Hilbert modular form data - 2.2.77.1-44.1-e

Formats: - HTML - YAML - JSON - 2023-03-28T11:33:58.046255

• 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': 77, 'field_bad_primes': [7, 11], 'field_label': '2.2.77.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.77.1-44.1-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [2, 11], 'level_ideal': '[44, 22, 2*w + 10]', 'level_label': '44.1', 'level_norm': 44, 'parallel_weight': 2, 'short_label': '44.1-e', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4, 2, 2]', -1], ['[11, 11, w + 5]', -1]], 'hecke_eigenvalues': [1, 0, 2, 1, 2, -2, 0, 0, 2, -2, 0, 0, 6, 2, 2, -8, 8, 2, 2, -10, 10, 12, 12, -4, -4, 12, -12, 18, -18, 6, -6, -10, -10, 2, -2, 22, 22, 14, -14, -12, -12, 12, -12, -6, 6, 12, 12, 12, 12, 6, -6, 8, -8, 16, -16, 2, -2, 26, -26, 14, -14, 30, 30, 12, 12, -14, 14, -28, -28, -10, -10, -18, -18, 16, -16, 34, 34, 16, -16, 12, 12, 30, 30, -6, 6, -4, -4, 36, -36, -8, -8, -20, -20, 8, -8, 34, -34, -22, 22, 20, -20, -28, -28, -4, 4, 32, -32, 18, 18, -28, -28, 18, 18, -18, -18, -42, 42, 4, 4, 14, 14, -6, 6, 0, 0, 30, 30, -8, 8, 40, -40, 14, -14, 50, -50, -20, -20, -22, -42, 42, 48, -48, -52, -52, -52, -52, -20, 20, -4, -4, 32, 32, 20, -20, -42, 42, 12, 12, 46, 2, 2, 52, 52, 62, -62, -38, -38, 40, -40, -10, 10, -56, -56, -42, 42, 54, 54, -52, 52, -40, -40, 4, -4, -20, -20, -30, -30, 4, -4, -16, 16, -28, 28, 12, -12, -40, -40, -16, 16, 24, -24, 12, 12, -34, -34, 48, -48, 46, 46, -8, -8, 18, -18, 8, 8, 40, -40, 26, 26, 46, -46, 32, -32, -4, -4, -4, -4, 14, -14, 34, 34, -44, 44, -44, 44, -12, 12, -4, -4, 74, -74, -62, -62, 66, -66, -56, 56, 66, -66, -14, 14, -78, -78, -52, -52, 52, -52, -52, -52, -26, 26, -24, 24, -52, -52, -4, 4, 58, 62, -62, 30, -30, 48, 48, -34, -34, 12, -12, 50, 50, -26, 26, -74, 74, -74, 74, 42, -42, -16, 16, 36, 36, 52, 52, -2, -2, -28, -28, -72, -72, 24, -24, -42, -42, 76, 76, -76, 76, -18, 18, 42, 42, 66, -66, -68, -68, -36, -36, -50, 58, 58, -44, 44, -2, 2, -78, -78, -4, 4, 52, -52, -58, -58, 42, 42, -30, 30, 12, 12, 30, 30, -4, -4, -8, 8, -62, 62, 38, 38, -26, -26, -60, 60, -44, 44, 46, -46, -24, -24, 12, -12, -32, -32, -14, -14, 22, -22, -4, -4, 32, -32, -38, -38, 52, -52, 40, -40, 56, -56, -54, -54, -34, 34, 100, 100, 26, 26, -52, -52, 48, 48, -20, 20, -4, -4, -18, 18, 34, 34, -30, 30, -12, 12, -10, -10, 12, -12, -12, -12, 56, -56, 54, 54, -14, 14, -68, -68, -66, 66, -36, -36, 52, -52, 28, 28, 62, 62, -68, -68, -108, 108, 10, 10, -12, 12, -38, 38, 92, -92, -62, 62, 88, -88, 58, 58, 6, 6, -30, 30, 50, -50, -82, -82, -60, -60, 112, 112, 22, 22, -42, 42, -12, -12, -60, -60, 86, -86, -14, -14, -104, 104, -30, -30, -60, 60, -38, 38, 58, 58, 18, -98, 98, 112, -112, 6, 6, 46, -46, -114, 114, 38, 38, 4, -4, -40, 40, -34, -34, -36, -36, 26, -26, 110, -110, -16, 16, -76, 76, 22, 22, -66, -66, -86, 86, -24, -24, 86, 86, -60, -60, -72, 72, 98, -98, 70, -70, -22, -22, 44, 44, -16, 16, -32, 32, 30, 30, 6, -6, -60, -60, 24, 24, 44, -44, -6, 6, -34, 34, 82, 82, 52, 52, -110, 110, -4, -4, -2, -2, 34, -34, -94, 94, -52, -52, -30, 30, -40, -40, 68, -68, -12, -12, 106, -106, 54, 54, -68, 68, -88, 88, 98, -98, 40, 40, 68, -68, 108, -108, 116, 116, 50, 50, -42, -42, -34, 34, 104, -104, -92, -92, 90, -90, -12, 12, 6, 6, -10, 10, -106, 106, 8, 8, 12, 12, 106, -106, -8, 8, 36, -36, -110, 110, -132, -132, -42, -42, 42, -42, -88, 88, -132, -132, -2, -2, -110, -110, 124, 124, -60, 60, -52, 52, 106, 106, -36, 36, 84, -84, 36, 36, -98, 98, -90, -90, 40, -40, 36, 36, 30, -30, 28, -28, 106, 106, -4, 4, -66, -66, 32, 32, 116, 116, 32, -32, 48, 48, -18, -18, -18, 18, -94, -94, -86, 86, -108, 108, -126, 126, -22, 22, -20, -20, -52, -52, 30, 30, 86, -86, 98, 98, 38, 38, -22, -22, -132, 132, 84, 84, 26, -26, -46, 46, 102, -102, 68, 68, 52, -52, 42, 42, -140, 140, 76, 76, -108, -108, -62, 62, 84, 84, 52, 52, -90, 90, -48, 48, 56, -56, -68, -68, 52, 52, -30, 30, 126, -126, 10, 10, -74, -74, -38, -38, 74, -74, 68, -68, 4, -4, -102, 102, -108, -108, 60, 60, -2, 2, -20, -20, 126, -126, -54, 54, -54, -54, -60, -60, -62, 62, 60, 60, 42, -42, -48, 48, -74, 74, 132, 132, -44, -44, 98, 98, -124, -124, -108, 108, 46, -46, -38, -38, -112, 112, 92, -92, 72, 72, 104, -104, 50, -50, 58, 58, -70, 70, -158, 112, -112, -46, 46, -50, 50, 110, 110, 124, 124, 150, 150, -82, -82, 56, 56, 126, -126, -140, -140, 38, 38, 140, 140, 134, 134, 68, -68, -36, -36, 6, 6, 36, -36, 0, 0, 140, -140, -70, -70, 48, -48, -68, 68, 142, 142, 84, 84, 66, 66, -80, -80, 158, -158, -52, 52, -20, -20, 12, 12, 124, -124, 26, 26, -54, -54, -76, 76, 62, 62, 26, -26, 24, 24, 90, 90, 62, -62, -110, 110, 76, 76, 2, -2, 36, 36, 100, -100, -26, -26, 6, 6, -102, 102, 4, 4, -2, 2, -96, 96, 102, 102, 30, 30, 140, 140, 10, 10, 114, -114, -20, -20, 54, -54, -78, 78, 112, 112, 74, 74, 18, 18, -24, 24, 132, 132, 8, 8, 8, -8, -14, -14, 78, -78, -138, -138, 96, -96, 4, 4, -106, 106, -162, -162, -64, 64, -36, -36, -8, 8, 70, 70, -48, -48, -36, 36, 32, 32, 126, 126, 76, 76, 30, -30, 98, -98, 86, -86, 92, 92, -50, 50, 82, 82, -126, -126, 76, -76, -150, 150, 90, 90, -30, 30, -118, 118, -64, 64, -18, -18, 4, 4, -164, -164, 178, -36, 36, 144, -144, 20, -20, -10, -10, -82, -82, -90, 90, -132, 132, 10, 10, -170, -170, 74, -74, -20, 20, 84, 84, 98, -98, 86, 86, -76, -76, -144, 144, -126, 126, 94, -94, 54, 54, -6, -6, -120, 120, 146, 146, 62, 62, -8, 8, -52, -52, -2, 2, -146, -146, -84, 84, 14, -14, 162, 162, -180, 180, -124, -124, -48, 48, 124, -124, 4, -4, 160, -160, 108, 108, 58, 58, -70, 70, -114, -114, -134, 134, -144, 144, 86, 86, -140, -140, 124, 124, -106, 106, 8, 8, 32, -32, 14, 14, 170, -170, -86, 86, 114, 114, -50, -50, -84, 84, -10, -10, -8, -8, -154, -154, -56, 56, 132, 132, 132, -132, -70, -70, 68, -68, 158, 158, -102, 102, -158, 158, 184, 184, 114, -114, 94, 94, -84, -84, -24, 24, -10, -10, -96, 96, -38, -38, -28, 28, -42, -42, -28, -28, 66, -66, -142, 142, 174, -174, 94, 94, -68, -68, 50, 102, -102, -124, -124, 168, 168, -18, -18, 62, -62, 52, -52, 10, -10, 122, -122, 134, -134, -10, -10, -28, -28, 138, 138, -40, 40, -164, 164, -138, -138, -138, 138, 88, -88, 122, 122, 80, -80, 60, -60, -84, -84, 108, -108, 18, 18, -10, 10, 64, -64, 120, 120, 18, 18, -100, -100, 20, 20, -40, 40, -78, -78, 134, -134], 'hecke_polynomial': 'x', 'label': '2.2.77.1-44.1-e'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 77, 'ideals': ['[1, 1, 1]', '[4, 2, 2]', '[7, 7, -w - 3]', '[9, 3, 3]', '[11, 11, w + 5]', '[13, 13, w + 2]', '[13, 13, w - 3]', '[16, 4, 4]', '[17, 17, w + 1]', '[17, 17, -w + 2]', '[19, 19, w]', '[19, 19, w - 1]', '[23, 23, w + 6]', '[23, 23, -w + 7]', '[25, 5, -5]', '[28, 14, -2*w - 6]', '[36, 6, 6]', '[37, 37, -w - 7]', '[37, 37, w - 8]', '[41, 41, 2*w - 7]', '[41, 41, -2*w - 5]', '[44, 22, 2*w + 10]', '[49, 7, 7]', '[52, 26, 2*w + 4]', '[52, 26, 2*w - 6]', '[53, 53, -w - 8]', '[53, 53, w - 9]', '[61, 61, 2*w - 5]', '[61, 61, -2*w - 3]', '[63, 21, -3*w - 9]', '[64, 8, 8]', '[67, 67, 2*w - 13]', '[67, 67, -2*w - 11]', '[68, 34, 2*w + 2]', '[68, 34, -2*w + 4]', '[71, 71, -w - 9]', '[71, 71, w - 10]', '[73, 73, 2*w - 3]', '[73, 73, -2*w - 1]', '[76, 38, 2*w]', '[76, 38, 2*w - 2]', '[77, 77, -2*w + 1]', '[81, 9, 9]', '[83, 83, 3*w - 11]', '[83, 83, -3*w - 8]', '[91, 91, -w - 10]', '[91, 91, w - 11]', '[92, 46, 2*w + 12]', '[92, 46, -2*w + 14]', '[99, 33, 3*w + 15]', '[100, 10, -10]', '[101, 101, -3*w - 7]', '[101, 101, 3*w - 10]', '[112, 28, -4*w - 12]', '[113, 113, -w - 11]', '[113, 113, w - 12]', '[117, 39, 3*w + 6]', '[117, 39, 3*w - 9]', '[119, 119, 2*w - 15]', '[119, 119, 2*w + 13]', '[121, 11, 11]', '[131, 131, 3*w - 8]', '[131, 131, -3*w - 5]', '[133, 133, 3*w - 19]', '[133, 133, -3*w - 16]', '[137, 137, -w - 12]', '[137, 137, w - 13]', '[139, 139, 4*w - 15]', '[139, 139, -4*w - 11]', '[143, 143, 3*w + 4]', '[143, 143, 3*w - 7]', '[144, 12, 12]', '[148, 74, -2*w - 14]', '[148, 74, 2*w - 16]', '[153, 51, 3*w + 3]', '[153, 51, -3*w + 6]', '[161, 161, -3*w + 5]', '[161, 161, -3*w - 2]', '[163, 163, -w - 13]', '[163, 163, w - 14]', '[164, 82, 4*w - 14]', '[164, 82, -4*w - 10]', '[167, 167, -3*w - 1]', '[167, 167, 3*w - 4]', '[169, 13, 13]', '[169, 169, 3*w + 17]', '[169, 169, -3*w + 20]', '[171, 57, 3*w]', '[171, 57, 3*w - 3]', '[173, 173, 3*w - 2]', '[173, 173, 3*w - 1]', '[175, 35, 5*w + 15]', '[176, 44, 4*w + 20]', '[179, 179, 2*w - 17]', '[179, 179, -2*w - 15]', '[187, 187, -4*w - 9]', '[187, 187, 4*w - 13]', '[191, 191, -w - 14]', '[191, 191, w - 15]', '[196, 14, 14]', '[207, 69, 3*w + 18]', '[207, 69, -3*w + 21]', '[208, 52, 4*w + 8]', '[208, 52, 4*w - 12]', '[209, 209, 5*w - 19]', '[209, 209, 5*w + 14]', '[212, 106, -2*w - 16]', '[212, 106, 2*w - 18]', '[221, 221, -w - 15]', '[221, 221, 4*w - 25]', '[221, 221, 4*w + 21]', '[221, 221, -w + 16]', '[225, 15, -15]', '[227, 227, 4*w - 11]', '[227, 227, -4*w - 7]', '[241, 241, -5*w - 13]', '[241, 241, 5*w - 18]', '[244, 122, 4*w - 10]', '[244, 122, -4*w - 6]', '[247, 247, -3*w + 22]', '[247, 247, -2*w + 19]', '[247, 247, 2*w + 17]', '[247, 247, 3*w + 19]', '[252, 42, -6*w - 18]', '[253, 253, w + 16]', '[253, 253, -w + 17]', '[256, 16, 16]', '[259, 259, 4*w + 5]', '[259, 259, 11*w + 40]', '[268, 134, 4*w - 26]', '[268, 134, -4*w - 22]', '[271, 271, 5*w - 17]', '[271, 271, -5*w - 12]', '[272, 68, 4*w + 4]', '[272, 68, -4*w + 8]', '[275, 55, -5*w - 25]', '[283, 283, 4*w - 7]', '[283, 283, -4*w - 3]', '[284, 142, -2*w - 18]', '[284, 142, 2*w - 20]', '[287, 287, -w - 17]', '[287, 287, 13*w + 53]', '[289, 17, 17]', '[289, 289, 3*w + 20]', '[289, 289, -3*w + 23]', '[292, 146, 4*w - 6]', '[292, 146, -4*w - 2]', '[293, 293, 6*w - 23]', '[293, 293, -6*w - 17]', '[299, 299, 5*w + 11]', '[299, 299, 4*w + 1]', '[299, 299, 4*w - 5]', '[299, 299, 5*w - 16]', '[304, 76, 4*w]', '[304, 76, 4*w - 4]', '[307, 307, 4*w - 3]', '[307, 307, 4*w - 1]', '[308, 154, -4*w + 2]', '[317, 317, -4*w - 23]', '[317, 317, 4*w - 27]', '[323, 323, w + 18]', '[323, 323, 2*w - 21]', '[323, 323, 2*w + 19]', '[323, 323, w - 19]', '[324, 18, 18]', '[325, 65, -5*w - 10]', '[325, 65, -5*w + 15]', '[331, 331, 5*w - 31]', '[331, 331, -5*w - 26]', '[332, 166, 6*w - 22]', '[332, 166, -6*w - 16]', '[333, 111, -3*w - 21]', '[333, 111, 3*w - 24]', '[343, 49, -7*w - 21]', '[349, 349, 5*w - 14]', '[349, 349, -5*w - 9]', '[361, 19, 19]', '[361, 361, w + 19]', '[361, 361, -w + 20]', '[364, 182, -2*w - 20]', '[364, 182, 2*w - 22]', '[368, 92, 4*w + 24]', '[368, 92, -4*w + 28]', '[369, 123, 6*w - 21]', '[369, 123, -6*w - 15]', '[371, 371, 5*w + 8]', '[371, 371, 12*w + 43]', '[379, 379, 3*w - 25]', '[379, 379, -3*w - 22]', '[389, 389, -5*w - 27]', '[389, 389, 5*w - 32]', '[391, 391, 7*w - 27]', '[391, 391, 5*w - 12]', '[391, 391, -5*w - 7]', '[391, 391, -7*w - 20]', '[396, 66, 6*w + 30]', '[400, 20, -20]', '[401, 401, -w - 20]', '[401, 401, w - 21]', '[404, 202, -6*w - 14]', '[404, 202, 6*w - 20]', '[407, 407, -13*w - 54]', '[407, 407, -2*w - 21]', '[409, 409, -5*w - 6]', '[409, 409, 5*w - 11]', '[421, 421, 4*w - 29]', '[421, 421, -4*w - 25]', '[425, 85, -5*w - 5]', '[425, 85, 5*w - 10]', '[427, 427, -3*w - 23]', '[427, 427, 11*w + 47]', '[437, 437, 6*w + 13]', '[437, 437, 7*w + 19]', '[437, 437, 7*w - 26]', '[437, 437, 6*w - 19]', '[439, 439, 5*w - 9]', '[439, 439, -5*w - 4]', '[441, 21, 21]', '[443, 443, -w - 21]', '[443, 443, w - 22]', '[448, 56, -8*w - 24]', '[449, 449, 5*w - 33]', '[449, 449, -5*w - 28]', '[451, 451, 5*w + 3]', '[451, 451, -17*w - 63]', '[452, 226, -2*w - 22]', '[452, 226, 2*w - 24]', '[461, 461, 5*w - 7]', '[461, 461, -5*w - 2]', '[463, 463, -7*w - 34]', '[463, 463, 7*w - 41]', '[468, 78, 6*w + 12]', '[468, 78, 6*w - 18]', '[469, 469, 5*w + 1]', '[469, 469, 19*w + 71]', '[475, 95, -5*w]', '[475, 95, -5*w + 5]', '[476, 238, 4*w - 30]', '[476, 238, 4*w + 26]', '[477, 159, -3*w - 24]', '[477, 159, 3*w - 27]', '[479, 479, 5*w - 4]', '[479, 479, 5*w - 1]', '[481, 481, -10*w + 43]', '[481, 481, -5*w + 2]', '[481, 481, -5*w + 3]', '[481, 481, -10*w - 33]', '[484, 22, 22]', '[487, 487, -w - 22]', '[487, 487, w - 23]', '[497, 497, 13*w + 46]', '[497, 497, 6*w + 11]', '[499, 499, 2*w - 25]', '[499, 499, -2*w - 23]', '[503, 503, 9*w + 28]', '[503, 503, 8*w + 23]', '[511, 511, -5*w - 29]', '[511, 511, 9*w + 41]', '[523, 523, 7*w - 24]', '[523, 523, -7*w - 17]', '[524, 262, 6*w - 16]', '[524, 262, -6*w - 10]', '[529, 23, 23]', '[529, 529, -3*w + 28]', '[529, 529, 3*w + 25]', '[532, 266, 6*w - 38]', '[532, 266, -6*w - 32]', '[533, 533, -w - 23]', '[533, 533, -11*w + 59]', '[533, 533, -11*w - 48]', '[533, 533, -w + 24]', '[539, 77, 7*w + 35]', '[548, 274, -2*w - 24]', '[548, 274, 2*w - 26]', '[549, 183, 6*w - 15]', '[549, 183, -6*w - 9]', '[556, 278, 8*w - 30]', '[556, 278, -8*w - 22]', '[563, 563, 7*w - 23]', '[563, 563, -7*w - 16]', '[567, 63, -9*w - 27]', '[572, 286, 6*w + 8]', '[572, 286, 6*w - 14]', '[575, 115, -5*w - 30]', '[575, 115, 5*w - 35]', '[576, 24, 24]', '[581, 581, -w - 24]', '[581, 581, 20*w + 81]', '[583, 583, -3*w - 26]', '[583, 583, -14*w - 59]', '[592, 148, -4*w - 28]', '[592, 148, 4*w - 32]', '[593, 593, -6*w - 7]', '[593, 593, 6*w - 13]', '[599, 599, 2*w - 27]', '[599, 599, -2*w - 25]', '[601, 601, -7*w - 15]', '[601, 601, 7*w - 22]', '[603, 201, 6*w - 39]', '[603, 201, -6*w - 33]', '[607, 607, 8*w - 29]', '[607, 607, -8*w - 21]', '[612, 102, 6*w + 6]', '[612, 102, -6*w + 12]', '[617, 617, -8*w - 39]', '[617, 617, 8*w - 47]', '[625, 25, -25]', '[629, 629, 9*w - 35]', '[629, 629, -6*w + 11]', '[629, 629, 6*w + 5]', '[629, 629, -9*w - 26]', '[631, 631, -w - 25]', '[631, 631, w - 26]', '[637, 91, 7*w + 14]', '[637, 91, 7*w - 21]', '[639, 213, -3*w - 27]', '[639, 213, 3*w - 30]', '[641, 641, 5*w - 36]', '[641, 641, -5*w - 31]', '[644, 322, -6*w + 10]', '[644, 322, -6*w - 4]', '[652, 326, -2*w - 26]', '[652, 326, 2*w - 28]', '[653, 653, 4*w - 33]', '[653, 653, -4*w - 29]', '[656, 164, 8*w - 28]', '[656, 164, -8*w - 20]', '[657, 219, 6*w - 9]', '[657, 219, -6*w - 3]', '[668, 334, -6*w - 2]', '[668, 334, 6*w - 8]', '[671, 671, -15*w - 53]', '[671, 671, 7*w + 13]', '[676, 26, 26]', '[676, 338, 6*w + 34]', '[676, 338, -6*w + 40]', '[677, 677, -6*w - 1]', '[677, 677, 6*w - 7]', '[683, 683, -w - 26]', '[683, 683, w - 27]', '[684, 114, 6*w]', '[684, 114, 6*w - 6]', '[689, 689, -6*w + 5]', '[689, 689, -11*w + 46]', '[689, 689, -11*w - 35]', '[689, 689, -6*w + 1]', '[692, 346, 6*w - 4]', '[692, 346, 6*w - 2]', '[693, 231, -6*w + 3]', '[697, 697, -3*w + 31]', '[697, 697, 9*w - 52]', '[697, 697, -9*w - 43]', '[697, 697, 3*w + 28]', '[700, 70, 10*w + 30]', '[703, 703, -8*w - 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61]', '[5953, 5953, 22*w - 69]', '[5953, 5953, -22*w - 47]', '[5981, 5981, 18*w - 25]', '[5981, 5981, -18*w - 7]', '[5987, 5987, -w - 77]', '[5987, 5987, w - 78]', '[6007, 6007, 2*w - 79]', '[6007, 6007, -2*w - 77]', '[6029, 6029, -7*w - 80]', '[6029, 6029, 7*w - 87]', '[6043, 6043, 11*w - 97]', '[6043, 6043, -11*w - 86]', '[6047, 6047, -24*w - 59]', '[6047, 6047, 24*w - 83]', '[6067, 6067, 28*w + 81]', '[6067, 6067, 31*w + 96]', '[6073, 6073, -24*w - 119]', '[6073, 6073, 24*w - 143]', '[6079, 6079, -19*w - 20]', '[6079, 6079, 19*w - 39]', '[6089, 6089, 30*w + 91]', '[6089, 6089, 29*w + 86]', '[6143, 6143, -w - 78]', '[6143, 6143, w - 79]', '[6151, 6151, -23*w - 52]', '[6151, 6151, 23*w - 75]', '[6173, 6173, 18*w - 17]', '[6173, 6173, 18*w - 1]', '[6197, 6197, 7*w - 88]', '[6197, 6197, -7*w - 81]', '[6221, 6221, 18*w - 5]', '[6221, 6221, 18*w - 13]', '[6241, 79, -79]', '[6247, 6247, -19*w - 17]', '[6247, 6247, 19*w - 36]', '[6277, 6277, 23*w - 74]', '[6277, 6277, -23*w - 51]', '[6299, 6299, -19*w - 16]', '[6299, 6299, 19*w - 35]', '[6301, 6301, -w - 79]', '[6301, 6301, w - 80]', '[6323, 6323, 2*w - 81]', '[6323, 6323, -2*w - 79]', '[6329, 6329, 25*w - 148]', '[6329, 6329, -25*w - 123]', '[6337, 6337, 8*w - 91]', '[6337, 6337, -8*w - 83]', '[6367, 6367, 7*w - 89]', '[6367, 6367, -7*w - 82]', '[6397, 6397, 19*w - 33]', '[6397, 6397, -19*w - 14]', '[6427, 6427, -17*w - 101]', '[6427, 6427, 17*w - 118]', '[6449, 6449, 13*w - 105]', '[6449, 6449, -13*w - 92]', '[6451, 6451, -9*w - 85]', '[6451, 6451, 9*w - 94]', '[6469, 6469, -3*w - 80]', '[6469, 6469, 3*w - 83]', '[6481, 6481, 25*w - 87]', '[6481, 6481, -25*w - 62]', '[6491, 6491, 5*w - 86]', '[6491, 6491, -5*w - 81]', '[6521, 6521, -16*w - 99]', '[6521, 6521, 16*w - 115]', '[6529, 6529, -19*w - 11]', '[6529, 6529, 19*w - 30]', '[6551, 6551, -27*w - 73]', '[6551, 6551, 27*w - 100]', '[6569, 6569, -19*w - 10]', '[6569, 6569, 19*w - 29]', '[6581, 6581, 4*w - 85]', '[6581, 6581, -4*w - 81]', '[6599, 6599, -24*w - 55]', '[6599, 6599, 24*w - 79]', '[6607, 6607, 19*w - 28]', '[6607, 6607, -19*w - 9]', '[6637, 6637, -12*w - 91]', '[6637, 6637, 12*w - 103]', '[6659, 6659, -5*w - 82]', '[6659, 6659, 5*w - 87]', '[6689, 6689, -8*w - 85]', '[6689, 6689, 8*w - 93]', '[6703, 6703, -6*w - 83]', '[6703, 6703, 6*w - 89]', '[6709, 6709, 19*w - 25]', '[6709, 6709, -19*w - 6]', '[6761, 6761, -23*w - 47]', '[6761, 6761, 23*w - 70]', '[6763, 6763, 21*w - 134]', '[6763, 6763, -21*w - 113]', '[6791, 6791, -11*w - 90]', '[6791, 6791, 11*w - 101]', '[6793, 6793, 19*w - 22]', '[6793, 6793, -19*w - 3]', '[6829, 6829, 5*w - 88]', '[6829, 6829, -5*w - 83]', '[6857, 6857, 19*w - 127]', '[6857, 6857, -19*w - 108]', '[6863, 6863, -24*w - 53]', '[6863, 6863, 24*w - 77]', '[6869, 6869, 17*w - 120]', '[6869, 6869, -17*w - 103]', '[6907, 6907, 19*w - 3]', '[6907, 6907, 19*w - 16]', '[6911, 6911, -10*w - 89]', '[6911, 6911, 10*w - 99]', '[6917, 6917, -4*w - 83]', '[6917, 6917, 4*w - 87]', '[6947, 6947, 19*w - 8]', '[6947, 6947, 19*w - 11]', '[6949, 6949, 19*w - 9]', '[6949, 6949, 19*w - 10]', '[6967, 6967, -3*w - 83]', '[6967, 6967, 3*w - 86]', '[6971, 6971, 20*w - 37]', '[6971, 6971, -20*w - 17]', '[6983, 6983, 11*w - 102]', '[6983, 6983, -11*w - 91]', '[6991, 6991, 23*w - 68]', '[6991, 6991, -23*w - 45]', '[6997, 6997, 9*w - 97]', '[6997, 6997, -9*w - 88]', '[7001, 7001, -5*w - 84]', '[7001, 7001, 5*w - 89]', '[7013, 7013, -22*w - 37]', '[7013, 7013, 22*w - 59]', '[7043, 7043, -14*w - 97]', '[7043, 7043, 14*w - 111]', '[7069, 7069, 29*w - 110]', '[7069, 7069, -29*w - 81]', '[7103, 7103, -23*w - 44]', '[7103, 7103, 23*w - 67]', '[7109, 7109, -23*w - 120]', '[7109, 7109, 23*w - 143]', '[7121, 7121, -w - 84]', '[7121, 7121, w - 85]', '[7151, 7151, -26*w - 129]', '[7151, 7151, 26*w - 155]', '[7177, 7177, 11*w - 103]', '[7177, 7177, -11*w - 92]', '[7213, 7213, 23*w - 66]', '[7213, 7213, -23*w - 43]', '[7219, 7219, -18*w - 107]', '[7219, 7219, 18*w - 125]', '[7229, 7229, 21*w - 46]', '[7229, 7229, -21*w - 25]', '[7237, 7237, 26*w - 89]', '[7237, 7237, -26*w - 63]', '[7247, 7247, -7*w - 87]', '[7247, 7247, 7*w - 94]', '[7253, 7253, -13*w - 96]', '[7253, 7253, 13*w - 109]', '[7309, 7309, 3*w - 88]', '[7309, 7309, -3*w - 85]', '[7321, 7321, 23*w - 65]', '[7321, 7321, -23*w - 42]', '[7331, 7331, -19*w - 110]', '[7331, 7331, 19*w - 129]', '[7351, 7351, 5*w - 91]', '[7351, 7351, -5*w - 86]', '[7369, 7369, 31*w + 90]', '[7369, 7369, 34*w + 105]', '[7393, 7393, 16*w - 119]', '[7393, 7393, -16*w - 103]', '[7411, 7411, -20*w - 7]', '[7411, 7411, 20*w - 27]', '[7417, 7417, 8*w - 97]', '[7417, 7417, -8*w - 89]', '[7433, 7433, -21*w - 22]', '[7433, 7433, 21*w - 43]', '[7459, 7459, -13*w - 97]', '[7459, 7459, 13*w - 110]', '[7523, 7523, -28*w - 73]', '[7523, 7523, 28*w - 101]', '[7529, 7529, -5*w - 87]', '[7529, 7529, 5*w - 92]', '[7537, 7537, -26*w - 61]', '[7537, 7537, 26*w - 87]', '[7547, 7547, -17*w - 106]', '[7547, 7547, 17*w - 123]', '[7559, 7559, 21*w - 41]', '[7559, 7559, -21*w - 20]', '[7561, 7561, 9*w - 100]', '[7561, 7561, -9*w - 91]', '[7583, 7583, 22*w - 141]', '[7583, 7583, -22*w - 119]', '[7607, 7607, 24*w - 71]', '[7607, 7607, -24*w - 47]', '[7639, 7639, 23*w - 145]', '[7639, 7639, -23*w - 122]', '[7681, 7681, 24*w - 149]', '[7681, 7681, -24*w - 125]', '[7687, 7687, 18*w - 127]', '[7687, 7687, -18*w - 109]', '[7691, 7691, 20*w - 13]', '[7691, 7691, 20*w - 7]', '[7699, 7699, 20*w - 11]', '[7699, 7699, 20*w - 9]', '[7717, 7717, 22*w - 51]', '[7717, 7717, -22*w - 29]', '[7723, 7723, -27*w - 134]', '[7723, 7723, 27*w - 161]', '[7741, 7741, 25*w - 78]', '[7741, 7741, -25*w - 53]', '[7753, 7753, -9*w - 92]', '[7753, 7753, 9*w - 101]', '[7793, 7793, 8*w - 99]', '[7793, 7793, -8*w - 91]', '[7817, 7817, 29*w - 106]', '[7817, 7817, -29*w - 77]', '[7829, 7829, 26*w - 85]', '[7829, 7829, -26*w - 59]', '[7841, 7841, -16*w - 105]', '[7841, 7841, 16*w - 121]', '[7853, 7853, 34*w + 103]', '[7853, 7853, 33*w + 98]', '[7867, 7867, 28*w - 99]', '[7867, 7867, -28*w - 71]', '[7873, 7873, -22*w - 27]', '[7873, 7873, 22*w - 49]', '[7877, 7877, 13*w - 112]', '[7877, 7877, -13*w - 99]', '[7879, 7879, 15*w - 118]', '[7879, 7879, -15*w - 103]', '[7907, 7907, 23*w - 146]', '[7907, 7907, -23*w - 123]', '[7921, 89, -89]', '[7927, 7927, 23*w - 59]', '[7927, 7927, -23*w - 36]', '[7937, 7937, 21*w - 34]', '[7937, 7937, -21*w - 13]', '[7993, 7993, -31*w - 87]', '[7993, 7993, 31*w - 118]', '[8009, 8009, 17*w - 125]', '[8009, 8009, -17*w - 108]', '[8017, 8017, -3*w - 89]', '[8017, 8017, 3*w - 92]', '[8069, 8069, 21*w - 31]', '[8069, 8069, -21*w - 10]', '[8081, 8081, 33*w + 97]', '[8081, 8081, 35*w + 107]', '[8089, 8089, 13*w - 113]', '[8089, 8089, -13*w - 100]', '[8101, 8101, -15*w - 104]', '[8101, 8101, 15*w - 119]', '[8147, 8147, -21*w - 8]', '[8147, 8147, 21*w - 29]', '[8161, 8161, -22*w - 23]', '[8161, 8161, 22*w - 45]', '[8171, 8171, -w - 90]', '[8171, 8171, w - 91]', '[8179, 8179, -29*w - 75]', '[8179, 8179, 29*w - 104]', '[8233, 8233, 24*w - 151]', '[8233, 8233, -24*w - 127]', '[8243, 8243, 17*w - 126]', '[8243, 8243, -17*w - 109]', '[8263, 8263, 32*w - 123]', '[8263, 8263, -32*w - 91]', '[8291, 8291, 23*w - 55]', '[8291, 8291, -23*w - 32]', '[8293, 8293, 22*w - 43]', '[8293, 8293, -22*w - 21]', '[8297, 8297, 16*w - 123]', '[8297, 8297, -16*w - 107]', '[8317, 8317, -28*w - 139]', '[8317, 8317, 28*w - 167]', '[8329, 8329, 35*w + 106]', '[8329, 8329, 34*w + 101]', '[8353, 8353, -w - 91]', '[8353, 8353, w - 92]', '[8369, 8369, -7*w - 93]', '[8369, 8369, 7*w - 100]', '[8377, 8377, -23*w - 31]', '[8377, 8377, 23*w - 54]', '[8387, 8387, 2*w - 93]', '[8387, 8387, -2*w - 91]', '[8389, 8389, -26*w - 55]', '[8389, 8389, 26*w - 81]', '[8429, 8429, -20*w - 117]', '[8429, 8429, 20*w - 137]', '[8447, 8447, 21*w - 4]', '[8447, 8447, 21*w - 17]', '[8461, 8461, -23*w - 30]', '[8461, 8461, 23*w - 53]', '[8537, 8537, -w - 92]', '[8537, 8537, w - 93]', '[8543, 8543, -23*w - 29]', '[8543, 8543, 23*w - 52]', '[8563, 8563, -7*w - 94]', '[8563, 8563, 7*w - 101]', '[8599, 8599, 31*w - 115]', '[8599, 8599, -31*w - 84]', '[8609, 8609, -25*w - 46]', '[8609, 8609, 25*w - 71]', '[8623, 8623, 23*w - 51]', '[8623, 8623, -23*w - 28]', '[8641, 8641, -22*w - 15]', '[8641, 8641, 22*w - 37]', '[8647, 8647, -18*w - 113]', '[8647, 8647, 18*w - 131]', '[8677, 8677, 12*w - 113]', '[8677, 8677, -12*w - 101]', '[8707, 8707, 29*w - 101]', '[8707, 8707, -29*w - 72]', '[8737, 8737, -13*w - 103]', '[8737, 8737, 13*w - 116]', '[8741, 8741, 22*w - 35]', '[8741, 8741, -22*w - 13]', '[8753, 8753, -33*w - 94]', '[8753, 8753, 33*w - 127]', '[8761, 8761, 16*w - 125]', '[8761, 8761, -16*w - 109]', '[8779, 8779, -15*w - 107]', '[8779, 8779, 15*w - 122]', '[8803, 8803, 21*w - 142]', '[8803, 8803, -21*w - 121]', '[8819, 8819, 36*w + 109]', '[8819, 8819, 35*w + 104]', '[8831, 8831, -5*w - 94]', '[8831, 8831, 5*w - 99]', '[8839, 8839, -25*w - 44]', '[8839, 8839, 25*w - 69]', '[8849, 8849, -25*w - 132]', '[8849, 8849, 25*w - 157]', '[8861, 8861, 30*w - 107]', '[8861, 8861, -30*w - 77]', '[8923, 8923, -23*w - 24]', '[8923, 8923, 23*w - 47]', '[8933, 8933, -29*w - 144]', '[8933, 8933, 29*w - 173]', '[8941, 8941, -20*w - 119]', '[8941, 8941, 20*w - 139]', '[8951, 8951, -25*w - 43]', '[8951, 8951, 25*w - 68]', '[8969, 8969, 8*w - 105]', '[8969, 8969, -8*w - 97]', '[8999, 8999, 23*w - 150]', '[8999, 8999, -23*w - 127]', '[9013, 9013, -11*w - 101]', '[9013, 9013, 11*w - 112]', '[9049, 9049, 29*w - 99]', '[9049, 9049, -29*w - 70]', '[9067, 9067, 21*w - 143]', '[9067, 9067, -21*w - 122]', '[9103, 9103, -32*w - 87]', '[9103, 9103, 32*w - 119]', '[9109, 9109, -12*w - 103]', '[9109, 9109, 12*w - 115]', '[9127, 9127, -23*w - 21]', '[9127, 9127, 23*w - 44]', '[9157, 9157, -7*w - 97]', '[9157, 9157, 7*w - 104]', '[9173, 9173, -22*w - 1]', '[9173, 9173, 22*w - 23]', '[9187, 9187, 31*w - 112]', '[9187, 9187, -31*w - 81]', '[9199, 9199, -17*w - 113]', '[9199, 9199, 17*w - 130]', '[9203, 9203, 27*w - 83]', '[9203, 9203, -27*w - 56]', '[9221, 9221, 5*w - 101]', '[9221, 9221, -5*w - 96]', '[9227, 9227, 11*w - 113]', '[9227, 9227, -11*w - 102]', '[9239, 9239, -24*w - 31]', '[9239, 9239, 24*w - 55]', '[9241, 9241, 15*w - 124]', '[9241, 9241, -15*w - 109]', '[9257, 9257, 34*w - 131]', '[9257, 9257, -34*w - 97]', '[9277, 9277, -23*w - 128]', '[9277, 9277, 23*w - 151]', '[9281, 9281, 22*w - 17]', '[9281, 9281, 22*w - 5]', '[9293, 9293, -w - 96]', '[9293, 9293, w - 97]', '[9311, 9311, 10*w - 111]', '[9311, 9311, -10*w - 101]', '[9323, 9323, 37*w + 112]', '[9323, 9323, 36*w + 107]', '[9341, 9341, -27*w - 55]', '[9341, 9341, 27*w - 82]', '[9371, 9371, 23*w - 40]', '[9371, 9371, -23*w - 17]', '[9377, 9377, 8*w - 107]', '[9377, 9377, -8*w - 99]', '[9403, 9403, -13*w - 106]', '[9403, 9403, 13*w - 119]', '[9409, 97, -97]', '[9413, 9413, -26*w - 47]', '[9413, 9413, 26*w - 73]', '[9419, 9419, -5*w - 97]', '[9419, 9419, 5*w - 102]', '[9431, 9431, -25*w - 134]', '[9431, 9431, 25*w - 159]', '[9461, 9461, 20*w - 141]', '[9461, 9461, -20*w - 121]', '[9467, 9467, 28*w - 89]', '[9467, 9467, -28*w - 61]', '[9511, 9511, 32*w - 117]', '[9511, 9511, -32*w - 85]', '[9533, 9533, -23*w - 14]', '[9533, 9533, 23*w - 37]', '[9539, 9539, 35*w - 136]', '[9539, 9539, -35*w - 101]', '[9547, 9547, -29*w - 67]', '[9547, 9547, 29*w - 96]', '[9601, 9601, 21*w - 145]', '[9601, 9601, -21*w - 124]', '[9619, 9619, 5*w - 103]', '[9619, 9619, -5*w - 98]', '[9629, 9629, -13*w - 107]', '[9629, 9629, 13*w - 120]', '[9631, 9631, -23*w - 12]', '[9631, 9631, 23*w - 35]', '[9649, 9649, -26*w - 45]', '[9649, 9649, 26*w - 71]', '[9661, 9661, -11*w - 104]', '[9661, 9661, 11*w - 115]', '[9677, 9677, 23*w - 34]', '[9677, 9677, -23*w - 11]', '[9679, 9679, 25*w - 61]', '[9679, 9679, -25*w - 36]', '[9689, 9689, 17*w - 132]', '[9689, 9689, -17*w - 115]', '[9719, 9719, -24*w - 25]', '[9719, 9719, 24*w - 49]', '[9721, 9721, -23*w - 10]', '[9721, 9721, 23*w - 33]', '[9739, 9739, -10*w - 103]', '[9739, 9739, 10*w - 113]', '[9743, 9743, -27*w - 52]', '[9743, 9743, 27*w - 79]', '[9769, 9769, -7*w - 100]', '[9769, 9769, 7*w - 107]', '[9803, 9803, -23*w - 8]', '[9803, 9803, 23*w - 31]', '[9833, 9833, 33*w - 122]', '[9833, 9833, -33*w - 89]', '[9839, 9839, -23*w - 130]', '[9839, 9839, 23*w - 153]', '[9857, 9857, -13*w - 108]', '[9857, 9857, 13*w - 121]', '[9871, 9871, -21*w - 125]', '[9871, 9871, 21*w - 146]', '[9923, 9923, 2*w - 101]', '[9923, 9923, -2*w - 99]', '[9929, 9929, -30*w - 71]', '[9929, 9929, 30*w - 101]', '[9949, 9949, -15*w - 112]', '[9949, 9949, 15*w - 127]', '[9973, 9973, -23*w - 3]', '[9973, 9973, 23*w - 26]']}
• 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
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_label	text
  galt	integer
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  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
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-19, -1, 1], 'conductor': 77, 'degree': 2, 'dirichlet_group': [1, 76], 'disc_abs': 77, 'disc_rad': 77, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[2, 1]]], [5, [[2, 1]]], [7, [0]], [11, [0]], [13, [[1, 2]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[1, 2]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_label': '2T1', 'galt': 1, 'index': 1, 'inessentialp': [], 'is_galois': True, 'iso_number': 1, 'label': '2.2.77.1', 'local_algs': ['7.2.1.1', '11.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [7, 11], 'rd': 8.77496438739, 'regulator': {'__RealLiteral__': 0, 'data': '2.18464379161', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 4 \\)'], 'used_grh': False, 'zk': ['1', 'a']}