Hilbert modular form data - 4.4.9792.1-16.1-b

Formats: - HTML - YAML - JSON - 2024-06-04T11:34:08.608408

• 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': 4, 'disc': 9792, 'field_bad_primes': [2, 3, 17], 'field_label': '4.4.9792.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '4.4.9792.1-16.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2], 'level_ideal': '[16, 2, 2]', 'level_label': '16.1', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.1-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4, 2, w^3 - 3*w^2 - 3*w + 4]', 1]], 'hecke_eigenvalues': [0, '1/4*e^2 - 5', '1/4*e^2 - 5', 'e', 'e', '-1/8*e^3 + 7/2*e', '-1/8*e^3 + 7/2*e', 0, 0, '-1/4*e^2 + 5', '-1/4*e^2 + 5', '-1/8*e^3 + 7/2*e', '-1/8*e^3 + 7/2*e', '-1/4*e^2 + 15', '-1/4*e^3 + 5*e', '-1/4*e^3 + 5*e', '1/4*e^2 - 3', '1/4*e^2 - 3', '-3/4*e^2 + 15', '-3/4*e^2 + 15', '5/4*e^2 - 23', '5/4*e^2 - 23', '-1/4*e^3 + 6*e', '-1/4*e^3 + 6*e', '1/4*e^3 - 8*e', '1/4*e^3 - 4*e', '1/4*e^3 - 8*e', '1/4*e^3 - 4*e', '1/4*e^3 - 9*e', '1/4*e^3 - 9*e', '-1/4*e^2 - 1', '-1/4*e^2 - 1', '1/4*e^2 - 11', '1/4*e^2 - 11', '1/4*e^2 - 5', '1/4*e^2 - 5', '-3/4*e^2 + 7', '7/4*e^2 - 43', '7/4*e^2 - 43', '-3/4*e^2 + 7', '-1/8*e^3 - 1/2*e', '-1/8*e^3 - 1/2*e', 'e^2 - 10', 'e^2 - 10', '3/8*e^3 - 21/2*e', '-1/8*e^3 - 1/2*e', '3/8*e^3 - 21/2*e', '-1/8*e^3 - 1/2*e', '-1/4*e^3 + 13*e', '-1/4*e^3 + 13*e', '-4*e', '-4*e', '1/4*e^2 - 13', '1/4*e^2 - 13', '-3/4*e^2 - 1', '-3/4*e^2 - 1', '-1/8*e^3 - 1/2*e', '-1/8*e^3 - 1/2*e', '1/2*e^3 - 13*e', '1/2*e^3 - 13*e', '1/4*e^3 - 9*e', '1/4*e^3 - 9*e', '3/4*e^2 - 13', '3/4*e^2 - 13', '-e^2 + 22', '-e^2 + 22', '1/4*e^3 - 8*e', '3/8*e^3 - 21/2*e', '1/4*e^3 - 8*e', '3/8*e^3 - 21/2*e', '5/4*e^2 - 31', '5/4*e^2 - 31', '-7/4*e^2 + 51', '-7/4*e^2 + 51', '1/4*e^3 - 9*e', '1/4*e^3 - 9*e', '-1/2*e^3 + 14*e', '-1/2*e^3 + 14*e', '-1/2*e^3 + 15*e', '-1/2*e^3 + 15*e', '-1/2*e^3 + 14*e', '-1/2*e^3 + 14*e', '-e^2 + 22', '-e^2 + 22', '-3/4*e^2 + 1', '-3/4*e^2 + 1', '-1/4*e^2 + 13', '-1/4*e^2 + 13', '5*e', '5*e', '-5/4*e^2 + 19', '2*e^2 - 38', '-5/4*e^2 + 19', '2*e^2 - 38', '1/4*e^3 - e', '1/4*e^3 - e', '11/4*e^2 - 55', '11/4*e^2 - 55', '-4*e', '-4*e', '1/4*e^3 - 12*e', '1/4*e^3 - 12*e', '-9/4*e^2 + 63', '3/4*e^3 - 19*e', '3/4*e^3 - 19*e', '4*e', '4*e', '-3*e^2 + 62', '-3*e^2 + 62', '9/4*e^2 - 53', '9/4*e^2 - 53', '-1/8*e^3 + 15/2*e', '-1/8*e^3 + 15/2*e', '-2*e^2 + 58', '-3/4*e^2 + 23', '-3/4*e^2 + 23', '7/4*e^2 - 43', '7/4*e^2 - 43', '-1/8*e^3 + 23/2*e', '-1/8*e^3 + 23/2*e', '-e^2 + 30', '-e^2 + 30', '-1/4*e^3 + 5*e', '-1/4*e^3 + 5*e', '-1/4*e^2 + 29', '3/4*e^2 + 25', '3/4*e^2 + 25', '-1/4*e^2 + 29', '1/2*e^3 - 18*e', '1/2*e^3 - 18*e', '-7/4*e^2 + 11', '-7/4*e^2 + 11', '3/8*e^3 - 13/2*e', '3/8*e^3 - 29/2*e', '3/8*e^3 - 13/2*e', '3/8*e^3 - 29/2*e', '3/8*e^3 - 29/2*e', '3/8*e^3 - 29/2*e', '11/4*e^2 - 55', '11/4*e^2 - 55', '-3/4*e^3 + 15*e', '-3/4*e^3 + 15*e', '1/4*e^3 - 4*e', '1/4*e^3 - 4*e', '-3/4*e^3 + 15*e', '-3/4*e^3 + 15*e', '-1/2*e^3 + 14*e', '-1/2*e^3 + 14*e', '-1/4*e^3 + 10*e', '-1/4*e^3 + 10*e', 0, 0, '8*e', '8*e', '1/4*e^2 + 35', '-13/4*e^2 + 49', '-13/4*e^2 + 49', '1/4*e^2 + 35', '1/2*e^3 - 9*e', '1/2*e^3 - 9*e', '7/4*e^2 - 25', '-1/4*e^2 - 19', '15/4*e^2 - 83', '15/4*e^2 - 83', '-1/4*e^2 - 19', '-1/4*e^3 + 17*e', '-1/4*e^3 + 17*e', '3/4*e^2 - 7', '3/4*e^2 - 7', '-e^2 + 62', '-e^2 + 62', '-1/4*e^3 + 9*e', '-1/4*e^3 + 9*e', '-e^2 + 22', '-e^2 + 22', '-3/4*e^2 - 7', '-3/4*e^2 - 7', '-1/2*e^3 + 7*e', '-1/2*e^3 + 7*e', '5/4*e^2 - 65', '9/4*e^2 - 37', '9/4*e^2 - 37', '5/4*e^2 - 65', '-e^3 + 20*e', '-e^3 + 20*e', '3/4*e^3 - 27*e', '3/4*e^3 - 27*e', '11/4*e^2 - 53', '11/4*e^2 - 53', '1/2*e^3 - 14*e', '1/2*e^3 - 14*e', '7/4*e^2 - 81', '7/4*e^2 - 81', '-1/8*e^3 - 1/2*e', '-1/8*e^3 - 1/2*e', '7/4*e^2 - 25', '7/4*e^2 - 25', '1/4*e^3 - 12*e', '1/4*e^3 - 12*e', '5/4*e^3 - 29*e', '-1/4*e^3 + 13*e', '-1/4*e^3 + 13*e', '5/4*e^3 - 29*e', '-5/4*e^2 + 49', '-5/4*e^2 + 49', '-1/8*e^3 + 15/2*e', '-1/8*e^3 + 15/2*e', '3*e^2 - 34', '3*e^2 - 34', '3/4*e^2 + 17', '3/4*e^2 + 17', '-e^3 + 28*e', '-e^3 + 28*e', '3*e^2 - 74', '3*e^2 - 74', '4*e', '4*e', '11/4*e^2 - 63', '11/4*e^2 - 63', '1/2*e^3 - 13*e', '7/8*e^3 - 49/2*e', '1/2*e^3 - 13*e', '7/8*e^3 - 49/2*e', '13/4*e^2 - 65', '13/4*e^2 - 65', '-1/2*e^3 + 19*e', '-1/2*e^3 + 19*e', '-4*e', '-4*e', '-3/4*e^2 + 55', '-3/4*e^2 + 55', '3/4*e^2 - 31', '3/4*e^2 - 31', 'e^2 + 30', 'e^2 + 30', '-9/4*e^2 + 61', '-9/4*e^2 + 61', '-9/4*e^2 + 61', '-9/4*e^2 + 61', '-1/4*e^3 + 2*e', '-1/4*e^3 + 2*e', '-e^3 + 32*e', '-e^3 + 32*e', '-19/4*e^2 + 95', '-19/4*e^2 + 95', '-3/4*e^3 + 16*e', '-3/4*e^3 + 16*e', '1/4*e^3 - 17*e', '1/4*e^3 + 3*e', '1/4*e^3 - 17*e', '1/4*e^3 + 3*e', '3*e^2 - 26', '3*e^2 - 26', '-9/4*e^2 + 21', '-9/4*e^2 + 21', '2*e^2 - 54', '-1/2*e^3 + 11*e', '-1/2*e^3 + 11*e', '7/8*e^3 - 41/2*e', '7/8*e^3 - 41/2*e', '5*e', '5*e', '-e^2 + 86', '-e^2 + 86', '-5*e^2 + 78', '-5*e^2 + 78', '21/4*e^2 - 121', '21/4*e^2 - 121', '-9/4*e^2 + 53', '-9/4*e^2 + 53', '-1/4*e^2 - 19', '-7/4*e^2 + 19', '-1/4*e^2 - 19', '-7/4*e^2 + 19', '-e^2 + 30', '13/4*e^2 - 63', '13/4*e^2 - 63', '-e^2 + 30', '3/4*e^2 - 15', '3/4*e^2 - 15', 'e^3 - 20*e', 'e^3 - 20*e', 'e^2 - 58', 'e^2 - 58', '1/2*e^3 - 6*e', '-1/2*e^3 + 18*e', '1/2*e^3 - 6*e', '-1/2*e^3 + 18*e', '13/4*e^2 - 103', '13/4*e^2 - 103', '-9/8*e^3 + 55/2*e', '-9/8*e^3 + 55/2*e', '-1/8*e^3 + 15/2*e', '-1/8*e^3 + 15/2*e', '-1/4*e^2 - 9', '-1/4*e^2 - 9', '-3*e^2 + 54', '-3*e^2 + 54', '-13/4*e^2 + 17', '-13/4*e^2 + 17'], 'hecke_polynomial': 'x^4 - 40*x^2 + 272', 'label': '4.4.9792.1-16.1-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 9792, 'ideals': ['[1, 1, 1]', '[4, 2, w^3 - 3*w^2 - 3*w + 4]', '[7, 7, w]', '[7, 7, w^3 - 3*w^2 - 4*w + 5]', '[9, 3, w^3 - 4*w^2 - w + 9]', '[16, 2, 2]', '[17, 17, 2*w^3 - 6*w^2 - 7*w + 8]', '[17, 17, -w^3 + 3*w^2 + 4*w - 3]', '[17, 17, -w + 2]', '[23, 23, 2*w^3 - 7*w^2 - 4*w + 12]', '[23, 23, -w^2 + 2*w + 3]', '[28, 14, -w^3 + 4*w^2 + 2*w - 7]', '[28, 14, 2*w^3 - 7*w^2 - 5*w + 13]', '[31, 31, -2*w^3 + 7*w^2 + 5*w - 12]', '[31, 31, -w^3 + 4*w^2 + 2*w - 8]', '[36, 6, w^3 - 2*w^2 - 6*w + 1]', '[41, 41, 3*w^3 - 10*w^2 - 7*w + 16]', '[41, 41, 2*w^3 - 7*w^2 - 5*w + 10]', '[49, 7, 2*w^3 - 6*w^2 - 6*w + 7]', '[49, 7, 2*w^3 - 6*w^2 - 6*w + 9]', '[49, 49, -w^2 + 2*w + 7]', '[49, 49, -2*w^3 + 7*w^2 + 4*w - 8]', '[63, 21, -2*w^3 + 6*w^2 + 7*w - 7]', '[63, 21, w^3 - 3*w^2 - 2*w + 2]', '[64, 4, 2*w^3 - 6*w^2 - 6*w + 8]', '[68, 34, w^3 - 4*w^2 - 2*w + 11]', '[68, 34, w^2 - w - 5]', '[68, 34, 3*w^3 - 10*w^2 - 8*w + 15]', '[71, 71, w^2 - 2*w - 2]', '[71, 71, 2*w^3 - 7*w^2 - 4*w + 13]', '[73, 73, 3*w^3 - 11*w^2 - 5*w + 19]', '[73, 73, -4*w^3 + 13*w^2 + 10*w - 17]', '[79, 79, 3*w^3 - 9*w^2 - 10*w + 13]', '[79, 79, -2*w^3 + 6*w^2 + 5*w - 8]', '[81, 3, 3]', '[92, 46, w^2 - 3*w - 1]', '[92, 46, -w^3 + 4*w^2 - 9]', '[97, 97, 2*w^3 - 6*w^2 - 8*w + 9]', '[97, 97, 2*w - 1]', '[112, 14, 2*w]', '[112, 14, 2*w^3 - 6*w^2 - 8*w + 10]', '[113, 113, 2*w^3 - 6*w^2 - 7*w + 6]', '[113, 113, -w^3 + 3*w^2 + 2*w - 1]', '[119, 119, -4*w^3 + 13*w^2 + 12*w - 21]', '[119, 119, -w^2 + 2*w]', '[119, 119, -2*w^3 + 7*w^2 + 4*w - 14]', '[119, 119, -2*w^3 + 7*w^2 + 4*w - 15]', '[119, 119, w^2 - 4]', '[119, 119, -w^2 + 2*w + 1]', '[124, 62, -w^3 + 3*w^2 + 5*w - 6]', '[124, 62, -w^3 + 3*w^2 + 5*w - 4]', '[137, 137, w^3 - 2*w^2 - 5*w + 2]', '[137, 137, 2*w^3 - 7*w^2 - 3*w + 12]', '[137, 137, -3*w^3 + 10*w^2 + 7*w - 17]', '[137, 137, -w^3 + 2*w^2 + 6*w - 2]', '[144, 6, 2*w^3 - 8*w^2 - 2*w + 18]', '[153, 51, w^3 - 3*w^2 - 5*w + 5]', '[153, 51, -4*w^3 + 13*w^2 + 10*w - 18]', '[153, 51, -2*w^3 + 5*w^2 + 8*w - 3]', '[161, 161, -3*w^3 + 10*w^2 + 8*w - 14]', '[161, 161, -w^3 + 4*w^2 - 10]', '[161, 161, -w^2 + 3*w]', '[161, 161, w^2 - w - 6]', '[164, 82, w^2 - 3*w + 1]', '[164, 82, -w^3 + 3*w^2 + w - 2]', '[167, 167, -2*w^3 + 7*w^2 + 6*w - 10]', '[167, 167, 3*w^3 - 9*w^2 - 10*w + 10]', '[169, 13, -2*w^3 + 7*w^2 + 2*w - 9]', '[169, 13, -2*w^3 + 5*w^2 + 10*w - 4]', '[193, 193, -2*w^3 + 8*w^2 + 3*w - 13]', '[193, 193, -3*w^3 + 11*w^2 + 6*w - 22]', '[196, 14, -w^3 + 3*w^2 + 3*w - 8]', '[196, 14, -w^3 + 3*w^2 + 3*w]', '[196, 98, 3*w^3 - 8*w^2 - 12*w + 7]', '[196, 98, 4*w^3 - 13*w^2 - 9*w + 17]', '[199, 199, 5*w^3 - 16*w^2 - 14*w + 26]', '[199, 199, w^3 - 2*w^2 - 7*w + 3]', '[207, 69, -w^3 + 4*w^2 + w - 3]', '[207, 69, w^3 - 4*w^2 - w + 12]', '[217, 217, -4*w^3 + 12*w^2 + 13*w - 19]', '[217, 217, 3*w^3 - 9*w^2 - 8*w + 14]', '[217, 217, 2*w^3 - 5*w^2 - 6*w + 7]', '[217, 217, -6*w^3 + 19*w^2 + 18*w - 32]', '[223, 223, -3*w^3 + 8*w^2 + 12*w - 8]', '[223, 223, 3*w^3 - 11*w^2 - 6*w + 17]', '[223, 223, 2*w^3 - 8*w^2 - 3*w + 18]', '[223, 223, -4*w^3 + 13*w^2 + 9*w - 18]', '[233, 233, -3*w^3 + 10*w^2 + 6*w - 16]', '[233, 233, -2*w^3 + 5*w^2 + 9*w - 6]', '[241, 241, -3*w^3 + 9*w^2 + 8*w - 10]', '[241, 241, 4*w^3 - 12*w^2 - 13*w + 15]', '[252, 42, w^2 - w - 7]', '[252, 42, -3*w^3 + 10*w^2 + 8*w - 13]', '[256, 4, 4]', '[257, 257, 2*w^3 - 8*w^2 - w + 16]', '[257, 257, 4*w^3 - 13*w^2 - 11*w + 18]', '[257, 257, -w^3 + 5*w^2 - 2*w - 9]', '[257, 257, -w^3 + 2*w^2 + 4*w + 2]', '[263, 263, 4*w^3 - 14*w^2 - 9*w + 27]', '[263, 263, 5*w^3 - 15*w^2 - 17*w + 25]', '[263, 263, -2*w^3 + 7*w^2 + 6*w - 16]', '[263, 263, -2*w^3 + 7*w^2 + 6*w - 9]', '[271, 271, -w - 4]', '[271, 271, -w^3 + 3*w^2 + 4*w - 9]', '[271, 271, 5*w^3 - 16*w^2 - 14*w + 24]', '[271, 271, -4*w^3 + 14*w^2 + 9*w - 24]', '[272, 34, 4*w^3 - 12*w^2 - 14*w + 16]', '[272, 34, -2*w^3 + 6*w^2 + 8*w - 6]', '[272, 34, -2*w + 4]', '[279, 93, -2*w^3 + 7*w^2 + 6*w - 17]', '[279, 93, -w^3 + 5*w^2 - 16]', '[281, 281, -2*w^3 + 6*w^2 + 5*w - 4]', '[281, 281, -3*w^3 + 9*w^2 + 10*w - 9]', '[281, 281, 3*w^3 - 10*w^2 - 8*w + 12]', '[281, 281, w^2 - w - 8]', '[284, 142, 2*w^3 - 7*w^2 - 3*w + 13]', '[284, 142, w^3 - 2*w^2 - 6*w + 3]', '[287, 287, 4*w^3 - 13*w^2 - 10*w + 22]', '[287, 287, 7*w^3 - 23*w^2 - 20*w + 38]', '[287, 287, -3*w^3 + 9*w^2 + 6*w - 14]', '[287, 287, -4*w^3 + 14*w^2 + 10*w - 21]', '[289, 17, -4*w^3 + 14*w^2 + 9*w - 23]', '[289, 17, -3*w^3 + 9*w^2 + 9*w - 13]', '[289, 17, -w^3 + 5*w^2 - 12]', '[289, 17, -3*w^3 + 9*w^2 + 9*w - 11]', '[289, 289, 4*w^3 - 14*w^2 - 10*w + 27]', '[289, 289, 2*w^3 - 8*w^2 - 4*w + 13]', '[292, 146, -w^3 + 5*w^2 - 3*w - 8]', '[292, 146, -3*w^3 + 10*w^2 + 6*w - 9]', '[311, 311, w^2 - 5]', '[311, 311, -4*w^3 + 13*w^2 + 12*w - 20]', '[313, 313, 6*w^3 - 19*w^2 - 18*w + 31]', '[313, 313, -2*w^3 + 5*w^2 + 6*w - 6]', '[316, 158, 2*w^3 - 7*w^2 - 5*w + 17]', '[316, 158, w^3 - 4*w^2 - 2*w + 3]', '[324, 6, 3*w^3 - 9*w^2 - 9*w + 12]', '[337, 337, 3*w^3 - 11*w^2 - 3*w + 15]', '[337, 337, w^3 - w^2 - 9*w - 5]', '[343, 7, 2*w^3 - 8*w^2 - 5*w + 14]', '[343, 7, -5*w^3 + 17*w^2 + 14*w - 31]', '[343, 49, -2*w^3 + 8*w^2 + 3*w - 14]', '[343, 49, 3*w^3 - 11*w^2 - 6*w + 21]', '[343, 343, -w^3 + 2*w^2 + 7*w]', '[343, 343, -w^3 + 4*w^2 - w - 5]', '[353, 353, -w^3 + 2*w^2 + 5*w - 4]', '[353, 353, w^3 - w^2 - 8*w - 3]', '[353, 353, 3*w^3 - 10*w^2 - 7*w + 19]', '[353, 353, -4*w^3 + 14*w^2 + 7*w - 22]', '[361, 19, -3*w^3 + 11*w^2 + 6*w - 18]', '[361, 19, 2*w^3 - 8*w^2 - 3*w + 17]', '[367, 367, -4*w^3 + 12*w^2 + 13*w - 18]', '[367, 367, 3*w^3 - 9*w^2 - 8*w + 13]', '[368, 46, 4*w^3 - 14*w^2 - 8*w + 24]', '[368, 46, -2*w^2 + 4*w + 6]', '[369, 123, w^3 - 3*w^2 - 5*w + 11]', '[369, 123, w^2 - 4*w - 1]', '[383, 383, 5*w^3 - 17*w^2 - 12*w + 30]', '[383, 383, 2*w^2 - 3*w - 5]', '[383, 383, 3*w^3 - 9*w^2 - 11*w + 11]', '[383, 383, -w^3 + 3*w^2 + w - 1]', '[388, 194, 3*w^3 - 11*w^2 - 7*w + 22]', '[388, 194, -3*w^3 + 11*w^2 + 7*w - 18]', '[391, 391, -w^3 + 2*w^2 + 7*w - 1]', '[391, 391, w^3 - 4*w^2 + w + 6]', '[391, 391, -w^3 + 6*w^2 - 3*w - 18]', '[391, 391, -3*w^3 + 9*w^2 + 8*w - 11]', '[391, 391, -5*w^3 + 18*w^2 + 9*w - 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12*w^2 - 5*w + 26]', '[1783, 1783, -3*w^3 + 12*w^2 + 4*w - 24]', '[1791, 597, 7*w^3 - 21*w^2 - 26*w + 38]', '[1791, 597, 10*w^3 - 29*w^2 - 36*w + 34]', '[1792, 28, 4*w]', '[1792, 28, 4*w^3 - 12*w^2 - 16*w + 20]', '[1796, 898, w^3 - 8*w - 5]', '[1796, 898, -8*w^3 + 27*w^2 + 19*w - 45]', '[1799, 1799, 5*w^3 - 15*w^2 - 17*w + 17]', '[1799, 1799, -4*w^3 + 13*w^2 + 12*w - 14]', '[1799, 1799, 8*w^3 - 27*w^2 - 20*w + 48]', '[1799, 1799, -5*w^3 + 17*w^2 + 10*w - 28]', '[1799, 1799, -w^2 + 11]', '[1799, 1799, 2*w^3 - 4*w^2 - 11*w + 3]', '[1799, 1799, 3*w^3 - 9*w^2 - 7*w + 7]', '[1799, 1799, -3*w^2 + 4*w + 7]', '[1801, 1801, 8*w^3 - 24*w^2 - 27*w + 33]', '[1801, 1801, 4*w^3 - 12*w^2 - 16*w + 19]', '[1801, 1801, 4*w - 1]', '[1801, 1801, 7*w^3 - 21*w^2 - 23*w + 33]', '[1808, 226, 4*w^3 - 12*w^2 - 14*w + 12]', '[1808, 226, -2*w^3 + 6*w^2 + 4*w - 2]', '[1817, 1817, 5*w^3 - 14*w^2 - 18*w + 22]', '[1817, 1817, 4*w^3 - 13*w^2 - 15*w + 18]', '[1817, 1817, 3*w^3 - 10*w^2 - 12*w + 22]', '[1817, 1817, 6*w^3 - 19*w^2 - 15*w + 32]', '[1828, 914, 3*w^3 - 12*w^2 - 4*w + 23]', '[1828, 914, -w^3 + 6*w^2 - 6*w - 11]', '[1828, 914, 4*w^3 - 15*w^2 - 7*w + 27]', '[1828, 914, -9*w^3 + 29*w^2 + 25*w - 46]', '[1831, 1831, w^3 - 2*w^2 - 8*w + 2]', '[1831, 1831, w^2 - 5*w - 2]', '[1841, 1841, -6*w^3 + 19*w^2 + 19*w - 28]', '[1841, 1841, 17*w^3 - 56*w^2 - 51*w + 104]', '[1841, 1841, -11*w^3 + 34*w^2 + 37*w - 59]', '[1841, 1841, 3*w^3 - 8*w^2 - 5*w + 14]', '[1841, 1841, w^3 - 3*w^2 - 1]', '[1841, 1841, -5*w^3 + 18*w^2 + 15*w - 35]', '[1841, 1841, 3*w^3 - 8*w^2 - 12*w + 14]', '[1841, 1841, -4*w^3 + 13*w^2 + 9*w - 24]', '[1847, 1847, 6*w^3 - 20*w^2 - 15*w + 25]', '[1847, 1847, w^3 - w^2 - 6*w - 10]', '[1849, 43, -6*w^3 + 21*w^2 + 14*w - 37]', '[1849, 43, -2*w^3 + 9*w^2 + 2*w - 18]', '[1863, 69, 6*w^3 - 21*w^2 - 12*w + 36]', '[1863, 69, -3*w^2 + 6*w + 9]', '[1871, 1871, -4*w^3 + 13*w^2 + 8*w - 22]', '[1871, 1871, 4*w^3 - 13*w^2 - 12*w + 15]', '[1871, 1871, 4*w^3 - 11*w^2 - 16*w + 17]', '[1871, 1871, w^2 - 10]', '[1873, 1873, -w^3 + 5*w^2 - 20]', '[1873, 1873, -4*w^3 + 14*w^2 + 9*w - 15]', '[1897, 1897, w^3 - 3*w^2 - 7*w + 7]', '[1897, 1897, 12*w^3 - 40*w^2 - 33*w + 71]', '[1897, 1897, -11*w^3 + 35*w^2 + 33*w - 57]', '[1897, 1897, -3*w^3 + 9*w^2 + 13*w - 13]', '[1897, 1897, -6*w^3 + 21*w^2 + 14*w - 35]', '[1897, 1897, 6*w^3 - 19*w^2 - 16*w + 28]', '[1897, 1897, -w^2 - 4*w]', '[1897, 1897, -8*w^3 + 25*w^2 + 28*w - 45]', '[1904, 238, -8*w^3 + 26*w^2 + 24*w - 42]', '[1904, 238, -2*w^2 + 4*w]', '[1904, 238, -4*w^3 + 14*w^2 + 8*w - 28]', '[1904, 238, -4*w^3 + 14*w^2 + 8*w - 30]', '[1904, 238, 2*w^2 - 8]', '[1904, 238, -2*w^2 + 4*w + 2]', '[1913, 1913, -2*w^3 + 6*w^2 + 3*w - 4]', '[1913, 1913, 5*w^3 - 15*w^2 - 18*w + 19]', '[1913, 1913, 6*w^3 - 20*w^2 - 11*w + 30]', '[1913, 1913, 9*w^3 - 30*w^2 - 23*w + 45]', '[1916, 958, -6*w^3 + 17*w^2 + 23*w - 25]', '[1916, 958, 5*w^3 - 16*w^2 - 10*w + 25]', '[1921, 1921, w^3 - w^2 - 9*w - 11]', '[1921, 1921, -4*w^3 + 11*w^2 + 14*w - 11]', '[1921, 1921, -3*w^2 + 6*w + 20]', '[1921, 1921, 7*w^3 - 21*w^2 - 23*w + 27]', '[1921, 1921, 6*w^3 - 19*w^2 - 16*w + 26]', '[1921, 1921, -3*w^3 + 11*w^2 + 3*w - 9]', '[1948, 974, 3*w^2 - 9*w - 13]', '[1948, 974, 3*w^3 - 12*w^2 + 17]', '[1953, 651, 3*w^3 - 10*w^2 - 5*w + 19]', '[1953, 651, 3*w^3 - 8*w^2 - 13*w + 14]', '[1953, 651, 3*w^3 - 7*w^2 - 14*w + 7]', '[1953, 651, 6*w^3 - 20*w^2 - 13*w + 32]', '[1967, 1967, -4*w^3 + 13*w^2 + 6*w - 21]', '[1967, 1967, -6*w^3 + 17*w^2 + 24*w - 26]', '[1967, 1967, 2*w^3 - 9*w^2 + 14]', '[1967, 1967, 3*w^3 - 11*w^2 - 3*w + 21]', '[1967, 1967, 4*w^3 - 14*w^2 - 7*w + 25]', '[1967, 1967, w^3 - w^2 - 9*w + 1]', '[1967, 1967, -4*w^3 + 15*w^2 + 6*w - 31]', '[1967, 1967, w^3 - w^2 - 8*w]', '[1984, 124, -2*w^3 + 6*w^2 + 10*w - 12]', '[1984, 124, -2*w^3 + 6*w^2 + 10*w - 8]', '[1988, 994, -3*w^3 + 11*w^2 + 9*w - 14]', '[1988, 994, 5*w^3 - 16*w^2 - 16*w + 23]', '[1988, 994, w^2 + w - 7]', '[1988, 994, 5*w^3 - 17*w^2 - 15*w + 36]', '[1993, 1993, -8*w^3 + 28*w^2 + 17*w - 43]', '[1993, 1993, 4*w^3 - 13*w^2 - 16*w + 19]', '[1993, 1993, -6*w^3 + 21*w^2 + 14*w - 36]', '[1993, 1993, -2*w^3 + 9*w^2 + 2*w - 19]', '[1999, 1999, -7*w^3 + 22*w^2 + 20*w - 30]', '[1999, 1999, 4*w^3 - 11*w^2 - 13*w + 10]', '[2007, 669, -7*w^3 + 15*w^2 + 38*w - 2]', '[2007, 669, -2*w^3 + 6*w^2 + 4*w - 1]', '[2007, 669, 2*w^3 - 12*w^2 + 5*w + 43]', '[2007, 669, 2*w^3 - 9*w^2 + 2*w + 13]', '[2009, 287, -7*w^3 + 22*w^2 + 24*w - 34]', '[2009, 287, -3*w^3 + 12*w^2 + w - 14]', '[2009, 287, -4*w^3 + 13*w^2 + 7*w - 14]', '[2009, 287, 7*w^3 - 24*w^2 - 16*w + 32]', '[2009, 2009, 14*w^3 - 48*w^2 - 27*w + 68]', '[2009, 2009, 5*w^3 - 16*w^2 - 15*w + 21]', '[2009, 2009, 11*w^3 - 39*w^2 - 22*w + 53]', '[2009, 2009, 7*w^3 - 24*w^2 - 16*w + 42]', '[2012, 1006, -7*w^3 + 24*w^2 + 20*w - 39]', '[2012, 1006, -4*w^3 + 15*w^2 + 11*w - 31]', '[2017, 2017, 4*w^3 - 11*w^2 - 14*w + 12]', '[2017, 2017, -6*w^3 + 19*w^2 + 16*w - 27]', '[2023, 119, -7*w^3 + 24*w^2 + 18*w - 42]', '[2023, 119, 6*w^3 - 19*w^2 - 15*w + 28]', '[2023, 119, 3*w^3 - 12*w^2 - 5*w + 21]', '[2023, 119, 2*w^3 - 8*w^2 + w + 14]', '[2023, 119, w^3 - w^2 - 10*w - 1]', '[2023, 119, -5*w^3 + 14*w^2 + 18*w - 18]', '[2023, 119, 2*w^3 - 9*w^2 - 3*w + 18]', '[2023, 119, -5*w^3 + 18*w^2 + 11*w - 34]', '[2023, 2023, -w^3 + 2*w^2 + 5*w + 7]', '[2023, 2023, 6*w^3 - 19*w^2 - 15*w + 24]', '[2023, 2023, -5*w^3 + 14*w^2 + 18*w - 14]', '[2023, 2023, 3*w^3 - 10*w^2 - 7*w + 8]', '[2039, 2039, -w^3 + 5*w^2 + w - 17]', '[2039, 2039, 2*w^3 - 9*w^2 - 2*w + 26]', '[2039, 2039, -5*w^3 + 17*w^2 + 13*w - 23]', '[2039, 2039, -5*w^3 + 17*w^2 + 15*w - 37]', '[2044, 1022, w^3 - w^2 - 11*w + 4]', '[2044, 1022, 2*w^3 - 7*w^2 - 7*w + 23]', '[2044, 1022, 4*w^3 - 15*w^2 - 3*w + 21]', '[2044, 1022, 3*w^3 - 10*w^2 - 6*w + 7]', '[2063, 2063, 4*w^3 - 14*w^2 - 8*w + 29]', '[2063, 2063, 2*w^2 - 4*w - 1]', '[2081, 2081, w^3 - 3*w^2 + 2*w - 1]', '[2081, 2081, 6*w^3 - 18*w^2 - 23*w + 24]', '[2084, 1042, -4*w^3 + 11*w^2 + 11*w - 9]', '[2084, 1042, -3*w^3 + 7*w^2 + 13*w - 8]', '[2087, 2087, -6*w^3 + 19*w^2 + 14*w - 20]', '[2087, 2087, 2*w^2 - 6*w - 1]', '[2087, 2087, -2*w^3 + 8*w^2 - 19]', '[2087, 2087, 6*w^3 - 17*w^2 - 22*w + 15]', '[2097, 699, w^3 - 3*w^2 - 2*w - 4]', '[2097, 699, -8*w^3 + 21*w^2 + 34*w - 19]', '[2108, 1054, 2*w^3 - 7*w^2 - w + 19]', '[2108, 1054, -3*w^3 + 8*w^2 + 12*w - 15]', '[2108, 1054, -9*w^3 + 30*w^2 + 24*w - 55]', '[2108, 1054, 4*w^3 - 13*w^2 - 9*w + 25]', '[2108, 1054, -5*w^3 + 18*w^2 + 10*w - 39]', '[2108, 1054, -3*w^3 + 8*w^2 + 14*w - 19]', '[2111, 2111, -4*w^3 + 15*w^2 + 4*w - 27]', '[2111, 2111, -6*w^3 + 20*w^2 + 15*w - 37]', '[2113, 2113, 6*w^3 - 19*w^2 - 14*w + 27]', '[2113, 2113, -6*w^3 + 18*w^2 + 16*w - 19]', '[2116, 46, -5*w^3 + 15*w^2 + 15*w - 18]', '[2116, 46, 5*w^3 - 15*w^2 - 15*w + 22]', '[2116, 1058, 3*w^3 - 9*w^2 - 13*w + 16]', '[2116, 1058, w^3 - 3*w^2 - 7*w + 4]', '[2129, 2129, -2*w^3 + 5*w^2 + 5*w - 2]', '[2129, 2129, 5*w^3 - 18*w^2 - 10*w + 38]', '[2129, 2129, 7*w^3 - 22*w^2 - 22*w + 32]', '[2129, 2129, -7*w^3 + 24*w^2 + 17*w - 46]', '[2137, 2137, 4*w^3 - 15*w^2 - 8*w + 25]', '[2137, 2137, -4*w^3 + 15*w^2 + 8*w - 30]', '[2153, 2153, -3*w^3 + 8*w^2 + 14*w - 16]', '[2153, 2153, 2*w^3 - 7*w^2 - w + 16]', '[2161, 2161, -2*w^2 + 4*w - 3]', '[2161, 2161, -2*w^3 + 7*w^2 + 4*w - 19]', '[2161, 2161, -w^2 + 2*w - 4]', '[2161, 2161, -4*w^3 + 14*w^2 + 8*w - 33]', '[2169, 723, w^3 - 8*w^2 + 9*w + 22]', '[2169, 723, 5*w^3 - 10*w^2 - 30*w + 2]', '[2177, 2177, 5*w^3 - 16*w^2 - 12*w + 28]', '[2177, 2177, w^3 - 5*w]', '[2177, 2177, -11*w^3 + 36*w^2 + 31*w - 65]', '[2177, 2177, -4*w^3 + 11*w^2 + 15*w - 18]', '[2191, 2191, w^3 - 8*w^2 - 2*w + 14]', '[2191, 2191, 18*w^3 - 59*w^2 - 53*w + 106]', '[2191, 2191, -7*w^3 + 24*w^2 + 19*w - 42]', '[2191, 2191, -3*w^3 + 12*w^2 + 7*w - 23]', '[2192, 274, 2*w^3 - 4*w^2 - 10*w + 4]', '[2192, 274, 4*w^3 - 14*w^2 - 6*w + 24]', '[2192, 274, -6*w^3 + 20*w^2 + 14*w - 34]', '[2192, 274, -2*w^3 + 4*w^2 + 12*w - 4]', '[2201, 2201, w^3 - 6*w^2 + 6*w + 8]', '[2201, 2201, 2*w^3 - 8*w^2 - 5*w + 20]', '[2201, 2201, -5*w^3 + 17*w^2 + 14*w - 25]', '[2201, 2201, -8*w^3 + 26*w^2 + 21*w - 34]', '[2207, 2207, -2*w^3 + 9*w^2 - 9]', '[2207, 2207, 7*w^3 - 23*w^2 - 18*w + 30]', '[2209, 47, -w^3 + 3*w^2 + 3*w - 11]', '[2209, 47, w^3 - 3*w^2 - 3*w - 3]', '[2212, 1106, -3*w^3 + 9*w^2 + 13*w - 14]', '[2212, 1106, -5*w^3 + 18*w^2 + 12*w - 35]', '[2212, 1106, -4*w^3 + 15*w^2 + 9*w - 25]', '[2212, 1106, -w^3 + 3*w^2 + 7*w - 6]', '[2231, 2231, -8*w^3 + 27*w^2 + 20*w - 40]', '[2231, 2231, 3*w^2 - 4*w - 15]', '[2231, 2231, 8*w^3 - 25*w^2 - 26*w + 38]', '[2231, 2231, -2*w^3 + 5*w^2 + 4*w - 3]', '[2239, 2239, -5*w^3 + 18*w^2 + 11*w - 30]', '[2239, 2239, 3*w^3 - 12*w^2 - 5*w + 25]', '[2263, 2263, -9*w^3 + 28*w^2 + 28*w - 46]', '[2263, 2263, 2*w^2 - 7*w - 4]', '[2263, 2263, -w^3 + 5*w^2 - 4*w - 11]', '[2263, 2263, -3*w^3 + 10*w^2 + 8*w - 8]', '[2268, 42, -3*w^3 + 12*w^2 + 6*w - 21]', '[2268, 42, 6*w^3 - 21*w^2 - 15*w + 39]', '[2273, 2273, -5*w^3 + 16*w^2 + 10*w - 18]', '[2273, 2273, -6*w^3 + 17*w^2 + 23*w - 18]', '[2281, 2281, -w^3 + 3*w^2 + 7*w - 5]', '[2281, 2281, -3*w^3 + 9*w^2 + 13*w - 15]', '[2287, 2287, -5*w^3 + 18*w^2 + 12*w - 30]', '[2287, 2287, 6*w^3 - 18*w^2 - 19*w + 22]', '[2287, 2287, -4*w^3 + 15*w^2 + 9*w - 30]', '[2287, 2287, 5*w^3 - 15*w^2 - 14*w + 17]', '[2304, 12, 4*w^3 - 16*w^2 - 4*w + 36]', '[2313, 771, -4*w^3 + 8*w^2 + 21*w + 11]', '[2313, 771, 2*w^3 - 3*w^2 - 16*w + 1]', '[2313, 771, 8*w^3 - 22*w^2 - 30*w + 17]', '[2313, 771, w^3 - 9*w^2 + 10*w + 32]', '[2329, 2329, 2*w^3 - 6*w^2 - 10*w + 11]', '[2329, 2329, 7*w^3 - 25*w^2 - 14*w + 38]', '[2329, 2329, 2*w^3 - 10*w^2 + w + 27]', '[2329, 2329, -6*w^3 + 18*w^2 + 23*w - 31]', '[2329, 2329, 4*w^3 - 16*w^2 - 6*w + 37]', '[2329, 2329, w^3 - w^2 - 10*w - 2]', '[2329, 2329, 2*w^3 - 6*w^2 - 10*w + 9]', '[2329, 2329, -w^3 + 7*w^2 - 2*w - 20]', '[2329, 2329, -w^2 + 6*w + 6]', '[2329, 2329, -2*w^3 + 5*w^2 + 12*w - 11]', '[2329, 2329, -10*w^3 + 34*w^2 + 25*w - 55]', '[2329, 2329, -6*w^3 + 23*w^2 + 10*w - 51]', '[2351, 2351, 6*w^3 - 21*w^2 - 10*w + 33]', '[2351, 2351, -6*w^3 + 20*w^2 + 15*w - 39]', '[2359, 2359, -5*w^3 + 18*w^2 + 9*w - 21]', '[2359, 2359, w^3 - 2*w^2 - 7*w - 7]', '[2359, 2359, w^3 - 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3*w + 7]', '[2401, 2401, 2*w^3 - 6*w^2 - 8*w + 17]', '[2401, 2401, 2*w + 7]', '[2404, 1202, 2*w^3 - 5*w^2 - 7*w + 13]', '[2404, 1202, 5*w^3 - 16*w^2 - 14*w + 33]', '[2417, 2417, -3*w^3 + 8*w^2 + 13*w - 15]', '[2417, 2417, 3*w^3 - 10*w^2 - 5*w + 20]', '[2423, 2423, -5*w^3 + 17*w^2 + 11*w - 31]', '[2423, 2423, 3*w^3 - 9*w^2 - 6*w + 8]', '[2423, 2423, -w^3 + w^2 + 7*w - 1]', '[2423, 2423, -6*w^3 + 18*w^2 + 21*w - 23]', '[2428, 1214, -5*w^3 + 14*w^2 + 18*w - 17]', '[2428, 1214, 6*w^3 - 19*w^2 - 15*w + 27]', '[2439, 813, -2*w^3 + 10*w^2 - 3*w - 29]', '[2439, 813, -8*w^3 + 28*w^2 + 18*w - 53]', '[2439, 813, 5*w^3 - 13*w^2 - 24*w + 20]', '[2439, 813, -2*w^3 + 8*w^2 + 5*w - 27]', '[2441, 2441, -3*w^3 + 11*w^2 + 8*w - 27]', '[2441, 2441, -4*w^3 + 14*w^2 + 11*w - 18]', '[2448, 102, 2*w^3 - 6*w^2 - 10*w + 10]', '[2448, 102, -8*w^3 + 26*w^2 + 20*w - 36]', '[2448, 102, -4*w^3 + 10*w^2 + 16*w - 6]', '[2449, 2449, -6*w^3 + 22*w^2 + 11*w - 41]', '[2449, 2449, 3*w^3 - 11*w^2 - w + 19]', '[2449, 2449, -3*w^3 + 7*w^2 + 17*w - 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29*w + 64]', '[2788, 1394, -3*w^3 + 12*w^2 + 2*w - 11]', '[2788, 1394, 7*w^3 - 22*w^2 - 20*w + 33]', '[2788, 1394, -5*w^3 + 18*w^2 + 12*w - 31]', '[2788, 1394, -4*w^3 + 11*w^2 + 11*w - 15]', '[2788, 1394, -w^3 + 5*w^2 - 7*w + 2]', '[2791, 2791, -7*w^3 + 22*w^2 + 20*w - 32]', '[2791, 2791, -4*w^3 + 11*w^2 + 13*w - 12]', '[2799, 933, -3*w^3 + 13*w^2 + 2*w - 31]', '[2799, 933, -6*w^3 + 17*w^2 + 25*w - 26]', '[2801, 2801, -9*w^3 + 30*w^2 + 25*w - 48]', '[2801, 2801, 3*w^3 - 12*w^2 - w + 25]', '[2801, 2801, 7*w^3 - 23*w^2 - 18*w + 41]', '[2801, 2801, -7*w^3 + 25*w^2 + 14*w - 47]', '[2807, 2807, -6*w^3 + 17*w^2 + 14*w - 28]', '[2807, 2807, -5*w^3 + 13*w^2 + 17*w - 21]', '[2807, 2807, 11*w^3 - 35*w^2 - 31*w + 61]', '[2807, 2807, 14*w^3 - 43*w^2 - 46*w + 73]', '[2809, 53, -2*w^3 + 7*w^2 - 10]', '[2809, 53, 4*w^3 - 11*w^2 - 18*w + 15]', '[2817, 939, 11*w^3 - 33*w^2 - 40*w + 55]', '[2817, 939, -2*w^3 + 3*w^2 + 13*w + 2]', '[2833, 2833, 6*w^3 - 18*w^2 - 19*w + 23]', '[2833, 2833, -5*w^3 + 15*w^2 + 14*w - 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49]', '[4879, 4879, -6*w^3 + 22*w^2 + 15*w - 36]', '[4879, 4879, -3*w^3 + 8*w^2 + 13*w - 21]', '[4889, 4889, 6*w^3 - 21*w^2 - 11*w + 36]', '[4889, 4889, w^3 - 10*w - 4]', '[4892, 2446, 5*w^3 - 18*w^2 - 6*w + 31]', '[4892, 2446, -w^3 + 7*w^2 - w - 22]', '[4892, 2446, -7*w^3 + 20*w^2 + 26*w - 31]', '[4892, 2446, 2*w^3 - 3*w^2 - 15*w + 1]', '[4903, 4903, -6*w^3 + 17*w^2 + 21*w - 22]', '[4903, 4903, 7*w^3 - 22*w^2 - 18*w + 32]', '[4913, 17, -9*w^3 + 30*w^2 + 23*w - 43]', '[4913, 17, -w^3 + 7*w + 12]', '[4913, 17, 5*w^3 - 18*w^2 - 13*w + 24]', '[4913, 289, -w^3 + 6*w^2 - w - 25]', '[4913, 289, w^3 - 6*w^2 - w + 18]', '[4913, 289, 2*w^3 - 4*w^2 - 11*w + 6]', '[4913, 289, -5*w^3 + 17*w^2 + 10*w - 31]', '[4913, 289, -9*w^3 + 30*w^2 + 25*w - 47]', '[4913, 4913, 3*w^3 - 10*w^2 - 12*w + 24]', '[4913, 4913, -4*w^3 + 13*w^2 + 15*w - 16]', '[4919, 4919, -8*w^3 + 27*w^2 + 20*w - 38]', '[4919, 4919, 3*w^2 - 4*w - 17]', '[4924, 2462, 2*w^3 - 5*w^2 - 11*w - 5]', '[4924, 2462, w^3 - 4*w^2 + 2*w - 5]', '[4932, 822, w^3 - 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22]', '[5167, 5167, 9*w^3 - 31*w^2 - 22*w + 53]', '[5167, 5167, 5*w^3 - 20*w^2 - 7*w + 46]', '[5177, 5177, 7*w^3 - 24*w^2 - 13*w + 38]', '[5177, 5177, -2*w^3 + 4*w^2 + 13*w - 8]', '[5177, 5177, -3*w^3 + 11*w^2 + 2*w - 23]', '[5177, 5177, 3*w^3 - 6*w^2 - 17*w + 3]', '[5183, 5183, -2*w^3 + 7*w^2 + 8*w - 20]', '[5183, 5183, -3*w^3 + 11*w^2 + 3*w - 25]', '[5183, 5183, -w^3 + w^2 + 9*w - 5]', '[5183, 5183, -4*w^3 + 13*w^2 + 14*w - 15]', '[5184, 12, 6*w^3 - 18*w^2 - 18*w + 24]', '[5188, 2594, 2*w^3 - 7*w^2 - 5*w + 3]', '[5188, 2594, -w^3 + 4*w^2 + 2*w - 17]', '[5201, 5201, -6*w^3 + 21*w^2 + 15*w - 28]', '[5201, 5201, 8*w^3 - 26*w^2 - 23*w + 38]', '[5201, 5201, w^3 - w^2 - 4*w - 7]', '[5201, 5201, 3*w^3 - 12*w^2 - 6*w + 32]', '[5209, 5209, -4*w^3 + 13*w^2 + 12*w - 30]', '[5209, 5209, -w^2 - 5]', '[5212, 2606, -7*w^3 + 20*w^2 + 24*w - 29]', '[5212, 2606, -8*w^3 + 25*w^2 + 21*w - 39]', '[5231, 5231, 2*w^3 - 5*w^2 - 6*w - 5]', '[5231, 5231, 6*w^3 - 19*w^2 - 18*w + 20]', '[5233, 5233, 7*w^3 - 25*w^2 - 15*w + 45]', '[5233, 5233, -3*w^3 + 13*w^2 + 3*w - 25]', '[5239, 403, 3*w^3 - 9*w^2 - 14*w + 13]', '[5239, 403, w^3 - 9*w - 18]', '[5239, 403, -2*w^3 + 6*w^2 + 11*w - 12]', '[5239, 403, 9*w^3 - 26*w^2 - 32*w + 30]', '[5257, 5257, -6*w^3 + 18*w^2 + 17*w - 21]', '[5257, 5257, 8*w^3 - 24*w^2 - 26*w + 31]', '[5257, 5257, -6*w^3 + 18*w^2 + 16*w - 21]', '[5257, 5257, 7*w^3 - 21*w^2 - 22*w + 26]', '[5273, 5273, 3*w^3 - 8*w^2 - 8*w + 4]', '[5273, 5273, -8*w^3 + 25*w^2 + 25*w - 34]', '[5276, 2638, 6*w^3 - 23*w^2 - 5*w + 31]', '[5276, 2638, w^3 - 8*w^2 + 10*w + 29]', '[5281, 5281, 9*w^3 - 31*w^2 - 23*w + 57]', '[5281, 5281, -12*w^3 + 39*w^2 + 32*w - 61]', '[5284, 2642, -6*w^3 + 17*w^2 + 21*w - 19]', '[5284, 2642, -7*w^3 + 22*w^2 + 18*w - 29]', '[5287, 5287, -w^3 + 2*w^2 + 5*w - 10]', '[5287, 5287, 3*w^3 - 10*w^2 - 7*w + 25]', '[5287, 5287, 4*w^3 - 9*w^2 - 15*w + 8]', '[5287, 5287, -9*w^3 + 30*w^2 + 26*w - 62]', '[5287, 5287, -7*w^3 + 20*w^2 + 25*w - 26]', '[5287, 5287, -13*w^3 + 42*w^2 + 36*w - 68]', '[5297, 5297, 3*w^3 - 12*w^2 + 26]', '[5297, 5297, 3*w^2 - 9*w - 4]', '[5321, 5321, -w^3 - 2*w^2 + 5*w + 11]', '[5321, 5321, -6*w^3 + 21*w^2 + 17*w - 44]', '[5321, 5321, -5*w^3 + 18*w^2 + 14*w - 26]', '[5321, 5321, 19*w^3 - 62*w^2 - 55*w + 104]', '[5321, 5321, -w^3 + 6*w^2 - 20]', '[5321, 5321, 17*w^3 - 56*w^2 - 51*w + 108]', '[5327, 5327, 12*w^3 - 38*w^2 - 41*w + 61]', '[5327, 5327, -4*w^3 + 15*w^2 + 16*w - 21]', '[5327, 5327, 8*w^3 - 26*w^2 - 25*w + 41]', '[5327, 5327, -4*w^3 + 15*w^2 + 12*w - 21]', '[5327, 5327, -16*w^3 + 52*w^2 + 46*w - 97]', '[5327, 5327, 6*w^3 - 18*w^2 - 15*w + 35]', '[5327, 5327, -8*w^3 + 27*w^2 + 24*w - 54]', '[5327, 5327, w^3 - 5*w^2 - 4*w + 14]', '[5329, 73, -7*w^3 + 21*w^2 + 21*w - 33]', '[5329, 73, 7*w^3 - 21*w^2 - 21*w + 23]', '[5329, 5329, -w^3 + 3*w^2 + 8*w - 6]', '[5329, 5329, 4*w^3 - 12*w^2 - 17*w + 19]', '[5359, 5359, 6*w^3 - 18*w^2 - 15*w + 22]', '[5359, 5359, -w^3 + 11*w + 17]', '[5359, 5359, 5*w^3 - 18*w^2 - 7*w + 18]', '[5359, 5359, -9*w^3 + 27*w^2 + 30*w - 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47*w^2 - 47*w + 74]', '[5572, 2786, -3*w^3 + 10*w^2 + 14*w - 21]', '[5572, 2786, 16*w^3 - 51*w^2 - 53*w + 93]', '[5572, 2786, -8*w^3 + 25*w^2 + 23*w - 35]', '[5596, 2798, 9*w^3 - 29*w^2 - 23*w + 40]', '[5596, 2798, -5*w^3 + 13*w^2 + 19*w - 10]', '[5609, 5609, -5*w^3 + 18*w^2 + 9*w - 37]', '[5609, 5609, -w^3 + 6*w^2 - 3*w - 8]', '[5609, 5609, 8*w^3 - 23*w^2 - 31*w + 36]', '[5609, 5609, -5*w^3 + 16*w^2 + 8*w - 26]', '[5617, 5617, -6*w^3 + 17*w^2 + 20*w - 24]', '[5617, 5617, -4*w^3 + 16*w^2 + 9*w - 27]', '[5617, 5617, 3*w^3 - 13*w^2 - 4*w + 24]', '[5617, 5617, 8*w^3 - 28*w^2 - 19*w + 51]', '[5617, 5617, 7*w^3 - 25*w^2 - 15*w + 41]', '[5617, 5617, -9*w^3 + 31*w^2 + 24*w - 58]', '[5617, 5617, -8*w^3 + 25*w^2 + 22*w - 39]', '[5617, 5617, -3*w^3 + 13*w^2 + 3*w - 29]', '[5623, 5623, -11*w^3 + 38*w^2 + 25*w - 60]', '[5623, 5623, -7*w^3 + 22*w^2 + 17*w - 30]', '[5623, 5623, -7*w^3 + 20*w^2 + 25*w - 25]', '[5623, 5623, -11*w^3 + 34*w^2 + 35*w - 52]', '[5625, 15, -5*w^3 + 20*w^2 + 5*w - 45]', '[5636, 2818, -5*w^3 + 16*w^2 + 16*w - 19]', '[5636, 2818, 3*w^2 - 5*w - 5]', '[5636, 2818, w^2 + w - 11]', '[5636, 2818, -7*w^3 + 24*w^2 + 16*w - 45]', '[5639, 5639, -4*w^3 + 12*w^2 + 8*w - 25]', '[5639, 5639, -8*w^3 + 24*w^2 + 28*w - 45]', '[5641, 5641, -5*w^3 + 13*w^2 + 19*w - 13]', '[5641, 5641, -9*w^3 + 29*w^2 + 23*w - 43]', '[5647, 5647, -7*w^3 + 21*w^2 + 22*w - 31]', '[5647, 5647, 6*w^3 - 18*w^2 - 17*w + 26]', '[5648, 706, -2*w^3 + 4*w^2 + 10*w - 8]', '[5648, 706, 6*w^3 - 20*w^2 - 14*w + 40]', '[5648, 706, 6*w^3 - 20*w^2 - 14*w + 38]', '[5648, 706, -8*w^3 + 28*w^2 + 14*w - 44]', '[5663, 5663, 20*w^3 - 65*w^2 - 58*w + 115]', '[5663, 5663, -2*w^3 + 10*w^2 - 4*w - 29]', '[5663, 5663, -9*w^3 + 29*w^2 + 23*w - 49]', '[5663, 5663, 2*w^3 - 8*w^2 + 3*w + 21]', '[5679, 1893, -6*w^3 + 13*w^2 + 32*w - 4]', '[5679, 1893, -3*w^3 + 7*w^2 + 17*w - 13]', '[5679, 1893, -2*w^3 + 12*w^2 - 8*w - 37]', '[5679, 1893, -8*w^3 + 30*w^2 + 13*w - 61]', '[5689, 5689, -2*w^3 + 6*w^2 + 11*w - 9]', '[5689, 5689, -3*w^3 + 9*w^2 + 14*w - 16]', '[5692, 2846, 7*w^3 - 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22*w^2 - 14*w + 40]', '[9792, 204, 4*w^3 - 14*w^2 - 6*w + 10]', '[9792, 204, 2*w^3 - 4*w^2 - 12*w - 10]', '[9793, 9793, -4*w^3 + 10*w^2 + 21*w - 9]', '[9793, 9793, 4*w^3 - 11*w^2 - 20*w + 22]', '[9793, 9793, w^2 - 8*w - 7]', '[9793, 9793, 3*w^3 - 11*w^2 + 14]', '[9796, 4898, -2*w^3 + 3*w^2 + 17*w - 3]', '[9796, 4898, -5*w^3 + 21*w^2 + 5*w - 36]', '[9796, 4898, -9*w^3 + 33*w^2 + 17*w - 64]', '[9796, 4898, 3*w^3 - 12*w^2 + 2*w + 23]', '[9833, 9833, 7*w^3 - 24*w^2 - 18*w + 30]', '[9833, 9833, 2*w^3 - 9*w^2 - 3*w + 30]', '[9839, 9839, -8*w^3 + 27*w^2 + 18*w - 47]', '[9839, 9839, -2*w^3 + 3*w^2 + 12*w - 2]', '[9839, 9839, 8*w^3 - 28*w^2 - 19*w + 37]', '[9839, 9839, 6*w^3 - 21*w^2 - 16*w + 26]', '[9857, 9857, -w^3 + 9*w + 1]', '[9857, 9857, 7*w^3 - 24*w^2 - 15*w + 44]', '[9863, 9863, -4*w^3 + 10*w^2 + 18*w - 15]', '[9863, 9863, 6*w^3 - 20*w^2 - 12*w + 35]', '[9863, 9863, -11*w^3 + 37*w^2 + 28*w - 68]', '[9863, 9863, -4*w^3 + 16*w^2 + 12*w - 21]', '[9863, 9863, 7*w^3 - 23*w^2 - 22*w + 34]', '[9863, 9863, 2*w^3 - 8*w^2 - 7*w + 21]', '[9863, 9863, -12*w^3 + 40*w^2 + 36*w - 79]', '[9863, 9863, 4*w^2 - 5*w - 7]', '[9871, 9871, -5*w^3 + 22*w^2 + w - 52]', '[9871, 9871, -10*w^3 + 35*w^2 + 25*w - 68]', '[9872, 1234, -8*w^3 + 26*w^2 + 22*w - 32]', '[9872, 1234, 8*w^3 - 26*w^2 - 26*w + 40]', '[9881, 9881, 13*w^3 - 43*w^2 - 38*w + 71]', '[9881, 9881, -11*w^3 + 38*w^2 + 25*w - 68]', '[9881, 9881, -8*w^3 + 25*w^2 + 25*w - 32]', '[9881, 9881, -3*w^3 + 8*w^2 + 8*w - 2]', '[9884, 4942, 5*w^3 - 19*w^2 - 15*w + 28]', '[9884, 4942, 13*w^3 - 44*w^2 - 38*w + 85]', '[9884, 4942, -2*w^3 + 9*w^2 + 7*w - 21]', '[9884, 4942, w^3 - 3*w^2 + w - 6]', '[9884, 4942, -11*w^3 + 36*w^2 + 34*w - 59]', '[9884, 4942, 11*w^3 - 37*w^2 - 33*w + 72]', '[9884, 4942, -3*w^3 + 13*w^2 + 9*w - 28]', '[9884, 4942, -6*w^3 + 19*w^2 + 11*w - 21]', '[9887, 9887, 2*w^3 - 4*w^2 - 8*w - 11]', '[9887, 9887, 8*w^3 - 26*w^2 - 22*w + 29]', '[9913, 9913, -7*w^3 + 27*w^2 + 2*w - 30]', '[9913, 9913, 4*w^3 - 12*w^2 - 18*w + 17]', '[9913, 9913, -9*w^3 + 33*w^2 + 15*w - 53]', '[9913, 9913, 9*w^3 - 27*w^2 - 29*w + 41]', '[9927, 3309, -2*w^3 - 4*w^2 + 29*w + 48]', '[9927, 3309, 16*w^3 - 52*w^2 - 43*w + 78]', '[9927, 3309, 11*w^3 - 34*w^2 - 33*w + 44]', '[9927, 3309, w^3 + 4*w^2 - 18*w - 38]', '[9959, 9959, 4*w^3 - 14*w^2 - 3*w + 27]', '[9959, 9959, 3*w^3 - 9*w^2 - 6*w + 2]', '[9959, 9959, -6*w^3 + 18*w^2 + 21*w - 17]', '[9959, 9959, 3*w^3 - 13*w^2 + w + 17]', '[9959, 9959, 3*w^3 - 13*w^2 + w + 33]', '[9959, 9959, -w^3 + 3*w^2 - w + 9]', '[9959, 9959, 5*w^3 - 15*w^2 - 19*w + 11]', '[9959, 9959, -5*w^3 + 13*w^2 + 24*w - 22]', '[9961, 9961, 10*w^3 - 35*w^2 - 24*w + 56]', '[9961, 9961, -19*w^3 + 63*w^2 + 53*w - 109]', '[9961, 9961, -10*w^3 + 31*w^2 + 30*w - 49]', '[9961, 9961, 24*w^3 - 76*w^2 - 75*w + 129]', '[9967, 9967, -3*w^3 + 11*w^2 - 17]', '[9967, 9967, 4*w^3 - 10*w^2 - 21*w + 12]', '[10000, 10, -10]'], 'label': '4.4.9792.1', 'narrow_class_no': 2, 'primes': ['[4, 2, w^3 - 3*w^2 - 3*w + 4]', '[7, 7, w]', '[7, 7, w^3 - 3*w^2 - 4*w + 5]', '[9, 3, w^3 - 4*w^2 - 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3]', '[809, 809, -2*w^3 + 6*w^2 + 3*w - 12]', '[823, 823, -w^3 + 4*w^2 + 2*w - 2]', '[823, 823, 2*w^3 - 7*w^2 - 5*w + 18]', '[839, 839, 4*w^3 - 13*w^2 - 14*w + 27]', '[839, 839, -7*w^3 + 23*w^2 + 19*w - 41]', '[857, 857, -3*w^3 + 10*w^2 + 9*w - 12]', '[857, 857, -w^3 + 4*w^2 + 3*w - 13]', '[863, 863, 3*w^3 - 11*w^2 - 2*w + 20]', '[863, 863, -2*w^3 + 4*w^2 + 13*w - 5]', '[863, 863, 6*w^3 - 19*w^2 - 18*w + 27]', '[863, 863, -2*w^3 + 5*w^2 + 6*w - 2]', '[881, 881, -3*w^3 + 10*w^2 + 5*w - 17]', '[881, 881, -3*w^3 + 8*w^2 + 13*w - 12]', '[887, 887, -3*w^3 + 9*w^2 + 11*w - 9]', '[887, 887, w^3 - 3*w^2 - w - 1]', '[911, 911, 4*w^3 - 14*w^2 - 10*w + 17]', '[911, 911, 5*w^3 - 17*w^2 - 12*w + 22]', '[919, 919, -4*w^3 + 15*w^2 + 7*w - 30]', '[919, 919, -2*w^2 + 7*w + 2]', '[919, 919, w^3 - 5*w^2 + 4*w + 13]', '[919, 919, 3*w^3 - 12*w^2 - 4*w + 20]', '[929, 929, -4*w^3 + 13*w^2 + 9*w - 22]', '[929, 929, 3*w^3 - 8*w^2 - 12*w + 12]', '[961, 31, 4*w^3 - 12*w^2 - 12*w + 17]', '[967, 967, -2*w^3 + 6*w^2 + 7*w - 2]', '[967, 967, -3*w^3 + 8*w^2 + 15*w - 6]', '[967, 967, w^3 - 2*w^2 - 5*w - 6]', '[967, 967, 7*w^3 - 22*w^2 - 21*w + 36]', '[983, 983, 5*w^3 - 17*w^2 - 13*w + 25]', '[983, 983, w^3 - 5*w^2 - w + 15]', '[991, 991, -6*w^3 + 21*w^2 + 13*w - 34]', '[991, 991, 7*w^3 - 22*w^2 - 21*w + 33]', '[1009, 1009, w^2 - 2*w + 3]', '[1009, 1009, -2*w^3 + 7*w^2 + 4*w - 18]', '[1031, 1031, -4*w^3 + 15*w^2 + 4*w - 26]', '[1031, 1031, 3*w^2 - 8*w - 9]', '[1033, 1033, 2*w^3 - 4*w^2 - 13*w + 3]', '[1033, 1033, -5*w^3 + 15*w^2 + 19*w - 23]', '[1033, 1033, w^3 - w^2 - 8*w - 10]', '[1033, 1033, 4*w^3 - 14*w^2 - 7*w + 15]', '[1049, 1049, -7*w^3 + 24*w^2 + 16*w - 34]', '[1049, 1049, -5*w^3 + 16*w^2 + 18*w - 24]', '[1063, 1063, w^3 - 4*w^2 + 2*w + 8]', '[1063, 1063, w^3 - 2*w^2 - 4*w - 8]', '[1063, 1063, 7*w^3 - 24*w^2 - 17*w + 39]', '[1063, 1063, w^3 - 2*w^2 - 7*w - 6]', '[1103, 1103, w^3 - 5*w^2 + 3*w + 17]', '[1103, 1103, -w^3 + 5*w^2 - 3*w - 3]', '[1103, 1103, -w^3 + 5*w^2 - 2*w - 6]', '[1103, 1103, -2*w^3 + 8*w^2 + w - 19]', '[1129, 1129, -6*w^3 + 18*w^2 + 20*w - 27]', '[1129, 1129, -4*w^3 + 12*w^2 + 10*w - 17]', '[1151, 1151, w^3 - w^2 - 7*w - 1]', '[1151, 1151, 5*w^3 - 17*w^2 - 11*w + 29]', '[1153, 1153, -2*w^3 + 8*w^2 + 3*w - 23]', '[1153, 1153, -6*w^3 + 18*w^2 + 20*w - 25]', '[1193, 1193, -2*w^3 + 5*w^2 + 9*w - 10]', '[1193, 1193, 3*w^3 - 10*w^2 - 6*w + 20]', '[1201, 1201, 6*w^3 - 19*w^2 - 16*w + 24]', '[1201, 1201, 4*w^3 - 11*w^2 - 14*w + 9]', '[1217, 1217, 7*w^3 - 22*w^2 - 21*w + 30]', '[1217, 1217, 7*w^3 - 23*w^2 - 18*w + 39]', '[1223, 1223, -2*w^3 + 9*w^2 - 15]', '[1223, 1223, -3*w^3 + 9*w^2 + 13*w - 9]', '[1223, 1223, -5*w^3 + 17*w^2 + 12*w - 34]', '[1223, 1223, 4*w^3 - 15*w^2 - 6*w + 30]', '[1231, 1231, -3*w^3 + 7*w^2 + 12*w - 3]', '[1231, 1231, -8*w^3 + 26*w^2 + 21*w - 38]', '[1289, 1289, -4*w^3 + 14*w^2 + 7*w - 24]', '[1289, 1289, -w^3 + w^2 + 8*w + 1]', '[1297, 1297, -4*w^3 + 12*w^2 + 11*w - 15]', '[1297, 1297, -5*w^3 + 15*w^2 + 16*w - 20]', '[1303, 1303, -3*w^3 + 10*w^2 + 7*w - 23]', '[1303, 1303, -w^3 + 2*w^2 + 5*w - 8]', '[1319, 1319, -8*w^3 + 28*w^2 + 15*w - 43]', '[1319, 1319, w^3 + w^2 - 12*w - 12]', '[1321, 1321, w^2 - 2*w - 10]', '[1321, 1321, 2*w^3 - 7*w^2 - 4*w + 5]', '[1367, 1367, -5*w^3 + 17*w^2 + 14*w - 26]', '[1367, 1367, 2*w^3 - 8*w^2 - 5*w + 19]', '[1399, 1399, -2*w^3 + 7*w^2 + 3*w - 4]', '[1399, 1399, w^3 - 2*w^2 - 6*w - 6]', '[1409, 1409, w^3 - 2*w^2 - 3*w - 3]', '[1409, 1409, 3*w^3 - 10*w^2 - 5*w + 18]', '[1409, 1409, -5*w^3 + 16*w^2 + 15*w - 22]', '[1409, 1409, -3*w^3 + 8*w^2 + 13*w - 13]', '[1423, 1423, 7*w^3 - 24*w^2 - 18*w + 44]', '[1423, 1423, -8*w^3 + 26*w^2 + 21*w - 40]', '[1433, 1433, -7*w^3 + 24*w^2 + 17*w - 45]', '[1433, 1433, -3*w^3 + 12*w^2 + 3*w - 29]', '[1439, 1439, -2*w^3 + 6*w^2 + 4*w - 3]', '[1439, 1439, -4*w^3 + 12*w^2 + 14*w - 13]', '[1471, 1471, -w - 6]', '[1471, 1471, -w^3 + 3*w^2 + 4*w - 11]', '[1471, 1471, w^3 - 2*w^2 - 8*w + 4]', '[1471, 1471, w^2 - 5*w - 4]', '[1489, 1489, -2*w^3 + 9*w^2 + 2*w - 17]', '[1489, 1489, -6*w^3 + 21*w^2 + 14*w - 38]', '[1543, 1543, -7*w^3 + 24*w^2 + 19*w - 45]', '[1543, 1543, 2*w^3 - 3*w^2 - 15*w - 4]', '[1543, 1543, -5*w^3 + 18*w^2 + 6*w - 26]', '[1543, 1543, -3*w^3 + 12*w^2 + 7*w - 20]', '[1553, 1553, -4*w^3 + 14*w^2 + 11*w - 20]', '[1553, 1553, -3*w^3 + 11*w^2 + 8*w - 25]', '[1559, 1559, 2*w^2 - 4*w - 3]', '[1559, 1559, 4*w^3 - 14*w^2 - 8*w + 27]', '[1567, 1567, -4*w^3 + 15*w^2 + 3*w - 20]', '[1567, 1567, w^3 - 12*w - 10]', '[1601, 1601, -3*w^3 + 10*w^2 + 10*w - 12]', '[1601, 1601, 2*w^3 - 7*w^2 - 7*w + 18]', '[1607, 1607, -7*w^3 + 23*w^2 + 20*w - 36]', '[1607, 1607, -6*w^3 + 19*w^2 + 18*w - 26]', '[1607, 1607, 2*w^2 - w - 9]', '[1607, 1607, -2*w^3 + 5*w^2 + 6*w - 1]', '[1609, 1609, -4*w^3 + 15*w^2 + 8*w - 24]', '[1609, 1609, 4*w^3 - 15*w^2 - 8*w + 31]', '[1663, 1663, -6*w^3 + 19*w^2 + 13*w - 26]', '[1663, 1663, -7*w^3 + 20*w^2 + 26*w - 26]', '[1681, 41, -5*w^3 + 15*w^2 + 15*w - 17]', '[1697, 1697, -w^3 + 9*w + 6]', '[1697, 1697, -7*w^3 + 24*w^2 + 15*w - 39]', '[1721, 1721, -5*w^3 + 18*w^2 + 13*w - 38]', '[1721, 1721, -w^3 + 6*w^2 - 5*w - 20]', '[1721, 1721, -w^3 + w^2 + 6*w + 11]', '[1721, 1721, 6*w^3 - 20*w^2 - 15*w + 24]', '[1753, 1753, -3*w^3 + 9*w^2 + 13*w - 17]', '[1753, 1753, w^3 - 3*w^2 - 7*w + 3]', '[1753, 1753, -6*w^3 + 22*w^2 + 12*w - 45]', '[1753, 1753, -6*w^3 + 21*w^2 + 16*w - 40]', '[1759, 1759, -2*w^3 + 6*w^2 + w - 8]', '[1759, 1759, 7*w^3 - 21*w^2 - 26*w + 33]', '[1759, 1759, -3*w^3 + 10*w^2 + 10*w - 26]', '[1759, 1759, -5*w^3 + 17*w^2 + 12*w - 37]', '[1783, 1783, -5*w^3 + 18*w^2 + 11*w - 29]', '[1783, 1783, 4*w^3 - 15*w^2 - 7*w + 26]', '[1783, 1783, 3*w^3 - 12*w^2 - 5*w + 26]', '[1783, 1783, -3*w^3 + 12*w^2 + 4*w - 24]', '[1801, 1801, 8*w^3 - 24*w^2 - 27*w + 33]', '[1801, 1801, 4*w^3 - 12*w^2 - 16*w + 19]', '[1801, 1801, 4*w - 1]', '[1801, 1801, 7*w^3 - 21*w^2 - 23*w + 33]', '[1831, 1831, w^3 - 2*w^2 - 8*w + 2]', '[1831, 1831, w^2 - 5*w - 2]', '[1847, 1847, 6*w^3 - 20*w^2 - 15*w + 25]', '[1847, 1847, w^3 - w^2 - 6*w - 10]', '[1849, 43, -6*w^3 + 21*w^2 + 14*w - 37]', '[1849, 43, -2*w^3 + 9*w^2 + 2*w - 18]', '[1871, 1871, -4*w^3 + 13*w^2 + 8*w - 22]', '[1871, 1871, 4*w^3 - 13*w^2 - 12*w + 15]', '[1871, 1871, 4*w^3 - 11*w^2 - 16*w + 17]', '[1871, 1871, w^2 - 10]', '[1873, 1873, -w^3 + 5*w^2 - 20]', '[1873, 1873, -4*w^3 + 14*w^2 + 9*w - 15]', '[1913, 1913, -2*w^3 + 6*w^2 + 3*w - 4]', '[1913, 1913, 5*w^3 - 15*w^2 - 18*w + 19]', '[1913, 1913, 6*w^3 - 20*w^2 - 11*w + 30]', '[1913, 1913, 9*w^3 - 30*w^2 - 23*w + 45]', '[1993, 1993, -8*w^3 + 28*w^2 + 17*w - 43]', '[1993, 1993, 4*w^3 - 13*w^2 - 16*w + 19]', '[1993, 1993, -6*w^3 + 21*w^2 + 14*w - 36]', '[1993, 1993, -2*w^3 + 9*w^2 + 2*w - 19]', '[1999, 1999, -7*w^3 + 22*w^2 + 20*w - 30]', '[1999, 1999, 4*w^3 - 11*w^2 - 13*w + 10]']}
• 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': [7, 2, -7, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 9792, 'disc_rad': 102, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 1]]], [7, [[2, 1], [1, 2]]], [11, [[4, 1]]], [13, [[2, 2]]], [17, [0]], [19, [[2, 2]]], [23, [[2, 1], [1, 2]]], [29, [[4, 1]]], [31, [[2, 1], [1, 2]]], [37, [[4, 1]]], [41, [[2, 1], [1, 2]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 20.199009876724155, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.9792.1', 'local_algs': ['2.4.6.1', '3.4.2.2', '17.1.0.1', '17.1.0.1', '17.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 17], 'rd': 9.94758940723, 'regulator': {'__RealLiteral__': 0, 'data': '4.9482532611', 'prec': 40}, 'res': {'gal': ['-36,144,-114,-108,91,26,-19,-2,1'], 'sib': ['-2,10,-7,-1,1', '-36,144,-114,-108,91,26,-19,-2,1']}, 'subfield_mults': [1], 'subfields': ['-2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} - 3 a^{2} - 3 a + 3 \\)', '\\( a + 1 \\)', '\\( a^{2} - 2 a - 5 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}