac[jca56, jp] = (
       -rho*Y[jca56]*rate_eval.p_Ca56__He4_K53
       -rho*Y[jca56]*rate_eval.p_Ca56__n_Sc56
       -rho*Y[jca56]*rate_eval.p_Ca56__Sc57
       +rho*Y[jk56]*rate_eval.p_K56__n_Ca56
       +rho*Y[jsc59]*rate_eval.p_Sc59__He4_Ca56
       +rho*Y[jk55]*rate_eval.p_K55__Ca56
       )

    jac[jca56, jhe4] = (
       -rho*Y[jca56]*rate_eval.He4_Ca56__Ti60
       -rho*Y[jca56]*rate_eval.He4_Ca56__n_Ti59
       +rho*Y[jar52]*rate_eval.He4_Ar52__Ca56
       +rho*Y[jar53]*rate_eval.He4_Ar53__n_Ca56
       )

    jac[jca56, jar52] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar52__Ca56
       )

    jac[jca56, jar53] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar53__n_Ca56
       )

    jac[jca56, jk55] = (
       +rho*Y[jp]*rate_eval.p_K55__Ca56
       )

    jac[jca56, jk56] = (
       +rho*Y[jp]*rate_eval.p_K56__n_Ca56
       +rate_eval.K56__Ca56__weak__mo03
       )

    jac[jca56, jk57] = (
       +rate_eval.K57__n_Ca56__weak__mp17
       )

    jac[jca56, jk58] = (
       +rate_eval.K58__n_n_Ca56__weak__mp17
       )

    jac[jca56, jk59] = (
       +rate_eval.K59__n_n_n_Ca56__weak__mo03
       )

    jac[jca56, jca55] = (
       +rho*Y[jn]*rate_eval.n_Ca55__Ca56
       )

    jac[jca56, jca56] = (
       -rate_eval.Ca56__n_n_n_Sc53__weak__mo03
       -rho*Y[jp]*rate_eval.p_Ca56__He4_K53
       -rho*Y[jp]*rate_eval.p_Ca56__n_Sc56
       -rho*Y[jn]*rate_eval.n_Ca56__Ca57
       -rho*Y[jp]*rate_eval.p_Ca56__Sc57
       -rho*Y[jhe4]*rate_eval.He4_Ca56__Ti60
       -rate_eval.Ca56__n_Sc55__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ca56__n_Ti59
       -rate_eval.Ca56__Sc56__weak__wc17
       )

    jac[jca56, jsc59] = (
       +rho*Y[jp]*rate_eval.p_Sc59__He4_Ca56
       )

    jac[jca57, jn] = (
       -rho*Y[jca57]*rate_eval.n_Ca57__Ca58
       +rho*Y[jca56]*rate_eval.n_Ca56__Ca57
       )

    jac[jca57, jp] = (
       -rho*Y[jca57]*rate_eval.p_Ca57__Sc58
       -rho*Y[jca57]*rate_eval.p_Ca57__He4_K54
       -rho*Y[jca57]*rate_eval.p_Ca57__n_Sc57
       +rho*Y[jsc60]*rate_eval.p_Sc60__He4_Ca57
       +rho*Y[jk57]*rate_eval.p_K57__n_Ca57
       +rho*Y[jk56]*rate_eval.p_K56__Ca57
       )

    jac[jca57, jhe4] = (
       -rho*Y[jca57]*rate_eval.He4_Ca57__n_Ti60
       -rho*Y[jca57]*rate_eval.He4_Ca57__Ti61
       +rho*Y[jar53]*rate_eval.He4_Ar53__Ca57
       +rho*Y[jar54]*rate_eval.He4_Ar54__n_Ca57
       )

    jac[jca57, jar53] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar53__Ca57
       )

    jac[jca57, jar54] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar54__n_Ca57
       )

    jac[jca57, jk56] = (
       +rho*Y[jp]*rate_eval.p_K56__Ca57
       )

    jac[jca57, jk57] = (
       +rho*Y[jp]*rate_eval.p_K57__n_Ca57
       +rate_eval.K57__Ca57__weak__mo03
       )

    jac[jca57, jk58] = (
       +rate_eval.K58__n_Ca57__weak__mp17
       )

    jac[jca57, jk59] = (
       +rate_eval.K59__n_n_Ca57__weak__mp17
       )

    jac[jca57, jca56] = (
       +rho*Y[jn]*rate_eval.n_Ca56__Ca57
       )

    jac[jca57, jca57] = (
       -rate_eval.Ca57__n_n_n_Sc54__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Ca57__n_Ti60
       -rate_eval.Ca57__n_n_Sc55__weak__mp17
       -rho*Y[jp]*rate_eval.p_Ca57__Sc58
       -rho*Y[jn]*rate_eval.n_Ca57__Ca58
       -rate_eval.Ca57__Sc57__weak__mo03
       -rho*Y[jp]*rate_eval.p_Ca57__He4_K54
       -rate_eval.Ca57__n_Sc56__weak__mp17
       -rho*Y[jp]*rate_eval.p_Ca57__n_Sc57
       -rho*Y[jhe4]*rate_eval.He4_Ca57__Ti61
       )

    jac[jca57, jsc60] = (
       +rho*Y[jp]*rate_eval.p_Sc60__He4_Ca57
       )

    jac[jca58, jn] = (
       -rho*Y[jca58]*rate_eval.n_Ca58__Ca59
       +rho*Y[jca57]*rate_eval.n_Ca57__Ca58
       )

    jac[jca58, jp] = (
       -rho*Y[jca58]*rate_eval.p_Ca58__He4_K55
       -rho*Y[jca58]*rate_eval.p_Ca58__n_Sc58
       -rho*Y[jca58]*rate_eval.p_Ca58__Sc59
       +rho*Y[jk58]*rate_eval.p_K58__n_Ca58
       +rho*Y[jk57]*rate_eval.p_K57__Ca58
       +rho*Y[jsc61]*rate_eval.p_Sc61__He4_Ca58
       )

    jac[jca58, jhe4] = (
       -rho*Y[jca58]*rate_eval.He4_Ca58__n_Ti61
       -rho*Y[jca58]*rate_eval.He4_Ca58__Ti62
       +rho*Y[jar54]*rate_eval.He4_Ar54__Ca58
       )

    jac[jca58, jar54] = (
       +rho*Y[jhe4]*rate_eval.He4_Ar54__Ca58
       )

    jac[jca58, jk57] = (
       +rho*Y[jp]*rate_eval.p_K57__Ca58
       )

    jac[jca58, jk58] = (
       +rho*Y[jp]*rate_eval.p_K58__n_Ca58
       +rate_eval.K58__Ca58__weak__mo03
       )

    jac[jca58, jk59] = (
       +rate_eval.K59__n_Ca58__weak__mp17
       )

    jac[jca58, jca57] = (
       +rho*Y[jn]*rate_eval.n_Ca57__Ca58
       )

    jac[jca58, jca58] = (
       -rate_eval.Ca58__n_n_n_Sc55__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Ca58__n_Ti61
       -rho*Y[jp]*rate_eval.p_Ca58__He4_K55
       -rho*Y[jp]*rate_eval.p_Ca58__n_Sc58
       -rho*Y[jp]*rate_eval.p_Ca58__Sc59
       -rho*Y[jhe4]*rate_eval.He4_Ca58__Ti62
       -rate_eval.Ca58__n_Sc57__weak__mp17
       -rate_eval.Ca58__n_n_Sc56__weak__mp17
       -rho*Y[jn]*rate_eval.n_Ca58__Ca59
       -rate_eval.Ca58__Sc58__weak__mo03
       )

    jac[jca58, jsc61] = (
       +rho*Y[jp]*rate_eval.p_Sc61__He4_Ca58
       )

    jac[jca59, jn] = (
       -rho*Y[jca59]*rate_eval.n_Ca59__Ca60
       +rho*Y[jca58]*rate_eval.n_Ca58__Ca59
       )

    jac[jca59, jp] = (
       -rho*Y[jca59]*rate_eval.p_Ca59__n_Sc59
       -rho*Y[jca59]*rate_eval.p_Ca59__Sc60
       -rho*Y[jca59]*rate_eval.p_Ca59__He4_K56
       +rho*Y[jk59]*rate_eval.p_K59__n_Ca59
       +rho*Y[jk58]*rate_eval.p_K58__Ca59
       +rho*Y[jsc62]*rate_eval.p_Sc62__He4_Ca59
       )

    jac[jca59, jhe4] = (
       -rho*Y[jca59]*rate_eval.He4_Ca59__Ti63
       -rho*Y[jca59]*rate_eval.He4_Ca59__n_Ti62
       )

    jac[jca59, jk58] = (
       +rho*Y[jp]*rate_eval.p_K58__Ca59
       )

    jac[jca59, jk59] = (
       +rho*Y[jp]*rate_eval.p_K59__n_Ca59
       +rate_eval.K59__Ca59__weak__mo03
       )

    jac[jca59, jca58] = (
       +rho*Y[jn]*rate_eval.n_Ca58__Ca59
       )

    jac[jca59, jca59] = (
       -rate_eval.Ca59__n_n_n_Sc56__weak__mo03
       -rho*Y[jp]*rate_eval.p_Ca59__n_Sc59
       -rho*Y[jhe4]*rate_eval.He4_Ca59__Ti63
       -rho*Y[jp]*rate_eval.p_Ca59__Sc60
       -rate_eval.Ca59__n_n_Sc57__weak__mp17
       -rho*Y[jn]*rate_eval.n_Ca59__Ca60
       -rate_eval.Ca59__n_Sc58__weak__mp17
       -rate_eval.Ca59__Sc59__weak__mo03
       -rho*Y[jp]*rate_eval.p_Ca59__He4_K56
       -rho*Y[jhe4]*rate_eval.He4_Ca59__n_Ti62
       )

    jac[jca59, jsc62] = (
       +rho*Y[jp]*rate_eval.p_Sc62__He4_Ca59
       )

    jac[jca60, jn] = (
       -rho*Y[jca60]*rate_eval.n_Ca60__Ca61
       +rho*Y[jca59]*rate_eval.n_Ca59__Ca60
       )

    jac[jca60, jp] = (
       -rho*Y[jca60]*rate_eval.p_Ca60__n_Sc60
       -rho*Y[jca60]*rate_eval.p_Ca60__Sc61
       -rho*Y[jca60]*rate_eval.p_Ca60__He4_K57
       +rho*Y[jk59]*rate_eval.p_K59__Ca60
       +rho*Y[jsc63]*rate_eval.p_Sc63__He4_Ca60
       )

    jac[jca60, jhe4] = (
       -rho*Y[jca60]*rate_eval.He4_Ca60__n_Ti63
       -rho*Y[jca60]*rate_eval.He4_Ca60__Ti64
       )

    jac[jca60, jk59] = (
       +rho*Y[jp]*rate_eval.p_K59__Ca60
       )

    jac[jca60, jca59] = (
       +rho*Y[jn]*rate_eval.n_Ca59__Ca60
       )

    jac[jca60, jca60] = (
       -rate_eval.Ca60__n_n_n_Sc57__weak__mo03
       -rho*Y[jp]*rate_eval.p_Ca60__n_Sc60
       -rho*Y[jhe4]*rate_eval.He4_Ca60__n_Ti63
       -rho*Y[jp]*rate_eval.p_Ca60__Sc61
       -rho*Y[jn]*rate_eval.n_Ca60__Ca61
       -rho*Y[jhe4]*rate_eval.He4_Ca60__Ti64
       -rho*Y[jp]*rate_eval.p_Ca60__He4_K57
       -rate_eval.Ca60__n_Sc59__weak__mp17
       -rate_eval.Ca60__Sc60__weak__mo03
       -rate_eval.Ca60__n_n_Sc58__weak__mp17
       )

    jac[jca60, jsc63] = (
       +rho*Y[jp]*rate_eval.p_Sc63__He4_Ca60
       )

    jac[jca61, jn] = (
       +rho*Y[jca60]*rate_eval.n_Ca60__Ca61
       )

    jac[jca61, jp] = (
       -rho*Y[jca61]*rate_eval.p_Ca61__Sc62
       -rho*Y[jca61]*rate_eval.p_Ca61__He4_K58
       -rho*Y[jca61]*rate_eval.p_Ca61__n_Sc61
       )

    jac[jca61, jhe4] = (
       -rho*Y[jca61]*rate_eval.He4_Ca61__n_Ti64
       -rho*Y[jca61]*rate_eval.He4_Ca61__Ti65
       )

    jac[jca61, jca60] = (
       +rho*Y[jn]*rate_eval.n_Ca60__Ca61
       )

    jac[jca61, jca61] = (
       -rho*Y[jp]*rate_eval.p_Ca61__Sc62
       -rho*Y[jp]*rate_eval.p_Ca61__He4_K58
       -rho*Y[jp]*rate_eval.p_Ca61__n_Sc61
       -rho*Y[jhe4]*rate_eval.He4_Ca61__n_Ti64
       -rate_eval.Ca61__n_n_n_Sc58__weak__mo03
       -rate_eval.Ca61__n_Sc60__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ca61__Ti65
       -rate_eval.Ca61__Sc61__weak__mo03
       -rate_eval.Ca61__n_n_Sc59__weak__mp17
       )

    jac[jsc35, jn] = (
       -rho*Y[jsc35]*rate_eval.n_Sc35__He4_K32
       -rho*Y[jsc35]*rate_eval.n_Sc35__p_Ca35
       -rho*Y[jsc35]*rate_eval.n_Sc35__Sc36
       )

    jac[jsc35, jp] = (
       +rho*Y[jca34]*rate_eval.p_Ca34__Sc35
       )

    jac[jsc35, jhe4] = (
       -rho*Y[jsc35]*rate_eval.He4_Sc35__p_Ti38
       -rho*Y[jsc35]*rate_eval.He4_Sc35__V39
       +rho*Y[jk31]*rate_eval.He4_K31__Sc35
       )

    jac[jsc35, jk31] = (
       +rho*Y[jhe4]*rate_eval.He4_K31__Sc35
       )

    jac[jsc35, jca34] = (
       +rho*Y[jp]*rate_eval.p_Ca34__Sc35
       )

    jac[jsc35, jsc35] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc35__p_Ti38
       -rho*Y[jn]*rate_eval.n_Sc35__He4_K32
       -rho*Y[jn]*rate_eval.n_Sc35__p_Ca35
       -rho*Y[jhe4]*rate_eval.He4_Sc35__V39
       -rho*Y[jn]*rate_eval.n_Sc35__Sc36
       -rate_eval.Sc35__Ca35__weak__bqa_pos_
       )

    jac[jsc36, jn] = (
       -rho*Y[jsc36]*rate_eval.n_Sc36__p_Ca36
       -rho*Y[jsc36]*rate_eval.n_Sc36__He4_K33
       -rho*Y[jsc36]*rate_eval.n_Sc36__Sc37
       +rho*Y[jsc35]*rate_eval.n_Sc35__Sc36
       +rho*Y[jv39]*rate_eval.n_V39__He4_Sc36
       )

    jac[jsc36, jp] = (
       -rho*Y[jsc36]*rate_eval.p_Sc36__Ti37
       +rho*Y[jca35]*rate_eval.p_Ca35__Sc36
       )

    jac[jsc36, jhe4] = (
       -rho*Y[jsc36]*rate_eval.He4_Sc36__p_Ti39
       -rho*Y[jsc36]*rate_eval.He4_Sc36__V40
       +rho*Y[jk32]*rate_eval.He4_K32__Sc36
       +rho*Y[jca33]*rate_eval.He4_Ca33__p_Sc36
       )

    jac[jsc36, jk32] = (
       +rho*Y[jhe4]*rate_eval.He4_K32__Sc36
       )

    jac[jsc36, jca33] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca33__p_Sc36
       )

    jac[jsc36, jca35] = (
       +rho*Y[jp]*rate_eval.p_Ca35__Sc36
       )

    jac[jsc36, jsc35] = (
       +rho*Y[jn]*rate_eval.n_Sc35__Sc36
       )

    jac[jsc36, jsc36] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc36__p_Ti39
       -rho*Y[jp]*rate_eval.p_Sc36__Ti37
       -rho*Y[jhe4]*rate_eval.He4_Sc36__V40
       -rho*Y[jn]*rate_eval.n_Sc36__p_Ca36
       -rho*Y[jn]*rate_eval.n_Sc36__He4_K33
       -rho*Y[jn]*rate_eval.n_Sc36__Sc37
       -rate_eval.Sc36__Ca36__weak__bqa_pos_
       )

    jac[jsc36, jv39] = (
       +rho*Y[jn]*rate_eval.n_V39__He4_Sc36
       )

    jac[jsc37, jn] = (
       -rho*Y[jsc37]*rate_eval.n_Sc37__He4_K34
       -rho*Y[jsc37]*rate_eval.n_Sc37__p_Ca37
       -rho*Y[jsc37]*rate_eval.n_Sc37__Sc38
       +rho*Y[jv40]*rate_eval.n_V40__He4_Sc37
       +rho*Y[jti37]*rate_eval.n_Ti37__p_Sc37
       +rho*Y[jsc36]*rate_eval.n_Sc36__Sc37
       )

    jac[jsc37, jp] = (
       -rho*Y[jsc37]*rate_eval.p_Sc37__Ti38
       +rho*Y[jca36]*rate_eval.p_Ca36__Sc37
       )

    jac[jsc37, jhe4] = (
       -rho*Y[jsc37]*rate_eval.He4_Sc37__p_Ti40
       -rho*Y[jsc37]*rate_eval.He4_Sc37__V41
       +rho*Y[jk33]*rate_eval.He4_K33__Sc37
       +rho*Y[jca34]*rate_eval.He4_Ca34__p_Sc37
       )

    jac[jsc37, jk33] = (
       +rho*Y[jhe4]*rate_eval.He4_K33__Sc37
       )

    jac[jsc37, jca34] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca34__p_Sc37
       )

    jac[jsc37, jca36] = (
       +rho*Y[jp]*rate_eval.p_Ca36__Sc37
       )

    jac[jsc37, jsc36] = (
       +rho*Y[jn]*rate_eval.n_Sc36__Sc37
       )

    jac[jsc37, jsc37] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc37__p_Ti40
       -rho*Y[jn]*rate_eval.n_Sc37__He4_K34
       -rho*Y[jn]*rate_eval.n_Sc37__p_Ca37
       -rho*Y[jp]*rate_eval.p_Sc37__Ti38
       -rho*Y[jn]*rate_eval.n_Sc37__Sc38
       -rate_eval.Sc37__Ca37__weak__bqa_pos_
       -rho*Y[jhe4]*rate_eval.He4_Sc37__V41
       )

    jac[jsc37, jti37] = (
       +rho*Y[jn]*rate_eval.n_Ti37__p_Sc37
       +rate_eval.Ti37__Sc37__weak__bqa_pos_
       )

    jac[jsc37, jv40] = (
       +rho*Y[jn]*rate_eval.n_V40__He4_Sc37
       )

    jac[jsc38, jn] = (
       -rho*Y[jsc38]*rate_eval.n_Sc38__Sc39
       -rho*Y[jsc38]*rate_eval.n_Sc38__p_Ca38
       -rho*Y[jsc38]*rate_eval.n_Sc38__He4_K35
       +rho*Y[jv41]*rate_eval.n_V41__He4_Sc38
       +rho*Y[jti38]*rate_eval.n_Ti38__p_Sc38
       +rho*Y[jsc37]*rate_eval.n_Sc37__Sc38
       )

    jac[jsc38, jp] = (
       -rho*Y[jsc38]*rate_eval.p_Sc38__Ti39
       +rho*Y[jca37]*rate_eval.p_Ca37__Sc38
       )

    jac[jsc38, jhe4] = (
       -rho*Y[jsc38]*rate_eval.He4_Sc38__p_Ti41
       -rho*Y[jsc38]*rate_eval.He4_Sc38__V42
       +rho*Y[jca35]*rate_eval.He4_Ca35__p_Sc38
       +rho*Y[jk34]*rate_eval.He4_K34__Sc38
       )

    jac[jsc38, jk34] = (
       +rho*Y[jhe4]*rate_eval.He4_K34__Sc38
       )

    jac[jsc38, jca35] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca35__p_Sc38
       )

    jac[jsc38, jca37] = (
       +rho*Y[jp]*rate_eval.p_Ca37__Sc38
       )

    jac[jsc38, jsc37] = (
       +rho*Y[jn]*rate_eval.n_Sc37__Sc38
       )

    jac[jsc38, jsc38] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc38__p_Ti41
       -rate_eval.Sc38__Ca38__weak__mo97
       -rho*Y[jhe4]*rate_eval.He4_Sc38__V42
       -rho*Y[jp]*rate_eval.p_Sc38__Ti39
       -rho*Y[jn]*rate_eval.n_Sc38__Sc39
       -rho*Y[jn]*rate_eval.n_Sc38__p_Ca38
       -rho*Y[jn]*rate_eval.n_Sc38__He4_K35
       )

    jac[jsc38, jti38] = (
       +rho*Y[jn]*rate_eval.n_Ti38__p_Sc38
       +rate_eval.Ti38__Sc38__weak__mo97
       )

    jac[jsc38, jv41] = (
       +rho*Y[jn]*rate_eval.n_V41__He4_Sc38
       )

    jac[jsc39, jn] = (
       -rho*Y[jsc39]*rate_eval.n_Sc39__He4_K36
       -rho*Y[jsc39]*rate_eval.n_Sc39__Sc40
       -rho*Y[jsc39]*rate_eval.n_Sc39__p_Ca39
       +rho*Y[jv42]*rate_eval.n_V42__He4_Sc39
       +rho*Y[jti39]*rate_eval.n_Ti39__p_Sc39
       +rho*Y[jsc38]*rate_eval.n_Sc38__Sc39
       )

    jac[jsc39, jp] = (
       -rho*Y[jsc39]*rate_eval.p_Sc39__Ti40
       +rho*Y[jca38]*rate_eval.p_Ca38__Sc39
       )

    jac[jsc39, jhe4] = (
       -rho*Y[jsc39]*rate_eval.He4_Sc39__p_Ti42
       -rho*Y[jsc39]*rate_eval.He4_Sc39__V43
       +rho*Y[jca36]*rate_eval.He4_Ca36__p_Sc39
       +rho*Y[jk35]*rate_eval.He4_K35__Sc39
       )

    jac[jsc39, jk35] = (
       +rho*Y[jhe4]*rate_eval.He4_K35__Sc39
       )

    jac[jsc39, jca36] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca36__p_Sc39
       )

    jac[jsc39, jca38] = (
       +rho*Y[jp]*rate_eval.p_Ca38__Sc39
       )

    jac[jsc39, jsc38] = (
       +rho*Y[jn]*rate_eval.n_Sc38__Sc39
       )

    jac[jsc39, jsc39] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc39__p_Ti42
       -rho*Y[jn]*rate_eval.n_Sc39__He4_K36
       -rho*Y[jhe4]*rate_eval.He4_Sc39__V43
       -rho*Y[jn]*rate_eval.n_Sc39__Sc40
       -rho*Y[jp]*rate_eval.p_Sc39__Ti40
       -rate_eval.Sc39__Ca39__weak__mo97
       -rho*Y[jn]*rate_eval.n_Sc39__p_Ca39
       )

    jac[jsc39, jti39] = (
       +rho*Y[jn]*rate_eval.n_Ti39__p_Sc39
       +rate_eval.Ti39__Sc39__weak__wc17
       )

    jac[jsc39, jv42] = (
       +rho*Y[jn]*rate_eval.n_V42__He4_Sc39
       )

    jac[jsc40, jn] = (
       -rho*Y[jsc40]*rate_eval.n_Sc40__Sc41
       -rho*Y[jsc40]*rate_eval.n_Sc40__p_Ca40
       -rho*Y[jsc40]*rate_eval.n_Sc40__He4_K37
       +rho*Y[jv43]*rate_eval.n_V43__He4_Sc40
       +rho*Y[jsc39]*rate_eval.n_Sc39__Sc40
       +rho*Y[jti40]*rate_eval.n_Ti40__p_Sc40
       )

    jac[jsc40, jp] = (
       -rho*Y[jsc40]*rate_eval.p_Sc40__Ti41
       +rho*Y[jca39]*rate_eval.p_Ca39__Sc40
       )

    jac[jsc40, jhe4] = (
       -rho*Y[jsc40]*rate_eval.He4_Sc40__p_Ti43
       -rho*Y[jsc40]*rate_eval.He4_Sc40__V44
       +rho*Y[jk36]*rate_eval.He4_K36__Sc40
       +rho*Y[jca37]*rate_eval.He4_Ca37__p_Sc40
       )

    jac[jsc40, jk36] = (
       +rho*Y[jhe4]*rate_eval.He4_K36__Sc40
       )

    jac[jsc40, jca37] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca37__p_Sc40
       )

    jac[jsc40, jca39] = (
       +rho*Y[jp]*rate_eval.p_Ca39__Sc40
       )

    jac[jsc40, jsc39] = (
       +rho*Y[jn]*rate_eval.n_Sc39__Sc40
       )

    jac[jsc40, jsc40] = (
       -rho*Y[jn]*rate_eval.n_Sc40__Sc41
       -rho*Y[jhe4]*rate_eval.He4_Sc40__p_Ti43
       -rho*Y[jn]*rate_eval.n_Sc40__p_Ca40
       -rho*Y[jp]*rate_eval.p_Sc40__Ti41
       -rate_eval.Sc40__Ca40__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Sc40__V44
       -rate_eval.Sc40__He4_Ar36__weak__wc12
       -rate_eval.Sc40__p_K39__weak__wc12
       -rho*Y[jn]*rate_eval.n_Sc40__He4_K37
       )

    jac[jsc40, jti40] = (
       +rho*Y[jn]*rate_eval.n_Ti40__p_Sc40
       )

    jac[jsc40, jv43] = (
       +rho*Y[jn]*rate_eval.n_V43__He4_Sc40
       )

    jac[jsc41, jn] = (
       -rho*Y[jsc41]*rate_eval.n_Sc41__He4_K38
       -rho*Y[jsc41]*rate_eval.n_Sc41__Sc42
       -rho*Y[jsc41]*rate_eval.n_Sc41__p_Ca41
       +rho*Y[jsc40]*rate_eval.n_Sc40__Sc41
       +rho*Y[jv44]*rate_eval.n_V44__He4_Sc41
       +rho*Y[jti41]*rate_eval.n_Ti41__p_Sc41
       )

    jac[jsc41, jp] = (
       -rho*Y[jsc41]*rate_eval.p_Sc41__Ti42
       +rho*Y[jca40]*rate_eval.p_Ca40__Sc41
       )

    jac[jsc41, jhe4] = (
       -rho*Y[jsc41]*rate_eval.He4_Sc41__V45
       -rho*Y[jsc41]*rate_eval.He4_Sc41__p_Ti44
       +rho*Y[jca38]*rate_eval.He4_Ca38__p_Sc41
       +rho*Y[jk37]*rate_eval.He4_K37__Sc41
       )

    jac[jsc41, jk37] = (
       +rho*Y[jhe4]*rate_eval.He4_K37__Sc41
       )

    jac[jsc41, jca38] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca38__p_Sc41
       )

    jac[jsc41, jca40] = (
       +rho*Y[jp]*rate_eval.p_Ca40__Sc41
       )

    jac[jsc41, jsc40] = (
       +rho*Y[jn]*rate_eval.n_Sc40__Sc41
       )

    jac[jsc41, jsc41] = (
       -rho*Y[jn]*rate_eval.n_Sc41__He4_K38
       -rho*Y[jhe4]*rate_eval.He4_Sc41__V45
       -rho*Y[jp]*rate_eval.p_Sc41__Ti42
       -rho*Y[jn]*rate_eval.n_Sc41__Sc42
       -rho*Y[jhe4]*rate_eval.He4_Sc41__p_Ti44
       -rate_eval.Sc41__Ca41__weak__wc12
       -rho*Y[jn]*rate_eval.n_Sc41__p_Ca41
       )

    jac[jsc41, jti41] = (
       +rho*Y[jn]*rate_eval.n_Ti41__p_Sc41
       +rate_eval.Ti41__Sc41__weak__wc17
       )

    jac[jsc41, jv44] = (
       +rho*Y[jn]*rate_eval.n_V44__He4_Sc41
       )

    jac[jsc41, jcr43] = (
       +rate_eval.Cr43__p_p_Sc41__weak__wc12
       )

    jac[jsc42, jn] = (
       -rho*Y[jsc42]*rate_eval.n_Sc42__He4_K39
       -rho*Y[jsc42]*rate_eval.n_Sc42__p_Ca42
       -rho*Y[jsc42]*rate_eval.n_Sc42__Sc43
       +rho*Y[jv45]*rate_eval.n_V45__He4_Sc42
       +rho*Y[jti42]*rate_eval.n_Ti42__p_Sc42
       +rho*Y[jsc41]*rate_eval.n_Sc41__Sc42
       )

    jac[jsc42, jp] = (
       -rho*Y[jsc42]*rate_eval.p_Sc42__Ti43
       -rho*Y[jsc42]*rate_eval.p_Sc42__He4_Ca39
       +rho*Y[jca41]*rate_eval.p_Ca41__Sc42
       )

    jac[jsc42, jhe4] = (
       -rho*Y[jsc42]*rate_eval.He4_Sc42__p_Ti45
       -rho*Y[jsc42]*rate_eval.He4_Sc42__V46
       +rho*Y[jk38]*rate_eval.He4_K38__Sc42
       )

    jac[jsc42, jk38] = (
       +rho*Y[jhe4]*rate_eval.He4_K38__Sc42
       )

    jac[jsc42, jca41] = (
       +rho*Y[jp]*rate_eval.p_Ca41__Sc42
       )

    jac[jsc42, jsc41] = (
       +rho*Y[jn]*rate_eval.n_Sc41__Sc42
       )

    jac[jsc42, jsc42] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc42__p_Ti45
       -rho*Y[jn]*rate_eval.n_Sc42__He4_K39
       -rho*Y[jn]*rate_eval.n_Sc42__p_Ca42
       -rho*Y[jhe4]*rate_eval.He4_Sc42__V46
       -rho*Y[jp]*rate_eval.p_Sc42__Ti43
       -rho*Y[jn]*rate_eval.n_Sc42__Sc43
       -rate_eval.Sc42__Ca42__weak__wc12
       -rho*Y[jp]*rate_eval.p_Sc42__He4_Ca39
       )

    jac[jsc42, jti42] = (
       +rho*Y[jn]*rate_eval.n_Ti42__p_Sc42
       +rate_eval.Ti42__Sc42__weak__wc12
       )

    jac[jsc42, jv45] = (
       +rho*Y[jn]*rate_eval.n_V45__He4_Sc42
       )

    jac[jsc43, jn] = (
       -rho*Y[jsc43]*rate_eval.n_Sc43__He4_K40
       -rho*Y[jsc43]*rate_eval.n_Sc43__p_Ca43
       -rho*Y[jsc43]*rate_eval.n_Sc43__Sc44
       +rho*Y[jv46]*rate_eval.n_V46__He4_Sc43
       +rho*Y[jsc42]*rate_eval.n_Sc42__Sc43
       +rho*Y[jti43]*rate_eval.n_Ti43__p_Sc43
       )

    jac[jsc43, jp] = (
       -rho*Y[jsc43]*rate_eval.p_Sc43__Ti44
       -rho*Y[jsc43]*rate_eval.p_Sc43__He4_Ca40
       +rho*Y[jca42]*rate_eval.p_Ca42__Sc43
       )

    jac[jsc43, jhe4] = (
       -rho*Y[jsc43]*rate_eval.He4_Sc43__p_Ti46
       -rho*Y[jsc43]*rate_eval.He4_Sc43__V47
       +rho*Y[jk39]*rate_eval.He4_K39__Sc43
       )

    jac[jsc43, jk39] = (
       +rho*Y[jhe4]*rate_eval.He4_K39__Sc43
       )

    jac[jsc43, jca42] = (
       +rho*Y[jp]*rate_eval.p_Ca42__Sc43
       )

    jac[jsc43, jsc42] = (
       +rho*Y[jn]*rate_eval.n_Sc42__Sc43
       )

    jac[jsc43, jsc43] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc43__p_Ti46
       -rho*Y[jn]*rate_eval.n_Sc43__He4_K40
       -rho*Y[jn]*rate_eval.n_Sc43__p_Ca43
       -rho*Y[jhe4]*rate_eval.He4_Sc43__V47
       -rho*Y[jn]*rate_eval.n_Sc43__Sc44
       -rho*Y[jp]*rate_eval.p_Sc43__Ti44
       -rho*Y[jp]*rate_eval.p_Sc43__He4_Ca40
       -rate_eval.Sc43__Ca43__weak__wc12
       )

    jac[jsc43, jti43] = (
       +rate_eval.Ti43__Sc43__weak__wc12
       +rho*Y[jn]*rate_eval.n_Ti43__p_Sc43
       )

    jac[jsc43, jv46] = (
       +rho*Y[jn]*rate_eval.n_V46__He4_Sc43
       )

    jac[jsc44, jn] = (
       -rho*Y[jsc44]*rate_eval.n_Sc44__p_Ca44
       -rho*Y[jsc44]*rate_eval.n_Sc44__Sc45
       +rho*Y[jv47]*rate_eval.n_V47__He4_Sc44
       +rho*Y[jti44]*rate_eval.n_Ti44__p_Sc44
       +rho*Y[jsc43]*rate_eval.n_Sc43__Sc44
       )

    jac[jsc44, jp] = (
       -rho*Y[jsc44]*rate_eval.p_Sc44__He4_Ca41
       -rho*Y[jsc44]*rate_eval.p_Sc44__Ti45
       +rho*Y[jca43]*rate_eval.p_Ca43__Sc44
       )

    jac[jsc44, jhe4] = (
       -rho*Y[jsc44]*rate_eval.He4_Sc44__p_Ti47
       -rho*Y[jsc44]*rate_eval.He4_Sc44__V48
       +rho*Y[jk41]*rate_eval.He4_K41__n_Sc44
       +rho*Y[jk40]*rate_eval.He4_K40__Sc44
       )

    jac[jsc44, jk40] = (
       +rho*Y[jhe4]*rate_eval.He4_K40__Sc44
       )

    jac[jsc44, jk41] = (
       +rho*Y[jhe4]*rate_eval.He4_K41__n_Sc44
       )

    jac[jsc44, jca43] = (
       +rho*Y[jp]*rate_eval.p_Ca43__Sc44
       )

    jac[jsc44, jsc43] = (
       +rho*Y[jn]*rate_eval.n_Sc43__Sc44
       )

    jac[jsc44, jsc44] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc44__p_Ti47
       -rho*Y[jp]*rate_eval.p_Sc44__He4_Ca41
       -rho*Y[jn]*rate_eval.n_Sc44__p_Ca44
       -rho*Y[jhe4]*rate_eval.He4_Sc44__V48
       -rho*Y[jn]*rate_eval.n_Sc44__Sc45
       -rate_eval.Sc44__Ca44__weak__wc12
       -rho*Y[jp]*rate_eval.p_Sc44__Ti45
       )

    jac[jsc44, jti44] = (
       +rho*Y[jn]*rate_eval.n_Ti44__p_Sc44
       +rate_eval.Ti44__Sc44__weak__wc12
       )

    jac[jsc44, jv47] = (
       +rho*Y[jn]*rate_eval.n_V47__He4_Sc44
       )

    jac[jsc45, jn] = (
       -rho*Y[jsc45]*rate_eval.n_Sc45__p_Ca45
       -rho*Y[jsc45]*rate_eval.n_Sc45__Sc46
       +rho*Y[jti45]*rate_eval.n_Ti45__p_Sc45
       +rho*Y[jsc44]*rate_eval.n_Sc44__Sc45
       +rho*Y[jv48]*rate_eval.n_V48__He4_Sc45
       )

    jac[jsc45, jp] = (
       -rho*Y[jsc45]*rate_eval.p_Sc45__He4_Ca42
       -rho*Y[jsc45]*rate_eval.p_Sc45__Ti46
       +rho*Y[jca44]*rate_eval.p_Ca44__Sc45
       )

    jac[jsc45, jhe4] = (
       -rho*Y[jsc45]*rate_eval.He4_Sc45__p_Ti48
       -rho*Y[jsc45]*rate_eval.He4_Sc45__V49
       +rho*Y[jk42]*rate_eval.He4_K42__n_Sc45
       +rho*Y[jk41]*rate_eval.He4_K41__Sc45
       )

    jac[jsc45, jk41] = (
       +rho*Y[jhe4]*rate_eval.He4_K41__Sc45
       )

    jac[jsc45, jk42] = (
       +rho*Y[jhe4]*rate_eval.He4_K42__n_Sc45
       )

    jac[jsc45, jca44] = (
       +rho*Y[jp]*rate_eval.p_Ca44__Sc45
       )

    jac[jsc45, jca45] = (
       +rate_eval.Ca45__Sc45__weak__wc12
       )

    jac[jsc45, jsc44] = (
       +rho*Y[jn]*rate_eval.n_Sc44__Sc45
       )

    jac[jsc45, jsc45] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc45__p_Ti48
       -rho*Y[jp]*rate_eval.p_Sc45__He4_Ca42
       -rho*Y[jn]*rate_eval.n_Sc45__p_Ca45
       -rho*Y[jp]*rate_eval.p_Sc45__Ti46
       -rho*Y[jhe4]*rate_eval.He4_Sc45__V49
       -rho*Y[jn]*rate_eval.n_Sc45__Sc46
       )

    jac[jsc45, jti45] = (
       +rho*Y[jn]*rate_eval.n_Ti45__p_Sc45
       +rate_eval.Ti45__Sc45__weak__wc12
       )

    jac[jsc45, jv48] = (
       +rho*Y[jn]*rate_eval.n_V48__He4_Sc45
       )

    jac[jsc46, jn] = (
       -rho*Y[jsc46]*rate_eval.n_Sc46__p_Ca46
       -rho*Y[jsc46]*rate_eval.n_Sc46__He4_K43
       -rho*Y[jsc46]*rate_eval.n_Sc46__Sc47
       +rho*Y[jsc45]*rate_eval.n_Sc45__Sc46
       )

    jac[jsc46, jp] = (
       -rho*Y[jsc46]*rate_eval.p_Sc46__He4_Ca43
       -rho*Y[jsc46]*rate_eval.p_Sc46__n_Ti46
       -rho*Y[jsc46]*rate_eval.p_Sc46__Ti47
       +rho*Y[jca45]*rate_eval.p_Ca45__Sc46
       )

    jac[jsc46, jhe4] = (
       -rho*Y[jsc46]*rate_eval.He4_Sc46__p_Ti49
       -rho*Y[jsc46]*rate_eval.He4_Sc46__n_V49
       -rho*Y[jsc46]*rate_eval.He4_Sc46__V50
       +rho*Y[jk42]*rate_eval.He4_K42__Sc46
       )

    jac[jsc46, jk42] = (
       +rho*Y[jhe4]*rate_eval.He4_K42__Sc46
       )

    jac[jsc46, jca45] = (
       +rho*Y[jp]*rate_eval.p_Ca45__Sc46
       )

    jac[jsc46, jsc45] = (
       +rho*Y[jn]*rate_eval.n_Sc45__Sc46
       )

    jac[jsc46, jsc46] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc46__p_Ti49
       -rho*Y[jp]*rate_eval.p_Sc46__He4_Ca43
       -rho*Y[jn]*rate_eval.n_Sc46__p_Ca46
       -rho*Y[jn]*rate_eval.n_Sc46__He4_K43
       -rho*Y[jp]*rate_eval.p_Sc46__n_Ti46
       -rho*Y[jp]*rate_eval.p_Sc46__Ti47
       -rho*Y[jn]*rate_eval.n_Sc46__Sc47
       -rho*Y[jhe4]*rate_eval.He4_Sc46__n_V49
       -rate_eval.Sc46__Ti46__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Sc46__V50
       )

    jac[jsc47, jn] = (
       -rho*Y[jsc47]*rate_eval.n_Sc47__Sc48
       +rho*Y[jv50]*rate_eval.n_V50__He4_Sc47
       +rho*Y[jsc46]*rate_eval.n_Sc46__Sc47
       +rho*Y[jti47]*rate_eval.n_Ti47__p_Sc47
       )

    jac[jsc47, jp] = (
       -rho*Y[jsc47]*rate_eval.p_Sc47__He4_Ca44
       -rho*Y[jsc47]*rate_eval.p_Sc47__Ti48
       +rho*Y[jca47]*rate_eval.p_Ca47__n_Sc47
       +rho*Y[jca46]*rate_eval.p_Ca46__Sc47
       )

    jac[jsc47, jhe4] = (
       -rho*Y[jsc47]*rate_eval.He4_Sc47__p_Ti50
       -rho*Y[jsc47]*rate_eval.He4_Sc47__V51
       +rho*Y[jk43]*rate_eval.He4_K43__Sc47
       +rho*Y[jk44]*rate_eval.He4_K44__n_Sc47
       )

    jac[jsc47, jk43] = (
       +rho*Y[jhe4]*rate_eval.He4_K43__Sc47
       )

    jac[jsc47, jk44] = (
       +rho*Y[jhe4]*rate_eval.He4_K44__n_Sc47
       )

    jac[jsc47, jca46] = (
       +rho*Y[jp]*rate_eval.p_Ca46__Sc47
       )

    jac[jsc47, jca47] = (
       +rho*Y[jp]*rate_eval.p_Ca47__n_Sc47
       +rate_eval.Ca47__Sc47__weak__wc12
       )

    jac[jsc47, jsc46] = (
       +rho*Y[jn]*rate_eval.n_Sc46__Sc47
       )

    jac[jsc47, jsc47] = (
       -rate_eval.Sc47__Ti47__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Sc47__p_Ti50
       -rho*Y[jp]*rate_eval.p_Sc47__He4_Ca44
       -rho*Y[jhe4]*rate_eval.He4_Sc47__V51
       -rho*Y[jp]*rate_eval.p_Sc47__Ti48
       -rho*Y[jn]*rate_eval.n_Sc47__Sc48
       )

    jac[jsc47, jti47] = (
       +rho*Y[jn]*rate_eval.n_Ti47__p_Sc47
       )

    jac[jsc47, jv50] = (
       +rho*Y[jn]*rate_eval.n_V50__He4_Sc47
       )

    jac[jsc48, jn] = (
       -rho*Y[jsc48]*rate_eval.n_Sc48__p_Ca48
       -rho*Y[jsc48]*rate_eval.n_Sc48__Sc49
       +rho*Y[jsc47]*rate_eval.n_Sc47__Sc48
       )

    jac[jsc48, jp] = (
       -rho*Y[jsc48]*rate_eval.p_Sc48__He4_Ca45
       -rho*Y[jsc48]*rate_eval.p_Sc48__n_Ti48
       -rho*Y[jsc48]*rate_eval.p_Sc48__Ti49
       +rho*Y[jca47]*rate_eval.p_Ca47__Sc48
       )

    jac[jsc48, jhe4] = (
       -rho*Y[jsc48]*rate_eval.He4_Sc48__n_V51
       -rho*Y[jsc48]*rate_eval.He4_Sc48__V52
       -rho*Y[jsc48]*rate_eval.He4_Sc48__p_Ti51
       +rho*Y[jk44]*rate_eval.He4_K44__Sc48
       +rho*Y[jk45]*rate_eval.He4_K45__n_Sc48
       )

    jac[jsc48, jk44] = (
       +rho*Y[jhe4]*rate_eval.He4_K44__Sc48
       )

    jac[jsc48, jk45] = (
       +rho*Y[jhe4]*rate_eval.He4_K45__n_Sc48
       )

    jac[jsc48, jca47] = (
       +rho*Y[jp]*rate_eval.p_Ca47__Sc48
       )

    jac[jsc48, jca48] = (
       +rate_eval.Ca48__Sc48__weak__mo03
       )

    jac[jsc48, jsc47] = (
       +rho*Y[jn]*rate_eval.n_Sc47__Sc48
       )

    jac[jsc48, jsc48] = (
       -rho*Y[jp]*rate_eval.p_Sc48__He4_Ca45
       -rho*Y[jn]*rate_eval.n_Sc48__p_Ca48
       -rho*Y[jhe4]*rate_eval.He4_Sc48__n_V51
       -rho*Y[jp]*rate_eval.p_Sc48__n_Ti48
       -rho*Y[jhe4]*rate_eval.He4_Sc48__V52
       -rho*Y[jp]*rate_eval.p_Sc48__Ti49
       -rho*Y[jn]*rate_eval.n_Sc48__Sc49
       -rho*Y[jhe4]*rate_eval.He4_Sc48__p_Ti51
       -rate_eval.Sc48__Ti48__weak__wc12
       )

    jac[jsc49, jn] = (
       -rho*Y[jsc49]*rate_eval.n_Sc49__Sc50
       +rho*Y[jsc48]*rate_eval.n_Sc48__Sc49
       +rho*Y[jv52]*rate_eval.n_V52__He4_Sc49
       )

    jac[jsc49, jp] = (
       -rho*Y[jsc49]*rate_eval.p_Sc49__He4_Ca46
       -rho*Y[jsc49]*rate_eval.p_Sc49__n_Ti49
       -rho*Y[jsc49]*rate_eval.p_Sc49__Ti50
       +rho*Y[jti52]*rate_eval.p_Ti52__He4_Sc49
       +rho*Y[jca49]*rate_eval.p_Ca49__n_Sc49
       +rho*Y[jca48]*rate_eval.p_Ca48__Sc49
       )

    jac[jsc49, jhe4] = (
       -rho*Y[jsc49]*rate_eval.He4_Sc49__V53
       +rho*Y[jk45]*rate_eval.He4_K45__Sc49
       +rho*Y[jk46]*rate_eval.He4_K46__n_Sc49
       )

    jac[jsc49, jk45] = (
       +rho*Y[jhe4]*rate_eval.He4_K45__Sc49
       )

    jac[jsc49, jk46] = (
       +rho*Y[jhe4]*rate_eval.He4_K46__n_Sc49
       )

    jac[jsc49, jca48] = (
       +rho*Y[jp]*rate_eval.p_Ca48__Sc49
       )

    jac[jsc49, jca49] = (
       +rho*Y[jp]*rate_eval.p_Ca49__n_Sc49
       +rate_eval.Ca49__Sc49__weak__wc12
       )

    jac[jsc49, jsc48] = (
       +rho*Y[jn]*rate_eval.n_Sc48__Sc49
       )

    jac[jsc49, jsc49] = (
       -rho*Y[jp]*rate_eval.p_Sc49__He4_Ca46
       -rho*Y[jp]*rate_eval.p_Sc49__n_Ti49
       -rho*Y[jhe4]*rate_eval.He4_Sc49__V53
       -rho*Y[jp]*rate_eval.p_Sc49__Ti50
       -rho*Y[jn]*rate_eval.n_Sc49__Sc50
       -rate_eval.Sc49__Ti49__weak__wc12
       )

    jac[jsc49, jti52] = (
       +rho*Y[jp]*rate_eval.p_Ti52__He4_Sc49
       )

    jac[jsc49, jv52] = (
       +rho*Y[jn]*rate_eval.n_V52__He4_Sc49
       )

    jac[jsc50, jn] = (
       -rho*Y[jsc50]*rate_eval.n_Sc50__Sc51
       +rho*Y[jsc49]*rate_eval.n_Sc49__Sc50
       )

    jac[jsc50, jp] = (
       -rho*Y[jsc50]*rate_eval.p_Sc50__Ti51
       -rho*Y[jsc50]*rate_eval.p_Sc50__n_Ti50
       -rho*Y[jsc50]*rate_eval.p_Sc50__He4_Ca47
       +rho*Y[jti53]*rate_eval.p_Ti53__He4_Sc50
       +rho*Y[jca49]*rate_eval.p_Ca49__Sc50
       +rho*Y[jca50]*rate_eval.p_Ca50__n_Sc50
       )

    jac[jsc50, jhe4] = (
       -rho*Y[jsc50]*rate_eval.He4_Sc50__V54
       -rho*Y[jsc50]*rate_eval.He4_Sc50__n_V53
       +rho*Y[jk47]*rate_eval.He4_K47__n_Sc50
       +rho*Y[jk46]*rate_eval.He4_K46__Sc50
       )

    jac[jsc50, jk46] = (
       +rho*Y[jhe4]*rate_eval.He4_K46__Sc50
       )

    jac[jsc50, jk47] = (
       +rho*Y[jhe4]*rate_eval.He4_K47__n_Sc50
       )

    jac[jsc50, jca49] = (
       +rho*Y[jp]*rate_eval.p_Ca49__Sc50
       )

    jac[jsc50, jca50] = (
       +rho*Y[jp]*rate_eval.p_Ca50__n_Sc50
       +rate_eval.Ca50__Sc50__weak__wc12
       )

    jac[jsc50, jsc49] = (
       +rho*Y[jn]*rate_eval.n_Sc49__Sc50
       )

    jac[jsc50, jsc50] = (
       -rho*Y[jp]*rate_eval.p_Sc50__Ti51
       -rho*Y[jp]*rate_eval.p_Sc50__n_Ti50
       -rho*Y[jn]*rate_eval.n_Sc50__Sc51
       -rho*Y[jp]*rate_eval.p_Sc50__He4_Ca47
       -rate_eval.Sc50__Ti50__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Sc50__V54
       -rho*Y[jhe4]*rate_eval.He4_Sc50__n_V53
       )

    jac[jsc50, jti53] = (
       +rho*Y[jp]*rate_eval.p_Ti53__He4_Sc50
       )

    jac[jsc51, jn] = (
       -rho*Y[jsc51]*rate_eval.n_Sc51__Sc52
       +rho*Y[jsc50]*rate_eval.n_Sc50__Sc51
       )

    jac[jsc51, jp] = (
       -rho*Y[jsc51]*rate_eval.p_Sc51__He4_Ca48
       -rho*Y[jsc51]*rate_eval.p_Sc51__n_Ti51
       -rho*Y[jsc51]*rate_eval.p_Sc51__Ti52
       +rho*Y[jti54]*rate_eval.p_Ti54__He4_Sc51
       +rho*Y[jca51]*rate_eval.p_Ca51__n_Sc51
       +rho*Y[jca50]*rate_eval.p_Ca50__Sc51
       )

    jac[jsc51, jhe4] = (
       -rho*Y[jsc51]*rate_eval.He4_Sc51__n_V54
       -rho*Y[jsc51]*rate_eval.He4_Sc51__V55
       +rho*Y[jk48]*rate_eval.He4_K48__n_Sc51
       +rho*Y[jk47]*rate_eval.He4_K47__Sc51
       )

    jac[jsc51, jk47] = (
       +rho*Y[jhe4]*rate_eval.He4_K47__Sc51
       )

    jac[jsc51, jk48] = (
       +rho*Y[jhe4]*rate_eval.He4_K48__n_Sc51
       )

    jac[jsc51, jca50] = (
       +rho*Y[jp]*rate_eval.p_Ca50__Sc51
       )

    jac[jsc51, jca51] = (
       +rate_eval.Ca51__Sc51__weak__wc12
       +rho*Y[jp]*rate_eval.p_Ca51__n_Sc51
       )

    jac[jsc51, jca52] = (
       +rate_eval.Ca52__n_Sc51__weak__wc12
       )

    jac[jsc51, jsc50] = (
       +rho*Y[jn]*rate_eval.n_Sc50__Sc51
       )

    jac[jsc51, jsc51] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc51__n_V54
       -rho*Y[jp]*rate_eval.p_Sc51__He4_Ca48
       -rho*Y[jp]*rate_eval.p_Sc51__n_Ti51
       -rho*Y[jp]*rate_eval.p_Sc51__Ti52
       -rho*Y[jhe4]*rate_eval.He4_Sc51__V55
       -rho*Y[jn]*rate_eval.n_Sc51__Sc52
       -rate_eval.Sc51__Ti51__weak__wc12
       )

    jac[jsc51, jti54] = (
       +rho*Y[jp]*rate_eval.p_Ti54__He4_Sc51
       )

    jac[jsc52, jn] = (
       -rho*Y[jsc52]*rate_eval.n_Sc52__Sc53
       +rho*Y[jsc51]*rate_eval.n_Sc51__Sc52
       )

    jac[jsc52, jp] = (
       -rho*Y[jsc52]*rate_eval.p_Sc52__Ti53
       -rho*Y[jsc52]*rate_eval.p_Sc52__He4_Ca49
       -rho*Y[jsc52]*rate_eval.p_Sc52__n_Ti52
       +rho*Y[jca52]*rate_eval.p_Ca52__n_Sc52
       +rho*Y[jca51]*rate_eval.p_Ca51__Sc52
       +rho*Y[jti55]*rate_eval.p_Ti55__He4_Sc52
       )

    jac[jsc52, jhe4] = (
       -rho*Y[jsc52]*rate_eval.He4_Sc52__n_V55
       -rho*Y[jsc52]*rate_eval.He4_Sc52__V56
       +rho*Y[jk49]*rate_eval.He4_K49__n_Sc52
       +rho*Y[jk48]*rate_eval.He4_K48__Sc52
       )

    jac[jsc52, jk48] = (
       +rho*Y[jhe4]*rate_eval.He4_K48__Sc52
       )

    jac[jsc52, jk49] = (
       +rho*Y[jhe4]*rate_eval.He4_K49__n_Sc52
       )

    jac[jsc52, jca51] = (
       +rho*Y[jp]*rate_eval.p_Ca51__Sc52
       )

    jac[jsc52, jca52] = (
       +rho*Y[jp]*rate_eval.p_Ca52__n_Sc52
       +rate_eval.Ca52__Sc52__weak__wc12
       )

    jac[jsc52, jca53] = (
       +rate_eval.Ca53__n_Sc52__weak__wc12
       )

    jac[jsc52, jsc51] = (
       +rho*Y[jn]*rate_eval.n_Sc51__Sc52
       )

    jac[jsc52, jsc52] = (
       -rho*Y[jp]*rate_eval.p_Sc52__Ti53
       -rho*Y[jhe4]*rate_eval.He4_Sc52__n_V55
       -rho*Y[jp]*rate_eval.p_Sc52__He4_Ca49
       -rho*Y[jp]*rate_eval.p_Sc52__n_Ti52
       -rho*Y[jn]*rate_eval.n_Sc52__Sc53
       -rho*Y[jhe4]*rate_eval.He4_Sc52__V56
       -rate_eval.Sc52__Ti52__weak__wc12
       )

    jac[jsc52, jti55] = (
       +rho*Y[jp]*rate_eval.p_Ti55__He4_Sc52
       )

    jac[jsc53, jn] = (
       -rho*Y[jsc53]*rate_eval.n_Sc53__Sc54
       +rho*Y[jsc52]*rate_eval.n_Sc52__Sc53
       )

    jac[jsc53, jp] = (
       -rho*Y[jsc53]*rate_eval.p_Sc53__n_Ti53
       -rho*Y[jsc53]*rate_eval.p_Sc53__Ti54
       -rho*Y[jsc53]*rate_eval.p_Sc53__He4_Ca50
       +rho*Y[jca53]*rate_eval.p_Ca53__n_Sc53
       +rho*Y[jti56]*rate_eval.p_Ti56__He4_Sc53
       +rho*Y[jca52]*rate_eval.p_Ca52__Sc53
       )

    jac[jsc53, jhe4] = (
       -rho*Y[jsc53]*rate_eval.He4_Sc53__n_V56
       -rho*Y[jsc53]*rate_eval.He4_Sc53__V57
       +rho*Y[jk50]*rate_eval.He4_K50__n_Sc53
       +rho*Y[jk49]*rate_eval.He4_K49__Sc53
       )

    jac[jsc53, jk49] = (
       +rho*Y[jhe4]*rate_eval.He4_K49__Sc53
       )

    jac[jsc53, jk50] = (
       +rho*Y[jhe4]*rate_eval.He4_K50__n_Sc53
       )

    jac[jsc53, jca52] = (
       +rho*Y[jp]*rate_eval.p_Ca52__Sc53
       )

    jac[jsc53, jca53] = (
       +rho*Y[jp]*rate_eval.p_Ca53__n_Sc53
       +rate_eval.Ca53__Sc53__weak__wc12
       )

    jac[jsc53, jca54] = (
       +rate_eval.Ca54__n_Sc53__weak__mp17
       )

    jac[jsc53, jca56] = (
       +rate_eval.Ca56__n_n_n_Sc53__weak__mo03
       )

    jac[jsc53, jsc52] = (
       +rho*Y[jn]*rate_eval.n_Sc52__Sc53
       )

    jac[jsc53, jsc53] = (
       -rho*Y[jp]*rate_eval.p_Sc53__n_Ti53
       -rate_eval.Sc53__Ti53__weak__wc12
       -rho*Y[jp]*rate_eval.p_Sc53__Ti54
       -rho*Y[jn]*rate_eval.n_Sc53__Sc54
       -rho*Y[jhe4]*rate_eval.He4_Sc53__n_V56
       -rho*Y[jp]*rate_eval.p_Sc53__He4_Ca50
       -rho*Y[jhe4]*rate_eval.He4_Sc53__V57
       )

    jac[jsc53, jti56] = (
       +rho*Y[jp]*rate_eval.p_Ti56__He4_Sc53
       )

    jac[jsc54, jn] = (
       -rho*Y[jsc54]*rate_eval.n_Sc54__Sc55
       +rho*Y[jsc53]*rate_eval.n_Sc53__Sc54
       )

    jac[jsc54, jp] = (
       -rho*Y[jsc54]*rate_eval.p_Sc54__n_Ti54
       -rho*Y[jsc54]*rate_eval.p_Sc54__Ti55
       -rho*Y[jsc54]*rate_eval.p_Sc54__He4_Ca51
       +rho*Y[jti57]*rate_eval.p_Ti57__He4_Sc54
       +rho*Y[jca54]*rate_eval.p_Ca54__n_Sc54
       +rho*Y[jca53]*rate_eval.p_Ca53__Sc54
       )

    jac[jsc54, jhe4] = (
       -rho*Y[jsc54]*rate_eval.He4_Sc54__n_V57
       -rho*Y[jsc54]*rate_eval.He4_Sc54__V58
       +rho*Y[jk51]*rate_eval.He4_K51__n_Sc54
       +rho*Y[jk50]*rate_eval.He4_K50__Sc54
       )

    jac[jsc54, jk50] = (
       +rho*Y[jhe4]*rate_eval.He4_K50__Sc54
       )

    jac[jsc54, jk51] = (
       +rho*Y[jhe4]*rate_eval.He4_K51__n_Sc54
       )

    jac[jsc54, jca53] = (
       +rho*Y[jp]*rate_eval.p_Ca53__Sc54
       )

    jac[jsc54, jca54] = (
       +rho*Y[jp]*rate_eval.p_Ca54__n_Sc54
       +rate_eval.Ca54__Sc54__weak__wc17
       )

    jac[jsc54, jca55] = (
       +rate_eval.Ca55__n_Sc54__weak__mp17
       )

    jac[jsc54, jca57] = (
       +rate_eval.Ca57__n_n_n_Sc54__weak__mo03
       )

    jac[jsc54, jsc53] = (
       +rho*Y[jn]*rate_eval.n_Sc53__Sc54
       )

    jac[jsc54, jsc54] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc54__n_V57
       -rho*Y[jp]*rate_eval.p_Sc54__n_Ti54
       -rho*Y[jhe4]*rate_eval.He4_Sc54__V58
       -rate_eval.Sc54__Ti54__weak__wc17
       -rho*Y[jn]*rate_eval.n_Sc54__Sc55
       -rate_eval.Sc54__n_Ti53__weak__mp17
       -rho*Y[jp]*rate_eval.p_Sc54__Ti55
       -rho*Y[jp]*rate_eval.p_Sc54__He4_Ca51
       )

    jac[jsc54, jti57] = (
       +rho*Y[jp]*rate_eval.p_Ti57__He4_Sc54
       )

    jac[jsc55, jn] = (
       -rho*Y[jsc55]*rate_eval.n_Sc55__Sc56
       +rho*Y[jsc54]*rate_eval.n_Sc54__Sc55
       )

    jac[jsc55, jp] = (
       -rho*Y[jsc55]*rate_eval.p_Sc55__He4_Ca52
       -rho*Y[jsc55]*rate_eval.p_Sc55__n_Ti55
       -rho*Y[jsc55]*rate_eval.p_Sc55__Ti56
       +rho*Y[jca55]*rate_eval.p_Ca55__n_Sc55
       +rho*Y[jca54]*rate_eval.p_Ca54__Sc55
       +rho*Y[jti58]*rate_eval.p_Ti58__He4_Sc55
       )

    jac[jsc55, jhe4] = (
       -rho*Y[jsc55]*rate_eval.He4_Sc55__n_V58
       -rho*Y[jsc55]*rate_eval.He4_Sc55__V59
       +rho*Y[jk52]*rate_eval.He4_K52__n_Sc55
       +rho*Y[jk51]*rate_eval.He4_K51__Sc55
       )

    jac[jsc55, jk51] = (
       +rho*Y[jhe4]*rate_eval.He4_K51__Sc55
       )

    jac[jsc55, jk52] = (
       +rho*Y[jhe4]*rate_eval.He4_K52__n_Sc55
       )

    jac[jsc55, jca54] = (
       +rho*Y[jp]*rate_eval.p_Ca54__Sc55
       )

    jac[jsc55, jca55] = (
       +rho*Y[jp]*rate_eval.p_Ca55__n_Sc55
       +rate_eval.Ca55__Sc55__weak__wc12
       )

    jac[jsc55, jca56] = (
       +rate_eval.Ca56__n_Sc55__weak__mp17
       )

    jac[jsc55, jca57] = (
       +rate_eval.Ca57__n_n_Sc55__weak__mp17
       )

    jac[jsc55, jca58] = (
       +rate_eval.Ca58__n_n_n_Sc55__weak__mo03
       )

    jac[jsc55, jsc54] = (
       +rho*Y[jn]*rate_eval.n_Sc54__Sc55
       )

    jac[jsc55, jsc55] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc55__n_V58
       -rho*Y[jp]*rate_eval.p_Sc55__He4_Ca52
       -rho*Y[jp]*rate_eval.p_Sc55__n_Ti55
       -rho*Y[jn]*rate_eval.n_Sc55__Sc56
       -rho*Y[jhe4]*rate_eval.He4_Sc55__V59
       -rho*Y[jp]*rate_eval.p_Sc55__Ti56
       -rate_eval.Sc55__n_Ti54__weak__wc12
       -rate_eval.Sc55__Ti55__weak__wc12
       )

    jac[jsc55, jti58] = (
       +rho*Y[jp]*rate_eval.p_Ti58__He4_Sc55
       )

    jac[jsc56, jn] = (
       -rho*Y[jsc56]*rate_eval.n_Sc56__Sc57
       +rho*Y[jsc55]*rate_eval.n_Sc55__Sc56
       )

    jac[jsc56, jp] = (
       -rho*Y[jsc56]*rate_eval.p_Sc56__Ti57
       -rho*Y[jsc56]*rate_eval.p_Sc56__He4_Ca53
       -rho*Y[jsc56]*rate_eval.p_Sc56__n_Ti56
       +rho*Y[jca56]*rate_eval.p_Ca56__n_Sc56
       +rho*Y[jca55]*rate_eval.p_Ca55__Sc56
       +rho*Y[jti59]*rate_eval.p_Ti59__He4_Sc56
       )

    jac[jsc56, jhe4] = (
       -rho*Y[jsc56]*rate_eval.He4_Sc56__n_V59
       -rho*Y[jsc56]*rate_eval.He4_Sc56__V60
       +rho*Y[jk53]*rate_eval.He4_K53__n_Sc56
       +rho*Y[jk52]*rate_eval.He4_K52__Sc56
       )

    jac[jsc56, jk52] = (
       +rho*Y[jhe4]*rate_eval.He4_K52__Sc56
       )

    jac[jsc56, jk53] = (
       +rho*Y[jhe4]*rate_eval.He4_K53__n_Sc56
       )

    jac[jsc56, jca55] = (
       +rho*Y[jp]*rate_eval.p_Ca55__Sc56
       )

    jac[jsc56, jca56] = (
       +rho*Y[jp]*rate_eval.p_Ca56__n_Sc56
       +rate_eval.Ca56__Sc56__weak__wc17
       )

    jac[jsc56, jca57] = (
       +rate_eval.Ca57__n_Sc56__weak__mp17
       )

    jac[jsc56, jca58] = (
       +rate_eval.Ca58__n_n_Sc56__weak__mp17
       )

    jac[jsc56, jca59] = (
       +rate_eval.Ca59__n_n_n_Sc56__weak__mo03
       )

    jac[jsc56, jsc55] = (
       +rho*Y[jn]*rate_eval.n_Sc55__Sc56
       )

    jac[jsc56, jsc56] = (
       -rate_eval.Sc56__n_Ti55__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Sc56__n_V59
       -rho*Y[jhe4]*rate_eval.He4_Sc56__V60
       -rho*Y[jp]*rate_eval.p_Sc56__Ti57
       -rho*Y[jn]*rate_eval.n_Sc56__Sc57
       -rho*Y[jp]*rate_eval.p_Sc56__He4_Ca53
       -rate_eval.Sc56__Ti56__weak__wc17
       -rho*Y[jp]*rate_eval.p_Sc56__n_Ti56
       )

    jac[jsc56, jti59] = (
       +rho*Y[jp]*rate_eval.p_Ti59__He4_Sc56
       )

    jac[jsc57, jn] = (
       -rho*Y[jsc57]*rate_eval.n_Sc57__Sc58
       +rho*Y[jsc56]*rate_eval.n_Sc56__Sc57
       )

    jac[jsc57, jp] = (
       -rho*Y[jsc57]*rate_eval.p_Sc57__He4_Ca54
       -rho*Y[jsc57]*rate_eval.p_Sc57__n_Ti57
       -rho*Y[jsc57]*rate_eval.p_Sc57__Ti58
       +rho*Y[jca56]*rate_eval.p_Ca56__Sc57
       +rho*Y[jti60]*rate_eval.p_Ti60__He4_Sc57
       +rho*Y[jca57]*rate_eval.p_Ca57__n_Sc57
       )

    jac[jsc57, jhe4] = (
       -rho*Y[jsc57]*rate_eval.He4_Sc57__n_V60
       -rho*Y[jsc57]*rate_eval.He4_Sc57__V61
       +rho*Y[jk54]*rate_eval.He4_K54__n_Sc57
       +rho*Y[jk53]*rate_eval.He4_K53__Sc57
       )

    jac[jsc57, jk53] = (
       +rho*Y[jhe4]*rate_eval.He4_K53__Sc57
       )

    jac[jsc57, jk54] = (
       +rho*Y[jhe4]*rate_eval.He4_K54__n_Sc57
       )

    jac[jsc57, jca56] = (
       +rho*Y[jp]*rate_eval.p_Ca56__Sc57
       )

    jac[jsc57, jca57] = (
       +rate_eval.Ca57__Sc57__weak__mo03
       +rho*Y[jp]*rate_eval.p_Ca57__n_Sc57
       )

    jac[jsc57, jca58] = (
       +rate_eval.Ca58__n_Sc57__weak__mp17
       )

    jac[jsc57, jca59] = (
       +rate_eval.Ca59__n_n_Sc57__weak__mp17
       )

    jac[jsc57, jca60] = (
       +rate_eval.Ca60__n_n_n_Sc57__weak__mo03
       )

    jac[jsc57, jsc56] = (
       +rho*Y[jn]*rate_eval.n_Sc56__Sc57
       )

    jac[jsc57, jsc57] = (
       -rate_eval.Sc57__n_n_n_Ti54__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Sc57__n_V60
       -rho*Y[jp]*rate_eval.p_Sc57__He4_Ca54
       -rho*Y[jp]*rate_eval.p_Sc57__n_Ti57
       -rho*Y[jhe4]*rate_eval.He4_Sc57__V61
       -rho*Y[jp]*rate_eval.p_Sc57__Ti58
       -rate_eval.Sc57__Ti57__weak__wc17
       -rate_eval.Sc57__n_Ti56__weak__mp17
       -rho*Y[jn]*rate_eval.n_Sc57__Sc58
       )

    jac[jsc57, jti60] = (
       +rho*Y[jp]*rate_eval.p_Ti60__He4_Sc57
       )

    jac[jsc58, jn] = (
       -rho*Y[jsc58]*rate_eval.n_Sc58__Sc59
       +rho*Y[jsc57]*rate_eval.n_Sc57__Sc58
       )

    jac[jsc58, jp] = (
       -rho*Y[jsc58]*rate_eval.p_Sc58__He4_Ca55
       -rho*Y[jsc58]*rate_eval.p_Sc58__n_Ti58
       -rho*Y[jsc58]*rate_eval.p_Sc58__Ti59
       +rho*Y[jca58]*rate_eval.p_Ca58__n_Sc58
       +rho*Y[jca57]*rate_eval.p_Ca57__Sc58
       +rho*Y[jti61]*rate_eval.p_Ti61__He4_Sc58
       )

    jac[jsc58, jhe4] = (
       -rho*Y[jsc58]*rate_eval.He4_Sc58__n_V61
       -rho*Y[jsc58]*rate_eval.He4_Sc58__V62
       +rho*Y[jk55]*rate_eval.He4_K55__n_Sc58
       +rho*Y[jk54]*rate_eval.He4_K54__Sc58
       )

    jac[jsc58, jk54] = (
       +rho*Y[jhe4]*rate_eval.He4_K54__Sc58
       )

    jac[jsc58, jk55] = (
       +rho*Y[jhe4]*rate_eval.He4_K55__n_Sc58
       )

    jac[jsc58, jca57] = (
       +rho*Y[jp]*rate_eval.p_Ca57__Sc58
       )

    jac[jsc58, jca58] = (
       +rho*Y[jp]*rate_eval.p_Ca58__n_Sc58
       +rate_eval.Ca58__Sc58__weak__mo03
       )

    jac[jsc58, jca59] = (
       +rate_eval.Ca59__n_Sc58__weak__mp17
       )

    jac[jsc58, jca60] = (
       +rate_eval.Ca60__n_n_Sc58__weak__mp17
       )

    jac[jsc58, jca61] = (
       +rate_eval.Ca61__n_n_n_Sc58__weak__mo03
       )

    jac[jsc58, jsc57] = (
       +rho*Y[jn]*rate_eval.n_Sc57__Sc58
       )

    jac[jsc58, jsc58] = (
       -rate_eval.Sc58__n_n_n_Ti55__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Sc58__n_V61
       -rho*Y[jp]*rate_eval.p_Sc58__He4_Ca55
       -rho*Y[jp]*rate_eval.p_Sc58__n_Ti58
       -rho*Y[jhe4]*rate_eval.He4_Sc58__V62
       -rho*Y[jp]*rate_eval.p_Sc58__Ti59
       -rho*Y[jn]*rate_eval.n_Sc58__Sc59
       -rate_eval.Sc58__n_Ti57__weak__mp17
       -rate_eval.Sc58__n_n_Ti56__weak__mp17
       -rate_eval.Sc58__Ti58__weak__wc17
       )

    jac[jsc58, jti61] = (
       +rho*Y[jp]*rate_eval.p_Ti61__He4_Sc58
       )

    jac[jsc59, jn] = (
       -rho*Y[jsc59]*rate_eval.n_Sc59__Sc60
       +rho*Y[jsc58]*rate_eval.n_Sc58__Sc59
       )

    jac[jsc59, jp] = (
       -rho*Y[jsc59]*rate_eval.p_Sc59__He4_Ca56
       -rho*Y[jsc59]*rate_eval.p_Sc59__Ti60
       -rho*Y[jsc59]*rate_eval.p_Sc59__n_Ti59
       +rho*Y[jca59]*rate_eval.p_Ca59__n_Sc59
       +rho*Y[jca58]*rate_eval.p_Ca58__Sc59
       +rho*Y[jti62]*rate_eval.p_Ti62__He4_Sc59
       )

    jac[jsc59, jhe4] = (
       -rho*Y[jsc59]*rate_eval.He4_Sc59__V63
       -rho*Y[jsc59]*rate_eval.He4_Sc59__n_V62
       +rho*Y[jk56]*rate_eval.He4_K56__n_Sc59
       +rho*Y[jk55]*rate_eval.He4_K55__Sc59
       )

    jac[jsc59, jk55] = (
       +rho*Y[jhe4]*rate_eval.He4_K55__Sc59
       )

    jac[jsc59, jk56] = (
       +rho*Y[jhe4]*rate_eval.He4_K56__n_Sc59
       )

    jac[jsc59, jca58] = (
       +rho*Y[jp]*rate_eval.p_Ca58__Sc59
       )

    jac[jsc59, jca59] = (
       +rho*Y[jp]*rate_eval.p_Ca59__n_Sc59
       +rate_eval.Ca59__Sc59__weak__mo03
       )

    jac[jsc59, jca60] = (
       +rate_eval.Ca60__n_Sc59__weak__mp17
       )

    jac[jsc59, jca61] = (
       +rate_eval.Ca61__n_n_Sc59__weak__mp17
       )

    jac[jsc59, jsc58] = (
       +rho*Y[jn]*rate_eval.n_Sc58__Sc59
       )

    jac[jsc59, jsc59] = (
       -rate_eval.Sc59__n_n_n_Ti56__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Sc59__V63
       -rho*Y[jhe4]*rate_eval.He4_Sc59__n_V62
       -rho*Y[jn]*rate_eval.n_Sc59__Sc60
       -rho*Y[jp]*rate_eval.p_Sc59__He4_Ca56
       -rate_eval.Sc59__n_n_Ti57__weak__mp17
       -rate_eval.Sc59__n_Ti58__weak__mp17
       -rate_eval.Sc59__Ti59__weak__mo03
       -rho*Y[jp]*rate_eval.p_Sc59__Ti60
       -rho*Y[jp]*rate_eval.p_Sc59__n_Ti59
       )

    jac[jsc59, jti62] = (
       +rho*Y[jp]*rate_eval.p_Ti62__He4_Sc59
       )

    jac[jsc60, jn] = (
       -rho*Y[jsc60]*rate_eval.n_Sc60__Sc61
       +rho*Y[jsc59]*rate_eval.n_Sc59__Sc60
       )

    jac[jsc60, jp] = (
       -rho*Y[jsc60]*rate_eval.p_Sc60__He4_Ca57
       -rho*Y[jsc60]*rate_eval.p_Sc60__n_Ti60
       -rho*Y[jsc60]*rate_eval.p_Sc60__Ti61
       +rho*Y[jti63]*rate_eval.p_Ti63__He4_Sc60
       +rho*Y[jca60]*rate_eval.p_Ca60__n_Sc60
       +rho*Y[jca59]*rate_eval.p_Ca59__Sc60
       )

    jac[jsc60, jhe4] = (
       -rho*Y[jsc60]*rate_eval.He4_Sc60__n_V63
       -rho*Y[jsc60]*rate_eval.He4_Sc60__V64
       +rho*Y[jk57]*rate_eval.He4_K57__n_Sc60
       +rho*Y[jk56]*rate_eval.He4_K56__Sc60
       )

    jac[jsc60, jk56] = (
       +rho*Y[jhe4]*rate_eval.He4_K56__Sc60
       )

    jac[jsc60, jk57] = (
       +rho*Y[jhe4]*rate_eval.He4_K57__n_Sc60
       )

    jac[jsc60, jca59] = (
       +rho*Y[jp]*rate_eval.p_Ca59__Sc60
       )

    jac[jsc60, jca60] = (
       +rho*Y[jp]*rate_eval.p_Ca60__n_Sc60
       +rate_eval.Ca60__Sc60__weak__mo03
       )

    jac[jsc60, jca61] = (
       +rate_eval.Ca61__n_Sc60__weak__mp17
       )

    jac[jsc60, jsc59] = (
       +rho*Y[jn]*rate_eval.n_Sc59__Sc60
       )

    jac[jsc60, jsc60] = (
       -rho*Y[jhe4]*rate_eval.He4_Sc60__n_V63
       -rho*Y[jp]*rate_eval.p_Sc60__He4_Ca57
       -rho*Y[jp]*rate_eval.p_Sc60__n_Ti60
       -rho*Y[jhe4]*rate_eval.He4_Sc60__V64
       -rho*Y[jp]*rate_eval.p_Sc60__Ti61
       -rate_eval.Sc60__n_n_Ti58__weak__mp17
       -rate_eval.Sc60__n_Ti59__weak__mp17
       -rate_eval.Sc60__n_n_n_Ti57__weak__mo03
       -rho*Y[jn]*rate_eval.n_Sc60__Sc61
       -rate_eval.Sc60__Ti60__weak__mo03
       )

    jac[jsc60, jti63] = (
       +rho*Y[jp]*rate_eval.p_Ti63__He4_Sc60
       )

    jac[jsc61, jn] = (
       -rho*Y[jsc61]*rate_eval.n_Sc61__Sc62
       +rho*Y[jsc60]*rate_eval.n_Sc60__Sc61
       )

    jac[jsc61, jp] = (
       -rho*Y[jsc61]*rate_eval.p_Sc61__n_Ti61
       -rho*Y[jsc61]*rate_eval.p_Sc61__Ti62
       -rho*Y[jsc61]*rate_eval.p_Sc61__He4_Ca58
       +rho*Y[jti64]*rate_eval.p_Ti64__He4_Sc61
       +rho*Y[jca61]*rate_eval.p_Ca61__n_Sc61
       +rho*Y[jca60]*rate_eval.p_Ca60__Sc61
       )

    jac[jsc61, jhe4] = (
       -rho*Y[jsc61]*rate_eval.He4_Sc61__n_V64
       -rho*Y[jsc61]*rate_eval.He4_Sc61__V65
       +rho*Y[jk57]*rate_eval.He4_K57__Sc61
       +rho*Y[jk58]*rate_eval.He4_K58__n_Sc61
       )

    jac[jsc61, jk57] = (
       +rho*Y[jhe4]*rate_eval.He4_K57__Sc61
       )

    jac[jsc61, jk58] = (
       +rho*Y[jhe4]*rate_eval.He4_K58__n_Sc61
       )

    jac[jsc61, jca60] = (
       +rho*Y[jp]*rate_eval.p_Ca60__Sc61
       )

    jac[jsc61, jca61] = (
       +rho*Y[jp]*rate_eval.p_Ca61__n_Sc61
       +rate_eval.Ca61__Sc61__weak__mo03
       )

    jac[jsc61, jsc60] = (
       +rho*Y[jn]*rate_eval.n_Sc60__Sc61
       )

    jac[jsc61, jsc61] = (
       -rate_eval.Sc61__n_n_n_Ti58__weak__mo03
       -rate_eval.Sc61__n_n_Ti59__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Sc61__n_V64
       -rho*Y[jp]*rate_eval.p_Sc61__n_Ti61
       -rho*Y[jp]*rate_eval.p_Sc61__Ti62
       -rate_eval.Sc61__n_Ti60__weak__mp17
       -rho*Y[jp]*rate_eval.p_Sc61__He4_Ca58
       -rho*Y[jn]*rate_eval.n_Sc61__Sc62
       -rho*Y[jhe4]*rate_eval.He4_Sc61__V65
       -rate_eval.Sc61__Ti61__weak__mo03
       )

    jac[jsc61, jti64] = (
       +rho*Y[jp]*rate_eval.p_Ti64__He4_Sc61
       )

    jac[jsc62, jn] = (
       -rho*Y[jsc62]*rate_eval.n_Sc62__Sc63
       +rho*Y[jsc61]*rate_eval.n_Sc61__Sc62
       )

    jac[jsc62, jp] = (
       -rho*Y[jsc62]*rate_eval.p_Sc62__n_Ti62
       -rho*Y[jsc62]*rate_eval.p_Sc62__Ti63
       -rho*Y[jsc62]*rate_eval.p_Sc62__He4_Ca59
       +rho*Y[jca61]*rate_eval.p_Ca61__Sc62
       +rho*Y[jti65]*rate_eval.p_Ti65__He4_Sc62
       )

    jac[jsc62, jhe4] = (
       -rho*Y[jsc62]*rate_eval.He4_Sc62__n_V65
       -rho*Y[jsc62]*rate_eval.He4_Sc62__V66
       +rho*Y[jk58]*rate_eval.He4_K58__Sc62
       +rho*Y[jk59]*rate_eval.He4_K59__n_Sc62
       )

    jac[jsc62, jk58] = (
       +rho*Y[jhe4]*rate_eval.He4_K58__Sc62
       )

    jac[jsc62, jk59] = (
       +rho*Y[jhe4]*rate_eval.He4_K59__n_Sc62
       )

    jac[jsc62, jca61] = (
       +rho*Y[jp]*rate_eval.p_Ca61__Sc62
       )

    jac[jsc62, jsc61] = (
       +rho*Y[jn]*rate_eval.n_Sc61__Sc62
       )

    jac[jsc62, jsc62] = (
       -rate_eval.Sc62__n_n_n_Ti59__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Sc62__n_V65
       -rho*Y[jp]*rate_eval.p_Sc62__n_Ti62
       -rate_eval.Sc62__Ti62__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Sc62__V66
       -rate_eval.Sc62__n_n_Ti60__weak__mp17
       -rho*Y[jn]*rate_eval.n_Sc62__Sc63
       -rho*Y[jp]*rate_eval.p_Sc62__Ti63
       -rate_eval.Sc62__n_Ti61__weak__mp17
       -rho*Y[jp]*rate_eval.p_Sc62__He4_Ca59
       )

    jac[jsc62, jti65] = (
       +rho*Y[jp]*rate_eval.p_Ti65__He4_Sc62
       )

    jac[jsc63, jn] = (
       +rho*Y[jsc62]*rate_eval.n_Sc62__Sc63
       )

    jac[jsc63, jp] = (
       -rho*Y[jsc63]*rate_eval.p_Sc63__Ti64
       -rho*Y[jsc63]*rate_eval.p_Sc63__He4_Ca60
       -rho*Y[jsc63]*rate_eval.p_Sc63__n_Ti63
       )

    jac[jsc63, jhe4] = (
       -rho*Y[jsc63]*rate_eval.He4_Sc63__n_V66
       -rho*Y[jsc63]*rate_eval.He4_Sc63__V67
       +rho*Y[jk59]*rate_eval.He4_K59__Sc63
       )

    jac[jsc63, jk59] = (
       +rho*Y[jhe4]*rate_eval.He4_K59__Sc63
       )

    jac[jsc63, jsc62] = (
       +rho*Y[jn]*rate_eval.n_Sc62__Sc63
       )

    jac[jsc63, jsc63] = (
       -rate_eval.Sc63__n_n_n_Ti60__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Sc63__n_V66
       -rho*Y[jp]*rate_eval.p_Sc63__Ti64
       -rho*Y[jp]*rate_eval.p_Sc63__He4_Ca60
       -rate_eval.Sc63__Ti63__weak__mo03
       -rate_eval.Sc63__n_Ti62__weak__mp17
       -rate_eval.Sc63__n_n_Ti61__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Sc63__V67
       -rho*Y[jp]*rate_eval.p_Sc63__n_Ti63
       )

    jac[jti37, jn] = (
       -rho*Y[jti37]*rate_eval.n_Ti37__He4_Ca34
       -rho*Y[jti37]*rate_eval.n_Ti37__Ti38
       -rho*Y[jti37]*rate_eval.n_Ti37__p_Sc37
       )

    jac[jti37, jp] = (
       +rho*Y[jsc36]*rate_eval.p_Sc36__Ti37
       )

    jac[jti37, jhe4] = (
       -rho*Y[jti37]*rate_eval.He4_Ti37__p_V40
       -rho*Y[jti37]*rate_eval.He4_Ti37__Cr41
       +rho*Y[jca33]*rate_eval.He4_Ca33__Ti37
       )

    jac[jti37, jca33] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca33__Ti37
       )

    jac[jti37, jsc36] = (
       +rho*Y[jp]*rate_eval.p_Sc36__Ti37
       )

    jac[jti37, jti37] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti37__p_V40
       -rho*Y[jn]*rate_eval.n_Ti37__He4_Ca34
       -rho*Y[jn]*rate_eval.n_Ti37__Ti38
       -rho*Y[jn]*rate_eval.n_Ti37__p_Sc37
       -rho*Y[jhe4]*rate_eval.He4_Ti37__Cr41
       -rate_eval.Ti37__Sc37__weak__bqa_pos_
       )

    jac[jti38, jn] = (
       -rho*Y[jti38]*rate_eval.n_Ti38__He4_Ca35
       -rho*Y[jti38]*rate_eval.n_Ti38__p_Sc38
       -rho*Y[jti38]*rate_eval.n_Ti38__Ti39
       +rho*Y[jcr41]*rate_eval.n_Cr41__He4_Ti38
       +rho*Y[jti37]*rate_eval.n_Ti37__Ti38
       )

    jac[jti38, jp] = (
       -rho*Y[jti38]*rate_eval.p_Ti38__V39
       +rho*Y[jsc37]*rate_eval.p_Sc37__Ti38
       )

    jac[jti38, jhe4] = (
       -rho*Y[jti38]*rate_eval.He4_Ti38__p_V41
       -rho*Y[jti38]*rate_eval.He4_Ti38__Cr42
       +rho*Y[jsc35]*rate_eval.He4_Sc35__p_Ti38
       +rho*Y[jca34]*rate_eval.He4_Ca34__Ti38
       )

    jac[jti38, jca34] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca34__Ti38
       )

    jac[jti38, jsc35] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc35__p_Ti38
       )

    jac[jti38, jsc37] = (
       +rho*Y[jp]*rate_eval.p_Sc37__Ti38
       )

    jac[jti38, jti37] = (
       +rho*Y[jn]*rate_eval.n_Ti37__Ti38
       )

    jac[jti38, jti38] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti38__p_V41
       -rho*Y[jn]*rate_eval.n_Ti38__He4_Ca35
       -rho*Y[jn]*rate_eval.n_Ti38__p_Sc38
       -rho*Y[jp]*rate_eval.p_Ti38__V39
       -rate_eval.Ti38__Sc38__weak__mo97
       -rho*Y[jhe4]*rate_eval.He4_Ti38__Cr42
       -rho*Y[jn]*rate_eval.n_Ti38__Ti39
       )

    jac[jti38, jcr41] = (
       +rho*Y[jn]*rate_eval.n_Cr41__He4_Ti38
       )

    jac[jti39, jn] = (
       -rho*Y[jti39]*rate_eval.n_Ti39__p_Sc39
       -rho*Y[jti39]*rate_eval.n_Ti39__He4_Ca36
       -rho*Y[jti39]*rate_eval.n_Ti39__Ti40
       +rho*Y[jcr42]*rate_eval.n_Cr42__He4_Ti39
       +rho*Y[jv39]*rate_eval.n_V39__p_Ti39
       +rho*Y[jti38]*rate_eval.n_Ti38__Ti39
       )

    jac[jti39, jp] = (
       -rho*Y[jti39]*rate_eval.p_Ti39__V40
       +rho*Y[jsc38]*rate_eval.p_Sc38__Ti39
       )

    jac[jti39, jhe4] = (
       -rho*Y[jti39]*rate_eval.He4_Ti39__p_V42
       -rho*Y[jti39]*rate_eval.He4_Ti39__Cr43
       +rho*Y[jsc36]*rate_eval.He4_Sc36__p_Ti39
       +rho*Y[jca35]*rate_eval.He4_Ca35__Ti39
       )

    jac[jti39, jca35] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca35__Ti39
       )

    jac[jti39, jsc36] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc36__p_Ti39
       )

    jac[jti39, jsc38] = (
       +rho*Y[jp]*rate_eval.p_Sc38__Ti39
       )

    jac[jti39, jti38] = (
       +rho*Y[jn]*rate_eval.n_Ti38__Ti39
       )

    jac[jti39, jti39] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti39__p_V42
       -rho*Y[jn]*rate_eval.n_Ti39__p_Sc39
       -rho*Y[jn]*rate_eval.n_Ti39__He4_Ca36
       -rho*Y[jp]*rate_eval.p_Ti39__V40
       -rate_eval.Ti39__p_Ca38__weak__wc12
       -rate_eval.Ti39__Sc39__weak__wc17
       -rho*Y[jn]*rate_eval.n_Ti39__Ti40
       -rho*Y[jhe4]*rate_eval.He4_Ti39__Cr43
       )

    jac[jti39, jv39] = (
       +rho*Y[jn]*rate_eval.n_V39__p_Ti39
       +rate_eval.V39__Ti39__weak__bqa_pos_
       )

    jac[jti39, jcr42] = (
       +rho*Y[jn]*rate_eval.n_Cr42__He4_Ti39
       )

    jac[jti40, jn] = (
       -rho*Y[jti40]*rate_eval.n_Ti40__Ti41
       -rho*Y[jti40]*rate_eval.n_Ti40__p_Sc40
       -rho*Y[jti40]*rate_eval.n_Ti40__He4_Ca37
       +rho*Y[jv40]*rate_eval.n_V40__p_Ti40
       +rho*Y[jcr43]*rate_eval.n_Cr43__He4_Ti40
       +rho*Y[jti39]*rate_eval.n_Ti39__Ti40
       )

    jac[jti40, jp] = (
       -rho*Y[jti40]*rate_eval.p_Ti40__V41
       +rho*Y[jsc39]*rate_eval.p_Sc39__Ti40
       )

    jac[jti40, jhe4] = (
       -rho*Y[jti40]*rate_eval.He4_Ti40__p_V43
       -rho*Y[jti40]*rate_eval.He4_Ti40__Cr44
       +rho*Y[jsc37]*rate_eval.He4_Sc37__p_Ti40
       +rho*Y[jca36]*rate_eval.He4_Ca36__Ti40
       )

    jac[jti40, jca36] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca36__Ti40
       )

    jac[jti40, jsc37] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc37__p_Ti40
       )

    jac[jti40, jsc39] = (
       +rho*Y[jp]*rate_eval.p_Sc39__Ti40
       )

    jac[jti40, jti39] = (
       +rho*Y[jn]*rate_eval.n_Ti39__Ti40
       )

    jac[jti40, jti40] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti40__p_V43
       -rho*Y[jhe4]*rate_eval.He4_Ti40__Cr44
       -rho*Y[jp]*rate_eval.p_Ti40__V41
       -rho*Y[jn]*rate_eval.n_Ti40__Ti41
       -rho*Y[jn]*rate_eval.n_Ti40__p_Sc40
       -rate_eval.Ti40__p_Ca39__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ti40__He4_Ca37
       )

    jac[jti40, jv40] = (
       +rho*Y[jn]*rate_eval.n_V40__p_Ti40
       +rate_eval.V40__Ti40__weak__bqa_pos_
       )

    jac[jti40, jcr43] = (
       +rho*Y[jn]*rate_eval.n_Cr43__He4_Ti40
       )

    jac[jti41, jn] = (
       -rho*Y[jti41]*rate_eval.n_Ti41__He4_Ca38
       -rho*Y[jti41]*rate_eval.n_Ti41__p_Sc41
       -rho*Y[jti41]*rate_eval.n_Ti41__Ti42
       +rho*Y[jcr44]*rate_eval.n_Cr44__He4_Ti41
       +rho*Y[jti40]*rate_eval.n_Ti40__Ti41
       +rho*Y[jv41]*rate_eval.n_V41__p_Ti41
       )

    jac[jti41, jp] = (
       -rho*Y[jti41]*rate_eval.p_Ti41__V42
       +rho*Y[jsc40]*rate_eval.p_Sc40__Ti41
       )

    jac[jti41, jhe4] = (
       -rho*Y[jti41]*rate_eval.He4_Ti41__Cr45
       -rho*Y[jti41]*rate_eval.He4_Ti41__p_V44
       +rho*Y[jsc38]*rate_eval.He4_Sc38__p_Ti41
       +rho*Y[jca37]*rate_eval.He4_Ca37__Ti41
       )

    jac[jti41, jca37] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca37__Ti41
       )

    jac[jti41, jsc38] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc38__p_Ti41
       )

    jac[jti41, jsc40] = (
       +rho*Y[jp]*rate_eval.p_Sc40__Ti41
       )

    jac[jti41, jti40] = (
       +rho*Y[jn]*rate_eval.n_Ti40__Ti41
       )

    jac[jti41, jti41] = (
       -rho*Y[jn]*rate_eval.n_Ti41__He4_Ca38
       -rho*Y[jn]*rate_eval.n_Ti41__p_Sc41
       -rho*Y[jhe4]*rate_eval.He4_Ti41__Cr45
       -rho*Y[jp]*rate_eval.p_Ti41__V42
       -rho*Y[jn]*rate_eval.n_Ti41__Ti42
       -rate_eval.Ti41__p_Ca40__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ti41__p_V44
       -rate_eval.Ti41__Sc41__weak__wc17
       )

    jac[jti41, jv41] = (
       +rho*Y[jn]*rate_eval.n_V41__p_Ti41
       +rate_eval.V41__Ti41__weak__bqa_pos_
       )

    jac[jti41, jcr42] = (
       +rate_eval.Cr42__p_Ti41__weak__wc12
       )

    jac[jti41, jcr44] = (
       +rho*Y[jn]*rate_eval.n_Cr44__He4_Ti41
       )

    jac[jti42, jn] = (
       -rho*Y[jti42]*rate_eval.n_Ti42__p_Sc42
       -rho*Y[jti42]*rate_eval.n_Ti42__He4_Ca39
       -rho*Y[jti42]*rate_eval.n_Ti42__Ti43
       +rho*Y[jcr45]*rate_eval.n_Cr45__He4_Ti42
       +rho*Y[jti41]*rate_eval.n_Ti41__Ti42
       +rho*Y[jv42]*rate_eval.n_V42__p_Ti42
       )

    jac[jti42, jp] = (
       -rho*Y[jti42]*rate_eval.p_Ti42__V43
       +rho*Y[jsc41]*rate_eval.p_Sc41__Ti42
       )

    jac[jti42, jhe4] = (
       -rho*Y[jti42]*rate_eval.He4_Ti42__p_V45
       -rho*Y[jti42]*rate_eval.He4_Ti42__Cr46
       +rho*Y[jsc39]*rate_eval.He4_Sc39__p_Ti42
       +rho*Y[jca38]*rate_eval.He4_Ca38__Ti42
       )

    jac[jti42, jca38] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca38__Ti42
       )

    jac[jti42, jsc39] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc39__p_Ti42
       )

    jac[jti42, jsc41] = (
       +rho*Y[jp]*rate_eval.p_Sc41__Ti42
       )

    jac[jti42, jti41] = (
       +rho*Y[jn]*rate_eval.n_Ti41__Ti42
       )

    jac[jti42, jti42] = (
       -rho*Y[jn]*rate_eval.n_Ti42__p_Sc42
       -rho*Y[jhe4]*rate_eval.He4_Ti42__p_V45
       -rho*Y[jn]*rate_eval.n_Ti42__He4_Ca39
       -rho*Y[jp]*rate_eval.p_Ti42__V43
       -rho*Y[jhe4]*rate_eval.He4_Ti42__Cr46
       -rho*Y[jn]*rate_eval.n_Ti42__Ti43
       -rate_eval.Ti42__Sc42__weak__wc12
       )

    jac[jti42, jv42] = (
       +rho*Y[jn]*rate_eval.n_V42__p_Ti42
       +rate_eval.V42__Ti42__weak__mo97
       )

    jac[jti42, jcr43] = (
       +rate_eval.Cr43__p_Ti42__weak__wc17
       )

    jac[jti42, jcr45] = (
       +rho*Y[jn]*rate_eval.n_Cr45__He4_Ti42
       )

    jac[jti42, jfe45] = (
       +rate_eval.Fe45__p_p_p_Ti42__weak__wc12
       )

    jac[jti43, jn] = (
       -rho*Y[jti43]*rate_eval.n_Ti43__He4_Ca40
       -rho*Y[jti43]*rate_eval.n_Ti43__Ti44
       -rho*Y[jti43]*rate_eval.n_Ti43__p_Sc43
       +rho*Y[jcr46]*rate_eval.n_Cr46__He4_Ti43
       +rho*Y[jv43]*rate_eval.n_V43__p_Ti43
       +rho*Y[jti42]*rate_eval.n_Ti42__Ti43
       )

    jac[jti43, jp] = (
       -rho*Y[jti43]*rate_eval.p_Ti43__V44
       +rho*Y[jsc42]*rate_eval.p_Sc42__Ti43
       )

    jac[jti43, jhe4] = (
       -rho*Y[jti43]*rate_eval.He4_Ti43__p_V46
       -rho*Y[jti43]*rate_eval.He4_Ti43__Cr47
       +rho*Y[jsc40]*rate_eval.He4_Sc40__p_Ti43
       +rho*Y[jca39]*rate_eval.He4_Ca39__Ti43
       )

    jac[jti43, jca39] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca39__Ti43
       )

    jac[jti43, jsc40] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc40__p_Ti43
       )

    jac[jti43, jsc42] = (
       +rho*Y[jp]*rate_eval.p_Sc42__Ti43
       )

    jac[jti43, jti42] = (
       +rho*Y[jn]*rate_eval.n_Ti42__Ti43
       )

    jac[jti43, jti43] = (
       -rate_eval.Ti43__Sc43__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ti43__p_V46
       -rho*Y[jn]*rate_eval.n_Ti43__He4_Ca40
       -rho*Y[jp]*rate_eval.p_Ti43__V44
       -rho*Y[jhe4]*rate_eval.He4_Ti43__Cr47
       -rho*Y[jn]*rate_eval.n_Ti43__Ti44
       -rho*Y[jn]*rate_eval.n_Ti43__p_Sc43
       )

    jac[jti43, jv43] = (
       +rho*Y[jn]*rate_eval.n_V43__p_Ti43
       +rate_eval.V43__Ti43__weak__wc12
       )

    jac[jti43, jcr44] = (
       +rate_eval.Cr44__p_Ti43__weak__wc12
       )

    jac[jti43, jcr46] = (
       +rho*Y[jn]*rate_eval.n_Cr46__He4_Ti43
       )

    jac[jti44, jn] = (
       -rho*Y[jti44]*rate_eval.n_Ti44__p_Sc44
       -rho*Y[jti44]*rate_eval.n_Ti44__Ti45
       -rho*Y[jti44]*rate_eval.n_Ti44__He4_Ca41
       +rho*Y[jv44]*rate_eval.n_V44__p_Ti44
       +rho*Y[jcr47]*rate_eval.n_Cr47__He4_Ti44
       +rho*Y[jti43]*rate_eval.n_Ti43__Ti44
       )

    jac[jti44, jp] = (
       -rho*Y[jti44]*rate_eval.p_Ti44__V45
       +rho*Y[jsc43]*rate_eval.p_Sc43__Ti44
       )

    jac[jti44, jhe4] = (
       -rho*Y[jti44]*rate_eval.He4_Ti44__p_V47
       -rho*Y[jti44]*rate_eval.He4_Ti44__Cr48
       +rho*Y[jca40]*rate_eval.He4_Ca40__Ti44
       +rho*Y[jsc41]*rate_eval.He4_Sc41__p_Ti44
       )

    jac[jti44, jca40] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca40__Ti44
       )

    jac[jti44, jsc41] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc41__p_Ti44
       )

    jac[jti44, jsc43] = (
       +rho*Y[jp]*rate_eval.p_Sc43__Ti44
       )

    jac[jti44, jti43] = (
       +rho*Y[jn]*rate_eval.n_Ti43__Ti44
       )

    jac[jti44, jti44] = (
       -rho*Y[jn]*rate_eval.n_Ti44__p_Sc44
       -rho*Y[jhe4]*rate_eval.He4_Ti44__p_V47
       -rho*Y[jhe4]*rate_eval.He4_Ti44__Cr48
       -rho*Y[jp]*rate_eval.p_Ti44__V45
       -rho*Y[jn]*rate_eval.n_Ti44__Ti45
       -rate_eval.Ti44__Sc44__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ti44__He4_Ca41
       )

    jac[jti44, jv44] = (
       +rho*Y[jn]*rate_eval.n_V44__p_Ti44
       +rate_eval.V44__Ti44__weak__wc12
       )

    jac[jti44, jcr45] = (
       +rate_eval.Cr45__p_Ti44__weak__wc12
       )

    jac[jti44, jcr47] = (
       +rho*Y[jn]*rate_eval.n_Cr47__He4_Ti44
       )

    jac[jti45, jn] = (
       -rho*Y[jti45]*rate_eval.n_Ti45__p_Sc45
       -rho*Y[jti45]*rate_eval.n_Ti45__He4_Ca42
       -rho*Y[jti45]*rate_eval.n_Ti45__Ti46
       +rho*Y[jti44]*rate_eval.n_Ti44__Ti45
       +rho*Y[jv45]*rate_eval.n_V45__p_Ti45
       +rho*Y[jcr48]*rate_eval.n_Cr48__He4_Ti45
       )

    jac[jti45, jp] = (
       -rho*Y[jti45]*rate_eval.p_Ti45__V46
       +rho*Y[jsc44]*rate_eval.p_Sc44__Ti45
       )

    jac[jti45, jhe4] = (
       -rho*Y[jti45]*rate_eval.He4_Ti45__p_V48
       -rho*Y[jti45]*rate_eval.He4_Ti45__Cr49
       +rho*Y[jsc42]*rate_eval.He4_Sc42__p_Ti45
       +rho*Y[jca41]*rate_eval.He4_Ca41__Ti45
       )

    jac[jti45, jca41] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca41__Ti45
       )

    jac[jti45, jsc42] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc42__p_Ti45
       )

    jac[jti45, jsc44] = (
       +rho*Y[jp]*rate_eval.p_Sc44__Ti45
       )

    jac[jti45, jti44] = (
       +rho*Y[jn]*rate_eval.n_Ti44__Ti45
       )

    jac[jti45, jti45] = (
       -rho*Y[jn]*rate_eval.n_Ti45__p_Sc45
       -rho*Y[jhe4]*rate_eval.He4_Ti45__p_V48
       -rho*Y[jn]*rate_eval.n_Ti45__He4_Ca42
       -rho*Y[jhe4]*rate_eval.He4_Ti45__Cr49
       -rho*Y[jn]*rate_eval.n_Ti45__Ti46
       -rate_eval.Ti45__Sc45__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ti45__V46
       )

    jac[jti45, jv45] = (
       +rate_eval.V45__Ti45__weak__wc12
       +rho*Y[jn]*rate_eval.n_V45__p_Ti45
       )

    jac[jti45, jcr48] = (
       +rho*Y[jn]*rate_eval.n_Cr48__He4_Ti45
       )

    jac[jti46, jn] = (
       -rho*Y[jti46]*rate_eval.n_Ti46__Ti47
       +rho*Y[jv46]*rate_eval.n_V46__p_Ti46
       +rho*Y[jti45]*rate_eval.n_Ti45__Ti46
       +rho*Y[jcr49]*rate_eval.n_Cr49__He4_Ti46
       )

    jac[jti46, jp] = (
       -rho*Y[jti46]*rate_eval.p_Ti46__V47
       +rho*Y[jv49]*rate_eval.p_V49__He4_Ti46
       +rho*Y[jsc45]*rate_eval.p_Sc45__Ti46
       +rho*Y[jsc46]*rate_eval.p_Sc46__n_Ti46
       )

    jac[jti46, jhe4] = (
       -rho*Y[jti46]*rate_eval.He4_Ti46__Cr50
       +rho*Y[jsc43]*rate_eval.He4_Sc43__p_Ti46
       +rho*Y[jca43]*rate_eval.He4_Ca43__n_Ti46
       +rho*Y[jca42]*rate_eval.He4_Ca42__Ti46
       )

    jac[jti46, jca42] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca42__Ti46
       )

    jac[jti46, jca43] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca43__n_Ti46
       )

    jac[jti46, jsc43] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc43__p_Ti46
       )

    jac[jti46, jsc45] = (
       +rho*Y[jp]*rate_eval.p_Sc45__Ti46
       )

    jac[jti46, jsc46] = (
       +rho*Y[jp]*rate_eval.p_Sc46__n_Ti46
       +rate_eval.Sc46__Ti46__weak__wc12
       )

    jac[jti46, jti45] = (
       +rho*Y[jn]*rate_eval.n_Ti45__Ti46
       )

    jac[jti46, jti46] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti46__Cr50
       -rho*Y[jn]*rate_eval.n_Ti46__Ti47
       -rho*Y[jp]*rate_eval.p_Ti46__V47
       )

    jac[jti46, jv46] = (
       +rho*Y[jn]*rate_eval.n_V46__p_Ti46
       +rate_eval.V46__Ti46__weak__wc12
       )

    jac[jti46, jv49] = (
       +rho*Y[jp]*rate_eval.p_V49__He4_Ti46
       )

    jac[jti46, jcr49] = (
       +rho*Y[jn]*rate_eval.n_Cr49__He4_Ti46
       )

    jac[jti47, jn] = (
       -rho*Y[jti47]*rate_eval.n_Ti47__He4_Ca44
       -rho*Y[jti47]*rate_eval.n_Ti47__Ti48
       -rho*Y[jti47]*rate_eval.n_Ti47__p_Sc47
       +rho*Y[jcr50]*rate_eval.n_Cr50__He4_Ti47
       +rho*Y[jti46]*rate_eval.n_Ti46__Ti47
       +rho*Y[jv47]*rate_eval.n_V47__p_Ti47
       )

    jac[jti47, jp] = (
       -rho*Y[jti47]*rate_eval.p_Ti47__V48
       +rho*Y[jv50]*rate_eval.p_V50__He4_Ti47
       +rho*Y[jsc46]*rate_eval.p_Sc46__Ti47
       )

    jac[jti47, jhe4] = (
       -rho*Y[jti47]*rate_eval.He4_Ti47__Cr51
       +rho*Y[jca43]*rate_eval.He4_Ca43__Ti47
       +rho*Y[jsc44]*rate_eval.He4_Sc44__p_Ti47
       )

    jac[jti47, jca43] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca43__Ti47
       )

    jac[jti47, jsc44] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc44__p_Ti47
       )

    jac[jti47, jsc46] = (
       +rho*Y[jp]*rate_eval.p_Sc46__Ti47
       )

    jac[jti47, jsc47] = (
       +rate_eval.Sc47__Ti47__weak__wc12
       )

    jac[jti47, jti46] = (
       +rho*Y[jn]*rate_eval.n_Ti46__Ti47
       )

    jac[jti47, jti47] = (
       -rho*Y[jn]*rate_eval.n_Ti47__He4_Ca44
       -rho*Y[jp]*rate_eval.p_Ti47__V48
       -rho*Y[jn]*rate_eval.n_Ti47__Ti48
       -rho*Y[jhe4]*rate_eval.He4_Ti47__Cr51
       -rho*Y[jn]*rate_eval.n_Ti47__p_Sc47
       )

    jac[jti47, jv47] = (
       +rho*Y[jn]*rate_eval.n_V47__p_Ti47
       +rate_eval.V47__Ti47__weak__wc12
       )

    jac[jti47, jv50] = (
       +rho*Y[jp]*rate_eval.p_V50__He4_Ti47
       )

    jac[jti47, jcr50] = (
       +rho*Y[jn]*rate_eval.n_Cr50__He4_Ti47
       )

    jac[jti48, jn] = (
       -rho*Y[jti48]*rate_eval.n_Ti48__Ti49
       +rho*Y[jcr51]*rate_eval.n_Cr51__He4_Ti48
       +rho*Y[jv48]*rate_eval.n_V48__p_Ti48
       +rho*Y[jti47]*rate_eval.n_Ti47__Ti48
       )

    jac[jti48, jp] = (
       -rho*Y[jti48]*rate_eval.p_Ti48__V49
       +rho*Y[jv51]*rate_eval.p_V51__He4_Ti48
       +rho*Y[jsc48]*rate_eval.p_Sc48__n_Ti48
       +rho*Y[jsc47]*rate_eval.p_Sc47__Ti48
       )

    jac[jti48, jhe4] = (
       -rho*Y[jti48]*rate_eval.He4_Ti48__Cr52
       +rho*Y[jsc45]*rate_eval.He4_Sc45__p_Ti48
       +rho*Y[jca44]*rate_eval.He4_Ca44__Ti48
       +rho*Y[jca45]*rate_eval.He4_Ca45__n_Ti48
       )

    jac[jti48, jca44] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca44__Ti48
       )

    jac[jti48, jca45] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca45__n_Ti48
       )

    jac[jti48, jsc45] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc45__p_Ti48
       )

    jac[jti48, jsc47] = (
       +rho*Y[jp]*rate_eval.p_Sc47__Ti48
       )

    jac[jti48, jsc48] = (
       +rho*Y[jp]*rate_eval.p_Sc48__n_Ti48
       +rate_eval.Sc48__Ti48__weak__wc12
       )

    jac[jti48, jti47] = (
       +rho*Y[jn]*rate_eval.n_Ti47__Ti48
       )

    jac[jti48, jti48] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti48__Cr52
       -rho*Y[jp]*rate_eval.p_Ti48__V49
       -rho*Y[jn]*rate_eval.n_Ti48__Ti49
       )

    jac[jti48, jv48] = (
       +rho*Y[jn]*rate_eval.n_V48__p_Ti48
       +rate_eval.V48__Ti48__weak__wc12
       )

    jac[jti48, jv51] = (
       +rho*Y[jp]*rate_eval.p_V51__He4_Ti48
       )

    jac[jti48, jcr51] = (
       +rho*Y[jn]*rate_eval.n_Cr51__He4_Ti48
       )

    jac[jti49, jn] = (
       -rho*Y[jti49]*rate_eval.n_Ti49__He4_Ca46
       -rho*Y[jti49]*rate_eval.n_Ti49__Ti50
       +rho*Y[jv49]*rate_eval.n_V49__p_Ti49
       +rho*Y[jti48]*rate_eval.n_Ti48__Ti49
       )

    jac[jti49, jp] = (
       -rho*Y[jti49]*rate_eval.p_Ti49__V50
       +rho*Y[jv52]*rate_eval.p_V52__He4_Ti49
       +rho*Y[jsc49]*rate_eval.p_Sc49__n_Ti49
       +rho*Y[jsc48]*rate_eval.p_Sc48__Ti49
       )

    jac[jti49, jhe4] = (
       -rho*Y[jti49]*rate_eval.He4_Ti49__n_Cr52
       -rho*Y[jti49]*rate_eval.He4_Ti49__Cr53
       +rho*Y[jsc46]*rate_eval.He4_Sc46__p_Ti49
       +rho*Y[jca45]*rate_eval.He4_Ca45__Ti49
       )

    jac[jti49, jca45] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca45__Ti49
       )

    jac[jti49, jsc46] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc46__p_Ti49
       )

    jac[jti49, jsc48] = (
       +rho*Y[jp]*rate_eval.p_Sc48__Ti49
       )

    jac[jti49, jsc49] = (
       +rho*Y[jp]*rate_eval.p_Sc49__n_Ti49
       +rate_eval.Sc49__Ti49__weak__wc12
       )

    jac[jti49, jti48] = (
       +rho*Y[jn]*rate_eval.n_Ti48__Ti49
       )

    jac[jti49, jti49] = (
       -rho*Y[jn]*rate_eval.n_Ti49__He4_Ca46
       -rho*Y[jp]*rate_eval.p_Ti49__V50
       -rho*Y[jn]*rate_eval.n_Ti49__Ti50
       -rho*Y[jhe4]*rate_eval.He4_Ti49__n_Cr52
       -rho*Y[jhe4]*rate_eval.He4_Ti49__Cr53
       )

    jac[jti49, jv49] = (
       +rho*Y[jn]*rate_eval.n_V49__p_Ti49
       +rate_eval.V49__Ti49__weak__wc12
       )

    jac[jti49, jv52] = (
       +rho*Y[jp]*rate_eval.p_V52__He4_Ti49
       )

    jac[jti50, jn] = (
       -rho*Y[jti50]*rate_eval.n_Ti50__Ti51
       +rho*Y[jcr53]*rate_eval.n_Cr53__He4_Ti50
       +rho*Y[jv50]*rate_eval.n_V50__p_Ti50
       +rho*Y[jti49]*rate_eval.n_Ti49__Ti50
       )

    jac[jti50, jp] = (
       -rho*Y[jti50]*rate_eval.p_Ti50__V51
       +rho*Y[jsc50]*rate_eval.p_Sc50__n_Ti50
       +rho*Y[jv53]*rate_eval.p_V53__He4_Ti50
       +rho*Y[jsc49]*rate_eval.p_Sc49__Ti50
       )

    jac[jti50, jhe4] = (
       -rho*Y[jti50]*rate_eval.He4_Ti50__Cr54
       +rho*Y[jsc47]*rate_eval.He4_Sc47__p_Ti50
       +rho*Y[jca47]*rate_eval.He4_Ca47__n_Ti50
       +rho*Y[jca46]*rate_eval.He4_Ca46__Ti50
       )

    jac[jti50, jca46] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca46__Ti50
       )

    jac[jti50, jca47] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca47__n_Ti50
       )

    jac[jti50, jsc47] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc47__p_Ti50
       )

    jac[jti50, jsc49] = (
       +rho*Y[jp]*rate_eval.p_Sc49__Ti50
       )

    jac[jti50, jsc50] = (
       +rho*Y[jp]*rate_eval.p_Sc50__n_Ti50
       +rate_eval.Sc50__Ti50__weak__wc12
       )

    jac[jti50, jti49] = (
       +rho*Y[jn]*rate_eval.n_Ti49__Ti50
       )

    jac[jti50, jti50] = (
       -rho*Y[jp]*rate_eval.p_Ti50__V51
       -rho*Y[jhe4]*rate_eval.He4_Ti50__Cr54
       -rho*Y[jn]*rate_eval.n_Ti50__Ti51
       )

    jac[jti50, jv50] = (
       +rho*Y[jn]*rate_eval.n_V50__p_Ti50
       +rate_eval.V50__Ti50__weak__mo03
       )

    jac[jti50, jv53] = (
       +rho*Y[jp]*rate_eval.p_V53__He4_Ti50
       )

    jac[jti50, jcr53] = (
       +rho*Y[jn]*rate_eval.n_Cr53__He4_Ti50
       )

    jac[jti51, jn] = (
       -rho*Y[jti51]*rate_eval.n_Ti51__He4_Ca48
       -rho*Y[jti51]*rate_eval.n_Ti51__Ti52
       +rho*Y[jti50]*rate_eval.n_Ti50__Ti51
       )

    jac[jti51, jp] = (
       -rho*Y[jti51]*rate_eval.p_Ti51__n_V51
       -rho*Y[jti51]*rate_eval.p_Ti51__V52
       +rho*Y[jsc50]*rate_eval.p_Sc50__Ti51
       +rho*Y[jsc51]*rate_eval.p_Sc51__n_Ti51
       +rho*Y[jv54]*rate_eval.p_V54__He4_Ti51
       )

    jac[jti51, jhe4] = (
       -rho*Y[jti51]*rate_eval.He4_Ti51__n_Cr54
       -rho*Y[jti51]*rate_eval.He4_Ti51__Cr55
       +rho*Y[jca47]*rate_eval.He4_Ca47__Ti51
       +rho*Y[jsc48]*rate_eval.He4_Sc48__p_Ti51
       )

    jac[jti51, jca47] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca47__Ti51
       )

    jac[jti51, jsc48] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc48__p_Ti51
       )

    jac[jti51, jsc50] = (
       +rho*Y[jp]*rate_eval.p_Sc50__Ti51
       )

    jac[jti51, jsc51] = (
       +rho*Y[jp]*rate_eval.p_Sc51__n_Ti51
       +rate_eval.Sc51__Ti51__weak__wc12
       )

    jac[jti51, jti50] = (
       +rho*Y[jn]*rate_eval.n_Ti50__Ti51
       )

    jac[jti51, jti51] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti51__n_Cr54
       -rho*Y[jp]*rate_eval.p_Ti51__n_V51
       -rho*Y[jn]*rate_eval.n_Ti51__He4_Ca48
       -rho*Y[jhe4]*rate_eval.He4_Ti51__Cr55
       -rho*Y[jp]*rate_eval.p_Ti51__V52
       -rate_eval.Ti51__V51__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ti51__Ti52
       )

    jac[jti51, jv54] = (
       +rho*Y[jp]*rate_eval.p_V54__He4_Ti51
       )

    jac[jti52, jn] = (
       -rho*Y[jti52]*rate_eval.n_Ti52__Ti53
       +rho*Y[jcr55]*rate_eval.n_Cr55__He4_Ti52
       +rho*Y[jti51]*rate_eval.n_Ti51__Ti52
       )

    jac[jti52, jp] = (
       -rho*Y[jti52]*rate_eval.p_Ti52__He4_Sc49
       -rho*Y[jti52]*rate_eval.p_Ti52__n_V52
       -rho*Y[jti52]*rate_eval.p_Ti52__V53
       +rho*Y[jsc52]*rate_eval.p_Sc52__n_Ti52
       +rho*Y[jsc51]*rate_eval.p_Sc51__Ti52
       +rho*Y[jv55]*rate_eval.p_V55__He4_Ti52
       )

    jac[jti52, jhe4] = (
       -rho*Y[jti52]*rate_eval.He4_Ti52__Cr56
       +rho*Y[jca48]*rate_eval.He4_Ca48__Ti52
       +rho*Y[jca49]*rate_eval.He4_Ca49__n_Ti52
       )

    jac[jti52, jca48] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca48__Ti52
       )

    jac[jti52, jca49] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca49__n_Ti52
       )

    jac[jti52, jsc51] = (
       +rho*Y[jp]*rate_eval.p_Sc51__Ti52
       )

    jac[jti52, jsc52] = (
       +rho*Y[jp]*rate_eval.p_Sc52__n_Ti52
       +rate_eval.Sc52__Ti52__weak__wc12
       )

    jac[jti52, jti51] = (
       +rho*Y[jn]*rate_eval.n_Ti51__Ti52
       )

    jac[jti52, jti52] = (
       -rho*Y[jp]*rate_eval.p_Ti52__He4_Sc49
       -rho*Y[jp]*rate_eval.p_Ti52__n_V52
       -rho*Y[jhe4]*rate_eval.He4_Ti52__Cr56
       -rho*Y[jp]*rate_eval.p_Ti52__V53
       -rho*Y[jn]*rate_eval.n_Ti52__Ti53
       -rate_eval.Ti52__V52__weak__wc12
       )

    jac[jti52, jv55] = (
       +rho*Y[jp]*rate_eval.p_V55__He4_Ti52
       )

    jac[jti52, jcr55] = (
       +rho*Y[jn]*rate_eval.n_Cr55__He4_Ti52
       )

    jac[jti53, jn] = (
       -rho*Y[jti53]*rate_eval.n_Ti53__Ti54
       +rho*Y[jti52]*rate_eval.n_Ti52__Ti53
       )

    jac[jti53, jp] = (
       -rho*Y[jti53]*rate_eval.p_Ti53__He4_Sc50
       -rho*Y[jti53]*rate_eval.p_Ti53__n_V53
       -rho*Y[jti53]*rate_eval.p_Ti53__V54
       +rho*Y[jsc52]*rate_eval.p_Sc52__Ti53
       +rho*Y[jsc53]*rate_eval.p_Sc53__n_Ti53
       +rho*Y[jv56]*rate_eval.p_V56__He4_Ti53
       )

    jac[jti53, jhe4] = (
       -rho*Y[jti53]*rate_eval.He4_Ti53__n_Cr56
       -rho*Y[jti53]*rate_eval.He4_Ti53__Cr57
       +rho*Y[jca50]*rate_eval.He4_Ca50__n_Ti53
       +rho*Y[jca49]*rate_eval.He4_Ca49__Ti53
       )

    jac[jti53, jca49] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca49__Ti53
       )

    jac[jti53, jca50] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca50__n_Ti53
       )

    jac[jti53, jsc52] = (
       +rho*Y[jp]*rate_eval.p_Sc52__Ti53
       )

    jac[jti53, jsc53] = (
       +rho*Y[jp]*rate_eval.p_Sc53__n_Ti53
       +rate_eval.Sc53__Ti53__weak__wc12
       )

    jac[jti53, jsc54] = (
       +rate_eval.Sc54__n_Ti53__weak__mp17
       )

    jac[jti53, jti52] = (
       +rho*Y[jn]*rate_eval.n_Ti52__Ti53
       )

    jac[jti53, jti53] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti53__n_Cr56
       -rho*Y[jp]*rate_eval.p_Ti53__He4_Sc50
       -rho*Y[jp]*rate_eval.p_Ti53__n_V53
       -rho*Y[jhe4]*rate_eval.He4_Ti53__Cr57
       -rho*Y[jp]*rate_eval.p_Ti53__V54
       -rho*Y[jn]*rate_eval.n_Ti53__Ti54
       -rate_eval.Ti53__V53__weak__wc12
       )

    jac[jti53, jv56] = (
       +rho*Y[jp]*rate_eval.p_V56__He4_Ti53
       )

    jac[jti54, jn] = (
       -rho*Y[jti54]*rate_eval.n_Ti54__Ti55
       +rho*Y[jti53]*rate_eval.n_Ti53__Ti54
       )

    jac[jti54, jp] = (
       -rho*Y[jti54]*rate_eval.p_Ti54__He4_Sc51
       -rho*Y[jti54]*rate_eval.p_Ti54__n_V54
       -rho*Y[jti54]*rate_eval.p_Ti54__V55
       +rho*Y[jv57]*rate_eval.p_V57__He4_Ti54
       +rho*Y[jsc54]*rate_eval.p_Sc54__n_Ti54
       +rho*Y[jsc53]*rate_eval.p_Sc53__Ti54
       )

    jac[jti54, jhe4] = (
       -rho*Y[jti54]*rate_eval.He4_Ti54__n_Cr57
       -rho*Y[jti54]*rate_eval.He4_Ti54__Cr58
       +rho*Y[jca51]*rate_eval.He4_Ca51__n_Ti54
       +rho*Y[jca50]*rate_eval.He4_Ca50__Ti54
       )

    jac[jti54, jca50] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca50__Ti54
       )

    jac[jti54, jca51] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca51__n_Ti54
       )

    jac[jti54, jsc53] = (
       +rho*Y[jp]*rate_eval.p_Sc53__Ti54
       )

    jac[jti54, jsc54] = (
       +rho*Y[jp]*rate_eval.p_Sc54__n_Ti54
       +rate_eval.Sc54__Ti54__weak__wc17
       )

    jac[jti54, jsc55] = (
       +rate_eval.Sc55__n_Ti54__weak__wc12
       )

    jac[jti54, jsc57] = (
       +rate_eval.Sc57__n_n_n_Ti54__weak__mo03
       )

    jac[jti54, jti53] = (
       +rho*Y[jn]*rate_eval.n_Ti53__Ti54
       )

    jac[jti54, jti54] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti54__n_Cr57
       -rho*Y[jp]*rate_eval.p_Ti54__He4_Sc51
       -rho*Y[jp]*rate_eval.p_Ti54__n_V54
       -rho*Y[jn]*rate_eval.n_Ti54__Ti55
       -rho*Y[jhe4]*rate_eval.He4_Ti54__Cr58
       -rho*Y[jp]*rate_eval.p_Ti54__V55
       -rate_eval.Ti54__V54__weak__wc12
       )

    jac[jti54, jv57] = (
       +rho*Y[jp]*rate_eval.p_V57__He4_Ti54
       )

    jac[jti55, jn] = (
       -rho*Y[jti55]*rate_eval.n_Ti55__Ti56
       +rho*Y[jti54]*rate_eval.n_Ti54__Ti55
       )

    jac[jti55, jp] = (
       -rho*Y[jti55]*rate_eval.p_Ti55__n_V55
       -rho*Y[jti55]*rate_eval.p_Ti55__V56
       -rho*Y[jti55]*rate_eval.p_Ti55__He4_Sc52
       +rho*Y[jv58]*rate_eval.p_V58__He4_Ti55
       +rho*Y[jsc55]*rate_eval.p_Sc55__n_Ti55
       +rho*Y[jsc54]*rate_eval.p_Sc54__Ti55
       )

    jac[jti55, jhe4] = (
       -rho*Y[jti55]*rate_eval.He4_Ti55__n_Cr58
       -rho*Y[jti55]*rate_eval.He4_Ti55__Cr59
       +rho*Y[jca51]*rate_eval.He4_Ca51__Ti55
       +rho*Y[jca52]*rate_eval.He4_Ca52__n_Ti55
       )

    jac[jti55, jca51] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca51__Ti55
       )

    jac[jti55, jca52] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca52__n_Ti55
       )

    jac[jti55, jsc54] = (
       +rho*Y[jp]*rate_eval.p_Sc54__Ti55
       )

    jac[jti55, jsc55] = (
       +rho*Y[jp]*rate_eval.p_Sc55__n_Ti55
       +rate_eval.Sc55__Ti55__weak__wc12
       )

    jac[jti55, jsc56] = (
       +rate_eval.Sc56__n_Ti55__weak__mp17
       )

    jac[jti55, jsc58] = (
       +rate_eval.Sc58__n_n_n_Ti55__weak__mo03
       )

    jac[jti55, jti54] = (
       +rho*Y[jn]*rate_eval.n_Ti54__Ti55
       )

    jac[jti55, jti55] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti55__n_Cr58
       -rho*Y[jp]*rate_eval.p_Ti55__n_V55
       -rho*Y[jp]*rate_eval.p_Ti55__V56
       -rho*Y[jn]*rate_eval.n_Ti55__Ti56
       -rho*Y[jhe4]*rate_eval.He4_Ti55__Cr59
       -rate_eval.Ti55__V55__weak__wc12
       -rho*Y[jp]*rate_eval.p_Ti55__He4_Sc52
       )

    jac[jti55, jv58] = (
       +rho*Y[jp]*rate_eval.p_V58__He4_Ti55
       )

    jac[jti56, jn] = (
       -rho*Y[jti56]*rate_eval.n_Ti56__Ti57
       +rho*Y[jti55]*rate_eval.n_Ti55__Ti56
       )

    jac[jti56, jp] = (
       -rho*Y[jti56]*rate_eval.p_Ti56__He4_Sc53
       -rho*Y[jti56]*rate_eval.p_Ti56__V57
       -rho*Y[jti56]*rate_eval.p_Ti56__n_V56
       +rho*Y[jsc55]*rate_eval.p_Sc55__Ti56
       +rho*Y[jsc56]*rate_eval.p_Sc56__n_Ti56
       +rho*Y[jv59]*rate_eval.p_V59__He4_Ti56
       )

    jac[jti56, jhe4] = (
       -rho*Y[jti56]*rate_eval.He4_Ti56__Cr60
       -rho*Y[jti56]*rate_eval.He4_Ti56__n_Cr59
       +rho*Y[jca52]*rate_eval.He4_Ca52__Ti56
       +rho*Y[jca53]*rate_eval.He4_Ca53__n_Ti56
       )

    jac[jti56, jca52] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca52__Ti56
       )

    jac[jti56, jca53] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca53__n_Ti56
       )

    jac[jti56, jsc55] = (
       +rho*Y[jp]*rate_eval.p_Sc55__Ti56
       )

    jac[jti56, jsc56] = (
       +rate_eval.Sc56__Ti56__weak__wc17
       +rho*Y[jp]*rate_eval.p_Sc56__n_Ti56
       )

    jac[jti56, jsc57] = (
       +rate_eval.Sc57__n_Ti56__weak__mp17
       )

    jac[jti56, jsc58] = (
       +rate_eval.Sc58__n_n_Ti56__weak__mp17
       )

    jac[jti56, jsc59] = (
       +rate_eval.Sc59__n_n_n_Ti56__weak__mo03
       )

    jac[jti56, jti55] = (
       +rho*Y[jn]*rate_eval.n_Ti55__Ti56
       )

    jac[jti56, jti56] = (
       -rho*Y[jp]*rate_eval.p_Ti56__He4_Sc53
       -rho*Y[jp]*rate_eval.p_Ti56__V57
       -rho*Y[jhe4]*rate_eval.He4_Ti56__Cr60
       -rho*Y[jhe4]*rate_eval.He4_Ti56__n_Cr59
       -rate_eval.Ti56__V56__weak__wc12
       -rho*Y[jn]*rate_eval.n_Ti56__Ti57
       -rho*Y[jp]*rate_eval.p_Ti56__n_V56
       )

    jac[jti56, jv59] = (
       +rho*Y[jp]*rate_eval.p_V59__He4_Ti56
       )

    jac[jti57, jn] = (
       -rho*Y[jti57]*rate_eval.n_Ti57__Ti58
       +rho*Y[jti56]*rate_eval.n_Ti56__Ti57
       )

    jac[jti57, jp] = (
       -rho*Y[jti57]*rate_eval.p_Ti57__He4_Sc54
       -rho*Y[jti57]*rate_eval.p_Ti57__n_V57
       -rho*Y[jti57]*rate_eval.p_Ti57__V58
       +rho*Y[jv60]*rate_eval.p_V60__He4_Ti57
       +rho*Y[jsc57]*rate_eval.p_Sc57__n_Ti57
       +rho*Y[jsc56]*rate_eval.p_Sc56__Ti57
       )

    jac[jti57, jhe4] = (
       -rho*Y[jti57]*rate_eval.He4_Ti57__n_Cr60
       -rho*Y[jti57]*rate_eval.He4_Ti57__Cr61
       +rho*Y[jca53]*rate_eval.He4_Ca53__Ti57
       +rho*Y[jca54]*rate_eval.He4_Ca54__n_Ti57
       )

    jac[jti57, jca53] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca53__Ti57
       )

    jac[jti57, jca54] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca54__n_Ti57
       )

    jac[jti57, jsc56] = (
       +rho*Y[jp]*rate_eval.p_Sc56__Ti57
       )

    jac[jti57, jsc57] = (
       +rho*Y[jp]*rate_eval.p_Sc57__n_Ti57
       +rate_eval.Sc57__Ti57__weak__wc17
       )

    jac[jti57, jsc58] = (
       +rate_eval.Sc58__n_Ti57__weak__mp17
       )

    jac[jti57, jsc59] = (
       +rate_eval.Sc59__n_n_Ti57__weak__mp17
       )

    jac[jti57, jsc60] = (
       +rate_eval.Sc60__n_n_n_Ti57__weak__mo03
       )

    jac[jti57, jti56] = (
       +rho*Y[jn]*rate_eval.n_Ti56__Ti57
       )

    jac[jti57, jti57] = (
       -rho*Y[jp]*rate_eval.p_Ti57__He4_Sc54
       -rho*Y[jp]*rate_eval.p_Ti57__n_V57
       -rho*Y[jp]*rate_eval.p_Ti57__V58
       -rho*Y[jn]*rate_eval.n_Ti57__Ti58
       -rho*Y[jhe4]*rate_eval.He4_Ti57__n_Cr60
       -rate_eval.Ti57__V57__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Ti57__Cr61
       )

    jac[jti57, jv60] = (
       +rho*Y[jp]*rate_eval.p_V60__He4_Ti57
       )

    jac[jti58, jn] = (
       -rho*Y[jti58]*rate_eval.n_Ti58__Ti59
       +rho*Y[jti57]*rate_eval.n_Ti57__Ti58
       )

    jac[jti58, jp] = (
       -rho*Y[jti58]*rate_eval.p_Ti58__n_V58
       -rho*Y[jti58]*rate_eval.p_Ti58__V59
       -rho*Y[jti58]*rate_eval.p_Ti58__He4_Sc55
       +rho*Y[jsc58]*rate_eval.p_Sc58__n_Ti58
       +rho*Y[jv61]*rate_eval.p_V61__He4_Ti58
       +rho*Y[jsc57]*rate_eval.p_Sc57__Ti58
       )

    jac[jti58, jhe4] = (
       -rho*Y[jti58]*rate_eval.He4_Ti58__n_Cr61
       -rho*Y[jti58]*rate_eval.He4_Ti58__Cr62
       +rho*Y[jca54]*rate_eval.He4_Ca54__Ti58
       +rho*Y[jca55]*rate_eval.He4_Ca55__n_Ti58
       )

    jac[jti58, jca54] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca54__Ti58
       )

    jac[jti58, jca55] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca55__n_Ti58
       )

    jac[jti58, jsc57] = (
       +rho*Y[jp]*rate_eval.p_Sc57__Ti58
       )

    jac[jti58, jsc58] = (
       +rho*Y[jp]*rate_eval.p_Sc58__n_Ti58
       +rate_eval.Sc58__Ti58__weak__wc17
       )

    jac[jti58, jsc59] = (
       +rate_eval.Sc59__n_Ti58__weak__mp17
       )

    jac[jti58, jsc60] = (
       +rate_eval.Sc60__n_n_Ti58__weak__mp17
       )

    jac[jti58, jsc61] = (
       +rate_eval.Sc61__n_n_n_Ti58__weak__mo03
       )

    jac[jti58, jti57] = (
       +rho*Y[jn]*rate_eval.n_Ti57__Ti58
       )

    jac[jti58, jti58] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti58__n_Cr61
       -rho*Y[jp]*rate_eval.p_Ti58__n_V58
       -rho*Y[jn]*rate_eval.n_Ti58__Ti59
       -rho*Y[jp]*rate_eval.p_Ti58__V59
       -rate_eval.Ti58__V58__weak__wc12
       -rate_eval.Ti58__n_V57__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ti58__Cr62
       -rho*Y[jp]*rate_eval.p_Ti58__He4_Sc55
       )

    jac[jti58, jv61] = (
       +rho*Y[jp]*rate_eval.p_V61__He4_Ti58
       )

    jac[jti59, jn] = (
       -rho*Y[jti59]*rate_eval.n_Ti59__Ti60
       +rho*Y[jti58]*rate_eval.n_Ti58__Ti59
       )

    jac[jti59, jp] = (
       -rho*Y[jti59]*rate_eval.p_Ti59__n_V59
       -rho*Y[jti59]*rate_eval.p_Ti59__V60
       -rho*Y[jti59]*rate_eval.p_Ti59__He4_Sc56
       +rho*Y[jsc58]*rate_eval.p_Sc58__Ti59
       +rho*Y[jv62]*rate_eval.p_V62__He4_Ti59
       +rho*Y[jsc59]*rate_eval.p_Sc59__n_Ti59
       )

    jac[jti59, jhe4] = (
       -rho*Y[jti59]*rate_eval.He4_Ti59__n_Cr62
       -rho*Y[jti59]*rate_eval.He4_Ti59__Cr63
       +rho*Y[jca55]*rate_eval.He4_Ca55__Ti59
       +rho*Y[jca56]*rate_eval.He4_Ca56__n_Ti59
       )

    jac[jti59, jca55] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca55__Ti59
       )

    jac[jti59, jca56] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca56__n_Ti59
       )

    jac[jti59, jsc58] = (
       +rho*Y[jp]*rate_eval.p_Sc58__Ti59
       )

    jac[jti59, jsc59] = (
       +rate_eval.Sc59__Ti59__weak__mo03
       +rho*Y[jp]*rate_eval.p_Sc59__n_Ti59
       )

    jac[jti59, jsc60] = (
       +rate_eval.Sc60__n_Ti59__weak__mp17
       )

    jac[jti59, jsc61] = (
       +rate_eval.Sc61__n_n_Ti59__weak__mp17
       )

    jac[jti59, jsc62] = (
       +rate_eval.Sc62__n_n_n_Ti59__weak__mo03
       )

    jac[jti59, jti58] = (
       +rho*Y[jn]*rate_eval.n_Ti58__Ti59
       )

    jac[jti59, jti59] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti59__n_Cr62
       -rho*Y[jp]*rate_eval.p_Ti59__n_V59
       -rho*Y[jn]*rate_eval.n_Ti59__Ti60
       -rho*Y[jp]*rate_eval.p_Ti59__V60
       -rho*Y[jhe4]*rate_eval.He4_Ti59__Cr63
       -rho*Y[jp]*rate_eval.p_Ti59__He4_Sc56
       -rate_eval.Ti59__V59__weak__wc12
       )

    jac[jti59, jv62] = (
       +rho*Y[jp]*rate_eval.p_V62__He4_Ti59
       )

    jac[jti60, jn] = (
       -rho*Y[jti60]*rate_eval.n_Ti60__Ti61
       +rho*Y[jti59]*rate_eval.n_Ti59__Ti60
       )

    jac[jti60, jp] = (
       -rho*Y[jti60]*rate_eval.p_Ti60__n_V60
       -rho*Y[jti60]*rate_eval.p_Ti60__V61
       -rho*Y[jti60]*rate_eval.p_Ti60__He4_Sc57
       +rho*Y[jsc60]*rate_eval.p_Sc60__n_Ti60
       +rho*Y[jv63]*rate_eval.p_V63__He4_Ti60
       +rho*Y[jsc59]*rate_eval.p_Sc59__Ti60
       )

    jac[jti60, jhe4] = (
       -rho*Y[jti60]*rate_eval.He4_Ti60__n_Cr63
       -rho*Y[jti60]*rate_eval.He4_Ti60__Cr64
       +rho*Y[jca57]*rate_eval.He4_Ca57__n_Ti60
       +rho*Y[jca56]*rate_eval.He4_Ca56__Ti60
       )

    jac[jti60, jca56] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca56__Ti60
       )

    jac[jti60, jca57] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca57__n_Ti60
       )

    jac[jti60, jsc59] = (
       +rho*Y[jp]*rate_eval.p_Sc59__Ti60
       )

    jac[jti60, jsc60] = (
       +rho*Y[jp]*rate_eval.p_Sc60__n_Ti60
       +rate_eval.Sc60__Ti60__weak__mo03
       )

    jac[jti60, jsc61] = (
       +rate_eval.Sc61__n_Ti60__weak__mp17
       )

    jac[jti60, jsc62] = (
       +rate_eval.Sc62__n_n_Ti60__weak__mp17
       )

    jac[jti60, jsc63] = (
       +rate_eval.Sc63__n_n_n_Ti60__weak__mo03
       )

    jac[jti60, jti59] = (
       +rho*Y[jn]*rate_eval.n_Ti59__Ti60
       )

    jac[jti60, jti60] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti60__n_Cr63
       -rho*Y[jp]*rate_eval.p_Ti60__n_V60
       -rho*Y[jhe4]*rate_eval.He4_Ti60__Cr64
       -rho*Y[jp]*rate_eval.p_Ti60__V61
       -rho*Y[jn]*rate_eval.n_Ti60__Ti61
       -rate_eval.Ti60__n_V59__weak__mp17
       -rho*Y[jp]*rate_eval.p_Ti60__He4_Sc57
       -rate_eval.Ti60__V60__weak__wc17
       )

    jac[jti60, jv63] = (
       +rho*Y[jp]*rate_eval.p_V63__He4_Ti60
       )

    jac[jti61, jn] = (
       -rho*Y[jti61]*rate_eval.n_Ti61__Ti62
       +rho*Y[jti60]*rate_eval.n_Ti60__Ti61
       )

    jac[jti61, jp] = (
       -rho*Y[jti61]*rate_eval.p_Ti61__n_V61
       -rho*Y[jti61]*rate_eval.p_Ti61__V62
       -rho*Y[jti61]*rate_eval.p_Ti61__He4_Sc58
       +rho*Y[jv64]*rate_eval.p_V64__He4_Ti61
       +rho*Y[jsc61]*rate_eval.p_Sc61__n_Ti61
       +rho*Y[jsc60]*rate_eval.p_Sc60__Ti61
       )

    jac[jti61, jhe4] = (
       -rho*Y[jti61]*rate_eval.He4_Ti61__n_Cr64
       -rho*Y[jti61]*rate_eval.He4_Ti61__Cr65
       +rho*Y[jca58]*rate_eval.He4_Ca58__n_Ti61
       +rho*Y[jca57]*rate_eval.He4_Ca57__Ti61
       )

    jac[jti61, jca57] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca57__Ti61
       )

    jac[jti61, jca58] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca58__n_Ti61
       )

    jac[jti61, jsc60] = (
       +rho*Y[jp]*rate_eval.p_Sc60__Ti61
       )

    jac[jti61, jsc61] = (
       +rho*Y[jp]*rate_eval.p_Sc61__n_Ti61
       +rate_eval.Sc61__Ti61__weak__mo03
       )

    jac[jti61, jsc62] = (
       +rate_eval.Sc62__n_Ti61__weak__mp17
       )

    jac[jti61, jsc63] = (
       +rate_eval.Sc63__n_n_Ti61__weak__mp17
       )

    jac[jti61, jti60] = (
       +rho*Y[jn]*rate_eval.n_Ti60__Ti61
       )

    jac[jti61, jti61] = (
       -rho*Y[jp]*rate_eval.p_Ti61__n_V61
       -rho*Y[jhe4]*rate_eval.He4_Ti61__n_Cr64
       -rho*Y[jhe4]*rate_eval.He4_Ti61__Cr65
       -rho*Y[jp]*rate_eval.p_Ti61__V62
       -rate_eval.Ti61__V61__weak__wc17
       -rate_eval.Ti61__n_V60__weak__mp17
       -rho*Y[jp]*rate_eval.p_Ti61__He4_Sc58
       -rho*Y[jn]*rate_eval.n_Ti61__Ti62
       )

    jac[jti61, jv64] = (
       +rho*Y[jp]*rate_eval.p_V64__He4_Ti61
       )

    jac[jti62, jn] = (
       -rho*Y[jti62]*rate_eval.n_Ti62__Ti63
       +rho*Y[jti61]*rate_eval.n_Ti61__Ti62
       )

    jac[jti62, jp] = (
       -rho*Y[jti62]*rate_eval.p_Ti62__n_V62
       -rho*Y[jti62]*rate_eval.p_Ti62__V63
       -rho*Y[jti62]*rate_eval.p_Ti62__He4_Sc59
       +rho*Y[jv65]*rate_eval.p_V65__He4_Ti62
       +rho*Y[jsc62]*rate_eval.p_Sc62__n_Ti62
       +rho*Y[jsc61]*rate_eval.p_Sc61__Ti62
       )

    jac[jti62, jhe4] = (
       -rho*Y[jti62]*rate_eval.He4_Ti62__n_Cr65
       -rho*Y[jti62]*rate_eval.He4_Ti62__Cr66
       +rho*Y[jca58]*rate_eval.He4_Ca58__Ti62
       +rho*Y[jca59]*rate_eval.He4_Ca59__n_Ti62
       )

    jac[jti62, jca58] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca58__Ti62
       )

    jac[jti62, jca59] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca59__n_Ti62
       )

    jac[jti62, jsc61] = (
       +rho*Y[jp]*rate_eval.p_Sc61__Ti62
       )

    jac[jti62, jsc62] = (
       +rho*Y[jp]*rate_eval.p_Sc62__n_Ti62
       +rate_eval.Sc62__Ti62__weak__mo03
       )

    jac[jti62, jsc63] = (
       +rate_eval.Sc63__n_Ti62__weak__mp17
       )

    jac[jti62, jti61] = (
       +rho*Y[jn]*rate_eval.n_Ti61__Ti62
       )

    jac[jti62, jti62] = (
       -rho*Y[jp]*rate_eval.p_Ti62__n_V62
       -rho*Y[jp]*rate_eval.p_Ti62__V63
       -rho*Y[jhe4]*rate_eval.He4_Ti62__n_Cr65
       -rho*Y[jhe4]*rate_eval.He4_Ti62__Cr66
       -rate_eval.Ti62__n_V61__weak__mp17
       -rho*Y[jn]*rate_eval.n_Ti62__Ti63
       -rate_eval.Ti62__V62__weak__mo03
       -rho*Y[jp]*rate_eval.p_Ti62__He4_Sc59
       )

    jac[jti62, jv65] = (
       +rho*Y[jp]*rate_eval.p_V65__He4_Ti62
       )

    jac[jti63, jn] = (
       -rho*Y[jti63]*rate_eval.n_Ti63__Ti64
       +rho*Y[jti62]*rate_eval.n_Ti62__Ti63
       )

    jac[jti63, jp] = (
       -rho*Y[jti63]*rate_eval.p_Ti63__He4_Sc60
       -rho*Y[jti63]*rate_eval.p_Ti63__n_V63
       -rho*Y[jti63]*rate_eval.p_Ti63__V64
       +rho*Y[jsc62]*rate_eval.p_Sc62__Ti63
       +rho*Y[jsc63]*rate_eval.p_Sc63__n_Ti63
       +rho*Y[jv66]*rate_eval.p_V66__He4_Ti63
       )

    jac[jti63, jhe4] = (
       -rho*Y[jti63]*rate_eval.He4_Ti63__n_Cr66
       -rho*Y[jti63]*rate_eval.He4_Ti63__Cr67
       +rho*Y[jca60]*rate_eval.He4_Ca60__n_Ti63
       +rho*Y[jca59]*rate_eval.He4_Ca59__Ti63
       )

    jac[jti63, jca59] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca59__Ti63
       )

    jac[jti63, jca60] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca60__n_Ti63
       )

    jac[jti63, jsc62] = (
       +rho*Y[jp]*rate_eval.p_Sc62__Ti63
       )

    jac[jti63, jsc63] = (
       +rate_eval.Sc63__Ti63__weak__mo03
       +rho*Y[jp]*rate_eval.p_Sc63__n_Ti63
       )

    jac[jti63, jti62] = (
       +rho*Y[jn]*rate_eval.n_Ti62__Ti63
       )

    jac[jti63, jti63] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti63__n_Cr66
       -rho*Y[jp]*rate_eval.p_Ti63__He4_Sc60
       -rho*Y[jp]*rate_eval.p_Ti63__n_V63
       -rho*Y[jhe4]*rate_eval.He4_Ti63__Cr67
       -rho*Y[jp]*rate_eval.p_Ti63__V64
       -rate_eval.Ti63__n_V62__weak__mp17
       -rate_eval.Ti63__V63__weak__mo03
       -rho*Y[jn]*rate_eval.n_Ti63__Ti64
       -rate_eval.Ti63__n_n_V61__weak__mp17
       )

    jac[jti63, jv66] = (
       +rho*Y[jp]*rate_eval.p_V66__He4_Ti63
       )

    jac[jti64, jn] = (
       -rho*Y[jti64]*rate_eval.n_Ti64__Ti65
       +rho*Y[jti63]*rate_eval.n_Ti63__Ti64
       )

    jac[jti64, jp] = (
       -rho*Y[jti64]*rate_eval.p_Ti64__He4_Sc61
       -rho*Y[jti64]*rate_eval.p_Ti64__n_V64
       -rho*Y[jti64]*rate_eval.p_Ti64__V65
       +rho*Y[jv67]*rate_eval.p_V67__He4_Ti64
       +rho*Y[jsc63]*rate_eval.p_Sc63__Ti64
       )

    jac[jti64, jhe4] = (
       -rho*Y[jti64]*rate_eval.He4_Ti64__n_Cr67
       -rho*Y[jti64]*rate_eval.He4_Ti64__Cr68
       +rho*Y[jca61]*rate_eval.He4_Ca61__n_Ti64
       +rho*Y[jca60]*rate_eval.He4_Ca60__Ti64
       )

    jac[jti64, jca60] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca60__Ti64
       )

    jac[jti64, jca61] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca61__n_Ti64
       )

    jac[jti64, jsc63] = (
       +rho*Y[jp]*rate_eval.p_Sc63__Ti64
       )

    jac[jti64, jti63] = (
       +rho*Y[jn]*rate_eval.n_Ti63__Ti64
       )

    jac[jti64, jti64] = (
       -rho*Y[jhe4]*rate_eval.He4_Ti64__n_Cr67
       -rho*Y[jp]*rate_eval.p_Ti64__He4_Sc61
       -rho*Y[jn]*rate_eval.n_Ti64__Ti65
       -rho*Y[jp]*rate_eval.p_Ti64__n_V64
       -rate_eval.Ti64__n_n_V62__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ti64__Cr68
       -rate_eval.Ti64__n_V63__weak__mp17
       -rate_eval.Ti64__V64__weak__mo03
       -rho*Y[jp]*rate_eval.p_Ti64__V65
       -rate_eval.Ti64__n_n_n_V61__weak__mo03
       )

    jac[jti64, jv67] = (
       +rho*Y[jp]*rate_eval.p_V67__He4_Ti64
       )

    jac[jti65, jn] = (
       +rho*Y[jti64]*rate_eval.n_Ti64__Ti65
       )

    jac[jti65, jp] = (
       -rho*Y[jti65]*rate_eval.p_Ti65__He4_Sc62
       -rho*Y[jti65]*rate_eval.p_Ti65__V66
       -rho*Y[jti65]*rate_eval.p_Ti65__n_V65
       )

    jac[jti65, jhe4] = (
       -rho*Y[jti65]*rate_eval.He4_Ti65__n_Cr68
       -rho*Y[jti65]*rate_eval.He4_Ti65__Cr69
       +rho*Y[jca61]*rate_eval.He4_Ca61__Ti65
       )

    jac[jti65, jca61] = (
       +rho*Y[jhe4]*rate_eval.He4_Ca61__Ti65
       )

    jac[jti65, jti64] = (
       +rho*Y[jn]*rate_eval.n_Ti64__Ti65
       )

    jac[jti65, jti65] = (
       -rate_eval.Ti65__n_n_n_V62__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Ti65__n_Cr68
       -rate_eval.Ti65__n_V64__weak__mp17
       -rho*Y[jp]*rate_eval.p_Ti65__He4_Sc62
       -rho*Y[jp]*rate_eval.p_Ti65__V66
       -rho*Y[jp]*rate_eval.p_Ti65__n_V65
       -rate_eval.Ti65__n_n_V63__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Ti65__Cr69
       -rate_eval.Ti65__V65__weak__mo03
       )

    jac[jv39, jn] = (
       -rho*Y[jv39]*rate_eval.n_V39__V40
       -rho*Y[jv39]*rate_eval.n_V39__p_Ti39
       -rho*Y[jv39]*rate_eval.n_V39__He4_Sc36
       )

    jac[jv39, jp] = (
       +rho*Y[jti38]*rate_eval.p_Ti38__V39
       )

    jac[jv39, jhe4] = (
       -rho*Y[jv39]*rate_eval.He4_V39__p_Cr42
       -rho*Y[jv39]*rate_eval.He4_V39__Mn43
       +rho*Y[jsc35]*rate_eval.He4_Sc35__V39
       )

    jac[jv39, jsc35] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc35__V39
       )

    jac[jv39, jti38] = (
       +rho*Y[jp]*rate_eval.p_Ti38__V39
       )

    jac[jv39, jv39] = (
       -rho*Y[jhe4]*rate_eval.He4_V39__p_Cr42
       -rho*Y[jn]*rate_eval.n_V39__V40
       -rho*Y[jn]*rate_eval.n_V39__p_Ti39
       -rho*Y[jhe4]*rate_eval.He4_V39__Mn43
       -rate_eval.V39__Ti39__weak__bqa_pos_
       -rho*Y[jn]*rate_eval.n_V39__He4_Sc36
       )

    jac[jv40, jn] = (
       -rho*Y[jv40]*rate_eval.n_V40__p_Ti40
       -rho*Y[jv40]*rate_eval.n_V40__He4_Sc37
       -rho*Y[jv40]*rate_eval.n_V40__V41
       +rho*Y[jmn43]*rate_eval.n_Mn43__He4_V40
       +rho*Y[jv39]*rate_eval.n_V39__V40
       )

    jac[jv40, jp] = (
       -rho*Y[jv40]*rate_eval.p_V40__Cr41
       +rho*Y[jti39]*rate_eval.p_Ti39__V40
       )

    jac[jv40, jhe4] = (
       -rho*Y[jv40]*rate_eval.He4_V40__p_Cr43
       -rho*Y[jv40]*rate_eval.He4_V40__Mn44
       +rho*Y[jti37]*rate_eval.He4_Ti37__p_V40
       +rho*Y[jsc36]*rate_eval.He4_Sc36__V40
       )

    jac[jv40, jsc36] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc36__V40
       )

    jac[jv40, jti37] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti37__p_V40
       )

    jac[jv40, jti39] = (
       +rho*Y[jp]*rate_eval.p_Ti39__V40
       )

    jac[jv40, jv39] = (
       +rho*Y[jn]*rate_eval.n_V39__V40
       )

    jac[jv40, jv40] = (
       -rho*Y[jn]*rate_eval.n_V40__p_Ti40
       -rho*Y[jhe4]*rate_eval.He4_V40__p_Cr43
       -rho*Y[jn]*rate_eval.n_V40__He4_Sc37
       -rho*Y[jp]*rate_eval.p_V40__Cr41
       -rate_eval.V40__Ti40__weak__bqa_pos_
       -rho*Y[jhe4]*rate_eval.He4_V40__Mn44
       -rho*Y[jn]*rate_eval.n_V40__V41
       )

    jac[jv40, jmn43] = (
       +rho*Y[jn]*rate_eval.n_Mn43__He4_V40
       )

    jac[jv41, jn] = (
       -rho*Y[jv41]*rate_eval.n_V41__He4_Sc38
       -rho*Y[jv41]*rate_eval.n_V41__V42
       -rho*Y[jv41]*rate_eval.n_V41__p_Ti41
       +rho*Y[jmn44]*rate_eval.n_Mn44__He4_V41
       +rho*Y[jcr41]*rate_eval.n_Cr41__p_V41
       +rho*Y[jv40]*rate_eval.n_V40__V41
       )

    jac[jv41, jp] = (
       -rho*Y[jv41]*rate_eval.p_V41__Cr42
       +rho*Y[jti40]*rate_eval.p_Ti40__V41
       )

    jac[jv41, jhe4] = (
       -rho*Y[jv41]*rate_eval.He4_V41__Mn45
       -rho*Y[jv41]*rate_eval.He4_V41__p_Cr44
       +rho*Y[jti38]*rate_eval.He4_Ti38__p_V41
       +rho*Y[jsc37]*rate_eval.He4_Sc37__V41
       )

    jac[jv41, jsc37] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc37__V41
       )

    jac[jv41, jti38] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti38__p_V41
       )

    jac[jv41, jti40] = (
       +rho*Y[jp]*rate_eval.p_Ti40__V41
       )

    jac[jv41, jv40] = (
       +rho*Y[jn]*rate_eval.n_V40__V41
       )

    jac[jv41, jv41] = (
       -rho*Y[jn]*rate_eval.n_V41__He4_Sc38
       -rho*Y[jhe4]*rate_eval.He4_V41__Mn45
       -rho*Y[jp]*rate_eval.p_V41__Cr42
       -rho*Y[jn]*rate_eval.n_V41__V42
       -rho*Y[jn]*rate_eval.n_V41__p_Ti41
       -rate_eval.V41__Ti41__weak__bqa_pos_
       -rho*Y[jhe4]*rate_eval.He4_V41__p_Cr44
       )

    jac[jv41, jcr41] = (
       +rho*Y[jn]*rate_eval.n_Cr41__p_V41
       +rate_eval.Cr41__V41__weak__bqa_pos_
       )

    jac[jv41, jmn44] = (
       +rho*Y[jn]*rate_eval.n_Mn44__He4_V41
       )

    jac[jv42, jn] = (
       -rho*Y[jv42]*rate_eval.n_V42__He4_Sc39
       -rho*Y[jv42]*rate_eval.n_V42__V43
       -rho*Y[jv42]*rate_eval.n_V42__p_Ti42
       +rho*Y[jcr42]*rate_eval.n_Cr42__p_V42
       +rho*Y[jv41]*rate_eval.n_V41__V42
       +rho*Y[jmn45]*rate_eval.n_Mn45__He4_V42
       )

    jac[jv42, jp] = (
       -rho*Y[jv42]*rate_eval.p_V42__Cr43
       +rho*Y[jti41]*rate_eval.p_Ti41__V42
       )

    jac[jv42, jhe4] = (
       -rho*Y[jv42]*rate_eval.He4_V42__p_Cr45
       -rho*Y[jv42]*rate_eval.He4_V42__Mn46
       +rho*Y[jti39]*rate_eval.He4_Ti39__p_V42
       +rho*Y[jsc38]*rate_eval.He4_Sc38__V42
       )

    jac[jv42, jsc38] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc38__V42
       )

    jac[jv42, jti39] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti39__p_V42
       )

    jac[jv42, jti41] = (
       +rho*Y[jp]*rate_eval.p_Ti41__V42
       )

    jac[jv42, jv41] = (
       +rho*Y[jn]*rate_eval.n_V41__V42
       )

    jac[jv42, jv42] = (
       -rho*Y[jhe4]*rate_eval.He4_V42__p_Cr45
       -rho*Y[jn]*rate_eval.n_V42__He4_Sc39
       -rho*Y[jp]*rate_eval.p_V42__Cr43
       -rho*Y[jn]*rate_eval.n_V42__V43
       -rho*Y[jn]*rate_eval.n_V42__p_Ti42
       -rho*Y[jhe4]*rate_eval.He4_V42__Mn46
       -rate_eval.V42__Ti42__weak__mo97
       )

    jac[jv42, jcr42] = (
       +rho*Y[jn]*rate_eval.n_Cr42__p_V42
       +rate_eval.Cr42__V42__weak__wc12
       )

    jac[jv42, jmn45] = (
       +rho*Y[jn]*rate_eval.n_Mn45__He4_V42
       )

    jac[jv43, jn] = (
       -rho*Y[jv43]*rate_eval.n_V43__p_Ti43
       -rho*Y[jv43]*rate_eval.n_V43__He4_Sc40
       -rho*Y[jv43]*rate_eval.n_V43__V44
       +rho*Y[jmn46]*rate_eval.n_Mn46__He4_V43
       +rho*Y[jcr43]*rate_eval.n_Cr43__p_V43
       +rho*Y[jv42]*rate_eval.n_V42__V43
       )

    jac[jv43, jp] = (
       -rho*Y[jv43]*rate_eval.p_V43__Cr44
       +rho*Y[jti42]*rate_eval.p_Ti42__V43
       )

    jac[jv43, jhe4] = (
       -rho*Y[jv43]*rate_eval.He4_V43__p_Cr46
       -rho*Y[jv43]*rate_eval.He4_V43__Mn47
       +rho*Y[jti40]*rate_eval.He4_Ti40__p_V43
       +rho*Y[jsc39]*rate_eval.He4_Sc39__V43
       )

    jac[jv43, jsc39] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc39__V43
       )

    jac[jv43, jti40] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti40__p_V43
       )

    jac[jv43, jti42] = (
       +rho*Y[jp]*rate_eval.p_Ti42__V43
       )

    jac[jv43, jv42] = (
       +rho*Y[jn]*rate_eval.n_V42__V43
       )

    jac[jv43, jv43] = (
       -rho*Y[jhe4]*rate_eval.He4_V43__p_Cr46
       -rho*Y[jn]*rate_eval.n_V43__p_Ti43
       -rho*Y[jn]*rate_eval.n_V43__He4_Sc40
       -rho*Y[jhe4]*rate_eval.He4_V43__Mn47
       -rho*Y[jp]*rate_eval.p_V43__Cr44
       -rho*Y[jn]*rate_eval.n_V43__V44
       -rate_eval.V43__Ti43__weak__wc12
       )

    jac[jv43, jcr43] = (
       +rho*Y[jn]*rate_eval.n_Cr43__p_V43
       +rate_eval.Cr43__V43__weak__wc12
       )

    jac[jv43, jmn46] = (
       +rho*Y[jn]*rate_eval.n_Mn46__He4_V43
       )

    jac[jv43, jfe45] = (
       +rate_eval.Fe45__p_p_V43__weak__wc12
       )

    jac[jv44, jn] = (
       -rho*Y[jv44]*rate_eval.n_V44__He4_Sc41
       -rho*Y[jv44]*rate_eval.n_V44__p_Ti44
       -rho*Y[jv44]*rate_eval.n_V44__V45
       +rho*Y[jmn47]*rate_eval.n_Mn47__He4_V44
       +rho*Y[jv43]*rate_eval.n_V43__V44
       +rho*Y[jcr44]*rate_eval.n_Cr44__p_V44
       )

    jac[jv44, jp] = (
       -rho*Y[jv44]*rate_eval.p_V44__Cr45
       +rho*Y[jti43]*rate_eval.p_Ti43__V44
       )

    jac[jv44, jhe4] = (
       -rho*Y[jv44]*rate_eval.He4_V44__p_Cr47
       -rho*Y[jv44]*rate_eval.He4_V44__Mn48
       +rho*Y[jsc40]*rate_eval.He4_Sc40__V44
       +rho*Y[jti41]*rate_eval.He4_Ti41__p_V44
       )

    jac[jv44, jsc40] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc40__V44
       )

    jac[jv44, jti41] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti41__p_V44
       )

    jac[jv44, jti43] = (
       +rho*Y[jp]*rate_eval.p_Ti43__V44
       )

    jac[jv44, jv43] = (
       +rho*Y[jn]*rate_eval.n_V43__V44
       )

    jac[jv44, jv44] = (
       -rho*Y[jn]*rate_eval.n_V44__He4_Sc41
       -rho*Y[jn]*rate_eval.n_V44__p_Ti44
       -rho*Y[jhe4]*rate_eval.He4_V44__p_Cr47
       -rho*Y[jp]*rate_eval.p_V44__Cr45
       -rho*Y[jn]*rate_eval.n_V44__V45
       -rho*Y[jhe4]*rate_eval.He4_V44__Mn48
       -rate_eval.V44__Ti44__weak__wc12
       )

    jac[jv44, jcr44] = (
       +rate_eval.Cr44__V44__weak__wc12
       +rho*Y[jn]*rate_eval.n_Cr44__p_V44
       )

    jac[jv44, jmn47] = (
       +rho*Y[jn]*rate_eval.n_Mn47__He4_V44
       )

    jac[jv45, jn] = (
       -rho*Y[jv45]*rate_eval.n_V45__He4_Sc42
       -rho*Y[jv45]*rate_eval.n_V45__V46
       -rho*Y[jv45]*rate_eval.n_V45__p_Ti45
       +rho*Y[jmn48]*rate_eval.n_Mn48__He4_V45
       +rho*Y[jcr45]*rate_eval.n_Cr45__p_V45
       +rho*Y[jv44]*rate_eval.n_V44__V45
       )

    jac[jv45, jp] = (
       -rho*Y[jv45]*rate_eval.p_V45__Cr46
       +rho*Y[jti44]*rate_eval.p_Ti44__V45
       )

    jac[jv45, jhe4] = (
       -rho*Y[jv45]*rate_eval.He4_V45__Mn49
       -rho*Y[jv45]*rate_eval.He4_V45__p_Cr48
       +rho*Y[jti42]*rate_eval.He4_Ti42__p_V45
       +rho*Y[jsc41]*rate_eval.He4_Sc41__V45
       )

    jac[jv45, jsc41] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc41__V45
       )

    jac[jv45, jti42] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti42__p_V45
       )

    jac[jv45, jti44] = (
       +rho*Y[jp]*rate_eval.p_Ti44__V45
       )

    jac[jv45, jv44] = (
       +rho*Y[jn]*rate_eval.n_V44__V45
       )

    jac[jv45, jv45] = (
       -rho*Y[jn]*rate_eval.n_V45__He4_Sc42
       -rho*Y[jhe4]*rate_eval.He4_V45__Mn49
       -rho*Y[jn]*rate_eval.n_V45__V46
       -rate_eval.V45__Ti45__weak__wc12
       -rho*Y[jp]*rate_eval.p_V45__Cr46
       -rho*Y[jhe4]*rate_eval.He4_V45__p_Cr48
       -rho*Y[jn]*rate_eval.n_V45__p_Ti45
       )

    jac[jv45, jcr45] = (
       +rho*Y[jn]*rate_eval.n_Cr45__p_V45
       +rate_eval.Cr45__V45__weak__wc12
       )

    jac[jv45, jmn46] = (
       +rate_eval.Mn46__p_V45__weak__wc12
       )

    jac[jv45, jmn48] = (
       +rho*Y[jn]*rate_eval.n_Mn48__He4_V45
       )

    jac[jv46, jn] = (
       -rho*Y[jv46]*rate_eval.n_V46__He4_Sc43
       -rho*Y[jv46]*rate_eval.n_V46__p_Ti46
       -rho*Y[jv46]*rate_eval.n_V46__V47
       +rho*Y[jcr46]*rate_eval.n_Cr46__p_V46
       +rho*Y[jmn49]*rate_eval.n_Mn49__He4_V46
       +rho*Y[jv45]*rate_eval.n_V45__V46
       )

    jac[jv46, jp] = (
       -rho*Y[jv46]*rate_eval.p_V46__Cr47
       +rho*Y[jti45]*rate_eval.p_Ti45__V46
       )

    jac[jv46, jhe4] = (
       -rho*Y[jv46]*rate_eval.He4_V46__p_Cr49
       -rho*Y[jv46]*rate_eval.He4_V46__Mn50
       +rho*Y[jti43]*rate_eval.He4_Ti43__p_V46
       +rho*Y[jsc42]*rate_eval.He4_Sc42__V46
       )

    jac[jv46, jsc42] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc42__V46
       )

    jac[jv46, jti43] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti43__p_V46
       )

    jac[jv46, jti45] = (
       +rho*Y[jp]*rate_eval.p_Ti45__V46
       )

    jac[jv46, jv45] = (
       +rho*Y[jn]*rate_eval.n_V45__V46
       )

    jac[jv46, jv46] = (
       -rho*Y[jhe4]*rate_eval.He4_V46__p_Cr49
       -rho*Y[jn]*rate_eval.n_V46__He4_Sc43
       -rho*Y[jn]*rate_eval.n_V46__p_Ti46
       -rho*Y[jhe4]*rate_eval.He4_V46__Mn50
       -rho*Y[jp]*rate_eval.p_V46__Cr47
       -rho*Y[jn]*rate_eval.n_V46__V47
       -rate_eval.V46__Ti46__weak__wc12
       )

    jac[jv46, jcr46] = (
       +rho*Y[jn]*rate_eval.n_Cr46__p_V46
       +rate_eval.Cr46__V46__weak__wc12
       )

    jac[jv46, jmn49] = (
       +rho*Y[jn]*rate_eval.n_Mn49__He4_V46
       )

    jac[jv47, jn] = (
       -rho*Y[jv47]*rate_eval.n_V47__He4_Sc44
       -rho*Y[jv47]*rate_eval.n_V47__V48
       -rho*Y[jv47]*rate_eval.n_V47__p_Ti47
       +rho*Y[jmn50]*rate_eval.n_Mn50__He4_V47
       +rho*Y[jcr47]*rate_eval.n_Cr47__p_V47
       +rho*Y[jv46]*rate_eval.n_V46__V47
       )

    jac[jv47, jp] = (
       -rho*Y[jv47]*rate_eval.p_V47__Cr48
       +rho*Y[jti46]*rate_eval.p_Ti46__V47
       )

    jac[jv47, jhe4] = (
       -rho*Y[jv47]*rate_eval.He4_V47__p_Cr50
       -rho*Y[jv47]*rate_eval.He4_V47__Mn51
       +rho*Y[jsc43]*rate_eval.He4_Sc43__V47
       +rho*Y[jti44]*rate_eval.He4_Ti44__p_V47
       )

    jac[jv47, jsc43] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc43__V47
       )

    jac[jv47, jti44] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti44__p_V47
       )

    jac[jv47, jti46] = (
       +rho*Y[jp]*rate_eval.p_Ti46__V47
       )

    jac[jv47, jv46] = (
       +rho*Y[jn]*rate_eval.n_V46__V47
       )

    jac[jv47, jv47] = (
       -rho*Y[jhe4]*rate_eval.He4_V47__p_Cr50
       -rho*Y[jn]*rate_eval.n_V47__He4_Sc44
       -rho*Y[jhe4]*rate_eval.He4_V47__Mn51
       -rho*Y[jn]*rate_eval.n_V47__V48
       -rho*Y[jn]*rate_eval.n_V47__p_Ti47
       -rate_eval.V47__Ti47__weak__wc12
       -rho*Y[jp]*rate_eval.p_V47__Cr48
       )

    jac[jv47, jcr47] = (
       +rho*Y[jn]*rate_eval.n_Cr47__p_V47
       +rate_eval.Cr47__V47__weak__wc12
       )

    jac[jv47, jmn48] = (
       +rate_eval.Mn48__p_V47__weak__wc12
       )

    jac[jv47, jmn50] = (
       +rho*Y[jn]*rate_eval.n_Mn50__He4_V47
       )

    jac[jv48, jn] = (
       -rho*Y[jv48]*rate_eval.n_V48__p_Ti48
       -rho*Y[jv48]*rate_eval.n_V48__V49
       -rho*Y[jv48]*rate_eval.n_V48__He4_Sc45
       +rho*Y[jcr48]*rate_eval.n_Cr48__p_V48
       +rho*Y[jmn51]*rate_eval.n_Mn51__He4_V48
       +rho*Y[jv47]*rate_eval.n_V47__V48
       )

    jac[jv48, jp] = (
       -rho*Y[jv48]*rate_eval.p_V48__Cr49
       +rho*Y[jti47]*rate_eval.p_Ti47__V48
       )

    jac[jv48, jhe4] = (
       -rho*Y[jv48]*rate_eval.He4_V48__p_Cr51
       -rho*Y[jv48]*rate_eval.He4_V48__Mn52
       +rho*Y[jti45]*rate_eval.He4_Ti45__p_V48
       +rho*Y[jsc44]*rate_eval.He4_Sc44__V48
       )

    jac[jv48, jsc44] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc44__V48
       )

    jac[jv48, jti45] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti45__p_V48
       )

    jac[jv48, jti47] = (
       +rho*Y[jp]*rate_eval.p_Ti47__V48
       )

    jac[jv48, jv47] = (
       +rho*Y[jn]*rate_eval.n_V47__V48
       )

    jac[jv48, jv48] = (
       -rho*Y[jn]*rate_eval.n_V48__p_Ti48
       -rho*Y[jp]*rate_eval.p_V48__Cr49
       -rho*Y[jn]*rate_eval.n_V48__V49
       -rho*Y[jhe4]*rate_eval.He4_V48__p_Cr51
       -rho*Y[jn]*rate_eval.n_V48__He4_Sc45
       -rho*Y[jhe4]*rate_eval.He4_V48__Mn52
       -rate_eval.V48__Ti48__weak__wc12
       )

    jac[jv48, jcr48] = (
       +rho*Y[jn]*rate_eval.n_Cr48__p_V48
       +rate_eval.Cr48__V48__weak__wc12
       )

    jac[jv48, jmn51] = (
       +rho*Y[jn]*rate_eval.n_Mn51__He4_V48
       )

    jac[jv49, jn] = (
       -rho*Y[jv49]*rate_eval.n_V49__p_Ti49
       -rho*Y[jv49]*rate_eval.n_V49__V50
       +rho*Y[jmn52]*rate_eval.n_Mn52__He4_V49
       +rho*Y[jcr49]*rate_eval.n_Cr49__p_V49
       +rho*Y[jv48]*rate_eval.n_V48__V49
       )

    jac[jv49, jp] = (
       -rho*Y[jv49]*rate_eval.p_V49__He4_Ti46
       -rho*Y[jv49]*rate_eval.p_V49__Cr50
       +rho*Y[jti48]*rate_eval.p_Ti48__V49
       )

    jac[jv49, jhe4] = (
       -rho*Y[jv49]*rate_eval.He4_V49__Mn53
       -rho*Y[jv49]*rate_eval.He4_V49__p_Cr52
       +rho*Y[jsc45]*rate_eval.He4_Sc45__V49
       +rho*Y[jsc46]*rate_eval.He4_Sc46__n_V49
       )

    jac[jv49, jsc45] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc45__V49
       )

    jac[jv49, jsc46] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc46__n_V49
       )

    jac[jv49, jti48] = (
       +rho*Y[jp]*rate_eval.p_Ti48__V49
       )

    jac[jv49, jv48] = (
       +rho*Y[jn]*rate_eval.n_V48__V49
       )

    jac[jv49, jv49] = (
       -rho*Y[jp]*rate_eval.p_V49__He4_Ti46
       -rho*Y[jhe4]*rate_eval.He4_V49__Mn53
       -rho*Y[jn]*rate_eval.n_V49__p_Ti49
       -rho*Y[jp]*rate_eval.p_V49__Cr50
       -rho*Y[jhe4]*rate_eval.He4_V49__p_Cr52
       -rho*Y[jn]*rate_eval.n_V49__V50
       -rate_eval.V49__Ti49__weak__wc12
       )

    jac[jv49, jcr49] = (
       +rho*Y[jn]*rate_eval.n_Cr49__p_V49
       +rate_eval.Cr49__V49__weak__wc12
       )

    jac[jv49, jmn52] = (
       +rho*Y[jn]*rate_eval.n_Mn52__He4_V49
       )

    jac[jv50, jn] = (
       -rho*Y[jv50]*rate_eval.n_V50__p_Ti50
       -rho*Y[jv50]*rate_eval.n_V50__He4_Sc47
       -rho*Y[jv50]*rate_eval.n_V50__V51
       +rho*Y[jmn53]*rate_eval.n_Mn53__He4_V50
       +rho*Y[jv49]*rate_eval.n_V49__V50
       )

    jac[jv50, jp] = (
       -rho*Y[jv50]*rate_eval.p_V50__He4_Ti47
       -rho*Y[jv50]*rate_eval.p_V50__n_Cr50
       -rho*Y[jv50]*rate_eval.p_V50__Cr51
       +rho*Y[jti49]*rate_eval.p_Ti49__V50
       )

    jac[jv50, jhe4] = (
       -rho*Y[jv50]*rate_eval.He4_V50__p_Cr53
       -rho*Y[jv50]*rate_eval.He4_V50__Mn54
       +rho*Y[jsc46]*rate_eval.He4_Sc46__V50
       )

    jac[jv50, jsc46] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc46__V50
       )

    jac[jv50, jti49] = (
       +rho*Y[jp]*rate_eval.p_Ti49__V50
       )

    jac[jv50, jv49] = (
       +rho*Y[jn]*rate_eval.n_V49__V50
       )

    jac[jv50, jv50] = (
       -rho*Y[jhe4]*rate_eval.He4_V50__p_Cr53
       -rho*Y[jp]*rate_eval.p_V50__He4_Ti47
       -rho*Y[jp]*rate_eval.p_V50__n_Cr50
       -rho*Y[jn]*rate_eval.n_V50__p_Ti50
       -rho*Y[jn]*rate_eval.n_V50__He4_Sc47
       -rho*Y[jhe4]*rate_eval.He4_V50__Mn54
       -rho*Y[jp]*rate_eval.p_V50__Cr51
       -rho*Y[jn]*rate_eval.n_V50__V51
       -rate_eval.V50__Ti50__weak__mo03
       )

    jac[jv50, jmn53] = (
       +rho*Y[jn]*rate_eval.n_Mn53__He4_V50
       )

    jac[jv51, jn] = (
       -rho*Y[jv51]*rate_eval.n_V51__V52
       +rho*Y[jmn54]*rate_eval.n_Mn54__He4_V51
       +rho*Y[jv50]*rate_eval.n_V50__V51
       +rho*Y[jcr51]*rate_eval.n_Cr51__p_V51
       )

    jac[jv51, jp] = (
       -rho*Y[jv51]*rate_eval.p_V51__He4_Ti48
       -rho*Y[jv51]*rate_eval.p_V51__Cr52
       +rho*Y[jcr54]*rate_eval.p_Cr54__He4_V51
       +rho*Y[jti51]*rate_eval.p_Ti51__n_V51
       +rho*Y[jti50]*rate_eval.p_Ti50__V51
       )

    jac[jv51, jhe4] = (
       -rho*Y[jv51]*rate_eval.He4_V51__Mn55
       +rho*Y[jsc48]*rate_eval.He4_Sc48__n_V51
       +rho*Y[jsc47]*rate_eval.He4_Sc47__V51
       )

    jac[jv51, jsc47] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc47__V51
       )

    jac[jv51, jsc48] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc48__n_V51
       )

    jac[jv51, jti50] = (
       +rho*Y[jp]*rate_eval.p_Ti50__V51
       )

    jac[jv51, jti51] = (
       +rho*Y[jp]*rate_eval.p_Ti51__n_V51
       +rate_eval.Ti51__V51__weak__wc12
       )

    jac[jv51, jv50] = (
       +rho*Y[jn]*rate_eval.n_V50__V51
       )

    jac[jv51, jv51] = (
       -rho*Y[jp]*rate_eval.p_V51__He4_Ti48
       -rho*Y[jhe4]*rate_eval.He4_V51__Mn55
       -rho*Y[jn]*rate_eval.n_V51__V52
       -rho*Y[jp]*rate_eval.p_V51__Cr52
       )

    jac[jv51, jcr51] = (
       +rho*Y[jn]*rate_eval.n_Cr51__p_V51
       +rate_eval.Cr51__V51__weak__wc12
       )

    jac[jv51, jcr54] = (
       +rho*Y[jp]*rate_eval.p_Cr54__He4_V51
       )

    jac[jv51, jmn54] = (
       +rho*Y[jn]*rate_eval.n_Mn54__He4_V51
       )

    jac[jv52, jn] = (
       -rho*Y[jv52]*rate_eval.n_V52__V53
       -rho*Y[jv52]*rate_eval.n_V52__He4_Sc49
       +rho*Y[jv51]*rate_eval.n_V51__V52
       )

    jac[jv52, jp] = (
       -rho*Y[jv52]*rate_eval.p_V52__He4_Ti49
       -rho*Y[jv52]*rate_eval.p_V52__n_Cr52
       -rho*Y[jv52]*rate_eval.p_V52__Cr53
       +rho*Y[jti52]*rate_eval.p_Ti52__n_V52
       +rho*Y[jcr55]*rate_eval.p_Cr55__He4_V52
       +rho*Y[jti51]*rate_eval.p_Ti51__V52
       )

    jac[jv52, jhe4] = (
       -rho*Y[jv52]*rate_eval.He4_V52__Mn56
       -rho*Y[jv52]*rate_eval.He4_V52__n_Mn55
       +rho*Y[jsc48]*rate_eval.He4_Sc48__V52
       )

    jac[jv52, jsc48] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc48__V52
       )

    jac[jv52, jti51] = (
       +rho*Y[jp]*rate_eval.p_Ti51__V52
       )

    jac[jv52, jti52] = (
       +rho*Y[jp]*rate_eval.p_Ti52__n_V52
       +rate_eval.Ti52__V52__weak__wc12
       )

    jac[jv52, jv51] = (
       +rho*Y[jn]*rate_eval.n_V51__V52
       )

    jac[jv52, jv52] = (
       -rho*Y[jp]*rate_eval.p_V52__He4_Ti49
       -rho*Y[jp]*rate_eval.p_V52__n_Cr52
       -rho*Y[jhe4]*rate_eval.He4_V52__Mn56
       -rho*Y[jp]*rate_eval.p_V52__Cr53
       -rate_eval.V52__Cr52__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_V52__n_Mn55
       -rho*Y[jn]*rate_eval.n_V52__V53
       -rho*Y[jn]*rate_eval.n_V52__He4_Sc49
       )

    jac[jv52, jcr55] = (
       +rho*Y[jp]*rate_eval.p_Cr55__He4_V52
       )

    jac[jv53, jn] = (
       -rho*Y[jv53]*rate_eval.n_V53__V54
       +rho*Y[jv52]*rate_eval.n_V52__V53
       +rho*Y[jmn56]*rate_eval.n_Mn56__He4_V53
       )

    jac[jv53, jp] = (
       -rho*Y[jv53]*rate_eval.p_V53__n_Cr53
       -rho*Y[jv53]*rate_eval.p_V53__He4_Ti50
       -rho*Y[jv53]*rate_eval.p_V53__Cr54
       +rho*Y[jcr56]*rate_eval.p_Cr56__He4_V53
       +rho*Y[jti53]*rate_eval.p_Ti53__n_V53
       +rho*Y[jti52]*rate_eval.p_Ti52__V53
       )

    jac[jv53, jhe4] = (
       -rho*Y[jv53]*rate_eval.He4_V53__Mn57
       +rho*Y[jsc49]*rate_eval.He4_Sc49__V53
       +rho*Y[jsc50]*rate_eval.He4_Sc50__n_V53
       )

    jac[jv53, jsc49] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc49__V53
       )

    jac[jv53, jsc50] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc50__n_V53
       )

    jac[jv53, jti52] = (
       +rho*Y[jp]*rate_eval.p_Ti52__V53
       )

    jac[jv53, jti53] = (
       +rho*Y[jp]*rate_eval.p_Ti53__n_V53
       +rate_eval.Ti53__V53__weak__wc12
       )

    jac[jv53, jv52] = (
       +rho*Y[jn]*rate_eval.n_V52__V53
       )

    jac[jv53, jv53] = (
       -rho*Y[jp]*rate_eval.p_V53__n_Cr53
       -rho*Y[jp]*rate_eval.p_V53__He4_Ti50
       -rho*Y[jhe4]*rate_eval.He4_V53__Mn57
       -rho*Y[jp]*rate_eval.p_V53__Cr54
       -rho*Y[jn]*rate_eval.n_V53__V54
       -rate_eval.V53__Cr53__weak__wc12
       )

    jac[jv53, jcr56] = (
       +rho*Y[jp]*rate_eval.p_Cr56__He4_V53
       )

    jac[jv53, jmn56] = (
       +rho*Y[jn]*rate_eval.n_Mn56__He4_V53
       )

    jac[jv54, jn] = (
       -rho*Y[jv54]*rate_eval.n_V54__V55
       +rho*Y[jv53]*rate_eval.n_V53__V54
       )

    jac[jv54, jp] = (
       -rho*Y[jv54]*rate_eval.p_V54__n_Cr54
       -rho*Y[jv54]*rate_eval.p_V54__Cr55
       -rho*Y[jv54]*rate_eval.p_V54__He4_Ti51
       +rho*Y[jcr57]*rate_eval.p_Cr57__He4_V54
       +rho*Y[jti54]*rate_eval.p_Ti54__n_V54
       +rho*Y[jti53]*rate_eval.p_Ti53__V54
       )

    jac[jv54, jhe4] = (
       -rho*Y[jv54]*rate_eval.He4_V54__n_Mn57
       -rho*Y[jv54]*rate_eval.He4_V54__Mn58
       +rho*Y[jsc51]*rate_eval.He4_Sc51__n_V54
       +rho*Y[jsc50]*rate_eval.He4_Sc50__V54
       )

    jac[jv54, jsc50] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc50__V54
       )

    jac[jv54, jsc51] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc51__n_V54
       )

    jac[jv54, jti53] = (
       +rho*Y[jp]*rate_eval.p_Ti53__V54
       )

    jac[jv54, jti54] = (
       +rho*Y[jp]*rate_eval.p_Ti54__n_V54
       +rate_eval.Ti54__V54__weak__wc12
       )

    jac[jv54, jv53] = (
       +rho*Y[jn]*rate_eval.n_V53__V54
       )

    jac[jv54, jv54] = (
       -rho*Y[jhe4]*rate_eval.He4_V54__n_Mn57
       -rho*Y[jp]*rate_eval.p_V54__n_Cr54
       -rho*Y[jhe4]*rate_eval.He4_V54__Mn58
       -rho*Y[jp]*rate_eval.p_V54__Cr55
       -rate_eval.V54__Cr54__weak__wc12
       -rho*Y[jn]*rate_eval.n_V54__V55
       -rho*Y[jp]*rate_eval.p_V54__He4_Ti51
       )

    jac[jv54, jcr57] = (
       +rho*Y[jp]*rate_eval.p_Cr57__He4_V54
       )

    jac[jv55, jn] = (
       -rho*Y[jv55]*rate_eval.n_V55__V56
       +rho*Y[jv54]*rate_eval.n_V54__V55
       )

    jac[jv55, jp] = (
       -rho*Y[jv55]*rate_eval.p_V55__n_Cr55
       -rho*Y[jv55]*rate_eval.p_V55__Cr56
       -rho*Y[jv55]*rate_eval.p_V55__He4_Ti52
       +rho*Y[jti55]*rate_eval.p_Ti55__n_V55
       +rho*Y[jti54]*rate_eval.p_Ti54__V55
       +rho*Y[jcr58]*rate_eval.p_Cr58__He4_V55
       )

    jac[jv55, jhe4] = (
       -rho*Y[jv55]*rate_eval.He4_V55__n_Mn58
       -rho*Y[jv55]*rate_eval.He4_V55__Mn59
       +rho*Y[jsc52]*rate_eval.He4_Sc52__n_V55
       +rho*Y[jsc51]*rate_eval.He4_Sc51__V55
       )

    jac[jv55, jsc51] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc51__V55
       )

    jac[jv55, jsc52] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc52__n_V55
       )

    jac[jv55, jti54] = (
       +rho*Y[jp]*rate_eval.p_Ti54__V55
       )

    jac[jv55, jti55] = (
       +rho*Y[jp]*rate_eval.p_Ti55__n_V55
       +rate_eval.Ti55__V55__weak__wc12
       )

    jac[jv55, jv54] = (
       +rho*Y[jn]*rate_eval.n_V54__V55
       )

    jac[jv55, jv55] = (
       -rho*Y[jhe4]*rate_eval.He4_V55__n_Mn58
       -rho*Y[jp]*rate_eval.p_V55__n_Cr55
       -rho*Y[jp]*rate_eval.p_V55__Cr56
       -rho*Y[jn]*rate_eval.n_V55__V56
       -rate_eval.V55__Cr55__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_V55__Mn59
       -rho*Y[jp]*rate_eval.p_V55__He4_Ti52
       )

    jac[jv55, jcr58] = (
       +rho*Y[jp]*rate_eval.p_Cr58__He4_V55
       )

    jac[jv56, jn] = (
       -rho*Y[jv56]*rate_eval.n_V56__V57
       +rho*Y[jv55]*rate_eval.n_V55__V56
       )

    jac[jv56, jp] = (
       -rho*Y[jv56]*rate_eval.p_V56__He4_Ti53
       -rho*Y[jv56]*rate_eval.p_V56__Cr57
       -rho*Y[jv56]*rate_eval.p_V56__n_Cr56
       +rho*Y[jti55]*rate_eval.p_Ti55__V56
       +rho*Y[jcr59]*rate_eval.p_Cr59__He4_V56
       +rho*Y[jti56]*rate_eval.p_Ti56__n_V56
       )

    jac[jv56, jhe4] = (
       -rho*Y[jv56]*rate_eval.He4_V56__n_Mn59
       -rho*Y[jv56]*rate_eval.He4_V56__Mn60
       +rho*Y[jsc52]*rate_eval.He4_Sc52__V56
       +rho*Y[jsc53]*rate_eval.He4_Sc53__n_V56
       )

    jac[jv56, jsc52] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc52__V56
       )

    jac[jv56, jsc53] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc53__n_V56
       )

    jac[jv56, jti55] = (
       +rho*Y[jp]*rate_eval.p_Ti55__V56
       )

    jac[jv56, jti56] = (
       +rate_eval.Ti56__V56__weak__wc12
       +rho*Y[jp]*rate_eval.p_Ti56__n_V56
       )

    jac[jv56, jv55] = (
       +rho*Y[jn]*rate_eval.n_V55__V56
       )

    jac[jv56, jv56] = (
       -rho*Y[jhe4]*rate_eval.He4_V56__n_Mn59
       -rho*Y[jn]*rate_eval.n_V56__V57
       -rho*Y[jp]*rate_eval.p_V56__He4_Ti53
       -rho*Y[jp]*rate_eval.p_V56__Cr57
       -rho*Y[jhe4]*rate_eval.He4_V56__Mn60
       -rho*Y[jp]*rate_eval.p_V56__n_Cr56
       -rate_eval.V56__Cr56__weak__wc12
       )

    jac[jv56, jcr59] = (
       +rho*Y[jp]*rate_eval.p_Cr59__He4_V56
       )

    jac[jv57, jn] = (
       -rho*Y[jv57]*rate_eval.n_V57__V58
       +rho*Y[jv56]*rate_eval.n_V56__V57
       )

    jac[jv57, jp] = (
       -rho*Y[jv57]*rate_eval.p_V57__He4_Ti54
       -rho*Y[jv57]*rate_eval.p_V57__n_Cr57
       -rho*Y[jv57]*rate_eval.p_V57__Cr58
       +rho*Y[jcr60]*rate_eval.p_Cr60__He4_V57
       +rho*Y[jti57]*rate_eval.p_Ti57__n_V57
       +rho*Y[jti56]*rate_eval.p_Ti56__V57
       )

    jac[jv57, jhe4] = (
       -rho*Y[jv57]*rate_eval.He4_V57__n_Mn60
       -rho*Y[jv57]*rate_eval.He4_V57__Mn61
       +rho*Y[jsc54]*rate_eval.He4_Sc54__n_V57
       +rho*Y[jsc53]*rate_eval.He4_Sc53__V57
       )

    jac[jv57, jsc53] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc53__V57
       )

    jac[jv57, jsc54] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc54__n_V57
       )

    jac[jv57, jti56] = (
       +rho*Y[jp]*rate_eval.p_Ti56__V57
       )

    jac[jv57, jti57] = (
       +rho*Y[jp]*rate_eval.p_Ti57__n_V57
       +rate_eval.Ti57__V57__weak__wc12
       )

    jac[jv57, jti58] = (
       +rate_eval.Ti58__n_V57__weak__mp17
       )

    jac[jv57, jv56] = (
       +rho*Y[jn]*rate_eval.n_V56__V57
       )

    jac[jv57, jv57] = (
       -rho*Y[jp]*rate_eval.p_V57__He4_Ti54
       -rho*Y[jp]*rate_eval.p_V57__n_Cr57
       -rho*Y[jhe4]*rate_eval.He4_V57__n_Mn60
       -rho*Y[jhe4]*rate_eval.He4_V57__Mn61
       -rho*Y[jp]*rate_eval.p_V57__Cr58
       -rho*Y[jn]*rate_eval.n_V57__V58
       -rate_eval.V57__Cr57__weak__wc12
       )

    jac[jv57, jcr60] = (
       +rho*Y[jp]*rate_eval.p_Cr60__He4_V57
       )

    jac[jv58, jn] = (
       -rho*Y[jv58]*rate_eval.n_V58__V59
       +rho*Y[jv57]*rate_eval.n_V57__V58
       )

    jac[jv58, jp] = (
       -rho*Y[jv58]*rate_eval.p_V58__He4_Ti55
       -rho*Y[jv58]*rate_eval.p_V58__n_Cr58
       -rho*Y[jv58]*rate_eval.p_V58__Cr59
       +rho*Y[jti58]*rate_eval.p_Ti58__n_V58
       +rho*Y[jcr61]*rate_eval.p_Cr61__He4_V58
       +rho*Y[jti57]*rate_eval.p_Ti57__V58
       )

    jac[jv58, jhe4] = (
       -rho*Y[jv58]*rate_eval.He4_V58__n_Mn61
       -rho*Y[jv58]*rate_eval.He4_V58__Mn62
       +rho*Y[jsc55]*rate_eval.He4_Sc55__n_V58
       +rho*Y[jsc54]*rate_eval.He4_Sc54__V58
       )

    jac[jv58, jsc54] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc54__V58
       )

    jac[jv58, jsc55] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc55__n_V58
       )

    jac[jv58, jti57] = (
       +rho*Y[jp]*rate_eval.p_Ti57__V58
       )

    jac[jv58, jti58] = (
       +rho*Y[jp]*rate_eval.p_Ti58__n_V58
       +rate_eval.Ti58__V58__weak__wc12
       )

    jac[jv58, jv57] = (
       +rho*Y[jn]*rate_eval.n_V57__V58
       )

    jac[jv58, jv58] = (
       -rho*Y[jhe4]*rate_eval.He4_V58__n_Mn61
       -rho*Y[jp]*rate_eval.p_V58__He4_Ti55
       -rho*Y[jp]*rate_eval.p_V58__n_Cr58
       -rho*Y[jhe4]*rate_eval.He4_V58__Mn62
       -rho*Y[jp]*rate_eval.p_V58__Cr59
       -rate_eval.V58__n_Cr57__weak__mp17
       -rate_eval.V58__Cr58__weak__wc17
       -rho*Y[jn]*rate_eval.n_V58__V59
       )

    jac[jv58, jcr61] = (
       +rho*Y[jp]*rate_eval.p_Cr61__He4_V58
       )

    jac[jv59, jn] = (
       -rho*Y[jv59]*rate_eval.n_V59__V60
       +rho*Y[jv58]*rate_eval.n_V58__V59
       )

    jac[jv59, jp] = (
       -rho*Y[jv59]*rate_eval.p_V59__n_Cr59
       -rho*Y[jv59]*rate_eval.p_V59__Cr60
       -rho*Y[jv59]*rate_eval.p_V59__He4_Ti56
       +rho*Y[jcr62]*rate_eval.p_Cr62__He4_V59
       +rho*Y[jti59]*rate_eval.p_Ti59__n_V59
       +rho*Y[jti58]*rate_eval.p_Ti58__V59
       )

    jac[jv59, jhe4] = (
       -rho*Y[jv59]*rate_eval.He4_V59__n_Mn62
       -rho*Y[jv59]*rate_eval.He4_V59__Mn63
       +rho*Y[jsc56]*rate_eval.He4_Sc56__n_V59
       +rho*Y[jsc55]*rate_eval.He4_Sc55__V59
       )

    jac[jv59, jsc55] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc55__V59
       )

    jac[jv59, jsc56] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc56__n_V59
       )

    jac[jv59, jti58] = (
       +rho*Y[jp]*rate_eval.p_Ti58__V59
       )

    jac[jv59, jti59] = (
       +rho*Y[jp]*rate_eval.p_Ti59__n_V59
       +rate_eval.Ti59__V59__weak__wc12
       )

    jac[jv59, jti60] = (
       +rate_eval.Ti60__n_V59__weak__mp17
       )

    jac[jv59, jv58] = (
       +rho*Y[jn]*rate_eval.n_V58__V59
       )

    jac[jv59, jv59] = (
       -rho*Y[jhe4]*rate_eval.He4_V59__n_Mn62
       -rho*Y[jp]*rate_eval.p_V59__n_Cr59
       -rho*Y[jp]*rate_eval.p_V59__Cr60
       -rho*Y[jn]*rate_eval.n_V59__V60
       -rho*Y[jhe4]*rate_eval.He4_V59__Mn63
       -rate_eval.V59__n_Cr58__weak__wc12
       -rate_eval.V59__Cr59__weak__wc12
       -rho*Y[jp]*rate_eval.p_V59__He4_Ti56
       )

    jac[jv59, jcr62] = (
       +rho*Y[jp]*rate_eval.p_Cr62__He4_V59
       )

    jac[jv60, jn] = (
       -rho*Y[jv60]*rate_eval.n_V60__V61
       +rho*Y[jv59]*rate_eval.n_V59__V60
       )

    jac[jv60, jp] = (
       -rho*Y[jv60]*rate_eval.p_V60__He4_Ti57
       -rho*Y[jv60]*rate_eval.p_V60__n_Cr60
       -rho*Y[jv60]*rate_eval.p_V60__Cr61
       +rho*Y[jti60]*rate_eval.p_Ti60__n_V60
       +rho*Y[jti59]*rate_eval.p_Ti59__V60
       +rho*Y[jcr63]*rate_eval.p_Cr63__He4_V60
       )

    jac[jv60, jhe4] = (
       -rho*Y[jv60]*rate_eval.He4_V60__n_Mn63
       -rho*Y[jv60]*rate_eval.He4_V60__Mn64
       +rho*Y[jsc57]*rate_eval.He4_Sc57__n_V60
       +rho*Y[jsc56]*rate_eval.He4_Sc56__V60
       )

    jac[jv60, jsc56] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc56__V60
       )

    jac[jv60, jsc57] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc57__n_V60
       )

    jac[jv60, jti59] = (
       +rho*Y[jp]*rate_eval.p_Ti59__V60
       )

    jac[jv60, jti60] = (
       +rho*Y[jp]*rate_eval.p_Ti60__n_V60
       +rate_eval.Ti60__V60__weak__wc17
       )

    jac[jv60, jti61] = (
       +rate_eval.Ti61__n_V60__weak__mp17
       )

    jac[jv60, jv59] = (
       +rho*Y[jn]*rate_eval.n_V59__V60
       )

    jac[jv60, jv60] = (
       -rho*Y[jp]*rate_eval.p_V60__He4_Ti57
       -rho*Y[jp]*rate_eval.p_V60__n_Cr60
       -rho*Y[jhe4]*rate_eval.He4_V60__n_Mn63
       -rho*Y[jhe4]*rate_eval.He4_V60__Mn64
       -rho*Y[jp]*rate_eval.p_V60__Cr61
       -rate_eval.V60__Cr60__weak__wc17
       -rate_eval.V60__n_Cr59__weak__mp17
       -rho*Y[jn]*rate_eval.n_V60__V61
       )

    jac[jv60, jcr63] = (
       +rho*Y[jp]*rate_eval.p_Cr63__He4_V60
       )

    jac[jv61, jn] = (
       -rho*Y[jv61]*rate_eval.n_V61__V62
       +rho*Y[jv60]*rate_eval.n_V60__V61
       )

    jac[jv61, jp] = (
       -rho*Y[jv61]*rate_eval.p_V61__n_Cr61
       -rho*Y[jv61]*rate_eval.p_V61__He4_Ti58
       -rho*Y[jv61]*rate_eval.p_V61__Cr62
       +rho*Y[jti61]*rate_eval.p_Ti61__n_V61
       +rho*Y[jti60]*rate_eval.p_Ti60__V61
       +rho*Y[jcr64]*rate_eval.p_Cr64__He4_V61
       )

    jac[jv61, jhe4] = (
       -rho*Y[jv61]*rate_eval.He4_V61__n_Mn64
       -rho*Y[jv61]*rate_eval.He4_V61__Mn65
       +rho*Y[jsc58]*rate_eval.He4_Sc58__n_V61
       +rho*Y[jsc57]*rate_eval.He4_Sc57__V61
       )

    jac[jv61, jsc57] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc57__V61
       )

    jac[jv61, jsc58] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc58__n_V61
       )

    jac[jv61, jti60] = (
       +rho*Y[jp]*rate_eval.p_Ti60__V61
       )

    jac[jv61, jti61] = (
       +rho*Y[jp]*rate_eval.p_Ti61__n_V61
       +rate_eval.Ti61__V61__weak__wc17
       )

    jac[jv61, jti62] = (
       +rate_eval.Ti62__n_V61__weak__mp17
       )

    jac[jv61, jti63] = (
       +rate_eval.Ti63__n_n_V61__weak__mp17
       )

    jac[jv61, jti64] = (
       +rate_eval.Ti64__n_n_n_V61__weak__mo03
       )

    jac[jv61, jv60] = (
       +rho*Y[jn]*rate_eval.n_V60__V61
       )

    jac[jv61, jv61] = (
       -rho*Y[jhe4]*rate_eval.He4_V61__n_Mn64
       -rho*Y[jp]*rate_eval.p_V61__n_Cr61
       -rho*Y[jp]*rate_eval.p_V61__He4_Ti58
       -rho*Y[jhe4]*rate_eval.He4_V61__Mn65
       -rho*Y[jn]*rate_eval.n_V61__V62
       -rate_eval.V61__n_Cr60__weak__wc12
       -rho*Y[jp]*rate_eval.p_V61__Cr62
       -rate_eval.V61__Cr61__weak__wc12
       )

    jac[jv61, jcr64] = (
       +rho*Y[jp]*rate_eval.p_Cr64__He4_V61
       )

    jac[jv62, jn] = (
       -rho*Y[jv62]*rate_eval.n_V62__V63
       +rho*Y[jv61]*rate_eval.n_V61__V62
       )

    jac[jv62, jp] = (
       -rho*Y[jv62]*rate_eval.p_V62__n_Cr62
       -rho*Y[jv62]*rate_eval.p_V62__He4_Ti59
       -rho*Y[jv62]*rate_eval.p_V62__Cr63
       +rho*Y[jcr65]*rate_eval.p_Cr65__He4_V62
       +rho*Y[jti62]*rate_eval.p_Ti62__n_V62
       +rho*Y[jti61]*rate_eval.p_Ti61__V62
       )

    jac[jv62, jhe4] = (
       -rho*Y[jv62]*rate_eval.He4_V62__n_Mn65
       -rho*Y[jv62]*rate_eval.He4_V62__Mn66
       +rho*Y[jsc59]*rate_eval.He4_Sc59__n_V62
       +rho*Y[jsc58]*rate_eval.He4_Sc58__V62
       )

    jac[jv62, jsc58] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc58__V62
       )

    jac[jv62, jsc59] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc59__n_V62
       )

    jac[jv62, jti61] = (
       +rho*Y[jp]*rate_eval.p_Ti61__V62
       )

    jac[jv62, jti62] = (
       +rho*Y[jp]*rate_eval.p_Ti62__n_V62
       +rate_eval.Ti62__V62__weak__mo03
       )

    jac[jv62, jti63] = (
       +rate_eval.Ti63__n_V62__weak__mp17
       )

    jac[jv62, jti64] = (
       +rate_eval.Ti64__n_n_V62__weak__mp17
       )

    jac[jv62, jti65] = (
       +rate_eval.Ti65__n_n_n_V62__weak__mo03
       )

    jac[jv62, jv61] = (
       +rho*Y[jn]*rate_eval.n_V61__V62
       )

    jac[jv62, jv62] = (
       -rho*Y[jhe4]*rate_eval.He4_V62__n_Mn65
       -rho*Y[jn]*rate_eval.n_V62__V63
       -rho*Y[jp]*rate_eval.p_V62__n_Cr62
       -rate_eval.V62__n_Cr61__weak__mp17
       -rate_eval.V62__Cr62__weak__wc17
       -rho*Y[jp]*rate_eval.p_V62__He4_Ti59
       -rho*Y[jhe4]*rate_eval.He4_V62__Mn66
       -rho*Y[jp]*rate_eval.p_V62__Cr63
       )

    jac[jv62, jcr65] = (
       +rho*Y[jp]*rate_eval.p_Cr65__He4_V62
       )

    jac[jv63, jn] = (
       -rho*Y[jv63]*rate_eval.n_V63__V64
       +rho*Y[jv62]*rate_eval.n_V62__V63
       )

    jac[jv63, jp] = (
       -rho*Y[jv63]*rate_eval.p_V63__n_Cr63
       -rho*Y[jv63]*rate_eval.p_V63__He4_Ti60
       -rho*Y[jv63]*rate_eval.p_V63__Cr64
       +rho*Y[jcr66]*rate_eval.p_Cr66__He4_V63
       +rho*Y[jti63]*rate_eval.p_Ti63__n_V63
       +rho*Y[jti62]*rate_eval.p_Ti62__V63
       )

    jac[jv63, jhe4] = (
       -rho*Y[jv63]*rate_eval.He4_V63__Mn67
       -rho*Y[jv63]*rate_eval.He4_V63__n_Mn66
       +rho*Y[jsc59]*rate_eval.He4_Sc59__V63
       +rho*Y[jsc60]*rate_eval.He4_Sc60__n_V63
       )

    jac[jv63, jsc59] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc59__V63
       )

    jac[jv63, jsc60] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc60__n_V63
       )

    jac[jv63, jti62] = (
       +rho*Y[jp]*rate_eval.p_Ti62__V63
       )

    jac[jv63, jti63] = (
       +rho*Y[jp]*rate_eval.p_Ti63__n_V63
       +rate_eval.Ti63__V63__weak__mo03
       )

    jac[jv63, jti64] = (
       +rate_eval.Ti64__n_V63__weak__mp17
       )

    jac[jv63, jti65] = (
       +rate_eval.Ti65__n_n_V63__weak__mp17
       )

    jac[jv63, jv62] = (
       +rho*Y[jn]*rate_eval.n_V62__V63
       )

    jac[jv63, jv63] = (
       -rho*Y[jp]*rate_eval.p_V63__n_Cr63
       -rho*Y[jhe4]*rate_eval.He4_V63__Mn67
       -rho*Y[jhe4]*rate_eval.He4_V63__n_Mn66
       -rho*Y[jp]*rate_eval.p_V63__He4_Ti60
       -rho*Y[jp]*rate_eval.p_V63__Cr64
       -rate_eval.V63__n_Cr62__weak__wc12
       -rho*Y[jn]*rate_eval.n_V63__V64
       -rate_eval.V63__Cr63__weak__wc12
       )

    jac[jv63, jcr66] = (
       +rho*Y[jp]*rate_eval.p_Cr66__He4_V63
       )

    jac[jv64, jn] = (
       -rho*Y[jv64]*rate_eval.n_V64__V65
       +rho*Y[jv63]*rate_eval.n_V63__V64
       )

    jac[jv64, jp] = (
       -rho*Y[jv64]*rate_eval.p_V64__He4_Ti61
       -rho*Y[jv64]*rate_eval.p_V64__n_Cr64
       -rho*Y[jv64]*rate_eval.p_V64__Cr65
       +rho*Y[jcr67]*rate_eval.p_Cr67__He4_V64
       +rho*Y[jti63]*rate_eval.p_Ti63__V64
       +rho*Y[jti64]*rate_eval.p_Ti64__n_V64
       )

    jac[jv64, jhe4] = (
       -rho*Y[jv64]*rate_eval.He4_V64__n_Mn67
       -rho*Y[jv64]*rate_eval.He4_V64__Mn68
       +rho*Y[jsc61]*rate_eval.He4_Sc61__n_V64
       +rho*Y[jsc60]*rate_eval.He4_Sc60__V64
       )

    jac[jv64, jsc60] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc60__V64
       )

    jac[jv64, jsc61] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc61__n_V64
       )

    jac[jv64, jti63] = (
       +rho*Y[jp]*rate_eval.p_Ti63__V64
       )

    jac[jv64, jti64] = (
       +rho*Y[jp]*rate_eval.p_Ti64__n_V64
       +rate_eval.Ti64__V64__weak__mo03
       )

    jac[jv64, jti65] = (
       +rate_eval.Ti65__n_V64__weak__mp17
       )

    jac[jv64, jv63] = (
       +rho*Y[jn]*rate_eval.n_V63__V64
       )

    jac[jv64, jv64] = (
       -rho*Y[jhe4]*rate_eval.He4_V64__n_Mn67
       -rho*Y[jp]*rate_eval.p_V64__He4_Ti61
       -rate_eval.V64__n_n_Cr62__weak__mp17
       -rho*Y[jp]*rate_eval.p_V64__n_Cr64
       -rho*Y[jhe4]*rate_eval.He4_V64__Mn68
       -rho*Y[jp]*rate_eval.p_V64__Cr65
       -rho*Y[jn]*rate_eval.n_V64__V65
       -rate_eval.V64__n_Cr63__weak__mp17
       -rate_eval.V64__Cr64__weak__wc17
       )

    jac[jv64, jcr67] = (
       +rho*Y[jp]*rate_eval.p_Cr67__He4_V64
       )

    jac[jv65, jn] = (
       -rho*Y[jv65]*rate_eval.n_V65__V66
       +rho*Y[jv64]*rate_eval.n_V64__V65
       )

    jac[jv65, jp] = (
       -rho*Y[jv65]*rate_eval.p_V65__He4_Ti62
       -rho*Y[jv65]*rate_eval.p_V65__Cr66
       -rho*Y[jv65]*rate_eval.p_V65__n_Cr65
       +rho*Y[jcr68]*rate_eval.p_Cr68__He4_V65
       +rho*Y[jti65]*rate_eval.p_Ti65__n_V65
       +rho*Y[jti64]*rate_eval.p_Ti64__V65
       )

    jac[jv65, jhe4] = (
       -rho*Y[jv65]*rate_eval.He4_V65__Mn69
       -rho*Y[jv65]*rate_eval.He4_V65__n_Mn68
       +rho*Y[jsc62]*rate_eval.He4_Sc62__n_V65
       +rho*Y[jsc61]*rate_eval.He4_Sc61__V65
       )

    jac[jv65, jsc61] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc61__V65
       )

    jac[jv65, jsc62] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc62__n_V65
       )

    jac[jv65, jti64] = (
       +rho*Y[jp]*rate_eval.p_Ti64__V65
       )

    jac[jv65, jti65] = (
       +rho*Y[jp]*rate_eval.p_Ti65__n_V65
       +rate_eval.Ti65__V65__weak__mo03
       )

    jac[jv65, jv64] = (
       +rho*Y[jn]*rate_eval.n_V64__V65
       )

    jac[jv65, jv65] = (
       -rate_eval.V65__n_n_n_Cr62__weak__mo03
       -rho*Y[jp]*rate_eval.p_V65__He4_Ti62
       -rho*Y[jp]*rate_eval.p_V65__Cr66
       -rho*Y[jhe4]*rate_eval.He4_V65__Mn69
       -rate_eval.V65__Cr65__weak__mo03
       -rate_eval.V65__n_Cr64__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_V65__n_Mn68
       -rate_eval.V65__n_n_Cr63__weak__mp17
       -rho*Y[jn]*rate_eval.n_V65__V66
       -rho*Y[jp]*rate_eval.p_V65__n_Cr65
       )

    jac[jv65, jcr68] = (
       +rho*Y[jp]*rate_eval.p_Cr68__He4_V65
       )

    jac[jv66, jn] = (
       -rho*Y[jv66]*rate_eval.n_V66__V67
       +rho*Y[jv65]*rate_eval.n_V65__V66
       )

    jac[jv66, jp] = (
       -rho*Y[jv66]*rate_eval.p_V66__n_Cr66
       -rho*Y[jv66]*rate_eval.p_V66__Cr67
       -rho*Y[jv66]*rate_eval.p_V66__He4_Ti63
       +rho*Y[jcr69]*rate_eval.p_Cr69__He4_V66
       +rho*Y[jti65]*rate_eval.p_Ti65__V66
       )

    jac[jv66, jhe4] = (
       -rho*Y[jv66]*rate_eval.He4_V66__n_Mn69
       -rho*Y[jv66]*rate_eval.He4_V66__Mn70
       +rho*Y[jsc63]*rate_eval.He4_Sc63__n_V66
       +rho*Y[jsc62]*rate_eval.He4_Sc62__V66
       )

    jac[jv66, jsc62] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc62__V66
       )

    jac[jv66, jsc63] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc63__n_V66
       )

    jac[jv66, jti65] = (
       +rho*Y[jp]*rate_eval.p_Ti65__V66
       )

    jac[jv66, jv65] = (
       +rho*Y[jn]*rate_eval.n_V65__V66
       )

    jac[jv66, jv66] = (
       -rate_eval.V66__n_n_n_Cr63__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_V66__n_Mn69
       -rho*Y[jp]*rate_eval.p_V66__n_Cr66
       -rho*Y[jhe4]*rate_eval.He4_V66__Mn70
       -rho*Y[jp]*rate_eval.p_V66__Cr67
       -rate_eval.V66__Cr66__weak__mo03
       -rate_eval.V66__n_Cr65__weak__mp17
       -rho*Y[jn]*rate_eval.n_V66__V67
       -rate_eval.V66__n_n_Cr64__weak__mp17
       -rho*Y[jp]*rate_eval.p_V66__He4_Ti63
       )

    jac[jv66, jcr69] = (
       +rho*Y[jp]*rate_eval.p_Cr69__He4_V66
       )

    jac[jv67, jn] = (
       +rho*Y[jv66]*rate_eval.n_V66__V67
       )

    jac[jv67, jp] = (
       -rho*Y[jv67]*rate_eval.p_V67__n_Cr67
       -rho*Y[jv67]*rate_eval.p_V67__He4_Ti64
       -rho*Y[jv67]*rate_eval.p_V67__Cr68
       +rho*Y[jcr70]*rate_eval.p_Cr70__He4_V67
       )

    jac[jv67, jhe4] = (
       -rho*Y[jv67]*rate_eval.He4_V67__n_Mn70
       -rho*Y[jv67]*rate_eval.He4_V67__Mn71
       +rho*Y[jsc63]*rate_eval.He4_Sc63__V67
       )

    jac[jv67, jsc63] = (
       +rho*Y[jhe4]*rate_eval.He4_Sc63__V67
       )

    jac[jv67, jv66] = (
       +rho*Y[jn]*rate_eval.n_V66__V67
       )

    jac[jv67, jv67] = (
       -rho*Y[jhe4]*rate_eval.He4_V67__n_Mn70
       -rho*Y[jp]*rate_eval.p_V67__n_Cr67
       -rate_eval.V67__n_n_n_Cr64__weak__mo03
       -rho*Y[jp]*rate_eval.p_V67__He4_Ti64
       -rho*Y[jhe4]*rate_eval.He4_V67__Mn71
       -rho*Y[jp]*rate_eval.p_V67__Cr68
       -rate_eval.V67__Cr67__weak__mo03
       -rate_eval.V67__n_Cr66__weak__mp17
       -rate_eval.V67__n_n_Cr65__weak__mp17
       )

    jac[jv67, jcr70] = (
       +rho*Y[jp]*rate_eval.p_Cr70__He4_V67
       )

    jac[jcr41, jn] = (
       -rho*Y[jcr41]*rate_eval.n_Cr41__He4_Ti38
       -rho*Y[jcr41]*rate_eval.n_Cr41__Cr42
       -rho*Y[jcr41]*rate_eval.n_Cr41__p_V41
       )

    jac[jcr41, jp] = (
       +rho*Y[jv40]*rate_eval.p_V40__Cr41
       )

    jac[jcr41, jhe4] = (
       -rho*Y[jcr41]*rate_eval.He4_Cr41__p_Mn44
       -rho*Y[jcr41]*rate_eval.He4_Cr41__Fe45
       +rho*Y[jti37]*rate_eval.He4_Ti37__Cr41
       )

    jac[jcr41, jti37] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti37__Cr41
       )

    jac[jcr41, jv40] = (
       +rho*Y[jp]*rate_eval.p_V40__Cr41
       )

    jac[jcr41, jcr41] = (
       -rho*Y[jn]*rate_eval.n_Cr41__He4_Ti38
       -rho*Y[jn]*rate_eval.n_Cr41__Cr42
       -rho*Y[jhe4]*rate_eval.He4_Cr41__p_Mn44
       -rho*Y[jhe4]*rate_eval.He4_Cr41__Fe45
       -rho*Y[jn]*rate_eval.n_Cr41__p_V41
       -rate_eval.Cr41__V41__weak__bqa_pos_
       )

    jac[jcr42, jn] = (
       -rho*Y[jcr42]*rate_eval.n_Cr42__He4_Ti39
       -rho*Y[jcr42]*rate_eval.n_Cr42__p_V42
       -rho*Y[jcr42]*rate_eval.n_Cr42__Cr43
       +rho*Y[jcr41]*rate_eval.n_Cr41__Cr42
       +rho*Y[jfe45]*rate_eval.n_Fe45__He4_Cr42
       )

    jac[jcr42, jp] = (
       -rho*Y[jcr42]*rate_eval.p_Cr42__Mn43
       +rho*Y[jv41]*rate_eval.p_V41__Cr42
       )

    jac[jcr42, jhe4] = (
       -rho*Y[jcr42]*rate_eval.He4_Cr42__p_Mn45
       -rho*Y[jcr42]*rate_eval.He4_Cr42__Fe46
       +rho*Y[jv39]*rate_eval.He4_V39__p_Cr42
       +rho*Y[jti38]*rate_eval.He4_Ti38__Cr42
       )

    jac[jcr42, jti38] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti38__Cr42
       )

    jac[jcr42, jv39] = (
       +rho*Y[jhe4]*rate_eval.He4_V39__p_Cr42
       )

    jac[jcr42, jv41] = (
       +rho*Y[jp]*rate_eval.p_V41__Cr42
       )

    jac[jcr42, jcr41] = (
       +rho*Y[jn]*rate_eval.n_Cr41__Cr42
       )

    jac[jcr42, jcr42] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr42__p_Mn45
       -rho*Y[jn]*rate_eval.n_Cr42__He4_Ti39
       -rho*Y[jn]*rate_eval.n_Cr42__p_V42
       -rho*Y[jhe4]*rate_eval.He4_Cr42__Fe46
       -rho*Y[jn]*rate_eval.n_Cr42__Cr43
       -rate_eval.Cr42__p_Ti41__weak__wc12
       -rho*Y[jp]*rate_eval.p_Cr42__Mn43
       -rate_eval.Cr42__V42__weak__wc12
       )

    jac[jcr42, jfe45] = (
       +rho*Y[jn]*rate_eval.n_Fe45__He4_Cr42
       )

    jac[jcr43, jn] = (
       -rho*Y[jcr43]*rate_eval.n_Cr43__p_V43
       -rho*Y[jcr43]*rate_eval.n_Cr43__He4_Ti40
       -rho*Y[jcr43]*rate_eval.n_Cr43__Cr44
       +rho*Y[jfe46]*rate_eval.n_Fe46__He4_Cr43
       +rho*Y[jmn43]*rate_eval.n_Mn43__p_Cr43
       +rho*Y[jcr42]*rate_eval.n_Cr42__Cr43
       )

    jac[jcr43, jp] = (
       -rho*Y[jcr43]*rate_eval.p_Cr43__Mn44
       +rho*Y[jv42]*rate_eval.p_V42__Cr43
       )

    jac[jcr43, jhe4] = (
       -rho*Y[jcr43]*rate_eval.He4_Cr43__p_Mn46
       -rho*Y[jcr43]*rate_eval.He4_Cr43__Fe47
       +rho*Y[jv40]*rate_eval.He4_V40__p_Cr43
       +rho*Y[jti39]*rate_eval.He4_Ti39__Cr43
       )

    jac[jcr43, jti39] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti39__Cr43
       )

    jac[jcr43, jv40] = (
       +rho*Y[jhe4]*rate_eval.He4_V40__p_Cr43
       )

    jac[jcr43, jv42] = (
       +rho*Y[jp]*rate_eval.p_V42__Cr43
       )

    jac[jcr43, jcr42] = (
       +rho*Y[jn]*rate_eval.n_Cr42__Cr43
       )

    jac[jcr43, jcr43] = (
       -rate_eval.Cr43__p_p_p_Ca40__weak__wc12
       -rate_eval.Cr43__p_p_Sc41__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Cr43__p_Mn46
       -rho*Y[jn]*rate_eval.n_Cr43__p_V43
       -rho*Y[jn]*rate_eval.n_Cr43__He4_Ti40
       -rho*Y[jhe4]*rate_eval.He4_Cr43__Fe47
       -rho*Y[jn]*rate_eval.n_Cr43__Cr44
       -rate_eval.Cr43__p_Ti42__weak__wc17
       -rho*Y[jp]*rate_eval.p_Cr43__Mn44
       -rate_eval.Cr43__V43__weak__wc12
       )

    jac[jcr43, jmn43] = (
       +rate_eval.Mn43__Cr43__weak__bqa_pos_
       +rho*Y[jn]*rate_eval.n_Mn43__p_Cr43
       )

    jac[jcr43, jfe46] = (
       +rho*Y[jn]*rate_eval.n_Fe46__He4_Cr43
       )

    jac[jcr44, jn] = (
       -rho*Y[jcr44]*rate_eval.n_Cr44__He4_Ti41
       -rho*Y[jcr44]*rate_eval.n_Cr44__Cr45
       -rho*Y[jcr44]*rate_eval.n_Cr44__p_V44
       +rho*Y[jfe47]*rate_eval.n_Fe47__He4_Cr44
       +rho*Y[jcr43]*rate_eval.n_Cr43__Cr44
       +rho*Y[jmn44]*rate_eval.n_Mn44__p_Cr44
       )

    jac[jcr44, jp] = (
       -rho*Y[jcr44]*rate_eval.p_Cr44__Mn45
       +rho*Y[jv43]*rate_eval.p_V43__Cr44
       )

    jac[jcr44, jhe4] = (
       -rho*Y[jcr44]*rate_eval.He4_Cr44__p_Mn47
       -rho*Y[jcr44]*rate_eval.He4_Cr44__Fe48
       +rho*Y[jti40]*rate_eval.He4_Ti40__Cr44
       +rho*Y[jv41]*rate_eval.He4_V41__p_Cr44
       )

    jac[jcr44, jti40] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti40__Cr44
       )

    jac[jcr44, jv41] = (
       +rho*Y[jhe4]*rate_eval.He4_V41__p_Cr44
       )

    jac[jcr44, jv43] = (
       +rho*Y[jp]*rate_eval.p_V43__Cr44
       )

    jac[jcr44, jcr43] = (
       +rho*Y[jn]*rate_eval.n_Cr43__Cr44
       )

    jac[jcr44, jcr44] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr44__p_Mn47
       -rho*Y[jn]*rate_eval.n_Cr44__He4_Ti41
       -rate_eval.Cr44__V44__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Cr44__Fe48
       -rho*Y[jn]*rate_eval.n_Cr44__Cr45
       -rho*Y[jn]*rate_eval.n_Cr44__p_V44
       -rate_eval.Cr44__p_Ti43__weak__wc12
       -rho*Y[jp]*rate_eval.p_Cr44__Mn45
       )

    jac[jcr44, jmn44] = (
       +rho*Y[jn]*rate_eval.n_Mn44__p_Cr44
       +rate_eval.Mn44__Cr44__weak__bqa_pos_
       )

    jac[jcr44, jfe45] = (
       +rate_eval.Fe45__p_Cr44__weak__wc17
       )

    jac[jcr44, jfe47] = (
       +rho*Y[jn]*rate_eval.n_Fe47__He4_Cr44
       )

    jac[jcr45, jn] = (
       -rho*Y[jcr45]*rate_eval.n_Cr45__He4_Ti42
       -rho*Y[jcr45]*rate_eval.n_Cr45__Cr46
       -rho*Y[jcr45]*rate_eval.n_Cr45__p_V45
       +rho*Y[jmn45]*rate_eval.n_Mn45__p_Cr45
       +rho*Y[jfe48]*rate_eval.n_Fe48__He4_Cr45
       +rho*Y[jcr44]*rate_eval.n_Cr44__Cr45
       )

    jac[jcr45, jp] = (
       -rho*Y[jcr45]*rate_eval.p_Cr45__Mn46
       +rho*Y[jv44]*rate_eval.p_V44__Cr45
       )

    jac[jcr45, jhe4] = (
       -rho*Y[jcr45]*rate_eval.He4_Cr45__p_Mn48
       -rho*Y[jcr45]*rate_eval.He4_Cr45__Fe49
       +rho*Y[jv42]*rate_eval.He4_V42__p_Cr45
       +rho*Y[jti41]*rate_eval.He4_Ti41__Cr45
       )

    jac[jcr45, jti41] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti41__Cr45
       )

    jac[jcr45, jv42] = (
       +rho*Y[jhe4]*rate_eval.He4_V42__p_Cr45
       )

    jac[jcr45, jv44] = (
       +rho*Y[jp]*rate_eval.p_V44__Cr45
       )

    jac[jcr45, jcr44] = (
       +rho*Y[jn]*rate_eval.n_Cr44__Cr45
       )

    jac[jcr45, jcr45] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr45__p_Mn48
       -rho*Y[jn]*rate_eval.n_Cr45__He4_Ti42
       -rho*Y[jhe4]*rate_eval.He4_Cr45__Fe49
       -rho*Y[jn]*rate_eval.n_Cr45__Cr46
       -rho*Y[jp]*rate_eval.p_Cr45__Mn46
       -rate_eval.Cr45__p_Ti44__weak__wc12
       -rho*Y[jn]*rate_eval.n_Cr45__p_V45
       -rate_eval.Cr45__V45__weak__wc12
       )

    jac[jcr45, jmn45] = (
       +rho*Y[jn]*rate_eval.n_Mn45__p_Cr45
       +rate_eval.Mn45__Cr45__weak__bqa_pos_
       )

    jac[jcr45, jfe46] = (
       +rate_eval.Fe46__p_Cr45__weak__wc12
       )

    jac[jcr45, jfe48] = (
       +rho*Y[jn]*rate_eval.n_Fe48__He4_Cr45
       )

    jac[jcr46, jn] = (
       -rho*Y[jcr46]*rate_eval.n_Cr46__He4_Ti43
       -rho*Y[jcr46]*rate_eval.n_Cr46__p_V46
       -rho*Y[jcr46]*rate_eval.n_Cr46__Cr47
       +rho*Y[jfe49]*rate_eval.n_Fe49__He4_Cr46
       +rho*Y[jmn46]*rate_eval.n_Mn46__p_Cr46
       +rho*Y[jcr45]*rate_eval.n_Cr45__Cr46
       )

    jac[jcr46, jp] = (
       -rho*Y[jcr46]*rate_eval.p_Cr46__Mn47
       +rho*Y[jv45]*rate_eval.p_V45__Cr46
       )

    jac[jcr46, jhe4] = (
       -rho*Y[jcr46]*rate_eval.He4_Cr46__p_Mn49
       -rho*Y[jcr46]*rate_eval.He4_Cr46__Fe50
       +rho*Y[jv43]*rate_eval.He4_V43__p_Cr46
       +rho*Y[jti42]*rate_eval.He4_Ti42__Cr46
       )

    jac[jcr46, jti42] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti42__Cr46
       )

    jac[jcr46, jv43] = (
       +rho*Y[jhe4]*rate_eval.He4_V43__p_Cr46
       )

    jac[jcr46, jv45] = (
       +rho*Y[jp]*rate_eval.p_V45__Cr46
       )

    jac[jcr46, jcr45] = (
       +rho*Y[jn]*rate_eval.n_Cr45__Cr46
       )

    jac[jcr46, jcr46] = (
       -rho*Y[jn]*rate_eval.n_Cr46__He4_Ti43
       -rho*Y[jn]*rate_eval.n_Cr46__p_V46
       -rho*Y[jhe4]*rate_eval.He4_Cr46__p_Mn49
       -rho*Y[jhe4]*rate_eval.He4_Cr46__Fe50
       -rho*Y[jp]*rate_eval.p_Cr46__Mn47
       -rho*Y[jn]*rate_eval.n_Cr46__Cr47
       -rate_eval.Cr46__V46__weak__wc12
       )

    jac[jcr46, jmn46] = (
       +rho*Y[jn]*rate_eval.n_Mn46__p_Cr46
       +rate_eval.Mn46__Cr46__weak__wc12
       )

    jac[jcr46, jfe47] = (
       +rate_eval.Fe47__p_Cr46__weak__wc12
       )

    jac[jcr46, jfe49] = (
       +rho*Y[jn]*rate_eval.n_Fe49__He4_Cr46
       )

    jac[jcr47, jn] = (
       -rho*Y[jcr47]*rate_eval.n_Cr47__He4_Ti44
       -rho*Y[jcr47]*rate_eval.n_Cr47__p_V47
       -rho*Y[jcr47]*rate_eval.n_Cr47__Cr48
       +rho*Y[jfe50]*rate_eval.n_Fe50__He4_Cr47
       +rho*Y[jmn47]*rate_eval.n_Mn47__p_Cr47
       +rho*Y[jcr46]*rate_eval.n_Cr46__Cr47
       )

    jac[jcr47, jp] = (
       -rho*Y[jcr47]*rate_eval.p_Cr47__Mn48
       +rho*Y[jv46]*rate_eval.p_V46__Cr47
       )

    jac[jcr47, jhe4] = (
       -rho*Y[jcr47]*rate_eval.He4_Cr47__p_Mn50
       -rho*Y[jcr47]*rate_eval.He4_Cr47__Fe51
       +rho*Y[jti43]*rate_eval.He4_Ti43__Cr47
       +rho*Y[jv44]*rate_eval.He4_V44__p_Cr47
       )

    jac[jcr47, jti43] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti43__Cr47
       )

    jac[jcr47, jv44] = (
       +rho*Y[jhe4]*rate_eval.He4_V44__p_Cr47
       )

    jac[jcr47, jv46] = (
       +rho*Y[jp]*rate_eval.p_V46__Cr47
       )

    jac[jcr47, jcr46] = (
       +rho*Y[jn]*rate_eval.n_Cr46__Cr47
       )

    jac[jcr47, jcr47] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr47__p_Mn50
       -rho*Y[jn]*rate_eval.n_Cr47__He4_Ti44
       -rho*Y[jn]*rate_eval.n_Cr47__p_V47
       -rate_eval.Cr47__V47__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Cr47__Fe51
       -rho*Y[jp]*rate_eval.p_Cr47__Mn48
       -rho*Y[jn]*rate_eval.n_Cr47__Cr48
       )

    jac[jcr47, jmn47] = (
       +rho*Y[jn]*rate_eval.n_Mn47__p_Cr47
       +rate_eval.Mn47__Cr47__weak__wc17
       )

    jac[jcr47, jfe48] = (
       +rate_eval.Fe48__p_Cr47__weak__wc12
       )

    jac[jcr47, jfe50] = (
       +rho*Y[jn]*rate_eval.n_Fe50__He4_Cr47
       )

    jac[jcr48, jn] = (
       -rho*Y[jcr48]*rate_eval.n_Cr48__p_V48
       -rho*Y[jcr48]*rate_eval.n_Cr48__Cr49
       -rho*Y[jcr48]*rate_eval.n_Cr48__He4_Ti45
       +rho*Y[jfe51]*rate_eval.n_Fe51__He4_Cr48
       +rho*Y[jcr47]*rate_eval.n_Cr47__Cr48
       +rho*Y[jmn48]*rate_eval.n_Mn48__p_Cr48
       )

    jac[jcr48, jp] = (
       -rho*Y[jcr48]*rate_eval.p_Cr48__Mn49
       +rho*Y[jv47]*rate_eval.p_V47__Cr48
       )

    jac[jcr48, jhe4] = (
       -rho*Y[jcr48]*rate_eval.He4_Cr48__p_Mn51
       -rho*Y[jcr48]*rate_eval.He4_Cr48__Fe52
       +rho*Y[jti44]*rate_eval.He4_Ti44__Cr48
       +rho*Y[jv45]*rate_eval.He4_V45__p_Cr48
       )

    jac[jcr48, jti44] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti44__Cr48
       )

    jac[jcr48, jv45] = (
       +rho*Y[jhe4]*rate_eval.He4_V45__p_Cr48
       )

    jac[jcr48, jv47] = (
       +rho*Y[jp]*rate_eval.p_V47__Cr48
       )

    jac[jcr48, jcr47] = (
       +rho*Y[jn]*rate_eval.n_Cr47__Cr48
       )

    jac[jcr48, jcr48] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr48__p_Mn51
       -rho*Y[jn]*rate_eval.n_Cr48__p_V48
       -rho*Y[jhe4]*rate_eval.He4_Cr48__Fe52
       -rho*Y[jn]*rate_eval.n_Cr48__Cr49
       -rate_eval.Cr48__V48__weak__wc12
       -rho*Y[jp]*rate_eval.p_Cr48__Mn49
       -rho*Y[jn]*rate_eval.n_Cr48__He4_Ti45
       )

    jac[jcr48, jmn48] = (
       +rate_eval.Mn48__Cr48__weak__wc12
       +rho*Y[jn]*rate_eval.n_Mn48__p_Cr48
       )

    jac[jcr48, jfe49] = (
       +rate_eval.Fe49__p_Cr48__weak__wc12
       )

    jac[jcr48, jfe51] = (
       +rho*Y[jn]*rate_eval.n_Fe51__He4_Cr48
       )

    jac[jcr49, jn] = (
       -rho*Y[jcr49]*rate_eval.n_Cr49__p_V49
       -rho*Y[jcr49]*rate_eval.n_Cr49__He4_Ti46
       -rho*Y[jcr49]*rate_eval.n_Cr49__Cr50
       +rho*Y[jfe52]*rate_eval.n_Fe52__He4_Cr49
       +rho*Y[jmn49]*rate_eval.n_Mn49__p_Cr49
       +rho*Y[jcr48]*rate_eval.n_Cr48__Cr49
       )

    jac[jcr49, jp] = (
       -rho*Y[jcr49]*rate_eval.p_Cr49__Mn50
       +rho*Y[jv48]*rate_eval.p_V48__Cr49
       )

    jac[jcr49, jhe4] = (
       -rho*Y[jcr49]*rate_eval.He4_Cr49__p_Mn52
       -rho*Y[jcr49]*rate_eval.He4_Cr49__Fe53
       +rho*Y[jv46]*rate_eval.He4_V46__p_Cr49
       +rho*Y[jti45]*rate_eval.He4_Ti45__Cr49
       )

    jac[jcr49, jti45] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti45__Cr49
       )

    jac[jcr49, jv46] = (
       +rho*Y[jhe4]*rate_eval.He4_V46__p_Cr49
       )

    jac[jcr49, jv48] = (
       +rho*Y[jp]*rate_eval.p_V48__Cr49
       )

    jac[jcr49, jcr48] = (
       +rho*Y[jn]*rate_eval.n_Cr48__Cr49
       )

    jac[jcr49, jcr49] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr49__p_Mn52
       -rho*Y[jn]*rate_eval.n_Cr49__p_V49
       -rho*Y[jp]*rate_eval.p_Cr49__Mn50
       -rho*Y[jhe4]*rate_eval.He4_Cr49__Fe53
       -rho*Y[jn]*rate_eval.n_Cr49__He4_Ti46
       -rho*Y[jn]*rate_eval.n_Cr49__Cr50
       -rate_eval.Cr49__V49__weak__wc12
       )

    jac[jcr49, jmn49] = (
       +rho*Y[jn]*rate_eval.n_Mn49__p_Cr49
       +rate_eval.Mn49__Cr49__weak__wc12
       )

    jac[jcr49, jfe52] = (
       +rho*Y[jn]*rate_eval.n_Fe52__He4_Cr49
       )

    jac[jcr50, jn] = (
       -rho*Y[jcr50]*rate_eval.n_Cr50__He4_Ti47
       -rho*Y[jcr50]*rate_eval.n_Cr50__Cr51
       +rho*Y[jfe53]*rate_eval.n_Fe53__He4_Cr50
       +rho*Y[jmn50]*rate_eval.n_Mn50__p_Cr50
       +rho*Y[jcr49]*rate_eval.n_Cr49__Cr50
       )

    jac[jcr50, jp] = (
       -rho*Y[jcr50]*rate_eval.p_Cr50__Mn51
       +rho*Y[jmn53]*rate_eval.p_Mn53__He4_Cr50
       +rho*Y[jv50]*rate_eval.p_V50__n_Cr50
       +rho*Y[jv49]*rate_eval.p_V49__Cr50
       )

    jac[jcr50, jhe4] = (
       -rho*Y[jcr50]*rate_eval.He4_Cr50__Fe54
       +rho*Y[jv47]*rate_eval.He4_V47__p_Cr50
       +rho*Y[jti46]*rate_eval.He4_Ti46__Cr50
       )

    jac[jcr50, jti46] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti46__Cr50
       )

    jac[jcr50, jv47] = (
       +rho*Y[jhe4]*rate_eval.He4_V47__p_Cr50
       )

    jac[jcr50, jv49] = (
       +rho*Y[jp]*rate_eval.p_V49__Cr50
       )

    jac[jcr50, jv50] = (
       +rho*Y[jp]*rate_eval.p_V50__n_Cr50
       )

    jac[jcr50, jcr49] = (
       +rho*Y[jn]*rate_eval.n_Cr49__Cr50
       )

    jac[jcr50, jcr50] = (
       -rho*Y[jn]*rate_eval.n_Cr50__He4_Ti47
       -rho*Y[jp]*rate_eval.p_Cr50__Mn51
       -rho*Y[jhe4]*rate_eval.He4_Cr50__Fe54
       -rho*Y[jn]*rate_eval.n_Cr50__Cr51
       )

    jac[jcr50, jmn50] = (
       +rho*Y[jn]*rate_eval.n_Mn50__p_Cr50
       +rate_eval.Mn50__Cr50__weak__wc12
       )

    jac[jcr50, jmn53] = (
       +rho*Y[jp]*rate_eval.p_Mn53__He4_Cr50
       )

    jac[jcr50, jfe53] = (
       +rho*Y[jn]*rate_eval.n_Fe53__He4_Cr50
       )

    jac[jcr51, jn] = (
       -rho*Y[jcr51]*rate_eval.n_Cr51__He4_Ti48
       -rho*Y[jcr51]*rate_eval.n_Cr51__Cr52
       -rho*Y[jcr51]*rate_eval.n_Cr51__p_V51
       +rho*Y[jmn51]*rate_eval.n_Mn51__p_Cr51
       +rho*Y[jfe54]*rate_eval.n_Fe54__He4_Cr51
       +rho*Y[jcr50]*rate_eval.n_Cr50__Cr51
       )

    jac[jcr51, jp] = (
       -rho*Y[jcr51]*rate_eval.p_Cr51__Mn52
       +rho*Y[jmn54]*rate_eval.p_Mn54__He4_Cr51
       +rho*Y[jv50]*rate_eval.p_V50__Cr51
       )

    jac[jcr51, jhe4] = (
       -rho*Y[jcr51]*rate_eval.He4_Cr51__Fe55
       +rho*Y[jv48]*rate_eval.He4_V48__p_Cr51
       +rho*Y[jti47]*rate_eval.He4_Ti47__Cr51
       )

    jac[jcr51, jti47] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti47__Cr51
       )

    jac[jcr51, jv48] = (
       +rho*Y[jhe4]*rate_eval.He4_V48__p_Cr51
       )

    jac[jcr51, jv50] = (
       +rho*Y[jp]*rate_eval.p_V50__Cr51
       )

    jac[jcr51, jcr50] = (
       +rho*Y[jn]*rate_eval.n_Cr50__Cr51
       )

    jac[jcr51, jcr51] = (
       -rho*Y[jn]*rate_eval.n_Cr51__He4_Ti48
       -rho*Y[jp]*rate_eval.p_Cr51__Mn52
       -rho*Y[jn]*rate_eval.n_Cr51__Cr52
       -rho*Y[jhe4]*rate_eval.He4_Cr51__Fe55
       -rho*Y[jn]*rate_eval.n_Cr51__p_V51
       -rate_eval.Cr51__V51__weak__wc12
       )

    jac[jcr51, jmn51] = (
       +rho*Y[jn]*rate_eval.n_Mn51__p_Cr51
       +rate_eval.Mn51__Cr51__weak__wc12
       )

    jac[jcr51, jmn54] = (
       +rho*Y[jp]*rate_eval.p_Mn54__He4_Cr51
       )

    jac[jcr51, jfe54] = (
       +rho*Y[jn]*rate_eval.n_Fe54__He4_Cr51
       )

    jac[jcr52, jn] = (
       -rho*Y[jcr52]*rate_eval.n_Cr52__Cr53
       +rho*Y[jmn52]*rate_eval.n_Mn52__p_Cr52
       +rho*Y[jfe55]*rate_eval.n_Fe55__He4_Cr52
       +rho*Y[jcr51]*rate_eval.n_Cr51__Cr52
       )

    jac[jcr52, jp] = (
       -rho*Y[jcr52]*rate_eval.p_Cr52__Mn53
       +rho*Y[jmn55]*rate_eval.p_Mn55__He4_Cr52
       +rho*Y[jv52]*rate_eval.p_V52__n_Cr52
       +rho*Y[jv51]*rate_eval.p_V51__Cr52
       )

    jac[jcr52, jhe4] = (
       -rho*Y[jcr52]*rate_eval.He4_Cr52__Fe56
       +rho*Y[jv49]*rate_eval.He4_V49__p_Cr52
       +rho*Y[jti48]*rate_eval.He4_Ti48__Cr52
       +rho*Y[jti49]*rate_eval.He4_Ti49__n_Cr52
       )

    jac[jcr52, jti48] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti48__Cr52
       )

    jac[jcr52, jti49] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti49__n_Cr52
       )

    jac[jcr52, jv49] = (
       +rho*Y[jhe4]*rate_eval.He4_V49__p_Cr52
       )

    jac[jcr52, jv51] = (
       +rho*Y[jp]*rate_eval.p_V51__Cr52
       )

    jac[jcr52, jv52] = (
       +rho*Y[jp]*rate_eval.p_V52__n_Cr52
       +rate_eval.V52__Cr52__weak__wc12
       )

    jac[jcr52, jcr51] = (
       +rho*Y[jn]*rate_eval.n_Cr51__Cr52
       )

    jac[jcr52, jcr52] = (
       -rho*Y[jp]*rate_eval.p_Cr52__Mn53
       -rho*Y[jn]*rate_eval.n_Cr52__Cr53
       -rho*Y[jhe4]*rate_eval.He4_Cr52__Fe56
       )

    jac[jcr52, jmn52] = (
       +rho*Y[jn]*rate_eval.n_Mn52__p_Cr52
       +rate_eval.Mn52__Cr52__weak__wc12
       )

    jac[jcr52, jmn55] = (
       +rho*Y[jp]*rate_eval.p_Mn55__He4_Cr52
       )

    jac[jcr52, jfe55] = (
       +rho*Y[jn]*rate_eval.n_Fe55__He4_Cr52
       )

    jac[jcr53, jn] = (
       -rho*Y[jcr53]*rate_eval.n_Cr53__He4_Ti50
       -rho*Y[jcr53]*rate_eval.n_Cr53__Cr54
       +rho*Y[jfe56]*rate_eval.n_Fe56__He4_Cr53
       +rho*Y[jmn53]*rate_eval.n_Mn53__p_Cr53
       +rho*Y[jcr52]*rate_eval.n_Cr52__Cr53
       )

    jac[jcr53, jp] = (
       -rho*Y[jcr53]*rate_eval.p_Cr53__Mn54
       +rho*Y[jmn56]*rate_eval.p_Mn56__He4_Cr53
       +rho*Y[jv53]*rate_eval.p_V53__n_Cr53
       +rho*Y[jv52]*rate_eval.p_V52__Cr53
       )

    jac[jcr53, jhe4] = (
       -rho*Y[jcr53]*rate_eval.He4_Cr53__Fe57
       +rho*Y[jv50]*rate_eval.He4_V50__p_Cr53
       +rho*Y[jti49]*rate_eval.He4_Ti49__Cr53
       )

    jac[jcr53, jti49] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti49__Cr53
       )

    jac[jcr53, jv50] = (
       +rho*Y[jhe4]*rate_eval.He4_V50__p_Cr53
       )

    jac[jcr53, jv52] = (
       +rho*Y[jp]*rate_eval.p_V52__Cr53
       )

    jac[jcr53, jv53] = (
       +rho*Y[jp]*rate_eval.p_V53__n_Cr53
       +rate_eval.V53__Cr53__weak__wc12
       )

    jac[jcr53, jcr52] = (
       +rho*Y[jn]*rate_eval.n_Cr52__Cr53
       )

    jac[jcr53, jcr53] = (
       -rho*Y[jn]*rate_eval.n_Cr53__He4_Ti50
       -rho*Y[jhe4]*rate_eval.He4_Cr53__Fe57
       -rho*Y[jp]*rate_eval.p_Cr53__Mn54
       -rho*Y[jn]*rate_eval.n_Cr53__Cr54
       )

    jac[jcr53, jmn53] = (
       +rho*Y[jn]*rate_eval.n_Mn53__p_Cr53
       +rate_eval.Mn53__Cr53__weak__wc12
       )

    jac[jcr53, jmn56] = (
       +rho*Y[jp]*rate_eval.p_Mn56__He4_Cr53
       )

    jac[jcr53, jfe56] = (
       +rho*Y[jn]*rate_eval.n_Fe56__He4_Cr53
       )

    jac[jcr54, jn] = (
       -rho*Y[jcr54]*rate_eval.n_Cr54__Cr55
       +rho*Y[jmn54]*rate_eval.n_Mn54__p_Cr54
       +rho*Y[jcr53]*rate_eval.n_Cr53__Cr54
       +rho*Y[jfe57]*rate_eval.n_Fe57__He4_Cr54
       )

    jac[jcr54, jp] = (
       -rho*Y[jcr54]*rate_eval.p_Cr54__He4_V51
       -rho*Y[jcr54]*rate_eval.p_Cr54__Mn55
       +rho*Y[jv54]*rate_eval.p_V54__n_Cr54
       +rho*Y[jv53]*rate_eval.p_V53__Cr54
       +rho*Y[jmn57]*rate_eval.p_Mn57__He4_Cr54
       )

    jac[jcr54, jhe4] = (
       -rho*Y[jcr54]*rate_eval.He4_Cr54__Fe58
       +rho*Y[jti51]*rate_eval.He4_Ti51__n_Cr54
       +rho*Y[jti50]*rate_eval.He4_Ti50__Cr54
       )

    jac[jcr54, jti50] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti50__Cr54
       )

    jac[jcr54, jti51] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti51__n_Cr54
       )

    jac[jcr54, jv53] = (
       +rho*Y[jp]*rate_eval.p_V53__Cr54
       )

    jac[jcr54, jv54] = (
       +rho*Y[jp]*rate_eval.p_V54__n_Cr54
       +rate_eval.V54__Cr54__weak__wc12
       )

    jac[jcr54, jcr53] = (
       +rho*Y[jn]*rate_eval.n_Cr53__Cr54
       )

    jac[jcr54, jcr54] = (
       -rho*Y[jp]*rate_eval.p_Cr54__He4_V51
       -rho*Y[jhe4]*rate_eval.He4_Cr54__Fe58
       -rho*Y[jp]*rate_eval.p_Cr54__Mn55
       -rho*Y[jn]*rate_eval.n_Cr54__Cr55
       )

    jac[jcr54, jmn54] = (
       +rate_eval.Mn54__Cr54__weak__wc12
       +rho*Y[jn]*rate_eval.n_Mn54__p_Cr54
       )

    jac[jcr54, jmn57] = (
       +rho*Y[jp]*rate_eval.p_Mn57__He4_Cr54
       )

    jac[jcr54, jfe57] = (
       +rho*Y[jn]*rate_eval.n_Fe57__He4_Cr54
       )

    jac[jcr55, jn] = (
       -rho*Y[jcr55]*rate_eval.n_Cr55__He4_Ti52
       -rho*Y[jcr55]*rate_eval.n_Cr55__Cr56
       +rho*Y[jcr54]*rate_eval.n_Cr54__Cr55
       )

    jac[jcr55, jp] = (
       -rho*Y[jcr55]*rate_eval.p_Cr55__n_Mn55
       -rho*Y[jcr55]*rate_eval.p_Cr55__He4_V52
       -rho*Y[jcr55]*rate_eval.p_Cr55__Mn56
       +rho*Y[jv55]*rate_eval.p_V55__n_Cr55
       +rho*Y[jv54]*rate_eval.p_V54__Cr55
       +rho*Y[jmn58]*rate_eval.p_Mn58__He4_Cr55
       )

    jac[jcr55, jhe4] = (
       -rho*Y[jcr55]*rate_eval.He4_Cr55__n_Fe58
       -rho*Y[jcr55]*rate_eval.He4_Cr55__Fe59
       +rho*Y[jti51]*rate_eval.He4_Ti51__Cr55
       )

    jac[jcr55, jti51] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti51__Cr55
       )

    jac[jcr55, jv54] = (
       +rho*Y[jp]*rate_eval.p_V54__Cr55
       )

    jac[jcr55, jv55] = (
       +rho*Y[jp]*rate_eval.p_V55__n_Cr55
       +rate_eval.V55__Cr55__weak__wc12
       )

    jac[jcr55, jcr54] = (
       +rho*Y[jn]*rate_eval.n_Cr54__Cr55
       )

    jac[jcr55, jcr55] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr55__n_Fe58
       -rho*Y[jn]*rate_eval.n_Cr55__He4_Ti52
       -rho*Y[jp]*rate_eval.p_Cr55__n_Mn55
       -rho*Y[jp]*rate_eval.p_Cr55__He4_V52
       -rho*Y[jn]*rate_eval.n_Cr55__Cr56
       -rho*Y[jhe4]*rate_eval.He4_Cr55__Fe59
       -rho*Y[jp]*rate_eval.p_Cr55__Mn56
       -rate_eval.Cr55__Mn55__weak__wc12
       )

    jac[jcr55, jmn58] = (
       +rho*Y[jp]*rate_eval.p_Mn58__He4_Cr55
       )

    jac[jcr56, jn] = (
       -rho*Y[jcr56]*rate_eval.n_Cr56__Cr57
       +rho*Y[jcr55]*rate_eval.n_Cr55__Cr56
       +rho*Y[jfe59]*rate_eval.n_Fe59__He4_Cr56
       )

    jac[jcr56, jp] = (
       -rho*Y[jcr56]*rate_eval.p_Cr56__n_Mn56
       -rho*Y[jcr56]*rate_eval.p_Cr56__He4_V53
       -rho*Y[jcr56]*rate_eval.p_Cr56__Mn57
       +rho*Y[jmn59]*rate_eval.p_Mn59__He4_Cr56
       +rho*Y[jv55]*rate_eval.p_V55__Cr56
       +rho*Y[jv56]*rate_eval.p_V56__n_Cr56
       )

    jac[jcr56, jhe4] = (
       -rho*Y[jcr56]*rate_eval.He4_Cr56__Fe60
       +rho*Y[jti53]*rate_eval.He4_Ti53__n_Cr56
       +rho*Y[jti52]*rate_eval.He4_Ti52__Cr56
       )

    jac[jcr56, jti52] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti52__Cr56
       )

    jac[jcr56, jti53] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti53__n_Cr56
       )

    jac[jcr56, jv55] = (
       +rho*Y[jp]*rate_eval.p_V55__Cr56
       )

    jac[jcr56, jv56] = (
       +rho*Y[jp]*rate_eval.p_V56__n_Cr56
       +rate_eval.V56__Cr56__weak__wc12
       )

    jac[jcr56, jcr55] = (
       +rho*Y[jn]*rate_eval.n_Cr55__Cr56
       )

    jac[jcr56, jcr56] = (
       -rho*Y[jp]*rate_eval.p_Cr56__n_Mn56
       -rho*Y[jp]*rate_eval.p_Cr56__He4_V53
       -rho*Y[jp]*rate_eval.p_Cr56__Mn57
       -rho*Y[jn]*rate_eval.n_Cr56__Cr57
       -rho*Y[jhe4]*rate_eval.He4_Cr56__Fe60
       -rate_eval.Cr56__Mn56__weak__wc12
       )

    jac[jcr56, jmn59] = (
       +rho*Y[jp]*rate_eval.p_Mn59__He4_Cr56
       )

    jac[jcr56, jfe59] = (
       +rho*Y[jn]*rate_eval.n_Fe59__He4_Cr56
       )

    jac[jcr57, jn] = (
       -rho*Y[jcr57]*rate_eval.n_Cr57__Cr58
       +rho*Y[jcr56]*rate_eval.n_Cr56__Cr57
       )

    jac[jcr57, jp] = (
       -rho*Y[jcr57]*rate_eval.p_Cr57__n_Mn57
       -rho*Y[jcr57]*rate_eval.p_Cr57__He4_V54
       -rho*Y[jcr57]*rate_eval.p_Cr57__Mn58
       +rho*Y[jmn60]*rate_eval.p_Mn60__He4_Cr57
       +rho*Y[jv57]*rate_eval.p_V57__n_Cr57
       +rho*Y[jv56]*rate_eval.p_V56__Cr57
       )

    jac[jcr57, jhe4] = (
       -rho*Y[jcr57]*rate_eval.He4_Cr57__n_Fe60
       -rho*Y[jcr57]*rate_eval.He4_Cr57__Fe61
       +rho*Y[jti54]*rate_eval.He4_Ti54__n_Cr57
       +rho*Y[jti53]*rate_eval.He4_Ti53__Cr57
       )

    jac[jcr57, jti53] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti53__Cr57
       )

    jac[jcr57, jti54] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti54__n_Cr57
       )

    jac[jcr57, jv56] = (
       +rho*Y[jp]*rate_eval.p_V56__Cr57
       )

    jac[jcr57, jv57] = (
       +rho*Y[jp]*rate_eval.p_V57__n_Cr57
       +rate_eval.V57__Cr57__weak__wc12
       )

    jac[jcr57, jv58] = (
       +rate_eval.V58__n_Cr57__weak__mp17
       )

    jac[jcr57, jcr56] = (
       +rho*Y[jn]*rate_eval.n_Cr56__Cr57
       )

    jac[jcr57, jcr57] = (
       -rho*Y[jp]*rate_eval.p_Cr57__n_Mn57
       -rho*Y[jp]*rate_eval.p_Cr57__He4_V54
       -rho*Y[jhe4]*rate_eval.He4_Cr57__n_Fe60
       -rho*Y[jn]*rate_eval.n_Cr57__Cr58
       -rho*Y[jhe4]*rate_eval.He4_Cr57__Fe61
       -rho*Y[jp]*rate_eval.p_Cr57__Mn58
       -rate_eval.Cr57__Mn57__weak__wc12
       )

    jac[jcr57, jmn60] = (
       +rho*Y[jp]*rate_eval.p_Mn60__He4_Cr57
       )

    jac[jcr58, jn] = (
       -rho*Y[jcr58]*rate_eval.n_Cr58__Cr59
       +rho*Y[jcr57]*rate_eval.n_Cr57__Cr58
       )

    jac[jcr58, jp] = (
       -rho*Y[jcr58]*rate_eval.p_Cr58__Mn59
       -rho*Y[jcr58]*rate_eval.p_Cr58__n_Mn58
       -rho*Y[jcr58]*rate_eval.p_Cr58__He4_V55
       +rho*Y[jv58]*rate_eval.p_V58__n_Cr58
       +rho*Y[jv57]*rate_eval.p_V57__Cr58
       +rho*Y[jmn61]*rate_eval.p_Mn61__He4_Cr58
       )

    jac[jcr58, jhe4] = (
       -rho*Y[jcr58]*rate_eval.He4_Cr58__Fe62
       -rho*Y[jcr58]*rate_eval.He4_Cr58__n_Fe61
       +rho*Y[jti55]*rate_eval.He4_Ti55__n_Cr58
       +rho*Y[jti54]*rate_eval.He4_Ti54__Cr58
       )

    jac[jcr58, jti54] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti54__Cr58
       )

    jac[jcr58, jti55] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti55__n_Cr58
       )

    jac[jcr58, jv57] = (
       +rho*Y[jp]*rate_eval.p_V57__Cr58
       )

    jac[jcr58, jv58] = (
       +rho*Y[jp]*rate_eval.p_V58__n_Cr58
       +rate_eval.V58__Cr58__weak__wc17
       )

    jac[jcr58, jv59] = (
       +rate_eval.V59__n_Cr58__weak__wc12
       )

    jac[jcr58, jcr57] = (
       +rho*Y[jn]*rate_eval.n_Cr57__Cr58
       )

    jac[jcr58, jcr58] = (
       -rate_eval.Cr58__Mn58__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Cr58__Fe62
       -rho*Y[jp]*rate_eval.p_Cr58__Mn59
       -rho*Y[jp]*rate_eval.p_Cr58__n_Mn58
       -rho*Y[jn]*rate_eval.n_Cr58__Cr59
       -rho*Y[jhe4]*rate_eval.He4_Cr58__n_Fe61
       -rho*Y[jp]*rate_eval.p_Cr58__He4_V55
       )

    jac[jcr58, jmn61] = (
       +rho*Y[jp]*rate_eval.p_Mn61__He4_Cr58
       )

    jac[jcr59, jn] = (
       -rho*Y[jcr59]*rate_eval.n_Cr59__Cr60
       +rho*Y[jcr58]*rate_eval.n_Cr58__Cr59
       )

    jac[jcr59, jp] = (
       -rho*Y[jcr59]*rate_eval.p_Cr59__n_Mn59
       -rho*Y[jcr59]*rate_eval.p_Cr59__Mn60
       -rho*Y[jcr59]*rate_eval.p_Cr59__He4_V56
       +rho*Y[jmn62]*rate_eval.p_Mn62__He4_Cr59
       +rho*Y[jv59]*rate_eval.p_V59__n_Cr59
       +rho*Y[jv58]*rate_eval.p_V58__Cr59
       )

    jac[jcr59, jhe4] = (
       -rho*Y[jcr59]*rate_eval.He4_Cr59__n_Fe62
       -rho*Y[jcr59]*rate_eval.He4_Cr59__Fe63
       +rho*Y[jti56]*rate_eval.He4_Ti56__n_Cr59
       +rho*Y[jti55]*rate_eval.He4_Ti55__Cr59
       )

    jac[jcr59, jti55] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti55__Cr59
       )

    jac[jcr59, jti56] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti56__n_Cr59
       )

    jac[jcr59, jv58] = (
       +rho*Y[jp]*rate_eval.p_V58__Cr59
       )

    jac[jcr59, jv59] = (
       +rho*Y[jp]*rate_eval.p_V59__n_Cr59
       +rate_eval.V59__Cr59__weak__wc12
       )

    jac[jcr59, jv60] = (
       +rate_eval.V60__n_Cr59__weak__mp17
       )

    jac[jcr59, jcr58] = (
       +rho*Y[jn]*rate_eval.n_Cr58__Cr59
       )

    jac[jcr59, jcr59] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr59__n_Fe62
       -rho*Y[jp]*rate_eval.p_Cr59__n_Mn59
       -rho*Y[jhe4]*rate_eval.He4_Cr59__Fe63
       -rho*Y[jp]*rate_eval.p_Cr59__Mn60
       -rho*Y[jn]*rate_eval.n_Cr59__Cr60
       -rho*Y[jp]*rate_eval.p_Cr59__He4_V56
       -rate_eval.Cr59__Mn59__weak__wc12
       )

    jac[jcr59, jmn62] = (
       +rho*Y[jp]*rate_eval.p_Mn62__He4_Cr59
       )

    jac[jcr60, jn] = (
       -rho*Y[jcr60]*rate_eval.n_Cr60__Cr61
       +rho*Y[jcr59]*rate_eval.n_Cr59__Cr60
       )

    jac[jcr60, jp] = (
       -rho*Y[jcr60]*rate_eval.p_Cr60__He4_V57
       -rho*Y[jcr60]*rate_eval.p_Cr60__Mn61
       -rho*Y[jcr60]*rate_eval.p_Cr60__n_Mn60
       +rho*Y[jv60]*rate_eval.p_V60__n_Cr60
       +rho*Y[jv59]*rate_eval.p_V59__Cr60
       +rho*Y[jmn63]*rate_eval.p_Mn63__He4_Cr60
       )

    jac[jcr60, jhe4] = (
       -rho*Y[jcr60]*rate_eval.He4_Cr60__Fe64
       -rho*Y[jcr60]*rate_eval.He4_Cr60__n_Fe63
       +rho*Y[jti57]*rate_eval.He4_Ti57__n_Cr60
       +rho*Y[jti56]*rate_eval.He4_Ti56__Cr60
       )

    jac[jcr60, jti56] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti56__Cr60
       )

    jac[jcr60, jti57] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti57__n_Cr60
       )

    jac[jcr60, jv59] = (
       +rho*Y[jp]*rate_eval.p_V59__Cr60
       )

    jac[jcr60, jv60] = (
       +rho*Y[jp]*rate_eval.p_V60__n_Cr60
       +rate_eval.V60__Cr60__weak__wc17
       )

    jac[jcr60, jv61] = (
       +rate_eval.V61__n_Cr60__weak__wc12
       )

    jac[jcr60, jcr59] = (
       +rho*Y[jn]*rate_eval.n_Cr59__Cr60
       )

    jac[jcr60, jcr60] = (
       -rho*Y[jp]*rate_eval.p_Cr60__He4_V57
       -rho*Y[jp]*rate_eval.p_Cr60__Mn61
       -rho*Y[jp]*rate_eval.p_Cr60__n_Mn60
       -rho*Y[jhe4]*rate_eval.He4_Cr60__Fe64
       -rho*Y[jn]*rate_eval.n_Cr60__Cr61
       -rho*Y[jhe4]*rate_eval.He4_Cr60__n_Fe63
       -rate_eval.Cr60__Mn60__weak__wc12
       )

    jac[jcr60, jmn63] = (
       +rho*Y[jp]*rate_eval.p_Mn63__He4_Cr60
       )

    jac[jcr61, jn] = (
       -rho*Y[jcr61]*rate_eval.n_Cr61__Cr62
       +rho*Y[jcr60]*rate_eval.n_Cr60__Cr61
       )

    jac[jcr61, jp] = (
       -rho*Y[jcr61]*rate_eval.p_Cr61__He4_V58
       -rho*Y[jcr61]*rate_eval.p_Cr61__Mn62
       -rho*Y[jcr61]*rate_eval.p_Cr61__n_Mn61
       +rho*Y[jmn64]*rate_eval.p_Mn64__He4_Cr61
       +rho*Y[jv61]*rate_eval.p_V61__n_Cr61
       +rho*Y[jv60]*rate_eval.p_V60__Cr61
       )

    jac[jcr61, jhe4] = (
       -rho*Y[jcr61]*rate_eval.He4_Cr61__n_Fe64
       -rho*Y[jcr61]*rate_eval.He4_Cr61__Fe65
       +rho*Y[jti58]*rate_eval.He4_Ti58__n_Cr61
       +rho*Y[jti57]*rate_eval.He4_Ti57__Cr61
       )

    jac[jcr61, jti57] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti57__Cr61
       )

    jac[jcr61, jti58] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti58__n_Cr61
       )

    jac[jcr61, jv60] = (
       +rho*Y[jp]*rate_eval.p_V60__Cr61
       )

    jac[jcr61, jv61] = (
       +rho*Y[jp]*rate_eval.p_V61__n_Cr61
       +rate_eval.V61__Cr61__weak__wc12
       )

    jac[jcr61, jv62] = (
       +rate_eval.V62__n_Cr61__weak__mp17
       )

    jac[jcr61, jcr60] = (
       +rho*Y[jn]*rate_eval.n_Cr60__Cr61
       )

    jac[jcr61, jcr61] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr61__n_Fe64
       -rho*Y[jp]*rate_eval.p_Cr61__He4_V58
       -rho*Y[jn]*rate_eval.n_Cr61__Cr62
       -rho*Y[jp]*rate_eval.p_Cr61__Mn62
       -rate_eval.Cr61__Mn61__weak__wc12
       -rate_eval.Cr61__n_Mn60__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Cr61__Fe65
       -rho*Y[jp]*rate_eval.p_Cr61__n_Mn61
       )

    jac[jcr61, jmn64] = (
       +rho*Y[jp]*rate_eval.p_Mn64__He4_Cr61
       )

    jac[jcr62, jn] = (
       -rho*Y[jcr62]*rate_eval.n_Cr62__Cr63
       +rho*Y[jcr61]*rate_eval.n_Cr61__Cr62
       )

    jac[jcr62, jp] = (
       -rho*Y[jcr62]*rate_eval.p_Cr62__He4_V59
       -rho*Y[jcr62]*rate_eval.p_Cr62__Mn63
       -rho*Y[jcr62]*rate_eval.p_Cr62__n_Mn62
       +rho*Y[jmn65]*rate_eval.p_Mn65__He4_Cr62
       +rho*Y[jv62]*rate_eval.p_V62__n_Cr62
       +rho*Y[jv61]*rate_eval.p_V61__Cr62
       )

    jac[jcr62, jhe4] = (
       -rho*Y[jcr62]*rate_eval.He4_Cr62__n_Fe65
       -rho*Y[jcr62]*rate_eval.He4_Cr62__Fe66
       +rho*Y[jti59]*rate_eval.He4_Ti59__n_Cr62
       +rho*Y[jti58]*rate_eval.He4_Ti58__Cr62
       )

    jac[jcr62, jti58] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti58__Cr62
       )

    jac[jcr62, jti59] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti59__n_Cr62
       )

    jac[jcr62, jv61] = (
       +rho*Y[jp]*rate_eval.p_V61__Cr62
       )

    jac[jcr62, jv62] = (
       +rho*Y[jp]*rate_eval.p_V62__n_Cr62
       +rate_eval.V62__Cr62__weak__wc17
       )

    jac[jcr62, jv63] = (
       +rate_eval.V63__n_Cr62__weak__wc12
       )

    jac[jcr62, jv64] = (
       +rate_eval.V64__n_n_Cr62__weak__mp17
       )

    jac[jcr62, jv65] = (
       +rate_eval.V65__n_n_n_Cr62__weak__mo03
       )

    jac[jcr62, jcr61] = (
       +rho*Y[jn]*rate_eval.n_Cr61__Cr62
       )

    jac[jcr62, jcr62] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr62__n_Fe65
       -rho*Y[jp]*rate_eval.p_Cr62__He4_V59
       -rho*Y[jp]*rate_eval.p_Cr62__Mn63
       -rho*Y[jp]*rate_eval.p_Cr62__n_Mn62
       -rho*Y[jhe4]*rate_eval.He4_Cr62__Fe66
       -rho*Y[jn]*rate_eval.n_Cr62__Cr63
       -rate_eval.Cr62__n_Mn61__weak__mp17
       -rate_eval.Cr62__Mn62__weak__wc12
       )

    jac[jcr62, jmn65] = (
       +rho*Y[jp]*rate_eval.p_Mn65__He4_Cr62
       )

    jac[jcr63, jn] = (
       -rho*Y[jcr63]*rate_eval.n_Cr63__Cr64
       +rho*Y[jcr62]*rate_eval.n_Cr62__Cr63
       )

    jac[jcr63, jp] = (
       -rho*Y[jcr63]*rate_eval.p_Cr63__n_Mn63
       -rho*Y[jcr63]*rate_eval.p_Cr63__Mn64
       -rho*Y[jcr63]*rate_eval.p_Cr63__He4_V60
       +rho*Y[jmn66]*rate_eval.p_Mn66__He4_Cr63
       +rho*Y[jv63]*rate_eval.p_V63__n_Cr63
       +rho*Y[jv62]*rate_eval.p_V62__Cr63
       )

    jac[jcr63, jhe4] = (
       -rho*Y[jcr63]*rate_eval.He4_Cr63__n_Fe66
       -rho*Y[jcr63]*rate_eval.He4_Cr63__Fe67
       +rho*Y[jti60]*rate_eval.He4_Ti60__n_Cr63
       +rho*Y[jti59]*rate_eval.He4_Ti59__Cr63
       )

    jac[jcr63, jti59] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti59__Cr63
       )

    jac[jcr63, jti60] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti60__n_Cr63
       )

    jac[jcr63, jv62] = (
       +rho*Y[jp]*rate_eval.p_V62__Cr63
       )

    jac[jcr63, jv63] = (
       +rho*Y[jp]*rate_eval.p_V63__n_Cr63
       +rate_eval.V63__Cr63__weak__wc12
       )

    jac[jcr63, jv64] = (
       +rate_eval.V64__n_Cr63__weak__mp17
       )

    jac[jcr63, jv65] = (
       +rate_eval.V65__n_n_Cr63__weak__mp17
       )

    jac[jcr63, jv66] = (
       +rate_eval.V66__n_n_n_Cr63__weak__mo03
       )

    jac[jcr63, jcr62] = (
       +rho*Y[jn]*rate_eval.n_Cr62__Cr63
       )

    jac[jcr63, jcr63] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr63__n_Fe66
       -rho*Y[jp]*rate_eval.p_Cr63__n_Mn63
       -rho*Y[jhe4]*rate_eval.He4_Cr63__Fe67
       -rho*Y[jp]*rate_eval.p_Cr63__Mn64
       -rho*Y[jn]*rate_eval.n_Cr63__Cr64
       -rate_eval.Cr63__n_Mn62__weak__mp17
       -rate_eval.Cr63__Mn63__weak__wc17
       -rho*Y[jp]*rate_eval.p_Cr63__He4_V60
       )

    jac[jcr63, jmn66] = (
       +rho*Y[jp]*rate_eval.p_Mn66__He4_Cr63
       )

    jac[jcr64, jn] = (
       -rho*Y[jcr64]*rate_eval.n_Cr64__Cr65
       +rho*Y[jcr63]*rate_eval.n_Cr63__Cr64
       )

    jac[jcr64, jp] = (
       -rho*Y[jcr64]*rate_eval.p_Cr64__n_Mn64
       -rho*Y[jcr64]*rate_eval.p_Cr64__Mn65
       -rho*Y[jcr64]*rate_eval.p_Cr64__He4_V61
       +rho*Y[jmn67]*rate_eval.p_Mn67__He4_Cr64
       +rho*Y[jv64]*rate_eval.p_V64__n_Cr64
       +rho*Y[jv63]*rate_eval.p_V63__Cr64
       )

    jac[jcr64, jhe4] = (
       -rho*Y[jcr64]*rate_eval.He4_Cr64__n_Fe67
       -rho*Y[jcr64]*rate_eval.He4_Cr64__Fe68
       +rho*Y[jti60]*rate_eval.He4_Ti60__Cr64
       +rho*Y[jti61]*rate_eval.He4_Ti61__n_Cr64
       )

    jac[jcr64, jti60] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti60__Cr64
       )

    jac[jcr64, jti61] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti61__n_Cr64
       )

    jac[jcr64, jv63] = (
       +rho*Y[jp]*rate_eval.p_V63__Cr64
       )

    jac[jcr64, jv64] = (
       +rho*Y[jp]*rate_eval.p_V64__n_Cr64
       +rate_eval.V64__Cr64__weak__wc17
       )

    jac[jcr64, jv65] = (
       +rate_eval.V65__n_Cr64__weak__mp17
       )

    jac[jcr64, jv66] = (
       +rate_eval.V66__n_n_Cr64__weak__mp17
       )

    jac[jcr64, jv67] = (
       +rate_eval.V67__n_n_n_Cr64__weak__mo03
       )

    jac[jcr64, jcr63] = (
       +rho*Y[jn]*rate_eval.n_Cr63__Cr64
       )

    jac[jcr64, jcr64] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr64__n_Fe67
       -rho*Y[jhe4]*rate_eval.He4_Cr64__Fe68
       -rho*Y[jp]*rate_eval.p_Cr64__n_Mn64
       -rho*Y[jp]*rate_eval.p_Cr64__Mn65
       -rho*Y[jn]*rate_eval.n_Cr64__Cr65
       -rho*Y[jp]*rate_eval.p_Cr64__He4_V61
       -rate_eval.Cr64__n_Mn63__weak__mp17
       -rate_eval.Cr64__Mn64__weak__wc12
       )

    jac[jcr64, jmn67] = (
       +rho*Y[jp]*rate_eval.p_Mn67__He4_Cr64
       )

    jac[jcr65, jn] = (
       -rho*Y[jcr65]*rate_eval.n_Cr65__Cr66
       +rho*Y[jcr64]*rate_eval.n_Cr64__Cr65
       )

    jac[jcr65, jp] = (
       -rho*Y[jcr65]*rate_eval.p_Cr65__He4_V62
       -rho*Y[jcr65]*rate_eval.p_Cr65__Mn66
       -rho*Y[jcr65]*rate_eval.p_Cr65__n_Mn65
       +rho*Y[jv64]*rate_eval.p_V64__Cr65
       +rho*Y[jv65]*rate_eval.p_V65__n_Cr65
       +rho*Y[jmn68]*rate_eval.p_Mn68__He4_Cr65
       )

    jac[jcr65, jhe4] = (
       -rho*Y[jcr65]*rate_eval.He4_Cr65__n_Fe68
       -rho*Y[jcr65]*rate_eval.He4_Cr65__Fe69
       +rho*Y[jti61]*rate_eval.He4_Ti61__Cr65
       +rho*Y[jti62]*rate_eval.He4_Ti62__n_Cr65
       )

    jac[jcr65, jti61] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti61__Cr65
       )

    jac[jcr65, jti62] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti62__n_Cr65
       )

    jac[jcr65, jv64] = (
       +rho*Y[jp]*rate_eval.p_V64__Cr65
       )

    jac[jcr65, jv65] = (
       +rate_eval.V65__Cr65__weak__mo03
       +rho*Y[jp]*rate_eval.p_V65__n_Cr65
       )

    jac[jcr65, jv66] = (
       +rate_eval.V66__n_Cr65__weak__mp17
       )

    jac[jcr65, jv67] = (
       +rate_eval.V67__n_n_Cr65__weak__mp17
       )

    jac[jcr65, jcr64] = (
       +rho*Y[jn]*rate_eval.n_Cr64__Cr65
       )

    jac[jcr65, jcr65] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr65__n_Fe68
       -rho*Y[jp]*rate_eval.p_Cr65__He4_V62
       -rho*Y[jp]*rate_eval.p_Cr65__Mn66
       -rho*Y[jhe4]*rate_eval.He4_Cr65__Fe69
       -rho*Y[jp]*rate_eval.p_Cr65__n_Mn65
       -rho*Y[jn]*rate_eval.n_Cr65__Cr66
       -rate_eval.Cr65__n_Mn64__weak__mp17
       -rate_eval.Cr65__Mn65__weak__wc17
       )

    jac[jcr65, jmn68] = (
       +rho*Y[jp]*rate_eval.p_Mn68__He4_Cr65
       )

    jac[jcr66, jn] = (
       -rho*Y[jcr66]*rate_eval.n_Cr66__Cr67
       +rho*Y[jcr65]*rate_eval.n_Cr65__Cr66
       )

    jac[jcr66, jp] = (
       -rho*Y[jcr66]*rate_eval.p_Cr66__He4_V63
       -rho*Y[jcr66]*rate_eval.p_Cr66__Mn67
       -rho*Y[jcr66]*rate_eval.p_Cr66__n_Mn66
       +rho*Y[jmn69]*rate_eval.p_Mn69__He4_Cr66
       +rho*Y[jv66]*rate_eval.p_V66__n_Cr66
       +rho*Y[jv65]*rate_eval.p_V65__Cr66
       )

    jac[jcr66, jhe4] = (
       -rho*Y[jcr66]*rate_eval.He4_Cr66__Fe70
       -rho*Y[jcr66]*rate_eval.He4_Cr66__n_Fe69
       +rho*Y[jti63]*rate_eval.He4_Ti63__n_Cr66
       +rho*Y[jti62]*rate_eval.He4_Ti62__Cr66
       )

    jac[jcr66, jti62] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti62__Cr66
       )

    jac[jcr66, jti63] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti63__n_Cr66
       )

    jac[jcr66, jv65] = (
       +rho*Y[jp]*rate_eval.p_V65__Cr66
       )

    jac[jcr66, jv66] = (
       +rho*Y[jp]*rate_eval.p_V66__n_Cr66
       +rate_eval.V66__Cr66__weak__mo03
       )

    jac[jcr66, jv67] = (
       +rate_eval.V67__n_Cr66__weak__mp17
       )

    jac[jcr66, jcr65] = (
       +rho*Y[jn]*rate_eval.n_Cr65__Cr66
       )

    jac[jcr66, jcr66] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr66__Fe70
       -rho*Y[jhe4]*rate_eval.He4_Cr66__n_Fe69
       -rho*Y[jp]*rate_eval.p_Cr66__He4_V63
       -rho*Y[jn]*rate_eval.n_Cr66__Cr67
       -rho*Y[jp]*rate_eval.p_Cr66__Mn67
       -rate_eval.Cr66__n_Mn65__weak__mp17
       -rho*Y[jp]*rate_eval.p_Cr66__n_Mn66
       -rate_eval.Cr66__Mn66__weak__wc17
       )

    jac[jcr66, jmn69] = (
       +rho*Y[jp]*rate_eval.p_Mn69__He4_Cr66
       )

    jac[jcr67, jn] = (
       -rho*Y[jcr67]*rate_eval.n_Cr67__Cr68
       +rho*Y[jcr66]*rate_eval.n_Cr66__Cr67
       )

    jac[jcr67, jp] = (
       -rho*Y[jcr67]*rate_eval.p_Cr67__n_Mn67
       -rho*Y[jcr67]*rate_eval.p_Cr67__He4_V64
       -rho*Y[jcr67]*rate_eval.p_Cr67__Mn68
       +rho*Y[jv67]*rate_eval.p_V67__n_Cr67
       +rho*Y[jv66]*rate_eval.p_V66__Cr67
       +rho*Y[jmn70]*rate_eval.p_Mn70__He4_Cr67
       )

    jac[jcr67, jhe4] = (
       -rho*Y[jcr67]*rate_eval.He4_Cr67__Fe71
       -rho*Y[jcr67]*rate_eval.He4_Cr67__n_Fe70
       +rho*Y[jti64]*rate_eval.He4_Ti64__n_Cr67
       +rho*Y[jti63]*rate_eval.He4_Ti63__Cr67
       )

    jac[jcr67, jti63] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti63__Cr67
       )

    jac[jcr67, jti64] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti64__n_Cr67
       )

    jac[jcr67, jv66] = (
       +rho*Y[jp]*rate_eval.p_V66__Cr67
       )

    jac[jcr67, jv67] = (
       +rho*Y[jp]*rate_eval.p_V67__n_Cr67
       +rate_eval.V67__Cr67__weak__mo03
       )

    jac[jcr67, jcr66] = (
       +rho*Y[jn]*rate_eval.n_Cr66__Cr67
       )

    jac[jcr67, jcr67] = (
       -rho*Y[jp]*rate_eval.p_Cr67__n_Mn67
       -rate_eval.Cr67__Mn67__weak__mo03
       -rho*Y[jp]*rate_eval.p_Cr67__He4_V64
       -rho*Y[jhe4]*rate_eval.He4_Cr67__Fe71
       -rate_eval.Cr67__n_Mn66__weak__mp17
       -rho*Y[jn]*rate_eval.n_Cr67__Cr68
       -rho*Y[jhe4]*rate_eval.He4_Cr67__n_Fe70
       -rho*Y[jp]*rate_eval.p_Cr67__Mn68
       )

    jac[jcr67, jmn70] = (
       +rho*Y[jp]*rate_eval.p_Mn70__He4_Cr67
       )

    jac[jcr68, jn] = (
       -rho*Y[jcr68]*rate_eval.n_Cr68__Cr69
       +rho*Y[jcr67]*rate_eval.n_Cr67__Cr68
       )

    jac[jcr68, jp] = (
       -rho*Y[jcr68]*rate_eval.p_Cr68__He4_V65
       -rho*Y[jcr68]*rate_eval.p_Cr68__n_Mn68
       -rho*Y[jcr68]*rate_eval.p_Cr68__Mn69
       +rho*Y[jmn71]*rate_eval.p_Mn71__He4_Cr68
       +rho*Y[jv67]*rate_eval.p_V67__Cr68
       )

    jac[jcr68, jhe4] = (
       -rho*Y[jcr68]*rate_eval.He4_Cr68__n_Fe71
       -rho*Y[jcr68]*rate_eval.He4_Cr68__Fe72
       +rho*Y[jti65]*rate_eval.He4_Ti65__n_Cr68
       +rho*Y[jti64]*rate_eval.He4_Ti64__Cr68
       )

    jac[jcr68, jti64] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti64__Cr68
       )

    jac[jcr68, jti65] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti65__n_Cr68
       )

    jac[jcr68, jv67] = (
       +rho*Y[jp]*rate_eval.p_V67__Cr68
       )

    jac[jcr68, jcr67] = (
       +rho*Y[jn]*rate_eval.n_Cr67__Cr68
       )

    jac[jcr68, jcr68] = (
       -rho*Y[jp]*rate_eval.p_Cr68__He4_V65
       -rho*Y[jp]*rate_eval.p_Cr68__n_Mn68
       -rate_eval.Cr68__Mn68__weak__mo03
       -rho*Y[jp]*rate_eval.p_Cr68__Mn69
       -rate_eval.Cr68__n_Mn67__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Cr68__n_Fe71
       -rho*Y[jn]*rate_eval.n_Cr68__Cr69
       -rho*Y[jhe4]*rate_eval.He4_Cr68__Fe72
       )

    jac[jcr68, jmn71] = (
       +rho*Y[jp]*rate_eval.p_Mn71__He4_Cr68
       )

    jac[jcr69, jn] = (
       -rho*Y[jcr69]*rate_eval.n_Cr69__Cr70
       +rho*Y[jcr68]*rate_eval.n_Cr68__Cr69
       )

    jac[jcr69, jp] = (
       -rho*Y[jcr69]*rate_eval.p_Cr69__He4_V66
       -rho*Y[jcr69]*rate_eval.p_Cr69__Mn70
       -rho*Y[jcr69]*rate_eval.p_Cr69__n_Mn69
       +rho*Y[jmn72]*rate_eval.p_Mn72__He4_Cr69
       )

    jac[jcr69, jhe4] = (
       -rho*Y[jcr69]*rate_eval.He4_Cr69__n_Fe72
       -rho*Y[jcr69]*rate_eval.He4_Cr69__Fe73
       +rho*Y[jti65]*rate_eval.He4_Ti65__Cr69
       )

    jac[jcr69, jti65] = (
       +rho*Y[jhe4]*rate_eval.He4_Ti65__Cr69
       )

    jac[jcr69, jcr68] = (
       +rho*Y[jn]*rate_eval.n_Cr68__Cr69
       )

    jac[jcr69, jcr69] = (
       -rho*Y[jhe4]*rate_eval.He4_Cr69__n_Fe72
       -rho*Y[jp]*rate_eval.p_Cr69__He4_V66
       -rate_eval.Cr69__Mn69__weak__mo03
       -rho*Y[jp]*rate_eval.p_Cr69__Mn70
       -rho*Y[jn]*rate_eval.n_Cr69__Cr70
       -rate_eval.Cr69__n_Mn68__weak__mp17
       -rate_eval.Cr69__n_n_Mn67__weak__mp17
       -rho*Y[jp]*rate_eval.p_Cr69__n_Mn69
       -rho*Y[jhe4]*rate_eval.He4_Cr69__Fe73
       )

    jac[jcr69, jmn72] = (
       +rho*Y[jp]*rate_eval.p_Mn72__He4_Cr69
       )

    jac[jcr70, jn] = (
       +rho*Y[jcr69]*rate_eval.n_Cr69__Cr70
       )

    jac[jcr70, jp] = (
       -rho*Y[jcr70]*rate_eval.p_Cr70__Mn71
       -rho*Y[jcr70]*rate_eval.p_Cr70__n_Mn70
       -rho*Y[jcr70]*rate_eval.p_Cr70__He4_V67
       +rho*Y[jmn73]*rate_eval.p_Mn73__He4_Cr70
       )

    jac[jcr70, jhe4] = (
       -rho*Y[jcr70]*rate_eval.He4_Cr70__n_Fe73
       -rho*Y[jcr70]*rate_eval.He4_Cr70__Fe74
       )

    jac[jcr70, jcr69] = (
       +rho*Y[jn]*rate_eval.n_Cr69__Cr70
       )

    jac[jcr70, jcr70] = (
       -rate_eval.Cr70__n_n_n_Mn67__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Cr70__n_Fe73
       -rho*Y[jp]*rate_eval.p_Cr70__Mn71
       -rho*Y[jhe4]*rate_eval.He4_Cr70__Fe74
       -rate_eval.Cr70__Mn70__weak__mo03
       -rho*Y[jp]*rate_eval.p_Cr70__n_Mn70
       -rate_eval.Cr70__n_Mn69__weak__mp17
       -rate_eval.Cr70__n_n_Mn68__weak__mp17
       -rho*Y[jp]*rate_eval.p_Cr70__He4_V67
       )

    jac[jcr70, jmn73] = (
       +rho*Y[jp]*rate_eval.p_Mn73__He4_Cr70
       )

    jac[jmn43, jn] = (
       -rho*Y[jmn43]*rate_eval.n_Mn43__He4_V40
       -rho*Y[jmn43]*rate_eval.n_Mn43__p_Cr43
       -rho*Y[jmn43]*rate_eval.n_Mn43__Mn44
       )

    jac[jmn43, jp] = (
       +rho*Y[jcr42]*rate_eval.p_Cr42__Mn43
       )

    jac[jmn43, jhe4] = (
       -rho*Y[jmn43]*rate_eval.He4_Mn43__Co47
       -rho*Y[jmn43]*rate_eval.He4_Mn43__p_Fe46
       +rho*Y[jv39]*rate_eval.He4_V39__Mn43
       )

    jac[jmn43, jv39] = (
       +rho*Y[jhe4]*rate_eval.He4_V39__Mn43
       )

    jac[jmn43, jcr42] = (
       +rho*Y[jp]*rate_eval.p_Cr42__Mn43
       )

    jac[jmn43, jmn43] = (
       -rate_eval.Mn43__Cr43__weak__bqa_pos_
       -rho*Y[jn]*rate_eval.n_Mn43__He4_V40
       -rho*Y[jhe4]*rate_eval.He4_Mn43__Co47
       -rho*Y[jn]*rate_eval.n_Mn43__p_Cr43
       -rho*Y[jhe4]*rate_eval.He4_Mn43__p_Fe46
       -rho*Y[jn]*rate_eval.n_Mn43__Mn44
       )

    jac[jmn44, jn] = (
       -rho*Y[jmn44]*rate_eval.n_Mn44__Mn45
       -rho*Y[jmn44]*rate_eval.n_Mn44__p_Cr44
       -rho*Y[jmn44]*rate_eval.n_Mn44__He4_V41
       +rho*Y[jmn43]*rate_eval.n_Mn43__Mn44
       )

    jac[jmn44, jp] = (
       -rho*Y[jmn44]*rate_eval.p_Mn44__Fe45
       +rho*Y[jcr43]*rate_eval.p_Cr43__Mn44
       )

    jac[jmn44, jhe4] = (
       -rho*Y[jmn44]*rate_eval.He4_Mn44__p_Fe47
       -rho*Y[jmn44]*rate_eval.He4_Mn44__Co48
       +rho*Y[jcr41]*rate_eval.He4_Cr41__p_Mn44
       +rho*Y[jv40]*rate_eval.He4_V40__Mn44
       )

    jac[jmn44, jv40] = (
       +rho*Y[jhe4]*rate_eval.He4_V40__Mn44
       )

    jac[jmn44, jcr41] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr41__p_Mn44
       )

    jac[jmn44, jcr43] = (
       +rho*Y[jp]*rate_eval.p_Cr43__Mn44
       )

    jac[jmn44, jmn43] = (
       +rho*Y[jn]*rate_eval.n_Mn43__Mn44
       )

    jac[jmn44, jmn44] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn44__p_Fe47
       -rho*Y[jn]*rate_eval.n_Mn44__Mn45
       -rho*Y[jn]*rate_eval.n_Mn44__p_Cr44
       -rho*Y[jp]*rate_eval.p_Mn44__Fe45
       -rho*Y[jhe4]*rate_eval.He4_Mn44__Co48
       -rho*Y[jn]*rate_eval.n_Mn44__He4_V41
       -rate_eval.Mn44__Cr44__weak__bqa_pos_
       )

    jac[jmn45, jn] = (
       -rho*Y[jmn45]*rate_eval.n_Mn45__p_Cr45
       -rho*Y[jmn45]*rate_eval.n_Mn45__Mn46
       -rho*Y[jmn45]*rate_eval.n_Mn45__He4_V42
       +rho*Y[jmn44]*rate_eval.n_Mn44__Mn45
       +rho*Y[jfe45]*rate_eval.n_Fe45__p_Mn45
       )

    jac[jmn45, jp] = (
       -rho*Y[jmn45]*rate_eval.p_Mn45__Fe46
       +rho*Y[jcr44]*rate_eval.p_Cr44__Mn45
       )

    jac[jmn45, jhe4] = (
       -rho*Y[jmn45]*rate_eval.He4_Mn45__p_Fe48
       -rho*Y[jmn45]*rate_eval.He4_Mn45__Co49
       +rho*Y[jcr42]*rate_eval.He4_Cr42__p_Mn45
       +rho*Y[jv41]*rate_eval.He4_V41__Mn45
       )

    jac[jmn45, jv41] = (
       +rho*Y[jhe4]*rate_eval.He4_V41__Mn45
       )

    jac[jmn45, jcr42] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr42__p_Mn45
       )

    jac[jmn45, jcr44] = (
       +rho*Y[jp]*rate_eval.p_Cr44__Mn45
       )

    jac[jmn45, jmn44] = (
       +rho*Y[jn]*rate_eval.n_Mn44__Mn45
       )

    jac[jmn45, jmn45] = (
       -rho*Y[jn]*rate_eval.n_Mn45__p_Cr45
       -rho*Y[jhe4]*rate_eval.He4_Mn45__p_Fe48
       -rho*Y[jhe4]*rate_eval.He4_Mn45__Co49
       -rho*Y[jp]*rate_eval.p_Mn45__Fe46
       -rho*Y[jn]*rate_eval.n_Mn45__Mn46
       -rho*Y[jn]*rate_eval.n_Mn45__He4_V42
       -rate_eval.Mn45__Cr45__weak__bqa_pos_
       )

    jac[jmn45, jfe45] = (
       +rho*Y[jn]*rate_eval.n_Fe45__p_Mn45
       +rate_eval.Fe45__Mn45__weak__wc17
       )

    jac[jmn46, jn] = (
       -rho*Y[jmn46]*rate_eval.n_Mn46__He4_V43
       -rho*Y[jmn46]*rate_eval.n_Mn46__p_Cr46
       -rho*Y[jmn46]*rate_eval.n_Mn46__Mn47
       +rho*Y[jfe46]*rate_eval.n_Fe46__p_Mn46
       +rho*Y[jmn45]*rate_eval.n_Mn45__Mn46
       )

    jac[jmn46, jp] = (
       -rho*Y[jmn46]*rate_eval.p_Mn46__Fe47
       +rho*Y[jcr45]*rate_eval.p_Cr45__Mn46
       )

    jac[jmn46, jhe4] = (
       -rho*Y[jmn46]*rate_eval.He4_Mn46__p_Fe49
       -rho*Y[jmn46]*rate_eval.He4_Mn46__Co50
       +rho*Y[jcr43]*rate_eval.He4_Cr43__p_Mn46
       +rho*Y[jv42]*rate_eval.He4_V42__Mn46
       )

    jac[jmn46, jv42] = (
       +rho*Y[jhe4]*rate_eval.He4_V42__Mn46
       )

    jac[jmn46, jcr43] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr43__p_Mn46
       )

    jac[jmn46, jcr45] = (
       +rho*Y[jp]*rate_eval.p_Cr45__Mn46
       )

    jac[jmn46, jmn45] = (
       +rho*Y[jn]*rate_eval.n_Mn45__Mn46
       )

    jac[jmn46, jmn46] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn46__p_Fe49
       -rho*Y[jn]*rate_eval.n_Mn46__He4_V43
       -rho*Y[jn]*rate_eval.n_Mn46__p_Cr46
       -rho*Y[jhe4]*rate_eval.He4_Mn46__Co50
       -rho*Y[jp]*rate_eval.p_Mn46__Fe47
       -rate_eval.Mn46__p_V45__weak__wc12
       -rho*Y[jn]*rate_eval.n_Mn46__Mn47
       -rate_eval.Mn46__Cr46__weak__wc12
       )

    jac[jmn46, jfe46] = (
       +rho*Y[jn]*rate_eval.n_Fe46__p_Mn46
       +rate_eval.Fe46__Mn46__weak__wc12
       )

    jac[jmn47, jn] = (
       -rho*Y[jmn47]*rate_eval.n_Mn47__p_Cr47
       -rho*Y[jmn47]*rate_eval.n_Mn47__He4_V44
       -rho*Y[jmn47]*rate_eval.n_Mn47__Mn48
       +rho*Y[jfe47]*rate_eval.n_Fe47__p_Mn47
       +rho*Y[jmn46]*rate_eval.n_Mn46__Mn47
       )

    jac[jmn47, jp] = (
       -rho*Y[jmn47]*rate_eval.p_Mn47__Fe48
       +rho*Y[jcr46]*rate_eval.p_Cr46__Mn47
       )

    jac[jmn47, jhe4] = (
       -rho*Y[jmn47]*rate_eval.He4_Mn47__p_Fe50
       -rho*Y[jmn47]*rate_eval.He4_Mn47__Co51
       +rho*Y[jcr44]*rate_eval.He4_Cr44__p_Mn47
       +rho*Y[jv43]*rate_eval.He4_V43__Mn47
       )

    jac[jmn47, jv43] = (
       +rho*Y[jhe4]*rate_eval.He4_V43__Mn47
       )

    jac[jmn47, jcr44] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr44__p_Mn47
       )

    jac[jmn47, jcr46] = (
       +rho*Y[jp]*rate_eval.p_Cr46__Mn47
       )

    jac[jmn47, jmn46] = (
       +rho*Y[jn]*rate_eval.n_Mn46__Mn47
       )

    jac[jmn47, jmn47] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn47__p_Fe50
       -rho*Y[jn]*rate_eval.n_Mn47__p_Cr47
       -rho*Y[jhe4]*rate_eval.He4_Mn47__Co51
       -rho*Y[jn]*rate_eval.n_Mn47__He4_V44
       -rho*Y[jp]*rate_eval.p_Mn47__Fe48
       -rate_eval.Mn47__Cr47__weak__wc17
       -rho*Y[jn]*rate_eval.n_Mn47__Mn48
       )

    jac[jmn47, jfe47] = (
       +rho*Y[jn]*rate_eval.n_Fe47__p_Mn47
       +rate_eval.Fe47__Mn47__weak__wc12
       )

    jac[jmn48, jn] = (
       -rho*Y[jmn48]*rate_eval.n_Mn48__He4_V45
       -rho*Y[jmn48]*rate_eval.n_Mn48__p_Cr48
       -rho*Y[jmn48]*rate_eval.n_Mn48__Mn49
       +rho*Y[jfe48]*rate_eval.n_Fe48__p_Mn48
       +rho*Y[jmn47]*rate_eval.n_Mn47__Mn48
       )

    jac[jmn48, jp] = (
       -rho*Y[jmn48]*rate_eval.p_Mn48__Fe49
       +rho*Y[jcr47]*rate_eval.p_Cr47__Mn48
       )

    jac[jmn48, jhe4] = (
       -rho*Y[jmn48]*rate_eval.He4_Mn48__Co52
       -rho*Y[jmn48]*rate_eval.He4_Mn48__p_Fe51
       +rho*Y[jcr45]*rate_eval.He4_Cr45__p_Mn48
       +rho*Y[jv44]*rate_eval.He4_V44__Mn48
       )

    jac[jmn48, jv44] = (
       +rho*Y[jhe4]*rate_eval.He4_V44__Mn48
       )

    jac[jmn48, jcr45] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr45__p_Mn48
       )

    jac[jmn48, jcr47] = (
       +rho*Y[jp]*rate_eval.p_Cr47__Mn48
       )

    jac[jmn48, jmn47] = (
       +rho*Y[jn]*rate_eval.n_Mn47__Mn48
       )

    jac[jmn48, jmn48] = (
       -rho*Y[jn]*rate_eval.n_Mn48__He4_V45
       -rho*Y[jhe4]*rate_eval.He4_Mn48__Co52
       -rho*Y[jp]*rate_eval.p_Mn48__Fe49
       -rho*Y[jhe4]*rate_eval.He4_Mn48__p_Fe51
       -rate_eval.Mn48__Cr48__weak__wc12
       -rho*Y[jn]*rate_eval.n_Mn48__p_Cr48
       -rho*Y[jn]*rate_eval.n_Mn48__Mn49
       -rate_eval.Mn48__p_V47__weak__wc12
       )

    jac[jmn48, jfe48] = (
       +rho*Y[jn]*rate_eval.n_Fe48__p_Mn48
       +rate_eval.Fe48__Mn48__weak__wc12
       )

    jac[jmn49, jn] = (
       -rho*Y[jmn49]*rate_eval.n_Mn49__He4_V46
       -rho*Y[jmn49]*rate_eval.n_Mn49__Mn50
       -rho*Y[jmn49]*rate_eval.n_Mn49__p_Cr49
       +rho*Y[jfe49]*rate_eval.n_Fe49__p_Mn49
       +rho*Y[jmn48]*rate_eval.n_Mn48__Mn49
       )

    jac[jmn49, jp] = (
       -rho*Y[jmn49]*rate_eval.p_Mn49__Fe50
       +rho*Y[jcr48]*rate_eval.p_Cr48__Mn49
       )

    jac[jmn49, jhe4] = (
       -rho*Y[jmn49]*rate_eval.He4_Mn49__p_Fe52
       -rho*Y[jmn49]*rate_eval.He4_Mn49__Co53
       +rho*Y[jcr46]*rate_eval.He4_Cr46__p_Mn49
       +rho*Y[jv45]*rate_eval.He4_V45__Mn49
       )

    jac[jmn49, jv45] = (
       +rho*Y[jhe4]*rate_eval.He4_V45__Mn49
       )

    jac[jmn49, jcr46] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr46__p_Mn49
       )

    jac[jmn49, jcr48] = (
       +rho*Y[jp]*rate_eval.p_Cr48__Mn49
       )

    jac[jmn49, jmn48] = (
       +rho*Y[jn]*rate_eval.n_Mn48__Mn49
       )

    jac[jmn49, jmn49] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn49__p_Fe52
       -rho*Y[jn]*rate_eval.n_Mn49__He4_V46
       -rho*Y[jhe4]*rate_eval.He4_Mn49__Co53
       -rho*Y[jp]*rate_eval.p_Mn49__Fe50
       -rho*Y[jn]*rate_eval.n_Mn49__Mn50
       -rho*Y[jn]*rate_eval.n_Mn49__p_Cr49
       -rate_eval.Mn49__Cr49__weak__wc12
       )

    jac[jmn49, jfe49] = (
       +rho*Y[jn]*rate_eval.n_Fe49__p_Mn49
       +rate_eval.Fe49__Mn49__weak__wc12
       )

    jac[jmn50, jn] = (
       -rho*Y[jmn50]*rate_eval.n_Mn50__He4_V47
       -rho*Y[jmn50]*rate_eval.n_Mn50__Mn51
       -rho*Y[jmn50]*rate_eval.n_Mn50__p_Cr50
       +rho*Y[jfe50]*rate_eval.n_Fe50__p_Mn50
       +rho*Y[jmn49]*rate_eval.n_Mn49__Mn50
       )

    jac[jmn50, jp] = (
       -rho*Y[jmn50]*rate_eval.p_Mn50__Fe51
       +rho*Y[jcr49]*rate_eval.p_Cr49__Mn50
       )

    jac[jmn50, jhe4] = (
       -rho*Y[jmn50]*rate_eval.He4_Mn50__Co54
       -rho*Y[jmn50]*rate_eval.He4_Mn50__p_Fe53
       +rho*Y[jcr47]*rate_eval.He4_Cr47__p_Mn50
       +rho*Y[jv46]*rate_eval.He4_V46__Mn50
       )

    jac[jmn50, jv46] = (
       +rho*Y[jhe4]*rate_eval.He4_V46__Mn50
       )

    jac[jmn50, jcr47] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr47__p_Mn50
       )

    jac[jmn50, jcr49] = (
       +rho*Y[jp]*rate_eval.p_Cr49__Mn50
       )

    jac[jmn50, jmn49] = (
       +rho*Y[jn]*rate_eval.n_Mn49__Mn50
       )

    jac[jmn50, jmn50] = (
       -rho*Y[jn]*rate_eval.n_Mn50__He4_V47
       -rho*Y[jn]*rate_eval.n_Mn50__Mn51
       -rho*Y[jhe4]*rate_eval.He4_Mn50__Co54
       -rho*Y[jp]*rate_eval.p_Mn50__Fe51
       -rho*Y[jn]*rate_eval.n_Mn50__p_Cr50
       -rate_eval.Mn50__Cr50__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Mn50__p_Fe53
       )

    jac[jmn50, jfe50] = (
       +rho*Y[jn]*rate_eval.n_Fe50__p_Mn50
       +rate_eval.Fe50__Mn50__weak__wc12
       )

    jac[jmn51, jn] = (
       -rho*Y[jmn51]*rate_eval.n_Mn51__p_Cr51
       -rho*Y[jmn51]*rate_eval.n_Mn51__He4_V48
       -rho*Y[jmn51]*rate_eval.n_Mn51__Mn52
       +rho*Y[jmn50]*rate_eval.n_Mn50__Mn51
       +rho*Y[jfe51]*rate_eval.n_Fe51__p_Mn51
       )

    jac[jmn51, jp] = (
       -rho*Y[jmn51]*rate_eval.p_Mn51__Fe52
       +rho*Y[jcr50]*rate_eval.p_Cr50__Mn51
       )

    jac[jmn51, jhe4] = (
       -rho*Y[jmn51]*rate_eval.He4_Mn51__p_Fe54
       -rho*Y[jmn51]*rate_eval.He4_Mn51__Co55
       +rho*Y[jcr48]*rate_eval.He4_Cr48__p_Mn51
       +rho*Y[jv47]*rate_eval.He4_V47__Mn51
       )

    jac[jmn51, jv47] = (
       +rho*Y[jhe4]*rate_eval.He4_V47__Mn51
       )

    jac[jmn51, jcr48] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr48__p_Mn51
       )

    jac[jmn51, jcr50] = (
       +rho*Y[jp]*rate_eval.p_Cr50__Mn51
       )

    jac[jmn51, jmn50] = (
       +rho*Y[jn]*rate_eval.n_Mn50__Mn51
       )

    jac[jmn51, jmn51] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn51__p_Fe54
       -rho*Y[jn]*rate_eval.n_Mn51__p_Cr51
       -rho*Y[jp]*rate_eval.p_Mn51__Fe52
       -rho*Y[jn]*rate_eval.n_Mn51__He4_V48
       -rho*Y[jn]*rate_eval.n_Mn51__Mn52
       -rho*Y[jhe4]*rate_eval.He4_Mn51__Co55
       -rate_eval.Mn51__Cr51__weak__wc12
       )

    jac[jmn51, jfe51] = (
       +rho*Y[jn]*rate_eval.n_Fe51__p_Mn51
       +rate_eval.Fe51__Mn51__weak__wc12
       )

    jac[jmn52, jn] = (
       -rho*Y[jmn52]*rate_eval.n_Mn52__He4_V49
       -rho*Y[jmn52]*rate_eval.n_Mn52__p_Cr52
       -rho*Y[jmn52]*rate_eval.n_Mn52__Mn53
       +rho*Y[jmn51]*rate_eval.n_Mn51__Mn52
       +rho*Y[jfe52]*rate_eval.n_Fe52__p_Mn52
       )

    jac[jmn52, jp] = (
       -rho*Y[jmn52]*rate_eval.p_Mn52__Fe53
       +rho*Y[jcr51]*rate_eval.p_Cr51__Mn52
       )

    jac[jmn52, jhe4] = (
       -rho*Y[jmn52]*rate_eval.He4_Mn52__Co56
       -rho*Y[jmn52]*rate_eval.He4_Mn52__p_Fe55
       +rho*Y[jcr49]*rate_eval.He4_Cr49__p_Mn52
       +rho*Y[jv48]*rate_eval.He4_V48__Mn52
       )

    jac[jmn52, jv48] = (
       +rho*Y[jhe4]*rate_eval.He4_V48__Mn52
       )

    jac[jmn52, jcr49] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr49__p_Mn52
       )

    jac[jmn52, jcr51] = (
       +rho*Y[jp]*rate_eval.p_Cr51__Mn52
       )

    jac[jmn52, jmn51] = (
       +rho*Y[jn]*rate_eval.n_Mn51__Mn52
       )

    jac[jmn52, jmn52] = (
       -rho*Y[jn]*rate_eval.n_Mn52__He4_V49
       -rho*Y[jn]*rate_eval.n_Mn52__p_Cr52
       -rho*Y[jn]*rate_eval.n_Mn52__Mn53
       -rho*Y[jhe4]*rate_eval.He4_Mn52__Co56
       -rate_eval.Mn52__Cr52__weak__wc12
       -rho*Y[jp]*rate_eval.p_Mn52__Fe53
       -rho*Y[jhe4]*rate_eval.He4_Mn52__p_Fe55
       )

    jac[jmn52, jfe52] = (
       +rho*Y[jn]*rate_eval.n_Fe52__p_Mn52
       +rate_eval.Fe52__Mn52__weak__wc12
       )

    jac[jmn53, jn] = (
       -rho*Y[jmn53]*rate_eval.n_Mn53__p_Cr53
       -rho*Y[jmn53]*rate_eval.n_Mn53__He4_V50
       -rho*Y[jmn53]*rate_eval.n_Mn53__Mn54
       +rho*Y[jfe53]*rate_eval.n_Fe53__p_Mn53
       +rho*Y[jmn52]*rate_eval.n_Mn52__Mn53
       )

    jac[jmn53, jp] = (
       -rho*Y[jmn53]*rate_eval.p_Mn53__He4_Cr50
       -rho*Y[jmn53]*rate_eval.p_Mn53__Fe54
       +rho*Y[jcr52]*rate_eval.p_Cr52__Mn53
       )

    jac[jmn53, jhe4] = (
       -rho*Y[jmn53]*rate_eval.He4_Mn53__p_Fe56
       -rho*Y[jmn53]*rate_eval.He4_Mn53__Co57
       +rho*Y[jv49]*rate_eval.He4_V49__Mn53
       )

    jac[jmn53, jv49] = (
       +rho*Y[jhe4]*rate_eval.He4_V49__Mn53
       )

    jac[jmn53, jcr52] = (
       +rho*Y[jp]*rate_eval.p_Cr52__Mn53
       )

    jac[jmn53, jmn52] = (
       +rho*Y[jn]*rate_eval.n_Mn52__Mn53
       )

    jac[jmn53, jmn53] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn53__p_Fe56
       -rho*Y[jp]*rate_eval.p_Mn53__He4_Cr50
       -rho*Y[jn]*rate_eval.n_Mn53__p_Cr53
       -rho*Y[jn]*rate_eval.n_Mn53__He4_V50
       -rho*Y[jhe4]*rate_eval.He4_Mn53__Co57
       -rho*Y[jp]*rate_eval.p_Mn53__Fe54
       -rho*Y[jn]*rate_eval.n_Mn53__Mn54
       -rate_eval.Mn53__Cr53__weak__wc12
       )

    jac[jmn53, jfe53] = (
       +rho*Y[jn]*rate_eval.n_Fe53__p_Mn53
       +rate_eval.Fe53__Mn53__weak__wc12
       )

    jac[jmn54, jn] = (
       -rho*Y[jmn54]*rate_eval.n_Mn54__p_Cr54
       -rho*Y[jmn54]*rate_eval.n_Mn54__He4_V51
       -rho*Y[jmn54]*rate_eval.n_Mn54__Mn55
       +rho*Y[jfe54]*rate_eval.n_Fe54__p_Mn54
       +rho*Y[jmn53]*rate_eval.n_Mn53__Mn54
       )

    jac[jmn54, jp] = (
       -rho*Y[jmn54]*rate_eval.p_Mn54__He4_Cr51
       -rho*Y[jmn54]*rate_eval.p_Mn54__Fe55
       +rho*Y[jfe57]*rate_eval.p_Fe57__He4_Mn54
       +rho*Y[jcr53]*rate_eval.p_Cr53__Mn54
       )

    jac[jmn54, jhe4] = (
       -rho*Y[jmn54]*rate_eval.He4_Mn54__Co58
       +rho*Y[jv50]*rate_eval.He4_V50__Mn54
       )

    jac[jmn54, jv50] = (
       +rho*Y[jhe4]*rate_eval.He4_V50__Mn54
       )

    jac[jmn54, jcr53] = (
       +rho*Y[jp]*rate_eval.p_Cr53__Mn54
       )

    jac[jmn54, jmn53] = (
       +rho*Y[jn]*rate_eval.n_Mn53__Mn54
       )

    jac[jmn54, jmn54] = (
       -rho*Y[jp]*rate_eval.p_Mn54__He4_Cr51
       -rate_eval.Mn54__Cr54__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Mn54__Co58
       -rho*Y[jn]*rate_eval.n_Mn54__p_Cr54
       -rho*Y[jn]*rate_eval.n_Mn54__He4_V51
       -rho*Y[jn]*rate_eval.n_Mn54__Mn55
       -rho*Y[jp]*rate_eval.p_Mn54__Fe55
       )

    jac[jmn54, jfe54] = (
       +rho*Y[jn]*rate_eval.n_Fe54__p_Mn54
       )

    jac[jmn54, jfe57] = (
       +rho*Y[jp]*rate_eval.p_Fe57__He4_Mn54
       )

    jac[jmn55, jn] = (
       -rho*Y[jmn55]*rate_eval.n_Mn55__Mn56
       +rho*Y[jfe55]*rate_eval.n_Fe55__p_Mn55
       +rho*Y[jmn54]*rate_eval.n_Mn54__Mn55
       )

    jac[jmn55, jp] = (
       -rho*Y[jmn55]*rate_eval.p_Mn55__He4_Cr52
       -rho*Y[jmn55]*rate_eval.p_Mn55__Fe56
       +rho*Y[jcr55]*rate_eval.p_Cr55__n_Mn55
       +rho*Y[jcr54]*rate_eval.p_Cr54__Mn55
       +rho*Y[jfe58]*rate_eval.p_Fe58__He4_Mn55
       )

    jac[jmn55, jhe4] = (
       -rho*Y[jmn55]*rate_eval.He4_Mn55__Co59
       +rho*Y[jv51]*rate_eval.He4_V51__Mn55
       +rho*Y[jv52]*rate_eval.He4_V52__n_Mn55
       )

    jac[jmn55, jv51] = (
       +rho*Y[jhe4]*rate_eval.He4_V51__Mn55
       )

    jac[jmn55, jv52] = (
       +rho*Y[jhe4]*rate_eval.He4_V52__n_Mn55
       )

    jac[jmn55, jcr54] = (
       +rho*Y[jp]*rate_eval.p_Cr54__Mn55
       )

    jac[jmn55, jcr55] = (
       +rho*Y[jp]*rate_eval.p_Cr55__n_Mn55
       +rate_eval.Cr55__Mn55__weak__wc12
       )

    jac[jmn55, jmn54] = (
       +rho*Y[jn]*rate_eval.n_Mn54__Mn55
       )

    jac[jmn55, jmn55] = (
       -rho*Y[jp]*rate_eval.p_Mn55__He4_Cr52
       -rho*Y[jn]*rate_eval.n_Mn55__Mn56
       -rho*Y[jhe4]*rate_eval.He4_Mn55__Co59
       -rho*Y[jp]*rate_eval.p_Mn55__Fe56
       )

    jac[jmn55, jfe55] = (
       +rho*Y[jn]*rate_eval.n_Fe55__p_Mn55
       +rate_eval.Fe55__Mn55__weak__wc12
       )

    jac[jmn55, jfe58] = (
       +rho*Y[jp]*rate_eval.p_Fe58__He4_Mn55
       )

    jac[jmn56, jn] = (
       -rho*Y[jmn56]*rate_eval.n_Mn56__Mn57
       -rho*Y[jmn56]*rate_eval.n_Mn56__He4_V53
       +rho*Y[jmn55]*rate_eval.n_Mn55__Mn56
       )

    jac[jmn56, jp] = (
       -rho*Y[jmn56]*rate_eval.p_Mn56__He4_Cr53
       -rho*Y[jmn56]*rate_eval.p_Mn56__Fe57
       -rho*Y[jmn56]*rate_eval.p_Mn56__n_Fe56
       +rho*Y[jfe59]*rate_eval.p_Fe59__He4_Mn56
       +rho*Y[jcr56]*rate_eval.p_Cr56__n_Mn56
       +rho*Y[jcr55]*rate_eval.p_Cr55__Mn56
       )

    jac[jmn56, jhe4] = (
       -rho*Y[jmn56]*rate_eval.He4_Mn56__Co60
       +rho*Y[jv52]*rate_eval.He4_V52__Mn56
       )

    jac[jmn56, jv52] = (
       +rho*Y[jhe4]*rate_eval.He4_V52__Mn56
       )

    jac[jmn56, jcr55] = (
       +rho*Y[jp]*rate_eval.p_Cr55__Mn56
       )

    jac[jmn56, jcr56] = (
       +rho*Y[jp]*rate_eval.p_Cr56__n_Mn56
       +rate_eval.Cr56__Mn56__weak__wc12
       )

    jac[jmn56, jmn55] = (
       +rho*Y[jn]*rate_eval.n_Mn55__Mn56
       )

    jac[jmn56, jmn56] = (
       -rho*Y[jp]*rate_eval.p_Mn56__He4_Cr53
       -rho*Y[jp]*rate_eval.p_Mn56__Fe57
       -rho*Y[jn]*rate_eval.n_Mn56__Mn57
       -rho*Y[jhe4]*rate_eval.He4_Mn56__Co60
       -rho*Y[jn]*rate_eval.n_Mn56__He4_V53
       -rate_eval.Mn56__Fe56__weak__wc12
       -rho*Y[jp]*rate_eval.p_Mn56__n_Fe56
       )

    jac[jmn56, jfe59] = (
       +rho*Y[jp]*rate_eval.p_Fe59__He4_Mn56
       )

    jac[jmn57, jn] = (
       -rho*Y[jmn57]*rate_eval.n_Mn57__Mn58
       +rho*Y[jmn56]*rate_eval.n_Mn56__Mn57
       )

    jac[jmn57, jp] = (
       -rho*Y[jmn57]*rate_eval.p_Mn57__n_Fe57
       -rho*Y[jmn57]*rate_eval.p_Mn57__He4_Cr54
       -rho*Y[jmn57]*rate_eval.p_Mn57__Fe58
       +rho*Y[jfe60]*rate_eval.p_Fe60__He4_Mn57
       +rho*Y[jcr57]*rate_eval.p_Cr57__n_Mn57
       +rho*Y[jcr56]*rate_eval.p_Cr56__Mn57
       )

    jac[jmn57, jhe4] = (
       -rho*Y[jmn57]*rate_eval.He4_Mn57__Co61
       +rho*Y[jv54]*rate_eval.He4_V54__n_Mn57
       +rho*Y[jv53]*rate_eval.He4_V53__Mn57
       )

    jac[jmn57, jv53] = (
       +rho*Y[jhe4]*rate_eval.He4_V53__Mn57
       )

    jac[jmn57, jv54] = (
       +rho*Y[jhe4]*rate_eval.He4_V54__n_Mn57
       )

    jac[jmn57, jcr56] = (
       +rho*Y[jp]*rate_eval.p_Cr56__Mn57
       )

    jac[jmn57, jcr57] = (
       +rho*Y[jp]*rate_eval.p_Cr57__n_Mn57
       +rate_eval.Cr57__Mn57__weak__wc12
       )

    jac[jmn57, jmn56] = (
       +rho*Y[jn]*rate_eval.n_Mn56__Mn57
       )

    jac[jmn57, jmn57] = (
       -rho*Y[jp]*rate_eval.p_Mn57__n_Fe57
       -rho*Y[jp]*rate_eval.p_Mn57__He4_Cr54
       -rho*Y[jp]*rate_eval.p_Mn57__Fe58
       -rho*Y[jn]*rate_eval.n_Mn57__Mn58
       -rate_eval.Mn57__Fe57__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Mn57__Co61
       )

    jac[jmn57, jfe60] = (
       +rho*Y[jp]*rate_eval.p_Fe60__He4_Mn57
       )

    jac[jmn58, jn] = (
       -rho*Y[jmn58]*rate_eval.n_Mn58__Mn59
       +rho*Y[jmn57]*rate_eval.n_Mn57__Mn58
       )

    jac[jmn58, jp] = (
       -rho*Y[jmn58]*rate_eval.p_Mn58__Fe59
       -rho*Y[jmn58]*rate_eval.p_Mn58__n_Fe58
       -rho*Y[jmn58]*rate_eval.p_Mn58__He4_Cr55
       +rho*Y[jfe61]*rate_eval.p_Fe61__He4_Mn58
       +rho*Y[jcr57]*rate_eval.p_Cr57__Mn58
       +rho*Y[jcr58]*rate_eval.p_Cr58__n_Mn58
       )

    jac[jmn58, jhe4] = (
       -rho*Y[jmn58]*rate_eval.He4_Mn58__Co62
       -rho*Y[jmn58]*rate_eval.He4_Mn58__n_Co61
       +rho*Y[jv55]*rate_eval.He4_V55__n_Mn58
       +rho*Y[jv54]*rate_eval.He4_V54__Mn58
       )

    jac[jmn58, jv54] = (
       +rho*Y[jhe4]*rate_eval.He4_V54__Mn58
       )

    jac[jmn58, jv55] = (
       +rho*Y[jhe4]*rate_eval.He4_V55__n_Mn58
       )

    jac[jmn58, jcr57] = (
       +rho*Y[jp]*rate_eval.p_Cr57__Mn58
       )

    jac[jmn58, jcr58] = (
       +rate_eval.Cr58__Mn58__weak__wc12
       +rho*Y[jp]*rate_eval.p_Cr58__n_Mn58
       )

    jac[jmn58, jmn57] = (
       +rho*Y[jn]*rate_eval.n_Mn57__Mn58
       )

    jac[jmn58, jmn58] = (
       -rate_eval.Mn58__Fe58__weak__wc12
       -rho*Y[jp]*rate_eval.p_Mn58__Fe59
       -rho*Y[jn]*rate_eval.n_Mn58__Mn59
       -rho*Y[jhe4]*rate_eval.He4_Mn58__Co62
       -rho*Y[jp]*rate_eval.p_Mn58__n_Fe58
       -rho*Y[jp]*rate_eval.p_Mn58__He4_Cr55
       -rho*Y[jhe4]*rate_eval.He4_Mn58__n_Co61
       )

    jac[jmn58, jfe61] = (
       +rho*Y[jp]*rate_eval.p_Fe61__He4_Mn58
       )

    jac[jmn59, jn] = (
       -rho*Y[jmn59]*rate_eval.n_Mn59__Mn60
       +rho*Y[jmn58]*rate_eval.n_Mn58__Mn59
       )

    jac[jmn59, jp] = (
       -rho*Y[jmn59]*rate_eval.p_Mn59__He4_Cr56
       -rho*Y[jmn59]*rate_eval.p_Mn59__n_Fe59
       -rho*Y[jmn59]*rate_eval.p_Mn59__Fe60
       +rho*Y[jfe62]*rate_eval.p_Fe62__He4_Mn59
       +rho*Y[jcr59]*rate_eval.p_Cr59__n_Mn59
       +rho*Y[jcr58]*rate_eval.p_Cr58__Mn59
       )

    jac[jmn59, jhe4] = (
       -rho*Y[jmn59]*rate_eval.He4_Mn59__Co63
       -rho*Y[jmn59]*rate_eval.He4_Mn59__n_Co62
       +rho*Y[jv56]*rate_eval.He4_V56__n_Mn59
       +rho*Y[jv55]*rate_eval.He4_V55__Mn59
       )

    jac[jmn59, jv55] = (
       +rho*Y[jhe4]*rate_eval.He4_V55__Mn59
       )

    jac[jmn59, jv56] = (
       +rho*Y[jhe4]*rate_eval.He4_V56__n_Mn59
       )

    jac[jmn59, jcr58] = (
       +rho*Y[jp]*rate_eval.p_Cr58__Mn59
       )

    jac[jmn59, jcr59] = (
       +rho*Y[jp]*rate_eval.p_Cr59__n_Mn59
       +rate_eval.Cr59__Mn59__weak__wc12
       )

    jac[jmn59, jmn58] = (
       +rho*Y[jn]*rate_eval.n_Mn58__Mn59
       )

    jac[jmn59, jmn59] = (
       -rho*Y[jp]*rate_eval.p_Mn59__He4_Cr56
       -rho*Y[jhe4]*rate_eval.He4_Mn59__Co63
       -rho*Y[jp]*rate_eval.p_Mn59__n_Fe59
       -rho*Y[jn]*rate_eval.n_Mn59__Mn60
       -rho*Y[jhe4]*rate_eval.He4_Mn59__n_Co62
       -rho*Y[jp]*rate_eval.p_Mn59__Fe60
       -rate_eval.Mn59__Fe59__weak__wc12
       )

    jac[jmn59, jfe62] = (
       +rho*Y[jp]*rate_eval.p_Fe62__He4_Mn59
       )

    jac[jmn60, jn] = (
       -rho*Y[jmn60]*rate_eval.n_Mn60__Mn61
       +rho*Y[jmn59]*rate_eval.n_Mn59__Mn60
       )

    jac[jmn60, jp] = (
       -rho*Y[jmn60]*rate_eval.p_Mn60__He4_Cr57
       -rho*Y[jmn60]*rate_eval.p_Mn60__n_Fe60
       -rho*Y[jmn60]*rate_eval.p_Mn60__Fe61
       +rho*Y[jfe63]*rate_eval.p_Fe63__He4_Mn60
       +rho*Y[jcr60]*rate_eval.p_Cr60__n_Mn60
       +rho*Y[jcr59]*rate_eval.p_Cr59__Mn60
       )

    jac[jmn60, jhe4] = (
       -rho*Y[jmn60]*rate_eval.He4_Mn60__n_Co63
       -rho*Y[jmn60]*rate_eval.He4_Mn60__Co64
       +rho*Y[jv57]*rate_eval.He4_V57__n_Mn60
       +rho*Y[jv56]*rate_eval.He4_V56__Mn60
       )

    jac[jmn60, jv56] = (
       +rho*Y[jhe4]*rate_eval.He4_V56__Mn60
       )

    jac[jmn60, jv57] = (
       +rho*Y[jhe4]*rate_eval.He4_V57__n_Mn60
       )

    jac[jmn60, jcr59] = (
       +rho*Y[jp]*rate_eval.p_Cr59__Mn60
       )

    jac[jmn60, jcr60] = (
       +rho*Y[jp]*rate_eval.p_Cr60__n_Mn60
       +rate_eval.Cr60__Mn60__weak__wc12
       )

    jac[jmn60, jcr61] = (
       +rate_eval.Cr61__n_Mn60__weak__mp17
       )

    jac[jmn60, jmn59] = (
       +rho*Y[jn]*rate_eval.n_Mn59__Mn60
       )

    jac[jmn60, jmn60] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn60__n_Co63
       -rho*Y[jp]*rate_eval.p_Mn60__He4_Cr57
       -rho*Y[jp]*rate_eval.p_Mn60__n_Fe60
       -rho*Y[jhe4]*rate_eval.He4_Mn60__Co64
       -rho*Y[jn]*rate_eval.n_Mn60__Mn61
       -rho*Y[jp]*rate_eval.p_Mn60__Fe61
       -rate_eval.Mn60__Fe60__weak__wc12
       )

    jac[jmn60, jfe63] = (
       +rho*Y[jp]*rate_eval.p_Fe63__He4_Mn60
       )

    jac[jmn61, jn] = (
       -rho*Y[jmn61]*rate_eval.n_Mn61__Mn62
       +rho*Y[jmn60]*rate_eval.n_Mn60__Mn61
       )

    jac[jmn61, jp] = (
       -rho*Y[jmn61]*rate_eval.p_Mn61__n_Fe61
       -rho*Y[jmn61]*rate_eval.p_Mn61__Fe62
       -rho*Y[jmn61]*rate_eval.p_Mn61__He4_Cr58
       +rho*Y[jfe64]*rate_eval.p_Fe64__He4_Mn61
       +rho*Y[jcr60]*rate_eval.p_Cr60__Mn61
       +rho*Y[jcr61]*rate_eval.p_Cr61__n_Mn61
       )

    jac[jmn61, jhe4] = (
       -rho*Y[jmn61]*rate_eval.He4_Mn61__Co65
       -rho*Y[jmn61]*rate_eval.He4_Mn61__n_Co64
       +rho*Y[jv58]*rate_eval.He4_V58__n_Mn61
       +rho*Y[jv57]*rate_eval.He4_V57__Mn61
       )

    jac[jmn61, jv57] = (
       +rho*Y[jhe4]*rate_eval.He4_V57__Mn61
       )

    jac[jmn61, jv58] = (
       +rho*Y[jhe4]*rate_eval.He4_V58__n_Mn61
       )

    jac[jmn61, jcr60] = (
       +rho*Y[jp]*rate_eval.p_Cr60__Mn61
       )

    jac[jmn61, jcr61] = (
       +rate_eval.Cr61__Mn61__weak__wc12
       +rho*Y[jp]*rate_eval.p_Cr61__n_Mn61
       )

    jac[jmn61, jcr62] = (
       +rate_eval.Cr62__n_Mn61__weak__mp17
       )

    jac[jmn61, jmn60] = (
       +rho*Y[jn]*rate_eval.n_Mn60__Mn61
       )

    jac[jmn61, jmn61] = (
       -rho*Y[jp]*rate_eval.p_Mn61__n_Fe61
       -rho*Y[jhe4]*rate_eval.He4_Mn61__Co65
       -rho*Y[jp]*rate_eval.p_Mn61__Fe62
       -rate_eval.Mn61__Fe61__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Mn61__n_Co64
       -rho*Y[jp]*rate_eval.p_Mn61__He4_Cr58
       -rho*Y[jn]*rate_eval.n_Mn61__Mn62
       )

    jac[jmn61, jfe64] = (
       +rho*Y[jp]*rate_eval.p_Fe64__He4_Mn61
       )

    jac[jmn62, jn] = (
       -rho*Y[jmn62]*rate_eval.n_Mn62__Mn63
       +rho*Y[jmn61]*rate_eval.n_Mn61__Mn62
       )

    jac[jmn62, jp] = (
       -rho*Y[jmn62]*rate_eval.p_Mn62__He4_Cr59
       -rho*Y[jmn62]*rate_eval.p_Mn62__Fe63
       -rho*Y[jmn62]*rate_eval.p_Mn62__n_Fe62
       +rho*Y[jfe65]*rate_eval.p_Fe65__He4_Mn62
       +rho*Y[jcr62]*rate_eval.p_Cr62__n_Mn62
       +rho*Y[jcr61]*rate_eval.p_Cr61__Mn62
       )

    jac[jmn62, jhe4] = (
       -rho*Y[jmn62]*rate_eval.He4_Mn62__n_Co65
       -rho*Y[jmn62]*rate_eval.He4_Mn62__Co66
       +rho*Y[jv59]*rate_eval.He4_V59__n_Mn62
       +rho*Y[jv58]*rate_eval.He4_V58__Mn62
       )

    jac[jmn62, jv58] = (
       +rho*Y[jhe4]*rate_eval.He4_V58__Mn62
       )

    jac[jmn62, jv59] = (
       +rho*Y[jhe4]*rate_eval.He4_V59__n_Mn62
       )

    jac[jmn62, jcr61] = (
       +rho*Y[jp]*rate_eval.p_Cr61__Mn62
       )

    jac[jmn62, jcr62] = (
       +rho*Y[jp]*rate_eval.p_Cr62__n_Mn62
       +rate_eval.Cr62__Mn62__weak__wc12
       )

    jac[jmn62, jcr63] = (
       +rate_eval.Cr63__n_Mn62__weak__mp17
       )

    jac[jmn62, jmn61] = (
       +rho*Y[jn]*rate_eval.n_Mn61__Mn62
       )

    jac[jmn62, jmn62] = (
       -rho*Y[jp]*rate_eval.p_Mn62__He4_Cr59
       -rho*Y[jhe4]*rate_eval.He4_Mn62__n_Co65
       -rho*Y[jn]*rate_eval.n_Mn62__Mn63
       -rho*Y[jp]*rate_eval.p_Mn62__Fe63
       -rate_eval.Mn62__Fe62__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Mn62__Co66
       -rho*Y[jp]*rate_eval.p_Mn62__n_Fe62
       )

    jac[jmn62, jfe65] = (
       +rho*Y[jp]*rate_eval.p_Fe65__He4_Mn62
       )

    jac[jmn63, jn] = (
       -rho*Y[jmn63]*rate_eval.n_Mn63__Mn64
       +rho*Y[jmn62]*rate_eval.n_Mn62__Mn63
       )

    jac[jmn63, jp] = (
       -rho*Y[jmn63]*rate_eval.p_Mn63__Fe64
       -rho*Y[jmn63]*rate_eval.p_Mn63__He4_Cr60
       -rho*Y[jmn63]*rate_eval.p_Mn63__n_Fe63
       +rho*Y[jcr63]*rate_eval.p_Cr63__n_Mn63
       +rho*Y[jcr62]*rate_eval.p_Cr62__Mn63
       +rho*Y[jfe66]*rate_eval.p_Fe66__He4_Mn63
       )

    jac[jmn63, jhe4] = (
       -rho*Y[jmn63]*rate_eval.He4_Mn63__Co67
       -rho*Y[jmn63]*rate_eval.He4_Mn63__n_Co66
       +rho*Y[jv60]*rate_eval.He4_V60__n_Mn63
       +rho*Y[jv59]*rate_eval.He4_V59__Mn63
       )

    jac[jmn63, jv59] = (
       +rho*Y[jhe4]*rate_eval.He4_V59__Mn63
       )

    jac[jmn63, jv60] = (
       +rho*Y[jhe4]*rate_eval.He4_V60__n_Mn63
       )

    jac[jmn63, jcr62] = (
       +rho*Y[jp]*rate_eval.p_Cr62__Mn63
       )

    jac[jmn63, jcr63] = (
       +rho*Y[jp]*rate_eval.p_Cr63__n_Mn63
       +rate_eval.Cr63__Mn63__weak__wc17
       )

    jac[jmn63, jcr64] = (
       +rate_eval.Cr64__n_Mn63__weak__mp17
       )

    jac[jmn63, jmn62] = (
       +rho*Y[jn]*rate_eval.n_Mn62__Mn63
       )

    jac[jmn63, jmn63] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn63__Co67
       -rho*Y[jn]*rate_eval.n_Mn63__Mn64
       -rho*Y[jp]*rate_eval.p_Mn63__Fe64
       -rho*Y[jp]*rate_eval.p_Mn63__He4_Cr60
       -rho*Y[jp]*rate_eval.p_Mn63__n_Fe63
       -rho*Y[jhe4]*rate_eval.He4_Mn63__n_Co66
       -rate_eval.Mn63__Fe63__weak__wc12
       -rate_eval.Mn63__n_Fe62__weak__mp17
       )

    jac[jmn63, jfe66] = (
       +rho*Y[jp]*rate_eval.p_Fe66__He4_Mn63
       )

    jac[jmn64, jn] = (
       -rho*Y[jmn64]*rate_eval.n_Mn64__Mn65
       +rho*Y[jmn63]*rate_eval.n_Mn63__Mn64
       )

    jac[jmn64, jp] = (
       -rho*Y[jmn64]*rate_eval.p_Mn64__He4_Cr61
       -rho*Y[jmn64]*rate_eval.p_Mn64__n_Fe64
       -rho*Y[jmn64]*rate_eval.p_Mn64__Fe65
       +rho*Y[jfe67]*rate_eval.p_Fe67__He4_Mn64
       +rho*Y[jcr63]*rate_eval.p_Cr63__Mn64
       +rho*Y[jcr64]*rate_eval.p_Cr64__n_Mn64
       )

    jac[jmn64, jhe4] = (
       -rho*Y[jmn64]*rate_eval.He4_Mn64__Co68
       -rho*Y[jmn64]*rate_eval.He4_Mn64__n_Co67
       +rho*Y[jv61]*rate_eval.He4_V61__n_Mn64
       +rho*Y[jv60]*rate_eval.He4_V60__Mn64
       )

    jac[jmn64, jv60] = (
       +rho*Y[jhe4]*rate_eval.He4_V60__Mn64
       )

    jac[jmn64, jv61] = (
       +rho*Y[jhe4]*rate_eval.He4_V61__n_Mn64
       )

    jac[jmn64, jcr63] = (
       +rho*Y[jp]*rate_eval.p_Cr63__Mn64
       )

    jac[jmn64, jcr64] = (
       +rho*Y[jp]*rate_eval.p_Cr64__n_Mn64
       +rate_eval.Cr64__Mn64__weak__wc12
       )

    jac[jmn64, jcr65] = (
       +rate_eval.Cr65__n_Mn64__weak__mp17
       )

    jac[jmn64, jmn63] = (
       +rho*Y[jn]*rate_eval.n_Mn63__Mn64
       )

    jac[jmn64, jmn64] = (
       -rho*Y[jp]*rate_eval.p_Mn64__He4_Cr61
       -rho*Y[jp]*rate_eval.p_Mn64__n_Fe64
       -rho*Y[jhe4]*rate_eval.He4_Mn64__Co68
       -rho*Y[jp]*rate_eval.p_Mn64__Fe65
       -rho*Y[jn]*rate_eval.n_Mn64__Mn65
       -rate_eval.Mn64__Fe64__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Mn64__n_Co67
       -rate_eval.Mn64__n_Fe63__weak__wc12
       )

    jac[jmn64, jfe67] = (
       +rho*Y[jp]*rate_eval.p_Fe67__He4_Mn64
       )

    jac[jmn65, jn] = (
       -rho*Y[jmn65]*rate_eval.n_Mn65__Mn66
       +rho*Y[jmn64]*rate_eval.n_Mn64__Mn65
       )

    jac[jmn65, jp] = (
       -rho*Y[jmn65]*rate_eval.p_Mn65__He4_Cr62
       -rho*Y[jmn65]*rate_eval.p_Mn65__n_Fe65
       -rho*Y[jmn65]*rate_eval.p_Mn65__Fe66
       +rho*Y[jfe68]*rate_eval.p_Fe68__He4_Mn65
       +rho*Y[jcr64]*rate_eval.p_Cr64__Mn65
       +rho*Y[jcr65]*rate_eval.p_Cr65__n_Mn65
       )

    jac[jmn65, jhe4] = (
       -rho*Y[jmn65]*rate_eval.He4_Mn65__n_Co68
       -rho*Y[jmn65]*rate_eval.He4_Mn65__Co69
       +rho*Y[jv62]*rate_eval.He4_V62__n_Mn65
       +rho*Y[jv61]*rate_eval.He4_V61__Mn65
       )

    jac[jmn65, jv61] = (
       +rho*Y[jhe4]*rate_eval.He4_V61__Mn65
       )

    jac[jmn65, jv62] = (
       +rho*Y[jhe4]*rate_eval.He4_V62__n_Mn65
       )

    jac[jmn65, jcr64] = (
       +rho*Y[jp]*rate_eval.p_Cr64__Mn65
       )

    jac[jmn65, jcr65] = (
       +rho*Y[jp]*rate_eval.p_Cr65__n_Mn65
       +rate_eval.Cr65__Mn65__weak__wc17
       )

    jac[jmn65, jcr66] = (
       +rate_eval.Cr66__n_Mn65__weak__mp17
       )

    jac[jmn65, jmn64] = (
       +rho*Y[jn]*rate_eval.n_Mn64__Mn65
       )

    jac[jmn65, jmn65] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn65__n_Co68
       -rho*Y[jp]*rate_eval.p_Mn65__He4_Cr62
       -rho*Y[jn]*rate_eval.n_Mn65__Mn66
       -rho*Y[jhe4]*rate_eval.He4_Mn65__Co69
       -rate_eval.Mn65__n_Fe64__weak__mp17
       -rho*Y[jp]*rate_eval.p_Mn65__n_Fe65
       -rate_eval.Mn65__Fe65__weak__wc17
       -rho*Y[jp]*rate_eval.p_Mn65__Fe66
       )

    jac[jmn65, jfe68] = (
       +rho*Y[jp]*rate_eval.p_Fe68__He4_Mn65
       )

    jac[jmn66, jn] = (
       -rho*Y[jmn66]*rate_eval.n_Mn66__Mn67
       +rho*Y[jmn65]*rate_eval.n_Mn65__Mn66
       )

    jac[jmn66, jp] = (
       -rho*Y[jmn66]*rate_eval.p_Mn66__He4_Cr63
       -rho*Y[jmn66]*rate_eval.p_Mn66__n_Fe66
       -rho*Y[jmn66]*rate_eval.p_Mn66__Fe67
       +rho*Y[jfe69]*rate_eval.p_Fe69__He4_Mn66
       +rho*Y[jcr65]*rate_eval.p_Cr65__Mn66
       +rho*Y[jcr66]*rate_eval.p_Cr66__n_Mn66
       )

    jac[jmn66, jhe4] = (
       -rho*Y[jmn66]*rate_eval.He4_Mn66__Co70
       -rho*Y[jmn66]*rate_eval.He4_Mn66__n_Co69
       +rho*Y[jv63]*rate_eval.He4_V63__n_Mn66
       +rho*Y[jv62]*rate_eval.He4_V62__Mn66
       )

    jac[jmn66, jv62] = (
       +rho*Y[jhe4]*rate_eval.He4_V62__Mn66
       )

    jac[jmn66, jv63] = (
       +rho*Y[jhe4]*rate_eval.He4_V63__n_Mn66
       )

    jac[jmn66, jcr65] = (
       +rho*Y[jp]*rate_eval.p_Cr65__Mn66
       )

    jac[jmn66, jcr66] = (
       +rho*Y[jp]*rate_eval.p_Cr66__n_Mn66
       +rate_eval.Cr66__Mn66__weak__wc17
       )

    jac[jmn66, jcr67] = (
       +rate_eval.Cr67__n_Mn66__weak__mp17
       )

    jac[jmn66, jmn65] = (
       +rho*Y[jn]*rate_eval.n_Mn65__Mn66
       )

    jac[jmn66, jmn66] = (
       -rho*Y[jp]*rate_eval.p_Mn66__He4_Cr63
       -rho*Y[jp]*rate_eval.p_Mn66__n_Fe66
       -rho*Y[jhe4]*rate_eval.He4_Mn66__Co70
       -rho*Y[jp]*rate_eval.p_Mn66__Fe67
       -rate_eval.Mn66__Fe66__weak__wc17
       -rate_eval.Mn66__n_Fe65__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Mn66__n_Co69
       -rho*Y[jn]*rate_eval.n_Mn66__Mn67
       )

    jac[jmn66, jfe69] = (
       +rho*Y[jp]*rate_eval.p_Fe69__He4_Mn66
       )

    jac[jmn67, jn] = (
       -rho*Y[jmn67]*rate_eval.n_Mn67__Mn68
       +rho*Y[jmn66]*rate_eval.n_Mn66__Mn67
       )

    jac[jmn67, jp] = (
       -rho*Y[jmn67]*rate_eval.p_Mn67__He4_Cr64
       -rho*Y[jmn67]*rate_eval.p_Mn67__Fe68
       -rho*Y[jmn67]*rate_eval.p_Mn67__n_Fe67
       +rho*Y[jfe70]*rate_eval.p_Fe70__He4_Mn67
       +rho*Y[jcr67]*rate_eval.p_Cr67__n_Mn67
       +rho*Y[jcr66]*rate_eval.p_Cr66__Mn67
       )

    jac[jmn67, jhe4] = (
       -rho*Y[jmn67]*rate_eval.He4_Mn67__n_Co70
       -rho*Y[jmn67]*rate_eval.He4_Mn67__Co71
       +rho*Y[jv64]*rate_eval.He4_V64__n_Mn67
       +rho*Y[jv63]*rate_eval.He4_V63__Mn67
       )

    jac[jmn67, jv63] = (
       +rho*Y[jhe4]*rate_eval.He4_V63__Mn67
       )

    jac[jmn67, jv64] = (
       +rho*Y[jhe4]*rate_eval.He4_V64__n_Mn67
       )

    jac[jmn67, jcr66] = (
       +rho*Y[jp]*rate_eval.p_Cr66__Mn67
       )

    jac[jmn67, jcr67] = (
       +rho*Y[jp]*rate_eval.p_Cr67__n_Mn67
       +rate_eval.Cr67__Mn67__weak__mo03
       )

    jac[jmn67, jcr68] = (
       +rate_eval.Cr68__n_Mn67__weak__mp17
       )

    jac[jmn67, jcr69] = (
       +rate_eval.Cr69__n_n_Mn67__weak__mp17
       )

    jac[jmn67, jcr70] = (
       +rate_eval.Cr70__n_n_n_Mn67__weak__mo03
       )

    jac[jmn67, jmn66] = (
       +rho*Y[jn]*rate_eval.n_Mn66__Mn67
       )

    jac[jmn67, jmn67] = (
       -rho*Y[jp]*rate_eval.p_Mn67__He4_Cr64
       -rho*Y[jhe4]*rate_eval.He4_Mn67__n_Co70
       -rho*Y[jhe4]*rate_eval.He4_Mn67__Co71
       -rho*Y[jp]*rate_eval.p_Mn67__Fe68
       -rho*Y[jn]*rate_eval.n_Mn67__Mn68
       -rate_eval.Mn67__Fe67__weak__wc17
       -rate_eval.Mn67__n_Fe66__weak__mp17
       -rho*Y[jp]*rate_eval.p_Mn67__n_Fe67
       )

    jac[jmn67, jfe70] = (
       +rho*Y[jp]*rate_eval.p_Fe70__He4_Mn67
       )

    jac[jmn68, jn] = (
       -rho*Y[jmn68]*rate_eval.n_Mn68__Mn69
       +rho*Y[jmn67]*rate_eval.n_Mn67__Mn68
       )

    jac[jmn68, jp] = (
       -rho*Y[jmn68]*rate_eval.p_Mn68__n_Fe68
       -rho*Y[jmn68]*rate_eval.p_Mn68__Fe69
       -rho*Y[jmn68]*rate_eval.p_Mn68__He4_Cr65
       +rho*Y[jfe71]*rate_eval.p_Fe71__He4_Mn68
       +rho*Y[jcr68]*rate_eval.p_Cr68__n_Mn68
       +rho*Y[jcr67]*rate_eval.p_Cr67__Mn68
       )

    jac[jmn68, jhe4] = (
       -rho*Y[jmn68]*rate_eval.He4_Mn68__n_Co71
       -rho*Y[jmn68]*rate_eval.He4_Mn68__Co72
       +rho*Y[jv64]*rate_eval.He4_V64__Mn68
       +rho*Y[jv65]*rate_eval.He4_V65__n_Mn68
       )

    jac[jmn68, jv64] = (
       +rho*Y[jhe4]*rate_eval.He4_V64__Mn68
       )

    jac[jmn68, jv65] = (
       +rho*Y[jhe4]*rate_eval.He4_V65__n_Mn68
       )

    jac[jmn68, jcr67] = (
       +rho*Y[jp]*rate_eval.p_Cr67__Mn68
       )

    jac[jmn68, jcr68] = (
       +rho*Y[jp]*rate_eval.p_Cr68__n_Mn68
       +rate_eval.Cr68__Mn68__weak__mo03
       )

    jac[jmn68, jcr69] = (
       +rate_eval.Cr69__n_Mn68__weak__mp17
       )

    jac[jmn68, jcr70] = (
       +rate_eval.Cr70__n_n_Mn68__weak__mp17
       )

    jac[jmn68, jmn67] = (
       +rho*Y[jn]*rate_eval.n_Mn67__Mn68
       )

    jac[jmn68, jmn68] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn68__n_Co71
       -rho*Y[jp]*rate_eval.p_Mn68__n_Fe68
       -rho*Y[jhe4]*rate_eval.He4_Mn68__Co72
       -rate_eval.Mn68__Fe68__weak__wc17
       -rho*Y[jn]*rate_eval.n_Mn68__Mn69
       -rho*Y[jp]*rate_eval.p_Mn68__Fe69
       -rate_eval.Mn68__n_n_Fe66__weak__mp17
       -rate_eval.Mn68__n_Fe67__weak__mp17
       -rho*Y[jp]*rate_eval.p_Mn68__He4_Cr65
       )

    jac[jmn68, jfe71] = (
       +rho*Y[jp]*rate_eval.p_Fe71__He4_Mn68
       )

    jac[jmn69, jn] = (
       -rho*Y[jmn69]*rate_eval.n_Mn69__Mn70
       +rho*Y[jmn68]*rate_eval.n_Mn68__Mn69
       )

    jac[jmn69, jp] = (
       -rho*Y[jmn69]*rate_eval.p_Mn69__He4_Cr66
       -rho*Y[jmn69]*rate_eval.p_Mn69__n_Fe69
       -rho*Y[jmn69]*rate_eval.p_Mn69__Fe70
       +rho*Y[jfe72]*rate_eval.p_Fe72__He4_Mn69
       +rho*Y[jcr68]*rate_eval.p_Cr68__Mn69
       +rho*Y[jcr69]*rate_eval.p_Cr69__n_Mn69
       )

    jac[jmn69, jhe4] = (
       -rho*Y[jmn69]*rate_eval.He4_Mn69__n_Co72
       -rho*Y[jmn69]*rate_eval.He4_Mn69__Co73
       +rho*Y[jv66]*rate_eval.He4_V66__n_Mn69
       +rho*Y[jv65]*rate_eval.He4_V65__Mn69
       )

    jac[jmn69, jv65] = (
       +rho*Y[jhe4]*rate_eval.He4_V65__Mn69
       )

    jac[jmn69, jv66] = (
       +rho*Y[jhe4]*rate_eval.He4_V66__n_Mn69
       )

    jac[jmn69, jcr68] = (
       +rho*Y[jp]*rate_eval.p_Cr68__Mn69
       )

    jac[jmn69, jcr69] = (
       +rate_eval.Cr69__Mn69__weak__mo03
       +rho*Y[jp]*rate_eval.p_Cr69__n_Mn69
       )

    jac[jmn69, jcr70] = (
       +rate_eval.Cr70__n_Mn69__weak__mp17
       )

    jac[jmn69, jmn68] = (
       +rho*Y[jn]*rate_eval.n_Mn68__Mn69
       )

    jac[jmn69, jmn69] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn69__n_Co72
       -rho*Y[jp]*rate_eval.p_Mn69__He4_Cr66
       -rho*Y[jn]*rate_eval.n_Mn69__Mn70
       -rho*Y[jp]*rate_eval.p_Mn69__n_Fe69
       -rho*Y[jhe4]*rate_eval.He4_Mn69__Co73
       -rho*Y[jp]*rate_eval.p_Mn69__Fe70
       -rate_eval.Mn69__n_Fe68__weak__mp17
       -rate_eval.Mn69__Fe69__weak__wc17
       )

    jac[jmn69, jfe72] = (
       +rho*Y[jp]*rate_eval.p_Fe72__He4_Mn69
       )

    jac[jmn70, jn] = (
       -rho*Y[jmn70]*rate_eval.n_Mn70__Mn71
       +rho*Y[jmn69]*rate_eval.n_Mn69__Mn70
       )

    jac[jmn70, jp] = (
       -rho*Y[jmn70]*rate_eval.p_Mn70__Fe71
       -rho*Y[jmn70]*rate_eval.p_Mn70__He4_Cr67
       -rho*Y[jmn70]*rate_eval.p_Mn70__n_Fe70
       +rho*Y[jfe73]*rate_eval.p_Fe73__He4_Mn70
       +rho*Y[jcr69]*rate_eval.p_Cr69__Mn70
       +rho*Y[jcr70]*rate_eval.p_Cr70__n_Mn70
       )

    jac[jmn70, jhe4] = (
       -rho*Y[jmn70]*rate_eval.He4_Mn70__Co74
       -rho*Y[jmn70]*rate_eval.He4_Mn70__n_Co73
       +rho*Y[jv67]*rate_eval.He4_V67__n_Mn70
       +rho*Y[jv66]*rate_eval.He4_V66__Mn70
       )

    jac[jmn70, jv66] = (
       +rho*Y[jhe4]*rate_eval.He4_V66__Mn70
       )

    jac[jmn70, jv67] = (
       +rho*Y[jhe4]*rate_eval.He4_V67__n_Mn70
       )

    jac[jmn70, jcr69] = (
       +rho*Y[jp]*rate_eval.p_Cr69__Mn70
       )

    jac[jmn70, jcr70] = (
       +rate_eval.Cr70__Mn70__weak__mo03
       +rho*Y[jp]*rate_eval.p_Cr70__n_Mn70
       )

    jac[jmn70, jmn69] = (
       +rho*Y[jn]*rate_eval.n_Mn69__Mn70
       )

    jac[jmn70, jmn70] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn70__Co74
       -rho*Y[jn]*rate_eval.n_Mn70__Mn71
       -rate_eval.Mn70__n_Fe69__weak__mp17
       -rho*Y[jp]*rate_eval.p_Mn70__Fe71
       -rate_eval.Mn70__Fe70__weak__mo03
       -rate_eval.Mn70__n_n_Fe68__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Mn70__n_Co73
       -rho*Y[jp]*rate_eval.p_Mn70__He4_Cr67
       -rho*Y[jp]*rate_eval.p_Mn70__n_Fe70
       )

    jac[jmn70, jfe73] = (
       +rho*Y[jp]*rate_eval.p_Fe73__He4_Mn70
       )

    jac[jmn71, jn] = (
       -rho*Y[jmn71]*rate_eval.n_Mn71__Mn72
       +rho*Y[jmn70]*rate_eval.n_Mn70__Mn71
       )

    jac[jmn71, jp] = (
       -rho*Y[jmn71]*rate_eval.p_Mn71__He4_Cr68
       -rho*Y[jmn71]*rate_eval.p_Mn71__Fe72
       -rho*Y[jmn71]*rate_eval.p_Mn71__n_Fe71
       +rho*Y[jfe74]*rate_eval.p_Fe74__He4_Mn71
       +rho*Y[jcr70]*rate_eval.p_Cr70__Mn71
       )

    jac[jmn71, jhe4] = (
       -rho*Y[jmn71]*rate_eval.He4_Mn71__Co75
       -rho*Y[jmn71]*rate_eval.He4_Mn71__n_Co74
       +rho*Y[jv67]*rate_eval.He4_V67__Mn71
       )

    jac[jmn71, jv67] = (
       +rho*Y[jhe4]*rate_eval.He4_V67__Mn71
       )

    jac[jmn71, jcr70] = (
       +rho*Y[jp]*rate_eval.p_Cr70__Mn71
       )

    jac[jmn71, jmn70] = (
       +rho*Y[jn]*rate_eval.n_Mn70__Mn71
       )

    jac[jmn71, jmn71] = (
       -rate_eval.Mn71__n_n_n_Fe68__weak__mo03
       -rho*Y[jp]*rate_eval.p_Mn71__He4_Cr68
       -rho*Y[jn]*rate_eval.n_Mn71__Mn72
       -rho*Y[jp]*rate_eval.p_Mn71__Fe72
       -rho*Y[jp]*rate_eval.p_Mn71__n_Fe71
       -rate_eval.Mn71__n_n_Fe69__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Mn71__Co75
       -rho*Y[jhe4]*rate_eval.He4_Mn71__n_Co74
       -rate_eval.Mn71__n_Fe70__weak__mp17
       -rate_eval.Mn71__Fe71__weak__mo03
       )

    jac[jmn71, jfe74] = (
       +rho*Y[jp]*rate_eval.p_Fe74__He4_Mn71
       )

    jac[jmn72, jn] = (
       -rho*Y[jmn72]*rate_eval.n_Mn72__Mn73
       +rho*Y[jmn71]*rate_eval.n_Mn71__Mn72
       )

    jac[jmn72, jp] = (
       -rho*Y[jmn72]*rate_eval.p_Mn72__He4_Cr69
       -rho*Y[jmn72]*rate_eval.p_Mn72__n_Fe72
       -rho*Y[jmn72]*rate_eval.p_Mn72__Fe73
       +rho*Y[jfe75]*rate_eval.p_Fe75__He4_Mn72
       )

    jac[jmn72, jhe4] = (
       -rho*Y[jmn72]*rate_eval.He4_Mn72__n_Co75
       -rho*Y[jmn72]*rate_eval.He4_Mn72__Co76
       )

    jac[jmn72, jmn71] = (
       +rho*Y[jn]*rate_eval.n_Mn71__Mn72
       )

    jac[jmn72, jmn72] = (
       -rho*Y[jhe4]*rate_eval.He4_Mn72__n_Co75
       -rho*Y[jp]*rate_eval.p_Mn72__He4_Cr69
       -rho*Y[jp]*rate_eval.p_Mn72__n_Fe72
       -rho*Y[jhe4]*rate_eval.He4_Mn72__Co76
       -rho*Y[jn]*rate_eval.n_Mn72__Mn73
       -rho*Y[jp]*rate_eval.p_Mn72__Fe73
       -rate_eval.Mn72__n_n_Fe70__weak__mp17
       -rate_eval.Mn72__n_Fe71__weak__mp17
       -rate_eval.Mn72__n_n_n_Fe69__weak__mo03
       -rate_eval.Mn72__Fe72__weak__mo03
       )

    jac[jmn72, jfe75] = (
       +rho*Y[jp]*rate_eval.p_Fe75__He4_Mn72
       )

    jac[jmn73, jn] = (
       +rho*Y[jmn72]*rate_eval.n_Mn72__Mn73
       )

    jac[jmn73, jp] = (
       -rho*Y[jmn73]*rate_eval.p_Mn73__He4_Cr70
       -rho*Y[jmn73]*rate_eval.p_Mn73__Fe74
       -rho*Y[jmn73]*rate_eval.p_Mn73__n_Fe73
       +rho*Y[jfe76]*rate_eval.p_Fe76__He4_Mn73
       )

    jac[jmn73, jhe4] = (
       -rho*Y[jmn73]*rate_eval.He4_Mn73__n_Co76
       -rho*Y[jmn73]*rate_eval.He4_Mn73__Co77
       )

    jac[jmn73, jmn72] = (
       +rho*Y[jn]*rate_eval.n_Mn72__Mn73
       )

    jac[jmn73, jmn73] = (
       -rate_eval.Mn73__n_n_n_Fe70__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Mn73__n_Co76
       -rho*Y[jp]*rate_eval.p_Mn73__He4_Cr70
       -rho*Y[jp]*rate_eval.p_Mn73__Fe74
       -rho*Y[jp]*rate_eval.p_Mn73__n_Fe73
       -rate_eval.Mn73__n_n_Fe71__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Mn73__Co77
       -rate_eval.Mn73__n_Fe72__weak__mp17
       -rate_eval.Mn73__Fe73__weak__mo03
       )

    jac[jmn73, jfe76] = (
       +rho*Y[jp]*rate_eval.p_Fe76__He4_Mn73
       )

    jac[jfe45, jn] = (
       -rho*Y[jfe45]*rate_eval.n_Fe45__p_Mn45
       -rho*Y[jfe45]*rate_eval.n_Fe45__Fe46
       -rho*Y[jfe45]*rate_eval.n_Fe45__He4_Cr42
       )

    jac[jfe45, jp] = (
       +rho*Y[jmn44]*rate_eval.p_Mn44__Fe45
       )

    jac[jfe45, jhe4] = (
       -rho*Y[jfe45]*rate_eval.He4_Fe45__Ni49
       -rho*Y[jfe45]*rate_eval.He4_Fe45__p_Co48
       +rho*Y[jcr41]*rate_eval.He4_Cr41__Fe45
       )

    jac[jfe45, jcr41] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr41__Fe45
       )

    jac[jfe45, jmn44] = (
       +rho*Y[jp]*rate_eval.p_Mn44__Fe45
       )

    jac[jfe45, jfe45] = (
       -rate_eval.Fe45__p_p_p_Ti42__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Fe45__Ni49
       -rho*Y[jhe4]*rate_eval.He4_Fe45__p_Co48
       -rate_eval.Fe45__p_Cr44__weak__wc17
       -rho*Y[jn]*rate_eval.n_Fe45__p_Mn45
       -rho*Y[jn]*rate_eval.n_Fe45__Fe46
       -rate_eval.Fe45__p_p_V43__weak__wc12
       -rho*Y[jn]*rate_eval.n_Fe45__He4_Cr42
       -rate_eval.Fe45__Mn45__weak__wc17
       )

    jac[jfe46, jn] = (
       -rho*Y[jfe46]*rate_eval.n_Fe46__He4_Cr43
       -rho*Y[jfe46]*rate_eval.n_Fe46__p_Mn46
       -rho*Y[jfe46]*rate_eval.n_Fe46__Fe47
       +rho*Y[jfe45]*rate_eval.n_Fe45__Fe46
       )

    jac[jfe46, jp] = (
       -rho*Y[jfe46]*rate_eval.p_Fe46__Co47
       +rho*Y[jmn45]*rate_eval.p_Mn45__Fe46
       )

    jac[jfe46, jhe4] = (
       -rho*Y[jfe46]*rate_eval.He4_Fe46__p_Co49
       -rho*Y[jfe46]*rate_eval.He4_Fe46__Ni50
       +rho*Y[jcr42]*rate_eval.He4_Cr42__Fe46
       +rho*Y[jmn43]*rate_eval.He4_Mn43__p_Fe46
       )

    jac[jfe46, jcr42] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr42__Fe46
       )

    jac[jfe46, jmn43] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn43__p_Fe46
       )

    jac[jfe46, jmn45] = (
       +rho*Y[jp]*rate_eval.p_Mn45__Fe46
       )

    jac[jfe46, jfe45] = (
       +rho*Y[jn]*rate_eval.n_Fe45__Fe46
       )

    jac[jfe46, jfe46] = (
       -rho*Y[jn]*rate_eval.n_Fe46__He4_Cr43
       -rho*Y[jn]*rate_eval.n_Fe46__p_Mn46
       -rho*Y[jhe4]*rate_eval.He4_Fe46__p_Co49
       -rho*Y[jhe4]*rate_eval.He4_Fe46__Ni50
       -rho*Y[jp]*rate_eval.p_Fe46__Co47
       -rate_eval.Fe46__p_Cr45__weak__wc12
       -rho*Y[jn]*rate_eval.n_Fe46__Fe47
       -rate_eval.Fe46__Mn46__weak__wc12
       )

    jac[jfe47, jn] = (
       -rho*Y[jfe47]*rate_eval.n_Fe47__He4_Cr44
       -rho*Y[jfe47]*rate_eval.n_Fe47__Fe48
       -rho*Y[jfe47]*rate_eval.n_Fe47__p_Mn47
       +rho*Y[jfe46]*rate_eval.n_Fe46__Fe47
       )

    jac[jfe47, jp] = (
       -rho*Y[jfe47]*rate_eval.p_Fe47__Co48
       +rho*Y[jmn46]*rate_eval.p_Mn46__Fe47
       )

    jac[jfe47, jhe4] = (
       -rho*Y[jfe47]*rate_eval.He4_Fe47__Ni51
       -rho*Y[jfe47]*rate_eval.He4_Fe47__p_Co50
       +rho*Y[jmn44]*rate_eval.He4_Mn44__p_Fe47
       +rho*Y[jcr43]*rate_eval.He4_Cr43__Fe47
       )

    jac[jfe47, jcr43] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr43__Fe47
       )

    jac[jfe47, jmn44] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn44__p_Fe47
       )

    jac[jfe47, jmn46] = (
       +rho*Y[jp]*rate_eval.p_Mn46__Fe47
       )

    jac[jfe47, jfe46] = (
       +rho*Y[jn]*rate_eval.n_Fe46__Fe47
       )

    jac[jfe47, jfe47] = (
       -rho*Y[jn]*rate_eval.n_Fe47__He4_Cr44
       -rho*Y[jp]*rate_eval.p_Fe47__Co48
       -rho*Y[jhe4]*rate_eval.He4_Fe47__Ni51
       -rho*Y[jn]*rate_eval.n_Fe47__Fe48
       -rho*Y[jn]*rate_eval.n_Fe47__p_Mn47
       -rate_eval.Fe47__p_Cr46__weak__wc12
       -rate_eval.Fe47__Mn47__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Fe47__p_Co50
       )

    jac[jfe48, jn] = (
       -rho*Y[jfe48]*rate_eval.n_Fe48__p_Mn48
       -rho*Y[jfe48]*rate_eval.n_Fe48__Fe49
       -rho*Y[jfe48]*rate_eval.n_Fe48__He4_Cr45
       +rho*Y[jfe47]*rate_eval.n_Fe47__Fe48
       )

    jac[jfe48, jp] = (
       -rho*Y[jfe48]*rate_eval.p_Fe48__Co49
       +rho*Y[jmn47]*rate_eval.p_Mn47__Fe48
       )

    jac[jfe48, jhe4] = (
       -rho*Y[jfe48]*rate_eval.He4_Fe48__p_Co51
       -rho*Y[jfe48]*rate_eval.He4_Fe48__Ni52
       +rho*Y[jmn45]*rate_eval.He4_Mn45__p_Fe48
       +rho*Y[jcr44]*rate_eval.He4_Cr44__Fe48
       )

    jac[jfe48, jcr44] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr44__Fe48
       )

    jac[jfe48, jmn45] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn45__p_Fe48
       )

    jac[jfe48, jmn47] = (
       +rho*Y[jp]*rate_eval.p_Mn47__Fe48
       )

    jac[jfe48, jfe47] = (
       +rho*Y[jn]*rate_eval.n_Fe47__Fe48
       )

    jac[jfe48, jfe48] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe48__p_Co51
       -rho*Y[jn]*rate_eval.n_Fe48__p_Mn48
       -rho*Y[jn]*rate_eval.n_Fe48__Fe49
       -rho*Y[jn]*rate_eval.n_Fe48__He4_Cr45
       -rho*Y[jp]*rate_eval.p_Fe48__Co49
       -rate_eval.Fe48__Mn48__weak__wc12
       -rate_eval.Fe48__p_Cr47__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Fe48__Ni52
       )

    jac[jfe49, jn] = (
       -rho*Y[jfe49]*rate_eval.n_Fe49__He4_Cr46
       -rho*Y[jfe49]*rate_eval.n_Fe49__p_Mn49
       -rho*Y[jfe49]*rate_eval.n_Fe49__Fe50
       +rho*Y[jfe48]*rate_eval.n_Fe48__Fe49
       )

    jac[jfe49, jp] = (
       -rho*Y[jfe49]*rate_eval.p_Fe49__Co50
       +rho*Y[jmn48]*rate_eval.p_Mn48__Fe49
       )

    jac[jfe49, jhe4] = (
       -rho*Y[jfe49]*rate_eval.He4_Fe49__p_Co52
       -rho*Y[jfe49]*rate_eval.He4_Fe49__Ni53
       +rho*Y[jmn46]*rate_eval.He4_Mn46__p_Fe49
       +rho*Y[jcr45]*rate_eval.He4_Cr45__Fe49
       )

    jac[jfe49, jcr45] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr45__Fe49
       )

    jac[jfe49, jmn46] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn46__p_Fe49
       )

    jac[jfe49, jmn48] = (
       +rho*Y[jp]*rate_eval.p_Mn48__Fe49
       )

    jac[jfe49, jfe48] = (
       +rho*Y[jn]*rate_eval.n_Fe48__Fe49
       )

    jac[jfe49, jfe49] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe49__p_Co52
       -rho*Y[jn]*rate_eval.n_Fe49__He4_Cr46
       -rho*Y[jn]*rate_eval.n_Fe49__p_Mn49
       -rate_eval.Fe49__Mn49__weak__wc12
       -rho*Y[jn]*rate_eval.n_Fe49__Fe50
       -rho*Y[jp]*rate_eval.p_Fe49__Co50
       -rho*Y[jhe4]*rate_eval.He4_Fe49__Ni53
       -rate_eval.Fe49__p_Cr48__weak__wc12
       )

    jac[jfe50, jn] = (
       -rho*Y[jfe50]*rate_eval.n_Fe50__He4_Cr47
       -rho*Y[jfe50]*rate_eval.n_Fe50__Fe51
       -rho*Y[jfe50]*rate_eval.n_Fe50__p_Mn50
       +rho*Y[jfe49]*rate_eval.n_Fe49__Fe50
       )

    jac[jfe50, jp] = (
       -rho*Y[jfe50]*rate_eval.p_Fe50__Co51
       +rho*Y[jmn49]*rate_eval.p_Mn49__Fe50
       )

    jac[jfe50, jhe4] = (
       -rho*Y[jfe50]*rate_eval.He4_Fe50__p_Co53
       -rho*Y[jfe50]*rate_eval.He4_Fe50__Ni54
       +rho*Y[jmn47]*rate_eval.He4_Mn47__p_Fe50
       +rho*Y[jcr46]*rate_eval.He4_Cr46__Fe50
       )

    jac[jfe50, jcr46] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr46__Fe50
       )

    jac[jfe50, jmn47] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn47__p_Fe50
       )

    jac[jfe50, jmn49] = (
       +rho*Y[jp]*rate_eval.p_Mn49__Fe50
       )

    jac[jfe50, jfe49] = (
       +rho*Y[jn]*rate_eval.n_Fe49__Fe50
       )

    jac[jfe50, jfe50] = (
       -rho*Y[jn]*rate_eval.n_Fe50__He4_Cr47
       -rho*Y[jn]*rate_eval.n_Fe50__Fe51
       -rho*Y[jhe4]*rate_eval.He4_Fe50__p_Co53
       -rho*Y[jn]*rate_eval.n_Fe50__p_Mn50
       -rho*Y[jp]*rate_eval.p_Fe50__Co51
       -rate_eval.Fe50__Mn50__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Fe50__Ni54
       )

    jac[jfe51, jn] = (
       -rho*Y[jfe51]*rate_eval.n_Fe51__He4_Cr48
       -rho*Y[jfe51]*rate_eval.n_Fe51__p_Mn51
       -rho*Y[jfe51]*rate_eval.n_Fe51__Fe52
       +rho*Y[jfe50]*rate_eval.n_Fe50__Fe51
       )

    jac[jfe51, jp] = (
       -rho*Y[jfe51]*rate_eval.p_Fe51__Co52
       +rho*Y[jmn50]*rate_eval.p_Mn50__Fe51
       )

    jac[jfe51, jhe4] = (
       -rho*Y[jfe51]*rate_eval.He4_Fe51__Ni55
       -rho*Y[jfe51]*rate_eval.He4_Fe51__p_Co54
       +rho*Y[jcr47]*rate_eval.He4_Cr47__Fe51
       +rho*Y[jmn48]*rate_eval.He4_Mn48__p_Fe51
       )

    jac[jfe51, jcr47] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr47__Fe51
       )

    jac[jfe51, jmn48] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn48__p_Fe51
       )

    jac[jfe51, jmn50] = (
       +rho*Y[jp]*rate_eval.p_Mn50__Fe51
       )

    jac[jfe51, jfe50] = (
       +rho*Y[jn]*rate_eval.n_Fe50__Fe51
       )

    jac[jfe51, jfe51] = (
       -rho*Y[jn]*rate_eval.n_Fe51__He4_Cr48
       -rho*Y[jhe4]*rate_eval.He4_Fe51__Ni55
       -rho*Y[jn]*rate_eval.n_Fe51__p_Mn51
       -rho*Y[jn]*rate_eval.n_Fe51__Fe52
       -rho*Y[jp]*rate_eval.p_Fe51__Co52
       -rho*Y[jhe4]*rate_eval.He4_Fe51__p_Co54
       -rate_eval.Fe51__Mn51__weak__wc12
       )

    jac[jfe52, jn] = (
       -rho*Y[jfe52]*rate_eval.n_Fe52__He4_Cr49
       -rho*Y[jfe52]*rate_eval.n_Fe52__p_Mn52
       -rho*Y[jfe52]*rate_eval.n_Fe52__Fe53
       +rho*Y[jfe51]*rate_eval.n_Fe51__Fe52
       )

    jac[jfe52, jp] = (
       -rho*Y[jfe52]*rate_eval.p_Fe52__Co53
       +rho*Y[jmn51]*rate_eval.p_Mn51__Fe52
       )

    jac[jfe52, jhe4] = (
       -rho*Y[jfe52]*rate_eval.He4_Fe52__p_Co55
       -rho*Y[jfe52]*rate_eval.He4_Fe52__Ni56
       +rho*Y[jmn49]*rate_eval.He4_Mn49__p_Fe52
       +rho*Y[jcr48]*rate_eval.He4_Cr48__Fe52
       )

    jac[jfe52, jcr48] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr48__Fe52
       )

    jac[jfe52, jmn49] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn49__p_Fe52
       )

    jac[jfe52, jmn51] = (
       +rho*Y[jp]*rate_eval.p_Mn51__Fe52
       )

    jac[jfe52, jfe51] = (
       +rho*Y[jn]*rate_eval.n_Fe51__Fe52
       )

    jac[jfe52, jfe52] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe52__p_Co55
       -rho*Y[jn]*rate_eval.n_Fe52__He4_Cr49
       -rho*Y[jhe4]*rate_eval.He4_Fe52__Ni56
       -rho*Y[jp]*rate_eval.p_Fe52__Co53
       -rho*Y[jn]*rate_eval.n_Fe52__p_Mn52
       -rate_eval.Fe52__Mn52__weak__wc12
       -rho*Y[jn]*rate_eval.n_Fe52__Fe53
       )

    jac[jfe53, jn] = (
       -rho*Y[jfe53]*rate_eval.n_Fe53__He4_Cr50
       -rho*Y[jfe53]*rate_eval.n_Fe53__p_Mn53
       -rho*Y[jfe53]*rate_eval.n_Fe53__Fe54
       +rho*Y[jfe52]*rate_eval.n_Fe52__Fe53
       )

    jac[jfe53, jp] = (
       -rho*Y[jfe53]*rate_eval.p_Fe53__Co54
       +rho*Y[jmn52]*rate_eval.p_Mn52__Fe53
       )

    jac[jfe53, jhe4] = (
       -rho*Y[jfe53]*rate_eval.He4_Fe53__p_Co56
       -rho*Y[jfe53]*rate_eval.He4_Fe53__Ni57
       +rho*Y[jcr49]*rate_eval.He4_Cr49__Fe53
       +rho*Y[jmn50]*rate_eval.He4_Mn50__p_Fe53
       )

    jac[jfe53, jcr49] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr49__Fe53
       )

    jac[jfe53, jmn50] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn50__p_Fe53
       )

    jac[jfe53, jmn52] = (
       +rho*Y[jp]*rate_eval.p_Mn52__Fe53
       )

    jac[jfe53, jfe52] = (
       +rho*Y[jn]*rate_eval.n_Fe52__Fe53
       )

    jac[jfe53, jfe53] = (
       -rho*Y[jn]*rate_eval.n_Fe53__He4_Cr50
       -rho*Y[jn]*rate_eval.n_Fe53__p_Mn53
       -rho*Y[jhe4]*rate_eval.He4_Fe53__p_Co56
       -rate_eval.Fe53__Mn53__weak__wc12
       -rho*Y[jn]*rate_eval.n_Fe53__Fe54
       -rho*Y[jp]*rate_eval.p_Fe53__Co54
       -rho*Y[jhe4]*rate_eval.He4_Fe53__Ni57
       )

    jac[jfe54, jn] = (
       -rho*Y[jfe54]*rate_eval.n_Fe54__p_Mn54
       -rho*Y[jfe54]*rate_eval.n_Fe54__He4_Cr51
       -rho*Y[jfe54]*rate_eval.n_Fe54__Fe55
       +rho*Y[jfe53]*rate_eval.n_Fe53__Fe54
       )

    jac[jfe54, jp] = (
       -rho*Y[jfe54]*rate_eval.p_Fe54__Co55
       +rho*Y[jmn53]*rate_eval.p_Mn53__Fe54
       )

    jac[jfe54, jhe4] = (
       -rho*Y[jfe54]*rate_eval.He4_Fe54__Ni58
       +rho*Y[jmn51]*rate_eval.He4_Mn51__p_Fe54
       +rho*Y[jcr50]*rate_eval.He4_Cr50__Fe54
       )

    jac[jfe54, jcr50] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr50__Fe54
       )

    jac[jfe54, jmn51] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn51__p_Fe54
       )

    jac[jfe54, jmn53] = (
       +rho*Y[jp]*rate_eval.p_Mn53__Fe54
       )

    jac[jfe54, jfe53] = (
       +rho*Y[jn]*rate_eval.n_Fe53__Fe54
       )

    jac[jfe54, jfe54] = (
       -rho*Y[jn]*rate_eval.n_Fe54__p_Mn54
       -rho*Y[jn]*rate_eval.n_Fe54__He4_Cr51
       -rho*Y[jhe4]*rate_eval.He4_Fe54__Ni58
       -rho*Y[jn]*rate_eval.n_Fe54__Fe55
       -rho*Y[jp]*rate_eval.p_Fe54__Co55
       )

    jac[jfe55, jn] = (
       -rho*Y[jfe55]*rate_eval.n_Fe55__p_Mn55
       -rho*Y[jfe55]*rate_eval.n_Fe55__He4_Cr52
       -rho*Y[jfe55]*rate_eval.n_Fe55__Fe56
       +rho*Y[jfe54]*rate_eval.n_Fe54__Fe55
       )

    jac[jfe55, jp] = (
       -rho*Y[jfe55]*rate_eval.p_Fe55__Co56
       +rho*Y[jmn54]*rate_eval.p_Mn54__Fe55
       )

    jac[jfe55, jhe4] = (
       -rho*Y[jfe55]*rate_eval.He4_Fe55__Ni59
       +rho*Y[jcr51]*rate_eval.He4_Cr51__Fe55
       +rho*Y[jmn52]*rate_eval.He4_Mn52__p_Fe55
       )

    jac[jfe55, jcr51] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr51__Fe55
       )

    jac[jfe55, jmn52] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn52__p_Fe55
       )

    jac[jfe55, jmn54] = (
       +rho*Y[jp]*rate_eval.p_Mn54__Fe55
       )

    jac[jfe55, jfe54] = (
       +rho*Y[jn]*rate_eval.n_Fe54__Fe55
       )

    jac[jfe55, jfe55] = (
       -rho*Y[jn]*rate_eval.n_Fe55__p_Mn55
       -rho*Y[jn]*rate_eval.n_Fe55__He4_Cr52
       -rho*Y[jp]*rate_eval.p_Fe55__Co56
       -rho*Y[jhe4]*rate_eval.He4_Fe55__Ni59
       -rate_eval.Fe55__Mn55__weak__wc12
       -rho*Y[jn]*rate_eval.n_Fe55__Fe56
       )

    jac[jfe56, jn] = (
       -rho*Y[jfe56]*rate_eval.n_Fe56__He4_Cr53
       -rho*Y[jfe56]*rate_eval.n_Fe56__Fe57
       +rho*Y[jfe55]*rate_eval.n_Fe55__Fe56
       )

    jac[jfe56, jp] = (
       -rho*Y[jfe56]*rate_eval.p_Fe56__Co57
       +rho*Y[jmn55]*rate_eval.p_Mn55__Fe56
       +rho*Y[jmn56]*rate_eval.p_Mn56__n_Fe56
       )

    jac[jfe56, jhe4] = (
       -rho*Y[jfe56]*rate_eval.He4_Fe56__Ni60
       +rho*Y[jmn53]*rate_eval.He4_Mn53__p_Fe56
       +rho*Y[jcr52]*rate_eval.He4_Cr52__Fe56
       )

    jac[jfe56, jcr52] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr52__Fe56
       )

    jac[jfe56, jmn53] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn53__p_Fe56
       )

    jac[jfe56, jmn55] = (
       +rho*Y[jp]*rate_eval.p_Mn55__Fe56
       )

    jac[jfe56, jmn56] = (
       +rate_eval.Mn56__Fe56__weak__wc12
       +rho*Y[jp]*rate_eval.p_Mn56__n_Fe56
       )

    jac[jfe56, jfe55] = (
       +rho*Y[jn]*rate_eval.n_Fe55__Fe56
       )

    jac[jfe56, jfe56] = (
       -rho*Y[jn]*rate_eval.n_Fe56__He4_Cr53
       -rho*Y[jhe4]*rate_eval.He4_Fe56__Ni60
       -rho*Y[jp]*rate_eval.p_Fe56__Co57
       -rho*Y[jn]*rate_eval.n_Fe56__Fe57
       )

    jac[jfe57, jn] = (
       -rho*Y[jfe57]*rate_eval.n_Fe57__Fe58
       -rho*Y[jfe57]*rate_eval.n_Fe57__He4_Cr54
       +rho*Y[jfe56]*rate_eval.n_Fe56__Fe57
       )

    jac[jfe57, jp] = (
       -rho*Y[jfe57]*rate_eval.p_Fe57__He4_Mn54
       -rho*Y[jfe57]*rate_eval.p_Fe57__Co58
       +rho*Y[jmn57]*rate_eval.p_Mn57__n_Fe57
       +rho*Y[jmn56]*rate_eval.p_Mn56__Fe57
       )

    jac[jfe57, jhe4] = (
       -rho*Y[jfe57]*rate_eval.He4_Fe57__Ni61
       +rho*Y[jcr53]*rate_eval.He4_Cr53__Fe57
       )

    jac[jfe57, jcr53] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr53__Fe57
       )

    jac[jfe57, jmn56] = (
       +rho*Y[jp]*rate_eval.p_Mn56__Fe57
       )

    jac[jfe57, jmn57] = (
       +rho*Y[jp]*rate_eval.p_Mn57__n_Fe57
       +rate_eval.Mn57__Fe57__weak__wc12
       )

    jac[jfe57, jfe56] = (
       +rho*Y[jn]*rate_eval.n_Fe56__Fe57
       )

    jac[jfe57, jfe57] = (
       -rho*Y[jp]*rate_eval.p_Fe57__He4_Mn54
       -rho*Y[jp]*rate_eval.p_Fe57__Co58
       -rho*Y[jn]*rate_eval.n_Fe57__Fe58
       -rho*Y[jhe4]*rate_eval.He4_Fe57__Ni61
       -rho*Y[jn]*rate_eval.n_Fe57__He4_Cr54
       )

    jac[jfe58, jn] = (
       -rho*Y[jfe58]*rate_eval.n_Fe58__Fe59
       +rho*Y[jfe57]*rate_eval.n_Fe57__Fe58
       )

    jac[jfe58, jp] = (
       -rho*Y[jfe58]*rate_eval.p_Fe58__Co59
       -rho*Y[jfe58]*rate_eval.p_Fe58__He4_Mn55
       +rho*Y[jmn57]*rate_eval.p_Mn57__Fe58
       +rho*Y[jmn58]*rate_eval.p_Mn58__n_Fe58
       )

    jac[jfe58, jhe4] = (
       -rho*Y[jfe58]*rate_eval.He4_Fe58__Ni62
       +rho*Y[jcr55]*rate_eval.He4_Cr55__n_Fe58
       +rho*Y[jcr54]*rate_eval.He4_Cr54__Fe58
       )

    jac[jfe58, jcr54] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr54__Fe58
       )

    jac[jfe58, jcr55] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr55__n_Fe58
       )

    jac[jfe58, jmn57] = (
       +rho*Y[jp]*rate_eval.p_Mn57__Fe58
       )

    jac[jfe58, jmn58] = (
       +rate_eval.Mn58__Fe58__weak__wc12
       +rho*Y[jp]*rate_eval.p_Mn58__n_Fe58
       )

    jac[jfe58, jfe57] = (
       +rho*Y[jn]*rate_eval.n_Fe57__Fe58
       )

    jac[jfe58, jfe58] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe58__Ni62
       -rho*Y[jn]*rate_eval.n_Fe58__Fe59
       -rho*Y[jp]*rate_eval.p_Fe58__Co59
       -rho*Y[jp]*rate_eval.p_Fe58__He4_Mn55
       )

    jac[jfe59, jn] = (
       -rho*Y[jfe59]*rate_eval.n_Fe59__Fe60
       -rho*Y[jfe59]*rate_eval.n_Fe59__He4_Cr56
       +rho*Y[jfe58]*rate_eval.n_Fe58__Fe59
       )

    jac[jfe59, jp] = (
       -rho*Y[jfe59]*rate_eval.p_Fe59__He4_Mn56
       -rho*Y[jfe59]*rate_eval.p_Fe59__n_Co59
       -rho*Y[jfe59]*rate_eval.p_Fe59__Co60
       +rho*Y[jmn58]*rate_eval.p_Mn58__Fe59
       +rho*Y[jmn59]*rate_eval.p_Mn59__n_Fe59
       )

    jac[jfe59, jhe4] = (
       -rho*Y[jfe59]*rate_eval.He4_Fe59__n_Ni62
       -rho*Y[jfe59]*rate_eval.He4_Fe59__Ni63
       +rho*Y[jcr55]*rate_eval.He4_Cr55__Fe59
       )

    jac[jfe59, jcr55] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr55__Fe59
       )

    jac[jfe59, jmn58] = (
       +rho*Y[jp]*rate_eval.p_Mn58__Fe59
       )

    jac[jfe59, jmn59] = (
       +rho*Y[jp]*rate_eval.p_Mn59__n_Fe59
       +rate_eval.Mn59__Fe59__weak__wc12
       )

    jac[jfe59, jfe58] = (
       +rho*Y[jn]*rate_eval.n_Fe58__Fe59
       )

    jac[jfe59, jfe59] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe59__n_Ni62
       -rho*Y[jp]*rate_eval.p_Fe59__He4_Mn56
       -rho*Y[jp]*rate_eval.p_Fe59__n_Co59
       -rho*Y[jhe4]*rate_eval.He4_Fe59__Ni63
       -rho*Y[jp]*rate_eval.p_Fe59__Co60
       -rate_eval.Fe59__Co59__weak__wc12
       -rho*Y[jn]*rate_eval.n_Fe59__Fe60
       -rho*Y[jn]*rate_eval.n_Fe59__He4_Cr56
       )

    jac[jfe60, jn] = (
       -rho*Y[jfe60]*rate_eval.n_Fe60__Fe61
       +rho*Y[jfe59]*rate_eval.n_Fe59__Fe60
       )

    jac[jfe60, jp] = (
       -rho*Y[jfe60]*rate_eval.p_Fe60__He4_Mn57
       -rho*Y[jfe60]*rate_eval.p_Fe60__Co61
       +rho*Y[jmn60]*rate_eval.p_Mn60__n_Fe60
       +rho*Y[jmn59]*rate_eval.p_Mn59__Fe60
       )

    jac[jfe60, jhe4] = (
       -rho*Y[jfe60]*rate_eval.He4_Fe60__Ni64
       +rho*Y[jcr57]*rate_eval.He4_Cr57__n_Fe60
       +rho*Y[jcr56]*rate_eval.He4_Cr56__Fe60
       )

    jac[jfe60, jcr56] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr56__Fe60
       )

    jac[jfe60, jcr57] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr57__n_Fe60
       )

    jac[jfe60, jmn59] = (
       +rho*Y[jp]*rate_eval.p_Mn59__Fe60
       )

    jac[jfe60, jmn60] = (
       +rho*Y[jp]*rate_eval.p_Mn60__n_Fe60
       +rate_eval.Mn60__Fe60__weak__wc12
       )

    jac[jfe60, jfe59] = (
       +rho*Y[jn]*rate_eval.n_Fe59__Fe60
       )

    jac[jfe60, jfe60] = (
       -rho*Y[jp]*rate_eval.p_Fe60__He4_Mn57
       -rho*Y[jp]*rate_eval.p_Fe60__Co61
       -rate_eval.Fe60__Co60__weak__wc12
       -rho*Y[jn]*rate_eval.n_Fe60__Fe61
       -rho*Y[jhe4]*rate_eval.He4_Fe60__Ni64
       )

    jac[jfe61, jn] = (
       -rho*Y[jfe61]*rate_eval.n_Fe61__Fe62
       +rho*Y[jfe60]*rate_eval.n_Fe60__Fe61
       )

    jac[jfe61, jp] = (
       -rho*Y[jfe61]*rate_eval.p_Fe61__He4_Mn58
       -rho*Y[jfe61]*rate_eval.p_Fe61__n_Co61
       -rho*Y[jfe61]*rate_eval.p_Fe61__Co62
       +rho*Y[jmn61]*rate_eval.p_Mn61__n_Fe61
       +rho*Y[jmn60]*rate_eval.p_Mn60__Fe61
       )

    jac[jfe61, jhe4] = (
       -rho*Y[jfe61]*rate_eval.He4_Fe61__Ni65
       -rho*Y[jfe61]*rate_eval.He4_Fe61__n_Ni64
       +rho*Y[jcr57]*rate_eval.He4_Cr57__Fe61
       +rho*Y[jcr58]*rate_eval.He4_Cr58__n_Fe61
       )

    jac[jfe61, jcr57] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr57__Fe61
       )

    jac[jfe61, jcr58] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr58__n_Fe61
       )

    jac[jfe61, jmn60] = (
       +rho*Y[jp]*rate_eval.p_Mn60__Fe61
       )

    jac[jfe61, jmn61] = (
       +rho*Y[jp]*rate_eval.p_Mn61__n_Fe61
       +rate_eval.Mn61__Fe61__weak__wc12
       )

    jac[jfe61, jfe60] = (
       +rho*Y[jn]*rate_eval.n_Fe60__Fe61
       )

    jac[jfe61, jfe61] = (
       -rho*Y[jp]*rate_eval.p_Fe61__He4_Mn58
       -rho*Y[jp]*rate_eval.p_Fe61__n_Co61
       -rho*Y[jp]*rate_eval.p_Fe61__Co62
       -rho*Y[jhe4]*rate_eval.He4_Fe61__Ni65
       -rho*Y[jhe4]*rate_eval.He4_Fe61__n_Ni64
       -rho*Y[jn]*rate_eval.n_Fe61__Fe62
       -rate_eval.Fe61__Co61__weak__wc12
       )

    jac[jfe62, jn] = (
       -rho*Y[jfe62]*rate_eval.n_Fe62__Fe63
       +rho*Y[jfe61]*rate_eval.n_Fe61__Fe62
       )

    jac[jfe62, jp] = (
       -rho*Y[jfe62]*rate_eval.p_Fe62__He4_Mn59
       -rho*Y[jfe62]*rate_eval.p_Fe62__n_Co62
       -rho*Y[jfe62]*rate_eval.p_Fe62__Co63
       +rho*Y[jmn61]*rate_eval.p_Mn61__Fe62
       +rho*Y[jmn62]*rate_eval.p_Mn62__n_Fe62
       )

    jac[jfe62, jhe4] = (
       -rho*Y[jfe62]*rate_eval.He4_Fe62__n_Ni65
       -rho*Y[jfe62]*rate_eval.He4_Fe62__Ni66
       +rho*Y[jcr59]*rate_eval.He4_Cr59__n_Fe62
       +rho*Y[jcr58]*rate_eval.He4_Cr58__Fe62
       )

    jac[jfe62, jcr58] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr58__Fe62
       )

    jac[jfe62, jcr59] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr59__n_Fe62
       )

    jac[jfe62, jmn61] = (
       +rho*Y[jp]*rate_eval.p_Mn61__Fe62
       )

    jac[jfe62, jmn62] = (
       +rate_eval.Mn62__Fe62__weak__mo03
       +rho*Y[jp]*rate_eval.p_Mn62__n_Fe62
       )

    jac[jfe62, jmn63] = (
       +rate_eval.Mn63__n_Fe62__weak__mp17
       )

    jac[jfe62, jfe61] = (
       +rho*Y[jn]*rate_eval.n_Fe61__Fe62
       )

    jac[jfe62, jfe62] = (
       -rho*Y[jp]*rate_eval.p_Fe62__He4_Mn59
       -rho*Y[jp]*rate_eval.p_Fe62__n_Co62
       -rho*Y[jn]*rate_eval.n_Fe62__Fe63
       -rho*Y[jhe4]*rate_eval.He4_Fe62__n_Ni65
       -rho*Y[jhe4]*rate_eval.He4_Fe62__Ni66
       -rate_eval.Fe62__Co62__weak__wc12
       -rho*Y[jp]*rate_eval.p_Fe62__Co63
       )

    jac[jfe63, jn] = (
       -rho*Y[jfe63]*rate_eval.n_Fe63__Fe64
       +rho*Y[jfe62]*rate_eval.n_Fe62__Fe63
       )

    jac[jfe63, jp] = (
       -rho*Y[jfe63]*rate_eval.p_Fe63__He4_Mn60
       -rho*Y[jfe63]*rate_eval.p_Fe63__Co64
       -rho*Y[jfe63]*rate_eval.p_Fe63__n_Co63
       +rho*Y[jmn62]*rate_eval.p_Mn62__Fe63
       +rho*Y[jmn63]*rate_eval.p_Mn63__n_Fe63
       )

    jac[jfe63, jhe4] = (
       -rho*Y[jfe63]*rate_eval.He4_Fe63__n_Ni66
       -rho*Y[jfe63]*rate_eval.He4_Fe63__Ni67
       +rho*Y[jcr59]*rate_eval.He4_Cr59__Fe63
       +rho*Y[jcr60]*rate_eval.He4_Cr60__n_Fe63
       )

    jac[jfe63, jcr59] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr59__Fe63
       )

    jac[jfe63, jcr60] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr60__n_Fe63
       )

    jac[jfe63, jmn62] = (
       +rho*Y[jp]*rate_eval.p_Mn62__Fe63
       )

    jac[jfe63, jmn63] = (
       +rho*Y[jp]*rate_eval.p_Mn63__n_Fe63
       +rate_eval.Mn63__Fe63__weak__wc12
       )

    jac[jfe63, jmn64] = (
       +rate_eval.Mn64__n_Fe63__weak__wc12
       )

    jac[jfe63, jfe62] = (
       +rho*Y[jn]*rate_eval.n_Fe62__Fe63
       )

    jac[jfe63, jfe63] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe63__n_Ni66
       -rho*Y[jp]*rate_eval.p_Fe63__He4_Mn60
       -rho*Y[jp]*rate_eval.p_Fe63__Co64
       -rho*Y[jn]*rate_eval.n_Fe63__Fe64
       -rho*Y[jp]*rate_eval.p_Fe63__n_Co63
       -rho*Y[jhe4]*rate_eval.He4_Fe63__Ni67
       -rate_eval.Fe63__Co63__weak__wc12
       )

    jac[jfe64, jn] = (
       -rho*Y[jfe64]*rate_eval.n_Fe64__Fe65
       +rho*Y[jfe63]*rate_eval.n_Fe63__Fe64
       )

    jac[jfe64, jp] = (
       -rho*Y[jfe64]*rate_eval.p_Fe64__He4_Mn61
       -rho*Y[jfe64]*rate_eval.p_Fe64__n_Co64
       -rho*Y[jfe64]*rate_eval.p_Fe64__Co65
       +rho*Y[jmn64]*rate_eval.p_Mn64__n_Fe64
       +rho*Y[jmn63]*rate_eval.p_Mn63__Fe64
       )

    jac[jfe64, jhe4] = (
       -rho*Y[jfe64]*rate_eval.He4_Fe64__n_Ni67
       -rho*Y[jfe64]*rate_eval.He4_Fe64__Ni68
       +rho*Y[jcr61]*rate_eval.He4_Cr61__n_Fe64
       +rho*Y[jcr60]*rate_eval.He4_Cr60__Fe64
       )

    jac[jfe64, jcr60] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr60__Fe64
       )

    jac[jfe64, jcr61] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr61__n_Fe64
       )

    jac[jfe64, jmn63] = (
       +rho*Y[jp]*rate_eval.p_Mn63__Fe64
       )

    jac[jfe64, jmn64] = (
       +rho*Y[jp]*rate_eval.p_Mn64__n_Fe64
       +rate_eval.Mn64__Fe64__weak__wc12
       )

    jac[jfe64, jmn65] = (
       +rate_eval.Mn65__n_Fe64__weak__mp17
       )

    jac[jfe64, jfe63] = (
       +rho*Y[jn]*rate_eval.n_Fe63__Fe64
       )

    jac[jfe64, jfe64] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe64__n_Ni67
       -rho*Y[jp]*rate_eval.p_Fe64__He4_Mn61
       -rho*Y[jhe4]*rate_eval.He4_Fe64__Ni68
       -rho*Y[jp]*rate_eval.p_Fe64__n_Co64
       -rho*Y[jp]*rate_eval.p_Fe64__Co65
       -rate_eval.Fe64__Co64__weak__wc12
       -rho*Y[jn]*rate_eval.n_Fe64__Fe65
       )

    jac[jfe65, jn] = (
       -rho*Y[jfe65]*rate_eval.n_Fe65__Fe66
       +rho*Y[jfe64]*rate_eval.n_Fe64__Fe65
       )

    jac[jfe65, jp] = (
       -rho*Y[jfe65]*rate_eval.p_Fe65__He4_Mn62
       -rho*Y[jfe65]*rate_eval.p_Fe65__Co66
       -rho*Y[jfe65]*rate_eval.p_Fe65__n_Co65
       +rho*Y[jmn64]*rate_eval.p_Mn64__Fe65
       +rho*Y[jmn65]*rate_eval.p_Mn65__n_Fe65
       )

    jac[jfe65, jhe4] = (
       -rho*Y[jfe65]*rate_eval.He4_Fe65__Ni69
       -rho*Y[jfe65]*rate_eval.He4_Fe65__n_Ni68
       +rho*Y[jcr62]*rate_eval.He4_Cr62__n_Fe65
       +rho*Y[jcr61]*rate_eval.He4_Cr61__Fe65
       )

    jac[jfe65, jcr61] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr61__Fe65
       )

    jac[jfe65, jcr62] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr62__n_Fe65
       )

    jac[jfe65, jmn64] = (
       +rho*Y[jp]*rate_eval.p_Mn64__Fe65
       )

    jac[jfe65, jmn65] = (
       +rho*Y[jp]*rate_eval.p_Mn65__n_Fe65
       +rate_eval.Mn65__Fe65__weak__wc17
       )

    jac[jfe65, jmn66] = (
       +rate_eval.Mn66__n_Fe65__weak__mp17
       )

    jac[jfe65, jfe64] = (
       +rho*Y[jn]*rate_eval.n_Fe64__Fe65
       )

    jac[jfe65, jfe65] = (
       -rho*Y[jp]*rate_eval.p_Fe65__He4_Mn62
       -rho*Y[jhe4]*rate_eval.He4_Fe65__Ni69
       -rho*Y[jp]*rate_eval.p_Fe65__Co66
       -rho*Y[jn]*rate_eval.n_Fe65__Fe66
       -rho*Y[jp]*rate_eval.p_Fe65__n_Co65
       -rho*Y[jhe4]*rate_eval.He4_Fe65__n_Ni68
       -rate_eval.Fe65__Co65__weak__wc12
       )

    jac[jfe66, jn] = (
       -rho*Y[jfe66]*rate_eval.n_Fe66__Fe67
       +rho*Y[jfe65]*rate_eval.n_Fe65__Fe66
       )

    jac[jfe66, jp] = (
       -rho*Y[jfe66]*rate_eval.p_Fe66__He4_Mn63
       -rho*Y[jfe66]*rate_eval.p_Fe66__n_Co66
       -rho*Y[jfe66]*rate_eval.p_Fe66__Co67
       +rho*Y[jmn66]*rate_eval.p_Mn66__n_Fe66
       +rho*Y[jmn65]*rate_eval.p_Mn65__Fe66
       )

    jac[jfe66, jhe4] = (
       -rho*Y[jfe66]*rate_eval.He4_Fe66__n_Ni69
       -rho*Y[jfe66]*rate_eval.He4_Fe66__Ni70
       +rho*Y[jcr63]*rate_eval.He4_Cr63__n_Fe66
       +rho*Y[jcr62]*rate_eval.He4_Cr62__Fe66
       )

    jac[jfe66, jcr62] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr62__Fe66
       )

    jac[jfe66, jcr63] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr63__n_Fe66
       )

    jac[jfe66, jmn65] = (
       +rho*Y[jp]*rate_eval.p_Mn65__Fe66
       )

    jac[jfe66, jmn66] = (
       +rho*Y[jp]*rate_eval.p_Mn66__n_Fe66
       +rate_eval.Mn66__Fe66__weak__wc17
       )

    jac[jfe66, jmn67] = (
       +rate_eval.Mn67__n_Fe66__weak__mp17
       )

    jac[jfe66, jmn68] = (
       +rate_eval.Mn68__n_n_Fe66__weak__mp17
       )

    jac[jfe66, jfe65] = (
       +rho*Y[jn]*rate_eval.n_Fe65__Fe66
       )

    jac[jfe66, jfe66] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe66__n_Ni69
       -rho*Y[jp]*rate_eval.p_Fe66__He4_Mn63
       -rho*Y[jn]*rate_eval.n_Fe66__Fe67
       -rho*Y[jp]*rate_eval.p_Fe66__n_Co66
       -rho*Y[jp]*rate_eval.p_Fe66__Co67
       -rate_eval.Fe66__Co66__weak__wc12
       -rho*Y[jhe4]*rate_eval.He4_Fe66__Ni70
       )

    jac[jfe67, jn] = (
       -rho*Y[jfe67]*rate_eval.n_Fe67__Fe68
       +rho*Y[jfe66]*rate_eval.n_Fe66__Fe67
       )

    jac[jfe67, jp] = (
       -rho*Y[jfe67]*rate_eval.p_Fe67__He4_Mn64
       -rho*Y[jfe67]*rate_eval.p_Fe67__n_Co67
       -rho*Y[jfe67]*rate_eval.p_Fe67__Co68
       +rho*Y[jmn66]*rate_eval.p_Mn66__Fe67
       +rho*Y[jmn67]*rate_eval.p_Mn67__n_Fe67
       )

    jac[jfe67, jhe4] = (
       -rho*Y[jfe67]*rate_eval.He4_Fe67__Ni71
       -rho*Y[jfe67]*rate_eval.He4_Fe67__n_Ni70
       +rho*Y[jcr64]*rate_eval.He4_Cr64__n_Fe67
       +rho*Y[jcr63]*rate_eval.He4_Cr63__Fe67
       )

    jac[jfe67, jcr63] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr63__Fe67
       )

    jac[jfe67, jcr64] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr64__n_Fe67
       )

    jac[jfe67, jmn66] = (
       +rho*Y[jp]*rate_eval.p_Mn66__Fe67
       )

    jac[jfe67, jmn67] = (
       +rate_eval.Mn67__Fe67__weak__wc17
       +rho*Y[jp]*rate_eval.p_Mn67__n_Fe67
       )

    jac[jfe67, jmn68] = (
       +rate_eval.Mn68__n_Fe67__weak__mp17
       )

    jac[jfe67, jfe66] = (
       +rho*Y[jn]*rate_eval.n_Fe66__Fe67
       )

    jac[jfe67, jfe67] = (
       -rho*Y[jp]*rate_eval.p_Fe67__He4_Mn64
       -rate_eval.Fe67__Co67__weak__wc12
       -rho*Y[jp]*rate_eval.p_Fe67__n_Co67
       -rho*Y[jhe4]*rate_eval.He4_Fe67__Ni71
       -rho*Y[jn]*rate_eval.n_Fe67__Fe68
       -rho*Y[jp]*rate_eval.p_Fe67__Co68
       -rho*Y[jhe4]*rate_eval.He4_Fe67__n_Ni70
       )

    jac[jfe68, jn] = (
       -rho*Y[jfe68]*rate_eval.n_Fe68__Fe69
       +rho*Y[jfe67]*rate_eval.n_Fe67__Fe68
       )

    jac[jfe68, jp] = (
       -rho*Y[jfe68]*rate_eval.p_Fe68__He4_Mn65
       -rho*Y[jfe68]*rate_eval.p_Fe68__Co69
       -rho*Y[jfe68]*rate_eval.p_Fe68__n_Co68
       +rho*Y[jmn68]*rate_eval.p_Mn68__n_Fe68
       +rho*Y[jmn67]*rate_eval.p_Mn67__Fe68
       )

    jac[jfe68, jhe4] = (
       -rho*Y[jfe68]*rate_eval.He4_Fe68__n_Ni71
       -rho*Y[jfe68]*rate_eval.He4_Fe68__Ni72
       +rho*Y[jcr65]*rate_eval.He4_Cr65__n_Fe68
       +rho*Y[jcr64]*rate_eval.He4_Cr64__Fe68
       )

    jac[jfe68, jcr64] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr64__Fe68
       )

    jac[jfe68, jcr65] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr65__n_Fe68
       )

    jac[jfe68, jmn67] = (
       +rho*Y[jp]*rate_eval.p_Mn67__Fe68
       )

    jac[jfe68, jmn68] = (
       +rho*Y[jp]*rate_eval.p_Mn68__n_Fe68
       +rate_eval.Mn68__Fe68__weak__wc17
       )

    jac[jfe68, jmn69] = (
       +rate_eval.Mn69__n_Fe68__weak__mp17
       )

    jac[jfe68, jmn70] = (
       +rate_eval.Mn70__n_n_Fe68__weak__mp17
       )

    jac[jfe68, jmn71] = (
       +rate_eval.Mn71__n_n_n_Fe68__weak__mo03
       )

    jac[jfe68, jfe67] = (
       +rho*Y[jn]*rate_eval.n_Fe67__Fe68
       )

    jac[jfe68, jfe68] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe68__n_Ni71
       -rho*Y[jp]*rate_eval.p_Fe68__He4_Mn65
       -rho*Y[jhe4]*rate_eval.He4_Fe68__Ni72
       -rho*Y[jp]*rate_eval.p_Fe68__Co69
       -rho*Y[jn]*rate_eval.n_Fe68__Fe69
       -rate_eval.Fe68__n_Co67__weak__mp17
       -rho*Y[jp]*rate_eval.p_Fe68__n_Co68
       -rate_eval.Fe68__Co68__weak__wc12
       )

    jac[jfe69, jn] = (
       -rho*Y[jfe69]*rate_eval.n_Fe69__Fe70
       +rho*Y[jfe68]*rate_eval.n_Fe68__Fe69
       )

    jac[jfe69, jp] = (
       -rho*Y[jfe69]*rate_eval.p_Fe69__He4_Mn66
       -rho*Y[jfe69]*rate_eval.p_Fe69__n_Co69
       -rho*Y[jfe69]*rate_eval.p_Fe69__Co70
       +rho*Y[jmn69]*rate_eval.p_Mn69__n_Fe69
       +rho*Y[jmn68]*rate_eval.p_Mn68__Fe69
       )

    jac[jfe69, jhe4] = (
       -rho*Y[jfe69]*rate_eval.He4_Fe69__Ni73
       -rho*Y[jfe69]*rate_eval.He4_Fe69__n_Ni72
       +rho*Y[jcr66]*rate_eval.He4_Cr66__n_Fe69
       +rho*Y[jcr65]*rate_eval.He4_Cr65__Fe69
       )

    jac[jfe69, jcr65] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr65__Fe69
       )

    jac[jfe69, jcr66] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr66__n_Fe69
       )

    jac[jfe69, jmn68] = (
       +rho*Y[jp]*rate_eval.p_Mn68__Fe69
       )

    jac[jfe69, jmn69] = (
       +rho*Y[jp]*rate_eval.p_Mn69__n_Fe69
       +rate_eval.Mn69__Fe69__weak__wc17
       )

    jac[jfe69, jmn70] = (
       +rate_eval.Mn70__n_Fe69__weak__mp17
       )

    jac[jfe69, jmn71] = (
       +rate_eval.Mn71__n_n_Fe69__weak__mp17
       )

    jac[jfe69, jmn72] = (
       +rate_eval.Mn72__n_n_n_Fe69__weak__mo03
       )

    jac[jfe69, jfe68] = (
       +rho*Y[jn]*rate_eval.n_Fe68__Fe69
       )

    jac[jfe69, jfe69] = (
       -rho*Y[jp]*rate_eval.p_Fe69__He4_Mn66
       -rho*Y[jp]*rate_eval.p_Fe69__n_Co69
       -rho*Y[jp]*rate_eval.p_Fe69__Co70
       -rho*Y[jhe4]*rate_eval.He4_Fe69__Ni73
       -rho*Y[jn]*rate_eval.n_Fe69__Fe70
       -rate_eval.Fe69__Co69__weak__wc17
       -rate_eval.Fe69__n_Co68__weak__mp17
       -rho*Y[jhe4]*rate_eval.He4_Fe69__n_Ni72
       )

    jac[jfe70, jn] = (
       -rho*Y[jfe70]*rate_eval.n_Fe70__Fe71
       +rho*Y[jfe69]*rate_eval.n_Fe69__Fe70
       )

    jac[jfe70, jp] = (
       -rho*Y[jfe70]*rate_eval.p_Fe70__He4_Mn67
       -rho*Y[jfe70]*rate_eval.p_Fe70__n_Co70
       -rho*Y[jfe70]*rate_eval.p_Fe70__Co71
       +rho*Y[jmn69]*rate_eval.p_Mn69__Fe70
       +rho*Y[jmn70]*rate_eval.p_Mn70__n_Fe70
       )

    jac[jfe70, jhe4] = (
       -rho*Y[jfe70]*rate_eval.He4_Fe70__n_Ni73
       -rho*Y[jfe70]*rate_eval.He4_Fe70__Ni74
       +rho*Y[jcr66]*rate_eval.He4_Cr66__Fe70
       +rho*Y[jcr67]*rate_eval.He4_Cr67__n_Fe70
       )

    jac[jfe70, jcr66] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr66__Fe70
       )

    jac[jfe70, jcr67] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr67__n_Fe70
       )

    jac[jfe70, jmn69] = (
       +rho*Y[jp]*rate_eval.p_Mn69__Fe70
       )

    jac[jfe70, jmn70] = (
       +rate_eval.Mn70__Fe70__weak__mo03
       +rho*Y[jp]*rate_eval.p_Mn70__n_Fe70
       )

    jac[jfe70, jmn71] = (
       +rate_eval.Mn71__n_Fe70__weak__mp17
       )

    jac[jfe70, jmn72] = (
       +rate_eval.Mn72__n_n_Fe70__weak__mp17
       )

    jac[jfe70, jmn73] = (
       +rate_eval.Mn73__n_n_n_Fe70__weak__mo03
       )

    jac[jfe70, jfe69] = (
       +rho*Y[jn]*rate_eval.n_Fe69__Fe70
       )

    jac[jfe70, jfe70] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe70__n_Ni73
       -rho*Y[jp]*rate_eval.p_Fe70__He4_Mn67
       -rho*Y[jp]*rate_eval.p_Fe70__n_Co70
       -rho*Y[jhe4]*rate_eval.He4_Fe70__Ni74
       -rho*Y[jp]*rate_eval.p_Fe70__Co71
       -rho*Y[jn]*rate_eval.n_Fe70__Fe71
       -rate_eval.Fe70__n_Co69__weak__mp17
       -rate_eval.Fe70__Co70__weak__wc17
       )

    jac[jfe71, jn] = (
       -rho*Y[jfe71]*rate_eval.n_Fe71__Fe72
       +rho*Y[jfe70]*rate_eval.n_Fe70__Fe71
       )

    jac[jfe71, jp] = (
       -rho*Y[jfe71]*rate_eval.p_Fe71__He4_Mn68
       -rho*Y[jfe71]*rate_eval.p_Fe71__n_Co71
       -rho*Y[jfe71]*rate_eval.p_Fe71__Co72
       +rho*Y[jmn70]*rate_eval.p_Mn70__Fe71
       +rho*Y[jmn71]*rate_eval.p_Mn71__n_Fe71
       )

    jac[jfe71, jhe4] = (
       -rho*Y[jfe71]*rate_eval.He4_Fe71__n_Ni74
       -rho*Y[jfe71]*rate_eval.He4_Fe71__Ni75
       +rho*Y[jcr67]*rate_eval.He4_Cr67__Fe71
       +rho*Y[jcr68]*rate_eval.He4_Cr68__n_Fe71
       )

    jac[jfe71, jcr67] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr67__Fe71
       )

    jac[jfe71, jcr68] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr68__n_Fe71
       )

    jac[jfe71, jmn70] = (
       +rho*Y[jp]*rate_eval.p_Mn70__Fe71
       )

    jac[jfe71, jmn71] = (
       +rho*Y[jp]*rate_eval.p_Mn71__n_Fe71
       +rate_eval.Mn71__Fe71__weak__mo03
       )

    jac[jfe71, jmn72] = (
       +rate_eval.Mn72__n_Fe71__weak__mp17
       )

    jac[jfe71, jmn73] = (
       +rate_eval.Mn73__n_n_Fe71__weak__mp17
       )

    jac[jfe71, jfe70] = (
       +rho*Y[jn]*rate_eval.n_Fe70__Fe71
       )

    jac[jfe71, jfe71] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe71__n_Ni74
       -rho*Y[jp]*rate_eval.p_Fe71__He4_Mn68
       -rho*Y[jp]*rate_eval.p_Fe71__n_Co71
       -rho*Y[jn]*rate_eval.n_Fe71__Fe72
       -rho*Y[jhe4]*rate_eval.He4_Fe71__Ni75
       -rho*Y[jp]*rate_eval.p_Fe71__Co72
       -rate_eval.Fe71__n_Co70__weak__mp17
       -rate_eval.Fe71__Co71__weak__wc17
       )

    jac[jfe72, jn] = (
       -rho*Y[jfe72]*rate_eval.n_Fe72__Fe73
       +rho*Y[jfe71]*rate_eval.n_Fe71__Fe72
       )

    jac[jfe72, jp] = (
       -rho*Y[jfe72]*rate_eval.p_Fe72__He4_Mn69
       -rho*Y[jfe72]*rate_eval.p_Fe72__n_Co72
       -rho*Y[jfe72]*rate_eval.p_Fe72__Co73
       +rho*Y[jmn72]*rate_eval.p_Mn72__n_Fe72
       +rho*Y[jmn71]*rate_eval.p_Mn71__Fe72
       )

    jac[jfe72, jhe4] = (
       -rho*Y[jfe72]*rate_eval.He4_Fe72__n_Ni75
       -rho*Y[jfe72]*rate_eval.He4_Fe72__Ni76
       +rho*Y[jcr69]*rate_eval.He4_Cr69__n_Fe72
       +rho*Y[jcr68]*rate_eval.He4_Cr68__Fe72
       )

    jac[jfe72, jcr68] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr68__Fe72
       )

    jac[jfe72, jcr69] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr69__n_Fe72
       )

    jac[jfe72, jmn71] = (
       +rho*Y[jp]*rate_eval.p_Mn71__Fe72
       )

    jac[jfe72, jmn72] = (
       +rho*Y[jp]*rate_eval.p_Mn72__n_Fe72
       +rate_eval.Mn72__Fe72__weak__mo03
       )

    jac[jfe72, jmn73] = (
       +rate_eval.Mn73__n_Fe72__weak__mp17
       )

    jac[jfe72, jfe71] = (
       +rho*Y[jn]*rate_eval.n_Fe71__Fe72
       )

    jac[jfe72, jfe72] = (
       -rho*Y[jp]*rate_eval.p_Fe72__He4_Mn69
       -rho*Y[jp]*rate_eval.p_Fe72__n_Co72
       -rho*Y[jn]*rate_eval.n_Fe72__Fe73
       -rho*Y[jp]*rate_eval.p_Fe72__Co73
       -rate_eval.Fe72__n_Co71__weak__mp17
       -rate_eval.Fe72__Co72__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Fe72__n_Ni75
       -rho*Y[jhe4]*rate_eval.He4_Fe72__Ni76
       )

    jac[jfe73, jn] = (
       -rho*Y[jfe73]*rate_eval.n_Fe73__Fe74
       +rho*Y[jfe72]*rate_eval.n_Fe72__Fe73
       )

    jac[jfe73, jp] = (
       -rho*Y[jfe73]*rate_eval.p_Fe73__He4_Mn70
       -rho*Y[jfe73]*rate_eval.p_Fe73__n_Co73
       -rho*Y[jfe73]*rate_eval.p_Fe73__Co74
       +rho*Y[jmn73]*rate_eval.p_Mn73__n_Fe73
       +rho*Y[jmn72]*rate_eval.p_Mn72__Fe73
       )

    jac[jfe73, jhe4] = (
       -rho*Y[jfe73]*rate_eval.He4_Fe73__n_Ni76
       -rho*Y[jfe73]*rate_eval.He4_Fe73__Ni77
       +rho*Y[jcr70]*rate_eval.He4_Cr70__n_Fe73
       +rho*Y[jcr69]*rate_eval.He4_Cr69__Fe73
       )

    jac[jfe73, jcr69] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr69__Fe73
       )

    jac[jfe73, jcr70] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr70__n_Fe73
       )

    jac[jfe73, jmn72] = (
       +rho*Y[jp]*rate_eval.p_Mn72__Fe73
       )

    jac[jfe73, jmn73] = (
       +rho*Y[jp]*rate_eval.p_Mn73__n_Fe73
       +rate_eval.Mn73__Fe73__weak__mo03
       )

    jac[jfe73, jfe72] = (
       +rho*Y[jn]*rate_eval.n_Fe72__Fe73
       )

    jac[jfe73, jfe73] = (
       -rho*Y[jp]*rate_eval.p_Fe73__He4_Mn70
       -rho*Y[jp]*rate_eval.p_Fe73__n_Co73
       -rho*Y[jhe4]*rate_eval.He4_Fe73__n_Ni76
       -rho*Y[jhe4]*rate_eval.He4_Fe73__Ni77
       -rho*Y[jp]*rate_eval.p_Fe73__Co74
       -rho*Y[jn]*rate_eval.n_Fe73__Fe74
       -rate_eval.Fe73__n_n_Co71__weak__mp17
       -rate_eval.Fe73__n_Co72__weak__mp17
       -rate_eval.Fe73__Co73__weak__mo03
       )

    jac[jfe74, jn] = (
       -rho*Y[jfe74]*rate_eval.n_Fe74__Fe75
       +rho*Y[jfe73]*rate_eval.n_Fe73__Fe74
       )

    jac[jfe74, jp] = (
       -rho*Y[jfe74]*rate_eval.p_Fe74__He4_Mn71
       -rho*Y[jfe74]*rate_eval.p_Fe74__n_Co74
       -rho*Y[jfe74]*rate_eval.p_Fe74__Co75
       +rho*Y[jmn73]*rate_eval.p_Mn73__Fe74
       )

    jac[jfe74, jhe4] = (
       -rho*Y[jfe74]*rate_eval.He4_Fe74__n_Ni77
       -rho*Y[jfe74]*rate_eval.He4_Fe74__Ni78
       +rho*Y[jcr70]*rate_eval.He4_Cr70__Fe74
       )

    jac[jfe74, jcr70] = (
       +rho*Y[jhe4]*rate_eval.He4_Cr70__Fe74
       )

    jac[jfe74, jmn73] = (
       +rho*Y[jp]*rate_eval.p_Mn73__Fe74
       )

    jac[jfe74, jfe73] = (
       +rho*Y[jn]*rate_eval.n_Fe73__Fe74
       )

    jac[jfe74, jfe74] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe74__n_Ni77
       -rho*Y[jp]*rate_eval.p_Fe74__He4_Mn71
       -rho*Y[jp]*rate_eval.p_Fe74__n_Co74
       -rho*Y[jn]*rate_eval.n_Fe74__Fe75
       -rate_eval.Fe74__Co74__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Fe74__Ni78
       -rate_eval.Fe74__n_Co73__weak__mp17
       -rho*Y[jp]*rate_eval.p_Fe74__Co75
       )

    jac[jfe75, jn] = (
       -rho*Y[jfe75]*rate_eval.n_Fe75__Fe76
       +rho*Y[jfe74]*rate_eval.n_Fe74__Fe75
       )

    jac[jfe75, jp] = (
       -rho*Y[jfe75]*rate_eval.p_Fe75__He4_Mn72
       -rho*Y[jfe75]*rate_eval.p_Fe75__n_Co75
       -rho*Y[jfe75]*rate_eval.p_Fe75__Co76
       )

    jac[jfe75, jhe4] = (
       -rho*Y[jfe75]*rate_eval.He4_Fe75__n_Ni78
       -rho*Y[jfe75]*rate_eval.He4_Fe75__Ni79
       )

    jac[jfe75, jfe74] = (
       +rho*Y[jn]*rate_eval.n_Fe74__Fe75
       )

    jac[jfe75, jfe75] = (
       -rate_eval.Fe75__n_n_n_Co72__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Fe75__n_Ni78
       -rho*Y[jp]*rate_eval.p_Fe75__He4_Mn72
       -rho*Y[jp]*rate_eval.p_Fe75__n_Co75
       -rho*Y[jn]*rate_eval.n_Fe75__Fe76
       -rho*Y[jhe4]*rate_eval.He4_Fe75__Ni79
       -rate_eval.Fe75__n_n_Co73__weak__mp17
       -rate_eval.Fe75__n_Co74__weak__mp17
       -rate_eval.Fe75__Co75__weak__mo03
       -rho*Y[jp]*rate_eval.p_Fe75__Co76
       )

    jac[jfe76, jn] = (
       +rho*Y[jfe75]*rate_eval.n_Fe75__Fe76
       )

    jac[jfe76, jp] = (
       -rho*Y[jfe76]*rate_eval.p_Fe76__He4_Mn73
       -rho*Y[jfe76]*rate_eval.p_Fe76__Co77
       -rho*Y[jfe76]*rate_eval.p_Fe76__n_Co76
       )

    jac[jfe76, jhe4] = (
       -rho*Y[jfe76]*rate_eval.He4_Fe76__n_Ni79
       -rho*Y[jfe76]*rate_eval.He4_Fe76__Ni80
       )

    jac[jfe76, jfe75] = (
       +rho*Y[jn]*rate_eval.n_Fe75__Fe76
       )

    jac[jfe76, jfe76] = (
       -rho*Y[jhe4]*rate_eval.He4_Fe76__n_Ni79
       -rho*Y[jp]*rate_eval.p_Fe76__He4_Mn73
       -rate_eval.Fe76__n_n_n_Co73__weak__mo03
       -rho*Y[jhe4]*rate_eval.He4_Fe76__Ni80
       -rho*Y[jp]*rate_eval.p_Fe76__Co77
       -rate_eval.Fe76__n_n_Co74__weak__mp17
       -rho*Y[jp]*rate_eval.p_Fe76__n_Co76
       -rate_eval.Fe76__n_Co75__weak__mp17
       -rate_eval.Fe76__Co76__weak__mo03
       )

    jac[jco47, jp] = (
       +rho*Y[jfe46]*rate_eval.p_Fe46__Co47
       )

    jac[jco47, jhe4] = (
       +rho*Y[jmn43]*rate_eval.He4_Mn43__Co47
       )

    jac[jco47, jmn43] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn43__Co47
       )

    jac[jco47, jfe46] = (
       +rho*Y[jp]*rate_eval.p_Fe46__Co47
       )

    jac[jco48, jp] = (
       +rho*Y[jfe47]*rate_eval.p_Fe47__Co48
       )

    jac[jco48, jhe4] = (
       +rho*Y[jmn44]*rate_eval.He4_Mn44__Co48
       +rho*Y[jfe45]*rate_eval.He4_Fe45__p_Co48
       )

    jac[jco48, jmn44] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn44__Co48
       )

    jac[jco48, jfe45] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe45__p_Co48
       )

    jac[jco48, jfe47] = (
       +rho*Y[jp]*rate_eval.p_Fe47__Co48
       )

    jac[jco49, jp] = (
       +rho*Y[jfe48]*rate_eval.p_Fe48__Co49
       )

    jac[jco49, jhe4] = (
       +rho*Y[jfe46]*rate_eval.He4_Fe46__p_Co49
       +rho*Y[jmn45]*rate_eval.He4_Mn45__Co49
       )

    jac[jco49, jmn45] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn45__Co49
       )

    jac[jco49, jfe46] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe46__p_Co49
       )

    jac[jco49, jfe48] = (
       +rho*Y[jp]*rate_eval.p_Fe48__Co49
       )

    jac[jco50, jp] = (
       +rho*Y[jfe49]*rate_eval.p_Fe49__Co50
       )

    jac[jco50, jhe4] = (
       +rho*Y[jmn46]*rate_eval.He4_Mn46__Co50
       +rho*Y[jfe47]*rate_eval.He4_Fe47__p_Co50
       )

    jac[jco50, jmn46] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn46__Co50
       )

    jac[jco50, jfe47] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe47__p_Co50
       )

    jac[jco50, jfe49] = (
       +rho*Y[jp]*rate_eval.p_Fe49__Co50
       )

    jac[jco51, jp] = (
       +rho*Y[jfe50]*rate_eval.p_Fe50__Co51
       )

    jac[jco51, jhe4] = (
       +rho*Y[jfe48]*rate_eval.He4_Fe48__p_Co51
       +rho*Y[jmn47]*rate_eval.He4_Mn47__Co51
       )

    jac[jco51, jmn47] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn47__Co51
       )

    jac[jco51, jfe48] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe48__p_Co51
       )

    jac[jco51, jfe50] = (
       +rho*Y[jp]*rate_eval.p_Fe50__Co51
       )

    jac[jco52, jp] = (
       +rho*Y[jfe51]*rate_eval.p_Fe51__Co52
       )

    jac[jco52, jhe4] = (
       +rho*Y[jfe49]*rate_eval.He4_Fe49__p_Co52
       +rho*Y[jmn48]*rate_eval.He4_Mn48__Co52
       )

    jac[jco52, jmn48] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn48__Co52
       )

    jac[jco52, jfe49] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe49__p_Co52
       )

    jac[jco52, jfe51] = (
       +rho*Y[jp]*rate_eval.p_Fe51__Co52
       )

    jac[jco53, jp] = (
       +rho*Y[jfe52]*rate_eval.p_Fe52__Co53
       )

    jac[jco53, jhe4] = (
       +rho*Y[jfe50]*rate_eval.He4_Fe50__p_Co53
       +rho*Y[jmn49]*rate_eval.He4_Mn49__Co53
       )

    jac[jco53, jmn49] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn49__Co53
       )

    jac[jco53, jfe50] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe50__p_Co53
       )

    jac[jco53, jfe52] = (
       +rho*Y[jp]*rate_eval.p_Fe52__Co53
       )

    jac[jco54, jp] = (
       +rho*Y[jfe53]*rate_eval.p_Fe53__Co54
       )

    jac[jco54, jhe4] = (
       +rho*Y[jmn50]*rate_eval.He4_Mn50__Co54
       +rho*Y[jfe51]*rate_eval.He4_Fe51__p_Co54
       )

    jac[jco54, jmn50] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn50__Co54
       )

    jac[jco54, jfe51] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe51__p_Co54
       )

    jac[jco54, jfe53] = (
       +rho*Y[jp]*rate_eval.p_Fe53__Co54
       )

    jac[jco55, jp] = (
       +rho*Y[jfe54]*rate_eval.p_Fe54__Co55
       )

    jac[jco55, jhe4] = (
       +rho*Y[jfe52]*rate_eval.He4_Fe52__p_Co55
       +rho*Y[jmn51]*rate_eval.He4_Mn51__Co55
       )

    jac[jco55, jmn51] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn51__Co55
       )

    jac[jco55, jfe52] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe52__p_Co55
       )

    jac[jco55, jfe54] = (
       +rho*Y[jp]*rate_eval.p_Fe54__Co55
       )

    jac[jco56, jp] = (
       +rho*Y[jfe55]*rate_eval.p_Fe55__Co56
       )

    jac[jco56, jhe4] = (
       +rho*Y[jfe53]*rate_eval.He4_Fe53__p_Co56
       +rho*Y[jmn52]*rate_eval.He4_Mn52__Co56
       )

    jac[jco56, jmn52] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn52__Co56
       )

    jac[jco56, jfe53] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe53__p_Co56
       )

    jac[jco56, jfe55] = (
       +rho*Y[jp]*rate_eval.p_Fe55__Co56
       )

    jac[jco57, jp] = (
       +rho*Y[jfe56]*rate_eval.p_Fe56__Co57
       )

    jac[jco57, jhe4] = (
       +rho*Y[jmn53]*rate_eval.He4_Mn53__Co57
       )

    jac[jco57, jmn53] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn53__Co57
       )

    jac[jco57, jfe56] = (
       +rho*Y[jp]*rate_eval.p_Fe56__Co57
       )

    jac[jco58, jp] = (
       +rho*Y[jfe57]*rate_eval.p_Fe57__Co58
       )

    jac[jco58, jhe4] = (
       +rho*Y[jmn54]*rate_eval.He4_Mn54__Co58
       )

    jac[jco58, jmn54] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn54__Co58
       )

    jac[jco58, jfe57] = (
       +rho*Y[jp]*rate_eval.p_Fe57__Co58
       )

    jac[jco59, jp] = (
       +rho*Y[jfe59]*rate_eval.p_Fe59__n_Co59
       +rho*Y[jfe58]*rate_eval.p_Fe58__Co59
       )

    jac[jco59, jhe4] = (
       +rho*Y[jmn55]*rate_eval.He4_Mn55__Co59
       )

    jac[jco59, jmn55] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn55__Co59
       )

    jac[jco59, jfe58] = (
       +rho*Y[jp]*rate_eval.p_Fe58__Co59
       )

    jac[jco59, jfe59] = (
       +rho*Y[jp]*rate_eval.p_Fe59__n_Co59
       +rate_eval.Fe59__Co59__weak__wc12
       )

    jac[jco60, jp] = (
       +rho*Y[jfe59]*rate_eval.p_Fe59__Co60
       )

    jac[jco60, jhe4] = (
       +rho*Y[jmn56]*rate_eval.He4_Mn56__Co60
       )

    jac[jco60, jmn56] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn56__Co60
       )

    jac[jco60, jfe59] = (
       +rho*Y[jp]*rate_eval.p_Fe59__Co60
       )

    jac[jco60, jfe60] = (
       +rate_eval.Fe60__Co60__weak__wc12
       )

    jac[jco61, jp] = (
       +rho*Y[jfe61]*rate_eval.p_Fe61__n_Co61
       +rho*Y[jfe60]*rate_eval.p_Fe60__Co61
       )

    jac[jco61, jhe4] = (
       +rho*Y[jmn58]*rate_eval.He4_Mn58__n_Co61
       +rho*Y[jmn57]*rate_eval.He4_Mn57__Co61
       )

    jac[jco61, jmn57] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn57__Co61
       )

    jac[jco61, jmn58] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn58__n_Co61
       )

    jac[jco61, jfe60] = (
       +rho*Y[jp]*rate_eval.p_Fe60__Co61
       )

    jac[jco61, jfe61] = (
       +rho*Y[jp]*rate_eval.p_Fe61__n_Co61
       +rate_eval.Fe61__Co61__weak__wc12
       )

    jac[jco62, jp] = (
       +rho*Y[jfe62]*rate_eval.p_Fe62__n_Co62
       +rho*Y[jfe61]*rate_eval.p_Fe61__Co62
       )

    jac[jco62, jhe4] = (
       +rho*Y[jmn59]*rate_eval.He4_Mn59__n_Co62
       +rho*Y[jmn58]*rate_eval.He4_Mn58__Co62
       )

    jac[jco62, jmn58] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn58__Co62
       )

    jac[jco62, jmn59] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn59__n_Co62
       )

    jac[jco62, jfe61] = (
       +rho*Y[jp]*rate_eval.p_Fe61__Co62
       )

    jac[jco62, jfe62] = (
       +rho*Y[jp]*rate_eval.p_Fe62__n_Co62
       +rate_eval.Fe62__Co62__weak__wc12
       )

    jac[jco63, jp] = (
       +rho*Y[jfe63]*rate_eval.p_Fe63__n_Co63
       +rho*Y[jfe62]*rate_eval.p_Fe62__Co63
       )

    jac[jco63, jhe4] = (
       +rho*Y[jmn60]*rate_eval.He4_Mn60__n_Co63
       +rho*Y[jmn59]*rate_eval.He4_Mn59__Co63
       )

    jac[jco63, jmn59] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn59__Co63
       )

    jac[jco63, jmn60] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn60__n_Co63
       )

    jac[jco63, jfe62] = (
       +rho*Y[jp]*rate_eval.p_Fe62__Co63
       )

    jac[jco63, jfe63] = (
       +rho*Y[jp]*rate_eval.p_Fe63__n_Co63
       +rate_eval.Fe63__Co63__weak__wc12
       )

    jac[jco64, jp] = (
       +rho*Y[jfe63]*rate_eval.p_Fe63__Co64
       +rho*Y[jfe64]*rate_eval.p_Fe64__n_Co64
       )

    jac[jco64, jhe4] = (
       +rho*Y[jmn60]*rate_eval.He4_Mn60__Co64
       +rho*Y[jmn61]*rate_eval.He4_Mn61__n_Co64
       )

    jac[jco64, jmn60] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn60__Co64
       )

    jac[jco64, jmn61] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn61__n_Co64
       )

    jac[jco64, jfe63] = (
       +rho*Y[jp]*rate_eval.p_Fe63__Co64
       )

    jac[jco64, jfe64] = (
       +rho*Y[jp]*rate_eval.p_Fe64__n_Co64
       +rate_eval.Fe64__Co64__weak__wc12
       )

    jac[jco65, jp] = (
       +rho*Y[jfe64]*rate_eval.p_Fe64__Co65
       +rho*Y[jfe65]*rate_eval.p_Fe65__n_Co65
       )

    jac[jco65, jhe4] = (
       +rho*Y[jmn62]*rate_eval.He4_Mn62__n_Co65
       +rho*Y[jmn61]*rate_eval.He4_Mn61__Co65
       )

    jac[jco65, jmn61] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn61__Co65
       )

    jac[jco65, jmn62] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn62__n_Co65
       )

    jac[jco65, jfe64] = (
       +rho*Y[jp]*rate_eval.p_Fe64__Co65
       )

    jac[jco65, jfe65] = (
       +rho*Y[jp]*rate_eval.p_Fe65__n_Co65
       +rate_eval.Fe65__Co65__weak__wc12
       )

    jac[jco66, jp] = (
       +rho*Y[jfe66]*rate_eval.p_Fe66__n_Co66
       +rho*Y[jfe65]*rate_eval.p_Fe65__Co66
       )

    jac[jco66, jhe4] = (
       +rho*Y[jmn62]*rate_eval.He4_Mn62__Co66
       +rho*Y[jmn63]*rate_eval.He4_Mn63__n_Co66
       )

    jac[jco66, jmn62] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn62__Co66
       )

    jac[jco66, jmn63] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn63__n_Co66
       )

    jac[jco66, jfe65] = (
       +rho*Y[jp]*rate_eval.p_Fe65__Co66
       )

    jac[jco66, jfe66] = (
       +rho*Y[jp]*rate_eval.p_Fe66__n_Co66
       +rate_eval.Fe66__Co66__weak__wc12
       )

    jac[jco67, jp] = (
       +rho*Y[jfe67]*rate_eval.p_Fe67__n_Co67
       +rho*Y[jfe66]*rate_eval.p_Fe66__Co67
       )

    jac[jco67, jhe4] = (
       +rho*Y[jmn63]*rate_eval.He4_Mn63__Co67
       +rho*Y[jmn64]*rate_eval.He4_Mn64__n_Co67
       )

    jac[jco67, jmn63] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn63__Co67
       )

    jac[jco67, jmn64] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn64__n_Co67
       )

    jac[jco67, jfe66] = (
       +rho*Y[jp]*rate_eval.p_Fe66__Co67
       )

    jac[jco67, jfe67] = (
       +rate_eval.Fe67__Co67__weak__wc12
       +rho*Y[jp]*rate_eval.p_Fe67__n_Co67
       )

    jac[jco67, jfe68] = (
       +rate_eval.Fe68__n_Co67__weak__mp17
       )

    jac[jco68, jp] = (
       +rho*Y[jfe67]*rate_eval.p_Fe67__Co68
       +rho*Y[jfe68]*rate_eval.p_Fe68__n_Co68
       )

    jac[jco68, jhe4] = (
       +rho*Y[jmn65]*rate_eval.He4_Mn65__n_Co68
       +rho*Y[jmn64]*rate_eval.He4_Mn64__Co68
       )

    jac[jco68, jmn64] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn64__Co68
       )

    jac[jco68, jmn65] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn65__n_Co68
       )

    jac[jco68, jfe67] = (
       +rho*Y[jp]*rate_eval.p_Fe67__Co68
       )

    jac[jco68, jfe68] = (
       +rho*Y[jp]*rate_eval.p_Fe68__n_Co68
       +rate_eval.Fe68__Co68__weak__wc12
       )

    jac[jco68, jfe69] = (
       +rate_eval.Fe69__n_Co68__weak__mp17
       )

    jac[jco69, jp] = (
       +rho*Y[jfe69]*rate_eval.p_Fe69__n_Co69
       +rho*Y[jfe68]*rate_eval.p_Fe68__Co69
       )

    jac[jco69, jhe4] = (
       +rho*Y[jmn65]*rate_eval.He4_Mn65__Co69
       +rho*Y[jmn66]*rate_eval.He4_Mn66__n_Co69
       )

    jac[jco69, jmn65] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn65__Co69
       )

    jac[jco69, jmn66] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn66__n_Co69
       )

    jac[jco69, jfe68] = (
       +rho*Y[jp]*rate_eval.p_Fe68__Co69
       )

    jac[jco69, jfe69] = (
       +rho*Y[jp]*rate_eval.p_Fe69__n_Co69
       +rate_eval.Fe69__Co69__weak__wc17
       )

    jac[jco69, jfe70] = (
       +rate_eval.Fe70__n_Co69__weak__mp17
       )

    jac[jco70, jp] = (
       +rho*Y[jfe70]*rate_eval.p_Fe70__n_Co70
       +rho*Y[jfe69]*rate_eval.p_Fe69__Co70
       )

    jac[jco70, jhe4] = (
       +rho*Y[jmn67]*rate_eval.He4_Mn67__n_Co70
       +rho*Y[jmn66]*rate_eval.He4_Mn66__Co70
       )

    jac[jco70, jmn66] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn66__Co70
       )

    jac[jco70, jmn67] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn67__n_Co70
       )

    jac[jco70, jfe69] = (
       +rho*Y[jp]*rate_eval.p_Fe69__Co70
       )

    jac[jco70, jfe70] = (
       +rho*Y[jp]*rate_eval.p_Fe70__n_Co70
       +rate_eval.Fe70__Co70__weak__wc17
       )

    jac[jco70, jfe71] = (
       +rate_eval.Fe71__n_Co70__weak__mp17
       )

    jac[jco71, jp] = (
       +rho*Y[jfe71]*rate_eval.p_Fe71__n_Co71
       +rho*Y[jfe70]*rate_eval.p_Fe70__Co71
       )

    jac[jco71, jhe4] = (
       +rho*Y[jmn68]*rate_eval.He4_Mn68__n_Co71
       +rho*Y[jmn67]*rate_eval.He4_Mn67__Co71
       )

    jac[jco71, jmn67] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn67__Co71
       )

    jac[jco71, jmn68] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn68__n_Co71
       )

    jac[jco71, jfe70] = (
       +rho*Y[jp]*rate_eval.p_Fe70__Co71
       )

    jac[jco71, jfe71] = (
       +rho*Y[jp]*rate_eval.p_Fe71__n_Co71
       +rate_eval.Fe71__Co71__weak__wc17
       )

    jac[jco71, jfe72] = (
       +rate_eval.Fe72__n_Co71__weak__mp17
       )

    jac[jco71, jfe73] = (
       +rate_eval.Fe73__n_n_Co71__weak__mp17
       )

    jac[jco72, jp] = (
       +rho*Y[jfe72]*rate_eval.p_Fe72__n_Co72
       +rho*Y[jfe71]*rate_eval.p_Fe71__Co72
       )

    jac[jco72, jhe4] = (
       +rho*Y[jmn69]*rate_eval.He4_Mn69__n_Co72
       +rho*Y[jmn68]*rate_eval.He4_Mn68__Co72
       )

    jac[jco72, jmn68] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn68__Co72
       )

    jac[jco72, jmn69] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn69__n_Co72
       )

    jac[jco72, jfe71] = (
       +rho*Y[jp]*rate_eval.p_Fe71__Co72
       )

    jac[jco72, jfe72] = (
       +rho*Y[jp]*rate_eval.p_Fe72__n_Co72
       +rate_eval.Fe72__Co72__weak__mo03
       )

    jac[jco72, jfe73] = (
       +rate_eval.Fe73__n_Co72__weak__mp17
       )

    jac[jco72, jfe75] = (
       +rate_eval.Fe75__n_n_n_Co72__weak__mo03
       )

    jac[jco73, jp] = (
       +rho*Y[jfe73]*rate_eval.p_Fe73__n_Co73
       +rho*Y[jfe72]*rate_eval.p_Fe72__Co73
       )

    jac[jco73, jhe4] = (
       +rho*Y[jmn69]*rate_eval.He4_Mn69__Co73
       +rho*Y[jmn70]*rate_eval.He4_Mn70__n_Co73
       )

    jac[jco73, jmn69] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn69__Co73
       )

    jac[jco73, jmn70] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn70__n_Co73
       )

    jac[jco73, jfe72] = (
       +rho*Y[jp]*rate_eval.p_Fe72__Co73
       )

    jac[jco73, jfe73] = (
       +rho*Y[jp]*rate_eval.p_Fe73__n_Co73
       +rate_eval.Fe73__Co73__weak__mo03
       )

    jac[jco73, jfe74] = (
       +rate_eval.Fe74__n_Co73__weak__mp17
       )

    jac[jco73, jfe75] = (
       +rate_eval.Fe75__n_n_Co73__weak__mp17
       )

    jac[jco73, jfe76] = (
       +rate_eval.Fe76__n_n_n_Co73__weak__mo03
       )

    jac[jco74, jp] = (
       +rho*Y[jfe74]*rate_eval.p_Fe74__n_Co74
       +rho*Y[jfe73]*rate_eval.p_Fe73__Co74
       )

    jac[jco74, jhe4] = (
       +rho*Y[jmn70]*rate_eval.He4_Mn70__Co74
       +rho*Y[jmn71]*rate_eval.He4_Mn71__n_Co74
       )

    jac[jco74, jmn70] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn70__Co74
       )

    jac[jco74, jmn71] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn71__n_Co74
       )

    jac[jco74, jfe73] = (
       +rho*Y[jp]*rate_eval.p_Fe73__Co74
       )

    jac[jco74, jfe74] = (
       +rho*Y[jp]*rate_eval.p_Fe74__n_Co74
       +rate_eval.Fe74__Co74__weak__mo03
       )

    jac[jco74, jfe75] = (
       +rate_eval.Fe75__n_Co74__weak__mp17
       )

    jac[jco74, jfe76] = (
       +rate_eval.Fe76__n_n_Co74__weak__mp17
       )

    jac[jco75, jp] = (
       +rho*Y[jfe75]*rate_eval.p_Fe75__n_Co75
       +rho*Y[jfe74]*rate_eval.p_Fe74__Co75
       )

    jac[jco75, jhe4] = (
       +rho*Y[jmn72]*rate_eval.He4_Mn72__n_Co75
       +rho*Y[jmn71]*rate_eval.He4_Mn71__Co75
       )

    jac[jco75, jmn71] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn71__Co75
       )

    jac[jco75, jmn72] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn72__n_Co75
       )

    jac[jco75, jfe74] = (
       +rho*Y[jp]*rate_eval.p_Fe74__Co75
       )

    jac[jco75, jfe75] = (
       +rho*Y[jp]*rate_eval.p_Fe75__n_Co75
       +rate_eval.Fe75__Co75__weak__mo03
       )

    jac[jco75, jfe76] = (
       +rate_eval.Fe76__n_Co75__weak__mp17
       )

    jac[jco76, jp] = (
       +rho*Y[jfe76]*rate_eval.p_Fe76__n_Co76
       +rho*Y[jfe75]*rate_eval.p_Fe75__Co76
       )

    jac[jco76, jhe4] = (
       +rho*Y[jmn73]*rate_eval.He4_Mn73__n_Co76
       +rho*Y[jmn72]*rate_eval.He4_Mn72__Co76
       )

    jac[jco76, jmn72] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn72__Co76
       )

    jac[jco76, jmn73] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn73__n_Co76
       )

    jac[jco76, jfe75] = (
       +rho*Y[jp]*rate_eval.p_Fe75__Co76
       )

    jac[jco76, jfe76] = (
       +rho*Y[jp]*rate_eval.p_Fe76__n_Co76
       +rate_eval.Fe76__Co76__weak__mo03
       )

    jac[jco77, jp] = (
       +rho*Y[jfe76]*rate_eval.p_Fe76__Co77
       )

    jac[jco77, jhe4] = (
       +rho*Y[jmn73]*rate_eval.He4_Mn73__Co77
       )

    jac[jco77, jmn73] = (
       +rho*Y[jhe4]*rate_eval.He4_Mn73__Co77
       )

    jac[jco77, jfe76] = (
       +rho*Y[jp]*rate_eval.p_Fe76__Co77
       )

    jac[jni49, jhe4] = (
       +rho*Y[jfe45]*rate_eval.He4_Fe45__Ni49
       )

    jac[jni49, jfe45] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe45__Ni49
       )

    jac[jni50, jhe4] = (
       +rho*Y[jfe46]*rate_eval.He4_Fe46__Ni50
       )

    jac[jni50, jfe46] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe46__Ni50
       )

    jac[jni51, jhe4] = (
       +rho*Y[jfe47]*rate_eval.He4_Fe47__Ni51
       )

    jac[jni51, jfe47] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe47__Ni51
       )

    jac[jni52, jhe4] = (
       +rho*Y[jfe48]*rate_eval.He4_Fe48__Ni52
       )

    jac[jni52, jfe48] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe48__Ni52
       )

    jac[jni53, jhe4] = (
       +rho*Y[jfe49]*rate_eval.He4_Fe49__Ni53
       )

    jac[jni53, jfe49] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe49__Ni53
       )

    jac[jni54, jhe4] = (
       +rho*Y[jfe50]*rate_eval.He4_Fe50__Ni54
       )

    jac[jni54, jfe50] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe50__Ni54
       )

    jac[jni55, jhe4] = (
       +rho*Y[jfe51]*rate_eval.He4_Fe51__Ni55
       )

    jac[jni55, jfe51] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe51__Ni55
       )

    jac[jni56, jhe4] = (
       +rho*Y[jfe52]*rate_eval.He4_Fe52__Ni56
       )

    jac[jni56, jfe52] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe52__Ni56
       )

    jac[jni57, jhe4] = (
       +rho*Y[jfe53]*rate_eval.He4_Fe53__Ni57
       )

    jac[jni57, jfe53] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe53__Ni57
       )

    jac[jni58, jhe4] = (
       +rho*Y[jfe54]*rate_eval.He4_Fe54__Ni58
       )

    jac[jni58, jfe54] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe54__Ni58
       )

    jac[jni59, jhe4] = (
       +rho*Y[jfe55]*rate_eval.He4_Fe55__Ni59
       )

    jac[jni59, jfe55] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe55__Ni59
       )

    jac[jni60, jhe4] = (
       +rho*Y[jfe56]*rate_eval.He4_Fe56__Ni60
       )

    jac[jni60, jfe56] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe56__Ni60
       )

    jac[jni61, jhe4] = (
       +rho*Y[jfe57]*rate_eval.He4_Fe57__Ni61
       )

    jac[jni61, jfe57] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe57__Ni61
       )

    jac[jni62, jhe4] = (
       +rho*Y[jfe59]*rate_eval.He4_Fe59__n_Ni62
       +rho*Y[jfe58]*rate_eval.He4_Fe58__Ni62
       )

    jac[jni62, jfe58] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe58__Ni62
       )

    jac[jni62, jfe59] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe59__n_Ni62
       )

    jac[jni63, jhe4] = (
       +rho*Y[jfe59]*rate_eval.He4_Fe59__Ni63
       )

    jac[jni63, jfe59] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe59__Ni63
       )

    jac[jni64, jhe4] = (
       +rho*Y[jfe61]*rate_eval.He4_Fe61__n_Ni64
       +rho*Y[jfe60]*rate_eval.He4_Fe60__Ni64
       )

    jac[jni64, jfe60] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe60__Ni64
       )

    jac[jni64, jfe61] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe61__n_Ni64
       )

    jac[jni65, jhe4] = (
       +rho*Y[jfe62]*rate_eval.He4_Fe62__n_Ni65
       +rho*Y[jfe61]*rate_eval.He4_Fe61__Ni65
       )

    jac[jni65, jfe61] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe61__Ni65
       )

    jac[jni65, jfe62] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe62__n_Ni65
       )

    jac[jni66, jhe4] = (
       +rho*Y[jfe63]*rate_eval.He4_Fe63__n_Ni66
       +rho*Y[jfe62]*rate_eval.He4_Fe62__Ni66
       )

    jac[jni66, jfe62] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe62__Ni66
       )

    jac[jni66, jfe63] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe63__n_Ni66
       )

    jac[jni67, jhe4] = (
       +rho*Y[jfe64]*rate_eval.He4_Fe64__n_Ni67
       +rho*Y[jfe63]*rate_eval.He4_Fe63__Ni67
       )

    jac[jni67, jfe63] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe63__Ni67
       )

    jac[jni67, jfe64] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe64__n_Ni67
       )

    jac[jni68, jhe4] = (
       +rho*Y[jfe64]*rate_eval.He4_Fe64__Ni68
       +rho*Y[jfe65]*rate_eval.He4_Fe65__n_Ni68
       )

    jac[jni68, jfe64] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe64__Ni68
       )

    jac[jni68, jfe65] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe65__n_Ni68
       )

    jac[jni69, jhe4] = (
       +rho*Y[jfe65]*rate_eval.He4_Fe65__Ni69
       +rho*Y[jfe66]*rate_eval.He4_Fe66__n_Ni69
       )

    jac[jni69, jfe65] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe65__Ni69
       )

    jac[jni69, jfe66] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe66__n_Ni69
       )

    jac[jni70, jhe4] = (
       +rho*Y[jfe66]*rate_eval.He4_Fe66__Ni70
       +rho*Y[jfe67]*rate_eval.He4_Fe67__n_Ni70
       )

    jac[jni70, jfe66] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe66__Ni70
       )

    jac[jni70, jfe67] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe67__n_Ni70
       )

    jac[jni71, jhe4] = (
       +rho*Y[jfe68]*rate_eval.He4_Fe68__n_Ni71
       +rho*Y[jfe67]*rate_eval.He4_Fe67__Ni71
       )

    jac[jni71, jfe67] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe67__Ni71
       )

    jac[jni71, jfe68] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe68__n_Ni71
       )

    jac[jni72, jhe4] = (
       +rho*Y[jfe68]*rate_eval.He4_Fe68__Ni72
       +rho*Y[jfe69]*rate_eval.He4_Fe69__n_Ni72
       )

    jac[jni72, jfe68] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe68__Ni72
       )

    jac[jni72, jfe69] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe69__n_Ni72
       )

    jac[jni73, jhe4] = (
       +rho*Y[jfe70]*rate_eval.He4_Fe70__n_Ni73
       +rho*Y[jfe69]*rate_eval.He4_Fe69__Ni73
       )

    jac[jni73, jfe69] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe69__Ni73
       )

    jac[jni73, jfe70] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe70__n_Ni73
       )

    jac[jni74, jhe4] = (
       +rho*Y[jfe71]*rate_eval.He4_Fe71__n_Ni74
       +rho*Y[jfe70]*rate_eval.He4_Fe70__Ni74
       )

    jac[jni74, jfe70] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe70__Ni74
       )

    jac[jni74, jfe71] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe71__n_Ni74
       )

    jac[jni75, jhe4] = (
       +rho*Y[jfe71]*rate_eval.He4_Fe71__Ni75
       +rho*Y[jfe72]*rate_eval.He4_Fe72__n_Ni75
       )

    jac[jni75, jfe71] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe71__Ni75
       )

    jac[jni75, jfe72] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe72__n_Ni75
       )

    jac[jni76, jhe4] = (
       +rho*Y[jfe73]*rate_eval.He4_Fe73__n_Ni76
       +rho*Y[jfe72]*rate_eval.He4_Fe72__Ni76
       )

    jac[jni76, jfe72] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe72__Ni76
       )

    jac[jni76, jfe73] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe73__n_Ni76
       )

    jac[jni77, jhe4] = (
       +rho*Y[jfe74]*rate_eval.He4_Fe74__n_Ni77
       +rho*Y[jfe73]*rate_eval.He4_Fe73__Ni77
       )

    jac[jni77, jfe73] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe73__Ni77
       )

    jac[jni77, jfe74] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe74__n_Ni77
       )

    jac[jni78, jhe4] = (
       +rho*Y[jfe75]*rate_eval.He4_Fe75__n_Ni78
       +rho*Y[jfe74]*rate_eval.He4_Fe74__Ni78
       )

    jac[jni78, jfe74] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe74__Ni78
       )

    jac[jni78, jfe75] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe75__n_Ni78
       )

    jac[jni79, jhe4] = (
       +rho*Y[jfe76]*rate_eval.He4_Fe76__n_Ni79
       +rho*Y[jfe75]*rate_eval.He4_Fe75__Ni79
       )

    jac[jni79, jfe75] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe75__Ni79
       )

    jac[jni79, jfe76] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe76__n_Ni79
       )

    jac[jni80, jhe4] = (
       +rho*Y[jfe76]*rate_eval.He4_Fe76__Ni80
       )

    jac[jni80, jfe76] = (
       +rho*Y[jhe4]*rate_eval.He4_Fe76__Ni80
       )

    return jac
