Hilbert modular form data - 4.4.19225.1-16.1-g

Formats: - HTML - YAML - JSON - 2024-06-04T00:22:09.780186

• 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': 7, 'disc': 19225, 'field_bad_primes': [5, 769], 'field_label': '4.4.19225.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '4.4.19225.1-16.1-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [2], 'level_ideal': '[16, 2, 2]', 'level_label': '16.1', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.1-g', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4, 2, w + 2]', 1], ['[4, 2, -1/2*w^3 + 3/2*w^2 + 9/2*w - 10]', 1]], 'hecke_eigenvalues': [-1, -1, 'e', 'e', '1/135*e^6 - 1/9*e^5 - 8/45*e^4 + 167/45*e^3 - 7/9*e^2 - 172/15*e - 122/27', '1/135*e^6 - 1/9*e^5 - 8/45*e^4 + 167/45*e^3 - 7/9*e^2 - 172/15*e - 122/27', '-2/135*e^6 + 1/45*e^5 + 22/45*e^4 - 22/45*e^3 - 47/45*e^2 - 4*e - 8/27', '4/135*e^6 - 7/45*e^5 - 13/15*e^4 + 26/5*e^3 - 7/15*e^2 - 154/9*e - 80/27', '4/135*e^6 - 7/45*e^5 - 13/15*e^4 + 26/5*e^3 - 7/15*e^2 - 154/9*e - 80/27', '-2/135*e^6 + 1/5*e^5 + 4/9*e^4 - 311/45*e^3 - 43/45*e^2 + 1199/45*e + 358/27', '4/135*e^6 - 4/45*e^5 - 17/15*e^4 + 3*e^3 + 116/15*e^2 - 521/45*e - 332/27', '4/135*e^6 - 4/45*e^5 - 17/15*e^4 + 3*e^3 + 116/15*e^2 - 521/45*e - 332/27', '-2/135*e^6 + 1/5*e^5 + 4/9*e^4 - 311/45*e^3 - 43/45*e^2 + 1199/45*e + 358/27', '1/135*e^6 - 1/15*e^5 - 16/45*e^4 + 106/45*e^3 + 206/45*e^2 - 95/9*e - 440/27', '1/135*e^6 - 1/15*e^5 - 16/45*e^4 + 106/45*e^3 + 206/45*e^2 - 95/9*e - 440/27', '-8/135*e^6 + 4/15*e^5 + 86/45*e^4 - 392/45*e^3 - 214/45*e^2 + 1214/45*e + 298/27', '-8/135*e^6 + 4/15*e^5 + 86/45*e^4 - 392/45*e^3 - 214/45*e^2 + 1214/45*e + 298/27', '1/135*e^6 + 1/9*e^5 - 2/5*e^4 - 61/15*e^3 + 14/3*e^2 + 904/45*e + 88/27', '1/135*e^6 + 1/9*e^5 - 2/5*e^4 - 61/15*e^3 + 14/3*e^2 + 904/45*e + 88/27', '1/45*e^6 - 4/45*e^5 - 38/45*e^4 + 128/45*e^3 + 253/45*e^2 - 59/9*e - 10', '1/45*e^6 - 4/45*e^5 - 38/45*e^4 + 128/45*e^3 + 253/45*e^2 - 59/9*e - 10', '8/135*e^6 - 11/45*e^5 - 2*e^4 + 41/5*e^3 + 109/15*e^2 - 1381/45*e - 412/27', '8/135*e^6 - 11/45*e^5 - 2*e^4 + 41/5*e^3 + 109/15*e^2 - 1381/45*e - 412/27', '1/15*e^6 - 4/15*e^5 - 11/5*e^4 + 133/15*e^3 + 103/15*e^2 - 30*e - 70/3', '1/15*e^6 - 4/15*e^5 - 11/5*e^4 + 133/15*e^3 + 103/15*e^2 - 30*e - 70/3', '4/135*e^6 - 7/45*e^5 - 13/15*e^4 + 26/5*e^3 - 7/15*e^2 - 172/9*e + 244/27', '-1/45*e^6 - 1/45*e^5 + 43/45*e^4 + 32/45*e^3 - 383/45*e^2 + 1/9*e + 70/9', '-1/45*e^6 - 1/45*e^5 + 43/45*e^4 + 32/45*e^3 - 383/45*e^2 + 1/9*e + 70/9', '2/135*e^6 - 2/15*e^5 - 17/45*e^4 + 197/45*e^3 - 98/45*e^2 - 97/9*e + 200/27', '-11/135*e^6 + 2/5*e^5 + 116/45*e^4 - 596/45*e^3 - 211/45*e^2 + 367/9*e + 160/27', '2/135*e^6 - 2/15*e^5 - 17/45*e^4 + 197/45*e^3 - 98/45*e^2 - 97/9*e + 200/27', '-11/135*e^6 + 2/5*e^5 + 116/45*e^4 - 596/45*e^3 - 211/45*e^2 + 367/9*e + 160/27', '-1/15*e^6 + 2/9*e^5 + 107/45*e^4 - 323/45*e^3 - 113/9*e^2 + 934/45*e + 256/9', '-1/15*e^6 + 2/9*e^5 + 107/45*e^4 - 323/45*e^3 - 113/9*e^2 + 934/45*e + 256/9', '8/135*e^6 - 14/45*e^5 - 26/15*e^4 + 151/15*e^3 - 8/5*e^2 - 233/9*e + 290/27', '8/135*e^6 - 14/45*e^5 - 26/15*e^4 + 151/15*e^3 - 8/5*e^2 - 233/9*e + 290/27', '-1/27*e^6 + 1/3*e^5 + 10/9*e^4 - 103/9*e^3 - 8/9*e^2 + 400/9*e + 490/27', '11/135*e^6 - 23/45*e^5 - 37/15*e^4 + 84/5*e^3 + 14/5*e^2 - 461/9*e - 760/27', '-1/27*e^6 + 1/3*e^5 + 10/9*e^4 - 103/9*e^3 - 8/9*e^2 + 400/9*e + 490/27', '11/135*e^6 - 23/45*e^5 - 37/15*e^4 + 84/5*e^3 + 14/5*e^2 - 461/9*e - 760/27', '-11/135*e^6 + 2/5*e^5 + 116/45*e^4 - 596/45*e^3 - 211/45*e^2 + 385/9*e + 430/27', '-11/135*e^6 + 2/5*e^5 + 116/45*e^4 - 596/45*e^3 - 211/45*e^2 + 385/9*e + 430/27', '1/135*e^6 - 1/3*e^5 + 2/45*e^4 + 502/45*e^3 - 62/9*e^2 - 1471/45*e - 152/27', '1/135*e^6 - 1/3*e^5 + 2/45*e^4 + 502/45*e^3 - 62/9*e^2 - 1471/45*e - 152/27', '2/45*e^6 - 4/9*e^5 - 58/45*e^4 + 697/45*e^3 - 2/9*e^2 - 2891/45*e - 58/3', '-8/135*e^6 + 14/45*e^5 + 31/15*e^4 - 161/15*e^3 - 52/5*e^2 + 428/9*e + 754/27', '-8/135*e^6 + 14/45*e^5 + 31/15*e^4 - 161/15*e^3 - 52/5*e^2 + 428/9*e + 754/27', '2/45*e^6 - 4/9*e^5 - 58/45*e^4 + 697/45*e^3 - 2/9*e^2 - 2891/45*e - 58/3', '4/27*e^6 - 2/3*e^5 - 43/9*e^4 + 199/9*e^3 + 104/9*e^2 - 655/9*e - 1006/27', '4/27*e^6 - 2/3*e^5 - 43/9*e^4 + 199/9*e^3 + 104/9*e^2 - 655/9*e - 1006/27', '11/135*e^6 - 5/9*e^5 - 133/45*e^4 + 862/45*e^3 + 169/9*e^2 - 1157/15*e - 1432/27', '11/135*e^6 - 5/9*e^5 - 133/45*e^4 + 862/45*e^3 + 169/9*e^2 - 1157/15*e - 1432/27', '4/135*e^6 - 2/45*e^5 - 44/45*e^4 + 44/45*e^3 + 94/45*e^2 + 9*e + 340/27', '4/135*e^6 - 2/45*e^5 - 44/45*e^4 + 44/45*e^3 + 94/45*e^2 + 9*e + 340/27', '1/135*e^6 + 2/9*e^5 - 8/45*e^4 - 358/45*e^3 - 25/9*e^2 + 523/15*e + 688/27', '1/27*e^6 - 22/45*e^5 - 22/45*e^4 + 736/45*e^3 - 811/45*e^2 - 259/5*e + 398/27', '1/135*e^6 + 2/9*e^5 - 8/45*e^4 - 358/45*e^3 - 25/9*e^2 + 523/15*e + 688/27', '1/27*e^6 - 22/45*e^5 - 22/45*e^4 + 736/45*e^3 - 811/45*e^2 - 259/5*e + 398/27', '11/135*e^6 - 4/9*e^5 - 12/5*e^4 + 214/15*e^3 - 4/3*e^2 - 1681/45*e + 338/27', '11/135*e^6 - 4/9*e^5 - 12/5*e^4 + 214/15*e^3 - 4/3*e^2 - 1681/45*e + 338/27', '13/135*e^6 - 14/45*e^5 - 143/45*e^4 + 443/45*e^3 + 403/45*e^2 - 24*e - 20/27', '13/135*e^6 - 14/45*e^5 - 143/45*e^4 + 443/45*e^3 + 403/45*e^2 - 24*e - 20/27', '-1/135*e^6 + 1/45*e^5 + 8/15*e^4 - 1/3*e^3 - 48/5*e^2 - 496/45*e + 938/27', '17/135*e^6 - 2/5*e^5 - 179/45*e^4 + 563/45*e^3 + 241/45*e^2 - 1226/45*e + 728/27', '-2/27*e^6 + 5/9*e^5 + 7/3*e^4 - 19*e^3 - 5*e^2 + 649/9*e + 1010/27', '-2/27*e^6 + 5/9*e^5 + 7/3*e^4 - 19*e^3 - 5*e^2 + 649/9*e + 1010/27', '-1/45*e^6 + 14/45*e^5 + 28/45*e^4 - 478/45*e^3 - 53/45*e^2 + 370/9*e + 268/9', '-1/45*e^6 + 14/45*e^5 + 28/45*e^4 - 478/45*e^3 - 53/45*e^2 + 370/9*e + 268/9', '-7/135*e^6 + 1/45*e^5 + 8/5*e^4 + 1/15*e^3 - 4/15*e^2 - 119/9*e - 400/27', '1/27*e^6 - 1/9*e^5 - 4/3*e^4 + 11/3*e^3 + 19/3*e^2 - 134/9*e - 10/27', '-7/135*e^6 + 1/45*e^5 + 8/5*e^4 + 1/15*e^3 - 4/15*e^2 - 119/9*e - 400/27', '1/27*e^6 - 1/9*e^5 - 4/3*e^4 + 11/3*e^3 + 19/3*e^2 - 134/9*e - 10/27', '7/135*e^6 - 11/45*e^5 - 77/45*e^4 + 377/45*e^3 + 262/45*e^2 - 38*e - 530/27', '7/135*e^6 - 11/45*e^5 - 77/45*e^4 + 377/45*e^3 + 262/45*e^2 - 38*e - 530/27', '7/135*e^6 - 1/45*e^5 - 29/15*e^4 + 4/15*e^3 + 58/5*e^2 + 17/9*e - 356/27', '7/135*e^6 - 1/45*e^5 - 29/15*e^4 + 4/15*e^3 + 58/5*e^2 + 17/9*e - 356/27', '-1/45*e^6 + 14/45*e^5 + 28/45*e^4 - 478/45*e^3 + 37/45*e^2 + 325/9*e - 20/9', '-1/45*e^6 + 14/45*e^5 + 28/45*e^4 - 478/45*e^3 + 37/45*e^2 + 325/9*e - 20/9', '-1/15*e^6 + 1/9*e^5 + 112/45*e^4 - 163/45*e^3 - 130/9*e^2 + 554/45*e + 236/9', '8/135*e^6 + 4/45*e^5 - 7/3*e^4 - 19/5*e^3 + 244/15*e^2 + 1079/45*e + 218/27', '8/135*e^6 + 4/45*e^5 - 7/3*e^4 - 19/5*e^3 + 244/15*e^2 + 1079/45*e + 218/27', '-1/15*e^6 + 1/9*e^5 + 112/45*e^4 - 163/45*e^3 - 130/9*e^2 + 554/45*e + 236/9', '-16/135*e^6 + 38/45*e^5 + 161/45*e^4 - 1271/45*e^3 - 166/45*e^2 + 269/3*e + 1250/27', '-16/135*e^6 + 38/45*e^5 + 161/45*e^4 - 1271/45*e^3 - 166/45*e^2 + 269/3*e + 1250/27', '-17/135*e^6 + 19/45*e^5 + 38/9*e^4 - 631/45*e^3 - 608/45*e^2 + 713/15*e + 598/27', '-17/135*e^6 + 19/45*e^5 + 38/9*e^4 - 631/45*e^3 - 608/45*e^2 + 713/15*e + 598/27', '-14/135*e^6 + 22/45*e^5 + 154/45*e^4 - 724/45*e^3 - 464/45*e^2 + 157/3*e + 700/27', '-14/135*e^6 + 22/45*e^5 + 154/45*e^4 - 724/45*e^3 - 464/45*e^2 + 157/3*e + 700/27', '-1/27*e^6 + 2/9*e^5 + 8/9*e^4 - 62/9*e^3 + 53/9*e^2 + 10*e - 200/27', '-1/27*e^6 + 2/9*e^5 + 8/9*e^4 - 62/9*e^3 + 53/9*e^2 + 10*e - 200/27', '8/45*e^6 - 32/45*e^5 - 259/45*e^4 + 1039/45*e^3 + 614/45*e^2 - 583/9*e - 80/3', '8/45*e^6 - 32/45*e^5 - 259/45*e^4 + 1039/45*e^3 + 614/45*e^2 - 583/9*e - 80/3', '-2/135*e^6 - 4/45*e^5 + 3/5*e^4 + 41/15*e^3 - 28/5*e^2 + 8/9*e + 544/27', '1/45*e^6 - 11/45*e^5 - 5/9*e^4 + 379/45*e^3 - 148/45*e^2 - 1466/45*e + 146/9', '-2/135*e^6 - 4/45*e^5 + 3/5*e^4 + 41/15*e^3 - 28/5*e^2 + 8/9*e + 544/27', '1/45*e^6 - 11/45*e^5 - 5/9*e^4 + 379/45*e^3 - 148/45*e^2 - 1466/45*e + 146/9', '4/135*e^6 - 17/45*e^5 - 29/45*e^4 + 584/45*e^3 - 311/45*e^2 - 146/3*e + 34/27', '-22/135*e^6 + 19/45*e^5 + 6*e^4 - 69/5*e^3 - 521/15*e^2 + 2009/45*e + 1538/27', '4/135*e^6 - 17/45*e^5 - 29/45*e^4 + 584/45*e^3 - 311/45*e^2 - 146/3*e + 34/27', '-22/135*e^6 + 19/45*e^5 + 6*e^4 - 69/5*e^3 - 521/15*e^2 + 2009/45*e + 1538/27', '-16/135*e^6 + 28/45*e^5 + 19/5*e^4 - 302/15*e^3 - 142/15*e^2 + 484/9*e + 644/27', '-16/135*e^6 + 28/45*e^5 + 19/5*e^4 - 302/15*e^3 - 142/15*e^2 + 484/9*e + 644/27', '2/45*e^6 - 2/5*e^5 - 17/15*e^4 + 197/15*e^3 - 98/15*e^2 - 115/3*e + 200/9', '14/135*e^6 - 22/45*e^5 - 139/45*e^4 + 709/45*e^3 + 44/45*e^2 - 43*e - 430/27', '14/135*e^6 - 22/45*e^5 - 139/45*e^4 + 709/45*e^3 + 44/45*e^2 - 43*e - 430/27', '2/45*e^6 - 2/5*e^5 - 17/15*e^4 + 197/15*e^3 - 98/15*e^2 - 115/3*e + 200/9', '-11/135*e^6 + 11/15*e^5 + 116/45*e^4 - 1121/45*e^3 - 301/45*e^2 + 784/9*e + 754/27', '-11/135*e^6 + 11/15*e^5 + 116/45*e^4 - 1121/45*e^3 - 301/45*e^2 + 784/9*e + 754/27', '19/135*e^6 - 14/15*e^5 - 184/45*e^4 + 1399/45*e^3 - 61/45*e^2 - 938/9*e - 620/27', '1/45*e^6 + 1/45*e^5 - 43/45*e^4 - 32/45*e^3 + 383/45*e^2 - 37/9*e + 20/9', '1/45*e^6 + 1/45*e^5 - 43/45*e^4 - 32/45*e^3 + 383/45*e^2 - 37/9*e + 20/9', '19/135*e^6 - 14/15*e^5 - 184/45*e^4 + 1399/45*e^3 - 61/45*e^2 - 938/9*e - 620/27', '-1/27*e^6 + 13/45*e^5 + 43/45*e^4 - 424/45*e^3 + 214/45*e^2 + 313/15*e - 182/27', '-1/27*e^6 + 13/45*e^5 + 43/45*e^4 - 424/45*e^3 + 214/45*e^2 + 313/15*e - 182/27', '2/135*e^6 - 28/45*e^5 + 11/45*e^4 + 928/45*e^3 - 844/45*e^2 - 902/15*e + 458/27', '2/135*e^6 - 28/45*e^5 + 11/45*e^4 + 928/45*e^3 - 844/45*e^2 - 902/15*e + 458/27', '1/27*e^6 + 1/9*e^5 - 11/9*e^4 - 43/9*e^3 + 16/9*e^2 + 124/3*e + 434/27', '1/27*e^6 + 1/9*e^5 - 11/9*e^4 - 43/9*e^3 + 16/9*e^2 + 124/3*e + 434/27', '1/135*e^6 + 2/45*e^5 - 7/15*e^4 - 23/15*e^3 + 34/5*e^2 + 20/9*e - 200/27', '1/135*e^6 + 2/45*e^5 - 7/15*e^4 - 23/15*e^3 + 34/5*e^2 + 20/9*e - 200/27', '-14/135*e^6 + 7/9*e^5 + 49/15*e^4 - 132/5*e^3 - 9*e^2 + 4444/45*e + 1738/27', '4/45*e^6 - 11/15*e^5 - 38/15*e^4 + 371/15*e^3 - 23/15*e^2 - 449/5*e - 344/9', '-14/135*e^6 + 7/9*e^5 + 49/15*e^4 - 132/5*e^3 - 9*e^2 + 4444/45*e + 1738/27', '4/45*e^6 - 11/15*e^5 - 38/15*e^4 + 371/15*e^3 - 23/15*e^2 - 449/5*e - 344/9', '-1/45*e^6 - 2/5*e^5 + 4/5*e^4 + 72/5*e^3 - 13/15*e^2 - 314/5*e - 424/9', '-1/45*e^6 - 2/5*e^5 + 4/5*e^4 + 72/5*e^3 - 13/15*e^2 - 314/5*e - 424/9', '-1/15*e^6 + 3/5*e^5 + 11/5*e^4 - 308/15*e^3 - 118/15*e^2 + 217/3*e + 100/3', '-1/3*e^5 + 2/3*e^4 + 11*e^3 - 59/3*e^2 - 77/3*e + 30', '-1/15*e^6 + 3/5*e^5 + 11/5*e^4 - 308/15*e^3 - 118/15*e^2 + 217/3*e + 100/3', '-1/3*e^5 + 2/3*e^4 + 11*e^3 - 59/3*e^2 - 77/3*e + 30', '-2/45*e^6 + 2/5*e^5 + 4/5*e^4 - 64/5*e^3 + 238/15*e^2 + 27*e - 200/9', '-2/45*e^6 + 2/5*e^5 + 4/5*e^4 - 64/5*e^3 + 238/15*e^2 + 27*e - 200/9', '37/135*e^6 - 46/45*e^5 - 139/15*e^4 + 509/15*e^3 + 514/15*e^2 - 1060/9*e - 2180/27', '37/135*e^6 - 46/45*e^5 - 139/15*e^4 + 509/15*e^3 + 514/15*e^2 - 1060/9*e - 2180/27', '-29/135*e^6 + 8/9*e^5 + 322/45*e^4 - 1318/45*e^3 - 217/9*e^2 + 1403/15*e + 1558/27', '-29/135*e^6 + 8/9*e^5 + 322/45*e^4 - 1318/45*e^3 - 217/9*e^2 + 1403/15*e + 1558/27', '1/135*e^6 - 2/5*e^5 - 1/45*e^4 + 631/45*e^3 - 229/45*e^2 - 494/9*e - 296/27', '1/135*e^6 - 2/5*e^5 - 1/45*e^4 + 631/45*e^3 - 229/45*e^2 - 494/9*e - 296/27', '-28/135*e^6 + 52/45*e^5 + 97/15*e^4 - 193/5*e^3 - 178/15*e^2 + 5864/45*e + 2108/27', '-28/135*e^6 + 52/45*e^5 + 97/15*e^4 - 193/5*e^3 - 178/15*e^2 + 5864/45*e + 2108/27', '-2/45*e^6 + 1/15*e^5 + 32/15*e^4 - 37/15*e^3 - 382/15*e^2 + 15*e + 358/9', '-2/45*e^6 + 1/15*e^5 + 32/15*e^4 - 37/15*e^3 - 382/15*e^2 + 15*e + 358/9', '2/135*e^6 - 2/15*e^5 - 32/45*e^4 + 242/45*e^3 + 472/45*e^2 - 304/9*e - 1510/27', '-5/27*e^6 + 16/15*e^5 + 283/45*e^4 - 1639/45*e^3 - 1166/45*e^2 + 6094/45*e + 2108/27', '-5/27*e^6 + 16/15*e^5 + 283/45*e^4 - 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3896/45*e - 1562/27', '-4/15*e^6 + 73/45*e^5 + 371/45*e^4 - 2396/45*e^3 - 541/45*e^2 + 1397/9*e + 400/9', '1/9*e^6 - 8/9*e^5 - 25/9*e^4 + 268/9*e^3 - 133/9*e^2 - 899/9*e - 140/9', '1/9*e^6 - 8/9*e^5 - 25/9*e^4 + 268/9*e^3 - 133/9*e^2 - 899/9*e - 140/9', '-4/15*e^6 + 73/45*e^5 + 371/45*e^4 - 2396/45*e^3 - 541/45*e^2 + 1397/9*e + 400/9', '-26/135*e^6 + 23/45*e^5 + 97/15*e^4 - 242/15*e^3 - 99/5*e^2 + 329/9*e - 290/27', '-26/135*e^6 + 23/45*e^5 + 97/15*e^4 - 242/15*e^3 - 99/5*e^2 + 329/9*e - 290/27', '26/135*e^6 - 23/45*e^5 - 34/5*e^4 + 79/5*e^3 + 169/5*e^2 - 317/9*e - 1726/27', '-1/45*e^6 - 16/45*e^5 + 43/45*e^4 + 557/45*e^3 - 293/45*e^2 - 398/9*e - 92/9', '26/135*e^6 - 23/45*e^5 - 34/5*e^4 + 79/5*e^3 + 169/5*e^2 - 317/9*e - 1726/27', '-1/45*e^6 - 16/45*e^5 + 43/45*e^4 + 557/45*e^3 - 293/45*e^2 - 398/9*e - 92/9', '1/135*e^6 + 4/9*e^5 - 1/15*e^4 - 251/15*e^3 - 10*e^2 + 4654/45*e + 2068/27', '1/135*e^6 + 4/9*e^5 - 1/15*e^4 - 251/15*e^3 - 10*e^2 + 4654/45*e + 2068/27', '-1/45*e^6 - 1/45*e^5 + 58/45*e^4 + 17/45*e^3 - 938/45*e^2 + 94/9*e + 520/9', '-1/45*e^6 - 1/45*e^5 + 58/45*e^4 + 17/45*e^3 - 938/45*e^2 + 94/9*e + 520/9', '-1/45*e^6 + 29/45*e^5 + 43/45*e^4 - 1018/45*e^3 - 608/45*e^2 + 835/9*e + 610/9', '-1/45*e^6 + 29/45*e^5 + 43/45*e^4 - 1018/45*e^3 - 608/45*e^2 + 835/9*e + 610/9', '7/45*e^6 - 11/9*e^5 - 218/45*e^4 + 1832/45*e^3 + 110/9*e^2 - 5791/45*e - 238/3', '7/45*e^6 - 11/9*e^5 - 218/45*e^4 + 1832/45*e^3 + 110/9*e^2 - 5791/45*e - 238/3', '-11/45*e^6 + 82/45*e^5 + 326/45*e^4 - 2732/45*e^3 - 94/45*e^2 + 8419/45*e + 476/9', '-11/45*e^6 + 82/45*e^5 + 326/45*e^4 - 2732/45*e^3 - 94/45*e^2 + 8419/45*e + 476/9', '4/9*e^5 - 4/9*e^4 - 134/9*e^3 + 110/9*e^2 + 391/9*e + 20/9', '4/9*e^5 - 4/9*e^4 - 134/9*e^3 + 110/9*e^2 + 391/9*e + 20/9', '-31/135*e^6 + 11/15*e^5 + 331/45*e^4 - 1036/45*e^3 - 626/45*e^2 + 491/9*e - 706/27', '-31/135*e^6 + 11/15*e^5 + 331/45*e^4 - 1036/45*e^3 - 626/45*e^2 + 491/9*e - 706/27', '32/135*e^6 - 16/45*e^5 - 367/45*e^4 + 457/45*e^3 + 1352/45*e^2 - 37/3*e + 614/27', '-23/135*e^6 + 13/15*e^5 + 278/45*e^4 - 1313/45*e^3 - 1618/45*e^2 + 994/9*e + 3064/27', '38/135*e^6 - 41/45*e^5 - 31/3*e^4 + 458/15*e^3 + 303/5*e^2 - 5326/45*e - 2632/27', '38/135*e^6 - 41/45*e^5 - 31/3*e^4 + 458/15*e^3 + 303/5*e^2 - 5326/45*e - 2632/27', '16/135*e^6 - 58/45*e^5 - 14/5*e^4 + 652/15*e^3 - 278/15*e^2 - 1318/9*e - 590/27', '16/135*e^6 - 58/45*e^5 - 14/5*e^4 + 652/15*e^3 - 278/15*e^2 - 1318/9*e - 590/27', '14/135*e^6 - 37/45*e^5 - 109/45*e^4 + 1174/45*e^3 - 901/45*e^2 - 50*e + 1064/27', '14/135*e^6 - 37/45*e^5 - 109/45*e^4 + 1174/45*e^3 - 901/45*e^2 - 50*e + 1064/27', '19/135*e^6 - 14/15*e^5 - 184/45*e^4 + 1384/45*e^3 - 46/45*e^2 - 809/9*e - 1520/27', '19/135*e^6 - 14/15*e^5 - 184/45*e^4 + 1384/45*e^3 - 46/45*e^2 - 809/9*e - 1520/27', '37/135*e^6 - 22/15*e^5 - 382/45*e^4 + 2182/45*e^3 + 437/45*e^2 - 1331/9*e - 1106/27', '37/135*e^6 - 22/15*e^5 - 382/45*e^4 + 2182/45*e^3 + 437/45*e^2 - 1331/9*e - 1106/27', '-2/45*e^6 + 13/45*e^5 + 71/45*e^4 - 416/45*e^3 - 331/45*e^2 + 122/9*e + 110/9', '-2/45*e^6 + 13/45*e^5 + 71/45*e^4 - 416/45*e^3 - 331/45*e^2 + 122/9*e + 110/9', '7/45*e^6 - 38/45*e^5 - 256/45*e^4 + 1336/45*e^3 + 1526/45*e^2 - 1201/9*e - 880/9', '7/45*e^6 - 38/45*e^5 - 256/45*e^4 + 1336/45*e^3 + 1526/45*e^2 - 1201/9*e - 880/9', '1/135*e^6 - 4/9*e^5 + 7/45*e^4 + 707/45*e^3 - 79/9*e^2 - 1022/15*e - 482/27', '-2/45*e^6 + 7/15*e^5 + 8/15*e^4 - 15*e^3 + 391/15*e^2 + 563/15*e - 644/9', '-2/45*e^6 + 7/15*e^5 + 8/15*e^4 - 15*e^3 + 391/15*e^2 + 563/15*e - 644/9', '1/135*e^6 - 4/9*e^5 + 7/45*e^4 + 707/45*e^3 - 79/9*e^2 - 1022/15*e - 482/27', '10/27*e^6 - 77/45*e^5 - 58/5*e^4 + 847/15*e^3 + 238/15*e^2 - 7861/45*e - 982/27', '2/15*e^6 - 74/45*e^5 - 193/45*e^4 + 2548/45*e^3 + 788/45*e^2 - 1978/9*e - 1112/9', '2/15*e^6 - 74/45*e^5 - 193/45*e^4 + 2548/45*e^3 + 788/45*e^2 - 1978/9*e - 1112/9', '10/27*e^6 - 77/45*e^5 - 58/5*e^4 + 847/15*e^3 + 238/15*e^2 - 7861/45*e - 982/27', '14/45*e^6 - 22/15*e^5 - 154/15*e^4 + 724/15*e^3 + 494/15*e^2 - 154*e - 610/9', '14/45*e^6 - 22/15*e^5 - 154/15*e^4 + 724/15*e^3 + 494/15*e^2 - 154*e - 610/9', '-16/135*e^6 + 28/45*e^5 + 19/5*e^4 - 317/15*e^3 - 142/15*e^2 + 790/9*e + 1400/27', '-7/27*e^6 + 14/9*e^5 + 74/9*e^4 - 464/9*e^3 - 175/9*e^2 + 457/3*e + 2290/27', '-7/27*e^6 + 14/9*e^5 + 74/9*e^4 - 464/9*e^3 - 175/9*e^2 + 457/3*e + 2290/27', '-16/135*e^6 + 28/45*e^5 + 19/5*e^4 - 317/15*e^3 - 142/15*e^2 + 790/9*e + 1400/27'], 'hecke_polynomial': 'x^7 - 5*x^6 - 39*x^5 + 171*x^4 + 315*x^3 - 663*x^2 - 1105*x - 250', 'label': '4.4.19225.1-16.1-g'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 19225, 'ideals': ['[1, 1, 1]', '[4, 2, w + 2]', '[4, 2, -1/2*w^3 + 3/2*w^2 + 9/2*w - 10]', '[9, 3, 1/2*w^3 - 5/2*w^2 - 5/2*w + 17]', '[9, 3, 3/2*w^3 - 11/2*w^2 - 19/2*w + 28]', '[11, 11, 1/2*w^3 - 3/2*w^2 - 9/2*w + 11]', '[11, 11, -w - 3]', '[16, 2, 2]', '[16, 4, w^3 - 3*w^2 - 8*w + 16]', '[16, 4, -1/2*w^3 + 3/2*w^2 + 5/2*w - 8]', '[25, 5, w^3 - 3*w^2 - 7*w + 15]', '[29, 29, w + 1]', '[29, 29, 1/2*w^3 - 3/2*w^2 - 9/2*w + 9]', '[31, 31, -1/2*w^3 + 5/2*w^2 + 5/2*w - 16]', '[31, 31, 1/2*w^3 - 3/2*w^2 - 9/2*w + 5]', '[31, 31, -w + 3]', '[31, 31, 3/2*w^3 - 11/2*w^2 - 19/2*w + 29]', '[36, 6, 2*w^3 - 7*w^2 - 13*w + 35]', '[36, 6, w^2 - w - 10]', '[36, 6, -w^3 + 3*w^2 + 8*w - 18]', '[36, 6, 1/2*w^3 - 3/2*w^2 - 5/2*w + 10]', '[44, 22, w]', '[44, 22, -3/2*w^3 + 9/2*w^2 + 23/2*w - 22]', '[44, 22, 1/2*w^3 - 3/2*w^2 - 9/2*w + 8]', '[44, 22, w^3 - 3*w^2 - 6*w + 14]', '[59, 59, 2*w^2 - w - 13]', '[59, 59, 9/2*w^3 - 31/2*w^2 - 61/2*w + 85]', '[61, 61, 2*w^3 - 6*w^2 - 15*w + 31]', '[61, 61, -3/2*w^3 + 11/2*w^2 + 21/2*w - 34]', '[64, 4, 2*w + 4]', '[64, 4, -w^3 + 3*w^2 + 9*w - 20]', '[64, 8, 3/2*w^3 - 11/2*w^2 - 17/2*w + 25]', '[64, 8, w^2 - 2*w - 12]', '[71, 71, 3/2*w^3 - 11/2*w^2 - 19/2*w + 32]', '[71, 71, -1/2*w^3 + 5/2*w^2 + 5/2*w - 13]', '[79, 79, -3*w^3 + 10*w^2 + 19*w - 51]', '[79, 79, 15/2*w^3 - 51/2*w^2 - 103/2*w + 139]', '[81, 3, 3]', '[81, 9, 2*w^2 - 2*w - 17]', '[81, 9, -4*w^3 + 14*w^2 + 26*w - 73]', '[99, 33, -1/2*w^3 + 1/2*w^2 + 7/2*w]', '[99, 33, -5/2*w^3 + 17/2*w^2 + 31/2*w - 44]', '[99, 33, -w^3 + 2*w^2 + 9*w - 7]', '[99, 33, 3*w^3 - 10*w^2 - 21*w + 53]', '[100, 10, -9/2*w^3 + 31/2*w^2 + 61/2*w - 84]', '[100, 10, 2*w^2 - w - 14]', '[101, 101, -2*w^3 + 7*w^2 + 14*w - 37]', '[101, 101, -1/2*w^3 + 5/2*w^2 + 7/2*w - 16]', '[109, 109, w^3 - 3*w^2 - 6*w + 19]', '[109, 109, -w^3 + 4*w^2 + 5*w - 19]', '[116, 58, 1/2*w^3 - 3/2*w^2 - 9/2*w + 12]', '[116, 58, -w - 4]', '[116, 58, -1/2*w^3 + 7/2*w^2 + 1/2*w - 28]', '[116, 58, 3*w^3 - 11*w^2 - 18*w + 54]', '[121, 11, 3/2*w^3 - 9/2*w^2 - 21/2*w + 22]', '[121, 11, -3/2*w^3 + 9/2*w^2 + 21/2*w - 23]', '[121, 121, 1/2*w^3 - 5/2*w^2 - 5/2*w + 12]', '[121, 121, 3/2*w^3 - 11/2*w^2 - 19/2*w + 33]', '[124, 62, 7/2*w^3 - 23/2*w^2 - 49/2*w + 61]', '[124, 62, -w^2 + w + 6]', '[124, 62, -w^3 + 2*w^2 + 7*w - 8]', '[124, 62, -2*w^3 + 7*w^2 + 13*w - 39]', '[124, 62, -w^3 + 4*w^2 + 5*w - 18]', '[124, 62, w^3 - 4*w^2 - 6*w + 18]', '[124, 62, w^3 - 4*w^2 - 6*w + 27]', '[124, 62, 1/2*w^3 - 5/2*w^2 - 3/2*w + 19]', '[139, 139, -w^3 + 4*w^2 + 7*w - 25]', '[139, 139, -5/2*w^3 + 17/2*w^2 + 33/2*w - 41]', '[144, 6, w^3 - 5*w^2 - 5*w + 34]', '[144, 6, 3*w^3 - 11*w^2 - 19*w + 56]', '[144, 12, -w^2 + 8]', '[144, 12, w^3 - 2*w^2 - 8*w + 7]', '[144, 12, 3*w^3 - 10*w^2 - 20*w + 52]', '[144, 12, -1/2*w^3 + 3/2*w^2 + 5/2*w - 4]', '[149, 149, 1/2*w^3 + 1/2*w^2 - 11/2*w - 8]', '[149, 149, 5/2*w^3 - 19/2*w^2 - 35/2*w + 50]', '[149, 149, -9/2*w^3 + 31/2*w^2 + 59/2*w - 82]', '[149, 149, -5/2*w^3 + 19/2*w^2 + 35/2*w - 56]', '[151, 151, -1/2*w^3 + 3/2*w^2 + 3/2*w - 12]', '[151, 151, 3/2*w^3 - 9/2*w^2 - 25/2*w + 28]', '[176, 22, w^3 - 3*w^2 - 9*w + 22]', '[176, 22, -2*w - 6]', '[176, 44, w^2 + 2*w]', '[176, 44, -2*w^3 + 7*w^2 + 11*w - 33]', '[176, 44, -7/2*w^3 + 23/2*w^2 + 53/2*w - 69]', '[176, 44, -w^3 + 2*w^2 + 10*w - 4]', '[179, 179, -1/2*w^3 + 3/2*w^2 + 9/2*w - 3]', '[179, 179, w - 5]', '[225, 15, -5/2*w^3 + 17/2*w^2 + 29/2*w - 42]', '[225, 15, 3/2*w^3 - 7/2*w^2 - 27/2*w + 13]', '[229, 229, -15/2*w^3 + 51/2*w^2 + 105/2*w - 142]', '[229, 229, 1/2*w^3 - 7/2*w^2 - 7/2*w + 19]', '[229, 229, -17/2*w^3 + 57/2*w^2 + 119/2*w - 156]', '[229, 229, -9/2*w^3 + 33/2*w^2 + 55/2*w - 82]', '[236, 118, 3/2*w^3 - 9/2*w^2 - 19/2*w + 20]', '[236, 118, -3/2*w^3 + 11/2*w^2 + 17/2*w - 31]', '[236, 118, -w^2 + 2*w + 6]', '[236, 118, -2*w^3 + 6*w^2 + 15*w - 28]', '[239, 239, -9*w^3 + 31*w^2 + 59*w - 161]', '[239, 239, w^3 + w^2 - 11*w - 19]', '[241, 241, 5/2*w^3 - 15/2*w^2 - 37/2*w + 37]', '[241, 241, -2*w^3 + 6*w^2 + 13*w - 29]', '[244, 122, -21/2*w^3 + 71/2*w^2 + 149/2*w - 200]', '[244, 122, 21/2*w^3 - 69/2*w^2 - 155/2*w + 197]', '[244, 122, 3*w^2 - 3*w - 26]', '[244, 122, w^3 - w^2 - 10*w - 2]', '[251, 251, -7/2*w^3 + 25/2*w^2 + 45/2*w - 67]', '[251, 251, 1/2*w^3 - 5/2*w^2 - 13/2*w + 7]', '[251, 251, -1/2*w^3 + 1/2*w^2 + 13/2*w + 4]', '[251, 251, -1/2*w^3 + 7/2*w^2 + 3/2*w - 23]', '[256, 4, 4]', '[256, 8, 2*w^3 - 6*w^2 - 16*w + 32]', '[256, 8, -w^3 + 3*w^2 + 5*w - 16]', '[256, 16, 2*w^3 - 7*w^2 - 14*w + 36]', '[256, 16, 3/2*w^3 - 9/2*w^2 - 23/2*w + 20]', '[261, 87, -3/2*w^3 + 5/2*w^2 + 27/2*w - 5]', '[261, 87, -w^3 + 4*w^2 + 7*w - 27]', '[261, 87, -3/2*w^3 + 11/2*w^2 + 21/2*w - 26]', '[261, 87, 5*w^3 - 17*w^2 - 32*w + 87]', '[271, 271, -w^3 + 4*w^2 + 5*w - 25]', '[271, 271, -5/2*w^3 + 17/2*w^2 + 33/2*w - 47]', '[275, 55, 11/2*w^3 - 37/2*w^2 - 75/2*w + 99]', '[275, 55, -w^3 + w^2 + 8*w - 1]', '[279, 93, 3/2*w^3 - 11/2*w^2 - 19/2*w + 25]', '[279, 93, -1/2*w^3 + 5/2*w^2 + 11/2*w - 8]', '[279, 93, -2*w^3 + 6*w^2 + 16*w - 31]', '[279, 93, 6*w^3 - 20*w^2 - 42*w + 109]', '[279, 93, -w^3 + 3*w^2 + 5*w - 15]', '[279, 93, -w^3 + w^2 + 7*w - 3]', '[279, 93, -3*w^3 + 10*w^2 + 23*w - 61]', '[279, 93, 1/2*w^3 - 5/2*w^2 - 5/2*w + 20]', '[281, 281, 5/2*w^3 - 15/2*w^2 - 39/2*w + 41]', '[281, 281, 3/2*w^3 - 7/2*w^2 - 27/2*w + 14]', '[284, 142, -17/2*w^3 + 57/2*w^2 + 119/2*w - 155]', '[284, 142, w^3 - 7*w - 4]', '[284, 142, -w^3 + 2*w^2 + 10*w - 2]', '[284, 142, 2*w^3 - 7*w^2 - 11*w + 31]', '[289, 17, -7/2*w^3 + 25/2*w^2 + 45/2*w - 62]', '[289, 17, 5/2*w^3 - 15/2*w^2 - 39/2*w + 37]', '[311, 311, -19/2*w^3 + 65/2*w^2 + 129/2*w - 175]', '[311, 311, -7/2*w^3 + 25/2*w^2 + 47/2*w - 71]', '[311, 311, 7/2*w^3 - 25/2*w^2 - 49/2*w + 67]', '[311, 311, -3/2*w^3 + 11/2*w^2 + 15/2*w - 31]', '[316, 158, w^3 - 2*w^2 - 9*w + 8]', '[316, 158, -w^3 + 4*w^2 + 8*w - 19]', '[316, 158, -5/2*w^3 + 17/2*w^2 + 31/2*w - 45]', '[316, 158, -3*w^3 + 10*w^2 + 21*w - 52]', '[319, 319, 3/2*w^3 - 7/2*w^2 - 27/2*w + 11]', '[319, 319, 7/2*w^3 - 25/2*w^2 - 45/2*w + 66]', '[319, 319, 1/2*w^3 - 7/2*w^2 - 3/2*w + 24]', '[319, 319, 5/2*w^3 - 17/2*w^2 - 29/2*w + 40]', '[324, 6, 3*w + 6]', '[324, 6, -3/2*w^3 + 9/2*w^2 + 27/2*w - 30]', '[324, 18, 5/2*w^3 - 15/2*w^2 - 37/2*w + 38]', '[324, 18, 1/2*w^3 - 1/2*w^2 - 11/2*w + 1]', '[324, 18, -2*w^3 + 7*w^2 + 12*w - 38]', '[324, 18, 2*w^3 - 6*w^2 - 13*w + 30]', '[331, 331, 19/2*w^3 - 65/2*w^2 - 127/2*w + 173]', '[331, 331, -w^3 - w^2 + 10*w + 15]', '[341, 341, -4*w^3 + 14*w^2 + 27*w - 77]', '[341, 341, w^3 - 5*w^2 - 5*w + 33]', '[341, 341, -w^3 + 3*w^2 + 9*w - 11]', '[341, 341, -2*w + 5]', '[341, 341, 5/2*w^3 - 17/2*w^2 - 35/2*w + 44]', '[341, 341, w^2 - 9]', '[341, 341, -1/2*w^3 + 7/2*w^2 + 5/2*w - 21]', '[341, 341, 3*w^3 - 11*w^2 - 19*w + 57]', '[349, 349, -5/2*w^3 + 15/2*w^2 + 33/2*w - 35]', '[349, 349, 3/2*w^3 - 11/2*w^2 - 21/2*w + 36]', '[361, 19, 2*w^3 - 6*w^2 - 14*w + 29]', '[361, 19, 2*w^3 - 6*w^2 - 14*w + 31]', '[379, 379, 1/2*w^3 - 5/2*w^2 - 1/2*w + 20]', '[379, 379, -1/2*w^3 + 5/2*w^2 + 1/2*w - 9]', '[396, 66, 1/2*w^3 - 5/2*w^2 - 3/2*w + 11]', '[396, 66, -2*w^3 + 5*w^2 + 16*w - 22]', '[396, 66, -2*w^3 + 7*w^2 + 15*w - 44]', '[396, 66, -1/2*w^3 + 7/2*w^2 + 5/2*w - 22]', '[396, 66, 7/2*w^3 - 23/2*w^2 - 45/2*w + 59]', '[396, 66, -w^3 + 4*w^2 + 8*w - 17]', '[396, 66, 4*w^3 - 14*w^2 - 27*w + 76]', '[396, 66, -w^3 + 4*w^2 + 5*w - 26]', '[400, 10, 2*w^3 - 6*w^2 - 14*w + 30]', '[400, 20, 3/2*w^3 - 13/2*w^2 - 19/2*w + 34]', '[400, 20, 3*w^3 - 11*w^2 - 20*w + 64]', '[401, 401, -7/2*w^3 + 25/2*w^2 + 45/2*w - 69]', '[401, 401, w^3 - 3*w^2 - 5*w + 19]', '[404, 202, w^3 - 2*w^2 - 5*w + 14]', '[404, 202, 21/2*w^3 - 71/2*w^2 - 145/2*w + 194]', '[404, 202, w^3 + w^2 - 8*w - 10]', '[404, 202, 9/2*w^3 - 29/2*w^2 - 67/2*w + 83]', '[409, 409, 3/2*w^3 - 7/2*w^2 - 23/2*w + 13]', '[409, 409, -11/2*w^3 + 37/2*w^2 + 77/2*w - 100]', '[409, 409, 7/2*w^3 - 23/2*w^2 - 47/2*w + 58]', '[409, 409, -w^3 + 3*w^2 + 9*w - 9]', '[419, 419, 3/2*w^3 - 13/2*w^2 - 17/2*w + 36]', '[419, 419, -5/2*w^3 + 19/2*w^2 + 31/2*w - 54]', '[421, 421, -w^3 + 4*w^2 + 5*w - 27]', '[421, 421, 7/2*w^3 - 23/2*w^2 - 47/2*w + 63]', '[436, 218, -11/2*w^3 + 37/2*w^2 + 79/2*w - 102]', '[436, 218, 3*w^2 + 5*w - 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5*w^2 - 3*w + 38]', '[1984, 248, 5*w^3 - 18*w^2 - 32*w + 95]', '[1984, 248, -w^3 + 5*w^2 + 6*w - 36]', '[1984, 248, -w^3 + 6*w^2 + 4*w - 40]', '[1984, 248, -7/2*w^3 + 25/2*w^2 + 47/2*w - 62]', '[1984, 248, 3*w^3 - 10*w^2 - 24*w + 64]', '[1984, 248, -w^3 + 3*w^2 + 10*w - 20]', '[1984, 248, 1/2*w^3 - 3/2*w^2 - 13/2*w + 4]', '[1984, 248, w^3 - 4*w^2 - 10*w + 13]', '[1996, 998, 37/2*w^3 - 123/2*w^2 - 265/2*w + 344]', '[1996, 998, 23/2*w^3 - 79/2*w^2 - 149/2*w + 203]', '[1996, 998, -4*w^3 + 15*w^2 + 25*w - 78]', '[1996, 998, -29*w^3 + 98*w^2 + 202*w - 537]', '[1996, 998, 2*w^3 - 2*w^2 - 15*w + 6]', '[1996, 998, 2*w^3 - 3*w^2 - 14*w + 10]', '[1996, 998, -2*w^3 + 8*w^2 + 15*w - 40]', '[1996, 998, -6*w^3 + 19*w^2 + 37*w - 95]', '[2011, 2011, -3/2*w^3 + 11/2*w^2 + 23/2*w - 21]', '[2011, 2011, -3/2*w^3 + 11/2*w^2 + 23/2*w - 40]', '[2025, 15, 3*w^3 - 9*w^2 - 21*w + 45]', '[2025, 45, -w^3 + w^2 + 13*w + 9]', '[2025, 45, 3*w^3 - 11*w^2 - 15*w + 49]', '[2029, 2029, 4*w^3 - 15*w^2 - 28*w + 81]', '[2029, 2029, 2*w^3 - 6*w^2 - 17*w + 29]', '[2036, 1018, 2*w^2 + 3*w - 8]', '[2036, 1018, -11*w^3 + 36*w^2 + 84*w - 213]', '[2036, 1018, -13/2*w^3 + 43/2*w^2 + 97/2*w - 122]', '[2036, 1018, 3*w^2 + 7*w - 2]', '[2039, 2039, -w - 7]', '[2039, 2039, 1/2*w^3 - 3/2*w^2 - 9/2*w + 15]', '[2059, 2059, 7*w^3 - 23*w^2 - 50*w + 123]', '[2059, 2059, -5/2*w^3 + 15/2*w^2 + 39/2*w - 34]', '[2059, 2059, -3/2*w^3 + 9/2*w^2 + 17/2*w - 18]', '[2059, 2059, 3/2*w^3 - 5/2*w^2 - 19/2*w + 9]', '[2061, 687, -w^3 + 3*w^2 + 5*w - 9]', '[2061, 687, 3/2*w^3 - 5/2*w^2 - 25/2*w + 10]', '[2061, 687, 7/2*w^3 - 23/2*w^2 - 51/2*w + 59]', '[2061, 687, 11*w^3 - 37*w^2 - 76*w + 203]', '[2061, 687, 1/2*w^3 - 7/2*w^2 - 7/2*w + 24]', '[2061, 687, -2*w^3 + 8*w^2 + 10*w - 37]', '[2061, 687, 3*w^3 - 10*w^2 - 21*w + 47]', '[2061, 687, -w^3 - 2*w^2 + 13*w + 27]', '[2069, 2069, 7/2*w^3 - 21/2*w^2 - 51/2*w + 53]', '[2069, 2069, 3*w^3 - 9*w^2 - 20*w + 45]', '[2081, 2081, 9/2*w^3 - 31/2*w^2 - 59/2*w + 85]', '[2081, 2081, 1/2*w^3 + 1/2*w^2 - 11/2*w - 5]', '[2081, 2081, 19/2*w^3 - 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123]', '[2224, 556, -4*w^3 + 15*w^2 + 24*w - 84]', '[2239, 2239, -5/2*w^3 + 19/2*w^2 + 35/2*w - 61]', '[2239, 2239, -w^3 + 3*w^2 + 12*w - 3]', '[2239, 2239, -7/2*w^3 + 21/2*w^2 + 45/2*w - 48]', '[2239, 2239, -3/2*w^3 + 9/2*w^2 + 31/2*w - 37]', '[2251, 2251, 7/2*w^3 - 27/2*w^2 - 45/2*w + 70]', '[2251, 2251, -3*w^3 + 12*w^2 + 19*w - 73]', '[2259, 753, 13*w^3 - 46*w^2 - 79*w + 225]', '[2259, 753, -5/2*w^3 + 21/2*w^2 + 31/2*w - 72]', '[2259, 753, 5/2*w^3 - 23/2*w^2 - 29/2*w + 75]', '[2259, 753, 11*w^3 - 36*w^2 - 79*w + 201]', '[2259, 753, -5/2*w^3 + 13/2*w^2 + 33/2*w - 31]', '[2259, 753, -4*w^3 + 2*w^2 + 44*w + 35]', '[2259, 753, -7/2*w^3 + 19/2*w^2 + 55/2*w - 39]', '[2259, 753, -9*w^3 + 31*w^2 + 60*w - 167]', '[2269, 2269, -5/2*w^3 + 19/2*w^2 + 35/2*w - 46]', '[2269, 2269, 5/2*w^3 - 19/2*w^2 - 35/2*w + 60]', '[2269, 2269, 7/2*w^3 - 27/2*w^2 - 43/2*w + 71]', '[2269, 2269, -5/2*w^3 + 21/2*w^2 + 29/2*w - 64]', '[2281, 2281, -6*w^3 + 20*w^2 + 40*w - 103]', '[2281, 2281, 2*w^3 - 4*w^2 - 16*w + 13]', '[2284, 1142, 3*w^3 - 8*w^2 - 23*w + 34]', '[2284, 1142, 1/2*w^3 - 3/2*w^2 - 1/2*w + 10]', '[2284, 1142, -w^3 + 4*w^2 + 6*w - 15]', '[2284, 1142, 2*w^3 - 6*w^2 - 17*w + 34]', '[2291, 2291, 7/2*w^3 - 17/2*w^2 - 61/2*w + 35]', '[2291, 2291, -21/2*w^3 + 71/2*w^2 + 145/2*w - 191]', '[2291, 2291, -19/2*w^3 + 67/2*w^2 + 123/2*w - 173]', '[2291, 2291, 7/2*w^3 - 21/2*w^2 - 55/2*w + 59]', '[2304, 12, 2*w^3 - 10*w^2 - 10*w + 68]', '[2304, 12, 6*w^3 - 22*w^2 - 38*w + 112]', '[2304, 24, -2*w^2 + 16]', '[2304, 24, 2*w^3 - 4*w^2 - 16*w + 14]', '[2304, 24, 6*w^3 - 20*w^2 - 40*w + 104]', '[2304, 24, -w^3 + 3*w^2 + 5*w - 8]', '[2304, 48, -2*w^3 + 9*w^2 + 10*w - 60]', '[2304, 48, -7/2*w^3 + 27/2*w^2 + 41/2*w - 67]', '[2304, 48, 9*w^3 - 31*w^2 - 62*w + 172]', '[2304, 48, 1/2*w^3 - 11/2*w^2 - 5/2*w + 32]', '[2309, 2309, -w^3 + 5*w^2 + 5*w - 39]', '[2309, 2309, -7/2*w^3 + 25/2*w^2 + 45/2*w - 72]', '[2309, 2309, 3*w^3 - 11*w^2 - 19*w + 51]', '[2309, 2309, 1/2*w^3 - 7/2*w^2 - 3/2*w + 18]', '[2349, 87, 3*w + 3]', '[2349, 87, 3/2*w^3 - 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2*w - 34]', '[2396, 1198, 25/2*w^3 - 87/2*w^2 - 165/2*w + 228]', '[2396, 1198, 5/2*w^3 - 21/2*w^2 - 35/2*w + 51]', '[2396, 1198, 5/2*w^3 - 19/2*w^2 - 29/2*w + 56]', '[2396, 1198, -19/2*w^3 + 67/2*w^2 + 117/2*w - 171]', '[2396, 1198, -8*w^2 - 3*w + 38]', '[2399, 2399, 11/2*w^3 - 39/2*w^2 - 71/2*w + 107]', '[2399, 2399, 1/2*w^3 - 9/2*w^2 - 1/2*w + 28]', '[2401, 7, -7]', '[2404, 1202, 2*w^3 - w^2 - 10*w + 6]', '[2404, 1202, -8*w^3 + 27*w^2 + 51*w - 133]', '[2404, 1202, 9/2*w^3 - 33/2*w^2 - 43/2*w + 69]', '[2404, 1202, w^2 - 4*w - 2]', '[2411, 2411, -25/2*w^3 + 85/2*w^2 + 175/2*w - 236]', '[2411, 2411, -5*w^2 + 29]', '[2416, 302, -w^3 + 3*w^2 + 3*w - 24]', '[2416, 302, 3*w^3 - 9*w^2 - 25*w + 56]', '[2416, 604, -2*w^3 + 5*w^2 + 18*w - 16]', '[2416, 604, w^3 + 2*w^2 - 10*w - 20]', '[2416, 604, -12*w^3 + 41*w^2 + 81*w - 221]', '[2416, 604, -5/2*w^3 + 17/2*w^2 + 27/2*w - 37]', '[2439, 813, 9/2*w^3 - 29/2*w^2 - 55/2*w + 70]', '[2439, 813, 1/2*w^3 + 9/2*w^2 - 23/2*w - 51]', '[2439, 813, -7/2*w^3 + 27/2*w^2 + 47/2*w - 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173/2*w + 233]', '[821, 821, 19/2*w^3 - 63/2*w^2 - 135/2*w + 173]', '[829, 829, -7/2*w^3 + 27/2*w^2 + 43/2*w - 79]', '[829, 829, 10*w^3 - 34*w^2 - 67*w + 179]', '[829, 829, -3/2*w^3 + 1/2*w^2 + 27/2*w + 9]', '[829, 829, 5/2*w^3 - 13/2*w^2 - 41/2*w + 31]', '[839, 839, -3/2*w^3 + 11/2*w^2 + 25/2*w - 26]', '[839, 839, 2*w^3 - 7*w^2 - 16*w + 43]', '[841, 29, 5/2*w^3 - 15/2*w^2 - 35/2*w + 39]', '[881, 881, -8*w^3 + 27*w^2 + 56*w - 151]', '[881, 881, -w^3 + 3*w^2 + 4*w - 21]', '[911, 911, 5/2*w^3 - 19/2*w^2 - 33/2*w + 51]', '[911, 911, 2*w^3 - 8*w^2 - 13*w + 47]', '[919, 919, 3/2*w^3 - 9/2*w^2 - 27/2*w + 29]', '[919, 919, -3*w - 5]', '[919, 919, 1/2*w^3 - 7/2*w^2 - 5/2*w + 17]', '[919, 919, -4*w^3 + 14*w^2 + 27*w - 81]', '[929, 929, 7/2*w^3 - 23/2*w^2 - 49/2*w + 58]', '[929, 929, 13*w^3 - 44*w^2 - 89*w + 237]', '[929, 929, 9/2*w^3 - 29/2*w^2 - 59/2*w + 78]', '[929, 929, -w^3 + 2*w^2 + 7*w - 5]', '[941, 941, 5/2*w^3 - 19/2*w^2 - 31/2*w + 59]', '[941, 941, -3/2*w^3 + 13/2*w^2 + 17/2*w - 31]', '[941, 941, w^3 - 3*w^2 - 10*w + 7]', '[941, 941, -8*w^3 + 27*w^2 + 56*w - 147]', '[971, 971, -9/2*w^3 + 29/2*w^2 + 73/2*w - 92]', '[971, 971, -1/2*w^3 + 5/2*w^2 + 17/2*w - 1]', '[991, 991, w^3 - 4*w^2 - 3*w + 15]', '[991, 991, -1/2*w^3 + 1/2*w^2 + 15/2*w + 6]', '[1019, 1019, 3*w^3 - 9*w^2 - 19*w + 45]', '[1019, 1019, 3*w^3 - 11*w^2 - 20*w + 53]', '[1019, 1019, -1/2*w^3 + 1/2*w^2 + 17/2*w + 9]', '[1019, 1019, -1/2*w^3 + 5/2*w^2 - 3/2*w - 4]', '[1021, 1021, -3/2*w^3 + 13/2*w^2 + 19/2*w - 37]', '[1021, 1021, 3*w^3 - 11*w^2 - 20*w + 61]', '[1049, 1049, w^3 - 4*w^2 - 9*w + 15]', '[1049, 1049, 5/2*w^3 - 17/2*w^2 - 39/2*w + 54]', '[1051, 1051, 3/2*w^3 - 11/2*w^2 - 15/2*w + 21]', '[1051, 1051, -1/2*w^3 + 7/2*w^2 + 7/2*w - 23]', '[1051, 1051, 9/2*w^3 - 31/2*w^2 - 63/2*w + 83]', '[1051, 1051, -1/2*w^3 + 1/2*w^2 + 13/2*w + 8]', '[1061, 1061, 2*w^3 - 5*w^2 - 14*w + 19]', '[1061, 1061, 9/2*w^3 - 29/2*w^2 - 63/2*w + 72]', '[1091, 1091, 3/2*w^3 - 5/2*w^2 - 21/2*w + 10]', '[1091, 1091, 3/2*w^3 - 3/2*w^2 - 19/2*w + 7]', '[1091, 1091, -13/2*w^3 + 43/2*w^2 + 91/2*w - 116]', '[1091, 1091, 19/2*w^3 - 63/2*w^2 - 135/2*w + 174]', '[1109, 1109, -5/2*w^3 + 17/2*w^2 + 33/2*w - 53]', '[1109, 1109, 4*w^3 - 13*w^2 - 26*w + 67]', '[1109, 1109, -3/2*w^3 + 11/2*w^2 + 23/2*w - 25]', '[1109, 1109, 4*w^3 - 13*w^2 - 28*w + 65]', '[1171, 1171, 1/2*w^3 - 1/2*w^2 + 3/2*w + 12]', '[1171, 1171, 11/2*w^3 - 35/2*w^2 - 87/2*w + 105]', '[1181, 1181, 2*w^3 - 8*w^2 - 13*w + 45]', '[1181, 1181, -5/2*w^3 + 19/2*w^2 + 33/2*w - 53]', '[1201, 1201, -5/2*w^3 + 15/2*w^2 + 39/2*w - 45]', '[1201, 1201, -1/2*w^3 + 3/2*w^2 + 13/2*w - 3]', '[1201, 1201, -w^3 + 3*w^2 + 10*w - 21]', '[1201, 1201, 3/2*w^3 - 9/2*w^2 - 17/2*w + 29]', '[1229, 1229, -5*w^3 + 17*w^2 + 35*w - 91]', '[1229, 1229, 3/2*w^3 - 9/2*w^2 - 25/2*w + 17]', '[1249, 1249, 5/2*w^3 - 17/2*w^2 - 35/2*w + 40]', '[1249, 1249, 3/2*w^3 - 3/2*w^2 - 21/2*w + 4]', '[1249, 1249, w^2 - 13]', '[1249, 1249, 9*w^3 - 30*w^2 - 63*w + 163]', '[1289, 1289, 3/2*w^3 - 1/2*w^2 - 23/2*w - 3]', '[1289, 1289, 11*w^3 - 37*w^2 - 76*w + 201]', '[1291, 1291, -1/2*w^3 - 7/2*w^2 + 13/2*w + 29]', '[1291, 1291, 23/2*w^3 - 79/2*w^2 - 155/2*w + 212]', '[1301, 1301, 11*w^3 - 38*w^2 - 73*w + 201]', '[1301, 1301, 1/2*w^3 - 5/2*w^2 - 17/2*w + 3]', '[1319, 1319, 12*w^3 - 40*w^2 - 85*w + 219]', '[1319, 1319, 3/2*w^3 - 1/2*w^2 - 19/2*w - 1]', '[1321, 1321, -1/2*w^3 - 1/2*w^2 - 1/2*w - 7]', '[1321, 1321, -3*w^3 + 11*w^2 + 15*w - 45]', '[1361, 1361, -3*w^3 + 11*w^2 + 21*w - 57]', '[1361, 1361, 5/2*w^3 - 15/2*w^2 - 39/2*w + 35]', '[1381, 1381, -3*w^3 + 9*w^2 + 23*w - 43]', '[1381, 1381, 2*w^3 - 6*w^2 - 12*w + 27]', '[1381, 1381, -1/2*w^3 + 3/2*w^2 + 9/2*w - 1]', '[1381, 1381, w - 7]', '[1399, 1399, 9/2*w^3 - 33/2*w^2 - 57/2*w + 85]', '[1399, 1399, -5/2*w^3 + 15/2*w^2 + 41/2*w - 37]', '[1409, 1409, 3/2*w^3 - 1/2*w^2 - 21/2*w - 1]', '[1409, 1409, -23/2*w^3 + 77/2*w^2 + 161/2*w - 211]', '[1409, 1409, 11/2*w^3 - 39/2*w^2 - 71/2*w + 98]', '[1409, 1409, 1/2*w^3 - 9/2*w^2 - 1/2*w + 37]', '[1429, 1429, 3/2*w^3 - 5/2*w^2 - 33/2*w - 5]', '[1429, 1429, 7/2*w^3 - 25/2*w^2 - 37/2*w + 53]', '[1439, 1439, -7*w^3 + 23*w^2 + 52*w - 135]', '[1439, 1439, -1/2*w^3 - 1/2*w^2 + 1/2*w - 5]', '[1451, 1451, 1/2*w^3 + 3/2*w^2 - 13/2*w - 15]', '[1451, 1451, -13/2*w^3 + 45/2*w^2 + 85/2*w - 120]', '[1459, 1459, -7/2*w^3 + 27/2*w^2 + 43/2*w - 70]', '[1459, 1459, 5/2*w^3 - 21/2*w^2 - 29/2*w + 65]', '[1471, 1471, 5/2*w^3 - 17/2*w^2 - 37/2*w + 43]', '[1471, 1471, -3*w^3 + 10*w^2 + 21*w - 49]', '[1481, 1481, -6*w^3 + 21*w^2 + 40*w - 113]', '[1481, 1481, -16*w^3 + 54*w^2 + 112*w - 299]', '[1481, 1481, 9*w^3 - 30*w^2 - 63*w + 161]', '[1481, 1481, 1/2*w^3 - 9/2*w^2 - 3/2*w + 30]', '[1489, 1489, -8*w^3 + 26*w^2 + 60*w - 151]', '[1489, 1489, -w^3 + 5*w^2 + 6*w - 35]', '[1489, 1489, 7/2*w^3 - 25/2*w^2 - 47/2*w + 63]', '[1489, 1489, -w^3 + w^2 + 3*w - 13]', '[1499, 1499, 3*w^3 - 10*w^2 - 21*w + 45]', '[1499, 1499, 9/2*w^3 - 29/2*w^2 - 65/2*w + 75]', '[1511, 1511, -11/2*w^3 + 35/2*w^2 + 79/2*w - 91]', '[1511, 1511, -5/2*w^3 + 21/2*w^2 + 33/2*w - 54]', '[1511, 1511, 7/2*w^3 - 19/2*w^2 - 57/2*w + 42]', '[1511, 1511, 5/2*w^3 - 15/2*w^2 - 29/2*w + 41]', '[1531, 1531, -4*w^2 + 2*w + 29]', '[1531, 1531, 9*w^3 - 31*w^2 - 61*w + 167]', '[1549, 1549, -1/2*w^3 + 1/2*w^2 + 13/2*w - 5]', '[1549, 1549, -3/2*w^3 + 11/2*w^2 + 15/2*w - 34]', '[1559, 1559, 9/2*w^3 - 29/2*w^2 - 63/2*w + 76]', '[1559, 1559, 2*w^3 - 5*w^2 - 14*w + 23]', '[1571, 1571, 3*w^3 - 9*w^2 - 20*w + 43]', '[1571, 1571, 2*w^3 - 7*w^2 - 14*w + 45]', '[1601, 1601, -27/2*w^3 + 93/2*w^2 + 179/2*w - 247]', '[1601, 1601, 1/2*w^3 - 1/2*w^2 + 5/2*w + 16]', '[1609, 1609, -1/2*w^3 + 7/2*w^2 + 1/2*w - 31]', '[1609, 1609, 3/2*w^3 - 7/2*w^2 - 23/2*w + 25]', '[1621, 1621, 7/2*w^3 - 25/2*w^2 - 45/2*w + 71]', '[1621, 1621, -1/2*w^3 + 7/2*w^2 + 3/2*w - 19]', '[1681, 41, -3*w^3 + 9*w^2 + 21*w - 43]', '[1681, 41, 3*w^3 - 9*w^2 - 21*w + 47]', '[1721, 1721, -1/2*w^3 - 3/2*w^2 + 21/2*w + 25]', '[1721, 1721, -9/2*w^3 + 33/2*w^2 + 49/2*w - 78]', '[1759, 1759, 4*w^3 - 14*w^2 - 25*w + 75]', '[1759, 1759, 2*w^3 - 7*w^2 - 12*w + 43]', '[1831, 1831, -3/2*w^3 + 7/2*w^2 + 29/2*w - 6]', '[1831, 1831, 15/2*w^3 - 51/2*w^2 - 103/2*w + 136]', '[1849, 43, -1/2*w^3 + 7/2*w^2 - 3/2*w - 31]', '[1849, 43, 15/2*w^3 - 51/2*w^2 - 101/2*w + 138]', '[1871, 1871, 3*w^3 - 9*w^2 - 18*w + 43]', '[1871, 1871, -7/2*w^3 + 21/2*w^2 + 45/2*w - 51]', '[1879, 1879, 21/2*w^3 - 71/2*w^2 - 145/2*w + 195]', '[1879, 1879, -w^3 - w^2 + 8*w + 9]', '[1889, 1889, 2*w^3 - 4*w^2 - 16*w + 15]', '[1889, 1889, -6*w^3 + 20*w^2 + 40*w - 105]', '[1901, 1901, 2*w^2 - 7*w - 29]', '[1901, 1901, -19/2*w^3 + 65/2*w^2 + 133/2*w - 182]', '[1901, 1901, 1/2*w^3 - 11/2*w^2 - 7/2*w + 30]', '[1901, 1901, -1/2*w^3 + 5/2*w^2 + 1/2*w - 24]', '[1931, 1931, -1/2*w^3 + 9/2*w^2 + 3/2*w - 34]', '[1931, 1931, -5/2*w^3 + 19/2*w^2 + 35/2*w - 59]', '[1931, 1931, -5/2*w^3 + 19/2*w^2 + 35/2*w - 47]', '[1931, 1931, 6*w^3 - 21*w^2 - 40*w + 109]', '[1949, 1949, -3/2*w^3 + 15/2*w^2 + 19/2*w - 46]', '[1949, 1949, -11/2*w^3 + 39/2*w^2 + 75/2*w - 105]', '[1979, 1979, -7/2*w^3 + 21/2*w^2 + 55/2*w - 51]', '[1979, 1979, 3/2*w^3 - 5/2*w^2 - 29/2*w + 7]', '[1979, 1979, 9/2*w^3 - 31/2*w^2 - 55/2*w + 81]', '[1979, 1979, -2*w^3 + 6*w^2 + 11*w - 27]']}
• 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': [44, 2, -15, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 19225, 'disc_rad': 3845, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[2, 2]]], [5, [0]], [7, [[4, 1]]], [11, [[2, 1], [1, 2]]], [13, [[4, 1]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[4, 1]]], [29, [[2, 1], [1, 2]]], [31, [[1, 4]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[4, 1]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 62.00806399170998, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.19225.1', 'local_algs': ['5.4.2.1', 'm769.1.2.0', 'm769.2.1.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 769], 'rd': 11.7751537671, 'regulator': {'__RealLiteral__': 0, 'data': '8.07845723656', 'prec': 44}, 'res': {'gal': ['-36,366,-335,-806,712,126,-62,-2,1'], 'sib': ['18,29,-28,-2,1', '-36,366,-335,-806,712,126,-62,-2,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{3} - \\frac{3}{2} a^{2} - \\frac{7}{2} a + 8 \\)', '\\( a^{3} - 3 a^{2} - 6 a + 15 \\)', '\\( \\frac{1}{2} a^{3} + \\frac{1}{2} a^{2} - \\frac{11}{2} a - 9 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2 - 1/2*a']}