Hilbert modular form data - 4.4.18625.1-20.2-a

Formats: - HTML - YAML - JSON - 2026-03-19T10:54:13.354573

• 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': 18625, 'field_bad_primes': [5, 149], 'field_label': '4.4.18625.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.18625.1-20.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2, 5], 'level_ideal': '[20,10,1/6*w^3 - 7/3*w + 7/6]', 'level_label': '20.2', 'level_norm': 20, 'parallel_weight': 2, 'short_label': '20.2-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4,2,1/6*w^3 - 7/3*w - 17/6]', -1], ['[5,5,-1/2*w^3 - w^2 + 5*w + 21/2]', 1]], 'hecke_eigenvalues': [1, 1, -1, 4, 0, 0, -4, -12, 4, -4, -12, 2, 2, 0, 4, 0, -4, 0, -4, 0, -12, -4, -16, 12, -4, 8, 16, -4, -20, -8, -6, 0, 8, -4, -8, -22, 10, 0, 16, 4, -24, 0, -20, 20, -8, -6, 6, 10, 6, 12, 8, 12, -20, 12, -16, 8, 24, 22, -26, 24, -12, -32, 4, -24, -12, -28, 20, -36, 28, -24, -20, -16, -12, 6, 6, -2, -36, -18, 12, 26, -22, 32, 40, -18, -2, -12, 40, 16, -24, 12, -20, 4, 12, 36, 12, 6, 6, -18, 14, -16, -44, -24, -4, 36, -40, -36, 4, 0, -24, 16, 24, -20, 12, -44, 16, 24, 4, 4, -44, -32, -4, 48, -20, -24, -6, 26, 32, -4, 20, 16, 32, 10, -6, 42, -38, 40, 28, -10, 44, 22, 0, 30, 30, 24, 12, -6, -38, 12, -4, -40, 28, 0, -24, -40, 8, 48, -28, 32, -48, -4, -32, -16, 50, -30, -20, -36, 4, 16, 4, 8, -56, 34, 34, 0, -4, -30, 34, -28, -24, -58, -58, 48, 36, 12, 12, 6, -26, 44, 12, -16, -48, -8, 24, 44, 52, -2, -18, 62, 2, 30, 18, -24, -12, -32, -4, 4, -64, 48, 20, -26, 6, -36, -16, -10, -10, -6, 22, -42, 26, 26, 58, 16, 40, 4, 30, 16, 46, 72, -32, -4, 76, -36, 8, -32, 52, 12, -20, 50, -14, -28, -56, 0, 0, 74, 28, 74, 32, 60, -80, -60, 0, 6, -42, 18, -28, 36, 60, -20, -52, 52, -52, -60, -46, 52, -46, 0, 36, -62, 60, 82, 22, 6, -24, 52, -16, 76, -36, -80, 0, -36, 80, -40, 82, 66, -34, -46, -78, 46, 36, -84, -4, -36, -34, -66, 8, 56, -16, -40], 'hecke_polynomial': 'x', 'label': '4.4.18625.1-20.2-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 18625, 'ideals': ['[1, 1, 1]', '[4, 2, 1/6*w^3 - 7/3*w - 17/6]', '[4, 2, w - 3]', '[5, 5, -1/6*w^3 + w^2 + 1/3*w - 25/6]', '[9, 3, 1/6*w^3 - 7/3*w + 13/6]', '[9, 3, -w - 2]', '[11, 11, -1/6*w^3 + 7/3*w + 11/6]', '[11, 11, -w + 2]', '[16, 2, 2]', '[16, 4, -1/6*w^3 + 1/3*w + 5/6]', '[16, 4, 1/3*w^3 - 11/3*w - 2/3]', '[20, 10, w + 1]', '[20, 10, -1/6*w^3 + 7/3*w - 7/6]', '[25, 5, -1/3*w^3 + 8/3*w + 2/3]', '[36, 6, -1/6*w^3 + 7/3*w + 5/6]', '[36, 6, 1/3*w^3 + w^2 - 11/3*w - 35/3]', '[36, 6, -w^2 + w + 3]', '[36, 6, w - 1]', '[41, 41, -w]', '[41, 41, 1/6*w^3 - 7/3*w + 1/6]', '[44, 22, 1/3*w^3 - 11/3*w + 4/3]', '[44, 22, 1/3*w^3 - 11/3*w - 8/3]', '[44, 22, -1/6*w^3 + 1/3*w + 17/6]', '[44, 22, 1/6*w^3 - 1/3*w + 7/6]', '[45, 15, -1/6*w^3 + 7/3*w + 23/6]', '[45, 15, -w + 4]', '[55, 55, 1/3*w^3 - 5/3*w + 1/3]', '[55, 55, 1/2*w^3 - 5*w + 1/2]', '[59, 59, -1/6*w^3 + 1/3*w + 23/6]', '[59, 59, -1/3*w^3 + 11/3*w + 11/3]', '[61, 61, -5/3*w^3 - 3*w^2 + 46/3*w + 79/3]', '[61, 61, 5/6*w^3 + w^2 - 23/3*w - 55/6]', '[61, 61, w^3 + 2*w^2 - 9*w - 17]', '[61, 61, -1/6*w^3 + 10/3*w + 35/6]', '[64, 4, 1/3*w^3 - 14/3*w - 17/3]', '[64, 4, 2*w - 6]', '[64, 8, 1/6*w^3 + w^2 - 4/3*w - 59/6]', '[64, 8, -w^2 + 5]', '[71, 71, -1/2*w^3 + 2*w^2 + 4*w - 33/2]', '[71, 71, 1/6*w^3 - w^2 - 4/3*w + 67/6]', '[79, 79, 1/2*w^3 - 3*w + 1/2]', '[79, 79, -2/3*w^3 + 19/3*w - 2/3]', '[80, 10, -1/3*w^3 + 2*w^2 + 2/3*w - 25/3]', '[80, 20, -1/3*w^3 + w^2 + 5/3*w - 19/3]', '[80, 20, 2/3*w^3 + w^2 - 19/3*w - 25/3]', '[81, 3, 3]', '[81, 9, -1/3*w^3 + 2*w^2 + 2/3*w - 28/3]', '[81, 9, w^3 + 2*w^2 - 10*w - 20]', '[89, 89, 1/2*w^3 + w^2 - 5*w - 15/2]', '[89, 89, 1/3*w^3 - 11/3*w + 7/3]', '[99, 33, -w^2 + 2*w + 2]', '[99, 33, 1/6*w^3 + w^2 - 4/3*w - 65/6]', '[99, 33, w^2 - 4]', '[99, 33, 1/2*w^3 + w^2 - 6*w - 25/2]', '[100, 10, 7/6*w^3 + 2*w^2 - 31/3*w - 107/6]', '[100, 10, 2/3*w^3 - 2*w^2 - 13/3*w + 35/3]', '[101, 101, -5/6*w^3 - w^2 + 23/3*w + 61/6]', '[101, 101, 1/2*w^3 - w^2 - 3*w + 9/2]', '[109, 109, 1/2*w^3 - w^2 - 4*w + 11/2]', '[109, 109, -2/3*w^3 - w^2 + 16/3*w + 28/3]', '[121, 11, 1/2*w^3 - 4*w - 3/2]', '[121, 11, -1/2*w^3 + 4*w + 1/2]', '[121, 121, 1/6*w^3 - 10/3*w + 25/6]', '[121, 121, 1/6*w^3 - 10/3*w - 23/6]', '[125, 5, -1/2*w^3 + w^2 + w - 1/2]', '[131, 131, 2*w - 7]', '[131, 131, -7/6*w^3 - 2*w^2 + 28/3*w + 89/6]', '[139, 139, -1/6*w^3 + w^2 + 4/3*w - 31/6]', '[139, 139, 1/3*w^3 + w^2 - 8/3*w - 29/3]', '[144, 6, 1/3*w^3 - 14/3*w + 13/3]', '[144, 6, -2*w - 4]', '[144, 12, -1/3*w^3 + w^2 - 1/3*w + 2/3]', '[144, 12, -1/3*w^3 + 5/3*w - 4/3]', '[144, 12, 1/2*w^3 - 5*w + 3/2]', '[144, 12, -w^3 - 2*w^2 + 9*w + 18]', '[149, 149, 1/6*w^3 - 2*w^2 + 5/3*w + 37/6]', '[151, 151, -7/6*w^3 + 3*w^2 + 28/3*w - 133/6]', '[151, 151, 5/3*w^3 + 3*w^2 - 40/3*w - 67/3]', '[164, 82, 1/2*w^3 + 2*w^2 - 5*w - 41/2]', '[164, 82, 2/3*w^3 - 2*w^2 - 13/3*w + 41/3]', '[164, 82, -7/6*w^3 - 2*w^2 + 31/3*w + 95/6]', '[164, 82, -2*w^2 + w + 9]', '[169, 13, -1/6*w^3 - 2/3*w + 29/6]', '[169, 13, 7/6*w^3 - 4*w^2 - 19/3*w + 139/6]', '[176, 22, -1/3*w^3 + 14/3*w + 11/3]', '[176, 22, -2*w + 4]', '[176, 44, 2/3*w^3 - w^2 - 10/3*w + 11/3]', '[176, 44, 1/3*w^3 - w^2 - 11/3*w + 37/3]', '[176, 44, -1/3*w^3 - w^2 + 5/3*w + 8/3]', '[176, 44, -7/6*w^3 - w^2 + 34/3*w + 65/6]', '[180, 30, 1/3*w^3 - w^2 - 8/3*w + 16/3]', '[180, 30, 1/2*w^3 - w^2 - 2*w + 9/2]', '[180, 30, -w^3 - w^2 + 10*w + 10]', '[180, 30, 1/2*w^3 + w^2 - 4*w - 19/2]', '[181, 181, -2/3*w^3 + 13/3*w + 10/3]', '[181, 181, 5/6*w^3 - 23/3*w - 19/6]', '[191, 191, 5/6*w^3 + w^2 - 32/3*w - 97/6]', '[191, 191, w^3 - 9*w - 5]', '[191, 191, -w^2 + 4*w - 2]', '[191, 191, 5/6*w^3 + w^2 - 17/3*w - 43/6]', '[199, 199, 1/2*w^3 - 2*w - 7/2]', '[199, 199, 7/6*w^3 - 5*w^2 - 7/3*w + 109/6]', '[205, 205, 3/2*w^3 + 2*w^2 - 15*w - 41/2]', '[205, 205, -2/3*w^3 + 2*w^2 + 7/3*w - 26/3]', '[211, 211, -1/6*w^3 + w^2 + 7/3*w - 79/6]', '[211, 211, 1/2*w^3 + 2*w^2 - 6*w - 37/2]', '[220, 110, -w^2 + w + 2]', '[220, 110, -1/3*w^3 - w^2 + 11/3*w + 38/3]', '[220, 110, -5/3*w^3 - 3*w^2 + 49/3*w + 88/3]', '[220, 110, -2/3*w^3 + 3*w^2 + 7/3*w - 44/3]', '[225, 15, -1/2*w^3 + 2*w^2 + 3*w - 29/2]', '[225, 15, w^3 + 2*w^2 - 9*w - 15]', '[229, 229, -1/2*w^3 + 5*w - 5/2]', '[229, 229, 1/2*w^3 - 2*w^2 - 2*w + 23/2]', '[229, 229, 1/6*w^3 + w^2 - 10/3*w - 53/6]', '[229, 229, -7/6*w^3 - 2*w^2 + 34/3*w + 107/6]', '[236, 118, 1/6*w^3 - 7/3*w - 29/6]', '[236, 118, -w^3 - w^2 + 11*w + 13]', '[236, 118, 1/3*w^3 - w^2 + 1/3*w + 4/3]', '[236, 118, w - 5]', '[239, 239, 2*w^3 + 3*w^2 - 22*w - 36]', '[239, 239, -7/3*w^3 - 3*w^2 + 74/3*w + 113/3]', '[241, 241, -1/3*w^3 - w^2 + 2/3*w + 11/3]', '[241, 241, -1/2*w^3 + w^2 + 6*w - 23/2]', '[244, 122, -2/3*w^3 + 19/3*w - 5/3]', '[244, 122, 1/3*w^3 - w^2 - 11/3*w + 19/3]', '[244, 122, -2/3*w^3 - w^2 + 13/3*w + 25/3]', '[244, 122, 2/3*w^3 + w^2 - 19/3*w - 22/3]', '[244, 122, -25/6*w^3 - 7*w^2 + 118/3*w + 395/6]', '[244, 122, 1/3*w^3 + w^2 - 5/3*w - 26/3]', '[244, 122, -2/3*w^3 + w^2 + 19/3*w - 20/3]', '[244, 122, 1/2*w^3 - 3*w + 3/2]', '[256, 4, 4]', '[256, 8, -1/3*w^3 + 2/3*w + 5/3]', '[256, 8, 2/3*w^3 - 22/3*w - 4/3]', '[256, 16, 1/6*w^3 - 13/3*w + 43/6]', '[256, 16, 1/3*w^3 - 17/3*w - 20/3]', '[271, 271, -5/6*w^3 - w^2 + 20/3*w + 49/6]', '[271, 271, 1/6*w^3 - 1/3*w - 35/6]', '[275, 55, -5/6*w^3 - 2*w^2 + 23/3*w + 103/6]', '[275, 55, -1/3*w^3 + 2*w^2 + 5/3*w - 37/3]', '[281, 281, -1/6*w^3 - w^2 + 7/3*w + 11/6]', '[281, 281, -w^3 + 9*w - 1]', '[281, 281, -1/2*w^3 + 8*w + 19/2]', '[281, 281, w^3 - 4*w^2 - 4*w + 20]', '[284, 142, 4/3*w^3 - 41/3*w - 11/3]', '[284, 142, -4/3*w^3 + 4*w^2 + 41/3*w - 121/3]', '[284, 142, -w^2 + w + 11]', '[284, 142, 7/6*w^3 + w^2 - 40/3*w - 101/6]', '[295, 295, 1/3*w^3 - 17/3*w + 19/3]', '[295, 295, 1/6*w^3 - 13/3*w - 35/6]', '[305, 305, 1/3*w^3 + w^2 - 8/3*w - 35/3]', '[305, 305, -1/2*w^3 + 2*w^2 + 4*w - 37/2]', '[305, 305, 1/3*w^3 - 2*w^2 - 11/3*w + 61/3]', '[305, 305, 1/2*w^3 + w^2 - 3*w - 17/2]', '[311, 311, 2*w^2 - 13]', '[311, 311, -1/3*w^3 - 2*w^2 + 8/3*w + 50/3]', '[316, 158, 2/3*w^3 - 3*w^2 + 5/3*w + 14/3]', '[316, 158, -7/6*w^3 - 3*w^2 + 28/3*w + 113/6]', '[316, 158, -7/3*w^3 - 3*w^2 + 77/3*w + 116/3]', '[316, 158, 2/3*w^3 - 3*w^2 - 16/3*w + 77/3]', '[320, 20, 2*w + 2]', '[320, 20, -1/3*w^3 + 14/3*w - 7/3]', '[320, 40, w^3 + w^2 - 9*w - 9]', '[320, 40, 2/3*w^3 - w^2 - 13/3*w + 17/3]', '[324, 6, 1/2*w^3 - 7*w - 17/2]', '[324, 6, 3*w - 9]', '[324, 18, w^2 + w - 13]', '[324, 18, -w^2 - w + 4]', '[324, 18, 1/2*w^3 - w^2 - 4*w + 9/2]', '[324, 18, -w^2 - w + 2]', '[331, 331, 1/2*w^3 + w^2 - 4*w - 5/2]', '[331, 331, -1/2*w^3 - w^2 + 5*w + 27/2]', '[331, 331, 1/6*w^3 - 2*w^2 + 2/3*w + 73/6]', '[331, 331, 5/6*w^3 + 2*w^2 - 26/3*w - 103/6]', '[349, 349, -1/2*w^3 - w^2 + 4*w + 21/2]', '[349, 349, 1/6*w^3 + w^2 - 1/3*w - 59/6]', '[355, 355, -1/2*w^3 + 6*w + 11/2]', '[355, 355, -1/2*w^3 + 2*w^2 + 4*w - 27/2]', '[356, 178, 17/6*w^3 + 5*w^2 - 80/3*w - 271/6]', '[356, 178, -2/3*w^3 + w^2 + 31/3*w - 62/3]', '[356, 178, w^2 - 3*w - 2]', '[356, 178, -5/6*w^3 - 2*w^2 + 23/3*w + 97/6]', '[361, 19, 2/3*w^3 - 16/3*w - 7/3]', '[361, 19, 1/6*w^3 - 4/3*w - 29/6]', '[369, 123, -2/3*w^3 + 2*w^2 + 16/3*w - 41/3]', '[369, 123, w^3 - 10*w]', '[369, 123, -2/3*w^3 + 10/3*w + 1/3]', '[369, 123, -w^3 - 2*w^2 + 8*w + 16]', '[379, 379, 1/6*w^3 + w^2 - 10/3*w - 17/6]', '[379, 379, -5/6*w^3 - 2*w^2 + 23/3*w + 115/6]', '[379, 379, -1/3*w^3 + 2*w^2 + 5/3*w - 31/3]', '[379, 379, 1/3*w^3 + w^2 - 14/3*w - 35/3]', '[389, 389, -1/3*w^3 + 2/3*w + 14/3]', '[389, 389, 1/2*w^3 + 2*w^2 - 4*w - 35/2]', '[395, 395, -7/6*w^3 + 7*w^2 + 1/3*w - 157/6]', '[395, 395, -2*w + 3]', '[396, 66, w + 5]', '[396, 66, -1/2*w^3 - w^2 + 2*w + 11/2]', '[396, 66, 2*w^2 - w - 11]', '[396, 66, -2/3*w^3 + w^2 + 22/3*w - 29/3]', '[396, 66, -2/3*w^3 - w^2 + 25/3*w + 49/3]', '[396, 66, -1/2*w^3 - 2*w^2 + 5*w + 37/2]', '[396, 66, -w^2 + 3*w - 2]', '[396, 66, -1/6*w^3 + 7/3*w - 31/6]', '[400, 10, -2/3*w^3 + 16/3*w + 4/3]', '[400, 20, 1/6*w^3 + 2*w^2 - 7/3*w - 65/6]', '[400, 20, 1/3*w^3 + 2*w^2 - 11/3*w - 56/3]', '[401, 401, 1/3*w^3 + 2*w^2 - 14/3*w - 38/3]', '[401, 401, 5/6*w^3 - 4*w^2 - 5/3*w + 101/6]', '[401, 401, -1/3*w^3 - 2*w^2 + 14/3*w + 50/3]', '[401, 401, -5/6*w^3 + 2*w^2 + 5/3*w - 29/6]', '[404, 202, 13/3*w^3 + 7*w^2 - 125/3*w - 206/3]', '[404, 202, w^2 + w - 3]', '[404, 202, 2/3*w^3 - w^2 - 16/3*w + 11/3]', '[404, 202, 1/3*w^3 + w^2 - 14/3*w - 38/3]', '[405, 15, -1/2*w^3 + 3*w^2 + w - 25/2]', '[405, 45, -1/6*w^3 + w^2 + 1/3*w - 55/6]', '[405, 45, 1/2*w^3 + w^2 - 5*w - 11/2]', '[409, 409, -1/2*w^3 + 6*w - 7/2]', '[409, 409, 5/6*w^3 + 2*w^2 - 26/3*w - 91/6]', '[436, 218, -5/6*w^3 - w^2 + 26/3*w + 91/6]', '[436, 218, -2*w^3 + 6*w^2 + 13*w - 37]', '[436, 218, 7/2*w^3 + 6*w^2 - 31*w - 103/2]', '[436, 218, 1/3*w^3 - w^2 - 2/3*w - 2/3]', '[439, 439, 1/3*w^3 + 2*w^2 - 14/3*w - 32/3]', '[439, 439, 1/3*w^3 + 2*w^2 - 14/3*w - 56/3]', '[445, 445, 1/6*w^3 - 3*w^2 + 5/3*w + 79/6]', '[445, 445, -5/6*w^3 + 4*w^2 + 8/3*w - 113/6]', '[449, 449, -11/6*w^3 - 3*w^2 + 47/3*w + 157/6]', '[449, 449, -7/6*w^3 + 3*w^2 + 25/3*w - 109/6]', '[451, 451, 1/6*w^3 - 10/3*w + 43/6]', '[451, 451, 1/6*w^3 - 10/3*w - 41/6]', '[451, 451, 1/2*w^3 + w^2 - 6*w - 29/2]', '[451, 451, w^2 - 2*w]', '[461, 461, 1/6*w^3 + 2*w^2 - 4/3*w - 77/6]', '[461, 461, 2/3*w^3 + 2*w^2 - 22/3*w - 55/3]', '[479, 479, 2/3*w^3 - 2*w^2 - 13/3*w + 32/3]', '[479, 479, -7/6*w^3 - 2*w^2 + 31/3*w + 113/6]', '[484, 22, w^2 + 3*w + 1]', '[484, 22, 5/3*w^3 + 3*w^2 - 43/3*w - 76/3]', '[484, 22, w^3 - 3*w^2 - 7*w + 19]', '[484, 22, 1/3*w^3 - w^2 - 17/3*w + 49/3]', '[484, 242, -2/3*w^3 - w^2 + 19/3*w + 19/3]', '[484, 242, 1/6*w^3 - 2*w^2 - 1/3*w + 55/6]', '[484, 242, 2/3*w^3 + 2*w^2 - 19/3*w - 61/3]', '[484, 242, 1/3*w^3 - w^2 - 5/3*w + 25/3]', '[491, 491, 1/3*w^3 + 2*w^2 - 11/3*w - 35/3]', '[491, 491, 1/6*w^3 + 2*w^2 - 7/3*w - 107/6]', '[495, 165, 5/6*w^3 - 2*w^2 - 14/3*w + 59/6]', '[495, 165, -1/2*w^3 + 6*w + 1/2]', '[495, 165, -3/2*w^3 - 2*w^2 + 14*w + 39/2]', '[495, 165, -1/6*w^3 - 2/3*w + 5/6]', '[499, 499, 4/3*w^3 + 2*w^2 - 38/3*w - 53/3]', '[499, 499, 5/6*w^3 - 4*w^2 - 2/3*w + 101/6]', '[500, 10, 1/6*w^3 - 2*w^2 - 1/3*w + 91/6]', '[500, 10, -2/3*w^3 - 2*w^2 + 19/3*w + 43/3]', '[505, 505, -2/3*w^3 + 10/3*w + 13/3]', '[505, 505, w^3 - 10*w - 4]', '[509, 509, -2/3*w^3 + 31/3*w + 40/3]', '[509, 509, 1/6*w^3 - 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5*w^2 + 35*w + 115/2]', '[1899, 633, 7/2*w^3 + 7*w^2 - 36*w - 151/2]', '[1899, 633, -w^3 - w^2 + 10*w + 7]', '[1899, 633, -13/6*w^3 + 3*w^2 + 55/3*w - 97/6]', '[1901, 1901, w^2 + 2*w + 2]', '[1901, 1901, 1/2*w^3 - 3*w^2 + w + 13/2]', '[1901, 1901, -1/6*w^3 + 4*w^2 - 11/3*w - 73/6]', '[1901, 1901, 1/6*w^3 - w^2 - 10/3*w + 103/6]', '[1916, 958, w^3 - w^2 - 8*w + 6]', '[1916, 958, -7/6*w^3 - w^2 + 28/3*w + 53/6]', '[1916, 958, w^3 + 3*w^2 - 10*w - 28]', '[1916, 958, 1/6*w^3 - 3*w^2 + 2/3*w + 97/6]', '[1931, 1931, 7/6*w^3 - w^2 - 28/3*w + 13/6]', '[1931, 1931, 4/3*w^3 + w^2 - 32/3*w - 38/3]', '[1931, 1931, -7/6*w^3 - 3*w^2 + 31/3*w + 137/6]', '[1931, 1931, 1/2*w^3 - 3*w^2 - 3*w + 43/2]', '[1936, 22, w^3 - 8*w - 3]', '[1936, 22, -w^3 + 8*w + 1]', '[1936, 44, 1/3*w^3 + 3*w^2 - 11/3*w - 50/3]', '[1936, 44, -1/6*w^3 - 3*w^2 + 10/3*w + 95/6]', '[1936, 44, -2/3*w^3 - 3*w^2 + 22/3*w + 85/3]', '[1936, 44, 1/3*w^3 + 3*w^2 - 11/3*w - 83/3]', '[1936, 242, 1/3*w^3 - 20/3*w + 25/3]', '[1936, 242, 1/3*w^3 - 20/3*w - 23/3]', '[1936, 484, -1/2*w^3 + 3*w^2 - 2*w - 9/2]', '[1936, 484, 5/6*w^3 - 29/3*w - 1/6]', '[1936, 484, -1/3*w^3 - 1/3*w + 2/3]', '[1936, 484, -2*w^3 - 3*w^2 + 22*w + 39]', '[1945, 1945, -17/6*w^3 + 9*w^2 + 23/3*w - 185/6]', '[1945, 1945, 7/6*w^3 - 25/3*w + 7/6]', '[1949, 1949, 4/3*w^3 - 3*w^2 - 32/3*w + 58/3]', '[1949, 1949, 11/6*w^3 + 3*w^2 - 44/3*w - 151/6]', '[1951, 1951, 11/6*w^3 - 5*w^2 - 20/3*w + 113/6]', '[1951, 1951, -4/3*w^3 + 26/3*w - 1/3]', '[1964, 982, 4/3*w^3 - 5*w^2 - 11/3*w + 64/3]', '[1964, 982, -17/6*w^3 - 6*w^2 + 71/3*w + 253/6]', '[1964, 982, -10/3*w^3 - 5*w^2 + 101/3*w + 155/3]', '[1964, 982, 5/3*w^3 - 6*w^2 - 37/3*w + 140/3]', '[1975, 395, -5/6*w^3 + w^2 + 11/3*w - 29/6]', '[1975, 395, 3/2*w^3 + w^2 - 15*w - 19/2]', '[1980, 330, 3*w^2 - w - 14]', '[1980, 330, 4/3*w^3 - 4*w^2 - 23/3*w + 73/3]', '[1980, 330, 1/6*w^3 + 2*w^2 - 1/3*w - 53/6]', '[1980, 330, 5/2*w^3 + 4*w^2 - 23*w - 69/2]', '[1980, 330, -1/2*w^3 - w^2 + 6*w + 3/2]', '[1980, 330, 2/3*w^3 + 3*w^2 - 19/3*w - 91/3]', '[1980, 330, w^2 - 2*w - 13]', '[1980, 330, 2*w^2 + w - 21]', '[1991, 1991, 5/2*w^3 + 5*w^2 - 26*w - 105/2]', '[1991, 1991, 5/6*w^3 - 4*w^2 - 14/3*w + 167/6]', '[1991, 1991, -11/6*w^3 - 4*w^2 + 50/3*w + 187/6]', '[1991, 1991, -2/3*w^3 + 5*w^2 - 2/3*w - 62/3]', '[1996, 998, -2/3*w^3 + 25/3*w - 5/3]', '[1996, 998, -43/6*w^3 - 12*w^2 + 205/3*w + 683/6]', '[1996, 998, 2/3*w^3 + 3*w^2 - 25/3*w - 61/3]', '[1996, 998, -2*w^3 - 2*w^2 + 19*w + 25]', '[1999, 1999, -1/6*w^3 + 3*w^2 - 2/3*w - 151/6]', '[1999, 1999, 1/2*w^3 + 2*w^2 - 4*w - 49/2]', '[2000, 10, -w^3 + 2*w^2 + 2*w - 1]', '[2000, 20, 1/3*w^3 + w^2 - 17/3*w - 44/3]', '[2000, 20, 1/3*w^3 + w^2 - 17/3*w + 1/3]', '[2005, 2005, -3/2*w^3 + 9*w^2 - w - 63/2]', '[2005, 2005, 1/6*w^3 - 2*w^2 + 2/3*w + 97/6]', '[2005, 2005, 5/6*w^3 + 2*w^2 - 26/3*w - 79/6]', '[2005, 2005, 5/6*w^3 - 5*w^2 + 7/3*w + 89/6]', '[2011, 2011, -1/3*w^3 + 2*w^2 + 17/3*w - 37/3]', '[2011, 2011, 1/6*w^3 + 2*w^2 + 5/3*w - 107/6]', '[2020, 1010, -1/3*w^3 - 1/3*w + 8/3]', '[2020, 1010, -w^3 - 3*w^2 + 11*w + 28]', '[2020, 1010, -7/2*w^3 - 5*w^2 + 34*w + 101/2]', '[2020, 1010, -8/3*w^3 - 5*w^2 + 76/3*w + 133/3]', '[2025, 15, -w^3 + 8*w + 2]', '[2025, 45, -2/3*w^3 + 2*w^2 - 2/3*w - 5/3]', '[2025, 45, 2*w^3 + 2*w^2 - 22*w - 27]', '[2029, 2029, -11/3*w^3 - 6*w^2 + 100/3*w + 166/3]', '[2029, 2029, 5/6*w^3 - 2*w^2 - 38/3*w + 197/6]', '[2036, 1018, -w - 7]', '[2036, 1018, 2/3*w^3 + w^2 - 7/3*w - 19/3]', '[2036, 1018, -1/6*w^3 + 7/3*w - 43/6]', '[2036, 1018, -w^3 + w^2 + 11*w - 9]', '[2039, 2039, -11/6*w^3 - 3*w^2 + 47/3*w + 163/6]', '[2039, 2039, -1/6*w^3 + 3*w^2 + 1/3*w - 91/6]', '[2039, 2039, 7/6*w^3 - 3*w^2 - 25/3*w + 103/6]', '[2039, 2039, w^3 - 6*w^2 - 2*w + 26]', '[2045, 2045, -1/2*w^3 + 6*w^2 - 3*w - 49/2]', '[2045, 2045, 5/3*w^3 - 7*w^2 - 16/3*w + 95/3]', '[2061, 687, -7/6*w^3 + 3*w^2 + 40/3*w - 217/6]', '[2061, 687, 4/3*w^3 - 4*w^2 - 5/3*w + 28/3]', '[2061, 687, -4/3*w^3 + 2*w^2 + 26/3*w - 13/3]', '[2061, 687, 7/6*w^3 - 31/3*w - 17/6]', '[2061, 687, 3/2*w^3 + 2*w^2 - 12*w - 31/2]', '[2061, 687, w^3 - 7*w - 3]', '[2061, 687, -3/2*w^3 - w^2 + 17*w + 49/2]', '[2061, 687, -7/2*w^3 - 4*w^2 + 37*w + 97/2]', '[2084, 1042, 29/6*w^3 + 8*w^2 - 137/3*w - 445/6]', '[2084, 1042, -w^3 + w^2 + 16*w - 30]', '[2084, 1042, -2/3*w^3 + 3*w^2 + 13/3*w - 74/3]', '[2084, 1042, 7/6*w^3 + 2*w^2 - 19/3*w - 47/6]', '[2089, 2089, 3*w^2 - 4*w - 10]', '[2089, 2089, 2/3*w^3 - 5*w^2 + 8/3*w + 44/3]', '[2096, 262, 4*w - 14]', '[2096, 262, -7/3*w^3 - 4*w^2 + 56/3*w + 89/3]', '[2096, 524, 10/3*w^3 + 5*w^2 - 95/3*w - 149/3]', '[2096, 524, 1/2*w^3 - w^2 - 4*w + 29/2]', '[2096, 524, w^3 - 7*w - 2]', '[2096, 524, 1/3*w^3 - 23/3*w + 46/3]', '[2099, 2099, -7/6*w^3 - w^2 + 25/3*w + 77/6]', '[2099, 2099, 2*w^2 + w - 22]', '[2101, 2101, 19/6*w^3 + 6*w^2 - 100/3*w - 383/6]', '[2101, 2101, w^3 - 5*w^2 - 4*w + 31]', '[2101, 2101, 1/6*w^3 + 5/3*w - 23/6]', '[2101, 2101, -1/6*w^3 - w^2 + 1/3*w + 101/6]', '[2101, 2101, -3/2*w^3 - 2*w^2 + 11*w + 29/2]', '[2101, 2101, -7/6*w^3 - 3*w^2 + 37/3*w + 167/6]', '[2101, 2101, 8/3*w^3 + 6*w^2 - 61/3*w - 118/3]', '[2101, 2101, -1/6*w^3 - 4*w^2 + 10/3*w + 119/6]', '[2111, 2111, 3*w^2 - 2*w - 24]', '[2111, 2111, 5/6*w^3 + 3*w^2 - 26/3*w - 121/6]', '[2111, 2111, 2*w^3 - 6*w^2 - 12*w + 35]', '[2111, 2111, -11/3*w^3 - 6*w^2 + 100/3*w + 160/3]', '[2116, 46, -14/3*w^3 - 9*w^2 + 121/3*w + 211/3]', '[2116, 46, -3/2*w^3 - 2*w^2 + 17*w + 47/2]', '[2116, 46, 8/3*w^3 - 9*w^2 - 55/3*w + 188/3]', '[2116, 46, 1/3*w^3 - 2*w^2 + 7/3*w + 16/3]', '[2124, 354, 4*w^3 + 7*w^2 - 37*w - 64]', '[2124, 354, -w^2 + 3*w + 10]', '[2124, 354, -1/2*w^3 + 11*w + 33/2]', '[2124, 354, -2/3*w^3 - w^2 + 25/3*w + 13/3]', '[2124, 354, -w^3 + w^2 + 11*w - 14]', '[2124, 354, 2/3*w^3 + w^2 - 7/3*w - 4/3]', '[2124, 354, 7/6*w^3 - 5*w^2 + 8/3*w + 31/6]', '[2124, 354, -2/3*w^3 + 37/3*w - 53/3]', '[2129, 2129, 1/6*w^3 + 2*w^2 - 10/3*w - 119/6]', '[2129, 2129, -1/3*w^3 + 2*w^2 - 4/3*w - 34/3]', '[2131, 2131, 1/2*w^3 + 3*w^2 - 4*w - 37/2]', '[2131, 2131, -5/2*w^3 - 5*w^2 + 22*w + 81/2]', '[2131, 2131, 5/6*w^3 + 3*w^2 - 29/3*w - 163/6]', '[2131, 2131, 1/6*w^3 - 2*w^2 + 17/3*w - 11/6]', '[2141, 2141, -1/6*w^3 + 2*w^2 + 4/3*w - 139/6]', '[2141, 2141, 1/2*w^3 + 2*w^2 - 4*w - 13/2]', '[2151, 717, -1/2*w^3 + 2*w^2 - w - 13/2]', '[2151, 717, -1/2*w^3 + 2*w^2 + w - 5/2]', '[2151, 717, -4/3*w^3 - 2*w^2 + 41/3*w + 80/3]', '[2151, 717, 5/3*w^3 + 2*w^2 - 55/3*w - 67/3]', '[2161, 2161, 3/2*w^3 - w^2 - 14*w + 13/2]', '[2161, 2161, 4/3*w^3 + w^2 - 26/3*w - 26/3]', '[2164, 1082, 1/3*w^3 + w^2 - 32/3*w + 40/3]', '[2164, 1082, -1/3*w^3 - w^2 + 20/3*w - 4/3]', '[2164, 1082, 1/2*w^3 + w^2 - 8*w - 31/2]', '[2164, 1082, -7/6*w^3 - w^2 + 52/3*w + 161/6]', '[2169, 723, -1/3*w^3 + 2*w^2 + 11/3*w - 37/3]', '[2169, 723, 1/2*w^3 + 2*w^2 - 3*w - 35/2]', '[2169, 723, 2*w^3 + 2*w^2 - 19*w - 18]', '[2169, 723, -8/3*w^3 - 2*w^2 + 79/3*w + 64/3]', '[2179, 2179, 5/6*w^3 - 4*w^2 - 8/3*w + 101/6]', '[2179, 2179, w^3 - 6*w^2 - w + 23]', '[2180, 1090, -7/6*w^3 + 5*w^2 + 22/3*w - 223/6]', '[2180, 1090, -7/3*w^3 - 5*w^2 + 62/3*w + 110/3]', '[2180, 1090, -5/6*w^3 - 2*w^2 + 29/3*w + 85/6]', '[2180, 1090, 2*w^2 - 3*w - 15]', '[2189, 2189, -1/6*w^3 - 2*w^2 + 10/3*w + 137/6]', '[2189, 2189, -5/6*w^3 + 2*w^2 + 8/3*w - 53/6]', '[2189, 2189, -w^3 + 11*w - 3]', '[2189, 2189, 4/3*w^3 + 3*w^2 - 32/3*w - 50/3]', '[2195, 2195, -1/2*w^3 + 3*w^2 - 3*w - 13/2]', '[2195, 2195, -11/6*w^3 + 11*w^2 - 1/3*w - 239/6]', '[2196, 366, -4/3*w^3 + 4*w^2 + 41/3*w - 127/3]', '[2196, 366, 4/3*w^3 - 5*w^2 - 35/3*w + 130/3]', '[2196, 366, -1/6*w^3 + w^2 - 8/3*w - 1/6]', '[2196, 366, -w^3 + 3*w^2 + 9*w - 32]', '[2196, 366, 1/2*w^3 - 4*w^2 - 5*w + 71/2]', '[2196, 366, -w^2 - w + 16]', '[2196, 366, 5/2*w^3 + 5*w^2 - 24*w - 95/2]', '[2196, 366, 2*w^3 + 3*w^2 - 17*w - 24]', '[2196, 366, -1/2*w^3 + w^2 + 8*w - 33/2]', '[2196, 366, w^2 + 4*w + 1]', '[2196, 366, -w^2 + w + 15]', '[2196, 366, -17/3*w^3 - 7*w^2 + 172/3*w + 232/3]', '[2196, 366, 4/3*w^3 - 3*w^2 - 29/3*w + 61/3]', '[2196, 366, -3*w^3 - 5*w^2 + 26*w + 42]', '[2196, 366, -3/2*w^3 - 2*w^2 + 11*w + 27/2]', '[2196, 366, w^3 + 3*w^2 - 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3*w^2 + 34/3*w + 167/6]', '[1381, 1381, 1/3*w^3 - 3*w^2 - 2/3*w + 49/3]', '[1399, 1399, 7/6*w^3 - 4*w^2 - 22/3*w + 163/6]', '[1399, 1399, 13/6*w^3 + 4*w^2 - 58/3*w - 191/6]', '[1409, 1409, -3/2*w^3 + 4*w^2 + 10*w - 45/2]', '[1409, 1409, 2*w^2 - 9]', '[1409, 1409, -5/2*w^3 - 4*w^2 + 22*w + 73/2]', '[1409, 1409, 1/3*w^3 + 2*w^2 - 8/3*w - 62/3]', '[1439, 1439, 7/6*w^3 - 37/3*w + 7/6]', '[1439, 1439, -1/2*w^3 - 3*w^2 + 7*w + 33/2]', '[1459, 1459, 2*w^2 - 2*w - 17]', '[1459, 1459, -5/6*w^3 + 26/3*w + 55/6]', '[1459, 1459, 2/3*w^3 + 2*w^2 - 22/3*w - 37/3]', '[1459, 1459, -1/2*w^3 + 2*w + 19/2]', '[1511, 1511, 3/2*w^3 - 6*w^2 - 8*w + 75/2]', '[1511, 1511, -19/6*w^3 - 6*w^2 + 88/3*w + 305/6]', '[1531, 1531, 5/2*w^3 + 3*w^2 - 29*w - 87/2]', '[1531, 1531, -13/6*w^3 - 3*w^2 + 61/3*w + 179/6]', '[1549, 1549, 1/2*w^3 + 2*w^2 - 6*w - 21/2]', '[1549, 1549, w^3 - 10*w + 2]', '[1579, 1579, -1/2*w^3 + w^2 + 3*w - 21/2]', '[1579, 1579, 5/6*w^3 + w^2 - 23/3*w - 25/6]', '[1601, 1601, 1/3*w^3 + w^2 - 20/3*w - 5/3]', '[1601, 1601, -7/6*w^3 - 3*w^2 + 31/3*w + 131/6]', '[1609, 1609, 5/6*w^3 - w^2 - 23/3*w + 23/6]', '[1609, 1609, -11/6*w^3 - 3*w^2 + 50/3*w + 175/6]', '[1609, 1609, -5/6*w^3 - w^2 + 17/3*w + 67/6]', '[1609, 1609, -w^3 + 3*w^2 + 6*w - 15]', '[1619, 1619, 1/3*w^3 + 2*w^2 - 5/3*w - 53/3]', '[1619, 1619, 2/3*w^3 - w^2 - 16/3*w + 2/3]', '[1619, 1619, 3/2*w^3 + 2*w^2 - 12*w - 39/2]', '[1619, 1619, 1/3*w^3 - 2*w^2 - 14/3*w + 70/3]', '[1621, 1621, 1/6*w^3 + 3*w^2 - 4/3*w - 113/6]', '[1621, 1621, -1/3*w^3 - 3*w^2 + 8/3*w + 77/3]', '[1681, 41, w^3 - 8*w - 4]', '[1699, 1699, 5/6*w^3 + w^2 - 29/3*w - 37/6]', '[1699, 1699, -1/6*w^3 + w^2 - 5/3*w - 49/6]', '[1709, 1709, -1/6*w^3 - 2*w^2 + 13/3*w + 35/6]', '[1709, 1709, -3/2*w^3 - w^2 + 14*w + 15/2]', '[1721, 1721, -5/6*w^3 - w^2 + 35/3*w + 103/6]', '[1721, 1721, 5/3*w^3 + 2*w^2 - 43/3*w - 61/3]', '[1721, 1721, -7/6*w^3 + 2*w^2 + 25/3*w - 55/6]', '[1721, 1721, -1/6*w^3 - w^2 + 19/3*w - 19/6]', '[1741, 1741, 1/6*w^3 - 3*w^2 + 5/3*w + 115/6]', '[1741, 1741, -1/2*w^3 + 4*w^2 - w - 25/2]', '[1741, 1741, 7/6*w^3 + 3*w^2 - 37/3*w - 149/6]', '[1741, 1741, -11/6*w^3 + 6*w^2 + 17/3*w - 131/6]', '[1789, 1789, 1/6*w^3 - w^2 - 13/3*w + 103/6]', '[1789, 1789, w^3 + 2*w^2 - 8*w - 18]', '[1789, 1789, -2*w^3 - 3*w^2 + 18*w + 30]', '[1789, 1789, -2/3*w^3 + 2*w^2 + 16/3*w - 35/3]', '[1801, 1801, -7/6*w^3 - w^2 + 28/3*w + 47/6]', '[1801, 1801, -w^3 + w^2 + 8*w - 7]', '[1811, 1811, 4/3*w^3 - 29/3*w - 26/3]', '[1811, 1811, -7/6*w^3 + w^2 + 31/3*w - 43/6]', '[1831, 1831, -1/3*w^3 + 2/3*w + 32/3]', '[1831, 1831, -3/2*w^3 - 2*w^2 + 12*w + 33/2]', '[1849, 43, -7/6*w^3 - 2*w^2 + 31/3*w + 125/6]', '[1849, 43, -1/2*w^3 + 3*w^2 + 5*w - 43/2]', '[1871, 1871, -3/2*w^3 - 2*w^2 + 12*w + 29/2]', '[1871, 1871, 7/6*w^3 - 2*w^2 - 28/3*w + 91/6]', '[1879, 1879, 3/2*w^3 + 3*w^2 - 13*w - 53/2]', '[1879, 1879, -5/6*w^3 + 3*w^2 + 17/3*w - 107/6]', '[1889, 1889, -1/2*w^3 - w^2 + 6*w + 5/2]', '[1889, 1889, w^2 - 2*w - 12]', '[1901, 1901, w^2 + 2*w + 2]', '[1901, 1901, 1/2*w^3 - 3*w^2 + w + 13/2]', '[1901, 1901, -1/6*w^3 + 4*w^2 - 11/3*w - 73/6]', '[1901, 1901, 1/6*w^3 - w^2 - 10/3*w + 103/6]', '[1931, 1931, 7/6*w^3 - w^2 - 28/3*w + 13/6]', '[1931, 1931, 4/3*w^3 + w^2 - 32/3*w - 38/3]', '[1931, 1931, -7/6*w^3 - 3*w^2 + 31/3*w + 137/6]', '[1931, 1931, 1/2*w^3 - 3*w^2 - 3*w + 43/2]', '[1949, 1949, 4/3*w^3 - 3*w^2 - 32/3*w + 58/3]', '[1949, 1949, 11/6*w^3 + 3*w^2 - 44/3*w - 151/6]', '[1951, 1951, 11/6*w^3 - 5*w^2 - 20/3*w + 113/6]', '[1951, 1951, -4/3*w^3 + 26/3*w - 1/3]', '[1999, 1999, -1/6*w^3 + 3*w^2 - 2/3*w - 151/6]', '[1999, 1999, 1/2*w^3 + 2*w^2 - 4*w - 49/2]']}
• 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[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [41, 9, -14, -1, 1], 'conductor': 0, 'degree': 4, 'disc_abs': 18625, 'disc_rad': 745, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 40.81507862588707, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.18625.1', 'local_algs': ['5.1.4.3a1.4', '149.2.1.0a1.1', '149.1.2.1a1.2'], 'monogenic': -1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [5, 149], 'rd': 11.6821847546, 'regulator': {'__RealLiteral__': 0, 'data': '8.81065543235', 'prec': 44}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_order': 2, 'unit_signature_rank': 3, 'used_grh': False}