Hilbert modular form data - 4.4.15125.1-16.1-g

Formats: - HTML - YAML - JSON - 2024-05-22T07:47:46.282114

• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 4, 'dimension': 2, 'disc': 15125, 'field_bad_primes': [5, 11], 'field_label': '4.4.15125.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '4.4.15125.1-16.1-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [2], 'level_ideal': '[16, 2, 2]', 'level_label': '16.1', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.1-g', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[16, 2, 2]', 1]], 'hecke_eigenvalues': [-4, '-e - 2', 'e', -1, 4, 4, 4, 4, '-e + 4', '-e + 4', 'e + 6', 'e + 6', 'e', '-e - 2', 'e', '-e - 2', '2*e', '-2*e - 4', '-2*e - 4', '2*e', 'e + 12', '-e + 10', 'e + 12', '-e + 10', 14, 4, 4, 4, 4, '-3*e + 2', '-3*e + 2', '3*e + 8', '3*e + 8', '2*e - 4', '2*e - 4', '-2*e - 8', '-2*e - 8', -2, -2, -2, -2, 'e + 2', 'e + 2', '-e', '-e', '3*e', '-3*e - 6', '-3*e - 6', '3*e', -12, -12, -12, -12, 16, 16, 16, 16, '-3*e - 18', '-3*e - 18', '3*e - 12', '3*e - 12', '3*e + 10', '-3*e + 4', '-3*e + 4', '3*e + 10', '-e + 2', 'e + 4', '-e + 2', 'e + 4', -12, -12, -12, -12, '3*e - 2', '3*e - 2', '-3*e - 8', '-3*e - 8', '4*e + 24', '-4*e + 16', '4*e + 24', '-4*e + 16', '4*e', '-4*e - 8', '4*e', '-4*e - 8', '-e - 26', '-e - 26', 'e - 24', 'e - 24', '-4*e - 8', '4*e', '-4*e - 8', '4*e', '-e - 40', '-e - 40', 'e - 38', 'e - 38', '-2*e - 12', '2*e - 8', '-2*e - 12', '2*e - 8', 34, 34, 34, 34, '-9*e - 14', '-9*e - 14', '9*e + 4', '9*e + 4', '6*e - 6', '-6*e - 18', '6*e - 6', '-6*e - 18', '2*e - 8', '-2*e - 12', '2*e - 8', '-2*e - 12', '-3*e + 20', '3*e + 26', '3*e + 26', '-3*e + 20', '-8*e - 16', '-8*e - 16', '8*e', '8*e', '4*e - 4', '4*e - 4', '-4*e - 12', '-4*e - 12', '4*e + 4', '-4*e - 4', '-4*e - 4', '4*e + 4', -46, -46, -46, -46, '-e - 22', '-e - 22', 'e - 20', 'e - 20', '-4*e + 32', '4*e + 40', '-4*e + 32', '4*e + 40', '-5*e - 26', '-5*e - 26', '5*e - 16', '5*e - 16', '7*e + 12', '-7*e - 2', '-7*e - 2', '7*e + 12'], 'hecke_polynomial': 'x^2 + 2*x - 20', 'label': '4.4.15125.1-16.1-g'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 15125, 'ideals': ['[1, 1, 1]', '[5, 5, 4*w^3 + 7*w^2 - 37*w - 45]', '[11, 11, 2*w^3 + 3*w^2 - 18*w - 16]', '[11, 11, -w + 2]', '[16, 2, 2]', '[19, 19, 4*w^3 + 7*w^2 - 36*w - 45]', '[19, 19, -w^3 - w^2 + 9*w + 3]', '[19, 19, -2*w^3 - 4*w^2 + 17*w + 23]', '[19, 19, w^3 + 2*w^2 - 10*w - 10]', '[25, 5, 2*w^3 + 4*w^2 - 18*w - 25]', '[29, 29, -w - 2]', '[29, 29, -w^3 - 2*w^2 + 8*w + 15]', '[29, 29, 2*w^3 + 3*w^2 - 18*w - 20]', '[29, 29, -3*w^3 - 5*w^2 + 27*w + 28]', '[31, 31, 3*w^3 + 5*w^2 - 27*w - 31]', '[31, 31, -3*w^3 - 5*w^2 + 27*w + 30]', '[31, 31, -2*w^3 - 3*w^2 + 18*w + 17]', '[31, 31, 2*w^3 + 3*w^2 - 18*w - 18]', '[55, 55, 2*w^3 + 3*w^2 - 18*w - 14]', '[55, 55, w - 4]', '[71, 71, -w^3 - 2*w^2 + 10*w + 8]', '[71, 71, 4*w^3 + 8*w^2 - 35*w - 50]', '[71, 71, -4*w^3 - 7*w^2 + 36*w + 47]', '[71, 71, -w^3 - 2*w^2 + 8*w + 17]', '[79, 79, w^3 + 2*w^2 - 10*w - 14]', '[79, 79, -w^3 - w^2 + 9*w + 7]', '[79, 79, -2*w^3 - 4*w^2 + 17*w + 27]', '[79, 79, -4*w^3 - 7*w^2 + 36*w + 41]', '[80, 10, 8*w^3 + 14*w^2 - 74*w - 90]', '[81, 3, -3]', '[95, 95, -2*w^3 - 4*w^2 + 19*w + 26]', '[95, 95, -3*w^3 - 6*w^2 + 26*w + 39]', '[95, 95, 5*w^3 + 9*w^2 - 45*w - 54]', '[95, 95, -w^2 + 6]', '[109, 109, -2*w^3 - 3*w^2 + 19*w + 13]', '[109, 109, 3*w^3 + 5*w^2 - 26*w - 26]', '[109, 109, 2*w^3 + 3*w^2 - 19*w - 22]', '[109, 109, 3*w^3 + 5*w^2 - 26*w - 35]', '[121, 11, 3*w^3 + 6*w^2 - 27*w - 38]', '[121, 11, 3*w^3 + 6*w^2 - 27*w - 37]', '[121, 11, -10*w^3 - 18*w^2 + 91*w + 113]', '[125, 5, -12*w^3 - 21*w^2 + 109*w + 133]', '[139, 139, 4*w^3 + 7*w^2 - 36*w - 40]', '[139, 139, -w^3 - w^2 + 9*w + 8]', '[139, 139, -w^3 - 2*w^2 + 10*w + 15]', '[139, 139, 2*w^3 + 4*w^2 - 17*w - 28]', '[145, 145, -19*w^3 - 33*w^2 + 175*w + 214]', '[145, 145, 5*w^3 + 9*w^2 - 46*w - 55]', '[145, 145, -22*w^3 - 39*w^2 + 202*w + 249]', '[145, 145, 10*w^3 + 18*w^2 - 90*w - 113]', '[149, 149, 4*w^3 + 8*w^2 - 35*w - 52]', '[149, 149, -3*w^3 - 5*w^2 + 26*w + 34]', '[149, 149, -2*w^3 - 3*w^2 + 19*w + 14]', '[149, 149, -6*w^3 - 11*w^2 + 54*w + 66]', '[155, 155, -22*w^3 - 39*w^2 + 201*w + 248]', '[155, 155, -14*w^3 - 25*w^2 + 128*w + 159]', '[155, 155, 18*w^3 + 32*w^2 - 164*w - 203]', '[155, 155, 10*w^3 + 18*w^2 - 91*w - 114]', '[176, 22, 4*w^3 + 6*w^2 - 36*w - 32]', '[176, 22, -2*w + 4]', '[181, 181, w^3 + 2*w^2 - 11*w - 13]', '[181, 181, -3*w^3 - 4*w^2 + 27*w + 24]', '[181, 181, -7*w^3 - 12*w^2 + 63*w + 72]', '[181, 181, 3*w^3 + 6*w^2 - 25*w - 39]', '[191, 191, -7*w^3 - 12*w^2 + 66*w + 80]', '[191, 191, 5*w^3 + 9*w^2 - 47*w - 57]', '[191, 191, -2*w^3 - 2*w^2 + 18*w + 9]', '[191, 191, 2*w^3 + 2*w^2 - 17*w - 13]', '[209, 209, 5*w^3 + 10*w^2 - 43*w - 60]', '[209, 209, 2*w^3 + 4*w^2 - 19*w - 27]', '[209, 209, 5*w^3 + 9*w^2 - 45*w - 53]', '[209, 209, -9*w^3 - 16*w^2 + 81*w + 101]', '[209, 209, -3*w^3 - 6*w^2 + 29*w + 34]', '[209, 209, -w^2 + 5]', '[209, 209, 3*w^3 + 6*w^2 - 26*w - 40]', '[209, 209, w^3 - 9*w + 5]', '[239, 239, 7*w^3 + 13*w^2 - 62*w - 81]', '[239, 239, -2*w^3 - 5*w^2 + 17*w + 32]', '[239, 239, 6*w^3 + 11*w^2 - 55*w - 67]', '[239, 239, -w^3 - 3*w^2 + 10*w + 20]', '[251, 251, 7*w^3 + 13*w^2 - 63*w - 82]', '[251, 251, -5*w^3 - 10*w^2 + 44*w + 61]', '[251, 251, 4*w^3 + 8*w^2 - 37*w - 48]', '[251, 251, -2*w^3 - 5*w^2 + 18*w + 34]', '[256, 4, 4]', '[275, 55, 2*w^3 + 5*w^2 - 16*w - 34]', '[275, 55, -2*w^3 - 2*w^2 + 17*w + 12]', '[304, 38, 8*w^3 + 14*w^2 - 72*w - 90]', '[304, 38, -2*w^3 - 2*w^2 + 18*w + 6]', '[304, 38, -4*w^3 - 8*w^2 + 34*w + 46]', '[304, 38, 2*w^3 + 4*w^2 - 20*w - 20]', '[311, 311, 5*w^3 + 9*w^2 - 44*w - 50]', '[311, 311, -4*w^3 - 7*w^2 + 37*w + 48]', '[311, 311, 2*w^3 + 4*w^2 - 19*w - 19]', '[311, 311, w^3 + w^2 - 8*w - 11]', '[319, 319, -w^3 - 4*w^2 + 12*w + 22]', '[319, 319, w^2 - 4]', '[319, 319, w^3 + 2*w^2 - 13*w - 1]', '[319, 319, 2*w^3 + 5*w^2 - 16*w - 37]', '[319, 319, -3*w^3 - 6*w^2 + 26*w + 41]', '[319, 319, -9*w^3 - 16*w^2 + 80*w + 94]', '[319, 319, -w^3 - 5*w^2 + 7*w + 39]', '[319, 319, -7*w^3 - 10*w^2 + 63*w + 48]', '[331, 331, 4*w^3 + 6*w^2 - 36*w - 37]', '[331, 331, -6*w^3 - 10*w^2 + 54*w + 59]', '[331, 331, -2*w - 1]', '[331, 331, -2*w^3 - 4*w^2 + 16*w + 27]', '[341, 341, -3*w^3 - 3*w^2 + 28*w + 7]', '[341, 341, -2*w^3 - 5*w^2 + 19*w + 31]', '[341, 341, w^3 + w^2 - 9*w]', '[341, 341, 2*w^3 + 5*w^2 - 18*w - 33]', '[341, 341, -3*w^3 - 4*w^2 + 27*w + 16]', '[341, 341, -w^3 - 4*w^2 + 10*w + 26]', '[341, 341, w^3 - 10*w + 9]', '[341, 341, w^3 + 4*w^2 - 9*w - 28]', '[349, 349, -3*w^3 - 5*w^2 + 28*w + 27]', '[349, 349, 4*w^3 + 8*w^2 - 35*w - 53]', '[349, 349, -3*w^3 - 6*w^2 + 28*w + 40]', '[349, 349, 6*w^3 + 11*w^2 - 54*w - 65]', '[355, 355, 42*w^3 + 74*w^2 - 385*w - 472]', '[355, 355, -w^3 - 2*w^2 + 11*w + 12]', '[355, 355, -13*w^3 - 23*w^2 + 117*w + 142]', '[355, 355, 13*w^3 + 23*w^2 - 120*w - 145]', '[359, 359, -w^3 - 3*w^2 + 8*w + 19]', '[359, 359, -6*w^3 - 11*w^2 + 53*w + 69]', '[359, 359, 5*w^3 + 9*w^2 - 46*w - 54]', '[359, 359, w^2 - w - 8]', '[361, 19, w^3 + 3*w^2 - 7*w - 23]', '[361, 19, -4*w^3 - 7*w^2 + 38*w + 45]', '[361, 19, -4*w^3 - 8*w^2 + 36*w + 51]', '[361, 19, -8*w^3 - 14*w^2 + 71*w + 83]', '[361, 19, -3*w^3 - 4*w^2 + 26*w + 26]', '[361, 19, -4*w^3 - 8*w^2 + 36*w + 49]', '[361, 361, w + 5]', '[361, 361, -2*w^3 - 3*w^2 + 18*w + 23]', '[361, 361, 3*w^3 + 5*w^2 - 27*w - 25]', '[361, 361, -w^3 - 2*w^2 + 8*w + 18]', '[395, 395, -23*w^3 - 40*w^2 + 211*w + 258]', '[395, 395, 14*w^3 + 25*w^2 - 129*w - 160]', '[395, 395, 9*w^3 + 16*w^2 - 82*w - 99]', '[395, 395, 18*w^3 + 32*w^2 - 163*w - 202]', '[400, 10, 4*w^3 + 8*w^2 - 36*w - 50]', '[401, 401, 5*w^3 + 8*w^2 - 45*w - 50]', '[401, 401, w^3 + 2*w^2 - 7*w - 15]', '[401, 401, w^3 + 2*w^2 - 7*w - 11]', '[401, 401, 5*w^3 + 8*w^2 - 45*w - 46]', '[405, 15, -12*w^3 - 21*w^2 + 111*w + 135]', '[409, 409, -9*w^3 - 16*w^2 + 81*w + 97]', '[409, 409, w^3 + w^2 - 11*w - 10]', '[409, 409, 6*w^3 + 10*w^2 - 53*w - 66]', '[409, 409, -3*w^3 - 6*w^2 + 29*w + 38]', '[421, 421, -3*w^3 - 4*w^2 + 26*w + 23]', '[421, 421, -4*w^3 - 6*w^2 + 35*w + 39]', '[421, 421, 8*w^3 + 14*w^2 - 71*w - 86]', '[421, 421, -7*w^3 - 12*w^2 + 62*w + 70]', '[439, 439, w^3 + w^2 - 10*w - 9]', '[439, 439, -4*w^3 - 7*w^2 + 35*w + 47]', '[439, 439, 3*w^3 + 5*w^2 - 28*w - 26]', '[439, 439, 2*w^3 + 3*w^2 - 17*w - 14]', '[464, 58, -2*w - 4]', '[464, 58, -2*w^3 - 4*w^2 + 16*w + 30]', '[464, 58, 4*w^3 + 6*w^2 - 36*w - 40]', '[464, 58, -6*w^3 - 10*w^2 + 54*w + 56]', '[475, 95, -6*w^3 - 11*w^2 + 56*w + 71]', '[475, 95, -3*w^3 - 7*w^2 + 25*w + 49]', '[475, 95, -10*w^3 - 18*w^2 + 89*w + 107]', '[475, 95, -w^3 + 8*w + 2]', '[479, 479, 3*w^3 + 6*w^2 - 29*w - 33]', '[479, 479, 5*w^3 + 10*w^2 - 43*w - 59]', '[479, 479, w^3 - 9*w + 6]', '[479, 479, 9*w^3 + 16*w^2 - 81*w - 102]', '[496, 62, 6*w^3 + 10*w^2 - 54*w - 62]', '[496, 62, -6*w^3 - 10*w^2 + 54*w + 60]', '[496, 62, -4*w^3 - 6*w^2 + 36*w + 34]', '[496, 62, 4*w^3 + 6*w^2 - 36*w - 36]', '[521, 521, 4*w^3 + 7*w^2 - 38*w - 44]', '[521, 521, 3*w^3 + 4*w^2 - 26*w - 25]', '[521, 521, 5*w^3 + 8*w^2 - 44*w - 46]', '[521, 521, -8*w^3 - 14*w^2 + 71*w + 84]', '[545, 545, -41*w^3 - 72*w^2 + 377*w + 463]', '[545, 545, -27*w^3 - 48*w^2 + 248*w + 304]', '[545, 545, 5*w^3 + 9*w^2 - 44*w - 58]', '[545, 545, 9*w^3 + 15*w^2 - 85*w - 101]', '[551, 551, -w^3 - w^2 + 11*w + 2]', '[551, 551, -5*w^3 - 8*w^2 + 44*w + 51]', '[551, 551, 2*w^3 + 3*w^2 - 20*w - 20]', '[551, 551, 2*w^3 + 3*w^2 - 17*w - 24]', '[551, 551, -3*w^3 - 5*w^2 + 28*w + 36]', '[551, 551, -19*w^3 - 34*w^2 + 173*w + 214]', '[551, 551, -3*w^3 - 8*w^2 + 31*w + 45]', '[551, 551, 7*w^3 + 9*w^2 - 64*w - 40]', '[551, 551, -17*w^3 - 29*w^2 + 154*w + 187]', '[551, 551, w^3 + 6*w^2 - 7*w - 48]', '[551, 551, 17*w^3 + 32*w^2 - 149*w - 193]', '[551, 551, 4*w^3 + 7*w^2 - 35*w - 37]', '[551, 551, -w^3 - w^2 + 10*w - 1]', '[551, 551, 6*w^3 + 10*w^2 - 53*w - 58]', '[551, 551, 10*w^3 + 19*w^2 - 85*w - 108]', '[551, 551, w^2 - 5*w + 5]', '[569, 569, 21*w^3 + 37*w^2 - 191*w - 236]', '[569, 569, -13*w^3 - 23*w^2 + 120*w + 149]', '[569, 569, 10*w^3 + 17*w^2 - 92*w - 111]', '[569, 569, -18*w^3 - 32*w^2 + 164*w + 201]', '[589, 589, -7*w^3 - 13*w^2 + 62*w + 82]', '[589, 589, -2*w^3 - 5*w^2 + 20*w + 31]', '[589, 589, 9*w^3 + 17*w^2 - 79*w - 105]', '[589, 589, -14*w^3 - 24*w^2 + 128*w + 155]', '[589, 589, 13*w^3 + 24*w^2 - 115*w - 147]', '[589, 589, -3*w^3 - 3*w^2 + 29*w + 8]', '[589, 589, 4*w^3 + 4*w^2 - 38*w - 11]', '[589, 589, 5*w^3 + 7*w^2 - 46*w - 34]', '[589, 589, -w^3 - 4*w^2 + 11*w + 25]', '[589, 589, 2*w^2 - w - 15]', '[589, 589, -9*w^3 - 15*w^2 + 82*w + 97]', '[589, 589, 5*w^3 + 8*w^2 - 46*w - 52]', '[589, 589, w^3 + 3*w^2 - 10*w - 21]', '[589, 589, -11*w^3 - 20*w^2 + 98*w + 124]', '[589, 589, 10*w^3 + 17*w^2 - 92*w - 110]', '[589, 589, -4*w^3 - 6*w^2 + 37*w + 31]', '[605, 55, 5*w^3 + 8*w^2 - 45*w - 48]', '[605, 55, -w^3 - 4*w^2 + 6*w + 34]', '[605, 55, -3*w^3 - 2*w^2 + 28*w + 2]', '[625, 5, 5]', '[631, 631, -2*w^3 - 3*w^2 + 20*w + 25]', '[631, 631, 7*w^3 + 12*w^2 - 64*w - 80]', '[631, 631, -9*w^3 - 17*w^2 + 80*w + 106]', '[631, 631, 19*w^3 + 33*w^2 - 175*w - 215]', '[641, 641, 4*w^3 + 6*w^2 - 35*w - 35]', '[641, 641, 4*w^3 + 6*w^2 - 35*w - 38]', '[641, 641, 7*w^3 + 12*w^2 - 62*w - 71]', '[641, 641, 7*w^3 + 12*w^2 - 62*w - 74]', '[659, 659, 6*w^3 + 11*w^2 - 54*w - 63]', '[659, 659, 4*w^3 + 6*w^2 - 37*w - 38]', '[659, 659, 4*w^3 + 8*w^2 - 35*w - 55]', '[659, 659, 3*w^3 + 6*w^2 - 28*w - 42]', '[661, 661, -27*w^3 - 48*w^2 + 247*w + 306]', '[661, 661, 14*w^3 + 24*w^2 - 129*w - 158]', '[661, 661, 11*w^3 + 19*w^2 - 102*w - 126]', '[661, 661, 2*w^3 + 3*w^2 - 19*w - 24]', '[691, 691, 6*w^3 + 12*w^2 - 53*w - 73]', '[691, 691, 8*w^3 + 15*w^2 - 72*w - 95]', '[691, 691, -5*w^3 - 10*w^2 + 46*w + 60]', '[691, 691, -3*w^3 - 7*w^2 + 27*w + 47]', '[695, 695, -14*w^3 - 25*w^2 + 126*w + 157]', '[695, 695, 18*w^3 + 32*w^2 - 166*w - 205]', '[695, 695, 27*w^3 + 47*w^2 - 248*w - 303]', '[695, 695, -13*w^3 - 23*w^2 + 119*w + 144]', '[725, 145, -10*w^3 - 18*w^2 + 89*w + 112]', '[725, 145, -w^3 + 8*w - 3]', '[725, 145, -6*w^3 - 11*w^2 + 56*w + 66]', '[725, 145, -3*w^3 - 7*w^2 + 25*w + 44]', '[739, 739, -2*w^3 - 5*w^2 + 19*w + 34]', '[739, 739, 7*w^3 + 13*w^2 - 64*w - 78]', '[739, 739, -3*w^3 - 7*w^2 + 26*w + 43]', '[739, 739, 8*w^3 + 15*w^2 - 71*w - 95]', '[745, 745, -21*w^3 - 37*w^2 + 191*w + 232]', '[745, 745, 9*w^3 + 16*w^2 - 81*w - 103]', '[745, 745, 30*w^3 + 53*w^2 - 272*w - 335]', '[745, 745, 23*w^3 + 41*w^2 - 211*w - 259]', '[751, 751, -4*w^3 - 9*w^2 + 37*w + 59]', '[751, 751, -5*w^3 - 9*w^2 + 43*w + 48]', '[751, 751, -6*w^3 - 10*w^2 + 55*w + 68]', '[751, 751, -10*w^3 - 17*w^2 + 93*w + 114]', '[769, 769, 6*w^3 + 11*w^2 - 52*w - 69]', '[769, 769, w^3 + w^2 - 7*w - 5]', '[769, 769, 2*w^3 + 2*w^2 - 19*w - 11]', '[769, 769, 7*w^3 + 12*w^2 - 64*w - 72]', '[775, 155, -3*w^3 - 5*w^2 + 29*w + 31]', '[775, 155, w^3 + w^2 - 11*w - 6]', '[775, 155, -w^2 - 2*w + 9]', '[775, 155, -2*w^3 - 3*w^2 + 20*w + 16]', '[781, 781, w^3 - 2*w - 15]', '[781, 781, 3*w^3 + w^2 - 29*w + 7]', '[781, 781, -5*w^3 - 6*w^2 + 45*w + 27]', '[781, 781, -4*w^3 - 5*w^2 + 36*w + 24]', '[781, 781, 3*w^3 + 6*w^2 - 31*w - 30]', '[781, 781, 9*w^3 + 20*w^2 - 76*w - 130]', '[781, 781, 5*w^3 + 7*w^2 - 46*w - 39]', '[781, 781, w^3 + 2*w^2 - 15*w + 3]', '[809, 809, -3*w^3 - 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3*w - 29]', '[1595, 1595, w^3 - 10*w + 1]', '[1595, 1595, -3*w^3 - 9*w^2 + 23*w + 69]', '[1595, 1595, 4*w^3 + 5*w^2 - 38*w - 19]', '[1595, 1595, -13*w^3 - 20*w^2 + 117*w + 104]', '[1595, 1595, -w^2 + 2*w + 8]', '[1619, 1619, 9*w^3 + 17*w^2 - 80*w - 109]', '[1619, 1619, -3*w^3 - 7*w^2 + 28*w + 48]', '[1619, 1619, 8*w^3 + 15*w^2 - 73*w - 89]', '[1619, 1619, 4*w^3 + 9*w^2 - 35*w - 54]', '[1621, 1621, -5*w^3 - 10*w^2 + 42*w + 61]', '[1621, 1621, 6*w^3 + 9*w^2 - 51*w - 55]', '[1621, 1621, 12*w^3 + 21*w^2 - 105*w - 128]', '[1621, 1621, 7*w^3 + 11*w^2 - 63*w - 69]', '[1639, 1639, -2*w^2 - w + 14]', '[1639, 1639, 5*w^3 + 8*w^2 - 42*w - 54]', '[1639, 1639, -4*w^3 - 2*w^2 + 38*w - 7]', '[1639, 1639, 5*w^3 + 14*w^2 - 40*w - 98]', '[1639, 1639, 2*w^3 + 6*w^2 - 24*w - 25]', '[1639, 1639, w^3 + 3*w^2 - 4*w - 34]', '[1639, 1639, -4*w^3 - 5*w^2 + 38*w + 20]', '[1639, 1639, -9*w^3 - 16*w^2 + 78*w + 91]', '[1655, 1655, -26*w^3 - 45*w^2 + 239*w + 293]', '[1655, 1655, -2*w^3 - 3*w^2 + 19*w + 25]', '[1655, 1655, -32*w^3 - 57*w^2 + 293*w + 363]', '[1655, 1655, 32*w^3 + 57*w^2 - 291*w - 361]', '[1669, 1669, 5*w^3 + 7*w^2 - 44*w - 49]', '[1669, 1669, -13*w^3 - 24*w^2 + 115*w + 148]', '[1669, 1669, -15*w^3 - 27*w^2 + 133*w + 166]', '[1669, 1669, 3*w^3 + 8*w^2 - 24*w - 53]', '[1681, 41, 6*w^3 + 12*w^2 - 54*w - 77]', '[1681, 41, 6*w^3 + 12*w^2 - 54*w - 73]', '[1705, 1705, 7*w^3 + 11*w^2 - 63*w - 62]', '[1705, 1705, 4*w^3 + 5*w^2 - 36*w - 27]', '[1705, 1705, -3*w^3 - 2*w^2 + 26*w + 10]', '[1705, 1705, -9*w^3 - 14*w^2 + 81*w + 76]', '[1705, 1705, 5*w^3 + 6*w^2 - 46*w - 27]', '[1705, 1705, 3*w^3 + 2*w^2 - 27*w - 6]', '[1705, 1705, -7*w^3 - 9*w^2 + 64*w + 41]', '[1705, 1705, -4*w^3 - 5*w^2 + 35*w + 31]', '[1721, 1721, -32*w^3 - 56*w^2 + 293*w + 361]', '[1721, 1721, -20*w^3 - 35*w^2 + 183*w + 227]', '[1721, 1721, -7*w^3 - 12*w^2 + 62*w + 83]', '[1721, 1721, -16*w^3 - 28*w^2 + 147*w + 183]', '[1741, 1741, 40*w^3 + 71*w^2 - 365*w - 450]', '[1741, 1741, 23*w^3 + 40*w^2 - 210*w - 259]', '[1741, 1741, 15*w^3 + 26*w^2 - 139*w - 172]', '[1741, 1741, 12*w^3 + 22*w^2 - 109*w - 138]', '[1744, 218, -4*w^3 - 6*w^2 + 38*w + 26]', '[1744, 218, 6*w^3 + 10*w^2 - 52*w - 52]', '[1744, 218, 4*w^3 + 6*w^2 - 38*w - 44]', '[1744, 218, 6*w^3 + 10*w^2 - 52*w - 70]', '[1745, 1745, -25*w^3 - 44*w^2 + 228*w + 277]', '[1745, 1745, 17*w^3 + 30*w^2 - 154*w - 192]', '[1745, 1745, 39*w^3 + 68*w^2 - 357*w - 436]', '[1745, 1745, -26*w^3 - 46*w^2 + 235*w + 290]', '[1759, 1759, -8*w^3 - 13*w^2 + 73*w + 85]', '[1759, 1759, 6*w^3 + 9*w^2 - 55*w - 46]', '[1759, 1759, 12*w^3 + 22*w^2 - 107*w - 138]', '[1759, 1759, -3*w^3 - 5*w^2 + 24*w + 38]', '[1775, 355, -3*w^3 - 8*w^2 + 28*w + 48]', '[1775, 355, 6*w^3 + 10*w^2 - 53*w - 52]', '[1775, 355, 10*w^3 + 19*w^2 - 92*w - 121]', '[1775, 355, 3*w^3 + 8*w^2 - 28*w - 53]', '[1789, 1789, -8*w^3 - 14*w^2 + 72*w + 81]', '[1789, 1789, -9*w^3 - 16*w^2 + 79*w + 100]', '[1789, 1789, 3*w^3 + 4*w^2 - 25*w - 22]', '[1789, 1789, -7*w^3 - 12*w^2 + 65*w + 71]', '[1795, 1795, 31*w^3 + 55*w^2 - 282*w - 346]', '[1795, 1795, -13*w^3 - 22*w^2 + 119*w + 143]', '[1795, 1795, -37*w^3 - 65*w^2 + 337*w + 415]', '[1795, 1795, -9*w^3 - 16*w^2 + 84*w + 106]', '[1805, 95, 20*w^3 + 35*w^2 - 181*w - 221]', '[1805, 95, -9*w^3 - 17*w^2 + 81*w + 104]', '[1805, 95, 6*w^3 + 12*w^2 - 55*w - 76]', '[1805, 95, 5*w^3 + 9*w^2 - 44*w - 48]', '[1805, 95, -4*w^3 - 9*w^2 + 36*w + 56]', '[1805, 95, -12*w^3 - 21*w^2 + 112*w + 136]', '[1805, 1805, -7*w^3 - 11*w^2 + 62*w + 71]', '[1805, 1805, -w^2 - 3*w + 13]', '[1805, 1805, 2*w^3 + 3*w^2 - 21*w - 22]', '[1805, 1805, -9*w^3 - 15*w^2 + 80*w + 86]', '[1831, 1831, -10*w^3 - 17*w^2 + 89*w + 99]', '[1831, 1831, 12*w^3 + 21*w^2 - 106*w - 129]', '[1831, 1831, 5*w^3 + 7*w^2 - 43*w - 41]', '[1831, 1831, 7*w^3 + 12*w^2 - 66*w - 72]', '[1871, 1871, -12*w^3 - 20*w^2 + 109*w + 120]', '[1871, 1871, 4*w^3 + 5*w^2 - 34*w - 33]', '[1871, 1871, 7*w^3 + 13*w^2 - 59*w - 82]', '[1871, 1871, -8*w^3 - 14*w^2 + 75*w + 89]', '[1889, 1889, 8*w^3 + 13*w^2 - 73*w - 86]', '[1889, 1889, -15*w^3 - 27*w^2 + 134*w + 168]', '[1889, 1889, -13*w^3 - 24*w^2 + 116*w + 151]', '[1889, 1889, 8*w^3 + 15*w^2 - 75*w - 90]', '[1901, 1901, 9*w^3 + 17*w^2 - 81*w - 107]', '[1901, 1901, 6*w^3 + 12*w^2 - 55*w - 73]', '[1901, 1901, -7*w^3 - 14*w^2 + 62*w + 86]', '[1901, 1901, -4*w^3 - 9*w^2 + 36*w + 59]', '[1936, 22, 6*w^3 + 12*w^2 - 54*w - 76]', '[1936, 22, 6*w^3 + 12*w^2 - 54*w - 74]', '[1936, 22, -20*w^3 - 36*w^2 + 182*w + 226]', '[1949, 1949, -12*w^3 - 21*w^2 + 107*w + 133]', '[1949, 1949, 7*w^3 + 13*w^2 - 59*w - 84]', '[1949, 1949, 7*w^3 + 10*w^2 - 64*w - 61]', '[1949, 1949, 12*w^3 + 20*w^2 - 109*w - 118]', '[1951, 1951, 7*w^3 + 14*w^2 - 65*w - 88]', '[1951, 1951, -13*w^3 - 24*w^2 + 117*w + 147]', '[1951, 1951, 31*w^3 + 54*w^2 - 284*w - 349]', '[1951, 1951, -9*w^3 - 18*w^2 + 79*w + 114]', '[1975, 395, -9*w^3 - 16*w^2 + 80*w + 102]', '[1975, 395, 5*w^3 + 9*w^2 - 47*w - 51]', '[1975, 395, -2*w^3 - 2*w^2 + 17*w + 7]', '[1975, 395, -2*w^3 - 5*w^2 + 16*w + 29]', '[1979, 1979, -7*w^3 - 14*w^2 + 60*w + 90]', '[1979, 1979, 13*w^3 + 23*w^2 - 117*w - 139]', '[1979, 1979, 2*w^3 + w^2 - 18*w - 5]', '[1979, 1979, 4*w^3 + 8*w^2 - 39*w - 51]', '[1991, 1991, -10*w^3 - 19*w^2 + 89*w + 115]', '[1991, 1991, -8*w^3 - 12*w^2 + 71*w + 57]', '[1991, 1991, w^3 + 7*w^2 - 12*w - 45]', '[1991, 1991, -3*w^3 - 5*w^2 + 31*w + 15]', '[1991, 1991, -w^3 + w^2 + 5*w + 5]', '[1991, 1991, 4*w^2 + 3*w - 43]', '[1991, 1991, 5*w^3 + 11*w^2 - 44*w - 73]', '[1991, 1991, 10*w^3 + 23*w^2 - 85*w - 151]', '[1999, 1999, 4*w^3 + 7*w^2 - 38*w - 37]', '[1999, 1999, 3*w^3 + 4*w^2 - 26*w - 18]', '[1999, 1999, w^3 + 3*w^2 - 7*w - 15]', '[1999, 1999, -8*w^3 - 14*w^2 + 71*w + 91]', '[2000, 10, -24*w^3 - 42*w^2 + 218*w + 266]', '[2005, 2005, 22*w^3 + 38*w^2 - 203*w - 249]', '[2005, 2005, -40*w^3 - 71*w^2 + 366*w + 452]', '[2005, 2005, 6*w^3 + 10*w^2 - 55*w - 69]', '[2005, 2005, -24*w^3 - 43*w^2 + 218*w + 272]', '[2011, 2011, 6*w^3 + 9*w^2 - 54*w - 55]', '[2011, 2011, 9*w^3 + 15*w^2 - 81*w - 89]', '[2011, 2011, -3*w - 1]', '[2011, 2011, -3*w^3 - 6*w^2 + 24*w + 40]', '[2025, 15, -6*w^3 - 12*w^2 + 54*w + 75]', '[2045, 2045, -52*w^3 - 92*w^2 + 473*w + 583]', '[2045, 2045, -48*w^3 - 84*w^2 + 442*w + 543]', '[2045, 2045, -49*w^3 - 87*w^2 + 449*w + 552]', '[2045, 2045, 42*w^3 + 73*w^2 - 384*w - 470]', '[2059, 2059, -38*w^3 - 67*w^2 + 349*w + 430]', '[2059, 2059, 13*w^3 + 22*w^2 - 121*w - 146]', '[2059, 2059, -2*w^3 - 5*w^2 + 17*w + 28]', '[2059, 2059, 30*w^3 + 52*w^2 - 275*w - 336]', '[2059, 2059, -6*w^3 - 11*w^2 + 52*w + 71]', '[2059, 2059, 3*w^3 + 7*w^2 - 30*w - 43]', '[2059, 2059, -6*w^3 - 11*w^2 + 55*w + 63]', '[2059, 2059, 14*w^3 + 25*w^2 - 127*w - 154]', '[2059, 2059, 6*w^3 + 10*w^2 - 52*w - 67]', '[2059, 2059, -11*w^3 - 21*w^2 + 96*w + 130]', '[2059, 2059, 6*w^3 + 10*w^2 - 52*w - 55]', '[2059, 2059, -11*w^3 - 20*w^2 + 99*w + 120]', '[2059, 2059, 12*w^3 + 21*w^2 - 107*w - 122]', '[2059, 2059, -4*w^3 - 6*w^2 + 38*w + 29]', '[2059, 2059, 7*w^3 + 13*w^2 - 62*w - 85]', '[2059, 2059, 5*w^3 + 9*w^2 - 48*w - 61]', '[2071, 2071, 6*w^3 + 9*w^2 - 54*w - 50]', '[2071, 2071, -3*w^3 - 9*w^2 + 36*w + 40]', '[2071, 2071, 11*w^3 + 22*w^2 - 96*w - 135]', '[2071, 2071, -27*w^3 - 51*w^2 + 234*w + 301]', '[2071, 2071, -36*w^3 - 63*w^2 + 327*w + 401]', '[2071, 2071, -9*w^3 - 15*w^2 + 81*w + 94]', '[2071, 2071, -3*w + 4]', '[2071, 2071, 3*w^3 + 6*w^2 - 24*w - 35]', '[2071, 2071, 6*w^3 + 3*w^2 - 57*w + 8]', '[2071, 2071, 17*w^3 + 31*w^2 - 153*w - 194]', '[2071, 2071, -19*w^3 - 32*w^2 + 171*w + 211]', '[2071, 2071, -11*w^3 - 16*w^2 + 99*w + 77]', '[2071, 2071, -2*w^3 - 7*w^2 + 18*w + 50]', '[2071, 2071, -8*w^3 - 16*w^2 + 75*w + 96]', '[2071, 2071, -w^3 - 2*w^2 + 15*w - 6]', '[2071, 2071, 7*w^3 + 14*w^2 - 57*w - 72]', '[2089, 2089, -13*w^3 - 23*w^2 + 121*w + 150]', '[2089, 2089, 13*w^3 + 22*w^2 - 120*w - 145]', '[2089, 2089, 26*w^3 + 46*w^2 - 239*w - 296]', '[2089, 2089, 22*w^3 + 38*w^2 - 202*w - 245]', '[2101, 2101, 4*w^3 + 6*w^2 - 37*w - 26]', '[2101, 2101, -7*w^2 + 7*w + 36]', '[2101, 2101, 2*w^3 + 4*w^2 - 19*w - 17]', '[2101, 2101, -3*w^3 - 5*w^2 + 25*w + 40]', '[2101, 2101, -2*w^2 + 6*w - 3]', '[2101, 2101, w^3 - w^2 - 12*w + 22]', '[2101, 2101, -14*w^3 - 25*w^2 + 123*w + 142]', '[2101, 2101, w^2 - 15]', '[2105, 2105, 21*w^3 + 38*w^2 - 189*w - 236]', '[2105, 2105, 29*w^3 + 52*w^2 - 266*w - 329]', '[2105, 2105, 9*w^3 + 17*w^2 - 82*w - 105]', '[2105, 2105, -41*w^3 - 73*w^2 + 373*w + 460]', '[2129, 2129, -8*w^3 - 15*w^2 + 71*w + 97]', '[2129, 2129, -5*w^3 - 9*w^2 + 43*w + 60]', '[2129, 2129, -6*w^3 - 10*w^2 + 55*w + 56]', '[2129, 2129, -7*w^3 - 13*w^2 + 64*w + 76]', '[2161, 2161, -3*w^3 - 4*w^2 + 30*w + 18]', '[2161, 2161, 9*w^3 + 15*w^2 - 79*w - 87]', '[2161, 2161, 8*w^3 + 13*w^2 - 70*w - 83]', '[2161, 2161, 12*w^3 + 21*w^2 - 107*w - 127]', '[2195, 2195, -33*w^3 - 58*w^2 + 304*w + 374]', '[2195, 2195, 31*w^3 + 55*w^2 - 284*w - 348]', '[2195, 2195, 13*w^3 + 22*w^2 - 121*w - 145]', '[2195, 2195, -13*w^3 - 23*w^2 + 117*w + 147]', '[2201, 2201, 5*w^3 + 9*w^2 - 41*w - 59]', '[2201, 2201, 4*w^3 + 5*w^2 - 34*w - 31]', '[2201, 2201, w^3 + 4*w^2 - 6*w - 30]', '[2201, 2201, 13*w^3 + 22*w^2 - 117*w - 130]', '[2201, 2201, 16*w^3 + 28*w^2 - 148*w - 179]', '[2201, 2201, 12*w^3 + 21*w^2 - 106*w - 124]', '[2201, 2201, -8*w^3 - 14*w^2 + 75*w + 88]', '[2201, 2201, -28*w^3 - 49*w^2 + 258*w + 315]', '[2201, 2201, -4*w^3 - 7*w^2 + 32*w + 41]', '[2201, 2201, 8*w^3 + 14*w^2 - 75*w - 87]', '[2201, 2201, w^3 + 4*w^2 - 6*w - 31]', '[2201, 2201, 4*w^3 + 5*w^2 - 34*w - 32]', '[2201, 2201, -13*w^3 - 22*w^2 + 118*w + 134]', '[2201, 2201, 5*w^3 + 7*w^2 - 43*w - 46]', '[2201, 2201, 7*w^3 + 10*w^2 - 63*w - 62]', '[2201, 2201, -13*w^3 - 23*w^2 + 115*w + 139]', '[2224, 278, 8*w^3 + 14*w^2 - 72*w - 80]', '[2224, 278, -2*w^3 - 2*w^2 + 18*w + 16]', '[2224, 278, -2*w^3 - 4*w^2 + 20*w + 30]', '[2224, 278, 4*w^3 + 8*w^2 - 34*w - 56]', '[2239, 2239, 6*w^3 + 10*w^2 - 56*w - 57]', '[2239, 2239, -9*w^3 - 16*w^2 + 81*w + 94]', '[2239, 2239, 8*w^3 + 14*w^2 - 70*w - 89]', '[2239, 2239, -4*w^3 - 6*w^2 + 34*w + 33]', '[2281, 2281, -7*w^3 - 11*w^2 + 63*w + 68]', '[2281, 2281, 2*w^3 + 4*w^2 - 15*w - 28]', '[2281, 2281, -8*w^3 - 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16*w^2 + 89*w + 92]', '[9641, 9641, -w^3 + 13*w]', '[9641, 9641, 35*w^3 + 61*w^2 - 323*w - 393]', '[9641, 9641, -11*w^3 - 17*w^2 + 98*w + 93]', '[9641, 9641, -33*w^3 - 58*w^2 + 305*w + 373]', '[9641, 9641, -4*w^3 - 6*w^2 + 41*w + 44]', '[9641, 9641, w^2 + 4*w - 4]', '[9641, 9641, -33*w^3 - 58*w^2 + 304*w + 370]', '[9641, 9641, -11*w^3 - 18*w^2 + 98*w + 113]', '[9641, 9641, 2*w^3 + 5*w^2 - 13*w - 25]', '[9641, 9641, w^3 + w^2 - 13*w]', '[9649, 9649, w^3 + 3*w^2 - 13*w - 21]', '[9649, 9649, 15*w^3 + 26*w^2 - 136*w - 156]', '[9649, 9649, 10*w^3 + 19*w^2 - 86*w - 121]', '[9649, 9649, 4*w^3 + 4*w^2 - 37*w - 23]', '[9661, 9661, 33*w^3 + 58*w^2 - 298*w - 365]', '[9661, 9661, 23*w^3 + 40*w^2 - 207*w - 252]', '[9661, 9661, -56*w^3 - 98*w^2 + 511*w + 624]', '[9661, 9661, -11*w^3 - 16*w^2 + 99*w + 100]', '[9679, 9679, 4*w^3 + 5*w^2 - 37*w - 41]', '[9679, 9679, 10*w^3 + 17*w^2 - 91*w - 90]', '[9679, 9679, 7*w^3 + 13*w^2 - 60*w - 94]', '[9679, 9679, -w^3 - w^2 + 6*w - 7]', '[9680, 110, 10*w^3 + 16*w^2 - 90*w - 96]', '[9680, 110, -2*w^3 - 8*w^2 + 12*w + 68]', '[9680, 110, -6*w^3 - 4*w^2 + 56*w + 4]', '[9691, 9691, 6*w - 13]', '[9691, 9691, w^3 - 2*w - 12]', '[9691, 9691, -6*w^3 - 14*w^2 + 49*w + 94]', '[9691, 9691, 2*w^3 + 3*w^2 - 12*w - 29]', '[9691, 9691, -9*w^3 - 18*w^2 + 76*w + 113]', '[9691, 9691, -13*w^3 - 26*w^2 + 111*w + 162]', '[9691, 9691, -6*w^3 - 7*w^2 + 54*w + 38]', '[9691, 9691, 11*w^3 + 16*w^2 - 100*w - 84]', '[9719, 9719, 43*w^3 + 76*w^2 - 394*w - 481]', '[9719, 9719, 18*w^3 + 32*w^2 - 161*w - 202]', '[9719, 9719, 37*w^3 + 64*w^2 - 341*w - 414]', '[9719, 9719, -38*w^3 - 67*w^2 + 351*w + 432]', '[9745, 9745, 83*w^3 + 147*w^2 - 758*w - 932]', '[9745, 9745, -75*w^3 - 133*w^2 + 683*w + 846]', '[9745, 9745, -14*w^3 - 26*w^2 + 126*w + 153]', '[9745, 9745, 67*w^3 + 119*w^2 - 614*w - 761]', '[9755, 9755, 76*w^3 + 134*w^2 - 691*w - 849]', '[9755, 9755, 38*w^3 + 67*w^2 - 344*w - 418]', '[9755, 9755, -66*w^3 - 115*w^2 + 602*w + 736]', '[9755, 9755, 12*w^3 + 20*w^2 - 107*w - 125]', '[9791, 9791, 2*w^3 + 4*w^2 - 16*w - 37]', '[9791, 9791, -4*w^3 - 6*w^2 + 36*w + 47]', '[9791, 9791, -2*w - 11]', '[9791, 9791, -6*w^3 - 10*w^2 + 54*w + 49]', '[9801, 33, -9*w^3 - 18*w^2 + 81*w + 114]', '[9801, 33, -9*w^3 - 18*w^2 + 81*w + 111]', '[9801, 33, 30*w^3 + 54*w^2 - 273*w - 339]', '[9829, 9829, -5*w^3 - 7*w^2 + 46*w + 49]', '[9829, 9829, -9*w^3 - 15*w^2 + 82*w + 82]', '[9829, 9829, -6*w^3 - 11*w^2 + 51*w + 77]', '[9829, 9829, 2*w^3 + 3*w^2 - 15*w - 10]', '[9869, 9869, 6*w^3 + 14*w^2 - 53*w - 84]', '[9869, 9869, 4*w^3 + 5*w^2 - 33*w - 27]', '[9869, 9869, -7*w^3 - 14*w^2 + 68*w + 88]', '[9869, 9869, -14*w^3 - 25*w^2 + 123*w + 156]', '[9869, 9869, -11*w^3 - 21*w^2 + 103*w + 134]', '[9869, 9869, 22*w^3 + 39*w^2 - 198*w - 237]', '[9869, 9869, 14*w^3 + 27*w^2 - 124*w - 174]', '[9869, 9869, 21*w^3 + 38*w^2 - 191*w - 234]', '[9869, 9869, 15*w^3 + 28*w^2 - 136*w - 167]', '[9869, 9869, 11*w^3 + 20*w^2 - 97*w - 138]', '[9869, 9869, 12*w^3 + 21*w^2 - 108*w - 121]', '[9869, 9869, 7*w^3 + 15*w^2 - 65*w - 100]', '[9869, 9869, -9*w^3 - 16*w^2 + 83*w + 83]', '[9869, 9869, 21*w^3 + 38*w^2 - 188*w - 229]', '[9869, 9869, 19*w^3 + 36*w^2 - 167*w - 223]', '[9869, 9869, -11*w^3 - 19*w^2 + 102*w + 113]', '[9871, 9871, -4*w^3 - 11*w^2 + 36*w + 75]', '[9871, 9871, 13*w^3 + 26*w^2 - 114*w - 160]', '[9871, 9871, 10*w^3 + 20*w^2 - 93*w - 121]', '[9871, 9871, 19*w^3 + 35*w^2 - 171*w - 219]', '[9875, 395, 61*w^3 + 108*w^2 - 557*w - 684]', '[9875, 395, -36*w^3 - 63*w^2 + 327*w + 404]', '[9875, 395, -11*w^3 - 18*w^2 + 102*w + 119]', '[9875, 395, -24*w^3 - 42*w^2 + 223*w + 276]', '[9889, 9889, -8*w^3 - 9*w^2 + 73*w + 31]', '[9889, 9889, 4*w^3 + 8*w^2 - 43*w - 33]', '[9889, 9889, -5*w^3 - 7*w^2 + 41*w + 41]', '[9889, 9889, -3*w^3 - 5*w^2 + 19*w + 50]', '[9889, 9889, -3*w^3 - w^2 + 15*w + 31]', '[9889, 9889, -12*w^3 - 12*w^2 + 113*w + 35]', '[9889, 9889, 8*w^3 + 17*w^2 - 69*w - 115]', '[9889, 9889, 3*w^3 + 7*w^2 - 34*w - 25]', '[9889, 9889, 16*w^3 + 24*w^2 - 145*w - 124]', '[9889, 9889, -w^3 + 5*w^2 + 12*w - 47]', '[9889, 9889, -12*w^3 - 22*w^2 + 108*w + 127]', '[9889, 9889, w^3 + 5*w^2 - 10*w - 27]', '[9889, 9889, 16*w^3 + 30*w^2 - 140*w - 185]', '[9889, 9889, -10*w^3 - 16*w^2 + 91*w + 83]', '[9889, 9889, 6*w^3 + 13*w^2 - 52*w - 76]', '[9889, 9889, 23*w^3 + 41*w^2 - 201*w - 235]', '[9889, 9889, -4*w^2 - 2*w + 31]', '[9889, 9889, 5*w^3 + 12*w^2 - 40*w - 88]', '[9889, 9889, -5*w^3 - 20*w^2 + 36*w + 155]', '[9889, 9889, -w^3 + 5*w^2 - 12]', '[9889, 9889, w^3 - 3*w^2 - 9*w + 31]', '[9889, 9889, -14*w^3 - 28*w^2 + 121*w + 169]', '[9889, 9889, 2*w^3 - w^2 - 21*w + 16]', '[9889, 9889, -w^3 + w^2 + 4*w - 4]', '[9889, 9889, 26*w^3 + 49*w^2 - 227*w - 297]', '[9889, 9889, 10*w^3 + 13*w^2 - 90*w - 59]', '[9889, 9889, 6*w^3 + 7*w^2 - 53*w - 31]', '[9889, 9889, -4*w^3 - 12*w^2 + 45*w + 56]', '[9889, 9889, -9*w^3 - 16*w^2 + 77*w + 103]', '[9889, 9889, -5*w^3 - 9*w^2 + 41*w + 69]', '[9889, 9889, -2*w^3 + 5*w^2 + 8*w - 20]', '[9889, 9889, 5*w^3 + 4*w^2 - 50*w]', '[9895, 9895, -22*w^3 - 40*w^2 + 203*w + 256]', '[9895, 9895, 19*w^3 + 34*w^2 - 171*w - 206]', '[9895, 9895, -74*w^3 - 131*w^2 + 673*w + 830]', '[9895, 9895, -61*w^3 - 106*w^2 + 558*w + 683]', '[9899, 9899, -3*w^3 - 5*w^2 + 32*w + 42]', '[9899, 9899, -30*w^3 - 56*w^2 + 262*w + 337]', '[9899, 9899, -10*w^3 - 15*w^2 + 89*w + 102]', '[9899, 9899, -w^3 + 6*w - 3]', '[9899, 9899, -41*w^3 - 73*w^2 + 376*w + 461]', '[9899, 9899, 2*w^2 + w - 7]', '[9899, 9899, 16*w^3 + 27*w^2 - 143*w - 151]', '[9899, 9899, -7*w^2 + 9*w + 33]', '[9899, 9899, 44*w^3 + 81*w^2 - 387*w - 486]', '[9899, 9899, -5*w^3 - 6*w^2 + 49*w + 18]', '[9899, 9899, -9*w^3 - 14*w^2 + 77*w + 99]', '[9899, 9899, 3*w^3 + w^2 - 23*w - 5]', '[9899, 9899, 11*w^3 + 18*w^2 - 103*w - 122]', '[9899, 9899, -w^3 + w^2 + 11*w - 8]', '[9899, 9899, -12*w^3 - 17*w^2 + 110*w + 79]', '[9899, 9899, -12*w^3 - 22*w^2 + 105*w + 138]', '[9901, 9901, 16*w^3 + 30*w^2 - 143*w - 183]', '[9901, 9901, 12*w^3 + 23*w^2 - 110*w - 145]', '[9901, 9901, -8*w^3 - 14*w^2 + 71*w + 74]', '[9901, 9901, 5*w^3 + 12*w^2 - 46*w - 74]', '[9929, 9929, -7*w^3 - 15*w^2 + 66*w + 97]', '[9929, 9929, -18*w^3 - 33*w^2 + 163*w + 200]', '[9929, 9929, -4*w^3 - 11*w^2 + 35*w + 69]', '[9929, 9929, 15*w^3 + 29*w^2 - 132*w - 184]', '[9931, 9931, -w^3 + w^2 + 11*w - 23]', '[9931, 9931, 12*w^3 + 21*w^2 - 110*w - 141]', '[9931, 9931, 8*w^3 + 15*w^2 - 71*w - 106]', '[9931, 9931, -14*w^3 - 27*w^2 + 124*w + 168]', '[9955, 9955, -6*w^3 - 4*w^2 + 57*w + 5]', '[9955, 9955, 16*w^3 + 35*w^2 - 135*w - 229]', '[9955, 9955, -22*w^3 - 36*w^2 + 197*w + 201]', '[9955, 9955, -8*w^3 - 15*w^2 + 67*w + 89]', '[9955, 9955, 5*w^3 + w^2 - 42*w - 3]', '[9955, 9955, -3*w^3 - 7*w^2 + 19*w + 63]', '[9955, 9955, 9*w^3 + 13*w^2 - 82*w - 71]', '[9955, 9955, -w^3 - 5*w^2 + 17*w + 21]', '[9995, 9995, -24*w^3 - 42*w^2 + 217*w + 270]', '[9995, 9995, 36*w^3 + 63*w^2 - 333*w - 410]', '[9995, 9995, 11*w^3 + 18*w^2 - 103*w - 120]', '[9995, 9995, 61*w^3 + 108*w^2 - 558*w - 685]', '[10000, 10, 10]'], 'label': '4.4.15125.1', 'narrow_class_no': 4, 'primes': ['[5, 5, 4*w^3 + 7*w^2 - 37*w - 45]', '[11, 11, 2*w^3 + 3*w^2 - 18*w - 16]', '[11, 11, -w + 2]', '[16, 2, 2]', '[19, 19, 4*w^3 + 7*w^2 - 36*w - 45]', '[19, 19, -w^3 - w^2 + 9*w + 3]', '[19, 19, -2*w^3 - 4*w^2 + 17*w + 23]', '[19, 19, w^3 + 2*w^2 - 10*w - 10]', '[29, 29, -w - 2]', '[29, 29, -w^3 - 2*w^2 + 8*w + 15]', '[29, 29, 2*w^3 + 3*w^2 - 18*w - 20]', '[29, 29, -3*w^3 - 5*w^2 + 27*w + 28]', '[31, 31, 3*w^3 + 5*w^2 - 27*w - 31]', '[31, 31, -3*w^3 - 5*w^2 + 27*w + 30]', '[31, 31, -2*w^3 - 3*w^2 + 18*w + 17]', '[31, 31, 2*w^3 + 3*w^2 - 18*w - 18]', '[71, 71, -w^3 - 2*w^2 + 10*w + 8]', '[71, 71, 4*w^3 + 8*w^2 - 35*w - 50]', '[71, 71, -4*w^3 - 7*w^2 + 36*w + 47]', '[71, 71, -w^3 - 2*w^2 + 8*w + 17]', '[79, 79, w^3 + 2*w^2 - 10*w - 14]', '[79, 79, -w^3 - w^2 + 9*w + 7]', '[79, 79, -2*w^3 - 4*w^2 + 17*w + 27]', '[79, 79, -4*w^3 - 7*w^2 + 36*w + 41]', '[81, 3, -3]', '[109, 109, -2*w^3 - 3*w^2 + 19*w + 13]', '[109, 109, 3*w^3 + 5*w^2 - 26*w - 26]', '[109, 109, 2*w^3 + 3*w^2 - 19*w - 22]', '[109, 109, 3*w^3 + 5*w^2 - 26*w - 35]', '[139, 139, 4*w^3 + 7*w^2 - 36*w - 40]', '[139, 139, -w^3 - w^2 + 9*w + 8]', '[139, 139, -w^3 - 2*w^2 + 10*w + 15]', '[139, 139, 2*w^3 + 4*w^2 - 17*w - 28]', '[149, 149, 4*w^3 + 8*w^2 - 35*w - 52]', '[149, 149, -3*w^3 - 5*w^2 + 26*w + 34]', '[149, 149, -2*w^3 - 3*w^2 + 19*w + 14]', '[149, 149, -6*w^3 - 11*w^2 + 54*w + 66]', '[181, 181, w^3 + 2*w^2 - 11*w - 13]', '[181, 181, -3*w^3 - 4*w^2 + 27*w + 24]', '[181, 181, -7*w^3 - 12*w^2 + 63*w + 72]', '[181, 181, 3*w^3 + 6*w^2 - 25*w - 39]', '[191, 191, -7*w^3 - 12*w^2 + 66*w + 80]', '[191, 191, 5*w^3 + 9*w^2 - 47*w - 57]', '[191, 191, -2*w^3 - 2*w^2 + 18*w + 9]', '[191, 191, 2*w^3 + 2*w^2 - 17*w - 13]', '[239, 239, 7*w^3 + 13*w^2 - 62*w - 81]', '[239, 239, -2*w^3 - 5*w^2 + 17*w + 32]', '[239, 239, 6*w^3 + 11*w^2 - 55*w - 67]', '[239, 239, -w^3 - 3*w^2 + 10*w + 20]', '[251, 251, 7*w^3 + 13*w^2 - 63*w - 82]', '[251, 251, -5*w^3 - 10*w^2 + 44*w + 61]', '[251, 251, 4*w^3 + 8*w^2 - 37*w - 48]', '[251, 251, -2*w^3 - 5*w^2 + 18*w + 34]', '[311, 311, 5*w^3 + 9*w^2 - 44*w - 50]', '[311, 311, -4*w^3 - 7*w^2 + 37*w + 48]', '[311, 311, 2*w^3 + 4*w^2 - 19*w - 19]', '[311, 311, w^3 + w^2 - 8*w - 11]', '[331, 331, 4*w^3 + 6*w^2 - 36*w - 37]', '[331, 331, -6*w^3 - 10*w^2 + 54*w + 59]', '[331, 331, -2*w - 1]', '[331, 331, -2*w^3 - 4*w^2 + 16*w + 27]', '[349, 349, -3*w^3 - 5*w^2 + 28*w + 27]', '[349, 349, 4*w^3 + 8*w^2 - 35*w - 53]', '[349, 349, -3*w^3 - 6*w^2 + 28*w + 40]', '[349, 349, 6*w^3 + 11*w^2 - 54*w - 65]', '[359, 359, -w^3 - 3*w^2 + 8*w + 19]', '[359, 359, -6*w^3 - 11*w^2 + 53*w + 69]', '[359, 359, 5*w^3 + 9*w^2 - 46*w - 54]', '[359, 359, w^2 - w - 8]', '[401, 401, 5*w^3 + 8*w^2 - 45*w - 50]', '[401, 401, w^3 + 2*w^2 - 7*w - 15]', '[401, 401, w^3 + 2*w^2 - 7*w - 11]', '[401, 401, 5*w^3 + 8*w^2 - 45*w - 46]', '[409, 409, -9*w^3 - 16*w^2 + 81*w + 97]', '[409, 409, w^3 + w^2 - 11*w - 10]', '[409, 409, 6*w^3 + 10*w^2 - 53*w - 66]', '[409, 409, -3*w^3 - 6*w^2 + 29*w + 38]', '[421, 421, -3*w^3 - 4*w^2 + 26*w + 23]', '[421, 421, -4*w^3 - 6*w^2 + 35*w + 39]', '[421, 421, 8*w^3 + 14*w^2 - 71*w - 86]', '[421, 421, -7*w^3 - 12*w^2 + 62*w + 70]', '[439, 439, w^3 + w^2 - 10*w - 9]', '[439, 439, -4*w^3 - 7*w^2 + 35*w + 47]', '[439, 439, 3*w^3 + 5*w^2 - 28*w - 26]', '[439, 439, 2*w^3 + 3*w^2 - 17*w - 14]', '[479, 479, 3*w^3 + 6*w^2 - 29*w - 33]', '[479, 479, 5*w^3 + 10*w^2 - 43*w - 59]', '[479, 479, w^3 - 9*w + 6]', '[479, 479, 9*w^3 + 16*w^2 - 81*w - 102]', '[521, 521, 4*w^3 + 7*w^2 - 38*w - 44]', '[521, 521, 3*w^3 + 4*w^2 - 26*w - 25]', '[521, 521, 5*w^3 + 8*w^2 - 44*w - 46]', '[521, 521, -8*w^3 - 14*w^2 + 71*w + 84]', '[569, 569, 21*w^3 + 37*w^2 - 191*w - 236]', '[569, 569, -13*w^3 - 23*w^2 + 120*w + 149]', '[569, 569, 10*w^3 + 17*w^2 - 92*w - 111]', '[569, 569, -18*w^3 - 32*w^2 + 164*w + 201]', '[631, 631, -2*w^3 - 3*w^2 + 20*w + 25]', '[631, 631, 7*w^3 + 12*w^2 - 64*w - 80]', '[631, 631, -9*w^3 - 17*w^2 + 80*w + 106]', '[631, 631, 19*w^3 + 33*w^2 - 175*w - 215]', '[641, 641, 4*w^3 + 6*w^2 - 35*w - 35]', '[641, 641, 4*w^3 + 6*w^2 - 35*w - 38]', '[641, 641, 7*w^3 + 12*w^2 - 62*w - 71]', '[641, 641, 7*w^3 + 12*w^2 - 62*w - 74]', '[659, 659, 6*w^3 + 11*w^2 - 54*w - 63]', '[659, 659, 4*w^3 + 6*w^2 - 37*w - 38]', '[659, 659, 4*w^3 + 8*w^2 - 35*w - 55]', '[659, 659, 3*w^3 + 6*w^2 - 28*w - 42]', '[661, 661, -27*w^3 - 48*w^2 + 247*w + 306]', '[661, 661, 14*w^3 + 24*w^2 - 129*w - 158]', '[661, 661, 11*w^3 + 19*w^2 - 102*w - 126]', '[661, 661, 2*w^3 + 3*w^2 - 19*w - 24]', '[691, 691, 6*w^3 + 12*w^2 - 53*w - 73]', '[691, 691, 8*w^3 + 15*w^2 - 72*w - 95]', '[691, 691, -5*w^3 - 10*w^2 + 46*w + 60]', '[691, 691, -3*w^3 - 7*w^2 + 27*w + 47]', '[739, 739, -2*w^3 - 5*w^2 + 19*w + 34]', '[739, 739, 7*w^3 + 13*w^2 - 64*w - 78]', '[739, 739, -3*w^3 - 7*w^2 + 26*w + 43]', '[739, 739, 8*w^3 + 15*w^2 - 71*w - 95]', '[751, 751, -4*w^3 - 9*w^2 + 37*w + 59]', '[751, 751, -5*w^3 - 9*w^2 + 43*w + 48]', '[751, 751, -6*w^3 - 10*w^2 + 55*w + 68]', '[751, 751, -10*w^3 - 17*w^2 + 93*w + 114]', '[769, 769, 6*w^3 + 11*w^2 - 52*w - 69]', '[769, 769, w^3 + w^2 - 7*w - 5]', '[769, 769, 2*w^3 + 2*w^2 - 19*w - 11]', '[769, 769, 7*w^3 + 12*w^2 - 64*w - 72]', '[809, 809, -3*w^3 - 4*w^2 + 29*w + 17]', '[809, 809, -5*w^3 - 8*w^2 + 43*w + 54]', '[809, 809, w^3 - 9*w + 9]', '[809, 809, 10*w^3 + 18*w^2 - 90*w - 109]', '[881, 881, -10*w^3 - 17*w^2 + 92*w + 113]', '[881, 881, -6*w^3 - 10*w^2 + 56*w + 69]', '[881, 881, -31*w^3 - 55*w^2 + 283*w + 350]', '[881, 881, -11*w^3 - 19*w^2 + 101*w + 125]', '[911, 911, 5*w^3 + 8*w^2 - 44*w - 49]', '[911, 911, -6*w^3 - 10*w^2 + 53*w + 60]', '[911, 911, 5*w^3 + 8*w^2 - 44*w - 48]', '[911, 911, 6*w^3 + 10*w^2 - 53*w - 61]', '[919, 919, 4*w^3 + 7*w^2 - 37*w - 38]', '[919, 919, 5*w^3 + 9*w^2 - 44*w - 60]', '[919, 919, 8*w^3 + 14*w^2 - 73*w - 85]', '[919, 919, -7*w^3 - 13*w^2 + 61*w + 81]', '[971, 971, 28*w^3 + 49*w^2 - 255*w - 312]', '[971, 971, 16*w^3 + 28*w^2 - 145*w - 176]', '[971, 971, -25*w^3 - 44*w^2 + 227*w + 278]', '[971, 971, 15*w^3 + 26*w^2 - 136*w - 165]', '[991, 991, 5*w^3 + 10*w^2 - 42*w - 64]', '[991, 991, -4*w^3 - 5*w^2 + 36*w + 29]', '[991, 991, -11*w^3 - 19*w^2 + 99*w + 115]', '[991, 991, 10*w^3 + 17*w^2 - 90*w - 108]']}
• 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': [31, 14, -14, -1, 1], 'conductor': 55, 'degree': 4, 'dirichlet_group': [32, 1, 34, 43], 'disc_abs': 15125, 'disc_rad': 55, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[4, 1]]], [5, [0]], [7, [[4, 1]]], [11, [0]], [13, [[4, 1]]], [17, [[4, 1]]], [19, [[1, 4]]], [23, [[4, 1]]], [29, [[1, 4]]], [31, [[1, 4]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[4, 1]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 2], 'galois_label': '4T1', 'galt': 1, 'grd': 11.08980336897316, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.15125.1', 'local_algs': ['5.4.3.2', '11.2.1.2', '11.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 11], 'rd': 11.089803369, 'regulator': {'__RealLiteral__': 0, 'data': '5.29445586371', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} + 2 a^{2} - 9 a - 13 \\)', '\\( a - 3 \\)', '\\( 2 a^{3} + 3 a^{2} - 18 a - 15 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}