Hilbert modular form data - 2.2.168.1-21.1-a

Formats: - HTML - YAML - JSON - 2025-05-24T02:55:33.369950

• 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': 1, 'disc': 168, 'field_bad_primes': [2, 3, 7], 'field_label': '2.2.168.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.168.1-21.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [3, 7], 'level_ideal': '[21, 21, w]', 'level_label': '21.1', 'level_norm': 21, 'parallel_weight': 2, 'short_label': '21.1-a', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, w]', 1], ['[7, 7, w - 7]', 1]], 'hecke_eigenvalues': [1, -1, -1, -4, -4, 2, 2, -6, -6, -4, -4, -6, 2, 2, 2, 2, 0, 0, -6, -6, 2, 2, -16, -16, -14, -14, -4, -4, 0, 0, -12, -12, -6, -6, 8, 8, 2, 2, -8, -8, 4, 4, 26, 26, 2, 2, -22, -22, 10, 10, 26, 26, 20, 20, -4, -4, -24, -24, 18, 18, -14, -14, 28, 28, 2, 2, 10, 10, 0, 0, -6, -6, 18, 18, -36, -36, 10, 10, 16, 16, -16, -16, -8, -8, -20, -20, 24, 24, 18, 18, 20, 20, -46, 2, 2, -6, -6, 20, 20, -40, -40, -20, -20, -40, -40, 18, 18, -12, -12, -22, -22, 34, 34, 12, 12, -20, -20, -30, -30, -48, -48, 18, 18, -32, -32, 18, 18, 44, 44, -44, -44, -38, -38, 24, 24, 12, 12, -14, -14, -8, -8, 10, 10, -14, -14, -44, -44, -6, -6, 8, 8, 8, 8, 26, 26, -44, -44, -62, 40, 40, 24, 24, -16, -16, 26, 26], 'hecke_polynomial': 'x', 'label': '2.2.168.1-21.1-a'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 168, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[3, 3, w]', '[4, 2, 2]', '[6, 6, -w + 6]', '[7, 7, w - 7]', '[8, 4, 2*w]', '[9, 3, 3]', '[11, 11, w + 3]', '[11, 11, w + 8]', '[12, 6, 2*w]', '[13, 13, w + 4]', '[13, 13, w + 9]', '[14, 14, w]', '[16, 4, 4]', '[17, 17, -w - 5]', '[17, 17, -w + 5]', '[18, 6, 3*w]', '[19, 19, w + 2]', '[19, 19, w + 17]', '[21, 21, w]', '[22, 22, -w - 8]', '[22, 22, w - 8]', '[24, 12, -2*w + 12]', '[25, 5, 5]', '[26, 26, w + 4]', '[26, 26, -w + 4]', '[27, 9, 3*w]', '[28, 14, 2*w - 14]', '[29, 29, w + 10]', '[29, 29, w + 19]', '[32, 8, 4*w]', '[33, 33, w + 3]', '[33, 33, w - 3]', '[34, 34, w + 12]', '[34, 34, w + 22]', '[36, 6, 6]', '[38, 38, -w - 2]', '[38, 38, w - 2]', '[39, 39, w + 9]', '[39, 39, w - 9]', '[41, 41, -w - 1]', '[41, 41, w - 1]', '[42, 42, w]', '[44, 22, 2*w + 6]', '[44, 22, 2*w + 16]', '[47, 47, -2*w + 11]', '[47, 47, 4*w - 25]', '[48, 12, 4*w]', '[49, 7, 7]', '[50, 10, 5*w]', '[51, 51, w + 12]', '[51, 51, w + 39]', '[52, 26, 2*w + 8]', '[52, 26, 2*w + 18]', '[53, 53, w + 25]', '[53, 53, w + 28]', '[54, 18, -3*w + 18]', '[56, 28, 2*w]', '[57, 57, -2*w + 15]', '[57, 57, -2*w - 15]', '[58, 58, -w - 10]', '[58, 58, w - 10]', '[61, 61, w + 15]', '[61, 61, w + 46]', '[63, 21, 3*w - 21]', '[64, 8, 8]', '[66, 66, w + 30]', '[66, 66, w + 36]', '[68, 34, -2*w - 10]', '[68, 34, -2*w + 10]', '[72, 12, 6*w]', '[75, 15, 5*w]', '[76, 38, 2*w + 4]', '[76, 38, 2*w + 34]', '[77, 77, w + 14]', '[77, 77, w + 63]', '[78, 78, w + 30]', '[78, 78, w + 48]', '[79, 79, -w - 11]', '[79, 79, w - 11]', '[81, 9, 9]', '[82, 82, w + 40]', '[82, 82, w + 42]', '[84, 42, 2*w]', '[87, 87, 2*w - 9]', '[87, 87, 8*w - 51]', '[88, 44, -2*w - 16]', '[88, 44, 2*w - 16]', '[89, 89, 3*w - 17]', '[89, 89, 5*w - 31]', '[91, 91, w + 35]', '[91, 91, w + 56]', '[94, 94, w + 18]', '[94, 94, w + 76]', '[96, 24, -4*w + 24]', '[98, 14, 7*w]', '[99, 33, 3*w + 9]', '[99, 33, 3*w + 24]', '[100, 10, 10]', '[102, 102, w + 12]', '[102, 102, -w + 12]', '[104, 52, 2*w + 8]', '[104, 52, -2*w + 8]', '[106, 106, -3*w + 22]', '[106, 106, 5*w - 34]', '[107, 107, w + 16]', '[107, 107, w + 91]', '[108, 18, 6*w]', '[112, 28, 4*w - 28]', '[114, 114, w + 36]', '[114, 114, w + 78]', '[116, 58, 2*w + 20]', '[116, 58, 2*w + 38]', '[117, 39, 3*w + 12]', '[117, 39, 3*w + 27]', '[119, 119, 2*w - 7]', '[119, 119, 2*w + 7]', '[121, 11, 11]', '[121, 121, -2*w + 17]', '[121, 121, 2*w + 17]', '[122, 122, 7*w - 44]', '[122, 122, 3*w - 16]', '[123, 123, w + 42]', '[123, 123, w + 81]', '[126, 42, 3*w]', '[127, 127, -w - 13]', '[127, 127, w - 13]', '[128, 16, 8*w]', '[132, 66, 2*w + 6]', '[132, 66, 2*w - 6]', '[133, 133, w + 21]', '[133, 133, w + 112]', '[136, 68, 2*w + 24]', '[136, 68, 2*w + 44]', '[139, 139, w + 43]', '[139, 139, w + 96]', '[141, 141, w + 18]', '[141, 141, w + 123]', '[143, 143, -4*w + 23]', '[143, 143, -2*w + 5]', '[143, 143, 2*w + 5]', '[143, 143, 4*w + 23]', '[144, 12, 12]', '[147, 21, 7*w]', '[149, 149, w + 41]', '[149, 149, w + 108]', '[150, 30, -5*w + 30]', '[151, 151, 3*w + 23]', '[151, 151, -3*w + 23]', '[152, 76, -2*w - 4]', '[152, 76, 2*w - 4]', '[153, 51, -3*w - 15]', '[153, 51, -3*w + 15]', '[154, 154, w + 14]', '[154, 154, -w + 14]', '[156, 78, 2*w + 18]', '[156, 78, 2*w - 18]', '[157, 157, w + 55]', '[157, 157, w + 102]', '[158, 158, w + 68]', '[158, 158, w + 90]', '[159, 159, 2*w - 3]', '[159, 159, -2*w - 3]', '[162, 18, 9*w]', '[164, 82, -2*w - 2]', '[164, 82, 2*w - 2]', '[167, 167, 2*w - 1]', '[167, 167, -2*w - 1]', '[168, 84, 2*w]', '[169, 13, 13]', '[169, 169, -4*w + 29]', '[169, 169, 4*w + 29]', '[171, 57, 3*w + 6]', '[171, 57, 3*w + 51]', '[174, 174, w + 48]', '[174, 174, w + 126]', '[175, 35, 5*w - 35]', '[176, 44, 4*w + 12]', '[176, 44, 4*w + 32]', '[178, 178, w + 24]', '[178, 178, w + 154]', '[179, 179, w + 20]', '[179, 179, w + 159]', '[181, 181, w + 59]', '[181, 181, w + 122]', '[182, 182, -3*w + 14]', '[182, 182, 3*w + 14]', '[183, 183, -w - 15]', '[183, 183, w - 15]', '[187, 187, w + 63]', '[187, 187, w + 80]', '[187, 187, w + 107]', '[187, 187, w + 124]', '[188, 94, -4*w + 22]', '[188, 94, 8*w - 50]', '[189, 63, 3*w]', '[192, 24, 8*w]', '[193, 193, 2*w - 19]', '[193, 193, -2*w - 19]', '[196, 14, 14]', '[197, 197, w + 47]', '[197, 197, w + 150]', '[198, 66, -3*w - 24]', '[198, 66, 3*w - 24]', '[200, 20, 10*w]', '[203, 203, w + 77]', '[203, 203, w + 126]', '[204, 102, 2*w + 24]', '[204, 102, 2*w + 78]', '[208, 52, 4*w + 16]', '[208, 52, 4*w + 36]', '[209, 209, -5*w + 29]', '[209, 209, -3*w - 13]', '[209, 209, 3*w - 13]', '[209, 209, 5*w + 29]', '[212, 106, 2*w + 50]', '[212, 106, 2*w + 56]', '[214, 214, -w - 16]', '[214, 214, w - 16]', '[216, 36, -6*w + 36]', '[221, 221, w + 22]', '[221, 221, w + 56]', '[221, 221, w + 165]', '[221, 221, w + 199]', '[224, 56, 4*w]', '[225, 15, 15]', '[228, 114, -4*w + 30]', '[228, 114, -4*w - 30]', '[229, 229, w + 27]', '[229, 229, w + 202]', '[231, 231, -4*w - 21]', '[231, 231, -4*w + 21]', '[232, 116, -2*w - 20]', '[232, 116, 2*w - 20]', '[234, 78, 3*w + 12]', '[234, 78, -3*w + 12]', '[237, 237, w + 90]', '[237, 237, w + 147]', '[238, 238, w + 56]', '[238, 238, w + 182]', '[242, 22, 11*w]', '[242, 242, w + 52]', '[242, 242, w + 190]', '[243, 27, 9*w]', '[244, 122, 2*w + 30]', '[244, 122, 2*w + 92]', '[246, 246, -5*w + 36]', '[246, 246, 7*w - 48]', '[247, 247, w + 17]', '[247, 247, 3*w - 25]', '[247, 247, -3*w - 25]', '[247, 247, -w + 17]', '[252, 42, 6*w - 42]', '[254, 254, w + 114]', '[254, 254, w + 140]', '[256, 16, 16]', '[257, 257, 3*w - 11]', '[257, 257, -3*w - 11]', '[261, 87, 3*w + 30]', '[261, 87, 3*w + 57]', '[264, 132, 2*w + 60]', '[264, 132, 2*w + 72]', '[266, 266, -5*w - 28]', '[266, 266, 5*w - 28]', '[267, 267, w + 24]', '[267, 267, w + 243]', '[272, 68, -4*w - 20]', '[272, 68, -4*w + 20]', '[273, 273, 2*w - 21]', '[273, 273, 2*w + 21]', '[275, 55, 5*w + 15]', '[275, 55, 5*w + 40]', '[278, 278, -3*w - 10]', '[278, 278, 3*w - 10]', '[282, 282, w + 18]', '[282, 282, w - 18]', '[283, 283, w + 61]', '[283, 283, w + 222]', '[286, 286, w + 30]', '[286, 286, w + 74]', '[286, 286, w + 212]', '[286, 286, w + 256]', '[287, 287, 6*w - 35]', '[287, 287, -8*w + 49]', '[288, 24, 12*w]', '[289, 17, 17]', '[289, 289, 4*w + 31]', '[289, 289, -4*w + 31]', '[294, 42, -7*w + 42]', '[297, 99, 3*w + 9]', '[297, 99, 3*w - 9]', '[298, 298, 3*w + 26]', '[298, 298, -3*w + 26]', '[300, 30, 10*w]', '[302, 302, w + 58]', '[302, 302, w + 244]', '[304, 76, 4*w + 8]', '[304, 76, 4*w + 68]', '[306, 102, 3*w + 36]', '[306, 102, 3*w + 66]', '[307, 307, w + 137]', '[307, 307, w + 170]', '[308, 154, 2*w + 28]', '[308, 154, 2*w + 126]', '[311, 311, 4*w - 19]', '[311, 311, -4*w - 19]', '[312, 156, 2*w + 60]', '[312, 156, 2*w + 96]', '[314, 314, 3*w - 8]', '[314, 314, -3*w - 8]', '[316, 158, -2*w - 22]', '[316, 158, 2*w - 22]', '[317, 317, w + 26]', '[317, 317, w + 291]', '[318, 318, w + 78]', '[318, 318, w + 240]', '[319, 319, w + 19]', '[319, 319, -9*w + 61]', '[319, 319, 9*w + 61]', '[319, 319, -w + 19]', '[321, 321, 5*w - 27]', '[321, 321, 11*w - 69]', '[323, 323, w + 97]', '[323, 323, w + 131]', '[323, 323, w + 192]', '[323, 323, w + 226]', '[324, 18, 18]', '[325, 65, 5*w + 20]', '[325, 65, 5*w + 45]', '[328, 164, 2*w + 80]', '[328, 164, 2*w + 84]', '[329, 329, 3*w + 7]', '[329, 329, -3*w + 7]', '[334, 334, w + 84]', '[334, 334, w + 250]', '[336, 84, 4*w]', '[337, 337, -6*w + 43]', '[337, 337, -8*w + 55]', '[338, 26, 13*w]', '[338, 338, w + 134]', '[338, 338, w + 204]', '[342, 114, -3*w - 6]', '[342, 114, 3*w - 6]', '[343, 49, 7*w - 49]', '[347, 347, w + 70]', '[347, 347, w + 277]', '[348, 174, 4*w - 18]', '[348, 174, 16*w - 102]', '[349, 349, w + 33]', '[349, 349, w + 316]', '[350, 70, 5*w]', '[351, 117, 3*w + 27]', '[351, 117, 3*w - 27]', '[352, 88, -4*w - 32]', '[352, 88, 4*w - 32]', '[353, 353, 3*w - 5]', '[353, 353, -3*w - 5]', '[356, 178, 6*w - 34]', '[356, 178, 10*w - 62]', '[357, 357, w + 63]', '[357, 357, w + 294]', '[358, 358, -w - 20]', '[358, 358, w - 20]', '[361, 19, 19]', '[361, 361, -2*w + 23]', '[361, 361, 2*w + 23]', '[362, 362, -3*w - 4]', '[362, 362, 3*w - 4]', '[363, 33, 11*w]', '[363, 363, w + 69]', '[363, 363, w + 294]', '[364, 182, 2*w + 70]', '[364, 182, 2*w + 112]', '[366, 366, w + 168]', '[366, 366, w + 198]', '[369, 123, -3*w - 3]', '[369, 123, 3*w - 3]', '[371, 371, w + 28]', '[371, 371, w + 343]', '[374, 374, 5*w + 26]', '[374, 374, 3*w - 2]', '[374, 374, 3*w + 2]', '[374, 374, 5*w - 26]', '[376, 188, 2*w + 36]', '[376, 188, 2*w + 152]', '[377, 377, 7*w - 41]', '[377, 377, 3*w + 1]', '[377, 377, -3*w + 1]', '[377, 377, -7*w - 41]', '[378, 126, 3*w]', '[381, 381, w + 114]', '[381, 381, w + 267]', '[383, 383, -4*w - 17]', '[383, 383, 4*w - 17]', '[384, 48, -8*w + 48]', '[386, 386, w + 106]', '[386, 386, w + 280]', '[389, 389, w + 141]', '[389, 389, w + 248]', '[392, 28, 14*w]', '[394, 394, -5*w + 38]', '[394, 394, 11*w - 74]', '[396, 66, 6*w + 18]', '[396, 66, 6*w + 48]', '[397, 397, w + 162]', '[397, 397, w + 235]', '[399, 399, -w - 21]', '[399, 399, -w + 21]', '[400, 20, 20]', '[406, 406, -3*w + 28]', '[406, 406, -17*w + 112]', '[408, 204, 2*w + 24]', '[408, 204, -2*w + 24]', '[416, 104, 4*w + 16]', '[416, 104, -4*w + 16]', '[417, 417, -4*w + 33]', '[417, 417, 14*w - 93]', '[418, 418, w + 36]', '[418, 418, w + 74]', '[418, 418, w + 344]', '[418, 418, w + 382]', '[423, 141, -6*w + 33]', '[423, 141, 12*w - 75]', '[424, 212, -6*w + 44]', '[424, 212, 10*w - 68]', '[425, 85, -5*w - 25]', '[425, 85, -5*w + 25]', '[427, 427, w + 168]', '[427, 427, w + 259]', '[428, 214, 2*w + 32]', '[428, 214, 2*w + 182]', '[429, 429, w + 30]', '[429, 429, w + 69]', '[429, 429, w + 360]', '[429, 429, w + 399]', '[432, 36, 12*w]', '[441, 21, 21]', '[442, 442, w + 22]', '[442, 442, 7*w - 50]', '[442, 442, 7*w + 50]', '[442, 442, w - 22]', '[443, 443, w + 186]', '[443, 443, w + 257]', '[447, 447, -4*w + 15]', '[447, 447, -22*w + 141]', '[448, 56, 8*w - 56]', '[450, 30, 15*w]', '[451, 451, w + 124]', '[451, 451, w + 206]', '[451, 451, w + 245]', '[451, 451, w + 327]', '[453, 453, w + 93]', '[453, 453, w + 360]', '[456, 228, 2*w + 72]', '[456, 228, 2*w + 156]', '[457, 457, 2*w - 25]', '[457, 457, -2*w - 25]', '[458, 458, 11*w - 68]', '[458, 458, 7*w - 40]', '[459, 153, 3*w + 36]', '[459, 153, 3*w + 117]', '[462, 462, w + 168]', '[462, 462, w + 294]', '[463, 463, -3*w - 29]', '[463, 463, 3*w - 29]', '[464, 116, 4*w + 40]', '[464, 116, 4*w + 76]', '[468, 78, 6*w + 24]', '[468, 78, 6*w + 54]', '[471, 471, 13*w - 87]', '[471, 471, -5*w + 39]', '[474, 474, 5*w - 24]', '[474, 474, 17*w - 108]', '[475, 95, 5*w + 10]', '[475, 95, 5*w + 85]', '[476, 238, 4*w - 14]', '[476, 238, 4*w + 14]', '[477, 159, 3*w + 75]', '[477, 159, 3*w + 84]', '[479, 479, 8*w - 47]', '[479, 479, 10*w - 61]', '[484, 22, 22]', '[484, 242, -4*w + 34]', '[484, 242, 4*w + 34]', '[486, 54, -9*w + 54]', '[487, 487, -w - 23]', '[487, 487, w - 23]', '[488, 244, 14*w - 88]', '[488, 244, 6*w - 32]', '[491, 491, w + 32]', '[491, 491, w + 459]', '[492, 246, 2*w + 84]', '[492, 246, 2*w + 162]', '[493, 493, w + 39]', '[493, 493, w + 97]', '[493, 493, w + 396]', '[493, 493, w + 454]', '[494, 494, w + 74]', '[494, 494, w + 230]', '[494, 494, w + 264]', '[494, 494, w + 420]', '[501, 501, w + 84]', '[501, 501, w + 417]', '[503, 503, -4*w - 13]', '[503, 503, 4*w - 13]', '[504, 84, 6*w]', '[507, 39, 13*w]', '[507, 507, w + 204]', '[507, 507, w + 303]', '[508, 254, -2*w - 26]', '[508, 254, 2*w - 26]', '[512, 32, 16*w]', '[513, 171, -6*w + 45]', '[513, 171, -6*w - 45]', '[514, 514, w + 82]', '[514, 514, w + 432]', '[517, 517, w + 206]', '[517, 517, w + 217]', '[517, 517, w + 300]', '[517, 517, w + 311]', '[521, 521, -5*w - 23]', '[521, 521, 5*w - 23]', '[522, 174, -3*w - 30]', '[522, 174, 3*w - 30]', '[523, 523, w + 105]', '[523, 523, w + 418]', '[525, 105, 5*w]', '[528, 132, 4*w + 12]', '[528, 132, 4*w - 12]', '[529, 23, -23]', '[532, 266, 2*w + 42]', '[532, 266, 2*w + 224]', '[533, 533, w + 165]', '[533, 533, w + 204]', '[533, 533, w + 329]', '[533, 533, w + 368]', '[534, 534, -w - 24]', '[534, 534, w - 24]', '[537, 537, 13*w - 81]', '[537, 537, 7*w - 39]', '[539, 77, 7*w + 21]', '[539, 77, 7*w + 56]', '[543, 543, 11*w - 75]', '[543, 543, -7*w + 51]', '[544, 136, 4*w + 48]', '[544, 136, 4*w + 88]', '[546, 546, w + 126]', '[546, 546, w + 420]', '[549, 183, 3*w + 45]', '[549, 183, 3*w + 138]', '[550, 110, -5*w - 40]', '[550, 110, 5*w - 40]', '[551, 551, 6*w + 31]', '[551, 551, 4*w - 11]', '[551, 551, -4*w - 11]', '[551, 551, -6*w + 31]', '[553, 553, -18*w + 119]', '[553, 553, -4*w + 35]', '[556, 278, 2*w + 86]', '[556, 278, 2*w + 192]', '[557, 557, w + 34]', '[557, 557, w + 523]', '[561, 561, 8*w - 57]', '[561, 561, 2*w - 27]', '[561, 561, -2*w - 27]', '[561, 561, -8*w - 57]', '[564, 282, 2*w + 36]', '[564, 282, 2*w + 246]', '[566, 566, 5*w - 22]', '[566, 566, -5*w - 22]', '[567, 63, 9*w - 63]', '[572, 286, -8*w + 46]', '[572, 286, -4*w + 10]', '[572, 286, 4*w + 10]', '[572, 286, 8*w + 46]', '[574, 574, w + 42]', '[574, 574, w + 532]', '[576, 24, 24]', '[578, 34, 17*w]', '[578, 578, w + 80]', '[578, 578, w + 498]', '[579, 579, w + 87]', '[579, 579, w + 492]', '[583, 583, w + 25]', '[583, 583, -3*w + 31]', '[583, 583, -3*w - 31]', '[583, 583, w - 25]', '[588, 42, 14*w]', '[591, 591, -4*w - 9]', '[591, 591, 4*w - 9]', '[593, 593, 9*w - 53]', '[593, 593, 11*w - 67]', '[594, 198, 3*w + 90]', '[594, 198, 3*w + 108]', '[596, 298, 2*w + 82]', '[596, 298, 2*w + 216]', '[600, 60, -10*w + 60]', '[604, 302, 6*w + 46]', '[604, 302, -6*w + 46]', '[608, 152, -4*w - 8]', '[608, 152, 4*w - 8]', '[609, 609, -5*w - 21]', '[609, 609, -5*w + 21]', '[611, 611, w + 217]', '[611, 611, w + 264]', '[611, 611, w + 347]', '[611, 611, w + 394]', '[612, 102, -6*w - 30]', '[612, 102, -6*w + 30]', '[614, 614, 7*w - 38]', '[614, 614, 15*w - 94]', '[616, 308, 2*w + 28]', '[616, 308, -2*w + 28]', '[619, 619, w + 287]', '[619, 619, w + 332]', '[622, 622, w + 238]', '[622, 622, w + 384]', '[623, 623, -4*w + 7]', '[623, 623, -4*w - 7]', '[624, 156, 4*w + 36]', '[624, 156, 4*w - 36]', '[625, 25, 25]', '[627, 627, w + 36]', '[627, 627, w + 135]', '[627, 627, w + 492]', '[627, 627, w + 591]', '[628, 314, 2*w + 110]', '[628, 314, 2*w + 204]', '[631, 631, 5*w - 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182]', '[9887, 9887, 18*w - 61]', '[9887, 9887, -18*w - 61]', '[9891, 3297, 3*w + 777]', '[9891, 3297, 3*w + 2520]', '[9892, 4946, -44*w + 302]', '[9892, 4946, -32*w + 230]', '[9893, 9893, w + 1062]', '[9893, 9893, w + 3345]', '[9893, 9893, w + 6548]', '[9893, 9893, w + 8831]', '[9896, 4948, 26*w - 136]', '[9896, 4948, 66*w - 416]', '[9897, 9897, 23*w - 111]', '[9897, 9897, 77*w - 489]', '[9899, 9899, w + 2297]', '[9899, 9899, w + 2392]', '[9899, 9899, w + 7507]', '[9899, 9899, w + 7602]', '[9900, 330, 30*w + 90]', '[9900, 330, 30*w + 240]', '[9901, 9901, w + 4771]', '[9901, 9901, w + 5130]', '[9902, 9902, w + 1626]', '[9902, 9902, w + 8276]', '[9904, 2476, 4*w + 1148]', '[9904, 2476, 4*w + 1328]', '[9906, 9906, w + 2934]', '[9906, 9906, w + 3696]', '[9906, 9906, w + 6210]', '[9906, 9906, w + 6972]', '[9911, 9911, -46*w + 281]', '[9911, 9911, 30*w - 167]', '[9911, 9911, -16*w - 29]', '[9911, 9911, 20*w + 83]', '[9911, 9911, -20*w + 83]', '[9911, 9911, 16*w - 29]', '[9911, 9911, -30*w - 167]', '[9911, 9911, 46*w + 281]', '[9918, 3306, 3*w + 1248]', '[9918, 3306, 3*w + 1362]', '[9918, 3306, 3*w + 1944]', '[9918, 3306, 3*w + 2058]', '[9921, 9921, 50*w - 339]', '[9921, 9921, -28*w + 207]', '[9922, 902, 11*w + 440]', '[9922, 902, 11*w + 462]', '[9922, 9922, w + 778]', '[9922, 9922, w + 4304]', '[9922, 9922, w + 5618]', '[9922, 9922, w + 9144]', '[9923, 9923, w + 2814]', '[9923, 9923, w + 7109]', '[9924, 4962, 22*w - 102]', '[9924, 4962, 82*w - 522]', '[9925, 1985, 5*w + 810]', '[9925, 1985, 5*w + 1175]', '[9929, 9929, -17*w - 47]', '[9929, 9929, 17*w - 47]', '[9931, 9931, w + 2142]', '[9931, 9931, w + 7789]', '[9937, 9937, 6*w + 107]', '[9937, 9937, -4*w - 103]', '[9937, 9937, 4*w - 103]', '[9937, 9937, -6*w + 107]', '[9939, 9939, w + 1686]', '[9939, 9939, w + 8253]', '[9941, 9941, w + 4533]', '[9941, 9941, w + 5408]', '[9947, 1421, 7*w + 539]', '[9947, 1421, 7*w + 882]', '[9948, 4974, 62*w - 414]', '[9948, 4974, -22*w + 174]', '[9952, 2488, 4*w + 952]', '[9952, 2488, 4*w + 1536]', '[9954, 3318, 3*w + 1218]', '[9954, 3318, 3*w + 2100]', '[9957, 9957, w + 435]', '[9957, 9957, w + 9522]', '[9958, 9958, w + 100]', '[9958, 9958, -33*w - 236]', '[9958, 9958, 33*w - 236]', '[9958, 9958, -w + 100]', '[9961, 9961, -108*w + 707]', '[9961, 9961, -10*w + 119]', '[9963, 1107, 9*w + 378]', '[9963, 1107, 9*w + 729]', '[9964, 4982, 2*w + 904]', '[9964, 4982, 2*w + 1540]', '[9964, 4982, 2*w + 3442]', '[9964, 4982, 2*w + 4078]', '[9966, 9966, w + 360]', '[9966, 9966, w + 3264]', '[9966, 9966, w + 6702]', '[9966, 9966, w + 9606]', '[9968, 2492, -16*w + 28]', '[9968, 2492, -16*w - 28]', '[9973, 9973, w + 2403]', '[9973, 9973, w + 7570]', '[9974, 9974, 45*w - 274]', '[9974, 9974, 37*w - 218]', '[9975, 1995, -5*w - 105]', '[9975, 1995, -5*w + 105]', '[9978, 9978, 19*w - 72]', '[9978, 9978, 103*w - 660]', '[9984, 624, 16*w + 144]', '[9984, 624, 16*w - 144]', '[9986, 9986, w + 3218]', '[9986, 9986, w + 6768]', '[9993, 9993, 88*w - 579]', '[9993, 9993, -14*w + 135]', '[9996, 714, 14*w + 168]', '[9996, 714, 14*w + 546]', '[9998, 9998, w + 4928]', '[9998, 9998, w + 5070]', '[10000, 100, 100]'], 'label': '2.2.168.1', 'narrow_class_no': 4, 'primes': ['[2, 2, w]', '[3, 3, w]', '[7, 7, w - 7]', '[11, 11, w + 3]', '[11, 11, w + 8]', '[13, 13, w + 4]', '[13, 13, w + 9]', '[17, 17, -w - 5]', '[17, 17, -w + 5]', '[19, 19, w + 2]', '[19, 19, w + 17]', '[25, 5, 5]', '[29, 29, w + 10]', '[29, 29, w + 19]', '[41, 41, -w - 1]', '[41, 41, w - 1]', '[47, 47, -2*w + 11]', '[47, 47, 4*w - 25]', '[53, 53, w + 25]', '[53, 53, w + 28]', '[61, 61, w + 15]', '[61, 61, w + 46]', '[79, 79, -w - 11]', '[79, 79, w - 11]', '[89, 89, 3*w - 17]', '[89, 89, 5*w - 31]', '[107, 107, w + 16]', '[107, 107, w + 91]', '[127, 127, -w - 13]', '[127, 127, w - 13]', '[139, 139, w + 43]', '[139, 139, w + 96]', '[149, 149, w + 41]', '[149, 149, w + 108]', '[151, 151, 3*w + 23]', '[151, 151, -3*w + 23]', '[157, 157, w + 55]', '[157, 157, w + 102]', '[167, 167, 2*w - 1]', '[167, 167, -2*w - 1]', '[179, 179, w + 20]', '[179, 179, w + 159]', '[181, 181, w + 59]', '[181, 181, w + 122]', '[193, 193, 2*w - 19]', '[193, 193, -2*w - 19]', '[197, 197, w + 47]', '[197, 197, w + 150]', '[229, 229, w + 27]', '[229, 229, w + 202]', '[257, 257, 3*w - 11]', '[257, 257, -3*w - 11]', '[283, 283, w + 61]', '[283, 283, w + 222]', '[307, 307, w + 137]', '[307, 307, w + 170]', '[311, 311, 4*w - 19]', '[311, 311, -4*w - 19]', '[317, 317, w + 26]', '[317, 317, w + 291]', '[337, 337, -6*w + 43]', '[337, 337, -8*w + 55]', '[347, 347, w + 70]', '[347, 347, w + 277]', '[349, 349, w + 33]', '[349, 349, w + 316]', '[353, 353, 3*w - 5]', '[353, 353, -3*w - 5]', '[383, 383, -4*w - 17]', '[383, 383, 4*w - 17]', '[389, 389, w + 141]', '[389, 389, w + 248]', '[397, 397, w + 162]', '[397, 397, w + 235]', '[443, 443, w + 186]', '[443, 443, w + 257]', '[457, 457, 2*w - 25]', '[457, 457, -2*w - 25]', '[463, 463, -3*w - 29]', '[463, 463, 3*w - 29]', '[479, 479, 8*w - 47]', '[479, 479, 10*w - 61]', '[487, 487, -w - 23]', '[487, 487, w - 23]', '[491, 491, w + 32]', '[491, 491, w + 459]', '[503, 503, -4*w - 13]', '[503, 503, 4*w - 13]', '[521, 521, -5*w - 23]', '[521, 521, 5*w - 23]', '[523, 523, w + 105]', '[523, 523, w + 418]', '[529, 23, -23]', '[557, 557, w + 34]', '[557, 557, w + 523]', '[593, 593, 9*w - 53]', '[593, 593, 11*w - 67]', '[619, 619, w + 287]', '[619, 619, w + 332]', '[631, 631, 5*w - 41]', '[631, 631, -5*w - 41]', '[643, 643, w + 148]', '[643, 643, w + 495]', '[647, 647, -4*w - 5]', '[647, 647, 4*w - 5]', '[653, 653, w + 85]', '[653, 653, w + 568]', '[659, 659, w + 187]', '[659, 659, w + 472]', '[661, 661, w + 45]', '[661, 661, w + 616]', '[673, 673, 2*w - 29]', '[673, 673, -2*w - 29]', '[683, 683, w + 98]', '[683, 683, w + 585]', '[691, 691, w + 95]', '[691, 691, w + 596]', '[701, 701, w + 38]', '[701, 701, w + 663]', '[719, 719, 10*w - 59]', '[719, 719, 12*w - 73]', '[733, 733, w + 158]', '[733, 733, w + 575]', '[751, 751, 7*w - 53]', '[751, 751, -7*w - 53]', '[761, 761, 5*w - 17]', '[761, 761, -5*w - 17]', '[787, 787, w + 228]', '[787, 787, w + 559]', '[811, 811, w + 380]', '[811, 811, w + 431]', '[821, 821, w + 306]', '[821, 821, w + 515]', '[823, 823, -13*w + 89]', '[823, 823, -9*w + 65]', '[827, 827, w + 155]', '[827, 827, w + 672]', '[829, 829, w + 234]', '[829, 829, w + 595]', '[839, 839, -8*w - 43]', '[839, 839, 8*w - 43]', '[853, 853, w + 51]', '[853, 853, w + 802]', '[857, 857, 11*w - 65]', '[857, 857, 13*w - 79]', '[859, 859, w + 229]', '[859, 859, w + 630]', '[881, 881, -5*w - 13]', '[881, 881, 5*w - 13]', '[887, 887, -6*w - 25]', '[887, 887, 6*w - 25]', '[919, 919, -w - 31]', '[919, 919, w - 31]', '[929, 929, -5*w - 11]', '[929, 929, 5*w - 11]', '[947, 947, w + 44]', '[947, 947, w + 903]', '[961, 31, -31]', '[967, 967, -7*w - 55]', '[967, 967, 7*w - 55]', '[983, 983, 6*w - 23]', '[983, 983, -6*w - 23]', '[991, 991, 3*w - 37]', '[991, 991, -3*w - 37]', '[997, 997, w + 286]', '[997, 997, w + 711]']}
• 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
  relative_class_number	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': [-42, 0, 1], 'conductor': 168, 'degree': 2, 'dirichlet_group': [1, 125], 'disc_abs': 168, 'disc_rad': 42, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 1]]], [7, [0]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[1, 2]]], [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': 12.96148139681572, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.168.1', 'local_algs': ['2.2.3.2', '3.2.1.2', '7.2.1.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 7], 'rd': 12.9614813968, 'regulator': {'__RealLiteral__': 0, 'data': '3.2566139548', 'prec': 40}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 2 a - 13 \\)'], 'used_grh': False, 'zk': ['1', 'a']}