Hilbert modular form data - 3.3.1944.1-6.1-a

Formats: - HTML - YAML - JSON - 2024-05-06T23:48:23.595394

• 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': 1944, 'field_bad_primes': [2, 3], 'field_label': '3.3.1944.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1944.1-6.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2, 3], 'level_ideal': '[6, 6, w]', 'level_label': '6.1', 'level_norm': 6, 'parallel_weight': 2, 'short_label': '6.1-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^2 + 2*w + 2]', 1], ['[3, 3, w^2 - w - 9]', 1]], 'hecke_eigenvalues': [-1, 2, -1, -4, -2, 2, 0, 8, -6, 0, -2, -4, 10, -8, 14, 10, -8, -10, -6, -12, 12, -2, 16, -4, -14, -12, 4, -12, -4, -12, -12, 2, 14, -2, -8, -22, -24, 20, -22, -6, 4, 16, 2, -2, 2, 4, 10, -4, 18, 8, -28, -10, 14, -8, -14, 0, 4, 6, 8, 4, 0, -10, 6, 6, -28, -6, -12, 16, -18, -30, -18, 12, 10, -18, -8, -10, -18, 34, -26, 18, 0, 18, 6, -26, -28, 28, -26, -10, 30, 16, -22, -20, -40, 32, -8, -14, 6, -10, -10, -38, -22, -22, 6, 36, -44, 12, -26, 32, 12, 34, -6, 4, -12, -10, 30, -10, 50, 18, -30, -18, 46, 18, 34, -4, 28, 16, -20, 2, -42, 52, -34, 12, 54, -46, -48, -44, -28, -26, -2, 38, 26, 8, -38, -4, 58, -8, -24, 0, 56, -30, 24, -10, 20, -36, 38, -14, 52, 36, 44, 8, -12, -48, -20, -10], 'hecke_polynomial': 'x', 'label': '3.3.1944.1-6.1-a'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 1944, 'ideals': ['[1, 1, 1]', '[2, 2, -w^2 + 2*w + 2]', '[2, 2, w + 1]', '[3, 3, w^2 - w - 9]', '[4, 2, -w^2 + w + 8]', '[4, 2, -3*w^2 + 2*w + 25]', '[4, 4, -w - 2]', '[6, 6, w]', '[6, 6, -w - 3]', '[7, 7, w^2 - w - 7]', '[8, 2, 2]', '[8, 4, w^2 - 3*w - 2]', '[8, 4, -w^2 + 7]', '[8, 8, 4*w^2 - 3*w - 34]', '[9, 3, w^2 - 3*w - 3]', '[11, 11, w^2 - w - 1]', '[12, 6, w^2 + w]', '[12, 6, -w^2 + 2*w + 3]', '[12, 12, 2*w^2 - w - 18]', '[13, 13, -2*w - 1]', '[14, 14, -2*w^2 + 5*w + 4]', '[14, 14, w - 1]', '[16, 4, -2*w^2 + 4*w + 4]', '[16, 4, w^2 - 2*w - 5]', '[16, 4, 2*w + 2]', '[16, 8, w^2 - w - 10]', '[16, 16, w - 2]', '[17, 17, -2*w^2 + 6*w + 5]', '[18, 6, -w^2 + 6]', '[18, 6, 4*w^2 - 3*w - 33]', '[21, 21, 4*w + 3]', '[22, 22, -2*w^2 + w + 17]', '[22, 22, -w + 4]', '[24, 6, 2*w^2 - 2*w - 18]', '[24, 12, w^2 - w - 6]', '[24, 12, w^2 - 4*w - 3]', '[24, 24, -w^2 - 2*w]', '[26, 26, -4*w^2 + 3*w + 35]', '[26, 26, -w^2 + 10]', '[27, 3, 3]', '[28, 14, -3*w^2 + 3*w + 28]', '[28, 14, w^2 - 1]', '[28, 28, -w^2 + 8]', '[31, 31, -2*w^2 + 2*w + 19]', '[32, 4, -2*w^2 + 2*w + 16]', '[32, 4, -6*w^2 + 4*w + 50]', '[32, 8, -2*w - 4]', '[32, 8, -w^2 + 2*w + 1]', '[32, 16, w^2 - w - 2]', '[32, 32, -5*w^2 + 4*w + 44]', '[33, 33, -2*w - 3]', '[34, 34, w + 4]', '[34, 34, 2*w^2 - w - 19]', '[36, 6, -w^2 + 3*w]', '[36, 6, w^2 - 9]', '[36, 12, w^2]', '[37, 37, 2*w^2 - 13]', '[39, 39, w^2 + w - 3]', '[41, 41, w^2 - w - 5]', '[42, 42, -w^2 + 2*w + 6]', '[42, 42, -2*w^2 + w + 15]', '[43, 43, 2*w^2 - 2*w - 17]', '[43, 43, -2*w + 7]', '[43, 43, 12*w^2 - 8*w - 101]', '[44, 22, -w^2 + 3*w + 4]', '[44, 22, -w^2 + 5]', '[44, 44, -w^2 - 6*w - 4]', '[48, 12, 2*w]', '[48, 12, -3*w^2 + 2*w + 27]', '[48, 12, -2*w - 6]', '[48, 24, -3*w^2 + 7*w + 6]', '[48, 48, -3*w^2 + 2*w + 24]', '[49, 7, w^2 + w - 1]', '[49, 49, 3*w^2 - w - 23]', '[51, 51, -w^2 + w + 3]', '[52, 26, -w^2 + 2*w + 11]', '[52, 26, -w^2 + w + 4]', '[52, 52, -3*w^2 + 8*w + 8]', '[54, 6, -3*w^2 + 6*w + 6]', '[54, 6, 3*w + 3]', '[56, 14, 2*w^2 - 2*w - 14]', '[56, 28, -w^2 - w + 2]', '[56, 28, 5*w^2 - 4*w - 43]', '[56, 56, -w^2 + 4*w + 4]', '[59, 59, -w^2 + w + 11]', '[61, 61, -w^2 - w - 1]', '[62, 62, 2*w^2 - 3*w - 11]', '[62, 62, -w^2 + 2]', '[63, 21, -w^2 - 3*w - 3]', '[64, 4, 4]', '[64, 8, w^2 - 6*w - 5]', '[64, 8, 2*w^2 - 6*w - 4]', '[64, 8, -2*w^2 + 14]', '[64, 16, 8*w^2 - 6*w - 68]', '[64, 32, 3*w^2 - 3*w - 22]', '[64, 64, -w^2 + 4]', '[66, 66, 5*w^2 - 4*w - 42]', '[66, 66, 4*w^2 - 11*w - 9]', '[68, 34, w^2 - 2*w - 7]', '[68, 34, 3*w^2 - 7*w - 8]', '[68, 68, -2*w^2 + w + 2]', '[72, 6, 2*w^2 - 6*w - 6]', '[72, 12, -5*w^2 + 3*w + 42]', '[72, 12, w^2 - 3]', '[72, 24, -w^2 + 12]', '[74, 74, -w^2 - 2*w - 2]', '[74, 74, -w + 5]', '[77, 77, 2*w^2 - 4*w - 5]', '[78, 78, 2*w^2 - 5*w - 3]', '[78, 78, -2*w^2 - w]', '[79, 79, -2*w^2 + 4*w + 7]', '[81, 9, 3*w^2 - 3*w - 27]', '[82, 82, -4*w^2 + 9*w + 8]', '[82, 82, 3*w + 1]', '[83, 83, 2*w - 1]', '[84, 42, w^2 - w]', '[84, 42, -w^2 - 2*w + 3]', '[84, 84, 5*w^2 - 14*w - 12]', '[86, 86, -w - 5]', '[86, 86, 16*w^2 - 11*w - 136]', '[86, 86, w^2 - 2*w - 10]', '[86, 86, -w^2 + 4*w + 2]', '[86, 86, -2*w^2 + 5*w + 7]', '[86, 86, 4*w^2 - w - 29]', '[88, 22, 2*w^2 - 2*w - 2]', '[88, 44, -w^2 - 4*w - 1]', '[88, 44, 3*w^2 - w - 22]', '[88, 88, w^2 - 2*w - 8]', '[89, 89, 5*w^2 - 3*w - 43]', '[91, 91, w^2 - 3*w - 5]', '[93, 93, 2*w^2 - 4*w - 3]', '[96, 12, 2*w^2 + 2*w]', '[96, 12, -2*w^2 + 4*w + 6]', '[96, 24, 4*w^2 - 2*w - 36]', '[96, 24, -w^2 + 2*w + 9]', '[96, 48, -w^2 - w + 6]', '[96, 96, w^2 - 2*w]', '[98, 14, -4*w^2 + 3*w + 4]', '[98, 14, 2*w^2 + 9*w + 5]', '[98, 98, -3*w - 4]', '[98, 98, -2*w^2 + 3*w + 13]', '[99, 33, 2*w^2 - 21]', '[102, 102, -5*w - 3]', '[102, 102, -6*w^2 + 5*w + 48]', '[103, 103, -2*w + 5]', '[104, 26, -4*w - 2]', '[104, 52, -w^2 + 4*w - 1]', '[104, 52, 5*w^2 - 5*w - 46]', '[104, 104, 2*w^2 - w - 14]', '[107, 107, -w^2 - 3*w + 1]', '[108, 6, -3*w^2 + 3*w + 24]', '[108, 6, -9*w^2 + 6*w + 75]', '[108, 12, -3*w - 6]', '[109, 109, w^2 - 3*w + 1]', '[111, 111, 2*w^2 - 2*w - 3]', '[112, 28, -4*w^2 + 10*w + 8]', '[112, 28, w^2 - 2*w - 13]', '[112, 28, 2*w - 2]', '[112, 56, -7*w^2 + 5*w + 58]', '[112, 112, 2*w^2 + w - 10]', '[113, 113, -2*w^2 + 8*w + 7]', '[117, 39, 5*w^2 - 3*w - 45]', '[118, 118, 3*w + 5]', '[118, 118, -2*w^2 + 3*w + 4]', '[119, 119, 2*w^2 + 4*w + 1]', '[121, 11, -7*w^2 + 5*w + 61]', '[121, 121, -2*w^2 + 2*w + 13]', '[122, 122, 2*w^2 - w - 20]', '[122, 122, 8*w^2 - 5*w - 67]', '[123, 123, -4*w^2 + 2*w + 33]', '[124, 62, -w^2 + 4*w + 1]', '[124, 62, -w^2 - 7*w - 4]', '[124, 124, -5*w^2 + 4*w + 40]', '[125, 5, -5]', '[126, 42, 4*w^2 - 3*w - 36]', '[126, 42, -4*w^2 + 9*w + 9]', '[127, 127, 18*w^2 - 12*w - 151]', '[128, 8, -4*w^2 + 8*w + 8]', '[128, 8, 2*w^2 - 4*w - 10]', '[128, 8, 4*w + 4]', '[128, 16, 2*w^2 - 2*w - 20]', '[128, 16, 3*w^2 - 2*w - 23]', '[128, 32, 2*w - 4]', '[128, 64, -w^2 - 5*w - 2]', '[128, 128, 3*w^2 - 4*w - 4]', '[129, 129, 9*w^2 - 7*w - 75]', '[129, 129, -3*w^2 - 7*w - 3]', '[129, 129, 2*w - 3]', '[131, 131, w^2 + w - 13]', '[132, 66, w^2 - w - 12]', '[132, 66, 5*w^2 - 2*w - 39]', '[132, 132, -w^2 + 4*w]', '[136, 34, -4*w^2 + 12*w + 10]', '[136, 68, -3*w^2 + 3*w + 26]', '[136, 68, -w^2 - 1]', '[136, 136, -2*w^2 + 3*w + 10]', '[137, 137, 4*w^2 - 4*w - 31]', '[139, 139, -2*w - 7]', '[139, 139, 4*w^2 - 2*w - 31]', '[139, 139, -19*w^2 + 13*w + 161]', '[143, 143, -3*w^2 + 3*w + 25]', '[144, 12, -2*w^2 + 12]', '[144, 12, w^2 + 6*w + 3]', '[144, 12, 8*w^2 - 6*w - 66]', '[144, 24, -w^2 + 3*w + 6]', '[144, 48, -5*w^2 + 12*w + 12]', '[147, 21, -2*w^2 - 2*w + 9]', '[147, 147, -w^2 + 5*w + 3]', '[148, 74, -7*w^2 + 17*w + 16]', '[148, 74, -w^2 + 4*w + 5]', '[148, 148, 3*w^2 - 2*w - 28]', '[149, 149, w^2 + w - 7]', '[149, 149, w^2 - 7*w - 5]', '[149, 149, 6*w^2 - 4*w - 53]', '[151, 151, w^2 - 5*w - 5]', '[153, 51, 2*w^2 - 15]', '[154, 154, -2*w^2 + 3*w + 20]', '[154, 154, -2*w^2 + 9*w + 7]', '[156, 78, -3*w^2 + 10*w + 9]', '[156, 78, 3*w^2 - w - 24]', '[156, 156, w - 6]', '[157, 157, 20*w^2 - 14*w - 169]', '[158, 158, 6*w^2 - 5*w - 52]', '[158, 158, 2*w^2 - 7*w - 5]', '[162, 18, 3*w]', '[162, 18, -3*w - 9]', '[164, 82, 11*w^2 - 8*w - 95]', '[164, 82, 3*w^2 - w - 28]', '[164, 164, -w^2 - 2*w + 4]', '[166, 166, 2*w^2 + w - 1]', '[166, 166, 5*w^2 - 16*w - 14]', '[168, 42, 8*w + 6]', '[168, 84, -3*w^2 + w + 30]', '[168, 84, 3*w^2 - 8*w - 9]', '[168, 168, -w - 6]', '[169, 13, 4*w^2 - 2*w - 35]', '[169, 169, -6*w^2 + 4*w + 49]', '[172, 86, -w^2 - 6*w - 5]', '[172, 86, 3*w^2 - 3*w - 4]', '[172, 86, 5*w^2 - 3*w - 40]', '[172, 86, 3*w^2 - 6*w - 5]', '[172, 86, -w^2 - 3*w - 4]', '[172, 86, -w^2 + 13]', '[172, 172, 2*w^2 - 3*w - 14]', '[172, 172, -w^2 + 6*w + 4]', '[172, 172, -2*w^2 + 3*w + 22]', '[176, 44, -4*w^2 + 2*w + 34]', '[176, 44, 5*w^2 - 14*w - 13]', '[176, 44, -2*w + 8]', '[176, 88, -w^2 - w - 2]', '[176, 176, -3*w^2 + 10*w + 8]', '[177, 177, 10*w^2 - 8*w - 87]', '[178, 178, 2*w^2 - w - 13]', '[178, 178, 2*w^2 - 5*w - 8]', '[179, 179, w^2 - 3*w - 13]', '[181, 181, 4*w^2 - 12*w - 11]', '[182, 182, -5*w^2 + 2*w + 38]', '[182, 182, -2*w^2 + w + 1]', '[183, 183, 4*w + 9]', '[186, 186, 2*w^2 + w - 12]', '[186, 186, -8*w^2 + 5*w + 69]', '[187, 187, -2*w^2 - 2*w + 7]', '[189, 21, 3*w^2 - 3*w - 21]', '[192, 12, 4*w^2 - 4*w - 36]', '[192, 24, w^2 + 2*w + 3]', '[192, 24, 2*w^2 - 2*w - 12]', '[192, 24, 2*w^2 - 8*w - 6]', '[192, 48, -2*w^2 - 4*w]', '[192, 96, -w^2 + 7*w + 6]', '[192, 192, 4*w^2 - w - 30]', '[193, 193, -3*w^2 + 7*w + 11]', '[193, 193, 2*w^2 - 4*w - 23]', '[193, 193, -w^2 + w - 1]', '[196, 14, w^2 + w - 8]', '[196, 14, 3*w^2 - 4*w - 31]', '[196, 28, -3*w^2 - 10*w - 4]', '[196, 98, 7*w^2 - 19*w - 16]', '[196, 98, w^2 - 2*w + 1]', '[196, 196, 6*w^2 - 5*w - 50]', '[197, 197, 3*w^2 - 3*w - 29]', '[197, 197, -2*w^2 + 6*w + 7]', '[197, 197, w^2 - 3*w - 7]', '[198, 66, 2*w^2 - 3*w - 9]', '[198, 66, -2*w^2 - 3*w]', '[199, 199, 26*w^2 - 18*w - 221]', '[204, 102, -5*w^2 + 4*w + 45]', '[204, 102, -w^2 - w + 12]', '[204, 204, w^2 + 4*w]', '[206, 206, -2*w^2 + 3*w + 5]', '[206, 206, 12*w^2 - 9*w - 104]', '[208, 52, -8*w^2 + 6*w + 70]', '[208, 52, 3*w^2 - 6*w - 7]', '[208, 52, -2*w^2 + 20]', '[208, 104, w^2 + 3*w - 2]', '[208, 208, -2*w^2 + 3*w + 2]', '[211, 211, -4*w - 5]', '[211, 211, 9*w^2 - 7*w - 77]', '[211, 211, 3*w^2 - 7*w - 5]', '[214, 214, -8*w^2 + 5*w + 68]', '[214, 214, 4*w^2 - 11*w - 11]', '[216, 6, 6]', '[216, 12, 3*w^2 - 9*w - 6]', '[216, 12, -3*w^2 + 21]', '[216, 24, 12*w^2 - 9*w - 102]', '[217, 217, 13*w^2 - 9*w - 109]', '[218, 218, -2*w^2 + 7*w + 7]', '[218, 218, 7*w^2 - 4*w - 58]', '[221, 221, 4*w^2 - 4*w - 29]', '[222, 222, 6*w^2 - 5*w - 51]', '[222, 222, 3*w^2 - 4*w - 18]', '[223, 223, 11*w^2 - 7*w - 91]', '[224, 28, -6*w^2 + 6*w + 56]', '[224, 28, 2*w^2 - 2]', '[224, 56, -2*w^2 + 16]', '[224, 56, -3*w^2 + 6*w + 11]', '[224, 112, w^2 - 3*w + 2]', '[224, 224, -2*w^2 - 3*w - 2]', '[226, 226, -4*w^2 + 3*w + 31]', '[226, 226, -3*w^2 + 6*w + 14]', '[227, 227, 3*w^2 - w - 25]', '[229, 229, 2*w^2 - 4*w - 11]', '[231, 231, -w^2 - w + 9]', '[233, 233, 2*w^2 + 6*w + 5]', '[234, 78, 2*w^2 - 3*w - 15]', '[234, 78, w^2 + 6*w + 6]', '[236, 118, -9*w^2 + 7*w + 76]', '[236, 118, 3*w^2 + 8*w + 5]', '[236, 236, w^2 - 4*w - 16]', '[237, 237, 3*w^2 - w - 27]', '[238, 238, 8*w^2 - 7*w - 71]', '[238, 238, 3*w^2 - 2*w - 22]', '[241, 241, w^2 - w - 13]', '[241, 241, w^2 + w - 11]', '[241, 241, 4*w + 1]', '[242, 22, -2*w^2 + 3*w + 8]', '[242, 22, -2*w^2 + 3*w + 19]', '[242, 242, 5*w^2 - 12*w - 10]', '[242, 242, -3*w + 1]', '[243, 9, 3*w^2 - 9*w - 9]', '[244, 122, w^2 - 3*w - 8]', '[244, 122, 3*w^2 - 19]', '[244, 244, 4*w^2 - 9*w - 10]', '[246, 246, -w^2 + 4*w + 6]', '[246, 246, -2*w^2 - w + 9]', '[248, 62, -4*w^2 + 4*w + 38]', '[248, 124, 3*w^2 - 4*w - 5]', '[248, 124, -w^2 - w + 10]', '[248, 248, 3*w^2 - 8*w - 4]', '[249, 249, -3*w^2 + w + 21]', '[250, 10, 5*w^2 - 10*w - 10]', '[250, 10, -5*w - 5]', '[251, 251, 2*w^2 - 11]', '[252, 42, w^2 - 3*w - 12]', '[252, 42, -7*w^2 + 6*w + 57]', '[252, 84, 2*w^2 - 3*w - 6]', '[254, 254, 6*w^2 - w - 43]', '[254, 254, w^2 - 2*w - 14]', '[256, 8, -4*w^2 + 4*w + 32]', '[256, 8, -12*w^2 + 8*w + 100]', '[256, 16, w^2 + 2*w - 5]', '[256, 16, -4*w - 8]', '[256, 16, -2*w^2 + 4*w + 2]', '[256, 32, 2*w^2 - 2*w - 4]', '[256, 64, -10*w^2 + 8*w + 88]', '[256, 128, -3*w^2 + w + 26]', '[256, 256, w^2 - 4*w + 4]', '[257, 257, 4*w^2 - 8*w - 7]', '[258, 258, -2*w^2 + 7*w]', '[258, 258, -2*w^2 + w + 12]', '[258, 258, 2*w^2 - w - 3]', '[258, 258, 2*w^2 - w - 21]', '[258, 258, -4*w^2 + 5*w + 39]', '[258, 258, -8*w^2 + 7*w + 72]', '[259, 259, -9*w^2 + 7*w + 79]', '[262, 262, 2*w^2 - 3*w - 7]', '[262, 262, 8*w^2 - 21*w - 20]', '[263, 263, 5*w^2 - 5*w - 47]', '[263, 263, 5*w^2 - 11*w - 11]', '[263, 263, 2*w^2 - 2*w - 11]', '[264, 66, -4*w - 6]', '[264, 132, 3*w^2 - 5*w - 6]', '[264, 132, -3*w^2 + 4*w + 21]', '[264, 264, -6*w^2 + 5*w + 54]', '[267, 267, 2*w^2 + 4*w + 3]', '[269, 269, 6*w^2 - 6*w - 55]', '[269, 269, 8*w^2 - 18*w - 17]', '[269, 269, -2*w^2 + 19]', '[271, 271, 2*w^2 - 17]', '[272, 68, 2*w + 8]', '[272, 68, -w^2 - 10*w - 7]', '[272, 68, 4*w^2 - 2*w - 38]', '[272, 136, w^2 - 5*w - 2]', '[272, 272, 13*w^2 - 10*w - 112]', '[273, 273, -2*w^2 + 2*w + 21]', '[274, 274, -5*w^2 + 14*w + 10]', '[274, 274, w - 7]', '[277, 277, 2*w^2 + 2*w - 1]', '[278, 278, -2*w^2 - 9*w - 7]', '[278, 278, 2*w^2 + 3*w - 7]', '[278, 278, -2*w^2 + 3*w + 16]', '[278, 278, 3*w^2 - 2]', '[278, 278, -w^2 - 2]', '[278, 278, -6*w^2 + 3*w + 47]', '[279, 93, w^2 - 3*w - 9]', '[281, 281, 4*w + 7]', '[286, 286, w + 7]', '[286, 286, 2*w^2 - 7*w - 4]', '[287, 287, -2*w^2 + 23]', '[288, 12, -2*w^2 + 6*w]', '[288, 12, 2*w^2 - 18]', '[288, 24, 2*w^2]', '[288, 24, 7*w^2 - 6*w - 63]', '[288, 48, 7*w^2 - 3*w - 54]', '[288, 96, 2*w^2 - 3*w - 18]', '[289, 17, 10*w^2 - 6*w - 83]', '[289, 289, w^2 - 3*w - 11]', '[294, 42, w^2 + 8*w + 6]', '[294, 42, -4*w^2 - 11*w - 3]', '[294, 294, -w^2 + 4*w + 18]', '[294, 294, 10*w^2 - 7*w - 87]', '[296, 74, 4*w^2 - 26]', '[296, 148, w^2 - 3*w - 10]', '[296, 148, 3*w^2 - 1]', '[296, 296, 3*w^2 - 6*w - 8]', '[297, 33, 3*w^2 - 3*w - 3]', '[298, 298, 2*w^2 + 3*w - 1]', '[298, 298, -4*w^2 + 3*w + 37]', '[298, 298, 2*w^2 - 3*w - 17]', '[298, 298, 2*w^2 - 9*w - 8]', '[298, 298, -3*w + 8]', '[298, 298, 3*w^2 - 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10*w - 3]', '[1857, 1857, -18*w^2 + 10*w + 147]', '[1857, 1857, 12*w^2 - 28*w - 39]', '[1858, 1858, -22*w^2 + 17*w + 181]', '[1858, 1858, 5*w^2 - 2*w - 34]', '[1859, 143, -w^2 + 7*w - 1]', '[1859, 1859, -3*w^2 + w + 11]', '[1861, 1861, 8*w^2 - 4*w - 61]', '[1864, 466, 4*w^2 + 12*w + 10]', '[1864, 932, w^2 - 15*w - 10]', '[1864, 932, w^2 - 19]', '[1864, 1864, 6*w^2 - 9*w - 62]', '[1867, 1867, 5*w^2 - w - 41]', '[1867, 1867, -4*w^2 + 10*w + 17]', '[1867, 1867, 3*w^2 + w - 7]', '[1868, 934, 11*w^2 - 5*w - 88]', '[1868, 934, 33*w^2 - 28*w - 293]', '[1868, 1868, -9*w^2 - 22*w + 4]', '[1869, 1869, 3*w^2 - w - 9]', '[1871, 1871, 5*w^2 + 15*w + 11]', '[1871, 1871, -13*w^2 + 27*w + 25]', '[1871, 1871, 4*w^2 - 6*w - 11]', '[1872, 156, 4*w^2 - 6*w - 30]', '[1872, 156, 11*w^2 - 6*w - 87]', '[1872, 156, 2*w^2 + 12*w + 12]', '[1872, 312, -5*w^2 + 3*w + 6]', '[1872, 624, 8*w^2 - 9*w - 78]', '[1874, 1874, -21*w^2 + 16*w + 178]', '[1874, 1874, -11*w^2 + 26*w + 26]', '[1874, 1874, -4*w^2 + w + 1]', '[1874, 1874, -8*w^2 + 23*w + 17]', '[1874, 1874, -2*w^2 + 7*w + 13]', '[1874, 1874, -15*w^2 + 44*w + 38]', '[1879, 1879, 13*w^2 - 11*w - 113]', '[1883, 1883, 3*w^2 + 19*w + 13]', '[1883, 1883, 15*w^2 - 13*w - 121]', '[1883, 1883, 17*w^2 - 43*w - 37]', '[1884, 942, 21*w^2 - 14*w - 183]', '[1884, 942, -3*w^2 + 5*w + 36]', '[1884, 1884, -5*w + 6]', '[1887, 1887, w^2 - 7*w - 27]', '[1888, 236, -18*w^2 + 14*w + 152]', '[1888, 236, 6*w^2 + 16*w + 10]', '[1888, 472, -w^2 + 2*w - 7]', '[1888, 472, 2*w^2 - 8*w - 32]', '[1888, 944, 3*w^2 - w - 10]', '[1888, 1888, 7*w^2 - 20*w - 20]', '[1889, 1889, -7*w^2 + 15*w + 17]', '[1891, 1891, -6*w + 17]', '[1892, 946, -7*w^2 + 8*w + 47]', '[1892, 946, 3*w^2 + w - 8]', '[1892, 946, 17*w^2 - 11*w - 140]', '[1892, 946, 5*w^2 - 10*w - 7]', '[1892, 946, 9*w^2 - 4*w - 73]', '[1892, 946, w^2 + w - 20]', '[1892, 1892, 5*w^2 - 16*w - 16]', '[1892, 1892, 6*w^2 - 7*w - 46]', '[1892, 1892, 3*w^2 + 8*w + 8]', '[1893, 1893, -8*w^2 + 2*w + 57]', '[1894, 1894, -13*w^2 + 34*w + 26]', '[1894, 1894, 5*w - 11]', '[1896, 474, 6*w^2 - 2*w - 54]', '[1896, 948, -3*w^2 - 7*w + 6]', '[1896, 948, 21*w^2 - 16*w - 183]', '[1896, 1896, 3*w^2 - 2*w]', '[1897, 1897, -13*w^2 + 11*w + 107]', '[1899, 633, -29*w^2 + 21*w + 243]', '[1899, 633, -2*w^2 + 27]', '[1899, 633, -11*w^2 + 9*w + 99]', '[1902, 1902, -2*w^2 + w - 3]', '[1902, 1902, -4*w^2 + 5*w + 9]', '[1902, 1902, -16*w^2 + 11*w + 132]', '[1902, 1902, -10*w^2 + 29*w + 24]', '[1902, 1902, 22*w^2 - 17*w - 192]', '[1902, 1902, -8*w^2 + 19*w + 15]', '[1904, 476, 16*w^2 - 14*w - 142]', '[1904, 476, w^2 - 10*w - 5]', '[1904, 476, 6*w^2 - 4*w - 44]', '[1904, 952, 5*w^2 - 11*w - 22]', '[1904, 1904, 11*w + 10]', '[1906, 1906, 4*w^2 + 5*w - 1]', '[1906, 1906, 6*w^2 - 23*w - 20]', '[1907, 1907, -7*w^2 + 15*w + 23]', '[1911, 273, 6*w^2 + 20*w + 15]', '[1911, 1911, 15*w^2 - 11*w - 123]', '[1913, 1913, 17*w^2 - 13*w - 149]', '[1916, 958, 15*w^2 - 12*w - 127]', '[1916, 958, 7*w^2 - 9*w - 44]', '[1916, 958, 19*w^2 - 51*w - 44]', '[1916, 958, 3*w^2 - 6*w - 1]', '[1916, 958, -5*w^2 + 9*w + 28]', '[1916, 958, -9*w^2 + 6*w + 71]', '[1916, 1916, 10*w^2 - 9*w - 82]', '[1916, 1916, -9*w - 10]', '[1916, 1916, -3*w^2 + 8]', '[1918, 1918, 3*w^2 - 10]', '[1918, 1918, -8*w^2 + 9*w + 55]', '[1921, 1921, -2*w^2 + 10*w - 13]', '[1922, 62, 4*w^2 + w - 28]', '[1922, 62, -18*w^2 + 11*w + 157]', '[1922, 1922, -5*w^2 - 2*w + 26]', '[1922, 1922, 18*w^2 - 13*w - 149]', '[1923, 1923, 22*w + 15]', '[1924, 962, 3*w^2 - 7*w - 40]', '[1924, 962, -23*w^2 + 16*w + 199]', '[1924, 1924, w^2 + 4*w - 8]', '[1926, 642, 5*w^2 - 6*w - 30]', '[1926, 642, 10*w^2 - 9*w - 87]', '[1928, 482, 2*w^2 - 2*w - 26]', '[1928, 482, 2*w^2 + 2*w - 22]', '[1928, 482, 8*w + 2]', '[1928, 964, -3*w^2 + 11*w + 2]', '[1928, 964, 9*w^2 - 8*w - 83]', '[1928, 964, w^2 - 8*w + 13]', '[1928, 964, 11*w^2 - 4*w - 85]', '[1928, 964, -7*w^2 + 19*w + 10]', '[1928, 964, -11*w^2 + 25*w + 22]', '[1928, 1928, -8*w^2 + 5*w + 62]', '[1928, 1928, -45*w^2 + 32*w + 380]', '[1928, 1928, -47*w^2 + 34*w + 400]', '[1931, 1931, 3*w^2 - 5*w - 1]', '[1933, 1933, -8*w - 11]', '[1934, 1934, 2*w^2 + 3*w - 13]', '[1934, 1934, -4*w^2 + 9*w + 4]', '[1936, 44, 23*w^2 - 18*w - 191]', '[1936, 44, -4*w^2 + 6*w + 16]', '[1936, 44, -4*w^2 + 6*w + 38]', '[1936, 88, 5*w^2 + 9*w + 2]', '[1936, 176, 19*w^2 - 12*w - 164]', '[1936, 484, 10*w^2 - 24*w - 20]', '[1936, 484, -w^2 + 6*w + 25]', '[1936, 484, -6*w + 2]', '[1936, 968, 13*w^2 - 9*w - 106]', '[1936, 1936, 6*w^2 - 9*w - 38]', '[1937, 1937, -7*w^2 + 5*w + 53]', '[1937, 1937, 2*w^2 + 2*w - 19]', '[1937, 1937, -3*w^2 - 5*w - 5]', '[1939, 1939, w^2 - w + 7]', '[1942, 1942, 12*w^2 - 11*w - 107]', '[1942, 1942, 5*w^2 - 4*w - 34]', '[1944, 18, 6*w^2 - 18*w - 18]', '[1944, 36, -15*w^2 + 9*w + 126]', '[1944, 36, 3*w^2 - 9]', '[1944, 72, -3*w^2 + 36]', '[1946, 1946, -2*w^2 - 5*w + 7]', '[1946, 1946, 32*w^2 - 23*w - 275]', '[1946, 1946, -6*w^2 + 7*w + 55]', '[1946, 1946, 4*w^2 - 7*w - 4]', '[1946, 1946, 9*w^2 - 4*w - 82]', '[1946, 1946, -4*w^2 + 5*w + 20]', '[1947, 1947, w^2 - 7*w - 21]', '[1948, 974, 11*w^2 - 37*w - 32]', '[1948, 974, 5*w^2 + 4*w - 1]', '[1948, 1948, -3*w^2 - 2*w + 20]', '[1949, 1949, 5*w^2 - 11*w - 7]', '[1949, 1949, 4*w^2 + 4*w - 19]', '[1949, 1949, 3*w^2 + w - 31]', '[1951, 1951, -11*w^2 + 29*w + 29]', '[1952, 244, 2*w^2 - 6*w - 16]', '[1952, 244, 6*w^2 - 38]', '[1952, 488, 8*w^2 - 18*w - 20]', '[1952, 488, 7*w^2 - 6*w - 7]', '[1952, 976, -21*w^2 + 15*w + 182]', '[1952, 1952, -5*w^2 + 52]', '[1953, 651, -4*w^2 + 39]', '[1954, 1954, w^2 - 18*w - 14]', '[1954, 1954, 6*w^2 + 15*w + 5]', '[1958, 1958, 4*w^2 - w - 5]', '[1958, 1958, -14*w^2 + 13*w + 128]', '[1959, 1959, -8*w^2 - 20*w - 9]', '[1959, 1959, 11*w^2 - 7*w - 99]', '[1959, 1959, 5*w^2 - 7*w - 27]', '[1962, 654, -8*w^2 + 9*w + 75]', '[1962, 654, -4*w^2 + 3*w + 24]', '[1963, 1963, 13*w^2 - 9*w - 115]', '[1964, 982, -19*w^2 + 47*w + 44]', '[1964, 982, -3*w^2 + 10*w + 13]', '[1964, 1964, 8*w^2 - 5*w - 74]', '[1966, 1966, 14*w^2 - 11*w - 124]', '[1966, 1966, 3*w^2 - 16*w - 14]', '[1966, 1966, -2*w^2 - 13*w - 11]', '[1966, 1966, -6*w^2 + 11*w + 13]', '[1966, 1966, 4*w^2 + 7*w - 1]', '[1966, 1966, 7*w^2 - 8*w - 10]', '[1967, 1967, 3*w^2 + w - 25]', '[1968, 492, -2*w^2 + 8*w + 12]', '[1968, 492, 13*w^2 - 10*w - 105]', '[1968, 492, -4*w^2 - 2*w + 18]', '[1968, 984, -13*w^2 + 31*w + 30]', '[1968, 1968, 10*w^2 - 7*w - 90]', '[1969, 1969, -2*w^2 - 14*w - 11]', '[1973, 1973, w^2 + 11*w + 5]', '[1973, 1973, -6*w^2 + 16*w + 19]', '[1973, 1973, 25*w^2 - 17*w - 209]', '[1977, 1977, -6*w^2 + 2*w + 51]', '[1979, 1979, 23*w^2 - 15*w - 191]', '[1982, 1982, 5*w - 7]', '[1982, 1982, -11*w^2 + 28*w + 22]', '[1983, 1983, 2*w^2 + 2*w - 21]', '[1984, 124, -8*w^2 + 8*w + 76]', '[1984, 248, 6*w^2 - 8*w - 10]', '[1984, 248, -w^2 - 10*w - 11]', '[1984, 248, -2*w^2 - 2*w + 20]', '[1984, 496, 6*w^2 - 16*w - 8]', '[1984, 992, -5*w^2 + w + 2]', '[1984, 1984, -9*w^2 + 2*w + 64]', '[1987, 1987, -3*w^2 - 7*w - 7]', '[1987, 1987, 2*w^2 + 2*w - 31]', '[1987, 1987, w^2 - w - 19]', '[1989, 663, -2*w^2 - 6*w - 9]', '[1991, 1991, w^2 + 5*w - 25]', '[1992, 498, -6*w^2 + 2*w + 42]', '[1992, 996, -9*w^2 + 16*w + 15]', '[1992, 996, -3*w^2 + 7*w + 18]', '[1992, 1992, -3*w^2 - 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w - 1]', '[79, 79, -2*w^2 + 4*w + 7]', '[83, 83, 2*w - 1]', '[89, 89, 5*w^2 - 3*w - 43]', '[103, 103, -2*w + 5]', '[107, 107, -w^2 - 3*w + 1]', '[109, 109, w^2 - 3*w + 1]', '[113, 113, -2*w^2 + 8*w + 7]', '[121, 11, -7*w^2 + 5*w + 61]', '[125, 5, -5]', '[127, 127, 18*w^2 - 12*w - 151]', '[131, 131, w^2 + w - 13]', '[137, 137, 4*w^2 - 4*w - 31]', '[139, 139, -2*w - 7]', '[139, 139, 4*w^2 - 2*w - 31]', '[139, 139, -19*w^2 + 13*w + 161]', '[149, 149, w^2 + w - 7]', '[149, 149, w^2 - 7*w - 5]', '[149, 149, 6*w^2 - 4*w - 53]', '[151, 151, w^2 - 5*w - 5]', '[157, 157, 20*w^2 - 14*w - 169]', '[169, 13, 4*w^2 - 2*w - 35]', '[179, 179, w^2 - 3*w - 13]', '[181, 181, 4*w^2 - 12*w - 11]', '[193, 193, -3*w^2 + 7*w + 11]', '[193, 193, 2*w^2 - 4*w - 23]', '[193, 193, -w^2 + w - 1]', '[197, 197, 3*w^2 - 3*w - 29]', '[197, 197, -2*w^2 + 6*w + 7]', '[197, 197, w^2 - 3*w - 7]', '[199, 199, 26*w^2 - 18*w - 221]', '[211, 211, -4*w - 5]', '[211, 211, 9*w^2 - 7*w - 77]', '[211, 211, 3*w^2 - 7*w - 5]', '[223, 223, 11*w^2 - 7*w - 91]', '[227, 227, 3*w^2 - w - 25]', '[229, 229, 2*w^2 - 4*w - 11]', '[233, 233, 2*w^2 + 6*w + 5]', '[241, 241, w^2 - w - 13]', '[241, 241, w^2 + w - 11]', '[241, 241, 4*w + 1]', '[251, 251, 2*w^2 - 11]', '[257, 257, 4*w^2 - 8*w - 7]', '[263, 263, 5*w^2 - 5*w - 47]', '[263, 263, 5*w^2 - 11*w - 11]', '[263, 263, 2*w^2 - 2*w - 11]', '[269, 269, 6*w^2 - 6*w - 55]', '[269, 269, 8*w^2 - 18*w - 17]', '[269, 269, -2*w^2 + 19]', '[271, 271, 2*w^2 - 17]', '[277, 277, 2*w^2 + 2*w - 1]', '[281, 281, 4*w + 7]', '[289, 17, 10*w^2 - 6*w - 83]', '[317, 317, 2*w^2 + 10*w + 7]', '[317, 317, 22*w^2 - 16*w - 187]', '[317, 317, 4*w^2 - 10*w - 7]', '[347, 347, 2*w^2 - 2*w - 1]', '[349, 349, 4*w^2 - 16*w - 13]', '[353, 353, 2*w^2 - 2*w - 5]', '[367, 367, 23*w^2 - 17*w - 197]', '[373, 373, w^2 - 5*w - 1]', '[397, 397, -6*w^2 + 12*w + 11]', '[401, 401, 2*w^2 + 2*w - 5]', '[419, 419, -3*w^2 - 5*w - 1]', '[421, 421, 14*w^2 - 10*w - 121]', '[439, 439, 3*w^2 - w - 31]', '[443, 443, 2*w^2 - 4*w - 13]', '[449, 449, 29*w^2 - 21*w - 247]', '[457, 457, 2*w^2 - 4*w - 25]', '[457, 457, 9*w^2 - 7*w - 73]', '[457, 457, 7*w^2 - 13*w - 13]', '[461, 461, 6*w^2 - 14*w - 17]', '[461, 461, 2*w^2 - 8*w - 5]', '[461, 461, 15*w^2 - 11*w - 125]', '[463, 463, -3*w^2 + 5*w + 7]', '[467, 467, 3*w^2 + 3*w - 11]', '[479, 479, -w^2 + 5*w - 1]', '[479, 479, 5*w^2 - w - 37]', '[479, 479, 2*w^2 - 4*w - 1]', '[487, 487, 3*w^2 - 3*w - 19]', '[491, 491, 5*w^2 - w - 35]', '[521, 521, -w^2 - 9*w - 7]', '[541, 541, 2*w^2 - 6*w + 1]', '[557, 557, 47*w^2 - 33*w - 401]', '[557, 557, 2*w^2 - 5]', '[557, 557, -13*w^2 + 9*w + 113]', '[563, 563, 10*w^2 - 8*w - 85]', '[569, 569, 4*w^2 - 2*w - 29]', '[587, 587, -3*w^2 + 7*w + 13]', '[593, 593, w^2 - 3*w - 17]', '[607, 607, 8*w^2 - 4*w - 65]', '[613, 613, 6*w^2 - 6*w - 47]', '[617, 617, -8*w - 7]', '[619, 619, 5*w^2 - 5*w - 41]', '[619, 619, 3*w^2 - w - 19]', '[619, 619, 36*w^2 - 26*w - 305]', '[631, 631, w^2 + 3*w - 5]', '[641, 641, -w^2 - w + 17]', '[653, 653, 5*w^2 - 5*w - 43]', '[653, 653, -3*w^2 - 7*w - 5]', '[653, 653, -4*w^2 + 8*w + 19]', '[659, 659, 3*w^2 - 5*w - 11]', '[661, 661, -5*w^2 + 11*w + 13]', '[683, 683, 5*w^2 - 3*w - 47]', '[701, 701, 11*w^2 - 9*w - 91]', '[701, 701, 6*w + 17]', '[701, 701, 7*w^2 - 21*w - 19]', '[709, 709, w^2 - 7*w + 11]', '[719, 719, -23*w^2 + 15*w + 193]', '[719, 719, -5*w^2 + 9*w + 23]', '[719, 719, 10*w^2 - 6*w - 85]', '[727, 727, -6*w^2 + 4*w + 55]', '[733, 733, -4*w^2 + 8*w + 13]', '[739, 739, 3*w^2 - 3*w - 31]', '[739, 739, 16*w^2 - 12*w - 139]', '[739, 739, 9*w^2 - 9*w - 67]', '[751, 751, 2*w^2 - 4*w - 17]', '[757, 757, 3*w^2 + 3*w - 1]', '[761, 761, -3*w^2 + 5*w + 31]', '[809, 809, 3*w^2 - 3*w - 17]', '[823, 823, -6*w^2 + 16*w + 17]', '[827, 827, -9*w^2 + 27*w + 23]', '[829, 829, -3*w^2 + 9*w + 11]', '[853, 853, 6*w^2 - 2*w - 47]', '[857, 857, 10*w^2 - 8*w - 89]', '[877, 877, -3*w^2 - w + 37]', '[881, 881, -w^2 + 3*w - 5]', '[883, 883, -w^2 - 3*w - 7]', '[883, 883, -2*w^2 - 6*w - 7]', '[883, 883, 4*w^2 - 29]', '[887, 887, -4*w^2 + 14*w + 13]', '[887, 887, 8*w^2 - 8*w - 73]', '[887, 887, 2*w - 11]', '[919, 919, -6*w^2 + 6*w + 53]', '[929, 929, -7*w^2 + 19*w + 19]', '[937, 937, 7*w^2 - 15*w - 25]', '[937, 937, 2*w^2 - 25]', '[937, 937, 2*w^2 - 6*w - 11]', '[947, 947, 8*w^2 - 8*w - 59]', '[953, 953, w^2 + 3*w - 7]', '[961, 31, 6*w^2 - 14*w - 11]', '[967, 967, 7*w^2 - 5*w - 55]', '[971, 971, 42*w^2 - 30*w - 359]', '[977, 977, 2*w^2 + 4*w - 7]', '[983, 983, 2*w^2 - 8*w + 1]', '[983, 983, 2*w^2 + 2*w - 13]', '[983, 983, -2*w - 11]', '[991, 991, 6*w^2 - 6*w - 43]', '[997, 997, w^2 - 5*w - 11]']}
• 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': [-6, -9, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1944, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[3, 1]]], [7, [[2, 1], [1, 1]]], [11, [[2, 1], [1, 1]]], [13, [[2, 1], [1, 1]]], [17, [[2, 1], [1, 1]]], [19, [[3, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [[2, 1], [1, 1]]], [37, [[2, 1], [1, 1]]], [41, [[2, 1], [1, 1]]], [43, [[1, 3]]], [47, [[3, 1]]], [53, [[3, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [9, 11], 'galois_label': '3T2', 'galt': 2, 'grd': 21.196653174008656, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1944.1', 'local_algs': ['2.1.0.1', '2.2.3.4', '3.3.5.3'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 3], 'rd': 12.4805029383, 'regulator': {'__RealLiteral__': 0, 'data': '15.6005131144', 'prec': 44}, 'res': {'gal': ['-6,36,27,-24,-18,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 3 a - 1 \\)', '\\( 2 a^{2} - 1 \\)'], 'unitsGmodule': [[4, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}