Hilbert modular form data - 4.4.9301.1-21.1-a

Formats: - HTML - YAML - JSON - 2024-05-18T17:54:00.191350

• 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': 9301, 'field_bad_primes': [71, 131], 'field_label': '4.4.9301.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.9301.1-21.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [3, 7], 'level_ideal': '[21, 21, -w^3 + w^2 + 5*w]', 'level_label': '21.1', 'level_norm': 21, 'parallel_weight': 2, 'short_label': '21.1-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], ['[7, 7, -w^2 + 2]', 1]], 'hecke_eigenvalues': [1, 0, -1, -2, -5, 6, 0, -2, -2, -4, -10, 10, 2, -4, 0, 6, -6, 4, -14, -12, -8, -18, -12, -2, 18, -18, 12, -12, -12, -20, 20, -20, -4, 6, -12, -2, -18, -28, -8, 0, -14, 20, -6, 24, 12, -20, 12, 6, 6, 24, 18, 18, -16, 10, 20, -20, -10, 28, -2, 26, -6, -22, 14, -24, 6, 16, 4, -24, -14, 34, 12, -30, -20, 32, 28, 10, 16, 2, -12, -12, 12, 14, -2, 6, -2, -14, 26, -6, 18, -36, -28, -20, 12, 24, 30, 36, -38, 4, -30, 36, 8, 20, 38, -16, 30, 6, -12, 18, -6, 22, -32, -46, -36, 14, 34, 42, -6, 4, -8, -40, -22, -42, 24, 44, -28, -8, -46, 34, 34, -36, -16, -12, -18, 46, 42, 6, -52, 30, -30, -42, 18, 36, 20, -54, 48, 50, 52, -28, 28, 12, 24, -48, 18, -42, -6, -54, -42, -36, -10, 26, -56, -30, 12, -60, -4, 2, 20, -12, -24, -26, -18, 18, 28, 16, 14, -22, -16, -44, 58, 56, -24, -30, 16, -10, -42, -24, 34, 28, -48, -6, -30, 30, -50, -2, 26, 50, 2, 42, -18, 2, -6, -22, 4, 52, 42, 46, 72, -36, -50, -6, 60, -18, -40, 4, 62, -2, -44, -34, -54, -44, -62, -34, -10, -24, -48, -22, -14, 18, -36, 24, 12, 14, -72, 32, 56, 0, 66, 38, -64, 30, 24, -62, -66, 30, 26, 34, 52, 4, 16, 12, 10, -26, 2, -18, 52, -18, 42, 42, 10, -26, 22, 40, -66, -62, -34, -60, -42, -18, 14, 18, -50, -20, -62, 60, 72, 2, -42, -42, 30, 78, -78, 66, 18, -46, 54, 78, -18, 36, -8, 26, 18, -18, 16, -16], 'hecke_polynomial': 'x', 'label': '4.4.9301.1-21.1-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 9301, 'ideals': ['[1, 1, 1]', '[3, 3, w]', '[5, 5, -w^3 + w^2 + 4*w + 1]', '[7, 7, -w^2 + 2]', '[7, 7, -w^2 + w + 2]', '[9, 9, -w^2 + w + 3]', '[15, 15, -w^2 + 2*w + 3]', '[16, 2, 2]', '[17, 17, -w^3 + w^2 + 4*w - 2]', '[21, 21, -w^3 + w^2 + 5*w]', '[21, 21, w^2 - 2*w]', '[23, 23, -w^3 + 2*w^2 + 3*w - 2]', '[25, 25, -w^3 + w^2 + 3*w - 1]', '[27, 3, -w^3 + w^2 + 5*w - 1]', '[27, 27, -w^3 + w^2 + 3*w]', '[35, 35, -w^2 + 4]', '[35, 35, -w^3 + 5*w + 2]', '[37, 37, -w^3 + 4*w + 1]', '[37, 37, -w^3 + w^2 + 2*w + 1]', '[45, 45, w^2 - 3*w]', '[48, 6, 2*w]', '[49, 7, -w^3 + 2*w^2 + 2*w - 4]', '[49, 7, -w^3 + 3*w^2 + 2*w - 4]', '[49, 49, w^3 - 2*w^2 - 3*w + 1]', '[49, 49, -w^3 + 3*w^2 - 4]', '[51, 51, -w^2 - w + 3]', '[61, 61, -w^3 + 2*w^2 + 4*w - 2]', '[61, 61, -w^3 + 3*w^2 + 2*w - 7]', '[63, 63, w + 3]', '[63, 63, -w^3 + w^2 + 4*w + 3]', '[67, 67, w^2 - 3*w - 2]', '[69, 69, w^3 - 2*w^2 - w + 3]', '[71, 71, -w^2 + 5]', '[71, 71, 2*w^3 - w^2 - 9*w - 2]', '[71, 71, w^2 - 2*w - 5]', '[75, 75, -w^2 + w + 6]', '[79, 79, w^2 - 3*w - 1]', '[79, 79, w^3 - 6*w - 1]', '[80, 10, -2*w^3 + 2*w^2 + 8*w + 2]', '[81, 3, 3]', '[81, 81, 2*w - 3]', '[85, 85, w^2 + 1]', '[89, 89, -w^3 + 3*w^2 + 3*w - 7]', '[97, 97, -w^3 + 2*w^2 + 2*w - 5]', '[101, 101, -w^3 + 3*w^2 + 2*w - 5]', '[105, 105, -w^3 + 4*w]', '[105, 105, -w^3 + 3*w^2 + 2*w - 6]', '[107, 107, 2*w^3 - 2*w^2 - 9*w - 1]', '[109, 109, -w^3 + 5*w + 1]', '[111, 111, w^3 + w^2 - 2*w - 3]', '[111, 111, -3*w^2 + 2*w + 3]', '[112, 14, -2*w^2 + 4]', '[112, 14, -2*w^2 + 2*w + 4]', '[115, 115, w^3 - 2*w^2 - 5*w + 1]', '[119, 119, -w^3 + 2*w^2 + 4*w - 1]', '[119, 119, w - 4]', '[125, 5, 2*w^3 - w^2 - 8*w - 2]', '[125, 125, -w^3 + 4*w + 5]', '[131, 131, -2*w^3 + 3*w^2 + 7*w - 2]', '[131, 131, 2*w^2 - 3*w - 7]', '[131, 131, 2*w^3 - 3*w^2 - 6*w + 2]', '[135, 15, -w^3 + w^2 + 2*w + 2]', '[135, 135, -2*w^3 + 2*w^2 + 8*w - 3]', '[137, 137, w^3 - 2*w^2 - 3*w + 7]', '[139, 139, w^3 - 4*w + 2]', '[144, 18, -2*w^2 + 2*w + 6]', '[147, 21, 2*w^3 - 3*w^2 - 3*w + 3]', '[147, 21, 2*w^3 - 2*w^2 - 9*w + 3]', '[147, 147, w^3 - 4*w - 6]', '[147, 147, -2*w^2 + w + 6]', '[151, 151, w^2 + w - 4]', '[153, 153, -2*w^3 + 3*w^2 + 8*w - 3]', '[157, 157, 2*w^2 - 2*w - 5]', '[157, 157, w^3 - 2*w^2 - 5*w + 7]', '[161, 161, -2*w^2 + 3*w + 2]', '[161, 161, -w^3 + 4*w - 1]', '[173, 173, 2*w^3 - 3*w^2 - 6*w + 4]', '[175, 175, -w^3 + 3*w^2 - 5]', '[175, 175, 2*w^3 - 4*w^2 - 6*w + 5]', '[179, 179, 2*w^3 - 3*w^2 - 9*w + 4]', '[181, 181, w^3 + w^2 - 7*w - 4]', '[183, 183, 2*w^3 - 3*w^2 - 6*w + 3]', '[183, 183, w^3 - w^2 - w + 3]', '[185, 185, -3*w^3 + 3*w^2 + 10*w + 4]', '[185, 185, 2*w^3 + w^2 - 11*w - 10]', '[189, 21, -2*w^3 + 2*w^2 + 7*w - 2]', '[189, 21, -2*w^3 + 2*w^2 + 7*w + 1]', '[189, 189, 2*w^3 - 4*w^2 - 5*w + 3]', '[189, 189, 2*w^3 - 4*w^2 - 7*w + 6]', '[197, 197, w^3 - 3*w^2 - w + 7]', '[201, 201, w^3 - 3*w^2 - 2*w]', '[207, 207, -w^3 + 6*w]', '[213, 213, w^3 - 2*w^2 - 5*w]', '[213, 213, w^3 + w^2 - 4*w - 6]', '[213, 213, -w^3 + 5*w]', '[223, 223, 3*w^3 - 4*w^2 - 11*w + 4]', '[223, 223, -w^3 + w^2 + 4*w - 5]', '[225, 225, -w^3 + w^2 + 6*w]', '[227, 227, 2*w^3 - 2*w^2 - 9*w - 2]', '[229, 229, w^3 - w^2 - 6*w + 2]', '[229, 229, 4*w^3 - 6*w^2 - 14*w + 7]', '[233, 233, 2*w^3 - 3*w^2 - 5*w + 1]', '[237, 237, w^3 - 3*w^2 - w]', '[237, 237, -w^3 + w^2 + 2*w + 3]', '[239, 239, -w - 4]', '[239, 239, -2*w^3 + 4*w^2 + 5*w - 8]', '[240, 30, -2*w^2 + 4*w + 6]', '[241, 241, -2*w^3 + w^2 + 10*w + 1]', '[243, 9, 3*w]', '[243, 243, -w^3 + 7*w + 3]', '[245, 35, w^3 - 7*w - 1]', '[245, 35, 2*w^2 - 4*w - 1]', '[245, 245, 2*w^3 - 3*w^2 - 9*w + 5]', '[245, 245, -w^2 + 3*w + 5]', '[251, 251, -w^3 + 2*w^2 + 2*w - 8]', '[251, 251, -2*w^3 + 5*w^2 + 5*w - 8]', '[255, 255, -2*w^3 + 2*w^2 + 7*w]', '[256, 4, 4]', '[257, 257, 2*w^3 - 2*w^2 - 7*w + 1]', '[259, 259, -3*w^2 - 4*w + 1]', '[259, 259, w^3 - 2*w^2 - 6*w - 2]', '[259, 259, w^3 + w + 2]', '[259, 259, w^3 - 3*w^2 + 3*w + 5]', '[263, 263, w^3 - 4*w^2 - 4*w + 7]', '[267, 267, 2*w^3 - 2*w^2 - 6*w + 3]', '[269, 269, w^2 + 2*w - 4]', '[269, 269, 2*w^2 - 7]', '[271, 271, 2*w^3 - 3*w^2 - 7*w + 1]', '[271, 271, w^2 + 3*w - 2]', '[271, 271, 3*w^3 - 5*w^2 - 11*w + 13]', '[271, 271, -2*w^3 + 3*w^2 + 9*w - 2]', '[272, 34, -2*w^3 + 2*w^2 + 8*w - 4]', '[277, 277, w^2 - w - 7]', '[277, 277, 3*w^3 - 4*w^2 - 13*w + 5]', '[277, 277, -w^3 + w^2 + 3*w - 5]', '[277, 277, w^3 - 3*w - 4]', '[281, 281, w^3 - 2*w^2 - 2*w - 2]', '[283, 283, w^2 + 3*w - 1]', '[283, 283, w^3 - w^2 - 2*w - 4]', '[289, 289, -w^3 + 7*w + 2]', '[291, 291, w^3 - 3*w^2 - 4*w + 3]', '[293, 293, 3*w^3 - 4*w^2 - 12*w + 8]', '[293, 293, w^2 + w - 5]', '[303, 303, 2*w^3 - 3*w^2 - 4*w + 3]', '[305, 305, 3*w^3 - w^2 - 16*w - 4]', '[305, 305, -w^3 + 5*w + 7]', '[307, 307, 2*w^3 - 2*w^2 - 6*w - 1]', '[307, 307, -w^2 - 2]', '[311, 311, -w^3 + 5*w - 1]', '[313, 313, 2*w^3 - 2*w^2 - 8*w - 5]', '[313, 313, -2*w^3 + 3*w^2 + 5*w - 2]', '[315, 315, -2*w^2 + 3*w + 9]', '[315, 315, 2*w^3 - 3*w^2 - 5*w + 3]', '[317, 317, 2*w^3 - 2*w^2 - 9*w + 4]', '[317, 317, w^3 - 2*w^2 - 3*w - 2]', '[321, 321, w^2 - 3*w - 6]', '[327, 327, -w^3 + 2*w + 3]', '[331, 331, -w^3 + 2*w^2 + w - 5]', '[333, 333, -2*w^2 + 5*w + 6]', '[333, 333, 2*w^3 - 2*w^2 - 10*w - 3]', '[335, 335, w^3 + 3*w^2 - 11*w - 11]', '[336, 42, -2*w^3 + 2*w^2 + 10*w]', '[336, 42, 2*w^2 - 4*w]', '[337, 337, -2*w^3 + 3*w^2 + 5*w - 7]', '[337, 337, w^3 - 4*w^2 - w + 5]', '[343, 7, w^3 - 4*w^2 + 1]', '[343, 7, -w^3 - w^2 + 3*w - 2]', '[343, 49, 2*w^2 + 2*w - 5]', '[343, 49, w^3 - w^2 - w - 2]', '[343, 343, w^3 + w^2 - 4*w - 1]', '[343, 343, w^3 - 5*w + 2]', '[345, 345, -2*w^2 + 5*w + 3]', '[349, 349, -2*w^3 + w^2 + 11*w + 1]', '[355, 355, -w^2 + 4*w + 2]', '[355, 355, 5*w^3 + w^2 - 27*w - 23]', '[355, 355, 4*w^3 - w^2 - 21*w - 11]', '[357, 357, w^2 - 4*w]', '[357, 357, -w^3 - w^2 + 5*w + 9]', '[367, 367, -2*w^3 + 2*w^2 + 8*w - 5]', '[368, 46, -2*w^3 + 4*w^2 + 6*w - 4]', '[375, 15, w^3 + 2*w^2 - 4*w - 6]', '[375, 375, -w^3 - w^2 + 6*w + 3]', '[379, 379, -w^3 + 2*w^2 - 4]', '[383, 383, -3*w^3 + 6*w^2 + 9*w - 14]', '[383, 383, w - 5]', '[389, 389, 4*w^3 - 6*w^2 - 14*w + 11]', '[391, 391, 2*w^3 - 5*w^2 - 6*w + 10]', '[393, 393, w^3 - 3*w^2 + 6]', '[393, 393, -w^3 + 4*w^2 - 6]', '[393, 393, 2*w^3 - 3*w^2 - 7*w]', '[395, 395, 4*w^2 - 7*w - 10]', '[395, 395, -2*w^3 - 3*w^2 + 15*w + 16]', '[397, 397, -2*w^3 + w^2 + 11*w - 1]', '[397, 397, -3*w^3 + 2*w^2 + 12*w + 1]', '[400, 50, -2*w^3 + 2*w^2 + 6*w - 2]', '[401, 401, 3*w - 7]', '[405, 15, -3*w^3 + 3*w^2 + 12*w + 3]', '[405, 405, -2*w^2 - w + 6]', '[409, 409, w^2 - 4*w - 1]', '[411, 411, -w^3 + 2*w^2 + 6*w - 3]', '[417, 417, -2*w^3 + 4*w^2 + 5*w - 9]', '[421, 421, -2*w^3 + 4*w^2 + 7*w - 5]', '[421, 421, -2*w^3 + 4*w^2 + 4*w - 7]', '[425, 425, -2*w^3 + 3*w^2 + 7*w + 1]', '[427, 427, -w^3 - w^2 + 5*w + 2]', '[427, 427, w^3 - w^2 - 3*w - 5]', '[427, 427, -2*w^3 + 6*w - 1]', '[427, 427, -w^3 + 2*w^2 + 3*w - 8]', '[432, 6, -2*w^3 + 2*w^2 + 10*w - 2]', '[432, 54, -2*w^3 + 2*w^2 + 6*w]', '[441, 63, -w^2 + 2*w - 3]', '[441, 63, w^2 + w - 6]', '[441, 441, w^3 + w^2 - 7*w - 3]', '[441, 441, -2*w^3 + w^2 + 6*w]', '[443, 443, 2*w^3 - 2*w^2 - 10*w + 1]', '[445, 445, 3*w^3 - 2*w^2 - 14*w - 1]', '[449, 449, -w^3 - w^2 + 2*w - 2]', '[453, 453, w^3 + w^2 - 4*w]', '[459, 51, 2*w^3 - 5*w^2 - 7*w + 14]', '[459, 459, w^3 - 2*w^2 - w + 6]', '[461, 461, 3*w^3 - 3*w^2 - 12*w + 4]', '[463, 463, -2*w^3 + 2*w^2 + 6*w - 1]', '[463, 463, -3*w^2 + 5*w + 4]', '[467, 467, w^2 + w - 10]', '[467, 467, 3*w^3 - 3*w^2 - 14*w + 1]', '[469, 469, 3*w^3 - 4*w^2 - 7*w - 1]', '[469, 469, 2*w^3 - w^2 - 5*w - 1]', '[471, 471, -w^3 + 6*w - 3]', '[471, 471, 2*w^3 - 2*w^2 - 5*w]', '[479, 479, -2*w^3 + w^2 + 6*w + 1]', '[483, 483, -3*w^2 + 5*w + 9]', '[483, 483, w^3 - 3*w^2 - w + 9]', '[485, 485, 2*w^3 - w^2 - 11*w - 2]', '[491, 491, w^3 + 2*w^2 - 7*w - 8]', '[497, 497, w^3 - 2*w^2 - w + 7]', '[497, 497, w^3 + 2*w^2 - 3*w - 7]', '[497, 497, -2*w^2 + 4*w + 7]', '[497, 497, 2*w^3 - 3*w^2 - 11*w - 1]', '[497, 497, 2*w^3 - 8*w - 7]', '[497, 497, 3*w^3 - 2*w^2 - 15*w - 7]', '[499, 499, 4*w^3 - 5*w^2 - 16*w + 8]', '[499, 499, w^3 - 3*w - 5]', '[503, 503, -w^3 + 3*w^2 + w - 10]', '[503, 503, w^3 - 3*w^2 - 4*w + 1]', '[505, 505, w^3 + w^2 - 8*w - 2]', '[519, 519, -w^3 + 4*w^2 + 2*w - 6]', '[523, 523, -w^3 + 4*w - 4]', '[525, 525, -w^3 - 2*w^2 + 7*w + 9]', '[525, 525, 2*w^3 - 5*w^2 - 4*w + 3]', '[529, 529, w^2 - 3*w + 4]', '[535, 535, 5*w^3 - 26*w - 22]', '[537, 537, -w^3 + w^2 + 2*w - 6]', '[541, 541, w^3 - 5*w^2 + 2*w + 10]', '[543, 543, 2*w^3 - 2*w^2 - 5*w - 3]', '[545, 545, -2*w^3 - 2*w^2 + 13*w + 13]', '[547, 547, -3*w^3 + 6*w^2 + 11*w - 10]', '[547, 547, -3*w^3 + 6*w^2 + 7*w - 10]', '[549, 549, 2*w^2 - w - 12]', '[549, 549, -2*w^3 + w^2 + 9*w]', '[553, 553, -3*w^3 + 4*w^2 + 10*w + 2]', '[553, 553, 2*w^3 - 2*w^2 - 5*w + 1]', '[553, 553, 3*w^3 - 5*w^2 - 6*w + 1]', '[553, 553, -2*w^3 + 3*w^2 + 8*w - 1]', '[555, 555, -5*w^2 + 7*w + 9]', '[555, 555, 3*w^3 - w^2 - 12*w - 6]', '[557, 557, -w^3 + 3*w^2 + 4*w - 10]', '[557, 557, 3*w^2 - 6*w - 8]', '[557, 557, -w^3 + 4*w^2 - 11]', '[557, 557, -2*w^3 + 4*w^2 + 5*w - 11]', '[560, 70, -2*w^2 + 8]', '[560, 70, -2*w^3 + 10*w + 4]', '[567, 21, -3*w^2 + 6]', '[567, 21, -3*w^2 + 3*w + 6]', '[567, 567, -3*w^3 + 3*w^2 + 11*w - 3]', '[567, 567, -w^3 - 2*w^2 + 6*w + 9]', '[569, 569, w^3 + w^2 - 6*w - 11]', '[571, 571, 3*w^3 - 4*w^2 - 10*w + 2]', '[571, 571, w^3 - 3*w^2 - 5*w + 2]', '[575, 575, -w^2 - 2*w + 5]', '[577, 577, 2*w^3 - w^2 - 7*w + 4]', '[587, 587, 2*w^3 - 11*w - 4]', '[591, 591, -2*w^3 + 4*w^2 + 6*w - 3]', '[592, 74, -2*w^3 + 8*w + 2]', '[592, 74, -2*w^3 + 2*w^2 + 4*w + 2]', '[595, 595, w^3 - 2*w^2 + w - 2]', '[595, 595, -w^2 + 2*w + 8]', '[603, 603, 3*w^3 - 3*w^2 - 10*w - 3]', '[607, 607, 2*w^3 - 3*w^2 - 9*w + 1]', '[613, 613, -3*w^3 + 3*w^2 + 14*w - 5]', '[617, 617, 2*w^3 - 3*w^2 - 8*w + 10]', '[617, 617, 3*w^3 - 5*w^2 - 8*w + 10]', '[621, 69, w^3 - w^2 - 5*w - 5]', '[621, 621, -w^3 + w^2 + w + 3]', '[623, 623, -w - 5]', '[623, 623, -2*w^3 + 2*w^2 + 5*w - 8]', '[625, 5, 5]', '[625, 625, w^3 - 2*w + 4]', '[629, 629, 4*w + 1]', '[629, 629, -w^3 + w^2 + w - 7]', '[639, 639, 5*w^3 - 3*w^2 - 24*w - 9]', '[639, 639, 2*w^3 + w^2 - 10*w - 12]', '[639, 639, -w^3 + w + 3]', '[643, 643, -w^3 + w^2 + 7*w + 1]', '[643, 643, w^3 + 2*w^2 - 6*w - 8]', '[655, 655, 5*w^3 - 28*w - 16]', '[655, 655, -3*w^3 + w^2 + 13*w + 13]', '[655, 655, 3*w^3 - 2*w^2 - 11*w - 10]', '[661, 661, -3*w^3 + 5*w^2 + 8*w - 7]', '[669, 669, -w^3 + 4*w^2 + w - 9]', '[669, 669, -w^2 - 4*w + 3]', '[673, 673, -3*w^3 + 3*w^2 + 13*w - 4]', '[675, 75, w^3 - 4*w^2 - 2*w + 10]', '[675, 675, w^2 + w + 3]', '[679, 679, w^3 - 2*w - 4]', '[679, 679, 3*w^2 + 2*w - 7]', '[681, 681, w^2 - 4*w - 6]', '[683, 683, -w^3 + 2*w^2 - 5]', '[683, 683, w^3 - w^2 - 4*w - 5]', '[685, 685, -w^3 - w^2 + 5*w + 1]', '[687, 687, 3*w^3 - 3*w^2 - 11*w + 6]', '[687, 687, -w^2 + w - 3]', '[691, 691, w^3 + w^2 - 6*w - 2]', '[691, 691, -w^3 + 3*w^2 - 7]', '[695, 695, -w^3 + 4*w^2 + w - 7]', '[699, 699, w^3 - 5*w^2 + w + 6]', '[707, 707, -w^3 + 3*w - 4]', '[707, 707, w^3 - 3*w^2 - w - 1]', '[709, 709, w^2 - w - 8]', '[711, 711, -4*w^3 + 4*w^2 + 16*w + 3]', '[711, 711, 3*w^3 - 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11]', '[1757, 1757, 6*w^2 + 2*w - 13]', '[1757, 1757, -2*w^3 + w^2 + 7*w - 7]', '[1757, 1757, w^3 + 3*w^2 - 5*w - 10]', '[1757, 1757, w^3 - 4*w^2 + w - 1]', '[1759, 1759, w^3 + 2*w^2 - 8*w - 4]', '[1761, 1761, 2*w^3 - w^2 - 6*w - 6]', '[1773, 1773, 2*w^3 - 4*w^2 - w + 6]', '[1775, 1775, -3*w^3 + 5*w^2 + 12*w - 5]', '[1775, 1775, 2*w^2 - 5*w - 13]', '[1775, 1775, 3*w^3 - w^2 - 12*w - 1]', '[1776, 222, 2*w^3 + 2*w^2 - 4*w - 6]', '[1776, 222, -6*w^2 + 4*w + 6]', '[1777, 1777, 2*w^3 + w^2 - 15*w - 10]', '[1785, 1785, 4*w^3 - 7*w^2 - 12*w + 6]', '[1785, 1785, -w^3 + 2*w^2 + 8*w]', '[1787, 1787, w^3 - w^2 - 8*w - 1]', '[1789, 1789, 2*w^3 - 4*w^2 - 4*w + 11]', '[1792, 28, -4*w^2 + 8]', '[1792, 28, -4*w^2 + 4*w + 8]', '[1799, 1799, w^3 - 9*w - 4]', '[1799, 1799, w^3 - 3*w^2 - 8*w + 2]', '[1801, 1801, -w^3 + 5*w^2 - w - 16]', '[1809, 201, 2*w^3 - 2*w^2 - 7*w - 7]', '[1809, 1809, 5*w^2 - 6*w - 9]', '[1811, 1811, 2*w^3 - 3*w^2 - 5*w - 5]', '[1813, 259, -w^3 + 5*w^2 + 5*w - 5]', '[1813, 259, -3*w^3 + 2*w^2 + 9*w - 2]', '[1813, 259, 5*w^3 - 5*w^2 - 23*w + 1]', '[1813, 259, -w^3 + 6*w^2 - w - 7]', '[1813, 1813, -w^3 - 3*w^2 + 5*w + 8]', '[1813, 1813, 4*w^3 - 6*w^2 - 7*w + 1]', '[1813, 1813, -3*w^3 + 3*w^2 + 9*w + 1]', '[1813, 1813, -4*w^3 + 14*w^2 - 2*w - 13]', '[1817, 1817, -3*w^3 + 8*w^2 + 2*w - 10]', '[1817, 1817, 2*w^3 - 7*w^2 - w + 13]', '[1819, 1819, -w^3 + 6*w^2 + w - 19]', '[1821, 1821, -w^3 + w^2 - w - 6]', '[1823, 1823, 3*w^2 - 11]', '[1823, 1823, w - 7]', '[1831, 1831, w^3 - 2*w^2 - 3*w - 4]', '[1835, 1835, w^3 - 5*w^2 + 13]', '[1839, 1839, -w^2 - 2*w + 9]', '[1840, 230, 2*w^3 - 4*w^2 - 10*w + 2]', '[1841, 1841, w^3 + 2*w^2 - 2*w + 2]', '[1841, 1841, 4*w^3 + w^2 - 8*w + 5]', '[1847, 1847, -w^3 - w^2 + 9*w - 2]', '[1849, 43, 6*w^3 - 9*w^2 - 21*w + 11]', '[1849, 43, -2*w^3 + w^2 + 9*w - 5]', '[1851, 1851, -2*w^3 + 7*w^2 + 7*w - 9]', '[1851, 1851, -w^3 + 2*w^2 + 8*w - 6]', '[1853, 1853, w^3 - 2*w^2 - 2*w + 10]', '[1861, 1861, 2*w^3 - 3*w^2 - 11*w + 2]', '[1863, 69, -3*w^3 + 6*w^2 + 9*w - 6]', '[1863, 1863, -4*w^3 + 5*w^2 + 15*w]', '[1869, 1869, 6*w^3 - 7*w^2 - 23*w + 9]', '[1869, 1869, -4*w^3 + 8*w^2 + 13*w - 12]', '[1871, 1871, 5*w - 1]', '[1871, 1871, 3*w^3 - 6*w^2 - 14*w + 13]', '[1873, 1873, 2*w^3 - 11*w - 2]', '[1875, 15, 5*w^3 - 25*w - 15]', '[1875, 1875, -4*w^3 + 4*w^2 + 15*w - 3]', '[1877, 1877, w^2 - 5*w + 8]', '[1877, 1877, 3*w^3 - 2*w^2 - 6*w + 7]', '[1883, 1883, w^2 - 5*w - 8]', '[1883, 1883, -3*w^3 + w^2 + 5*w - 5]', '[1883, 1883, -2*w^3 + w^2 + 2*w - 8]', '[1883, 1883, -2*w^3 + 3*w^2 + w - 5]', '[1887, 1887, 4*w^2 + w]', '[1887, 1887, -4*w^2 - 6*w + 3]', '[1889, 1889, 2*w^3 - w^2 - 9*w + 4]', '[1895, 1895, w^3 + 2*w^2 - 11*w - 7]', '[1897, 1897, w^3 + 3*w^2 - 10*w - 7]', '[1897, 1897, -3*w^3 + 2*w^2 + 5*w - 1]', '[1897, 1897, 2*w^3 - 9*w - 1]', '[1897, 1897, -4*w^3 - w^2 + 7*w - 1]', '[1897, 1897, -3*w^3 + 13*w + 5]', '[1897, 1897, -4*w^3 + w^2 + 13*w - 1]', '[1897, 1897, 2*w^3 - 6*w^2 - 5*w + 11]', '[1897, 1897, -3*w^3 + 4*w^2 + 8*w - 2]', '[1901, 1901, -w^3 - w^2 + 7*w - 1]', '[1901, 1901, -3*w^3 + 3*w^2 + 12*w - 8]', '[1901, 1901, -2*w^3 + 6*w^2 + 5*w - 13]', '[1901, 1901, -4*w^3 + 3*w^2 + 15*w - 1]', '[1904, 238, -2*w^3 + 4*w^2 + 8*w - 2]', '[1904, 238, 2*w - 8]', '[1915, 1915, 3*w^3 - 4*w^2 - 8*w + 4]', '[1915, 1915, 5*w^3 - 6*w^2 - 18*w - 2]', '[1917, 213, -2*w^3 + 5*w^2 + 7*w - 5]', '[1917, 213, 2*w^3 + 4*w^2 - 13*w - 25]', '[1917, 213, 5*w^3 - 5*w^2 - 22*w - 1]', '[1917, 1917, 2*w^3 + w^2 - 14*w - 15]', '[1917, 1917, 3*w^3 - 14*w - 6]', '[1917, 1917, -3*w^3 + 4*w^2 + 12*w]', '[1929, 1929, 3*w^3 - w^2 - 9*w - 3]', '[1929, 1929, -2*w^2 - 2*w - 3]', '[1933, 1933, -3*w^3 + 2*w^2 + 10*w + 2]', '[1939, 1939, w^3 + 3*w^2 - 8*w - 11]', '[1939, 1939, 4*w^3 - 3*w^2 - 16*w - 2]', '[1939, 1939, 4*w^2 - w - 7]', '[1939, 1939, 2*w^2 - 7*w - 8]', '[1939, 1939, 4*w^2 - w - 11]', '[1939, 1939, 5*w^3 - 5*w^2 - 18*w + 7]', '[1939, 1939, 6*w^2 + 3*w - 10]', '[1939, 1939, -w^3 - 2*w - 5]', '[1945, 1945, -2*w^3 + 3*w^2 + 3*w - 7]', '[1949, 1949, 3*w^3 - 3*w^2 - 15*w - 5]', '[1949, 1949, -w^3 + 5*w^2 + 2*w - 8]', '[1955, 1955, -3*w^3 + 2*w^2 + 15*w - 2]', '[1965, 1965, -2*w^3 - 2*w^2 + 16*w + 9]', '[1965, 1965, w^3 + 4*w^2 - 13*w - 9]', '[1965, 1965, 5*w^3 - 3*w^2 - 21*w - 15]', '[1967, 1967, -w^3 + 7*w^2 - 5*w - 10]', '[1967, 1967, 4*w^2 - 2*w - 7]', '[1973, 1973, -w^3 + w^2 + 5*w - 8]', '[1975, 1975, w^3 - 4*w^2 + w + 11]', '[1975, 1975, -w^3 + 5*w^2 - 8]', '[1979, 1979, -2*w^3 + 5*w^2 + 3*w - 11]', '[1981, 1981, -4*w^3 - 2*w^2 + 7*w + 1]', '[1981, 1981, -3*w^3 + w^2 + 6*w + 1]', '[1981, 1981, -w^3 + 3*w^2 - w - 8]', '[1981, 1981, -w^3 + 6*w^2 - 6*w - 11]', '[1983, 1983, 2*w^3 - 7*w^2 - 4*w + 9]', '[1985, 1985, -6*w^3 - w^2 + 31*w + 28]', '[1985, 1985, -2*w^3 - 6*w^2 + 19*w + 26]', '[1987, 1987, -w^3 + w^2 - 3*w - 1]', '[1993, 1993, -2*w^3 + 6*w^2 + 2*w - 13]', '[1997, 1997, -4*w^3 + 8*w^2 + 10*w - 7]', '[1997, 1997, w^3 - w - 5]', '[1999, 1999, -w^3 + 2*w^2 - w - 11]', '[1999, 1999, w^2 - 10]', '[2000, 10, 4*w^3 - 2*w^2 - 16*w - 4]', '[2000, 250, -2*w^3 + 8*w + 10]', '[2005, 2005, 7*w^3 - 10*w^2 - 22*w + 2]', '[2007, 2007, 3*w^3 - 4*w^2 - 8*w + 3]', '[2007, 2007, -2*w^3 + 6*w^2 + 5*w - 12]', '[2017, 2017, 4*w^3 - 7*w^2 - 16*w + 10]', '[2019, 2019, -2*w^2 - w + 9]', '[2023, 2023, w^3 - 5*w^2 - 3*w + 11]', '[2023, 2023, -3*w^3 + 2*w^2 + 10*w + 1]', '[2025, 75, -3*w^3 + 3*w^2 + 9*w - 3]', '[2025, 2025, -4*w^3 + 3*w^2 + 16*w + 3]', '[2029, 2029, -w^3 + 5*w^2 + 7*w - 11]', '[2029, 2029, -w^3 + 3*w^2 + 8*w - 7]', '[2037, 2037, -4*w^3 + 7*w^2 + 10*w - 9]', '[2037, 2037, 4*w^3 - 6*w^2 - 17*w + 6]', '[2039, 2039, -w^3 + 5*w^2 + 2*w - 13]', '[2039, 2039, -3*w^3 + 4*w^2 + 7*w - 4]', '[2043, 2043, 5*w^3 - w^2 - 25*w - 12]', '[2045, 2045, 5*w^2 - 9*w - 13]', '[2047, 2047, 4*w^3 - 5*w^2 - 16*w + 11]', '[2049, 2049, w^3 - 5*w^2 - 4*w + 3]', '[2049, 2049, w^2 - 6*w - 3]', '[2051, 2051, -w^3 + 3*w^2 - 2*w - 7]', '[2051, 2051, 3*w^3 - 5*w^2 - 11*w + 4]', '[2051, 2051, -2*w^3 + 2*w^2 + 3*w - 7]', '[2051, 2051, 4*w^3 - 8*w^2 - 16*w + 13]', '[2055, 2055, -3*w^2 + 5*w + 12]', '[2061, 2061, -3*w^3 + 8*w^2 + 7*w - 24]', '[2061, 2061, 4*w^3 - 5*w^2 - 14*w + 3]', '[2073, 2073, 2*w^3 - 5*w^2 - 6*w + 3]', '[2073, 2073, 2*w^3 - w^2 - 3*w - 3]', '[2081, 2081, w^3 - 9*w + 2]', '[2085, 2085, 3*w^3 - 4*w^2 - 6*w + 3]', '[2087, 2087, 2*w^3 - 6*w^2 - w + 11]', '[2096, 262, -4*w^3 + 6*w^2 + 14*w - 4]', '[2096, 262, 4*w^2 - 6*w - 14]', '[2096, 262, 4*w^3 - 6*w^2 - 12*w + 4]', '[2097, 2097, -w^3 - 2*w^2 + 11*w + 6]', '[2099, 2099, -2*w - 7]', '[2105, 2105, -w^3 + 4*w + 10]', '[2105, 2105, w^3 + w^2 - 10*w - 1]', '[2111, 2111, -4*w^3 + 5*w^2 + 11*w + 2]', '[2111, 2111, 5*w^3 - 5*w^2 - 20*w + 2]', '[2113, 2113, w^3 - w^2 - 3*w - 7]', '[2113, 2113, -3*w^3 + 7*w^2 + 4*w - 10]', '[2121, 2121, 4*w^3 - 5*w^2 - 14*w + 6]', '[2121, 2121, -5*w^3 + 12*w^2 + 9*w - 12]', '[2125, 85, -w^3 + 3*w^2 - w - 14]', '[2125, 2125, -3*w^3 + 3*w^2 + 15*w - 1]', '[2127, 2127, w^3 - w^2 - 8*w]', '[2129, 2129, -w^3 + 5*w^2 + w - 8]', '[2129, 2129, -w^2 + 2*w - 5]', '[2133, 237, w^3 - w^2 - 2*w - 8]', '[2133, 237, -w^3 - 2*w^2 + 5*w + 17]', '[2133, 2133, -4*w^2 + 7*w + 12]', '[2133, 2133, -w^3 + 6*w^2 - 3*w - 9]', '[2135, 2135, -3*w^3 + 8*w^2 + 7*w - 22]', '[2135, 2135, -w^3 - 3*w^2 + 6*w + 11]', '[2135, 2135, 5*w^3 - 5*w^2 - 21*w - 2]', '[2135, 2135, -4*w^3 + 4*w^2 + 14*w - 5]', '[2137, 2137, w^3 + w^2 - 3*w - 8]', '[2137, 2137, 5*w^3 - 7*w^2 - 17*w + 5]', '[2149, 2149, w^3 + 5*w^2 - w - 7]', '[2149, 2149, -w^2 - 6*w - 2]', '[2149, 2149, 5*w^2 - 3*w - 7]', '[2149, 2149, 3*w^2 - 9*w - 8]', '[2151, 2151, -w^3 + 3*w^2 + 5*w - 12]', '[2151, 2151, w^3 + 3*w^2 - 7*w - 12]', '[2160, 30, -2*w^3 + 2*w^2 + 4*w + 4]', '[2160, 270, -4*w^3 + 4*w^2 + 16*w - 6]', '[2161, 2161, 2*w^3 - 4*w^2 - 9*w + 2]', '[2161, 2161, 2*w^3 - w^2 - 11*w + 4]', '[2169, 2169, -6*w^3 + 5*w^2 + 26*w + 6]', '[2177, 2177, -w^3 + 5*w^2 + 6*w - 5]', '[2177, 2177, -2*w^3 + 5*w^2 + 6*w - 2]', '[2181, 2181, 2*w^3 - 3*w^2 - 2*w + 6]', '[2187, 9, -3*w^3 + 3*w^2 + 15*w - 3]', '[2187, 81, -3*w^3 + 3*w^2 + 9*w]', '[2187, 2187, 3*w^3 - 7*w^2 - 7*w + 6]', '[2191, 2191, w^2 + 5*w - 1]', '[2191, 2191, 2*w^3 + 5*w^2 - 17*w - 16]', '[2191, 2191, 2*w^3 + 3*w^2 - 10*w - 10]', '[2191, 2191, w^3 - 4*w^2 + 5*w + 5]', '[2192, 274, 2*w^3 - 4*w^2 - 6*w + 14]', '[2199, 2199, -2*w^3 + 8*w^2 - w - 9]', '[2203, 2203, -w^3 + 3*w^2 + 6*w - 10]', '[2205, 315, -w^3 + 3*w^2 - 4*w - 3]', '[2205, 315, -7*w^3 + 16*w^2 + 10*w - 15]', '[2205, 2205, 5*w^3 - 6*w^2 - 19*w + 6]', '[2205, 2205, -2*w^2 + 2*w - 3]', '[2209, 47, -6*w^3 + 7*w^2 + 25*w - 4]', '[2209, 47, -2*w^3 + 12*w + 1]', '[2213, 2213, -4*w^2 + 2*w + 17]', '[2215, 2215, 3*w^3 + 3*w^2 - 20*w - 23]', '[2217, 2217, 3*w^3 - 4*w^2 - 7*w + 3]', '[2219, 2219, 3*w^3 - 5*w^2 - 10*w + 2]', '[2219, 2219, w^3 + 4*w^2 - 4*w - 7]', '[2219, 2219, 6*w^2 - 7*w - 10]', '[2219, 2219, 3*w^3 - 6*w^2 - 12*w + 8]', '[2221, 2221, 2*w^3 - w^2 - 11*w - 10]', '[2224, 278, 2*w^3 - 8*w + 4]', '[2225, 2225, 3*w^3 - 6*w^2 - 14*w + 10]', '[2227, 2227, 3*w^3 - 8*w^2 - 8*w + 19]', '[2227, 2227, 5*w^3 - 6*w^2 - 19*w + 5]', '[2227, 2227, -3*w^3 + 7*w^2 + 7*w - 16]', '[2229, 2229, -w^3 + 5*w - 6]', '[2231, 2231, 2*w^3 - 3*w^2 - 11*w + 7]', '[2243, 2243, 3*w^3 - 5*w^2 - 4*w + 7]', '[2243, 2243, 3*w^3 - 4*w^2 - 15*w - 1]', '[2245, 2245, 2*w^3 - 4*w^2 - 8*w + 1]', '[2247, 2247, w^3 - 5*w^2 + 12]', '[2247, 2247, 3*w^3 + 3*w^2 - 20*w - 27]', '[2251, 2251, 4*w^2 - 3*w - 13]', '[2251, 2251, -w^3 + 2*w^2 - w - 7]', '[2253, 2253, 3*w^3 - 3*w^2 - 7*w]', '[2257, 2257, 3*w^3 - 2*w^2 - 7*w - 1]', '[2257, 2257, -4*w^3 + 8*w^2 + 15*w - 13]', '[2257, 2257, 2*w^3 + w^2 - 13*w - 5]', '[2257, 2257, 4*w^3 - 5*w^2 - 17*w + 2]', '[2259, 2259, -w^3 + w^2 + 6*w - 9]', '[2259, 2259, 5*w^2 - 3*w - 18]', '[2265, 2265, 4*w^2 - 4*w - 9]', '[2267, 2267, -w^3 + w^2 + 8*w - 2]', '[2273, 2273, -5*w^2 + 7*w + 11]', '[2283, 2283, w^3 + 3*w^2 - 5*w]', '[2287, 2287, -3*w^3 + 3*w^2 + 9*w - 2]', '[2289, 2289, w^3 - 3*w^2 - 3]', '[2289, 2289, -2*w^3 - 2*w^2 + 10*w + 15]', '[2293, 2293, 3*w^3 - 3*w^2 - 15*w + 2]', '[2293, 2293, -w^3 + 4*w^2 + 4*w - 13]', '[2293, 2293, 4*w^3 - 4*w^2 - 15*w + 2]', '[2293, 2293, 3*w^3 - 2*w^2 - 9*w + 1]', '[2295, 255, -w^3 + w^2 + 8*w - 1]', '[2295, 2295, -3*w^3 + w^2 + 17*w + 6]', '[2304, 36, -4*w^2 + 4*w + 12]', '[2305, 2305, 2*w^3 + 4*w^2 - 14*w - 23]', '[2309, 2309, w^3 - w^2 - 5]', '[2309, 2309, -2*w^3 + 5*w^2 + 8*w - 16]', '[2311, 2311, 2*w^3 - w^2 - 10*w + 4]', '[2311, 2311, 4*w^2 - 3*w - 8]', '[2313, 2313, 3*w^3 - 2*w^2 - 16*w - 3]', '[2315, 2315, -w^3 - 7*w^2 + 17*w + 19]', '[2315, 2315, -3*w^3 + w^2 + 12*w + 11]', '[2317, 2317, w^3 + 3*w^2 - 7]', '[2317, 2317, 2*w^3 - w^2 - 4*w - 4]', '[2319, 2319, 3*w^3 - w^2 - 8*w]', '[2323, 2323, w^3 + w^2 - 9*w + 4]', '[2329, 2329, -2*w^3 + 8*w + 11]', '[2331, 2331, 4*w^3 + w^2 - 19*w - 12]', '[2331, 2331, -5*w^3 + 5*w^2 + 14*w + 6]', '[2331, 2331, 4*w^3 + w^2 - 14*w - 6]', '[2331, 2331, -3*w^3 + 8*w + 6]', '[2333, 2333, 4*w^3 - 5*w^2 - 14*w + 5]', '[2335, 2335, 9*w^3 - 9*w^2 - 35*w - 7]', '[2335, 2335, 2*w^3 - 7*w - 8]', '[2341, 2341, -2*w^3 + 5*w^2 + 8*w - 17]', '[2341, 2341, 2*w^3 - 6*w^2 - 9*w + 8]', '[2345, 2345, 2*w^3 + w^2 - 11*w - 5]', '[2345, 2345, 4*w^3 - 2*w^2 - 15*w - 10]', '[2347, 2347, -3*w^3 + 4*w^2 + 7*w - 10]', '[2347, 2347, -3*w^3 + 3*w^2 + 9*w - 1]', '[2352, 42, 4*w^3 - 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6*w^2 + 4*w + 2]', '[2401, 49, -5*w^3 + 13*w^2 - 5]', '[2401, 343, -w^2 + 6*w - 1]', '[2401, 343, 5*w^3 - 6*w^2 - 20*w + 10]', '[2401, 2401, -2*w^3 + 5*w^2 + 3*w + 1]', '[2401, 2401, 3*w^3 - w^2 - 16*w - 2]', '[2403, 267, 7*w^3 - 10*w^2 - 26*w + 16]', '[2403, 2403, 2*w^3 - 3*w^2 - 11*w + 3]', '[2411, 2411, 3*w^3 - 2*w^2 - 13*w + 2]', '[2411, 2411, 5*w^2 - 7*w - 7]', '[2415, 2415, w^3 - 5*w^2 - 2*w + 9]', '[2415, 2415, -3*w^3 + 3*w^2 + 8*w]', '[2416, 302, 2*w^2 + 2*w - 8]', '[2417, 2417, w^3 + 2*w^2 - 5*w - 19]', '[2421, 2421, 3*w^2 - 5*w - 15]', '[2421, 2421, -2*w^3 + 4*w^2 + 3*w - 9]', '[2425, 2425, 3*w^3 - 2*w^2 - 11*w + 5]', '[2427, 2427, -w^3 + 4*w^2 - 7*w - 9]', '[2433, 2433, 3*w^3 - 4*w^2 - 13*w]', '[2437, 2437, 6*w^3 - 8*w^2 - 21*w + 4]', '[2439, 2439, 5*w^3 - 11*w^2 - 16*w + 24]', '[2439, 2439, -5*w^3 + 3*w^2 + 22*w + 3]', '[2439, 2439, 3*w^3 - 17*w - 6]', '[2439, 2439, -3*w^3 + 3*w^2 + 8*w - 3]', '[2441, 2441, 2*w^2 - 5*w - 10]', '[2441, 2441, w^3 - 7*w - 10]', '[2443, 2443, -4*w^3 + 4*w^2 + 15*w - 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25*w - 6]', '[5943, 5943, 3*w^3 - 11*w^2 + 7*w + 6]', '[5949, 5949, -2*w^3 + 2*w^2 + 13*w - 6]', '[5953, 5953, -3*w^3 + 3*w^2 + 4*w - 7]', '[5955, 5955, -8*w^3 + 9*w^2 + 28*w + 6]', '[5955, 5955, -7*w^3 + w^2 + 34*w + 18]', '[5957, 5957, 2*w^3 - w^2 + 3*w + 2]', '[5957, 5957, w^3 - 3*w^2 - 6*w - 5]', '[5957, 5957, -2*w^3 - 2*w^2 + w - 5]', '[5957, 5957, 4*w^3 - 11*w^2 + 4*w + 11]', '[5961, 5961, -8*w^2 + 3]', '[5963, 5963, -4*w^3 + 4*w^2 + 13*w - 1]', '[5965, 5965, -w^3 + 7]', '[5965, 5965, 2*w^3 + 3*w^2 - 18*w - 7]', '[5975, 5975, 4*w^3 - 2*w^2 - 12*w + 1]', '[5975, 5975, 4*w^3 - 4*w^2 - 16*w + 11]', '[5979, 5979, 4*w^3 - 8*w^2 - 11*w + 6]', '[5981, 5981, -w^3 + 10*w + 1]', '[5981, 5981, -2*w^3 + 4*w^2 + 7*w - 16]', '[5981, 5981, 4*w^2 - w - 17]', '[5981, 5981, 6*w^3 - 7*w^2 - 23*w - 1]', '[5987, 5987, w^3 + 4*w^2 - 8*w - 13]', '[5987, 5987, -6*w^3 + 7*w^2 + 28*w - 13]', '[5987, 5987, w^3 + w^2 - 7]', '[5987, 5987, -6*w^3 + 5*w^2 + 27*w - 2]', '[5991, 5991, 4*w^3 - 10*w^2 - 3*w + 12]', '[5991, 5991, w^3 + 4*w^2 - 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w^2 - 6*w + 2]', '[229, 229, 4*w^3 - 6*w^2 - 14*w + 7]', '[233, 233, 2*w^3 - 3*w^2 - 5*w + 1]', '[239, 239, -w - 4]', '[239, 239, -2*w^3 + 4*w^2 + 5*w - 8]', '[241, 241, -2*w^3 + w^2 + 10*w + 1]', '[251, 251, -w^3 + 2*w^2 + 2*w - 8]', '[251, 251, -2*w^3 + 5*w^2 + 5*w - 8]', '[257, 257, 2*w^3 - 2*w^2 - 7*w + 1]', '[263, 263, w^3 - 4*w^2 - 4*w + 7]', '[269, 269, w^2 + 2*w - 4]', '[269, 269, 2*w^2 - 7]', '[271, 271, 2*w^3 - 3*w^2 - 7*w + 1]', '[271, 271, w^2 + 3*w - 2]', '[271, 271, 3*w^3 - 5*w^2 - 11*w + 13]', '[271, 271, -2*w^3 + 3*w^2 + 9*w - 2]', '[277, 277, w^2 - w - 7]', '[277, 277, 3*w^3 - 4*w^2 - 13*w + 5]', '[277, 277, -w^3 + w^2 + 3*w - 5]', '[277, 277, w^3 - 3*w - 4]', '[281, 281, w^3 - 2*w^2 - 2*w - 2]', '[283, 283, w^2 + 3*w - 1]', '[283, 283, w^3 - w^2 - 2*w - 4]', '[293, 293, 3*w^3 - 4*w^2 - 12*w + 8]', '[293, 293, w^2 + w - 5]', '[307, 307, 2*w^3 - 2*w^2 - 6*w - 1]', '[307, 307, -w^2 - 2]', '[311, 311, -w^3 + 5*w - 1]', '[313, 313, 2*w^3 - 2*w^2 - 8*w - 5]', '[313, 313, -2*w^3 + 3*w^2 + 5*w - 2]', '[317, 317, 2*w^3 - 2*w^2 - 9*w + 4]', '[317, 317, w^3 - 2*w^2 - 3*w - 2]', '[331, 331, -w^3 + 2*w^2 + w - 5]', '[337, 337, -2*w^3 + 3*w^2 + 5*w - 7]', '[337, 337, w^3 - 4*w^2 - w + 5]', '[349, 349, -2*w^3 + w^2 + 11*w + 1]', '[367, 367, -2*w^3 + 2*w^2 + 8*w - 5]', '[379, 379, -w^3 + 2*w^2 - 4]', '[383, 383, -3*w^3 + 6*w^2 + 9*w - 14]', '[383, 383, w - 5]', '[389, 389, 4*w^3 - 6*w^2 - 14*w + 11]', '[397, 397, -2*w^3 + w^2 + 11*w - 1]', '[397, 397, -3*w^3 + 2*w^2 + 12*w + 1]', '[401, 401, 3*w - 7]', '[409, 409, w^2 - 4*w - 1]', '[421, 421, -2*w^3 + 4*w^2 + 7*w - 5]', '[421, 421, -2*w^3 + 4*w^2 + 4*w - 7]', '[443, 443, 2*w^3 - 2*w^2 - 10*w + 1]', '[449, 449, -w^3 - w^2 + 2*w - 2]', '[461, 461, 3*w^3 - 3*w^2 - 12*w + 4]', '[463, 463, -2*w^3 + 2*w^2 + 6*w - 1]', '[463, 463, -3*w^2 + 5*w + 4]', '[467, 467, w^2 + w - 10]', '[467, 467, 3*w^3 - 3*w^2 - 14*w + 1]', '[479, 479, -2*w^3 + w^2 + 6*w + 1]', '[491, 491, w^3 + 2*w^2 - 7*w - 8]', '[499, 499, 4*w^3 - 5*w^2 - 16*w + 8]', '[499, 499, w^3 - 3*w - 5]', '[503, 503, -w^3 + 3*w^2 + w - 10]', '[503, 503, w^3 - 3*w^2 - 4*w + 1]', '[523, 523, -w^3 + 4*w - 4]', '[541, 541, w^3 - 5*w^2 + 2*w + 10]', '[547, 547, -3*w^3 + 6*w^2 + 11*w - 10]', '[547, 547, -3*w^3 + 6*w^2 + 7*w - 10]', '[557, 557, -w^3 + 3*w^2 + 4*w - 10]', '[557, 557, 3*w^2 - 6*w - 8]', '[557, 557, -w^3 + 4*w^2 - 11]', '[557, 557, -2*w^3 + 4*w^2 + 5*w - 11]', '[569, 569, w^3 + w^2 - 6*w - 11]', '[571, 571, 3*w^3 - 4*w^2 - 10*w + 2]', '[571, 571, w^3 - 3*w^2 - 5*w + 2]', '[577, 577, 2*w^3 - w^2 - 7*w + 4]', '[587, 587, 2*w^3 - 11*w - 4]', '[607, 607, 2*w^3 - 3*w^2 - 9*w + 1]', '[613, 613, -3*w^3 + 3*w^2 + 14*w - 5]', '[617, 617, 2*w^3 - 3*w^2 - 8*w + 10]', '[617, 617, 3*w^3 - 5*w^2 - 8*w + 10]', '[643, 643, -w^3 + w^2 + 7*w + 1]', '[643, 643, w^3 + 2*w^2 - 6*w - 8]', '[661, 661, -3*w^3 + 5*w^2 + 8*w - 7]', '[673, 673, -3*w^3 + 3*w^2 + 13*w - 4]', '[683, 683, -w^3 + 2*w^2 - 5]', '[683, 683, w^3 - w^2 - 4*w - 5]', '[691, 691, w^3 + w^2 - 6*w - 2]', '[691, 691, -w^3 + 3*w^2 - 7]', '[709, 709, w^2 - w - 8]', '[727, 727, -2*w^3 + 4*w^2 + 7*w - 4]', '[733, 733, 3*w^3 - 5*w^2 - 7*w + 2]', '[739, 739, -w^3 + 4*w^2 + w - 8]', '[743, 743, 2*w^3 - 3*w^2 - 10*w + 7]', '[751, 751, 3*w^2 - 3*w - 7]', '[761, 761, w^2 + 3*w - 5]', '[773, 773, 3*w^2 - w - 8]', '[787, 787, w^3 - 5*w - 8]', '[797, 797, -w^3 - w^2 + 7*w + 2]', '[809, 809, 3*w^3 - 4*w^2 - 11*w - 4]', '[811, 811, 3*w^2 - 4*w - 13]', '[827, 827, -4*w^3 + 7*w^2 + 12*w - 7]', '[827, 827, 2*w^2 + w - 7]', '[839, 839, -2*w^2 + 5*w + 7]', '[857, 857, -3*w^3 + 4*w^2 + 10*w - 4]', '[857, 857, 2*w^3 - 3*w^2 - 8*w - 1]', '[859, 859, -5*w^3 + 9*w^2 + 18*w - 16]', '[863, 863, -2*w^3 + 4*w^2 + 6*w - 1]', '[863, 863, -2*w^3 + w^2 + 8*w - 2]', '[877, 877, w^3 - 3*w - 7]', '[883, 883, -w^3 + w^2 + 7*w - 2]', '[907, 907, 2*w^3 - w^2 - 12*w - 5]', '[907, 907, 3*w^3 - 14*w - 7]', '[911, 911, 5*w^3 - 5*w^2 - 21*w + 4]', '[911, 911, w^3 - w^2 - w - 4]', '[929, 929, 3*w^2 - 2*w - 7]', '[941, 941, 4*w^3 - 5*w^2 - 14*w + 1]', '[941, 941, 2*w^3 - 5*w^2 - 8*w + 7]', '[953, 953, -w^3 - 3*w^2 + 9*w + 10]', '[953, 953, -3*w^3 + 2*w^2 + 15*w - 1]', '[953, 953, -3*w^3 + 5*w^2 + 9*w - 2]', '[953, 953, 3*w^3 - 3*w^2 - 11*w + 1]', '[961, 31, -3*w^2 + 5*w + 10]', '[961, 31, -2*w^3 + 3*w^2 + 4*w - 7]', '[967, 967, -w^3 - w^2 + 8*w + 1]', '[977, 977, -2*w^3 + 3*w^2 + 10*w - 4]', '[983, 983, 4*w^3 - 6*w^2 - 12*w + 11]', '[983, 983, -w^3 + 2*w^2 + 7*w - 5]', '[997, 997, 3*w^3 - 8*w^2 - 5*w + 13]', '[1009, 1009, -2*w^3 + 4*w^2 + 6*w - 13]', '[1009, 1009, 4*w^3 - 5*w^2 - 15*w + 1]', '[1019, 1019, w^3 - 4*w^2 - w + 16]', '[1031, 1031, -w^3 - w^2 + 6*w + 1]', '[1033, 1033, -w^3 + 3*w^2 - 8]', '[1049, 1049, -2*w^3 + 6*w^2 + 3*w - 11]', '[1049, 1049, -2*w^3 + 4*w^2 + 3*w - 7]', '[1051, 1051, -2*w^3 + 3*w^2 + 10*w - 5]', '[1063, 1063, -3*w^3 + 3*w^2 + 11*w - 8]', '[1063, 1063, -w^2 + 2*w - 4]', '[1069, 1069, -3*w^3 + 4*w^2 + 9*w - 1]', '[1087, 1087, w^2 - 5*w - 2]', '[1087, 1087, 3*w^3 - 3*w^2 - 9*w + 5]', '[1093, 1093, -2*w^3 + w^2 + 7*w + 8]', '[1093, 1093, w^3 - 8*w - 2]', '[1109, 1109, -5*w^3 + 8*w^2 + 17*w - 14]', '[1109, 1109, -4*w^3 + 7*w^2 + 15*w - 11]', '[1123, 1123, 4*w^3 - 6*w^2 - 14*w + 5]', '[1129, 1129, 3*w^3 - 2*w^2 - 8*w + 4]', '[1151, 1151, 4*w^3 - 5*w^2 - 12*w + 10]', '[1151, 1151, -w^3 - 3*w^2 + 9*w + 11]', '[1171, 1171, -w^3 - 3*w^2 + 8*w + 14]', '[1171, 1171, -3*w^3 + 3*w^2 + 7*w - 8]', '[1181, 1181, -4*w^2 + 5*w + 5]', '[1181, 1181, -3*w^3 + 6*w^2 + 9*w - 7]', '[1193, 1193, -2*w^3 + 6*w^2 + 3*w - 10]', '[1193, 1193, -4*w^3 + 6*w^2 + 17*w - 11]', '[1201, 1201, 3*w^3 - 4*w^2 - 6*w + 5]', '[1201, 1201, -3*w^3 + 3*w^2 + 15*w - 5]', '[1201, 1201, -2*w^3 + 5*w^2 + 4*w - 16]', '[1201, 1201, 3*w^3 - 3*w^2 - 8*w - 4]', '[1213, 1213, -3*w^3 + 4*w^2 + 14*w - 4]', '[1217, 1217, -w^3 + 4*w^2 - 13]', '[1229, 1229, -4*w^3 + 4*w^2 + 18*w - 5]', '[1231, 1231, -w^3 + 2*w^2 + 7*w - 4]', '[1277, 1277, 3*w^3 - 5*w^2 - 9*w - 1]', '[1279, 1279, 4*w^3 - 5*w^2 - 14*w - 2]', '[1291, 1291, 3*w^3 - 6*w^2 - 8*w + 5]', '[1291, 1291, w^3 - 5*w^2 + 14]', '[1301, 1301, -4*w^3 + 9*w^2 + 13*w - 20]', '[1321, 1321, 3*w^3 - 4*w^2 - 9*w + 5]', '[1367, 1367, -3*w^3 + 4*w^2 + 11*w + 1]', '[1367, 1367, -w^3 + 2*w^2 - 8]', '[1369, 37, -3*w^3 + 5*w^2 + 11*w - 5]', '[1373, 1373, -2*w^3 - w^2 + 6*w - 1]', '[1409, 1409, -2*w^3 + 6*w^2 + 4*w - 13]', '[1439, 1439, -2*w^3 + 5*w^2 + 5*w - 17]', '[1447, 1447, 6*w^3 - 9*w^2 - 23*w + 19]', '[1447, 1447, 2*w^3 - 3*w^2 - 8*w + 11]', '[1453, 1453, -w^3 + w^2 - 3*w - 2]', '[1453, 1453, 2*w^3 - w^2 - 10*w + 2]', '[1459, 1459, 3*w^3 - 2*w^2 - 5*w + 5]', '[1471, 1471, -w^3 - w^2 + 6*w - 1]', '[1481, 1481, w^3 - 6*w^2 + 20]', '[1483, 1483, 2*w^3 - 4*w^2 - 5*w + 14]', '[1483, 1483, -2*w^3 + 5*w^2 + 6*w - 17]', '[1483, 1483, w^3 - 2*w^2 - 4*w + 10]', '[1483, 1483, 3*w^3 - 4*w^2 - 9*w + 4]', '[1487, 1487, -w^3 + 5*w^2 - 7]', '[1487, 1487, -3*w^3 + 5*w^2 + 13*w - 5]', '[1489, 1489, -w^2 - w - 4]', '[1489, 1489, w^2 + 3*w + 5]', '[1493, 1493, -3*w^3 + 2*w^2 + 12*w - 2]', '[1499, 1499, -w^3 + 5*w^2 - w - 11]', '[1511, 1511, 2*w^2 + 2*w - 7]', '[1511, 1511, -w^3 + 5*w^2 - w - 8]', '[1549, 1549, 2*w^3 - 4*w^2 - 7*w + 1]', '[1559, 1559, w^3 - 2*w^2 - 2*w - 4]', '[1567, 1567, 3*w^2 - w - 13]', '[1567, 1567, -w^3 + w^2 + 3*w - 7]', '[1583, 1583, -2*w^3 + 6*w^2 + 6*w - 11]', '[1583, 1583, w^3 - 5*w^2 - 8*w + 8]', '[1597, 1597, -4*w^3 + 5*w^2 + 10*w + 2]', '[1597, 1597, 4*w^3 - 6*w^2 - 11*w + 1]', '[1601, 1601, 5*w - 2]', '[1607, 1607, -3*w^3 + 6*w^2 + 6*w - 10]', '[1609, 1609, -2*w^3 + 6*w^2 + 5*w - 14]', '[1613, 1613, 3*w^3 - 3*w^2 - 10*w + 2]', '[1613, 1613, -4*w^3 + 9*w^2 + 12*w - 17]', '[1621, 1621, -w^2 - 4]', '[1621, 1621, 4*w^3 - 5*w^2 - 18*w + 5]', '[1627, 1627, -3*w^3 + 4*w^2 + 8*w - 5]', '[1627, 1627, -2*w^3 + 5*w - 5]', '[1663, 1663, 4*w^3 - 2*w^2 - 19*w - 4]', '[1667, 1667, 3*w^3 - 7*w^2 - 6*w + 4]', '[1669, 1669, -5*w^3 + 9*w^2 + 14*w - 14]', '[1669, 1669, -3*w^3 + 6*w^2 + 13*w - 8]', '[1693, 1693, w^3 + w^2 - 4*w - 10]', '[1697, 1697, 3*w^3 - 2*w^2 - 14*w - 10]', '[1699, 1699, -2*w^3 + 4*w^2 + 3*w - 8]', '[1709, 1709, -4*w^3 + 5*w^2 + 14*w - 7]', '[1709, 1709, 4*w^3 - 6*w^2 - 13*w + 8]', '[1721, 1721, w^3 - 2*w^2 - 4*w - 4]', '[1753, 1753, w^3 - 3*w^2 - 2*w - 2]', '[1753, 1753, -2*w^3 + 6*w^2 + 4*w - 11]', '[1759, 1759, w^3 + 2*w^2 - 8*w - 4]', '[1777, 1777, 2*w^3 + w^2 - 15*w - 10]', '[1787, 1787, w^3 - w^2 - 8*w - 1]', '[1789, 1789, 2*w^3 - 4*w^2 - 4*w + 11]', '[1801, 1801, -w^3 + 5*w^2 - w - 16]', '[1811, 1811, 2*w^3 - 3*w^2 - 5*w - 5]', '[1823, 1823, 3*w^2 - 11]', '[1823, 1823, w - 7]', '[1831, 1831, w^3 - 2*w^2 - 3*w - 4]', '[1847, 1847, -w^3 - w^2 + 9*w - 2]', '[1849, 43, 6*w^3 - 9*w^2 - 21*w + 11]', '[1849, 43, -2*w^3 + w^2 + 9*w - 5]', '[1861, 1861, 2*w^3 - 3*w^2 - 11*w + 2]', '[1871, 1871, 5*w - 1]', '[1871, 1871, 3*w^3 - 6*w^2 - 14*w + 13]', '[1873, 1873, 2*w^3 - 11*w - 2]', '[1877, 1877, w^2 - 5*w + 8]', '[1877, 1877, 3*w^3 - 2*w^2 - 6*w + 7]', '[1889, 1889, 2*w^3 - w^2 - 9*w + 4]', '[1901, 1901, -w^3 - w^2 + 7*w - 1]', '[1901, 1901, -3*w^3 + 3*w^2 + 12*w - 8]', '[1901, 1901, -2*w^3 + 6*w^2 + 5*w - 13]', '[1901, 1901, -4*w^3 + 3*w^2 + 15*w - 1]', '[1933, 1933, -3*w^3 + 2*w^2 + 10*w + 2]', '[1949, 1949, 3*w^3 - 3*w^2 - 15*w - 5]', '[1949, 1949, -w^3 + 5*w^2 + 2*w - 8]', '[1973, 1973, -w^3 + w^2 + 5*w - 8]', '[1979, 1979, -2*w^3 + 5*w^2 + 3*w - 11]', '[1987, 1987, -w^3 + w^2 - 3*w - 1]', '[1993, 1993, -2*w^3 + 6*w^2 + 2*w - 13]', '[1997, 1997, -4*w^3 + 8*w^2 + 10*w - 7]', '[1997, 1997, w^3 - w - 5]', '[1999, 1999, -w^3 + 2*w^2 - w - 11]', '[1999, 1999, w^2 - 10]']}
• 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, 1, -5, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 9301, 'disc_rad': 9301, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[3, 1], [1, 1]]], [5, [[3, 1], [1, 1]]], [7, [[2, 1], [1, 2]]], [11, [[4, 1]]], [13, [[4, 1]]], [17, [[3, 1], [1, 1]]], [19, [[4, 1]]], [23, [[3, 1], [1, 1]]], [29, [[4, 1]]], [31, [[2, 2]]], [37, [[2, 1], [1, 2]]], [41, [[4, 1]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[4, 1]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 96.44169222903547, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.9301.1', 'local_algs': ['71.1.0.1', '71.1.0.1', '71.2.1.1', '131.1.0.1', '131.1.0.1', '131.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [71, 131], 'rd': 9.82047311635, 'regulator': {'__RealLiteral__': 0, 'data': '5.65473750217', 'prec': 44}, 'res': {'gal': ['24491673,9096930,-170112264,-54835066,410965558,141273276,-496163845,-186675668,341663866,138845122,-142461750,-61306290,37059531,16512490,-6137958,-2742654,661816,279814,-47635,-17032,2306,568,-70,-8,1'], 'sib': ['-5177,27485,13906,-67353,-3223,39665,-5740,-5998,988,330,-55,-6,1', '1,-12,2,19,-7,-3,1', '207609,193993,-90949,-20793,7514,405,-163,-2,1', '37,527,1790,-1086,-3559,2144,1691,-1499,113,151,-29,-4,1', '64,-382,359,173,-83,-1,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a - 1 \\)', '\\( a^{2} - 2 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}