Hilbert modular form data - 4.4.9301.1-25.1-e

Formats: - HTML - YAML - JSON - 2024-05-30T00:18:38.421764

• 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': 9301, 'field_bad_primes': [71, 131], 'field_label': '4.4.9301.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.9301.1-25.1-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [5], 'level_ideal': '[25, 25, -w^3 + w^2 + 3*w - 1]', 'level_label': '25.1', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.1-e', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5, 5, -w^3 + w^2 + 4*w + 1]', 1]], 'hecke_eigenvalues': ['e', 0, 'e - 1', 'e - 1', 'e^2 - 4*e - 3', '-e^2 + 4', 'e^2 - 2*e + 1', '2*e^2 - 4*e - 8', '-e^2 + 4*e + 3', '-3*e + 5', -5, '-3*e + 9', '-e^2 - e + 12', '-e^2 + 5*e + 4', '3*e^2 - 4*e - 5', '-2*e^2 + e + 10', '-e^2 + e + 9', '-3*e^2 + 5*e + 13', '4*e - 1', '2*e^2 - 4*e - 1', '4*e^2 - 5*e - 11', '-3*e^2 - e + 19', 'e^2 - e + 6', 'e^2 - 7*e - 3', '6*e - 3', '-2*e^2 - e + 18', '-4*e^2 + 5*e + 11', 'e^2 - e', '-3*e^2 + 3*e + 9', '5*e^2 - 12*e - 17', '-3*e^2 + 12*e + 7', '-2*e^2 + e + 1', 'e^2 - 2*e - 10', '3*e + 12', '-e^2 + 5*e - 4', '2*e^2 - 4*e - 19', '-2*e^2 + 10*e + 10', '5*e^2 - 7*e - 23', '2*e^2 - 9*e - 17', '-e^2 - 4*e + 20', '-2*e^2 - 2*e + 25', '-7*e^2 + 14*e + 21', '-2*e^2 + e + 7', '4*e^2 - 8*e - 17', 'e^2 - 4*e - 15', '-5*e^2 + 12*e + 14', '-2*e^2 + 8*e - 3', 'e^2 - 4*e - 3', '3*e^2 - 3*e - 18', '3*e - 3', '-4*e^2 + 14*e + 8', 'e^2 + e - 5', '2*e^2 - e + 9', '6*e^2 - 7*e - 11', '-2*e^2 + e + 5', '3*e^2 - 6', '2*e^2 - 10*e - 9', '-2*e^2 - 3*e + 17', '-2*e^2 + 11*e + 6', '-2*e^2 + e + 6', '2*e^2 - 2*e - 12', '-3*e^2 - 3*e + 19', '5*e^2 - e - 32', '2*e^2 + 4*e - 9', '-3*e^2 + 6*e + 3', '-2*e^2 + e + 1', 'e^2 - 6*e + 11', '-5*e^2 + 4*e + 31', 'e^2 - 6*e + 17', '-6*e^2 + 10*e + 5', '-e^2 - e - 7', '-4*e^2 - e + 11', '-5*e^2 + 4*e + 16', '-3*e^2 - 3*e + 13', '-4*e^2 + 4*e + 21', '3*e^2 - 5*e + 2', '2*e^2 - e - 25', '3*e^2 - 12*e - 20', '-e^2 + 10', '-5*e^2 + 17*e + 21', '-4*e^2 + 2*e + 11', '-e^2 - e - 2', '2*e^2 + 1', '3*e^2 - 3*e - 9', '2*e^2 - 6*e - 8', '-5*e^2 - 2*e + 40', '-3*e^2 + 6*e + 1', '-4*e^2 + 11*e + 14', '-4*e^2 + 9*e - 2', '7*e^2 - 17*e - 17', '2*e^2 + 8*e - 20', '-2*e^2 + 4*e + 10', '-9*e^2 + 9*e + 36', '6*e^2 - 15*e - 3', '6*e + 21', '-3*e^2 + 2*e - 8', '-e^2 + e + 27', '4*e^2 - 15*e - 4', '7*e^2 - 11*e - 29', 'e^2 - 11*e - 8', '7*e^2 - 14*e - 7', '-11*e^2 + 19*e + 32', '-e^2 - 7*e + 7', '-2*e^2 + e + 26', '-5*e^2 + 7*e - 5', '-8*e^2 + 13*e + 34', '-5*e^2 + 12*e + 35', '-3*e^2 - 2*e - 1', '8*e^2 - 9*e - 32', '4*e + 11', '-8*e^2 + 15*e + 5', '-5*e^2 + 13*e + 36', '-4*e^2 + 7*e + 9', 'e^2 + 7*e - 16', '-3*e^2 + 2*e - 11', '-4*e^2 + 11*e - 7', '8*e^2 - 7*e - 37', '-4*e^2 + 11*e + 29', '3*e^2 - 10*e + 1', '-2*e^2 + 7*e - 9', 'e^2 - 5*e - 37', '-e^2 + 4*e - 36', '-7*e^2 + 7*e + 33', '10*e^2 - 14*e - 37', 'e^2 + e + 12', '7*e^2 - 6*e - 13', 'e^2 - 14*e - 7', '7*e^2 - 11*e - 29', '2*e^2 - 3*e + 10', 9, '-11*e^2 + 13*e + 36', '-3*e^2 + 16*e - 4', '-2*e^2 + 13*e - 11', '4*e^2 + 7*e - 44', '-3*e^2 - 6*e + 15', '-e^2 + 10*e + 6', '15*e + 2', '-4*e^2 + 8*e + 20', '3*e^2 - 6*e - 6', 'e^2 - 14*e + 10', 'e^2 - 8*e - 11', 'e^2 + 7*e - 11', 'e^2 + e - 45', '-e^2 - 13*e + 17', '-4*e^2 + 15*e + 43', '12*e^2 - 9*e - 43', 'e^2 - 14*e + 4', '-e^2 + 2*e - 44', '-11*e^2 + 14*e + 33', '3*e - 30', '-6*e^2 + 6*e + 24', '3*e - 12', '6*e - 12', '-5*e^2 + 19*e + 1', '-11*e^2 + 7*e + 37', '-4*e^2 + 5*e - 22', '-8*e^2 + 9*e + 26', '-2*e^2 + 4*e - 5', '7*e^2 - 8*e - 3', '-7*e^2 + 11*e + 40', '-6*e^2 + 6*e + 30', '-10*e^2 + 20*e + 38', '-7*e^2 + 9*e + 40', '-5*e^2 + 9*e + 38', '7*e^2 - 5*e - 39', '9*e - 1', '9*e^2 - 49', '18*e + 3', '-3*e^2 + 18*e - 12', '-6*e^2 + 13*e - 7', '-11*e^2 + 23*e + 39', '2*e^2 + 17*e - 25', '14*e^2 - 23*e - 30', '-8*e^2 + 15*e + 47', '4*e^2 - 11*e - 16', 'e^2 + 10*e - 31', -17, '8*e^2 - 18*e - 8', 'e^2 - 10*e + 33', '-7*e^2 + 17*e + 28', '-e^2 + 6*e + 22', 'e^2 - 19*e', '-7*e^2 - 6*e + 55', '4*e^2 - 5*e - 4', '-e^2 + 17*e + 5', '-e^2 - 3*e + 10', '3*e^2 + 9*e - 27', '-5*e^2 + 9*e + 41', '4*e^2 - 17*e - 14', '3*e - 15', '6*e^2 - 12*e - 9', '-5*e^2 - 2*e + 22', '9*e^2 - 6*e - 33', '7*e^2 - 9*e - 49', '-9*e^2 - 9*e + 67', '-7*e^2 - 4*e + 55', '12*e^2 - 18*e - 16', '3*e^2 - 9*e - 24', '13*e^2 - 16*e - 39', '3*e^2 - 3*e + 41', '-7*e^2 - 5*e + 60', '-6*e^2 - 3*e + 23', '3*e^2 + 6*e', '12*e^2 - 2*e - 67', 'e^2 - 11*e - 5', '7*e^2 - 9*e + 11', '10*e^2 - 39*e - 46', '13*e^2 - 22*e - 57', '3*e^2 + 27', '-2*e^2 + e + 67', '-6*e + 54', 'e^2 - 3*e - 19', '4*e^2 + 4*e - 27', '6*e^2 - 16*e - 14', '-5*e^2 - 5*e + 39', '-4*e^2 - 3*e + 40', '7*e^2 - 11*e - 8', '-4*e^2 + 11*e + 22', '4*e^2 + 18*e - 34', '9*e^2 - 23*e - 13', '2*e^2 - 14*e - 42', '4*e^2 - 17*e - 52', '6*e^2 - 6*e - 38', 'e^2 - 14*e - 2', '5*e^2 - 12*e + 16', '18*e^2 - 36*e - 49', '14*e^2 - 20*e - 54', '14*e^2 - 18*e - 53', '-7*e^2 + 13*e - 15', '9*e^2 - 3*e - 45', '5*e^2 - 7*e - 25', '8*e^2 - 16*e + 16', '-6*e^2 - 3*e + 33', '-3*e^2 - 12*e + 19', '-3*e^2 + 24*e - 5', '-9*e^2 + 23*e + 16', '4*e^2 - 20*e - 20', '-6*e^2 + 6*e + 40', '2*e^2 + 5*e + 36', '-e^2 - 5*e + 48', '-e^2 - 16*e + 23', '-11*e^2 + 19*e + 40', '-3*e^2 + 21*e + 33', '-7*e^2 + 25*e + 36', '10*e^2 - 20*e - 58', '-12*e^2 + 4*e + 38', '12*e^2 - e - 65', '-16*e^2 + 12*e + 61', '-4*e^2 + 25*e + 33', '8*e^2 + 2*e - 58', '-7*e^2 + 32*e + 14', '-2*e^2 + 11*e + 33', '-8*e^2 + 19*e + 26', '-e^2 - e - 37', '-e^2 + 15*e + 1', '-15*e + 45', '18*e^2 - 38*e - 61', '-3*e^2 + 18*e + 33', '14*e^2 - 6*e - 56', '9*e^2 + 10*e - 70', '6*e^2 - 5*e + 14', '-10*e^2 + 24*e + 52', '-4*e^2 - 4*e + 68', '-6*e^2 + 19*e + 5', '-15*e^2 + 15*e + 77', '7*e^2 - 7*e - 57', '14*e^2 - 32*e - 42', '12*e^2 - 42*e - 30', '-10*e^2 - e + 46', '-15*e^2 + 18*e + 66', '-e^2 + 6*e - 23', '15*e^2 - 23*e - 28', '11*e^2 - 33*e - 17', '6*e^2 + 6*e - 48', '-3*e^2 + 6*e - 24', '13*e^2 - 50*e - 54', '13*e^2 - 27*e - 7', '-9*e^2 + 3*e + 15', '-4*e^2 + 20*e - 1', '-4*e^2 + 35*e + 11', '-14*e^2 + 32*e + 63', '-9*e^2 - 6*e + 45', '-4*e^2 - 10*e + 41', '4*e^2 - 14*e + 26', '-2*e^2 + 16*e - 2', '-e^2 + 6*e - 53', '-18*e^2 + 43*e + 65', '11*e^2 + 9*e - 92', '8*e^2 - 10*e + 5', '-15*e^2 + 12*e + 71', '-2*e^2 + 19*e - 11', '-7*e^2 + 7*e + 12', '-15*e^2 + 26*e + 31', '-12*e^2 + 6*e + 43'], 'hecke_polynomial': 'x^3 - 2*x^2 - 5*x + 3', 'label': '4.4.9301.1-25.1-e'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 9301, 'ideals': ['[1, 1, 1]', '[3, 3, w]', '[5, 5, -w^3 + w^2 + 4*w + 1]', '[7, 7, -w^2 + 2]', '[7, 7, -w^2 + w + 2]', '[9, 9, -w^2 + w + 3]', '[15, 15, -w^2 + 2*w + 3]', '[16, 2, 2]', '[17, 17, -w^3 + w^2 + 4*w - 2]', '[21, 21, -w^3 + w^2 + 5*w]', '[21, 21, w^2 - 2*w]', '[23, 23, -w^3 + 2*w^2 + 3*w - 2]', '[25, 25, -w^3 + w^2 + 3*w - 1]', '[27, 3, -w^3 + w^2 + 5*w - 1]', '[27, 27, -w^3 + w^2 + 3*w]', '[35, 35, -w^2 + 4]', '[35, 35, -w^3 + 5*w + 2]', '[37, 37, -w^3 + 4*w + 1]', '[37, 37, -w^3 + w^2 + 2*w + 1]', '[45, 45, w^2 - 3*w]', '[48, 6, 2*w]', '[49, 7, -w^3 + 2*w^2 + 2*w - 4]', '[49, 7, -w^3 + 3*w^2 + 2*w - 4]', '[49, 49, w^3 - 2*w^2 - 3*w + 1]', '[49, 49, -w^3 + 3*w^2 - 4]', '[51, 51, -w^2 - w + 3]', '[61, 61, -w^3 + 2*w^2 + 4*w - 2]', '[61, 61, -w^3 + 3*w^2 + 2*w - 7]', '[63, 63, w + 3]', '[63, 63, -w^3 + w^2 + 4*w + 3]', '[67, 67, w^2 - 3*w - 2]', '[69, 69, w^3 - 2*w^2 - w + 3]', '[71, 71, -w^2 + 5]', '[71, 71, 2*w^3 - w^2 - 9*w - 2]', '[71, 71, w^2 - 2*w - 5]', '[75, 75, -w^2 + w + 6]', '[79, 79, w^2 - 3*w - 1]', '[79, 79, w^3 - 6*w - 1]', '[80, 10, -2*w^3 + 2*w^2 + 8*w + 2]', '[81, 3, 3]', '[81, 81, 2*w - 3]', '[85, 85, w^2 + 1]', '[89, 89, -w^3 + 3*w^2 + 3*w - 7]', '[97, 97, -w^3 + 2*w^2 + 2*w - 5]', '[101, 101, -w^3 + 3*w^2 + 2*w - 5]', '[105, 105, -w^3 + 4*w]', '[105, 105, -w^3 + 3*w^2 + 2*w - 6]', '[107, 107, 2*w^3 - 2*w^2 - 9*w - 1]', '[109, 109, -w^3 + 5*w + 1]', '[111, 111, w^3 + w^2 - 2*w - 3]', '[111, 111, -3*w^2 + 2*w + 3]', '[112, 14, -2*w^2 + 4]', '[112, 14, -2*w^2 + 2*w + 4]', '[115, 115, w^3 - 2*w^2 - 5*w + 1]', '[119, 119, -w^3 + 2*w^2 + 4*w - 1]', '[119, 119, w - 4]', '[125, 5, 2*w^3 - w^2 - 8*w - 2]', '[125, 125, -w^3 + 4*w + 5]', '[131, 131, -2*w^3 + 3*w^2 + 7*w - 2]', '[131, 131, 2*w^2 - 3*w - 7]', '[131, 131, 2*w^3 - 3*w^2 - 6*w + 2]', '[135, 15, -w^3 + w^2 + 2*w + 2]', '[135, 135, -2*w^3 + 2*w^2 + 8*w - 3]', '[137, 137, w^3 - 2*w^2 - 3*w + 7]', '[139, 139, w^3 - 4*w + 2]', '[144, 18, -2*w^2 + 2*w + 6]', '[147, 21, 2*w^3 - 3*w^2 - 3*w + 3]', '[147, 21, 2*w^3 - 2*w^2 - 9*w + 3]', '[147, 147, w^3 - 4*w - 6]', '[147, 147, -2*w^2 + w + 6]', '[151, 151, w^2 + w - 4]', '[153, 153, -2*w^3 + 3*w^2 + 8*w - 3]', '[157, 157, 2*w^2 - 2*w - 5]', '[157, 157, w^3 - 2*w^2 - 5*w + 7]', '[161, 161, -2*w^2 + 3*w + 2]', '[161, 161, -w^3 + 4*w - 1]', '[173, 173, 2*w^3 - 3*w^2 - 6*w + 4]', '[175, 175, -w^3 + 3*w^2 - 5]', '[175, 175, 2*w^3 - 4*w^2 - 6*w + 5]', '[179, 179, 2*w^3 - 3*w^2 - 9*w + 4]', '[181, 181, w^3 + w^2 - 7*w - 4]', '[183, 183, 2*w^3 - 3*w^2 - 6*w + 3]', '[183, 183, w^3 - w^2 - w + 3]', '[185, 185, -3*w^3 + 3*w^2 + 10*w + 4]', '[185, 185, 2*w^3 + w^2 - 11*w - 10]', '[189, 21, -2*w^3 + 2*w^2 + 7*w - 2]', '[189, 21, -2*w^3 + 2*w^2 + 7*w + 1]', '[189, 189, 2*w^3 - 4*w^2 - 5*w + 3]', '[189, 189, 2*w^3 - 4*w^2 - 7*w + 6]', '[197, 197, w^3 - 3*w^2 - w + 7]', '[201, 201, w^3 - 3*w^2 - 2*w]', '[207, 207, -w^3 + 6*w]', '[213, 213, w^3 - 2*w^2 - 5*w]', '[213, 213, w^3 + w^2 - 4*w - 6]', '[213, 213, -w^3 + 5*w]', '[223, 223, 3*w^3 - 4*w^2 - 11*w + 4]', '[223, 223, -w^3 + w^2 + 4*w - 5]', '[225, 225, -w^3 + w^2 + 6*w]', '[227, 227, 2*w^3 - 2*w^2 - 9*w - 2]', '[229, 229, w^3 - w^2 - 6*w + 2]', '[229, 229, 4*w^3 - 6*w^2 - 14*w + 7]', '[233, 233, 2*w^3 - 3*w^2 - 5*w + 1]', '[237, 237, w^3 - 3*w^2 - w]', '[237, 237, -w^3 + w^2 + 2*w + 3]', '[239, 239, -w - 4]', '[239, 239, -2*w^3 + 4*w^2 + 5*w - 8]', '[240, 30, -2*w^2 + 4*w + 6]', '[241, 241, -2*w^3 + w^2 + 10*w + 1]', '[243, 9, 3*w]', '[243, 243, -w^3 + 7*w + 3]', '[245, 35, w^3 - 7*w - 1]', '[245, 35, 2*w^2 - 4*w - 1]', '[245, 245, 2*w^3 - 3*w^2 - 9*w + 5]', '[245, 245, -w^2 + 3*w + 5]', '[251, 251, -w^3 + 2*w^2 + 2*w - 8]', '[251, 251, -2*w^3 + 5*w^2 + 5*w - 8]', '[255, 255, -2*w^3 + 2*w^2 + 7*w]', '[256, 4, 4]', '[257, 257, 2*w^3 - 2*w^2 - 7*w + 1]', '[259, 259, -3*w^2 - 4*w + 1]', '[259, 259, w^3 - 2*w^2 - 6*w - 2]', '[259, 259, w^3 + w + 2]', '[259, 259, w^3 - 3*w^2 + 3*w + 5]', '[263, 263, w^3 - 4*w^2 - 4*w + 7]', '[267, 267, 2*w^3 - 2*w^2 - 6*w + 3]', '[269, 269, w^2 + 2*w - 4]', '[269, 269, 2*w^2 - 7]', '[271, 271, 2*w^3 - 3*w^2 - 7*w + 1]', '[271, 271, w^2 + 3*w - 2]', '[271, 271, 3*w^3 - 5*w^2 - 11*w + 13]', '[271, 271, -2*w^3 + 3*w^2 + 9*w - 2]', '[272, 34, -2*w^3 + 2*w^2 + 8*w - 4]', '[277, 277, w^2 - w - 7]', '[277, 277, 3*w^3 - 4*w^2 - 13*w + 5]', '[277, 277, -w^3 + w^2 + 3*w - 5]', '[277, 277, w^3 - 3*w - 4]', '[281, 281, w^3 - 2*w^2 - 2*w - 2]', '[283, 283, w^2 + 3*w - 1]', '[283, 283, w^3 - w^2 - 2*w - 4]', '[289, 289, -w^3 + 7*w + 2]', '[291, 291, w^3 - 3*w^2 - 4*w + 3]', '[293, 293, 3*w^3 - 4*w^2 - 12*w + 8]', '[293, 293, w^2 + w - 5]', '[303, 303, 2*w^3 - 3*w^2 - 4*w + 3]', '[305, 305, 3*w^3 - w^2 - 16*w - 4]', '[305, 305, -w^3 + 5*w + 7]', '[307, 307, 2*w^3 - 2*w^2 - 6*w - 1]', '[307, 307, -w^2 - 2]', '[311, 311, -w^3 + 5*w - 1]', '[313, 313, 2*w^3 - 2*w^2 - 8*w - 5]', '[313, 313, -2*w^3 + 3*w^2 + 5*w - 2]', '[315, 315, -2*w^2 + 3*w + 9]', '[315, 315, 2*w^3 - 3*w^2 - 5*w + 3]', '[317, 317, 2*w^3 - 2*w^2 - 9*w + 4]', '[317, 317, w^3 - 2*w^2 - 3*w - 2]', '[321, 321, w^2 - 3*w - 6]', '[327, 327, -w^3 + 2*w + 3]', '[331, 331, -w^3 + 2*w^2 + w - 5]', '[333, 333, -2*w^2 + 5*w + 6]', '[333, 333, 2*w^3 - 2*w^2 - 10*w - 3]', '[335, 335, w^3 + 3*w^2 - 11*w - 11]', '[336, 42, -2*w^3 + 2*w^2 + 10*w]', '[336, 42, 2*w^2 - 4*w]', '[337, 337, -2*w^3 + 3*w^2 + 5*w - 7]', '[337, 337, w^3 - 4*w^2 - w + 5]', '[343, 7, w^3 - 4*w^2 + 1]', '[343, 7, -w^3 - w^2 + 3*w - 2]', '[343, 49, 2*w^2 + 2*w - 5]', '[343, 49, w^3 - w^2 - w - 2]', '[343, 343, w^3 + w^2 - 4*w - 1]', '[343, 343, w^3 - 5*w + 2]', '[345, 345, -2*w^2 + 5*w + 3]', '[349, 349, -2*w^3 + w^2 + 11*w + 1]', '[355, 355, -w^2 + 4*w + 2]', '[355, 355, 5*w^3 + w^2 - 27*w - 23]', '[355, 355, 4*w^3 - w^2 - 21*w - 11]', '[357, 357, w^2 - 4*w]', '[357, 357, -w^3 - w^2 + 5*w + 9]', '[367, 367, -2*w^3 + 2*w^2 + 8*w - 5]', '[368, 46, -2*w^3 + 4*w^2 + 6*w - 4]', '[375, 15, w^3 + 2*w^2 - 4*w - 6]', '[375, 375, -w^3 - w^2 + 6*w + 3]', '[379, 379, -w^3 + 2*w^2 - 4]', '[383, 383, -3*w^3 + 6*w^2 + 9*w - 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3*w^2 - 9*w + 4]', '[1605, 1605, 5*w^3 - w^2 - 27*w - 15]', '[1607, 1607, -3*w^3 + 6*w^2 + 6*w - 10]', '[1609, 1609, -2*w^3 + 6*w^2 + 5*w - 14]', '[1611, 1611, 5*w^3 - 5*w^2 - 20*w + 3]', '[1613, 1613, 3*w^3 - 3*w^2 - 10*w + 2]', '[1613, 1613, -4*w^3 + 9*w^2 + 12*w - 17]', '[1616, 202, -2*w^3 + 6*w^2 + 4*w - 10]', '[1621, 1621, -w^2 - 4]', '[1621, 1621, 4*w^3 - 5*w^2 - 18*w + 5]', '[1623, 1623, -4*w^3 + 7*w^2 + 9*w - 3]', '[1627, 1627, -3*w^3 + 4*w^2 + 8*w - 5]', '[1627, 1627, -2*w^3 + 5*w - 5]', '[1629, 1629, 5*w^3 - 4*w^2 - 21*w - 9]', '[1631, 1631, 5*w + 1]', '[1631, 1631, w^3 - 5*w^2 + 6*w + 7]', '[1633, 1633, 2*w^3 + w^2 - 10*w - 5]', '[1633, 1633, 2*w^3 - 2*w^2 - 11*w + 1]', '[1633, 1633, 4*w^2 - 3*w - 14]', '[1635, 1635, -4*w^3 + 3*w^2 + 15*w + 6]', '[1641, 1641, 3*w^3 - 4*w^2 - 7*w + 9]', '[1641, 1641, 3*w^3 - 8*w^2 - 7*w + 9]', '[1647, 183, 2*w^3 - 5*w^2 - 4*w + 14]', '[1647, 183, 7*w^3 - 10*w^2 - 26*w + 13]', '[1647, 1647, 2*w^3 - w^2 - 12*w]', '[1647, 1647, -w^3 - w^2 + 2*w + 6]', '[1649, 1649, 5*w^3 - 7*w^2 - 17*w + 13]', '[1655, 1655, 2*w^3 - 13*w - 5]', '[1659, 1659, 2*w^3 - 5*w^2 - 3]', '[1659, 1659, -4*w^3 + 10*w^2 + w - 3]', '[1659, 1659, -2*w^3 - 2*w^2 + 11*w + 18]', '[1659, 1659, w^3 - 5*w - 9]', '[1663, 1663, 4*w^3 - 2*w^2 - 19*w - 4]', '[1665, 1665, -3*w^3 + 11*w^2 - 3*w - 9]', '[1665, 1665, -w^3 + 2*w + 6]', '[1667, 1667, 3*w^3 - 7*w^2 - 6*w + 4]', '[1669, 1669, -5*w^3 + 9*w^2 + 14*w - 14]', '[1669, 1669, -3*w^3 + 6*w^2 + 13*w - 8]', '[1671, 1671, 3*w^3 - 6*w^2 - 8*w]', '[1671, 1671, 2*w^3 - 5*w^2 - 9*w + 6]', '[1671, 1671, 3*w^3 - 5*w^2 - 10*w + 3]', '[1671, 1671, 2*w^3 - w^2 - 9*w + 3]', '[1673, 1673, -w^3 + 4*w^2 + 6*w - 10]', '[1673, 1673, w^3 + 3*w^2 - 6*w - 8]', '[1673, 1673, w^3 - w^2 - 4]', '[1673, 1673, w^3 + 4*w^2 - 2*w - 8]', '[1675, 1675, 4*w^2 - 3*w - 7]', '[1680, 210, -2*w^3 + 8*w]', '[1680, 210, -2*w^3 + 6*w^2 + 4*w - 12]', '[1685, 1685, -4*w^2 + 7*w + 5]', '[1685, 1685, 2*w^3 - 2*w^2 - 11*w + 2]', '[1687, 1687, -3*w^3 + 4*w^2 + 13*w - 1]', '[1687, 1687, -4*w^3 + 4*w^2 + 16*w + 5]', '[1693, 1693, w^3 + w^2 - 4*w - 10]', '[1697, 1697, 3*w^3 - 2*w^2 - 14*w - 10]', '[1699, 1699, -2*w^3 + 4*w^2 + 3*w - 8]', '[1701, 63, -3*w^3 + 3*w^2 + 15*w]', '[1701, 63, 3*w^2 - 6*w]', '[1701, 1701, -4*w^2 + 9]', '[1701, 1701, 3*w^3 - 3*w^2 - 13*w + 6]', '[1707, 1707, 2*w^3 - w^2 - 12*w - 3]', '[1709, 1709, -4*w^3 + 5*w^2 + 14*w - 7]', '[1709, 1709, 4*w^3 - 6*w^2 - 13*w + 8]', '[1712, 214, 4*w^3 - 4*w^2 - 18*w - 2]', '[1713, 1713, -2*w^3 + w - 3]', '[1713, 1713, -w^3 + 5*w^2 - w - 9]', '[1715, 35, -3*w^3 + 5*w^2 + 7*w - 10]', '[1715, 35, 2*w^3 - 5*w^2 - 6*w + 4]', '[1715, 245, -2*w^3 + 6*w^2 + 6*w - 13]', '[1715, 245, 3*w^3 - 3*w^2 - 10*w + 1]', '[1715, 1715, w^3 + 3*w^2 - 8*w - 10]', '[1715, 1715, -w^3 + 5*w^2 - w - 10]', '[1717, 1717, 4*w^3 - 8*w^2 - 14*w + 13]', '[1721, 1721, w^3 - 2*w^2 - 4*w - 4]', '[1725, 1725, -4*w^3 + 6*w^2 + 15*w - 6]', '[1731, 1731, -3*w^3 + 6*w^2 + 8*w - 15]', '[1744, 218, -2*w^3 + 10*w + 2]', '[1745, 1745, -4*w^3 - 4*w^2 + 27*w + 28]', '[1753, 1753, w^3 - 3*w^2 - 2*w - 2]', '[1753, 1753, -2*w^3 + 6*w^2 + 4*w - 11]', '[1757, 1757, 6*w^2 + 2*w - 13]', '[1757, 1757, -2*w^3 + w^2 + 7*w - 7]', '[1757, 1757, w^3 + 3*w^2 - 5*w - 10]', '[1757, 1757, w^3 - 4*w^2 + w - 1]', '[1759, 1759, w^3 + 2*w^2 - 8*w - 4]', '[1761, 1761, 2*w^3 - w^2 - 6*w - 6]', '[1773, 1773, 2*w^3 - 4*w^2 - w + 6]', '[1775, 1775, -3*w^3 + 5*w^2 + 12*w - 5]', '[1775, 1775, 2*w^2 - 5*w - 13]', '[1775, 1775, 3*w^3 - w^2 - 12*w - 1]', '[1776, 222, 2*w^3 + 2*w^2 - 4*w - 6]', '[1776, 222, -6*w^2 + 4*w + 6]', '[1777, 1777, 2*w^3 + w^2 - 15*w - 10]', '[1785, 1785, 4*w^3 - 7*w^2 - 12*w + 6]', '[1785, 1785, -w^3 + 2*w^2 + 8*w]', '[1787, 1787, w^3 - w^2 - 8*w - 1]', '[1789, 1789, 2*w^3 - 4*w^2 - 4*w + 11]', '[1792, 28, -4*w^2 + 8]', '[1792, 28, -4*w^2 + 4*w + 8]', '[1799, 1799, w^3 - 9*w - 4]', '[1799, 1799, w^3 - 3*w^2 - 8*w + 2]', '[1801, 1801, -w^3 + 5*w^2 - w - 16]', '[1809, 201, 2*w^3 - 2*w^2 - 7*w - 7]', '[1809, 1809, 5*w^2 - 6*w - 9]', '[1811, 1811, 2*w^3 - 3*w^2 - 5*w - 5]', '[1813, 259, -w^3 + 5*w^2 + 5*w - 5]', '[1813, 259, -3*w^3 + 2*w^2 + 9*w - 2]', '[1813, 259, 5*w^3 - 5*w^2 - 23*w + 1]', '[1813, 259, -w^3 + 6*w^2 - w - 7]', '[1813, 1813, -w^3 - 3*w^2 + 5*w + 8]', '[1813, 1813, 4*w^3 - 6*w^2 - 7*w + 1]', '[1813, 1813, -3*w^3 + 3*w^2 + 9*w + 1]', '[1813, 1813, -4*w^3 + 14*w^2 - 2*w - 13]', '[1817, 1817, -3*w^3 + 8*w^2 + 2*w - 10]', '[1817, 1817, 2*w^3 - 7*w^2 - w + 13]', '[1819, 1819, -w^3 + 6*w^2 + w - 19]', '[1821, 1821, -w^3 + w^2 - w - 6]', '[1823, 1823, 3*w^2 - 11]', '[1823, 1823, w - 7]', '[1831, 1831, w^3 - 2*w^2 - 3*w - 4]', '[1835, 1835, w^3 - 5*w^2 + 13]', '[1839, 1839, -w^2 - 2*w + 9]', '[1840, 230, 2*w^3 - 4*w^2 - 10*w + 2]', '[1841, 1841, w^3 + 2*w^2 - 2*w + 2]', '[1841, 1841, 4*w^3 + w^2 - 8*w + 5]', '[1847, 1847, -w^3 - w^2 + 9*w - 2]', '[1849, 43, 6*w^3 - 9*w^2 - 21*w + 11]', '[1849, 43, -2*w^3 + w^2 + 9*w - 5]', '[1851, 1851, -2*w^3 + 7*w^2 + 7*w - 9]', '[1851, 1851, -w^3 + 2*w^2 + 8*w - 6]', '[1853, 1853, w^3 - 2*w^2 - 2*w + 10]', '[1861, 1861, 2*w^3 - 3*w^2 - 11*w + 2]', '[1863, 69, -3*w^3 + 6*w^2 + 9*w - 6]', '[1863, 1863, -4*w^3 + 5*w^2 + 15*w]', '[1869, 1869, 6*w^3 - 7*w^2 - 23*w + 9]', '[1869, 1869, -4*w^3 + 8*w^2 + 13*w - 12]', '[1871, 1871, 5*w - 1]', '[1871, 1871, 3*w^3 - 6*w^2 - 14*w + 13]', '[1873, 1873, 2*w^3 - 11*w - 2]', '[1875, 15, 5*w^3 - 25*w - 15]', '[1875, 1875, -4*w^3 + 4*w^2 + 15*w - 3]', '[1877, 1877, w^2 - 5*w + 8]', '[1877, 1877, 3*w^3 - 2*w^2 - 6*w + 7]', '[1883, 1883, w^2 - 5*w - 8]', '[1883, 1883, -3*w^3 + w^2 + 5*w - 5]', '[1883, 1883, -2*w^3 + w^2 + 2*w - 8]', '[1883, 1883, -2*w^3 + 3*w^2 + w - 5]', '[1887, 1887, 4*w^2 + w]', '[1887, 1887, -4*w^2 - 6*w + 3]', '[1889, 1889, 2*w^3 - w^2 - 9*w + 4]', '[1895, 1895, w^3 + 2*w^2 - 11*w - 7]', '[1897, 1897, w^3 + 3*w^2 - 10*w - 7]', '[1897, 1897, -3*w^3 + 2*w^2 + 5*w - 1]', '[1897, 1897, 2*w^3 - 9*w - 1]', '[1897, 1897, -4*w^3 - w^2 + 7*w - 1]', '[1897, 1897, -3*w^3 + 13*w + 5]', '[1897, 1897, -4*w^3 + w^2 + 13*w - 1]', '[1897, 1897, 2*w^3 - 6*w^2 - 5*w + 11]', '[1897, 1897, -3*w^3 + 4*w^2 + 8*w - 2]', '[1901, 1901, -w^3 - w^2 + 7*w - 1]', '[1901, 1901, -3*w^3 + 3*w^2 + 12*w - 8]', '[1901, 1901, -2*w^3 + 6*w^2 + 5*w - 13]', '[1901, 1901, -4*w^3 + 3*w^2 + 15*w - 1]', '[1904, 238, -2*w^3 + 4*w^2 + 8*w - 2]', '[1904, 238, 2*w - 8]', '[1915, 1915, 3*w^3 - 4*w^2 - 8*w + 4]', '[1915, 1915, 5*w^3 - 6*w^2 - 18*w - 2]', '[1917, 213, -2*w^3 + 5*w^2 + 7*w - 5]', '[1917, 213, 2*w^3 + 4*w^2 - 13*w - 25]', '[1917, 213, 5*w^3 - 5*w^2 - 22*w - 1]', '[1917, 1917, 2*w^3 + w^2 - 14*w - 15]', '[1917, 1917, 3*w^3 - 14*w - 6]', '[1917, 1917, -3*w^3 + 4*w^2 + 12*w]', '[1929, 1929, 3*w^3 - w^2 - 9*w - 3]', '[1929, 1929, -2*w^2 - 2*w - 3]', '[1933, 1933, -3*w^3 + 2*w^2 + 10*w + 2]', '[1939, 1939, w^3 + 3*w^2 - 8*w - 11]', '[1939, 1939, 4*w^3 - 3*w^2 - 16*w - 2]', '[1939, 1939, 4*w^2 - w - 7]', '[1939, 1939, 2*w^2 - 7*w - 8]', '[1939, 1939, 4*w^2 - w - 11]', '[1939, 1939, 5*w^3 - 5*w^2 - 18*w + 7]', '[1939, 1939, 6*w^2 + 3*w - 10]', '[1939, 1939, -w^3 - 2*w - 5]', '[1945, 1945, -2*w^3 + 3*w^2 + 3*w - 7]', '[1949, 1949, 3*w^3 - 3*w^2 - 15*w - 5]', '[1949, 1949, -w^3 + 5*w^2 + 2*w - 8]', '[1955, 1955, -3*w^3 + 2*w^2 + 15*w - 2]', '[1965, 1965, -2*w^3 - 2*w^2 + 16*w + 9]', '[1965, 1965, w^3 + 4*w^2 - 13*w - 9]', '[1965, 1965, 5*w^3 - 3*w^2 - 21*w - 15]', '[1967, 1967, -w^3 + 7*w^2 - 5*w - 10]', '[1967, 1967, 4*w^2 - 2*w - 7]', '[1973, 1973, -w^3 + w^2 + 5*w - 8]', '[1975, 1975, w^3 - 4*w^2 + w + 11]', '[1975, 1975, -w^3 + 5*w^2 - 8]', '[1979, 1979, -2*w^3 + 5*w^2 + 3*w - 11]', '[1981, 1981, -4*w^3 - 2*w^2 + 7*w + 1]', '[1981, 1981, -3*w^3 + w^2 + 6*w + 1]', '[1981, 1981, -w^3 + 3*w^2 - w - 8]', '[1981, 1981, -w^3 + 6*w^2 - 6*w - 11]', '[1983, 1983, 2*w^3 - 7*w^2 - 4*w + 9]', '[1985, 1985, -6*w^3 - w^2 + 31*w + 28]', '[1985, 1985, -2*w^3 - 6*w^2 + 19*w + 26]', '[1987, 1987, -w^3 + w^2 - 3*w - 1]', '[1993, 1993, -2*w^3 + 6*w^2 + 2*w - 13]', '[1997, 1997, -4*w^3 + 8*w^2 + 10*w - 7]', '[1997, 1997, w^3 - w - 5]', '[1999, 1999, -w^3 + 2*w^2 - w - 11]', '[1999, 1999, w^2 - 10]', '[2000, 10, 4*w^3 - 2*w^2 - 16*w - 4]', '[2000, 250, -2*w^3 + 8*w + 10]', '[2005, 2005, 7*w^3 - 10*w^2 - 22*w + 2]', '[2007, 2007, 3*w^3 - 4*w^2 - 8*w + 3]', '[2007, 2007, -2*w^3 + 6*w^2 + 5*w - 12]', '[2017, 2017, 4*w^3 - 7*w^2 - 16*w + 10]', '[2019, 2019, -2*w^2 - w + 9]', '[2023, 2023, w^3 - 5*w^2 - 3*w + 11]', '[2023, 2023, -3*w^3 + 2*w^2 + 10*w + 1]', '[2025, 75, -3*w^3 + 3*w^2 + 9*w - 3]', '[2025, 2025, -4*w^3 + 3*w^2 + 16*w + 3]', '[2029, 2029, -w^3 + 5*w^2 + 7*w - 11]', '[2029, 2029, -w^3 + 3*w^2 + 8*w - 7]', '[2037, 2037, -4*w^3 + 7*w^2 + 10*w - 9]', '[2037, 2037, 4*w^3 - 6*w^2 - 17*w + 6]', '[2039, 2039, -w^3 + 5*w^2 + 2*w - 13]', '[2039, 2039, -3*w^3 + 4*w^2 + 7*w - 4]', '[2043, 2043, 5*w^3 - w^2 - 25*w - 12]', '[2045, 2045, 5*w^2 - 9*w - 13]', '[2047, 2047, 4*w^3 - 5*w^2 - 16*w + 11]', '[2049, 2049, w^3 - 5*w^2 - 4*w + 3]', '[2049, 2049, w^2 - 6*w - 3]', '[2051, 2051, -w^3 + 3*w^2 - 2*w - 7]', '[2051, 2051, 3*w^3 - 5*w^2 - 11*w + 4]', '[2051, 2051, -2*w^3 + 2*w^2 + 3*w - 7]', '[2051, 2051, 4*w^3 - 8*w^2 - 16*w + 13]', '[2055, 2055, -3*w^2 + 5*w + 12]', '[2061, 2061, -3*w^3 + 8*w^2 + 7*w - 24]', '[2061, 2061, 4*w^3 - 5*w^2 - 14*w + 3]', '[2073, 2073, 2*w^3 - 5*w^2 - 6*w + 3]', '[2073, 2073, 2*w^3 - w^2 - 3*w - 3]', '[2081, 2081, w^3 - 9*w + 2]', '[2085, 2085, 3*w^3 - 4*w^2 - 6*w + 3]', '[2087, 2087, 2*w^3 - 6*w^2 - w + 11]', '[2096, 262, -4*w^3 + 6*w^2 + 14*w - 4]', '[2096, 262, 4*w^2 - 6*w - 14]', '[2096, 262, 4*w^3 - 6*w^2 - 12*w + 4]', '[2097, 2097, -w^3 - 2*w^2 + 11*w + 6]', '[2099, 2099, -2*w - 7]', '[2105, 2105, -w^3 + 4*w + 10]', '[2105, 2105, w^3 + w^2 - 10*w - 1]', '[2111, 2111, -4*w^3 + 5*w^2 + 11*w + 2]', '[2111, 2111, 5*w^3 - 5*w^2 - 20*w + 2]', '[2113, 2113, w^3 - w^2 - 3*w - 7]', '[2113, 2113, -3*w^3 + 7*w^2 + 4*w - 10]', '[2121, 2121, 4*w^3 - 5*w^2 - 14*w + 6]', '[2121, 2121, -5*w^3 + 12*w^2 + 9*w - 12]', '[2125, 85, -w^3 + 3*w^2 - w - 14]', '[2125, 2125, -3*w^3 + 3*w^2 + 15*w - 1]', '[2127, 2127, w^3 - w^2 - 8*w]', '[2129, 2129, -w^3 + 5*w^2 + w - 8]', '[2129, 2129, -w^2 + 2*w - 5]', '[2133, 237, w^3 - w^2 - 2*w - 8]', '[2133, 237, -w^3 - 2*w^2 + 5*w + 17]', '[2133, 2133, -4*w^2 + 7*w + 12]', '[2133, 2133, -w^3 + 6*w^2 - 3*w - 9]', '[2135, 2135, -3*w^3 + 8*w^2 + 7*w - 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4*w^2 + 5*w + 5]', '[2192, 274, 2*w^3 - 4*w^2 - 6*w + 14]', '[2199, 2199, -2*w^3 + 8*w^2 - w - 9]', '[2203, 2203, -w^3 + 3*w^2 + 6*w - 10]', '[2205, 315, -w^3 + 3*w^2 - 4*w - 3]', '[2205, 315, -7*w^3 + 16*w^2 + 10*w - 15]', '[2205, 2205, 5*w^3 - 6*w^2 - 19*w + 6]', '[2205, 2205, -2*w^2 + 2*w - 3]', '[2209, 47, -6*w^3 + 7*w^2 + 25*w - 4]', '[2209, 47, -2*w^3 + 12*w + 1]', '[2213, 2213, -4*w^2 + 2*w + 17]', '[2215, 2215, 3*w^3 + 3*w^2 - 20*w - 23]', '[2217, 2217, 3*w^3 - 4*w^2 - 7*w + 3]', '[2219, 2219, 3*w^3 - 5*w^2 - 10*w + 2]', '[2219, 2219, w^3 + 4*w^2 - 4*w - 7]', '[2219, 2219, 6*w^2 - 7*w - 10]', '[2219, 2219, 3*w^3 - 6*w^2 - 12*w + 8]', '[2221, 2221, 2*w^3 - w^2 - 11*w - 10]', '[2224, 278, 2*w^3 - 8*w + 4]', '[2225, 2225, 3*w^3 - 6*w^2 - 14*w + 10]', '[2227, 2227, 3*w^3 - 8*w^2 - 8*w + 19]', '[2227, 2227, 5*w^3 - 6*w^2 - 19*w + 5]', '[2227, 2227, -3*w^3 + 7*w^2 + 7*w - 16]', '[2229, 2229, -w^3 + 5*w - 6]', '[2231, 2231, 2*w^3 - 3*w^2 - 11*w + 7]', '[2243, 2243, 3*w^3 - 5*w^2 - 4*w + 7]', '[2243, 2243, 3*w^3 - 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21]', '[5271, 5271, -4*w^3 + 4*w^2 + 16*w - 9]', '[5273, 5273, -w^3 + 2*w^2 + 5*w - 13]', '[5277, 5277, 3*w^3 - 3*w^2 - 5*w - 3]', '[5279, 5279, 6*w^3 - 5*w^2 - 26*w - 8]', '[5281, 5281, 3*w^3 - 5*w^2 - 15*w + 7]', '[5283, 5283, w^3 + 4*w^2 - 8*w - 6]', '[5285, 5285, -2*w^3 + 3*w^2 + 5*w - 13]', '[5285, 5285, 2*w^3 - 2*w^2 - 13*w - 2]', '[5287, 5287, 3*w^3 - 4*w^2 - 10*w + 14]', '[5293, 5293, w^3 - 2*w^2 - 9*w + 5]', '[5293, 5293, -4*w^3 + 4*w^2 + 17*w - 8]', '[5296, 662, -2*w^3 + 4*w^2 + 2*w - 10]', '[5297, 5297, -3*w^3 + 9*w^2 + 8*w - 23]', '[5297, 5297, w^3 + w^2 - 11*w - 5]', '[5303, 5303, -2*w^3 + 7*w^2 + 5*w - 16]', '[5315, 5315, 5*w^3 - 8*w^2 - 15*w + 2]', '[5315, 5315, 2*w^3 - 7*w^2 - 4*w + 16]', '[5319, 591, -w^3 - 2*w^2 + 8*w - 1]', '[5319, 5319, -2*w^3 - w^2 + 13*w + 3]', '[5321, 5321, 3*w^3 + w^2 - 16*w - 8]', '[5321, 5321, 3*w^3 - 6*w^2 - 6*w + 13]', '[5325, 5325, 2*w^3 + 4*w^2 - 16*w - 27]', '[5325, 5325, 2*w^3 - 3*w^2 - 2*w + 9]', '[5325, 5325, 11*w^3 - 6*w^2 - 51*w - 15]', '[5327, 5327, -3*w^3 + 5*w^2 + 2*w - 7]', '[5327, 5327, -4*w^3 + 2*w^2 + 7*w - 7]', '[5328, 666, -4*w^2 + 10*w + 12]', '[5328, 666, 4*w^3 - 4*w^2 - 20*w - 6]', '[5331, 5331, 3*w^3 - 5*w^2 - 12*w - 6]', '[5341, 763, 4*w^3 - 5*w^2 - 12*w + 5]', '[5341, 763, 3*w^3 - 8*w^2 - 8*w + 8]', '[5341, 5341, 5*w^3 - 8*w^2 - 12*w + 2]', '[5341, 5341, 5*w^2 - 5*w - 11]', '[5345, 5345, -6*w^3 + 4*w^2 + 23*w + 17]', '[5351, 5351, -4*w^3 + 3*w^2 + 13*w - 2]', '[5355, 5355, -3*w^3 + 8*w^2 + 2*w - 12]', '[5355, 5355, -4*w^3 + 7*w^2 + 10*w - 15]', '[5359, 5359, -3*w^3 + 6*w^2 + 2*w + 2]', '[5360, 670, 2*w^3 + 6*w^2 - 22*w - 22]', '[5361, 5361, -3*w^2 - 2*w - 3]', '[5367, 5367, -2*w^3 + 6*w^2 + 9*w - 6]', '[5376, 84, -4*w^3 + 4*w^2 + 20*w]', '[5376, 84, 4*w^2 - 8*w]', '[5381, 5381, w^3 - 6*w - 11]', '[5387, 5387, -8*w^3 + 13*w^2 + 27*w - 16]', '[5387, 5387, 4*w^3 - 4*w^2 - 22*w - 5]', '[5389, 5389, -6*w^3 + 11*w^2 + 21*w - 29]', '[5389, 5389, 2*w^3 + w^2 - 10*w - 2]', '[5392, 674, -4*w^3 + 6*w^2 + 10*w - 14]', '[5392, 674, 2*w^3 - 8*w^2 - 2*w + 10]', '[5393, 5393, -2*w^3 + 7*w^2 + 5*w - 13]', '[5397, 5397, w^3 + 5*w^2 - 8*w - 21]', '[5397, 5397, 3*w^3 - 7*w^2 - 4*w + 12]', '[5403, 5403, 4*w^3 - 6*w^2 - 15*w + 3]', '[5411, 5411, -2*w^3 - w^2 + w - 7]', '[5411, 5411, w^3 - 2*w^2 - 7*w - 7]', '[5413, 5413, 4*w^3 - 5*w^2 - 20*w - 2]', '[5427, 201, 3*w^2 - 9*w - 6]', '[5427, 5427, 2*w^3 - 9*w^2 + 5*w + 6]', '[5429, 5429, -6*w^3 + 7*w^2 + 22*w - 14]', '[5429, 5429, 3*w^3 - 9*w^2 - 10*w + 16]', '[5433, 5433, -w^3 + 5*w^2 - 7*w - 6]', '[5435, 5435, w^3 + 5*w^2 - 15*w - 17]', '[5435, 5435, w^3 + 2*w^2 - 4*w - 13]', '[5437, 5437, -4*w^3 + 4*w^2 + 12*w - 5]', '[5439, 777, -3*w^2 + 4*w + 18]', '[5439, 777, -3*w^2 - w + 12]', '[5439, 777, 2*w^2 - 4*w - 15]', '[5439, 777, w^3 + 2*w^2 - 12*w - 6]', '[5439, 5439, 5*w^3 - 6*w^2 - 17*w - 9]', '[5439, 5439, 3*w^3 - 5*w^2 - 18*w - 3]', '[5439, 5439, -5*w^3 + 2*w^2 + 27*w + 12]', '[5439, 5439, -w^2 + 8*w + 9]', '[5441, 5441, -3*w^3 + 7*w^2 + 8*w - 4]', '[5441, 5441, 4*w^3 - 5*w^2 - 19*w + 8]', '[5443, 5443, -7*w^3 + 9*w^2 + 25*w - 4]', '[5443, 5443, -w^3 - 4*w^2 + 7*w + 11]', '[5443, 5443, 2*w^3 + w^2 - 9*w - 20]', '[5443, 5443, 5*w^2 - 4*w - 10]', '[5449, 5449, 2*w^3 - 7*w - 11]', '[5451, 5451, -5*w^3 + 9*w^2 + 11*w - 6]', '[5451, 5451, 5*w^3 - 13*w^2 - 7*w + 9]', '[5457, 5457, 5*w^3 - 4*w^2 - 18*w + 3]', '[5463, 5463, 5*w^3 - 2*w^2 - 23*w - 6]', '[5465, 5465, w^3 - 7*w^2 + 10*w + 11]', '[5465, 5465, 3*w^3 + 4*w^2 - 23*w - 23]', '[5469, 5469, w^2 - 7*w]', '[5469, 5469, 3*w^3 - 11*w]', '[5477, 5477, 4*w^3 - 3*w^2 - 22*w - 7]', '[5477, 5477, 5*w^3 - 10*w^2 - 18*w + 16]', '[5483, 5483, 3*w^3 - 3*w^2 - 16*w + 1]', '[5488, 14, 2*w^3 - 8*w^2 + 2]', '[5488, 14, -2*w^3 - 2*w^2 + 6*w - 4]', '[5488, 98, 4*w^2 + 4*w - 10]', '[5488, 98, 2*w^3 - 2*w^2 - 2*w - 4]', '[5488, 686, 2*w^3 + 2*w^2 - 8*w - 2]', '[5488, 686, 2*w^3 - 10*w + 4]', '[5493, 5493, -w^3 + 2*w^2 - 5*w - 3]', '[5495, 5495, 5*w^3 - 9*w^2 - 18*w + 25]', '[5495, 5495, 5*w^3 - 4*w^2 - 23*w - 10]', '[5495, 5495, -3*w^3 + 3*w^2 + 16*w - 4]', '[5495, 5495, 3*w^2 - 6*w - 14]', '[5497, 5497, 3*w^3 - 6*w^2 - 11*w + 5]', '[5497, 5497, 3*w^3 - 4*w^2 - 17*w + 13]', '[5503, 5503, -4*w^3 + 8*w^2 + 17*w - 22]', '[5503, 5503, 5*w^3 - w^2 - 22*w - 8]', '[5503, 5503, -7*w^3 + 6*w^2 + 30*w - 2]', '[5503, 5503, w^2 - 7*w - 1]', '[5505, 5505, -4*w^3 + 5*w^2 + 12*w - 3]', '[5509, 5509, -w^3 - 4*w^2 + 6*w + 13]', '[5509, 5509, -2*w^3 - 4*w^2 + 15*w + 16]', '[5517, 5517, -8*w^3 + 10*w^2 + 31*w - 6]', '[5519, 5519, -3*w^3 + 5*w^2 + 12*w - 1]', '[5520, 690, -4*w^2 + 10*w + 6]', '[5521, 5521, -w^3 + 5*w^2 - 5*w - 11]', '[5521, 5521, w^3 - 7*w^2 - 4*w + 11]', '[5523, 5523, 4*w^3 - 11*w^2 - 12*w + 15]', '[5523, 5523, -6*w^3 + 6*w^2 + 19*w - 12]', '[5527, 5527, 3*w^3 - 4*w^2 - 8*w - 8]', '[5531, 5531, -3*w^3 + w^2 + 17*w - 1]', '[5531, 5531, -w^3 + 6*w^2 - 10]', '[5541, 5541, -2*w^3 + 4*w^2 - w + 3]', '[5543, 5543, 2*w^3 - 8*w^2 - w + 19]', '[5545, 5545, 3*w^3 - 6*w^2 - 4*w + 10]', '[5545, 5545, w^3 - 6*w^2 - w + 10]', '[5547, 129, -3*w^3 + 9*w^2 + 5*w - 18]', '[5547, 129, -w^3 - w^2 - 3*w + 6]', '[5553, 5553, 2*w^3 - 5*w^2 - 10*w + 15]', '[5553, 5553, 4*w^3 - 10*w^2 - 11*w + 21]', '[5557, 5557, -3*w^3 + 5*w^2 + 15*w - 10]', '[5559, 5559, -w^3 + 3*w^2 + 9*w - 3]', '[5563, 5563, 5*w^3 - 5*w^2 - 18*w + 5]', '[5569, 5569, 7*w^3 - 9*w^2 - 26*w + 13]', '[5573, 5573, -4*w^3 + 5*w^2 + 12*w - 4]', '[5575, 5575, -2*w^3 + 5*w^2 + 6*w - 19]', '[5575, 5575, 5*w^3 - 6*w^2 - 14*w + 11]', '[5579, 5579, -4*w^3 + 7*w^2 + 12*w + 1]', '[5579, 5579, -2*w^3 + 5*w^2 + 9*w - 2]', '[5581, 5581, w^3 + 2*w^2 - 12*w - 5]', '[5581, 5581, -5*w^3 + 5*w^2 + 22*w - 7]', '[5583, 5583, -w^3 - w^2 - 6]', '[5584, 698, -4*w^3 + 2*w^2 + 22*w + 2]', '[5587, 5587, -7*w^3 + 13*w^2 + 26*w - 23]', '[5587, 5587, -2*w^3 + 6*w^2 + 8*w - 25]', '[5589, 207, 3*w^3 - 6*w^2 - 3*w + 9]', '[5589, 5589, w^3 - 5*w^2 + 4*w + 12]', '[5607, 5607, -w^3 + 7*w^2 + 3*w - 18]', '[5607, 5607, w^3 + 4*w^2 - 8*w - 15]', '[5609, 5609, -2*w^3 + 5*w^2 + 9*w - 17]', '[5609, 5609, -2*w^3 - w^2 + 14*w + 2]', '[5609, 5609, -4*w^3 + 6*w^2 + 9*w - 4]', '[5609, 5609, -4*w^3 + 5*w^2 + 16*w + 2]', '[5609, 5609, 5*w^3 - 10*w^2 - 15*w + 13]', '[5609, 5609, -w^3 + 6*w - 8]', '[5613, 5613, -3*w^3 + w^2 + 10*w - 9]', '[5613, 5613, 5*w^2 - w]', '[5615, 5615, -2*w^3 + 9*w^2 - 3*w - 13]', '[5619, 5619, 2*w^3 - w^2 - 4*w - 6]', '[5625, 45, -5*w^2 + 5*w + 15]', '[5625, 5625, -5*w^2 + w + 12]', '[5627, 5627, 5*w^3 - 6*w^2 - 16*w + 10]', '[5631, 5631, w^3 - 5*w^2 + 8*w]', '[5631, 5631, -5*w^3 + 5*w^2 + 19*w - 9]', '[5635, 805, -3*w^3 + 10*w - 4]', '[5635, 805, -2*w^3 + 5*w^2 + 12*w - 7]', '[5635, 5635, -5*w^3 + 10*w^2 + 14*w - 22]', '[5635, 5635, -w^3 + 10*w + 2]', '[5639, 5639, -4*w^3 + 6*w^2 + 17*w - 4]', '[5639, 5639, -4*w^3 + 7*w^2 + 13*w - 5]', '[5645, 5645, w^3 + 2*w^2 - 3*w - 11]', '[5649, 5649, -2*w^3 + 3*w^2 + 12*w - 6]', '[5649, 5649, 4*w^3 - 3*w^2 - 15*w + 6]', '[5649, 5649, w^3 - 3*w^2 + 7*w - 3]', '[5649, 5649, 7*w^3 - 5*w^2 - 29*w]', '[5651, 5651, -5*w^3 + 12*w^2 + 16*w - 28]', '[5653, 5653, 4*w^2 + w - 13]', '[5653, 5653, 5*w^3 - 2*w^2 - 22*w - 5]', '[5657, 5657, -4*w^3 + 6*w^2 + 9*w - 5]', '[5657, 5657, 3*w^3 - 7*w^2 - 10*w - 1]', '[5661, 5661, -4*w^3 + 3*w^2 + 13*w + 3]', '[5661, 5661, w^3 + 5*w^2 - 6*w - 18]', '[5663, 5663, 2*w^3 + 8*w^2 - 21*w - 20]', '[5663, 5663, 3*w^3 + 4*w^2 - 14*w - 11]', '[5667, 5667, w^3 + w^2 + 2*w - 6]', '[5669, 5669, -3*w^3 + w^2 + 12*w - 2]', '[5675, 5675, 2*w^3 + 2*w^2 - 8*w - 13]', '[5677, 5677, 4*w^3 - 18*w - 17]', '[5677, 5677, w^3 + 4*w^2 - 5*w - 17]', '[5680, 710, -2*w^2 + 8*w + 4]', '[5680, 710, 10*w^3 + 2*w^2 - 54*w - 46]', '[5680, 710, 8*w^3 - 2*w^2 - 42*w - 22]', '[5685, 5685, 3*w^3 - 6*w^2 - 8*w - 3]', '[5689, 5689, -w^3 + 10*w - 1]', '[5689, 5689, w^3 - 2*w^2 - 9*w + 2]', '[5691, 5691, -4*w^3 + 5*w^2 + 9*w - 6]', '[5691, 5691, w^3 + 4*w^2 - 11*w - 21]', '[5691, 5691, 2*w^3 - w^2 - 4*w + 9]', '[5691, 5691, -5*w^2 + 8*w + 27]', '[5691, 5691, 4*w^3 - 12*w^2 - 3*w + 15]', '[5691, 5691, 2*w^3 - 3*w^2 + 3*w - 3]', '[5691, 5691, -2*w^3 + 7*w^2 + 5*w - 15]', '[5691, 5691, -w^2 + 8*w - 9]', '[5695, 5695, -2*w^3 + 4*w^2 - 4*w - 5]', '[5703, 5703, -2*w^3 - 2*w^2 + 15*w + 6]', '[5703, 5703, -2*w^3 + 2*w^2 + 3]', '[5703, 5703, 5*w^3 - 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14]', '[5773, 5773, 5*w^3 - 9*w^2 - 20*w + 13]', '[5773, 5773, 2*w^3 - 15*w + 10]', '[5779, 5779, 4*w^2 - 8*w - 13]', '[5779, 5779, -w^3 + 6*w^2 + w - 16]', '[5783, 5783, -4*w^3 + 10*w^2 + 15*w - 25]', '[5783, 5783, 5*w^3 - w^2 - 26*w - 10]', '[5787, 5787, 5*w^3 - 3*w^2 - 20*w - 6]', '[5787, 5787, 4*w^3 - w^2 - 21*w - 18]', '[5789, 5789, -3*w^3 + w^2 + 4*w - 8]', '[5789, 5789, -w^3 + 2*w^2 - 3*w - 8]', '[5789, 5789, -3*w^3 + 2*w^2 + 15*w - 5]', '[5789, 5789, -6*w^2 + 12*w + 7]', '[5791, 5791, w^3 - 7*w^2 - w + 25]', '[5799, 5799, -w^3 - 5*w^2 + 5*w + 9]', '[5807, 5807, 2*w^3 - w^2 - 3*w - 5]', '[5807, 5807, -5*w^3 + 5*w^2 + 21*w - 7]', '[5809, 5809, w^3 - 5*w^2 + 8*w + 11]', '[5809, 5809, -w^3 + 8*w^2 - 5*w - 22]', '[5809, 5809, 4*w^3 - 5*w^2 - 19*w + 7]', '[5809, 5809, 3*w^3 - 5*w^2 - 15*w + 8]', '[5813, 5813, w^3 - 7*w^2 + 5*w + 5]', '[5813, 5813, -4*w^3 + 11*w^2 + 12*w - 28]', '[5817, 5817, w^3 - 4*w^2 + 6*w + 3]', '[5817, 5817, 5*w^3 - w^2 - 23*w - 9]', '[5817, 5817, -2*w^3 + 13*w - 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20]', '[1321, 1321, 3*w^3 - 4*w^2 - 9*w + 5]', '[1367, 1367, -3*w^3 + 4*w^2 + 11*w + 1]', '[1367, 1367, -w^3 + 2*w^2 - 8]', '[1369, 37, -3*w^3 + 5*w^2 + 11*w - 5]', '[1373, 1373, -2*w^3 - w^2 + 6*w - 1]', '[1409, 1409, -2*w^3 + 6*w^2 + 4*w - 13]', '[1439, 1439, -2*w^3 + 5*w^2 + 5*w - 17]', '[1447, 1447, 6*w^3 - 9*w^2 - 23*w + 19]', '[1447, 1447, 2*w^3 - 3*w^2 - 8*w + 11]', '[1453, 1453, -w^3 + w^2 - 3*w - 2]', '[1453, 1453, 2*w^3 - w^2 - 10*w + 2]', '[1459, 1459, 3*w^3 - 2*w^2 - 5*w + 5]', '[1471, 1471, -w^3 - w^2 + 6*w - 1]', '[1481, 1481, w^3 - 6*w^2 + 20]', '[1483, 1483, 2*w^3 - 4*w^2 - 5*w + 14]', '[1483, 1483, -2*w^3 + 5*w^2 + 6*w - 17]', '[1483, 1483, w^3 - 2*w^2 - 4*w + 10]', '[1483, 1483, 3*w^3 - 4*w^2 - 9*w + 4]', '[1487, 1487, -w^3 + 5*w^2 - 7]', '[1487, 1487, -3*w^3 + 5*w^2 + 13*w - 5]', '[1489, 1489, -w^2 - w - 4]', '[1489, 1489, w^2 + 3*w + 5]', '[1493, 1493, -3*w^3 + 2*w^2 + 12*w - 2]', '[1499, 1499, -w^3 + 5*w^2 - w - 11]', '[1511, 1511, 2*w^2 + 2*w - 7]', '[1511, 1511, -w^3 + 5*w^2 - w - 8]', '[1549, 1549, 2*w^3 - 4*w^2 - 7*w + 1]', '[1559, 1559, w^3 - 2*w^2 - 2*w - 4]', '[1567, 1567, 3*w^2 - w - 13]', '[1567, 1567, -w^3 + w^2 + 3*w - 7]', '[1583, 1583, -2*w^3 + 6*w^2 + 6*w - 11]', '[1583, 1583, w^3 - 5*w^2 - 8*w + 8]', '[1597, 1597, -4*w^3 + 5*w^2 + 10*w + 2]', '[1597, 1597, 4*w^3 - 6*w^2 - 11*w + 1]', '[1601, 1601, 5*w - 2]', '[1607, 1607, -3*w^3 + 6*w^2 + 6*w - 10]', '[1609, 1609, -2*w^3 + 6*w^2 + 5*w - 14]', '[1613, 1613, 3*w^3 - 3*w^2 - 10*w + 2]', '[1613, 1613, -4*w^3 + 9*w^2 + 12*w - 17]', '[1621, 1621, -w^2 - 4]', '[1621, 1621, 4*w^3 - 5*w^2 - 18*w + 5]', '[1627, 1627, -3*w^3 + 4*w^2 + 8*w - 5]', '[1627, 1627, -2*w^3 + 5*w - 5]', '[1663, 1663, 4*w^3 - 2*w^2 - 19*w - 4]', '[1667, 1667, 3*w^3 - 7*w^2 - 6*w + 4]', '[1669, 1669, -5*w^3 + 9*w^2 + 14*w - 14]', '[1669, 1669, -3*w^3 + 6*w^2 + 13*w - 8]', '[1693, 1693, w^3 + w^2 - 4*w - 10]', '[1697, 1697, 3*w^3 - 2*w^2 - 14*w - 10]', '[1699, 1699, -2*w^3 + 4*w^2 + 3*w - 8]', '[1709, 1709, -4*w^3 + 5*w^2 + 14*w - 7]', '[1709, 1709, 4*w^3 - 6*w^2 - 13*w + 8]', '[1721, 1721, w^3 - 2*w^2 - 4*w - 4]', '[1753, 1753, w^3 - 3*w^2 - 2*w - 2]', '[1753, 1753, -2*w^3 + 6*w^2 + 4*w - 11]', '[1759, 1759, w^3 + 2*w^2 - 8*w - 4]', '[1777, 1777, 2*w^3 + w^2 - 15*w - 10]', '[1787, 1787, w^3 - w^2 - 8*w - 1]', '[1789, 1789, 2*w^3 - 4*w^2 - 4*w + 11]', '[1801, 1801, -w^3 + 5*w^2 - w - 16]', '[1811, 1811, 2*w^3 - 3*w^2 - 5*w - 5]', '[1823, 1823, 3*w^2 - 11]', '[1823, 1823, w - 7]', '[1831, 1831, w^3 - 2*w^2 - 3*w - 4]', '[1847, 1847, -w^3 - w^2 + 9*w - 2]', '[1849, 43, 6*w^3 - 9*w^2 - 21*w + 11]', '[1849, 43, -2*w^3 + w^2 + 9*w - 5]', '[1861, 1861, 2*w^3 - 3*w^2 - 11*w + 2]', '[1871, 1871, 5*w - 1]', '[1871, 1871, 3*w^3 - 6*w^2 - 14*w + 13]', '[1873, 1873, 2*w^3 - 11*w - 2]', '[1877, 1877, w^2 - 5*w + 8]', '[1877, 1877, 3*w^3 - 2*w^2 - 6*w + 7]', '[1889, 1889, 2*w^3 - w^2 - 9*w + 4]', '[1901, 1901, -w^3 - w^2 + 7*w - 1]', '[1901, 1901, -3*w^3 + 3*w^2 + 12*w - 8]', '[1901, 1901, -2*w^3 + 6*w^2 + 5*w - 13]', '[1901, 1901, -4*w^3 + 3*w^2 + 15*w - 1]', '[1933, 1933, -3*w^3 + 2*w^2 + 10*w + 2]', '[1949, 1949, 3*w^3 - 3*w^2 - 15*w - 5]', '[1949, 1949, -w^3 + 5*w^2 + 2*w - 8]', '[1973, 1973, -w^3 + w^2 + 5*w - 8]', '[1979, 1979, -2*w^3 + 5*w^2 + 3*w - 11]', '[1987, 1987, -w^3 + w^2 - 3*w - 1]', '[1993, 1993, -2*w^3 + 6*w^2 + 2*w - 13]', '[1997, 1997, -4*w^3 + 8*w^2 + 10*w - 7]', '[1997, 1997, w^3 - w - 5]', '[1999, 1999, -w^3 + 2*w^2 - w - 11]', '[1999, 1999, w^2 - 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': [3, 1, -5, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 9301, 'disc_rad': 9301, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[3, 1], [1, 1]]], [5, [[3, 1], [1, 1]]], [7, [[2, 1], [1, 2]]], [11, [[4, 1]]], [13, [[4, 1]]], [17, [[3, 1], [1, 1]]], [19, [[4, 1]]], [23, [[3, 1], [1, 1]]], [29, [[4, 1]]], [31, [[2, 2]]], [37, [[2, 1], [1, 2]]], [41, [[4, 1]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[4, 1]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 96.44169222903547, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.9301.1', 'local_algs': ['71.1.0.1', '71.1.0.1', '71.2.1.1', '131.1.0.1', '131.1.0.1', '131.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [71, 131], 'rd': 9.82047311635, 'regulator': {'__RealLiteral__': 0, 'data': '5.65473750217', 'prec': 44}, 'res': {'gal': ['24491673,9096930,-170112264,-54835066,410965558,141273276,-496163845,-186675668,341663866,138845122,-142461750,-61306290,37059531,16512490,-6137958,-2742654,661816,279814,-47635,-17032,2306,568,-70,-8,1'], 'sib': ['-5177,27485,13906,-67353,-3223,39665,-5740,-5998,988,330,-55,-6,1', '1,-12,2,19,-7,-3,1', '207609,193993,-90949,-20793,7514,405,-163,-2,1', '37,527,1790,-1086,-3559,2144,1691,-1499,113,151,-29,-4,1', '64,-382,359,173,-83,-1,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a - 1 \\)', '\\( a^{2} - 2 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}