Hilbert modular form data - 3.3.1509.1-9.2-c

Formats: - HTML - YAML - JSON - 2024-05-04T21:31:58.467196

• 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': 3, 'dimension': 4, 'disc': 1509, 'field_bad_primes': [3, 503], 'field_label': '3.3.1509.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1509.1-9.2-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [3], 'level_ideal': '[9, 3, w^2 - 7]', 'level_label': '9.2', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.2-c', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, -2*w^2 + w + 15]', 1], ['[3, 3, w - 1]', -1]], 'hecke_eigenvalues': ['e', -1, 1, 'e^3 - 2*e^2 - 3*e + 3', 'e^3 - 2*e^2 - 3*e + 4', '-e^3 + 4*e^2 + e - 4', '-e^3 + e^2 + e + 3', '-2*e^3 + 3*e^2 + 6*e - 3', '2*e^2 - 6*e - 6', '-3*e^3 + 3*e^2 + 13*e - 5', 'e^3 - 3*e^2 + e + 1', 'e^3 - 3*e^2 - 3*e + 5', '2*e^3 - 6*e^2 + 12', 'e^3 + e^2 - 9*e - 5', 'e^3 + 3*e^2 - 9*e - 11', '-e^3 - 3*e^2 + 7*e + 13', '-e^3 + e^2 + 5*e + 7', '3*e^3 - 7*e^2 - 5*e + 13', '-3*e^3 + 6*e^2 + 11*e - 4', '3*e^3 - 5*e^2 - 7*e + 3', '-2*e^3 + 6*e^2 + 2*e - 8', '6*e^2 - 10*e - 16', '2*e^3 + 3*e^2 - 18*e - 7', '-e^2 - 4*e + 5', '-4*e^3 + 3*e^2 + 12*e + 9', '6*e^3 - 11*e^2 - 14*e + 9', 'e^3 - 3*e^2 - e + 1', '-7*e^3 + 12*e^2 + 17*e - 12', '2*e + 8', '-4*e^3 + 3*e^2 + 12*e + 9', '-3*e^3 + 11*e^2 + 3*e - 15', '-e^3 + 5*e^2 - e - 13', '-2*e^3 + e^2 + 6*e + 17', '-e^3 - 4*e^2 + 13*e + 14', 'e^3 - 3*e^2 + 3*e - 5', '6*e^3 - 12*e^2 - 18*e + 16', 'e^3 - e^2 - 13*e + 7', '-2*e^3 + 5*e^2 + 14*e - 17', '-2*e^3 - 6*e^2 + 16*e + 24', '-3*e^3 + 10*e^2 + 3*e - 22', '-5*e^3 + 6*e^2 + 17*e - 10', '8*e^3 - 14*e^2 - 20*e + 16', '7*e^3 - 15*e^2 - 13*e + 15', '-5*e^3 + 8*e^2 + 9*e - 2', 'e^2 + 9', '-e^3 - e^2 + 11*e + 7', '-3*e^3 - e^2 + 19*e + 9', '-2*e^3 + 6*e^2 + 10*e - 14', 'e^3 + 5*e^2 - 13*e - 17', '4*e - 6', '-4*e^3 + 11*e^2 + 4*e - 9', 'e^3 - 11*e^2 + 15*e + 25', '-4*e^3 + 13*e^2 - 4*e - 17', '4*e^3 - 7*e^2 - 22*e + 17', '6*e^3 - 15*e^2 - 10*e + 7', '-2*e^3 + 8*e^2 + 6*e - 12', '-3*e^3 + 5*e^2 + 7*e + 9', '3*e^3 - 4*e^2 - 15*e + 18', '-6*e^3 + 9*e^2 + 14*e + 13', '-5*e^3 + 17*e^2 - 3*e - 29', '-11*e^3 + 21*e^2 + 29*e - 23', '-e^3 - 5*e^2 + 13*e + 25', '-3*e^3 + 10*e^2 + 11*e - 18', '-5*e^3 + 5*e^2 + 21*e - 7', '-6*e^3 + 14*e^2 + 14*e - 28', '-5*e^3 + 4*e^2 + 15*e + 14', '-5*e^3 + 7*e^2 + 17*e - 25', '-e^3 + 2*e^2 - e - 24', '11*e^3 - 24*e^2 - 23*e + 28', '-5*e^3 + 12*e^2 + 21*e - 20', '-7*e^2 + 12*e + 3', '7*e^3 - 11*e^2 - 13*e - 5', '-5*e^3 + 11*e^2 + e - 5', '2*e^3 - 9*e^2 + 2*e + 15', '2*e^3 + e^2 - 14*e + 13', '-e^3 - 3*e^2 + e + 17', '-4*e^3 - e^2 + 20*e + 1', '8*e + 4', '-4*e^3 + 6*e^2 + 2*e - 4', '6*e^3 - 21*e^2 - 10*e + 33', '2*e^3 - 7*e^2 + 23', '-8*e^3 + 14*e^2 + 24*e - 24', '4*e^3 - 3*e^2 - 14*e - 5', 'e^3 + 2*e^2 - 9*e - 4', '-3*e^2 + 2*e + 7', 'e^3 + 2*e^2 - 5*e', '4*e^3 - 6*e^2 - 4*e + 6', '2*e^3 - 3*e^2 - 12*e + 21', '-e^3 + 7*e^2 - 11*e - 13', '7*e^3 - 13*e^2 - 31*e + 29', '-9*e^3 + 27*e^2 + 5*e - 35', '-4*e^3 + 10*e^2 + 20*e - 18', '3*e^3 - 11*e^2 + 11*e + 9', '-2*e^3 + 3*e^2 + 14*e - 7', '-4*e^3 + 8*e^2 + 12*e + 12', '-3*e^3 + 3*e^2 + 3*e - 3', '2*e^3 + 3*e^2 - 20*e + 5', '-7*e^3 + 15*e^2 + 27*e - 33', '-2*e^3 - 2*e^2 + 2*e + 38', '-6*e^3 + 4*e^2 + 38*e - 2', '6*e^3 - 12*e^2 - 24*e + 24', 'e^3 - 4*e^2 - 5*e + 18', '3*e^3 + 6*e^2 - 27*e - 28', '2*e^3 - 12*e^2 + 6*e + 24', '-4*e^3 + 8*e^2 + 8*e - 14', '-5*e^3 + 12*e^2 + 7*e - 38', '4*e^3 + 7*e^2 - 28*e - 35', '-7*e^3 + 22*e^2 + e - 24', '-e^3 - 11*e^2 + 23*e + 33', '4*e^3 - 16*e^2 - 2*e + 34', '3*e^3 - e^2 - 19*e - 13', '-5*e^3 + 16*e^2 + 5*e - 32', '-e^3 + 12*e^2 - 11*e - 34', '-4*e^3 + 18*e - 6', 'e^3 + 2*e^2 - 5*e - 10', '-7*e^3 + 25*e^2 - e - 31', '-e^3 + 6*e^2 + e - 22', '5*e^3 - 24*e^2 + 3*e + 48', '-3*e^3 + 15*e^2 + 11*e - 51', '-7*e^3 + 12*e^2 + 19*e - 8', '3*e^3 - 12*e^2 - 17*e + 36', '-7*e^3 + 22*e^2 - 5*e - 40', '9*e^2 - 18*e - 3', '-3*e^3 + 15*e^2 + e - 51', '2*e^3 - e^2 + 2*e - 7', '2*e^3 + e^2 - 10*e - 13', '-e^3 - 12*e^2 + 21*e + 4', '-3*e^3 + 12*e^2 + 3*e - 24', '3*e^3 + 16*e^2 - 35*e - 38', 'e^3 - 3*e^2 + 7*e - 15', '-3*e^3 - 5*e^2 + 31*e + 11', '4*e^3 - 10*e^2 - 16*e + 18', '-11*e^3 + 23*e^2 + 27*e - 13', '-10*e^3 + 21*e^2 + 26*e - 25', 'e^3 - 8*e^2 + 13*e + 2', '7*e^3 - 23*e^2 - 13*e + 51', '5*e^3 - e^2 - 21*e - 11', '6*e^3 - 22*e - 14', '12*e^3 - 25*e^2 - 24*e + 35', '3*e^3 + 4*e^2 - 11*e - 42', '-8*e^3 + 23*e^2 + 10*e - 15', '-5*e^3 + 9*e^2 + 15*e - 19', '-20*e^2 + 40*e + 46', '4*e^3 + 11*e^2 - 24*e - 57', 'e^3 + e^2 + 3*e - 17', '8*e^3 - 29*e^2 - 10*e + 43', '-e^3 - 8*e^2 + 9*e + 56', '-5*e^3 + 6*e^2 + 27*e - 24', '-15*e^3 + 28*e^2 + 39*e - 36', '-e^3 + 11*e^2 - 9*e - 19', '13*e^3 - 37*e^2 - 9*e + 55', '4*e^3 - 2*e^2 - 20*e - 40', '-5*e^3 + 11*e^2 + 17*e - 37', '-12*e^3 + 16*e^2 + 52*e - 34', '5*e^3 + 2*e^2 - 33*e + 4', '15*e^3 - 37*e^2 - 23*e + 35', '3*e^3 - 5*e^2 - 35*e + 29', '15*e^3 - 22*e^2 - 51*e + 38', '-7*e^3 + 5*e^2 + 17*e + 19', '-8*e^3 + 21*e^2 + 30*e - 35', '7*e^3 - 5*e^2 - 47*e + 13', '5*e^3 - 22*e^2 + 7*e + 38', 'e^3 + 6*e^2 + 5*e - 50'], 'hecke_polynomial': 'x^4 - 3*x^3 - 2*x^2 + 7*x + 1', 'label': '3.3.1509.1-9.2-c'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 1509, 'ideals': ['[1, 1, 1]', '[2, 2, -w^2 + 6]', '[3, 3, -2*w^2 + w + 15]', '[3, 3, w - 1]', '[4, 2, -w^2 + 3*w - 1]', '[4, 4, w]', '[6, 6, -w - 2]', '[6, 6, -w + 2]', '[8, 2, 2]', '[8, 8, -w^2 + 8]', '[9, 3, w^2 - 2*w + 1]', '[9, 3, w^2 - 7]', '[9, 9, w + 1]', '[11, 11, w + 3]', '[12, 6, -w^2 + w + 5]', '[12, 6, w^2 - w - 9]', '[12, 12, -w^2 + w + 8]', '[12, 12, w^2 - w]', '[16, 4, -2*w^2 + 12]', '[16, 4, -w^2 + w + 7]', '[16, 16, w^2]', '[18, 6, -w^2 + 3*w - 2]', '[18, 6, -w^2 - w + 2]', '[18, 18, -3*w^2 + w + 22]', '[19, 19, -w^2 + 5]', '[22, 22, -3*w + 2]', '[23, 23, -2*w^2 + 2*w + 17]', '[24, 6, -4*w^2 + 2*w + 30]', '[24, 6, 2*w - 2]', '[24, 24, -w^2 + 2*w]', '[24, 24, w - 4]', '[27, 3, 3]', '[27, 9, w^2 - 1]', '[27, 9, 2*w^2 - w - 13]', '[27, 27, -3*w^2 + 2*w + 23]', '[31, 31, -w^2 + 2*w + 1]', '[32, 4, -2*w^2 + 6*w - 2]', '[32, 8, 2*w]', '[32, 32, -w^2 + w + 4]', '[33, 33, w^2 + 2*w - 3]', '[33, 33, -w^2 + 4*w - 1]', '[36, 6, -w^2 - w + 5]', '[36, 6, w^2 - 3*w - 1]', '[36, 12, -2*w^2 + w + 16]', '[36, 12, w^2 - 4]', '[36, 18, w^2 - 5*w + 3]', '[36, 36, w^2 + w]', '[37, 37, 2*w^2 - 13]', '[38, 38, -w^2 + 5*w - 2]', '[43, 43, 5*w^2 - 2*w - 35]', '[43, 43, 3*w - 1]', '[43, 43, 2*w - 3]', '[44, 22, -w^2 + w + 1]', '[44, 44, -w^2 + 2*w + 4]', '[46, 46, -w^2 + 2]', '[47, 47, w^2 - 3]', '[48, 12, -2*w - 4]', '[48, 12, w^2 - w + 1]', '[48, 12, -2*w + 4]', '[48, 12, w^2 - w - 3]', '[48, 48, w + 4]', '[48, 48, 3*w^2 - w - 20]', '[54, 6, -3*w^2 + 18]', '[54, 18, -w^2 - 4*w + 2]', '[54, 18, w^2 - 10]', '[54, 54, -w^2 + w + 2]', '[57, 57, -w^2 - 4*w + 3]', '[57, 57, -2*w - 1]', '[59, 59, -3*w^2 + 2*w + 21]', '[62, 62, -w^2 + w + 10]', '[64, 4, 4]', '[64, 8, -w^2 - 3*w + 3]', '[64, 16, -2*w^2 + 16]', '[64, 64, -3*w^2 + 2*w + 24]', '[66, 66, 3*w^2 - 2*w - 22]', '[66, 66, -w^2 - w + 6]', '[69, 69, 2*w^2 + w - 9]', '[69, 69, -w + 5]', '[71, 71, 2*w + 3]', '[71, 71, 3*w^2 - 19]', '[71, 71, 4*w^2 - 13*w + 5]', '[72, 6, 2*w^2 - 4*w + 2]', '[72, 6, 2*w^2 - 14]', '[72, 18, 2*w + 2]', '[72, 24, w^2 - 5*w + 4]', '[72, 24, 7*w^2 - 3*w - 52]', '[72, 72, -2*w^2 + w + 12]', '[74, 74, -w^2 + 2*w - 2]', '[76, 38, w^2 - 3*w + 3]', '[76, 76, -w^2 - 2*w + 4]', '[81, 9, -w^2 + 2*w + 5]', '[81, 9, -6*w^2 + 3*w + 45]', '[81, 9, 3*w - 3]', '[81, 27, 2*w^2 - 11]', '[81, 81, w^2 + 2*w + 1]', '[83, 83, 2*w^2 - 15]', '[86, 86, w^2 - 3*w - 2]', '[86, 86, -2*w^2 - 3*w + 6]', '[86, 86, w^2 - 2*w - 10]', '[88, 22, 2*w + 6]', '[88, 88, -4*w^2 + w + 28]', '[89, 89, -w^2 - 1]', '[89, 89, 2*w^2 - 4*w + 1]', '[89, 89, -4*w + 3]', '[92, 46, -w^2 - w + 7]', '[92, 92, -3*w^2 + w + 24]', '[93, 93, -4*w^2 + 2*w + 27]', '[93, 93, 2*w^2 - 8*w + 3]', '[94, 94, w^2 - 3*w - 14]', '[96, 12, -2*w^2 + 2*w + 10]', '[96, 12, 2*w^2 - 2*w - 18]', '[96, 24, -2*w^2 + 2*w + 16]', '[96, 24, 2*w^2 - 2*w]', '[96, 96, w^2 - 4*w]', '[96, 96, w^2 - 7*w + 4]', '[99, 33, 4*w^2 - 25]', '[99, 33, 2*w^2 + 2*w - 1]', '[99, 99, -2*w^2 + 2*w + 13]', '[103, 103, 2*w^2 - 5*w + 1]', '[107, 107, -2*w^2 + w + 17]', '[107, 107, -2*w^2 + 9*w - 5]', '[107, 107, 2*w^2 + w - 11]', '[108, 6, -3*w^2 + 9*w - 3]', '[108, 12, 3*w]', '[108, 18, 5*w^2 - 3*w - 35]', '[108, 18, -w^2 - w - 1]', '[108, 36, w^2 + 6*w - 4]', '[108, 36, w^2 + w - 8]', '[108, 54, -w^2 - w + 9]', '[108, 108, -w^2 + 2*w + 12]', '[109, 109, 3*w^2 - 8*w + 3]', '[111, 111, w + 5]', '[111, 111, 2*w^2 + 2*w - 3]', '[113, 113, -2*w^2 + 2*w - 1]', '[114, 114, -w^2 + 2*w + 6]', '[114, 114, 4*w^2 - w - 30]', '[118, 118, -3*w^2 + 9*w - 2]', '[121, 11, -w^2 + 4*w - 5]', '[121, 121, -4*w^2 + 2*w + 31]', '[124, 62, -5*w^2 + 3*w + 37]', '[124, 124, w^2 - 6*w + 4]', '[125, 5, -5]', '[127, 127, w^2 - 11]', '[128, 8, -4*w^2 + 24]', '[128, 8, -2*w^2 + 2*w + 14]', '[128, 32, 2*w^2]', '[128, 128, -3*w + 4]', '[129, 129, -2*w^2 + 2*w + 15]', '[129, 129, 6*w^2 - 2*w - 43]', '[129, 129, 2*w^2 - 5*w + 3]', '[129, 129, w^2 + 2*w - 5]', '[129, 129, -w^2 + 2*w + 9]', '[129, 129, 4*w^2 - w - 29]', '[131, 131, 2*w^2 - w - 11]', '[132, 66, w^2 - 7*w + 3]', '[132, 66, -3*w^2 + w + 19]', '[132, 132, 2*w^2 - 5*w]', '[132, 132, 3*w^2 - 8*w + 4]', '[137, 137, -w^2 + 2*w + 7]', '[137, 137, 3*w - 7]', '[137, 137, 2*w^2 - 3*w - 7]', '[138, 138, -4*w^2 + w + 26]', '[138, 138, -5*w + 2]', '[139, 139, -2*w^2 + 6*w + 1]', '[141, 141, 4*w - 1]', '[141, 141, 6*w^2 - 2*w - 41]', '[142, 142, -3*w^2 + 6*w - 2]', '[142, 142, -w^2 + w - 2]', '[142, 142, w - 6]', '[144, 12, -w^2 + 5*w - 1]', '[144, 12, -2*w^2 + 6*w - 4]', '[144, 12, 7*w^2 - 3*w - 49]', '[144, 12, -2*w^2 - 2*w + 4]', '[144, 36, -w^2 + w + 11]', '[144, 36, -6*w^2 + 2*w + 44]', '[144, 48, -w^2 + 2*w + 8]', '[144, 48, w^2 + 3*w - 4]', '[144, 144, -3*w^2 + 11*w - 4]', '[148, 74, w^2 - 3*w - 3]', '[148, 148, 2*w^2 + w - 8]', '[151, 151, 2*w^2 - 3*w - 19]', '[152, 38, -2*w^2 + 10]', '[152, 152, -5*w^2 + 3*w + 36]', '[157, 157, 3*w - 5]', '[162, 18, -5*w^2 + w + 34]', '[162, 18, -3*w - 6]', '[162, 18, -3*w + 6]', '[162, 54, w^2 - 6*w + 2]', '[162, 162, -5*w^2 + 2*w + 34]', '[163, 163, 2*w^2 - 7*w + 1]', '[166, 166, -3*w^2 + 10*w - 6]', '[167, 167, -3*w - 1]', '[167, 167, 4*w^2 - 14*w + 5]', '[167, 167, 3*w^2 - 12*w + 5]', '[171, 57, 4*w^2 - 3*w - 31]', '[171, 57, -2*w^2 + w + 1]', '[171, 171, -2*w^2 - 2*w + 9]', '[172, 86, w^2 + w - 13]', '[172, 86, -3*w^2 - w + 15]', '[172, 86, 7*w^2 - 25*w + 11]', '[172, 172, 3*w^2 - 20]', '[172, 172, 2*w^2 - 3*w]', '[172, 172, -7*w^2 + 4*w + 52]', '[173, 173, -3*w^2 + 12*w - 7]', '[176, 44, -3*w^2 + 3*w + 25]', '[176, 44, -6*w + 4]', '[176, 176, w^2 - 3*w + 4]', '[177, 177, w^2 - 2*w + 3]', '[177, 177, 2*w^2 - 2*w - 9]', '[178, 178, -w^2 - 2*w - 2]', '[178, 178, w^2 + 4*w + 2]', '[178, 178, 3*w^2 + 3*w - 10]', '[181, 181, w^2 - 4*w - 1]', '[184, 46, -4*w^2 + 4*w + 34]', '[184, 184, -w^2 - 5*w + 4]', '[186, 186, w^2 + 5*w - 2]', '[186, 186, w^2 + 2*w - 6]', '[188, 94, -3*w^2 + 9*w - 5]', '[188, 188, w^2 + 4*w - 4]', '[192, 12, -8*w^2 + 4*w + 60]', '[192, 12, 4*w - 4]', '[192, 24, -3*w^2 - w + 17]', '[192, 24, -3*w^2 - w + 1]', '[192, 48, -2*w^2 + 4*w]', '[192, 48, 2*w - 8]', '[192, 192, 2*w^2 + w - 12]', '[192, 192, w^2 + 4*w]', '[193, 193, -w^2 - 2*w + 13]', '[197, 197, -3*w^2 + 17]', '[198, 66, -w^2 - 2]', '[198, 66, -2*w^2 + w + 10]', '[198, 198, -3*w^2 - w + 2]', '[206, 206, -w - 6]', '[207, 69, w^2 + 4*w + 1]', '[207, 69, -w^2 + 6*w - 5]', '[207, 207, -9*w^2 + 4*w + 67]', '[209, 209, -6*w^2 + 3*w + 41]', '[211, 211, -4*w^2 + 3*w + 27]', '[213, 213, 4*w^2 - 13*w + 7]', '[213, 213, -3*w^2 + 2*w + 25]', '[213, 213, 2*w + 7]', '[213, 213, 3*w^2 - 4*w - 13]', '[213, 213, 2*w^2 + w - 3]', '[213, 213, 2*w^2 - 4*w - 3]', '[214, 214, 2*w^2 - 9*w + 6]', '[214, 214, -3*w - 2]', '[214, 214, 6*w^2 - 7*w - 54]', '[216, 6, 6]', '[216, 18, 2*w^2 - 2]', '[216, 18, 4*w^2 - 2*w - 26]', '[216, 24, -3*w^2 + 24]', '[216, 54, -6*w^2 + 4*w + 46]', '[216, 72, w^2 - 3*w - 4]', '[216, 72, 5*w^2 - 4*w - 40]', '[216, 216, -5*w + 4]', '[218, 218, -w^2 - w - 2]', '[222, 222, -11*w^2 + 5*w + 78]', '[222, 222, 2*w^2 - w - 18]', '[223, 223, w^2 - 6*w + 7]', '[223, 223, 3*w + 5]', '[223, 223, 2*w^2 - 9]', '[226, 226, 3*w^2 + 4*w - 6]', '[228, 114, -3*w^2 + w + 25]', '[228, 114, -3*w^2 + 13*w - 7]', '[228, 228, -6*w^2 + w + 40]', '[228, 228, -2*w^2 - w]', '[233, 233, 2*w^2 - 19]', '[236, 118, -w^2 - 3*w + 5]', '[236, 236, -w^2 + 12]', '[241, 241, w^2 + 2*w - 7]', '[242, 22, 3*w^2 - w - 18]', '[242, 242, w^2 - 6*w + 6]', '[243, 9, 3*w^2 - 6*w + 3]', '[243, 9, 3*w^2 - 21]', '[243, 27, 3*w + 3]', '[243, 27, 2*w^2 - 4*w - 1]', '[243, 81, -2*w^2 + 9*w - 7]', '[243, 243, -4*w^2 + 4*w + 35]', '[248, 62, -2*w^2 + 4*w + 2]', '[248, 248, 3*w + 4]', '[249, 249, 2*w^2 - 2*w - 1]', '[249, 249, -w + 7]', '[250, 10, 5*w^2 - 30]', '[253, 253, 2*w^2 - w + 1]', '[254, 254, 9*w^2 - 3*w - 62]', '[256, 8, -4*w^2 + 12*w - 4]', '[256, 16, 4*w]', '[256, 16, -7*w^2 + 3*w + 53]', '[256, 64, -2*w^2 + 2*w + 8]', '[256, 256, -w^2 + 3*w + 12]', '[257, 257, -8*w^2 + 29*w - 13]', '[258, 258, -3*w^2 + 8*w - 2]', '[258, 258, -3*w^2 - 5*w + 2]', '[258, 258, -2*w^2 - w + 6]', '[258, 258, 7*w^2 - 4*w - 50]', '[258, 258, -9*w^2 + w + 58]', '[258, 258, -2*w^2 + 7*w - 6]', '[262, 262, 8*w^2 - 5*w - 62]', '[263, 263, -7*w^2 + 2*w + 49]', '[264, 66, 2*w^2 + 4*w - 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3*w + 53]', '[1879, 1879, 6*w^2 - 6*w - 31]', '[1881, 627, -4*w^2 + 8*w + 5]', '[1881, 627, -5*w^2 + 12*w - 7]', '[1881, 1881, -9*w^2 + 2*w + 65]', '[1882, 1882, 14*w^2 + 5*w - 74]', '[1884, 942, 5*w^2 - 11*w - 13]', '[1884, 942, -5*w^2 - w + 33]', '[1884, 1884, -5*w^2 + 26*w - 12]', '[1884, 1884, 5*w^2 - 2*w - 28]', '[1888, 236, -2*w^2 - 6*w + 10]', '[1888, 472, -2*w^2 + 24]', '[1888, 1888, -12*w^2 + 3*w + 92]', '[1889, 1889, -16*w^2 + 58*w - 29]', '[1892, 946, -17*w^2 + 7*w + 119]', '[1892, 946, 5*w^2 - 3*w - 43]', '[1892, 946, 3*w^2 - 15*w + 5]', '[1892, 1892, 8*w^2 - 21*w + 8]', '[1892, 1892, -24*w^2 + 15*w + 184]', '[1892, 1892, 5*w^2 - 12*w - 4]', '[1899, 633, 26*w^2 - 12*w - 185]', '[1899, 633, -4*w^2 + 14*w - 1]', '[1899, 1899, -5*w^2 + 2*w + 43]', '[1901, 1901, 4*w^2 - 7*w - 1]', '[1902, 1902, 17*w^2 - 5*w - 118]', '[1902, 1902, 3*w^2 + w + 2]', '[1903, 1903, 8*w - 9]', '[1906, 1906, 8*w^2 + 5*w - 38]', '[1907, 1907, 4*w^2 + 2*w - 13]', '[1909, 1909, -4*w^2 + 18*w - 13]', '[1913, 1913, -3*w^2 + 24*w - 13]', '[1913, 1913, w^2 + 6*w - 23]', '[1913, 1913, 5*w^2 - 20*w + 7]', '[1917, 213, 6*w + 9]', '[1917, 213, 9*w^2 - 57]', '[1917, 213, 12*w^2 - 39*w + 15]', '[1917, 639, -2*w^2 + 12*w - 13]', '[1917, 639, 2*w^2 - w + 5]', '[1917, 639, 5*w^2 + 2*w - 1]', '[1917, 639, -14*w^2 + 9*w + 95]', '[1917, 639, 8*w^2 - w - 55]', '[1917, 639, -5*w^2 + 6*w + 29]', '[1917, 1917, -5*w^2 + 22*w - 9]', '[1917, 1917, 7*w - 11]', '[1917, 1917, 2*w^2 + 4*w - 25]', '[1922, 62, 10*w^2 - 13*w - 94]', '[1922, 1922, -4*w^2 + 3*w + 18]', '[1923, 1923, 4*w^2 - 4*w + 3]', '[1923, 1923, 10*w^2 - 2*w - 69]', '[1926, 642, -5*w^2 - 2*w + 22]', '[1926, 642, -w^2 + 6*w - 14]', '[1926, 642, w^2 - 20*w + 10]', '[1926, 642, -5*w^2 + 26]', '[1926, 642, -w^2 - 6*w + 10]', '[1926, 642, -5*w^2 - 14*w - 2]', '[1926, 1926, -5*w^2 + 11*w - 2]', '[1926, 1926, -3*w^2 - 5*w - 2]', '[1926, 1926, 29*w^2 - 14*w - 214]', '[1928, 482, 2*w^2 + 4*w - 14]', '[1928, 1928, 5*w^2 - w - 44]', '[1929, 1929, -6*w^2 + 4*w + 35]', '[1929, 1929, -w^2 + 2*w - 9]', '[1933, 1933, -w^2 + 4*w - 11]', '[1934, 1934, 9*w^2 + 9*w - 34]', '[1936, 44, -w^2 - 7*w - 5]', '[1936, 44, 6*w^2 - 2*w - 36]', '[1936, 176, 19*w^2 - 10*w - 136]', '[1936, 484, 5*w^2 - 9*w + 5]', '[1936, 484, 2*w^2 - 12*w + 12]', '[1936, 1936, w^2 + 2*w + 8]', '[1941, 1941, 4*w^2 - 2*w - 3]', '[1941, 1941, -w + 13]', '[1942, 1942, 4*w^2 + 11*w - 10]', '[1944, 18, 6*w^2 - 12*w + 6]', '[1944, 18, 6*w^2 - 42]', '[1944, 54, 6*w + 6]', '[1944, 54, 4*w^2 - 8*w - 2]', '[1944, 72, 3*w^2 - 15*w + 12]', '[1944, 72, 21*w^2 - 9*w - 156]', '[1944, 162, -4*w^2 + 18*w - 14]', '[1944, 216, -6*w^2 + 3*w + 36]', '[1944, 216, -w^2 - 7*w - 4]', '[1944, 486, -8*w^2 + 8*w + 70]', '[1944, 648, -w^2 - 8]', '[1944, 1944, -5*w^2 - w + 4]', '[1947, 1947, -7*w + 23]', '[1947, 1947, 6*w^2 - w - 35]', '[1948, 974, w^2 + 5*w - 13]', '[1948, 1948, 4*w^2 + w - 40]', '[1949, 1949, -2*w^2 + 6*w - 9]', '[1949, 1949, 10*w^2 - 4*w - 67]', '[1949, 1949, 4*w^2 + 2*w - 7]', '[1951, 1951, 3*w^2 - 12*w + 1]', '[1954, 1954, -w^2 - 9*w + 2]', '[1956, 978, w^2 + 7*w - 9]', '[1956, 978, -3*w^2 + 5*w + 19]', '[1956, 1956, w^2 + 2*w - 20]', '[1956, 1956, -7*w^2 - 2*w + 36]', '[1957, 1957, -2*w^2 + 4*w - 7]', '[1958, 1958, 3*w^2 - w - 30]', '[1958, 1958, w^2 + 24*w - 14]', '[1958, 1958, -5*w^2 + 5*w + 38]', '[1959, 1959, 9*w^2 + 2*w - 49]', '[1959, 1959, 5*w^2 + 16*w - 9]', '[1962, 654, 11*w^2 - 7*w - 82]', '[1962, 654, -4*w^2 - 3*w + 22]', '[1962, 1962, 4*w^2 - 11*w - 6]', '[1964, 982, -5*w^2 - 7*w + 17]', '[1964, 982, 11*w^2 - 31*w + 13]', '[1964, 982, 9*w^2 - 3*w - 59]', '[1964, 1964, -5*w^2 + 4*w + 44]', '[1964, 1964, 10*w^2 - 11*w - 88]', '[1964, 1964, -3*w^2 - 15*w + 8]', '[1973, 1973, -5*w^2 + 2*w - 1]', '[1973, 1973, 7*w - 15]', '[1973, 1973, 14*w^2 - 46*w + 19]', '[1977, 1977, -2*w^2 + 5*w + 19]', '[1977, 1977, 13*w^2 - 4*w - 93]', '[1978, 1978, 7*w^2 - 5*w - 58]', '[1978, 1978, -23*w^2 + 9*w + 162]', '[1978, 1978, w^2 - 10*w + 2]', '[1982, 1982, 2*w^2 - 5*w - 14]', '[1982, 1982, w^2 - 18]', '[1982, 1982, 5*w^2 - 4*w - 26]', '[1984, 124, -4*w^2 + 8*w + 4]', '[1984, 248, -w^2 + 13*w - 5]', '[1984, 496, 6*w + 8]', '[1984, 1984, -7*w^2 + 3*w + 44]', '[1986, 1986, w^2 - 2*w - 18]', '[1986, 1986, -12*w^2 + 5*w + 82]', '[1987, 1987, 5*w^2 - 8*w + 1]', '[1991, 1991, -6*w - 7]', '[1992, 498, 4*w^2 - 4*w - 2]', '[1992, 498, -2*w + 14]', '[1992, 1992, 3*w^2 - 8*w - 8]', '[1992, 1992, -6*w^2 - w + 52]', '[1994, 1994, -w^2 + 3*w - 10]', '[1996, 998, -11*w^2 + 3*w + 79]', '[1996, 1996, -15*w^2 + 11*w + 120]', '[1997, 1997, -8*w^2 + 29*w - 19]', '[1998, 222, -3*w^2 + 6*w - 6]', '[1998, 666, -4*w^2 + 5*w + 14]', '[1998, 666, -17*w^2 + 6*w + 122]', '[1998, 1998, 3*w^2 - 5*w - 26]', '[1999, 1999, 6*w^2 - 47]', '[2000, 20, 10*w^2 - 60]', '[2000, 20, 5*w^2 - 5*w - 35]', '[2000, 80, -5*w^2]', '[2003, 2003, -5*w^2 + 22*w - 13]', '[2003, 2003, 2*w^2 - 6*w - 9]', '[2003, 2003, 12*w^2 - w - 75]', '[2004, 1002, -w^2 + 7*w + 21]', '[2004, 1002, -w^2 + 11*w - 9]', '[2004, 1002, w^2 + 5*w - 17]', '[2004, 1002, -w^2 + 7*w + 3]', '[2004, 1002, -3*w^2 + 7*w + 11]', '[2004, 1002, -11*w^2 + 41*w - 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12*w + 5]', '[173, 173, -3*w^2 + 12*w - 7]', '[181, 181, w^2 - 4*w - 1]', '[193, 193, -w^2 - 2*w + 13]', '[197, 197, -3*w^2 + 17]', '[211, 211, -4*w^2 + 3*w + 27]', '[223, 223, w^2 - 6*w + 7]', '[223, 223, 3*w + 5]', '[223, 223, 2*w^2 - 9]', '[233, 233, 2*w^2 - 19]', '[241, 241, w^2 + 2*w - 7]', '[257, 257, -8*w^2 + 29*w - 13]', '[263, 263, -7*w^2 + 2*w + 49]', '[271, 271, w^2 - 2*w - 13]', '[271, 271, -w^2 + 8*w - 5]', '[271, 271, 3*w^2 - 23]', '[277, 277, 2*w^2 + w - 5]', '[281, 281, 2*w^2 - 3*w - 1]', '[293, 293, 4*w^2 - 12*w + 3]', '[307, 307, -7*w^2 + 24*w - 9]', '[311, 311, 4*w^2 - 3*w - 29]', '[311, 311, -4*w^2 + w + 25]', '[311, 311, -2*w^2 + 13*w - 7]', '[313, 313, 2*w^2 - 3]', '[317, 317, 2*w^2 - 9*w + 3]', '[331, 331, 3*w^2 + 2*w - 15]', '[337, 337, 2*w^2 - 6*w + 5]', '[343, 7, -7]', '[347, 347, 2*w - 9]', '[347, 347, -4*w + 9]', '[347, 347, 2*w^2 + w - 17]', '[349, 349, -w^2 - 3]', '[353, 353, w^2 - 6*w + 1]', '[353, 353, 2*w^2 - 4*w - 23]', '[353, 353, -2*w^2 + 5*w + 5]', '[361, 19, 2*w^2 - 3*w - 3]', '[379, 379, -4*w^2 + 23]', '[379, 379, 4*w^2 - 2*w - 25]', '[379, 379, -4*w^2 + 6*w + 39]', '[383, 383, 3*w - 11]', '[389, 389, 8*w^2 - 3*w - 55]', '[401, 401, 4*w^2 - 16*w + 11]', '[409, 409, 2*w^2 + 2*w - 11]', '[421, 421, 2*w^2 - 2*w - 5]', '[421, 421, -6*w^2 + 4*w + 45]', '[421, 421, 6*w - 5]', '[439, 439, -2*w^2 + 3*w + 13]', '[443, 443, 2*w^2 - w - 5]', '[457, 457, -4*w^2 + 27]', '[487, 487, 3*w^2 - 4*w - 27]', '[491, 491, -11*w^2 + 6*w + 81]', '[491, 491, -2*w^2 - w - 1]', '[491, 491, 2*w^2 - 8*w + 1]', '[499, 499, 2*w^2 - 7*w + 7]', '[503, 503, -2*w^2 + 3*w + 15]', '[503, 503, -2*w^2 + 3*w - 3]', '[509, 509, 5*w^2 - 6*w - 45]', '[521, 521, -w^2 + 2*w - 5]', '[523, 523, 8*w^2 - 2*w - 53]', '[529, 23, 6*w^2 - 22*w + 9]', '[541, 541, -2*w^2 - 2*w - 1]', '[557, 557, 10*w^2 - 2*w - 67]', '[569, 569, -6*w^2 + 3*w + 47]', '[571, 571, -w^2 + 12*w - 7]', '[577, 577, -2*w^2 + 11*w - 7]', '[587, 587, -7*w^2 + 24*w - 13]', '[599, 599, -4*w^2 + 12*w - 7]', '[607, 607, 6*w - 1]', '[607, 607, w^2 + 6*w + 7]', '[607, 607, -2*w - 9]', '[613, 613, 3*w^2 - 2*w - 15]', '[619, 619, 2*w^2 - 12*w + 5]', '[641, 641, w^2 + 4*w - 7]', '[643, 643, -6*w^2 + 15*w - 7]', '[647, 647, 4*w^2 - 29]', '[653, 653, 4*w^2 + 5*w - 7]', '[659, 659, 8*w - 3]', '[691, 691, 2*w^2 - 21]', '[691, 691, 4*w^2 - 2*w - 1]', '[691, 691, 6*w^2 - 2*w - 39]', '[701, 701, 3*w^2 + 2*w - 9]', '[709, 709, -3*w^2 + 2*w + 27]', '[719, 719, 5*w^2 - 4*w - 29]', '[733, 733, -w^2 + 4*w + 13]', '[743, 743, -w - 9]', '[743, 743, 7*w^2 - 26*w + 11]', '[743, 743, 8*w^2 - 6*w - 63]', '[751, 751, 5*w - 9]', '[757, 757, -4*w^2 + 6*w - 3]', '[761, 761, -8*w^2 + 5*w + 59]', '[769, 769, -w^2 - 2*w - 5]', '[787, 787, 2*w^2 - 4*w - 11]', '[797, 797, -7*w^2 + 4*w + 55]', '[823, 823, 6*w^2 + 2*w - 33]', '[827, 827, -4*w^2 - w + 25]', '[829, 829, 3*w^2 - 13]', '[839, 839, w^2 - 15]', '[853, 853, -3*w^2 + 14*w - 9]', '[853, 853, 6*w^2 - w - 45]', '[853, 853, 2*w^2 + w - 23]', '[857, 857, 2*w^2 - 5*w - 23]', '[859, 859, 3*w^2 - 6*w - 11]', '[877, 877, 6*w^2 + w - 33]', '[881, 881, -3*w^2 + 16*w - 9]', '[883, 883, -5*w^2 + 20*w - 13]', '[883, 883, -5*w^2 + 2*w + 41]', '[883, 883, 2*w^2 + 2*w - 17]', '[887, 887, 10*w^2 - 3*w - 71]', '[907, 907, -3*w^2 + 4*w - 3]', '[929, 929, 6*w^2 - 5*w - 39]', '[929, 929, -4*w^2 + 21]', '[929, 929, w^2 + 10*w - 7]', '[937, 937, -4*w^2 + 4*w + 31]', '[941, 941, -5*w - 9]', '[953, 953, -5*w - 3]', '[961, 31, 4*w^2 + w - 19]', '[967, 967, -w^2 - 6*w - 1]', '[971, 971, 4*w^2 - 23*w + 11]', '[977, 977, 7*w^2 + 2*w - 37]', '[991, 991, -4*w^2 + 17*w - 11]', '[991, 991, 6*w^2 - 18*w + 5]', '[991, 991, -6*w^2 + 22*w - 15]', '[997, 997, 11*w^2 - 36*w + 15]']}
• 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': [4, -7, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1509, 'disc_rad': 1509, 'disc_sign': 1, 'frobs': [[2, [[2, 1], [1, 1]]], [3, [0]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[2, 1], [1, 1]]], [13, [[3, 1]]], [17, [[3, 1]]], [19, [[2, 1], [1, 1]]], [23, [[2, 1], [1, 1]]], [29, [[3, 1]]], [31, [[2, 1], [1, 1]]], [37, [[2, 1], [1, 1]]], [41, [[3, 1]]], [43, [[1, 3]]], [47, [[2, 1], [1, 1]]], [53, [[3, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 38.84584919911006, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1509.1', 'local_algs': ['3.1.0.1', '3.2.1.2', 'm503.1.1.0', 'm503.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 503], 'rd': 11.4699910738, 'regulator': {'__RealLiteral__': 0, 'data': '11.2956582948', 'prec': 44}, 'res': {'gal': ['-1509,0,484,0,-44,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 3 \\)', '\\( a^{2} - 6 a + 3 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}