Hilbert modular form data - 4.4.10304.1-16.4-b

Formats: - HTML - YAML - JSON - 2024-04-28T08:51:38.884267

• 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': 10304, 'field_bad_primes': [2, 7, 23], 'field_label': '4.4.10304.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.10304.1-16.4-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2], 'level_ideal': '[16,4,-w^2 + 2*w + 3]', 'level_label': '16.4', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.4-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2,2,1/2*w^2 - 3/2*w - 1]', 1]], 'hecke_eigenvalues': [-1, 0, 0, 0, 2, 2, -8, 8, -6, -6, 8, -8, -6, -6, -6, 8, -8, 10, 10, 10, 10, 10, 2, 2, 2, 2, -6, -6, -16, 0, 0, 16, 2, 2, 8, -8, -24, 24, 8, 16, -16, -8, 24, -24, 26, -6, -6, 26, 18, -30, -30, 18, 18, 18, 0, 0, 0, 0, 26, 26, 26, 26, 16, -16, -14, 2, 2, -14, 34, 34, 2, 2, -24, 24, 26, 26, 18, 18, 26, 26, 0, 0, -32, 32, 2, 2, 40, 8, -8, -40, 26, -22, -22, 10, 10, -22, -22, 48, -24, 24, -48, 10, 10, -8, 8, 10, 10, 16, -16, 34, 34, -24, 24, 8, -8, -8, 8, -8, 8, -48, 48, -16, 16, -38, -38, 32, -24, 24, -32, 34, 34, -38, -38, 32, 24, -24, -32, 8, -8, -16, 16, 40, -40, -46, -46, 26, -22, -22, 26, 58, 58, -30, 18, 18, -56, 24, -24, 56, -8, 8, -8, 8, 50, 50, -32, 32, 26, 26, 0, 0, -6, -38, -38, -6, 16, 40, -40, -16, -6, -6, -24, 24, 16, -16, -6, -6, -62, -62, 18, 42, 42, 18, 48, -48, 40, -40, -14, -38, -38, -14, 56, 40, -40, -56, 10, 26, 26, 10, 18, -14, -14, 18, -8, 8, -24, 24, -38, 2, 2, -38, -56, 40, -40, 56, -46, -46, 48, -48, 40, 16, -16, -40, -30, 50, 50, -30, -32, 32, -38, -6, -6, -38, 0, 56, -56, 0, 16, -8, 8, -16, 32, -32, -30, -62, -62, -30, -32, 32, -16, 16, -46, -46, -24, 24, -16, 16, 8, -8, 80, -80, -30, -30, 32, -32, -46, 18, 18, -16, 16, -38, -38, -48, 48, -22, -22, 24, -24, 32, -32, -72, -32, 32, 72, -62, -62, -56, 56, 50, 50, 74, 74, 74, 74, 24, -24], 'hecke_polynomial': 'x', 'label': '4.4.10304.1-16.4-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 10304, 'ideals': ['[1, 1, 1]', '[2, 2, 1/2*w^2 + 1/2*w - 2]', '[2, 2, -1/2*w^3 + 1/2*w^2 + 3*w + 1]', '[4, 2, -w + 2]', '[4, 2, -1/2*w^2 + 1/2*w + 2]', '[4, 2, w + 1]', '[7, 7, -1/2*w^3 + 3/2*w^2 + w - 3]', '[8, 2, -1/2*w^3 + 1/2*w^2 + 2*w - 2]', '[8, 2, -1/2*w^3 + 9/2*w + 2]', '[8, 4, -1/2*w^3 + 1/2*w^2 + 3*w]', '[8, 4, w - 1]', '[14, 14, -1/2*w^2 - 1/2*w + 3]', '[14, 14, -1/2*w^2 + 3/2*w + 2]', '[16, 2, 2]', '[16, 4, 1/2*w^3 - 3/2*w^2 - w + 4]', '[16, 4, -w^2 + 4]', '[16, 4, -w^2 + 2*w + 3]', '[16, 4, -1/2*w^3 + 5/2*w + 2]', '[23, 23, 1/2*w^3 + 1/2*w^2 - 3*w - 3]', '[25, 5, -1/2*w^3 + 9/2*w + 1]', '[25, 5, -1/2*w^3 + 5/2*w - 1]', '[28, 14, -1/2*w^3 + w^2 + 5/2*w - 1]', '[28, 14, -1/2*w^2 + 5/2*w - 2]', '[28, 14, -1/2*w^3 + 1/2*w^2 + 3*w - 2]', '[31, 31, -1/2*w^3 + 1/2*w^2 + 2*w - 1]', '[31, 31, 1/2*w^3 - w^2 - 3/2*w + 1]', '[32, 4, w^2 + w - 4]', '[32, 4, -1/2*w^3 + 1/2*w^2 + 4*w]', '[32, 4, -1/2*w^3 + w^2 + 3/2*w - 2]', '[32, 4, -w^3 + w^2 + 6*w + 2]', '[32, 8, -1/2*w^3 + 3/2*w^2 + 2*w - 4]', '[32, 8, -1/2*w^3 + 7/2*w + 1]', '[41, 41, 3/2*w^3 - w^2 - 21/2*w - 5]', '[41, 41, 1/2*w^3 - 2*w^2 - 5/2*w + 7]', '[46, 46, 1/2*w^3 - 1/2*w^2 - 3*w + 3]', '[46, 46, 1/2*w^3 - w^2 - 5/2*w]', '[47, 47, -w^2 - w + 5]', '[47, 47, -w^3 + 1/2*w^2 + 13/2*w + 5]', '[49, 7, -w^2 + w + 5]', '[49, 7, 1/2*w^2 - 1/2*w - 5]', '[50, 10, 1/2*w^3 - 2*w^2 - 3/2*w + 8]', '[50, 10, -1/2*w^2 - 1/2*w + 4]', '[50, 10, -1/2*w^3 - 1/2*w^2 + 4*w + 5]', '[50, 10, -1/2*w^2 + 3/2*w + 3]', '[56, 14, 1/2*w^3 - w^2 - 3/2*w + 4]', '[56, 14, -1/2*w^3 + 1/2*w^2 + 2*w + 2]', '[56, 28, w + 3]', '[56, 28, -w + 4]', '[62, 62, 1/2*w^3 - 2*w^2 + 1/2*w + 4]', '[62, 62, -1/2*w^3 + w^2 + 5/2*w - 6]', '[62, 62, -1/2*w^3 + 1/2*w^2 + 3*w + 3]', '[62, 62, 1/2*w^3 + 1/2*w^2 - 2*w - 3]', '[64, 4, -2*w + 4]', '[64, 4, -w^2 + w + 4]', '[64, 4, 2*w + 2]', '[64, 8, 1/2*w^3 - 1/2*w^2 - 2*w + 4]', '[64, 8, -1/2*w^3 - 1/2*w^2 + 4*w + 4]', '[64, 8, 1/2*w^3 - 2*w^2 - 3/2*w + 7]', '[64, 8, -1/2*w^3 + w^2 + 3/2*w + 2]', '[73, 73, -1/2*w^3 + 1/2*w^2 + 4*w - 3]', '[73, 73, 1/2*w^3 - w^2 - 7/2*w + 1]', '[79, 79, w^2 - 3*w + 1]', '[79, 79, w^2 + w - 1]', '[81, 3, -3]', '[82, 82, w^3 + 1/2*w^2 - 13/2*w - 5]', '[82, 82, 1/2*w^2 + 1/2*w - 5]', '[82, 82, 1/2*w^2 - 3/2*w - 4]', '[82, 82, -w^3 + 7/2*w^2 + 5/2*w - 10]', '[89, 89, -1/2*w^3 + 3*w^2 + 7/2*w - 11]', '[89, 89, 1/2*w^3 - 5/2*w - 3]', '[89, 89, -1/2*w^3 + 3/2*w^2 + w - 5]', '[89, 89, 5/2*w^3 - 2*w^2 - 33/2*w - 7]', '[92, 46, w^2 - 2*w - 5]', '[92, 46, -1/2*w^2 - 3/2*w - 2]', '[92, 46, w^2 - 6]', '[94, 94, -1/2*w^2 + 7/2*w - 4]', '[94, 94, -1/2*w^3 + 7/2*w]', '[94, 94, -1/2*w^3 + 3/2*w^2 + 2*w - 3]', '[94, 94, 1/2*w^2 + 5/2*w + 1]', '[97, 97, -1/2*w^3 + w^2 + 3/2*w - 5]', '[97, 97, -1/2*w^2 - 3/2*w + 3]', '[97, 97, w^3 - w^2 - 6*w - 1]', '[97, 97, 1/2*w^3 - 1/2*w^2 - 2*w - 3]', '[98, 14, 1/2*w^3 - 2*w^2 - 7/2*w + 8]', '[98, 14, -w^3 + 3/2*w^2 + 9/2*w - 6]', '[98, 14, -w^3 + 3/2*w^2 + 9/2*w + 1]', '[98, 14, 2*w^3 - 3/2*w^2 - 27/2*w - 5]', '[100, 10, -1/2*w^3 + 1/2*w^2 + 5*w + 2]', '[100, 10, 3/2*w^2 + 1/2*w - 4]', '[100, 10, -1/2*w^3 - 1/2*w^2 + 4*w + 2]', '[100, 10, -w^3 + 3/2*w^2 + 11/2*w]', '[100, 10, -w^3 + 2*w^2 + 6*w - 9]', '[100, 10, -1/2*w^3 + w^2 + 9/2*w - 7]', '[112, 14, -w^3 + 3*w^2 + 2*w - 6]', '[112, 28, -1/2*w^3 + 9/2*w]', '[112, 28, -w^3 + 3*w^2 + 5*w - 11]', '[112, 28, -w^3 + 8*w + 4]', '[112, 28, -1/2*w^3 + 3/2*w^2 + 3*w - 4]', '[113, 113, w^3 - 3*w^2 - 6*w + 13]', '[113, 113, 3*w^3 - 3/2*w^2 - 43/2*w - 11]', '[124, 62, -w^3 + 2*w^2 + 6*w - 10]', '[124, 62, 1/2*w^2 + 3/2*w - 2]', '[124, 62, w^3 - 6*w - 2]', '[124, 62, -w^3 + 3*w^2 + 3*w - 7]', '[124, 62, 1/2*w^2 - 5/2*w]', '[124, 62, w^3 - w^2 - 7*w - 3]', '[127, 127, -1/2*w^3 + w^2 + 3/2*w - 7]', '[127, 127, 3/2*w^3 - w^2 - 13/2*w + 7]', '[127, 127, 3/2*w^3 + w^2 - 29/2*w - 11]', '[127, 127, 1/2*w^3 - 1/2*w^2 - 2*w - 5]', '[128, 4, -w^3 + w^2 + 4*w - 4]', '[128, 4, -w^3 + 9*w + 4]', '[128, 8, -w^3 + w^2 + 6*w]', '[128, 8, -1/2*w^3 + 1/2*w^2 + 4*w - 4]', '[128, 8, -1/2*w^3 + w^2 + 7/2*w]', '[128, 8, 2*w - 2]', '[128, 16, -w^3 + 2*w^2 + 4*w]', '[128, 16, -w^3 + w^2 + 5*w - 5]', '[137, 137, 2*w^3 - 3/2*w^2 - 25/2*w - 9]', '[137, 137, -3*w^2 - w + 11]', '[146, 146, -1/2*w^3 + 2*w^2 + 7/2*w - 10]', '[146, 146, -w^3 + 1/2*w^2 + 7/2*w - 4]', '[146, 146, 1/2*w^3 + 3/2*w^2 - 7*w - 9]', '[146, 146, 2*w^3 - 1/2*w^2 - 29/2*w - 11]', '[158, 158, w^3 + 1/2*w^2 - 17/2*w - 8]', '[158, 158, -1/2*w^3 + 7/2*w + 6]', '[158, 158, 3/2*w^2 - 1/2*w - 5]', '[158, 158, 1/2*w^3 - 1/2*w^2 - 3*w + 5]', '[161, 161, -2*w + 1]', '[162, 6, -3/2*w^2 - 3/2*w + 6]', '[162, 6, 3/2*w^3 - 3/2*w^2 - 9*w - 3]', '[164, 82, 1/2*w^3 - 7/2*w + 1]', '[164, 82, 3/2*w^3 - 2*w^2 - 17/2*w - 1]', '[164, 82, 2*w^3 - 1/2*w^2 - 31/2*w - 8]', '[164, 82, w^3 - 3/2*w^2 - 11/2*w + 8]', '[164, 82, -2*w^2 - w + 6]', '[164, 82, w^3 - w^2 - 7*w + 2]', '[167, 167, 1/2*w^2 + 3/2*w - 5]', '[167, 167, 1/2*w^2 - 5/2*w - 3]', '[175, 35, 1/2*w^3 - 5/2*w^2 - 2*w + 9]', '[175, 35, -1/2*w^3 - w^2 + 11/2*w + 5]', '[178, 178, -3/2*w^2 + 1/2*w + 9]', '[178, 178, 2*w^3 - 3/2*w^2 - 27/2*w - 7]', '[178, 178, 1/2*w^3 + 1/2*w^2 - 6*w - 1]', '[178, 178, w^3 + 1/2*w^2 - 17/2*w - 7]', '[178, 178, w^3 - 7/2*w^2 - 9/2*w + 14]', '[178, 178, w^3 + 1/2*w^2 - 9/2*w]', '[178, 178, 1/2*w^3 - 3*w^2 - 5/2*w + 10]', '[178, 178, 3/2*w^2 - 5/2*w - 8]', '[184, 46, 1/2*w^3 + 1/2*w^2 - 5*w - 2]', '[184, 46, 1/2*w^3 - 2*w^2 - 5/2*w + 6]', '[184, 92, 1/2*w^3 - w^2 - 9/2*w + 1]', '[184, 92, 1/2*w^3 - 1/2*w^2 - 5*w + 4]', '[188, 94, -w^2 + 2*w + 6]', '[188, 94, -1/2*w^3 - 3/2*w^2 + w + 6]', '[188, 94, w^3 - 3/2*w^2 - 7/2*w + 6]', '[188, 94, -w^3 - 1/2*w^2 + 19/2*w + 8]', '[188, 94, -w^3 + w^2 + 5*w + 5]', '[188, 94, 1/2*w^3 - w^2 - 1/2*w + 3]', '[191, 191, 2*w^3 - w^2 - 15*w - 5]', '[191, 191, -w^3 + 3/2*w^2 + 11/2*w - 7]', '[194, 194, -w^3 + 5/2*w^2 + 7/2*w - 6]', '[194, 194, 3/2*w^2 - 5/2*w - 5]', '[194, 194, 7/2*w^3 - 3/2*w^2 - 25*w - 17]', '[194, 194, 1/2*w^3 - 7/2*w + 2]', '[194, 194, -w^3 + 1/2*w^2 + 15/2*w + 1]', '[194, 194, 1/2*w^3 - 2*w^2 + 5/2*w - 2]', '[194, 194, 3/2*w^2 - 1/2*w - 6]', '[194, 194, 5/2*w^3 - 5/2*w^2 - 15*w - 7]', '[196, 14, w^3 - 3*w^2 - 3*w + 10]', '[196, 14, 3/2*w^2 - 3/2*w - 8]', '[196, 14, -1/2*w^3 + 3/2*w^2 + 4*w - 10]', '[196, 14, -1/2*w^2 + 1/2*w + 6]', '[196, 14, -w^3 + 6*w + 5]', '[196, 14, 1/2*w^3 - 11/2*w - 5]', '[199, 199, -1/2*w^3 - w^2 + 11/2*w + 7]', '[199, 199, 5/2*w^3 - 3/2*w^2 - 17*w - 9]', '[199, 199, 1/2*w^3 - 5/2*w^2 - 4*w + 11]', '[199, 199, 1/2*w^3 - 5/2*w + 3]', '[200, 10, 1/2*w^3 - 3/2*w^2 - w + 6]', '[200, 10, -1/2*w^3 + 9/2*w + 6]', '[200, 10, -1/2*w^3 + 5/2*w + 4]', '[200, 10, 1/2*w^3 - 3/2*w^2 - 3*w + 10]', '[200, 20, 1/2*w^3 - 1/2*w^2 - w + 4]', '[200, 20, -w^3 + w^2 + 5*w + 4]', '[200, 20, -1/2*w^3 + w^2 + 1/2*w + 3]', '[200, 20, w^3 - 2*w^2 - 4*w + 9]', '[217, 217, w^3 - 7/2*w^2 - 7/2*w + 13]', '[217, 217, w^3 + 1/2*w^2 - 15/2*w - 7]', '[223, 223, -w^3 + 2*w^2 + 5*w - 3]', '[223, 223, w^3 - w^2 - 6*w + 3]', '[224, 28, -1/2*w^3 - w^2 + 7/2*w + 6]', '[224, 28, -w^2 - w + 6]', '[224, 28, -w^2 + 3*w + 4]', '[224, 28, 1/2*w^3 - 5/2*w^2 + 8]', '[224, 56, 1/2*w^3 - 2*w^2 + 1/2*w + 5]', '[224, 56, -1/2*w^3 - 1/2*w^2 + 2*w + 4]', '[226, 226, -w^3 + 5/2*w^2 + 15/2*w - 16]', '[226, 226, 1/2*w^3 + w^2 - 9/2*w - 8]', '[226, 226, -1/2*w^3 + 5/2*w^2 + w - 11]', '[226, 226, w^3 - 1/2*w^2 - 19/2*w - 7]', '[233, 233, -2*w^2 + 7]', '[233, 233, w^3 + w^2 - 6*w - 5]', '[233, 233, -5/2*w^3 + w^2 + 35/2*w + 13]', '[233, 233, -w^3 + 1/2*w^2 + 13/2*w + 7]', '[241, 241, w^3 + w^2 - 10*w - 9]', '[241, 241, -1/2*w^3 + 3/2*w^2 + 3*w - 3]', '[241, 241, -1/2*w^3 + 9/2*w - 1]', '[241, 241, w^3 - 1/2*w^2 - 9/2*w + 5]', '[248, 62, -1/2*w^3 + 3/2*w^2 - w + 2]', '[248, 62, -1/2*w^3 - w^2 + 11/2*w + 6]', '[248, 62, -1/2*w^3 + 5/2*w^2 + 2*w - 10]', '[248, 62, -1/2*w^3 + 1/2*w - 2]', '[248, 124, w + 4]', '[248, 124, 1/2*w^3 - w^2 - 5/2*w + 7]', '[248, 124, 1/2*w^3 - 1/2*w^2 - 3*w - 4]', '[248, 124, w - 5]', '[254, 254, 2*w^3 - 3/2*w^2 - 27/2*w - 3]', '[254, 254, -w^3 + 3/2*w^2 + 9/2*w - 5]', '[254, 254, w^3 - 3/2*w^2 - 13/2*w - 3]', '[254, 254, -1/2*w^3 - 1/2*w^2 + 4*w + 1]', '[254, 254, -9/2*w^2 - 5/2*w + 16]', '[254, 254, -w^3 + 3/2*w^2 + 13/2*w - 10]', '[254, 254, w^3 - 3/2*w^2 - 9/2*w]', '[254, 254, -w^3 + 5/2*w^2 + 3/2*w - 4]', '[256, 4, 4]', '[256, 8, w^3 - 3*w^2 - 2*w + 8]', '[256, 8, -2*w^2 + 8]', '[256, 8, -2*w^2 + 4*w + 6]', '[256, 8, -w^3 + 5*w + 4]', '[256, 16, -1/2*w^3 + 1/2*w^2 + 4*w + 4]', '[256, 16, -w^2 + 8]', '[256, 16, -w^2 + 2*w + 7]', '[256, 16, 1/2*w^3 - w^2 - 7/2*w + 8]', '[257, 257, w^3 - w^2 - 8*w + 3]', '[257, 257, 5/2*w^3 - w^2 - 39/2*w - 7]', '[263, 263, w^3 - 5*w + 3]', '[263, 263, w^3 + 1/2*w^2 - 19/2*w - 5]', '[271, 271, -1/2*w^3 + 2*w^2 + 5/2*w - 13]', '[271, 271, -2*w^3 + 7/2*w^2 + 17/2*w - 15]', '[274, 274, w^3 + 1/2*w^2 - 17/2*w - 5]', '[274, 274, -w^3 - 1/2*w^2 + 21/2*w + 3]', '[274, 274, 1/2*w^3 - 11/2*w]', '[274, 274, -w^3 + 7/2*w^2 + 9/2*w - 12]', '[281, 281, 1/2*w^3 - 5/2*w - 7]', '[281, 281, -1/2*w^3 + 3/2*w^2 + w - 9]', '[287, 287, -1/2*w^3 + 1/2*w^2 + 2*w - 5]', '[287, 287, 1/2*w^3 - w^2 - 3/2*w - 3]', '[289, 17, 3/2*w^2 - 3/2*w - 5]', '[289, 17, 3/2*w^2 - 3/2*w - 7]', '[292, 146, 1/2*w^3 - 1/2*w^2 - 7*w + 10]', '[292, 146, w^3 - 5/2*w^2 - 9/2*w + 6]', '[292, 146, w^3 - 2*w^2 - 4*w + 6]', '[292, 146, w^3 - w^2 - 5*w - 1]', '[292, 146, w^3 - 1/2*w^2 - 13/2*w]', '[292, 146, 1/2*w^3 - w^2 - 13/2*w - 3]', '[311, 311, w^3 - 3*w^2 - 2*w + 3]', '[311, 311, -w^3 + 5*w - 1]', '[313, 313, 7/2*w^3 - w^2 - 53/2*w - 15]', '[313, 313, -1/2*w^3 + 3/2*w^2 + w - 7]', '[313, 313, 1/2*w^3 - 5/2*w - 5]', '[313, 313, 3/2*w^3 - 3*w^2 - 17/2*w + 15]', '[316, 158, w^3 - w^2 - 5*w + 2]', '[316, 158, -1/2*w^3 + 3/2*w^2 + 4*w - 6]', '[316, 158, w^3 - 7/2*w^2 - 3/2*w + 6]', '[316, 158, -w^3 - 1/2*w^2 + 11/2*w + 2]', '[316, 158, 1/2*w^3 - 11/2*w - 1]', '[316, 158, -w^3 + 2*w^2 + 4*w - 3]', '[322, 322, -1/2*w^3 + 3*w^2 + 5/2*w - 12]', '[322, 322, 1/2*w^3 + 3/2*w^2 - 7*w - 7]', '[324, 6, 3*w - 6]', '[324, 6, 3/2*w^2 - 3/2*w - 6]', '[324, 6, -3*w - 3]', '[328, 82, 1/2*w^3 - w^2 - 11/2*w - 4]', '[328, 82, 1/2*w^3 + 1/2*w^2 - 3*w - 6]', '[328, 82, -1/2*w^3 + 1/2*w^2 + 6*w - 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19/2*w + 1]', '[1823, 1823, -1/2*w^3 + 1/2*w^2 + 8*w - 11]', '[1823, 1823, 2*w^3 - 7*w^2 - 11*w + 27]', '[1825, 365, w^3 - 1/2*w^2 - 9/2*w - 13]', '[1825, 365, -w^3 + 3/2*w^2 + 11/2*w - 11]', '[1825, 365, 2*w^3 + w^2 - 17*w - 17]', '[1825, 365, w^3 + 3*w^2 - 4*w - 11]', '[1828, 914, -3/2*w^3 + w^2 + 11/2*w + 1]', '[1828, 914, w^2 + 6*w + 3]', '[1828, 914, -w^3 + 7/2*w^2 + 7/2*w - 8]', '[1828, 914, -w^3 - 1/2*w^2 + 15/2*w + 2]', '[1828, 914, -w^2 + 8*w - 10]', '[1828, 914, -3/2*w^3 + 7/2*w^2 + 3*w - 6]', '[1831, 1831, -1/2*w^3 + w^2 + 11/2*w - 5]', '[1831, 1831, -1/2*w^3 + 1/2*w^2 + 6*w - 1]', '[1838, 1838, 3/2*w^3 - 3/2*w^2 - 13*w - 9]', '[1838, 1838, -w^3 + 7/2*w^2 + 5/2*w - 15]', '[1838, 1838, w^3 + 1/2*w^2 - 13/2*w - 10]', '[1838, 1838, -3/2*w^3 + 3*w^2 + 23/2*w - 22]', '[1841, 1841, 3*w^2 - 5*w - 7]', '[1841, 1841, 3*w^2 - w - 9]', '[1847, 1847, 5/2*w^3 - 2*w^2 - 33/2*w - 11]', '[1847, 1847, -1/2*w^3 + 1/2*w^2 + 6*w - 3]', '[1847, 1847, -1/2*w^3 + w^2 + 11/2*w - 3]', '[1847, 1847, 1/2*w^2 - 9/2*w - 5]', '[1858, 1858, -3/2*w^2 - 3/2*w - 2]', '[1858, 1858, -3/2*w^3 + 2*w^2 + 13/2*w + 8]', '[1858, 1858, -1/2*w^3 + 7/2*w^2 - 4*w - 9]', '[1858, 1858, 3/2*w^2 - 9/2*w + 5]', '[1863, 69, -3/2*w^3 - 3/2*w^2 + 9*w + 9]', '[1864, 466, -3/2*w^3 + 2*w^2 + 15/2*w - 2]', '[1864, 466, -1/2*w^3 - 1/2*w^2 + 7*w - 6]', '[1864, 466, 5/2*w^3 - 5/2*w^2 - 16*w - 6]', '[1864, 466, 1/2*w^3 - 3*w^2 - 3/2*w + 6]', '[1864, 466, -3/2*w^3 + 5/2*w^2 + 9*w - 2]', '[1864, 466, -5/2*w^3 + w^2 + 31/2*w + 8]', '[1864, 466, -1/2*w^3 + 2*w^2 + 9/2*w]', '[1864, 466, -3/2*w^3 + 5/2*w^2 + 7*w - 6]', '[1864, 932, -3/2*w^3 - w^2 + 31/2*w + 7]', '[1864, 932, -w^3 + 2*w^2 + 8*w + 3]', '[1864, 932, -1/2*w^3 + 1/2*w^2 + 7*w - 8]', '[1864, 932, -1/2*w^3 - w^2 + 17/2*w + 1]', '[1864, 932, -1/2*w^3 + 5/2*w^2 + 5*w - 8]', '[1864, 932, 1/2*w^3 - w^2 - 13/2*w - 1]', '[1864, 932, -w^3 + w^2 + 9*w - 12]', '[1864, 932, 2*w^3 - 9*w + 4]', '[1873, 1873, -w^2 + 3*w - 5]', '[1873, 1873, -w^2 - w - 3]', '[1874, 1874, 3/2*w^2 - 13/2*w + 3]', '[1874, 1874, -2*w^3 + 1/2*w^2 + 25/2*w + 19]', '[1874, 1874, 6*w^3 - 3/2*w^2 - 91/2*w - 33]', '[1874, 1874, 4*w^3 + 1/2*w^2 - 71/2*w - 23]', '[1874, 1874, 7/2*w^3 - 5*w^2 - 27/2*w + 20]', '[1874, 1874, 5/2*w^3 - 8*w^2 - 23/2*w + 32]', '[1874, 1874, 1/2*w^3 + 4*w^2 - 3/2*w - 16]', '[1874, 1874, 5/2*w^3 + w^2 - 17/2*w - 4]', '[1879, 1879, 2*w^3 + 1/2*w^2 - 25/2*w - 11]', '[1879, 1879, 4*w + 7]', '[1886, 1886, -1/2*w^2 + 7/2*w + 7]', '[1886, 1886, -w^3 - 3/2*w^2 + 19/2*w + 13]', '[1886, 1886, w^3 - 9/2*w^2 - 7/2*w + 20]', '[1886, 1886, -5/2*w^3 - w^2 + 29/2*w + 12]', '[1889, 1889, 4*w^3 - 5*w^2 - 21*w - 9]', '[1889, 1889, w^3 + 11/2*w^2 - 1/2*w - 19]', '[1897, 1897, 4*w^3 - 23/2*w^2 - 29/2*w + 35]', '[1897, 1897, 1/2*w^2 - 9/2*w + 3]', '[1906, 1906, -2*w^3 + 11/2*w^2 + 11/2*w - 14]', '[1906, 1906, -w^3 + 5/2*w^2 + 11/2*w - 4]', '[1906, 1906, -w^3 + 1/2*w^2 + 15/2*w - 3]', '[1906, 1906, -2*w^3 + 1/2*w^2 + 21/2*w + 5]', '[1913, 1913, 2*w^3 - 5/2*w^2 - 23/2*w + 1]', '[1913, 1913, 1/2*w^2 - 9/2*w - 1]', '[1913, 1913, 1/2*w^2 + 7/2*w - 5]', '[1913, 1913, w^2 + 3*w - 5]', '[1918, 1918, -2*w^3 + 17/2*w^2 - 3/2*w - 16]', '[1918, 1918, -w^3 + 5/2*w^2 + 3/2*w + 4]', '[1918, 1918, 3/2*w^3 - 3/2*w^2 - 7*w - 9]', '[1918, 1918, 3/2*w^3 - 11/2*w^2 - 5*w + 19]', '[1922, 62, 2*w^3 - 3/2*w^2 - 15/2*w + 6]', '[1922, 62, 2*w^3 - 5/2*w^2 - 17/2*w + 10]', '[1922, 62, 2*w^3 - 7/2*w^2 - 15/2*w - 1]', '[1922, 62, 3/2*w^3 + 1/2*w^2 - 15*w - 7]', '[1922, 1922, -3/2*w^3 + 4*w^2 + 13/2*w - 10]', '[1922, 1922, -3/2*w^3 + 3*w^2 + 11/2*w - 8]', '[1922, 1922, -3/2*w^3 + 3/2*w^2 + 7*w + 1]', '[1922, 1922, -3/2*w^3 + 1/2*w^2 + 10*w + 1]', '[1927, 1927, 2*w^3 - 4*w^2 - 10*w + 7]', '[1927, 1927, -3/2*w^3 + 5/2*w^2 + 7*w - 5]', '[1927, 1927, -3/2*w^3 + 2*w^2 + 15/2*w - 3]', '[1927, 1927, 7/2*w^3 - w^2 - 57/2*w - 11]', '[1928, 482, 3/2*w^3 + w^2 - 21/2*w - 6]', '[1928, 482, 1/2*w^3 - 1/2*w^2 - 6*w + 2]', '[1928, 482, -1/2*w^3 - 7/2*w^2 + 14]', '[1928, 482, -3/2*w^3 - w^2 + 29/2*w + 14]', '[1928, 482, 3/2*w^3 - 5/2*w^2 - 5*w + 10]', '[1928, 482, -5/2*w^3 + 2*w^2 + 29/2*w + 12]', '[1928, 482, -1/2*w^3 + w^2 + 11/2*w - 4]', '[1928, 482, -3/2*w^3 + 11/2*w^2 + 4*w - 14]', '[1928, 964, -3/2*w^3 - w^2 + 19/2*w + 5]', '[1928, 964, w^3 - 2*w^2 - 2*w + 7]', '[1928, 964, -1/2*w^3 + w^2 - 3/2*w + 5]', '[1928, 964, -2*w^3 + 2*w^2 + 9*w - 8]', '[1928, 964, 2*w^3 - 4*w^2 - 7*w + 1]', '[1928, 964, -w^3 - w^2 + 7*w + 12]', '[1928, 964, -1/2*w^3 - 3/2*w^2 + 7*w + 12]', '[1928, 964, 3/2*w^3 - 11/2*w^2 - 3*w + 12]', '[1948, 974, -3/2*w^3 + 3/2*w^2 + 5*w - 10]', '[1948, 974, -w^3 + 9/2*w^2 + 5/2*w - 14]', '[1948, 974, w^3 - 2*w^2 - 8*w - 5]', '[1948, 974, w^3 - 1/2*w^2 - 9/2*w - 6]', '[1948, 974, w^3 + 2*w^2 - 6*w - 7]', '[1948, 974, -1/2*w^3 + 5/2*w^2 - w - 10]', '[1948, 974, 1/2*w^3 + w^2 - 5/2*w - 9]', '[1948, 974, -w^3 + 5*w^2 - w - 10]', '[1948, 974, -w^3 + 5/2*w^2 + 5/2*w - 10]', '[1948, 974, -w^3 + w^2 + 9*w - 14]', '[1948, 974, w^3 + 3/2*w^2 - 17/2*w - 8]', '[1948, 974, 3/2*w^3 - 3*w^2 - 7/2*w - 5]', '[1954, 1954, 5/2*w^3 - 5*w^2 - 29/2*w + 26]', '[1954, 1954, -w^3 - 7/2*w^2 + 3/2*w + 8]', '[1954, 1954, 5/2*w^3 - 11/2*w^2 - 10*w + 7]', '[1954, 1954, 6*w^3 - 3/2*w^2 - 91/2*w - 27]', '[1966, 1966, 5/2*w^2 - 3/2*w - 9]', '[1966, 1966, 5/2*w^3 - 6*w^2 - 23/2*w + 22]', '[1966, 1966, -2*w^3 + 7/2*w^2 + 23/2*w - 6]', '[1966, 1966, -3/2*w^3 + 5/2*w^2 + 8*w - 15]', '[1966, 1966, 3*w^3 + 1/2*w^2 - 49/2*w - 20]', '[1966, 1966, 2*w^3 - 5/2*w^2 - 25/2*w + 7]', '[1966, 1966, -5/2*w^3 + 3/2*w^2 + 16*w + 7]', '[1966, 1966, 1/2*w^3 + w^2 - 9/2*w - 14]', '[1967, 1967, 3*w^3 - 19/2*w^2 - 11/2*w + 17]', '[1967, 1967, 2*w^3 - 4*w^2 - 12*w + 19]', '[1975, 395, 2*w^3 - 3/2*w^2 - 21/2*w - 7]', '[1975, 395, 5/2*w^3 - 3/2*w^2 - 19*w - 13]', '[1975, 395, 3*w^3 - 9*w^2 - 16*w + 41]', '[1975, 395, 5/2*w^3 - 6*w^2 - 29/2*w + 31]', '[1982, 1982, -3/2*w^2 + 9/2*w + 7]', '[1982, 1982, w^3 + 1/2*w^2 - 21/2*w - 10]', '[1982, 1982, -5/2*w^2 + 11/2*w + 10]', '[1982, 1982, 1/2*w^3 + 3/2*w^2 - w + 1]', '[1982, 1982, -1/2*w^3 + 3*w^2 - 7/2*w + 2]', '[1982, 1982, -3/2*w^3 + 1/2*w^2 + 4*w - 3]', '[1982, 1982, -3/2*w^3 - 3/2*w^2 + 14*w + 11]', '[1982, 1982, -3/2*w^2 - 3/2*w + 10]', '[1984, 124, -2*w^3 + 4*w^2 + 12*w - 20]', '[1984, 124, w^2 + 3*w - 4]', '[1984, 124, 2*w^3 - 12*w - 4]', '[1984, 124, -2*w^3 + 6*w^2 + 6*w - 14]', '[1984, 124, w^2 - 5*w]', '[1984, 124, 2*w^3 - 2*w^2 - 14*w - 6]', '[1984, 248, -3/2*w^3 + 7/2*w^2 + 6*w - 4]', '[1984, 248, w^2 + 4*w]', '[1984, 248, -3/2*w^3 + 3*w^2 + 9/2*w - 2]', '[1984, 248, 1/2*w^3 + 1/2*w^2 - 8*w - 4]', '[1984, 248, -1/2*w^3 + 2*w^2 + 11/2*w - 11]', '[1984, 248, 3/2*w^3 - 3/2*w^2 - 6*w + 4]', '[1984, 248, w^2 - 6*w + 5]', '[1984, 248, 3/2*w^3 - w^2 - 17/2*w + 4]', '[1999, 1999, 3/2*w^3 - 3*w^2 - 9/2*w + 7]', '[1999, 1999, 3/2*w^3 - w^2 - 25/2*w - 3]', '[2009, 287, -w^3 + 5/2*w^2 + 17/2*w - 15]', '[2009, 287, 5/2*w^3 - 5/2*w^2 - 16*w - 7]', '[2009, 287, -w^3 + 1/2*w^2 + 21/2*w + 5]', '[2009, 287, 5/2*w^3 - 5*w^2 - 27/2*w + 23]', '[2017, 2017, -3/2*w^3 + 11/2*w^2 - 11]', '[2017, 2017, -w^3 + 11/2*w^2 - 1/2*w - 11]', '[2017, 2017, w^3 + 5/2*w^2 - 15/2*w - 7]', '[2017, 2017, -3/2*w^3 - w^2 + 13/2*w + 7]', '[2018, 2018, -1/2*w^3 + 2*w^2 + 11/2*w - 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37/2*w - 11]', '[641, 641, -2*w^3 + 2*w^2 + 8*w - 9]', '[647, 647, w^3 - 2*w^2 - 5*w + 1]', '[647, 647, -w^3 + w^2 + 6*w - 5]', '[719, 719, -1/2*w^3 + 3/2*w^2 + 5*w - 9]', '[719, 719, w^3 - 1/2*w^2 - 13/2*w + 7]', '[727, 727, -3*w^2 - w + 9]', '[727, 727, -1/2*w^3 + w^2 + 7/2*w - 9]', '[727, 727, 1/2*w^3 - 1/2*w^2 - 4*w - 5]', '[727, 727, 2*w^3 - 5/2*w^2 - 23/2*w - 3]', '[743, 743, w^3 - 3*w^2 - 2*w + 9]', '[743, 743, w^3 + 1/2*w^2 - 19/2*w - 11]', '[751, 751, -1/2*w^3 + 3*w^2 - 1/2*w - 11]', '[751, 751, 1/2*w^3 + 3/2*w^2 - 4*w - 9]', '[761, 761, w^3 + w^2 - 8*w - 7]', '[761, 761, -w^3 + 4*w^2 + 3*w - 13]', '[823, 823, 3/2*w^3 - 7/2*w^2 - 6*w + 11]', '[823, 823, -3/2*w^3 + 5/2*w^2 + 7*w - 9]', '[823, 823, 5/2*w^3 - 3/2*w^2 - 19*w - 5]', '[823, 823, 5/2*w^3 - 3/2*w^2 - 19*w - 7]', '[841, 29, 1/2*w^3 + 1/2*w^2 - 3*w - 9]', '[841, 29, -1/2*w^3 + 2*w^2 + 1/2*w - 11]', '[857, 857, -3/2*w^3 + 4*w^2 + 11/2*w - 15]', '[857, 857, -w^3 + w^2 + 6*w - 9]', '[863, 863, -2*w^3 + w^2 + 9*w - 7]', '[863, 863, -1/2*w^3 + 2*w^2 + 9/2*w - 9]', '[863, 863, 5/2*w^3 - 2*w^2 - 33/2*w - 5]', '[863, 863, 2*w^3 + 1/2*w^2 - 37/2*w - 9]', '[887, 887, 1/2*w^3 + 1/2*w^2 - 3*w + 3]', '[887, 887, -1/2*w^3 - 3/2*w^2 + 6*w + 9]', '[911, 911, -1/2*w^3 - 3/2*w^2 + 6*w + 7]', '[911, 911, -1/2*w^3 + 3*w^2 + 3/2*w - 11]', '[919, 919, 4*w^3 - w^2 - 31*w - 17]', '[919, 919, 2*w^3 - 7/2*w^2 - 21/2*w + 17]', '[929, 929, 1/2*w^3 + 1/2*w^2 - 5*w + 3]', '[929, 929, -1/2*w^3 + 2*w^2 + 5/2*w - 1]', '[937, 937, -w^3 + 9/2*w^2 + 5/2*w - 13]', '[937, 937, -2*w^3 + 9/2*w^2 + 19/2*w - 13]', '[937, 937, 2*w^3 - 3/2*w^2 - 25/2*w - 1]', '[937, 937, w^3 + 3/2*w^2 - 17/2*w - 7]', '[953, 953, 3/2*w^3 - 2*w^2 - 11/2*w + 9]', '[953, 953, -3/2*w^3 - w^2 + 29/2*w + 13]', '[961, 31, 2*w^2 - 2*w - 7]', '[977, 977, -1/2*w^3 + 3/2*w^2 + 5*w - 13]', '[977, 977, 1/2*w^3 - 13/2*w - 7]', '[983, 983, 2*w^3 + 1/2*w^2 - 25/2*w - 7]', '[983, 983, -2*w^3 + 7/2*w^2 + 17/2*w - 17]', '[983, 983, -3*w^3 - w^2 + 26*w + 23]', '[983, 983, 2*w^3 - 3/2*w^2 - 25/2*w + 1]', '[991, 991, -w^3 - 1/2*w^2 + 11/2*w - 1]', '[991, 991, -11/2*w^2 - 5/2*w + 19]', '[991, 991, -4*w^3 + 4*w^2 + 24*w + 11]', '[991, 991, -w^3 + 9*w + 1]', '[1009, 1009, 1/2*w^3 + 1/2*w^2 - 7*w + 3]', '[1009, 1009, -1/2*w^3 + 2*w^2 + 9/2*w - 3]', '[1031, 1031, -4*w^2 - 2*w + 13]', '[1031, 1031, -3/2*w^3 + 3/2*w^2 + 8*w - 3]', '[1033, 1033, -1/2*w^3 - 2*w^2 + 9/2*w + 15]', '[1033, 1033, -1/2*w^3 + 7/2*w^2 - w - 17]', '[1039, 1039, -1/2*w^3 + 3*w^2 - 1/2*w - 9]', '[1039, 1039, -1/2*w^3 - 3/2*w^2 + 4*w + 7]', '[1049, 1049, 3/2*w^2 - 11/2*w - 3]', '[1049, 1049, -w^3 + 3/2*w^2 + 15/2*w - 13]', '[1049, 1049, 3/2*w^3 - 7/2*w^2 - 6*w + 15]', '[1049, 1049, 3/2*w^2 + 5/2*w - 7]', '[1063, 1063, 7/2*w^3 - 2*w^2 - 47/2*w - 13]', '[1063, 1063, -w^3 + 1/2*w^2 + 21/2*w + 9]', '[1063, 1063, -w^3 - w^2 + 6*w + 9]', '[1063, 1063, w^3 + 1/2*w^2 - 15/2*w - 3]', '[1097, 1097, -3/2*w^3 + 4*w^2 + 7/2*w - 11]', '[1097, 1097, w^3 - 9/2*w^2 - 9/2*w + 17]', '[1103, 1103, w^2 - 3*w - 7]', '[1103, 1103, w^2 + w - 9]', '[1151, 1151, -w^3 + 7/2*w^2 + 3/2*w - 11]', '[1151, 1151, w^3 + 1/2*w^2 - 11/2*w - 7]', '[1153, 1153, 3/2*w^3 - 2*w^2 - 19/2*w - 1]', '[1153, 1153, -3/2*w^3 + 5/2*w^2 + 9*w - 11]', '[1201, 1201, 3/2*w^3 - 9/2*w^2 - 7*w + 15]', '[1201, 1201, w^3 - 7/2*w^2 - 15/2*w + 17]', '[1217, 1217, 1/2*w^3 + w^2 - 11/2*w - 1]', '[1217, 1217, -1/2*w^3 - 2*w^2 + 1/2*w + 9]', '[1217, 1217, -3/2*w^3 + w^2 + 17/2*w + 9]', '[1217, 1217, -1/2*w^3 + 5/2*w^2 + 2*w - 5]', '[1223, 1223, -1/2*w^3 + w^2 + 11/2*w - 1]', '[1223, 1223, -1/2*w^3 + 1/2*w^2 + 6*w - 5]', '[1231, 1231, -1/2*w^3 - 5/2*w^2 + 9*w + 11]', '[1231, 1231, 3/2*w^3 + 1/2*w^2 - 6*w + 3]', '[1249, 1249, -5*w^3 + 3*w^2 + 34*w + 19]', '[1249, 1249, -1/2*w^3 + 9/2*w^2 + 4*w - 19]', '[1249, 1249, 7/2*w^3 - 3/2*w^2 - 24*w - 19]', '[1249, 1249, -3*w^3 - w^2 + 28*w + 17]', '[1279, 1279, 3/2*w^3 - w^2 - 25/2*w + 1]', '[1279, 1279, -w^3 - w^2 + 10*w + 13]', '[1279, 1279, -w^3 + 5/2*w^2 + 5/2*w - 9]', '[1279, 1279, 3/2*w^3 - 7/2*w^2 - 10*w + 11]', '[1289, 1289, 3/2*w^2 - 11/2*w - 1]', '[1289, 1289, 2*w^3 - 1/2*w^2 - 15/2*w + 3]', '[1289, 1289, w^3 + w^2 - 12*w - 5]', '[1289, 1289, 2*w^3 - 3*w^2 - 11*w + 9]', '[1297, 1297, 1/2*w^3 - 7/2*w^2 - 3*w + 11]', '[1297, 1297, 4*w^3 - 5/2*w^2 - 55/2*w - 13]', '[1297, 1297, w^3 - 4*w^2 - 7*w + 17]', '[1297, 1297, 5/2*w^3 - 5/2*w^2 - 16*w - 5]', '[1303, 1303, -w^3 + 2*w^2 + 3*w - 9]', '[1303, 1303, w^3 - w^2 - 4*w - 5]', '[1319, 1319, w^2 + w - 11]', '[1319, 1319, w^2 - 3*w - 9]', '[1321, 1321, 3*w^2 + 3*w - 13]', '[1321, 1321, -2*w^3 + w^2 + 13*w + 13]', '[1321, 1321, 7/2*w^2 + 1/2*w - 13]', '[1321, 1321, 3*w^3 - 5/2*w^2 - 37/2*w - 9]', '[1327, 1327, -w^3 + 1/2*w^2 + 13/2*w - 3]', '[1327, 1327, 3/2*w^3 - 3/2*w^2 - 6*w + 5]', '[1327, 1327, 3/2*w^3 - 1/2*w^2 - 13*w - 3]', '[1327, 1327, w^3 - 5/2*w^2 - 9/2*w + 3]', '[1361, 1361, 1/2*w^3 + w^2 - 7/2*w - 11]', '[1361, 1361, -1/2*w^3 + 5/2*w^2 - 13]', '[1367, 1367, -3/2*w^3 + 3*w^2 + 13/2*w - 9]', '[1367, 1367, 3/2*w^3 - 3/2*w^2 - 8*w - 1]', '[1399, 1399, 3/2*w^3 - 1/2*w^2 - 7*w + 7]', '[1399, 1399, 3/2*w^3 - 4*w^2 - 7/2*w + 7]', '[1399, 1399, 5*w^3 - w^2 - 40*w - 21]', '[1399, 1399, 3/2*w^3 + 3/2*w^2 - 15*w - 13]', '[1409, 1409, -w^3 + 3*w^2 + 6*w - 19]', '[1409, 1409, w^3 + 2*w^2 - 11*w - 9]', '[1409, 1409, -5/2*w^3 + 37/2*w + 17]', '[1409, 1409, w^3 - 9*w - 11]', '[1423, 1423, 2*w^3 - 5/2*w^2 - 15/2*w + 11]', '[1423, 1423, -2*w^3 - w^2 + 19*w + 15]', '[1433, 1433, 2*w^3 - 9/2*w^2 - 19/2*w + 15]', '[1433, 1433, 3*w^2 - 5*w - 13]', '[1433, 1433, 3*w^2 - w - 15]', '[1433, 1433, 2*w^3 - 3/2*w^2 - 25/2*w - 3]', '[1439, 1439, 1/2*w^3 - 4*w^2 - 5/2*w + 15]', '[1439, 1439, 1/2*w^3 - 1/2*w^2 - 2*w - 7]', '[1439, 1439, -1/2*w^3 + w^2 + 3/2*w - 9]', '[1439, 1439, 5/2*w^3 - w^2 - 35/2*w - 15]', '[1447, 1447, -3/2*w^3 + 1/2*w^2 + 13*w + 5]', '[1447, 1447, -1/2*w^3 + 5/2*w - 5]', '[1447, 1447, 1/2*w^3 - 3/2*w^2 - w - 3]', '[1447, 1447, 2*w^3 - 2*w^2 - 14*w - 7]', '[1471, 1471, -1/2*w^3 + 3/2*w^2 + 5*w - 7]', '[1471, 1471, 1/2*w^3 - 13/2*w - 1]', '[1489, 1489, -2*w^3 + 7*w^2 + 5*w - 21]', '[1489, 1489, 1/2*w^3 - 5*w^2 - 7/2*w + 17]', '[1489, 1489, 7/2*w^3 - 3*w^2 - 45/2*w - 11]', '[1489, 1489, 2*w^3 + w^2 - 13*w - 11]', '[1511, 1511, w^3 - w^2 - 4*w - 7]', '[1511, 1511, -1/2*w^3 - 3*w^2 + 19/2*w + 15]', '[1543, 1543, w^3 + 1/2*w^2 - 19/2*w - 3]', '[1543, 1543, -w^3 + 7/2*w^2 + 11/2*w - 11]', '[1553, 1553, 1/2*w^3 - 1/2*w^2 - 5]', '[1553, 1553, -1/2*w^3 + w^2 - 1/2*w - 5]', '[1559, 1559, 7/2*w^3 - 5/2*w^2 - 23*w - 11]', '[1559, 1559, 1/2*w^3 - 7/2*w^2 - 5*w + 15]', '[1567, 1567, 1/2*w^3 - 7/2*w^2 - w + 11]', '[1567, 1567, -1/2*w^3 - 2*w^2 + 13/2*w + 7]', '[1583, 1583, 3/2*w^3 - 3/2*w^2 - 8*w + 1]', '[1583, 1583, -3/2*w^3 + 3*w^2 + 13/2*w - 7]', '[1607, 1607, -w^3 + 5/2*w^2 + 13/2*w - 5]', '[1607, 1607, -w^3 + 1/2*w^2 + 17/2*w - 3]', '[1657, 1657, 1/2*w^3 + 3/2*w^2 - 8*w - 9]', '[1657, 1657, 3/2*w^3 - 3/2*w^2 - 4*w + 5]', '[1663, 1663, 1/2*w^3 - w^2 - 3/2*w - 5]', '[1663, 1663, -1/2*w^3 + 1/2*w^2 + 2*w - 7]', '[1681, 41, 5/2*w^2 - 5/2*w - 13]', '[1697, 1697, -1/2*w^3 + 4*w^2 - 11/2*w - 9]', '[1697, 1697, 5/2*w^3 + w^2 - 15/2*w - 1]', '[1759, 1759, 3/2*w^2 - 7/2*w - 9]', '[1759, 1759, 3/2*w^2 + 1/2*w - 11]', '[1777, 1777, 3/2*w^3 - 5*w^2 - 9/2*w + 19]', '[1777, 1777, 3/2*w^3 + 1/2*w^2 - 10*w - 11]', '[1783, 1783, -3/2*w^3 + 7/2*w^2 + 8*w - 19]', '[1783, 1783, -7/2*w^3 - 1/2*w^2 + 28*w + 25]', '[1801, 1801, 9/2*w^3 - 9/2*w^2 - 28*w - 9]', '[1801, 1801, 1/2*w^3 - 11/2*w^2 - 5*w + 19]', '[1823, 1823, -1/2*w^3 + 1/2*w^2 + 8*w - 11]', '[1823, 1823, 2*w^3 - 7*w^2 - 11*w + 27]', '[1831, 1831, -1/2*w^3 + w^2 + 11/2*w - 5]', '[1831, 1831, -1/2*w^3 + 1/2*w^2 + 6*w - 1]', '[1847, 1847, 5/2*w^3 - 2*w^2 - 33/2*w - 11]', '[1847, 1847, -1/2*w^3 + 1/2*w^2 + 6*w - 3]', '[1847, 1847, -1/2*w^3 + w^2 + 11/2*w - 3]', '[1847, 1847, 1/2*w^2 - 9/2*w - 5]', '[1873, 1873, -w^2 + 3*w - 5]', '[1873, 1873, -w^2 - w - 3]', '[1879, 1879, 2*w^3 + 1/2*w^2 - 25/2*w - 11]', '[1879, 1879, 4*w + 7]', '[1889, 1889, 4*w^3 - 5*w^2 - 21*w - 9]', '[1889, 1889, w^3 + 11/2*w^2 - 1/2*w - 19]', '[1913, 1913, 2*w^3 - 5/2*w^2 - 23/2*w + 1]', '[1913, 1913, 1/2*w^2 - 9/2*w - 1]', '[1913, 1913, 1/2*w^2 + 7/2*w - 5]', '[1913, 1913, w^2 + 3*w - 5]', '[1999, 1999, 3/2*w^3 - 3*w^2 - 9/2*w + 7]', '[1999, 1999, 3/2*w^3 - w^2 - 25/2*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': [8, 8, -7, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 10304, 'disc_rad': 322, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [[2, 2]]], [7, [0]], [11, [[4, 1]]], [13, [[4, 1]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [0]], [29, [[2, 2]]], [31, [[2, 1], [1, 2]]], [37, [[4, 1]]], [41, [[2, 1], [1, 2]]], [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': [12, 4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 35.888716889852724, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.10304.1', 'local_algs': ['2.2.3.1', '2.2.3.1', '7.2.1.2', '7.2.0.1', '23.2.0.1', '23.2.1.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 7, 23], 'rd': 10.0751486502, 'regulator': {'__RealLiteral__': 0, 'data': '10.8638173525', 'prec': 44}, 'res': {'gal': ['32,-16,-158,40,183,-36,-38,0,1'], 'sib': ['32,0,-17,0,1', '32,-16,-158,40,183,-36,-38,0,1']}, 'subfield_mults': [1], 'subfields': ['-2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{2} - \\frac{1}{2} a - 1 \\)', '\\( \\frac{1}{2} a^{3} - \\frac{9}{2} a - 3 \\)', '\\( \\frac{1}{2} a^{3} - \\frac{1}{2} a^{2} - 2 a + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2*a', '1/2*a^3 - 1/2*a']}