Hilbert modular form data - 4.4.1600.1-79.4-a

Formats: - HTML - YAML - JSON - 2024-06-08T14:44:15.304751

• 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': 4, 'dimension': 3, 'disc': 1600, 'field_bad_primes': [2, 5], 'field_label': '4.4.1600.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.1600.1-79.4-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [79], 'level_ideal': '[79,79,-1/2*w^3 + 3/2*w^2 + 2*w - 4]', 'level_label': '79.4', 'level_norm': 79, 'parallel_weight': 2, 'short_label': '79.4-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[79,79,-1/2*w^3 + 3/2*w^2 + 2*w - 4]', 1]], 'hecke_eigenvalues': ['e', 'e^2 + e - 6', '-1/2*e^2 - e + 11/2', '-3*e^2 - 4*e + 21', '-5/2*e^2 - 3*e + 35/2', '-2*e^2 - 2*e + 8', 4, '3*e^2 + 4*e - 19', '5/2*e^2 + e - 35/2', '-2*e^2 + 8', '-2*e - 4', '2*e + 4', '3*e^2 + 2*e - 19', '-2*e^2 + 16', '4*e^2 + 4*e - 20', '-3*e + 1', '-4*e^2 - 6*e + 30', '9/2*e^2 + 5*e - 59/2', '9/2*e^2 + 3*e - 51/2', '-11/2*e^2 - 5*e + 73/2', '-7/2*e^2 - 5*e + 57/2', -1, '-e^2 - 3*e + 4', 'e^2 + 2*e - 13', '-5/2*e^2 - 3*e + 39/2', '5*e^2 + 2*e - 29', 'e^2 + 2*e - 9', '-3/2*e^2 + e + 17/2', 'e^2 - 4*e - 9', '-2*e^2 - e + 9', '7*e^2 + 8*e - 47', '-7/2*e^2 + e + 57/2', '-4*e^2 - 2*e + 24', '9*e^2 + 10*e - 61', '2*e^2 - 22', '9*e^2 + 8*e - 53', 'e^2 - 6*e - 11', '3*e + 11', 'e^2 + 2*e - 15', '-3/2*e^2 + 5*e + 21/2', '-3*e^2 - 8*e + 19', '7/2*e^2 + 7*e - 49/2', '-7*e^2 - 10*e + 53', '-5*e^2 - 2*e + 23', 'e + 9', '7*e^2 + 8*e - 43', '-5*e^2 - 8*e + 27', '-e^2 + 6*e + 1', '-13/2*e^2 - e + 75/2', 'e^2 - 19', '5/2*e^2 + 5*e - 55/2', '-3*e^2 - 2*e + 9', '-5/2*e^2 - 5*e + 59/2', '3*e^2 - 11', '-5/2*e^2 + 5*e + 35/2', '-4*e^2 - 4*e + 34', '3*e^2 - 4*e - 13', 'e^2 - 2*e - 1', '-4*e + 2', '-13/2*e^2 - 7*e + 63/2', '-8*e^2 - 12*e + 60', '2*e + 18', '8*e^2 + 7*e - 61', '-23/2*e^2 - 17*e + 185/2', '4*e^2 + 9*e - 31', '13/2*e^2 + 9*e - 63/2', '3*e^2 - 8*e - 23', '4*e^2 - 2*e - 34', '4*e^2 + 6*e - 16', '-5/2*e^2 + 3*e + 27/2', 'e^2 - 3', '6*e^2 + 2*e - 38', '9/2*e^2 + 3*e - 79/2', '-10*e', '3*e^2 - 2*e - 3', '7/2*e^2 + 5*e - 77/2', '-11*e^2 - 7*e + 62', '10*e^2 + 8*e - 68', '11/2*e^2 + 13*e - 101/2', '-10*e^2 - 19*e + 71', '-5*e^2 - 6*e + 39', '-11/2*e^2 + e + 53/2', -8, '1/2*e^2 - e - 43/2', '-7*e^2 - 4*e + 31', '-4*e^2 - 3*e + 21', '4*e^2 + 2*e - 24', '4*e^2 - 2*e - 32', '-2*e - 16', '-15/2*e^2 - 3*e + 81/2', '-1/2*e^2 + 7*e + 3/2', '-6*e^2 - 11*e + 35', '8*e^2 + 8*e - 40', '-13*e^2 - 14*e + 95', '15/2*e^2 + 13*e - 105/2', '9/2*e^2 + 13*e - 43/2', '15/2*e^2 + 3*e - 69/2', '7*e^2 + 2*e - 63', '25/2*e^2 + 13*e - 139/2', '-4*e^2 + 18', '15*e^2 + 14*e - 103', '-2*e^2 - 2*e - 10', '9*e^2 + 6*e - 57', '-11/2*e^2 - e + 69/2', '-8*e^2 + 44', '-10*e^2 - 8*e + 74', '1/2*e^2 + 5*e + 21/2', '18*e^2 + 14*e - 108', '-9*e^2 - 12*e + 79', '-8*e^2 - 10*e + 60', '-13*e^2 - 2*e + 77', '-6*e^2 - 8*e + 56', '6*e^2 + 18*e - 48', '9*e^2 + 8*e - 61', '-8*e', '-10*e^2 - 8*e + 78', '-15*e^2 - 9*e + 92', '-13*e^2 - 8*e + 67', '-10*e - 8', '15/2*e^2 + 9*e - 133/2', '10*e^2 + 10*e - 56', '-10*e^2 - 10*e + 60', '2*e^2 - 6', '-3*e^2 - 8*e + 55', '-3*e^2 - 2*e + 33', '-8*e^2 - 5*e + 47', '-5*e^2 - 12*e + 21', '17*e^2 + 20*e - 117', '-3*e^2 - 15*e + 26', '-9*e^2 - 10*e + 41', '-e^2 + 9*e + 28', '3*e^2 + 10*e - 43', '-e^2 - 3*e - 16', '4*e^2 + 4*e - 22', '-29/2*e^2 - 3*e + 171/2', 'e^2 - 7*e + 6', 'e^2 + 2*e - 49', '-7*e^2 - 2*e + 51', '-17/2*e^2 + 5*e + 123/2', '7/2*e^2 - 15*e - 53/2', '-2*e^2 + 4*e + 54', '12*e^2 + 19*e - 105', '7*e^2 + 12*e - 23', '-9*e^2 - 12*e + 69', '13*e^2 + 15*e - 116', '-6*e^2 + 44', '2*e^2 - 8', '3/2*e^2 + e - 65/2', '-9*e^2 - 15*e + 44', '-14*e^2 - 2*e + 90', '-7/2*e^2 + 9*e + 97/2', '-1/2*e^2 + e + 3/2', '29/2*e^2 + 13*e - 183/2', '3*e^2 - 2*e - 9', '7/2*e^2 + 5*e + 3/2', '-18*e - 2', '-11*e^2 - 24*e + 87', '2*e^2 + 20*e - 10', '11*e^2 + 14*e - 71', '21*e^2 + 22*e - 133', '15/2*e^2 + 5*e - 93/2', '-14*e + 12', '-6*e^2 + 7*e + 41', '20*e^2 + 23*e - 145', '7/2*e^2 + 3*e + 47/2', '20*e^2 + 23*e - 145'], 'hecke_polynomial': 'x^3 - x^2 - 9*x + 13', 'label': '4.4.1600.1-79.4-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 1600, 'ideals': ['[1, 1, 1]', '[4, 2, 1/2*w^3 - 2*w]', '[9, 3, -1/2*w^3 + 1/2*w^2 + 2*w - 3]', '[9, 3, 1/2*w^3 + 1/2*w^2 - 2*w - 3]', '[16, 2, 2]', '[25, 5, w^2 - 3]', '[31, 31, 1/2*w^3 + 1/2*w^2 - 3*w]', '[31, 31, -1/2*w^2 - w + 3]', '[31, 31, -1/2*w^2 + w + 3]', '[31, 31, 1/2*w^3 - 1/2*w^2 - 3*w]', '[36, 6, -w^3 + 5*w + 2]', '[36, 6, -w^3 + 5*w - 2]', '[41, 41, 1/2*w^3 - w^2 - w + 3]', '[41, 41, w^3 + w^2 - 5*w - 3]', '[41, 41, -3/2*w^2 - w + 5]', '[41, 41, -1/2*w^3 - w^2 + w + 3]', '[49, 7, -1/2*w^3 + 2*w - 3]', '[49, 7, 1/2*w^3 - 2*w - 3]', '[64, 4, w^3 - 4*w]', '[71, 71, 1/2*w^3 + 1/2*w^2 - 2*w - 5]', '[71, 71, 1/2*w^3 + 3/2*w^2 - 3*w - 5]', '[71, 71, 1/2*w^3 - 3/2*w^2 - 3*w + 5]', '[71, 71, -1/2*w^3 + 1/2*w^2 + 2*w - 5]', '[79, 79, 1/2*w^3 + 3/2*w^2 - 2*w - 4]', '[79, 79, -w^3 - 1/2*w^2 + 6*w]', '[79, 79, w^3 - 1/2*w^2 - 6*w]', '[79, 79, 1/2*w^3 - 3/2*w^2 - 2*w + 4]', '[81, 3, 3]', '[81, 9, -1/2*w^3 + 4*w - 1]', '[81, 9, -1/2*w^3 + 4*w + 1]', '[89, 89, w^2 + w - 5]', '[89, 89, -w^3 + 1/2*w^2 + 5*w]', '[89, 89, w^3 + 1/2*w^2 - 5*w]', '[89, 89, w^2 - w - 5]', '[100, 10, -1/2*w^3 + 4*w]', '[121, 11, 3/2*w^2 - 5]', '[121, 11, 1/2*w^2 - 5]', '[124, 62, w^3 + w^2 - 5*w - 2]', '[124, 62, -1/2*w^3 - w^2 + w + 4]', '[124, 62, 1/2*w^3 - w^2 - w + 4]', '[124, 62, w^3 - w^2 - 5*w + 2]', '[144, 6, -w^3 + w^2 + 4*w - 6]', '[144, 6, w^3 + w^2 - 4*w - 6]', '[151, 151, -w^3 + 1/2*w^2 + 5*w + 1]', '[151, 151, 1/2*w^3 + 1/2*w^2 - w - 4]', '[151, 151, -1/2*w^3 + 1/2*w^2 + w - 4]', '[151, 151, -w^3 - 1/2*w^2 + 5*w - 1]', '[164, 82, 1/2*w^3 + w^2 - 5*w - 4]', '[164, 82, -1/2*w^3 - w^2 + 4*w + 6]', '[164, 82, w^3 - w^2 - 7*w + 2]', '[164, 82, 1/2*w^3 - w^2 - 4*w]', '[169, 13, -1/2*w^3 - 2*w^2 + 3*w + 3]', '[169, 13, 2*w^2 - w - 9]', '[191, 191, -w^3 - 2*w^2 + 5*w + 7]', '[191, 191, 3/2*w^3 - 1/2*w^2 - 5*w + 3]', '[191, 191, -3/2*w^3 - 1/2*w^2 + 5*w + 3]', '[191, 191, w^3 - 2*w^2 - 5*w + 7]', '[196, 14, -3/2*w^3 + 6*w + 2]', '[196, 14, -3/2*w^3 + 6*w - 2]', '[199, 199, -1/2*w^3 + w^2 + 4*w - 7]', '[199, 199, -3/2*w^3 + 3/2*w^2 + 7*w - 4]', '[199, 199, 3/2*w^3 + 3/2*w^2 - 7*w - 4]', '[199, 199, 1/2*w^3 + w^2 - 4*w - 7]', '[225, 15, -1/2*w^3 - 3/2*w^2 + 4*w + 7]', '[225, 15, 1/2*w^3 - 3/2*w^2 - 4*w + 7]', '[239, 239, 2*w^3 - w^2 - 9*w + 3]', '[239, 239, -3/2*w^3 - w^2 + 5*w + 3]', '[239, 239, 3/2*w^3 - w^2 - 5*w + 3]', '[239, 239, 2*w^3 + w^2 - 9*w - 3]', '[241, 241, -w^3 + w^2 + 5*w - 1]', '[241, 241, -1/2*w^3 + w^2 + w - 5]', '[241, 241, 1/2*w^3 + w^2 - w - 5]', '[241, 241, w^3 + w^2 - 5*w - 1]', '[256, 4, 4]', '[271, 271, 3/2*w^3 - 9*w - 1]', '[271, 271, 3*w - 1]', '[271, 271, -3*w - 1]', '[271, 271, 1/2*w^2 - 3*w]', '[279, 93, -w^3 + 1/2*w^2 + 6*w + 2]', '[279, 93, 1/2*w^3 - 2*w^2 - 3*w + 7]', '[279, 93, 1/2*w^2 - 2*w - 5]', '[279, 93, 2*w^2 - w - 5]', '[279, 93, 2*w^2 + w - 5]', '[279, 93, 1/2*w^2 + 2*w - 5]', '[279, 93, -w^3 - 1/2*w^2 + 6*w - 2]', '[279, 93, -1/2*w^3 - 2*w^2 + 3*w + 7]', '[281, 281, 1/2*w^3 + 2*w^2 - 2*w - 7]', '[281, 281, -1/2*w^3 + 1/2*w^2 + 3*w - 6]', '[281, 281, 1/2*w^3 + 1/2*w^2 - 3*w - 6]', '[281, 281, -1/2*w^3 + 2*w^2 + 2*w - 7]', '[284, 142, w^3 + w^2 - 7*w - 4]', '[284, 142, -2*w^3 + 9*w - 2]', '[284, 142, -2*w^3 + 9*w + 2]', '[284, 142, -w^3 + w^2 + 7*w - 4]', '[289, 17, 1/2*w^2 + 3*w - 1]', '[289, 17, 1/2*w^2 - 3*w - 1]', '[311, 311, w^3 - 1/2*w^2 - 2*w + 3]', '[311, 311, 2*w^3 + 1/2*w^2 - 10*w]', '[311, 311, -2*w^3 + 1/2*w^2 + 10*w]', '[311, 311, -w^3 - 1/2*w^2 + 2*w + 3]', '[316, 158, -1/2*w^3 + 5*w + 2]', '[316, 158, -1/2*w^3 - 2*w^2 + w + 8]', '[316, 158, -1/2*w^3 + 2*w^2 + w - 8]', '[316, 158, 1/2*w^3 - 5*w + 2]', '[324, 6, 3/2*w^3 - 6*w]', '[324, 18, 1/2*w^3 + 2*w^2 - 2*w - 6]', '[324, 18, -1/2*w^3 + 2*w^2 + 2*w - 6]', '[356, 178, 1/2*w^3 + w^2 - w - 6]', '[356, 178, -3/2*w^3 - w^2 + 8*w + 2]', '[356, 178, -3/2*w^3 + w^2 + 8*w - 2]', '[356, 178, 1/2*w^3 - w^2 - w + 6]', '[359, 359, w^3 - 3/2*w^2 - 6*w + 3]', '[359, 359, -3/2*w^3 - 1/2*w^2 + 7*w - 2]', '[359, 359, 3/2*w^3 - 1/2*w^2 - 7*w - 2]', '[359, 359, w^3 - 1/2*w^2 - 3*w + 5]', '[361, 19, 2*w^2 - 7]', '[361, 19, 1/2*w^2 - 6]', '[369, 123, w^3 + w^2 - 3*w - 5]', '[369, 123, 2*w^3 + 3*w^2 - 13*w - 13]', '[369, 123, -3*w^3 - 5/2*w^2 + 17*w + 13]', '[369, 123, -2*w^3 - 1/2*w^2 + 9*w + 1]', '[369, 123, -3/2*w^3 + 7/2*w^2 + 10*w - 14]', '[369, 123, 1/2*w^3 + 3/2*w^2 - 4*w - 10]', '[369, 123, w^3 + 1/2*w^2 - 6*w - 7]', '[369, 123, 5/2*w^2 + 2*w - 7]', '[400, 10, 2*w^2 - 6]', '[401, 401, -2*w^3 - 1/2*w^2 + 9*w + 3]', '[401, 401, 3/2*w^3 + 1/2*w^2 - 5*w]', '[401, 401, -3/2*w^3 + 1/2*w^2 + 5*w]', '[401, 401, 2*w^3 - 1/2*w^2 - 9*w + 3]', '[409, 409, 3/2*w^3 + 3/2*w^2 - 8*w - 4]', '[409, 409, -1/2*w^3 - 3/2*w^2 + 5]', '[409, 409, 1/2*w^3 - 3/2*w^2 + 5]', '[409, 409, -3/2*w^3 + 3/2*w^2 + 8*w - 4]', '[431, 431, -2*w^3 + 9*w + 1]', '[431, 431, -3/2*w^3 + 5*w + 1]', '[431, 431, 3/2*w^3 - 5*w + 1]', '[431, 431, 2*w^3 - 9*w + 1]', '[439, 439, -3/2*w^3 + 1/2*w^2 + 5*w - 1]', '[439, 439, -2*w^3 + 1/2*w^2 + 9*w - 2]', '[439, 439, -2*w^3 - 1/2*w^2 + 9*w + 2]', '[439, 439, -3/2*w^3 - 1/2*w^2 + 5*w + 1]', '[441, 21, 1/2*w^3 - 3/2*w^2 - w + 7]', '[441, 21, 5/2*w^3 - 3/2*w^2 - 11*w + 11]', '[441, 21, -5/2*w^3 - 3/2*w^2 + 11*w + 11]', '[441, 21, -1/2*w^3 - 3/2*w^2 + w + 7]', '[449, 449, -w^3 - 3/2*w^2 + 3*w + 6]', '[449, 449, 3/2*w^3 + 3/2*w^2 - 7*w - 3]', '[449, 449, -3/2*w^3 + 3/2*w^2 + 7*w - 3]', '[449, 449, w^3 - 3/2*w^2 - 3*w + 6]', '[479, 479, -w - 5]', '[479, 479, 1/2*w^3 - 3*w - 5]', '[479, 479, -1/2*w^3 + 3*w - 5]', '[479, 479, w - 5]', '[484, 22, -w^3 + 7*w]', '[484, 22, -2*w^3 + 9*w]', '[496, 62, w^3 + w^2 - 6*w]', '[496, 62, -w^2 - 2*w + 6]', '[496, 62, -w^2 + 2*w + 6]', '[496, 62, w^3 - w^2 - 6*w]', '[521, 521, -5/2*w^3 - 1/2*w^2 + 12*w - 1]', '[521, 521, 3/2*w^3 - 3/2*w^2 - 6*w + 1]', '[521, 521, -3/2*w^3 - 3/2*w^2 + 6*w + 1]', '[521, 521, 5/2*w^3 - 1/2*w^2 - 12*w - 1]', '[529, 23, -1/2*w^3 + 2*w - 5]', '[529, 23, 1/2*w^3 - 2*w - 5]', '[569, 569, 2*w^3 + 2*w^2 - 9*w - 5]', '[569, 569, -2*w^3 + w^2 + 12*w - 3]', '[569, 569, 2*w^3 + w^2 - 12*w - 3]', '[569, 569, -2*w^3 + 2*w^2 + 9*w - 5]', '[576, 12, -2*w^3 + 10*w + 4]', '[576, 12, -2*w^3 + 10*w - 4]', '[599, 599, 3/2*w^3 + 2*w^2 - 6*w - 3]', '[599, 599, w^3 - 5/2*w^2 - 5*w + 8]', '[599, 599, -w^3 - 5/2*w^2 + 5*w + 8]', '[599, 599, -3/2*w^3 + 2*w^2 + 6*w - 3]', '[601, 601, 5/2*w^3 - 3/2*w^2 - 12*w + 4]', '[601, 601, -3/2*w^3 - 3/2*w^2 + 4*w + 5]', '[601, 601, 3/2*w^3 - 3/2*w^2 - 4*w + 5]', '[601, 601, -5/2*w^3 - 3/2*w^2 + 12*w + 4]', '[604, 302, w^3 + w^2 - 3*w - 6]', '[604, 302, -3/2*w^3 - w^2 + 7*w]', '[604, 302, -3/2*w^3 + w^2 + 7*w]', '[604, 302, -w^3 + w^2 + 3*w - 6]', '[625, 5, 5]', '[631, 631, 2*w^3 - 1/2*w^2 - 9*w - 3]', '[631, 631, -3/2*w^3 + 1/2*w^2 + 5*w - 6]', '[631, 631, 3/2*w^3 + 1/2*w^2 - 5*w - 6]', '[631, 631, -2*w^3 - 1/2*w^2 + 9*w - 3]', '[639, 213, w^3 - 5/2*w^2 - 4*w + 12]', '[639, 213, -3*w^3 - 5/2*w^2 + 14*w + 16]', '[639, 213, 5/2*w^3 + 7/2*w^2 - 15*w - 16]', '[639, 213, 1/2*w^3 + 3/2*w^2 - w - 8]', '[639, 213, 1/2*w^3 - 3/2*w^2 - w + 8]', '[639, 213, 5/2*w^3 - 7/2*w^2 - 15*w + 16]', '[639, 213, -w^3 - 5/2*w^2 + 4*w + 12]', '[639, 213, 3*w^3 - 5/2*w^2 - 14*w + 16]', '[641, 641, w^3 - 2*w^2 - 5*w + 3]', '[641, 641, 1/2*w^3 - 2*w^2 - w + 9]', '[641, 641, -1/2*w^3 - 2*w^2 + w + 9]', '[641, 641, -w^3 - 2*w^2 + 5*w + 3]', '[656, 82, -w^3 - 3*w^2 + 6*w + 8]', '[656, 82, 2*w^3 + 2*w^2 - 10*w - 6]', '[656, 82, -3*w^2 - 2*w + 10]', '[656, 82, -w^3 - 2*w^2 + 2*w + 6]', '[676, 26, -1/2*w^3 + w^2 - 2*w - 4]', '[676, 26, -5/2*w^3 - w^2 + 14*w + 2]', '[711, 237, -1/2*w^3 - 2*w^2 + 7]', '[711, 237, -3/2*w^3 - 2*w^2 + 10*w + 11]', '[711, 237, 7/2*w^3 - 2*w^2 - 17*w + 9]', '[711, 237, 5/2*w^3 + 2*w^2 - 15*w - 7]', '[711, 237, -7/2*w^3 - 2*w^2 + 17*w + 9]', '[711, 237, -5/2*w^3 + 2*w^2 + 15*w - 7]', '[711, 237, -3/2*w^3 + 2*w^2 + 10*w - 11]', '[711, 237, -1/2*w^3 + 2*w^2 - 7]', '[719, 719, -1/2*w^3 + 5/2*w^2 + 3*w - 9]', '[719, 719, -5/2*w^2 - w + 6]', '[719, 719, -5/2*w^2 + w + 6]', '[719, 719, 1/2*w^3 + 5/2*w^2 - 3*w - 9]', '[729, 9, -3/2*w^3 + 3/2*w^2 + 6*w - 9]', '[729, 9, 3/2*w^3 + 3/2*w^2 - 6*w - 9]', '[729, 27, 2*w^3 - w^2 - 8*w + 3]', '[729, 27, 2*w^3 + w^2 - 8*w - 3]', '[751, 751, -w^3 + w^2 + 5*w - 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5*w - 3]', '[41, 41, -3/2*w^2 - w + 5]', '[41, 41, -1/2*w^3 - w^2 + w + 3]', '[49, 7, -1/2*w^3 + 2*w - 3]', '[49, 7, 1/2*w^3 - 2*w - 3]', '[71, 71, 1/2*w^3 + 1/2*w^2 - 2*w - 5]', '[71, 71, 1/2*w^3 + 3/2*w^2 - 3*w - 5]', '[71, 71, 1/2*w^3 - 3/2*w^2 - 3*w + 5]', '[71, 71, -1/2*w^3 + 1/2*w^2 + 2*w - 5]', '[79, 79, 1/2*w^3 + 3/2*w^2 - 2*w - 4]', '[79, 79, -w^3 - 1/2*w^2 + 6*w]', '[79, 79, w^3 - 1/2*w^2 - 6*w]', '[79, 79, 1/2*w^3 - 3/2*w^2 - 2*w + 4]', '[89, 89, w^2 + w - 5]', '[89, 89, -w^3 + 1/2*w^2 + 5*w]', '[89, 89, w^3 + 1/2*w^2 - 5*w]', '[89, 89, w^2 - w - 5]', '[121, 11, 3/2*w^2 - 5]', '[121, 11, 1/2*w^2 - 5]', '[151, 151, -w^3 + 1/2*w^2 + 5*w + 1]', '[151, 151, 1/2*w^3 + 1/2*w^2 - w - 4]', '[151, 151, -1/2*w^3 + 1/2*w^2 + w - 4]', '[151, 151, -w^3 - 1/2*w^2 + 5*w - 1]', '[169, 13, -1/2*w^3 - 2*w^2 + 3*w + 3]', '[169, 13, 2*w^2 - w - 9]', '[191, 191, -w^3 - 2*w^2 + 5*w + 7]', '[191, 191, 3/2*w^3 - 1/2*w^2 - 5*w + 3]', '[191, 191, -3/2*w^3 - 1/2*w^2 + 5*w + 3]', '[191, 191, w^3 - 2*w^2 - 5*w + 7]', '[199, 199, -1/2*w^3 + w^2 + 4*w - 7]', '[199, 199, -3/2*w^3 + 3/2*w^2 + 7*w - 4]', '[199, 199, 3/2*w^3 + 3/2*w^2 - 7*w - 4]', '[199, 199, 1/2*w^3 + w^2 - 4*w - 7]', '[239, 239, 2*w^3 - w^2 - 9*w + 3]', '[239, 239, -3/2*w^3 - w^2 + 5*w + 3]', '[239, 239, 3/2*w^3 - w^2 - 5*w + 3]', '[239, 239, 2*w^3 + w^2 - 9*w - 3]', '[241, 241, -w^3 + w^2 + 5*w - 1]', '[241, 241, -1/2*w^3 + w^2 + w - 5]', '[241, 241, 1/2*w^3 + w^2 - w - 5]', '[241, 241, w^3 + w^2 - 5*w - 1]', '[271, 271, 3/2*w^3 - 9*w - 1]', '[271, 271, 3*w - 1]', '[271, 271, -3*w - 1]', '[271, 271, 1/2*w^2 - 3*w]', '[281, 281, 1/2*w^3 + 2*w^2 - 2*w - 7]', '[281, 281, -1/2*w^3 + 1/2*w^2 + 3*w - 6]', '[281, 281, 1/2*w^3 + 1/2*w^2 - 3*w - 6]', '[281, 281, -1/2*w^3 + 2*w^2 + 2*w - 7]', '[289, 17, 1/2*w^2 + 3*w - 1]', '[289, 17, 1/2*w^2 - 3*w - 1]', '[311, 311, w^3 - 1/2*w^2 - 2*w + 3]', '[311, 311, 2*w^3 + 1/2*w^2 - 10*w]', '[311, 311, -2*w^3 + 1/2*w^2 + 10*w]', '[311, 311, -w^3 - 1/2*w^2 + 2*w + 3]', '[359, 359, w^3 - 3/2*w^2 - 6*w + 3]', '[359, 359, -3/2*w^3 - 1/2*w^2 + 7*w - 2]', '[359, 359, 3/2*w^3 - 1/2*w^2 - 7*w - 2]', '[359, 359, w^3 - 1/2*w^2 - 3*w + 5]', '[361, 19, 2*w^2 - 7]', '[361, 19, 1/2*w^2 - 6]', '[401, 401, -2*w^3 - 1/2*w^2 + 9*w + 3]', '[401, 401, 3/2*w^3 + 1/2*w^2 - 5*w]', '[401, 401, -3/2*w^3 + 1/2*w^2 + 5*w]', '[401, 401, 2*w^3 - 1/2*w^2 - 9*w + 3]', '[409, 409, 3/2*w^3 + 3/2*w^2 - 8*w - 4]', '[409, 409, -1/2*w^3 - 3/2*w^2 + 5]', '[409, 409, 1/2*w^3 - 3/2*w^2 + 5]', '[409, 409, -3/2*w^3 + 3/2*w^2 + 8*w - 4]', '[431, 431, -2*w^3 + 9*w + 1]', '[431, 431, -3/2*w^3 + 5*w + 1]', '[431, 431, 3/2*w^3 - 5*w + 1]', '[431, 431, 2*w^3 - 9*w + 1]', '[439, 439, -3/2*w^3 + 1/2*w^2 + 5*w - 1]', '[439, 439, -2*w^3 + 1/2*w^2 + 9*w - 2]', '[439, 439, -2*w^3 - 1/2*w^2 + 9*w + 2]', '[439, 439, -3/2*w^3 - 1/2*w^2 + 5*w + 1]', '[449, 449, -w^3 - 3/2*w^2 + 3*w + 6]', '[449, 449, 3/2*w^3 + 3/2*w^2 - 7*w - 3]', '[449, 449, -3/2*w^3 + 3/2*w^2 + 7*w - 3]', '[449, 449, w^3 - 3/2*w^2 - 3*w + 6]', '[479, 479, -w - 5]', '[479, 479, 1/2*w^3 - 3*w - 5]', '[479, 479, -1/2*w^3 + 3*w - 5]', '[479, 479, w - 5]', '[521, 521, -5/2*w^3 - 1/2*w^2 + 12*w - 1]', '[521, 521, 3/2*w^3 - 3/2*w^2 - 6*w + 1]', '[521, 521, -3/2*w^3 - 3/2*w^2 + 6*w + 1]', '[521, 521, 5/2*w^3 - 1/2*w^2 - 12*w - 1]', '[529, 23, -1/2*w^3 + 2*w - 5]', '[529, 23, 1/2*w^3 - 2*w - 5]', '[569, 569, 2*w^3 + 2*w^2 - 9*w - 5]', '[569, 569, -2*w^3 + w^2 + 12*w - 3]', '[569, 569, 2*w^3 + w^2 - 12*w - 3]', '[569, 569, -2*w^3 + 2*w^2 + 9*w - 5]', '[599, 599, 3/2*w^3 + 2*w^2 - 6*w - 3]', '[599, 599, w^3 - 5/2*w^2 - 5*w + 8]', '[599, 599, -w^3 - 5/2*w^2 + 5*w + 8]', '[599, 599, -3/2*w^3 + 2*w^2 + 6*w - 3]', '[601, 601, 5/2*w^3 - 3/2*w^2 - 12*w + 4]', '[601, 601, -3/2*w^3 - 3/2*w^2 + 4*w + 5]', '[601, 601, 3/2*w^3 - 3/2*w^2 - 4*w + 5]', '[601, 601, -5/2*w^3 - 3/2*w^2 + 12*w + 4]', '[631, 631, 2*w^3 - 1/2*w^2 - 9*w - 3]', '[631, 631, -3/2*w^3 + 1/2*w^2 + 5*w - 6]', '[631, 631, 3/2*w^3 + 1/2*w^2 - 5*w - 6]', '[631, 631, -2*w^3 - 1/2*w^2 + 9*w - 3]', '[641, 641, w^3 - 2*w^2 - 5*w + 3]', '[641, 641, 1/2*w^3 - 2*w^2 - w + 9]', '[641, 641, -1/2*w^3 - 2*w^2 + w + 9]', '[641, 641, -w^3 - 2*w^2 + 5*w + 3]', '[719, 719, -1/2*w^3 + 5/2*w^2 + 3*w - 9]', '[719, 719, -5/2*w^2 - w + 6]', '[719, 719, -5/2*w^2 + w + 6]', '[719, 719, 1/2*w^3 + 5/2*w^2 - 3*w - 9]', '[751, 751, -w^3 + w^2 + 5*w - 9]', '[751, 751, 1/2*w^3 - w^2 - w - 3]', '[751, 751, -1/2*w^3 - w^2 + w - 3]', '[751, 751, w^3 + w^2 - 5*w - 9]', '[761, 761, 3/2*w^3 + 3/2*w^2 - 8*w - 3]', '[761, 761, -1/2*w^3 + 3/2*w^2 + w - 9]', '[761, 761, 1/2*w^3 + 3/2*w^2 - w - 9]', '[761, 761, -3/2*w^3 + 3/2*w^2 + 8*w - 3]', '[769, 769, -1/2*w^3 + 1/2*w^2 - 6]', '[769, 769, -3/2*w^3 - 1/2*w^2 + 8*w - 3]', '[769, 769, 3/2*w^3 - 1/2*w^2 - 8*w - 3]', '[769, 769, 1/2*w^3 + 1/2*w^2 - 6]', '[809, 809, -3/2*w^3 + 2*w^2 + 9*w - 5]', '[809, 809, -2*w^3 - 3/2*w^2 + 11*w + 4]', '[809, 809, 2*w^3 - 3/2*w^2 - 11*w + 4]', '[809, 809, 3/2*w^3 + 2*w^2 - 9*w - 5]', '[839, 839, -1/2*w^3 + 5/2*w^2 + 2*w - 8]', '[839, 839, -1/2*w^3 + w^2 + 3*w - 9]', '[839, 839, 1/2*w^3 + w^2 - 3*w - 9]', '[839, 839, 1/2*w^3 + 5/2*w^2 - 2*w - 8]', '[841, 29, 5/2*w^2 - 9]', '[841, 29, -5/2*w^2 + 6]', '[881, 881, -w^3 + w^2 + 8*w - 5]', '[881, 881, -w^3 - w^2 + 8*w + 1]', '[881, 881, w^3 - w^2 - 8*w + 1]', '[881, 881, w^3 + w^2 - 8*w - 5]', '[911, 911, w^3 - 3/2*w^2 - 7*w + 1]', '[911, 911, -1/2*w^3 + 3/2*w^2 + 5*w - 8]', '[911, 911, 1/2*w^3 + 3/2*w^2 - 5*w - 8]', '[911, 911, -w^3 - 3/2*w^2 + 7*w + 1]', '[919, 919, -w^3 - w^2 + 2*w + 5]', '[919, 919, -2*w^3 + w^2 + 10*w - 1]', '[919, 919, 2*w^3 + w^2 - 10*w - 1]', '[919, 919, w^3 - w^2 - 2*w + 5]', '[929, 929, 2*w^3 - 12*w - 1]', '[929, 929, 4*w - 1]', '[929, 929, -4*w - 1]', '[929, 929, 2*w^3 - 12*w + 1]', '[991, 991, -2*w^3 + 1/2*w^2 + 10*w + 2]', '[991, 991, -2*w^2 + 2*w + 9]', '[991, 991, -2*w^2 - 2*w + 9]', '[991, 991, 2*w^3 + 1/2*w^2 - 10*w + 2]']}
• 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, 0, -6, 0, 1], 'conductor': 40, 'degree': 4, 'dirichlet_group': [1, 9, 29, 21], 'disc_abs': 1600, 'disc_rad': 10, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 2]]], [5, [0]], [7, [[2, 2]]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[1, 4]]], [37, [[2, 2]]], [41, [[1, 4]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 6.324555320336759, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.1600.1', 'local_algs': ['2.4.6.1', '5.4.2.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 5], 'rd': 6.32455532034, 'regulator': {'__RealLiteral__': 0, 'data': '1.54250590983', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-10.0.1', '-2.0.1', '-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{2} - 1 \\)', '\\( \\frac{1}{2} a^{3} - 2 a - 1 \\)', '\\( \\frac{1}{2} a^{3} + \\frac{1}{2} a^{2} - 2 a - 1 \\)'], 'unitsGmodule': [[14, 1]], 'unitsType': 'Type IV', 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2', '1/2*a^3']}