Hilbert modular form data - 3.3.81.1-8.1-a

Formats: - HTML - YAML - JSON - 2025-06-18T14:38:58.909427

• 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': 81, 'field_bad_primes': [3], 'field_label': '3.3.81.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '3.3.81.1-8.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2], 'level_ideal': '[8, 2, 2]', 'level_label': '8.1', 'level_norm': 8, 'parallel_weight': 2, 'short_label': '8.1-a', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[8, 2, 2]', -1]], 'hecke_eigenvalues': [-3, 1, -3, -3, -3, -1, -1, -1, -4, -4, -4, 12, 12, 12, -12, -12, -12, 11, 11, 11, 6, 6, 6, 3, 3, 3, -16, -16, -16, 0, 2, 2, 2, -4, -4, -4, 12, 12, 12, 14, 14, 14, -12, -12, -12, -10, -10, -10, 3, 3, 3, 21, 21, 21, -24, -24, -24, 20, 20, 20, -7, -7, -7, -34, -18, -18, -18, 23, 23, 23, 20, 20, 20, -30, -30, -30, -7, -7, -7, 9, 9, 9, -15, -15, -15, 26, 26, 26, 0, 0, 0, -3, -3, -3, 20, 20, 20, -4, -4, -4, -30, -30, -30, 11, 11, 11, 6, 6, 6, -16, -16, -16, -40, -40, -40, 18, 18, 18, -9, -9, -9, 30, 30, 30, -36, -36, -36, 47, 47, 47, 2, 2, 2, 18, 18, 18, 33, 33, 33, -7, -7, -7, -12, -12, -12, -10, -10, -10, 24, 24, 24, -42, -42, -42, -19, -19, -19, 38, 38, 38, 14, 14, 14, 9, 9, 9, -36, -36, -36, -16, -16, -16], 'hecke_polynomial': 'x', 'label': '3.3.81.1-8.1-a'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 81, 'ideals': ['[1, 1, 1]', '[3, 3, -w + 1]', '[8, 2, 2]', '[9, 3, -w^2 - w + 2]', '[17, 17, -2*w^2 + w + 3]', '[17, 17, -w^2 - w + 3]', '[17, 17, -w^2 + 2*w + 3]', '[19, 19, -2*w^2 + 2*w + 5]', '[19, 19, -2*w^2 + 3]', '[19, 19, -2*w + 1]', '[24, 6, -2*w + 2]', '[27, 3, 3]', '[37, 37, -w^2 + 3*w + 3]', '[37, 37, 2*w^2 + w - 5]', '[37, 37, 3*w^2 - 2*w - 5]', '[51, 51, -3*w^2 + 2*w + 4]', '[51, 51, -2*w^2 - w + 6]', '[51, 51, -w^2 + 3*w + 4]', '[53, 53, -w - 4]', '[53, 53, -w^2 + w - 2]', '[53, 53, w^2 - 6]', '[57, 57, -2*w^2 + 3*w + 5]', '[57, 57, -w^2 - 2*w + 3]', '[57, 57, -3*w^2 + w + 5]', '[64, 4, 4]', '[71, 71, w^2 + w - 7]', '[71, 71, w^2 - 2*w - 7]', '[71, 71, -2*w^2 + w - 1]', '[72, 6, -2*w^2 - 2*w + 4]', '[73, 73, 3*w^2 - 3*w - 8]', '[73, 73, 2*w^2 - 3*w - 7]', '[73, 73, w^2 + 2*w - 5]', '[81, 9, -3*w + 3]', '[89, 89, -w^2 + 4*w + 4]', '[89, 89, 3*w^2 + w - 8]', '[89, 89, 2*w^2 - w - 9]', '[107, 107, 2*w^2 - 4*w - 5]', '[107, 107, 4*w^2 - 2*w - 7]', '[107, 107, 2*w^2 + 2*w - 5]', '[109, 109, w^2 - w - 7]', '[109, 109, -w^2 - 3]', '[109, 109, w - 5]', '[111, 111, -4*w^2 + 3*w + 4]', '[111, 111, 5*w^2 - 6*w - 8]', '[111, 111, w^2 - 7]', '[125, 5, -5]', '[127, 127, -5*w^2 + 4*w + 8]', '[127, 127, 4*w^2 + w - 10]', '[127, 127, -w^2 + 5*w + 4]', '[136, 34, -4*w^2 + 2*w + 6]', '[136, 34, -2*w^2 - 2*w + 6]', '[136, 34, -2*w^2 + 4*w + 6]', '[152, 38, -4*w^2 + 4*w + 10]', '[152, 38, -4*w^2 + 6]', '[152, 38, -4*w + 2]', '[153, 51, -2*w^2 + 4*w + 7]', '[153, 51, -4*w^2 + 2*w + 5]', '[153, 51, -2*w^2 - 2*w + 7]', '[159, 159, -2*w^2 + 6*w - 1]', '[159, 159, w^2 + 3*w - 7]', '[159, 159, w^2 + 3*w - 4]', '[163, 163, 5*w^2 - 2*w - 10]', '[163, 163, 5*w^2 - 3*w - 9]', '[163, 163, 3*w^2 + 2*w - 7]', '[171, 57, w^2 - 2*w + 4]', '[171, 57, -2*w^2 + w + 10]', '[171, 57, w^2 + w + 4]', '[179, 179, 3*w^2 - 4*w - 9]', '[179, 179, 4*w^2 - w - 5]', '[179, 179, w^2 + 3*w - 5]', '[181, 181, w^2 + 3*w - 6]', '[181, 181, 4*w^2 - 4*w - 11]', '[181, 181, 3*w^2 - 4*w - 10]', '[192, 12, -4*w + 4]', '[197, 197, w^2 - w - 8]', '[197, 197, -w^2 - 4]', '[197, 197, w - 6]', '[199, 199, -w - 6]', '[199, 199, -w^2 + w - 4]', '[199, 199, w^2 - 8]', '[213, 213, 5*w - 8]', '[213, 213, 3*w^2 + 2*w - 8]', '[213, 213, -3*w^2 + 8*w + 1]', '[216, 6, 6]', '[219, 219, -w^2 + 4*w - 6]', '[219, 219, 6*w^2 - 4*w - 11]', '[219, 219, 5*w^2 - 2*w - 9]', '[233, 233, 5*w^2 + w - 13]', '[233, 233, -6*w^2 + 5*w + 9]', '[233, 233, -w^2 + 6*w + 5]', '[243, 9, -3*w^2 - 3*w + 6]', '[251, 251, 3*w^2 + 2*w - 9]', '[251, 251, 2*w^2 - 2*w - 11]', '[251, 251, 2*w^2 - 5*w - 7]', '[267, 267, 2*w^2 - 11]', '[267, 267, 3*w^2 + 2*w - 11]', '[267, 267, -5*w^2 + 3*w + 5]', '[269, 269, -5*w^2 + 2*w + 8]', '[269, 269, 3*w^2 - 5*w - 8]', '[269, 269, 2*w^2 + 3*w - 6]', '[271, 271, w^2 + w - 9]', '[271, 271, 6*w^2 - 5*w - 15]', '[271, 271, 3*w^2 + 2*w - 10]', '[289, 17, -4*w^2 + 5*w + 10]', '[289, 17, -5*w^2 + w + 8]', '[289, 17, -w^2 - 4*w + 4]', '[289, 289, w^2 - 2*w + 5]', '[289, 289, w^2 + w + 5]', '[289, 289, -2*w^2 + w + 11]', '[296, 74, -2*w^2 + 6*w + 6]', '[296, 74, 4*w^2 + 2*w - 10]', '[296, 74, 6*w^2 - 4*w - 10]', '[307, 307, 3*w^2 - 5*w - 9]', '[307, 307, 5*w^2 - 2*w - 7]', '[307, 307, 2*w^2 + 3*w - 7]', '[321, 321, 6*w^2 - 5*w - 7]', '[321, 321, 6*w^2 - 7*w - 11]', '[321, 321, w - 7]', '[323, 323, w + 7]', '[323, 323, -5*w^2 + 7]', '[323, 323, w^2 - w + 5]', '[323, 323, -5*w + 3]', '[323, 323, -3*w^2 + 6*w + 7]', '[323, 323, -5*w^2 + 5*w + 13]', '[323, 323, -6*w^2 + 3*w + 11]', '[323, 323, -w^2 + 9]', '[323, 323, -3*w^2 - 3*w + 7]', '[327, 327, 2*w^2 + 3*w - 8]', '[327, 327, -w^2 + 6*w - 5]', '[327, 327, -w^2 + 6*w - 2]', '[333, 111, -5*w^2 - 2*w + 4]', '[333, 111, 2*w^2 - 4*w - 13]', '[333, 111, 4*w^2 - 5*w - 11]', '[343, 7, -7]', '[359, 359, -w^2 + 6*w - 3]', '[359, 359, 6*w^2 - 5*w - 17]', '[359, 359, 5*w^2 - 5*w - 16]', '[361, 19, -4*w^2 - 2*w + 11]', '[361, 19, -2*w^2 + 6*w + 7]', '[361, 19, -6*w^2 + 4*w + 9]', '[361, 361, -5*w^2 + 6]', '[361, 361, -5*w^2 + 5*w + 14]', '[361, 361, -5*w + 4]', '[375, 15, 5*w - 5]', '[379, 379, -2*w^2 + 7*w + 6]', '[379, 379, 7*w^2 - 5*w - 12]', '[379, 379, 5*w^2 + 2*w - 12]', '[381, 381, -6*w^2 + 4*w + 5]', '[381, 381, -9*w^2 + 11*w + 13]', '[381, 381, 3*w^2 - w - 14]', '[397, 397, 8*w^2 - 5*w - 16]', '[397, 397, 6*w^2 - 3*w - 10]', '[397, 397, 3*w^2 - 6*w - 8]', '[408, 102, -6*w^2 + 4*w + 8]', '[408, 102, -4*w^2 - 2*w + 12]', '[408, 102, -2*w^2 + 6*w + 8]', '[424, 106, -2*w - 8]', '[424, 106, -2*w^2 + 2*w - 4]', '[424, 106, 2*w^2 - 12]', '[431, 431, -w^2 + 7*w - 1]', '[431, 431, -6*w^2 + 4*w + 7]', '[431, 431, 4*w^2 + 2*w - 13]', '[433, 433, -4*w^2 - 4*w + 7]', '[433, 433, 7*w^2 - 4*w - 13]', '[433, 433, 8*w^2 - 4*w - 17]', '[449, 449, 7*w^2 - w - 14]', '[449, 449, 6*w^2 - 7*w - 12]', '[449, 449, 2*w^2 - w - 12]', '[456, 114, -4*w^2 + 6*w + 10]', '[456, 114, -2*w^2 - 4*w + 6]', '[456, 114, -6*w^2 + 2*w + 10]', '[459, 51, -6*w^2 + 3*w + 9]', '[459, 51, -3*w^2 - 3*w + 9]', '[459, 51, -3*w^2 + 6*w + 9]', '[467, 467, w^2 + 5*w - 4]', '[467, 467, 6*w^2 - w - 10]', '[467, 467, 5*w^2 - 6*w - 12]', '[477, 159, 5*w^2 + 5*w - 7]', '[477, 159, 2*w^2 + 5*w - 4]', '[477, 159, 5*w^2 + 2*w - 13]', '[487, 487, w^2 - w - 10]', '[487, 487, -w^2 - 6]', '[487, 487, w - 8]', '[489, 489, 7*w^2 - 7*w - 15]', '[489, 489, 8*w^2 - 9*w - 14]', '[489, 489, w^2 - 10]', '[503, 503, w^2 + 2*w - 11]', '[503, 503, 2*w^2 - 3*w - 13]', '[503, 503, -3*w^2 + w - 3]', '[512, 8, 8]', '[513, 57, -6*w^2 + 6*w + 15]', '[513, 57, -6*w^2 + 9]', '[513, 57, -6*w + 3]', '[521, 521, 5*w^2 - 6*w - 18]', '[521, 521, 3*w^2 - 4*w - 16]', '[521, 521, w^2 + 3*w - 12]', '[523, 523, 7*w^2 - 6*w - 18]', '[523, 523, 3*w^2 + 3*w - 11]', '[523, 523, 2*w^2 + w - 13]', '[537, 537, 7*w^2 - 4*w - 12]', '[537, 537, 5*w^2 - 8*w - 9]', '[537, 537, -2*w^2 + 5*w - 6]', '[541, 541, 2*w^2 + 4*w - 11]', '[541, 541, 6*w^2 - 2*w - 5]', '[541, 541, 4*w^2 - 6*w - 15]', '[543, 543, -2*w^2 + 6*w - 7]', '[543, 543, 8*w^2 - 5*w - 15]', '[543, 543, 7*w^2 - 3*w - 13]', '[557, 557, 8*w^2 - 2*w - 17]', '[557, 557, -6*w^2 + 8*w + 11]', '[557, 557, 3*w^2 - 2*w - 15]', '[568, 142, 2*w^2 + 2*w - 14]', '[568, 142, 2*w^2 - 4*w - 14]', '[568, 142, -4*w^2 + 2*w - 2]', '[576, 12, -4*w^2 - 4*w + 8]', '[577, 577, -6*w^2 + 7*w + 13]', '[577, 577, 7*w^2 - w - 13]', '[577, 577, 3*w^2 - w - 15]', '[584, 146, 6*w^2 - 6*w - 16]', '[584, 146, 4*w^2 - 6*w - 14]', '[584, 146, 2*w^2 + 4*w - 10]', '[591, 591, -w^2 + 7*w - 6]', '[591, 591, 2*w^2 + 4*w - 9]', '[591, 591, -w^2 + 7*w - 3]', '[593, 593, 8*w^2 - 6*w - 13]', '[593, 593, -2*w^2 + 8*w + 7]', '[593, 593, 6*w^2 + 2*w - 15]', '[597, 597, -2*w^2 + 8*w - 3]', '[597, 597, w^2 + 5*w - 6]', '[597, 597, w^2 + 5*w - 9]', '[613, 613, 2*w^2 - 7*w - 9]', '[613, 613, 5*w^2 + 2*w - 15]', '[613, 613, -7*w^2 + 5*w + 9]', '[629, 629, 3*w^2 + w + 4]', '[629, 629, 5*w^2 - 6*w - 15]', '[629, 629, -w^2 + 4*w - 8]', '[629, 629, 4*w^2 - 3*w - 18]', '[629, 629, 7*w^2 - 7*w - 16]', '[629, 629, -7*w + 2]', '[629, 629, 7*w^2 - 12]', '[629, 629, -6*w^2 + w + 7]', '[629, 629, w^2 + 5*w - 7]', '[631, 631, w^2 + 5*w - 8]', '[631, 631, 6*w^2 - 6*w - 17]', '[631, 631, 5*w^2 - 6*w - 16]', '[639, 213, 5*w^2 + 2*w - 16]', '[639, 213, 8*w^2 + 5*w - 13]', '[639, 213, 2*w^2 + 8*w - 1]', '[647, 647, 6*w^2 + 3*w - 13]', '[647, 647, -3*w^2 + 9*w + 7]', '[647, 647, 9*w^2 - 6*w - 17]', '[648, 18, -6*w + 6]', '[657, 219, 8*w^2 - w - 16]', '[657, 219, 8*w^2 + 2*w - 13]', '[657, 219, 2*w^2 - w - 13]', '[683, 683, 5*w^2 + 3*w - 12]', '[683, 683, 8*w^2 - 5*w - 14]', '[683, 683, 8*w^2 - 3*w - 16]', '[699, 699, 4*w^2 - w - 18]', '[699, 699, -11*w^2 + 14*w + 15]', '[699, 699, -7*w^2 + 4*w + 6]', '[701, 701, w^2 - w - 11]', '[701, 701, -w^2 - 7]', '[701, 701, w - 9]', '[703, 703, -w - 9]', '[703, 703, 3*w^2 + 4*w - 15]', '[703, 703, w^2 - w + 7]', '[703, 703, 4*w^2 - 7*w - 17]', '[703, 703, 10*w^2 - 3*w - 23]', '[703, 703, 7*w^2 - 10*w - 11]', '[703, 703, -7*w^2 + 3*w + 5]', '[703, 703, w^2 - 11]', '[703, 703, -3*w^2 - 7*w + 3]', '[712, 178, -2*w^2 + 8*w + 8]', '[712, 178, 6*w^2 + 2*w - 16]', '[712, 178, 4*w^2 - 2*w - 18]', '[719, 719, 9*w^2 - 4*w - 19]', '[719, 719, 8*w^2 - 4*w - 15]', '[719, 719, 9*w^2 - 5*w - 18]', '[729, 9, 9]', '[739, 739, 7*w^2 + 3*w - 15]', '[739, 739, -3*w^2 + 10*w + 7]', '[739, 739, 10*w^2 - 7*w - 19]', '[753, 753, w^2 + 2*w - 12]', '[753, 753, 7*w^2 - 4*w - 9]', '[753, 753, 4*w^2 + 3*w - 13]', '[757, 757, 3*w^2 - 16]', '[757, 757, -7*w^2 + 4*w + 7]', '[757, 757, 4*w^2 + 3*w - 15]', '[773, 773, 4*w^2 + 3*w - 14]', '[773, 773, 2*w^2 + w - 14]', '[773, 773, 8*w^2 - 7*w - 20]', '[801, 267, -7*w^2 - 4*w + 5]', '[801, 267, 4*w^2 - 5*w - 20]', '[801, 267, 8*w^2 + 2*w - 19]', '[807, 807, 7*w^2 - 9*w - 13]', '[807, 807, 8*w^2 - 6*w - 11]', '[807, 807, -w^2 + 3*w - 8]', '[809, 809, 3*w^2 + 4*w - 14]', '[809, 809, 7*w^2 - 3*w - 6]', '[809, 809, 4*w^2 - 7*w - 16]', '[811, 811, 9*w^2 - 3*w - 19]', '[811, 811, -6*w^2 + 9*w + 11]', '[811, 811, 5*w^2 - 3*w - 21]', '[813, 813, 11*w^2 - 8*w - 21]', '[813, 813, 7*w - 10]', '[813, 813, w^2 + 3*w - 13]', '[827, 827, -7*w^2 + 8*w + 15]', '[827, 827, 8*w^2 - w - 15]', '[827, 827, 3*w^2 - w - 16]', '[829, 829, 6*w^2 + 3*w - 14]', '[829, 829, -3*w^2 + 9*w + 8]', '[829, 829, 9*w^2 - 6*w - 16]', '[856, 214, 4*w^2 - 8*w - 10]', '[856, 214, 8*w^2 - 4*w - 14]', '[856, 214, 4*w^2 + 4*w - 10]', '[863, 863, 2*w^2 - 4*w - 15]', '[863, 863, -4*w^2 + 2*w - 3]', '[863, 863, 2*w^2 + 2*w - 15]', '[867, 51, -8*w^2 + 2*w + 15]', '[867, 51, -2*w^2 - 6*w + 5]', '[867, 51, -6*w^2 + 8*w + 13]', '[867, 867, -7*w + 4]', '[867, 867, -7*w^2 + 7*w + 18]', '[867, 867, -7*w^2 + 10]', '[872, 218, 2*w^2 - 2*w - 14]', '[872, 218, -2*w^2 - 6]', '[872, 218, 2*w - 10]', '[881, 881, 2*w^2 + 5*w - 8]', '[881, 881, 5*w^2 - 7*w - 14]', '[881, 881, 7*w^2 - 2*w - 10]', '[883, 883, -4*w^2 + 3*w - 3]', '[883, 883, 3*w^2 + w - 17]', '[883, 883, 8*w^2 - 7*w - 21]', '[888, 222, -8*w^2 + 6*w + 8]', '[888, 222, 10*w^2 - 12*w - 16]', '[888, 222, 2*w^2 - 14]', '[901, 901, 4*w^2 - 9*w - 9]', '[901, 901, 9*w^2 - 5*w - 17]', '[901, 901, 2*w^2 - 8*w - 11]', '[901, 901, 8*w^2 - 6*w - 9]', '[901, 901, 6*w^2 + 2*w - 19]', '[901, 901, w^2 + 6*w - 6]', '[901, 901, 7*w^2 - w - 10]', '[901, 901, 5*w^2 + 4*w - 11]', '[901, 901, 6*w^2 - 7*w - 16]', '[919, 919, 9*w^2 - w - 18]', '[919, 919, -8*w^2 + 9*w + 16]', '[919, 919, w^2 + 8*w - 2]', '[921, 921, 8*w^2 - 5*w - 12]', '[921, 921, -w^2 + 4*w - 9]', '[921, 921, 7*w^2 - 10*w - 12]', '[937, 937, 5*w^2 - 7*w - 15]', '[937, 937, 2*w^2 + 5*w - 9]', '[937, 937, 7*w^2 - 2*w - 9]', '[953, 953, 2*w^2 + 5*w - 11]', '[953, 953, 7*w^2 - 7*w - 19]', '[953, 953, 5*w^2 - 7*w - 17]', '[963, 321, 7*w^2 + w - 8]', '[963, 321, 5*w^2 - 7*w - 16]', '[963, 321, w^2 - 5*w - 14]', '[969, 969, -5*w^2 + 8*w + 12]', '[969, 969, -6*w^2 + 7*w + 17]', '[969, 969, -w^2 + w + 12]', '[969, 969, -3*w^2 - 5*w + 8]', '[969, 969, -7*w^2 + w + 9]', '[969, 969, -w^2 - 6*w + 7]', '[969, 969, -8*w^2 + 3*w + 14]', '[969, 969, w^2 + 8]', '[969, 969, -w + 10]', '[971, 971, -w - 10]', '[971, 971, -w^2 + w - 8]', '[971, 971, w^2 - 12]', '[981, 327, 7*w^2 + 4*w - 14]', '[981, 327, 4*w^2 + 7*w - 5]', '[981, 327, 4*w^2 + 4*w - 11]', '[991, 991, 4*w^2 - w - 19]', '[991, 991, -7*w^2 + 8*w + 16]', '[991, 991, 8*w^2 - w - 14]', '[999, 111, -3*w^2 + 9*w + 9]', '[999, 111, 6*w^2 + 3*w - 15]', '[999, 111, 9*w^2 - 6*w - 15]', '[1000, 10, -10]', '[1007, 1007, 8*w^2 + 3*w - 10]', '[1007, 1007, 6*w^2 - 7*w - 18]', '[1007, 1007, -3*w^2 + 11*w]', '[1007, 1007, 9*w^2 - 2*w - 18]', '[1007, 1007, 11*w^2 - 8*w - 28]', '[1007, 1007, 2*w^2 + 7*w - 4]', '[1007, 1007, 7*w^2 - w - 8]', '[1007, 1007, w^2 + 6*w - 8]', '[1007, 1007, 7*w^2 - 9*w - 14]', '[1009, 1009, 8*w^2 - 7*w - 24]', '[1009, 1009, 7*w^2 - 7*w - 20]', '[1009, 1009, 6*w^2 - 7*w - 19]', '[1016, 254, -10*w^2 + 8*w + 16]', '[1016, 254, 8*w^2 + 2*w - 20]', '[1016, 254, -2*w^2 + 10*w + 8]', '[1029, 21, 7*w - 7]', '[1061, 1061, 5*w^2 + 3*w - 18]', '[1061, 1061, -8*w^2 + 5*w + 8]', '[1061, 1061, 3*w^2 - 17]', '[1063, 1063, w^2 + 2*w - 13]', '[1063, 1063, -8*w^2 + 5*w + 10]', '[1063, 1063, 5*w^2 + 3*w - 16]', '[1077, 1077, -7*w^2 + 12*w - 2]', '[1077, 1077, 11*w^2 - 6*w - 23]', '[1077, 1077, 10*w^2 - 4*w - 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16*w - 43]', '[9873, 3291, 7*w^2 - 17*w - 47]', '[9873, 3291, -16*w^2 - 7*w + 8]', '[9879, 9879, 23*w^2 - 26*w - 39]', '[9879, 9879, 22*w^2 - 16*w - 39]', '[9879, 9879, -19*w^2 + 16*w + 18]', '[9879, 9879, 4*w^2 - w - 30]', '[9879, 9879, -9*w^2 + 26*w + 1]', '[9879, 9879, 9*w^2 + 8*w - 26]', '[9879, 9879, 17*w - 26]', '[9879, 9879, -w^2 + 12*w - 26]', '[9879, 9879, 6*w^2 + 11*w - 35]', '[9883, 9883, 21*w^2 - 14*w - 38]', '[9883, 9883, 14*w^2 + 7*w - 32]', '[9883, 9883, -7*w^2 + 21*w + 18]', '[9899, 9899, 11*w^2 + 10*w - 22]', '[9899, 9899, -5*w^2 + 21*w - 14]', '[9899, 9899, 21*w^2 - 16*w - 66]', '[9899, 9899, 21*w^2 + 8*w - 42]', '[9899, 9899, 29*w^2 - 23*w - 64]', '[9899, 9899, 17*w^2 - 28]', '[9899, 9899, 23*w^2 + 6*w - 40]', '[9899, 9899, 19*w^2 - 10*w - 68]', '[9899, 9899, 21*w^2 - 11*w - 42]', '[9901, 9901, 3*w^2 + 6*w - 31]', '[9901, 9901, -9*w^2 + 3*w - 7]', '[9901, 9901, 6*w^2 - 9*w - 37]', '[9928, 2482, 2*w^2 - 8*w - 28]', '[9928, 2482, 6*w^2 + 2*w - 36]', '[9928, 2482, 10*w^2 + 8*w - 26]', '[9928, 2482, 22*w^2 - 8*w - 48]', '[9928, 2482, 18*w^2 - 10*w - 30]', '[9928, 2482, 20*w^2 - 2*w - 40]', '[9928, 2482, 18*w^2 - 20*w - 36]', '[9928, 2482, 4*w^2 - 2*w - 30]', '[9928, 2482, 8*w^2 + 8*w - 30]', '[9937, 9937, 13*w^2 - 15*w - 39]', '[9937, 9937, 26*w^2 - 19*w - 63]', '[9937, 9937, 17*w^2 - 2*w - 64]', '[9937, 9937, -3*w^2 + 7*w - 17]', '[9937, 9937, 20*w^2 - 7*w - 41]', '[9937, 9937, 25*w^2 - 13*w - 55]', '[9937, 9937, 15*w^2 + 4*w - 42]', '[9937, 9937, 15*w - 17]', '[9937, 9937, 19*w^2 - 12*w - 32]', '[9939, 9939, -7*w^2 + 24*w - 14]', '[9939, 9939, 11*w^2 + 6*w - 35]', '[9939, 9939, -4*w^2 + 21*w - 2]', '[9953, 9953, 17*w^2 - 15*w - 51]', '[9953, 9953, 7*w^2 - 7*w - 38]', '[9953, 9953, 18*w^2 - 2*w - 33]', '[9953, 9953, 15*w^2 - 15*w - 43]', '[9953, 9953, 10*w^2 + 7*w - 30]', '[9953, 9953, 7*w^2 - 17*w - 24]', '[9953, 9953, 13*w^2 - 15*w - 41]', '[9953, 9953, -16*w^2 + 18*w + 35]', '[9953, 9953, 7*w^2 - 2*w - 37]', '[9973, 9973, 13*w^2 - 16*w - 47]', '[9973, 9973, 3*w^2 + 13*w - 27]', '[9973, 9973, 16*w^2 - 3*w - 11]', '[9987, 9987, -w^2 + 16*w - 15]', '[9987, 9987, 2*w^2 + 13*w - 18]', '[9987, 9987, -w^2 + 16*w - 12]', '[9993, 9993, -2*w^2 + 17*w - 12]', '[9993, 9993, w^2 + 14*w - 15]', '[9993, 9993, w^2 + 14*w - 18]'], 'label': '3.3.81.1', 'narrow_class_no': 1, 'primes': ['[3, 3, -w + 1]', '[8, 2, 2]', '[17, 17, -2*w^2 + w + 3]', '[17, 17, -w^2 - w + 3]', '[17, 17, -w^2 + 2*w + 3]', '[19, 19, -2*w^2 + 2*w + 5]', '[19, 19, -2*w^2 + 3]', '[19, 19, -2*w + 1]', '[37, 37, -w^2 + 3*w + 3]', '[37, 37, 2*w^2 + w - 5]', '[37, 37, 3*w^2 - 2*w - 5]', '[53, 53, -w - 4]', '[53, 53, -w^2 + w - 2]', '[53, 53, w^2 - 6]', '[71, 71, w^2 + w - 7]', '[71, 71, w^2 - 2*w - 7]', '[71, 71, -2*w^2 + w - 1]', '[73, 73, 3*w^2 - 3*w - 8]', '[73, 73, 2*w^2 - 3*w - 7]', '[73, 73, w^2 + 2*w - 5]', '[89, 89, -w^2 + 4*w + 4]', '[89, 89, 3*w^2 + w - 8]', '[89, 89, 2*w^2 - w - 9]', '[107, 107, 2*w^2 - 4*w - 5]', '[107, 107, 4*w^2 - 2*w - 7]', '[107, 107, 2*w^2 + 2*w - 5]', '[109, 109, w^2 - w - 7]', '[109, 109, -w^2 - 3]', '[109, 109, w - 5]', '[125, 5, -5]', '[127, 127, -5*w^2 + 4*w + 8]', '[127, 127, 4*w^2 + w - 10]', '[127, 127, -w^2 + 5*w + 4]', '[163, 163, 5*w^2 - 2*w - 10]', '[163, 163, 5*w^2 - 3*w - 9]', '[163, 163, 3*w^2 + 2*w - 7]', '[179, 179, 3*w^2 - 4*w - 9]', '[179, 179, 4*w^2 - w - 5]', '[179, 179, w^2 + 3*w - 5]', '[181, 181, w^2 + 3*w - 6]', '[181, 181, 4*w^2 - 4*w - 11]', '[181, 181, 3*w^2 - 4*w - 10]', '[197, 197, w^2 - w - 8]', '[197, 197, -w^2 - 4]', '[197, 197, w - 6]', '[199, 199, -w - 6]', '[199, 199, -w^2 + w - 4]', '[199, 199, w^2 - 8]', '[233, 233, 5*w^2 + w - 13]', '[233, 233, -6*w^2 + 5*w + 9]', '[233, 233, -w^2 + 6*w + 5]', '[251, 251, 3*w^2 + 2*w - 9]', '[251, 251, 2*w^2 - 2*w - 11]', '[251, 251, 2*w^2 - 5*w - 7]', '[269, 269, -5*w^2 + 2*w + 8]', '[269, 269, 3*w^2 - 5*w - 8]', '[269, 269, 2*w^2 + 3*w - 6]', '[271, 271, w^2 + w - 9]', '[271, 271, 6*w^2 - 5*w - 15]', '[271, 271, 3*w^2 + 2*w - 10]', '[307, 307, 3*w^2 - 5*w - 9]', '[307, 307, 5*w^2 - 2*w - 7]', '[307, 307, 2*w^2 + 3*w - 7]', '[343, 7, -7]', '[359, 359, -w^2 + 6*w - 3]', '[359, 359, 6*w^2 - 5*w - 17]', '[359, 359, 5*w^2 - 5*w - 16]', '[379, 379, -2*w^2 + 7*w + 6]', '[379, 379, 7*w^2 - 5*w - 12]', '[379, 379, 5*w^2 + 2*w - 12]', '[397, 397, 8*w^2 - 5*w - 16]', '[397, 397, 6*w^2 - 3*w - 10]', '[397, 397, 3*w^2 - 6*w - 8]', '[431, 431, -w^2 + 7*w - 1]', '[431, 431, -6*w^2 + 4*w + 7]', '[431, 431, 4*w^2 + 2*w - 13]', '[433, 433, -4*w^2 - 4*w + 7]', '[433, 433, 7*w^2 - 4*w - 13]', '[433, 433, 8*w^2 - 4*w - 17]', '[449, 449, 7*w^2 - w - 14]', '[449, 449, 6*w^2 - 7*w - 12]', '[449, 449, 2*w^2 - w - 12]', '[467, 467, w^2 + 5*w - 4]', '[467, 467, 6*w^2 - w - 10]', '[467, 467, 5*w^2 - 6*w - 12]', '[487, 487, w^2 - w - 10]', '[487, 487, -w^2 - 6]', '[487, 487, w - 8]', '[503, 503, w^2 + 2*w - 11]', '[503, 503, 2*w^2 - 3*w - 13]', '[503, 503, -3*w^2 + w - 3]', '[521, 521, 5*w^2 - 6*w - 18]', '[521, 521, 3*w^2 - 4*w - 16]', '[521, 521, w^2 + 3*w - 12]', '[523, 523, 7*w^2 - 6*w - 18]', '[523, 523, 3*w^2 + 3*w - 11]', '[523, 523, 2*w^2 + w - 13]', '[541, 541, 2*w^2 + 4*w - 11]', '[541, 541, 6*w^2 - 2*w - 5]', '[541, 541, 4*w^2 - 6*w - 15]', '[557, 557, 8*w^2 - 2*w - 17]', '[557, 557, -6*w^2 + 8*w + 11]', '[557, 557, 3*w^2 - 2*w - 15]', '[577, 577, -6*w^2 + 7*w + 13]', '[577, 577, 7*w^2 - w - 13]', '[577, 577, 3*w^2 - w - 15]', '[593, 593, 8*w^2 - 6*w - 13]', '[593, 593, -2*w^2 + 8*w + 7]', '[593, 593, 6*w^2 + 2*w - 15]', '[613, 613, 2*w^2 - 7*w - 9]', '[613, 613, 5*w^2 + 2*w - 15]', '[613, 613, -7*w^2 + 5*w + 9]', '[631, 631, w^2 + 5*w - 8]', '[631, 631, 6*w^2 - 6*w - 17]', '[631, 631, 5*w^2 - 6*w - 16]', '[647, 647, 6*w^2 + 3*w - 13]', '[647, 647, -3*w^2 + 9*w + 7]', '[647, 647, 9*w^2 - 6*w - 17]', '[683, 683, 5*w^2 + 3*w - 12]', '[683, 683, 8*w^2 - 5*w - 14]', '[683, 683, 8*w^2 - 3*w - 16]', '[701, 701, w^2 - w - 11]', '[701, 701, -w^2 - 7]', '[701, 701, w - 9]', '[719, 719, 9*w^2 - 4*w - 19]', '[719, 719, 8*w^2 - 4*w - 15]', '[719, 719, 9*w^2 - 5*w - 18]', '[739, 739, 7*w^2 + 3*w - 15]', '[739, 739, -3*w^2 + 10*w + 7]', '[739, 739, 10*w^2 - 7*w - 19]', '[757, 757, 3*w^2 - 16]', '[757, 757, -7*w^2 + 4*w + 7]', '[757, 757, 4*w^2 + 3*w - 15]', '[773, 773, 4*w^2 + 3*w - 14]', '[773, 773, 2*w^2 + w - 14]', '[773, 773, 8*w^2 - 7*w - 20]', '[809, 809, 3*w^2 + 4*w - 14]', '[809, 809, 7*w^2 - 3*w - 6]', '[809, 809, 4*w^2 - 7*w - 16]', '[811, 811, 9*w^2 - 3*w - 19]', '[811, 811, -6*w^2 + 9*w + 11]', '[811, 811, 5*w^2 - 3*w - 21]', '[827, 827, -7*w^2 + 8*w + 15]', '[827, 827, 8*w^2 - w - 15]', '[827, 827, 3*w^2 - w - 16]', '[829, 829, 6*w^2 + 3*w - 14]', '[829, 829, -3*w^2 + 9*w + 8]', '[829, 829, 9*w^2 - 6*w - 16]', '[863, 863, 2*w^2 - 4*w - 15]', '[863, 863, -4*w^2 + 2*w - 3]', '[863, 863, 2*w^2 + 2*w - 15]', '[881, 881, 2*w^2 + 5*w - 8]', '[881, 881, 5*w^2 - 7*w - 14]', '[881, 881, 7*w^2 - 2*w - 10]', '[883, 883, -4*w^2 + 3*w - 3]', '[883, 883, 3*w^2 + w - 17]', '[883, 883, 8*w^2 - 7*w - 21]', '[919, 919, 9*w^2 - w - 18]', '[919, 919, -8*w^2 + 9*w + 16]', '[919, 919, w^2 + 8*w - 2]', '[937, 937, 5*w^2 - 7*w - 15]', '[937, 937, 2*w^2 + 5*w - 9]', '[937, 937, 7*w^2 - 2*w - 9]', '[953, 953, 2*w^2 + 5*w - 11]', '[953, 953, 7*w^2 - 7*w - 19]', '[953, 953, 5*w^2 - 7*w - 17]', '[971, 971, -w - 10]', '[971, 971, -w^2 + w - 8]', '[971, 971, w^2 - 12]', '[991, 991, 4*w^2 - w - 19]', '[991, 991, -7*w^2 + 8*w + 16]', '[991, 991, 8*w^2 - w - 14]']}
• 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': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -3, 0, 1], 'conductor': 9, 'degree': 3, 'dirichlet_group': [1, 4, 7], 'disc_abs': 81, 'disc_rad': 3, 'disc_sign': 1, 'frobs': [[2, [[3, 1]]], [3, [0]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[3, 1]]], [13, [[3, 1]]], [17, [[1, 3]]], [19, [[1, 3]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [[3, 1]]], [37, [[1, 3]]], [41, [[3, 1]]], [43, [[3, 1]]], [47, [[3, 1]]], [53, [[1, 3]]], [59, [[3, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [4], 'galois_label': '3T1', 'galt': 1, 'grd': 4.326748710922225, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.81.1', 'local_algs': ['3.3.4.2'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [3], 'rd': 4.32674871092, 'regulator': {'__RealLiteral__': 0, 'data': '0.849287450646', 'prec': 47}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 2 \\)', '\\( a^{2} - a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}