Hilbert modular form data - 5.5.24217.1-43.1-a

Formats: - HTML - YAML - JSON - 2026-01-10T21:14:35.120934

• 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': 5, 'dimension': 1, 'disc': 24217, 'field_bad_primes': [61, 397], 'field_label': '5.5.24217.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '5.5.24217.1-43.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [43], 'level_ideal': '[43, 43, -3*w^4 + w^3 + 14*w^2 - 3*w - 6]', 'level_label': '43.1', 'level_norm': 43, 'parallel_weight': 2, 'short_label': '43.1-a', 'weight': '[2, 2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[43, 43, -3*w^4 + w^3 + 14*w^2 - 3*w - 6]', -1]], 'hecke_eigenvalues': [1, -3, -5, 4, 1, 1, 7, 5, 1, 4, 5, -3, -6, 12, 7, -3, 11, -4, -16, 3, 14, 15, -8, 2, 19, -7, -18, 6, 4, 14, 9, -10, -11, 6, 13, 2, 10, -24, -14, 11, 10, -19, -8, 26, -20, 21, -26, -20, -18, 2, -2, 18, -16, 8, 30, -22, 19, 4, -32, 24, 29, -29, -10, 21, 1, -10, -10, -20, -22, -17, -26, -18, -23, 23, -24, -30, 2, 12, -6, 9, -7, -30, 20, -18, -18, -18, -22, -34, 44, -30, 7, 2, 42, -38, 25, -37, 34, 43, 26, 27, -25, 22, 3, -27, -12, 1, 46, -21, -20, -38, 10, 3, -7, 38, 12, -48, 13, 10, 38, -11, -6, -26, -28, -22, 2, 49, -33, 16, -8, 10, 30, 30, -25, 51, -49, -26, 27, 34, 18, 21, -53, 14, -38, -29, -26, 18, -12, 44, 27, -39, 18, -34, -24, 18, -36, -6, 54, -27, -8, -7, 30, 32, 20, 6, 30, 6, -42, 42, 52, 14, -20, -2], 'hecke_polynomial': 'x', 'label': '5.5.24217.1-43.1-a'}
• hmf_fields •

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

  
  {'degree': 5, 'discriminant': 24217, 'ideals': ['[1, 1, 1]', '[5, 5, -2*w^4 + w^3 + 9*w^2 - 2*w - 3]', '[17, 17, -2*w^4 + w^3 + 9*w^2 - 3*w - 5]', '[17, 17, w^2 - 2]', '[23, 23, w^3 - 3*w]', '[25, 25, 2*w^4 - w^3 - 10*w^2 + 2*w + 7]', '[29, 29, 2*w^4 - w^3 - 10*w^2 + 2*w + 4]', '[32, 2, 2]', '[37, 37, -w^4 + w^3 + 4*w^2 - 2*w]', '[41, 41, -3*w^4 + 2*w^3 + 14*w^2 - 5*w - 7]', '[43, 43, -3*w^4 + w^3 + 14*w^2 - 3*w - 6]', '[47, 47, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 6]', '[53, 53, 2*w^4 - w^3 - 8*w^2 + 2*w + 1]', '[53, 53, -2*w^4 + w^3 + 10*w^2 - 4*w - 6]', '[59, 59, -w^4 + 4*w^2 + 1]', '[59, 59, -3*w^4 + 2*w^3 + 14*w^2 - 6*w - 8]', '[61, 61, 4*w^4 - 2*w^3 - 18*w^2 + 5*w + 7]', '[61, 61, 3*w^4 - w^3 - 15*w^2 + 2*w + 7]', '[73, 73, -4*w^4 + 2*w^3 + 18*w^2 - 7*w - 6]', '[83, 83, -2*w^4 + 9*w^2 + 2*w - 4]', '[83, 83, -2*w^4 + 2*w^3 + 10*w^2 - 7*w - 6]', '[85, 85, 3*w^4 - w^3 - 14*w^2 + 3*w + 5]', '[85, 85, w^4 - 5*w^2 - 2*w + 3]', '[97, 97, -2*w^4 + w^3 + 8*w^2 - 3*w + 1]', '[97, 97, -w^3 + w^2 + 4*w - 1]', '[101, 101, 2*w^4 - 9*w^2 - w + 5]', '[103, 103, 2*w^4 - 2*w^3 - 9*w^2 + 8*w + 2]', '[107, 107, -3*w^4 + w^3 + 15*w^2 - 4*w - 8]', '[109, 109, -3*w^4 + w^3 + 13*w^2 - 2*w - 4]', '[113, 113, 4*w^4 - 3*w^3 - 18*w^2 + 8*w + 8]', '[115, 115, -2*w^4 + 2*w^3 + 10*w^2 - 7*w - 5]', '[121, 11, -w^4 - w^3 + 5*w^2 + 4*w - 2]', '[125, 125, -2*w^4 + 2*w^3 + 9*w^2 - 5*w - 5]', '[131, 131, -4*w^4 + w^3 + 18*w^2 - 5]', '[139, 139, 2*w^3 - w^2 - 8*w + 1]', '[139, 139, -2*w^4 + w^3 + 9*w^2 - 3]', '[145, 145, w^4 - w^3 - 4*w^2 + 2*w - 1]', '[149, 149, 5*w^4 - 2*w^3 - 23*w^2 + 4*w + 11]', '[149, 149, w^4 - 4*w^2 - 3]', '[149, 149, 4*w^4 - 3*w^3 - 19*w^2 + 10*w + 8]', '[151, 151, 2*w^4 - w^3 - 9*w^2 + 5*w + 4]', '[157, 157, -2*w^4 - w^3 + 10*w^2 + 5*w - 4]', '[157, 157, 5*w^4 - 3*w^3 - 24*w^2 + 8*w + 13]', '[160, 10, -4*w^4 + 2*w^3 + 18*w^2 - 4*w - 6]', '[163, 163, -2*w^4 + 11*w^2 + w - 7]', '[167, 167, w^4 - 3*w^2 - 2*w - 3]', '[167, 167, -3*w^4 + 3*w^3 + 14*w^2 - 10*w - 9]', '[169, 13, 3*w^4 - 2*w^3 - 14*w^2 + 6*w + 3]', '[185, 185, 2*w^4 - 2*w^3 - 9*w^2 + 7*w + 6]', '[191, 191, -3*w^4 + w^3 + 15*w^2 - w - 6]', '[193, 193, 3*w^4 - 2*w^3 - 14*w^2 + 4*w + 5]', '[199, 199, -5*w^4 + 2*w^3 + 23*w^2 - 3*w - 10]', '[205, 205, -w^4 - w^3 + 5*w^2 + 3*w - 2]', '[215, 215, -w^4 + w^3 + 3*w^2 - 3*w + 2]', '[223, 223, -4*w^4 + w^3 + 20*w^2 - w - 9]', '[223, 223, -w^4 + 3*w^2 + 2]', '[233, 233, w^3 - 4*w - 4]', '[235, 235, 4*w^4 - 4*w^3 - 17*w^2 + 13*w + 5]', '[241, 241, -3*w^4 + 2*w^3 + 15*w^2 - 7*w - 7]', '[243, 3, -3]', '[251, 251, -3*w^4 + 3*w^3 + 13*w^2 - 8*w - 6]', '[257, 257, -4*w^4 + w^3 + 20*w^2 - 2*w - 9]', '[257, 257, -3*w^4 + 2*w^3 + 15*w^2 - 5*w - 11]', '[265, 265, -w^4 - w^3 + 6*w^2 + 4*w - 3]', '[265, 265, 5*w^4 - 2*w^3 - 23*w^2 + 6*w + 6]', '[269, 269, 2*w^4 - 11*w^2 - w + 6]', '[271, 271, w^4 + w^3 - 5*w^2 - 6*w + 2]', '[271, 271, 3*w^4 - w^3 - 15*w^2 + 8]', '[277, 277, -w^4 - w^3 + 6*w^2 + 3*w - 5]', '[283, 283, -5*w^4 + 3*w^3 + 23*w^2 - 10*w - 10]', '[289, 17, -3*w^4 + w^3 + 14*w^2 - 4]', '[289, 289, -w^4 + 4*w^2 - w + 1]', '[289, 289, -2*w^3 + 7*w + 1]', '[293, 293, -w^4 + w^3 + 6*w^2 - 3*w - 8]', '[295, 295, w^4 + w^3 - 5*w^2 - 6*w + 3]', '[295, 295, -5*w^4 + 2*w^3 + 22*w^2 - 4*w - 6]', '[305, 305, -w^4 + 6*w^2 - w - 6]', '[305, 305, 3*w^4 - 2*w^3 - 13*w^2 + 7*w + 1]', '[307, 307, -w^4 - w^3 + 6*w^2 + 4*w - 2]', '[311, 311, -w^3 + 2*w^2 + 3*w - 2]', '[311, 311, 2*w^4 - w^3 - 10*w^2 + 5*w + 7]', '[313, 313, -5*w^4 + 4*w^3 + 23*w^2 - 12*w - 11]', '[313, 313, -w^4 - w^3 + 5*w^2 + 3*w - 3]', '[347, 347, -w^4 + 2*w^3 + 3*w^2 - 7*w + 1]', '[353, 353, -3*w^4 + 14*w^2 + 3*w - 7]', '[353, 353, -3*w^4 + 3*w^3 + 13*w^2 - 9*w - 7]', '[365, 365, -7*w^4 + 5*w^3 + 30*w^2 - 15*w - 8]', '[367, 367, -w^4 + w^3 + 5*w^2 - 6*w - 4]', '[367, 367, -3*w^4 + w^3 + 15*w^2 - 3*w - 5]', '[379, 379, 5*w^4 - 2*w^3 - 23*w^2 + 6*w + 9]', '[383, 383, 4*w^4 - 2*w^3 - 19*w^2 + 7*w + 11]', '[391, 391, -w^4 + 5*w^2 - 6]', '[391, 391, w^4 + w^3 - 4*w^2 - 6*w + 1]', '[397, 397, w^4 - 3*w^2 - w - 3]', '[397, 397, -2*w^3 + w^2 + 8*w]', '[401, 401, 2*w^4 - 2*w^3 - 8*w^2 + 5*w]', '[415, 415, 2*w^4 - 3*w^3 - 8*w^2 + 11*w + 2]', '[415, 415, -w^4 + 3*w^3 + 4*w^2 - 11*w - 2]', '[421, 421, -4*w^4 + 2*w^3 + 17*w^2 - 5*w - 6]', '[421, 421, -w^4 + 2*w^3 + 6*w^2 - 8*w - 5]', '[425, 425, 2*w^4 + w^3 - 9*w^2 - 6*w + 3]', '[425, 425, -4*w^4 + 3*w^3 + 18*w^2 - 9*w - 9]', '[431, 431, 5*w^4 - 2*w^3 - 22*w^2 + 5*w + 7]', '[431, 431, -w^4 - w^3 + 6*w^2 + 5*w - 4]', '[439, 439, 4*w^4 - 2*w^3 - 19*w^2 + 7*w + 10]', '[443, 443, 4*w^4 - w^3 - 19*w^2 + 3*w + 8]', '[457, 457, -3*w^4 + 3*w^3 + 15*w^2 - 10*w - 9]', '[461, 461, -w^3 + 6*w]', '[461, 461, 3*w^4 - 3*w^3 - 14*w^2 + 9*w + 8]', '[463, 463, 5*w^4 - 3*w^3 - 23*w^2 + 7*w + 8]', '[485, 485, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 9]', '[485, 485, -10*w^4 + 5*w^3 + 45*w^2 - 13*w - 14]', '[493, 493, 5*w^4 - 2*w^3 - 23*w^2 + 3*w + 9]', '[493, 493, 2*w^3 - w^2 - 7*w + 1]', '[499, 499, 6*w^4 - 3*w^3 - 27*w^2 + 7*w + 11]', '[505, 505, -4*w^4 + 3*w^3 + 19*w^2 - 8*w - 10]', '[509, 509, 2*w^4 - w^3 - 8*w^2 + w - 1]', '[509, 509, 3*w^4 - 2*w^3 - 13*w^2 + 6*w + 7]', '[515, 515, 9*w^4 - 7*w^3 - 40*w^2 + 21*w + 15]', '[521, 521, w^3 - 6*w + 1]', '[523, 523, 4*w^4 - 2*w^3 - 18*w^2 + 3*w + 7]', '[529, 529, 4*w^4 - 2*w^3 - 17*w^2 + 4*w + 6]', '[535, 535, w^4 + w^3 - 7*w^2 - 3*w + 5]', '[541, 541, w^2 + w - 5]', '[544, 34, -4*w^4 + 2*w^3 + 18*w^2 - 6*w - 10]', '[544, 34, 2*w^2 - 4]', '[545, 545, -3*w^4 + w^3 + 13*w^2 - 3*w - 1]', '[547, 547, 5*w^4 - 2*w^3 - 25*w^2 + 4*w + 12]', '[547, 547, -6*w^4 + 3*w^3 + 27*w^2 - 10*w - 9]', '[557, 557, -4*w^4 + 3*w^3 + 18*w^2 - 10*w - 9]', '[557, 557, -4*w^4 + w^3 + 19*w^2 - 3*w - 6]', '[557, 557, 3*w^4 - 2*w^3 - 14*w^2 + 8*w + 7]', '[563, 563, -w^4 + 3*w^3 + 4*w^2 - 11*w + 1]', '[565, 565, 3*w^4 - 3*w^3 - 14*w^2 + 12*w + 3]', '[569, 569, w^2 + 3*w - 2]', '[575, 575, 2*w^4 - 11*w^2 - 2*w + 6]', '[577, 577, -5*w^4 + 2*w^3 + 23*w^2 - 6*w - 8]', '[587, 587, -2*w^4 + 10*w^2 + 3*w - 6]', '[593, 593, 4*w^4 - 3*w^3 - 19*w^2 + 8*w + 11]', '[601, 601, -4*w^4 + w^3 + 18*w^2 - 3*w - 6]', '[601, 601, -5*w^4 + 3*w^3 + 24*w^2 - 10*w - 13]', '[601, 601, -w^4 + 5*w^2 + 3*w - 3]', '[605, 55, 3*w^4 - 3*w^3 - 15*w^2 + 11*w + 9]', '[607, 607, -3*w^4 + 2*w^3 + 15*w^2 - 8*w - 9]', '[613, 613, 3*w^4 - 14*w^2 - 2*w + 8]', '[617, 617, -4*w^4 + w^3 + 19*w^2 - 3*w - 7]', '[619, 619, w^3 + w^2 - 3*w - 5]', '[625, 5, 4*w^4 - 2*w^3 - 19*w^2 + 3*w + 8]', '[625, 625, 5*w^4 - 2*w^3 - 23*w^2 + 3*w + 7]', '[629, 629, -w^4 - w^3 + 5*w^2 + 5*w - 5]', '[629, 629, 4*w^4 - w^3 - 17*w^2 + w + 4]', '[631, 631, 3*w^4 - w^3 - 12*w^2 - 1]', '[641, 641, -w^4 + 2*w^3 + 3*w^2 - 7*w]', '[647, 647, 2*w^2 - w - 5]', '[647, 647, -2*w^3 + w^2 + 8*w - 5]', '[647, 647, 5*w^4 - 3*w^3 - 23*w^2 + 9*w + 12]', '[655, 655, 3*w^4 - 13*w^2 - 2*w - 2]', '[661, 661, -8*w^4 + 3*w^3 + 39*w^2 - 7*w - 19]', '[667, 667, w^4 - 5*w^2 - 3*w + 4]', '[677, 677, -7*w^4 + 4*w^3 + 34*w^2 - 11*w - 17]', '[691, 691, w^2 + 2*w - 4]', '[691, 691, -5*w^4 + 2*w^3 + 23*w^2 - 3*w - 8]', '[691, 691, -7*w^4 + 5*w^3 + 32*w^2 - 14*w - 15]', '[695, 695, -w^3 + w^2 + 3*w + 3]', '[695, 695, -7*w^4 + 6*w^3 + 33*w^2 - 21*w - 16]', '[697, 697, -5*w^4 + 2*w^3 + 22*w^2 - 4*w - 7]', '[697, 697, -w^4 - w^3 + 6*w^2 + 5*w - 3]', '[701, 701, w - 4]', '[709, 709, -3*w^4 + 3*w^3 + 14*w^2 - 8*w - 7]', '[709, 709, 5*w^4 - 2*w^3 - 24*w^2 + 5*w + 9]', '[709, 709, -w^4 + w^3 + 5*w^2 - 3*w - 7]', '[719, 719, -3*w^4 + 13*w^2 + w - 7]', '[719, 719, -3*w^4 + 14*w^2 - 4]', '[725, 725, 6*w^4 - 3*w^3 - 28*w^2 + 8*w + 9]', '[727, 727, -7*w^4 + 4*w^3 + 32*w^2 - 10*w - 16]', '[727, 727, -3*w^4 + w^3 + 14*w^2 - 5*w - 8]', '[731, 731, -w - 4]', '[731, 731, -3*w^4 + 3*w^3 + 15*w^2 - 10*w - 8]', '[733, 733, -3*w^4 + 2*w^3 + 15*w^2 - 8*w - 10]', '[733, 733, -3*w^4 + 3*w^3 + 13*w^2 - 10*w - 7]', '[733, 733, 8*w^4 - 4*w^3 - 38*w^2 + 9*w + 15]', '[736, 46, 2*w^3 - 6*w]', '[739, 739, 4*w^4 - 3*w^3 - 20*w^2 + 9*w + 11]', '[739, 739, -w^4 + w^3 + 5*w^2 - 3*w + 1]', '[743, 743, -5*w^4 + 4*w^3 + 24*w^2 - 13*w - 16]', '[743, 743, w^4 - 7*w^2 - 2*w + 5]', '[745, 745, 3*w^3 - w^2 - 12*w - 1]', '[745, 745, 9*w^4 - 4*w^3 - 40*w^2 + 8*w + 12]', '[745, 745, 6*w^4 - 6*w^3 - 26*w^2 + 19*w + 8]', '[751, 751, -w^4 + 2*w^3 + 3*w^2 - 7*w - 1]', '[755, 755, 3*w^4 - 3*w^3 - 12*w^2 + 10*w + 4]', '[757, 757, 5*w^4 - 2*w^3 - 22*w^2 + 5*w + 8]', '[757, 757, w^4 + w^3 - 6*w^2 - 5*w + 2]', '[761, 761, 8*w^4 - 3*w^3 - 38*w^2 + 8*w + 18]', '[761, 761, 3*w^4 - w^3 - 14*w^2 + 2*w + 10]', '[761, 761, -4*w^4 + 3*w^3 + 19*w^2 - 7*w - 10]', '[769, 769, -w^4 + 2*w^3 + 5*w^2 - 8*w - 1]', '[773, 773, 9*w^4 - 4*w^3 - 41*w^2 + 9*w + 15]', '[773, 773, 4*w^4 - 2*w^3 - 18*w^2 + 3*w + 6]', '[773, 773, 2*w^2 - 5]', '[785, 785, 4*w^4 - 4*w^3 - 20*w^2 + 15*w + 13]', '[785, 785, -2*w^4 - w^3 + 10*w^2 + 6*w - 7]', '[787, 787, -w^4 + 6*w^2 - w - 7]', '[787, 787, w^4 - w^3 - 6*w^2 + w + 6]', '[799, 799, -w^3 + w^2 + 2*w - 4]', '[799, 799, -5*w^4 + 4*w^3 + 23*w^2 - 11*w - 10]', '[800, 50, 4*w^4 - 2*w^3 - 20*w^2 + 4*w + 14]', '[815, 815, 6*w^4 - 3*w^3 - 29*w^2 + 10*w + 14]', '[821, 821, 2*w^4 - w^3 - 9*w^2 + 4*w + 8]', '[823, 823, 6*w^4 - w^3 - 27*w^2 - w + 8]', '[827, 827, -3*w^4 + 2*w^3 + 16*w^2 - 6*w - 9]', '[827, 827, -8*w^4 + 5*w^3 + 37*w^2 - 16*w - 17]', '[835, 835, 3*w^3 - 14*w - 1]', '[835, 835, 6*w^4 - w^3 - 28*w^2 + w + 7]', '[839, 839, 2*w^4 - 10*w^2 + w + 8]', '[841, 841, -4*w^4 + 3*w^3 + 19*w^2 - 11*w - 10]', '[845, 65, 9*w^4 - 6*w^3 - 40*w^2 + 16*w + 12]', '[851, 851, -4*w^4 + w^3 + 20*w^2 - 2*w - 8]', '[853, 853, 2*w^4 - 2*w^3 - 11*w^2 + 7*w + 7]', '[857, 857, 5*w^4 - 2*w^3 - 24*w^2 + 7*w + 14]', '[877, 877, -w^4 + 2*w^3 + 5*w^2 - 10*w - 6]', '[883, 883, 3*w^4 - 3*w^3 - 15*w^2 + 12*w + 10]', '[887, 887, -4*w^4 + w^3 + 17*w^2 - w - 7]', '[901, 901, 2*w^4 - 2*w^3 - 11*w^2 + 7*w + 6]', '[901, 901, -2*w^4 + w^3 + 10*w^2 - 3*w - 1]', '[901, 901, -4*w^4 + w^3 + 20*w^2 - 4*w - 13]', '[901, 901, -4*w^4 + 3*w^3 + 19*w^2 - 7*w - 11]', '[907, 907, 2*w^4 - 11*w^2 - w + 2]', '[907, 907, -2*w^4 - w^3 + 10*w^2 + 4*w - 5]', '[911, 911, -9*w^4 + 4*w^3 + 43*w^2 - 9*w - 19]', '[919, 919, 4*w^4 - w^3 - 20*w^2 + w + 8]', '[925, 925, w^4 - 7*w^2 + 7]', '[928, 58, 4*w^4 - 2*w^3 - 20*w^2 + 4*w + 8]', '[937, 937, w^4 - 7*w^2 - 2*w + 4]', '[943, 943, -4*w^4 + 2*w^3 + 20*w^2 - 5*w - 8]', '[947, 947, 2*w^4 + 2*w^3 - 10*w^2 - 9*w + 3]', '[953, 953, -2*w^3 + 5*w + 4]', '[955, 955, -w^2 + 2*w + 5]', '[961, 31, -4*w^4 + w^3 + 19*w^2 - w - 4]', '[965, 965, 3*w^4 - 2*w^3 - 14*w^2 + 6*w + 2]', '[967, 967, 8*w^4 - 5*w^3 - 37*w^2 + 13*w + 18]', '[967, 967, 3*w^4 - w^3 - 13*w^2 - 2*w + 3]', '[971, 971, -4*w^4 + 3*w^3 + 21*w^2 - 10*w - 15]', '[971, 971, -3*w^4 + 12*w^2 + 3*w - 4]', '[971, 971, w^4 - 6*w^2 + 3*w + 6]', '[983, 983, -7*w^4 + 2*w^3 + 34*w^2 - 5*w - 16]', '[983, 983, w^4 - 7*w^2 - w + 8]', '[989, 989, -3*w^4 + 2*w^3 + 12*w^2 - 4*w]', '[991, 991, -4*w^4 + 4*w^3 + 19*w^2 - 15*w - 12]', '[991, 991, -8*w^4 + 3*w^3 + 37*w^2 - 5*w - 15]', '[991, 991, -w^4 + w^3 + 7*w^2 - 3*w - 7]', '[995, 995, w^4 - w^3 - 5*w^2 + 2*w + 8]', '[997, 997, -8*w^4 + 5*w^3 + 37*w^2 - 16*w - 16]', '[1003, 1003, 5*w^4 - 3*w^3 - 25*w^2 + 9*w + 14]', '[1003, 1003, w^4 - w^3 - 4*w^2 + w - 2]', '[1003, 1003, 5*w^4 - 2*w^3 - 24*w^2 + 5*w + 16]', '[1003, 1003, -3*w^4 + 3*w^3 + 15*w^2 - 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9*w - 13]', '[1357, 1357, -5*w^4 + w^3 + 23*w^2 - 2*w - 8]', '[1357, 1357, -w^4 + 2*w^3 + 3*w^2 - 9*w - 2]', '[1361, 1361, -7*w^4 + 3*w^3 + 34*w^2 - 6*w - 15]', '[1363, 1363, -2*w^4 + 2*w^3 + 8*w^2 - 9*w - 1]', '[1367, 1367, 3*w^4 + w^3 - 13*w^2 - 6*w + 4]', '[1369, 1369, -w^4 + 6*w^2 - w - 8]', '[1373, 1373, 6*w^4 - 2*w^3 - 27*w^2 + 2*w + 7]', '[1373, 1373, 6*w^4 - 3*w^3 - 28*w^2 + 6*w + 10]', '[1376, 86, -6*w^4 + 2*w^3 + 28*w^2 - 6*w - 12]', '[1385, 1385, -5*w^4 + 5*w^3 + 21*w^2 - 15*w - 9]', '[1399, 1399, 3*w^4 - w^3 - 14*w^2 + 2*w + 1]', '[1403, 1403, 5*w^4 - 3*w^3 - 23*w^2 + 11*w + 10]', '[1403, 1403, 3*w^4 - 3*w^3 - 15*w^2 + 7*w + 9]', '[1411, 1411, w^4 - w^3 - 7*w^2 + 3*w + 8]', '[1411, 1411, -5*w^4 + 4*w^3 + 24*w^2 - 11*w - 12]', '[1411, 1411, -2*w^4 + 10*w^2 - w - 9]', '[1411, 1411, 4*w^4 - 3*w^3 - 18*w^2 + 10*w + 10]', '[1415, 1415, -5*w^4 + 5*w^3 + 21*w^2 - 17*w - 5]', '[1427, 1427, 7*w^4 - 2*w^3 - 32*w^2 + 4*w + 11]', '[1429, 1429, 3*w^4 - 3*w^3 - 13*w^2 + 12*w + 3]', '[1429, 1429, -w^4 + w^3 + 7*w^2 - 4*w - 10]', '[1445, 85, -2*w^4 - w^3 + 10*w^2 + 3*w - 6]', '[1445, 1445, -5*w^4 + 3*w^3 + 23*w^2 - 6*w - 9]', '[1445, 1445, -6*w^4 + 3*w^3 + 26*w^2 - 7*w - 8]', '[1447, 1447, -6*w^4 + 4*w^3 + 29*w^2 - 10*w - 15]', '[1451, 1451, 5*w^4 - 4*w^3 - 23*w^2 + 14*w + 13]', '[1451, 1451, 3*w^4 - 3*w^3 - 14*w^2 + 11*w + 11]', '[1459, 1459, 6*w^4 - 2*w^3 - 27*w^2 + 6*w + 10]', '[1459, 1459, 2*w^4 - w^3 - 12*w^2 + 4*w + 10]', '[1465, 1465, 9*w^4 - 3*w^3 - 41*w^2 + 5*w + 14]', '[1471, 1471, -3*w^4 + w^3 + 16*w^2 - 3*w - 6]', '[1475, 1475, 2*w^4 - w^3 - 10*w^2 + 3*w + 10]', '[1475, 1475, -12*w^4 + 6*w^3 + 58*w^2 - 15*w - 33]', '[1481, 1481, -7*w^4 + 5*w^3 + 32*w^2 - 16*w - 15]', '[1483, 1483, -4*w^4 + 2*w^3 + 20*w^2 - 8*w - 13]', '[1487, 1487, 5*w^4 - w^3 - 22*w^2 + 7]', '[1487, 1487, 4*w^4 - 3*w^3 - 20*w^2 + 10*w + 9]', '[1504, 94, -6*w^4 + 4*w^3 + 28*w^2 - 14*w - 12]', '[1511, 1511, -6*w^4 + 4*w^3 + 28*w^2 - 10*w - 15]', '[1517, 1517, 6*w^4 - 2*w^3 - 27*w^2 + 4*w + 12]', '[1523, 1523, -6*w^4 + 4*w^3 + 29*w^2 - 13*w - 12]', '[1523, 1523, -4*w^4 + 18*w^2 + w - 4]', '[1523, 1523, -2*w^4 - 2*w^3 + 10*w^2 + 9*w - 4]', '[1525, 1525, 13*w^4 - 4*w^3 - 63*w^2 + 9*w + 33]', '[1525, 1525, 11*w^4 - 5*w^3 - 52*w^2 + 11*w + 25]', '[1531, 1531, 6*w^4 - 2*w^3 - 30*w^2 + 5*w + 14]', '[1535, 1535, 2*w^4 - 2*w^3 - 11*w^2 + 10*w + 8]', '[1537, 1537, 3*w^4 - w^3 - 15*w^2 - w + 8]', '[1537, 1537, -5*w^4 + 2*w^3 + 21*w^2 - 5*w - 6]', '[1555, 1555, -2*w^4 - w^3 + 11*w^2 + 5*w - 4]', '[1555, 1555, 4*w^4 - 2*w^3 - 20*w^2 + 9*w + 9]', '[1565, 1565, -4*w^4 + 5*w^3 + 18*w^2 - 19*w - 5]', '[1565, 1565, 4*w^4 - 3*w^3 - 20*w^2 + 10*w + 10]', '[1579, 1579, 2*w^4 - 7*w^2 - w - 3]', '[1579, 1579, -6*w^4 + 2*w^3 + 27*w^2 - 3*w - 11]', '[1579, 1579, 5*w^4 - w^3 - 22*w^2 + 8]', '[1591, 1591, -w^4 - w^3 + 3*w^2 + 7*w]', '[1597, 1597, 7*w^4 - 3*w^3 - 33*w^2 + 7*w + 12]', '[1601, 1601, w^4 - 6*w^2 + w + 9]', '[1607, 1607, -6*w^4 + 3*w^3 + 26*w^2 - 8*w - 9]', '[1609, 1609, -6*w^4 + w^3 + 29*w^2 - 2*w - 13]', '[1609, 1609, 4*w^4 - 3*w^3 - 17*w^2 + 9*w + 8]', '[1627, 1627, -2*w^4 + w^3 + 11*w^2 - w - 10]', '[1649, 1649, 5*w^4 - 2*w^3 - 25*w^2 + 4*w + 11]', '[1649, 1649, w^4 + w^3 - 4*w^2 - 5*w + 3]', '[1649, 1649, -7*w^4 + 5*w^3 + 34*w^2 - 14*w - 18]', '[1649, 1649, 2*w^4 - 2*w^3 - 8*w^2 + 5*w - 3]', '[1657, 1657, w^4 - 2*w^3 - 5*w^2 + 9*w]', '[1667, 1667, 6*w^4 - 3*w^3 - 27*w^2 + 8*w + 14]', '[1669, 1669, 5*w^4 - 3*w^3 - 23*w^2 + 11*w + 12]', '[1679, 1679, -7*w^4 + 4*w^3 + 29*w^2 - 14*w - 10]', '[1681, 1681, 2*w^4 + w^3 - 8*w^2 - 6*w + 2]', '[1696, 106, 4*w^4 - 2*w^3 - 16*w^2 + 4*w + 2]', '[1696, 106, -4*w^4 + 2*w^3 + 20*w^2 - 8*w - 12]', '[1697, 1697, 2*w^2 - 2*w - 7]', '[1697, 1697, -w^4 - w^3 + 7*w^2 + 4*w - 5]', '[1699, 1699, w^2 + 2*w - 5]', '[1699, 1699, -7*w^4 + 5*w^3 + 32*w^2 - 13*w - 14]', '[1711, 1711, 5*w^4 - w^3 - 22*w^2 + 3*w + 7]', '[1711, 1711, -3*w^4 + 16*w^2 + 3*w - 9]', '[1717, 1717, -w^4 - w^3 + 3*w^2 + 3*w + 4]', '[1717, 1717, -5*w^4 + 3*w^3 + 23*w^2 - 6*w - 8]', '[1735, 1735, -9*w^4 + 6*w^3 + 42*w^2 - 20*w - 17]', '[1739, 1739, 8*w^4 - 6*w^3 - 35*w^2 + 18*w + 13]', '[1741, 1741, -3*w^4 + 15*w^2 + 4*w - 8]', '[1751, 1751, 7*w^4 - 4*w^3 - 32*w^2 + 9*w + 13]', '[1751, 1751, -3*w^4 + 4*w^3 + 12*w^2 - 12*w - 2]', '[1759, 1759, 3*w^4 - 3*w^3 - 13*w^2 + 9*w + 9]', '[1759, 1759, -w^4 + 3*w^3 + 4*w^2 - 9*w - 2]', '[1759, 1759, -6*w^4 + 4*w^3 + 29*w^2 - 14*w - 15]', '[1763, 1763, 2*w^4 - w^3 - 8*w^2 + 4*w - 2]', '[1765, 1765, 6*w^4 - 5*w^3 - 28*w^2 + 15*w + 16]', '[1765, 1765, -2*w^4 + 3*w^3 + 10*w^2 - 14*w - 4]', '[1769, 1769, 4*w^4 - w^3 - 18*w^2 + 3*w + 12]', '[1769, 1769, -w^4 + w^3 + 2*w^2 - 4*w + 4]', '[1777, 1777, 2*w^4 + w^3 - 10*w^2 - 6*w + 8]', '[1783, 1783, 4*w^4 - 2*w^3 - 19*w^2 + 8*w + 10]', '[1783, 1783, 2*w^4 - w^3 - 7*w^2 + 2*w - 2]', '[1789, 1789, -w^4 - w^3 + 5*w^2 + 7*w - 2]', '[1801, 1801, w^4 + 2*w^3 - 6*w^2 - 6*w + 2]', '[1819, 1819, 6*w^4 - 4*w^3 - 28*w^2 + 8*w + 15]', '[1819, 1819, 6*w^4 - w^3 - 30*w^2 + 4*w + 18]', '[1825, 1825, -7*w^4 + 4*w^3 + 34*w^2 - 11*w - 14]', '[1835, 1835, -w^4 + 3*w^3 + 3*w^2 - 11*w - 3]', '[1835, 1835, -2*w^4 + 4*w^3 + 7*w^2 - 14*w]', '[1849, 1849, 4*w^4 - 3*w^3 - 18*w^2 + 9*w + 11]', '[1853, 1853, 2*w^4 + w^3 - 8*w^2 - 4*w + 4]', '[1853, 1853, 4*w^4 - 2*w^3 - 20*w^2 + 4*w + 7]', '[1861, 1861, 7*w^4 - 2*w^3 - 32*w^2 + 3*w + 14]', '[1861, 1861, 3*w^4 - w^3 - 16*w^2 + 2*w + 6]', '[1861, 1861, 3*w^4 - 3*w^3 - 16*w^2 + 11*w + 12]', '[1871, 1871, -w^4 - 2*w^3 + 6*w^2 + 7*w - 3]', '[1873, 1873, -5*w^4 + w^3 + 24*w^2 - 3*w - 10]', '[1873, 1873, -3*w^4 + w^3 + 16*w^2 - 4*w - 13]', '[1879, 1879, -6*w^4 + 4*w^3 + 27*w^2 - 9*w - 10]', '[1879, 1879, w^4 + w^3 - 4*w^2 - 7*w + 3]', '[1888, 118, -2*w^4 + 8*w^2 + 2]', '[1888, 118, -6*w^4 + 4*w^3 + 28*w^2 - 12*w - 16]', '[1895, 1895, 4*w^4 - 3*w^3 - 16*w^2 + 9*w + 1]', '[1901, 1901, -7*w^4 + 3*w^3 + 34*w^2 - 7*w - 15]', '[1901, 1901, -8*w^4 + 4*w^3 + 38*w^2 - 11*w - 15]', '[1909, 1909, -5*w^4 + 2*w^3 + 23*w^2 - 2*w - 6]', '[1909, 1909, 6*w^4 - 2*w^3 - 26*w^2 + 5*w + 8]', '[1913, 1913, -4*w^4 + 3*w^3 + 19*w^2 - 12*w - 9]', '[1915, 1915, -2*w^4 - w^3 + 11*w^2 + 6*w - 6]', '[1921, 1921, -6*w^4 + 3*w^3 + 29*w^2 - 11*w - 13]', '[1921, 1921, -2*w^4 + w^3 + 10*w^2 - 9]', '[1927, 1927, 3*w^4 - 3*w^3 - 11*w^2 + 9*w - 1]', '[1931, 1931, 7*w^4 - 3*w^3 - 31*w^2 + 8*w + 11]', '[1933, 1933, -w^3 + w^2 + w - 4]', '[1933, 1933, -w^4 + 2*w^3 + 4*w^2 - 10*w - 2]', '[1933, 1933, 3*w^4 - 13*w^2 - 2*w + 7]', '[1951, 1951, -6*w^4 + 5*w^3 + 27*w^2 - 14*w - 12]', '[1952, 122, 8*w^4 - 4*w^3 - 36*w^2 + 10*w + 14]', '[1952, 122, 6*w^4 - 2*w^3 - 30*w^2 + 4*w + 14]', '[1955, 1955, 8*w^4 - 4*w^3 - 37*w^2 + 9*w + 14]', '[1955, 1955, -w^4 + 2*w^2 + 3]', '[1961, 1961, 4*w^4 - 3*w^3 - 17*w^2 + 8*w + 9]', '[1961, 1961, 5*w^4 - 2*w^3 - 23*w^2 + 8*w + 5]', '[1979, 1979, 3*w^4 + w^3 - 15*w^2 - 5*w + 8]', '[1985, 1985, 7*w^4 - 2*w^3 - 32*w^2 + 4*w + 9]', '[1985, 1985, 5*w^4 - 5*w^3 - 24*w^2 + 19*w + 13]', '[1987, 1987, w^2 - 7]', '[1987, 1987, -6*w^4 + 4*w^3 + 28*w^2 - 13*w - 16]', '[1993, 1993, -7*w^4 + 3*w^3 + 31*w^2 - 6*w - 10]', '[1997, 1997, 2*w^4 - w^3 - 8*w^2 + 5*w - 1]', '[2003, 2003, 7*w^4 - 3*w^3 - 33*w^2 + 8*w + 11]', '[2005, 2005, 9*w^4 - 5*w^3 - 42*w^2 + 15*w + 14]', '[2011, 2011, -3*w^4 + w^3 + 15*w^2 + w - 9]', '[2021, 2021, 2*w^4 - 3*w^3 - 9*w^2 + 11*w]', '[2027, 2027, -2*w^4 + w^3 + 12*w^2 - 3*w - 10]', '[2027, 2027, 2*w^4 - 3*w^3 - 11*w^2 + 11*w + 8]', '[2029, 2029, 5*w^4 - 2*w^3 - 25*w^2 + 6*w + 10]', '[2029, 2029, 2*w^4 - 3*w^3 - 11*w^2 + 11*w + 7]', '[2039, 2039, 4*w^4 - 4*w^3 - 18*w^2 + 11*w + 9]', '[2039, 2039, w^3 + w^2 - 2*w - 5]', '[2053, 2053, -7*w^4 + w^3 + 34*w^2 - w - 19]', '[2057, 187, 6*w^4 - w^3 - 28*w^2 + 2*w + 12]', '[2057, 187, 2*w^4 - 10*w^2 - 4*w + 5]', '[2063, 2063, -w^4 - w^3 + 7*w^2 + 4*w - 4]', '[2069, 2069, -6*w^4 + 2*w^3 + 26*w^2 - 4*w - 7]', '[2075, 2075, -7*w^4 + 4*w^3 + 34*w^2 - 13*w - 20]', '[2075, 2075, 9*w^4 - 5*w^3 - 44*w^2 + 14*w + 24]', '[2081, 2081, -w^4 - w^3 + 7*w^2 + 5*w - 6]', '[2081, 2081, -w^4 - 2*w^3 + 6*w^2 + 9*w - 2]', '[2087, 2087, -4*w^4 + 5*w^3 + 20*w^2 - 18*w - 14]', '[2087, 2087, 4*w^4 - w^3 - 16*w^2 + w - 2]', '[2089, 2089, -2*w^4 - w^3 + 8*w^2 + 5*w - 3]', '[2089, 2089, -7*w^4 + w^3 + 35*w^2 - w - 20]', '[2105, 2105, -w^4 + 4*w^3 + 4*w^2 - 14*w - 4]', '[2105, 2105, -4*w^4 + 2*w^3 + 18*w^2 - 8*w - 3]', '[2111, 2111, -5*w^4 + 24*w^2 + 3*w - 14]', '[2117, 2117, 5*w^4 - 2*w^3 - 20*w^2 + 10*w + 4]', '[2125, 2125, -w^4 - 2*w^3 + 6*w^2 + 9*w]', '[2125, 2125, 8*w^4 - 3*w^3 - 39*w^2 + 7*w + 18]', '[2129, 2129, 5*w^4 - 4*w^3 - 25*w^2 + 12*w + 14]', '[2137, 2137, 3*w^3 - w^2 - 11*w]', '[2137, 2137, -6*w^4 + 4*w^3 + 29*w^2 - 10*w - 16]', '[2143, 2143, 8*w^4 - 4*w^3 - 36*w^2 + 10*w + 15]', '[2153, 2153, -w^4 + w^3 + 6*w^2 - w - 7]', '[2155, 2155, 7*w^4 - 5*w^3 - 33*w^2 + 17*w + 16]', '[2155, 2155, -6*w^4 + 3*w^3 + 26*w^2 - 9*w - 4]', '[2161, 2161, 7*w^4 - 3*w^3 - 32*w^2 + 9*w + 11]', '[2161, 2161, -6*w^4 + 3*w^3 + 26*w^2 - 7*w - 9]', '[2161, 2161, 2*w^3 + w^2 - 9*w - 1]', '[2173, 2173, 5*w^4 - 3*w^3 - 24*w^2 + 12*w + 10]', '[2173, 2173, -4*w^4 + w^3 + 22*w^2 - 3*w - 15]', '[2183, 2183, -5*w^4 + 3*w^3 + 24*w^2 - 11*w - 12]', '[2183, 2183, -4*w^4 + 2*w^3 + 16*w^2 - 5*w - 2]', '[2195, 2195, 2*w^3 - 2*w^2 - 8*w + 3]', '[2197, 13, 3*w^4 - w^3 - 14*w^2 - 2*w + 6]', '[2203, 2203, 3*w^4 - 15*w^2 - 4*w + 9]', '[2207, 2207, 6*w^4 - 2*w^3 - 28*w^2 + 6*w + 11]', '[2207, 2207, w^4 - 2*w^3 - 2*w^2 + 7*w - 2]', '[2209, 47, -8*w^4 + 3*w^3 + 38*w^2 - 6*w - 15]', '[2209, 47, -8*w^4 + 3*w^3 + 37*w^2 - 8*w - 15]', '[2209, 2209, 3*w^4 - 2*w^3 - 13*w^2 + 3*w + 1]', '[2213, 2213, w^4 - w^3 - 2*w^2 + 2*w - 5]', '[2215, 2215, w^4 - w^3 - 2*w^2 + 2*w - 4]', '[2221, 2221, w^3 - w - 4]', '[2227, 2227, -4*w^4 + 19*w^2 + 5*w - 8]', '[2227, 2227, -6*w^4 + w^3 + 28*w^2 - w - 9]', '[2231, 2231, -3*w^4 + 4*w^3 + 12*w^2 - 16*w - 4]', '[2231, 2231, 2*w^4 - 8*w^2 + w - 1]', '[2237, 2237, -3*w^4 + w^3 + 12*w^2 + w - 7]', '[2239, 2239, 3*w^4 - 16*w^2 - 3*w + 8]', '[2251, 2251, -4*w^4 + 4*w^3 + 19*w^2 - 12*w - 11]', '[2251, 2251, -6*w^4 + 5*w^3 + 28*w^2 - 15*w - 14]', '[2251, 2251, -w^4 - w^3 + 5*w^2 + 7*w - 4]', '[2257, 2257, 5*w^4 - 3*w^3 - 23*w^2 + 5*w + 10]', '[2257, 2257, 8*w^4 - 4*w^3 - 37*w^2 + 13*w + 13]', '[2267, 2267, w^4 - 3*w^3 - 3*w^2 + 11*w + 2]', '[2269, 2269, -7*w^4 + 5*w^3 + 33*w^2 - 14*w - 16]', '[2273, 2273, -w^3 + 3*w^2 + 3*w - 6]', '[2279, 2279, 6*w^4 - 4*w^3 - 27*w^2 + 9*w + 9]', '[2279, 2279, -5*w^4 + w^3 + 23*w^2 - 13]', '[2281, 2281, -w^4 - w^3 + 5*w^2 + 7*w - 3]', '[2281, 2281, -w^4 + 5*w^2 + 4*w - 3]', '[2285, 2285, -w^4 + 4*w^3 + 4*w^2 - 15*w - 2]', '[2293, 2293, -3*w^4 + 13*w^2 + 4*w - 6]', '[2297, 2297, -w^4 - w^3 + 6*w^2 + 2*w - 7]', '[2305, 2305, -5*w^4 + 5*w^3 + 22*w^2 - 16*w - 11]', '[2305, 2305, w^4 - 3*w^3 - 5*w^2 + 13*w + 2]', '[2309, 2309, 3*w^4 - 4*w^3 - 14*w^2 + 12*w + 8]', '[2309, 2309, 5*w^4 - w^3 - 26*w^2 + 15]', '[2311, 2311, 6*w^4 - 2*w^3 - 27*w^2 + 6*w + 9]', '[2315, 2315, 6*w^4 - 4*w^3 - 27*w^2 + 12*w + 5]', '[2323, 2323, 7*w^4 - 2*w^3 - 34*w^2 + 6*w + 16]', '[2333, 2333, -6*w^4 + w^3 + 31*w^2 - w - 17]', '[2333, 2333, 5*w^4 - 21*w^2 - 4*w + 3]', '[2336, 146, -8*w^4 + 4*w^3 + 36*w^2 - 14*w - 12]', '[2339, 2339, 5*w^4 - 2*w^3 - 23*w^2 + 2*w + 7]', '[2341, 2341, 2*w^4 - 3*w^3 - 7*w^2 + 10*w + 1]', '[2341, 2341, 6*w^4 - 3*w^3 - 29*w^2 + 8*w + 11]', '[2347, 2347, 8*w^4 - 4*w^3 - 38*w^2 + 10*w + 15]', '[2351, 2351, 4*w^4 - 4*w^3 - 20*w^2 + 13*w + 11]', '[2357, 2357, -6*w^4 + 2*w^3 + 29*w^2 - w - 15]', '[2363, 2363, -9*w^4 + 3*w^3 + 43*w^2 - 6*w - 18]', '[2363, 2363, 3*w^4 + w^3 - 14*w^2 - w + 5]', '[2363, 2363, 3*w^4 - 2*w^3 - 15*w^2 + 7]', '[2363, 2363, -w^4 - 2*w^3 + 5*w^2 + 10*w - 4]', '[2369, 2369, 6*w^4 - 4*w^3 - 25*w^2 + 11*w + 5]', '[2371, 2371, -w^4 - w^3 + 4*w^2 + 6*w - 3]', '[2371, 2371, 5*w^4 - w^3 - 24*w^2 + 3*w + 9]', '[2371, 2371, -4*w^4 + 4*w^3 + 18*w^2 - 11*w - 10]', '[2381, 2381, -4*w^4 + 3*w^3 + 18*w^2 - 9*w - 12]', '[2393, 2393, 3*w^4 - 2*w^3 - 12*w^2 + 4*w - 1]', '[2393, 2393, -4*w^4 + w^3 + 20*w^2 - 4*w - 14]', '[2399, 2399, 5*w^4 - w^3 - 25*w^2 + w + 10]', '[2407, 2407, -w^4 - 2*w^3 + 4*w^2 + 8*w - 2]', '[2407, 2407, w^3 - 2*w^2 - 7*w + 3]', '[2411, 2411, 7*w^4 - 2*w^3 - 32*w^2 + w + 11]', '[2417, 2417, w^4 + 2*w^3 - 6*w^2 - 9*w + 1]', '[2419, 2419, -6*w^4 + 4*w^3 + 27*w^2 - 12*w - 13]', '[2419, 2419, 5*w^4 - 2*w^3 - 25*w^2 + 3*w + 18]', '[2425, 2425, 4*w^4 - w^3 - 21*w^2 + 2*w + 19]', '[2425, 2425, -5*w^4 + 25*w^2 + 2*w - 14]', '[2437, 2437, 5*w^4 - 2*w^3 - 21*w^2 + 3*w + 6]', '[2441, 2441, -w^4 - w^3 + 4*w^2 + 5*w - 4]', '[2459, 2459, 6*w^4 - w^3 - 29*w^2 + 2*w + 12]', '[2461, 2461, -5*w^4 + 2*w^3 + 21*w^2 - 4*w - 9]', '[2465, 2465, 5*w^4 - 2*w^3 - 23*w^2 + 8*w + 12]', '[2465, 2465, -w^4 + 3*w^2 - 2*w + 3]', '[2467, 2467, 5*w^4 - 4*w^3 - 24*w^2 + 10*w + 12]', '[2467, 2467, -2*w^4 - w^3 + 8*w^2 + 7*w - 2]', '[2473, 2473, 8*w^4 - 5*w^3 - 36*w^2 + 13*w + 17]', '[2477, 2477, 7*w^4 - 2*w^3 - 34*w^2 + 4*w + 14]', '[2477, 2477, 12*w^4 - 7*w^3 - 57*w^2 + 20*w + 26]', '[2491, 2491, 5*w^4 - 3*w^3 - 22*w^2 + 9*w + 11]', '[2491, 2491, w - 5]', '[2495, 2495, 3*w^4 - 2*w^3 - 13*w^2 + 8*w - 1]', '[2501, 2501, -w^4 - w^3 + 6*w^2 + 7*w - 8]', '[2501, 2501, -7*w^4 + w^3 + 35*w^2 - 2*w - 20]', '[2507, 2507, -3*w^4 + 2*w^3 + 13*w^2 - 10*w - 7]', '[2525, 2525, 2*w^3 - 9*w + 2]', '[2533, 2533, 7*w^4 - 5*w^3 - 33*w^2 + 14*w + 19]', '[2533, 2533, w^4 - w^3 - 2*w^2 + 3*w - 4]', '[2533, 2533, 2*w^4 - w^3 - 11*w^2 + 5*w + 11]', '[2533, 2533, -w^4 + w^3 + 2*w^2 - w + 6]', '[2533, 2533, -7*w^4 + 5*w^3 + 31*w^2 - 15*w - 13]', '[2533, 2533, 4*w^4 - 4*w^3 - 19*w^2 + 12*w + 12]', '[2537, 2537, -6*w^4 + 3*w^3 + 29*w^2 - 7*w - 11]', '[2537, 2537, 5*w^4 - 25*w^2 - 2*w + 15]', '[2539, 2539, -w - 5]', '[2539, 2539, -4*w^4 + w^3 + 20*w^2 - 2*w - 16]', '[2543, 2543, 7*w^4 - 4*w^3 - 32*w^2 + 9*w + 12]', '[2545, 2545, -w^3 + 7*w - 1]', '[2545, 2545, 8*w^4 - 3*w^3 - 37*w^2 + 7*w + 10]', '[2549, 2549, w^4 - w^3 - 5*w^2 + 3*w - 2]', '[2567, 2567, -3*w^4 + 4*w^3 + 15*w^2 - 9*w - 7]', '[2567, 2567, -2*w^3 - w^2 + 2*w - 2]', '[2575, 2575, -2*w^4 - w^3 + 10*w^2 + 7*w - 9]', '[2593, 2593, -2*w^3 + 11*w - 4]', '[2599, 2599, 6*w^4 - 3*w^3 - 29*w^2 + 9*w + 10]', '[2605, 2605, -7*w^4 + 6*w^3 + 31*w^2 - 18*w - 14]', '[2609, 2609, 5*w^4 - w^3 - 24*w^2 + 7]', '[2615, 2615, w^4 - 5*w^2 + w - 3]', '[2623, 2623, -6*w^4 + 3*w^3 + 30*w^2 - 5*w - 19]', '[2623, 2623, -2*w^3 + 2*w^2 + 6*w - 7]', '[2645, 2645, 2*w^4 + 2*w^3 - 10*w^2 - 8*w + 3]', '[2656, 166, -4*w^4 + 18*w^2 + 4*w - 8]', '[2656, 166, -4*w^4 + 4*w^3 + 20*w^2 - 14*w - 12]', '[2657, 2657, 2*w^4 - 2*w^3 - 8*w^2 + 4*w - 1]', '[2657, 2657, 6*w^4 - 2*w^3 - 28*w^2 + 6*w + 9]', '[2669, 2669, 9*w^4 - 2*w^3 - 43*w^2 + 3*w + 19]', '[2669, 2669, -9*w^4 + 4*w^3 + 43*w^2 - 12*w - 23]', '[2669, 2669, 4*w^4 - 19*w^2 - 5*w + 9]', '[2669, 2669, -9*w^4 + 4*w^3 + 45*w^2 - 8*w - 28]', '[2671, 2671, 4*w^4 - 2*w^3 - 20*w^2 + 3*w + 5]', '[2675, 2675, -13*w^4 + 5*w^3 + 65*w^2 - 13*w - 36]', '[2677, 2677, -2*w^4 + w^3 + 12*w^2 - 3*w - 11]', '[2683, 2683, 5*w^4 - 4*w^3 - 24*w^2 + 11*w + 15]', '[2683, 2683, 5*w^4 - 4*w^3 - 25*w^2 + 13*w + 15]', '[2683, 2683, -5*w^4 + 2*w^3 + 24*w^2 - 8*w - 12]', '[2687, 2687, -w^4 + 5*w^2 + 4*w - 4]', '[2687, 2687, -10*w^4 + 7*w^3 + 46*w^2 - 20*w - 23]', '[2689, 2689, -8*w^4 + 6*w^3 + 37*w^2 - 20*w - 19]', '[2693, 2693, -5*w^4 + 2*w^3 + 24*w^2 - 4*w - 7]', '[2699, 2699, 6*w^4 - 2*w^3 - 29*w^2 + 4*w + 11]', '[2701, 2701, -11*w^4 + 7*w^3 + 47*w^2 - 21*w - 15]', '[2705, 2705, 10*w^4 - 5*w^3 - 45*w^2 + 12*w + 16]', '[2707, 2707, 7*w^4 - 2*w^3 - 35*w^2 + 2*w + 16]', '[2720, 170, 6*w^4 - 2*w^3 - 28*w^2 + 6*w + 10]', '[2720, 170, 2*w^4 - 10*w^2 - 4*w + 6]', '[2725, 2725, -7*w^4 + 3*w^3 + 33*w^2 - 5*w - 14]', '[2729, 2729, 7*w^4 - 4*w^3 - 32*w^2 + 12*w + 16]', '[2731, 2731, 7*w^4 - 2*w^3 - 31*w^2 + w + 10]', '[2731, 2731, 5*w^4 - 4*w^3 - 23*w^2 + 10*w + 12]', '[2735, 2735, -10*w^4 + 7*w^3 + 43*w^2 - 21*w - 11]', '[2735, 2735, -2*w^4 + 11*w^2 - w - 10]', '[2741, 2741, -w^4 - 2*w^3 + 5*w^2 + 6*w - 2]', '[2749, 2749, 4*w^4 - 19*w^2 + 6]', '[2749, 2749, w^4 - 2*w^2 - 4]', '[2771, 2771, 5*w^4 - w^3 - 23*w^2 + 14]', '[2771, 2771, 10*w^4 - 4*w^3 - 50*w^2 + 9*w + 26]', '[2773, 2773, 2*w^4 - 13*w^2 + w + 10]', '[2773, 2773, -2*w^4 + 3*w^3 + 7*w^2 - 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w^3 + 10*w^2 + 8*w - 4]', '[4321, 4321, -9*w^4 + 3*w^3 + 42*w^2 - 7*w - 15]', '[4321, 4321, -3*w^4 + 4*w^3 + 14*w^2 - 14*w - 3]', '[4337, 4337, 6*w^4 - 6*w^3 - 28*w^2 + 19*w + 14]', '[4339, 4339, 8*w^4 - 6*w^3 - 37*w^2 + 18*w + 20]', '[4343, 4343, 7*w^4 - 2*w^3 - 31*w^2 + 4*w + 11]', '[4357, 4357, 3*w^4 + w^3 - 16*w^2 - 3*w + 10]', '[4369, 4369, 8*w^4 - 2*w^3 - 41*w^2 + 3*w + 22]', '[4369, 4369, 8*w^4 - 3*w^3 - 36*w^2 + 5*w + 17]', '[4369, 4369, -2*w^4 - w^3 + 8*w^2 - w - 7]', '[4369, 4369, -3*w^4 + 4*w^3 + 16*w^2 - 9*w - 9]', '[4379, 4379, -2*w^4 + 6*w^2 - 6*w - 1]', '[4385, 4385, 4*w^3 - w^2 - 17*w - 4]', '[4387, 4387, 6*w^4 - w^3 - 33*w^2 + 3*w + 21]', '[4393, 4393, -2*w^4 + 4*w^3 + 12*w^2 - 10*w - 9]', '[4399, 4399, 3*w^4 - 4*w^3 - 11*w^2 + 13*w + 1]', '[4399, 4399, -10*w^4 + 6*w^3 + 48*w^2 - 18*w - 23]', '[4399, 4399, -3*w^3 + 2*w^2 + 11*w + 1]', '[4399, 4399, 9*w^4 - 4*w^3 - 42*w^2 + 9*w + 14]', '[4409, 4409, 3*w^4 - 5*w^3 - 14*w^2 + 16*w + 9]', '[4415, 4415, w^4 - 5*w^3 - 3*w^2 + 19*w + 3]', '[4423, 4423, 7*w^4 - 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4*w + 7]', '[4505, 4505, 2*w^4 - 4*w^3 - 8*w^2 + 12*w + 3]', '[4505, 4505, 7*w^4 - 2*w^3 - 35*w^2 + 4*w + 16]', '[4507, 4507, -6*w^4 + 3*w^3 + 30*w^2 - 11*w - 18]', '[4519, 4519, 6*w^4 - 5*w^3 - 29*w^2 + 14*w + 15]', '[4535, 4535, 5*w^4 - 4*w^3 - 25*w^2 + 14*w + 14]', '[4535, 4535, 4*w^4 - 2*w^3 - 16*w^2 + 1]', '[4547, 4547, 2*w^4 - w^3 - 7*w^2 + 5*w - 3]', '[4547, 4547, 7*w^4 - 3*w^3 - 30*w^2 + 6*w + 8]', '[4549, 4549, 7*w^4 - 5*w^3 - 34*w^2 + 15*w + 15]', '[4553, 4553, -6*w^4 + 5*w^3 + 29*w^2 - 15*w - 18]', '[4553, 4553, 6*w^4 - 29*w^2 - 2*w + 17]', '[4555, 4555, -w^4 + 2*w^3 + 2*w^2 - 6*w + 9]', '[4559, 4559, -w^4 - 2*w^3 + 6*w^2 + 5*w - 5]', '[4559, 4559, 4*w^4 - w^3 - 20*w^2 + 5]', '[4561, 4561, -5*w^4 + 4*w^3 + 24*w^2 - 9*w - 14]', '[4561, 4561, 4*w^4 - w^3 - 18*w^2 + w]', '[4561, 4561, -7*w^4 + 3*w^3 + 31*w^2 - 4*w - 10]', '[4567, 4567, -3*w^4 + 16*w^2 - 14]', '[4567, 4567, 4*w^4 - 2*w^3 - 18*w^2 + 5*w + 13]', '[4573, 4573, -8*w^4 + 3*w^3 + 41*w^2 - 6*w - 21]', '[4573, 4573, -5*w^4 + w^3 + 22*w^2 - 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23*w - 17]', '[4747, 4747, 4*w^4 - 2*w^3 - 18*w^2 + 4*w + 13]', '[4751, 4751, -w^4 + 5*w^2 + w - 8]', '[4765, 4765, 5*w^4 - w^3 - 20*w^2 - 3*w + 4]', '[4768, 298, 10*w^4 - 4*w^3 - 46*w^2 + 8*w + 22]', '[4768, 298, 2*w^4 - 8*w^2 - 6]', '[4768, 298, 8*w^4 - 6*w^3 - 38*w^2 + 20*w + 16]', '[4775, 4775, -12*w^4 + 3*w^3 + 57*w^2 - 6*w - 28]', '[4783, 4783, -7*w^4 + w^3 + 31*w^2 + w - 9]', '[4783, 4783, 2*w^4 - w^3 - 7*w^2 - 4]', '[4787, 4787, 6*w^4 - w^3 - 27*w^2 - w + 13]', '[4789, 4789, 4*w^4 - 4*w^3 - 19*w^2 + 10*w + 13]', '[4805, 155, -7*w^4 + 3*w^3 + 30*w^2 - 4*w - 4]', '[4811, 4811, 8*w^4 - 6*w^3 - 38*w^2 + 16*w + 17]', '[4811, 4811, 2*w^4 + w^3 - 10*w^2 - 2*w + 10]', '[4813, 4813, 5*w^4 - 23*w^2 - w + 7]', '[4825, 4825, 8*w^4 - 3*w^3 - 36*w^2 + 7*w + 16]', '[4831, 4831, 2*w^4 + w^3 - 11*w^2 - 2*w + 10]', '[4831, 4831, -4*w^4 + 2*w^3 + 22*w^2 - 5*w - 16]', '[4832, 302, 4*w^4 - 2*w^3 - 18*w^2 + 10*w + 8]', '[4835, 4835, w^4 - 3*w^3 - 4*w^2 + 14*w - 4]', '[4835, 4835, w^4 + 2*w^3 - 6*w^2 - 7*w - 4]', '[4841, 4841, -7*w^4 + 4*w^3 + 31*w^2 - 8*w - 9]', '[4843, 4843, -2*w^4 - 2*w^3 + 11*w^2 + 10*w - 5]', '[4843, 4843, -7*w^4 + 2*w^3 + 31*w^2 - 2*w - 10]', '[4847, 4847, 7*w^4 - 2*w^3 - 33*w^2 + 4*w + 9]', '[4855, 4855, -4*w^4 + 21*w^2 + w - 7]', '[4855, 4855, 2*w^4 - 4*w^3 - 9*w^2 + 11*w + 9]', '[4855, 4855, 6*w^4 + w^3 - 29*w^2 - 7*w + 11]', '[4859, 4859, w^4 - 3*w^3 - w^2 + 10*w - 5]', '[4877, 4877, 10*w^4 - 6*w^3 - 46*w^2 + 17*w + 22]', '[4889, 4889, 6*w^4 - 2*w^3 - 29*w^2 + 4*w + 10]', '[4897, 4897, 3*w^4 - 4*w^3 - 14*w^2 + 11*w + 11]', '[4897, 4897, -4*w^4 + 3*w^3 + 16*w^2 - 6*w - 1]', '[4897, 4897, -w^4 - 3*w^3 + 5*w^2 + 11*w]', '[4897, 4897, 4*w^4 - w^3 - 21*w^2 + 5*w + 15]', '[4901, 377, -7*w^4 + 5*w^3 + 34*w^2 - 13*w - 11]', '[4909, 4909, 5*w^4 - 24*w^2 - 6*w + 10]', '[4909, 4909, -10*w^4 + 4*w^3 + 46*w^2 - 8*w - 21]', '[4913, 17, 9*w^4 - 5*w^3 - 41*w^2 + 11*w + 17]', '[4913, 289, -2*w^4 - w^3 + 12*w^2 + 6*w - 9]', '[4913, 289, -10*w^4 + 5*w^3 + 45*w^2 - 13*w - 17]', '[4913, 4913, 6*w^4 - 5*w^3 - 27*w^2 + 13*w + 14]', '[4913, 4913, -2*w^4 + w^3 + 6*w^2 + 4]', '[4915, 4915, 2*w^4 - 13*w^2 + w + 13]', '[4915, 4915, 7*w^4 - 3*w^3 - 32*w^2 + 10*w + 5]', '[4919, 4919, -5*w^4 + w^3 + 25*w^2 - w - 9]', '[4919, 4919, 6*w^4 - 4*w^3 - 29*w^2 + 15*w + 14]', '[4919, 4919, -7*w^4 + 6*w^3 + 32*w^2 - 19*w - 17]', '[4933, 4933, 8*w^4 - 4*w^3 - 39*w^2 + 13*w + 22]', '[4937, 4937, -3*w^4 + 3*w^3 + 15*w^2 - 8*w - 14]', '[4943, 4943, w^4 + 2*w^3 - 4*w^2 - 8*w + 3]', '[4943, 4943, w^4 - 3*w^2 - 3*w - 7]', '[4943, 4943, -w^4 - 2*w^3 + 7*w^2 + 9*w - 6]', '[4945, 4945, -2*w^4 + 2*w^3 + 8*w^2 - 10*w - 1]', '[4955, 4955, -w^4 + 3*w^2 + 9]', '[4955, 4955, 6*w^4 - w^3 - 28*w^2 + 2*w + 10]', '[4955, 4955, -2*w^4 + 6*w^3 + 8*w^2 - 24*w - 5]', '[4957, 4957, w^4 - 2*w^3 - 2*w^2 + 8*w - 1]', '[4961, 451, 8*w^4 - 3*w^3 - 39*w^2 + 7*w + 17]', '[4967, 4967, 2*w^4 - 4*w^3 - 8*w^2 + 13*w]', '[4969, 4969, 5*w^4 - w^3 - 24*w^2 + 5]', '[4973, 4973, 5*w^4 - 5*w^3 - 24*w^2 + 15*w + 13]', '[4975, 4975, -19*w^4 + 7*w^3 + 90*w^2 - 13*w - 46]', '[4981, 4981, 3*w^4 - w^3 - 16*w^2 + 4*w + 15]', '[4981, 4981, 10*w^4 - 6*w^3 - 49*w^2 + 16*w + 29]', '[4985, 4985, -8*w^4 + 8*w^3 + 34*w^2 - 27*w - 8]', '[5003, 5003, -6*w^4 + w^3 + 26*w^2 + w - 7]', '[5015, 5015, -2*w^4 - 2*w^3 + 11*w^2 + 8*w - 7]', '[5015, 5015, 7*w^4 - 3*w^3 - 33*w^2 + 7*w + 10]', '[5015, 5015, -10*w^4 + 4*w^3 + 47*w^2 - 7*w - 21]', '[5015, 5015, w^4 + 2*w^3 - 4*w^2 - 9*w + 2]', '[5021, 5021, 9*w^4 - 3*w^3 - 43*w^2 + 8*w + 19]', '[5024, 314, -4*w^4 - 2*w^3 + 20*w^2 + 10*w - 8]', '[5024, 314, 10*w^4 - 6*w^3 - 48*w^2 + 16*w + 26]', '[5029, 5029, -9*w^4 + 6*w^3 + 43*w^2 - 16*w - 21]', '[5045, 5045, -w^4 + 2*w^3 + 7*w^2 - 12*w - 9]', '[5051, 5051, -6*w^4 + 3*w^3 + 29*w^2 - 11*w - 18]', '[5051, 5051, -10*w^4 + 4*w^3 + 45*w^2 - 9*w - 15]', '[5063, 5063, 6*w^4 - 5*w^3 - 28*w^2 + 14*w + 17]', '[5063, 5063, -8*w^4 + 5*w^3 + 37*w^2 - 17*w - 18]', '[5063, 5063, -8*w^4 + 5*w^3 + 37*w^2 - 14*w - 20]', '[5063, 5063, 5*w^4 - w^3 - 25*w^2 - 2*w + 14]', '[5065, 5065, -5*w^4 + w^3 + 23*w^2 + 2*w - 14]', '[5077, 5077, 7*w^4 - 5*w^3 - 33*w^2 + 16*w + 20]', '[5081, 5081, 7*w^4 - 6*w^3 - 33*w^2 + 18*w + 16]', '[5087, 5087, 4*w^4 - 5*w^3 - 18*w^2 + 15*w + 10]', '[5087, 5087, -w^4 + 2*w^3 + 5*w^2 - 11*w - 2]', '[5095, 5095, 6*w^4 - 2*w^3 - 26*w^2 + 5*w - 1]', '[5095, 5095, 13*w^4 - 10*w^3 - 60*w^2 + 33*w + 26]', '[5095, 5095, -14*w^4 + 7*w^3 + 62*w^2 - 16*w - 18]', '[5099, 5099, w^4 + 3*w^3 - 6*w^2 - 12*w + 4]', '[5105, 5105, -3*w^4 + 15*w^2 + 5*w - 12]', '[5113, 5113, -2*w^4 + 4*w^3 + 8*w^2 - 11*w - 3]', '[5120, 20, -8*w^4 + 4*w^3 + 36*w^2 - 8*w - 12]', '[5123, 5123, -10*w^4 + 4*w^3 + 46*w^2 - 7*w - 18]', '[5125, 5125, 7*w^4 - 5*w^3 - 34*w^2 + 13*w + 18]', '[5129, 5129, -w^4 + w^3 + 2*w^2 - 9*w - 1]', '[5129, 5129, -3*w^4 + 4*w^3 + 16*w^2 - 10*w - 12]', '[5141, 5141, 6*w^4 - w^3 - 27*w^2 + 2*w + 8]', '[5141, 5141, 3*w^4 - w^3 - 15*w^2 - 2*w + 8]', '[5141, 5141, 6*w^4 - 3*w^3 - 29*w^2 + 11*w + 15]', '[5141, 5141, 7*w^4 - 3*w^3 - 32*w^2 + 4*w + 13]', '[5143, 5143, -4*w^4 + 5*w^3 + 18*w^2 - 20*w - 5]', '[5143, 5143, -2*w^4 + 13*w^2 - 4]', '[5147, 5147, 4*w^4 - 3*w^3 - 21*w^2 + 10*w + 12]', '[5153, 5153, -w^4 - w^3 + 7*w^2 + 2*w - 9]', '[5155, 5155, -5*w^4 + 6*w^3 + 24*w^2 - 22*w - 10]', '[5165, 5165, -11*w^4 + 8*w^3 + 50*w^2 - 27*w - 19]', '[5171, 5171, -2*w^4 + 13*w^2 - 11]', '[5179, 5179, 3*w^4 - w^3 - 12*w^2 - w - 2]', '[5185, 5185, 8*w^4 - 3*w^3 - 39*w^2 + 10*w + 22]', '[5185, 5185, -4*w^4 + 4*w^3 + 16*w^2 - 11*w]', '[5185, 5185, 3*w^4 - 2*w^3 - 15*w^2 + 3*w + 12]', '[5185, 5185, 9*w^4 - 6*w^3 - 42*w^2 + 16*w + 20]', '[5189, 5189, -6*w^4 + 2*w^3 + 26*w^2 - 3*w - 9]', '[5203, 473, 7*w^4 - 4*w^3 - 32*w^2 + 12*w + 17]', '[5209, 5209, 4*w^4 - 21*w^2 - 4*w + 11]', '[5216, 326, -4*w^4 + 22*w^2 + 2*w - 14]', '[5219, 5219, 5*w^4 - w^3 - 26*w^2 + w + 11]', '[5219, 5219, 3*w^4 - 12*w^2 - 4*w + 5]', '[5227, 5227, -4*w^4 + w^3 + 18*w^2 + 3*w - 8]', '[5255, 5255, -2*w^4 + 11*w^2 - w]', '[5261, 5261, -3*w^4 + 3*w^3 + 13*w^2 - 13*w - 3]', '[5261, 5261, -7*w^4 + 4*w^3 + 33*w^2 - 8*w - 14]', '[5273, 5273, -w^4 + 2*w^3 + 3*w^2 - 10*w + 2]', '[5279, 5279, 4*w^4 - 2*w^3 - 19*w^2 + 9*w + 11]', '[5287, 5287, -4*w^4 + 4*w^3 + 20*w^2 - 9*w - 13]', '[5287, 5287, -5*w^4 + w^3 + 24*w^2 - 6*w - 16]', '[5287, 5287, 2*w^4 - 7*w^2 - 3*w + 5]', '[5287, 5287, 5*w^4 - 2*w^3 - 27*w^2 + 5*w + 13]', '[5297, 5297, 9*w^4 - 5*w^3 - 43*w^2 + 16*w + 22]', '[5297, 5297, 3*w^2 - w - 7]', '[5297, 5297, -5*w^4 + 3*w^3 + 26*w^2 - 11*w - 15]', '[5305, 5305, -4*w^4 - 2*w^3 + 19*w^2 + 10*w - 6]', '[5305, 5305, 4*w^4 - 6*w^3 - 15*w^2 + 19*w + 1]', '[5311, 5311, -w^4 - 2*w^3 + 5*w^2 + 10*w - 5]', '[5315, 5315, 11*w^4 - 6*w^3 - 51*w^2 + 18*w + 15]', '[5315, 5315, 7*w^4 - 4*w^3 - 29*w^2 + 10*w + 6]', '[5321, 5321, 7*w^4 - w^3 - 32*w^2 + 4*w + 15]', '[5321, 5321, 8*w^4 - 5*w^3 - 38*w^2 + 17*w + 18]', '[5321, 5321, 2*w^4 - w^3 - 11*w^2 + w + 12]', '[5321, 5321, 2*w^4 - w^3 - 11*w^2 - 2*w + 7]', '[5323, 5323, -4*w^4 - w^3 + 20*w^2 + 4*w - 9]', '[5329, 73, -w^4 + w^3 + 4*w^2 - 4*w - 7]', '[5329, 73, -w^4 + 8*w^2 + w - 9]', '[5329, 5329, 7*w^4 - 5*w^3 - 32*w^2 + 18*w + 14]', '[5333, 5333, 7*w^4 - 2*w^3 - 32*w^2 + 5*w + 9]', '[5344, 334, 2*w^4 - 6*w^2 - 4*w - 6]', '[5344, 334, -6*w^4 + 6*w^3 + 28*w^2 - 20*w - 18]', '[5347, 5347, -3*w^4 + 4*w^3 + 14*w^2 - 10*w - 8]', '[5347, 5347, 8*w^4 - 2*w^3 - 37*w^2 + 4*w + 14]', '[5353, 5353, -6*w^4 + 2*w^3 + 29*w^2 - 5*w - 9]', '[5353, 5353, -w^4 + 2*w^3 + 2*w^2 - 8*w]', '[5359, 5359, -2*w^4 - 3*w^3 + 9*w^2 + 11*w]', '[5365, 5365, 7*w^4 - 4*w^3 - 35*w^2 + 13*w + 19]', '[5371, 5371, -3*w^4 - w^3 + 14*w^2 + 8*w - 8]', '[5375, 5375, 3*w^4 - 13*w^2 - 1]', '[5381, 5381, w^3 + 3*w^2 - 4*w - 10]', '[5381, 5381, 5*w^4 - 23*w^2 - 3*w + 12]', '[5381, 5381, 8*w^4 - 4*w^3 - 37*w^2 + 14*w + 16]', '[5393, 5393, -5*w^4 + 2*w^3 + 25*w^2 - 3*w - 9]', '[5405, 5405, 9*w^4 - 5*w^3 - 40*w^2 + 16*w + 9]', '[5407, 5407, -8*w^4 + 5*w^3 + 37*w^2 - 17*w - 17]', '[5407, 5407, -2*w^4 + 10*w^2 + 2*w - 11]', '[5408, 26, 6*w^4 - 4*w^3 - 28*w^2 + 12*w + 6]', '[5417, 5417, -3*w^4 - w^3 + 12*w^2 + 7*w - 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16*w - 14]', '[5479, 5479, -9*w^4 + 4*w^3 + 40*w^2 - 11*w - 15]', '[5479, 5479, 8*w^4 - 3*w^3 - 36*w^2 + 5*w + 16]', '[5485, 5485, -4*w^4 + 7*w^3 + 18*w^2 - 25*w - 9]', '[5501, 5501, -7*w^4 + 4*w^3 + 31*w^2 - 10*w - 16]', '[5513, 5513, -5*w^4 + 5*w^3 + 22*w^2 - 16*w - 12]', '[5513, 5513, 6*w^4 - 4*w^3 - 24*w^2 + 9*w + 2]', '[5513, 5513, 11*w^4 - 9*w^3 - 49*w^2 + 26*w + 18]', '[5521, 5521, 2*w^4 - w^3 - 6*w^2 + 3*w - 2]', '[5527, 5527, 9*w^4 - 3*w^3 - 43*w^2 + 8*w + 18]', '[5539, 5539, -3*w^4 + 12*w^2 - 3*w - 10]', '[5543, 5543, -6*w^4 + 4*w^3 + 27*w^2 - 8*w - 9]', '[5545, 5545, w^4 - 6*w^2 + 2*w + 9]', '[5557, 5557, -5*w^4 + 4*w^3 + 25*w^2 - 13*w - 12]', '[5557, 5557, 7*w^4 - 2*w^3 - 31*w^2 + 4*w + 12]', '[5557, 5557, 7*w^4 - 3*w^3 - 35*w^2 + 6*w + 16]', '[5563, 5563, 2*w^4 - 2*w^3 - 6*w^2 + 5*w - 4]', '[5563, 5563, 4*w^4 - 3*w^3 - 21*w^2 + 10*w + 11]', '[5563, 5563, -w^4 - 2*w^3 + 3*w^2 + 9*w]', '[5569, 5569, -4*w^4 + 2*w^3 + 21*w^2 - 3*w - 16]', '[5575, 5575, -18*w^4 + 5*w^3 + 87*w^2 - 10*w - 45]', '[5575, 5575, 4*w^4 - w^3 - 20*w^2 + 4*w + 16]', '[5581, 5581, -8*w^4 + 4*w^3 + 37*w^2 - 7*w - 17]', '[5581, 5581, 5*w^4 - 4*w^3 - 22*w^2 + 12*w + 12]', '[5581, 5581, 6*w^4 - 6*w^3 - 27*w^2 + 18*w + 13]', '[5587, 5587, 6*w^4 - 4*w^3 - 24*w^2 + 13*w + 9]', '[5589, 69, -3*w^3 + 9*w]', '[5591, 5591, -8*w^4 + 5*w^3 + 36*w^2 - 13*w - 18]', '[5597, 5597, -w^4 + 3*w^3 + 6*w^2 - 5*w + 1]', '[5615, 5615, -w^4 + w^3 + 5*w^2 - 8*w - 1]', '[5623, 5623, 4*w^4 - 5*w^3 - 19*w^2 + 16*w + 12]', '[5633, 5633, 3*w^2 - w - 9]', '[5639, 5639, 5*w^4 - 4*w^3 - 25*w^2 + 14*w + 11]', '[5639, 5639, 6*w^4 - w^3 - 27*w^2 + 2*w + 7]', '[5641, 5641, -7*w^4 + 4*w^3 + 35*w^2 - 12*w - 17]', '[5641, 5641, w^4 - w^3 - 3*w^2 - 4]', '[5641, 5641, -8*w^4 + 4*w^3 + 37*w^2 - 8*w - 12]', '[5645, 5645, 9*w^4 - 5*w^3 - 44*w^2 + 15*w + 22]', '[5645, 5645, 11*w^4 - 5*w^3 - 53*w^2 + 14*w + 23]', '[5651, 5651, 4*w^4 - 4*w^3 - 19*w^2 + 10*w + 11]', '[5651, 5651, -9*w^4 + 6*w^3 + 41*w^2 - 19*w - 19]', '[5657, 5657, -11*w^4 + 5*w^3 + 50*w^2 - 12*w - 19]', '[5671, 5671, 5*w^4 - 24*w^2 + 9]', '[5671, 5671, 6*w^4 - 5*w^3 - 27*w^2 + 16*w + 14]', '[5687, 517, 4*w^4 - 5*w^3 - 18*w^2 + 14*w + 9]', '[5693, 5693, 5*w^4 - 23*w^2 - w + 6]', '[5693, 5693, 6*w^4 - 4*w^3 - 26*w^2 + 6*w + 5]', '[5693, 5693, -6*w^4 + w^3 + 28*w^2 - 2*w - 9]', '[5699, 5699, 4*w^4 - w^3 - 16*w^2 - w + 8]', '[5699, 5699, -14*w^4 + 6*w^3 + 66*w^2 - 16*w - 27]', '[5701, 5701, -4*w^4 + 3*w^3 + 20*w^2 - 13*w - 11]', '[5701, 5701, 7*w^4 - 5*w^3 - 31*w^2 + 15*w + 14]', '[5711, 5711, -w^4 - w^3 + 7*w^2 + w - 8]', '[5717, 5717, 3*w^4 - 4*w^3 - 14*w^2 + 11*w + 10]', '[5717, 5717, -7*w^4 + 5*w^3 + 33*w^2 - 13*w - 17]', '[5723, 5723, -w^4 + 4*w^3 + 7*w^2 - 16*w - 9]', '[5723, 5723, 9*w^4 - 3*w^3 - 43*w^2 + 6*w + 17]', '[5723, 5723, w^4 - 2*w^3 - 5*w^2 + 11*w + 1]', '[5723, 5723, -w^4 + 4*w^3 + 4*w^2 - 14*w - 2]', '[5741, 5741, -2*w^4 - w^3 + 9*w^2 + 7*w - 6]', '[5743, 5743, -3*w^4 + 3*w^3 + 15*w^2 - 14*w - 9]', '[5749, 5749, 3*w^4 + w^3 - 16*w^2 - 7*w + 8]', '[5765, 5765, 5*w^4 - 4*w^3 - 21*w^2 + 15*w + 1]', '[5771, 5771, -4*w^4 + w^3 + 21*w^2 - 4*w - 16]', '[5773, 5773, -5*w^4 + 2*w^3 + 25*w^2 - 6*w - 7]', '[5777, 5777, -2*w^4 - 2*w^3 + 10*w^2 + 7*w - 4]', '[5777, 5777, -10*w^4 + 5*w^3 + 45*w^2 - 13*w - 18]', '[5779, 5779, 6*w^4 - 4*w^3 - 30*w^2 + 13*w + 13]', '[5779, 5779, 4*w^4 - w^3 - 20*w^2 - 2*w + 11]', '[5783, 5783, 5*w^4 - 3*w^3 - 22*w^2 + 9*w + 13]', '[5783, 5783, w^2 - 8]', '[5791, 5791, -8*w^4 + 4*w^3 + 35*w^2 - 10*w - 12]', '[5791, 5791, -7*w^4 + 2*w^3 + 31*w^2 - 2*w - 13]', '[5791, 5791, -8*w^4 + 2*w^3 + 36*w^2 - 4*w - 11]', '[5801, 5801, 7*w^4 - 5*w^3 - 34*w^2 + 17*w + 16]', '[5807, 5807, -w^4 - 2*w^3 + 7*w^2 + 8*w - 4]', '[5809, 5809, 8*w^4 - 5*w^3 - 39*w^2 + 15*w + 19]', '[5809, 5809, -w^4 - 2*w^3 + 4*w^2 + 11*w - 2]', '[5813, 5813, 2*w^4 + 2*w^3 - 11*w^2 - 8*w + 8]', '[5825, 5825, -5*w^4 + 4*w^3 + 25*w^2 - 11*w - 20]', '[5827, 5827, 5*w^4 - 4*w^3 - 25*w^2 + 14*w + 13]', '[5839, 5839, w^2 + 3*w - 6]', '[5843, 5843, -3*w^4 + 4*w^3 + 16*w^2 - 14*w - 11]', '[5855, 5855, w^4 - 4*w^2 + 2*w - 4]', '[5867, 5867, 2*w^4 - 3*w^3 - 9*w^2 + 14*w + 4]', '[5869, 5869, w^4 - w^3 - 3*w^2 + 6*w - 5]', '[5875, 5875, 4*w^4 - 3*w^3 - 15*w^2 + 7*w + 1]', '[5881, 5881, 5*w^4 - 2*w^3 - 22*w^2 + 7*w + 3]', '[5899, 5899, -9*w^4 + 4*w^3 + 44*w^2 - 10*w - 20]', '[5899, 5899, -2*w^3 + 9*w - 4]', '[5903, 5903, w^4 - 6*w^2 - w - 2]', '[5905, 5905, 9*w^4 - 7*w^3 - 39*w^2 + 20*w + 8]', '[5905, 5905, 6*w^4 - w^3 - 26*w^2 - w + 8]', '[5911, 5911, -4*w^4 + 4*w^3 + 19*w^2 - 10*w - 12]', '[5911, 5911, 5*w^4 - 19*w^2 + w + 5]', '[5917, 5917, 7*w^4 - 4*w^3 - 32*w^2 + 11*w + 18]', '[5917, 5917, 3*w^3 - w^2 - 10*w + 1]', '[5917, 5917, -10*w^4 + 3*w^3 + 46*w^2 - 5*w - 19]', '[5917, 5917, 4*w^4 - w^3 - 19*w^2 - 3*w + 8]', '[5920, 370, 4*w^4 - 4*w^3 - 18*w^2 + 14*w + 12]', '[5927, 5927, 3*w^4 - 4*w^3 - 13*w^2 + 14*w + 10]', '[5935, 5935, -w^4 + 3*w^3 + 2*w^2 - 10*w - 1]', '[5939, 5939, -w^4 + 4*w^3 + 4*w^2 - 13*w - 3]', '[5945, 5945, 8*w^4 - 5*w^3 - 39*w^2 + 15*w + 18]', '[5953, 5953, 8*w^4 - 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10*w - 9]', '[169, 13, 3*w^4 - 2*w^3 - 14*w^2 + 6*w + 3]', '[191, 191, -3*w^4 + w^3 + 15*w^2 - w - 6]', '[193, 193, 3*w^4 - 2*w^3 - 14*w^2 + 4*w + 5]', '[199, 199, -5*w^4 + 2*w^3 + 23*w^2 - 3*w - 10]', '[223, 223, -4*w^4 + w^3 + 20*w^2 - w - 9]', '[223, 223, -w^4 + 3*w^2 + 2]', '[233, 233, w^3 - 4*w - 4]', '[241, 241, -3*w^4 + 2*w^3 + 15*w^2 - 7*w - 7]', '[243, 3, -3]', '[251, 251, -3*w^4 + 3*w^3 + 13*w^2 - 8*w - 6]', '[257, 257, -4*w^4 + w^3 + 20*w^2 - 2*w - 9]', '[257, 257, -3*w^4 + 2*w^3 + 15*w^2 - 5*w - 11]', '[269, 269, 2*w^4 - 11*w^2 - w + 6]', '[271, 271, w^4 + w^3 - 5*w^2 - 6*w + 2]', '[271, 271, 3*w^4 - w^3 - 15*w^2 + 8]', '[277, 277, -w^4 - w^3 + 6*w^2 + 3*w - 5]', '[283, 283, -5*w^4 + 3*w^3 + 23*w^2 - 10*w - 10]', '[293, 293, -w^4 + w^3 + 6*w^2 - 3*w - 8]', '[307, 307, -w^4 - w^3 + 6*w^2 + 4*w - 2]', '[311, 311, -w^3 + 2*w^2 + 3*w - 2]', '[311, 311, 2*w^4 - w^3 - 10*w^2 + 5*w + 7]', '[313, 313, -5*w^4 + 4*w^3 + 23*w^2 - 12*w - 11]', '[313, 313, -w^4 - w^3 + 5*w^2 + 3*w - 3]', '[347, 347, -w^4 + 2*w^3 + 3*w^2 - 7*w + 1]', '[353, 353, -3*w^4 + 14*w^2 + 3*w - 7]', '[353, 353, -3*w^4 + 3*w^3 + 13*w^2 - 9*w - 7]', '[367, 367, -w^4 + w^3 + 5*w^2 - 6*w - 4]', '[367, 367, -3*w^4 + w^3 + 15*w^2 - 3*w - 5]', '[379, 379, 5*w^4 - 2*w^3 - 23*w^2 + 6*w + 9]', '[383, 383, 4*w^4 - 2*w^3 - 19*w^2 + 7*w + 11]', '[397, 397, w^4 - 3*w^2 - w - 3]', '[397, 397, -2*w^3 + w^2 + 8*w]', '[401, 401, 2*w^4 - 2*w^3 - 8*w^2 + 5*w]', '[421, 421, -4*w^4 + 2*w^3 + 17*w^2 - 5*w - 6]', '[421, 421, -w^4 + 2*w^3 + 6*w^2 - 8*w - 5]', '[431, 431, 5*w^4 - 2*w^3 - 22*w^2 + 5*w + 7]', '[431, 431, -w^4 - w^3 + 6*w^2 + 5*w - 4]', '[439, 439, 4*w^4 - 2*w^3 - 19*w^2 + 7*w + 10]', '[443, 443, 4*w^4 - w^3 - 19*w^2 + 3*w + 8]', '[457, 457, -3*w^4 + 3*w^3 + 15*w^2 - 10*w - 9]', '[461, 461, -w^3 + 6*w]', '[461, 461, 3*w^4 - 3*w^3 - 14*w^2 + 9*w + 8]', '[463, 463, 5*w^4 - 3*w^3 - 23*w^2 + 7*w + 8]', '[499, 499, 6*w^4 - 3*w^3 - 27*w^2 + 7*w + 11]', '[509, 509, 2*w^4 - w^3 - 8*w^2 + w - 1]', '[509, 509, 3*w^4 - 2*w^3 - 13*w^2 + 6*w + 7]', '[521, 521, w^3 - 6*w + 1]', '[523, 523, 4*w^4 - 2*w^3 - 18*w^2 + 3*w + 7]', '[541, 541, w^2 + w - 5]', '[547, 547, 5*w^4 - 2*w^3 - 25*w^2 + 4*w + 12]', '[547, 547, -6*w^4 + 3*w^3 + 27*w^2 - 10*w - 9]', '[557, 557, -4*w^4 + 3*w^3 + 18*w^2 - 10*w - 9]', '[557, 557, -4*w^4 + w^3 + 19*w^2 - 3*w - 6]', '[557, 557, 3*w^4 - 2*w^3 - 14*w^2 + 8*w + 7]', '[563, 563, -w^4 + 3*w^3 + 4*w^2 - 11*w + 1]', '[569, 569, w^2 + 3*w - 2]', '[577, 577, -5*w^4 + 2*w^3 + 23*w^2 - 6*w - 8]', '[587, 587, -2*w^4 + 10*w^2 + 3*w - 6]', '[593, 593, 4*w^4 - 3*w^3 - 19*w^2 + 8*w + 11]', '[601, 601, -4*w^4 + w^3 + 18*w^2 - 3*w - 6]', '[601, 601, -5*w^4 + 3*w^3 + 24*w^2 - 10*w - 13]', '[601, 601, -w^4 + 5*w^2 + 3*w - 3]', '[607, 607, -3*w^4 + 2*w^3 + 15*w^2 - 8*w - 9]', '[613, 613, 3*w^4 - 14*w^2 - 2*w + 8]', '[617, 617, -4*w^4 + w^3 + 19*w^2 - 3*w - 7]', '[619, 619, w^3 + w^2 - 3*w - 5]', '[625, 5, 4*w^4 - 2*w^3 - 19*w^2 + 3*w + 8]', '[631, 631, 3*w^4 - w^3 - 12*w^2 - 1]', '[641, 641, -w^4 + 2*w^3 + 3*w^2 - 7*w]', '[647, 647, 2*w^2 - w - 5]', '[647, 647, -2*w^3 + w^2 + 8*w - 5]', '[647, 647, 5*w^4 - 3*w^3 - 23*w^2 + 9*w + 12]', '[661, 661, -8*w^4 + 3*w^3 + 39*w^2 - 7*w - 19]', '[677, 677, -7*w^4 + 4*w^3 + 34*w^2 - 11*w - 17]', '[691, 691, w^2 + 2*w - 4]', '[691, 691, -5*w^4 + 2*w^3 + 23*w^2 - 3*w - 8]', '[691, 691, -7*w^4 + 5*w^3 + 32*w^2 - 14*w - 15]', '[701, 701, w - 4]', '[709, 709, -3*w^4 + 3*w^3 + 14*w^2 - 8*w - 7]', '[709, 709, 5*w^4 - 2*w^3 - 24*w^2 + 5*w + 9]', '[709, 709, -w^4 + w^3 + 5*w^2 - 3*w - 7]', '[719, 719, -3*w^4 + 13*w^2 + w - 7]', '[719, 719, -3*w^4 + 14*w^2 - 4]', '[727, 727, -7*w^4 + 4*w^3 + 32*w^2 - 10*w - 16]', '[727, 727, -3*w^4 + w^3 + 14*w^2 - 5*w - 8]', '[733, 733, -3*w^4 + 2*w^3 + 15*w^2 - 8*w - 10]', '[733, 733, -3*w^4 + 3*w^3 + 13*w^2 - 10*w - 7]', '[733, 733, 8*w^4 - 4*w^3 - 38*w^2 + 9*w + 15]', '[739, 739, 4*w^4 - 3*w^3 - 20*w^2 + 9*w + 11]', '[739, 739, -w^4 + w^3 + 5*w^2 - 3*w + 1]', '[743, 743, -5*w^4 + 4*w^3 + 24*w^2 - 13*w - 16]', '[743, 743, w^4 - 7*w^2 - 2*w + 5]', '[751, 751, -w^4 + 2*w^3 + 3*w^2 - 7*w - 1]', '[757, 757, 5*w^4 - 2*w^3 - 22*w^2 + 5*w + 8]', '[757, 757, w^4 + w^3 - 6*w^2 - 5*w + 2]', '[761, 761, 8*w^4 - 3*w^3 - 38*w^2 + 8*w + 18]', '[761, 761, 3*w^4 - w^3 - 14*w^2 + 2*w + 10]', '[761, 761, -4*w^4 + 3*w^3 + 19*w^2 - 7*w - 10]', '[769, 769, -w^4 + 2*w^3 + 5*w^2 - 8*w - 1]', '[773, 773, 9*w^4 - 4*w^3 - 41*w^2 + 9*w + 15]', '[773, 773, 4*w^4 - 2*w^3 - 18*w^2 + 3*w + 6]', '[773, 773, 2*w^2 - 5]', '[787, 787, -w^4 + 6*w^2 - w - 7]', '[787, 787, w^4 - w^3 - 6*w^2 + w + 6]', '[821, 821, 2*w^4 - w^3 - 9*w^2 + 4*w + 8]', '[823, 823, 6*w^4 - w^3 - 27*w^2 - w + 8]', '[827, 827, -3*w^4 + 2*w^3 + 16*w^2 - 6*w - 9]', '[827, 827, -8*w^4 + 5*w^3 + 37*w^2 - 16*w - 17]', '[839, 839, 2*w^4 - 10*w^2 + w + 8]', '[853, 853, 2*w^4 - 2*w^3 - 11*w^2 + 7*w + 7]', '[857, 857, 5*w^4 - 2*w^3 - 24*w^2 + 7*w + 14]', '[877, 877, -w^4 + 2*w^3 + 5*w^2 - 10*w - 6]', '[883, 883, 3*w^4 - 3*w^3 - 15*w^2 + 12*w + 10]', '[887, 887, -4*w^4 + w^3 + 17*w^2 - w - 7]', '[907, 907, 2*w^4 - 11*w^2 - w + 2]', '[907, 907, -2*w^4 - w^3 + 10*w^2 + 4*w - 5]', '[911, 911, -9*w^4 + 4*w^3 + 43*w^2 - 9*w - 19]', '[919, 919, 4*w^4 - w^3 - 20*w^2 + w + 8]', '[937, 937, w^4 - 7*w^2 - 2*w + 4]', '[947, 947, 2*w^4 + 2*w^3 - 10*w^2 - 9*w + 3]', '[953, 953, -2*w^3 + 5*w + 4]', '[961, 31, -4*w^4 + w^3 + 19*w^2 - w - 4]', '[967, 967, 8*w^4 - 5*w^3 - 37*w^2 + 13*w + 18]', '[967, 967, 3*w^4 - w^3 - 13*w^2 - 2*w + 3]', '[971, 971, -4*w^4 + 3*w^3 + 21*w^2 - 10*w - 15]', '[971, 971, -3*w^4 + 12*w^2 + 3*w - 4]', '[971, 971, w^4 - 6*w^2 + 3*w + 6]', '[983, 983, -7*w^4 + 2*w^3 + 34*w^2 - 5*w - 16]', '[983, 983, w^4 - 7*w^2 - w + 8]', '[991, 991, -4*w^4 + 4*w^3 + 19*w^2 - 15*w - 12]', '[991, 991, -8*w^4 + 3*w^3 + 37*w^2 - 5*w - 15]', '[991, 991, -w^4 + w^3 + 7*w^2 - 3*w - 7]', '[997, 997, -8*w^4 + 5*w^3 + 37*w^2 - 16*w - 16]']}
• 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[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	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': [1, 3, -1, -5, 0, 1], 'conductor': 0, 'degree': 5, 'dirichlet_group': [], 'disc_abs': 24217, 'disc_rad': 24217, 'disc_sign': 1, 'frobs': [[2, [[5, 1]]], [3, [[5, 1]]], [5, [[4, 1], [1, 1]]], [7, [[5, 1]]], [11, [[3, 1], [2, 1]]], [13, [[3, 1], [2, 1]]], [17, [[3, 1], [1, 2]]], [19, [[5, 1]]], [23, [[4, 1], [1, 1]]], [29, [[4, 1], [1, 1]]], [31, [[3, 1], [2, 1]]], [37, [[4, 1], [1, 1]]], [41, [[4, 1], [1, 1]]], [43, [[4, 1], [1, 1]]], [47, [[2, 2], [1, 1]]], [53, [[3, 1], [1, 2]]], [59, [[3, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [60, 60], 'galois_label': '5T5', 'galt': 5, 'grd': 155.6181223379848, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.5.24217.1', 'local_algs': ['61.1.1.0a1.1', '61.2.1.0a1.1', '61.1.2.1a1.1', 'm397.1.1.0', 'm397.1.2.0', 'm397.2.1.1'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 0, 'ramps': [61, 397], 'rd': 7.53050443021, 'regulator': {'__RealLiteral__': 0, 'data': '2.39942113132', 'prec': 44}, 'res': {'sib': ['-1,-8,12,46,-31,-63,37,22,-12,-2,1', '-13128328481,-694902330,801840653,27841534,-17595569,-351928,167185,1940,-690,-4,1', '-1458721,5979084,59373425,120396557,58257106,-75816874,-83152146,6975698,34290002,4784761,-7157001,-1533179,888222,195662,-69404,-12550,3335,399,-89,-5,1', '-214183646389,7536468901741,-44439392735563,-316456028979400,1630156105457635,416496053224371,-9197470763385765,5963684093067987,18068262691464551,-18399419059787322,-16952425591591497,23405069972524379,8332375533199041,-16945698321571115,-1758181618961603,7875261827567487,-307259505770013,-2495305159848087,335329287332387,556476628095961,-116047864419827,-88487702995891,24495393676673,9981746274321,-3535150819383,-772579398867,361947870147,36781587329,-26489897051,-572889747,1367923365,-52266560,-47987048,4244492,1049459,-147990,-11228,2660,-10,-20,1', '-2875,19332,-15606,-53958,61054,33376,-54570,-834,17803,-2938,-2424,594,143,-42,-3,1', '-504,-1411,26525,-40057,-4155,25597,-3006,-4382,659,280,-45,-6,1', '-5062,1645,2810,117,-133,-3,1', '-68104425073,-520266843437,-514140326757,270946627261,339384145499,-48216220209,-88426276914,2489334784,12173346893,239526263,-979922921,-38955404,48033732,2151727,-1441019,-58392,25660,775,-248,-4,1', '1,-20,122,-79,-1409,2421,5722,-9236,-9814,15113,7421,-12596,-2045,5483,-186,-1199,180,117,-25,-4,1', '1,-43,420,634,-15398,-6509,184846,113995,-1010122,-910475,2706738,3047768,-3909204,-5236499,3260508,5184708,-1662824,-3157721,563350,1228449,-144965,-309402,31587,49807,-5446,-4896,621,265,-39,-6,1', '1222047,-52775064,450780930,-359233200,-8902234881,27102168481,27540470439,-178357148375,30047861576,434715643754,-139463683421,-516970377056,75852788905,301523466518,128610059,-93303801573,-9329328112,16059073469,2699904727,-1566497261,-344084594,87051155,23413046,-2690600,-897758,42746,19344,-271,-218,0,1', '38304,286380,-5771483,18166717,222565,-61600681,38945858,80057601,-70467371,-50573866,56193099,14952259,-24244329,-859917,5907957,-619848,-794075,162201,54051,-16512,-1321,748,-22,-12,1', '64010773,560566921,-55681926896,-105515619697,413877755358,204084477896,-897670408049,-91677568626,944609065256,-72095414915,-573185557372,100952922540,217492637701,-52104908088,-53871296433,15383221845,8898058425,-2897895486,-981888390,363787344,70560252,-30825390,-3029593,1742268,54329,-62920,1126,1312,-72,-12,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( 2 a^{4} - a^{3} - 9 a^{2} + 3 a + 3 \\)', '\\( a^{4} - 5 a^{2} - a + 2 \\)', '\\( a^{4} - 5 a^{2} + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4']}