r = 5 (values in 1/16Z, m = r + 2 = 7): {'TRIV': 2176, 'CERT': 5818, 'THM_F': 186, 'THM_F+': 10}
  candidates not in TRIV/CERT/THM_F, by (F+ applies, F# applies): {(True, True): 10}
  THM_F: h(++,+-,-+,--) = ('-1', '1/16', '1/16', '-3/4'), mu = -13/32, hat h(12) = -15/32, rho = 17/21
  THM_F: h(++,+-,-+,--) = ('-1', '1/16', '1/16', '-5/8'), mu = -3/8, hat h(12) = -7/16, rho = 17/23
  THM_F: h(++,+-,-+,--) = ('-1', '1/16', '1/16', '-1/2'), mu = -11/32, hat h(12) = -13/32, rho = 17/25
  THM_F: h(++,+-,-+,--) = ('-1', '1/16', '1/16', '-3/8'), mu = -5/16, hat h(12) = -3/8, rho = 17/27
  THM_F: h(++,+-,-+,--) = ('-1', '1/16', '1/16', '-1/4'), mu = -9/32, hat h(12) = -11/32, rho = 17/29
  THM_F: h(++,+-,-+,--) = ('-15/16', '1/16', '1/16', '-13/16'), mu = -13/32, hat h(12) = -15/32, rho = 143/180
  THM_F: h(++,+-,-+,--) = ('-15/16', '1/16', '1/16', '-11/16'), mu = -3/8, hat h(12) = -7/16, rho = 71/99
  THM_F: h(++,+-,-+,--) = ('-15/16', '1/16', '1/16', '-9/16'), mu = -11/32, hat h(12) = -13/32, rho = 47/72
  THM_F: h(++,+-,-+,--) = ('-15/16', '1/16', '1/16', '-7/16'), mu = -5/16, hat h(12) = -3/8, rho = 70/117
  THM_F: h(++,+-,-+,--) = ('-15/16', '1/16', '1/16', '-5/16'), mu = -9/32, hat h(12) = -11/32, rho = 139/252
  THM_F: h(++,+-,-+,--) = ('-15/16', '1/16', '1/16', '-3/16'), mu = -1/4, hat h(12) = -5/16, rho = 23/45
  THM_F: h(++,+-,-+,--) = ('-15/16', '1/8', '1/8', '-9/16'), mu = -5/16, hat h(12) = -7/16, rho = 317/475
  THM_F: h(++,+-,-+,--) = ('-15/16', '1/8', '1/8', '-7/16'), mu = -9/32, hat h(12) = -13/32, rho = 35/57
  THM_F: h(++,+-,-+,--) = ('-7/8', '1/16', '1/16', '-3/4'), mu = -3/8, hat h(12) = -7/16, rho = 281/399
  THM_F: h(++,+-,-+,--) = ('-7/8', '1/16', '1/16', '-5/8'), mu = -11/32, hat h(12) = -13/32, rho = 277/437
  THM_F: h(++,+-,-+,--) = ('-7/8', '1/16', '1/16', '-1/2'), mu = -5/16, hat h(12) = -3/8, rho = 273/475
  THM_F: h(++,+-,-+,--) = ('-7/8', '1/16', '1/16', '-3/8'), mu = -9/32, hat h(12) = -11/32, rho = 269/513
  THM_F: h(++,+-,-+,--) = ('-7/8', '1/16', '1/16', '-1/4'), mu = -1/4, hat h(12) = -5/16, rho = 265/551
  THM_F: h(++,+-,-+,--) = ('-7/8', '1/16', '1/16', '-1/8'), mu = -7/32, hat h(12) = -9/32, rho = 261/589
  THM_F: h(++,+-,-+,--) = ('-7/8', '1/8', '1/8', '-3/4'), mu = -11/32, hat h(12) = -15/32, rho = 79/110
  THM_F: h(++,+-,-+,--) = ('-7/8', '1/8', '1/8', '-5/8'), mu = -5/16, hat h(12) = -7/16, rho = 13/20
  THM_F: h(++,+-,-+,--) = ('-7/8', '1/8', '1/8', '-1/2'), mu = -9/32, hat h(12) = -13/32, rho = 77/130
  THM_F: h(++,+-,-+,--) = ('-7/8', '1/8', '1/8', '-3/8'), mu = -1/4, hat h(12) = -3/8, rho = 19/35
  THM_F+ [D=+1, a=1/2, a2=1/8, Mp=101/748, A=1/8, M=101/748, q=2/5]: h(++,+-,-+,--) = ('-7/8', '1/8', '1/8', '-1/4'), mu = -7/32, hat h(12) = -11/32, rho = 1/2
  THM_F: h(++,+-,-+,--) = ('-13/16', '1/16', '1/16', '-15/16'), mu = -13/32, hat h(12) = -15/32, rho = 143/180
  THM_F: h(++,+-,-+,--) = ('-13/16', '1/16', '1/16', '-11/16'), mu = -11/32, hat h(12) = -13/32, rho = 137/220
  THM_F: h(++,+-,-+,--) = ('-13/16', '1/16', '1/16', '-9/16'), mu = -5/16, hat h(12) = -3/8, rho = 67/120
  THM_F: h(++,+-,-+,--) = ('-13/16', '1/16', '1/16', '-7/16'), mu = -9/32, hat h(12) = -11/32, rho = 131/260
  THM_F: h(++,+-,-+,--) = ('-13/16', '1/16', '1/16', '-5/16'), mu = -1/4, hat h(12) = -5/16, rho = 16/35
  THM_F: h(++,+-,-+,--) = ('-13/16', '1/16', '1/16', '-3/16'), mu = -7/32, hat h(12) = -9/32, rho = 5/12
  THM_F+ [D=+1, a=61/160, a2=226981/4096000, Mp=4087/56320, A=226981/4096000, M=4087/56320, q=5/13]: h(++,+-,-+,--) = ('-13/16', '1/16', '1/16', '-1/16'), mu = -3/16, hat h(12) = -1/4, rho = 61/160
  THM_F: h(++,+-,-+,--) = ('-13/16', '1/8', '1/8', '-11/16'), mu = -5/16, hat h(12) = -7/16, rho = 103/161
  THM_F: h(++,+-,-+,--) = ('-13/16', '1/8', '1/8', '-9/16'), mu = -9/32, hat h(12) = -13/32, rho = 101/175
  THM_F: h(++,+-,-+,--) = ('-13/16', '1/8', '1/8', '-7/16'), mu = -1/4, hat h(12) = -3/8, rho = 11/21
  THM_F: h(++,+-,-+,--) = ('-13/16', '1/8', '1/8', '-5/16'), mu = -7/32, hat h(12) = -11/32, rho = 97/203
  THM_F+ [D=+1, a=95/217, a2=857375/10218313, Mp=33725/307923, A=857375/10218313, M=33725/307923, q=21/52]: h(++,+-,-+,--) = ('-13/16', '1/8', '1/8', '-3/16'), mu = -3/16, hat h(12) = -5/16, rho = 95/217
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/16', '1/16', '-1'), mu = -13/32, hat h(12) = -15/32, rho = 17/21
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/16', '1/16', '-7/8'), mu = -3/8, hat h(12) = -7/16, rho = 281/399
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/16', '1/16', '-5/8'), mu = -5/16, hat h(12) = -3/8, rho = 265/483
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/16', '1/16', '-1/2'), mu = -9/32, hat h(12) = -11/32, rho = 257/525
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/16', '1/16', '-3/8'), mu = -1/4, hat h(12) = -5/16, rho = 83/189
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/16', '1/16', '-1/4'), mu = -7/32, hat h(12) = -9/32, rho = 241/609
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/16', '1/16', '-1/8'), mu = -3/16, hat h(12) = -1/4, rho = 233/651
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/8', '1/8', '-7/8'), mu = -11/32, hat h(12) = -15/32, rho = 79/110
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/8', '1/8', '-5/8'), mu = -9/32, hat h(12) = -13/32, rho = 25/44
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/8', '1/8', '-1/2'), mu = -1/4, hat h(12) = -3/8, rho = 73/143
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/8', '1/8', '-3/8'), mu = -7/32, hat h(12) = -11/32, rho = 71/154
  THM_F: h(++,+-,-+,--) = ('-3/4', '1/8', '1/8', '-1/4'), mu = -3/16, hat h(12) = -5/16, rho = 23/55
  THM_F+ [D=+1, a=67/176, a2=300763/5451776, Mp=67/768, A=300763/5451776, M=67/768, q=11/27]: h(++,+-,-+,--) = ('-3/4', '1/8', '1/8', '-1/8'), mu = -5/32, hat h(12) = -9/32, rho = 67/176
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/16', '1/16', '-15/16'), mu = -3/8, hat h(12) = -7/16, rho = 71/99
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/16', '1/16', '-13/16'), mu = -11/32, hat h(12) = -13/32, rho = 137/220
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/16', '1/16', '-9/16'), mu = -9/32, hat h(12) = -11/32, rho = 127/264
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/16', '1/16', '-7/16'), mu = -1/4, hat h(12) = -5/16, rho = 61/143
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/16', '1/16', '-5/16'), mu = -7/32, hat h(12) = -9/32, rho = 117/308
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/16', '1/16', '-3/16'), mu = -3/16, hat h(12) = -1/4, rho = 56/165
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/16', '1/16', '-1/16'), mu = -5/32, hat h(12) = -7/32, rho = 107/352
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/8', '1/8', '-13/16'), mu = -5/16, hat h(12) = -7/16, rho = 103/161
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/8', '1/8', '-9/16'), mu = -1/4, hat h(12) = -3/8, rho = 289/575
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/8', '1/8', '-7/16'), mu = -7/32, hat h(12) = -11/32, rho = 31/69
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/8', '1/8', '-5/16'), mu = -3/16, hat h(12) = -5/16, rho = 269/667
  THM_F: h(++,+-,-+,--) = ('-11/16', '1/8', '1/8', '-3/16'), mu = -5/32, hat h(12) = -9/32, rho = 259/713
  THM_F: h(++,+-,-+,--) = ('-11/16', '3/16', '3/16', '-9/16'), mu = -7/32, hat h(12) = -13/32, rho = 163/312
  THM_F: h(++,+-,-+,--) = ('-11/16', '3/16', '3/16', '-7/16'), mu = -3/16, hat h(12) = -3/8, rho = 79/168
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/16', '1/16', '-1'), mu = -3/8, hat h(12) = -7/16, rho = 17/23
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/16', '1/16', '-7/8'), mu = -11/32, hat h(12) = -13/32, rho = 277/437
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/16', '1/16', '-3/4'), mu = -5/16, hat h(12) = -3/8, rho = 265/483
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/16', '1/16', '-1/2'), mu = -1/4, hat h(12) = -5/16, rho = 241/575
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/16', '1/16', '-3/8'), mu = -7/32, hat h(12) = -9/32, rho = 229/621
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/16', '1/16', '-1/4'), mu = -3/16, hat h(12) = -1/4, rho = 217/667
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/16', '1/16', '-1/8'), mu = -5/32, hat h(12) = -7/32, rho = 205/713
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/8', '1/8', '-7/8'), mu = -5/16, hat h(12) = -7/16, rho = 13/20
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/8', '1/8', '-3/4'), mu = -9/32, hat h(12) = -13/32, rho = 25/44
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/8', '1/8', '-1/2'), mu = -7/32, hat h(12) = -11/32, rho = 23/52
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/8', '1/8', '-3/8'), mu = -3/16, hat h(12) = -5/16, rho = 11/28
  THM_F: h(++,+-,-+,--) = ('-5/8', '1/8', '1/8', '-1/4'), mu = -5/32, hat h(12) = -9/32, rho = 7/20
  THM_F+ [D=+1, a=5/16, a2=125/4096, Mp=17/256, A=125/4096, M=17/256, q=3/7]: h(++,+-,-+,--) = ('-5/8', '1/8', '1/8', '-1/8'), mu = -1/8, hat h(12) = -1/4, rho = 5/16
  THM_F: h(++,+-,-+,--) = ('-5/8', '3/16', '3/16', '-1/2'), mu = -3/16, hat h(12) = -3/8, rho = 313/675
  THM_F: h(++,+-,-+,--) = ('-5/8', '3/16', '3/16', '-3/8'), mu = -5/32, hat h(12) = -11/32, rho = 301/725
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/16', '1/16', '-15/16'), mu = -11/32, hat h(12) = -13/32, rho = 47/72
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/16', '1/16', '-13/16'), mu = -5/16, hat h(12) = -3/8, rho = 67/120
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/16', '1/16', '-11/16'), mu = -9/32, hat h(12) = -11/32, rho = 127/264
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/16', '1/16', '-7/16'), mu = -7/32, hat h(12) = -9/32, rho = 113/312
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/16', '1/16', '-5/16'), mu = -3/16, hat h(12) = -1/4, rho = 53/168
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/16', '1/16', '-3/16'), mu = -5/32, hat h(12) = -7/32, rho = 11/40
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/16', '1/16', '-1/16'), mu = -1/8, hat h(12) = -3/16, rho = 23/96
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/8', '1/8', '-15/16'), mu = -5/16, hat h(12) = -7/16, rho = 317/475
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/8', '1/8', '-13/16'), mu = -9/32, hat h(12) = -13/32, rho = 101/175
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/8', '1/8', '-11/16'), mu = -1/4, hat h(12) = -3/8, rho = 289/575
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/8', '1/8', '-7/16'), mu = -3/16, hat h(12) = -5/16, rho = 29/75
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/8', '1/8', '-5/16'), mu = -5/32, hat h(12) = -9/32, rho = 247/725
  THM_F: h(++,+-,-+,--) = ('-9/16', '1/8', '1/8', '-3/16'), mu = -1/8, hat h(12) = -1/4, rho = 233/775
  THM_F: h(++,+-,-+,--) = ('-9/16', '3/16', '3/16', '-11/16'), mu = -7/32, hat h(12) = -13/32, rho = 163/312
  THM_F: h(++,+-,-+,--) = ('-9/16', '3/16', '3/16', '-7/16'), mu = -5/32, hat h(12) = -11/32, rho = 149/364
  THM_F: h(++,+-,-+,--) = ('-9/16', '3/16', '3/16', '-5/16'), mu = -1/8, hat h(12) = -5/16, rho = 71/195
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/16', '1/16', '-1'), mu = -11/32, hat h(12) = -13/32, rho = 17/25
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/16', '1/16', '-7/8'), mu = -5/16, hat h(12) = -3/8, rho = 273/475
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/16', '1/16', '-3/4'), mu = -9/32, hat h(12) = -11/32, rho = 257/525
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/16', '1/16', '-5/8'), mu = -1/4, hat h(12) = -5/16, rho = 241/575
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/16', '1/16', '-3/8'), mu = -3/16, hat h(12) = -1/4, rho = 209/675
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/16', '1/16', '-1/4'), mu = -5/32, hat h(12) = -7/32, rho = 193/725
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/16', '1/16', '-1/8'), mu = -1/8, hat h(12) = -3/16, rho = 177/775
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/8', '1/8', '-7/8'), mu = -9/32, hat h(12) = -13/32, rho = 77/130
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/8', '1/8', '-3/4'), mu = -1/4, hat h(12) = -3/8, rho = 73/143
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/8', '1/8', '-5/8'), mu = -7/32, hat h(12) = -11/32, rho = 23/52
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/8', '1/8', '-3/8'), mu = -5/32, hat h(12) = -9/32, rho = 61/182
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/8', '1/8', '-1/4'), mu = -1/8, hat h(12) = -1/4, rho = 19/65
  THM_F: h(++,+-,-+,--) = ('-1/2', '1/8', '1/8', '-1/8'), mu = -3/32, hat h(12) = -7/32, rho = 53/208
  THM_F: h(++,+-,-+,--) = ('-1/2', '3/16', '3/16', '-5/8'), mu = -3/16, hat h(12) = -3/8, rho = 313/675
  THM_F: h(++,+-,-+,--) = ('-1/2', '3/16', '3/16', '-3/8'), mu = -1/8, hat h(12) = -5/16, rho = 281/783
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/16', '1/16', '-15/16'), mu = -5/16, hat h(12) = -3/8, rho = 70/117
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/16', '1/16', '-13/16'), mu = -9/32, hat h(12) = -11/32, rho = 131/260
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/16', '1/16', '-11/16'), mu = -1/4, hat h(12) = -5/16, rho = 61/143
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/16', '1/16', '-9/16'), mu = -7/32, hat h(12) = -9/32, rho = 113/312
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/16', '1/16', '-5/16'), mu = -5/32, hat h(12) = -7/32, rho = 95/364
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/16', '1/16', '-3/16'), mu = -1/8, hat h(12) = -3/16, rho = 43/195
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/16', '1/16', '-1/16'), mu = -3/32, hat h(12) = -5/32, rho = 77/416
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/8', '1/8', '-15/16'), mu = -9/32, hat h(12) = -13/32, rho = 35/57
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/8', '1/8', '-13/16'), mu = -1/4, hat h(12) = -3/8, rho = 11/21
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/8', '1/8', '-11/16'), mu = -7/32, hat h(12) = -11/32, rho = 31/69
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/8', '1/8', '-9/16'), mu = -3/16, hat h(12) = -5/16, rho = 29/75
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/8', '1/8', '-5/16'), mu = -1/8, hat h(12) = -1/4, rho = 25/87
  THM_F: h(++,+-,-+,--) = ('-7/16', '1/8', '1/8', '-3/16'), mu = -3/32, hat h(12) = -7/32, rho = 23/93
  THM_F: h(++,+-,-+,--) = ('-7/16', '3/16', '3/16', '-11/16'), mu = -3/16, hat h(12) = -3/8, rho = 79/168
  THM_F: h(++,+-,-+,--) = ('-7/16', '3/16', '3/16', '-9/16'), mu = -5/32, hat h(12) = -11/32, rho = 149/364
  THM_F: h(++,+-,-+,--) = ('-7/16', '3/16', '3/16', '-5/16'), mu = -3/32, hat h(12) = -9/32, rho = 131/420
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/16', '1/16', '-1'), mu = -5/16, hat h(12) = -3/8, rho = 17/27
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/16', '1/16', '-7/8'), mu = -9/32, hat h(12) = -11/32, rho = 269/513
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/16', '1/16', '-3/4'), mu = -1/4, hat h(12) = -5/16, rho = 83/189
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/16', '1/16', '-5/8'), mu = -7/32, hat h(12) = -9/32, rho = 229/621
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/16', '1/16', '-1/2'), mu = -3/16, hat h(12) = -1/4, rho = 209/675
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/16', '1/16', '-1/4'), mu = -1/8, hat h(12) = -3/16, rho = 169/783
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/16', '1/16', '-1/8'), mu = -3/32, hat h(12) = -5/32, rho = 149/837
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/8', '1/8', '-7/8'), mu = -1/4, hat h(12) = -3/8, rho = 19/35
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/8', '1/8', '-3/4'), mu = -7/32, hat h(12) = -11/32, rho = 71/154
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/8', '1/8', '-5/8'), mu = -3/16, hat h(12) = -5/16, rho = 11/28
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/8', '1/8', '-1/2'), mu = -5/32, hat h(12) = -9/32, rho = 61/182
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/8', '1/8', '-1/4'), mu = -3/32, hat h(12) = -7/32, rho = 17/70
  THM_F: h(++,+-,-+,--) = ('-3/8', '1/8', '1/8', '-1/8'), mu = -1/16, hat h(12) = -3/16, rho = 23/112
  THM_F: h(++,+-,-+,--) = ('-3/8', '3/16', '3/16', '-5/8'), mu = -5/32, hat h(12) = -11/32, rho = 301/725
  THM_F: h(++,+-,-+,--) = ('-3/8', '3/16', '3/16', '-1/2'), mu = -1/8, hat h(12) = -5/16, rho = 281/783
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/16', '1/16', '-15/16'), mu = -9/32, hat h(12) = -11/32, rho = 139/252
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/16', '1/16', '-13/16'), mu = -1/4, hat h(12) = -5/16, rho = 16/35
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/16', '1/16', '-11/16'), mu = -7/32, hat h(12) = -9/32, rho = 117/308
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/16', '1/16', '-9/16'), mu = -3/16, hat h(12) = -1/4, rho = 53/168
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/16', '1/16', '-7/16'), mu = -5/32, hat h(12) = -7/32, rho = 95/364
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/16', '1/16', '-3/16'), mu = -3/32, hat h(12) = -5/32, rho = 73/420
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/16', '1/16', '-1/16'), mu = -1/16, hat h(12) = -1/8, rho = 31/224
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/8', '1/8', '-13/16'), mu = -7/32, hat h(12) = -11/32, rho = 97/203
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/8', '1/8', '-11/16'), mu = -3/16, hat h(12) = -5/16, rho = 269/667
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/8', '1/8', '-9/16'), mu = -5/32, hat h(12) = -9/32, rho = 247/725
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/8', '1/8', '-7/16'), mu = -1/8, hat h(12) = -1/4, rho = 25/87
  THM_F: h(++,+-,-+,--) = ('-5/16', '1/8', '1/8', '-3/16'), mu = -1/16, hat h(12) = -3/16, rho = 181/899
  THM_F: h(++,+-,-+,--) = ('-5/16', '3/16', '3/16', '-9/16'), mu = -1/8, hat h(12) = -5/16, rho = 71/195
  THM_F: h(++,+-,-+,--) = ('-5/16', '3/16', '3/16', '-7/16'), mu = -3/32, hat h(12) = -9/32, rho = 131/420
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/16', '1/16', '-1'), mu = -9/32, hat h(12) = -11/32, rho = 17/29
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/16', '1/16', '-7/8'), mu = -1/4, hat h(12) = -5/16, rho = 265/551
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/16', '1/16', '-3/4'), mu = -7/32, hat h(12) = -9/32, rho = 241/609
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/16', '1/16', '-5/8'), mu = -3/16, hat h(12) = -1/4, rho = 217/667
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/16', '1/16', '-1/2'), mu = -5/32, hat h(12) = -7/32, rho = 193/725
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/16', '1/16', '-3/8'), mu = -1/8, hat h(12) = -3/16, rho = 169/783
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/16', '1/16', '-1/8'), mu = -1/16, hat h(12) = -1/8, rho = 121/899
  THM_F+ [D=+1, a=1/2, a2=1/8, Mp=101/748, A=1/8, M=101/748, q=2/5]: h(++,+-,-+,--) = ('-1/4', '1/8', '1/8', '-7/8'), mu = -7/32, hat h(12) = -11/32, rho = 1/2
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/8', '1/8', '-3/4'), mu = -3/16, hat h(12) = -5/16, rho = 23/55
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/8', '1/8', '-5/8'), mu = -5/32, hat h(12) = -9/32, rho = 7/20
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/8', '1/8', '-1/2'), mu = -1/8, hat h(12) = -1/4, rho = 19/65
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/8', '1/8', '-3/8'), mu = -3/32, hat h(12) = -7/32, rho = 17/70
  THM_F: h(++,+-,-+,--) = ('-1/4', '1/8', '1/8', '-1/8'), mu = -1/32, hat h(12) = -5/32, rho = 13/80
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/16', '1/16', '-15/16'), mu = -1/4, hat h(12) = -5/16, rho = 23/45
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/16', '1/16', '-13/16'), mu = -7/32, hat h(12) = -9/32, rho = 5/12
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/16', '1/16', '-11/16'), mu = -3/16, hat h(12) = -1/4, rho = 56/165
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/16', '1/16', '-9/16'), mu = -5/32, hat h(12) = -7/32, rho = 11/40
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/16', '1/16', '-7/16'), mu = -1/8, hat h(12) = -3/16, rho = 43/195
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/16', '1/16', '-5/16'), mu = -3/32, hat h(12) = -5/32, rho = 73/420
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/16', '1/16', '-1/16'), mu = -1/32, hat h(12) = -3/32, rho = 47/480
  THM_F+ [D=+1, a=95/217, a2=857375/10218313, Mp=33725/307923, A=857375/10218313, M=33725/307923, q=21/52]: h(++,+-,-+,--) = ('-3/16', '1/8', '1/8', '-13/16'), mu = -3/16, hat h(12) = -5/16, rho = 95/217
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/8', '1/8', '-11/16'), mu = -5/32, hat h(12) = -9/32, rho = 259/713
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/8', '1/8', '-9/16'), mu = -1/8, hat h(12) = -1/4, rho = 233/775
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/8', '1/8', '-7/16'), mu = -3/32, hat h(12) = -7/32, rho = 23/93
  THM_F: h(++,+-,-+,--) = ('-3/16', '1/8', '1/8', '-5/16'), mu = -1/16, hat h(12) = -3/16, rho = 181/899
  THM_F: h(++,+-,-+,--) = ('-1/8', '1/16', '1/16', '-7/8'), mu = -7/32, hat h(12) = -9/32, rho = 261/589
  THM_F: h(++,+-,-+,--) = ('-1/8', '1/16', '1/16', '-3/4'), mu = -3/16, hat h(12) = -1/4, rho = 233/651
  THM_F: h(++,+-,-+,--) = ('-1/8', '1/16', '1/16', '-5/8'), mu = -5/32, hat h(12) = -7/32, rho = 205/713
  THM_F: h(++,+-,-+,--) = ('-1/8', '1/16', '1/16', '-1/2'), mu = -1/8, hat h(12) = -3/16, rho = 177/775
  THM_F: h(++,+-,-+,--) = ('-1/8', '1/16', '1/16', '-3/8'), mu = -3/32, hat h(12) = -5/32, rho = 149/837
  THM_F: h(++,+-,-+,--) = ('-1/8', '1/16', '1/16', '-1/4'), mu = -1/16, hat h(12) = -1/8, rho = 121/899
  THM_F+ [D=+1, a=67/176, a2=300763/5451776, Mp=67/768, A=300763/5451776, M=67/768, q=11/27]: h(++,+-,-+,--) = ('-1/8', '1/8', '1/8', '-3/4'), mu = -5/32, hat h(12) = -9/32, rho = 67/176
  THM_F+ [D=+1, a=5/16, a2=125/4096, Mp=17/256, A=125/4096, M=17/256, q=3/7]: h(++,+-,-+,--) = ('-1/8', '1/8', '1/8', '-5/8'), mu = -1/8, hat h(12) = -1/4, rho = 5/16
  THM_F: h(++,+-,-+,--) = ('-1/8', '1/8', '1/8', '-1/2'), mu = -3/32, hat h(12) = -7/32, rho = 53/208
  THM_F: h(++,+-,-+,--) = ('-1/8', '1/8', '1/8', '-3/8'), mu = -1/16, hat h(12) = -3/16, rho = 23/112
  THM_F: h(++,+-,-+,--) = ('-1/8', '1/8', '1/8', '-1/4'), mu = -1/32, hat h(12) = -5/32, rho = 13/80
  THM_F+ [D=+1, a=61/160, a2=226981/4096000, Mp=4087/56320, A=226981/4096000, M=4087/56320, q=5/13]: h(++,+-,-+,--) = ('-1/16', '1/16', '1/16', '-13/16'), mu = -3/16, hat h(12) = -1/4, rho = 61/160
  THM_F: h(++,+-,-+,--) = ('-1/16', '1/16', '1/16', '-11/16'), mu = -5/32, hat h(12) = -7/32, rho = 107/352
  THM_F: h(++,+-,-+,--) = ('-1/16', '1/16', '1/16', '-9/16'), mu = -1/8, hat h(12) = -3/16, rho = 23/96
  THM_F: h(++,+-,-+,--) = ('-1/16', '1/16', '1/16', '-7/16'), mu = -3/32, hat h(12) = -5/32, rho = 77/416
  THM_F: h(++,+-,-+,--) = ('-1/16', '1/16', '1/16', '-5/16'), mu = -1/16, hat h(12) = -1/8, rho = 31/224
  THM_F: h(++,+-,-+,--) = ('-1/16', '1/16', '1/16', '-3/16'), mu = -1/32, hat h(12) = -3/32, rho = 47/480
