Hilbert modular form data - 4.4.10816.1-23.3-c

Formats: - HTML - YAML - JSON - 2024-05-01T08:40:47.189870

• 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': 1, 'disc': 10816, 'field_bad_primes': [2, 13], 'field_label': '4.4.10816.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.10816.1-23.3-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [23], 'level_ideal': '[23,23,1/5*w^3 - 4/5*w^2 - 6/5*w + 12/5]', 'level_label': '23.3', 'level_norm': 23, 'parallel_weight': 2, 'short_label': '23.3-c', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[23,23,1/5*w^3 - 4/5*w^2 - 6/5*w + 12/5]', -1]], 'hecke_eigenvalues': [-1, 1, -4, -3, 2, -3, 2, -1, -1, 1, -1, -3, 2, 4, 4, 4, 9, 4, -11, -1, -6, 9, 4, -9, -9, 6, 11, 10, -20, 13, -7, -12, 13, -4, 13, -12, 8, 8, 20, 5, 5, -10, 16, 1, -9, 16, -2, 18, -12, -27, 24, -16, 4, 9, 2, 12, -13, -18, -26, -26, -26, -1, -8, -13, -28, -8, -10, -15, -32, -32, -22, -2, -11, -21, 14, 14, -34, 16, -9, 11, 11, -14, -24, -9, 40, -30, 15, -30, -30, 45, -15, 10, -10, -30, 30, 0, 30, 0, 25, -25, 48, 38, 8, 8, -50, -35, -30, -35, 32, 32, 2, -28, 31, -44, 1, -34, 24, 44, -26, -26, -8, 12, -28, -8, 40, 20, -35, -40, 45, -15, -10, 5, 11, -34, -29, -4, -7, -7, -28, -18, 7, -13, -32, 18, -2, -7, 42, 12, 27, 42, -28, 47, 12, 37, 10, 10, 5, -40, 2, 52, 32, -38, -41, -6, 14, -51, -13, 2, -5, -40, 50, 20, 12, 12, -38, 42, -59, -34, 56, -34, 14, -36, -6, 39, -44, 26, -14, 26, 49, -26, 34, 34, 14, -61, -16, 34, -44, 56, -4, 16, 50, -10, 0, 50, -16, 39, 19, 34, 32, -8, 22, 52, 46, -44, 46, 26, 17, -38, 32, -58, 30, -25, -65, -50, 6, 36, 6, 6, 21, -49, -29, -39, -24, -9, -13, -43, -63, 32, -42, 38, 3, 18, 5, -40, 55, 0, -59, 66, -49, -69, -36, 24, 39, 24, -4, 56, -69, -24, -50, -35, -70, -30, -19, -64, 6, 56, -48, 2, 15, -5, -30, 20, -38, -38, 37, 2, -24, -24, 16, -14, 18, -42, -17, 3, 36, 16, 20, -75, -85, -75, -54, 16, 16, 81, 34, 34, 9, -66, -3, 27, 17, 67, -44, 66, 36, 6, 65, 25, -30, -70], 'hecke_polynomial': 'x', 'label': '4.4.10816.1-23.3-c'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 10816, 'ideals': ['[1, 1, 1]', '[4, 2, -2/5*w^3 + 3/5*w^2 + 17/5*w - 9/5]', '[9, 3, -2/5*w^3 + 3/5*w^2 + 22/5*w - 9/5]', '[9, 3, 2/5*w^3 - 3/5*w^2 - 22/5*w + 14/5]', '[16, 2, 2]', '[17, 17, w + 1]', '[17, 17, -4/5*w^3 + 6/5*w^2 + 39/5*w - 13/5]', '[17, 17, -4/5*w^3 + 6/5*w^2 + 39/5*w - 28/5]', '[17, 17, -w + 2]', '[23, 23, -1/5*w^3 + 4/5*w^2 + 6/5*w - 22/5]', '[23, 23, -1/5*w^3 - 1/5*w^2 + 11/5*w + 3/5]', '[23, 23, -1/5*w^3 + 4/5*w^2 + 6/5*w - 12/5]', '[23, 23, -1/5*w^3 - 1/5*w^2 + 11/5*w + 13/5]', '[25, 5, -4/5*w^3 + 6/5*w^2 + 39/5*w - 33/5]', '[25, 5, -w^3 + w^2 + 10*w - 2]', '[36, 6, -1/5*w^3 - 1/5*w^2 + 11/5*w + 8/5]', '[36, 6, -1/5*w^3 + 4/5*w^2 + 6/5*w - 17/5]', '[49, 7, -4/5*w^3 + 6/5*w^2 + 34/5*w - 23/5]', '[49, 7, 4/5*w^3 - 6/5*w^2 - 34/5*w + 13/5]', '[64, 4, -4/5*w^3 + 6/5*w^2 + 34/5*w - 18/5]', '[68, 34, -3/5*w^3 + 2/5*w^2 + 28/5*w - 11/5]', '[68, 34, -3/5*w^3 + 2/5*w^2 + 28/5*w + 9/5]', '[68, 34, 3/5*w^3 - 7/5*w^2 - 23/5*w + 36/5]', '[68, 34, -3/5*w^3 + 7/5*w^2 + 23/5*w - 16/5]', '[79, 79, 3/5*w^3 - 7/5*w^2 - 28/5*w + 21/5]', '[79, 79, 1/5*w^3 + 1/5*w^2 - 16/5*w - 13/5]', '[79, 79, -1/5*w^3 + 4/5*w^2 + 11/5*w - 27/5]', '[79, 79, 3/5*w^3 - 2/5*w^2 - 33/5*w + 11/5]', '[81, 3, 3]', '[81, 9, 2/5*w^3 - 3/5*w^2 - 22/5*w + 29/5]', '[81, 9, -2/5*w^3 + 3/5*w^2 + 22/5*w + 6/5]', '[92, 46, 6/5*w^3 - 9/5*w^2 - 61/5*w + 37/5]', '[92, 46, -2/5*w^3 + 3/5*w^2 + 27/5*w - 9/5]', '[92, 46, 2/5*w^3 - 3/5*w^2 - 27/5*w + 19/5]', '[92, 46, -6/5*w^3 + 9/5*w^2 + 61/5*w - 27/5]', '[100, 10, w^3 - 2*w^2 - 8*w + 9]', '[100, 10, -w^3 + w^2 + 11*w]', '[103, 103, -1/5*w^3 + 4/5*w^2 + 1/5*w - 17/5]', '[103, 103, -w^3 + 2*w^2 + 9*w - 7]', '[103, 103, w^3 - w^2 - 10*w + 3]', '[103, 103, 1/5*w^3 + 1/5*w^2 - 6/5*w - 13/5]', '[113, 113, w^2 - 7]', '[113, 113, -7/5*w^3 + 13/5*w^2 + 67/5*w - 49/5]', '[113, 113, 7/5*w^3 - 8/5*w^2 - 72/5*w + 24/5]', '[113, 113, -3/5*w^3 + 2/5*w^2 + 33/5*w + 19/5]', '[121, 11, 6/5*w^3 - 9/5*w^2 - 61/5*w + 32/5]', '[121, 11, -2/5*w^3 + 3/5*w^2 + 27/5*w - 14/5]', '[127, 127, -1/5*w^3 - 1/5*w^2 + 6/5*w - 12/5]', '[127, 127, -w^3 + w^2 + 10*w + 2]', '[127, 127, -w^3 + 2*w^2 + 9*w - 12]', '[127, 127, 1/5*w^3 - 4/5*w^2 - 1/5*w - 8/5]', '[144, 6, -4/5*w^3 + 6/5*w^2 + 44/5*w - 18/5]', '[144, 6, 4/5*w^3 - 6/5*w^2 - 44/5*w + 28/5]', '[153, 51, -3/5*w^3 + 7/5*w^2 + 18/5*w - 26/5]', '[153, 51, 3/5*w^3 - 7/5*w^2 - 28/5*w + 16/5]', '[153, 51, 1/5*w^3 + 1/5*w^2 - 16/5*w - 18/5]', '[153, 51, 7/5*w^3 - 13/5*w^2 - 62/5*w + 44/5]', '[153, 51, 1/5*w^3 - 4/5*w^2 - 11/5*w + 32/5]', '[153, 51, -7/5*w^3 + 8/5*w^2 + 67/5*w - 24/5]', '[153, 51, -3/5*w^3 + 2/5*w^2 + 23/5*w + 4/5]', '[153, 51, -3/5*w^3 + 2/5*w^2 + 33/5*w - 16/5]', '[169, 13, -4/5*w^3 + 6/5*w^2 + 44/5*w - 23/5]', '[191, 191, 2/5*w^3 + 2/5*w^2 - 27/5*w - 26/5]', '[191, 191, -2/5*w^3 + 8/5*w^2 + 17/5*w - 24/5]', '[191, 191, -2/5*w^3 - 2/5*w^2 + 27/5*w + 1/5]', '[191, 191, 2/5*w^3 - 8/5*w^2 - 17/5*w + 49/5]', '[196, 14, 2/5*w^3 - 3/5*w^2 - 17/5*w - 11/5]', '[196, 14, 2/5*w^3 - 3/5*w^2 - 17/5*w + 29/5]', '[199, 199, -w - 4]', '[199, 199, 4/5*w^3 - 6/5*w^2 - 39/5*w - 2/5]', '[199, 199, -4/5*w^3 + 6/5*w^2 + 39/5*w - 43/5]', '[199, 199, w - 5]', '[207, 69, 6/5*w^3 - 4/5*w^2 - 61/5*w - 8/5]', '[207, 69, 8/5*w^3 - 12/5*w^2 - 73/5*w + 36/5]', '[207, 69, 4/5*w^3 - 6/5*w^2 - 29/5*w + 13/5]', '[207, 69, -2/5*w^3 + 8/5*w^2 + 7/5*w - 19/5]', '[207, 69, 2/5*w^3 + 2/5*w^2 - 17/5*w - 6/5]', '[207, 69, 4/5*w^3 - 6/5*w^2 - 29/5*w + 18/5]', '[207, 69, -6/5*w^3 + 14/5*w^2 + 51/5*w - 67/5]', '[207, 69, 8/5*w^3 - 12/5*w^2 - 73/5*w + 41/5]', '[225, 15, -w^3 + 2*w^2 + 8*w - 4]', '[225, 15, -3/5*w^3 + 2/5*w^2 + 38/5*w + 4/5]', '[225, 15, w^3 - w^2 - 11*w + 5]', '[225, 15, w^3 - w^2 - 9*w - 1]', '[233, 233, -w^3 + 2*w^2 + 9*w - 6]', '[233, 233, 1/5*w^3 + 1/5*w^2 - 6/5*w - 18/5]', '[233, 233, -1/5*w^3 + 4/5*w^2 + 1/5*w - 22/5]', '[233, 233, w^3 - w^2 - 10*w + 4]', '[256, 4, 4]', '[257, 257, -9/5*w^3 + 16/5*w^2 + 79/5*w - 63/5]', '[257, 257, w^3 - w^2 - 8*w + 3]', '[257, 257, 2/5*w^3 - 8/5*w^2 - 17/5*w + 59/5]', '[257, 257, -9/5*w^3 + 11/5*w^2 + 84/5*w - 23/5]', '[263, 263, 7/5*w^3 - 13/5*w^2 - 57/5*w + 39/5]', '[263, 263, -7/5*w^3 + 8/5*w^2 + 77/5*w - 14/5]', '[263, 263, -7/5*w^3 + 13/5*w^2 + 72/5*w - 64/5]', '[263, 263, -7/5*w^3 + 8/5*w^2 + 62/5*w - 24/5]', '[272, 34, 2*w + 2]', '[272, 34, -8/5*w^3 + 12/5*w^2 + 78/5*w - 26/5]', '[272, 34, -8/5*w^3 + 12/5*w^2 + 78/5*w - 56/5]', '[272, 34, -2*w + 4]', '[289, 17, -6/5*w^3 + 9/5*w^2 + 51/5*w - 22/5]', '[289, 17, -2/5*w^3 + 3/5*w^2 + 22/5*w - 34/5]', '[289, 17, -w^2 + w + 8]', '[289, 17, -6/5*w^3 + 9/5*w^2 + 51/5*w - 32/5]', '[289, 17, 2/5*w^3 - 3/5*w^2 - 22/5*w - 11/5]', '[289, 17, -w^2 + w + 2]', '[289, 289, -9/5*w^3 + 16/5*w^2 + 84/5*w - 58/5]', '[289, 289, -1/5*w^3 - 1/5*w^2 + 1/5*w + 13/5]', '[289, 289, -1/5*w^3 + 4/5*w^2 - 4/5*w - 12/5]', '[289, 289, 9/5*w^3 - 11/5*w^2 - 89/5*w + 33/5]', '[311, 311, 1/5*w^3 + 1/5*w^2 - 11/5*w - 33/5]', '[311, 311, 1/5*w^3 - 4/5*w^2 - 6/5*w - 8/5]', '[311, 311, -1/5*w^3 - 1/5*w^2 + 11/5*w - 17/5]', '[311, 311, -1/5*w^3 + 4/5*w^2 + 6/5*w - 42/5]', '[313, 313, -9/5*w^3 + 11/5*w^2 + 94/5*w - 33/5]', '[313, 313, -11/5*w^3 + 19/5*w^2 + 96/5*w - 52/5]', '[313, 313, -11/5*w^3 + 19/5*w^2 + 101/5*w - 67/5]', '[313, 313, -9/5*w^3 + 16/5*w^2 + 89/5*w - 63/5]', '[316, 158, -1/5*w^3 + 4/5*w^2 + 16/5*w - 27/5]', '[316, 158, 7/5*w^3 - 8/5*w^2 - 72/5*w + 29/5]', '[316, 158, 7/5*w^3 - 13/5*w^2 - 67/5*w + 44/5]', '[316, 158, 1/5*w^3 + 1/5*w^2 - 21/5*w - 8/5]', '[324, 6, 6/5*w^3 - 9/5*w^2 - 51/5*w + 27/5]', '[324, 18, -7/5*w^3 + 13/5*w^2 + 57/5*w - 44/5]', '[324, 18, -7/5*w^3 + 8/5*w^2 + 62/5*w - 19/5]', '[337, 337, -4/5*w^3 + 1/5*w^2 + 44/5*w + 2/5]', '[337, 337, w^2 - 2*w - 5]', '[337, 337, w^2 - 6]', '[337, 337, -4/5*w^3 + 11/5*w^2 + 34/5*w - 43/5]', '[361, 19, 2/5*w^3 + 2/5*w^2 - 17/5*w - 26/5]', '[361, 19, 12/5*w^3 - 18/5*w^2 - 112/5*w + 59/5]', '[367, 367, -3/5*w^3 + 7/5*w^2 + 18/5*w - 31/5]', '[367, 367, 7/5*w^3 - 8/5*w^2 - 67/5*w + 29/5]', '[367, 367, -7/5*w^3 + 13/5*w^2 + 62/5*w - 39/5]', '[367, 367, 3/5*w^3 - 2/5*w^2 - 23/5*w - 9/5]', '[368, 46, -2/5*w^3 + 8/5*w^2 + 12/5*w - 44/5]', '[368, 46, -2/5*w^3 - 2/5*w^2 + 22/5*w + 6/5]', '[368, 46, -2/5*w^3 + 8/5*w^2 + 12/5*w - 24/5]', '[368, 46, -2/5*w^3 - 2/5*w^2 + 22/5*w + 26/5]', '[391, 391, -8/5*w^3 + 12/5*w^2 + 83/5*w - 31/5]', '[391, 391, -8/5*w^3 + 12/5*w^2 + 78/5*w - 21/5]', '[391, 391, -w^3 + 2*w^2 + 9*w - 5]', '[391, 391, 2/5*w^3 - 8/5*w^2 - 17/5*w + 29/5]', '[391, 391, 1/5*w^3 - 4/5*w^2 - 1/5*w + 27/5]', '[391, 391, 2/5*w^3 + 2/5*w^2 - 27/5*w - 21/5]', '[391, 391, 4/5*w^3 - 6/5*w^2 - 49/5*w + 13/5]', '[391, 391, 2*w - 5]', '[391, 391, 2*w + 3]', '[391, 391, 4/5*w^3 - 6/5*w^2 - 49/5*w + 38/5]', '[391, 391, -2/5*w^3 + 8/5*w^2 + 17/5*w - 44/5]', '[391, 391, 1/5*w^3 + 1/5*w^2 - 6/5*w - 23/5]', '[391, 391, -2/5*w^3 - 2/5*w^2 + 27/5*w + 6/5]', '[391, 391, w^3 - w^2 - 10*w + 5]', '[391, 391, 8/5*w^3 - 12/5*w^2 - 78/5*w + 61/5]', '[391, 391, -8/5*w^3 + 12/5*w^2 + 83/5*w - 56/5]', '[400, 10, -8/5*w^3 + 12/5*w^2 + 78/5*w - 66/5]', '[400, 10, -2*w^3 + 2*w^2 + 20*w - 4]', '[412, 206, w^3 - w^2 - 11*w + 6]', '[412, 206, 3/5*w^3 - 7/5*w^2 - 33/5*w + 46/5]', '[412, 206, 3/5*w^3 - 2/5*w^2 - 38/5*w - 9/5]', '[412, 206, w^3 - 2*w^2 - 10*w + 5]', '[425, 85, -1/5*w^3 + 4/5*w^2 + 1/5*w + 13/5]', '[425, 85, -w^3 + w^2 + 10*w + 3]', '[425, 85, 4/5*w^3 - 11/5*w^2 - 34/5*w + 53/5]', '[425, 85, -w^2 + 4]', '[425, 85, 4/5*w^3 - 1/5*w^2 - 44/5*w - 12/5]', '[425, 85, w^2 - 2*w - 3]', '[425, 85, -w^3 + 2*w^2 + 9*w - 13]', '[425, 85, -1/5*w^3 - 1/5*w^2 + 6/5*w - 17/5]', '[433, 433, w^3 - w^2 - 11*w + 9]', '[433, 433, 2/5*w^3 - 3/5*w^2 - 32/5*w + 19/5]', '[433, 433, 1/5*w^3 + 1/5*w^2 - 6/5*w - 38/5]', '[433, 433, w^3 - 2*w^2 - 10*w + 2]', '[439, 439, -11/5*w^3 + 14/5*w^2 + 111/5*w - 47/5]', '[439, 439, -1/5*w^3 + 4/5*w^2 + 21/5*w - 27/5]', '[439, 439, -3/5*w^3 + 7/5*w^2 + 28/5*w - 56/5]', '[439, 439, -11/5*w^3 + 19/5*w^2 + 106/5*w - 67/5]', '[441, 21, -4/5*w^3 + 11/5*w^2 + 34/5*w - 48/5]', '[441, 21, 4/5*w^3 - 1/5*w^2 - 44/5*w - 7/5]', '[441, 21, -w^2 + 5]', '[441, 21, -w^2 + 2*w + 4]', '[452, 226, 11/5*w^3 - 19/5*w^2 - 111/5*w + 62/5]', '[452, 226, 4/5*w^3 - 11/5*w^2 - 39/5*w + 63/5]', '[452, 226, 4/5*w^3 - 1/5*w^2 - 49/5*w - 17/5]', '[452, 226, -13/5*w^3 + 17/5*w^2 + 123/5*w - 46/5]', '[484, 22, w^2 - w - 7]', '[484, 22, -w^2 + w + 3]', '[503, 503, -2/5*w^3 + 8/5*w^2 + 17/5*w - 34/5]', '[503, 503, -2/5*w^3 + 8/5*w^2 + 17/5*w - 39/5]', '[503, 503, 2/5*w^3 + 2/5*w^2 - 27/5*w - 16/5]', '[503, 503, 2/5*w^3 + 2/5*w^2 - 27/5*w - 11/5]', '[508, 254, w^3 - w^2 - 7*w + 4]', '[508, 254, -13/5*w^3 + 17/5*w^2 + 123/5*w - 36/5]', '[508, 254, 13/5*w^3 - 22/5*w^2 - 118/5*w + 91/5]', '[508, 254, w^3 - 2*w^2 - 6*w + 3]', '[521, 521, -2/5*w^3 + 8/5*w^2 + 12/5*w - 39/5]', '[521, 521, -2/5*w^3 + 8/5*w^2 + 12/5*w - 29/5]', '[521, 521, 2/5*w^3 + 2/5*w^2 - 22/5*w - 11/5]', '[521, 521, 2/5*w^3 + 2/5*w^2 - 22/5*w - 21/5]', '[529, 23, -7/5*w^3 + 8/5*w^2 + 77/5*w - 44/5]', '[529, 23, 2/5*w^3 - 3/5*w^2 - 17/5*w - 16/5]', '[529, 23, 6/5*w^3 - 9/5*w^2 - 66/5*w + 47/5]', '[529, 23, 6/5*w^3 - 14/5*w^2 - 41/5*w + 27/5]', '[529, 23, 6/5*w^3 - 9/5*w^2 - 66/5*w + 22/5]', '[529, 23, -2/5*w^3 + 3/5*w^2 + 17/5*w - 34/5]', '[529, 529, -w^3 + 2*w^2 + 9*w - 4]', '[529, 529, -1/5*w^3 - 1/5*w^2 + 6/5*w + 28/5]', '[529, 529, -1/5*w^3 + 4/5*w^2 + 1/5*w - 32/5]', '[529, 529, w^3 - w^2 - 10*w + 6]', '[569, 569, 2*w^3 - 4*w^2 - 17*w + 14]', '[569, 569, 6/5*w^3 - 4/5*w^2 - 51/5*w - 3/5]', '[569, 569, -6/5*w^3 + 14/5*w^2 + 41/5*w - 52/5]', '[569, 569, 2*w^3 - 2*w^2 - 19*w + 5]', '[575, 115, 1/5*w^3 - 4/5*w^2 - 1/5*w + 37/5]', '[575, 115, w^3 - w^2 - 10*w + 7]', '[575, 115, w^2 - 2*w - 8]', '[575, 115, -4/5*w^3 + 11/5*w^2 + 34/5*w - 28/5]', '[575, 115, -4/5*w^3 + 1/5*w^2 + 44/5*w - 13/5]', '[575, 115, w^2 - 9]', '[575, 115, w^3 - 2*w^2 - 9*w + 3]', '[575, 115, -1/5*w^3 - 1/5*w^2 + 6/5*w + 33/5]', '[576, 12, -2/5*w^3 - 2/5*w^2 + 22/5*w + 16/5]', '[576, 12, -2/5*w^3 + 8/5*w^2 + 12/5*w - 34/5]', '[599, 599, -11/5*w^3 + 14/5*w^2 + 101/5*w - 22/5]', '[599, 599, -7/5*w^3 + 8/5*w^2 + 57/5*w - 34/5]', '[599, 599, -7/5*w^3 + 13/5*w^2 + 52/5*w - 24/5]', '[599, 599, -11/5*w^3 + 19/5*w^2 + 96/5*w - 82/5]', '[601, 601, 7/5*w^3 - 13/5*w^2 - 67/5*w + 39/5]', '[601, 601, -1/5*w^3 + 4/5*w^2 + 16/5*w - 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26/5*w^2 - 134/5*w + 103/5]', '[809, 809, 2*w^3 - 3*w^2 - 18*w + 9]', '[809, 809, -6/5*w^3 + 9/5*w^2 + 46/5*w - 22/5]', '[809, 809, 6/5*w^3 - 9/5*w^2 - 46/5*w + 27/5]', '[809, 809, -2*w^3 + 3*w^2 + 18*w - 10]', '[823, 823, 3/5*w^3 - 2/5*w^2 - 23/5*w - 44/5]', '[823, 823, 12/5*w^3 - 18/5*w^2 - 112/5*w + 39/5]', '[823, 823, -12/5*w^3 + 18/5*w^2 + 112/5*w - 79/5]', '[823, 823, 7/5*w^3 - 18/5*w^2 - 57/5*w + 94/5]', '[841, 29, -6/5*w^3 + 9/5*w^2 + 66/5*w - 32/5]', '[841, 29, 6/5*w^3 - 9/5*w^2 - 66/5*w + 37/5]', '[857, 857, -w^3 + 3*w^2 + 6*w - 11]', '[857, 857, 9/5*w^3 - 6/5*w^2 - 89/5*w + 3/5]', '[857, 857, -9/5*w^3 + 21/5*w^2 + 74/5*w - 83/5]', '[857, 857, -w^3 + 9*w + 3]', '[881, 881, 7/5*w^3 - 18/5*w^2 - 67/5*w + 64/5]', '[881, 881, -w^3 + 13*w + 4]', '[881, 881, w^3 - 3*w^2 - 10*w + 16]', '[881, 881, -7/5*w^3 + 3/5*w^2 + 82/5*w - 14/5]', '[887, 887, 8/5*w^3 - 7/5*w^2 - 78/5*w + 21/5]', '[887, 887, -4/5*w^3 + 11/5*w^2 + 24/5*w - 48/5]', '[887, 887, -4/5*w^3 + 1/5*w^2 + 34/5*w + 17/5]', '[887, 887, -8/5*w^3 + 17/5*w^2 + 68/5*w - 56/5]', '[911, 911, 2*w^3 - 3*w^2 - 20*w + 4]', '[911, 911, 2/5*w^3 - 3/5*w^2 - 32/5*w - 16/5]', '[911, 911, 2/5*w^3 - 3/5*w^2 - 32/5*w + 49/5]', '[911, 911, -2*w^3 + 3*w^2 + 20*w - 17]', '[919, 919, -w^3 + w^2 + 10*w - 10]', '[919, 919, 1/5*w^3 + 1/5*w^2 - 6/5*w - 48/5]', '[919, 919, w^3 - 3*w^2 - 7*w + 15]', '[919, 919, -w^3 + 3*w^2 + 7*w - 9]', '[937, 937, 13/5*w^3 - 22/5*w^2 - 123/5*w + 76/5]', '[937, 937, 12/5*w^3 - 18/5*w^2 - 122/5*w + 49/5]', '[937, 937, -12/5*w^3 + 18/5*w^2 + 122/5*w - 79/5]', '[937, 937, 4/5*w^3 - 6/5*w^2 - 54/5*w + 43/5]', '[953, 953, w^3 - 3*w^2 - 6*w + 9]', '[953, 953, -9/5*w^3 + 21/5*w^2 + 74/5*w - 93/5]', '[953, 953, 9/5*w^3 - 6/5*w^2 - 89/5*w - 7/5]', '[953, 953, w^3 - 9*w - 1]', '[961, 31, 8/5*w^3 - 12/5*w^2 - 68/5*w + 31/5]', '[961, 31, -8/5*w^3 + 12/5*w^2 + 68/5*w - 41/5]', '[991, 991, 7/5*w^3 - 18/5*w^2 - 52/5*w + 74/5]', '[991, 991, -7/5*w^3 + 18/5*w^2 + 52/5*w - 64/5]', '[991, 991, -8/5*w^3 + 12/5*w^2 + 73/5*w - 76/5]', '[991, 991, -7/5*w^3 + 3/5*w^2 + 67/5*w + 11/5]', '[1031, 1031, -16/5*w^3 + 24/5*w^2 + 156/5*w - 67/5]', '[1031, 1031, -4*w - 1]', '[1031, 1031, 4*w - 5]', '[1031, 1031, -16/5*w^3 + 24/5*w^2 + 156/5*w - 97/5]', '[1039, 1039, -8/5*w^3 + 17/5*w^2 + 78/5*w - 96/5]', '[1039, 1039, -4/5*w^3 + 1/5*w^2 + 54/5*w - 28/5]', '[1039, 1039, 1/5*w^3 - 9/5*w^2 - 1/5*w + 67/5]', '[1039, 1039, 8/5*w^3 - 7/5*w^2 - 88/5*w - 9/5]', '[1049, 1049, -9/5*w^3 + 16/5*w^2 + 84/5*w - 48/5]', '[1049, 1049, -1/5*w^3 + 4/5*w^2 - 4/5*w - 22/5]', '[1049, 1049, 1/5*w^3 + 1/5*w^2 - 1/5*w - 23/5]', '[1049, 1049, 9/5*w^3 - 11/5*w^2 - 89/5*w + 43/5]', '[1063, 1063, -9/5*w^3 + 11/5*w^2 + 79/5*w - 33/5]', '[1063, 1063, -9/5*w^3 + 16/5*w^2 + 74/5*w - 58/5]', '[1063, 1063, 9/5*w^3 - 11/5*w^2 - 79/5*w + 23/5]', '[1063, 1063, 9/5*w^3 - 16/5*w^2 - 74/5*w + 48/5]', '[1153, 1153, -7/5*w^3 + 8/5*w^2 + 67/5*w - 44/5]', '[1153, 1153, 3/5*w^3 - 2/5*w^2 - 23/5*w - 24/5]', '[1153, 1153, -3/5*w^3 + 7/5*w^2 + 18/5*w - 46/5]', '[1153, 1153, 7/5*w^3 - 13/5*w^2 - 62/5*w + 24/5]', '[1193, 1193, w^3 - w^2 - 8*w - 2]', '[1193, 1193, -9/5*w^3 + 16/5*w^2 + 79/5*w - 38/5]', '[1193, 1193, -9/5*w^3 + 11/5*w^2 + 84/5*w - 48/5]', '[1193, 1193, -w^3 + 2*w^2 + 7*w - 10]', '[1223, 1223, w^2 - 4*w - 3]', '[1223, 1223, -12/5*w^3 + 23/5*w^2 + 112/5*w - 89/5]', '[1223, 1223, 12/5*w^3 - 13/5*w^2 - 122/5*w + 34/5]', '[1223, 1223, w^2 + 2*w - 6]', '[1231, 1231, 4/5*w^3 - 11/5*w^2 - 44/5*w + 18/5]', '[1231, 1231, -8/5*w^3 + 17/5*w^2 + 78/5*w - 101/5]', '[1231, 1231, -8/5*w^3 + 7/5*w^2 + 88/5*w + 14/5]', '[1231, 1231, 6/5*w^3 - 4/5*w^2 - 46/5*w - 3/5]', '[1249, 1249, 1/5*w^3 - 4/5*w^2 - 16/5*w + 42/5]', '[1249, 1249, -7/5*w^3 + 8/5*w^2 + 72/5*w - 44/5]', '[1249, 1249, 7/5*w^3 - 13/5*w^2 - 67/5*w + 29/5]', '[1249, 1249, 1/5*w^3 + 1/5*w^2 - 21/5*w - 23/5]', '[1297, 1297, -13/5*w^3 + 17/5*w^2 + 123/5*w - 61/5]', '[1297, 1297, -w^3 + 2*w^2 + 6*w - 8]', '[1297, 1297, w^3 - w^2 - 7*w - 1]', '[1297, 1297, 13/5*w^3 - 22/5*w^2 - 118/5*w + 66/5]', '[1303, 1303, 12/5*w^3 - 13/5*w^2 - 117/5*w + 34/5]', '[1303, 1303, -4/5*w^3 + 1/5*w^2 + 29/5*w + 12/5]', '[1303, 1303, -4/5*w^3 + 11/5*w^2 + 19/5*w - 38/5]', '[1303, 1303, -12/5*w^3 + 23/5*w^2 + 107/5*w - 84/5]', '[1327, 1327, -3/5*w^3 + 2/5*w^2 + 28/5*w - 36/5]', '[1327, 1327, -3/5*w^3 + 7/5*w^2 + 23/5*w - 61/5]', '[1327, 1327, 3/5*w^3 - 2/5*w^2 - 28/5*w - 34/5]', '[1327, 1327, -3/5*w^3 + 7/5*w^2 + 23/5*w + 9/5]', '[1361, 1361, 3/5*w^3 + 3/5*w^2 - 48/5*w + 16/5]', '[1361, 1361, 9/5*w^3 - 21/5*w^2 - 84/5*w + 118/5]', '[1361, 1361, -9/5*w^3 + 6/5*w^2 + 99/5*w + 22/5]', '[1361, 1361, -12/5*w^3 + 13/5*w^2 + 132/5*w - 49/5]', '[1369, 37, 6/5*w^3 - 9/5*w^2 - 41/5*w + 22/5]', '[1369, 37, 14/5*w^3 - 21/5*w^2 - 129/5*w + 68/5]', '[1433, 1433, -8/5*w^3 + 17/5*w^2 + 53/5*w - 36/5]', '[1433, 1433, 16/5*w^3 - 29/5*w^2 - 141/5*w + 122/5]', '[1433, 1433, -16/5*w^3 + 19/5*w^2 + 151/5*w - 32/5]', '[1433, 1433, 8/5*w^3 - 7/5*w^2 - 63/5*w + 26/5]', '[1439, 1439, 9/5*w^3 - 11/5*w^2 - 94/5*w + 53/5]', '[1439, 1439, -3/5*w^3 + 7/5*w^2 + 38/5*w - 51/5]', '[1439, 1439, 3/5*w^3 - 2/5*w^2 - 43/5*w - 9/5]', '[1439, 1439, 9/5*w^3 - 16/5*w^2 - 89/5*w + 43/5]', '[1447, 1447, 11/5*w^3 - 14/5*w^2 - 116/5*w + 32/5]', '[1447, 1447, -w^3 + w^2 + 13*w - 7]', '[1447, 1447, -w^3 + 2*w^2 + 12*w - 6]', '[1447, 1447, -11/5*w^3 + 19/5*w^2 + 111/5*w - 87/5]', '[1481, 1481, 1/5*w^3 - 4/5*w^2 - 16/5*w + 52/5]', '[1481, 1481, 7/5*w^3 - 13/5*w^2 - 67/5*w + 19/5]', '[1481, 1481, -7/5*w^3 + 8/5*w^2 + 72/5*w - 54/5]', '[1481, 1481, 1/5*w^3 + 1/5*w^2 - 21/5*w - 33/5]', '[1511, 1511, 6/5*w^3 - 4/5*w^2 - 56/5*w + 27/5]', '[1511, 1511, -6/5*w^3 + 14/5*w^2 + 46/5*w - 77/5]', '[1511, 1511, -6/5*w^3 + 4/5*w^2 + 56/5*w + 23/5]', '[1511, 1511, 6/5*w^3 - 14/5*w^2 - 46/5*w + 27/5]', '[1543, 1543, -8/5*w^3 + 17/5*w^2 + 68/5*w - 51/5]', '[1543, 1543, -4/5*w^3 + 1/5*w^2 + 34/5*w + 22/5]', '[1543, 1543, -4/5*w^3 + 11/5*w^2 + 24/5*w - 53/5]', '[1543, 1543, 8/5*w^3 - 7/5*w^2 - 78/5*w + 26/5]', '[1559, 1559, -12/5*w^3 + 18/5*w^2 + 107/5*w - 44/5]', '[1559, 1559, 8/5*w^3 - 12/5*w^2 - 63/5*w + 21/5]', '[1559, 1559, -8/5*w^3 + 12/5*w^2 + 63/5*w - 46/5]', '[1559, 1559, -12/5*w^3 + 18/5*w^2 + 107/5*w - 69/5]', '[1583, 1583, w^2 + w - 8]', '[1583, 1583, 8/5*w^3 - 7/5*w^2 - 83/5*w + 26/5]', '[1583, 1583, -8/5*w^3 + 17/5*w^2 + 73/5*w - 56/5]', '[1583, 1583, w^2 - 3*w - 6]', '[1609, 1609, -6/5*w^3 + 9/5*w^2 + 71/5*w - 52/5]', '[1609, 1609, 2*w^3 - 3*w^2 - 21*w + 8]', '[1609, 1609, -2*w^3 + 3*w^2 + 21*w - 14]', '[1609, 1609, -6/5*w^3 + 9/5*w^2 + 71/5*w - 22/5]', '[1663, 1663, -8/5*w^3 + 17/5*w^2 + 78/5*w - 56/5]', '[1663, 1663, -9/5*w^3 + 11/5*w^2 + 84/5*w - 53/5]', '[1663, 1663, -4/5*w^3 + 11/5*w^2 + 44/5*w - 63/5]', '[1663, 1663, 8/5*w^3 - 7/5*w^2 - 88/5*w + 31/5]', '[1681, 41, 2*w^3 - 3*w^2 - 17*w + 6]', '[1681, 41, -2*w^3 + 3*w^2 + 17*w - 12]', '[1759, 1759, 1/5*w^3 + 1/5*w^2 - 26/5*w - 13/5]', '[1759, 1759, -11/5*w^3 + 19/5*w^2 + 106/5*w - 57/5]', '[1759, 1759, 11/5*w^3 - 14/5*w^2 - 111/5*w + 57/5]', '[1759, 1759, -1/5*w^3 + 4/5*w^2 + 21/5*w - 37/5]', '[1777, 1777, -9/5*w^3 + 6/5*w^2 + 89/5*w - 18/5]', '[1777, 1777, 1/5*w^3 + 6/5*w^2 - 6/5*w - 48/5]', '[1777, 1777, w^3 - 9*w - 6]', '[1777, 1777, -18/5*w^3 + 27/5*w^2 + 168/5*w - 86/5]', '[1823, 1823, -14/5*w^3 + 26/5*w^2 + 139/5*w - 123/5]', '[1823, 1823, -6/5*w^3 + 4/5*w^2 + 81/5*w - 37/5]', '[1823, 1823, 6/5*w^3 - 14/5*w^2 - 71/5*w + 42/5]', '[1823, 1823, 14/5*w^3 - 16/5*w^2 - 149/5*w + 28/5]', '[1847, 1847, 4/5*w^3 - 16/5*w^2 - 39/5*w + 88/5]', '[1847, 1847, -16/5*w^3 + 29/5*w^2 + 151/5*w - 112/5]', '[1847, 1847, 16/5*w^3 - 19/5*w^2 - 161/5*w + 52/5]', '[1847, 1847, -17/5*w^3 + 28/5*w^2 + 167/5*w - 124/5]', '[1849, 43, -8/5*w^3 + 12/5*w^2 + 88/5*w - 61/5]', '[1849, 43, 8/5*w^3 - 12/5*w^2 - 88/5*w + 31/5]', '[1871, 1871, -6/5*w^3 + 4/5*w^2 + 66/5*w - 27/5]', '[1871, 1871, 2/5*w^3 + 2/5*w^2 - 32/5*w - 31/5]', '[1871, 1871, 2/5*w^3 - 8/5*w^2 - 22/5*w + 59/5]', '[1871, 1871, 6/5*w^3 - 14/5*w^2 - 56/5*w + 37/5]', '[1873, 1873, -1/5*w^3 + 9/5*w^2 - 4/5*w - 47/5]', '[1873, 1873, -w^3 + 11*w + 1]', '[1873, 1873, -w^3 + 3*w^2 + 8*w - 11]', '[1873, 1873, 1/5*w^3 + 6/5*w^2 - 11/5*w - 43/5]', '[1889, 1889, -16/5*w^3 + 29/5*w^2 + 156/5*w - 122/5]', '[1889, 1889, -17/5*w^3 + 28/5*w^2 + 152/5*w - 74/5]', '[1889, 1889, -18/5*w^3 + 32/5*w^2 + 163/5*w - 116/5]', '[1889, 1889, 16/5*w^3 - 19/5*w^2 - 166/5*w + 47/5]', '[1951, 1951, 8/5*w^3 - 12/5*w^2 - 63/5*w + 41/5]', '[1951, 1951, -12/5*w^3 + 18/5*w^2 + 107/5*w - 64/5]', '[1951, 1951, 12/5*w^3 - 18/5*w^2 - 107/5*w + 49/5]', '[1951, 1951, -8/5*w^3 + 12/5*w^2 + 63/5*w - 26/5]', '[1993, 1993, 4/5*w^3 - 11/5*w^2 - 34/5*w + 88/5]', '[1993, 1993, 13/5*w^3 - 22/5*w^2 - 133/5*w + 56/5]', '[1993, 1993, 13/5*w^3 - 22/5*w^2 - 128/5*w + 66/5]', '[1993, 1993, -3/5*w^3 + 7/5*w^2 + 43/5*w - 51/5]', '[1999, 1999, -7/5*w^3 + 13/5*w^2 + 77/5*w - 49/5]', '[1999, 1999, -9/5*w^3 + 16/5*w^2 + 94/5*w - 68/5]', '[1999, 1999, 9/5*w^3 - 11/5*w^2 - 99/5*w + 33/5]', '[1999, 1999, -7/5*w^3 + 8/5*w^2 + 82/5*w - 34/5]']}
• 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, 10, -9, -2, 1], 'conductor': 104, 'degree': 4, 'dirichlet_group': [1, 53, 77, 25], 'disc_abs': 10816, 'disc_rad': 26, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 2]]], [5, [[2, 2]]], [7, [[2, 2]]], [11, [[2, 2]]], [13, [0]], [17, [[1, 4]]], [19, [[2, 2]]], [23, [[1, 4]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 10.198039027185569, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.10816.1', 'local_algs': ['2.4.6.1', '13.4.2.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 13], 'rd': 10.1980390272, 'regulator': {'__RealLiteral__': 0, 'data': '4.87014657656', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-3.-1.1', '-2.0.1', '-26.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2}{5} a^{3} - \\frac{3}{5} a^{2} - \\frac{17}{5} a + \\frac{4}{5} \\)', '\\( \\frac{2}{5} a^{3} - \\frac{3}{5} a^{2} - \\frac{22}{5} a + \\frac{4}{5} \\)', '\\( \\frac{4}{5} a^{3} - \\frac{6}{5} a^{2} - \\frac{39}{5} a + \\frac{18}{5} \\)'], 'unitsGmodule': [[14, 1]], 'unitsType': 'Type IV', 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/5*a^3 + 1/5*a^2 - 1/5*a + 2/5']}