Hilbert modular form data - 2.2.28.1-676.1-a

Formats: - HTML - YAML - JSON - 2024-09-15T01:05:33.208546

• 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': 28, 'field_bad_primes': [2, 7], 'field_label': '2.2.28.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.28.1-676.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2, 13], 'level_ideal': '[676, 26, -26]', 'level_label': '676.1', 'level_norm': 676, 'parallel_weight': 2, 'short_label': '676.1-a', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, w - 3]', -1], ['[169, 13, -13]', -1]], 'hecke_eigenvalues': [0, -3, 1, -4, 6, 6, 6, 10, -6, 5, 7, 7, 9, -11, -9, 8, -4, -8, 0, -6, -6, -4, 16, -10, 2, 15, -1, -15, -4, 12, 8, -4, -8, 16, -9, 9, 16, 16, 1, 2, -10, 15, -15, -20, 20, -21, 9, -2, -26, 3, -13, -17, 19, 17, -29, -8, 24, 0, 32, -7, -11, 18, 8, 28, -16, -20, -13, -11, 17, -23, 14, -26, 8, -20, -25, 29, 6, -30, 0, 24, 5, 1, -11, 35, 4, 40, 4, -12, -28, 40, -20, -36, 4, 20, -6, 14, -27, -15, 15, -2, 10, -13, 13, 21, -7, 13, -3, -20, 36, -18, 30, 23, 25, -24, 4, -8, 4, -7, 33, 28, -40, 18, 46, -24, 24, -25, -25, 40, 20, 22, -22, -35, 43, -18, 34, 8, 16, -24, -48, 8, 32, 18, -30, -50, 34, -54, -26, -1, 21, 29, 17, 33, 15, 8, -12, 22, 54, 35, -17, -52, -44, 24, -40, 46, -10, 26, -34, -6, -42, 22, -30, 2, -46, -37, 63, -4, 16, -38, -22, 24, 28, -20, 28, 31, 37, 2, -2, 4, -44, -36, 8, 35, -19, 44, 4, -8, -60, 16, 64, -10, -46, -21, 23, -37, 11, -4, -12, 31, -43, 39, -15, 34, 58, -7, -5, 54, 54, 45, 33, -32, -16, 22, 74, 2, 46, -44, -20, -15, -31, 19, -25, -31, -21, 27, -59, -24, 4, -69, -9, -32, 36, -70, -50, 64, 4, 5, -73, 42, 14, -19, -5, -24, -36, 48, 12, -63, 4, 28, -69, 61, 44, 40, -56, -72, 19, -75, -22, 26, 36, 36, -34, -18, 58, 42, -38, -6, 78, 19, 43, -42, 10, 37, -17, 30, 30, -45, 23, 0, -12, -30, -26, 68, -80, -8, 12, 77, 9, 52, -52, -47, -33, -64, 44, 36, 48, 8, 52, 6, 50, -67, 85, -34, 26, 15, 7, 55, 19, -52, 68, -66, 26, 28, -36, -6, 74, 15, 9, -10, -54, 22, 10, 60, 36, -30, 14, -50, 50, 76, 28, -82, 90, -27, -75, -51, -85, -31, -93, 52, 52, 0, -12, 77, 43, 20, -28, -24, 68, -71, 59, -42, -18, -7, -47, -18, 42, -37, 7, -79, 73, 43, -69, 65, -19, 2, -26, -78, 90, 12, 60, -56, -8, -48, -44, 2, 6, -68, -16, -88, -16, -26, 18, 78, -66, -80, -8, 61, 37, 75, -79, -18, 90, -30, 2, 2, 70, -1, 73, -54, 78, -2, -14, 30, 42, 38, 22, -17, -73, 38, 86, 48, 36, -4, -60, 36, 12, -22, 94, -38, -38, 66, 74, 11, -7, 38, 106, -13, 37, -91, -25, 14, 42, -22, 42, -99, 75, 50, -62, 44, -44, -32, 112, 72, -80, -22, 58, 54, 14, -33, 9, -51, -39, 14, -90, -86, -10, 28, -52, 110, 42, 24, 12, -62, 58, 16, 40, 63, 45, 64, -68, 12, 40, -67, 71, 28, 108, -5, 5, 20, 20, 61, 83, 72, 0, -52, -56, 8, -8, -4, -56, 34, -2, -42, 74, 14, 94, 13, -45, -57, 69, -106, 62, -38, 106, 32, -20, 66, -18, -39, -19, 18, -38, 15, -115, 99, -27, -44, -64, 31, -52, 32, 106, 86, -99, -99, -97, 3, -28, 0, -7, -101, 90, 70, 89, 3, 66, -34, -64, -16, -103, -3, -69, -85, 114, 18, -3, -9, -30, 18, -71, 29, -70, 10, 34, 46, -110, 2, 39, -9, -82, 42, -99, 57, 6, 18, -52, -76, -64, 20, 72, -48, -19, -49, 93, 3, -6, 54, -14, -74, -46, 18, -13, -73, -71, -65, -40, -48, -12, 56, 70, -46, -108, 36, 87, 15, 10, -74, -71, -7, -35, 122, 102, 102, 118, -132, 48, 51, 49, 8, -8, -114, -78, 32, 80, -90, -78, 83, -17, 117, -67, 54, 74, 46, -82, -108, -108, -40, -112, -35, -115, -94, -62, 108, -84, -10, 66, 53, 57, -53, 109, -72, -96, -110, 34, 44, 84, -77, -55, 50, -50, 13, 71, -57, -85, -90, -18, -82, -38, 4, 16, 129, -15, 34, 30, -85, 91, 26, 102, 120, -4, 69, -33, -18, 4, -68, 53, 91, 102, -34, 12, -84, 72, -80, 40, -112, 136, 16, 39, 89, 23, -49, 63, -21, -50, 18, 18, 6, 40, 108, 68, 4, 108, 32, -55, -52, 12, -23, 3, -90, -114, -83, -29, -26, 22, 126, 22, -69, -63, -24, 124, -16, -56, 85, -55, -46, 70, -98, -2, 62, 50, 60, 108, 135, 85, -49, -55, -138, 90, -53, -65, 114, -54, -36, 124, 90, -6, 145, -103, 111, 57, -32, -28, -66, 66, 50, 2, -68, -148, 66, 22, -11, -123, -31, 5, 75, -99, 36, -72, 62, 38, 12, -72, 100, -88, 12, 84, -60, 60, 27, 33, -13, -121, -20, -116, -105, -123, 70, 26, 39, 7, -44, -16, 4, 44, -23, 35, 81, -35, -48, -60, 67, 67, -25, 51, -111, -16, 64, -136, 112, 112, -56, 28, 84, 82, -58, -30, -90, 28, -68, 66, 138, -69, -31, -38, 2, -75, -3, 69, 123, -100, -108, 48, -60, 106, -62, -62, 70, -42, 6, 138, -66, -77, 9, -14, -38, 58, 70, 89, -17, -38, 34, 86, -6, 79, 43, 81, 63, 36, -60, 56, -48, 11, 39, -140, 4, 50, 94, 44, 32, 26, 82, 90, 122, 36, 28, 90, -42, -132, 148, -12, 12, -48, -60, -108, -52, 22, 110, 92, 92, 124, 160, -147, 113, -96, -48, 38, -30, 41, -133, -77, 149, 87, 47, -20, 148, -38, 74, -150, -126, -49, -161, 22, -2, 136, -12, 1, -115, 105, -19, 22, -82, 122, -46, 110, 46, -65, 83, -18, 42, -84, 52, -20, -88, 58, -106, -26, -118, 36, 60, -126, -30, -100, 68, -153, -155, 36, -108, 168, -116, 76, 104, 33, -21, 33, -51, 12, -12, -78, 2, -114, 30, 14, 98, -85, -41, -40, -56, -16, 88, -54, 86, -6, -150, 3, 105, -6, -118, -114, -110, 52, 8, 18, -90, 110, -90, 18, -104, 68, 50, 78, -77, 73, -13, -69, 4, -68, 35, 83, 88, 168, -151, 97, -6, 70, -177, -15, -28, -108, -143, 111, -16, -156, -117, 7, 76, 4, 86, -46, -32, 144, 138, -46, 109, -97, -118, 126, -163, -105, 65, 45, 170, 26, -128, -152, 64, -116, -113, -21, 93, -123, -34, 98, 30, -78, -88, 8, 50, -62, -156, -44, -60, -80, 2, -62, -134, 50, -175, -101, 98, 78, -40, 24, 172, 56, 4, -80, -71, -137, -155, -67, 22, 154, 8, -120, -55, -91, -33, 63, -122, 166, -113, -59, -40, 24, -89, 113, 28, -16, -143, -159, 60, 84, 122, 58, 68, -28, 9, 95, -86, -82, -13, 153, 0, 36, -155, -59, -129, 117, -58, -178, 32, 128, -96, 108, 55, -133, -96, -96, 140, -44, -38, -118, -142, 114, 173, -29, 62, 146, -57, -93, 9, 189, -10, 66, -12, -12, 184, 12, 42, -126, -115, -77, 14, 146, 76, 44, 38, 38, 85, 131, 54, 90, 62, -114, 41, -64, 4, 118, 98, 106, 178, 58, -14, 4, 36, 9, -75, 186, 162, -12, -92, -88, -136, 8, -4, 163, -105, -58, -146, 160, 28, 152, -60, 70, -70, 6, -126, -6, 122, -112, 80, 146, -146, 103, 69, 15, 135, 47, -97, -131, -81, 56, -144, 16, 56, -91, -37, -21, -135, -84, -100, 170, -10, 87, 111, 44, -140, -97, -61, -147, 119, -140, -100, -14, 22, -18, -150, 40, -16], 'hecke_polynomial': 'x', 'label': '2.2.28.1-676.1-a'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 28, 'ideals': ['[1, 1, 1]', '[2, 2, w - 3]', '[3, 3, w - 2]', '[3, 3, w + 2]', '[4, 2, 2]', '[6, 6, -w - 1]', '[6, 6, -w + 1]', '[7, 7, w]', '[8, 4, 2*w - 6]', '[9, 3, 3]', '[9, 9, w + 4]', '[9, 9, -w + 4]', '[12, 6, 2*w - 4]', '[12, 6, 2*w + 4]', '[14, 14, -3*w + 7]', '[16, 4, 4]', '[18, 6, 3*w - 9]', '[18, 18, -w - 5]', '[18, 18, w - 5]', '[19, 19, 2*w - 3]', '[19, 19, 2*w + 3]', '[21, 21, -2*w + 7]', '[21, 21, 2*w + 7]', '[24, 12, -2*w - 2]', '[24, 12, -2*w + 2]', '[25, 5, 5]', '[27, 9, 3*w - 6]', '[27, 9, 3*w + 6]', '[27, 27, 2*w - 1]', '[27, 27, 2*w + 1]', '[28, 14, 2*w]', '[29, 29, -w - 6]', '[29, 29, w - 6]', '[31, 31, 4*w + 9]', '[31, 31, -4*w + 9]', '[32, 8, 4*w - 12]', '[36, 6, 6]', '[36, 18, 2*w + 8]', '[36, 18, -2*w + 8]', '[37, 37, -3*w + 10]', '[37, 37, -6*w + 17]', '[38, 38, -3*w + 5]', '[38, 38, -3*w - 5]', '[42, 42, -w - 7]', '[42, 42, w - 7]', '[47, 47, -3*w - 4]', '[47, 47, 3*w - 4]', '[48, 12, 4*w - 8]', '[48, 12, 4*w + 8]', '[49, 7, 7]', '[50, 10, 5*w - 15]', '[53, 53, 2*w - 9]', '[53, 53, 2*w + 9]', '[54, 18, -3*w - 3]', '[54, 18, -3*w + 3]', '[54, 54, -5*w - 11]', '[54, 54, -5*w + 11]', '[56, 28, -6*w + 14]', '[57, 57, w + 8]', '[57, 57, -4*w + 13]', '[57, 57, 4*w + 13]', '[57, 57, -w + 8]', '[58, 58, 3*w + 11]', '[58, 58, -3*w + 11]', '[59, 59, 3*w - 2]', '[59, 59, -3*w - 2]', '[62, 62, 3*w + 1]', '[62, 62, -3*w + 1]', '[63, 21, 3*w]', '[63, 63, 4*w - 7]', '[63, 63, 4*w + 7]', '[64, 8, 8]', '[72, 12, 6*w - 18]', '[72, 36, -2*w - 10]', '[72, 36, 2*w - 10]', '[74, 74, -w - 9]', '[74, 74, w - 9]', '[75, 15, 5*w - 10]', '[75, 15, 5*w + 10]', '[76, 38, 4*w - 6]', '[76, 38, 4*w + 6]', '[81, 9, 9]', '[81, 27, 3*w + 12]', '[81, 27, -3*w + 12]', '[81, 81, -5*w + 16]', '[81, 81, 5*w + 16]', '[83, 83, -6*w - 13]', '[83, 83, -6*w + 13]', '[84, 42, -4*w + 14]', '[84, 42, 4*w + 14]', '[87, 87, -4*w - 5]', '[87, 87, -7*w + 16]', '[87, 87, -7*w - 16]', '[87, 87, -4*w + 5]', '[93, 93, w + 10]', '[93, 93, -2*w + 11]', '[93, 93, -2*w - 11]', '[93, 93, w - 10]', '[94, 94, 5*w - 9]', '[94, 94, -13*w + 33]', '[96, 24, -4*w - 4]', '[96, 24, -4*w + 4]', '[98, 14, 7*w - 21]', '[100, 10, 10]', '[103, 103, 4*w - 3]', '[103, 103, -4*w - 3]', '[106, 106, 3*w - 13]', '[106, 106, 3*w + 13]', '[108, 18, 6*w - 12]', '[108, 18, 6*w + 12]', '[108, 54, 4*w - 2]', '[108, 54, 4*w + 2]', '[109, 109, -6*w + 19]', '[109, 109, -6*w - 19]', '[111, 111, 4*w + 1]', '[111, 111, 5*w + 8]', '[111, 111, 5*w - 8]', '[111, 111, 4*w - 1]', '[112, 28, 4*w]', '[113, 113, -13*w + 36]', '[113, 113, -4*w + 15]', '[114, 114, -w - 11]', '[114, 114, -5*w - 17]', '[114, 114, 5*w - 17]', '[114, 114, w - 11]', '[116, 58, -2*w - 12]', '[116, 58, 2*w - 12]', '[118, 118, -11*w + 27]', '[118, 118, 7*w - 15]', '[121, 11, -11]', '[124, 62, 8*w + 18]', '[124, 62, -8*w + 18]', '[126, 42, -9*w + 21]', '[126, 126, -5*w + 7]', '[126, 126, -5*w - 7]', '[128, 16, 8*w - 24]', '[131, 131, -6*w + 11]', '[131, 131, -6*w - 11]', '[133, 133, 3*w + 14]', '[133, 133, -3*w + 14]', '[137, 137, -w - 12]', '[137, 137, w - 12]', '[139, 139, -5*w - 6]', '[139, 139, 5*w - 6]', '[141, 141, -10*w - 29]', '[141, 141, 2*w - 13]', '[141, 141, 2*w + 13]', '[141, 141, -10*w + 29]', '[144, 12, 12]', '[144, 36, 4*w + 16]', '[144, 36, -4*w + 16]', '[147, 21, 7*w - 14]', '[147, 21, 7*w + 14]', '[148, 74, -6*w + 20]', '[148, 74, -12*w + 34]', '[149, 149, -5*w + 18]', '[149, 149, -14*w + 39]', '[150, 30, -5*w - 5]', '[150, 30, -5*w + 5]', '[152, 76, -6*w + 10]', '[152, 76, -6*w - 10]', '[159, 159, -8*w - 17]', '[159, 159, 5*w - 4]', '[159, 159, -5*w - 4]', '[159, 159, 8*w - 17]', '[162, 18, 9*w - 27]', '[162, 54, -3*w - 15]', '[162, 54, 3*w - 15]', '[162, 162, -w - 13]', '[162, 162, w - 13]', '[166, 166, 5*w + 3]', '[166, 166, 5*w - 3]', '[167, 167, -9*w + 20]', '[167, 167, -9*w - 20]', '[168, 84, -2*w - 14]', '[168, 84, 2*w - 14]', '[169, 13, -13]', '[171, 57, 6*w - 9]', '[171, 57, 6*w + 9]', '[171, 171, 10*w - 23]', '[171, 171, 5*w - 2]', '[171, 171, 5*w + 2]', '[171, 171, 10*w + 23]', '[174, 174, 7*w - 13]', '[174, 174, 5*w + 1]', '[174, 174, 5*w - 1]', '[174, 174, 7*w + 13]', '[175, 35, 5*w]', '[177, 177, -8*w + 25]', '[177, 177, 4*w - 17]', '[177, 177, 4*w + 17]', '[177, 177, -8*w - 25]', '[186, 186, -5*w - 19]', '[186, 186, 7*w + 23]', '[186, 186, 7*w - 23]', '[186, 186, -5*w + 19]', '[188, 94, -6*w - 8]', '[188, 94, 6*w - 8]', '[189, 63, -6*w + 21]', '[189, 63, 6*w + 21]', '[189, 189, w + 14]', '[189, 189, -w + 14]', '[192, 24, 8*w - 16]', '[192, 24, 8*w + 16]', '[193, 193, 3*w - 16]', '[193, 193, -3*w - 16]', '[196, 14, 14]', '[197, 197, 2*w - 15]', '[197, 197, -2*w - 15]', '[199, 199, -7*w - 12]', '[199, 199, -7*w + 12]', '[200, 20, 10*w - 30]', '[203, 203, -6*w - 7]', '[203, 203, -6*w + 7]', '[206, 206, -15*w + 37]', '[206, 206, 9*w - 19]', '[212, 106, 4*w - 18]', '[212, 106, 4*w + 18]', '[216, 36, -6*w - 6]', '[216, 36, -6*w + 6]', '[216, 108, -10*w - 22]', '[216, 108, -10*w + 22]', '[217, 217, 9*w - 28]', '[217, 217, 9*w + 28]', '[218, 218, -w - 15]', '[218, 218, -w + 15]', '[222, 222, -7*w - 11]', '[222, 222, -11*w - 25]', '[222, 222, -11*w + 25]', '[222, 222, -7*w + 11]', '[223, 223, -8*w + 15]', '[223, 223, -8*w - 15]', '[224, 56, -12*w + 28]', '[225, 15, 15]', '[225, 45, 5*w + 20]', '[225, 45, -5*w + 20]', '[226, 226, -3*w - 17]', '[226, 226, 3*w - 17]', '[227, 227, 6*w - 5]', '[227, 227, -6*w - 5]', '[228, 114, 2*w + 16]', '[228, 114, -8*w + 26]', '[228, 114, 8*w + 26]', '[228, 114, -2*w + 16]', '[232, 116, 6*w + 22]', '[232, 116, -6*w + 22]', '[233, 233, -16*w + 45]', '[233, 233, -7*w + 24]', '[236, 118, 6*w - 4]', '[236, 118, -6*w - 4]', '[242, 22, -11*w + 33]', '[243, 27, 9*w - 18]', '[243, 27, 9*w + 18]', '[243, 81, 6*w - 3]', '[243, 81, 6*w + 3]', '[243, 243, 7*w - 10]', '[243, 243, 7*w + 10]', '[248, 124, 6*w + 2]', '[248, 124, -6*w + 2]', '[249, 249, -w - 16]', '[249, 249, -4*w - 19]', '[249, 249, 4*w - 19]', '[249, 249, w - 16]', '[251, 251, -6*w - 1]', '[251, 251, 6*w - 1]', '[252, 42, 6*w]', '[252, 126, 8*w - 14]', '[252, 126, 8*w + 14]', '[256, 16, 16]', '[259, 259, 17*w - 42]', '[259, 259, 10*w - 21]', '[261, 87, -3*w - 18]', '[261, 87, 3*w - 18]', '[261, 261, 10*w - 31]', '[261, 261, 2*w - 17]', '[261, 261, -2*w - 17]', '[261, 261, -10*w - 31]', '[262, 262, 7*w - 9]', '[262, 262, 7*w + 9]', '[266, 266, 5*w - 21]', '[266, 266, -5*w - 21]', '[271, 271, -11*w + 24]', '[271, 271, -11*w - 24]', '[274, 274, -15*w + 43]', '[274, 274, -9*w + 29]', '[277, 277, -21*w + 58]', '[277, 277, -6*w + 23]', '[278, 278, 9*w - 17]', '[278, 278, -21*w + 53]', '[279, 93, 12*w + 27]', '[279, 93, -12*w + 27]', '[279, 279, 7*w + 8]', '[279, 279, 8*w - 13]', '[279, 279, -8*w - 13]', '[279, 279, -7*w + 8]', '[281, 281, -8*w + 27]', '[281, 281, -17*w + 48]', '[282, 282, w + 17]', '[282, 282, 7*w - 25]', '[282, 282, 7*w + 25]', '[282, 282, w - 17]', '[283, 283, 13*w - 30]', '[283, 283, -14*w + 33]', '[288, 24, 12*w - 36]', '[288, 72, -4*w - 20]', '[288, 72, 4*w - 20]', '[289, 17, -17]', '[294, 42, -7*w - 7]', '[294, 42, -7*w + 7]', '[296, 148, -2*w - 18]', '[296, 148, 2*w - 18]', '[298, 298, 3*w - 19]', '[298, 298, -3*w - 19]', '[300, 30, 10*w - 20]', '[300, 30, 10*w + 20]', '[304, 76, 8*w - 12]', '[304, 76, 8*w + 12]', '[307, 307, 7*w - 6]', '[307, 307, -7*w - 6]', '[309, 309, -11*w + 34]', '[309, 309, 5*w + 22]', '[309, 309, 5*w - 22]', '[309, 309, -11*w - 34]', '[311, 311, -9*w - 16]', '[311, 311, -9*w + 16]', '[317, 317, -w - 18]', '[317, 317, w - 18]', '[318, 318, -19*w + 47]', '[318, 318, -7*w - 5]', '[318, 318, 7*w - 5]', '[318, 318, 11*w - 23]', '[324, 18, 18]', '[324, 54, 6*w + 24]', '[324, 54, -6*w + 24]', '[324, 162, -10*w + 32]', '[324, 162, 10*w + 32]', '[327, 327, -7*w - 4]', '[327, 327, 8*w + 11]', '[327, 327, -8*w + 11]', '[327, 327, 7*w - 4]', '[329, 329, -4*w + 21]', '[329, 329, -4*w - 21]', '[332, 166, -12*w - 26]', '[332, 166, -12*w + 26]', '[333, 111, -9*w + 30]', '[333, 111, -18*w + 51]', '[333, 333, -7*w + 26]', '[333, 333, -2*w + 19]', '[333, 333, 2*w + 19]', '[333, 333, 7*w + 26]', '[334, 334, 7*w - 3]', '[334, 334, 7*w + 3]', '[336, 84, -8*w + 28]', '[336, 84, 8*w + 28]', '[337, 337, -3*w - 20]', '[337, 337, 3*w - 20]', '[338, 26, -13*w + 39]', '[339, 339, 10*w - 19]', '[339, 339, 7*w - 2]', '[339, 339, 7*w + 2]', '[339, 339, 10*w + 19]', '[342, 114, -9*w + 15]', '[342, 114, -9*w - 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106]', '[6971, 6971, -51*w + 106]', '[6991, 6991, -44*w + 81]', '[6991, 6991, -44*w - 81]', '[6997, 6997, -114*w + 313]', '[6997, 6997, -27*w + 110]', '[7001, 7001, -20*w - 99]', '[7001, 7001, 20*w - 99]', '[7019, 7019, -42*w - 73]', '[7019, 7019, -42*w + 73]', '[7027, 7027, -62*w - 141]', '[7027, 7027, -62*w + 141]', '[7057, 7057, -93*w + 260]', '[7057, 7057, -36*w + 127]', '[7103, 7103, -48*w + 95]', '[7103, 7103, -48*w - 95]', '[7109, 7109, -29*w + 114]', '[7109, 7109, -110*w + 303]', '[7121, 7121, -8*w - 87]', '[7121, 7121, 8*w - 87]', '[7159, 7159, -32*w - 3]', '[7159, 7159, 32*w - 3]', '[7177, 7177, 9*w - 88]', '[7177, 7177, -9*w - 88]', '[7187, 7187, -54*w + 115]', '[7187, 7187, -54*w - 115]', '[7193, 7193, -17*w - 96]', '[7193, 7193, 17*w - 96]', '[7243, 7243, -46*w - 87]', '[7243, 7243, -46*w + 87]', '[7253, 7253, -11*w - 90]', '[7253, 7253, 11*w - 90]', '[7283, 7283, 39*w - 58]', '[7283, 7283, -39*w - 58]', '[7307, 7307, -42*w + 71]', '[7307, 7307, -42*w - 71]', '[7309, 7309, -39*w - 134]', '[7309, 7309, 39*w - 134]', '[7333, 7333, -3*w - 86]', '[7333, 7333, 3*w - 86]', '[7393, 7393, -51*w + 160]', '[7393, 7393, -51*w - 160]', '[7411, 7411, -41*w + 66]', '[7411, 7411, -41*w - 66]', '[7417, 7417, 24*w - 107]', '[7417, 7417, 24*w + 107]', '[7451, 7451, -45*w + 82]', '[7451, 7451, -45*w - 82]', '[7457, 7457, -4*w - 87]', '[7457, 7457, 4*w - 87]', '[7477, 7477, -54*w + 167]', '[7477, 7477, -54*w - 167]', '[7507, 7507, -38*w - 51]', '[7507, 7507, 38*w - 51]', '[7523, 7523, -33*w - 10]', '[7523, 7523, 33*w - 10]', '[7529, 7529, -49*w + 156]', '[7529, 7529, -49*w - 156]', '[7541, 7541, 2*w - 87]', '[7541, 7541, -2*w - 87]', '[7559, 7559, 33*w - 8]', '[7559, 7559, -33*w - 8]', '[7561, 7561, -60*w + 181]', '[7561, 7561, -60*w - 181]', '[7589, 7589, 26*w + 111]', '[7589, 7589, 26*w - 111]', '[7591, 7591, -49*w - 96]', '[7591, 7591, -49*w + 96]', '[7607, 7607, 33*w - 4]', '[7607, 7607, -33*w - 4]', '[7643, 7643, -54*w - 113]', '[7643, 7643, -54*w + 113]', '[7669, 7669, -6*w - 89]', '[7669, 7669, 6*w - 89]', '[7673, 7673, -112*w + 309]', '[7673, 7673, -31*w + 120]', '[7681, 7681, 3*w - 88]', '[7681, 7681, -3*w - 88]', '[7691, 7691, -66*w - 151]', '[7691, 7691, -66*w + 151]', '[7699, 7699, -50*w + 99]', '[7699, 7699, -50*w - 99]', '[7703, 7703, -36*w - 37]', '[7703, 7703, 36*w - 37]', '[7727, 7727, -69*w - 160]', '[7727, 7727, -69*w + 160]', '[7753, 7753, -33*w + 124]', '[7753, 7753, -108*w + 299]', '[7757, 7757, -7*w - 90]', '[7757, 7757, 7*w - 90]', '[7759, 7759, -43*w - 72]', '[7759, 7759, -43*w + 72]', '[7793, 7793, -88*w + 249]', '[7793, 7793, -43*w + 144]', '[7841, 7841, -100*w + 279]', '[7841, 7841, -37*w + 132]', '[7867, 7867, 34*w - 15]', '[7867, 7867, -34*w - 15]', '[7877, 7877, -19*w - 102]', '[7877, 7877, 19*w - 102]', '[7921, 89, -89]', '[7927, 7927, -44*w + 75]', '[7927, 7927, -44*w - 75]', '[7933, 7933, 18*w - 101]', '[7933, 7933, -18*w - 101]', '[7949, 7949, -10*w - 93]', '[7949, 7949, 10*w - 93]', '[7951, 7951, 40*w - 57]', '[7951, 7951, -40*w - 57]', '[8009, 8009, -16*w - 99]', '[8009, 8009, 16*w - 99]', '[8011, 8011, 34*w - 9]', '[8011, 8011, -34*w - 9]', '[8017, 8017, -12*w - 95]', '[8017, 8017, 12*w - 95]', '[8039, 8039, -60*w - 131]', '[8039, 8039, -60*w + 131]', '[8089, 8089, -36*w + 131]', '[8089, 8089, -105*w + 292]', '[8093, 8093, -w - 90]', '[8093, 8093, w - 90]', '[8101, 8101, -42*w + 143]', '[8101, 8101, -93*w + 262]', '[8111, 8111, -36*w - 31]', '[8111, 8111, 36*w - 31]', '[8117, 8117, -101*w + 282]', '[8117, 8117, -38*w + 135]', '[8123, 8123, -42*w - 65]', '[8123, 8123, -42*w + 65]', '[8147, 8147, 39*w - 50]', '[8147, 8147, -39*w - 50]', '[8167, 8167, -41*w - 60]', '[8167, 8167, 41*w - 60]', '[8179, 8179, -55*w - 114]', '[8179, 8179, -55*w + 114]', '[8231, 8231, -36*w - 29]', '[8231, 8231, 36*w - 29]', '[8233, 8233, -57*w + 176]', '[8233, 8233, -57*w - 176]', '[8263, 8263, -56*w + 117]', '[8263, 8263, -56*w - 117]', '[8269, 8269, -9*w - 94]', '[8269, 8269, 9*w - 94]', '[8287, 8287, 37*w - 36]', '[8287, 8287, -37*w - 36]', '[8291, 8291, -66*w + 149]', '[8291, 8291, -66*w - 149]', '[8297, 8297, -52*w - 165]', '[8297, 8297, -52*w + 165]', '[8317, 8317, -63*w + 190]', '[8317, 8317, -63*w - 190]', '[8353, 8353, 27*w + 116]', '[8353, 8353, 27*w - 116]', '[8363, 8363, -69*w + 158]', '[8363, 8363, -69*w - 158]', '[8369, 8369, -11*w - 96]', '[8369, 8369, 11*w - 96]', '[8419, 8419, -58*w - 123]', '[8419, 8419, -58*w + 123]', '[8429, 8429, 14*w - 99]', '[8429, 8429, -14*w - 99]', '[8431, 8431, -35*w - 12]', '[8431, 8431, 35*w - 12]', '[8447, 8447, -36*w - 25]', '[8447, 8447, 36*w - 25]', '[8513, 8513, -128*w + 351]', '[8513, 8513, -29*w + 120]', '[8521, 8521, -48*w - 157]', '[8521, 8521, -48*w + 157]', '[8537, 8537, 4*w - 93]', '[8537, 8537, -4*w - 93]', '[8539, 8539, -35*w - 6]', '[8539, 8539, 35*w - 6]', '[8543, 8543, -36*w - 23]', '[8543, 8543, 36*w - 23]', '[8597, 8597, -91*w + 258]', '[8597, 8597, -46*w + 153]', '[8599, 8599, -40*w - 51]', '[8599, 8599, 40*w - 51]', '[8623, 8623, -61*w + 132]', '[8623, 8623, -61*w - 132]', '[8627, 8627, 42*w - 61]', '[8627, 8627, -42*w - 61]', '[8677, 8677, -42*w - 145]', '[8677, 8677, 42*w - 145]', '[8681, 8681, -103*w + 288]', '[8681, 8681, -40*w + 141]', '[8689, 8689, -51*w + 164]', '[8689, 8689, -51*w - 164]', '[8699, 8699, -45*w - 74]', '[8699, 8699, -45*w + 74]', '[8707, 8707, -49*w - 90]', '[8707, 8707, -49*w + 90]', '[8737, 8737, -24*w - 113]', '[8737, 8737, 24*w - 113]', '[8761, 8761, -33*w + 128]', '[8761, 8761, -120*w + 331]', '[8783, 8783, -36*w - 17]', '[8783, 8783, 36*w - 17]', '[8819, 8819, -57*w + 118]', '[8819, 8819, -57*w - 118]', '[8821, 8821, 27*w + 118]', '[8821, 8821, 27*w - 118]', '[8839, 8839, -65*w - 144]', '[8839, 8839, -65*w + 144]', '[8849, 8849, -35*w + 132]', '[8849, 8849, -116*w + 321]', '[8867, 8867, -42*w - 59]', '[8867, 8867, 42*w - 59]', '[8923, 8923, -67*w - 150]', '[8923, 8923, -67*w + 150]', '[8929, 8929, -45*w + 152]', '[8929, 8929, -96*w + 271]', '[8933, 8933, 22*w - 111]', '[8933, 8933, -22*w - 111]', '[8941, 8941, -57*w - 178]', '[8941, 8941, -57*w + 178]', '[8951, 8951, 36*w - 11]', '[8951, 8951, -36*w - 11]', '[8963, 8963, -54*w + 107]', '[8963, 8963, -54*w - 107]', '[8969, 8969, -41*w + 144]', '[8969, 8969, -104*w + 291]', '[9007, 9007, -37*w - 24]', '[9007, 9007, 37*w - 24]', '[9013, 9013, -21*w - 110]', '[9013, 9013, 21*w - 110]', '[9041, 9041, 5*w - 96]', '[9041, 9041, -5*w - 96]', '[9043, 9043, -71*w - 162]', '[9043, 9043, -71*w + 162]', '[9091, 9091, -74*w - 171]', '[9091, 9091, -74*w + 171]', '[9103, 9103, -76*w + 177]', '[9103, 9103, -76*w - 177]', '[9109, 9109, -66*w + 199]', '[9109, 9109, -66*w - 199]', '[9127, 9127, -52*w + 99]', '[9127, 9127, -52*w - 99]', '[9137, 9137, 19*w - 108]', '[9137, 9137, -19*w - 108]', '[9157, 9157, 6*w - 97]', '[9157, 9157, -6*w - 97]', '[9181, 9181, -18*w - 107]', '[9181, 9181, 18*w - 107]', '[9187, 9187, -46*w + 75]', '[9187, 9187, -46*w - 75]', '[9203, 9203, 39*w - 38]', '[9203, 9203, -39*w - 38]', '[9209, 9209, -w - 96]', '[9209, 9209, w - 96]', '[9221, 9221, 13*w - 102]', '[9221, 9221, -13*w - 102]', '[9239, 9239, -48*w - 83]', '[9239, 9239, -48*w + 83]', '[9241, 9241, -15*w - 104]', '[9241, 9241, 15*w - 104]', '[9277, 9277, -33*w + 130]', '[9277, 9277, -126*w + 347]', '[9293, 9293, -23*w - 114]', '[9293, 9293, 23*w - 114]', '[9323, 9323, -42*w - 55]', '[9323, 9323, 42*w - 55]', '[9343, 9343, 43*w - 60]', '[9343, 9343, -43*w - 60]', '[9349, 9349, -51*w + 166]', '[9349, 9349, -51*w - 166]', '[9371, 9371, -51*w - 94]', '[9371, 9371, -51*w + 94]', '[9377, 9377, -56*w + 177]', '[9377, 9377, -56*w - 177]', '[9409, 97, -97]', '[9433, 9433, 9*w - 100]', '[9433, 9433, -9*w - 100]', '[9437, 9437, -94*w + 267]', '[9437, 9437, -49*w + 162]', '[9439, 9439, 37*w - 12]', '[9439, 9439, -37*w - 12]', '[9461, 9461, -37*w + 138]', '[9461, 9461, -118*w + 327]', '[9463, 9463, -41*w - 48]', '[9463, 9463, 41*w - 48]', '[9467, 9467, -66*w + 145]', '[9467, 9467, -66*w - 145]', '[9473, 9473, -32*w + 129]', '[9473, 9473, -131*w + 360]', '[9491, 9491, 39*w - 34]', '[9491, 9491, -39*w - 34]', '[9511, 9511, -55*w - 108]', '[9511, 9511, -55*w + 108]', '[9521, 9521, -20*w - 111]', '[9521, 9521, 20*w - 111]', '[9539, 9539, 42*w - 53]', '[9539, 9539, -42*w - 53]', '[9547, 9547, 37*w - 6]', '[9547, 9547, -37*w - 6]', '[9551, 9551, -45*w - 68]', '[9551, 9551, 45*w - 68]', '[9601, 9601, -12*w - 103]', '[9601, 9601, 12*w - 103]', '[9613, 9613, 18*w - 109]', '[9613, 9613, -18*w - 109]', '[9623, 9623, -39*w - 32]', '[9623, 9623, 39*w - 32]', '[9629, 9629, -65*w + 198]', '[9629, 9629, -65*w - 198]', '[9631, 9631, -56*w + 111]', '[9631, 9631, -56*w - 111]', '[9661, 9661, 15*w - 106]', '[9661, 9661, -15*w - 106]', '[9679, 9679, 40*w - 39]', '[9679, 9679, -40*w - 39]', '[9689, 9689, -4*w - 99]', '[9689, 9689, 4*w - 99]', '[9697, 9697, -36*w + 137]', '[9697, 9697, -123*w + 340]', '[9719, 9719, -72*w - 163]', '[9719, 9719, -72*w + 163]', '[9743, 9743, -51*w - 92]', '[9743, 9743, -51*w + 92]', '[9769, 9769, -60*w - 187]', '[9769, 9769, -60*w + 187]', '[9781, 9781, 27*w - 122]', '[9781, 9781, 27*w + 122]', '[9791, 9791, -75*w + 172]', '[9791, 9791, -75*w - 172]', '[9803, 9803, -54*w + 103]', '[9803, 9803, -54*w - 103]', '[9829, 9829, -30*w + 127]', '[9829, 9829, -141*w + 386]', '[9857, 9857, 44*w - 153]', '[9857, 9857, -44*w - 153]', '[9859, 9859, -58*w - 117]', '[9859, 9859, -58*w + 117]', '[9883, 9883, 38*w - 15]', '[9883, 9883, -38*w - 15]', '[9887, 9887, -48*w + 79]', '[9887, 9887, -48*w - 79]', '[9931, 9931, -50*w - 87]', '[9931, 9931, -50*w + 87]', '[9941, 9941, -58*w + 183]', '[9941, 9941, -58*w - 183]', '[9949, 9949, -6*w - 101]', '[9949, 9949, 6*w - 101]', '[9967, 9967, -59*w + 120]', '[9967, 9967, -59*w - 120]']}
• 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[]
  minimal_sibling	numeric[]
  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': [-7, 0, 1], 'conductor': 28, 'degree': 2, 'dirichlet_group': [1, 27], 'disc_abs': 28, 'disc_rad': 14, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[1, 2]]], [5, [[2, 1]]], [7, [0]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[2, 1]]], [19, [[1, 2]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[1, 2]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[1, 2]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 5.291502622129181, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.28.1', 'local_algs': ['2.2.2.1', '7.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 7], 'rd': 5.29150262213, 'regulator': {'__RealLiteral__': 0, 'data': '2.76865938331', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 3 a - 8 \\)'], 'used_grh': False, 'zk': ['1', 'a']}