Hilbert modular form data - 4.4.11525.1-25.3-d

Formats: - HTML - YAML - JSON - 2024-05-03T14:53:01.170564

• 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': 4, 'disc': 11525, 'field_bad_primes': [5, 461], 'field_label': '4.4.11525.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.11525.1-25.3-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [5], 'level_ideal': '[25,5,1/5*w^3 - 1/5*w^2 - 11/5*w + 1]', 'level_label': '25.3', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.3-d', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5,5,1/5*w^3 - 6/5*w^2 - 1/5*w + 4]', -1]], 'hecke_eigenvalues': ['e', 0, '2/5*e^3 - 1/5*e^2 - 19/5*e - 6/5', '-3/5*e^3 + 4/5*e^2 + 31/5*e - 36/5', '2/5*e^3 - 6/5*e^2 - 24/5*e + 34/5', '6/5*e^3 - 8/5*e^2 - 67/5*e + 52/5', '3/5*e^3 - 4/5*e^2 - 31/5*e + 1/5', '-3/5*e^3 + 4/5*e^2 + 26/5*e - 26/5', '-3/5*e^3 + 4/5*e^2 + 31/5*e - 26/5', '-8/5*e^3 + 9/5*e^2 + 96/5*e - 66/5', '-3/5*e^3 - 1/5*e^2 + 31/5*e + 24/5', '2/5*e^3 - 6/5*e^2 - 14/5*e + 34/5', '-2/5*e^3 + 6/5*e^2 + 14/5*e - 29/5', '4/5*e^3 - 2/5*e^2 - 63/5*e + 13/5', '3/5*e^3 - 9/5*e^2 - 16/5*e + 46/5', '2*e^3 - 2*e^2 - 21*e + 14', '-11/5*e^3 + 13/5*e^2 + 102/5*e - 47/5', '12/5*e^3 - 16/5*e^2 - 139/5*e + 99/5', 'e^3 - e^2 - 10*e', '1/5*e^3 + 2/5*e^2 - 32/5*e - 38/5', '-4/5*e^3 + 2/5*e^2 + 48/5*e - 38/5', 'e^2 - 5', '1/5*e^3 + 12/5*e^2 - 17/5*e - 78/5', '-e^3 + 2*e^2 + 11*e - 15', '-11/5*e^3 + 13/5*e^2 + 112/5*e - 77/5', '2/5*e^3 + 9/5*e^2 - 19/5*e - 81/5', '-4/5*e^3 - 3/5*e^2 + 43/5*e + 27/5', '16/5*e^3 - 18/5*e^2 - 172/5*e + 117/5', '-9/5*e^3 + 17/5*e^2 + 93/5*e - 48/5', '-3*e^3 + 4*e^2 + 29*e - 22', '4/5*e^3 - 7/5*e^2 - 58/5*e + 43/5', '13/5*e^3 - 19/5*e^2 - 141/5*e + 106/5', '2*e^3 - 2*e^2 - 19*e + 8', '-8/5*e^3 + 9/5*e^2 + 101/5*e - 36/5', '7/5*e^3 - 16/5*e^2 - 54/5*e + 69/5', '-4*e^3 + 7*e^2 + 38*e - 37', '-9/5*e^3 + 12/5*e^2 + 98/5*e - 98/5', '11/5*e^3 - 23/5*e^2 - 112/5*e + 97/5', '-e^2 + e + 5', '-8/5*e^3 + 14/5*e^2 + 66/5*e - 56/5', '-13/5*e^3 + 24/5*e^2 + 116/5*e - 101/5', '-e^3 + 15*e + 6', '-18/5*e^3 + 24/5*e^2 + 191/5*e - 126/5', '-11/5*e^3 + 13/5*e^2 + 102/5*e - 47/5', '1/5*e^3 - 8/5*e^2 - 17/5*e + 97/5', '-18/5*e^3 + 29/5*e^2 + 191/5*e - 171/5', '19/5*e^3 - 22/5*e^2 - 183/5*e + 63/5', '13/5*e^3 - 4/5*e^2 - 136/5*e + 6/5', '24/5*e^3 - 32/5*e^2 - 248/5*e + 183/5', '13/5*e^3 - 24/5*e^2 - 141/5*e + 106/5', '-14/5*e^3 + 32/5*e^2 + 123/5*e - 188/5', 'e^3 - 2*e^2 - 16*e + 9', '28/5*e^3 - 39/5*e^2 - 286/5*e + 216/5', '13/5*e^3 - 9/5*e^2 - 146/5*e + 81/5', '-1/5*e^3 + 8/5*e^2 + 12/5*e - 12/5', '-4/5*e^3 + 7/5*e^2 + 48/5*e - 83/5', '-12/5*e^3 + 11/5*e^2 + 159/5*e - 104/5', '4*e^3 - 7*e^2 - 43*e + 24', '-18/5*e^3 + 24/5*e^2 + 171/5*e - 51/5', '27/5*e^3 - 41/5*e^2 - 274/5*e + 204/5', '-1/5*e^3 - 7/5*e^2 + 22/5*e + 138/5', '28/5*e^3 - 39/5*e^2 - 301/5*e + 166/5', '17/5*e^3 - 36/5*e^2 - 179/5*e + 169/5', 'e^3 + e^2 - 15*e - 18', '-3/5*e^3 - 1/5*e^2 + 46/5*e - 51/5', '6/5*e^3 - 23/5*e^2 - 62/5*e + 87/5', '13/5*e^3 - 19/5*e^2 - 181/5*e + 141/5', '19/5*e^3 - 17/5*e^2 - 183/5*e + 58/5', 'e^3 - e^2 - 12*e - 1', '-12/5*e^3 + 31/5*e^2 + 119/5*e - 159/5', '-37/5*e^3 + 36/5*e^2 + 394/5*e - 279/5', '-27/5*e^3 + 41/5*e^2 + 259/5*e - 204/5', '-17/5*e^3 + 31/5*e^2 + 159/5*e - 144/5', '1/5*e^3 - 3/5*e^2 + 3/5*e - 53/5', '-4/5*e^3 - 18/5*e^2 + 63/5*e + 52/5', '1/5*e^3 - 8/5*e^2 + 18/5*e + 42/5', '-21/5*e^3 + 23/5*e^2 + 227/5*e - 222/5', '-3/5*e^3 + 4/5*e^2 + 56/5*e - 146/5', '-3*e^3 + e^2 + 31*e - 16', '-1/5*e^3 + 8/5*e^2 - 23/5*e - 32/5', '-24/5*e^3 + 32/5*e^2 + 263/5*e - 188/5', '3/5*e^3 + 6/5*e^2 - 36/5*e - 14/5', '4/5*e^3 + 8/5*e^2 - 78/5*e - 62/5', '-4/5*e^3 - 3/5*e^2 + 33/5*e + 12/5', '2/5*e^3 + 4/5*e^2 - 49/5*e - 66/5', '-29/5*e^3 + 32/5*e^2 + 273/5*e - 168/5', '-22/5*e^3 + 16/5*e^2 + 259/5*e - 144/5', '17/5*e^3 - 21/5*e^2 - 139/5*e + 114/5', '-6*e^3 + 7*e^2 + 65*e - 36', '-27/5*e^3 + 41/5*e^2 + 254/5*e - 264/5', '-3*e^3 + 4*e^2 + 34*e - 40', '16/5*e^3 - 28/5*e^2 - 157/5*e + 187/5', '-6/5*e^3 + 18/5*e^2 + 62/5*e - 192/5', '32/5*e^3 - 26/5*e^2 - 324/5*e + 129/5', '18/5*e^3 - 29/5*e^2 - 141/5*e + 126/5', '-3*e^3 + 39*e - 3', '-32/5*e^3 + 36/5*e^2 + 364/5*e - 209/5', '26/5*e^3 - 43/5*e^2 - 297/5*e + 202/5', '26/5*e^3 - 33/5*e^2 - 287/5*e + 187/5', '24/5*e^3 - 32/5*e^2 - 228/5*e + 193/5', '-2*e^3 + 3*e^2 + 21*e - 40', '-28/5*e^3 + 24/5*e^2 + 286/5*e - 101/5', '-6/5*e^3 + 13/5*e^2 + 67/5*e - 87/5', '-e^3 + 4*e^2 + 17*e - 21', '-14/5*e^3 + 7/5*e^2 + 153/5*e - 68/5', '2/5*e^3 + 14/5*e^2 - 39/5*e - 11/5', '-14/5*e^3 - 3/5*e^2 + 183/5*e + 7/5', '-3*e^3 + 6*e^2 + 36*e - 25', 'e^3 - 3*e^2 - 12*e + 14', '-14/5*e^3 - 3/5*e^2 + 153/5*e + 37/5', '34/5*e^3 - 57/5*e^2 - 358/5*e + 223/5', '-16/5*e^3 + 3/5*e^2 + 202/5*e - 32/5', '-31/5*e^3 + 33/5*e^2 + 327/5*e - 167/5', '13/5*e^3 + 11/5*e^2 - 171/5*e - 29/5', '-3*e^3 + 7*e^2 + 25*e - 40', '-2*e^3 + 8*e^2 + 17*e - 40', '-16/5*e^3 + 13/5*e^2 + 202/5*e - 117/5', '18/5*e^3 - 4/5*e^2 - 201/5*e + 51/5', '-e^3 + 3*e^2 + 10*e - 1', '8/5*e^3 - 9/5*e^2 - 81/5*e + 166/5', 'e^3 + 2*e^2 - 10*e - 34', '18/5*e^3 - 39/5*e^2 - 171/5*e + 241/5', '23/5*e^3 - 34/5*e^2 - 276/5*e + 306/5', '-6/5*e^3 - 12/5*e^2 + 87/5*e + 153/5', '2/5*e^3 - 1/5*e^2 - 14/5*e + 9/5', '-16/5*e^3 + 33/5*e^2 + 102/5*e - 237/5', '2/5*e^3 - 11/5*e^2 + 11/5*e + 199/5', '16/5*e^3 - 13/5*e^2 - 107/5*e + 7/5', '3*e^3 + e^2 - 38*e + 9', '41/5*e^3 - 53/5*e^2 - 427/5*e + 282/5', '3/5*e^3 - 4/5*e^2 - 31/5*e + 16/5', '8*e^3 - 13*e^2 - 87*e + 65', '-23/5*e^3 + 14/5*e^2 + 261/5*e - 86/5', '8/5*e^3 + 6/5*e^2 - 156/5*e - 119/5', '-3*e^3 + 5*e^2 + 24*e - 33', '-13/5*e^3 + 9/5*e^2 + 176/5*e + 24/5', '19/5*e^3 - 32/5*e^2 - 193/5*e + 3/5', '-14/5*e^3 + 22/5*e^2 + 188/5*e - 183/5', '29/5*e^3 - 22/5*e^2 - 343/5*e + 213/5', '7*e^3 - 9*e^2 - 68*e + 57', '17/5*e^3 - 6/5*e^2 - 174/5*e + 79/5', '-4/5*e^3 + 7/5*e^2 + 33/5*e - 53/5', '11/5*e^3 - 8/5*e^2 - 187/5*e + 97/5', '-17/5*e^3 - 4/5*e^2 + 189/5*e + 1/5', '-3*e^3 + 6*e^2 + 39*e - 54', '-43/5*e^3 + 69/5*e^2 + 436/5*e - 306/5', '7/5*e^3 + 9/5*e^2 - 44/5*e - 71/5', '-3/5*e^3 + 4/5*e^2 + 91/5*e - 11/5', '17/5*e^3 - 31/5*e^2 - 149/5*e + 49/5', '32/5*e^3 - 36/5*e^2 - 279/5*e + 114/5', '-12/5*e^3 + 36/5*e^2 + 169/5*e - 249/5', '3*e^3 - 9*e^2 - 33*e + 54', '-8/5*e^3 + 24/5*e^2 + 71/5*e - 111/5', '29/5*e^3 - 42/5*e^2 - 283/5*e + 273/5', '24/5*e^3 - 32/5*e^2 - 253/5*e + 228/5', '4/5*e^3 + 3/5*e^2 - 78/5*e - 17/5', '19/5*e^3 + 3/5*e^2 - 183/5*e - 77/5', '-27/5*e^3 + 46/5*e^2 + 264/5*e - 204/5', '-19/5*e^3 + 22/5*e^2 + 138/5*e - 123/5', '4/5*e^3 + 8/5*e^2 - 108/5*e - 77/5', '-11/5*e^3 - 2/5*e^2 + 77/5*e + 93/5', '-33/5*e^3 + 64/5*e^2 + 361/5*e - 336/5', '7/5*e^3 + 14/5*e^2 - 54/5*e - 96/5', '-6*e^3 + 13*e^2 + 65*e - 75', '-1/5*e^3 - 17/5*e^2 + 27/5*e + 43/5', '-24/5*e^3 + 22/5*e^2 + 258/5*e - 173/5'], 'hecke_polynomial': 'x^4 - 2*x^3 - 10*x^2 + 15*x - 3', 'label': '4.4.11525.1-25.3-d'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 11525, 'ideals': ['[1, 1, 1]', '[5, 5, 1/5*w^3 + 4/5*w^2 - 11/5*w - 7]', '[5, 5, 1/5*w^3 - 6/5*w^2 - 1/5*w + 4]', '[11, 11, w + 1]', '[11, 11, 1/5*w^3 - 1/5*w^2 - 11/5*w + 2]', '[16, 2, 2]', '[19, 19, -1/5*w^3 + 1/5*w^2 + 1/5*w + 1]', '[19, 19, 1/5*w^3 - 1/5*w^2 - 11/5*w]', '[19, 19, -2/5*w^3 + 2/5*w^2 + 17/5*w]', '[19, 19, w - 1]', '[25, 5, w]', '[25, 5, 2/5*w^3 - 2/5*w^2 - 12/5*w + 1]', '[25, 5, -1/5*w^3 + 1/5*w^2 + 11/5*w - 1]', '[29, 29, w^2 - w - 8]', '[29, 29, 2/5*w^3 - 2/5*w^2 - 7/5*w + 2]', '[31, 31, 1/5*w^3 - 1/5*w^2 - 1/5*w + 2]', '[31, 31, 2/5*w^3 - 2/5*w^2 - 17/5*w + 3]', '[55, 55, -2/5*w^3 + 7/5*w^2 + 7/5*w - 7]', '[55, 55, -2/5*w^3 + 2/5*w^2 + 17/5*w + 1]', '[55, 55, -1/5*w^3 + 1/5*w^2 + 1/5*w + 2]', '[55, 55, 2/5*w^3 + 3/5*w^2 - 17/5*w - 4]', '[61, 61, -2/5*w^3 - 3/5*w^2 + 12/5*w + 5]', '[61, 61, -4/5*w^3 - 6/5*w^2 + 39/5*w + 15]', '[61, 61, 3/5*w^3 + 2/5*w^2 - 18/5*w - 3]', '[61, 61, 7/5*w^3 + 3/5*w^2 - 62/5*w - 13]', '[71, 71, 1/5*w^3 - 6/5*w^2 - 6/5*w + 4]', '[71, 71, w^2 - 8]', '[79, 79, 3/5*w^3 + 12/5*w^2 - 33/5*w - 22]', '[79, 79, 1/5*w^3 + 4/5*w^2 - 11/5*w - 9]', '[80, 10, 2/5*w^3 + 8/5*w^2 - 22/5*w - 14]', '[80, 10, 2/5*w^3 - 12/5*w^2 - 2/5*w + 8]', '[81, 3, -3]', '[95, 95, -2/5*w^3 + 7/5*w^2 + 17/5*w - 11]', '[95, 95, -w^2 + 9]', '[95, 95, 1/5*w^3 - 6/5*w^2 - 6/5*w + 3]', '[95, 95, -w^2 - w + 2]', '[95, 95, -1/5*w^3 + 6/5*w^2 + 1/5*w - 8]', '[95, 95, 3/5*w^3 - 3/5*w^2 - 13/5*w + 1]', '[95, 95, 4/5*w^3 - 4/5*w^2 - 29/5*w + 2]', '[95, 95, -1/5*w^3 - 4/5*w^2 + 11/5*w + 3]', '[101, 101, 3/5*w^3 + 7/5*w^2 - 28/5*w - 15]', '[101, 101, 1/5*w^3 + 9/5*w^2 - 16/5*w - 16]', '[121, 11, 3/5*w^3 - 3/5*w^2 - 18/5*w + 2]', '[121, 11, 3/5*w^3 - 3/5*w^2 - 18/5*w + 1]', '[121, 121, -3/5*w^3 + 8/5*w^2 + 8/5*w - 6]', '[121, 121, 4/5*w^3 + 1/5*w^2 - 34/5*w - 4]', '[125, 5, -w^3 + 9*w + 5]', '[125, 5, -3/5*w^3 + 8/5*w^2 + 3/5*w - 4]', '[125, 25, w^2 - w - 10]', '[125, 25, -4/5*w^3 + 9/5*w^2 + 14/5*w - 5]', '[131, 131, 1/5*w^3 + 4/5*w^2 - 16/5*w - 8]', '[131, 131, w^2 - 2*w - 2]', '[145, 145, -8/5*w^3 - 17/5*w^2 + 78/5*w + 36]', '[145, 145, -7/5*w^3 + 12/5*w^2 + 17/5*w - 5]', '[145, 145, 2/5*w^3 - 2/5*w^2 - 7/5*w - 2]', '[145, 145, 1/5*w^3 + 4/5*w^2 - 6/5*w - 7]', '[149, 149, 4/5*w^3 + 1/5*w^2 - 29/5*w - 5]', '[149, 149, 4/5*w^3 - 9/5*w^2 - 19/5*w + 6]', '[151, 151, 2/5*w^3 + 3/5*w^2 - 17/5*w - 3]', '[151, 151, -2/5*w^3 + 7/5*w^2 + 7/5*w - 8]', '[151, 151, 4/5*w^3 + 1/5*w^2 - 29/5*w - 2]', '[151, 151, -4/5*w^3 + 9/5*w^2 + 19/5*w - 9]', '[155, 155, 4/5*w^3 + 6/5*w^2 - 34/5*w - 13]', '[155, 155, -w^3 + w^2 + 3*w - 1]', '[155, 155, -8/5*w^3 + 8/5*w^2 + 63/5*w - 4]', '[155, 155, 4/5*w^3 - 14/5*w^2 - 14/5*w + 9]', '[176, 22, 2*w + 2]', '[176, 22, 2/5*w^3 - 2/5*w^2 - 22/5*w + 4]', '[179, 179, -3/5*w^3 + 8/5*w^2 + 18/5*w - 6]', '[179, 179, 2/5*w^3 + 3/5*w^2 - 12/5*w - 6]', '[209, 209, w^2 - 1]', '[209, 209, -1/5*w^3 - 9/5*w^2 + 11/5*w + 15]', '[209, 209, -2/5*w^3 + 12/5*w^2 + 7/5*w - 8]', '[209, 209, 1/5*w^3 - 6/5*w^2 - 6/5*w + 11]', '[209, 209, -1/5*w^3 + 1/5*w^2 - 4/5*w + 1]', '[209, 209, -3/5*w^3 + 8/5*w^2 + 23/5*w - 13]', '[209, 209, 1/5*w^3 + 4/5*w^2 - 1/5*w]', '[209, 209, -3/5*w^3 + 3/5*w^2 + 28/5*w - 1]', '[211, 211, 1/5*w^3 + 4/5*w^2 - 6/5*w - 10]', '[211, 211, 2/5*w^3 - 7/5*w^2 - 12/5*w + 2]', '[229, 229, 6/5*w^3 - 11/5*w^2 - 41/5*w + 11]', '[229, 229, 2*w^2 - 2*w - 9]', '[229, 229, -4/5*w^3 - 1/5*w^2 + 19/5*w + 2]', '[229, 229, -3/5*w^3 + 3/5*w^2 + 28/5*w - 3]', '[239, 239, 11/5*w^3 + 4/5*w^2 - 96/5*w - 19]', '[239, 239, -6/5*w^3 + 1/5*w^2 + 51/5*w + 3]', '[241, 241, 1/5*w^3 + 4/5*w^2 - 1/5*w - 6]', '[241, 241, 4/5*w^3 - 4/5*w^2 - 29/5*w - 1]', '[251, 251, -1/5*w^3 + 6/5*w^2 + 11/5*w - 12]', '[251, 251, -1/5*w^3 + 11/5*w^2 + 1/5*w - 15]', '[256, 4, 4]', '[269, 269, 2/5*w^3 + 3/5*w^2 - 17/5*w - 2]', '[269, 269, -2/5*w^3 + 7/5*w^2 + 7/5*w - 9]', '[271, 271, 1/5*w^3 - 1/5*w^2 + 4/5*w]', '[271, 271, 3/5*w^3 - 3/5*w^2 - 28/5*w + 2]', '[275, 55, -1/5*w^3 + 1/5*w^2 + 11/5*w + 4]', '[275, 55, 2/5*w^3 + 8/5*w^2 - 17/5*w - 9]', '[275, 55, 3/5*w^3 - 13/5*w^2 - 13/5*w + 14]', '[275, 55, 3/5*w^3 - 3/5*w^2 - 8/5*w + 3]', '[275, 55, w^3 - w^2 - 8*w + 5]', '[275, 55, w - 5]', '[281, 281, w^3 - 3*w^2 - 4*w + 13]', '[281, 281, -3/5*w^3 + 3/5*w^2 + 28/5*w - 6]', '[281, 281, -6/5*w^3 + 26/5*w^2 + 11/5*w - 16]', '[281, 281, w^3 + w^2 - 8*w - 9]', '[289, 17, 2/5*w^3 + 3/5*w^2 - 7/5*w - 5]', '[289, 17, 4/5*w^3 - 9/5*w^2 - 29/5*w + 8]', '[304, 38, -2/5*w^3 + 2/5*w^2 + 2/5*w + 2]', '[304, 38, 2/5*w^3 - 2/5*w^2 - 22/5*w]', '[304, 38, -4/5*w^3 + 4/5*w^2 + 34/5*w]', '[304, 38, 2*w - 2]', '[305, 305, 4/5*w^3 + 1/5*w^2 - 24/5*w - 3]', '[305, 305, 1/5*w^3 - 6/5*w^2 - 11/5*w + 10]', '[305, 305, w^2 - 2*w - 8]', '[305, 305, -1/5*w^3 + 1/5*w^2 + 16/5*w - 3]', '[305, 305, -1/5*w^3 + 1/5*w^2 + 16/5*w + 1]', '[305, 305, -3/5*w^3 + 8/5*w^2 + 13/5*w - 9]', '[305, 305, -3/5*w^3 - 2/5*w^2 + 18/5*w + 6]', '[305, 305, w^3 - 2*w^2 - 6*w + 9]', '[311, 311, -w^2 + 2*w + 11]', '[311, 311, -1/5*w^3 + 6/5*w^2 + 1/5*w - 1]', '[311, 311, 1/5*w^3 + 4/5*w^2 - 16/5*w + 1]', '[311, 311, -1/5*w^3 - 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31]', '[1919, 1919, -2/5*w^3 + 7/5*w^2 - 8/5*w - 5]', '[1919, 1919, 1/5*w^3 + 4/5*w^2 - 6/5*w - 13]', '[1919, 1919, 9/5*w^3 - 14/5*w^2 - 69/5*w + 11]', '[1919, 1919, -9/5*w^3 + 24/5*w^2 + 64/5*w - 34]', '[1919, 1919, 6/5*w^3 - 1/5*w^2 - 31/5*w - 1]', '[1931, 1931, -4/5*w^3 + 29/5*w^2 - 1/5*w - 19]', '[1931, 1931, 2/5*w^3 - 17/5*w^2 - 2/5*w + 14]', '[1931, 1931, 1/5*w^3 + 14/5*w^2 - 16/5*w - 20]', '[1931, 1931, 4/5*w^3 + 21/5*w^2 - 49/5*w - 36]', '[1936, 22, 6/5*w^3 - 6/5*w^2 - 36/5*w + 4]', '[1936, 22, 6/5*w^3 - 6/5*w^2 - 36/5*w + 2]', '[1936, 242, -6/5*w^3 + 16/5*w^2 + 16/5*w - 12]', '[1936, 242, 8/5*w^3 + 2/5*w^2 - 68/5*w - 8]', '[1945, 1945, 12/5*w^3 - 22/5*w^2 - 37/5*w + 8]', '[1945, 1945, 7/5*w^3 - 22/5*w^2 - 7/5*w + 7]', '[1945, 1945, -18/5*w^3 - 17/5*w^2 + 158/5*w + 46]', '[1945, 1945, 1/5*w^3 - 26/5*w^2 + 4/5*w + 43]', '[1969, 1969, -9/5*w^3 + 29/5*w^2 + 44/5*w - 30]', '[1969, 1969, -4/5*w^3 - 1/5*w^2 + 39/5*w]', '[1969, 1969, 2/5*w^3 - 7/5*w^2 + 3/5*w + 9]', '[1969, 1969, 7/5*w^3 + 13/5*w^2 - 52/5*w - 16]', '[1975, 395, 4*w^2 - 3*w - 35]', '[1975, 395, -2/5*w^3 + 7/5*w^2 - 8/5*w - 3]', '[1975, 395, -17/5*w^3 + 2/5*w^2 + 147/5*w + 14]', '[1975, 395, 9/5*w^3 - 4/5*w^2 - 79/5*w - 2]', '[1975, 395, -9/5*w^3 + 4/5*w^2 + 69/5*w + 3]', '[1975, 395, w^3 - 10*w - 5]', '[1979, 1979, 1/5*w^3 + 4/5*w^2 + 4/5*w - 9]', '[1979, 1979, 4/5*w^3 - 9/5*w^2 - 34/5*w + 5]', '[1999, 1999, -2/5*w^3 + 12/5*w^2 + 2/5*w - 17]', '[1999, 1999, 2/5*w^3 + 8/5*w^2 - 22/5*w - 5]', '[2000, 10, -2*w^3 + 18*w + 10]', '[2000, 10, -6/5*w^3 + 16/5*w^2 + 6/5*w - 8]', '[2000, 50, 2*w^2 - 2*w - 20]', '[2000, 50, -8/5*w^3 + 18/5*w^2 + 28/5*w - 10]', '[2005, 2005, 1/5*w^3 - 1/5*w^2 - 21/5*w + 3]', '[2005, 2005, -2/5*w^3 + 2/5*w^2 + 27/5*w]', '[2005, 2005, -7/5*w^3 + 12/5*w^2 + 42/5*w - 10]', '[2005, 2005, 6/5*w^3 - 1/5*w^2 - 36/5*w - 2]', '[2025, 15, -3*w]', '[2025, 15, -6/5*w^3 + 6/5*w^2 + 36/5*w - 3]', '[2025, 15, 3/5*w^3 - 3/5*w^2 - 33/5*w + 3]', '[2029, 2029, 13/5*w^3 + 2/5*w^2 - 113/5*w - 19]', '[2029, 2029, -w^3 + 5*w^2 + 3*w - 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w^2 - 9*w + 10]', '[2375, 475, -2*w^3 + 4*w^2 + 13*w - 20]', '[2375, 475, -3/5*w^3 - 2/5*w^2 + 13/5*w + 8]', '[2384, 298, 8/5*w^3 + 2/5*w^2 - 58/5*w - 10]', '[2384, 298, 8/5*w^3 - 18/5*w^2 - 38/5*w + 12]', '[2395, 2395, 11/5*w^3 - 16/5*w^2 - 86/5*w + 18]', '[2395, 2395, -1/5*w^3 - 19/5*w^2 + 21/5*w + 14]', '[2395, 2395, 22/5*w^3 + 18/5*w^2 - 197/5*w - 49]', '[2395, 2395, 6/5*w^3 - 31/5*w^2 + 4/5*w + 14]', '[2401, 7, -7]', '[2411, 2411, -3*w^3 + 9*w^2 + 6*w - 22]', '[2411, 2411, 2/5*w^3 - 7/5*w^2 - 22/5*w + 17]', '[2416, 302, 4/5*w^3 + 6/5*w^2 - 34/5*w - 6]', '[2416, 302, -4/5*w^3 + 14/5*w^2 + 14/5*w - 16]', '[2416, 302, 8/5*w^3 + 2/5*w^2 - 58/5*w - 4]', '[2416, 302, -8/5*w^3 + 18/5*w^2 + 38/5*w - 18]', '[2441, 2441, -4/5*w^3 + 24/5*w^2 - 6/5*w - 13]', '[2441, 2441, -3/5*w^3 + 13/5*w^2 + 8/5*w - 22]', '[2449, 2449, -6/5*w^3 + 26/5*w^2 + 31/5*w - 24]', '[2449, 2449, -2*w^3 + 8*w^2 + 5*w - 24]', '[2449, 2449, -11/5*w^3 - 19/5*w^2 + 101/5*w + 41]', '[2449, 2449, -3/5*w^3 - 17/5*w^2 + 23/5*w + 23]', '[2459, 2459, 7/5*w^3 - 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15]', '[529, 23, 2/5*w^3 + 13/5*w^2 - 27/5*w - 21]', '[541, 541, 1/5*w^3 - 11/5*w^2 - 1/5*w + 10]', '[541, 541, 3/5*w^3 - 8/5*w^2 - 13/5*w + 13]', '[541, 541, -2*w^2 + w + 13]', '[541, 541, 3/5*w^3 + 2/5*w^2 - 23/5*w + 2]', '[569, 569, w^3 - 2*w^2 - 5*w + 7]', '[569, 569, -1/5*w^3 + 1/5*w^2 + 1/5*w - 6]', '[571, 571, w^2 + w - 9]', '[571, 571, -2/5*w^3 + 12/5*w^2 + 7/5*w - 12]', '[571, 571, 1/5*w^3 + 9/5*w^2 - 11/5*w - 11]', '[571, 571, -2/5*w^3 + 7/5*w^2 + 17/5*w - 4]', '[601, 601, -3/5*w^3 + 13/5*w^2 + 18/5*w - 11]', '[601, 601, -4/5*w^3 + 4/5*w^2 + 34/5*w + 1]', '[631, 631, 2/5*w^3 + 18/5*w^2 - 27/5*w - 30]', '[631, 631, 3/5*w^3 - 23/5*w^2 - 3/5*w + 15]', '[661, 661, -2*w^3 + 17*w + 12]', '[661, 661, -9/5*w^3 + 4/5*w^2 + 74/5*w + 1]', '[691, 691, -7/5*w^3 - 18/5*w^2 + 72/5*w + 35]', '[691, 691, 6/5*w^3 - 31/5*w^2 - 6/5*w + 19]', '[701, 701, -1/5*w^3 + 6/5*w^2 + 16/5*w - 6]', '[701, 701, 2/5*w^3 - 7/5*w^2 - 22/5*w + 8]', '[709, 709, -3/5*w^3 + 13/5*w^2 + 13/5*w - 18]', '[709, 709, 1/5*w^3 + 14/5*w^2 - 11/5*w - 20]', '[709, 709, -2/5*w^3 - 8/5*w^2 + 17/5*w + 5]', '[709, 709, 1/5*w^3 + 4/5*w^2 - 21/5*w - 10]', '[719, 719, -3/5*w^3 + 8/5*w^2 + 13/5*w - 12]', '[719, 719, 3/5*w^3 + 2/5*w^2 - 23/5*w + 1]', '[719, 719, -7/5*w^3 + 17/5*w^2 + 32/5*w - 14]', '[719, 719, 7/5*w^3 + 3/5*w^2 - 52/5*w - 8]', '[739, 739, 1/5*w^3 - 1/5*w^2 - 11/5*w - 5]', '[739, 739, w - 6]', '[761, 761, -4/5*w^3 + 9/5*w^2 + 19/5*w - 11]', '[761, 761, 4/5*w^3 + 1/5*w^2 - 29/5*w]', '[769, 769, 3/5*w^3 - 13/5*w^2 - 13/5*w + 8]', '[769, 769, -2/5*w^3 - 8/5*w^2 + 17/5*w + 15]', '[769, 769, 7/5*w^3 - 17/5*w^2 - 37/5*w + 18]', '[769, 769, -6/5*w^3 - 4/5*w^2 + 41/5*w + 5]', '[809, 809, -1/5*w^3 + 6/5*w^2 - 4/5*w - 14]', '[809, 809, -2/5*w^3 - 3/5*w^2 + 22/5*w - 4]', '[809, 809, -6/5*w^3 + 6/5*w^2 + 41/5*w - 5]', '[809, 809, w^3 - w^2 - 5*w + 4]', '[821, 821, -3/5*w^3 - 17/5*w^2 + 33/5*w + 30]', '[821, 821, -4/5*w^3 + 24/5*w^2 + 9/5*w - 15]', '[829, 829, 7/5*w^3 - 12/5*w^2 - 52/5*w + 10]', '[829, 829, -1/5*w^3 + 11/5*w^2 - 4/5*w - 19]', '[829, 829, -13/5*w^3 + 3/5*w^2 + 108/5*w + 10]', '[829, 829, -w^3 + 4*w^2 + 5*w - 23]', '[839, 839, 4/5*w^3 - 9/5*w^2 - 24/5*w + 4]', '[839, 839, 3/5*w^3 + 2/5*w^2 - 18/5*w - 8]', '[841, 29, -w^3 + w^2 + 6*w - 4]', '[859, 859, 6/5*w^3 - 11/5*w^2 - 36/5*w + 9]', '[859, 859, w^3 - 6*w - 3]', '[881, 881, 4/5*w^3 - 4/5*w^2 - 9/5*w - 1]', '[881, 881, 9/5*w^3 - 24/5*w^2 - 19/5*w + 14]', '[881, 881, -w^3 + 6*w + 2]', '[881, 881, 1/5*w^3 - 1/5*w^2 - 1/5*w - 6]', '[911, 911, w^3 - w^2 - 5*w + 1]', '[911, 911, 6/5*w^3 - 6/5*w^2 - 41/5*w + 2]', '[919, 919, -7/5*w^3 + 12/5*w^2 + 42/5*w - 7]', '[919, 919, -6/5*w^3 + 1/5*w^2 + 36/5*w + 5]', '[929, 929, -2/5*w^3 - 8/5*w^2 + 17/5*w + 16]', '[929, 929, -3/5*w^3 + 13/5*w^2 + 13/5*w - 7]', '[961, 31, w^3 - w^2 - 6*w + 2]', '[971, 971, 8/5*w^3 - 13/5*w^2 - 48/5*w + 6]', '[971, 971, -2/5*w^3 - 3/5*w^2 + 22/5*w]', '[971, 971, 7/5*w^3 - 7/5*w^2 - 57/5*w + 7]', '[971, 971, -1/5*w^3 + 6/5*w^2 - 4/5*w - 10]', '[991, 991, 2/5*w^3 + 8/5*w^2 - 22/5*w - 7]', '[991, 991, -2/5*w^3 + 12/5*w^2 + 2/5*w - 15]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [25, 5, -11, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 11525, 'disc_rad': 2305, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[4, 1]]], [5, [0]], [7, [[4, 1]]], [11, [[2, 1], [1, 2]]], [13, [[4, 1]]], [17, [[2, 2]]], [19, [[1, 4]]], [23, [[2, 2]]], [29, [[2, 1], [1, 2]]], [31, [[2, 1], [1, 2]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[4, 1]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 48.010415536631214, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.11525.1', 'local_algs': ['5.2.1.1', '5.2.1.1', 'm461.1.1.0', 'm461.1.1.0', 'm461.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 461], 'rd': 10.3612042142, 'regulator': {'__RealLiteral__': 0, 'data': '5.17238740407', 'prec': 44}, 'res': {'gal': ['625,0,-1105,0,526,0,-48,0,1'], 'sib': ['-5,21,-20,-2,1', '625,0,-1105,0,526,0,-48,0,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{5} a^{3} - \\frac{1}{5} a^{2} - \\frac{6}{5} a \\)', '\\( \\frac{2}{5} a^{3} + \\frac{3}{5} a^{2} - \\frac{17}{5} a - 6 \\)', '\\( \\frac{2}{5} a^{3} - \\frac{7}{5} a^{2} - \\frac{12}{5} a + 9 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/5*a^3 - 1/5*a^2 - 1/5*a']}