Hilbert modular form data - 4.4.13768.1-16.3-c

Formats: - HTML - YAML - JSON - 2024-04-30T11:21:19.832328

• 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': 3, 'disc': 13768, 'field_bad_primes': [2, 1721], 'field_label': '4.4.13768.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.13768.1-16.3-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [2], 'level_ideal': '[16, 4, w^2 - 2]', 'level_label': '16.3', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.3-c', '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]], 'hecke_eigenvalues': [0, 'e', 'e - 1', '-e + 4', 0, 'e^2 + e - 4', 'e^2 - e', 'e^2 - 4', 'e^2 - 2*e - 4', '2*e^2 - e - 4', '-2*e^2 + 3*e + 8', '-e^2 + 3*e + 4', '-e^2 + 4', '3*e', 'e - 10', '-e^2 - e + 8', '-e^2 + e', 'e^2 + e - 2', '-e^2 - 4*e + 4', '-2*e^2 + e + 2', '-3*e^2 + 3*e + 6', '2*e^2 + 3*e - 8', '-5*e^2 + e + 20', '2*e^2 - 5*e - 12', '-2*e^2 + 2*e + 12', '-3*e', '-3*e^2 - e + 16', '-6*e', '5*e^2 - 3*e - 20', '-2*e^2 - 5*e + 16', '-3*e^2 + 3*e + 12', '-3*e^2 + 3*e + 12', '-3*e^2 + 16', '-e^2 + 2*e + 16', '-e^2 - 7*e + 8', '-3*e^2 - 3*e + 12', '-6*e', '3*e^2 + 3*e - 18', '6*e + 6', '3*e^2 - 20', '-3*e^2 + 24', '-5*e^2 + 5*e + 24', 'e^2 - 5*e - 2', '-2*e^2 + 5*e + 12', '2*e^2 - 5*e - 6', '3*e^2 + 6*e - 30', '2*e^2 + 5*e - 8', '4*e^2 - 5*e - 26', '-2*e^2 + 5*e + 12', '-3*e^2 + 24', '-e^2 + 3*e - 14', '3*e^2 + 3*e - 12', '3*e^2 - 2*e - 10', -8, '-5*e^2 - 3*e + 32', 'e^2 - 2*e - 16', '3*e^2 + 3*e - 4', 'e^2 - 9*e - 4', '-5*e^2 - 3*e + 20', -6, '-2*e^2 - 5*e + 8', '-3*e^2 - 3*e + 36', '2*e^2 - 4*e + 4', '-3*e^2 - 3*e + 24', '-2*e^2 + 3*e + 26', '-e^2 + 2*e + 8', '-e^2 + 3*e - 8', '-2*e^2 + 4*e + 14', '-3*e^2 + 9*e + 24', 12, '-e^2 + e + 12', '3*e^2 - 9*e - 20', '6*e^2 - 3*e - 24', '3*e^2 - 6*e - 18', '-3*e^2 + 3*e + 4', '3*e^2 + 2', '-e^2 + e + 18', '3*e^2 - 7*e - 8', '-4*e^2 - 4*e + 20', '3*e^2 + 6*e - 36', '-4*e^2 - 9*e + 40', 12, '3*e^2', '-3*e^2 + 3*e + 16', '-3*e^2 + 6*e + 12', '-4*e^2 - 3*e + 40', '3*e^2 - 3*e - 30', '-3*e^2 - e + 28', '-e^2 - 7*e + 4', '-e^2 - 2*e + 18', '-6*e + 14', '8*e^2 - 3*e - 26', '2*e^2 + 3*e - 32', '2*e^2 + 2*e + 4', '6*e^2 - 9*e - 20', 'e^2 - 5*e + 16', 'e^2 - 8*e - 2', '7*e^2 + e - 40', '-e^2 + 28', '-4*e^2 - 3*e + 16', '4*e^2 + 4*e - 44', '3*e + 12', '-8*e^2 - 6*e + 38', '3*e - 10', '5*e^2 - 13*e - 20', 36, '-e^2 - 10*e + 20', '-3*e^2 + 4*e + 2', '-5*e^2 - 2*e + 44', '6*e^2 + 3*e - 44', '-6*e^2 + 18', '-5*e^2 + 3*e + 26', '3*e^2 + 3*e - 36', '-8*e - 22', '6*e^2 - 6*e - 44', '5*e^2 - e - 8', '-6*e^2 + 10*e + 26', '6*e^2 - 6*e - 12', '6*e^2 + e - 40', 'e^2 + 7*e + 2', '5*e^2 - 6*e - 8', '-3*e^2 - 3*e + 20', '-e^2 + 13*e + 18', '-3*e^2 + 14*e + 16', '-3*e^2 + 15*e + 20', '-3*e^2 + 12*e + 6', '-3*e^2 + 9*e + 16', '2*e^2 - 6*e - 8', '7*e^2 + 3*e - 22', '6*e^2 - 42', '6*e - 12', '7*e^2 - 2*e - 28', '5*e^2 - 14*e - 12', '7*e^2 + 6*e - 46', '-2*e^2 + 12*e + 26', '-3*e^2 + 6*e + 32', '-3*e^2 - 9*e + 16', '-6*e^2 + 12*e + 36', '-5*e^2 + 7*e + 14', '-4*e^2 - 2*e + 30', '-5*e^2 + 13*e + 26', '3*e^2 - 6*e', '3*e + 36', '-15*e + 8', '4*e^2 + 3*e - 4', '-e^2 + 13*e + 6', '3*e^2 - 9*e - 6', '2*e^2 - 20*e - 12', '3*e^2 - 6*e - 8', '8*e^2 - 3*e - 20', '-2*e^2 + 8*e + 12', 'e^2 + 9*e - 28', '-3*e^2 + 16', '-e^2 + 8*e - 4', '-4*e^2 + 9*e + 22', '-6*e^2 + 12*e + 28', '3*e^2 + 9*e', '-e^2 + 3*e + 22', '-e^2 - 4*e - 8', '6*e^2 + 6*e - 36', '9*e^2 + 6*e - 48', '-7*e^2 + 2*e + 20', '11*e^2 + 5*e - 52'], 'hecke_polynomial': 'x^3 - x^2 - 7*x + 4', 'label': '4.4.13768.1-16.3-c'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 13768, 'ideals': ['[1, 1, 1]', '[2, 2, -w]', '[3, 3, w + 1]', '[4, 2, w^3 - w^2 - 4*w]', '[4, 2, -w^2 - w + 1]', '[6, 6, w - 2]', '[8, 2, w^3 - w^2 - 5*w + 2]', '[8, 4, -w^3 + w^2 + 4*w - 2]', '[9, 9, -w^3 + w^2 + 4*w - 1]', '[12, 6, -w^2 + 2*w]', '[12, 6, -w^3 + 2*w^2 + 4*w - 5]', '[13, 13, -w^2 + 3]', '[16, 2, 2]', '[16, 4, w^2 - w - 3]', '[16, 4, w^2 - 2]', '[17, 17, -w + 3]', '[18, 18, w^2 - w - 2]', '[24, 6, w^3 - w^2 - 5*w]', '[24, 12, -w^3 + 4*w]', '[26, 26, w^3 - 3*w]', '[27, 3, w^3 - 2*w^2 - 3*w + 5]', '[27, 27, -w^3 + 5*w + 1]', '[31, 31, -w^2 - 2*w + 1]', '[32, 4, -2*w]', '[32, 4, -w^3 + w^2 + 3*w]', '[32, 8, -w^3 + 2*w]', '[34, 34, w^2 - 3*w]', '[36, 18, -w^3 + w^2 + 2*w]', '[36, 18, w^2 + w - 3]', '[39, 39, -3*w^3 + 4*w^2 + 13*w - 9]', '[41, 41, -w^2 + 5]', '[43, 43, w^3 - w^2 - 5*w - 1]', '[43, 43, w^3 - w^2 - 3*w + 1]', '[48, 6, 2*w + 2]', '[48, 12, 2*w^3 - 3*w^2 - 8*w + 6]', '[48, 12, w^3 - 4*w - 3]', '[51, 51, -w^2 + 2*w + 3]', '[52, 26, -w^2 - w - 1]', '[52, 26, -w^3 + w^2 + 6*w - 4]', '[54, 6, w^3 - 2*w^2 - 3*w + 2]', '[54, 54, w^3 - 3*w - 2]', '[59, 59, -w - 3]', '[59, 59, -2*w^3 + 2*w^2 + 9*w - 5]', '[59, 59, -w^3 - 3*w^2 - w + 3]', '[59, 59, w^3 - 7*w + 1]', '[61, 61, -w^3 + w^2 + 2*w + 5]', '[61, 61, -w^3 - w^2 + 4*w + 3]', '[62, 62, 2*w^3 - 2*w^2 - 9*w + 2]', '[64, 4, 2*w^3 - 2*w^2 - 8*w]', '[64, 4, -2*w^2 - 2*w + 2]', '[64, 8, -w^3 + 6*w]', '[64, 8, -w^3 + 4*w - 1]', '[67, 67, 4*w^3 - 4*w^2 - 18*w + 7]', '[68, 34, w^3 - 2*w^2 - 4*w + 3]', '[68, 34, w^3 - w^2 - 6*w]', '[72, 18, -w^3 - w^2 + 3*w]', '[72, 36, w^3 - 2*w^2 - 4*w + 8]', '[73, 73, -2*w^3 + 6*w - 3]', '[73, 73, -2*w + 3]', '[78, 78, -w^3 + 2*w^2 + 3*w - 6]', '[81, 3, 3]', '[81, 81, -w^2 + 7]', '[82, 82, w^3 - 5*w]', '[86, 86, -2*w^2 + w + 2]', '[86, 86, 3*w + 2]', '[93, 93, -w^3 + 2*w^2 + 5*w - 7]', '[96, 12, -w^3 - w^2 + 5*w + 2]', '[96, 12, 2*w - 4]', '[96, 24, w^3 - 2*w^2 - 2*w + 4]', '[97, 97, w^3 - 2*w^2 - 5*w + 3]', '[101, 101, w^3 + w^2 - 5*w - 7]', '[101, 101, -w^3 - w^2 + 4*w + 5]', '[102, 102, w^3 - 2*w^2 - 3*w]', '[103, 103, 2*w^3 - 8*w - 1]', '[103, 103, w^2 - 2*w - 7]', '[104, 26, w^3 - 3*w^2 - w + 4]', '[104, 52, -w^3 + 4*w + 4]', '[108, 6, w^3 + w^2 - 6*w - 4]', '[108, 6, -2*w^3 + w^2 + 9*w - 1]', '[108, 54, -3*w^3 + 4*w^2 + 12*w - 10]', '[108, 54, 3*w^3 - 4*w^2 - 14*w + 11]', '[109, 109, -w^3 + 2*w^2 + 3*w - 7]', '[113, 113, -w^3 + w^2 + 6*w - 3]', '[117, 117, -2*w^3 + 2*w^2 + 10*w - 3]', '[118, 118, w^2 + w - 4]', '[118, 118, 2*w^3 - 3*w^2 - 9*w + 6]', '[118, 118, -w^3 + 2*w^2 + w + 2]', '[118, 118, w^2 + 3*w]', '[122, 122, -w^3 + 2*w^2 + 5*w - 8]', '[122, 122, 2*w^3 + w^2 - 5*w - 2]', '[123, 123, -w^3 + w^2 + 2*w - 3]', '[124, 62, w^3 - 4*w - 5]', '[124, 62, -w^2 + 2*w + 4]', '[127, 127, -w^3 + w^2 + 6*w - 1]', '[128, 4, 2*w^3 - 2*w^2 - 10*w + 4]', '[128, 8, -3*w^3 + 3*w^2 + 13*w - 4]', '[128, 8, -2*w^3 + 2*w^2 + 8*w - 4]', '[128, 16, w^3 - w^2 - 2*w - 2]', '[129, 129, w^3 - w^2 - 8*w - 3]', '[129, 129, w^3 + w^2 - 4*w - 1]', '[131, 131, -2*w^3 + 3*w^2 + 10*w - 11]', '[134, 134, -2*w^2 + w + 8]', '[136, 34, w^3 + w^2 - 5*w - 4]', '[136, 68, w^2 + 2*w + 2]', '[137, 137, w^3 + w^2 - 6*w - 5]', '[139, 139, -3*w^3 + 2*w^2 + 15*w - 1]', '[144, 18, -2*w^3 + 2*w^2 + 8*w - 2]', '[144, 36, w^3 - w^2 - 6*w + 2]', '[144, 36, 2*w^3 - w^2 - 11*w + 1]', '[146, 146, -4*w^3 + 5*w^2 + 17*w - 12]', '[146, 146, -2*w^2 + 3*w]', '[149, 149, w^3 - 3*w^2 - 4*w + 11]', '[149, 149, -w^3 + 5*w - 1]', '[153, 153, -w^3 + w^2 + 5*w + 3]', '[156, 78, w^3 - 6*w + 1]', '[156, 78, -w^3 + 2*w^2 + 4*w - 2]', '[157, 157, -2*w^3 + 3*w^2 + 6*w - 1]', '[162, 6, -3*w]', '[162, 162, w^3 - 7*w]', '[163, 163, 2*w^2 - 3]', '[163, 163, -2*w^3 + 2*w^2 + 7*w - 5]', '[164, 82, -w^3 + 2*w + 2]', '[164, 82, w^2 - 3*w - 3]', '[167, 167, -2*w^3 + 2*w^2 + 8*w - 3]', '[167, 167, -2*w^2 + 2*w + 9]', '[169, 169, -3*w + 1]', '[172, 86, w^3 + 2*w^2 + 1]', '[172, 86, -3*w^3 + w^2 + 14*w + 8]', '[172, 86, -w^3 - 2*w^2 + 3]', '[172, 86, -w^3 + w^2 + 2*w + 4]', '[173, 173, 2*w^3 - w^2 - 8*w + 3]', '[173, 173, 2*w^3 - 3*w^2 - 6*w + 3]', '[177, 177, -2*w^3 + w^2 + 8*w - 1]', '[177, 177, -2*w^3 + 4*w^2 + 10*w - 11]', '[177, 177, 2*w^3 - 2*w^2 - 8*w - 1]', '[177, 177, -w^2 - 4*w - 3]', '[181, 181, 2*w^3 - 3*w^2 - 8*w + 5]', '[183, 183, -3*w^3 - 2*w^2 + 9*w + 5]', '[183, 183, -2*w^3 + 6*w^2 - 5]', '[186, 186, -w^3 + 5*w - 2]', '[191, 191, -2*w^3 + w^2 + 10*w - 1]', '[192, 12, -2*w^2 + 4*w]', '[192, 12, -2*w^3 + 4*w^2 + 8*w - 10]', '[192, 24, 2*w^3 - 3*w^2 - 9*w + 11]', '[192, 24, -2*w^3 + w^2 + 8*w + 2]', '[193, 193, -w^3 + 3*w^2 + 2*w - 7]', '[193, 193, w^3 - 3*w - 3]', '[193, 193, 2*w^2 - 2*w - 3]', '[193, 193, w^3 - 7*w - 1]', '[194, 194, w^3 - w + 2]', '[197, 197, w^2 - 2*w - 5]', '[201, 201, 4*w^3 - 2*w^2 - 19*w - 1]', '[202, 202, -2*w^3 + 9*w + 2]', '[202, 202, 2*w^3 + w^2 - 7*w - 2]', '[204, 102, -w^3 + 3*w^2 + 4*w - 12]', '[204, 102, -w^2 - 3*w + 1]', '[206, 206, -w^3 + 2*w^2 + 7*w]', '[206, 206, 3*w^3 - 4*w^2 - 13*w + 8]', '[208, 26, -2*w^2 + 6]', '[208, 52, w^2 - w - 7]', '[208, 52, w^3 + w^2 - 6*w - 2]', '[211, 211, w^2 - 4*w - 1]', '[216, 6, w^3 + w^2 - 3*w - 4]', '[216, 12, -4*w^3 + 5*w^2 + 18*w - 14]', '[216, 54, w^3 - w^2 - 5*w + 6]', '[216, 108, -w^2 + 2*w + 6]', '[218, 218, -w^3 + 2*w^2 + 5*w - 2]', '[219, 219, 5*w^3 - 7*w^2 - 21*w + 21]', '[219, 219, 2*w^2 - w - 3]', '[221, 221, w^3 - 3*w^2 - 3*w + 9]', '[226, 226, -w^2 + w - 2]', '[229, 229, -w^3 + w^2 + 6*w - 7]', '[229, 229, -4*w^3 + 6*w^2 + 16*w - 13]', '[233, 233, 3*w^2 + 2*w - 5]', '[233, 233, 2*w^3 - 2*w^2 - 11*w + 7]', '[234, 234, -w - 4]', '[236, 118, -3*w^3 + 2*w^2 + 14*w + 2]', '[236, 118, w^3 + 4*w^2 + 2*w - 3]', '[236, 118, w^3 - 2*w^2 - 4*w + 1]', '[236, 118, -w^3 - w^2 + 4*w]', '[236, 118, w^3 - w^2 - 2*w + 4]', '[236, 118, w^2 + w - 5]', '[236, 118, 2*w^3 + w^2 - 11*w - 9]', '[236, 118, -3*w^3 - w^2 + 18*w + 8]', '[239, 239, -w^3 + w^2 + 7*w + 1]', '[241, 241, w^3 - 3*w^2 - 2*w + 9]', '[241, 241, w^3 + w^2 - 9*w - 5]', '[243, 9, 3*w + 3]', '[243, 243, -w^3 + 3*w^2 + 2*w - 5]', '[244, 122, 2*w^3 - 3*w^2 - 7*w + 3]', '[244, 122, -w^3 + 6*w - 2]', '[244, 122, 4*w^3 + 5*w^2 - 7*w - 3]', '[244, 122, 3*w^3 - 16*w - 6]', '[246, 246, 2*w^3 - 7*w - 2]', '[248, 62, -w^3 - w^2 + 7*w + 2]', '[248, 124, w^3 - 2*w^2 - 4*w]', '[251, 251, 2*w^3 - 6*w + 1]', '[254, 254, -w^2 - w - 2]', '[256, 4, 4]', '[256, 8, 2*w^2 - 2*w - 6]', '[256, 8, 2*w^2 - 4]', '[256, 16, -w^3 + 4*w + 7]', '[256, 16, w^3 + w^2 - 2*w + 2]', '[258, 258, -2*w^3 + 2*w^2 + 7*w]', '[258, 258, -2*w^3 + 4*w^2 + 5*w - 4]', '[262, 262, -w^3 + 7*w - 4]', '[268, 134, 2*w^3 - w^2 - 8*w]', '[268, 134, -2*w^3 + w^2 + 11*w + 1]', '[271, 271, 2*w^3 - w^2 - 8*w - 1]', '[271, 271, -2*w^2 + w + 7]', '[272, 34, -2*w + 6]', '[272, 68, w^3 - 8*w - 3]', '[272, 68, -w^3 + 3*w^2 + 2*w - 6]', '[274, 274, -2*w^3 + w^2 + 7*w + 2]', '[278, 278, -3*w + 4]', '[279, 279, 2*w^2 - 5]', '[281, 281, 2*w^3 + 2*w^2 - 5*w - 1]', '[288, 36, 2*w^2 - 2*w - 4]', '[288, 36, -w^3 + w^2 + 3*w + 4]', '[288, 72, w^2 + 2]', '[289, 289, w^3 - w^2 - 2*w + 5]', '[291, 291, -2*w^2 - 4*w + 1]', '[292, 146, -w^3 + 3*w^2 + 4*w - 8]', '[292, 146, w^3 - 2*w^2 - 4*w + 9]', '[292, 146, -w^3 + 2*w^2 + 4*w + 2]', '[292, 146, w^3 - 2*w^2 - 6*w + 1]', '[293, 293, w^3 + w^2 - 5*w - 1]', '[293, 293, -3*w + 7]', '[298, 298, 2*w^3 - w^2 - 9*w + 2]', '[298, 298, w^3 - w - 2]', '[303, 303, -3*w^3 - 2*w^2 + 11*w + 7]', '[303, 303, 3*w^3 + w^2 - 14*w - 9]', '[306, 306, 4*w^3 - 6*w^2 - 17*w + 14]', '[307, 307, -w^3 - 2*w^2 + 3*w + 5]', '[309, 309, w^3 - 3*w^2 - 3*w + 13]', '[309, 309, w^3 - w^2 - 9*w - 7]', '[311, 311, -w^3 + 3*w^2 + 4*w - 7]', '[312, 78, -w^3 + w^2 + w + 2]', '[312, 156, -w^3 + w^2 - 2]', '[313, 313, 2*w^2 - 2*w - 5]', '[314, 314, 2*w^3 - 2*w^2 - 7*w + 4]', '[317, 317, -2*w^3 + 4*w^2 + 7*w - 13]', '[317, 317, -2*w^3 + 3*w^2 + 8*w - 11]', '[324, 6, 3*w^3 - 3*w^2 - 12*w]', '[324, 6, -3*w^2 - 3*w + 3]', '[324, 162, -2*w^3 + w^2 + 8*w - 4]', '[324, 162, 2*w^3 - 3*w^2 - 9*w + 5]', '[326, 326, 3*w^2 + w - 4]', '[326, 326, -2*w^3 + 3*w]', '[327, 327, -2*w - 5]', '[328, 82, -w^3 - 3*w^2 + w + 4]', '[328, 164, -w^3 - 2*w^2 + 8*w + 8]', '[334, 334, 2*w^2 - w - 4]', '[334, 334, 2*w^3 - 2*w^2 - 9*w]', '[337, 337, 3*w^3 + 2*w^2 - 7*w + 1]', '[338, 338, 2*w^3 - 7*w - 4]', '[339, 339, -w^3 + 2*w^2 + 5*w - 1]', '[344, 86, -w^3 - w^2 + 7*w + 8]', '[344, 86, w^3 - 3*w^2 - 3*w + 8]', '[344, 172, -w^3 + w^2 + 4*w - 6]', '[344, 172, w^3 + w^2 - 4*w - 6]', '[346, 346, -w^3 - 2*w^2 + w + 4]', '[346, 346, w^3 - 4*w^2 + w + 4]', '[347, 347, 2*w^3 - 2*w^2 - 11*w + 1]', '[349, 349, -5*w^3 + 6*w^2 + 23*w - 13]', '[351, 39, 2*w^3 - 4*w^2 - 9*w + 13]', '[351, 351, 2*w^3 - w^2 - 6*w + 3]', '[354, 354, w^3 + 2*w^2 - 3*w - 4]', '[354, 354, w^3 - 2*w^2 - 7*w + 2]', '[354, 354, -2*w^2 + 5*w + 4]', '[354, 354, -w^2 - w + 6]', '[359, 359, 2*w^3 - 2*w^2 - 12*w + 9]', '[359, 359, -2*w^3 + 8*w + 5]', '[362, 362, w^3 - 2*w^2 - w + 4]', '[366, 366, w^2 - 3*w - 4]', '[366, 366, 2*w^2 - w - 6]', '[367, 367, -4*w^3 + 4*w^2 + 19*w - 5]', '[367, 367, 2*w^3 + w^2 - 10*w - 7]', '[369, 369, -4*w^3 + 4*w^2 + 18*w - 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10*w - 8]', '[1873, 1873, w^3 + 5*w^2 + 2*w - 3]', '[1874, 1874, 3*w^2 - w - 8]', '[1875, 15, -5*w - 5]', '[1877, 1877, 6*w^3 - w^2 - 32*w - 9]', '[1877, 1877, -w^3 + w^2 + 8*w + 7]', '[1878, 1878, 2*w^3 - 6*w^2 - w + 10]', '[1879, 1879, 4*w^2 - w - 15]', '[1884, 942, -w^3 - 2*w - 3]', '[1884, 942, -4*w^3 + 7*w^2 + 14*w - 12]', '[1888, 236, 3*w^3 - w^2 - 11*w - 2]', '[1888, 236, 2*w^2 + 2*w - 8]', '[1888, 236, w^3 - 3*w^2 - w + 10]', '[1888, 236, 4*w^3 - 6*w^2 - 18*w + 12]', '[1888, 236, -2*w^3 + 4*w^2 + 2*w + 4]', '[1888, 236, 2*w^2 + 6*w]', '[1888, 236, -5*w^3 + 5*w^2 + 23*w - 12]', '[1888, 236, -w^3 + 7*w^2 - 7*w - 10]', '[1888, 472, 2*w^3 - w^2 - 4*w + 6]', '[1888, 472, -4*w^3 + 3*w^2 + 16*w - 10]', '[1888, 472, -4*w^3 - w^2 + 24*w + 14]', '[1888, 472, 4*w^3 + 3*w^2 - 8*w - 2]', '[1889, 1889, -6*w^3 + 9*w^2 + 24*w - 19]', '[1891, 1891, 6*w^3 + 6*w^2 - 12*w - 5]', '[1891, 1891, 2*w^3 - 14*w + 1]', '[1898, 1898, -w^3 + 4*w^2 + 5*w - 4]', '[1898, 1898, -2*w^3 + 2*w^2 + 11*w - 12]', '[1899, 1899, 4*w^2 - 6*w - 7]', '[1902, 1902, 5*w^3 - 8*w^2 - 23*w + 26]', '[1902, 1902, -w^3 + 2*w^2 + 9*w]', '[1906, 1906, 3*w^2 - 9*w - 4]', '[1906, 1906, w^3 - 4*w^2 + 3*w + 6]', '[1907, 1907, 3*w^2 - 2*w - 7]', '[1912, 478, w^3 + w^2 - 7*w - 12]', '[1912, 956, -w^3 - 3*w^2 + 4*w + 10]', '[1913, 1913, 4*w^3 - 4*w^2 - 21*w + 1]', '[1913, 1913, -w^3 - w^2 + w + 5]', '[1916, 958, 4*w^3 - 3*w^2 - 17*w + 3]', '[1916, 958, -3*w^3 + 2*w^2 + 10*w + 6]', '[1921, 1921, -3*w^3 + 2*w^2 + 19*w - 11]', '[1922, 1922, w^3 - 2*w^2 - w + 10]', '[1928, 482, w^3 + w^2 - 3*w + 4]', '[1928, 482, w^3 + 3*w^2 - 5*w - 12]', '[1928, 964, -3*w^3 + 3*w^2 + 8*w + 10]', '[1928, 964, w^3 + 8]', '[1929, 1929, -3*w^3 + 2*w^2 + 11*w - 3]', '[1929, 1929, -w^3 + 4*w^2 + 3*w - 11]', '[1934, 1934, -2*w^3 - 3*w^2 + 5*w + 8]', '[1937, 1937, 3*w^3 - 5*w^2 - 11*w + 7]', '[1937, 1937, -2*w^3 + 4*w^2 + 11*w - 5]', '[1942, 1942, -4*w^3 + 4*w^2 + 19*w - 12]', '[1944, 18, 3*w^3 - 3*w^2 - 15*w]', '[1944, 36, -3*w^3 + 12*w]', '[1944, 486, -5*w^3 + 7*w^2 + 19*w - 14]', '[1944, 972, 3*w^3 - 4*w^2 - 16*w + 12]', '[1948, 974, 4*w^3 - w^2 - 21*w - 3]', '[1948, 974, -3*w^3 + 3*w^2 + 14*w]', '[1949, 1949, 2*w^3 + 4*w^2 - w + 1]', '[1951, 1951, -w^3 + 3*w^2 + 6*w - 11]', '[1951, 1951, 3*w^3 - 17*w - 3]', '[1952, 244, -2*w^3 + 4*w^2 + 10*w - 16]', '[1952, 244, 3*w^3 - 7*w^2 - 9*w + 20]', '[1952, 244, -w^3 + w^2 + 11*w + 4]', '[1952, 244, 4*w^3 + 2*w^2 - 10*w - 4]', '[1952, 488, -4*w^3 + 7*w^2 + 8*w - 2]', '[1952, 488, 4*w^3 + 7*w^2 - 2]', '[1956, 978, 2*w^3 - 7*w^2 - 2*w + 4]', '[1956, 978, 3*w^3 - 2*w^2 - 12*w + 11]', '[1956, 978, 8*w^3 - 13*w^2 - 37*w + 35]', '[1956, 978, 3*w^3 - 5*w^2 - 6*w + 8]', '[1959, 1959, -w^3 + 5*w^2 + 14*w + 5]', '[1959, 1959, 2*w^3 - 5*w^2 + 2*w - 3]', '[1962, 1962, -2*w^2 - w + 10]', '[1966, 1966, 4*w^3 - 2*w^2 - 17*w - 4]', '[1968, 246, -2*w^3 + 2*w^2 + 4*w - 6]', '[1968, 492, -w^2 - 4*w - 6]', '[1968, 492, -w^2 - 3*w + 7]', '[1971, 219, 5*w^3 - 7*w^2 - 24*w + 13]', '[1971, 219, -w^3 - w^2 - 3*w + 1]', '[1971, 1971, -14*w^3 + 20*w^2 + 59*w - 53]', '[1971, 1971, w^3 - 9*w + 1]', '[1973, 1973, -w^2 + 2*w - 5]', '[1977, 1977, -w^3 + 2*w^2 + 7*w - 11]', '[1979, 1979, -3*w^3 + w^2 + 14*w - 1]', '[1982, 1982, -w^3 + 2*w^2 + 5*w - 12]', '[1982, 1982, -2*w^3 + 5*w^2 + w + 2]', '[1983, 1983, -3*w^3 + 3*w^2 + 16*w + 1]', '[1983, 1983, 3*w^3 - w^2 - 20*w - 13]', '[1984, 124, 2*w^3 - 8*w - 10]', '[1984, 124, -2*w^2 + 4*w + 8]', '[1984, 248, -3*w^3 + 8*w^2 + 4*w - 11]', '[1984, 248, w^3 + w^2 - 2*w - 6]', '[1987, 1987, -6*w - 1]', '[1989, 1989, -2*w^3 + 2*w - 3]', '[1993, 1993, 4*w^2 + w - 11]', '[1996, 998, -w^3 + 4*w^2 + 2*w - 10]', '[1996, 998, -w^2 - w + 11]', '[1996, 998, w^3 - 4*w^2 - 2*w + 19]', '[1996, 998, 4*w^3 - 3*w^2 - 18*w - 4]', '[1997, 1997, 7*w^3 - 11*w^2 - 28*w + 25]', '[1997, 1997, 3*w^3 - 2*w^2 - 11*w - 1]', '[2003, 2003, 6*w^3 - 3*w^2 - 30*w - 1]', '[2003, 2003, 3*w^3 + 2*w^2 - 9*w - 1]', '[2004, 1002, -4*w^3 + 5*w^2 + 14*w - 4]', '[2004, 1002, 3*w^3 + 2*w^2 - 16*w - 9]', '[2004, 1002, 2*w^3 - 5*w^2 - 2*w + 8]', '[2004, 1002, 7*w^3 - 10*w^2 - 32*w + 27]', '[2006, 2006, -w^3 + 2*w^2 + 7*w - 12]', '[2006, 2006, -4*w^3 + 5*w^2 + 9*w + 2]', '[2006, 2006, -w^3 + 9*w]', '[2006, 2006, 2*w^3 + 2*w^2 - 5*w - 6]', '[2008, 502, w^3 - 5*w^2 - 5*w + 14]', '[2008, 1004, 2*w^3 + w^2 - 10*w - 2]', '[2011, 2011, 4*w^3 - 4*w^2 - 16*w - 1]', '[2017, 2017, -2*w^3 + 9*w - 3]', '[2017, 2017, -9*w^3 + 11*w^2 + 39*w - 25]', '[2018, 2018, -3*w^3 + 5*w]', '[2018, 2018, -4*w^3 + 8*w^2 + 15*w - 22]', '[2019, 2019, w^3 - 5*w^2 - 15*w - 3]', '[2019, 2019, -3*w^3 + w^2 + 11*w + 1]', '[2022, 2022, 4*w^3 - w^2 - 17*w]', '[2026, 2026, 2*w^3 - w^2 - 13*w + 4]', '[2026, 2026, 3*w^3 - 2*w^2 - 17*w - 2]', '[2027, 2027, -2*w - 7]', '[2027, 2027, -w^3 + 2*w^2 + w - 9]', '[2028, 1014, 3*w^3 - 4*w^2 - 14*w + 5]', '[2028, 1014, -3*w^3 + w^2 + 12*w - 4]', '[2032, 254, -2*w^3 + 2*w^2 + 12*w - 2]', '[2032, 508, 4*w^3 - 3*w^2 - 17*w + 1]', '[2032, 508, 3*w^3 - w^2 - 10*w + 2]', '[2034, 2034, 3*w^3 - 4*w^2 - 9*w + 4]', '[2041, 2041, w^3 - 11*w + 7]', '[2048, 8, 4*w^3 - 4*w^2 - 20*w + 8]', '[2048, 16, -6*w^3 + 6*w^2 + 26*w - 8]', '[2048, 16, -4*w^3 + 4*w^2 + 16*w - 8]', '[2048, 32, w^3 - w^2 + w + 4]', '[2048, 32, 2*w^3 - 2*w^2 - 4*w - 4]', '[2048, 64, w^3 - 2*w^2 + 2*w + 4]', '[2049, 2049, -2*w^3 + 3*w - 5]', '[2061, 2061, -2*w^2 - 2*w - 3]', '[2061, 2061, 3*w^3 - 3*w^2 - 7*w + 5]', '[2062, 2062, 2*w^3 - 6*w^2 - 5*w + 20]', '[2063, 2063, -w^3 + 4*w^2 + 3*w - 9]', '[2064, 258, 2*w^3 - 2*w^2 - 16*w - 6]', '[2064, 258, 2*w^3 + 2*w^2 - 8*w - 2]', '[2064, 516, -6*w^3 + w^2 + 27*w + 11]', '[2064, 516, -w^2 + 10]', '[2064, 516, -2*w^3 + 3*w^2 + 9*w + 1]', '[2064, 516, 2*w^3 - 3*w^2 - 12*w + 14]', '[2066, 2066, -w^2 - 7*w - 2]', '[2069, 2069, w^3 - w^2 - 5]', '[2069, 2069, -2*w^3 + 11*w - 1]', '[2073, 2073, 5*w^3 - w^2 - 21*w - 3]', '[2074, 2074, 3*w^3 - 2*w^2 - 9*w - 2]', '[2074, 2074, 2*w^3 - 3*w^2 - 9*w]', '[2076, 1038, -w^3 + 4*w - 6]', '[2076, 1038, -7*w^3 + 12*w^2 + 32*w - 29]', '[2076, 1038, -5*w^3 + 6*w^2 + 26*w - 21]', '[2076, 1038, -5*w^3 + 14*w^2 - 10]', '[2077, 2077, -5*w^3 + 3*w^2 + 24*w + 5]', '[2081, 2081, 5*w^3 - 4*w^2 - 25*w + 3]', '[2082, 2082, -4*w^3 + 3*w^2 + 19*w - 6]', '[2083, 2083, -4*w^3 + 2*w^2 + 16*w + 5]', '[2087, 2087, 3*w^3 - 5*w^2 - 9*w + 3]', '[2087, 2087, w^2 - 4*w - 7]', '[2091, 2091, -w^3 - 3*w^2 + 8*w + 13]', '[2094, 2094, -5*w - 8]', '[2096, 262, -4*w^3 + 6*w^2 + 20*w - 22]', '[2096, 524, 5*w^3 - 8*w^2 - 18*w + 20]', '[2096, 524, -2*w^3 - w^2 + 9*w + 1]', '[2097, 2097, 2*w^3 - 4*w^2 - 12*w + 9]', '[2097, 2097, w^3 - w^2 - 9*w - 1]', '[2098, 2098, -2*w^3 + 3*w^2 + 11*w - 16]', '[2098, 2098, -w^3 + 4*w^2 + 5*w - 14]', '[2098, 2098, -w^3 + 4*w^2 + 3*w - 10]', '[2098, 2098, 3*w^3 - 6*w^2 - 7*w + 4]', '[2102, 2102, 4*w^3 - 2*w^2 - 17*w]', '[2106, 78, 3*w^3 - 9*w]', '[2106, 2106, 4*w^3 - 3*w^2 - 17*w + 2]', '[2108, 1054, w^3 - 5*w^2 + 2*w + 12]', '[2108, 1054, 2*w^3 + 3*w^2 - 7*w - 9]', '[2119, 2119, -2*w^3 - w^2 + 4*w - 5]', '[2119, 2119, -3*w^3 + 7*w^2 + 17*w - 15]', '[2122, 2122, -3*w^3 + 11*w - 2]', '[2124, 1062, 3*w^3 - 8*w - 2]', '[2124, 1062, -w^3 - 4*w^2 + 9]', '[2124, 1062, w^3 - 2*w^2 + 6]', '[2124, 1062, w^3 - 2*w - 7]', '[2124, 1062, -2*w^3 + 9*w^2 - 6*w - 8]', '[2124, 1062, -3*w^3 + 2*w^2 + 16*w - 7]', '[2124, 1062, 4*w^3 - 5*w^2 - 17*w + 7]', '[2124, 1062, -3*w^3 + 2*w^2 + 14*w - 6]', '[2127, 2127, 2*w^3 + 2*w^2 - 12*w - 9]', '[2132, 1066, w^3 + w^2 + 2*w + 4]', '[2132, 1066, 2*w^3 + w^2 - 7*w - 7]', '[2137, 2137, -4*w^3 + 4*w^2 + 20*w - 7]', '[2137, 2137, 8*w^3 - 9*w^2 - 36*w + 21]', '[2138, 2138, 5*w^2 - 9*w - 4]', '[2138, 2138, -4*w^3 + 5*w^2 + 15*w - 10]', '[2141, 2141, -4*w^3 + w^2 + 16*w + 1]', '[2141, 2141, -2*w^3 - 2*w^2 + 13*w + 5]', '[2143, 2143, -2*w^3 + 3*w^2 + 12*w - 15]', '[2143, 2143, -2*w^3 + 2*w^2 + 12*w - 5]', '[2144, 268, w^3 + 3*w^2 - 7*w - 20]', '[2144, 268, -4*w^2 + 2*w + 16]', '[2144, 536, -w^3 + 2*w^2 + 2*w - 12]', '[2151, 2151, -2*w^3 - 2*w^2 + 11*w + 11]', '[2153, 2153, 4*w^3 - 4*w^2 - 21*w + 3]', '[2153, 2153, 2*w^3 - w^2 - 4*w + 7]', '[2154, 2154, 2*w^3 - 2*w^2 - 7*w - 6]', '[2154, 2154, 2*w^3 - 3*w^2 - w + 4]', '[2157, 2157, -3*w^3 + 5*w^2 + 13*w - 19]', '[2159, 2159, -3*w^3 + 2*w^2 + 17*w - 5]', '[2161, 2161, -w^3 + 4*w^2 + 9*w - 7]', '[2164, 1082, 3*w^2 - 20]', '[2164, 1082, -3*w^3 + 2*w^2 + 10*w - 11]', '[2168, 542, -w^3 - 3*w^2 + 7*w + 14]', '[2168, 542, -3*w^3 - 5*w^2 + 3*w + 6]', '[2168, 1084, w^2 - 2*w - 10]', '[2168, 1084, -3*w^3 + w^2 + 12*w + 10]', '[2169, 2169, 4*w^2 - w - 5]', '[2169, 2169, -w^3 + 7*w + 9]', '[2171, 2171, -4*w^3 + 5*w^2 + 20*w - 9]', '[2171, 2171, w^3 + 2*w^2 - 11*w + 1]', '[2172, 1086, 3*w^3 + 2*w^2 - 4*w + 3]', '[2172, 1086, -w^3 - 3*w^2 + 10*w + 12]', '[2174, 2174, -3*w^3 + 2*w^2 + w - 2]', '[2176, 68, 2*w^3 + 2*w^2 - 10*w - 8]', '[2176, 136, 2*w^2 + 4*w + 4]', '[2176, 136, w^3 - w^2 + w - 4]', '[2176, 272, 4*w^3 - 5*w^2 - 20*w + 14]', '[2179, 2179, -4*w^3 + 8*w^2 + 17*w - 27]', '[2179, 2179, -4*w^3 + 6*w^2 + 15*w - 9]', '[2181, 2181, 4*w^2 - 13]', '[2182, 2182, 2*w^3 - 2*w^2 - w - 2]', '[2186, 2186, 3*w^3 - 2*w^2 - 15*w + 6]', '[2187, 9, 3*w^3 - 6*w^2 - 9*w + 15]', '[2187, 81, -3*w^3 + 15*w + 3]', '[2187, 2187, 2*w^3 - w^2 - 14*w + 7]', '[2188, 1094, w^3 + 2*w^2 - 12*w + 3]', '[2188, 1094, -3*w^3 + 6*w^2 + 8*w - 6]', '[2192, 274, 2*w^3 + 2*w^2 - 12*w - 10]', '[2192, 548, -4*w^3 + w^2 + 19*w + 13]', '[2192, 548, -w^3 + w^2 + 6*w + 6]', '[2193, 2193, w^3 + 2*w^2 - 9*w - 1]', '[2193, 2193, 3*w^3 - 19*w - 7]', '[2196, 1098, -2*w^3 - 3*w^2 - w - 3]', '[2196, 1098, w^3 + 2*w^2 + 6*w + 2]', '[2196, 1098, 2*w^3 - 5*w^2 - 4*w + 12]', '[2196, 1098, w^2 + 3*w - 13]', '[2197, 13, -w^3 + 5*w^2 - 2*w - 7]', '[2197, 2197, 3*w^3 - w^2 - 9*w + 3]', '[2199, 2199, -4*w^3 + 6*w^2 + 13*w - 9]', '[2202, 2202, -w^3 - 2*w^2 + 9*w + 10]', '[2202, 2202, w^3 - 2*w^2 - 11*w - 8]', '[2206, 2206, -w^3 + 2*w^2 + 5*w + 4]', '[2213, 2213, -w^3 + 5*w^2 + 5*w - 9]', '[2214, 246, 4*w^3 - 5*w^2 - 15*w + 8]', '[2214, 2214, 2*w^3 - w^2 - 11*w - 8]', '[2217, 2217, -w^3 - w^2 - 2*w - 5]', '[2221, 2221, 5*w^3 - 9*w^2 - 19*w + 27]', '[2221, 2221, -4*w^3 + 4*w^2 + 19*w - 3]', '[2224, 278, 4*w^3 - 4*w^2 - 20*w + 14]', '[2224, 556, -4*w^3 + 7*w^2 + 16*w - 14]', '[2224, 556, -6*w^3 + 9*w^2 + 23*w - 17]', '[2227, 2227, 2*w^3 - 4*w^2 - 7*w + 3]', '[2228, 1114, -w^3 + 5*w^2 - 4*w - 8]', '[2228, 1114, -4*w^3 - 3*w^2 + 5*w - 1]', '[2232, 558, -5*w^3 + 5*w^2 + 21*w - 10]', '[2232, 1116, 2*w^3 - w^2 - 6*w - 6]', '[2234, 2234, -3*w^3 + 3*w - 2]', '[2236, 1118, -w^3 + 4*w^2 + 10*w + 3]', '[2236, 1118, -w^3 + 3*w^2 - 8]', '[2236, 1118, -3*w^3 + 6*w + 1]', '[2236, 1118, -3*w^3 + 7*w^2 + 8*w - 12]', '[2237, 2237, 3*w^3 - 5*w^2 - 15*w + 19]', '[2239, 2239, 2*w^3 - 15*w + 7]', '[2243, 2243, -4*w^3 + 6*w^2 + 14*w - 7]', '[2246, 2246, 3*w^3 - 2*w^2 - 11*w + 2]', '[2246, 2246, -4*w^3 + 6*w^2 + 13*w - 10]', '[2248, 562, 3*w^3 + w^2 - 9*w + 6]', '[2248, 1124, w^2 - 6*w + 10]', '[2249, 2249, 3*w^3 - 3*w^2 - 16*w + 7]', '[2249, 2249, 3*w^3 - 7*w^2 - 18*w + 11]', '[2252, 1126, -4*w^3 + 3*w^2 + 14*w + 8]', '[2252, 1126, -4*w^3 - 5*w^2 + 5*w + 5]', '[2253, 2253, -w^3 - w^2 - 3*w - 3]', '[2259, 2259, -w^3 + w^2 + 2*w - 9]', '[2263, 2263, w^3 - 4*w^2 - w + 15]', '[2263, 2263, -2*w^3 - w^2 + 8*w - 3]', '[2267, 2267, 3*w^3 - 5*w^2 - 10*w + 5]', '[2267, 2267, 3*w^3 - 4*w^2 - 11*w + 1]', '[2267, 2267, -2*w^3 + 2*w^2 + 12*w - 3]', '[2267, 2267, -w^3 + 3*w^2 + 9*w - 3]', '[2273, 2273, 3*w^3 - 3*w^2 - 10*w + 1]', '[2278, 2278, 2*w^3 - 7*w^2 - 5*w + 24]', '[2284, 1142, -3*w^3 + 6*w - 1]', '[2284, 1142, -5*w^3 + 7*w^2 + 14*w]', '[2286, 2286, 3*w^3 - 2*w^2 - 11*w]', '[2287, 2287, 3*w^3 - 7*w^2 - 10*w + 25]', '[2292, 1146, 2*w^3 - 7*w^2 + 8*w - 4]', '[2292, 1146, -10*w^3 + 15*w^2 + 39*w - 37]', '[2293, 2293, -2*w^3 - w^2 + 8*w - 1]', '[2297, 2297, 3*w^3 + 2*w^2 - 21*w - 7]', '[2298, 2298, -4*w^3 + 7*w^2 + 11*w - 6]', '[2301, 2301, 8*w^3 - 10*w^2 - 36*w + 21]', '[2301, 2301, -2*w^2 + w - 3]', '[2301, 2301, 4*w^3 - w^2 - 20*w - 3]', '[2301, 2301, 3*w^3 - 3*w^2 - 10*w + 5]', '[2302, 2302, -w^3 - 2*w^2 + 7*w]', '[2302, 2302, -2*w^3 + w^2 + 13*w + 2]', '[2304, 36, -4*w^3 + 4*w^2 + 16*w - 4]', '[2304, 72, 2*w^3 - 2*w^2 - 12*w + 4]', '[2304, 72, 4*w^3 - 2*w^2 - 22*w + 2]', '[2304, 144, 2*w^3 - w^2 - 3*w - 3]', '[2304, 144, -3*w^3 + 2*w^2 + 10*w - 4]', '[2309, 2309, 5*w^3 - 4*w^2 - 21*w - 1]', '[2311, 2311, 2*w^3 - 4*w^2 - 9*w + 5]', '[2311, 2311, -4*w^3 + 6*w^2 + 19*w - 23]', '[2312, 578, w^3 + 3*w^2 - 9*w - 10]', '[2312, 1156, -w^3 + w^2 + 4*w + 6]', '[2316, 1158, -3*w^3 + 8*w - 1]', '[2316, 1158, -6*w^3 + 5*w^2 + 24*w + 4]', '[2316, 1158, 2*w^3 - 3*w^2 - 5*w + 9]', '[2316, 1158, -w^3 + 4*w^2 - 6*w - 2]', '[2316, 1158, 4*w^3 - 11*w^2 - 2*w + 4]', '[2316, 1158, w^3 - 6*w + 7]', '[2316, 1158, -3*w^3 + 6*w^2 + 2*w + 2]', '[2316, 1158, 4*w^3 - 5*w^2 - 15*w + 9]', '[2319, 2319, 2*w^3 - 3*w^2 - 12*w - 1]', '[2322, 258, -w^3 + 2*w^2 - 3*w + 4]', '[2322, 258, -w^3 + 2*w^2 + 3*w + 4]', '[2322, 2322, -5*w^3 + 19*w + 8]', '[2322, 2322, -w^3 + 4*w^2 + 5*w]', '[2328, 582, w^3 - w^2 - w + 10]', '[2328, 1164, w^3 + 5*w^2 - 10]', '[2329, 2329, w^3 + 4*w^2 - 11*w - 13]', '[2333, 2333, -2*w^3 + 6*w^2 + 6*w - 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2*w + 4]', '[5344, 1336, -3*w^3 + 14*w]', '[5347, 5347, 2*w^3 - 3*w^2 - 14*w + 1]', '[5356, 2678, -2*w^3 + 5*w^2 + 5*w - 19]', '[5356, 2678, w^3 - 5*w^2 - 6*w + 16]', '[5356, 2678, 8*w^3 - 11*w^2 - 36*w + 24]', '[5356, 2678, 3*w^2 + 11*w + 9]', '[5363, 5363, -3*w^3 - 9*w^2 + 13]', '[5363, 5363, w^3 - 5*w^2 - 2*w + 9]', '[5364, 2682, 2*w^3 - 3*w^2 + 2*w + 4]', '[5364, 2682, w^3 - 4*w^2 - 10*w + 7]', '[5364, 2682, -3*w^3 + 4*w^2 + 14*w - 2]', '[5364, 2682, 4*w^3 - w^2 - 21*w - 1]', '[5366, 5366, -3*w^3 - 2*w^2 + 13*w + 4]', '[5366, 5366, -4*w^3 + 8*w^2 + 13*w - 22]', '[5371, 5371, 4*w^3 - w^2 - 14*w + 1]', '[5378, 5378, 6*w^3 - 8*w^2 - 25*w + 14]', '[5378, 5378, 6*w^3 - 5*w^2 - 27*w]', '[5378, 5378, -3*w^3 + 4*w^2 + 15*w - 2]', '[5378, 5378, -2*w^3 + 6*w^2 + 5*w - 14]', '[5381, 5381, 2*w^3 - 7*w^2 - 10*w + 15]', '[5384, 1346, w^3 - 5*w^2 + w + 26]', '[5384, 1346, -3*w^3 + 7*w^2 + 13*w - 26]', '[5384, 2692, 7*w^2 + 2*w - 22]', '[5384, 2692, 4*w^3 - 7*w^2 - 14*w + 22]', '[5386, 5386, -w^3 + 2*w^2 - 3*w + 8]', '[5387, 5387, w^3 - w^2 + 5*w - 1]', '[5388, 2694, -3*w^3 + 9*w^2 + 4*w - 20]', '[5388, 2694, -4*w^3 + 3*w^2 + 11*w - 11]', '[5388, 2694, w^3 + 3*w^2 - 14*w + 8]', '[5388, 2694, 14*w^3 - 23*w^2 - 59*w + 59]', '[5389, 5389, 4*w^3 - 18*w - 3]', '[5389, 5389, -7*w^3 + 11*w^2 + 31*w - 37]', '[5392, 674, 6*w^3 + 4*w^2 - 14*w + 2]', '[5392, 1348, 5*w^3 - 2*w^2 - 26*w]', '[5392, 1348, -w^3 + 6*w^2 + 10*w - 7]', '[5398, 5398, -2*w^3 + 6*w^2 + 3*w - 16]', '[5403, 5403, w^2 - 6*w + 11]', '[5407, 5407, -4*w^3 + 6*w^2 + 11*w - 7]', '[5407, 5407, -3*w^3 + 4*w^2 + 13*w - 1]', '[5407, 5407, -6*w^3 + 8*w^2 + 22*w - 11]', '[5407, 5407, 3*w^3 + w^2 - 22*w - 1]', '[5408, 676, 4*w^3 - 14*w - 8]', '[5408, 676, -3*w^3 - w^2 + 21*w + 12]', '[5408, 1352, -3*w^3 + w^2 + 18*w - 6]', '[5414, 5414, -6*w^2 + w + 6]', '[5417, 5417, -w^3 + 5*w^2 + 2*w - 15]', '[5421, 5421, -2*w^3 + 8*w^2 - 4*w + 1]', '[5422, 5422, -5*w^2 + 3*w + 6]', '[5424, 678, -2*w^3 + 4*w^2 + 10*w - 2]', '[5424, 1356, 3*w^3 - 16*w - 1]', '[5424, 1356, -9*w^3 + 15*w^2 + 34*w - 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w + 10]', '[5464, 2732, -2*w^3 + 5*w^2 + 2*w - 10]', '[5466, 5466, 2*w^3 - 9*w^2 + 5*w + 10]', '[5468, 2734, 3*w^3 - 5*w^2 - 16*w + 20]', '[5468, 2734, 3*w^3 + 2*w^2 - 12*w - 3]', '[5469, 5469, w^3 - 3*w^2 - 10*w + 3]', '[5469, 5469, -3*w^2 + 8*w - 7]', '[5471, 5471, -4*w^3 + 4*w^2 + 12*w - 13]', '[5471, 5471, 7*w^3 - 8*w^2 - 35*w + 29]', '[5476, 74, -11*w^3 + 3*w^2 + 56*w + 16]', '[5476, 74, w^3 - 7*w^2 - 2*w + 32]', '[5476, 74, -6*w^3 - 3*w^2 + 17*w + 1]', '[5476, 74, w^3 - 10*w^2 - 12*w + 21]', '[5483, 5483, 3*w^3 - w^2 - 19*w - 5]', '[5483, 5483, -w^3 + 4*w^2 + w - 21]', '[5484, 2742, 4*w^3 - 5*w^2 - 19*w - 7]', '[5484, 2742, w^3 - 6*w^2 + 6*w + 10]', '[5484, 2742, w^3 - 2*w^2 - 12*w - 3]', '[5484, 2742, 2*w^3 - 3*w^2 - 10*w + 16]', '[5484, 2742, -5*w^3 + 24*w + 22]', '[5484, 2742, 2*w^3 + w^2 - 3*w + 7]', '[5484, 2742, 2*w^3 - w^2 - 12*w + 12]', '[5484, 2742, 16*w^3 - 25*w^2 - 69*w + 65]', '[5486, 5486, -2*w^3 - 5*w^2 + 7*w + 6]', '[5487, 5487, 2*w^3 - 4*w^2 - 12*w - 3]', '[5487, 5487, -w^2 + 6*w + 7]', '[5487, 5487, 2*w^3 - 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7]', '[5541, 5541, -4*w^3 + 6*w^2 + 15*w - 7]', '[5542, 5542, -3*w^3 + 8*w^2 + 7*w - 12]', '[5542, 5542, -4*w^3 + 7*w^2 + 5*w - 4]', '[5547, 129, -3*w^3 + w^2 + 19*w - 3]', '[5547, 129, -4*w^2 + w + 11]', '[5547, 5547, 6*w^3 + 2*w^2 - 28*w - 15]', '[5547, 5547, -6*w^3 + 11*w^2 + 28*w - 31]', '[5552, 694, 4*w^3 - 4*w^2 - 22*w + 2]', '[5552, 1388, -5*w^3 + w^2 + 18*w - 2]', '[5552, 1388, -7*w^3 + 4*w^2 + 32*w + 1]', '[5553, 5553, 5*w^3 - 4*w^2 - 21*w + 3]', '[5554, 5554, 4*w^2 - 3*w - 12]', '[5554, 5554, -w^3 + 2*w^2 + 7*w + 6]', '[5559, 5559, 2*w^2 - w - 15]', '[5562, 618, -4*w^3 + 5*w^2 + 21*w - 8]', '[5562, 618, w^3 + 4*w^2 - 3*w - 10]', '[5562, 5562, 5*w^2 - 3*w - 20]', '[5562, 5562, -6*w^3 - 3*w^2 + 25*w + 16]', '[5563, 5563, -w^3 - 3*w^2 + 9*w + 1]', '[5563, 5563, -8*w^3 + 14*w^2 + 31*w - 35]', '[5569, 5569, w^3 + w^2 - 4*w - 15]', '[5571, 5571, 3*w^3 - 5*w^2 - 15*w + 23]', '[5574, 5574, -5*w^3 + 2*w^2 + 29*w + 10]', '[5576, 1394, w^3 - 5*w^2 - 3*w + 10]', '[5576, 2788, -2*w^3 - w^2 + 6*w - 6]', '[5582, 5582, 3*w^3 - 8*w^2 - 9*w + 28]', '[5583, 5583, -4*w^3 + 2*w^2 + 23*w + 5]', '[5584, 698, -10*w^3 + 12*w^2 + 46*w - 26]', '[5584, 1396, 13*w^3 - 14*w^2 - 58*w + 27]', '[5584, 1396, 9*w^3 - 10*w^2 - 38*w + 24]', '[5591, 5591, -4*w^3 + 3*w^2 + 22*w - 7]', '[5592, 1398, -w^3 + 3*w^2 + 5*w + 4]', '[5592, 1398, 3*w^3 - 7*w^2 - 9*w + 22]', '[5592, 2796, 3*w^3 - 2*w^2 - 20*w + 12]', '[5592, 2796, -2*w^3 + 5*w^2 + 10*w - 18]', '[5594, 5594, -4*w^3 - 2*w^2 + 27*w + 8]', '[5594, 5594, 2*w^3 - w - 4]', '[5594, 5594, -w^3 - 4*w^2 + 3*w + 8]', '[5594, 5594, -w^3 + w + 10]', '[5596, 2798, 6*w^3 - 5*w^2 - 22*w - 12]', '[5596, 2798, -2*w^3 - 5*w^2 + w - 1]', '[5598, 5598, w^3 - 5*w + 8]', '[5601, 5601, -2*w^3 - 3*w^2 - 5]', '[5602, 5602, 5*w^2 + w - 8]', '[5602, 5602, -6*w^3 + 3*w^2 + 27*w + 4]', '[5603, 5603, 8*w^3 - 6*w^2 - 38*w + 1]', '[5603, 5603, 8*w^3 - 12*w^2 - 30*w + 25]', '[5611, 5611, 3*w^3 - 3*w^2 - 8*w + 11]', '[5613, 5613, -3*w^3 + 8*w^2 - w + 3]', '[5613, 5613, -5*w^3 - 5*w^2 + 12*w + 9]', '[5616, 78, 4*w^3 - 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9]', '[9963, 9963, -4*w^3 + 8*w^2 + 12*w - 21]', '[9969, 9969, w^3 + 3*w^2 - 9*w - 23]', '[9969, 9969, 2*w^3 + 5*w^2 - 2*w - 11]', '[9969, 9969, 6*w^3 - 10*w^2 - 28*w + 33]', '[9969, 9969, w^3 + 7*w + 5]', '[9971, 9971, -2*w^3 + 5*w^2 + 12*w - 17]', '[9971, 9971, 3*w^2 + 8*w - 3]', '[9971, 9971, 9*w^3 - 14*w^2 - 39*w + 33]', '[9971, 9971, 7*w^3 - 2*w^2 - 31*w - 21]', '[9973, 9973, -2*w^3 + 2*w^2 + 15*w + 1]', '[9973, 9973, w^3 + 4*w^2 - 15*w - 11]', '[9979, 9979, -6*w^3 + 6*w^2 + 25*w - 1]', '[9983, 9983, 5*w^3 - 12*w^2 - 17*w + 43]', '[9983, 9983, 5*w^3 - 23*w - 5]', '[9984, 156, -12*w^3 + 16*w^2 + 52*w - 36]', '[9984, 312, 2*w^3 - 2*w^2 - 4*w - 12]', '[9984, 312, -6*w^2 - 2*w + 10]', '[9984, 624, w^3 - 6*w^2 + 2*w + 12]', '[9984, 624, -w^3 + 4*w - 9]', '[9986, 9986, -4*w^3 + 4*w^2 + 13*w + 10]', '[9991, 9991, w^3 - 5*w^2 - 5*w + 27]', '[9991, 9991, -w^3 - w^2 + 4*w - 7]', '[9993, 9993, 4*w^3 - 27*w - 11]', '[9993, 9993, 7*w^3 - 3*w^2 - 31*w - 9]', '[9998, 9998, 4*w^3 - 3*w^2 - 13*w + 4]', '[10000, 10, 10]', '[10000, 20, -5*w^2 + 5*w + 15]', '[10000, 20, -5*w^2 + 10]'], 'label': '4.4.13768.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -w]', '[3, 3, w + 1]', '[4, 2, -w^2 - w + 1]', '[13, 13, -w^2 + 3]', '[17, 17, -w + 3]', '[27, 3, w^3 - 2*w^2 - 3*w + 5]', '[31, 31, -w^2 - 2*w + 1]', '[41, 41, -w^2 + 5]', '[43, 43, w^3 - w^2 - 5*w - 1]', '[43, 43, w^3 - w^2 - 3*w + 1]', '[59, 59, -w - 3]', '[59, 59, -2*w^3 + 2*w^2 + 9*w - 5]', '[59, 59, -w^3 - 3*w^2 - w + 3]', '[59, 59, w^3 - 7*w + 1]', '[61, 61, -w^3 + w^2 + 2*w + 5]', '[61, 61, -w^3 - w^2 + 4*w + 3]', '[67, 67, 4*w^3 - 4*w^2 - 18*w + 7]', '[73, 73, -2*w^3 + 6*w - 3]', '[73, 73, -2*w + 3]', '[97, 97, w^3 - 2*w^2 - 5*w + 3]', '[101, 101, w^3 + w^2 - 5*w - 7]', '[101, 101, -w^3 - w^2 + 4*w + 5]', '[103, 103, 2*w^3 - 8*w - 1]', '[103, 103, w^2 - 2*w - 7]', '[109, 109, -w^3 + 2*w^2 + 3*w - 7]', '[113, 113, -w^3 + w^2 + 6*w - 3]', '[127, 127, -w^3 + w^2 + 6*w - 1]', '[131, 131, -2*w^3 + 3*w^2 + 10*w - 11]', '[137, 137, w^3 + w^2 - 6*w - 5]', '[139, 139, -3*w^3 + 2*w^2 + 15*w - 1]', '[149, 149, w^3 - 3*w^2 - 4*w + 11]', '[149, 149, -w^3 + 5*w - 1]', '[157, 157, -2*w^3 + 3*w^2 + 6*w - 1]', '[163, 163, 2*w^2 - 3]', '[163, 163, -2*w^3 + 2*w^2 + 7*w - 5]', '[167, 167, -2*w^3 + 2*w^2 + 8*w - 3]', '[167, 167, -2*w^2 + 2*w + 9]', '[173, 173, 2*w^3 - w^2 - 8*w + 3]', '[173, 173, 2*w^3 - 3*w^2 - 6*w + 3]', '[181, 181, 2*w^3 - 3*w^2 - 8*w + 5]', '[191, 191, -2*w^3 + w^2 + 10*w - 1]', '[193, 193, -w^3 + 3*w^2 + 2*w - 7]', '[193, 193, w^3 - 3*w - 3]', '[193, 193, 2*w^2 - 2*w - 3]', '[193, 193, w^3 - 7*w - 1]', '[197, 197, w^2 - 2*w - 5]', '[211, 211, w^2 - 4*w - 1]', '[229, 229, -w^3 + w^2 + 6*w - 7]', '[229, 229, -4*w^3 + 6*w^2 + 16*w - 13]', '[233, 233, 3*w^2 + 2*w - 5]', '[233, 233, 2*w^3 - 2*w^2 - 11*w + 7]', '[239, 239, -w^3 + w^2 + 7*w + 1]', '[241, 241, w^3 - 3*w^2 - 2*w + 9]', '[241, 241, w^3 + w^2 - 9*w - 5]', '[251, 251, 2*w^3 - 6*w + 1]', '[271, 271, 2*w^3 - w^2 - 8*w - 1]', '[271, 271, -2*w^2 + w + 7]', '[281, 281, 2*w^3 + 2*w^2 - 5*w - 1]', '[293, 293, w^3 + w^2 - 5*w - 1]', '[293, 293, -3*w + 7]', '[307, 307, -w^3 - 2*w^2 + 3*w + 5]', '[311, 311, -w^3 + 3*w^2 + 4*w - 7]', '[313, 313, 2*w^2 - 2*w - 5]', '[317, 317, -2*w^3 + 4*w^2 + 7*w - 13]', '[317, 317, -2*w^3 + 3*w^2 + 8*w - 11]', '[337, 337, 3*w^3 + 2*w^2 - 7*w + 1]', '[347, 347, 2*w^3 - 2*w^2 - 11*w + 1]', '[349, 349, -5*w^3 + 6*w^2 + 23*w - 13]', '[359, 359, 2*w^3 - 2*w^2 - 12*w + 9]', '[359, 359, -2*w^3 + 8*w + 5]', '[367, 367, -4*w^3 + 4*w^2 + 19*w - 5]', '[367, 367, 2*w^3 + w^2 - 10*w - 7]', '[383, 383, 2*w^3 - 2*w^2 - 7*w + 1]', '[389, 389, 2*w^2 - w - 5]', '[397, 397, 3*w^3 - 4*w^2 - 11*w + 9]', '[397, 397, 3*w^3 - 3*w^2 - 12*w + 7]', '[397, 397, 2*w^3 - 4*w^2 - 8*w + 15]', '[397, 397, -w^3 + 3*w^2 + w - 7]', '[409, 409, -w^3 - w^2 + 9*w - 1]', '[419, 419, 2*w^2 - 3*w - 7]', '[419, 419, 4*w^3 - 3*w^2 - 18*w + 3]', '[431, 431, -3*w^3 + w^2 + 17*w - 1]', '[431, 431, 3*w^3 - w^2 - 16*w - 1]', '[433, 433, -2*w^3 + 5*w^2 + 8*w - 19]', '[443, 443, 3*w - 5]', '[449, 449, -2*w^3 + 2*w^2 + 9*w - 9]', '[449, 449, -5*w^3 + 8*w^2 + 19*w - 17]', '[457, 457, -3*w^3 + 3*w^2 + 13*w - 9]', '[457, 457, -3*w^3 + 2*w^2 + 13*w + 1]', '[457, 457, -2*w^3 + w^2 + 8*w + 7]', '[457, 457, 3*w^3 - 3*w^2 - 15*w + 7]', '[461, 461, -2*w^3 + 2*w^2 + 9*w + 1]', '[479, 479, -w^3 + w^2 + 7*w - 9]', '[487, 487, -w^3 - w^2 + w - 3]', '[499, 499, -2*w^3 + 7*w - 3]', '[499, 499, -5*w^3 + 7*w^2 + 20*w - 15]', '[541, 541, -3*w^3 + 4*w^2 + 13*w - 7]', '[547, 547, -w^3 - w^2 + 3*w + 5]', '[557, 557, 4*w - 1]', '[563, 563, 2*w^3 - w^2 - 6*w - 1]', '[571, 571, w^3 - w^2 - w - 3]', '[587, 587, -2*w^3 + 2*w^2 + 10*w + 1]', '[593, 593, 2*w^3 - 2*w^2 - 6*w + 3]', '[613, 613, -5*w^3 + 5*w^2 + 23*w - 7]', '[613, 613, -w^3 + w^2 + 5*w - 7]', '[617, 617, -w - 5]', '[619, 619, -3*w^3 + 4*w^2 + 11*w - 7]', '[625, 5, -5]', '[643, 643, -3*w^3 + 3*w^2 + 14*w - 9]', '[643, 643, -3*w^2 - 4*w + 1]', '[653, 653, -w^3 + w^2 + 9*w + 3]', '[653, 653, -4*w^2 + 6*w + 11]', '[659, 659, -w^2 - 4*w + 1]', '[661, 661, -3*w^3 + 3*w^2 + 15*w - 5]', '[661, 661, w^3 + w^2 - 7*w - 11]', '[673, 673, 2*w^3 - 3*w^2 - 12*w + 1]', '[673, 673, -2*w^3 + w^2 + 10*w - 3]', '[683, 683, -w^3 - 2*w^2 + 5*w + 11]', '[691, 691, 4*w^3 - 3*w^2 - 18*w + 5]', '[709, 709, w^3 - 3*w - 7]', '[719, 719, 2*w^3 - 8*w + 1]', '[727, 727, -3*w^3 + 6*w^2 + 13*w - 19]', '[733, 733, w^3 - w^2 + 3]', '[739, 739, -w^3 + w^2 + 3*w - 7]', '[751, 751, -w^2 - 3]', '[773, 773, 2*w^3 - 2*w^2 - 11*w + 3]', '[787, 787, w^3 - w^2 - 3*w - 5]', '[797, 797, -2*w^3 + 2*w^2 + 5*w - 1]', '[797, 797, -7*w^3 + 8*w^2 + 31*w - 15]', '[809, 809, 4*w^3 - 6*w^2 - 17*w + 13]', '[809, 809, 3*w^2 - 4*w - 5]', '[811, 811, 2*w^2 + 4*w + 3]', '[811, 811, -3*w^3 + 3*w^2 + 12*w - 5]', '[821, 821, 2*w^3 - 10*w - 1]', '[821, 821, 6*w^3 - 10*w^2 - 24*w + 29]', '[823, 823, -5*w^3 + 3*w^2 + 24*w - 1]', '[823, 823, w^3 + w^2 + w + 3]', '[827, 827, -4*w^3 + 3*w^2 + 16*w - 7]', '[829, 829, 2*w^3 - 4*w^2 - 6*w + 11]', '[841, 29, w^3 - 3*w^2 - 5*w + 3]', '[841, 29, -3*w^3 + 3*w^2 + 13*w - 1]', '[857, 857, -4*w^3 + 6*w^2 + 13*w - 7]', '[857, 857, -3*w^3 + w^2 + 15*w + 1]', '[859, 859, -4*w^2 + 3*w + 17]', '[863, 863, -4*w^3 + 8*w^2 + 14*w - 21]', '[877, 877, -w^3 - w^2 + 6*w - 1]', '[881, 881, -5*w - 1]', '[883, 883, -4*w^3 + 4*w^2 + 21*w - 13]', '[883, 883, 2*w^3 - 11*w - 1]', '[887, 887, -3*w^3 - w^2 + 8*w - 5]', '[907, 907, w^3 - w^2 - w + 5]', '[911, 911, 2*w^2 - 5*w - 5]', '[919, 919, -w^3 + 3*w^2 + 6*w - 3]', '[919, 919, 5*w^2 + 4*w - 9]', '[929, 929, w^3 + 3*w^2 - 8*w - 17]', '[937, 937, -4*w^3 + 4*w^2 + 17*w - 7]', '[953, 953, -2*w^3 + 2*w^2 + 7*w + 5]', '[953, 953, 3*w^3 - 4*w^2 - 11*w + 3]', '[967, 967, 4*w^3 - 2*w^2 - 17*w + 3]', '[971, 971, w^3 - 3*w^2 - 8*w + 1]', '[983, 983, -2*w^3 - 2*w^2 + 12*w + 13]', '[991, 991, -2*w^3 - 2*w^2 + 8*w + 7]', '[991, 991, w^3 + w^2 - 10*w + 1]']}
• 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': [2, 2, -5, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 13768, 'disc_rad': 3442, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1], [1, 1]]], [5, [[4, 1]]], [7, [[4, 1]]], [11, [[4, 1]]], [13, [[3, 1], [1, 1]]], [17, [[3, 1], [1, 1]]], [19, [[4, 1]]], [23, [[4, 1]]], [29, [[2, 2]]], [31, [[3, 1], [1, 1]]], [37, [[2, 2]]], [41, [[3, 1], [1, 1]]], [43, [[2, 1], [1, 2]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 117.33712115098103, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.13768.1', 'local_algs': ['2.2.3.2', '2.2.0.1', 'm1721.1.2.0', 'm1721.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 1721], 'rd': 10.8322260478, 'regulator': {'__RealLiteral__': 0, 'data': '11.1695196331', 'prec': 44}, 'res': {'gal': ['-2792956,28638520,-35656322,-96895532,143784041,150958324,-221178940,-145468272,182592413,94515424,-89522234,-41412560,27009099,11852292,-5081710,-2139220,605783,237176,-46500,-15528,2307,548,-70,-8,1'], 'sib': ['-4,146,-631,140,1615,-610,-1429,280,427,-18,-39,0,1', '2394543,390802,-280173,-22462,11088,394,-179,-2,1', '4,-15,5,19,-7,-3,1', '5426,-7400,-209,974,-151,-2,1', '632,9952,17712,-43536,-6312,29840,-3711,-4966,775,300,-49,-6,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a^{3} - a^{2} - 4 a + 3 \\)', '\\( 2 a^{3} - 3 a^{2} - 8 a + 7 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}