Hilbert modular form data - 3.3.564.1-12.2-a

Formats: - HTML - YAML - JSON - 2024-05-28T04:20:09.902318

• 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': 3, 'dimension': 1, 'disc': 564, 'field_bad_primes': [2, 3, 47], 'field_label': '3.3.564.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.564.1-12.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2, 3], 'level_ideal': '[12, 6, w^2 - 1]', 'level_label': '12.2', 'level_norm': 12, 'parallel_weight': 2, 'short_label': '12.2-a', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, w - 1]', -1], ['[3, 3, w - 2]', 1]], 'hecke_eigenvalues': [0, 0, -1, -2, -2, 0, 8, 10, 10, 2, -4, 8, 12, -6, -4, -2, -6, 6, -4, -4, 14, -4, 2, -10, -14, -2, 10, 6, 6, 20, 12, -6, 2, 10, 12, 22, -4, -4, -14, -10, 2, 16, -14, 6, 0, 4, -16, -2, -16, 20, -16, -18, -26, 22, 22, 26, -30, 4, 28, 4, -24, -12, -26, 18, 10, -24, -2, 0, -30, 30, 6, -18, -14, -18, -6, -18, 6, 16, 30, 36, 36, -36, -32, -24, 16, 4, 8, 12, 4, -22, 30, -34, -6, -10, 18, 22, -12, -16, -4, 28, 44, -12, 4, -42, -16, 44, 4, -6, 42, -14, -16, -18, -36, -20, -12, 28, 20, -34, -12, -42, 30, 22, 26, -26, 6, 22, -20, -40, 44, 4, 48, -16, -16, 32, 38, -34, 34, -2, 38, -34, -12, 42, -42, -2, 12, -2, -46, 38, -34, -8, 24, -50, 20, -16, -16, 8, 0, 36, -24, -48, -34, -22, 38, 52, 10, -14, -52, -24, 32, -50], 'hecke_polynomial': 'x', 'label': '3.3.564.1-12.2-a'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 564, 'ideals': ['[1, 1, 1]', '[2, 2, w - 1]', '[3, 3, w]', '[3, 3, w - 2]', '[4, 2, w^2 - 5]', '[6, 6, w + 1]', '[6, 6, -w + 3]', '[8, 2, 2]', '[9, 3, w^2 + w - 3]', '[9, 3, -w^2 + w + 5]', '[9, 9, w^2 - w - 3]', '[12, 6, w^2 - 3]', '[12, 6, w^2 - 1]', '[13, 13, w^2 - 2*w - 2]', '[16, 4, 2*w - 2]', '[17, 17, -w^2 + 2]', '[18, 6, 2*w^2 - w - 9]', '[18, 6, w^2 - w - 2]', '[18, 18, w + 3]', '[19, 19, -w^2 + w + 1]', '[24, 6, 2*w]', '[24, 6, 2*w - 4]', '[26, 26, -w^2 - w + 4]', '[27, 3, 3]', '[27, 9, -2*w^2 + w + 12]', '[27, 9, w^2 - w + 1]', '[27, 27, 2*w - 3]', '[31, 31, -w + 4]', '[32, 4, 2*w^2 - 10]', '[34, 34, -w^2 - w + 8]', '[36, 6, w^2 + 2*w + 1]', '[36, 6, -w^2 + 2*w + 3]', '[36, 18, w^2 + 2*w - 3]', '[38, 38, -3*w^2 + w + 14]', '[39, 39, -2*w - 3]', '[39, 39, -2*w^2 + 11]', '[41, 41, -w^2 + 2*w - 2]', '[41, 41, -2*w^2 - 3*w + 4]', '[41, 41, 2*w + 1]', '[43, 43, -w^2 - w + 5]', '[47, 47, -w^2 + 8]', '[47, 47, 2*w^2 - w - 8]', '[48, 12, 2*w + 2]', '[48, 12, -2*w + 6]', '[51, 51, w^2 - 3*w - 1]', '[51, 51, 2*w^2 - 2*w - 9]', '[52, 26, -w^2 - 1]', '[53, 53, w^2 + w - 7]', '[54, 6, 3*w - 3]', '[54, 18, -w^2 + w + 8]', '[54, 18, w^2 + w - 6]', '[54, 54, w^2 + 3*w]', '[57, 57, -w - 4]', '[57, 57, 2*w^2 - 3*w - 6]', '[59, 59, w^2 - 2*w - 4]', '[61, 61, -3*w^2 + 14]', '[61, 61, 4*w^2 - 2*w - 19]', '[61, 61, -2*w^2 + 7]', '[62, 62, 2*w^2 + w - 5]', '[64, 4, 4]', '[67, 67, -2*w^2 - w + 8]', '[68, 34, w^2 - 2*w - 7]', '[71, 71, w^2 + 2*w - 4]', '[72, 6, 2*w^2 + 2*w - 6]', '[72, 6, -2*w^2 + 2*w + 10]', '[72, 18, 2*w^2 - 2*w - 6]', '[73, 73, -2*w^2 + 2*w + 11]', '[76, 38, w^2 - 2*w - 5]', '[78, 78, -2*w^2 - w + 3]', '[78, 78, w - 5]', '[81, 9, 3*w]', '[81, 9, 2*w^2 + w - 4]', '[81, 9, 3*w - 6]', '[81, 27, -w^2 + 2*w + 6]', '[81, 81, 2*w^2 - 3*w]', '[82, 82, -2*w^2 + w + 7]', '[82, 82, -w^2 - w + 10]', '[82, 82, 2*w^2 - w - 13]', '[83, 83, -3*w + 4]', '[86, 86, -w^2 + w - 2]', '[89, 89, -3*w^2 - 3*w + 5]', '[93, 93, -w^2 + 4*w]', '[93, 93, 3*w^2 - w - 13]', '[94, 94, 3*w - 5]', '[94, 94, -w^2 + 3*w + 2]', '[96, 12, 2*w^2 - 6]', '[96, 12, 2*w^2 - 2]', '[101, 101, w^2 + 2*w + 2]', '[102, 102, -2*w^2 + 3*w + 3]', '[102, 102, -2*w^2 - 3*w + 5]', '[104, 26, 2*w^2 - 4*w - 4]', '[106, 106, w^2 - 3*w + 4]', '[108, 6, 3*w^2 - 15]', '[108, 18, w^2 - 2*w + 3]', '[108, 18, w^2 + 2*w - 5]', '[108, 54, -w^2 + 9]', '[109, 109, 4*w - 1]', '[113, 113, 2*w^2 - 2*w - 5]', '[113, 113, -w^2 - 2*w + 10]', '[113, 113, -5*w^2 + w + 25]', '[114, 114, -w^2 - 3*w + 4]', '[114, 114, -2*w^2 - w + 9]', '[117, 39, -2*w^2 + 2*w + 1]', '[117, 39, -2*w^2 + w + 6]', '[117, 117, -2*w^2 - 3*w]', '[118, 118, -2*w^2 + 3*w + 1]', '[122, 122, -w - 5]', '[122, 122, -3*w - 1]', '[122, 122, -2*w^2 + 3*w + 7]', '[123, 123, 3*w^2 - 2*w - 12]', '[123, 123, -2*w^2 + 5]', '[123, 123, -w^2 - 2]', '[123, 123, -4*w^2 + w + 18]', '[123, 123, w^2 - w - 9]', '[123, 123, 2*w^2 - 3*w - 2]', '[124, 62, 3*w^2 - 17]', '[125, 5, -5]', '[127, 127, -2*w^2 - 4*w - 1]', '[128, 8, 4*w - 4]', '[129, 129, -2*w^2 + 3]', '[129, 129, 2*w - 7]', '[131, 131, -3*w^2 + 16]', '[134, 134, -6*w^2 + 3*w + 29]', '[136, 34, -2*w^2 + 4]', '[137, 137, -3*w^2 + 3*w + 13]', '[137, 137, 2*w^2 - w - 2]', '[137, 137, 2*w^2 + 2*w - 7]', '[139, 139, w^2 - 2*w - 10]', '[141, 141, w^2 + 2*w - 6]', '[141, 141, -w^2 + 6*w - 2]', '[141, 141, -w^2 + 3*w + 3]', '[141, 141, -3*w^2 + 4*w + 10]', '[142, 142, 2*w^2 - w + 1]', '[144, 12, 4*w^2 - 2*w - 18]', '[144, 12, 2*w^2 - 2*w - 4]', '[144, 36, 2*w + 6]', '[146, 146, 2*w^2 - w - 5]', '[149, 149, -3*w - 4]', '[151, 151, -3*w - 2]', '[152, 38, -2*w^2 + 2*w + 2]', '[153, 51, -2*w^2 + 4*w - 3]', '[153, 51, -2*w^2 - w + 10]', '[153, 153, w - 6]', '[156, 78, -w^2 - 2*w + 9]', '[156, 78, -3*w^2 - 2*w + 7]', '[159, 159, -4*w + 11]', '[159, 159, 2*w^2 - 2*w - 3]', '[162, 18, 3*w + 3]', '[162, 18, -3*w + 9]', '[162, 18, 2*w^2 + w - 13]', '[162, 54, 2*w^2 - w - 3]', '[162, 162, 3*w^2 - w - 12]', '[163, 163, 2*w^2 - w - 4]', '[164, 82, -w^2 - 2*w + 7]', '[164, 82, w^2 - 4*w - 1]', '[164, 82, 3*w^2 - 11]', '[166, 166, -5*w^2 + w + 26]', '[169, 13, w^2 + 4*w + 2]', '[169, 169, 2*w^2 + 4*w - 5]', '[171, 57, -w^2 - 4*w]', '[171, 57, -w^2 - 2*w + 8]', '[171, 171, w^2 - 3*w - 9]', '[172, 86, 3*w^2 - 2*w - 19]', '[173, 173, 2*w^2 - w - 14]', '[177, 177, -3*w^2 + 5*w + 5]', '[177, 177, -w^2 + w - 3]', '[178, 178, -2*w^2 - w + 11]', '[181, 181, w^2 + 3*w - 5]', '[183, 183, -3*w^2 - w + 9]', '[183, 183, 2*w^2 + w - 12]', '[183, 183, -2*w^2 - 3*w + 6]', '[183, 183, -3*w^2 - 2*w + 4]', '[183, 183, 4*w - 5]', '[183, 183, -2*w^2 - 6*w + 5]', '[186, 186, -4*w^2 + 3*w + 21]', '[186, 186, -w^2 + 3*w + 4]', '[188, 94, w^2 + 4*w + 1]', '[188, 94, -7*w^2 + 4*w + 37]', '[191, 191, w^2 + w - 11]', '[192, 12, 4*w]', '[192, 12, 4*w - 8]', '[193, 193, 2*w^2 - 4*w - 5]', '[197, 197, 3*w^2 + w - 13]', '[199, 199, 6*w^2 - 3*w - 34]', '[201, 201, 7*w^2 - 3*w - 39]', '[201, 201, w^2 - 10]', '[202, 202, -3*w^2 + 3*w + 14]', '[204, 102, -3*w^2 + 2*w + 11]', '[204, 102, -w^2 - 2*w - 3]', '[208, 52, -2*w^2 - 2*w + 8]', '[211, 211, -w^2 + 2*w - 4]', '[212, 106, -5*w^2 + 2*w + 29]', '[213, 213, w^2 - 3*w + 5]', '[213, 213, 3*w^2 + w - 3]', '[216, 6, 6]', '[216, 18, -4*w^2 + 2*w + 24]', '[216, 18, 2*w^2 - 2*w + 2]', '[216, 54, 4*w - 6]', '[218, 218, 4*w^2 - 5*w + 1]', '[219, 219, w + 6]', '[219, 219, 2*w^2 + 1]', '[221, 221, 4*w - 7]', '[223, 223, w^2 - 3*w - 5]', '[226, 226, w^2 - w - 10]', '[226, 226, -2*w^2 + 7*w - 1]', '[226, 226, -w^2 + 3*w + 8]', '[228, 114, -3*w^2 + 4*w + 7]', '[228, 114, -w^2 - 3]', '[229, 229, -3*w^2 + 3*w + 17]', '[234, 78, -4*w^2 + w + 17]', '[234, 78, w^2 - 5*w]', '[234, 234, 2*w^2 - 3*w - 9]', '[236, 118, -5*w^2 + 2*w + 23]', '[239, 239, 3*w^2 - w - 11]', '[243, 9, 3*w^2 + 3*w - 9]', '[243, 9, -3*w^2 + 3*w + 15]', '[243, 27, 3*w^2 - 3*w - 9]', '[243, 27, -w^2 + 4*w + 2]', '[243, 81, w^2 + w + 3]', '[243, 243, -2*w^2 + 2*w + 15]', '[244, 122, -w^2 - 4*w + 5]', '[244, 122, 3*w^2 + 2*w - 11]', '[244, 122, -3*w^2 + 2*w + 1]', '[246, 246, -2*w^2 + 5*w + 3]', '[246, 246, -5*w + 1]', '[246, 246, -w^2 - 3*w + 6]', '[246, 246, 2*w^2 + 3*w + 1]', '[246, 246, 3*w^2 - 5*w - 8]', '[246, 246, w^2 - 3*w - 6]', '[247, 247, 3*w^2 - 10]', '[248, 62, -2*w + 8]', '[249, 249, w^2 + 3*w - 15]', '[249, 249, w^2 - 3*w - 7]', '[250, 10, -5*w + 5]', '[251, 251, 4*w^2 - 2*w - 17]', '[254, 254, 3*w^2 - 3*w - 16]', '[256, 8, 4*w^2 - 20]', '[258, 258, -3*w^2 - w + 8]', '[258, 258, -w^2 - 3*w + 12]', '[262, 262, w - 7]', '[263, 263, 3*w + 8]', '[267, 267, -4*w - 1]', '[267, 267, 2*w^2 - 3*w - 12]', '[268, 134, 3*w^2 - 4*w - 11]', '[269, 269, -2*w^2 + 3*w + 10]', '[272, 68, -2*w^2 - 2*w + 16]', '[274, 274, 2*w^2 + w + 1]', '[274, 274, 3*w^2 - 5*w - 4]', '[274, 274, -w^2 + 9*w - 4]', '[277, 277, -2*w - 7]', '[277, 277, 4*w^2 - 23]', '[277, 277, 7*w^2 - 4*w - 40]', '[278, 278, -2*w^2 - 3*w + 7]', '[279, 93, w^2 + 5*w - 5]', '[279, 93, 2*w^2 + 2*w - 9]', '[279, 279, 6*w^2 - w - 30]', '[282, 282, -2*w^2 + 3*w + 11]', '[282, 282, 5*w^2 - 5*w - 18]', '[282, 282, 3*w^2 - 5*w]', '[282, 282, 3*w^2 + w - 14]', '[284, 142, -w^2 + 2*w + 11]', '[288, 12, 2*w^2 + 4*w + 2]', '[288, 12, -2*w^2 + 4*w + 6]', '[288, 36, 2*w^2 + 4*w - 6]', '[289, 17, 3*w^2 - 2*w - 10]', '[289, 289, 2*w^2 + 2*w + 1]', '[292, 146, -w^2 + 6*w - 1]', '[298, 298, 4*w^2 - w - 25]', '[302, 302, -3*w^2 + w + 2]', '[303, 303, w^2 + 3*w - 7]', '[303, 303, 4*w^2 - 21]', '[304, 76, -6*w^2 + 2*w + 28]', '[306, 102, -w^2 + w - 4]', '[306, 102, 2*w^2 - w - 15]', '[306, 306, w^2 - 7*w + 6]', '[312, 78, -4*w - 6]', '[312, 78, -4*w^2 + 22]', '[313, 313, 3*w^2 + w - 7]', '[318, 318, 3*w^2 - w - 10]', '[318, 318, w^2 + 5*w - 18]', '[323, 323, 2*w^2 - w + 2]', '[324, 18, w^2 - 4*w + 7]', '[324, 18, 3*w^2 - 9]', '[324, 18, 3*w^2 - 3]', '[324, 54, w^2 + 4*w - 15]', '[324, 162, -w^2 + 4*w + 3]', '[326, 326, -w^2 + 7*w - 2]', '[327, 327, 4*w^2 - w]', '[327, 327, 4*w^2 - 9*w + 2]', '[328, 82, -2*w^2 + 4*w - 4]', '[328, 82, -4*w^2 - 6*w + 8]', '[328, 82, 4*w + 2]', '[331, 331, -3*w^2 + 3*w + 1]', '[331, 331, -3*w^2 + 4*w + 20]', '[331, 331, -w^2 - 3*w + 11]', '[332, 166, w^2 - 11]', '[338, 26, -3*w^2 + w + 20]', '[338, 338, 3*w^2 - 3*w - 8]', '[339, 339, 4*w^2 + 2*w - 15]', '[339, 339, -3*w^2 - w + 5]', '[339, 339, -4*w^2 + 9*w + 4]', '[339, 339, -4*w^2 + 15]', '[339, 339, 5*w - 6]', '[339, 339, 3*w^2 + 5*w - 7]', '[342, 114, -2*w^2 + 5*w - 5]', '[342, 114, w^2 + w - 12]', '[342, 342, -3*w^2 - w + 6]', '[343, 7, -7]', '[344, 86, -2*w^2 - 2*w + 10]', '[346, 346, -w^2 - 3*w + 8]', '[347, 347, -3*w^2 - w + 19]', '[349, 349, 4*w^2 + 4*w - 11]', '[351, 39, 3*w^2 - 6*w - 6]', '[351, 117, -w^2 - 4*w + 6]', '[351, 117, -w^2 - 2*w - 4]', '[351, 351, -3*w^2 - w + 15]', '[353, 353, w^2 - 5*w - 1]', '[354, 354, -w - 7]', '[354, 354, 4*w^2 - 7*w - 9]', '[356, 178, -w^2 + 2*w - 5]', '[361, 19, 4*w^2 - w - 16]', '[361, 361, 3*w^2 + 7*w - 1]', '[362, 362, 3*w^2 - 3*w + 2]', '[366, 366, w^2 - 3*w + 6]', '[366, 366, -w^2 - 3*w + 10]', '[366, 366, -3*w^2 + 5*w + 2]', '[366, 366, -w^2 - 5*w]', '[366, 366, -3*w^2 - w]', '[366, 366, 6*w^2 - w - 31]', '[367, 367, -4*w - 5]', '[369, 123, 2*w^2 - 5*w - 4]', '[369, 123, -2*w^2 - 5*w + 6]', '[369, 123, -2*w^2 - 2*w + 15]', '[369, 123, -4*w^2 - 2*w + 11]', '[369, 123, -w^2 + w + 11]', '[369, 123, -w^2 + 8*w - 6]', '[369, 369, w^2 + 3*w - 9]', '[369, 369, -4*w - 3]', '[369, 369, -3*w^2 - 2*w + 12]', '[372, 186, 3*w^2 - 2*w - 9]', '[372, 186, 3*w^2 - 4*w - 1]', '[373, 373, -w^2 - 4]', '[375, 15, -5*w]', '[375, 15, -5*w + 10]', '[376, 94, -2*w^2 + 16]', '[376, 94, 4*w^2 - 2*w - 16]', '[381, 381, -5*w^2 + 24]', '[381, 381, -2*w^2 - 3*w + 8]', '[382, 382, w^2 - 7*w + 8]', '[383, 383, 2*w^2 - 4*w - 7]', '[384, 24, 4*w + 4]', '[384, 24, -4*w + 12]', '[386, 386, -4*w^2 + 9*w - 1]', '[387, 129, -5*w^2 + 2*w + 22]', '[387, 129, 2*w^2 - 7*w]', '[387, 387, 3*w^2 - 4*w - 12]', '[389, 389, -5*w^2 + 4*w + 28]', '[389, 389, 3*w^2 - 8]', '[389, 389, -9*w^2 + 4*w + 50]', '[393, 393, -3*w^2 + 2*w + 2]', '[393, 393, -3*w^2 + w + 9]', '[394, 394, w^2 + w + 4]', '[397, 397, -8*w^2 + w + 38]', '[397, 397, 6*w^2 - w - 32]', '[397, 397, 2*w^2 + 2*w - 11]', '[398, 398, -3*w^2 - w + 16]', '[401, 401, w^2 - 4*w - 4]', '[402, 402, -5*w + 7]', '[402, 402, -3*w^2 - w + 18]', '[403, 403, 4*w^2 - 2*w - 25]', '[404, 202, 3*w^2 - 4*w - 5]', '[408, 102, 2*w^2 - 6*w - 2]', '[408, 102, 4*w^2 - 4*w - 18]', '[409, 409, 5*w^2 - w - 31]', '[411, 411, 6*w^2 - 8*w - 17]', '[411, 411, 4*w^2 + 3*w - 6]', '[411, 411, -2*w + 9]', '[411, 411, -3*w^2 + 10*w - 2]', '[411, 411, w^2 + 8*w - 6]', '[411, 411, -w + 8]', '[416, 52, -2*w^2 - 2]', '[417, 417, -3*w^2 - 8*w + 4]', '[417, 417, -w^2 - 5*w - 3]', '[421, 421, 3*w^2 - 3*w - 7]', '[422, 422, 2*w^2 - 11*w + 7]', '[423, 141, 4*w^2 - 8*w - 3]', '[423, 141, 2*w^2 + 4*w - 7]', '[423, 141, 8*w^2 - 2*w - 43]', '[423, 141, -2*w^2 + 4*w + 15]', '[423, 423, -4*w^2 + 27]', '[423, 423, 2*w^2 - 2*w + 3]', '[424, 106, 2*w^2 + 2*w - 14]', '[426, 426, 4*w^2 + 3*w - 7]', '[426, 426, 5*w - 9]', '[431, 431, -2*w^2 - 3*w - 2]', '[432, 12, 6*w - 6]', '[432, 36, -2*w^2 + 2*w + 16]', '[432, 36, 2*w^2 + 2*w - 12]', '[432, 108, 2*w^2 + 6*w]', '[433, 433, 5*w^2 + 2*w - 16]', '[436, 218, 3*w^2 - 7]', '[438, 438, -3*w^2 + 7*w + 4]', '[438, 438, w^2 + 5*w - 6]', '[442, 442, w^2 + 5*w + 2]', '[443, 443, w^2 - 4*w - 10]', '[443, 443, 2*w^2 + 2*w - 13]', '[443, 443, -3*w^2 + 4*w + 2]', '[446, 446, -3*w^2 + 3*w + 2]', '[447, 447, -7*w^2 + 3*w + 33]', '[447, 447, -3*w^2 + 2*w + 8]', '[452, 226, -5*w^2 + 4*w + 25]', '[452, 226, 3*w^2 - 5]', '[452, 226, -w^2 - 4*w + 7]', '[453, 453, -3*w^2 - 2*w]', '[453, 453, -3*w^2 + 4*w + 4]', '[456, 114, -2*w - 8]', '[456, 114, 4*w^2 - 6*w - 12]', '[458, 458, 3*w^2 - w - 8]', '[459, 51, -3*w^2 + 6]', '[459, 153, w^2 + 2*w - 14]', '[459, 153, -5*w^2 + w + 21]', '[459, 459, w^2 - 6*w]', '[463, 463, 6*w - 1]', '[468, 78, 5*w^2 - 4*w - 27]', '[468, 78, w^2 - 4*w - 5]', '[468, 234, -3*w^2 + 4*w + 3]', '[472, 118, 2*w^2 - 4*w - 8]', '[477, 159, -w^2 + 2*w + 12]', '[477, 159, 7*w^2 - 4*w - 32]', '[477, 477, -5*w^2 + 6*w + 18]', '[478, 478, -w^2 + 5*w + 2]', '[479, 479, -w^2 + w - 5]', '[486, 18, 6*w^2 - 3*w - 27]', '[486, 18, 3*w^2 - 3*w - 6]', '[486, 54, 3*w + 9]', '[486, 54, 5*w^2 + 7*w - 10]', '[486, 162, -4*w^2 + 5*w + 15]', '[486, 486, 2*w^2 + 3*w - 9]', '[487, 487, 5*w^2 - 4*w - 26]', '[487, 487, -w^2 - 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3*w - 5]', '[229, 229, -3*w^2 + 3*w + 17]', '[239, 239, 3*w^2 - w - 11]', '[251, 251, 4*w^2 - 2*w - 17]', '[263, 263, 3*w + 8]', '[269, 269, -2*w^2 + 3*w + 10]', '[277, 277, -2*w - 7]', '[277, 277, 4*w^2 - 23]', '[277, 277, 7*w^2 - 4*w - 40]', '[289, 17, 3*w^2 - 2*w - 10]', '[313, 313, 3*w^2 + w - 7]', '[331, 331, -3*w^2 + 3*w + 1]', '[331, 331, -3*w^2 + 4*w + 20]', '[331, 331, -w^2 - 3*w + 11]', '[343, 7, -7]', '[347, 347, -3*w^2 - w + 19]', '[349, 349, 4*w^2 + 4*w - 11]', '[353, 353, w^2 - 5*w - 1]', '[361, 19, 4*w^2 - w - 16]', '[367, 367, -4*w - 5]', '[373, 373, -w^2 - 4]', '[383, 383, 2*w^2 - 4*w - 7]', '[389, 389, -5*w^2 + 4*w + 28]', '[389, 389, 3*w^2 - 8]', '[389, 389, -9*w^2 + 4*w + 50]', '[397, 397, -8*w^2 + w + 38]', '[397, 397, 6*w^2 - w - 32]', '[397, 397, 2*w^2 + 2*w - 11]', '[401, 401, w^2 - 4*w - 4]', '[409, 409, 5*w^2 - w - 31]', '[421, 421, 3*w^2 - 3*w - 7]', '[431, 431, -2*w^2 - 3*w - 2]', '[433, 433, 5*w^2 + 2*w - 16]', '[443, 443, w^2 - 4*w - 10]', '[443, 443, 2*w^2 + 2*w - 13]', '[443, 443, -3*w^2 + 4*w + 2]', '[463, 463, 6*w - 1]', '[479, 479, -w^2 + w - 5]', '[487, 487, 5*w^2 - 4*w - 26]', '[487, 487, -w^2 - 4*w + 14]', '[487, 487, 2*w^2 - w - 16]', '[491, 491, -4*w^2 - 5*w + 10]', '[499, 499, 2*w^2 - 8*w + 1]', '[509, 509, -4*w^2 + 3*w + 26]', '[509, 509, -6*w^2 + w + 26]', '[509, 509, 4*w^2 - 4*w - 19]', '[521, 521, 4*w^2 - 3*w - 14]', '[541, 541, w^2 + 4*w - 8]', '[541, 541, w^2 + w - 13]', '[541, 541, 3*w^2 + 3*w - 11]', '[547, 547, 3*w^2 - 2*w - 4]', '[563, 563, 2*w^2 - 4*w + 5]', '[563, 563, -3*w^2 + 2*w - 2]', '[563, 563, -6*w + 7]', '[571, 571, -3*w^2 - 5*w - 1]', '[571, 571, -w^2 + 3*w - 7]', '[571, 571, 3*w^2 - 22]', '[577, 577, 3*w^2 - 4*w - 14]', '[587, 587, -3*w^2 - 6*w - 2]', '[587, 587, 2*w^2 + 3*w - 10]', '[587, 587, -7*w^2 + 2*w + 32]', '[593, 593, -w^2 - w - 5]', '[593, 593, 5*w^2 - 28]', '[593, 593, w^2 + 5*w - 7]', '[607, 607, 3*w^2 + 2*w - 14]', '[617, 617, -2*w^2 + 4*w + 13]', '[631, 631, w^2 - 8*w + 8]', '[643, 643, -9*w^2 + 3*w + 43]', '[643, 643, -2*w^2 + 4*w + 11]', '[643, 643, -5*w^2 + 3*w + 31]', '[647, 647, -4*w^2 + 7*w + 10]', '[653, 653, 6*w^2 - 5*w - 28]', '[659, 659, w^2 + 4*w - 10]', '[661, 661, -8*w^2 + 3*w + 46]', '[661, 661, 4*w^2 + w - 20]', '[661, 661, 2*w^2 - 4*w - 19]', '[673, 673, -4*w + 13]', '[677, 677, -5*w^2 - w + 17]', '[677, 677, -3*w^2 - 4*w + 10]', '[677, 677, 2*w^2 - 2*w - 17]', '[683, 683, 4*w^2 - 5*w - 16]', '[691, 691, 5*w^2 + 2*w - 20]', '[719, 719, 6*w^2 - 3*w - 26]', '[727, 727, -6*w^2 - w + 22]', '[743, 743, -7*w^2 + w + 37]', '[743, 743, 7*w^2 - 3*w - 41]', '[743, 743, 4*w + 11]', '[751, 751, 2*w^2 + 5*w - 8]', '[757, 757, 3*w^2 - 6*w - 8]', '[761, 761, 5*w^2 - 2*w - 20]', '[769, 769, 4*w^2 + w - 10]', '[769, 769, -5*w^2 - w + 23]', '[769, 769, -3*w - 10]', '[773, 773, 2*w^2 + 3*w - 16]', '[787, 787, 5*w^2 + 7*w - 11]', '[821, 821, -6*w - 1]', '[821, 821, -11*w^2 + 7*w + 61]', '[821, 821, -w^2 - 6*w - 4]', '[827, 827, -4*w^2 - 4*w + 13]', '[829, 829, w^2 - 5*w - 5]', '[853, 853, -2*w^2 + w - 4]', '[853, 853, -3*w^2 + 2*w + 22]', '[853, 853, w - 10]', '[859, 859, 6*w^2 - 35]', '[863, 863, 3*w^2 + 3*w - 13]', '[877, 877, 5*w^2 - w - 19]', '[883, 883, 5*w^2 - 5*w - 23]', '[883, 883, 3*w^2 - 4*w + 4]', '[883, 883, w^2 - 5*w - 11]', '[887, 887, 4*w^2 - 11]', '[887, 887, -6*w^2 + 6*w + 37]', '[887, 887, 4*w^2 + w - 8]', '[911, 911, 5*w^2 + 2*w - 14]', '[919, 919, w^2 + 6*w - 8]', '[929, 929, 6*w^2 - w - 38]', '[937, 937, 12*w^2 - 6*w - 67]', '[941, 941, 7*w^2 - 5*w - 29]', '[947, 947, -8*w^2 + w + 40]', '[961, 31, w^2 + 3*w + 7]', '[977, 977, 6*w^2 - 23]', '[983, 983, -4*w^2 + 5*w + 2]', '[983, 983, w^2 - 5*w - 7]', '[983, 983, 6*w^2 - 31]', '[997, 997, -6*w^2 + 2*w + 37]']}
• 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': [3, -5, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 564, 'disc_rad': 282, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[3, 1]]], [13, [[2, 1], [1, 1]]], [17, [[2, 1], [1, 1]]], [19, [[2, 1], [1, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [[2, 1], [1, 1]]], [37, [[3, 1]]], [41, [[1, 3]]], [43, [[2, 1], [1, 1]]], [47, [0]], [53, [[2, 1], [1, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 3, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 18.849343120394256, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.564.1', 'local_algs': ['2.3.2.1', '3.1.0.1', '3.2.1.2', '47.1.0.1', '47.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 47], 'rd': 8.26214922567, 'regulator': {'__RealLiteral__': 0, 'data': '5.40274790998', 'prec': 44}, 'res': {'gal': ['81,-135,30,45,-20,-1,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 2 \\)', '\\( 2 a^{2} - a - 10 \\)'], 'unitsGmodule': [[4, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}