Hilbert modular form data - 4.4.8468.1-16.3-e

Formats: - HTML - YAML - JSON - 2024-06-04T13:21:06.131754

• 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': 2, 'disc': 8468, 'field_bad_primes': [2, 29, 73], 'field_label': '4.4.8468.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.8468.1-16.3-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [2], 'level_ideal': '[16, 4, w^3 - w^2 - 3*w + 1]', 'level_label': '16.3', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.3-e', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, w - 1]', 1]], 'hecke_eigenvalues': ['e', 0, 2, 4, '-4*e + 6', '-4*e', '4*e', '4*e - 4', '-4*e + 8', '2*e - 6', '4*e', '-8*e + 8', 4, '-4*e + 4', '4*e - 4', '2*e + 2', '-4*e + 12', '-2*e - 10', '8*e - 14', '4*e - 12', '-4*e', '8*e - 4', -14, '-4*e + 16', '2*e + 6', 4, -8, '-4*e + 8', '-2*e + 10', 2, '-4*e + 10', -2, '-6*e - 2', '-2*e - 2', '4*e + 8', '-8*e + 8', 20, '12*e - 8', -16, -4, '-8*e + 20', '-10*e + 10', '4*e - 16', '-8*e + 8', '-4*e + 20', -18, '16*e - 20', '4*e - 4', '-4*e - 8', '4*e + 8', '-12*e + 20', '-12*e + 20', '4*e - 8', '8*e - 12', '8*e - 20', '-8*e + 2', '12*e - 10', '-4*e + 16', '2*e + 6', '4*e + 12', '-20*e + 16', '4*e - 8', '4*e - 12', '-12*e - 4', '-4*e + 20', '-4*e + 32', '-24*e + 24', '-4*e + 16', '10*e + 6', '20*e - 12', '-10*e + 14', '8*e - 34', -22, '-12*e + 24', '-12*e + 16', '20*e - 24', '-8*e + 6', '-8*e - 4', '-8*e + 6', '-6*e - 14', -14, '-12*e - 8', '8*e - 6', '20*e - 30', '-4*e + 28', '-12*e - 10', '12*e + 4', '12*e - 6', '-12*e + 20', 6, '8*e - 12', '8*e + 20', '2*e - 18', '16*e - 26', '-4*e - 8', '12*e - 24', '-20*e + 12', '-8*e + 16', '-10*e - 6', '-8*e - 4', '-16*e + 22', '-16*e + 2', '-12*e - 16', '20*e - 8', '12*e - 32', '-8*e + 20', '24*e - 36', '-8*e - 20', '-24*e + 22', '20*e - 20', '20*e', '4*e - 28', '-8*e + 16', '18*e - 6', 34, '-2*e + 2', '-10*e + 6', -22, '-8*e - 4', '4*e + 20', '-12*e + 20', '-16*e + 8', -16, '-8*e + 34', '8*e - 16', -4, '16*e - 6', '4*e - 4', -28, '18*e - 34', '-8*e - 20', '16*e - 22', '4*e - 16', '-12*e + 36', 12, 0, '-4*e + 46', '16*e + 8', '-16*e + 24', '26*e - 38', '16*e - 36', '-12*e + 48', '-8*e - 6', '24*e - 20', '-8*e + 42', '14*e + 14', -14, '16*e + 6', '-18*e + 30', '8*e - 48', '4*e + 28', '8*e - 10', '8*e - 44', '8*e - 16', '20*e - 34', '-4*e + 34', '-12*e - 8', '-10*e + 38', '10*e + 6', '12*e - 44', '16*e - 38', '20*e - 36', '-12*e + 8', '-12*e + 8', '-8*e - 20', '20*e - 22', '-32*e + 46', '16*e - 4', '32*e - 26'], 'hecke_polynomial': 'x^2 - 2*x - 1', 'label': '4.4.8468.1-16.3-e'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 8468, 'ideals': ['[1, 1, 1]', '[2, 2, w^3 - 4*w - 2]', '[2, 2, w - 1]', '[4, 2, w^2 - w - 2]', '[4, 2, -w^2 + 3]', '[4, 4, -w]', '[8, 2, w^3 - 5*w - 2]', '[8, 2, -w^3 + w^2 + 3*w - 3]', '[8, 4, -w^3 + w^2 + 4*w - 4]', '[8, 8, w^2 - 2*w]', '[11, 11, -w^3 + 5*w + 1]', '[16, 2, 2]', '[16, 4, w^3 - 3*w]', '[16, 4, w^3 - w^2 - 3*w + 1]', '[16, 8, w^2 - w - 4]', '[16, 16, w^3 - 4*w]', '[17, 17, -w^3 + 3*w + 1]', '[22, 22, -w^3 + w^2 + 3*w - 2]', '[22, 22, -w + 3]', '[23, 23, w^3 + w^2 - 4*w - 5]', '[29, 29, -w^3 + w^2 + 2*w - 1]', '[29, 29, w^3 + w^2 - 6*w - 5]', '[29, 29, w^3 - w^2 - 4*w + 1]', '[32, 4, -2*w^3 + 8*w + 4]', '[32, 4, -w^3 - w^2 + 5*w + 3]', '[32, 4, -2*w + 2]', '[32, 8, w^3 - 2*w^2 - 3*w + 4]', '[32, 16, w^2 + w - 4]', '[32, 32, w^3 - w^2 - 5*w + 4]', '[34, 34, w^3 - 2*w^2 - 4*w + 5]', '[34, 34, -w^3 + 2*w^2 + 2*w - 2]', '[44, 22, w^3 + w^2 - 4*w - 2]', '[44, 22, w^2 - 2*w - 3]', '[44, 44, w^3 - 4*w - 4]', '[46, 46, w^2 - 6]', '[46, 46, w^3 - 4*w + 1]', '[47, 47, w^3 - 3*w - 3]', '[53, 53, 2*w^2 - 2*w - 5]', '[53, 53, -w^3 + 2*w^2 + 5*w - 7]', '[58, 58, w + 3]', '[58, 58, -w^3 + w^2 + 5*w - 2]', '[58, 58, -w^3 + 2*w^2 + 2*w - 5]', '[58, 58, -2*w^3 + 9*w + 2]', '[58, 58, -2*w^2 + w + 7]', '[58, 58, w^3 - 4*w + 2]', '[59, 59, 2*w^3 - 8*w - 3]', '[59, 59, w^3 - w^2 - 2*w + 3]', '[64, 4, -2*w^2 + 2*w + 4]', '[64, 4, w^3 - w^2 - 5*w + 3]', '[64, 4, 2*w^2 - 6]', '[64, 8, 2*w]', '[64, 16, -w^3 + 3*w + 4]', '[64, 32, -w^3 + w^2 + 4*w]', '[64, 64, -w^3 - w^2 + 3*w + 4]', '[67, 67, 2*w - 1]', '[68, 34, w^2 + 2*w - 1]', '[68, 34, -w^3 - w^2 + 4*w + 6]', '[68, 68, -w^3 + w^2 + 5*w]', '[71, 71, 2*w^2 - 5]', '[73, 73, -w^3 + w^2 + 4*w + 1]', '[73, 73, -2*w^3 + 8*w + 1]', '[73, 73, -w^3 + 5*w - 1]', '[79, 79, w^2 - w + 1]', '[79, 79, w^3 + w^2 - 4*w - 7]', '[81, 3, -3]', '[83, 83, 2*w^3 + w^2 - 9*w - 5]', '[83, 83, w^2 + w - 5]', '[88, 22, w^3 - 3*w^2 - 3*w + 9]', '[88, 22, -w^3 + 2*w^2 + 5*w - 6]', '[88, 44, w^2 - 3*w]', '[88, 88, 2*w^2 - w - 4]', '[92, 46, -w^3 - w^2 + 6*w + 6]', '[92, 46, -2*w^3 - w^2 + 10*w + 5]', '[92, 92, -w^3 + 3*w^2 + 3*w - 8]', '[94, 94, 2*w^2 - 3*w - 1]', '[94, 94, -4*w^3 + 17*w + 10]', '[97, 97, 4*w^3 + w^2 - 19*w - 11]', '[97, 97, -2*w^3 + 3*w^2 + 7*w - 7]', '[101, 101, -w^3 + 2*w^2 + 3*w - 3]', '[103, 103, w^3 + w^2 - 4*w - 1]', '[103, 103, -2*w^3 + w^2 + 7*w - 5]', '[106, 106, -3*w^3 - 2*w^2 + 16*w + 10]', '[106, 106, 2*w^2 - w - 6]', '[106, 106, 2*w^3 - 4*w^2 - 3*w + 5]', '[106, 106, w^3 - 6*w + 1]', '[109, 109, w^3 - w^2 - 2*w - 3]', '[113, 113, 2*w^2 - 9]', '[116, 58, w^2 + 2*w - 3]', '[116, 58, -w^2 - w + 6]', '[116, 58, 2*w^3 + w^2 - 8*w - 7]', '[116, 58, w^3 - w^2 - 4*w + 6]', '[116, 58, w^2 + 1]', '[116, 58, -w^3 - w^2 + 6*w + 2]', '[116, 116, -2*w^3 + w^2 + 6*w - 4]', '[116, 116, -w^3 + 2*w^2 + 4*w - 4]', '[116, 116, -w^2 + 2*w + 4]', '[118, 118, -w^2 - 2*w + 2]', '[118, 118, 2*w^2 - 3*w - 5]', '[118, 118, 2*w^2 - w - 5]', '[118, 118, w^3 + w^2 - 5*w - 2]', '[121, 121, -w^3 - w^2 + 6*w + 7]', '[128, 4, -2*w^3 + 10*w + 4]', '[128, 4, 2*w^3 - 2*w^2 - 6*w + 6]', '[128, 8, 2*w^3 - 2*w^2 - 8*w + 8]', '[128, 8, -w^3 + w^2 + 5*w + 1]', '[128, 16, -2*w^2 + 4*w]', '[128, 32, w^3 - 2*w^2 - w + 4]', '[128, 64, -w^3 - w^2 + 4*w]', '[128, 128, -w + 4]', '[131, 131, -2*w^2 + 2*w + 7]', '[134, 134, 2*w^2 - 3*w + 1]', '[134, 134, w^3 + 2*w^2 - 6*w - 6]', '[136, 34, -w^3 + 5*w - 2]', '[136, 34, w^3 + w^2 - 3*w + 1]', '[136, 68, w^3 - w^2 - 2*w + 4]', '[136, 136, -2*w^3 + 2*w^2 + 7*w - 4]', '[137, 137, -2*w^3 + w^2 + 9*w - 3]', '[137, 137, 2*w^3 - w^2 - 9*w - 1]', '[142, 142, 2*w^3 - 2*w^2 - 5*w + 5]', '[142, 142, -w^3 + 6*w + 2]', '[146, 146, w^3 - 2*w^2 + 3]', '[146, 146, -2*w^2 - w + 7]', '[146, 146, -3*w + 5]', '[146, 146, 5*w^3 + w^2 - 21*w - 14]', '[146, 146, 5*w^3 + 2*w^2 - 24*w - 18]', '[146, 146, 2*w^3 + 2*w^2 - 11*w - 10]', '[149, 149, 2*w^3 - w^2 - 7*w - 1]', '[157, 157, w^3 - 5*w + 3]', '[158, 158, w^3 - 2*w^2 + 2*w - 1]', '[158, 158, -w^3 + 6*w - 3]', '[158, 158, 2*w^3 - w^2 - 6*w - 2]', '[158, 158, w^3 - 2*w^2 - 2*w + 6]', '[162, 6, -3*w^3 + 12*w + 6]', '[162, 6, -3*w + 3]', '[163, 163, -w^3 + 3*w^2 + 4*w - 7]', '[166, 166, -2*w^2 - w + 2]', '[166, 166, w^3 - 6*w + 5]', '[166, 166, w^3 - 2*w - 3]', '[166, 166, -2*w^3 + w^2 + 8*w + 2]', '[173, 173, w^3 + 2*w^2 - 3*w - 7]', '[176, 22, 2*w^3 - 10*w - 2]', '[176, 44, w^3 + 2*w^2 - 5*w - 8]', '[176, 44, w^3 + w^2 - 3*w - 5]', '[176, 88, w^3 - w^2 - 6*w]', '[176, 176, -w^3 - w^2 + 7*w + 4]', '[179, 179, w^3 - w^2 - 2*w + 5]', '[179, 179, w^3 - 5*w - 5]', '[184, 46, -w^3 + w^2 + w + 3]', '[184, 46, -w^3 + 2*w^2 + 3*w - 2]', '[184, 92, -w^3 - w^2 + 2*w + 4]', '[184, 184, -w^3 + 6*w]', '[187, 187, -2*w^3 - 2*w^2 + 10*w + 9]', '[188, 94, w^2 - 2*w - 5]', '[188, 94, -3*w^2 + 5*w + 6]', '[188, 188, -w^3 - 2*w^2 + 6*w + 4]', '[191, 191, 2*w^2 + 2*w - 7]', '[194, 194, 2*w^3 - 7*w - 2]', '[194, 194, 3*w^3 - 6*w^2 - 8*w + 15]', '[194, 194, w^3 - 4*w - 5]', '[194, 194, 2*w^3 + w^2 - 8*w - 10]', '[197, 197, 3*w^2 - w - 5]', '[197, 197, -2*w^3 + w^2 + 7*w - 7]', '[202, 202, 2*w^3 - 7*w - 6]', '[202, 202, 2*w^3 - 4*w^2 - 3*w + 7]', '[206, 206, -w^3 - w^2 + 7*w + 6]', '[206, 206, w^3 - 4*w^2 - 6*w + 13]', '[206, 206, w^3 - 3]', '[206, 206, w^2 - 2*w - 6]', '[212, 106, -2*w^3 + 3*w^2 + 3*w + 2]', '[212, 106, w^2 - 7]', '[212, 106, -2*w^3 + w^2 + 8*w + 3]', '[212, 106, 2*w^3 - 3*w^2 - 5*w + 6]', '[212, 212, -3*w^3 - w^2 + 15*w + 8]', '[212, 212, -2*w^3 + 2*w^2 + 5*w]', '[218, 218, -3*w^3 + 5*w^2 + 11*w - 14]', '[218, 218, 4*w^3 - 17*w - 7]', '[223, 223, 2*w^3 - 2*w^2 - 8*w + 3]', '[226, 226, 2*w^3 - 2*w^2 - 9*w + 9]', '[226, 226, -5*w^3 + 22*w + 10]', '[227, 227, w^2 + 3*w - 5]', '[232, 58, w^3 + w^2 - 7*w - 3]', '[232, 58, w^3 + 2*w^2 - 5*w - 6]', '[232, 58, -w^3 + w - 2]', '[232, 58, w^3 + w^2 - 5*w - 1]', '[232, 58, -w^3 + 2*w^2 - w + 2]', '[232, 58, -w^3 + 3*w^2 + 5*w - 11]', '[232, 116, 2*w^3 - w^2 - 7*w]', '[232, 116, -w^2 - 3*w]', '[232, 116, -w^3 + 3*w^2 + 2*w - 4]', '[232, 232, -w - 4]', '[232, 232, 2*w^3 + w^2 - 8*w - 8]', '[232, 232, -w^3 - w^2 + w + 4]', '[233, 233, -3*w^3 - w^2 + 12*w + 9]', '[233, 233, 3*w^2 - w - 11]', '[236, 118, 2*w^3 - 3*w^2 - 4*w + 5]', '[236, 118, -2*w^3 - w^2 + 11*w + 6]', '[236, 118, w^3 - w^2 - 2]', '[236, 118, -2*w^3 + w^2 + 8*w + 5]', '[236, 236, w^3 - 6*w + 4]', '[236, 236, -3*w^3 - 2*w^2 + 16*w + 12]', '[239, 239, w^3 - 5*w + 5]', '[239, 239, w^3 + 2*w^2 - 5*w - 3]', '[241, 241, -w^3 + w^2 + 6*w - 5]', '[241, 241, w^3 + 2*w^2 - 5*w - 7]', '[242, 242, -w^3 - 2*w^2 + 2*w + 6]', '[242, 242, -w^3 + 2*w^2 + 4*w - 3]', '[251, 251, 3*w^3 - 13*w - 3]', '[251, 251, w^3 - 2*w^2 - 5*w + 3]', '[253, 253, 2*w^3 - 4*w^2 - 4*w + 5]', '[256, 4, 4]', '[256, 8, -2*w^3 + 6*w]', '[256, 8, w^3 - w^2 - w + 3]', '[256, 8, -2*w^3 + 2*w^2 + 6*w - 2]', '[256, 16, -2*w^2 + 2*w + 8]', '[256, 32, -2*w^3 + 8*w]', '[256, 64, w^3 + 2*w^2 - 7*w - 4]', '[256, 128, w^2 - 3*w - 4]', '[256, 256, 2*w^3 + 2*w^2 - 7*w - 4]', '[257, 257, -2*w^3 + w^2 + 7*w - 1]', '[262, 262, 2*w^3 - 9*w - 7]', '[262, 262, -w^2 - 2*w + 6]', '[268, 134, 2*w^3 - 3*w^2 - 3*w + 2]', '[268, 134, -2*w^3 + w^2 + 6*w - 3]', '[268, 268, -2*w^2 + w]', '[271, 271, -2*w^3 + 2*w^2 + 6*w - 5]', '[272, 34, 2*w^3 - 6*w - 2]', '[272, 68, w^3 - w^2 - 3*w - 3]', '[272, 68, w^3 + 2*w^2 - 7*w - 8]', '[272, 136, 2*w^3 + w^2 - 9*w - 4]', '[272, 272, -3*w - 4]', '[274, 274, 3*w^3 - 12*w - 5]', '[274, 274, -8*w^3 - 3*w^2 + 36*w + 26]', '[274, 274, -2*w^3 + 4*w^2 + 7*w - 10]', '[274, 274, -w^3 + 2*w^2 + 2*w - 7]', '[277, 277, w^3 - w - 3]', '[277, 277, -w^3 - w^2 + 6*w + 1]', '[283, 283, -w^3 + 4*w^2 + w - 7]', '[284, 142, -2*w^3 + w^2 + 6*w - 7]', '[284, 142, w^2 - w + 2]', '[284, 284, -2*w^3 + 5*w]', '[289, 289, 2*w^3 - 5*w^2 - 7*w + 15]', '[292, 146, -2*w^3 - w^2 + 8*w + 3]', '[292, 146, w^3 + 3*w^2 - 8*w - 6]', '[292, 146, -2*w^3 + 3*w^2 + 10*w - 5]', '[292, 146, 2*w^3 - w^2 - 9*w - 2]', '[292, 146, 2*w^3 - 3*w^2 - 5*w + 2]', '[292, 146, -2*w^3 + 3*w^2 + 8*w - 7]', '[292, 292, w^2 - 4*w - 4]', '[292, 292, w^3 - 2*w - 4]', '[292, 292, 2*w^3 + 2*w^2 - 7*w - 8]', '[293, 293, 4*w^3 - 18*w - 9]', '[293, 293, 3*w^3 - w^2 - 12*w - 1]', '[298, 298, -w^3 + 4*w^2 - 7]', '[298, 298, -6*w^3 - w^2 + 26*w + 18]', '[307, 307, 3*w^3 - 15*w - 7]', '[313, 313, 2*w^3 - 6*w - 1]', '[313, 313, w^3 + w^2 - 4*w - 9]', '[314, 314, -2*w^2 + 3*w + 6]', '[314, 314, -w^3 - 2*w^2 + 8*w + 3]', '[316, 158, -3*w^2 + 7]', '[316, 158, -w^3 + 5*w^2 - 2*w - 6]', '[316, 158, w^3 + 3*w^2 - 8*w - 10]', '[316, 158, w^2 - 6*w + 7]', '[316, 316, -w^3 + w^2 - w]', '[316, 316, 3*w^3 - 7*w^2 - 7*w + 16]', '[317, 317, -3*w^2 - w + 5]', '[317, 317, 2*w^3 - w^2 - 7*w - 5]', '[319, 319, -2*w - 5]', '[319, 319, -3*w^2 + 3*w + 7]', '[319, 319, w^3 - 2*w^2 - w + 5]', '[324, 6, -3*w^2 + 3*w + 6]', '[324, 6, 3*w^2 - 9]', '[324, 12, 3*w]', '[326, 326, w^3 + w^2 - 3*w - 6]', '[326, 326, 3*w^3 - 4*w^2 - 8*w + 11]', '[331, 331, 2*w^2 - 2*w - 9]', '[332, 166, -3*w^3 + w^2 + 12*w + 6]', '[332, 166, 3*w^2 - 4*w - 1]', '[332, 166, -2*w^3 + 3*w^2 + 6*w - 11]', '[332, 166, w^3 - 3*w^2 + 6]', '[332, 332, 2*w^3 - 3*w^2 - 4*w + 4]', '[332, 332, -w^3 - w^2 + 5*w]', '[337, 337, w^3 - w^2 - 6*w + 1]', '[346, 346, 2*w^3 - 7*w + 3]', '[346, 346, -4*w^3 + 19*w + 10]', '[347, 347, -2*w^3 + 2*w^2 + 6*w - 3]', '[349, 349, 2*w^3 - 2*w^2 - 4*w + 3]', '[352, 44, 2*w^3 - 2*w^2 - 6*w + 4]', '[352, 44, w^3 + w^2 - 5*w + 1]', '[352, 44, 2*w - 6]', '[352, 88, -w^3 + 3*w - 4]', '[352, 176, 2*w^3 - w^2 - 9*w + 4]', '[352, 352, -w^3 + 2*w^2 + 2*w - 8]', '[358, 358, -w^3 + 4*w^2 + 4*w - 9]', '[358, 358, -3*w + 1]', '[358, 358, 3*w^3 + w^2 - 13*w - 6]', '[358, 358, -8*w^3 - 2*w^2 + 35*w + 22]', '[368, 46, -2*w^3 - 2*w^2 + 8*w + 10]', '[368, 92, 3*w^3 - 11*w - 8]', '[368, 92, -3*w^3 + w^2 + 13*w + 3]', '[368, 184, w^2 - 3*w + 4]', '[368, 368, -2*w^3 + 2*w^2 + 5*w - 4]', '[373, 373, 6*w^3 + 2*w^2 - 26*w - 15]', '[374, 374, -2*w^3 + 2*w^2 + 5*w - 1]', '[374, 374, w^2 + 2]', '[376, 94, -5*w^3 - 2*w^2 + 23*w + 14]', '[376, 94, w^3 - 3*w^2 - 3*w + 5]', '[376, 188, w^3 - w^2 - 6*w + 4]', '[376, 376, w^3 - 5*w^2 + 5*w + 4]', '[379, 379, 3*w^3 - w^2 - 12*w - 5]', '[382, 382, 2*w^3 - 9*w + 7]', '[382, 382, -w^3 + 2*w^2 + 4*w - 2]', '[388, 194, w^2 - 4*w + 1]', '[388, 194, -7*w^3 - w^2 + 30*w + 18]', '[388, 194, w^3 + w^2 - 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14*w + 9]', '[1796, 1796, w^2 + 4]', '[1802, 1802, -3*w^3 + 2*w^2 + 14*w - 9]', '[1802, 1802, w^3 + 4*w^2 - 8*w - 11]', '[1802, 1802, -w^3 + 8*w^2 - 10*w - 6]', '[1802, 1802, w^3 - 8*w - 2]', '[1808, 226, -4*w^2 + 18]', '[1808, 452, -5*w^3 + 5*w^2 + 19*w - 9]', '[1808, 452, -3*w^3 + 4*w^2 + 13*w - 8]', '[1808, 904, -7*w^2 + 3*w + 28]', '[1808, 1808, -5*w^3 + 4*w^2 + 22*w - 8]', '[1816, 454, -w^3 + 3*w - 6]', '[1816, 454, 3*w^3 - 3*w^2 - 9*w + 5]', '[1816, 908, -2*w^3 + 5*w^2 + w]', '[1816, 1816, -3*w^3 + 2*w^2 + 6*w]', '[1817, 1817, -2*w^3 + 7*w^2 + w - 13]', '[1817, 1817, 2*w^3 + 2*w^2 - 6*w - 9]', '[1822, 1822, 5*w^3 - 2*w^2 - 20*w - 1]', '[1822, 1822, 2*w^3 - 11*w + 9]', '[1822, 1822, w^3 + 2*w^2 - 6*w - 14]', '[1822, 1822, -3*w^3 + 2*w^2 + 12*w + 2]', '[1823, 1823, -4*w^3 + w^2 + 19*w + 1]', '[1826, 1826, -w^3 + 2*w^2 + 8*w - 15]', '[1826, 1826, w^3 + 2*w^2 - 8*w - 10]', '[1826, 1826, 3*w^3 - 6*w^2 - 10*w + 14]', '[1826, 1826, 3*w^3 + 2*w^2 - 16*w - 7]', '[1828, 914, 3*w^3 + w^2 - 10*w + 2]', '[1828, 914, -2*w^3 + 3*w^2 + 4*w - 9]', '[1828, 1828, -w^3 + 2*w^2 + 4*w - 12]', '[1831, 1831, 9*w^3 + w^2 - 42*w - 21]', '[1831, 1831, w^3 + 5*w^2 - 10*w - 11]', '[1831, 1831, -3*w^3 + 8*w^2 + 11*w - 25]', '[1831, 1831, 5*w^3 - 23*w - 5]', '[1838, 1838, 2*w^3 - 5*w^2 - 4*w + 6]', '[1838, 1838, 3*w^3 - w^2 - 9*w + 2]', '[1838, 1838, 2*w^3 - 4*w^2 + w - 3]', '[1838, 1838, w - 7]', '[1844, 922, -4*w^3 - w^2 + 17*w + 6]', '[1844, 922, 2*w^3 - 7*w^2 - 8*w + 17]', '[1844, 922, 2*w^3 + w^2 - 2*w + 5]', '[1844, 922, w^2 - 5*w - 6]', '[1844, 1844, 4*w^3 + 4*w^2 - 13*w - 8]', '[1844, 1844, 3*w^3 - 6*w^2 - 14*w + 20]', '[1847, 1847, 4*w^3 - 7*w^2 - 15*w + 19]', '[1847, 1847, -2*w^3 - 2*w^2 + 12*w + 13]', '[1849, 43, -w^3 + 6*w^2 + 3*w - 11]', '[1849, 43, -3*w^3 + 3*w^2 + 8*w - 11]', '[1852, 926, -2*w^3 - w^2 + 10*w + 1]', '[1852, 926, -w^3 + 9*w^2 - 10*w - 10]', '[1852, 1852, -w^3 + 5*w^2 - 5*w - 8]', '[1853, 1853, -2*w^3 - 4*w^2 + 12*w + 19]', '[1856, 116, -w^3 + 5*w^2 + w - 11]', '[1856, 116, -2*w^2 - 4*w + 6]', '[1856, 116, 2*w^2 + 2*w - 12]', '[1856, 116, -4*w^3 - 2*w^2 + 16*w + 14]', '[1856, 116, -5*w^3 + w^2 + 21*w + 9]', '[1856, 116, -2*w^3 + 2*w^2 + 8*w - 12]', '[1856, 116, -2*w^2 - 2]', '[1856, 116, 3*w^3 - 3*w^2 - 7*w + 1]', '[1856, 116, 2*w^3 + 2*w^2 - 12*w - 4]', '[1856, 232, 4*w^3 - 2*w^2 - 12*w + 8]', '[1856, 232, 2*w^3 - 4*w^2 - 8*w + 8]', '[1856, 232, 2*w^2 - 4*w - 8]', '[1856, 464, -3*w^3 + 6*w^2 + 9*w - 20]', '[1856, 464, w^3 + 4*w^2 - w - 12]', '[1856, 464, 3*w^3 + 2*w^2 - 11*w - 4]', '[1856, 928, 2*w^3 + w^2 - 9*w - 12]', '[1856, 928, 4*w^3 - 3*w^2 - 15*w + 12]', '[1856, 928, -2*w^3 + w^2 + 3*w + 4]', '[1856, 1856, 4*w^2 + w - 4]', '[1856, 1856, -w^3 - 2*w^2 + 8*w]', '[1856, 1856, 4*w^3 - 15*w - 4]', '[1863, 69, -3*w^3 - 3*w^2 + 12*w + 15]', '[1864, 466, 3*w^3 - 6*w^2 - 5*w + 2]', '[1864, 466, -w^3 + 3*w^2 + 5*w - 3]', '[1864, 466, -9*w^3 + 39*w + 14]', '[1864, 466, 5*w^3 - 9*w^2 - 21*w + 29]', '[1864, 932, 3*w^3 - w^2 - 6*w - 4]', '[1864, 932, 8*w^3 - 13*w^2 - 31*w + 40]', '[1864, 1864, w^3 + 4*w^2 - 12*w - 8]', '[1864, 1864, -4*w^3 + 6*w^2 + 13*w - 12]', '[1867, 1867, -w^3 - 2*w^2 + 9*w + 9]', '[1868, 934, -4*w^3 + 5*w^2 + 13*w - 14]', '[1868, 934, 4*w^3 - w^2 - 18*w - 7]', '[1868, 1868, 7*w^3 + w^2 - 33*w - 16]', '[1874, 1874, 5*w^3 + w^2 - 21*w - 18]', '[1874, 1874, 3*w^3 - 8*w^2 - 6*w + 17]', '[1877, 1877, w^3 - 3*w^2 + 4*w + 1]', '[1879, 1879, 4*w^2 - 2*w - 11]', '[1888, 236, 2*w^2 + 4*w - 4]', '[1888, 236, -w^3 - w^2 + 9*w - 1]', '[1888, 236, -4*w^2 + 6*w + 10]', '[1888, 236, -3*w^3 + w^2 + 7*w + 1]', '[1888, 236, -4*w^2 + 2*w + 10]', '[1888, 236, -2*w^3 - 2*w^2 + 10*w + 4]', '[1888, 472, -w^3 - 2*w^2 + 3*w + 12]', '[1888, 472, w^3 + w + 4]', '[1888, 944, -2*w^3 + 3*w^2 + 9*w - 4]', '[1888, 944, -4*w^3 + w^2 + 15*w + 4]', '[1888, 1888, 3*w^3 - 4*w^2 - 8*w]', '[1888, 1888, -w^3 + 6*w + 8]', '[1889, 1889, w^3 + 2*w^2 - 3*w - 13]', '[1901, 1901, 4*w^3 - 5*w^2 - 11*w + 15]', '[1903, 1903, 6*w^3 - 26*w - 7]', '[1906, 1906, -2*w^3 + 2*w^2 + 11*w - 2]', '[1906, 1906, -w^3 - 4*w^2 + 6*w + 15]', '[1907, 1907, 9*w^3 + w^2 - 40*w - 17]', '[1907, 1907, -w^3 + w^2 + 4*w - 9]', '[1907, 1907, -w^3 + w^2 + 8*w - 7]', '[1907, 1907, w^3 - 2*w^2 - 7*w + 5]', '[1909, 1909, -3*w^3 + 3*w^2 + 6*w - 1]', '[1909, 1909, -2*w^2 + 2*w + 13]', '[1912, 478, w^3 - 2*w^2 - 7*w + 6]', '[1912, 478, -w^3 + 5*w^2 + w - 13]', '[1912, 478, -3*w^3 + w^2 + 5*w - 3]', '[1912, 478, -5*w^3 - 2*w^2 + 19*w + 14]', '[1912, 956, w^3 - 5*w^2 + 6*w + 4]', '[1912, 956, -w^3 - w^2 + 4*w - 4]', '[1912, 1912, -5*w^2 + 4*w + 8]', '[1912, 1912, -3*w^3 + 9*w^2 - w - 4]', '[1913, 1913, 4*w^3 - 20*w - 3]', '[1913, 1913, -4*w^3 + 18*w + 3]', '[1921, 1921, 3*w^3 - 2*w^2 - 13*w - 1]', '[1922, 62, -2*w^3 + w^2 + 4*w + 6]', '[1922, 62, 3*w^3 + 2*w^2 - 10*w - 2]', '[1922, 62, -w^3 + 2*w^2 - 7]', '[1922, 62, -5*w^3 + 10*w^2 + 8*w - 17]', '[1928, 482, w^3 + 2*w^2 - 5*w - 14]', '[1928, 482, 5*w^3 - 11*w^2 - 17*w + 31]', '[1928, 482, -9*w^3 - 2*w^2 + 39*w + 22]', '[1928, 482, w^3 - 3*w^2 - 7*w + 9]', '[1928, 964, 6*w^3 - 11*w^2 - 25*w + 40]', '[1928, 964, 3*w^3 - 5*w^2 - 12*w + 12]', '[1928, 1928, -3*w^3 + 5*w^2 + 7*w - 4]', '[1928, 1928, w^3 - 4*w^2 + 8*w - 8]', '[1931, 1931, -w^3 + 4*w^2 + 3*w - 5]', '[1934, 1934, 2*w^3 - 4*w^2 - 5*w + 3]', '[1934, 1934, -3*w^3 - 3*w^2 + 11*w + 6]', '[1934, 1934, 2*w^3 + w^2 - 4*w - 6]', '[1934, 1934, -2*w^2 + 5*w + 7]', '[1936, 242, 2*w^3 + 2*w^2 - 12*w - 14]', '[1936, 484, 3*w^3 - 8*w^2 - 11*w + 24]', '[1936, 484, 5*w^3 + w^2 - 23*w - 9]', '[1936, 968, -2*w^3 + 7*w^2 + w - 12]', '[1936, 1936, -5*w + 4]', '[1943, 1943, 3*w^3 - 3*w^2 - 10*w - 3]', '[1943, 1943, w^3 - 7*w^2 + 2*w + 9]', '[1943, 1943, -w^3 + 3*w^2 - 9]', '[1948, 974, 2*w^3 + 3*w^2 - 6*w - 11]', '[1948, 974, -3*w^3 + w^2 + 8*w + 6]', '[1948, 1948, -w^3 + 3*w^2 + 5*w]', '[1951, 1951, 3*w^3 + 4*w^2 - 11*w - 13]', '[1954, 1954, -2*w^3 + 4*w^2 + 7*w - 7]', '[1954, 1954, -w^2 - 4*w - 6]', '[1954, 1954, 12*w^3 + 4*w^2 - 55*w - 34]', '[1954, 1954, 4*w^3 - 15*w - 5]', '[1964, 982, -w^3 + 3*w^2 - 4*w - 2]', '[1964, 982, 3*w^2 + 4*w - 7]', '[1964, 1964, w^3 + 5*w^2 - 5*w - 8]', '[1966, 1966, -5*w^3 + 6*w^2 + 18*w - 18]', '[1966, 1966, 7*w^3 - 32*w - 15]', '[1969, 1969, w^3 + 4*w^2 - 7*w - 9]', '[1969, 1969, 8*w^3 + 2*w^2 - 38*w - 21]', '[1972, 986, w^2 - 4*w - 9]', '[1972, 986, -w^3 - 3*w^2 + 10*w + 10]', '[1972, 986, -2*w^3 + w^2 + 4*w + 7]', '[1972, 986, -2*w^3 + 3*w^2 + 7*w - 2]', '[1972, 986, -3*w^3 + w^2 + 8*w - 2]', '[1972, 986, w^2 - 2*w + 5]', '[1972, 1972, -3*w^3 - 3*w^2 + 13*w + 8]', '[1972, 1972, -2*w^3 - 2*w^2 + 5*w + 8]', '[1972, 1972, w^3 - 4*w^2 + 12]', '[1979, 1979, -2*w^3 - 4*w^2 + 8*w + 9]', '[1979, 1979, -4*w^3 + 5*w^2 + 11*w - 5]', '[1979, 1979, -w^3 + 5*w - 7]', '[1979, 1979, -2*w^3 + 3*w^2 + 11*w - 5]', '[1982, 1982, w^3 + 2*w - 2]', '[1982, 1982, -w^3 + 2*w^2 + 8*w - 1]', '[1982, 1982, w^3 - 6*w^2 + 2*w + 9]', '[1982, 1982, 5*w^3 - 4*w^2 - 18*w + 18]', '[1987, 1987, w^3 - w^2 - 8*w - 1]', '[1987, 1987, -w^3 + 5*w^2 + 6*w - 17]', '[1993, 1993, -2*w^3 + w^2 + 11*w - 3]', '[1994, 1994, -w^3 + 4*w^2 - 2*w + 1]', '[1994, 1994, 5*w^3 - 4*w^2 - 16*w - 1]', '[1994, 1994, 7*w^3 + 5*w^2 - 35*w - 26]', '[1994, 1994, 2*w^3 - 7*w - 10]', '[1996, 998, -w^2 + 4*w - 7]', '[1996, 998, 3*w^3 - 3*w^2 - 8*w + 6]', '[1996, 1996, -2*w^3 - w^2 + 6*w - 4]', '[1999, 1999, w^3 + 3*w^2 - 2*w - 11]', '[2003, 2003, -2*w - 7]', '[2003, 2003, 2*w^2 + 4*w - 5]', '[2006, 2006, 2*w^3 + 4*w^2 - 13*w - 9]', '[2006, 2006, 3*w^3 - 10*w - 10]', '[2006, 2006, w^2 - 6*w - 6]', '[2006, 2006, -5*w - 1]', '[2008, 502, -3*w^3 + 5*w^2 + 9*w - 19]', '[2008, 502, w^3 - 4*w^2 + w + 10]', '[2008, 502, 3*w^3 - w^2 - 13*w - 9]', '[2008, 502, -w^3 - w + 6]', '[2008, 1004, -2*w^3 - w^2 + 9*w]', '[2008, 1004, 5*w^3 + 3*w^2 - 26*w - 20]', '[2008, 2008, -w^3 - w^2 + 3*w + 12]', '[2008, 2008, w^3 - 5*w^2 - w + 12]', '[2011, 2011, 7*w^3 + 4*w^2 - 29*w - 23]', '[2012, 1006, w^3 - 5*w^2 - 2*w + 14]', '[2012, 1006, -2*w^3 + w^2 + 12*w - 7]', '[2012, 1006, 5*w^2 - 6*w - 3]', '[2012, 1006, -6*w^3 + w^2 + 25*w + 14]', '[2012, 2012, 3*w^3 - 4*w^2 - 6*w + 4]', '[2012, 2012, -w^3 + 3*w^2 + 7*w - 8]', '[2017, 2017, -2*w^3 + 3*w^2 + 7*w + 1]', '[2017, 2017, w^3 + w^2 - 4*w - 11]', '[2017, 2017, 3*w^3 - 4*w^2 - 11*w + 7]', '[2017, 2017, -3*w^3 + 9*w - 7]', '[2024, 506, -3*w^3 + w^2 + 9*w + 1]', '[2024, 506, w^3 + 2*w^2 - w + 2]', '[2024, 1012, -3*w^3 - w^2 + 14*w + 4]', '[2024, 2024, -w^2 + 4*w + 8]', '[2026, 2026, -w^3 + w^2 + w - 10]', '[2026, 2026, 5*w^3 - 6*w^2 - 14*w + 18]', '[2026, 2026, 4*w^3 - 2*w^2 - 15*w + 3]', '[2026, 2026, w^3 + 4*w^2 - 4*w - 9]', '[2027, 2027, 6*w^3 + 4*w^2 - 28*w - 21]', '[2036, 1018, 3*w^3 - 5*w^2 - 10*w + 10]', '[2036, 1018, 5*w^2 - 11]', '[2036, 2036, 3*w^2 + 2*w - 12]', '[2042, 2042, -7*w^3 - 3*w^2 + 35*w + 22]', '[2042, 2042, 3*w^3 - 4*w^2 - 6*w + 5]', '[2048, 8, 4*w^3 - 20*w - 8]', '[2048, 8, -4*w^3 + 4*w^2 + 12*w - 12]', '[2048, 16, -4*w^3 + 4*w^2 + 16*w - 16]', '[2048, 16, 3*w^3 + w^2 - 11*w - 11]', '[2048, 16, 2*w^3 - 2*w^2 - 10*w - 2]', '[2048, 32, 4*w^2 - 8*w]', '[2048, 64, -2*w^3 + 4*w^2 + 2*w - 8]', '[2048, 128, 2*w^3 + 2*w^2 - 8*w]', '[2048, 256, 2*w - 8]', '[2048, 512, 3*w^3 - 2*w^2 - 9*w + 4]', '[2048, 1024, -2*w^3 - w^2 + 5*w - 4]', '[2048, 2048, 3*w^3 - w^2 - 13*w + 4]', '[2056, 514, 3*w^3 - 3*w^2 - 11*w + 15]', '[2056, 514, 5*w^3 + 4*w^2 - 23*w - 22]', '[2056, 1028, 4*w^3 - 7*w^2 - 13*w + 24]', '[2056, 2056, -2*w^3 + 6*w^2 + w - 12]', '[2057, 2057, -w^3 + 5*w^2 + 2*w - 13]', '[2059, 2059, -w^3 - w^2 - 2*w + 5]', '[2059, 2059, -3*w^3 - w^2 + 10*w + 9]', '[2059, 2059, -3*w^3 + w^2 + 12*w - 5]', '[2062, 2062, 4*w^3 - 5*w^2 - 16*w + 22]', '[2062, 2062, 2*w^3 + 2*w^2 - 7*w - 11]', '[2063, 2063, 4*w^3 - 4*w^2 - 10*w - 1]', '[2068, 1034, -2*w^3 - 5*w^2 + 14*w + 13]', '[2068, 1034, -w^3 - w^2 + 10*w + 6]', '[2068, 2068, -6*w^3 + 23*w + 16]', '[2069, 2069, w^3 - 2*w^2 - 5*w + 13]', '[2069, 2069, -2*w^3 - w^2 + 13*w + 7]', '[2078, 2078, -w^3 + 8*w - 2]', '[2078, 2078, 4*w^3 - 12*w^2 - 3*w + 15]', '[2078, 2078, 6*w^3 - 10*w^2 - 15*w + 23]', '[2078, 2078, -w^3 - 4*w^2 + 10*w + 6]', '[2083, 2083, 3*w^3 + 4*w^2 - 11*w - 11]', '[2083, 2083, w^3 + w^2 - 7]', '[2087, 2087, w^3 + 2*w^2 - 7*w - 15]', '[2087, 2087, 3*w^3 - 2*w^2 - 9*w + 1]', '[2092, 1046, 2*w^3 - w^2 - 12*w - 3]', '[2092, 1046, -2*w^3 - 3*w^2 + 15*w + 10]', '[2092, 2092, -3*w^3 - 4*w^2 + 14*w + 12]', '[2096, 262, 4*w^2 - 4*w - 14]', '[2096, 524, 3*w^3 - w^2 - 9*w + 1]', '[2096, 524, 3*w^3 - 13*w]', '[2096, 1048, -w^3 - 5*w^2 + 12*w + 8]', '[2096, 2096, -3*w^2 + 6*w + 8]', '[2098, 2098, -5*w^3 + 6*w^2 + 20*w - 22]', '[2098, 2098, 5*w^3 - 24*w - 9]', '[2099, 2099, w^3 + w^2 + 2*w - 1]', '[2099, 2099, 2*w^3 + w^2 - 5*w - 7]', '[2101, 2101, 3*w^3 - 2*w^2 - 13*w + 9]', '[2102, 2102, 5*w^2 - 2*w - 18]', '[2102, 2102, 4*w^3 - w^2 - 14*w + 6]', '[2102, 2102, 4*w^3 - 2*w^2 - 19*w + 5]', '[2102, 2102, -2*w^3 + 4*w^2 + 5*w - 15]', '[2111, 2111, 4*w^3 - 4*w^2 - 16*w + 7]', '[2116, 1058, 2*w^3 - w^2 - 6*w + 9]', '[2116, 1058, w^3 - 3*w^2 - 2]', '[2116, 2116, 3*w^3 - w^2 - 7*w]', '[2117, 2117, 6*w^3 - w^2 - 23*w - 11]', '[2117, 2117, 3*w^3 + 5*w^2 - 14*w - 23]', '[2117, 2117, w^3 - w^2 + 7]', '[2117, 2117, 11*w^3 + 3*w^2 - 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18*w - 5]', '[4364, 4364, -w^3 - 4*w^2 + 12*w + 12]', '[4364, 4364, -10*w^3 - 2*w^2 + 43*w + 24]', '[4367, 4367, 6*w^3 + 8*w^2 - 32*w - 39]', '[4369, 4369, -w^3 + w^2 + 6*w + 7]', '[4373, 4373, -2*w^3 + 5*w^2 - w + 3]', '[4373, 4373, -3*w^3 + 4*w^2 + 11*w - 5]', '[4384, 548, -6*w^3 + 24*w + 10]', '[4384, 548, -5*w^3 - w^2 + 21*w + 19]', '[4384, 548, 16*w^3 + 6*w^2 - 72*w - 52]', '[4384, 548, 9*w^3 + 5*w^2 - 41*w - 31]', '[4384, 548, 4*w^3 - 8*w^2 - 14*w + 20]', '[4384, 548, 2*w^3 - 4*w^2 - 4*w + 14]', '[4384, 1096, w^3 - 4*w^2 - 3*w + 20]', '[4384, 1096, -9*w^3 - 2*w^2 + 41*w + 20]', '[4384, 2192, -5*w^3 + 3*w^2 + 18*w - 8]', '[4384, 2192, 5*w^3 - 7*w^2 - 22*w + 24]', '[4384, 4384, w^3 - 8*w^2 + 32]', '[4384, 4384, -5*w^2 + 12*w]', '[4388, 2194, -2*w^3 - w^2 + 11*w - 2]', '[4388, 2194, 2*w^3 + 3*w^2 - 6*w + 1]', '[4388, 2194, -2*w^3 + 5*w^2 + 3*w - 14]', '[4388, 2194, 4*w^3 - w^2 - 10*w + 3]', '[4388, 2194, -4*w^3 + 7*w^2 + 18*w - 21]', '[4388, 2194, w^3 + w^2 - 10*w + 2]', '[4388, 2194, -4*w^3 + 7*w^2 + 16*w - 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18*w + 23]', '[5198, 5198, -5*w^3 + 6*w^2 + 22*w - 17]', '[5198, 5198, 2*w^3 - 11*w^2 - 6*w + 46]', '[5209, 5209, 6*w^2 - 2*w - 21]', '[5212, 2606, -6*w^3 + w^2 + 20*w - 5]', '[5212, 2606, 4*w^3 - w^2 - 13*w - 2]', '[5212, 5212, -w^3 - 2*w^2 - 4]', '[5216, 652, -2*w^3 - 2*w^2 + 6*w + 12]', '[5216, 652, -w^3 - 5*w^2 + 5*w + 11]', '[5216, 652, -6*w^3 + 8*w^2 + 16*w - 22]', '[5216, 1304, -5*w^3 + 6*w^2 + 21*w - 28]', '[5216, 2608, 7*w^3 - 7*w^2 - 22*w + 24]', '[5216, 5216, -8*w^3 + 14*w^2 + 27*w - 44]', '[5219, 5219, -3*w^3 + 13*w - 3]', '[5221, 5221, 3*w^3 - 10*w^2 + 3*w + 13]', '[5224, 1306, -7*w^3 + 19*w^2 + 31*w - 59]', '[5224, 1306, w^3 - 4*w^2 + w + 22]', '[5224, 1306, -3*w^3 - 4*w^2 + 9*w + 14]', '[5224, 1306, -3*w^3 + 3*w^2 + 13*w - 1]', '[5224, 2612, -12*w^3 + 25*w^2 + 47*w - 80]', '[5224, 2612, -5*w^3 + w^2 + 24*w + 4]', '[5224, 5224, -3*w^3 - 5*w^2 + 13*w + 20]', '[5224, 5224, 4*w^3 - 10*w^2 - 13*w + 28]', '[5228, 2614, 3*w^3 - 9*w^2 - 8*w + 18]', '[5228, 2614, -4*w^3 + w^2 + 12*w + 3]', '[5228, 5228, -4*w^3 - 2*w^2 + 19*w + 8]', '[5233, 5233, -2*w^3 + 6*w^2 + 10*w - 13]', '[5234, 5234, 2*w^2 - 5*w - 10]', '[5234, 5234, 4*w^2 - 5*w - 14]', '[5234, 5234, 3*w^3 + 2*w^2 - 16*w - 5]', '[5234, 5234, 3*w^3 + 2*w^2 - 18*w - 3]', '[5237, 5237, -5*w^3 + 4*w^2 + 15*w - 13]', '[5237, 5237, -w^3 - 5*w^2 + 4*w + 13]', '[5242, 5242, 7*w - 13]', '[5242, 5242, -8*w^3 - 6*w^2 + 41*w + 34]', '[5258, 5258, w^3 + 6*w^2 - 10*w - 18]', '[5258, 5258, 6*w^2 - 9*w - 5]', '[5258, 5258, 2*w^3 - 4*w^2 - 7*w + 3]', '[5258, 5258, -2*w^3 + 3*w^2 - 6]', '[5261, 5261, w^3 + 7*w^2 - 4*w - 27]', '[5272, 1318, w^3 + 6*w^2 - 3*w - 18]', '[5272, 1318, 3*w^3 - 3*w^2 - 15*w + 7]', '[5272, 1318, w^3 + 2*w^2 + 3*w - 2]', '[5272, 1318, -w^3 - 5*w^2 + 7*w + 11]', '[5272, 2636, -w^3 - 5*w^2 + 8*w + 12]', '[5272, 2636, -3*w^3 - w^2 + 10*w + 12]', '[5272, 5272, w^2 + 6*w]', '[5272, 5272, -2*w^3 + 3*w^2 + 10*w]', '[5276, 2638, -3*w^2 + 8*w + 9]', '[5276, 2638, -2*w^3 + 9*w^2 + w - 14]', '[5276, 5276, -4*w^3 + w^2 + 16*w + 12]', '[5288, 1322, 3*w^3 - 5*w^2 - 11*w + 9]', '[5288, 1322, w^3 + 4*w^2 - w - 14]', '[5288, 2644, -3*w^3 + 3*w^2 + 4*w + 4]', '[5288, 5288, -w^3 + 5*w^2 + 3*w - 4]', '[5293, 5293, 13*w^3 + 3*w^2 - 60*w - 31]', '[5293, 5293, 3*w^3 + w^2 - 16*w - 1]', '[5296, 662, -4*w^2 + 4*w + 18]', '[5296, 1324, -5*w^3 + 19*w]', '[5296, 1324, -5*w^3 + w^2 + 23*w - 1]', '[5296, 2648, -2*w^3 - 5*w^2 + 11*w + 28]', '[5296, 5296, -7*w^3 + 2*w^2 + 28*w]', '[5302, 5302, 4*w^3 - 10*w^2 - 11*w + 26]', '[5302, 5302, 2*w^3 - w^2 - 12*w + 2]', '[5302, 5302, -3*w^3 + 2*w^2 + 20*w - 19]', '[5302, 5302, 6*w^2 - 5*w - 17]', '[5309, 5309, -5*w^3 + 6*w^2 + 15*w - 21]', '[5311, 5311, -3*w^3 + 7*w^2 + 16*w - 25]', '[5312, 332, w^3 + 3*w^2 - 13*w - 9]', '[5312, 332, 6*w^3 - 2*w^2 - 24*w - 12]', '[5312, 332, -6*w^2 + 8*w + 2]', '[5312, 332, 4*w^3 - 6*w^2 - 12*w + 22]', '[5312, 332, -5*w^3 + 5*w^2 + 21*w - 19]', '[5312, 332, -2*w^3 + 6*w^2 - 12]', '[5312, 664, -4*w^3 + 6*w^2 + 8*w - 8]', '[5312, 664, 2*w^3 + 2*w^2 - 10*w]', '[5312, 1328, w^3 + 2*w^2 - 5*w + 4]', '[5312, 1328, w^3 - w - 12]', '[5312, 2656, -2*w^3 - w^2 + 13*w - 4]', '[5312, 2656, 4*w^3 - 3*w^2 - 13*w + 4]', '[5312, 5312, 2*w^3 - 4*w^2 - 3*w + 12]', '[5312, 5312, -w^3 + 2*w - 8]', '[5314, 5314, 5*w^3 + 2*w^2 - 24*w - 22]', '[5314, 5314, 2*w^3 - 8*w^2 - 7*w + 21]', '[5318, 5318, -w^3 - 6*w + 11]', '[5318, 5318, 4*w^3 - 10*w^2 + 3*w + 1]', '[5318, 5318, 3*w^2 - 6*w - 10]', '[5318, 5318, -6*w^3 - 8*w^2 + 37*w + 30]', '[5321, 5321, 6*w^3 - w^2 - 23*w - 9]', '[5321, 5321, -w^3 - 4*w^2 - w - 1]', '[5323, 5323, -w^3 - w^2 + 10*w - 1]', '[5324, 22, -3*w^3 + 5*w^2 + 8*w - 18]', '[5324, 22, 4*w^3 - 3*w^2 - 18*w + 13]', '[5324, 44, 5*w^3 - w^2 - 17*w + 8]', '[5324, 2662, -4*w^3 + 7*w^2 + 12*w - 13]', '[5324, 2662, -3*w^2 - 3*w + 14]', '[5324, 5324, -w^3 + 6*w^2 + 6*w - 12]', '[5326, 5326, 4*w^3 - 4*w^2 - 11*w + 9]', '[5326, 5326, -8*w^3 - 2*w^2 + 39*w + 22]', '[5329, 73, 13*w^3 + 2*w^2 - 57*w - 31]', '[5329, 73, -5*w^3 + 4*w^2 + 11*w - 9]', '[5329, 73, -3*w^3 - 3*w^2 + 14*w + 7]', '[5329, 73, -4*w^3 + 3*w^2 + 17*w - 13]', '[5329, 5329, 13*w^3 + 2*w^2 - 59*w - 35]', '[5329, 5329, -3*w^3 + 9*w^2 + 8*w - 27]', '[5333, 5333, -3*w^3 - 6*w^2 + 13*w + 27]', '[5333, 5333, -w^3 + 5*w^2 + 4*w - 7]', '[5336, 1334, w^3 - 3*w - 10]', '[5336, 1334, 3*w^3 + 3*w^2 - 11*w - 3]', '[5336, 1334, 5*w^3 - 4*w^2 - 19*w + 18]', '[5336, 1334, -3*w^3 + w^2 + 17*w + 5]', '[5336, 1334, 3*w^3 - 4*w^2 - 15*w + 14]', '[5336, 1334, w^3 + 5*w^2 + w - 15]', '[5336, 2668, 4*w^3 - w^2 - 13*w]', '[5336, 2668, -w^3 + 7*w^2 + 4*w - 20]', '[5336, 2668, -5*w^2 + 9*w]', '[5336, 5336, w^3 - 7*w^2 + 3*w + 12]', '[5336, 5336, 3*w^3 - 4*w^2 - 4*w + 8]', '[5336, 5336, w^3 + 5*w^2 - 9*w - 20]', '[5338, 5338, -w^3 - 6*w^2 + 14*w + 15]', '[5338, 5338, -3*w^3 - 4*w^2 + 16*w + 10]', '[5342, 5342, 6*w^3 - 4*w^2 - 25*w + 11]', '[5342, 5342, -2*w^3 + 5*w^2 + 4*w - 22]', '[5351, 5351, 2*w^3 + 5*w^2 - 7*w - 13]', '[5353, 5353, -4*w^3 + 6*w^2 + 12*w - 23]', '[5353, 5353, -w^3 + 2*w^2 + 9*w - 1]', '[5354, 5354, 5*w^3 - 4*w^2 - 16*w + 13]', '[5354, 5354, -4*w^3 + 6*w^2 + 7*w - 6]', '[5357, 5357, 7*w^3 - w^2 - 30*w - 13]', '[5359, 5359, -4*w^3 - 6*w^2 + 22*w + 35]', '[5359, 5359, 7*w^2 - 7*w - 11]', '[5372, 2686, -6*w^3 + 13*w^2 + 20*w - 39]', '[5372, 2686, 5*w^3 - 15*w^2 - 2*w + 22]', '[5372, 2686, 2*w^3 + 3*w^2 - 5]', '[5372, 2686, -2*w^3 - w^2 + 5*w + 10]', '[5372, 5372, -3*w^2 + 10*w - 4]', '[5372, 5372, -w^3 + 4*w^2 + 6*w - 4]', '[5374, 5374, 2*w^3 - 2*w^2 - 3*w + 9]', '[5374, 5374, -5*w^3 + 4*w^2 + 18*w - 6]', '[5378, 5378, 4*w^3 - 6*w^2 - 7*w + 7]', '[5378, 5378, -11*w^3 - 5*w^2 + 53*w + 42]', '[5378, 5378, -8*w^3 - 4*w^2 + 41*w + 26]', '[5378, 5378, -w^3 + 6*w^2 + 6*w - 21]', '[5386, 5386, 4*w^3 - 4*w^2 - 11*w + 3]', '[5386, 5386, -w^2 - 6]', '[5387, 5387, 2*w^3 - 8*w - 11]', '[5387, 5387, -4*w^3 + 3*w^2 + 13*w - 5]', '[5389, 5389, 4*w^3 - 4*w^2 - 20*w + 17]', '[5389, 5389, 6*w^2 - 6*w - 13]', '[5392, 674, -2*w^3 + 2*w^2 + 12*w - 2]', '[5392, 1348, -w^3 - 5*w^2 + 7*w + 17]', '[5392, 1348, -3*w^3 - 6*w^2 + 9*w + 16]', '[5392, 2696, -5*w^3 + 3*w^2 + 22*w]', '[5392, 5392, -3*w^3 - 5*w^2 + 11*w + 20]', '[5393, 5393, 5*w^3 - 5*w^2 - 14*w + 1]', '[5399, 5399, 4*w^3 - 2*w^2 - 12*w + 5]', '[5401, 5401, -w^3 - 5*w^2 + 8*w + 15]', '[5407, 5407, 3*w^3 - 3*w^2 - 12*w + 17]', '[5407, 5407, 3*w^3 - 9*w^2 - 6*w + 19]', '[5413, 5413, -3*w^3 + 7*w^2 + 12*w - 17]', '[5416, 1354, -w^3 - w^2 - 3*w + 5]', '[5416, 1354, -9*w^3 - 2*w^2 + 37*w + 22]', '[5416, 1354, 5*w^3 - 13*w^2 - 21*w + 37]', '[5416, 1354, -7*w^3 + 29*w + 6]', '[5416, 1354, 3*w^3 - 9*w^2 - 5*w + 19]', '[5416, 1354, 9*w^3 + 2*w^2 - 39*w - 30]', '[5416, 1354, 5*w^3 - 13*w^2 - 7*w + 19]', '[5416, 1354, -3*w^3 - 4*w^2 + 19*w + 10]', '[5416, 2708, 8*w^3 - 15*w^2 - 33*w + 48]', '[5416, 2708, w^3 - 3*w^2 - 8*w + 20]', '[5416, 2708, 2*w^3 - 5*w^2 - 7*w + 8]', '[5416, 2708, w^3 + w^2 - 14*w + 12]', '[5416, 5416, -5*w^3 + 12*w^2 + 4*w - 8]', '[5416, 5416, 7*w^3 - 17*w^2 + w + 4]', '[5416, 5416, -2*w^3 + 2*w^2 + 13*w - 12]', '[5416, 5416, -3*w^3 + 9*w^2 + 7*w - 20]', '[5417, 5417, -6*w^3 - w^2 + 23*w + 17]', '[5417, 5417, -3*w^3 + 4*w^2 + 7*w - 13]', '[5419, 5419, 5*w^3 - w^2 - 24*w - 3]', '[5419, 5419, 5*w^3 + w^2 - 14*w - 7]', '[5422, 5422, 8*w^3 + 3*w^2 - 34*w - 26]', '[5422, 5422, 3*w^3 - 4*w^2 - 6*w + 11]', '[5423, 5423, -w^3 - 3*w^2 + 12*w + 7]', '[5423, 5423, -w^3 + 3*w^2 + 2*w - 17]', '[5423, 5423, -4*w^2 - 4*w + 15]', '[5426, 5426, 4*w^3 - w^2 - 12*w - 10]', '[5426, 5426, 5*w^3 - 10*w^2 - 6*w + 15]', '[5427, 201, 6*w - 3]', '[5428, 2714, -2*w^3 + 5*w^2 + 8*w - 9]', '[5428, 2714, w^3 - 7*w^2 + 22]', '[5428, 2714, w^2 + w + 6]', '[5428, 2714, -4*w^3 + 3*w^2 + 12*w - 1]', '[5428, 5428, -3*w^3 + 3*w^2 + 15*w - 8]', '[5428, 5428, -4*w^3 - w^2 + 20*w + 4]', '[5431, 5431, 4*w^3 + 5*w^2 - 17*w - 21]', '[5438, 5438, -6*w^3 + 3*w^2 + 22*w + 10]', '[5438, 5438, -w^3 + 8*w^2 - 8*w - 3]', '[5441, 5441, 4*w^3 - w^2 - 13*w - 1]', '[5443, 5443, -3*w^3 + w^2 + 10*w - 11]', '[5443, 5443, -3*w^3 - 2*w^2 + 15*w + 5]', '[5443, 5443, 2*w^3 - w^2 - 13*w - 3]', '[5443, 5443, -10*w^3 - 2*w^2 + 42*w + 25]', '[5452, 2726, -8*w^3 - w^2 + 36*w + 25]', '[5452, 2726, w^3 + w^2 - 10]', '[5452, 2726, 2*w^3 + 3*w^2 - 10*w - 3]', '[5452, 2726, 2*w^3 - w^2 - 5*w - 10]', '[5452, 2726, 3*w^3 + 5*w^2 - 22*w - 14]', '[5452, 2726, 4*w^3 - w^2 - 10*w - 7]', '[5452, 5452, w^3 - 5*w^2 - 5*w + 8]', '[5452, 5452, 4*w^3 - 2*w^2 - 13*w]', '[5452, 5452, 3*w^3 + 5*w^2 - 17*w - 16]', '[5458, 5458, 4*w^3 - w^2 - 12*w + 2]', '[5458, 5458, w - 9]', '[5459, 5459, w^3 - w^2 - 4*w - 7]', '[5459, 5459, 4*w^3 - 7*w^2 - 15*w + 17]', '[5459, 5459, 5*w^2 + 5*w - 17]', '[5459, 5459, w^3 - 8*w^2 - w + 29]', '[5462, 5462, 8*w^3 - 13*w^2 - 30*w + 38]', '[5462, 5462, 3*w^3 - 4*w^2 - 10*w - 2]', '[5462, 5462, -10*w^3 + 43*w + 17]', '[5462, 5462, 5*w^3 - 4*w^2 - 12*w - 7]', '[5477, 5477, -4*w^3 + 2*w^2 + 16*w - 9]', '[5479, 5479, -5*w^3 + 4*w^2 + 19*w - 17]', '[5479, 5479, -2*w^3 + 3*w^2 + w - 7]', '[5482, 5482, 3*w^3 - 7*w^2 - 5*w + 6]', '[5482, 5482, -2*w^3 + 6*w^2 + 9*w - 13]', '[5483, 5483, 5*w^3 - 8*w^2 - 13*w + 17]', '[5483, 5483, -2*w^3 - 2*w^2 + 10*w + 17]', '[5489, 5489, w^3 + 4*w^2 - 9*w - 3]', '[5492, 2746, 5*w^2 - 6*w + 1]', '[5492, 2746, 4*w^3 + 5*w^2 - 21*w - 18]', '[5492, 5492, 3*w^3 - 6*w^2 - 4*w + 12]', '[5497, 5497, -2*w^3 + w^2 + 15*w + 7]', '[5497, 5497, -5*w^3 + 11*w^2 + 6*w - 9]', '[5501, 5501, 2*w^2 + 4*w - 13]', '[5501, 5501, -w^3 + 2*w^2 - w - 9]', '[5506, 5506, 4*w^3 - 4*w^2 - 13*w - 1]', '[5506, 5506, 3*w^3 + w^2 - 9*w - 10]', '[5508, 102, -3*w^2 - 6*w + 3]', '[5508, 102, 3*w^3 + 3*w^2 - 12*w - 18]', '[5508, 204, 3*w^3 - 3*w^2 - 15*w]', '[5522, 5522, 5*w^2 + 2*w - 18]', '[5522, 5522, 6*w^3 - 2*w^2 - 27*w + 3]', '[5522, 5522, 4*w^3 - 6*w^2 - 15*w + 13]', '[5522, 5522, 5*w^2 - 4*w - 22]', '[5524, 2762, 6*w^3 - 15*w^2 - 11*w + 26]', '[5524, 2762, -4*w^3 + 5*w^2 + 8*w - 3]', '[5524, 2762, 2*w^3 - 5*w^2 - 11*w + 22]', '[5524, 2762, 4*w^3 + w^2 - 18*w - 17]', '[5524, 5524, 7*w^3 + 5*w^2 - 35*w - 32]', '[5524, 5524, -2*w^3 - 3*w^2 + 14*w + 4]', '[5531, 5531, -8*w^3 + 36*w + 19]', '[5531, 5531, -4*w^3 + 8*w^2 + 16*w - 21]', '[5531, 5531, 5*w^3 - 6*w^2 - 23*w + 13]', '[5531, 5531, -5*w^3 + w^2 + 16*w + 7]', '[5533, 5533, -2*w^3 + 4*w + 9]', '[5533, 5533, -3*w^3 - 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4*w^2 - 25*w - 3]', '[9833, 9833, 13*w^3 + w^2 - 56*w - 23]', '[9833, 9833, 3*w^3 - 7*w - 9]', '[9836, 4918, 2*w^3 + 7*w^2 - 2*w - 19]', '[9836, 4918, -3*w^3 + w^2 + 4*w + 6]', '[9836, 9836, w^3 + 7*w^2 - w - 8]', '[9838, 9838, 6*w^3 + w^2 - 20*w - 10]', '[9838, 9838, 4*w^3 - 2*w^2 - 15*w - 11]', '[9839, 9839, 8*w^3 - w^2 - 37*w - 15]', '[9839, 9839, w^3 + 6*w^2 - 7*w - 21]', '[9851, 9851, -8*w^3 - 4*w^2 + 38*w + 35]', '[9859, 9859, -5*w^3 + 5*w^2 + 10*w + 7]', '[9862, 9862, 3*w^3 - 10*w^2 - 4*w + 19]', '[9862, 9862, 2*w^3 + 2*w^2 - 13*w + 7]', '[9862, 9862, 8*w^3 + w^2 - 34*w - 26]', '[9862, 9862, -6*w^3 + 2*w^2 + 25*w + 10]', '[9866, 9866, 5*w^3 + w^2 - 19*w - 2]', '[9866, 9866, -3*w^3 + 14*w^2 + 14*w - 35]', '[9868, 4934, -w^3 - w^2 + 4*w + 14]', '[9868, 4934, -4*w^3 + 7*w^2 + 12*w - 31]', '[9868, 9868, -5*w^3 + w^2 + 17*w]', '[9872, 1234, -12*w^3 + 56*w + 26]', '[9872, 2468, 9*w^3 - 10*w^2 - 33*w + 32]', '[9872, 2468, 7*w^3 - 5*w^2 - 25*w + 21]', '[9872, 4936, -5*w^3 + 5*w^2 + 16*w - 8]', '[9872, 9872, w^3 - w^2 - 3*w + 12]', '[9878, 9878, -2*w^3 + 8*w^2 + 5*w - 22]', '[9878, 9878, 3*w^3 - 2*w^2 - 18*w + 13]', '[9883, 9883, 2*w^3 - 6*w^2 + 6*w + 3]', '[9883, 9883, -4*w^3 + 16*w - 3]', '[9887, 9887, 2*w - 11]', '[9887, 9887, -w^3 + 4*w^2 + 9*w - 9]', '[9901, 9901, -8*w^3 + 8*w^2 + 28*w - 27]', '[9901, 9901, -4*w^3 - 3*w^2 + 19*w + 9]', '[9902, 9902, -6*w^2 - 7*w + 6]', '[9902, 9902, -9*w^3 + 12*w^2 + 28*w - 38]', '[9902, 9902, 2*w^3 - w^2 - 10*w - 10]', '[9902, 9902, 4*w^3 + 2*w^2 - 23*w - 11]', '[9902, 9902, 3*w^3 + 4*w^2 - 10*w - 17]', '[9902, 9902, -w^3 - 6*w^2 + 4*w + 15]', '[9902, 9902, 6*w^3 - 2*w^2 - 21*w - 7]', '[9902, 9902, 4*w^3 + 5*w^2 - 18*w - 18]', '[9904, 1238, 2*w^3 - 4*w^2 - 10*w - 2]', '[9904, 1238, -6*w^2 + 10*w + 14]', '[9904, 2476, 5*w^3 - w^2 - 15*w - 11]', '[9904, 2476, -3*w^3 - 4*w^2 + 15*w + 8]', '[9904, 2476, 7*w^3 + 6*w^2 - 19*w - 16]', '[9904, 2476, -w^3 + 3*w^2 - w - 15]', '[9904, 4952, -5*w^3 + w^2 + 18*w + 16]', '[9904, 4952, 4*w^3 + w^2 - 23*w - 12]', '[9904, 9904, -6*w^3 + w^2 + 22*w + 8]', '[9904, 9904, 6*w^3 + 6*w^2 - 23*w - 20]', '[9907, 9907, -5*w^3 + 5*w^2 + 24*w - 19]', '[9908, 4954, -4*w^3 + w^2 + 11*w + 10]', '[9908, 4954, 2*w^3 + 5*w^2 - 6*w - 19]', '[9908, 9908, -2*w^3 + 4*w^2 + 9*w]', '[9911, 9911, 10*w^3 - 40*w - 29]', '[9911, 9911, -5*w^3 + 4*w^2 + 17*w - 7]', '[9914, 9914, 5*w^3 + w^2 - 17*w + 2]', '[9914, 9914, -2*w^3 + 4*w^2 + 3*w - 15]', '[9923, 9923, 3*w^3 + 2*w^2 - 15*w - 3]', '[9923, 9923, 14*w^3 + 7*w^2 - 65*w - 47]', '[9928, 2482, w^3 + 7*w^2 - w - 7]', '[9928, 2482, -w^3 - 6*w^2 + 9*w + 14]', '[9928, 2482, w^3 - 4*w^2 - w + 22]', '[9928, 2482, -7*w^3 - 3*w^2 + 21*w + 1]', '[9928, 2482, -3*w^3 - w^2 + 13*w - 5]', '[9928, 2482, w^3 - 2*w^2 - 7*w + 18]', '[9928, 4964, -7*w^3 + w^2 + 24*w - 4]', '[9928, 4964, -5*w^3 + 5*w^2 + 16*w - 12]', '[9928, 4964, w^2 + 7*w]', '[9928, 9928, -8*w^2 + 5*w + 36]', '[9928, 9928, 3*w^3 - 10*w^2 - 6*w + 32]', '[9928, 9928, -4*w^3 - w^2 + 14*w + 16]', '[9931, 9931, -2*w^3 - 2*w^2 + 16*w - 5]', '[9938, 9938, 4*w^3 - 8*w^2 - 19*w + 23]', '[9938, 9938, -19*w^3 - 4*w^2 + 84*w + 46]', '[9941, 9941, 2*w^3 + 6*w^2 - 12*w - 23]', '[9941, 9941, 5*w^3 - 4*w^2 - 21*w + 3]', '[9944, 2486, 11*w^3 - 14*w^2 - 43*w + 46]', '[9944, 2486, -9*w^3 + 19*w^2 + 31*w - 65]', '[9944, 4972, -4*w^3 + w^2 + 21*w - 8]', '[9944, 9944, 2*w^3 - 6*w^2 - 3*w + 20]', '[9949, 9949, 7*w^2 - w - 23]', '[9962, 9962, 2*w^3 - 10*w^2 - 7*w + 39]', '[9962, 9962, 4*w^3 + 4*w^2 - 19*w - 11]', '[9962, 9962, 3*w^3 + w^2 - 9*w - 18]', '[9962, 9962, 7*w^3 - 28*w - 22]', '[9964, 4982, -4*w^3 + 9*w^2 + 7*w - 10]', '[9964, 4982, 4*w^3 - 9*w^2 - 16*w + 23]', '[9964, 4982, 4*w^3 - 3*w^2 - 17*w - 2]', '[9964, 4982, -4*w^3 + 7*w^2 + 20*w - 13]', '[9964, 9964, -2*w^3 + w + 8]', '[9964, 9964, 4*w^3 + 4*w^2 - 13*w - 16]', '[9973, 9973, -7*w^3 + 9*w^2 + 24*w - 21]', '[9983, 9983, -w^3 + 7*w^2 + 10*w - 15]', '[9988, 4994, 2*w^3 - 9*w^2 - 2*w + 11]', '[9988, 4994, -3*w^3 + 11*w^2 - 18]', '[9988, 9988, w^2 - 8*w + 4]', '[9991, 9991, -4*w^3 + 7*w^2 + 7*w - 15]', '[9991, 9991, -5*w^3 + 6*w^2 + 15*w - 11]', '[9991, 9991, 3*w^3 - 9*w^2 - 8*w + 17]', '[9991, 9991, -2*w^3 + 8*w^2 + 4*w - 21]', '[10000, 10, 10]', '[10000, 20, -5*w^3 + 15*w]', '[10000, 20, -5*w^3 + 5*w^2 + 15*w - 5]', '[10000, 40, -5*w^2 + 5*w + 20]', '[10000, 80, -5*w^3 + 20*w]'], 'label': '4.4.8468.1', 'narrow_class_no': 1, 'primes': ['[2, 2, w^3 - 4*w - 2]', '[2, 2, w - 1]', '[11, 11, -w^3 + 5*w + 1]', '[17, 17, -w^3 + 3*w + 1]', '[23, 23, w^3 + w^2 - 4*w - 5]', '[29, 29, -w^3 + w^2 + 2*w - 1]', '[29, 29, w^3 + w^2 - 6*w - 5]', '[29, 29, w^3 - w^2 - 4*w + 1]', '[47, 47, w^3 - 3*w - 3]', '[53, 53, 2*w^2 - 2*w - 5]', '[53, 53, -w^3 + 2*w^2 + 5*w - 7]', '[59, 59, 2*w^3 - 8*w - 3]', '[59, 59, w^3 - w^2 - 2*w + 3]', '[67, 67, 2*w - 1]', '[71, 71, 2*w^2 - 5]', '[73, 73, -w^3 + w^2 + 4*w + 1]', '[73, 73, -2*w^3 + 8*w + 1]', '[73, 73, -w^3 + 5*w - 1]', '[79, 79, w^2 - w + 1]', '[79, 79, w^3 + w^2 - 4*w - 7]', '[81, 3, -3]', '[83, 83, 2*w^3 + w^2 - 9*w - 5]', '[83, 83, w^2 + w - 5]', '[97, 97, 4*w^3 + w^2 - 19*w - 11]', '[97, 97, -2*w^3 + 3*w^2 + 7*w - 7]', '[101, 101, -w^3 + 2*w^2 + 3*w - 3]', '[103, 103, w^3 + w^2 - 4*w - 1]', '[103, 103, -2*w^3 + w^2 + 7*w - 5]', '[109, 109, w^3 - w^2 - 2*w - 3]', '[113, 113, 2*w^2 - 9]', '[131, 131, -2*w^2 + 2*w + 7]', '[137, 137, -2*w^3 + w^2 + 9*w - 3]', '[137, 137, 2*w^3 - w^2 - 9*w - 1]', '[149, 149, 2*w^3 - w^2 - 7*w - 1]', '[157, 157, w^3 - 5*w + 3]', '[163, 163, -w^3 + 3*w^2 + 4*w - 7]', '[173, 173, w^3 + 2*w^2 - 3*w - 7]', '[179, 179, w^3 - w^2 - 2*w + 5]', '[179, 179, w^3 - 5*w - 5]', '[191, 191, 2*w^2 + 2*w - 7]', '[197, 197, 3*w^2 - w - 5]', '[197, 197, -2*w^3 + w^2 + 7*w - 7]', '[223, 223, 2*w^3 - 2*w^2 - 8*w + 3]', '[227, 227, w^2 + 3*w - 5]', '[233, 233, -3*w^3 - w^2 + 12*w + 9]', '[233, 233, 3*w^2 - w - 11]', '[239, 239, w^3 - 5*w + 5]', '[239, 239, w^3 + 2*w^2 - 5*w - 3]', '[241, 241, -w^3 + w^2 + 6*w - 5]', '[241, 241, w^3 + 2*w^2 - 5*w - 7]', '[251, 251, 3*w^3 - 13*w - 3]', '[251, 251, w^3 - 2*w^2 - 5*w + 3]', '[257, 257, -2*w^3 + w^2 + 7*w - 1]', '[271, 271, -2*w^3 + 2*w^2 + 6*w - 5]', '[277, 277, w^3 - w - 3]', '[277, 277, -w^3 - w^2 + 6*w + 1]', '[283, 283, -w^3 + 4*w^2 + w - 7]', '[293, 293, 4*w^3 - 18*w - 9]', '[293, 293, 3*w^3 - w^2 - 12*w - 1]', '[307, 307, 3*w^3 - 15*w - 7]', '[313, 313, 2*w^3 - 6*w - 1]', '[313, 313, w^3 + w^2 - 4*w - 9]', '[317, 317, -3*w^2 - w + 5]', '[317, 317, 2*w^3 - w^2 - 7*w - 5]', '[331, 331, 2*w^2 - 2*w - 9]', '[337, 337, w^3 - w^2 - 6*w + 1]', '[347, 347, -2*w^3 + 2*w^2 + 6*w - 3]', '[349, 349, 2*w^3 - 2*w^2 - 4*w + 3]', '[373, 373, 6*w^3 + 2*w^2 - 26*w - 15]', '[379, 379, 3*w^3 - w^2 - 12*w - 5]', '[389, 389, -2*w^3 + 4*w^2 + 4*w - 9]', '[389, 389, 3*w^3 + 2*w^2 - 13*w - 13]', '[397, 397, -3*w^3 + 2*w^2 + 11*w - 1]', '[401, 401, 2*w^3 - w^2 - 9*w - 3]', '[409, 409, w^3 + w^2 - 2*w - 5]', '[419, 419, 3*w^3 - 2*w^2 - 11*w - 1]', '[421, 421, -w^3 + 3*w^2 + 2*w - 11]', '[439, 439, 2*w^3 - 6*w - 5]', '[449, 449, -w^3 + w^2 + 6*w - 3]', '[457, 457, w^3 - w^2 - 3]', '[461, 461, 2*w^3 - 2*w^2 - 10*w + 1]', '[461, 461, -2*w^3 - 2*w^2 + 6*w + 7]', '[463, 463, -2*w^3 + 3*w^2 + 5*w - 1]', '[467, 467, 3*w^3 - 6*w^2 - 13*w + 19]', '[487, 487, w^2 - 3*w - 5]', '[491, 491, -2*w^3 + w^2 + 5*w - 1]', '[499, 499, -w^3 + 3*w^2 + 6*w - 9]', '[503, 503, -2*w^3 + 3*w^2 + 7*w - 13]', '[503, 503, 4*w^3 + 2*w^2 - 18*w - 11]', '[509, 509, -3*w^3 + 3*w^2 + 12*w - 11]', '[523, 523, 3*w^3 - 11*w - 5]', '[541, 541, 3*w^2 - w - 9]', '[541, 541, -w^3 - 2*w^2 + 7*w + 9]', '[541, 541, -3*w^3 + 2*w^2 + 11*w - 5]', '[541, 541, -w^3 + 4*w^2 + 3*w - 11]', '[569, 569, -3*w^3 + 3*w^2 + 12*w - 13]', '[571, 571, 4*w^3 - w^2 - 17*w - 5]', '[571, 571, w^2 + 3*w - 3]', '[577, 577, -w^3 - 2*w^2 + 7*w + 3]', '[593, 593, -2*w^3 + w^2 + 9*w - 5]', '[601, 601, -2*w^3 + 6*w - 5]', '[607, 607, 2*w^3 - 2*w^2 - 10*w + 3]', '[607, 607, 2*w^3 - 3*w^2 - 5*w + 9]', '[613, 613, 2*w^3 - w^2 - 5*w - 5]', '[613, 613, w^2 + w - 9]', '[617, 617, 6*w^3 - 28*w - 13]', '[619, 619, -w^3 + 2*w^2 + 5*w + 1]', '[619, 619, 3*w^2 - 5*w - 7]', '[625, 5, -5]', '[653, 653, 2*w^3 - 5*w^2 - 9*w + 13]', '[653, 653, 2*w^3 + w^2 - 7*w + 1]', '[659, 659, -3*w^3 + 2*w^2 + 9*w - 7]', '[659, 659, -3*w^3 - 2*w^2 + 17*w + 11]', '[661, 661, -2*w^3 + 8*w - 5]', '[677, 677, -w^3 - 3*w^2 + 6*w + 7]', '[677, 677, 3*w^2 + w - 11]', '[677, 677, -w^3 - 2*w^2 + 9*w + 3]', '[677, 677, 2*w^3 - 4*w^2 - 1]', '[719, 719, -w^3 + 3*w^2 - 7]', '[719, 719, -w^2 + w - 3]', '[727, 727, -w^3 + 5*w^2 + 4*w - 13]', '[727, 727, 3*w^3 - 11*w - 3]', '[739, 739, 2*w^3 + 2*w^2 - 8*w - 11]', '[739, 739, -w^3 + 3*w^2 + 4*w - 5]', '[743, 743, w^3 + 3*w^2 - 4*w - 7]', '[751, 751, -2*w^3 + 2*w^2 + 8*w - 1]', '[757, 757, w^3 + 3*w^2 - 6*w - 11]', '[757, 757, -4*w - 1]', '[769, 769, 2*w^3 - 2*w^2 - 8*w + 11]', '[773, 773, -w^3 + 7*w - 1]', '[787, 787, w^2 - 3*w - 7]', '[797, 797, 4*w^3 - 16*w - 7]', '[797, 797, w^3 - 7*w - 1]', '[809, 809, 3*w^3 - 3*w^2 - 12*w + 5]', '[809, 809, w^3 - 5*w^2 - 2*w + 17]', '[811, 811, w^3 - 2*w^2 - 7*w + 9]', '[823, 823, -2*w^3 + 3*w^2 + w + 1]', '[827, 827, -3*w^3 + w^2 + 12*w - 3]', '[827, 827, 8*w^3 - 36*w - 15]', '[829, 829, -w^2 - w - 3]', '[853, 853, 4*w^3 + w^2 - 17*w - 7]', '[853, 853, 4*w - 3]', '[857, 857, 2*w^3 + 3*w^2 - 11*w - 11]', '[859, 859, w^3 - 5*w^2 - 4*w + 15]', '[877, 877, -4*w^3 + w^2 + 15*w - 3]', '[881, 881, -4*w^2 + 6*w + 9]', '[881, 881, -w^3 + 3*w - 5]', '[881, 881, 3*w^2 - 3*w - 11]', '[881, 881, -w^3 + 4*w^2 + w - 13]', '[883, 883, 2*w^3 - 3*w^2 - 3*w - 3]', '[883, 883, w^3 - 5*w^2 + 13]', '[887, 887, -w^3 + 2*w^2 + w - 7]', '[911, 911, -4*w^3 + 4*w^2 + 14*w - 13]', '[911, 911, 2*w^2 + 2*w - 9]', '[919, 919, -w^2 - 5*w + 9]', '[919, 919, 3*w^3 - 15*w - 5]', '[937, 937, -3*w^3 + 3*w^2 + 10*w - 5]', '[953, 953, -8*w^3 - w^2 + 35*w + 17]', '[961, 31, 3*w^3 - w^2 - 14*w - 5]', '[961, 31, 2*w^3 - 5*w^2 - 5*w + 9]', '[967, 967, 5*w^2 + w - 9]', '[967, 967, -5*w^3 + 23*w + 13]', '[977, 977, -w^3 - 2*w^2 + 7*w + 11]', '[977, 977, -3*w^3 + 2*w^2 + 13*w - 7]', '[983, 983, 2*w^3 - 6*w - 7]', '[991, 991, 6*w^2 - 11]', '[991, 991, 3*w^3 - 5*w^2 - 12*w + 13]', '[997, 997, w^3 + w^2 - 8*w - 3]', '[997, 997, -3*w^3 + 4*w^2 + 9*w - 9]']}
• 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': [4, 3, -5, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 8468, 'disc_rad': 4234, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [[4, 1]]], [7, [[4, 1]]], [11, [[3, 1], [1, 1]]], [13, [[4, 1]]], [17, [[3, 1], [1, 1]]], [19, [[4, 1]]], [23, [[3, 1], [1, 1]]], [29, [0]], [31, [[2, 2]]], [37, [[4, 1]]], [41, [[4, 1]]], [43, [[2, 2]]], [47, [[3, 1], [1, 1]]], [53, [[2, 1], [1, 2]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 73.03770071172075, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.8468.1', 'local_algs': ['2.1.0.1', '2.3.2.1', '29.1.0.1', '29.1.0.1', '29.2.1.2', '73.1.0.1', '73.1.0.1', '73.2.1.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 29, 73], 'rd': 9.59279607636, 'regulator': {'__RealLiteral__': 0, 'data': '9.39000564978', 'prec': 44}, 'res': {'gal': ['16,0,-3728,0,168912,0,-2418328,0,12305100,0,-16563700,0,9931749,0,-3138062,0,560787,0,-57608,0,3291,0,-94,0,1'], 'sib': ['-961,-4628,3749,44034,58644,9600,-16491,-3230,1912,160,-79,-2,1', '1097,1745,686,-47,-52,-1,1', '1363,-8352,-14522,-1942,1937,230,-88,-4,1', '2,-6,-4,19,-7,-3,1', '8,-64,-124,950,988,-972,-997,250,299,-16,-31,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} - a^{2} - 4 a + 3 \\)', '\\( a^{2} - a - 3 \\)', '\\( a^{3} - 5 a - 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}