Hilbert modular form data - 4.4.18688.1-1.1-a

Formats: - HTML - YAML - JSON - 2024-04-30T08:27:19.455314

• 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': 18688, 'field_bad_primes': [2, 73], 'field_label': '4.4.18688.1', 'is_CM': 'yes', 'is_base_change': 'yes', 'label': '4.4.18688.1-1.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [], 'level_ideal': '[1, 1, 1]', 'level_label': '1.1', 'level_norm': 1, 'parallel_weight': 2, 'short_label': '1.1-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [], 'hecke_eigenvalues': [0, 0, 0, 2, 2, 6, 6, 0, 0, -6, -6, 6, 6, 0, 0, 14, -2, -2, -2, 0, 0, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, -22, 0, 0, 0, 0, 0, 0, 30, 30, 0, 0, -26, -26, -30, -30, 30, 30, 0, 0, 0, 0, -18, -18, 2, 0, 0, 0, 0, 10, 10, -14, -14, 0, 0, 0, 0, -34, -34, 22, 22, 0, 0, -38, -38, 0, 0, 0, 0, 42, 42, -26, 26, -26, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 46, 46, -42, -42, -34, -34, 0, 0, -46, -46, 30, 30, 50, 0, 0, 42, 42, -42, -42, 0, 0, 10, 10, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54, 54, -22, -22, 0, 0, 54, 54, 54, 54, 0, 0, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 54, 54, -34, 34, -34, 34, 62, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, -38, -38, 0, 0, 0, 0, 62, 62, 0, 0, 0, 0, 0, 0, 66, 66, 66, 66, -58, -58, 0, 0, 2, 2, 14, 14, 0, 0, 0, 0, 0, 0, 70, 70, 0, 0, 0, 0, 26, 26, 0, 0, -6, -6, 0, 0, -74, -74, 42, 42, 0, 0, 0, 0, -18, 18, -18, 18, 0, 0, 0, 0, 0, 0, 66, 66, -58, -58, 0, 0, 0, 0, 78, 78, 0, 0, 0, 0, -66, -66, 0, 0, 0, 0, -74, -74, 54, 54, 54, 54, -78, -78, 82, -82, 82, -82, 0, 0, 50, -50, 50, -50, 0, 0, 0, 0, 0, 0, 0, 0, 66, 66, 66, 66, -78, -78, 0, 0, 58, 58, 0, 0], 'hecke_polynomial': 'x', 'label': '4.4.18688.1-1.1-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 18688, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 2]', '[4, 2, -1/3*w^3 + 1/3*w^2 + 2*w - 2/3]', '[7, 7, -2/3*w^3 + 2/3*w^2 + 5*w - 7/3]', '[7, 7, -1/3*w^3 + 1/3*w^2 + w - 5/3]', '[8, 2, 1/3*w^3 + 2/3*w^2 - 2*w - 10/3]', '[9, 3, -1/3*w^3 + 1/3*w^2 + 3*w - 5/3]', '[9, 3, w + 1]', '[14, 14, w]', '[14, 14, 1/3*w^3 - 1/3*w^2 - 3*w + 2/3]', '[16, 2, 2]', '[17, 17, w + 3]', '[17, 17, -1/3*w^3 + 1/3*w^2 + 3*w - 11/3]', '[18, 6, 1/3*w^3 - 1/3*w^2 - 3*w - 4/3]', '[18, 6, w - 2]', '[28, 14, 2/3*w^3 - 5/3*w^2 - 4*w + 28/3]', '[28, 14, w^2 - 2]', '[31, 31, 1/3*w^3 - 1/3*w^2 - w - 1/3]', '[31, 31, -2/3*w^3 + 2/3*w^2 + 5*w - 1/3]', '[32, 4, -2*w - 4]', '[34, 34, 1/3*w^3 - 1/3*w^2 - w + 8/3]', '[34, 34, 2/3*w^3 - 2/3*w^2 - 5*w + 10/3]', '[36, 6, 2/3*w^3 - 5/3*w^2 - 4*w + 22/3]', '[36, 6, -w^2 + 4]', '[41, 41, -2/3*w^3 + 5/3*w^2 + 4*w - 19/3]', '[41, 41, w^2 - 5]', '[41, 41, 2*w + 3]', '[41, 41, 2/3*w^3 + 4/3*w^2 - 5*w - 29/3]', '[47, 47, -2/3*w^3 + 5/3*w^2 + 3*w - 19/3]', '[47, 47, 1/3*w^3 + 2/3*w^2 - 3*w - 13/3]', '[49, 7, 2/3*w^3 - 2/3*w^2 - 4*w + 7/3]', '[49, 7, -1/3*w^3 + 1/3*w^2 + 2*w - 11/3]', '[49, 49, -w^3 + w^2 + 7*w - 3]', '[49, 49, -2/3*w^3 + 2/3*w^2 + 3*w - 7/3]', '[56, 14, 1/3*w^3 - 4/3*w^2 - 2*w + 14/3]', '[56, 14, -1/3*w^3 + 4/3*w^2 + 2*w - 20/3]', '[62, 62, -2/3*w^3 + 2/3*w^2 + 3*w - 4/3]', '[62, 62, w^3 - w^2 - 7*w + 2]', '[63, 21, 1/3*w^3 + 2/3*w^2 - 2*w - 7/3]', '[63, 21, w^3 - 2*w^2 - 6*w + 9]', '[63, 21, -w^2 + 7]', '[63, 21, 2/3*w^3 - 5/3*w^2 - 4*w + 13/3]', '[64, 4, -2/3*w^3 + 2/3*w^2 + 4*w - 4/3]', '[68, 34, -2/3*w^3 - 1/3*w^2 + 4*w + 8/3]', '[68, 34, 4/3*w^3 - 7/3*w^2 - 8*w + 26/3]', '[72, 6, 1/3*w^3 + 2/3*w^2 - 2*w - 16/3]', '[72, 6, w^3 - 2*w^2 - 6*w + 6]', '[73, 73, -1/3*w^3 + 1/3*w^2 + 5*w + 19/3]', '[73, 73, -2/3*w^3 - 1/3*w^2 + 4*w + 11/3]', '[73, 73, -1/3*w^3 + 4/3*w^2 + 2*w - 17/3]', '[81, 3, 3]', '[81, 9, -1/3*w^3 + 1/3*w^2 - 5/3]', '[81, 9, w^3 - w^2 - 8*w + 3]', '[82, 82, 1/3*w^3 - 1/3*w^2 - w - 4/3]', '[82, 82, -2/3*w^3 + 2/3*w^2 + 5*w + 2/3]', '[82, 82, -1/3*w^3 - 2/3*w^2 + w + 10/3]', '[82, 82, -w^3 - 2*w^2 + 5*w + 10]', '[94, 94, -1/3*w^3 + 1/3*w^2 + 3*w + 10/3]', '[94, 94, -4/3*w^3 - 5/3*w^2 + 9*w + 40/3]', '[98, 14, -2/3*w^3 - 4/3*w^2 + 3*w + 14/3]', '[98, 14, 1/3*w^3 + 2/3*w^2 + w + 8/3]', '[98, 98, -1/3*w^3 + 4/3*w^2 + 3*w - 8/3]', '[98, 98, 2/3*w^3 - 5/3*w^2 - 5*w + 28/3]', '[103, 103, -1/3*w^3 + 4/3*w^2 + w - 23/3]', '[103, 103, w^2 - w - 3]', '[112, 14, -4/3*w^3 + 4/3*w^2 + 10*w - 14/3]', '[112, 14, -2/3*w^3 + 2/3*w^2 + 2*w - 10/3]', '[113, 113, -2/3*w^3 + 2/3*w^2 + 5*w + 11/3]', '[113, 113, 1/3*w^3 - 1/3*w^2 - w - 13/3]', '[119, 119, -2/3*w^3 + 2/3*w^2 + 5*w + 5/3]', '[119, 119, 2/3*w^3 - 5/3*w^2 - 4*w + 7/3]', '[119, 119, w^2 - 9]', '[119, 119, -1/3*w^3 + 1/3*w^2 + w + 7/3]', '[124, 62, 2/3*w^3 - 5/3*w^2 - 4*w + 10/3]', '[124, 62, -w^2 + 8]', '[126, 42, 1/3*w^3 - 1/3*w^2 - 3*w + 14/3]', '[126, 42, -w - 4]', '[126, 42, -w^3 + 2*w^2 + 7*w - 12]', '[126, 42, w^2 + w]', '[127, 127, 2/3*w^3 + 1/3*w^2 - 9*w - 41/3]', '[127, 127, -2/3*w^3 + 5/3*w^2 + 5*w - 31/3]', '[127, 127, -1/3*w^3 + 1/3*w^2 - 11/3]', '[127, 127, 4/3*w^3 + 5/3*w^2 - 10*w - 43/3]', '[128, 4, 2/3*w^3 + 4/3*w^2 - 4*w - 20/3]', '[136, 34, -w^3 + 2*w^2 + 6*w - 10]', '[136, 34, -1/3*w^3 - 2/3*w^2 + 2*w + 4/3]', '[144, 6, -2/3*w^3 + 2/3*w^2 + 6*w - 10/3]', '[144, 6, 2*w + 2]', '[146, 146, 1/3*w^3 + 2/3*w^2 - 3*w - 10/3]', '[146, 146, -2/3*w^3 + 5/3*w^2 + 3*w - 22/3]', '[146, 146, -2/3*w^3 - 4/3*w^2 + 3*w + 20/3]', '[151, 151, -1/3*w^3 + 4/3*w^2 + w - 29/3]', '[151, 151, 2/3*w^3 - 2/3*w^2 - 6*w - 5/3]', '[153, 51, -2/3*w^3 + 2/3*w^2 + 6*w - 1/3]', '[153, 51, 1/3*w^3 + 5/3*w^2 - w - 19/3]', '[153, 51, -2*w + 1]', '[153, 51, 2*w^3 - 4*w^2 - 13*w + 17]', '[162, 6, -3*w - 6]', '[162, 18, -1/3*w^3 + 4/3*w^2 + w - 26/3]', '[162, 18, w^2 - w - 2]', '[164, 82, 1/3*w^3 - 1/3*w^2 - 4*w + 8/3]', '[164, 82, 1/3*w^3 - 1/3*w^2 - 4*w - 4/3]', '[164, 82, -1/3*w^3 - 5/3*w^2 + 2*w + 22/3]', '[164, 82, 2/3*w^3 + 1/3*w^2 - 8*w - 32/3]', '[167, 167, -2/3*w^3 + 5/3*w^2 + 2*w - 19/3]', '[167, 167, 2/3*w^3 + 1/3*w^2 - 6*w - 11/3]', '[188, 94, w^2 - 2*w - 2]', '[188, 94, w^2 - 2*w - 8]', '[191, 191, -w^3 + 2*w^2 + 6*w - 5]', '[191, 191, 1/3*w^3 + 2/3*w^2 - 2*w - 19/3]', '[193, 193, -1/3*w^3 + 1/3*w^2 + 5*w + 13/3]', '[193, 193, 2/3*w^3 + 7/3*w^2 - 2*w - 23/3]', '[196, 14, -1/3*w^3 + 1/3*w^2 + 2*w - 14/3]', '[196, 14, w^3 - w^2 - 6*w + 4]', '[196, 98, 2/3*w^3 - 5/3*w^2 - 4*w + 34/3]', '[196, 98, w^2]', '[199, 199, 1/3*w^3 + 2/3*w^2 + 2*w + 11/3]', '[199, 199, 1/3*w^3 + 2/3*w^2 - 5*w - 31/3]', '[206, 206, -2/3*w^3 - 1/3*w^2 + 7*w + 32/3]', '[206, 206, -w^3 - w^2 + 5*w + 6]', '[217, 217, 2/3*w^3 - 2/3*w^2 - 6*w + 7/3]', '[217, 217, -2*w - 1]', '[217, 217, 2/3*w^3 - 2/3*w^2 - w + 7/3]', '[217, 217, -5/3*w^3 + 5/3*w^2 + 13*w - 13/3]', '[223, 223, -2/3*w^3 + 5/3*w^2 + 5*w - 13/3]', '[223, 223, 4/3*w^3 - 7/3*w^2 - 8*w + 17/3]', '[223, 223, 2/3*w^3 + 1/3*w^2 - 4*w - 17/3]', '[223, 223, w^3 - w^2 - 7*w - 1]', '[224, 28, 2*w]', '[224, 28, 2/3*w^3 - 2/3*w^2 - 6*w + 4/3]', '[226, 226, 2/3*w^3 + 1/3*w^2 - 11*w - 50/3]', '[226, 226, -1/3*w^3 - 5/3*w^2 + 5*w + 40/3]', '[233, 233, -1/3*w^3 + 1/3*w^2 + w - 17/3]', '[233, 233, -2/3*w^3 + 2/3*w^2 + 5*w - 19/3]', '[238, 238, 1/3*w^3 + 2/3*w^2 - 3*w - 28/3]', '[238, 238, 2/3*w^3 - 5/3*w^2 - 3*w + 4/3]', '[238, 238, -4/3*w^3 + 10/3*w^2 + 7*w - 38/3]', '[238, 238, 1/3*w^3 + 5/3*w^2 - 3*w - 28/3]', '[239, 239, 5/3*w^3 + 7/3*w^2 - 10*w - 41/3]', '[239, 239, -5/3*w^3 - 7/3*w^2 + 12*w + 59/3]', '[241, 241, -1/3*w^3 + 7/3*w^2 + w - 23/3]', '[241, 241, 5/3*w^3 + 10/3*w^2 - 10*w - 59/3]', '[248, 62, -1/3*w^3 + 4/3*w^2 + 2*w - 32/3]', '[248, 62, -1/3*w^3 + 4/3*w^2 + 2*w - 2/3]', '[252, 42, -1/3*w^3 + 1/3*w^2 - 14/3]', '[252, 42, -w^3 + w^2 + 8*w - 6]', '[252, 42, -w^3 + w^2 + 8*w]', '[252, 42, 1/3*w^3 - 1/3*w^2 - 4/3]', '[254, 254, -w^3 + 7*w + 4]', '[254, 254, -w^2 + w + 10]', '[254, 254, -1/3*w^3 - 5/3*w^2 + 3*w + 34/3]', '[254, 254, -4/3*w^3 + 7/3*w^2 + 7*w - 20/3]', '[256, 4, 4]', '[257, 257, -1/3*w^3 + 1/3*w^2 + 4*w - 5/3]', '[257, 257, 1/3*w^3 - 1/3*w^2 - 4*w - 1/3]', '[257, 257, 2/3*w^3 + 1/3*w^2 - 7*w - 23/3]', '[257, 257, -4/3*w^3 + 1/3*w^2 + 10*w + 13/3]', '[263, 263, -4/3*w^3 + 7/3*w^2 + 9*w - 23/3]', '[263, 263, 1/3*w^3 + 2/3*w^2 - w - 13/3]', '[271, 271, 5/3*w^3 - 5/3*w^2 - 12*w + 19/3]', '[271, 271, w^3 - w^2 - 4*w + 5]', '[272, 34, 2*w + 6]', '[272, 34, -2/3*w^3 + 2/3*w^2 + 6*w - 22/3]', '[279, 93, 2*w^2 - 5]', '[279, 93, -w^2 + 2*w + 9]', '[279, 93, w^2 - 2*w - 1]', '[279, 93, 4/3*w^3 - 10/3*w^2 - 8*w + 53/3]', '[281, 281, w^2 + 5*w + 5]', '[281, 281, -1/3*w^3 - 5/3*w^2 + 2*w + 25/3]', '[287, 287, -2/3*w^3 + 2/3*w^2 + w - 1/3]', '[287, 287, -w^3 + 2*w^2 + 4*w - 7]', '[287, 287, -1/3*w^3 - 2/3*w^2 + 3*w + 7/3]', '[287, 287, -2/3*w^3 - 4/3*w^2 + w + 11/3]', '[287, 287, 3*w^3 - 5*w^2 - 21*w + 21]', '[287, 287, 2/3*w^3 - 5/3*w^2 - 3*w + 25/3]', '[287, 287, w^3 - 8*w - 3]', '[287, 287, 5/3*w^3 - 5/3*w^2 - 13*w + 7/3]', '[288, 12, 2/3*w^3 - 2/3*w^2 - 6*w - 8/3]', '[288, 12, 2*w - 4]', '[289, 17, w^3 - w^2 - 6*w + 3]', '[289, 17, -w^3 + w^2 + 6*w - 1]', '[289, 289, 1/3*w^3 - 4/3*w^2 - 3*w - 1/3]', '[289, 289, -2/3*w^3 + 5/3*w^2 + 5*w - 37/3]', '[292, 146, -4/3*w^3 - 5/3*w^2 + 8*w + 34/3]', '[292, 146, -1/3*w^3 + 1/3*w^2 + 4*w + 16/3]', '[292, 146, 1/3*w^3 - 1/3*w^2 - 4*w + 2/3]', '[302, 302, -2/3*w^3 - 1/3*w^2 + 9*w + 44/3]', '[302, 302, -2/3*w^3 + 2/3*w^2 + 11*w + 38/3]', '[306, 102, -w^3 + 2*w^2 + 7*w - 6]', '[306, 102, -1/3*w^3 - 5/3*w^2 + w + 10/3]', '[306, 102, -2*w^3 + 4*w^2 + 13*w - 20]', '[306, 102, w^2 + w - 6]', '[311, 311, 1/3*w^3 - 7/3*w^2 + 41/3]', '[311, 311, -2*w + 5]', '[311, 311, -w^3 - 2*w^2 + 7*w + 15]', '[311, 311, 2/3*w^3 - 2/3*w^2 - 6*w - 11/3]', '[313, 313, w^3 - w^2 - 5*w + 1]', '[313, 313, -4/3*w^3 + 4/3*w^2 + 9*w - 5/3]', '[324, 6, -w^3 + w^2 + 6*w - 2]', '[324, 18, -1/3*w^3 + 7/3*w^2 + 2*w - 20/3]', '[324, 18, -w^3 + 3*w^2 + 6*w - 16]', '[328, 82, -1/3*w^3 + 4/3*w^2 + 4*w - 2/3]', '[328, 82, -1/3*w^3 + 4/3*w^2 + 8*w + 22/3]', '[328, 82, w^3 - 2*w^2 - 6*w + 4]', '[328, 82, -1/3*w^3 - 2/3*w^2 + 2*w + 22/3]', '[329, 329, -w^3 + 3*w^2 + 4*w - 5]', '[329, 329, 7/3*w^3 - 10/3*w^2 - 16*w + 35/3]', '[329, 329, -w^3 + 4*w + 1]', '[329, 329, 1/3*w^3 + 5/3*w^2 - 4*w - 49/3]', '[334, 334, -1/3*w^3 + 4/3*w^2 + 5*w + 10/3]', '[334, 334, -5/3*w^3 - 4/3*w^2 + 13*w + 50/3]', '[337, 337, 4/3*w^3 - 4/3*w^2 - 11*w + 5/3]', '[337, 337, 2/3*w^3 + 1/3*w^2 - 6*w - 29/3]', '[343, 7, 8/3*w^3 - 11/3*w^2 - 19*w + 49/3]', '[343, 7, w^3 - 3*w + 3]', '[343, 49, -4/3*w^3 + 1/3*w^2 + 11*w + 7/3]', '[343, 49, -w^3 + 2*w^2 + 3*w - 7]', '[343, 343, 1/3*w^3 + 2/3*w^2 - 4*w - 7/3]', '[343, 343, 1/3*w^3 - 4/3*w^2 + 23/3]', '[359, 359, -w^3 - w^2 + 12*w + 19]', '[359, 359, -1/3*w^3 + 4/3*w^2 + 5*w + 1/3]', '[359, 359, -1/3*w^3 - 8/3*w^2 - 4*w + 1/3]', '[359, 359, w^2 - 3*w - 9]', '[361, 19, 2*w^2 - w - 13]', '[361, 19, -w^3 + 3*w^2 + 5*w - 9]', '[369, 123, w^3 + w^2 - 5*w - 5]', '[369, 123, -2*w^3 + 4*w^2 + 10*w - 11]', '[369, 123, 8/3*w^3 - 14/3*w^2 - 17*w + 55/3]', '[369, 123, 4/3*w^3 - 4/3*w^2 - 9*w + 11/3]', '[369, 123, w^3 - w^2 - 5*w + 3]', '[369, 123, -1/3*w^3 + 1/3*w^2 + 3*w + 13/3]', '[369, 123, 4/3*w^3 + 2/3*w^2 - 10*w - 31/3]', '[369, 123, w - 5]', '[376, 94, -w^3 + 6*w + 4]', '[376, 94, -w^3 + 12*w + 16]', '[382, 382, -3*w - 4]', '[382, 382, -4/3*w^3 - 8/3*w^2 + 9*w + 52/3]', '[386, 386, -1/3*w^3 + 4/3*w^2 + 3*w - 26/3]', '[386, 386, -2/3*w^3 + 5/3*w^2 + 5*w - 10/3]', '[392, 14, 1/3*w^3 + 2/3*w^2 + 2*w + 14/3]', '[392, 14, -w^3 - 2*w^2 + 4*w + 6]', '[392, 98, -1/3*w^3 - 2/3*w^2 + 10/3]', '[392, 98, -5/3*w^3 + 8/3*w^2 + 12*w - 28/3]', '[398, 398, w^3 - w^2 - 5*w + 2]', '[398, 398, -4/3*w^3 + 4/3*w^2 + 9*w - 8/3]', '[409, 409, -w - 5]', '[409, 409, -1/3*w^3 + 1/3*w^2 + 3*w - 17/3]', '[412, 206, 2/3*w^3 + 1/3*w^2 - 6*w - 8/3]', '[412, 206, -2/3*w^3 + 5/3*w^2 + 2*w - 22/3]', '[423, 141, 7/3*w^3 - 13/3*w^2 - 14*w + 41/3]', '[423, 141, w^3 + w^2 - 6*w - 9]', '[423, 141, w^3 - 2*w^2 - 6*w + 3]', '[423, 141, 1/3*w^3 + 2/3*w^2 - 2*w - 25/3]', '[431, 431, -w^3 - 3*w^2 + 2*w + 9]', '[431, 431, 2/3*w^3 + 7/3*w^2 - w - 23/3]', '[433, 433, -1/3*w^3 + 1/3*w^2 + 6*w + 19/3]', '[433, 433, 2/3*w^3 + 7/3*w^2 - 3*w - 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13/3]', '[1897, 1897, -1/3*w^3 - 20/3*w^2 - 3*w + 31/3]', '[1897, 1897, -20/3*w^3 + 41/3*w^2 + 45*w - 217/3]', '[1897, 1897, -8/3*w^3 + 11/3*w^2 + 17*w - 49/3]', '[1904, 238, -4/3*w^3 + 4/3*w^2 + 10*w + 10/3]', '[1904, 238, 4/3*w^3 - 10/3*w^2 - 8*w + 14/3]', '[1904, 238, 2*w^2 - 18]', '[1904, 238, -2/3*w^3 + 2/3*w^2 + 2*w + 14/3]', '[1912, 478, -7/3*w^3 + 4/3*w^2 + 16*w - 8/3]', '[1912, 478, 1/3*w^3 + 8/3*w^2 - 4*w - 52/3]', '[1913, 1913, 5/3*w^3 - 5/3*w^2 - 9*w + 1/3]', '[1913, 1913, -4/3*w^3 + 7/3*w^2 + 9*w - 47/3]', '[1921, 1921, -4/3*w^3 + 1/3*w^2 + 16*w + 61/3]', '[1921, 1921, 4/3*w^3 - 10/3*w^2 - 6*w + 11/3]', '[1921, 1921, 2/3*w^3 + 4/3*w^2 - 6*w - 53/3]', '[1921, 1921, 2/3*w^3 + 1/3*w^2 - 12*w + 43/3]', '[1922, 62, -4/3*w^3 - 8/3*w^2 + 7*w + 34/3]', '[1922, 62, -4/3*w^3 - 8/3*w^2 + 9*w + 46/3]', '[1922, 1922, -2/3*w^3 - 1/3*w^2 + 3*w + 20/3]', '[1922, 1922, -5/3*w^3 + 8/3*w^2 + 11*w - 16/3]', '[1927, 1927, -2/3*w^3 + 11/3*w^2 + 2*w - 73/3]', '[1927, 1927, -2/3*w^3 + 5/3*w^2 + 8*w + 5/3]', '[1927, 1927, 1/3*w^3 + 2/3*w^2 - w - 25/3]', '[1927, 1927, -7/3*w^3 - 8/3*w^2 + 15*w + 67/3]', '[1927, 1927, -4/3*w^3 + 7/3*w^2 + 9*w - 11/3]', '[1927, 1927, 1/3*w^3 + 2/3*w^2 - w - 37/3]', '[1927, 1927, -4/3*w^3 + 7/3*w^2 + 9*w + 1/3]', '[1927, 1927, 2/3*w^3 - 11/3*w^2 - 2*w + 25/3]', '[1928, 482, 1/3*w^3 + 8/3*w^2 - 6*w - 64/3]', '[1928, 482, -1/3*w^3 - 8/3*w^2 + 2*w + 52/3]', '[1934, 1934, -7/3*w^3 + 10/3*w^2 + 15*w - 32/3]', '[1934, 1934, -1/3*w^3 + 1/3*w^2 + 7*w + 22/3]', '[1934, 1934, -4/3*w^3 - 11/3*w^2 + 7*w + 52/3]', '[1934, 1934, 4/3*w^3 - 1/3*w^2 - 7*w - 4/3]', '[1948, 974, w^2 + 8*w + 12]', '[1948, 974, 1/3*w^3 + 5/3*w^2 - 6*w - 52/3]', '[1948, 974, 1/3*w^3 - 1/3*w^2 + 2*w + 26/3]', '[1948, 974, 1/3*w^3 - 7/3*w^2 + 2*w + 8/3]', '[1951, 1951, -7/3*w^3 - 8/3*w^2 + 17*w + 67/3]', '[1951, 1951, 4/3*w^3 - 10/3*w^2 - 10*w + 59/3]', '[1953, 651, -w - 7]', '[1953, 651, -7/3*w^3 + 13/3*w^2 + 17*w - 77/3]', '[1953, 651, -2*w^2 - 3*w - 1]', '[1953, 651, -2*w^3 + 5*w^2 + 11*w - 17]', '[1953, 651, -1/3*w^3 + 1/3*w^2 + 3*w - 23/3]', '[1953, 651, 1/3*w^3 + 8/3*w^2 - 3*w - 49/3]', '[1953, 651, w^3 - w^2 - 10*w + 7]', '[1953, 651, 1/3*w^3 - 1/3*w^2 - 6*w - 13/3]', '[1954, 1954, 4/3*w^3 - 10/3*w^2 - 5*w + 38/3]', '[1954, 1954, -w^3 - w^2 + 9*w + 8]', '[1966, 1966, 2*w^3 + 2*w^2 - 11*w - 10]', '[1966, 1966, -4/3*w^3 - 14/3*w^2 - w + 10/3]', '[1967, 1967, -2*w^3 + 2*w^2 + 15*w - 9]', '[1967, 1967, -w^3 + w^2 + 3*w - 7]', '[1967, 1967, 2/3*w^3 + 1/3*w^2 - 6*w + 7/3]', '[1967, 1967, 2/3*w^3 - 5/3*w^2 - 2*w + 37/3]', '[1982, 1982, -5/3*w^3 - 7/3*w^2 + 7*w + 26/3]', '[1982, 1982, w^2 + 5*w + 8]', '[1984, 124, 4/3*w^3 - 10/3*w^2 - 8*w + 20/3]', '[1984, 124, -2*w^2 + 16]', '[1993, 1993, -8/3*w^3 + 8/3*w^2 + 19*w - 19/3]', '[1993, 1993, 5/3*w^3 - 5/3*w^2 - 7*w + 13/3]', '[1999, 1999, 2/3*w^3 + 1/3*w^2 - 3*w - 41/3]', '[1999, 1999, -5/3*w^3 + 8/3*w^2 + 11*w + 5/3]', '[2007, 669, 7/3*w^3 - 13/3*w^2 - 14*w + 59/3]', '[2007, 669, 2*w^2 - 4*w - 15]', '[2007, 669, w^3 - 2*w + 5]', '[2007, 669, -10/3*w^3 + 22/3*w^2 + 19*w - 89/3]', '[2007, 669, 2/3*w^3 + 4/3*w^2 - 7*w - 23/3]', '[2007, 669, -4/3*w^3 + 13/3*w^2 + 6*w - 65/3]', '[2007, 669, -w^3 + 3*w^2 + 3*w - 13]', '[2007, 669, w^3 + 3*w^2 - 7*w - 15]', '[2009, 287, -7/3*w^3 - 17/3*w^2 + 11*w + 73/3]', '[2009, 287, -4/3*w^3 + 7/3*w^2 + 12*w - 35/3]', '[2009, 287, -2/3*w^3 - 1/3*w^2 + 8*w + 23/3]', '[2009, 287, -2/3*w^3 + 5/3*w^2 + 8*w - 7/3]', '[2009, 287, 2/3*w^3 + 10/3*w^2 - 2*w - 35/3]', '[2009, 287, 1/3*w^3 + 5/3*w^2 + 4*w + 5/3]', '[2009, 287, -4/3*w^3 - 11/3*w^2 + 7*w + 55/3]', '[2009, 287, -2/3*w^3 + 2/3*w^2 + 11*w + 35/3]', '[2009, 2009, w^3 - 3*w^2 - 6*w + 21]', '[2009, 2009, -1/3*w^3 + 1/3*w^2 - 3*w + 7/3]', '[2009, 2009, 1/3*w^3 - 7/3*w^2 - 2*w + 5/3]', '[2009, 2009, 2*w^3 - 2*w^2 - 17*w + 1]', '[2009, 2009, -4/3*w^3 + 1/3*w^2 + 7*w + 1/3]', '[2009, 2009, 10/3*w^3 - 16/3*w^2 - 25*w + 71/3]', '[2009, 2009, 7/3*w^3 - 10/3*w^2 - 15*w + 35/3]', '[2009, 2009, -1/3*w^3 - 5/3*w^2 - 3*w + 7/3]', '[2012, 1006, w^3 - w^2 - 10*w - 6]', '[2012, 1006, 7/3*w^3 + 11/3*w^2 - 16*w - 76/3]', '[2012, 1006, -2/3*w^3 - 7/3*w^2 + 4*w + 26/3]', '[2012, 1006, 3*w^2 + 8*w + 4]', '[2016, 84, 2/3*w^3 - 2/3*w^2 - 6*w + 28/3]', '[2016, 84, -2*w - 8]', '[2016, 84, -2*w^3 + 4*w^2 + 14*w - 24]', '[2016, 84, 2*w^2 + 2*w]', '[2017, 2017, -7/3*w^3 + 16/3*w^2 + 14*w - 65/3]', '[2017, 2017, -1/3*w^3 + 1/3*w^2 - 2*w - 11/3]', '[2017, 2017, 5/3*w^3 - 5/3*w^2 - 14*w + 19/3]', '[2017, 2017, -1/3*w^3 - 8/3*w^2 + 2*w + 37/3]', '[2018, 2018, w^3 - 5*w - 6]', '[2018, 2018, -2*w^3 + 3*w^2 + 13*w - 6]', '[2023, 119, 4/3*w^3 - 13/3*w^2 - 7*w + 77/3]', '[2023, 119, -8/3*w^3 + 17/3*w^2 + 17*w - 91/3]', '[2023, 119, -1/3*w^3 + 10/3*w^2 + w - 23/3]', '[2023, 119, -1/3*w^3 - 8/3*w^2 + w + 13/3]', '[2023, 2023, 5/3*w^3 - 11/3*w^2 - 8*w + 43/3]', '[2023, 2023, w^3 + w^2 - 8*w - 7]', '[2023, 2023, 2*w^3 - 4*w^2 - 12*w + 11]', '[2023, 2023, -2/3*w^3 - 4/3*w^2 + 4*w + 35/3]', '[2032, 254, 4/3*w^3 + 2/3*w^2 - 18*w - 82/3]', '[2032, 254, -4/3*w^3 + 10/3*w^2 + 10*w - 62/3]', '[2032, 254, -2/3*w^3 + 2/3*w^2 - 22/3]', '[2032, 254, 8/3*w^3 + 10/3*w^2 - 20*w - 86/3]', '[2034, 678, 2*w^3 - 3*w^2 - 9*w + 2]', '[2034, 678, -w^3 + 3*w^2 - w + 4]', '[2034, 678, 2*w^3 - 19*w - 22]', '[2034, 678, -7/3*w^3 + 4/3*w^2 + 17*w + 22/3]', '[2039, 2039, -5/3*w^3 - 13/3*w^2 + 7*w + 47/3]', '[2039, 2039, -4/3*w^3 - 5/3*w^2 + 10*w + 37/3]', '[2044, 1022, -2/3*w^3 + 11/3*w^2 + 6*w - 22/3]', '[2044, 1022, -2*w^3 + 3*w^2 + 14*w - 8]', '[2044, 1022, -2*w^3 + 5*w^2 + 14*w - 28]', '[2044, 1022, 5/3*w^3 - 11/3*w^2 - 10*w + 28/3]', '[2044, 1022, -1/3*w^3 - 5/3*w^2 + 2*w + 40/3]', '[2044, 1022, 2/3*w^3 + 1/3*w^2 - 2*w - 14/3]', '[2048, 8, 4/3*w^3 + 8/3*w^2 - 8*w - 40/3]', '[2056, 514, w^3 + 2*w^2 - 4*w - 10]', '[2056, 514, -5/3*w^3 - 10/3*w^2 + 8*w + 50/3]', '[2056, 514, -11/3*w^3 - 16/3*w^2 + 26*w + 128/3]', '[2056, 514, 7/3*w^3 + 8/3*w^2 - 24*w - 118/3]', '[2062, 2062, 5/3*w^3 + 4/3*w^2 - 19*w - 92/3]', '[2062, 2062, -2/3*w^3 - 1/3*w^2 + 7*w + 38/3]', '[2062, 2062, -w^3 + w^2 + 17*w + 20]', '[2062, 2062, -7/3*w^3 - 11/3*w^2 + 11*w + 52/3]', '[2066, 2066, -5/3*w^3 + 8/3*w^2 + 9*w - 40/3]', '[2066, 2066, 1/3*w^3 - 7/3*w^2 + w + 44/3]', '[2078, 2078, -2/3*w^3 - 10/3*w^2 + 3*w + 50/3]', '[2078, 2078, -4/3*w^3 - 14/3*w^2 - 3*w + 10/3]', '[2084, 1042, -8/3*w^3 - 13/3*w^2 + 14*w + 68/3]', '[2084, 1042, 1/3*w^3 - 1/3*w^2 - 4*w - 22/3]', '[2087, 2087, -5/3*w^3 - 13/3*w^2 + 6*w + 41/3]', '[2087, 2087, 4/3*w^3 + 5/3*w^2 - 9*w - 31/3]', '[2089, 2089, -4/3*w^3 + 13/3*w^2 + 6*w - 41/3]', '[2089, 2089, -5/3*w^3 + 8/3*w^2 + 14*w - 25/3]', '[2097, 699, 2*w^3 - 3*w^2 - 16*w + 11]', '[2097, 699, 10/3*w^3 - 16/3*w^2 - 26*w + 83/3]', '[2097, 699, -2*w^2 - 6*w - 1]', '[2097, 699, -w^2 - 4*w + 3]', '[2104, 526, 1/3*w^3 + 8/3*w^2 - 2*w - 40/3]', '[2104, 526, 1/3*w^3 + 8/3*w^2 + 8*w + 20/3]', '[2108, 1054, 1/3*w^3 - 7/3*w^2 - 6*w + 2/3]', '[2108, 1054, -4/3*w^3 + 7/3*w^2 + 6*w - 32/3]', '[2108, 1054, 4/3*w^3 - 1/3*w^2 - 10*w + 2/3]', '[2108, 1054, -7/3*w^3 + 13/3*w^2 + 18*w - 74/3]', '[2111, 2111, -5/3*w^3 + 14/3*w^2 + 7*w - 55/3]', '[2111, 2111, 2/3*w^3 + 7/3*w^2 - 7*w - 41/3]', '[2111, 2111, -4/3*w^3 + 10/3*w^2 + 7*w - 65/3]', '[2111, 2111, -w^3 + 2*w^2 + 10*w - 1]', '[2114, 2114, -8/3*w^3 + 8/3*w^2 + 21*w - 10/3]', '[2114, 2114, 4/3*w^3 - 7/3*w^2 - 11*w + 14/3]', '[2114, 2114, 1/3*w^3 - 7/3*w^2 + w + 62/3]', '[2114, 2114, -2/3*w^3 + 2/3*w^2 + w - 28/3]', '[2116, 46, 5/3*w^3 - 5/3*w^2 - 10*w + 4/3]', '[2116, 46, 5/3*w^3 - 5/3*w^2 - 10*w + 16/3]', '[2126, 2126, -1/3*w^3 + 4/3*w^2 + 13*w + 58/3]', '[2126, 2126, -4/3*w^3 - 2/3*w^2 + 11*w + 52/3]', '[2126, 2126, 10/3*w^3 + 14/3*w^2 - 19*w - 88/3]', '[2126, 2126, -8/3*w^3 - 13/3*w^2 + 21*w + 110/3]', '[2137, 2137, -3*w^2 + 11]', '[2137, 2137, -2*w^3 + 5*w^2 + 12*w - 23]', '[2142, 714, -w^3 + 2*w^2 + w - 8]', '[2142, 714, 2*w^3 - w^2 - 17*w]', '[2142, 714, -2/3*w^3 + 8/3*w^2 - w - 16/3]', '[2142, 714, w^3 + w^2 - 11*w - 14]', '[2142, 714, 2*w^3 - 3*w^2 - 11*w + 6]', '[2142, 714, 5/3*w^3 - 17/3*w^2 - 7*w + 46/3]', '[2142, 714, 5/3*w^3 - 2/3*w^2 - 11*w - 14/3]', '[2142, 714, -4*w^2 + 3*w + 28]', '[2143, 2143, 1/3*w^3 + 8/3*w^2 - 3*w - 61/3]', '[2143, 2143, -2*w^3 + 5*w^2 + 11*w - 13]', '[2151, 717, 3*w^3 - 5*w^2 - 22*w + 19]', '[2151, 717, w^3 + 4*w^2 - 7*w - 27]', '[2151, 717, -7/3*w^3 - 8/3*w^2 + 19*w + 79/3]', '[2151, 717, w^3 - 3*w^2 - 4*w + 15]', '[2153, 2153, -1/3*w^3 - 5/3*w^2 - w - 5/3]', '[2153, 2153, 2/3*w^3 + 10/3*w^2 - 2*w - 41/3]', '[2153, 2153, 8/3*w^3 - 11/3*w^2 - 17*w + 25/3]', '[2153, 2153, 2/3*w^3 + 10/3*w^2 + 5*w + 1/3]', '[2159, 2159, -4/3*w^3 - 2/3*w^2 + 9*w + 13/3]', '[2159, 2159, 2*w^3 - w^2 - 15*w + 1]', '[2159, 2159, 5/3*w^3 - 5/3*w^2 - 14*w + 37/3]', '[2159, 2159, 1/3*w^3 - 1/3*w^2 + 2*w + 29/3]', '[2159, 2159, -1/3*w^3 + 10/3*w^2 + 2*w - 65/3]', '[2159, 2159, -2*w^3 + 5*w^2 + 12*w - 29]', '[2159, 2159, 5/3*w^3 - 8/3*w^2 - 7*w + 31/3]', '[2159, 2159, 17/3*w^3 - 29/3*w^2 - 42*w + 151/3]', '[2161, 2161, 2*w^2 - w - 19]', '[2161, 2161, w^3 - 3*w^2 - 5*w + 3]', '[2168, 542, -1/3*w^3 - 2/3*w^2 + 8*w + 58/3]', '[2168, 542, 7/3*w^3 + 14/3*w^2 - 4*w - 22/3]', '[2169, 723, w^3 - 4*w^2 - 4*w + 19]', '[2169, 723, 2*w^3 - 3*w^2 - 10*w + 5]', '[2169, 723, 8/3*w^3 + 7/3*w^2 - 19*w - 65/3]', '[2169, 723, -w^3 + 2*w^2 + 6*w - 15]', '[2176, 68, -2*w^3 + 4*w^2 + 12*w - 20]', '[2176, 68, -2/3*w^3 - 4/3*w^2 + 4*w + 8/3]', '[2177, 2177, 2/3*w^3 + 10/3*w^2 - 7*w - 77/3]', '[2177, 2177, w^3 - 2*w^2 - 5*w - 1]', '[2177, 2177, -14/3*w^3 + 11/3*w^2 + 35*w - 7/3]', '[2177, 2177, -7/3*w^3 + 19/3*w^2 + 11*w - 53/3]', '[2177, 2177, -10/3*w^3 + 10/3*w^2 + 24*w - 29/3]', '[2177, 2177, -14/3*w^3 + 20/3*w^2 + 35*w - 91/3]', '[2177, 2177, 2*w^3 - 2*w^2 - 13*w + 7]', '[2177, 2177, w^3 + w^2 + w + 3]', '[2191, 2191, 2/3*w^3 - 17/3*w^2 - 4*w + 37/3]', '[2191, 2191, 8/3*w^3 - 23/3*w^2 - 16*w + 133/3]', '[2191, 2191, -2/3*w^3 + 8/3*w^2 + 2*w - 49/3]', '[2191, 2191, 2*w^2 - 2*w - 5]', '[2194, 2194, -2/3*w^3 - 10/3*w^2 + 3*w + 32/3]', '[2194, 2194, -4/3*w^3 - 8/3*w^2 + 7*w + 46/3]', '[2194, 2194, 1/3*w^3 + 2/3*w^2 + 5*w + 38/3]', '[2194, 2194, -4/3*w^3 - 8/3*w^2 + 5*w + 34/3]', '[2207, 2207, 4/3*w^3 - 4/3*w^2 - 5*w + 23/3]', '[2207, 2207, 7/3*w^3 - 7/3*w^2 - 17*w + 29/3]', '[2209, 47, -1/3*w^3 + 1/3*w^2 + 2*w - 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2*w^2 - 3*w + 1]', '[857, 857, w^2 - 3*w - 5]', '[857, 857, -2/3*w^3 - 1/3*w^2 + 8*w - 1/3]', '[857, 857, 1/3*w^3 + 2/3*w^2 - 5*w - 13/3]', '[857, 857, w^2 - 4*w - 9]', '[863, 863, -4/3*w^3 + 7/3*w^2 + 8*w - 5/3]', '[863, 863, 2/3*w^3 + 1/3*w^2 - 4*w - 29/3]', '[881, 881, -5/3*w^3 - 4/3*w^2 + 11*w + 41/3]', '[881, 881, -4/3*w^3 - 5/3*w^2 + 6*w + 19/3]', '[887, 887, -4/3*w^3 + 4/3*w^2 + 10*w + 1/3]', '[887, 887, 2/3*w^3 - 2/3*w^2 - 2*w - 5/3]', '[911, 911, w^3 - 9*w - 1]', '[911, 911, 5/3*w^3 + 10/3*w^2 - 12*w - 65/3]', '[911, 911, 1/3*w^3 - 1/3*w^2 + w + 23/3]', '[911, 911, -2/3*w^3 + 5/3*w^2 + w - 25/3]', '[919, 919, -2/3*w^3 + 8/3*w^2 - 37/3]', '[919, 919, 2/3*w^3 + 4/3*w^2 - 8*w - 23/3]', '[929, 929, -2*w^3 - 3*w^2 + 11*w + 17]', '[929, 929, 1/3*w^3 - 1/3*w^2 - 4*w - 19/3]', '[937, 937, 4/3*w^3 - 1/3*w^2 - 9*w - 13/3]', '[937, 937, 3*w - 1]', '[937, 937, -w^3 + w^2 + 7*w - 9]', '[937, 937, w^3 - w^2 - 9*w + 1]', '[961, 31, 4/3*w^3 - 4/3*w^2 - 8*w + 11/3]', '[967, 967, w^2 - 3*w - 11]', '[967, 967, 1/3*w^3 + 2/3*w^2 - w - 19/3]', '[967, 967, 1/3*w^3 + 5/3*w^2 + 6*w + 23/3]', '[967, 967, 4/3*w^3 - 7/3*w^2 - 9*w + 17/3]', '[977, 977, w^3 - 4*w^2 - 5*w + 23]', '[977, 977, 2/3*w^3 - 11/3*w^2 - 3*w + 31/3]', '[983, 983, 4/3*w^3 - 4/3*w^2 - 6*w + 23/3]', '[983, 983, -2*w^3 + 2*w^2 + 14*w - 9]', '[991, 991, 2/3*w^3 + 1/3*w^2 - 5*w + 1/3]', '[991, 991, -w^3 + 2*w^2 + 5*w - 11]', '[1009, 1009, -1/3*w^3 + 1/3*w^2 + 9*w + 37/3]', '[1009, 1009, 2/3*w^3 + 7/3*w^2 - 6*w - 47/3]', '[1031, 1031, -4/3*w^3 + 10/3*w^2 + 7*w - 47/3]', '[1031, 1031, w^3 - w^2 - 9*w - 3]', '[1031, 1031, 1/3*w^3 - 7/3*w^2 + 53/3]', '[1031, 1031, 1/3*w^3 + 5/3*w^2 - 3*w - 19/3]', '[1033, 1033, -4/3*w^3 - 5/3*w^2 + 5*w + 13/3]', '[1033, 1033, 2*w^3 + 2*w^2 - 14*w - 19]', '[1039, 1039, -4/3*w^3 + 10/3*w^2 + 10*w - 53/3]', '[1039, 1039, -2/3*w^3 + 8/3*w^2 + 6*w - 19/3]', '[1063, 1063, -1/3*w^3 - 8/3*w^2 + 4*w + 37/3]', '[1063, 1063, -2/3*w^3 + 5/3*w^2 + 2*w - 43/3]', '[1063, 1063, -5/3*w^3 + 14/3*w^2 + 8*w - 61/3]', '[1063, 1063, 2/3*w^3 + 4/3*w^2 - 5*w - 41/3]', '[1097, 1097, -4/3*w^3 + 7/3*w^2 + 8*w - 47/3]', '[1097, 1097, 5/3*w^3 - 8/3*w^2 - 8*w + 19/3]', '[1097, 1097, -2/3*w^3 + 8/3*w^2 + 4*w - 31/3]', '[1097, 1097, -2/3*w^3 + 8/3*w^2 + 4*w - 37/3]', '[1129, 1129, 2/3*w^3 + 10/3*w^2 - w - 29/3]', '[1129, 1129, -2/3*w^3 + 2/3*w^2 + 10*w + 29/3]', '[1151, 1151, -w^3 + w^2 + 15*w + 17]', '[1151, 1151, -2/3*w^3 + 5/3*w^2 + 6*w - 1/3]', '[1153, 1153, w^3 - w^2 - 9*w + 3]', '[1153, 1153, -3*w - 1]', '[1201, 1201, 1/3*w^3 + 8/3*w^2 - 4*w - 43/3]', '[1201, 1201, -5/3*w^3 - 13/3*w^2 + 7*w + 53/3]', '[1231, 1231, 2/3*w^3 + 1/3*w^2 - 3*w - 17/3]', '[1231, 1231, -5/3*w^3 + 8/3*w^2 + 11*w - 19/3]', '[1279, 1279, 4/3*w^3 - 1/3*w^2 - 10*w - 1/3]', '[1279, 1279, -4/3*w^3 + 7/3*w^2 + 6*w - 29/3]', '[1279, 1279, 2/3*w^3 + 1/3*w^2 - 7*w + 1/3]', '[1279, 1279, -1/3*w^3 + 4/3*w^2 - w - 29/3]', '[1297, 1297, -2*w^3 - 3*w^2 + 9*w + 11]', '[1297, 1297, w^3 + 3*w^2 - 1]', '[1303, 1303, 8/3*w^3 - 11/3*w^2 - 17*w + 19/3]', '[1303, 1303, 4/3*w^3 + 2/3*w^2 - 13*w - 19/3]', '[1319, 1319, 5/3*w^3 - 8/3*w^2 - 9*w + 37/3]', '[1319, 1319, 4/3*w^3 - 1/3*w^2 - 9*w + 5/3]', '[1321, 1321, -1/3*w^3 + 1/3*w^2 + 5*w - 5/3]', '[1321, 1321, 2/3*w^3 - 2/3*w^2 - 7*w + 1/3]', '[1327, 1327, 2/3*w^3 + 1/3*w^2 - 11*w - 53/3]', '[1327, 1327, -1/3*w^3 + 1/3*w^2 - 2*w - 23/3]', '[1361, 1361, 2/3*w^3 + 1/3*w^2 - 8*w - 41/3]', '[1361, 1361, -5/3*w^3 - 7/3*w^2 + 7*w + 29/3]', '[1367, 1367, -1/3*w^3 + 7/3*w^2 + 3*w - 41/3]', '[1367, 1367, 4/3*w^3 - 10/3*w^2 - 9*w + 29/3]', '[1369, 37, -4/3*w^3 + 10/3*w^2 + 9*w - 65/3]', '[1369, 37, 1/3*w^3 - 7/3*w^2 - 3*w + 5/3]', '[1409, 1409, -2/3*w^3 - 13/3*w^2 - w + 29/3]', '[1409, 1409, -4/3*w^3 - 2/3*w^2 + 5*w + 1/3]', '[1423, 1423, 2/3*w^3 + 1/3*w^2 + 19/3]', '[1423, 1423, 7/3*w^3 - 16/3*w^2 - 12*w + 59/3]', '[1423, 1423, -4/3*w^3 - 2/3*w^2 + 9*w + 37/3]', '[1423, 1423, 7/3*w^3 - 13/3*w^2 - 13*w + 29/3]', '[1433, 1433, 1/3*w^3 - 1/3*w^2 - w - 19/3]', '[1433, 1433, -2*w^3 - 2*w^2 + 13*w + 15]', '[1433, 1433, 2/3*w^3 - 2/3*w^2 - 5*w - 17/3]', '[1433, 1433, -2/3*w^3 + 11/3*w^2 + 2*w - 61/3]', '[1439, 1439, 2/3*w^3 + 4/3*w^2 - 6*w - 23/3]', '[1439, 1439, -4/3*w^3 + 10/3*w^2 + 6*w - 41/3]', '[1447, 1447, -5/3*w^3 + 11/3*w^2 + 7*w - 37/3]', '[1447, 1447, 2/3*w^3 - 5/3*w^2 - 8*w + 31/3]', '[1471, 1471, 5/3*w^3 - 2/3*w^2 - 14*w + 1/3]', '[1471, 1471, -w^3 + 2*w^2 + 2*w - 9]', '[1481, 1481, -1/3*w^3 - 5/3*w^2 + 7*w + 43/3]', '[1481, 1481, -8/3*w^3 + 17/3*w^2 + 17*w - 73/3]', '[1489, 1489, 4*w + 5]', '[1489, 1489, 4/3*w^3 - 4/3*w^2 - 12*w + 23/3]', '[1511, 1511, w^3 - 4*w^2 - 3*w + 9]', '[1511, 1511, 3*w^2 - 3*w - 23]', '[1543, 1543, 2/3*w^3 + 1/3*w^2 - 6*w + 1/3]', '[1543, 1543, -2/3*w^3 + 5/3*w^2 + 2*w - 31/3]', '[1553, 1553, -7/3*w^3 + 10/3*w^2 + 13*w - 41/3]', '[1553, 1553, 2*w^3 - w^2 - 13*w + 3]', '[1559, 1559, 2*w^2 - 15]', '[1559, 1559, -4/3*w^3 + 10/3*w^2 + 8*w - 23/3]', '[1567, 1567, -1/3*w^3 - 2/3*w^2 - 4*w - 23/3]', '[1567, 1567, -1/3*w^3 - 2/3*w^2 + 7*w + 43/3]', '[1601, 1601, -2/3*w^3 + 2/3*w^2 + 5*w - 25/3]', '[1601, 1601, -1/3*w^3 + 1/3*w^2 + w - 23/3]', '[1607, 1607, -7/3*w^3 + 10/3*w^2 + 18*w - 29/3]', '[1607, 1607, -2*w^3 + 4*w^2 + 12*w - 19]', '[1607, 1607, -2/3*w^3 - 4/3*w^2 + 4*w + 11/3]', '[1607, 1607, -4/3*w^3 - 5/3*w^2 + 11*w + 43/3]', '[1657, 1657, -4/3*w^3 + 1/3*w^2 + 6*w - 5/3]', '[1657, 1657, 8/3*w^3 - 11/3*w^2 - 18*w + 43/3]', '[1697, 1697, 2/3*w^3 - 2/3*w^2 - 8*w - 11/3]', '[1697, 1697, -2/3*w^3 - 1/3*w^2 + 10*w + 41/3]', '[1697, 1697, -w^3 - 3*w^2 + 7*w + 17]', '[1697, 1697, -2/3*w^3 - 1/3*w^2 + 13*w + 59/3]', '[1721, 1721, -2/3*w^3 - 7/3*w^2 - 4*w - 19/3]', '[1721, 1721, -5/3*w^3 - 7/3*w^2 + 5*w + 11/3]', '[1753, 1753, -7/3*w^3 - 14/3*w^2 + 15*w + 85/3]', '[1753, 1753, -5/3*w^3 - 13/3*w^2 + 11*w + 71/3]', '[1753, 1753, 1/3*w^3 + 2/3*w^2 - 6*w - 25/3]', '[1753, 1753, 1/3*w^3 + 8/3*w^2 - 2*w - 43/3]', '[1759, 1759, -1/3*w^3 + 4/3*w^2 + 4*w - 29/3]', '[1759, 1759, -w^3 + 2*w^2 + 8*w - 3]', '[1777, 1777, -2/3*w^3 + 11/3*w^2 + 4*w - 31/3]', '[1777, 1777, -5/3*w^3 + 14/3*w^2 + 12*w - 67/3]', '[1777, 1777, -4/3*w^3 + 13/3*w^2 + 8*w - 71/3]', '[1777, 1777, w^3 - 4*w^2 - 8*w + 13]', '[1783, 1783, -5/3*w^3 + 2/3*w^2 + 13*w + 29/3]', '[1783, 1783, 4/3*w^3 - 7/3*w^2 - 5*w - 1/3]', '[1831, 1831, -1/3*w^3 - 5/3*w^2 + 25/3]', '[1831, 1831, 4/3*w^3 + 2/3*w^2 - 7*w - 25/3]', '[1831, 1831, -7/3*w^3 + 13/3*w^2 + 16*w - 47/3]', '[1831, 1831, 3*w^3 - 5*w^2 - 19*w + 15]', '[1847, 1847, -4/3*w^3 - 2/3*w^2 + 8*w + 31/3]', '[1847, 1847, -8/3*w^3 - 10/3*w^2 + 19*w + 89/3]', '[1889, 1889, -2/3*w^3 - 1/3*w^2 + 10*w + 53/3]', '[1889, 1889, 2/3*w^3 + 7/3*w^2 + 3*w + 13/3]', '[1889, 1889, 3*w^3 - 2*w^2 - 24*w + 1]', '[1889, 1889, -5/3*w^3 - 7/3*w^2 + 5*w + 17/3]', '[1913, 1913, 5/3*w^3 - 5/3*w^2 - 9*w + 1/3]', '[1913, 1913, -4/3*w^3 + 7/3*w^2 + 9*w - 47/3]', '[1951, 1951, -7/3*w^3 - 8/3*w^2 + 17*w + 67/3]', '[1951, 1951, 4/3*w^3 - 10/3*w^2 - 10*w + 59/3]', '[1993, 1993, -8/3*w^3 + 8/3*w^2 + 19*w - 19/3]', '[1993, 1993, 5/3*w^3 - 5/3*w^2 - 7*w + 13/3]', '[1999, 1999, 2/3*w^3 + 1/3*w^2 - 3*w - 41/3]', '[1999, 1999, -5/3*w^3 + 8/3*w^2 + 11*w + 5/3]']}
• 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': [14, -4, -10, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 18688, 'disc_rad': 146, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 2]]], [5, [[4, 1]]], [7, [[2, 1], [1, 2]]], [11, [[4, 1]]], [13, [[4, 1]]], [17, [[2, 1], [1, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[4, 1]]], [31, [[2, 1], [1, 2]]], [37, [[2, 2]]], [41, [[1, 4]]], [43, [[4, 1]]], [47, [[2, 1], [1, 2]]], [53, [[4, 1]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 34.17601498127012, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.18688.1', 'local_algs': ['2.4.8.3', '73.1.0.1', '73.1.0.1', '73.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 73], 'rd': 11.6920511428, 'regulator': {'__RealLiteral__': 0, 'data': '10.5562587685', 'prec': 44}, 'res': {'gal': ['144,0,-272,0,145,0,-26,0,1'], 'sib': ['2,0,-9,0,1', '144,0,-272,0,145,0,-26,0,1']}, 'subfield_mults': [1], 'subfields': ['-2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{3} a^{3} - \\frac{1}{3} a^{2} - 2 a + \\frac{5}{3} \\)', '\\( \\frac{2}{3} a^{3} - \\frac{5}{3} a^{2} - 3 a + \\frac{13}{3} \\)', '\\( \\frac{1}{3} a^{3} + \\frac{2}{3} a^{2} - \\frac{1}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/3*a^3 - 1/3*a^2 - 1/3']}