Hilbert modular form data - 4.4.14400.1-1.1-c

Formats: - HTML - YAML - JSON - 2024-06-07T15:18:04.730789

• 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': 14400, 'field_bad_primes': [2, 3, 5], 'field_label': '4.4.14400.1', 'is_CM': 'yes', 'is_base_change': 'yes', 'label': '4.4.14400.1-1.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [], 'level_ideal': '[1, 1, 1]', 'level_label': '1.1', 'level_norm': 1, 'parallel_weight': 2, 'short_label': '1.1-c', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [], 'hecke_eigenvalues': [-4, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, -22, -22, -22, -22, 0, 0, 0, 0, 26, 26, 0, 0, 0, 0, 14, 14, 14, 14, 0, 0, 0, 0, 26, 26, 26, 26, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 26, 26, 26, 26, 0, 0, 0, 0, 38, 38, 38, 38, 0, 0, 0, 0, -22, -22, -22, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 0, 0, 0, 0, -46, -46, -22, -22, -22, -22, 0, 0, 0, 0, -46, -46, -46, -46, 26, 26, 26, 26, -46, -46, -46, -46, 0, 0, 0, 0, 0, 0, 0, 0, -34, -34, -34, -34, -22, -22, -22, -22, 38, 38, 38, 38, 0, 0, 0, 0, 0, 0, 0, 0, -58, -58, -58, -58, 0, 0, 0, 0, 0, 0, 0, 0, 62, 62], 'hecke_polynomial': 'x', 'label': '4.4.14400.1-1.1-c'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 14400, 'ideals': ['[1, 1, 1]', '[4, 2, -2/19*w^3 + 3/19*w^2 + 37/19*w - 3]', '[5, 5, 3/19*w^3 + 5/19*w^2 - 27/19*w - 1]', '[5, 5, -3/19*w^3 + 14/19*w^2 + 8/19*w - 2]', '[9, 3, -2/19*w^3 + 3/19*w^2 + 37/19*w - 4]', '[16, 2, 2]', '[19, 19, -w]', '[19, 19, 4/19*w^3 - 6/19*w^2 - 55/19*w + 1]', '[19, 19, 4/19*w^3 - 6/19*w^2 - 55/19*w + 2]', '[19, 19, w - 1]', '[20, 10, 2/19*w^3 - 3/19*w^2 + 1/19*w - 1]', '[20, 10, 2/19*w^3 - 3/19*w^2 + 1/19*w + 1]', '[25, 5, -2/19*w^3 + 3/19*w^2 + 37/19*w - 2]', '[25, 5, 4/19*w^3 - 6/19*w^2 - 36/19*w + 1]', '[25, 5, -2/19*w^3 + 3/19*w^2 + 37/19*w]', '[29, 29, -5/19*w^3 - 2/19*w^2 + 64/19*w + 2]', '[29, 29, 10/19*w^3 - 34/19*w^2 - 71/19*w + 9]', '[29, 29, 4/19*w^3 - 6/19*w^2 - 55/19*w + 4]', '[29, 29, -w + 3]', '[36, 6, 2/19*w^3 - 3/19*w^2 - 37/19*w + 1]', '[45, 15, -1/19*w^3 - 8/19*w^2 + 28/19*w]', '[45, 15, 1/19*w^3 - 11/19*w^2 - 9/19*w + 1]', '[49, 7, 5/19*w^3 - 17/19*w^2 - 64/19*w + 11]', '[49, 7, 6/19*w^3 - 9/19*w^2 - 92/19*w - 1]', '[64, 4, -4/19*w^3 + 6/19*w^2 + 74/19*w - 6]', '[71, 71, 3/19*w^3 + 5/19*w^2 - 46/19*w - 1]', '[71, 71, 6/19*w^3 - 9/19*w^2 - 73/19*w]', '[71, 71, 6/19*w^3 - 9/19*w^2 - 73/19*w + 4]', '[71, 71, -3/19*w^3 + 14/19*w^2 + 27/19*w - 3]', '[76, 38, 1/19*w^3 - 11/19*w^2 + 29/19*w - 2]', '[76, 38, -7/19*w^3 + 20/19*w^2 + 82/19*w - 11]', '[76, 38, 7/19*w^3 - 1/19*w^2 - 101/19*w - 6]', '[76, 38, 1/19*w^3 + 8/19*w^2 + 10/19*w + 1]', '[80, 10, 6/19*w^3 + 10/19*w^2 - 54/19*w - 2]', '[80, 10, -6/19*w^3 + 28/19*w^2 + 16/19*w - 4]', '[81, 3, 3]', '[95, 95, -6/19*w^3 + 9/19*w^2 + 92/19*w + 2]', '[95, 95, -5/19*w^3 + 17/19*w^2 + 26/19*w - 5]', '[95, 95, 2/19*w^3 - 3/19*w^2 - 56/19*w - 3]', '[95, 95, 7/19*w^3 - 20/19*w^2 - 63/19*w + 5]', '[95, 95, 7/19*w^3 - 1/19*w^2 - 82/19*w - 1]', '[95, 95, 2/19*w^3 - 3/19*w^2 - 56/19*w + 6]', '[95, 95, -5/19*w^3 - 2/19*w^2 + 45/19*w + 3]', '[95, 95, -6/19*w^3 + 9/19*w^2 + 92/19*w - 7]', '[100, 10, -2/19*w^3 + 3/19*w^2 + 37/19*w + 3]', '[100, 10, -8/19*w^3 + 31/19*w^2 + 53/19*w - 9]', '[100, 10, 2/19*w^3 - 3/19*w^2 - 37/19*w + 5]', '[101, 101, 7/19*w^3 - 1/19*w^2 - 63/19*w - 3]', '[101, 101, -9/19*w^3 + 23/19*w^2 + 81/19*w - 5]', '[101, 101, 9/19*w^3 - 4/19*w^2 - 100/19*w]', '[101, 101, 7/19*w^3 - 20/19*w^2 - 44/19*w + 6]', '[116, 58, 2/19*w^3 - 3/19*w^2 + 1/19*w - 3]', '[116, 58, -3/19*w^3 + 14/19*w^2 + 8/19*w - 5]', '[116, 58, 3/19*w^3 + 5/19*w^2 - 27/19*w - 4]', '[116, 58, -5/19*w^3 - 2/19*w^2 + 64/19*w + 1]', '[121, 11, 6/19*w^3 - 9/19*w^2 - 54/19*w + 1]', '[121, 11, -6/19*w^3 + 9/19*w^2 + 54/19*w - 2]', '[125, 5, 3/19*w^3 - 14/19*w^2 + 30/19*w - 2]', '[125, 5, 3/19*w^3 + 5/19*w^2 + 11/19*w + 1]', '[125, 25, 5/19*w^3 + 2/19*w^2 - 26/19*w - 2]', '[125, 25, 5/19*w^3 - 17/19*w^2 - 7/19*w + 3]', '[139, 139, 9/19*w^3 - 4/19*w^2 - 100/19*w - 2]', '[139, 139, -7/19*w^3 + 1/19*w^2 + 63/19*w + 1]', '[139, 139, 7/19*w^3 - 20/19*w^2 - 44/19*w + 4]', '[139, 139, w - 5]', '[144, 6, -4/19*w^3 + 6/19*w^2 + 74/19*w - 8]', '[145, 145, 1/19*w^3 - 11/19*w^2 + 10/19*w - 1]', '[145, 145, -2/19*w^3 + 3/19*w^2 - 20/19*w]', '[145, 145, w^2 + 3*w + 2]', '[145, 145, 4/19*w^3 - 25/19*w^2 + 2/19*w + 4]', '[145, 145, 4/19*w^3 + 13/19*w^2 - 36/19*w - 3]', '[145, 145, -7/19*w^3 + 1/19*w^2 + 44/19*w + 1]', '[145, 145, -2/19*w^3 + 22/19*w^2 - 20/19*w - 3]', '[145, 145, 1/19*w^3 + 8/19*w^2 - 9/19*w + 1]', '[149, 149, -1/19*w^3 + 11/19*w^2 - 10/19*w - 6]', '[149, 149, -3/19*w^3 - 5/19*w^2 + 46/19*w]', '[149, 149, -3/19*w^3 + 14/19*w^2 + 27/19*w - 2]', '[149, 149, 1/19*w^3 + 8/19*w^2 - 9/19*w - 6]', '[169, 13, 14/19*w^3 - 40/19*w^2 - 126/19*w + 13]', '[169, 13, 10/19*w^3 - 34/19*w^2 - 52/19*w + 7]', '[171, 57, 1/19*w^3 - 11/19*w^2 + 48/19*w - 2]', '[171, 57, -11/19*w^3 + 26/19*w^2 + 137/19*w - 12]', '[171, 57, -11/19*w^3 + 7/19*w^2 + 156/19*w + 4]', '[171, 57, -1/19*w^3 - 8/19*w^2 - 29/19*w]', '[180, 30, -8/19*w^3 - 7/19*w^2 + 53/19*w + 3]', '[180, 30, -8/19*w^3 + 31/19*w^2 + 15/19*w - 5]', '[191, 191, -10/19*w^3 + 15/19*w^2 + 109/19*w - 6]', '[191, 191, 6/19*w^3 - 9/19*w^2 - 35/19*w - 2]', '[191, 191, -6/19*w^3 + 9/19*w^2 + 35/19*w - 4]', '[191, 191, 10/19*w^3 - 15/19*w^2 - 109/19*w]', '[196, 14, -3/19*w^3 + 14/19*w^2 + 8/19*w + 1]', '[196, 14, -3/19*w^3 - 5/19*w^2 - 11/19*w + 2]', '[211, 211, 1/19*w^3 + 8/19*w^2 - 28/19*w - 8]', '[211, 211, 1/19*w^3 - 11/19*w^2 - 9/19*w - 1]', '[211, 211, -1/19*w^3 - 8/19*w^2 + 28/19*w - 2]', '[211, 211, -1/19*w^3 + 11/19*w^2 + 9/19*w - 9]', '[225, 15, -12/19*w^3 + 37/19*w^2 + 89/19*w - 10]', '[225, 15, 4/19*w^3 - 6/19*w^2 - 74/19*w - 1]', '[225, 15, 4/19*w^3 - 6/19*w^2 - 74/19*w + 5]', '[239, 239, 4/19*w^3 - 25/19*w^2 - 17/19*w + 12]', '[239, 239, -1/19*w^3 - 8/19*w^2 - 29/19*w + 5]', '[239, 239, 10/19*w^3 - 15/19*w^2 - 128/19*w + 1]', '[239, 239, -4/19*w^3 - 13/19*w^2 + 55/19*w + 10]', '[241, 241, -2/19*w^3 + 3/19*w^2 + 56/19*w - 4]', '[241, 241, -6/19*w^3 + 9/19*w^2 + 92/19*w]', '[241, 241, 6/19*w^3 - 9/19*w^2 - 92/19*w + 5]', '[241, 241, -2/19*w^3 + 3/19*w^2 + 56/19*w + 1]', '[245, 35, 5/19*w^3 + 2/19*w^2 - 83/19*w]', '[245, 35, 1/19*w^3 - 11/19*w^2 - 28/19*w + 6]', '[245, 35, -4/19*w^3 + 6/19*w^2 + 17/19*w - 4]', '[245, 35, -8/19*w^3 + 12/19*w^2 + 91/19*w + 1]', '[256, 4, 4]', '[261, 87, -3/19*w^3 - 5/19*w^2 + 65/19*w - 1]', '[261, 87, -7/19*w^3 + 20/19*w^2 + 63/19*w - 4]', '[261, 87, -7/19*w^3 + 1/19*w^2 + 82/19*w]', '[261, 87, 5/19*w^3 + 2/19*w^2 - 45/19*w - 4]', '[269, 269, -10/19*w^3 + 34/19*w^2 + 71/19*w - 11]', '[269, 269, 8/19*w^3 - 12/19*w^2 - 129/19*w + 11]', '[269, 269, -10/19*w^3 + 34/19*w^2 + 71/19*w - 8]', '[269, 269, -13/19*w^3 + 48/19*w^2 + 60/19*w - 8]', '[284, 142, 3/19*w^3 - 14/19*w^2 + 30/19*w - 3]', '[284, 142, -8/19*w^3 + 31/19*w^2 + 53/19*w - 11]', '[284, 142, -16/19*w^3 + 43/19*w^2 + 201/19*w - 23]', '[284, 142, 15/19*w^3 - 51/19*w^2 - 97/19*w + 14]', '[289, 17, 30/19*w^3 - 7/19*w^2 - 384/19*w - 14]', '[289, 17, 11/19*w^3 - 45/19*w^2 - 80/19*w + 17]', '[304, 38, -2*w]', '[304, 38, 8/19*w^3 - 12/19*w^2 - 110/19*w + 2]', '[304, 38, 8/19*w^3 - 12/19*w^2 - 110/19*w + 4]', '[304, 38, 2*w - 2]', '[311, 311, -12/19*w^3 + 37/19*w^2 + 108/19*w - 15]', '[311, 311, -24/19*w^3 + 55/19*w^2 + 273/19*w - 22]', '[311, 311, -8/19*w^3 - 7/19*w^2 + 110/19*w + 4]', '[311, 311, 4/19*w^3 + 13/19*w^2 - 36/19*w - 7]', '[320, 20, 4/19*w^3 - 6/19*w^2 + 2/19*w - 2]', '[320, 20, 4/19*w^3 - 6/19*w^2 + 2/19*w + 2]', '[324, 6, -6/19*w^3 + 9/19*w^2 + 111/19*w - 9]', '[331, 331, -1/19*w^3 - 8/19*w^2 + 66/19*w - 2]', '[331, 331, -6/19*w^3 + 28/19*w^2 + 35/19*w - 9]', '[331, 331, 20/19*w^3 - 68/19*w^2 - 161/19*w + 22]', '[331, 331, 16/19*w^3 - 62/19*w^2 - 87/19*w + 15]', '[355, 355, -11/19*w^3 + 45/19*w^2 + 61/19*w - 11]', '[355, 355, 3/19*w^3 + 24/19*w^2 + 11/19*w]', '[355, 355, 1/19*w^3 - 11/19*w^2 + 29/19*w - 3]', '[355, 355, 8/19*w^3 + 26/19*w^2 - 53/19*w - 4]', '[355, 355, -8/19*w^3 + 50/19*w^2 - 23/19*w - 5]', '[355, 355, 1/19*w^3 + 8/19*w^2 + 10/19*w + 2]', '[355, 355, -3/19*w^3 + 33/19*w^2 - 68/19*w + 2]', '[355, 355, -11/19*w^3 - 12/19*w^2 + 118/19*w + 6]', '[359, 359, 13/19*w^3 - 48/19*w^2 - 79/19*w + 11]', '[359, 359, -7/19*w^3 + 20/19*w^2 + 101/19*w - 13]', '[359, 359, -15/19*w^3 + 51/19*w^2 + 116/19*w - 17]', '[359, 359, 3/19*w^3 + 5/19*w^2 - 84/19*w + 5]', '[361, 19, -2/19*w^3 + 3/19*w^2 + 37/19*w + 4]', '[361, 19, -8/19*w^3 + 12/19*w^2 + 72/19*w - 3]', '[361, 19, 8/19*w^3 - 12/19*w^2 - 110/19*w + 3]', '[361, 19, -2/19*w^3 + 3/19*w^2 + 37/19*w - 6]', '[361, 19, 8/19*w^3 - 12/19*w^2 - 72/19*w + 1]', '[361, 19, 2*w - 1]', '[361, 361, -4/19*w^3 - 13/19*w^2 + 55/19*w + 4]', '[361, 361, 4/19*w^3 - 25/19*w^2 - 17/19*w + 10]', '[361, 361, -4/19*w^3 - 13/19*w^2 + 55/19*w + 8]', '[361, 361, 4/19*w^3 - 25/19*w^2 - 17/19*w + 6]', '[379, 379, 3/19*w^3 + 5/19*w^2 - 65/19*w - 9]', '[379, 379, 25/19*w^3 - 9/19*w^2 - 339/19*w - 11]', '[379, 379, -25/19*w^3 + 66/19*w^2 + 282/19*w - 28]', '[379, 379, 3/19*w^3 - 14/19*w^2 - 46/19*w + 12]', '[380, 190, 3/19*w^3 - 14/19*w^2 - 8/19*w + 7]', '[380, 190, 3/19*w^3 - 14/19*w^2 - 46/19*w + 1]', '[380, 190, 5/19*w^3 - 17/19*w^2 - 45/19*w + 2]', '[380, 190, 3/19*w^3 + 5/19*w^2 - 65/19*w - 6]', '[380, 190, -3/19*w^3 + 14/19*w^2 + 46/19*w - 9]', '[380, 190, -5/19*w^3 - 2/19*w^2 + 64/19*w - 1]', '[380, 190, -3/19*w^3 - 5/19*w^2 + 65/19*w - 2]', '[380, 190, -3/19*w^3 - 5/19*w^2 + 27/19*w + 6]', '[389, 389, -13/19*w^3 + 48/19*w^2 + 136/19*w - 24]', '[389, 389, 11/19*w^3 - 7/19*w^2 - 118/19*w + 2]', '[389, 389, -3/19*w^3 + 14/19*w^2 + 46/19*w - 10]', '[389, 389, -13/19*w^3 - 9/19*w^2 + 193/19*w + 15]', '[400, 10, -4/19*w^3 + 6/19*w^2 + 74/19*w - 4]', '[400, 10, 8/19*w^3 - 12/19*w^2 - 72/19*w + 2]', '[400, 10, -4/19*w^3 + 6/19*w^2 + 74/19*w]', '[404, 202, w^2 - 3*w - 1]', '[404, 202, 28/19*w^3 - 99/19*w^2 - 195/19*w + 29]', '[404, 202, -8/19*w^3 + 31/19*w^2 + 91/19*w - 15]', '[404, 202, -28/19*w^3 + 99/19*w^2 + 195/19*w - 27]', '[405, 15, 9/19*w^3 + 15/19*w^2 - 81/19*w - 3]', '[405, 15, -9/19*w^3 + 42/19*w^2 + 24/19*w - 6]', '[409, 409, 2/19*w^3 - 3/19*w^2 - 56/19*w]', '[409, 409, 6/19*w^3 - 9/19*w^2 - 92/19*w + 4]', '[409, 409, -6/19*w^3 + 9/19*w^2 + 92/19*w - 1]', '[409, 409, -2/19*w^3 + 3/19*w^2 + 56/19*w - 3]', '[431, 431, -6/19*w^3 + 9/19*w^2 + 130/19*w - 13]', '[431, 431, 12/19*w^3 - 37/19*w^2 - 108/19*w + 11]', '[431, 431, 10/19*w^3 - 15/19*w^2 - 166/19*w + 14]', '[431, 431, -8/19*w^3 + 31/19*w^2 + 34/19*w - 8]', '[441, 21, 4/19*w^3 + 13/19*w^2 - 36/19*w + 1]', '[441, 21, -1/19*w^3 + 11/19*w^2 - 48/19*w - 1]', '[461, 461, 5/19*w^3 - 17/19*w^2 - 45/19*w + 1]', '[461, 461, -3/19*w^3 + 14/19*w^2 + 8/19*w - 8]', '[461, 461, 3/19*w^3 + 5/19*w^2 - 27/19*w - 7]', '[461, 461, 5/19*w^3 + 2/19*w^2 - 64/19*w + 2]', '[464, 58, 10/19*w^3 + 4/19*w^2 - 128/19*w - 4]', '[464, 58, 20/19*w^3 - 68/19*w^2 - 142/19*w + 18]', '[464, 58, 8/19*w^3 - 12/19*w^2 - 110/19*w + 8]', '[464, 58, -2*w + 6]', '[475, 95, 1/19*w^3 - 11/19*w^2 - 28/19*w - 2]', '[475, 95, -2/19*w^3 - 16/19*w^2 + 37/19*w + 4]', '[475, 95, 1/19*w^3 - 11/19*w^2 + 10/19*w - 2]', '[475, 95, 5/19*w^3 + 2/19*w^2 - 83/19*w - 8]', '[475, 95, 3/19*w^3 + 5/19*w^2 - 46/19*w - 8]', '[475, 95, -3/19*w^3 + 14/19*w^2 + 27/19*w - 10]', '[475, 95, -5/19*w^3 + 17/19*w^2 + 64/19*w - 12]', '[475, 95, -2/19*w^3 - 16/19*w^2 + 37/19*w + 9]', '[475, 95, 2/19*w^3 - 22/19*w^2 + 1/19*w + 10]', '[475, 95, 1/19*w^3 + 8/19*w^2 - 47/19*w + 4]', '[475, 95, -2/19*w^3 + 22/19*w^2 - 1/19*w - 5]', '[475, 95, 1/19*w^3 + 8/19*w^2 - 9/19*w + 2]', '[479, 479, 5/19*w^3 - 17/19*w^2 - 26/19*w + 7]', '[479, 479, 1/19*w^3 - 11/19*w^2 - 28/19*w + 7]', '[479, 479, 7/19*w^3 - 1/19*w^2 - 82/19*w + 1]', '[479, 479, -5/19*w^3 + 17/19*w^2 + 64/19*w - 3]', '[484, 22, -11/19*w^3 + 45/19*w^2 + 61/19*w - 12]', '[484, 22, 13/19*w^3 - 48/19*w^2 - 98/19*w + 15]', '[499, 499, -11/19*w^3 + 7/19*w^2 + 118/19*w + 2]', '[499, 499, 9/19*w^3 - 23/19*w^2 - 62/19*w + 4]', '[499, 499, -9/19*w^3 + 4/19*w^2 + 81/19*w]', '[499, 499, -11/19*w^3 + 26/19*w^2 + 99/19*w - 8]', '[500, 10, -4/19*w^3 + 25/19*w^2 + 17/19*w - 3]', '[500, 10, 4/19*w^3 + 13/19*w^2 - 55/19*w - 1]', '[500, 50, w^2 - 3*w + 1]', '[500, 50, w^2 + w - 1]', '[505, 505, 8/19*w^3 + 26/19*w^2 + 42/19*w + 1]', '[505, 505, 6/19*w^3 + 29/19*w^2 + 41/19*w + 2]', '[505, 505, 12/19*w^3 - 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12]', '[9869, 9869, -3/19*w^3 + 14/19*w^2 - 30/19*w - 12]', '[9869, 9869, -13/19*w^3 + 10/19*w^2 + 174/19*w - 10]', '[9869, 9869, 60/19*w^3 - 14/19*w^2 - 749/19*w - 22]', '[9869, 9869, -28/19*w^3 + 118/19*w^2 + 81/19*w - 23]', '[9904, 1238, -10/19*w^3 + 34/19*w^2 + 90/19*w - 22]', '[9904, 1238, 10/19*w^3 - 34/19*w^2 - 52/19*w - 4]', '[9904, 1238, -10/19*w^3 - 4/19*w^2 + 90/19*w - 8]', '[9904, 1238, -14/19*w^3 + 40/19*w^2 + 126/19*w - 24]', '[9931, 9931, 21/19*w^3 - 3/19*w^2 - 189/19*w - 1]', '[9931, 9931, -27/19*w^3 + 12/19*w^2 + 300/19*w + 8]', '[9931, 9931, -27/19*w^3 + 69/19*w^2 + 243/19*w - 23]', '[9931, 9931, -21/19*w^3 + 60/19*w^2 + 132/19*w - 10]', '[9941, 9941, -7/19*w^3 + 1/19*w^2 + 234/19*w - 22]', '[9941, 9941, 33/19*w^3 - 97/19*w^2 - 316/19*w + 32]', '[9941, 9941, -33/19*w^3 + 2/19*w^2 + 411/19*w + 12]', '[9941, 9941, -58/19*w^3 + 144/19*w^2 + 617/19*w - 51]', '[9980, 4990, -7/19*w^3 - 18/19*w^2 + 120/19*w - 3]', '[9980, 4990, -1/19*w^3 + 49/19*w^2 - 105/19*w - 2]', '[9980, 4990, -w^3 - 2*w^2 + 8*w + 5]', '[9980, 4990, -15/19*w^3 - 25/19*w^2 + 173/19*w + 6]', '[9980, 4990, 15/19*w^3 - 70/19*w^2 - 78/19*w + 13]', '[9980, 4990, -w^3 + 5*w^2 + w - 10]', '[9980, 4990, -1/19*w^3 - 46/19*w^2 - 10/19*w + 5]', '[9980, 4990, 7/19*w^3 - 39/19*w^2 - 63/19*w + 2]', '[9981, 3327, 41/19*w^3 - 90/19*w^2 - 616/19*w + 64]', '[9981, 3327, 13/19*w^3 - 48/19*w^2 - 98/19*w + 8]', '[9981, 3327, -13/19*w^3 - 9/19*w^2 + 155/19*w + 1]', '[9981, 3327, 11/19*w^3 - 45/19*w^2 - 61/19*w + 19]', '[10000, 10, 10]', '[10000, 50, -8/19*w^3 + 12/19*w^2 + 148/19*w + 10]', '[10000, 50, 8/19*w^3 - 12/19*w^2 - 148/19*w + 18]', '[10000, 50, -8/19*w^3 + 50/19*w^2 + 34/19*w - 16]', '[10000, 50, 8/19*w^3 + 26/19*w^2 - 110/19*w - 12]'], 'label': '4.4.14400.1', 'narrow_class_no': 2, 'primes': ['[4, 2, -2/19*w^3 + 3/19*w^2 + 37/19*w - 3]', '[5, 5, 3/19*w^3 + 5/19*w^2 - 27/19*w - 1]', '[5, 5, -3/19*w^3 + 14/19*w^2 + 8/19*w - 2]', '[9, 3, -2/19*w^3 + 3/19*w^2 + 37/19*w - 4]', '[19, 19, -w]', '[19, 19, 4/19*w^3 - 6/19*w^2 - 55/19*w + 1]', '[19, 19, 4/19*w^3 - 6/19*w^2 - 55/19*w + 2]', '[19, 19, w - 1]', '[29, 29, -5/19*w^3 - 2/19*w^2 + 64/19*w + 2]', '[29, 29, 10/19*w^3 - 34/19*w^2 - 71/19*w + 9]', '[29, 29, 4/19*w^3 - 6/19*w^2 - 55/19*w + 4]', '[29, 29, -w + 3]', '[49, 7, 5/19*w^3 - 17/19*w^2 - 64/19*w + 11]', '[49, 7, 6/19*w^3 - 9/19*w^2 - 92/19*w - 1]', '[71, 71, 3/19*w^3 + 5/19*w^2 - 46/19*w - 1]', '[71, 71, 6/19*w^3 - 9/19*w^2 - 73/19*w]', '[71, 71, 6/19*w^3 - 9/19*w^2 - 73/19*w + 4]', '[71, 71, -3/19*w^3 + 14/19*w^2 + 27/19*w - 3]', '[101, 101, 7/19*w^3 - 1/19*w^2 - 63/19*w - 3]', '[101, 101, -9/19*w^3 + 23/19*w^2 + 81/19*w - 5]', '[101, 101, 9/19*w^3 - 4/19*w^2 - 100/19*w]', '[101, 101, 7/19*w^3 - 20/19*w^2 - 44/19*w + 6]', '[121, 11, 6/19*w^3 - 9/19*w^2 - 54/19*w + 1]', '[121, 11, -6/19*w^3 + 9/19*w^2 + 54/19*w - 2]', '[139, 139, 9/19*w^3 - 4/19*w^2 - 100/19*w - 2]', '[139, 139, -7/19*w^3 + 1/19*w^2 + 63/19*w + 1]', '[139, 139, 7/19*w^3 - 20/19*w^2 - 44/19*w + 4]', '[139, 139, w - 5]', '[149, 149, -1/19*w^3 + 11/19*w^2 - 10/19*w - 6]', '[149, 149, -3/19*w^3 - 5/19*w^2 + 46/19*w]', '[149, 149, -3/19*w^3 + 14/19*w^2 + 27/19*w - 2]', '[149, 149, 1/19*w^3 + 8/19*w^2 - 9/19*w - 6]', '[169, 13, 14/19*w^3 - 40/19*w^2 - 126/19*w + 13]', '[169, 13, 10/19*w^3 - 34/19*w^2 - 52/19*w + 7]', '[191, 191, -10/19*w^3 + 15/19*w^2 + 109/19*w - 6]', '[191, 191, 6/19*w^3 - 9/19*w^2 - 35/19*w - 2]', '[191, 191, -6/19*w^3 + 9/19*w^2 + 35/19*w - 4]', '[191, 191, 10/19*w^3 - 15/19*w^2 - 109/19*w]', '[211, 211, 1/19*w^3 + 8/19*w^2 - 28/19*w - 8]', '[211, 211, 1/19*w^3 - 11/19*w^2 - 9/19*w - 1]', '[211, 211, -1/19*w^3 - 8/19*w^2 + 28/19*w - 2]', '[211, 211, -1/19*w^3 + 11/19*w^2 + 9/19*w - 9]', '[239, 239, 4/19*w^3 - 25/19*w^2 - 17/19*w + 12]', '[239, 239, -1/19*w^3 - 8/19*w^2 - 29/19*w + 5]', '[239, 239, 10/19*w^3 - 15/19*w^2 - 128/19*w + 1]', '[239, 239, -4/19*w^3 - 13/19*w^2 + 55/19*w + 10]', '[241, 241, -2/19*w^3 + 3/19*w^2 + 56/19*w - 4]', '[241, 241, -6/19*w^3 + 9/19*w^2 + 92/19*w]', '[241, 241, 6/19*w^3 - 9/19*w^2 - 92/19*w + 5]', '[241, 241, -2/19*w^3 + 3/19*w^2 + 56/19*w + 1]', '[269, 269, -10/19*w^3 + 34/19*w^2 + 71/19*w - 11]', '[269, 269, 8/19*w^3 - 12/19*w^2 - 129/19*w + 11]', '[269, 269, -10/19*w^3 + 34/19*w^2 + 71/19*w - 8]', '[269, 269, -13/19*w^3 + 48/19*w^2 + 60/19*w - 8]', '[289, 17, 30/19*w^3 - 7/19*w^2 - 384/19*w - 14]', '[289, 17, 11/19*w^3 - 45/19*w^2 - 80/19*w + 17]', '[311, 311, -12/19*w^3 + 37/19*w^2 + 108/19*w - 15]', '[311, 311, -24/19*w^3 + 55/19*w^2 + 273/19*w - 22]', '[311, 311, -8/19*w^3 - 7/19*w^2 + 110/19*w + 4]', '[311, 311, 4/19*w^3 + 13/19*w^2 - 36/19*w - 7]', '[331, 331, -1/19*w^3 - 8/19*w^2 + 66/19*w - 2]', '[331, 331, -6/19*w^3 + 28/19*w^2 + 35/19*w - 9]', '[331, 331, 20/19*w^3 - 68/19*w^2 - 161/19*w + 22]', '[331, 331, 16/19*w^3 - 62/19*w^2 - 87/19*w + 15]', '[359, 359, 13/19*w^3 - 48/19*w^2 - 79/19*w + 11]', '[359, 359, -7/19*w^3 + 20/19*w^2 + 101/19*w - 13]', '[359, 359, -15/19*w^3 + 51/19*w^2 + 116/19*w - 17]', '[359, 359, 3/19*w^3 + 5/19*w^2 - 84/19*w + 5]', '[379, 379, 3/19*w^3 + 5/19*w^2 - 65/19*w - 9]', '[379, 379, 25/19*w^3 - 9/19*w^2 - 339/19*w - 11]', '[379, 379, -25/19*w^3 + 66/19*w^2 + 282/19*w - 28]', '[379, 379, 3/19*w^3 - 14/19*w^2 - 46/19*w + 12]', '[389, 389, -13/19*w^3 + 48/19*w^2 + 136/19*w - 24]', '[389, 389, 11/19*w^3 - 7/19*w^2 - 118/19*w + 2]', '[389, 389, -3/19*w^3 + 14/19*w^2 + 46/19*w - 10]', '[389, 389, -13/19*w^3 - 9/19*w^2 + 193/19*w + 15]', '[409, 409, 2/19*w^3 - 3/19*w^2 - 56/19*w]', '[409, 409, 6/19*w^3 - 9/19*w^2 - 92/19*w + 4]', '[409, 409, -6/19*w^3 + 9/19*w^2 + 92/19*w - 1]', '[409, 409, -2/19*w^3 + 3/19*w^2 + 56/19*w - 3]', '[431, 431, -6/19*w^3 + 9/19*w^2 + 130/19*w - 13]', '[431, 431, 12/19*w^3 - 37/19*w^2 - 108/19*w + 11]', '[431, 431, 10/19*w^3 - 15/19*w^2 - 166/19*w + 14]', '[431, 431, -8/19*w^3 + 31/19*w^2 + 34/19*w - 8]', '[461, 461, 5/19*w^3 - 17/19*w^2 - 45/19*w + 1]', '[461, 461, -3/19*w^3 + 14/19*w^2 + 8/19*w - 8]', '[461, 461, 3/19*w^3 + 5/19*w^2 - 27/19*w - 7]', '[461, 461, 5/19*w^3 + 2/19*w^2 - 64/19*w + 2]', '[479, 479, 5/19*w^3 - 17/19*w^2 - 26/19*w + 7]', '[479, 479, 1/19*w^3 - 11/19*w^2 - 28/19*w + 7]', '[479, 479, 7/19*w^3 - 1/19*w^2 - 82/19*w + 1]', '[479, 479, -5/19*w^3 + 17/19*w^2 + 64/19*w - 3]', '[499, 499, -11/19*w^3 + 7/19*w^2 + 118/19*w + 2]', '[499, 499, 9/19*w^3 - 23/19*w^2 - 62/19*w + 4]', '[499, 499, -9/19*w^3 + 4/19*w^2 + 81/19*w]', '[499, 499, -11/19*w^3 + 26/19*w^2 + 99/19*w - 8]', '[509, 509, -6/19*w^3 - 10/19*w^2 + 73/19*w + 9]', '[509, 509, -1/19*w^3 + 11/19*w^2 + 47/19*w - 7]', '[509, 509, -6/19*w^3 - 10/19*w^2 + 73/19*w + 2]', '[509, 509, -9/19*w^3 + 4/19*w^2 + 138/19*w - 2]', '[529, 23, -4/19*w^3 + 6/19*w^2 + 74/19*w - 1]', '[529, 23, 4/19*w^3 - 6/19*w^2 - 74/19*w + 3]', '[571, 571, 1/19*w^3 + 8/19*w^2 - 66/19*w + 6]', '[571, 571, -9/19*w^3 + 23/19*w^2 + 119/19*w - 15]', '[571, 571, -11/19*w^3 + 26/19*w^2 + 156/19*w - 18]', '[571, 571, 3/19*w^3 + 5/19*w^2 - 103/19*w + 9]', '[599, 599, 6/19*w^3 - 9/19*w^2 - 16/19*w - 2]', '[599, 599, -14/19*w^3 + 21/19*w^2 + 164/19*w - 7]', '[599, 599, -2/19*w^3 + 22/19*w^2 + 18/19*w - 13]', '[599, 599, -6/19*w^3 + 9/19*w^2 + 16/19*w - 3]', '[601, 601, 23/19*w^3 - 63/19*w^2 - 264/19*w + 31]', '[601, 601, -36/19*w^3 - 3/19*w^2 + 476/19*w + 23]', '[601, 601, 36/19*w^3 - 111/19*w^2 - 362/19*w + 46]', '[601, 601, -16/19*w^3 + 43/19*w^2 + 125/19*w - 8]', '[619, 619, -5/19*w^3 + 17/19*w^2 + 45/19*w - 11]', '[619, 619, 5/19*w^3 - 17/19*w^2 - 26/19*w - 2]', '[619, 619, -5/19*w^3 - 2/19*w^2 + 45/19*w - 4]', '[619, 619, -7/19*w^3 + 20/19*w^2 + 63/19*w - 12]', '[691, 691, 7/19*w^3 - 1/19*w^2 - 120/19*w]', '[691, 691, 3/19*w^3 - 14/19*w^2 - 65/19*w + 6]', '[691, 691, -3/19*w^3 - 5/19*w^2 + 84/19*w + 2]', '[691, 691, 7/19*w^3 - 20/19*w^2 - 101/19*w + 6]', '[701, 701, -7/19*w^3 + 20/19*w^2 + 63/19*w - 2]', '[701, 701, 5/19*w^3 - 17/19*w^2 - 26/19*w + 8]', '[701, 701, -7/19*w^3 + 20/19*w^2 + 82/19*w - 4]', '[701, 701, -7/19*w^3 + 1/19*w^2 + 82/19*w - 2]', '[719, 719, -8/19*w^3 + 31/19*w^2 + 53/19*w - 12]', '[719, 719, 8/19*w^3 - 31/19*w^2 - 53/19*w + 6]', '[719, 719, -8/19*w^3 - 7/19*w^2 + 91/19*w + 2]', '[719, 719, 8/19*w^3 + 7/19*w^2 - 91/19*w - 8]', '[739, 739, 9/19*w^3 - 23/19*w^2 - 43/19*w + 3]', '[739, 739, -16/19*w^3 + 24/19*w^2 + 163/19*w - 9]', '[739, 739, 16/19*w^3 - 24/19*w^2 - 163/19*w]', '[739, 739, -9/19*w^3 + 4/19*w^2 + 62/19*w]', '[769, 769, 24/19*w^3 - 74/19*w^2 - 254/19*w + 35]', '[769, 769, -3/19*w^3 + 33/19*w^2 - 30/19*w - 11]', '[769, 769, 3/19*w^3 + 24/19*w^2 - 27/19*w - 11]', '[769, 769, 24/19*w^3 + 2/19*w^2 - 330/19*w - 19]', '[811, 811, 5/19*w^3 + 2/19*w^2 - 102/19*w]', '[811, 811, -5/19*w^3 + 17/19*w^2 + 83/19*w - 7]', '[811, 811, 5/19*w^3 + 2/19*w^2 - 102/19*w - 2]', '[811, 811, -5/19*w^3 + 17/19*w^2 + 83/19*w - 5]', '[821, 821, -6/19*w^3 - 10/19*w^2 + 111/19*w + 13]', '[821, 821, 1/19*w^3 + 8/19*w^2 + 10/19*w - 12]', '[821, 821, -1/19*w^3 + 11/19*w^2 - 29/19*w - 11]', '[821, 821, -6/19*w^3 + 28/19*w^2 + 73/19*w - 18]', '[839, 839, -2*w^3 + 26*w + 23]', '[839, 839, 18/19*w^3 - 65/19*w^2 - 143/19*w + 24]', '[839, 839, -18/19*w^3 - 11/19*w^2 + 219/19*w + 14]', '[839, 839, 2*w^3 - 6*w^2 - 20*w + 47]', '[859, 859, 10/19*w^3 - 34/19*w^2 - 109/19*w + 19]', '[859, 859, 3/19*w^3 + 24/19*w^2 - 46/19*w - 14]', '[859, 859, -17/19*w^3 + 35/19*w^2 + 210/19*w - 14]', '[859, 859, -10/19*w^3 - 4/19*w^2 + 147/19*w + 12]', '[911, 911, -1/19*w^3 + 11/19*w^2 + 28/19*w - 9]', '[911, 911, -5/19*w^3 + 17/19*w^2 + 64/19*w - 1]', '[911, 911, 5/19*w^3 + 2/19*w^2 - 83/19*w + 3]', '[911, 911, 1/19*w^3 + 8/19*w^2 - 47/19*w - 7]', '[941, 941, 11/19*w^3 - 7/19*w^2 - 99/19*w - 5]', '[941, 941, -1/19*w^3 + 11/19*w^2 + 28/19*w - 10]', '[941, 941, -13/19*w^3 + 10/19*w^2 + 136/19*w - 4]', '[941, 941, -6/19*w^3 + 28/19*w^2 - 3/19*w - 6]', '[961, 31, 10/19*w^3 - 15/19*w^2 - 90/19*w + 2]', '[961, 31, -10/19*w^3 + 15/19*w^2 + 90/19*w - 3]']}
• 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': [19, 14, -13, -2, 1], 'conductor': 120, 'degree': 4, 'dirichlet_group': [1, 11, 59, 49], 'disc_abs': 14400, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[2, 2]]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[1, 4]]], [23, [[2, 2]]], [29, [[1, 4]]], [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, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 10.954451150103322, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.14400.1', 'local_algs': ['2.4.6.2', '3.4.2.1', '5.2.1.1', '5.2.1.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 5], 'rd': 10.9544511501, 'regulator': {'__RealLiteral__': 0, 'data': '6.81516481705', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-30.0.1', '-6.0.1', '-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2}{19} a^{3} - \\frac{3}{19} a^{2} - \\frac{18}{19} a + 1 \\)', '\\( \\frac{6}{19} a^{3} - \\frac{9}{19} a^{2} - \\frac{73}{19} a + 2 \\)', '\\( \\frac{4}{19} a^{3} - \\frac{6}{19} a^{2} - \\frac{74}{19} a + 7 \\)'], 'unitsGmodule': [[1, 1], [2, 1], [3, 1]], 'unitsType': 'Type I (ii)', 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/19*a^3 + 8/19*a^2 - 9/19*a']}