Hilbert modular form data - 2.2.157.1-3.2-b

Formats: - HTML - YAML - JSON - 2024-05-18T23:28:36.427695

• 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': 2, 'disc': 157, 'field_bad_primes': [157], 'field_label': '2.2.157.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.157.1-3.2-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [3], 'level_ideal': '[3,3,-w + 7]', 'level_label': '3.2', 'level_norm': 3, 'parallel_weight': 2, 'short_label': '3.2-b', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3,3,-w + 7]', -1]], 'hecke_eigenvalues': ['e', 1, -2, '-2*e', '-e - 4', 'e + 4', '-e - 5', '2*e + 2', '-e - 3', 6, '2*e - 2', '-2*e - 4', -2, -2, '-2*e', '6*e + 2', '-5*e - 7', '-2*e - 2', '-e - 5', '4*e', '-e + 3', -2, 'e - 6', 'e + 1', -12, '5*e - 5', '-2*e + 6', '8*e + 2', '-6*e - 10', -6, '-2*e + 2', '4*e - 10', '-6*e - 4', '9*e + 4', '4*e + 12', '7*e', '-3*e - 15', '-4*e + 6', '-e - 8', '7*e + 11', 'e - 4', '-4*e + 16', 'e - 4', '5*e + 14', '10*e + 6', '5*e + 9', '7*e - 4', '-10*e - 4', '5*e - 12', '-12*e - 12', '9*e - 6', '12*e + 16', '-4*e - 2', '-4*e - 2', '3*e + 3', '10*e - 8', '2*e + 6', 14, '-7*e - 4', 2, '-2*e + 30', '12*e + 8', '-2*e + 6', '-15*e - 10', '-8*e - 4', '3*e - 14', '-3*e - 2', '-6*e - 24', '-13*e - 1', '4*e - 18', '3*e + 23', '-18*e - 12', '-e + 2', -2, '16*e - 2', '-3*e + 6', '-12*e + 12', '12*e + 18', '-5*e - 20', 'e + 24', '6*e - 22', '-9*e + 4', '-8*e - 22', '-3*e + 9', '-17*e - 7', '-5*e - 21', '8*e + 18', '8*e + 18', '18*e + 8', '-4*e - 2', '-6*e - 28', '-e + 27', '-4*e - 12', '3*e - 14', '-9*e + 17', '-4*e', 18, '-9*e - 27', 22, '-11*e + 19', '3*e + 14', '4*e - 30', '-e - 10', '-20*e - 2', '10*e + 14', -32, '-11*e + 12', '-6*e - 24', '-19*e - 23', '-21*e - 3', '-2*e + 6', '5*e - 29', '14*e + 20', '-22*e - 14', '-17*e', '-8*e - 14', '4*e + 40', '15*e + 18', '2*e + 2', '5*e + 39', '-e + 29', '-17*e - 12', '19*e + 14', '-2*e - 2', '-24*e - 16', '2*e - 12', '-2*e + 4', '2*e - 44', '15*e - 11', 32, '2*e - 10', '4*e + 6', '3*e - 24', '14*e + 2', '9*e + 22', '-16*e - 6', '-9*e - 17', '19*e - 7', '-18*e - 12', '6*e - 16', '4*e - 8', '-22*e', '-22*e - 6', '12*e + 28', '-e - 32', '-24*e - 8', '4*e - 6', '-19*e - 33', '-3*e - 28', '-6*e - 16', '11*e - 29', '-2*e + 40', '6*e - 12', '-4*e - 6', '17*e', '-15*e + 9', '5*e - 18', '4*e - 14', '-3*e - 34', '13*e - 13'], 'hecke_polynomial': 'x^2 + x - 3', 'label': '2.2.157.1-3.2-b'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 157, 'ideals': ['[1, 1, 1]', '[3, 3, w + 6]', '[3, 3, -w + 7]', '[4, 2, 2]', '[9, 3, 3]', '[9, 9, -w + 6]', '[9, 9, -w - 5]', '[11, 11, -3*w - 17]', '[11, 11, 3*w - 20]', '[12, 6, 2*w + 12]', '[12, 6, -2*w + 14]', '[13, 13, 2*w - 13]', '[13, 13, 2*w + 11]', '[16, 4, 4]', '[17, 17, w + 7]', '[17, 17, -w + 8]', '[19, 19, -w - 4]', '[19, 19, -w + 5]', '[25, 5, 5]', '[27, 9, 3*w + 18]', '[27, 9, -3*w + 21]', '[27, 27, -w - 3]', '[27, 27, -w + 4]', '[31, 31, -6*w - 35]', '[31, 31, -6*w + 41]', '[33, 33, -w - 2]', '[33, 33, -w - 8]', '[33, 33, -w + 9]', '[33, 33, w - 3]', '[36, 6, 6]', '[36, 18, -2*w + 12]', '[36, 18, -2*w - 10]', '[37, 37, -w - 1]', '[37, 37, w - 2]', '[39, 39, w]', '[39, 39, 2*w - 15]', '[39, 39, -2*w - 13]', '[39, 39, w - 1]', '[44, 22, -6*w - 34]', '[44, 22, 6*w - 40]', '[47, 47, 3*w + 16]', '[47, 47, -3*w + 19]', '[48, 12, 4*w + 24]', '[48, 12, -4*w + 28]', '[49, 7, -7]', '[51, 51, w + 9]', '[51, 51, -5*w + 33]', '[51, 51, -5*w - 28]', '[51, 51, -w + 10]', '[52, 26, 4*w - 26]', '[52, 26, 4*w + 22]', '[57, 57, 7*w + 41]', '[57, 57, -2*w + 11]', '[57, 57, -2*w - 9]', '[57, 57, -7*w + 48]', '[64, 8, 8]', '[67, 67, 3*w - 22]', '[67, 67, -3*w - 19]', '[68, 34, 2*w + 14]', '[68, 34, -2*w + 16]', '[71, 71, -w - 10]', '[71, 71, w - 11]', '[75, 15, 5*w + 30]', '[75, 15, -5*w + 35]', '[76, 38, -2*w - 8]', '[76, 38, -2*w + 10]', '[81, 9, 9]', '[81, 27, -3*w + 18]', '[81, 27, -3*w - 15]', '[81, 81, -10*w - 57]', '[81, 81, -10*w + 67]', '[89, 89, -8*w - 47]', '[89, 89, 8*w - 55]', '[93, 93, -w - 11]', '[93, 93, 2*w - 9]', '[93, 93, -2*w - 7]', '[93, 93, -w + 12]', '[99, 33, -9*w - 51]', '[99, 33, 9*w - 60]', '[99, 99, 4*w + 21]', '[99, 99, 2*w - 17]', '[99, 99, 2*w + 15]', '[99, 99, -4*w + 25]', '[100, 10, 10]', '[101, 101, 4*w - 29]', '[101, 101, -4*w - 25]', '[108, 18, 6*w + 36]', '[108, 18, -6*w + 42]', '[108, 54, -2*w - 6]', '[108, 54, -2*w + 8]', '[109, 109, -3*w - 20]', '[109, 109, 3*w - 23]', '[111, 111, 8*w - 53]', '[111, 111, -5*w + 32]', '[111, 111, 5*w + 27]', '[111, 111, -8*w - 45]', '[113, 113, 3*w - 17]', '[113, 113, -3*w - 14]', '[117, 39, 6*w - 39]', '[117, 39, 6*w + 33]', '[117, 117, -w - 12]', '[117, 117, 7*w + 39]', '[117, 117, 7*w - 46]', '[117, 117, w - 13]', '[121, 11, 11]', '[121, 121, -2*w + 7]', '[121, 121, -2*w - 5]', '[124, 62, -12*w - 70]', '[124, 62, -12*w + 82]', '[127, 127, -9*w - 53]', '[127, 127, 9*w - 62]', '[132, 66, -2*w - 4]', '[132, 66, -2*w - 16]', '[132, 66, -2*w + 18]', '[132, 66, 2*w - 6]', '[141, 141, 5*w - 36]', '[141, 141, 2*w - 5]', '[141, 141, -2*w - 3]', '[141, 141, 5*w + 31]', '[143, 143, -w - 13]', '[143, 143, -3*w - 13]', '[143, 143, 3*w - 16]', '[143, 143, -w + 14]', '[144, 12, 12]', '[144, 36, -4*w + 24]', '[144, 36, -4*w - 20]', '[147, 21, -7*w - 42]', '[147, 21, 7*w - 49]', '[148, 74, -2*w - 2]', '[148, 74, 2*w - 4]', '[153, 51, 3*w + 21]', '[153, 51, -3*w + 24]', '[153, 153, -13*w - 74]', '[153, 153, -2*w + 3]', '[153, 153, -2*w - 1]', '[153, 153, -13*w + 87]', '[156, 78, 2*w]', '[156, 78, 4*w - 30]', '[156, 78, -4*w - 26]', '[156, 78, 2*w - 2]', '[157, 157, 2*w - 1]', '[167, 167, 2*w - 19]', '[167, 167, -2*w - 17]', '[169, 13, 13]', '[169, 169, -5*w - 26]', '[169, 169, -5*w + 31]', '[171, 57, -3*w - 12]', '[171, 57, -3*w + 15]', '[171, 171, w + 14]', '[171, 171, 10*w + 59]', '[171, 171, -10*w + 69]', '[171, 171, -w + 15]', '[173, 173, 13*w - 89]', '[173, 173, -13*w - 76]', '[176, 44, -12*w - 68]', '[176, 44, 12*w - 80]', '[187, 187, -6*w + 43]', '[187, 187, 4*w - 23]', '[187, 187, -4*w - 19]', '[187, 187, -6*w - 37]', '[188, 94, 6*w + 32]', '[188, 94, -6*w + 38]', '[192, 24, 8*w + 48]', '[192, 24, -8*w + 56]', '[193, 193, 11*w - 73]', '[193, 193, -11*w - 62]', '[196, 14, -14]', '[197, 197, 3*w - 14]', '[197, 197, -3*w - 11]', '[199, 199, 3*w - 25]', '[199, 199, -3*w - 22]', '[201, 201, -w - 15]', '[201, 201, 7*w - 45]', '[201, 201, 7*w + 38]', '[201, 201, w - 16]', '[204, 102, 2*w + 18]', '[204, 102, -10*w + 66]', '[204, 102, -10*w - 56]', '[204, 102, -2*w + 20]', '[208, 52, 8*w - 52]', '[208, 52, 8*w + 44]', '[209, 209, 9*w + 50]', '[209, 209, 5*w + 32]', '[209, 209, 5*w - 37]', '[209, 209, -9*w + 59]', '[213, 213, -4*w - 27]', '[213, 213, -17*w - 99]', '[213, 213, 17*w - 116]', '[213, 213, 4*w - 31]', '[221, 221, -11*w - 65]', '[221, 221, 3*w + 10]', '[221, 221, 3*w - 13]', '[221, 221, 11*w - 76]', '[225, 15, 15]', '[225, 45, -5*w + 30]', '[225, 45, -5*w - 25]', '[228, 114, 14*w + 82]', '[228, 114, -4*w + 22]', '[228, 114, -4*w - 18]', '[228, 114, -14*w + 96]', '[233, 233, -w - 16]', '[233, 233, w - 17]', '[239, 239, 7*w - 50]', '[239, 239, -7*w - 43]', '[243, 27, 9*w + 54]', '[243, 27, -9*w + 63]', '[243, 81, -3*w - 9]', '[243, 81, -3*w + 12]', '[243, 243, -2*w + 21]', '[243, 243, 2*w + 19]', '[247, 247, 16*w + 91]', '[247, 247, -3*w - 23]', '[247, 247, 3*w - 26]', '[247, 247, 16*w - 107]', '[256, 16, 16]', '[257, 257, 6*w + 31]', '[257, 257, -6*w + 37]', '[263, 263, 3*w - 11]', '[263, 263, -3*w - 8]', '[267, 267, -w - 17]', '[267, 267, 4*w + 17]', '[267, 267, 4*w - 21]', '[267, 267, w - 18]', '[268, 134, 6*w - 44]', '[268, 134, -6*w - 38]', '[272, 68, 4*w + 28]', '[272, 68, -4*w + 32]', '[275, 55, -15*w - 85]', '[275, 55, 15*w - 100]', '[277, 277, -12*w - 71]', '[277, 277, 12*w - 83]', '[279, 93, -18*w - 105]', '[279, 93, -18*w + 123]', '[279, 279, -5*w + 29]', '[279, 279, 5*w - 38]', '[279, 279, 5*w + 33]', '[279, 279, 5*w + 24]', '[281, 281, -3*w - 7]', '[281, 281, 3*w - 10]', '[283, 283, -7*w + 44]', '[283, 283, 7*w + 37]', '[284, 142, -2*w - 20]', '[284, 142, 2*w - 22]', '[289, 17, 17]', '[289, 289, -15*w + 103]', '[289, 289, 15*w + 88]', '[297, 99, -3*w - 6]', '[297, 99, -3*w - 24]', '[297, 99, -3*w + 27]', '[297, 99, 3*w - 9]', '[297, 297, 8*w - 57]', '[297, 297, -14*w + 93]', '[297, 297, 14*w + 79]', '[297, 297, 8*w + 49]', '[300, 30, 10*w + 60]', '[300, 30, -10*w + 70]', '[303, 303, -w - 18]', '[303, 303, 8*w + 43]', '[303, 303, 8*w - 51]', '[303, 303, w - 19]', '[304, 76, -4*w - 16]', '[304, 76, -4*w + 20]', '[311, 311, 3*w - 8]', '[311, 311, -3*w - 5]', '[313, 313, -13*w - 73]', '[313, 313, 13*w - 86]', '[317, 317, -9*w + 58]', '[317, 317, 9*w + 49]', '[323, 323, -3*w - 4]', '[323, 323, -12*w + 79]', '[323, 323, -12*w - 67]', '[323, 323, -3*w + 7]', '[324, 18, 18]', '[324, 54, -6*w + 36]', '[324, 54, -6*w - 30]', '[324, 162, -20*w - 114]', '[324, 162, -20*w + 134]', '[325, 65, 10*w - 65]', '[325, 65, 10*w + 55]', '[327, 327, 11*w + 61]', '[327, 327, 2*w - 23]', '[327, 327, -2*w - 21]', '[327, 327, 11*w - 72]', '[331, 331, -5*w - 23]', '[331, 331, 5*w - 28]', '[333, 111, -3*w - 3]', '[333, 111, 3*w - 6]', '[333, 333, -4*w + 33]', '[333, 333, 7*w + 44]', '[333, 333, 7*w - 51]', '[333, 333, -4*w - 29]', '[339, 339, 35*w - 236]', '[339, 339, -4*w + 19]', '[339, 339, 4*w + 15]', '[339, 339, -35*w - 201]', '[341, 341, -w - 19]', '[341, 341, -3*w + 5]', '[341, 341, -3*w - 2]', '[341, 341, w - 20]', '[347, 347, -3*w - 1]', '[347, 347, 3*w - 4]', '[349, 349, 3*w - 28]', '[349, 349, -3*w - 25]', '[351, 117, 3*w]', '[351, 117, 6*w - 45]', '[351, 117, -6*w - 39]', '[351, 117, 3*w - 3]', '[351, 351, -5*w - 34]', '[351, 351, 19*w - 130]', '[351, 351, -19*w - 111]', '[351, 351, 5*w - 39]', '[353, 353, 3*w - 2]', '[353, 353, 3*w - 1]', '[356, 178, -16*w - 94]', '[356, 178, 16*w - 110]', '[361, 19, 19]', '[361, 361, -9*w + 64]', '[361, 361, 9*w + 55]', '[363, 33, -11*w - 66]', '[363, 33, 11*w - 77]', '[363, 363, -7*w - 36]', '[363, 363, -19*w - 108]', '[363, 363, -19*w + 127]', '[363, 363, -7*w + 43]', '[372, 186, -2*w - 22]', '[372, 186, 4*w - 18]', '[372, 186, -4*w - 14]', '[372, 186, -2*w + 24]', '[381, 381, -w - 20]', '[381, 381, 5*w - 27]', '[381, 381, 5*w + 22]', '[381, 381, w - 21]', '[389, 389, 6*w - 35]', '[389, 389, 6*w + 29]', '[396, 66, -18*w - 102]', '[396, 66, 18*w - 120]', '[396, 198, 8*w + 42]', '[396, 198, 4*w - 34]', '[396, 198, 4*w + 30]', '[396, 198, -8*w + 50]', '[400, 20, 20]', '[403, 403, -4*w - 13]', '[403, 403, -3*w - 26]', '[403, 403, -3*w + 29]', '[403, 403, 4*w - 17]', '[404, 202, 8*w - 58]', '[404, 202, -8*w - 50]', '[407, 407, -14*w - 83]', '[407, 407, 23*w + 134]', '[407, 407, -23*w + 157]', '[407, 407, 14*w - 97]', '[419, 419, 2*w - 25]', '[419, 419, -2*w - 23]', '[423, 141, 9*w + 48]', '[423, 141, -9*w + 57]', '[423, 423, -w - 21]', '[423, 423, 17*w - 113]', '[423, 423, -17*w - 96]', '[423, 423, -w + 22]', '[425, 85, 5*w + 35]', '[425, 85, -5*w + 40]', '[429, 429, 5*w + 21]', '[429, 429, 7*w + 45]', '[429, 429, -20*w - 117]', '[429, 429, -17*w + 117]', '[429, 429, -17*w - 100]', '[429, 429, -20*w + 137]', '[429, 429, 7*w - 52]', '[429, 429, -5*w + 26]', '[431, 431, 10*w - 71]', '[431, 431, -10*w - 61]', '[432, 36, 12*w + 72]', '[432, 36, -12*w + 84]', '[432, 108, -4*w - 12]', '[432, 108, -4*w + 16]', '[436, 218, -6*w - 40]', '[436, 218, 6*w - 46]', '[441, 21, 21]', '[441, 63, 7*w - 42]', '[441, 63, 7*w + 35]', '[444, 222, 16*w - 106]', '[444, 222, -10*w + 64]', '[444, 222, 10*w + 54]', '[444, 222, -16*w - 90]', '[452, 226, 6*w - 34]', '[452, 226, -6*w - 28]', '[457, 457, 27*w + 157]', '[457, 457, 27*w - 184]', '[459, 153, 3*w + 27]', '[459, 153, -15*w + 99]', '[459, 153, -15*w - 84]', '[459, 153, -3*w + 30]', '[459, 459, -11*w + 71]', '[459, 459, -4*w + 15]', '[459, 459, -4*w - 11]', '[459, 459, -11*w - 60]', '[461, 461, -4*w - 31]', '[461, 461, 4*w - 35]', '[467, 467, -w - 22]', '[467, 467, w - 23]', '[468, 78, 12*w - 78]', '[468, 78, 12*w + 66]', '[468, 234, -2*w - 24]', '[468, 234, 14*w + 78]', '[468, 234, 14*w - 92]', '[468, 234, 2*w - 26]', '[471, 471, 13*w + 72]', '[471, 471, 13*w - 85]', '[475, 95, -5*w - 20]', '[475, 95, -5*w + 25]', '[481, 481, -15*w - 89]', '[481, 481, 9*w + 56]', '[481, 481, 9*w - 65]', '[481, 481, -15*w + 104]', '[484, 22, 22]', '[484, 242, -4*w + 14]', '[484, 242, -4*w - 10]', '[487, 487, 8*w + 41]', '[487, 487, -8*w + 49]', '[496, 124, -24*w - 140]', '[496, 124, -24*w + 164]', '[501, 501, 31*w - 211]', '[501, 501, 5*w - 41]', '[501, 501, -5*w - 36]', '[501, 501, -31*w - 180]', '[507, 39, 13*w + 78]', '[507, 39, -13*w + 91]', '[507, 507, -11*w + 78]', '[507, 507, -4*w - 9]', '[507, 507, -4*w + 13]', '[507, 507, 11*w + 67]', '[508, 254, -18*w - 106]', '[508, 254, 18*w - 124]', '[513, 171, 21*w + 123]', '[513, 171, -6*w + 33]', '[513, 171, -6*w - 27]', '[513, 171, -21*w + 144]', '[513, 513, w + 23]', '[513, 513, -8*w + 59]', '[513, 513, 8*w + 51]', '[513, 513, -w + 24]', '[517, 517, 7*w - 41]', '[517, 517, -3*w + 31]', '[517, 517, 3*w + 28]', '[517, 517, 7*w + 34]', '[519, 519, 5*w - 24]', '[519, 519, 2*w - 27]', '[519, 519, -2*w - 25]', '[519, 519, 5*w + 19]', '[523, 523, -6*w - 41]', '[523, 523, 6*w - 47]', '[527, 527, -7*w + 53]', '[527, 527, 9*w - 56]', '[527, 527, -9*w - 47]', '[527, 527, -7*w - 46]', '[528, 132, -4*w - 8]', '[528, 132, -4*w - 32]', '[528, 132, -4*w + 36]', '[528, 132, 4*w - 12]', '[529, 23, -23]', '[539, 77, 21*w + 119]', '[539, 77, -21*w + 140]', '[547, 547, 4*w - 11]', '[547, 547, -4*w - 7]', '[557, 557, 28*w - 191]', '[557, 557, -28*w - 163]', '[561, 561, w + 24]', '[561, 561, -16*w - 95]', '[561, 561, 10*w - 63]', '[561, 561, 5*w + 18]', '[561, 561, -5*w + 23]', '[561, 561, -10*w - 53]', '[561, 561, -16*w + 111]', '[561, 561, w - 25]', '[564, 282, 10*w - 72]', '[564, 282, 4*w - 10]', '[564, 282, -4*w - 6]', '[564, 282, 10*w + 62]', '[571, 571, 20*w - 133]', '[571, 571, -20*w - 113]', '[572, 286, -2*w - 26]', '[572, 286, -6*w - 26]', '[572, 286, 6*w - 32]', '[572, 286, -2*w + 28]', '[576, 24, 24]', '[576, 72, -8*w + 48]', '[576, 72, -8*w - 40]', '[577, 577, -3*w - 29]', '[577, 577, 3*w - 32]', '[579, 579, -4*w - 5]', '[579, 579, -5*w - 37]', '[579, 579, -5*w + 42]', '[579, 579, 4*w - 9]', '[588, 42, -14*w - 84]', '[588, 42, 14*w - 98]', '[589, 589, 12*w - 85]', '[589, 589, 11*w + 59]', '[589, 589, -11*w + 70]', '[589, 589, 12*w + 73]', '[591, 591, -32*w - 183]', '[591, 591, 7*w + 33]', '[591, 591, -7*w + 40]', '[591, 591, 32*w - 215]', '[592, 148, -4*w - 4]', '[592, 148, 4*w - 8]', '[593, 593, 19*w - 131]', '[593, 593, -19*w - 112]', '[597, 597, 4*w - 37]', '[597, 597, 43*w - 292]', '[597, 597, -43*w - 249]', '[597, 597, -4*w - 33]', '[601, 601, 5*w - 22]', '[601, 601, -5*w - 17]', '[603, 201, 9*w - 66]', '[603, 201, -9*w - 57]', '[603, 603, 4*w - 7]', '[603, 603, 22*w - 151]', '[603, 603, -22*w - 129]', '[603, 603, 4*w + 3]', '[611, 611, -w - 25]', '[611, 611, 12*w + 65]', '[611, 611, -12*w + 77]', '[611, 611, -w + 26]', '[612, 102, 6*w + 42]', '[612, 102, -6*w + 48]', '[612, 306, -26*w - 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458]', '[9652, 4826, -66*w - 392]', '[9652, 4826, 34*w - 206]', '[9653, 1379, 21*w - 98]', '[9653, 1379, -21*w - 77]', '[9659, 9659, -36*w + 221]', '[9659, 9659, -84*w + 559]', '[9659, 9659, -84*w - 475]', '[9659, 9659, -36*w - 185]', '[9663, 9663, -w - 98]', '[9663, 9663, 31*w + 152]', '[9663, 9663, 31*w - 183]', '[9663, 9663, w - 99]', '[9677, 9677, -59*w - 353]', '[9677, 9677, 59*w - 412]', '[9687, 9687, -16*w - 11]', '[9687, 9687, -23*w - 163]', '[9687, 9687, -23*w + 186]', '[9687, 9687, 16*w - 27]', '[9692, 4846, -18*w - 46]', '[9692, 4846, 18*w - 64]', '[9697, 9697, 47*w + 254]', '[9697, 9697, -47*w + 301]', '[9701, 9701, 42*w + 223]', '[9701, 9701, 19*w - 164]', '[9701, 9701, -19*w - 145]', '[9701, 9701, -42*w + 265]', '[9703, 9703, 9*w - 118]', '[9703, 9703, -17*w - 32]', '[9703, 9703, 17*w - 49]', '[9703, 9703, -9*w - 109]', '[9707, 9707, 27*w - 151]', '[9707, 9707, -47*w + 334]', '[9707, 9707, -47*w - 287]', '[9707, 9707, -27*w - 124]', '[9721, 9721, 98*w - 655]', '[9721, 9721, -98*w - 557]', '[9724, 4862, 12*w + 118]', '[9724, 4862, 74*w - 490]', '[9724, 4862, -42*w - 260]', '[9724, 4862, -16*w + 26]', '[9724, 4862, 16*w + 10]', '[9724, 4862, -42*w + 302]', '[9724, 4862, -74*w - 416]', '[9724, 4862, 12*w - 130]', '[9725, 1945, 30*w - 175]', '[9725, 1945, 30*w + 145]', '[9731, 9731, -14*w - 125]', '[9731, 9731, 5*w - 106]', '[9731, 9731, -5*w - 101]', '[9731, 9731, 14*w - 139]', '[9733, 9733, 39*w - 283]', '[9733, 9733, -39*w - 244]', '[9743, 9743, 74*w - 511]', '[9743, 9743, -74*w - 437]', '[9747, 171, 57*w + 342]', '[9747, 171, -57*w + 399]', '[9747, 513, -19*w - 57]', '[9747, 513, -19*w + 76]', '[9747, 3249, 3*w + 99]', '[9747, 3249, -39*w + 243]', '[9747, 3249, -39*w - 204]', '[9747, 3249, -3*w + 102]', '[9747, 9747, -91*w - 516]', '[9747, 9747, -28*w - 131]', '[9747, 9747, -28*w + 159]', '[9747, 9747, -91*w + 607]', '[9748, 4874, 114*w - 778]', '[9748, 4874, -116*w + 778]', '[9751, 1393, 21*w - 175]', '[9751, 1393, -21*w - 154]', '[9753, 9753, 29*w + 138]', '[9753, 9753, 127*w - 853]', '[9753, 9753, -127*w - 726]', '[9753, 9753, -29*w + 167]', '[9759, 9759, 35*w + 223]', '[9759, 9759, 16*w - 25]', '[9759, 9759, -16*w - 9]', '[9759, 9759, 35*w - 258]', '[9764, 4882, 10*w - 122]', '[9764, 4882, -10*w - 112]', '[9767, 9767, -49*w - 298]', '[9767, 9767, 49*w - 347]', '[9769, 9769, 25*w - 134]', '[9769, 9769, -25*w - 109]', '[9771, 9771, -20*w - 67]', '[9771, 9771, 11*w + 115]', '[9771, 9771, -11*w + 126]', '[9771, 9771, -20*w + 87]', '[9776, 2444, -4*w - 100]', '[9776, 2444, 48*w + 260]', '[9776, 2444, -48*w + 308]', '[9776, 2444, -4*w + 104]', '[9781, 9781, -22*w - 85]', '[9781, 9781, 22*w - 107]', '[9783, 3261, -18*w - 141]', '[9783, 3261, 18*w - 159]', '[9783, 9783, 83*w + 469]', '[9783, 9783, 17*w - 48]', '[9783, 9783, 17*w + 31]', '[9783, 9783, 83*w - 552]', '[9791, 9791, 55*w - 386]', '[9791, 9791, -55*w - 331]', '[9792, 408, 24*w + 168]', '[9792, 408, -24*w + 192]', '[9792, 1224, -104*w - 592]', '[9792, 1224, -16*w + 24]', '[9792, 1224, -16*w - 8]', '[9792, 1224, -104*w + 696]', '[9801, 99, 99]', '[9801, 297, 33*w - 198]', '[9801, 297, 33*w + 165]', '[9801, 891, 110*w + 627]', '[9801, 891, 110*w - 737]', '[9801, 1089, -18*w + 63]', '[9801, 1089, -18*w - 45]', '[9801, 3267, -51*w + 360]', '[9801, 3267, -15*w + 144]', '[9801, 3267, 15*w + 129]', '[9801, 3267, 51*w + 309]', '[9801, 9801, -73*w - 410]', '[9801, 9801, -64*w + 445]', '[9801, 9801, 64*w + 381]', '[9801, 9801, -73*w + 483]', '[9809, 9809, 8*w - 115]', '[9809, 9809, -53*w - 320]', '[9809, 9809, 53*w - 373]', '[9809, 9809, -8*w - 107]', '[9823, 9823, -43*w + 272]', '[9823, 9823, 6*w - 109]', '[9823, 9823, -69*w - 409]', '[9823, 9823, -16*w - 7]', '[9823, 9823, -16*w + 23]', '[9823, 9823, 69*w - 478]', '[9823, 9823, -6*w - 103]', '[9823, 9823, -43*w - 229]', '[9827, 9827, 17*w - 154]', '[9827, 9827, 21*w - 97]', '[9827, 9827, -21*w - 76]', '[9827, 9827, -17*w - 137]', '[9833, 9833, -16*w - 133]', '[9833, 9833, 16*w - 149]', '[9839, 9839, -24*w - 101]', '[9839, 9839, 24*w - 125]', '[9843, 9843, 23*w + 93]', '[9843, 9843, 37*w - 228]', '[9843, 9843, -77*w - 454]', '[9843, 9843, 2*w - 101]', '[9843, 9843, 2*w + 99]', '[9843, 9843, -77*w + 531]', '[9843, 9843, -37*w - 191]', '[9843, 9843, -23*w + 116]', '[9849, 1407, -7*w - 105]', '[9849, 1407, 49*w - 315]', '[9849, 1407, 49*w + 266]', '[9849, 1407, 7*w - 112]', '[9851, 9851, -132*w + 887]', '[9851, 9851, 132*w + 755]', '[9852, 4926, 34*w - 252]', '[9852, 4926, -16*w - 6]', '[9852, 4926, 16*w - 22]', '[9852, 4926, 34*w + 218]', '[9861, 9861, -w - 99]', '[9861, 9861, 17*w + 30]', '[9861, 9861, 35*w + 178]', '[9861, 9861, 44*w - 315]', '[9861, 9861, -44*w - 271]', '[9861, 9861, 35*w - 213]', '[9861, 9861, 17*w - 47]', '[9861, 9861, w - 100]', '[9872, 2468, -72*w - 404]', '[9872, 2468, 72*w - 476]', '[9879, 9879, 19*w - 75]', '[9879, 9879, 16*w - 21]', '[9879, 9879, -13*w - 122]', '[9879, 9879, -25*w + 198]', '[9879, 9879, -25*w - 173]', '[9879, 9879, 13*w - 135]', '[9879, 9879, -16*w - 5]', '[9879, 9879, 19*w + 56]', '[9887, 9887, 38*w - 277]', '[9887, 9887, -38*w - 239]', '[9892, 4946, 26*w - 142]', '[9892, 4946, -26*w - 116]', '[9900, 330, -90*w - 510]', '[9900, 330, 90*w - 600]', '[9900, 990, 40*w + 210]', '[9900, 990, 20*w - 170]', '[9900, 990, 20*w + 150]', '[9900, 990, -40*w + 250]', '[9901, 9901, 82*w - 545]', '[9901, 9901, -82*w - 463]', '[9903, 9903, 139*w - 946]', '[9903, 9903, 22*w - 181]', '[9903, 9903, -22*w - 159]', '[9903, 9903, -139*w - 807]', '[9904, 2476, -16*w - 4]', '[9904, 2476, 16*w - 20]', '[9907, 9907, -111*w + 758]', '[9907, 9907, -121*w + 812]', '[9908, 4954, 18*w - 62]', '[9908, 4954, -18*w - 44]', '[9916, 4958, -32*w + 190]', '[9916, 4958, -50*w + 322]', '[9916, 4958, 50*w + 272]', '[9916, 4958, -32*w - 158]', '[9921, 9921, -80*w - 471]', '[9921, 9921, -41*w - 255]', '[9921, 9921, 41*w - 296]', '[9921, 9921, 80*w - 551]', '[9924, 4962, 214*w - 1444]', '[9924, 4962, -20*w + 86]', '[9924, 4962, 20*w + 66]', '[9924, 4962, -214*w - 1230]', '[9927, 3309, -33*w - 213]', '[9927, 3309, 33*w - 246]', '[9927, 9927, 98*w - 671]', '[9927, 9927, 16*w - 19]', '[9927, 9927, 16*w + 3]', '[9927, 9927, -98*w - 573]', '[9931, 9931, -9*w - 110]', '[9931, 9931, 9*w - 119]', '[9937, 9937, 17*w - 46]', '[9937, 9937, -192*w - 1111]', '[9937, 9937, 192*w - 1303]', '[9937, 9937, 17*w + 29]', '[9939, 9939, 44*w + 235]', '[9939, 9939, -5*w - 102]', '[9939, 9939, 5*w - 107]', '[9939, 9939, 44*w - 279]', '[9948, 4974, -16*w - 2]', '[9948, 4974, -26*w + 204]', '[9948, 4974, -26*w - 178]', '[9948, 4974, 16*w - 18]', '[9949, 9949, 3*w - 103]', '[9949, 9949, -3*w - 100]', '[9967, 9967, -16*w - 1]', '[9967, 9967, 16*w - 17]', '[9972, 1662, -72*w - 426]', '[9972, 1662, 72*w - 498]', '[9972, 4986, 46*w - 328]', '[9972, 4986, 22*w + 84]', '[9972, 4986, 22*w - 106]', '[9972, 4986, -46*w - 282]', '[9973, 9973, -12*w - 119]', '[9973, 9973, 12*w - 131]', '[9977, 9977, -162*w + 1091]', '[9977, 9977, 51*w + 278]', '[9977, 9977, -51*w + 329]', '[9977, 9977, 162*w + 929]', '[9981, 3327, -27*w - 123]', '[9981, 3327, 27*w - 150]', '[9981, 9981, -4*w + 105]', '[9981, 9981, 95*w + 556]', '[9981, 9981, 95*w - 651]', '[9981, 9981, -4*w - 101]', '[9984, 624, 16*w]', '[9984, 624, 32*w - 240]', '[9984, 624, -32*w - 208]', '[9984, 624, 16*w - 16]', '[9996, 714, -14*w - 126]', '[9996, 714, 70*w - 462]', '[9996, 714, 70*w + 392]', '[9996, 714, 14*w - 140]', '[9997, 9997, -31*w + 182]', '[9997, 9997, -103*w + 689]', '[9997, 9997, -103*w - 586]', '[9997, 9997, -31*w - 151]', '[9999, 3333, 21*w + 75]', '[9999, 3333, 27*w - 210]', '[9999, 3333, 27*w + 183]', '[9999, 3333, -21*w + 96]', '[9999, 9999, -16*w + 15]', '[9999, 9999, -67*w - 398]', '[9999, 9999, 10*w + 113]', '[9999, 9999, 115*w - 771]', '[9999, 9999, -115*w - 656]', '[9999, 9999, 10*w - 123]', '[9999, 9999, -67*w + 465]', '[9999, 9999, 16*w - 1]', '[10000, 100, 100]'], 'label': '2.2.157.1', 'narrow_class_no': 1, 'primes': ['[3, 3, w + 6]', '[3, 3, -w + 7]', '[4, 2, 2]', '[11, 11, -3*w - 17]', '[11, 11, 3*w - 20]', '[13, 13, 2*w - 13]', '[13, 13, 2*w + 11]', '[17, 17, w + 7]', '[17, 17, -w + 8]', '[19, 19, -w - 4]', '[19, 19, -w + 5]', '[25, 5, 5]', '[31, 31, -6*w - 35]', '[31, 31, -6*w + 41]', '[37, 37, -w - 1]', '[37, 37, w - 2]', '[47, 47, 3*w + 16]', '[47, 47, -3*w + 19]', '[49, 7, -7]', '[67, 67, 3*w - 22]', '[67, 67, -3*w - 19]', '[71, 71, -w - 10]', '[71, 71, w - 11]', '[89, 89, -8*w - 47]', '[89, 89, 8*w - 55]', '[101, 101, 4*w - 29]', '[101, 101, -4*w - 25]', '[109, 109, -3*w - 20]', '[109, 109, 3*w - 23]', '[113, 113, 3*w - 17]', '[113, 113, -3*w - 14]', '[127, 127, -9*w - 53]', '[127, 127, 9*w - 62]', '[157, 157, 2*w - 1]', '[167, 167, 2*w - 19]', '[167, 167, -2*w - 17]', '[173, 173, 13*w - 89]', '[173, 173, -13*w - 76]', '[193, 193, 11*w - 73]', '[193, 193, -11*w - 62]', '[197, 197, 3*w - 14]', '[197, 197, -3*w - 11]', '[199, 199, 3*w - 25]', '[199, 199, -3*w - 22]', '[233, 233, -w - 16]', '[233, 233, w - 17]', '[239, 239, 7*w - 50]', '[239, 239, -7*w - 43]', '[257, 257, 6*w + 31]', '[257, 257, -6*w + 37]', '[263, 263, 3*w - 11]', '[263, 263, -3*w - 8]', '[277, 277, -12*w - 71]', '[277, 277, 12*w - 83]', '[281, 281, -3*w - 7]', '[281, 281, 3*w - 10]', '[283, 283, -7*w + 44]', '[283, 283, 7*w + 37]', '[311, 311, 3*w - 8]', '[311, 311, -3*w - 5]', '[313, 313, -13*w - 73]', '[313, 313, 13*w - 86]', '[317, 317, -9*w + 58]', '[317, 317, 9*w + 49]', '[331, 331, -5*w - 23]', '[331, 331, 5*w - 28]', '[347, 347, -3*w - 1]', '[347, 347, 3*w - 4]', '[349, 349, 3*w - 28]', '[349, 349, -3*w - 25]', '[353, 353, 3*w - 2]', '[353, 353, 3*w - 1]', '[389, 389, 6*w - 35]', '[389, 389, 6*w + 29]', '[419, 419, 2*w - 25]', '[419, 419, -2*w - 23]', '[431, 431, 10*w - 71]', '[431, 431, -10*w - 61]', '[457, 457, 27*w + 157]', '[457, 457, 27*w - 184]', '[461, 461, -4*w - 31]', '[461, 461, 4*w - 35]', '[467, 467, -w - 22]', '[467, 467, w - 23]', '[487, 487, 8*w + 41]', '[487, 487, -8*w + 49]', '[523, 523, -6*w - 41]', '[523, 523, 6*w - 47]', '[529, 23, -23]', '[547, 547, 4*w - 11]', '[547, 547, -4*w - 7]', '[557, 557, 28*w - 191]', '[557, 557, -28*w - 163]', '[571, 571, 20*w - 133]', '[571, 571, -20*w - 113]', '[577, 577, -3*w - 29]', '[577, 577, 3*w - 32]', '[593, 593, 19*w - 131]', '[593, 593, -19*w - 112]', '[601, 601, 5*w - 22]', '[601, 601, -5*w - 17]', '[617, 617, -18*w - 101]', '[617, 617, 18*w - 119]', '[619, 619, -4*w - 1]', '[619, 619, 4*w - 5]', '[631, 631, 17*w - 112]', '[631, 631, -17*w - 95]', '[641, 641, 15*w + 83]', '[641, 641, 15*w - 98]', '[647, 647, -17*w - 101]', '[647, 647, 17*w - 118]', '[653, 653, -11*w - 68]', '[653, 653, 11*w - 79]', '[659, 659, 5*w - 43]', '[659, 659, -5*w - 38]', '[661, 661, -25*w - 142]', '[661, 661, 25*w - 167]', '[677, 677, 13*w - 92]', '[677, 677, -13*w - 79]', '[709, 709, 5*w - 19]', '[709, 709, -5*w - 14]', '[727, 727, -9*w - 58]', '[727, 727, 9*w - 67]', '[733, 733, 7*w - 38]', '[733, 733, -7*w - 31]', '[739, 739, -18*w - 107]', '[739, 739, 18*w - 125]', '[743, 743, 2*w - 31]', '[743, 743, -2*w - 29]', '[769, 769, -3*w - 32]', '[769, 769, 3*w - 35]', '[773, 773, -w - 28]', '[773, 773, w - 29]', '[797, 797, 21*w - 139]', '[797, 797, -21*w - 118]', '[821, 821, -15*w + 97]', '[821, 821, 15*w + 82]', '[827, 827, 9*w - 53]', '[827, 827, -9*w - 44]', '[829, 829, -19*w - 106]', '[829, 829, 19*w - 125]', '[841, 29, -29]', '[853, 853, 9*w - 68]', '[853, 853, -9*w - 59]', '[907, 907, 3*w - 37]', '[907, 907, -3*w - 34]', '[911, 911, 5*w - 46]', '[911, 911, -5*w - 41]', '[929, 929, -6*w - 19]', '[929, 929, 6*w - 25]', '[941, 941, -20*w - 119]', '[941, 941, 20*w - 139]', '[953, 953, -w - 31]', '[953, 953, w - 32]', '[967, 967, 11*w + 56]', '[967, 967, -11*w + 67]', '[977, 977, 16*w - 113]', '[977, 977, -16*w - 97]', '[991, 991, -8*w - 35]', '[991, 991, 8*w - 43]']}
• 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': [-39, -1, 1], 'conductor': 157, 'degree': 2, 'dirichlet_group': [1, 156], 'disc_abs': 157, 'disc_rad': 157, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[1, 2]]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[2, 1]]], [29, [[2, 1]]], [31, [[1, 2]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1], 'galois_label': '2T1', 'galt': 1, 'grd': 12.529964086141668, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.157.1', 'local_algs': ['157.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [157], 'rd': 12.5299640861, 'regulator': {'__RealLiteral__': 0, 'data': '5.36131420646', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 17 a + 98 \\)'], 'used_grh': False, 'zk': ['1', 'a']}