Hilbert modular form data - 2.2.33.1-539.1-e

Formats: - HTML - YAML - JSON - 2023-10-04T19:48:24.049627

• 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': 33, 'field_bad_primes': [3, 11], 'field_label': '2.2.33.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.33.1-539.1-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [7, 11], 'level_ideal': '[539, 77, -28*w + 91]', 'level_label': '539.1', 'level_norm': 539, 'parallel_weight': 2, 'short_label': '539.1-e', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[11, 11, 4*w - 13]', 1], ['[49, 7, -7]', -1]], 'hecke_eigenvalues': [-1, -1, 2, -1, -4, -4, -6, 6, 6, 10, 10, -6, -6, -4, -4, 1, 8, 8, 0, 0, -10, -10, 4, 4, 14, 14, -12, -12, -12, -12, 10, 10, 14, 14, -8, -8, 0, 0, -10, -12, -12, 10, 10, -22, -22, -18, -18, 22, 22, -12, -12, 18, 18, 18, 18, 0, 0, -8, -8, -6, -6, 24, 24, 2, 2, -20, -20, -4, -4, -16, -16, -38, 22, 22, -8, -8, 22, 22, -14, -14, 0, 0, -26, -26, 0, 0, 4, 4, 4, 4, -28, -28, -28, -28, -16, -16, -4, -4, -30, -22, -22, 32, 32, -30, -30, -18, -18, -32, -32, 14, 14, -8, -8, 14, 14, -4, -4, 22, 22, 12, 12, -46, -46, 22, 22, -34, -34, 18, 18, 8, 8, -20, -20, -10, -10, -48, -48, 30, 30, -46, -46, 24, 24, 28, 28, -2, -2, -56, -56, 6, 6, 28, 28, 28, 28, 0, 0, 24, 24, -34, -34, 52, 52, 52, 52, 22, 22, 16, 16, -34, -34, 8, 8, 64, 64, 6, 6, -12, -12, -18, -18, -8, -8, 14, 14, 20, 20, -24, -24, 60, 60, 34, 34, 48, 48, 28, 28, -30, -30, -30, -30, -18, -18, -60, -60, -42, -42, -14, -14, -24, -24, 60, 60, -70, -70, 24, 24, -64, -64, 12, 12, -52, -52, -14, -14, -50, -50, 70, 70, -28, -28, 6, 6, 66, 66, -54, -54, -54, -54, 44, 44, -48, -48, -46, -46, 8, 8, 64, 64, 2, 2, 0, 0, -76, -76, -38, -38, 36, 36, -26, -26, -66, -66, 62, 62, 48, 48, -26, -26, -34, -34, 48, 48, -16, -16, -4, -4, -20, -20, 58, -18, -18, -78, -78, -74, -74, 68, 68, -6, -6, 48, 48, -32, -32, 82, 82, -48, -48, 6, 6, -16, -16, 46, 46, 54, 54, -72, -72, -6, -6, -4, -4, -72, -72, -40, -40, -50, -50, -62, -62, -14, -14, 40, 40, 8, 8, -10, -10, 50, 50, -48, -48, 62, 62, 24, 24, 6, -34, -34, -64, -64, -14, -14, -76, -76, -38, -38, -10, -10, 60, 60, 8, 8, 20, 20, 58, 58, 56, 56, -24, -24, -18, -18, -84, -84, 28, 28, 22, 22, 12, 12, 44, 44, -18, -18, 22, 22, 36, 36, 42, 42, 8, 8, 98, 98, -38, -38, 16, 16, -84, -84, -50, -50, -96, -96, -34, -34, -82, -82, -26, -26, -56, -56, -2, -2, -28, -28, 78, 78, 62, 62, 98, 98, -70, 38, 38, -32, -32, -54, -54, 96, 96, -52, -52, 58, 58, -94, -94, 34, 34, 20, 20, 18, 18, 28, 28, 52, 52, -98, -98, 70, 70, 16, 16, 24, 24, 46, 46, -24, -24, 30, 30, 60, 60, 28, 28, -58, -58, 60, 60, 108, 108, -36, -36, -52, -52, 86, 86, -14, -14, -34, -34, 14, 14, -96, -96, 42, 42, 68, 68, -54, -54, 32, 32, 18, 18, -92, -92, 50, 50, -114, -26, -26, 12, 12, -74, -74, 72, 72, 4, 4, -46, -46, -74, -74, 62, 62, -2, -2, 86, 86, 0, 0, -48, -48, -106, -106, -122, -70, -70, -18, -18, 70, 70, -60, -60, 22, 22, 64, 64, 76, 76, 50, 50, 36, 36, -38, -38, 84, 84, 90, 90, 48, 48, -66, -66, -16, -16, 36, 36, -84, -84, 6, 6, 124, 124, -102, -102, -86, -86, -20, -20, -14, -14, 0, 0, -22, -22, 8, 8, -108, -108, -56, -56, -92, -92, 94, 94, -100, -100, 82, 82, -14, -14, -108, -108, 28, 28, -74, -74, 42, 42, -84, -84, 96, 96, 102, 102, 18, 18, 58, 58, 32, 32, 96, 96, -84, -84, 72, 72, 26, 26, -38, -38, 104, 104, 108, 108, -48, -48, -38, -38, 104, 104, -10, -10, 0, 0, -118, -118, 98, 98, -2, -2, 84, 84, -112, -112, -66, -66, 36, 36, 64, 64, -56, -56, 86, 86, -24, -24, 86, 86, 30, 30, -110, -110, -84, -84, -74, -74, 96, 96, 40, 40, -74, -74, 64, 64, 2, 60, 60, 24, 24, 4, 4, 4, 4, -34, -34, 24, 24, -12, -12, -30, -30, -46, -46, 26, 26, -24, -24, 16, 16, 54, 54, -104, -104, 20, 20, -82, 62, 62, 36, 36, 20, 20, 50, 50, -86, -86, -78, -78, 64, 64, -14, -14, -56, -56, 10, 10, 136, 136, 60, 60, 108, 108, 32, 32, -58, -58, 22, 22, -50, -50, 120, 120, -10, -10, 50, 50, 60, 60, 10, 10, 14, 14, -130, -130, -12, -12, 36, 36, -22, -22, 46, 46, 16, 16, -104, -104, 32, 32, -40, -40, -20, -20, 96, 96, -26, -26, 82, 82, 72, 72, -64, -64, -76, -76, 48, 48, -112, -112, 18, 18, 148, 148, -36, -36, -26, -26, 52, 52, 30, 30, 118, 118, -74, -74, -82, -82, 68, 68, 44, 44, -88, -88, 14, 14, -94, -78, -78, -2, -2, 96, 96, -48, -48, -50, -50, -96, -96, 50, 50, -142, -142, 18, 18, -108, -108, -74, -74, 68, 68, -140, -140, 38, 38, 20, 20, -76, -76, 104, 104, 134, 134, -4, -4, 94, 94, -2, -2, 90, 90, -88, -88, 14, 14, -68, -68, 68, 68, 130, 130, -146, -146, 156, 156, 26, 26, -78, -78, 140, 140, 84, 84, 84, 84, 120, 120, -46, -46, 80, 80, 32, 32, -130, -130, 24, 24, -34, -34, 0, 0, 60, 60, 24, 24, 74, 74, 42, 42, 38, 38, 18, 18, 60, 60, 28, 28, 104, 104, -18, -18, 78, 78, 2, 2, 24, 24, 90, 90, 58, 58, -36, -36, 106, 106, -12, -12, 24, 24, 142, 142, 84, 84, 54, 54, -36, -36, 62, 62, 90, 90, -108, -108, -90, -90, -74, -74, 14, 14, 30, 30, 100, 100, 34, 34, -80, -80, -66, -66, 2, 2, 76, 76, -120, -120, -124, -124, -74, -74, 38, 38, -50, -50, -30, -30, 116, 116, -128, -128, 60, 60, -84, -84, 72, 72, -36, -36, 136, 136, -142, 12, 12, -6, -6, -126, -126, 2, 2, 94, 94, -46, -46, 16, 16, -72, -72, 0, 0, 90, 90, -106, -106, -154, -154, 66, 66, -104, -104, -30, -30, -146, -146, 84, 84, 78, 78, -26, -26, 126, 126, 168, 168, 42, 42, -94, -94, -42, -42, -48, -48, 14, 14, -148, -148, -162, -162, 34, 34, -24, -24, -40, -40, 42, 42, 78, 78, -40, -40, -98, -98, 20, 20, -16, -16, -166, -166, 102, 102, -70, -70, -14, -14, -36, -36, -76, -76, -72, -72, 110, 110, -152, -152, 124, 124, 96, 96, 28, 28, 12, 12, -70, -70, 38, 38, -52, -52, 70, 70, 78, 78, 44, 44, -34, -34, 186, 186, 66, 66, -76, -76, 24, 24, 22, 22, -38, -38, 82, 82, 66, 66, -66, -66, 24, 24, -100, -100, -176, -176, -6, -6, 48, 48, -106, -106, 20, 20, -62, -62, 192, 192, -44, -44, 158, 158, -108, -108, 122, 122, 108, 108, 122, 122, -76, -76, -176, -176, -138, -138, -182, -182, -46, -46, 142, 142, 40, 40, 42, 42, -48, -48, -126, -126, -96, -96, -12, -12, -108, -108, 130, 130, -56, -56, 158, 158, 168, 168, 136, 136, -98, -98, 56, 56, 16, 16, 120, 120, 166, 166, 48, 48, 102, 102, -68, -68, -108, -108, 74, 74, -164, -164, 186, 186, 102, 102, 48, 48, -90, -90, 114, 114, -94, -94, -158, -158], 'hecke_polynomial': 'x', 'label': '2.2.33.1-539.1-e'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 33, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 2]', '[2, 2, -w + 3]', '[3, 3, 2*w - 7]', '[4, 2, 2]', '[4, 4, -w + 4]', '[4, 4, w + 3]', '[6, 6, w + 1]', '[6, 6, w - 2]', '[8, 4, -2*w - 4]', '[8, 4, -2*w + 6]', '[8, 8, -w]', '[8, 8, -w + 1]', '[9, 3, 3]', '[11, 11, 4*w - 13]', '[12, 6, 4*w - 14]', '[12, 12, -w - 4]', '[12, 12, w - 5]', '[16, 4, 4]', '[16, 8, -2*w + 8]', '[16, 8, 2*w + 6]', '[16, 16, -3*w + 11]', '[16, 16, 3*w + 8]', '[17, 17, -2*w + 5]', '[17, 17, 2*w + 3]', '[18, 6, -3*w - 6]', '[18, 6, -3*w + 9]', '[22, 22, -w - 5]', '[22, 22, w - 6]', '[24, 12, 2*w + 2]', '[24, 12, 2*w - 4]', '[24, 24, 5*w + 11]', '[24, 24, 5*w - 16]', '[25, 5, 5]', '[27, 9, 6*w - 21]', '[29, 29, -2*w + 3]', '[29, 29, 2*w + 1]', '[31, 31, -2*w + 9]', '[31, 31, 2*w + 7]', '[32, 8, -4*w - 8]', '[32, 8, -4*w + 12]', '[32, 16, -2*w]', '[32, 16, -2*w + 2]', '[32, 32, -3*w + 8]', '[32, 32, -3*w - 5]', '[33, 33, -2*w + 1]', '[34, 34, w + 6]', '[34, 34, 5*w - 18]', '[34, 34, 5*w + 13]', '[34, 34, w - 7]', '[36, 6, 6]', '[36, 12, -3*w + 12]', '[36, 12, 3*w + 9]', '[37, 37, -4*w - 11]', '[37, 37, 4*w - 15]', '[41, 41, -10*w + 33]', '[41, 41, 6*w - 19]', '[44, 22, 8*w - 26]', '[44, 44, 3*w + 4]', '[44, 44, 3*w - 7]', '[48, 12, 8*w - 28]', '[48, 24, -2*w - 8]', '[48, 24, 2*w - 10]', '[48, 48, -w - 7]', '[48, 48, w - 8]', '[49, 7, -7]', '[50, 10, -5*w - 10]', '[50, 10, -5*w + 15]', '[51, 51, -4*w + 11]', '[51, 51, 4*w + 7]', '[54, 18, 3*w + 3]', '[54, 18, 3*w - 6]', '[58, 58, -7*w + 25]', '[58, 58, 3*w - 13]', '[58, 58, 3*w + 10]', '[58, 58, -7*w - 18]', '[62, 62, -7*w - 15]', '[62, 62, -3*w + 5]', '[62, 62, -3*w - 2]', '[62, 62, -7*w + 22]', '[64, 8, 8]', '[64, 16, -4*w + 16]', '[64, 16, 4*w + 12]', '[64, 32, -6*w + 22]', '[64, 32, 6*w + 16]', '[64, 64, w + 8]', '[64, 64, -w + 9]', '[66, 66, 5*w + 14]', '[66, 66, -5*w + 19]', '[67, 67, 2*w - 11]', '[67, 67, -2*w - 9]', '[68, 34, -4*w + 10]', '[68, 34, 4*w + 6]', '[68, 68, -3*w - 1]', '[68, 68, 9*w - 29]', '[68, 68, -9*w - 20]', '[68, 68, 3*w - 4]', '[72, 12, -6*w - 12]', '[72, 12, -6*w + 18]', '[72, 24, -3*w]', '[72, 24, -3*w + 3]', '[74, 74, 5*w - 14]', '[74, 74, 3*w - 2]', '[74, 74, 3*w - 1]', '[74, 74, 5*w + 9]', '[75, 15, 10*w - 35]', '[81, 9, 9]', '[82, 82, w + 9]', '[82, 82, -3*w - 11]', '[82, 82, -3*w + 14]', '[82, 82, w - 10]', '[83, 83, 4*w + 5]', '[83, 83, 4*w - 9]', '[87, 87, 8*w + 17]', '[87, 87, -8*w + 25]', '[88, 44, -2*w - 10]', '[88, 44, 2*w - 12]', '[88, 88, 9*w - 32]', '[88, 88, -9*w - 23]', '[93, 93, 4*w - 17]', '[93, 93, -4*w - 13]', '[96, 24, 4*w + 4]', '[96, 24, 4*w - 8]', '[96, 48, 10*w + 22]', '[96, 48, 10*w - 32]', '[96, 96, 5*w + 8]', '[96, 96, 5*w - 13]', '[97, 97, 8*w + 21]', '[97, 97, 8*w - 29]', '[98, 14, 7*w + 14]', '[98, 14, 7*w - 21]', '[99, 33, 12*w - 39]', '[100, 10, 10]', '[100, 20, -5*w + 20]', '[100, 20, 5*w + 15]', '[101, 101, 6*w - 17]', '[101, 101, 6*w + 11]', '[102, 102, w + 10]', '[102, 102, 7*w - 26]', '[102, 102, 7*w + 19]', '[102, 102, w - 11]', '[103, 103, -6*w - 17]', '[103, 103, 6*w - 23]', '[107, 107, 4*w - 7]', '[107, 107, -4*w - 3]', '[108, 18, 12*w - 42]', '[108, 36, -3*w - 12]', '[108, 36, 3*w - 15]', '[111, 111, -2*w + 13]', '[111, 111, 2*w + 11]', '[116, 58, -4*w + 6]', '[116, 58, 4*w + 2]', '[116, 116, 9*w + 19]', '[116, 116, 5*w - 12]', '[116, 116, -5*w - 7]', '[116, 116, -9*w + 28]', '[121, 11, 11]', '[123, 123, -4*w - 1]', '[123, 123, 4*w - 5]', '[124, 62, -4*w + 18]', '[124, 62, 4*w + 14]', '[124, 124, w + 11]', '[124, 124, -11*w + 39]', '[124, 124, 11*w + 28]', '[124, 124, -w + 12]', '[128, 16, -8*w - 16]', '[128, 16, -8*w + 24]', '[128, 32, -4*w]', '[128, 32, -4*w + 4]', '[128, 64, -6*w + 16]', '[128, 64, -6*w - 10]', '[128, 128, -11*w + 35]', '[128, 128, -11*w - 24]', '[131, 131, 4*w - 3]', '[131, 131, 4*w - 1]', '[132, 66, -4*w + 2]', '[132, 132, -7*w + 20]', '[132, 132, -7*w - 13]', '[134, 134, 5*w + 6]', '[134, 134, 15*w + 34]', '[134, 134, 15*w - 49]', '[134, 134, 5*w - 11]', '[136, 68, 2*w + 12]', '[136, 68, 10*w - 36]', '[136, 68, 10*w + 26]', '[136, 68, 2*w - 14]', '[136, 136, -5*w + 21]', '[136, 136, -3*w + 16]', '[136, 136, -3*w - 13]', '[136, 136, -5*w - 16]', '[144, 12, 12]', '[144, 24, -6*w + 24]', '[144, 24, 6*w + 18]', '[144, 48, -9*w + 33]', '[144, 48, 9*w + 24]', '[147, 21, -14*w + 49]', '[148, 74, -8*w - 22]', '[148, 74, 8*w - 30]', '[148, 148, -w - 12]', '[148, 148, -7*w - 20]', '[148, 148, 7*w - 27]', '[148, 148, w - 13]', '[149, 149, 10*w + 21]', '[149, 149, 10*w - 31]', '[150, 30, 5*w + 5]', '[150, 30, 5*w - 10]', '[153, 51, -6*w + 15]', '[153, 51, 6*w + 9]', '[157, 157, 4*w + 15]', '[157, 157, 4*w - 19]', '[162, 18, -9*w - 18]', '[162, 18, -9*w + 27]', '[163, 163, 2*w - 15]', '[163, 163, -2*w - 13]', '[164, 82, -20*w + 66]', '[164, 82, 12*w - 38]', '[164, 164, 5*w - 9]', '[164, 164, 7*w + 12]', '[164, 164, -7*w + 19]', '[164, 164, -5*w - 4]', '[166, 166, 13*w - 46]', '[166, 166, -3*w - 14]', '[166, 166, 3*w - 17]', '[166, 166, -13*w - 33]', '[167, 167, 8*w - 23]', '[167, 167, 8*w + 15]', '[169, 13, -13]', '[173, 173, 14*w + 31]', '[173, 173, 14*w - 45]', '[174, 174, -w - 13]', '[174, 174, 5*w + 17]', '[174, 174, 5*w - 22]', '[174, 174, -w + 14]', '[176, 44, 16*w - 52]', '[176, 88, 6*w + 8]', '[176, 88, 6*w - 14]', '[176, 176, 5*w + 3]', '[176, 176, 5*w - 8]', '[181, 181, -20*w + 69]', '[181, 181, -12*w + 43]', '[186, 186, 11*w + 23]', '[186, 186, 5*w - 7]', '[186, 186, 5*w + 2]', '[186, 186, 11*w - 34]', '[187, 187, -6*w + 25]', '[187, 187, -6*w - 19]', '[192, 24, 16*w - 56]', '[192, 48, -4*w - 16]', '[192, 48, 4*w - 20]', '[192, 96, -2*w - 14]', '[192, 96, 2*w - 16]', '[192, 192, -11*w - 29]', '[192, 192, 11*w - 40]', '[194, 194, -5*w - 1]', '[194, 194, 7*w + 11]', '[194, 194, -7*w + 18]', '[194, 194, 5*w - 6]', '[196, 14, 14]', '[196, 28, 7*w - 28]', '[196, 28, -7*w - 21]', '[197, 197, -6*w - 7]', '[197, 197, 6*w - 13]', '[198, 66, -3*w - 15]', '[198, 66, 3*w - 18]', '[199, 199, 10*w - 37]', '[199, 199, -10*w - 27]', '[200, 20, -10*w - 20]', '[200, 20, -10*w + 30]', '[200, 40, -5*w]', '[200, 40, -5*w + 5]', '[201, 201, -32*w + 109]', '[201, 201, -8*w + 31]', '[202, 202, -w - 14]', '[202, 202, 9*w - 34]', '[202, 202, -9*w - 25]', '[202, 202, w - 15]', '[204, 102, -8*w + 22]', '[204, 102, 8*w + 14]', '[204, 204, 5*w - 4]', '[204, 204, 13*w - 41]', '[204, 204, -13*w - 28]', '[204, 204, -5*w + 1]', '[206, 206, 9*w - 26]', '[206, 206, 5*w - 2]', '[206, 206, 5*w - 3]', '[206, 206, 9*w + 17]', '[214, 214, 15*w - 53]', '[214, 214, -5*w + 23]', '[214, 214, -5*w - 18]', '[214, 214, 15*w + 38]', '[216, 36, 6*w + 6]', '[216, 36, 6*w - 12]', '[216, 72, 15*w + 33]', '[216, 72, 15*w - 48]', '[222, 222, -17*w + 55]', '[222, 222, -7*w + 17]', '[222, 222, -7*w - 10]', '[222, 222, -19*w + 62]', '[223, 223, 2*w - 17]', '[223, 223, -2*w - 15]', '[225, 15, 15]', '[227, 227, 12*w + 25]', '[227, 227, 12*w - 37]', '[229, 229, -4*w + 21]', '[229, 229, -4*w - 17]', '[232, 116, -14*w + 50]', '[232, 116, 6*w - 26]', '[232, 116, 6*w + 20]', '[232, 116, -14*w - 36]', '[232, 232, -w - 15]', '[232, 232, -3*w + 19]', '[232, 232, -3*w - 16]', '[232, 232, -w + 16]', '[233, 233, 6*w - 11]', '[233, 233, -6*w - 5]', '[239, 239, -8*w + 21]', '[239, 239, 8*w + 13]', '[242, 22, -11*w - 22]', '[242, 22, -11*w + 33]', '[243, 27, 18*w - 63]', '[246, 246, -7*w + 29]', '[246, 246, 13*w - 47]', '[246, 246, 13*w + 34]', '[246, 246, -7*w - 22]', '[248, 124, -14*w - 30]', '[248, 124, -6*w + 10]', '[248, 124, -6*w - 4]', '[248, 124, -14*w + 44]', '[248, 248, -7*w + 16]', '[248, 248, -9*w - 16]', '[248, 248, -9*w + 25]', '[248, 248, -7*w - 9]', '[249, 249, -10*w + 29]', '[249, 249, -10*w - 19]', '[256, 16, 16]', '[256, 32, -8*w + 32]', '[256, 32, 8*w + 24]', '[256, 64, -12*w + 44]', '[256, 64, 12*w + 32]', '[256, 128, 2*w + 16]', '[256, 128, -2*w + 18]', '[256, 256, 5*w + 19]', '[256, 256, -5*w + 24]', '[261, 87, -6*w + 9]', '[261, 87, 6*w + 3]', '[262, 262, -9*w - 26]', '[262, 262, -11*w - 30]', '[262, 262, 11*w - 41]', '[262, 262, 9*w - 35]', '[263, 263, 16*w - 51]', '[263, 263, 16*w + 35]', '[264, 132, 10*w + 28]', '[264, 132, -10*w + 38]', '[264, 264, w + 16]', '[264, 264, -w + 17]', '[268, 134, 4*w - 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101]', '[8053, 8053, -44*w + 177]', '[8053, 8053, -44*w - 133]', '[8069, 8069, 38*w - 81]', '[8069, 8069, -38*w - 43]', '[8081, 8081, 50*w + 87]', '[8081, 8081, 50*w - 137]', '[8087, 8087, -32*w - 3]', '[8087, 8087, 32*w - 35]', '[8089, 8089, 16*w - 109]', '[8089, 8089, -16*w - 93]', '[8093, 8093, -34*w - 21]', '[8093, 8093, 34*w - 55]', '[8101, 8101, -108*w + 377]', '[8101, 8101, -100*w + 351]', '[8117, 8117, -138*w + 455]', '[8117, 8117, 86*w - 273]', '[8147, 8147, 52*w - 145]', '[8147, 8147, 52*w + 93]', '[8167, 8167, -6*w - 89]', '[8167, 8167, 6*w - 95]', '[8209, 8209, -136*w + 469]', '[8209, 8209, -80*w + 287]', '[8219, 8219, 68*w + 139]', '[8219, 8219, 68*w - 207]', '[8221, 8221, -12*w - 91]', '[8221, 8221, 12*w - 103]', '[8233, 8233, -64*w - 173]', '[8233, 8233, 64*w - 237]', '[8287, 8287, -62*w - 169]', '[8287, 8287, 62*w - 231]', '[8291, 8291, -36*w - 31]', '[8291, 8291, 36*w - 67]', '[8317, 8317, -52*w - 149]', '[8317, 8317, 52*w - 201]', '[8353, 8353, 56*w - 213]', '[8353, 8353, -56*w - 157]', '[8419, 8419, -34*w - 117]', '[8419, 8419, 34*w - 151]', '[8423, 8423, 32*w - 21]', '[8423, 8423, 32*w - 11]', '[8431, 8431, 2*w - 93]', '[8431, 8431, -2*w - 91]', '[8447, 8447, 32*w - 17]', '[8447, 8447, 32*w - 15]', '[8513, 8513, 34*w - 49]', '[8513, 8513, -34*w - 15]', '[8539, 8539, 6*w - 97]', '[8539, 8539, -6*w - 91]', '[8543, 8543, 72*w + 149]', '[8543, 8543, 72*w - 221]', '[8563, 8563, -18*w - 97]', '[8563, 8563, 18*w - 115]', '[8581, 8581, -20*w - 99]', '[8581, 8581, 20*w - 119]', '[8597, 8597, 118*w - 385]', '[8597, 8597, 106*w - 343]', '[8609, 8609, 62*w - 183]', '[8609, 8609, 62*w + 121]', '[8629, 8629, -36*w - 121]', '[8629, 8629, 36*w - 157]', '[8647, 8647, -154*w + 529]', '[8647, 8647, -74*w + 269]', '[8663, 8663, 88*w - 279]', '[8663, 8663, -144*w + 475]', '[8677, 8677, -44*w + 179]', '[8677, 8677, -44*w - 135]', '[8681, 8681, 54*w - 151]', '[8681, 8681, 54*w + 97]', '[8713, 8713, -32*w - 115]', '[8713, 8713, 32*w - 147]', '[8737, 8737, -112*w + 391]', '[8737, 8737, -104*w + 365]', '[8741, 8741, 70*w - 213]', '[8741, 8741, 70*w + 143]', '[8747, 8747, 44*w + 63]', '[8747, 8747, 44*w - 107]', '[8753, 8753, 34*w - 45]', '[8753, 8753, -34*w - 11]', '[8761, 8761, -72*w + 263]', '[8761, 8761, -160*w + 549]', '[8779, 8779, -10*w - 93]', '[8779, 8779, 10*w - 103]', '[8803, 8803, 2*w - 95]', '[8803, 8803, -2*w - 93]', '[8807, 8807, 48*w + 77]', '[8807, 8807, -48*w + 125]', '[8819, 8819, 92*w - 293]', '[8819, 8819, 92*w + 201]', '[8861, 8861, 34*w - 43]', '[8861, 8861, -34*w - 9]', '[8893, 8893, 4*w - 97]', '[8893, 8893, -4*w - 93]', '[8941, 8941, -68*w - 183]', '[8941, 8941, 68*w - 251]', '[8951, 8951, 96*w - 307]', '[8951, 8951, 96*w + 211]', '[9001, 9001, -40*w + 169]', '[9001, 9001, -40*w - 129]', '[9007, 9007, -66*w - 179]', '[9007, 9007, 66*w - 245]', '[9011, 9011, -36*w - 23]', '[9011, 9011, 36*w - 59]', '[9013, 9013, -12*w - 95]', '[9013, 9013, 12*w - 107]', '[9041, 9041, 66*w - 197]', '[9041, 9041, 66*w + 131]', '[9043, 9043, -146*w + 503]', '[9043, 9043, -82*w + 295]', '[9059, 9059, 100*w - 321]', '[9059, 9059, 100*w + 221]', '[9067, 9067, 54*w - 209]', '[9067, 9067, -54*w - 155]', '[9091, 9091, -62*w - 171]', '[9091, 9091, 62*w - 233]', '[9109, 9109, 60*w - 227]', '[9109, 9109, -60*w - 167]', '[9133, 9133, -132*w + 457]', '[9133, 9133, -92*w + 327]', '[9137, 9137, 34*w - 37]', '[9137, 9137, -34*w - 3]', '[9157, 9157, 28*w + 111]', '[9157, 9157, -28*w + 139]', '[9173, 9173, 54*w - 149]', '[9173, 9173, 54*w + 95]', '[9199, 9199, -14*w - 97]', '[9199, 9199, 14*w - 111]', '[9203, 9203, 108*w + 241]', '[9203, 9203, 108*w - 349]', '[9209, 9209, -38*w - 33]', '[9209, 9209, 38*w - 71]', '[9239, 9239, 112*w - 363]', '[9239, 9239, 120*w - 391]', '[9241, 9241, 32*w + 117]', '[9241, 9241, 32*w - 149]', '[9257, 9257, 58*w - 165]', '[9257, 9257, 58*w + 107]', '[9277, 9277, -4*w - 95]', '[9277, 9277, 4*w - 99]', '[9281, 9281, 34*w - 33]', '[9281, 9281, 34*w - 1]', '[9323, 9323, 36*w - 55]', '[9323, 9323, -36*w - 19]', '[9337, 9337, -16*w - 99]', '[9337, 9337, 16*w - 115]', '[9341, 9341, 34*w - 3]', '[9341, 9341, 34*w - 31]', '[9343, 9343, -158*w + 543]', '[9343, 9343, -78*w + 283]', '[9371, 9371, 164*w - 543]', '[9371, 9371, 84*w - 263]', '[9397, 9397, -116*w + 405]', '[9397, 9397, -108*w + 379]', '[9403, 9403, 38*w - 165]', '[9403, 9403, -38*w - 127]', '[9413, 9413, 38*w - 69]', '[9413, 9413, -38*w - 31]', '[9421, 9421, 12*w - 109]', '[9421, 9421, -12*w - 97]', '[9437, 9437, 34*w - 27]', '[9437, 9437, 34*w - 7]', '[9439, 9439, -46*w - 141]', '[9439, 9439, -46*w + 187]', '[9463, 9463, -22*w - 105]', '[9463, 9463, 22*w - 127]', '[9467, 9467, -36*w - 17]', '[9467, 9467, 36*w - 53]', '[9473, 9473, 34*w - 9]', '[9473, 9473, 34*w - 25]', '[9479, 9479, -40*w - 41]', '[9479, 9479, 40*w - 81]', '[9521, 9521, 34*w - 13]', '[9521, 9521, 34*w - 21]', '[9533, 9533, 34*w - 15]', '[9533, 9533, 34*w - 19]', '[9539, 9539, 52*w + 87]', '[9539, 9539, 52*w - 139]', '[9587, 9587, 68*w - 203]', '[9587, 9587, 68*w + 135]', '[9601, 9601, 40*w - 171]', '[9601, 9601, -40*w - 131]', '[9619, 9619, 14*w - 113]', '[9619, 9619, -14*w - 99]', '[9661, 9661, -28*w + 141]', '[9661, 9661, -28*w - 113]', '[9677, 9677, 82*w - 255]', '[9677, 9677, 82*w + 173]', '[9719, 9719, 40*w - 79]', '[9719, 9719, -40*w - 39]', '[9733, 9733, 52*w - 205]', '[9733, 9733, -52*w - 153]', '[9739, 9739, -86*w + 309]', '[9739, 9739, -150*w + 517]', '[9743, 9743, 56*w - 155]', '[9743, 9743, 56*w + 99]', '[9767, 9767, 64*w - 187]', '[9767, 9767, 64*w + 123]', '[9769, 9769, -16*w - 101]', '[9769, 9769, 16*w - 117]', '[9803, 9803, 156*w - 515]', '[9803, 9803, 92*w - 291]', '[9817, 9817, -96*w + 341]', '[9817, 9817, -136*w + 471]', '[9833, 9833, 74*w + 151]', '[9833, 9833, 74*w - 225]', '[9851, 9851, 36*w - 47]', '[9851, 9851, -36*w - 11]', '[9859, 9859, 66*w - 247]', '[9859, 9859, -66*w - 181]', '[9871, 9871, 18*w - 121]', '[9871, 9871, -18*w - 103]', '[9883, 9883, -58*w - 165]', '[9883, 9883, 58*w - 223]', '[9901, 9901, -60*w - 169]', '[9901, 9901, 60*w - 229]', '[9929, 9929, -42*w - 47]', '[9929, 9929, 42*w - 89]', '[9931, 9931, 22*w - 129]', '[9931, 9931, -22*w - 107]', '[9941, 9941, 86*w - 269]', '[9941, 9941, 170*w - 563]', '[9949, 9949, -44*w + 183]', '[9949, 9949, -44*w - 139]', '[9967, 9967, 2*w - 101]', '[9967, 9967, -2*w - 99]']}
• 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_label	text
  galt	integer
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	integer[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-8, -1, 1], 'conductor': 33, 'degree': 2, 'dirichlet_group': [1, 32], 'disc_abs': 33, 'disc_rad': 33, 'disc_sign': 1, 'frobs': [[2, [[1, 2]]], [3, [0]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [0]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[1, 2]]], [37, [[1, 2]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[2, 1]]], [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': '2.2.33.1', 'local_algs': ['3.2.1.2', '11.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 11], 'rd': 5.74456264654, 'regulator': {'__RealLiteral__': 0, 'data': '3.82816847133', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 8 a + 19 \\)'], 'used_grh': False, 'zk': ['1', 'a']}