Hilbert modular form data - 4.4.8000.1-25.1-b

Formats: - HTML - YAML - JSON - 2026-02-09T08:06:01.004478

• 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': 8000, 'field_bad_primes': [2, 5], 'field_label': '4.4.8000.1', 'is_CM': 'yes', 'is_base_change': 'yes', 'label': '4.4.8000.1-25.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [5], 'level_ideal': '[25, 5, -w^2 + 5]', 'level_label': '25.1', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.1-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5, 5, w^2 - w - 5]', 1]], 'hecke_eigenvalues': [0, 0, -6, -6, -6, -6, 0, 0, 0, 0, -6, -6, -6, -6, 0, 0, 0, 0, 14, 0, 0, 0, 0, -18, -18, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, -26, -26, -26, -26, -6, -6, -6, -6, 0, 0, 0, 0, -18, -18, -18, -18, -26, -26, -26, -26, 0, 0, 0, 0, 0, 0, 0, 0, 34, 34, 0, 0, 0, 0, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 42, 42, 42, 42, 0, 0, 0, 0, -6, -6, -6, -6, 22, 22, 22, 22, 0, 0, 0, 0, -46, -46, -46, -46, 42, 42, 42, 42, -46, -46, -46, -46, 0, 0, 0, 0, 0, 0, 0, 0, 54, 54, 54, 54, -38, -38, -38, -38, 0, 0, 0, 0, 0, 0, 0, 0, -18, -18, -18, -18, 0, 0, 0, 0, 62, 62, 54, 54, 54, 54], 'hecke_polynomial': 'x', 'label': '4.4.8000.1-25.1-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 8000, 'ideals': ['[1, 1, 1]', '[4, 2, 1/2*w^3 - 3*w + 2]', '[5, 5, w^2 - w - 5]', '[11, 11, -1/2*w^3 - 1/2*w^2 + 3*w + 3]', '[11, 11, -1/2*w^2 + w + 2]', '[11, 11, -1/2*w^2 - w + 2]', '[11, 11, 1/2*w^3 - 1/2*w^2 - 3*w + 3]', '[16, 2, 2]', '[20, 10, w]', '[25, 5, -w^2 + 5]', '[29, 29, -1/2*w^2 - w + 4]', '[29, 29, -1/2*w^3 + 1/2*w^2 + 3*w - 1]', '[29, 29, -1/2*w^3 - 1/2*w^2 + 3*w + 1]', '[29, 29, -1/2*w^2 + w + 4]', '[41, 41, w^3 - 1/2*w^2 - 6*w + 6]', '[41, 41, -1/2*w^3 + 5/2*w^2 + 5*w - 14]', '[41, 41, 1/2*w^3 - 1/2*w^2 - 3*w + 6]', '[41, 41, -3/2*w^2 - 2*w + 6]', '[44, 22, -w^2 + w + 6]', '[44, 22, -1/2*w^3 - w^2 + 3*w + 4]', '[44, 22, 1/2*w^3 - w^2 - 3*w + 4]', '[44, 22, w^2 + w - 6]', '[55, 55, -1/2*w^2 + w + 5]', '[55, 55, 1/2*w^3 + 1/2*w^2 - 3*w]', '[55, 55, -1/2*w^3 + 1/2*w^2 + 3*w]', '[55, 55, 1/2*w^2 + w - 5]', '[64, 4, w^3 - 6*w + 4]', '[79, 79, -w^3 - w^2 + 4*w - 1]', '[79, 79, -3/2*w^2 - w + 9]', '[79, 79, -w^3 + 7/2*w^2 + 9*w - 21]', '[79, 79, w^3 - w^2 - 6*w + 9]', '[80, 10, 2*w^2 + 2*w - 10]', '[81, 3, -3]', '[100, 10, 1/2*w^3 - 2*w^2 - 5*w + 10]', '[109, 109, w^2 - w - 7]', '[109, 109, -1/2*w^3 + 1/2*w^2 + 4*w - 1]', '[109, 109, 1/2*w^3 + 1/2*w^2 - 4*w - 1]', '[109, 109, w^2 + w - 7]', '[116, 58, -w - 4]', '[116, 58, 1/2*w^3 - 3*w - 4]', '[116, 58, -1/2*w^3 + 3*w - 4]', '[116, 58, w - 4]', '[121, 11, 3/2*w^2 - 8]', '[121, 11, -w^2 - 2*w + 3]', '[121, 11, w^2 - 2*w - 3]', '[121, 11, 3/2*w^2 - 7]', '[121, 11, -w^3 + w^2 + 6*w - 7]', '[121, 11, -w^3 - w^2 + 6*w + 7]', '[121, 121, -w^3 + 1/2*w^2 + 5*w + 1]', '[121, 121, -1/2*w^3 + 1/2*w^2 + 5*w - 6]', '[121, 121, -1/2*w^3 - 1/2*w^2 + 5*w + 6]', '[121, 121, -w^3 - 1/2*w^2 + 5*w - 1]', '[125, 5, w^3 - 5*w - 5]', '[131, 131, -1/2*w^3 - 1/2*w^2 + 4*w + 7]', '[131, 131, -1/2*w^3 + 7/2*w^2 + 6*w - 18]', '[131, 131, 1/2*w^3 + 1/2*w^2 - 2*w + 2]', '[131, 131, 1/2*w^3 - 1/2*w^2 - 4*w + 7]', '[145, 145, w^3 + 1/2*w^2 - 6*w - 5]', '[145, 145, 1/2*w^2 - 2*w]', '[145, 145, -1/2*w^2 - 2*w]', '[145, 145, w^3 - 1/2*w^2 - 6*w + 5]', '[149, 149, w^3 + w^2 - 5*w - 7]', '[149, 149, 1/2*w^3 - w^2 - 5*w + 3]', '[149, 149, -1/2*w^3 - w^2 + 5*w + 3]', '[149, 149, -w^3 + w^2 + 5*w - 7]', '[164, 82, 1/2*w^3 - w^2 - 2*w + 6]', '[164, 82, 1/2*w^3 + w^2 - 4*w - 4]', '[164, 82, -1/2*w^3 + w^2 + 4*w - 4]', '[164, 82, -1/2*w^3 - w^2 + 2*w + 6]', '[176, 22, -w^3 - w^2 + 6*w + 6]', '[176, 22, -w^2 + 2*w + 4]', '[176, 22, -w^2 - 2*w + 4]', '[176, 22, w^3 - w^2 - 6*w + 6]', '[199, 199, -w^3 - w^2 + 6*w + 3]', '[199, 199, -w^2 + 2*w + 7]', '[199, 199, -w^2 - 2*w + 7]', '[199, 199, w^3 - w^2 - 6*w + 3]', '[205, 205, -1/2*w^3 + 3/2*w^2 + 3*w - 5]', '[205, 205, 1/2*w^3 - 1/2*w^2 - 2*w + 5]', '[205, 205, 1/2*w^3 + 1/2*w^2 - 2*w - 5]', '[205, 205, -1/2*w^3 - 3/2*w^2 + 3*w + 5]', '[211, 211, 1/2*w^3 - 2*w^2 - 3*w + 11]', '[211, 211, -1/2*w^3 - 1/2*w^2 + 3*w + 7]', '[211, 211, 1/2*w^3 - 1/2*w^2 - 3*w + 7]', '[211, 211, 1/2*w^3 + 2*w^2 - 3*w - 11]', '[220, 110, -1/2*w^3 + 2*w^2 + 3*w - 10]', '[220, 110, 2*w^2 + w - 10]', '[220, 110, -2*w^2 + w + 10]', '[220, 110, -1/2*w^3 - 2*w^2 + 3*w + 10]', '[229, 229, -1/2*w^3 - 1/2*w^2 + 4*w - 2]', '[229, 229, 1/2*w^3 + 1/2*w^2 - 2*w - 7]', '[229, 229, 1/2*w^3 - 1/2*w^2 - 2*w + 7]', '[229, 229, 1/2*w^3 - 1/2*w^2 - 4*w - 2]', '[239, 239, 1/2*w^2 + 2*w - 6]', '[239, 239, -w^3 - 1/2*w^2 + 6*w - 1]', '[239, 239, w^3 - 1/2*w^2 - 6*w - 1]', '[239, 239, 1/2*w^2 - 2*w - 6]', '[241, 241, -w^3 + 1/2*w^2 + 6*w - 2]', '[241, 241, -w^3 - 1/2*w^2 + 6*w + 4]', '[241, 241, w^3 - 1/2*w^2 - 6*w + 4]', '[241, 241, w^3 + 1/2*w^2 - 6*w - 2]', '[251, 251, 1/2*w^3 + w^2 - 5*w - 7]', '[251, 251, w^3 + w^2 - 5*w - 3]', '[251, 251, -w^3 + w^2 + 5*w - 3]', '[251, 251, -1/2*w^3 + w^2 + 5*w - 7]', '[256, 4, 4]', '[269, 269, 1/2*w^3 + 1/2*w^2 - 2*w - 6]', '[269, 269, 1/2*w^3 - 1/2*w^2 - 4*w - 1]', '[269, 269, -1/2*w^3 - 1/2*w^2 + 4*w - 1]', '[269, 269, -1/2*w^3 + 1/2*w^2 + 2*w - 6]', '[275, 55, -1/2*w^3 - 1/2*w^2 + 5*w + 5]', '[275, 55, -w^3 + 1/2*w^2 + 5*w]', '[275, 55, w^3 + 1/2*w^2 - 5*w]', '[275, 55, 1/2*w^3 - 1/2*w^2 - 5*w + 5]', '[281, 281, w^3 - 6*w + 1]', '[281, 281, w^3 - 1/2*w^2 - 6*w + 3]', '[281, 281, -w^3 - 1/2*w^2 + 6*w + 3]', '[281, 281, -w^3 + 6*w + 1]', '[316, 158, 1/2*w^3 + w^2 - 5*w - 6]', '[316, 158, w^3 - w^2 - 5*w + 4]', '[316, 158, -w^3 - w^2 + 5*w + 4]', '[316, 158, -1/2*w^3 + w^2 + 5*w - 6]', '[319, 319, 1/2*w^3 - 3/2*w^2 - 5*w + 12]', '[319, 319, 1/2*w^3 + w^2 - 4*w - 3]', '[319, 319, -3/2*w^2 + 2*w + 9]', '[319, 319, -w^3 + 3/2*w^2 + 5*w - 3]', '[319, 319, -w^3 + 3/2*w^2 + 6*w - 6]', '[319, 319, -1/2*w^3 + w^2 + 2*w - 7]', '[319, 319, w^3 - 2*w^2 - 6*w + 9]', '[319, 319, 2*w^2 - 2*w - 11]', '[319, 319, -2*w^2 - 2*w + 11]', '[319, 319, -w^3 - 2*w^2 + 6*w + 9]', '[319, 319, -1/2*w^3 - w^2 + 2*w + 7]', '[319, 319, w^3 + 3/2*w^2 - 6*w - 6]', '[319, 319, w^3 + 3/2*w^2 - 5*w - 3]', '[319, 319, 3/2*w^2 + 2*w - 9]', '[319, 319, -1/2*w^3 + w^2 + 4*w - 3]', '[319, 319, 1/2*w^3 + 3/2*w^2 - 5*w - 12]', '[320, 20, 2*w]', '[324, 6, -3/2*w^3 + 9*w - 6]', '[331, 331, 3/2*w^3 + w^2 - 7*w + 1]', '[331, 331, -1/2*w^3 + 3*w^2 + 5*w - 17]', '[331, 331, -3/2*w^3 + w^2 + 9*w - 13]', '[331, 331, 1/2*w^3 + 3*w^2 + w - 11]', '[349, 349, 1/2*w^3 + 3/2*w^2 - 2*w - 9]', '[349, 349, -1/2*w^3 + 3/2*w^2 + 4*w - 6]', '[349, 349, 1/2*w^3 + 3/2*w^2 - 4*w - 6]', '[349, 349, -1/2*w^3 + 3/2*w^2 + 2*w - 9]', '[359, 359, -w^3 + 7/2*w^2 + 9*w - 19]', '[359, 359, w^3 - 2*w^2 - 8*w + 11]', '[359, 359, w^3 - 1/2*w^2 - 6*w - 2]', '[359, 359, -5/2*w^2 - 3*w + 9]', '[361, 19, 2*w^2 - 11]', '[361, 19, -1/2*w^2 + 7]', '[389, 389, -1/2*w^3 + 5/2*w^2 + 6*w - 11]', '[389, 389, 5/2*w^3 - 3/2*w^2 - 16*w + 17]', '[389, 389, 3/2*w^3 - 1/2*w^2 - 10*w + 7]', '[389, 389, -3/2*w^3 + 7/2*w^2 + 12*w - 21]', '[395, 395, -1/2*w^3 - 5/2*w^2 + 2*w + 10]', '[395, 395, 1/2*w^3 - 3*w + 5]', '[395, 395, 1/2*w^3 - 3*w - 5]', '[395, 395, -1/2*w^3 + 5/2*w^2 + 2*w - 10]', '[400, 10, -2*w^2 + 10]', '[401, 401, -w^3 + 1/2*w^2 + 5*w - 1]', '[401, 401, 1/2*w^3 + 1/2*w^2 - 5*w - 4]', '[401, 401, -1/2*w^3 + 1/2*w^2 + 5*w - 4]', '[401, 401, w^3 + 1/2*w^2 - 5*w - 1]', '[405, 15, -3*w^2 + 3*w + 15]', '[436, 218, 3/2*w^3 - 2*w^2 - 10*w + 18]', '[436, 218, -3/2*w^3 + 4*w^2 + 13*w - 24]', '[436, 218, -3/2*w^3 + 9*w - 4]', '[436, 218, 1/2*w^3 - 4*w^2 - 6*w + 22]', '[439, 439, -2*w^3 + 3/2*w^2 + 12*w - 16]', '[439, 439, -w^3 + 1/2*w^2 + 5*w - 7]', '[439, 439, w^3 + 1/2*w^2 - 5*w - 7]', '[439, 439, w^3 + 1/2*w^2 - 4*w + 4]', '[451, 451, -w^3 - 1/2*w^2 + 5*w + 2]', '[451, 451, -1/2*w^3 - 1/2*w^2 + 5*w + 3]', '[451, 451, 3/2*w^3 + 1/2*w^2 - 9*w - 7]', '[451, 451, -1/2*w^3 - 1/2*w^2 + 2*w - 3]', '[451, 451, 1/2*w^2 - 3*w + 2]', '[451, 451, -1/2*w^3 - 5/2*w^2 + 2*w + 12]', '[451, 451, 1/2*w^3 + 1/2*w^2 - 4*w - 8]', '[451, 451, -1/2*w^3 - 5/2*w^2 + 4*w + 13]', '[451, 451, -1/2*w^3 + 5/2*w^2 + 4*w - 13]', '[451, 451, -1/2*w^3 + 1/2*w^2 + 4*w - 8]', '[451, 451, 1/2*w^3 - 5/2*w^2 - 2*w + 12]', '[451, 451, 1/2*w^2 + 3*w + 2]', '[451, 451, -1/2*w^3 + 1/2*w^2 + 2*w + 3]', '[451, 451, 3/2*w^3 - 1/2*w^2 - 9*w + 7]', '[451, 451, -1/2*w^3 + 1/2*w^2 + 5*w - 3]', '[451, 451, w^3 - 1/2*w^2 - 5*w + 2]', '[464, 58, -w^2 - 2*w + 8]', '[464, 58, -w^3 + w^2 + 6*w - 2]', '[464, 58, -w^3 - w^2 + 6*w + 2]', '[464, 58, -w^2 + 2*w + 8]', '[479, 479, -w^3 + 9/2*w^2 + 10*w - 26]', '[479, 479, -3/2*w^3 + 3/2*w^2 + 9*w - 14]', '[479, 479, -3/2*w^3 - 1/2*w^2 + 7*w - 6]', '[479, 479, -5/2*w^2 - 2*w + 14]', '[484, 22, -3/2*w^3 + w^2 + 8*w + 2]', '[484, 22, w^3 - w^2 - 5*w + 8]', '[484, 22, -1/2*w^3 - 2*w^2 + 5*w + 14]', '[484, 22, -1/2*w^3 - 3*w^2 + 6*w + 14]', '[484, 22, 1/2*w^3 + w^2 - 5*w - 2]', '[484, 22, w^3 + 2*w^2 - 5*w - 6]', '[484, 242, 1/2*w^3 - w^2 - 4*w + 2]', '[484, 242, 1/2*w^3 + w^2 - 2*w - 8]', '[484, 242, -1/2*w^3 + w^2 + 2*w - 8]', '[484, 242, 1/2*w^3 + w^2 - 4*w - 2]', '[491, 491, 1/2*w^3 + 5/2*w^2 - 4*w - 14]', '[491, 491, 1/2*w^3 + 5/2*w^2 - 2*w - 11]', '[491, 491, -1/2*w^3 + 5/2*w^2 + 2*w - 11]', '[491, 491, -1/2*w^3 + 5/2*w^2 + 4*w - 14]', '[500, 10, -w^3 + 5*w]', '[509, 509, 1/2*w^3 - 1/2*w^2 - 5*w - 3]', '[509, 509, -w^3 + 1/2*w^2 + 5*w - 8]', '[509, 509, w^3 + 1/2*w^2 - 5*w - 8]', '[509, 509, -7/2*w^2 - 3*w + 18]', '[521, 521, -9/2*w^2 - 4*w + 21]', '[521, 521, -5/2*w^3 + 2*w^2 + 16*w - 19]', '[521, 521, -1/2*w^3 + 2*w^2 + 6*w - 9]', '[521, 521, w^3 - 7/2*w^2 - 8*w + 22]', '[524, 262, 3/2*w^3 + 2*w^2 - 8*w - 6]', '[524, 262, 1/2*w^3 + 2*w^2 - 4*w - 8]', '[524, 262, -1/2*w^3 + 2*w^2 + 4*w - 8]', '[524, 262, 7/2*w^3 - 4*w^2 - 24*w + 34]', '[545, 545, -w^3 - 5/2*w^2 + 9*w + 15]', '[545, 545, -3*w^2 + 2*w + 15]', '[545, 545, -2*w^3 - w^2 + 12*w + 15]', '[545, 545, -2*w^3 + 1/2*w^2 + 11*w + 5]', '[571, 571, 1/2*w^3 - 1/2*w^2 - 4*w - 4]', '[571, 571, 3/2*w^3 - 3/2*w^2 - 9*w + 7]', '[571, 571, -3/2*w^3 - 3/2*w^2 + 9*w + 7]', '[571, 571, -1/2*w^3 - 1/2*w^2 + 4*w - 4]', '[580, 290, -1/2*w^3 - 2*w^2 + w + 10]', '[580, 290, -w^3 + 2*w^2 + 7*w - 10]', '[580, 290, -w^3 - 2*w^2 + 7*w + 10]', '[580, 290, 1/2*w^3 - 2*w^2 - w + 10]', '[596, 298, 1/2*w^3 + 2*w^2 + w - 4]', '[596, 298, 1/2*w^3 - 7*w^2 - 9*w + 36]', '[596, 298, -3/2*w^3 + 3*w^2 + 11*w - 24]', '[596, 298, -7/2*w^3 + 2*w^2 + 21*w - 24]', '[599, 599, 1/2*w^3 + w^2 - 2*w - 9]', '[599, 599, -1/2*w^3 + w^2 + 4*w - 1]', '[599, 599, 1/2*w^3 + w^2 - 4*w - 1]', '[599, 599, -1/2*w^3 + w^2 + 2*w - 9]', '[601, 601, 5/2*w^2 + w - 11]', '[601, 601, 1/2*w^3 - 5/2*w^2 - 3*w + 14]', '[601, 601, -1/2*w^3 - 5/2*w^2 + 3*w + 14]', '[601, 601, 5/2*w^2 - w - 11]', '[605, 55, -3/2*w^3 + 1/2*w^2 + 7*w + 5]', '[605, 55, -w^3 + 7*w + 5]', '[605, 55, -w^3 + 7*w - 5]', '[605, 55, -1/2*w^3 + w - 5]', '[605, 55, 1/2*w^3 - w - 5]', '[605, 55, -3/2*w^3 - 1/2*w^2 + 8*w + 10]', '[605, 605, 1/2*w^3 + 3/2*w^2 - 2*w - 10]', '[605, 605, 1/2*w^3 + 3/2*w^2 - 4*w - 5]', '[605, 605, 1/2*w^3 - 3/2*w^2 - 4*w + 5]', '[605, 605, -1/2*w^3 + 3/2*w^2 + 2*w - 10]', '[625, 5, 5]', '[641, 641, 5/2*w^2 + w - 13]', '[641, 641, -1/2*w^3 + 5/2*w^2 + 3*w - 12]', '[641, 641, 1/2*w^3 + 5/2*w^2 - 3*w - 12]', '[641, 641, 5/2*w^2 - w - 13]', '[655, 655, 2*w^3 + 11/2*w^2 - 17*w - 35]', '[655, 655, w^3 + 1/2*w^2 - 4*w - 5]', '[655, 655, w^3 - 1/2*w^2 - 4*w + 5]', '[655, 655, -w^3 + 7/2*w^2 + 3*w - 15]', '[656, 82, 2*w^3 - w^2 - 12*w + 12]', '[656, 82, -w^3 + 5*w^2 + 10*w - 28]', '[656, 82, w^3 - w^2 - 6*w + 12]', '[656, 82, -3*w^2 - 4*w + 12]', '[691, 691, 1/2*w^3 + 5/2*w^2 - 3*w - 13]', '[691, 691, -1/2*w^3 - w^2 + 3*w + 11]', '[691, 691, 1/2*w^3 - w^2 - 3*w + 11]', '[691, 691, -1/2*w^3 + 5/2*w^2 + 3*w - 13]', '[704, 44, -2*w^2 + 2*w + 12]', '[704, 44, -w^3 - 2*w^2 + 6*w + 8]', '[704, 44, w^3 - 2*w^2 - 6*w + 8]', '[704, 44, 2*w^2 + 2*w - 12]', '[709, 709, 3/2*w^3 - 3/2*w^2 - 8*w + 2]', '[709, 709, -1/2*w^3 + 3/2*w^2 + 6*w - 13]', '[709, 709, 1/2*w^3 + 3/2*w^2 - 6*w - 13]', '[709, 709, -3/2*w^3 - 3/2*w^2 + 8*w + 2]', '[719, 719, w^2 + 2*w - 9]', '[719, 719, w^3 + w^2 - 6*w - 1]', '[719, 719, -w^3 + w^2 + 6*w - 1]', '[719, 719, w^2 - 2*w - 9]', '[725, 145, w^3 - 3/2*w^2 - 5*w + 10]', '[725, 145, -1/2*w^3 - 3/2*w^2 + 5*w + 5]', '[725, 145, -1/2*w^3 + 3/2*w^2 + 5*w - 5]', '[725, 145, -w^3 - 3/2*w^2 + 5*w + 10]', '[745, 745, 7/2*w^3 - 2*w^2 - 18*w - 5]', '[745, 745, -w^3 + 3*w^2 + 2*w - 5]', '[745, 745, -w^3 - 7*w^2 + 12*w + 35]', '[745, 745, -3/2*w^3 - 2*w^2 + 12*w + 15]', '[761, 761, 1/2*w^3 + w^2 - 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5*w - 3]', '[251, 251, -w^3 + w^2 + 5*w - 3]', '[251, 251, -1/2*w^3 + w^2 + 5*w - 7]', '[269, 269, 1/2*w^3 + 1/2*w^2 - 2*w - 6]', '[269, 269, 1/2*w^3 - 1/2*w^2 - 4*w - 1]', '[269, 269, -1/2*w^3 - 1/2*w^2 + 4*w - 1]', '[269, 269, -1/2*w^3 + 1/2*w^2 + 2*w - 6]', '[281, 281, w^3 - 6*w + 1]', '[281, 281, w^3 - 1/2*w^2 - 6*w + 3]', '[281, 281, -w^3 - 1/2*w^2 + 6*w + 3]', '[281, 281, -w^3 + 6*w + 1]', '[331, 331, 3/2*w^3 + w^2 - 7*w + 1]', '[331, 331, -1/2*w^3 + 3*w^2 + 5*w - 17]', '[331, 331, -3/2*w^3 + w^2 + 9*w - 13]', '[331, 331, 1/2*w^3 + 3*w^2 + w - 11]', '[349, 349, 1/2*w^3 + 3/2*w^2 - 2*w - 9]', '[349, 349, -1/2*w^3 + 3/2*w^2 + 4*w - 6]', '[349, 349, 1/2*w^3 + 3/2*w^2 - 4*w - 6]', '[349, 349, -1/2*w^3 + 3/2*w^2 + 2*w - 9]', '[359, 359, -w^3 + 7/2*w^2 + 9*w - 19]', '[359, 359, w^3 - 2*w^2 - 8*w + 11]', '[359, 359, w^3 - 1/2*w^2 - 6*w - 2]', '[359, 359, -5/2*w^2 - 3*w + 9]', '[361, 19, 2*w^2 - 11]', '[361, 19, -1/2*w^2 + 7]', '[389, 389, -1/2*w^3 + 5/2*w^2 + 6*w - 11]', '[389, 389, 5/2*w^3 - 3/2*w^2 - 16*w + 17]', '[389, 389, 3/2*w^3 - 1/2*w^2 - 10*w + 7]', '[389, 389, -3/2*w^3 + 7/2*w^2 + 12*w - 21]', '[401, 401, -w^3 + 1/2*w^2 + 5*w - 1]', '[401, 401, 1/2*w^3 + 1/2*w^2 - 5*w - 4]', '[401, 401, -1/2*w^3 + 1/2*w^2 + 5*w - 4]', '[401, 401, w^3 + 1/2*w^2 - 5*w - 1]', '[439, 439, -2*w^3 + 3/2*w^2 + 12*w - 16]', '[439, 439, -w^3 + 1/2*w^2 + 5*w - 7]', '[439, 439, w^3 + 1/2*w^2 - 5*w - 7]', '[439, 439, w^3 + 1/2*w^2 - 4*w + 4]', '[479, 479, -w^3 + 9/2*w^2 + 10*w - 26]', '[479, 479, -3/2*w^3 + 3/2*w^2 + 9*w - 14]', '[479, 479, -3/2*w^3 - 1/2*w^2 + 7*w - 6]', '[479, 479, -5/2*w^2 - 2*w + 14]', '[491, 491, 1/2*w^3 + 5/2*w^2 - 4*w - 14]', '[491, 491, 1/2*w^3 + 5/2*w^2 - 2*w - 11]', '[491, 491, -1/2*w^3 + 5/2*w^2 + 2*w - 11]', '[491, 491, -1/2*w^3 + 5/2*w^2 + 4*w - 14]', '[509, 509, 1/2*w^3 - 1/2*w^2 - 5*w - 3]', '[509, 509, -w^3 + 1/2*w^2 + 5*w - 8]', '[509, 509, w^3 + 1/2*w^2 - 5*w - 8]', '[509, 509, -7/2*w^2 - 3*w + 18]', '[521, 521, -9/2*w^2 - 4*w + 21]', '[521, 521, -5/2*w^3 + 2*w^2 + 16*w - 19]', '[521, 521, -1/2*w^3 + 2*w^2 + 6*w - 9]', '[521, 521, w^3 - 7/2*w^2 - 8*w + 22]', '[571, 571, 1/2*w^3 - 1/2*w^2 - 4*w - 4]', '[571, 571, 3/2*w^3 - 3/2*w^2 - 9*w + 7]', '[571, 571, -3/2*w^3 - 3/2*w^2 + 9*w + 7]', '[571, 571, -1/2*w^3 - 1/2*w^2 + 4*w - 4]', '[599, 599, 1/2*w^3 + w^2 - 2*w - 9]', '[599, 599, -1/2*w^3 + w^2 + 4*w - 1]', '[599, 599, 1/2*w^3 + w^2 - 4*w - 1]', '[599, 599, -1/2*w^3 + w^2 + 2*w - 9]', '[601, 601, 5/2*w^2 + w - 11]', '[601, 601, 1/2*w^3 - 5/2*w^2 - 3*w + 14]', '[601, 601, -1/2*w^3 - 5/2*w^2 + 3*w + 14]', '[601, 601, 5/2*w^2 - w - 11]', '[641, 641, 5/2*w^2 + w - 13]', '[641, 641, -1/2*w^3 + 5/2*w^2 + 3*w - 12]', '[641, 641, 1/2*w^3 + 5/2*w^2 - 3*w - 12]', '[641, 641, 5/2*w^2 - w - 13]', '[691, 691, 1/2*w^3 + 5/2*w^2 - 3*w - 13]', '[691, 691, -1/2*w^3 - w^2 + 3*w + 11]', '[691, 691, 1/2*w^3 - w^2 - 3*w + 11]', '[691, 691, -1/2*w^3 + 5/2*w^2 + 3*w - 13]', '[709, 709, 3/2*w^3 - 3/2*w^2 - 8*w + 2]', '[709, 709, -1/2*w^3 + 3/2*w^2 + 6*w - 13]', '[709, 709, 1/2*w^3 + 3/2*w^2 - 6*w - 13]', '[709, 709, -3/2*w^3 - 3/2*w^2 + 8*w + 2]', '[719, 719, w^2 + 2*w - 9]', '[719, 719, w^3 + w^2 - 6*w - 1]', '[719, 719, -w^3 + w^2 + 6*w - 1]', '[719, 719, w^2 - 2*w - 9]', '[761, 761, 1/2*w^3 + w^2 - 6*w - 9]', '[761, 761, 3/2*w^3 + w^2 - 8*w - 1]', '[761, 761, 3/2*w^3 - 5*w^2 - 14*w + 29]', '[761, 761, -1/2*w^3 + w^2 + 6*w - 9]', '[811, 811, 3/2*w^3 - 1/2*w^2 - 8*w + 12]', '[811, 811, w^3 - 2*w^2 - 9*w + 11]', '[811, 811, -w^3 - 2*w^2 + 9*w + 11]', '[811, 811, -3/2*w^3 + 9/2*w^2 + 12*w - 28]', '[829, 829, w^3 + w^2 - 5*w - 9]', '[829, 829, 1/2*w^3 - w^2 - 5*w + 1]', '[829, 829, -1/2*w^3 - w^2 + 5*w + 1]', '[829, 829, -w^3 + w^2 + 5*w - 9]', '[839, 839, w^3 - 5/2*w^2 - 8*w + 13]', '[839, 839, 2*w^3 - 1/2*w^2 - 13*w - 1]', '[839, 839, -2*w^3 - 1/2*w^2 + 13*w - 1]', '[839, 839, w^3 + 5/2*w^2 - 8*w - 13]', '[881, 881, -w^3 + 9/2*w^2 + 9*w - 27]', '[881, 881, -2*w^3 + 1/2*w^2 + 12*w - 9]', '[881, 881, w^3 - 7/2*w^2 - 10*w + 19]', '[881, 881, 2*w^3 - 5/2*w^2 - 13*w + 23]', '[919, 919, 1/2*w^3 + 2*w^2 - 4*w - 7]', '[919, 919, 1/2*w^3 + 2*w^2 - 2*w - 13]', '[919, 919, -1/2*w^3 + 2*w^2 + 2*w - 13]', '[919, 919, -1/2*w^3 + 2*w^2 + 4*w - 7]', '[961, 31, -w^2 + 11]', '[961, 31, 5/2*w^2 - 13]', '[971, 971, 1/2*w^3 + 7/2*w^2 - 5*w - 17]', '[971, 971, 2*w^3 - 13*w - 3]', '[971, 971, -2*w^3 + 13*w - 3]', '[971, 971, -1/2*w^3 + 7/2*w^2 + 5*w - 17]']}
• 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
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [20, 0, -10, 0, 1], 'conductor': 40, 'degree': 4, 'dirichlet_group': [3, 1, 27, 9], 'disc_abs': 8000, 'disc_rad': 10, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [0]], [7, [[4, 1]]], [11, [[1, 4]]], [13, [[4, 1]]], [17, [[4, 1]]], [19, [[2, 2]]], [23, [[4, 1]]], [29, [[1, 4]]], [31, [[2, 2]]], [37, [[4, 1]]], [41, [[1, 4]]], [43, [[4, 1]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 3], 'galois_label': '4T1', 'galt': 1, 'grd': 9.457416090031758, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.8000.1', 'local_algs': ['2.2.2.6a1.2', '5.1.4.3a1.4'], 'monogenic': -1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [2, 5], 'rd': 9.45741609003, 'regulator': {'__RealLiteral__': 0, 'data': '4.50325854125', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{2} - 3 \\)', '\\( \\frac{1}{2} a^{3} - a^{2} - 4 a + 7 \\)', '\\( \\frac{1}{2} a^{3} + a^{2} - 2 a - 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2', '1/2*a^3']}