Hilbert modular form data - 4.4.7625.1-16.3-b

Formats: - HTML - YAML - JSON - 2024-06-06T11:51:35.546856

• 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': 6, 'disc': 7625, 'field_bad_primes': [5, 61], 'field_label': '4.4.7625.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.7625.1-16.3-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2], 'level_ideal': '[16,4,1/4*w^3 - 1/4*w^2 - 9/4*w + 1]', 'level_label': '16.3', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.3-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4,2,1/2*w^3 + 1/2*w^2 - 7/2*w - 5]', 1]], 'hecke_eigenvalues': ['e', 0, '-1/8*e^4 + 13/8*e^2 - 2', '1/8*e^4 - 21/8*e^2 + 11', '-1/8*e^4 + 21/8*e^2 - 7', '-1/8*e^5 + 21/8*e^3 - 11*e', '1/4*e^5 - 17/4*e^3 + 13*e', '-7/8*e^4 + 107/8*e^2 - 36', '3/8*e^4 - 55/8*e^2 + 24', '1/8*e^5 - 13/8*e^3 + 2*e', '1/2*e^5 - 17/2*e^3 + 26*e', '1/4*e^5 - 17/4*e^3 + 17*e', '1/8*e^5 - 13/8*e^3 + 2*e', '1/2*e^4 - 17/2*e^2 + 26', '-3/8*e^4 + 39/8*e^2 - 10', '3/8*e^4 - 39/8*e^2 + 14', '-1/2*e^5 + 17/2*e^3 - 30*e', '3/8*e^5 - 47/8*e^3 + 15*e', '7/8*e^4 - 123/8*e^2 + 48', '-1/2*e^5 + 15/2*e^3 - 19*e', '2*e', '7/8*e^4 - 115/8*e^2 + 41', '3/8*e^4 - 31/8*e^2 + 5', '-5/8*e^5 + 81/8*e^3 - 30*e', '-e^3 + 13*e', '-1/4*e^5 + 17/4*e^3 - 15*e', '-1/4*e^5 + 17/4*e^3 - 17*e', '2*e^2 - 14', '-1/4*e^5 + 17/4*e^3 - 13*e', '-3/8*e^5 + 55/8*e^3 - 28*e', '3/8*e^4 - 31/8*e^2 + 5', '9/8*e^4 - 157/8*e^2 + 59', '9/8*e^4 - 157/8*e^2 + 55', '5/8*e^4 - 73/8*e^2 + 19', '11/8*e^4 - 183/8*e^2 + 67', '-3/8*e^4 + 15/8*e^2 + 25', '5/8*e^5 - 89/8*e^3 + 37*e', '3/8*e^5 - 47/8*e^3 + 11*e', '-1/4*e^5 + 21/4*e^3 - 22*e', '5/8*e^5 - 89/8*e^3 + 37*e', '9/8*e^4 - 141/8*e^2 + 45', '-13/8*e^4 + 225/8*e^2 - 93', '-e^3 + 7*e', '3/8*e^5 - 63/8*e^3 + 33*e', '-1/4*e^5 + 13/4*e^3 - 2*e', '-7/8*e^5 + 107/8*e^3 - 36*e', '-1/4*e^5 + 17/4*e^3 - 21*e', '1/2*e^5 - 17/2*e^3 + 30*e', '1/8*e^5 - 13/8*e^3 + 6*e', 'e^3 - 9*e', '-1/2*e^4 + 13/2*e^2 + 4', '3/2*e^4 - 47/2*e^2 + 76', '-1/8*e^5 + 21/8*e^3 - 9*e', '-3/8*e^5 + 55/8*e^3 - 32*e', '-1/8*e^5 - 3/8*e^3 + 18*e', '-7/8*e^5 + 123/8*e^3 - 50*e', '-3/2*e^4 + 55/2*e^2 - 96', '3/2*e^4 - 47/2*e^2 + 72', '-3/8*e^4 + 39/8*e^2 + 6', '3/8*e^4 - 39/8*e^2 + 30', '1/8*e^4 - 37/8*e^2 + 17', '-3/8*e^4 + 47/8*e^2 - 19', '-9/8*e^5 + 149/8*e^3 - 58*e', '-1/4*e^5 + 17/4*e^3 - 13*e', '-3/8*e^4 + 55/8*e^2 - 4', '7/8*e^4 - 107/8*e^2 + 32', '-13/8*e^4 + 217/8*e^2 - 68', '-3/8*e^4 + 55/8*e^2 - 32', '-5/8*e^5 + 89/8*e^3 - 43*e', '1/4*e^5 - 21/4*e^3 + 20*e', '-3/8*e^5 + 55/8*e^3 - 20*e', '-3/8*e^5 + 39/8*e^3 - 2*e', '19/8*e^4 - 303/8*e^2 + 101', '-11/8*e^4 + 191/8*e^2 - 80', '9/8*e^5 - 157/8*e^3 + 59*e', '-e^5 + 17*e^3 - 52*e', '1/8*e^5 + 3/8*e^3 - 16*e', '-5/8*e^5 + 81/8*e^3 - 28*e', '1/4*e^5 - 17/4*e^3 + 7*e', '-1/2*e^5 + 15/2*e^3 - 11*e', '-15/8*e^4 + 275/8*e^2 - 116', '-15/8*e^4 + 275/8*e^2 - 116', '1/8*e^5 - 21/8*e^3 + 7*e', '1/4*e^5 - 13/4*e^3 + 4*e', '-3/8*e^5 + 63/8*e^3 - 33*e', '-3/4*e^5 + 51/4*e^3 - 39*e', '-17/8*e^4 + 261/8*e^2 - 93', '-1/8*e^4 + 21/8*e^2 - 21', '5/8*e^4 - 89/8*e^2 + 29', '-11/8*e^4 + 175/8*e^2 - 74', '19/8*e^4 - 287/8*e^2 + 95', '3/8*e^4 - 71/8*e^2 + 46', '-17/8*e^4 + 277/8*e^2 - 103', '7/8*e^4 - 75/8*e^2 + 8', '-5/8*e^4 + 81/8*e^2 - 40', '-5/8*e^4 + 25/8*e^2 + 29', 'e^5 - 16*e^3 + 43*e', '13/8*e^5 - 209/8*e^3 + 79*e', '-1/4*e^5 + 9/4*e^3 + 11*e', '5/8*e^5 - 89/8*e^3 + 35*e', '3/8*e^4 - 47/8*e^2 + 25', '3/8*e^4 - 47/8*e^2 + 25', '-5/8*e^5 + 89/8*e^3 - 39*e', '-5/8*e^5 + 89/8*e^3 - 51*e', '-7/8*e^4 + 91/8*e^2 - 20', '5/8*e^4 - 65/8*e^2 + 4', '1/8*e^5 - 21/8*e^3 + 5*e', '3/4*e^5 - 39/4*e^3 + 14*e', '-3/4*e^5 + 47/4*e^3 - 28*e', '9/8*e^5 - 157/8*e^3 + 65*e', '-1/2*e^5 + 15/2*e^3 - 25*e', '1/8*e^5 - 29/8*e^3 + 32*e', '-11/8*e^4 + 207/8*e^2 - 102', '-3/8*e^4 + 23/8*e^2 - 10', '-15/8*e^4 + 195/8*e^2 - 30', '-7/8*e^4 + 107/8*e^2 - 58', '19/8*e^4 - 311/8*e^2 + 102', '-27/8*e^4 + 415/8*e^2 - 138', '13/8*e^4 - 217/8*e^2 + 98', '-23/8*e^4 + 347/8*e^2 - 118', '13/8*e^4 - 193/8*e^2 + 57', '13/8*e^4 - 193/8*e^2 + 57', '-7/8*e^4 + 115/8*e^2 - 47', '1/8*e^4 + 43/8*e^2 - 47', '5/8*e^5 - 97/8*e^3 + 52*e', '-7/8*e^5 + 99/8*e^3 - 29*e', '5/8*e^5 - 97/8*e^3 + 42*e', '3/4*e^5 - 59/4*e^3 + 57*e', '-7/8*e^4 + 147/8*e^2 - 77', '-15/8*e^4 + 315/8*e^2 - 149', '3/8*e^5 - 47/8*e^3 + 23*e', '1/4*e^5 - 21/4*e^3 + 26*e', '-3/2*e^5 + 55/2*e^3 - 92*e', '-1/2*e^5 + 15/2*e^3 - 17*e', '-5/8*e^5 + 81/8*e^3 - 26*e', '11/8*e^5 - 199/8*e^3 + 91*e', '13/8*e^4 - 217/8*e^2 + 88', '3/8*e^4 - 55/8*e^2 + 4', '1/2*e^4 - 13/2*e^2 + 22', '-5/2*e^4 + 89/2*e^2 - 146', '5/8*e^4 - 89/8*e^2 + 27', '-5/8*e^5 + 89/8*e^3 - 45*e', '7/8*e^5 - 91/8*e^3 + 18*e', 'e^5 - 17*e^3 + 48*e', '-1/4*e^5 + 21/4*e^3 - 18*e', '-33/8*e^4 + 509/8*e^2 - 170', '-5/8*e^4 + 113/8*e^2 - 50', '11/8*e^4 - 127/8*e^2 + 2', '-9/8*e^4 + 101/8*e^2 + 2', '19/8*e^4 - 327/8*e^2 + 100', '-9/8*e^4 + 165/8*e^2 - 44', 'e^4 - 19*e^2 + 26', '9/8*e^4 - 157/8*e^2 + 75', '1/8*e^4 - 61/8*e^2 + 28', '3/8*e^4 - 55/8*e^2 + 40', '11/8*e^4 - 199/8*e^2 + 69'], 'hecke_polynomial': 'x^6 - 21*x^4 + 120*x^2 - 192', 'label': '4.4.7625.1-16.3-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 7625, 'ideals': ['[1, 1, 1]', '[4, 2, 1/2*w^3 - 3/2*w^2 - 3/2*w + 4]', '[4, 2, 1/2*w^3 + 1/2*w^2 - 7/2*w - 5]', '[5, 5, -1/4*w^3 - 3/4*w^2 + 5/4*w + 3]', '[11, 11, -1/4*w^3 + 1/4*w^2 + 9/4*w]', '[11, 11, w - 1]', '[16, 2, 2]', '[16, 4, w]', '[16, 4, -1/4*w^3 + 1/4*w^2 + 9/4*w - 1]', '[20, 10, 1/4*w^3 - 1/4*w^2 - 1/4*w - 1]', '[20, 10, 1/2*w^3 - 1/2*w^2 - 7/2*w]', '[25, 5, -1/2*w^3 + 1/2*w^2 + 5/2*w - 1]', '[29, 29, 1/4*w^3 - 1/4*w^2 - 1/4*w + 2]', '[29, 29, 1/2*w^3 - 1/2*w^2 - 7/2*w + 3]', '[31, 31, -3/4*w^3 - 1/4*w^2 + 19/4*w + 4]', '[31, 31, -3/4*w^3 + 7/4*w^2 + 11/4*w - 5]', '[44, 22, -1/2*w^3 + 3/2*w^2 + 3/2*w - 6]', '[44, 22, 3/4*w^3 - 7/4*w^2 - 15/4*w + 6]', '[44, 22, 1/2*w^3 + 1/2*w^2 - 5/2*w - 4]', '[44, 22, 1/2*w^3 + 1/2*w^2 - 7/2*w - 3]', '[49, 7, -1/2*w^3 + 3/2*w^2 + 5/2*w - 5]', '[49, 7, 1/2*w^3 - 1/2*w^2 - 7/2*w - 1]', '[55, 55, w^2 - 1]', '[55, 55, 1/4*w^3 - 5/4*w^2 - 5/4*w + 9]', '[59, 59, -1/4*w^3 + 5/4*w^2 + 5/4*w - 3]', '[59, 59, w^2 - 7]', '[61, 61, -5/4*w^3 - 7/4*w^2 + 37/4*w + 15]', '[64, 4, w^3 - 3*w^2 - 3*w + 8]', '[64, 4, w^3 + w^2 - 7*w - 10]', '[64, 8, w^2 - 8]', '[64, 8, 1/2*w^3 + 1/2*w^2 - 3/2*w - 3]', '[71, 71, 3/4*w^3 + 9/4*w^2 - 11/4*w - 7]', '[71, 71, 1/4*w^3 - 1/4*w^2 - 13/4*w - 2]', '[79, 79, -1/4*w^3 + 5/4*w^2 + 1/4*w - 7]', '[79, 79, 1/4*w^3 + 3/4*w^2 - 9/4*w - 2]', '[80, 10, -1/2*w^3 - 3/2*w^2 + 5/2*w + 6]', '[80, 20, -3/4*w^3 - 1/4*w^2 + 15/4*w + 2]', '[80, 20, -w^3 + 2*w^2 + 5*w - 8]', '[81, 3, -3]', '[89, 89, -w^2 + 2*w + 1]', '[89, 89, 1/4*w^3 + 3/4*w^2 - 13/4*w - 7]', '[100, 10, w^3 - 8*w - 7]', '[100, 10, 1/2*w^3 - 3/2*w^2 + 1/2*w]', '[101, 101, -1/4*w^3 + 9/4*w^2 + 5/4*w - 12]', '[101, 101, -1/4*w^3 + 9/4*w^2 + 5/4*w - 8]', '[109, 109, 1/4*w^3 + 3/4*w^2 - 9/4*w - 1]', '[109, 109, -5/4*w^3 - 3/4*w^2 + 33/4*w + 7]', '[109, 109, -1/4*w^3 + 5/4*w^2 + 1/4*w - 8]', '[109, 109, 1/4*w^3 + 3/4*w^2 - 5/4*w - 9]', '[116, 58, 1/4*w^3 - 5/4*w^2 + 3/4*w]', '[116, 58, -1/2*w^3 - 1/2*w^2 + 9/2*w + 8]', '[116, 58, -3/4*w^3 + 3/4*w^2 + 11/4*w - 1]', '[116, 58, w^3 - w^2 - 6*w + 2]', '[121, 11, -3/4*w^3 + 3/4*w^2 + 15/4*w - 1]', '[121, 11, -3/4*w^3 + 3/4*w^2 + 15/4*w - 2]', '[121, 121, -3/4*w^3 + 3/4*w^2 + 23/4*w - 3]', '[121, 121, 1/4*w^3 - 1/4*w^2 + 3/4*w + 1]', '[124, 62, -1/2*w^3 + 3/2*w^2 + 3/2*w - 7]', '[124, 62, 1/4*w^3 + 3/4*w^2 - 5/4*w - 6]', '[124, 62, 1/2*w^3 - 3/2*w^2 - 5/2*w + 4]', '[124, 62, 1/2*w^3 + 1/2*w^2 - 7/2*w - 2]', '[125, 5, 1/4*w^3 + 3/4*w^2 + 3/4*w - 1]', '[139, 139, 1/2*w^3 + 3/2*w^2 - 9/2*w - 7]', '[139, 139, -1/2*w^3 + 5/2*w^2 + 1/2*w - 11]', '[145, 145, 1/2*w^3 + 1/2*w^2 - 5/2*w - 5]', '[145, 145, -3/4*w^3 + 7/4*w^2 + 15/4*w - 5]', '[151, 151, 7/4*w^3 - 19/4*w^2 - 23/4*w + 14]', '[151, 151, -3/4*w^3 + 11/4*w^2 + 11/4*w - 10]', '[155, 155, 1/4*w^3 - 1/4*w^2 + 3/4*w]', '[155, 155, -3/4*w^3 + 3/4*w^2 + 23/4*w - 2]', '[176, 22, -1/2*w^3 + 1/2*w^2 + 9/2*w]', '[176, 22, 2*w - 2]', '[176, 44, w + 4]', '[176, 44, -w^2 + w + 9]', '[176, 44, w^2 - w]', '[176, 44, 1/4*w^3 - 1/4*w^2 - 9/4*w + 5]', '[181, 181, -3/4*w^3 + 11/4*w^2 + 15/4*w - 12]', '[181, 181, 1/2*w^3 + 3/2*w^2 - 9/2*w - 9]', '[191, 191, 1/4*w^3 + 7/4*w^2 - 13/4*w - 8]', '[191, 191, -1/4*w^3 + 9/4*w^2 - 3/4*w - 10]', '[196, 14, w^3 - 6*w - 3]', '[196, 14, -1/2*w^3 + 3/2*w^2 + 1/2*w]', '[196, 14, 1/2*w^3 - 5/2*w^2 + 5/2*w]', '[196, 14, -3*w^3 - 2*w^2 + 22*w + 25]', '[199, 199, -3/4*w^3 + 11/4*w^2 + 15/4*w - 10]', '[199, 199, 1/4*w^3 + 3/4*w^2 - 5/4*w - 7]', '[199, 199, -1/2*w^3 + 3/2*w^2 + 5/2*w - 3]', '[199, 199, 3/4*w^3 - 3/4*w^2 - 23/4*w - 1]', '[211, 211, -5/4*w^3 + 17/4*w^2 + 13/4*w - 13]', '[211, 211, -1/4*w^3 + 5/4*w^2 - 7/4*w + 2]', '[220, 110, 1/2*w^3 + 1/2*w^2 - 3/2*w - 4]', '[220, 110, w^3 - 2*w^2 - 6*w + 7]', '[220, 110, 1/2*w^3 + 1/2*w^2 - 7/2*w - 1]', '[220, 110, -1/2*w^3 + 3/2*w^2 + 3/2*w - 8]', '[229, 229, -1/4*w^3 + 5/4*w^2 + 9/4*w - 9]', '[229, 229, 1/4*w^3 - 9/4*w^2 + 11/4*w + 1]', '[229, 229, 3/4*w^3 + 1/4*w^2 - 15/4*w - 5]', '[229, 229, 1/2*w^3 + 5/2*w^2 - 1/2*w - 7]', '[236, 118, w^3 - 4*w^2 + 6]', '[236, 118, 5/4*w^3 + 3/4*w^2 - 29/4*w - 7]', '[236, 118, -3/2*w^3 - 3/2*w^2 + 25/2*w + 19]', '[236, 118, -3/2*w^3 + 7/2*w^2 + 13/2*w - 12]', '[239, 239, 5/4*w^3 - 1/4*w^2 - 37/4*w - 6]', '[239, 239, -3/4*w^3 + 7/4*w^2 + 11/4*w - 8]', '[239, 239, w^2 - 2*w - 7]', '[239, 239, -5/2*w^3 - 5/2*w^2 + 37/2*w + 23]', '[244, 122, 5/4*w^3 - 9/4*w^2 - 33/4*w + 8]', '[244, 122, -1/2*w^3 + 3/2*w^2 + 3/2*w - 10]', '[245, 35, 5/4*w^3 + 7/4*w^2 - 29/4*w - 9]', '[245, 35, -3/4*w^3 - 5/4*w^2 + 15/4*w + 3]', '[251, 251, -1/4*w^3 + 9/4*w^2 + 5/4*w - 11]', '[251, 251, -1/4*w^3 + 9/4*w^2 + 5/4*w - 9]', '[256, 4, 4]', '[256, 8, 2*w]', '[256, 8, -1/2*w^3 + 1/2*w^2 + 9/2*w - 2]', '[256, 16, w^2]', '[256, 16, 1/4*w^3 - 5/4*w^2 - 5/4*w + 10]', '[269, 269, -7/4*w^3 - 1/4*w^2 + 59/4*w + 14]', '[269, 269, -1/2*w^3 - 3/2*w^2 + 7/2*w + 5]', '[269, 269, 3/4*w^3 - 11/4*w^2 + 9/4*w]', '[269, 269, -5/4*w^3 - 7/4*w^2 + 25/4*w + 7]', '[271, 271, 2*w^2 - w - 7]', '[271, 271, -1/4*w^3 + 9/4*w^2 + 1/4*w - 12]', '[271, 271, -1/2*w^3 + 5/2*w^2 + 5/2*w - 11]', '[271, 271, 1/4*w^3 + 7/4*w^2 - 13/4*w - 9]', '[275, 55, -1/4*w^3 - 7/4*w^2 + 9/4*w + 10]', '[275, 55, 1/2*w^3 - 5/2*w^2 - 3/2*w + 9]', '[281, 281, w^3 - 5*w - 3]', '[281, 281, 5/4*w^3 + 3/4*w^2 - 25/4*w - 6]', '[284, 142, -1/2*w^3 + 3/2*w^2 + 7/2*w - 4]', '[284, 142, -3/4*w^3 + 3/4*w^2 + 3/4*w + 1]', '[284, 142, -w^2 - w + 7]', '[284, 142, -1/2*w^3 - 1/2*w^2 + 7/2*w]', '[289, 17, 1/4*w^3 + 7/4*w^2 - 9/4*w - 14]', '[289, 17, -5/4*w^3 - 7/4*w^2 + 45/4*w + 17]', '[295, 295, -5/4*w^3 - 11/4*w^2 + 21/4*w + 8]', '[295, 295, -1/4*w^3 + 1/4*w^2 - 3/4*w - 5]', '[305, 305, 1/4*w^3 - 9/4*w^2 - 5/4*w + 10]', '[311, 311, 1/4*w^3 - 1/4*w^2 - 9/4*w - 4]', '[311, 311, w - 5]', '[316, 158, -7/4*w^3 - 9/4*w^2 + 55/4*w + 21]', '[316, 158, 3/2*w^3 - 11/2*w^2 - 5/2*w + 14]', '[316, 158, -3/4*w^3 - 1/4*w^2 + 31/4*w + 8]', '[316, 158, -w^2 + 4*w - 2]', '[319, 319, -3/4*w^3 + 3/4*w^2 + 7/4*w + 1]', '[319, 319, 5/4*w^3 - 5/4*w^2 - 33/4*w + 1]', '[319, 319, 5/4*w^3 - 13/4*w^2 - 21/4*w + 10]', '[319, 319, -w^3 - w^2 + 6*w + 9]', '[320, 20, 1/2*w^3 - 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3*w - 15]', '[1901, 1901, 5/4*w^3 - 21/4*w^2 - 9/4*w + 16]', '[1901, 1901, -1/4*w^3 - 15/4*w^2 + 5/4*w + 19]', '[1931, 1931, 3/4*w^3 + 13/4*w^2 - 19/4*w - 18]', '[1931, 1931, 3/2*w^3 - 11/2*w^2 - 13/2*w + 21]', '[1936, 22, -3/2*w^3 + 3/2*w^2 + 15/2*w - 2]', '[1936, 22, -3/2*w^3 + 3/2*w^2 + 15/2*w - 4]', '[1936, 44, 1/4*w^3 - 13/4*w^2 + 3/4*w + 16]', '[1936, 44, 1/2*w^3 - 7/2*w^2 - 3/2*w + 17]', '[1936, 44, -3*w^2 + 2*w + 12]', '[1936, 44, -3*w^2 + w + 12]', '[1936, 242, -3/2*w^3 + 3/2*w^2 + 23/2*w - 6]', '[1936, 242, 1/2*w^3 - 1/2*w^2 + 3/2*w + 2]', '[1936, 484, 3/4*w^3 - 15/4*w^2 - 15/4*w + 26]', '[1936, 484, 3*w^2 - 4]', '[1936, 484, -w^2 + 12]', '[1936, 484, -1/4*w^3 + 5/4*w^2 + 5/4*w + 2]', '[1945, 1945, -5/4*w^3 - 3/4*w^2 + 33/4*w + 4]', '[1945, 1945, 5/4*w^3 - 13/4*w^2 - 17/4*w + 14]', '[1949, 1949, 5/4*w^3 - 9/4*w^2 - 29/4*w + 4]', '[1949, 1949, -1/2*w^3 - 7/2*w^2 - 1/2*w + 9]', '[1949, 1949, 3/4*w^3 + 1/4*w^2 - 11/4*w - 7]', '[1949, 1949, 2*w^3 + 4*w^2 - 7*w - 15]', '[1975, 395, 5/4*w^3 - 1/4*w^2 - 37/4*w + 1]', '[1975, 395, -3/4*w^3 + 7/4*w^2 + 3/4*w - 8]', '[1984, 124, -w^3 + 3*w^2 + 3*w - 14]', '[1984, 124, 1/2*w^3 + 3/2*w^2 - 5/2*w - 12]', '[1984, 124, w^3 - 3*w^2 - 5*w + 8]', '[1984, 124, w^3 + w^2 - 7*w - 4]', '[1984, 248, 7/4*w^3 - 15/4*w^2 - 39/4*w + 13]', '[1984, 248, 3/2*w^3 - 1/2*w^2 - 21/2*w + 1]', '[1984, 248, w^3 + w^2 - 4*w - 8]', '[1984, 248, -w^3 + 2*w^2 + 2*w - 8]', '[1991, 1991, 3/2*w^3 - 3/2*w^2 - 13/2*w + 1]', '[1991, 1991, 11/4*w^3 + 5/4*w^2 - 75/4*w - 18]', '[1991, 1991, 11/4*w^3 - 23/4*w^2 - 51/4*w + 24]', '[1991, 1991, 9/4*w^3 - 13/4*w^2 - 49/4*w + 15]', '[1996, 998, 3/2*w^3 - 1/2*w^2 - 15/2*w]', '[1996, 998, 7/4*w^3 - 11/4*w^2 - 35/4*w + 10]', '[1996, 998, -1/2*w^3 + 7/2*w^2 + 3/2*w - 14]', '[1996, 998, 3*w^2 - w - 15]', '[2000, 10, 1/2*w^3 + 3/2*w^2 + 3/2*w - 2]', '[2000, 20, w^3 - 2*w^2 - 7*w + 16]', '[2000, 20, 1/4*w^3 + 3/4*w^2 + 3/4*w + 4]', '[2005, 2005, -5/4*w^3 - 7/4*w^2 + 5/4*w + 3]', '[2005, 2005, 1/2*w^3 - 1/2*w^2 - 13/2*w - 3]', '[2011, 2011, 1/4*w^3 + 11/4*w^2 - 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9]', '[229, 229, 1/4*w^3 - 9/4*w^2 + 11/4*w + 1]', '[229, 229, 3/4*w^3 + 1/4*w^2 - 15/4*w - 5]', '[229, 229, 1/2*w^3 + 5/2*w^2 - 1/2*w - 7]', '[239, 239, 5/4*w^3 - 1/4*w^2 - 37/4*w - 6]', '[239, 239, -3/4*w^3 + 7/4*w^2 + 11/4*w - 8]', '[239, 239, w^2 - 2*w - 7]', '[239, 239, -5/2*w^3 - 5/2*w^2 + 37/2*w + 23]', '[251, 251, -1/4*w^3 + 9/4*w^2 + 5/4*w - 11]', '[251, 251, -1/4*w^3 + 9/4*w^2 + 5/4*w - 9]', '[269, 269, -7/4*w^3 - 1/4*w^2 + 59/4*w + 14]', '[269, 269, -1/2*w^3 - 3/2*w^2 + 7/2*w + 5]', '[269, 269, 3/4*w^3 - 11/4*w^2 + 9/4*w]', '[269, 269, -5/4*w^3 - 7/4*w^2 + 25/4*w + 7]', '[271, 271, 2*w^2 - w - 7]', '[271, 271, -1/4*w^3 + 9/4*w^2 + 1/4*w - 12]', '[271, 271, -1/2*w^3 + 5/2*w^2 + 5/2*w - 11]', '[271, 271, 1/4*w^3 + 7/4*w^2 - 13/4*w - 9]', '[281, 281, w^3 - 5*w - 3]', '[281, 281, 5/4*w^3 + 3/4*w^2 - 25/4*w - 6]', '[289, 17, 1/4*w^3 + 7/4*w^2 - 9/4*w - 14]', '[289, 17, -5/4*w^3 - 7/4*w^2 + 45/4*w + 17]', '[311, 311, 1/4*w^3 - 1/4*w^2 - 9/4*w - 4]', '[311, 311, w - 5]', '[331, 331, 2*w^2 - w - 11]', '[331, 331, -1/4*w^3 + 9/4*w^2 + 1/4*w - 8]', '[349, 349, 1/4*w^3 - 9/4*w^2 + 19/4*w - 2]', '[349, 349, -5/4*w^3 - 3/4*w^2 + 49/4*w + 16]', '[359, 359, -7/4*w^3 - 5/4*w^2 + 63/4*w + 20]', '[359, 359, 3/4*w^3 + 5/4*w^2 - 19/4*w - 10]', '[361, 19, -1/4*w^3 + 1/4*w^2 + 5/4*w - 5]', '[361, 19, -w^3 + w^2 + 5*w - 3]', '[379, 379, -1/4*w^3 - 3/4*w^2 + 17/4*w - 1]', '[379, 379, -2*w^3 - 2*w^2 + 17*w + 23]', '[379, 379, -1/4*w^3 + 9/4*w^2 + 5/4*w - 16]', '[379, 379, 1/4*w^3 + 3/4*w^2 - 17/4*w - 8]', '[389, 389, -3/2*w^3 - 5/2*w^2 + 13/2*w + 11]', '[389, 389, -5/4*w^3 - 7/4*w^2 + 45/4*w + 19]', '[401, 401, 5/4*w^3 - 5/4*w^2 - 29/4*w + 2]', '[401, 401, w^3 - w^2 - 4*w + 1]', '[409, 409, -1/4*w^3 + 5/4*w^2 - 3/4*w - 7]', '[409, 409, -3/4*w^3 + 7/4*w^2 + 11/4*w - 9]', '[419, 419, 1/4*w^3 + 3/4*w^2 - 1/4*w - 6]', '[419, 419, 1/2*w^3 + 1/2*w^2 - 5/2*w - 7]', '[421, 421, 3/4*w^3 - 11/4*w^2 + 1/4*w + 2]', '[421, 421, 3/2*w^3 + 1/2*w^2 - 19/2*w - 7]', '[431, 431, 1/4*w^3 - 5/4*w^2 + 3/4*w - 1]', '[431, 431, -5/4*w^3 - 3/4*w^2 + 21/4*w + 4]', '[431, 431, -1/2*w^3 - 1/2*w^2 + 9/2*w + 9]', '[431, 431, 1/2*w^3 - 1/2*w^2 - 9/2*w - 5]', '[461, 461, 1/4*w^3 + 3/4*w^2 - 17/4*w - 4]', '[461, 461, -3/2*w^3 - 1/2*w^2 + 25/2*w + 15]', '[461, 461, -7/4*w^3 - 9/4*w^2 + 55/4*w + 20]', '[461, 461, 1/4*w^3 + 3/4*w^2 - 17/4*w - 3]', '[499, 499, -1/4*w^3 + 5/4*w^2 - 15/4*w + 5]', '[499, 499, -1/4*w^3 - 3/4*w^2 + 17/4*w - 2]', '[509, 509, 5/4*w^3 + 3/4*w^2 - 33/4*w - 6]', '[509, 509, 1/4*w^3 - 9/4*w^2 + 11/4*w + 3]', '[521, 521, -5/4*w^3 + 1/4*w^2 + 25/4*w - 1]', '[521, 521, 5/4*w^3 - 9/4*w^2 - 21/4*w + 5]', '[529, 23, 5/4*w^3 - 5/4*w^2 - 33/4*w + 6]', '[529, 23, 1/4*w^3 + 7/4*w^2 - 13/4*w - 5]', '[541, 541, -5/4*w^3 + 17/4*w^2 + 5/4*w - 6]', '[541, 541, w^2 - 2*w - 11]', '[569, 569, -3/4*w^3 + 11/4*w^2 + 15/4*w - 9]', '[569, 569, 1/2*w^3 - 3/2*w^2 + 3/2*w - 3]', '[569, 569, -w^3 + w^2 + 7*w + 1]', '[569, 569, 3/4*w^3 - 15/4*w^2 + 9/4*w + 5]', '[599, 599, 5/4*w^3 - 1/4*w^2 - 37/4*w - 1]', '[599, 599, -3/4*w^3 + 7/4*w^2 + 3/4*w - 6]', '[601, 601, 1/4*w^3 + 11/4*w^2 - 17/4*w - 11]', '[601, 601, 5/4*w^3 - 5/4*w^2 - 17/4*w + 1]', '[601, 601, 1/4*w^3 - 13/4*w^2 + 7/4*w + 16]', '[601, 601, -7/4*w^3 + 7/4*w^2 + 43/4*w - 3]', '[631, 631, -1/4*w^3 + 1/4*w^2 + 1/4*w - 6]', '[631, 631, -1/2*w^3 + 1/2*w^2 + 7/2*w - 7]', '[641, 641, -1/4*w^3 - 3/4*w^2 + 9/4*w - 2]', '[641, 641, -1/4*w^3 + 5/4*w^2 + 1/4*w - 11]', '[661, 661, -3/4*w^3 - 9/4*w^2 + 27/4*w + 16]', '[661, 661, 1/2*w^3 + 3/2*w^2 - 9/2*w - 15]', '[701, 701, 3/2*w^3 - 3/2*w^2 - 17/2*w + 1]', '[701, 701, -5/4*w^3 + 5/4*w^2 + 21/4*w]', '[709, 709, -3/2*w^3 + 3/2*w^2 + 11/2*w - 7]', '[709, 709, -2*w^3 + 2*w^2 + 12*w - 9]', '[739, 739, -1/4*w^3 + 5/4*w^2 - 3/4*w - 9]', '[739, 739, -1/2*w^3 - 1/2*w^2 + 9/2*w - 1]', '[761, 761, -7/2*w^3 - 7/2*w^2 + 55/2*w + 37]', '[761, 761, 1/2*w^3 + 1/2*w^2 - 5/2*w - 11]', '[769, 769, -1/4*w^3 + 9/4*w^2 - 3/4*w - 14]', '[769, 769, 1/4*w^3 + 7/4*w^2 - 13/4*w - 4]', '[809, 809, 1/4*w^3 + 3/4*w^2 - 21/4*w - 9]', '[809, 809, 1/2*w^3 + 1/2*w^2 - 13/2*w + 3]', '[809, 809, -5/4*w^3 + 9/4*w^2 + 29/4*w - 6]', '[809, 809, 3/4*w^3 + 1/4*w^2 - 11/4*w - 5]', '[811, 811, -1/2*w^3 + 1/2*w^2 + 11/2*w - 5]', '[811, 811, 1/4*w^3 - 1/4*w^2 - 17/4*w - 2]', '[821, 821, -1/4*w^3 - 7/4*w^2 - 7/4*w + 4]', '[821, 821, 7/4*w^3 + 5/4*w^2 - 63/4*w - 22]', '[841, 29, 5/4*w^3 - 5/4*w^2 - 25/4*w + 1]', '[859, 859, -3/4*w^3 - 13/4*w^2 + 3/4*w + 8]', '[859, 859, -1/2*w^3 + 5/2*w^2 + 1/2*w - 13]', '[859, 859, 5/4*w^3 + 11/4*w^2 - 17/4*w - 11]', '[859, 859, 1/2*w^3 + 3/2*w^2 - 9/2*w - 5]', '[881, 881, 5/4*w^3 - 5/4*w^2 - 21/4*w + 4]', '[881, 881, 1/4*w^3 + 3/4*w^2 - 9/4*w - 10]', '[881, 881, -5/4*w^3 + 1/4*w^2 + 45/4*w + 8]', '[881, 881, -1/4*w^3 + 9/4*w^2 + 5/4*w - 18]', '[941, 941, 9/4*w^3 - 33/4*w^2 - 13/4*w + 20]', '[941, 941, -11/4*w^3 - 13/4*w^2 + 87/4*w + 32]', '[961, 31, -1/2*w^3 + 1/2*w^2 + 5/2*w - 7]', '[991, 991, -w^3 + w^2 + 8*w - 3]', '[991, 991, -7/4*w^3 + 15/4*w^2 + 27/4*w - 9]', '[991, 991, -11/4*w^3 + 35/4*w^2 + 31/4*w - 26]', '[991, 991, -1/4*w^3 + 1/4*w^2 - 7/4*w]']}
• 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': [16, 4, -9, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 7625, 'disc_rad': 305, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[4, 1]]], [5, [0]], [7, [[2, 2]]], [11, [[2, 1], [1, 2]]], [13, [[4, 1]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 1], [1, 2]]], [31, [[2, 1], [1, 2]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[4, 1]]], [53, [[2, 2]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 26.115143751039085, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.7625.1', 'local_algs': ['5.4.3.2', '61.2.1.2', '61.2.0.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 61], 'rd': 9.34458377794, 'regulator': {'__RealLiteral__': 0, 'data': '4.88717250406', 'prec': 44}, 'res': {'gal': ['1,0,-29,0,136,0,-29,0,1'], 'sib': ['-4,17,-16,-2,1', '1,0,-29,0,136,0,-29,0,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{4} a^{3} - \\frac{1}{4} a^{2} - \\frac{5}{4} a \\)', '\\( \\frac{1}{4} a^{3} + \\frac{3}{4} a^{2} - \\frac{9}{4} a - 6 \\)', '\\( \\frac{1}{4} a^{3} + \\frac{3}{4} a^{2} - \\frac{1}{4} a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/4*a^3 - 1/4*a^2 - 1/4*a']}