Hilbert modular form data - 2.2.380.1-2.1-e

Formats: - HTML - YAML - JSON - 2024-06-13T20:14:39.045948

• 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': 380, 'field_bad_primes': [2, 5, 19], 'field_label': '2.2.380.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.380.1-2.1-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [2], 'level_ideal': '[2, 2, w + 1]', 'level_label': '2.1', 'level_norm': 2, 'parallel_weight': 2, 'short_label': '2.1-e', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, w + 1]', '-1/42*e^3 - 29/42*e']], 'hecke_eigenvalues': ['1/42*e^3 + 29/42*e', 0, 'e', '1/7*e^3 + 22/7*e', 1, '1/14*e^3 + 1/14*e', '-3/14*e^3 - 59/14*e', -2, '2/7*e^3 + 37/7*e', '-1/7*e^3 - 8/7*e', -6, -6, '1/7*e^3 + 1/7*e', '-3/7*e^3 - 59/7*e', '-2/7*e^3 - 30/7*e', '2/7*e^3 + 30/7*e', '-1/7*e^3 - 29/7*e', '-1/7*e^3 - 29/7*e', '-5/14*e^3 - 61/14*e', '1/2*e^3 + 17/2*e', '1/2*e^2 + 17/2', '-1/2*e^2 - 5/2', 'e^2 + 11', '-e^2 - 11', '-e^2 - 17', 'e^2 + 5', -10, -10, '3/7*e^3 + 45/7*e', '-3/7*e^3 - 45/7*e', '-2*e', '-2/7*e^3 - 44/7*e', 'e^2 + 5', '-e^2 - 17', '1/7*e^3 + 29/7*e', '1/7*e^3 + 29/7*e', -6, '-e^2 - 5', 'e^2 + 17', '-e^2 - 17', 'e^2 + 5', '-3/7*e^3 - 59/7*e', '1/7*e^3 + 1/7*e', '-5/7*e^3 - 61/7*e', 'e^3 + 17*e', '2*e^2 + 28', '-2*e^2 - 16', '3/7*e^3 + 59/7*e', '-1/7*e^3 - 1/7*e', '-3/2*e^2 - 23/2', '3/2*e^2 + 43/2', -24, -24, '-6/7*e^3 - 90/7*e', '6/7*e^3 + 90/7*e', '-5/7*e^3 - 61/7*e', 'e^3 + 17*e', '-1/7*e^3 - 15/7*e', '1/7*e^3 + 15/7*e', 7, '5/14*e^3 + 145/14*e', '5/14*e^3 + 145/14*e', '5/14*e^3 + 61/14*e', '-1/2*e^3 - 17/2*e', '1/2*e^2 + 41/2', '-1/2*e^2 + 19/2', '-2/7*e^3 - 2/7*e', '6/7*e^3 + 118/7*e', '-12/7*e^3 - 180/7*e', '12/7*e^3 + 180/7*e', '3*e^2 + 43', '-3*e^2 - 23', '-5/7*e^3 - 89/7*e', '3/7*e^3 + 31/7*e', '1/14*e^3 - 83/14*e', '-15/14*e^3 - 323/14*e', '7/2*e^2 + 59/2', '-7/2*e^2 - 95/2', '-e^2 - 29', 'e^2 - 7', 'e^2 - 1', '-e^2 - 23', '2/7*e^3 + 30/7*e', '-2/7*e^3 - 30/7*e', '-3*e^2 - 41', '3*e^2 + 25', '1/7*e^3 + 29/7*e', '1/7*e^3 + 29/7*e', '-3*e^2 - 21', '3*e^2 + 45', '1/7*e^3 + 1/7*e', '-3/7*e^3 - 59/7*e', '8/7*e^3 + 190/7*e', '2/7*e^3 + 100/7*e', '-11/7*e^3 - 214/7*e', '4/7*e^3 + 11/7*e', 20, 20, '11/7*e^3 + 193/7*e', '-e^3 - 11*e', '3*e^2 + 33', '-3*e^2 - 33', '-5/7*e^3 - 117/7*e', '-1/7*e^3 - 57/7*e', '4/7*e^3 + 11/7*e', '-11/7*e^3 - 214/7*e', '-1/2*e^2 - 17/2', '1/2*e^2 + 5/2', '2/7*e^3 + 44/7*e', '2*e', '1/2*e^3 + 17/2*e', '-5/14*e^3 - 61/14*e', '-2*e^2 - 10', '2*e^2 + 34', '-2*e^2 + 14', '2*e^2 + 58', '4/7*e^3 + 39/7*e', '-e^3 - 18*e', '-e^2 + 19', 'e^2 + 41', -3, -3, '3*e^2 + 20', '-3*e^2 - 46', '3/14*e^3 + 3/14*e', '-9/14*e^3 - 177/14*e', '-15/14*e^3 - 183/14*e', '3/2*e^3 + 51/2*e', '-2*e^2 - 25', '2*e^2 + 19', '-3/2*e^2 - 91/2', '3/2*e^2 - 25/2', '2*e^2 + 4', '-2*e^2 - 40', '-6/7*e^3 - 167/7*e', '-5/7*e^3 - 152/7*e', '-3*e^2 - 57', '3*e^2 + 9', -39, '-8/7*e^3 - 148/7*e', '4/7*e^3 + 32/7*e', '-17/14*e^3 - 269/14*e', '15/14*e^3 + 211/14*e', '2*e^2 + 52', '-2*e^2 + 8', '-8*e', '-8/7*e^3 - 176/7*e', 'e^2 - 1', '-e^2 - 23', '4*e^2 + 35', '-4*e^2 - 53', '11/7*e^3 + 277/7*e', '5/7*e^3 + 187/7*e', '-8/7*e^3 - 64/7*e', '16/7*e^3 + 296/7*e', '11/7*e^3 + 179/7*e', '-9/7*e^3 - 121/7*e', '-2*e^2 - 52', '2*e^2 - 8', '-4/7*e^3 - 74/7*e', '2/7*e^3 + 16/7*e', -20, -20], 'hecke_polynomial': 'x^4 + 22*x^2 + 49', 'label': '2.2.380.1-2.1-e'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 380, 'ideals': ['[1, 1, 1]', '[2, 2, w + 1]', '[4, 2, 2]', '[5, 5, -w + 10]', '[7, 7, w + 2]', '[7, 7, w + 5]', '[8, 4, 2*w + 2]', '[9, 3, 3]', '[10, 10, w + 5]', '[13, 13, w + 2]', '[13, 13, w + 11]', '[14, 14, -w + 9]', '[14, 14, -w - 9]', '[16, 4, 4]', '[18, 6, 3*w + 3]', '[19, 19, 2*w - 19]', '[20, 10, -2*w + 20]', '[23, 23, w + 7]', '[23, 23, w + 16]', '[25, 5, 5]', '[26, 26, -w - 11]', '[26, 26, w - 11]', '[28, 14, 2*w + 4]', '[28, 14, 2*w + 10]', '[31, 31, -w - 8]', '[31, 31, w - 8]', '[32, 8, 4*w + 4]', '[35, 35, w + 5]', '[35, 35, w + 30]', '[36, 6, 6]', '[37, 37, w + 13]', '[37, 37, w + 24]', '[38, 38, w + 19]', '[40, 20, 2*w + 10]', '[43, 43, w + 3]', '[43, 43, w + 40]', '[45, 15, -3*w + 30]', '[46, 46, -w - 7]', '[46, 46, w - 7]', '[47, 47, w + 1]', '[47, 47, w + 46]', '[49, 7, 7]', '[49, 49, w + 12]', '[49, 49, -w + 12]', '[50, 10, 5*w + 5]', '[52, 26, 2*w + 4]', '[52, 26, 2*w + 22]', '[53, 53, w + 25]', '[53, 53, w + 28]', '[56, 28, -2*w + 18]', '[56, 28, -2*w - 18]', '[59, 59, -w - 6]', '[59, 59, w - 6]', '[61, 61, 2*w - 21]', '[61, 61, 6*w - 59]', '[62, 62, w + 23]', '[62, 62, w + 39]', '[63, 21, 3*w + 6]', '[63, 21, 3*w + 15]', '[64, 8, 8]', '[65, 65, w + 15]', '[65, 65, w + 50]', '[70, 70, -w - 5]', '[70, 70, -w + 5]', '[71, 71, 5*w - 48]', '[71, 71, -3*w + 28]', '[72, 12, 6*w + 6]', '[74, 74, -w - 13]', '[74, 74, w - 13]', '[76, 38, 4*w - 38]', '[79, 79, -w - 4]', '[79, 79, w - 4]', '[80, 20, -4*w + 40]', '[81, 9, 9]', '[83, 83, w + 26]', '[83, 83, w + 57]', '[86, 86, -w - 3]', '[86, 86, w - 3]', '[90, 30, 3*w + 15]', '[91, 91, w + 2]', '[91, 91, 2*w - 17]', '[91, 91, 2*w + 17]', '[91, 91, w - 2]', '[92, 46, 2*w + 14]', '[92, 46, 2*w + 32]', '[94, 94, -w - 1]', '[94, 94, w - 1]', '[95, 95, w]', '[97, 97, w + 17]', '[97, 97, w + 80]', '[98, 14, 7*w + 7]', '[98, 98, w + 37]', '[98, 98, w + 61]', '[100, 10, 10]', '[101, 101, -w - 14]', '[101, 101, w - 14]', '[104, 52, -2*w - 22]', '[104, 52, 2*w - 22]', '[106, 106, 3*w - 31]', '[106, 106, 3*w + 31]', '[112, 28, 4*w + 8]', '[112, 28, 4*w + 20]', '[113, 113, w + 35]', '[113, 113, w + 78]', '[115, 115, w + 30]', '[115, 115, w + 85]', '[117, 39, 3*w + 6]', '[117, 39, 3*w + 33]', '[118, 118, w + 53]', '[118, 118, w + 65]', '[121, 11, -11]', '[122, 122, w + 41]', '[122, 122, w + 81]', '[124, 62, -2*w - 16]', '[124, 62, 2*w - 16]', '[125, 25, -5*w + 50]', '[126, 42, -3*w + 27]', '[126, 42, -3*w - 27]', '[128, 16, 8*w + 8]', '[130, 130, -w - 15]', '[130, 130, w - 15]', '[133, 133, w + 19]', '[133, 133, w + 114]', '[140, 70, 2*w + 10]', '[140, 70, 2*w + 60]', '[142, 142, w + 33]', '[142, 142, w + 109]', '[144, 12, 12]', '[148, 74, 2*w + 26]', '[148, 74, 2*w + 48]', '[149, 149, 2*w - 23]', '[149, 149, -2*w - 23]', '[151, 151, 8*w - 77]', '[151, 151, -4*w + 37]', '[152, 76, 2*w + 38]', '[155, 155, -2*w + 15]', '[155, 155, 18*w - 175]', '[158, 158, w + 75]', '[158, 158, w + 83]', '[160, 40, 4*w + 20]', '[161, 161, -w - 16]', '[161, 161, 8*w + 79]', '[161, 161, 8*w - 79]', '[161, 161, -w + 16]', '[162, 18, 9*w + 9]', '[163, 163, w + 62]', '[163, 163, w + 101]', '[166, 166, 5*w - 47]', '[166, 166, 5*w + 47]', '[169, 13, 13]', '[169, 169, 3*w + 32]', '[169, 169, -3*w + 32]', '[171, 57, 6*w - 57]', '[172, 86, 2*w + 6]', '[172, 86, 2*w + 80]', '[173, 173, w + 21]', '[173, 173, w + 152]', '[175, 35, 5*w + 10]', '[175, 35, 5*w + 25]', '[179, 179, 3*w - 26]', '[179, 179, -13*w + 126]', '[180, 30, -6*w + 60]', '[182, 182, w + 37]', '[182, 182, w + 89]', '[182, 182, w + 93]', '[182, 182, w + 145]', '[184, 92, -2*w - 14]', '[184, 92, 2*w - 14]', '[185, 185, w + 50]', '[185, 185, w + 135]', '[188, 94, 2*w + 2]', '[188, 94, 2*w + 92]', '[190, 190, w + 95]', '[193, 193, w + 45]', '[193, 193, w + 148]', '[194, 194, -w - 17]', '[194, 194, w - 17]', '[196, 14, 14]', '[196, 98, 2*w + 24]', '[196, 98, -2*w + 24]', '[200, 20, 10*w + 10]', '[202, 202, w + 87]', '[202, 202, w + 115]', '[207, 69, 3*w + 21]', '[207, 69, 3*w + 48]', '[208, 52, 4*w + 8]', '[208, 52, 4*w + 44]', '[211, 211, 2*w - 13]', '[211, 211, -2*w - 13]', '[212, 106, 2*w + 50]', '[212, 106, 2*w + 56]', '[215, 215, w + 40]', '[215, 215, w + 175]', '[217, 217, w + 23]', '[217, 217, w + 54]', '[217, 217, w + 163]', '[217, 217, w + 194]', '[224, 56, -4*w + 36]', '[224, 56, -4*w - 36]', '[225, 15, 15]', '[226, 226, 5*w - 51]', '[226, 226, 9*w - 89]', '[229, 229, -w - 18]', '[229, 229, w - 18]', '[230, 230, 17*w - 165]', '[230, 230, -3*w + 25]', '[234, 78, -3*w - 33]', '[234, 78, 3*w - 33]', '[235, 235, w + 95]', '[235, 235, w + 140]', '[236, 118, -2*w - 12]', '[236, 118, 2*w - 12]', '[242, 22, 11*w + 11]', '[244, 122, 4*w - 42]', '[244, 122, 12*w - 118]', '[245, 35, -7*w + 70]', '[245, 245, -2*w + 25]', '[245, 245, 2*w + 25]', '[247, 247, w + 76]', '[247, 247, w + 171]', '[248, 124, 2*w + 46]', '[248, 124, 2*w + 78]', '[250, 50, 5*w + 25]', '[252, 42, 6*w + 12]', '[252, 42, 6*w + 30]', '[256, 16, 16]', '[257, 257, w + 98]', '[257, 257, w + 159]', '[259, 259, 11*w - 106]', '[259, 259, 2*w - 11]', '[259, 259, 2*w + 11]', '[259, 259, 11*w + 106]', '[260, 130, 2*w + 30]', '[260, 130, 2*w + 100]', '[263, 263, w + 44]', '[263, 263, w + 219]', '[265, 265, w + 25]', '[265, 265, w + 240]', '[266, 266, -w - 19]', '[266, 266, w - 19]', '[279, 93, -3*w - 24]', '[279, 93, 3*w - 24]', '[280, 140, -2*w - 10]', '[280, 140, -2*w + 10]', '[283, 283, w + 100]', '[283, 283, w + 183]', '[284, 142, 10*w - 96]', '[284, 142, -6*w + 56]', '[288, 24, 12*w + 12]', '[289, 17, -17]', '[293, 293, w + 55]', '[293, 293, w + 238]', '[295, 295, -4*w + 35]', '[295, 295, 16*w - 155]', '[296, 148, -2*w - 26]', '[296, 148, 2*w - 26]', '[298, 298, w + 63]', '[298, 298, w + 235]', '[299, 299, 9*w + 86]', '[299, 299, 2*w - 9]', '[299, 299, -2*w - 9]', '[299, 299, -9*w + 86]', '[301, 301, 6*w - 61]', '[301, 301, -3*w + 34]', '[301, 301, -3*w - 34]', '[301, 301, 6*w + 61]', '[302, 302, w + 47]', '[302, 302, w + 255]', '[304, 76, 8*w - 76]', '[305, 305, -w - 20]', '[305, 305, w - 20]', '[310, 310, w + 85]', '[310, 310, w + 225]', '[315, 105, 3*w + 15]', '[315, 105, 3*w + 90]', '[316, 158, -2*w - 8]', '[316, 158, 2*w - 8]', '[317, 317, w + 27]', '[317, 317, w + 290]', '[320, 40, -8*w + 80]', '[322, 322, w + 131]', '[322, 322, w + 145]', '[322, 322, w + 177]', '[322, 322, w + 191]', '[324, 18, 18]', '[325, 65, 5*w + 10]', '[325, 65, 5*w + 55]', '[326, 326, -3*w + 23]', '[326, 326, -3*w - 23]', '[329, 329, -4*w - 43]', '[329, 329, 5*w + 52]', '[329, 329, 5*w - 52]', '[329, 329, -4*w + 43]', '[331, 331, 2*w - 7]', '[331, 331, -2*w - 7]', '[332, 166, 2*w + 52]', '[332, 166, 2*w + 114]', '[333, 111, 3*w + 39]', '[333, 111, 3*w + 72]', '[337, 337, w + 134]', '[337, 337, w + 203]', '[338, 26, 13*w + 13]', '[338, 338, w + 67]', '[338, 338, w + 271]', '[342, 114, 3*w + 57]', '[343, 49, 7*w + 14]', '[343, 49, 7*w + 35]', '[343, 343, w + 110]', '[343, 343, w + 233]', '[344, 172, -2*w - 6]', '[344, 172, 2*w - 6]', '[346, 346, -w - 21]', '[346, 346, w - 21]', '[347, 347, w + 147]', '[347, 347, w + 200]', '[349, 349, 2*w - 27]', '[349, 349, -2*w - 27]', '[350, 70, -5*w + 45]', '[350, 70, -5*w - 45]', '[355, 355, 2*w - 5]', '[355, 355, -2*w - 5]', '[358, 358, w + 51]', '[358, 358, w + 307]', '[360, 60, 6*w + 30]', '[361, 19, 19]', '[364, 182, 2*w + 4]', '[364, 182, 4*w - 34]', '[364, 182, 4*w + 34]', '[364, 182, 2*w - 4]', '[367, 367, w + 126]', '[367, 367, w + 241]', '[368, 92, 4*w + 28]', '[368, 92, 4*w + 64]', '[370, 370, 23*w - 225]', '[370, 370, 3*w - 35]', '[371, 371, 3*w + 22]', '[371, 371, 2*w - 3]', '[371, 371, -2*w - 3]', '[371, 371, -3*w + 22]', '[373, 373, w + 29]', '[373, 373, w + 344]', '[376, 188, -2*w - 2]', '[376, 188, 2*w - 2]', '[379, 379, 2*w - 1]', '[379, 379, -2*w - 1]', '[380, 190, 2*w]', '[386, 386, 7*w - 71]', '[386, 386, 11*w - 109]', '[387, 129, 3*w + 9]', '[387, 129, 3*w + 120]', '[388, 194, 2*w + 34]', '[388, 194, 2*w + 160]', '[389, 389, -w - 22]', '[389, 389, w - 22]', '[392, 28, 14*w + 14]', '[392, 196, 2*w + 74]', '[392, 196, 2*w + 122]', '[395, 395, 14*w - 135]', '[395, 395, -6*w + 55]', '[400, 20, 20]', '[403, 403, w + 54]', '[403, 403, w + 132]', '[403, 403, w + 271]', '[403, 403, w + 349]', '[404, 202, -2*w - 28]', '[404, 202, 2*w - 28]', '[405, 45, -9*w + 90]', '[413, 413, w + 65]', '[413, 413, w + 124]', '[413, 413, w + 289]', '[413, 413, w + 348]', '[414, 138, -3*w - 21]', '[414, 138, 3*w - 21]', '[415, 415, w + 140]', '[415, 415, w + 275]', '[416, 104, -4*w - 44]', '[416, 104, 4*w - 44]', '[422, 422, w + 99]', '[422, 422, w + 323]', '[423, 141, 3*w + 3]', '[423, 141, 3*w + 138]', '[424, 212, 6*w - 62]', '[424, 212, 6*w + 62]', '[427, 427, w + 142]', '[427, 427, w + 163]', '[427, 427, w + 264]', '[427, 427, w + 285]', '[430, 430, -7*w + 65]', '[430, 430, 13*w - 125]', '[431, 431, -4*w - 33]', '[431, 431, 4*w - 33]', '[433, 433, w + 31]', '[433, 433, w + 402]', '[434, 434, -w - 23]', '[434, 434, 17*w + 167]', '[434, 434, 17*w - 167]', '[434, 434, -w + 23]', '[437, 437, w + 76]', '[437, 437, w + 361]', '[439, 439, 5*w - 44]', '[439, 439, -19*w + 184]', '[441, 21, 21]', '[441, 147, 3*w + 36]', '[441, 147, -3*w + 36]', '[443, 443, w + 192]', '[443, 443, w + 251]', '[448, 56, 8*w + 16]', '[448, 56, 8*w + 40]', '[450, 30, 15*w + 15]', '[452, 226, 2*w + 70]', '[452, 226, 2*w + 156]', '[455, 455, 3*w - 20]', '[455, 455, 8*w + 75]', '[455, 455, 8*w - 75]', '[455, 455, 3*w + 20]', '[458, 458, w + 211]', '[458, 458, w + 247]', '[460, 230, 2*w + 60]', '[460, 230, 2*w + 170]', '[461, 461, 2*w - 29]', '[461, 461, -2*w - 29]', '[463, 463, w + 133]', '[463, 463, w + 330]', '[467, 467, w + 58]', '[467, 467, w + 409]', '[468, 78, 6*w + 12]', '[468, 78, 6*w + 66]', '[470, 470, -9*w + 85]', '[470, 470, 11*w - 105]', '[472, 236, 2*w + 106]', '[472, 236, 2*w + 130]', '[475, 95, 10*w - 95]', '[477, 159, 3*w + 75]', '[477, 159, 3*w + 84]', '[481, 481, w + 24]', '[481, 481, 12*w + 119]', '[481, 481, -12*w + 119]', '[481, 481, -w + 24]', '[484, 22, -22]', '[485, 485, w + 80]', '[485, 485, w + 405]', '[488, 244, 2*w + 82]', '[488, 244, 2*w + 162]', '[490, 70, 7*w + 35]', '[490, 490, w + 135]', '[490, 490, w + 355]', '[494, 494, -3*w - 19]', '[494, 494, -3*w + 19]', '[496, 124, -4*w - 32]', '[496, 124, 4*w - 32]', '[497, 497, w + 33]', '[497, 497, w + 180]', '[497, 497, w + 317]', '[497, 497, w + 464]', '[500, 50, -10*w + 100]', '[503, 503, w + 108]', '[503, 503, w + 395]', '[504, 84, -6*w + 54]', '[504, 84, -6*w - 54]', '[505, 505, 4*w - 45]', '[505, 505, 24*w - 235]', '[512, 32, 16*w + 16]', '[514, 514, 3*w - 37]', '[514, 514, 3*w + 37]', '[518, 518, w + 61]', '[518, 518, w + 135]', '[518, 518, w + 383]', '[518, 518, w + 457]', '[520, 260, -2*w - 30]', '[520, 260, 2*w - 30]', '[526, 526, 5*w + 43]', '[526, 526, 5*w - 43]', '[529, 23, 23]', '[529, 529, 15*w - 148]', '[529, 529, 7*w - 72]', '[530, 530, -w - 25]', '[530, 530, -w + 25]', '[531, 177, -3*w - 18]', '[531, 177, 3*w - 18]', '[532, 266, 2*w + 38]', '[532, 266, 2*w + 228]', '[541, 541, 21*w - 206]', '[541, 541, 5*w - 54]', '[549, 183, 6*w - 63]', '[549, 183, 18*w - 177]', '[553, 553, w + 75]', '[553, 553, w + 233]', '[553, 553, w + 320]', '[553, 553, w + 478]', '[558, 186, 3*w + 69]', '[558, 186, 3*w + 117]', '[559, 559, 7*w + 64]', '[559, 559, 4*w - 31]', '[559, 559, -4*w - 31]', '[559, 559, -7*w + 64]', '[560, 140, 4*w + 20]', '[560, 140, 4*w + 120]', '[565, 565, w + 35]', '[565, 565, w + 530]', '[566, 566, 3*w - 17]', '[566, 566, -3*w - 17]', '[567, 63, 9*w + 18]', '[567, 63, 9*w + 45]', '[568, 284, 2*w + 66]', '[568, 284, 2*w + 218]', '[575, 115, 5*w + 35]', '[575, 115, 5*w + 80]', '[576, 24, 24]', '[578, 34, 17*w + 17]', '[581, 581, -w - 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179]', '[9854, 9854, -23*w + 201]', '[9854, 9854, 23*w + 201]', '[9854, 9854, 21*w - 179]', '[9857, 9857, w + 2920]', '[9857, 9857, w + 6937]', '[9862, 9862, w + 1065]', '[9862, 9862, w + 8797]', '[9866, 9866, 13*w + 161]', '[9866, 9866, 13*w - 161]', '[9868, 4934, 2*w + 2228]', '[9868, 4934, 2*w + 2706]', '[9871, 9871, -40*w + 377]', '[9871, 9871, 52*w - 497]', '[9873, 3291, 3*w + 1464]', '[9873, 3291, 3*w + 1827]', '[9875, 1975, 70*w - 675]', '[9875, 1975, -30*w + 275]', '[9880, 4940, -22*w + 190]', '[9880, 4940, -22*w - 190]', '[9882, 1098, 9*w + 369]', '[9882, 1098, 9*w + 729]', '[9887, 9887, w + 783]', '[9887, 9887, w + 9104]', '[9890, 9890, w + 605]', '[9890, 9890, w + 1465]', '[9890, 9890, w + 8425]', '[9890, 9890, w + 9285]', '[9892, 4946, 2*w + 142]', '[9892, 4946, 2*w + 4804]', '[9893, 9893, w + 141]', '[9893, 9893, w + 3664]', '[9893, 9893, w + 6229]', '[9893, 9893, w + 9752]', '[9895, 9895, 11*w - 40]', '[9895, 9895, -11*w - 40]', '[9896, 4948, -34*w + 346]', '[9896, 4948, -58*w + 574]', '[9898, 1414, 7*w + 609]', '[9898, 1414, 7*w + 805]', '[9898, 9898, w + 1703]', '[9898, 9898, w + 2511]', '[9898, 9898, w + 7387]', '[9898, 9898, w + 8195]', '[9905, 9905, w + 100]', '[9905, 9905, 16*w + 185]', '[9905, 9905, 16*w - 185]', '[9905, 9905, w - 100]', '[9910, 9910, w + 3215]', '[9910, 9910, w + 6695]', '[9913, 9913, w + 315]', '[9913, 9913, w + 3995]', '[9913, 9913, w + 5918]', '[9913, 9913, w + 9598]', '[9917, 9917, w + 1787]', '[9917, 9917, w + 2631]', '[9917, 9917, w + 7286]', '[9917, 9917, w + 8130]', '[9920, 1240, -16*w + 120]', '[9920, 1240, 144*w - 1400]', '[9923, 9923, w + 3005]', '[9923, 9923, w + 6918]', '[9926, 9926, 51*w - 487]', '[9926, 9926, 15*w - 107]', '[9926, 9926, 15*w + 107]', '[9926, 9926, 51*w + 487]', '[9927, 3309, 3*w + 654]', '[9927, 3309, 3*w + 2655]', '[9929, 9929, -4*w - 107]', '[9929, 9929, 4*w - 107]', '[9931, 9931, -26*w + 233]', '[9931, 9931, 26*w + 233]', '[9935, 9935, w + 3760]', '[9935, 9935, w + 6175]', '[9940, 4970, 2*w + 360]', '[9940, 4970, 2*w + 1060]', '[9940, 4970, 2*w + 3910]', '[9940, 4970, 2*w + 4610]', '[9941, 9941, 14*w - 169]', '[9941, 9941, -14*w - 169]', '[9943, 9943, w + 264]', '[9943, 9943, w + 590]', '[9943, 9943, w + 9353]', '[9943, 9943, w + 9679]', '[9946, 9946, 5*w - 111]', '[9946, 9946, -5*w - 111]', '[9954, 3318, 39*w - 393]', '[9954, 3318, -15*w - 177]', '[9954, 3318, -15*w + 177]', '[9954, 3318, 39*w + 393]', '[9959, 9959, -12*w - 61]', '[9959, 9959, -19*w - 156]', '[9959, 9959, 19*w - 156]', '[9959, 9959, 12*w - 61]', '[9961, 9961, -20*w - 219]', '[9961, 9961, -3*w - 104]', '[9961, 9961, -3*w + 104]', '[9961, 9961, -20*w + 219]', '[9964, 4982, 28*w + 254]', '[9964, 4982, 62*w - 596]', '[9964, 4982, -34*w + 316]', '[9964, 4982, 28*w - 254]', '[9967, 9967, w + 2425]', '[9967, 9967, w + 7542]', '[9971, 767, -13*w - 78]', '[9971, 767, 13*w - 78]', '[9971, 9971, -14*w + 93]', '[9971, 9971, -50*w - 477]', '[9971, 9971, 50*w - 477]', '[9971, 9971, 14*w + 93]', '[9974, 9974, -11*w - 39]', '[9974, 9974, 11*w - 39]', '[9981, 3327, 66*w - 651]', '[9981, 3327, 30*w - 309]', '[9982, 9982, w + 1465]', '[9982, 9982, w + 2767]', '[9982, 9982, w + 4317]', '[9982, 9982, w + 4363]', '[9982, 9982, w + 5619]', '[9982, 9982, w + 5665]', '[9982, 9982, w + 7215]', '[9982, 9982, w + 8517]', '[9985, 9985, w + 1725]', '[9985, 9985, w + 8260]', '[9986, 9986, -7*w - 121]', '[9986, 9986, 7*w - 121]', '[9994, 9994, -9*w + 133]', '[9994, 9994, 9*w + 133]', '[9997, 9997, w + 4197]', '[9997, 9997, w + 4262]', '[9997, 9997, w + 5735]', '[9997, 9997, w + 5800]', '[9998, 9998, w + 4053]', '[9998, 9998, w + 5945]', '[10000, 100, 100]'], 'label': '2.2.380.1', 'narrow_class_no': 4, 'primes': ['[2, 2, w + 1]', '[5, 5, -w + 10]', '[7, 7, w + 2]', '[7, 7, w + 5]', '[9, 3, 3]', '[13, 13, w + 2]', '[13, 13, w + 11]', '[19, 19, 2*w - 19]', '[23, 23, w + 7]', '[23, 23, w + 16]', '[31, 31, -w - 8]', '[31, 31, w - 8]', '[37, 37, w + 13]', '[37, 37, w + 24]', '[43, 43, w + 3]', '[43, 43, w + 40]', '[47, 47, w + 1]', '[47, 47, w + 46]', '[53, 53, w + 25]', '[53, 53, w + 28]', '[59, 59, -w - 6]', '[59, 59, w - 6]', '[61, 61, 2*w - 21]', '[61, 61, 6*w - 59]', '[71, 71, 5*w - 48]', '[71, 71, -3*w + 28]', '[79, 79, -w - 4]', '[79, 79, w - 4]', '[83, 83, w + 26]', '[83, 83, w + 57]', '[97, 97, w + 17]', '[97, 97, w + 80]', '[101, 101, -w - 14]', '[101, 101, w - 14]', '[113, 113, w + 35]', '[113, 113, w + 78]', '[121, 11, -11]', '[149, 149, 2*w - 23]', '[149, 149, -2*w - 23]', '[151, 151, 8*w - 77]', '[151, 151, -4*w + 37]', '[163, 163, w + 62]', '[163, 163, w + 101]', '[173, 173, w + 21]', '[173, 173, w + 152]', '[179, 179, 3*w - 26]', '[179, 179, -13*w + 126]', '[193, 193, w + 45]', '[193, 193, w + 148]', '[211, 211, 2*w - 13]', '[211, 211, -2*w - 13]', '[229, 229, -w - 18]', '[229, 229, w - 18]', '[257, 257, w + 98]', '[257, 257, w + 159]', '[263, 263, w + 44]', '[263, 263, w + 219]', '[283, 283, w + 100]', '[283, 283, w + 183]', '[289, 17, -17]', '[293, 293, w + 55]', '[293, 293, w + 238]', '[317, 317, w + 27]', '[317, 317, w + 290]', '[331, 331, 2*w - 7]', '[331, 331, -2*w - 7]', '[337, 337, w + 134]', '[337, 337, w + 203]', '[347, 347, w + 147]', '[347, 347, w + 200]', '[349, 349, 2*w - 27]', '[349, 349, -2*w - 27]', '[367, 367, w + 126]', '[367, 367, w + 241]', '[373, 373, w + 29]', '[373, 373, w + 344]', '[379, 379, 2*w - 1]', '[379, 379, -2*w - 1]', '[389, 389, -w - 22]', '[389, 389, w - 22]', '[431, 431, -4*w - 33]', '[431, 431, 4*w - 33]', '[433, 433, w + 31]', '[433, 433, w + 402]', '[439, 439, 5*w - 44]', '[439, 439, -19*w + 184]', '[443, 443, w + 192]', '[443, 443, w + 251]', '[461, 461, 2*w - 29]', '[461, 461, -2*w - 29]', '[463, 463, w + 133]', '[463, 463, w + 330]', '[467, 467, w + 58]', '[467, 467, w + 409]', '[503, 503, w + 108]', '[503, 503, w + 395]', '[541, 541, 21*w - 206]', '[541, 541, 5*w - 54]', '[587, 587, w + 260]', '[587, 587, w + 327]', '[599, 599, -3*w - 16]', '[599, 599, 3*w - 16]', '[643, 643, w + 122]', '[643, 643, w + 521]', '[647, 647, w + 68]', '[647, 647, w + 579]', '[659, 659, 3*w - 14]', '[659, 659, -3*w - 14]', '[673, 673, w + 257]', '[673, 673, w + 416]', '[677, 677, w + 210]', '[677, 677, w + 467]', '[701, 701, 10*w - 101]', '[701, 701, 14*w - 139]', '[709, 709, 2*w - 33]', '[709, 709, -2*w - 33]', '[727, 727, w + 72]', '[727, 727, w + 655]', '[751, 751, 20*w - 193]', '[751, 751, -8*w + 73]', '[761, 761, -5*w + 56]', '[761, 761, 5*w + 56]', '[769, 769, 17*w - 168]', '[769, 769, 9*w - 92]', '[773, 773, w + 274]', '[773, 773, w + 499]', '[797, 797, w + 172]', '[797, 797, w + 625]', '[809, 809, 8*w - 83]', '[809, 809, 20*w - 197]', '[811, 811, 7*w - 62]', '[811, 811, 7*w + 62]', '[821, 821, -7*w + 74]', '[821, 821, -7*w - 74]', '[823, 823, w + 170]', '[823, 823, w + 653]', '[839, 839, -3*w - 4]', '[839, 839, 3*w - 4]', '[841, 29, -29]', '[857, 857, w + 106]', '[857, 857, w + 751]', '[877, 877, w + 43]', '[877, 877, w + 834]', '[881, 881, 4*w - 49]', '[881, 881, -4*w - 49]', '[883, 883, w + 401]', '[883, 883, w + 482]', '[911, 911, 16*w - 153]', '[911, 911, -12*w + 113]', '[929, 929, -w - 32]', '[929, 929, w - 32]', '[947, 947, w + 82]', '[947, 947, w + 865]', '[953, 953, w + 420]', '[953, 953, w + 533]', '[967, 967, w + 391]', '[967, 967, w + 576]', '[971, 971, 23*w - 222]', '[971, 971, -9*w + 82]', '[977, 977, w + 308]', '[977, 977, w + 669]', '[991, 991, 4*w - 23]', '[991, 991, -4*w - 23]']}
• 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': [-95, 0, 1], 'conductor': 380, 'degree': 2, 'dirichlet_group': [1, 379], 'disc_abs': 380, 'disc_rad': 190, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 1]]], [5, [0]], [7, [[1, 2]]], [11, [[2, 1]]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [0]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[1, 2]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[1, 2]]], [47, [[1, 2]]], [53, [[1, 2]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 19.493588689617926, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.380.1', 'local_algs': ['2.2.2.1', '5.2.1.1', '19.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 5, 19], 'rd': 19.4935886896, 'regulator': {'__RealLiteral__': 0, 'data': '4.3565444206', 'prec': 40}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 4 a + 39 \\)'], 'used_grh': False, 'zk': ['1', 'a']}