Hilbert modular form data - 4.4.11197.1-21.1-e

Formats: - HTML - YAML - JSON - 2024-05-27T02:59:48.069189

• 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': 5, 'disc': 11197, 'field_bad_primes': [11197], 'field_label': '4.4.11197.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.11197.1-21.1-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [3, 7], 'level_ideal': '[21, 21, w^3 - w^2 - 5*w]', 'level_label': '21.1', 'level_norm': 21, 'parallel_weight': 2, 'short_label': '21.1-e', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, w + 1]', -1], ['[7, 7, w^3 - 2*w^2 - 3*w + 1]', -1]], 'hecke_eigenvalues': [1, 1, 'e', '-e + 3', '-1/4*e^3 + 5/4*e^2 + 9/4*e - 45/4', '1/8*e^4 - 3/4*e^3 - e^2 + 29/4*e + 3/8', '-1/4*e^3 + 7/4*e^2 + 5/4*e - 51/4', '1/4*e^3 - 3/4*e^2 - 13/4*e + 27/4', '-1/4*e^3 + 3/4*e^2 + 17/4*e - 23/4', '-1/8*e^4 + e^3 - 1/4*e^2 - 19/2*e + 55/8', '-1/4*e^3 + 3/4*e^2 + 13/4*e - 7/4', '1/8*e^4 - 3/4*e^3 + 21/4*e - 69/8', '-1/4*e^4 + 5/4*e^3 + 9/4*e^2 - 41/4*e + 1', '-e^2 + e + 12', '-1/8*e^4 + 1/2*e^3 + 9/4*e^2 - 5*e - 77/8', '-1/8*e^4 + 1/2*e^3 + 5/4*e^2 - 5*e + 59/8', '1/4*e^4 - e^3 - 7/2*e^2 + 9*e + 37/4', '3/4*e^3 - 13/4*e^2 - 31/4*e + 105/4', '3/4*e^3 - 13/4*e^2 - 31/4*e + 101/4', '-1/8*e^4 + e^3 - 1/4*e^2 - 13/2*e + 47/8', '1/4*e^4 - 3/2*e^3 - e^2 + 23/2*e - 61/4', '-1/2*e^3 + 3/2*e^2 + 9/2*e - 11/2', '-3/4*e^3 + 15/4*e^2 + 31/4*e - 131/4', '-1/4*e^4 + 3/2*e^3 - 21/2*e + 69/4', '5/4*e^3 - 21/4*e^2 - 49/4*e + 153/4', '1/2*e^3 - 5/2*e^2 - 11/2*e + 53/2', '1/8*e^4 + 1/4*e^3 - 6*e^2 + 1/4*e + 299/8', '-1/8*e^4 + e^3 - 1/4*e^2 - 19/2*e + 167/8', '1/4*e^4 - 5/4*e^3 - 15/4*e^2 + 49/4*e + 29/2', '1/2*e^3 - 5/2*e^2 - 3/2*e + 39/2', '1/4*e^3 - 5/4*e^2 - 1/4*e + 53/4', '-1/4*e^4 + 7/4*e^3 + 3/4*e^2 - 75/4*e + 17/2', '-1/8*e^4 + 19/4*e^2 - 5/2*e - 225/8', '1/8*e^4 - e^3 + 1/4*e^2 + 13/2*e - 63/8', '1/8*e^4 - 3/4*e^3 - 2*e^2 + 29/4*e + 107/8', '-1/4*e^4 + 3/4*e^3 + 17/4*e^2 - 27/4*e - 17', 'e^3 - 5*e^2 - 10*e + 40', '1/8*e^4 - 1/2*e^3 - 13/4*e^2 + 6*e + 77/8', '1/2*e^4 - 11/4*e^3 - 17/4*e^2 + 95/4*e + 19/4', '-1/4*e^4 + 3/2*e^3 + 3*e^2 - 35/2*e - 19/4', '-1/4*e^4 + 5/4*e^3 + 15/4*e^2 - 53/4*e - 27/2', '1/4*e^4 - 3/4*e^3 - 17/4*e^2 + 19/4*e + 13', '-1/4*e^4 + 7/4*e^3 + 1/4*e^2 - 67/4*e + 12', '1/4*e^4 - 5/4*e^3 - 11/4*e^2 + 49/4*e + 13/2', '1/4*e^3 - 7/4*e^2 - 1/4*e + 51/4', '-2*e^2 + 4*e + 26', '-1/8*e^4 + 9/4*e^3 - 11/2*e^2 - 79/4*e + 377/8', '1/2*e^4 - 9/4*e^3 - 21/4*e^2 + 73/4*e + 3/4', '1/8*e^4 - 1/2*e^3 - 9/4*e^2 + 5*e - 3/8', '1/2*e^3 - 5/2*e^2 - 17/2*e + 53/2', '-3/8*e^4 + 3/2*e^3 + 19/4*e^2 - 9*e - 119/8', '-3/4*e^3 + 11/4*e^2 + 43/4*e - 67/4', '-1/4*e^4 + 1/4*e^3 + 29/4*e^2 + 7/4*e - 45', '1/4*e^3 - 9/4*e^2 + 15/4*e + 49/4', '1/4*e^3 - 7/4*e^2 - 25/4*e + 83/4', '-1/4*e^4 + e^3 + 3/2*e^2 - 5*e + 91/4', '-1/4*e^4 + e^3 + 9/2*e^2 - 9*e - 61/4', '-1/2*e^4 + 7/4*e^3 + 29/4*e^2 - 47/4*e - 99/4', '-1/8*e^4 + 1/2*e^3 + 9/4*e^2 - 165/8', '3/8*e^4 - 7/4*e^3 - 7/2*e^2 + 49/4*e + 21/8', '-1/4*e^4 + e^3 + 9/2*e^2 - 9*e - 65/4', '-3/2*e^3 + 15/2*e^2 + 23/2*e - 103/2', '1/4*e^4 + 1/2*e^3 - 11*e^2 - 13/2*e + 283/4', 'e^3 - 3*e^2 - 13*e + 25', '1/4*e^4 + 1/2*e^3 - 11*e^2 - 11/2*e + 263/4', '3/4*e^3 - 13/4*e^2 - 31/4*e + 137/4', '-1/2*e^4 + 3*e^3 + e^2 - 23*e + 65/2', '1/4*e^4 - 5/4*e^3 - 9/4*e^2 + 41/4*e - 5', '1/4*e^4 - 1/4*e^3 - 23/4*e^2 + 5/4*e + 45/2', '-3/4*e^3 + 17/4*e^2 + 23/4*e - 121/4', '-1/2*e^4 + 5/2*e^3 + 9/2*e^2 - 37/2*e - 2', '1/8*e^4 - 5/4*e^3 + 5/2*e^2 + 39/4*e - 345/8', '1/2*e^3 + 1/2*e^2 - 19/2*e - 19/2', '-1/4*e^4 + 3/2*e^3 + 3*e^2 - 33/2*e - 31/4', '1/2*e^4 - 11/4*e^3 - 25/4*e^2 + 119/4*e + 51/4', '-1/4*e^4 + 1/2*e^3 + 7*e^2 + 3/2*e - 219/4', '3/8*e^4 - 3/2*e^3 - 19/4*e^2 + 15*e + 7/8', '-1/4*e^4 + 1/2*e^3 + 3*e^2 + 5/2*e - 31/4', '1/2*e^4 - 5/2*e^3 - 13/2*e^2 + 59/2*e + 15', '1/4*e^4 - e^3 - 1/2*e^2 + 5*e - 151/4', '1/2*e^4 - 4*e^3 + 2*e^2 + 36*e - 81/2', '1/4*e^4 - e^3 - 1/2*e^2 + e - 55/4', '-5/8*e^4 + 7/2*e^3 + 17/4*e^2 - 32*e + 55/8', '-1/4*e^4 + 7/4*e^3 + 5/4*e^2 - 63/4*e - 1', 'e^3 - 2*e^2 - 14*e - 3', '-1/4*e^4 + 3/2*e^3 + e^2 - 19/2*e + 29/4', '1/4*e^4 + 1/2*e^3 - 12*e^2 - 9/2*e + 319/4', '-5/4*e^3 + 23/4*e^2 + 53/4*e - 167/4', '-1/4*e^4 + 9/4*e^3 - 1/4*e^2 - 101/4*e + 39/2', '-1/4*e^4 + 2*e^3 - 1/2*e^2 - 17*e + 79/4', '-2*e^2 + e + 41', '-1/4*e^4 - 1/4*e^3 + 37/4*e^2 + 21/4*e - 53', '1/4*e^4 - 3*e^3 + 9/2*e^2 + 28*e - 135/4', '1/2*e^4 - 3*e^3 - 5*e^2 + 29*e - 3/2', '-1/2*e^3 + 3/2*e^2 + 15/2*e - 61/2', '-1/4*e^4 + 17/2*e^2 + 6*e - 225/4', '3/4*e^3 - 5/4*e^2 - 35/4*e + 45/4', '2*e^2 - 2*e - 14', '-1/4*e^4 + 3/4*e^3 + 13/4*e^2 - 35/4*e + 2', '1/8*e^4 - e^3 + 1/4*e^2 + 9/2*e - 159/8', '-1/2*e^3 + 3/2*e^2 + 7/2*e + 23/2', '-1/2*e^4 + 2*e^3 + 6*e^2 - 15*e - 29/2', '-1/4*e^4 + 7/2*e^3 - 9*e^2 - 55/2*e + 373/4', '-1/2*e^3 - 1/2*e^2 + 19/2*e + 21/2', '-1/2*e^4 + 5/2*e^3 + 13/2*e^2 - 35/2*e - 29', '1/4*e^3 + 7/4*e^2 - 13/4*e - 123/4', '1/2*e^4 - 4*e^3 + 2*e^2 + 32*e - 101/2', '-1/4*e^4 + 3*e^3 - 9/2*e^2 - 27*e + 163/4', '-1/2*e^4 + e^3 + 11*e^2 - 7*e - 101/2', '-1/2*e^4 + 3/2*e^3 + 15/2*e^2 - 13/2*e - 28', '9/4*e^3 - 33/4*e^2 - 101/4*e + 189/4', '-3/2*e^3 + 15/2*e^2 + 19/2*e - 105/2', '3/4*e^4 - 17/4*e^3 - 23/4*e^2 + 129/4*e + 1', '3/4*e^4 - 4*e^3 - 13/2*e^2 + 37*e + 27/4', '1/2*e^4 - 7/4*e^3 - 39/4*e^2 + 43/4*e + 189/4', '1/2*e^4 - 5/2*e^3 - 5/2*e^2 + 27/2*e - 22', '5/8*e^4 - 3*e^3 - 23/4*e^2 + 37/2*e - 19/8', '1/4*e^4 - 21/2*e^2 + 8*e + 225/4', '1/8*e^4 - 3/4*e^3 - 3*e^2 + 37/4*e + 275/8', '1/4*e^4 - 7/4*e^3 + 15/4*e^2 + 39/4*e - 53', '1/2*e^3 - 5/2*e^2 - 13/2*e + 5/2', '-3/4*e^4 + 19/4*e^3 + 21/4*e^2 - 171/4*e + 23/2', '-1/8*e^4 - 1/4*e^3 + 5*e^2 + 31/4*e - 307/8', '3/2*e^3 - 11/2*e^2 - 33/2*e + 41/2', '-3/8*e^4 + 2*e^3 + 21/4*e^2 - 43/2*e - 299/8', 'e^2 - 6*e - 21', '-e^2 + 7*e - 14', '1/4*e^4 - 3/2*e^3 - 2*e^2 + 41/2*e - 61/4', '3/4*e^4 - 4*e^3 - 7/2*e^2 + 30*e - 97/4', '1/2*e^4 - 3/2*e^3 - 19/2*e^2 + 27/2*e + 37', '3/8*e^4 - 9/4*e^3 - 4*e^2 + 99/4*e + 57/8', '-3*e - 1', '-1/2*e^4 + 11/4*e^3 + 7/4*e^2 - 99/4*e + 95/4', '1/4*e^4 - 3*e^3 + 11/2*e^2 + 26*e - 227/4', '-e^3 + 4*e^2 + 3*e - 12', '-1/4*e^4 + 3/2*e^3 + 3*e^2 - 45/2*e + 41/4', '-1/4*e^4 + 11/4*e^3 - 19/4*e^2 - 87/4*e + 58', '1/4*e^4 - 4*e^3 + 23/2*e^2 + 32*e - 415/4', '1/8*e^4 - 1/4*e^3 - 1/2*e^2 - 1/4*e - 153/8', '1/2*e^4 - 5/4*e^3 - 45/4*e^2 + 37/4*e + 195/4', '-1/4*e^4 + 5/4*e^3 - 7/4*e^2 - 13/4*e + 58', '-e^4 + 15/4*e^3 + 59/4*e^2 - 123/4*e - 179/4', '-1/2*e^4 + 5/2*e^3 + 7/2*e^2 - 39/2*e - 8', '-3/4*e^4 + 5/2*e^3 + 13*e^2 - 43/2*e - 161/4', '1/8*e^4 - 5/4*e^3 + 5/2*e^2 + 63/4*e - 281/8', '-1/2*e^4 + 11/4*e^3 + 23/4*e^2 - 99/4*e - 113/4', '-1/4*e^3 - 5/4*e^2 + 21/4*e + 173/4', '-1/4*e^4 + e^3 + 3/2*e^2 - 5*e + 63/4', '5/4*e^3 - 15/4*e^2 - 61/4*e + 99/4', '-e^4 + 21/4*e^3 + 39/4*e^2 - 205/4*e - 51/4', '1/4*e^4 + 3/4*e^3 - 55/4*e^2 - 27/4*e + 149/2', '-1/4*e^4 + 1/2*e^3 + 5*e^2 - 5/2*e - 19/4', '1/2*e^4 - 5/2*e^3 - 11/2*e^2 + 51/2*e + 19', '-3/4*e^4 + 13/4*e^3 + 39/4*e^2 - 141/4*e - 27', '3/4*e^4 - 9/2*e^3 - 2*e^2 + 65/2*e - 219/4', '1/4*e^4 - e^3 - 11/2*e^2 + 14*e + 193/4', '1/4*e^4 - 5/2*e^3 + e^2 + 55/2*e - 61/4', '5/8*e^4 - 17/4*e^3 - 5/2*e^2 + 151/4*e - 13/8', '1/4*e^4 - 2*e^3 + 7/2*e^2 + 6*e - 215/4', '-3/4*e^4 + 15/4*e^3 + 29/4*e^2 - 119/4*e + 23/2', '-3/4*e^4 + 23/4*e^3 - 13/4*e^2 - 199/4*e + 76', '-5/4*e^4 + 11/2*e^3 + 15*e^2 - 91/2*e - 79/4', '-1/4*e^4 - 1/2*e^3 + 12*e^2 - 3/2*e - 311/4', '-1/2*e^4 + 2*e^3 + 9*e^2 - 17*e - 39/2', '1/4*e^4 + 2*e^3 - 37/2*e^2 - 24*e + 557/4', '-3/8*e^4 + e^3 + 21/4*e^2 - 11/2*e - 35/8', '3/8*e^4 - 1/2*e^3 - 47/4*e^2 + 9*e + 519/8', '1/8*e^4 - 3/2*e^3 + 23/4*e^2 + 5*e - 379/8', '-1/2*e^4 + 3/2*e^3 + 15/2*e^2 - 27/2*e + 3', '-3/4*e^3 + 15/4*e^2 + 35/4*e - 191/4', '-1/8*e^4 + 1/2*e^3 + 21/4*e^2 - 7*e - 341/8', '5/8*e^4 - 21/4*e^3 + 3/2*e^2 + 207/4*e - 261/8', '-3/4*e^3 + 1/4*e^2 + 71/4*e - 73/4', '-5/4*e^3 + 27/4*e^2 + 21/4*e - 139/4', '1/2*e^4 - 2*e^3 - 10*e^2 + 26*e + 59/2', '-1/4*e^4 + 3*e^3 - 13/2*e^2 - 24*e + 263/4', '-1/8*e^4 + 3/4*e^3 + 2*e^2 - 49/4*e - 355/8', '3/4*e^4 - 11/4*e^3 - 51/4*e^2 + 75/4*e + 42', '3/4*e^4 - 9/2*e^3 - 2*e^2 + 73/2*e - 107/4', '1/4*e^4 - 9/4*e^3 + 1/4*e^2 + 57/4*e + 11/2', 'e^4 - 6*e^3 - 6*e^2 + 50*e - 11', '5/4*e^3 - 11/4*e^2 - 45/4*e - 125/4', '1/4*e^4 - 1/2*e^3 - 6*e^2 + 9/2*e + 115/4', '1/8*e^4 - 5/4*e^3 - 5/2*e^2 + 107/4*e + 215/8', '-1/4*e^4 + 5/4*e^3 + 7/4*e^2 - 61/4*e + 31/2', '-5/8*e^4 + 11/4*e^3 + 11*e^2 - 121/4*e - 295/8', '11/4*e^3 - 59/4*e^2 - 95/4*e + 447/4', '-1/2*e^4 + 7/2*e^3 - 9/2*e^2 - 39/2*e + 95', '-3/8*e^4 + 13/4*e^3 - 155/4*e + 207/8', '-5/8*e^4 + 23/4*e^3 - e^2 - 229/4*e + 217/8', '1/4*e^4 - e^3 - 11/2*e^2 + 5*e + 165/4', '-3/4*e^4 + 11/2*e^3 + 3*e^2 - 97/2*e - 13/4', '1/2*e^4 - 2*e^3 - 10*e^2 + 17*e + 119/2', '-e^3 + e^2 + 14*e - 14', '-1/4*e^4 - 9/4*e^3 + 75/4*e^2 + 97/4*e - 253/2', 'e^4 - 9/2*e^3 - 21/2*e^2 + 67/2*e + 45/2', '1/4*e^4 - 11/4*e^3 + 23/4*e^2 + 51/4*e - 64', '-e^3 + 3*e^2 + 15*e - 27', '-3/4*e^4 + 17/4*e^3 + 5/4*e^2 - 133/4*e + 145/2', '1/8*e^4 - 1/2*e^3 - 5/4*e^2 + 13*e - 123/8', '-1/4*e^4 + 5/2*e^3 - 7*e^2 - 25/2*e + 317/4', '-1/4*e^4 + 7/4*e^3 + 17/4*e^2 - 91/4*e - 49', '1/2*e^4 - 3/2*e^3 - 19/2*e^2 + 35/2*e + 39', '-5/4*e^3 + 23/4*e^2 + 61/4*e - 227/4', '-1/4*e^4 + 1/4*e^3 + 29/4*e^2 + 7/4*e - 23', '1/4*e^4 - 15/4*e^3 + 27/4*e^2 + 151/4*e - 66', 'e^3 - 5*e^2 - 9*e + 49', '-1/4*e^4 + e^3 + 3/2*e^2 - 10*e + 199/4', '3/4*e^4 - 4*e^3 - 11/2*e^2 + 24*e - 77/4', '-5/4*e^4 + 21/4*e^3 + 63/4*e^2 - 173/4*e - 97/2', '5/8*e^4 - 7/2*e^3 - 29/4*e^2 + 34*e + 161/8', '-5/8*e^4 + 7/2*e^3 + 21/4*e^2 - 34*e + 15/8', '-1/2*e^4 + 3*e^3 - 20*e + 95/2', '1/2*e^4 - 1/2*e^3 - 25/2*e^2 - 17/2*e + 81', '3/8*e^4 - e^3 - 25/4*e^2 + 23/2*e - 5/8', 'e^4 - 25/4*e^3 - 11/4*e^2 + 233/4*e - 145/4', '3/4*e^4 - 6*e^3 - 5/2*e^2 + 61*e - 61/4', '-3/4*e^4 + 5*e^3 + 9/2*e^2 - 48*e + 121/4', '7/8*e^4 - 6*e^3 - 5/4*e^2 + 99/2*e - 585/8', '-1/4*e^4 + 13/4*e^3 - 21/4*e^2 - 117/4*e + 55/2', '-1/4*e^4 - 1/4*e^3 + 35/4*e^2 - 7/4*e - 69/2', '-1/2*e^4 + 3/4*e^3 + 53/4*e^2 - 3/4*e - 203/4', '-1/4*e^4 - 1/2*e^3 + 9*e^2 + 15/2*e - 295/4', '-e^4 + 7/2*e^3 + 39/2*e^2 - 75/2*e - 143/2', '-1/4*e^4 - e^3 + 29/2*e^2 + 7*e - 225/4', '5/8*e^4 - 5/2*e^3 - 25/4*e^2 + 24*e - 191/8', '-1/4*e^4 + 3*e^3 - 15/2*e^2 - 27*e + 199/4', '3/4*e^4 - 13/4*e^3 - 31/4*e^2 + 89/4*e - 24', '-1/8*e^4 + 23/4*e^2 - 9/2*e - 489/8', '-3/4*e^4 + 5*e^3 + 9/2*e^2 - 46*e - 3/4', '1/8*e^4 + 3/2*e^3 - 49/4*e^2 - 6*e + 677/8', '1/4*e^4 + 7/4*e^3 - 61/4*e^2 - 91/4*e + 112', '1/8*e^4 - 5/4*e^3 + 9/2*e^2 + 19/4*e - 497/8', '-1/4*e^4 - 5/4*e^3 + 53/4*e^2 + 45/4*e - 65', '-5/8*e^4 + 4*e^3 + 35/4*e^2 - 97/2*e - 125/8', '-7/8*e^4 + 5*e^3 + 9/4*e^2 - 83/2*e + 361/8', '-1/4*e^4 + 5/2*e^3 + 2*e^2 - 57/2*e - 63/4', '3/4*e^4 - 5/2*e^3 - 11*e^2 + 31/2*e + 165/4', '-2*e^3 + 10*e^2 + 23*e - 41', '1/4*e^4 - 3*e^3 + 13/2*e^2 + 24*e - 183/4', '-e^4 + 27/4*e^3 - 1/4*e^2 - 231/4*e + 269/4', '1/2*e^4 - 5/4*e^3 - 21/4*e^2 - 23/4*e + 23/4', '1/4*e^4 + 3/2*e^3 - 17*e^2 - 23/2*e + 339/4', '-e^4 + 23/4*e^3 + 35/4*e^2 - 203/4*e - 71/4', '-1/4*e^4 + 3/4*e^3 + 19/4*e^2 - 15/4*e - 51/2', '-1/2*e^4 + 5/2*e^3 + 15/2*e^2 - 59/2*e - 37', '-1/2*e^3 - 5/2*e^2 + 47/2*e + 67/2', '3/4*e^4 - 5/2*e^3 - 16*e^2 + 43/2*e + 369/4', '1/4*e^4 - 3/2*e^3 - 4*e^2 + 23/2*e + 127/4', '2*e^3 - 13*e^2 - 8*e + 115', '-3/4*e^4 + 15/4*e^3 + 49/4*e^2 - 155/4*e - 59/2', '-e^4 + 11/2*e^3 + 17/2*e^2 - 99/2*e - 43/2', '-1/4*e^4 + 4*e^3 - 29/2*e^2 - 39*e + 543/4', '3/4*e^4 - 25/4*e^3 + 17/4*e^2 + 193/4*e - 85', '1/2*e^4 - 1/2*e^3 - 27/2*e^2 - 3/2*e + 111', '-e^3 + 4*e^2 + 16*e - 25', '9/4*e^3 - 29/4*e^2 - 133/4*e + 169/4', 'e^4 - 11/2*e^3 - 9/2*e^2 + 77/2*e - 55/2', '5/8*e^4 - 5/4*e^3 - 31/2*e^2 + 31/4*e + 371/8', '1/2*e^4 - 4*e^3 - 3*e^2 + 40*e + 17/2', '1/2*e^4 - 15/4*e^3 + 1/4*e^2 + 135/4*e - 19/4', '-e^4 + 4*e^3 + 14*e^2 - 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85/2*e + 219/4', '3/4*e^4 - 19/4*e^3 - 13/4*e^2 + 143/4*e - 73/2', '3/4*e^4 - 19/4*e^3 - 7/4*e^2 + 147/4*e - 51', '1/4*e^4 - 13/4*e^3 + 33/4*e^2 + 85/4*e - 183/2', '-9/8*e^4 + 13/2*e^3 + 25/4*e^2 - 52*e + 115/8', '-3/4*e^3 + 21/4*e^2 + 71/4*e - 213/4', '1/2*e^4 - 19/4*e^3 + 13/4*e^2 + 183/4*e - 67/4', '-1/2*e^4 + 3*e^3 + 5*e^2 - 23*e - 93/2', '1/4*e^4 - 3*e^3 + 7/2*e^2 + 28*e - 195/4', '3/4*e^4 - 9/2*e^3 - 8*e^2 + 73/2*e + 125/4', '-1/4*e^4 + 2*e^3 + 3/2*e^2 - 32*e + 75/4', '3/8*e^4 - 5/2*e^3 - 3/4*e^2 + 18*e - 25/8', 'e^4 - 11/2*e^3 - 15/2*e^2 + 111/2*e - 19/2', '1/4*e^4 - 11/4*e^3 + 3/4*e^2 + 163/4*e - 16', '-3/2*e^4 + 37/4*e^3 + 31/4*e^2 - 341/4*e + 71/4', '1/2*e^4 - 4*e^3 + e^2 + 31*e - 13/2', '1/4*e^4 + e^3 - 19/2*e^2 - 13*e + 149/4', '-e^4 + 27/4*e^3 + 1/4*e^2 - 223/4*e + 279/4', '-1/4*e^4 - 5/2*e^3 + 19*e^2 + 57/2*e - 475/4', '-e^4 + 3*e^3 + 19*e^2 - 19*e - 86', '-1/2*e^4 + 11/2*e^3 - 11/2*e^2 - 101/2*e + 61', '-7/8*e^4 + 3*e^3 + 57/4*e^2 - 39/2*e - 327/8', '5/4*e^4 - 21/4*e^3 - 67/4*e^2 + 189/4*e + 99/2', '-3/4*e^3 + 33/4*e^2 - 21/4*e - 237/4', '-3/4*e^4 + 5*e^3 + 5/2*e^2 - 52*e - 3/4', '1/4*e^4 - 5/4*e^3 - 15/4*e^2 + 101/4*e - 25/2', '3/4*e^4 - 5/2*e^3 - 8*e^2 + 23/2*e - 143/4', 'e^4 - 19/4*e^3 - 47/4*e^2 + 179/4*e + 11/4', '-3/4*e^4 + 2*e^3 + 27/2*e^2 - 11*e - 263/4', '-1/8*e^4 - 1/4*e^3 + 5*e^2 + 39/4*e - 531/8', '1/4*e^4 - 7/2*e^2 - 2*e - 75/4', '3/2*e^4 - 15/2*e^3 - 19/2*e^2 + 109/2*e - 23', '-7/8*e^4 + 4*e^3 + 13/4*e^2 - 53/2*e + 641/8', '-1/8*e^4 + 1/2*e^3 + 1/4*e^2 - 5*e + 19/8', '2*e^3 - 6*e^2 - 27*e + 59', '5/8*e^4 - 4*e^3 - 7/4*e^2 + 71/2*e - 99/8', '-1/4*e^4 + 13/4*e^3 - 15/4*e^2 - 165/4*e + 50', 'e^4 - 9/2*e^3 - 31/2*e^2 + 97/2*e + 109/2', '9/4*e^3 - 39/4*e^2 - 101/4*e + 383/4', 'e^4 - 6*e^3 - 5*e^2 + 59*e - 27', '1/2*e^4 - 7/2*e^3 + 5/2*e^2 + 35/2*e - 63', '-1/4*e^4 + 3/2*e^3 + e^2 - 41/2*e - 55/4', '-3/8*e^4 - 3/2*e^3 + 55/4*e^2 + 32*e - 751/8', '-3/4*e^4 + 9/2*e^3 + 4*e^2 - 107/2*e + 79/4', '1/4*e^4 - 13/4*e^3 + 47/4*e^2 + 49/4*e - 121', '1/4*e^4 - 5/4*e^3 + 5/4*e^2 + 5/4*e + 5/2', '-3/4*e^4 + 4*e^3 + 15/2*e^2 - 37*e + 113/4', '3/4*e^4 - 9/4*e^3 - 67/4*e^2 + 93/4*e + 97', '5/4*e^3 - 29/4*e^2 - 49/4*e + 49/4', '3/8*e^4 - e^3 - 45/4*e^2 + 29/2*e + 459/8', '-1/4*e^4 + 5/4*e^3 + 1/4*e^2 - 49/4*e + 61', '1/2*e^4 - 23/4*e^3 + 37/4*e^2 + 223/4*e - 263/4', '-3/2*e^4 + 11/2*e^3 + 51/2*e^2 - 83/2*e - 98', '3/4*e^4 - 23/4*e^3 - 5/4*e^2 + 227/4*e - 43/2', 'e^4 - 19/2*e^3 + 11/2*e^2 + 183/2*e - 143/2', '7/4*e^4 - 41/4*e^3 - 55/4*e^2 + 345/4*e - 14', '-1/4*e^4 - 5/4*e^3 + 53/4*e^2 + 13/4*e - 86', '3/8*e^4 - 17/4*e^3 + 12*e^2 + 103/4*e - 1023/8', '-1/8*e^4 + 3/2*e^3 - 15/4*e^2 - 14*e + 371/8', '-1/4*e^4 + 19/4*e^3 - 63/4*e^2 - 167/4*e + 164', '3/4*e^4 - 19/4*e^3 + 1/4*e^2 + 163/4*e - 51', '-1/4*e^3 - 1/4*e^2 + 17/4*e + 121/4', 'e^4 - 11/4*e^3 - 67/4*e^2 + 75/4*e + 239/4', '5/4*e^4 - 15/2*e^3 - 2*e^2 + 111/2*e - 333/4', '-1/2*e^4 + 1/2*e^3 + 25/2*e^2 + 9/2*e - 47', '-1/2*e^4 + 17/4*e^3 - 15/4*e^2 - 197/4*e + 161/4', '-1/2*e^4 + 11/4*e^3 + 13/4*e^2 - 131/4*e + 189/4', '-5/4*e^4 + 9*e^3 + 9/2*e^2 - 81*e + 143/4', '-7/4*e^4 + 37/4*e^3 + 67/4*e^2 - 305/4*e - 2', '3/4*e^4 - 5/2*e^3 - 16*e^2 + 75/2*e + 281/4', '-1/4*e^4 + 9/2*e^2 - e + 51/4', '3/4*e^4 - 17/4*e^3 - 11/4*e^2 + 137/4*e - 55', '1/2*e^3 - 3/2*e^2 - 43/2*e - 19/2', '3/4*e^4 - 8*e^3 + 19/2*e^2 + 74*e - 393/4', '-e^4 + 5*e^3 + 12*e^2 - 41*e - 41', '-3/8*e^4 + 3/2*e^3 + 15/4*e^2 - 7*e + 225/8', '1/4*e^4 + 2*e^3 - 31/2*e^2 - 30*e + 477/4', '-1/2*e^4 + 1/2*e^3 + 29/2*e^2 + 15/2*e - 106', '1/4*e^4 - 5/4*e^3 - 23/4*e^2 + 17/4*e + 113/2', '1/4*e^4 + 1/4*e^3 - 47/4*e^2 - 17/4*e + 151/2', '-e^4 + 5/2*e^3 + 49/2*e^2 - 49/2*e - 235/2', '-1/4*e^4 + 3*e^3 - 3/2*e^2 - 35*e + 47/4', '3/8*e^4 - 1/2*e^3 - 43/4*e^2 - 5*e + 991/8', '1/2*e^4 - 5/2*e^3 - 3/2*e^2 + 21/2*e - 34', '-9/4*e^3 + 13/4*e^2 + 129/4*e - 45/4', '-e^4 + 9/2*e^3 + 15/2*e^2 - 51/2*e + 73/2', '-1/4*e^4 + 2*e^3 - 1/2*e^2 - 20*e + 67/4', '-1/4*e^4 + 1/4*e^3 + 29/4*e^2 + 39/4*e - 37', '1/2*e^4 - 13/4*e^3 - 27/4*e^2 + 117/4*e + 113/4', '-1/2*e^4 + 9/2*e^3 - 9/2*e^2 - 85/2*e + 85', '-3/4*e^4 + 3*e^3 + 23/2*e^2 - 24*e - 71/4', '-3/8*e^4 - e^3 + 81/4*e^2 + 39/2*e - 1075/8', '-1/4*e^3 - 5/4*e^2 + 17/4*e - 79/4', '-3/4*e^4 - e^3 + 55/2*e^2 + 10*e - 567/4', '-1/4*e^4 + 11/4*e^3 - 3/4*e^2 - 99/4*e + 16', '-1/2*e^4 - 5/4*e^3 + 99/4*e^2 + 25/4*e - 617/4', '5/4*e^3 - 11/4*e^2 - 85/4*e - 77/4', '-3/2*e^4 + 23/4*e^3 + 75/4*e^2 - 191/4*e - 5/4', '3/4*e^3 - 5/4*e^2 - 63/4*e - 7/4', 'e^4 - 33*e^2 - 4*e + 182', '3/4*e^4 - 19/4*e^3 - 33/4*e^2 + 167/4*e + 123/2', '1/8*e^4 + 1/4*e^2 - 23/2*e - 199/8', '1/4*e^4 - 13/4*e^3 + 37/4*e^2 + 109/4*e - 223/2', '-3/4*e^4 + 1/4*e^3 + 105/4*e^2 + 19/4*e - 333/2', '3/2*e^4 - 6*e^3 - 18*e^2 + 41*e + 31/2', '-1/4*e^4 + 25/2*e^2 - 289/4', '-3/4*e^4 + 37/4*e^3 - 69/4*e^2 - 361/4*e + 160', '1/2*e^4 - 1/2*e^3 - 19/2*e^2 - 1/2*e - 24', '5/4*e^3 - 31/4*e^2 + 3/4*e + 263/4', '-1/2*e^4 + 1/2*e^3 + 9/2*e^2 + 45/2*e + 11', '-e^4 + 25/4*e^3 - 3/4*e^2 - 189/4*e + 271/4', '-1/4*e^4 + 3/4*e^3 + 13/4*e^2 + 25/4*e - 38', '-1/8*e^4 - 2*e^3 + 71/4*e^2 + 41/2*e - 1217/8', '1/2*e^4 - 9/2*e^3 + 11/2*e^2 + 73/2*e - 84', '-e^4 + 11/4*e^3 + 91/4*e^2 - 79/4*e - 483/4', '1/4*e^4 - 5/4*e^3 - 19/4*e^2 + 109/4*e + 59/2', '1/4*e^4 - 5/2*e^3 + 7*e^2 + 23/2*e - 225/4', '-5/2*e^3 + 21/2*e^2 + 35/2*e - 83/2', '-1/4*e^4 - 3/4*e^3 + 57/4*e^2 + 43/4*e - 106', '5/4*e^3 - 15/4*e^2 - 49/4*e + 51/4', '-e^4 + 23/4*e^3 + 43/4*e^2 - 243/4*e - 3/4', '1/4*e^3 + 3/4*e^2 + 11/4*e + 17/4', '5/4*e^4 - 17/2*e^3 - 5*e^2 + 161/2*e - 185/4', '-5/8*e^4 + 9*e^3 - 65/4*e^2 - 171/2*e + 1067/8', '-1/4*e^4 + 15/4*e^3 - 25/4*e^2 - 195/4*e + 55/2', '1/2*e^4 - 6*e^3 + 9*e^2 + 72*e - 163/2', '3/4*e^4 - 9/2*e^3 - 2*e^2 + 73/2*e - 243/4', '-1/4*e^4 - 3/4*e^3 + 59/4*e^2 + 47/4*e - 207/2', '1/2*e^4 - 13/4*e^3 + 13/4*e^2 + 73/4*e - 323/4', '-7/8*e^4 + 19/4*e^3 + 19/2*e^2 - 149/4*e - 17/8', '3/4*e^3 - 5/4*e^2 - 27/4*e - 235/4', '1/2*e^4 - 7/4*e^3 - 11/4*e^2 + 27/4*e - 271/4', '-5/4*e^4 + 6*e^3 + 33/2*e^2 - 56*e - 201/4', '1/8*e^4 - 5/4*e^3 + 9/2*e^2 + 19/4*e - 545/8', '-1/2*e^4 + 5/2*e^3 + 13/2*e^2 - 49/2*e - 64', '-e^4 + 9/2*e^3 + 31/2*e^2 - 63/2*e - 105/2', '-5/8*e^4 + 4*e^3 + 23/4*e^2 - 79/2*e - 29/8', '5/4*e^4 - 15/4*e^3 - 103/4*e^2 + 159/4*e + 129/2', '1/4*e^4 - 1/4*e^3 - 3/4*e^2 - 55/4*e - 141/2', '7/4*e^4 - 9*e^3 - 25/2*e^2 + 74*e - 97/4', '-3/2*e^4 + 8*e^3 + 13*e^2 - 64*e - 19/2', '3/4*e^4 - 11/4*e^3 - 67/4*e^2 + 131/4*e + 70', 'e^4 - 6*e^3 - 3*e^2 + 44*e - 80', '-3/4*e^4 + 5/2*e^3 + 8*e^2 - 21/2*e + 99/4', '1/2*e^4 - 5/2*e^3 - 15/2*e^2 + 79/2*e + 48', '3/4*e^4 - 15/2*e^3 + 6*e^2 + 169/2*e - 307/4', '-7/8*e^4 + 5*e^3 + 1/4*e^2 - 57/2*e + 433/8', '1/4*e^4 - 13/4*e^3 + 41/4*e^2 + 113/4*e - 129/2', '3/4*e^4 - 15/4*e^3 - 37/4*e^2 + 127/4*e + 115/2', '1/2*e^4 - 33/4*e^3 + 83/4*e^2 + 301/4*e - 769/4', '3/4*e^4 - 2*e^3 - 31/2*e^2 + 20*e + 115/4', '5/8*e^4 - 7/2*e^3 - 29/4*e^2 + 39*e + 393/8', '-3/8*e^4 + 49/4*e^2 + 43/2*e - 875/8', '-e^4 + 6*e^3 - 42*e + 43', '3/4*e^4 - 9/2*e^3 + e^2 + 57/2*e - 183/4', '-1/2*e^4 + 5/2*e^3 + 5/2*e^2 - 7/2*e + 29', '-e^4 + 11/2*e^3 + 31/2*e^2 - 123/2*e - 109/2', '1/2*e^4 - 6*e^3 + 14*e^2 + 49*e - 331/2', '1/2*e^4 - 7/2*e^3 - 11/2*e^2 + 81/2*e - 11', '1/4*e^4 - 13/2*e^3 + 20*e^2 + 115/2*e - 629/4', '1/2*e^4 - 6*e^3 + 5*e^2 + 77*e - 117/2', '-1/4*e^4 + 4*e^3 - 33/2*e^2 - 24*e + 643/4', '-3/4*e^4 - 1/4*e^3 + 113/4*e^2 - 31/4*e - 321/2', 'e^4 - 4*e^3 - 11*e^2 + 32*e + 15', '-1/2*e^4 + 6*e^3 - 9*e^2 - 50*e + 207/2', '1/2*e^3 - 11/2*e^2 + 21/2*e + 121/2', '1/2*e^4 - 23/4*e^3 + 39/4*e^2 + 187/4*e - 301/4', '1/4*e^4 - 3/2*e^3 - 5*e^2 + 15/2*e + 123/4', '3/4*e^4 - 13/2*e^3 + 4*e^2 + 115/2*e - 391/4', '9/8*e^4 - 21/4*e^3 - 37/2*e^2 + 195/4*e + 495/8', '3/4*e^4 - 3/4*e^3 - 77/4*e^2 + 3/4*e + 205/2', '-1/2*e^4 + 7/2*e^3 + 11/2*e^2 - 111/2*e - 31', '-1/8*e^4 - 3/2*e^3 + 25/4*e^2 + 21*e - 221/8', '3/4*e^4 - 11/4*e^3 - 45/4*e^2 + 115/4*e - 39/2', '1/4*e^4 + 5/4*e^3 - 67/4*e^2 - 85/4*e + 277/2', '1/4*e^4 - 9/4*e^3 - 7/4*e^2 + 141/4*e + 59/2', '1/2*e^4 - 11/2*e^3 + 13/2*e^2 + 95/2*e - 83', '-1/4*e^4 - 7/2*e^3 + 21*e^2 + 57/2*e - 407/4', '1/4*e^4 + 3*e^3 - 47/2*e^2 - 37*e + 629/4', '-1/8*e^4 + 2*e^3 + 3/4*e^2 - 71/2*e - 201/8', '9/4*e^4 - 12*e^3 - 35/2*e^2 + 105*e - 15/4', '3/2*e^3 - 13/2*e^2 - 1/2*e + 87/2', 'e^4 - 10*e^3 + 6*e^2 + 93*e - 64', '-5/8*e^4 + 5/4*e^3 + 23/2*e^2 - 15/4*e - 195/8', '-3/4*e^4 + 17/4*e^3 + 45/4*e^2 - 225/4*e - 77/2', '1/4*e^4 - 4*e^3 + 21/2*e^2 + 50*e - 459/4', '9/2*e^3 - 47/2*e^2 - 99/2*e + 345/2', '-1/4*e^4 + 15/4*e^3 - 63/4*e^2 - 67/4*e + 156', '1/2*e^4 + 1/2*e^3 - 37/2*e^2 + 5/2*e + 59', '3/4*e^4 - 17/2*e^3 + 17*e^2 + 125/2*e - 791/4', '-17/8*e^4 + 33/4*e^3 + 65/2*e^2 - 279/4*e - 759/8', '3/8*e^4 + 1/2*e^3 - 59/4*e^2 + 5*e + 231/8', '-5/8*e^4 + 11/2*e^3 - 11/4*e^2 - 55*e + 455/8', '-9/8*e^4 + 6*e^3 + 51/4*e^2 - 111/2*e - 561/8', '-1/8*e^4 + 11/4*e^3 - 12*e^2 - 65/4*e + 669/8', '-3/4*e^4 + 7*e^3 - 11/2*e^2 - 60*e + 277/4', '1/2*e^4 - 11/2*e^3 + 1/2*e^2 + 131/2*e + 5', 'e^4 - 2*e^3 - 23*e^2 + 12*e + 74', '1/2*e^4 - 11/2*e^3 + 27/2*e^2 + 103/2*e - 168', '-1/4*e^4 + e^3 + 19/2*e^2 - 8*e - 345/4', '1/4*e^4 + 3/4*e^3 - 39/4*e^2 - 15/4*e + 135/2', '-7/4*e^3 + 45/4*e^2 - 13/4*e - 381/4', '-1/2*e^4 - 3/4*e^3 + 107/4*e^2 - 5/4*e - 529/4', '-e^4 + 5/4*e^3 + 117/4*e^2 - 117/4*e - 529/4', '-1/4*e^4 + 17/4*e^3 - 77/4*e^2 - 113/4*e + 373/2', '5/4*e^3 - 41/4*e^2 + 39/4*e + 269/4', '11/4*e^3 - 75/4*e^2 - 63/4*e + 535/4', '3/8*e^4 - 1/2*e^3 - 23/4*e^2 - 3*e - 73/8', '-5/8*e^4 - 1/2*e^3 + 101/4*e^2 + 11*e - 1481/8', '1/2*e^4 - 5*e^3 + 7*e^2 + 37*e - 195/2', '5/4*e^4 - 7*e^3 + 3/2*e^2 + 42*e - 503/4', '-1/4*e^4 - 4*e^3 + 51/2*e^2 + 34*e - 605/4', '-e^4 + 7/2*e^3 + 47/2*e^2 - 75/2*e - 237/2', '-3/4*e^4 + 3/2*e^3 + 19*e^2 - 17/2*e - 445/4', '-2*e^4 + 41/4*e^3 + 65/4*e^2 - 325/4*e + 7/4', '-3/4*e^4 + 21/4*e^3 - 5/4*e^2 - 117/4*e + 56', '1/4*e^4 + 3/4*e^3 - 61/4*e^2 + 29/4*e + 133', '-1/2*e^4 - 3/2*e^3 + 51/2*e^2 + 41/2*e - 178', '-3/8*e^4 + 1/4*e^3 + 10*e^2 + 49/4*e - 641/8', '-1/2*e^4 - 7/4*e^3 + 93/4*e^2 + 27/4*e - 503/4', '1/8*e^4 - 2*e^3 - 11/4*e^2 + 65/2*e + 305/8', '-11/8*e^4 + 27/4*e^3 + 15/2*e^2 - 169/4*e + 475/8', '3/2*e^4 - 21/2*e^3 + 5/2*e^2 + 167/2*e - 149', '-1/8*e^4 - 3/2*e^3 + 41/4*e^2 + 11*e - 877/8', '1/2*e^4 - 5*e^3 + 2*e^2 + 44*e - 47/2', '5/4*e^4 - 4*e^3 - 39/2*e^2 + 35*e + 245/4', '5/4*e^4 - 13/2*e^3 - 3*e^2 + 81/2*e - 393/4', '-1/2*e^4 + 2*e^3 + 10*e^2 - 32*e - 171/2', '7/4*e^4 - 17/2*e^3 - 14*e^2 + 125/2*e + 9/4', 'e^4 - 9/2*e^3 - 29/2*e^2 + 107/2*e + 57/2', '-5/4*e^4 + 31/4*e^3 + 41/4*e^2 - 271/4*e - 15', '-e^4 + 9/2*e^3 + 27/2*e^2 - 65/2*e - 101/2', '-5/4*e^4 + 17/4*e^3 + 83/4*e^2 - 81/4*e - 171/2', '1/2*e^4 - 13/4*e^3 - 11/4*e^2 + 157/4*e + 105/4', '-5/4*e^4 + 33/4*e^3 - 17/4*e^2 - 249/4*e + 273/2', '1/2*e^4 - 9/2*e^3 + 9/2*e^2 + 75/2*e - 30', '5/4*e^4 - 3*e^3 - 43/2*e^2 + 24*e + 117/4', '13/4*e^3 - 47/4*e^2 - 133/4*e + 255/4', '1/2*e^4 - 15/4*e^3 + 7/4*e^2 + 187/4*e - 221/4', '1/4*e^4 + 17/4*e^3 - 91/4*e^2 - 217/4*e + 353/2', '1/4*e^4 - e^3 - 1/2*e^2 + 3*e - 347/4', '-1/8*e^4 + 7/4*e^3 + 3*e^2 - 165/4*e + 165/8', '5/4*e^4 - 17/4*e^3 - 89/4*e^2 + 157/4*e + 32', '-5/4*e^4 + 11/2*e^3 + 9*e^2 - 63/2*e + 105/4', '-7/8*e^4 + 7/2*e^3 + 75/4*e^2 - 39*e - 611/8', '-1/4*e^4 - 3/2*e^3 + 23*e^2 + 7/2*e - 651/4', '3/4*e^4 - 5*e^3 + 5/2*e^2 + 46*e - 453/4', '-3/4*e^4 + 13/4*e^3 + 45/4*e^2 - 101/4*e - 213/2', '-3/8*e^4 + 3/4*e^3 + 15/2*e^2 + 11/4*e - 37/8', '1/4*e^4 + e^3 - 19/2*e^2 - 21*e + 93/4', '-17/8*e^4 + 21/2*e^3 + 81/4*e^2 - 96*e - 309/8', '3/4*e^4 - 23/4*e^3 + 13/4*e^2 + 239/4*e - 74', '-9/8*e^4 + 5/4*e^3 + 63/2*e^2 - 19/4*e - 1271/8', '-1/2*e^4 + 3/2*e^3 + 31/2*e^2 - 43/2*e - 85', '-6*e^3 + 29*e^2 + 48*e - 229', '-1/4*e^4 - 3*e^3 + 59/2*e^2 + 23*e - 821/4', '-3/2*e^3 + 3/2*e^2 + 47/2*e - 67/2', '1/2*e^4 - 9/2*e^3 - 5/2*e^2 + 113/2*e', '5/4*e^4 - 25/4*e^3 - 47/4*e^2 + 149/4*e + 1/2', '3/4*e^4 - 4*e^3 - 5/2*e^2 + 41*e - 381/4', '3/2*e^4 - 23/4*e^3 - 85/4*e^2 + 179/4*e + 323/4', '-3/4*e^4 + 13/4*e^3 + 37/4*e^2 - 41/4*e - 43/2', '1/4*e^3 - 3/4*e^2 - 9/4*e - 153/4', '1/2*e^4 - 1/2*e^3 - 27/2*e^2 - 33/2*e + 62', '-3*e^3 + 15*e^2 + 20*e - 82', '-e^4 + 10*e^3 - 5*e^2 - 101*e + 87', '5/8*e^4 - 3/2*e^3 - 61/4*e^2 + 6*e + 705/8', '1/4*e^4 + 1/2*e^3 - 9*e^2 - 35/2*e + 263/4', '1/4*e^4 - 3*e^3 + 19/2*e^2 + 13*e - 419/4'], 'hecke_polynomial': 'x^5 - 5*x^4 - 18*x^3 + 78*x^2 + 89*x - 257', 'label': '4.4.11197.1-21.1-e'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 11197, 'ideals': ['[1, 1, 1]', '[3, 3, w + 1]', '[7, 7, w^3 - 2*w^2 - 3*w + 1]', '[9, 9, -w + 2]', '[11, 11, -w - 2]', '[11, 11, -w^3 + 2*w^2 + 3*w - 2]', '[13, 13, -w^2 + 2*w + 2]', '[16, 2, 2]', '[19, 19, -w^3 + 2*w^2 + 4*w - 1]', '[21, 21, w^3 - w^2 - 5*w]', '[23, 23, -w^2 + w + 3]', '[23, 23, -w^2 + 3]', '[27, 3, w^3 - 3*w^2 - w + 4]', '[27, 27, -w^2 + w + 2]', '[29, 29, -w^3 + 3*w^2 + 3*w - 5]', '[29, 29, w^3 - 2*w^2 - 4*w]', '[33, 33, -w^3 + w^2 + 4*w - 1]', '[33, 33, w^3 - 2*w^2 - 2*w + 1]', '[39, 39, w^3 - 2*w^2 - 5*w + 4]', '[47, 47, -w^3 + 2*w^2 + 3*w - 5]', '[47, 47, w^2 - 3*w - 2]', '[48, 6, 2*w + 2]', '[49, 49, w^3 - 2*w^2 - 5*w + 2]', '[57, 57, -w^3 + 3*w^2 + 4*w - 6]', '[61, 61, -w^3 + 2*w^2 + 5*w - 3]', '[63, 63, w^3 - 2*w^2 - 2*w + 4]', '[67, 67, -w^3 + w^2 + 5*w - 1]', '[67, 67, -2*w^3 + 3*w^2 + 11*w - 7]', '[69, 69, 2*w^3 - 3*w^2 - 8*w]', '[69, 69, -w^2 + 4*w - 1]', '[77, 77, -2*w^3 + 3*w^2 + 8*w - 1]', '[77, 77, w - 4]', '[81, 3, 3]', '[81, 81, -2*w^3 + 3*w^2 + 8*w - 3]', '[83, 83, -2*w + 3]', '[87, 87, -w^3 + w^2 + 6*w - 2]', '[87, 87, -w^2 - w + 3]', '[89, 89, 3*w^3 - 7*w^2 - 9*w + 9]', '[91, 91, w + 3]', '[97, 97, w^3 - w^2 - 4*w - 3]', '[97, 97, -w^3 + 5*w + 3]', '[99, 99, -2*w^3 + 5*w^2 + 5*w - 5]', '[99, 99, w^2 - 4]', '[103, 103, -w^3 + 3*w^2 + w - 5]', '[103, 103, -w^3 + 2*w^2 + 3*w + 2]', '[112, 14, 2*w^3 - 4*w^2 - 6*w + 2]', '[117, 117, w^3 - 3*w^2 - 4*w + 3]', '[121, 11, 2*w^3 - 3*w^2 - 7*w + 3]', '[121, 11, 2*w^3 - 5*w^2 - 3*w + 2]', '[121, 121, w^3 - 2*w^2 - 4*w + 6]', '[121, 121, -w^3 + w^2 + 5*w - 2]', '[127, 127, -2*w^3 + 4*w^2 + 6*w - 5]', '[131, 131, w^2 - 3*w - 3]', '[133, 133, w^3 - w^2 - 4*w - 4]', '[137, 137, -2*w^3 + 3*w^2 + 9*w - 3]', '[139, 139, 2*w - 5]', '[141, 141, -w^3 + w^2 + w - 4]', '[141, 141, w^3 - 2*w^2 - 5*w - 2]', '[143, 143, -w^3 + w^2 + 7*w - 2]', '[143, 143, w^3 - 6*w - 4]', '[144, 18, -2*w + 4]', '[147, 147, -w^3 + 8*w + 4]', '[149, 149, -2*w^3 + 4*w^2 + 9*w - 4]', '[151, 151, 3*w^3 - 5*w^2 - 12*w + 3]', '[151, 151, w^3 - w^2 - 6*w + 3]', '[161, 161, 2*w^3 - 4*w^2 - 8*w + 3]', '[161, 161, 2*w^3 - 3*w^2 - 10*w + 2]', '[163, 163, -2*w^3 + 5*w^2 + 5*w - 9]', '[167, 167, -w^3 + 2*w^2 + 6*w - 7]', '[169, 169, w^3 - 2*w^2 - 6*w + 1]', '[171, 171, -2*w^3 + 4*w^2 + 6*w - 3]', '[176, 22, -2*w - 4]', '[176, 22, -2*w^3 + 4*w^2 + 6*w - 4]', '[179, 179, -w^3 + 4*w^2 - w - 5]', '[179, 179, -3*w^3 + 8*w^2 + 7*w - 12]', '[181, 181, 2*w^3 - 5*w^2 - 4*w + 2]', '[183, 183, -w^3 + 3*w^2 + 5*w - 2]', '[189, 21, w^3 - 3*w^2 - 4*w + 7]', '[189, 189, w^3 - w^2 - 7*w + 1]', '[199, 199, w^3 - 5*w - 5]', '[201, 201, -3*w^3 + 6*w^2 + 10*w - 5]', '[201, 201, -2*w^3 + 2*w^2 + 7*w]', '[203, 203, -2*w^3 + 3*w^2 + 7*w + 3]', '[203, 203, -2*w^3 + 4*w^2 + 9*w - 7]', '[207, 207, w^3 - 2*w^2 - 3*w + 6]', '[207, 207, w^3 - 3*w^2 - w + 6]', '[208, 26, -2*w^2 + 4*w + 4]', '[209, 209, -w^2 + 5]', '[209, 209, -w^3 + 4*w^2 - w - 4]', '[211, 211, 2*w^2 - 3*w - 7]', '[223, 223, -2*w^3 + 3*w^2 + 8*w - 4]', '[223, 223, -2*w^3 + 3*w^2 + 10*w - 5]', '[223, 223, w^3 - 2*w^2 - 6*w + 8]', '[223, 223, 2*w^3 - 2*w^2 - 9*w]', '[227, 227, 2*w^3 - 3*w^2 - 7*w + 2]', '[229, 229, -w^3 + 3*w^2 + 4*w - 2]', '[229, 229, -2*w^3 + 2*w^2 + 8*w - 1]', '[231, 231, w^2 - 3*w - 4]', '[231, 231, -w^3 + 3*w^2 + 2]', '[233, 233, -2*w^3 + 4*w^2 + 7*w - 1]', '[243, 9, 3*w + 3]', '[243, 243, w^3 - 3*w^2 + 4]', '[247, 247, -2*w^3 + 2*w^2 + 11*w]', '[249, 249, 2*w^2 - w - 3]', '[251, 251, w^2 + w - 4]', '[253, 253, 2*w^3 - 5*w^2 - 4*w + 1]', '[253, 253, -2*w^3 + 4*w^2 + 9*w - 5]', '[253, 253, w^3 - 2*w^2 - 6*w + 4]', '[253, 253, 2*w^3 - 5*w^2 - 5*w + 4]', '[256, 4, 4]', '[257, 257, -2*w^3 + 4*w^2 + 9*w - 2]', '[261, 261, -2*w^3 + 3*w^2 + 7*w - 1]', '[261, 261, 2*w^3 - 4*w^2 - 5*w + 1]', '[263, 263, -w^3 + 2*w^2 + 6*w - 2]', '[263, 263, w^2 - 3*w - 6]', '[263, 263, 2*w^3 - 4*w^2 - 7*w]', '[263, 263, -w^3 + 8*w]', '[267, 267, 2*w^3 - 4*w^2 - 9*w + 6]', '[271, 271, 2*w^2 - w - 5]', '[271, 271, -3*w^3 + 7*w^2 + 8*w - 6]', '[273, 273, -2*w^3 + 5*w^2 + 2*w - 2]', '[277, 277, -w^3 + 2*w^2 + w - 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14*w + 5]', '[1671, 1671, -3*w^3 + 6*w^2 + 11*w - 1]', '[1671, 1671, 5*w^3 - 8*w^2 - 20*w + 2]', '[1681, 41, -3*w^3 + 5*w^2 + 15*w - 7]', '[1681, 41, -w^3 + 2*w^2 + 8*w - 2]', '[1689, 1689, -w^3 + 6*w^2 + 4*w - 9]', '[1689, 1689, -3*w^3 + 7*w^2 + 15*w - 4]', '[1691, 1691, -3*w^3 + 7*w^2 + 11*w - 18]', '[1693, 1693, w^3 - w^2 - w - 4]', '[1697, 1697, 3*w^3 - 6*w^2 - 11*w]', '[1697, 1697, 5*w^3 - 7*w^2 - 21*w + 1]', '[1699, 1699, 2*w^2 - 5*w - 8]', '[1701, 63, 3*w^3 - 3*w^2 - 15*w]', '[1701, 1701, w^3 + w^2 - 12*w + 3]', '[1703, 1703, 3*w^3 - 5*w^2 - 9*w - 5]', '[1709, 1709, -2*w^3 + 7*w^2 + 6*w - 13]', '[1713, 1713, -4*w^3 + 6*w^2 + 23*w + 4]', '[1713, 1713, -w^3 + w^2 - w - 6]', '[1721, 1721, -2*w^3 + w^2 + 13*w]', '[1723, 1723, 2*w^2 - 5*w - 11]', '[1723, 1723, -2*w^3 + 4*w^2 + 6*w - 11]', '[1729, 1729, -3*w^3 + 6*w^2 + 14*w - 2]', '[1731, 1731, -w^3 + 4*w^2 + 8*w - 3]', '[1731, 1731, 4*w^2 + 5*w - 5]', '[1733, 1733, -4*w^3 + 7*w^2 + 14*w - 2]', '[1733, 1733, -2*w^3 + 2*w^2 + 9*w - 5]', '[1743, 1743, -w^3 + w^2 + 9*w - 2]', '[1747, 1747, w^3 - 2*w^2 - 3*w - 5]', '[1747, 1747, -4*w^3 + 9*w^2 + 10*w - 14]', '[1757, 1757, -3*w^3 + 7*w^2 + 9*w - 5]', '[1759, 1759, 2*w^3 - 3*w^2 - 12*w - 6]', '[1759, 1759, -2*w^3 + 4*w^2 + 3*w - 7]', '[1761, 1761, w^3 + 2*w^2 - 2*w - 6]', '[1761, 1761, 3*w^3 - 7*w^2 - 12*w + 7]', '[1769, 1769, 6*w^3 - 12*w^2 - 19*w + 19]', '[1769, 1769, w^2 - 5*w - 5]', '[1771, 1771, 3*w^3 - 5*w^2 - 9*w + 1]', '[1771, 1771, -w^3 + 4*w^2 + 3*w - 12]', '[1771, 1771, 3*w^3 - 4*w^2 - 11*w + 7]', '[1771, 1771, 2*w^3 - 7*w^2 - w + 9]', '[1777, 1777, -3*w^3 + 4*w^2 + 14*w - 4]', '[1781, 1781, -5*w^3 + 9*w^2 + 19*w - 3]', '[1783, 1783, -2*w^3 + 6*w^2 + w - 8]', '[1787, 1787, -6*w^3 + 10*w^2 + 23*w - 10]', '[1787, 1787, 2*w^3 - w^2 - 18*w + 11]', '[1789, 1789, -w^3 + 2*w^2 + 4*w - 9]', '[1791, 1791, w^2 - 2*w - 9]', '[1792, 28, 4*w^3 - 8*w^2 - 12*w + 4]', '[1793, 1793, 3*w^3 - 7*w^2 - 7*w + 16]', '[1793, 1793, 6*w^3 - 12*w^2 - 23*w + 21]', '[1797, 1797, -3*w^3 + 2*w^2 + 9*w - 5]', '[1799, 1799, 2*w^3 - w^2 - 10*w - 9]', '[1807, 1807, -2*w^3 + 9*w^2 - 6*w - 10]', '[1809, 201, -4*w^3 + 9*w^2 + 10*w - 7]', '[1809, 201, -5*w^3 + 9*w^2 + 20*w - 5]', '[1809, 1809, -2*w^3 + 5*w^2 + 8*w - 2]', '[1809, 1809, -6*w^3 + 14*w^2 + 16*w - 13]', '[1823, 1823, -5*w^3 + 9*w^2 + 22*w - 8]', '[1827, 1827, -2*w^3 + 5*w^2 + 5*w - 14]', '[1827, 1827, 2*w^3 - 3*w^2 - 8*w - 6]', '[1831, 1831, -6*w^3 + 17*w^2 + 9*w - 18]', '[1831, 1831, -4*w^3 + 11*w^2 + 9*w - 16]', '[1833, 1833, -6*w^3 + 14*w^2 + 23*w - 24]', '[1833, 1833, -3*w^3 + 8*w^2 + 6*w - 5]', '[1837, 1837, -3*w^2 + 5*w + 6]', '[1837, 1837, 2*w^3 - 6*w^2 - 8*w + 13]', '[1841, 1841, -4*w^3 + 7*w^2 + 12*w + 5]', '[1841, 1841, 5*w^2 - 13*w - 7]', '[1841, 1841, 3*w^2 - 5*w - 7]', '[1841, 1841, -5*w^3 + 7*w^2 + 23*w - 3]', '[1843, 1843, 5*w^3 - 7*w^2 - 21*w - 1]', '[1843, 1843, -5*w^3 + 5*w^2 + 22*w + 2]', '[1849, 43, -w^3 + 5*w^2 - 2*w - 9]', '[1849, 43, 3*w^2 - 2*w - 6]', '[1851, 1851, -5*w^3 + 6*w^2 + 24*w + 1]', '[1851, 1851, w^3 + w^2 - 2*w - 5]', '[1859, 1859, 3*w^2 - 2*w - 7]', '[1859, 1859, -w^3 + 2*w^2 - w + 4]', '[1861, 1861, -w^2 + 2*w - 5]', '[1863, 69, -3*w^2 + 3*w + 9]', '[1863, 69, -3*w^2 + 9]', '[1863, 1863, 2*w^3 - 5*w^2 - 9*w + 13]', '[1863, 1863, 3*w^3 - 9*w^2 - 5*w + 13]', '[1867, 1867, w^3 - 2*w^2 - 2*w - 6]', '[1867, 1867, 5*w^3 - 7*w^2 - 24*w + 4]', '[1867, 1867, -2*w^3 + 5*w^2 + 2*w - 7]', '[1867, 1867, 6*w^3 - 13*w^2 - 18*w + 12]', '[1869, 1869, 2*w^3 - 7*w^2 - 2*w + 13]', '[1871, 1871, 2*w^2 - w - 11]', '[1872, 234, 2*w^3 - 6*w^2 - 8*w + 6]', '[1873, 1873, -w^3 + 5*w^2 - 2*w - 6]', '[1873, 1873, -w^3 + 2*w^2 + 8*w - 3]', '[1875, 15, -5*w - 5]', '[1877, 1877, -4*w^3 + 4*w^2 + 21*w + 2]', '[1879, 1879, 4*w - 7]', '[1879, 1879, 5*w^3 - 9*w^2 - 22*w + 5]', '[1879, 1879, 3*w^2 - 3*w - 5]', '[1879, 1879, -3*w^3 + 7*w^2 + 12*w - 20]', '[1881, 1881, w^3 - 2*w^2 - 5*w + 10]', '[1881, 1881, 4*w^3 - 6*w^2 - 15*w + 4]', '[1893, 1893, w^3 - 3*w^2 - 8*w - 4]', '[1897, 1897, -3*w^3 + 5*w^2 + 15*w - 4]', '[1897, 1897, -4*w^3 + 7*w^2 + 16*w - 11]', '[1899, 1899, -2*w^3 + 7*w^2 + w - 14]', '[1901, 1901, 3*w^2 - 4*w - 5]', '[1907, 1907, -2*w^3 + 8*w^2 - 2*w - 11]', '[1909, 1909, -2*w^3 + 5*w^2 + 3*w - 9]', '[1909, 1909, -2*w^3 + 3*w^2 + 6*w - 9]', '[1911, 1911, 3*w^3 - 6*w^2 - 10*w + 14]', '[1923, 1923, -4*w^3 + 5*w^2 + 14*w - 4]', '[1923, 1923, -3*w^3 + 6*w^2 + 16*w + 1]', '[1929, 1929, w^3 - w^2 - 6*w - 7]', '[1931, 1931, -w^3 + 4*w - 5]', '[1933, 1933, -w^3 + 4*w^2 - w - 11]', '[1933, 1933, w^3 - 4*w - 7]', '[1933, 1933, 6*w^3 - 16*w^2 - 9*w + 12]', '[1933, 1933, -4*w^2 + 13*w - 6]', '[1936, 22, 4*w^3 - 6*w^2 - 14*w + 6]', '[1936, 22, 4*w^3 - 10*w^2 - 6*w + 4]', '[1936, 242, 2*w^3 - 4*w^2 - 8*w + 12]', '[1936, 242, -2*w^3 + 2*w^2 + 10*w - 4]', '[1937, 1937, -5*w^3 + 8*w^2 + 20*w - 4]', '[1939, 1939, -2*w^3 + 2*w^2 + 11*w - 4]', '[1941, 1941, 5*w^3 - 7*w^2 - 21*w]', '[1941, 1941, 2*w^3 - 2*w^2 - 8*w - 7]', '[1943, 1943, -4*w^2 + 7*w + 13]', '[1943, 1943, 3*w^3 - 8*w^2 - 11*w + 10]', '[1943, 1943, -w^3 + 7*w^2 - 8*w - 11]', '[1943, 1943, 2*w^3 - 12*w - 5]', '[1949, 1949, 2*w^3 - 2*w^2 - 12*w + 5]', '[1949, 1949, -w^3 + 2*w^2 - w - 5]', '[1951, 1951, -3*w^3 + 6*w^2 + 15*w - 4]', '[1951, 1951, 4*w^3 - 8*w^2 - 10*w + 13]', '[1957, 1957, -4*w^3 + 7*w^2 + 16*w + 1]', '[1957, 1957, 3*w^3 - 5*w^2 - 15*w + 6]', '[1963, 1963, 6*w^3 - 8*w^2 - 30*w + 1]', '[1963, 1963, 4*w^3 - 10*w^2 - 8*w + 5]', '[1969, 1969, -2*w^3 + 2*w^2 + 8*w + 9]', '[1969, 1969, 4*w^3 - 11*w^2 - 11*w + 21]', '[1969, 1969, 2*w^3 - 2*w^2 - 15*w + 8]', '[1969, 1969, -3*w^2 + 4*w + 9]', '[1973, 1973, -w^3 - w^2 + 13*w - 1]', '[1979, 1979, 3*w^3 - 6*w^2 - 12*w - 1]', '[1979, 1979, 4*w^3 - 6*w^2 - 20*w + 9]', '[1981, 1981, -w^3 + 5*w^2 - 3*w - 11]', '[1983, 1983, -2*w^3 + w^2 + 12*w]', '[1983, 1983, 4*w^3 - 4*w^2 - 15*w - 1]', '[1991, 1991, 3*w^3 - 6*w^2 - 12*w + 2]', '[1991, 1991, 4*w^3 - 3*w^2 - 26*w - 5]', '[1993, 1993, 2*w^2 - 5*w - 9]', '[2001, 2001, 2*w^3 - 3*w^2 - 12*w + 5]', '[2001, 2001, -3*w^3 + 6*w^2 + 14*w - 7]', '[2001, 2001, 4*w^3 - 9*w^2 - 11*w + 5]', '[2001, 2001, -4*w^3 + 8*w^2 + 15*w - 6]', '[2007, 2007, -3*w^3 + 6*w^2 + 14*w - 10]', '[2007, 2007, -3*w^3 + 4*w^2 + 19*w - 12]', '[2007, 2007, -w^3 - w^2 + 3*w + 6]', '[2007, 2007, 2*w^3 - 3*w^2 - 12*w + 2]', '[2013, 2013, -3*w^2 - w + 8]', '[2013, 2013, -w^3 + 5*w^2 - 6]', '[2027, 2027, -w^3 - w^2 + 13*w - 6]', '[2027, 2027, -7*w^3 + 17*w^2 + 18*w - 19]', '[2027, 2027, -3*w^3 + 8*w^2 + 11*w - 17]', '[2027, 2027, 5*w^3 - 9*w^2 - 18*w + 4]', '[2031, 2031, -3*w^3 + 2*w^2 + 5*w - 9]', '[2032, 254, -4*w^3 + 8*w^2 + 12*w - 10]', '[2037, 2037, 5*w^3 - 8*w^2 - 26*w - 4]', '[2037, 2037, -5*w^3 + 6*w^2 + 27*w + 4]', '[2039, 2039, -3*w^3 + 4*w^2 + 15*w - 5]', '[2043, 2043, 3*w^3 - 7*w^2 - 10*w + 6]', '[2047, 2047, w^2 + 2*w - 7]', '[2047, 2047, 8*w^3 - 17*w^2 - 27*w + 26]', '[2049, 2049, 2*w^3 - 5*w^2 - 10*w]', '[2049, 2049, 2*w^3 - 5*w^2 - 18*w - 8]', '[2061, 2061, -3*w^3 + 6*w^2 + 7*w - 5]', '[2061, 2061, -2*w^3 + 4*w^2 + 11*w - 4]', '[2079, 231, -2*w^3 + 3*w^2 + 5*w + 4]', '[2079, 231, 2*w^3 - 11*w - 7]', '[2079, 2079, -3*w^3 + 5*w^2 + 16*w - 1]', '[2079, 2079, -w^3 + 5*w^2 - 2*w - 8]', '[2081, 2081, -w^3 + 5*w^2 - 2*w - 7]', '[2081, 2081, -6*w^3 + 16*w^2 + 12*w - 21]', '[2083, 2083, -4*w^3 + 6*w^2 + 15*w - 8]', '[2093, 2093, 4*w^3 - 5*w^2 - 20*w + 2]', '[2093, 2093, -4*w^3 + 11*w^2 + 6*w - 7]', '[2096, 262, 2*w^2 - 6*w - 6]', '[2097, 2097, -4*w^3 + 9*w^2 + 9*w - 4]', '[2099, 2099, -4*w^3 + 9*w^2 + 10*w - 8]', '[2103, 2103, w^3 - w^2 - 3*w - 10]', '[2103, 2103, -2*w^3 + 2*w^2 + 14*w + 1]', '[2103, 2103, -6*w^3 + 10*w^2 + 25*w - 3]', '[2103, 2103, 2*w^3 - 5*w^2 - 9*w + 1]', '[2113, 2113, 3*w^3 - 5*w^2 - 9*w + 3]', '[2113, 2113, -w^3 + w^2 + 11*w - 11]', '[2119, 2119, -w^3 + 3*w^2 + 5*w - 13]', '[2127, 2127, 5*w^3 - 9*w^2 - 27*w - 1]', '[2128, 266, 2*w^3 - 2*w^2 - 8*w - 8]', '[2131, 2131, -w^3 + 5*w^2 - w - 6]', '[2131, 2131, -w^3 + 3*w^2 - 2*w - 5]', '[2137, 2137, 2*w^3 - 5*w^2 - 3]', '[2143, 2143, -3*w^3 + 9*w^2 + 8*w - 18]', '[2143, 2143, -3*w^3 + 5*w^2 + 8*w - 5]', '[2149, 2149, -5*w^3 + 8*w^2 + 22*w - 8]', '[2153, 2153, 6*w^3 - 15*w^2 - 12*w + 10]', '[2153, 2153, -7*w^3 + 16*w^2 + 21*w - 19]', '[2157, 2157, -w^2 - 7*w - 3]', '[2161, 2161, 3*w^3 - 6*w^2 - 7*w + 3]', '[2163, 2163, -4*w^3 + 7*w^2 + 14*w - 3]', '[2163, 2163, 4*w^3 - 3*w^2 - 23*w - 4]', '[2171, 2171, -3*w^3 + 9*w^2 + 11*w - 12]', '[2177, 2177, -w^3 - 4*w^2 + 19*w + 3]', '[2179, 2179, 3*w^3 - 6*w^2 - 7*w + 13]', '[2179, 2179, -w^3 + 4*w^2 - 3*w - 6]', '[2181, 2181, -3*w^3 + 7*w^2 + 13*w - 6]', '[2187, 9, 3*w^3 - 9*w^2 - 3*w + 12]', '[2187, 81, -3*w^2 + 3*w + 6]', '[2187, 2187, w^3 + 2*w^2 - 12*w - 10]', '[2189, 2189, 4*w^3 - 8*w^2 - 17*w + 6]', '[2189, 2189, -4*w^3 + w^2 + 18*w + 11]', '[2191, 2191, -3*w^3 + 6*w^2 + 15*w - 20]', '[2191, 2191, -6*w^3 + 10*w^2 + 24*w - 5]', '[2191, 2191, -3*w^2 + 3*w + 8]', '[2191, 2191, 3*w^3 - 8*w^2 - 9*w + 21]', '[2192, 274, -4*w^3 + 6*w^2 + 18*w - 6]', '[2197, 13, 5*w^3 - 12*w^2 - 10*w + 6]', '[2197, 2197, 4*w^3 - 6*w^2 - 15*w]', '[2199, 2199, 7*w^3 - 6*w^2 - 30*w - 5]', '[2203, 2203, 3*w^2 - 4*w - 6]', '[2207, 2207, 2*w^3 - 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7*w - 12]', '[5349, 5349, -w^2 - w - 6]', '[5357, 5357, 10*w^3 - 13*w^2 - 42*w + 4]', '[5357, 5357, 8*w^3 - 17*w^2 - 32*w + 31]', '[5357, 5357, 4*w^3 - 12*w^2 - 12*w + 23]', '[5357, 5357, 2*w^3 - 7*w^2 - w + 21]', '[5359, 5359, -5*w^3 + 7*w^2 + 19*w - 3]', '[5359, 5359, -5*w^3 + 6*w^2 + 24*w - 1]', '[5361, 5361, -8*w^3 + 9*w^2 + 31*w - 4]', '[5361, 5361, 5*w^3 - 11*w^2 - 13*w + 9]', '[5367, 5367, -w^3 + 2*w^2 - 2*w - 8]', '[5373, 597, -w^3 + 6*w^2 - 2*w - 16]', '[5373, 5373, w^3 - w^2 - 11*w - 9]', '[5376, 84, 4*w^3 - 4*w^2 - 20*w]', '[5377, 5377, -4*w^2 + 5*w + 13]', '[5379, 5379, -3*w^3 + 4*w^2 + 15*w - 10]', '[5379, 5379, 6*w^3 - 11*w^2 - 20*w + 15]', '[5387, 5387, -4*w^3 + 6*w^2 + 21*w - 2]', '[5391, 5391, -6*w^3 + 16*w^2 + 15*w - 19]', '[5397, 5397, 5*w^3 - 3*w^2 - 25*w - 11]', '[5399, 5399, 2*w^3 - 7*w^2 - 2*w + 23]', '[5399, 5399, -2*w^3 + 15*w]', '[5401, 5401, 3*w^3 - 5*w^2 - 17*w + 11]', '[5401, 5401, -4*w^2 + 3*w + 11]', '[5407, 5407, -2*w^3 + 6*w^2 + w - 11]', '[5411, 5411, 3*w^3 - 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7]', '[1511, 1511, -5*w^3 + 7*w^2 + 22*w - 3]', '[1531, 1531, -3*w^3 + 6*w^2 + 14*w - 6]', '[1549, 1549, w^2 - 3*w - 9]', '[1549, 1549, 5*w^3 - 10*w^2 - 16*w + 6]', '[1553, 1553, 3*w^3 - 3*w^2 - 16*w]', '[1553, 1553, -4*w^3 + 11*w^2 + 5*w - 5]', '[1559, 1559, -5*w^3 + 12*w^2 + 12*w - 13]', '[1567, 1567, -w - 6]', '[1571, 1571, -2*w^3 + w^2 + 16*w + 5]', '[1571, 1571, -3*w^3 + 6*w^2 + 15*w - 1]', '[1579, 1579, -4*w^3 + 8*w^2 + 16*w - 7]', '[1597, 1597, -w^3 + 2*w^2 + 8*w - 5]', '[1597, 1597, -w^3 + 3*w^2 + 3*w - 12]', '[1601, 1601, 3*w^3 - 6*w^2 - 14*w + 11]', '[1607, 1607, -3*w^3 + 4*w^2 + 13*w - 4]', '[1619, 1619, 4*w^2 - 3*w - 15]', '[1621, 1621, -2*w^3 + 4*w^2 + 11*w - 3]', '[1621, 1621, -w^2 - w - 4]', '[1637, 1637, -2*w^3 + 3*w^2 + 15*w - 18]', '[1637, 1637, 7*w^3 - 18*w^2 - 14*w + 19]', '[1657, 1657, -2*w^3 + w^2 + 19*w - 12]', '[1657, 1657, -3*w^3 + 4*w^2 + 10*w - 2]', '[1657, 1657, 3*w^3 - 3*w^2 - 20*w + 8]', '[1657, 1657, -3*w^3 + 6*w^2 + 7*w - 6]', '[1667, 1667, -w^3 + 3*w^2 + 6*w - 9]', '[1667, 1667, -w^3 + 3*w^2 - w - 6]', '[1669, 1669, 3*w^2 - 7*w - 8]', '[1669, 1669, 4*w^2 - 14*w + 5]', '[1681, 41, -3*w^3 + 5*w^2 + 15*w - 7]', '[1681, 41, -w^3 + 2*w^2 + 8*w - 2]', '[1693, 1693, w^3 - w^2 - w - 4]', '[1697, 1697, 3*w^3 - 6*w^2 - 11*w]', '[1697, 1697, 5*w^3 - 7*w^2 - 21*w + 1]', '[1699, 1699, 2*w^2 - 5*w - 8]', '[1709, 1709, -2*w^3 + 7*w^2 + 6*w - 13]', '[1721, 1721, -2*w^3 + w^2 + 13*w]', '[1723, 1723, 2*w^2 - 5*w - 11]', '[1723, 1723, -2*w^3 + 4*w^2 + 6*w - 11]', '[1733, 1733, -4*w^3 + 7*w^2 + 14*w - 2]', '[1733, 1733, -2*w^3 + 2*w^2 + 9*w - 5]', '[1747, 1747, w^3 - 2*w^2 - 3*w - 5]', '[1747, 1747, -4*w^3 + 9*w^2 + 10*w - 14]', '[1759, 1759, 2*w^3 - 3*w^2 - 12*w - 6]', '[1759, 1759, -2*w^3 + 4*w^2 + 3*w - 7]', '[1777, 1777, -3*w^3 + 4*w^2 + 14*w - 4]', '[1783, 1783, -2*w^3 + 6*w^2 + w - 8]', '[1787, 1787, -6*w^3 + 10*w^2 + 23*w - 10]', '[1787, 1787, 2*w^3 - w^2 - 18*w + 11]', '[1789, 1789, -w^3 + 2*w^2 + 4*w - 9]', '[1823, 1823, -5*w^3 + 9*w^2 + 22*w - 8]', '[1831, 1831, -6*w^3 + 17*w^2 + 9*w - 18]', '[1831, 1831, -4*w^3 + 11*w^2 + 9*w - 16]', '[1849, 43, -w^3 + 5*w^2 - 2*w - 9]', '[1849, 43, 3*w^2 - 2*w - 6]', '[1861, 1861, -w^2 + 2*w - 5]', '[1867, 1867, w^3 - 2*w^2 - 2*w - 6]', '[1867, 1867, 5*w^3 - 7*w^2 - 24*w + 4]', '[1867, 1867, -2*w^3 + 5*w^2 + 2*w - 7]', '[1867, 1867, 6*w^3 - 13*w^2 - 18*w + 12]', '[1871, 1871, 2*w^2 - w - 11]', '[1873, 1873, -w^3 + 5*w^2 - 2*w - 6]', '[1873, 1873, -w^3 + 2*w^2 + 8*w - 3]', '[1877, 1877, -4*w^3 + 4*w^2 + 21*w + 2]', '[1879, 1879, 4*w - 7]', '[1879, 1879, 5*w^3 - 9*w^2 - 22*w + 5]', '[1879, 1879, 3*w^2 - 3*w - 5]', '[1879, 1879, -3*w^3 + 7*w^2 + 12*w - 20]', '[1901, 1901, 3*w^2 - 4*w - 5]', '[1907, 1907, -2*w^3 + 8*w^2 - 2*w - 11]', '[1931, 1931, -w^3 + 4*w - 5]', '[1933, 1933, -w^3 + 4*w^2 - w - 11]', '[1933, 1933, w^3 - 4*w - 7]', '[1933, 1933, 6*w^3 - 16*w^2 - 9*w + 12]', '[1933, 1933, -4*w^2 + 13*w - 6]', '[1949, 1949, 2*w^3 - 2*w^2 - 12*w + 5]', '[1949, 1949, -w^3 + 2*w^2 - w - 5]', '[1951, 1951, -3*w^3 + 6*w^2 + 15*w - 4]', '[1951, 1951, 4*w^3 - 8*w^2 - 10*w + 13]', '[1973, 1973, -w^3 - w^2 + 13*w - 1]', '[1979, 1979, 3*w^3 - 6*w^2 - 12*w - 1]', '[1979, 1979, 4*w^3 - 6*w^2 - 20*w + 9]', '[1993, 1993, 2*w^2 - 5*w - 9]', '[2027, 2027, -w^3 - w^2 + 13*w - 6]', '[2027, 2027, -7*w^3 + 17*w^2 + 18*w - 19]', '[2027, 2027, -3*w^3 + 8*w^2 + 11*w - 17]', '[2027, 2027, 5*w^3 - 9*w^2 - 18*w + 4]', '[2039, 2039, -3*w^3 + 4*w^2 + 15*w - 5]', '[2081, 2081, -w^3 + 5*w^2 - 2*w - 7]', '[2081, 2081, -6*w^3 + 16*w^2 + 12*w - 21]', '[2083, 2083, -4*w^3 + 6*w^2 + 15*w - 8]', '[2099, 2099, -4*w^3 + 9*w^2 + 10*w - 8]', '[2113, 2113, 3*w^3 - 5*w^2 - 9*w + 3]', '[2113, 2113, -w^3 + w^2 + 11*w - 11]', '[2131, 2131, -w^3 + 5*w^2 - w - 6]', '[2131, 2131, -w^3 + 3*w^2 - 2*w - 5]', '[2137, 2137, 2*w^3 - 5*w^2 - 3]', '[2143, 2143, -3*w^3 + 9*w^2 + 8*w - 18]', '[2143, 2143, -3*w^3 + 5*w^2 + 8*w - 5]', '[2153, 2153, 6*w^3 - 15*w^2 - 12*w + 10]', '[2153, 2153, -7*w^3 + 16*w^2 + 21*w - 19]', '[2161, 2161, 3*w^3 - 6*w^2 - 7*w + 3]', '[2179, 2179, 3*w^3 - 6*w^2 - 7*w + 13]', '[2179, 2179, -w^3 + 4*w^2 - 3*w - 6]', '[2197, 13, 5*w^3 - 12*w^2 - 10*w + 6]', '[2203, 2203, 3*w^2 - 4*w - 6]', '[2207, 2207, 2*w^3 - 7*w^2 + w + 9]', '[2209, 47, -w^3 + 4*w^2 - 2*w - 8]', '[2213, 2213, -3*w^3 + 2*w^2 + 18*w + 2]', '[2221, 2221, -2*w^3 + 2*w^2 + 10*w - 5]', '[2237, 2237, 3*w^2 - 4*w - 8]', '[2237, 2237, -3*w^3 + 6*w^2 + 14*w - 8]', '[2243, 2243, -w^3 + 3*w^2 + 5*w - 12]', '[2273, 2273, -3*w^3 + 4*w^2 + 8*w - 4]', '[2287, 2287, 4*w^3 - 8*w^2 - 18*w + 5]', '[2287, 2287, -3*w^3 + 6*w^2 + 14*w - 18]', '[2309, 2309, -2*w^3 + 5*w^2 + 7]', '[2311, 2311, -w^3 + 5*w^2 - w - 11]', '[2311, 2311, 3*w^3 - 5*w^2 - 12*w - 5]', '[2333, 2333, -3*w^3 + 4*w^2 + 13*w - 5]', '[2333, 2333, w^2 - 5*w - 8]', '[2347, 2347, -w^2 + 7*w - 8]', '[2347, 2347, 4*w^3 - 7*w^2 - 16*w + 12]', '[2351, 2351, 5*w^3 - 13*w^2 - 8*w + 6]', '[2351, 2351, -4*w^3 + 7*w^2 + 18*w - 1]', '[2357, 2357, -4*w^3 + 8*w^2 + 12*w - 5]', '[2357, 2357, -w^3 + 4*w^2 - w - 16]', '[2371, 2371, -5*w^3 + 7*w^2 + 20*w - 3]', '[2371, 2371, -6*w^3 + 16*w^2 + 11*w - 19]', '[2377, 2377, 4*w^3 - 6*w^2 - 15*w + 3]', '[2377, 2377, -4*w^3 + 7*w^2 + 16*w - 14]', '[2381, 2381, 5*w^3 - 9*w^2 - 18*w + 10]', '[2381, 2381, w^3 - 3*w - 6]', '[2383, 2383, w^3 - 3*w^2 - 8*w + 3]', '[2383, 2383, -2*w^3 + 4*w^2 + 11*w - 6]', '[2383, 2383, -w^3 + 3*w^2 + 8*w - 6]', '[2383, 2383, w^3 + 2*w^2 - 16*w + 5]', '[2423, 2423, 2*w^2 - 9]', '[2423, 2423, 4*w^3 - 7*w^2 - 14*w + 4]', '[2441, 2441, -2*w^3 + 5*w^2 + 9*w - 14]', '[2441, 2441, -3*w^3 + 4*w^2 + 16*w - 7]', '[2447, 2447, -4*w^3 + 9*w^2 + 17*w - 9]', '[2447, 2447, -w^3 - w^2 + 12*w - 4]', '[2459, 2459, w^2 - w - 10]', '[2473, 2473, -2*w^3 + 7*w^2 + 2*w - 9]', '[2477, 2477, 4*w^3 - 7*w^2 - 14*w + 5]', '[2503, 2503, -2*w^3 + 6*w^2 + 7*w - 5]', '[2521, 2521, w^3 + 2*w^2 - 17*w + 8]', '[2521, 2521, -w^3 + 7*w^2 - 11*w + 1]', '[2531, 2531, -5*w^3 + 10*w^2 + 18*w - 8]', '[2539, 2539, 6*w^3 - 11*w^2 - 29*w + 25]', '[2551, 2551, 2*w^3 + w^2 - 15*w - 3]', '[2557, 2557, -3*w^3 + 3*w^2 + 16*w - 1]', '[2557, 2557, 4*w^3 - 6*w^2 - 20*w + 3]', '[2579, 2579, w^3 + w^2 - 6*w - 11]', '[2591, 2591, 4*w^3 - 6*w^2 - 15*w + 2]', '[2591, 2591, 4*w^3 - 5*w^2 - 22*w + 6]', '[2609, 2609, 6*w^3 - 15*w^2 - 14*w + 15]', '[2609, 2609, w^3 + w^2 - 5*w - 9]', '[2617, 2617, -2*w^3 + 2*w^2 + 11*w - 6]', '[2617, 2617, -2*w^3 + 3*w^2 + 9*w + 6]', '[2617, 2617, 3*w^3 - 6*w^2 - 6*w + 4]', '[2617, 2617, 3*w^3 - 6*w^2 - 13*w + 1]', '[2621, 2621, 2*w^3 + w^2 - 11*w - 11]', '[2659, 2659, -2*w^3 + 3*w^2 + 13*w - 15]', '[2663, 2663, w^3 + 2*w^2 - 11*w - 7]', '[2671, 2671, 4*w^3 - 5*w^2 - 15*w + 1]', '[2683, 2683, -2*w^3 + 7*w^2 + 3*w - 14]', '[2687, 2687, -2*w^3 + w^2 + 13*w - 1]', '[2699, 2699, -2*w^3 + 7*w^2 + 2*w - 11]', '[2699, 2699, -4*w^3 + 5*w^2 + 17*w - 3]', '[2707, 2707, -4*w^3 + 10*w^2 + 10*w - 9]', '[2711, 2711, -4*w^3 + 7*w^2 + 13*w - 8]', '[2713, 2713, 4*w^3 - 7*w^2 - 17*w + 13]', '[2729, 2729, -2*w^3 + 3*w^2 + 13*w - 8]', '[2731, 2731, -2*w^3 + 4*w^2 + 10*w - 15]', '[2741, 2741, 3*w^3 - 3*w^2 - 15*w + 1]', '[2749, 2749, -2*w^3 + 4*w^2 + 3*w - 10]', '[2749, 2749, 5*w^2 - 14*w]', '[2753, 2753, -3*w^3 + 8*w^2 + 7*w - 21]', '[2767, 2767, -2*w^3 + 7*w^2 + 4*w - 10]', '[2777, 2777, -w^3 + 5*w^2 - 4*w - 9]', '[2789, 2789, -w^3 + w^2 + 10*w - 5]', '[2797, 2797, -2*w^3 + 5*w^2 + 3*w + 4]', '[2797, 2797, -7*w^3 + 18*w^2 + 18*w - 27]', '[2797, 2797, -3*w^3 + 9*w^2 + 6*w - 13]', '[2797, 2797, w^3 - w^2 - 2*w - 8]', '[2801, 2801, -5*w^3 + 14*w^2 + 11*w - 24]', '[2803, 2803, -2*w^3 + w^2 + 14*w - 2]', '[2803, 2803, w^3 + w^2 - 9*w + 2]', '[2837, 2837, -4*w^3 + 7*w^2 + 19*w - 5]', '[2837, 2837, -2*w - 7]', '[2843, 2843, 5*w^3 - 14*w^2 - 6*w + 8]', '[2843, 2843, -3*w^3 + 6*w^2 + 14*w]', '[2843, 2843, -w^3 + 5*w^2 + w - 10]', '[2843, 2843, -w^3 + 5*w^2 - 11]', '[2851, 2851, -w^3 + w^2 + 3*w - 7]', '[2851, 2851, -w^3 + 3*w^2 - w - 10]', '[2857, 2857, 2*w^3 - 3*w^2 - 10*w - 6]', '[2857, 2857, -5*w^3 + 9*w^2 + 20*w - 4]', '[2861, 2861, -w^2 - 2*w - 5]', '[2879, 2879, 4*w^2 - 11]', '[2903, 2903, -3*w^3 + 4*w^2 + 15*w - 6]', '[2903, 2903, 2*w^2 - 6*w - 7]', '[2909, 2909, w^3 + w^2 - 11*w + 3]', '[2927, 2927, -3*w^3 + 2*w^2 + 11*w - 2]', '[2927, 2927, -w^3 + 3*w^2 - w - 9]', '[2939, 2939, w^3 - w^2 - 5*w - 8]', '[2953, 2953, 2*w^2 - 10*w + 13]', '[2953, 2953, 4*w^3 - 9*w^2 - 11*w + 4]', '[2957, 2957, 2*w^3 - w^2 - 16*w + 6]', '[2999, 2999, 6*w^3 - 12*w^2 - 20*w + 17]', '[3001, 3001, 4*w^3 - 7*w^2 - 15*w - 5]', '[3001, 3001, 3*w^2 - 8*w - 7]', '[3011, 3011, 3*w^3 - 2*w^2 - 11*w - 5]', '[3023, 3023, -5*w^3 + 8*w^2 + 26*w - 16]', '[3037, 3037, -w^3 + 4*w^2 - 2*w - 9]', '[3037, 3037, -5*w^3 + 9*w^2 + 18*w - 9]', '[3041, 3041, 5*w^3 - 10*w^2 - 15*w + 4]', '[3061, 3061, -5*w^3 + 7*w^2 + 17*w + 3]', '[3061, 3061, -3*w^3 + 6*w^2 + 15*w - 5]', '[3061, 3061, 5*w^3 - 10*w^2 - 16*w + 13]', '[3061, 3061, 5*w^3 - 9*w^2 - 25*w + 21]', '[3067, 3067, -5*w^3 + 12*w^2 + 13*w - 11]', '[3067, 3067, 7*w^3 - 12*w^2 - 27*w + 12]', '[3079, 3079, 3*w^2 - 2*w - 13]', '[3089, 3089, 3*w^3 - 3*w^2 - 19*w + 6]', '[3089, 3089, -2*w^3 + 8*w^2 - 3*w - 11]', '[3089, 3089, 2*w^3 - 5*w^2 - w - 7]', '[3089, 3089, 5*w^3 - 8*w^2 - 17*w + 10]', '[3109, 3109, -5*w^3 + 11*w^2 + 21*w - 14]', '[3119, 3119, 2*w^2 + 3*w - 7]', '[3121, 3121, -w^3 + 5*w^2 - 10]', '[3121, 3121, -3*w^3 + 10*w^2 + 7*w - 23]', '[3137, 3137, -6*w^3 + 17*w^2 + 6*w - 9]', '[3167, 3167, w^3 - w^2 - 4*w - 9]', '[3187, 3187, -7*w^3 + 18*w^2 + 12*w - 12]', '[3187, 3187, -5*w^3 + 10*w^2 + 23*w - 27]', '[3187, 3187, w^3 + 2*w^2 - 14*w + 1]', '[3187, 3187, -4*w^3 + 8*w^2 + 11*w - 3]', '[3203, 3203, 4*w^3 - 7*w^2 - 20*w + 14]', '[3203, 3203, -5*w^3 + 6*w^2 + 28*w - 6]', '[3203, 3203, 6*w^3 - 9*w^2 - 24*w + 8]', '[3203, 3203, -w^3 + 5*w^2 - 9*w + 10]', '[3221, 3221, -3*w^3 + 9*w^2 + 7*w - 16]', '[3221, 3221, -w^3 + 2*w^2 + 4*w - 10]', '[3229, 3229, -4*w^3 + 10*w^2 + 15*w - 21]', '[3229, 3229, 6*w^3 - 11*w^2 - 21*w + 4]', '[3251, 3251, w^3 + 2*w^2 - 10*w - 10]', '[3271, 3271, 3*w^3 - 8*w^2 - 14*w + 11]', '[3299, 3299, 4*w^3 - 7*w^2 - 17*w - 5]', '[3301, 3301, w^2 - 2*w - 10]', '[3307, 3307, -4*w^3 + 9*w^2 + 13*w - 8]', '[3313, 3313, -4*w^3 + 9*w^2 + 8*w - 3]', '[3313, 3313, w^3 - 10*w - 7]', '[3323, 3323, 5*w^3 - 7*w^2 - 20*w + 2]', '[3331, 3331, -4*w^3 + 6*w^2 + 19*w - 8]', '[3343, 3343, -3*w^3 + 4*w^2 + 14*w - 6]', '[3343, 3343, 3*w^3 - 4*w^2 - 18*w + 8]', '[3347, 3347, 2*w^3 - 7*w^2 - 9*w + 14]', '[3361, 3361, -2*w^3 + 7*w^2 + 3*w - 11]', '[3373, 3373, -2*w^3 + 7*w^2 + 4*w - 13]', '[3391, 3391, -3*w^3 + 8*w^2 + 7*w - 5]', '[3407, 3407, -3*w^3 + 5*w^2 + 16*w - 9]', '[3449, 3449, -w^3 + w^2 + 10*w - 2]', '[3457, 3457, 4*w^2 - 8*w - 7]', '[3457, 3457, w^3 - 2*w^2 - 2*w - 7]', '[3467, 3467, -5*w^3 + 7*w^2 + 20*w + 1]', '[3469, 3469, -w^3 + 2*w^2 + 5*w - 11]', '[3469, 3469, -2*w^3 + 7*w^2 + 4*w - 12]', '[3481, 59, w^3 - 3*w - 7]', '[3481, 59, w^2 + 2*w - 9]', '[3491, 3491, -4*w^3 + 8*w^2 + 20*w - 23]', '[3499, 3499, -5*w^3 + 11*w^2 + 14*w - 21]', '[3527, 3527, w^3 + 2*w^2 - 10*w - 6]', '[3529, 3529, -4*w^3 + 10*w^2 + 11*w - 10]', '[3533, 3533, -4*w^3 + 7*w^2 + 19*w - 6]', '[3539, 3539, 5*w^3 - 11*w^2 - 21*w + 26]', '[3547, 3547, -2*w^3 + 5*w^2 + w - 7]', '[3559, 3559, -w^3 - w^2 + 3*w + 7]', '[3571, 3571, -3*w^3 + 3*w^2 + 14*w - 2]', '[3581, 3581, w^3 - w^2 - 5]', '[3581, 3581, -5*w^3 + 8*w^2 + 17*w + 2]', '[3593, 3593, -4*w^3 + 8*w^2 + 17*w - 5]', '[3607, 3607, -w^3 + 3*w^2 + 6*w - 11]', '[3617, 3617, -6*w^3 + 10*w^2 + 30*w - 21]', '[3631, 3631, 5*w^2 - 10*w - 13]', '[3637, 3637, 2*w^3 + w^2 - 19*w - 8]', '[3643, 3643, -4*w^3 + 7*w^2 + 21*w - 1]', '[3643, 3643, 3*w^2 - 3*w - 19]', '[3659, 3659, 2*w^3 + w^2 - 18*w - 10]', '[3671, 3671, 4*w^3 - 8*w^2 - 14*w - 1]', '[3677, 3677, -3*w^3 + 7*w^2 + 6*w - 12]', '[3677, 3677, -3*w^3 + 4*w^2 + 13*w - 7]', '[3691, 3691, 2*w^3 - 17*w + 1]', '[3691, 3691, -5*w^3 + 10*w^2 + 16*w - 12]', '[3697, 3697, -5*w^3 + 16*w^2 + 2*w - 17]', '[3701, 3701, 2*w^3 - 18*w + 3]', '[3709, 3709, w^3 - 4*w - 10]', '[3727, 3727, 6*w^3 - 11*w^2 - 26*w + 11]', '[3767, 3767, 7*w^3 - 18*w^2 - 15*w + 18]', '[3767, 3767, -w^3 - 2*w^2 + 7*w + 9]', '[3779, 3779, 7*w^3 - 14*w^2 - 28*w + 15]', '[3779, 3779, -3*w^3 + 5*w^2 + 16*w - 3]', '[3797, 3797, -7*w^3 + 19*w^2 + 14*w - 23]', '[3821, 3821, -3*w^3 + 10*w^2 + 2*w - 13]', '[3821, 3821, -6*w^3 + 10*w^2 + 24*w + 1]', '[3851, 3851, -4*w^3 + 8*w^2 + 15*w - 4]', '[3863, 3863, -w^3 + 5*w^2 - 7*w - 5]', '[3863, 3863, -2*w^3 + 8*w^2 - w - 13]', '[3881, 3881, -3*w^3 + 7*w^2 + 12*w - 5]', '[3881, 3881, 4*w^3 - 5*w^2 - 23*w + 9]', '[3889, 3889, 4*w^3 - 8*w^2 - 18*w + 13]', '[3889, 3889, w^3 - w^2 - 11*w - 5]', '[3907, 3907, -7*w^3 + 20*w^2 + 10*w - 21]', '[3911, 3911, 4*w^3 - 7*w^2 - 13*w + 3]', '[3917, 3917, 3*w^3 - 2*w^2 - 22*w + 3]', '[3917, 3917, 6*w^3 - 11*w^2 - 27*w + 22]', '[3923, 3923, -3*w^3 + 8*w^2 + 11*w - 19]', '[3923, 3923, -3*w^3 + 9*w^2 + 9*w - 22]', '[3931, 3931, -5*w^3 + 8*w^2 + 21*w - 9]', '[3943, 3943, -5*w^3 + 10*w^2 + 18*w - 7]', '[3989, 3989, 7*w^3 - 13*w^2 - 30*w + 22]', '[3989, 3989, -w^2 + 4*w - 8]']}
• 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': [1, 3, -4, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 11197, 'disc_rad': 11197, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[3, 1], [1, 1]]], [5, [[4, 1]]], [7, [[3, 1], [1, 1]]], [11, [[2, 1], [1, 2]]], [13, [[3, 1], [1, 1]]], [17, [[4, 1]]], [19, [[3, 1], [1, 1]]], [23, [[2, 1], [1, 2]]], [29, [[2, 1], [1, 2]]], [31, [[4, 1]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[2, 1], [1, 2]]], [53, [[4, 1]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12], 'galois_label': '4T5', 'galt': 5, 'grd': 105.8158778255891, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.11197.1', 'local_algs': ['m11197.1.1.0', 'm11197.1.1.0', 'm11197.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [11197], 'rd': 10.2866844914, 'regulator': {'__RealLiteral__': 0, 'data': '5.67295698421', 'prec': 44}, 'res': {'gal': ['-96336,80568,6512340,13036642,-37412473,-65538308,91068555,111754924,-124883636,-79806354,97786367,19927508,-40515976,1781916,8764120,-1742086,-932931,314428,36818,-23802,659,748,-68,-8,1'], 'sib': ['-4,0,25,0,-11,0,1', '1,14,-1,-221,162,443,-336,-289,196,61,-29,-3,1', '1259,-2266,935,75,-67,-1,1', '256,0,-5533,0,30401,0,-10234,0,1195,0,-58,0,1', '437703,28333,-91709,-5293,5770,193,-133,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a - 1 \\)', '\\( a^{2} - 3 a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}