Hilbert modular form data - 4.4.4205.1-13.1-a

Formats: - HTML - YAML - JSON - 2024-05-05T10:39:21.714298

• 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': 4205, 'field_bad_primes': [5, 29], 'field_label': '4.4.4205.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.4205.1-13.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [13], 'level_ideal': '[13, 13, -w^2 + w + 3]', 'level_label': '13.1', 'level_norm': 13, 'parallel_weight': 2, 'short_label': '13.1-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[13, 13, -w^2 + w + 3]', -1]], 'hecke_eigenvalues': [-3, 2, -3, 1, -6, 3, -4, -9, 4, -5, 6, 6, 3, -7, -7, -11, -1, -4, -9, -2, -17, 10, -5, -10, 10, -18, 2, -15, 15, -20, 0, 20, -10, -10, 10, 8, -22, 15, -11, -26, 20, -10, 0, 0, 22, -13, -1, 4, -18, -8, -4, 6, 12, 7, 2, 17, -12, 13, 18, -22, -11, 9, -16, -31, 18, 18, -21, -31, 28, -22, 4, 19, 31, 16, 33, 8, -12, 33, 33, -17, -8, 12, 1, 6, 2, -18, 30, 20, -5, -40, 0, 0, -30, -35, 18, 18, -42, 18, -34, -4, -20, 8, -2, 33, 18, -3, -28, 22, -28, 18, 18, 34, -26, 19, -26, 17, 12, -28, 37, 46, -24, -18, -8, 16, 26, -16, -1, -50, 35, -5, 40, -28, 17, -2, -22, -2, -37, -3, 12, 37, -33, -32, 17, 17, 44, 39, 27, -23, -34, -54, 0, -20, -50, 35, 58, -32, 27, -13, 2, 32, -9, 46, -13, 42, 3, -42], 'hecke_polynomial': 'x', 'label': '4.4.4205.1-13.1-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 4205, 'ideals': ['[1, 1, 1]', '[5, 5, -w^3 + w^2 + 5*w]', '[7, 7, -w^3 + 2*w^2 + 3*w - 3]', '[7, 7, w^3 - 2*w^2 - 3*w]', '[13, 13, -w^2 + w + 3]', '[13, 13, -w^2 + w + 2]', '[16, 2, 2]', '[23, 23, -w^2 + 3*w + 1]', '[23, 23, -2*w^3 + 3*w^2 + 9*w - 2]', '[25, 5, w^3 - 2*w^2 - 4*w]', '[25, 5, w^3 - 2*w^2 - 2*w + 2]', '[35, 35, -w^3 + 3*w^2 + w - 3]', '[35, 35, 2*w^3 - 4*w^2 - 7*w + 4]', '[49, 7, w^3 - w^2 - 6*w - 1]', '[49, 7, -w^3 + w^2 + 6*w]', '[49, 49, -2*w^3 + 3*w^2 + 7*w - 1]', '[49, 49, -2*w^3 + 3*w^2 + 7*w]', '[53, 53, 2*w^3 - 2*w^2 - 8*w - 3]', '[53, 53, 2*w^3 - 2*w^2 - 8*w - 1]', '[65, 65, -w^3 + 2*w^2 + 2*w - 3]', '[65, 65, -2*w^3 + 3*w^2 + 8*w + 1]', '[67, 67, 2*w^3 - 4*w^2 - 7*w + 2]', '[67, 67, -2*w^3 + 4*w^2 + 6*w - 1]', '[80, 10, -2*w^3 + 2*w^2 + 10*w]', '[81, 3, -3]', '[83, 83, 2*w^3 - 3*w^2 - 6*w - 1]', '[83, 83, 3*w^3 - 4*w^2 - 12*w + 1]', '[91, 91, -w^3 + 2*w^2 + 2*w - 4]', '[91, 91, w^3 - 6*w - 2]', '[91, 91, w^2 - 4]', '[91, 91, 2*w^3 - 3*w^2 - 8*w - 2]', '[103, 103, 3*w^3 - 4*w^2 - 12*w - 1]', '[103, 103, 2*w^3 - 3*w^2 - 6*w + 1]', '[107, 107, w^3 - w^2 - 3*w - 3]', '[107, 107, 2*w^3 - 2*w^2 - 9*w]', '[109, 109, -3*w^3 + 5*w^2 + 10*w - 5]', '[109, 109, -2*w^3 + 3*w^2 + 9*w + 1]', '[109, 109, -2*w^3 + 2*w^2 + 7*w]', '[109, 109, w^2 - 3*w - 4]', '[112, 14, -2*w^3 + 4*w^2 + 6*w - 6]', '[112, 14, 2*w^3 - 4*w^2 - 6*w]', '[115, 115, w^3 - 3*w^2 - 3*w + 5]', '[115, 115, -2*w^2 + 3*w + 4]', '[121, 11, 3*w^3 - 4*w^2 - 12*w]', '[121, 11, 2*w^2 - 3*w - 6]', '[125, 5, w^3 - 5*w - 6]', '[125, 25, -w^3 + 3*w^2 + 2*w - 4]', '[139, 139, w^3 - 7*w - 1]', '[139, 139, -w^3 + 2*w^2 + 5*w - 4]', '[139, 139, 3*w^3 - 3*w^2 - 14*w - 2]', '[139, 139, -3*w^3 + 5*w^2 + 13*w - 2]', '[149, 149, -w^2 + 4*w + 1]', '[149, 149, -3*w^3 + 4*w^2 + 14*w - 1]', '[149, 149, 2*w^2 - 3*w - 5]', '[149, 149, -w^3 + 3*w^2 + 3*w - 4]', '[161, 161, 3*w^3 - 5*w^2 - 11*w + 1]', '[161, 161, 2*w^3 - 2*w^2 - 10*w + 1]', '[161, 161, 2*w - 3]', '[161, 161, -2*w^3 + 4*w^2 + 5*w - 4]', '[167, 167, -w^3 - w^2 + 7*w + 4]', '[167, 167, -4*w^3 + 6*w^2 + 15*w - 4]', '[169, 13, w^3 - w^2 - 6*w + 4]', '[169, 13, 2*w^3 - 4*w^2 - 7*w + 1]', '[169, 169, w^3 - 3*w^2 + 4]', '[169, 169, 3*w^3 - 5*w^2 - 12*w + 2]', '[173, 173, w^2 - 3*w - 5]', '[173, 173, 2*w^3 - 2*w^2 - 11*w]', '[175, 35, -2*w^3 + 3*w^2 + 10*w - 1]', '[175, 35, -2*w^3 + 3*w^2 + 8*w - 5]', '[175, 35, -w^3 + 2*w^2 + 2*w + 3]', '[175, 35, w^3 - 8*w - 3]', '[179, 179, 2*w^3 - 2*w^2 - 9*w + 1]', '[179, 179, w^3 - w^2 - 3*w - 4]', '[179, 179, w^2 - 5]', '[179, 179, w^3 - 6*w - 1]', '[197, 197, w^3 + w^2 - 7*w - 6]', '[197, 197, 2*w^3 - 2*w^2 - 9*w + 2]', '[208, 26, -2*w^2 + 2*w + 6]', '[208, 26, -2*w^2 + 2*w + 4]', '[223, 223, -w^2 + 7]', '[223, 223, 2*w^2 - w - 4]', '[227, 227, 2*w^3 - 2*w^2 - 11*w - 2]', '[227, 227, w^3 - w^2 - 7*w - 1]', '[233, 233, w^3 - w^2 - 7*w]', '[233, 233, -2*w^3 + 2*w^2 + 11*w + 1]', '[245, 35, -2*w^2 + 2*w + 5]', '[245, 35, w^2 - 6]', '[245, 245, w + 4]', '[245, 245, -w^3 + w^2 + 5*w + 5]', '[256, 4, 4]', '[257, 257, -2*w^3 + 4*w^2 + 8*w - 1]', '[257, 257, 2*w^2 - 4*w - 7]', '[265, 265, w^3 + w^2 - 9*w - 8]', '[265, 265, -w^3 + 3*w^2 + w - 8]', '[277, 277, -4*w^3 + 6*w^2 + 15*w - 3]', '[277, 277, -3*w^3 + 5*w^2 + 9*w]', '[281, 281, -2*w^3 + 5*w^2 + 3*w - 5]', '[281, 281, -2*w^3 + 5*w^2 + 5*w - 7]', '[281, 281, 2*w^3 - 5*w^2 - 5*w + 4]', '[281, 281, -4*w^3 + 7*w^2 + 15*w - 4]', '[283, 283, 3*w^3 - 4*w^2 - 13*w - 3]', '[283, 283, -w^3 + 2*w^2 + w - 4]', '[299, 299, w^3 - 2*w^2 - 3*w + 6]', '[299, 299, -3*w^3 + 4*w^2 + 11*w - 1]', '[299, 299, -3*w^3 + 4*w^2 + 11*w + 2]', '[299, 299, -w^3 + 2*w^2 + 3*w + 3]', '[313, 313, -2*w^3 + 4*w^2 + 5*w - 5]', '[313, 313, 3*w^3 - 5*w^2 - 11*w]', '[325, 65, 4*w^3 - 6*w^2 - 15*w + 2]', '[325, 65, -w^2 - w + 4]', '[325, 65, 3*w^3 - 5*w^2 - 9*w + 1]', '[325, 65, 2*w^3 - w^2 - 11*w - 3]', '[335, 335, 3*w^3 - 7*w^2 - 7*w + 6]', '[335, 335, -4*w^3 + 8*w^2 + 13*w - 7]', '[343, 7, -4*w^3 + 6*w^2 + 17*w - 1]', '[343, 7, w^3 - 3*w^2 + w + 4]', '[343, 49, 5*w^3 - 8*w^2 - 20*w + 4]', '[343, 49, -2*w^3 + 5*w^2 + 2*w - 4]', '[343, 343, w^3 - 2*w^2 - 6*w + 4]', '[343, 343, -2*w^3 + w^2 + 12*w + 2]', '[347, 347, -w^3 + 2*w^2 + w - 5]', '[347, 347, 3*w^3 - 4*w^2 - 13*w - 4]', '[353, 353, 3*w^3 - 5*w^2 - 12*w + 1]', '[353, 353, -w^3 + 3*w^2 - 5]', '[361, 19, 3*w^3 - 3*w^2 - 13*w - 9]', '[361, 19, 2*w^3 - 2*w^2 - 7*w + 4]', '[368, 46, -2*w^2 + 6*w + 2]', '[368, 46, -4*w^3 + 6*w^2 + 18*w - 4]', '[371, 371, -3*w^3 + 4*w^2 + 9*w + 4]', '[371, 371, -w^3 + 3*w + 4]', '[371, 371, -3*w^3 + 2*w^2 + 15*w + 5]', '[371, 371, -5*w^3 + 6*w^2 + 21*w - 1]', '[373, 373, -3*w^3 + 4*w^2 + 11*w + 1]', '[373, 373, -3*w^3 + 4*w^2 + 11*w]', '[383, 383, 3*w^3 - 5*w^2 - 13*w + 1]', '[383, 383, 2*w^2 - 5*w - 6]', '[397, 397, 4*w^3 - 5*w^2 - 19*w - 1]', '[397, 397, 2*w^3 - 2*w^2 - 9*w - 7]', '[400, 10, 2*w^3 - 4*w^2 - 8*w]', '[400, 10, 2*w^3 - 4*w^2 - 4*w + 4]', '[405, 15, 3*w^3 - 3*w^2 - 15*w]', '[415, 415, -w^3 + 4*w^2 - 2*w - 6]', '[415, 415, -4*w^3 + 8*w^2 + 13*w - 12]', '[431, 431, 2*w^3 - 2*w^2 - 7*w - 5]', '[431, 431, 3*w^3 - 6*w^2 - 11*w + 3]', '[431, 431, 3*w^3 - 3*w^2 - 13*w]', '[431, 431, w^3 - 4*w^2 + w + 8]', '[455, 455, -3*w^3 + 5*w^2 + 8*w]', '[455, 455, w^3 - w^2 - 4*w - 6]', '[455, 455, w^3 - w^2 - 4*w + 4]', '[455, 455, 5*w^3 - 7*w^2 - 20*w + 2]', '[457, 457, 4*w^3 - 7*w^2 - 13*w]', '[457, 457, -3*w^2 + 4*w + 5]', '[463, 463, -3*w^3 + 5*w^2 + 11*w + 1]', '[463, 463, 2*w^3 - 4*w^2 - 5*w + 6]', '[469, 469, -w^3 + 4*w^2 - w + 1]', '[469, 469, 3*w^3 - 8*w^2 - 3*w]', '[469, 469, -5*w^3 + 8*w^2 + 22*w - 7]', '[469, 469, 3*w^3 - 4*w^2 - 15*w + 3]', '[487, 487, -w^3 + 4*w^2 - 7]', '[487, 487, -2*w^3 + 5*w^2 + 6*w - 5]', '[499, 499, -6*w^3 + 8*w^2 + 25*w - 1]', '[499, 499, -w^3 + 4*w^2 - 5]', '[499, 499, -2*w^3 + 5*w^2 + 6*w - 7]', '[499, 499, 3*w^3 - 5*w^2 - 7*w]', '[509, 509, -4*w^3 + 8*w^2 + 15*w - 8]', '[509, 509, 3*w^3 - 4*w^2 - 10*w - 2]', '[509, 509, -3*w^3 + 3*w^2 + 11*w + 6]', '[509, 509, 4*w^3 - 5*w^2 - 16*w]', '[515, 515, -2*w^3 + 6*w^2 + 3*w - 12]', '[515, 515, -3*w^3 + 6*w^2 + 8*w - 6]', '[521, 521, -4*w^3 + 5*w^2 + 15*w - 2]', '[521, 521, w^3 - w^2 - 8*w + 1]', '[521, 521, -4*w^3 + 7*w^2 + 12*w - 6]', '[521, 521, 3*w^3 - 3*w^2 - 16*w - 1]', '[523, 523, 3*w^3 - w^2 - 17*w - 8]', '[523, 523, -5*w^3 + 5*w^2 + 23*w + 4]', '[529, 23, 4*w^3 - 5*w^2 - 18*w - 4]', '[529, 23, 3*w^3 - 6*w^2 - 10*w + 2]', '[529, 529, -2*w^3 + w^2 + 10*w + 2]', '[529, 529, w^3 - 4*w - 6]', '[535, 535, 2*w^3 - w^2 - 13*w - 3]', '[535, 535, -2*w^3 + 4*w^2 + 7*w - 9]', '[545, 545, 4*w^3 - 5*w^2 - 16*w - 3]', '[545, 545, 8*w^3 - 13*w^2 - 30*w + 10]', '[545, 545, -w^3 + 4*w^2 + w - 9]', '[545, 545, 2*w^3 - 4*w^2 - 5*w + 7]', '[547, 547, -2*w^3 + 5*w^2 + 6*w - 6]', '[547, 547, -w^3 + 4*w^2 - 6]', '[557, 557, -3*w^3 + 6*w^2 + 9*w - 10]', '[557, 557, 3*w^3 - 6*w^2 - 9*w - 1]', '[560, 70, -2*w^3 + 6*w^2 + 2*w - 6]', '[560, 70, 4*w^3 - 8*w^2 - 14*w + 8]', '[567, 21, 3*w^3 - 6*w^2 - 9*w + 9]', '[567, 21, -3*w^3 + 6*w^2 + 9*w]', '[571, 571, 4*w^3 - 4*w^2 - 17*w - 6]', '[571, 571, -2*w^3 + 6*w^2 + 3*w - 10]', '[571, 571, 4*w^3 - 5*w^2 - 18*w + 3]', '[571, 571, -3*w^3 + 7*w^2 + 9*w - 5]', '[575, 115, 4*w^3 - 5*w^2 - 17*w + 3]', '[575, 115, 2*w^3 - 3*w^2 - 8*w - 5]', '[575, 115, -w^3 + 2*w^2 + 2*w - 7]', '[575, 115, -2*w^3 + 3*w^2 + 5*w + 4]', '[581, 581, -w^2 - w + 5]', '[581, 581, -4*w^3 + 8*w^2 + 7*w + 1]', '[581, 581, -9*w^3 + 13*w^2 + 37*w - 8]', '[581, 581, -2*w^3 + w^2 + 11*w + 2]', '[587, 587, 3*w^3 - 3*w^2 - 14*w]', '[587, 587, w^3 - w^2 - 2*w - 4]', '[593, 593, -w^3 + 3*w^2 + 2*w - 10]', '[593, 593, -5*w^3 + 7*w^2 + 19*w - 4]', '[605, 55, -3*w^3 + 7*w^2 + 8*w - 12]', '[605, 55, 6*w^3 - 8*w^2 - 25*w - 3]', '[613, 613, 3*w^3 - 5*w^2 - 12*w - 4]', '[613, 613, -w^3 + 3*w^2 - 10]', '[625, 5, 5]', '[625, 25, 2*w^3 - 2*w^2 - 12*w - 3]', '[625, 25, 2*w^3 - 2*w^2 - 12*w + 1]', '[631, 631, 4*w^3 - 8*w^2 - 13*w + 4]', '[631, 631, 3*w^3 - 4*w^2 - 15*w + 2]', '[631, 631, w^3 - 9*w - 1]', '[631, 631, 3*w^3 - 7*w^2 - 7*w + 9]', '[637, 91, 4*w^3 - 4*w^2 - 17*w - 4]', '[637, 91, -4*w^3 + 5*w^2 + 16*w + 1]', '[637, 91, 3*w^3 - 3*w^2 - 11*w - 3]', '[637, 91, -3*w^3 + 4*w^2 + 10*w + 1]', '[637, 637, -w^3 + 9*w + 3]', '[637, 637, -w^3 + w^2 + 8*w + 1]', '[637, 637, -3*w^3 + 3*w^2 + 16*w + 3]', '[637, 637, -3*w^3 + 4*w^2 + 15*w]', '[643, 643, 3*w^3 - 3*w^2 - 16*w - 2]', '[643, 643, w^3 - w^2 - 8*w]', '[647, 647, -w^3 + 4*w^2 + 2*w - 4]', '[647, 647, -3*w^2 + 4*w + 10]', '[673, 673, w^3 + 2*w^2 - 9*w - 8]', '[673, 673, -w^3 + 4*w^2 + 3*w - 7]', '[683, 683, 3*w^3 - 3*w^2 - 11*w - 2]', '[683, 683, 4*w^3 - 4*w^2 - 17*w - 5]', '[689, 689, 2*w^3 - 3*w^2 - 13*w - 4]', '[689, 689, 2*w^3 - w^2 - 15*w - 8]', '[689, 689, 4*w^3 - 5*w^2 - 21*w - 5]', '[689, 689, 4*w^3 - 3*w^2 - 23*w - 11]', '[695, 695, 5*w^3 - 7*w^2 - 23*w + 5]', '[695, 695, -w^3 + 4*w^2 + w - 14]', '[695, 695, 2*w - 7]', '[695, 695, -6*w^3 + 11*w^2 + 19*w - 4]', '[709, 709, -5*w^3 + 7*w^2 + 21*w + 1]', '[709, 709, -3*w^3 + 2*w^2 + 16*w + 4]', '[709, 709, 4*w^3 - 4*w^2 - 19*w - 2]', '[709, 709, -2*w^3 + 4*w^2 + 3*w - 4]', '[721, 721, -4*w^3 + 5*w^2 + 17*w - 4]', '[721, 721, -2*w^3 + 3*w^2 + 5*w + 5]', '[721, 721, -7*w^3 + 9*w^2 + 31*w - 2]', '[721, 721, -2*w^3 + 4*w^2 + w + 1]', '[745, 745, 5*w^3 - 8*w^2 - 20*w + 3]', '[745, 745, 4*w^3 - 5*w^2 - 18*w + 4]', '[745, 745, -w^3 + 2*w^2 + 4]', '[745, 745, 5*w^3 - 7*w^2 - 20*w - 3]', '[749, 749, w^3 - 4*w^2 - w + 8]', '[749, 749, -4*w^3 + 7*w^2 + 10*w + 1]', '[749, 749, -7*w^3 + 10*w^2 + 28*w - 5]', '[749, 749, w^3 - 4*w^2 - w + 5]', '[763, 763, -w^3 + w^2 + 9*w - 2]', '[763, 763, -2*w^2 + 7*w + 4]', '[763, 763, 5*w^3 - 6*w^2 - 20*w + 3]', '[763, 763, -w^3 + 2*w^2 + 4*w + 4]', '[763, 763, 10*w^3 - 16*w^2 - 39*w + 17]', '[763, 763, -w^2 + 2*w + 8]', '[763, 763, -5*w^3 + 7*w^2 + 23*w - 1]', '[763, 763, w^3 - w - 3]', '[784, 14, 2*w^3 - 2*w^2 - 12*w - 2]', '[784, 14, -2*w^3 + 2*w^2 + 12*w]', '[784, 98, -4*w^3 + 6*w^2 + 14*w - 2]', '[784, 98, -4*w^3 + 6*w^2 + 14*w]', '[787, 787, 2*w^2 - w - 9]', '[787, 787, w^3 + w^2 - 7*w - 2]', '[805, 805, 3*w^3 - 5*w^2 - 12*w - 1]', '[805, 805, -w^3 + 3*w^2 - 7]', '[805, 805, 2*w^3 - w^2 - 10*w - 1]', '[805, 805, w^3 - 4*w - 7]', '[811, 811, 4*w^3 - 7*w^2 - 11*w]', '[811, 811, 3*w^3 - 4*w^2 - 9*w - 1]', '[811, 811, -6*w^3 + 9*w^2 + 23*w - 5]', '[811, 811, 5*w^3 - 6*w^2 - 21*w - 2]', '[821, 821, -3*w^3 + 6*w^2 + 11*w - 2]', '[821, 821, 2*w^3 - 13*w - 5]', '[821, 821, -w^3 + 4*w^2 - w - 9]', '[821, 821, -w^3 + 3*w^2 + 5*w - 6]', '[835, 835, 8*w^3 - 14*w^2 - 29*w + 15]', '[835, 835, -3*w^3 + 4*w^2 + 12*w + 7]', '[841, 29, 2*w^3 - 2*w^2 - 12*w - 1]', '[845, 65, -5*w^3 + 6*w^2 + 25*w - 6]', '[845, 65, -3*w^3 + 7*w^2 + 8*w - 7]', '[845, 845, -2*w^3 + 12*w + 5]', '[845, 845, 2*w^2 - 7]', '[847, 77, -8*w^3 + 11*w^2 + 34*w - 5]', '[847, 77, w^3 - 4*w^2 - 2*w + 13]', '[847, 77, -w^3 + w^2 + 2*w + 5]', '[847, 77, -w^3 - 2*w^2 + 11*w + 5]', '[848, 106, 4*w^3 - 4*w^2 - 16*w - 6]', '[848, 106, 4*w^3 - 4*w^2 - 16*w - 2]', '[857, 857, w^3 - 4*w^2 + 3*w + 6]', '[857, 857, -5*w^3 + 8*w^2 + 21*w - 3]', '[863, 863, -w^3 + 4*w^2 + w - 7]', '[863, 863, -w^3 + 4*w^2 + w - 6]', '[865, 865, 3*w^2 - 4*w - 9]', '[865, 865, 5*w^3 - 6*w^2 - 21*w - 3]', '[871, 871, -2*w^3 + w^2 + 11*w + 1]', '[871, 871, w^3 + w^2 - 6*w]', '[871, 871, 3*w^3 - 3*w^2 - 13*w + 2]', '[871, 871, -3*w^2 + 5*w + 2]', '[875, 35, 4*w^3 - 5*w^2 - 15*w + 1]', '[875, 35, -4*w^3 + 5*w^2 + 15*w + 4]', '[875, 175, -3*w^2 + 6*w + 2]', '[875, 175, 3*w^3 - 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7]', '[1495, 1495, 4*w^3 - 8*w^2 - 12*w + 11]', '[1499, 1499, 3*w^3 - 6*w^2 - 13*w + 9]', '[1499, 1499, 5*w^3 - 9*w^2 - 20*w + 5]', '[1499, 1499, 3*w^2 - 7*w - 9]', '[1499, 1499, 4*w^3 - 7*w^2 - 17*w + 2]', '[1541, 1541, 6*w^3 - 11*w^2 - 19*w + 10]', '[1541, 1541, -9*w^3 + 15*w^2 + 32*w - 14]', '[1541, 1541, 6*w^3 - 15*w^2 - 7*w + 7]', '[1541, 1541, -5*w^3 + 11*w^2 + 9*w - 6]', '[1543, 1543, -4*w^3 + 9*w^2 + 11*w - 8]', '[1543, 1543, -4*w^3 + 9*w^2 + 11*w - 9]', '[1553, 1553, -w^3 + 2*w^2 + 3*w - 8]', '[1553, 1553, w^3 - 2*w^2 - 3*w - 5]', '[1559, 1559, -4*w^3 + 7*w^2 + 15*w - 1]', '[1559, 1559, 3*w^2 - 6*w - 11]', '[1559, 1559, -2*w^3 + 5*w^2 + 3*w - 8]', '[1559, 1559, -3*w^3 + 6*w^2 + 12*w - 1]', '[1561, 1561, w^3 - 4*w^2 - 4*w + 9]', '[1561, 1561, 6*w^3 - 10*w^2 - 19*w - 1]', '[1561, 1561, -6*w^3 + 13*w^2 + 19*w - 20]', '[1561, 1561, -w^3 - 2*w^2 + 7*w + 3]', '[1565, 1565, 7*w^3 - 11*w^2 - 26*w + 5]', '[1565, 1565, -3*w^3 + 8*w^2 + 6*w - 11]', '[1567, 1567, -w^3 + 3*w^2 - w - 7]', '[1567, 1567, 4*w^3 - 6*w^2 - 17*w - 2]', '[1573, 143, 6*w^3 - 7*w^2 - 29*w - 4]', '[1573, 143, 3*w^3 - w^2 - 17*w - 16]', '[1573, 143, 3*w^3 - 3*w^2 - 17*w - 4]', '[1573, 143, 3*w^3 - 3*w^2 - 14*w - 10]', '[1589, 1589, w^3 - 4*w^2 + 3*w + 7]', '[1589, 1589, 2*w^3 - 5*w^2 + 5]', '[1589, 1589, -7*w^3 + 10*w^2 + 30*w - 1]', '[1589, 1589, -5*w^3 + 8*w^2 + 21*w - 2]', '[1619, 1619, -w^3 + 3*w^2 + 6*w - 6]', '[1619, 1619, -4*w^3 + 7*w^2 + 14*w + 1]', '[1619, 1619, -3*w^3 + w^2 + 18*w + 6]', '[1619, 1619, 3*w^3 - 6*w^2 - 8*w + 9]', '[1625, 65, -4*w^3 + 5*w^2 + 20*w - 1]', '[1625, 65, -w^3 + 10*w + 1]', '[1625, 325, w^2 - 2*w - 9]', '[1625, 325, w^3 - 2*w^2 - 4*w - 5]', '[1631, 1631, -6*w^3 + 10*w^2 + 24*w - 5]', '[1631, 1631, 3*w^3 - 7*w^2 - 3*w + 5]', '[1631, 1631, 8*w^3 - 12*w^2 - 33*w + 4]', '[1631, 1631, -2*w^3 + 6*w^2 - 7]', '[1637, 1637, w^2 - 3*w + 5]', '[1637, 1637, -2*w^3 + 3*w^2 + 9*w - 8]', '[1648, 206, 6*w^3 - 8*w^2 - 24*w - 2]', '[1648, 206, 4*w^3 - 6*w^2 - 12*w + 2]', '[1657, 1657, -2*w^3 + 6*w^2 + 5*w - 11]', '[1657, 1657, -w^3 + 5*w^2 - w - 6]', '[1669, 1669, 2*w^3 - 2*w^2 - 13*w + 1]', '[1669, 1669, 3*w^3 - 3*w^2 - 17*w]', '[1669, 1669, 5*w^3 - 6*w^2 - 20*w - 1]', '[1669, 1669, 4*w^3 - 5*w^2 - 14*w - 3]', '[1675, 335, w^3 - w^2 - 11*w + 3]', '[1675, 335, w^3 + w^2 - 5*w + 3]', '[1675, 335, w^3 - 4*w^2 + 6*w]', '[1675, 335, w^3 - 4*w^2 - 2]', '[1681, 41, w^3 - 10*w - 2]', '[1681, 41, 4*w^3 - 5*w^2 - 20*w]', '[1712, 214, 2*w^3 - 2*w^2 - 6*w - 6]', '[1712, 214, 4*w^3 - 4*w^2 - 18*w]', '[1715, 35, -5*w^3 + 8*w^2 + 16*w + 1]', '[1715, 35, 6*w^3 - 9*w^2 - 22*w + 5]', '[1715, 245, w^3 + 2*w^2 - 9*w - 4]', '[1715, 245, -w^3 + 4*w^2 + 3*w - 11]', '[1715, 1715, -w^3 - 2*w^2 + 11*w + 12]', '[1715, 1715, -3*w^3 + 6*w^2 + 13*w - 1]', '[1733, 1733, -2*w^3 + w^2 + 14*w + 4]', '[1733, 1733, 3*w^3 - 4*w^2 - 16*w]', '[1735, 1735, w^3 + 3*w^2 - 11*w - 13]', '[1735, 1735, 6*w^3 - 8*w^2 - 24*w + 1]', '[1744, 218, -6*w^3 + 10*w^2 + 20*w - 10]', '[1744, 218, -4*w^3 + 6*w^2 + 18*w + 2]', '[1744, 218, -4*w^3 + 4*w^2 + 14*w]', '[1744, 218, 2*w^2 - 6*w - 8]', '[1747, 1747, 4*w^3 - 3*w^2 - 22*w - 3]', '[1747, 1747, 5*w^3 - 6*w^2 - 23*w + 3]', '[1753, 1753, 3*w^3 - 3*w^2 - 11*w - 8]', '[1753, 1753, 4*w^3 - 4*w^2 - 17*w + 1]', '[1765, 1765, -4*w^3 + 9*w^2 + 12*w - 12]', '[1765, 1765, 6*w^3 - 9*w^2 - 22*w]', '[1792, 28, -4*w^3 + 8*w^2 + 12*w - 12]', '[1792, 28, 4*w^3 - 8*w^2 - 12*w]', '[1799, 1799, w^3 - 4*w^2 - w - 2]', '[1799, 1799, 5*w^3 - 8*w^2 - 23*w + 5]', '[1799, 1799, -w^3 - 2*w^2 + 13*w + 6]', '[1799, 1799, w^3 - 4*w^2 - w + 15]', '[1805, 95, 6*w^3 - 3*w^2 - 35*w - 13]', '[1805, 95, -6*w^3 + 8*w^2 + 25*w - 7]', '[1807, 1807, 5*w^3 - 6*w^2 - 24*w - 7]', '[1807, 1807, -2*w^3 + 5*w^2 + 3*w + 3]', '[1807, 1807, 5*w^3 - 7*w^2 - 21*w - 3]', '[1807, 1807, 4*w^3 - 7*w^2 - 14*w - 2]', '[1807, 1807, -3*w^3 + 6*w^2 + 8*w - 10]', '[1807, 1807, -2*w^3 + 4*w^2 + 3*w - 6]', '[1807, 1807, 8*w^3 - 9*w^2 - 38*w - 9]', '[1807, 1807, -w + 7]', '[1823, 1823, -5*w^3 + 8*w^2 + 19*w]', '[1823, 1823, -3*w^3 + 6*w^2 + 7*w - 7]', '[1831, 1831, 2*w^3 - 5*w^2 - 8*w + 10]', '[1831, 1831, w^3 + 2*w^2 - 10*w - 4]', '[1831, 1831, w^3 - w^2 - w - 5]', '[1831, 1831, 4*w^3 - 4*w^2 - 19*w]', '[1840, 230, 2*w^3 - 6*w^2 - 6*w + 10]', '[1840, 230, -4*w^2 + 6*w + 8]', '[1847, 1847, 3*w^3 - 2*w^2 - 16*w - 2]', '[1847, 1847, w^2 + 2*w - 6]', '[1855, 1855, -w^3 - 3*w^2 + 15*w + 9]', '[1855, 1855, 2*w^3 - 2*w^2 - 13*w - 2]', '[1855, 1855, -3*w^3 + 3*w^2 + 17*w + 3]', '[1855, 1855, 6*w^3 - 10*w^2 - 27*w + 6]', '[1861, 1861, 3*w^3 - 2*w^2 - 17*w - 1]', '[1861, 1861, -6*w^3 + 10*w^2 + 20*w - 3]', '[1861, 1861, 6*w^3 - 10*w^2 - 20*w + 5]', '[1861, 1861, w^3 - 2*w^2 - 7*w + 6]', '[1863, 69, 3*w^2 - 9*w - 3]', '[1863, 69, 6*w^3 - 9*w^2 - 27*w + 6]', '[1865, 1865, 2*w^3 - 6*w^2 - 2*w + 11]', '[1865, 1865, 3*w^3 - 7*w^2 - 7*w + 11]', '[1879, 1879, 7*w^3 - 8*w^2 - 33*w - 8]', '[1879, 1879, 4*w^3 - 7*w^2 - 19*w + 9]', '[1879, 1879, -5*w^3 + 5*w^2 + 20*w - 1]', '[1879, 1879, -6*w^3 + 10*w^2 + 19*w - 9]', '[1907, 1907, 6*w^3 - 8*w^2 - 24*w - 1]', '[1907, 1907, 4*w^3 - 6*w^2 - 12*w + 1]', '[1909, 1909, -4*w^3 + 13*w^2 - 8]', '[1909, 1909, -11*w^3 + 20*w^2 + 42*w - 22]', '[1909, 1909, -2*w^3 + 6*w^2 + 4*w - 9]', '[1909, 1909, -2*w^3 + 6*w^2 + 4*w - 7]', '[1913, 1913, 3*w^3 - 2*w^2 - 15*w - 2]', '[1913, 1913, w^3 - 3*w - 7]', '[1915, 1915, -6*w^3 + 8*w^2 + 23*w + 5]', '[1915, 1915, -4*w^3 + 9*w^2 + 13*w - 13]', '[1936, 22, 6*w^3 - 8*w^2 - 24*w]', '[1936, 22, 4*w^2 - 6*w - 12]', '[1937, 1937, -w^2 - 2*w - 5]', '[1937, 1937, -5*w^3 + 6*w^2 + 20*w + 2]', '[1937, 1937, 3*w^3 - 2*w^2 - 16*w - 13]', '[1937, 1937, -4*w^3 + 5*w^2 + 14*w + 2]', '[1937, 1937, 3*w^3 - 4*w^2 - 13*w - 8]', '[1937, 1937, 2*w^3 - 3*w^2 - 6*w + 8]', '[1937, 1937, -w^3 + 2*w^2 + w - 9]', '[1937, 1937, -3*w^3 + 4*w^2 + 12*w + 8]', '[1939, 1939, 12*w^3 - 18*w^2 - 49*w + 14]', '[1939, 1939, 4*w^3 - 4*w^2 - 20*w + 1]', '[1939, 1939, 4*w - 5]', '[1939, 1939, 5*w^3 - 11*w^2 - 7*w - 1]', '[1967, 1967, 10*w^3 - 14*w^2 - 43*w + 8]', '[1967, 1967, -2*w^2 + 5*w - 4]', '[1967, 1967, 3*w^3 - 5*w^2 - 13*w + 11]', '[1967, 1967, 7*w^3 - 13*w^2 - 27*w + 19]', '[1967, 1967, 2*w^3 - 4*w^2 - 2*w - 5]', '[1967, 1967, 3*w^3 - 10*w^2 + 4*w + 4]', '[1967, 1967, -w^3 - 2*w^2 + 12*w + 2]', '[1967, 1967, 12*w^3 - 19*w^2 - 50*w + 16]', '[1973, 1973, -3*w^3 + 3*w^2 + 17*w + 2]', '[1973, 1973, 2*w^3 - 2*w^2 - 13*w - 1]', '[1981, 1981, 3*w^3 - 5*w^2 - 10*w + 10]', '[1981, 1981, -3*w^3 + 5*w^2 + 10*w + 6]', '[1981, 1981, -w^2 + 7*w + 2]', '[1981, 1981, -6*w^3 + 7*w^2 + 29*w + 3]', '[1985, 1985, -3*w^3 + 8*w^2 + 9*w - 19]', '[1985, 1985, 5*w^3 - 3*w^2 - 28*w - 9]', '[1997, 1997, 4*w^3 - 5*w^2 - 14*w - 1]', '[1997, 1997, 5*w^3 - 6*w^2 - 20*w - 3]', '[2000, 10, 2*w^3 - 10*w - 12]', '[2000, 50, -2*w^3 + 6*w^2 + 4*w - 8]', '[2017, 2017, 4*w^3 - 7*w^2 - 11*w + 7]', '[2017, 2017, 6*w^3 - 9*w^2 - 23*w - 2]', '[2025, 15, -3*w^3 + 6*w^2 + 12*w]', '[2025, 15, -3*w^3 + 6*w^2 + 6*w - 6]', '[2053, 2053, 5*w^3 - 8*w^2 - 20*w + 1]', '[2053, 2053, -2*w^3 + 5*w^2 + 2*w - 7]', '[2063, 2063, w^3 - w^2 - 4*w - 8]', '[2063, 2063, -w^3 + w^2 + 4*w - 6]', '[2075, 415, -3*w^3 + 4*w^2 + 6*w + 3]', '[2075, 415, -w^3 + 6*w^2 - 4*w - 3]', '[2075, 415, w^3 - 4*w^2 - 5*w + 8]', '[2075, 415, 5*w^3 - 6*w^2 - 21*w + 4]', '[2083, 2083, -w^3 + 4*w^2 - 2*w - 9]', '[2083, 2083, 4*w^3 - 7*w^2 - 16*w + 1]', '[2087, 2087, -2*w^3 + 6*w^2 + 5*w - 10]', '[2087, 2087, -w^3 + 5*w^2 - w - 7]', '[2093, 2093, -4*w^3 + 3*w^2 + 21*w + 4]', '[2093, 2093, 6*w^3 - 9*w^2 - 25*w + 1]', '[2093, 2093, -2*w^3 + 5*w^2 + 3*w - 9]', '[2093, 2093, 4*w^3 - 7*w^2 - 15*w]', '[2093, 2093, -2*w^3 + 5*w^2 + w - 6]', '[2093, 2093, -w^2 - 3*w + 5]', '[2093, 2093, 2*w^3 - 13*w - 3]', '[2093, 2093, -w^3 + 3*w^2 + 5*w - 8]', '[2111, 2111, -5*w^3 + 9*w^2 + 19*w - 4]', '[2111, 2111, -8*w^3 + 13*w^2 + 29*w - 8]', '[2111, 2111, -2*w^3 + 6*w^2 + w - 9]', '[2111, 2111, -3*w^3 + 9*w^2 + 4*w - 14]', '[2113, 2113, 4*w^3 - 3*w^2 - 19*w - 4]', '[2113, 2113, -3*w^3 + 8*w^2 + 6*w - 10]', '[2137, 2137, -6*w^3 + 9*w^2 + 22*w - 4]', '[2137, 2137, -5*w^3 + 8*w^2 + 16*w]', '[2141, 2141, 2*w^3 + 2*w^2 - 15*w - 12]', '[2141, 2141, -6*w^3 + 7*w^2 + 25*w - 2]', '[2141, 2141, 6*w^3 - 8*w^2 - 27*w - 3]', '[2141, 2141, 5*w^3 - 6*w^2 - 21*w + 6]', '[2153, 2153, -2*w^3 + 12*w + 3]', '[2153, 2153, 2*w^2 - 9]', '[2155, 2155, -9*w^3 + 13*w^2 + 35*w + 1]', '[2155, 2155, 3*w^3 - w^2 - 20*w - 7]', '[2155, 2155, -6*w^3 + 12*w^2 + 20*w - 11]', '[2155, 2155, -3*w^3 + 6*w^2 + 10*w - 13]', '[2171, 2171, -4*w^3 + 7*w^2 + 18*w + 7]', '[2171, 2171, -7*w^3 + 11*w^2 + 31*w - 6]', '[2171, 2171, -3*w^3 + 5*w^2 + 16*w - 2]', '[2171, 2171, -5*w^3 + 6*w^2 + 25*w + 11]', '[2179, 2179, -2*w - 7]', '[2179, 2179, -w^3 - 3*w^2 + 10*w + 6]', '[2179, 2179, -2*w^3 + 2*w^2 + 10*w + 9]', '[2179, 2179, 2*w^3 - 6*w^2 - w - 2]', '[2191, 2191, -3*w^3 + 7*w^2 + 5*w + 3]', '[2191, 2191, -6*w^3 + 8*w^2 + 28*w - 3]', '[2191, 2191, -2*w^2 + 8*w + 1]', '[2191, 2191, 6*w^3 - 10*w^2 - 23*w + 14]', '[2197, 13, 4*w^3 - 9*w^2 - 12*w + 11]', '[2197, 13, 3*w^3 - 8*w^2 - 6*w + 7]', '[2197, 169, 3*w^3 - 2*w^2 - 14*w - 1]', '[2197, 169, -2*w^3 + w^2 + 8*w + 9]', '[2197, 2197, -6*w^3 + 9*w^2 + 26*w - 1]', '[2197, 2197, -w^3 + 4*w^2 - 4*w - 7]', '[2203, 2203, -5*w^3 + 8*w^2 + 16*w - 3]', '[2203, 2203, 6*w^3 - 9*w^2 - 22*w + 1]', '[2213, 2213, 4*w^3 - 6*w^2 - 17*w - 4]', '[2213, 2213, -w^3 + 3*w^2 - w - 9]', '[2224, 278, 2*w^3 - 14*w - 2]', '[2224, 278, -2*w^3 + 4*w^2 + 10*w - 8]', '[2224, 278, 6*w^3 - 6*w^2 - 28*w - 4]', '[2224, 278, -6*w^3 + 10*w^2 + 26*w - 4]', '[2237, 2237, 7*w^3 - 7*w^2 - 31*w - 7]', '[2237, 2237, -6*w^3 + 11*w^2 + 24*w - 7]', '[2239, 2239, 2*w^3 - 3*w^2 - 8*w + 8]', '[2239, 2239, -4*w^2 + 6*w + 9]', '[2239, 2239, w^3 - 2*w^2 - 2*w - 6]', '[2239, 2239, -2*w^3 + 6*w^2 + 6*w - 9]', '[2249, 2249, 3*w^3 - w^2 - 12*w - 9]', '[2249, 2249, 3*w^3 - 15*w - 14]', '[2249, 2249, 3*w^3 - 15*w - 7]', '[2249, 2249, 5*w^3 - 3*w^2 - 24*w - 9]', '[2267, 2267, -5*w^3 + 9*w^2 + 18*w - 3]', '[2267, 2267, -3*w^3 + 7*w^2 + 6*w - 9]', '[2275, 455, -7*w^3 + 12*w^2 + 27*w - 7]', '[2275, 455, -6*w^3 + 8*w^2 + 28*w - 1]', '[2275, 455, -4*w^2 + 6*w + 11]', '[2275, 455, -w^3 + 2*w^2 - w + 5]', '[2275, 455, -5*w^3 + 6*w^2 + 23*w - 4]', '[2275, 455, -2*w^3 + 6*w^2 + 6*w - 7]', '[2275, 455, 2*w^2 - 8*w - 3]', '[2275, 455, 3*w^3 - 8*w^2 - 3*w + 8]', '[2285, 2285, -4*w^3 + 11*w^2 + 6*w - 13]', '[2285, 2285, -5*w^3 + 8*w^2 + 18*w + 4]', '[2287, 2287, 5*w^3 - 3*w^2 - 29*w - 10]', '[2287, 2287, 5*w^3 - 9*w^2 - 12*w]', '[2297, 2297, -w^2 + 2*w - 5]', '[2297, 2297, w^3 - 2*w^2 - 4*w + 9]', '[2311, 2311, -5*w^3 + 9*w^2 + 16*w + 1]', '[2311, 2311, 6*w^3 - 7*w^2 - 30*w - 6]', '[2311, 2311, 4*w^3 - 7*w^2 - 17*w + 1]', '[2311, 2311, 3*w^2 - 7*w - 10]', '[2315, 2315, -8*w^3 + 12*w^2 + 31*w - 5]', '[2315, 2315, 2*w^3 - 7*w^2 - w + 11]', '[2327, 2327, 5*w^3 - 8*w^2 - 22*w + 1]', '[2327, 2327, 3*w^2 - 6*w - 14]', '[2327, 2327, 3*w^3 - 6*w^2 - 12*w - 2]', '[2327, 2327, 3*w^2 - 8*w - 9]', '[2327, 2327, 3*w^3 - 6*w^2 - 13*w]', '[2327, 2327, 2*w^2 - 6*w - 9]', '[2327, 2327, 4*w^3 - 6*w^2 - 18*w - 3]', '[2327, 2327, w^3 + 2*w^2 - 11*w - 13]', '[2333, 2333, 2*w^3 - 2*w^2 - 6*w - 7]', '[2333, 2333, 4*w^3 - 4*w^2 - 18*w + 1]', '[2345, 2345, -3*w^3 + 11*w^2 - 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6]', '[2411, 2411, -2*w^3 + 16*w + 7]', '[2411, 2411, 2*w^3 - 7*w^2 - 2*w + 14]', '[2423, 2423, -3*w^3 + 8*w^2 + 6*w - 8]', '[2423, 2423, 4*w^3 - 9*w^2 - 12*w + 10]', '[2429, 2429, 4*w^3 - 7*w^2 - 13*w + 13]', '[2429, 2429, -4*w^3 + 7*w^2 + 13*w + 6]', '[2429, 2429, -w^3 + w^2 + 10*w + 2]', '[2429, 2429, -5*w^3 + 5*w^2 + 26*w + 6]', '[2435, 2435, 7*w^3 - 12*w^2 - 26*w + 6]', '[2435, 2435, 8*w^3 - 12*w^2 - 31*w]', '[2437, 2437, -6*w^3 + 12*w^2 + 21*w - 14]', '[2437, 2437, 4*w^3 - w^2 - 23*w - 11]', '[2441, 2441, 5*w^3 - 5*w^2 - 20*w - 3]', '[2441, 2441, 2*w^3 - 2*w^2 - 11*w + 7]', '[2441, 2441, 5*w^3 - 5*w^2 - 20*w - 7]', '[2441, 2441, -w^3 + w^2 + 7*w - 8]', '[2459, 2459, -5*w^3 + 11*w^2 + 14*w - 9]', '[2459, 2459, -5*w^3 + 11*w^2 + 14*w - 11]', '[2459, 2459, 5*w^3 - 6*w^2 - 22*w + 4]', '[2459, 2459, 2*w^3 - 3*w^2 - 4*w - 6]', '[2461, 2461, 4*w^3 - 4*w^2 - 19*w + 1]', '[2461, 2461, -7*w^3 + 13*w^2 + 28*w - 16]', '[2461, 2461, -w^3 + 7*w^2 - 8*w - 6]', '[2461, 2461, w^3 - w^2 - w - 6]', '[2471, 2471, w^3 - 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9]', '[3899, 3899, -2*w^3 + w^2 + 15*w + 3]', '[3899, 3899, 13*w^3 - 23*w^2 - 48*w + 30]', '[3899, 3899, -7*w^3 + 17*w^2 + 12*w]', '[3899, 3899, -4*w^3 + 5*w^2 + 21*w]', '[3920, 70, -4*w^2 + 4*w + 10]', '[3920, 70, 2*w^2 - 12]', '[3920, 490, 2*w + 8]', '[3920, 490, -2*w^3 + 2*w^2 + 10*w + 10]', '[3935, 3935, 9*w^3 - 11*w^2 - 42*w - 1]', '[3935, 3935, w^3 - 2*w^2 - 2*w - 7]', '[3943, 3943, w^3 + 3*w^2 - 9*w - 12]', '[3943, 3943, 4*w^2 - 3*w - 9]', '[3967, 3967, -3*w^3 - w^2 + 17*w + 9]', '[3967, 3967, -5*w^3 + 7*w^2 + 23*w + 9]', '[3969, 21, 3*w^3 - 3*w^2 - 18*w - 3]', '[3969, 21, 3*w^3 - 3*w^2 - 18*w]', '[3969, 147, 6*w^3 - 9*w^2 - 21*w + 3]', '[3969, 147, 6*w^3 - 9*w^2 - 21*w]', '[3979, 3979, -3*w^3 + 6*w^2 + 7*w - 11]', '[3979, 3979, 5*w^3 - 8*w^2 - 19*w - 4]', '[3979, 3979, -w^3 + 5*w^2 - 6*w - 9]', '[3979, 3979, 7*w^3 - 11*w^2 - 30*w + 3]', '[3997, 3997, 7*w^3 - 9*w^2 - 32*w + 7]', '[3997, 3997, 4*w^3 - 10*w^2 - 9*w + 9]', '[3997, 3997, 2*w^3 - 9*w^2 + 4*w + 1]', '[3997, 3997, -5*w^3 + 6*w^2 + 17*w + 9]', '[3997, 3997, -16*w^3 + 25*w^2 + 63*w - 18]', '[3997, 3997, 5*w^3 - 12*w^2 - 4*w - 1]', '[3997, 3997, 7*w^3 - 12*w^2 - 31*w + 14]', '[3997, 3997, -7*w^3 + 6*w^2 + 34*w + 9]', '[4001, 4001, -w^3 + 3*w^2 + 5*w - 11]', '[4001, 4001, -2*w^3 + 13*w]', '[4001, 4001, 9*w^3 - 14*w^2 - 32*w - 1]', '[4001, 4001, 8*w^3 - 9*w^2 - 36*w - 2]', '[4003, 4003, w^2 + 2*w - 10]', '[4003, 4003, 3*w^3 - 2*w^2 - 16*w + 2]', '[4007, 4007, -w^3 + 2*w^2 - w + 11]', '[4007, 4007, -2*w^3 - 2*w^2 + 17*w + 8]', '[4025, 805, -3*w^2 + 7*w + 12]', '[4025, 805, w^2 - 2*w + 6]', '[4025, 805, 3*w^3 - 8*w^2 - 8*w + 8]', '[4025, 805, -w^3 - w^2 + 4*w + 10]', '[4025, 805, -2*w^3 + 7*w^2 + 2*w - 12]', '[4025, 805, -3*w^3 + w^2 + 16*w + 4]', '[4025, 805, -w^3 + 2*w^2 + 4*w - 10]', '[4025, 805, -4*w^3 + 7*w^2 + 17*w + 1]', '[4027, 4027, 4*w^3 - 7*w^2 - 16*w - 3]', '[4027, 4027, -w^3 + 4*w^2 - 2*w - 13]', '[4055, 4055, -2*w^3 + 6*w^2 - 9]', '[4055, 4055, 11*w^3 - 20*w^2 - 39*w + 23]', '[4055, 4055, -4*w^3 + 11*w^2 + 4*w - 11]', '[4055, 4055, -3*w^3 + 9*w^2 + 5*w - 21]', '[4067, 581, -6*w^3 + 8*w^2 + 29*w + 1]', '[4067, 581, -2*w^3 + 8*w^2 - 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14*w + 3]', '[4259, 4259, -w^3 + 6*w^2 - 4*w - 17]', '[4259, 4259, 2*w^2 + w - 9]', '[4259, 4259, -3*w^3 + w^2 + 17*w + 4]', '[4283, 4283, 7*w^3 - 9*w^2 - 28*w - 4]', '[4283, 4283, -5*w^3 + 7*w^2 + 16*w - 2]', '[4285, 4285, 8*w^3 - 12*w^2 - 29*w + 8]', '[4285, 4285, -7*w^3 + 11*w^2 + 23*w + 3]', '[4291, 4291, -3*w^3 + 2*w^2 + 20*w + 8]', '[4291, 4291, 7*w^3 - 14*w^2 - 22*w + 26]', '[4291, 4291, -6*w^3 + 13*w^2 + 16*w + 4]', '[4291, 4291, -4*w^3 + 5*w^2 + 22*w + 4]', '[4293, 159, 3*w^3 - 21*w - 6]', '[4293, 159, 3*w^3 - 6*w^2 - 15*w + 9]', '[4297, 4297, -w - 8]', '[4297, 4297, w^3 - w^2 - 5*w - 9]', '[4315, 4315, 7*w^3 - 11*w^2 - 27*w + 1]', '[4315, 4315, 8*w^3 - 12*w^2 - 32*w + 1]', '[4325, 865, -w^2 - w - 6]', '[4325, 865, -2*w^3 + 3*w^2 + 15*w + 4]', '[4325, 865, -w^3 + 3*w^2 + 7*w + 6]', '[4325, 865, w^3 - w^2 - 11*w - 2]', '[4327, 4327, 7*w^3 - 9*w^2 - 27*w - 7]', '[4327, 4327, 6*w^3 - 8*w^2 - 21*w + 4]', '[4337, 4337, -3*w^3 + 4*w^2 + 10*w - 9]', '[4337, 4337, 4*w^3 - 5*w^2 - 16*w - 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3*w^2 - 6*w - 9]', '[4963, 4963, -13*w^3 + 18*w^2 + 54*w - 5]', '[4963, 4963, 3*w^3 - 4*w^2 - 12*w + 9]', '[4963, 4963, 10*w^3 - 13*w^2 - 42*w - 1]', '[4963, 4963, w^3 - 6*w^2 + 3*w + 11]', '[4963, 4963, 3*w^3 - 8*w^2 + 3*w + 3]', '[4963, 4963, -w^3 + 7*w^2 - 6*w - 11]', '[4963, 4963, 13*w^3 - 18*w^2 - 57*w + 6]', '[4979, 4979, -5*w^3 + 5*w^2 + 18*w + 10]', '[4979, 4979, 7*w^3 - 7*w^2 - 30*w - 2]', '[4979, 4979, 4*w^3 - 2*w^2 - 17*w - 3]', '[4979, 4979, -5*w^3 + 3*w^2 + 23*w + 16]', '[4987, 4987, 3*w^2 - 8*w - 11]', '[4987, 4987, 5*w^3 - 8*w^2 - 22*w - 1]', '[4993, 4993, w^3 + 3*w^2 - 16*w - 5]', '[4993, 4993, 2*w^3 - 5*w^2 - 2*w + 14]', '[5008, 626, -4*w^3 + 8*w^2 + 10*w - 10]', '[5008, 626, 6*w^3 - 10*w^2 - 22*w]', '[5011, 5011, -2*w^3 + 17*w + 7]', '[5011, 5011, 5*w^3 - 7*w^2 - 25*w]', '[5011, 5011, -3*w^3 + 9*w^2 + 4*w - 9]', '[5011, 5011, -5*w^3 + 11*w^2 + 16*w - 13]', '[5021, 5021, -2*w^3 + 7*w^2 + 6*w - 12]', '[5021, 5021, 3*w^2 - 7*w - 15]', '[5021, 5021, 4*w^3 - 7*w^2 - 17*w - 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7*w - 14]', '[5105, 5105, 8*w^3 - 10*w^2 - 33*w - 5]', '[5105, 5105, 10*w^3 - 14*w^2 - 45*w + 9]', '[5105, 5105, -w^2 + 5*w - 9]', '[5105, 5105, -2*w^3 + 7*w^2 + 3*w - 13]', '[5113, 5113, w^2 - 2*w - 11]', '[5113, 5113, w^3 - 2*w^2 - 4*w - 7]', '[5129, 5129, -2*w^3 - 3*w^2 + 22*w + 6]', '[5129, 5129, 7*w^3 - 9*w^2 - 26*w + 4]', '[5129, 5129, 5*w^3 - 7*w^2 - 15*w - 2]', '[5129, 5129, -14*w^3 + 20*w^2 + 60*w - 13]', '[5153, 5153, -w^3 + 3*w^2 + 6*w - 9]', '[5153, 5153, -3*w^3 + w^2 + 18*w + 3]', '[5161, 5161, 7*w^3 - 7*w^2 - 30*w - 7]', '[5161, 5161, 11*w^3 - 12*w^2 - 49*w - 8]', '[5161, 5161, 3*w^3 + 2*w^2 - 21*w - 16]', '[5161, 5161, 5*w^3 - 30*w - 23]', '[5167, 5167, 3*w^2 - w - 13]', '[5167, 5167, -2*w^3 - w^2 + 13*w + 4]', '[5171, 5171, 4*w^3 - 7*w^2 - 18*w - 2]', '[5171, 5171, -8*w^3 + 14*w^2 + 25*w + 2]', '[5171, 5171, w^3 + 2*w^2 - 12*w - 14]', '[5171, 5171, -9*w^3 + 15*w^2 + 31*w - 15]', '[5197, 5197, w^3 - 12*w]', '[5197, 5197, 6*w^3 - 7*w^2 - 30*w]', '[5200, 130, 8*w^3 - 12*w^2 - 30*w + 4]', '[5200, 130, -2*w^2 - 2*w + 8]', '[5200, 130, 6*w^3 - 10*w^2 - 18*w + 2]', '[5200, 130, 4*w^3 - 2*w^2 - 22*w - 6]', '[5215, 5215, -w^3 + 4*w^2 - 3*w + 5]', '[5215, 5215, -5*w^3 + 9*w^2 + 13*w + 8]', '[5215, 5215, w^2 - 3*w + 7]', '[5215, 5215, 9*w^3 - 14*w^2 - 33*w + 3]', '[5215, 5215, -6*w^3 + 13*w^2 + 18*w - 15]', '[5215, 5215, -2*w^3 + 3*w^2 + 9*w - 10]', '[5215, 5215, -8*w^3 + 12*w^2 + 31*w - 15]', '[5215, 5215, -5*w^3 + 8*w^2 + 21*w - 14]', '[5221, 5221, -4*w^3 + 6*w^2 + 15*w - 11]', '[5221, 5221, 3*w^3 - 7*w^2 - 6*w - 4]', '[5221, 5221, -5*w^3 + 9*w^2 + 18*w - 16]', '[5221, 5221, 3*w^3 - 5*w^2 - 9*w - 8]', '[5227, 5227, -2*w^3 + 7*w^2 - w - 12]', '[5227, 5227, 6*w^3 - 11*w^2 - 23*w + 5]', '[5233, 5233, w^3 - 5*w^2 + 3*w + 18]', '[5233, 5233, -9*w^3 + 14*w^2 + 32*w - 10]', '[5243, 749, 3*w^3 - 18*w - 7]', '[5243, 749, 2*w^3 + w^2 - 15*w - 4]', '[5243, 749, 3*w^2 - 11]', '[5243, 749, -2*w^3 + 5*w^2 + 9*w - 11]', '[5243, 5243, 5*w^3 - 9*w^2 - 18*w]', '[5243, 5243, -3*w^3 + 7*w^2 + 6*w - 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w^2 - 16*w - 3]', '[5341, 5341, w^3 - w^2 - 2*w + 8]', '[5341, 5341, 7*w^3 - 9*w^2 - 31*w + 9]', '[5341, 5341, 3*w^3 - 19*w - 7]', '[5341, 5341, -w^3 + 4*w^2 + 5*w - 10]', '[5341, 5341, w^3 + w^2 - 4*w - 11]', '[5359, 5359, -3*w^3 + 6*w^2 + 6*w + 7]', '[5359, 5359, 3*w^3 - 8*w^2 - 3*w - 3]', '[5359, 5359, 7*w^3 - 12*w^2 - 27*w + 18]', '[5359, 5359, -6*w^3 + 9*w^2 + 24*w - 13]', '[5360, 670, 6*w^3 - 14*w^2 - 14*w + 12]', '[5360, 670, -8*w^3 + 16*w^2 + 26*w - 14]', '[5381, 5381, -4*w^3 + 10*w^2 + 10*w - 13]', '[5381, 5381, 3*w^3 - 4*w^2 - 18*w - 2]', '[5381, 5381, -4*w^3 + 3*w^2 + 24*w + 8]', '[5381, 5381, -9*w^3 + 13*w^2 + 35*w - 1]', '[5387, 5387, -7*w^3 + 14*w^2 + 25*w - 15]', '[5387, 5387, 10*w^3 - 13*w^2 - 40*w - 9]', '[5393, 5393, -7*w^3 + 11*w^2 + 24*w - 5]', '[5393, 5393, -7*w^3 + 11*w^2 + 24*w - 1]', '[5395, 5395, -8*w^3 + 10*w^2 + 33*w - 5]', '[5395, 5395, 5*w^3 - 7*w^2 - 15*w - 8]', '[5395, 5395, -w^3 - 3*w^2 + 10*w + 4]', '[5395, 5395, -w^3 + 5*w^2 + 2*w - 16]', '[5407, 5407, -2*w^3 + 7*w^2 + w - 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8]', '[5488, 686, 2*w^3 - 4*w^2 - 12*w + 8]', '[5488, 686, -4*w^3 + 2*w^2 + 24*w + 4]', '[5503, 5503, -5*w^3 + 10*w^2 + 12*w - 9]', '[5503, 5503, -8*w^3 + 13*w^2 + 30*w - 3]', '[5509, 5509, 3*w^3 - 11*w^2 - w + 7]', '[5509, 5509, 6*w^3 - 14*w^2 - 19*w + 24]', '[5509, 5509, -6*w^3 + 8*w^2 + 22*w - 1]', '[5509, 5509, -6*w^3 + 8*w^2 + 22*w + 3]', '[5515, 5515, 12*w^3 - 13*w^2 - 56*w - 8]', '[5515, 5515, 7*w^3 - 13*w^2 - 23*w + 19]', '[5545, 5545, 17*w^3 - 27*w^2 - 68*w + 18]', '[5545, 5545, 10*w^3 - 15*w^2 - 46*w + 16]', '[5545, 5545, 8*w^3 - 15*w^2 - 23*w]', '[5545, 5545, w^3 + 5*w^2 - 16*w - 20]', '[5552, 694, -2*w^3 + 4*w^2 + 2*w - 10]', '[5552, 694, 6*w^3 - 8*w^2 - 26*w - 8]', '[5561, 5561, -7*w^3 + 12*w^2 + 27*w - 5]', '[5561, 5561, -3*w^3 + 8*w^2 + 3*w - 10]', '[5561, 5561, -3*w^3 + 6*w^2 + 14*w - 11]', '[5561, 5561, 2*w^3 + w^2 - 16*w - 3]', '[5563, 5563, 3*w^3 - 4*w^2 - 8*w - 8]', '[5563, 5563, 6*w^3 - 7*w^2 - 26*w + 4]', '[5573, 5573, 7*w^3 - 8*w^2 - 29*w - 4]', '[5573, 5573, -3*w^3 + w^2 + 20*w]', '[5575, 1115, 7*w^3 - 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8]', '[5717, 5717, 4*w^3 - 3*w^2 - 21*w - 1]', '[5737, 5737, -6*w^3 + 12*w^2 + 16*w - 11]', '[5737, 5737, -8*w^3 + 14*w^2 + 28*w - 5]', '[5743, 5743, -2*w^3 + 5*w^2 + 2*w - 12]', '[5743, 5743, 5*w^3 - 8*w^2 - 20*w - 4]', '[5747, 5747, 7*w^3 - 11*w^2 - 32*w + 8]', '[5747, 5747, 2*w^3 - 7*w^2 - w - 2]', '[5747, 5747, 4*w^3 - 9*w^2 - 13*w + 21]', '[5747, 5747, 8*w^3 - 16*w^2 - 30*w + 19]', '[5747, 5747, -w^3 - 3*w^2 + 16*w + 6]', '[5747, 5747, -5*w^3 + 7*w^2 + 15*w - 1]', '[5747, 5747, -8*w^3 + 10*w^2 + 33*w + 4]', '[5747, 5747, 2*w^3 - 10*w^2 + 6*w + 11]', '[5755, 5755, 4*w^3 - 2*w^2 - 25*w - 2]', '[5755, 5755, -9*w^3 + 12*w^2 + 40*w - 8]', '[5755, 5755, -4*w^3 + 9*w^2 + 10*w - 15]', '[5755, 5755, w^3 - 6*w^2 + 5*w + 15]', '[5765, 5765, 10*w^3 - 13*w^2 - 46*w + 4]', '[5765, 5765, -w^2 + 4*w - 8]', '[5776, 38, 6*w^3 - 6*w^2 - 26*w - 18]', '[5776, 38, 4*w^3 - 4*w^2 - 14*w + 8]', '[5777, 5777, 2*w^3 - 17*w - 6]', '[5777, 5777, 5*w^3 - 7*w^2 - 25*w + 1]', '[5777, 5777, -w^3 + 4*w^2 - 3*w - 11]', '[5777, 5777, 8*w^3 - 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15*w - 7]', '[5941, 5941, -4*w^3 + 8*w^2 + 16*w + 7]', '[5941, 5941, 5*w^3 - 3*w^2 - 28*w - 7]', '[5941, 5941, -4*w^3 + 5*w^2 + 20*w + 12]', '[5965, 5965, 9*w^3 - 17*w^2 - 29*w + 17]', '[5965, 5965, 6*w^3 - 14*w^2 - 14*w + 17]', '[5968, 746, -6*w^3 + 8*w^2 + 22*w + 2]', '[5968, 746, -6*w^3 + 8*w^2 + 22*w]', '[5981, 5981, -7*w^3 + 10*w^2 + 25*w - 5]', '[5981, 5981, 8*w^3 - 10*w^2 - 33*w - 3]', '[5981, 5981, -7*w^3 + 10*w^2 + 25*w + 4]', '[5981, 5981, 5*w^3 - 7*w^2 - 15*w]', '[5987, 5987, -2*w^3 + 6*w^2 + 7*w - 15]', '[5987, 5987, w^3 + 3*w^2 - 11*w - 4]', '[5999, 5999, -2*w^3 + 7*w^2 + 3*w - 10]', '[5999, 5999, w^3 - w^2 - 4*w - 10]', '[5999, 5999, -w^3 + w^2 + 4*w - 8]', '[5999, 5999, -2*w^3 + 7*w^2 + 3*w - 11]', '[6007, 6007, -4*w^3 + 2*w^2 + 23*w + 5]', '[6007, 6007, w^3 - 3*w^2 - 7*w + 8]', '[6019, 6019, -2*w^3 - 2*w^2 + 15*w + 7]', '[6019, 6019, -5*w^3 + 3*w^2 + 26*w + 8]', '[6019, 6019, -w^3 - w^2 + 2*w + 8]', '[6019, 6019, w^3 - 5*w^2 - 3*w + 14]', '[6037, 6037, -4*w^3 + 8*w^2 + 9*w - 9]', '[6037, 6037, -7*w^3 + 11*w^2 + 27*w]', '[6041, 6041, 3*w^3 - 7*w^2 - 12*w + 14]', '[6041, 6041, -5*w^2 + 9*w + 4]', '[6041, 6041, 4*w^3 - 9*w^2 - 15*w + 17]', '[6041, 6041, -w^3 - 3*w^2 + 12*w + 4]', '[6055, 6055, 5*w^3 - 5*w^2 - 22*w + 2]', '[6055, 6055, -3*w^3 + 7*w^2 + 13*w - 12]', '[6055, 6055, -2*w^3 - 2*w^2 + 17*w + 7]', '[6055, 6055, -3*w^3 + 3*w^2 + 10*w + 10]', '[6065, 6065, 7*w^3 - 12*w^2 - 21*w + 1]', '[6065, 6065, w^3 + 3*w^2 - 7*w - 17]', '[6067, 6067, -3*w^3 + 7*w^2 + 6*w - 13]', '[6067, 6067, -5*w^3 + 9*w^2 + 18*w + 1]', '[6085, 6085, -10*w^3 + 17*w^2 + 37*w - 9]', '[6085, 6085, 10*w^3 - 16*w^2 - 37*w + 3]', '[6091, 6091, 7*w^3 - 11*w^2 - 29*w + 2]', '[6091, 6091, -4*w^3 + 7*w^2 + 10*w - 9]', '[6091, 6091, -2*w^3 + 6*w^2 - w - 9]', '[6091, 6091, -7*w^3 + 10*w^2 + 28*w + 5]', '[6095, 6095, 4*w^3 - 31*w - 18]', '[6095, 6095, 4*w^3 - 4*w^2 - 25*w - 10]', '[6095, 6095, 5*w^3 - 5*w^2 - 29*w - 11]', '[6095, 6095, 7*w^3 - 11*w^2 - 35*w - 1]', '[6097, 6097, 3*w^3 - 4*w^2 - 18*w + 2]', '[6097, 6097, 4*w^3 - 9*w^2 - 8*w - 4]', '[6097, 6097, -5*w^3 + 9*w^2 + 25*w - 7]', '[6097, 6097, -w^3 + 4*w^2 + 4]', '[6097, 6097, 6*w^3 - 9*w^2 - 20*w + 2]', '[6097, 6097, -3*w^3 + 10*w^2 + 2*w - 8]', '[6097, 6097, -7*w^3 + 10*w^2 + 24*w - 6]', '[6097, 6097, 3*w^3 - 9*w^2 - 7*w + 7]', '[6113, 6113, 6*w^3 - 12*w^2 - 19*w + 4]', '[6113, 6113, 6*w^3 - 12*w^2 - 20*w + 5]', '[6115, 6115, -2*w^2 + w + 16]', '[6115, 6115, 5*w^3 - 6*w^2 - 26*w + 2]', '[6125, 35, -7*w^3 + 5*w^2 + 35*w + 12]', '[6125, 35, -w^3 + 6]', '[6125, 175, 7*w^3 - 11*w^2 - 24*w + 3]', '[6125, 175, -6*w^3 + 8*w^2 + 22*w + 1]', '[6125, 245, 7*w^3 - 10*w^2 - 30*w - 2]', '[6125, 245, 2*w^3 - 5*w^2 + 8]', '[6125, 1225, 4*w^3 - 5*w^2 - 22*w + 3]', '[6125, 1225, 3*w^3 - 2*w^2 - 20*w - 1]', '[6128, 766, 6*w^3 - 10*w^2 - 26*w + 2]', '[6128, 766, 4*w^2 - 10*w - 12]', '[6139, 6139, 9*w^3 - 18*w^2 - 32*w + 24]', '[6139, 6139, -6*w^3 + 9*w^2 + 20*w]', '[6139, 6139, 7*w^3 - 10*w^2 - 26*w + 2]', '[6139, 6139, -4*w^3 + 13*w^2 + 2*w - 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33*w + 9]', '[9931, 9931, -8*w^3 + 17*w^2 + 27*w - 13]', '[9931, 9931, -4*w^3 + 13*w^2 + 3*w - 20]', '[9931, 9931, 9*w^3 - 10*w^2 - 45*w - 10]', '[9967, 9967, -4*w^3 + 5*w^2 + 23*w + 3]', '[9967, 9967, -4*w^3 + 3*w^2 + 25*w + 8]', '[9983, 9983, 6*w^2 - 8*w - 11]', '[9983, 9983, -2*w^3 + 5*w^2 + 9*w - 15]', '[9983, 9983, -2*w^3 + 8*w^2 + 4*w - 17]', '[9983, 9983, -9*w^3 + 17*w^2 + 30*w - 22]', '[9983, 9983, 11*w^3 - 12*w^2 - 48*w - 7]', '[9983, 9983, -5*w^3 + 13*w^2 + 10*w - 21]', '[9983, 9983, 8*w^3 - 8*w^2 - 41*w - 10]', '[9983, 9983, -2*w^3 - w^2 + 15*w]', '[9985, 9985, -3*w^3 + 8*w^2 + 4*w - 14]', '[9985, 9985, -2*w^3 + 8*w^2 - w - 20]', '[9989, 9989, 13*w^3 - 20*w^2 - 56*w + 16]', '[9989, 9989, 7*w^3 - 12*w^2 - 28*w + 20]', '[9989, 9989, 2*w^3 - 7*w^2 + 2*w - 4]', '[9989, 9989, 2*w^3 - 9*w^2 + 10*w + 4]', '[10000, 10, 10]', '[10000, 50, 4*w^3 - 4*w^2 - 24*w - 6]', '[10000, 50, 4*w^3 - 4*w^2 - 24*w + 2]'], 'label': '4.4.4205.1', 'narrow_class_no': 1, 'primes': ['[5, 5, -w^3 + w^2 + 5*w]', '[7, 7, -w^3 + 2*w^2 + 3*w - 3]', '[7, 7, w^3 - 2*w^2 - 3*w]', '[13, 13, -w^2 + w + 3]', '[13, 13, -w^2 + w + 2]', '[16, 2, 2]', '[23, 23, -w^2 + 3*w + 1]', '[23, 23, -2*w^3 + 3*w^2 + 9*w - 2]', '[25, 5, w^3 - 2*w^2 - 2*w + 2]', '[49, 7, w^3 - w^2 - 6*w - 1]', '[53, 53, 2*w^3 - 2*w^2 - 8*w - 3]', '[53, 53, 2*w^3 - 2*w^2 - 8*w - 1]', '[67, 67, 2*w^3 - 4*w^2 - 7*w + 2]', '[67, 67, -2*w^3 + 4*w^2 + 6*w - 1]', '[81, 3, -3]', '[83, 83, 2*w^3 - 3*w^2 - 6*w - 1]', '[83, 83, 3*w^3 - 4*w^2 - 12*w + 1]', '[103, 103, 3*w^3 - 4*w^2 - 12*w - 1]', '[103, 103, 2*w^3 - 3*w^2 - 6*w + 1]', '[107, 107, w^3 - w^2 - 3*w - 3]', '[107, 107, 2*w^3 - 2*w^2 - 9*w]', '[109, 109, -3*w^3 + 5*w^2 + 10*w - 5]', '[109, 109, -2*w^3 + 3*w^2 + 9*w + 1]', '[109, 109, -2*w^3 + 2*w^2 + 7*w]', '[109, 109, w^2 - 3*w - 4]', '[121, 11, 3*w^3 - 4*w^2 - 12*w]', '[121, 11, 2*w^2 - 3*w - 6]', '[139, 139, w^3 - 7*w - 1]', '[139, 139, -w^3 + 2*w^2 + 5*w - 4]', '[139, 139, 3*w^3 - 3*w^2 - 14*w - 2]', '[139, 139, -3*w^3 + 5*w^2 + 13*w - 2]', '[149, 149, -w^2 + 4*w + 1]', '[149, 149, -3*w^3 + 4*w^2 + 14*w - 1]', '[149, 149, 2*w^2 - 3*w - 5]', '[149, 149, -w^3 + 3*w^2 + 3*w - 4]', '[167, 167, -w^3 - w^2 + 7*w + 4]', '[167, 167, -4*w^3 + 6*w^2 + 15*w - 4]', '[169, 13, w^3 - w^2 - 6*w + 4]', '[173, 173, w^2 - 3*w - 5]', '[173, 173, 2*w^3 - 2*w^2 - 11*w]', '[179, 179, 2*w^3 - 2*w^2 - 9*w + 1]', '[179, 179, w^3 - w^2 - 3*w - 4]', '[179, 179, w^2 - 5]', '[179, 179, w^3 - 6*w - 1]', '[197, 197, w^3 + w^2 - 7*w - 6]', '[197, 197, 2*w^3 - 2*w^2 - 9*w + 2]', '[223, 223, -w^2 + 7]', '[223, 223, 2*w^2 - w - 4]', '[227, 227, 2*w^3 - 2*w^2 - 11*w - 2]', '[227, 227, w^3 - w^2 - 7*w - 1]', '[233, 233, w^3 - w^2 - 7*w]', '[233, 233, -2*w^3 + 2*w^2 + 11*w + 1]', '[257, 257, -2*w^3 + 4*w^2 + 8*w - 1]', '[257, 257, 2*w^2 - 4*w - 7]', '[277, 277, -4*w^3 + 6*w^2 + 15*w - 3]', '[277, 277, -3*w^3 + 5*w^2 + 9*w]', '[281, 281, -2*w^3 + 5*w^2 + 3*w - 5]', '[281, 281, -2*w^3 + 5*w^2 + 5*w - 7]', '[281, 281, 2*w^3 - 5*w^2 - 5*w + 4]', '[281, 281, -4*w^3 + 7*w^2 + 15*w - 4]', '[283, 283, 3*w^3 - 4*w^2 - 13*w - 3]', '[283, 283, -w^3 + 2*w^2 + w - 4]', '[313, 313, -2*w^3 + 4*w^2 + 5*w - 5]', '[313, 313, 3*w^3 - 5*w^2 - 11*w]', '[347, 347, -w^3 + 2*w^2 + w - 5]', '[347, 347, 3*w^3 - 4*w^2 - 13*w - 4]', '[353, 353, 3*w^3 - 5*w^2 - 12*w + 1]', '[353, 353, -w^3 + 3*w^2 - 5]', '[361, 19, 3*w^3 - 3*w^2 - 13*w - 9]', '[361, 19, 2*w^3 - 2*w^2 - 7*w + 4]', '[373, 373, -3*w^3 + 4*w^2 + 11*w + 1]', '[373, 373, -3*w^3 + 4*w^2 + 11*w]', '[383, 383, 3*w^3 - 5*w^2 - 13*w + 1]', '[383, 383, 2*w^2 - 5*w - 6]', '[397, 397, 4*w^3 - 5*w^2 - 19*w - 1]', '[397, 397, 2*w^3 - 2*w^2 - 9*w - 7]', '[431, 431, 2*w^3 - 2*w^2 - 7*w - 5]', '[431, 431, 3*w^3 - 6*w^2 - 11*w + 3]', '[431, 431, 3*w^3 - 3*w^2 - 13*w]', '[431, 431, w^3 - 4*w^2 + w + 8]', '[457, 457, 4*w^3 - 7*w^2 - 13*w]', '[457, 457, -3*w^2 + 4*w + 5]', '[463, 463, -3*w^3 + 5*w^2 + 11*w + 1]', '[463, 463, 2*w^3 - 4*w^2 - 5*w + 6]', '[487, 487, -w^3 + 4*w^2 - 7]', '[487, 487, -2*w^3 + 5*w^2 + 6*w - 5]', '[499, 499, -6*w^3 + 8*w^2 + 25*w - 1]', '[499, 499, -w^3 + 4*w^2 - 5]', '[499, 499, -2*w^3 + 5*w^2 + 6*w - 7]', '[499, 499, 3*w^3 - 5*w^2 - 7*w]', '[509, 509, -4*w^3 + 8*w^2 + 15*w - 8]', '[509, 509, 3*w^3 - 4*w^2 - 10*w - 2]', '[509, 509, -3*w^3 + 3*w^2 + 11*w + 6]', '[509, 509, 4*w^3 - 5*w^2 - 16*w]', '[521, 521, -4*w^3 + 5*w^2 + 15*w - 2]', '[521, 521, w^3 - w^2 - 8*w + 1]', '[521, 521, -4*w^3 + 7*w^2 + 12*w - 6]', '[521, 521, 3*w^3 - 3*w^2 - 16*w - 1]', '[523, 523, 3*w^3 - w^2 - 17*w - 8]', '[523, 523, -5*w^3 + 5*w^2 + 23*w + 4]', '[529, 23, 3*w^3 - 6*w^2 - 10*w + 2]', '[547, 547, -2*w^3 + 5*w^2 + 6*w - 6]', '[547, 547, -w^3 + 4*w^2 - 6]', '[557, 557, -3*w^3 + 6*w^2 + 9*w - 10]', '[557, 557, 3*w^3 - 6*w^2 - 9*w - 1]', '[571, 571, 4*w^3 - 4*w^2 - 17*w - 6]', '[571, 571, -2*w^3 + 6*w^2 + 3*w - 10]', '[571, 571, 4*w^3 - 5*w^2 - 18*w + 3]', '[571, 571, -3*w^3 + 7*w^2 + 9*w - 5]', '[587, 587, 3*w^3 - 3*w^2 - 14*w]', '[587, 587, w^3 - w^2 - 2*w - 4]', '[593, 593, -w^3 + 3*w^2 + 2*w - 10]', '[593, 593, -5*w^3 + 7*w^2 + 19*w - 4]', '[613, 613, 3*w^3 - 5*w^2 - 12*w - 4]', '[613, 613, -w^3 + 3*w^2 - 10]', '[631, 631, 4*w^3 - 8*w^2 - 13*w + 4]', '[631, 631, 3*w^3 - 4*w^2 - 15*w + 2]', '[631, 631, w^3 - 9*w - 1]', '[631, 631, 3*w^3 - 7*w^2 - 7*w + 9]', '[643, 643, 3*w^3 - 3*w^2 - 16*w - 2]', '[643, 643, w^3 - w^2 - 8*w]', '[647, 647, -w^3 + 4*w^2 + 2*w - 4]', '[647, 647, -3*w^2 + 4*w + 10]', '[673, 673, w^3 + 2*w^2 - 9*w - 8]', '[673, 673, -w^3 + 4*w^2 + 3*w - 7]', '[683, 683, 3*w^3 - 3*w^2 - 11*w - 2]', '[683, 683, 4*w^3 - 4*w^2 - 17*w - 5]', '[709, 709, -5*w^3 + 7*w^2 + 21*w + 1]', '[709, 709, -3*w^3 + 2*w^2 + 16*w + 4]', '[709, 709, 4*w^3 - 4*w^2 - 19*w - 2]', '[709, 709, -2*w^3 + 4*w^2 + 3*w - 4]', '[787, 787, 2*w^2 - w - 9]', '[787, 787, w^3 + w^2 - 7*w - 2]', '[811, 811, 4*w^3 - 7*w^2 - 11*w]', '[811, 811, 3*w^3 - 4*w^2 - 9*w - 1]', '[811, 811, -6*w^3 + 9*w^2 + 23*w - 5]', '[811, 811, 5*w^3 - 6*w^2 - 21*w - 2]', '[821, 821, -3*w^3 + 6*w^2 + 11*w - 2]', '[821, 821, 2*w^3 - 13*w - 5]', '[821, 821, -w^3 + 4*w^2 - w - 9]', '[821, 821, -w^3 + 3*w^2 + 5*w - 6]', '[841, 29, 2*w^3 - 2*w^2 - 12*w - 1]', '[857, 857, w^3 - 4*w^2 + 3*w + 6]', '[857, 857, -5*w^3 + 8*w^2 + 21*w - 3]', '[863, 863, -w^3 + 4*w^2 + w - 7]', '[863, 863, -w^3 + 4*w^2 + w - 6]', '[877, 877, -w^3 - w^2 + 8*w + 2]', '[877, 877, -w^3 + 3*w^2 + 4*w - 8]', '[883, 883, 4*w^3 - 7*w^2 - 14*w + 1]', '[883, 883, 3*w^3 - 6*w^2 - 8*w + 7]', '[929, 929, 3*w^3 - 5*w^2 - 12*w - 3]', '[929, 929, -w^3 + 3*w^2 - 9]', '[929, 929, 3*w - 5]', '[929, 929, 3*w^3 - 3*w^2 - 15*w + 2]', '[937, 937, w^3 - 2*w^2 - 6*w + 6]', '[937, 937, 2*w^3 - w^2 - 12*w]', '[941, 941, -w^3 + 4*w^2 + 2*w - 7]', '[941, 941, -4*w^3 + 6*w^2 + 13*w - 3]', '[941, 941, -5*w^3 + 7*w^2 + 19*w + 2]', '[941, 941, 3*w^2 - 4*w - 7]', '[953, 953, 3*w^3 - 5*w^2 - 12*w - 2]', '[953, 953, -w^3 + 3*w^2 - 8]', '[961, 31, 4*w^3 - 6*w^2 - 13*w - 2]', '[961, 31, 5*w^3 - 7*w^2 - 19*w + 3]', '[977, 977, -4*w^3 + 7*w^2 + 19*w - 6]', '[977, 977, -3*w^3 + 7*w^2 + 10*w - 6]']}
• 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': [1, -1, -5, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 4205, 'disc_rad': 145, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[4, 1]]], [5, [0]], [7, [[2, 1], [1, 2]]], [11, [[2, 2]]], [13, [[2, 1], [1, 2]]], [17, [[4, 1]]], [19, [[2, 2]]], [23, [[2, 1], [1, 2]]], [29, [0]], [31, [[2, 2]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[4, 1]]], [47, [[4, 1]]], [53, [[2, 1], [1, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 12.041594578792296, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '4.4.4205.1', 'local_algs': ['5.2.0.1', '5.2.1.2', '29.4.2.1'], 'minimal_sibling': [1, 1, -3, -1, 1], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 29], 'rd': 8.05269963102, 'regulator': {'__RealLiteral__': 0, 'data': '2.8242845114', 'prec': 40}, 'res': {'gal': ['-1,11,-5,-36,17,26,-12,-2,1'], 'sib': ['1,1,-3,-1,1', '-1,11,-5,-36,17,26,-12,-2,1']}, 'subfield_mults': [1], 'subfields': ['-7.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{3} - 2 a^{2} - 3 a + 2 \\)', '\\( a^{2} - 2 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}