Hilbert modular form data - 2.2.77.1-44.1-d

Formats: - HTML - YAML - JSON - 2025-12-18T23:55:02.883866

• 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-d', 'label_nsuffix': 3, 'label_suffix': 'd', '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-d', '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, -2, 0, 1, -1, 4, -2, 3, 0, -5, -6, -1, 1, -7, -2, 7, 12, 9, -11, -8, 7, -12, 8, -8, -3, -6, 14, -16, 4, 2, 2, -6, 4, 12, -18, 13, 3, -15, -5, -6, -16, -12, -22, 9, 4, 15, 0, -18, 12, -2, -2, 22, 7, -13, -28, 14, 14, 9, -16, -2, -2, -27, 23, -8, -13, -30, 10, 20, -5, -30, -15, 12, 2, -25, -10, -8, 32, -25, 0, -31, 24, -20, -20, 12, 37, -26, -31, 25, 0, 3, 18, 0, 35, 24, -11, -6, -16, 24, -21, -21, -36, 45, 10, 37, -18, -32, 38, 33, -37, -18, 7, -48, -38, -26, 24, 8, -2, -6, -1, 40, 40, 9, -6, 7, 22, 23, -42, 22, 7, 40, -30, -47, -47, -28, -38, 54, 49, 32, 4, 34, -7, 18, 54, -56, -31, 34, 3, 33, 53, -2, -38, -48, -2, -7, -8, 17, 18, -37, -38, -12, -12, -23, 2, 38, -32, 37, -3, -41, 44, -5, 0, 43, -12, 17, 37, -21, -6, 38, 23, 49, -16, 62, -38, 62, -3, -31, -31, -52, 3, 39, 49, -48, 52, -25, -60, -46, -21, 45, 0, -63, 62, 63, 18, 4, -6, -40, 40, -10, -50, 49, -66, -2, -12, 70, 0, -17, 23, -6, 54, -20, 20, -32, 3, 60, -15, 34, -11, 57, 57, 10, -50, 44, 14, -30, 20, -13, 12, -72, -32, -21, 14, 62, 62, -7, -37, -2, 18, 10, -70, -16, 29, -15, -50, -32, -12, -32, 33, 83, 18, -28, -43, 54, 14, -28, 37, 53, 43, -5, -23, -28, -37, -12, 2, 12, 49, 39, -40, 15, 12, 22, -53, -33, -65, 30, -60, 35, -27, 73, 34, 4, -66, 29, -73, 52, 48, -2, -2, 13, -60, 20, 54, 54, -35, 75, -51, 24, -10, 5, 12, -28, -22, -2, 42, 52, 79, 74, 25, 0, 10, 38, -12, -60, 40, -11, -56, 30, 10, 24, 69, 43, 13, -21, 69, -2, 48, 75, -30, 72, -68, -66, 4, 8, -37, -28, 12, 77, 67, -42, -2, -28, 52, -11, -31, -91, 54, 42, 12, 24, -1, -78, 82, 58, 28, -46, -26, -52, 33, -13, 42, 72, 12, 28, -72, -46, -66, -40, 55, 83, 38, 84, 34, -35, 65, -58, 47, -55, 15, 35, 30, 37, 72, 0, -80, 2, -53, -70, 70, -36, -56, -45, 0, 62, -8, 43, 33, 99, 44, -11, -16, -36, -46, -80, 40, 98, -2, -72, 48, 0, -50, -41, 24, 75, -15, 70, 25, -53, 42, 68, -32, 20, -40, -70, -65, 62, -28, -41, -21, -12, -32, 7, -18, -80, 50, 38, -22, 42, -83, 42, -48, 49, 4, 48, -112, -40, -65, -38, 52, -8, 62, -77, 68, 18, 23, -93, -8, 49, 64, -30, 30, 108, 68, -36, -6, -70, -65, -58, -68, 55, -5, -28, -87, -92, 108, 8, 90, -55, -41, 84, 2, 77, -22, -82, 40, 10, -66, -46, -41, 29, 64, -56, -36, 54, -15, -20, -38, 22, 34, 34, 53, 3, 68, -62, -45, 70, 0, 95, -46, 4, -22, -12, 10, 15, 0, -90, 78, -42, -6, 29, 2, -68, 19, -61, -88, -48, 38, -52, 9, -41, 72, -43, 4, 64, 73, -57, 50, -80, 89, 44, -36, -16, -15, -60, -108, 17, -12, -92, -67, -67, 92, -58, 114, -66, -60, -80, -22, -7, -70, 95, -62, -102, 12, -78, -100, -125, -90, 5, -108, 12, -33, 42, -40, -80, 72, -103, -90, 60, 73, -72, 38, -92, -32, 58, 50, -80, -6, -106, 17, -38, 48, -32, -28, -43, 23, -42, -18, -118, 4, 19, 108, -12, 45, 80, -12, 3, -15, 100, -32, -42, -36, -56, -12, 38, -26, 9, 112, -58, -102, 38, -40, 75, 19, -76, -62, 118, -61, -41, 82, -23, 79, 79, 102, -98, 64, -6, 87, -53, 80, 0, 34, 49, -17, 48, -35, -45, 9, -6, 15, -90, -98, -108, 94, 14, 85, -35, -55, -75, 58, -17, 69, -36, -53, 72, -5, 130, -120, 10, -15, -75, 52, -48, -128, 72, -140, -125, -88, -18, 30, 30, -58, -93, -112, -27, -40, -60, -96, 54, -127, -132, -27, -47, 12, 12, 114, -6, -27, -102, 74, -71, 50, 70, -56, -136, -78, 102, -70, -60, 18, -2, 104, 24, -93, -43, 124, 94, -103, 52, 108, 93, -111, -36, 104, 94, -72, 108, -25, 125, -78, 122, -67, 88, -108, 32, -142, -122, 29, 79, 140, -90, 82, -18, -2, -117, -46, 24, 60, -115, -63, 17, 78, -102, -20, 80, -38, -73, 68, -22, -75, -10, -71, -21, -48, 152, 132, -118, 48, 48, -125, -10, -76, -31, 40, 60, 119, 44, 132, -18, 8, 28, 43, -52, -120, 90, 109, -56, 33, 73, 48, 8, 129, -61, 125, 0, 75, -60, 9, -56, 132, 22, -26, 24, 118, 108, 27, 12, -83, 78, -112, -107, 88, -15, -140, -3, -133, 44, 24, 70, -55, -97, 98, -52, -27, 143, -82, 108, -122, -120, 0, 82, -13, -25, -50, -38, 42, -88, 87, -58, -43, 70, 5, 97, -23, 120, 15, -93, -118, -75, 5, 48, -32, 58, -42, -30, -5, 5, 85, -71, -46, 75, -10, 152, -63, 119, -106, -78, 72, -36, 19, -80, 70, 58, -12, -81, 64, -15, -65, 48, -2, -88, -108, 158, -92, 108, -72, -10, 85, 18, 73, 97, 47, 4, -121, -28, 82, 18, -92, 32, 132, 94, -151, 124, 94, 90, 95, 119, 149, -120, 0, 7, -38, -33, 72, -87, 78, 14, 49, -125, -130, 50, 105, -57, -122, 68, 123, -91, 109, 75, -70, 22, 122, -88, 17, 22, 147, -120, -75, -46, 54, -13, -93, -22, 103, -81, 54, -60, 95, -16, 74, 0, 80, -112, -22, -52, -132, 85, 80, 102, 32, -6, 24, -77, -57, -145, 150, -38, -123, 118, -77, -33, 17, 160, 120, 48, -137, -91, -106, 62, 132, 34, -66, 14, -111, -72, -102, -150, -150, -3, 87, 14, -111, 28, 43, -126, -66, 18, 78, 145, 90, -72, -127, -33, 28, -2, 18, 88, 84, 119, -170, -80, -142, 103, 90, 140, -58, -138, 15, 35, 7, -138, -112, 28, -8, -93, -78, -153, 100, 60, -146, -151, -31, 84, 114, -56, 177, 17, -76, -91, 108, -162, -72, 48, -90, -40, -21, 94, -160, 130, 38, 118, -32, 8, -90, 75, 135, -35, -32, 48, -153, 62, -157, -107, 54, -96, 104, -101, -85, 145, 75, 20, 34, 124, -28, -123, 128, 48, 138, 123, -112, -142, 103, 83, -8, -33, -26, -66, 2, -138, 25, 40, -46, -131, 100, 110, 32, -93, 0, 160, -55, -50, 37, 92, 104, -66, 54, -106, -28, -38, -43, 57, 30, -130, 40, -95, 54, 44, 175, 20, 3, 78, -31, -116, -170, 60, -67, -17, 58, 8, -36, -41, -2, 128, 55, -100, 179, 9, -73, -23, -167, -2, -140, 170, 42, 92, -2, -87, 13, -82, 182, 42, 39, 9, -78, 112, 84, -96, 172, -18, 82, -38, 158, 18, -136, 129, -55, -11, 64, 100, 0, 112, 47, -78, 177, 163, -67, -53, -8, -91, 4, -90, 120, -32, 118, -73, 87, 75, 80, 0, -30, 77, -143, 165, 20, -88, -18, -67, -102, -130, -140, 40, 40, -150, -60, 82, 62, -190, -115, -46, 14, 130, -140, -91, 49, 84, -91, 100, -30, -82, 13, -128, 97, -76, -176, 0, 50, -20, -80, -141, -46], 'hecke_polynomial': 'x', 'label': '2.2.77.1-44.1-d'}
• 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
  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[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  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': [-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_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 8.774964387392123, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.77.1', 'local_algs': ['7.1.2.1a1.2', '11.1.2.1a1.1'], 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, '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']}