Hilbert modular form data - 2.2.53.1-1156.1-a

Formats: - HTML - YAML - JSON - 2025-12-27T01:17:15.634127

• 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': 53, 'field_bad_primes': [53], 'field_label': '2.2.53.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.53.1-1156.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2, 17], 'level_ideal': '[1156, 34, 34]', 'level_label': '1156.1', 'level_norm': 1156, 'parallel_weight': 2, 'short_label': '1156.1-a', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4, 2, 2]', -1], ['[17, 17, -w - 5]', 1], ['[17, 17, w - 6]', 1]], 'hecke_eigenvalues': [1, -4, -4, -2, 6, 6, 2, 2, -1, -1, -10, 0, 0, -4, -4, 8, 8, 0, 0, -6, 0, 0, -6, -6, 14, 14, -6, -6, -6, -6, -6, -6, 6, 6, 2, 2, -12, -12, -16, -16, -10, -10, 8, 8, -6, -6, 14, 14, -10, -10, -24, -24, 8, 8, 6, 6, 6, 6, 20, 20, 12, 12, -12, -12, -16, -16, 18, 18, -22, -16, -16, -10, -10, 24, 24, 2, 2, 8, 8, -18, -18, -6, -6, 12, 12, 8, 8, -18, -18, -16, -16, -46, 20, 20, 2, 2, 14, 14, 12, 12, -30, -30, -24, -24, 20, 20, 26, 26, 14, 14, -48, -48, 24, 24, -46, -46, 38, 38, 30, 30, 8, 8, -22, -22, -36, -36, 8, 8, -10, -10, 38, 38, -16, -16, -36, -36, -18, -18, -16, -16, 48, 48, 32, 32, -58, -58, 12, 12, -18, -18, -58, -58, -36, -36, 18, 18, -30, -30, -46, -40, -40, -24, -24, 0, 0, -16, -16, -28, -28, 36, 36, 60, 60, -54, -54, -10, -10, -12, -12, -10, -10, 42, 42, 48, 48, -30, -30, 44, 44, 44, 44, 38, 38, 60, 60, -22, -22, -18, -18, 44, 44, -48, -48, -60, -60, -12, -12, 8, 8, 12, 12, 42, 42, -10, -10, 54, 54, -36, -36, 14, 14, 66, 66, -12, -12, 0, 0, 32, 32, 38, 38, -40, -40, 56, 56, -36, -36, -30, -30, -28, -28, -40, -40, -6, -6, 32, 32, -24, -24, -58, -58, -6, -6, 24, 24, 72, 72, -10, -10, 12, 12, -12, -12, -46, -18, -18, 18, 18, 78, 78, -18, -18, 26, 26, 8, 8, 14, 14, -48, -48, -46, -46, -70, -70, 0, 0, -4, -4, -70, -70, -24, -24, 56, 56, -48, -48, -42, -42, 44, 44, 8, 8, -18, -18, 20, 20, -18, -18, -12, -12, -52, -52, 48, 48, -48, -48, -4, -4, 12, 12, 26, 26, 6, 6, 2, 2, -58, -58, 74, 74, 60, 60, -12, -12, 8, 8, -36, -36, 2, 2, -22, -22, 66, 66, -30, -30, 66, 66, 20, 20, 8, 8, 12, 12, 78, 78, -34, -34, 48, 48, 44, 44, -48, -48, 20, 20, -24, -24, 0, 0, 32, 32, 32, 32, -84, -84, -10, -10, 0, 0, 54, 54, -78, -78, -46, -46, -84, -84, 72, 72, -84, -84, 60, 60, 44, 44, -10, -10, -40, -40, 14, 14, 42, 42, 68, 68, -40, -40, 32, 32, -42, -42, 26, 26, -18, -18, -22, -22, -12, -12, -24, -24, 20, 20, -78, -78, 12, 12, -34, -34, 6, 6, -78, -78, 12, 12, -16, -16, -46, -46, -70, -70, -82, -82, 90, 90, -30, -30, -70, -70, -30, -30, 32, 32, 36, 36, 86, 86, -58, -58, -16, -16, 48, 48, -30, -30, 2, 2, 26, 26, 42, 42, -40, -40, 72, 72, 92, 92, 108, 108, -90, -90, -40, -40, -64, -64, 84, 84, -6, -6, -60, -60, 50, 50, 78, 78, -34, -34, -88, -88, -24, -24, 32, 32, -106, -106, -90, -90, -66, -66, 62, 62, -78, -78, -34, -34, 110, 110, -72, -72, -88, -88, 24, 24, -106, -40, -40, -88, -88, 84, 84, -34, -34, -54, -54, -102, -102, 80, 80, 42, 42, 20, 20, -48, -48, -46, -46, 0, 0, 96, 96, 54, 54, 80, 80, 42, 42, -64, -64, 42, 42, -18, -18, -46, -46, 32, 32, 98, 98, -6, -6, 48, 48, -18, -18, -76, -76, 2, 2, 30, 30, -30, -30, -16, -16, -6, -6, -84, -84, 60, 60, 114, 114, -34, -34, -18, -18, -124, -124, -52, -52, 74, 74, 114, 114, -40, -40, 2, 2, -54, -54, -120, -120, 90, 90, -70, -108, -108, 68, 68, 104, 104, -48, -48, -112, -112, 32, 32, -54, -54, 62, 62, -58, -58, -88, -88, -78, -78, -72, -72, -102, -102, -94, -94, 96, 96, 8, 8, -112, -112, -126, -126, -60, -60, 134, 134, -126, -126, 26, 26, -114, -114, -66, -66, -120, -120, -76, -76, -4, -4, 108, 108, 62, 62, 42, 42, 98, 98, -16, -16, 104, 104, -48, -48, -142, 108, 108, -106, -106, -40, -40, 42, 42, -24, -24, 72, 72, -10, -10, 74, 74, 36, 36, 110, 110, -46, -46, 60, 60, 30, 30, -120, -120, -142, -88, -88, -42, -42, 114, 114, 108, 108, 104, 104, 32, 32, 78, 78, 56, 56, -40, -40, 122, 122, -58, -58, -24, -24, 96, 96, -76, -76, -120, -120, -34, -34, 32, 32, -46, -46, -88, -88, -76, -76, -48, -48, 0, 0, 14, 14, -24, -24, 8, 8, 96, 96, 54, 54, -138, -138, 8, 8, 80, 80, 30, 30, -48, -48, -24, -24, 98, 98, 84, 84, 14, 14, -60, -60, -52, -52, -54, -54, -4, -4, -76, -76, 90, 90, 98, 98, 18, 18, -6, -6, -130, -130, 116, 116, -6, -6, 102, 102, -142, -142, 62, 62, -76, -76, -94, 32, 32, 36, 36, 66, 66, -136, -136, 56, 56, 0, 0, -84, -84, 60, 60, 80, 80, -54, -54, -96, -96, -118, -118, -88, -88, 110, 110, 60, 60, -124, -124, 90, 90, -100, -100, -150, -150, -46, -46, -42, -42, -154, -154, -16, -16, 96, 96, 140, 140, -54, -54, -142, -142, 156, 156, 128, 128, -88, -88, 54, 54, 38, 38, -64, -64, 78, 78, -120, -120, 50, 50, 66, 66, -78, -78, 74, 74, 20, 20, -166, -66, -66, -22, -22, -138, -138, 146, 146, 36, 36, -88, -88, -108, -108, 24, 24, 68, 68, -138, -138, 8, 8, -114, -114, 84, 84, 24, 24, -48, -48, 12, 12, 128, 128, 54, 54, 8, 8, -10, -10, -88, -88, 158, 158, 138, 138, 86, 86, 72, 72, -52, -52, -28, -28, 90, 90, -18, -18, 20, 20, 110, 110, 24, 24, -58, -58, 120, 120, -10, -10, -96, -96, -12, -12, -76, -76, 0, 0, 104, 104, -28, -28, -114, -114, -114, -114, 26, 26, -10, -10, 102, 102, 38, 38, -48, -48, 122, 122, -126, -126, 18, 18, 98, 98, 174, 174, 48, 48, 44, 44, 66, 66, 108, 108, -28, -28, -46, -46, -70, -70, -150, -150, 24, 24, 60, 60, 42, 42, 6, 6, 84, 84, -34, -34, 102, 102, 104, 104, -16, -16, 50, 50, -36, -36, 140, 140, 180, 180, 12, 12, -124, -124, 104, 104, 66, 66, 8, 8, 110, 110, 48, 48, -54, -54, 110, 110, -24, -24, 8, 8, -46, -46, -112, -112, 8, 8, -102, -102, 86, 86, -96, -96, 96, 96, 84, 84, 164, 164, -112, -112, -136, -136, -36, -36, 20, 20, -66, -66, -156, -156, 138, 138, 122, 122, -120, -120, 122, 122, 108, 108, 96, 96, 90, 90, 30, 30, 8, 8, 2, 2, -34, -34, -150, -150, 86, 86, -144, -144, -24, -24, 180, 180, -22, -22, -72, -72, -48, -48, 50, 50, -16, -16, -16, -16, 164, 164, 80, 80, -46, -46, -48, -48, 66, 66, 60, 60, -72, -72, 66, 66, 72, 72, 80, 80, -130, -130, -186, -186, -4, -4, 96, 96, 90, 90, -100, -100, 2, 2, -120, -120, 164, 164, 146, 146, -40, -40, -42, -42, 6, 6, 80, 80, 138, 138, 108, 108, -166, -166, -144, -144, 156, 156, 96, 96, -88, -88, -148, -148, 6, 6, 56, 56, -24, -24, 192, 192, -22, -22, -136, -136, -124, -124, -100, -100, -162, -162, -120, -120, 102, 102, -100, -100, 92, 92, 2, 2, 180, 180, -100, -100, -148, -148, -70, -70, -16, -16], 'hecke_polynomial': 'x', 'label': '2.2.53.1-1156.1-a'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 53, 'ideals': ['[1, 1, 1]', '[4, 2, 2]', '[7, 7, w + 2]', '[7, 7, w - 3]', '[9, 3, 3]', '[11, 11, w + 1]', '[11, 11, w - 2]', '[13, 13, w]', '[13, 13, w - 1]', '[16, 4, 4]', '[17, 17, -w - 5]', '[17, 17, w - 6]', '[25, 5, -5]', '[28, 14, 2*w + 4]', '[28, 14, 2*w - 6]', '[29, 29, -w - 6]', '[29, 29, w - 7]', '[36, 6, 6]', '[37, 37, 2*w - 5]', '[37, 37, -2*w - 3]', '[43, 43, -w - 7]', '[43, 43, w - 8]', '[44, 22, 2*w + 2]', '[44, 22, 2*w - 4]', '[47, 47, 3*w + 7]', '[47, 47, 3*w - 10]', '[49, 7, 7]', '[49, 49, -2*w + 3]', '[49, 49, -2*w - 1]', '[52, 26, 2*w]', '[52, 26, 2*w - 2]', '[53, 53, 2*w - 1]', '[59, 59, -w - 8]', '[59, 59, w - 9]', '[63, 21, 3*w + 6]', '[63, 21, 3*w - 9]', '[64, 8, 8]', '[68, 34, -2*w - 10]', '[68, 34, 2*w - 12]', '[77, 77, w + 9]', '[77, 77, -3*w + 8]', '[77, 77, -3*w - 5]', '[77, 77, -w + 10]', '[81, 9, 9]', '[89, 89, -3*w - 4]', '[89, 89, 3*w - 7]', '[91, 91, -3*w + 16]', '[91, 91, -2*w + 13]', '[91, 91, 2*w + 11]', '[91, 91, 3*w + 13]', '[97, 97, -w - 10]', '[97, 97, w - 11]', '[99, 33, 3*w + 3]', '[99, 33, 3*w - 6]', '[100, 10, -10]', '[107, 107, 3*w - 5]', '[107, 107, -3*w - 2]', '[112, 28, 4*w + 8]', '[112, 28, 4*w - 12]', '[113, 113, -3*w - 1]', '[113, 113, 3*w - 4]', '[116, 58, -2*w - 12]', '[116, 58, 2*w - 14]', '[117, 39, 3*w]', '[117, 39, 3*w - 3]', '[119, 119, -8*w + 31]', '[119, 119, -3*w + 2]', '[119, 119, -3*w + 1]', '[119, 119, -8*w - 23]', '[121, 11, 11]', '[121, 121, 3*w + 14]', '[121, 121, -3*w + 17]', '[131, 131, 4*w - 11]', '[131, 131, -4*w - 7]', '[143, 143, w + 12]', '[143, 143, -2*w + 15]', '[143, 143, 2*w + 13]', '[143, 143, -w + 13]', '[144, 12, 12]', '[148, 74, 4*w - 10]', '[148, 74, -4*w - 6]', '[149, 149, 4*w - 21]', '[149, 149, -4*w - 17]', '[153, 51, -3*w - 15]', '[153, 51, 3*w - 18]', '[163, 163, -4*w - 5]', '[163, 163, 4*w - 9]', '[169, 13, 13]', '[169, 169, w + 13]', '[169, 169, -w + 14]', '[172, 86, -2*w - 14]', '[172, 86, 2*w - 16]', '[175, 35, -5*w - 10]', '[175, 35, -5*w + 15]', '[176, 44, 4*w + 4]', '[176, 44, 4*w - 8]', '[187, 187, -4*w + 7]', '[187, 187, -7*w - 18]', '[187, 187, -7*w + 25]', '[187, 187, -4*w - 3]', '[188, 94, 6*w + 14]', '[188, 94, 6*w - 20]', '[196, 14, 14]', '[196, 98, -4*w + 6]', '[196, 98, -4*w - 2]', '[197, 197, -w - 14]', '[197, 197, w - 15]', '[199, 199, 5*w - 14]', '[199, 199, -5*w - 9]', '[203, 203, -4*w - 1]', '[203, 203, -9*w - 25]', '[203, 203, -9*w + 34]', '[203, 203, -4*w + 5]', '[208, 52, 4*w]', '[208, 52, 4*w - 4]', '[211, 211, 4*w - 3]', '[211, 211, 4*w - 1]', '[212, 106, 4*w - 2]', '[221, 221, -6*w - 13]', '[221, 221, -5*w - 8]', '[221, 221, -5*w + 13]', '[221, 221, -6*w + 19]', '[223, 223, -3*w - 17]', '[223, 223, 3*w - 20]', '[225, 15, -15]', '[227, 227, -w - 15]', '[227, 227, w - 16]', '[229, 229, -4*w - 19]', '[229, 229, 4*w - 23]', '[236, 118, -2*w - 16]', '[236, 118, 2*w - 18]', '[241, 241, 5*w - 12]', '[241, 241, -5*w - 7]', '[252, 42, 6*w + 12]', '[252, 42, 6*w - 18]', '[256, 16, 16]', '[259, 259, w + 16]', '[259, 259, -9*w + 41]', '[259, 259, -9*w - 32]', '[259, 259, w - 17]', '[261, 87, -3*w - 18]', '[261, 87, 3*w - 21]', '[269, 269, -5*w - 22]', '[269, 269, 5*w - 27]', '[271, 271, 2*w - 19]', '[271, 271, -2*w - 17]', '[272, 68, -4*w - 20]', '[272, 68, 4*w - 24]', '[275, 55, -5*w - 5]', '[275, 55, -5*w + 10]', '[281, 281, 6*w - 17]', '[281, 281, -6*w - 11]', '[289, 17, 17]', '[289, 289, 5*w - 9]', '[289, 289, -5*w - 4]', '[293, 293, -w - 17]', '[293, 293, w - 18]', '[301, 301, -10*w - 27]', '[301, 301, -5*w - 3]', '[301, 301, -5*w + 8]', '[301, 301, -10*w + 37]', '[307, 307, -7*w - 15]', '[307, 307, 7*w - 22]', '[308, 154, 2*w + 18]', '[308, 154, -6*w + 16]', '[308, 154, -6*w - 10]', '[308, 154, -2*w + 20]', '[311, 311, 5*w - 7]', '[311, 311, -5*w - 2]', '[317, 317, 4*w - 25]', '[317, 317, -4*w - 21]', '[319, 319, -5*w - 1]', '[319, 319, -8*w - 19]', '[319, 319, -8*w + 27]', '[319, 319, -5*w + 6]', '[324, 18, 18]', '[325, 65, -5*w]', '[325, 65, -5*w + 5]', '[329, 329, w + 18]', '[329, 329, 16*w + 53]', '[329, 329, -16*w + 69]', '[329, 329, -w + 19]', '[331, 331, 5*w - 2]', '[331, 331, 5*w - 3]', '[333, 111, 6*w - 15]', '[333, 111, -6*w - 9]', '[343, 49, 7*w + 14]', '[343, 49, 7*w - 21]', '[343, 343, -3*w - 20]', '[343, 343, 3*w - 23]', '[347, 347, 2*w - 21]', '[347, 347, -2*w - 19]', '[356, 178, -6*w - 8]', '[356, 178, 6*w - 14]', '[361, 19, -19]', '[364, 182, -6*w + 32]', '[364, 182, -4*w + 26]', '[364, 182, 4*w + 22]', '[364, 182, 6*w + 26]', '[367, 367, -w - 19]', '[367, 367, w - 20]', '[371, 371, 5*w + 24]', '[371, 371, -5*w + 29]', '[377, 377, -7*w + 20]', '[377, 377, -6*w - 7]', '[377, 377, -6*w + 13]', '[377, 377, -7*w - 13]', '[387, 129, -3*w - 21]', '[387, 129, 3*w - 24]', '[388, 194, -2*w - 20]', '[388, 194, 2*w - 22]', '[396, 66, 6*w + 6]', '[396, 66, 6*w - 12]', '[400, 20, -20]', '[407, 407, -w - 20]', '[407, 407, -7*w + 36]', '[407, 407, -7*w - 29]', '[407, 407, -w + 21]', '[409, 409, -7*w - 12]', '[409, 409, 7*w - 19]', '[413, 413, -6*w + 11]', '[413, 413, -11*w + 40]', '[413, 413, -11*w - 29]', '[413, 413, -6*w - 5]', '[423, 141, 9*w + 21]', '[423, 141, 9*w - 30]', '[425, 85, -5*w - 25]', '[425, 85, 5*w - 30]', '[428, 214, 6*w - 10]', '[428, 214, -6*w - 4]', '[431, 431, 2*w - 23]', '[431, 431, -2*w - 21]', '[433, 433, 3*w - 25]', '[433, 433, -3*w - 22]', '[439, 439, -7*w - 11]', '[439, 439, 7*w - 18]', '[441, 21, 21]', '[441, 147, -6*w + 9]', '[441, 147, -6*w - 3]', '[448, 56, 8*w + 16]', '[448, 56, 8*w - 24]', '[449, 449, -w - 21]', '[449, 449, w - 22]', '[452, 226, -6*w - 2]', '[452, 226, 6*w - 8]', '[461, 461, -6*w - 1]', '[461, 461, 6*w - 7]', '[464, 116, -4*w - 24]', '[464, 116, 4*w - 28]', '[467, 467, 7*w - 17]', '[467, 467, -7*w - 10]', '[468, 78, 6*w]', '[468, 78, 6*w - 6]', '[473, 473, -6*w + 5]', '[473, 473, -9*w + 29]', '[473, 473, -9*w - 20]', '[473, 473, -6*w + 1]', '[476, 238, -16*w + 62]', '[476, 238, -6*w + 4]', '[476, 238, -6*w + 2]', '[476, 238, -16*w - 46]', '[477, 159, 6*w - 3]', '[481, 481, -5*w + 31]', '[481, 481, -3*w - 23]', '[481, 481, -3*w + 26]', '[481, 481, -5*w - 26]', '[484, 22, 22]', '[484, 242, 6*w + 28]', '[484, 242, -6*w + 34]', '[487, 487, 8*w - 23]', '[487, 487, -8*w - 15]', '[493, 493, -w - 22]', '[493, 493, 7*w - 16]', '[493, 493, -7*w - 9]', '[493, 493, w - 23]', '[517, 517, -13*w + 59]', '[517, 517, -4*w + 29]', '[517, 517, 4*w + 25]', '[517, 517, 13*w + 46]', '[521, 521, -9*w - 19]', '[521, 521, 9*w - 28]', '[523, 523, 2*w - 25]', '[523, 523, -2*w - 23]', '[524, 262, 8*w - 22]', '[524, 262, -8*w - 14]', '[529, 23, -23]', '[531, 177, -3*w - 24]', '[531, 177, 3*w - 27]', '[539, 77, 7*w + 7]', '[539, 77, 7*w - 14]', '[539, 539, -w - 23]', '[539, 539, -5*w - 27]', '[539, 539, 5*w - 32]', '[539, 539, w - 24]', '[541, 541, 10*w - 33]', '[541, 541, 10*w + 23]', '[547, 547, -6*w - 29]', '[547, 547, 6*w - 35]', '[559, 559, -7*w + 13]', '[559, 559, -8*w + 21]', '[559, 559, -8*w - 13]', '[559, 559, -7*w - 6]', '[567, 63, 9*w + 18]', '[567, 63, 9*w - 27]', '[572, 286, 2*w + 24]', '[572, 286, -4*w + 30]', '[572, 286, 4*w + 26]', '[572, 286, -2*w + 26]', '[576, 24, 24]', '[577, 577, -7*w - 5]', '[577, 577, 7*w - 12]', '[583, 583, -3*w + 28]', '[583, 583, 3*w + 25]', '[587, 587, -w - 24]', '[587, 587, w - 25]', '[592, 148, 8*w - 20]', '[592, 148, -8*w - 12]', '[593, 593, -7*w - 4]', '[593, 593, 7*w - 11]', '[596, 298, 8*w - 42]', '[596, 298, -8*w - 34]', '[599, 599, 5*w - 33]', '[599, 599, -5*w - 28]', '[607, 607, 7*w - 10]', '[607, 607, -7*w - 3]', '[611, 611, 10*w + 39]', '[611, 611, -7*w + 39]', '[611, 611, 7*w + 32]', '[611, 611, -10*w + 49]', '[612, 102, -6*w - 30]', '[612, 102, 6*w - 36]', '[619, 619, 7*w - 9]', '[619, 619, -7*w - 2]', '[623, 623, -13*w + 60]', '[623, 623, 2*w - 27]', '[623, 623, 2*w + 25]', '[623, 623, -13*w - 47]', '[625, 25, -25]', '[629, 629, -7*w - 1]', '[629, 629, -4*w - 27]', '[629, 629, 4*w - 31]', '[629, 629, 7*w - 8]', '[637, 91, 7*w]', '[637, 91, 7*w - 7]', '[637, 637, -w - 25]', '[637, 637, -3*w - 26]', '[637, 637, 3*w - 29]', '[637, 637, w - 26]', '[643, 643, 7*w - 6]', '[643, 643, 7*w - 1]', '[647, 647, 7*w - 2]', '[647, 647, 7*w - 5]', '[649, 649, -10*w - 21]', '[649, 649, -7*w + 3]', '[649, 649, -7*w + 4]', '[649, 649, -10*w + 31]', '[652, 326, -8*w - 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7]', '[6397, 6397, 22*w - 15]', '[6449, 6449, 30*w - 89]', '[6449, 6449, -30*w - 59]', '[6451, 6451, -29*w - 54]', '[6451, 6451, 29*w - 83]', '[6473, 6473, -17*w - 93]', '[6473, 6473, 17*w - 110]', '[6481, 6481, 34*w - 111]', '[6481, 6481, 34*w + 77]', '[6491, 6491, 7*w - 88]', '[6491, 6491, -7*w - 81]', '[6529, 6529, 24*w - 131]', '[6529, 6529, -24*w - 107]', '[6547, 6547, -23*w - 10]', '[6547, 6547, 23*w - 33]', '[6563, 6563, -23*w - 105]', '[6563, 6563, 23*w - 128]', '[6571, 6571, -31*w - 63]', '[6571, 6571, 31*w - 94]', '[6581, 6581, -20*w - 99]', '[6581, 6581, 20*w - 119]', '[6619, 6619, 14*w - 103]', '[6619, 6619, -14*w - 89]', '[6653, 6653, -26*w - 35]', '[6653, 6653, 26*w - 61]', '[6661, 6661, 7*w - 89]', '[6661, 6661, -7*w - 82]', '[6679, 6679, -32*w - 67]', '[6679, 6679, 32*w - 99]', '[6689, 6689, -27*w - 41]', '[6689, 6689, 27*w - 68]', '[6691, 6691, 13*w - 101]', '[6691, 6691, -13*w - 88]', '[6703, 6703, -23*w - 6]', '[6703, 6703, 23*w - 29]', '[6737, 6737, 23*w - 28]', '[6737, 6737, -23*w - 5]', '[6791, 6791, 24*w - 41]', '[6791, 6791, -24*w - 17]', '[6793, 6793, -w - 82]', '[6793, 6793, w - 83]', '[6827, 6827, 23*w - 25]', '[6827, 6827, -23*w - 2]', '[6833, 6833, -7*w - 83]', '[6833, 6833, 7*w - 90]', '[6841, 6841, 26*w - 59]', '[6841, 6841, -26*w - 33]', '[6883, 6883, -17*w - 95]', '[6883, 6883, 17*w - 112]', '[6889, 83, -83]', '[6899, 6899, 23*w - 22]', '[6899, 6899, 23*w - 1]', '[6907, 6907, -28*w - 45]', '[6907, 6907, 28*w - 73]', '[6947, 6947, 33*w - 103]', '[6947, 6947, -33*w - 70]', '[6949, 6949, 25*w - 49]', '[6949, 6949, -25*w - 24]', '[6959, 6959, -w - 83]', '[6959, 6959, w - 84]', '[6967, 6967, 23*w - 5]', '[6967, 6967, 23*w - 18]', '[6971, 6971, 36*w - 119]', '[6971, 6971, 36*w + 83]', '[6983, 6983, 29*w - 79]', '[6983, 6983, -29*w - 50]', '[6997, 6997, 23*w - 15]', '[6997, 6997, 23*w - 8]', '[7013, 7013, -4*w - 83]', '[7013, 7013, 4*w - 87]', '[7039, 7039, 21*w - 124]', '[7039, 7039, -21*w - 103]', '[7043, 7043, -22*w - 105]', '[7043, 7043, 22*w - 127]', '[7103, 7103, -24*w - 11]', '[7103, 7103, 24*w - 35]', '[7109, 7109, 27*w - 64]', '[7109, 7109, -27*w - 37]', '[7127, 7127, -w - 84]', '[7127, 7127, w - 85]', '[7151, 7151, -5*w - 84]', '[7151, 7151, 5*w - 89]', '[7159, 7159, -25*w - 21]', '[7159, 7159, 25*w - 46]', '[7193, 7193, -26*w - 29]', '[7193, 7193, 26*w - 55]', '[7207, 7207, 19*w - 119]', '[7207, 7207, -19*w - 100]', '[7219, 7219, -25*w - 112]', '[7219, 7219, 25*w - 137]', '[7237, 7237, 29*w - 77]', '[7237, 7237, -29*w - 48]', '[7297, 7297, -w - 85]', '[7297, 7297, w - 86]', '[7307, 7307, 27*w - 62]', '[7307, 7307, -27*w - 35]', '[7321, 7321, 15*w - 109]', '[7321, 7321, -15*w - 94]', '[7331, 7331, 31*w - 89]', '[7331, 7331, -31*w - 58]', '[7351, 7351, -25*w - 18]', '[7351, 7351, 25*w - 43]', '[7411, 7411, -25*w - 17]', '[7411, 7411, 25*w - 42]', '[7433, 7433, -8*w - 87]', '[7433, 7433, 8*w - 95]', '[7457, 7457, -33*w - 67]', '[7457, 7457, 33*w - 100]', '[7477, 7477, -31*w - 57]', '[7477, 7477, 31*w - 88]', '[7489, 7489, -35*w - 76]', '[7489, 7489, 35*w - 111]', '[7517, 7517, -11*w - 90]', '[7517, 7517, 11*w - 101]', '[7537, 7537, -3*w - 86]', '[7537, 7537, 3*w - 89]', '[7541, 7541, -7*w - 87]', '[7541, 7541, 7*w - 94]', '[7573, 7573, 34*w - 105]', '[7573, 7573, -34*w - 71]', '[7583, 7583, 24*w - 19]', '[7583, 7583, 24*w - 5]', '[7589, 7589, -27*w - 32]', '[7589, 7589, 27*w - 59]', '[7603, 7603, 29*w - 74]', '[7603, 7603, -29*w - 45]', '[7607, 7607, 24*w - 17]', '[7607, 7607, 24*w - 7]', '[7621, 7621, -31*w - 56]', '[7621, 7621, 31*w - 87]', '[7639, 7639, 32*w - 93]', '[7639, 7639, -32*w - 61]', '[7643, 7643, -w - 87]', '[7643, 7643, w - 88]', '[7649, 7649, -19*w - 102]', '[7649, 7649, 19*w - 121]', '[7669, 7669, -9*w - 89]', '[7669, 7669, 9*w - 98]', '[7681, 7681, 25*w - 37]', '[7681, 7681, -25*w - 12]', '[7691, 7691, 2*w - 89]', '[7691, 7691, -2*w - 87]', '[7723, 7723, 7*w - 95]', '[7723, 7723, -7*w - 88]', '[7727, 7727, -17*w - 99]', '[7727, 7727, 17*w - 116]', '[7753, 7753, 23*w - 133]', '[7753, 7753, -23*w - 110]', '[7829, 7829, 30*w - 79]', '[7829, 7829, -30*w - 49]', '[7853, 7853, 27*w - 56]', '[7853, 7853, -27*w - 29]', '[7873, 7873, -19*w - 103]', '[7873, 7873, 19*w - 122]', '[7901, 7901, 25*w - 32]', '[7901, 7901, -25*w - 7]', '[7907, 7907, 7*w - 96]', '[7907, 7907, -7*w - 89]', '[7933, 7933, -26*w - 19]', '[7933, 7933, 26*w - 45]', '[7937, 7937, -27*w - 28]', '[7937, 7937, 27*w - 55]', '[7949, 7949, -33*w - 64]', '[7949, 7949, 33*w - 97]', '[7951, 7951, -29*w - 42]', '[7951, 7951, 29*w - 71]', '[7963, 7963, -21*w - 107]', '[7963, 7963, 21*w - 128]', '[7993, 7993, -24*w - 113]', '[7993, 7993, 24*w - 137]', '[8009, 8009, 25*w - 29]', '[8009, 8009, -25*w - 4]', '[8039, 8039, 29*w - 153]', '[8039, 8039, -29*w - 124]', '[8069, 8069, 4*w - 93]', '[8069, 8069, -4*w - 89]', '[8081, 8081, 30*w - 77]', '[8081, 8081, -30*w - 47]', '[8093, 8093, -7*w - 90]', '[8093, 8093, 7*w - 97]', '[8147, 8147, 36*w - 113]', '[8147, 8147, -36*w - 77]', '[8161, 8161, -17*w - 101]', '[8161, 8161, 17*w - 118]', '[8171, 8171, 25*w - 2]', '[8171, 8171, 25*w - 23]', '[8179, 8179, 28*w - 61]', '[8179, 8179, -28*w - 33]', '[8191, 8191, 25*w - 3]', '[8191, 8191, 25*w - 22]', '[8209, 8209, 25*w - 4]', '[8209, 8209, 25*w - 21]', '[8219, 8219, -14*w - 97]', '[8219, 8219, 14*w - 111]', '[8221, 8221, 35*w - 107]', '[8221, 8221, -35*w - 72]', '[8231, 8231, 25*w - 141]', '[8231, 8231, -25*w - 116]', '[8243, 8243, -23*w - 112]', '[8243, 8243, 23*w - 135]', '[8269, 8269, 25*w - 9]', '[8269, 8269, 25*w - 16]', '[8293, 8293, -12*w - 95]', '[8293, 8293, 12*w - 107]', '[8297, 8297, 11*w - 105]', '[8297, 8297, -11*w - 94]', '[8311, 8311, -31*w - 51]', '[8311, 8311, 31*w - 82]', '[8317, 8317, 29*w - 154]', '[8317, 8317, -29*w - 125]', '[8363, 8363, 28*w - 59]', '[8363, 8363, -28*w - 31]', '[8387, 8387, -29*w - 38]', '[8387, 8387, 29*w - 67]', '[8389, 8389, 20*w - 127]', '[8389, 8389, -20*w - 107]', '[8423, 8423, -33*w - 61]', '[8423, 8423, 33*w - 94]', '[8431, 8431, -27*w - 121]', '[8431, 8431, 27*w - 148]', '[8443, 8443, 31*w - 81]', '[8443, 8443, -31*w - 50]', '[8467, 8467, 26*w - 145]', '[8467, 8467, -26*w - 119]', '[8527, 8527, -32*w - 55]', '[8527, 8527, 32*w - 87]', '[8537, 8537, 27*w - 47]', '[8537, 8537, -27*w - 20]', '[8539, 8539, -28*w - 29]', '[8539, 8539, 28*w - 57]', '[8543, 8543, -w - 92]', '[8543, 8543, w - 93]', '[8573, 8573, 31*w - 80]', '[8573, 8573, -31*w - 49]', '[8597, 8597, 39*w + 88]', '[8597, 8597, 39*w - 127]', '[8599, 8599, -5*w - 92]', '[8599, 8599, 5*w - 97]', '[8623, 8623, -3*w - 92]', '[8623, 8623, 3*w - 95]', '[8629, 8629, -9*w - 94]', '[8629, 8629, 9*w - 103]', '[8663, 8663, -7*w - 93]', '[8663, 8663, 7*w - 100]', '[8677, 8677, -21*w - 110]', '[8677, 8677, 21*w - 131]', '[8681, 8681, 13*w - 111]', '[8681, 8681, -13*w - 98]', '[8693, 8693, -29*w - 35]', '[8693, 8693, 29*w - 64]', '[8699, 8699, -11*w - 96]', '[8699, 8699, 11*w - 107]', '[8707, 8707, 28*w - 55]', '[8707, 8707, -28*w - 27]', '[8741, 8741, -23*w - 114]', '[8741, 8741, 23*w - 137]', '[8761, 8761, -26*w - 1]', '[8761, 8761, 26*w - 27]', '[8783, 8783, 2*w - 95]', '[8783, 8783, -2*w - 93]', '[8807, 8807, 32*w - 85]', '[8807, 8807, -32*w - 53]', '[8861, 8861, 20*w - 129]', '[8861, 8861, -20*w - 109]', '[8867, 8867, -28*w - 25]', '[8867, 8867, 28*w - 53]', '[8887, 8887, 29*w - 62]', '[8887, 8887, -29*w - 33]', '[8893, 8893, 26*w - 5]', '[8893, 8893, 26*w - 21]', '[8929, 8929, 16*w - 119]', '[8929, 8929, -16*w - 103]', '[8933, 8933, 28*w - 153]', '[8933, 8933, -28*w - 125]', '[8941, 8941, 26*w - 17]', '[8941, 8941, 26*w - 9]', '[8951, 8951, 31*w - 77]', '[8951, 8951, -31*w - 46]', '[8963, 8963, -22*w - 113]', '[8963, 8963, 22*w - 135]', '[8999, 8999, -26*w - 121]', '[8999, 8999, 26*w - 147]', '[9001, 9001, 3*w - 97]', '[9001, 9001, -3*w - 94]', '[9011, 9011, 25*w - 144]', '[9011, 9011, -25*w - 119]', '[9059, 9059, -27*w - 11]', '[9059, 9059, 27*w - 38]', '[9067, 9067, 14*w - 115]', '[9067, 9067, -14*w - 101]', '[9091, 9091, 35*w - 102]', '[9091, 9091, -35*w - 67]', '[9103, 9103, 13*w - 113]', '[9103, 9103, -13*w - 100]', '[9109, 9109, -11*w - 98]', '[9109, 9109, 11*w - 109]', '[9127, 9127, -6*w - 95]', '[9127, 9127, 6*w - 101]', '[9133, 9133, 38*w - 119]', '[9133, 9133, -38*w - 81]', '[9173, 9173, 33*w - 89]', '[9173, 9173, -33*w - 56]', '[9209, 9209, 37*w - 113]', '[9209, 9209, -37*w - 76]', '[9221, 9221, -30*w - 37]', '[9221, 9221, 30*w - 67]', '[9239, 9239, -27*w - 7]', '[9239, 9239, 27*w - 34]', '[9281, 9281, -17*w - 106]', '[9281, 9281, 17*w - 123]', '[9311, 9311, -31*w - 43]', '[9311, 9311, 31*w - 74]', '[9319, 9319, 31*w - 164]', '[9319, 9319, -31*w - 133]', '[9337, 9337, 29*w - 57]', '[9337, 9337, -29*w - 28]', '[9341, 9341, -20*w - 111]', '[9341, 9341, 20*w - 131]', '[9343, 9343, 32*w - 81]', '[9343, 9343, -32*w - 49]', '[9371, 9371, 5*w - 101]', '[9371, 9371, -5*w - 96]', '[9377, 9377, -16*w - 105]', '[9377, 9377, 16*w - 121]', '[9391, 9391, 41*w + 93]', '[9391, 9391, 41*w - 134]', '[9397, 9397, -37*w - 75]', '[9397, 9397, 37*w - 112]', '[9419, 9419, 27*w - 29]', '[9419, 9419, -27*w - 2]', '[9421, 9421, -29*w - 27]', '[9421, 9421, 29*w - 56]', '[9433, 9433, -9*w - 98]', '[9433, 9433, 9*w - 107]', '[9463, 9463, 22*w - 137]', '[9463, 9463, -22*w - 115]', '[9491, 9491, -10*w - 99]', '[9491, 9491, 10*w - 109]', '[9497, 9497, -19*w - 110]', '[9497, 9497, 19*w - 129]', '[9511, 9511, 17*w - 124]', '[9511, 9511, -17*w - 107]', '[9533, 9533, 13*w - 115]', '[9533, 9533, -13*w - 102]', '[9539, 9539, 26*w - 149]', '[9539, 9539, -26*w - 123]', '[9547, 9547, 28*w - 43]', '[9547, 9547, -28*w - 15]', '[9551, 9551, 2*w - 99]', '[9551, 9551, -2*w - 97]', '[9587, 9587, 27*w - 22]', '[9587, 9587, 27*w - 5]', '[9629, 9629, 27*w - 8]', '[9629, 9629, 27*w - 19]', '[9631, 9631, 18*w - 127]', '[9631, 9631, -18*w - 109]', '[9661, 9661, 29*w - 53]', '[9661, 9661, -29*w - 24]', '[9689, 9689, -w - 98]', '[9689, 9689, w - 99]', '[9739, 9739, -11*w - 101]', '[9739, 9739, 11*w - 112]', '[9743, 9743, 17*w - 125]', '[9743, 9743, -17*w - 108]', '[9767, 9767, 37*w - 110]', '[9767, 9767, -37*w - 73]', '[9769, 9769, 5*w - 103]', '[9769, 9769, -5*w - 98]', '[9781, 9781, -3*w - 98]', '[9781, 9781, 3*w - 101]', '[9811, 9811, -29*w - 22]', '[9811, 9811, 29*w - 51]', '[9829, 9829, -20*w - 113]', '[9829, 9829, 20*w - 133]', '[9833, 9833, 16*w - 123]', '[9833, 9833, -16*w - 107]', '[9851, 9851, -39*w - 82]', '[9851, 9851, 39*w - 121]', '[9857, 9857, 7*w - 106]', '[9857, 9857, -7*w - 99]', '[9859, 9859, 28*w - 37]', '[9859, 9859, -28*w - 9]', '[9871, 9871, -31*w - 38]', '[9871, 9871, 31*w - 69]', '[9883, 9883, 29*w - 50]', '[9883, 9883, -29*w - 21]', '[9887, 9887, -w - 99]', '[9887, 9887, w - 100]', '[9901, 9901, 15*w - 121]', '[9901, 9901, -15*w - 106]', '[9907, 9907, -21*w - 115]', '[9907, 9907, 21*w - 136]', '[9949, 9949, -37*w - 72]', '[9949, 9949, 37*w - 109]', '[9973, 9973, -12*w - 103]', '[9973, 9973, 12*w - 115]']}
• 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': [-13, -1, 1], 'conductor': 53, 'degree': 2, 'dirichlet_group': [1, 52], 'disc_abs': 53, 'disc_rad': 53, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[2, 1]]], [5, [[2, 1]]], [7, [[1, 2]]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[1, 2]]], [47, [[1, 2]]], [53, [0]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1], 'galois_label': '2T1', 'galt': 1, 'grd': 7.280109889280518, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.53.1', 'local_algs': ['53.1.2.1a1.1'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 0, 'ramps': [53], 'rd': 7.28010988928, 'regulator': {'__RealLiteral__': 0, 'data': '1.96572047165', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a']}