Hilbert modular form data - 4.4.16609.1-15.1-g

Formats: - HTML - YAML - JSON - 2024-04-29T13:55:25.506703

• 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': 5, 'disc': 16609, 'field_bad_primes': [17, 977], 'field_label': '4.4.16609.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.16609.1-15.1-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [3, 5], 'level_ideal': '[15, 15, w^3 - 5*w - 3]', 'level_label': '15.1', 'level_norm': 15, 'parallel_weight': 2, 'short_label': '15.1-g', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, -w^2 + w + 3]', -1], ['[5, 5, w^2 - 4]', 1]], 'hecke_eigenvalues': ['e', 1, -1, '-e^4 - 2*e^3 + 4*e^2 + 8*e', '2*e^4 + 5*e^3 - 9*e^2 - 19*e - 1', 'e^4 + 3*e^3 - 2*e^2 - 11*e - 7', '-e^4 - 5*e^3 + e^2 + 19*e + 4', '-e^3 - e^2 + 5*e + 1', 'e^4 + 3*e^3 - 4*e^2 - 11*e + 1', '-2*e^4 - 3*e^3 + 9*e^2 + 9*e - 1', '-e^4 - 2*e^3 + 2*e^2 + 4*e + 5', '-2*e^4 - 4*e^3 + 12*e^2 + 16*e - 10', 'e^4 + e^3 - 4*e^2 - e - 3', 'e^4 + 5*e^3 - 4*e^2 - 23*e - 3', '-5*e^4 - 13*e^3 + 18*e^2 + 47*e + 5', '-3*e^4 - 7*e^3 + 11*e^2 + 25*e - 2', 'e^3 + 2*e^2 - 3*e - 4', '3*e^4 + 7*e^3 - 9*e^2 - 25*e - 14', 'e^4 + e^3 - 6*e^2 - 7*e - 1', '-e^2 - 4*e + 5', '-3*e^4 - 3*e^3 + 17*e^2 + 13*e - 8', '3*e^4 + 3*e^3 - 17*e^2 - 9*e + 10', '-e^4 + 6*e^2 - 4*e - 13', '4*e^4 + 11*e^3 - 14*e^2 - 45*e - 8', '4*e^4 + 6*e^3 - 19*e^2 - 20*e + 7', '-e^4 + 2*e^3 + 10*e^2 - 10*e - 19', '3*e^4 + 8*e^3 - 8*e^2 - 30*e - 9', '-7*e^4 - 17*e^3 + 28*e^2 + 63*e + 5', 'e^4 + 5*e^3 + e^2 - 19*e - 16', '2*e^4 + 2*e^3 - 13*e^2 - 10*e + 9', '3*e^4 + 5*e^3 - 17*e^2 - 19*e + 12', '-2*e^3 + e^2 + 6*e - 13', '-e^4 - e^3 + 3*e^2 + 3*e + 2', '-2*e^4 - e^3 + 10*e^2 - 5*e - 14', '7*e^4 + 14*e^3 - 27*e^2 - 48*e - 10', '-4*e^4 - 9*e^3 + 15*e^2 + 25*e + 3', '2*e^4 + 6*e^3 - 6*e^2 - 32*e - 10', '-3*e^4 - 11*e^3 + 10*e^2 + 41*e + 3', '7*e^4 + 15*e^3 - 29*e^2 - 61*e - 8', '4*e^4 + 8*e^3 - 16*e^2 - 24*e + 6', '-e^3 + e^2 + 7*e - 3', '-e^4 - e^3 + 3*e^2 - e + 8', '-e^4 - 2*e^3 + 4*e^2 - 2*e - 3', '-4*e^4 - 6*e^3 + 22*e^2 + 22*e - 16', '2*e^4 - e^3 - 12*e^2 + 15*e + 12', '4*e^4 + 14*e^3 - 9*e^2 - 54*e - 13', '-4*e^4 - 15*e^3 + 14*e^2 + 69*e + 10', '2*e^4 + 8*e^3 - 9*e^2 - 36*e - 1', 'e^4 + 7*e^3 + e^2 - 25*e - 14', 'e^4 + 3*e^3 - 2*e^2 - 3*e + 3', '-4*e^4 - 8*e^3 + 13*e^2 + 28*e + 13', '-e^4 - e^3 + 8*e^2 + 5*e + 11', '3*e^2 - 2*e - 1', '-2*e^4 - 3*e^3 + 15*e^2 + 17*e - 13', '9*e^4 + 21*e^3 - 32*e^2 - 71*e - 19', '-e^4 - 5*e^3 + e^2 + 25*e + 10', '-e^4 - 2*e^3 + 2*e^2 + 6*e - 9', '-e^4 - 4*e^3 + 7*e^2 + 24*e', '3*e^4 - 19*e^2 + 12*e + 18', '-e^4 - 4*e^3 + e^2 + 16*e - 4', '2*e^4 + 3*e^3 - 14*e^2 - 9*e + 22', 'e^4 + 2*e^3 - 3*e^2 + 2*e - 10', '-4*e^4 - 9*e^3 + 14*e^2 + 35*e', 'e^4 + 2*e^3 + 6*e^2 + 2*e - 25', '-3*e^4 - 7*e^3 + 15*e^2 + 41*e - 4', '-4*e^4 - 15*e^3 + 12*e^2 + 69*e + 16', '-4*e^4 - 2*e^3 + 25*e^2 + 2*e - 15', '-3*e^3 + 4*e^2 + 19*e', '5*e^4 + 10*e^3 - 27*e^2 - 38*e + 16', '-2*e^4 - 4*e^3 + 6*e^2 + 12*e + 20', '-5*e^4 - 13*e^3 + 23*e^2 + 57*e + 8', '-5*e^4 - 9*e^3 + 21*e^2 + 27*e - 12', '6*e^4 + 15*e^3 - 25*e^2 - 61*e - 17', '-7*e^4 - 21*e^3 + 30*e^2 + 87*e + 5', '-4*e^4 - 15*e^3 + 6*e^2 + 61*e + 14', '-e^4 - 10*e^3 - 5*e^2 + 36*e + 10', '5*e^4 + 13*e^3 - 20*e^2 - 55*e - 21', '-2*e^4 - 6*e^3 + 6*e^2 + 12*e - 4', '3*e^4 + 10*e^3 - 5*e^2 - 26*e - 22', '5*e^4 + 7*e^3 - 25*e^2 - 21*e + 12', '-11*e^4 - 25*e^3 + 43*e^2 + 91*e - 2', '4*e^4 + 13*e^3 - 14*e^2 - 47*e - 14', '6*e^4 + 21*e^3 - 25*e^2 - 89*e - 5', '-11*e^4 - 26*e^3 + 45*e^2 + 98*e + 4', '4*e^4 + 8*e^3 - 15*e^2 - 24*e - 11', '8*e^4 + 13*e^3 - 34*e^2 - 53*e - 26', '6*e^4 + 17*e^3 - 25*e^2 - 63*e + 9', '-12*e^4 - 25*e^3 + 52*e^2 + 101*e + 6', '2*e^4 + 6*e^3 - 11*e^2 - 28*e + 9', '5*e^4 + 15*e^3 - 16*e^2 - 63*e - 7', '-e^4 - 6*e^3 - 2*e^2 + 26*e + 35', '-2*e^4 - e^3 + 9*e^2 - e + 1', '-e^4 - 11*e^3 - 8*e^2 + 51*e + 29', '9*e^4 + 24*e^3 - 29*e^2 - 92*e - 6', '-2*e^4 + 2*e^3 + 19*e^2 + 2*e - 27', '8*e^4 + 18*e^3 - 29*e^2 - 74*e - 27', '-12*e^4 - 25*e^3 + 48*e^2 + 89*e + 4', '-2*e^4 + 4*e^3 + 25*e^2 - 18*e - 29', '4*e^4 + 7*e^3 - 26*e^2 - 17*e + 26', '8*e^4 + 20*e^3 - 33*e^2 - 84*e - 15', '-4*e^4 - 6*e^3 + 22*e^2 + 20*e - 32', '-e^4 - 9*e^3 - e^2 + 45*e + 26', '3*e^3 + 14*e^2 - 5*e - 28', 'e^4 + 3*e^3 - 4*e^2 - 11*e - 1', '4*e^4 + e^3 - 25*e^2 - 7*e + 1', '-2*e^4 - 3*e^3 + 3*e^2 + e + 11', '-6*e^4 - 15*e^3 + 17*e^2 + 59*e + 19', '-2*e^4 - 4*e^3 + 7*e^2 + 8*e + 9', '-7*e^4 - 21*e^3 + 19*e^2 + 83*e + 14', '-9*e^4 - 14*e^3 + 38*e^2 + 50*e + 11', '4*e^3 + 4*e^2 - 6*e - 6', '-12*e^4 - 27*e^3 + 47*e^2 + 107*e + 25', '5*e^4 + 7*e^3 - 28*e^2 - 17*e + 23', '-8*e^4 - 27*e^3 + 26*e^2 + 113*e + 18', '-e^4 - 2*e^3 - 6*e^2 + 2*e + 29', '-2*e^4 - 11*e^3 - 2*e^2 + 53*e + 16', '-4*e^4 - e^3 + 29*e^2 - 13*e - 43', '-e^4 + e^3 + 11*e^2 - 21*e - 30', 'e^4 + 13*e^3 + 9*e^2 - 53*e - 26', '-e^4 + 2*e^3 + 6*e^2 - 10*e - 5', '-12*e^4 - 24*e^3 + 55*e^2 + 92*e + 1', '3*e^3 + 4*e^2 - 13*e - 26', '8*e^4 + 22*e^3 - 25*e^2 - 82*e - 29', '7*e^4 + 9*e^3 - 25*e^2 - 29*e - 32', '-15*e^4 - 41*e^3 + 51*e^2 + 143*e + 28', '3*e^4 + 11*e^3 - 15*e^2 - 45*e + 4', '5*e^4 + 22*e^3 - 8*e^2 - 82*e - 19', '-9*e^4 - 28*e^3 + 27*e^2 + 116*e + 32', '9*e^4 + 23*e^3 - 32*e^2 - 95*e - 13', '12*e^4 + 19*e^3 - 55*e^2 - 69*e + 1', '10*e^4 + 23*e^3 - 38*e^2 - 75*e + 10', '10*e^4 + 26*e^3 - 34*e^2 - 98*e - 10', '-15*e^4 - 32*e^3 + 60*e^2 + 112*e + 15', '-5*e^3 - 7*e^2 + 31*e + 15', '4*e^4 + 3*e^3 - 27*e^2 - e + 25', '-e^4 - 5*e^3 + 3*e^2 + 23*e - 12', '-6*e^4 - 15*e^3 + 30*e^2 + 55*e - 22', '-5*e^4 - 22*e^3 + 7*e^2 + 78*e + 34', '3*e^4 - 2*e^3 - 23*e^2 + 30*e + 42', '-4*e^4 + e^3 + 26*e^2 - 15*e - 22', '7*e^4 + 7*e^3 - 29*e^2 - 5*e + 12', '14*e^4 + 30*e^3 - 53*e^2 - 106*e - 15', '16*e^4 + 41*e^3 - 64*e^2 - 157*e - 12', '-2*e^4 - 5*e^3 + 8*e^2 + 31*e + 26', '7*e^4 + 15*e^3 - 29*e^2 - 43*e + 6', '-2*e^4 + 5*e^3 + 17*e^2 - 31*e - 33', '-6*e^4 - 12*e^3 + 21*e^2 + 28*e + 3', '14*e^4 + 18*e^3 - 75*e^2 - 62*e + 35', '-8*e^4 - 20*e^3 + 38*e^2 + 64*e - 34', '-6*e^4 - 19*e^3 + 19*e^2 + 89*e + 17', '17*e^4 + 40*e^3 - 74*e^2 - 164*e - 15', '15*e^4 + 23*e^3 - 73*e^2 - 65*e + 42', '-7*e^4 - 25*e^3 + 18*e^2 + 83*e + 23', '4*e^4 + 4*e^3 - 23*e^2 - 20*e + 21', '-5*e^4 - 10*e^3 + 32*e^2 + 30*e - 31', '-11*e^4 - 24*e^3 + 44*e^2 + 82*e - 7', '-6*e^4 - 8*e^3 + 32*e^2 + 36*e - 24', '-8*e^4 - 22*e^3 + 31*e^2 + 86*e - 5', '-2*e^4 - 9*e^3 + 16*e^2 + 39*e - 34', '-8*e^4 - 9*e^3 + 30*e^2 + 11*e + 10', '-6*e^4 - 15*e^3 + 18*e^2 + 55*e - 8'], 'hecke_polynomial': 'x^5 + 3*x^4 - 3*x^3 - 12*x^2 - 4*x + 1', 'label': '4.4.16609.1-15.1-g'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 16609, 'ideals': ['[1, 1, 1]', '[2, 2, -w^2 + w + 4]', '[3, 3, -w^2 + w + 3]', '[4, 4, w + 1]', '[5, 5, w^2 - 4]', '[6, 6, -w^2 + 3]', '[8, 2, w^3 - w^2 - 4*w + 5]', '[8, 8, -w^3 + w^2 + 5*w - 5]', '[9, 9, w]', '[10, 10, w^3 - w^2 - 4*w + 4]', '[12, 12, -w^3 + w^2 + 3*w - 3]', '[15, 15, w^3 - 5*w - 3]', '[16, 2, 2]', '[16, 16, -w^3 + w^2 + 4*w - 2]', '[17, 17, -w^2 + w + 5]', '[18, 18, -w^3 + w^2 + 4*w]', '[20, 20, w^2 - w - 2]', '[24, 6, -w^3 + w^2 + 4*w - 3]', '[24, 24, -w^2 + w + 6]', '[25, 25, -w^3 + w^2 + 3*w - 2]', '[27, 3, -w^3 + 4*w - 2]', '[27, 27, -w^3 + w^2 + 3*w]', '[29, 29, -w^2 + w + 1]', '[29, 29, -w^3 + 4*w + 2]', '[30, 30, -w^3 + 2*w^2 + 3*w - 6]', '[32, 4, -2*w^2 + 2*w + 8]', '[32, 32, -w^2 - w + 4]', '[34, 34, -w^3 + 2*w^2 + 4*w - 5]', '[36, 36, -w^3 + 5*w]', '[37, 37, -2*w^3 + 3*w^2 + 9*w - 13]', '[40, 10, w^3 + w^2 - 6*w - 5]', '[40, 40, 2*w^2 + w - 5]', '[41, 41, w^3 - w^2 - 5*w + 2]', '[43, 43, -w^3 + w^2 + 3*w - 4]', '[45, 45, w^3 - 4*w]', '[48, 6, -2*w^2 + 2*w + 6]', '[48, 48, -w^3 + 2*w^2 + 5*w - 6]', '[50, 50, -w^3 + 2*w^2 + 6*w - 7]', '[51, 51, -2*w^2 - w + 6]', '[54, 6, -w^3 + 4*w + 1]', '[54, 54, -w^3 + 3*w]', '[58, 58, -2*w^3 + 3*w^2 + 6*w - 5]', '[58, 58, w^3 - 3*w^2 - 3*w + 7]', '[60, 60, -w^2 - 2*w + 3]', '[61, 61, w^2 - 2*w - 2]', '[61, 61, 2*w^2 - w - 8]', '[64, 4, -w^3 + w^2 + 6*w - 5]', '[64, 8, 2*w + 2]', '[64, 64, -2*w^2 + w + 7]', '[67, 67, -4*w^3 + 5*w^2 + 18*w - 22]', '[68, 68, w^3 - 3*w^2 - w + 7]', '[72, 18, w^3 - 3*w^2 - 2*w + 9]', '[72, 72, w^3 - 2*w^2 - 6*w + 9]', '[73, 73, -w^2 - 2*w + 2]', '[74, 74, w^2 - 7]', '[75, 75, 2*w^3 - 4*w^2 - 10*w + 15]', '[79, 79, w^2 - 2*w - 4]', '[80, 10, 2*w^2 - 8]', '[80, 80, w^3 - 6*w - 1]', '[81, 3, 3]', '[81, 81, w^2]', '[82, 82, w^3 + 2*w^2 - 7*w - 10]', '[85, 85, -w^3 + 3*w^2 + 3*w - 10]', '[86, 86, w^3 - 2*w^2 - 3*w + 2]', '[87, 87, 2*w^2 + 2*w - 3]', '[87, 87, -w^2 + 2*w + 6]', '[89, 89, w^2 + w - 5]', '[89, 89, 2*w^3 - 2*w^2 - 9*w + 8]', '[89, 89, w^3 - 5*w - 5]', '[89, 89, -w^3 + 2*w^2 + 4*w - 4]', '[90, 90, w^3 + 2*w^2 - 6*w - 9]', '[96, 12, -2*w^2 + 6]', '[96, 96, -w^2 + 2*w + 3]', '[97, 97, w^3 + w^2 - 5*w - 4]', '[100, 100, -w^3 + w^2 + 5*w - 1]', '[101, 101, -2*w^3 + 2*w^2 + 8*w - 11]', '[102, 102, -w^3 - w^2 + 4*w + 6]', '[103, 103, w^3 - 5*w + 1]', '[108, 12, w^3 - 3*w^2 - 4*w + 8]', '[108, 108, -w^3 - w^2 + 5*w + 9]', '[109, 109, 2*w - 1]', '[109, 109, -w^3 + 2*w^2 + 3*w - 7]', '[111, 111, 2*w^3 - 2*w^2 - 9*w + 6]', '[113, 113, 2*w^2 - 7]', '[116, 116, -w^3 + w^2 + 6*w - 4]', '[116, 116, -2*w^3 - w^2 + 11*w + 10]', '[120, 30, w^3 - w^2 - 6*w + 3]', '[120, 120, w^3 - 2*w^2 - 4*w + 3]', '[122, 122, 3*w^3 + 4*w^2 - 18*w - 25]', '[122, 122, 3*w^3 + w^2 - 14*w - 14]', '[123, 123, 3*w^2 - 2*w - 12]', '[125, 5, -w^3 + 3*w^2 + 3*w - 8]', '[125, 125, -2*w - 1]', '[127, 127, 2*w^3 - 4*w^2 - 11*w + 16]', '[128, 4, 2*w^3 - 2*w^2 - 8*w + 10]', '[128, 16, -2*w^3 + 2*w^2 + 10*w - 10]', '[128, 128, -w^3 - 2*w^2 + 3*w + 4]', '[129, 129, 2*w^3 - 3*w^2 - 6*w + 6]', '[131, 131, 3*w^2 + 2*w - 8]', '[131, 131, -2*w^3 + 4*w^2 + 8*w - 13]', '[134, 134, -w^3 + w^2 + 5*w - 7]', '[135, 15, 2*w^3 - 3*w^2 - 11*w + 13]', '[135, 135, 2*w^2 - 2*w - 9]', '[136, 34, w^3 - w^2 - 4*w + 7]', '[136, 136, -2*w^3 + 2*w^2 + 9*w - 7]', '[137, 137, w^3 - 3*w^2 - 7*w + 10]', '[144, 18, 2*w]', '[144, 144, w^3 - 3*w^2 - 3*w + 9]', '[145, 145, w^3 - 2*w^2 - 5*w + 5]', '[145, 145, 2*w^3 - 3*w^2 - 7*w + 5]', '[146, 146, w^3 - w^2 - 5*w - 1]', '[148, 148, w^3 + 4*w^2 - 8*w - 19]', '[149, 149, -w^3 + 4*w - 4]', '[149, 149, w^2 - 2*w - 8]', '[150, 150, -w^2 - w + 6]', '[153, 153, -w^3 + w^2 + 5*w]', '[157, 157, -w - 4]', '[158, 158, 3*w^3 - w^2 - 13*w - 7]', '[160, 20, 2*w^3 - 2*w^2 - 8*w + 8]', '[160, 160, -w^3 + w^2 + 3*w - 7]', '[162, 6, -3*w^2 + 3*w + 12]', '[162, 162, -2*w^3 + w^2 + 9*w]', '[163, 163, -w^3 + 2*w^2 + 6*w - 10]', '[164, 164, w^2 - 2*w - 7]', '[167, 167, -w^3 + 2*w^2 + 5*w - 11]', '[167, 167, -3*w^2 - 2*w + 10]', '[167, 167, -w^2 - w + 7]', '[167, 167, 2*w^2 - 2*w - 5]', '[170, 170, w^3 - 5*w + 2]', '[172, 172, -3*w^2 - 2*w + 5]', '[173, 173, -3*w^3 + 2*w^2 + 13*w - 11]', '[174, 174, 2*w^3 - 4*w^2 - 9*w + 15]', '[174, 174, -w^3 - 2*w^2 + 5*w + 12]', '[178, 178, 3*w^2 - 2*w - 11]', '[178, 178, w^3 - 4*w^2 + 11]', '[178, 178, w^3 + w^2 - 6*w - 4]', '[178, 178, -w^3 + 2*w^2 + w - 4]', '[179, 179, w^3 - 3*w^2 - 5*w + 10]', '[180, 180, w^3 - w^2 - 2*w]', '[183, 183, 2*w^3 + 4*w^2 - 12*w - 21]', '[183, 183, 3*w^3 - w^2 - 13*w - 6]', '[185, 185, -3*w^3 - 2*w^2 + 17*w + 13]', '[191, 191, -2*w^3 - 3*w^2 + 10*w + 14]', '[191, 191, 3*w^2 + w - 7]', '[192, 12, -w^3 - 3*w^2 + 6*w + 15]', '[192, 24, -2*w^3 + 2*w^2 + 6*w - 6]', '[192, 192, w^3 - 2*w + 3]', '[193, 193, w^2 - w + 1]', '[193, 193, -w^2 - w - 1]', '[194, 194, 3*w^3 + 2*w^2 - 15*w - 16]', '[200, 50, -w^3 - 3*w^2 + 6*w + 13]', '[200, 200, 2*w^3 - 3*w^2 - 7*w + 10]', '[201, 201, 3*w^3 - 4*w^2 - 13*w + 15]', '[202, 202, w^2 - w - 8]', '[204, 204, -2*w^2 + w + 3]', '[205, 205, -2*w^3 + 10*w + 1]', '[206, 206, 2*w^3 - 9*w - 5]', '[215, 215, -2*w^2 - 2*w + 7]', '[216, 6, w^3 - 3*w^2 - 4*w + 11]', '[216, 24, -2*w^3 + 3*w^2 + 5*w - 4]', '[216, 54, w^3 - 3*w^2 - 4*w + 9]', '[216, 216, -w^3 + w^2 + 6*w]', '[218, 218, 2*w^3 - 2*w^2 - 7*w - 1]', '[218, 218, -2*w^3 + 3*w^2 + 7*w - 4]', '[219, 219, w^3 - 3*w - 3]', '[222, 222, w^3 + 3*w^2 - 8*w - 12]', '[225, 225, -2*w^3 + 3*w^2 + 9*w - 9]', '[226, 226, 2*w^3 + w^2 - 9*w - 10]', '[227, 227, 4*w^3 - 4*w^2 - 17*w + 20]', '[227, 227, -3*w^3 + 4*w^2 + 13*w - 17]', '[229, 229, -w^3 + 6*w - 2]', '[232, 58, -w^3 - w^2 + 4*w + 7]', '[232, 58, -w^3 - w^2 + 4*w + 1]', '[232, 232, -2*w^3 + w^2 + 9*w + 2]', '[232, 232, w^3 - 2*w^2 - 3*w + 8]', '[233, 233, -3*w^3 + 3*w^2 + 13*w - 16]', '[237, 237, 3*w^3 - 2*w^2 - 11*w - 3]', '[240, 30, 2*w^3 - 10*w - 6]', '[240, 240, 2*w^3 - w^2 - 9*w + 6]', '[241, 241, -w^2 + 2*w - 2]', '[243, 9, -3*w^2 + 3*w + 9]', '[243, 243, w^3 - 4*w^2 - w + 9]', '[244, 244, w^3 + w^2 - 9*w - 13]', '[244, 244, 2*w^3 + w^2 - 9*w - 8]', '[246, 246, w^3 + w^2 - 5*w - 3]', '[250, 10, w^3 + 2*w^2 - 3*w - 2]', '[250, 250, -2*w^2 + w + 1]', '[254, 254, w^3 - 3*w^2 - 4*w + 10]', '[255, 255, -2*w^3 + 3*w^2 + 8*w - 12]', '[256, 4, 4]', '[256, 32, -2*w^3 + 2*w^2 + 8*w - 4]', '[256, 256, -w^3 - 3*w^2 + 7*w + 17]', '[258, 258, w^3 + w^2 - w - 3]', '[261, 261, -w^3 + w^2 + w]', '[261, 261, -2*w^3 + w^2 + 10*w]', '[262, 262, w^3 + w^2 - 3*w - 5]', '[262, 262, 2*w^3 - w^2 - 9*w + 8]', '[263, 263, 2*w^3 - 5*w^2 - 12*w + 16]', '[263, 263, -3*w^3 + 4*w^2 + 13*w - 19]', '[267, 267, 2*w^3 - 6*w^2 - 4*w + 15]', '[267, 267, -w^3 + 3*w^2 + 3*w - 12]', '[267, 267, w^3 + 2*w^2 - 2*w - 6]', '[267, 267, 2*w^2 - 3*w - 6]', '[268, 268, -w^3 + 3*w^2 + 2*w - 10]', '[269, 269, w^3 + 2*w^2 - 5*w - 7]', '[269, 269, -w^3 - 2*w^2 + w + 5]', '[270, 30, 2*w^3 - 3*w^2 - 8*w + 7]', '[270, 270, -w^2 - 3*w]', '[272, 34, -2*w^2 + 2*w + 10]', '[272, 272, -w^3 - 2*w^2 + 7*w + 8]', '[274, 274, w^3 - 2*w^2 - 5*w + 4]', '[281, 281, 2*w^3 - 2*w^2 - 8*w + 1]', '[281, 281, w^2 - 8]', '[288, 36, -2*w^3 + 2*w^2 + 8*w]', '[288, 288, -w^3 - 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w^2 + w]', '[1737, 1737, -w^3 - w^2 - w]', '[1740, 1740, 3*w^3 - 4*w^2 - 15*w + 12]', '[1740, 1740, 5*w^2 - 3*w - 24]', '[1741, 1741, -4*w^2 - 3*w + 14]', '[1744, 218, 4*w - 2]', '[1744, 218, -2*w^3 + 4*w^2 + 6*w - 14]', '[1744, 1744, 3*w^3 - 7*w^2 - 10*w + 20]', '[1744, 1744, 3*w^2 - 5*w - 4]', '[1745, 1745, w^3 + 6*w^2 - 9*w - 29]', '[1746, 1746, 2*w^3 + 6*w^2 - 13*w - 27]', '[1747, 1747, w^3 + w^2 - 3*w - 10]', '[1747, 1747, 3*w^3 - 2*w^2 - 13*w + 7]', '[1751, 1751, 3*w^3 - 14*w - 4]', '[1752, 438, -w^3 + 5*w^2 + 6*w - 15]', '[1752, 1752, w^3 - w^2 - 8*w + 6]', '[1756, 1756, 6*w^3 - 3*w^2 - 24*w - 11]', '[1756, 1756, 3*w^2 + w - 2]', '[1763, 1763, -w^3 + 2*w^2 + 8*w - 8]', '[1765, 1765, -3*w^3 - 6*w^2 + 19*w + 35]', '[1766, 1766, 2*w^3 + 2*w^2 - 13*w - 11]', '[1769, 1769, 2*w^3 + 5*w^2 - 15*w - 25]', '[1769, 1769, 4*w^2 - 13]', '[1769, 1769, 5*w^3 + 6*w^2 - 25*w - 35]', '[1769, 1769, 3*w^3 - 5*w^2 - 11*w + 10]', '[1772, 1772, w^3 + 7*w^2 - 14]', '[1772, 1772, w^3 + 4*w^2 + 2*w - 1]', '[1774, 1774, w^3 + 2*w^2 - 6*w - 5]', '[1776, 222, 4*w^3 - 4*w^2 - 18*w + 12]', '[1776, 1776, w^3 + 6*w^2 - 8*w - 33]', '[1777, 1777, -2*w^3 + 4*w^2 + 8*w - 7]', '[1780, 1780, -w^2 + 4*w + 1]', '[1780, 1780, 3*w^3 - 5*w^2 - 12*w + 20]', '[1780, 1780, -3*w^3 + 8*w^2 + 8*w - 19]', '[1780, 1780, -6*w^2 + 5*w + 19]', '[1783, 1783, -w^2 + 2*w - 4]', '[1783, 1783, -2*w^3 + 3*w^2 + 9*w - 17]', '[1787, 1787, 2*w^3 + w^2 - 7*w + 5]', '[1787, 1787, 4*w^3 - 5*w^2 - 15*w + 17]', '[1788, 1788, 2*w^3 + 3*w^2 - 6*w - 3]', '[1788, 1788, -5*w^3 + 2*w^2 + 15*w - 12]', '[1789, 1789, -3*w^3 + 12*w - 2]', '[1790, 1790, 4*w^3 - 8*w^2 - 23*w + 31]', '[1795, 1795, -3*w^3 + 3*w^2 + 11*w - 10]', '[1795, 1795, 3*w^2 - 2]', '[1796, 1796, 3*w^3 - 2*w^2 - 12*w + 1]', '[1797, 1797, -w^3 + 3*w^2 + w - 12]', '[1797, 1797, 2*w^3 - 2*w^2 - 13*w + 12]', '[1800, 450, -w^3 - 5*w^2 + 8*w + 27]', '[1800, 1800, -3*w^3 + w^2 + 13*w + 9]', '[1801, 1801, -w^3 + 8*w - 2]', '[1808, 226, 4*w^2 - 14]', '[1808, 1808, w^3 + w^2 - 8*w - 4]', '[1809, 201, -5*w^3 + 9*w^2 + 23*w - 34]', '[1809, 1809, -4*w^3 + 8*w^2 + 18*w - 27]', '[1811, 1811, -2*w^3 + 7*w^2 + 12*w - 22]', '[1811, 1811, w^3 - 2*w^2 - 3*w - 1]', '[1814, 1814, 5*w^2 - 6*w - 17]', '[1816, 454, -5*w^3 + 7*w^2 + 26*w - 29]', '[1816, 454, 3*w^3 - 3*w^2 - 18*w + 17]', '[1816, 1816, 2*w^2 + 5*w - 1]', '[1816, 1816, w^2 - 4*w - 5]', '[1818, 1818, w^3 - w^2 - 8*w]', '[1822, 1822, 6*w^3 + 3*w^2 - 30*w - 29]', '[1823, 1823, 3*w^3 - 5*w^2 - 13*w + 14]', '[1825, 1825, 6*w^2 + 2*w - 13]', '[1828, 1828, -2*w^3 + 3*w^2 + 7*w - 14]', '[1830, 1830, -2*w^3 + 2*w^2 + 5*w + 3]', '[1830, 1830, -w^3 - w^2 + 8*w + 6]', '[1831, 1831, -6*w^2 - 7*w + 14]', '[1831, 1831, -3*w^3 + 4*w^2 + 12*w - 20]', '[1832, 458, -w^3 - 3*w^2 + 10*w + 17]', '[1832, 1832, -w^3 - 7*w^2 + 10*w + 28]', '[1835, 1835, 2*w^3 - w^2 - 12*w + 2]', '[1835, 1835, 4*w^3 + 2*w^2 - 23*w - 14]', '[1835, 1835, -3*w^3 - w^2 + 13*w + 2]', '[1835, 1835, 3*w^3 - 2*w^2 - 9*w + 7]', '[1836, 204, -w^3 + w + 4]', '[1836, 1836, -3*w^3 + 4*w^2 + 17*w - 18]', '[1838, 1838, w^3 + w^2 - 8*w - 14]', '[1842, 1842, w^2 + 4*w - 3]', '[1842, 1842, 2*w^3 - w^2 - 11*w - 6]', '[1845, 1845, -4*w^2 - w + 18]', '[1847, 1847, -4*w^3 + 7*w^2 + 13*w - 13]', '[1847, 1847, 4*w^2 + 4*w - 13]', '[1849, 1849, 5*w^2 - 2*w - 22]', '[1850, 1850, 3*w^3 - 3*w^2 - 11*w + 5]', '[1851, 1851, -2*w^3 - 6*w^2 + 13*w + 30]', '[1853, 1853, -2*w^3 + 3*w^2 + 9*w - 5]', '[1853, 1853, w^3 - 4*w - 8]', '[1854, 1854, 5*w^2 - 3*w - 18]', '[1856, 116, w^3 - 5*w^2 - 6*w + 17]', '[1856, 116, w^3 - 5*w^2 - 2*w + 17]', '[1856, 232, -2*w^3 + 2*w^2 + 12*w - 8]', '[1856, 232, -4*w^3 - 2*w^2 + 22*w + 20]', '[1856, 1856, -3*w^3 + 6*w^2 + 10*w - 11]', '[1856, 1856, 3*w^3 - 3*w^2 - 8*w + 10]', '[1858, 1858, 4*w^3 - 2*w^2 - 15*w - 7]', '[1864, 466, 5*w^3 - 7*w^2 - 24*w + 25]', '[1864, 1864, w^3 - 2*w^2 - 8*w - 1]', '[1865, 1865, 5*w^2 - 3*w - 19]', '[1865, 1865, -4*w^3 + 5*w^2 + 16*w - 10]', '[1873, 1873, -2*w^3 + 7*w^2 + 6*w - 28]', '[1873, 1873, -2*w^3 - 3*w^2 + 11*w + 13]', '[1874, 1874, 2*w^3 + 8*w^2 - 17*w - 37]', '[1874, 1874, -w^3 - 3*w^2 + 9*w + 13]', '[1875, 15, -5*w^2 + 5*w + 15]', '[1875, 1875, -w^3 - 4*w^2 + 9*w + 21]', '[1877, 1877, -2*w^3 - w^2 + 8*w - 2]', '[1877, 1877, -2*w^3 + 6*w^2 + 12*w - 23]', '[1878, 1878, -4*w^3 + 9*w^2 + 11*w - 24]', '[1878, 1878, 2*w^3 + w^2 - 10*w - 3]', '[1884, 1884, 3*w^3 - 8*w + 3]', '[1887, 1887, 3*w^3 + w^2 - 17*w - 6]', '[1889, 1889, 3*w^3 - 2*w^2 - 17*w + 1]', '[1893, 1893, 2*w^3 + 2*w^2 - 13*w - 12]', '[1893, 1893, w^3 + 2*w^2 - 5*w - 3]', '[1896, 474, -w^3 + 5*w^2 + 2*w - 15]', '[1896, 1896, 3*w^3 + w^2 - 17*w - 15]', '[1901, 1901, -w^2 + 3*w - 5]', '[1905, 1905, 4*w^3 - 4*w^2 - 18*w + 15]', '[1907, 1907, 3*w^3 - 12*w + 8]', '[1907, 1907, -5*w^3 + 8*w^2 + 20*w - 28]', '[1910, 1910, -w^3 - 7]', '[1910, 1910, -2*w^2 + 5*w + 13]', '[1913, 1913, -3*w^3 + 6*w^2 + 16*w - 26]', '[1913, 1913, -2*w^3 + 2*w^2 + 11*w - 2]', '[1915, 1915, -8*w^2 - w + 34]', '[1915, 1915, -2*w^3 - 5*w^2 + 10*w + 26]', '[1916, 1916, 3*w^3 - 16*w - 13]', '[1916, 1916, -2*w^3 - w^2 + 8*w + 11]', '[1916, 1916, 2*w^3 - 2*w^2 - 5*w - 1]', '[1916, 1916, -w^3 - 3*w^2 + 8*w + 10]', '[1920, 60, 2*w^3 - 2*w^2 - 12*w + 6]', '[1920, 240, 2*w^3 - 4*w^2 - 8*w + 6]', '[1920, 1920, 3*w^3 - 4*w^2 - 8*w + 3]', '[1921, 1921, 2*w^3 + 3*w^2 - 9*w - 17]', '[1928, 482, w^3 + w^2 - 8*w - 5]', '[1928, 1928, 5*w^3 - 4*w^2 - 21*w + 20]', '[1930, 1930, 5*w^3 - 6*w^2 - 19*w + 22]', '[1930, 1930, -3*w^3 + 9*w - 4]', '[1931, 1931, -5*w^2 - 4*w + 16]', '[1933, 1933, 6*w^3 - 7*w^2 - 28*w + 28]', '[1933, 1933, 2*w^3 - 7*w^2 - 13*w + 25]', '[1933, 1933, -w^3 - 5*w^2 + 5*w + 14]', '[1933, 1933, 8*w^3 - 12*w^2 - 37*w + 50]', '[1935, 1935, -2*w^3 - 2*w^2 + 7*w]', '[1940, 1940, -w^3 + 5*w + 8]', '[1941, 1941, 4*w^3 + 5*w^2 - 21*w - 33]', '[1942, 1942, 5*w^3 - 5*w^2 - 22*w + 22]', '[1942, 1942, -3*w^3 + 3*w^2 + 12*w - 8]', '[1943, 1943, 3*w^3 - w^2 - 13*w + 10]', '[1943, 1943, 2*w^2 + 2*w - 11]', '[1944, 18, -3*w^3 + 3*w^2 + 12*w - 9]', '[1944, 72, -3*w^2 + 3*w + 18]', '[1944, 486, -3*w^3 + 3*w^2 + 10*w - 9]', '[1944, 1944, w^3 - w^2 - w + 9]', '[1945, 1945, -w^3 - 9*w^2 + 9*w + 46]', '[1945, 1945, -6*w^3 - 4*w^2 + 31*w + 32]', '[1948, 1948, 2*w^3 - 3*w^2 - 3*w + 10]', '[1952, 244, 6*w^3 + 8*w^2 - 36*w - 50]', '[1952, 244, 6*w^3 + 2*w^2 - 28*w - 28]', '[1952, 1952, 3*w^3 + 2*w^2 - 12*w - 7]', '[1952, 1952, -w^3 + 3*w^2 + 2*w - 14]', '[1954, 1954, -w^3 + 5*w^2 + 2*w - 22]', '[1956, 1956, 2*w^3 - 2*w^2 - 7*w - 3]', '[1962, 1962, -2*w^3 + 7*w^2 + w - 18]', '[1962, 1962, 3*w^3 - 7*w^2 - 6*w + 18]', '[1964, 1964, 3*w^3 + 2*w^2 - 12*w - 11]', '[1964, 1964, 5*w^3 - 3*w^2 - 20*w - 4]', '[1965, 1965, -2*w^3 - 2*w^2 + 9*w + 6]', '[1965, 1965, -4*w^3 + 8*w^2 + 11*w - 12]', '[1966, 1966, w^2 - 5*w - 8]', '[1968, 246, 6*w^2 - 4*w - 24]', '[1968, 1968, -3*w^3 + 4*w^2 + 14*w - 21]', '[1971, 219, w^3 + 3*w^2 - 7*w - 10]', '[1971, 1971, 4*w^2 - 2*w - 9]', '[1972, 1972, 3*w^3 - 4*w^2 - 12*w + 19]', '[1972, 1972, -3*w^3 + 2*w^2 + 15*w - 2]', '[1975, 1975, -2*w^3 + 8*w^2 + 4*w - 19]', '[1982, 1982, -2*w^3 + 3*w^2 + 7*w - 16]', '[1982, 1982, -3*w^3 + 4*w^2 + 14*w - 11]', '[1994, 1994, -w^3 + 2*w^2 + 8*w - 5]', '[1997, 1997, -4*w^2 - 6*w + 7]', '[1998, 222, 4*w^3 - 3*w^2 - 19*w + 14]', '[1998, 1998, 3*w^3 - w^2 - 11*w - 9]', '[2000, 10, -2*w^3 + 6*w^2 + 6*w - 16]', '[2000, 80, 2*w^3 - w^2 - 11*w - 4]', '[2000, 250, -4*w - 2]', '[2000, 2000, -w^3 + 5*w^2 + 2*w - 16]', '[2003, 2003, -w^3 - 6*w^2 + 16]', '[2003, 2003, -2*w^3 + 6*w^2 + 6*w - 19]', '[2004, 2004, 5*w^3 - 7*w^2 - 20*w + 24]', '[2004, 2004, -5*w^3 + 9*w^2 + 13*w - 21]', '[2004, 2004, -w^3 + 9*w + 12]', '[2004, 2004, -4*w^3 + w^2 + 17*w + 12]', '[2005, 2005, -w^3 - 3*w^2 + 9*w + 22]', '[2005, 2005, -3*w^3 + 13*w + 13]', '[2010, 2010, -3*w^3 + 3*w^2 + 14*w - 6]', '[2011, 2011, -5*w^3 + 10*w^2 + 26*w - 40]', '[2011, 2011, -2*w^3 + 2*w^2 + 12*w - 7]', '[2017, 2017, -2*w^3 + 5*w^2 + 2*w - 10]', '[2017, 2017, w^3 - 9*w^2 - 11*w + 26]', '[2018, 2018, w^3 + w^2 + w - 1]', '[2018, 2018, -3*w^2 - 5*w + 8]', '[2020, 2020, -4*w^3 + 3*w^2 + 17*w - 14]', '[2022, 2022, -2*w^3 + w^2 + 3*w - 6]', '[2025, 75, -3*w^3 + 3*w^2 + 9*w - 6]', '[2025, 2025, 3*w^3 - 5*w^2 - 11*w + 18]', '[2027, 2027, 3*w^2 - 3*w - 17]', '[2027, 2027, -4*w^3 + 6*w^2 + 18*w - 19]', '[2031, 2031, -4*w^3 + 9*w^2 + 21*w - 33]', '[2032, 254, 4*w^3 - 8*w^2 - 22*w + 32]', '[2032, 2032, -7*w^3 + 11*w^2 + 33*w - 41]', '[2034, 2034, w^3 + 5*w^2 - 8*w - 18]', '[2040, 510, 3*w^3 - w^2 - 16*w - 3]', '[2040, 2040, 3*w^2 - 5*w - 12]', '[2042, 2042, 4*w^3 - 17*w - 11]', '[2043, 2043, 2*w^3 - 5*w^2 - 6*w + 18]', '[2043, 2043, -4*w^3 + 10*w^2 + 10*w - 27]', '[2045, 2045, -2*w^3 + 7*w^2 + 4*w - 20]', '[2048, 8, 4*w^3 - 4*w^2 - 16*w + 20]', '[2048, 32, -4*w^3 + 4*w^2 + 20*w - 20]', '[2048, 256, -2*w^3 - 4*w^2 + 6*w + 8]', '[2048, 2048, w^3 - 2*w^2 - w + 10]', '[2050, 2050, -5*w^3 + 7*w^2 + 22*w - 32]', '[2053, 2053, 4*w^3 - 2*w^2 - 17*w + 14]', '[2055, 2055, 2*w^3 - 3*w^2 - 7*w + 15]', '[2060, 2060, -w + 7]', '[2061, 2061, -w^2 - 3*w + 9]', '[2062, 2062, 7*w^3 + 4*w^2 - 34*w - 37]', '[2064, 258, 4*w^3 - 6*w^2 - 12*w + 12]', '[2064, 2064, w^3 - 4*w^2 - 10*w + 15]', '[2066, 2066, 2*w^3 + w^2 - 13*w - 10]', '[2073, 2073, 4*w^3 - w^2 - 18*w - 6]', '[2074, 2074, -w - 7]', '[2074, 2074, 3*w^2 - 4*w - 5]', '[2076, 2076, -w^3 + w^2 + 9*w + 3]', '[2078, 2078, -2*w^3 + 7*w^2 + 4*w - 19]', '[2081, 2081, -2*w^3 + 2*w^2 + 10*w - 1]', '[2081, 2081, 4*w^3 - 15*w + 10]', '[2082, 2082, 3*w^3 - 2*w^2 - 10*w - 3]', '[2083, 2083, -6*w^3 + 4*w^2 + 25*w - 26]', '[2083, 2083, w^2 - 4*w - 2]', '[2084, 2084, -3*w^2 - 4*w + 11]', '[2084, 2084, 3*w^2 + 2*w - 13]', '[2087, 2087, 3*w^2 - 3*w - 5]', '[2087, 2087, -w^3 + w^2 + 5*w - 10]', '[2088, 522, -w^3 - 3*w^2 + 6*w + 9]', '[2088, 522, -w^3 - 3*w^2 + 9]', '[2088, 2088, -2*w^3 + 4*w^2 + 9*w - 9]', '[2088, 2088, w^3 - 5*w^2 + 18]', '[2089, 2089, -4*w^3 + 7*w^2 + 21*w - 31]', '[2091, 2091, 3*w^3 - 13*w + 3]', '[2092, 2092, -3*w^3 + w^2 + 8*w - 4]', '[2094, 2094, w^3 - 7*w^2 + 2*w + 24]', '[2095, 2095, 2*w^3 + 6*w^2 - 12*w - 31]', '[2095, 2095, -3*w^3 + 2*w^2 + 13*w - 5]', '[2096, 262, 6*w^2 + 4*w - 16]', '[2096, 262, -4*w^3 + 8*w^2 + 16*w - 26]', '[2096, 2096, w^3 - 2*w^2 - 8*w + 7]', '[2096, 2096, 5*w^2 - 13]', '[2097, 2097, w^3 - 3*w - 9]', '[2102, 2102, 2*w^3 + w^2 - 8*w - 13]', '[2104, 526, -3*w^3 + 5*w^2 + 14*w - 25]', '[2104, 526, 5*w^3 - 5*w^2 - 26*w + 19]', '[2104, 2104, -2*w^3 + 4*w^2 + 5*w - 13]', '[2104, 2104, 3*w^3 - 4*w^2 - 12*w + 7]', '[2105, 2105, -2*w^3 + 4*w^2 + 13*w - 16]', '[2111, 2111, -w^3 + 6*w^2 + 11*w - 19]', '[2111, 2111, -w^3 + 5*w^2 + 5*w - 14]', '[2113, 2113, 2*w^3 - 11*w + 2]', '[2113, 2113, w^2 - 4*w - 4]', '[2116, 92, w^3 + 5*w^2 - 7*w - 23]', '[2116, 92, 3*w^3 + 9*w^2 - 22*w - 44]', '[2117, 2117, w^3 + 5*w^2 - 3*w - 14]', '[2117, 2117, 4*w^3 + 2*w^2 - 18*w - 17]', '[2118, 2118, w^3 + 5*w^2 - 10*w - 24]', '[2122, 2122, 3*w^2 + w - 16]', '[2125, 85, 2*w^3 - w^2 - 6*w - 4]', '[2125, 2125, 2*w^3 - w^2 - 11*w - 5]', '[2129, 2129, 4*w - 1]', '[2131, 2131, 4*w^3 - 6*w^2 - 12*w + 17]', '[2131, 2131, 3*w^2 - w - 19]', '[2133, 237, w^3 + 3*w^2 - w - 10]', '[2133, 2133, -2*w^3 + 10*w^2 - 27]', '[2136, 534, -w^3 + w^2 + 3]', '[2136, 534, 7*w^3 + 5*w^2 - 38*w - 39]', '[2136, 534, 3*w^3 - w^2 - 12*w - 3]', '[2136, 534, 3*w^3 - 5*w^2 - 14*w + 15]', '[2136, 2136, -3*w^3 + 5*w^2 + 9*w - 15]', '[2136, 2136, w^3 - 4*w^2 - 9*w + 12]', '[2136, 2136, -w^3 + 8*w + 3]', '[2136, 2136, 5*w^2 - 21]', '[2137, 2137, -2*w^3 - w^2 + 10*w + 14]', '[2143, 2143, 2*w^3 + w^2 - 9*w - 1]', '[2143, 2143, w^3 + 6*w^2 - 14]', '[2144, 268, -2*w^3 + 2*w^2 + 10*w - 14]', '[2144, 2144, 5*w^3 - 7*w^2 - 21*w + 23]', '[2146, 2146, 4*w^3 + w^2 - 19*w - 14]', '[2146, 2146, w^3 + w^2 - 8*w + 2]', '[2148, 2148, 3*w^2 + 7*w - 12]', '[2150, 2150, 3*w^3 - 9*w^2 - 18*w + 28]', '[2152, 538, 3*w^3 + w^2 - 10*w + 1]', '[2152, 538, 3*w^3 - 3*w^2 - 10*w + 5]', '[2152, 2152, -w^3 + w^2 + 4*w - 10]', '[2152, 2152, 4*w^3 + 3*w^2 - 12*w - 11]', '[2153, 2153, 3*w^3 - 6*w^2 - 15*w + 19]', '[2153, 2153, w^3 + 2*w^2 - 7*w - 5]', '[2153, 2153, -4*w^3 + 4*w^2 + 18*w - 13]', '[2153, 2153, 7*w^3 - 8*w^2 - 31*w + 35]', '[2154, 2154, w^3 + w^2 - 7*w + 3]', '[2154, 2154, 5*w^3 - w^2 - 20*w - 12]', '[2155, 2155, 7*w^2 - 3*w - 37]', '[2155, 2155, -4*w^2 + 3*w + 20]', '[2159, 2159, 3*w^3 - 7*w^2 - 15*w + 26]', '[2160, 30, 4*w^3 - 6*w^2 - 22*w + 26]', '[2160, 240, -w^3 - 3*w^2 - 2*w + 4]', '[2160, 270, 4*w^2 - 4*w - 18]', '[2160, 2160, -w^3 + 5*w^2 + 8*w - 18]', '[2161, 2161, -w^3 + 3*w - 7]', '[2161, 2161, -w^3 - 5*w^2 + 7*w + 20]', '[2164, 2164, w^3 + 2*w^2 - 5*w - 2]', '[2164, 2164, -2*w^3 - 3*w^2 + 2*w + 7]', '[2165, 2165, w^3 + 2*w^2 - 5*w - 1]', '[2169, 2169, -w^3 + 2*w^2 - 2*w]', '[2174, 2174, -7*w^2 - 4*w + 13]', '[2174, 2174, -3*w^3 + 12*w^2 + 2*w - 31]', '[2175, 2175, -w^3 - w^2 + 5*w + 12]', '[2175, 2175, -w^3 + 2*w^2 + 8*w - 6]', '[2176, 68, 2*w^3 - 2*w^2 - 8*w + 14]', '[2176, 272, -4*w^3 + 4*w^2 + 18*w - 14]', '[2176, 2176, w^3 - 5*w^2 + 10]', '[2180, 2180, -4*w^3 + 6*w^2 + 13*w - 13]', '[2180, 2180, 2*w^3 - 3*w^2 - 3*w + 2]', '[2186, 2186, -w^3 + 3*w^2 + 8*w - 14]', '[2186, 2186, 2*w^3 - 8*w^2 - w + 19]', '[2187, 9, -3*w^3 + 12*w - 6]', '[2187, 81, -3*w^3 + 3*w^2 + 9*w]', '[2187, 2187, -w^3 - 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19]', '[5157, 5157, -4*w^3 + 7*w^2 + 8*w - 18]', '[5157, 5157, -5*w^3 - w^2 + 21*w]', '[5160, 1290, -3*w^3 + 7*w^2 + 16*w - 21]', '[5160, 5160, 3*w^3 - 3*w^2 - 4*w + 6]', '[5162, 5162, w^3 - 2*w^2 - w - 4]', '[5162, 5162, 4*w^3 - 4*w^2 - 17*w + 5]', '[5162, 5162, -4*w^3 + 6*w^2 + 11*w - 17]', '[5162, 5162, -10*w^3 + 19*w^2 + 25*w - 34]', '[5162, 5162, 2*w^3 + 7*w^2 - 16*w - 35]', '[5162, 5162, 5*w^3 - 14*w^2 - 11*w + 26]', '[5162, 5162, 3*w^3 - 5*w^2 - 16*w + 14]', '[5162, 5162, 5*w^3 - 9*w^2 - 16*w + 16]', '[5164, 5164, -4*w^3 + 3*w^2 + 17*w + 2]', '[5164, 5164, w^3 + w^2 - 13*w - 17]', '[5164, 5164, 7*w^2 - 4*w - 23]', '[5164, 5164, 2*w^3 + 5*w^2 - 10*w - 17]', '[5165, 5165, -8*w^3 + 10*w^2 + 37*w - 40]', '[5169, 5169, -2*w^3 - 3*w^2 + 8*w + 6]', '[5171, 5171, w^3 - 4*w^2 - 8*w + 2]', '[5172, 5172, -4*w^3 + 7*w^2 + 18*w - 21]', '[5172, 5172, -w^3 - 3*w^2 - 3*w + 3]', '[5176, 1294, 5*w^3 + w^2 - 22*w - 17]', '[5176, 5176, 6*w^3 - w^2 - 26*w - 19]', '[5178, 5178, -w^2 - 6*w - 3]', '[5179, 5179, w^3 + 6*w^2 - 3*w - 17]', '[5182, 5182, 2*w^3 + w^2 - 14*w - 11]', '[5184, 12, -3*w^3 + 3*w^2 + 18*w - 15]', '[5184, 24, 6*w + 6]', '[5184, 192, -6*w^2 + 3*w + 21]', '[5184, 324, -w^3 + w^2 + 10*w - 9]', '[5184, 648, -4*w^2 - 2*w + 18]', '[5184, 5184, -4*w^3 + 4*w^2 + 19*w - 9]', '[5185, 5185, -3*w^3 + 11*w + 17]', '[5185, 5185, -4*w^3 - 4*w^2 + 23*w + 22]', '[5186, 5186, 5*w^3 - 4*w^2 - 22*w + 17]', '[5188, 5188, -5*w^3 - 7*w^2 + 17*w + 23]', '[5189, 5189, -4*w^3 + 9*w^2 + 23*w - 29]', '[5189, 5189, -w^3 + 6*w^2 + 6*w - 20]', '[5190, 5190, 5*w^3 + 8*w^2 - 27*w - 48]', '[5191, 5191, -4*w^3 + 9*w^2 + 18*w - 26]', '[5191, 5191, 5*w + 2]', '[5193, 5193, w^3 + 7*w^2 - 3*w - 18]', '[5195, 5195, 3*w^3 - 4*w^2 - 11*w + 19]', '[5196, 5196, 3*w^3 - 8*w^2 - 7*w + 24]', '[5199, 5199, -w^3 + 6]', '[5199, 5199, -6*w^3 + 10*w^2 + 32*w - 39]', '[5202, 306, 6*w^2 + w - 27]', '[5202, 306, -w^3 + 3*w^2 + 2*w]', '[5204, 5204, 5*w^3 - w^2 - 23*w - 13]', '[5205, 5205, -3*w^3 - 11*w^2 + 25*w + 48]', '[5207, 5207, -3*w^3 + 10*w^2 + 9*w - 37]', '[5210, 5210, 2*w^3 - w^2 - 13*w + 4]', '[5210, 5210, -4*w^3 - w^2 + 23*w + 10]', '[5211, 579, -4*w^3 + 16*w - 11]', '[5211, 579, 4*w^3 + 6*w^2 - 10*w - 7]', '[5211, 5211, 4*w^3 - 3*w^2 - 12*w]', '[5211, 5211, -6*w^3 + 11*w^2 + 14*w - 18]', '[5212, 5212, 2*w^3 + w^2 - 15*w - 14]', '[5216, 652, 6*w^3 - 4*w^2 - 24*w + 22]', '[5216, 5216, -5*w^3 + 6*w^2 + 24*w - 31]', '[5218, 5218, -3*w^3 + 12*w^2 + 2*w - 35]', '[5218, 5218, -2*w^3 + 7*w^2 + w - 22]', '[5219, 5219, -w^3 + 4*w^2 + 9*w - 17]', '[5219, 5219, -2*w^3 - w^2 + 11*w + 1]', '[5220, 5220, -2*w^3 + 7*w^2 + 10*w - 27]', '[5220, 5220, -w^3 + 7*w^2 + w - 27]', '[5223, 5223, -w^3 - w^2 + 9*w + 6]', '[5227, 5227, 5*w^3 + 2*w^2 - 18*w + 2]', '[5227, 5227, 9*w^3 - 9*w^2 - 41*w + 40]', '[5228, 5228, -7*w^3 - 3*w^2 + 36*w + 32]', '[5230, 5230, 3*w^3 - 6*w^2 - 22*w + 29]', '[5231, 5231, -2*w^3 + 2*w^2 + 12*w - 17]', '[5232, 654, -4*w^3 + 6*w^2 + 10*w - 6]', '[5232, 654, 6*w^3 - 8*w^2 - 20*w + 12]', '[5232, 5232, 2*w^3 - 3*w^2 - 14*w + 15]', '[5232, 5232, 5*w^3 - 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15*w - 17]', '[5321, 5321, 4*w^3 + w^2 - 23*w - 11]', '[5321, 5321, 8*w^3 - 10*w^2 - 36*w + 41]', '[5322, 5322, 4*w^3 - 3*w^2 - 15*w - 6]', '[5323, 5323, 3*w^3 - 11*w^2 - 19*w + 34]', '[5326, 5326, -w^3 + 5*w^2 - 20]', '[5326, 5326, 5*w - 1]', '[5328, 666, -2*w^3 + 10*w^2 + 2*w - 36]', '[5328, 5328, -6*w^3 + 10*w^2 + 31*w - 45]', '[5329, 5329, -5*w^3 + 6*w^2 + 16*w - 20]', '[5331, 5331, 4*w^3 - 13*w^2 - 7*w + 33]', '[5338, 5338, 2*w^3 - 5*w^2 - 10*w + 11]', '[5340, 5340, -5*w^3 + 6*w^2 + 19*w - 12]', '[5340, 5340, -3*w^3 - w^2 + 12*w - 6]', '[5340, 5340, -4*w^3 + 3*w^2 + 11*w - 12]', '[5340, 5340, w^3 + 2*w + 3]', '[5344, 668, 8*w^2 - 6*w - 34]', '[5344, 668, -4*w^3 + 2*w^2 + 16*w - 10]', '[5344, 668, -2*w^3 - 6*w^2 + 10*w + 26]', '[5344, 668, 8*w^3 - 6*w^2 - 30*w - 4]', '[5344, 5344, w^2 - 5*w - 2]', '[5344, 5344, -4*w^3 + 8*w^2 + 21*w - 35]', '[5344, 5344, 2*w^3 - 3*w^2 - 10*w + 19]', '[5344, 5344, -3*w^3 - 3*w^2 + 19*w + 19]', '[5349, 5349, -3*w^3 + 10*w^2 + 3*w - 21]', '[5349, 5349, 2*w^3 + 2*w^2 - 13*w - 6]', '[5354, 5354, 2*w^3 + 6*w^2 - 9*w - 23]', '[5360, 670, -4*w^3 + 2*w^2 + 22*w - 10]', '[5360, 5360, 2*w^3 - 9*w^2 - 13*w + 26]', '[5361, 5361, -4*w^2 + 3*w + 6]', '[5361, 5361, -w^2 - 2*w - 6]', '[5364, 5364, -5*w^3 + 3*w^2 + 22*w - 18]', '[5364, 5364, 6*w^3 + 3*w^2 - 29*w - 18]', '[5365, 5365, -4*w^3 + 4*w^2 + 23*w - 20]', '[5365, 5365, -w^3 - 2*w^2 + 2*w + 22]', '[5366, 5366, -w^3 - 6*w^2 + 2*w + 17]', '[5366, 5366, -3*w^3 + 13*w - 8]', '[5367, 5367, -4*w^2 + 4*w + 21]', '[5370, 5370, -w^3 + 2*w^2 + 10*w - 15]', '[5371, 5371, 5*w^3 - 2*w^2 - 23*w + 7]', '[5371, 5371, -7*w^3 + 10*w^2 + 29*w - 35]', '[5372, 5372, 8*w^3 - 13*w^2 - 24*w + 17]', '[5374, 5374, 9*w^2 - 7*w - 34]', '[5375, 215, 4*w^3 - 7*w^2 - 22*w + 22]', '[5375, 5375, -w^3 + 7*w^2 + 7*w - 14]', '[5378, 5378, -w^3 + 9*w - 2]', '[5378, 5378, -3*w^3 - 10*w^2 + 20*w + 41]', '[5380, 5380, 2*w^3 - w + 1]', '[5380, 5380, -4*w^3 - w^2 + 22*w + 7]', '[5381, 5381, -w^3 + 2*w^2 - 2*w - 2]', '[5385, 5385, -w^3 + 8*w + 12]', '[5385, 5385, 3*w^3 - 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20]', '[5442, 5442, w^3 + 3*w^2 - 6*w - 6]', '[5448, 1362, -w^3 - 7*w^2 + 6*w + 33]', '[5448, 1362, w^3 + 7*w^2 - 8*w - 33]', '[5448, 5448, -5*w^3 + 3*w^2 + 17*w - 15]', '[5448, 5448, 6*w^3 - 9*w^2 - 19*w + 24]', '[5450, 5450, 5*w^3 - 4*w^2 - 22*w + 25]', '[5450, 5450, 5*w^3 - 9*w^2 - 25*w + 31]', '[5454, 606, 5*w^3 - 20*w + 7]', '[5454, 5454, 3*w^3 + 2*w^2 - 13*w - 18]', '[5458, 5458, 6*w^3 - 8*w^2 - 27*w + 25]', '[5461, 5461, 2*w^3 + 2*w^2 - 10*w - 5]', '[5465, 5465, -3*w^3 + 2*w^2 + 18*w - 10]', '[5465, 5465, 2*w^3 - 2*w^2 - 13*w + 8]', '[5466, 5466, 3*w^3 - w^2 - 16*w - 6]', '[5469, 5469, 6*w^3 - 5*w^2 - 24*w + 24]', '[5470, 5470, w^3 - 7*w^2 - 7*w + 19]', '[5470, 5470, -2*w^3 - w^2 + 12*w + 1]', '[5470, 5470, -6*w^3 + 9*w^2 + 21*w - 20]', '[5470, 5470, 5*w^3 - 4*w^2 - 25*w + 26]', '[5471, 5471, -4*w^3 + 4*w^2 + 13*w - 16]', '[5475, 5475, 4*w^3 - 9*w^2 - 13*w + 15]', '[5476, 5476, -w^3 - 5*w^2 + 9*w + 17]', '[5477, 5477, -4*w^3 + 2*w^2 + 18*w - 5]', '[5480, 1370, w^3 + w^2 + 2*w - 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18*w + 20]', '[521, 521, -3*w^3 + 11*w - 5]', '[521, 521, 3*w^3 - 3*w^2 - 15*w + 14]', '[523, 523, -2*w^3 + 5*w^2 + 8*w - 14]', '[529, 23, -2*w^3 + 3*w^2 + 8*w - 14]', '[529, 23, 3*w^3 - 2*w^2 - 14*w + 4]', '[541, 541, -w^3 + 2*w^2 + 7*w - 11]', '[541, 541, -w^3 - w^2 + 5*w - 2]', '[547, 547, -3*w - 2]', '[547, 547, w^3 - 2*w^2 - 7*w + 7]', '[547, 547, w^3 - 4*w^2 - 8*w + 10]', '[547, 547, 2*w^3 - 3*w^2 - 7*w + 11]', '[563, 563, 2*w^3 - 4*w^2 - 12*w + 13]', '[563, 563, -w^3 + 4*w^2 + w - 7]', '[571, 571, -w^3 + 2*w^2 + 2*w - 8]', '[571, 571, 3*w^2 - 10]', '[577, 577, 2*w^3 + w^2 - 7*w - 5]', '[599, 599, 2*w^3 - 7*w + 2]', '[599, 599, -4*w^3 + 7*w^2 + 21*w - 29]', '[617, 617, -2*w^3 + w^2 + 11*w + 1]', '[631, 631, 3*w^2 + w - 13]', '[631, 631, 3*w^2 - 4*w - 10]', '[647, 647, 3*w^3 - 4*w^2 - 13*w + 11]', '[677, 677, -2*w^3 + 4*w^2 + 8*w - 17]', '[691, 691, -w^3 + 3*w^2 + 3*w - 14]', '[733, 733, -w^3 + 4*w^2 + 3*w - 11]', '[733, 733, 3*w^3 - w^2 - 15*w - 2]', '[733, 733, -w^3 + w^2 + 7*w - 2]', '[733, 733, 3*w^3 - 4*w^2 - 16*w + 16]', '[739, 739, -3*w^3 + w^2 + 11*w - 8]', '[743, 743, -3*w^3 + 2*w^2 + 12*w - 14]', '[751, 751, -2*w^3 + w^2 + 8*w - 2]', '[761, 761, -2*w^3 + 2*w^2 + 7*w - 10]', '[761, 761, 2*w^3 - 4*w^2 - 3*w + 8]', '[769, 769, -w^3 + w^2 + 7*w - 4]', '[769, 769, 2*w^3 + 2*w^2 - 8*w - 11]', '[787, 787, -2*w^3 + 3*w^2 + 6*w - 10]', '[787, 787, -2*w^2 - 3*w + 8]', '[797, 797, -2*w^3 + w^2 + 7*w - 1]', '[797, 797, -2*w^3 - 2*w^2 + 11*w + 10]', '[809, 809, -2*w^3 + 5*w^2 + 7*w - 19]', '[811, 811, 2*w^3 - 2*w^2 - 7*w - 2]', '[811, 811, 3*w^3 - 2*w^2 - 11*w - 1]', '[827, 827, 3*w^3 - 2*w^2 - 14*w + 10]', '[829, 829, 2*w^3 - 2*w^2 - 9*w + 2]', '[829, 829, 4*w^2 + 2*w - 11]', '[841, 29, 2*w^3 + w^2 - 6*w - 2]', '[863, 863, 2*w^3 - 8*w - 1]', '[883, 883, 3*w^3 - 4*w^2 - 15*w + 13]', '[887, 887, 3*w^3 - 2*w^2 - 12*w + 10]', '[907, 907, 2*w^3 - 3*w^2 - 9*w + 7]', '[911, 911, 2*w^3 + w^2 - 11*w - 5]', '[919, 919, -2*w^3 + 5*w - 8]', '[929, 929, -w^3 + 4*w^2 + 3*w - 13]', '[937, 937, w^3 - 5*w - 7]', '[937, 937, -2*w^3 + 3*w^2 + 10*w - 8]', '[971, 971, -2*w^3 + 4*w^2 + 11*w - 20]', '[971, 971, -4*w^3 + 4*w^2 + 19*w - 20]', '[977, 977, -4*w^3 + 6*w^2 + 19*w - 28]', '[983, 983, -4*w^2 - 4*w + 7]', '[991, 991, -5*w^3 + 8*w^2 + 26*w - 32]', '[991, 991, -6*w^3 + 6*w^2 + 26*w - 31]', '[997, 997, -3*w^3 + 8*w^2 + 18*w - 26]']}
• 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': [9, -1, -7, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 16609, 'disc_rad': 16609, 'disc_sign': 1, 'frobs': [[2, [[3, 1], [1, 1]]], [3, [[3, 1], [1, 1]]], [5, [[3, 1], [1, 1]]], [7, [[4, 1]]], [11, [[4, 1]]], [13, [[4, 1]]], [17, [0]], [19, [[4, 1]]], [23, [[2, 2]]], [29, [[2, 1], [1, 2]]], [31, [[4, 1]]], [37, [[3, 1], [1, 1]]], [41, [[3, 1], [1, 1]]], [43, [[3, 1], [1, 1]]], [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': 128.87590930814028, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.16609.1', 'local_algs': ['17.2.1.2', '17.2.0.1', 'm977.1.2.0', 'm977.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [17, 977], 'rd': 11.3523525891, 'regulator': {'__RealLiteral__': 0, 'data': '12.2374056104', 'prec': 44}, 'res': {'gal': ['1,0,-5494,0,240769,0,-1832394,0,5758862,0,-8923096,0,7148087,0,-3003142,0,653104,0,-73494,0,4136,0,-108,0,1'], 'sib': ['-1,0,14,0,-13,0,1', '-17672,102624,-4250,-168985,17780,72601,-12052,-9866,1790,440,-77,-6,1', '-8,60,14,-643,209,1637,-636,-972,165,139,-21,-6,1', '1029120,191447,-182018,-18686,8914,512,-166,-4,1', '8,144,-34,-147,-58,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} - a^{2} - 5 a + 4 \\)', '\\( a + 2 \\)', '\\( a^{3} - 2 a^{2} - 5 a + 7 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}