Hilbert modular form data - 4.4.8789.1-19.1-d

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• 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': 5, 'disc': 8789, 'field_bad_primes': [11, 17, 47], 'field_label': '4.4.8789.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.8789.1-19.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [19], 'level_ideal': '[19, 19, w^2 - w - 2]', 'level_label': '19.1', 'level_norm': 19, 'parallel_weight': 2, 'short_label': '19.1-d', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[19, 19, w^2 - w - 2]', 1]], 'hecke_eigenvalues': ['e', '-14/17*e^4 - 20/17*e^3 + 344/17*e^2 + 295/17*e - 110', '1/17*e^4 - 1/17*e^3 - 10/17*e^2 + 19/17*e - 2', '-1/17*e^4 + 1/17*e^3 + 27/17*e^2 - 19/17*e - 10', '-23/17*e^4 - 28/17*e^3 + 553/17*e^2 + 413/17*e - 168', '22/17*e^4 + 29/17*e^3 - 526/17*e^2 - 432/17*e + 163', '-8/17*e^4 - 9/17*e^3 + 182/17*e^2 + 137/17*e - 54', '9/17*e^4 + 8/17*e^3 - 209/17*e^2 - 101/17*e + 63', -1, '-12/17*e^4 - 22/17*e^3 + 290/17*e^2 + 316/17*e - 90', '15/17*e^4 + 19/17*e^3 - 371/17*e^2 - 310/17*e + 121', '-15/17*e^4 - 19/17*e^3 + 354/17*e^2 + 276/17*e - 108', '6/17*e^4 + 11/17*e^3 - 162/17*e^2 - 175/17*e + 60', '-33/17*e^4 - 35/17*e^3 + 772/17*e^2 + 512/17*e - 226', '-9/17*e^4 - 8/17*e^3 + 209/17*e^2 + 101/17*e - 61', '10/17*e^4 + 7/17*e^3 - 253/17*e^2 - 82/17*e + 77', '-2/17*e^4 + 2/17*e^3 + 54/17*e^2 - 4/17*e - 22', '22/17*e^4 + 29/17*e^3 - 543/17*e^2 - 449/17*e + 169', 'e^4 + e^3 - 22*e^2 - 14*e + 98', '8/17*e^4 + 9/17*e^3 - 199/17*e^2 - 154/17*e + 73', '-3/17*e^4 + 3/17*e^3 + 81/17*e^2 - 74/17*e - 25', '33/17*e^4 + 52/17*e^3 - 789/17*e^2 - 733/17*e + 245', '-4/17*e^4 - 13/17*e^3 + 91/17*e^2 + 196/17*e - 29', '-41/17*e^4 - 61/17*e^3 + 988/17*e^2 + 921/17*e - 312', '52/17*e^4 + 67/17*e^3 - 1251/17*e^2 - 950/17*e + 387', '-19/17*e^4 - 32/17*e^3 + 496/17*e^2 + 455/17*e - 173', '-14/17*e^4 - 37/17*e^3 + 327/17*e^2 + 499/17*e - 99', '71/17*e^4 + 99/17*e^3 - 1713/17*e^2 - 1456/17*e + 535', '-25/17*e^4 - 26/17*e^3 + 556/17*e^2 + 358/17*e - 152', '28/17*e^4 + 23/17*e^3 - 654/17*e^2 - 335/17*e + 196', '22/17*e^4 + 12/17*e^3 - 509/17*e^2 - 194/17*e + 140', '43/17*e^4 + 59/17*e^3 - 1008/17*e^2 - 849/17*e + 312', '-9/17*e^4 - 25/17*e^3 + 209/17*e^2 + 322/17*e - 63', '15/17*e^4 + 19/17*e^3 - 371/17*e^2 - 259/17*e + 124', '-12/17*e^4 - 22/17*e^3 + 290/17*e^2 + 316/17*e - 96', '28/17*e^4 + 40/17*e^3 - 671/17*e^2 - 573/17*e + 215', '36/17*e^4 + 49/17*e^3 - 853/17*e^2 - 676/17*e + 253', '-6/17*e^4 - 11/17*e^3 + 128/17*e^2 + 124/17*e - 29', '6/17*e^4 - 6/17*e^3 - 128/17*e^2 + 80/17*e + 28', '-81/17*e^4 - 106/17*e^3 + 1949/17*e^2 + 1521/17*e - 605', '-22/17*e^4 - 29/17*e^3 + 543/17*e^2 + 466/17*e - 161', '23/17*e^4 + 45/17*e^3 - 587/17*e^2 - 651/17*e + 198', '13/17*e^4 + 21/17*e^3 - 317/17*e^2 - 314/17*e + 105', '-45/17*e^4 - 57/17*e^3 + 1130/17*e^2 + 913/17*e - 370', '37/17*e^4 + 31/17*e^3 - 863/17*e^2 - 453/17*e + 254', '6/17*e^4 - 6/17*e^3 - 128/17*e^2 + 114/17*e + 20', '13/17*e^4 + 21/17*e^3 - 317/17*e^2 - 263/17*e + 94', '-16/17*e^4 - 18/17*e^3 + 381/17*e^2 + 240/17*e - 104', '33/17*e^4 + 52/17*e^3 - 789/17*e^2 - 852/17*e + 249', '11/17*e^4 + 23/17*e^3 - 280/17*e^2 - 369/17*e + 98', '-2*e^4 - 3*e^3 + 49*e^2 + 44*e - 263', '-1/17*e^4 + 1/17*e^3 - 41/17*e^2 - 70/17*e + 45', '-70/17*e^4 - 83/17*e^3 + 1669/17*e^2 + 1271/17*e - 503', '-22/17*e^4 - 12/17*e^3 + 492/17*e^2 + 194/17*e - 132', '-43/17*e^4 - 59/17*e^3 + 1059/17*e^2 + 951/17*e - 348', '-99/17*e^4 - 122/17*e^3 + 2350/17*e^2 + 1740/17*e - 714', '76/17*e^4 + 111/17*e^3 - 1831/17*e^2 - 1650/17*e + 589', '-48/17*e^4 - 54/17*e^3 + 1126/17*e^2 + 805/17*e - 334', '54/17*e^4 + 82/17*e^3 - 1305/17*e^2 - 1133/17*e + 417', '-37/17*e^4 - 31/17*e^3 + 846/17*e^2 + 453/17*e - 230', '-46/17*e^4 - 56/17*e^3 + 1106/17*e^2 + 826/17*e - 332', '59/17*e^4 + 60/17*e^3 - 1389/17*e^2 - 885/17*e + 405', '-114/17*e^4 - 124/17*e^3 + 2704/17*e^2 + 1846/17*e - 816', '5/17*e^4 + 12/17*e^3 - 135/17*e^2 - 245/17*e + 61', '41/17*e^4 + 61/17*e^3 - 1039/17*e^2 - 921/17*e + 344', '48/17*e^4 + 71/17*e^3 - 1177/17*e^2 - 1179/17*e + 375', '40/17*e^4 + 45/17*e^3 - 961/17*e^2 - 668/17*e + 301', '33/17*e^4 + 35/17*e^3 - 806/17*e^2 - 529/17*e + 258', '80/17*e^4 + 107/17*e^3 - 1905/17*e^2 - 1557/17*e + 577', '-54/17*e^4 - 65/17*e^3 + 1305/17*e^2 + 946/17*e - 401', '9/17*e^4 + 25/17*e^3 - 192/17*e^2 - 339/17*e + 72', '-116/17*e^4 - 139/17*e^3 + 2758/17*e^2 + 2080/17*e - 841', '52/17*e^4 + 50/17*e^3 - 1183/17*e^2 - 695/17*e + 335', '-8/17*e^4 + 8/17*e^3 + 114/17*e^2 - 186/17*e - 2', '35/17*e^4 + 67/17*e^3 - 860/17*e^2 - 933/17*e + 294', '128/17*e^4 + 178/17*e^3 - 3048/17*e^2 - 2634/17*e + 954', '-45/17*e^4 - 57/17*e^3 + 1113/17*e^2 + 879/17*e - 346', '57/17*e^4 + 96/17*e^3 - 1420/17*e^2 - 1433/17*e + 459', '22/17*e^4 + 12/17*e^3 - 526/17*e^2 - 194/17*e + 158', '-2*e^4 - 3*e^3 + 52*e^2 + 45*e - 308', '140/17*e^4 + 183/17*e^3 - 3389/17*e^2 - 2746/17*e + 1059', '-19/17*e^4 - 32/17*e^3 + 479/17*e^2 + 387/17*e - 169', '-38/17*e^4 - 30/17*e^3 + 856/17*e^2 + 400/17*e - 236', '37/17*e^4 + 48/17*e^3 - 897/17*e^2 - 827/17*e + 277', '59/17*e^4 + 77/17*e^3 - 1474/17*e^2 - 1208/17*e + 488', '-27/17*e^4 - 7/17*e^3 + 610/17*e^2 + 99/17*e - 160', '42/17*e^4 + 43/17*e^3 - 1049/17*e^2 - 766/17*e + 349', '72/17*e^4 + 81/17*e^3 - 1740/17*e^2 - 1199/17*e + 530', '-137/17*e^4 - 186/17*e^3 + 3308/17*e^2 + 2701/17*e - 1029', '98/17*e^4 + 140/17*e^3 - 2408/17*e^2 - 2082/17*e + 754', '75/17*e^4 + 95/17*e^3 - 1804/17*e^2 - 1465/17*e + 548', '-48/17*e^4 - 71/17*e^3 + 1194/17*e^2 + 1043/17*e - 388', 'e^4 + e^3 - 27*e^2 - 15*e + 158', '59/17*e^4 + 60/17*e^3 - 1355/17*e^2 - 817/17*e + 389', '-21/17*e^4 - 47/17*e^3 + 618/17*e^2 + 723/17*e - 248', '46/17*e^4 + 22/17*e^3 - 1106/17*e^2 - 384/17*e + 328', '-161/17*e^4 - 196/17*e^3 + 3837/17*e^2 + 2891/17*e - 1169', '-54/17*e^4 - 65/17*e^3 + 1322/17*e^2 + 929/17*e - 400', '-45/17*e^4 - 74/17*e^3 + 1130/17*e^2 + 1117/17*e - 369', '-30/17*e^4 - 55/17*e^3 + 691/17*e^2 + 756/17*e - 193', '56/17*e^4 + 97/17*e^3 - 1376/17*e^2 - 1435/17*e + 428', '24/17*e^4 + 27/17*e^3 - 597/17*e^2 - 428/17*e + 205', '43/17*e^4 + 59/17*e^3 - 1008/17*e^2 - 849/17*e + 332', '8/17*e^4 + 26/17*e^3 - 250/17*e^2 - 426/17*e + 112', '15/17*e^4 + 2/17*e^3 - 354/17*e^2 - 72/17*e + 80', '135/17*e^4 + 188/17*e^3 - 3237/17*e^2 - 2773/17*e + 1011', '109/17*e^4 + 163/17*e^3 - 2620/17*e^2 - 2315/17*e + 826', '-20/17*e^4 - 31/17*e^3 + 421/17*e^2 + 470/17*e - 103', '41/17*e^4 + 44/17*e^3 - 920/17*e^2 - 581/17*e + 255', '-30/17*e^4 - 38/17*e^3 + 742/17*e^2 + 603/17*e - 220', '-27/17*e^4 - 24/17*e^3 + 644/17*e^2 + 439/17*e - 177', '89/17*e^4 + 98/17*e^3 - 2131/17*e^2 - 1573/17*e + 639', '-7/17*e^4 - 10/17*e^3 + 172/17*e^2 + 122/17*e - 30', '132/17*e^4 + 157/17*e^3 - 3173/17*e^2 - 2235/17*e + 959', '77/17*e^4 + 93/17*e^3 - 1858/17*e^2 - 1291/17*e + 572', '82/17*e^4 + 105/17*e^3 - 1976/17*e^2 - 1655/17*e + 612', '-76/17*e^4 - 77/17*e^3 + 1797/17*e^2 + 1174/17*e - 525', '135/17*e^4 + 205/17*e^3 - 3271/17*e^2 - 2960/17*e + 1039', '-50/17*e^4 - 69/17*e^3 + 1282/17*e^2 + 1141/17*e - 444', '-28/17*e^4 - 40/17*e^3 + 620/17*e^2 + 692/17*e - 172', '4*e^4 + 4*e^3 - 92*e^2 - 56*e + 476', '16/17*e^4 + 18/17*e^3 - 432/17*e^2 - 274/17*e + 158', '14/17*e^4 + 54/17*e^3 - 310/17*e^2 - 720/17*e + 100', 'e^4 + 3*e^3 - 27*e^2 - 45*e + 174', '-71/17*e^4 - 99/17*e^3 + 1730/17*e^2 + 1439/17*e - 556', '-78/17*e^4 - 109/17*e^3 + 1885/17*e^2 + 1697/17*e - 605', '-89/17*e^4 - 98/17*e^3 + 2131/17*e^2 + 1505/17*e - 627', '121/17*e^4 + 168/17*e^3 - 2995/17*e^2 - 2495/17*e + 947', '-33/17*e^4 - 52/17*e^3 + 755/17*e^2 + 699/17*e - 237', '-2*e^4 - 2*e^3 + 45*e^2 + 22*e - 218', '-7/17*e^4 - 10/17*e^3 + 291/17*e^2 + 173/17*e - 125', '4/17*e^4 + 13/17*e^3 - 91/17*e^2 - 162/17*e + 7', '7*e^4 + 10*e^3 - 171*e^2 - 149*e + 925', '-5*e^4 - 7*e^3 + 121*e^2 + 104*e - 679', '139/17*e^4 + 184/17*e^3 - 3311/17*e^2 - 2629/17*e + 1005', '101/17*e^4 + 120/17*e^3 - 2387/17*e^2 - 1617/17*e + 715', '-53/17*e^4 - 83/17*e^3 + 1312/17*e^2 + 1271/17*e - 432', '96/17*e^4 + 142/17*e^3 - 2354/17*e^2 - 2086/17*e + 742', '80/17*e^4 + 90/17*e^3 - 1905/17*e^2 - 1200/17*e + 572', '15/17*e^4 + 19/17*e^3 - 388/17*e^2 - 259/17*e + 114', '129/17*e^4 + 160/17*e^3 - 3160/17*e^2 - 2292/17*e + 980', '-2*e^4 - 3*e^3 + 45*e^2 + 48*e - 223', '-14/17*e^4 - 3/17*e^3 + 361/17*e^2 + 40/17*e - 133', '-116/17*e^4 - 156/17*e^3 + 2809/17*e^2 + 2403/17*e - 887', '74/17*e^4 + 113/17*e^3 - 1760/17*e^2 - 1671/17*e + 564', '82/17*e^4 + 88/17*e^3 - 1942/17*e^2 - 1230/17*e + 576', '57/17*e^4 + 96/17*e^3 - 1403/17*e^2 - 1501/17*e + 435', '10/17*e^4 + 7/17*e^3 - 287/17*e^2 - 14/17*e + 85', '1/17*e^4 - 1/17*e^3 - 44/17*e^2 + 121/17*e + 38', '-39/17*e^4 - 63/17*e^3 + 968/17*e^2 + 993/17*e - 300', '18/17*e^4 - 18/17*e^3 - 367/17*e^2 + 257/17*e + 65', '-32/17*e^4 - 19/17*e^3 + 745/17*e^2 + 344/17*e - 217', '160/17*e^4 + 214/17*e^3 - 3844/17*e^2 - 3080/17*e + 1178', '49/17*e^4 + 70/17*e^3 - 1221/17*e^2 - 1177/17*e + 389', '-82/17*e^4 - 122/17*e^3 + 1942/17*e^2 + 1604/17*e - 592', '13/17*e^4 + 21/17*e^3 - 470/17*e^2 - 382/17*e + 214', '-101/17*e^4 - 103/17*e^3 + 2438/17*e^2 + 1634/17*e - 762', '98/17*e^4 + 123/17*e^3 - 2323/17*e^2 - 1878/17*e + 707'], 'hecke_polynomial': 'x^5 - x^4 - 27*x^3 + 36*x^2 + 170*x - 289', 'label': '4.4.8789.1-19.1-d'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 8789, 'ideals': ['[1, 1, 1]', '[5, 5, -w^3 + 2*w^2 + 3*w]', '[7, 7, w - 1]', '[11, 11, -w^3 + 2*w^2 + 4*w]', '[13, 13, -2*w^3 + 3*w^2 + 10*w - 2]', '[16, 2, 2]', '[17, 17, -w^3 + 2*w^2 + 5*w - 3]', '[17, 17, -w^3 + w^2 + 5*w]', '[17, 17, -w^2 + 2*w + 1]', '[19, 19, w^2 - w - 2]', '[25, 25, w^3 - w^2 - 6*w]', '[29, 29, w^3 - 2*w^2 - 5*w]', '[29, 29, w^2 - w - 3]', '[31, 31, -w^3 + 2*w^2 + 3*w - 2]', '[35, 35, 2*w^3 - 4*w^2 - 9*w + 4]', '[43, 43, 2*w^3 - 3*w^2 - 11*w]', '[47, 47, w^3 - 7*w - 4]', '[49, 49, w^3 - w^2 - 7*w]', '[53, 53, -2*w^3 + 3*w^2 + 9*w - 1]', '[55, 55, 2*w^3 - 3*w^2 - 11*w + 1]', '[61, 61, -w - 3]', '[65, 65, -w^3 + w^2 + 7*w + 2]', '[73, 73, -w^3 + 2*w^2 + 3*w - 3]', '[73, 73, w^3 - w^2 - 7*w - 1]', '[77, 77, w^3 - 3*w^2 - 2*w + 4]', '[80, 10, -2*w^3 + 4*w^2 + 6*w]', '[81, 3, -3]', '[83, 83, -2*w^3 + 3*w^2 + 9*w + 1]', '[83, 83, -w^3 + 3*w^2 + 2*w - 3]', '[85, 85, 2*w^3 - 3*w^2 - 10*w - 2]', '[85, 85, 2*w^3 - 3*w^2 - 9*w]', '[85, 85, w^3 - w^2 - 6*w - 5]', '[89, 89, w - 4]', '[91, 91, -w^3 + 2*w^2 + 3*w - 4]', '[95, 95, -w^3 + 3*w^2 - w - 2]', '[103, 103, w^3 - 2*w^2 - 6*w + 3]', '[112, 14, 2*w - 2]', '[113, 113, 2*w^3 - w^2 - 14*w - 6]', '[119, 119, -2*w^3 + 3*w^2 + 11*w + 2]', '[119, 119, -w^3 + 2*w^2 + 3*w + 3]', '[119, 119, w^3 - 2*w^2 - 4*w + 5]', '[121, 11, w^3 - 9*w - 3]', '[121, 11, -w^2 + 2*w + 7]', '[125, 5, -3*w^3 + 4*w^2 + 15*w + 1]', '[125, 125, w^3 - 9*w - 5]', '[133, 133, w^3 - 2*w^2 - w + 2]', '[139, 139, w^3 - 2*w^2 - 5*w - 3]', '[139, 139, w^3 - 5*w - 5]', '[143, 143, -2*w^3 + 2*w^2 + 11*w + 2]', '[145, 145, w^3 - 2*w^2 - w - 1]', '[145, 145, w^2 - 4*w - 2]', '[151, 151, w^3 - 9*w - 7]', '[155, 155, -w^3 + 4*w^2 - w - 1]', '[157, 157, -3*w^3 + 6*w^2 + 13*w - 6]', '[163, 163, w^3 - 3*w^2 - 2*w + 9]', '[167, 167, -w^3 + 7*w + 3]', '[167, 167, -3*w^3 + 4*w^2 + 15*w - 1]', '[169, 169, -w^3 + 3*w^2 + 3*w - 3]', '[173, 173, 2*w^3 - 3*w^2 - 7*w - 2]', '[175, 175, -w^2 + 3*w + 5]', '[176, 22, -2*w^3 + 4*w^2 + 8*w]', '[181, 181, -w^3 + 3*w^2 + 4*w - 5]', '[187, 187, 3*w^3 - 5*w^2 - 13*w + 2]', '[187, 187, 3*w^3 - 5*w^2 - 15*w + 1]', '[187, 187, 3*w^3 - 4*w^2 - 15*w - 2]', '[191, 191, w^3 - w^2 - 4*w - 4]', '[193, 193, -w^3 + w^2 + 7*w + 6]', '[193, 193, 2*w^3 - 2*w^2 - 13*w - 5]', '[199, 199, -2*w^3 + 5*w^2 + 5*w - 5]', '[203, 203, w^3 - 2*w^2 - 2*w + 3]', '[203, 203, -2*w^3 + 3*w^2 + 7*w - 1]', '[208, 26, -4*w^3 + 6*w^2 + 20*w - 4]', '[209, 209, 2*w^2 - 3*w - 2]', '[211, 211, w^3 - w^2 - 8*w - 3]', '[211, 211, -2*w^2 + 3*w + 8]', '[215, 215, -w^3 + 3*w^2 + 3*w - 4]', '[217, 217, 2*w^3 - 5*w^2 - 7*w + 3]', '[221, 221, -2*w^3 + 3*w^2 + 11*w + 3]', '[221, 221, -2*w^3 + 3*w^2 + 8*w + 1]', '[221, 221, -2*w + 3]', '[227, 227, -w^3 + 3*w^2 + 4*w - 4]', '[227, 227, w^2 - 3*w - 6]', '[229, 229, w^2 - 5]', '[229, 229, 3*w^3 - 4*w^2 - 17*w - 2]', '[233, 233, 3*w^3 - 6*w^2 - 13*w + 3]', '[233, 233, 3*w^3 - 4*w^2 - 16*w + 1]', '[235, 235, -w^3 + 4*w^2 - 3*w - 5]', '[241, 241, -2*w^3 + 4*w^2 + 8*w + 1]', '[245, 245, 2*w^3 - 3*w^2 - 12*w - 1]', '[247, 247, 2*w^3 - 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9]', '[1727, 1727, 4*w^3 - 5*w^2 - 23*w + 4]', '[1729, 1729, -w^3 - w^2 + 3*w + 6]', '[1735, 1735, 3*w^2 - 7*w - 1]', '[1745, 1745, 3*w^3 - 7*w^2 - 4*w - 1]', '[1747, 1747, -6*w^3 + 12*w^2 + 27*w - 14]', '[1751, 1751, -8*w^3 + 13*w^2 + 38*w - 13]', '[1751, 1751, -4*w^3 + 8*w^2 + 23*w - 5]', '[1751, 1751, -w^2 + 7*w]', '[1753, 1753, 2*w^3 - w^2 - 14*w - 2]', '[1757, 1757, -2*w^3 + 5*w^2 + 10*w + 1]', '[1759, 1759, 3*w^2 - 2*w - 13]', '[1765, 1765, 5*w^3 - 13*w^2 - 14*w + 4]', '[1765, 1765, -3*w^3 + 5*w^2 + 10*w + 6]', '[1765, 1765, w^2 - w + 4]', '[1765, 1765, 4*w^3 - 7*w^2 - 18*w - 1]', '[1769, 1769, -5*w^3 + 8*w^2 + 27*w - 4]', '[1769, 1769, -2*w^3 + 5*w^2 + 9*w - 11]', '[1783, 1783, 3*w^3 - 7*w^2 - 13*w + 7]', '[1783, 1783, -3*w^3 + 7*w^2 + 12*w - 7]', '[1787, 1787, 3*w^3 - 7*w^2 - 13*w + 14]', '[1792, 28, 4*w - 4]', '[1793, 1793, -5*w^3 + 7*w^2 + 28*w + 2]', '[1795, 1795, w^2 - 6*w + 4]', '[1801, 1801, 3*w^3 - 3*w^2 - 17*w - 1]', '[1801, 1801, -2*w^3 + 4*w^2 + 11*w - 8]', '[1801, 1801, -4*w^3 + 6*w^2 + 20*w + 5]', '[1801, 1801, -w^3 + 3*w^2 - w - 6]', '[1805, 1805, -4*w^3 + 13*w^2 + 2*w - 5]', '[1807, 1807, 4*w^3 - 7*w^2 - 23*w + 1]', '[1807, 1807, 2*w^3 - w^2 - 11*w - 1]', '[1808, 226, 4*w^3 - 2*w^2 - 28*w - 12]', '[1811, 1811, -4*w^3 + 6*w^2 + 17*w + 4]', '[1811, 1811, 3*w^2 - 6*w - 17]', '[1823, 1823, -2*w^3 + 17*w + 5]', '[1823, 1823, -5*w^3 + 9*w^2 + 23*w - 3]', '[1825, 1825, w^3 - 2*w^2 - 7*w + 7]', '[1825, 1825, -5*w^3 + 8*w^2 + 22*w - 3]', '[1835, 1835, 5*w^3 - 11*w^2 - 16*w + 2]', '[1837, 1837, 3*w^3 - 7*w^2 - 13*w + 8]', '[1837, 1837, w^3 - 5*w^2 + w + 6]', '[1847, 1847, w^3 - 4*w^2 - w + 16]', '[1849, 1849, 2*w^3 - w^2 - 12*w - 2]', '[1855, 1855, -11*w^3 + 19*w^2 + 55*w - 14]', '[1859, 1859, -w^3 + w^2 + 3*w + 8]', '[1865, 1865, -3*w^3 + 7*w^2 + 12*w - 8]', '[1867, 1867, 2*w^3 - 3*w^2 - 6*w - 5]', '[1867, 1867, -2*w^3 + 5*w^2 + 7*w - 14]', '[1867, 1867, -5*w^3 + 9*w^2 + 19*w - 7]', '[1867, 1867, -2*w^3 - w^2 + 16*w + 14]', '[1873, 1873, -3*w^3 + 6*w^2 + 13*w + 1]', '[1877, 1877, w^3 - w^2 - 10*w - 2]', '[1877, 1877, -7*w^3 + 8*w^2 + 37*w + 8]', '[1879, 1879, 2*w^3 - w^2 - 16*w - 4]', '[1879, 1879, -4*w^3 + 7*w^2 + 15*w - 1]', '[1885, 1885, 4*w^3 - 4*w^2 - 20*w - 7]', '[1885, 1885, -w^3 + 2*w^2 - 6]', '[1889, 1889, 4*w^2 - 11*w - 11]', '[1889, 1889, w^3 - 2*w^2 - 3*w - 6]', '[1891, 1891, -5*w^3 + 8*w^2 + 25*w - 10]', '[1895, 1895, 5*w^3 - 12*w^2 - 16*w + 6]', '[1895, 1895, 4*w^3 - 7*w^2 - 15*w]', '[1901, 1901, -4*w^3 + 6*w^2 + 23*w + 1]', '[1901, 1901, w^3 - 4*w - 7]', '[1903, 1903, 4*w^3 - 8*w^2 - 9*w - 2]', '[1904, 238, -4*w^3 + 6*w^2 + 22*w + 4]', '[1904, 238, -2*w^3 + 4*w^2 + 6*w + 6]', '[1904, 238, 2*w^3 - 4*w^2 - 8*w + 10]', '[1913, 1913, 3*w^2 - 4*w - 8]', '[1915, 1915, 4*w^3 - 8*w^2 - 15*w - 1]', '[1921, 1921, -6*w^3 + 7*w^2 + 35*w + 5]', '[1921, 1921, 5*w^3 - 9*w^2 - 18*w - 9]', '[1921, 1921, w^3 - 7*w - 12]', '[1925, 1925, -w^3 + 11*w + 4]', '[1933, 1933, -2*w^3 + 5*w^2 + 9*w - 15]', '[1936, 22, 2*w^3 - 18*w - 6]', '[1936, 22, -2*w^2 + 4*w + 14]', '[1939, 1939, -4*w^3 + 5*w^2 + 22*w - 2]', '[1945, 1945, 3*w^3 - 7*w^2 - 11*w]', '[1945, 1945, 7*w^3 - 16*w^2 - 17*w + 1]', '[1957, 1957, 4*w^3 - 6*w^2 - 21*w - 4]', '[1963, 1963, 4*w^3 - 5*w^2 - 19*w - 3]', '[1967, 1967, -2*w^3 + 7*w^2 - 4*w - 1]', '[1973, 1973, w^3 - 11*w - 2]', '[1973, 1973, -4*w^3 + 8*w^2 + 14*w - 7]', '[1981, 1981, 6*w^3 - 11*w^2 - 29*w + 6]', '[1985, 1985, -3*w^2 + 4*w + 10]', '[1985, 1985, -2*w^3 + 7*w^2 + 1]', '[1991, 1991, 3*w^3 - 3*w^2 - 16*w]', '[1993, 1993, 2*w^3 + w^2 - 20*w - 9]', '[1997, 1997, 3*w^3 - 5*w^2 - 16*w - 4]', '[1997, 1997, 4*w^3 - 5*w^2 - 24*w - 5]', '[1997, 1997, 2*w^3 - 6*w^2 - 8*w + 11]', '[1997, 1997, 4*w^3 - 7*w^2 - 19*w]', '[2000, 10, -6*w^3 + 8*w^2 + 30*w + 2]', '[2000, 250, 2*w^3 - 18*w - 10]', '[2011, 2011, 5*w^3 - 5*w^2 - 26*w - 8]', '[2011, 2011, 4*w^3 - 5*w^2 - 21*w + 2]', '[2015, 2015, 3*w^3 - 6*w^2 - 14*w]', '[2021, 2021, -4*w^3 + 6*w^2 + 17*w - 1]', '[2023, 119, -2*w^2 + 8*w + 1]', '[2023, 119, -3*w^2 + 3*w + 7]', '[2023, 119, -2*w^3 + 3*w^2 + 14*w - 1]', '[2023, 119, -2*w^3 + w^2 + 13*w + 2]', '[2023, 2023, -2*w^3 + w^2 + 16*w + 6]', '[2023, 2023, 5*w^3 - 7*w^2 - 25*w - 8]', '[2025, 75, -3*w^3 + 3*w^2 + 18*w]', '[2027, 2027, -2*w^3 + 5*w^2 + 5*w - 9]', '[2027, 2027, 2*w^2 - w - 11]', '[2027, 2027, -w^3 - w^2 + 14*w + 11]', '[2027, 2027, 5*w^3 - 7*w^2 - 24*w - 1]', '[2039, 2039, -2*w - 7]', '[2041, 2041, 22*w^3 - 38*w^2 - 105*w + 29]', '[2051, 2051, 6*w^3 - 12*w^2 - 20*w + 5]', '[2053, 2053, 4*w^3 - 5*w^2 - 21*w + 4]', '[2053, 2053, -3*w^2 + 4*w + 9]', '[2057, 187, -w^3 + 11*w + 3]', '[2057, 187, 4*w^3 - 5*w^2 - 19*w - 5]', '[2057, 187, -4*w^3 + 3*w^2 + 27*w + 13]', '[2057, 187, w^2 + w - 8]', '[2057, 187, -2*w^3 + 3*w^2 + 10*w - 7]', '[2057, 187, -3*w^3 + 2*w^2 + 18*w + 6]', '[2063, 2063, 5*w^3 - 8*w^2 - 21*w + 4]', '[2063, 2063, 2*w^3 - w^2 - 16*w - 5]', '[2063, 2063, 2*w^3 - 2*w^2 - 15*w - 5]', '[2063, 2063, -5*w^3 + 7*w^2 + 24*w + 4]', '[2069, 2069, w^2 + w - 11]', '[2069, 2069, 5*w^3 - 7*w^2 - 28*w + 1]', '[2075, 2075, -5*w^3 + 10*w^2 + 19*w - 2]', '[2075, 2075, -3*w^3 + 7*w^2 + 9*w - 9]', '[2083, 2083, -4*w^3 + 8*w^2 + 16*w - 1]', '[2083, 2083, 3*w^3 - 6*w^2 - 13*w - 2]', '[2089, 2089, -w^3 + 3*w^2 + 6*w - 7]', '[2089, 2089, -5*w^3 + 8*w^2 + 22*w + 1]', '[2095, 2095, -2*w^3 + 2*w^2 + 8*w + 7]', '[2095, 2095, -w^3 + 2*w^2 + 4]', '[2095, 2095, 3*w^3 - 7*w^2 - 5*w - 3]', '[2095, 2095, 6*w^3 - 12*w^2 - 17*w - 3]', '[2101, 2101, 4*w^3 - 7*w^2 - 14*w - 2]', '[2107, 2107, 5*w^3 - 9*w^2 - 23*w + 13]', '[2117, 2117, -2*w^3 + 4*w^2 + 5*w - 6]', '[2117, 2117, -4*w^3 + 7*w^2 + 16*w + 8]', '[2117, 2117, 2*w^3 - 4*w^2 - 14*w + 1]', '[2117, 2117, 4*w^3 - 5*w^2 - 19*w - 4]', '[2119, 2119, -3*w^3 + 6*w^2 + 10*w - 7]', '[2123, 2123, -3*w^3 + 5*w^2 + 16*w + 5]', '[2123, 2123, 2*w^2 - 6*w - 9]', '[2125, 85, 11*w^3 - 18*w^2 - 55*w + 8]', '[2125, 85, 4*w^3 - 7*w^2 - 15*w + 12]', '[2125, 85, w^3 - 3*w^2 + 8]', '[2125, 2125, 2*w^3 - 6*w^2 - 5*w + 10]', '[2125, 2125, 4*w^3 - 8*w^2 - 15*w + 9]', '[2125, 2125, -3*w^3 + 2*w^2 + 19*w + 6]', '[2128, 266, 2*w^3 - 4*w^2 - 2*w + 4]', '[2131, 2131, w^3 + w^2 - 9*w - 2]', '[2135, 2135, -4*w^3 + 9*w^2 + 19*w - 10]', '[2137, 2137, w^3 - 5*w^2 - w + 15]', '[2141, 2141, 2*w^3 - 3*w^2 - 9*w - 8]', '[2141, 2141, -4*w^3 + 9*w^2 + 13*w]', '[2141, 2141, -6*w^3 + 11*w^2 + 27*w - 5]', '[2141, 2141, -2*w^2 + 5*w + 15]', '[2143, 2143, 3*w^2 - 3*w - 10]', '[2147, 2147, 5*w^3 - 6*w^2 - 25*w - 4]', '[2149, 2149, -w^3 + 3*w^2 + w + 4]', '[2149, 2149, -w^3 - w^2 + 8*w + 1]', '[2153, 2153, 2*w^3 - 3*w^2 - 14*w - 1]', '[2153, 2153, -w^3 - w^2 + 11*w + 14]', '[2155, 2155, -3*w^3 + 7*w^2 + 6*w - 5]', '[2161, 2161, -4*w^3 + 7*w^2 + 19*w - 11]', '[2161, 2161, w^2 - 2*w - 10]', '[2165, 2165, -5*w^3 + 13*w^2 + 8*w - 6]', '[2165, 2165, -w^3 + 4*w^2 - 5*w - 4]', '[2171, 2171, 2*w^3 - 3*w^2 - 9*w + 7]', '[2171, 2171, 16*w^3 - 27*w^2 - 75*w + 25]', '[2177, 2177, 2*w^3 - 5*w^2 - 4*w + 7]', '[2179, 2179, -2*w^3 + 6*w^2 + 3*w - 10]', '[2179, 2179, -5*w^3 + 7*w^2 + 28*w + 1]', '[2189, 2189, -w^3 + 6*w^2 - 9*w - 2]', '[2191, 2191, w^3 + 2*w^2 - 16*w - 1]', '[2195, 2195, 5*w^3 - 11*w^2 - 16*w - 3]', '[2197, 13, -6*w^3 + 10*w^2 + 25*w + 4]', '[2197, 2197, -w^3 + 2*w^2 + 2*w - 9]', '[2203, 2203, -5*w^3 + 8*w^2 + 22*w - 2]', '[2209, 47, -3*w^3 + 7*w^2 + 13*w - 15]', '[2209, 47, 4*w^3 - 10*w^2 - 11*w + 7]', '[2215, 2215, 7*w^3 - 17*w^2 - 11*w + 2]', '[2215, 2215, w^3 - 3*w^2 + 5*w]', '[2219, 2219, 3*w^3 - 8*w^2 - 8*w + 6]', '[2221, 2221, w^3 - 4*w^2 + 2*w - 3]', '[2224, 278, 2*w^3 - 4*w^2 - 10*w - 6]', '[2224, 278, 2*w^3 - 10*w - 10]', '[2225, 2225, -4*w^3 + 4*w^2 + 26*w - 1]', '[2233, 2233, w^3 - w^2 - 5*w - 9]', '[2233, 2233, 2*w^3 - w^2 - 14*w - 1]', '[2249, 2249, -2*w^3 + 4*w^2 + 4*w - 5]', '[2251, 2251, -6*w^3 + 9*w^2 + 33*w + 1]', '[2261, 2261, 3*w^3 - w^2 - 16*w - 7]', '[2261, 2261, -w^3 + 6*w^2 - 4*w - 8]', '[2261, 2261, 3*w^2 - 2*w - 8]', '[2263, 2263, 4*w^3 - 8*w^2 - 17*w + 2]', '[2263, 2263, 5*w^3 - 7*w^2 - 28*w]', '[2267, 2267, 3*w^3 - 3*w^2 - 17*w]', '[2269, 2269, 5*w^3 - 7*w^2 - 29*w - 7]', '[2269, 2269, 2*w^3 - w^2 - 12*w - 1]', '[2273, 2273, 5*w^3 - 7*w^2 - 24*w - 3]', '[2273, 2273, 2*w^3 - 2*w^2 - 15*w]', '[2273, 2273, -3*w^3 + 5*w^2 + 13*w - 9]', '[2273, 2273, 2*w^3 - 4*w^2 - 4*w - 7]', '[2275, 2275, -6*w^3 + 9*w^2 + 28*w - 3]', '[2279, 2279, -w^3 + 4*w^2 - w - 10]', '[2285, 2285, -3*w^3 + 9*w^2 - w - 2]', '[2285, 2285, -3*w^3 + 11*w^2 + 2*w - 4]', '[2287, 2287, -2*w^3 + 6*w^2 + 9*w - 9]', '[2288, 286, -4*w^3 + 4*w^2 + 22*w + 4]', '[2293, 2293, -w^3 + 3*w^2 - 11]', '[2299, 209, 3*w^3 - 3*w^2 - 16*w + 1]', '[2299, 209, -5*w^3 + 8*w^2 + 20*w + 6]', '[2303, 2303, -3*w^3 + 4*w^2 + 12*w + 8]', '[2305, 2305, 2*w^3 - w^2 - 14*w + 2]', '[2309, 2309, 5*w^3 - 11*w^2 - 18*w + 9]', '[2311, 2311, -4*w^3 + 8*w^2 + 21*w - 9]', '[2317, 2317, -3*w^3 + 3*w^2 + 16*w - 2]', '[2320, 290, 2*w^3 - 4*w^2 - 2*w - 2]', '[2320, 290, 2*w^2 - 8*w - 4]', '[2321, 2321, -w^3 + 3*w^2 - 2*w - 6]', '[2321, 2321, -3*w^3 + 2*w^2 + 20*w + 5]', '[2339, 2339, 3*w^2 - 6*w - 16]', '[2341, 2341, -4*w^3 + 10*w^2 + 12*w - 15]', '[2347, 2347, -w^3 - w^2 + 6*w + 11]', '[2347, 2347, 5*w^3 - 6*w^2 - 27*w - 2]', '[2349, 87, -3*w^3 + 3*w^2 + 18*w - 6]', '[2349, 87, 3*w^2 - 3*w - 9]', '[2353, 2353, 12*w^3 - 21*w^2 - 59*w + 14]', '[2359, 2359, -w^3 - w^2 + 9*w]', '[2363, 2363, 2*w^3 - 5*w^2 - 17*w - 4]', '[2363, 2363, w^3 - w^2 - 12*w - 6]', '[2363, 2363, 2*w^3 + w^2 - 9*w - 4]', '[2363, 2363, -w^3 + 7*w^2 - 4*w - 6]', '[2363, 2363, w^3 - 2*w^2 - w + 10]', '[2363, 2363, -w^3 + 3*w + 6]', '[2365, 2365, 9*w^3 - 16*w^2 - 41*w + 19]', '[2371, 2371, 2*w^3 + w^2 - 20*w - 12]', '[2371, 2371, 2*w^3 - 7*w^2 - 2*w + 6]', '[2375, 95, 7*w^3 - 11*w^2 - 35*w + 1]', '[2375, 2375, -5*w^3 + 6*w^2 + 22*w + 10]', '[2377, 2377, 6*w^3 - 9*w^2 - 31*w - 2]', '[2377, 2377, 5*w^3 - 8*w^2 - 24*w - 2]', '[2387, 2387, -w^2 + 6*w - 5]', '[2389, 2389, 3*w^3 - 2*w^2 - 22*w - 11]', '[2389, 2389, -5*w^3 + 8*w^2 + 22*w - 1]', '[2389, 2389, 8*w^3 - 12*w^2 - 39*w + 3]', '[2389, 2389, w^3 + w^2 - 13*w - 11]', '[2393, 2393, 4*w^3 - 7*w^2 - 23*w + 8]', '[2395, 2395, -2*w^3 + w^2 + 12*w - 1]', '[2399, 2399, -5*w^3 + 5*w^2 + 26*w + 5]', '[2401, 7, 7]', '[2401, 2401, -2*w^3 + 5*w^2 + 3*w - 6]', '[2407, 2407, 3*w^3 - 3*w^2 - 20*w - 6]', '[2407, 2407, w^2 + 2*w - 6]', '[2407, 2407, w^3 - 2*w^2 - 4*w - 6]', '[2407, 2407, w^3 - 5*w - 11]', '[2411, 2411, 3*w^3 - 3*w^2 - 18*w + 1]', '[2411, 2411, w^3 + 2*w^2 - 9*w - 10]', '[2411, 2411, -5*w^3 + 7*w^2 + 28*w + 6]', '[2411, 2411, 5*w^3 - 7*w^2 - 25*w - 9]', '[2416, 302, 2*w^3 - 18*w - 14]', '[2429, 2429, 4*w^3 - 9*w^2 - 16*w + 7]', '[2431, 2431, 3*w^3 - w^2 - 22*w - 9]', '[2431, 2431, -w^3 + 2*w^2 + 5*w + 6]', '[2431, 2431, -3*w^3 + 3*w^2 + 14*w + 10]', '[2435, 2435, 5*w^2 - 9*w - 8]', '[2435, 2435, 4*w^3 - 7*w^2 - 20*w]', '[2437, 2437, -6*w^3 + 9*w^2 + 25*w - 6]', '[2437, 2437, -2*w^3 + 6*w^2 + 5*w - 7]', '[2443, 2443, -4*w^3 + 7*w^2 + 13*w - 2]', '[2447, 2447, 2*w^3 + 2*w^2 - 19*w - 17]', '[2447, 2447, w^3 + 3*w^2 - 17*w - 12]', '[2447, 2447, -3*w^3 + 8*w^2 + 7*w - 11]', '[2447, 2447, 3*w^3 - 6*w^2 - 19*w + 4]', '[2459, 2459, -6*w^3 + 10*w^2 + 29*w - 2]', '[2459, 2459, -5*w^3 + 7*w^2 + 25*w + 10]', '[2465, 2465, w + 7]', '[2465, 2465, -3*w^3 + 4*w^2 + 19*w + 3]', '[2465, 2465, w^3 - 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10]', '[2519, 2519, 4*w^3 - 6*w^2 - 17*w - 1]', '[2521, 2521, -w^3 + 5*w^2 - w - 7]', '[2521, 2521, 3*w^3 - 3*w^2 - 20*w - 3]', '[2527, 2527, 3*w^3 - 9*w^2 - 6*w + 5]', '[2531, 2531, -5*w^3 + 8*w^2 + 25*w + 1]', '[2531, 2531, 2*w^2 - 8*w - 3]', '[2539, 2539, -4*w^3 + 7*w^2 + 14*w + 1]', '[2539, 2539, -4*w^3 + 9*w^2 + 12*w - 8]', '[2549, 2549, -2*w^3 + 6*w^2 + 5*w - 8]', '[2551, 2551, -2*w^3 + 6*w^2 + w - 7]', '[2555, 2555, 8*w^3 - 13*w^2 - 37*w + 7]', '[2555, 2555, -7*w^3 + 13*w^2 + 35*w - 13]', '[2563, 2563, -w^3 - w^2 + 11*w - 4]', '[2563, 2563, -4*w^3 + 9*w^2 + 15*w - 9]', '[2567, 2567, 4*w^3 - 3*w^2 - 19*w - 8]', '[2567, 2567, 5*w^3 - 7*w^2 - 20*w - 8]', '[2567, 2567, -w^3 - 2*w^2 + 9*w + 12]', '[2569, 2569, 2*w^3 - 2*w^2 - 13*w + 6]', '[2573, 2573, -3*w^3 + 2*w^2 + 21*w + 3]', '[2573, 2573, -2*w^3 + w^2 + 14*w]', '[2575, 2575, 5*w^3 - 8*w^2 - 28*w + 6]', '[2579, 2579, -5*w^3 + 7*w^2 + 23*w - 1]', '[2581, 2581, -5*w^3 + 9*w^2 + 22*w - 1]', '[2581, 2581, 4*w^3 - 7*w^2 - 14*w + 1]', '[2585, 2585, -2*w^3 + w^2 + 10*w + 10]', '[2587, 2587, 12*w^3 - 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3*w^2 - 16*w - 4]', '[5075, 5075, 3*w^3 - w^2 - 16*w - 14]', '[5081, 5081, 2*w^3 - 3*w^2 - 5*w - 6]', '[5081, 5081, 5*w^3 - 7*w^2 - 29*w - 2]', '[5081, 5081, 5*w^3 - 6*w^2 - 30*w - 5]', '[5081, 5081, w^3 - 2*w^2 + w - 5]', '[5087, 5087, 8*w^3 - 15*w^2 - 38*w + 9]', '[5087, 5087, 3*w^2 - 8*w - 12]', '[5089, 5089, 5*w^3 - 9*w^2 - 19*w + 9]', '[5089, 5089, -5*w^3 + 10*w^2 + 24*w - 15]', '[5095, 5095, -6*w^3 + 12*w^2 + 19*w - 3]', '[5095, 5095, -4*w^3 + 11*w^2 + 6*w - 9]', '[5099, 5099, 5*w^3 - 6*w^2 - 24*w - 7]', '[5101, 5101, w^3 - 5*w^2 + w + 22]', '[5101, 5101, -4*w^3 + 8*w^2 + 17*w + 1]', '[5104, 638, -2*w^2 + 2*w - 4]', '[5104, 638, 2*w^3 - 14*w - 4]', '[5105, 5105, 3*w^3 - 6*w^2 - 10*w - 7]', '[5107, 5107, -4*w^3 + 9*w^2 + 11*w - 8]', '[5117, 5117, 5*w^3 - 6*w^2 - 30*w - 4]', '[5117, 5117, 12*w^3 - 19*w^2 - 62*w + 6]', '[5117, 5117, -3*w^3 + 7*w^2 + 8*w - 19]', '[5119, 5119, 9*w^3 - 16*w^2 - 43*w + 9]', '[5119, 5119, 2*w^2 + w - 9]', '[5131, 5131, 5*w^3 - 12*w^2 - 15*w + 1]', '[5131, 5131, -2*w^3 + 2*w^2 + 7*w - 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15*w - 9]', '[5363, 5363, -3*w^3 + 10*w^2 + 3*w - 14]', '[5375, 215, 4*w^3 - 7*w^2 - 20*w - 3]', '[5375, 5375, -3*w^3 + 2*w^2 + 20*w + 18]', '[5377, 5377, -10*w^3 + 17*w^2 + 48*w - 8]', '[5381, 5381, 4*w^2 - 5*w - 15]', '[5383, 5383, -6*w^3 + 9*w^2 + 27*w - 2]', '[5383, 5383, 4*w^3 - 6*w^2 - 14*w + 9]', '[5387, 5387, -w^3 + 5*w^2 + 3*w - 9]', '[5389, 5389, 5*w^3 - 7*w^2 - 22*w]', '[5389, 5389, 5*w^3 - 11*w^2 - 20*w + 13]', '[5389, 5389, 6*w^3 - 12*w^2 - 18*w - 1]', '[5392, 674, 2*w^3 - 2*w^2 - 16*w - 2]', '[5393, 5393, -w^3 + 5*w^2 + 2*w - 11]', '[5393, 5393, 2*w^3 - 17*w - 2]', '[5395, 5395, 5*w^3 - 8*w^2 - 20*w - 3]', '[5395, 5395, -4*w^2 + 6*w + 13]', '[5399, 5399, -w^3 + 2*w^2 + 4*w - 10]', '[5399, 5399, 4*w^3 - 7*w^2 - 14*w + 8]', '[5399, 5399, -w^3 - 3*w^2 + 12*w + 14]', '[5399, 5399, w^3 - w^2 - 2*w - 9]', '[5407, 5407, -6*w^3 + 8*w^2 + 29*w + 7]', '[5407, 5407, -2*w^3 + 4*w^2 + 7*w - 12]', '[5423, 5423, -4*w^3 + 6*w^2 + 24*w - 1]', '[5423, 5423, 4*w^3 - 6*w^2 - 17*w + 10]', '[5423, 5423, -6*w^3 + 7*w^2 + 36*w + 10]', '[5423, 5423, 3*w^3 - 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2*w - 11]', '[9985, 9985, -3*w^3 + 4*w^2 + 21*w + 2]', '[9985, 9985, 3*w^3 - 7*w^2 - 3*w - 4]', '[9997, 9997, -15*w^3 + 28*w^2 + 70*w - 28]', '[9997, 9997, 17*w^3 - 30*w^2 - 85*w + 19]', '[10000, 10, 10]', '[10000, 1250, -2*w^3 + 4*w^2 + 2*w - 8]'], 'label': '4.4.8789.1', 'narrow_class_no': 1, 'primes': ['[5, 5, -w^3 + 2*w^2 + 3*w]', '[7, 7, w - 1]', '[11, 11, -w^3 + 2*w^2 + 4*w]', '[13, 13, -2*w^3 + 3*w^2 + 10*w - 2]', '[16, 2, 2]', '[17, 17, -w^3 + 2*w^2 + 5*w - 3]', '[17, 17, -w^3 + w^2 + 5*w]', '[17, 17, -w^2 + 2*w + 1]', '[19, 19, w^2 - w - 2]', '[29, 29, w^3 - 2*w^2 - 5*w]', '[29, 29, w^2 - w - 3]', '[31, 31, -w^3 + 2*w^2 + 3*w - 2]', '[43, 43, 2*w^3 - 3*w^2 - 11*w]', '[47, 47, w^3 - 7*w - 4]', '[53, 53, -2*w^3 + 3*w^2 + 9*w - 1]', '[61, 61, -w - 3]', '[73, 73, -w^3 + 2*w^2 + 3*w - 3]', '[73, 73, w^3 - w^2 - 7*w - 1]', '[81, 3, -3]', '[83, 83, -2*w^3 + 3*w^2 + 9*w + 1]', '[83, 83, -w^3 + 3*w^2 + 2*w - 3]', '[89, 89, w - 4]', '[103, 103, w^3 - 2*w^2 - 6*w + 3]', '[113, 113, 2*w^3 - w^2 - 14*w - 6]', '[121, 11, -w^2 + 2*w + 7]', '[125, 5, -3*w^3 + 4*w^2 + 15*w + 1]', '[139, 139, w^3 - 2*w^2 - 5*w - 3]', '[139, 139, w^3 - 5*w - 5]', '[151, 151, w^3 - 9*w - 7]', '[157, 157, -3*w^3 + 6*w^2 + 13*w - 6]', '[163, 163, w^3 - 3*w^2 - 2*w + 9]', '[167, 167, -w^3 + 7*w + 3]', '[167, 167, -3*w^3 + 4*w^2 + 15*w - 1]', '[173, 173, 2*w^3 - 3*w^2 - 7*w - 2]', '[181, 181, -w^3 + 3*w^2 + 4*w - 5]', '[191, 191, w^3 - w^2 - 4*w - 4]', '[193, 193, -w^3 + w^2 + 7*w + 6]', '[193, 193, 2*w^3 - 2*w^2 - 13*w - 5]', '[199, 199, -2*w^3 + 5*w^2 + 5*w - 5]', '[211, 211, w^3 - w^2 - 8*w - 3]', '[211, 211, -2*w^2 + 3*w + 8]', '[227, 227, -w^3 + 3*w^2 + 4*w - 4]', '[227, 227, w^2 - 3*w - 6]', '[229, 229, w^2 - 5]', '[229, 229, 3*w^3 - 4*w^2 - 17*w - 2]', '[233, 233, 3*w^3 - 6*w^2 - 13*w + 3]', '[233, 233, 3*w^3 - 4*w^2 - 16*w + 1]', '[241, 241, -2*w^3 + 4*w^2 + 8*w + 1]', '[251, 251, 2*w^3 - 2*w^2 - 9*w - 3]', '[277, 277, 3*w^3 - 4*w^2 - 17*w - 1]', '[281, 281, -2*w^2 + 5*w + 1]', '[283, 283, -4*w^3 + 6*w^2 + 19*w - 2]', '[293, 293, -3*w^3 + 6*w^2 + 12*w - 2]', '[307, 307, w^3 - w^2 - 4*w - 5]', '[307, 307, w^3 - w^2 - 8*w - 2]', '[311, 311, 2*w^2 - 3*w - 7]', '[313, 313, -2*w^3 + w^2 + 15*w + 3]', '[317, 317, -w^3 + 3*w^2 + w - 5]', '[331, 331, 2*w^3 - 3*w^2 - 12*w]', '[337, 337, w^3 - w^2 - 8*w - 1]', '[343, 7, -w^3 + 6*w + 8]', '[347, 347, 2*w^3 - 4*w^2 - 7*w + 5]', '[349, 349, 2*w^3 - 4*w^2 - 9*w]', '[353, 353, -3*w^3 + 4*w^2 + 16*w + 5]', '[353, 353, -3*w^3 + 4*w^2 + 14*w]', '[353, 353, -w^3 + 3*w^2 + 4*w - 8]', '[353, 353, -w^3 + 2*w^2 + 8*w - 3]', '[359, 359, -4*w^3 + 7*w^2 + 19*w - 3]', '[367, 367, -w^3 + 2*w^2 + 6*w - 5]', '[373, 373, 5*w^3 - 8*w^2 - 26*w + 3]', '[379, 379, -3*w^3 + 5*w^2 + 17*w - 4]', '[379, 379, -w^3 + 2*w^2 + 4*w - 6]', '[383, 383, w^2 - 6]', '[389, 389, w^3 - 2*w^2 - 3*w - 4]', '[389, 389, w^2 + w - 4]', '[397, 397, -4*w^3 + 5*w^2 + 23*w + 5]', '[397, 397, -3*w^3 + 5*w^2 + 12*w - 2]', '[419, 419, -3*w^3 + 4*w^2 + 17*w + 5]', '[419, 419, -3*w^3 + 5*w^2 + 15*w]', '[419, 419, 3*w^3 - 5*w^2 - 14*w - 1]', '[419, 419, 2*w^3 - 3*w^2 - 10*w - 6]', '[431, 431, 2*w^3 - 2*w^2 - 11*w]', '[433, 433, w^3 - 8*w - 1]', '[433, 433, 2*w^2 - 2*w - 5]', '[439, 439, 2*w^3 - 2*w^2 - 9*w - 6]', '[443, 443, 2*w^3 - 5*w^2 - 7*w]', '[443, 443, 2*w^3 - 5*w^2 - 9*w + 4]', '[457, 457, -2*w^3 + 5*w^2 + 7*w - 4]', '[457, 457, -w^3 + 2*w^2 - 3]', '[461, 461, -4*w^3 + 7*w^2 + 17*w - 7]', '[479, 479, 3*w^3 - 5*w^2 - 12*w + 6]', '[487, 487, -2*w^3 + 5*w^2 + 9*w - 9]', '[487, 487, w^3 - 10*w - 8]', '[499, 499, 2*w^3 - 2*w^2 - 12*w + 1]', '[503, 503, w^2 - 7]', '[503, 503, w^3 + w^2 - 7*w - 8]', '[529, 23, -3*w^3 + 5*w^2 + 12*w + 1]', '[529, 23, 3*w^3 - 4*w^2 - 14*w - 1]', '[541, 541, w^3 - 4*w^2 - 2*w + 11]', '[563, 563, -2*w^3 + w^2 + 15*w + 6]', '[569, 569, w^3 - 2*w^2 - 4*w - 4]', '[601, 601, 3*w^3 - 5*w^2 - 17*w + 1]', '[607, 607, -2*w^3 + 5*w^2 + 7*w - 5]', '[607, 607, -w^3 + 3*w^2 + 6*w - 5]', '[613, 613, -4*w^3 + 5*w^2 + 21*w + 1]', '[613, 613, -5*w^3 + 8*w^2 + 23*w - 4]', '[619, 619, w^3 + w^2 - 9*w - 5]', '[619, 619, -3*w^3 + 4*w^2 + 14*w + 2]', '[641, 641, -6*w^3 + 8*w^2 + 31*w + 3]', '[643, 643, 3*w^3 - 4*w^2 - 17*w - 6]', '[643, 643, -2*w^3 + 5*w^2 + 7*w - 6]', '[647, 647, 3*w^3 - 4*w^2 - 13*w - 10]', '[653, 653, -3*w^3 + 5*w^2 + 14*w + 2]', '[653, 653, w^3 - 2*w^2 - w - 3]', '[661, 661, 5*w^3 - 9*w^2 - 24*w + 5]', '[683, 683, 2*w^3 - 3*w^2 - 13*w - 2]', '[683, 683, 4*w^3 - 7*w^2 - 18*w + 1]', '[719, 719, -w^3 + 2*w^2 + 3*w - 7]', '[719, 719, 3*w^3 - 5*w^2 - 16*w - 1]', '[727, 727, -2*w^3 + 5*w^2 + 8*w - 7]', '[727, 727, 2*w^3 - 5*w^2 - 7*w + 13]', '[733, 733, -2*w^2 + 7]', '[733, 733, -3*w^3 + 5*w^2 + 11*w + 2]', '[739, 739, -6*w^3 + 9*w^2 + 29*w - 3]', '[739, 739, -2*w^3 + 3*w^2 + 7*w + 5]', '[751, 751, 4*w^3 - 5*w^2 - 23*w - 3]', '[757, 757, -w^3 + 10*w + 4]', '[757, 757, 2*w^3 - w^2 - 14*w - 4]', '[769, 769, -w^3 + 4*w^2 + 4*w - 8]', '[769, 769, 4*w^3 - 6*w^2 - 21*w - 2]', '[787, 787, 3*w^3 - 3*w^2 - 19*w - 6]', '[787, 787, -2*w^2 + 6*w + 7]', '[839, 839, -3*w^3 + 3*w^2 + 19*w + 5]', '[841, 29, 3*w^3 - 4*w^2 - 13*w - 4]', '[853, 853, -3*w^3 + 5*w^2 + 14*w + 3]', '[853, 853, 2*w^2 - w - 9]', '[853, 853, 3*w^3 - 5*w^2 - 11*w + 1]', '[853, 853, w - 6]', '[857, 857, 2*w^3 - 2*w^2 - 9*w - 7]', '[857, 857, -4*w^3 + 8*w^2 + 13*w - 1]', '[859, 859, 2*w^3 - 4*w^2 - 13*w + 2]', '[859, 859, w^3 - w^2 - 9*w - 2]', '[863, 863, -2*w^3 - w^2 + 17*w + 11]', '[877, 877, 5*w^3 - 6*w^2 - 28*w - 9]', '[877, 877, -4*w^3 + 5*w^2 + 20*w + 6]', '[881, 881, 4*w^3 - 5*w^2 - 18*w - 8]', '[911, 911, -w^3 + 4*w^2 - w - 8]', '[911, 911, 2*w^3 - 3*w^2 - 13*w - 1]', '[919, 919, w^3 - w^2 - 7*w + 5]', '[929, 929, 2*w^3 - 3*w^2 - 13*w + 1]', '[929, 929, -2*w^3 + 5*w^2 + 6*w - 11]', '[941, 941, -3*w^3 + 7*w^2 + 12*w - 5]', '[953, 953, -2*w^3 + 5*w^2 + 5*w - 7]', '[971, 971, w^3 - w^2 - 3*w - 5]', '[971, 971, 3*w^3 - 7*w^2 - 12*w + 11]', '[977, 977, 3*w^3 - 5*w^2 - 11*w]', '[997, 997, -2*w^3 + 3*w^2 + 6*w - 5]', '[997, 997, -4*w^3 + 7*w^2 + 16*w - 2]']}
• 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[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -2, -6, -1, 1], 'conductor': 0, 'degree': 4, 'disc_abs': 8789, 'disc_rad': 8789, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 93.74966666607408, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.8789.1', 'local_algs': ['11.2.1.0a1.1', '11.1.2.1a1.2', '17.1.1.0a1.1', '17.1.1.0a1.1', '17.1.2.1a1.2', '47.2.1.0a1.1', '47.1.2.1a1.2'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 0, 'ramps': [11, 17, 47], 'rd': 9.68244115221, 'regulator': {'__RealLiteral__': 0, 'data': '4.20025231363', 'prec': 44}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 4, 'used_grh': False}