Hilbert modular form data - 4.4.17417.1-13.1-b

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• 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': 18, 'disc': 17417, 'field_bad_primes': [17417], 'field_label': '4.4.17417.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.17417.1-13.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', '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-b', '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': ['e', '-79516/43625*e^17 - 526408/43625*e^16 + 66131/8725*e^15 + 8633724/43625*e^14 + 9053253/43625*e^13 - 52270696/43625*e^12 - 18258339/8725*e^11 + 28799402/8725*e^10 + 342395314/43625*e^9 - 174606912/43625*e^8 - 618007117/43625*e^7 + 56441426/43625*e^6 + 556976069/43625*e^5 + 48743422/43625*e^4 - 229446894/43625*e^3 - 36263294/43625*e^2 + 1224543/1745*e + 275004/1745', '-24202/43625*e^17 - 164951/43625*e^16 + 14702/8725*e^15 + 2664078/43625*e^14 + 3192316/43625*e^13 - 15716262/43625*e^12 - 6074893/8725*e^11 + 8249494/8725*e^10 + 111255808/43625*e^9 - 44643314/43625*e^8 - 197209749/43625*e^7 + 6598622/43625*e^6 + 175158593/43625*e^5 + 18546559/43625*e^4 - 71386468/43625*e^3 - 9960568/43625*e^2 + 372333/1745*e + 73058/1745', '95387/43625*e^17 + 642331/43625*e^16 - 65652/8725*e^15 - 10413418/43625*e^14 - 11957196/43625*e^13 + 61755572/43625*e^12 + 23191453/8725*e^11 - 32610439/8725*e^10 - 427896923/43625*e^9 + 175645959/43625*e^8 + 762293419/43625*e^7 - 13858957/43625*e^6 - 679215483/43625*e^5 - 99340979/43625*e^4 + 277754808/43625*e^3 + 56972508/43625*e^2 - 1494087/1745*e - 383118/1745', 1, '-168707/43625*e^17 - 1149316/43625*e^16 + 103577/8725*e^15 + 18591523/43625*e^14 + 22287181/43625*e^13 - 109755642/43625*e^12 - 42635273/8725*e^11 + 57311579/8725*e^10 + 785738078/43625*e^9 - 296486024/43625*e^8 - 1404389409/43625*e^7 - 6552548/43625*e^6 + 1260165563/43625*e^5 + 204788344/43625*e^4 - 520995788/43625*e^3 - 111945688/43625*e^2 + 565778/349*e + 740598/1745', '111622/43625*e^17 + 744936/43625*e^16 - 85357/8725*e^15 - 12174958/43625*e^14 - 13405776/43625*e^13 + 73166582/43625*e^12 + 26651953/8725*e^11 - 39588809/8725*e^10 - 499504113/43625*e^9 + 226359154/43625*e^8 + 904873214/43625*e^7 - 42481442/43625*e^6 - 820604773/43625*e^5 - 100795924/43625*e^4 + 341033698/43625*e^3 + 62028073/43625*e^2 - 1842444/1745*e - 441028/1745', '-59557/43625*e^17 - 396966/43625*e^16 + 45167/8725*e^15 + 6467298/43625*e^14 + 7146881/43625*e^13 - 38666942/43625*e^12 - 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1301270692/43625*e^3 - 258797767/43625*e^2 + 7007319/1745*e + 1843547/1745'], 'hecke_polynomial': 'x^18 + 8*x^17 + 5*x^16 - 114*x^15 - 263*x^14 + 496*x^13 + 2040*x^12 - 210*x^11 - 6704*x^10 - 3748*x^9 + 10502*x^8 + 9904*x^7 - 7554*x^6 - 10072*x^5 + 1744*x^4 + 4314*x^3 + 330*x^2 - 600*x - 125', 'label': '4.4.17417.1-13.1-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 17417, 'ideals': ['[1, 1, 1]', '[2, 2, w^3 - 3*w^2 - w + 2]', '[4, 4, w]', '[5, 5, w^2 - 2*w - 3]', '[5, 5, w^3 - 3*w^2 - 3*w + 5]', '[8, 2, w^3 - 2*w^2 - 3*w + 3]', '[8, 8, -w^2 + w + 4]', '[10, 10, -w^3 + 3*w^2 + 2*w - 6]', '[10, 10, -w + 2]', '[13, 13, -w^2 + w + 3]', '[16, 2, 2]', '[16, 16, w^3 - 2*w^2 - 4*w]', '[17, 17, -w^2 + 3*w + 1]', '[20, 20, -2*w^3 + 5*w^2 + 7*w - 8]', '[20, 20, w^3 - 2*w^2 - 3*w]', '[23, 23, w^2 - 3]', '[25, 5, -w^3 + 2*w^2 + 4*w - 3]', '[25, 5, -w^2 + 2*w + 1]', '[25, 25, w^3 - 4*w^2 + 2*w + 3]', '[25, 25, w^3 - 3*w^2 - 2*w + 3]', '[26, 26, w^2 - 3*w - 2]', '[32, 4, 2*w^3 - 6*w^2 - 2*w + 4]', '[32, 32, 2*w^3 - 5*w^2 - 6*w + 8]', '[34, 34, w^3 - 2*w^2 - 3*w + 2]', '[37, 37, w^3 - 4*w^2 - 2*w + 9]', '[40, 10, -w^3 + 2*w^2 + 5*w - 1]', '[40, 10, w^3 - 2*w^2 - 3*w + 1]', '[40, 40, w^3 - 3*w^2 - 3*w + 4]', '[40, 40, -w^2 + 2*w]', '[41, 41, w^2 - w - 5]', '[46, 46, -w^3 + 3*w^2 + 2*w - 2]', '[49, 7, -w^3 + 2*w^2 + 2*w - 1]', '[49, 7, w^2 + w - 3]', '[50, 10, -w^2 + 2*w + 6]', '[50, 10, -w^3 + 4*w^2 - w - 6]', '[50, 50, w^3 - 2*w^2 - 2*w + 2]', '[50, 50, -w^3 + 4*w^2 + w - 10]', '[52, 52, w^3 - 2*w^2 - 4*w + 4]', '[59, 59, w^3 - 3*w^2 - 4*w + 5]', '[64, 4, -w^3 + 2*w^2 + 5*w - 3]', '[64, 8, 2*w]', '[64, 64, w^2 - 3*w - 4]', '[65, 65, -2*w + 1]', '[65, 65, -2*w^2 + 4*w + 5]', '[67, 67, -w^3 + 3*w^2 + w - 5]', '[68, 68, -w^3 + 3*w^2 + w]', '[71, 71, 2*w - 3]', '[71, 71, w^3 - 4*w^2 + 2*w + 5]', '[74, 74, w^3 - 2*w^2 - 5*w + 2]', '[79, 79, -w^3 + 5*w^2 - 4*w - 5]', '[79, 79, -2*w^3 + 7*w^2 + 5*w - 15]', '[80, 10, 2*w^2 - 4*w - 6]', '[80, 10, 2*w^3 - 6*w^2 - 6*w + 10]', '[80, 80, -w^3 + 3*w^2]', '[80, 80, w^3 - 3*w^2 - 2*w + 8]', '[81, 3, -3]', '[82, 82, -2*w^3 + 5*w^2 + 5*w - 2]', '[83, 83, -2*w^3 + 6*w^2 + 2*w - 5]', '[85, 85, w + 3]', '[85, 85, -2*w^3 + 6*w^2 + w - 3]', '[92, 92, -2*w^3 + 5*w^2 + 5*w - 8]', '[97, 97, w^3 - w^2 - 7*w - 3]', '[98, 14, -2*w^3 + 7*w^2 + w - 6]', '[98, 14, 3*w^3 - 10*w^2 - w + 6]', '[100, 20, 2*w^3 - 4*w^2 - 7*w]', '[100, 20, -w^2 + 4]', '[100, 100, -w^3 + 3*w^2 + w - 8]', '[100, 100, -w^3 + 3*w^2 - 4]', '[101, 101, -w^3 + 3*w^2 + 3*w - 3]', '[104, 26, w^3 - 2*w^2 - 3*w - 3]', '[104, 104, w^3 - 3*w^2 - 2*w]', '[107, 107, -w^3 + 4*w^2 - 7]', '[113, 113, w^3 - 3*w^2 - 5*w + 3]', '[115, 115, -w^2 + 3*w + 5]', '[115, 115, w^3 - 2*w^2 - 2*w - 1]', '[118, 118, w^3 - 4*w^2 + 6]', '[121, 11, -w^3 + 3*w^2 + 4*w - 3]', '[121, 11, 2*w^3 - 6*w^2 - 3*w + 5]', '[125, 5, -w^3 + 4*w^2 + 2*w - 7]', '[125, 5, 2*w^3 - 5*w^2 - 5*w + 1]', '[125, 25, w^2 + 1]', '[125, 25, -2*w^2 + 5*w + 3]', '[125, 125, -2*w^3 + 4*w^2 + 9*w - 3]', '[125, 125, 2*w^3 - 6*w^2 - 6*w + 13]', '[127, 127, -2*w^3 + 6*w^2 + 5*w - 9]', '[128, 4, 2*w^3 - 4*w^2 - 6*w + 6]', '[128, 16, -2*w^2 + 2*w + 8]', '[128, 128, -w^3 + 4*w^2 + 2*w - 8]', '[130, 130, -w^3 + 4*w^2 + 2*w - 10]', '[130, 130, w^3 - 3*w^2 - w + 6]', '[134, 134, 2*w^3 - 8*w^2 + 3*w + 6]', '[136, 34, -w^3 + 4*w^2 + w - 9]', '[136, 136, w^3 - 3*w^2 - 4*w + 8]', '[137, 137, -w^3 + 5*w^2 + 3*w - 9]', '[139, 139, w^3 - w^2 - 4*w + 1]', '[142, 142, -5*w^3 + 17*w^2 + w - 14]', '[142, 142, -7*w^3 + 26*w^2 - 5*w - 22]', '[148, 148, w^3 - 5*w^2 + 3*w + 8]', '[149, 149, w^3 - 3*w^2 - w + 9]', '[157, 157, w^2 - 4*w + 1]', '[158, 158, -w^3 + 3*w^2 + 3*w - 2]', '[158, 158, -2*w^3 + 5*w^2 + 7*w - 6]', '[160, 20, -2*w^3 + 6*w^2 + 4*w - 12]', '[160, 20, -2*w + 4]', '[160, 160, 2*w^3 - 5*w^2 - 5*w + 4]', '[160, 160, -w^3 + 2*w^2 + w - 4]', '[162, 6, -3*w^3 + 9*w^2 + 3*w - 6]', '[163, 163, -3*w^3 + 7*w^2 + 9*w - 13]', '[163, 163, w^3 - 3*w^2 - w + 7]', '[164, 164, w^3 - w^2 - 5*w]', '[166, 166, w^3 - 4*w^2 + 10]', '[169, 169, -2*w^3 + 6*w^2 + 4*w - 13]', '[170, 170, 2*w^3 - 5*w^2 - 4*w + 2]', '[170, 170, -w^3 + w^2 + 7*w + 2]', '[179, 179, -2*w^3 + 3*w^2 + 5*w - 5]', '[179, 179, -2*w^3 + 4*w^2 + 5*w - 9]', '[181, 181, -w^2 + 3*w - 3]', '[181, 181, 2*w^3 - 4*w^2 - 8*w + 5]', '[184, 46, w^3 - 4*w^2 + w + 7]', '[184, 184, w^3 - 3*w^2 + w + 4]', '[185, 185, -2*w^2 + 3*w + 7]', '[185, 185, 2*w^2 - 4*w - 11]', '[191, 191, 2*w - 5]', '[193, 193, -2*w^3 + 4*w^2 + 7*w + 3]', '[193, 193, -2*w^3 + 5*w^2 + 5*w - 7]', '[194, 194, -4*w^2 + 9*w + 10]', '[196, 28, w^3 - 4*w^2 - w + 8]', '[196, 28, -3*w^2 + 2*w + 4]', '[197, 197, -w^3 + 4*w^2 - 11]', '[199, 199, -2*w^3 + 8*w^2 + 6*w - 15]', '[200, 10, -w^3 + 4*w^2 - w - 1]', '[200, 10, -w^3 + 2*w^2 + w - 5]', '[200, 40, 3*w^3 - 8*w^2 - 9*w + 12]', '[200, 40, 2*w^3 - 6*w^2 - 3*w + 4]', '[200, 50, -w^3 + 4*w^2 + w - 7]', '[200, 50, w^3 - 4*w^2 - 3*w + 9]', '[200, 200, -w^3 + w^2 + 6*w]', '[200, 200, 2*w^3 - 4*w^2 - 7*w + 4]', '[202, 202, 2*w^3 - 6*w^2 - w + 2]', '[205, 205, -w^3 - w^2 + 10*w + 11]', '[205, 205, -4*w^3 + 10*w^2 + 12*w - 17]', '[208, 26, -2*w^2 + 2*w + 6]', '[208, 208, w^2 + w - 4]', '[211, 211, -2*w^3 + 3*w^2 + 6*w - 5]', '[211, 211, -4*w^3 + 10*w^2 + 12*w - 19]', '[214, 214, 3*w^3 - 12*w^2 + 5*w + 10]', '[221, 221, -2*w^3 + 4*w^2 + 7*w - 1]', '[226, 226, -2*w^2 + 3*w + 6]', '[229, 229, w^3 - 3*w^2 - 4*w + 9]', '[229, 229, w^2 - 5]', '[230, 230, 3*w^2 - 7*w - 6]', '[230, 230, -w^3 + 2*w^2 + 3*w - 6]', '[233, 233, w^2 - 2*w - 7]', '[236, 236, -4*w^3 + 15*w^2 - 4*w - 12]', '[239, 239, -3*w^3 + 10*w^2 + 2*w - 9]', '[239, 239, -2*w^3 + 5*w^2 + 5*w - 5]', '[242, 22, w^3 - 2*w^2 - 2*w - 2]', '[242, 22, -8*w^3 + 27*w^2 - 18]', '[245, 35, w^3 - 3*w^2 + 5]', '[245, 35, 2*w^2 - 6*w - 5]', '[245, 35, 2*w^3 - 6*w^2 + 3]', '[245, 35, 2*w^2 + w - 5]', '[250, 10, w^3 - 4*w^2 + 3*w + 2]', '[250, 10, 2*w^3 - 5*w^2 - 5*w + 6]', '[250, 50, 5*w^3 - 13*w^2 - 15*w + 22]', '[250, 50, w^3 - 3*w^2 - 4*w + 2]', '[250, 250, -2*w^2 + 3*w + 2]', '[250, 250, -w^2 + 4*w + 2]', '[254, 254, 2*w^3 - 7*w^2 + 2*w + 2]', '[256, 4, 4]', '[256, 32, 2*w^3 - 4*w^2 - 8*w]', '[256, 256, -w^2 + 4*w]', '[257, 257, -2*w^3 + 5*w^2 + 4*w - 9]', '[260, 260, -2*w^3 + 5*w^2 + 6*w - 4]', '[260, 260, -w^3 + 5*w^2 - 4*w - 4]', '[263, 263, w^3 - 2*w^2 - 4*w - 3]', '[263, 263, w^3 - 6*w - 7]', '[268, 268, w^3 - 4*w^2 - 2*w + 4]', '[269, 269, w^3 - 3*w^2 - w - 1]', '[269, 269, w - 5]', '[272, 34, -2*w^2 + 6*w + 2]', '[272, 272, w^3 - 4*w^2 + 3*w + 4]', '[274, 274, 3*w - 2]', '[278, 278, w^3 - 4*w^2 + 2*w + 6]', '[281, 281, -2*w + 7]', '[284, 284, 2*w^2 - 3*w]', '[284, 284, -2*w^3 + 7*w^2 + 2*w - 4]', '[289, 289, -2*w^3 + 5*w^2 + 8*w - 7]', '[293, 293, 2*w^2 - w - 7]', '[293, 293, -2*w^3 + 6*w^2 + 6*w - 9]', '[295, 295, w^2 - 4*w - 1]', '[295, 295, -2*w^3 + 4*w^2 + 7*w - 3]', '[296, 74, -w^3 + 4*w^2 + w - 13]', '[296, 296, -w - 4]', '[298, 298, -2*w^3 + 4*w^2 + 7*w - 2]', '[299, 299, 3*w^3 - 8*w^2 - 8*w + 17]', '[307, 307, -2*w^3 + 5*w^2 + 4*w - 11]', '[311, 311, -w^3 + 3*w^2 + 2*w - 9]', '[314, 314, 7*w^3 - 25*w^2 + 2*w + 22]', '[316, 316, -3*w^2 + 4*w + 12]', '[316, 316, w^3 - 2*w^2 - 2*w - 4]', '[317, 317, 4*w^3 - 15*w^2 + 3*w + 15]', '[317, 317, w^3 - 4*w^2 - 4*w + 9]', '[320, 20, -w^3 + 2*w^2 + w + 1]', '[320, 20, -5*w^3 + 14*w^2 + 13*w - 27]', '[320, 40, -4*w^3 + 10*w^2 + 14*w - 16]', '[320, 40, 2*w^3 - 4*w^2 - 6*w]', '[320, 320, -w^3 + 3*w^2 + 5*w - 4]', '[320, 320, w^3 - 5*w^2 + 3*w + 4]', '[324, 12, -3*w]', '[325, 65, -2*w^3 + 5*w^2 + 8*w - 5]', '[325, 65, w^3 - 2*w^2 - 6*w + 5]', '[325, 325, -2*w^3 + 5*w^2 + 4*w - 3]', '[325, 325, w^3 - w^2 - 5*w + 1]', '[326, 326, -2*w^3 + 6*w^2 + 3*w - 10]', '[326, 326, 2*w^2 - 5*w - 2]', '[328, 82, -3*w^3 + 8*w^2 + 11*w - 11]', '[328, 328, 3*w^2 - 6*w - 16]', '[331, 331, -w^3 + 4*w^2 + 2*w - 11]', '[331, 331, 2*w^3 - 7*w^2 - 5*w + 13]', '[332, 332, -w^3 + 5*w^2 + 2*w - 12]', '[335, 335, -3*w^3 + 9*w^2 + 10*w - 17]', '[335, 335, -w^3 + 2*w^2 + 2*w + 3]', '[337, 337, 2*w^3 - 4*w^2 - 8*w - 1]', '[338, 338, -w^3 + w^2 + 7*w - 2]', '[340, 340, 2*w^3 - 6*w^2 - 5*w + 8]', '[340, 340, -3*w^3 + 7*w^2 + 10*w - 12]', '[347, 347, -2*w^3 + 7*w^2 + 9*w - 9]', '[349, 349, -w^3 + 5*w^2 - 2*w - 11]', '[349, 349, 4*w^3 - 9*w^2 - 14*w + 13]', '[353, 353, -3*w^3 + 7*w^2 + 9*w - 11]', '[355, 355, 4*w^3 - 10*w^2 - 8*w + 1]', '[355, 355, -3*w + 1]', '[355, 355, 2*w^3 - 7*w^2 + 9]', '[355, 355, -5*w^3 + 13*w^2 + 13*w - 23]', '[358, 358, -w^2 + w - 2]', '[358, 358, -2*w^3 + 5*w^2 + 4*w - 6]', '[362, 362, -8*w^3 + 27*w^2 + w - 22]', '[362, 362, w^3 - 5*w^2 + 3*w + 10]', '[367, 367, 3*w^3 - 5*w^2 - 11*w + 5]', '[367, 367, -w^3 + 3*w^2 + 5*w - 1]', '[368, 46, 2*w^2 - 6]', '[368, 368, -2*w^3 + 3*w^2 + 8*w]', '[370, 370, 4*w^3 - 11*w^2 - 10*w + 22]', '[370, 370, -3*w^3 + 5*w^2 + 13*w + 2]', '[373, 373, w^3 - 2*w^2 - 6*w + 1]', '[379, 379, 2*w^3 - 5*w^2 - 7*w + 5]', '[382, 382, -7*w^3 + 23*w^2 + 3*w - 18]', '[383, 383, 2*w^3 - 3*w^2 - 11*w - 1]', '[383, 383, -2*w^3 + 5*w^2 + 3*w - 13]', '[386, 386, -w^2 + 6]', '[386, 386, 2*w^3 - 7*w^2 + w + 2]', '[388, 388, w^3 - 2*w^2 - 6*w - 4]', '[391, 391, w^3 - w^2 - 6*w + 1]', '[392, 14, -w^3 + w - 3]', '[392, 14, w^3 - 4*w^2 - w + 1]', '[392, 56, -2*w^3 + 5*w^2 + 6*w]', '[392, 56, -w^3 + 3*w^2 + 6*w]', '[394, 394, -w^3 + 9*w + 2]', '[395, 395, w^3 - 5*w^2 + 2*w + 17]', '[395, 395, 2*w^3 - 7*w^2 - 2*w + 11]', '[395, 395, -2*w^3 + 6*w^2 + 5*w - 15]', '[395, 395, 2*w^2 - 2*w - 9]', '[397, 397, -2*w^3 + 4*w^2 + 7*w - 7]', '[397, 397, 2*w^3 - 3*w^2 - 8*w - 5]', '[398, 398, -w^3 + 3*w^2 + 5*w - 6]', '[400, 10, -2*w^3 + 4*w^2 + 8*w - 6]', '[400, 10, -2*w^2 + 4*w + 2]', '[400, 50, 2*w^3 - 8*w^2 + 4*w + 6]', '[400, 50, 2*w^3 - 6*w^2 - 4*w + 6]', '[400, 80, 3*w^2 - 6*w - 8]', '[400, 80, 3*w^3 - 8*w^2 - 7*w + 12]', '[400, 400, -w^3 + 2*w^2 + 3*w + 4]', '[400, 400, -4*w^3 + 11*w^2 + 13*w - 20]', '[404, 404, w^3 - 2*w^2 + 4]', '[405, 15, -3*w^2 + 6*w + 9]', '[405, 15, -3*w^3 + 9*w^2 + 9*w - 15]', '[409, 409, w^3 - 3*w^2 + w - 1]', '[410, 410, -w^3 + 3*w^2 + 3*w - 10]', '[410, 410, 3*w^3 - 10*w^2 - 6*w + 22]', '[415, 415, 4*w^3 - 11*w^2 - 10*w + 21]', '[415, 415, 2*w^3 - 3*w^2 - 10*w + 1]', '[416, 52, 2*w^2 - 6*w - 4]', '[416, 416, -3*w^3 + 10*w^2 + 2*w - 8]', '[419, 419, -4*w^3 + 14*w^2 - w - 13]', '[421, 421, -3*w^2 + 2*w + 9]', '[421, 421, 2*w^2 - 6*w - 3]', '[422, 422, -w^3 + 3*w^2 - 6]', '[422, 422, -3*w^3 + 9*w^2 + 5*w - 14]', '[425, 85, 5*w^3 - 13*w^2 - 14*w + 23]', '[425, 85, 2*w^3 - 5*w^2 - 3*w + 5]', '[425, 425, -2*w^3 + 5*w^2 + 5*w + 1]', '[425, 425, -w^3 + 3*w^2 + 5*w - 5]', '[428, 428, 2*w^3 - 5*w^2 - 4*w + 4]', '[431, 431, -2*w^3 + 4*w^2 + 9*w - 7]', '[431, 431, -2*w^3 + 6*w^2 + 3*w - 15]', '[431, 431, -3*w^3 + 6*w^2 + 10*w - 9]', '[431, 431, -3*w^3 + 11*w^2 + 10*w - 19]', '[442, 442, -4*w^3 + 11*w^2 + 12*w - 18]', '[443, 443, 3*w^3 - 6*w^2 - 8*w + 13]', '[443, 443, -2*w^3 + 5*w^2 + 4*w - 5]', '[443, 443, -2*w^3 + 5*w^2 + 6*w - 3]', '[443, 443, 5*w^3 - 12*w^2 - 16*w + 19]', '[452, 452, -w^3 + 6*w^2 - 7*w - 8]', '[458, 458, 5*w^3 - 16*w^2 - 4*w + 14]', '[458, 458, -3*w^3 + 9*w^2 + 4*w - 6]', '[460, 460, -3*w^3 + 9*w^2 + 3*w - 8]', '[460, 460, w^3 - 2*w^2 - 6*w + 4]', '[461, 461, w^3 - 2*w^2 + 7]', '[461, 461, -3*w^2 + w + 7]', '[466, 466, -3*w^3 + 7*w^2 + 8*w - 2]', '[472, 118, -3*w^3 + 8*w^2 + 7*w - 9]', '[472, 472, -2*w^3 + 5*w^2 + 3*w - 4]', '[478, 478, -w^3 + 5*w + 6]', '[478, 478, 4*w^3 - 13*w^2 - w + 6]', '[479, 479, w^2 + w - 5]', '[481, 481, -2*w^3 + 2*w^2 + 13*w + 3]', '[484, 44, -2*w^3 + 7*w^2 - w - 8]', '[484, 44, w^3 - w^2 + 4]', '[485, 485, w^3 - 3*w^2 + 9]', '[485, 485, -5*w^3 + 6*w^2 + 26*w + 13]', '[487, 487, 2*w^2 - 4*w + 1]', '[487, 487, 2*w^3 - 8*w^2 + 4*w + 7]', '[490, 70, -3*w^3 + 12*w^2 - 4*w - 10]', '[490, 70, w^3 - w^2 - 5*w + 2]', '[490, 70, w^3 - 2*w^2 - 6*w + 2]', '[490, 70, -2*w^3 + 7*w^2 + 2*w - 6]', '[491, 491, -3*w^3 + 7*w^2 + 7*w - 1]', '[500, 20, -w^3 + 5*w^2 - 5*w - 8]', '[500, 20, w^3 - 4*w^2 - 2*w + 12]', '[500, 100, -2*w^3 + 5*w^2 + 3*w]', '[500, 100, 2*w^2 - 5*w - 8]', '[500, 500, -w^2 + 3*w + 8]', '[500, 500, -2*w^3 + 4*w^2 + 7*w - 8]', '[505, 505, w^3 - 8*w - 3]', '[505, 505, -3*w^3 + 7*w^2 + 8*w - 15]', '[508, 508, 3*w^3 - 7*w^2 - 12*w + 12]', '[509, 509, -2*w^3 + 9*w^2 + 5*w - 19]', '[509, 509, -3*w^3 + 6*w^2 + 10*w + 1]', '[512, 8, 4*w^3 - 12*w^2 - 4*w + 8]', '[512, 8, -3*w^3 + 10*w^2 - w - 5]', '[512, 64, 4*w^3 - 10*w^2 - 12*w + 16]', '[512, 512, w^3 - 5*w^2 + 16]', '[514, 514, w^3 - 5*w^2 + 4*w + 2]', '[520, 130, -w^3 + 6*w^2 - 5*w - 7]', '[520, 130, -3*w^3 + 8*w^2 + 9*w - 11]', '[520, 520, -w^3 + 4*w^2 + 3*w - 4]', '[520, 520, 2*w^3 - 3*w^2 - 7*w + 4]', '[521, 521, w^3 - 2*w^2 - 6*w + 3]', '[521, 521, 3*w - 5]', '[523, 523, -w^3 + 5*w^2 + 4*w - 7]', '[523, 523, -2*w^3 + 4*w^2 + 6*w - 1]', '[523, 523, w^2 - 7]', '[523, 523, -2*w^3 + 8*w^2 + 8*w - 13]', '[526, 526, -3*w^3 + 6*w^2 + 11*w + 2]', '[526, 526, -5*w^3 + 14*w^2 + 7*w - 6]', '[529, 529, w^3 - 5*w^2 + 5*w + 5]', '[533, 533, 2*w^2 - 5*w - 11]', '[535, 535, -2*w^3 + 4*w^2 + 6*w + 5]', '[535, 535, -4*w^3 + 10*w^2 + 13*w - 19]', '[536, 134, -3*w^3 + 6*w^2 + 9*w - 11]', '[536, 536, -w^3 + 5*w^2 + w - 12]', '[538, 538, -8*w^3 + 26*w^2 + 3*w - 18]', '[538, 538, -6*w^3 + 19*w^2 + 4*w - 14]', '[541, 541, -w^3 + 5*w^2 - w - 13]', '[544, 68, 2*w^3 - 4*w^2 - 6*w + 4]', '[544, 544, -w^3 + 6*w + 8]', '[547, 547, -2*w^3 + 7*w^2 + 3*w - 11]', '[547, 547, -w^3 + 4*w^2 + 2*w - 13]', '[547, 547, -2*w^3 + 2*w^2 + 6*w - 1]', '[547, 547, -w^3 + 6*w^2 - 6*w - 7]', '[548, 548, -5*w^3 + 18*w^2 - w - 16]', '[556, 556, w^3 + w^2 - 2*w - 4]', '[562, 562, 9*w^3 - 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6*w - 17]', '[1775, 1775, -4*w^3 + 15*w^2 - 5*w - 13]', '[1775, 1775, -5*w^3 + 15*w^2 + 6*w - 17]', '[1781, 1781, -w^3 + 5*w^2 - 6*w - 3]', '[1783, 1783, 4*w^3 - 11*w^2 - 10*w + 13]', '[1783, 1783, 3*w^3 - 5*w^2 - 16*w - 1]', '[1787, 1787, 4*w^3 - 11*w^2 - 11*w + 15]', '[1787, 1787, 4*w^3 - 15*w^2 - 14*w + 27]', '[1789, 1789, 4*w^3 - 10*w^2 - 11*w + 7]', '[1790, 1790, w^3 - 6*w^2 + 4*w + 10]', '[1790, 1790, -4*w^3 + 13*w^2 + 13*w - 26]', '[1790, 1790, -3*w^3 + 11*w^2 + 9*w - 18]', '[1790, 1790, 2*w^2 - 7*w - 2]', '[1807, 1807, w^3 - 5*w^2 - 7*w + 3]', '[1808, 226, 2*w^3 - 6*w^2 - 10*w + 6]', '[1808, 1808, -w^3 - w^2 + 12*w + 16]', '[1810, 1810, w^3 - 5*w^2 + 9*w - 6]', '[1810, 1810, 4*w^3 - 10*w^2 - 15*w + 18]', '[1810, 1810, 7*w^3 - 20*w^2 - 16*w + 34]', '[1810, 1810, -9*w^3 + 23*w^2 + 28*w - 38]', '[1813, 259, w^2 - 6*w - 3]', '[1813, 259, 4*w^3 - 11*w^2 - 6*w + 1]', '[1814, 1814, -w^3 - 2*w^2 + 14*w + 6]', '[1814, 1814, -6*w^3 + 19*w^2 + 6*w - 18]', '[1817, 1817, -2*w^2 + 7*w + 3]', '[1817, 1817, -3*w^3 + 6*w^2 + 14*w - 7]', '[1819, 1819, 6*w^3 - 17*w^2 - 10*w + 13]', '[1832, 458, 7*w^3 - 20*w^2 - 21*w + 35]', '[1832, 458, -3*w^3 + 10*w^2 + 11*w - 15]', '[1832, 1832, -w^3 + 4*w^2 - 2*w - 16]', '[1832, 1832, 4*w^3 - 12*w^2 - 9*w + 28]', '[1835, 1835, -5*w^3 + 8*w^2 + 26*w + 5]', '[1835, 1835, -3*w^3 + 5*w^2 + 6*w - 13]', '[1835, 1835, 3*w^3 - 3*w^2 - 16*w - 5]', '[1835, 1835, 3*w^3 - 2*w^2 - 18*w - 9]', '[1840, 230, -2*w^2 + 6*w + 10]', '[1840, 230, 2*w^3 - 4*w^2 - 4*w - 2]', '[1840, 1840, 3*w^3 - 12*w^2 + w + 12]', '[1840, 1840, -w^2 + w - 4]', '[1844, 1844, 5*w^3 - 20*w^2 + 6*w + 20]', '[1844, 1844, 3*w^3 - 13*w^2 + 7*w + 16]', '[1846, 1846, 2*w^3 - 9*w^2 + 5*w + 6]', '[1846, 1846, 7*w^3 - 21*w^2 - 8*w + 10]', '[1847, 1847, -w^3 + 6*w^2 - 6*w - 5]', '[1847, 1847, 4*w^3 - 10*w^2 - 11*w + 11]', '[1850, 370, w^3 - w^2 - 3*w - 6]', '[1850, 370, -2*w^3 + 8*w^2 + 3*w - 22]', '[1850, 1850, 2*w^3 - 7*w^2 - w + 14]', '[1850, 1850, 2*w^3 - 6*w^2 - w - 2]', '[1858, 1858, -3*w^2 + 8*w + 2]', '[1858, 1858, -2*w^3 + 8*w^2 + 3*w - 18]', '[1863, 69, -3*w^2 + 9]', '[1864, 466, -5*w^3 + 10*w^2 + 17*w - 13]', '[1864, 1864, w^3 + 4*w^2 - 12*w - 24]', '[1865, 1865, 4*w^3 - 10*w^2 - 9*w + 21]', '[1865, 1865, -4*w^3 + 6*w^2 + 18*w + 5]', '[1867, 1867, -2*w^3 + 3*w^2 + 8*w - 5]', '[1867, 1867, 3*w^3 - 7*w^2 - 6*w - 1]', '[1867, 1867, -4*w^2 + 9*w + 7]', '[1867, 1867, -w^3 + 7*w^2 + 2*w - 15]', '[1871, 1871, -4*w^2 + 11*w + 7]', '[1874, 1874, 9*w^3 - 28*w^2 - 6*w + 14]', '[1877, 1877, 4*w^3 - 11*w^2 - 8*w + 7]', '[1879, 1879, -5*w^2 + 3*w + 15]', '[1882, 1882, 3*w^3 - 14*w^2 + 10*w + 18]', '[1886, 1886, 3*w^3 - 6*w^2 - 10*w + 2]', '[1888, 236, 2*w^3 - 8*w^2 + 12]', '[1888, 1888, w^3 + w^2 - 11*w - 4]', '[1889, 1889, -3*w^3 + 13*w^2 - 7*w - 11]', '[1895, 1895, 6*w^3 - 16*w^2 - 16*w + 33]', '[1895, 1895, -3*w^3 + 3*w^2 + 18*w + 5]', '[1901, 1901, w^3 - 7*w^2 + w + 21]', '[1906, 1906, 3*w^3 - 17*w^2 + 17*w + 22]', '[1906, 1906, -3*w^3 + 8*w^2 + 3*w - 2]', '[1907, 1907, -2*w^3 + 8*w^2 + w - 17]', '[1909, 1909, 2*w^3 - 7*w^2 - 4*w + 7]', '[1910, 1910, -2*w^2 + 9*w - 10]', '[1910, 1910, 7*w^3 - 21*w^2 - 16*w + 38]', '[1912, 478, -3*w^3 + 4*w^2 + 15*w + 1]', '[1912, 478, -3*w^3 + 8*w^2 + 7*w - 19]', '[1912, 1912, -2*w^3 + 9*w + 4]', '[1912, 1912, -4*w^3 + 9*w^2 + 16*w - 8]', '[1913, 1913, -2*w^3 + 8*w^2 - 19]', '[1915, 1915, 2*w^2 - 6*w - 11]', '[1915, 1915, -7*w^3 + 9*w^2 + 36*w + 15]', '[1915, 1915, -w^3 - 3*w^2 + 10*w + 19]', '[1915, 1915, 4*w^3 - 12*w^2 - 8*w + 27]', '[1916, 1916, w^3 + w^2 - 5*w]', '[1921, 1921, 2*w^2 - 4*w - 13]', '[1924, 1924, -2*w^3 + 3*w^2 + 9*w + 8]', '[1930, 1930, 4*w^2 - 9*w - 14]', '[1930, 1930, -4*w^3 + 11*w^2 + 5*w - 2]', '[1930, 1930, 7*w^3 - 18*w^2 - 22*w + 34]', '[1930, 1930, -5*w^3 + 15*w^2 + 11*w - 22]', '[1933, 1933, w^3 + 2*w^2 - 10*w - 13]', '[1933, 1933, -4*w^3 + 8*w^2 + 14*w - 9]', '[1934, 1934, 2*w^3 - 11*w^2 + 11*w + 14]', '[1936, 22, -2*w^3 + 6*w^2 + 8*w - 6]', '[1936, 22, 4*w^3 - 12*w^2 - 6*w + 10]', '[1936, 176, -3*w^3 + 7*w^2 + 7*w + 4]', '[1936, 176, w^3 - 9*w - 12]', '[1937, 1937, 6*w^2 - 4*w - 19]', '[1940, 1940, -4*w^3 + w^2 + 28*w + 20]', '[1940, 1940, w^3 + 3*w^2 - 13*w - 24]', '[1942, 1942, 3*w^3 - 13*w^2 + 8*w + 14]', '[1942, 1942, 3*w^3 - 10*w^2 - 4*w + 10]', '[1948, 1948, -2*w^3 + 4*w^2 - w]', '[1948, 1948, -4*w^3 + 14*w^2 + w - 8]', '[1954, 1954, -3*w^3 + 6*w^2 + 14*w - 6]', '[1955, 1955, 4*w^3 - 13*w^2 - 2*w + 15]', '[1955, 1955, 4*w^3 - 13*w^2 - 10*w + 25]', '[1960, 70, 3*w^3 - 4*w^2 - 9*w + 7]', '[1960, 70, -w^3 - 2*w^2 + 7*w + 9]', '[1960, 70, -w^3 + 6*w^2 + 3*w - 7]', '[1960, 70, w^3 - 4*w^2 - 3*w - 1]', '[1960, 280, w^3 - w - 4]', '[1960, 280, -4*w^2 + 3*w + 12]', '[1960, 280, -w^2 - w - 4]', '[1960, 280, 3*w^3 - 8*w^2 + 8]', '[1964, 1964, w^3 - 8*w^2 + 8*w + 12]', '[1966, 1966, -4*w^3 + 9*w^2 + 14*w - 6]', '[1970, 1970, -4*w^3 + 13*w^2 + 8*w - 26]', '[1970, 1970, 7*w^3 - 21*w^2 - 17*w + 46]', '[1975, 395, 2*w^3 - 5*w^2 - 3*w - 5]', '[1975, 395, -4*w^2 + 8*w + 19]', '[1975, 395, 3*w^3 - 9*w^2 - 12*w + 13]', '[1975, 395, -3*w^3 + 9*w^2 + 7*w - 11]', '[1975, 1975, -7*w^3 + 17*w^2 + 21*w - 29]', '[1975, 1975, -2*w^3 + 9*w^2 + w - 27]', '[1975, 1975, 4*w^3 - 9*w^2 - 14*w + 15]', '[1975, 1975, w^3 - 6*w + 1]', '[1982, 1982, w^3 - 7*w^2 + 7*w + 14]', '[1982, 1982, 2*w^3 - 3*w^2 - 12*w + 2]', '[1985, 1985, 4*w^3 - 9*w^2 - 17*w + 9]', '[1985, 1985, -3*w^2 + 7*w + 3]', '[1985, 1985, 3*w^3 - 7*w^2 - 11*w + 5]', '[1985, 1985, -3*w^3 + 6*w^2 + 10*w - 5]', '[1987, 1987, -3*w^3 + 7*w^2 + 10*w - 3]', '[1990, 1990, 3*w^3 - 7*w^2 - 8*w + 6]', '[1990, 1990, -8*w^3 + 20*w^2 + 21*w - 38]', '[1993, 1993, w^3 - 2*w^2 - 6*w + 11]', '[1993, 1993, w^3 - 6*w^2 - 4*w + 13]', '[1994, 1994, -4*w^3 + 11*w^2 + 8*w - 14]', '[1997, 1997, -3*w^3 + 9*w^2 + 9*w - 13]', '[1999, 1999, 2*w^3 - 5*w^2 - 2*w - 1]', '[2000, 10, -2*w^3 + 8*w^2 + 4*w - 14]', '[2000, 10, 4*w^3 - 10*w^2 - 10*w + 2]', '[2000, 50, 2*w^2 + 2]', '[2000, 50, -4*w^2 + 10*w + 6]', '[2000, 80, 4*w^3 - 10*w^2 - 15*w + 12]', '[2000, 80, -2*w^3 + 3*w^2 + 9*w - 4]', '[2000, 250, -4*w^3 + 8*w^2 + 18*w - 6]', '[2000, 250, 4*w^3 - 12*w^2 - 12*w + 26]', '[2000, 400, -w^3 + w^2 + 9*w - 4]', '[2000, 400, w^3 - 7*w^2 + 6*w + 8]', '[2000, 2000, 4*w^3 - 11*w^2 - 12*w + 16]', '[2000, 2000, 5*w^3 - 12*w^2 - 16*w + 16]', '[2003, 2003, -4*w^3 + 10*w^2 + 16*w - 11]', '[2006, 2006, -6*w^3 + 18*w^2 + 7*w - 14]', '[2009, 287, 2*w^3 - 5*w^2 - 8*w + 1]', '[2009, 287, 2*w^3 - 4*w^2 - 5*w + 11]', '[2011, 2011, 3*w + 7]', '[2011, 2011, -4*w^3 + 12*w^2 + 8*w - 15]', '[2020, 2020, 5*w^3 - 15*w^2 - 11*w + 32]', '[2020, 2020, 2*w^3 - 3*w^2 - 6*w - 4]', '[2025, 15, 3*w^3 - 6*w^2 - 12*w + 9]', '[2025, 15, 3*w^2 - 6*w - 3]', '[2025, 75, -3*w^3 + 12*w^2 - 6*w - 9]', '[2025, 75, -3*w^3 + 9*w^2 + 6*w - 9]', '[2026, 2026, -w^3 + 4*w^2 - 2*w - 10]', '[2027, 2027, -3*w^3 + 7*w^2 + 7*w - 9]', '[2029, 2029, -3*w^3 + 13*w^2 + 10*w - 25]', '[2029, 2029, -2*w^3 + 2*w^2 + 12*w + 1]', '[2032, 254, -4*w^3 + 12*w^2 + 10*w - 18]', '[2032, 2032, -w^3 + 3*w^2 + 3*w - 12]', '[2036, 2036, -w^3 + 6*w^2 - 4*w - 12]', '[2036, 2036, -5*w^2 + 10*w + 12]', '[2038, 2038, -3*w^3 + 11*w^2 + w - 14]', '[2039, 2039, w^3 - 6*w^2 + 4*w + 11]', '[2039, 2039, w^2 + 2*w - 7]', '[2041, 2041, 3*w^3 - 7*w^2 - 8*w + 7]', '[2042, 2042, w^3 - 2*w^2 - 3*w - 6]', '[2045, 2045, -5*w^3 + 13*w^2 + 12*w - 21]', '[2045, 2045, 3*w^3 - 12*w^2 + 4*w + 15]', '[2048, 8, 4*w^3 - 8*w^2 - 12*w + 12]', '[2048, 32, -4*w^2 + 4*w + 16]', '[2048, 256, -2*w^3 + 8*w^2 + 4*w - 16]', '[2048, 2048, -3*w^3 + 5*w^2 + 13*w - 4]', '[2050, 410, w^3 + 4*w^2 - 13*w - 26]', '[2050, 410, w^3 - 7*w^2 + 6*w + 18]', '[2050, 2050, 3*w^3 - 13*w^2 + 38]', '[2050, 2050, -2*w^3 + 6*w^2 + 7*w - 6]', '[2054, 2054, -4*w^3 + 7*w^2 + 16*w - 6]', '[2054, 2054, 4*w^3 - 10*w^2 - 11*w + 14]', '[2056, 514, -7*w^3 + 14*w^2 + 19*w - 27]', '[2056, 2056, -3*w^3 + 12*w^2 + 8*w - 24]', '[2057, 187, -7*w^3 + 26*w^2 - 4*w - 27]', '[2057, 187, w^3 - 5*w^2 + 3*w + 13]', '[2063, 2063, -w^3 + 2*w^2 + 4*w - 9]', '[2069, 2069, -4*w^3 + 8*w^2 + 18*w - 9]', '[2069, 2069, 3*w^3 - 8*w^2 - 8*w + 1]', '[2075, 415, -2*w^3 + 6*w^2 + 3*w - 17]', '[2075, 415, w^3 - 3*w^2 - 4*w - 3]', '[2075, 2075, -2*w^3 + 7*w^2 + 5*w - 19]', '[2075, 2075, 5*w^3 - 16*w^2 - 12*w + 33]', '[2080, 260, -2*w^3 + 8*w^2 + 4*w - 20]', '[2080, 260, 2*w^3 - 6*w^2 - 2*w + 12]', '[2080, 2080, 2*w^3 - 3*w^2 - 12*w]', '[2080, 2080, 4*w^3 - 13*w^2 - 10*w + 24]', '[2081, 2081, -4*w^3 + 15*w^2 - w - 15]', '[2083, 2083, w^2 + w - 9]', '[2084, 2084, 3*w^2 - 5*w]', '[2084, 2084, w^2 + 4]', '[2087, 2087, -2*w^3 + 6*w^2 + 6*w + 1]', '[2087, 2087, 2*w^3 - 3*w^2 - 5*w + 9]', '[2092, 2092, -4*w^2 + 5*w + 8]', '[2092, 2092, w^3 - 7*w]', '[2092, 2092, -8*w^3 + 27*w^2 + 2*w - 20]', '[2092, 2092, w^3 - 5*w^2 + 6*w + 4]', '[2095, 2095, -w^3 + w^2 + 5*w + 9]', '[2095, 2095, 5*w^3 - 13*w^2 - 13*w + 21]', '[2098, 2098, 2*w^3 - 10*w^2 + 9*w + 10]', '[2099, 2099, -4*w^3 + 9*w^2 + 15*w - 15]', '[2102, 2102, 2*w^3 - 10*w^2 - 5*w + 22]', '[2104, 526, -3*w^3 + 4*w^2 + 11*w - 1]', '[2104, 526, -3*w^3 + 8*w^2 + 15*w - 5]', '[2104, 2104, 3*w^3 - w^2 - 24*w - 24]', '[2104, 2104, 3*w^3 - w^2 - 18*w - 16]', '[2105, 2105, 2*w^3 - w^2 - 15*w - 15]', '[2105, 2105, -6*w^3 + 13*w^2 + 18*w + 1]', '[2105, 2105, -w^3 - 2*w^2 + 10*w + 11]', '[2105, 2105, 3*w^3 - 9*w^2 - 5*w + 17]', '[2106, 78, -3*w^2 + 9*w + 6]', '[2110, 2110, -2*w^3 + 3*w^2 + 7*w + 6]', '[2110, 2110, -10*w^3 + 28*w^2 + 31*w - 54]', '[2110, 2110, -3*w^3 + 10*w^2 + 11*w - 18]', '[2110, 2110, -w^3 + 3*w^2 - 2*w + 6]', '[2111, 2111, 2*w^3 - w^2 - 14*w - 5]', '[2113, 2113, -4*w^3 + 9*w^2 + 13*w - 3]', '[2116, 2116, -3*w^3 + 10*w^2 + 2*w - 4]', '[2119, 2119, w^3 - 9*w^2 + 14*w + 13]', '[2119, 2119, 3*w^3 - 11*w^2 + 17]', '[2122, 2122, 4*w^3 - 11*w^2 - 7*w + 14]', '[2125, 85, 4*w^3 - 11*w^2 - 8*w + 13]', '[2125, 85, -4*w^3 + 10*w^2 + 15*w - 17]', '[2125, 425, -3*w^3 + 5*w^2 + 12*w - 5]', '[2125, 425, w^3 - 5*w^2 + 6*w + 5]', '[2125, 2125, 2*w^3 - 6*w^2 - 6*w + 5]', '[2125, 2125, 3*w^3 - 6*w^2 - 10*w + 3]', '[2126, 2126, -4*w^3 + 8*w^2 + 15*w - 6]', '[2132, 2132, -4*w^3 + 10*w^2 + 15*w - 16]', '[2140, 2140, -4*w^2 + 11*w + 8]', '[2140, 2140, 9*w^3 - 23*w^2 - 28*w + 36]', '[2141, 2141, 5*w^2 - 9*w - 9]', '[2144, 268, 4*w^3 - 16*w^2 + 6*w + 12]', '[2144, 2144, -6*w^3 + 15*w^2 + 19*w - 28]', '[2152, 538, -3*w^3 + 6*w^2 + 9*w - 7]', '[2152, 538, -5*w^3 + 12*w^2 + 15*w - 19]', '[2152, 2152, w^3 + w^2 - 7*w - 12]', '[2152, 2152, -w^3 + 6*w^2 - w - 20]', '[2153, 2153, w^2 - 6*w - 9]', '[2153, 2153, w^3 - 7*w^2 + 7*w + 13]', '[2155, 2155, -w^3 - 3*w^2 + 11*w + 21]', '[2155, 2155, 5*w^3 - 11*w^2 - 17*w + 5]', '[2155, 2155, 3*w^2 - 7*w - 13]', '[2155, 2155, 4*w^3 - 8*w^2 - 13*w + 13]', '[2155, 2155, -10*w^3 + 29*w^2 + 27*w - 55]', '[2155, 2155, 4*w^3 - 8*w^2 - 18*w + 3]', '[2155, 2155, -2*w^3 + 7*w^2 + 6*w - 9]', '[2155, 2155, -2*w^3 + 2*w^2 + 11*w + 1]', '[2158, 2158, -4*w^2 + 5*w + 18]', '[2159, 2159, 5*w^3 - 16*w^2 - 6*w + 23]', '[2161, 2161, 2*w^3 - 3*w^2 - 12*w + 1]', '[2164, 2164, 3*w^3 - 6*w^2 - 10*w + 4]', '[2174, 2174, -8*w^3 + 26*w^2 + 5*w - 22]', '[2176, 68, -2*w^3 + 8*w^2 + 2*w - 18]', '[2176, 272, 2*w^3 - 6*w^2 - 8*w + 16]', '[2176, 2176, 4*w^3 - 10*w^2 - 11*w + 12]', '[2183, 2183, -3*w^3 + 11*w^2 + 3*w - 23]', '[2188, 2188, -4*w^3 + 11*w^2 + 4*w - 4]', '[2188, 2188, 3*w^3 - 7*w^2 - 5*w + 8]', '[2188, 2188, -7*w^3 + 21*w^2 + 6*w - 12]', '[2188, 2188, 2*w^3 - 3*w^2 - 10*w + 4]', '[2192, 274, -2*w^3 + 10*w^2 + 6*w - 18]', '[2192, 2192, -3*w^3 + 5*w^2 + 10*w - 8]', '[2194, 2194, 3*w^3 - 9*w^2 - w + 2]', '[2197, 13, 3*w^3 - 11*w^2 - w + 15]', '[2197, 2197, 3*w^3 - 12*w^2 + 2*w + 13]', '[2203, 2203, -4*w^3 + 10*w^2 + 7*w - 1]', '[2209, 47, 2*w^3 - 7*w^2 + 3*w + 9]', '[2209, 47, w^2 - 5*w - 11]', '[2210, 2210, w^3 - 6*w^2 - w + 10]', '[2210, 2210, -4*w^3 + 11*w^2 + 9*w - 10]', '[2213, 2213, w^3 - 7*w^2 + 8*w + 15]', '[2215, 2215, -3*w^3 + 8*w^2 + 8*w - 19]', '[2215, 2215, -2*w^3 + 8*w^2 + 4*w - 15]', '[2215, 2215, 3*w^2 - 9*w - 5]', '[2215, 2215, -6*w^3 + 12*w^2 + 26*w - 9]', '[2215, 2215, 2*w^2 - 3*w + 3]', '[2215, 2215, 2*w^3 + w^2 - 19*w - 11]', '[2215, 2215, -3*w^3 + 10*w^2 + 10*w - 21]', '[2215, 2215, 4*w^3 - 8*w^2 - 15*w + 5]', '[2218, 2218, 3*w^3 - 16*w^2 + 13*w + 22]', '[2224, 278, 2*w^3 - 2*w^2 - 8*w + 2]', '[2224, 2224, -w^3 - 2*w^2 + 9*w + 12]', '[2231, 2231, -3*w^3 + 2*w^2 + 14*w + 5]', '[2234, 2234, 4*w^3 - 16*w^2 + 7*w + 14]', '[2234, 2234, -w^3 + 6*w - 2]', '[2237, 2237, -4*w^3 + 10*w^2 + 11*w - 13]', '[2248, 562, 7*w^3 - 18*w^2 - 21*w + 29]', '[2248, 2248, 2*w^3 - 9*w^2 - w + 28]', '[2251, 2251, 3*w^3 - 5*w^2 - 15*w + 5]', '[2251, 2251, -w^3 + 6*w^2 - 15]', '[2252, 2252, w^3 - 2*w^2 + 3*w]', '[2252, 2252, 2*w^3 - 5*w^2 - w]', '[2254, 322, -3*w^3 + 7*w^2 + 3*w - 2]', '[2254, 322, 3*w^3 - 6*w^2 - 4*w + 6]', '[2258, 2258, w^3 - 10*w^2 + 17*w + 14]', '[2258, 2258, w^2 - 6*w + 2]', '[2260, 2260, -w^3 + 5*w^2 + w - 16]', '[2260, 2260, 2*w^3 - 7*w^2 + 12]', '[2269, 2269, w^3 - 4*w - 7]', '[2272, 284, -10*w^3 + 34*w^2 + 2*w - 28]', '[2272, 284, -14*w^3 + 52*w^2 - 10*w - 44]', '[2272, 2272, w^3 - 8*w]', '[2272, 2272, -8*w^3 + 23*w^2 + 22*w - 40]', '[2273, 2273, 2*w^3 - 9*w^2 + 2*w + 19]', '[2276, 2276, -2*w^2 - 5*w]', '[2278, 2278, -2*w^3 + 3*w^2 + 8*w - 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4*w + 14]', '[5326, 5326, 3*w^3 - 4*w^2 - 7*w + 2]', '[5330, 5330, 4*w^3 - 14*w^2 - 5*w + 38]', '[5330, 5330, -2*w^3 + 9*w^2 + w - 22]', '[5338, 5338, 3*w^3 - 11*w^2 - 3*w + 18]', '[5342, 5342, w^3 - w^2 - 10*w - 2]', '[5342, 5342, -13*w^3 + 43*w^2 + 4*w - 34]', '[5347, 5347, -2*w^3 + 3*w^2 + 11*w - 9]', '[5350, 1070, -w^3 + 8*w^2 - 6*w - 26]', '[5350, 1070, -4*w^3 + 12*w^2 + w + 2]', '[5350, 5350, -w^2 + 7*w - 2]', '[5350, 5350, 4*w^3 - 14*w^2 - 7*w + 38]', '[5351, 5351, -3*w^3 + 11*w^2 + 3*w - 19]', '[5359, 5359, -5*w^2 + 3*w + 17]', '[5360, 670, -6*w^3 + 18*w^2 + 20*w - 34]', '[5360, 670, -2*w^3 + 4*w^2 + 4*w + 6]', '[5360, 5360, -5*w^3 + 18*w^2 + w - 20]', '[5360, 5360, -5*w^3 + 14*w^2 + 11*w - 28]', '[5366, 5366, -9*w^3 + 26*w^2 + 10*w - 10]', '[5366, 5366, 8*w^3 - 26*w^2 - 3*w + 14]', '[5372, 5372, 5*w^3 - 16*w^2 - 10*w + 28]', '[5372, 5372, -2*w^3 + 9*w^2 + 3*w - 24]', '[5378, 5378, -5*w^3 + 13*w^2 + 9*w - 6]', '[5378, 5378, -w^3 - w^2 + 9*w + 2]', '[5380, 5380, -6*w^3 + 15*w^2 + 12*w - 4]', '[5380, 5380, 5*w^3 - 11*w^2 - 21*w + 16]', '[5380, 5380, -5*w^3 + 12*w^2 + 12*w - 4]', '[5380, 5380, 11*w^3 - 28*w^2 - 37*w + 48]', '[5381, 5381, 4*w^3 - 12*w^2 - 11*w + 31]', '[5381, 5381, -4*w^3 + 10*w^2 + 17*w - 9]', '[5384, 1346, -w^3 + 2*w^2 + 5*w + 7]', '[5384, 5384, 5*w^3 - 8*w^2 - 24*w - 8]', '[5389, 5389, -2*w^3 + 3*w^2 + 12*w - 11]', '[5389, 5389, 2*w^3 - 7*w^2 + 15]', '[5392, 674, 4*w^3 - 8*w^2 - 16*w - 2]', '[5392, 5392, -7*w^3 + 8*w^2 + 38*w + 24]', '[5393, 5393, 8*w^3 - 20*w^2 - 21*w + 41]', '[5393, 5393, -4*w^2 - w + 11]', '[5393, 5393, -4*w^3 + 6*w^2 + 10*w - 9]', '[5393, 5393, -w^3 - 5*w^2 + 20*w + 21]', '[5395, 5395, 5*w^3 - 9*w^2 - 24*w - 1]', '[5395, 5395, 5*w^3 - 11*w^2 - 14*w + 1]', '[5398, 5398, -2*w^3 + 6*w^2 + w - 14]', '[5408, 676, -2*w^3 + 2*w^2 + 14*w - 4]', '[5408, 5408, -4*w^2 + 7*w + 4]', '[5410, 5410, -5*w^3 + 16*w^2 + 8*w - 30]', '[5410, 5410, 7*w^3 - 22*w^2 - 17*w + 50]', '[5413, 5413, -4*w^3 + 11*w^2 + 15*w - 19]', '[5413, 5413, 2*w^3 - 4*w^2 - 13*w - 1]', '[5414, 5414, 5*w^2 - 6*w - 10]', '[5414, 5414, 6*w^3 - 15*w^2 - 19*w + 18]', '[5416, 1354, 7*w^3 - 16*w^2 - 19*w + 33]', '[5416, 1354, 3*w^3 - 8*w^2 - 13*w + 11]', '[5416, 5416, -4*w^2 + 9*w + 20]', '[5416, 5416, 5*w^3 - 15*w^2 - 16*w + 24]', '[5422, 5422, 3*w^3 - 11*w^2 - 4*w + 22]', '[5426, 5426, 4*w^3 - 10*w^2 - 9*w - 2]', '[5426, 5426, w^3 - w^2 - w - 6]', '[5427, 201, -3*w^3 + 9*w^2 + 3*w - 15]', '[5428, 5428, 2*w^3 - 10*w^2 + 7*w + 8]', '[5435, 5435, -13*w^3 + 35*w^2 + 36*w - 63]', '[5435, 5435, 3*w^3 - 12*w^2 + 2*w + 21]', '[5437, 5437, -2*w^3 + 3*w^2 + w - 9]', '[5438, 5438, 19*w^3 - 66*w^2 + 4*w + 46]', '[5440, 340, -3*w^3 + 6*w^2 + 15*w - 5]', '[5440, 340, 3*w^3 - 14*w^2 + 9*w + 13]', '[5440, 680, 4*w^3 - 12*w^2 - 10*w + 16]', '[5440, 680, -6*w^3 + 14*w^2 + 20*w - 24]', '[5440, 5440, -w^2 + w + 12]', '[5440, 5440, -2*w^3 + 10*w^2 - w - 28]', '[5441, 5441, -5*w^3 + 9*w^2 + 24*w - 5]', '[5441, 5441, 6*w^3 - 12*w^2 - 25*w + 13]', '[5447, 5447, 3*w^3 - 8*w^2 - 2*w + 1]', '[5449, 5449, 4*w^3 - 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9]', '[5822, 5822, 3*w^3 - 9*w^2 - 4*w + 18]', '[5822, 5822, 8*w^3 - 25*w^2 - 7*w + 22]', '[5825, 1165, 2*w^3 - w^2 - 13*w - 3]', '[5825, 1165, 6*w^3 - 12*w^2 - 24*w + 13]', '[5825, 5825, 4*w^2 - 12*w - 5]', '[5825, 5825, -4*w^3 + 10*w^2 + 13*w - 9]', '[5834, 5834, -6*w^3 + 29*w^2 - 19*w - 34]', '[5836, 5836, -w^3 + 2*w^2 - 9*w - 8]', '[5836, 5836, -8*w^3 + 23*w^2 + 10*w - 12]', '[5839, 5839, -4*w^3 + 5*w^2 + 21*w + 3]', '[5839, 5839, 3*w^3 - 7*w^2 - 13*w - 3]', '[5842, 5842, 2*w^2 - 5*w + 6]', '[5846, 5846, -4*w^3 + 10*w^2 + 9*w - 10]', '[5846, 5846, -5*w^3 + 8*w^2 + 17*w - 10]', '[5851, 5851, 2*w^3 - 3*w^2 - 5*w - 5]', '[5851, 5851, -w^2 + 7*w - 1]', '[5860, 5860, -3*w^3 + 6*w^2 + 16*w + 4]', '[5860, 5860, 3*w^3 - 12*w^2 + 7*w]', '[5860, 5860, 6*w^3 - 19*w^2 - 11*w + 32]', '[5860, 5860, 11*w^3 - 26*w^2 - 37*w + 40]', '[5861, 5861, 3*w^3 - 3*w^2 - 20*w - 5]', '[5861, 5861, -2*w^3 + w^2 + 18*w - 5]', '[5864, 1466, 3*w^3 - 8*w^2 - 11*w + 7]', '[5864, 1466, -5*w^3 + 10*w^2 + 19*w + 1]', '[5864, 5864, -3*w^3 + 8*w^2 + 10*w]', '[5864, 5864, -2*w^3 + w^2 + 14*w + 16]', '[5869, 5869, w^3 - 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20]', '[9908, 9908, -5*w^3 + 17*w^2 + 5*w - 16]', '[9908, 9908, -10*w^3 + 27*w^2 + 30*w - 44]', '[9910, 9910, -14*w^3 + 42*w^2 + 37*w - 86]', '[9910, 9910, 4*w^3 - 8*w^2 - 17*w + 14]', '[9910, 9910, 8*w^3 - 23*w^2 - 19*w + 46]', '[9910, 9910, -9*w^3 + 23*w^2 + 30*w - 34]', '[9913, 9913, 5*w^3 - 13*w^2 - 19*w + 21]', '[9913, 9913, -6*w^3 + 13*w^2 + 20*w - 7]', '[9913, 9913, w^3 - w^2 - 4*w - 13]', '[9913, 9913, -4*w^3 + 14*w^2 + 6*w - 23]', '[9916, 9916, 4*w^3 - 12*w^2 - w]', '[9922, 902, -w^2 + 9*w - 6]', '[9922, 902, 11*w^3 - 34*w^2 - 7*w + 14]', '[9923, 9923, -2*w^3 + 9*w^2 - 9*w - 11]', '[9923, 9923, -3*w^3 + 13*w^2 - w - 35]', '[9923, 9923, 2*w^3 - 19*w - 9]', '[9923, 9923, -5*w^3 + 14*w^2 + 18*w - 19]', '[9925, 1985, w^3 - w^2 - 3*w + 9]', '[9925, 1985, -10*w^3 + 34*w^2 - 31]', '[9925, 1985, 4*w^3 - 4*w^2 - 26*w - 9]', '[9925, 1985, 4*w^3 - 9*w^2 - 7*w + 21]', '[9925, 9925, 4*w^3 - 14*w^2 - 8*w + 27]', '[9925, 9925, -4*w^3 + 14*w^2 + 8*w - 25]', '[9925, 9925, -w^3 + 3*w^2 - 4*w + 7]', '[9925, 9925, -6*w^3 + 20*w^2 + 17*w - 41]', '[9931, 9931, 5*w^3 - 10*w^2 - 18*w + 15]', '[9931, 9931, -5*w^3 + 12*w^2 + 10*w + 3]', '[9932, 9932, -5*w^3 + 12*w^2 + 22*w - 28]', '[9935, 9935, -4*w^3 + 11*w^2 + 10*w - 27]', '[9935, 9935, 4*w^3 - 33*w - 19]', '[9946, 9946, -w^3 + 4*w^2 + w - 18]', '[9950, 1990, 5*w^3 - 16*w^2 - 15*w + 34]', '[9950, 1990, -w^3 + w^2 - 2*w + 6]', '[9950, 9950, -5*w^3 + 14*w^2 + 8*w - 22]', '[9950, 9950, -3*w^3 + 12*w^2 - 5*w - 2]', '[9952, 1244, -6*w^3 + 16*w^2 + 12*w - 12]', '[9952, 9952, -15*w^3 + 39*w^2 + 45*w - 68]', '[9953, 9953, -7*w^3 + 23*w^2 + 16*w - 49]', '[9953, 9953, 2*w^3 - 10*w^2 - w + 25]', '[9958, 9958, -4*w^3 + 9*w^2 + 20*w - 2]', '[9958, 9958, -6*w^3 + 7*w^2 + 32*w + 22]', '[9962, 9962, -3*w^3 + 10*w^2 + 14*w - 10]', '[9962, 9962, -6*w^3 + 25*w^2 - 13*w - 18]', '[9965, 9965, 4*w^3 - 16*w^2 + 2*w + 25]', '[9965, 9965, -14*w^3 + 40*w^2 + 39*w - 71]', '[9965, 9965, -2*w^3 + 6*w^2 - 15]', '[9965, 9965, -2*w^3 + 4*w^2 + w + 3]', '[9967, 9967, -4*w^3 + 10*w^2 + 9*w + 3]', '[9970, 9970, -10*w^3 + 29*w^2 + 31*w - 58]', '[9970, 9970, 4*w^2 - 13*w - 2]', '[9971, 9971, -2*w^3 + 8*w^2 - 8*w - 1]', '[9973, 9973, -7*w^3 + 17*w^2 + 25*w - 21]', '[9983, 9983, -5*w^3 + 13*w^2 + 10*w - 29]', '[9985, 9985, 3*w^3 - 4*w^2 - 16*w + 3]', '[9985, 9985, -5*w^3 + 15*w^2 + 8*w - 11]', '[9986, 9986, -5*w^3 + 13*w^2 + 10*w - 10]', '[9995, 9995, -5*w^3 + 12*w^2 + 12*w - 17]', '[9995, 9995, 2*w^3 - 13*w^2 + 15*w + 23]', '[9998, 9998, -w^3 + 12*w + 2]', '[10000, 10, 10]', '[10000, 50, 6*w^3 - 18*w^2 - 14*w + 42]', '[10000, 50, -4*w^3 + 14*w^2 + 2*w - 6]', '[10000, 50, -2*w^3 + 10*w^2 - 26]', '[10000, 50, -4*w^3 + 16*w^2 - 2*w - 18]', '[10000, 80, 5*w^3 - 10*w^2 - 20*w]', '[10000, 250, 6*w^2 - 10*w - 14]', '[10000, 250, -4*w^3 + 14*w^2 + 6*w - 26]', '[10000, 400, 3*w^3 - 10*w^2 - 10*w + 24]', '[10000, 400, w^3 - 9*w^2 + 13*w + 12]', '[10000, 400, 2*w^3 - 3*w^2 - 3*w + 12]', '[10000, 400, 4*w^3 - 8*w^2 - 9*w + 20]', '[10000, 1250, -4*w^3 + 14*w^2 + 4*w - 30]', '[10000, 1250, -2*w^3 + 8*w^2 - 4*w + 2]', '[10000, 2000, -4*w^3 + 6*w^2 + 21*w - 4]', '[10000, 2000, -4*w^3 + 11*w^2 + w - 4]', '[10000, 10000, -2*w^3 + 6*w^2 - w - 12]', '[10000, 10000, 6*w^3 - 17*w^2 - 11*w + 12]'], 'label': '4.4.17417.1', 'narrow_class_no': 2, 'primes': ['[2, 2, w^3 - 3*w^2 - w + 2]', '[5, 5, w^2 - 2*w - 3]', '[5, 5, w^3 - 3*w^2 - 3*w + 5]', '[8, 2, w^3 - 2*w^2 - 3*w + 3]', '[13, 13, -w^2 + w + 3]', '[17, 17, -w^2 + 3*w + 1]', '[23, 23, w^2 - 3]', '[25, 5, -w^2 + 2*w + 1]', '[37, 37, w^3 - 4*w^2 - 2*w + 9]', '[41, 41, w^2 - w - 5]', '[49, 7, -w^3 + 2*w^2 + 2*w - 1]', '[49, 7, w^2 + w - 3]', '[59, 59, w^3 - 3*w^2 - 4*w + 5]', '[67, 67, -w^3 + 3*w^2 + w - 5]', '[71, 71, 2*w - 3]', '[71, 71, w^3 - 4*w^2 + 2*w + 5]', '[79, 79, -w^3 + 5*w^2 - 4*w - 5]', '[79, 79, -2*w^3 + 7*w^2 + 5*w - 15]', '[81, 3, -3]', '[83, 83, -2*w^3 + 6*w^2 + 2*w - 5]', '[97, 97, w^3 - w^2 - 7*w - 3]', '[101, 101, -w^3 + 3*w^2 + 3*w - 3]', '[107, 107, -w^3 + 4*w^2 - 7]', '[113, 113, w^3 - 3*w^2 - 5*w + 3]', '[121, 11, -w^3 + 3*w^2 + 4*w - 3]', '[121, 11, 2*w^3 - 6*w^2 - 3*w + 5]', '[127, 127, -2*w^3 + 6*w^2 + 5*w - 9]', '[137, 137, -w^3 + 5*w^2 + 3*w - 9]', '[139, 139, w^3 - w^2 - 4*w + 1]', '[149, 149, w^3 - 3*w^2 - w + 9]', '[157, 157, w^2 - 4*w + 1]', '[163, 163, -3*w^3 + 7*w^2 + 9*w - 13]', '[163, 163, w^3 - 3*w^2 - w + 7]', '[179, 179, -2*w^3 + 3*w^2 + 5*w - 5]', '[179, 179, -2*w^3 + 4*w^2 + 5*w - 9]', '[181, 181, -w^2 + 3*w - 3]', '[181, 181, 2*w^3 - 4*w^2 - 8*w + 5]', '[191, 191, 2*w - 5]', '[193, 193, -2*w^3 + 4*w^2 + 7*w + 3]', '[193, 193, -2*w^3 + 5*w^2 + 5*w - 7]', '[197, 197, -w^3 + 4*w^2 - 11]', '[199, 199, -2*w^3 + 8*w^2 + 6*w - 15]', '[211, 211, -2*w^3 + 3*w^2 + 6*w - 5]', '[211, 211, -4*w^3 + 10*w^2 + 12*w - 19]', '[229, 229, w^3 - 3*w^2 - 4*w + 9]', '[229, 229, w^2 - 5]', '[233, 233, w^2 - 2*w - 7]', '[239, 239, -3*w^3 + 10*w^2 + 2*w - 9]', '[239, 239, -2*w^3 + 5*w^2 + 5*w - 5]', '[257, 257, -2*w^3 + 5*w^2 + 4*w - 9]', '[263, 263, w^3 - 2*w^2 - 4*w - 3]', '[263, 263, w^3 - 6*w - 7]', '[269, 269, w^3 - 3*w^2 - w - 1]', '[269, 269, w - 5]', '[281, 281, -2*w + 7]', '[293, 293, 2*w^2 - w - 7]', '[293, 293, -2*w^3 + 6*w^2 + 6*w - 9]', '[307, 307, -2*w^3 + 5*w^2 + 4*w - 11]', '[311, 311, -w^3 + 3*w^2 + 2*w - 9]', '[317, 317, 4*w^3 - 15*w^2 + 3*w + 15]', '[317, 317, w^3 - 4*w^2 - 4*w + 9]', '[331, 331, -w^3 + 4*w^2 + 2*w - 11]', '[331, 331, 2*w^3 - 7*w^2 - 5*w + 13]', '[337, 337, 2*w^3 - 4*w^2 - 8*w - 1]', '[347, 347, -2*w^3 + 7*w^2 + 9*w - 9]', '[349, 349, -w^3 + 5*w^2 - 2*w - 11]', '[349, 349, 4*w^3 - 9*w^2 - 14*w + 13]', '[353, 353, -3*w^3 + 7*w^2 + 9*w - 11]', '[367, 367, 3*w^3 - 5*w^2 - 11*w + 5]', '[367, 367, -w^3 + 3*w^2 + 5*w - 1]', '[373, 373, w^3 - 2*w^2 - 6*w + 1]', '[379, 379, 2*w^3 - 5*w^2 - 7*w + 5]', '[383, 383, 2*w^3 - 3*w^2 - 11*w - 1]', '[383, 383, -2*w^3 + 5*w^2 + 3*w - 13]', '[397, 397, -2*w^3 + 4*w^2 + 7*w - 7]', '[397, 397, 2*w^3 - 3*w^2 - 8*w - 5]', '[409, 409, w^3 - 3*w^2 + w - 1]', '[419, 419, -4*w^3 + 14*w^2 - w - 13]', '[421, 421, -3*w^2 + 2*w + 9]', '[421, 421, 2*w^2 - 6*w - 3]', '[431, 431, -2*w^3 + 4*w^2 + 9*w - 7]', '[431, 431, -2*w^3 + 6*w^2 + 3*w - 15]', '[431, 431, -3*w^3 + 6*w^2 + 10*w - 9]', '[431, 431, -3*w^3 + 11*w^2 + 10*w - 19]', '[443, 443, 3*w^3 - 6*w^2 - 8*w + 13]', '[443, 443, -2*w^3 + 5*w^2 + 4*w - 5]', '[443, 443, -2*w^3 + 5*w^2 + 6*w - 3]', '[443, 443, 5*w^3 - 12*w^2 - 16*w + 19]', '[461, 461, w^3 - 2*w^2 + 7]', '[461, 461, -3*w^2 + w + 7]', '[479, 479, w^2 + w - 5]', '[487, 487, 2*w^2 - 4*w + 1]', '[487, 487, 2*w^3 - 8*w^2 + 4*w + 7]', '[491, 491, -3*w^3 + 7*w^2 + 7*w - 1]', '[509, 509, -2*w^3 + 9*w^2 + 5*w - 19]', '[509, 509, -3*w^3 + 6*w^2 + 10*w + 1]', '[521, 521, w^3 - 2*w^2 - 6*w + 3]', '[521, 521, 3*w - 5]', '[523, 523, -w^3 + 5*w^2 + 4*w - 7]', '[523, 523, -2*w^3 + 4*w^2 + 6*w - 1]', '[523, 523, w^2 - 7]', '[523, 523, -2*w^3 + 8*w^2 + 8*w - 13]', '[541, 541, -w^3 + 5*w^2 - w - 13]', '[547, 547, -2*w^3 + 7*w^2 + 3*w - 11]', '[547, 547, -w^3 + 4*w^2 + 2*w - 13]', '[547, 547, -2*w^3 + 2*w^2 + 6*w - 1]', '[547, 547, -w^3 + 6*w^2 - 6*w - 7]', '[563, 563, 2*w^2 - 5*w - 1]', '[563, 563, w^2 - 2*w + 3]', '[569, 569, -2*w - 5]', '[571, 571, -2*w^3 + 6*w^2 + 3*w - 11]', '[577, 577, -w^3 + 3*w^2 - 7]', '[593, 593, w^3 - w^2 - 5*w + 3]', '[601, 601, 2*w^3 - 6*w^2 - 4*w + 5]', '[607, 607, -6*w^2 + 15*w + 13]', '[607, 607, -w^3 + 4*w^2 - 2*w - 7]', '[613, 613, -2*w^3 + 6*w^2 + 2*w - 9]', '[617, 617, -3*w^3 + 9*w^2 + 5*w - 9]', '[617, 617, 3*w^3 - 6*w^2 - 12*w + 7]', '[619, 619, -2*w^3 + 8*w^2 + 7*w - 13]', '[619, 619, 2*w^3 - 4*w^2 - 5*w + 1]', '[641, 641, 2*w^3 - w^2 - 6*w + 1]', '[641, 641, -2*w^3 + 4*w^2 + 8*w - 7]', '[641, 641, -2*w^3 + 7*w^2 + 4*w - 13]', '[641, 641, -2*w^3 + 3*w^2 + 7*w - 1]', '[647, 647, -2*w^3 + 7*w^2 + 8*w - 11]', '[647, 647, -2*w^3 + 4*w^2 + 6*w - 3]', '[653, 653, -4*w^2 + 3*w + 13]', '[653, 653, 3*w^3 - 7*w^2 - 11*w + 7]', '[659, 659, -5*w^3 + 14*w^2 + 16*w - 25]', '[659, 659, -4*w^3 + 13*w^2 + 11*w - 25]', '[673, 673, 2*w^3 - 7*w^2 - 6*w + 15]', '[677, 677, 3*w^3 - 8*w^2 - 6*w + 11]', '[677, 677, w^3 - 5*w^2 + 2*w + 9]', '[683, 683, 2*w^2 - 5*w - 9]', '[683, 683, w^3 - w^2 - 4*w - 7]', '[709, 709, -2*w^3 + 6*w^2 + 4*w - 3]', '[733, 733, -2*w^3 + 5*w^2 + 3*w + 1]', '[733, 733, 2*w^3 - 2*w^2 - 9*w - 1]', '[739, 739, -w - 5]', '[751, 751, 3*w^3 - 7*w^2 - 7*w + 11]', '[757, 757, -2*w^3 + 3*w^2 + 8*w - 3]', '[757, 757, 2*w^3 - 3*w^2 - 12*w - 3]', '[761, 761, -3*w^3 + 7*w^2 + 12*w - 11]', '[761, 761, -3*w^3 + 9*w^2 + 6*w - 11]', '[787, 787, -3*w^3 + 5*w^2 + 12*w + 3]', '[787, 787, w^2 - w - 9]', '[797, 797, -3*w^3 + 7*w^2 + 6*w - 17]', '[827, 827, -2*w^3 + 4*w^2 + 9*w - 11]', '[827, 827, -6*w^3 + 17*w^2 + 19*w - 29]', '[853, 853, -3*w^3 + 10*w^2 + 6*w - 21]', '[857, 857, 3*w^3 - 12*w^2 + 4*w + 9]', '[857, 857, -3*w^3 + 9*w^2 + 4*w - 13]', '[863, 863, -3*w^3 + 10*w^2 + 4*w - 15]', '[863, 863, -4*w^2 + w + 11]', '[877, 877, -2*w^3 + 4*w^2 + 8*w - 9]', '[881, 881, -2*w^3 + 4*w^2 + 5*w - 3]', '[907, 907, -w^3 + 5*w^2 - 2*w - 15]', '[907, 907, -2*w^3 + 6*w^2 + 7*w - 15]', '[929, 929, -w^2 + 11]', '[929, 929, -2*w^3 + 6*w^2 + 3*w - 13]', '[937, 937, -3*w^3 + 7*w^2 + 8*w - 3]', '[941, 941, w^3 + w^2 - 8*w - 5]', '[953, 953, 4*w^2 - 8*w - 13]', '[953, 953, w^3 - 4*w^2 - 4*w + 3]', '[967, 967, 3*w^2 - 5*w - 9]', '[971, 971, 3*w^2 - 4*w - 7]', '[971, 971, w^3 - 5*w^2 - 4*w + 11]', '[977, 977, -3*w^3 + 11*w^2 + 6*w - 25]', '[983, 983, -2*w^3 + 8*w^2 + 3*w - 21]', '[991, 991, 2*w^3 - 4*w^2 - 10*w + 3]', '[991, 991, 2*w^3 - 8*w^2 - 3*w + 19]', '[997, 997, -4*w^3 + 10*w^2 + 11*w - 21]']}
• 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': [4, 3, -5, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 17417, 'disc_rad': 17417, 'disc_sign': 1, 'frobs': [[2, [[3, 1], [1, 1]]], [3, [[4, 1]]], [5, [[2, 1], [1, 2]]], [7, [[2, 2]]], [11, [[2, 2]]], [13, [[3, 1], [1, 1]]], [17, [[3, 1], [1, 1]]], [19, [[4, 1]]], [23, [[3, 1], [1, 1]]], [29, [[4, 1]]], [31, [[4, 1]]], [37, [[3, 1], [1, 1]]], [41, [[3, 1], [1, 1]]], [43, [[4, 1]]], [47, [[2, 2]]], [53, [[4, 1]]], [59, [[3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12], 'galois_label': '4T5', 'galt': 5, 'grd': 131.97348218486925, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.17417.1', 'local_algs': ['m17417.1.1.0', 'm17417.1.1.0', 'm17417.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [17417], 'rd': 11.4879711953, 'regulator': {'__RealLiteral__': 0, 'data': '11.0297540098', 'prec': 44}, 'res': {'gal': ['-7104857,541230878,970568429,-2529129614,-3248450651,4658507748,3705206704,-4450013504,-1889348486,2378106518,425977719,-730948894,-20282386,131905418,-8670071,-14084634,1763909,882278,-146011,-31254,6114,568,-126,-4,1'], 'sib': ['-200,-3648,-3906,8031,6075,-4527,-3090,870,617,-51,-47,0,1', '-33187,473874,-193653,-508960,129297,140458,-30849,-13094,2537,480,-85,-6,1', '-9,0,26,0,-13,0,1', '1077004,427217,-408720,-36738,17730,764,-250,-4,1', '567,1527,929,-65,-87,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a - 1 \\)', '\\( 2 a^{3} - 6 a^{2} - 6 a + 11 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}