Hilbert modular form data - 2.2.456.1-2.1-n

Formats: - HTML - YAML - JSON - 2024-06-04T07:58:19.822832

• 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': 2, 'dimension': 4, 'disc': 456, 'field_bad_primes': [2, 3, 19], 'field_label': '2.2.456.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.456.1-2.1-n', 'label_nsuffix': 13, 'label_suffix': 'n', 'level_bad_primes': [2], 'level_ideal': '[2, 2, -3*w - 32]', 'level_label': '2.1', 'level_norm': 2, 'parallel_weight': 2, 'short_label': '2.1-n', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, -3*w - 32]', 1]], 'hecke_eigenvalues': [-1, '1/6*e^3 - 4/3*e', 'e', '1/6*e^3 - 7/3*e', 'e^2 - 8', '-e^2 + 6', '-1/3*e^3 + 8/3*e', '-1/3*e^3 + 8/3*e', '-1/3*e^3 + 5/3*e', '-1/2*e^3 + 5*e', '-1/6*e^3 + 4/3*e', '1/2*e^3 - 5*e', '1/3*e^3 - 5/3*e', '-e^2 + 12', 'e^2 - 2', 0, 0, '-e^2 + 18', 'e^2 + 4', '2*e^2 - 8', '-2*e^2 + 20', '-5/6*e^3 + 20/3*e', '-5/6*e^3 + 20/3*e', '2*e^2 - 10', '-2*e^2 + 18', '5/6*e^3 - 17/3*e', 'e^3 - 9*e', '-3*e', '-1/2*e^3 + 7*e', '-2*e^2 + 24', '2*e^2 - 4', '1/6*e^3 - 4/3*e', '1/6*e^3 - 4/3*e', '11/6*e^3 - 47/3*e', '5/3*e^3 - 37/3*e', '2*e^2 - 20', '-2*e^2 + 8', '-11/6*e^3 + 47/3*e', '-5/3*e^3 + 37/3*e', '-4/3*e^3 + 41/3*e', '-5/6*e^3 + 11/3*e', 'e^2 - 28', '-e^2 - 14', '5/2*e^3 - 22*e', '13/6*e^3 - 46/3*e', '5/6*e^3 - 38/3*e', '-1/6*e^3 + 22/3*e', 12, 12, '2*e^2', '-2*e^2 + 28', '4*e^2 - 20', '-4*e^2 + 36', -16, 'e^3 - 4*e', '5/3*e^3 - 52/3*e', '-e^2 + 26', 'e^2 + 12', '1/3*e^3 + 16/3*e', '5/3*e^3 - 64/3*e', '2/3*e^3 - 28/3*e', '4*e', '-7*e^2 + 44', '7*e^2 - 54', '9*e', '3/2*e^3 - 21*e', '-4/3*e^3 + 56/3*e', '-8*e', '2*e^2 - 28', '-2*e^2', '-5/2*e^3 + 21*e', '-7/3*e^3 + 53/3*e', '5*e^2 - 28', '-5*e^2 + 42', '1/3*e^3 - 8/3*e', '1/3*e^3 - 8/3*e', '-8/3*e^3 + 91/3*e', '-7/6*e^3 + 1/3*e', '3*e^2 - 18', '-3*e^2 + 24', '-7/3*e^3 + 56/3*e', '-7/3*e^3 + 56/3*e', '4*e^2 - 50', '-4*e^2 + 6', '-4*e^2 + 14', '4*e^2 - 42', '-2*e^3 + 27*e', '-1/6*e^3 - 29/3*e', 'e^2 - 12', '-e^2 + 2', '1/2*e^3 - 6*e', '1/6*e^3 + 2/3*e', '-13/6*e^3 + 76/3*e', '-5/6*e^3 - 4/3*e', '-4*e^2 + 46', '4*e^2 - 10', '3*e^3 - 24*e', '3*e^3 - 24*e', -8, 'e^3 - 8*e', 'e^3 - 8*e', '-1/3*e^3 - 25/3*e', '-13/6*e^3 + 85/3*e', '8*e^2 - 42', '-8*e^2 + 70', 32, 32, '-2*e^3 + 8*e', '-10/3*e^3 + 104/3*e', '-9*e^2 + 68', '9*e^2 - 58', '3*e^2 - 14', '-3*e^2 + 28', 18, 18, '31/6*e^3 - 121/3*e', '16/3*e^3 - 131/3*e', '13/6*e^3 - 37/3*e', '3*e^3 - 29*e', '-7/6*e^3 - 11/3*e', '-10/3*e^3 + 119/3*e', '-6*e^2 + 56', '6*e^2 - 28', '8*e^2 - 72', '-8*e^2 + 40', '-e^2 + 20', 'e^2 + 6', '11/6*e^3 - 44/3*e', '11/6*e^3 - 44/3*e', '-8*e', '-4/3*e^3 + 56/3*e', '7/2*e^3 - 25*e', '4*e^3 - 35*e', '10*e^2 - 56', '-10*e^2 + 84', '-2*e^3 + 11*e', '-17/6*e^3 + 83/3*e', '13*e^2 - 86', '-13*e^2 + 96', 42, '4*e^2 - 54', '-4*e^2 + 2', '3*e^2 + 6', '-3*e^2 + 48', '4/3*e^3 - 29/3*e', '3/2*e^3 - 13*e', '-8*e^2 + 64', '8*e^2 - 48', '-4/3*e^3 + 92/3*e', '2*e^3 - 36*e', '-9*e^2 + 78', '9*e^2 - 48', '2*e^2 + 8', '-2*e^2 + 36', '-10*e^2 + 68', '10*e^2 - 72', '1/6*e^3 + 2/3*e', '1/2*e^3 - 6*e', 'e^2 - 4', '-e^2 + 10', 4, '-e^2 - 34', 'e^2 - 48', '-5*e^2 + 66', '5*e^2 - 4', 24, 24], 'hecke_polynomial': 'x^4 - 14*x^2 + 36', 'label': '2.2.456.1-2.1-n'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 456, 'ideals': ['[1, 1, 1]', '[2, 2, -3*w - 32]', '[3, 3, w]', '[4, 2, 2]', '[5, 5, w + 2]', '[5, 5, w + 3]', '[6, 6, w]', '[7, 7, -w + 11]', '[7, 7, w + 11]', '[8, 4, -6*w - 64]', '[9, 3, 3]', '[10, 10, w + 2]', '[10, 10, w + 8]', '[11, 11, w + 2]', '[11, 11, w + 9]', '[12, 6, 2*w]', '[13, 13, w + 6]', '[13, 13, w + 7]', '[14, 14, -w + 10]', '[14, 14, -w - 10]', '[15, 15, -2*w - 21]', '[15, 15, -2*w + 21]', '[16, 4, 4]', '[18, 6, -9*w - 96]', '[19, 19, w]', '[20, 10, 2*w + 4]', '[20, 10, 2*w + 6]', '[21, 21, w + 3]', '[21, 21, w + 18]', '[22, 22, w + 2]', '[22, 22, w + 20]', '[24, 12, 2*w]', '[25, 5, 5]', '[25, 25, -4*w + 43]', '[25, 25, 4*w + 43]', '[26, 26, w + 6]', '[26, 26, w + 20]', '[27, 9, 3*w]', '[28, 14, -2*w + 22]', '[28, 14, 2*w + 22]', '[30, 30, w + 12]', '[30, 30, -w + 12]', '[32, 8, -12*w - 128]', '[33, 33, w + 9]', '[33, 33, w - 9]', '[35, 35, w + 3]', '[35, 35, w + 17]', '[35, 35, w + 18]', '[35, 35, w + 32]', '[36, 6, 6]', '[37, 37, w + 15]', '[37, 37, w + 22]', '[38, 38, w]', '[39, 39, 7*w - 75]', '[39, 39, 7*w + 75]', '[40, 20, 2*w + 4]', '[40, 20, 2*w + 16]', '[41, 41, 37*w + 395]', '[41, 41, 5*w + 53]', '[42, 42, w + 18]', '[42, 42, w + 24]', '[44, 22, 2*w + 4]', '[44, 22, 2*w + 18]', '[45, 15, 3*w + 6]', '[45, 15, 3*w + 9]', '[48, 12, 4*w]', '[49, 7, 7]', '[49, 49, -10*w + 107]', '[49, 49, 10*w + 107]', '[50, 10, -15*w - 160]', '[50, 50, -w - 8]', '[50, 50, -w + 8]', '[52, 26, 2*w + 12]', '[52, 26, 2*w + 14]', '[54, 18, 3*w]', '[55, 55, 13*w - 139]', '[55, 55, -w - 13]', '[55, 55, w - 13]', '[55, 55, -13*w - 139]', '[56, 28, -2*w + 20]', '[56, 28, -2*w - 20]', '[57, 57, 16*w + 171]', '[60, 30, -4*w - 42]', '[60, 30, -4*w + 42]', '[63, 21, -3*w + 33]', '[63, 21, 3*w + 33]', '[64, 8, 8]', '[65, 65, -w - 7]', '[65, 65, 3*w + 31]', '[65, 65, -3*w + 31]', '[65, 65, w - 7]', '[66, 66, -5*w - 54]', '[66, 66, 5*w - 54]', '[67, 67, w + 28]', '[67, 67, w + 39]', '[70, 70, w + 18]', '[70, 70, w + 32]', '[70, 70, w + 38]', '[70, 70, w + 52]', '[71, 71, 40*w + 427]', '[71, 71, 8*w + 85]', '[72, 12, -18*w - 192]', '[73, 73, -2*w + 23]', '[73, 73, 2*w + 23]', '[74, 74, w + 22]', '[74, 74, w + 52]', '[75, 15, 5*w]', '[75, 75, w + 33]', '[75, 75, w + 42]', '[76, 38, 2*w]', '[77, 77, w + 24]', '[77, 77, w + 31]', '[77, 77, w + 46]', '[77, 77, w + 53]', '[78, 78, w + 6]', '[78, 78, -w + 6]', '[80, 20, 4*w + 8]', '[80, 20, 4*w + 12]', '[81, 9, 9]', '[82, 82, -w - 14]', '[82, 82, w - 14]', '[83, 83, w + 23]', '[83, 83, w + 60]', '[84, 42, 2*w + 6]', '[84, 42, 2*w + 36]', '[88, 44, 2*w + 4]', '[88, 44, 2*w + 40]', '[89, 89, -w - 5]', '[89, 89, w - 5]', '[90, 30, 3*w + 6]', '[90, 30, 3*w + 24]', '[91, 91, w + 32]', '[91, 91, w + 45]', '[91, 91, w + 46]', '[91, 91, w + 59]', '[95, 95, -2*w + 19]', '[95, 95, -2*w - 19]', '[96, 24, 4*w]', '[98, 14, -21*w - 224]', '[98, 98, -w - 4]', '[98, 98, -w + 4]', '[99, 33, 3*w + 6]', '[99, 33, 3*w + 27]', '[100, 10, 10]', '[100, 50, -8*w + 86]', '[100, 50, 8*w + 86]', '[101, 101, w + 35]', '[101, 101, w + 66]', '[104, 52, 2*w + 12]', '[104, 52, 2*w + 40]', '[105, 105, -w - 3]', '[105, 105, -11*w + 117]', '[105, 105, -11*w - 117]', '[105, 105, -w + 3]', '[108, 18, 6*w]', '[109, 109, w + 21]', '[109, 109, w + 88]', '[110, 110, w + 2]', '[110, 110, 7*w + 74]', '[110, 110, 7*w - 74]', '[110, 110, w - 2]', '[111, 111, w + 15]', '[111, 111, w - 15]', '[112, 28, -4*w + 44]', '[112, 28, 4*w + 44]', '[113, 113, -w - 1]', '[113, 113, w - 1]', '[114, 114, -w]', '[117, 39, 3*w + 18]', '[117, 39, 3*w + 21]', '[120, 60, 2*w + 24]', '[120, 60, -2*w + 24]', '[121, 11, 11]', '[121, 121, 6*w + 65]', '[121, 121, -6*w + 65]', '[123, 123, w + 27]', '[123, 123, w + 96]', '[125, 25, 5*w + 10]', '[125, 25, 5*w + 15]', '[125, 125, w + 58]', '[125, 125, w + 67]', '[126, 42, -3*w + 30]', '[126, 42, -3*w - 30]', '[128, 16, -24*w - 256]', '[130, 130, 3*w - 34]', '[130, 130, -11*w - 118]', '[130, 130, -11*w + 118]', '[130, 130, 3*w + 34]', '[131, 131, w + 30]', '[131, 131, w + 101]', '[132, 66, 2*w + 18]', '[132, 66, 2*w - 18]', '[133, 133, w + 38]', '[133, 133, w + 95]', '[134, 134, w + 28]', '[134, 134, w + 106]', '[135, 45, -6*w - 63]', '[135, 45, -6*w + 63]', '[140, 70, 2*w + 6]', '[140, 70, 2*w + 34]', '[140, 70, 2*w + 36]', '[140, 70, 2*w + 64]', '[142, 142, -w - 16]', '[142, 142, w - 16]', '[143, 143, 14*w - 149]', '[143, 143, 4*w + 41]', '[143, 143, -4*w + 41]', '[143, 143, -14*w - 149]', '[144, 12, 12]', '[146, 146, -133*w - 1420]', '[146, 146, -5*w - 52]', '[147, 21, 7*w]', '[147, 147, w + 45]', '[147, 147, w + 102]', '[148, 74, 2*w + 30]', '[148, 74, 2*w + 44]', '[149, 149, w + 73]', '[149, 149, w + 76]', '[150, 30, 5*w]', '[150, 150, w + 42]', '[150, 150, w + 108]', '[152, 76, 2*w]', '[154, 154, w + 24]', '[154, 154, w + 46]', '[154, 154, w + 108]', '[154, 154, w + 130]', '[156, 78, 14*w - 150]', '[156, 78, 14*w + 150]', '[160, 40, 4*w + 8]', '[160, 40, 4*w + 32]', '[162, 18, -27*w - 288]', '[164, 82, 74*w + 790]', '[164, 82, 10*w + 106]', '[165, 165, w + 42]', '[165, 165, w + 57]', '[165, 165, w + 108]', '[165, 165, w + 123]', '[166, 166, w + 60]', '[166, 166, w + 106]', '[167, 167, 2*w - 17]', '[167, 167, -2*w - 17]', '[168, 84, 2*w + 36]', '[168, 84, 2*w + 48]', '[169, 13, 13]', '[169, 169, -2*w + 25]', '[169, 169, 2*w + 25]', '[171, 57, 3*w]', '[175, 35, -5*w + 55]', '[175, 35, 5*w + 55]', '[175, 175, w + 17]', '[175, 175, -9*w + 97]', '[175, 175, 9*w + 97]', '[175, 175, -w + 17]', '[176, 44, 4*w + 8]', '[176, 44, 4*w + 36]', '[178, 178, -17*w - 182]', '[178, 178, 47*w + 502]', '[180, 30, 6*w + 12]', '[180, 30, 6*w + 18]', '[181, 181, w + 64]', '[181, 181, w + 117]', '[182, 182, w + 32]', '[182, 182, w + 46]', '[182, 182, w + 136]', '[182, 182, w + 150]', '[185, 185, 17*w - 181]', '[185, 185, -3*w + 29]', '[185, 185, 3*w + 29]', '[185, 185, -17*w - 181]', '[189, 63, 3*w + 9]', '[189, 63, 3*w + 54]', '[190, 190, 7*w + 76]', '[190, 190, -7*w + 76]', '[192, 24, 8*w]', '[195, 195, w + 33]', '[195, 195, w + 72]', '[195, 195, w + 123]', '[195, 195, w + 162]', '[196, 14, 14]', '[196, 98, -20*w + 214]', '[196, 98, 20*w + 214]', '[197, 197, w + 36]', '[197, 197, w + 161]', '[198, 66, 3*w + 6]', '[198, 66, 3*w + 60]', '[199, 199, -3*w - 35]', '[199, 199, 3*w - 35]', '[200, 20, -30*w - 320]', '[200, 100, -2*w - 16]', '[200, 100, -2*w + 16]', '[201, 201, 4*w - 45]', '[201, 201, -4*w - 45]', '[202, 202, w + 66]', '[202, 202, w + 136]', '[205, 205, w + 27]', '[205, 205, w + 68]', '[205, 205, w + 137]', '[205, 205, w + 178]', '[208, 52, 4*w + 24]', '[208, 52, 4*w + 28]', '[209, 209, 9*w + 95]', '[209, 209, 9*w - 95]', '[210, 210, w + 18]', '[210, 210, 23*w + 246]', '[210, 210, -23*w + 246]', '[210, 210, -w + 18]', '[211, 211, w + 89]', '[211, 211, w + 122]', '[213, 213, w + 87]', '[213, 213, w + 126]', '[216, 36, 6*w]', '[218, 218, w + 88]', '[218, 218, w + 130]', '[219, 219, w + 48]', '[219, 219, w + 171]', '[220, 110, 26*w - 278]', '[220, 110, -2*w - 26]', '[220, 110, 2*w - 26]', '[220, 110, -26*w - 278]', '[222, 222, 13*w + 138]', '[222, 222, -13*w + 138]', '[224, 56, -4*w + 40]', '[224, 56, -4*w - 40]', '[225, 15, 15]', '[225, 75, -12*w + 129]', '[225, 75, 12*w + 129]', '[226, 226, -29*w - 310]', '[226, 226, 35*w + 374]', '[228, 114, 32*w + 342]', '[231, 231, 20*w - 213]', '[231, 231, 2*w - 15]', '[231, 231, 2*w + 15]', '[231, 231, 20*w + 213]', '[234, 78, 3*w + 18]', '[234, 78, 3*w + 60]', '[240, 60, -8*w - 84]', '[240, 60, -8*w + 84]', '[242, 22, -33*w - 352]', '[242, 242, -3*w - 28]', '[242, 242, -3*w + 28]', '[243, 27, 9*w]', '[245, 35, 7*w + 14]', '[245, 35, 7*w + 21]', '[245, 245, w + 53]', '[245, 245, w + 102]', '[245, 245, w + 143]', '[245, 245, w + 192]', '[246, 246, w + 96]', '[246, 246, w + 150]', '[247, 247, -w - 19]', '[247, 247, -w + 19]', '[249, 249, -5*w - 51]', '[249, 249, -5*w + 51]', '[250, 50, 5*w + 10]', '[250, 50, 5*w + 40]', '[250, 250, w + 58]', '[250, 250, w + 192]', '[251, 251, w + 37]', '[251, 251, w + 214]', '[252, 42, -6*w + 66]', '[252, 42, 6*w + 66]', '[256, 16, 16]', '[257, 257, 7*w - 73]', '[257, 257, -7*w - 73]', '[259, 259, w + 52]', '[259, 259, w + 59]', '[259, 259, w + 200]', '[259, 259, w + 207]', '[260, 130, -2*w - 14]', '[260, 130, 6*w + 62]', '[260, 130, -6*w + 62]', '[260, 130, 2*w - 14]', '[262, 262, w + 30]', '[262, 262, w + 232]', '[264, 132, -10*w - 108]', '[264, 132, 10*w - 108]', '[266, 266, w + 38]', '[266, 266, w + 228]', '[267, 267, w + 84]', '[267, 267, w + 183]', '[268, 134, 2*w + 56]', '[268, 134, 2*w + 78]', '[270, 90, 3*w + 36]', '[270, 90, -3*w + 36]', '[271, 271, -15*w - 161]', '[271, 271, 81*w + 865]', '[273, 273, -8*w - 87]', '[273, 273, 2*w - 27]', '[273, 273, 2*w + 27]', '[273, 273, -8*w + 87]', '[275, 55, 5*w + 10]', '[275, 55, 5*w + 45]', '[275, 275, w + 42]', '[275, 275, w + 108]', '[275, 275, w + 167]', '[275, 275, w + 233]', '[280, 140, 2*w + 36]', '[280, 140, 2*w + 64]', '[280, 140, 2*w + 76]', '[280, 140, 2*w + 104]', '[281, 281, 55*w + 587]', '[281, 281, 23*w + 245]', '[284, 142, 80*w + 854]', '[284, 142, 16*w + 170]', '[285, 285, w + 57]', '[285, 285, w + 228]', '[286, 286, -w - 20]', '[286, 286, 5*w - 56]', '[286, 286, 5*w + 56]', '[286, 286, -w + 20]', '[287, 287, 12*w - 127]', '[287, 287, 2*w - 13]', '[287, 287, 2*w + 13]', '[287, 287, 12*w + 127]', '[288, 24, -36*w - 384]', '[289, 17, -17]', '[292, 146, -4*w + 46]', '[292, 146, 4*w + 46]', '[294, 42, 7*w]', '[294, 294, w + 102]', '[294, 294, w + 192]', '[296, 148, 2*w + 44]', '[296, 148, 2*w + 104]', '[297, 99, 3*w + 27]', '[297, 99, 3*w - 27]', '[298, 298, w + 76]', '[298, 298, w + 222]', '[300, 30, 10*w]', '[300, 150, 2*w + 66]', '[300, 150, 2*w + 84]', '[303, 303, -4*w + 39]', '[303, 303, -4*w - 39]', '[304, 76, 4*w]', '[307, 307, w + 81]', '[307, 307, w + 226]', '[308, 154, 2*w + 48]', '[308, 154, 2*w + 62]', '[308, 154, 2*w + 92]', '[308, 154, 2*w + 106]', '[312, 156, 2*w + 12]', '[312, 156, -2*w + 12]', '[313, 313, 78*w + 833]', '[313, 313, -18*w - 193]', '[315, 105, 3*w + 9]', '[315, 105, 3*w + 51]', '[315, 105, 3*w + 54]', '[315, 105, 3*w + 96]', '[320, 40, 8*w + 16]', '[320, 40, 8*w + 24]', '[324, 18, 18]', '[325, 65, 5*w + 30]', '[325, 65, 5*w + 35]', '[325, 325, w + 33]', '[325, 325, w + 58]', '[325, 325, w + 267]', '[325, 325, w + 292]', '[327, 327, -w - 21]', '[327, 327, w - 21]', '[328, 164, -2*w - 28]', '[328, 164, 2*w - 28]', '[330, 330, w + 42]', '[330, 330, w + 108]', '[330, 330, w + 222]', '[330, 330, w + 288]', '[331, 331, w + 86]', '[331, 331, w + 245]', '[332, 166, 2*w + 46]', '[332, 166, 2*w + 120]', '[333, 111, 3*w + 45]', '[333, 111, 3*w + 66]', '[334, 334, 115*w + 1228]', '[334, 334, -13*w - 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143]', '[1895, 1895, 14*w - 143]', '[1895, 1895, 6*w + 47]', '[1897, 1897, 26*w - 281]', '[1897, 1897, -4*w + 61]', '[1897, 1897, -4*w - 61]', '[1897, 1897, 26*w + 281]', '[1898, 1898, w + 98]', '[1898, 1898, w + 682]', '[1898, 1898, w + 1216]', '[1898, 1898, w + 1800]', '[1899, 633, 3*w + 267]', '[1899, 633, 3*w + 366]', '[1900, 190, 10*w]', '[1900, 950, 2*w + 266]', '[1900, 950, 2*w + 684]', '[1901, 1901, w + 145]', '[1901, 1901, w + 1756]', '[1906, 1906, 15*w - 166]', '[1906, 1906, -15*w - 166]', '[1907, 1907, w + 439]', '[1907, 1907, w + 1468]', '[1911, 273, 49*w - 525]', '[1911, 273, 49*w + 525]', '[1911, 1911, -w - 45]', '[1911, 1911, -5*w - 69]', '[1911, 1911, -5*w + 69]', '[1911, 1911, -w + 45]', '[1913, 1913, -11*w + 109]', '[1913, 1913, 11*w + 109]', '[1915, 1915, w + 457]', '[1915, 1915, w + 692]', '[1915, 1915, w + 1223]', '[1915, 1915, w + 1458]', '[1917, 639, 3*w + 261]', '[1917, 639, 3*w + 378]', '[1919, 1919, -20*w - 209]', '[1919, 1919, -20*w + 209]', '[1920, 240, 8*w + 96]', '[1920, 240, -8*w + 96]', '[1922, 62, 93*w + 992]', '[1923, 1923, w + 888]', '[1923, 1923, w + 1035]', '[1924, 962, -20*w - 218]', '[1924, 962, -72*w + 770]', '[1924, 962, 72*w + 770]', '[1924, 962, 20*w - 218]', '[1925, 385, 5*w + 120]', '[1925, 385, 5*w + 155]', '[1925, 385, 5*w + 230]', '[1925, 385, 5*w + 265]', '[1925, 1925, w + 108]', '[1925, 1925, w + 508]', '[1925, 1925, w + 592]', '[1925, 1925, w + 717]', '[1925, 1925, w + 1208]', '[1925, 1925, w + 1333]', '[1925, 1925, w + 1417]', '[1925, 1925, w + 1817]', '[1933, 1933, w + 368]', '[1933, 1933, w + 1565]', '[1934, 1934, 15*w + 154]', '[1934, 1934, 15*w - 154]', '[1936, 44, 44]', '[1936, 484, 24*w + 260]', '[1936, 484, -24*w + 260]', '[1937, 1937, 43*w + 457]', '[1937, 1937, -57*w + 607]', '[1937, 1937, -57*w - 607]', '[1937, 1937, 43*w - 457]', '[1944, 108, 18*w]', '[1945, 1945, 22*w - 239]', '[1945, 1945, 2*w - 49]', '[1945, 1945, -2*w - 49]', '[1945, 1945, -22*w - 239]', '[1949, 1949, w + 924]', '[1949, 1949, w + 1025]', '[1950, 390, 5*w + 30]', '[1950, 390, -5*w + 30]', '[1950, 1950, 19*w - 198]', '[1950, 1950, 67*w + 714]', '[1950, 1950, -67*w + 714]', '[1950, 1950, -19*w - 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532]', '[1976, 988, 50*w - 532]', '[1980, 330, 78*w - 834]', '[1980, 330, -6*w - 78]', '[1980, 330, 6*w - 78]', '[1980, 330, -78*w - 834]', '[1983, 1983, -7*w - 87]', '[1983, 1983, 7*w - 87]', '[1986, 1986, 7*w + 60]', '[1986, 1986, -7*w + 60]', '[1988, 994, 26*w + 274]', '[1988, 994, 6*w - 46]', '[1988, 994, 6*w + 46]', '[1988, 994, 26*w - 274]', '[1990, 1990, w + 78]', '[1990, 1990, w + 718]', '[1990, 1990, w + 1272]', '[1990, 1990, w + 1912]', '[1991, 1991, 112*w + 1195]', '[1991, 1991, 10*w + 97]', '[1991, 1991, -10*w + 97]', '[1991, 1991, -112*w + 1195]', '[1992, 996, -14*w + 156]', '[1992, 996, 14*w + 156]', '[1993, 1993, -52*w - 557]', '[1993, 1993, 172*w + 1837]', '[1995, 1995, w + 228]', '[1995, 1995, w + 627]', '[1995, 1995, w + 1368]', '[1995, 1995, w + 1767]', '[1998, 666, 39*w + 414]', '[1998, 666, -39*w + 414]', '[1999, 1999, 3*w - 55]', '[1999, 1999, -3*w - 55]', '[2000, 100, 20*w + 40]', '[2000, 100, 20*w + 60]', '[2000, 500, 4*w + 232]', '[2000, 500, 4*w + 268]', '[2002, 2002, -w - 46]', '[2002, 2002, -81*w - 866]', '[2002, 2002, -31*w - 334]', '[2002, 2002, 9*w - 106]', '[2002, 2002, 9*w + 106]', '[2002, 2002, -31*w + 334]', '[2002, 2002, -81*w + 866]', '[2002, 2002, -w + 46]', '[2004, 1002, 2*w + 150]', '[2004, 1002, 2*w + 852]', '[2005, 2005, w + 142]', '[2005, 2005, w + 543]', '[2005, 2005, w + 1462]', '[2005, 2005, w + 1863]', '[2008, 1004, 2*w + 428]', '[2008, 1004, 2*w + 576]', '[2009, 287, 259*w + 2765]', '[2009, 287, 35*w + 371]', '[2009, 2009, 5*w - 29]', '[2009, 2009, 9*w - 85]', '[2009, 2009, 9*w + 85]', '[2009, 2009, 5*w + 29]', '[2010, 2010, w + 162]', '[2010, 2010, w + 642]', '[2010, 2010, w + 1368]', '[2010, 2010, w + 1848]', '[2016, 168, -12*w + 120]', '[2016, 168, -12*w - 120]', '[2020, 1010, -108*w + 1154]', '[2020, 1010, -4*w + 62]', '[2020, 1010, 4*w + 62]', '[2020, 1010, 108*w + 1154]', '[2023, 119, 17*w - 187]', '[2023, 119, -17*w - 187]', '[2025, 45, 45]', '[2025, 225, -36*w + 387]', '[2025, 225, 36*w + 387]', '[2026, 2026, w + 274]', '[2026, 2026, w + 1752]', '[2028, 78, 26*w]', '[2028, 1014, 2*w + 144]', '[2028, 1014, 2*w + 870]', '[2029, 2029, w + 725]', '[2029, 2029, w + 1304]', '[2034, 678, -87*w - 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338]', '[9902, 9902, 33*w + 338]', '[9903, 9903, 17*w - 207]', '[9903, 9903, -17*w - 207]', '[9907, 9907, w + 4546]', '[9907, 9907, w + 5361]', '[9908, 4954, 2*w + 508]', '[9908, 4954, 2*w + 4446]', '[9909, 3303, 3*w + 468]', '[9909, 3303, 3*w + 2835]', '[9915, 9915, w + 2562]', '[9915, 9915, w + 3387]', '[9915, 9915, w + 6528]', '[9915, 9915, w + 7353]', '[9916, 4958, -70*w + 754]', '[9916, 4958, 10*w - 146]', '[9916, 4958, -10*w - 146]', '[9916, 4958, 70*w + 754]', '[9919, 9919, -23*w + 265]', '[9919, 9919, 85*w - 913]', '[9919, 9919, 27*w + 305]', '[9919, 9919, -5*w + 113]', '[9919, 9919, -5*w - 113]', '[9919, 9919, 27*w - 305]', '[9919, 9919, 85*w + 913]', '[9919, 9919, -23*w - 265]', '[9922, 902, -11*w - 154]', '[9922, 902, 11*w - 154]', '[9922, 9922, -149*w - 1594]', '[9922, 9922, 19*w - 226]', '[9922, 9922, -19*w - 226]', '[9922, 9922, 149*w - 1594]', '[9923, 9923, w + 223]', '[9923, 9923, w + 9700]', '[9930, 9930, w + 2562]', '[9930, 9930, w + 4548]', '[9930, 9930, w + 5382]', '[9930, 9930, w + 7368]', '[9931, 9931, w + 2785]', '[9931, 9931, w + 7146]', '[9934, 9934, 705*w + 7528]', '[9934, 9934, -63*w - 680]', '[9937, 9937, -354*w - 3781]', '[9937, 9937, -126*w - 1349]', '[9939, 9939, w + 2886]', '[9939, 9939, w + 7053]', '[9940, 4970, 2*w + 174]', '[9940, 4970, 2*w + 316]', '[9940, 4970, 2*w + 1814]', '[9940, 4970, 2*w + 2304]', '[9940, 4970, 2*w + 2666]', '[9940, 4970, 2*w + 3156]', '[9940, 4970, 2*w + 4654]', '[9940, 4970, 2*w + 4796]', '[9941, 9941, w + 2542]', '[9941, 9941, w + 7399]', '[9942, 9942, w + 4542]', '[9942, 9942, w + 5400]', '[9944, 4972, 2*w + 224]', '[9944, 4972, 2*w + 1580]', '[9944, 4972, 2*w + 3392]', '[9944, 4972, 2*w + 4748]', '[9948, 4974, -2*w - 102]', '[9948, 4974, 2*w - 102]', '[9949, 9949, w + 3789]', '[9949, 9949, w + 6160]', '[9950, 1990, 45*w - 470]', '[9950, 1990, 45*w + 470]', '[9950, 9950, 11*w - 62]', '[9950, 9950, 59*w + 622]', '[9950, 9950, 59*w - 622]', '[9950, 9950, 11*w + 62]', '[9955, 9955, w + 607]', '[9955, 9955, w + 1927]', '[9955, 9955, w + 2598]', '[9955, 9955, w + 3918]', '[9955, 9955, w + 6037]', '[9955, 9955, w + 7357]', '[9955, 9955, w + 8028]', '[9955, 9955, w + 9348]', '[9956, 4978, 10*w - 38]', '[9956, 4978, 10*w + 38]', '[9958, 9958, w + 1606]', '[9958, 9958, w + 2372]', '[9958, 9958, w + 7586]', '[9958, 9958, w + 8352]', '[9960, 4980, 2*w + 876]', '[9960, 4980, 2*w + 1116]', '[9960, 4980, 2*w + 3864]', '[9960, 4980, 2*w + 4104]', '[9961, 9961, 26*w - 295]', '[9961, 9961, -24*w + 275]', '[9961, 9961, -24*w - 275]', '[9961, 9961, 26*w + 295]', '[9963, 1107, 9*w + 243]', '[9963, 1107, 9*w + 864]', '[9965, 9965, w + 2272]', '[9965, 9965, w + 3707]', '[9965, 9965, w + 6258]', '[9965, 9965, w + 7693]', '[9967, 9967, 41*w - 449]', '[9967, 9967, -41*w - 449]', '[9968, 2492, -24*w + 236]', '[9968, 2492, 64*w - 676]', '[9968, 2492, -64*w - 676]', '[9968, 2492, 24*w + 236]', '[9969, 9969, -89*w - 945]', '[9969, 9969, -89*w + 945]', '[9975, 1995, 25*w + 285]', '[9975, 1995, -25*w + 285]', '[9975, 9975, -101*w + 1083]', '[9975, 9975, 13*w + 171]', '[9975, 9975, -13*w + 171]', '[9975, 9975, 101*w + 1083]', '[9977, 9977, -53*w - 557]', '[9977, 9977, 73*w + 773]', '[9977, 9977, -73*w + 773]', '[9977, 9977, 53*w - 557]', '[9981, 3327, 3*w + 1224]', '[9981, 3327, 3*w + 2103]', '[9983, 9983, 26*w - 259]', '[9983, 9983, -34*w + 349]', '[9983, 9983, 34*w + 349]', '[9983, 9983, 26*w + 259]', '[9984, 624, 112*w - 1200]', '[9984, 624, 112*w + 1200]', '[9990, 3330, 3*w + 954]', '[9990, 3330, 3*w + 1044]', '[9990, 3330, 3*w + 2286]', '[9990, 3330, 3*w + 2376]', '[9995, 9995, w + 648]', '[9995, 9995, w + 2647]', '[9995, 9995, w + 7348]', '[9995, 9995, w + 9347]', '[9997, 9997, w + 1905]', '[9997, 9997, w + 3478]', '[9997, 9997, w + 6519]', '[9997, 9997, w + 8092]', '[9999, 3333, -3*w - 105]', '[9999, 3333, 75*w - 807]', '[9999, 3333, -75*w - 807]', '[9999, 3333, 3*w - 105]', '[10000, 100, 100]', '[10000, 500, -80*w + 860]', '[10000, 500, 80*w + 860]', '[10000, 2500, -32*w + 356]', '[10000, 2500, 32*w + 356]'], 'label': '2.2.456.1', 'narrow_class_no': 4, 'primes': ['[2, 2, -3*w - 32]', '[3, 3, w]', '[5, 5, w + 2]', '[5, 5, w + 3]', '[7, 7, -w + 11]', '[7, 7, w + 11]', '[11, 11, w + 2]', '[11, 11, w + 9]', '[13, 13, w + 6]', '[13, 13, w + 7]', '[19, 19, w]', '[37, 37, w + 15]', '[37, 37, w + 22]', '[41, 41, 37*w + 395]', '[41, 41, 5*w + 53]', '[67, 67, w + 28]', '[67, 67, w + 39]', '[71, 71, 40*w + 427]', '[71, 71, 8*w + 85]', '[73, 73, -2*w + 23]', '[73, 73, 2*w + 23]', '[83, 83, w + 23]', '[83, 83, w + 60]', '[89, 89, -w - 5]', '[89, 89, w - 5]', '[101, 101, w + 35]', '[101, 101, w + 66]', '[109, 109, w + 21]', '[109, 109, w + 88]', '[113, 113, -w - 1]', '[113, 113, w - 1]', '[131, 131, w + 30]', '[131, 131, w + 101]', '[149, 149, w + 73]', '[149, 149, w + 76]', '[167, 167, 2*w - 17]', '[167, 167, -2*w - 17]', '[181, 181, w + 64]', '[181, 181, w + 117]', '[197, 197, w + 36]', '[197, 197, w + 161]', '[199, 199, -3*w - 35]', '[199, 199, 3*w - 35]', '[211, 211, w + 89]', '[211, 211, w + 122]', '[251, 251, w + 37]', '[251, 251, w + 214]', '[257, 257, 7*w - 73]', '[257, 257, -7*w - 73]', '[271, 271, -15*w - 161]', '[271, 271, 81*w + 865]', '[281, 281, 55*w + 587]', '[281, 281, 23*w + 245]', '[289, 17, -17]', '[307, 307, w + 81]', '[307, 307, w + 226]', '[313, 313, 78*w + 833]', '[313, 313, -18*w - 193]', '[331, 331, w + 86]', '[331, 331, w + 245]', '[347, 347, w + 43]', '[347, 347, w + 304]', '[367, 367, 11*w - 119]', '[367, 367, 11*w + 119]', '[373, 373, w + 62]', '[373, 373, w + 311]', '[379, 379, w + 71]', '[379, 379, w + 308]', '[383, 383, 6*w + 61]', '[383, 383, 6*w - 61]', '[389, 389, w + 170]', '[389, 389, w + 219]', '[401, 401, -3*w - 25]', '[401, 401, 3*w - 25]', '[419, 419, w + 47]', '[419, 419, w + 372]', '[421, 421, w + 172]', '[421, 421, w + 249]', '[431, 431, 2*w - 5]', '[431, 431, -2*w - 5]', '[443, 443, w + 185]', '[443, 443, w + 258]', '[449, 449, 5*w - 49]', '[449, 449, 5*w + 49]', '[457, 457, -14*w - 151]', '[457, 457, 14*w - 151]', '[461, 461, w + 110]', '[461, 461, w + 351]', '[463, 463, -33*w - 353]', '[463, 463, 63*w + 673]', '[467, 467, w + 54]', '[467, 467, w + 413]', '[491, 491, w + 144]', '[491, 491, w + 347]', '[521, 521, 67*w + 715]', '[521, 521, 35*w + 373]', '[523, 523, w + 239]', '[523, 523, w + 284]', '[529, 23, -23]', '[547, 547, w + 85]', '[547, 547, w + 462]', '[557, 557, w + 79]', '[557, 557, w + 478]', '[569, 569, 11*w - 115]', '[569, 569, -11*w - 115]', '[577, 577, 4*w - 49]', '[577, 577, -4*w - 49]', '[587, 587, w + 124]', '[587, 587, w + 463]', '[599, 599, 4*w - 35]', '[599, 599, -4*w - 35]', '[631, 631, -5*w - 59]', '[631, 631, 5*w - 59]', '[641, 641, 5*w - 47]', '[641, 641, -5*w - 47]', '[653, 653, w + 296]', '[653, 653, w + 357]', '[661, 661, w + 82]', '[661, 661, w + 579]', '[701, 701, w + 157]', '[701, 701, w + 544]', '[727, 727, -w - 29]', '[727, 727, w - 29]', '[743, 743, 76*w + 811]', '[743, 743, 44*w + 469]', '[769, 769, 2*w - 35]', '[769, 769, -2*w - 35]', '[787, 787, w + 129]', '[787, 787, w + 658]', '[811, 811, w + 134]', '[811, 811, w + 677]', '[821, 821, w + 186]', '[821, 821, w + 635]', '[823, 823, 3*w - 43]', '[823, 823, -3*w - 43]', '[829, 829, w + 51]', '[829, 829, w + 778]', '[839, 839, 126*w + 1345]', '[839, 839, 30*w + 319]', '[841, 29, -29]', '[857, 857, -3*w - 13]', '[857, 857, 3*w - 13]', '[863, 863, 4*w - 31]', '[863, 863, -4*w - 31]', '[877, 877, w + 248]', '[877, 877, w + 629]', '[887, 887, -22*w + 233]', '[887, 887, 22*w + 233]', '[907, 907, w + 387]', '[907, 907, w + 520]', '[911, 911, 82*w + 875]', '[911, 911, 50*w + 533]', '[919, 919, -15*w + 163]', '[919, 919, -15*w - 163]', '[937, 937, -6*w - 71]', '[937, 937, 6*w - 71]', '[947, 947, w + 190]', '[947, 947, w + 757]', '[953, 953, 9*w + 91]', '[953, 953, 9*w - 91]', '[961, 31, -31]', '[967, 967, -9*w - 101]', '[967, 967, 9*w - 101]', '[977, 977, -3*w - 7]', '[977, 977, 3*w - 7]', '[983, 983, -4*w - 29]', '[983, 983, 4*w - 29]']}
• 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': [2], 'class_number': 2, 'cm': False, 'coeffs': [-114, 0, 1], 'conductor': 456, 'degree': 2, 'dirichlet_group': [1, 341], 'disc_abs': 456, 'disc_rad': 114, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[1, 2]]], [7, [[1, 2]]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [0]], [23, [[2, 1]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 21.354156504062622, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.456.1', 'local_algs': ['2.2.3.1', '3.2.1.2', '19.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 19], 'rd': 21.3541565041, 'regulator': {'__RealLiteral__': 0, 'data': '7.62559483418', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 96 a + 1025 \\)'], 'used_grh': False, 'zk': ['1', 'a']}