Hilbert modular form data - 2.2.28.1-81.1-a

Formats: - HTML - YAML - JSON - 2025-09-02T17:23:06.039713

• 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': 'yes', 'is_base_change': 'yes', 'label': '2.2.28.1-81.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [3], 'level_ideal': '[81, 9, 9]', 'level_label': '81.1', 'level_norm': 81, 'parallel_weight': 2, 'short_label': '81.1-a', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, w - 2]', -1], ['[3, 3, w + 2]', -1]], 'hecke_eigenvalues': [1, 0, 0, 0, 0, 0, 10, 2, 2, 0, 0, 6, 6, 0, 0, 10, 10, 0, 0, 0, 0, 0, 0, -18, -18, -2, -2, -6, 0, 0, -10, -10, 0, 0, -22, -22, 0, 0, 26, 18, 18, 26, 26, 0, 0, 0, 0, 0, 0, 22, 22, 0, 0, 0, 0, -10, -10, -26, -26, 0, 0, 34, 0, 0, 0, 0, 34, 34, -30, -30, 0, 0, 22, 22, 0, 0, -38, -38, -34, -34, 0, 0, -26, -26, 0, 0, -2, -2, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 18, -34, -34, -46, -46, 0, 0, 22, 22, 0, 0, 0, 0, 38, 38, -26, -26, 0, 0, 46, 46, 0, 0, 0, 0, 50, 50, -30, -30, 0, 0, 2, 2, 6, 6, 0, 0, 0, 0, 54, 54, 0, 0, 38, 38, 0, 0, -22, -22, 0, 0, 0, 0, -50, -50, 0, 0, -58, -58, 0, 0, 46, 46, 0, 0, 2, 2, 10, 10, 0, 0, -38, -38, 0, 0, 0, 0, -58, -58, -66, -66, 0, 0, -22, -22, 0, 0, 66, 66, 62, 62, 0, 0, -46, -46, 0, 0, 0, 0, 0, 0, -58, -58, 0, 0, 34, 34, 0, 0, 0, 0, 2, 2, 6, 6, 0, 0, 62, 62, 0, 0, 54, 54, 0, 0, -18, -18, 0, 0, -74, -74, 0, 0, 0, 0, -22, -22, 0, 0, 0, 0, 0, 0, 78, 78, 0, 0, 0, 0, 0, 0, 30, 30, -74, -74, 0, 0, 82, 0, 0, 82, 82, -38, -38, 0, 0, -66, -66, -6, -6, 0, 0, 0, 0, 0, 0, 58, 0, 0, 18, 18, -86, -86, 0, 0, -46, -46, 0, 0, 22, 22, 0, 0, -82, -82, 0, 0, 0, 0, 0, 0, 50, 50, -30, -30, -90, -90, 0, 0, 74, 74, -34, -34, 0, 0, -82, -82, 0, 0, 90, 90, 38, 38, 0, 0, 58, 58, 78, 78, -94, -94, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -10, -10, 86, 86, -62, -62, 0, 0, 0, 0, 74, 74, 82, 82, 0, 0, 22, 22, 0, 0, 0, 0, -50, -50, -26, -26, 0, 0, 90, 90, -54, -54, 0, 0, -86, -86, 0, 0, -34, -34, 0, 0, -58, -58, 94, 94, 0, 0, 0, 0, 0, 0, 82, 82, 0, 0, -102, -102, 0, 0, 74, 74, 62, 62, 0, 0, 46, 46, -2, -2, 0, 0, 0, 0, 106, 106, -86, -86, 0, 0, 0, 0, -94, -94, 0, 0, -26, -26, 0, 0, 0, 0, 0, 0, -102, -102, -106, -106, 0, 0, 0, 0, -34, -34, -58, -58, 110, 110, 0, 0, 0, 0, 0, 0, -94, -94, -86, -86, 62, 62, 0, 0, -106, -106, 102, 102, 0, 0, -78, -78, 0, 0, 46, 46, 0, 0, 0, 0, 114, 114, 2, 2, 0, 0, 0, 0, 10, 10, 0, 0, -18, -18, 0, 0, 0, 0, 0, 0, -54, -54, 0, 0, 26, 26, 0, 0, -94, -94, 0, 0, 118, 118, 30, 30, 0, 0, -74, -74, 0, 0, 0, 0, 0, 0, 34, 34, 114, 114, 122, 0, 0, 118, 118, 62, 62, 0, 0, -122, -122, 0, 0, 66, 66, 0, 0, -46, -46, 0, 0, 0, 0, 118, 118, 0, 0, 0, 0, 94, 94, 0, 0, 0, 0, 50, 50, 0, 0, 10, 10, 0, 0, 0, 0, -22, -22, 26, 26, 0, 0, 58, 58, 0, 0, 130, 130, 0, 0, 0, 0, -130, -130, 0, 0, -62, -62, -110, -110, 122, 122, 0, 0, 0, 0, -82, -82, 0, 0, -118, 0, 0, -134, -134, -46, -46, 0, 0, 0, 0, 0, 0, -114, -114, 0, 0, 86, 86, 0, 0, 50, 50, -130, -130, 0, 0, 0, 0, 0, 0, 122, 122, 2, 2, 0, 0, 0, 0, 0, 0, -138, -138, -18, -18, 110, 110, 0, 0, 0, 0, 78, 78, 0, 0, 0, 0, 134, 134, 30, 30, 0, 0, -62, -62, 0, 0, 94, 94, 0, 0, 34, 34, 0, 0, 114, 0, 0, -106, -106, 0, 0, 0, 0, 142, 142, 0, 0, 0, 0, -134, -134, 138, 138, 0, 0, 130, 130, -86, -86, -46, -46, 118, 118, 0, 0, 146, 0, 0, 0, 0, 0, 0, -90, -90, 0, 0, -146, -146, 0, 0, 0, 0, 0, 0, 0, 0, 18, 18, 58, 58, -146, -146, 0, 0, 0, 0, 150, 150, -26, -26, 0, 0, 0, 0, -62, -62, 0, 0, -150, -150, -142, -142, 0, 0, 118, 118, -66, -66, 0, 0, 0, 0, 38, 38, 0, 0, -134, -134, 0, 0, -86, -86, 0, 0, 0, 0, 0, 0, 146, 146, 0, 0, 0, 0, -150, -150, 0, 0, 74, 74, -50, -50, 0, 0, -138, -138, 0, 0, 0, 0, 106, 106, -54, -54, -94, 0, 0, 0, 0, -158, -158, 0, 0, 0, 0, -2, -2, -58, -58, 146, 146, 158, 158, 0, 0, 22, 22, 62, 62, -26, -26, -122, -122, 0, 0, 138, 138, 0, 0, 66, 66, -86, -86, 0, 0, 0, 0, -114, -114, 38, 38, 162, 162, 158, 158, 0, 0, 146, 146, 0, 0, 0, 0, 0, 0, 0, 0, 46, 46, 142, 142, 106, 106, -74, -74, 0, 0, -118, -118, 0, 0, -166, -166, 0, 0, 0, 0, 0, 0, 150, 150, 166, 166, 0, 0, 0, 0, -110, -110, 0, 0, 122, 122, -146, -146, 0, 0, -6, -6, 0, 0, -10, -10, 0, 0, 170, 170, 0, 0, 0, 0, 142, 142, 102, 102, -30, -30, 0, 0, -150, -150, 0, 0, -34, -34, -170, -170, 0, 0, 0, 0, 38, 38, 106, 106, 0, 0, 138, 138, -166, -166, 0, 0, 0, 0, 0, 0, -74, -74, -170, -170, -174, -174, 0, 0, 0, 0, 0, 0, 0, 0, 122, 122, -110, -110, 0, 0, -50, -50, 142, 142, 0, 0, -134, -134, 178, 0, 0, -162, -162, 178, 178, 0, 0, -58, -58, 0, 0, -174, -174, 0, 0, -102, -102, 2, 2, 6, 6, 0, 0, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 170, 170, 0, 0, 174, 174, 0, 0, 0, 0, -106, -106, 30, 30, 162, 162, 0, 0, -178, -178, 0, 0, -142, -142, 0, 0, 0, 0, 110, 110, -134, -134, -74, -74, 0, 0, 0, 0, 170, 170, 0, 0, 0, 0, 0, 0, -186, -186, 166, 166, -78, -78, 0, 0, 0, 0, 114, 114, 186, 186, 0, 0, 0, 0, 54, 54, 0, 0, -82, -82, 0, 0, 0, 0, 178, 178, 58, 58, 174, 174, 0, 0, 0, 0, 118, 118, 0, 0, 150, 150, 158, 158, 0, 0, 0, 0, 0, 0, -106, -106, 0, 0, 190, 190, 166, 166, -66, -66, 0, 0, 0, 0, -122, -122, -134, -134, 0, 0, 26, 26, 190, 190, 178, 178, 0, 0, 0, 0, -186, -186, 0, 0, 94, 94, 194, -38, -38, 194, 194, 0, 0, 74, 74, 0, 0, 0, 0, 190, 190, 0, 0, 0, 0, -194, -194, 0, 0, 0, 0, 0, 0, -46, -46, 78, 78, 0, 0, -158, -158, 0, 0, -194, -194, 0, 0, 166, 166, 50, 50, 0, 0, 0, 0, -102, -102, 118, 118, 0, 0, 0, 0, 198, 198, -194, -194, 0, 0, 0, 0, 0, 0, 0, 0, -86, -86, -162, -162, 0, 0], 'hecke_polynomial': 'x', 'label': '2.2.28.1-81.1-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[]
  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': [-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': ['2.1.2.2a1.1', '7.1.2.1a1.2'], 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, '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']}