Hilbert modular form data - 4.4.18736.1-7.1-b

Formats: - HTML - YAML - JSON - 2024-05-16T22:01:26.806533

• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 4, 'dimension': 10, 'disc': 18736, 'field_bad_primes': [2, 1171], 'field_label': '4.4.18736.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.18736.1-7.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [7], 'level_ideal': '[7, 7, w - 2]', 'level_label': '7.1', 'level_norm': 7, 'parallel_weight': 2, 'short_label': '7.1-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[7, 7, w - 2]', 1]], 'hecke_eigenvalues': ['e', '-3/4*e^9 + 53/4*e^7 - 129/2*e^5 + 153/2*e^3 - 17*e', '1/4*e^9 - 9/2*e^7 + 23*e^5 - 33*e^3 + 14*e', -1, '-3/4*e^8 + 13*e^6 - 121/2*e^4 + 61*e^2 - 10', '3/4*e^9 - 27/2*e^7 + 69*e^5 - 98*e^3 + 37*e', '-1/4*e^9 + 9/2*e^7 - 23*e^5 + 32*e^3 - 5*e', '11/4*e^9 - 97/2*e^7 + 471/2*e^5 - 280*e^3 + 74*e', '3/4*e^8 - 27/2*e^6 + 137/2*e^4 - 92*e^2 + 28', '2*e^9 - 71/2*e^7 + 175*e^5 - 219*e^3 + 63*e', '-3/4*e^8 + 27/2*e^6 - 137/2*e^4 + 92*e^2 - 24', '3*e^9 - 53*e^7 + 517/2*e^5 - 312*e^3 + 83*e', '-9/4*e^9 + 40*e^7 - 198*e^5 + 251*e^3 - 73*e', '5/4*e^9 - 22*e^7 + 106*e^5 - 121*e^3 + 27*e', '3/2*e^9 - 26*e^7 + 121*e^5 - 122*e^3 + 22*e', '2*e^2 - 10', '1/2*e^9 - 8*e^7 + 29*e^5 + 10*e^3 - 36*e', '3/4*e^9 - 27/2*e^7 + 69*e^5 - 98*e^3 + 39*e', '2*e^8 - 35*e^6 + 167*e^4 - 186*e^2 + 42', '23/4*e^9 - 203/2*e^7 + 494*e^5 - 591*e^3 + 152*e', '-5/2*e^9 + 89/2*e^7 - 221*e^5 + 283*e^3 - 74*e', '-e^8 + 18*e^6 - 92*e^4 + 132*e^2 - 44', '-5/2*e^9 + 89/2*e^7 - 221*e^5 + 285*e^3 - 90*e', '-11/4*e^9 + 49*e^7 - 244*e^5 + 315*e^3 - 85*e', '-13/4*e^9 + 115/2*e^7 - 281*e^5 + 338*e^3 - 79*e', '17/4*e^8 - 149/2*e^6 + 715/2*e^4 - 410*e^2 + 98', '-3/2*e^8 + 26*e^6 - 122*e^4 + 133*e^2 - 34', '1/2*e^8 - 9*e^6 + 46*e^4 - 64*e^2 + 26', '-3/4*e^8 + 13*e^6 - 123/2*e^4 + 71*e^2 - 14', '1/4*e^8 - 5*e^6 + 61/2*e^4 - 55*e^2 + 6', '3*e^9 - 105/2*e^7 + 250*e^5 - 275*e^3 + 56*e', '3/2*e^8 - 27*e^6 + 136*e^4 - 175*e^2 + 42', '1/2*e^9 - 8*e^7 + 29*e^5 + 10*e^3 - 36*e', '1/4*e^8 - 9/2*e^6 + 47/2*e^4 - 38*e^2 + 28', '-9/2*e^8 + 79*e^6 - 379*e^4 + 430*e^2 - 102', '-1/4*e^8 + 5*e^6 - 63/2*e^4 + 71*e^2 - 34', '-2*e^8 + 35*e^6 - 167*e^4 + 186*e^2 - 46', '-1/2*e^9 + 17/2*e^7 - 38*e^5 + 33*e^3 - 2*e', '3/2*e^8 - 27*e^6 + 137*e^4 - 184*e^2 + 40', '15/4*e^9 - 131/2*e^7 + 621/2*e^5 - 336*e^3 + 74*e', '-3*e^8 + 53*e^6 - 259*e^4 + 316*e^2 - 78', '1/4*e^9 - 9/2*e^7 + 23*e^5 - 34*e^3 + 22*e', '3/4*e^9 - 13*e^7 + 60*e^5 - 55*e^3 - 5*e', '-e^4 + 10*e^2 - 12', '3/2*e^9 - 53/2*e^7 + 129*e^5 - 153*e^3 + 29*e', '1/2*e^9 - 9*e^7 + 46*e^5 - 66*e^3 + 26*e', '-3/4*e^9 + 27/2*e^7 - 69*e^5 + 100*e^3 - 53*e', '27/4*e^9 - 237/2*e^7 + 569*e^5 - 648*e^3 + 153*e', '1/2*e^8 - 9*e^6 + 47*e^4 - 76*e^2 + 30', '-19/4*e^9 + 84*e^7 - 410*e^5 + 490*e^3 - 106*e', 'e^8 - 17*e^6 + 77*e^4 - 80*e^2 + 40', '-5/4*e^8 + 22*e^6 - 215/2*e^4 + 135*e^2 - 28', '-1/4*e^9 + 7/2*e^7 - 6*e^5 - 42*e^3 + 41*e', '2*e^9 - 35*e^7 + 333/2*e^5 - 182*e^3 + 41*e', '27/4*e^9 - 118*e^7 + 561*e^5 - 616*e^3 + 130*e', '-3/4*e^9 + 25/2*e^7 - 52*e^5 + 20*e^3 + 45*e', '3/2*e^8 - 26*e^6 + 122*e^4 - 132*e^2 + 26', '-3/2*e^9 + 26*e^7 - 121*e^5 + 124*e^3 - 38*e', '2*e^8 - 35*e^6 + 165*e^4 - 168*e^2 + 24', 'e^8 - 18*e^6 + 92*e^4 - 126*e^2 + 24', '-39/4*e^9 + 343/2*e^7 - 827*e^5 + 956*e^3 - 239*e', '-1/2*e^8 + 8*e^6 - 31*e^4 + 12*e^2 + 2', '-7/2*e^8 + 61*e^6 - 289*e^4 + 318*e^2 - 68', '-2*e^2', '-1/4*e^9 + 11/2*e^7 - 40*e^5 + 108*e^3 - 75*e', '-e^8 + 18*e^6 - 92*e^4 + 130*e^2 - 18', '7/4*e^8 - 63/2*e^6 + 323/2*e^4 - 232*e^2 + 64', '-11/2*e^9 + 195/2*e^7 - 480*e^5 + 602*e^3 - 179*e', '-3/4*e^9 + 23/2*e^7 - 69/2*e^5 - 56*e^3 + 74*e', '-1/4*e^8 + 11/2*e^6 - 81/2*e^4 + 108*e^2 - 46', '-1/4*e^9 + 9/2*e^7 - 47/2*e^5 + 40*e^3 - 40*e', '7/2*e^8 - 61*e^6 + 288*e^4 - 307*e^2 + 50', '-21/4*e^8 + 185/2*e^6 - 897/2*e^4 + 528*e^2 - 120', '5/4*e^9 - 22*e^7 + 106*e^5 - 119*e^3 + 15*e', '7/4*e^9 - 63/2*e^7 + 323/2*e^5 - 238*e^3 + 124*e', '3/2*e^8 - 26*e^6 + 120*e^4 - 112*e^2 + 22', '-3/4*e^9 + 29/2*e^7 - 85*e^5 + 162*e^3 - 71*e', '13/4*e^9 - 115/2*e^7 + 282*e^5 - 350*e^3 + 99*e', '-1/2*e^8 + 9*e^6 - 47*e^4 + 78*e^2 - 46', '11/4*e^8 - 49*e^6 + 485/2*e^4 - 299*e^2 + 82', '3/2*e^8 - 28*e^6 + 153*e^4 - 246*e^2 + 88', '-5*e^9 + 88*e^7 - 424*e^5 + 480*e^3 - 86*e', '-4*e^8 + 70*e^6 - 334*e^4 + 372*e^2 - 76', '-2*e^8 + 34*e^6 - 151*e^4 + 122*e^2 - 12', '-7*e^9 + 249/2*e^7 - 617*e^5 + 786*e^3 - 231*e', '-9*e^9 + 319/2*e^7 - 783*e^5 + 962*e^3 - 255*e', '5/4*e^9 - 22*e^7 + 107*e^5 - 133*e^3 + 53*e', '-39/4*e^9 + 172*e^7 - 836*e^5 + 998*e^3 - 256*e', '3/2*e^9 - 26*e^7 + 121*e^5 - 124*e^3 + 38*e', '3/4*e^9 - 25/2*e^7 + 53*e^5 - 34*e^3 - e', '9/2*e^9 - 159/2*e^7 + 387*e^5 - 461*e^3 + 126*e', '-9/2*e^8 + 78*e^6 - 363*e^4 + 364*e^2 - 60', '-5/4*e^8 + 22*e^6 - 211/2*e^4 + 113*e^2 - 16', '-17/2*e^9 + 151*e^7 - 747*e^5 + 950*e^3 - 274*e', '1/4*e^8 - 7/2*e^6 + 13/2*e^4 + 36*e^2 - 26', 'e^8 - 17*e^6 + 74*e^4 - 48*e^2 + 8', '9/4*e^9 - 81/2*e^7 + 206*e^5 - 280*e^3 + 75*e', '5*e^9 - 89*e^7 + 883/2*e^5 - 562*e^3 + 151*e', '-5*e^8 + 89*e^6 - 440*e^4 + 548*e^2 - 140', '7/2*e^8 - 61*e^6 + 288*e^4 - 310*e^2 + 72', '1/2*e^8 - 10*e^6 + 61*e^4 - 118*e^2 + 34', '31/4*e^9 - 273/2*e^7 + 660*e^5 - 768*e^3 + 177*e', '15/4*e^8 - 133/2*e^6 + 649/2*e^4 - 380*e^2 + 92', '-7/2*e^8 + 61*e^6 - 288*e^4 + 307*e^2 - 46', '-5/4*e^8 + 22*e^6 - 215/2*e^4 + 137*e^2 - 34', '4*e^9 - 71*e^7 + 697/2*e^5 - 418*e^3 + 71*e', '5/2*e^8 - 44*e^6 + 211*e^4 - 234*e^2 + 46', 'e^8 - 18*e^6 + 93*e^4 - 138*e^2 + 36', '-15/4*e^9 + 131/2*e^7 - 623/2*e^5 + 348*e^3 - 94*e', '-5/4*e^8 + 45/2*e^6 - 233/2*e^4 + 178*e^2 - 60', '13/2*e^8 - 114*e^6 + 546*e^4 - 611*e^2 + 126', '-3/4*e^8 + 13*e^6 - 117/2*e^4 + 35*e^2 + 30', 'e^8 - 18*e^6 + 92*e^4 - 126*e^2 + 4', '-9/2*e^8 + 79*e^6 - 378*e^4 + 415*e^2 - 90', '-9/4*e^8 + 40*e^6 - 393/2*e^4 + 237*e^2 - 54', '-5/4*e^9 + 45/2*e^7 - 115*e^5 + 164*e^3 - 51*e', '-3*e^8 + 53*e^6 - 256*e^4 + 290*e^2 - 68', '-39/4*e^9 + 345/2*e^7 - 844*e^5 + 1028*e^3 - 277*e', '5/2*e^8 - 45*e^6 + 231*e^4 - 336*e^2 + 108', '-15/4*e^9 + 65*e^7 - 301*e^5 + 285*e^3 - 8*e', '5*e^8 - 87*e^6 + 410*e^4 - 438*e^2 + 82', '4*e^9 - 70*e^7 + 332*e^5 - 352*e^3 + 58*e', '-15/2*e^8 + 132*e^6 - 638*e^4 + 742*e^2 - 172', '-e^8 + 17*e^6 - 73*e^4 + 34*e^2 + 42', '3*e^8 - 52*e^6 + 243*e^4 - 256*e^2 + 52', '-5/4*e^9 + 47/2*e^7 - 131*e^5 + 224*e^3 - 79*e', '15/2*e^8 - 132*e^6 + 637*e^4 - 734*e^2 + 176', '31/4*e^9 - 273/2*e^7 + 661*e^5 - 780*e^3 + 203*e', '-7/4*e^9 + 61/2*e^7 - 144*e^5 + 157*e^3 - 60*e', '-13/4*e^8 + 58*e^6 - 577/2*e^4 + 361*e^2 - 90', '7/2*e^8 - 62*e^6 + 303*e^4 - 359*e^2 + 74', '3/4*e^9 - 13*e^7 + 60*e^5 - 53*e^3 - 3*e', '-17/4*e^9 + 75*e^7 - 364*e^5 + 427*e^3 - 102*e', '1/2*e^8 - 9*e^6 + 43*e^4 - 32*e^2 - 34', '-13/2*e^9 + 114*e^7 - 547*e^5 + 628*e^3 - 168*e', '-3/2*e^8 + 26*e^6 - 121*e^4 + 115*e^2 + 18', '7/2*e^8 - 61*e^6 + 288*e^4 - 305*e^2 + 46', '-1/2*e^8 + 9*e^6 - 47*e^4 + 78*e^2 - 32', '-2*e^9 + 34*e^7 - 149*e^5 + 102*e^3 + 15*e', '3*e^9 - 53*e^7 + 258*e^5 - 306*e^3 + 58*e', '5/4*e^8 - 43/2*e^6 + 195/2*e^4 - 90*e^2 + 16', '-9*e^9 + 315/2*e^7 - 750*e^5 + 825*e^3 - 162*e', '9/4*e^8 - 40*e^6 + 397/2*e^4 - 257*e^2 + 86', '13/2*e^9 - 231/2*e^7 + 570*e^5 - 707*e^3 + 172*e', '-45/4*e^9 + 399/2*e^7 - 981*e^5 + 1212*e^3 - 331*e', '7*e^8 - 124*e^6 + 609*e^4 - 754*e^2 + 196', '-5*e^8 + 88*e^6 - 427*e^4 + 510*e^2 - 108', '-1/4*e^9 + 11/2*e^7 - 81/2*e^5 + 114*e^3 - 86*e', '-e^9 + 19*e^7 - 109*e^5 + 205*e^3 - 91*e', '-9*e^8 + 158*e^6 - 757*e^4 + 849*e^2 - 204', '4*e^8 - 70*e^6 + 334*e^4 - 378*e^2 + 110', '-1/2*e^8 + 9*e^6 - 48*e^4 + 84*e^2 - 32', '-11/2*e^8 + 97*e^6 - 469*e^4 + 538*e^2 - 118', '-3/2*e^9 + 25*e^7 - 104*e^5 + 46*e^3 + 38*e', '6*e^8 - 106*e^6 + 515*e^4 - 606*e^2 + 156', '-8*e^9 + 285/2*e^7 - 707*e^5 + 891*e^3 - 216*e', '7/2*e^9 - 64*e^7 + 337*e^5 - 508*e^3 + 178*e', '-23/4*e^8 + 201/2*e^6 - 957/2*e^4 + 538*e^2 - 136', '5/2*e^8 - 45*e^6 + 227*e^4 - 296*e^2 + 64', '-47/4*e^9 + 207*e^7 - 1003*e^5 + 1183*e^3 - 299*e', '15*e^9 - 265*e^7 + 1291*e^5 - 1541*e^3 + 369*e', '-39/4*e^9 + 341/2*e^7 - 810*e^5 + 878*e^3 - 167*e', '-11/2*e^8 + 97*e^6 - 470*e^4 + 552*e^2 - 142', '-37/2*e^9 + 326*e^7 - 1579*e^5 + 1852*e^3 - 466*e', '-15/4*e^9 + 133/2*e^7 - 327*e^5 + 400*e^3 - 77*e', '27/4*e^9 - 118*e^7 + 561*e^5 - 617*e^3 + 126*e', '-49/4*e^9 + 215*e^7 - 1031*e^5 + 1166*e^3 - 262*e', '-5/2*e^8 + 45*e^6 - 230*e^4 + 328*e^2 - 98', '19/2*e^9 - 333/2*e^7 + 796*e^5 - 889*e^3 + 197*e', '5*e^8 - 87*e^6 + 410*e^4 - 435*e^2 + 66', '39/4*e^9 - 347/2*e^7 + 860*e^5 - 1090*e^3 + 285*e', '-17/4*e^8 + 74*e^6 - 697/2*e^4 + 375*e^2 - 90', '17/2*e^9 - 149*e^7 + 1427/2*e^5 - 808*e^3 + 191*e', '-37/4*e^8 + 164*e^6 - 1607/2*e^4 + 971*e^2 - 246', '9/4*e^8 - 77/2*e^6 + 343/2*e^4 - 126*e^2 - 16', '9*e^9 - 313/2*e^7 + 734*e^5 - 761*e^3 + 126*e', '1/2*e^9 - 9*e^7 + 47*e^5 - 78*e^3 + 52*e', '-7*e^9 + 123*e^7 - 1183/2*e^5 + 674*e^3 - 153*e', '-25/4*e^8 + 111*e^6 - 1093/2*e^4 + 667*e^2 - 158', '1/2*e^9 - 7*e^7 + 11*e^5 + 94*e^3 - 98*e', '-5/4*e^8 + 21*e^6 - 179/2*e^4 + 61*e^2 - 22', '-11/4*e^9 + 99/2*e^7 - 503/2*e^5 + 342*e^3 - 92*e', '3*e^8 - 53*e^6 + 258*e^4 - 308*e^2 + 90', '-17/2*e^9 + 149*e^7 - 1425/2*e^5 + 796*e^3 - 165*e', '-7/2*e^9 + 61*e^7 - 288*e^5 + 310*e^3 - 85*e', '7/2*e^9 - 60*e^7 + 270*e^5 - 221*e^3 - 29*e', '-15/2*e^8 + 133*e^6 - 652*e^4 + 786*e^2 - 192', '9/4*e^9 - 40*e^7 + 199*e^5 - 263*e^3 + 108*e', '5/2*e^9 - 43*e^7 + 391/2*e^5 - 172*e^3 - 11*e', '-7/2*e^8 + 60*e^6 - 271*e^4 + 238*e^2 - 2', '7*e^8 - 122*e^6 + 574*e^4 - 600*e^2 + 128', '19/4*e^9 - 165/2*e^7 + 385*e^5 - 384*e^3 + 39*e', '7*e^9 - 124*e^7 + 608*e^5 - 742*e^3 + 195*e', '19/4*e^8 - 83*e^6 + 787/2*e^4 - 421*e^2 + 92', '-37/2*e^9 + 327*e^7 - 1595*e^5 + 1912*e^3 - 474*e', '-1/2*e^8 + 8*e^6 - 28*e^4 - 15*e^2 - 6', '2*e^9 - 36*e^7 + 183*e^5 - 248*e^3 + 74*e', '-2*e^9 + 35*e^7 - 167*e^5 + 190*e^3 - 82*e', '3*e^8 - 52*e^6 + 239*e^4 - 218*e^2 + 48', '-7/4*e^9 + 63/2*e^7 - 161*e^5 + 224*e^3 - 43*e', '7*e^8 - 123*e^6 + 590*e^4 - 667*e^2 + 178', '5/2*e^9 - 47*e^7 + 263*e^5 - 466*e^3 + 216*e', '-21/4*e^9 + 185/2*e^7 - 447*e^5 + 515*e^3 - 114*e', 'e^9 - 33/2*e^7 + 66*e^5 - 17*e^3 - 12*e', '-4*e^2 + 22', '-7*e^8 + 123*e^6 - 592*e^4 + 681*e^2 - 142', '-17/2*e^9 + 305/2*e^7 - 770*e^5 + 1032*e^3 - 303*e', '4*e^8 - 70*e^6 + 335*e^4 - 389*e^2 + 106', '-17/4*e^9 + 149/2*e^7 - 358*e^5 + 422*e^3 - 154*e', '-5/2*e^8 + 46*e^6 - 241*e^4 + 336*e^2 - 60', '8*e^9 - 143*e^7 + 716*e^5 - 939*e^3 + 293*e', '1/4*e^9 - 3*e^7 - 4*e^5 + 101*e^3 - 135*e', '15/4*e^9 - 133/2*e^7 + 327*e^5 - 406*e^3 + 127*e', '73/4*e^9 - 645/2*e^7 + 1573*e^5 - 1892*e^3 + 473*e', '-9/4*e^9 + 79/2*e^7 - 379/2*e^5 + 214*e^3 - 40*e', '7*e^9 - 121*e^7 + 558*e^5 - 530*e^3 + 38*e', '21/2*e^8 - 185*e^6 + 897*e^4 - 1066*e^2 + 256', '-5/4*e^9 + 23*e^7 - 125*e^5 + 217*e^3 - 112*e', '5/2*e^8 - 46*e^6 + 245*e^4 - 374*e^2 + 104', '17/4*e^9 - 151/2*e^7 + 374*e^5 - 482*e^3 + 167*e', '-5/2*e^8 + 45*e^6 - 228*e^4 + 302*e^2 - 70', '-25/2*e^8 + 220*e^6 - 1061*e^4 + 1218*e^2 - 286', '3*e^8 - 53*e^6 + 256*e^4 - 290*e^2 + 72', '51/4*e^9 - 445/2*e^7 + 1053*e^5 - 1136*e^3 + 233*e', '-47/4*e^9 + 209*e^7 - 1036*e^5 + 1318*e^3 - 366*e', '27/2*e^8 - 237*e^6 + 1139*e^4 - 1301*e^2 + 306', '-21/2*e^8 + 185*e^6 - 896*e^4 + 1050*e^2 - 256', '19/4*e^9 - 167/2*e^7 + 402*e^5 - 454*e^3 + 39*e', '7/2*e^9 - 60*e^7 + 271*e^5 - 236*e^3 + 42*e', '-2*e^9 + 35*e^7 - 167*e^5 + 180*e^3 + 12*e', '15/2*e^9 - 265/2*e^7 + 644*e^5 - 753*e^3 + 153*e', '7*e^8 - 122*e^6 + 574*e^4 - 594*e^2 + 124', '-4*e^8 + 69*e^6 - 315*e^4 + 276*e^2 - 6', '2*e^9 - 75/2*e^7 + 209*e^5 - 365*e^3 + 152*e', '-6*e^8 + 105*e^6 - 501*e^4 + 557*e^2 - 118', '7*e^8 - 124*e^6 + 612*e^4 - 784*e^2 + 212', '-9/2*e^8 + 81*e^6 - 412*e^4 + 557*e^2 - 148', '49/4*e^8 - 429/2*e^6 + 2049/2*e^4 - 1150*e^2 + 272', '-5/2*e^8 + 44*e^6 - 216*e^4 + 288*e^2 - 122', '-39/4*e^9 + 173*e^7 - 853*e^5 + 1073*e^3 - 311*e', '35/4*e^9 - 155*e^7 + 761*e^5 - 941*e^3 + 273*e', '11/4*e^8 - 99/2*e^6 + 507/2*e^4 - 368*e^2 + 120', '25/2*e^9 - 220*e^7 + 1063*e^5 - 1242*e^3 + 324*e', '-3/4*e^8 + 31/2*e^6 - 207/2*e^4 + 246*e^2 - 116', '17/4*e^8 - 147/2*e^6 + 685/2*e^4 - 362*e^2 + 80', '-31/4*e^9 + 273/2*e^7 - 661*e^5 + 784*e^3 - 231*e', '-39/4*e^9 + 171*e^7 - 817*e^5 + 899*e^3 - 157*e', '23/2*e^9 - 202*e^7 + 972*e^5 - 1122*e^3 + 306*e', '-7*e^8 + 123*e^6 - 594*e^4 + 700*e^2 - 142', '43/4*e^9 - 379/2*e^7 + 1837/2*e^5 - 1084*e^3 + 300*e', '-6*e^8 + 107*e^6 - 534*e^4 + 700*e^2 - 188', '-51/4*e^9 + 445/2*e^7 - 1051*e^5 + 1110*e^3 - 197*e', '-43/4*e^8 + 189*e^6 - 1821/2*e^4 + 1053*e^2 - 226', '43/4*e^9 - 191*e^7 + 943*e^5 - 1174*e^3 + 280*e', '8*e^8 - 143*e^6 + 717*e^4 - 937*e^2 + 244', '5*e^8 - 88*e^6 + 427*e^4 - 512*e^2 + 134', '3*e^9 - 52*e^7 + 241*e^5 - 234*e^3 + 44*e', '-2*e^8 + 35*e^6 - 165*e^4 + 172*e^2 - 66', '11/2*e^9 - 195/2*e^7 + 481*e^5 - 619*e^3 + 226*e', '7*e^9 - 124*e^7 + 1219/2*e^5 - 764*e^3 + 253*e', '-35/4*e^9 + 309/2*e^7 - 754*e^5 + 928*e^3 - 313*e', '23/4*e^9 - 104*e^7 + 536*e^5 - 769*e^3 + 250*e', '-6*e^9 + 209/2*e^7 - 489*e^5 + 481*e^3 - 18*e', '17/4*e^8 - 77*e^6 + 795/2*e^4 - 575*e^2 + 186', '-69/4*e^9 + 306*e^7 - 1507*e^5 + 1877*e^3 - 498*e', '-11/4*e^9 + 93/2*e^7 - 202*e^5 + 134*e^3 + 47*e', '-9*e^9 + 158*e^7 - 758*e^5 + 860*e^3 - 233*e', '-1/4*e^8 + 3*e^6 + 7/2*e^4 - 83*e^2 + 24', '3/4*e^9 - 29/2*e^7 + 86*e^5 - 175*e^3 + 104*e', '57/4*e^9 - 253*e^7 + 1248*e^5 - 1561*e^3 + 403*e', '47/4*e^8 - 206*e^6 + 1969/2*e^4 - 1099*e^2 + 242', '-5/2*e^8 + 44*e^6 - 215*e^4 + 272*e^2 - 68', '25/2*e^9 - 222*e^7 + 1095*e^5 - 1362*e^3 + 346*e', '-69/4*e^9 + 607/2*e^7 - 1465*e^5 + 1698*e^3 - 373*e', '-1/2*e^8 + 11*e^6 - 79*e^4 + 204*e^2 - 110', '-3/2*e^8 + 27*e^6 - 141*e^4 + 226*e^2 - 98', '35/4*e^8 - 155*e^6 + 1523/2*e^4 - 951*e^2 + 262', '-7/2*e^9 + 62*e^7 - 304*e^5 + 372*e^3 - 111*e', '-10*e^8 + 174*e^6 - 815*e^4 + 833*e^2 - 142', '25/4*e^8 - 112*e^6 + 1127/2*e^4 - 741*e^2 + 202', '17*e^9 - 301*e^7 + 2951/2*e^5 - 1812*e^3 + 501*e', '35/2*e^9 - 619/2*e^7 + 1511*e^5 - 1811*e^3 + 414*e', '61/4*e^9 - 541/2*e^7 + 1333*e^5 - 1676*e^3 + 491*e', '-25/4*e^9 + 221/2*e^7 - 540*e^5 + 648*e^3 - 98*e', '41/2*e^9 - 362*e^7 + 1764*e^5 - 2124*e^3 + 550*e', '21*e^9 - 370*e^7 + 1793*e^5 - 2114*e^3 + 528*e', '-15/4*e^9 + 137/2*e^7 - 363*e^5 + 580*e^3 - 268*e', '15*e^8 - 263*e^6 + 1260*e^4 - 1432*e^2 + 352', '-5*e^8 + 88*e^6 - 424*e^4 + 478*e^2 - 90', -38, '-31/2*e^9 + 275*e^7 - 2707/2*e^5 + 1680*e^3 - 473*e', '-18*e^9 + 316*e^7 - 1518*e^5 + 1734*e^3 - 396*e', '-25/4*e^9 + 223/2*e^7 - 555*e^5 + 704*e^3 - 163*e', '-8*e^9 + 141*e^7 - 685*e^5 + 820*e^3 - 210*e'], 'hecke_polynomial': 'x^10 - 18*x^8 + 92*x^6 - 132*x^4 + 60*x^2 - 8', 'label': '4.4.18736.1-7.1-b'}
• hmf_fields •

  Column	Type
  degree	smallint
  discriminant	bigint
  ideals	jsonb
  label	text
  narrow_class_no	smallint
  primes	jsonb

  
  {'degree': 4, 'discriminant': 18736, 'ideals': ['[1, 1, 1]', '[3, 3, w - 1]', '[4, 2, -w^3 + 2*w^2 + 4*w - 3]', '[5, 5, w]', '[7, 7, w - 2]', '[9, 9, w^3 - 3*w^2 - 2*w + 7]', '[11, 11, w^2 - 2*w - 4]', '[12, 6, -w^2 + w + 3]', '[15, 15, -w^2 + 2*w + 5]', '[16, 2, 2]', '[20, 10, -w^2 + w + 5]', '[21, 21, w^3 - w^2 - 5*w - 1]', '[23, 23, -w^2 + 2*w + 1]', '[23, 23, w^3 - 2*w^2 - 3*w + 3]', '[25, 25, w^3 - 3*w^2 - w + 5]', '[27, 3, -w^3 + w^2 + 6*w + 2]', '[27, 27, -w^3 + 2*w^2 + 3*w - 1]', '[28, 14, w^3 - 2*w^2 - 4*w + 1]', '[31, 31, -w^3 + 3*w^2 + w - 1]', '[31, 31, -w^3 + 2*w^2 + 4*w - 4]', '[33, 33, w^3 - 3*w^2 - 2*w + 4]', '[35, 35, w^2 - 2*w]', '[36, 18, -w^2 + 3*w + 1]', '[37, 37, w^2 - 2*w - 6]', '[37, 37, w^3 - 2*w^2 - 3*w + 2]', '[43, 43, w^2 - 3*w - 2]', '[44, 22, w^3 - 2*w^2 - 2*w + 1]', '[45, 45, -w^3 + 3*w^2 + 3*w - 5]', '[48, 6, 2*w - 2]', '[49, 49, w^3 - 3*w^2 + 4]', '[55, 55, w^3 - 2*w^2 - 4*w]', '[60, 30, -w^3 + 2*w^2 + 4*w - 5]', '[61, 61, -w^3 + 2*w^2 + 2*w - 2]', '[63, 63, w^2 - 4]', '[64, 4, -2*w^3 + 4*w^2 + 8*w - 6]', '[69, 69, -2*w^2 + 3*w + 8]', '[69, 69, w - 4]', '[73, 73, w^3 - 3*w^2 - 2*w + 3]', '[75, 75, -2*w^3 + 5*w^2 + 7*w - 10]', '[77, 77, w^3 - 4*w^2 + 8]', '[80, 10, 2*w]', '[81, 3, 3]', '[81, 81, w^3 - 4*w^2 + 6]', '[83, 83, -w - 3]', '[84, 42, -w^3 + 3*w^2 + w - 6]', '[89, 89, -w^3 + 3*w^2 + 2*w - 2]', '[89, 89, 2*w - 1]', '[92, 46, w^3 - 4*w^2 - 2*w + 9]', '[92, 46, w^3 - 2*w^2 - 2*w - 1]', '[93, 93, -w^3 + w^2 + 4*w - 1]', '[93, 93, -w^3 + 2*w^2 + 3*w + 2]', '[99, 99, -w^3 + 4*w^2 + w - 13]', '[100, 50, -w^3 + w^2 + 5*w]', '[101, 101, w^3 - 4*w^2 + w + 7]', '[101, 101, 2*w^2 - 3*w - 3]', '[103, 103, w^3 - 7*w - 4]', '[105, 105, -w^3 + 4*w^2 + w - 10]', '[107, 107, 3*w^3 - 2*w^2 - 17*w - 12]', '[108, 6, w^3 - 4*w^2 + 7]', '[108, 54, w^3 - 4*w^2 - 2*w + 11]', '[109, 109, -w^3 + 2*w^2 + 5*w - 2]', '[111, 111, w^3 - 3*w^2 - 4*w + 6]', '[111, 111, -w^3 + 4*w^2 + w - 7]', '[112, 14, 2*w - 4]', '[113, 113, w^3 - 3*w^2 - 4*w + 4]', '[115, 115, -w^3 + 2*w^2 + w]', '[115, 115, 2*w^2 - w - 5]', '[121, 121, -2*w^2 + 2*w + 7]', '[124, 62, -w^3 + 3*w^2 + 3*w - 4]', '[124, 62, w^2 - w + 1]', '[125, 5, w^3 - 2*w^2 - 5*w + 4]', '[125, 125, -w^3 + 4*w^2 + w - 5]', '[129, 129, w^3 - 4*w^2 + w + 2]', '[132, 66, w^3 - 6*w - 7]', '[135, 15, w^3 - 4*w^2 + 10]', '[135, 135, -2*w^2 + 3*w + 5]', '[139, 139, -w^3 + 2*w^2 + w - 4]', '[139, 139, -2*w^2 + 3*w + 7]', '[140, 70, w^2 - 3*w - 5]', '[144, 18, 2*w^3 - 6*w^2 - 4*w + 14]', '[147, 147, -w^3 + 2*w^2 + 5*w - 3]', '[148, 74, 2*w^3 - 5*w^2 - 5*w + 9]', '[148, 74, -w^3 + 5*w^2 - w - 16]', '[149, 149, -w^3 + 3*w^2 + w - 7]', '[149, 149, -2*w^3 + 6*w^2 + 5*w - 16]', '[155, 155, -w^2 + 5]', '[155, 155, -2*w^3 + 4*w^2 + 7*w - 5]', '[157, 157, -2*w^3 + 6*w^2 + 3*w - 11]', '[157, 157, 2*w^3 - 3*w^2 - 10*w + 1]', '[161, 161, -2*w^3 + 6*w^2 + 5*w - 11]', '[161, 161, 2*w^3 - 4*w^2 - 7*w + 7]', '[163, 163, -w^3 + 4*w^2 + w - 9]', '[163, 163, 2*w^3 - 5*w^2 - 6*w + 7]', '[165, 165, -w^3 + 3*w^2 - 5]', '[167, 167, -w^3 + 4*w^2 - 2*w - 6]', '[169, 13, -w^3 + 4*w^2 + w - 8]', '[169, 13, 2*w^2 - 3*w - 6]', '[172, 86, w^3 - 6*w - 9]', '[173, 173, w^3 - w^2 - 4*w - 4]', '[175, 175, w^3 - 2*w^2]', '[176, 22, 2*w^2 - 4*w - 8]', '[180, 90, -w^3 + 3*w^2 + w]', '[181, 181, 2*w^3 - 4*w^2 - 7*w + 4]', '[181, 181, w^2 - 2*w + 2]', '[183, 183, w^3 - 5*w^2 + 7]', '[185, 185, 2*w^2 - 2*w - 5]', '[185, 185, 3*w^3 - 8*w^2 - 9*w + 15]', '[189, 21, w^3 - w^2 - 6*w + 1]', '[189, 189, 2*w^3 - 6*w^2 - 3*w + 7]', '[191, 191, 2*w^2 - 4*w - 3]', '[192, 12, -2*w^2 + 2*w + 6]', '[196, 98, -2*w^3 + 5*w^2 + 5*w - 7]', '[197, 197, w^3 - 5*w^2 + 17]', '[197, 197, -w^3 + w^2 + 4*w - 2]', '[207, 207, w^3 - 4*w^2 - w + 4]', '[207, 207, -2*w^3 + 5*w^2 + 5*w - 8]', '[211, 211, 2*w^3 - 4*w^2 - 8*w + 3]', '[211, 211, -w^3 + 6*w + 8]', '[215, 215, w^3 - 3*w^2 - 2*w]', '[217, 217, w^2 - 2*w - 7]', '[217, 217, w^3 - 3*w^2 - 3*w + 3]', '[219, 219, -2*w^3 + 6*w^2 + w - 8]', '[220, 110, w^3 - 3*w^2 + w]', '[223, 223, w^3 - 4*w^2 - 2*w + 6]', '[225, 225, -w^3 + w^2 + 4*w + 5]', '[227, 227, 2*w^3 - 3*w^2 - 10*w - 2]', '[229, 229, -w^3 + 3*w^2 + 3*w - 1]', '[231, 231, -2*w^2 + 3*w + 2]', '[233, 233, -w^3 + w^2 + 5*w - 1]', '[233, 233, -2*w^3 + 7*w^2 + 4*w - 17]', '[240, 30, -2*w^2 + 4*w + 10]', '[243, 9, 3*w - 3]', '[243, 243, -2*w^3 + 4*w^2 + 8*w - 7]', '[244, 122, w^3 - 4*w^2 + 11]', '[245, 245, -3*w^3 + 7*w^2 + 10*w - 10]', '[249, 249, -w^2 - 2*w + 3]', '[252, 126, 2*w^3 - 5*w^2 - 3*w + 3]', '[253, 253, 2*w^3 - 4*w^2 - 6*w + 1]', '[253, 253, -2*w^3 + 3*w^2 + 9*w - 2]', '[256, 4, 4]', '[257, 257, 2*w^3 - 5*w^2 - 5*w + 4]', '[259, 259, w^3 - 4*w^2 - 2*w + 12]', '[259, 259, -2*w^3 + 6*w^2 + 4*w - 9]', '[263, 263, w^2 - 6]', '[263, 263, 3*w^3 - 9*w^2 - 8*w + 24]', '[267, 267, 2*w^3 - 6*w^2 + 7]', '[267, 267, 2*w^2 - 3*w + 1]', '[275, 275, w - 5]', '[276, 138, -w^3 + 3*w^2 + 3*w - 2]', '[276, 138, -w^3 + 5*w^2 - 3*w - 4]', '[279, 279, w^3 - 4*w^2 + 3*w + 3]', '[279, 279, w^3 - 4*w^2 + w + 8]', '[281, 281, 3*w^3 - 4*w^2 - 14*w - 2]', '[281, 281, 2*w^3 - 3*w^2 - 8*w + 1]', '[289, 17, 2*w^3 - 4*w^2 - 9*w + 9]', '[289, 17, -2*w^3 + 5*w^2 + 4*w - 8]', '[292, 146, -w^3 + 5*w^2 - w - 14]', '[293, 293, -w - 4]', '[297, 33, -w^3 + 4*w^2 - 3*w - 4]', '[297, 297, w^3 - 3*w^2 - 4*w + 3]', '[300, 150, -w^2 - w + 5]', '[301, 301, w^3 - 5*w^2 + 4*w + 4]', '[303, 303, -3*w^3 + 10*w^2 + 2*w - 12]', '[303, 303, 2*w^3 - 5*w^2 + 3]', '[305, 305, -3*w^2 + 2*w + 5]', '[307, 307, 3*w^3 - 3*w^2 - 15*w - 7]', '[308, 154, -2*w^3 + 7*w^2 + w - 7]', '[309, 309, w^3 - 2*w^2 - w - 1]', '[311, 311, w^2 - 8]', '[311, 311, -w^3 + 5*w^2 - 2*w - 7]', '[315, 315, 2*w^3 - 4*w^2 - 7*w]', '[320, 20, -2*w^2 + 2*w + 10]', '[321, 321, w^3 - 7*w - 3]', '[324, 6, -3*w^3 + 6*w^2 + 12*w - 9]', '[324, 162, -w^3 + w^2 + 7*w + 2]', '[327, 327, w^3 - 2*w^2 - 3*w + 7]', '[332, 166, 3*w^3 - 5*w^2 - 13*w + 4]', '[333, 333, -2*w^3 + 4*w^2 + 6*w - 11]', '[333, 333, 3*w^3 - 7*w^2 - 10*w + 14]', '[336, 42, 2*w^3 - 2*w^2 - 10*w - 2]', '[337, 337, w^2 - 4*w - 2]', '[337, 337, -w^3 + 3*w^2 - 6]', '[339, 339, -2*w^3 + 4*w^2 + 4*w - 9]', '[341, 341, w^3 - w^2 - 2*w - 2]', '[341, 341, 3*w^3 - 6*w^2 - 11*w + 6]', '[343, 7, -2*w^3 + 7*w^2 + 3*w - 16]', '[343, 343, 2*w^2 - 2*w - 11]', '[345, 345, w^2 - 4*w]', '[345, 345, -2*w^3 + 3*w^2 + 8*w]', '[347, 347, w^3 - 2*w^2 - 3*w - 3]', '[349, 349, -2*w^3 + 5*w^2 + 2*w - 4]', '[353, 353, -2*w^3 + 7*w^2 + 4*w - 14]', '[353, 353, -w^3 + 4*w^2 - 14]', '[356, 178, -3*w^2 + 5*w + 11]', '[356, 178, w^3 - 4*w^2 - 2*w + 13]', '[359, 359, -w^3 + 3*w^2 - 2*w - 2]', '[363, 363, -w^3 + w^2 + 7*w - 1]', '[365, 365, -w^3 + 3*w^2 - w - 5]', '[367, 367, w^2 - 5*w - 4]', '[367, 367, w^2 - w - 8]', '[368, 46, -2*w^2 + 4*w + 2]', '[368, 46, 2*w^3 - 4*w^2 - 6*w + 6]', '[372, 186, -w^3 + 3*w^2 - w + 2]', '[372, 186, -2*w^3 + 5*w^2 + 7*w - 7]', '[375, 15, -w^3 + 2*w^2 + 5*w - 9]', '[375, 375, w^3 - 3*w^2 - 2*w + 10]', '[379, 379, 3*w^3 - 2*w^2 - 19*w - 11]', '[379, 379, -w^2 - w - 2]', '[379, 379, 3*w^3 - 21*w - 19]', '[379, 379, -2*w^3 + 3*w^2 + 10*w + 3]', '[383, 383, 3*w^3 - 6*w^2 - 11*w + 7]', '[383, 383, w^3 - 5*w^2 + w + 7]', '[385, 385, -2*w^3 + 5*w^2 + 4*w - 5]', '[387, 387, 2*w^3 - 5*w^2 - 6*w + 6]', '[389, 389, w^2 - 4*w - 1]', '[396, 198, w^3 - w^2 - 5*w + 2]', '[397, 397, -w^3 + w^2 + 6*w - 2]', '[397, 397, 2*w^3 - 2*w^2 - 11*w - 8]', '[400, 50, 2*w^3 - 6*w^2 - 2*w + 10]', '[401, 401, 3*w^2 - 4*w - 12]', '[404, 202, -4*w^3 + 9*w^2 + 13*w - 11]', '[404, 202, w^3 - w^2 - 5*w - 6]', '[405, 15, 3*w]', '[405, 405, -2*w^3 + 5*w^2 + 2*w - 5]', '[407, 407, w^2 - w + 2]', '[407, 407, -2*w^3 + 2*w^2 + 11*w + 2]', '[409, 409, -2*w^3 + 7*w^2 + 4*w - 16]', '[409, 409, 3*w - 2]', '[412, 206, 3*w^3 - w^2 - 19*w - 18]', '[415, 415, -w^2 - 3*w]', '[417, 417, w^3 - 6*w^2 - w + 9]', '[417, 417, -2*w^3 + 5*w^2 + 4*w - 7]', '[419, 419, 2*w^2 - w - 8]', '[420, 210, w^3 - 4*w^2 - 2*w + 5]', '[427, 427, 2*w^3 - 7*w^2 - 2*w + 9]', '[428, 214, 2*w^3 - 5*w^2 - 5*w + 3]', '[432, 6, -2*w^3 + 2*w^2 + 12*w + 4]', '[432, 54, -2*w^3 + 4*w^2 + 6*w - 2]', '[433, 433, -w^3 + 4*w^2 + w - 14]', '[436, 218, w^3 - 7*w^2 + 3*w + 26]', '[439, 439, w^3 - 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7]', '[1505, 1505, -3*w^3 + 9*w^2 - 5]', '[1509, 1509, 3*w^3 - 9*w^2 - 5*w + 11]', '[1509, 1509, 4*w^3 - 9*w^2 - 10*w + 18]', '[1515, 1515, -w^3 - w^2 + 8*w + 15]', '[1515, 1515, 3*w^3 - 3*w^2 - 13*w - 5]', '[1516, 758, -w^3 + 6*w^2 - 4*w - 11]', '[1516, 758, 3*w^3 - 4*w^2 - 14*w + 1]', '[1516, 758, w^3 - 10*w + 1]', '[1516, 758, 5*w^3 - 19*w^2 - 7*w + 56]', '[1519, 1519, -3*w^3 + 8*w^2 + 5*w - 11]', '[1519, 1519, w^3 - 4*w^2 - 3*w + 14]', '[1521, 117, -5*w^3 + 15*w^2 + 14*w - 36]', '[1521, 117, -w^3 + 5*w^2 + w - 17]', '[1525, 1525, -3*w^2 + 5*w]', '[1527, 1527, w^3 - w^2 - 8*w + 11]', '[1529, 1529, w + 6]', '[1529, 1529, -3*w^3 + 12*w^2 - 2*w - 14]', '[1531, 1531, 3*w^3 - 7*w^2 - 8*w + 8]', '[1531, 1531, 2*w^2 + w - 8]', '[1531, 1531, -3*w^3 + 7*w^2 + 8*w - 11]', '[1531, 1531, 2*w^3 - 3*w^2 - 6*w - 4]', '[1532, 766, -4*w^3 + 19*w^2 - w - 61]', '[1532, 766, -3*w^3 + 8*w^2 + 8*w - 11]', '[1533, 1533, -w^3 - 2*w^2 + 9*w + 12]', '[1535, 1535, w^3 - 5*w - 10]', '[1540, 770, 3*w^3 - 10*w^2 - 8*w + 25]', '[1545, 1545, 7*w^3 - 6*w^2 - 38*w - 20]', '[1548, 774, 4*w^3 - 11*w^2 - 5*w + 3]', '[1553, 1553, -w^3 + 6*w^2 - 4*w - 12]', '[1555, 1555, w^3 - 8*w]', '[1555, 1555, -2*w^3 + 9*w^2 - 6*w - 5]', '[1556, 778, 3*w^2 - 3*w - 17]', '[1557, 1557, -w^3 + 6*w^2 - 2*w - 18]', '[1561, 1561, -4*w^3 + 11*w^2 + 6*w - 17]', '[1563, 1563, -w^3 + 2*w^2 - w - 6]', '[1567, 1567, 4*w^3 - 5*w^2 - 20*w - 2]', '[1569, 1569, w^3 - 5*w^2 - 3*w + 7]', '[1569, 1569, 4*w^3 - 10*w^2 - 4*w + 13]', '[1571, 1571, 4*w^3 - 8*w^2 - 13*w + 13]', '[1571, 1571, 5*w^3 - 5*w^2 - 25*w - 9]', '[1575, 1575, -2*w^3 + 8*w^2 + 3*w - 15]', '[1579, 1579, -2*w^3 + 6*w^2 - 9]', '[1579, 1579, -3*w^3 + 8*w^2 + 5*w - 9]', '[1583, 1583, 4*w^2 - 4*w - 17]', '[1584, 198, -2*w^3 + 8*w^2 + 2*w - 26]', '[1587, 69, -w^3 + 6*w^2 - 7*w - 4]', '[1587, 69, 3*w^3 - 10*w^2 - 4*w + 14]', '[1587, 1587, -3*w^3 + 6*w^2 + 11*w - 2]', '[1587, 1587, -4*w^3 + 10*w^2 + 11*w - 17]', '[1588, 794, 2*w^3 - 9*w^2 - w + 31]', '[1588, 794, 3*w^3 - 8*w^2 - 4*w + 7]', '[1589, 1589, -3*w^3 + 6*w^2 + 10*w - 6]', '[1591, 1591, -5*w^3 + 12*w^2 + 16*w - 18]', '[1591, 1591, -4*w^3 + 11*w^2 + 8*w - 22]', '[1597, 1597, 3*w^3 - 6*w^2 - 9*w + 2]', '[1600, 100, -2*w^3 + 2*w^2 + 10*w]', '[1601, 1601, 2*w^2 - w - 11]', '[1603, 1603, -w^3 + 6*w^2 - 9*w + 2]', '[1604, 802, 2*w^3 - 5*w^2 - 9*w + 13]', '[1605, 1605, 2*w^3 - 2*w^2 - 7*w - 5]', '[1609, 1609, 4*w^3 - 5*w^2 - 18*w - 7]', '[1613, 1613, -w^3 + 6*w^2 - 3*w - 16]', '[1613, 1613, -2*w^3 + 8*w^2 - 13]', '[1616, 202, 2*w^3 - 8*w^2 + 2*w + 14]', '[1616, 202, 4*w^2 - 6*w - 6]', '[1617, 1617, 4*w^3 - 7*w^2 - 17*w + 2]', '[1619, 1619, w^3 - 2*w^2 - 7*w + 1]', '[1620, 30, -3*w^2 + 3*w + 15]', '[1620, 810, 2*w^3 - 7*w^2 - w + 15]', '[1621, 1621, -w^3 + w^2 + 2*w + 12]', '[1621, 1621, 6*w^3 - 11*w^2 - 25*w + 8]', '[1623, 1623, -w^2 - 4*w + 8]', '[1623, 1623, w^3 - w^2 - 8*w - 1]', '[1628, 814, -3*w^3 + 11*w^2 + 9*w - 22]', '[1628, 814, -w^3 + 3*w^2 + 3*w + 2]', '[1629, 1629, 5*w^3 - 14*w^2 - 11*w + 29]', '[1629, 1629, 7*w^3 - 17*w^2 - 23*w + 33]', '[1631, 1631, w^3 - 2*w^2 - 7*w + 7]', '[1631, 1631, 7*w^3 - 20*w^2 - 17*w + 44]', '[1635, 1635, -5*w^3 + 8*w^2 + 24*w]', '[1636, 818, 11*w^3 - 29*w^2 - 33*w + 58]', '[1636, 818, 2*w^3 - 7*w^2 - 5*w + 21]', '[1637, 1637, 3*w^3 - 5*w^2 - 14*w - 1]', '[1639, 1639, 2*w^3 - 5*w^2 + 7]', '[1639, 1639, -2*w^2 + 3*w + 13]', '[1641, 1641, 4*w^3 - 10*w^2 - 10*w + 19]', '[1641, 1641, -w^3 + 6*w^2 - 5*w - 3]', '[1647, 183, -w^3 - 2*w^2 + 9*w + 11]', '[1647, 1647, -w^3 + 3*w^2 + 2*w + 2]', '[1648, 206, 2*w^3 - 14*w - 8]', '[1660, 830, w^3 + 2*w^2 - 8*w - 15]', '[1665, 1665, 4*w^3 - 10*w^2 - 15*w + 15]', '[1665, 1665, -w^3 + 5*w^2 + 2*w - 15]', '[1668, 834, w^3 + 2*w^2 - 2*w - 7]', '[1668, 834, 4*w^3 - 13*w^2 - 7*w + 31]', '[1671, 1671, 2*w^3 - 8*w^2 - w + 13]', '[1671, 1671, -2*w^3 + 3*w^2 + 12*w - 16]', '[1676, 838, 6*w^3 - 13*w^2 - 23*w + 19]', '[1679, 1679, -2*w^2 + 9]', '[1679, 1679, -2*w^3 + 9*w^2 - 3*w - 12]', '[1680, 210, -2*w^3 + 8*w^2 + 2*w - 20]', '[1681, 41, -2*w^3 + 5*w^2 + 9*w - 4]', '[1681, 41, w^3 - 4*w^2 + 5*w + 6]', '[1685, 1685, w^3 - 5*w^2 - 2*w + 5]', '[1685, 1685, w^3 - 4*w^2 - 2*w]', '[1689, 1689, 3*w^3 - 7*w^2 - 2*w + 9]', '[1689, 1689, -4*w^3 + 12*w^2 + 3*w - 14]', '[1693, 1693, 3*w^3 - 3*w^2 - 14*w - 2]', '[1695, 1695, 4*w^3 - 8*w^2 - 19*w + 5]', '[1697, 1697, 2*w^3 + w^2 - 16*w - 21]', '[1697, 1697, w^3 + w^2 - 8*w - 4]', '[1701, 63, 3*w^3 - 3*w^2 - 15*w - 3]', '[1701, 1701, 2*w^3 - 5*w^2 - 7*w + 4]', '[1705, 1705, 4*w^2 - 6*w - 15]', '[1705, 1705, 3*w^3 - 8*w^2 - 4*w + 10]', '[1707, 1707, -w^3 + w^2 + 8*w - 2]', '[1708, 854, w^3 - 4*w - 7]', '[1712, 214, 6*w^3 - 4*w^2 - 34*w - 24]', '[1713, 1713, w^3 - 4*w^2 + 7*w - 4]', '[1715, 35, 3*w^3 - 7*w^2 - 8*w + 10]', '[1715, 1715, 2*w^3 - 2*w^2 - 11*w]', '[1719, 1719, 3*w^3 - 7*w^2 - 8*w + 9]', '[1721, 1721, -3*w^3 + 9*w^2 + 6*w - 13]', '[1723, 1723, 2*w^3 - 2*w^2 - 12*w + 1]', '[1723, 1723, 5*w^2 - 7*w - 26]', '[1725, 1725, w^3 - 4*w^2 - 3*w + 15]', '[1725, 1725, w^3 - 4*w^2]', '[1727, 1727, w^3 - 3*w^2 - 4*w + 14]', '[1727, 1727, -2*w^3 + 6*w^2 + 5*w - 2]', '[1728, 12, 2*w^3 - 8*w^2 + 14]', '[1728, 108, 2*w^3 - 8*w^2 - 4*w + 22]', '[1731, 1731, w^3 - 3*w^2 + 5*w - 3]', '[1732, 866, 11*w^3 - 25*w^2 - 39*w + 42]', '[1735, 1735, 2*w^2 - 7*w - 5]', '[1741, 1741, -2*w^3 + 2*w^2 + 9*w - 1]', '[1743, 1743, -4*w^3 + 3*w^2 + 20*w + 8]', '[1744, 218, -2*w^3 + 4*w^2 + 10*w - 4]', '[1745, 1745, w^3 - 8*w^2 + 4*w + 10]', '[1753, 1753, -w^3 + 4*w^2 + 5*w - 3]', '[1753, 1753, 3*w^3 + 2*w^2 - 24*w - 28]', '[1756, 878, -3*w^3 + 11*w^2 + w - 16]', '[1756, 878, -2*w^3 + 7*w^2 - w - 11]', '[1759, 1759, -w^3 + 7*w + 11]', '[1761, 1761, -w^3 - w^2 + 6*w + 2]', '[1761, 1761, 3*w^3 - 8*w^2 - 3*w + 8]', '[1764, 882, -3*w^3 + 5*w^2 + 11*w - 4]', '[1765, 1765, 2*w^3 - 5*w^2 - 10*w + 5]', '[1765, 1765, 3*w^3 - 6*w^2 - 6*w + 10]', '[1771, 1771, -w^3 + 6*w - 4]', '[1771, 1771, 3*w^3 - 7*w^2 - 12*w + 14]', '[1772, 886, w^3 - 6*w^2 + 4*w + 17]', '[1773, 1773, -w^3 + 2*w^2 + 2*w + 6]', '[1773, 1773, -5*w^3 + 12*w^2 + 14*w - 24]', '[1776, 222, 2*w^3 - 6*w^2 - 8*w + 12]', '[1776, 222, -2*w^3 + 8*w^2 + 2*w - 14]', '[1777, 1777, 2*w^3 - w^2 - 13*w - 4]', '[1777, 1777, -2*w^3 + 6*w^2 + 5*w - 7]', '[1780, 890, -3*w^3 + 5*w^2 + 11*w]', '[1780, 890, -2*w^3 + 3*w^2 + 9*w - 5]', '[1787, 1787, -w^3 + 2*w^2 + 3*w - 9]', '[1788, 894, 3*w^2 - w - 11]', '[1788, 894, w^2 + 5*w - 9]', '[1792, 28, 4*w - 8]', '[1793, 1793, -3*w^2 + 3*w + 16]', '[1793, 1793, -4*w^3 + 9*w^2 + 12*w - 16]', '[1795, 1795, w^3 - 7*w^2 + 2*w + 5]', '[1796, 898, 3*w^3 - 11*w^2 - 3*w + 28]', '[1799, 1799, 5*w^3 - 15*w^2 - 6*w + 18]', '[1801, 1801, -2*w^3 + 3*w^2 + 8*w + 7]', '[1808, 226, 2*w^3 - 6*w^2 - 8*w + 8]', '[1813, 1813, 3*w^2 - 5*w - 2]', '[1813, 1813, -w^3 + 3*w^2 - w - 9]', '[1815, 1815, -w^3 + 2*w^2 + 3*w + 5]', '[1825, 1825, -w^3 + 4*w^2 - 5*w]', '[1828, 914, 9*w^3 - 27*w^2 - 23*w + 66]', '[1835, 1835, w^3 - 5*w^2 - 4*w]', '[1835, 1835, w^3 - w^2 - 8*w]', '[1837, 1837, -3*w^3 + 6*w^2 + 9*w + 4]', '[1839, 1839, 2*w^3 - 3*w^2 - 8*w + 6]', '[1840, 230, -2*w^3 + 4*w^2 + 2*w]', '[1840, 230, 4*w^2 - 2*w - 10]', '[1841, 1841, -2*w^3 + 8*w^2 + w - 18]', '[1841, 1841, w^3 - 2*w^2 - 6*w + 12]', '[1844, 922, 2*w^3 + w^2 - 17*w - 17]', '[1849, 1849, -6*w^2 + 9*w + 26]', '[1851, 1851, w^3 - 4*w^2 + 3*w - 3]', '[1852, 926, w^3 - 5*w^2 - w + 18]', '[1852, 926, 2*w^3 - 3*w^2 - 11*w + 7]', '[1859, 143, -2*w^2 + w + 12]', '[1859, 143, -3*w^3 + 2*w^2 + 16*w + 14]', '[1860, 930, w^3 - 6*w^2 + 6*w + 5]', '[1860, 930, w^3 - 3*w^2 + w + 10]', '[1861, 1861, -2*w^3 - w^2 + 14*w + 14]', '[1863, 69, -3*w^2 + 6*w + 3]', '[1863, 69, 3*w^3 - 6*w^2 - 9*w + 9]', '[1863, 1863, w^3 - 3*w^2 - 6*w + 8]', '[1863, 1863, -3*w^3 + 5*w^2 + 10*w - 6]', '[1867, 1867, -w^3 + w^2 + 8*w - 1]', '[1869, 1869, 2*w^3 + w^2 - 14*w - 13]', '[1869, 1869, w^3 + w^2 - 5*w - 9]', '[1871, 1871, -w^3 + 3*w^2 + 2*w - 12]', '[1873, 1873, 3*w^3 - 8*w^2 - 9*w + 22]', '[1875, 15, 5*w^3 - 10*w^2 - 20*w + 10]', '[1875, 1875, -w^3 + 3*w^2 + 6*w - 5]', '[1877, 1877, -3*w^3 + 7*w^2 + 13*w - 7]', '[1877, 1877, 3*w^3 - w^2 - 19*w - 11]', '[1877, 1877, -7*w^3 + 17*w^2 + 23*w - 29]', '[1877, 1877, 5*w^2 - 7*w - 8]', '[1879, 1879, 4*w^3 - 8*w^2 - 16*w + 7]', '[1884, 942, 3*w^2 - 5*w - 1]', '[1884, 942, -w^3 + 4*w^2 + 4*w - 13]', '[1891, 1891, 2*w^3 - 6*w^2 - 2*w + 13]', '[1891, 1891, -4*w^3 + 11*w^2 + 3*w - 8]', '[1892, 946, w^3 - 8*w^2 + 8*w + 13]', '[1895, 1895, 4*w^2 - 8*w - 15]', '[1895, 1895, 4*w^3 - 6*w^2 - 20*w + 5]', '[1895, 1895, -w^2 + w + 10]', '[1895, 1895, -w^3 - w^2 - 2*w]', '[1899, 1899, 7*w^3 - 17*w^2 - 24*w + 31]', '[1899, 1899, -5*w + 8]', '[1903, 1903, -3*w^3 - w^2 + 23*w + 21]', '[1909, 1909, w^3 + w^2 - 7*w - 3]', '[1909, 1909, -3*w^3 + 4*w^2 + 10*w - 4]', '[1915, 1915, 4*w^2 - 5*w - 15]', '[1915, 1915, -3*w^3 + 6*w^2 + 3*w - 5]', '[1916, 958, 5*w^3 - 14*w^2 - 14*w + 27]', '[1925, 1925, w^3 - 6*w^2 + 3*w + 10]', '[1929, 1929, 2*w^3 - 7*w^2 - 3*w + 8]', '[1931, 1931, -2*w^3 + 6*w^2 + 9*w - 9]', '[1932, 966, -3*w^3 + 6*w^2 + 10*w - 13]', '[1932, 966, 3*w^3 - 8*w^2 - 4*w + 9]', '[1933, 1933, 5*w^3 - 13*w^2 - 14*w + 21]', '[1935, 1935, -w^3 + 4*w^2 - 2*w - 10]', '[1936, 242, -4*w^2 + 4*w + 14]', '[1945, 1945, w^3 - 4*w^2 - w]', '[1948, 974, 3*w^3 - 9*w^2 - w + 12]', '[1951, 1951, -w^2 + w - 4]', '[1953, 1953, 3*w^3 - 8*w^2 - 11*w + 16]', '[1953, 1953, 2*w^3 - 4*w^2 - 3*w - 1]', '[1956, 978, 3*w^3 - 5*w^2 - 13*w + 6]', '[1956, 978, -w^3 + 3*w^2 + w - 12]', '[1967, 1967, -3*w^3 + 8*w^2 + 9*w - 12]', '[1967, 1967, -4*w^3 + 9*w^2 + 14*w - 11]', '[1971, 219, w^3 + 2*w^2 - 12*w - 14]', '[1971, 1971, 2*w^3 - 4*w^2 - 4*w - 3]', '[1973, 1973, w^3 - 6*w - 12]', '[1973, 1973, 3*w^3 - 11*w^2 + 19]', '[1980, 990, w^3 - 2*w - 5]', '[1983, 1983, 4*w^3 - 15*w^2 - 2*w + 19]', '[1983, 1983, w^3 - w^2 - 4*w + 7]', '[1984, 124, -2*w^3 + 6*w^2 + 6*w - 8]', '[1984, 124, 2*w^2 - 2*w + 2]', '[1985, 1985, -w^3 + w^2 + 2*w + 5]', '[1985, 1985, 3*w^3 - 7*w^2 - 9*w + 5]', '[1991, 1991, -5*w^3 + 6*w^2 + 26*w + 4]', '[1991, 1991, -2*w^3 + 7*w^2 - 13]', '[1993, 1993, -5*w^3 + 12*w^2 + 17*w - 19]', '[1993, 1993, -6*w^3 + 15*w^2 + 19*w - 26]', '[1999, 1999, -3*w^3 + 7*w^2 + 4*w - 9]', '[1999, 1999, 3*w^3 - 8*w^2 - 11*w + 17]', '[2000, 10, 2*w^3 - 4*w^2 - 10*w + 8]', '[2000, 250, -2*w^3 + 8*w^2 + 2*w - 10]', '[2003, 2003, -2*w^3 + 9*w^2 - 2*w - 22]', '[2003, 2003, -w^3 + 10*w - 4]', '[2004, 1002, 2*w^3 - 3*w^2 - 5*w - 3]', '[2005, 2005, 5*w^3 - 12*w^2 - 17*w + 25]', '[2007, 2007, 4*w^3 - 12*w^2 - 13*w + 27]', '[2011, 2011, 3*w^3 - 6*w^2 - 11*w - 2]', '[2012, 1006, 8*w^3 - 13*w^2 - 35*w + 3]', '[2012, 1006, 9*w^3 - 22*w^2 - 30*w + 39]', '[2013, 2013, w^3 - 2*w^2 + w - 3]', '[2019, 2019, 3*w^3 - 7*w^2 - 9*w + 19]', '[2020, 1010, w^3 - 7*w^2 + 5*w + 20]', '[2020, 1010, w^3 - 10*w - 5]', '[2023, 119, -5*w^3 + 16*w^2 + 8*w - 26]', '[2023, 119, -4*w^3 + 9*w^2 + 19*w - 28]', '[2025, 75, 3*w^3 - 9*w^2 - 3*w + 15]', '[2025, 2025, 2*w^3 - 9*w^2 + 25]', '[2028, 78, -w^3 + 2*w^2 + 2*w - 9]', '[2028, 78, w^3 - w^2 - 7*w - 8]', '[2031, 2031, w^3 - 6*w + 2]', '[2035, 2035, -7*w^3 + 17*w^2 + 20*w - 35]', '[2035, 2035, -2*w^3 + w^2 + 10*w + 10]', '[2036, 1018, 5*w^3 - 16*w^2 - 12*w + 43]', '[2039, 2039, 4*w^3 - w^2 - 28*w - 22]', '[2043, 2043, 2*w^3 - 8*w^2 - 4*w + 13]', '[2044, 1022, -w^3 + w^2 + 5*w + 8]', '[2045, 2045, 3*w^3 - 6*w^2 - 8*w + 10]', '[2045, 2045, 3*w^2 - 2*w]', '[2047, 2047, 2*w^3 - 10*w^2 + 5*w + 13]', '[2047, 2047, w^3 - 3*w - 6]', '[2047, 2047, -2*w^3 + 5*w^2 - 1]', '[2047, 2047, -w^3 + 6*w^2 + w - 13]', '[2051, 2051, -w^2 - 2*w + 8]', '[2060, 1030, 5*w^3 - 4*w^2 - 30*w - 15]', '[2061, 2061, -6*w^3 + 17*w^2 + 15*w - 32]', '[2063, 2063, 3*w^3 - 11*w^2 - w + 17]', '[2064, 258, 2*w^3 - 8*w^2 + 2*w + 4]', '[2069, 2069, -w^3 + 2*w^2 + 7*w - 6]', '[2069, 2069, -5*w^3 + 17*w^2 + 8*w - 42]', '[2073, 2073, w^3 + w^2 - 2*w - 6]', '[2075, 2075, -2*w^3 + 5*w^2 + 2*w - 10]', '[2076, 1038, w^3 + w^2 - 11*w - 12]', '[2079, 231, -2*w^3 + 5*w^2 + 9*w - 8]', '[2079, 2079, -3*w^3 + 7*w^2 + 7*w - 11]', '[2084, 1042, w^3 - w^2 - w - 4]', '[2085, 2085, w^3 - 6*w^2 + w + 10]', '[2085, 2085, -w^3 + 2*w^2 - 10]', '[2087, 2087, w^3 - 2*w^2 - 4]', '[2087, 2087, -2*w^3 + 5*w^2 + 8*w - 4]', '[2089, 2089, -3*w^3 + 9*w^2 + 4*w - 17]', '[2092, 1046, 4*w^3 - 11*w^2 - 11*w + 19]', '[2092, 1046, 6*w^3 - 9*w^2 - 27*w + 1]', '[2095, 2095, 2*w^3 - w^2 - 8*w]', '[2097, 2097, -5*w^3 + 12*w^2 + 15*w - 22]', '[2097, 2097, -14*w^3 + 41*w^2 + 37*w - 94]', '[2100, 1050, 3*w^3 - 7*w^2 - 5*w]', '[2101, 2101, -4*w^3 + 7*w^2 + 14*w + 2]', '[2103, 2103, 3*w^3 - 7*w^2 - 3*w + 7]', '[2107, 2107, 4*w^3 - 14*w^2 - w + 12]', '[2111, 2111, w^3 - 3*w^2 - 6*w + 6]', '[2111, 2111, w^3 - 3*w^2 - 6*w + 7]', '[2112, 132, 2*w^3 - 12*w - 14]', '[2116, 46, 5*w^3 - 11*w^2 - 17*w + 16]', '[2116, 46, 6*w^3 - 13*w^2 - 21*w + 17]', '[2116, 1058, -2*w^3 + 5*w^2 + 7*w - 3]', '[2116, 1058, -2*w^3 + 7*w^2 + 5*w - 11]', '[2121, 2121, 4*w^3 - 6*w^2 - 17*w - 2]', '[2121, 2121, -2*w^3 + 3*w^2 + 12*w + 8]', '[2127, 2127, -2*w^3 + 8*w^2 + 5*w - 14]', '[2127, 2127, -w^3 + 4*w^2 + 5*w - 2]', '[2135, 2135, -3*w^3 + 8*w^2 + w - 10]', '[2139, 2139, w^2 + w + 4]', '[2139, 2139, -2*w^3 + 9*w^2 - w - 12]', '[2139, 2139, -w^3 + 6*w^2 + w - 6]', '[2139, 2139, 3*w^3 - 5*w^2 - 11*w + 1]', '[2140, 1070, -w^3 + 5*w^2 - 5*w - 10]', '[2141, 2141, w^3 - 2*w^2 - w - 8]', '[2143, 2143, -3*w^3 + 8*w^2 + 4*w - 14]', '[2149, 2149, -3*w^3 + 6*w^2 + 11*w - 1]', '[2156, 1078, 3*w^3 - 9*w^2 - 9*w + 16]', '[2157, 2157, -2*w^3 + 8*w^2 - 9*w + 3]', '[2160, 30, 2*w^3 - 8*w^2 + 20]', '[2160, 270, -4*w^2 + 6*w + 10]', '[2161, 2161, -2*w^3 + 8*w^2 + w - 14]', '[2163, 2163, -7*w^3 + 5*w^2 + 42*w + 29]', '[2164, 1082, 3*w^3 - 10*w^2 - 6*w + 29]', '[2164, 1082, 3*w^3 - 7*w^2 - 7*w + 6]', '[2165, 2165, 2*w^3 - 4*w^2 - 10*w + 5]', '[2167, 2167, 3*w^3 - 5*w^2 - 11*w + 3]', '[2167, 2167, 4*w^2 - 5*w - 9]', '[2172, 1086, w^3 - 6*w^2 + 11]', '[2172, 1086, 3*w^3 - 5*w^2 - 15*w + 2]', '[2177, 2177, w^3 - 6*w^2 + 16]', '[2177, 2177, w^3 - 2*w^2 - 8*w + 16]', '[2180, 1090, -5*w^3 + 8*w^2 + 22*w - 5]', '[2181, 2181, -2*w^3 + 6*w^2 - 3*w - 4]', '[2187, 9, -3*w^3 + 3*w^2 + 18*w + 6]', '[2187, 81, -3*w^3 + 6*w^2 + 9*w - 3]', '[2187, 2187, w^3 - 5*w^2 + 6*w + 4]', '[2188, 1094, 3*w^3 - 5*w^2 - 15*w + 6]', '[2188, 1094, 10*w^3 - 23*w^2 - 35*w + 37]', '[2195, 2195, -3*w^3 + 10*w^2 + 3*w - 20]', '[2195, 2195, -w^3 + 6*w^2 - 3*w - 15]', '[2196, 1098, 2*w^3 - 9*w^2 + 3*w + 13]', '[2203, 2203, 4*w^3 - 10*w^2 - 11*w + 12]', '[2205, 2205, w^2 + 4*w - 5]', '[2215, 2215, w^3 - 7*w^2 + 4*w + 10]', '[2220, 1110, 5*w^3 - 11*w^2 - 17*w + 20]', '[2220, 1110, -3*w^3 + 9*w^2 + 5*w - 20]', '[2221, 2221, -3*w^3 + 2*w^2 + 17*w + 16]', '[2221, 2221, -2*w^3 + 8*w^2 + 2*w - 19]', '[2224, 278, -2*w^3 + 4*w^2 + 2*w - 8]', '[2224, 278, -4*w^2 + 6*w + 14]', '[2225, 2225, -3*w^3 + 11*w^2 + 3*w - 15]', '[2225, 2225, 2*w^3 - 7*w^2 + 4*w + 5]', '[2228, 1114, w^3 - 8*w^2 + 6*w + 29]', '[2228, 1114, -9*w^3 + 24*w^2 + 28*w - 53]', '[2235, 2235, -3*w^3 + 7*w^2 + 10*w - 20]', '[2235, 2235, -w^3 + 5*w^2 - 2*w - 20]', '[2237, 2237, 4*w^3 - w^2 - 25*w - 24]', '[2237, 2237, -3*w^3 + 7*w^2 + 10*w - 7]', '[2240, 140, 2*w^2 - 6*w - 10]', '[2241, 249, 4*w^3 - 4*w^2 - 24*w - 11]', '[2241, 2241, 3*w^3 - 4*w^2 - 12*w - 2]', '[2243, 2243, -w^3 + 3*w^2 + 3*w - 13]', '[2243, 2243, -4*w^2 + 5*w + 4]', '[2245, 2245, w^3 - 6*w^2 + 2*w + 10]', '[2247, 2247, -2*w^2 + 7*w + 1]', '[2252, 1126, -5*w^3 + 11*w^2 + 17*w - 12]', '[2252, 1126, w^3 - 6*w^2 + 2*w + 17]', '[2253, 2253, w^3 - 5*w^2 - 4*w + 14]', '[2257, 2257, -w^2 - 4]', '[2257, 2257, 5*w^3 - 4*w^2 - 30*w - 14]', '[2260, 1130, 5*w^3 - 9*w^2 - 19*w + 10]', '[2263, 2263, -2*w^3 + 8*w^2 + w - 17]', '[2263, 2263, 5*w^3 - 16*w^2 - 3*w + 12]', '[2267, 2267, -w^3 + 5*w^2 - 6*w - 6]', '[2267, 2267, -w^3 - 4*w^2 + 13*w + 23]', '[2268, 42, 3*w^3 - 6*w^2 - 12*w + 3]', '[2268, 1134, w^3 - 8*w + 1]', '[2271, 2271, 4*w^2 - 5*w - 2]', '[2271, 2271, -2*w^3 + 6*w^2 + 5*w - 6]', '[2271, 2271, 3*w^2 - 2*w - 13]', '[2271, 2271, 3*w^3 - 8*w^2 - 5*w + 16]', '[2273, 2273, -w^3 + 7*w - 1]', '[2276, 1138, -4*w^3 + 11*w^2 + 7*w - 13]', '[2277, 2277, -2*w^2 + 7*w + 4]', '[2277, 2277, 3*w^3 - 5*w^2 - 14*w + 7]', '[2281, 2281, w^3 + w^2 - 4*w - 8]', '[2281, 2281, 3*w^3 - 3*w^2 - 16*w - 3]', '[2283, 2283, w^3 - w^2 - w + 7]', '[2284, 1142, -5*w^3 + 12*w^2 + 18*w - 27]', '[2285, 2285, w^3 - 2*w^2 - 4*w + 10]', '[2287, 2287, 4*w^3 - 8*w^2 - 17*w + 11]', '[2287, 2287, -2*w^3 + 3*w^2 + 8*w - 7]', '[2289, 2289, 3*w^3 + w^2 - 20*w - 23]', '[2292, 1146, 2*w^3 - 5*w^2 - 7*w + 1]', '[2293, 2293, -2*w^3 + 4*w^2 + 10*w - 7]', '[2293, 2293, 3*w^3 - 6*w^2 - 6*w + 2]', '[2297, 2297, -4*w^3 + 13*w^2 + 7*w - 32]', '[2297, 2297, 5*w^3 - 12*w^2 - 15*w + 18]', '[2300, 1150, -w^3 + 2*w^2 + 4*w + 5]', '[2300, 1150, -3*w^3 + 12*w^2 - 2*w - 15]', '[2304, 36, 4*w^3 - 12*w^2 - 8*w + 28]', '[2305, 2305, w^3 + 4*w^2 - 9*w - 10]', '[2307, 2307, 2*w^3 - 11*w - 12]', '[2307, 2307, -w^3 + 6*w^2 - 6*w - 2]', '[2308, 1154, -4*w^3 + 9*w^2 + 15*w - 19]', '[2313, 2313, -4*w^3 + 9*w^2 + 16*w - 18]', '[2315, 2315, 3*w^2 - w]', '[2315, 2315, 5*w^3 - 10*w^2 - 21*w + 15]', '[2319, 2319, 4*w^3 - 13*w^2 - 4*w + 16]', '[2321, 2321, 3*w^3 - 9*w^2 + 4]', '[2321, 2321, -6*w^3 + 7*w^2 + 32*w + 8]', '[2323, 2323, 2*w^3 - 3*w^2 - 10*w + 6]', '[2323, 2323, w^3 - 2*w^2 + 2*w + 6]', '[2323, 2323, -5*w^3 + 15*w^2 + 4*w - 13]', '[2323, 2323, 3*w^3 - 11*w^2 - w + 7]', '[2324, 1162, -3*w^3 + 5*w^2 + 15*w + 2]', '[2325, 2325, -w^3 + 10*w]', '[2325, 2325, 3*w^3 - 11*w^2 + 2*w + 15]', '[2331, 2331, -2*w^3 + 6*w^2 + 7*w - 8]', '[2331, 2331, -5*w^2 + 4*w + 19]', '[2333, 2333, 2*w^3 - 7*w^2 - w + 16]', '[2333, 2333, -2*w^3 + 10*w^2 - 2*w - 29]', '[2339, 2339, -2*w^3 + 6*w^2 + 2*w - 17]', '[2339, 2339, 2*w^3 - 2*w^2 - 8*w + 3]', '[2347, 2347, 2*w^3 - 6*w^2 - 8*w + 19]', '[2347, 2347, 5*w^3 - 3*w^2 - 32*w - 19]', '[2348, 1174, 5*w^3 - 8*w^2 - 22*w - 1]', '[2348, 1174, -2*w^3 + 7*w^2 + 3*w - 7]', '[2351, 2351, -5*w^3 + w^2 + 33*w + 27]', '[2351, 2351, w^3 - 2*w^2 - 7*w + 3]', '[2352, 294, -2*w^3 + 4*w^2 + 10*w - 6]', '[2355, 2355, -3*w^3 + 9*w^2 + 7*w - 25]', '[2355, 2355, w^3 - 2*w^2 - 7*w + 5]', '[2357, 2357, 2*w^3 - 5*w^2 - 7*w + 2]', '[2357, 2357, 4*w^3 - 5*w^2 - 18*w - 6]', '[2359, 2359, 3*w^3 - 11*w^2 - 2*w + 17]', '[2359, 2359, w^3 - 6*w^2 + 6*w + 4]', '[2361, 2361, 6*w^3 - 19*w^2 - 4*w + 23]', '[2361, 2361, 3*w^2 - 7*w - 2]', '[2361, 2361, -w^3 + 4*w^2 + w - 16]', '[2361, 2361, -2*w^3 + 8*w^2 + 3*w - 18]', '[2364, 1182, w^3 - w^2 - 5*w + 8]', '[2364, 1182, -w^3 + 5*w^2 + 5*w - 6]', '[2365, 2365, -w^3 - 3*w^2 + 15*w + 15]', '[2367, 2367, -5*w^3 + 16*w^2 + 11*w - 37]', '[2367, 2367, -2*w^3 + 7*w^2 - 4*w + 2]', '[2368, 148, 4*w^3 - 10*w^2 - 10*w + 18]', '[2368, 148, -2*w^3 + 10*w^2 - 2*w - 32]', '[2369, 2369, -w^3 - w^2 + 11*w + 13]', '[2369, 2369, 3*w^3 - 6*w^2 - 10*w - 4]', '[2373, 2373, -2*w^3 - 3*w^2 + 14*w + 21]', '[2377, 2377, -4*w^3 + 12*w^2 + 7*w - 17]', '[2377, 2377, w^2 - 6*w + 3]', '[2381, 2381, 2*w^3 - 8*w^2 - 3*w + 28]', '[2381, 2381, w^3 + w^2 - 3*w - 7]', '[2384, 298, -2*w^3 + 6*w^2 + 2*w - 14]', '[2384, 298, -4*w^3 + 12*w^2 + 10*w - 32]', '[2387, 2387, -w^3 + 5*w^2 - 2*w - 1]', '[2387, 2387, -2*w^3 + 2*w^2 + 13*w + 3]', '[2389, 2389, w^3 - 3*w^2 + 3*w + 7]', '[2391, 2391, 4*w^3 - 12*w^2 - 14*w + 31]', '[2391, 2391, 2*w^3 - 3*w^2 - 8*w + 9]', '[2393, 2393, w^3 - 7*w^2 + 5*w + 23]', '[2393, 2393, -2*w + 9]', '[2395, 2395, 3*w^3 - 4*w^2 - 5*w + 5]', '[2399, 2399, 5*w^3 - 9*w^2 - 20*w + 7]', '[2401, 7, 7]', '[2401, 2401, -3*w^2 + 7*w + 12]', '[2403, 267, -2*w^3 - w^2 + 18*w + 16]', '[2403, 267, -w^3 + w^2 + 6*w + 8]', '[2403, 2403, w^3 - 6*w^2 + 3*w + 11]', '[2403, 2403, -3*w^3 + 6*w^2 + 7*w + 2]', '[2409, 2409, -w^3 + 4*w^2 - 2*w + 2]', '[2411, 2411, 3*w^2 - 6*w - 2]', '[2415, 2415, 3*w^3 - 8*w^2 - 8*w + 10]', '[2415, 2415, -3*w^3 + 7*w^2 + 4*w - 5]', '[2417, 2417, 6*w^3 - 12*w^2 - 25*w + 18]', '[2417, 2417, -5*w^3 + 14*w^2 + 10*w - 24]', '[2420, 1210, 2*w^3 - 9*w^2 + 3*w + 15]', '[2429, 2429, -2*w^3 + 6*w^2 - w + 1]', '[2435, 2435, 2*w^3 - 8*w^2 - w + 15]', '[2437, 2437, -3*w^3 + 6*w^2 + 9*w - 8]', '[2443, 2443, 5*w^3 - 18*w^2 + 18]', '[2445, 2445, 3*w^3 - 10*w^2 - 5*w + 15]', '[2445, 2445, -w^3 + 7*w^2 - 2*w - 25]', '[2452, 1226, 3*w^3 - 9*w^2 - 7*w + 14]', '[2453, 2453, -w^3 + 2*w^2 + 7*w - 4]', '[2461, 2461, -5*w^3 + 12*w^2 + 10*w - 4]', '[2461, 2461, 2*w^3 - 3*w^2 - 9*w + 6]', '[2463, 2463, w^3 - w^2 - 9*w - 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17*w - 50]', '[5295, 5295, -4*w^3 + 14*w^2 + 10*w - 35]', '[5299, 5299, -w^3 + 5*w^2 - 3*w + 1]', '[5299, 5299, -4*w^3 + 7*w^2 + 19*w - 6]', '[5299, 5299, 5*w^3 - 13*w^2 - 12*w + 22]', '[5299, 5299, -w^3 + 7*w^2 - 5*w - 17]', '[5303, 5303, -w^3 - 4*w^2 + 13*w + 21]', '[5308, 2654, 6*w^3 - 15*w^2 - 21*w + 31]', '[5309, 5309, 5*w^3 - 12*w^2 - 14*w + 16]', '[5312, 332, 6*w^3 - 10*w^2 - 26*w + 8]', '[5313, 5313, 4*w^3 - 14*w^2 - 8*w + 33]', '[5313, 5313, -2*w^3 + 4*w^2 + w - 9]', '[5316, 2658, -w^2 + 7*w + 3]', '[5319, 591, -4*w^3 + 10*w^2 + 9*w - 13]', '[5319, 591, -2*w^3 - w^2 + 12*w + 16]', '[5319, 5319, -6*w^3 + 13*w^2 + 20*w - 24]', '[5319, 5319, w^3 - 4*w^2 + 3*w + 12]', '[5323, 5323, -3*w^3 + 4*w^2 + 13*w + 11]', '[5323, 5323, 4*w^3 - 15*w^2 - 6*w + 24]', '[5324, 22, 6*w^3 - 15*w^2 - 17*w + 27]', '[5324, 2662, 4*w^3 - 11*w^2 - 11*w + 17]', '[5327, 5327, 3*w^3 - 4*w^2 - 13*w + 4]', '[5328, 666, -4*w^3 + 8*w^2 + 12*w - 22]', '[5328, 666, 6*w^3 - 14*w^2 - 20*w + 28]', '[5329, 5329, w^3 + 4*w^2 - 9*w - 21]', '[5331, 5331, w^3 - 2*w^2 + w - 6]', '[5331, 5331, 4*w^3 - 11*w^2 - 4*w + 17]', '[5332, 2666, -2*w^3 + 7*w^2 - 5*w - 7]', '[5332, 2666, -w^3 + 5*w^2 - 5*w - 12]', '[5340, 2670, 2*w^3 - 9*w^2 + w + 15]', '[5340, 2670, w^3 - 4*w^2 - 6*w + 15]', '[5341, 5341, -2*w^3 + 7*w^2 + 5*w - 8]', '[5345, 5345, 3*w^3 - w^2 - 7*w - 5]', '[5345, 5345, -4*w^3 + 8*w^2 + 13*w - 10]', '[5347, 5347, 6*w^3 - 10*w^2 - 26*w + 1]', '[5348, 2674, -w^3 - 4*w^2 + 14*w + 17]', '[5351, 5351, -2*w^3 + 7*w^2 - 16]', '[5357, 5357, 5*w^3 - 15*w^2 - 14*w + 29]', '[5359, 5359, -9*w^3 + 25*w^2 + 28*w - 51]', '[5359, 5359, 4*w^3 - 11*w^2 - 12*w + 18]', '[5359, 5359, -2*w^3 + 6*w^2 + w - 18]', '[5359, 5359, -w^3 + 3*w^2 + 2*w + 4]', '[5361, 5361, w^3 - 4*w^2 - 8*w + 14]', '[5363, 5363, 3*w^3 - 4*w^2 - 17*w + 1]', '[5363, 5363, 6*w^3 - 13*w^2 - 14*w - 1]', '[5364, 2682, 4*w^3 - 11*w^2 - 9*w + 13]', '[5364, 2682, 8*w^3 - 21*w^2 - 21*w + 43]', '[5375, 215, -w^3 + 7*w^2 - 14]', '[5375, 5375, -4*w^3 + 13*w^2 - 2*w - 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14]', '[9907, 9907, -5*w^3 + 10*w^2 + 18*w - 18]', '[9907, 9907, w^3 - 5*w^2 - 2*w + 26]', '[9907, 9907, 3*w^3 - 6*w^2 - 4*w + 14]', '[9909, 1101, 8*w^3 - 8*w^2 - 45*w - 28]', '[9909, 1101, 8*w^3 - 8*w^2 - 45*w - 16]', '[9909, 9909, 6*w^3 - 11*w^2 - 22*w + 3]', '[9909, 9909, 2*w^3 + 5*w^2 - 22*w - 21]', '[9915, 9915, -6*w^3 + 10*w^2 + 29*w]', '[9915, 9915, -w^3 + 3*w^2 + w - 15]', '[9920, 620, -6*w^3 + 16*w^2 + 8*w - 10]', '[9920, 620, 2*w^3 - 4*w^2 + 10]', '[9923, 9923, -w^3 + 3*w^2 + 4*w - 17]', '[9923, 9923, -6*w^3 + 13*w^2 + 22*w - 24]', '[9924, 4962, 3*w^2 + w - 13]', '[9924, 4962, -w^3 + 2*w - 7]', '[9924, 4962, 4*w^3 - 7*w^2 - 17*w + 11]', '[9924, 4962, 5*w^3 - 10*w^2 - 20*w + 7]', '[9925, 9925, -w^3 + 6*w^2 - 7*w - 15]', '[9925, 9925, -6*w^3 + 17*w^2 + 10*w - 25]', '[9927, 9927, -16*w^3 + 42*w^2 + 48*w - 83]', '[9933, 9933, 5*w^3 - 13*w^2 - 4*w + 6]', '[9936, 138, 4*w^3 - 10*w^2 - 12*w + 28]', '[9936, 138, -4*w^3 + 16*w^2 - 6*w - 22]', '[9936, 1242, 2*w^2 - 4*w - 16]', '[9936, 1242, 2*w^3 - 10*w^2 + 8*w + 18]', '[9939, 9939, -3*w^3 + 10*w^2 + 9*w - 16]', '[9941, 9941, -5*w^3 + 17*w^2 + 7*w - 41]', '[9943, 9943, -w^3 + 3*w^2 + 8*w - 8]', '[9943, 9943, 2*w^2 + w - 14]', '[9951, 9951, 10*w^2 - 21*w - 22]', '[9951, 9951, w^3 + w^2 - 8*w - 18]', '[9955, 9955, -4*w^3 + w^2 + 24*w + 25]', '[9955, 9955, 3*w^3 - 10*w^2 - 5*w + 10]', '[9957, 9957, w^3 - w^2 + w - 7]', '[9959, 9959, -9*w^3 + 21*w^2 + 29*w - 37]', '[9959, 9959, 3*w^3 - 4*w^2 - 16*w + 6]', '[9961, 9961, 3*w^3 - 5*w^2 - 16*w + 14]', '[9965, 9965, 3*w^3 - 11*w^2 - 2*w + 30]', '[9965, 9965, 2*w^3 - 8*w^2 + w + 25]', '[9967, 9967, 5*w^3 - 21*w^2 - 4*w + 67]', '[9967, 9967, 4*w^3 - 7*w^2 - 13*w + 2]', '[9968, 1246, 6*w^3 - 18*w^2 - 4*w + 18]', '[9968, 1246, 4*w^2 - 10*w + 4]', '[9973, 9973, 3*w^2 - w - 16]', '[9987, 9987, -2*w^3 + 10*w^2 - 5*w - 24]', '[9987, 9987, -2*w^3 + 10*w + 1]', '[9987, 9987, w^3 - 2*w^2 - 17*w + 24]', '[9987, 9987, -4*w^3 + 19*w^2 + 2*w - 26]', '[9988, 4994, 3*w^3 - 5*w^2 - 7*w + 16]', '[9993, 9993, 3*w^3 - 5*w^2 - 12*w + 14]', '[9995, 9995, w^3 - 11*w^2 + 3*w + 15]', '[9995, 9995, -2*w^3 + 4*w^2 + 5*w - 15]', '[9999, 9999, -3*w^3 + 2*w^2 + 18*w + 4]', '[9999, 9999, -4*w^3 + 17*w^2 - 46]', '[10000, 10, 10]', '[10000, 1250, -2*w^3 + 16*w + 20]'], 'label': '4.4.18736.1', 'narrow_class_no': 2, 'primes': ['[3, 3, w - 1]', '[4, 2, -w^3 + 2*w^2 + 4*w - 3]', '[5, 5, w]', '[7, 7, w - 2]', '[11, 11, w^2 - 2*w - 4]', '[23, 23, -w^2 + 2*w + 1]', '[23, 23, w^3 - 2*w^2 - 3*w + 3]', '[27, 3, -w^3 + w^2 + 6*w + 2]', '[31, 31, -w^3 + 3*w^2 + w - 1]', '[31, 31, -w^3 + 2*w^2 + 4*w - 4]', '[37, 37, w^2 - 2*w - 6]', '[37, 37, w^3 - 2*w^2 - 3*w + 2]', '[43, 43, w^2 - 3*w - 2]', '[61, 61, -w^3 + 2*w^2 + 2*w - 2]', '[73, 73, w^3 - 3*w^2 - 2*w + 3]', '[83, 83, -w - 3]', '[89, 89, -w^3 + 3*w^2 + 2*w - 2]', '[89, 89, 2*w - 1]', '[101, 101, w^3 - 4*w^2 + w + 7]', '[101, 101, 2*w^2 - 3*w - 3]', '[103, 103, w^3 - 7*w - 4]', '[107, 107, 3*w^3 - 2*w^2 - 17*w - 12]', '[109, 109, -w^3 + 2*w^2 + 5*w - 2]', '[113, 113, w^3 - 3*w^2 - 4*w + 4]', '[125, 5, w^3 - 2*w^2 - 5*w + 4]', '[139, 139, -w^3 + 2*w^2 + w - 4]', '[139, 139, -2*w^2 + 3*w + 7]', '[149, 149, -w^3 + 3*w^2 + w - 7]', '[149, 149, -2*w^3 + 6*w^2 + 5*w - 16]', '[157, 157, -2*w^3 + 6*w^2 + 3*w - 11]', '[157, 157, 2*w^3 - 3*w^2 - 10*w + 1]', '[163, 163, -w^3 + 4*w^2 + w - 9]', '[163, 163, 2*w^3 - 5*w^2 - 6*w + 7]', '[167, 167, -w^3 + 4*w^2 - 2*w - 6]', '[169, 13, -w^3 + 4*w^2 + w - 8]', '[169, 13, 2*w^2 - 3*w - 6]', '[173, 173, w^3 - w^2 - 4*w - 4]', '[181, 181, 2*w^3 - 4*w^2 - 7*w + 4]', '[181, 181, w^2 - 2*w + 2]', '[191, 191, 2*w^2 - 4*w - 3]', '[197, 197, w^3 - 5*w^2 + 17]', '[197, 197, -w^3 + w^2 + 4*w - 2]', '[211, 211, 2*w^3 - 4*w^2 - 8*w + 3]', '[211, 211, -w^3 + 6*w + 8]', '[223, 223, w^3 - 4*w^2 - 2*w + 6]', '[227, 227, 2*w^3 - 3*w^2 - 10*w - 2]', '[229, 229, -w^3 + 3*w^2 + 3*w - 1]', '[233, 233, -w^3 + w^2 + 5*w - 1]', '[233, 233, -2*w^3 + 7*w^2 + 4*w - 17]', '[257, 257, 2*w^3 - 5*w^2 - 5*w + 4]', '[263, 263, w^2 - 6]', '[263, 263, 3*w^3 - 9*w^2 - 8*w + 24]', '[281, 281, 3*w^3 - 4*w^2 - 14*w - 2]', '[281, 281, 2*w^3 - 3*w^2 - 8*w + 1]', '[289, 17, 2*w^3 - 4*w^2 - 9*w + 9]', '[289, 17, -2*w^3 + 5*w^2 + 4*w - 8]', '[293, 293, -w - 4]', '[307, 307, 3*w^3 - 3*w^2 - 15*w - 7]', '[311, 311, w^2 - 8]', '[311, 311, -w^3 + 5*w^2 - 2*w - 7]', '[337, 337, w^2 - 4*w - 2]', '[337, 337, -w^3 + 3*w^2 - 6]', '[343, 7, -2*w^3 + 7*w^2 + 3*w - 16]', '[347, 347, w^3 - 2*w^2 - 3*w - 3]', '[349, 349, -2*w^3 + 5*w^2 + 2*w - 4]', '[353, 353, -2*w^3 + 7*w^2 + 4*w - 14]', '[353, 353, -w^3 + 4*w^2 - 14]', '[359, 359, -w^3 + 3*w^2 - 2*w - 2]', '[367, 367, w^2 - 5*w - 4]', '[367, 367, w^2 - w - 8]', '[379, 379, 3*w^3 - 2*w^2 - 19*w - 11]', '[379, 379, -w^2 - w - 2]', '[379, 379, 3*w^3 - 21*w - 19]', '[379, 379, -2*w^3 + 3*w^2 + 10*w + 3]', '[383, 383, 3*w^3 - 6*w^2 - 11*w + 7]', '[383, 383, w^3 - 5*w^2 + w + 7]', '[389, 389, w^2 - 4*w - 1]', '[397, 397, -w^3 + w^2 + 6*w - 2]', '[397, 397, 2*w^3 - 2*w^2 - 11*w - 8]', '[401, 401, 3*w^2 - 4*w - 12]', '[409, 409, -2*w^3 + 7*w^2 + 4*w - 16]', '[409, 409, 3*w - 2]', '[419, 419, 2*w^2 - w - 8]', '[433, 433, -w^3 + 4*w^2 + w - 14]', '[439, 439, w^3 - w^2 - 7*w - 1]', '[439, 439, 3*w^3 - 7*w^2 - 9*w + 9]', '[443, 443, -2*w^3 + 5*w^2 + 3*w - 4]', '[449, 449, -2*w^3 + 5*w^2 + 4*w - 6]', '[457, 457, -2*w^3 + 5*w^2 + 8*w - 12]', '[461, 461, 2*w^3 - 3*w^2 - 6*w - 1]', '[463, 463, 3*w - 1]', '[463, 463, 2*w^3 + w^2 - 16*w - 18]', '[479, 479, -w^3 + 5*w^2 + w - 9]', '[487, 487, -3*w^3 + 8*w^2 + 7*w - 13]', '[503, 503, 3*w^2 - 6*w - 11]', '[503, 503, -w^3 + 5*w^2 + w - 13]', '[509, 509, -w^3 + 2*w^2 + 6*w - 6]', '[521, 521, 2*w^3 - 4*w^2 - 9*w + 6]', '[523, 523, -w^3 + 5*w^2 - 8]', '[523, 523, w^2 - 4*w - 7]', '[529, 23, -w^3 + 4*w^2 - w - 9]', '[541, 541, -w^3 + w^2 + 5*w - 3]', '[541, 541, -w^3 + 6*w^2 - 3*w - 19]', '[547, 547, w^3 - 2*w^2 - w - 2]', '[547, 547, -w^3 + 5*w^2 - 14]', '[557, 557, -2*w^3 + 4*w^2 + 6*w - 3]', '[557, 557, w^3 - 3*w^2 - 5*w + 11]', '[563, 563, w^3 - 5*w^2 + 2*w + 9]', '[563, 563, -w^3 + 4*w^2 + 2*w - 4]', '[569, 569, -2*w^3 + w^2 + 12*w + 12]', '[571, 571, -w^2 + 3*w - 4]', '[577, 577, w^2 - 2*w + 3]', '[587, 587, 3*w^2 - 5*w - 8]', '[587, 587, w^3 - 5*w^2 + w + 13]', '[613, 613, w^3 + w^2 - 7*w - 11]', '[617, 617, w^3 - 9*w - 2]', '[643, 643, 2*w^2 - 5*w - 8]', '[661, 661, -w^3 + 2*w^2 + 6*w - 2]', '[661, 661, -2*w^3 + 6*w^2 + w - 9]', '[673, 673, -2*w^3 + 5*w^2 + 8*w - 9]', '[677, 677, w^3 - 5*w - 7]', '[691, 691, 3*w^3 - 7*w^2 - 9*w + 11]', '[701, 701, 3*w^2 - 4*w - 7]', '[709, 709, -2*w^2 + 3*w + 12]', '[709, 709, -w^3 + 3*w^2 - 9]', '[719, 719, -2*w^2 + 6*w - 3]', '[727, 727, w^3 - 3*w^2 - 2*w - 1]', '[751, 751, -2*w^3 + 3*w^2 + 8*w - 4]', '[757, 757, -2*w^3 + 5*w^2 + 7*w - 6]', '[757, 757, w^3 - w^2 - 2*w - 3]', '[757, 757, -w^3 - w^2 + 10*w + 11]', '[757, 757, 6*w^3 - 14*w^2 - 20*w + 23]', '[761, 761, -4*w^3 + 10*w^2 + 13*w - 17]', '[769, 769, w^3 - 2*w^2 - w - 3]', '[769, 769, 5*w^3 - 8*w^2 - 22*w + 2]', '[773, 773, -w^3 + 5*w^2 - 3*w - 11]', '[787, 787, -2*w^3 + 8*w^2 - w - 13]', '[787, 787, 2*w^3 - 2*w^2 - 9*w - 8]', '[787, 787, 3*w^3 - 5*w^2 - 12*w + 3]', '[787, 787, 4*w^3 - 5*w^2 - 21*w - 4]', '[797, 797, 2*w^2 - w - 9]', '[797, 797, -3*w^3 + 7*w^2 + 10*w - 16]', '[821, 821, 4*w^3 - 3*w^2 - 24*w - 17]', '[821, 821, 2*w^3 - w^2 - 14*w - 6]', '[823, 823, 3*w^3 - 5*w^2 - 12*w + 1]', '[827, 827, -w^3 + 5*w^2 - 9]', '[827, 827, -2*w^3 + 6*w^2 + 2*w - 11]', '[827, 827, -2*w^3 + 7*w^2 + 6*w - 13]', '[827, 827, w^3 - w^2 - 8*w - 3]', '[853, 853, -w^3 + 2*w^2 + 3*w - 8]', '[857, 857, -w^3 - 2*w^2 + 11*w + 17]', '[857, 857, 3*w^3 - w^2 - 18*w - 16]', '[859, 859, -w^3 + w^2 + 7*w + 7]', '[859, 859, 5*w^3 - 5*w^2 - 26*w - 12]', '[859, 859, 2*w^3 - 4*w^2 - 4*w - 1]', '[859, 859, -3*w^2 + 4*w + 3]', '[863, 863, w^3 - 3*w^2 - 6*w + 3]', '[877, 877, w^3 - 2*w^2 - 3*w - 4]', '[877, 877, -w^3 + 5*w^2 - 2*w - 18]', '[883, 883, 3*w^3 - 7*w^2 - 7*w + 13]', '[883, 883, -4*w^3 + 9*w^2 + 14*w - 12]', '[919, 919, -w^3 + 4*w^2 + 3*w - 2]', '[919, 919, -w^3 + 3*w^2 + 2*w - 11]', '[929, 929, 2*w^3 - 4*w^2 - 9*w + 1]', '[937, 937, 3*w^3 - 9*w^2 - 4*w + 9]', '[953, 953, -3*w^3 + 9*w^2 + 6*w - 14]', '[961, 31, -3*w^3 + 6*w^2 + 11*w - 3]', '[967, 967, -w^3 + 5*w^2 - w - 11]', '[967, 967, 3*w^3 - 6*w^2 - 9*w + 1]', '[977, 977, 2*w^3 - 6*w^2 - 3*w + 18]', '[977, 977, 7*w^3 - 16*w^2 - 24*w + 26]', '[991, 991, 3*w^2 - 3*w - 8]', '[997, 997, 3*w^3 - 5*w^2 - 13*w - 1]', '[1009, 1009, 3*w^3 - 12*w^2 - 3*w + 34]', '[1013, 1013, -2*w^3 + 8*w^2 + w - 12]', '[1013, 1013, -2*w^3 + 3*w^2 + 6*w - 2]', '[1049, 1049, 3*w^3 - 5*w^2 - 14*w + 6]', '[1069, 1069, w^3 + w^2 - 6*w - 3]', '[1069, 1069, 2*w^3 - 8*w^2 - 2*w + 21]', '[1087, 1087, 4*w^3 - 5*w^2 - 20*w - 8]', '[1091, 1091, -2*w^3 + 8*w^2 - w - 16]', '[1103, 1103, -3*w^3 + 6*w^2 + 13*w - 9]', '[1117, 1117, 4*w^2 - 5*w - 16]', '[1117, 1117, 6*w^3 - 15*w^2 - 18*w + 26]', '[1123, 1123, -2*w^3 + 7*w^2 + 2*w - 6]', '[1123, 1123, -3*w^3 + 7*w^2 + 5*w - 11]', '[1129, 1129, -2*w^2 + 3*w - 2]', '[1129, 1129, 5*w^3 - 9*w^2 - 21*w + 9]', '[1129, 1129, 3*w^3 - 4*w^2 - 16*w - 2]', '[1129, 1129, w^3 + 2*w^2 - 10*w - 12]', '[1151, 1151, 2*w^3 + 2*w^2 - 17*w - 21]', '[1153, 1153, 6*w^3 - 11*w^2 - 24*w + 7]', '[1163, 1163, 3*w^3 - 7*w^2 - 8*w + 7]', '[1163, 1163, -3*w^3 + 10*w^2 + 7*w - 28]', '[1171, 1171, -2*w^3 + 4*w^2 + 9*w - 12]', '[1187, 1187, -3*w^3 + 10*w^2 + 4*w - 22]', '[1187, 1187, 5*w^3 - 9*w^2 - 22*w + 9]', '[1193, 1193, 3*w^3 - 6*w^2 - 10*w + 8]', '[1193, 1193, 3*w^2 - 3*w - 14]', '[1193, 1193, 4*w - 3]', '[1193, 1193, 3*w^3 - 10*w^2 - 7*w + 27]', '[1201, 1201, 4*w^3 - 9*w^2 - 15*w + 18]', '[1213, 1213, -w^3 + 4*w^2 - 4*w - 4]', '[1213, 1213, w^3 - 9*w + 1]', '[1217, 1217, w^3 - w^2 - w - 3]', '[1217, 1217, -3*w^3 + 20*w + 18]', '[1223, 1223, 6*w^3 - 11*w^2 - 24*w + 6]', '[1223, 1223, 3*w^2 - 6*w - 13]', '[1229, 1229, 3*w^3 - 6*w^2 - 13*w + 8]', '[1231, 1231, -w^3 + 4*w^2 - w - 12]', '[1259, 1259, -2*w^3 + 6*w^2 + 5*w - 8]', '[1259, 1259, 3*w^2 - 6*w - 4]', '[1277, 1277, -4*w^3 + 11*w^2 + 8*w - 19]', '[1279, 1279, -3*w^3 + 5*w^2 + 11*w + 1]', '[1283, 1283, -4*w^3 + 9*w^2 + 13*w - 14]', '[1291, 1291, -2*w^3 + 6*w^2 + 6*w - 9]', '[1291, 1291, -2*w^3 - 2*w^2 + 18*w + 21]', '[1297, 1297, 3*w^3 - 8*w^2 - 5*w + 8]', '[1319, 1319, -w^3 + 6*w^2 - 3*w - 9]', '[1321, 1321, -4*w^3 + 9*w^2 + 15*w - 12]', '[1327, 1327, w^2 + 2*w - 7]', '[1331, 11, -2*w^3 + 5*w^2 + 2*w - 9]', '[1367, 1367, -w^3 + 7*w^2 - 6*w - 11]', '[1367, 1367, -w^3 + w^2 + 8*w - 3]', '[1369, 37, -2*w^3 + 6*w^2 + 7*w - 9]', '[1373, 1373, -2*w^3 + 6*w^2 + 2*w - 1]', '[1409, 1409, 5*w^3 - 16*w^2 - 11*w + 38]', '[1423, 1423, -2*w^3 + 3*w^2 + 11*w - 2]', '[1433, 1433, -2*w^3 + w^2 + 9*w + 2]', '[1439, 1439, w^3 - 3*w^2 - 6*w + 4]', '[1439, 1439, -3*w^3 + 6*w^2 + 12*w - 4]', '[1447, 1447, 4*w^3 - 13*w^2 - 7*w + 24]', '[1453, 1453, -w^3 + 5*w^2 - 2*w - 16]', '[1459, 1459, 3*w^3 - 7*w^2 - 4*w + 4]', '[1471, 1471, -w^3 + 4*w^2 - 3*w - 8]', '[1487, 1487, -2*w^2 + w + 14]', '[1489, 1489, -3*w^3 + 7*w^2 + 5*w - 13]', '[1489, 1489, -4*w^2 + 6*w + 21]', '[1493, 1493, -2*w^3 + 7*w^2 + 2*w - 3]', '[1499, 1499, 6*w^3 - 14*w^2 - 20*w + 21]', '[1531, 1531, 3*w^3 - 7*w^2 - 8*w + 8]', '[1531, 1531, 2*w^2 + w - 8]', '[1531, 1531, -3*w^3 + 7*w^2 + 8*w - 11]', '[1531, 1531, 2*w^3 - 3*w^2 - 6*w - 4]', '[1553, 1553, -w^3 + 6*w^2 - 4*w - 12]', '[1567, 1567, 4*w^3 - 5*w^2 - 20*w - 2]', '[1571, 1571, 4*w^3 - 8*w^2 - 13*w + 13]', '[1571, 1571, 5*w^3 - 5*w^2 - 25*w - 9]', '[1579, 1579, -2*w^3 + 6*w^2 - 9]', '[1579, 1579, -3*w^3 + 8*w^2 + 5*w - 9]', '[1583, 1583, 4*w^2 - 4*w - 17]', '[1597, 1597, 3*w^3 - 6*w^2 - 9*w + 2]', '[1601, 1601, 2*w^2 - w - 11]', '[1609, 1609, 4*w^3 - 5*w^2 - 18*w - 7]', '[1613, 1613, -w^3 + 6*w^2 - 3*w - 16]', '[1613, 1613, -2*w^3 + 8*w^2 - 13]', '[1619, 1619, w^3 - 2*w^2 - 7*w + 1]', '[1621, 1621, -w^3 + w^2 + 2*w + 12]', '[1621, 1621, 6*w^3 - 11*w^2 - 25*w + 8]', '[1637, 1637, 3*w^3 - 5*w^2 - 14*w - 1]', '[1681, 41, -2*w^3 + 5*w^2 + 9*w - 4]', '[1681, 41, w^3 - 4*w^2 + 5*w + 6]', '[1693, 1693, 3*w^3 - 3*w^2 - 14*w - 2]', '[1697, 1697, 2*w^3 + w^2 - 16*w - 21]', '[1697, 1697, w^3 + w^2 - 8*w - 4]', '[1721, 1721, -3*w^3 + 9*w^2 + 6*w - 13]', '[1723, 1723, 2*w^3 - 2*w^2 - 12*w + 1]', '[1723, 1723, 5*w^2 - 7*w - 26]', '[1741, 1741, -2*w^3 + 2*w^2 + 9*w - 1]', '[1753, 1753, -w^3 + 4*w^2 + 5*w - 3]', '[1753, 1753, 3*w^3 + 2*w^2 - 24*w - 28]', '[1759, 1759, -w^3 + 7*w + 11]', '[1777, 1777, 2*w^3 - w^2 - 13*w - 4]', '[1777, 1777, -2*w^3 + 6*w^2 + 5*w - 7]', '[1787, 1787, -w^3 + 2*w^2 + 3*w - 9]', '[1801, 1801, -2*w^3 + 3*w^2 + 8*w + 7]', '[1861, 1861, -2*w^3 - w^2 + 14*w + 14]', '[1867, 1867, -w^3 + w^2 + 8*w - 1]', '[1871, 1871, -w^3 + 3*w^2 + 2*w - 12]', '[1873, 1873, 3*w^3 - 8*w^2 - 9*w + 22]', '[1877, 1877, -3*w^3 + 7*w^2 + 13*w - 7]', '[1877, 1877, 3*w^3 - w^2 - 19*w - 11]', '[1877, 1877, -7*w^3 + 17*w^2 + 23*w - 29]', '[1877, 1877, 5*w^2 - 7*w - 8]', '[1879, 1879, 4*w^3 - 8*w^2 - 16*w + 7]', '[1931, 1931, -2*w^3 + 6*w^2 + 9*w - 9]', '[1933, 1933, 5*w^3 - 13*w^2 - 14*w + 21]', '[1951, 1951, -w^2 + w - 4]', '[1973, 1973, w^3 - 6*w - 12]', '[1973, 1973, 3*w^3 - 11*w^2 + 19]', '[1993, 1993, -5*w^3 + 12*w^2 + 17*w - 19]', '[1993, 1993, -6*w^3 + 15*w^2 + 19*w - 26]', '[1999, 1999, -3*w^3 + 7*w^2 + 4*w - 9]', '[1999, 1999, 3*w^3 - 8*w^2 - 11*w + 17]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [5, 4, -5, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 18736, 'disc_rad': 2342, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1], [1, 1]]], [5, [[3, 1], [1, 1]]], [7, [[3, 1], [1, 1]]], [11, [[3, 1], [1, 1]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[4, 1]]], [23, [[2, 1], [1, 2]]], [29, [[4, 1]]], [31, [[2, 1], [1, 2]]], [37, [[2, 1], [1, 2]]], [41, [[2, 2]]], [43, [[3, 1], [1, 1]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 96.78842906050289, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.18736.1', 'local_algs': ['2.4.4.4', 'm1171.1.2.0', 'm1171.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 1171], 'rd': 11.6995516606, 'regulator': {'__RealLiteral__': 0, 'data': '9.51542766482', 'prec': 44}, 'res': {'gal': ['-256204,-1427920,2841432,25154696,20387736,-72282408,-98465508,72030004,142746941,-27312368,-99906418,-158064,38534617,3171592,-8612930,-978004,1135244,132996,-88670,-9148,4021,308,-98,-4,1'], 'sib': ['-4,0,20,0,-13,0,1', '-4,52,974,-136,-2659,1434,1352,-1162,63,138,-26,-4,1', '20164,0,-83872,0,50873,0,-12356,0,1390,0,-68,0,1', '38500,-57888,-21424,14976,5516,-192,-156,0,1', '68,-872,-47,290,-64,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a^{2} - 2 a - 3 \\)', '\\( a^{2} - a - 4 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}