Hilbert modular form data - 3.3.49.1-127.2-a

Formats: - HTML - YAML - JSON - 2025-12-18T10:21:18.943935

• 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': 49, 'field_bad_primes': [7], 'field_label': '3.3.49.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.49.1-127.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [127], 'level_ideal': '[127,127,-2*w^2 + 2*w - 3]', 'level_label': '127.2', 'level_norm': 127, 'parallel_weight': 2, 'short_label': '127.2-a', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[127,127,-2*w^2 + 2*w - 3]', -1]], 'hecke_eigenvalues': [2, -3, 2, 2, -4, -2, -6, 6, 0, 6, 6, 0, -4, -4, -10, 0, -12, 0, 12, -12, -18, 8, 2, 2, 0, 18, 12, 18, -16, 1, -16, 8, -16, 14, 12, 12, 18, -10, 2, 2, 18, -12, 24, 20, 20, -4, 2, 8, 8, -6, 6, -6, -24, 24, -12, 6, 6, 0, 18, -6, 6, -28, 20, -28, 14, -10, -16, -28, -10, 8, -16, -34, 20, 12, -24, -24, 2, 8, -22, 38, 14, 14, 30, -6, 0, 30, 6, 30, 32, -22, 8, -18, -6, 30, -24, 12, 36, -40, 2, -28, -12, 30, -12, 26, 38, -28, -36, 30, 42, 8, 20, -34, -46, 20, 32, -12, 36, -48, 44, 26, -28, -6, -30, -30, -46, 8, 32, 48, -48, -42, -34, 8, 2, 14, -40, 14, -18, 6, 0, 44, -4, -40, 12, -24, -54, 12, 6, -36, -10, 2, -28, 30, -18, -42, -4, 2, 20, 48, -30, -12, 50, 2, 2, 12, -6, -18, 56, 32, 50], 'hecke_polynomial': 'x', 'label': '3.3.49.1-127.2-a'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 49, 'ideals': ['[1, 1, 1]', '[7, 7, 2*w^2 - w - 3]', '[8, 2, 2]', '[13, 13, -w^2 - w + 3]', '[13, 13, -w^2 + 2*w + 2]', '[13, 13, -2*w^2 + w + 2]', '[27, 3, 3]', '[29, 29, 3*w^2 - 2*w - 4]', '[29, 29, 2*w^2 + w - 4]', '[29, 29, -w^2 + 3*w + 1]', '[41, 41, w^2 - w - 5]', '[41, 41, 2*w^2 - 3*w - 4]', '[41, 41, -3*w^2 + w + 3]', '[43, 43, w^2 + 2*w - 5]', '[43, 43, 2*w^2 + w - 5]', '[43, 43, 3*w^2 - 2*w - 3]', '[49, 7, -w^2 + 3*w + 3]', '[56, 14, 4*w^2 - 2*w - 6]', '[64, 4, 4]', '[71, 71, 4*w^2 - 3*w - 5]', '[71, 71, 3*w^2 - 4*w - 5]', '[71, 71, -4*w^2 + w + 5]', '[83, 83, w^2 + w - 7]', '[83, 83, w^2 - 2*w - 6]', '[83, 83, -3*w^2 - 2*w + 5]', '[91, 91, w^2 - w - 6]', '[91, 91, -w^2 - 3]', '[91, 91, -w + 5]', '[97, 97, 3*w^2 + w - 7]', '[97, 97, 3*w^2 - 4*w - 7]', '[97, 97, 2*w^2 - w - 8]', '[104, 26, -2*w^2 - 2*w + 6]', '[104, 26, -2*w^2 + 4*w + 4]', '[104, 26, -4*w^2 + 2*w + 4]', '[113, 113, 3*w^2 + w - 8]', '[113, 113, 2*w^2 - 4*w - 5]', '[113, 113, 2*w^2 + 2*w - 7]', '[125, 5, -5]', '[127, 127, 2*w^2 - 9]', '[127, 127, -3*w^2 - 2*w + 6]', '[127, 127, -5*w^2 + 3*w + 7]', '[139, 139, 5*w^2 - 4*w - 6]', '[139, 139, 4*w^2 - 5*w - 7]', '[139, 139, -5*w^2 + w + 6]', '[167, 167, w^2 + w - 8]', '[167, 167, 6*w^2 - 4*w - 9]', '[167, 167, -4*w^2 - 2*w + 7]', '[169, 13, -3*w^2 - 2*w + 7]', '[169, 13, -5*w^2 + 3*w + 6]', '[169, 13, -2*w^2 + 5*w + 3]', '[169, 169, -w^2 + w + 7]', '[169, 169, w^2 + 4]', '[169, 169, -w + 6]', '[181, 181, 4*w^2 + w - 9]', '[181, 181, 4*w^2 - 5*w - 9]', '[181, 181, 2*w^2 - w - 9]', '[189, 21, 6*w^2 - 3*w - 9]', '[197, 197, 2*w - 7]', '[197, 197, 3*w^2 - 5*w - 6]', '[197, 197, 2*w^2 - 2*w - 9]', '[203, 203, 5*w^2 - 3*w - 5]', '[203, 203, 3*w^2 + 2*w - 8]', '[203, 203, -2*w^2 + 5*w + 4]', '[211, 211, 3*w^2 - 5*w - 7]', '[211, 211, 2*w^2 + 3*w - 8]', '[211, 211, 4*w^2 + w - 10]', '[216, 6, 6]', '[223, 223, 3*w^2 + 2*w - 9]', '[223, 223, 4*w^2 + w - 11]', '[223, 223, 3*w^2 + 2*w - 10]', '[232, 58, 6*w^2 - 4*w - 8]', '[232, 58, 4*w^2 + 2*w - 8]', '[232, 58, -2*w^2 + 6*w + 2]', '[239, 239, 6*w^2 - 5*w - 7]', '[239, 239, -5*w^2 + 6*w + 9]', '[239, 239, -6*w^2 + w + 7]', '[251, 251, w^2 - 3*w - 8]', '[251, 251, -3*w^2 + 2*w - 3]', '[251, 251, 2*w^2 + w - 11]', '[281, 281, -7*w^2 + 6*w + 9]', '[281, 281, 6*w^2 + w - 11]', '[281, 281, w^2 - 7*w]', '[287, 287, -7*w^2 + w + 16]', '[287, 287, w^2 - 2*w - 8]', '[287, 287, -9*w^2 + 4*w + 16]', '[293, 293, -7*w^2 + 2*w + 10]', '[293, 293, 5*w^2 - 7*w - 7]', '[293, 293, 2*w^2 + 5*w - 6]', '[301, 301, -6*w^2 + 7*w + 10]', '[301, 301, -w^2 - w - 5]', '[301, 301, -2*w^2 + w + 10]', '[307, 307, -3*w^2 + w - 3]', '[307, 307, 2*w^2 - 3*w - 10]', '[307, 307, w^2 + 2*w - 10]', '[328, 82, 2*w^2 - 2*w - 10]', '[328, 82, 4*w^2 - 6*w - 8]', '[328, 82, -6*w^2 + 2*w + 6]', '[337, 337, 7*w^2 - 3*w - 10]', '[337, 337, 7*w^2 - 4*w - 10]', '[337, 337, -4*w^2 - 3*w + 8]', '[343, 7, 7]', '[344, 86, 2*w^2 + 4*w - 10]', '[344, 86, 4*w^2 + 2*w - 10]', '[344, 86, 6*w^2 - 4*w - 6]', '[349, 349, 5*w^2 + w - 15]', '[349, 349, 7*w^2 - 8*w - 11]', '[349, 349, -6*w^2 + 5*w + 2]', '[351, 39, -3*w^2 - 3*w + 9]', '[351, 39, -3*w^2 + 6*w + 6]', '[351, 39, -6*w^2 + 3*w + 6]', '[377, 377, -w - 7]', '[377, 377, -3*w^2 - 3*w + 10]', '[377, 377, w^2 - w + 6]', '[377, 377, 3*w^2 - 6*w - 7]', '[377, 377, 6*w^2 - 3*w - 5]', '[377, 377, -7*w^2 + 5*w + 9]', '[377, 377, -2*w^2 + 7*w + 2]', '[377, 377, -5*w^2 - 2*w + 10]', '[377, 377, w^2 - 9]', '[379, 379, 3*w^2 + 3*w - 11]', '[379, 379, 4*w^2 + 2*w - 11]', '[379, 379, 5*w^2 + w - 14]', '[392, 14, -2*w^2 + 6*w + 6]', '[419, 419, -5*w^2 - 3*w + 9]', '[419, 419, 2*w^2 + w - 12]', '[419, 419, w^2 - 3*w - 9]', '[421, 421, 9*w^2 - 5*w - 15]', '[421, 421, 3*w^2 + 5*w - 7]', '[421, 421, 4*w^2 - w - 15]', '[433, 433, -8*w^2 + 7*w + 10]', '[433, 433, 7*w^2 + w - 13]', '[433, 433, w^2 - 8*w]', '[448, 28, 8*w^2 - 4*w - 12]', '[449, 449, -7*w^2 + 2*w + 8]', '[449, 449, 8*w^2 - 6*w - 11]', '[449, 449, -6*w^2 - 2*w + 11]', '[461, 461, 2*w^2 + 6*w - 7]', '[461, 461, -8*w^2 + 2*w + 11]', '[461, 461, 6*w^2 - 8*w - 9]', '[463, 463, -7*w^2 + 8*w + 12]', '[463, 463, w^2 + 7*w - 7]', '[463, 463, -8*w^2 + w + 10]', '[491, 491, w^2 + 2*w - 11]', '[491, 491, 4*w^2 - 7*w - 7]', '[491, 491, 2*w^2 - 3*w - 11]', '[497, 497, -8*w^2 + w + 20]', '[497, 497, -5*w^2 + 2*w + 17]', '[497, 497, 3*w^2 - 4*w - 13]', '[503, 503, 5*w^2 - 7*w - 10]', '[503, 503, 2*w^2 - 2*w - 11]', '[503, 503, -7*w^2 + 2*w + 7]', '[512, 8, 8]', '[533, 533, 3*w^2 - 2*w - 13]', '[533, 533, 6*w^2 + w - 14]', '[533, 533, 5*w^2 + 2*w - 12]', '[533, 533, -5*w^2 - 3*w + 10]', '[533, 533, 2*w^2 + w + 5]', '[533, 533, 8*w^2 - 5*w - 11]', '[533, 533, 5*w^2 - 7*w - 12]', '[533, 533, 8*w^2 - 3*w - 11]', '[533, 533, -2*w^2 + 7*w + 4]', '[547, 547, 4*w^2 + 3*w - 15]', '[547, 547, -3*w^2 + 10*w]', '[547, 547, -7*w^2 + 4*w + 3]', '[559, 559, 8*w^2 - 7*w - 9]', '[559, 559, -w^2 + w - 7]', '[559, 559, 4*w^2 + 3]', '[559, 559, 4*w - 11]', '[559, 559, 5*w^2 - 9*w - 5]', '[559, 559, 4*w^2 + 3*w - 11]', '[559, 559, -4*w^2 - 5*w + 8]', '[559, 559, 4*w^2 - 8*w - 5]', '[559, 559, -w^2 + 8*w + 1]', '[568, 142, 8*w^2 - 6*w - 10]', '[568, 142, 6*w^2 - 8*w - 10]', '[568, 142, -8*w^2 + 2*w + 10]', '[581, 581, -11*w^2 + 8*w + 18]', '[581, 581, -12*w^2 + 4*w + 21]', '[581, 581, 2*w^2 - 7*w - 8]', '[587, 587, 6*w^2 + w - 17]', '[587, 587, 5*w^2 - 3*w - 17]', '[587, 587, w^2 - 7*w - 6]', '[601, 601, 4*w^2 + 3*w - 14]', '[601, 601, 4*w^2 + 3*w - 12]', '[601, 601, 6*w^2 + w - 16]', '[617, 617, 5*w^2 + 2*w - 14]', '[617, 617, 4*w^2 + 3*w - 13]', '[617, 617, 5*w^2 + 2*w - 15]', '[631, 631, -9*w^2 + 8*w + 11]', '[631, 631, 8*w^2 + w - 15]', '[631, 631, w^2 - 9*w]', '[637, 91, -8*w^2 + 3*w + 10]', '[637, 91, 3*w^2 + 5*w - 9]', '[637, 91, 5*w^2 - 8*w - 8]', '[643, 643, 6*w^2 - 9*w - 8]', '[643, 643, 3*w^2 + 6*w - 8]', '[643, 643, 4*w^2 - w - 16]', '[659, 659, -8*w^2 + 2*w + 9]', '[659, 659, 9*w^2 - 7*w - 12]', '[659, 659, 7*w^2 + 2*w - 13]', '[664, 166, 2*w^2 + 2*w - 14]', '[664, 166, 2*w^2 - 4*w - 12]', '[664, 166, -6*w^2 - 4*w + 10]', '[673, 673, -8*w^2 + 9*w + 14]', '[673, 673, w^2 + 8*w - 8]', '[673, 673, -9*w^2 + w + 11]', '[679, 679, -12*w^2 + 3*w + 26]', '[679, 679, -7*w^2 + 8*w + 16]', '[679, 679, -13*w^2 + 7*w + 24]', '[701, 701, 9*w^2 - 4*w - 13]', '[701, 701, -5*w^2 - 4*w + 10]', '[701, 701, -4*w^2 - 5*w + 9]', '[727, 727, -7*w^2 - 3*w + 12]', '[727, 727, w^2 + 2*w - 12]', '[727, 727, 10*w^2 - 7*w - 15]', '[728, 182, 2*w^2 - 2*w - 12]', '[728, 182, -2*w^2 - 6]', '[728, 182, -2*w + 10]', '[729, 9, 9]', '[743, 743, 5*w^2 - 2*w - 18]', '[743, 743, 4*w^2 - 5*w - 16]', '[743, 743, w^2 + 4*w - 14]', '[757, 757, 11*w^2 - 7*w - 18]', '[757, 757, w^2 + 3*w - 13]', '[757, 757, 3*w^2 + 5*w - 15]', '[769, 769, 2*w^2 - 11*w + 1]', '[769, 769, -10*w^2 + w + 13]', '[769, 769, 9*w^2 + 2*w - 15]', '[776, 194, 6*w^2 + 2*w - 14]', '[776, 194, 6*w^2 - 8*w - 14]', '[776, 194, 4*w^2 - 2*w - 16]', '[783, 87, 9*w^2 - 6*w - 12]', '[783, 87, 6*w^2 + 3*w - 12]', '[783, 87, -3*w^2 + 9*w + 3]', '[791, 791, -9*w^2 + 9*w + 19]', '[791, 791, -8*w^2 + 9*w + 15]', '[791, 791, -10*w^2 + w + 21]', '[797, 797, -8*w^2 + 5*w + 3]', '[797, 797, -3*w^2 + 11*w]', '[797, 797, 5*w^2 + 3*w - 18]', '[811, 811, -9*w^2 + 2*w + 11]', '[811, 811, 7*w^2 - 9*w - 12]', '[811, 811, 9*w^2 - 7*w - 11]', '[827, 827, 3*w^2 + 5*w - 14]', '[827, 827, 5*w^2 + 3*w - 13]', '[827, 827, 8*w^2 - 21]', '[832, 52, -4*w^2 - 4*w + 12]', '[832, 52, -4*w^2 + 8*w + 8]', '[832, 52, -8*w^2 + 4*w + 8]', '[839, 839, -6*w^2 - 4*w + 11]', '[839, 839, w^2 - 4*w - 11]', '[839, 839, 3*w^2 + w - 16]', '[841, 29, 8*w^2 - 3*w - 7]', '[841, 29, -5*w^2 + 8*w + 11]', '[841, 29, 3*w^2 + 5*w - 12]', '[841, 841, -4*w^2 + 9*w + 5]', '[841, 841, 5*w^2 + 4*w - 11]', '[841, 841, 9*w^2 - 5*w - 12]', '[853, 853, -8*w^2 + 7*w + 3]', '[853, 853, 7*w^2 + w - 20]', '[853, 853, w^2 - 8*w - 7]', '[875, 35, -10*w^2 + 5*w + 15]', '[881, 881, -10*w^2 + 9*w + 12]', '[881, 881, 9*w^2 + w - 17]', '[881, 881, w^2 - 10*w]', '[883, 883, 7*w^2 + w - 18]', '[883, 883, -8*w^2 + 5*w + 4]', '[883, 883, 5*w^2 + 3*w - 17]', '[889, 889, 4*w^2 - 8*w - 11]', '[889, 889, -14*w^2 + 9*w + 25]', '[889, 889, -3*w^2 + 8*w + 7]', '[904, 226, 6*w^2 + 2*w - 16]', '[904, 226, 4*w^2 - 8*w - 10]', '[904, 226, 4*w^2 + 4*w - 14]', '[911, 911, 10*w^2 - 7*w - 14]', '[911, 911, 2*w^2 + w - 14]', '[911, 911, -7*w^2 - 3*w + 13]', '[923, 923, w^2 + w - 12]', '[923, 923, 10*w^2 - 8*w - 13]', '[923, 923, 6*w^2 + 2*w - 17]', '[923, 923, w^2 + 3*w + 8]', '[923, 923, 7*w^2 - 10*w - 10]', '[923, 923, 5*w^2 + 3*w - 15]', '[923, 923, -8*w^2 - 2*w + 15]', '[923, 923, 4*w^2 - w - 17]', '[923, 923, -3*w^2 + 8*w + 8]', '[937, 937, -9*w^2 + 10*w + 16]', '[937, 937, w^2 + 9*w - 9]', '[937, 937, -10*w^2 + w + 12]', '[953, 953, 9*w^2 - 7*w - 10]', '[953, 953, -10*w^2 + 2*w + 13]', '[953, 953, 8*w^2 - 10*w - 13]', '[967, 967, 2*w^2 + 2*w - 15]', '[967, 967, 11*w^2 - 7*w - 17]', '[967, 967, -7*w^2 - 4*w + 12]', '[973, 973, -11*w^2 + 2*w + 27]', '[973, 973, -6*w^2 + 2*w + 21]', '[973, 973, 3*w^2 - 5*w - 15]', '[1000, 10, -10]', '[1009, 1009, 2*w^2 - 11*w]', '[1009, 1009, 9*w^2 + 2*w - 16]', '[1009, 1009, -11*w^2 + 9*w + 15]', '[1016, 254, 4*w^2 - 18]', '[1016, 254, -6*w^2 - 4*w + 12]', '[1016, 254, -10*w^2 + 6*w + 14]', '[1021, 1021, 10*w^2 - w - 23]', '[1021, 1021, -8*w^2 - 3*w + 14]', '[1021, 1021, 11*w^2 - 8*w - 16]', '[1049, 1049, 4*w^2 + w - 19]', '[1049, 1049, w^2 - 5*w - 12]', '[1049, 1049, -5*w^2 + 4*w - 5]', '[1051, 1051, 3*w^2 + 8*w - 9]', '[1051, 1051, -11*w^2 + 3*w + 16]', '[1051, 1051, 8*w^2 - 11*w - 11]', '[1063, 1063, -11*w^2 + w + 14]', '[1063, 1063, 10*w^2 + 2*w - 17]', '[1063, 1063, 2*w^2 - 12*w + 1]', '[1079, 1079, 10*w^2 - 9*w - 11]', '[1079, 1079, 9*w^2 + w - 18]', '[1079, 1079, w^2 + 9*w + 3]', '[1079, 1079, 4*w^2 + 5*w - 18]', '[1079, 1079, 2*w^2 + 2*w + 7]', '[1079, 1079, 5*w^2 - 9*w - 15]', '[1079, 1079, 9*w^2 - 11*w - 14]', '[1079, 1079, -10*w^2 + w + 11]', '[1079, 1079, 11*w^2 - 2*w - 15]', '[1091, 1091, w^2 + 4*w - 15]', '[1091, 1091, 3*w^2 + 6*w - 16]', '[1091, 1091, 8*w^2 - 12*w - 9]', '[1093, 1093, 3*w^2 - 16]', '[1093, 1093, 7*w^2 - 10*w - 11]', '[1093, 1093, 10*w^2 - 7*w - 13]', '[1107, 123, 3*w^2 - 3*w - 15]', '[1107, 123, 6*w^2 - 9*w - 12]', '[1107, 123, -9*w^2 + 3*w + 9]', '[1112, 278, 10*w^2 - 8*w - 12]', '[1112, 278, 8*w^2 - 10*w - 14]', '[1112, 278, -10*w^2 + 2*w + 12]', '[1161, 129, 3*w^2 + 6*w - 15]', '[1161, 129, 6*w^2 + 3*w - 15]', '[1161, 129, 9*w^2 - 6*w - 9]', '[1163, 1163, 2*w^2 - 9*w - 10]', '[1163, 1163, 7*w^2 + 2*w - 22]', '[1163, 1163, -9*w^2 + 7*w + 3]', '[1169, 1169, 4*w^2 - 9*w - 13]', '[1169, 1169, -10*w^2 + 5*w + 29]', '[1169, 1169, -13*w^2 + 9*w + 21]', '[1183, 91, 7*w^2 + 2*w - 17]', '[1183, 91, -9*w^2 + 7*w + 8]', '[1183, 91, 2*w^2 - 9*w - 5]', '[1183, 1183, 4*w^2 + 6*w - 11]', '[1183, 1183, 10*w^2 - 4*w - 13]', '[1183, 1183, -6*w^2 + 10*w + 9]', '[1189, 1189, w^2 - w - 12]', '[1189, 1189, -9*w^2 + 23]', '[1189, 1189, 4*w^2 - 9*w - 8]', '[1189, 1189, -9*w - 5]', '[1189, 1189, -11*w^2 + 4*w + 16]', '[1189, 1189, -13*w^2 + 7*w + 22]', '[1189, 1189, -4*w^2 - 7*w + 10]', '[1189, 1189, -10*w^2 - w + 19]', '[1189, 1189, w - 11]', '[1217, 1217, 3*w^2 + 2*w - 18]', '[1217, 1217, 12*w^2 - 5*w - 19]', '[1217, 1217, 2*w^2 - 5*w - 14]', '[1231, 1231, 6*w^2 + 3*w - 20]', '[1231, 1231, 8*w^2 + w - 20]', '[1231, 1231, -9*w^2 + 6*w + 4]', '[1247, 1247, -w^2 - w + 13]', '[1247, 1247, 2*w^2 + 8*w - 11]', '[1247, 1247, -2*w^2 - w + 15]', '[1247, 1247, 10*w^2 - 12*w - 5]', '[1247, 1247, -10*w^2 + 13*w + 13]', '[1247, 1247, -2*w^2 - 10*w - 1]', '[1247, 1247, -3*w^2 - 10*w + 9]', '[1247, 1247, -2*w^2 + w - 8]', '[1247, 1247, -3*w^2 + 9*w + 7]', '[1259, 1259, -9*w^2 + 7*w + 4]', '[1259, 1259, 7*w^2 + 2*w - 18]', '[1259, 1259, 7*w^2 + 2*w - 21]', '[1261, 1261, 9*w^2 + w - 19]', '[1261, 1261, 9*w^2 - 10*w - 19]', '[1261, 1261, 8*w^2 + w - 21]', '[1261, 1261, 4*w^2 - 9*w - 9]', '[1261, 1261, 6*w^2 - 5*w - 21]', '[1261, 1261, 12*w^2 - 6*w - 19]', '[1261, 1261, 11*w^2 - 5*w - 16]', '[1261, 1261, 2*w^2 - w - 14]', '[1261, 1261, 11*w^2 - 6*w - 16]', '[1267, 1267, -9*w^2 + 10*w + 21]', '[1267, 1267, -15*w^2 + 8*w + 27]', '[1267, 1267, -15*w^2 + 4*w + 33]', '[1289, 1289, 10*w^2 - 8*w - 11]', '[1289, 1289, 9*w^2 - 11*w - 15]', '[1289, 1289, -11*w^2 + 2*w + 14]', '[1301, 1301, 6*w^2 + 3*w - 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36]', '[9869, 9869, -21*w^2 + 23*w + 36]', '[9869, 9869, 10*w^2 - w - 41]', '[9869, 9869, -24*w^2 + 19*w + 34]', '[9869, 9869, 19*w^2 + 5*w - 33]', '[9871, 9871, 24*w^2 - 17*w - 36]', '[9871, 9871, -17*w^2 - 7*w + 29]', '[9871, 9871, 21*w^2 - 2*w - 49]', '[9883, 9883, 9*w^2 - 2*w - 38]', '[9883, 9883, 7*w^2 + 15*w - 20]', '[9883, 9883, 15*w^2 - 22*w - 21]', '[9941, 9941, 18*w^2 + 6*w - 31]', '[9941, 9941, -19*w^2 + 6*w + 20]', '[9941, 9941, 24*w^2 - 18*w - 35]', '[9947, 203, 21*w^2 - 14*w - 28]', '[9947, 203, 14*w^2 + 7*w - 28]', '[9947, 203, -7*w^2 + 21*w + 7]', '[9967, 9967, -21*w^2 + 2*w + 23]', '[9967, 9967, 19*w^2 + 2*w - 38]', '[9967, 9967, 21*w^2 - 19*w - 23]', '[9976, 2494, -2*w^2 - 2*w + 26]', '[9976, 2494, 4*w^2 + 16*w - 22]', '[9976, 2494, -4*w^2 - 2*w + 30]', '[9976, 2494, 20*w^2 - 24*w - 10]', '[9976, 2494, -20*w^2 + 26*w + 26]', '[9976, 2494, -4*w^2 - 20*w - 2]', '[9976, 2494, -6*w^2 - 20*w + 18]', '[9976, 2494, -4*w^2 + 2*w - 16]', '[9976, 2494, -6*w^2 + 18*w + 14]', '[9989, 9989, 13*w^2 - 14*w - 45]', '[9989, 9989, -5*w^2 + 19*w + 9]', '[9989, 9989, -20*w^2 + w + 54]', '[9997, 9997, 26*w^2 - 3*w - 37]', '[9997, 9997, w^2 - 19*w - 17]', '[9997, 9997, 19*w^2 - 18*w - 4]', '[9997, 9997, -22*w^2 - 4*w + 37]', '[9997, 9997, 2*w^2 - 10*w - 25]', '[9997, 9997, 3*w^2 + 11*w + 18]', '[9997, 9997, -10*w^2 + 8*w - 11]', '[9997, 9997, 3*w^2 + 23*w - 18]', '[9997, 9997, -5*w^2 + 18*w + 20]'], 'label': '3.3.49.1', 'narrow_class_no': 1, 'primes': ['[7, 7, 2*w^2 - w - 3]', '[8, 2, 2]', '[13, 13, -w^2 - w + 3]', '[13, 13, -w^2 + 2*w + 2]', '[13, 13, -2*w^2 + w + 2]', '[27, 3, 3]', '[29, 29, 3*w^2 - 2*w - 4]', '[29, 29, 2*w^2 + w - 4]', '[29, 29, -w^2 + 3*w + 1]', '[41, 41, w^2 - w - 5]', '[41, 41, 2*w^2 - 3*w - 4]', '[41, 41, -3*w^2 + w + 3]', '[43, 43, w^2 + 2*w - 5]', '[43, 43, 2*w^2 + w - 5]', '[43, 43, 3*w^2 - 2*w - 3]', '[71, 71, 4*w^2 - 3*w - 5]', '[71, 71, 3*w^2 - 4*w - 5]', '[71, 71, -4*w^2 + w + 5]', '[83, 83, w^2 + w - 7]', '[83, 83, w^2 - 2*w - 6]', '[83, 83, -3*w^2 - 2*w + 5]', '[97, 97, 3*w^2 + w - 7]', '[97, 97, 3*w^2 - 4*w - 7]', '[97, 97, 2*w^2 - w - 8]', '[113, 113, 3*w^2 + w - 8]', '[113, 113, 2*w^2 - 4*w - 5]', '[113, 113, 2*w^2 + 2*w - 7]', '[125, 5, -5]', '[127, 127, 2*w^2 - 9]', '[127, 127, -3*w^2 - 2*w + 6]', '[127, 127, -5*w^2 + 3*w + 7]', '[139, 139, 5*w^2 - 4*w - 6]', '[139, 139, 4*w^2 - 5*w - 7]', '[139, 139, -5*w^2 + w + 6]', '[167, 167, w^2 + w - 8]', '[167, 167, 6*w^2 - 4*w - 9]', '[167, 167, -4*w^2 - 2*w + 7]', '[181, 181, 4*w^2 + w - 9]', '[181, 181, 4*w^2 - 5*w - 9]', '[181, 181, 2*w^2 - w - 9]', '[197, 197, 2*w - 7]', '[197, 197, 3*w^2 - 5*w - 6]', '[197, 197, 2*w^2 - 2*w - 9]', '[211, 211, 3*w^2 - 5*w - 7]', '[211, 211, 2*w^2 + 3*w - 8]', '[211, 211, 4*w^2 + w - 10]', '[223, 223, 3*w^2 + 2*w - 9]', '[223, 223, 4*w^2 + w - 11]', '[223, 223, 3*w^2 + 2*w - 10]', '[239, 239, 6*w^2 - 5*w - 7]', '[239, 239, -5*w^2 + 6*w + 9]', '[239, 239, -6*w^2 + w + 7]', '[251, 251, w^2 - 3*w - 8]', '[251, 251, -3*w^2 + 2*w - 3]', '[251, 251, 2*w^2 + w - 11]', '[281, 281, -7*w^2 + 6*w + 9]', '[281, 281, 6*w^2 + w - 11]', '[281, 281, w^2 - 7*w]', '[293, 293, -7*w^2 + 2*w + 10]', '[293, 293, 5*w^2 - 7*w - 7]', '[293, 293, 2*w^2 + 5*w - 6]', '[307, 307, -3*w^2 + w - 3]', '[307, 307, 2*w^2 - 3*w - 10]', '[307, 307, w^2 + 2*w - 10]', '[337, 337, 7*w^2 - 3*w - 10]', '[337, 337, 7*w^2 - 4*w - 10]', '[337, 337, -4*w^2 - 3*w + 8]', '[349, 349, 5*w^2 + w - 15]', '[349, 349, 7*w^2 - 8*w - 11]', '[349, 349, -6*w^2 + 5*w + 2]', '[379, 379, 3*w^2 + 3*w - 11]', '[379, 379, 4*w^2 + 2*w - 11]', '[379, 379, 5*w^2 + w - 14]', '[419, 419, -5*w^2 - 3*w + 9]', '[419, 419, 2*w^2 + w - 12]', '[419, 419, w^2 - 3*w - 9]', '[421, 421, 9*w^2 - 5*w - 15]', '[421, 421, 3*w^2 + 5*w - 7]', '[421, 421, 4*w^2 - w - 15]', '[433, 433, -8*w^2 + 7*w + 10]', '[433, 433, 7*w^2 + w - 13]', '[433, 433, w^2 - 8*w]', '[449, 449, -7*w^2 + 2*w + 8]', '[449, 449, 8*w^2 - 6*w - 11]', '[449, 449, -6*w^2 - 2*w + 11]', '[461, 461, 2*w^2 + 6*w - 7]', '[461, 461, -8*w^2 + 2*w + 11]', '[461, 461, 6*w^2 - 8*w - 9]', '[463, 463, -7*w^2 + 8*w + 12]', '[463, 463, w^2 + 7*w - 7]', '[463, 463, -8*w^2 + w + 10]', '[491, 491, w^2 + 2*w - 11]', '[491, 491, 4*w^2 - 7*w - 7]', '[491, 491, 2*w^2 - 3*w - 11]', '[503, 503, 5*w^2 - 7*w - 10]', '[503, 503, 2*w^2 - 2*w - 11]', '[503, 503, -7*w^2 + 2*w + 7]', '[547, 547, 4*w^2 + 3*w - 15]', '[547, 547, -3*w^2 + 10*w]', '[547, 547, -7*w^2 + 4*w + 3]', '[587, 587, 6*w^2 + w - 17]', '[587, 587, 5*w^2 - 3*w - 17]', '[587, 587, w^2 - 7*w - 6]', '[601, 601, 4*w^2 + 3*w - 14]', '[601, 601, 4*w^2 + 3*w - 12]', '[601, 601, 6*w^2 + w - 16]', '[617, 617, 5*w^2 + 2*w - 14]', '[617, 617, 4*w^2 + 3*w - 13]', '[617, 617, 5*w^2 + 2*w - 15]', '[631, 631, -9*w^2 + 8*w + 11]', '[631, 631, 8*w^2 + w - 15]', '[631, 631, w^2 - 9*w]', '[643, 643, 6*w^2 - 9*w - 8]', '[643, 643, 3*w^2 + 6*w - 8]', '[643, 643, 4*w^2 - w - 16]', '[659, 659, -8*w^2 + 2*w + 9]', '[659, 659, 9*w^2 - 7*w - 12]', '[659, 659, 7*w^2 + 2*w - 13]', '[673, 673, -8*w^2 + 9*w + 14]', '[673, 673, w^2 + 8*w - 8]', '[673, 673, -9*w^2 + w + 11]', '[701, 701, 9*w^2 - 4*w - 13]', '[701, 701, -5*w^2 - 4*w + 10]', '[701, 701, -4*w^2 - 5*w + 9]', '[727, 727, -7*w^2 - 3*w + 12]', '[727, 727, w^2 + 2*w - 12]', '[727, 727, 10*w^2 - 7*w - 15]', '[743, 743, 5*w^2 - 2*w - 18]', '[743, 743, 4*w^2 - 5*w - 16]', '[743, 743, w^2 + 4*w - 14]', '[757, 757, 11*w^2 - 7*w - 18]', '[757, 757, w^2 + 3*w - 13]', '[757, 757, 3*w^2 + 5*w - 15]', '[769, 769, 2*w^2 - 11*w + 1]', '[769, 769, -10*w^2 + w + 13]', '[769, 769, 9*w^2 + 2*w - 15]', '[797, 797, -8*w^2 + 5*w + 3]', '[797, 797, -3*w^2 + 11*w]', '[797, 797, 5*w^2 + 3*w - 18]', '[811, 811, -9*w^2 + 2*w + 11]', '[811, 811, 7*w^2 - 9*w - 12]', '[811, 811, 9*w^2 - 7*w - 11]', '[827, 827, 3*w^2 + 5*w - 14]', '[827, 827, 5*w^2 + 3*w - 13]', '[827, 827, 8*w^2 - 21]', '[839, 839, -6*w^2 - 4*w + 11]', '[839, 839, w^2 - 4*w - 11]', '[839, 839, 3*w^2 + w - 16]', '[853, 853, -8*w^2 + 7*w + 3]', '[853, 853, 7*w^2 + w - 20]', '[853, 853, w^2 - 8*w - 7]', '[881, 881, -10*w^2 + 9*w + 12]', '[881, 881, 9*w^2 + w - 17]', '[881, 881, w^2 - 10*w]', '[883, 883, 7*w^2 + w - 18]', '[883, 883, -8*w^2 + 5*w + 4]', '[883, 883, 5*w^2 + 3*w - 17]', '[911, 911, 10*w^2 - 7*w - 14]', '[911, 911, 2*w^2 + w - 14]', '[911, 911, -7*w^2 - 3*w + 13]', '[937, 937, -9*w^2 + 10*w + 16]', '[937, 937, w^2 + 9*w - 9]', '[937, 937, -10*w^2 + w + 12]', '[953, 953, 9*w^2 - 7*w - 10]', '[953, 953, -10*w^2 + 2*w + 13]', '[953, 953, 8*w^2 - 10*w - 13]', '[967, 967, 2*w^2 + 2*w - 15]', '[967, 967, 11*w^2 - 7*w - 17]', '[967, 967, -7*w^2 - 4*w + 12]']}
• 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': [1, -2, -1, 1], 'conductor': 7, 'degree': 3, 'dirichlet_group': [1, 2, 4], 'disc_abs': 49, 'disc_rad': 7, 'disc_sign': 1, 'frobs': [[2, [[3, 1]]], [3, [[3, 1]]], [5, [[3, 1]]], [7, [0]], [11, [[3, 1]]], [13, [[1, 3]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[3, 1]]], [29, [[1, 3]]], [31, [[3, 1]]], [37, [[3, 1]]], [41, [[1, 3]]], [43, [[1, 3]]], [47, [[3, 1]]], [53, [[3, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2], 'galois_label': '3T1', 'galt': 1, 'grd': 3.6593057100229713, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.49.1', 'local_algs': ['7.1.3.2a1.1'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 0, 'ramps': [7], 'rd': 3.65930571002, 'regulator': {'__RealLiteral__': 0, 'data': '0.525454682123', 'prec': 47}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 2 \\)', '\\( a^{2} - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}