Hilbert modular form data - 4.4.12357.1-9.2-a

Formats: - HTML - YAML - JSON - 2024-05-06T12:27:30.043301

• 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': 12357, 'field_bad_primes': [3, 1373], 'field_label': '4.4.12357.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.12357.1-9.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [3], 'level_ideal': '[9, 3, -w^3 + 4*w]', 'level_label': '9.2', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.2-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, w]', 1], ['[3, 3, w + 1]', 1]], 'hecke_eigenvalues': [-1, -1, -3, 1, -7, 0, 1, -1, -5, -6, -1, -13, 4, 10, 1, 6, 7, 13, -4, -11, 14, 13, -13, -2, -10, -18, 3, 5, -5, 22, 1, -1, 2, 4, -16, 17, 6, 11, 26, 4, 8, -26, 17, 27, -8, 17, 17, 25, 12, 0, -2, -20, -22, -20, 21, 10, -24, 19, 14, 16, 10, -10, -32, 0, 0, 9, 6, 26, 26, 2, 2, -4, -5, 29, -2, -24, -24, -21, -4, 4, 34, 33, -13, 13, -24, -36, -8, 32, -2, -20, 21, -2, -13, -4, -28, 44, 40, -12, 4, -3, 24, 18, -35, 8, 6, 36, -6, -17, -23, 0, 12, 46, 12, 0, 6, -46, -6, 15, 25, 39, 6, 4, 16, 35, 1, -12, 18, 4, -28, 20, 19, 20, -2, 2, 44, 44, 1, -3, 3, -39, 48, 29, 15, 24, 11, 9, -40, 7, -24, 16, -1, 34, -6, 34, -14, -51, 8, 47, -10, -12, -20, -13, -18, -6, -9, -30, 6, -45], 'hecke_polynomial': 'x', 'label': '4.4.12357.1-9.2-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 12357, 'ideals': ['[1, 1, 1]', '[3, 3, w]', '[3, 3, w + 1]', '[7, 7, -w^2 + 2]', '[9, 3, -w^2 + 3]', '[9, 3, -w^3 + 4*w]', '[9, 3, w^2 - w - 2]', '[11, 11, -w^2 - w + 1]', '[16, 2, 2]', '[17, 17, -w^2 + w + 4]', '[19, 19, -w^3 + w^2 + 5*w - 2]', '[21, 21, -w^3 + w^2 + 4*w - 1]', '[21, 21, -w + 3]', '[23, 23, -w^3 + w^2 + 3*w - 4]', '[27, 3, -w^3 + 2*w^2 + 3*w - 6]', '[27, 3, w^3 - w^2 - 5*w + 3]', '[27, 9, -w^3 + 3*w]', '[27, 9, w^2 - w - 5]', '[31, 31, w^3 - w^2 - 3*w + 1]', '[33, 33, -w^3 + w^2 + 3*w - 2]', '[33, 33, w^3 - 5*w]', '[41, 41, -w^3 + 4*w - 1]', '[43, 43, w^3 + w^2 - 5*w - 4]', '[48, 6, 2*w]', '[48, 6, 2*w + 2]', '[49, 49, -w^2 - 2*w + 1]', '[51, 51, -2*w + 1]', '[51, 51, -w^3 + w^2 + 4*w]', '[53, 53, w^3 - w^2 - 4*w - 1]', '[53, 53, -w^2 - w + 4]', '[57, 57, w + 3]', '[57, 57, w^3 - 2*w^2 - 2*w + 1]', '[59, 59, -w^3 + 4*w - 2]', '[63, 21, -w^2 + 2*w + 3]', '[63, 21, -w^2 + 3*w]', '[63, 21, -w^3 + 6*w + 2]', '[67, 67, -2*w^3 + w^2 + 8*w + 1]', '[69, 69, 2*w^3 - 2*w^2 - 8*w + 5]', '[69, 69, 2*w + 3]', '[77, 77, -w^3 + 2*w^2 + 3*w - 7]', '[81, 3, 3]', '[81, 9, w^3 - 2*w^2 - 3*w + 3]', '[81, 9, -w^3 + 6*w]', '[81, 9, w^2 + 2*w - 2]', '[81, 9, w^3 - w^2 - 5*w]', '[89, 89, -2*w^3 + 3*w^2 + 8*w - 8]', '[89, 89, w^3 - 5*w + 1]', '[93, 93, 2*w^2 - 2*w - 3]', '[93, 93, w^3 + w^2 - 5*w - 2]', '[97, 97, w^3 - 6*w - 1]', '[97, 97, -w^3 + 3*w^2 + 4*w - 10]', '[99, 33, w^3 - 3*w - 3]', '[99, 33, -2*w^2 + w + 3]', '[99, 33, -w^3 - w^2 + 4*w + 1]', '[101, 101, -w^3 + 6*w - 2]', '[101, 101, -w^3 + 2*w^2 + 3*w - 8]', '[107, 107, w^3 - 2*w^2 - 4*w + 4]', '[112, 14, -2*w^2 + 4]', '[113, 113, 2*w^3 - w^2 - 9*w - 1]', '[113, 113, -w^3 + w^2 + w - 2]', '[119, 119, -w^2 - w + 5]', '[121, 121, -2*w^3 + w^2 + 8*w - 2]', '[123, 123, -2*w^3 - w^2 + 6*w + 2]', '[123, 123, -w^3 - w^2 + 2*w + 3]', '[127, 127, w - 4]', '[129, 129, 3*w^3 + w^2 - 12*w - 7]', '[129, 129, 2*w^3 - 7*w - 3]', '[131, 131, -2*w^3 + 4*w^2 + 6*w - 11]', '[133, 133, -2*w^2 + 2*w + 5]', '[137, 137, 3*w^3 - 5*w^2 - 11*w + 16]', '[137, 137, w^3 + w^2 - 7*w - 5]', '[139, 139, -2*w^3 + 3*w^2 + 6*w - 7]', '[144, 6, -2*w^2 + 6]', '[144, 6, -2*w^3 + 8*w]', '[144, 6, 2*w^2 - 2*w - 4]', '[147, 147, 2*w^3 - w^2 - 8*w]', '[147, 147, -w^3 + 5*w - 2]', '[149, 149, w^2 - 2*w - 4]', '[149, 149, w^2 + w - 7]', '[151, 151, -w^3 + 2*w^2 + 6*w - 4]', '[151, 151, -2*w^3 + w^2 + 7*w + 2]', '[153, 51, -w^3 + 3*w^2 + 4*w - 9]', '[153, 51, -w^2 + 3*w + 3]', '[153, 51, 2*w^3 - w^2 - 8*w + 4]', '[157, 157, -w^3 + 3*w^2 + 2*w - 7]', '[159, 159, w^3 + 2*w^2 - 3*w - 4]', '[159, 159, -w^3 + 8*w + 4]', '[159, 159, w^3 + w^2 - 4*w]', '[159, 159, -w^2 + 4*w + 3]', '[161, 161, -w^3 + 3*w + 4]', '[167, 167, w^3 - 2*w^2 - 3*w + 2]', '[167, 167, w^3 - w - 2]', '[171, 57, 2*w^3 - w^2 - 8*w + 1]', '[171, 57, 2*w^3 - 3*w^2 - 6*w + 6]', '[171, 57, w^2 + w - 6]', '[176, 22, -2*w^2 - 2*w + 2]', '[177, 177, -2*w^3 - w^2 + 5*w + 1]', '[177, 177, -w^3 - w^2 + w + 3]', '[181, 181, 2*w^2 - w - 4]', '[187, 187, w^3 - w^2 - 6*w + 1]', '[189, 21, -2*w^3 + w^2 + 9*w - 3]', '[189, 21, 2*w^3 - 2*w^2 - 7*w + 6]', '[189, 63, 2*w^2 + w - 7]', '[189, 63, w^3 - 3*w^2 - 3*w + 9]', '[191, 191, w^2 - 2*w - 7]', '[197, 197, -w^3 + w^2 + 2*w - 4]', '[199, 199, 2*w^3 - w^2 - 10*w + 1]', '[199, 199, w^3 + 2*w^2 - 5*w - 4]', '[201, 201, -w^3 - 2*w^2 + 7*w + 6]', '[201, 201, w^3 - w^2 - w - 2]', '[207, 69, w^3 - 6*w + 3]', '[207, 69, 2*w^2 - w - 6]', '[207, 69, 2*w^3 - 9*w - 1]', '[209, 209, w^3 - 2*w^2 - w + 4]', '[217, 217, -3*w + 2]', '[223, 223, 2*w^2 - w - 5]', '[223, 223, w^3 - w^2 - 6*w + 4]', '[227, 227, w^3 + w^2 - 5*w - 1]', '[227, 227, 2*w^3 - 10*w - 1]', '[227, 227, -2*w^3 + 4*w^2 + 9*w - 11]', '[227, 227, 3*w^3 - 3*w^2 - 13*w + 10]', '[229, 229, -w^3 + 3*w^2 + 3*w - 8]', '[231, 231, -w - 4]', '[231, 231, w^3 - 2*w^2 - 4*w + 3]', '[239, 239, -w^3 + 3*w^2 + 3*w - 5]', '[239, 239, w^3 + w^2 - 4*w - 8]', '[241, 241, w^3 - 2*w^2 - 3*w + 10]', '[241, 241, w^3 + 2*w^2 - 4*w - 7]', '[243, 9, -3*w]', '[243, 9, -w^3 + 2*w^2 - 3]', '[243, 9, -2*w^3 + 2*w^2 + 7*w - 3]', '[243, 9, -3*w - 3]', '[243, 27, -w^3 + w^2 + 3*w + 3]', '[243, 27, -w^3 - w^2 + 4*w + 7]', '[251, 251, 2*w^3 - w^2 - 10*w + 4]', '[253, 253, w^2 - w + 2]', '[256, 4, 4]', '[267, 267, -w^3 + w^2 + 6*w - 2]', '[267, 267, 2*w^3 - 7*w - 2]', '[267, 267, w^3 - 2*w^2 - 2*w + 6]', '[267, 267, w^3 - 2*w - 3]', '[272, 34, -2*w^2 + 2*w + 8]', '[277, 277, 3*w - 1]', '[279, 93, w^3 - w^2 - 6*w + 3]', '[279, 93, -2*w^2 + 5*w + 1]', '[279, 93, w^2 - 2*w - 6]', '[281, 281, 2*w^3 - 3*w^2 - 8*w + 7]', '[283, 283, w^3 - 2*w^2 - 6*w + 5]', '[283, 283, 2*w^3 - 2*w^2 - 7*w + 5]', '[287, 287, 3*w^2 + 2*w - 5]', '[289, 289, -2*w^3 + 7*w + 1]', '[291, 291, 2*w^3 - w^2 - 7*w + 3]', '[291, 291, w^3 - w^2 - 4*w - 3]', '[291, 291, w^3 + 2*w^2 - 3*w - 7]', '[291, 291, 2*w^3 - w^2 - 10*w - 4]', '[293, 293, 2*w^3 - w^2 - 8*w + 5]', '[293, 293, -w^3 + w^2 + 2*w - 5]', '[297, 33, -2*w^3 + 2*w^2 + 7*w]', '[297, 33, -w^3 + 2*w^2 + 6*w - 6]', '[297, 99, w^2 - 4*w + 1]', '[297, 99, 2*w^3 - 2*w^2 - 9*w + 3]', '[301, 301, -w^2 - w - 2]', '[303, 303, -2*w^3 + w^2 + 7*w + 1]', '[303, 303, -2*w - 5]', '[303, 303, -2*w^3 + 7*w - 3]', '[303, 303, w^3 - 2*w^2 - 5*w + 3]', '[304, 38, -2*w^3 + 2*w^2 + 10*w - 4]', '[307, 307, 2*w^2 - w - 11]', '[307, 307, 2*w^3 - 2*w^2 - 7*w + 4]', '[307, 307, 3*w^3 - 3*w^2 - 12*w + 7]', '[307, 307, 2*w^3 - 2*w^2 - 11*w + 13]', '[311, 311, 3*w^2 - 2*w - 13]', '[311, 311, w^3 + w^2 - 6*w - 1]', '[313, 313, -w^3 + 7*w - 2]', '[313, 313, 2*w^3 + 2*w^2 - 11*w - 10]', '[313, 313, 3*w^3 - 4*w^2 - 11*w + 10]', '[313, 313, -2*w^3 + 6*w - 1]', '[317, 317, w^3 + w^2 - 3*w - 5]', '[321, 321, -w^2 - 3*w + 1]', '[321, 321, -w^3 + w^2 + w - 3]', '[323, 323, -2*w^3 - w^2 + 10*w + 4]', '[336, 42, -2*w^3 + 2*w^2 + 8*w - 2]', '[336, 42, -2*w + 6]', '[339, 339, 3*w^3 - 16*w - 7]', '[339, 339, -w^3 - 3*w^2 + 2*w + 1]', '[339, 339, w^3 + w^2 - 7*w - 6]', '[339, 339, -4*w^2 + w + 3]', '[341, 341, -w^3 - w^2 + 2*w + 4]', '[343, 7, 2*w^3 - 3*w^2 - 5*w + 5]', '[343, 343, -w^3 + 2*w^2 + 4*w - 10]', '[347, 347, -3*w^3 + w^2 + 14*w - 1]', '[349, 349, 2*w^3 - 5*w^2 - 7*w + 17]', '[349, 349, w^3 - 7*w - 2]', '[349, 349, 3*w^3 - 3*w^2 - 12*w + 8]', '[349, 349, 3*w^3 - 12*w - 2]', '[353, 353, w^3 - 2*w^2 - 6*w + 11]', '[357, 357, -w^3 - 2*w^2 + 4*w + 5]', '[357, 357, -w^3 - w^2 + 5*w]', '[361, 361, 2*w^3 - 5*w + 1]', '[363, 363, -w^3 - 2*w^2 + 4*w + 6]', '[363, 363, w^3 + 2*w^2 - w - 5]', '[368, 46, -2*w^3 + 2*w^2 + 6*w - 8]', '[369, 123, w^3 - 2*w^2 - 4*w + 2]', '[369, 123, w^3 - w + 6]', '[369, 123, -w^3 + 3*w^2 + 6*w - 6]', '[371, 371, -w^3 - 2*w^2 + 5*w + 2]', '[371, 371, -2*w^3 + w^2 + 5*w - 5]', '[373, 373, -w^3 + w^2 + 3*w - 7]', '[379, 379, 2*w^3 - 11*w - 2]', '[379, 379, -2*w^3 + 2*w^2 + 6*w - 5]', '[381, 381, w^2 - 4*w]', '[381, 381, w^2 - 3*w - 4]', '[383, 383, -2*w^3 + w^2 + 9*w - 4]', '[387, 129, 3*w^3 - w^2 - 16*w - 6]', '[387, 129, -2*w^3 + w^2 + 8*w + 5]', '[387, 129, w^3 - 6*w - 6]', '[389, 389, 2*w^3 - 8*w + 1]', '[391, 391, -2*w^3 + 3*w^2 + 8*w - 13]', '[393, 393, 2*w^3 - 4*w^2 - 5*w + 6]', '[393, 393, w - 5]', '[399, 399, -2*w^3 + 2*w^2 + 5*w]', '[399, 399, -2*w^3 + 7*w + 5]', '[409, 409, w^3 + 2*w^2 - 5*w - 5]', '[409, 409, -w^3 + 4*w^2 + 2*w - 13]', '[411, 411, 2*w^3 - 2*w^2 - 8*w - 3]', '[411, 411, w^3 - w^2 - 4*w + 7]', '[411, 411, -2*w^3 + 4*w^2 + 7*w - 9]', '[411, 411, 3*w^3 - w^2 - 15*w - 8]', '[413, 413, 4*w^2 + 2*w - 7]', '[417, 417, w^3 - 4*w^2 - w + 6]', '[417, 417, -w^3 - w^2 + 5*w - 1]', '[419, 419, 2*w^2 + w - 8]', '[431, 431, -3*w^3 + 13*w + 2]', '[432, 6, -2*w^3 + 4*w^2 + 6*w - 12]', '[432, 6, 2*w^3 - 2*w^2 - 10*w + 6]', '[432, 18, -2*w^3 + 6*w]', '[432, 18, 2*w^2 - 2*w - 10]', '[433, 433, 2*w^3 - 3*w^2 - 10*w + 8]', '[437, 437, -w^3 + 3*w^2 + 2*w - 10]', '[439, 439, -2*w^3 + 2*w^2 + 10*w - 5]', '[441, 147, w^3 + 2*w^2 - 6*w - 6]', '[441, 147, -2*w^3 + 6*w + 1]', '[441, 147, -w^3 + w + 3]', '[447, 447, w^3 - w^2 - 6*w - 4]', '[447, 447, w^3 - 2*w^2 - 4*w]', '[447, 447, w^3 + 2*w^2 - 6*w - 7]', '[447, 447, w^3 + w^2 - 7*w]', '[451, 451, 2*w^3 + 4*w^2 - 4*w - 7]', '[453, 453, -w^3 - 3*w^2 + 8*w + 6]', '[453, 453, -w^3 - w^2 + w - 3]', '[453, 453, -3*w^3 - 2*w^2 + 15*w + 8]', '[453, 453, -3*w^2 - 5*w + 1]', '[457, 457, -2*w^3 + w^2 + 7*w - 1]', '[459, 51, 2*w^3 - w^2 - 6*w + 3]', '[459, 51, w^3 + 2*w^2 - 2*w - 6]', '[459, 153, -2*w^3 + 3*w^2 + 3*w - 2]', '[459, 153, -2*w^3 + 9*w]', '[467, 467, -w^3 + 2*w^2 + 4*w - 1]', '[467, 467, -3*w^3 + 5*w^2 + 10*w - 11]', '[469, 469, -w^3 + 7*w - 1]', '[471, 471, 2*w^3 - 3*w^2 - 4*w + 3]', '[471, 471, w^3 - 2*w - 4]', '[473, 473, -3*w^3 - 2*w^2 + 11*w + 5]', '[477, 159, -2*w^3 - w^2 + 9*w + 3]', '[477, 159, w^3 + 3*w^2 - 9*w - 5]', '[477, 159, -3*w^3 - 2*w^2 + 13*w + 9]', '[477, 159, -2*w^3 + 2*w^2 + 6*w - 9]', '[477, 159, w^3 - 3*w^2 - 7*w + 6]', '[477, 159, w^3 - 2*w^2 - w + 5]', '[483, 483, 2*w^3 - 3*w^2 - 10*w + 10]', '[483, 483, -w^3 - 2*w^2 + 7*w + 3]', '[487, 487, w^3 - 7*w - 1]', '[496, 62, 2*w^3 - 2*w^2 - 6*w + 2]', '[499, 499, -3*w^3 + 2*w^2 + 11*w + 1]', '[499, 499, w^3 + 2*w^2 - 5*w - 7]', '[501, 501, -w^3 + 2*w^2 - w - 3]', '[501, 501, 2*w^3 + 4*w^2 - 6*w - 5]', '[501, 501, w^3 + 4*w^2 - 5*w - 3]', '[501, 501, -4*w - 1]', '[503, 503, w^3 - 2*w^2 - 5*w + 2]', '[509, 509, -4*w^3 + 5*w^2 + 18*w - 20]', '[513, 57, w^3 + 2*w^2 - 5*w - 6]', '[513, 57, w^3 + w^2 - 6*w]', '[513, 171, -3*w^3 + w^2 + 12*w + 3]', '[513, 171, -w^3 - w^2 + w + 4]', '[527, 527, 2*w^3 - 11*w + 1]', '[528, 66, -2*w^3 + 2*w^2 + 6*w - 4]', '[528, 66, 2*w^3 - 10*w]', '[529, 529, w^2 - 8]', '[531, 177, 2*w^3 - 5*w + 6]', '[531, 177, w^3 - 3*w^2 - 3*w + 4]', '[531, 177, -w^3 + 4*w^2 + 6*w - 9]', '[539, 539, -w^3 + 3*w^2 + 6*w - 11]', '[543, 543, 2*w^3 - w^2 - 4*w]', '[543, 543, 2*w^3 + w^2 - 5*w - 4]', '[561, 561, -w^2 - 2*w - 3]', '[561, 561, -2*w^3 + w^2 + 10*w - 5]', '[567, 21, 3*w^2 - 6]', '[567, 63, 2*w^3 + w^2 - 7*w]', '[567, 63, 2*w^3 - 3*w^2 - 9*w + 14]', '[567, 63, -2*w^3 + 2*w^2 + 6*w - 3]', '[567, 63, -w^3 - w^2 + 3*w + 6]', '[571, 571, -3*w^3 + 12*w + 4]', '[571, 571, 2*w^3 - 5*w^2 - 8*w + 16]', '[571, 571, 2*w^3 + 2*w^2 - 9*w - 7]', '[571, 571, 3*w^3 - 2*w^2 - 11*w + 7]', '[573, 573, w^3 - w^2 - 9*w - 7]', '[573, 573, w^3 - 2*w^2 - 7*w]', '[583, 583, -3*w^3 - w^2 + 8*w - 1]', '[583, 583, -2*w^2 - 3*w - 2]', '[587, 587, w^3 + 2*w^2 - 5*w - 1]', '[587, 587, 2*w^3 - 2*w^2 - 8*w + 1]', '[587, 587, -2*w^3 + 2*w^2 + 9*w - 2]', '[587, 587, 2*w^3 - w^2 - 9*w + 5]', '[589, 589, 3*w^2 - w - 11]', '[591, 591, -w^3 - 2*w^2 + w - 1]', '[591, 591, -3*w^2 - w + 3]', '[593, 593, -4*w^3 + 6*w^2 + 16*w - 17]', '[593, 593, -w^3 + 3*w^2 + w - 8]', '[597, 597, 3*w^3 - w^2 - 15*w - 5]', '[597, 597, 3*w^3 - 7*w - 3]', '[597, 597, w^3 - 5*w - 6]', '[597, 597, 4*w^3 + 2*w^2 - 12*w - 7]', '[599, 599, -w^2 - 2*w + 7]', '[599, 599, -w^3 + 2*w^2 - 4]', '[603, 201, -w^3 + w^2 + 6*w - 9]', '[603, 201, w^2 - w - 8]', '[603, 201, 2*w^3 - 3*w^2 - 8*w + 6]', '[607, 607, -2*w^3 + 2*w^2 + 5*w - 1]', '[607, 607, -w^3 + w^2 + 5*w - 8]', '[613, 613, -w - 5]', '[617, 617, 3*w^3 - 2*w^2 - 14*w + 1]', '[617, 617, -w^3 + 2*w^2 + 2*w - 8]', '[619, 619, -w^3 + 2*w^2 + 6*w - 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26]', '[1717, 1717, w^2 + 4]', '[1719, 573, 7*w^3 - 28*w - 3]', '[1719, 573, -2*w^3 - 2*w^2 + 8*w + 11]', '[1719, 573, w^3 + 5*w^2 - 3*w - 18]', '[1727, 1727, -2*w^3 + 9*w - 4]', '[1733, 1733, -5*w^3 + 6*w^2 + 22*w - 23]', '[1733, 1733, w^3 + 2*w^2 - 2*w - 8]', '[1733, 1733, -2*w^3 + 3*w^2 + 7*w - 2]', '[1733, 1733, 4*w^3 - 4*w^2 - 17*w + 16]', '[1749, 1749, 2*w^3 - 5*w^2 - 8*w + 11]', '[1749, 1749, 3*w^3 + 3*w^2 - 17*w - 12]', '[1749, 1749, -2*w^3 + w^2 + 4*w + 4]', '[1749, 1749, -2*w^3 + 2*w^2 + 11*w - 6]', '[1757, 1757, 3*w^3 - 5*w^2 - 11*w + 11]', '[1759, 1759, w^3 + 3*w^2 - 6*w - 7]', '[1761, 1761, 3*w^3 - 4*w - 3]', '[1761, 1761, 2*w^3 - 13*w - 5]', '[1761, 1761, w^3 + w^2 - w - 6]', '[1761, 1761, 2*w^2 - 5*w - 6]', '[1761, 1761, -2*w^3 + w^2 + 13*w + 4]', '[1761, 1761, 4*w^3 + 2*w^2 - 9*w - 4]', '[1761, 1761, -w^2 + 4*w + 6]', '[1761, 1761, 3*w^3 - 10*w - 1]', '[1763, 1763, -3*w^3 + 2*w^2 + 16*w - 11]', '[1767, 1767, 3*w^3 - w^2 - 11*w]', '[1767, 1767, -3*w^3 + 6*w^2 + w + 1]', '[1771, 1771, 3*w^3 - 10*w - 2]', '[1773, 591, 4*w^3 - 13*w + 3]', '[1773, 591, 4*w^2 + 3*w - 12]', '[1773, 591, -w^3 + 5]', '[1779, 1779, -2*w^3 + 2*w^2 + 11*w - 5]', '[1779, 1779, 2*w^3 - 4*w^2 - 5*w + 12]', '[1779, 1779, w^3 - w^2 - 4*w - 5]', '[1779, 1779, 2*w^3 - 4*w^2 - 5*w + 3]', '[1783, 1783, -3*w^3 + 13*w + 11]', '[1787, 1787, -3*w^3 + 6*w^2 + 14*w - 26]', '[1787, 1787, -2*w^3 + 4*w^2 + 11*w - 17]', '[1789, 1789, -3*w^3 + 5*w^2 + 14*w - 23]', '[1791, 597, 3*w^3 + 4*w^2 - 14*w - 21]', '[1791, 597, -4*w^3 + 2*w^2 + 16*w + 1]', '[1791, 597, 5*w^3 - 3*w^2 - 21*w + 6]', '[1791, 597, -2*w^3 + 4*w^2 + 5*w + 2]', '[1791, 597, w^3 - 3*w^2 - 10*w - 3]', '[1791, 597, -2*w^2 - 3*w - 3]', '[1792, 28, -4*w^2 + 8]', '[1797, 1797, -w^3 - 2*w^2 + 7*w]', '[1797, 1797, -3*w^2 - w - 1]', '[1797, 1797, w^3 - 5*w^2 - w + 3]', '[1797, 1797, -w^3 - 3*w^2 + 5*w + 7]', '[1801, 1801, -4*w^3 + 15*w + 1]', '[1808, 226, 4*w^3 - 2*w^2 - 18*w - 2]', '[1808, 226, -2*w^3 + 2*w^2 + 2*w - 4]', '[1809, 201, w^3 - w^2 - 8*w]', '[1809, 201, -w^3 + 2*w^2 - 6]', '[1809, 603, -2*w^3 + 9*w + 9]', '[1809, 603, w^3 - 3*w^2 - 6*w + 16]', '[1811, 1811, -w^3 + 3*w^2 - 8]', '[1811, 1811, -3*w^3 + 3*w^2 + 13*w - 4]', '[1819, 1819, 3*w^3 - 3*w^2 - 15*w + 10]', '[1821, 1821, 5*w^2 - 5*w - 6]', '[1821, 1821, 2*w^3 + 3*w^2 - 10*w - 5]', '[1821, 1821, -5*w + 3]', '[1821, 1821, -w^3 + w^2 - 5]', '[1823, 1823, 2*w^3 - 5*w - 5]', '[1823, 1823, -2*w^3 - w^2 + 7*w + 8]', '[1829, 1829, -2*w^3 + 3*w^2 + 4*w - 8]', '[1831, 1831, 3*w^3 + w^2 - 14*w - 14]', '[1831, 1831, -4*w^3 + 5*w^2 + 21*w - 23]', '[1837, 1837, w^3 + 2*w^2 - 2*w + 2]', '[1837, 1837, -5*w^3 - 4*w^2 + 10*w + 4]', '[1839, 1839, -w^2 - 5*w]', '[1839, 1839, -w^2 - 6*w - 5]', '[1843, 1843, 9*w^3 - 10*w^2 - 37*w + 32]', '[1843, 1843, 2*w^3 + 2*w^2 - 11*w - 16]', '[1849, 1849, -4*w^3 + 3*w^2 + 16*w - 7]', '[1851, 1851, w^3 + w^2 - 8*w - 9]', '[1851, 1851, -w^2 - 3*w - 5]', '[1851, 1851, w^3 - 3*w^2 - 5*w + 3]', '[1851, 1851, 4*w^3 - w^2 - 22*w - 8]', '[1857, 1857, 3*w^2 - 4*w - 10]', '[1857, 1857, -w^3 - 4*w^2 + 4*w + 6]', '[1857, 1857, -3*w^3 - 3*w^2 + 10*w + 4]', '[1857, 1857, w^3 + w^2 - 10*w + 3]', '[1861, 1861, 4*w^3 - 16*w - 5]', '[1863, 69, 3*w^3 - 3*w^2 - 9*w + 12]', '[1863, 207, -w^3 + w^2 + 2*w + 6]', '[1863, 207, -w^3 + 2*w^2 + 3*w - 12]', '[1863, 207, 3*w^3 - 5*w^2 - 12*w + 12]', '[1863, 207, -3*w^3 + 2*w^2 + 13*w + 2]', '[1867, 1867, 3*w^3 - 3*w^2 - 10*w + 7]', '[1869, 1869, 3*w^3 - 6*w^2 - 13*w + 26]', '[1869, 1869, 4*w^2 - 3*w - 13]', '[1869, 1869, -7*w^3 + 11*w^2 + 26*w - 30]', '[1869, 1869, 2*w^3 - 13*w + 6]', '[1871, 1871, 3*w^2 + 2*w - 11]', '[1871, 1871, -3*w^3 + w^2 + 13*w - 4]', '[1875, 15, -5*w]', '[1875, 15, -5*w - 5]', '[1877, 1877, -2*w^3 + 3*w^2 + 5*w - 10]', '[1877, 1877, 3*w^3 - 7*w^2 - 10*w + 25]', '[1881, 627, -2*w^2 - 3*w + 9]', '[1881, 627, -3*w^3 + w^2 + 10*w - 3]', '[1881, 627, -3*w^3 - 2*w^2 + 17*w + 7]', '[1889, 1889, -3*w^3 + 6*w^2 + 10*w - 13]', '[1889, 1889, -w^3 + 3*w^2 + 6*w - 14]', '[1893, 1893, -w^3 - w^2 - 2*w + 3]', '[1893, 1893, -2*w^3 - w^2 + 2*w - 2]', '[1904, 238, -2*w^2 - 2*w + 10]', '[1919, 1919, -3*w^2 + 6*w + 7]', '[1919, 1919, 7*w^3 - 9*w^2 - 31*w + 25]', '[1921, 1921, 7*w^3 - w^2 - 34*w - 7]', '[1921, 1921, -w^2 + 2*w - 5]', '[1923, 1923, -w^3 - 3*w^2 + 5*w + 10]', '[1923, 1923, -2*w^3 + 10*w - 3]', '[1931, 1931, 3*w^3 - 4*w^2 - 9*w + 2]', '[1931, 1931, 4*w^3 + w^2 - 20*w - 7]', '[1933, 1933, 5*w^3 - 6*w^2 - 19*w + 14]', '[1933, 1933, 3*w^3 - 7*w^2 - 9*w + 17]', '[1936, 242, -4*w^3 + 2*w^2 + 16*w - 4]', '[1939, 1939, -3*w^3 + w^2 + 6*w - 2]', '[1941, 1941, w^3 - 2*w^2 - 8*w - 5]', '[1941, 1941, w^3 - 3*w^2 - 5*w]', '[1947, 1947, -w^3 + w^2 + 4*w - 9]', '[1947, 1947, 3*w^3 - 3*w^2 - 8*w + 10]', '[1949, 1949, 3*w^3 + w^2 - 14*w - 4]', '[1951, 1951, 3*w^3 - w^2 - 10*w - 2]', '[1951, 1951, -w^3 + 5*w^2 - 13]', '[1953, 651, -2*w^3 + 8*w^2 - 3*w - 9]', '[1953, 651, w^3 + 3*w^2 - 10*w - 3]', '[1953, 651, 2*w^3 + 3*w^2 - 12*w - 10]', '[1959, 1959, -2*w^3 + 2*w^2 + 6*w + 5]', '[1959, 1959, -w^3 - w^2 - 2*w - 3]', '[1959, 1959, 2*w^3 - w^2 - 4*w + 6]', '[1959, 1959, -3*w^2 - 8*w - 2]', '[1967, 1967, 3*w^3 - 2*w^2 - 13*w + 11]', '[1968, 246, -4*w^3 - 2*w^2 + 12*w + 4]', '[1968, 246, -2*w^3 - 2*w^2 + 4*w + 6]', '[1973, 1973, 2*w^3 + w^2 - 10*w - 1]', '[1977, 1977, 2*w^3 + 3*w^2 - 10*w - 8]', '[1977, 1977, w^3 + 3*w^2 - 8*w - 3]', '[1979, 1979, -w^3 + 4*w^2 + 7*w - 14]', '[1979, 1979, -2*w^3 + 4*w^2 + 6*w - 5]', '[1981, 1981, 4*w^3 - w^2 - 12*w + 7]', '[1981, 1981, w^3 - 3*w^2 - 8*w + 10]', '[1983, 1983, 3*w^3 - 2*w^2 - 10*w]', '[1983, 1983, 3*w^3 + w^2 - 12*w - 10]', '[1987, 1987, -7*w^3 + 10*w^2 + 31*w - 35]', '[1987, 1987, -2*w - 7]', '[1991, 1991, -3*w^3 - 3*w^2 + 9*w + 2]', '[1993, 1993, 4*w^2 - 4*w - 7]', '[1993, 1993, 2*w^3 - 3*w^2 - 11*w + 8]', '[1997, 1997, w^3 - w - 7]', '[1999, 1999, w^3 - 4*w^2 - 8*w + 11]', '[1999, 1999, -w^3 - 4*w^2 + 8*w + 7]', '[2003, 2003, 2*w^3 - 6*w^2 - 9*w + 22]', '[2007, 669, -w^3 + 2*w^2 + w + 4]', '[2007, 669, -w^3 + w^2 + 3*w - 9]', '[2007, 669, 2*w^3 - 3*w^2 - 11*w + 3]', '[2007, 669, -3*w^3 + 4*w^2 + 8*w - 5]', '[2007, 669, -w^3 - 2*w - 3]', '[2007, 669, -w^3 + w^2 - 3*w]', '[2009, 2009, 3*w^3 + 5*w^2 - 6*w - 10]', '[2017, 2017, 5*w^2 + 2*w - 13]', '[2019, 2019, 3*w^3 - 8*w^2 - 7*w + 15]', '[2019, 2019, -2*w^3 + 10*w - 7]', '[2023, 2023, w^3 - 5*w^2 - 2*w + 17]', '[2027, 2027, -w^3 + 2*w^2 - w - 5]', '[2027, 2027, 3*w^3 + 2*w^2 - 16*w - 7]', '[2029, 2029, -w^3 + 9*w - 11]', '[2032, 254, 2*w - 8]', '[2033, 2033, -3*w^3 + 5*w^2 + 10*w - 20]', '[2037, 2037, 6*w^3 - 6*w^2 - 26*w + 19]', '[2037, 2037, 2*w^3 + w^2 - 14*w]', '[2037, 2037, 2*w^3 + 3*w^2 - 13*w - 14]', '[2037, 2037, -5*w^3 + 10*w^2 + 19*w - 33]', '[2043, 681, w^3 - 3*w^2 - 6*w + 3]', '[2043, 681, -2*w^3 + 4*w^2 + 5*w - 1]', '[2043, 681, -w^2 - 4*w - 6]', '[2043, 681, 3*w^3 + 2*w^2 - 16*w - 18]', '[2043, 681, 4*w^3 - 3*w^2 - 18*w + 3]', '[2043, 681, -4*w^3 + 3*w^2 + 15*w + 2]', '[2043, 681, -7*w^3 + 7*w^2 + 27*w - 27]', '[2043, 681, 3*w^3 - 2*w^2 - 13*w + 10]', '[2043, 681, 2*w^3 - 9*w^2 - 11*w + 27]', '[2043, 681, 2*w^3 + w^2 - 9*w]', '[2043, 681, -4*w^3 + 5*w^2 + 16*w - 11]', '[2043, 681, 2*w^3 + 3*w^2 - 8*w - 9]', '[2047, 2047, 8*w^3 - 13*w^2 - 35*w + 44]', '[2047, 2047, -4*w^3 + 4*w^2 + 14*w - 13]', '[2049, 2049, -2*w^3 + w^2 + 2*w + 3]', '[2049, 2049, 3*w^3 - w^2 - 5*w - 3]', '[2049, 2049, -3*w^3 + 8*w + 2]', '[2049, 2049, 4*w^3 + w^2 - 11*w - 5]', '[2051, 2051, -2*w^3 + 5*w^2 + w - 8]', '[2051, 2051, w^3 + 4*w^2 + w - 10]', '[2053, 2053, -w^3 + 5*w - 7]', '[2057, 2057, -3*w^3 + 2*w^2 + 13*w + 4]', '[2061, 687, -3*w^3 + 4*w^2 + 12*w - 18]', '[2061, 687, w^2 - 4*w + 7]', '[2061, 687, 3*w^3 - 5*w^2 - 14*w + 12]', '[2063, 2063, -2*w^3 + 3*w^2 + 9*w - 4]', '[2063, 2063, 3*w^3 + w^2 - 16*w - 4]', '[2064, 258, 6*w^3 + 2*w^2 - 24*w - 14]', '[2064, 258, 4*w^3 - 14*w - 6]', '[2069, 2069, -5*w^3 + 5*w^2 + 22*w - 17]', '[2069, 2069, w^3 + 2*w^2 - 8*w - 10]', '[2077, 2077, -3*w^3 + 3*w^2 + 15*w - 7]', '[2079, 231, -w^3 - 2*w^2 + 8*w]', '[2079, 231, 4*w^3 - 2*w^2 - 15*w - 3]', '[2079, 693, -w^3 - 3*w^2 + 6*w + 8]', '[2079, 693, 3*w^3 - w^2 - 12*w + 6]', '[2081, 2081, 3*w^2 + w - 13]', '[2081, 2081, -4*w^3 + 2*w^2 + 15*w - 10]', '[2083, 2083, w^3 + 3*w^2 - 6*w - 10]', '[2089, 2089, 3*w^3 - 2*w^2 - 16*w + 8]', '[2089, 2089, 2*w^3 + w^2 - 8*w - 14]', '[2091, 2091, -w^3 - 3*w^2 + 5*w + 9]', '[2091, 2091, w^3 + 2*w^2 - 7]', '[2096, 262, -4*w^3 + 8*w^2 + 12*w - 22]', '[2099, 2099, -4*w^3 + w^2 + 18*w - 1]', '[2101, 2101, 5*w^2 + 8*w - 4]', '[2103, 2103, 2*w^3 - w^2 - 10*w - 7]', '[2103, 2103, 2*w^3 - 3*w^2 - 7*w]', '[2107, 2107, -5*w^3 - 2*w^2 + 18*w + 8]', '[2121, 2121, 5*w - 1]', '[2121, 2121, 5*w^3 - 5*w^2 - 23*w + 14]', '[2121, 2121, 3*w^3 - 2*w^2 - 13*w - 3]', '[2121, 2121, -4*w^3 + 8*w^2 + 14*w - 27]', '[2127, 2127, w^3 - 5*w^2 + w + 9]', '[2127, 2127, -2*w^3 - w^2 + 11*w + 1]', '[2128, 266, -4*w^2 + 4*w + 10]', '[2137, 2137, -2*w^3 + 6*w^2 + 8*w - 19]', '[2139, 2139, w^3 - 3*w^2 - 5*w + 17]', '[2139, 2139, 3*w^3 + w^2 - 13*w - 3]', '[2143, 2143, -4*w^3 + 6*w^2 + 12*w - 11]', '[2147, 2147, 3*w^3 + 4*w^2 - 17*w - 25]', '[2147, 2147, w^3 - 4*w^2 - 6*w + 7]', '[2149, 2149, -2*w^3 - 3*w^2 + 11*w + 20]', '[2149, 2149, 4*w^3 - 5*w^2 - 14*w + 14]', '[2149, 2149, -w^3 + 5*w^2 + 4*w - 16]', '[2149, 2149, w^3 - 2*w^2 - 8*w + 8]', '[2151, 717, 4*w^2 - 7*w + 1]', '[2151, 717, -3*w^3 + w^2 + 12*w - 9]', '[2151, 717, -5*w^2 - 2*w + 12]', '[2151, 717, -w^3 - 4*w^2 + 10*w + 13]', '[2151, 717, 6*w^3 - 2*w^2 - 29*w - 3]', '[2151, 717, 4*w^2 - 3*w - 18]', '[2159, 2159, -w^3 + 5*w^2 - 16]', '[2161, 2161, w^3 - 5*w^2 + 8]', '[2167, 2167, 2*w^3 + 5*w^2 - 7]', '[2169, 723, -5*w^3 + 3*w^2 + 21*w - 3]', '[2169, 723, 4*w^2 - w - 14]', '[2169, 723, 3*w^3 - 2*w^2 - 14*w + 9]', '[2169, 723, -w^3 + w^2 - 12]', '[2169, 723, -w^3 + 6*w + 8]', '[2169, 723, 3*w^3 - 4*w^2 - 19*w]', '[2173, 2173, 2*w^3 + 3*w^2 - 9*w - 8]', '[2173, 2173, w^3 - 4*w^2 - 8*w + 10]', '[2177, 2177, w^3 - 4*w^2 - 3*w + 4]', '[2177, 2177, -w^3 + 4*w^2 + 5*w - 17]', '[2179, 2179, -w^3 + w^2 + 8*w - 5]', '[2181, 2181, w^3 - 3*w^2 - 5*w + 2]', '[2181, 2181, -7*w - 3]', '[2181, 2181, w^3 - w^2 - 12*w - 7]', '[2181, 2181, -2*w^2 + 2*w - 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9]', '[2211, 2211, -w^3 + 2*w + 10]', '[2219, 2219, -2*w^3 + 3*w - 4]', '[2224, 278, -4*w^3 + 6*w^2 + 12*w - 14]', '[2227, 2227, 3*w^3 - 3*w^2 - 9*w + 7]', '[2231, 2231, 7*w^3 - 14*w^2 - 31*w + 46]', '[2231, 2231, -2*w^3 + 4*w^2 + 9*w - 8]', '[2237, 2237, -5*w^3 + 4*w^2 + 21*w - 5]', '[2247, 2247, 4*w^3 - 7*w^2 - 13*w + 15]', '[2247, 2247, -w^3 + 2*w^2 + 5*w - 13]', '[2251, 2251, -w^3 + w^2 + 8*w - 1]', '[2251, 2251, -2*w^3 + 6*w^2 + 6*w - 19]', '[2253, 2253, 3*w^3 - 4*w^2 - 8*w + 6]', '[2253, 2253, w^3 + w^2 - 2*w - 8]', '[2259, 753, 4*w^2 - 2*w - 21]', '[2259, 753, 5*w^3 - 6*w^2 - 21*w + 15]', '[2259, 753, -4*w^3 + 5*w^2 + 13*w - 5]', '[2261, 2261, -w^3 + 3*w^2 + 5*w - 1]', '[2271, 2271, -w^3 - 2*w^2 - 2*w + 3]', '[2271, 2271, 3*w^3 - 7*w]', '[2271, 2271, -2*w^3 - 2*w^2 + w - 2]', '[2271, 2271, 3*w^3 + 3*w^2 - 7*w - 7]', '[2273, 2273, -4*w^3 + w^2 + 20*w - 2]', '[2277, 759, -3*w^3 - w^2 + 11*w]', '[2277, 759, -4*w^2 + 9]', '[2277, 759, -3*w^3 + 5*w^2 + 13*w - 22]', '[2279, 2279, -w^3 + 3*w^2 + w - 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3*w^2 - 22*w + 9]', '[4947, 4947, 3*w^3 + 3*w^2 - 19*w - 15]', '[4949, 4949, -2*w^3 + 6*w^2 + 13*w - 11]', '[4949, 4949, w^3 + 2*w^2 - 2*w - 11]', '[4957, 4957, -2*w^2 + w - 4]', '[4957, 4957, -w^3 + 10*w - 5]', '[4961, 4961, 2*w^3 - 3*w^2 - 4*w + 17]', '[4963, 4963, -2*w^3 + 2*w^2 + 14*w - 13]', '[4967, 4967, -9*w^3 + 12*w^2 + 40*w - 46]', '[4967, 4967, 7*w^3 - 8*w^2 - 30*w + 28]', '[4971, 4971, -5*w^3 - 3*w^2 + 19*w + 8]', '[4971, 4971, -2*w^3 - 4*w^2 + 8*w + 9]', '[4973, 4973, 5*w^2 + 3*w - 16]', '[4976, 622, 6*w^2 - 4*w - 26]', '[4976, 622, 2*w^3 + 2*w^2 - 12*w - 2]', '[4981, 4981, -w^3 + 3*w^2 + 3*w - 17]', '[4981, 4981, w^2 - 7*w - 1]', '[4983, 4983, -2*w^3 + 3*w^2 + 4*w + 5]', '[4983, 4983, -w^3 + 7*w^2 + 6*w - 20]', '[4983, 4983, 4*w^3 + 4*w^2 - 25*w - 18]', '[4983, 4983, -w^3 - 5*w^2 + 4*w + 21]', '[4987, 4987, 5*w^3 - 6*w^2 - 18*w + 13]', '[4991, 4991, 4*w^3 - 5*w^2 - 12*w + 1]', '[4993, 4993, -3*w^3 - 4*w^2 + 13*w + 10]', '[4993, 4993, -3*w^3 + w^2 + 12*w + 10]', '[4999, 4999, -4*w^3 + 2*w^2 + 15*w - 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13*w + 3]', '[5097, 5097, -w^3 - w^2 - 4*w]', '[5097, 5097, -8*w - 3]', '[5097, 5097, -w^3 - 2*w^2 - 5*w - 4]', '[5097, 5097, w^3 - w^2 - 13*w - 8]', '[5103, 63, 3*w^2 - 6*w - 9]', '[5103, 63, 3*w^2 - 9*w]', '[5103, 63, 3*w^3 - 18*w - 6]', '[5103, 189, -w^3 + 4*w^2 + 5*w - 3]', '[5103, 189, -2*w^3 + 3*w^2 + 12*w - 9]', '[5103, 189, 2*w^2 + 4*w + 5]', '[5103, 189, w^3 - 2*w^2 + 12]', '[5117, 5117, w^3 + 2*w^2 - 9*w - 11]', '[5119, 5119, 3*w^3 - 19*w - 8]', '[5127, 5127, 2*w^3 - w^2 - 13*w - 10]', '[5127, 5127, 2*w^3 - 3*w^2 - 10*w]', '[5127, 5127, -2*w^3 + w^2 + 13*w + 1]', '[5127, 5127, w^3 - 3*w^2 + w + 9]', '[5129, 5129, w^3 - 5*w^2 - 8*w + 17]', '[5129, 5129, 3*w^3 + w^2 - 8*w - 7]', '[5131, 5131, -2*w^2 + 3*w - 5]', '[5136, 642, -2*w^2 - 6*w + 2]', '[5136, 642, -2*w^3 + 2*w^2 + 2*w - 6]', '[5137, 5137, -2*w^3 + 2*w^2 + 9*w - 14]', '[5137, 5137, -2*w^3 - 4*w^2 + 2*w - 1]', '[5139, 1713, -3*w^3 + 2*w^2 + 18*w + 3]', '[5139, 1713, 3*w^3 + w^2 - 19*w - 8]', '[5139, 1713, -4*w^3 + 25*w + 18]', '[5139, 1713, -4*w^3 - 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9*w - 38]', '[5219, 5219, -3*w^3 - w^2 + 13*w - 8]', '[5221, 5221, 9*w^3 - 19*w^2 - 42*w + 59]', '[5221, 5221, -5*w^3 + 5*w^2 + 19*w - 14]', '[5221, 5221, -4*w^3 + w^2 + 11*w - 5]', '[5221, 5221, w^3 - 7*w - 10]', '[5227, 5227, 3*w^3 - 3*w^2 - 8*w - 7]', '[5231, 5231, 3*w^3 - 7*w^2 - 13*w + 17]', '[5231, 5231, 4*w^2 + 3*w - 14]', '[5237, 5237, 2*w^3 - 3*w^2 - 10*w - 1]', '[5243, 5243, 3*w^3 - 6*w + 7]', '[5247, 1749, w^2 + 6]', '[5247, 1749, -3*w^3 + 2*w^2 + 5*w - 6]', '[5247, 1749, -w^3 - 3*w^2 - 3*w + 5]', '[5247, 1749, -3*w^3 - 5*w^2 + 14*w + 10]', '[5247, 1749, 6*w^3 - 2*w^2 - 21*w - 9]', '[5247, 1749, -w^3 - 6*w^2 + 10*w + 6]', '[5251, 5251, w^3 - 10*w - 2]', '[5251, 5251, 2*w^3 - w^2 - 8*w + 11]', '[5257, 5257, -4*w^3 + 3*w^2 + 20*w - 7]', '[5263, 5263, w^3 - w^2 - 2*w + 11]', '[5267, 5267, 5*w^3 - 10*w^2 - 24*w + 35]', '[5271, 5271, -w^3 + 8*w^2 - w - 28]', '[5271, 5271, 5*w^3 - 3*w^2 - 28*w + 18]', '[5273, 5273, 6*w^3 - 10*w^2 - 25*w + 29]', '[5277, 5277, 5*w^3 + 2*w^2 - 16*w - 10]', '[5277, 5277, 4*w^3 - w^2 - 10*w - 3]', '[5281, 5281, -2*w^3 + 15*w - 7]', '[5283, 1761, -2*w^3 + 7*w^2 + 2*w - 4]', '[5283, 1761, -5*w^2 - 3*w + 6]', '[5283, 1761, -2*w^3 - 3*w^2 + 2*w - 3]', '[5283, 1761, 3*w^3 + 4*w^2 - 14*w - 18]', '[5283, 1761, -2*w^3 - 3*w^2 + 15*w + 4]', '[5283, 1761, 4*w^3 - w^2 - 18*w + 3]', '[5283, 1761, -3*w^3 - 5*w^2 + 13*w + 21]', '[5283, 1761, -5*w^3 + 2*w^2 + 21*w - 6]', '[5283, 1761, 3*w^3 + w^2 - 16*w - 2]', '[5283, 1761, 2*w^3 + 4*w^2 - 9*w - 3]', '[5283, 1761, -3*w^3 + 5*w^2 + 10*w - 7]', '[5283, 1761, 3*w^3 + 5*w^2 - 10*w - 9]', '[5287, 5287, 2*w^3 + 8*w^2 - 12*w - 43]', '[5287, 5287, 5*w^3 - 3*w^2 - 19*w - 1]', '[5289, 5289, -w^3 + w^2 - 2*w + 9]', '[5289, 5289, -4*w^3 + 3*w^2 + 14*w - 2]', '[5299, 5299, -3*w^3 - 2*w^2 + 9*w - 5]', '[5299, 5299, w^3 + 7*w^2 - 13]', '[5301, 1767, -w^3 - w^2 + 4*w + 13]', '[5301, 1767, 2*w^2 - 9*w + 12]', '[5301, 1767, -4*w^3 + 6*w^2 + 13*w - 9]', '[5309, 5309, 5*w^2 - 22]', '[5313, 5313, 4*w^3 + w^2 - 23*w - 6]', '[5313, 5313, -3*w^3 + 5*w^2 + 9*w - 5]', '[5319, 591, 4*w^3 - 5*w^2 - 18*w + 24]', '[5319, 591, -4*w^3 + 7*w^2 + 17*w - 18]', '[5319, 1773, 2*w^3 - 3*w^2 - 6*w + 17]', '[5319, 1773, 4*w^3 + 3*w^2 - 12*w]', '[5321, 5321, -4*w^3 + w^2 + 17*w - 4]', '[5321, 5321, -6*w^3 + 6*w^2 + 23*w - 8]', '[5321, 5321, -2*w^3 + 3*w^2 + 4*w - 11]', '[5321, 5321, 4*w^3 - 2*w^2 - 20*w - 7]', '[5327, 5327, -7*w^3 + 3*w^2 + 32*w - 4]', '[5333, 5333, w^2 - 5*w - 11]', '[5337, 1779, w^2 + w + 6]', '[5337, 1779, -2*w^3 + 3*w^2 + 12*w + 1]', '[5337, 1779, -2*w^3 + 5*w^2 + 6*w - 6]', '[5337, 1779, w^2 - 8*w - 3]', '[5337, 1779, -2*w^3 + 5*w^2 - 3*w - 6]', '[5337, 1779, w^3 - 12*w - 8]', '[5339, 5339, 2*w^3 + w^2 - 5*w - 8]', '[5347, 5347, -w^3 + w^2 + 9*w - 4]', '[5349, 5349, -3*w^3 - 2*w^2 + 20*w + 9]', '[5349, 5349, 2*w^3 - 5*w^2 - 5*w + 2]', '[5351, 5351, 3*w^3 + w^2 - 9*w - 8]', '[5351, 5351, 3*w^3 - 6*w^2 - 14*w + 14]', '[5351, 5351, -w^3 + 4*w^2 + 6*w - 4]', '[5351, 5351, 6*w^3 - 6*w^2 - 25*w + 22]', '[5353, 5353, -4*w^3 + w^2 + 14*w - 2]', '[5353, 5353, -5*w^3 + 6*w^2 + 17*w - 10]', '[5353, 5353, 3*w^3 - 3*w^2 - 17*w + 14]', '[5353, 5353, 3*w^3 - w^2 - 17*w - 2]', '[5357, 5357, w^3 + w^2 + 3*w + 5]', '[5361, 5361, 5*w^2 - 3*w - 17]', '[5361, 5361, 2*w^3 + w^2 - 11*w + 6]', '[5361, 5361, 3*w^3 - w^2 - 17*w + 9]', '[5361, 5361, 5*w^2 - 11]', '[5367, 5367, -w^3 + 4*w^2 - 14]', '[5367, 5367, 2*w^3 - w^2 - 14*w + 9]', '[5371, 5371, 7*w^3 - 10*w^2 - 26*w + 29]', '[5373, 597, -8*w^3 + 10*w^2 + 33*w - 27]', '[5373, 597, w^3 - 7*w^2 - 2*w + 33]', '[5373, 597, -4*w^3 + w^2 + 14*w + 3]', '[5373, 597, -2*w^3 + w^2 + 3*w + 6]', '[5373, 1791, -10*w^3 + 5*w^2 + 46*w - 2]', '[5373, 1791, -2*w^3 - 3*w^2 - 3*w]', '[5373, 1791, 2*w^3 + 4*w^2 - 9*w - 15]', '[5373, 1791, -5*w^3 - 2*w^2 + 20*w + 14]', '[5376, 84, -4*w^3 + 4*w^2 + 16*w - 4]', '[5376, 84, -4*w + 12]', '[5377, 5377, -3*w^3 + 9*w^2 + 12*w - 31]', '[5377, 5377, -4*w^3 + 6*w^2 + 13*w - 28]', '[5381, 5381, -3*w^3 + 7*w^2 + 6*w - 8]', '[5381, 5381, 3*w^3 + w^2 - 15*w - 2]', '[5387, 5387, -2*w^3 - 4*w^2 + 7*w + 16]', '[5389, 5389, 2*w^3 + 4*w^2 - 11*w - 17]', '[5391, 1797, -3*w^3 + 2*w^2 + 3*w + 3]', '[5391, 1797, -5*w^3 - 3*w^2 + 15*w + 10]', '[5391, 1797, -4*w^3 + 10*w + 3]', '[5391, 1797, 4*w^3 - 13*w]', '[5391, 1797, -3*w^3 + 5*w^2 + w + 2]', '[5391, 1797, w^3 + 2*w^2 - 9]', '[5393, 5393, -3*w^3 - w^2 + 12*w - 1]', '[5403, 5403, -4*w^3 - 5*w^2 + 13*w + 12]', '[5403, 5403, -8*w^3 - 5*w^2 + 28*w + 13]', '[5407, 5407, -7*w^3 + 2*w^2 + 30*w + 7]', '[5407, 5407, 3*w^3 - 4*w^2 - 13*w + 20]', '[5411, 5411, -4*w^3 + 7*w^2 + 20*w - 29]', '[5417, 5417, -3*w^3 + 7*w^2 + 15*w - 17]', '[5417, 5417, 3*w^3 - 2*w^2 - 5*w - 4]', '[5424, 678, 6*w^3 - 32*w - 14]', '[5424, 678, -2*w^3 - 6*w^2 + 4*w + 2]', '[5424, 678, 2*w^3 + 2*w^2 - 14*w - 12]', '[5424, 678, -8*w^2 + 2*w + 6]', '[5427, 201, 6*w^3 - 3*w^2 - 24*w - 3]', '[5427, 603, 2*w^3 - w^2 - 3*w - 12]', '[5427, 603, -2*w^3 - w^2 + 15*w + 6]', '[5427, 603, -w^3 - 4*w^2 + 7*w + 13]', '[5427, 603, -2*w^3 - w^2 + 13*w - 3]', '[5433, 5433, w^3 - 2*w^2 - 5*w - 5]', '[5433, 5433, -3*w^3 + w^2 + 18*w + 5]', '[5433, 5433, 2*w^3 - 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4*w - 8]', '[5537, 5537, -2*w^3 - w^2 + 14*w + 14]', '[5543, 5543, 5*w^3 - 7*w^2 - 20*w + 17]', '[5543, 5543, -8*w^2 - 5*w + 22]', '[5547, 5547, -w^3 - 4*w^2 + 5*w + 12]', '[5547, 5547, -5*w^3 - w^2 + 21*w + 5]', '[5552, 694, -6*w^3 + 2*w^2 + 28*w - 2]', '[5553, 1851, 7*w^3 - 3*w^2 - 30*w + 6]', '[5553, 1851, 5*w^3 + 6*w^2 - 23*w - 30]', '[5553, 1851, -5*w^3 + 24*w + 4]', '[5553, 1851, 6*w^3 - 2*w^2 - 23*w + 6]', '[5553, 1851, -w^3 - w^2 + w + 10]', '[5553, 1851, -w^3 + 6*w^2 + 6*w - 21]', '[5557, 5557, w^3 + 3*w^2 - 7*w - 20]', '[5563, 5563, w^3 - w^2 - 4*w - 7]', '[5567, 5567, 2*w^3 - 3*w^2 - 14*w + 20]', '[5567, 5567, 4*w^3 - 7*w^2 - 20*w + 16]', '[5569, 5569, -4*w^3 + 3*w^2 + 21*w - 2]', '[5571, 1857, 3*w^3 - 4*w^2 - 10*w]', '[5571, 1857, 3*w^3 - w^2 - 14*w - 10]', '[5571, 1857, 2*w^3 - 5*w^2 - 3]', '[5571, 1857, w^2 - 7*w + 1]', '[5571, 1857, -w^3 + 4*w^2 + 9*w - 9]', '[5571, 1857, 2*w^3 - 2*w + 9]', '[5573, 5573, 3*w^2 - 4*w - 14]', '[5581, 5581, w^2 + 6*w - 2]', '[5581, 5581, 5*w^2 - 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11*w]', '[5613, 5613, -2*w^3 - 2*w^2 + 5*w + 9]', '[5617, 5617, w^3 - w^2 - 5*w - 7]', '[5617, 5617, 5*w^3 - 7*w^2 - 20*w + 29]', '[5625, 15, 5*w^2 - 15]', '[5625, 15, 5*w^3 - 20*w]', '[5625, 15, -5*w^2 + 5*w + 10]', '[5631, 5631, -w^3 - 2*w^2 + w - 4]', '[5631, 5631, -w^3 - 2*w^2 + 6*w + 16]', '[5631, 5631, w^3 - 5*w^2 - 4*w + 6]', '[5631, 5631, -4*w^3 + 5*w^2 + 16*w - 9]', '[5633, 5633, -w^3 - w^2 + w + 14]', '[5643, 627, 4*w^3 - 7*w^2 - 14*w + 15]', '[5643, 627, -2*w^3 - 5*w^2 + 6*w + 9]', '[5643, 1881, -w^3 + 2*w^2 + 4*w - 14]', '[5643, 1881, -2*w^3 - 3*w^2 + 9*w]', '[5648, 706, 2*w^3 - 4*w^2 - 12*w + 22]', '[5651, 5651, 9*w^3 - 15*w^2 - 34*w + 49]', '[5657, 5657, -2*w^3 - w^2 + 16*w - 8]', '[5659, 5659, -3*w^3 - 4*w^2 + 13*w + 16]', '[5659, 5659, w^3 + 3*w^2 - 13*w - 2]', '[5663, 5663, -3*w^3 + 7*w^2 + 16*w - 16]', '[5667, 5667, 3*w^3 - 5*w^2 - 4*w + 9]', '[5667, 5667, 2*w^3 + w^2 - 11*w + 3]', '[5667, 5667, w^2 + 6*w - 4]', '[5667, 5667, w^3 + 4*w^2 - 5*w - 11]', '[5671, 5671, w^3 - 2*w^2 - 3*w - 5]', '[5671, 5671, -5*w^3 + 5*w^2 + 17*w - 16]', '[5679, 1893, -w^3 + 7*w^2 + 6*w - 18]', '[5679, 1893, 5*w^3 - 17*w + 6]', '[5679, 1893, w^3 - 6*w^2 + 10]', '[5699, 5699, -2*w^3 - 4*w^2 + 11*w + 5]', '[5701, 5701, 6*w^3 - 8*w^2 - 22*w + 23]', '[5711, 5711, -4*w^3 + 7*w^2 + 20*w - 32]', '[5712, 714, -2*w^3 - 4*w^2 + 8*w + 10]', '[5712, 714, -2*w^3 - 2*w^2 + 10*w]', '[5717, 5717, -2*w^3 + 6*w^2 + 5*w - 23]', '[5719, 5719, 5*w^3 - w^2 - 21*w - 14]', '[5723, 5723, -4*w^3 - 3*w^2 + 13*w + 11]', '[5723, 5723, w^3 + 2*w^2 - w - 10]', '[5737, 5737, -5*w^3 + 11*w^2 + 15*w - 26]', '[5737, 5737, -4*w^3 + 2*w^2 + 14*w - 5]', '[5741, 5741, 2*w^3 - 4*w^2 - 4*w + 13]', '[5743, 5743, -2*w^3 + 2*w^2 + 13*w - 1]', '[5747, 5747, -3*w^3 + 2*w^2 + 4*w - 5]', '[5749, 5749, 5*w^3 - 11*w^2 - 19*w + 37]', '[5757, 5757, 4*w^3 - 4*w^2 - 13*w + 10]', '[5757, 5757, -2*w^3 + 4*w^2 + 4*w - 21]', '[5757, 5757, -4*w^3 + w^2 + 19*w - 3]', '[5757, 5757, -2*w^3 + w^2 + 13*w - 5]', '[5761, 5761, -4*w^3 + 5*w^2 + 11*w - 5]', '[5761, 5761, -2*w^3 + 9*w^2 + 11*w - 25]', '[5763, 5763, 6*w^3 + w^2 - 28*w - 21]', '[5763, 5763, -w^3 + 2*w^2 - 5*w]', '[5763, 5763, -3*w^2 + 5*w + 11]', '[5763, 5763, -w^3 + 9*w^2 - w - 8]', '[5769, 1923, -4*w^3 + 13*w + 3]', '[5769, 1923, -2*w^3 + 3*w + 6]', '[5769, 1923, -2*w^3 + 6*w^2 + 3*w - 17]', '[5773, 5773, -8*w^3 + 11*w^2 + 31*w - 34]', '[5776, 722, 4*w^3 - 10*w + 2]', '[5779, 5779, -w^3 + w^2 + 4*w - 11]', '[5783, 5783, 3*w^3 + 2*w^2 - 16*w - 5]', '[5789, 5789, 6*w^3 + w^2 - 19*w + 5]', '[5789, 5789, 5*w^3 - 2*w^2 - 22*w + 5]', '[5791, 5791, 8*w^3 - 10*w^2 - 32*w + 29]', '[5791, 5791, 5*w^2 - 5*w - 11]', '[5793, 5793, 2*w^3 + 2*w^2 - 16*w - 7]', '[5793, 5793, -w^3 - 5*w^2 + 7*w + 8]', '[5793, 5793, -w^3 + 6*w^2 - 7*w - 9]', '[5793, 5793, 5*w^3 - 19*w - 12]', '[5797, 5797, -w^3 - 4*w^2 + 6*w + 13]', '[5799, 5799, -w^3 + 6*w^2 - w - 15]', '[5799, 5799, -4*w^3 + 6*w^2 + 8*w - 9]', '[5799, 5799, 4*w^3 - 20*w - 1]', '[5799, 5799, -w^3 - w^2 - w + 8]', '[5803, 5803, w^3 + 5*w^2 - 5*w - 8]', '[5803, 5803, w^3 + 4*w^2 - 6*w - 10]', '[5807, 5807, 7*w^3 - 6*w^2 - 32*w + 19]', '[5807, 5807, -5*w^3 + 9*w^2 + 23*w - 35]', '[5808, 726, -2*w^3 - 4*w^2 + 8*w + 12]', '[5808, 726, 2*w^3 + 4*w^2 - 2*w - 10]', '[5817, 5817, -3*w^2 + 10*w - 3]', '[5817, 5817, w^3 - 4*w^2 + 2*w + 10]', '[5819, 5819, -2*w^3 + 4*w^2 + 11*w - 5]', '[5821, 5821, 4*w^3 + 4*w^2 - 21*w - 14]', '[5821, 5821, 2*w^3 + w^2 - 13*w - 16]', '[5823, 1941, -3*w^3 + w^2 + 8*w + 7]', '[5823, 1941, 6*w^3 + w^2 - 23*w - 6]', '[5823, 1941, 2*w^3 + 3*w^2 - 6*w - 12]', '[5827, 5827, 2*w^3 + w^2 - 10*w - 14]', '[5827, 5827, -w^3 + 3*w^2 - 6*w - 2]', '[5831, 119, 3*w^3 - w^2 - 18*w + 11]', '[5831, 5831, 3*w^3 - 2*w^2 - 7*w - 7]', '[5833, 5833, 11*w^3 - 9*w^2 - 50*w + 19]', '[5833, 5833, -4*w^3 + 6*w^2 + 7*w - 8]', '[5833, 5833, -2*w^3 + 8*w^2 + 7*w - 29]', '[5833, 5833, 2*w^3 - 9*w - 11]', '[5841, 1947, -w^2 - 6*w + 3]', '[5841, 1947, 3*w^3 + 4*w^2 - 7*w + 1]', '[5841, 1947, 7*w^2 + w - 9]', '[5843, 5843, 5*w^3 - 3*w^2 - 20*w - 7]', '[5847, 5847, 7*w^3 + 2*w^2 - 27*w - 13]', '[5847, 5847, 4*w^3 + w^2 - 13*w - 9]', '[5851, 5851, -4*w^3 + 2*w^2 + 17*w + 10]', '[5853, 5853, 2*w^3 + 5*w^2 - 11*w - 9]', '[5853, 5853, 4*w^3 - 5*w^2 - 10*w + 3]', '[5853, 5853, 5*w^3 + 4*w^2 - 21*w - 11]', '[5853, 5853, 3*w^3 - 10*w - 10]', '[5857, 5857, -w^2 + 2*w - 7]', '[5859, 651, 2*w^3 - 2*w^2 - 10*w + 15]', '[5859, 651, -w^3 + 5*w^2 - 18]', '[5859, 1953, 3*w^3 - 2*w^2 - 18*w + 12]', '[5859, 1953, -3*w^3 + 5*w^2 + 13*w - 10]', '[5861, 5861, -w^3 + 2*w^2 - w - 8]', '[5867, 5867, 5*w^2 - 4*w - 25]', '[5873, 5873, -2*w^3 + 2*w^2 + 3*w - 8]', '[5873, 5873, -5*w^3 + 10*w^2 + 18*w - 37]', '[5877, 1959, -5*w^3 + 3*w^2 + 20*w - 3]', '[5877, 1959, 3*w^3 - w^2 - 14*w + 8]', '[5877, 1959, -2*w^2 - 3*w + 15]', '[5877, 1959, 5*w^3 + w^2 - 18*w]', '[5877, 1959, -3*w^3 - 2*w^2 + 14*w + 4]', '[5877, 1959, 5*w^3 + 6*w^2 - 17*w - 18]', '[5879, 5879, 5*w^3 - 7*w^2 - 23*w + 17]', '[5881, 5881, -4*w^3 + 2*w^2 + 14*w + 1]', '[5888, 92, -4*w^3 + 4*w^2 + 12*w - 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10]', '[9903, 9903, 4*w^3 - w^2 - 10*w]', '[9903, 9903, 4*w^3 + 3*w^2 - 11*w - 10]', '[9904, 1238, -2*w^3 + 4*w^2 + 12*w - 26]', '[9904, 1238, -4*w^3 + 2*w^2 + 12*w - 4]', '[9907, 9907, 4*w^3 + 2*w^2 - 25*w - 7]', '[9907, 9907, 2*w^3 - w^2 - 14*w - 1]', '[9911, 9911, -5*w^3 + w^2 + 19*w - 7]', '[9911, 9911, 3*w^3 + w^2 - 20*w - 14]', '[9913, 9913, 7*w^3 - 3*w^2 - 25*w + 13]', '[9921, 9921, -5*w^3 - 2*w^2 + 16*w - 2]', '[9921, 9921, -w^3 - 5*w^2 + 4*w + 12]', '[9921, 9921, -5*w^3 - 2*w^2 + 19*w + 4]', '[9921, 9921, -7*w^2 - 2*w + 15]', '[9923, 9923, 5*w^3 - 6*w^2 - 20*w + 11]', '[9923, 9923, 2*w^3 - 2*w - 7]', '[9931, 9931, 3*w^3 - 2*w^2 - 17*w + 5]', '[9931, 9931, -7*w^3 + 4*w^2 + 28*w + 1]', '[9933, 9933, -6*w^3 - 4*w^2 + 27*w + 19]', '[9933, 9933, -4*w^3 - 2*w^2 + 19*w + 6]', '[9936, 138, 4*w^3 + 2*w^2 - 14*w - 12]', '[9936, 138, 4*w^3 - 2*w^2 - 12*w]', '[9936, 414, -4*w^3 + 2*w^2 + 22*w - 8]', '[9936, 414, 2*w^3 - 2*w^2 - 6]', '[9951, 9951, w^3 + 5*w^2 - 6*w - 10]', '[9951, 9951, w^3 + 4*w^2 - 10*w]', '[9959, 9959, -8*w^3 + 17*w^2 + 37*w - 50]', '[9961, 9961, -4*w^2 + w - 2]', '[9961, 9961, w^2 + 7*w - 2]', '[9963, 369, 6*w^3 + 3*w^2 - 18*w - 6]', '[9963, 369, 2*w^3 - 5*w^2 - 4*w + 18]', '[9963, 369, 4*w^3 - 2*w^2 - 9*w + 3]', '[9963, 369, 3*w^3 + 3*w^2 - 6*w - 9]', '[9963, 1107, -4*w^3 + 3*w^2 + 21*w - 4]', '[9963, 1107, -3*w^3 - 2*w^2 + 15*w + 3]', '[9967, 9967, 3*w^3 - 2*w^2 - 17*w + 4]', '[9967, 9967, -5*w^3 + 5*w^2 + 18*w - 11]', '[9968, 1246, -6*w^3 + 6*w^2 + 26*w - 26]', '[9968, 1246, 2*w^3 - 6*w^2 - 8*w + 10]', '[9969, 9969, -3*w^3 - 3*w^2 + 19*w + 6]', '[9969, 9969, 6*w^3 - 37*w - 19]', '[9969, 9969, 4*w^3 - 5*w^2 - 8*w + 4]', '[9969, 9969, 2*w^3 + 2*w^2 - 19*w - 12]', '[9973, 9973, -4*w^3 + 4*w^2 + 11*w - 7]', '[9973, 9973, w^3 - 4*w^2 - 3*w + 22]', '[9979, 9979, 6*w^3 - w^2 - 31*w - 2]', '[9979, 9979, -7*w^3 + 3*w^2 + 34*w - 2]', '[9979, 9979, 4*w^3 - 3*w^2 - 12*w + 2]', '[9979, 9979, -3*w^3 - 3*w^2 + 6*w - 4]', '[9983, 9983, -5*w^3 + 3*w^2 + 20*w - 16]', '[9983, 9983, 3*w^3 - 9*w - 10]', '[9987, 9987, 2*w^3 + 8*w^2 - 19*w - 12]', '[9987, 9987, 3*w^3 - 3*w^2 - 14*w - 8]', '[9987, 9987, 6*w^3 + 6*w^2 - 31*w - 19]', '[9987, 9987, 3*w^3 - 6*w^2 - 8*w]', '[9989, 9989, 3*w^3 + w^2 - 14*w + 1]', '[9993, 9993, -w^3 + 5*w^2 + 5*w - 4]', '[9993, 9993, 4*w^2 - 4*w + 3]', '[9999, 3333, -2*w^3 + 2*w^2 + 6*w - 15]', '[9999, 3333, -w^3 + 2*w^2 + w + 7]', '[9999, 3333, 3*w^3 - 5*w^2 - 17*w + 6]', '[9999, 3333, -w^3 - 5*w^2 + 6*w + 18]', '[9999, 3333, 5*w^3 - w^2 - 17*w + 4]', '[9999, 3333, 4*w^2 + 4*w - 15]', '[10000, 10, -10]'], 'label': '4.4.12357.1', 'narrow_class_no': 2, 'primes': ['[3, 3, w]', '[3, 3, w + 1]', '[7, 7, -w^2 + 2]', '[11, 11, -w^2 - w + 1]', '[16, 2, 2]', '[17, 17, -w^2 + w + 4]', '[19, 19, -w^3 + w^2 + 5*w - 2]', '[23, 23, -w^3 + w^2 + 3*w - 4]', '[31, 31, w^3 - w^2 - 3*w + 1]', '[41, 41, -w^3 + 4*w - 1]', '[43, 43, w^3 + w^2 - 5*w - 4]', '[53, 53, w^3 - w^2 - 4*w - 1]', '[53, 53, -w^2 - w + 4]', '[59, 59, -w^3 + 4*w - 2]', '[67, 67, -2*w^3 + w^2 + 8*w + 1]', '[89, 89, -2*w^3 + 3*w^2 + 8*w - 8]', '[89, 89, w^3 - 5*w + 1]', '[97, 97, w^3 - 6*w - 1]', '[97, 97, -w^3 + 3*w^2 + 4*w - 10]', '[101, 101, -w^3 + 6*w - 2]', '[101, 101, -w^3 + 2*w^2 + 3*w - 8]', '[107, 107, w^3 - 2*w^2 - 4*w + 4]', '[113, 113, 2*w^3 - w^2 - 9*w - 1]', '[113, 113, -w^3 + w^2 + w - 2]', '[127, 127, w - 4]', '[131, 131, -2*w^3 + 4*w^2 + 6*w - 11]', '[137, 137, 3*w^3 - 5*w^2 - 11*w + 16]', '[137, 137, w^3 + w^2 - 7*w - 5]', '[139, 139, -2*w^3 + 3*w^2 + 6*w - 7]', '[149, 149, w^2 - 2*w - 4]', '[149, 149, w^2 + w - 7]', '[151, 151, -w^3 + 2*w^2 + 6*w - 4]', '[151, 151, -2*w^3 + w^2 + 7*w + 2]', '[157, 157, -w^3 + 3*w^2 + 2*w - 7]', '[167, 167, w^3 - 2*w^2 - 3*w + 2]', '[167, 167, w^3 - w - 2]', '[181, 181, 2*w^2 - w - 4]', '[191, 191, w^2 - 2*w - 7]', '[197, 197, -w^3 + w^2 + 2*w - 4]', '[199, 199, 2*w^3 - w^2 - 10*w + 1]', '[199, 199, w^3 + 2*w^2 - 5*w - 4]', '[223, 223, 2*w^2 - w - 5]', '[223, 223, w^3 - w^2 - 6*w + 4]', '[227, 227, w^3 + w^2 - 5*w - 1]', '[227, 227, 2*w^3 - 10*w - 1]', '[227, 227, -2*w^3 + 4*w^2 + 9*w - 11]', '[227, 227, 3*w^3 - 3*w^2 - 13*w + 10]', '[229, 229, -w^3 + 3*w^2 + 3*w - 8]', '[239, 239, -w^3 + 3*w^2 + 3*w - 5]', '[239, 239, w^3 + w^2 - 4*w - 8]', '[241, 241, w^3 - 2*w^2 - 3*w + 10]', '[241, 241, w^3 + 2*w^2 - 4*w - 7]', '[251, 251, 2*w^3 - w^2 - 10*w + 4]', '[277, 277, 3*w - 1]', '[281, 281, 2*w^3 - 3*w^2 - 8*w + 7]', '[283, 283, w^3 - 2*w^2 - 6*w + 5]', '[283, 283, 2*w^3 - 2*w^2 - 7*w + 5]', '[293, 293, 2*w^3 - w^2 - 8*w + 5]', '[293, 293, -w^3 + w^2 + 2*w - 5]', '[307, 307, 2*w^2 - w - 11]', '[307, 307, 2*w^3 - 2*w^2 - 7*w + 4]', '[307, 307, 3*w^3 - 3*w^2 - 12*w + 7]', '[307, 307, 2*w^3 - 2*w^2 - 11*w + 13]', '[311, 311, 3*w^2 - 2*w - 13]', '[311, 311, w^3 + w^2 - 6*w - 1]', '[313, 313, -w^3 + 7*w - 2]', '[313, 313, 2*w^3 + 2*w^2 - 11*w - 10]', '[313, 313, 3*w^3 - 4*w^2 - 11*w + 10]', '[313, 313, -2*w^3 + 6*w - 1]', '[317, 317, w^3 + w^2 - 3*w - 5]', '[343, 7, 2*w^3 - 3*w^2 - 5*w + 5]', '[347, 347, -3*w^3 + w^2 + 14*w - 1]', '[349, 349, 2*w^3 - 5*w^2 - 7*w + 17]', '[349, 349, w^3 - 7*w - 2]', '[349, 349, 3*w^3 - 3*w^2 - 12*w + 8]', '[349, 349, 3*w^3 - 12*w - 2]', '[353, 353, w^3 - 2*w^2 - 6*w + 11]', '[373, 373, -w^3 + w^2 + 3*w - 7]', '[379, 379, 2*w^3 - 11*w - 2]', '[379, 379, -2*w^3 + 2*w^2 + 6*w - 5]', '[383, 383, -2*w^3 + w^2 + 9*w - 4]', '[389, 389, 2*w^3 - 8*w + 1]', '[409, 409, w^3 + 2*w^2 - 5*w - 5]', '[409, 409, -w^3 + 4*w^2 + 2*w - 13]', '[419, 419, 2*w^2 + w - 8]', '[431, 431, -3*w^3 + 13*w + 2]', '[433, 433, 2*w^3 - 3*w^2 - 10*w + 8]', '[439, 439, -2*w^3 + 2*w^2 + 10*w - 5]', '[457, 457, -2*w^3 + w^2 + 7*w - 1]', '[467, 467, -w^3 + 2*w^2 + 4*w - 1]', '[467, 467, -3*w^3 + 5*w^2 + 10*w - 11]', '[487, 487, w^3 - 7*w - 1]', '[499, 499, -3*w^3 + 2*w^2 + 11*w + 1]', '[499, 499, w^3 + 2*w^2 - 5*w - 7]', '[503, 503, w^3 - 2*w^2 - 5*w + 2]', '[509, 509, -4*w^3 + 5*w^2 + 18*w - 20]', '[571, 571, -3*w^3 + 12*w + 4]', '[571, 571, 2*w^3 - 5*w^2 - 8*w + 16]', '[571, 571, 2*w^3 + 2*w^2 - 9*w - 7]', '[571, 571, 3*w^3 - 2*w^2 - 11*w + 7]', '[587, 587, w^3 + 2*w^2 - 5*w - 1]', '[587, 587, 2*w^3 - 2*w^2 - 8*w + 1]', '[587, 587, -2*w^3 + 2*w^2 + 9*w - 2]', '[587, 587, 2*w^3 - w^2 - 9*w + 5]', '[593, 593, -4*w^3 + 6*w^2 + 16*w - 17]', '[593, 593, -w^3 + 3*w^2 + w - 8]', '[599, 599, -w^2 - 2*w + 7]', '[599, 599, -w^3 + 2*w^2 - 4]', '[607, 607, -2*w^3 + 2*w^2 + 5*w - 1]', '[607, 607, -w^3 + w^2 + 5*w - 8]', '[613, 613, -w - 5]', '[617, 617, 3*w^3 - 2*w^2 - 14*w + 1]', '[617, 617, -w^3 + 2*w^2 + 2*w - 8]', '[619, 619, -w^3 + 2*w^2 + 6*w - 13]', '[619, 619, -2*w^3 + w^2 + 6*w - 2]', '[625, 5, -5]', '[631, 631, -w^3 + 4*w - 5]', '[641, 641, w^3 - 3*w^2 - 5*w + 13]', '[647, 647, w^2 - 3*w - 5]', '[653, 653, w^3 - 4*w^2 + w + 8]', '[653, 653, w^3 - 2*w^2 - 6*w + 1]', '[659, 659, w^3 - 2*w - 5]', '[661, 661, 3*w^2 - 2*w - 10]', '[673, 673, -5*w^3 + 8*w^2 + 17*w - 22]', '[683, 683, -w^3 - w^2 + 6*w - 1]', '[683, 683, w^3 + 2*w^2 - 6*w - 2]', '[701, 701, 2*w^2 - 3*w - 7]', '[709, 709, -3*w^3 + 4*w^2 + 10*w - 8]', '[727, 727, w^3 - w^2 - 7*w + 5]', '[727, 727, w^3 - w^2 - 5*w - 4]', '[733, 733, 3*w^2 - 3*w - 7]', '[751, 751, -2*w^3 + 5*w^2 + 6*w - 14]', '[757, 757, 3*w^2 - 7]', '[757, 757, -w^3 + 3*w - 5]', '[761, 761, -2*w^3 + 5*w^2 + 6*w - 17]', '[773, 773, -3*w^3 + 6*w^2 + 10*w - 19]', '[787, 787, 3*w^3 - 3*w^2 - 11*w + 5]', '[809, 809, -4*w^3 + 2*w^2 + 17*w - 5]', '[821, 821, w^3 - w - 4]', '[823, 823, -2*w^3 + 3*w^2 + 7*w - 14]', '[823, 823, -2*w^3 - w^2 + 13*w + 2]', '[827, 827, 2*w^3 - 4*w^2 - 6*w + 13]', '[827, 827, 2*w^3 - 3*w^2 - 11*w + 4]', '[829, 829, w^3 - w^2 - 4*w - 4]', '[829, 829, -2*w^3 + 9*w + 8]', '[839, 839, w^3 + w^2 - 3*w - 7]', '[839, 839, -6*w^3 + 8*w^2 + 26*w - 29]', '[859, 859, -w^3 + 9*w + 4]', '[859, 859, w^3 + 3*w^2 - 6*w - 13]', '[863, 863, 3*w^2 - 5*w - 7]', '[863, 863, 2*w^3 - 7*w - 7]', '[877, 877, 4*w - 1]', '[881, 881, -3*w^2 + 14]', '[881, 881, 3*w^3 - 3*w^2 - 14*w + 5]', '[883, 883, 3*w^3 - 4*w^2 - 12*w + 17]', '[887, 887, -w^3 + w^2 + w - 5]', '[911, 911, w^3 - 4*w^2 - 2*w + 16]', '[919, 919, -4*w^3 + 5*w^2 + 19*w - 19]', '[919, 919, -4*w^3 + 2*w^2 + 17*w - 2]', '[941, 941, w^3 - w^2 - w + 8]', '[941, 941, -5*w^3 + 6*w^2 + 21*w - 16]', '[947, 947, 3*w^3 - 3*w^2 - 12*w + 4]', '[953, 953, w^2 - 3*w - 8]', '[967, 967, -w^3 + 2*w^2 + 7*w - 7]', '[971, 971, 3*w^3 - 5*w^2 - 12*w + 13]', '[977, 977, -2*w^3 + 3*w^2 + 6*w - 13]', '[983, 983, 2*w^3 - 6*w - 5]', '[997, 997, -w^3 + w^2 + 7*w - 2]']}
• 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': [3, 3, -5, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 12357, 'disc_rad': 4119, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [0]], [5, [[4, 1]]], [7, [[3, 1], [1, 1]]], [11, [[3, 1], [1, 1]]], [13, [[4, 1]]], [17, [[3, 1], [1, 1]]], [19, [[3, 1], [1, 1]]], [23, [[3, 1], [1, 1]]], [29, [[4, 1]]], [31, [[3, 1], [1, 1]]], [37, [[2, 2]]], [41, [[3, 1], [1, 1]]], [43, [[3, 1], [1, 1]]], [47, [[4, 1]]], [53, [[2, 1], [1, 2]]], [59, [[3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 64.17943595888016, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.12357.1', 'local_algs': ['3.2.1.2', '3.2.1.1', 'm1373.1.1.0', 'm1373.1.1.0', 'm1373.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 1373], 'rd': 10.5433412105, 'regulator': {'__RealLiteral__': 0, 'data': '7.5176275835', 'prec': 40}, 'res': {'gal': ['17839,127651,-2920397,14063406,-23342535,-7568638,60299204,-33423132,-48154558,45784479,15994273,-25688718,-1124164,7861581,-755408,-1417179,244646,152139,-33016,-9416,2274,306,-77,-4,1'], 'sib': ['-1024,-244,733,45,-55,-1,1', '-37,-447,2486,-2137,-3319,4001,660,-1486,100,170,-23,-6,1', '3,-10,0,19,-7,-3,1', '313,-1639,1691,2052,-4554,1867,1115,-1013,80,118,-27,-3,1', '4912,1976,-6236,-2830,1149,283,-86,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a^{3} - 2 a^{2} - 4 a + 7 \\)', '\\( a^{2} + a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}