Hilbert modular form data - 2.2.5.1-401.1-b

Formats: - HTML - YAML - JSON - 2024-06-01T06:22:24.193947

• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 2, 'dimension': 6, 'disc': 5, 'field_bad_primes': [5], 'field_label': '2.2.5.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.5.1-401.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [401], 'level_ideal': '[401, 401, 7*w - 25]', 'level_label': '401.1', 'level_norm': 401, 'parallel_weight': 2, 'short_label': '401.1-b', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[401, 401, 7*w - 25]', 1]], 'hecke_eigenvalues': ['e', '-1/4*e^5 - 1/4*e^4 + 7/2*e^3 + 1/2*e^2 - 33/4*e - 5/4', '-1/2*e^5 - 1/2*e^4 + 6*e^3 - e^2 - 19/2*e + 3/2', 'e^5 + 3/2*e^4 - 12*e^3 - 5*e^2 + 22*e + 21/2', '1/4*e^5 - 1/4*e^4 - 4*e^3 + 5*e^2 + 27/4*e - 15/4', '-3/4*e^5 - 7/4*e^4 + 8*e^3 + 11*e^2 - 61/4*e - 77/4', 'e^5 + 2*e^4 - 12*e^3 - 13*e^2 + 25*e + 25', 'e^2 + 2*e - 5', '-2*e^5 - 4*e^4 + 23*e^3 + 22*e^2 - 47*e - 38', '-1/2*e^5 - 1/2*e^4 + 7*e^3 + 2*e^2 - 33/2*e - 15/2', '3/4*e^5 + 3/4*e^4 - 9*e^3 + e^2 + 49/4*e + 1/4', '3/2*e^5 + 5/2*e^4 - 18*e^3 - 11*e^2 + 73/2*e + 41/2', '1/2*e^5 + 3/2*e^4 - 6*e^3 - 14*e^2 + 35/2*e + 57/2', '5/4*e^5 + 9/4*e^4 - 27/2*e^3 - 17/2*e^2 + 89/4*e + 41/4', '1/4*e^5 + 3/4*e^4 - 3*e^3 - 8*e^2 + 31/4*e + 65/4', '-1/2*e^5 - 1/2*e^4 + 7*e^3 + 3*e^2 - 29/2*e - 29/2', '-5/4*e^5 - 5/4*e^4 + 31/2*e^3 - 1/2*e^2 - 97/4*e - 9/4', '-2*e^5 - 4*e^4 + 24*e^3 + 25*e^2 - 52*e - 47', 'e^4 - 14*e^2 + 8*e + 25', '-7/4*e^5 - 11/4*e^4 + 21*e^3 + 12*e^2 - 157/4*e - 101/4', '1/2*e^5 - 7*e^3 + 6*e^2 + 23/2*e - 11', 'e^5 + 2*e^4 - 12*e^3 - 11*e^2 + 29*e + 15', '5/4*e^5 + 9/4*e^4 - 27/2*e^3 - 13/2*e^2 + 85/4*e + 21/4', '-1/4*e^5 + 3/4*e^4 + 11/2*e^3 - 19/2*e^2 - 45/4*e + 35/4', '-7/4*e^5 - 7/4*e^4 + 45/2*e^3 + 3/2*e^2 - 155/4*e - 47/4', '2*e^5 + 4*e^4 - 22*e^3 - 20*e^2 + 40*e + 30', '-1/2*e^5 - 3/2*e^4 + 7*e^3 + 17*e^2 - 53/2*e - 63/2', '-3/2*e^5 - 5/2*e^4 + 17*e^3 + 9*e^2 - 51/2*e - 33/2', '-3/2*e^5 - 7/2*e^4 + 17*e^3 + 22*e^2 - 79/2*e - 53/2', '1/2*e^5 - e^4 - 8*e^3 + 17*e^2 + 21/2*e - 15', '-e^5 - e^4 + 13*e^3 - 28*e - 7', '5/2*e^5 + 5*e^4 - 28*e^3 - 25*e^2 + 105/2*e + 33', '-9/4*e^5 - 25/4*e^4 + 45/2*e^3 + 85/2*e^2 - 181/4*e - 261/4', '-1/4*e^5 - 5/4*e^4 + 3/2*e^3 + 17/2*e^2 - 13/4*e - 45/4', '3/2*e^5 + 3*e^4 - 19*e^3 - 22*e^2 + 89/2*e + 44', '-1/2*e^4 - e^3 + 6*e^2 + 10*e - 25/2', '-3*e^5 - 5*e^4 + 34*e^3 + 17*e^2 - 57*e - 28', '13/4*e^5 + 27/4*e^4 - 37*e^3 - 41*e^2 + 283/4*e + 317/4', '-7/4*e^5 - 5/4*e^4 + 22*e^3 - 8*e^2 - 117/4*e + 25/4', '-13/4*e^5 - 25/4*e^4 + 79/2*e^3 + 77/2*e^2 - 345/4*e - 273/4', '13/4*e^5 + 21/4*e^4 - 77/2*e^3 - 41/2*e^2 + 273/4*e + 145/4', '2*e^5 + 3*e^4 - 25*e^3 - 12*e^2 + 59*e + 21', '-9/4*e^5 - 15/4*e^4 + 27*e^3 + 18*e^2 - 199/4*e - 157/4', '17/4*e^5 + 23/4*e^4 - 53*e^3 - 22*e^2 + 391/4*e + 245/4', '9/2*e^5 + 15/2*e^4 - 52*e^3 - 31*e^2 + 179/2*e + 139/2', '3/4*e^5 + 3/4*e^4 - 10*e^3 - 4*e^2 + 53/4*e + 93/4', '-2*e^4 - 5*e^3 + 16*e^2 + 19*e - 16', '-4*e^5 - 7*e^4 + 47*e^3 + 30*e^2 - 93*e - 43', '-7/4*e^5 - 23/4*e^4 + 33/2*e^3 + 83/2*e^2 - 151/4*e - 203/4', '11/4*e^5 + 21/4*e^4 - 33*e^3 - 33*e^2 + 277/4*e + 283/4', '3/4*e^5 - 1/4*e^4 - 10*e^3 + 14*e^2 + 37/4*e - 87/4', '-15/4*e^5 - 23/4*e^4 + 89/2*e^3 + 43/2*e^2 - 331/4*e - 191/4', '3*e^5 + 6*e^4 - 33*e^3 - 32*e^2 + 56*e + 70', '2*e^4 + e^3 - 27*e^2 + 9*e + 43', '5/4*e^5 + 19/4*e^4 - 12*e^3 - 42*e^2 + 119/4*e + 265/4', '-5/4*e^5 - 13/4*e^4 + 25/2*e^3 + 41/2*e^2 - 97/4*e - 137/4', '1/2*e^5 - 3/2*e^4 - 9*e^3 + 23*e^2 + 33/2*e - 43/2', '-11/4*e^5 - 23/4*e^4 + 33*e^3 + 35*e^2 - 313/4*e - 221/4', '-e^5 + 13*e^3 - 13*e^2 - 12*e + 13', '-2*e^4 - 2*e^3 + 24*e^2 - 24', '-7/4*e^5 - 19/4*e^4 + 35/2*e^3 + 67/2*e^2 - 123/4*e - 191/4', '-2*e^5 - 4*e^4 + 23*e^3 + 23*e^2 - 51*e - 51', '2*e^5 + 4*e^4 - 22*e^3 - 23*e^2 + 38*e + 57', '-2*e^5 - 4*e^4 + 25*e^3 + 25*e^2 - 57*e - 31', '7/4*e^5 + 15/4*e^4 - 17*e^3 - 16*e^2 + 93/4*e + 81/4', '-17/4*e^5 - 31/4*e^4 + 49*e^3 + 37*e^2 - 359/4*e - 281/4', '-1/2*e^5 - 3/2*e^4 + 2*e^3 + 6*e^2 + 21/2*e - 29/2', '-13/4*e^5 - 17/4*e^4 + 87/2*e^3 + 39/2*e^2 - 393/4*e - 173/4', '5/2*e^5 + 5*e^4 - 30*e^3 - 31*e^2 + 129/2*e + 57', '-9/2*e^5 - 9/2*e^4 + 58*e^3 + 3*e^2 - 207/2*e - 49/2', '-4*e^5 - 11/2*e^4 + 47*e^3 + 12*e^2 - 82*e - 67/2', '-11/4*e^5 - 11/4*e^4 + 33*e^3 - 6*e^2 - 201/4*e + 3/4', '1/4*e^5 - 7/4*e^4 - 7/2*e^3 + 53/2*e^2 - 27/4*e - 99/4', '-e^5 + e^4 + 14*e^3 - 24*e^2 - 7*e + 33', -1, '13/4*e^5 + 29/4*e^4 - 75/2*e^3 - 99/2*e^2 + 305/4*e + 409/4', '-3*e^5 - 7*e^4 + 34*e^3 + 46*e^2 - 83*e - 71', '3*e^5 + 7*e^4 - 32*e^3 - 39*e^2 + 59*e + 50', '3*e^5 + 15/2*e^4 - 33*e^3 - 50*e^2 + 73*e + 155/2', '-1/2*e^5 + 9*e^3 - 2*e^2 - 67/2*e + 3', '5*e^5 + 9*e^4 - 57*e^3 - 41*e^2 + 104*e + 68', '7/2*e^5 + 13/2*e^4 - 42*e^3 - 35*e^2 + 185/2*e + 125/2', '3/4*e^5 + 3/4*e^4 - 12*e^3 - 5*e^2 + 125/4*e + 105/4', '-3*e^5 - 4*e^4 + 35*e^3 + 6*e^2 - 50*e - 8', '2*e^5 + 2*e^4 - 25*e^3 + 4*e^2 + 53*e - 12', '-7/4*e^5 - 13/4*e^4 + 18*e^3 + 8*e^2 - 101/4*e - 47/4', '5*e^5 + 6*e^4 - 60*e^3 - 6*e^2 + 99*e + 22', '-1/2*e^5 - 3/2*e^4 + 9*e^3 + 24*e^2 - 77/2*e - 113/2', '-5*e^5 - 10*e^4 + 59*e^3 + 60*e^2 - 128*e - 102', '-2*e^5 - e^4 + 26*e^3 - 13*e^2 - 32*e + 16', '2*e^5 + e^4 - 29*e^3 + 6*e^2 + 59*e + 1', '1/2*e^5 + 3/2*e^4 - 6*e^3 - 11*e^2 + 31/2*e - 1/2', '-2*e^5 - 4*e^4 + 24*e^3 + 25*e^2 - 50*e - 29', '2*e^5 - 25*e^3 + 31*e^2 + 23*e - 39', '3/2*e^5 + 1/2*e^4 - 15*e^3 + 26*e^2 - 5/2*e - 93/2', '-2*e^5 - 2*e^4 + 23*e^3 - 5*e^2 - 23*e + 5', '-9/2*e^5 - 13/2*e^4 + 57*e^3 + 25*e^2 - 233/2*e - 113/2', '1/4*e^5 - 15/4*e^4 - 17/2*e^3 + 83/2*e^2 + 5/4*e - 211/4', '-2*e^5 - 3*e^4 + 25*e^3 + 16*e^2 - 37*e - 53', '-7/2*e^5 - 11/2*e^4 + 42*e^3 + 19*e^2 - 177/2*e - 67/2', '11/2*e^5 + 17/2*e^4 - 65*e^3 - 28*e^2 + 247/2*e + 79/2', '7/4*e^5 - 5/4*e^4 - 49/2*e^3 + 77/2*e^2 + 119/4*e - 201/4', '13/4*e^5 + 9/4*e^4 - 91/2*e^3 + 7/2*e^2 + 365/4*e + 77/4', '3/2*e^5 + 3/2*e^4 - 20*e^3 + 2*e^2 + 85/2*e - 7/2', '-3/4*e^5 - 11/4*e^4 + 13/2*e^3 + 37/2*e^2 - 95/4*e - 31/4', '6*e^5 + 8*e^4 - 74*e^3 - 28*e^2 + 126*e + 78', '-27/4*e^5 - 47/4*e^4 + 80*e^3 + 56*e^2 - 629/4*e - 385/4', '5/4*e^5 + 5/4*e^4 - 14*e^3 + 5*e^2 + 83/4*e - 81/4', '9/4*e^5 + 19/4*e^4 - 24*e^3 - 29*e^2 + 131/4*e + 229/4', '-23/4*e^5 - 39/4*e^4 + 137/2*e^3 + 83/2*e^2 - 547/4*e - 255/4', '-e^5 + e^4 + 11*e^3 - 32*e^2 + 12*e + 55', '-1/4*e^5 + 3/4*e^4 + 3*e^3 - 14*e^2 + 53/4*e + 149/4', 'e^5 + 7/2*e^4 - 8*e^3 - 27*e^2 + 8*e + 49/2', '-1/2*e^5 - 1/2*e^4 + 7*e^3 + 4*e^2 - 17/2*e - 67/2', '3/4*e^5 + 9/4*e^4 - 9*e^3 - 17*e^2 + 125/4*e + 71/4', '-2*e^5 - 4*e^4 + 24*e^3 + 17*e^2 - 64*e - 11', '-3*e^5 - 4*e^4 + 40*e^3 + 20*e^2 - 89*e - 42', '-3*e^5 - 8*e^4 + 31*e^3 + 56*e^2 - 64*e - 104', '7*e^5 + 23/2*e^4 - 85*e^3 - 56*e^2 + 157*e + 247/2', '1/2*e^5 - 3/2*e^4 - 10*e^3 + 21*e^2 + 51/2*e - 71/2', '5*e^5 + 9*e^4 - 58*e^3 - 44*e^2 + 109*e + 81', '-1/2*e^5 - 3/2*e^4 + 7*e^3 + 12*e^2 - 49/2*e - 9/2', '13/2*e^5 + 21/2*e^4 - 75*e^3 - 36*e^2 + 265/2*e + 91/2', '3*e^5 + 6*e^4 - 35*e^3 - 33*e^2 + 70*e + 65', 'e^5 - 15*e^3 + 14*e^2 + 40*e - 26', '9/4*e^5 + 9/4*e^4 - 51/2*e^3 + 15/2*e^2 + 97/4*e - 99/4', '21/4*e^5 + 41/4*e^4 - 115/2*e^3 - 103/2*e^2 + 393/4*e + 341/4', '-21/4*e^5 - 25/4*e^4 + 64*e^3 + 6*e^2 - 395/4*e - 95/4', '-25/4*e^5 - 53/4*e^4 + 75*e^3 + 93*e^2 - 643/4*e - 743/4', '3/2*e^5 + 3*e^4 - 21*e^3 - 24*e^2 + 117/2*e + 58', '17/4*e^5 + 33/4*e^4 - 51*e^3 - 47*e^2 + 507/4*e + 291/4', '-1/2*e^5 + 1/2*e^4 + 6*e^3 - 16*e^2 + 13/2*e + 23/2', '-2*e^5 - 2*e^4 + 25*e^3 - 2*e^2 - 39*e + 12', '-11/2*e^5 - 17/2*e^4 + 60*e^3 + 16*e^2 - 181/2*e + 5/2', '5*e^5 + 7*e^4 - 62*e^3 - 23*e^2 + 115*e + 36', '2*e^5 + 5*e^4 - 22*e^3 - 31*e^2 + 52*e + 20', '-2*e^5 - 2*e^4 + 25*e^3 - 45*e + 10', '-3/4*e^5 + 5/4*e^4 + 29/2*e^3 - 27/2*e^2 - 143/4*e + 17/4', '8*e^5 + 16*e^4 - 94*e^3 - 96*e^2 + 190*e + 182', '-11/2*e^5 - 21/2*e^4 + 65*e^3 + 56*e^2 - 275/2*e - 175/2', '3/2*e^5 + 7/2*e^4 - 16*e^3 - 18*e^2 + 53/2*e + 13/2', '5/4*e^5 + 17/4*e^4 - 17/2*e^3 - 53/2*e^2 - 31/4*e + 173/4', '3/2*e^5 + 3/2*e^4 - 20*e^3 + 97/2*e + 1/2', '4*e^5 + 4*e^4 - 52*e^3 + 96*e + 24', '-1/4*e^5 + 3/4*e^4 + 3/2*e^3 - 37/2*e^2 + 51/4*e + 55/4', '2*e^5 + 5/2*e^4 - 23*e^3 - 2*e^2 + 20*e + 13/2', '17/2*e^5 + 23/2*e^4 - 105*e^3 - 40*e^2 + 381/2*e + 189/2', '-7/4*e^5 - 5/4*e^4 + 17*e^3 - 22*e^2 - 9/4*e + 209/4', '-7/4*e^5 - 13/4*e^4 + 18*e^3 + 15*e^2 - 85/4*e - 219/4', '-7*e^5 - 8*e^4 + 83*e^3 + 2*e^2 - 122*e - 14', '-e^5 + 15*e^3 - 12*e^2 - 32*e + 46', '-5/2*e^5 + 1/2*e^4 + 34*e^3 - 38*e^2 - 115/2*e + 79/2', '5/2*e^5 + 19/2*e^4 - 20*e^3 - 71*e^2 + 83/2*e + 147/2', '-7/2*e^5 - 6*e^4 + 41*e^3 + 28*e^2 - 137/2*e - 59', '9/2*e^5 + 5/2*e^4 - 61*e^3 + 17*e^2 + 209/2*e + 25/2', '-8*e^5 - 11*e^4 + 100*e^3 + 40*e^2 - 196*e - 83', '7*e^5 + 11*e^4 - 86*e^3 - 50*e^2 + 165*e + 105', '6*e^5 + 12*e^4 - 64*e^3 - 52*e^2 + 110*e + 58', '-3/4*e^5 + 5/4*e^4 + 29/2*e^3 - 37/2*e^2 - 147/4*e - 7/4', '3/2*e^5 + 5/2*e^4 - 18*e^3 - 10*e^2 + 65/2*e + 15/2', '3*e^5 + e^4 - 44*e^3 + 14*e^2 + 81*e + 5', '-e^5 + e^4 + 9*e^3 - 40*e^2 + 14*e + 81', '27/4*e^5 + 37/4*e^4 - 78*e^3 - 16*e^2 + 465/4*e + 135/4', '3/4*e^5 + 3/4*e^4 - 15/2*e^3 + 13/2*e^2 + 55/4*e - 97/4', '13/2*e^5 + 19/2*e^4 - 74*e^3 - 22*e^2 + 231/2*e + 125/2', '-15/2*e^5 - 17/2*e^4 + 93*e^3 + 11*e^2 - 331/2*e - 125/2', '1/4*e^5 - 9/4*e^4 - 10*e^3 + 24*e^2 + 147/4*e - 131/4', '11/2*e^5 + 31/2*e^4 - 61*e^3 - 124*e^2 + 303/2*e + 389/2', '-9/4*e^5 - 5/4*e^4 + 61/2*e^3 - 23/2*e^2 - 245/4*e - 49/4', '-3*e^5 - 1/2*e^4 + 44*e^3 - 15*e^2 - 82*e - 51/2', '3/4*e^5 + 9/4*e^4 - 12*e^3 - 26*e^2 + 161/4*e + 139/4', '5*e^5 + 7*e^4 - 59*e^3 - 15*e^2 + 106*e + 52', '9/2*e^5 + 25/2*e^4 - 49*e^3 - 90*e^2 + 221/2*e + 239/2', '5*e^5 + 9*e^4 - 63*e^3 - 52*e^2 + 140*e + 67', '1/2*e^5 - 3/2*e^4 - 9*e^3 + 18*e^2 + 13/2*e - 9/2', '11*e^5 + 18*e^4 - 133*e^3 - 83*e^2 + 262*e + 153', '-31/4*e^5 - 53/4*e^4 + 91*e^3 + 61*e^2 - 649/4*e - 443/4', '19/4*e^5 + 19/4*e^4 - 117/2*e^3 + 19/2*e^2 + 415/4*e - 41/4', '17/2*e^5 + 37/2*e^4 - 95*e^3 - 110*e^2 + 377/2*e + 407/2', '-e^5 + 15*e^3 - 14*e^2 - 34*e + 26', '-e^5 - 5*e^4 + 10*e^3 + 48*e^2 - 37*e - 37', '-13/4*e^5 - 29/4*e^4 + 32*e^3 + 32*e^2 - 179/4*e - 211/4', '5*e^5 + 25/2*e^4 - 53*e^3 - 82*e^2 + 107*e + 265/2', '7/2*e^5 + 3/2*e^4 - 48*e^3 + 17*e^2 + 169/2*e + 31/2', '-7/2*e^5 + 1/2*e^4 + 50*e^3 - 43*e^2 - 177/2*e + 69/2', '7/4*e^5 + 3/4*e^4 - 47/2*e^3 + 21/2*e^2 + 211/4*e + 63/4', '-2*e^5 + 28*e^3 - 22*e^2 - 54*e + 10', '-1/2*e^5 - 5/2*e^4 + e^3 + 14*e^2 + 19/2*e + 5/2', '31/4*e^5 + 53/4*e^4 - 89*e^3 - 56*e^2 + 625/4*e + 375/4', '3/4*e^5 - 1/4*e^4 - 11*e^3 + 15*e^2 + 121/4*e - 131/4', '1/2*e^5 - 2*e^4 - 8*e^3 + 33*e^2 - 7/2*e - 20', '13/2*e^5 + 23/2*e^4 - 74*e^3 - 53*e^2 + 251/2*e + 223/2', '9/2*e^5 + 13/2*e^4 - 52*e^3 - 13*e^2 + 175/2*e + 61/2', '-9/2*e^5 - 23/2*e^4 + 48*e^3 + 76*e^2 - 191/2*e - 225/2', '-5/2*e^5 - 21/2*e^4 + 23*e^3 + 93*e^2 - 137/2*e - 269/2', '15/2*e^5 + 25/2*e^4 - 89*e^3 - 57*e^2 + 363/2*e + 229/2', 'e^5 - 2*e^4 - 18*e^3 + 28*e^2 + 29*e - 44', '9/2*e^5 + 9*e^4 - 52*e^3 - 53*e^2 + 213/2*e + 93', '1/4*e^5 + 7/4*e^4 - 3*e^3 - 20*e^2 + 47/4*e + 157/4', '15/2*e^5 + 23/2*e^4 - 90*e^3 - 45*e^2 + 329/2*e + 267/2', '-11/4*e^5 - 15/4*e^4 + 63/2*e^3 + 11/2*e^2 - 143/4*e - 67/4', '8*e^5 + 31/2*e^4 - 94*e^3 - 91*e^2 + 189*e + 309/2', '31/4*e^5 + 51/4*e^4 - 96*e^3 - 62*e^2 + 801/4*e + 453/4', '-7/2*e^5 - 17/2*e^4 + 39*e^3 + 55*e^2 - 175/2*e - 149/2', '-3*e^5 - 7/2*e^4 + 40*e^3 + 7*e^2 - 100*e - 13/2', '2*e^4 + 3*e^3 - 14*e^2 + 3*e', '-19/2*e^5 - 39/2*e^4 + 114*e^3 + 123*e^2 - 517/2*e - 407/2', '-53/4*e^5 - 115/4*e^4 + 149*e^3 + 174*e^2 - 1235/4*e - 1177/4', '5/2*e^5 + 4*e^4 - 29*e^3 - 14*e^2 + 111/2*e + 37', '-9*e^5 - 18*e^4 + 102*e^3 + 98*e^2 - 201*e - 184', '7/2*e^5 + 19/2*e^4 - 34*e^3 - 55*e^2 + 129/2*e + 95/2', '9/2*e^5 + 9/2*e^4 - 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197*e^3 - 24*e^2 + 412*e + 75', '-25/4*e^5 - 25/4*e^4 + 155/2*e^3 + 13/2*e^2 - 373/4*e - 177/4', '-37/4*e^5 - 53/4*e^4 + 207/2*e^3 + 61/2*e^2 - 525/4*e - 521/4', '22*e^5 + 30*e^4 - 264*e^3 - 81*e^2 + 422*e + 201', '-2*e^5 - 9*e^4 + 25*e^3 + 102*e^2 - 89*e - 199', '-99/4*e^5 - 193/4*e^4 + 299*e^3 + 284*e^2 - 2629/4*e - 1723/4', '81/4*e^5 + 107/4*e^4 - 250*e^3 - 91*e^2 + 1731/4*e + 1125/4', '-21/4*e^5 - 41/4*e^4 + 61*e^3 + 63*e^2 - 351/4*e - 571/4', '-7*e^5 - 7*e^4 + 86*e^3 - 2*e^2 - 171*e - 55', '19/4*e^5 + 15/4*e^4 - 73*e^3 - 5*e^2 + 737/4*e + 29/4', '-23/4*e^5 - 83/4*e^4 + 149/2*e^3 + 425/2*e^2 - 1083/4*e - 1567/4', '81/4*e^5 + 125/4*e^4 - 497/2*e^3 - 257/2*e^2 + 2069/4*e + 921/4', '10*e^5 + 7*e^4 - 106*e^3 + 103*e^2 + 46*e - 204', '21/4*e^5 + 61/4*e^4 - 103/2*e^3 - 225/2*e^2 + 349/4*e + 857/4', '-11/4*e^5 - 51/4*e^4 + 29*e^3 + 119*e^2 - 409/4*e - 705/4', '27/2*e^5 + 28*e^4 - 144*e^3 - 139*e^2 + 435/2*e + 300', '-15*e^5 - 25*e^4 + 185*e^3 + 139*e^2 - 378*e - 290', '57/4*e^5 + 65/4*e^4 - 169*e^3 - 4*e^2 + 1051/4*e + 159/4', '-1/2*e^5 + 7/2*e^4 + 4*e^3 - 69*e^2 + 157/2*e + 371/2', '-11/2*e^5 - 11/2*e^4 + 79*e^3 + 34*e^2 - 379/2*e - 325/2', '5/4*e^5 - 25/4*e^4 - 28*e^3 + 72*e^2 + 135/4*e - 355/4', '-57/4*e^5 - 129/4*e^4 + 160*e^3 + 213*e^2 - 1287/4*e - 1787/4', '11/2*e^5 + 35/2*e^4 - 39*e^3 - 104*e^2 + 55/2*e + 225/2', '63/4*e^5 + 41/4*e^4 - 208*e^3 + 65*e^2 + 1365/4*e + 15/4', '3/4*e^5 - 45/4*e^4 - 69/2*e^3 + 203/2*e^2 + 303/4*e - 297/4', '-24*e^5 - 42*e^4 + 293*e^3 + 239*e^2 - 609*e - 475', '49/2*e^5 + 81/2*e^4 - 290*e^3 - 201*e^2 + 1031/2*e + 981/2', '9/2*e^5 + 7/2*e^4 - 54*e^3 + 28*e^2 + 187/2*e - 127/2', '-63/2*e^5 - 99/2*e^4 + 368*e^3 + 176*e^2 - 1325/2*e - 609/2', '-73/4*e^5 - 109/4*e^4 + 451/2*e^3 + 217/2*e^2 - 1893/4*e - 853/4', '-41/4*e^5 - 45/4*e^4 + 255/2*e^3 + 3/2*e^2 - 957/4*e - 25/4', '4*e^5 + 7*e^4 - 33*e^3 - 5*e^2 - 39*e - 4', '-73/4*e^5 - 149/4*e^4 + 218*e^3 + 254*e^2 - 1807/4*e - 2003/4', '-17*e^5 - 40*e^4 + 186*e^3 + 235*e^2 - 403*e - 333', '-37/4*e^5 - 65/4*e^4 + 221/2*e^3 + 185/2*e^2 - 713/4*e - 661/4', '3*e^5 - 2*e^4 - 47*e^3 + 53*e^2 + 120*e - 29', '-55/4*e^5 - 29/4*e^4 + 178*e^3 - 82*e^2 - 1205/4*e - 39/4', '-43/4*e^5 - 79/4*e^4 + 134*e^3 + 117*e^2 - 1341/4*e - 829/4', '12*e^5 + 26*e^4 - 154*e^3 - 214*e^2 + 384*e + 442', '-29/2*e^5 - 61/2*e^4 + 166*e^3 + 183*e^2 - 719/2*e - 537/2', '7*e^5 + 8*e^4 - 89*e^3 - 24*e^2 + 180*e + 188', '-6*e^5 + 3*e^4 + 77*e^3 - 133*e^2 - 41*e + 218', '15*e^5 + 36*e^4 - 173*e^3 - 259*e^2 + 424*e + 457', '33/4*e^5 + 81/4*e^4 - 89*e^3 - 123*e^2 + 899/4*e + 531/4', '-17/2*e^5 - 3/2*e^4 + 112*e^3 - 87*e^2 - 339/2*e + 185/2', '9*e^5 + 15*e^4 - 106*e^3 - 62*e^2 + 197*e + 85', '-95/4*e^5 - 175/4*e^4 + 553/2*e^3 + 445/2*e^2 - 2251/4*e - 1627/4', '55/2*e^5 + 93/2*e^4 - 317*e^3 - 192*e^2 + 1155/2*e + 603/2', '11*e^5 + 28*e^4 - 126*e^3 - 220*e^2 + 299*e + 380', '-12*e^5 - 15*e^4 + 141*e^3 + 14*e^2 - 223*e - 63', '47/4*e^5 + 61/4*e^4 - 149*e^3 - 34*e^2 + 1297/4*e + 375/4', '-41/2*e^5 - 29*e^4 + 249*e^3 + 108*e^2 - 919/2*e - 312', '3/2*e^5 + 5/2*e^4 - 20*e^3 - 16*e^2 + 117/2*e + 179/2', '41/4*e^5 + 65/4*e^4 - 123*e^3 - 56*e^2 + 1043/4*e + 255/4', '37/4*e^5 + 33/4*e^4 - 249/2*e^3 - 29/2*e^2 + 1009/4*e + 653/4', '3*e^4 + 13*e^3 - 8*e^2 - 59*e - 59', '-69/4*e^5 - 69/4*e^4 + 214*e^3 + e^2 - 1379/4*e - 487/4', '37/4*e^5 + 65/4*e^4 - 118*e^3 - 82*e^2 + 1219/4*e + 423/4', '-39/2*e^5 - 63/2*e^4 + 232*e^3 + 137*e^2 - 909/2*e - 527/2', '105/4*e^5 + 141/4*e^4 - 641/2*e^3 - 181/2*e^2 + 2333/4*e + 1009/4', '-2*e^4 + 9*e^3 + 48*e^2 - 83*e - 54', '19/2*e^5 + 25/2*e^4 - 112*e^3 - 21*e^2 + 357/2*e + 109/2', '2*e^5 + 33/2*e^4 + 5*e^3 - 116*e^2 - 36*e + 101/2', '21/2*e^5 + 79/2*e^4 - 103*e^3 - 341*e^2 + 605/2*e + 1063/2', '3*e^5 + e^4 - 43*e^3 + 20*e^2 + 74*e - 37', '97/4*e^5 + 137/4*e^4 - 619/2*e^3 - 277/2*e^2 + 2569/4*e + 1093/4', '-9*e^5 - 13*e^4 + 106*e^3 + 16*e^2 - 201*e - 3', '45/2*e^5 + 71/2*e^4 - 260*e^3 - 111*e^2 + 931/2*e + 375/2', '45/4*e^5 + 7/4*e^4 - 160*e^3 + 92*e^2 + 1183/4*e - 275/4', '-53/4*e^5 - 113/4*e^4 + 143*e^3 + 157*e^2 - 1063/4*e - 1099/4', '-23/2*e^5 - 17/2*e^4 + 154*e^3 - 30*e^2 - 649/2*e - 39/2', '-36*e^5 - 68*e^4 + 417*e^3 + 353*e^2 - 849*e - 601', '-21*e^5 - 38*e^4 + 232*e^3 + 147*e^2 - 407*e - 189', '5/2*e^5 + 11/2*e^4 - 39*e^3 - 60*e^2 + 285/2*e + 153/2', '-29/4*e^5 - 37/4*e^4 + 81*e^3 - 15*e^2 - 535/4*e + 505/4', '-111/4*e^5 - 173/4*e^4 + 328*e^3 + 166*e^2 - 2389/4*e - 1223/4', '45/2*e^5 + 105/2*e^4 - 254*e^3 - 344*e^2 + 1131/2*e + 1067/2', '-1/4*e^5 + 23/4*e^4 + 6*e^3 - 77*e^2 + 105/4*e + 725/4', '12*e^5 + 9*e^4 - 160*e^3 + 42*e^2 + 308*e - 25', '41/2*e^5 + 99/2*e^4 - 231*e^3 - 345*e^2 + 1017/2*e + 1243/2', '-10*e^5 - 29*e^4 + 111*e^3 + 224*e^2 - 275*e - 379', '-14*e^5 - 29*e^4 + 158*e^3 + 150*e^2 - 340*e - 155', '85/4*e^5 + 101/4*e^4 - 258*e^3 - 27*e^2 + 1811/4*e + 223/4', '-19/2*e^5 - 43/2*e^4 + 121*e^3 + 158*e^2 - 667/2*e - 573/2', 'e^5 - 5/2*e^4 - 14*e^3 + 47*e^2 + 6*e - 135/2', '13/2*e^5 + 3/2*e^4 - 71*e^3 + 97*e^2 + 33/2*e - 261/2', '-12*e^5 - 22*e^4 + 143*e^3 + 126*e^2 - 271*e - 282', '-3/2*e^5 + 29/2*e^4 + 49*e^3 - 147*e^2 - 167/2*e + 129/2', '-9*e^5 + 2*e^4 + 123*e^3 - 130*e^2 - 128*e + 154', '27/2*e^5 + 51/2*e^4 - 150*e^3 - 123*e^2 + 573/2*e + 463/2', '-15/2*e^5 - 17/2*e^4 + 94*e^3 - 7*e^2 - 361/2*e + 59/2', '-1/4*e^5 - 41/4*e^4 - 8*e^3 + 111*e^2 - 175/4*e - 315/4', '28*e^5 + 44*e^4 - 326*e^3 - 141*e^2 + 560*e + 227', '5*e^5 + 24*e^4 - 45*e^3 - 213*e^2 + 150*e + 271', '-23/4*e^5 - 75/4*e^4 + 67*e^3 + 189*e^2 - 661/4*e - 1393/4', '16*e^5 + 33*e^4 - 197*e^3 - 213*e^2 + 471*e + 334', '-113/4*e^5 - 197/4*e^4 + 691/2*e^3 + 525/2*e^2 - 2829/4*e - 2005/4', '4*e^5 + 5*e^4 - 35*e^3 + 23*e^2 - 29*e - 56', '-43/2*e^5 - 75/2*e^4 + 263*e^3 + 203*e^2 - 1135/2*e - 799/2', 'e^5 - 8*e^3 + 39*e^2 + 11*e - 95', '-9/4*e^5 - 85/4*e^4 - 4*e^3 + 185*e^2 + 57/4*e - 1015/4', '-29/2*e^5 - 55/2*e^4 + 160*e^3 + 132*e^2 - 579/2*e - 449/2', '-15*e^5 - 31*e^4 + 176*e^3 + 206*e^2 - 383*e - 393', '5/4*e^5 + 53/4*e^4 - 11/2*e^3 - 285/2*e^2 + 297/4*e + 565/4', '-21/4*e^5 - 69/4*e^4 + 111/2*e^3 + 257/2*e^2 - 701/4*e - 673/4', '-21*e^5 - 44*e^4 + 245*e^3 + 277*e^2 - 488*e - 517', '-41/4*e^5 - 59/4*e^4 + 129*e^3 + 51*e^2 - 975/4*e - 389/4', '-31/2*e^5 - 18*e^4 + 182*e^3 + 5*e^2 - 531/2*e - 12', '-89/4*e^5 - 143/4*e^4 + 265*e^3 + 150*e^2 - 2047/4*e - 1165/4', '-71/4*e^5 - 139/4*e^4 + 417/2*e^3 + 387/2*e^2 - 1783/4*e - 1223/4', '-12*e^5 - 12*e^4 + 156*e^3 + 4*e^2 - 300*e - 80', '97/4*e^5 + 145/4*e^4 - 294*e^3 - 138*e^2 + 2183/4*e + 1511/4', '57/4*e^5 + 101/4*e^4 - 175*e^3 - 141*e^2 + 1571/4*e + 855/4', '-45/2*e^5 - 71/2*e^4 + 264*e^3 + 142*e^2 - 875/2*e - 609/2', '-14*e^5 - 21*e^4 + 159*e^3 + 43*e^2 - 259*e - 50', '-12*e^5 - 19*e^4 + 131*e^3 + 33*e^2 - 225*e + 52', '23/2*e^5 + 61/2*e^4 - 126*e^3 - 221*e^2 + 617/2*e + 721/2', '-e^5 - 2*e^4 + 7*e^3 - 8*e^2 + 10*e + 34', '3*e^5 + 18*e^4 - 27*e^3 - 187*e^2 + 96*e + 213', '-27*e^5 - 50*e^4 + 317*e^3 + 272*e^2 - 620*e - 582', '-41/2*e^5 - 67/2*e^4 + 256*e^3 + 164*e^2 - 1115/2*e - 581/2', '7/4*e^5 + 57/4*e^4 - 12*e^3 - 161*e^2 + 253/4*e + 983/4', '13/4*e^5 + 35/4*e^4 - 55*e^3 - 104*e^2 + 867/4*e + 673/4', '-49/2*e^5 - 105/2*e^4 + 279*e^3 + 308*e^2 - 1161/2*e - 943/2', '-15/4*e^5 + 9/4*e^4 + 121/2*e^3 - 93/2*e^2 - 415/4*e - 331/4', '-35/2*e^5 - 41/2*e^4 + 214*e^3 + 37*e^2 - 697/2*e - 337/2', '131/4*e^5 + 263/4*e^4 - 377*e^3 - 361*e^2 + 3201/4*e + 2293/4', '-35/4*e^5 - 75/4*e^4 + 197/2*e^3 + 215/2*e^2 - 707/4*e - 687/4', '9/2*e^5 + 33/2*e^4 - 45*e^3 - 155*e^2 + 133/2*e + 553/2', '43/2*e^5 + 51/2*e^4 - 253*e^3 - 13*e^2 + 771/2*e + 107/2', '-103/4*e^5 - 179/4*e^4 + 315*e^3 + 237*e^2 - 2581/4*e - 1641/4', '41/2*e^5 + 85/2*e^4 - 244*e^3 - 280*e^2 + 1103/2*e + 999/2', '-11/2*e^5 - 15/2*e^4 + 73*e^3 + 26*e^2 - 379/2*e + 35/2', '-15/4*e^5 - 67/4*e^4 + 41/2*e^3 + 245/2*e^2 - 43/4*e - 583/4', '45/4*e^5 + 89/4*e^4 - 259/2*e^3 - 241/2*e^2 + 1105/4*e + 937/4', '8*e^5 + 5*e^4 - 109*e^3 + 22*e^2 + 231*e + 9', '3*e^5 - 7*e^4 - 44*e^3 + 121*e^2 - 3*e - 232', '-13*e^5 - 17*e^4 + 152*e^3 + 35*e^2 - 207*e - 142', '-11*e^5 - 47/2*e^4 + 128*e^3 + 163*e^2 - 256*e - 549/2', '29/4*e^5 + 61/4*e^4 - 77*e^3 - 76*e^2 + 439/4*e + 499/4', '-9/2*e^5 - 15/2*e^4 + 42*e^3 + 7*e^2 - 59/2*e - 63/2', '12*e^5 + 28*e^4 - 128*e^3 - 168*e^2 + 272*e + 202', '-77/4*e^5 - 157/4*e^4 + 447/2*e^3 + 485/2*e^2 - 1861/4*e - 1617/4', '11*e^5 + 16*e^4 - 125*e^3 - 25*e^2 + 212*e - 49', '-6*e^4 - 17*e^3 + 41*e^2 + 49*e - 27', '-21/2*e^5 - 47/2*e^4 + 127*e^3 + 169*e^2 - 617/2*e - 667/2', '-5/2*e^5 - 5*e^4 + 42*e^3 + 51*e^2 - 289/2*e - 21', '-3/4*e^5 - 3/4*e^4 + 11*e^3 - 18*e^2 - 137/4*e + 507/4', '-93/4*e^5 - 155/4*e^4 + 281*e^3 + 181*e^2 - 2379/4*e - 1165/4', '11/2*e^5 + 8*e^4 - 67*e^3 - 32*e^2 + 305/2*e + 117', '3*e^5 + 11/2*e^4 - 34*e^3 - 31*e^2 + 58*e + 105/2', '85/4*e^5 + 129/4*e^4 - 499/2*e^3 - 209/2*e^2 + 1561/4*e + 849/4', '-16*e^5 - 28*e^4 + 189*e^3 + 127*e^2 - 401*e - 189', '3*e^5 + 3*e^4 - 23*e^3 + 32*e^2 - 54*e - 47', '8*e^5 + e^4 - 105*e^3 + 86*e^2 + 99*e - 123', '-33/2*e^5 - 26*e^4 + 207*e^3 + 116*e^2 - 903/2*e - 229', '10*e^5 + 47/2*e^4 - 108*e^3 - 125*e^2 + 215*e + 93/2', '-26*e^5 - 53*e^4 + 300*e^3 + 313*e^2 - 596*e - 572', '-49/4*e^5 - 97/4*e^4 + 307/2*e^3 + 345/2*e^2 - 1513/4*e - 1221/4', '65/4*e^5 + 105/4*e^4 - 407/2*e^3 - 233/2*e^2 + 1857/4*e + 589/4', '-5*e^5 - 19*e^4 + 44*e^3 + 157*e^2 - 109*e - 240'], 'hecke_polynomial': 'x^6 - 15*x^4 + 12*x^3 + 39*x^2 - 24*x - 29', 'label': '2.2.5.1-401.1-b'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 5, 'ideals': ['[1, 1, 1]', '[4, 2, 2]', '[5, 5, -2*w + 1]', '[9, 3, 3]', '[11, 11, -3*w + 2]', '[11, 11, -3*w + 1]', '[16, 4, 4]', '[19, 19, -4*w + 3]', '[19, 19, -4*w + 1]', '[20, 10, -4*w + 2]', '[25, 5, 5]', '[29, 29, w + 5]', '[29, 29, -w + 6]', '[31, 31, -5*w + 2]', '[31, 31, -5*w + 3]', '[36, 6, 6]', '[41, 41, -6*w + 5]', '[41, 41, w - 7]', '[44, 22, -6*w + 4]', '[44, 22, -6*w + 2]', '[45, 15, -6*w + 3]', '[49, 7, -7]', '[55, 55, w + 7]', '[55, 55, -w + 8]', '[59, 59, 2*w - 9]', '[59, 59, 7*w - 5]', '[61, 61, 3*w - 10]', '[61, 61, -3*w - 7]', '[64, 8, 8]', '[71, 71, -8*w + 7]', '[71, 71, w - 9]', '[76, 38, -8*w + 6]', '[76, 38, -8*w + 2]', '[79, 79, 8*w - 5]', '[79, 79, 3*w - 11]', '[80, 20, -8*w + 4]', '[81, 9, 9]', '[89, 89, -10*w - 1]', '[89, 89, 10*w - 11]', '[95, 95, -2*w + 11]', '[95, 95, 2*w + 9]', '[99, 33, -9*w + 6]', '[99, 33, -9*w + 3]', '[100, 10, 10]', '[101, 101, 4*w - 13]', '[101, 101, 5*w - 14]', '[109, 109, -11*w - 1]', '[109, 109, 11*w - 12]', '[116, 58, 2*w + 10]', '[116, 58, -2*w + 12]', '[121, 11, 11]', '[121, 121, -10*w + 3]', '[121, 121, -10*w + 7]', '[124, 62, -10*w + 4]', '[124, 62, -10*w + 6]', '[125, 25, -10*w + 5]', '[131, 131, -12*w - 1]', '[131, 131, 12*w - 13]', '[139, 139, 2*w - 13]', '[139, 139, -11*w + 9]', '[144, 12, 12]', '[145, 145, -11*w + 8]', '[145, 145, -11*w + 3]', '[149, 149, 7*w - 18]', '[149, 149, 4*w - 15]', '[151, 151, 5*w - 16]', '[151, 151, 6*w - 17]', '[155, 155, w + 12]', '[155, 155, -w + 13]', '[164, 82, -12*w + 10]', '[164, 82, 2*w - 14]', '[169, 13, -13]', '[171, 57, -12*w + 9]', '[171, 57, -12*w + 3]', '[176, 44, -12*w + 8]', '[176, 44, -12*w + 4]', '[179, 179, 7*w - 19]', '[179, 179, 5*w - 17]', '[180, 30, -12*w + 6]', '[181, 181, -14*w - 1]', '[181, 181, 14*w - 15]', '[191, 191, 2*w - 15]', '[191, 191, -13*w + 11]', '[196, 14, -14]', '[199, 199, 3*w - 16]', '[199, 199, -13*w + 10]', '[205, 205, -4*w + 17]', '[205, 205, 13*w - 9]', '[209, 209, w + 14]', '[209, 209, -13*w + 5]', '[209, 209, -13*w + 8]', '[209, 209, -w + 15]', '[211, 211, 6*w - 19]', '[211, 211, 7*w - 20]', '[220, 110, 2*w + 14]', '[220, 110, -2*w + 16]', '[225, 15, 15]', '[229, 229, -14*w + 11]', '[229, 229, 3*w - 17]', '[236, 118, 4*w - 18]', '[236, 118, 14*w - 10]', '[239, 239, -16*w - 1]', '[239, 239, 16*w - 17]', '[241, 241, 9*w - 23]', '[241, 241, 5*w - 19]', '[244, 122, 6*w - 20]', '[244, 122, -6*w - 14]', '[245, 35, 14*w - 7]', '[251, 251, 2*w - 17]', '[251, 251, -15*w + 13]', '[256, 16, 16]', '[261, 87, 3*w + 15]', '[261, 87, -3*w + 18]', '[269, 269, 15*w - 11]', '[269, 269, 4*w - 19]', '[271, 271, -17*w - 1]', '[271, 271, 17*w - 18]', '[275, 55, -15*w + 10]', '[275, 55, -15*w + 5]', '[279, 93, -15*w + 6]', '[279, 93, -15*w + 9]', '[281, 281, 7*w - 22]', '[281, 281, 8*w - 23]', '[284, 142, -16*w + 14]', '[284, 142, 2*w - 18]', '[289, 17, -17]', '[295, 295, 3*w - 19]', '[295, 295, 16*w - 13]', '[304, 76, -16*w + 12]', '[304, 76, -16*w + 4]', '[305, 305, 17*w - 16]', '[305, 305, 17*w - 1]', '[311, 311, 5*w - 21]', '[311, 311, 16*w - 11]', '[316, 158, 16*w - 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81]', '[6079, 6079, -79*w - 2]', '[6089, 6089, 41*w - 111]', '[6089, 6089, 29*w - 99]', '[6091, 6091, 21*w - 92]', '[6091, 6091, 71*w - 50]', '[6101, 6101, 82*w - 89]', '[6101, 6101, -82*w - 7]', '[6121, 6121, 37*w - 107]', '[6121, 6121, 33*w - 103]', '[6131, 6131, 81*w - 86]', '[6131, 6131, -81*w - 5]', '[6151, 6151, -80*w - 3]', '[6151, 6151, 80*w - 83]', '[6199, 6199, 15*w - 88]', '[6199, 6199, -73*w + 58]', '[6211, 6211, 26*w - 97]', '[6211, 6211, 45*w - 116]', '[6221, 6221, 81*w - 85]', '[6221, 6221, -81*w - 4]', '[6229, 6229, 27*w - 98]', '[6229, 6229, 44*w - 115]', '[6269, 6269, 13*w - 87]', '[6269, 6269, -74*w + 61]', '[6271, 6271, 30*w - 101]', '[6271, 6271, 41*w - 112]', '[6299, 6299, 37*w - 108]', '[6299, 6299, 34*w - 105]', '[6301, 6301, 35*w - 106]', '[6301, 6301, 36*w - 107]', '[6311, 6311, 23*w - 95]', '[6311, 6311, 49*w - 121]', '[6329, 6329, 86*w - 97]', '[6329, 6329, -86*w - 11]', '[6359, 6359, 25*w - 97]', '[6359, 6359, 47*w - 119]', '[6361, 6361, -74*w + 59]', '[6361, 6361, 15*w - 89]', '[6379, 6379, -85*w - 9]', '[6379, 6379, 85*w - 94]', '[6389, 6389, 73*w - 53]', '[6389, 6389, 20*w - 93]', '[6421, 6421, 73*w - 52]', '[6421, 6421, 21*w - 94]', '[6449, 6449, 83*w - 88]', '[6449, 6449, -83*w - 5]', '[6451, 6451, 73*w - 51]', '[6451, 6451, 22*w - 95]', '[6469, 6469, 82*w - 85]', '[6469, 6469, -82*w - 3]', '[6481, 6481, -85*w - 8]', '[6481, 6481, 85*w - 93]', '[6491, 6491, -87*w - 11]', '[6491, 6491, 87*w - 98]', '[6521, 6521, 19*w - 93]', '[6521, 6521, 74*w - 55]', '[6529, 6529, 25*w - 98]', '[6529, 6529, 48*w - 121]', '[6551, 6551, 26*w - 99]', '[6551, 6551, 47*w - 120]', '[6569, 6569, 16*w - 91]', '[6569, 6569, -75*w + 59]', '[6571, 6571, 27*w - 100]', '[6571, 6571, 46*w - 119]', '[6581, 6581, 85*w - 92]', '[6581, 6581, -85*w - 7]', '[6599, 6599, 87*w - 97]', '[6599, 6599, -87*w - 10]', '[6619, 6619, 30*w - 103]', '[6619, 6619, 43*w - 116]', '[6659, 6659, 35*w - 108]', '[6659, 6659, 38*w - 111]', '[6661, 6661, 36*w - 109]', '[6661, 6661, 37*w - 110]', '[6679, 6679, 85*w - 91]', '[6679, 6679, -85*w - 6]', '[6689, 6689, 75*w - 56]', '[6689, 6689, 19*w - 94]', '[6691, 6691, 15*w - 91]', '[6691, 6691, -76*w + 61]', '[6701, 6701, 49*w - 123]', '[6701, 6701, 25*w - 99]', '[6709, 6709, 89*w - 101]', '[6709, 6709, -89*w - 12]', '[6719, 6719, 83*w - 85]', '[6719, 6719, -83*w - 2]', '[6761, 6761, -77*w + 64]', '[6761, 6761, 13*w - 90]', '[6779, 6779, -76*w + 59]', '[6779, 6779, 17*w - 93]', '[6781, 6781, 45*w - 119]', '[6781, 6781, 29*w - 103]', '[6791, 6791, 22*w - 97]', '[6791, 6791, 75*w - 53]', '[6829, 6829, 41*w - 115]', '[6829, 6829, 33*w - 107]', '[6841, 6841, 35*w - 109]', '[6841, 6841, 39*w - 113]', '[6869, 6869, 85*w - 89]', '[6869, 6869, -85*w - 4]', '[6871, 6871, 88*w - 97]', '[6871, 6871, -88*w - 9]', '[6889, 83, -83]', '[6899, 6899, 49*w - 124]', '[6899, 6899, 26*w - 101]', '[6911, 6911, -87*w - 7]', '[6911, 6911, 87*w - 94]', '[6949, 6949, 17*w - 94]', '[6949, 6949, -77*w + 60]', '[6959, 6959, 29*w - 104]', '[6959, 6959, 46*w - 121]', '[6961, 6961, 85*w - 88]', '[6961, 6961, -85*w - 3]', '[6971, 6971, -84*w - 1]', '[6971, 6971, 84*w - 85]', '[6991, 6991, -77*w + 59]', '[6991, 6991, 18*w - 95]', '[7001, 7001, 32*w - 107]', '[7001, 7001, 43*w - 118]', '[7019, 7019, 34*w - 109]', '[7019, 7019, 41*w - 116]', '[7039, 7039, -89*w - 9]', '[7039, 7039, 89*w - 98]', '[7069, 7069, 77*w - 57]', '[7069, 7069, 20*w - 97]', '[7079, 7079, 88*w - 95]', '[7079, 7079, -88*w - 7]', '[7109, 7109, -87*w - 5]', '[7109, 7109, 87*w - 92]', '[7121, 7121, -78*w + 61]', '[7121, 7121, 17*w - 95]', '[7129, 7129, -86*w - 3]', '[7129, 7129, 86*w - 89]', '[7151, 7151, -79*w + 65]', '[7151, 7151, 14*w - 93]', '[7159, 7159, 91*w - 102]', '[7159, 7159, -91*w - 11]', '[7211, 7211, 35*w - 111]', '[7211, 7211, 41*w - 117]', '[7219, 7219, 39*w - 115]', '[7219, 7219, 37*w - 113]', '[7229, 7229, 52*w - 129]', '[7229, 7229, 25*w - 102]', '[7309, 7309, -86*w - 1]', '[7309, 7309, 86*w - 87]', '[7321, 7321, 48*w - 125]', '[7321, 7321, 29*w - 106]', '[7331, 7331, 92*w - 103]', '[7331, 7331, -92*w - 11]', '[7349, 7349, 78*w - 55]', '[7349, 7349, 23*w - 101]', '[7351, 7351, -89*w - 6]', '[7351, 7351, 89*w - 95]', '[7369, 7369, 32*w - 109]', '[7369, 7369, 45*w - 122]', '[7411, 7411, 38*w - 115]', '[7411, 7411, 39*w - 116]', '[7451, 7451, -89*w - 5]', '[7451, 7451, 89*w - 94]', '[7459, 7459, 21*w - 100]', '[7459, 7459, 79*w - 58]', '[7481, 7481, -87*w - 1]', '[7481, 7481, 87*w - 88]', '[7489, 7489, 91*w - 99]', '[7489, 7489, -91*w - 8]', '[7499, 7499, -81*w + 67]', '[7499, 7499, 14*w - 95]', '[7529, 7529, 23*w - 102]', '[7529, 7529, 79*w - 56]', '[7541, 7541, 31*w - 109]', '[7541, 7541, 47*w - 125]', '[7549, 7549, 89*w - 93]', '[7549, 7549, -89*w - 4]', '[7559, 7559, 19*w - 99]', '[7559, 7559, 80*w - 61]', '[7561, 7561, 24*w - 103]', '[7561, 7561, 79*w - 55]', '[7589, 7589, 43*w - 121]', '[7589, 7589, 35*w - 113]', '[7591, 7591, 54*w - 133]', '[7591, 7591, 25*w - 104]', '[7621, 7621, -95*w - 13]', '[7621, 7621, 95*w - 108]', '[7639, 7639, 21*w - 101]', '[7639, 7639, 80*w - 59]', '[7649, 7649, 17*w - 98]', '[7649, 7649, -81*w + 64]', '[7669, 7669, 28*w - 107]', '[7669, 7669, 51*w - 130]', '[7681, 7681, 94*w - 105]', '[7681, 7681, -94*w - 11]', '[7691, 7691, 50*w - 129]', '[7691, 7691, 29*w - 108]', '[7699, 7699, 91*w - 97]', '[7699, 7699, -91*w - 6]', '[7741, 7741, -95*w - 12]', '[7741, 7741, 95*w - 107]', '[7759, 7759, 46*w - 125]', '[7759, 7759, 33*w - 112]', '[7789, 7789, 43*w - 122]', '[7789, 7789, 36*w - 115]', '[7829, 7829, -82*w + 65]', '[7829, 7829, 17*w - 99]', '[7841, 7841, -93*w - 8]', '[7841, 7841, 93*w - 101]', '[7879, 7879, 29*w - 109]', '[7879, 7879, 51*w - 131]', '[7901, 7901, -91*w - 4]', '[7901, 7901, 91*w - 95]', '[7919, 7919, 49*w - 129]', '[7919, 7919, 31*w - 111]', '[7949, 7949, -93*w - 7]', '[7949, 7949, 93*w - 100]', '[7951, 7951, 47*w - 127]', '[7951, 7951, 33*w - 113]', '[8009, 8009, -90*w - 1]', '[8009, 8009, 90*w - 91]', '[8011, 8011, 17*w - 100]', '[8011, 8011, -83*w + 66]', '[8039, 8039, -96*w - 11]', '[8039, 8039, 96*w - 107]', '[8059, 8059, 18*w - 101]', '[8059, 8059, -83*w + 65]', '[8069, 8069, 52*w - 133]', '[8069, 8069, 29*w - 110]', '[8081, 8081, 82*w - 59]', '[8081, 8081, 23*w - 105]', '[8089, 8089, 95*w - 104]', '[8089, 8089, -95*w - 9]', '[8101, 8101, 97*w - 109]', '[8101, 8101, -97*w - 12]', '[8111, 8111, 50*w - 131]', '[8111, 8111, 31*w - 112]', '[8161, 8161, 98*w - 111]', '[8161, 8161, -98*w - 13]', '[8171, 8171, 35*w - 116]', '[8171, 8171, 46*w - 127]', '[8179, 8179, -92*w - 3]', '[8179, 8179, 92*w - 95]', '[8191, 8191, 83*w - 62]', '[8191, 8191, 21*w - 104]', '[8209, 8209, 27*w - 109]', '[8209, 8209, 55*w - 137]', '[8219, 8219, 14*w - 99]', '[8219, 8219, -85*w + 71]', '[8221, 8221, 97*w - 108]', '[8221, 8221, -97*w - 11]', '[8231, 8231, 83*w - 61]', '[8231, 8231, 22*w - 105]', '[8269, 8269, 23*w - 106]', '[8269, 8269, 83*w - 60]', '[8291, 8291, -84*w + 65]', '[8291, 8291, 19*w - 103]', '[8311, 8311, 95*w - 102]', '[8311, 8311, -95*w - 7]', '[8329, 8329, -85*w + 69]', '[8329, 8329, 16*w - 101]', '[8369, 8369, 35*w - 117]', '[8369, 8369, 47*w - 129]', '[8389, 8389, 37*w - 119]', '[8389, 8389, 45*w - 127]', '[8419, 8419, -95*w - 6]', '[8419, 8419, 95*w - 101]', '[8429, 8429, 55*w - 138]', '[8429, 8429, 28*w - 111]', '[8431, 8431, 18*w - 103]', '[8431, 8431, -85*w + 67]', '[8461, 8461, -86*w + 71]', '[8461, 8461, 15*w - 101]', '[8501, 8501, 31*w - 114]', '[8501, 8501, 52*w - 135]', '[8521, 8521, 51*w - 134]', '[8521, 8521, 32*w - 115]', '[8539, 8539, 33*w - 116]', '[8539, 8539, 50*w - 133]', '[8581, 8581, 47*w - 130]', '[8581, 8581, 36*w - 119]', '[8599, 8599, 38*w - 121]', '[8599, 8599, 45*w - 128]', '[8609, 8609, 43*w - 126]', '[8609, 8609, 40*w - 123]', '[8629, 8629, -95*w - 4]', '[8629, 8629, 95*w - 99]', '[8641, 8641, -98*w - 9]', '[8641, 8641, 98*w - 107]', '[8669, 8669, 19*w - 105]', '[8669, 8669, -86*w + 67]', '[8681, 8681, -97*w - 7]', '[8681, 8681, 97*w - 104]', '[8689, 8689, 85*w - 61]', '[8689, 8689, 24*w - 109]', '[8699, 8699, 53*w - 137]', '[8699, 8699, 31*w - 115]', '[8719, 8719, 101*w - 114]', '[8719, 8719, -101*w - 13]', '[8731, 8731, -95*w - 3]', '[8731, 8731, 95*w - 98]', '[8741, 8741, -94*w - 1]', '[8741, 8741, 94*w - 95]', '[8761, 8761, 86*w - 65]', '[8761, 8761, 21*w - 107]', '[8779, 8779, 100*w - 111]', '[8779, 8779, -100*w - 11]', '[8819, 8819, 43*w - 127]', '[8819, 8819, 41*w - 125]', '[8821, 8821, 28*w - 113]', '[8821, 8821, 57*w - 142]', '[8831, 8831, 95*w - 97]', '[8831, 8831, -95*w - 2]', '[8839, 8839, 15*w - 103]', '[8839, 8839, -88*w + 73]', '[8849, 8849, 29*w - 114]', '[8849, 8849, 56*w - 141]', '[8861, 8861, 19*w - 106]', '[8861, 8861, -87*w + 68]', '[8929, 8929, -95*w - 1]', '[8929, 8929, 95*w - 96]', '[8941, 8941, 33*w - 118]', '[8941, 8941, 52*w - 137]', '[8951, 8951, 17*w - 105]', '[8951, 8951, -88*w + 71]', '[8969, 8969, -101*w - 11]', '[8969, 8969, 101*w - 112]', '[8971, 8971, 103*w - 117]', '[8971, 8971, -103*w - 14]', '[8999, 8999, 87*w - 65]', '[8999, 8999, 22*w - 109]', '[9001, 9001, 48*w - 133]', '[9001, 9001, 37*w - 122]', '[9011, 9011, 38*w - 123]', '[9011, 9011, 47*w - 132]', '[9029, 9029, 41*w - 126]', '[9029, 9029, 44*w - 129]', '[9041, 9041, 23*w - 110]', '[9041, 9041, 87*w - 64]', '[9049, 9049, 57*w - 143]', '[9049, 9049, 29*w - 115]', '[9059, 9059, 99*w - 106]', '[9059, 9059, -99*w - 7]', '[9091, 9091, 101*w - 111]', '[9091, 9091, -101*w - 10]', '[9109, 9109, 97*w - 100]', '[9109, 9109, -97*w - 3]', '[9151, 9151, 88*w - 67]', '[9151, 9151, 21*w - 109]', '[9161, 9161, 102*w - 113]', '[9161, 9161, -102*w - 11]', '[9181, 9181, 35*w - 121]', '[9181, 9181, 51*w - 137]', '[9199, 9199, -89*w + 71]', '[9199, 9199, 18*w - 107]', '[9209, 9209, 49*w - 135]', '[9209, 9209, 37*w - 123]', '[9221, 9221, 59*w - 146]', '[9221, 9221, 28*w - 115]', '[9239, 9239, 88*w - 65]', '[9239, 9239, 23*w - 111]', '[9241, 9241, 45*w - 131]', '[9241, 9241, 41*w - 127]', '[9281, 9281, -99*w - 5]', '[9281, 9281, 99*w - 104]', '[9311, 9311, -97*w - 1]', '[9311, 9311, 97*w - 98]', '[9319, 9319, 25*w - 113]', '[9319, 9319, 88*w - 63]', '[9341, 9341, 17*w - 107]', '[9341, 9341, -90*w + 73]', '[9349, 9349, -89*w + 68]', '[9349, 9349, 21*w - 110]', '[9371, 9371, 34*w - 121]', '[9371, 9371, 53*w - 140]', '[9391, 9391, 27*w - 115]', '[9391, 9391, 88*w - 61]', '[9409, 97, -97]', '[9419, 9419, 50*w - 137]', '[9419, 9419, 37*w - 124]', '[9421, 9421, 106*w - 121]', '[9421, 9421, -106*w - 15]', '[9431, 9431, 38*w - 125]', '[9431, 9431, 49*w - 136]', '[9439, 9439, 89*w - 66]', '[9439, 9439, 23*w - 112]', '[9461, 9461, 43*w - 130]', '[9461, 9461, 44*w - 131]', '[9479, 9479, -103*w - 10]', '[9479, 9479, 103*w - 113]', '[9491, 9491, 105*w - 118]', '[9491, 9491, -105*w - 13]', '[9511, 9511, 31*w - 119]', '[9511, 9511, 57*w - 145]', '[9521, 9521, 25*w - 114]', '[9521, 9521, 89*w - 64]', '[9539, 9539, 17*w - 108]', '[9539, 9539, -91*w + 74]', '[9551, 9551, -104*w - 11]', '[9551, 9551, 104*w - 115]', '[9601, 9601, -103*w - 9]', '[9601, 9601, 103*w - 112]', '[9619, 9619, -107*w - 15]', '[9619, 9619, 107*w - 122]', '[9629, 9629, 61*w - 150]', '[9629, 9629, 28*w - 117]', '[9631, 9631, 37*w - 125]', '[9631, 9631, 51*w - 139]', '[9649, 9649, -91*w + 72]', '[9649, 9649, 19*w - 110]', '[9661, 9661, 60*w - 149]', '[9661, 9661, 29*w - 118]', '[9679, 9679, 45*w - 133]', '[9679, 9679, 43*w - 131]', '[9689, 9689, -106*w - 13]', '[9689, 9689, 106*w - 119]', '[9719, 9719, 58*w - 147]', '[9719, 9719, 31*w - 120]', '[9721, 9721, -103*w - 8]', '[9721, 9721, 103*w - 111]', '[9739, 9739, 17*w - 109]', '[9739, 9739, -92*w + 75]', '[9749, 9749, 105*w - 116]', '[9749, 9749, -105*w - 11]', '[9769, 9769, 56*w - 145]', '[9769, 9769, 33*w - 122]', '[9781, 9781, 101*w - 105]', '[9781, 9781, -101*w - 4]', '[9791, 9791, 34*w - 123]', '[9791, 9791, 55*w - 144]', '[9811, 9811, 54*w - 143]', '[9811, 9811, 35*w - 124]', '[9829, 9829, 36*w - 125]', '[9829, 9829, 53*w - 142]', '[9839, 9839, 103*w - 110]', '[9839, 9839, -103*w - 7]', '[9851, 9851, 19*w - 111]', '[9851, 9851, -92*w + 73]', '[9859, 9859, 38*w - 127]', '[9859, 9859, 51*w - 140]', '[9871, 9871, 50*w - 139]', '[9871, 9871, 39*w - 128]', '[9901, 9901, 44*w - 133]', '[9901, 9901, 45*w - 134]', '[9929, 9929, 31*w - 121]', '[9929, 9929, 59*w - 149]', '[9931, 9931, 25*w - 116]', '[9931, 9931, 91*w - 66]', '[9941, 9941, -93*w + 76]', '[9941, 9941, 17*w - 110]', '[9949, 9949, -106*w - 11]', '[9949, 9949, 106*w - 117]']}
• 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, -1, 1], 'conductor': 5, 'degree': 2, 'dirichlet_group': [1, 4], 'disc_abs': 5, 'disc_rad': 5, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[2, 1]]], [5, [0]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [[2, 1]]], [19, [[1, 2]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[1, 2]]], [37, [[2, 1]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1], 'galois_label': '2T1', 'galt': 1, 'grd': 2.23606797749979, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.5.1', 'local_algs': ['5.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [5], 'rd': 2.2360679775, 'regulator': {'__RealLiteral__': 0, 'data': '0.48121182506', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)'], 'used_grh': False, 'zk': ['1', 'a']}