Hilbert modular form data - 2.2.8.1-686.2-f

Formats: - HTML - YAML - JSON - 2026-02-18T02:13:09.392753

• 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': 8, 'field_bad_primes': [2], 'field_label': '2.2.8.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.8.1-686.2-f', 'label_nsuffix': 5, 'label_suffix': 'f', 'level_bad_primes': [2, 7], 'level_ideal': '[686,98,-7*w + 28]', 'level_label': '686.2', 'level_norm': 686, 'parallel_weight': 2, 'short_label': '686.2-f', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2,2,w]', 1], ['[7,7,2*w + 1]', -1], ['[7,7,2*w - 1]', -1]], 'hecke_eigenvalues': [-1, 0, 1, 2, 4, -6, 8, -4, 2, 6, -2, -2, 0, 2, 10, 8, 12, -10, -4, -8, 4, -16, 18, -14, -12, -6, 18, 10, 18, 14, -8, 0, 6, -18, -8, 0, -2, -18, 6, 4, 24, -10, -14, -2, -26, -4, -4, 6, -14, -20, 8, -4, 18, 26, 24, 28, -24, 16, 0, 10, -10, 24, 0, -32, -10, -2, -18, -22, -24, 16, 0, 2, 28, 28, -30, -14, -34, -34, -38, -20, -40, 12, -2, -16, -32, -8, 18, -6, 22, -6, -16, -8, -26, 6, 4, 16, -12, 28, 16, -18, 38, -10, -22, -32, 22, 4, 40, -40, -46, 32, 8, 24, -34, 6, 32, -12, 42, -22, -26, -2, 14, 30, -34, -18, 42, -14, -48, 24, 8, -36, -14, -20, 16, 30, 26, -2, -32, 8, -30, -30, 34, -30, -4, -4, -24, -36, 14, -30, 2, -48, 48, 16, 8, -6, 12, -52, -34, 34, 26, -4, -32, 30, 6, -6, 2, -16, -40, 50, -26, -16, 4, 18, 38, 46, 46, 36, 30, 44, -44, 20, -48, -24, -62, 24, 24, -50, -26, 66, -6, 0, 2, -2, 44, -2, -34, 12, -10, 32, -8, 10, 42, -2, 28, 26, -14, 2, 18, 42, 42, 8, -64, 48, 24, 28, 26, 32, 40, 8, 46, 56, 24, -30, -16, -8, 18, -6, 20, 16, 24, 18, 32, 44, -28, 28, 40, -72, -66, 14, 24, -72, -22, 36, 28, 4, -60, 44, -10, 44, -2, -50, 16, 64, -64, -72, -38, 16, 24, 4, 18, 24, 34, 20, -32, -28, -54, -28, 50, -32, 12, 14, -8, -8, 16, -22, 76, -28, -38, 58, 20, 36, 48, -16, 82, 10, -34, 0, 64, -22, 50, 2, 74, 24, 18, -34, -26, -48, 48, 4, 58, 16, -64, -26, 22, -68, -24, 76, -52, 70, 78, -16, -12, 40, -14, -32, -24, -66, -4, 62, 26, 46, -50, -56, -28, 42, -42, 22, 80, -32, -24, 50, -46, -40, 42, 32, 34, -6, 34, -38, 10, 80, 68, -76, 36, -30, -86, 82, 82, 12, -82, -18, -90, -38, 58, 36, 24, -34, 28, -48, 32, -50, 46, 60, 56, 22, -38, -32, 24, -16, 8, -20, -24, -26, -36, 12, -6, -38, -68, -50, -22, 40, -32, -18, -18, 24, 16, -20, 32, -14, 2, 38, -10, 72, 88, 6, 46, -34, -82, 88, 38, -102, 66, -48, -24, 12, 42, -70, 34, 34, 6, -22, -44, 46, 42, 22, 48, 20, 10, -38, 18, 60, -92, -36, 80, -72, 102, 16, 82, -26, -10, 14, 94, -8, 8, -24, -48, 14, -10, -26, -54, -14, -42, 78, -32, 40, 18, 88, 18, 82, 62, 78, 40, -10, 48, -72, 44, 2, -78, 98, -102, 50, -32, 8, -102, -34, -20, 64, -18, 94, -36, -40, 96, 96, -38, 58, 88, -88, 100, -76, 22, -72, -48, 34, -72, 70, -94, 106, 2, -84, -16, 48, -24, -54, 106, -98, 62, -84, -20, -6, 42, -104, -64, -14, -12, -68, 72, 4, 36, -96, 40, -14, 8, -14, 34, 0, -120, 2, -68, 92, -78, 82, 36, -120, -74, 64, -86, 20, -40, -16, -90, -78, -72, 16, -48, 56, 18, 4, -50, -114, -40, 16, 112, -48, -38, 22, 72, -32, -74, -34, 14, -18, -80, 8, 66, 40, -18, -26, 48, 86, -36, -36, -32, -8, -96, -12, -48, 102, 38, -50, -72, 20, -20, -18, 70, -74, 82, 64, 58, 18, 112, -82, -96, 0, 2, -80, 60, -18, -80, 58, -60, -80, -2, 114, -24, 60, 24, -6, 16, 56, 46, -40, -56, 16, -120, -54, -36, -56, -2, 62, -6, 32, -22, -64, -124, 38, -90, -20, 116, 94, 30, 6, 14, 44, -68, 6, 102, -62, -46, -72, 76, -78, -38, -12, -36, -26, -114, -72, -118, 62, 110, 114, 114, 14, -74, -104, -76, -98, -24, 44, -80, -108, 78, -130, -34, 48, 40, -2, 54, -46, 4, 94, -42, 126, 22, -18, 94, -12, 8, 80, 40, 112, 108, 84, -94, -90, -10, 32, -56, -66, 50, -64, -24, 128, -96, 62, 28, -86, 2, -46, -40, 64, 64, -94, 66, 40, -40, -10, 30, -96, -48, -94, -38, -74, 138, -16, -132, 132, -62, 42, -32, 0, -16, 134, -98, 108, -58, 24, 56, 18, -38, -114, -72, 110, 94, -6, -102, 20, -46, 88, 80, 46, 86, -16, 60, 0, -144, -32, -98, 72, 16, -142, -54, 18, 66, 56, -64, 16, 8, -12, -118, 40, -40, 6, 22, -42, -140, -14, 18, -102, 106, -42, 62, -52, 48, 104, 120, -112, 62, -124, 0, 80, 108, 42, 50, 86, 80, 78, 142, -122, 102, -30, 20, 36, -40, 76, 4, -104, -74, 100, -72, -138, 78, -22, 110, -56, -56, 12, -82, 38, -62, -52, -2, 128, 16, 20, 44, 140, -40, 154, -62, 8, -112, -20, 34, -14, -54, -36, 12, 120, -24, 120, 64, -70, -6, 42, -70, 56, 152, 54, -82, 24, -112, -92, -58, -104, 24, 2, -46, 2, 84, 116, 110, -26, 130, 114, 72, 32, 72, -138, -114, 42, -144, -22, 42, 24, -96, 94, 86, -50, -94, 128, -152, -18, -70, 116, -40, -144, 0, 12, 10, -158, -96, 120, 32, 46, 4, -40, -144, -90, 86, 122, 114, -86, 10, -66, -42, -112, 128, -86, -24, 0, -24, 120, 4, 50, 48, 88, 86, 48, 24, 144, 2, 26, -110, -126, -144, -160, 50, 74, -120, 96, -64, 64, -66, 122, 16, -52, -160, 10, -96, -84, 140, 20, -82, -70, 102, -106, 48, 112, -48, 120, 130, -116, 130, 148, -84, 24, 14, -40, -118, 78, -42, 138, -72, 54, -58, 70, 116, -10, 132, -168, 116, -26, 66, 162, -90, 40, -84, 100, -122, 46, 158, 4, 72, -28, -56, -32, -62, -62, -32, 52, -136, 30, -18, 138, 14, 66, 112, -76, -62, -38, -52, 92, 94, 86, -16, 16, 54, -10, -92, -34, 56, 64, -130, 62, -56, 134, -56, 64, -44, 120, -154, -58, -114, 72, 140, -20, 68, -42, 30, -86, 26, -22, 54, -10, 70, 108, 76, -24, -90, 70, -50, 142, 68, 134, 102, -122, 128, 32, 146, -80, 114, 162, -138, -154, -72, -16, 84, 54, -10, -2, -46, -158, 4, 112, 68, 34, -38, 66, 126, -54, 98, -68, -112, 120, -86, -14, -50, 78, 50, -162, -122, -90, -104, 132, -158, -102, -150, -86, 112, 40, -162, 60, 18, 10, 44, 114, -64, -8, -40, 96, -102, 86, 166, -114, -36, 70, -72, -64, 86, -46, -36, 154, -10, -90, 146, 114, 112, 44, -24, 96, 80, 104, -50, 142, 148, 120, -148, 16, 158, -98, -50, -90, 138, -134, 160, 0, 130, -40, 88, -88, 26, 42, 138, -172, 186, -54, -2, 14, 174, 166, 112, 172, 120, -82, 136, -112, 22, -6, 108, 132, -26, -126, -32, -50, 78, 36, -24, 72, 16, 140, 124, -74, 70, -2, 6, -138, -124, -120, 40, 148, 50, 90, -170, -146, -16, 136, 46, 66, -72, -56, 62, 0, -34, 30, 6, -2, 50, 170, 54, -26, 120, -112, 60, -52, 128, 58, 76, -20, 74, 50, -22, -22, -144, 24, -60, 110, 38, -138, -180, 136, 70, -162, -42, 54, -138, -72, -84, -70, 60, -120, -106, -34, 48, -28, 48, 32, 136, -186, -112, 112], 'hecke_polynomial': 'x', 'label': '2.2.8.1-686.2-f'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 8, 'ideals': ['[1, 1, 1]', '[2, 2, -w]', '[4, 2, 2]', '[7, 7, -2*w + 1]', '[7, 7, -2*w - 1]', '[8, 4, -2*w]', '[9, 3, 3]', '[14, 14, w + 4]', '[14, 14, -w + 4]', '[16, 4, 4]', '[17, 17, 3*w + 1]', '[17, 17, 3*w - 1]', '[18, 6, -3*w]', '[23, 23, w + 5]', '[23, 23, -w + 5]', '[25, 5, 5]', '[28, 14, -4*w + 2]', '[28, 14, -4*w - 2]', '[31, 31, 4*w + 1]', '[31, 31, -4*w + 1]', '[32, 8, -4*w]', '[34, 34, -w - 6]', '[34, 34, w - 6]', '[36, 6, 6]', '[41, 41, 2*w - 7]', '[41, 41, -2*w - 7]', '[46, 46, -5*w + 2]', '[46, 46, -5*w - 2]', '[47, 47, -w - 7]', '[47, 47, w - 7]', '[49, 7, 7]', '[49, 49, 5*w + 1]', '[49, 49, 5*w - 1]', '[50, 10, -5*w]', '[56, 28, 2*w + 8]', '[56, 28, -2*w + 8]', '[62, 62, -w - 8]', '[62, 62, -w + 8]', '[63, 21, -6*w + 3]', '[63, 21, -6*w - 3]', '[64, 8, 8]', '[68, 34, 6*w + 2]', '[68, 34, 6*w - 2]', '[71, 71, -6*w - 1]', '[71, 71, 6*w - 1]', '[72, 12, -6*w]', '[73, 73, -7*w - 5]', '[73, 73, 7*w - 5]', '[79, 79, -w - 9]', '[79, 79, w - 9]', '[81, 9, 9]', '[82, 82, 7*w + 4]', '[82, 82, 7*w - 4]', '[89, 89, -4*w - 11]', '[89, 89, 4*w - 11]', '[92, 46, 2*w + 10]', '[92, 46, -2*w + 10]', '[94, 94, 7*w - 2]', '[94, 94, 7*w + 2]', '[97, 97, -7*w - 1]', '[97, 97, 7*w - 1]', '[98, 14, -7*w]', '[98, 98, -w - 10]', '[98, 98, w - 10]', '[100, 10, 10]', '[103, 103, -3*w - 11]', '[103, 103, 3*w - 11]', '[112, 28, -8*w + 4]', '[112, 28, -8*w - 4]', '[113, 113, 2*w - 11]', '[113, 113, -2*w - 11]', '[119, 119, -w - 11]', '[119, 119, -8*w - 3]', '[119, 119, -8*w + 3]', '[119, 119, w - 11]', '[121, 11, -11]', '[124, 62, 8*w + 2]', '[124, 62, -8*w + 2]', '[126, 42, 3*w + 12]', '[126, 42, -3*w + 12]', '[127, 127, -8*w - 1]', '[127, 127, 8*w - 1]', '[128, 16, -8*w]', '[136, 68, -2*w - 12]', '[136, 68, 2*w - 12]', '[137, 137, 4*w - 13]', '[137, 137, -4*w - 13]', '[142, 142, w + 12]', '[142, 142, w - 12]', '[144, 12, 12]', '[146, 146, 5*w + 14]', '[146, 146, 5*w - 14]', '[151, 151, 3*w - 13]', '[151, 151, -3*w - 13]', '[153, 51, 9*w + 3]', '[153, 51, 9*w - 3]', '[158, 158, 9*w - 2]', '[158, 158, 9*w + 2]', '[161, 161, -9*w - 1]', '[161, 161, 2*w - 13]', '[161, 161, -2*w - 13]', '[161, 161, -9*w + 1]', '[162, 18, -9*w]', '[164, 82, 4*w - 14]', '[164, 82, -4*w - 14]', '[167, 167, -w - 13]', '[167, 167, w - 13]', '[169, 13, -13]', '[175, 35, -10*w + 5]', '[175, 35, -10*w - 5]', '[178, 178, 11*w - 8]', '[178, 178, 11*w + 8]', '[184, 92, -10*w + 4]', '[184, 92, -10*w - 4]', '[188, 94, -2*w - 14]', '[188, 94, 2*w - 14]', '[191, 191, 10*w - 3]', '[191, 191, -10*w - 3]', '[193, 193, -4*w - 15]', '[193, 193, 4*w - 15]', '[194, 194, w + 14]', '[194, 194, w - 14]', '[196, 14, 14]', '[196, 98, 10*w + 2]', '[196, 98, 10*w - 2]', '[199, 199, -10*w - 1]', '[199, 199, 10*w - 1]', '[200, 20, -10*w]', '[206, 206, 11*w + 6]', '[206, 206, 11*w - 6]', '[207, 69, 3*w + 15]', '[207, 69, -3*w + 15]', '[217, 217, -11*w + 5]', '[217, 217, 2*w - 15]', '[217, 217, 2*w + 15]', '[217, 217, 11*w + 5]', '[223, 223, -w - 15]', '[223, 223, w - 15]', '[224, 56, 4*w + 16]', '[224, 56, -4*w + 16]', '[225, 15, 15]', '[226, 226, 11*w + 4]', '[226, 226, 11*w - 4]', '[233, 233, -11*w - 3]', '[233, 233, 11*w - 3]', '[238, 238, -3*w + 16]', '[238, 238, 11*w - 2]', '[238, 238, 11*w + 2]', '[238, 238, 3*w + 16]', '[239, 239, -5*w - 17]', '[239, 239, 5*w - 17]', '[241, 241, -11*w - 1]', '[241, 241, 11*w - 1]', '[242, 22, 11*w]', '[248, 124, -2*w - 16]', '[248, 124, -2*w + 16]', '[252, 42, -12*w + 6]', '[252, 42, -12*w - 6]', '[254, 254, w + 16]', '[254, 254, w - 16]', '[256, 16, 16]', '[257, 257, 4*w - 17]', '[257, 257, -4*w - 17]', '[263, 263, 7*w - 19]', '[263, 263, -7*w - 19]', '[271, 271, -3*w - 17]', '[271, 271, 3*w - 17]', '[272, 68, 12*w + 4]', '[272, 68, 12*w - 4]', '[274, 274, 13*w + 8]', '[274, 274, 13*w - 8]', '[279, 93, 12*w + 3]', '[279, 93, -12*w + 3]', '[281, 281, 2*w - 17]', '[281, 281, -2*w - 17]', '[284, 142, -12*w - 2]', '[284, 142, 12*w - 2]', '[287, 287, 16*w - 15]', '[287, 287, 12*w + 1]', '[287, 287, 12*w - 1]', '[287, 287, 16*w + 15]', '[288, 24, -12*w]', '[289, 17, 17]', '[289, 289, 13*w + 7]', '[289, 289, 13*w - 7]', '[292, 146, -14*w - 10]', '[292, 146, 14*w - 10]', '[302, 302, 13*w - 6]', '[302, 302, 13*w + 6]', '[306, 102, -3*w - 18]', '[306, 102, 3*w - 18]', '[311, 311, -5*w - 19]', '[311, 311, 5*w - 19]', '[313, 313, -8*w - 21]', '[313, 313, 8*w - 21]', '[316, 158, -2*w - 18]', '[316, 158, 2*w - 18]', '[322, 322, w + 18]', '[322, 322, 13*w - 4]', '[322, 322, 13*w + 4]', '[322, 322, -w + 18]', '[324, 18, 18]', '[328, 164, 14*w + 8]', '[328, 164, 14*w - 8]', '[329, 329, 15*w - 11]', '[329, 329, 13*w - 3]', '[329, 329, 13*w + 3]', '[329, 329, 15*w + 11]', '[334, 334, 13*w - 2]', '[334, 334, 13*w + 2]', '[337, 337, -13*w - 1]', '[337, 337, 13*w - 1]', '[338, 26, 13*w]', '[343, 49, -14*w + 7]', '[343, 49, -14*w - 7]', '[343, 343, 3*w - 19]', '[343, 343, -3*w - 19]', '[350, 70, 5*w + 20]', '[350, 70, -5*w + 20]', '[353, 353, 2*w - 19]', '[353, 353, -2*w - 19]', '[356, 178, -8*w - 22]', '[356, 178, 8*w - 22]', '[359, 359, -w - 19]', '[359, 359, w - 19]', '[361, 19, -19]', '[367, 367, 9*w - 23]', '[367, 367, -9*w - 23]', '[368, 92, 4*w + 20]', '[368, 92, -4*w + 20]', '[369, 123, 6*w - 21]', '[369, 123, -6*w - 21]', '[376, 188, 14*w - 4]', '[376, 188, 14*w + 4]', '[382, 382, 3*w + 20]', '[382, 382, 3*w - 20]', '[383, 383, -14*w - 3]', '[383, 383, 14*w - 3]', '[386, 386, 15*w + 8]', '[386, 386, 15*w - 8]', '[388, 194, -14*w - 2]', '[388, 194, 14*w - 2]', '[391, 391, 14*w + 1]', '[391, 391, -5*w + 21]', '[391, 391, 5*w + 21]', '[391, 391, 14*w - 1]', '[392, 28, -14*w]', '[392, 196, -2*w - 20]', '[392, 196, 2*w - 20]', '[398, 398, w + 20]', '[398, 398, w - 20]', '[400, 20, 20]', '[401, 401, -8*w - 23]', '[401, 401, 8*w - 23]', '[409, 409, -17*w - 13]', '[409, 409, 17*w - 13]', '[412, 206, -6*w - 22]', '[412, 206, 6*w - 22]', '[414, 138, -15*w + 6]', '[414, 138, -15*w - 6]', '[423, 141, -3*w - 21]', '[423, 141, 3*w - 21]', '[425, 85, 15*w + 5]', '[425, 85, 15*w - 5]', '[431, 431, -7*w - 23]', '[431, 431, 7*w - 23]', '[433, 433, 2*w - 21]', '[433, 433, -2*w - 21]', '[434, 434, -15*w - 4]', '[434, 434, -5*w - 22]', '[434, 434, -5*w + 22]', '[434, 434, 15*w - 4]', '[439, 439, -w - 21]', '[439, 439, w - 21]', '[441, 21, 21]', '[441, 147, 15*w + 3]', '[441, 147, 15*w - 3]', '[446, 446, 15*w - 2]', '[446, 446, 15*w + 2]', '[448, 56, -16*w + 8]', '[448, 56, -16*w - 8]', '[449, 449, -15*w - 1]', '[449, 449, 15*w - 1]', '[450, 30, -15*w]', '[452, 226, 4*w - 22]', '[452, 226, -4*w - 22]', '[457, 457, -6*w - 23]', '[457, 457, 6*w - 23]', '[463, 463, 9*w - 25]', '[463, 463, -9*w - 25]', '[466, 466, 3*w - 22]', '[466, 466, 3*w + 22]', '[476, 238, -2*w - 22]', '[476, 238, -16*w - 6]', '[476, 238, -16*w + 6]', '[476, 238, 2*w - 22]', '[478, 478, 17*w - 10]', '[478, 478, 17*w + 10]', '[479, 479, -18*w - 13]', '[479, 479, 18*w - 13]', '[482, 482, w + 22]', '[482, 482, w - 22]', '[484, 22, -22]', '[487, 487, 16*w - 5]', '[487, 487, -16*w - 5]', '[496, 124, 16*w + 4]', '[496, 124, -16*w + 4]', '[497, 497, 8*w - 25]', '[497, 497, -4*w - 23]', '[497, 497, -4*w + 23]', '[497, 497, 8*w + 25]', '[503, 503, 16*w - 3]', '[503, 503, -16*w - 3]', '[504, 84, 6*w + 24]', '[504, 84, -6*w + 24]', '[508, 254, -16*w - 2]', '[508, 254, 16*w - 2]', '[511, 511, 17*w + 33]', '[511, 511, 3*w + 23]', '[511, 511, 3*w - 23]', '[511, 511, 17*w - 33]', '[512, 32, -16*w]', '[514, 514, 17*w - 8]', '[514, 514, 17*w + 8]', '[521, 521, 2*w - 23]', '[521, 521, -2*w - 23]', '[526, 526, 19*w - 14]', '[526, 526, 19*w + 14]', '[527, 527, -w - 23]', '[527, 527, 7*w - 25]', '[527, 527, 7*w + 25]', '[527, 527, -w + 23]', '[529, 23, 23]', '[529, 529, 17*w + 7]', '[529, 529, 17*w - 7]', '[542, 542, 17*w + 6]', '[542, 542, 17*w - 6]', '[544, 136, -4*w - 24]', '[544, 136, 4*w - 24]', '[548, 274, 8*w - 26]', '[548, 274, -8*w - 26]', '[553, 553, 19*w + 13]', '[553, 553, 17*w + 5]', '[553, 553, 17*w - 5]', '[553, 553, 19*w - 13]', '[558, 186, -3*w - 24]', '[558, 186, -3*w + 24]', '[562, 562, 17*w - 4]', '[562, 562, 17*w + 4]', '[567, 63, -18*w + 9]', '[567, 63, -18*w - 9]', '[568, 284, 2*w + 24]', '[568, 284, 2*w - 24]', '[569, 569, -17*w - 3]', '[569, 569, 17*w - 3]', '[574, 574, -w - 24]', '[574, 574, -15*w - 32]', '[574, 574, 15*w - 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85]', '[7207, 7207, 3*w - 85]', '[7207, 7207, -3*w - 85]', '[7247, 7247, 41*w - 103]', '[7247, 7247, -41*w - 103]', '[7297, 7297, 26*w - 93]', '[7297, 7297, -26*w - 93]', '[7321, 7321, 61*w - 11]', '[7321, 7321, -61*w - 11]', '[7351, 7351, -35*w - 99]', '[7351, 7351, 35*w - 99]', '[7369, 7369, 10*w - 87]', '[7369, 7369, -10*w - 87]', '[7393, 7393, 61*w - 7]', '[7393, 7393, -61*w - 7]', '[7417, 7417, 61*w - 5]', '[7417, 7417, -61*w - 5]', '[7433, 7433, 61*w - 3]', '[7433, 7433, -61*w - 3]', '[7457, 7457, -28*w - 95]', '[7457, 7457, 28*w - 95]', '[7481, 7481, 71*w - 51]', '[7481, 7481, -71*w - 51]', '[7487, 7487, 31*w - 97]', '[7487, 7487, -31*w - 97]', '[7489, 7489, 34*w - 99]', '[7489, 7489, -34*w - 99]', '[7529, 7529, 14*w - 89]', '[7529, 7529, -14*w - 89]', '[7537, 7537, -4*w - 87]', '[7537, 7537, 4*w - 87]', '[7559, 7559, 72*w - 53]', '[7559, 7559, -72*w - 53]', '[7561, 7561, 2*w - 87]', '[7561, 7561, -2*w - 87]', '[7577, 7577, -63*w - 19]', '[7577, 7577, 63*w - 19]', '[7583, 7583, 13*w - 89]', '[7583, 7583, -13*w - 89]', '[7591, 7591, 23*w - 93]', '[7591, 7591, -23*w - 93]', '[7607, 7607, -62*w - 9]', '[7607, 7607, 62*w - 9]', '[7639, 7639, -62*w - 7]', '[7639, 7639, 62*w - 7]', '[7649, 7649, -63*w - 17]', '[7649, 7649, 63*w - 17]', '[7673, 7673, -26*w - 95]', '[7673, 7673, 26*w - 95]', '[7681, 7681, 22*w - 93]', '[7681, 7681, -22*w - 93]', '[7687, 7687, -62*w - 1]', '[7687, 7687, 62*w - 1]', '[7703, 7703, -74*w - 57]', '[7703, 7703, 74*w - 57]', '[7727, 7727, 29*w - 97]', '[7727, 7727, -29*w - 97]', '[7753, 7753, 32*w - 99]', '[7753, 7753, -32*w - 99]', '[7759, 7759, -9*w - 89]', '[7759, 7759, 9*w - 89]', '[7793, 7793, 8*w - 89]', '[7793, 7793, -8*w - 89]', '[7817, 7817, -63*w - 11]', '[7817, 7817, 63*w - 11]', '[7823, 7823, 7*w - 89]', '[7823, 7823, -7*w - 89]', '[7841, 7841, 28*w - 97]', '[7841, 7841, -28*w - 97]', '[7873, 7873, -24*w - 95]', '[7873, 7873, 24*w - 95]', '[7879, 7879, -31*w - 99]', '[7879, 7879, 31*w - 99]', '[7919, 7919, -w - 89]', '[7919, 7919, w - 89]', '[7927, 7927, -74*w - 55]', '[7927, 7927, 74*w - 55]', '[7937, 7937, -63*w - 1]', '[7937, 7937, 63*w - 1]', '[7951, 7951, -27*w - 97]', '[7951, 7951, 27*w - 97]', '[7993, 7993, -12*w - 91]', '[7993, 7993, 12*w - 91]', '[8009, 8009, 44*w - 109]', '[8009, 8009, -44*w - 109]', '[8017, 8017, 36*w - 103]', '[8017, 8017, -36*w - 103]', '[8039, 8039, 11*w - 91]', '[8039, 8039, -11*w - 91]', '[8081, 8081, 10*w - 91]', '[8081, 8081, -10*w - 91]', '[8087, 8087, -41*w - 107]', '[8087, 8087, 41*w - 107]', '[8089, 8089, -65*w - 19]', '[8089, 8089, 65*w - 19]', '[8111, 8111, 64*w - 9]', '[8111, 8111, -64*w - 9]', '[8161, 8161, -65*w - 17]', '[8161, 8161, 65*w - 17]', '[8167, 8167, -64*w - 5]', '[8167, 8167, 64*w - 5]', '[8191, 8191, -64*w - 1]', '[8191, 8191, 64*w - 1]', '[8209, 8209, 6*w - 91]', '[8209, 8209, -6*w - 91]', '[8231, 8231, 5*w - 91]', '[8231, 8231, -5*w - 91]', '[8233, 8233, -28*w - 99]', '[8233, 8233, 28*w - 99]', '[8263, 8263, 3*w - 91]', '[8263, 8263, -3*w - 91]', '[8273, 8273, 2*w - 91]', '[8273, 8273, -2*w - 91]', '[8287, 8287, 37*w - 105]', '[8287, 8287, -37*w - 105]', '[8297, 8297, 34*w - 103]', '[8297, 8297, -34*w - 103]', '[8311, 8311, -13*w - 93]', '[8311, 8311, 13*w - 93]', '[8329, 8329, -65*w - 11]', '[8329, 8329, 65*w - 11]', '[8353, 8353, -42*w - 109]', '[8353, 8353, 42*w - 109]', '[8369, 8369, -65*w - 9]', '[8369, 8369, 65*w - 9]', '[8377, 8377, 77*w - 59]', '[8377, 8377, -77*w - 59]', '[8423, 8423, 66*w - 17]', '[8423, 8423, -66*w - 17]', '[8431, 8431, -33*w - 103]', '[8431, 8431, 33*w - 103]', '[8447, 8447, 78*w - 61]', '[8447, 8447, -78*w - 61]', '[8513, 8513, -79*w + 63]', '[8513, 8513, 79*w + 63]', '[8521, 8521, -8*w - 93]', '[8521, 8521, 8*w - 93]', '[8527, 8527, 76*w - 55]', '[8527, 8527, -76*w - 55]', '[8537, 8537, -67*w - 21]', '[8537, 8537, 67*w - 21]', '[8543, 8543, 66*w - 13]', '[8543, 8543, -66*w - 13]', '[8599, 8599, 5*w - 93]', '[8599, 8599, -5*w - 93]', '[8609, 8609, 77*w - 57]', '[8609, 8609, -77*w - 57]', '[8623, 8623, -43*w - 111]', '[8623, 8623, 43*w - 111]', '[8641, 8641, 2*w - 93]', '[8641, 8641, -2*w - 93]', '[8647, 8647, -w - 93]', '[8647, 8647, w - 93]', '[8663, 8663, -66*w - 7]', '[8663, 8663, 66*w - 7]', '[8681, 8681, -40*w - 109]', '[8681, 8681, 40*w - 109]', '[8689, 8689, -67*w - 17]', '[8689, 8689, 67*w - 17]', '[8713, 8713, -34*w - 105]', '[8713, 8713, 34*w - 105]', '[8719, 8719, 45*w - 113]', '[8719, 8719, -45*w - 113]', '[8737, 8737, -12*w - 95]', '[8737, 8737, 12*w - 95]', '[8753, 8753, -67*w - 15]', '[8753, 8753, 67*w - 15]', '[8761, 8761, 79*w - 61]', '[8761, 8761, -79*w - 61]', '[8783, 8783, -11*w - 95]', '[8783, 8783, 11*w - 95]', '[8807, 8807, -68*w - 21]', '[8807, 8807, 68*w - 21]', '[8831, 8831, 80*w - 63]', '[8831, 8831, -80*w - 63]', '[8839, 8839, -39*w - 109]', '[8839, 8839, 39*w - 109]', '[8849, 8849, -26*w - 101]', '[8849, 8849, 26*w - 101]', '[8863, 8863, 9*w - 95]', '[8863, 8863, -9*w - 95]', '[8887, 8887, 68*w - 19]', '[8887, 8887, -68*w - 19]', '[8929, 8929, 67*w - 7]', '[8929, 8929, -67*w - 7]', '[8951, 8951, 25*w - 101]', '[8951, 8951, -25*w - 101]', '[8969, 8969, 67*w - 3]', '[8969, 8969, -67*w - 3]', '[8999, 8999, -35*w - 107]', '[8999, 8999, 35*w - 107]', '[9001, 9001, 79*w - 59]', '[9001, 9001, -79*w - 59]', '[9007, 9007, -3*w - 95]', '[9007, 9007, 3*w - 95]', '[9041, 9041, 28*w - 103]', '[9041, 9041, -28*w - 103]', '[9049, 9049, 24*w - 101]', '[9049, 9049, -24*w - 101]', '[9103, 9103, 31*w - 105]', '[9103, 9103, -31*w - 105]', '[9127, 9127, -68*w - 11]', '[9127, 9127, 68*w - 11]', '[9137, 9137, 34*w - 107]', '[9137, 9137, -34*w - 107]', '[9151, 9151, -27*w - 103]', '[9151, 9151, 27*w - 103]', '[9161, 9161, 69*w - 19]', '[9161, 9161, -69*w - 19]', '[9199, 9199, 68*w - 7]', '[9199, 9199, -68*w - 7]', '[9209, 9209, 10*w - 97]', '[9209, 9209, -10*w - 97]', '[9239, 9239, -68*w - 3]', '[9239, 9239, 68*w - 3]', '[9241, 9241, -42*w - 113]', '[9241, 9241, 42*w - 113]', '[9257, 9257, -26*w - 103]', '[9257, 9257, 26*w - 103]', '[9281, 9281, 8*w - 97]', '[9281, 9281, -8*w - 97]', '[9311, 9311, -7*w - 97]', '[9311, 9311, 7*w - 97]', '[9319, 9319, -80*w - 59]', '[9319, 9319, 80*w - 59]', '[9337, 9337, 6*w - 97]', '[9337, 9337, -6*w - 97]', '[9343, 9343, -29*w - 105]', '[9343, 9343, 29*w - 105]', '[9377, 9377, 4*w - 97]', '[9377, 9377, -4*w - 97]', '[9391, 9391, 3*w - 97]', '[9391, 9391, -3*w - 97]', '[9431, 9431, 35*w - 109]', '[9431, 9431, -35*w - 109]', '[9433, 9433, -38*w - 111]', '[9433, 9433, 38*w - 111]', '[9439, 9439, 70*w - 19]', '[9439, 9439, -70*w - 19]', '[9463, 9463, 13*w - 99]', '[9463, 9463, -13*w - 99]', '[9473, 9473, -69*w - 7]', '[9473, 9473, 69*w - 7]', '[9479, 9479, 82*w - 63]', '[9479, 9479, -82*w - 63]', '[9497, 9497, -69*w - 5]', '[9497, 9497, 69*w - 5]', '[9511, 9511, -70*w - 17]', '[9511, 9511, 70*w - 17]', '[9521, 9521, -69*w - 1]', '[9521, 9521, 69*w - 1]', '[9551, 9551, 80*w - 57]', '[9551, 9551, -80*w - 57]', '[9601, 9601, -10*w - 99]', '[9601, 9601, 10*w - 99]', '[9623, 9623, -84*w + 67]', '[9623, 9623, 84*w + 67]', '[9631, 9631, -70*w - 13]', '[9631, 9631, 70*w - 13]', '[9649, 9649, -30*w - 107]', '[9649, 9649, 30*w - 107]', '[9679, 9679, 70*w - 11]', '[9679, 9679, -70*w - 11]', '[9689, 9689, -16*w - 101]', '[9689, 9689, 16*w - 101]', '[9697, 9697, 42*w - 115]', '[9697, 9697, -42*w - 115]', '[9719, 9719, 70*w - 9]', '[9719, 9719, -70*w - 9]', '[9721, 9721, -71*w - 19]', '[9721, 9721, 71*w - 19]', '[9743, 9743, -47*w - 119]', '[9743, 9743, 47*w - 119]', '[9767, 9767, -29*w - 107]', '[9767, 9767, 29*w - 107]', '[9769, 9769, -4*w - 99]', '[9769, 9769, 4*w - 99]', '[9791, 9791, 70*w - 3]', '[9791, 9791, -70*w - 3]', '[9817, 9817, -44*w - 117]', '[9817, 9817, 44*w - 117]', '[9833, 9833, 32*w - 109]', '[9833, 9833, -32*w - 109]', '[9839, 9839, -49*w - 121]', '[9839, 9839, 49*w - 121]', '[9857, 9857, -71*w - 15]', '[9857, 9857, 71*w - 15]', '[9871, 9871, 35*w - 111]', '[9871, 9871, -35*w - 111]', '[9887, 9887, 84*w - 65]', '[9887, 9887, -84*w - 65]', '[9929, 9929, -46*w - 119]', '[9929, 9929, 46*w - 119]', '[9967, 9967, 82*w - 59]', '[9967, 9967, -82*w - 59]']}
• 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': [-2, 0, 1], 'conductor': 8, 'degree': 2, 'dirichlet_group': [1, 5], 'disc_abs': 8, 'disc_rad': 2, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 1]]], [5, [[2, 1]]], [7, [[1, 2]]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[1, 2]]], [37, [[2, 1]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3], 'galois_label': '2T1', 'galt': 1, 'grd': 2.8284271247461903, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.8.1', 'local_algs': ['2.1.2.3a1.3'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 0, 'ramps': [2], 'rd': 2.82842712475, 'regulator': {'__RealLiteral__': 0, 'data': '0.88137358702', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a']}