Hilbert modular form data - 2.2.21.1-192.1-g

Formats: - HTML - YAML - JSON - 2026-02-09T09:48:28.931938

• 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': 21, 'field_bad_primes': [3, 7], 'field_label': '2.2.21.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.21.1-192.1-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [2, 3], 'level_ideal': '[192, 24, 8*w + 8]', 'level_label': '192.1', 'level_norm': 192, 'parallel_weight': 2, 'short_label': '192.1-g', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, w + 1]', -1], ['[4, 2, 2]', -1]], 'hecke_eigenvalues': [1, 0, 0, 2, 2, 2, 4, 6, -10, -10, 0, 6, -2, 0, 12, -4, 12, -12, 8, -8, -4, -8, 12, 10, -12, -10, -12, 2, 2, -2, -12, -8, 8, 12, 2, 10, -8, -20, 16, 4, 6, 6, 4, -26, -2, 10, 10, -20, 12, 16, -12, -12, 26, 30, -12, -10, 18, -14, 8, -24, -8, -18, 6, 26, -14, 28, -6, 30, -22, 26, 2, 26, 16, 12, -36, -28, -26, -6, 18, 10, -26, 12, 4, -40, -20, 24, 40, 24, -2, 22, 18, 18, 16, 4, -32, -30, -8, -18, -26, 10, 30, 8, -20, 4, 0, -8, -4, -16, 4, -12, -38, -38, -6, -16, 28, -8, 24, -10, 38, -6, -24, -14, 10, 0, 48, 16, -20, -50, 14, 34, -22, 30, -32, 36, -26, -30, -24, 36, -24, 24, 4, -30, -48, -42, 54, 22, 30, -40, 14, -58, -28, -16, 22, -26, 22, 46, 50, -20, -12, 6, -46, 44, 8, -60, 36, -24, 36, 58, -30, -6, -2, 36, -42, 38, -6, 2, -4, 52, -64, -48, 20, -60, -64, -26, 34, 48, 38, 22, 28, 42, 58, -14, 38, -24, -8, 22, -10, 16, 10, 14, 32, -2, 46, -34, 10, -42, 32, 32, -40, 60, -8, 52, -42, 18, -62, 52, 22, 34, 2, -4, -68, -8, 48, -14, -30, 30, -8, -70, -14, -22, 18, -8, 28, 6, -42, 8, 14, -62, -22, -10, -58, 68, -32, -12, 72, 54, -10, -42, 56, 60, 8, 52, 24, -52, -40, 26, -70, 54, 8, -66, 76, 54, 58, -58, -60, -8, 68, -28, 18, -50, 56, 40, 4, 14, -2, 2, -78, -26, -50, 70, 70, 0, 52, -32, 56, -12, 64, 0, 72, -30, -54, -2, -8, -12, -16, -36, 28, -46, -46, 2, 64, 24, -30, 44, -68, -16, -44, -20, -32, -6, -22, -42, 30, 60, 40, -82, -34, 56, -60, -18, 6, 8, -6, -14, 2, 40, -4, -6, 82, -4, 64, 44, 88, 12, -12, 50, -46, -24, -42, 54, -10, -16, 74, 82, -30, -14, 82, 44, -48, 24, 18, 82, -10, -2, 14, -54, -28, -28, -16, 44, -80, -18, -18, 48, 22, 62, 62, -4, 30, 96, -84, -18, 78, -18, -6, -12, 60, -34, -96, 96, 74, -42, 70, 32, 48, 14, 14, -48, -60, -48, 40, -18, 34, 78, -84, -6, 2, 72, -42, -4, -64, -48, -4, 48, -66, -18, 92, 18, 46, 58, 60, -36, -86, 58, 10, -42, 88, 26, -92, 74, 96, -64, -92, 76, -40, 2, -24, 32, 40, 84, -76, 48, 102, 24, 66, 98, 22, 54, -20, 32, -80, -4, 26, 26, -56, 52, -72, -76, -12, -8, 90, 108, -50, 10, 10, -34, -60, -48, -86, -14, 28, -32, -58, -10, -46, 50, 14, -10, 60, 104, -76, -8, 72, -24, -22, -38, 56, 108, -72, -42, 70, -68, -6, 66, -28, -60, 108, 8, -40, 96, 14, 62, 20, -34, 0, -76, -22, -62, -58, -98, 90, -28, 22, 106, -44, 28, 24, -32, 116, -8, -106, 70, -86, -8, -70, 118, -118, 94, 78, 12, 48, 82, 16, -56, 50, 110, -58, -46, -30, 96, 24, 46, 72, 70, -34, -72, 4, 48, 88, -12, 104, 32, 4, 78, 86, 36, -20, 46, 36, 12, 48, -26, 118, -36, 58, -98, 94, -90, -112, 40, 44, -36, -108, 94, -58, -4, 24, 46, 44, 106, -6, 110, -4, -16, 52, -78, -106, -30, -116, -90, -104, -28, -56, 44, 60, -48, -20, 120, 70, 62, -58, 14, 102, 42, 72, -82, -80, -118, 82, -108, 12, -6, -84, -42, 84, -78, -118, -30, 2, 120, -116, -34, 6, -58, 22, 24, 50, 26, -18, -88, 92, -40, 36, -16, 124, -38, -60, 34, -10, 20, -112, -78, -70, 60, 0, -74, -34, 2, 36, 6, 78, -90, 46, 40, -56, 58, 8, 128, 30, 58, 42, 0, 76, -52, -12, -46, 34, -102, -22, 4, 38, 82, -66, -46, 34, -44, -100, 36, 16, 52, -96, -2, -86, 10, -86, -36, 20, 0, -36, -96, -4, 16, -80, -20, -64, -68, 52, -4, -26, 94, 66, -94, -84, -62, 0, -54, -50, 56, -54, 72, -28, -36, -66, 6, 24, -46, 122, -66, 48, 44, 88, 42, -6, -18, -68, -42, 12, -64, 20, -108, -116, 28, -96, 94, 62, 18, -30, 114, -110, 76, -48, -18, -50, -98, -66, 66, -40, 48, -140, 76, -42, -62, 82, -10, -86, 16, -60, -80, 84, -78, -76, -120, -110, 98, 138, -44, 96, -76, -52, -120, 4, -58, 74, -56, 30, -22, -6, -8, -8, -108, 28, 60, 126, -6, 106, -60, 48, 28, 32, 144, 40, -22, -104, 46, 150, 120, -106, -98, -34, 36, -12, -146, 6, -52, -42, -40, -20, -14, 58, -22, -22, 4, -146, -126, -76, 0, 20, -16, 84, -14, -34, 16, -62, 142, -98, 88, -44, 100, -40, 122, -6, 130, -78, 142, 28, -138, -38, -110, 18, 76, -120, -118, -154, -22, 92, -132, -48, -32, -64, -50, 30, 100, -62, -78, 98, 124, -24, -90, 6, -138, -122, 18, 24, -62, 54, -86, 2, 74, 122, 124, 80, 32, -80, 38, 152, 86, -72, -62, -22, 60, 100, 36, -36, 34, -142, -86, 22, 8, 24, -82, 86, 130, -126, -112, -20, 20, 0, -140, 12, 14, -104, -54, 122, -30, 160, -116, 156, -16, 60, 18, -158, 104, -100, -10, 150, 144, 108, -26, -98, -8, -52, -116, 6, -60, -116, -28, -4, 34, -126, -70, -62, 70, 100, -128, 12, 22, 102, -122, -98, 38, -56, 4, 28, -52, -112, -10, 10, 48, 38, -90, -12, -140, -72, -156, -160, -30, 10, -122, -48, -80, 84, 32, 24, 40, -116, -156, 12, 146, 60, -102, -10, -106, 150, -168, 148, 40, 100, -72, 144, 8, 12, 160, 120, 134, 18, 0, -66, -72, 34, 4, -114, -112, 108, -138, -68, -114, 6, -84, 66, 144, 12, -18, -10, 24, 24, -138, -74, 28, -50, 68, -166, -106, 126, -10, 38, -108, -8, -20, 84, 92, -52, 134, -2, 152, 16, -26, -90, 138, -96, -18, -34, 42, -180, 60, 132, -100, -56, 70, 78, 154, 2, 120, -12, 146, -126, 12, 64, -112, 52, 140, -98, -146, 62, 36, 8, -88, -120, -88, 76, -86, -120, 30, -24, -28, -88, 88, 172, 32, -6, 34, 178, 106, 10, 114, -48, 4, 172, 26, 170, -98, -2, 62, -58, -162, -108, 58, 92, -118, -22, -92, -104, -64, -64, 74, -182, -100, 76, -34, 70, 8, 138, 94, -140, -44, -144, -144, -20, -134, -62, 70, 86, -162, -74, 0, 84, -100, 24, 56, 100, -102, -14, 138, 120, 80, -12, -22, 106, 74, 98, -50, 46, -118, 28, -56, 122, 134, -66, 100, 16, 44, 4, -168, 48, -70, -182, 128, -10, -142, 158, 0, -90, -130, -82, 20, -168, 176, -68, 58, -120, -2, 62, -108, 16, -146, -154, -124, -160, -114, -78, 24, 166, -22, 144, -84, -4, -180, -30, 108, 112, 146, -108, 24, 84, 88, -130, 158, -110, 146, -194, -42, -176, 36, 66, -102, -158, -130, -54, -112, -150, 158, -72, 124, -36, 80, 16, -36, -164, 6, -110, 122, -98, -18, 94, 22, -68, 120, -20, 4, 4, 72, -70, 138, -184, -106, 82, 154, 72, -24, 54, 102, -32, 134, -26, -34], 'hecke_polynomial': 'x', 'label': '2.2.21.1-192.1-g'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 21, 'ideals': ['[1, 1, 1]', '[3, 3, w + 1]', '[4, 2, 2]', '[5, 5, w]', '[5, 5, w - 1]', '[7, 7, -w - 3]', '[9, 3, 3]', '[12, 6, 2*w + 2]', '[15, 15, w + 4]', '[15, 15, -w + 5]', '[16, 4, 4]', '[17, 17, -2*w + 3]', '[17, 17, -2*w - 1]', '[20, 10, 2*w]', '[20, 10, 2*w - 2]', '[21, 21, -2*w + 1]', '[25, 5, 5]', '[25, 25, w + 5]', '[25, 25, -w + 6]', '[27, 9, 3*w + 3]', '[28, 14, -2*w - 6]', '[35, 35, -3*w + 5]', '[35, 35, -3*w - 2]', '[36, 6, 6]', '[37, 37, w + 6]', '[37, 37, -w + 7]', '[41, 41, 3*w + 1]', '[41, 41, -3*w + 4]', '[43, 43, 3*w + 8]', '[43, 43, 3*w - 11]', '[45, 15, 3*w]', '[45, 15, 3*w - 3]', '[47, 47, 3*w - 2]', '[47, 47, 3*w - 1]', '[48, 12, 4*w + 4]', '[49, 7, 7]', '[51, 51, -w - 7]', '[51, 51, w - 8]', '[59, 59, -5*w - 6]', '[59, 59, -4*w - 3]', '[60, 30, 2*w + 8]', '[60, 30, -2*w + 10]', '[63, 21, -3*w - 9]', '[64, 8, 8]', '[67, 67, -w - 8]', '[67, 67, w - 9]', '[68, 34, -4*w + 6]', '[68, 34, -4*w - 2]', '[75, 15, 5*w + 5]', '[75, 75, 4*w + 1]', '[75, 75, 4*w - 5]', '[79, 79, 2*w - 11]', '[79, 79, -2*w - 9]', '[80, 20, 4*w]', '[80, 20, 4*w - 4]', '[81, 9, 9]', '[83, 83, 4*w - 3]', '[83, 83, 4*w - 1]', '[84, 42, -4*w + 2]', '[85, 85, -w - 9]', '[85, 85, 3*w - 13]', '[85, 85, -3*w - 10]', '[85, 85, w - 10]', '[89, 89, -6*w - 7]', '[89, 89, -5*w - 4]', '[100, 10, 10]', '[100, 50, 2*w + 10]', '[100, 50, -2*w + 12]', '[101, 101, -5*w - 3]', '[101, 101, 5*w - 8]', '[105, 105, -w - 10]', '[105, 105, w - 11]', '[108, 18, 6*w + 6]', '[109, 109, 5*w - 18]', '[109, 109, 5*w + 13]', '[111, 111, 5*w - 7]', '[111, 111, 5*w + 2]', '[112, 28, -4*w - 12]', '[119, 119, 5*w + 1]', '[119, 119, 5*w - 6]', '[121, 11, -11]', '[123, 123, -2*w + 13]', '[123, 123, -2*w - 11]', '[125, 25, 5*w]', '[125, 25, 5*w - 5]', '[125, 125, 6*w - 11]', '[125, 125, 6*w + 5]', '[127, 127, -w - 11]', '[127, 127, w - 12]', '[129, 129, -5*w + 4]', '[129, 129, 5*w - 1]', '[131, 131, 5*w - 2]', '[131, 131, 5*w - 3]', '[135, 45, 3*w + 12]', '[135, 45, -3*w + 15]', '[140, 70, -6*w + 10]', '[140, 70, -6*w - 4]', '[141, 141, 5*w + 14]', '[141, 141, 4*w + 13]', '[144, 12, 12]', '[147, 21, 7*w + 7]', '[148, 74, 2*w + 12]', '[148, 74, -2*w + 14]', '[151, 151, -w - 12]', '[151, 151, w - 13]', '[153, 51, -6*w + 9]', '[153, 51, -6*w - 3]', '[163, 163, 3*w - 16]', '[163, 163, -3*w - 13]', '[164, 82, 6*w + 2]', '[164, 82, -6*w + 8]', '[167, 167, -8*w - 9]', '[167, 167, -7*w - 6]', '[169, 13, -13]', '[172, 86, 6*w + 16]', '[172, 86, 6*w - 22]', '[173, 173, -6*w - 1]', '[173, 173, 6*w - 7]', '[175, 35, -5*w - 15]', '[175, 175, 2*w - 15]', '[175, 175, -2*w - 13]', '[177, 177, -w - 13]', '[177, 177, w - 14]', '[180, 30, 6*w]', '[180, 30, 6*w - 6]', '[185, 185, 6*w - 5]', '[185, 185, 7*w + 5]', '[185, 185, 7*w - 12]', '[185, 185, 6*w - 1]', '[188, 94, 6*w - 4]', '[188, 94, 6*w - 2]', '[189, 63, -6*w + 3]', '[192, 24, 8*w + 8]', '[193, 193, -3*w - 14]', '[193, 193, 3*w - 17]', '[196, 14, 14]', '[201, 201, -7*w - 4]', '[201, 201, -10*w - 13]', '[204, 102, -2*w - 14]', '[204, 102, 2*w - 16]', '[205, 205, w + 14]', '[205, 205, 4*w + 15]', '[205, 205, 4*w - 19]', '[205, 205, w - 15]', '[211, 211, 6*w + 17]', '[211, 211, 6*w - 23]', '[215, 215, -8*w + 15]', '[215, 215, 7*w - 10]', '[215, 215, -11*w + 26]', '[215, 215, 8*w + 7]', '[225, 15, 15]', '[225, 75, 3*w + 15]', '[225, 75, -3*w + 18]', '[227, 227, 7*w - 9]', '[227, 227, -7*w - 2]', '[235, 235, w + 15]', '[235, 235, -2*w + 17]', '[235, 235, 2*w + 15]', '[235, 235, -w + 16]', '[236, 118, -10*w - 12]', '[236, 118, -8*w - 6]', '[237, 237, -7*w - 1]', '[237, 237, -13*w - 19]', '[240, 60, 4*w + 16]', '[240, 60, -4*w + 20]', '[243, 27, 9*w + 9]', '[245, 35, 7*w]', '[245, 35, 7*w - 7]', '[249, 249, 5*w + 17]', '[249, 249, 7*w + 19]', '[251, 251, 7*w - 6]', '[251, 251, 7*w - 1]', '[252, 42, -6*w - 18]', '[255, 255, -8*w + 13]', '[255, 255, -7*w + 2]', '[255, 255, -7*w + 5]', '[255, 255, -8*w - 5]', '[256, 16, 16]', '[257, 257, 7*w - 3]', '[257, 257, 7*w - 4]', '[259, 259, 3*w - 19]', '[259, 259, -3*w - 16]', '[267, 267, -w - 16]', '[267, 267, w - 17]', '[268, 134, -2*w - 16]', '[268, 134, 2*w - 18]', '[269, 269, -10*w - 11]', '[269, 269, -9*w - 8]', '[272, 68, -8*w + 12]', '[272, 68, -8*w - 4]', '[277, 277, 4*w - 21]', '[277, 277, -4*w - 17]', '[287, 287, 8*w + 3]', '[287, 287, -8*w + 11]', '[289, 17, 17]', '[289, 289, -5*w + 23]', '[289, 289, 5*w + 18]', '[293, 293, -9*w - 7]', '[293, 293, 9*w - 16]', '[295, 295, 6*w - 25]', '[295, 295, -3*w - 17]', '[295, 295, 3*w - 20]', '[295, 295, -6*w - 19]', '[300, 30, 10*w + 10]', '[300, 150, 8*w + 2]', '[300, 150, 8*w - 10]', '[301, 301, -w - 17]', '[301, 301, -w + 18]', '[303, 303, -13*w - 28]', '[303, 303, 2*w + 17]', '[311, 311, -8*w - 1]', '[311, 311, 8*w - 9]', '[315, 105, -9*w + 15]', '[315, 105, -9*w - 6]', '[316, 158, 4*w - 22]', '[316, 158, -4*w - 18]', '[320, 40, 8*w]', '[320, 40, 8*w - 8]', '[324, 18, 18]', '[327, 327, -8*w + 7]', '[327, 327, 8*w - 1]', '[329, 329, -11*w - 12]', '[329, 329, -10*w - 9]', '[331, 331, -5*w - 19]', '[331, 331, 5*w - 24]', '[332, 166, 8*w - 6]', '[332, 166, 8*w - 2]', '[333, 111, 3*w + 18]', '[333, 111, -3*w + 21]', '[335, 335, -9*w - 5]', '[335, 335, -8*w + 5]', '[335, 335, -8*w + 3]', '[335, 335, -9*w + 14]', '[336, 84, -8*w + 4]', '[337, 337, -w - 18]', '[337, 337, w - 19]', '[340, 170, -2*w - 18]', '[340, 170, 6*w - 26]', '[340, 170, -6*w - 20]', '[340, 170, 2*w - 20]', '[343, 49, -7*w - 21]', '[353, 353, 9*w - 13]', '[353, 353, -9*w - 4]', '[356, 178, -12*w - 14]', '[356, 178, -10*w - 8]', '[357, 357, 4*w + 19]', '[357, 357, -4*w + 23]', '[361, 19, -19]', '[363, 33, -11*w - 11]', '[369, 123, 9*w + 3]', '[369, 123, -9*w + 12]', '[373, 373, 3*w - 22]', '[373, 373, -3*w - 19]', '[375, 75, 5*w + 20]', '[375, 75, -5*w + 25]', '[375, 375, w + 19]', '[375, 375, -w + 20]', '[379, 379, 2*w - 21]', '[379, 379, -2*w - 19]', '[381, 381, -10*w - 7]', '[381, 381, -13*w - 16]', '[383, 383, 9*w - 11]', '[383, 383, -9*w - 2]', '[387, 129, 9*w + 24]', '[387, 129, 9*w - 33]', '[393, 393, 8*w + 23]', '[393, 393, 7*w + 22]', '[395, 395, -11*w + 21]', '[395, 395, -9*w - 1]', '[395, 395, -9*w + 10]', '[395, 395, -11*w - 10]', '[400, 20, 20]', '[400, 100, 4*w + 20]', '[400, 100, -4*w + 24]', '[404, 202, -10*w - 6]', '[404, 202, 10*w - 16]', '[405, 45, 9*w]', '[405, 45, 9*w - 9]', '[413, 413, 9*w - 8]', '[413, 413, 9*w - 1]', '[415, 415, w + 20]', '[415, 415, 3*w + 20]', '[415, 415, -3*w + 23]', '[415, 415, -w + 21]', '[419, 419, 9*w - 2]', '[419, 419, 9*w - 7]', '[420, 210, -2*w - 20]', '[420, 210, 2*w - 22]', '[421, 421, 5*w - 26]', '[421, 421, -5*w - 21]', '[423, 141, 9*w - 6]', '[423, 141, 9*w - 3]', '[425, 85, -10*w + 15]', '[425, 85, -10*w - 5]', '[425, 425, -9*w + 4]', '[425, 425, -11*w - 9]', '[425, 425, -11*w + 20]', '[425, 425, -9*w + 5]', '[432, 36, 12*w + 12]', '[436, 218, 10*w - 36]', '[436, 218, 10*w + 26]', '[441, 21, 21]', '[444, 222, 10*w - 14]', '[444, 222, 10*w + 4]', '[445, 445, 4*w - 25]', '[445, 445, -7*w - 23]', '[445, 445, 7*w - 30]', '[445, 445, -4*w - 21]', '[448, 56, -8*w - 24]', '[453, 453, -14*w - 17]', '[453, 453, -11*w - 8]', '[457, 457, -w - 21]', '[457, 457, w - 22]', '[459, 153, -3*w - 21]', '[459, 153, 3*w - 24]', '[461, 461, 10*w - 13]', '[461, 461, -10*w - 3]', '[463, 463, 2*w - 23]', '[463, 463, -2*w - 21]', '[467, 467, -13*w - 14]', '[467, 467, -12*w - 11]', '[469, 469, 5*w + 22]', '[469, 469, 12*w + 29]', '[476, 238, 10*w + 2]', '[476, 238, 10*w - 12]', '[479, 479, 11*w - 18]', '[479, 479, -11*w - 7]', '[484, 22, -22]', '[487, 487, -6*w - 23]', '[487, 487, 6*w - 29]', '[489, 489, -10*w - 1]', '[489, 489, -19*w - 28]', '[492, 246, -4*w + 26]', '[492, 246, -4*w - 22]', '[499, 499, 10*w - 37]', '[499, 499, 10*w + 27]', '[500, 50, 10*w]', '[500, 50, 10*w - 10]', '[500, 250, 12*w - 22]', '[500, 250, 12*w + 10]', '[501, 501, -w - 22]', '[501, 501, w - 23]', '[503, 503, -11*w - 6]', '[503, 503, 11*w - 17]', '[505, 505, -8*w + 33]', '[505, 505, -3*w + 25]', '[505, 505, -3*w - 22]', '[505, 505, -8*w - 25]', '[507, 39, -13*w - 13]', '[508, 254, -2*w - 22]', '[508, 254, 2*w - 24]', '[509, 509, 10*w - 9]', '[509, 509, 10*w - 1]', '[516, 258, -10*w + 8]', '[516, 258, 10*w - 2]', '[519, 519, -13*w - 31]', '[519, 519, 5*w + 23]', '[521, 521, 10*w - 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16]', '[5717, 5717, 33*w - 17]', '[5737, 5737, -9*w - 74]', '[5737, 5737, 9*w - 83]', '[5749, 5749, 7*w - 81]', '[5749, 5749, -7*w - 74]', '[5779, 5779, 23*w - 104]', '[5779, 5779, -23*w - 81]', '[5791, 5791, 15*w - 91]', '[5791, 5791, -15*w - 76]', '[5801, 5801, -43*w - 41]', '[5801, 5801, -45*w - 47]', '[5813, 5813, 34*w - 33]', '[5813, 5813, 34*w - 1]', '[5821, 5821, -20*w - 79]', '[5821, 5821, 20*w - 99]', '[5839, 5839, 33*w - 124]', '[5839, 5839, 33*w + 91]', '[5843, 5843, 36*w - 49]', '[5843, 5843, -36*w - 13]', '[5879, 5879, -35*w - 6]', '[5879, 5879, 35*w - 41]', '[5881, 5881, 16*w - 93]', '[5881, 5881, -16*w - 77]', '[5897, 5897, -47*w - 52]', '[5897, 5897, -42*w - 37]', '[5923, 5923, 22*w - 103]', '[5923, 5923, -22*w - 81]', '[5927, 5927, 37*w - 54]', '[5927, 5927, -37*w - 17]', '[5939, 5939, -45*w - 46]', '[5939, 5939, -44*w - 43]', '[5981, 5981, 38*w - 59]', '[5981, 5981, -38*w - 21]', '[6007, 6007, -11*w - 76]', '[6007, 6007, 11*w - 87]', '[6011, 6011, -35*w - 3]', '[6011, 6011, 35*w - 38]', '[6043, 6043, -18*w - 79]', '[6043, 6043, 18*w - 97]', '[6047, 6047, -47*w - 51]', '[6047, 6047, -43*w - 39]', '[6053, 6053, 34*w - 13]', '[6053, 6053, 34*w - 21]', '[6073, 6073, 32*w + 91]', '[6073, 6073, 32*w - 123]', '[6089, 6089, -35*w - 1]', '[6089, 6089, 35*w - 36]', '[6091, 6091, 29*w - 117]', '[6091, 6091, 30*w - 119]', '[6131, 6131, -37*w - 14]', '[6131, 6131, 37*w - 51]', '[6133, 6133, 12*w - 89]', '[6133, 6133, -12*w - 77]', '[6173, 6173, -41*w - 31]', '[6173, 6173, 41*w - 72]', '[6199, 6199, 10*w - 87]', '[6199, 6199, -10*w - 77]', '[6211, 6211, -6*w - 77]', '[6211, 6211, 6*w - 83]', '[6217, 6217, 9*w - 86]', '[6217, 6217, -9*w - 77]', '[6221, 6221, 35*w - 32]', '[6221, 6221, 35*w - 3]', '[6257, 6257, 37*w - 49]', '[6257, 6257, -37*w - 12]', '[6263, 6263, -39*w - 22]', '[6263, 6263, 39*w - 61]', '[6299, 6299, 35*w - 29]', '[6299, 6299, 35*w - 6]', '[6301, 6301, 15*w - 94]', '[6301, 6301, -15*w - 79]', '[6317, 6317, 37*w - 48]', '[6317, 6317, -37*w - 11]', '[6337, 6337, 11*w - 89]', '[6337, 6337, -11*w - 78]', '[6343, 6343, -23*w - 84]', '[6343, 6343, 23*w - 107]', '[6359, 6359, 35*w - 26]', '[6359, 6359, 35*w - 9]', '[6367, 6367, -14*w - 79]', '[6367, 6367, 14*w - 93]', '[6379, 6379, 2*w - 81]', '[6379, 6379, -2*w - 79]', '[6389, 6389, 35*w - 24]', '[6389, 6389, 35*w - 11]', '[6421, 6421, 36*w - 133]', '[6421, 6421, 36*w + 97]', '[6427, 6427, -21*w - 83]', '[6427, 6427, 21*w - 104]', '[6451, 6451, 35*w + 96]', '[6451, 6451, 35*w - 131]', '[6469, 6469, -12*w - 79]', '[6469, 6469, 12*w - 91]', '[6473, 6473, 41*w - 69]', '[6473, 6473, -41*w - 28]', '[6547, 6547, 9*w - 88]', '[6547, 6547, -9*w - 79]', '[6551, 6551, -40*w - 23]', '[6551, 6551, 40*w - 63]', '[6553, 6553, -8*w - 79]', '[6553, 6553, 8*w - 87]', '[6569, 6569, 41*w - 68]', '[6569, 6569, -41*w - 27]', '[6577, 6577, 16*w - 97]', '[6577, 6577, -16*w - 81]', '[6599, 6599, -45*w - 41]', '[6599, 6599, -49*w - 53]', '[6619, 6619, 37*w - 136]', '[6619, 6619, 37*w + 99]', '[6637, 6637, -w - 81]', '[6637, 6637, w - 82]', '[6653, 6653, 39*w - 56]', '[6653, 6653, -39*w - 17]', '[6661, 6661, -19*w - 83]', '[6661, 6661, 19*w - 102]', '[6673, 6673, -17*w - 82]', '[6673, 6673, 17*w - 99]', '[6679, 6679, 35*w - 132]', '[6679, 6679, 35*w + 97]', '[6703, 6703, 2*w - 83]', '[6703, 6703, -2*w - 81]', '[6719, 6719, 40*w - 61]', '[6719, 6719, -40*w - 21]', '[6737, 6737, 43*w - 76]', '[6737, 6737, -43*w - 33]', '[6761, 6761, 42*w - 71]', '[6761, 6761, -42*w - 29]', '[6763, 6763, 18*w - 101]', '[6763, 6763, -18*w - 83]', '[6779, 6779, 36*w - 13]', '[6779, 6779, 36*w - 23]', '[6803, 6803, 36*w - 19]', '[6803, 6803, 36*w - 17]', '[6829, 6829, -15*w - 82]', '[6829, 6829, 15*w - 97]', '[6841, 6841, 5*w - 86]', '[6841, 6841, -5*w - 81]', '[6863, 6863, -39*w - 14]', '[6863, 6863, 39*w - 53]', '[6871, 6871, 10*w - 91]', '[6871, 6871, -10*w - 81]', '[6883, 6883, 7*w - 88]', '[6883, 6883, -7*w - 81]', '[6947, 6947, 37*w - 3]', '[6947, 6947, 37*w - 34]', '[6967, 6967, -w - 83]', '[6967, 6967, w - 84]', '[6971, 6971, -52*w - 59]', '[6971, 6971, -45*w - 38]', '[6977, 6977, 37*w - 4]', '[6977, 6977, 37*w - 33]', '[6997, 6997, -21*w - 86]', '[6997, 6997, 21*w - 107]', '[7013, 7013, -46*w - 41]', '[7013, 7013, -51*w - 56]', '[7019, 7019, 41*w - 63]', '[7019, 7019, -41*w - 22]', '[7039, 7039, -17*w - 84]', '[7039, 7039, 17*w - 101]', '[7057, 7057, 9*w - 91]', '[7057, 7057, -9*w - 82]', '[7103, 7103, -41*w - 21]', '[7103, 7103, 41*w - 62]', '[7177, 7177, -24*w - 89]', '[7177, 7177, 24*w - 113]', '[7187, 7187, 37*w - 18]', '[7187, 7187, 37*w - 19]', '[7207, 7207, -6*w - 83]', '[7207, 7207, 6*w - 89]', '[7219, 7219, -10*w - 83]', '[7219, 7219, 10*w - 93]', '[7229, 7229, -39*w - 8]', '[7229, 7229, 39*w - 47]', '[7283, 7283, 39*w - 46]', '[7283, 7283, -39*w - 7]', '[7307, 7307, -52*w - 57]', '[7307, 7307, -47*w - 42]', '[7309, 7309, 20*w - 107]', '[7309, 7309, -20*w - 87]', '[7333, 7333, 37*w - 139]', '[7333, 7333, 37*w + 102]', '[7349, 7349, -50*w - 51]', '[7349, 7349, -49*w - 48]', '[7351, 7351, -5*w - 84]', '[7351, 7351, 5*w - 89]', '[7393, 7393, 32*w - 129]', '[7393, 7393, 33*w - 131]', '[7417, 7417, 19*w - 106]', '[7417, 7417, -19*w - 87]', '[7433, 7433, -39*w - 4]', '[7433, 7433, 39*w - 43]', '[7451, 7451, -43*w - 26]', '[7451, 7451, 43*w - 69]', '[7459, 7459, 22*w - 111]', '[7459, 7459, -22*w - 89]', '[7477, 7477, -w - 86]', '[7477, 7477, w - 87]', '[7481, 7481, 38*w - 29]', '[7481, 7481, 38*w - 9]', '[7517, 7517, 38*w - 27]', '[7517, 7517, 38*w - 11]', '[7523, 7523, 39*w - 41]', '[7523, 7523, -39*w - 2]', '[7559, 7559, -40*w - 9]', '[7559, 7559, 40*w - 49]', '[7561, 7561, -15*w - 86]', '[7561, 7561, 15*w - 101]', '[7577, 7577, 38*w - 21]', '[7577, 7577, 38*w - 17]', '[7603, 7603, -17*w - 87]', '[7603, 7603, 17*w - 104]', '[7607, 7607, -48*w - 43]', '[7607, 7607, -53*w - 58]', '[7639, 7639, 25*w - 117]', '[7639, 7639, -25*w - 92]', '[7643, 7643, 39*w - 38]', '[7643, 7643, 39*w - 1]', '[7649, 7649, -51*w - 52]', '[7649, 7649, -50*w - 49]', '[7669, 7669, 13*w - 99]', '[7669, 7669, -13*w - 86]', '[7681, 7681, 16*w - 103]', '[7681, 7681, -16*w - 87]', '[7687, 7687, 26*w - 119]', '[7687, 7687, -26*w - 93]', '[7691, 7691, -55*w - 63]', '[7691, 7691, -47*w - 39]', '[7703, 7703, -41*w - 13]', '[7703, 7703, 41*w - 54]', '[7723, 7723, 2*w - 89]', '[7723, 7723, -2*w - 87]', '[7727, 7727, -43*w - 23]', '[7727, 7727, 43*w - 66]', '[7753, 7753, -7*w - 86]', '[7753, 7753, 7*w - 93]', '[7817, 7817, -42*w - 17]', '[7817, 7817, 42*w - 59]', '[7829, 7829, 39*w - 7]', '[7829, 7829, 39*w - 32]', '[7853, 7853, 39*w - 31]', '[7853, 7853, 39*w - 8]', '[7879, 7879, -5*w - 87]', '[7879, 7879, 5*w - 92]', '[7901, 7901, 43*w - 64]', '[7901, 7901, -43*w - 21]', '[7933, 7933, -7*w - 87]', '[7933, 7933, 7*w - 94]', '[7937, 7937, -47*w - 37]', '[7937, 7937, 47*w - 84]', '[7963, 7963, 3*w - 91]', '[7963, 7963, -3*w - 88]', '[8017, 8017, 39*w + 107]', '[8017, 8017, 39*w - 146]', '[8039, 8039, 40*w - 39]', '[8039, 8039, 40*w - 1]', '[8059, 8059, 5*w - 93]', '[8059, 8059, -5*w - 88]', '[8069, 8069, -41*w - 7]', '[8069, 8069, 41*w - 48]', '[8081, 8081, 45*w - 73]', '[8081, 8081, -45*w - 28]', '[8089, 8089, 35*w - 138]', '[8089, 8089, 33*w - 134]', '[8101, 8101, -20*w - 91]', '[8101, 8101, 20*w - 111]', '[8111, 8111, 40*w - 3]', '[8111, 8111, 40*w - 37]', '[8123, 8123, -41*w - 6]', '[8123, 8123, 41*w - 47]', '[8147, 8147, -43*w - 18]', '[8147, 8147, 43*w - 61]', '[8191, 8191, 21*w - 113]', '[8191, 8191, -21*w - 92]', '[8231, 8231, 40*w - 7]', '[8231, 8231, 40*w - 33]', '[8233, 8233, 13*w - 102]', '[8233, 8233, -13*w - 89]', '[8237, 8237, 42*w - 53]', '[8237, 8237, -42*w - 11]', '[8269, 8269, 12*w - 101]', '[8269, 8269, -12*w - 89]', '[8273, 8273, -41*w - 3]', '[8273, 8273, 41*w - 44]', '[8291, 8291, -47*w - 34]', '[8291, 8291, 47*w - 81]', '[8311, 8311, -10*w - 89]', '[8311, 8311, 10*w - 99]', '[8317, 8317, -9*w - 89]', '[8317, 8317, 9*w - 98]', '[8353, 8353, -23*w - 94]', '[8353, 8353, 23*w - 117]', '[8363, 8363, -41*w - 1]', '[8363, 8363, 41*w - 42]', '[8443, 8443, 2*w - 93]', '[8443, 8443, -2*w - 91]', '[8447, 8447, 43*w - 57]', '[8447, 8447, -43*w - 14]', '[8467, 8467, 41*w - 152]', '[8467, 8467, 41*w + 111]', '[8501, 8501, -50*w - 43]', '[8501, 8501, -57*w - 64]', '[8521, 8521, 15*w - 106]', '[8521, 8521, -15*w - 91]', '[8527, 8527, 39*w + 109]', '[8527, 8527, 39*w - 148]', '[8543, 8543, -51*w - 46]', '[8543, 8543, -56*w - 61]', '[8563, 8563, 37*w - 144]', '[8563, 8563, 33*w - 136]', '[8573, 8573, 49*w - 88]', '[8573, 8573, -49*w - 39]', '[8609, 8609, 46*w - 73]', '[8609, 8609, -46*w - 27]', '[8627, 8627, 47*w - 78]', '[8627, 8627, -47*w - 31]', '[8647, 8647, 6*w - 97]', '[8647, 8647, -6*w - 91]', '[8669, 8669, 41*w - 8]', '[8669, 8669, 41*w - 33]', '[8677, 8677, 11*w - 102]', '[8677, 8677, -11*w - 91]', '[8689, 8689, 8*w - 99]', '[8689, 8689, -8*w - 91]', '[8693, 8693, 41*w - 9]', '[8693, 8693, 41*w - 32]', '[8699, 8699, 49*w - 87]', '[8699, 8699, -49*w - 38]', '[8719, 8719, -15*w - 92]', '[8719, 8719, 15*w - 107]', '[8731, 8731, 41*w + 112]', '[8731, 8731, 41*w - 153]', '[8737, 8737, -w - 93]', '[8737, 8737, w - 94]', '[8741, 8741, -53*w - 51]', '[8741, 8741, -55*w - 57]', '[8753, 8753, 41*w - 12]', '[8753, 8753, 41*w - 29]', '[8761, 8761, 40*w + 111]', '[8761, 8761, 40*w - 151]', '[8779, 8779, 23*w - 119]', '[8779, 8779, -23*w - 96]', '[8783, 8783, 41*w - 27]', '[8783, 8783, 41*w - 14]', '[8803, 8803, 38*w - 147]', '[8803, 8803, 33*w - 137]', '[8819, 8819, 41*w - 23]', '[8819, 8819, 41*w - 18]', '[8821, 8821, 35*w - 141]', '[8821, 8821, 36*w - 143]', '[8837, 8837, 43*w - 51]', '[8837, 8837, -43*w - 8]', '[8861, 8861, 42*w - 41]', '[8861, 8861, 42*w - 1]', '[8863, 8863, 7*w - 99]', '[8863, 8863, -7*w - 92]', '[8867, 8867, -57*w - 62]', '[8867, 8867, -52*w - 47]', '[8887, 8887, -9*w - 92]', '[8887, 8887, 9*w - 101]', '[8929, 8929, 25*w - 123]', '[8929, 8929, -25*w - 98]', '[8941, 8941, 4*w - 97]', '[8941, 8941, -4*w - 93]', '[8951, 8951, 43*w - 49]', '[8951, 8951, -43*w - 6]', '[8963, 8963, -51*w - 43]', '[8963, 8963, -59*w - 67]', '[8971, 8971, -14*w - 93]', '[8971, 8971, 14*w - 107]', '[9013, 9013, -13*w - 93]', '[9013, 9013, 13*w - 106]', '[9029, 9029, -50*w - 39]', '[9029, 9029, 50*w - 89]', '[9067, 9067, -11*w - 93]', '[9067, 9067, 11*w - 104]', '[9109, 9109, 28*w - 129]', '[9109, 9109, -28*w - 101]', '[9151, 9151, -25*w - 99]', '[9151, 9151, 25*w - 124]', '[9157, 9157, 29*w - 131]', '[9157, 9157, -29*w - 102]', '[9161, 9161, 42*w - 11]', '[9161, 9161, 42*w - 31]', '[9173, 9173, -46*w - 21]', '[9173, 9173, 46*w - 67]', '[9181, 9181, -5*w - 94]', '[9181, 9181, 5*w - 99]', '[9199, 9199, 43*w + 116]', '[9199, 9199, 43*w - 159]', '[9203, 9203, -44*w - 9]', '[9203, 9203, 44*w - 53]', '[9239, 9239, -56*w - 57]', '[9239, 9239, -55*w - 54]', '[9241, 9241, -21*w - 97]', '[9241, 9241, 21*w - 118]', '[9257, 9257, 42*w - 19]', '[9257, 9257, 42*w - 23]', '[9277, 9277, -9*w - 94]', '[9277, 9277, 9*w - 103]', '[9281, 9281, -50*w - 37]', '[9281, 9281, 50*w - 87]', '[9283, 9283, -27*w - 101]', '[9283, 9283, 27*w - 128]', '[9319, 9319, 35*w - 143]', '[9319, 9319, 38*w - 149]', '[9323, 9323, -44*w - 7]', '[9323, 9323, 44*w - 51]', '[9341, 9341, -47*w - 24]', '[9341, 9341, 47*w - 71]', '[9349, 9349, -20*w - 97]', '[9349, 9349, 20*w - 117]', '[9371, 9371, -45*w - 13]', '[9371, 9371, 45*w - 58]', '[9391, 9391, -29*w - 103]', '[9391, 9391, 29*w - 132]', '[9403, 9403, -17*w - 96]', '[9403, 9403, 17*w - 113]', '[9409, 97, -97]', '[9413, 9413, -49*w - 32]', '[9413, 9413, 49*w - 81]', '[9433, 9433, 23*w - 122]', '[9433, 9433, -23*w - 99]', '[9467, 9467, 43*w - 6]', '[9467, 9467, 43*w - 37]', '[9491, 9491, -53*w - 46]', '[9491, 9491, -60*w - 67]', '[9497, 9497, 43*w - 7]', '[9497, 9497, 43*w - 36]', '[9533, 9533, -59*w - 64]', '[9533, 9533, -54*w - 49]', '[9539, 9539, -44*w - 3]', '[9539, 9539, 44*w - 47]', '[9551, 9551, 43*w - 9]', '[9551, 9551, 43*w - 34]', '[9601, 9601, 25*w - 126]', '[9601, 9601, -25*w - 101]', '[9613, 9613, -17*w - 97]', '[9613, 9613, 17*w - 114]', '[9619, 9619, -13*w - 96]', '[9619, 9619, 13*w - 109]', '[9623, 9623, 51*w - 89]', '[9623, 9623, -51*w - 38]', '[9643, 9643, 7*w - 103]', '[9643, 9643, -7*w - 96]', '[9661, 9661, -19*w - 98]', '[9661, 9661, 19*w - 117]', '[9677, 9677, 43*w - 16]', '[9677, 9677, 43*w - 27]', '[9697, 9697, -w - 98]', '[9697, 9697, w - 99]', '[9719, 9719, -59*w - 63]', '[9719, 9719, -55*w - 51]', '[9739, 9739, -15*w - 97]', '[9739, 9739, 15*w - 112]', '[9743, 9743, -49*w - 29]', '[9743, 9743, 49*w - 78]', '[9749, 9749, 51*w - 88]', '[9749, 9749, -51*w - 37]', '[9769, 9769, -5*w - 97]', '[9769, 9769, 5*w - 102]', '[9781, 9781, -20*w - 99]', '[9781, 9781, 20*w - 119]', '[9787, 9787, -14*w - 97]', '[9787, 9787, 14*w - 111]', '[9791, 9791, -47*w - 19]', '[9791, 9791, 47*w - 66]', '[9803, 9803, 44*w - 41]', '[9803, 9803, 44*w - 3]', '[9811, 9811, 6*w - 103]', '[9811, 9811, -6*w - 97]', '[9829, 9829, -25*w - 102]', '[9829, 9829, 25*w - 127]', '[9833, 9833, -54*w - 47]', '[9833, 9833, -61*w - 68]', '[9871, 9871, 11*w - 108]', '[9871, 9871, -11*w - 97]', '[9887, 9887, -48*w - 23]', '[9887, 9887, 48*w - 71]', '[9907, 9907, -26*w - 103]', '[9907, 9907, 26*w - 129]', '[9929, 9929, 45*w - 49]', '[9929, 9929, -45*w - 4]', '[9949, 9949, 15*w - 113]', '[9949, 9949, -15*w - 98]']}
• 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
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-5, -1, 1], 'conductor': 21, 'degree': 2, 'dirichlet_group': [1, 20], 'disc_abs': 21, 'disc_rad': 21, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [0]], [5, [[1, 2]]], [7, [0]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[1, 2]]], [43, [[1, 2]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 4.58257569495584, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.21.1', 'local_algs': ['3.1.2.1a1.2', '7.1.2.1a1.1'], 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [3, 7], 'rd': 4.58257569496, 'regulator': {'__RealLiteral__': 0, 'data': '1.56679923697', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 2 \\)'], 'used_grh': False, 'zk': ['1', 'a']}