Hilbert modular form data - 2.2.145.1-5.1-f

Formats: - HTML - YAML - JSON - 2024-06-10T13:52:24.595876

• 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': 6, 'disc': 145, 'field_bad_primes': [5, 29], 'field_label': '2.2.145.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.145.1-5.1-f', 'label_nsuffix': 5, 'label_suffix': 'f', 'level_bad_primes': [5], 'level_ideal': '[5, 5, w + 2]', 'level_label': '5.1', 'level_norm': 5, 'parallel_weight': 2, 'short_label': '5.1-f', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5, 5, w + 2]', 1]], 'hecke_eigenvalues': ['e', '-e', 'e^5 - 9*e^3 + 12*e', '-e^5 + 9*e^3 - 12*e', -1, 'e^3 - 7*e', '-e^3 + 7*e', '2*e^2 - 4', '-2*e^5 + 17*e^3 - 17*e', '2*e^5 - 17*e^3 + 17*e', '3*e^5 - 25*e^3 + 26*e', '-3*e^5 + 25*e^3 - 26*e', 'e^5 - 9*e^3 + 12*e', '-e^5 + 9*e^3 - 12*e', 'e^4 - 6*e^2 - 5', '-e^4 + 8*e^2 - 3', '-e^4 + 8*e^2 - 3', 'e^4 - 8*e^2 + 15', 'e^4 - 8*e^2 + 15', '3*e^5 - 27*e^3 + 42*e', '-3*e^5 + 27*e^3 - 42*e', '-e^5 + 9*e^3 - 14*e', 'e^5 - 9*e^3 + 14*e', 'e^4 - 10*e^2 + 3', 'e^4 - 10*e^2 + 3', '3*e^5 - 29*e^3 + 48*e', '-3*e^5 + 29*e^3 - 48*e', '-e^4 + 8*e^2 + 11', '-5*e^5 + 43*e^3 - 54*e', '5*e^5 - 43*e^3 + 54*e', '2*e^5 - 17*e^3 + 13*e', '-2*e^5 + 17*e^3 - 13*e', '-2*e^2 + 18', '-2*e^2 + 18', 6, 6, '-3*e^4 + 22*e^2 - 7', '-3*e^4 + 22*e^2 - 7', '-5*e^5 + 45*e^3 - 58*e', '5*e^5 - 45*e^3 + 58*e', '-5*e^5 + 43*e^3 - 54*e', '5*e^5 - 43*e^3 + 54*e', '-2*e^4 + 12*e^2 - 8', '-2*e^2 + 10', '-2*e^2 + 10', 'e^4 - 12*e^2 + 21', 'e^4 - 12*e^2 + 21', '4*e^5 - 37*e^3 + 55*e', '-4*e^5 + 37*e^3 - 55*e', 'e^4 - 6*e^2 + 9', 'e^4 - 6*e^2 + 9', 'e^4 - 8*e^2 - 9', 'e^4 - 8*e^2 - 9', -2, -2, '5*e^5 - 45*e^3 + 68*e', '-5*e^5 + 45*e^3 - 68*e', '3*e^4 - 26*e^2 + 13', '3*e^4 - 26*e^2 + 13', '-3*e^5 + 27*e^3 - 38*e', '3*e^5 - 27*e^3 + 38*e', '-e^5 + 13*e^3 - 40*e', 'e^5 - 13*e^3 + 40*e', '-6*e^5 + 51*e^3 - 59*e', '6*e^5 - 51*e^3 + 59*e', '-5*e^5 + 39*e^3 - 28*e', '5*e^5 - 39*e^3 + 28*e', '2*e^4 - 14*e^2 - 6', '2*e^4 - 14*e^2 - 6', 'e^4 - 12*e^2 + 37', '-7*e^5 + 61*e^3 - 82*e', '7*e^5 - 61*e^3 + 82*e', '7*e^4 - 52*e^2 + 43', '7*e^4 - 52*e^2 + 43', '-e^4 + 4*e^2 + 17', '-e^4 + 4*e^2 + 17', '-4*e^4 + 34*e^2 - 34', '-4*e^4 + 34*e^2 - 34', '4*e^5 - 35*e^3 + 57*e', '-4*e^5 + 35*e^3 - 57*e', '-3*e^4 + 16*e^2 + 11', '-3*e^4 + 16*e^2 + 11', '-7*e^5 + 61*e^3 - 86*e', '7*e^5 - 61*e^3 + 86*e', '5*e^5 - 43*e^3 + 62*e', '-5*e^5 + 43*e^3 - 62*e', '-6*e^4 + 44*e^2 - 26', '-6*e^4 + 44*e^2 - 26', '3*e^5 - 27*e^3 + 44*e', '-3*e^5 + 27*e^3 - 44*e', '-e^4 + 4*e^2 + 11', '-e^4 + 4*e^2 + 11', '-e^4 + 12*e^2 - 17', '-e^4 + 12*e^2 - 17', '-e^4 + 10*e^2 - 35', '-5*e^5 + 39*e^3 - 38*e', '5*e^5 - 39*e^3 + 38*e', '2*e^4 - 18*e^2', '2*e^4 - 18*e^2', '2*e^5 - 11*e^3 - 13*e', '-2*e^5 + 11*e^3 + 13*e', '5*e^5 - 49*e^3 + 96*e', '-5*e^5 + 49*e^3 - 96*e', 'e^5 - 7*e^3 + 8*e', '-e^5 + 7*e^3 - 8*e', '-2*e^4 + 20*e^2 - 18', '-2*e^4 + 20*e^2 - 18', '-e^5 + 3*e^3 + 24*e', 'e^5 - 3*e^3 - 24*e', '5*e^4 - 44*e^2 + 33', '5*e^4 - 44*e^2 + 33', '-13*e^5 + 117*e^3 - 178*e', '13*e^5 - 117*e^3 + 178*e', '-3*e^4 + 32*e^2 - 33', '-3*e^4 + 32*e^2 - 33', '-3*e^4 + 16*e^2 + 13', '-3*e^4 + 16*e^2 + 13', 'e^4 - 8*e^2 + 5', 'e^4 - 8*e^2 + 5', '3*e^4 - 30*e^2 + 39', '3*e^4 - 30*e^2 + 39', '-17*e^5 + 145*e^3 - 168*e', '17*e^5 - 145*e^3 + 168*e', '6*e^5 - 61*e^3 + 113*e', '-6*e^5 + 61*e^3 - 113*e', '-e^5 + 11*e^3 - 34*e', 'e^5 - 11*e^3 + 34*e', '-e^5 + 13*e^3 - 22*e', 'e^5 - 13*e^3 + 22*e', '2*e^4 - 6*e^2 - 26', '2*e^4 - 6*e^2 - 26', '8*e^5 - 75*e^3 + 129*e', '-8*e^5 + 75*e^3 - 129*e', '-7*e^5 + 67*e^3 - 122*e', '7*e^5 - 67*e^3 + 122*e', '4*e^4 - 34*e^2 + 30', '4*e^4 - 34*e^2 + 30', '-4*e^4 + 36*e^2 - 50', '-4*e^4 + 36*e^2 - 50', '9*e^5 - 75*e^3 + 90*e', '-9*e^5 + 75*e^3 - 90*e', '19*e^5 - 167*e^3 + 208*e', '-19*e^5 + 167*e^3 - 208*e', '2*e^5 - 15*e^3 + 19*e', '-2*e^5 + 15*e^3 - 19*e', '3*e^5 - 29*e^3 + 38*e', '-3*e^5 + 29*e^3 - 38*e', '-13*e^5 + 117*e^3 - 164*e', '13*e^5 - 117*e^3 + 164*e', '-7*e^4 + 44*e^2 - 5', '-7*e^4 + 44*e^2 - 5', '-8*e^4 + 56*e^2 - 14', '-8*e^4 + 56*e^2 - 14', '-8*e^4 + 64*e^2 - 42', '-8*e^4 + 64*e^2 - 42', '-7*e^5 + 57*e^3 - 66*e', '7*e^5 - 57*e^3 + 66*e', 'e^4 + 4*e^2 - 19', '-11*e^5 + 93*e^3 - 106*e', '11*e^5 - 93*e^3 + 106*e', '-e^5 + 13*e^3 - 36*e', 'e^5 - 13*e^3 + 36*e', 'e^4 - 10*e^2 + 29', 'e^4 - 10*e^2 + 29', '-9*e^5 + 75*e^3 - 72*e', '9*e^5 - 75*e^3 + 72*e'], 'hecke_polynomial': 'x^6 - 9*x^4 + 13*x^2 - 1', 'label': '2.2.145.1-5.1-f'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 145, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[2, 2, w + 1]', '[3, 3, w]', '[3, 3, w + 2]', '[4, 2, 2]', '[4, 4, w]', '[4, 4, w + 3]', '[5, 5, w + 2]', '[6, 6, -w + 6]', '[6, 6, w + 2]', '[6, 6, w + 3]', '[6, 6, -w - 5]', '[8, 4, 2*w]', '[8, 4, 2*w + 2]', '[8, 8, w + 3]', '[8, 8, w + 4]', '[9, 3, 3]', '[9, 9, w]', '[9, 9, w + 8]', '[10, 10, w + 2]', '[10, 10, w + 7]', '[12, 6, 2*w]', '[12, 6, 2*w + 4]', '[12, 12, w]', '[12, 12, w + 3]', '[12, 12, w + 8]', '[12, 12, w + 11]', '[15, 15, w + 2]', '[15, 15, w + 12]', '[16, 4, 4]', '[16, 8, 2*w]', '[16, 8, 2*w + 6]', '[16, 16, -w - 4]', '[16, 16, -w + 5]', '[17, 17, w + 1]', '[17, 17, w + 15]', '[18, 6, 3*w]', '[18, 6, 3*w + 3]', '[18, 18, w]', '[18, 18, w + 8]', '[18, 18, w + 9]', '[18, 18, w + 17]', '[20, 10, 2*w + 4]', '[20, 20, w + 7]', '[20, 20, -w + 8]', '[24, 12, -2*w + 12]', '[24, 12, 2*w + 4]', '[24, 12, 2*w + 6]', '[24, 12, -2*w - 10]', '[24, 24, -w - 3]', '[24, 24, w + 11]', '[24, 24, w + 12]', '[24, 24, -w + 4]', '[25, 5, 5]', '[27, 9, 3*w]', '[27, 9, 3*w + 6]', '[27, 27, w + 9]', '[27, 27, w + 17]', '[29, 29, w + 14]', '[30, 30, -w - 2]', '[30, 30, w + 12]', '[30, 30, w + 17]', '[30, 30, -w + 3]', '[32, 8, 4*w]', '[32, 8, 4*w + 4]', '[32, 16, 2*w + 6]', '[32, 16, 2*w + 8]', '[32, 32, w + 11]', '[32, 32, w + 20]', '[34, 34, w + 1]', '[34, 34, w + 15]', '[34, 34, w + 18]', '[34, 34, w - 2]', '[36, 6, 6]', '[36, 12, 3*w]', '[36, 12, 3*w + 9]', '[36, 18, 2*w]', '[36, 18, 2*w + 16]', '[36, 36, -w]', '[36, 36, w + 8]', '[36, 36, -w + 9]', '[36, 36, -w + 1]', '[37, 37, w + 10]', '[37, 37, w + 26]', '[40, 20, 2*w + 4]', '[40, 20, 2*w + 14]', '[40, 40, w + 12]', '[40, 40, w + 27]', '[43, 43, w + 19]', '[43, 43, w + 23]', '[45, 15, 3*w + 6]', '[45, 45, -2*w + 11]', '[45, 45, -2*w - 9]', '[47, 47, w + 22]', '[47, 47, w + 24]', '[48, 12, 4*w]', '[48, 12, 4*w + 8]', '[48, 24, 2*w]', '[48, 24, 2*w + 6]', '[48, 24, 2*w + 16]', '[48, 24, 2*w + 22]', '[48, 48, w + 11]', '[48, 48, w + 20]', '[48, 48, w + 27]', '[48, 48, w + 36]', '[49, 7, -7]', '[50, 10, 5*w]', '[50, 10, 5*w + 5]', '[51, 51, w + 15]', '[51, 51, 2*w - 15]', '[51, 51, -2*w - 13]', '[51, 51, w + 35]', '[54, 18, -3*w + 18]', '[54, 18, 3*w + 6]', '[54, 18, 3*w + 9]', '[54, 18, -3*w - 15]', '[54, 54, w + 9]', '[54, 54, w + 17]', '[54, 54, w + 36]', '[54, 54, -w + 10]', '[58, 58, w + 14]', '[58, 58, w + 43]', '[59, 59, w + 16]', '[59, 59, w + 42]', '[60, 30, 2*w + 4]', '[60, 30, 2*w + 24]', '[60, 60, w + 12]', '[60, 60, w + 27]', '[60, 60, w + 32]', '[60, 60, w + 47]', '[64, 8, 8]', '[64, 16, 4*w]', '[64, 16, 4*w + 12]', '[64, 32, -2*w - 8]', '[64, 32, -2*w + 10]', '[64, 64, w + 20]', '[64, 64, w + 43]', '[68, 34, 2*w + 2]', '[68, 34, 2*w + 30]', '[68, 68, w + 15]', '[68, 68, w + 32]', '[68, 68, w + 35]', '[68, 68, w + 52]', '[71, 71, w + 21]', '[71, 71, w + 49]', '[72, 12, 6*w]', '[72, 12, 6*w + 6]', '[72, 24, 3*w + 9]', '[72, 24, 3*w + 12]', '[72, 36, 2*w]', '[72, 36, 2*w + 16]', '[72, 36, 2*w + 18]', '[72, 36, 2*w + 34]', '[72, 72, w + 27]', '[72, 72, w + 35]', '[72, 72, w + 36]', '[72, 72, w + 44]', '[73, 73, w + 13]', '[73, 73, w + 59]', '[74, 74, -w - 10]', '[74, 74, w + 26]', '[74, 74, w + 47]', '[74, 74, w - 11]', '[75, 15, 5*w]', '[75, 15, 5*w + 10]', '[80, 20, 4*w + 8]', '[80, 40, 2*w + 14]', '[80, 40, -2*w + 16]', '[80, 80, w + 27]', '[80, 80, w + 52]', '[81, 9, 9]', '[81, 27, 3*w]', '[81, 27, 3*w + 24]', '[81, 81, -2*w + 9]', '[81, 81, -2*w - 7]', '[85, 85, w + 32]', '[85, 85, w + 52]', '[86, 86, w + 19]', '[86, 86, 5*w + 29]', '[86, 86, 5*w - 34]', '[86, 86, w + 66]', '[87, 87, w + 14]', '[87, 87, w + 72]', '[90, 30, 3*w + 6]', '[90, 30, 3*w + 21]', '[90, 90, w + 17]', '[90, 90, w + 27]', '[90, 90, w + 62]', '[90, 90, w + 72]', '[94, 94, w + 22]', '[94, 94, -3*w + 22]', '[94, 94, -3*w - 19]', '[94, 94, w + 71]', '[96, 24, -4*w + 24]', '[96, 24, 4*w + 8]', '[96, 24, 4*w + 12]', '[96, 24, -4*w - 20]', '[96, 48, -2*w - 6]', '[96, 48, 2*w + 22]', '[96, 48, 2*w + 24]', '[96, 48, -2*w + 8]', '[96, 96, w + 11]', '[96, 96, w + 20]', '[96, 96, w + 75]', '[96, 96, -w + 12]', '[97, 97, w + 28]', '[97, 97, w + 68]', '[98, 14, 7*w]', '[98, 14, 7*w + 7]', '[100, 10, 10]', '[100, 20, 5*w]', '[100, 20, 5*w + 15]', '[102, 102, w + 15]', '[102, 102, w + 18]', '[102, 102, w + 32]', '[102, 102, w + 35]', '[102, 102, w + 66]', '[102, 102, w + 69]', '[102, 102, w + 83]', '[102, 102, w + 86]', '[108, 18, 6*w]', '[108, 18, 6*w + 12]', '[108, 36, 3*w]', '[108, 36, 3*w + 9]', '[108, 36, 3*w + 24]', '[108, 36, 3*w + 33]', '[108, 54, 2*w + 18]', '[108, 54, 2*w + 34]', '[108, 108, w + 36]', '[108, 108, w + 44]', '[108, 108, w + 63]', '[108, 108, w + 71]', '[109, 109, 2*w - 7]', '[109, 109, -2*w - 5]', '[111, 111, w + 26]', '[111, 111, 8*w + 43]', '[111, 111, 8*w - 51]', '[111, 111, w + 84]', '[113, 113, w + 45]', '[113, 113, w + 67]', '[116, 58, 2*w + 28]', '[116, 116, -3*w - 13]', '[116, 116, -3*w + 16]', '[118, 118, w + 16]', '[118, 118, w + 42]', '[118, 118, w + 75]', '[118, 118, w + 101]', '[120, 60, -2*w - 4]', '[120, 60, 2*w + 24]', '[120, 60, 2*w + 34]', '[120, 60, -2*w + 6]', '[120, 120, w + 12]', '[120, 120, w + 27]', '[120, 120, w + 92]', '[120, 120, -w + 13]', '[121, 11, -11]', '[125, 25, 5*w + 10]', '[127, 127, w + 39]', '[127, 127, w + 87]', '[128, 16, 8*w]', '[128, 16, 8*w + 8]', '[128, 32, 4*w + 12]', '[128, 32, 4*w + 16]', '[128, 64, 2*w + 22]', '[128, 64, 2*w + 40]', '[128, 128, w + 20]', '[128, 128, w + 107]', '[129, 129, w + 23]', '[129, 129, 2*w - 5]', '[129, 129, -2*w - 3]', '[129, 129, w + 105]', '[135, 45, 3*w + 6]', '[135, 45, 3*w + 36]', '[135, 135, w + 17]', '[135, 135, w + 117]', '[136, 68, 2*w + 2]', '[136, 68, 2*w + 30]', '[136, 68, 2*w + 36]', '[136, 68, 2*w - 4]', '[136, 136, w + 35]', '[136, 136, -3*w - 20]', '[136, 136, 3*w - 23]', '[136, 136, w + 100]', '[137, 137, w + 37]', '[137, 137, w + 99]', '[139, 139, 4*w - 23]', '[139, 139, 4*w + 19]', '[141, 141, w + 24]', '[141, 141, 2*w - 3]', '[141, 141, -2*w - 1]', '[141, 141, w + 116]', '[142, 142, w + 21]', '[142, 142, w + 49]', '[142, 142, w + 92]', '[142, 142, w + 120]', '[144, 12, 12]', '[144, 24, 6*w]', '[144, 24, 6*w + 18]', '[144, 36, 4*w]', '[144, 36, 4*w + 32]', '[144, 48, -3*w - 12]', '[144, 48, -3*w + 15]', '[144, 72, -2*w]', '[144, 72, 2*w + 16]', '[144, 72, -2*w + 18]', '[144, 72, -2*w + 2]', '[144, 144, w + 27]', '[144, 144, w + 36]', '[144, 144, w + 107]', '[144, 144, w + 116]', '[145, 145, -2*w + 1]', '[146, 146, -w - 13]', '[146, 146, w + 59]', '[146, 146, w + 86]', '[146, 146, w - 14]', '[147, 21, 7*w]', '[147, 21, 7*w + 14]', '[148, 74, 2*w + 20]', '[148, 74, 2*w + 52]', '[148, 148, w + 47]', '[148, 148, w + 63]', '[148, 148, w + 84]', '[148, 148, w + 100]', '[149, 149, 6*w + 31]', '[149, 149, 6*w - 37]', '[150, 30, -5*w + 30]', '[150, 30, 5*w + 10]', '[150, 30, 5*w + 15]', '[150, 30, -5*w - 25]', '[151, 151, w + 60]', '[151, 151, w + 90]', '[153, 51, 3*w + 3]', '[153, 51, 3*w + 45]', '[153, 153, w + 18]', '[153, 153, w + 35]', '[153, 153, w + 117]', '[153, 153, w + 134]', '[157, 157, w + 53]', '[157, 157, w + 103]', '[160, 40, 4*w + 8]', '[160, 40, 4*w + 28]', '[160, 80, 2*w + 24]', '[160, 80, 2*w + 54]', '[160, 160, w + 52]', '[160, 160, w + 107]', '[162, 18, 9*w]', '[162, 18, 9*w + 9]', '[162, 54, 3*w]', '[162, 54, 3*w + 24]', '[162, 54, 3*w + 27]', '[162, 54, 3*w + 51]', '[162, 162, w + 36]', '[162, 162, w + 44]', '[162, 162, w + 117]', '[162, 162, w + 125]', '[163, 163, w + 54]', '[163, 163, w + 108]', '[169, 13, -13]', '[170, 170, w + 32]', '[170, 170, 3*w - 14]', '[170, 170, 3*w + 11]', '[170, 170, w + 137]', '[172, 86, 2*w + 38]', '[172, 86, 2*w + 46]', '[172, 172, w + 19]', '[172, 172, w + 23]', '[172, 172, w + 148]', '[172, 172, w + 152]', '[174, 174, w + 14]', '[174, 174, w + 72]', '[174, 174, w + 101]', '[174, 174, -w + 15]', '[177, 177, w + 42]', '[177, 177, w + 75]', '[177, 177, w + 101]', '[177, 177, w + 134]', '[179, 179, 2*w - 19]', '[179, 179, -2*w - 17]', '[180, 30, 6*w + 12]', '[180, 60, 3*w + 21]', '[180, 60, -3*w + 24]', '[180, 90, -4*w + 22]', '[180, 90, -4*w - 18]', '[180, 180, w + 27]', '[180, 180, w + 72]', '[180, 180, w + 107]', '[180, 180, w + 152]', '[181, 181, w + 33]', '[181, 181, w + 147]', '[185, 185, w + 47]', '[185, 185, w + 137]', '[188, 94, 2*w + 44]', '[188, 94, 2*w + 48]', '[188, 188, w + 24]', '[188, 188, w + 71]', '[188, 188, w + 116]', '[188, 188, w + 163]', '[192, 24, 8*w]', '[192, 24, 8*w + 16]', '[192, 48, 4*w]', '[192, 48, 4*w + 12]', '[192, 48, 4*w + 32]', '[192, 48, 4*w + 44]', '[192, 96, 2*w + 22]', '[192, 96, 2*w + 40]', '[192, 96, 2*w + 54]', '[192, 96, 2*w + 72]', '[192, 192, w + 20]', '[192, 192, w + 84]', '[192, 192, w + 107]', '[192, 192, w + 171]', '[193, 193, w + 48]', '[193, 193, w + 144]', '[194, 194, w + 28]', '[194, 194, -3*w - 10]', '[194, 194, 3*w - 13]', '[194, 194, w + 165]', '[196, 14, 14]', '[196, 28, 7*w]', '[196, 28, 7*w + 21]', '[199, 199, w + 77]', '[199, 199, w + 121]', '[200, 20, 10*w]', '[200, 20, 10*w + 10]', '[200, 40, 5*w + 15]', '[200, 40, 5*w + 20]', '[204, 102, 2*w + 30]', '[204, 102, 4*w - 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84]', '[1921, 1921, 24*w + 139]', '[1921, 1921, w + 610]', '[1921, 1921, w + 1310]', '[1921, 1921, -24*w + 163]', '[1922, 62, 31*w]', '[1922, 62, 31*w + 31]', '[1928, 964, 2*w + 76]', '[1928, 964, 2*w + 404]', '[1928, 964, 2*w + 558]', '[1928, 964, 2*w + 886]', '[1928, 1928, w + 443]', '[1928, 1928, w + 684]', '[1928, 1928, w + 1243]', '[1928, 1928, w + 1484]', '[1930, 1930, w + 337]', '[1930, 1930, 3*w - 49]', '[1930, 1930, -3*w - 46]', '[1930, 1930, w + 1592]', '[1933, 1933, w + 124]', '[1933, 1933, w + 1808]', '[1934, 1934, w + 256]', '[1934, 1934, 27*w - 170]', '[1934, 1934, 27*w + 143]', '[1934, 1934, w + 1677]', '[1935, 645, 3*w + 186]', '[1935, 645, 3*w + 456]', '[1935, 1935, w + 62]', '[1935, 1935, w + 152]', '[1935, 1935, w + 1782]', '[1935, 1935, w + 1872]', '[1936, 44, 44]', '[1936, 88, 22*w]', '[1936, 88, 22*w + 66]', '[1936, 176, 11*w + 44]', '[1936, 176, 11*w - 55]', '[1940, 970, 2*w + 444]', '[1940, 970, 2*w + 524]', '[1940, 1940, w + 707]', '[1940, 1940, w + 747]', '[1940, 1940, w + 1192]', '[1940, 1940, w + 1232]', '[1944, 108, -18*w + 108]', '[1944, 108, 18*w + 36]', '[1944, 108, 18*w + 54]', '[1944, 108, -18*w - 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109]', '[9950, 1990, 5*w + 385]', '[9950, 1990, 5*w + 605]', '[9950, 1990, 5*w + 1380]', '[9950, 1990, 5*w + 1600]', '[9957, 9957, w + 564]', '[9957, 9957, w + 2754]', '[9957, 9957, w + 7202]', '[9957, 9957, w + 9392]', '[9962, 9962, w + 423]', '[9962, 9962, w + 1888]', '[9962, 9962, w + 3092]', '[9962, 9962, w + 4557]', '[9962, 9962, w + 5404]', '[9962, 9962, w + 6869]', '[9962, 9962, w + 8073]', '[9962, 9962, w + 9538]', '[9965, 9965, w + 2182]', '[9965, 9965, w + 7782]', '[9969, 9969, 50*w - 309]', '[9969, 9969, w + 4458]', '[9969, 9969, w + 5510]', '[9969, 9969, 50*w + 259]', '[9970, 9970, w + 1467]', '[9970, 9970, 17*w - 31]', '[9970, 9970, 17*w + 14]', '[9970, 9970, w + 8502]', '[9971, 767, 13*w + 208]', '[9971, 767, 13*w + 546]', '[9973, 9973, w + 1474]', '[9973, 9973, w + 8498]', '[9976, 4988, 22*w - 98]', '[9976, 4988, 2*w + 1594]', '[9976, 4988, 2*w + 3392]', '[9976, 4988, -22*w - 76]', '[9976, 9976, w + 2044]', '[9976, 9976, -3*w + 103]', '[9976, 9976, -3*w - 100]', '[9976, 9976, w + 7931]', '[9978, 9978, w + 1547]', '[9978, 9978, w + 1778]', '[9978, 9978, w + 3210]', '[9978, 9978, w + 3441]', '[9978, 9978, w + 6536]', '[9978, 9978, w + 6767]', '[9978, 9978, w + 8199]', '[9978, 9978, w + 8430]', '[9980, 4990, 2*w + 244]', '[9980, 4990, 2*w + 4744]', '[9980, 9980, -21*w + 88]', '[9980, 9980, -39*w - 193]', '[9980, 9980, 39*w - 232]', '[9980, 9980, 21*w + 67]', '[9981, 3327, 18*w - 51]', '[9981, 3327, -18*w - 33]', '[9981, 9981, w + 926]', '[9981, 9981, w + 3509]', '[9981, 9981, w + 6471]', '[9981, 9981, w + 9054]', '[9987, 9987, w + 1968]', '[9987, 9987, w + 4689]', '[9987, 9987, w + 5297]', '[9987, 9987, w + 8018]', '[9990, 3330, 3*w + 141]', '[9990, 3330, 3*w + 411]', '[9990, 3330, 3*w + 1251]', '[9990, 3330, 3*w + 1521]', '[9990, 3330, 3*w + 1806]', '[9990, 3330, 3*w + 2076]', '[9990, 3330, 3*w + 2916]', '[9990, 3330, 3*w + 3186]', '[9990, 9990, w + 692]', '[9990, 9990, w + 1062]', '[9990, 9990, w + 3932]', '[9990, 9990, w + 4302]', '[9990, 9990, w + 5687]', '[9990, 9990, w + 6057]', '[9990, 9990, w + 8927]', '[9990, 9990, w + 9297]', '[9993, 9993, w + 141]', '[9993, 9993, w + 3189]', '[9993, 9993, w + 6803]', '[9993, 9993, w + 9851]', '[9996, 714, 14*w + 210]', '[9996, 714, -28*w + 210]', '[9996, 714, 28*w + 182]', '[9996, 714, 14*w + 490]', '[9996, 1428, 7*w + 105]', '[9996, 1428, 7*w + 224]', '[9996, 1428, -35*w + 203]', '[9996, 1428, 7*w + 581]', '[9996, 1428, 7*w + 840]', '[9996, 1428, -35*w - 168]', '[9996, 1428, 7*w + 1197]', '[9996, 1428, -7*w + 112]', '[10000, 100, 100]', '[10000, 200, 50*w]', '[10000, 200, 50*w + 150]', '[10000, 400, -25*w - 100]', '[10000, 400, -25*w + 125]'], 'label': '2.2.145.1', 'narrow_class_no': 4, 'primes': ['[2, 2, w]', '[2, 2, w + 1]', '[3, 3, w]', '[3, 3, w + 2]', '[5, 5, w + 2]', '[17, 17, w + 1]', '[17, 17, w + 15]', '[29, 29, w + 14]', '[37, 37, w + 10]', '[37, 37, w + 26]', '[43, 43, w + 19]', '[43, 43, w + 23]', '[47, 47, w + 22]', '[47, 47, w + 24]', '[49, 7, -7]', '[59, 59, w + 16]', '[59, 59, w + 42]', '[71, 71, w + 21]', '[71, 71, w + 49]', '[73, 73, w + 13]', '[73, 73, w + 59]', '[97, 97, w + 28]', '[97, 97, w + 68]', '[109, 109, 2*w - 7]', '[109, 109, -2*w - 5]', '[113, 113, w + 45]', '[113, 113, w + 67]', '[121, 11, -11]', '[127, 127, w + 39]', '[127, 127, w + 87]', '[137, 137, w + 37]', '[137, 137, w + 99]', '[139, 139, 4*w - 23]', '[139, 139, 4*w + 19]', '[149, 149, 6*w + 31]', '[149, 149, 6*w - 37]', '[151, 151, w + 60]', '[151, 151, w + 90]', '[157, 157, w + 53]', '[157, 157, w + 103]', '[163, 163, w + 54]', '[163, 163, w + 108]', '[169, 13, -13]', '[179, 179, 2*w - 19]', '[179, 179, -2*w - 17]', '[181, 181, w + 33]', '[181, 181, w + 147]', '[193, 193, w + 48]', '[193, 193, w + 144]', '[199, 199, w + 77]', '[199, 199, w + 121]', '[239, 239, w + 31]', '[239, 239, w + 207]', '[241, 241, w + 38]', '[241, 241, w + 202]', '[263, 263, w + 56]', '[263, 263, w + 206]', '[281, 281, 6*w - 35]', '[281, 281, 6*w + 29]', '[293, 293, w + 130]', '[293, 293, w + 162]', '[307, 307, w + 25]', '[307, 307, w + 281]', '[317, 317, w + 123]', '[317, 317, w + 193]', '[337, 337, w + 151]', '[337, 337, w + 185]', '[349, 349, w + 102]', '[349, 349, w + 246]', '[361, 19, -19]', '[367, 367, w + 81]', '[367, 367, w + 285]', '[401, 401, w + 40]', '[401, 401, w + 360]', '[419, 419, w + 50]', '[419, 419, w + 368]', '[431, 431, 2*w - 25]', '[431, 431, -2*w - 23]', '[433, 433, w + 197]', '[433, 433, w + 235]', '[439, 439, w + 187]', '[439, 439, w + 251]', '[443, 443, w + 89]', '[443, 443, w + 353]', '[467, 467, w + 167]', '[467, 467, w + 299]', '[499, 499, 4*w - 11]', '[499, 499, -4*w - 7]', '[503, 503, w + 155]', '[503, 503, w + 347]', '[509, 509, -4*w - 31]', '[509, 509, 4*w - 35]', '[521, 521, -6*w - 25]', '[521, 521, 6*w - 31]', '[529, 23, -23]', '[563, 563, w + 164]', '[563, 563, w + 398]', '[571, 571, -4*w - 1]', '[571, 571, 4*w - 5]', '[577, 577, w + 34]', '[577, 577, w + 542]', '[607, 607, w + 139]', '[607, 607, w + 467]', '[617, 617, w + 192]', '[617, 617, w + 424]', '[631, 631, 6*w + 41]', '[631, 631, -6*w + 47]', '[653, 653, w + 242]', '[653, 653, w + 410]', '[661, 661, w + 238]', '[661, 661, w + 422]', '[677, 677, w + 82]', '[677, 677, w + 594]', '[691, 691, w + 315]', '[691, 691, w + 375]', '[701, 701, w + 154]', '[701, 701, w + 546]', '[709, 709, 10*w - 59]', '[709, 709, 10*w + 49]', '[719, 719, w + 131]', '[719, 719, w + 587]', '[727, 727, w + 76]', '[727, 727, w + 650]', '[733, 733, w + 273]', '[733, 733, w + 459]', '[743, 743, w + 172]', '[743, 743, w + 570]', '[757, 757, w + 95]', '[757, 757, w + 661]', '[761, 761, w + 55]', '[761, 761, w + 705]', '[773, 773, w + 96]', '[773, 773, w + 676]', '[797, 797, w + 343]', '[797, 797, w + 453]', '[811, 811, 6*w - 49]', '[811, 811, -6*w - 43]', '[821, 821, -6*w - 19]', '[821, 821, 6*w - 25]', '[823, 823, w + 243]', '[823, 823, w + 579]', '[827, 827, w + 290]', '[827, 827, w + 536]', '[853, 853, w + 400]', '[853, 853, w + 452]', '[887, 887, w + 126]', '[887, 887, w + 760]', '[907, 907, w + 104]', '[907, 907, w + 802]', '[919, 919, w + 74]', '[919, 919, w + 844]', '[929, 929, 8*w + 53]', '[929, 929, 8*w - 61]', '[941, 941, 4*w - 41]', '[941, 941, -4*w - 37]', '[947, 947, w + 97]', '[947, 947, w + 849]', '[961, 31, -31]', '[967, 967, w + 256]', '[967, 967, w + 710]', '[983, 983, w + 297]', '[983, 983, w + 685]', '[991, 991, w + 308]', '[991, 991, w + 682]', '[997, 997, w + 470]', '[997, 997, w + 526]']}
• 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': [4], 'class_number': 4, 'cm': False, 'coeffs': [-36, -1, 1], 'conductor': 145, 'degree': 2, 'dirichlet_group': [1, 144], 'disc_abs': 145, 'disc_rad': 145, 'disc_sign': 1, 'frobs': [[2, [[1, 2]]], [3, [[1, 2]]], [5, [0]], [7, [[2, 1]]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [0]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[2, 1]]], [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': 12.041594578792296, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.145.1', 'local_algs': ['5.2.1.1', '29.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 29], 'rd': 12.0415945788, 'regulator': {'__RealLiteral__': 0, 'data': '3.1797854377', 'prec': 40}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 2 a + 11 \\)'], 'used_grh': False, 'zk': ['1', 'a']}