Hilbert modular form data - 4.4.18432.1-14.3-e

Formats: - HTML - YAML - JSON - 2024-05-02T08:22:47.447927

• 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': 6, 'disc': 18432, 'field_bad_primes': [2, 3], 'field_label': '4.4.18432.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.18432.1-14.3-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [2, 7], 'level_ideal': '[14,14,1/3*w^3 - 3*w + 2]', 'level_label': '14.3', 'level_norm': 14, 'parallel_weight': 2, 'short_label': '14.3-e', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2,2,1/3*w^2 + w]', 1], ['[7,7,1/3*w^3 + 1/3*w^2 - 3*w - 3]', -1]], 'hecke_eigenvalues': [-1, 1, 'e', '1/10*e^5 + 7/20*e^4 - 29/20*e^3 - 103/20*e^2 - 19/20*e + 53/10', '1/5*e^5 + 9/20*e^4 - 73/20*e^3 - 121/20*e^2 + 147/20*e + 61/10', '-1/5*e^5 - 9/20*e^4 + 73/20*e^3 + 121/20*e^2 - 147/20*e - 81/10', '1/20*e^5 + 1/20*e^4 - 17/20*e^3 + 1/20*e^2 - 21/10*e - 28/5', '3/20*e^5 + 2/5*e^4 - 14/5*e^3 - 61/10*e^2 + 149/20*e + 87/10', '1/10*e^5 + 7/20*e^4 - 39/20*e^3 - 103/20*e^2 + 131/20*e + 53/10', '3/20*e^5 + 2/5*e^4 - 14/5*e^3 - 61/10*e^2 + 149/20*e + 87/10', '-1/5*e^5 - 7/10*e^4 + 17/5*e^3 + 103/10*e^2 - 33/5*e - 58/5', '9/20*e^5 + 6/5*e^4 - 79/10*e^3 - 163/10*e^2 + 257/20*e + 151/10', '3/20*e^5 + 3/20*e^4 - 51/20*e^3 + 3/20*e^2 + 27/10*e - 54/5', '-13/20*e^5 - 33/20*e^4 + 231/20*e^3 + 447/20*e^2 - 106/5*e - 141/5', '2/5*e^5 + 7/5*e^4 - 34/5*e^3 - 103/5*e^2 + 46/5*e + 76/5', '-7/10*e^5 - 39/20*e^4 + 233/20*e^3 + 531/20*e^2 - 217/20*e - 221/10', '-3/5*e^5 - 21/10*e^4 + 97/10*e^3 + 309/10*e^2 - 83/10*e - 179/5', '-19/20*e^5 - 59/20*e^4 + 313/20*e^3 + 821/20*e^2 - 88/5*e - 183/5', '-11/10*e^5 - 67/20*e^4 + 369/20*e^3 + 963/20*e^2 - 461/20*e - 523/10', '-9/20*e^5 - 29/20*e^4 + 143/20*e^3 + 411/20*e^2 - 28/5*e - 93/5', '-1/20*e^5 - 1/20*e^4 + 17/20*e^3 + 19/20*e^2 + 21/10*e - 12/5', '13/20*e^5 + 43/20*e^4 - 211/20*e^3 - 617/20*e^2 + 61/5*e + 161/5', '3/10*e^5 + 21/20*e^4 - 97/20*e^3 - 309/20*e^2 + 53/20*e + 159/10', '-2/5*e^5 - 9/10*e^4 + 39/5*e^3 + 121/10*e^2 - 111/5*e - 76/5', '-2/5*e^5 - 9/10*e^4 + 34/5*e^3 + 111/10*e^2 - 31/5*e - 26/5', '11/20*e^5 + 13/10*e^4 - 101/10*e^3 - 91/5*e^2 + 403/20*e + 209/10', '11/10*e^5 + 18/5*e^4 - 91/5*e^3 - 267/5*e^2 + 203/10*e + 289/5', '-e^5 - 3*e^4 + 16*e^3 + 42*e^2 - 10*e - 46', '-3/5*e^5 - 11/10*e^4 + 56/5*e^3 + 139/10*e^2 - 119/5*e - 64/5', '9/20*e^5 + 29/20*e^4 - 143/20*e^3 - 411/20*e^2 + 3/5*e + 93/5', '19/20*e^5 + 27/10*e^4 - 82/5*e^3 - 194/5*e^2 + 457/20*e + 431/10', '9/20*e^5 + 19/20*e^4 - 163/20*e^3 - 241/20*e^2 + 83/5*e + 33/5', '7/5*e^5 + 39/10*e^4 - 119/5*e^3 - 541/10*e^2 + 146/5*e + 286/5', '-29/20*e^5 - 89/20*e^4 + 503/20*e^3 + 1291/20*e^2 - 213/5*e - 393/5', '6/5*e^5 + 69/20*e^4 - 413/20*e^3 - 1001/20*e^2 + 527/20*e + 631/10', '1/10*e^5 + 3/5*e^4 - 17/10*e^3 - 52/5*e^2 + 34/5*e + 114/5', '3/10*e^5 + 11/20*e^4 - 127/20*e^3 - 139/20*e^2 + 443/20*e + 109/10', '13/20*e^5 + 7/5*e^4 - 113/10*e^3 - 161/10*e^2 + 309/20*e + 17/10', '-6/5*e^5 - 37/10*e^4 + 97/5*e^3 + 513/10*e^2 - 88/5*e - 218/5', '1/4*e^5 + 1/2*e^4 - 11/2*e^3 - 8*e^2 + 81/4*e + 37/2', '-11/20*e^5 - 23/10*e^4 + 81/10*e^3 + 176/5*e^2 + 57/20*e - 359/10', '1/20*e^5 + 1/20*e^4 - 17/20*e^3 + 21/20*e^2 + 19/10*e - 58/5', '9/20*e^5 + 17/10*e^4 - 37/5*e^3 - 134/5*e^2 + 207/20*e + 381/10', '-11/20*e^5 - 41/20*e^4 + 167/20*e^3 + 619/20*e^2 - 9/10*e - 202/5', '2/5*e^5 + 7/5*e^4 - 63/10*e^3 - 103/5*e^2 + 37/10*e + 101/5', '-7/10*e^5 - 39/20*e^4 + 233/20*e^3 + 531/20*e^2 - 217/20*e - 241/10', '-3/10*e^5 - 21/20*e^4 + 107/20*e^3 + 349/20*e^2 - 203/20*e - 319/10', '2/5*e^5 + 9/10*e^4 - 39/5*e^3 - 121/10*e^2 + 126/5*e + 36/5', '-19/20*e^5 - 59/20*e^4 + 323/20*e^3 + 821/20*e^2 - 221/10*e - 178/5', '-1/5*e^5 + 3/10*e^4 + 49/10*e^3 - 67/10*e^2 - 201/10*e + 17/5', '3/20*e^5 + 3/20*e^4 - 61/20*e^3 - 17/20*e^2 + 41/5*e + 1/5', '-9/10*e^5 - 63/20*e^4 + 291/20*e^3 + 947/20*e^2 - 299/20*e - 567/10', '4/5*e^5 + 61/20*e^4 - 247/20*e^3 - 889/20*e^2 + 93/20*e + 479/10', '-1/4*e^5 - e^4 + 9/2*e^3 + 31/2*e^2 - 45/4*e - 55/2', '-7/5*e^5 - 73/20*e^4 + 481/20*e^3 + 997/20*e^2 - 639/20*e - 467/10', '11/20*e^5 + 41/20*e^4 - 177/20*e^3 - 619/20*e^2 + 32/5*e + 187/5', '-17/20*e^5 - 57/20*e^4 + 289/20*e^3 + 843/20*e^2 - 203/10*e - 184/5', '8/5*e^5 + 23/5*e^4 - 267/10*e^3 - 327/5*e^2 + 263/10*e + 339/5', '-17/20*e^5 - 57/20*e^4 + 279/20*e^3 + 823/20*e^2 - 89/5*e - 209/5', '8/5*e^5 + 23/5*e^4 - 136/5*e^3 - 327/5*e^2 + 189/5*e + 364/5', '17/20*e^5 + 21/10*e^4 - 76/5*e^3 - 147/5*e^2 + 611/20*e + 363/10', '-11/20*e^5 - 13/10*e^4 + 53/5*e^3 + 96/5*e^2 - 533/20*e - 289/10', '-e^5 - 11/4*e^4 + 71/4*e^3 + 159/4*e^2 - 109/4*e - 103/2', '-33/20*e^5 - 93/20*e^4 + 561/20*e^3 + 1287/20*e^2 - 327/10*e - 306/5', '-23/20*e^5 - 17/5*e^4 + 99/5*e^3 + 491/10*e^2 - 689/20*e - 607/10', '-19/20*e^5 - 49/20*e^4 + 323/20*e^3 + 631/20*e^2 - 231/10*e - 98/5', '-1/10*e^5 - 7/20*e^4 + 29/20*e^3 + 103/20*e^2 - 21/20*e - 83/10', '-29/20*e^5 - 79/20*e^4 + 503/20*e^3 + 1101/20*e^2 - 188/5*e - 293/5', '49/20*e^5 + 149/20*e^4 - 813/20*e^3 - 2091/20*e^2 + 431/10*e + 518/5', '-21/20*e^5 - 14/5*e^4 + 191/10*e^3 + 387/10*e^2 - 773/20*e - 429/10', '-41/20*e^5 - 121/20*e^4 + 697/20*e^3 + 1699/20*e^2 - 459/10*e - 392/5', '-13/20*e^5 - 19/10*e^4 + 54/5*e^3 + 133/5*e^2 - 299/20*e - 447/10', '11/4*e^5 + 31/4*e^4 - 189/4*e^3 - 437/4*e^2 + 67*e + 121', '-5/4*e^5 - 7/2*e^4 + 43/2*e^3 + 48*e^2 - 117/4*e - 89/2', '33/20*e^5 + 27/5*e^4 - 139/5*e^3 - 801/10*e^2 + 699/20*e + 817/10', '-3/20*e^5 - 9/10*e^4 + 23/10*e^3 + 78/5*e^2 + 21/20*e - 227/10', '3/5*e^5 + 37/20*e^4 - 209/20*e^3 - 533/20*e^2 + 331/20*e + 263/10', '-9/10*e^5 - 7/5*e^4 + 173/10*e^3 + 78/5*e^2 - 236/5*e - 56/5', '23/20*e^5 + 39/10*e^4 - 193/10*e^3 - 288/5*e^2 + 579/20*e + 657/10', '-11/20*e^5 - 13/10*e^4 + 91/10*e^3 + 76/5*e^2 - 103/20*e + 61/10', '-9/10*e^5 - 29/10*e^4 + 74/5*e^3 + 411/10*e^2 - 207/10*e - 231/5', '19/20*e^5 + 16/5*e^4 - 77/5*e^3 - 443/10*e^2 + 257/20*e + 281/10', '-6/5*e^5 - 27/10*e^4 + 209/10*e^3 + 313/10*e^2 - 291/10*e - 23/5', '4/5*e^5 + 51/20*e^4 - 257/20*e^3 - 759/20*e^2 + 143/20*e + 409/10', '1/4*e^4 + 5/4*e^3 - 9/4*e^2 - 67/4*e - 9/2', '-9/20*e^5 - 39/20*e^4 + 113/20*e^3 + 581/20*e^2 + 169/10*e - 188/5', '33/20*e^5 + 22/5*e^4 - 293/10*e^3 - 601/10*e^2 + 1009/20*e + 627/10', '1/4*e^5 - 1/4*e^4 - 25/4*e^3 + 27/4*e^2 + 59/2*e - 6', '3/5*e^5 + 11/10*e^4 - 107/10*e^3 - 109/10*e^2 + 223/10*e - 1/5', '-41/20*e^5 - 53/10*e^4 + 361/10*e^3 + 371/5*e^2 - 1253/20*e - 889/10', '3/5*e^5 + 11/10*e^4 - 56/5*e^3 - 119/10*e^2 + 84/5*e - 6/5', '-3/5*e^5 - 21/10*e^4 + 51/5*e^3 + 329/10*e^2 - 49/5*e - 244/5', '7/4*e^5 + 21/4*e^4 - 117/4*e^3 - 303/4*e^2 + 37*e + 91', '1/5*e^5 + 9/20*e^4 - 83/20*e^3 - 141/20*e^2 + 177/20*e + 31/10', '-7/4*e^5 - 21/4*e^4 + 119/4*e^3 + 311/4*e^2 - 83/2*e - 96', '7/10*e^5 + 11/5*e^4 - 119/10*e^3 - 154/5*e^2 + 93/5*e + 8/5', '7/5*e^5 + 83/20*e^4 - 481/20*e^3 - 1227/20*e^2 + 679/20*e + 747/10', '3/20*e^5 + 33/20*e^4 - 11/20*e^3 - 507/20*e^2 - 183/10*e + 86/5', '-3/20*e^5 - 23/20*e^4 + 41/20*e^3 + 377/20*e^2 - 6/5*e - 191/5', '-21/10*e^5 - 28/5*e^4 + 377/10*e^3 + 402/5*e^2 - 349/5*e - 514/5', '9/5*e^5 + 91/20*e^4 - 617/20*e^3 - 1199/20*e^2 + 783/20*e + 479/10', '-13/10*e^5 - 14/5*e^4 + 231/10*e^3 + 181/5*e^2 - 187/5*e - 152/5', '31/20*e^5 + 101/20*e^4 - 497/20*e^3 - 1399/20*e^2 + 107/5*e + 247/5', '43/20*e^5 + 123/20*e^4 - 741/20*e^3 - 1717/20*e^2 + 251/5*e + 431/5', '13/10*e^5 + 81/20*e^4 - 407/20*e^3 - 1109/20*e^2 + 123/20*e + 659/10', '1/4*e^5 + e^4 - 9/2*e^3 - 35/2*e^2 + 57/4*e + 63/2', '3/5*e^5 + 13/5*e^4 - 77/10*e^3 - 197/5*e^2 - 147/10*e + 249/5', '5/4*e^5 + 7/2*e^4 - 20*e^3 - 48*e^2 + 47/4*e + 91/2', '-7/4*e^5 - 11/2*e^4 + 59/2*e^3 + 80*e^2 - 163/4*e - 205/2', '13/10*e^5 + 19/5*e^4 - 221/10*e^3 - 276/5*e^2 + 127/5*e + 362/5', '31/10*e^5 + 91/10*e^4 - 517/10*e^3 - 1289/10*e^2 + 254/5*e + 624/5', '4/5*e^5 + 41/20*e^4 - 277/20*e^3 - 549/20*e^2 + 403/20*e + 459/10', '-7/10*e^5 - 27/10*e^4 + 109/10*e^3 + 393/10*e^2 - 18/5*e - 198/5', '3/20*e^5 + 13/20*e^4 - 61/20*e^3 - 127/20*e^2 + 86/5*e - 99/5', '-e^5 - 3*e^4 + 31/2*e^3 + 40*e^2 - 11/2*e - 23', '-57/20*e^5 - 157/20*e^4 + 979/20*e^3 + 2143/20*e^2 - 324/5*e - 499/5', '-4/5*e^5 - 14/5*e^4 + 68/5*e^3 + 201/5*e^2 - 112/5*e - 122/5', '-7/4*e^5 - 19/4*e^4 + 121/4*e^3 + 273/4*e^2 - 41*e - 89', '-23/10*e^5 - 63/10*e^4 + 381/10*e^3 + 857/10*e^2 - 177/5*e - 342/5', '11/20*e^5 + 23/10*e^4 - 91/10*e^3 - 181/5*e^2 + 383/20*e + 559/10', '-23/10*e^5 - 131/20*e^4 + 797/20*e^3 + 1879/20*e^2 - 1193/20*e - 989/10', '41/20*e^5 + 141/20*e^4 - 657/20*e^3 - 2099/20*e^2 + 269/10*e + 522/5', '13/20*e^5 + 33/20*e^4 - 251/20*e^3 - 487/20*e^2 + 206/5*e + 161/5', 'e^5 + 7/4*e^4 - 73/4*e^3 - 75/4*e^2 + 111/4*e - 29/2', '-11/20*e^5 - 1/20*e^4 + 237/20*e^3 - 81/20*e^2 - 207/5*e + 13/5', '13/20*e^5 + 53/20*e^4 - 171/20*e^3 - 767/20*e^2 - 64/5*e + 111/5', '29/20*e^5 + 37/10*e^4 - 122/5*e^3 - 239/5*e^2 + 407/20*e + 151/10', '29/20*e^5 + 21/5*e^4 - 127/5*e^3 - 583/10*e^2 + 967/20*e + 651/10', '33/20*e^5 + 83/20*e^4 - 571/20*e^3 - 1097/20*e^2 + 176/5*e + 121/5', '1/4*e^5 + e^4 - 7/2*e^3 - 23/2*e^2 + 21/4*e - 31/2', '3/20*e^5 + 3/20*e^4 - 61/20*e^3 - 17/20*e^2 - 4/5*e - 59/5', '3*e^5 + 9*e^4 - 103/2*e^3 - 129*e^2 + 149/2*e + 151', '-13/10*e^5 - 81/20*e^4 + 427/20*e^3 + 1189/20*e^2 - 363/20*e - 469/10', '-1/5*e^5 - 7/10*e^4 + 12/5*e^3 + 113/10*e^2 + 32/5*e - 88/5', '3/2*e^5 + 21/4*e^4 - 93/4*e^3 - 301/4*e^2 + 13/4*e + 123/2', '41/20*e^5 + 63/10*e^4 - 168/5*e^3 - 441/5*e^2 + 563/20*e + 889/10', '-2/5*e^5 + 1/10*e^4 + 73/10*e^3 - 69/10*e^2 - 57/10*e + 189/5', '-11/20*e^5 - 31/20*e^4 + 157/20*e^3 + 469/20*e^2 + 53/5*e - 227/5', '1/2*e^5 + 2*e^4 - 8*e^3 - 28*e^2 + 31/2*e + 15', '23/20*e^5 + 39/10*e^4 - 84/5*e^3 - 278/5*e^2 - 291/20*e + 527/10', '7/10*e^5 + 29/20*e^4 - 273/20*e^3 - 381/20*e^2 + 717/20*e + 91/10', '-7/20*e^5 - 8/5*e^4 + 47/10*e^3 + 259/10*e^2 + 89/20*e - 503/10', '9/10*e^5 + 29/10*e^4 - 74/5*e^3 - 391/10*e^2 + 207/10*e + 71/5', '9/10*e^5 + 17/5*e^4 - 69/5*e^3 - 258/5*e^2 + 67/10*e + 211/5', '-21/10*e^5 - 117/20*e^4 + 729/20*e^3 + 1633/20*e^2 - 1061/20*e - 723/10', '9/20*e^5 + 6/5*e^4 - 32/5*e^3 - 133/10*e^2 - 73/20*e - 169/10', '11/10*e^5 + 57/20*e^4 - 369/20*e^3 - 813/20*e^2 + 281/20*e + 563/10', '-1/20*e^5 - 3/10*e^4 + 1/10*e^3 + 41/5*e^2 + 187/20*e - 419/10', '51/20*e^5 + 141/20*e^4 - 847/20*e^3 - 1899/20*e^2 + 429/10*e + 412/5', '14/5*e^5 + 171/20*e^4 - 957/20*e^3 - 2499/20*e^2 + 1423/20*e + 1479/10', '-12/5*e^5 - 143/20*e^4 + 831/20*e^3 + 2087/20*e^2 - 1229/20*e - 1327/10', '23/10*e^5 + 29/5*e^4 - 401/10*e^3 - 406/5*e^2 + 297/5*e + 432/5', '-13/20*e^5 - 17/5*e^4 + 83/10*e^3 + 511/10*e^2 + 251/20*e - 467/10', '-51/20*e^5 - 73/10*e^4 + 451/10*e^3 + 536/5*e^2 - 1763/20*e - 1459/10', '3/20*e^5 + 19/10*e^4 + 7/10*e^3 - 158/5*e^2 - 701/20*e + 367/10', '8/5*e^5 + 87/20*e^4 - 539/20*e^3 - 1223/20*e^2 + 541/20*e + 503/10', '-11/20*e^5 - 31/20*e^4 + 177/20*e^3 + 409/20*e^2 + 3/5*e - 77/5', '11/20*e^5 + 51/20*e^4 - 167/20*e^3 - 769/20*e^2 + 9/10*e + 152/5', 'e^5 + 9/4*e^4 - 79/4*e^3 - 121/4*e^2 + 209/4*e + 43/2', '3/4*e^5 + 3*e^4 - 11*e^3 - 87/2*e^2 + 1/4*e + 103/2', '37/20*e^5 + 97/20*e^4 - 679/20*e^3 - 1363/20*e^2 + 424/5*e + 419/5', '-9/10*e^5 - 33/20*e^4 + 351/20*e^3 + 437/20*e^2 - 799/20*e - 487/10', '-7/5*e^5 - 73/20*e^4 + 461/20*e^3 + 957/20*e^2 - 239/20*e - 327/10', '27/20*e^5 + 87/20*e^4 - 439/20*e^3 - 1233/20*e^2 + 153/10*e + 234/5', '43/20*e^5 + 123/20*e^4 - 761/20*e^3 - 1777/20*e^2 + 376/5*e + 491/5', '13/10*e^5 + 43/10*e^4 - 108/5*e^3 - 617/10*e^2 + 359/10*e + 257/5', '3/5*e^5 + 11/10*e^4 - 56/5*e^3 - 129/10*e^2 + 149/5*e + 4/5', '-1/5*e^5 - 6/5*e^4 + 17/5*e^3 + 119/5*e^2 - 83/5*e - 338/5', '23/10*e^5 + 141/20*e^4 - 777/20*e^3 - 1969/20*e^2 + 933/20*e + 769/10', '-39/10*e^5 - 52/5*e^4 + 663/10*e^3 + 703/5*e^2 - 426/5*e - 636/5', '-3/5*e^5 - 13/5*e^4 + 56/5*e^3 + 207/5*e^2 - 179/5*e - 394/5', '3/10*e^5 + 13/10*e^4 - 41/10*e^3 - 187/10*e^2 - 48/5*e + 12/5', '11/20*e^5 + 1/20*e^4 - 237/20*e^3 + 21/20*e^2 + 207/5*e + 147/5', '63/20*e^5 + 42/5*e^4 - 553/10*e^3 - 1191/10*e^2 + 1979/20*e + 1507/10', '1/20*e^5 - 6/5*e^4 - 41/10*e^3 + 193/10*e^2 + 673/20*e - 181/10', '8/5*e^5 + 23/5*e^4 - 257/10*e^3 - 332/5*e^2 + 103/10*e + 309/5', '91/20*e^5 + 64/5*e^4 - 781/10*e^3 - 1817/10*e^2 + 2103/20*e + 1949/10', '1/2*e^5 + 3*e^4 - 9/2*e^3 - 45*e^2 - 33*e + 32', '3/4*e^5 + 13/4*e^4 - 43/4*e^3 - 191/4*e^2 - 1/2*e + 64', '-1/2*e^5 - 3/4*e^4 + 41/4*e^3 + 43/4*e^2 - 117/4*e - 75/2', '17/20*e^5 + 11/10*e^4 - 167/10*e^3 - 52/5*e^2 + 641/20*e - 187/10', '1/4*e^4 - 5/4*e^3 - 37/4*e^2 + 71/4*e + 53/2', '-79/20*e^5 - 56/5*e^4 + 337/5*e^3 + 1573/10*e^2 - 1797/20*e - 1631/10', '71/20*e^5 + 201/20*e^4 - 1207/20*e^3 - 2799/20*e^2 + 689/10*e + 572/5', '17/5*e^5 + 99/10*e^4 - 294/5*e^3 - 1431/10*e^2 + 436/5*e + 876/5', '-17/20*e^5 - 31/10*e^4 + 117/10*e^3 + 237/5*e^2 + 499/20*e - 503/10', '-57/20*e^5 - 157/20*e^4 + 959/20*e^3 + 2163/20*e^2 - 324/5*e - 579/5', '9/5*e^5 + 43/10*e^4 - 163/5*e^3 - 567/10*e^2 + 317/5*e + 232/5', '1/20*e^5 + 1/20*e^4 - 7/20*e^3 - 39/20*e^2 - 68/5*e - 43/5', '8/5*e^5 + 31/10*e^4 - 146/5*e^3 - 379/10*e^2 + 309/5*e + 194/5', '-3/20*e^5 - 3/20*e^4 + 51/20*e^3 - 23/20*e^2 - 17/10*e + 174/5', '1/20*e^5 + 11/20*e^4 - 27/20*e^3 - 269/20*e^2 + 2/5*e + 267/5', '-31/20*e^5 - 24/5*e^4 + 128/5*e^3 + 677/10*e^2 - 453/20*e - 889/10', '-19/20*e^5 - 11/5*e^4 + 87/5*e^3 + 303/10*e^2 - 837/20*e - 171/10', '3/2*e^5 + 19/4*e^4 - 97/4*e^3 - 263/4*e^2 + 61/4*e + 77/2', '-71/20*e^5 - 201/20*e^4 + 1237/20*e^3 + 2879/20*e^2 - 507/5*e - 827/5', '9/4*e^5 + 6*e^4 - 79/2*e^3 - 171/2*e^2 + 293/4*e + 241/2', '9/10*e^5 + 7/5*e^4 - 173/10*e^3 - 63/5*e^2 + 211/5*e - 124/5', '59/20*e^5 + 41/5*e^4 - 499/10*e^3 - 1153/10*e^2 + 1227/20*e + 1171/10', '-23/10*e^5 - 39/5*e^4 + 381/10*e^3 + 586/5*e^2 - 267/5*e - 732/5', '11/4*e^5 + 31/4*e^4 - 189/4*e^3 - 441/4*e^2 + 70*e + 129', '-31/10*e^5 - 101/10*e^4 + 517/10*e^3 + 1459/10*e^2 - 324/5*e - 704/5', '-1/2*e^5 - 5/4*e^4 + 31/4*e^3 + 61/4*e^2 + 29/4*e + 3/2', 'e^5 + 5/2*e^4 - 18*e^3 - 61/2*e^2 + 40*e - 6', '9/4*e^5 + 13/2*e^4 - 39*e^3 - 97*e^2 + 251/4*e + 289/2', '21/10*e^5 + 117/20*e^4 - 709/20*e^3 - 1673/20*e^2 + 941/20*e + 1283/10', '-6/5*e^5 - 89/20*e^4 + 393/20*e^3 + 1341/20*e^2 - 387/20*e - 671/10', '-39/20*e^5 - 89/20*e^4 + 693/20*e^3 + 1151/20*e^2 - 273/5*e - 283/5', '9/10*e^5 + 73/20*e^4 - 261/20*e^3 - 1037/20*e^2 - 31/20*e + 577/10', '3/2*e^5 + 19/4*e^4 - 97/4*e^3 - 259/4*e^2 + 117/4*e + 93/2', '-1/20*e^5 - 13/10*e^4 - 2/5*e^3 + 131/5*e^2 + 237/20*e - 619/10', '-14/5*e^5 - 39/5*e^4 + 248/5*e^3 + 561/5*e^2 - 412/5*e - 722/5', '-29/20*e^5 - 69/20*e^4 + 503/20*e^3 + 911/20*e^2 - 198/5*e - 223/5', '-29/20*e^5 - 47/10*e^4 + 112/5*e^3 + 329/5*e^2 - 67/20*e - 701/10', '1/5*e^5 + 17/10*e^4 - 9/10*e^3 - 293/10*e^2 - 219/10*e + 153/5', '83/20*e^5 + 253/20*e^4 - 1391/20*e^3 - 3607/20*e^2 + 867/10*e + 866/5', '-3/2*e^5 - 17/4*e^4 + 105/4*e^3 + 253/4*e^2 - 193/4*e - 177/2', '9/10*e^5 + 63/20*e^4 - 331/20*e^3 - 927/20*e^2 + 839/20*e + 397/10', '1/5*e^5 + 19/20*e^4 - 23/20*e^3 - 251/20*e^2 - 363/20*e - 189/10', '4/5*e^5 + 41/20*e^4 - 247/20*e^3 - 449/20*e^2 + 33/20*e - 31/10', '-1/2*e^5 - 3/2*e^4 + 7*e^3 + 43/2*e^2 + 37/2*e - 37', '1/10*e^5 + 37/20*e^4 + 41/20*e^3 - 633/20*e^2 - 1049/20*e + 223/10', '-7/20*e^5 - 21/10*e^4 + 47/10*e^3 + 172/5*e^2 + 189/20*e - 543/10', '-41/20*e^5 - 131/20*e^4 + 677/20*e^3 + 1909/20*e^2 - 409/10*e - 482/5', '-1/5*e^5 - 1/5*e^4 + 49/10*e^3 + 19/5*e^2 - 261/10*e - 23/5', '9/10*e^5 + 12/5*e^4 - 163/10*e^3 - 158/5*e^2 + 196/5*e + 86/5', '3/20*e^5 + 3/20*e^4 - 41/20*e^3 + 23/20*e^2 - 74/5*e - 219/5', '57/20*e^5 + 157/20*e^4 - 999/20*e^3 - 2263/20*e^2 + 374/5*e + 779/5', '-e^5 - 2*e^4 + 37/2*e^3 + 25*e^2 - 83/2*e - 49', '31/20*e^5 + 61/20*e^4 - 577/20*e^3 - 779/20*e^2 + 282/5*e + 107/5', '63/20*e^5 + 42/5*e^4 - 543/10*e^3 - 1151/10*e^2 + 1539/20*e + 1177/10', '-1/4*e^5 - 3/4*e^4 + 13/4*e^3 + 37/4*e^2 + 33/2*e - 10', '47/20*e^5 + 137/20*e^4 - 849/20*e^3 - 2023/20*e^2 + 444/5*e + 709/5', '8/5*e^5 + 18/5*e^4 - 141/5*e^3 - 212/5*e^2 + 179/5*e - 46/5', '-41/10*e^5 - 131/10*e^4 + 687/10*e^3 + 1929/10*e^2 - 454/5*e - 1074/5', '-11/20*e^5 - 14/5*e^4 + 48/5*e^3 + 497/10*e^2 - 493/20*e - 1079/10', '-13/10*e^5 - 71/20*e^4 + 467/20*e^3 + 1039/20*e^2 - 923/20*e - 579/10', '3/20*e^5 - 7/20*e^4 - 81/20*e^3 + 33/20*e^2 + 96/5*e + 241/5', '37/20*e^5 + 127/20*e^4 - 659/20*e^3 - 1913/20*e^2 + 369/5*e + 749/5', '-7/5*e^5 - 43/20*e^4 + 541/20*e^3 + 447/20*e^2 - 1539/20*e - 307/10', '23/10*e^5 + 34/5*e^4 - 371/10*e^3 - 461/5*e^2 + 172/5*e + 222/5', '-1/20*e^5 + 7/10*e^4 + 18/5*e^3 - 59/5*e^2 - 843/20*e + 291/10', '-3/4*e^5 - 11/4*e^4 + 45/4*e^3 + 149/4*e^2 + 4*e - 31', '13/20*e^5 + 53/20*e^4 - 201/20*e^3 - 767/20*e^2 - 3/10*e + 36/5', '-19/20*e^5 - 16/5*e^4 + 139/10*e^3 + 473/10*e^2 + 113/20*e - 641/10', '-63/20*e^5 - 42/5*e^4 + 279/5*e^3 + 1201/10*e^2 - 1829/20*e - 1637/10', '11/4*e^5 + 31/4*e^4 - 189/4*e^3 - 437/4*e^2 + 73*e + 97', '-81/20*e^5 - 251/20*e^4 + 1337/20*e^3 + 3529/20*e^2 - 739/10*e - 922/5', '3/5*e^5 + 13/5*e^4 - 41/5*e^3 - 187/5*e^2 - 66/5*e + 54/5', '13/10*e^5 + 19/5*e^4 - 113/5*e^3 - 266/5*e^2 + 489/10*e + 287/5', '-69/20*e^5 - 97/10*e^4 + 589/10*e^3 + 679/5*e^2 - 1617/20*e - 1581/10', '-5/2*e^5 - 15/2*e^4 + 42*e^3 + 215/2*e^2 - 105/2*e - 139', '-9/5*e^5 - 34/5*e^4 + 143/5*e^3 + 506/5*e^2 - 132/5*e - 492/5', '-37/20*e^5 - 28/5*e^4 + 161/5*e^3 + 789/10*e^2 - 1071/20*e - 663/10', '33/10*e^5 + 103/10*e^4 - 561/10*e^3 - 1497/10*e^2 + 417/5*e + 822/5', '33/10*e^5 + 44/5*e^4 - 561/10*e^3 - 616/5*e^2 + 307/5*e + 582/5', '33/20*e^5 + 49/10*e^4 - 283/10*e^3 - 358/5*e^2 + 1089/20*e + 957/10', '-1/4*e^5 + 1/4*e^4 + 27/4*e^3 - 39/4*e^2 - 34*e + 39', '-3/20*e^5 + 11/10*e^4 + 24/5*e^3 - 107/5*e^2 - 329/20*e + 453/10', '-37/20*e^5 - 87/20*e^4 + 699/20*e^3 + 1173/20*e^2 - 404/5*e - 359/5', '-63/20*e^5 - 183/20*e^4 + 1111/20*e^3 + 2637/20*e^2 - 927/10*e - 756/5', '3/2*e^4 + e^3 - 55/2*e^2 + 94', '57/20*e^5 + 38/5*e^4 - 241/5*e^3 - 1029/10*e^2 + 991/20*e + 853/10', '-63/20*e^5 - 193/20*e^4 + 1081/20*e^3 + 2767/20*e^2 - 456/5*e - 881/5', '51/10*e^5 + 68/5*e^4 - 897/10*e^3 - 957/5*e^2 + 769/5*e + 1194/5', '2*e^5 + 4*e^4 - 75/2*e^3 - 49*e^2 + 193/2*e + 47', '13/10*e^5 + 101/20*e^4 - 417/20*e^3 - 1609/20*e^2 + 373/20*e + 999/10', '-1/2*e^5 + 17/2*e^3 - 8*e^2 - 5*e + 60', '-3/10*e^5 - 3/10*e^4 + 51/10*e^3 + 37/10*e^2 - 17/5*e - 112/5', '-1/4*e^5 + 7*e^3 - 11/2*e^2 - 179/4*e + 53/2', '-61/20*e^5 - 44/5*e^4 + 263/5*e^3 + 1217/10*e^2 - 1683/20*e - 1199/10', '-3/20*e^5 - 9/10*e^4 - 7/10*e^3 + 48/5*e^2 + 661/20*e + 303/10', '-53/20*e^5 - 42/5*e^4 + 443/10*e^3 + 1181/10*e^2 - 1349/20*e - 947/10', '-12/5*e^5 - 32/5*e^4 + 219/5*e^3 + 458/5*e^2 - 501/5*e - 666/5', '-19/5*e^5 - 231/20*e^4 + 1267/20*e^3 + 3299/20*e^2 - 1713/20*e - 2009/10', '-19/10*e^5 - 39/10*e^4 + 353/10*e^3 + 481/10*e^2 - 326/5*e - 226/5', '7/20*e^5 + 57/20*e^4 - 69/20*e^3 - 963/20*e^2 - 91/5*e + 249/5', '6/5*e^5 + 49/20*e^4 - 413/20*e^3 - 601/20*e^2 + 447/20*e - 99/10', '17/20*e^5 + 27/20*e^4 - 349/20*e^3 - 453/20*e^2 + 503/10*e + 364/5', '3/20*e^5 + 33/20*e^4 - 1/20*e^3 - 447/20*e^2 - 79/5*e - 29/5', '77/20*e^5 + 207/20*e^4 - 1329/20*e^3 - 2893/20*e^2 + 1033/10*e + 804/5', '67/20*e^5 + 217/20*e^4 - 1159/20*e^3 - 3303/20*e^2 + 973/10*e + 1064/5', '-7/4*e^5 - 4*e^4 + 67/2*e^3 + 99/2*e^2 - 387/4*e - 89/2', '-49/10*e^5 - 149/10*e^4 + 414/5*e^3 + 2151/10*e^2 - 997/10*e - 1091/5', '29/20*e^5 + 47/10*e^4 - 219/10*e^3 - 339/5*e^2 - 163/20*e + 671/10', '-27/10*e^5 - 189/20*e^4 + 863/20*e^3 + 2841/20*e^2 - 587/20*e - 1391/10', '-23/10*e^5 - 141/20*e^4 + 767/20*e^3 + 2049/20*e^2 - 843/20*e - 1119/10', '-31/20*e^5 - 53/10*e^4 + 118/5*e^3 + 381/5*e^2 + 67/20*e - 659/10', '-21/20*e^5 - 13/10*e^4 + 221/10*e^3 + 76/5*e^2 - 1633/20*e - 339/10', '19/10*e^5 + 113/20*e^4 - 671/20*e^3 - 1757/20*e^2 + 1219/20*e + 1347/10', '-21/10*e^5 - 33/5*e^4 + 347/10*e^3 + 472/5*e^2 - 139/5*e - 564/5', '8/5*e^5 + 38/5*e^4 - 106/5*e^3 - 582/5*e^2 - 116/5*e + 594/5', '11/10*e^5 + 47/20*e^4 - 379/20*e^3 - 583/20*e^2 + 691/20*e + 393/10'], 'hecke_polynomial': 'x^6 + 4*x^5 - 14*x^4 - 60*x^3 - 19*x^2 + 72*x + 44', 'label': '4.4.18432.1-14.3-e'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 18432, 'ideals': ['[1, 1, 1]', '[2, 2, -1/3*w^3 - 1/3*w^2 + 3*w + 4]', '[4, 2, 1/3*w^2 - 2]', '[7, 7, 1/3*w^3 + 1/3*w^2 - 3*w - 3]', '[7, 7, -1/3*w^2 + w + 1]', '[7, 7, 1/3*w^2 + w - 1]', '[7, 7, 1/3*w^3 - 1/3*w^2 - 3*w + 3]', '[8, 2, -1/3*w^3 + 2/3*w^2 + 2*w - 2]', '[9, 3, w - 3]', '[14, 14, w + 2]', '[14, 14, 1/3*w^3 - 3*w - 2]', '[14, 14, -1/3*w^3 + 3*w - 2]', '[14, 14, w - 2]', '[16, 2, 2]', '[18, 6, 1/3*w^3 - 3*w]', '[28, 14, -1/3*w^3 - 1/3*w^2 + 4*w + 4]', '[28, 14, 1/3*w^3 - 1/3*w^2 - 2*w]', '[28, 14, 1/3*w^3 + 1/3*w^2 - 2*w]', '[28, 14, -1/3*w^3 + 1/3*w^2 + 4*w - 4]', '[32, 4, -2/3*w^3 - 2/3*w^2 + 6*w + 8]', '[36, 6, 1/3*w^3 - w^2 - 2*w + 6]', '[41, 41, 1/3*w^3 - 1/3*w^2 - 3*w + 1]', '[41, 41, -1/3*w^2 + w + 3]', '[41, 41, 1/3*w^2 + w - 3]', '[41, 41, -1/3*w^3 - 1/3*w^2 + 3*w + 1]', '[47, 47, 1/3*w^3 + 1/3*w^2 - 4*w - 1]', '[47, 47, -1/3*w^3 + 1/3*w^2 + 2*w - 3]', '[47, 47, 1/3*w^3 + 1/3*w^2 - 2*w - 3]', '[47, 47, 1/3*w^3 - 1/3*w^2 - 4*w + 1]', '[49, 7, 2/3*w^2 - 5]', '[49, 7, 2/3*w^2 - 3]', '[49, 7, -1/3*w^3 + w^2 + 4*w - 7]', '[49, 7, 1/3*w^3 + w^2 - 4*w - 7]', '[49, 7, -1/3*w^3 + w^2 + 2*w - 5]', '[49, 7, 1/3*w^3 + w^2 - 2*w - 5]', '[49, 49, 1/3*w^3 + 1/3*w^2 - 4*w - 3]', '[49, 49, -1/3*w^3 - 1/3*w^2 + 2*w + 1]', '[49, 49, -1/3*w^3 + 1/3*w^2 + 2*w - 1]', '[49, 49, 1/3*w^3 - 1/3*w^2 - 4*w + 3]', '[56, 14, 1/3*w^3 - 2/3*w^2 - 4*w + 4]', '[56, 14, 1/3*w^3 + 2/3*w^2 - 2*w - 4]', '[56, 14, 1/3*w^3 - 2/3*w^2 - 2*w + 4]', '[56, 14, -1/3*w^3 - 2/3*w^2 + 4*w + 4]', '[63, 21, -1/3*w^3 + 2*w + 3]', '[63, 21, -1/3*w^3 + 4*w + 3]', '[63, 21, 1/3*w^3 - 4*w + 3]', '[63, 21, -1/3*w^3 + 2*w - 3]', '[64, 4, 2/3*w^2 - 4]', '[72, 6, -1/3*w^3 + 4*w]', '[81, 3, 3]', '[82, 82, -w - 4]', '[82, 82, -1/3*w^3 + 3*w - 4]', '[82, 82, 1/3*w^3 - 3*w - 4]', '[82, 82, w - 4]', '[89, 89, -1/3*w^3 + 2/3*w^2 + 3*w - 3]', '[89, 89, 2/3*w^2 + w - 5]', '[89, 89, 2/3*w^2 - w - 5]', '[89, 89, 1/3*w^3 + 2/3*w^2 - 3*w - 3]', '[94, 94, 4/3*w^3 + w^2 - 13*w - 16]', '[94, 94, 4/3*w^3 + 5/3*w^2 - 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7*w - 13]', '[1927, 1927, 1/3*w^3 + 4/3*w^2 - 3*w - 17]', '[1927, 1927, -1/3*w^3 + 7*w - 7]', '[1927, 1927, 1/3*w^3 - 7*w - 7]', '[1927, 1927, 1/3*w^3 - 4/3*w^2 - 3*w + 17]', '[1927, 1927, 2/3*w^3 - 8/3*w^2 - 7*w + 13]', '[1927, 1927, -4/3*w^3 + 11*w - 7]', '[1927, 1927, 1/3*w^3 - 8/3*w^2 - w + 19]', '[1927, 1927, -4/3*w^2 + w - 1]', '[1927, 1927, -w^3 + 7*w + 5]', '[1927, 1927, 2/3*w^3 - 9*w - 5]', '[1928, 482, -1/3*w^3 + 2/3*w^2 - 2*w + 10]', '[1928, 482, -1/3*w^3 + 8*w - 14]', '[1928, 482, -1/3*w^3 + 10]', '[1928, 482, -1/3*w^3 + 2/3*w^2 + 6*w - 14]', '[1934, 1934, 4*w^3 + 14/3*w^2 - 41*w - 52]', '[1934, 1934, 5/3*w^3 + 4/3*w^2 - 17*w - 18]', '[1934, 1934, -13/3*w^3 - 14/3*w^2 + 43*w + 54]', '[1934, 1934, -2*w^3 - 4/3*w^2 + 19*w + 20]', '[1948, 974, -1/3*w^3 + 1/3*w^2 + 4*w + 6]', '[1948, 974, -1/3*w^3 - 1/3*w^2 + 2*w + 10]', '[1948, 974, -1/3*w^3 + 1/3*w^2 + 2*w - 10]', '[1948, 974, -1/3*w^3 - 1/3*w^2 + 4*w - 6]', '[1967, 1967, 1/3*w^3 - 5/3*w^2 + 9]', '[1967, 1967, -2/3*w^3 + 2/3*w^2 + 10*w - 15]', '[1967, 1967, 7/3*w^3 + 5/3*w^2 - 22*w - 25]', '[1967, 1967, -2/3*w^3 - 2/3*w^2 + 6*w - 1]', '[1967, 1967, 2/3*w^2 + 2*w - 9]', '[1967, 1967, 4/3*w^3 - 1/3*w^2 - 12*w - 3]', '[1967, 1967, w^3 - 8/3*w^2 - 6*w + 9]', '[1967, 1967, 2*w^3 + 5/3*w^2 - 20*w - 21]', '[1967, 1967, -2*w^3 + 5/3*w^2 + 20*w - 21]', '[1967, 1967, w^3 + 1/3*w^2 - 12*w - 11]', '[1967, 1967, -4/3*w^3 - 1/3*w^2 + 12*w - 3]', '[1967, 1967, -2/3*w^2 + 2*w + 9]', '[1967, 1967, 2/3*w^3 - 2/3*w^2 - 6*w - 1]', '[1967, 1967, 1/3*w^3 - 10/3*w^2 - 8*w + 15]', '[1967, 1967, -2/3*w^3 - 2/3*w^2 + 10*w + 15]', '[1967, 1967, -8/3*w^3 + 8/3*w^2 + 28*w - 35]', '[2009, 287, 2/3*w^3 - 4/3*w^2 - 5*w + 3]', '[2009, 287, -5/3*w^3 + 4/3*w^2 + 17*w - 19]', '[2009, 287, 1/3*w^3 - 1/3*w^2 - w + 9]', '[2009, 287, 1/3*w^3 - 4/3*w^2 - 7*w + 1]', '[2009, 287, -w^3 - 4/3*w^2 + 9*w + 7]', '[2009, 287, -1/3*w^3 - w^2 + 5*w + 1]', '[2009, 287, 2/3*w^3 + w^2 - 5*w - 11]', '[2009, 287, 4/3*w^3 - 4/3*w^2 - 11*w + 15]', '[2009, 287, 4/3*w^2 + 3*w - 9]', '[2009, 287, 2/3*w^3 - 4/3*w^2 - w - 3]', '[2009, 287, -2/3*w^3 - 1/3*w^2 + 7*w - 5]', '[2009, 287, -1/3*w^3 - 4/3*w^2 + 5*w + 13]', '[2009, 287, 2/3*w^3 - w^2 - 5*w + 11]', '[2009, 287, -4/3*w^2 + 3*w + 9]', '[2009, 287, 2/3*w^3 + 4/3*w^2 - w + 3]', '[2009, 287, 2/3*w^3 - 1/3*w^2 - 7*w - 5]', '[2009, 287, -1/3*w^3 + 4/3*w^2 + 5*w - 13]', '[2009, 287, 4/3*w^3 + 4/3*w^2 - 11*w - 15]', '[2009, 287, -2/3*w^3 - 4/3*w^2 + 5*w + 3]', '[2009, 287, 5/3*w^3 + 4/3*w^2 - 17*w - 19]', '[2009, 287, 1/3*w^3 + 1/3*w^2 - w - 9]', '[2009, 287, -1/3*w^3 - 4/3*w^2 + 7*w + 1]', '[2009, 287, w^3 - 4/3*w^2 - 9*w + 7]', '[2009, 287, 1/3*w^3 - w^2 - 5*w + 1]', '[2009, 2009, w^3 - 1/3*w^2 - 9*w - 3]', '[2009, 2009, -1/3*w^2 + 3*w + 7]', '[2009, 2009, 2/3*w^3 - 1/3*w^2 - 3*w - 5]', '[2009, 2009, 2/3*w^3 - 2/3*w^2 - 7*w + 1]', '[2009, 2009, 1/3*w^3 + 2/3*w^2 + w + 5]', '[2009, 2009, 1/3*w^3 + 2/3*w^2 - w - 7]', '[2009, 2009, 4/3*w^3 + 2/3*w^2 - 13*w - 13]', '[2009, 2009, -w^3 + 1/3*w^2 + 11*w - 9]', '[2009, 2009, w^3 + 1/3*w^2 - 11*w - 9]', '[2009, 2009, -4/3*w^3 + 2/3*w^2 + 13*w - 13]', '[2009, 2009, 1/3*w^3 - 2/3*w^2 - w + 7]', '[2009, 2009, 1/3*w^3 - 2/3*w^2 + w - 5]', '[2009, 2009, -2/3*w^3 - 2/3*w^2 + 7*w + 1]', '[2009, 2009, 2/3*w^3 + 1/3*w^2 - 3*w + 5]', '[2009, 2009, 1/3*w^2 + 3*w - 7]', '[2009, 2009, -w^3 - 1/3*w^2 + 9*w - 3]', '[2016, 84, -2/3*w^3 + 2*w^2 + 6*w - 12]', '[2016, 84, 2*w^2 + 2*w - 12]', '[2016, 84, 2*w^2 - 2*w - 12]', '[2016, 84, 2/3*w^3 + 2*w^2 - 6*w - 12]', '[2017, 2017, 4/3*w^3 + 7/3*w^2 - 16*w - 21]', '[2017, 2017, -5/3*w^3 - 10/3*w^2 + 18*w + 27]', '[2017, 2017, -5/3*w^3 - 4/3*w^2 + 16*w + 21]', '[2017, 2017, -2*w^3 - 5/3*w^2 + 18*w + 21]', '[2018, 2018, -w^2 - 3*w + 8]', '[2018, 2018, w^3 + w^2 - 9*w - 4]', '[2018, 2018, -w^3 + w^2 + 9*w - 4]', '[2018, 2018, -w^2 + 3*w + 8]', '[2023, 119, -4/3*w^3 - 4/3*w^2 + 15*w + 15]', '[2023, 119, -2/3*w^3 - 2/3*w^2 + 9*w + 9]', '[2023, 119, w^3 - 2/3*w^2 - 7*w - 1]', '[2023, 119, w^3 - 4/3*w^2 - 5*w + 1]', '[2023, 119, w^3 + 2/3*w^2 - 7*w + 1]', '[2023, 119, w^3 + 4/3*w^2 - 5*w - 1]', '[2023, 119, -4/3*w^3 + 4/3*w^2 + 15*w - 15]', '[2023, 119, -2/3*w^3 + 2/3*w^2 + 9*w - 9]', '[2048, 8, 4/3*w^3 + 8/3*w^2 - 16*w - 24]', '[2063, 2063, -w^3 - 4/3*w^2 + 6*w + 9]', '[2063, 2063, -w^3 - 4/3*w^2 + 12*w + 7]', '[2063, 2063, w^3 - 4/3*w^2 - 12*w + 7]', '[2063, 2063, w^3 - 4/3*w^2 - 6*w + 9]', '[2084, 1042, -1/3*w^3 - 7/3*w^2 + 6*w + 10]', '[2084, 1042, -7/3*w^3 - 7/3*w^2 + 24*w + 28]', '[2084, 1042, 11/3*w^3 + 11/3*w^2 - 36*w - 44]', '[2084, 1042, 5/3*w^3 + 11/3*w^2 - 18*w - 26]', '[2097, 699, 2*w^2 - 2*w - 9]', '[2097, 699, -2/3*w^3 + 2*w^2 + 6*w - 15]', '[2097, 699, -7/3*w^3 + 3*w^2 + 22*w - 27]', '[2097, 699, -2*w^2 - 2*w + 9]', '[2098, 2098, 8/3*w^3 + 10/3*w^2 - 25*w - 32]', '[2098, 2098, 4*w^3 + 4*w^2 - 39*w - 50]', '[2098, 2098, -2/3*w^3 - 2*w^2 + 7*w + 14]', '[2098, 2098, -2/3*w^3 - 8/3*w^2 + 11*w + 16]', '[2111, 2111, -5/3*w^3 - 11/3*w^2 + 20*w + 27]', '[2111, 2111, 2/3*w^3 - 2/3*w^2 - 6*w - 3]', '[2111, 2111, -10/3*w^3 - 8/3*w^2 + 32*w + 39]', '[2111, 2111, -3*w^3 - 13/3*w^2 + 30*w + 39]', '[2113, 2113, w^3 - 1/3*w^2 - 8*w - 1]', '[2113, 2113, 1/3*w^3 + 1/3*w^2 - 6*w - 5]', '[2113, 2113, -1/3*w^3 + 1/3*w^2 + 6*w - 5]', '[2113, 2113, w^3 + 1/3*w^2 - 8*w + 1]', '[2114, 2114, w^3 - 3*w^2 - 3*w + 10]', '[2114, 2114, 2/3*w^3 - w^2 - 9*w + 2]', '[2114, 2114, -2/3*w^3 - 3*w^2 + 11*w + 16]', '[2114, 2114, 5/3*w^3 + 3*w^2 - 13*w - 20]', '[2114, 2114, 2*w^3 - 3*w^2 - 21*w + 26]', '[2114, 2114, 1/3*w^3 + w^2 - w - 8]', '[2114, 2114, w^3 - w^2 - 7*w + 10]', '[2114, 2114, 2/3*w^3 - w^2 - 7*w + 4]', '[2114, 2114, -2/3*w^3 - w^2 + 7*w + 4]', '[2114, 2114, w^3 + w^2 - 7*w - 10]', '[2114, 2114, 1/3*w^3 - w^2 - w + 8]', '[2114, 2114, -2*w^3 - 3*w^2 + 21*w + 26]', '[2114, 2114, 5/3*w^3 - 3*w^2 - 13*w + 20]', '[2114, 2114, 2/3*w^3 - 3*w^2 - 11*w + 16]', '[2114, 2114, -2/3*w^3 - w^2 + 9*w + 2]', '[2114, 2114, w^3 + 3*w^2 - 3*w - 10]', '[2116, 46, -5/3*w^2 + 12]', '[2116, 46, -5/3*w^2 + 8]', '[2126, 2126, 2/3*w^3 - 4/3*w^2 - 5*w + 12]', '[2126, 2126, -1/3*w^3 - 4/3*w^2 + 5*w + 4]', '[2126, 2126, 1/3*w^3 - 4/3*w^2 - 5*w + 4]', '[2126, 2126, 2/3*w^3 + 4/3*w^2 - 5*w - 12]', '[2151, 717, 2*w^3 - 3*w^2 - 17*w + 21]', '[2151, 717, w^2 - w - 15]', '[2151, 717, w^2 + w - 15]', '[2151, 717, -3*w^2 + 7*w + 9]', '[2153, 2153, 3*w^3 + 5/3*w^2 - 27*w - 31]', '[2153, 2153, -2/3*w^3 - 2*w^2 + 9*w + 11]', '[2153, 2153, 4*w^3 + 6*w^2 - 41*w - 55]', '[2153, 2153, -w^3 - 1/3*w^2 + 11*w + 11]', '[2161, 2161, 4/3*w^3 - 2/3*w^2 - 12*w + 3]', '[2161, 2161, 4/3*w^3 + w^2 - 12*w - 11]', '[2161, 2161, -4/3*w^3 + w^2 + 12*w - 11]', '[2161, 2161, -4/3*w^3 - 2/3*w^2 + 12*w + 3]', '[2169, 723, -7/3*w^3 + 3*w^2 + 21*w - 21]', '[2169, 723, -2*w^3 + 2*w^2 + 19*w - 15]', '[2169, 723, 2*w^3 - 2*w^2 - 17*w + 9]', '[2169, 723, 5/3*w^3 - w^2 - 15*w + 3]', '[2192, 274, -2/3*w^3 - 2/3*w^2 + 6*w - 2]', '[2192, 274, 2/3*w^2 + 2*w - 10]', '[2192, 274, 2/3*w^2 - 2*w - 10]', '[2192, 274, 2/3*w^3 - 2/3*w^2 - 6*w - 2]', '[2194, 2194, 5/3*w^3 + 2/3*w^2 - 15*w - 18]', '[2194, 2194, 5/3*w^3 + 8/3*w^2 - 19*w - 24]', '[2194, 2194, -3*w^3 - 10/3*w^2 + 29*w + 36]', '[2194, 2194, w^3 + 8/3*w^2 - 11*w - 18]', '[2206, 2206, w^3 + 1/3*w^2 - 9*w - 12]', '[2206, 2206, -7/3*w^3 - 5/3*w^2 + 21*w + 24]', '[2206, 2206, 5/3*w^3 + 7/3*w^2 - 19*w - 24]', '[2206, 2206, 7/3*w^3 + 13/3*w^2 - 25*w - 36]', '[2207, 2207, -w^3 + 1/3*w^2 + 10*w + 1]', '[2207, 2207, 1/3*w^3 - 4/3*w^2 - 2*w + 13]', '[2207, 2207, -1/3*w^3 - 4/3*w^2 + 2*w + 13]', '[2207, 2207, w^3 + 1/3*w^2 - 10*w + 1]', '[2209, 47, -1/3*w^2 - 5]', '[2209, 47, -3*w^3 - 7/3*w^2 + 28*w + 35]', '[2209, 47, -w^3 - 7/3*w^2 + 10*w + 17]', '[2209, 47, 1/3*w^2 - 9]', '[2209, 47, -10/3*w^3 - 4*w^2 + 32*w + 41]', '[2209, 47, 2/3*w^3 + 2*w^2 - 10*w - 13]', '[2209, 2209, -2*w^3 - 11/3*w^2 + 20*w + 29]', '[2209, 2209, w^3 + 4/3*w^2 - 12*w - 13]', '[2209, 2209, -13/3*w^3 - 14/3*w^2 + 42*w + 53]', '[2209, 2209, -4/3*w^3 + 1/3*w^2 + 10*w + 11]', '[2248, 562, 1/3*w^3 - 2/3*w^2 - 4*w + 12]', '[2248, 562, 1/3*w^3 + 2/3*w^2 - 2*w + 4]', '[2248, 562, 1/3*w^3 + 4/3*w^2 - 12*w + 12]', '[2248, 562, -1/3*w^3 - 2/3*w^2 + 4*w + 12]', '[2268, 42, -w^3 - w^2 + 12*w + 12]', '[2268, 42, w^3 - w^2 - 6*w]', '[2268, 42, w^3 + w^2 - 6*w]', '[2268, 42, -w^3 + w^2 + 12*w - 12]', '[2276, 1138, -1/3*w^3 + 5/3*w^2 + 6*w - 6]', '[2276, 1138, -w^3 + 5/3*w^2 + 8*w - 14]', '[2276, 1138, w^3 + 5/3*w^2 - 8*w - 14]', '[2276, 1138, 1/3*w^3 + 5/3*w^2 - 6*w - 6]', '[2296, 574, 1/3*w^3 + 2*w^2 - 2*w - 14]', '[2296, 574, w^3 - 2/3*w^2 - 10*w + 14]', '[2296, 574, -1/3*w^3 + 2/3*w^2 + 6]', '[2296, 574, -w^3 + 2/3*w^2 + 6*w + 2]', '[2296, 574, -w^3 - 2/3*w^2 + 8*w + 6]', '[2296, 574, w^3 - 2/3*w^2 - 12*w + 10]', '[2296, 574, -1/3*w^3 + 2*w^2 + 4*w - 10]', '[2296, 574, 1/3*w^3 - 2/3*w^2 - 6*w + 2]', '[2296, 574, 1/3*w^3 + 2/3*w^2 - 6*w - 2]', '[2296, 574, 1/3*w^3 + 2*w^2 - 4*w - 10]', '[2296, 574, w^3 + 2/3*w^2 - 12*w - 10]', '[2296, 574, -w^3 + 2/3*w^2 + 8*w - 6]', '[2296, 574, -w^3 - 2/3*w^2 + 6*w - 2]', '[2296, 574, 1/3*w^3 + 2/3*w^2 + 6]', '[2296, 574, -w^3 - 2/3*w^2 + 10*w + 14]', '[2296, 574, -1/3*w^3 + 2*w^2 + 2*w - 14]', '[2297, 2297, 2*w^3 + 4/3*w^2 - 19*w - 21]', '[2297, 2297, w^3 + 7/3*w^2 - 11*w - 15]', '[2297, 2297, 5/3*w^3 + 11/3*w^2 - 19*w - 27]', '[2297, 2297, -8/3*w^3 - 8/3*w^2 + 27*w + 33]', '[2302, 2302, w^3 + 7/3*w^2 - 9*w - 16]', '[2302, 2302, -1/3*w^3 - 5/3*w^2 + 7*w + 8]', '[2302, 2302, 5*w^3 + 19/3*w^2 - 49*w - 64]', '[2302, 2302, 11/3*w^3 + 7/3*w^2 - 33*w - 40]', '[2303, 329, -2*w^3 + 8/3*w^2 + 20*w - 23]', '[2303, 329, -2*w^3 + 10/3*w^2 + 14*w - 13]', '[2303, 329, -4/3*w^3 - 2/3*w^2 + 14*w + 11]', '[2303, 329, -5/3*w^3 + 1/3*w^2 + 16*w + 1]', '[2303, 329, -8/3*w^3 - 4/3*w^2 + 24*w + 25]', '[2303, 329, -w^3 + w^2 + 8*w - 1]', '[2303, 329, -2/3*w^3 + 2/3*w^2 + 2*w + 3]', '[2303, 329, 4/3*w^2 - 8*w + 9]', '[2303, 329, 1/3*w^3 - w^2 - 6*w + 11]', '[2303, 329, -2/3*w^3 - 8/3*w^2 + 9]', '[2303, 329, 4/3*w^3 - 10/3*w^2 - 18*w + 27]', '[2303, 329, -1/3*w^3 - 1/3*w^2 - 2*w + 5]', '[2303, 329, 2/3*w^3 - 8/3*w^2 + 9]', '[2303, 329, -4/3*w^3 - 10/3*w^2 + 18*w + 27]', '[2303, 329, -1/3*w^3 - 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w - 5]', '[151, 151, 1/3*w^3 + w^2 - 3*w - 7]', '[151, 151, -1/3*w^3 + w^2 + 3*w - 7]', '[151, 151, w^2 + w - 5]', '[191, 191, 1/3*w^3 + 2/3*w^2 - 4*w - 3]', '[191, 191, 1/3*w^3 + 2/3*w^2 - 2*w - 5]', '[191, 191, -1/3*w^3 + 2/3*w^2 + 2*w - 5]', '[191, 191, -1/3*w^3 + 2/3*w^2 + 4*w - 3]', '[193, 193, 2/3*w^3 + w^2 - 8*w - 7]', '[193, 193, -1/3*w^3 - 1/3*w^2 + 4*w + 7]', '[193, 193, -7/3*w^3 - 13/3*w^2 + 26*w + 37]', '[193, 193, -2/3*w^3 + w^2 + 8*w - 7]', '[199, 199, 5/3*w^3 + 2*w^2 - 17*w - 23]', '[199, 199, -2/3*w^3 - 5/3*w^2 + 9*w + 13]', '[199, 199, -2/3*w^3 - 1/3*w^2 + 5*w + 5]', '[199, 199, -w^3 - 2*w^2 + 11*w + 17]', '[233, 233, 1/3*w^3 - 4/3*w^2 - 3*w + 5]', '[233, 233, 1/3*w^3 - 4/3*w^2 - 5*w + 7]', '[233, 233, 4/3*w^2 + w - 11]', '[233, 233, 1/3*w^3 + 4/3*w^2 - 3*w - 5]', '[239, 239, 1/3*w^3 + w^2 - 4*w - 5]', '[239, 239, 4/3*w^3 + 4/3*w^2 - 14*w - 17]', '[239, 239, 4/3*w^3 + 2/3*w^2 - 12*w - 13]', '[239, 239, -1/3*w^3 + w^2 + 4*w - 5]', '[241, 241, -2/3*w^3 + 6*w + 1]', '[241, 241, 2/3*w^3 - 1/3*w^2 - 6*w + 3]', '[241, 241, -2/3*w^3 - 1/3*w^2 + 6*w + 3]', '[241, 241, 2/3*w^3 - 6*w + 1]', '[281, 281, -w^3 - w^2 + 9*w + 13]', '[281, 281, -2/3*w^3 - 2/3*w^2 + 5*w + 7]', '[281, 281, -2/3*w^3 + 2/3*w^2 + 5*w - 7]', '[281, 281, -7/3*w^3 - 3*w^2 + 23*w + 31]', '[289, 17, w^2 - 5]', '[289, 17, w^2 - 7]', '[337, 337, -w^3 + 4/3*w^2 + 8*w - 7]', '[337, 337, -2*w + 7]', '[337, 337, 2/3*w^3 - 2*w^2 - 4*w + 11]', '[337, 337, 1/3*w^3 + 2/3*w^2 - 6*w + 1]', '[383, 383, 2/3*w^3 + 5/3*w^2 - 8*w - 11]', '[383, 383, -w^3 - 2/3*w^2 + 10*w + 11]', '[383, 383, -5/3*w^3 - 4/3*w^2 + 16*w + 19]', '[383, 383, -4/3*w^3 - 7/3*w^2 + 14*w + 19]', '[431, 431, -2/3*w^3 + 1/3*w^2 + 4*w - 5]', '[431, 431, -2/3*w^3 - 1/3*w^2 + 8*w - 1]', '[431, 431, 2/3*w^3 - 1/3*w^2 - 8*w - 1]', '[431, 431, 2/3*w^3 + 1/3*w^2 - 4*w - 5]', '[433, 433, 2/3*w^3 + 7/3*w^2 - 10*w - 15]', '[433, 433, -3*w^3 - 10/3*w^2 + 30*w + 39]', '[433, 433, -1/3*w^3 - 4/3*w^2 + 4*w + 9]', '[433, 433, -4/3*w^3 - 5/3*w^2 + 12*w + 15]', '[439, 439, -4/3*w^3 - 1/3*w^2 + 11*w + 13]', '[439, 439, 1/3*w^3 + 2/3*w^2 - 5*w - 5]', '[439, 439, -3*w^3 - 10/3*w^2 + 29*w + 37]', '[439, 439, -4/3*w^3 - 7/3*w^2 + 13*w + 19]', '[479, 479, 1/3*w^2 - 2*w - 5]', '[479, 479, 2/3*w^3 + 1/3*w^2 - 6*w + 1]', '[479, 479, 2/3*w^3 - 1/3*w^2 - 6*w - 1]', '[479, 479, -1/3*w^2 - 2*w + 5]', '[487, 487, 1/3*w^3 + 4/3*w^2 - 3*w - 7]', '[487, 487, 4/3*w^2 - w - 9]', '[487, 487, -4/3*w^2 - w + 9]', '[487, 487, 1/3*w^3 - 4/3*w^2 - 3*w + 7]', '[521, 521, 2/3*w^3 - 2/3*w^2 - 5*w - 3]', '[521, 521, 5/3*w^3 + 7/3*w^2 - 17*w - 21]', '[521, 521, -7/3*w^3 - 11/3*w^2 + 25*w + 33]', '[521, 521, -4/3*w^3 - 2/3*w^2 + 13*w + 15]', '[529, 23, -1/3*w^2 - 3]', '[529, 23, 1/3*w^2 - 7]', '[569, 569, 2/3*w^3 + 2/3*w^2 - 5*w + 1]', '[569, 569, 1/3*w^3 - 2/3*w^2 - 5*w + 9]', '[569, 569, -1/3*w^3 - 2/3*w^2 + 5*w + 9]', '[569, 569, -2/3*w^3 + 2/3*w^2 + 5*w + 1]', '[577, 577, -w^3 + 1/3*w^2 + 8*w + 3]', '[577, 577, -1/3*w^3 - 1/3*w^2 + 6*w + 7]', '[577, 577, 1/3*w^3 - 1/3*w^2 - 6*w + 7]', '[577, 577, w^3 + 1/3*w^2 - 8*w + 3]', '[617, 617, -2/3*w^3 - 5/3*w^2 + 5*w + 7]', '[617, 617, -5/3*w^2 + 3*w + 5]', '[617, 617, -8/3*w^3 - 13/3*w^2 + 27*w + 37]', '[617, 617, -w^3 - 5/3*w^2 + 9*w + 15]', '[625, 5, -5]', '[631, 631, -1/3*w^3 - 5/3*w^2 + 3*w + 7]', '[631, 631, -5/3*w^2 - w + 13]', '[631, 631, 5/3*w^2 - w - 13]', '[631, 631, 1/3*w^3 - 5/3*w^2 - 3*w + 7]', '[673, 673, 2/3*w^3 + 1/3*w^2 - 8*w - 1]', '[673, 673, -2/3*w^3 - 1/3*w^2 + 4*w + 3]', '[673, 673, -2/3*w^3 + 1/3*w^2 + 4*w - 3]', '[673, 673, 2/3*w^3 - 1/3*w^2 - 8*w + 1]', '[719, 719, 1/3*w^3 - 1/3*w^2 - 6*w + 9]', '[719, 719, w^3 - 1/3*w^2 - 8*w - 5]', '[719, 719, w^3 + 1/3*w^2 - 8*w + 5]', '[719, 719, -1/3*w^3 - 1/3*w^2 + 6*w + 9]', '[727, 727, 2/3*w^3 + 1/3*w^2 - 5*w - 1]', '[727, 727, -1/3*w^3 - 1/3*w^2 + 5*w + 3]', '[727, 727, 1/3*w^3 - 1/3*w^2 - 5*w + 3]', '[727, 727, -2/3*w^3 + 1/3*w^2 + 5*w - 1]', '[761, 761, -2/3*w^3 + 1/3*w^2 + 3*w + 3]', '[761, 761, 7/3*w^3 + 10/3*w^2 - 23*w - 33]', '[761, 761, 3*w^3 + 10/3*w^2 - 29*w - 39]', '[761, 761, -2*w^3 - 5/3*w^2 + 17*w + 21]', '[769, 769, -4/3*w^3 - w^2 + 12*w + 13]', '[769, 769, -w^3 - 2/3*w^2 + 10*w + 13]', '[769, 769, -w^3 - 8/3*w^2 + 12*w + 19]', '[769, 769, -2*w^3 - 3*w^2 + 22*w + 29]', '[809, 809, -2/3*w^3 - 2/3*w^2 + 7*w + 3]', '[809, 809, w^2 + w - 11]', '[809, 809, w^2 - w - 11]', '[809, 809, 2/3*w^3 - 2/3*w^2 - 7*w + 3]', '[823, 823, 1/3*w^3 - 5*w - 1]', '[823, 823, 2/3*w^3 - 5*w - 1]', '[823, 823, 2/3*w^3 - 5*w + 1]', '[823, 823, -1/3*w^3 + 5*w - 1]', '[857, 857, -5/3*w^2 + w + 15]', '[857, 857, -1/3*w^3 - 5/3*w^2 + 3*w + 5]', '[857, 857, 1/3*w^3 - 5/3*w^2 - 3*w + 5]', '[857, 857, 5/3*w^2 + w - 15]', '[863, 863, -2/3*w^3 - 5/3*w^2 + 10*w + 15]', '[863, 863, -5/3*w^3 - 8/3*w^2 + 18*w + 27]', '[863, 863, -3*w^3 - 14/3*w^2 + 32*w + 45]', '[863, 863, -5/3*w^2 + 4*w + 9]', '[911, 911, 1/3*w^3 - 2/3*w^2 - 4*w - 1]', '[911, 911, -1/3*w^3 + 2/3*w^2 + 2*w - 9]', '[911, 911, 1/3*w^3 + 2/3*w^2 - 2*w - 9]', '[911, 911, -1/3*w^3 - 2/3*w^2 + 4*w - 1]', '[919, 919, w^3 + 1/3*w^2 - 9*w - 1]', '[919, 919, -w^3 - 2/3*w^2 + 9*w + 7]', '[919, 919, w^3 - 2/3*w^2 - 9*w + 7]', '[919, 919, -w^3 + 1/3*w^2 + 9*w - 1]', '[953, 953, -w^3 - w^2 + 9*w + 5]', '[953, 953, -w^2 - 3*w + 7]', '[953, 953, w^2 - 3*w - 7]', '[953, 953, w^3 - w^2 - 9*w + 5]', '[961, 31, 4/3*w^2 - 7]', '[961, 31, 4/3*w^2 - 9]', '[967, 967, -w^3 - 1/3*w^2 + 9*w + 5]', '[967, 967, w^3 + 2/3*w^2 - 9*w - 5]', '[967, 967, -w^3 + 2/3*w^2 + 9*w - 5]', '[967, 967, w^3 - 1/3*w^2 - 9*w + 5]', '[1009, 1009, 1/3*w^3 + 5/3*w^2 - 4*w - 9]', '[1009, 1009, -8/3*w^3 - 10/3*w^2 + 26*w + 33]', '[1009, 1009, 4/3*w^3 + 8/3*w^2 - 16*w - 21]', '[1009, 1009, 7/3*w^3 + 5/3*w^2 - 22*w - 27]', '[1049, 1049, -2/3*w^3 + 2/3*w^2 + 5*w - 9]', '[1049, 1049, -1/3*w^3 - 2/3*w^2 + 5*w - 1]', '[1049, 1049, 1/3*w^3 - 2/3*w^2 - 5*w - 1]', '[1049, 1049, 2/3*w^3 + 2/3*w^2 - 5*w - 9]', '[1063, 1063, w^3 + 2/3*w^2 - 9*w - 13]', '[1063, 1063, 2*w^3 + w^2 - 17*w - 19]', '[1063, 1063, -2/3*w^3 - w^2 + 9*w + 11]', '[1063, 1063, -3*w^3 - 14/3*w^2 + 31*w + 43]', '[1097, 1097, -2/3*w^3 + 1/3*w^2 + 7*w + 1]', '[1097, 1097, 1/3*w^3 + 1/3*w^2 - w - 5]', '[1097, 1097, -1/3*w^3 + 1/3*w^2 + w - 5]', '[1097, 1097, 2/3*w^3 + 1/3*w^2 - 7*w + 1]', '[1103, 1103, 2/3*w^2 + 2*w - 7]', '[1103, 1103, 2/3*w^3 + 2/3*w^2 - 6*w - 1]', '[1103, 1103, -2/3*w^3 + 2/3*w^2 + 6*w - 1]', '[1103, 1103, 2/3*w^2 - 2*w - 7]', '[1151, 1151, -2/3*w^3 + 4*w - 7]', '[1151, 1151, 2/3*w^3 - 8*w - 7]', '[1151, 1151, -2/3*w^3 + 8*w - 7]', '[1151, 1151, 2/3*w^3 - 4*w - 7]', '[1153, 1153, -1/3*w^3 + 6*w - 5]', '[1153, 1153, -w^3 + 8*w + 5]', '[1153, 1153, -w^3 + 8*w - 5]', '[1153, 1153, 1/3*w^3 - 6*w - 5]', '[1193, 1193, -1/3*w^3 - 2/3*w^2 + 5*w - 3]', '[1193, 1193, 2/3*w^3 + 2/3*w^2 - 5*w - 11]', '[1193, 1193, -2/3*w^3 + 2/3*w^2 + 5*w - 11]', '[1193, 1193, 1/3*w^3 - 2/3*w^2 - 5*w - 3]', '[1201, 1201, -7/3*w^3 - 4/3*w^2 + 20*w + 23]', '[1201, 1201, -w^3 + 2/3*w^2 + 8*w - 1]', '[1201, 1201, w^3 + 2/3*w^2 - 8*w - 1]', '[1201, 1201, 1/3*w^3 + 2/3*w^2 - 6*w - 7]', '[1249, 1249, -2/3*w^3 + 2*w^2 + 6*w - 11]', '[1249, 1249, 2*w^2 + 2*w - 13]', '[1249, 1249, 2*w^2 - 2*w - 13]', '[1249, 1249, 2/3*w^3 + 2*w^2 - 6*w - 11]', '[1289, 1289, w^3 - 2/3*w^2 - 11*w + 3]', '[1289, 1289, 1/3*w^3 + w^2 - 5*w - 11]', '[1289, 1289, -1/3*w^3 + w^2 + 5*w - 11]', '[1289, 1289, -w^3 - 2/3*w^2 + 11*w + 3]', '[1297, 1297, -1/3*w^3 + 4*w - 7]', '[1297, 1297, -1/3*w^3 + 2*w - 7]', '[1297, 1297, 1/3*w^3 - 2*w - 7]', '[1297, 1297, 1/3*w^3 - 4*w - 7]', '[1303, 1303, 1/3*w^3 - 2/3*w^2 - 5*w + 13]', '[1303, 1303, -11/3*w^3 - 13/3*w^2 + 37*w + 49]', '[1303, 1303, -w^3 - 7/3*w^2 + 11*w + 19]', '[1303, 1303, -1/3*w^3 - 2/3*w^2 + 5*w + 13]', '[1399, 1399, 4/3*w^3 + 2/3*w^2 - 11*w + 1]', '[1399, 1399, -1/3*w^3 - 2/3*w^2 + 7*w + 9]', '[1399, 1399, 1/3*w^3 - 2/3*w^2 - 7*w + 9]', '[1399, 1399, -4/3*w^3 + 2/3*w^2 + 11*w + 1]', '[1433, 1433, w^3 - 9*w - 7]', '[1433, 1433, 4/3*w^3 + 11/3*w^2 - 17*w - 25]', '[1433, 1433, -4/3*w^3 - 7/3*w^2 + 13*w + 17]', '[1433, 1433, -w^3 + 9*w - 7]', '[1439, 1439, -1/3*w^3 - 4/3*w^2 + 6*w + 11]', '[1439, 1439, -2*w^3 - 3*w^2 + 22*w + 31]', '[1439, 1439, 4/3*w^3 + 3*w^2 - 16*w - 25]', '[1439, 1439, -5/3*w^3 - 10/3*w^2 + 20*w + 29]', '[1447, 1447, 1/3*w^2 + w - 9]', '[1447, 1447, 1/3*w^3 - 1/3*w^2 - 3*w - 5]', '[1447, 1447, -1/3*w^3 - 1/3*w^2 + 3*w - 5]', '[1447, 1447, 1/3*w^2 - w - 9]', '[1481, 1481, -2/3*w^3 + 5/3*w^2 + 7*w - 9]', '[1481, 1481, 1/3*w^3 + 5/3*w^2 - w - 11]', '[1481, 1481, -1/3*w^3 + 5/3*w^2 + w - 11]', '[1481, 1481, -2/3*w^3 - 5/3*w^2 + 7*w + 9]', '[1487, 1487, 2/3*w^3 + 8/3*w^2 - 10*w - 15]', '[1487, 1487, -w^3 - 1/3*w^2 + 10*w + 9]', '[1487, 1487, -w^3 + 1/3*w^2 + 10*w - 9]', '[1487, 1487, -2*w^3 - 10/3*w^2 + 20*w + 27]', '[1489, 1489, -1/3*w^3 + 5/3*w^2 + 2*w - 9]', '[1489, 1489, -1/3*w^3 + 5/3*w^2 + 4*w - 11]', '[1489, 1489, 1/3*w^3 + 5/3*w^2 - 4*w - 11]', '[1489, 1489, 1/3*w^3 + 5/3*w^2 - 2*w - 9]', '[1543, 1543, -4*w^3 - 13/3*w^2 + 39*w + 49]', '[1543, 1543, 4*w^3 + 5*w^2 - 41*w - 55]', '[1543, 1543, 2/3*w^3 - 2/3*w^2 - 9*w + 1]', '[1543, 1543, 4/3*w^3 + 5/3*w^2 - 15*w - 17]', '[1583, 1583, -1/3*w^3 + w^2 + 4*w + 1]', '[1583, 1583, 1/3*w^3 + w^2 - 2*w - 13]', '[1583, 1583, -1/3*w^3 + w^2 + 2*w - 13]', '[1583, 1583, -1/3*w^3 - w^2 + 4*w - 1]', '[1721, 1721, w^3 - 1/3*w^2 - 7*w + 9]', '[1721, 1721, 2/3*w^3 + 1/3*w^2 - 9*w + 5]', '[1721, 1721, -2/3*w^3 + 1/3*w^2 + 9*w + 5]', '[1721, 1721, w^3 + 1/3*w^2 - 7*w - 9]', '[1777, 1777, -8/3*w^3 - 3*w^2 + 28*w + 37]', '[1777, 1777, -w^3 - 2/3*w^2 + 8*w + 7]', '[1777, 1777, -w^3 + 2/3*w^2 + 8*w - 7]', '[1777, 1777, -2/3*w^3 - 3*w^2 + 10*w + 19]', '[1783, 1783, -1/3*w^2 - w - 5]', '[1783, 1783, -1/3*w^3 + 1/3*w^2 + 3*w - 9]', '[1783, 1783, 1/3*w^3 + 1/3*w^2 - 3*w - 9]', '[1783, 1783, -1/3*w^2 + w - 5]', '[1823, 1823, 2/3*w^3 - 4/3*w^2 - 4*w + 9]', '[1823, 1823, 2/3*w^3 - 4/3*w^2 - 8*w + 7]', '[1823, 1823, 2/3*w^3 + 4/3*w^2 - 8*w - 7]', '[1823, 1823, 2/3*w^3 + 4/3*w^2 - 4*w - 9]', '[1831, 1831, -w - 7]', '[1831, 1831, -1/3*w^3 + 3*w - 7]', '[1831, 1831, 1/3*w^3 - 3*w - 7]', '[1831, 1831, w - 7]', '[1871, 1871, -4*w^3 - 13/3*w^2 + 38*w + 49]', '[1871, 1871, -7/3*w^3 - 10/3*w^2 + 22*w + 31]', '[1871, 1871, -7/3*w^3 - 4/3*w^2 + 20*w + 25]', '[1871, 1871, 2/3*w^3 + 1/3*w^2 - 4*w - 7]', '[1873, 1873, -1/3*w^2 + 4*w - 3]', '[1873, 1873, 4/3*w^3 + 1/3*w^2 - 12*w - 7]', '[1873, 1873, 4/3*w^3 - 1/3*w^2 - 12*w + 7]', '[1873, 1873, 1/3*w^2 + 4*w + 3]', '[1879, 1879, -1/3*w^3 + 7/3*w^2 + 5*w - 11]', '[1879, 1879, 2/3*w^3 + 7/3*w^2 - 5*w - 17]', '[1879, 1879, -2/3*w^3 + 7/3*w^2 + 5*w - 17]', '[1879, 1879, 1/3*w^3 + 7/3*w^2 - 5*w - 11]', '[1913, 1913, 1/3*w^3 + 1/3*w^2 - w - 7]', '[1913, 1913, -2/3*w^3 - 1/3*w^2 + 7*w - 3]', '[1913, 1913, 2/3*w^3 - 1/3*w^2 - 7*w - 3]', '[1913, 1913, -1/3*w^3 + 1/3*w^2 + w - 7]']}
• 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': [18, 0, -12, 0, 1], 'conductor': 48, 'degree': 4, 'dirichlet_group': [1, 11, 35, 25], 'disc_abs': 18432, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 1]]], [7, [[1, 4]]], [11, [[4, 1]]], [13, [[4, 1]]], [17, [[2, 2]]], [19, [[4, 1]]], [23, [[2, 2]]], [29, [[4, 1]]], [31, [[2, 2]]], [37, [[4, 1]]], [41, [[1, 4]]], [43, [[4, 1]]], [47, [[1, 4]]], [53, [[4, 1]]], [59, [[4, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [11, 2], 'galois_label': '4T1', 'galt': 1, 'grd': 11.651802520975762, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.18432.1', 'local_algs': ['2.4.11.3', '3.4.2.2'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 3], 'rd': 11.651802521, 'regulator': {'__RealLiteral__': 0, 'data': '11.1753272808', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{3} a^{2} - 1 \\)', '\\( \\frac{1}{3} a^{3} - \\frac{1}{3} a^{2} - 4 a + 5 \\)', '\\( \\frac{1}{3} a^{3} - \\frac{1}{3} a^{2} - 2 a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/3*a^2', '1/3*a^3']}