Hilbert modular form data - 4.4.2525.1-55.3-b

Formats: - HTML - YAML - JSON - 2024-05-31T19:34:32.723985

• 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': 1, 'disc': 2525, 'field_bad_primes': [5, 101], 'field_label': '4.4.2525.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.2525.1-55.3-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [5, 11], 'level_ideal': '[55,55,w^2 - 3*w]', 'level_label': '55.3', 'level_norm': 55, 'parallel_weight': 2, 'short_label': '55.3-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5,5,-w^3 + w^2 + 3*w]', 1], ['[11,11,-w^2 + 2*w + 3]', 1]], 'hecke_eigenvalues': [-1, 0, 6, -1, -1, 0, 0, 6, 0, 6, 0, -10, 8, 12, -6, -12, 0, 8, 2, 2, -4, 4, 6, 6, 0, 6, 6, 2, 2, -10, -4, 8, -12, 18, 2, 14, 2, 14, 2, 2, -22, -10, 0, 18, 20, -16, -10, -22, 26, -10, -6, 0, -16, -16, 2, -22, -24, -12, 20, 20, 8, -10, 36, 30, -24, -24, 2, 20, -18, -6, 18, 0, -22, -22, -22, 14, -24, 24, 0, 18, -4, -16, -6, -6, -12, 18, 0, 6, 0, -18, -12, -12, 0, -24, -22, 20, -34, -4, -22, 38, 6, -36, -6, -42, -40, 26, -24, -12, -46, -28, -28, -40, 18, 30, -24, 30, 20, 26, 6, -42, 30, 6, -10, -46, -48, 0, -10, 44, -16, -4, 14, 14, 44, -4, 44, -4, 14, 38, -10, -28, 20, 6, -42, 24, 0, -16, -16, 0, 60, 8, -10, 30, -12, -16, 32, -40, 50], 'hecke_polynomial': 'x', 'label': '4.4.2525.1-55.3-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 2525, 'ideals': ['[1, 1, 1]', '[5, 5, w]', '[5, 5, w^3 - 2*w^2 - 2*w + 3]', '[11, 11, -w^2 + 4]', '[11, 11, w^2 - 2*w - 3]', '[16, 2, 2]', '[25, 5, -w^3 + 3*w^2 - 5]', '[25, 5, 2*w^2 - 2*w - 5]', '[25, 5, -w^3 + 3*w + 3]', '[29, 29, w^3 - 4*w - 1]', '[29, 29, w^3 - 3*w^2 - w + 4]', '[41, 41, w^3 - 2*w^2 - w + 4]', '[41, 41, -w^3 + w^2 + 2*w + 2]', '[55, 55, -w^3 + 5*w + 1]', '[55, 55, w^2 + w - 2]', '[55, 55, -w^2 + 3*w]', '[55, 55, w^3 - 3*w^2 - 2*w + 5]', '[59, 59, -2*w^3 + 4*w^2 + 4*w - 7]', '[59, 59, -3*w^2 + 2*w + 7]', '[61, 61, -w^3 + 4*w^2 - 6]', '[61, 61, w^3 + w^2 - 5*w - 3]', '[71, 71, w^3 + w^2 - 4*w - 6]', '[71, 71, 3*w^2 - 2*w - 8]', '[71, 71, 3*w^2 - 4*w - 7]', '[71, 71, w^3 - 4*w^2 + w + 8]', '[79, 79, -2*w^3 + 3*w^2 + 5*w - 2]', '[79, 79, 2*w^2 - 3*w - 7]', '[79, 79, 2*w^2 - w - 8]', '[79, 79, -2*w^3 + 3*w^2 + 5*w - 4]', '[80, 10, 2*w]', '[80, 10, 2*w^3 - 4*w^2 - 4*w + 6]', '[81, 3, -3]', '[89, 89, -w - 3]', '[89, 89, w - 4]', '[101, 101, w^3 - 6*w - 2]', '[101, 101, 2*w^3 - 3*w^2 - 5*w + 3]', '[101, 101, -w^3 + 3*w^2 + 3*w - 7]', '[109, 109, -3*w^2 + 5*w + 4]', '[109, 109, -2*w^3 + w^2 + 6*w + 4]', '[121, 11, 3*w^2 - 3*w - 8]', '[121, 11, 3*w^2 - 3*w - 7]', '[121, 121, 2*w^3 - 4*w^2 - 3*w + 4]', '[121, 121, 2*w^3 - 2*w^2 - 5*w + 1]', '[125, 5, 2*w^3 - 2*w^2 - 5*w]', '[125, 5, -w^3 + 2*w^2 + 4*w - 5]', '[125, 25, -w^3 + 5*w]', '[125, 25, w^3 - 3*w^2 - 2*w + 4]', '[139, 139, -w^3 - w^2 + 6*w + 3]', '[139, 139, w^3 - 4*w^2 - w + 7]', '[145, 145, -w^3 + 3*w + 5]', '[145, 145, w^3 + 2*w^2 - 6*w - 7]', '[145, 145, w^3 - 5*w^2 + w + 10]', '[145, 145, w^3 - 3*w^2 + 7]', '[149, 149, -2*w^3 + 6*w^2 + w - 11]', '[149, 149, 2*w^3 - 7*w - 6]', '[151, 151, -w^3 + 2*w^2 + 4*w - 4]', '[151, 151, w^3 - w^2 - 5*w + 1]', '[169, 13, -4*w^2 + 5*w + 11]', '[169, 13, 3*w^3 - 6*w^2 - 7*w + 8]', '[176, 22, -2*w^2 + 8]', '[176, 22, 2*w^2 - 4*w - 6]', '[181, 181, w^3 + w^2 - 4*w - 7]', '[181, 181, -2*w^2 + 5*w + 1]', '[181, 181, 3*w^3 - 3*w^2 - 9*w + 2]', '[181, 181, -w^3 + 4*w^2 - w - 9]', '[191, 191, w^3 - 5*w + 1]', '[191, 191, -w^3 + 3*w^2 + 2*w - 3]', '[199, 199, -2*w^3 + 2*w^2 + 5*w + 4]', '[199, 199, -2*w^3 + 9*w + 4]', '[205, 205, 2*w^3 - 5*w^2 - 3*w + 6]', '[205, 205, -3*w^2 + w + 10]', '[205, 205, -3*w^2 + 5*w + 8]', '[205, 205, 2*w^3 - w^2 - 7*w]', '[229, 229, 2*w^2 - 5*w - 4]', '[229, 229, -4*w^2 + 5*w + 8]', '[241, 241, -3*w^3 + 7*w^2 + 5*w - 12]', '[241, 241, -3*w^3 + 2*w^2 + 10*w + 3]', '[256, 4, 4]', '[269, 269, -w^3 + 6*w^2 - 3*w - 13]', '[269, 269, w^3 + 3*w^2 - 6*w - 11]', '[271, 271, 2*w^3 - 2*w^2 - 7*w + 3]', '[271, 271, -2*w^3 + 4*w^2 + 5*w - 4]', '[275, 55, -2*w^3 + 5*w^2 + 2*w - 10]', '[275, 55, -w^3 + 2*w^2 - 5]', '[275, 55, 4*w^2 - 3*w - 11]', '[275, 55, -w^3 + w^2 + w + 4]', '[275, 55, 4*w^2 - 5*w - 10]', '[275, 55, -2*w^3 + w^2 + 6*w + 5]', '[289, 17, w^3 - 6*w^2 + 2*w + 11]', '[289, 17, w^3 + 3*w^2 - 7*w - 8]', '[295, 295, -4*w^2 + 3*w + 10]', '[295, 295, -3*w^3 + 8*w^2 + 6*w - 21]', '[295, 295, -3*w^3 + 2*w^2 + 7*w]', '[295, 295, w^3 - 4*w^2 - 3*w + 11]', '[305, 305, w^2 + 2*w - 8]', '[305, 305, 2*w^3 - 4*w^2 - w + 5]', '[305, 305, w^3 - 3*w^2 + w + 6]', '[305, 305, 3*w^3 - w^2 - 8*w - 5]', '[311, 311, -2*w^3 + w^2 + 5*w + 4]', '[311, 311, 2*w^3 - 5*w^2 - w + 8]', '[319, 319, -2*w^2 - w + 6]', '[319, 319, w^3 - 6*w + 2]', '[319, 319, w^3 - 3*w^2 - 3*w + 3]', '[319, 319, -2*w^2 + 5*w + 3]', '[331, 331, 3*w^3 - 3*w^2 - 11*w - 3]', '[331, 331, -3*w^3 + 6*w^2 + 8*w - 14]', '[349, 349, -3*w^3 + 6*w^2 + 6*w - 8]', '[349, 349, 3*w^3 - 3*w^2 - 9*w + 1]', '[355, 355, 3*w^3 - 11*w - 5]', '[355, 355, 3*w^3 - 2*w^2 - 8*w]', '[355, 355, 3*w^3 - 4*w^2 - 7*w]', '[355, 355, -2*w^3 + 5*w^2 + 3*w - 5]', '[355, 355, -2*w^3 + 5*w^2 + 5*w - 8]', '[355, 355, -2*w^3 + 6*w^2 + 5*w - 14]', '[355, 355, -w^3 + 7*w - 1]', '[355, 355, 2*w^3 - 3*w^2 - 8*w + 9]', '[359, 359, -2*w^3 - w^2 + 7*w + 8]', '[359, 359, -2*w^3 + 6*w^2 + w - 12]', '[359, 359, 2*w^3 - 7*w - 7]', '[359, 359, -2*w^3 + 7*w^2 - w - 12]', '[361, 19, 4*w^2 - 4*w - 11]', '[361, 19, -4*w^2 + 4*w + 9]', '[389, 389, -w^3 + 4*w^2 - w - 11]', '[389, 389, w^3 + w^2 - 4*w - 9]', '[395, 395, 2*w^2 - w - 11]', '[395, 395, 2*w^3 - 6*w^2 - 3*w + 17]', '[395, 395, 2*w^3 - w^2 - 8*w]', '[395, 395, 2*w^3 - 3*w^2 - 7*w]', '[395, 395, -4*w^3 + 10*w^2 + 8*w - 19]', '[395, 395, -3*w^3 + 4*w^2 + 10*w - 6]', '[395, 395, -w^3 - 3*w^2 + 8*w + 10]', '[395, 395, w^3 + 3*w^2 - 6*w - 10]', '[400, 10, -2*w^3 + 6*w^2 - 10]', '[400, 10, 4*w^2 - 4*w - 10]', '[400, 10, -2*w^3 + 6*w + 6]', '[401, 401, w^2 - 8]', '[401, 401, w^2 - 2*w - 7]', '[405, 15, -3*w]', '[405, 15, -3*w^3 + 6*w^2 + 6*w - 9]', '[409, 409, -3*w^2 + 5*w + 9]', '[409, 409, -3*w^3 + w^2 + 12*w + 4]', '[409, 409, -w^3 + w^2 + 6*w + 1]', '[409, 409, 3*w^2 - w - 11]', '[419, 419, w^3 - 7*w - 3]', '[419, 419, -w^3 + 3*w^2 + 4*w - 9]', '[431, 431, -2*w^3 + 2*w^2 + 7*w - 4]', '[431, 431, w^3 + 2*w^2 - 7*w - 4]', '[439, 439, -2*w^3 + 5*w^2 + 2*w - 11]', '[439, 439, 2*w^3 - w^2 - 6*w - 6]', '[445, 445, w^2 - 4*w]', '[445, 445, -4*w^3 + 10*w^2 + 6*w - 17]', '[445, 445, -w^2 - 3*w]', '[445, 445, -3*w^3 + 4*w^2 + 8*w - 4]', '[449, 449, w^3 + 3*w^2 - 7*w - 9]', '[449, 449, w^3 - 6*w^2 + 5*w + 11]', '[449, 449, 3*w^3 - 7*w^2 - 3*w + 8]', '[449, 449, -w^3 + 6*w^2 - 2*w - 12]', '[451, 451, -w^2 - 2]', '[451, 451, w^2 - 4*w - 1]', '[451, 451, w^2 + 2*w - 4]', '[451, 451, w^2 - 2*w + 3]', '[461, 461, -3*w^3 + 8*w^2 + 4*w - 18]', '[461, 461, 3*w^3 - 4*w^2 - 5*w - 1]', '[464, 58, 2*w^3 - 8*w - 2]', '[464, 58, 2*w^3 - 6*w^2 - 2*w + 8]', '[479, 479, -w^3 + 5*w^2 - 2*w - 16]', '[479, 479, 2*w^3 - 4*w^2 - w - 1]', '[491, 491, -w^3 + 7*w^2 - w - 18]', '[491, 491, w^3 + 2*w^2 - 5*w - 11]', '[491, 491, -w^3 + 5*w^2 - 2*w - 13]', '[491, 491, w^3 + 4*w^2 - 10*w - 13]', '[499, 499, 3*w^3 - 4*w^2 - 8*w + 3]', '[499, 499, -w^3 + 4*w^2 + 2*w - 6]', '[499, 499, -w^3 - w^2 + 7*w + 1]', '[499, 499, 3*w^3 - 5*w^2 - 7*w + 6]', '[505, 505, w^3 + 3*w^2 - 7*w - 10]', '[505, 505, -5*w^2 + 6*w + 14]', '[505, 505, 2*w^3 - 2*w^2 - 7*w - 5]', '[505, 505, -3*w^3 + 11*w^2 + 3*w - 26]', '[505, 505, w^3 - w^2 - 2*w + 5]', '[505, 505, w^3 - 4*w^2 - w + 14]', '[529, 23, 4*w^3 - 3*w^2 - 13*w - 1]', '[529, 23, w^3 + 4*w^2 - 9*w - 8]', '[545, 545, -2*w^3 + 8*w^2 - 3*w - 13]', '[545, 545, 2*w^3 - 4*w^2 - 5*w + 2]', '[545, 545, -3*w^3 + 5*w^2 + 4*w]', '[545, 545, 3*w^3 - 6*w^2 - 4*w + 5]', '[569, 569, -3*w^3 + 7*w^2 + 4*w - 14]', '[569, 569, 3*w^3 - 4*w^2 - 7*w + 1]', '[569, 569, 3*w^3 - 5*w^2 - 6*w + 7]', '[569, 569, w^3 - 4*w^2 + 4*w + 7]', '[571, 571, -w^3 + 7*w^2 - w - 17]', '[571, 571, w^3 + 4*w^2 - 10*w - 12]', '[599, 599, 3*w^3 - 6*w^2 - 5*w + 7]', '[599, 599, 3*w^3 - 3*w^2 - 8*w + 1]', '[605, 55, -w^3 + w^2 + 6*w]', '[605, 55, 3*w^3 - 3*w^2 - 8*w]', '[605, 55, -2*w^3 + 4*w^2 + 7*w - 9]', '[605, 55, -w^3 + 2*w^2 + 5*w - 6]', '[605, 605, w^3 - 2*w^2 - 2*w + 8]', '[605, 605, 2*w^2 - 5*w - 7]', '[605, 605, -2*w^2 - w + 10]', '[605, 605, -w^3 + w^2 + 3*w + 5]', '[619, 619, -w^3 + 3*w^2 + 4*w - 7]', '[619, 619, 2*w^3 - 6*w^2 - w + 13]', '[619, 619, -w^3 + 3*w^2 - 2*w - 6]', '[619, 619, w^3 - 7*w - 1]', '[625, 5, 5]', '[625, 25, -w^3 + w^2 + 5]', '[625, 25, -2*w^3 + w^2 + 5*w + 5]', '[625, 25, -2*w^3 + 5*w^2 + w - 9]', '[625, 25, -w^3 + 2*w^2 - w - 5]', '[641, 641, 3*w^3 - 3*w^2 - 7*w + 1]', '[641, 641, -3*w^3 + 6*w^2 + 4*w - 6]', '[649, 649, 4*w^3 - 7*w^2 - 7*w + 13]', '[649, 649, -4*w^3 + 13*w^2 + 6*w - 28]', '[649, 649, 2*w^3 - 5*w - 6]', '[649, 649, 2*w^3 - w^2 - 8*w + 1]', '[656, 82, 2*w^3 - 4*w^2 - 2*w + 8]', '[656, 82, -2*w^3 + 2*w^2 + 4*w + 4]', '[659, 659, -2*w^3 + 5*w^2 + 6*w - 7]', '[659, 659, -2*w^3 + w^2 + 10*w - 2]', '[661, 661, 2*w^3 - 4*w^2 - w + 6]', '[661, 661, w^3 + 2*w^2 - 5*w - 12]', '[671, 671, -w^3 + 3]', '[671, 671, -4*w^3 + 3*w^2 + 11*w + 4]', '[671, 671, -4*w^3 + 9*w^2 + 5*w - 14]', '[671, 671, -w^3 + 3*w^2 - 3*w - 2]', '[695, 695, -w^3 + 5*w^2 - 3*w - 11]', '[695, 695, w^3 - 5*w^2 - 2*w + 16]', '[695, 695, -3*w^3 + 2*w^2 + 8*w + 5]', '[695, 695, -2*w^3 + 3*w^2 + 2*w - 5]', '[701, 701, -w^3 + 3*w^2 - w - 9]', '[701, 701, -2*w^3 + w^2 + 9*w - 1]', '[701, 701, 2*w^3 - 8*w - 1]', '[701, 701, w^3 - 2*w - 8]', '[709, 709, 2*w^3 - 2*w^2 - 9*w + 1]', '[709, 709, w^3 - w^2 + w - 2]', '[719, 719, -5*w^2 + 4*w + 14]', '[719, 719, -5*w^2 + 6*w + 13]', '[725, 145, w^3 - 2*w^2 - 5*w + 5]', '[725, 145, -w^3 + 4*w^2 + 2*w - 5]', '[725, 145, -2*w^3 + 7*w^2 + 2*w - 12]', '[725, 145, -2*w^3 - w^2 + 10*w + 5]', '[725, 145, -w^3 + w^2 + 6*w - 1]', '[725, 145, -w^3 - w^2 + 7*w]', '[739, 739, 4*w^3 - 6*w^2 - 11*w + 7]', '[739, 739, -4*w^3 + 6*w^2 + 11*w - 6]', '[745, 745, -3*w^3 + 6*w^2 + 10*w - 18]', '[745, 745, -2*w^3 + 4*w^2 + 6*w - 3]', '[745, 745, 2*w^3 - 7*w^2 - w + 10]', '[745, 745, 4*w^3 + w^2 - 16*w - 10]', '[751, 751, -w^3 + 7*w^2 - 4*w - 16]', '[751, 751, -w^3 - 4*w^2 + 7*w + 14]', '[755, 755, w + 5]', '[755, 755, w^3 - w^2 - 4*w - 5]', '[755, 755, -2*w^3 + 9*w^2 - 22]', '[755, 755, w^3 - 7*w^2 + 3*w + 18]', '[769, 769, w^3 - 3*w^2 - w + 11]', '[769, 769, -w^3 + 4*w + 8]', '[781, 781, -2*w^3 - w^2 + 7*w + 9]', '[781, 781, -3*w^3 - 2*w^2 + 14*w + 13]', '[781, 781, -4*w^3 + 8*w^2 + 7*w - 17]', '[781, 781, -2*w^3 + 3*w^2 + 4*w - 9]', '[781, 781, 2*w^3 - 3*w^2 - 4*w - 4]', '[781, 781, -4*w^3 + 4*w^2 + 11*w + 6]', '[781, 781, 3*w^3 - 11*w^2 - w + 22]', '[781, 781, -2*w^3 + 7*w^2 - w - 13]', '[811, 811, -w^3 + 4*w^2 - 14]', '[811, 811, -w^3 - w^2 + 5*w + 11]', '[829, 829, -w^3 + 2*w^2 - w - 6]', '[829, 829, w^2 + 3*w - 1]', '[829, 829, 3*w^3 - 13*w - 6]', '[829, 829, w^3 - w^2 - 6]', '[841, 29, 5*w^2 - 5*w - 14]', '[841, 29, w^2 - w - 8]', '[841, 841, -3*w^3 + 8*w^2 + 3*w - 16]', '[841, 841, -3*w^3 + w^2 + 10*w + 8]', '[845, 65, 5*w^2 - 7*w - 15]', '[845, 65, -4*w^3 + 5*w^2 + 11*w]', '[845, 65, 3*w^3 - 4*w^2 - 12*w + 8]', '[845, 65, 2*w^3 - 9*w^2 - 2*w + 29]', '[859, 859, -w^3 + 6*w^2 - 11]', '[859, 859, -3*w^3 + 5*w^2 + 8*w - 2]', '[869, 869, -w^3 + 7*w^2 - 2*w - 18]', '[869, 869, 3*w^3 - 10*w^2 - 5*w + 21]', '[869, 869, -3*w^3 + w^2 + 13*w + 11]', '[869, 869, -3*w^3 + 8*w^2 + 5*w - 13]', '[869, 869, -3*w^3 + w^2 + 12*w + 3]', '[869, 869, -3*w^3 + 8*w^2 + 6*w - 22]', '[869, 869, 3*w^3 + w^2 - 16*w - 9]', '[869, 869, -w^3 - 4*w^2 + 9*w + 14]', '[880, 110, -2*w^3 + 10*w + 2]', '[880, 110, 2*w^2 + 2*w - 4]', '[880, 110, -2*w^2 + 6*w]', '[880, 110, 2*w^3 - 6*w^2 - 4*w + 10]', '[881, 881, -3*w^3 + w^2 + 11*w + 2]', '[881, 881, -3*w^3 + 8*w^2 + 4*w - 11]', '[891, 33, 3*w^2 - 12]', '[891, 33, -3*w^2 + 6*w + 9]', '[905, 905, -3*w^3 + 7*w^2 + 7*w - 11]', '[905, 905, 2*w^3 - 5*w^2 - w]', '[905, 905, 3*w^3 + 3*w^2 - 13*w - 15]', '[905, 905, 3*w^3 - 12*w - 5]', '[905, 905, -3*w^3 + 5*w^2 + 10*w - 12]', '[905, 905, 3*w^3 - 12*w^2 + 2*w + 22]', '[905, 905, 2*w^3 - 7*w^2 - w + 21]', '[905, 905, 2*w^3 - 5*w^2 - 4*w + 5]', '[911, 911, -2*w^2 - w + 11]', '[911, 911, 2*w^2 - 5*w - 8]', '[919, 919, w^3 - 5*w^2 - w + 8]', '[919, 919, -w^3 - 2*w^2 + 8*w + 3]', '[941, 941, 2*w^3 + 2*w^2 - 11*w - 7]', '[941, 941, -2*w^3 + 8*w^2 + w - 14]', '[944, 118, -4*w^3 + 8*w^2 + 8*w - 14]', '[944, 118, -6*w^2 + 4*w + 14]', '[955, 955, 3*w^3 - 9*w^2 - 2*w + 18]', '[955, 955, 2*w^3 - w^2 - 4*w - 5]', '[955, 955, -w^3 - w^2 + 3*w + 9]', '[955, 955, -w^3 + 2*w^2 - 2*w - 5]', '[961, 31, -2*w^2 + 2*w + 11]', '[961, 31, 5*w^2 - 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w - 9]', '[1699, 1699, -w^3 + 3*w^2 - 2*w - 9]', '[1709, 1709, -w^3 + 6*w^2 - 5*w - 13]', '[1709, 1709, w^3 + 3*w^2 - 4*w - 13]', '[1711, 1711, -w^3 - 6*w^2 + 5*w + 13]', '[1711, 1711, 2*w^3 - 9*w + 3]', '[1711, 1711, -3*w^3 + 6*w^2 + 4*w - 13]', '[1711, 1711, -w^3 + 5*w^2 + 3*w - 18]', '[1721, 1721, 4*w^3 - 6*w^2 - 9*w + 3]', '[1721, 1721, -2*w^3 + 5*w^2 + w - 13]', '[1721, 1721, 2*w^3 - w^2 - 5*w - 9]', '[1721, 1721, 4*w^3 - 6*w^2 - 9*w + 8]', '[1744, 218, -6*w^2 + 10*w + 8]', '[1744, 218, -4*w^3 + 2*w^2 + 12*w + 8]', '[1745, 1745, 3*w^3 + 3*w^2 - 14*w - 15]', '[1745, 1745, w^3 - 5*w^2 + w + 18]', '[1745, 1745, -6*w^2 + 7*w + 15]', '[1745, 1745, -2*w^3 + 7*w^2 + 4*w - 24]', '[1759, 1759, -w^3 + 3*w^2 + 5*w - 9]', '[1759, 1759, w^3 - 8*w - 2]', '[1769, 1769, 7*w^2 - 6*w - 14]', '[1769, 1769, w^3 + 3*w^2 - 3*w - 2]', '[1769, 1769, w^3 - 6*w^2 + 6*w + 1]', '[1769, 1769, -7*w^2 + 8*w + 13]', '[1775, 355, w^3 - 3*w^2 + 2*w + 10]', '[1775, 355, -w^3 - w^2 - 3]', '[1775, 355, -6*w^2 + 5*w + 15]', '[1775, 355, -4*w^2 + 15]', '[1775, 355, 2*w^3 - 3*w^2 - 4*w + 10]', '[1775, 355, -3*w^3 + 2*w^2 + 5*w - 4]', '[1775, 355, -3*w^3 + 7*w^2]', '[1775, 355, -2*w^3 + 3*w^2 + 4*w + 5]', '[1775, 355, 4*w^2 - 8*w - 11]', '[1775, 355, w^3 - w - 10]', '[1775, 355, -6*w^2 + 7*w + 14]', '[1775, 355, w^3 - 4*w^2 + 5*w - 5]', '[1789, 1789, 3*w^3 - 3*w^2 - 10*w + 6]', '[1789, 1789, -w^3 - 4*w^2 + 10*w + 7]', '[1795, 1795, -4*w^3 + 8*w^2 + 12*w - 21]', '[1795, 1795, -3*w^3 + 6*w^2 + 8*w - 6]', '[1795, 1795, -5*w^3 + 7*w^2 + 7*w - 5]', '[1795, 1795, -w^2 - 5*w + 11]', '[1795, 1795, 3*w^3 - 9*w^2 - 2*w + 10]', '[1795, 1795, -2*w^3 + 2*w^2 + 11*w - 11]', '[1795, 1795, 2*w^3 - 7*w^2 - 2*w + 10]', '[1795, 1795, 4*w^3 + w^2 - 17*w - 10]', '[1801, 1801, -2*w^3 + 5*w^2 - w - 8]', '[1801, 1801, -w^3 - 5*w^2 + 10*w + 13]', '[1801, 1801, w^3 - 8*w^2 + 3*w + 17]', '[1801, 1801, 2*w^3 - w^2 - 3*w - 6]', '[1805, 95, 4*w^3 - 4*w^2 - 11*w]', '[1805, 95, -4*w^3 + 4*w^2 + 9*w]', '[1805, 95, -3*w^3 + 6*w^2 + 10*w - 13]', '[1805, 95, w^3 - 2*w^2 - 6*w + 7]', '[1811, 1811, 4*w^3 - 3*w^2 - 14*w + 1]', '[1811, 1811, 4*w^3 - 9*w^2 - 8*w + 12]', '[1831, 1831, -w^3 + 8*w - 1]', '[1831, 1831, 2*w^2 + 3*w - 3]', '[1831, 1831, 5*w^3 - 11*w^2 - 9*w + 16]', '[1831, 1831, -w^3 + 3*w^2 + 5*w - 6]', '[1849, 43, -2*w^3 + 6*w^2 + 3*w - 6]', '[1849, 43, 3*w^3 - 8*w^2 - 6*w + 13]', '[1859, 143, 3*w^3 - 11*w^2 + 24]', '[1859, 143, 7*w^3 - 17*w^2 - 13*w + 32]', '[1859, 143, 5*w^3 - 3*w^2 - 17*w - 13]', '[1859, 143, -4*w^3 + w^2 + 20*w + 6]', '[1871, 1871, -3*w^3 - w^2 + 11*w + 12]', '[1871, 1871, 3*w^3 + 3*w^2 - 16*w - 17]', '[1879, 1879, -w^3 + 6*w^2 - 9]', '[1879, 1879, -3*w^3 + 7*w^2 + 6*w - 8]', '[1901, 1901, -w^3 - w^2 + 2*w - 2]', '[1901, 1901, -2*w^3 + 10*w^2 - 3*w - 21]', '[1931, 1931, w^3 + 2*w^2 - 4*w - 13]', '[1931, 1931, w^3 - 5*w^2 + 3*w + 14]', '[1936, 22, 6*w^2 - 6*w - 16]', '[1936, 22, 6*w^2 - 6*w - 14]', '[1936, 242, 4*w^3 - 8*w^2 - 6*w + 8]', '[1936, 242, 4*w^3 - 4*w^2 - 10*w + 2]', '[1945, 1945, 2*w^3 - 5*w^2 - 6*w + 5]', '[1945, 1945, -5*w^3 + 9*w^2 + 14*w - 18]', '[1945, 1945, 3*w^3 - 14*w - 5]', '[1945, 1945, -5*w^3 + 11*w^2 + 11*w - 17]', '[1949, 1949, -w^3 + 2*w^2 + 6*w - 3]', '[1949, 1949, 2*w^3 - 8*w^2 + 2*w + 17]', '[1949, 1949, 2*w^3 + 2*w^2 - 8*w - 13]', '[1949, 1949, w^3 - w^2 - 7*w + 4]', '[1951, 1951, -3*w^3 + 12*w^2 - w - 27]', '[1951, 1951, -3*w^3 + 8*w^2 + 6*w - 23]', '[1975, 395, w^3 + 2*w^2 - 10*w]', '[1975, 395, -3*w^3 + 5*w^2 + 9*w - 1]', '[1975, 395, 2*w^3 - w^2 - 11*w]', '[1975, 395, 3*w^3 + 3*w^2 - 15*w - 16]', '[1975, 395, -2*w^3 - 2*w^2 + 9*w + 15]', '[1975, 395, -w^2 + 10]', '[1975, 395, 2*w^3 - 8*w^2 + w + 20]', '[1975, 395, w^2 - 2*w - 9]', '[1975, 395, 3*w^3 - 12*w^2 + 25]', '[1975, 395, w^3 - 5*w^2 - 3*w + 7]', '[1975, 395, -2*w^3 + 5*w^2 + 7*w - 10]', '[1975, 395, -3*w^3 + 4*w^2 + 10*w - 10]', '[1979, 1979, -4*w^3 + 6*w^2 + 7*w - 3]', '[1979, 1979, 4*w^3 - 6*w^2 - 7*w + 6]', '[1991, 1991, -6*w^3 + 2*w^2 + 23*w + 9]', '[1991, 1991, 3*w^3 - 11*w^2 - 6*w + 23]', '[1991, 1991, -2*w^3 + 2*w^2 + 6*w + 7]', '[1991, 1991, -3*w^3 + 12*w^2 + w - 26]', '[1991, 1991, -3*w^3 - 3*w^2 + 16*w + 16]', '[1991, 1991, -2*w^3 + 4*w^2 + 4*w - 13]', '[1991, 1991, -5*w^3 + 11*w^2 + 7*w - 7]', '[1991, 1991, w^3 + w^2 - 10*w + 6]', '[2000, 10, 4*w^3 - 4*w^2 - 10*w]', '[2000, 10, -2*w^3 + 4*w^2 + 8*w - 10]', '[2000, 50, -2*w^3 + 10*w]', '[2000, 50, 2*w^3 - 6*w^2 - 4*w + 8]', '[2005, 2005, -5*w^3 + 8*w^2 + 13*w - 11]', '[2005, 2005, w^3 - 2*w^2 - 7*w]', '[2005, 2005, -6*w^3 + 14*w^2 + 11*w - 24]', '[2005, 2005, w^3 - 8*w]', '[2011, 2011, 3*w^3 - 2*w^2 - 8*w - 7]', '[2011, 2011, -w^2 - w - 4]', '[2011, 2011, -w^2 + 3*w - 6]', '[2011, 2011, 3*w^3 - 7*w^2 - 3*w + 14]', '[2025, 15, 3*w^3 - 9*w^2 + 15]', '[2025, 15, -6*w^2 + 6*w + 15]', '[2025, 15, 3*w^3 - 9*w - 9]', '[2029, 2029, w^3 + 4*w^2 - 6*w - 17]', '[2029, 2029, w^3 - 2*w^2 - 3*w - 4]', '[2029, 2029, -w^3 + w^2 + 4*w - 8]', '[2029, 2029, w^3 - 7*w^2 + 5*w + 18]', '[2045, 2045, 3*w^3 - 5*w^2 - 9*w]', '[2045, 2045, -2*w^3 + 7*w^2 - w - 15]', '[2045, 2045, -3*w^3 + 2*w^2 + 13*w - 2]', '[2045, 2045, -w^3 + 8*w^2 - 4*w - 20]', '[2045, 2045, w^3 + 5*w^2 - 9*w - 17]', '[2045, 2045, 3*w^3 - w^2 - 11*w]', '[2045, 2045, -2*w^3 - w^2 + 7*w + 11]', '[2045, 2045, -5*w^3 + 14*w^2 + 9*w - 28]', '[2059, 2059, -3*w^3 + 6*w^2 + 7*w - 3]', '[2059, 2059, 3*w^2 - 9*w + 2]', '[2059, 2059, 6*w^2 - w - 12]', '[2059, 2059, -4*w^3 + 5*w^2 + 10*w - 4]', '[2059, 2059, 4*w^3 - 7*w^2 - 8*w + 7]', '[2059, 2059, -6*w^2 + 11*w + 7]', '[2059, 2059, 3*w^2 + 3*w - 4]', '[2059, 2059, -3*w^3 + 3*w^2 + 10*w - 7]', '[2069, 2069, w^3 - w^2 + 2*w - 3]', '[2069, 2069, -4*w^3 + 6*w^2 + 9*w - 7]', '[2069, 2069, 4*w^3 - 6*w^2 - 9*w + 4]', '[2069, 2069, -w^3 + 2*w^2 - 3*w - 1]', '[2081, 2081, 2*w^3 - 3*w^2 - 9*w + 7]', '[2081, 2081, -2*w^3 + 3*w^2 + 9*w - 3]', '[2089, 2089, w^3 - 3*w^2 - 2*w + 13]', '[2089, 2089, -w^3 + 5*w + 9]', '[2095, 2095, w^3 - 4*w + 5]', '[2095, 2095, -3*w^3 + 3*w^2 + 4*w - 4]', '[2095, 2095, 2*w^3 - 3*w^2 - 8*w - 5]', '[2095, 2095, -w^3 - 5*w^2 + 10*w + 16]', '[2101, 2101, -w^3 - w^2 + 10*w + 6]', '[2101, 2101, -4*w^3 + 6*w^2 + 8*w - 3]', '[2101, 2101, 4*w^3 - 6*w^2 - 8*w + 7]', '[2101, 2101, w^3 - 4*w^2 - 5*w + 14]', '[2111, 2111, -4*w^3 + 7*w^2 + 6*w - 7]', '[2111, 2111, -4*w^3 + 5*w^2 + 8*w - 2]', '[2129, 2129, w^3 + 5*w^2 - 10*w - 14]', '[2129, 2129, -w^3 + 8*w^2 - 3*w - 18]', '[2131, 2131, w^3 - 9*w^2 + 8*w + 17]', '[2131, 2131, 4*w^3 - 10*w^2 - 6*w + 13]', '[2155, 2155, 2*w^3 - 7*w^2 + 2*w + 13]', '[2155, 2155, 4*w^3 - 3*w^2 - 9*w - 5]', '[2155, 2155, -4*w^3 + 12*w^2 + 4*w - 27]', '[2155, 2155, -2*w^3 - w^2 + 6*w + 10]', '[2161, 2161, -4*w^3 + 7*w^2 + 8*w - 8]', '[2161, 2161, 4*w^3 - 5*w^2 - 10*w + 3]', '[2179, 2179, -3*w^3 + 10*w^2 + 3*w - 17]', '[2179, 2179, -2*w^3 + 7*w^2 + 4*w - 12]', '[2179, 2179, 2*w^3 + w^2 - 12*w - 3]', '[2179, 2179, 3*w^3 + w^2 - 14*w - 7]', '[2189, 2189, -w^3 + 2*w^2 + 6*w - 4]', '[2189, 2189, -w^3 + 2*w^2 + 6]', '[2189, 2189, 7*w^3 - 4*w^2 - 25*w - 12]', '[2189, 2189, 3*w^3 + 6*w^2 - 23*w - 22]', '[2195, 2195, 3*w^3 + 2*w^2 - 16*w - 10]', '[2195, 2195, -4*w^3 + 8*w^2 + 9*w - 8]', '[2195, 2195, w^3 - 6*w^2 - w + 10]', '[2195, 2195, -5*w^3 + 10*w^2 + 13*w - 23]', '[2209, 47, -3*w^3 - 4*w^2 + 13*w + 16]', '[2209, 47, 2*w^3 - 6*w^2 + 4*w + 9]', '[2221, 2221, -2*w^2 + w + 13]', '[2221, 2221, 3*w^3 - 4*w^2 - 7*w - 6]', '[2221, 2221, 4*w^3 - 12*w^2 - 3*w + 17]', '[2221, 2221, -2*w^2 + 3*w + 12]', '[2224, 278, -2*w^3 - 2*w^2 + 12*w + 6]', '[2224, 278, 2*w^3 - 8*w^2 - 2*w + 14]', '[2225, 445, 2*w^3 - 5*w^2 + 10]', '[2225, 445, -2*w^3 - 4*w^2 + 11*w + 15]', '[2225, 445, 5*w^3 + w^2 - 17*w - 14]', '[2225, 445, 2*w^3 - w^2 - 4*w - 7]', '[2225, 445, 2*w^3 - 10*w^2 + 3*w + 20]', '[2225, 445, 5*w^3 - 16*w^2 + 25]', '[2245, 2245, 4*w^3 - 8*w^2 - 3*w + 10]', '[2245, 2245, 4*w^3 - 6*w^2 - 7*w + 5]', '[2245, 2245, -w^3 + 4*w^2 + 6*w - 19]', '[2245, 2245, -2*w^3 + 5*w^2 + 8*w - 16]', '[2245, 2245, 5*w^3 - 3*w^2 - 14*w - 5]', '[2245, 2245, -w^3 + 9*w^2 - 7*w - 15]', '[2245, 2245, -w^3 + w^2 + 7*w - 2]', '[2245, 2245, w^2 - 5*w + 9]', '[2251, 2251, 4*w^3 - 11*w^2 - 2*w + 18]', '[2251, 2251, -5*w^3 + 5*w^2 + 14*w - 8]', '[2255, 2255, w^3 - 8*w^2 + 5*w + 17]', '[2255, 2255, -2*w^3 - 4*w^2 + 13*w + 15]', '[2255, 2255, -3*w^3 - w^2 + 13*w + 6]', '[2255, 2255, -4*w^3 + 6*w^2 + 9*w - 6]', '[2255, 2255, 4*w^3 - 6*w^2 - 9*w + 5]', '[2255, 2255, -3*w^3 + 10*w^2 + 2*w - 15]', '[2255, 2255, -2*w^3 + 10*w^2 - w - 22]', '[2255, 2255, w^3 + 5*w^2 - 8*w - 15]', '[2269, 2269, -3*w^3 + 8*w^2 + 5*w - 11]', '[2269, 2269, w^3 - 3*w^2 - 2*w - 2]', '[2269, 2269, -w^3 + 5*w - 6]', '[2269, 2269, -3*w^3 + w^2 + 12*w + 1]', '[2281, 2281, -2*w^3 + 7*w^2 + 3*w - 11]', '[2281, 2281, -2*w^3 - w^2 + 11*w + 3]', '[2291, 2291, -2*w^3 + 4*w^2 + 8*w - 7]', '[2291, 2291, 2*w^3 - 4*w^2 - w + 11]', '[2291, 2291, 4*w^2 - 7*w - 13]', '[2291, 2291, -5*w^3 + 4*w^2 + 16*w + 2]', '[2291, 2291, -5*w^3 + 11*w^2 + 9*w - 17]', '[2291, 2291, -4*w^2 + w + 16]', '[2291, 2291, 2*w^3 - 2*w^2 - 3*w - 8]', '[2291, 2291, -2*w^3 + 2*w^2 + 10*w - 3]', '[2305, 2305, -8*w^3 + 19*w^2 + 18*w - 44]', '[2305, 2305, 2*w^3 - 8*w^2 - 3*w + 15]', '[2305, 2305, -3*w^3 + 9*w^2 + 2*w - 8]', '[2305, 2305, 2*w^3 + 7*w^2 - 16*w - 15]', '[2311, 2311, -2*w^3 + 4*w^2 + 8*w - 9]', '[2311, 2311, 2*w^3 - 2*w^2 - 10*w + 1]', '[2320, 290, -2*w^3 + 6*w + 10]', '[2320, 290, 2*w^3 + 4*w^2 - 12*w - 14]', '[2320, 290, 2*w^3 - 10*w^2 + 2*w + 20]', '[2320, 290, 2*w^3 - 6*w^2 + 14]', '[2341, 2341, -w^3 + 3*w^2 - 3*w - 8]', '[2341, 2341, w^3 - 9]', '[2349, 87, -3*w^3 + 12*w + 3]', '[2349, 87, -3*w^3 + 9*w^2 + 3*w - 12]', '[2351, 2351, -2*w^3 + 7*w^2 + 2*w - 9]', '[2351, 2351, -3*w^3 + 7*w^2 + 7*w - 9]', '[2371, 2371, w^3 + 5*w^2 - 9*w - 16]', '[2371, 2371, -w^3 + 8*w^2 - 4*w - 19]', '[2384, 298, -4*w^3 + 12*w^2 + 2*w - 22]', '[2384, 298, 4*w^3 - 14*w - 12]', '[2389, 2389, -w^3 + 7*w^2 - 6*w - 16]', '[2389, 2389, w^3 + 4*w^2 - 5*w - 16]', '[2395, 2395, 3*w^3 - 6*w^2 - 11*w + 5]', '[2395, 2395, -8*w^3 + 15*w^2 + 21*w - 28]', '[2395, 2395, 7*w^2 - 11*w - 10]', '[2395, 2395, -5*w^3 + 14*w^2 + 4*w - 18]', '[2399, 2399, -5*w^3 + 10*w^2 + 8*w - 16]', '[2399, 2399, w^3 + 5*w^2 - 9*w - 14]', '[2399, 2399, w^3 - 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5*w^2 + 19]', '[2495, 2495, 5*w^2 - 2*w - 18]', '[2495, 2495, -3*w^3 + 3*w^2 + 6*w + 5]', '[2495, 2495, w^3 + 5*w^2 - 9*w - 15]', '[2495, 2495, -3*w^3 + 11*w^2 - w - 22]', '[2495, 2495, 2*w^3 - 7*w^2 - 3*w + 23]', '[2501, 2501, 5*w^3 - 3*w^2 - 12*w - 2]', '[2501, 2501, -w^3 + 4*w^2 - 6*w - 6]', '[2501, 2501, w^3 + w^2 + w - 9]', '[2501, 2501, -5*w^3 + 12*w^2 + 3*w - 12]', '[2519, 2519, -5*w^3 + 8*w^2 + 13*w + 2]', '[2519, 2519, w^3 + 4*w^2 - 10*w - 6]', '[2519, 2519, 5*w^3 - 6*w^2 - 11*w - 4]', '[2519, 2519, 3*w^3 - 8*w^2 + 12]', '[2525, 505, -5*w^3 + 6*w^2 + 14*w]', '[2525, 505, -4*w^3 + 10*w^2 + 5*w - 10]', '[2525, 505, 4*w^3 + w^2 - 19*w - 11]', '[2525, 505, -2*w^3 + w^2 + 10*w - 5]', '[2525, 505, -2*w^3 + 3*w^2 + 9*w - 5]', '[2525, 505, 2*w^3 - 5*w^2 - 6*w + 4]', '[2525, 505, -4*w^3 + 2*w^2 + 13*w - 1]', '[2525, 505, 4*w^3 - 13*w^2 - 5*w + 25]', '[2525, 505, 5*w^3 - 9*w^2 - 11*w + 15]', '[2539, 2539, -2*w^3 + 6*w^2 + 2*w - 19]', '[2539, 2539, 5*w^3 - 7*w^2 - 12*w + 1]', '[2539, 2539, -5*w^3 + 8*w^2 + 11*w - 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9*w - 30]', '[9955, 9955, 7*w^3 - 2*w^2 - 24*w - 6]', '[9955, 9955, 7*w^3 - 22*w^2 + 7*w + 10]', '[9955, 9955, 3*w^3 - 9*w^2 - 7*w + 13]', '[9955, 9955, 4*w^3 - 3*w^2 - 19*w - 2]', '[9955, 9955, -7*w^3 + 9*w^2 + 19*w - 10]', '[9971, 767, -w^3 + 13*w^2 - 3*w - 38]', '[9971, 767, -2*w^3 - 7*w^2 + 14*w + 19]', '[9971, 767, 2*w^3 - 13*w^2 + 6*w + 24]', '[9971, 767, w^3 + 5*w^2 - 13*w - 1]', '[10000, 10, 10]', '[10000, 50, -2*w^3 + 2*w^2 + 10]', '[10000, 50, -4*w^3 + 2*w^2 + 10*w + 10]', '[10000, 50, -4*w^3 + 10*w^2 + 2*w - 18]', '[10000, 50, -2*w^3 + 4*w^2 - 2*w - 10]'], 'label': '4.4.2525.1', 'narrow_class_no': 1, 'primes': ['[5, 5, w]', '[5, 5, w^3 - 2*w^2 - 2*w + 3]', '[11, 11, -w^2 + 4]', '[11, 11, w^2 - 2*w - 3]', '[16, 2, 2]', '[29, 29, w^3 - 4*w - 1]', '[29, 29, w^3 - 3*w^2 - w + 4]', '[41, 41, w^3 - 2*w^2 - w + 4]', '[41, 41, -w^3 + w^2 + 2*w + 2]', '[59, 59, -2*w^3 + 4*w^2 + 4*w - 7]', '[59, 59, -3*w^2 + 2*w + 7]', '[61, 61, -w^3 + 4*w^2 - 6]', '[61, 61, w^3 + w^2 - 5*w - 3]', '[71, 71, w^3 + w^2 - 4*w - 6]', '[71, 71, 3*w^2 - 2*w - 8]', '[71, 71, 3*w^2 - 4*w - 7]', '[71, 71, w^3 - 4*w^2 + w + 8]', '[79, 79, -2*w^3 + 3*w^2 + 5*w - 2]', '[79, 79, 2*w^2 - 3*w - 7]', '[79, 79, 2*w^2 - w - 8]', '[79, 79, -2*w^3 + 3*w^2 + 5*w - 4]', '[81, 3, -3]', '[89, 89, -w - 3]', '[89, 89, w - 4]', '[101, 101, w^3 - 6*w - 2]', '[101, 101, 2*w^3 - 3*w^2 - 5*w + 3]', '[101, 101, -w^3 + 3*w^2 + 3*w - 7]', '[109, 109, -3*w^2 + 5*w + 4]', '[109, 109, -2*w^3 + w^2 + 6*w + 4]', '[121, 11, 3*w^2 - 3*w - 8]', '[139, 139, -w^3 - w^2 + 6*w + 3]', '[139, 139, w^3 - 4*w^2 - w + 7]', '[149, 149, -2*w^3 + 6*w^2 + w - 11]', '[149, 149, 2*w^3 - 7*w - 6]', '[151, 151, -w^3 + 2*w^2 + 4*w - 4]', '[151, 151, w^3 - w^2 - 5*w + 1]', '[169, 13, -4*w^2 + 5*w + 11]', '[169, 13, 3*w^3 - 6*w^2 - 7*w + 8]', '[181, 181, w^3 + w^2 - 4*w - 7]', '[181, 181, -2*w^2 + 5*w + 1]', '[181, 181, 3*w^3 - 3*w^2 - 9*w + 2]', '[181, 181, -w^3 + 4*w^2 - w - 9]', '[191, 191, w^3 - 5*w + 1]', '[191, 191, -w^3 + 3*w^2 + 2*w - 3]', '[199, 199, -2*w^3 + 2*w^2 + 5*w + 4]', '[199, 199, -2*w^3 + 9*w + 4]', '[229, 229, 2*w^2 - 5*w - 4]', '[229, 229, -4*w^2 + 5*w + 8]', '[241, 241, -3*w^3 + 7*w^2 + 5*w - 12]', '[241, 241, -3*w^3 + 2*w^2 + 10*w + 3]', '[269, 269, -w^3 + 6*w^2 - 3*w - 13]', '[269, 269, w^3 + 3*w^2 - 6*w - 11]', '[271, 271, 2*w^3 - 2*w^2 - 7*w + 3]', '[271, 271, -2*w^3 + 4*w^2 + 5*w - 4]', '[289, 17, w^3 - 6*w^2 + 2*w + 11]', '[289, 17, w^3 + 3*w^2 - 7*w - 8]', '[311, 311, -2*w^3 + w^2 + 5*w + 4]', '[311, 311, 2*w^3 - 5*w^2 - w + 8]', '[331, 331, 3*w^3 - 3*w^2 - 11*w - 3]', '[331, 331, -3*w^3 + 6*w^2 + 8*w - 14]', '[349, 349, -3*w^3 + 6*w^2 + 6*w - 8]', '[349, 349, 3*w^3 - 3*w^2 - 9*w + 1]', '[359, 359, -2*w^3 - w^2 + 7*w + 8]', '[359, 359, -2*w^3 + 6*w^2 + w - 12]', '[359, 359, 2*w^3 - 7*w - 7]', '[359, 359, -2*w^3 + 7*w^2 - w - 12]', '[361, 19, 4*w^2 - 4*w - 11]', '[361, 19, -4*w^2 + 4*w + 9]', '[389, 389, -w^3 + 4*w^2 - w - 11]', '[389, 389, w^3 + w^2 - 4*w - 9]', '[401, 401, w^2 - 8]', '[401, 401, w^2 - 2*w - 7]', '[409, 409, -3*w^2 + 5*w + 9]', '[409, 409, -3*w^3 + w^2 + 12*w + 4]', '[409, 409, -w^3 + w^2 + 6*w + 1]', '[409, 409, 3*w^2 - w - 11]', '[419, 419, w^3 - 7*w - 3]', '[419, 419, -w^3 + 3*w^2 + 4*w - 9]', '[431, 431, -2*w^3 + 2*w^2 + 7*w - 4]', '[431, 431, w^3 + 2*w^2 - 7*w - 4]', '[439, 439, -2*w^3 + 5*w^2 + 2*w - 11]', '[439, 439, 2*w^3 - w^2 - 6*w - 6]', '[449, 449, w^3 + 3*w^2 - 7*w - 9]', '[449, 449, w^3 - 6*w^2 + 5*w + 11]', '[449, 449, 3*w^3 - 7*w^2 - 3*w + 8]', '[449, 449, -w^3 + 6*w^2 - 2*w - 12]', '[461, 461, -3*w^3 + 8*w^2 + 4*w - 18]', '[461, 461, 3*w^3 - 4*w^2 - 5*w - 1]', '[479, 479, -w^3 + 5*w^2 - 2*w - 16]', '[479, 479, 2*w^3 - 4*w^2 - w - 1]', '[491, 491, -w^3 + 7*w^2 - w - 18]', '[491, 491, w^3 + 2*w^2 - 5*w - 11]', '[491, 491, -w^3 + 5*w^2 - 2*w - 13]', '[491, 491, w^3 + 4*w^2 - 10*w - 13]', '[499, 499, 3*w^3 - 4*w^2 - 8*w + 3]', '[499, 499, -w^3 + 4*w^2 + 2*w - 6]', '[499, 499, -w^3 - w^2 + 7*w + 1]', '[499, 499, 3*w^3 - 5*w^2 - 7*w + 6]', '[529, 23, 4*w^3 - 3*w^2 - 13*w - 1]', '[529, 23, w^3 + 4*w^2 - 9*w - 8]', '[569, 569, -3*w^3 + 7*w^2 + 4*w - 14]', '[569, 569, 3*w^3 - 4*w^2 - 7*w + 1]', '[569, 569, 3*w^3 - 5*w^2 - 6*w + 7]', '[569, 569, w^3 - 4*w^2 + 4*w + 7]', '[571, 571, -w^3 + 7*w^2 - w - 17]', '[571, 571, w^3 + 4*w^2 - 10*w - 12]', '[599, 599, 3*w^3 - 6*w^2 - 5*w + 7]', '[599, 599, 3*w^3 - 3*w^2 - 8*w + 1]', '[619, 619, -w^3 + 3*w^2 + 4*w - 7]', '[619, 619, 2*w^3 - 6*w^2 - w + 13]', '[619, 619, -w^3 + 3*w^2 - 2*w - 6]', '[619, 619, w^3 - 7*w - 1]', '[641, 641, 3*w^3 - 3*w^2 - 7*w + 1]', '[641, 641, -3*w^3 + 6*w^2 + 4*w - 6]', '[659, 659, -2*w^3 + 5*w^2 + 6*w - 7]', '[659, 659, -2*w^3 + w^2 + 10*w - 2]', '[661, 661, 2*w^3 - 4*w^2 - w + 6]', '[661, 661, w^3 + 2*w^2 - 5*w - 12]', '[701, 701, -w^3 + 3*w^2 - w - 9]', '[701, 701, -2*w^3 + w^2 + 9*w - 1]', '[701, 701, 2*w^3 - 8*w - 1]', '[701, 701, w^3 - 2*w - 8]', '[709, 709, 2*w^3 - 2*w^2 - 9*w + 1]', '[709, 709, w^3 - w^2 + w - 2]', '[719, 719, -5*w^2 + 4*w + 14]', '[719, 719, -5*w^2 + 6*w + 13]', '[739, 739, 4*w^3 - 6*w^2 - 11*w + 7]', '[739, 739, -4*w^3 + 6*w^2 + 11*w - 6]', '[751, 751, -w^3 + 7*w^2 - 4*w - 16]', '[751, 751, -w^3 - 4*w^2 + 7*w + 14]', '[769, 769, w^3 - 3*w^2 - w + 11]', '[769, 769, -w^3 + 4*w + 8]', '[811, 811, -w^3 + 4*w^2 - 14]', '[811, 811, -w^3 - w^2 + 5*w + 11]', '[829, 829, -w^3 + 2*w^2 - w - 6]', '[829, 829, w^2 + 3*w - 1]', '[829, 829, 3*w^3 - 13*w - 6]', '[829, 829, w^3 - w^2 - 6]', '[841, 29, 5*w^2 - 5*w - 14]', '[859, 859, -w^3 + 6*w^2 - 11]', '[859, 859, -3*w^3 + 5*w^2 + 8*w - 2]', '[881, 881, -3*w^3 + w^2 + 11*w + 2]', '[881, 881, -3*w^3 + 8*w^2 + 4*w - 11]', '[911, 911, -2*w^2 - w + 11]', '[911, 911, 2*w^2 - 5*w - 8]', '[919, 919, w^3 - 5*w^2 - w + 8]', '[919, 919, -w^3 - 2*w^2 + 8*w + 3]', '[941, 941, 2*w^3 + 2*w^2 - 11*w - 7]', '[941, 941, -2*w^3 + 8*w^2 + w - 14]', '[961, 31, -2*w^2 + 2*w + 11]', '[961, 31, 5*w^2 - 5*w - 13]', '[971, 971, w^3 - 2*w^2 - 3*w - 3]', '[971, 971, -w^3 + w^2 + 4*w - 7]', '[991, 991, -w^3 + 4*w^2 + 2*w - 16]', '[991, 991, w^3 + 3*w^2 - 5*w - 13]', '[991, 991, -w^3 + 6*w^2 - 4*w - 14]', '[991, 991, 2*w^3 + 3*w^2 - 10*w - 12]']}
• 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': [5, 5, -4, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 2525, 'disc_rad': 505, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[4, 1]]], [5, [0]], [7, [[4, 1]]], [11, [[2, 1], [1, 2]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 1], [1, 2]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[2, 1], [1, 2]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[4, 1]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 22.47220505424423, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.2525.1', 'local_algs': ['5.2.1.1', '5.2.1.1', '101.1.0.1', '101.1.0.1', '101.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 101], 'rd': 7.08867957419, 'regulator': {'__RealLiteral__': 0, 'data': '2.09111887566', 'prec': 44}, 'res': {'gal': ['5,25,-19,-102,73,46,-22,-2,1'], 'sib': ['5,0,-11,0,1', '5,25,-19,-102,73,46,-22,-2,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a - 3 \\)', '\\( a^{3} - a^{2} - 3 a - 1 \\)', '\\( a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}