Hilbert modular form data - 4.4.16357.1-15.2-d

Formats: - HTML - YAML - JSON - 2024-04-28T10:30:43.469716

• 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': 16357, 'field_bad_primes': [11, 1487], 'field_label': '4.4.16357.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.16357.1-15.2-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [3, 5], 'level_ideal': '[15, 15, -w^3 + 6*w - 1]', 'level_label': '15.2', 'level_norm': 15, 'parallel_weight': 2, 'short_label': '15.2-d', '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]', 1], ['[5, 5, -w^3 + 5*w + 2]', -1]], 'hecke_eigenvalues': [-1, 1, 0, 0, -4, -5, 4, -4, -4, -2, 2, 6, -4, 6, 4, 4, 4, -8, -2, 14, 2, 6, 8, -2, -2, -20, -16, -14, -14, 2, -18, -6, -18, 12, 12, 10, 6, 18, 22, -6, -8, 18, 12, 24, 12, -24, 12, 0, -12, 24, -18, -20, 2, 16, -26, -6, -20, -16, -2, 2, 28, -6, 24, 4, 4, 28, -18, -6, 8, -14, -24, 0, -30, -30, -6, -32, -12, 0, -24, 0, -24, 8, -10, 18, -30, -22, -26, 30, 2, -12, 16, -4, 12, -36, 6, -18, 8, 10, -10, 30, 6, 6, -36, 6, 0, 24, 26, -22, -8, -38, -46, -18, -18, 40, -10, 20, -28, -48, -30, -10, -22, -12, 12, 30, 36, 40, 12, 24, -12, 18, -28, -2, -38, -16, -24, 4, 8, 34, -42, -40, -34, -6, -6, -22, 30, -18, 14, -24, -32, -2, 20, -34, -30, 6, -22, 10, 42, 36, 16, -22, 26, 30, 16, 6, -6, -52, -58, -38, 16, -30, -18, 12, -30, 18, 32, -6, 6, 14, 14], 'hecke_polynomial': 'x', 'label': '4.4.16357.1-15.2-d'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 16357, 'ideals': ['[1, 1, 1]', '[3, 3, w + 1]', '[5, 5, -w^3 + 5*w + 2]', '[5, 5, w - 1]', '[9, 9, w - 2]', '[11, 11, -w^3 + 5*w]', '[13, 13, -w^3 + w^2 + 6*w - 3]', '[15, 15, -w^3 + 5*w + 1]', '[15, 15, -w^3 + 6*w - 1]', '[16, 2, 2]', '[19, 19, 2*w^3 - w^2 - 11*w + 2]', '[25, 5, -w^2 + w + 3]', '[25, 5, w^2 + w - 2]', '[25, 25, w^3 - 7*w + 1]', '[25, 25, -w + 3]', '[27, 3, w^3 - w^2 - 5*w + 4]', '[27, 27, w^2 - w - 2]', '[31, 31, -w - 3]', '[33, 33, -w^3 - w^2 + 4*w + 1]', '[37, 37, -w^3 - w^2 + 6*w + 4]', '[39, 39, -w^3 + 5*w + 4]', '[41, 41, w^3 + w^2 - 6*w - 5]', '[43, 43, w^3 - 7*w - 2]', '[45, 45, w^2 - 4]', '[45, 45, -w^3 - w^2 + 5*w + 2]', '[47, 47, -2*w^3 + 11*w + 2]', '[48, 6, 2*w + 2]', '[55, 55, w^3 - w^2 - 6*w + 1]', '[55, 55, -w^3 + 6*w + 4]', '[57, 57, w^3 - 7*w]', '[61, 61, w^2 - 3]', '[65, 65, 2*w^3 - 12*w - 5]', '[65, 65, w^3 - 7*w - 1]', '[67, 67, w^2 + w - 4]', '[75, 15, 2*w^3 - w^2 - 12*w + 6]', '[75, 15, -w^3 + 4*w + 3]', '[75, 75, w^3 - w^2 - 5*w]', '[75, 75, -w^2 + 2*w + 3]', '[79, 79, -4*w^3 + 2*w^2 + 22*w - 9]', '[80, 10, -2*w^3 + 10*w + 4]', '[80, 10, 2*w - 2]', '[81, 3, 3]', '[81, 81, -2*w^3 - w^2 + 12*w + 5]', '[93, 93, 2*w^3 - w^2 - 10*w + 2]', '[95, 95, 2*w + 3]', '[95, 95, w^3 - 5*w + 3]', '[97, 97, -3*w^3 + 2*w^2 + 19*w - 6]', '[97, 97, -w^3 + 6*w - 3]', '[97, 97, -3*w^3 + 16*w]', '[97, 97, -w^3 + w^2 + 4*w - 3]', '[99, 99, 2*w^3 - w^2 - 11*w + 1]', '[101, 101, -2*w^3 + w^2 + 11*w - 6]', '[103, 103, w^3 - w^2 - 7*w]', '[109, 109, -w^3 - w^2 + 6*w + 2]', '[111, 111, -2*w^3 - w^2 + 9*w + 5]', '[117, 117, -w^3 - w^2 + 8*w + 5]', '[121, 11, -w^3 - w^2 + 7*w + 2]', '[121, 11, 2*w^3 - 11*w + 1]', '[123, 123, 2*w^3 + w^2 - 10*w - 6]', '[125, 5, 3*w^3 - w^2 - 16*w + 4]', '[125, 5, -w^3 - w^2 + 5*w + 6]', '[125, 25, w^3 - 8*w - 3]', '[125, 25, 2*w^3 - w^2 - 12*w + 1]', '[125, 125, w^3 - w^2 - 6*w]', '[125, 125, 2*w^3 - 13*w - 4]', '[127, 127, -2*w^3 + w^2 + 13*w - 1]', '[127, 127, w^3 - w^2 - 6*w - 2]', '[129, 129, w^3 - w^2 - 8*w - 3]', '[135, 15, w^3 - w^2 - 8*w + 1]', '[135, 15, w^3 - w^2 - 8*w - 2]', '[135, 135, w^3 + w^2 - 4*w - 4]', '[135, 135, 2*w^3 - w^2 - 10*w - 1]', '[141, 141, 2*w^3 + w^2 - 11*w - 4]', '[143, 143, 2*w - 3]', '[144, 18, 2*w - 4]', '[155, 155, -w^2 - 2*w + 3]', '[155, 155, 3*w^3 + w^2 - 16*w - 7]', '[157, 157, -2*w^3 + 2*w^2 + 10*w - 7]', '[157, 157, w - 4]', '[163, 163, 2*w^3 - w^2 - 13*w + 3]', '[165, 165, w + 4]', '[165, 165, 2*w^3 - w^2 - 10*w + 5]', '[169, 169, -2*w^3 + 13*w - 3]', '[171, 171, w^3 - w^2 - 6*w - 1]', '[173, 173, -2*w^3 + w^2 + 13*w - 6]', '[173, 173, 2*w^3 - 12*w + 1]', '[173, 173, 2*w^3 - 11*w + 2]', '[173, 173, w^2 + w - 5]', '[176, 22, -2*w^3 + 10*w]', '[179, 179, -2*w^3 + 10*w + 3]', '[181, 181, -w^3 - w^2 + 7*w + 8]', '[183, 183, w^3 + w^2 - 3*w - 3]', '[185, 185, -4*w^3 - 2*w^2 + 26*w + 13]', '[185, 185, w^2 - 3*w - 3]', '[191, 191, w^3 - 5*w - 5]', '[191, 191, 2*w^3 - w^2 - 9*w - 1]', '[193, 193, -3*w^3 + 3*w^2 + 19*w - 7]', '[195, 195, 2*w^3 - w^2 - 13*w + 2]', '[195, 195, w^3 - w^2 - 7*w - 2]', '[197, 197, -w^3 + w^2 + 6*w - 7]', '[201, 201, w^3 + 2*w^2 - 3*w - 4]', '[205, 205, 5*w^3 + 2*w^2 - 31*w - 15]', '[205, 205, -w^2 + 2*w + 4]', '[208, 26, -2*w^3 + 2*w^2 + 12*w - 6]', '[209, 209, -2*w^3 + 12*w - 3]', '[215, 215, 3*w^3 + 2*w^2 - 18*w - 10]', '[215, 215, -w^3 - w^2 + 6*w + 1]', '[223, 223, w^3 + w^2 - 6*w + 1]', '[225, 45, w^3 - w^2 - 4*w + 4]', '[225, 45, 2*w^3 - 2*w^2 - 11*w + 5]', '[225, 225, 3*w^3 + w^2 - 19*w - 8]', '[225, 225, -w^3 + 6*w + 5]', '[227, 227, 6*w^3 - 3*w^2 - 34*w + 9]', '[227, 227, w^3 + w^2 - 8*w]', '[233, 233, 2*w^3 - 13*w - 3]', '[233, 233, -w^3 + 2*w^2 + 4*w - 6]', '[235, 235, 4*w^3 + w^2 - 23*w - 13]', '[235, 235, -2*w^3 + w^2 + 11*w]', '[237, 237, -w^3 - w^2 + 5*w + 8]', '[239, 239, -2*w^3 + 10*w + 1]', '[239, 239, w^3 - 8*w - 2]', '[240, 30, -2*w^3 + 10*w + 2]', '[240, 30, -2*w^3 + 12*w - 2]', '[243, 9, 3*w + 3]', '[243, 243, -3*w^3 + w^2 + 16*w - 3]', '[247, 247, -2*w^3 - w^2 + 12*w + 4]', '[251, 251, -3*w^3 + w^2 + 18*w]', '[251, 251, -5*w^3 + 2*w^2 + 30*w - 11]', '[256, 4, 4]', '[263, 263, -2*w^3 + w^2 + 10*w + 2]', '[269, 269, 3*w^3 - 18*w - 8]', '[271, 271, 2*w^3 + w^2 - 10*w - 2]', '[271, 271, -3*w^3 + 19*w]', '[275, 55, -2*w^3 + 13*w + 1]', '[275, 55, w^3 - 3*w - 3]', '[275, 275, -3*w^3 + w^2 + 16*w - 1]', '[275, 275, -2*w^3 + 2*w^2 + 11*w - 6]', '[277, 277, -w^3 + w^2 + 4*w - 8]', '[277, 277, 2*w^3 + w^2 - 14*w - 8]', '[279, 279, -w^2 - w + 6]', '[281, 281, w^3 - 8*w]', '[285, 285, -w^3 - w^2 + 8*w - 1]', '[285, 285, 2*w^3 - w^2 - 13*w - 1]', '[291, 291, 2*w^3 - w^2 - 9*w]', '[291, 291, -w^3 + 2*w - 2]', '[291, 291, -3*w^3 - 2*w^2 + 13*w + 3]', '[291, 291, -w^2 - 2]', '[297, 33, -w^3 + w^2 + 8*w - 4]', '[297, 297, w^3 - 8*w - 1]', '[303, 303, -2*w^3 - 2*w^2 + 13*w + 10]', '[304, 38, 4*w^3 - 2*w^2 - 22*w + 4]', '[305, 305, w^3 - w^2 - 3*w + 3]', '[305, 305, 2*w^3 + w^2 - 14*w - 6]', '[307, 307, 3*w^3 - w^2 - 16*w + 2]', '[307, 307, 2*w^3 - w^2 - 9*w + 1]', '[307, 307, -2*w^3 + 2*w^2 + 13*w - 7]', '[307, 307, -w^3 + w^2 + 7*w - 6]', '[309, 309, -2*w^2 - 6*w - 1]', '[313, 313, -3*w^3 + w^2 + 15*w + 4]', '[317, 317, -4*w^3 + w^2 + 22*w - 3]', '[317, 317, 2*w^3 - w^2 - 10*w - 3]', '[325, 65, -2*w^3 + w^2 + 12*w - 7]', '[325, 65, -w^3 - w^2 + 7*w]', '[325, 325, -2*w^3 + 9*w + 3]', '[325, 325, 2*w^3 + 2*w^2 - 13*w - 8]', '[327, 327, -2*w^3 - w^2 + 7*w + 3]', '[333, 333, w^3 + 2*w^2 - 9*w - 7]', '[335, 335, 3*w^3 - 18*w - 7]', '[335, 335, w^3 - 5*w + 4]', '[337, 337, w^3 + w^2 - 4*w - 5]', '[341, 341, w^3 + w^2 - 8*w - 6]', '[349, 349, -2*w^3 - w^2 + 11*w + 3]', '[349, 349, -4*w^3 + 2*w^2 + 24*w - 11]', '[351, 39, 2*w^3 + w^2 - 10*w - 7]', '[351, 351, w^3 - 6*w + 4]', '[353, 353, 3*w^3 - w^2 - 17*w + 7]', '[353, 353, -3*w^3 - 2*w^2 + 17*w + 11]', '[361, 361, w^2 + 2*w - 4]', '[363, 33, 3*w^3 + 2*w^2 - 18*w - 11]', '[363, 33, 2*w^3 + w^2 - 8*w - 1]', '[367, 367, 2*w^3 - 11*w - 7]', '[369, 369, -w^3 - 2*w^2 + 8*w + 9]', '[373, 373, -w^3 + w^2 + 4*w - 5]', '[375, 15, -3*w^3 + 2*w^2 + 15*w - 2]', '[375, 15, -2*w^3 - w^2 + 14*w + 4]', '[375, 75, w^3 - w^2 - 9*w - 1]', '[375, 75, 2*w^3 - 2*w^2 - 13*w + 3]', '[375, 375, -w^3 + 7*w + 6]', '[375, 375, -w^3 + 2*w^2 + 4*w - 5]', '[381, 381, -w^3 + 2*w^2 + 10*w + 1]', '[381, 381, -w^2 - 7*w - 3]', '[383, 383, -4*w^3 + 3*w^2 + 23*w - 9]', '[383, 383, 4*w^3 - w^2 - 22*w]', '[387, 387, -2*w^3 - w^2 + 13*w + 3]', '[389, 389, w^2 - 2*w - 5]', '[395, 395, 4*w^3 + w^2 - 22*w - 8]', '[395, 395, 3*w^3 - 17*w]', '[400, 10, -2*w^2 + 2*w + 6]', '[400, 10, 2*w^2 + 2*w - 4]', '[400, 50, 2*w^3 - 14*w + 2]', '[400, 50, -2*w + 6]', '[401, 401, -3*w^3 + 2*w^2 + 16*w - 9]', '[401, 401, 2*w^3 - w^2 - 14*w - 1]', '[403, 403, -2*w^3 + w^2 + 11*w + 1]', '[405, 15, -3*w^3 + 15*w + 6]', '[405, 15, 3*w - 3]', '[405, 405, w^3 + w^2 - 9*w - 3]', '[405, 405, 2*w^3 - 2*w^2 - 9*w + 1]', '[407, 407, -2*w^3 + 14*w + 5]', '[409, 409, 2*w^3 + 2*w^2 - 13*w - 9]', '[419, 419, -4*w^3 + 24*w + 7]', '[419, 419, 2*w^2 + 2*w - 7]', '[419, 419, -w^3 + 2*w^2 + 8*w - 6]', '[419, 419, 6*w^3 - 3*w^2 - 33*w + 13]', '[423, 423, -4*w^3 + w^2 + 22*w + 2]', '[429, 429, -3*w^3 + 16*w + 4]', '[431, 431, 2*w^3 - w^2 - 12*w - 5]', '[432, 6, 2*w^3 - 2*w^2 - 10*w + 8]', '[432, 54, 2*w^2 - 2*w - 4]', '[439, 439, -3*w^3 + 2*w^2 + 18*w - 4]', '[439, 439, w^3 + 2*w^2 - 7*w - 3]', '[443, 443, 6*w^3 - 3*w^2 - 33*w + 7]', '[449, 449, -3*w^3 + w^2 + 14*w - 4]', '[451, 451, 3*w^3 - 19*w - 5]', '[457, 457, 2*w^3 - 9*w]', '[457, 457, 3*w^3 - w^2 - 16*w - 2]', '[465, 465, 3*w^3 + w^2 - 15*w - 4]', '[465, 465, 3*w^3 - 16*w + 2]', '[471, 471, w^2 - 3*w - 4]', '[471, 471, w - 5]', '[473, 473, w^3 + 2*w^2 - 4*w - 6]', '[475, 95, -4*w^3 + w^2 + 23*w - 5]', '[475, 95, -w^3 + 9*w + 3]', '[475, 475, -3*w^3 + 16*w + 2]', '[475, 475, -2*w^3 + 9*w + 2]', '[479, 479, 3*w^3 - w^2 - 19*w + 4]', '[481, 481, -w - 5]', '[485, 485, w^3 - 2*w^2 - 6*w + 4]', '[485, 485, w^3 - 10*w + 4]', '[485, 485, -w^3 - w^2 + 3*w + 4]', '[485, 485, w^3 + 2*w^2 - 9*w - 3]', '[485, 485, -3*w^3 - w^2 + 19*w + 13]', '[485, 485, 2*w^3 - 3*w^2 - 8*w + 4]', '[485, 485, 3*w^3 - 2*w^2 - 19*w + 3]', '[485, 485, 2*w^3 - w^2 - 8*w - 1]', '[487, 487, -w^3 + w^2 + 4*w - 6]', '[489, 489, -3*w^3 + w^2 + 14*w + 4]', '[491, 491, 3*w^3 + w^2 - 17*w - 5]', '[495, 495, -3*w^3 + 2*w^2 + 14*w - 3]', '[495, 495, 3*w^3 - w^2 - 19*w]', '[496, 62, -2*w - 6]', '[499, 499, 5*w^3 - 3*w^2 - 28*w + 8]', '[499, 499, 2*w^3 - w^2 - 12*w - 1]', '[503, 503, -2*w^3 - w^2 + 12*w + 3]', '[503, 503, w^3 - 3*w - 4]', '[505, 505, 3*w^3 - 16*w - 3]', '[505, 505, 5*w^3 + 2*w^2 - 29*w - 13]', '[507, 507, -w^3 + 2*w^2 + 5*w - 7]', '[509, 509, -3*w - 5]', '[509, 509, -4*w^3 + 3*w^2 + 25*w - 10]', '[513, 57, -2*w^3 - w^2 + 10*w + 1]', '[513, 513, -2*w^3 + 13*w + 8]', '[515, 515, 2*w^3 + w^2 - 9*w - 6]', '[515, 515, -2*w^3 + 8*w - 1]', '[517, 517, w^2 - w - 9]', '[519, 519, -3*w^3 + w^2 + 15*w + 5]', '[519, 519, -w^3 + 2*w^2 + 5*w - 4]', '[519, 519, 2*w^3 - 9*w - 1]', '[519, 519, w^3 + 2*w^2 - 4*w - 5]', '[523, 523, -2*w^3 + w^2 + 14*w - 6]', '[528, 66, -2*w^3 - 2*w^2 + 8*w + 2]', '[529, 23, 4*w^3 - 2*w^2 - 21*w + 5]', '[529, 23, -3*w^3 - w^2 + 15*w + 6]', '[533, 533, w^3 - w^2 - 5*w + 8]', '[537, 537, -2*w^3 - 2*w^2 + 11*w + 5]', '[543, 543, -3*w^3 + 19*w - 2]', '[545, 545, -2*w^3 - 2*w^2 + 16*w + 9]', '[545, 545, w^2 - 5*w - 1]', '[549, 549, w^3 - 2*w^2 - 3*w + 6]', '[555, 555, -3*w^3 - w^2 + 20*w + 9]', '[555, 555, -2*w^3 + w^2 + 11*w + 2]', '[557, 557, -2*w^3 + w^2 + 13*w + 2]', '[557, 557, 3*w^3 - 2*w^2 - 16*w + 3]', '[559, 559, -3*w^3 + 15*w - 1]', '[569, 569, 2*w^2 - w - 8]', '[573, 573, w^3 + w^2 - 9*w - 6]', '[573, 573, w^3 + 2*w^2 - 8*w - 3]', '[579, 579, w^2 - 2*w + 3]', '[585, 585, -2*w^3 - w^2 + 14*w + 1]', '[585, 585, w^3 - 2*w^2 - 9*w]', '[587, 587, w^3 + 2*w^2 - 5*w - 16]', '[587, 587, -4*w^3 + w^2 + 25*w - 5]', '[589, 589, -2*w^3 + w^2 + 9*w - 5]', '[591, 591, w^2 - 2*w - 6]', '[592, 74, -2*w^3 - 2*w^2 + 12*w + 8]', '[599, 599, w^3 + 2*w^2 - 6*w - 5]', '[599, 599, -5*w^3 + 3*w^2 + 30*w - 15]', '[601, 601, w^3 - 6*w - 6]', '[603, 603, w^3 - w^2 - 6*w + 8]', '[605, 55, -3*w^3 - w^2 + 15*w + 5]', '[605, 55, w^3 + w^2 - 8*w - 7]', '[605, 55, -w^3 + 4*w + 7]', '[605, 55, -2*w^3 + w^2 + 14*w - 3]', '[607, 607, -w^3 + w^2 + 3*w - 4]', '[607, 607, -w^3 + 2*w - 3]', '[611, 611, -5*w^3 + 2*w^2 + 30*w - 5]', '[613, 613, 6*w^3 - 2*w^2 - 31*w + 11]', '[613, 613, w^3 + w^2 - 4*w - 6]', '[615, 615, 4*w^3 + w^2 - 25*w - 10]', '[615, 615, 3*w^3 - w^2 - 17*w - 1]', '[617, 617, 5*w^3 - w^2 - 30*w + 2]', '[617, 617, -2*w^3 + 2*w^2 + 9*w + 3]', '[619, 619, -w^3 + 2*w^2 + 6*w - 5]', '[619, 619, 2*w^3 - w^2 - 11*w - 3]', '[624, 78, -2*w^3 + 10*w + 8]', '[625, 5, 5]', '[625, 25, -w^3 + w^2 + 8*w - 5]', '[625, 25, 2*w^3 + w^2 - 10*w - 8]', '[625, 25, -3*w^3 + 2*w^2 + 15*w - 7]', '[625, 25, 2*w^3 + w^2 - 14*w - 9]', '[625, 125, -3*w^3 + w^2 + 15*w - 3]', '[625, 125, -w^3 + 2*w^2 + 5*w - 6]', '[625, 625, 2*w^3 - 8*w - 5]', '[625, 625, -2*w^3 - w^2 + 11*w + 2]', '[627, 627, -w^3 + 2*w^2 + 6*w - 6]', '[631, 631, -w^3 + 2*w^2 + 5*w - 5]', '[631, 631, -3*w^3 - w^2 + 18*w + 5]', '[635, 635, -2*w^3 - 2*w^2 + 11*w + 9]', '[635, 635, 3*w^3 - 16*w + 3]', '[635, 635, 4*w^3 - 18*w - 9]', '[635, 635, -2*w^3 + w^2 + 5*w + 1]', '[645, 645, w^2 + 2*w - 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6]', '[1761, 1761, 3*w^3 + 3*w^2 - 20*w - 17]', '[1761, 1761, -3*w^3 + 2*w^2 + 16*w - 1]', '[1763, 1763, 5*w^3 - 4*w^2 - 29*w + 12]', '[1765, 1765, -w^3 + 6*w - 6]', '[1765, 1765, -3*w^3 - 2*w^2 + 18*w + 7]', '[1765, 1765, -3*w^3 + w^2 + 14*w]', '[1765, 1765, w^3 + w^2 - 9*w - 8]', '[1767, 1767, -3*w^3 + w^2 + 20*w + 1]', '[1773, 1773, w^3 - w^2 - 8*w - 6]', '[1776, 222, -4*w^3 - 2*w^2 + 18*w + 10]', '[1787, 1787, 5*w^3 - 3*w^2 - 25*w + 6]', '[1789, 1789, -2*w^3 - w^2 + 15*w + 10]', '[1793, 1793, 3*w^3 - 3*w^2 - 13*w + 1]', '[1797, 1797, 3*w^3 + 2*w^2 - 10*w - 6]', '[1797, 1797, -2*w^3 + 3*w^2 + 10*w - 10]', '[1801, 1801, -5*w^3 + 26*w + 10]', '[1803, 1803, w^3 - 11*w - 7]', '[1805, 1805, 3*w^3 - w^2 - 17*w - 6]', '[1805, 1805, 4*w^3 - w^2 - 25*w + 2]', '[1809, 201, -4*w^3 + 4*w^2 + 23*w - 16]', '[1809, 1809, -w^2 + 3*w + 7]', '[1811, 1811, -w^3 + 2*w^2 + 3*w - 8]', '[1811, 1811, 3*w^3 + w^2 - 18*w - 3]', '[1815, 165, -w^3 - 2*w^2 + 10*w + 8]', '[1815, 165, -w^3 + w^2 + 3*w - 8]', '[1815, 165, w^2 - 3*w + 5]', '[1815, 165, -5*w^3 + 2*w^2 + 28*w - 12]', '[1821, 1821, -2*w^2 - 2*w - 3]', '[1821, 1821, -w^3 - 4*w^2 - 2*w - 2]', '[1831, 1831, 3*w^3 - 14*w]', '[1831, 1831, -3*w^3 + w^2 + 20*w + 8]', '[1833, 1833, 8*w^3 + w^2 - 45*w - 17]', '[1835, 1835, 9*w^3 + w^2 - 48*w - 23]', '[1835, 1835, -2*w^3 + w^2 + 6*w + 5]', '[1839, 1839, 2*w^3 + 3*w^2 - 9*w - 7]', '[1839, 1839, -5*w^3 + 22*w + 11]', '[1843, 1843, -10*w^3 + 6*w^2 + 55*w - 17]', '[1843, 1843, -w^3 + w^2 + 2*w - 5]', '[1843, 1843, -7*w^3 + 2*w^2 + 44*w - 12]', '[1843, 1843, -10*w^3 + 7*w^2 + 58*w - 29]', '[1845, 1845, 5*w^3 - 31*w - 14]', '[1845, 1845, -4*w^3 - 2*w^2 + 24*w + 19]', '[1847, 1847, -3*w^3 - 2*w^2 + 13*w + 1]', '[1849, 1849, 4*w^3 - 3*w^2 - 27*w + 8]', '[1851, 1851, -4*w^3 + w^2 + 23*w + 3]', '[1851, 1851, -w^2 + 10*w + 5]', '[1857, 1857, w^3 + 2*w^2 - 4]', '[1857, 1857, -w^3 + 12*w + 5]', '[1859, 1859, 5*w^3 - 3*w^2 - 26*w + 11]', '[1861, 1861, 3*w^3 - 20*w]', '[1861, 1861, 3*w^3 + w^2 - 20*w - 1]', '[1865, 1865, 2*w^3 - 3*w^2 - 10*w + 6]', '[1865, 1865, 3*w^3 + 2*w^2 - 19*w - 7]', '[1867, 1867, 4*w^3 + w^2 - 23*w - 15]', '[1867, 1867, -2*w^3 - 3*w^2 + 16*w + 12]', '[1871, 1871, 7*w^3 - w^2 - 42*w + 3]', '[1872, 234, -2*w^3 - 2*w^2 + 16*w + 10]', '[1873, 1873, -6*w^3 + 2*w^2 + 36*w - 1]', '[1873, 1873, -3*w^3 + w^2 + 18*w - 9]', '[1875, 15, -5*w - 5]', '[1875, 75, -3*w^3 + w^2 + 16*w - 9]', '[1875, 75, -5*w^3 + 4*w^2 + 29*w - 13]', '[1875, 75, -4*w^3 + 21*w + 2]', '[1875, 75, -4*w^3 + w^2 + 25*w - 1]', '[1875, 375, 2*w^2 + 2*w - 9]', '[1875, 375, w^3 + w^2 - 2*w - 5]', '[1875, 1875, -2*w^3 + 3*w^2 + 11*w - 6]', '[1875, 1875, 4*w^3 + 3*w^2 - 22*w - 15]', '[1877, 1877, 6*w^3 - w^2 - 33*w - 6]', '[1877, 1877, 3*w^3 + 2*w^2 - 14*w - 3]', '[1881, 1881, w^3 + 2*w^2 - w - 5]', '[1891, 1891, -w^3 - 3*w^2 + 3*w + 9]', '[1893, 1893, -4*w^3 - w^2 + 20*w + 8]', '[1893, 1893, w^3 + w^2 - w - 4]', '[1901, 1901, -6*w^3 + w^2 + 32*w - 9]', '[1903, 1903, 4*w^3 - 2*w^2 - 18*w + 7]', '[1903, 1903, -2*w^3 + 3*w^2 + 13*w - 3]', '[1903, 1903, 3*w^3 - 2*w^2 - 12*w]', '[1903, 1903, 4*w^3 - 2*w^2 - 25*w + 1]', '[1905, 1905, -3*w^2 - 2*w + 10]', '[1905, 1905, 3*w^2 - w - 4]', '[1905, 1905, 5*w^3 - 4*w^2 - 31*w + 14]', '[1905, 1905, 3*w^3 + w^2 - 12*w - 7]', '[1907, 1907, 9*w^3 - 4*w^2 - 52*w + 11]', '[1907, 1907, w^3 - w^2 - 9*w + 6]', '[1913, 1913, -10*w^3 + 5*w^2 + 56*w - 14]', '[1913, 1913, 2*w^3 - w^2 - 15*w + 2]', '[1915, 1915, 3*w^3 - w^2 - 17*w - 5]', '[1915, 1915, 2*w^3 - 15*w + 1]', '[1915, 1915, -3*w^3 - 3*w^2 + 15*w + 11]', '[1915, 1915, -2*w^2 - 3*w + 7]', '[1919, 1919, -5*w^3 + 29*w + 10]', '[1927, 1927, 2*w^3 - 12*w - 9]', '[1931, 1931, -6*w^3 + w^2 + 33*w - 2]', '[1931, 1931, 5*w^3 + w^2 - 27*w - 10]', '[1935, 1935, -5*w^3 - w^2 + 27*w + 8]', '[1935, 1935, 4*w^3 + 3*w^2 - 17*w - 10]', '[1936, 22, -2*w^3 - 2*w^2 + 14*w + 4]', '[1936, 22, 4*w^3 - 22*w + 2]', '[1941, 1941, 5*w^3 - w^2 - 28*w - 4]', '[1945, 1945, 4*w^3 + 3*w^2 - 26*w - 12]', '[1945, 1945, w^3 - 3*w^2 - 3*w + 5]', '[1957, 1957, 4*w^3 - 2*w^2 - 23*w + 12]', '[1968, 246, 4*w^3 + 2*w^2 - 20*w - 12]', '[1969, 1969, -w^3 + 7*w + 8]', '[1975, 395, -3*w^3 + w^2 + 20*w - 3]', '[1975, 395, -8*w^3 + 5*w^2 + 47*w - 21]', '[1975, 1975, -3*w^3 + w^2 + 18*w + 4]', '[1975, 1975, 3*w^3 + 2*w^2 - 20*w - 14]', '[1977, 1977, 4*w^3 - 2*w^2 - 18*w - 3]', '[1979, 1979, 6*w^3 - w^2 - 37*w + 4]', '[1983, 1983, 2*w^3 + w^2 - 5*w - 4]', '[1987, 1987, 3*w^3 + 2*w^2 - 22*w - 10]', '[1991, 1991, w^3 + 3*w^2 - 6]', '[1993, 1993, 7*w^3 - 5*w^2 - 37*w + 16]', '[1993, 1993, -2*w^3 + w^2 + 8*w - 6]', '[1997, 1997, 2*w^3 - w^2 - 11*w + 9]', '[2000, 10, 6*w^3 - 2*w^2 - 32*w + 8]', '[2000, 10, -2*w^3 - 2*w^2 + 10*w + 12]', '[2000, 50, 2*w^3 - 16*w - 6]', '[2000, 50, 4*w^3 - 2*w^2 - 24*w + 2]', '[2000, 250, 2*w^3 - 2*w^2 - 12*w]', '[2000, 250, 4*w^3 - 26*w - 8]', '[2005, 2005, -w^3 + 4*w^2 + 15*w + 2]', '[2005, 2005, 4*w^3 + 3*w^2 - 22*w - 14]', '[2005, 2005, -3*w^3 - w^2 + 15*w - 1]', '[2005, 2005, -2*w^3 + 4*w^2 + 19*w - 4]', '[2007, 2007, -w^3 - 2*w^2 + 14*w - 3]', '[2013, 2013, w^3 - 3*w^2 - 12*w - 2]', '[2015, 2015, 3*w^3 - 2*w^2 - 12*w + 1]', '[2015, 2015, -3*w^3 + w^2 + 21*w + 4]', '[2017, 2017, 3*w^3 - 14*w - 3]', '[2019, 2019, 3*w^3 - w^2 - 24*w - 14]', '[2021, 2021, -4*w^3 - 3*w^2 + 23*w + 17]', '[2025, 15, -3*w^2 + 3*w + 9]', '[2025, 15, 3*w^2 + 3*w - 6]', '[2025, 75, 3*w^3 - 21*w + 3]', '[2025, 75, -3*w + 9]', '[2025, 405, 3*w^3 - w^2 - 20*w - 7]', '[2025, 405, 3*w^3 + w^2 - 13*w - 2]', '[2025, 2025, 2*w^3 - w^2 - 15*w]', '[2025, 2025, 2*w^3 - 8*w - 9]', '[2027, 2027, -3*w^3 + 3*w^2 + 19*w - 12]', '[2027, 2027, -2*w^3 - 3*w^2 + 15*w + 14]', '[2029, 2029, 8*w^3 - 3*w^2 - 48*w + 12]', '[2031, 2031, 5*w^3 + 4*w^2 - 20*w - 10]', '[2031, 2031, -2*w^3 - 2*w^2 + 13*w + 4]', '[2032, 254, -4*w^3 + 2*w^2 + 26*w - 2]', '[2032, 254, 2*w^3 - 2*w^2 - 12*w - 4]', '[2035, 2035, -7*w^3 - 4*w^2 + 41*w + 22]', '[2035, 2035, 2*w^3 + 2*w^2 - 11*w - 3]', '[2039, 2039, 6*w^3 - 3*w^2 - 37*w + 15]', '[2041, 2041, -3*w^3 - 3*w^2 + 18*w + 11]', '[2041, 2041, -3*w^3 - w^2 + 15*w + 11]', '[2043, 2043, 2*w^3 - 2*w^2 - 13*w]', '[2043, 2043, w^3 + 4*w^2 - 6*w - 3]', '[2045, 2045, -3*w^2 + 6*w + 7]', '[2045, 2045, 9*w^3 + 5*w^2 - 58*w - 29]', '[2049, 2049, 2*w^3 - 2*w^2 - 11*w - 1]', '[2049, 2049, 2*w^3 - 11*w - 9]', '[2064, 258, 2*w^3 - 2*w^2 - 16*w - 6]', '[2071, 2071, -w^3 + 3*w^2 + 3*w - 8]', '[2073, 2073, -7*w^3 + 38*w + 13]', '[2077, 2077, -w^3 - 4*w^2 + w + 12]', '[2081, 2081, w^2 + 3*w - 6]', '[2081, 2081, 5*w^3 - w^2 - 27*w + 2]', '[2089, 2089, 10*w^3 - 4*w^2 - 57*w + 10]', '[2089, 2089, 3*w^3 - 14*w - 1]', '[2089, 2089, 2*w^3 - w^2 - 15*w + 1]', '[2089, 2089, -5*w^3 + w^2 + 30*w - 8]', '[2095, 2095, 3*w^3 - 15*w + 7]', '[2095, 2095, -4*w^3 + 23*w - 1]', '[2095, 2095, -4*w^3 + 21*w + 3]', '[2095, 2095, 2*w^3 - 9*w + 7]', '[2095, 2095, 3*w^3 - w^2 - 19*w - 5]', '[2095, 2095, -5*w^3 - w^2 + 27*w + 9]', '[2095, 2095, -5*w^3 + w^2 + 29*w - 6]', '[2095, 2095, 5*w^3 - 31*w - 12]', '[2097, 2097, 4*w^3 - 6*w^2 - 15*w + 13]', '[2097, 2097, w^3 - w^2 - 4]', '[2101, 2101, 4*w^3 - 21*w - 4]', '[2101, 2101, w - 7]', '[2103, 2103, -3*w^3 - 2*w^2 + 21*w + 5]', '[2103, 2103, -w^3 + w^2 + 12*w + 4]', '[2109, 2109, 4*w^3 - 20*w - 7]', '[2111, 2111, 2*w^2 - 4*w - 7]', '[2113, 2113, 3*w^3 + w^2 - 16*w - 1]', '[2115, 2115, -7*w^3 + 42*w + 8]', '[2115, 2115, 3*w^3 + w^2 - 21*w - 13]', '[2119, 2119, -3*w^3 - 2*w^2 + 11*w + 3]', '[2123, 2123, -w^3 + 12*w - 5]', '[2129, 2129, 3*w^3 + w^2 - 22*w - 10]', '[2129, 2129, 2*w^2 - 5*w - 6]', '[2131, 2131, 3*w^3 - 12*w + 2]', '[2131, 2131, w^2 + w - 11]', '[2133, 237, 2*w^3 + w^2 - 13*w - 13]', '[2133, 2133, 4*w^3 - 3*w^2 - 25*w + 12]', '[2145, 2145, 3*w^3 - 2*w^2 - 15*w - 1]', '[2145, 2145, 3*w^3 - 22*w + 5]', '[2151, 2151, 4*w^3 - 2*w^2 - 21*w]', '[2151, 2151, -2*w^3 - 2*w^2 + 15*w + 3]', '[2155, 2155, -3*w^3 + w^2 + 9*w + 3]', '[2155, 2155, 8*w^3 + w^2 - 40*w - 20]', '[2157, 2157, 3*w^3 - 14*w - 2]', '[2157, 2157, 2*w^3 - 2*w^2 - 15*w - 2]', '[2160, 30, 2*w^3 - 2*w^2 - 16*w + 2]', '[2160, 30, 2*w^3 - 2*w^2 - 16*w - 4]', '[2160, 270, 2*w^3 + 2*w^2 - 8*w - 8]', '[2160, 270, 4*w^3 - 2*w^2 - 20*w - 2]', '[2161, 2161, -w^3 + w^2 + 3*w - 12]', '[2161, 2161, 3*w^3 - w^2 - 20*w]', '[2167, 2167, 2*w^3 - 3*w^2 - 12*w + 7]', '[2179, 2179, 2*w^3 - w^2 - 13*w + 10]', '[2179, 2179, 3*w^3 + 3*w^2 - 17*w - 16]', '[2181, 2181, -3*w^3 - 5*w^2 + 9*w + 11]', '[2181, 2181, 3*w^3 - 13*w - 4]', '[2187, 9, 3*w^3 - 3*w^2 - 15*w + 12]', '[2187, 81, 3*w^2 - 3*w - 6]', '[2187, 2187, 2*w^3 + 3*w^2 - 9*w - 10]', '[2195, 2195, 5*w^3 - 2*w^2 - 25*w + 7]', '[2195, 2195, w^3 - 3*w^2 + 5*w + 2]', '[2195, 2195, -w^3 - w^2 + 3*w + 7]', '[2195, 2195, 2*w^3 + 4*w^2 - 21*w - 12]', '[2197, 13, 2*w^3 + 3*w^2 - 14*w - 10]', '[2197, 2197, -2*w^3 - 2*w^2 + 14*w + 13]', '[2199, 2199, -w^3 + w^2 - w + 3]', '[2207, 2207, 2*w^3 + 2*w^2 - 15*w - 11]', '[2207, 2207, -3*w^3 + 2*w^2 + 18*w - 13]', '[2207, 2207, 3*w^3 - 12*w - 7]', '[2207, 2207, -3*w^3 + 3*w^2 + 14*w - 2]', '[2209, 2209, 3*w^3 - 20*w - 4]', '[2211, 2211, w^3 - 4*w^2 - 16*w - 2]', '[2213, 2213, 3*w^3 - 2*w^2 - 11*w + 2]', '[2213, 2213, 4*w^3 - 2*w^2 - 23*w + 2]', '[2215, 2215, -w^2 + 3*w + 8]', '[2215, 2215, 3*w^3 - w^2 - 17*w + 9]', '[2217, 2217, -3*w^3 - 2*w^2 + 7*w - 3]', '[2223, 2223, -3*w^3 - w^2 + 15*w - 2]', '[2229, 2229, -5*w^3 + 29*w + 12]', '[2239, 2239, 3*w^2 + w - 12]', '[2239, 2239, 2*w^3 - 15*w - 3]', '[2245, 2245, 4*w^3 - 5*w^2 - 21*w + 7]', '[2245, 2245, 2*w^2 - 2*w + 3]', '[2249, 2249, -3*w^3 + w^2 + 19*w + 7]', '[2249, 2249, 6*w^3 - 3*w^2 - 32*w + 15]', '[2249, 2249, -w^3 + 3*w^2 + 12*w + 3]', '[2249, 2249, -w^2 + 4*w + 6]', '[2251, 2251, 6*w^3 - w^2 - 33*w - 3]', '[2253, 2253, w^3 - w^2 - 9*w - 7]', '[2253, 2253, -3*w^3 - 3*w^2 + 17*w + 8]', '[2255, 2255, 8*w^3 + 4*w^2 - 47*w - 26]', '[2255, 2255, -3*w^3 - w^2 + 17*w + 2]', '[2256, 282, 4*w^3 + 2*w^2 - 22*w - 8]', '[2257, 2257, 3*w^3 - 18*w - 11]', '[2259, 2259, 7*w^3 - 2*w^2 - 39*w + 3]', '[2259, 2259, -w^3 - 2*w^2 + 5*w - 3]', '[2267, 2267, 2*w^3 + 3*w^2 - 13*w - 15]', '[2269, 2269, 4*w^3 + w^2 - 21*w - 2]', '[2271, 2271, 3*w^3 - w^2 - 18*w - 5]', '[2281, 2281, 2*w^3 - 15*w]', '[2281, 2281, -w^3 + 3*w^2 + 6*w - 12]', '[2283, 2283, 2*w^3 + 3*w^2 - 4*w - 5]', '[2285, 2285, 2*w^3 - w^2 - 11*w - 7]', '[2285, 2285, w^2 + 2*w + 5]', '[2285, 2285, -2*w^3 + 3*w^2 + 11*w - 2]', '[2285, 2285, -2*w^3 + 17*w + 10]', '[2288, 286, 4*w - 6]', '[2297, 2297, 3*w^3 - w^2 - 18*w - 6]', '[2297, 2297, w^3 - 8*w - 9]', '[2299, 209, 5*w^3 - 31*w - 13]', '[2299, 209, 9*w^3 - 6*w^2 - 51*w + 22]', '[2304, 36, 4*w - 8]', '[2307, 2307, -w^3 + 3*w^2 + 3*w - 7]', '[2307, 2307, 2*w^3 + w^2 - 8*w - 7]', '[2311, 2311, 3*w^3 + 2*w^2 - 21*w - 13]', '[2319, 2319, w^3 + 3*w^2 - 8*w - 7]', '[2319, 2319, -8*w - 5]', '[2325, 465, -3*w^3 + 2*w^2 + 21*w - 5]', '[2325, 465, 3*w^3 + 2*w^2 - 14*w - 10]', '[2325, 2325, w^3 + w^2 - 9*w - 9]', '[2325, 2325, -2*w^3 + 2*w^2 + 14*w + 1]', '[2327, 2327, 3*w^3 - w^2 - 20*w + 1]', '[2333, 2333, 4*w^3 + w^2 - 19*w - 8]', '[2337, 2337, -5*w^3 + 27*w + 7]', '[2339, 2339, -5*w^3 + 3*w^2 + 29*w - 16]', '[2339, 2339, w^3 - 5*w - 8]', '[2347, 2347, w^3 + w^2 - 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w^2 - 27*w - 1]', '[2399, 2399, 5*w^3 - 30*w - 11]', '[2401, 7, -7]', '[2405, 2405, 5*w^3 + w^2 - 26*w - 11]', '[2405, 2405, 11*w^3 + 5*w^2 - 64*w - 32]', '[2413, 2413, -w^3 + w^2 + 3*w + 6]', '[2413, 2413, -10*w^3 + 6*w^2 + 56*w - 25]', '[2421, 2421, -6*w^3 + 31*w + 13]', '[2423, 2423, 5*w^3 - 2*w^2 - 27*w]', '[2423, 2423, -7*w^3 + 5*w^2 + 39*w - 16]', '[2425, 485, -8*w^3 + 4*w^2 + 43*w - 13]', '[2425, 485, -3*w^3 + 2*w^2 + 11*w - 5]', '[2425, 485, -3*w^3 + 4*w^2 + 13*w - 8]', '[2425, 485, 2*w^3 - 4*w^2 - 15*w + 7]', '[2425, 485, 4*w^3 - 5*w^2 - 32*w + 3]', '[2425, 485, -7*w^3 + w^2 + 42*w + 3]', '[2425, 485, -w^2 + 6*w - 7]', '[2425, 485, w^3 - 2*w^2 - 10*w + 6]', '[2425, 2425, -9*w^3 + 2*w^2 + 51*w - 3]', '[2425, 2425, -6*w^3 + 5*w^2 + 35*w - 19]', '[2425, 2425, -w^3 - w^2 + 11*w + 3]', '[2425, 2425, -2*w^2 - 3]', '[2425, 2425, -3*w^3 + 22*w - 10]', '[2425, 2425, -5*w^3 + w^2 + 34*w - 10]', '[2425, 2425, -4*w^3 + 5*w^2 + 16*w - 10]', '[2425, 2425, -6*w^3 + 5*w^2 + 29*w - 8]', '[2427, 2427, -4*w^3 + w^2 + 22*w + 5]', '[2433, 2433, w^3 - 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6]', '[5335, 5335, -9*w^3 - 3*w^2 + 48*w + 16]', '[5335, 5335, -4*w^3 + 6*w^2 + 29*w - 16]', '[5335, 5335, -w^2 - 6]', '[5339, 5339, 6*w^3 - 5*w^2 - 30*w + 15]', '[5345, 5345, 10*w^3 + 2*w^2 - 61*w - 25]', '[5345, 5345, 10*w^3 + 3*w^2 - 56*w - 24]', '[5345, 5345, 3*w^3 - 2*w^2 - 14*w + 13]', '[5345, 5345, w^3 - 3*w^2 - 9*w + 11]', '[5347, 5347, -w^3 + 6*w - 8]', '[5351, 5351, -5*w^3 + 2*w^2 + 25*w - 1]', '[5357, 5357, 6*w^3 - 32*w + 3]', '[5360, 670, 6*w^3 - 36*w - 14]', '[5360, 670, 2*w^3 - 10*w + 8]', '[5361, 5361, 2*w^3 + 2*w^2 - 14*w + 1]', '[5363, 5363, -w^3 - 4*w^2 + 2*w + 15]', '[5363, 5363, -w^3 + w^2 + 4*w + 7]', '[5363, 5363, 3*w^2 + 7*w - 6]', '[5363, 5363, 4*w^3 + w^2 - 21*w + 5]', '[5367, 5367, 3*w^3 - 2*w^2 - 23*w - 12]', '[5375, 215, 8*w^3 + 3*w^2 - 45*w - 18]', '[5375, 215, 2*w^3 - 4*w^2 - 14*w + 11]', '[5375, 1075, -4*w^3 + w^2 + 28*w + 15]', '[5375, 1075, -w^2 + 4*w + 12]', '[5375, 5375, 6*w + 7]', '[5375, 5375, -6*w^3 - w^2 + 39*w + 23]', '[5379, 5379, -2*w^3 + 10*w + 11]', '[5381, 5381, -6*w^3 + 38*w - 3]', '[5387, 5387, -4*w^3 - 4*w^2 + 25*w + 15]', '[5391, 5391, -4*w^2 + 8*w + 9]', '[5391, 5391, w^3 + w^2 - 2*w - 8]', '[5392, 674, 2*w^3 + 2*w^2 - 8*w - 10]', '[5393, 5393, 5*w^3 - w^2 - 26*w - 1]', '[5399, 5399, 2*w^3 - w^2 - 17*w + 3]', '[5401, 5401, -w^3 + 4*w^2 + 13*w + 1]', '[5403, 5403, -5*w^3 - 4*w^2 + 31*w + 15]', '[5407, 5407, 4*w^3 - 3*w^2 - 15*w + 3]', '[5409, 5409, -2*w^3 + 7*w + 11]', '[5413, 5413, 5*w^3 - 3*w^2 - 33*w + 9]', '[5415, 5415, 4*w^3 - 2*w^2 - 27*w + 6]', '[5415, 5415, 3*w^3 - 2*w^2 - 19*w - 2]', '[5419, 5419, -5*w^3 + w^2 + 33*w - 7]', '[5427, 201, 3*w^2 + 3*w - 12]', '[5427, 5427, 7*w^3 + w^2 - 44*w - 17]', '[5431, 5431, -10*w^3 + 5*w^2 + 60*w - 17]', '[5433, 5433, 4*w^3 + w^2 - 18*w - 6]', '[5433, 5433, w^3 - w^2 - 6*w - 7]', '[5435, 5435, 3*w^3 - w^2 - 11*w - 9]', '[5435, 5435, 6*w^3 + w^2 - 31*w - 13]', '[5435, 5435, -5*w^3 + 4*w^2 + 21*w - 5]', '[5435, 5435, -w^2 - 5*w + 6]', '[5441, 5441, 11*w^3 - 4*w^2 - 63*w + 19]', '[5445, 495, -7*w^3 + 3*w^2 + 42*w - 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2*w^2 - 21*w - 8]', '[5503, 5503, -5*w^3 + w^2 + 29*w + 6]', '[5505, 5505, 7*w^3 + w^2 - 37*w - 16]', '[5505, 5505, 3*w^3 + 2*w^2 - 20*w - 4]', '[5507, 5507, 9*w^3 - 4*w^2 - 51*w + 9]', '[5507, 5507, -4*w^3 + 5*w^2 + 22*w - 9]', '[5507, 5507, 3*w^3 - 2*w^2 - 17*w - 5]', '[5507, 5507, 3*w^3 - 5*w^2 - 19*w + 8]', '[5517, 5517, -w^3 + 3*w + 11]', '[5517, 5517, w^3 + 9*w^2 - 23*w - 16]', '[5519, 5519, 2*w^3 - 16*w + 11]', '[5519, 5519, 6*w^3 - 2*w^2 - 37*w + 5]', '[5521, 5521, 8*w^3 - 5*w^2 - 49*w + 19]', '[5521, 5521, 5*w^3 - 32*w - 1]', '[5527, 5527, 8*w^3 - 3*w^2 - 42*w]', '[5529, 5529, -4*w^3 + w^2 + 28*w - 7]', '[5529, 5529, -3*w^2 - 4*w - 4]', '[5529, 5529, -5*w^3 + 4*w^2 + 25*w - 5]', '[5529, 5529, -3*w^3 + 5*w^2 + 19*w - 19]', '[5531, 5531, -5*w^3 + 2*w^2 + 26*w - 15]', '[5531, 5531, 4*w^3 - w^2 - 19*w]', '[5533, 5533, 3*w^3 - 2*w^2 - 18*w - 2]', '[5533, 5533, -w^2 + 4*w + 10]', '[5535, 615, -5*w^3 - w^2 + 25*w + 4]', '[5535, 615, -8*w^3 - 4*w^2 + 43*w + 19]', '[5535, 5535, -6*w^3 - 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w^2 - 6*w - 2]', '[157, 157, -2*w^3 + 2*w^2 + 10*w - 7]', '[157, 157, w - 4]', '[163, 163, 2*w^3 - w^2 - 13*w + 3]', '[173, 173, -2*w^3 + w^2 + 13*w - 6]', '[173, 173, 2*w^3 - 12*w + 1]', '[173, 173, 2*w^3 - 11*w + 2]', '[173, 173, w^2 + w - 5]', '[179, 179, -2*w^3 + 10*w + 3]', '[181, 181, -w^3 - w^2 + 7*w + 8]', '[191, 191, w^3 - 5*w - 5]', '[191, 191, 2*w^3 - w^2 - 9*w - 1]', '[193, 193, -3*w^3 + 3*w^2 + 19*w - 7]', '[197, 197, -w^3 + w^2 + 6*w - 7]', '[223, 223, w^3 + w^2 - 6*w + 1]', '[227, 227, 6*w^3 - 3*w^2 - 34*w + 9]', '[227, 227, w^3 + w^2 - 8*w]', '[233, 233, 2*w^3 - 13*w - 3]', '[233, 233, -w^3 + 2*w^2 + 4*w - 6]', '[239, 239, -2*w^3 + 10*w + 1]', '[239, 239, w^3 - 8*w - 2]', '[251, 251, -3*w^3 + w^2 + 18*w]', '[251, 251, -5*w^3 + 2*w^2 + 30*w - 11]', '[263, 263, -2*w^3 + w^2 + 10*w + 2]', '[269, 269, 3*w^3 - 18*w - 8]', '[271, 271, 2*w^3 + w^2 - 10*w - 2]', '[271, 271, -3*w^3 + 19*w]', '[277, 277, -w^3 + w^2 + 4*w - 8]', '[277, 277, 2*w^3 + w^2 - 14*w - 8]', '[281, 281, w^3 - 8*w]', '[307, 307, 3*w^3 - w^2 - 16*w + 2]', '[307, 307, 2*w^3 - w^2 - 9*w + 1]', '[307, 307, -2*w^3 + 2*w^2 + 13*w - 7]', '[307, 307, -w^3 + w^2 + 7*w - 6]', '[313, 313, -3*w^3 + w^2 + 15*w + 4]', '[317, 317, -4*w^3 + w^2 + 22*w - 3]', '[317, 317, 2*w^3 - w^2 - 10*w - 3]', '[337, 337, w^3 + w^2 - 4*w - 5]', '[349, 349, -2*w^3 - w^2 + 11*w + 3]', '[349, 349, -4*w^3 + 2*w^2 + 24*w - 11]', '[353, 353, 3*w^3 - w^2 - 17*w + 7]', '[353, 353, -3*w^3 - 2*w^2 + 17*w + 11]', '[367, 367, 2*w^3 - 11*w - 7]', '[373, 373, -w^3 + w^2 + 4*w - 5]', '[383, 383, -4*w^3 + 3*w^2 + 23*w - 9]', '[383, 383, 4*w^3 - w^2 - 22*w]', '[389, 389, w^2 - 2*w - 5]', '[401, 401, -3*w^3 + 2*w^2 + 16*w - 9]', '[401, 401, 2*w^3 - w^2 - 14*w - 1]', '[409, 409, 2*w^3 + 2*w^2 - 13*w - 9]', '[419, 419, -4*w^3 + 24*w + 7]', '[419, 419, 2*w^2 + 2*w - 7]', '[419, 419, -w^3 + 2*w^2 + 8*w - 6]', '[419, 419, 6*w^3 - 3*w^2 - 33*w + 13]', '[431, 431, 2*w^3 - w^2 - 12*w - 5]', '[439, 439, -3*w^3 + 2*w^2 + 18*w - 4]', '[439, 439, w^3 + 2*w^2 - 7*w - 3]', '[443, 443, 6*w^3 - 3*w^2 - 33*w + 7]', '[449, 449, -3*w^3 + w^2 + 14*w - 4]', '[457, 457, 2*w^3 - 9*w]', '[457, 457, 3*w^3 - w^2 - 16*w - 2]', '[479, 479, 3*w^3 - w^2 - 19*w + 4]', '[487, 487, -w^3 + w^2 + 4*w - 6]', '[491, 491, 3*w^3 + w^2 - 17*w - 5]', '[499, 499, 5*w^3 - 3*w^2 - 28*w + 8]', '[499, 499, 2*w^3 - w^2 - 12*w - 1]', '[503, 503, -2*w^3 - w^2 + 12*w + 3]', '[503, 503, w^3 - 3*w - 4]', '[509, 509, -3*w - 5]', '[509, 509, -4*w^3 + 3*w^2 + 25*w - 10]', '[523, 523, -2*w^3 + w^2 + 14*w - 6]', '[529, 23, 4*w^3 - 2*w^2 - 21*w + 5]', '[529, 23, -3*w^3 - w^2 + 15*w + 6]', '[557, 557, -2*w^3 + w^2 + 13*w + 2]', '[557, 557, 3*w^3 - 2*w^2 - 16*w + 3]', '[569, 569, 2*w^2 - w - 8]', '[587, 587, w^3 + 2*w^2 - 5*w - 16]', '[587, 587, -4*w^3 + w^2 + 25*w - 5]', '[599, 599, w^3 + 2*w^2 - 6*w - 5]', '[599, 599, -5*w^3 + 3*w^2 + 30*w - 15]', '[601, 601, w^3 - 6*w - 6]', '[607, 607, -w^3 + w^2 + 3*w - 4]', '[607, 607, -w^3 + 2*w - 3]', '[613, 613, 6*w^3 - 2*w^2 - 31*w + 11]', '[613, 613, w^3 + w^2 - 4*w - 6]', '[617, 617, 5*w^3 - w^2 - 30*w + 2]', '[617, 617, -2*w^3 + 2*w^2 + 9*w + 3]', '[619, 619, -w^3 + 2*w^2 + 6*w - 5]', '[619, 619, 2*w^3 - w^2 - 11*w - 3]', '[631, 631, -w^3 + 2*w^2 + 5*w - 5]', '[631, 631, -3*w^3 - w^2 + 18*w + 5]', '[647, 647, 6*w^3 - w^2 - 36*w + 2]', '[659, 659, 4*w^3 + w^2 - 24*w - 14]', '[661, 661, 2*w^2 - w - 4]', '[673, 673, 2*w^3 + w^2 - 14*w - 12]', '[677, 677, 3*w^3 + 2*w^2 - 16*w - 7]', '[677, 677, -3*w^3 + w^2 + 15*w + 1]', '[683, 683, 2*w^2 - 2*w - 9]', '[683, 683, 2*w^3 - 14*w + 1]', '[691, 691, 5*w^3 - 2*w^2 - 30*w + 6]', '[701, 701, -2*w^3 + w^2 + 12*w + 2]', '[701, 701, -5*w^3 + 2*w^2 + 26*w]', '[719, 719, 3*w^3 - 18*w + 1]', '[719, 719, 3*w^3 - w^2 - 19*w + 1]', '[727, 727, -3*w^2 - 2*w + 11]', '[727, 727, 2*w^3 + w^2 - 13*w - 2]', '[733, 733, 2*w^3 - 3*w^2 - 8*w + 5]', '[739, 739, -3*w^3 + 16*w - 6]', '[743, 743, -4*w^3 - w^2 + 25*w + 8]', '[751, 751, w^2 - 2*w - 7]', '[751, 751, -3*w^3 + 15*w + 5]', '[757, 757, 3*w^3 - 19*w - 2]', '[761, 761, 2*w^2 + w - 5]', '[769, 769, -2*w^3 + w^2 + 14*w - 9]', '[769, 769, 2*w^2 - w - 7]', '[773, 773, w^3 - w^2 - 5*w - 4]', '[773, 773, w^3 - 3*w - 6]', '[787, 787, 3*w^3 - 19*w - 3]', '[797, 797, 8*w^3 - 3*w^2 - 47*w + 10]', '[809, 809, 4*w^3 - 25*w - 1]', '[811, 811, w^3 - 9*w - 1]', '[821, 821, 6*w^3 - 3*w^2 - 35*w + 8]', '[823, 823, 2*w^3 + w^2 - 10*w + 1]', '[823, 823, -2*w^3 + 2*w^2 + 7*w - 4]', '[829, 829, -5*w^3 + w^2 + 27*w - 4]', '[829, 829, 5*w^3 - 2*w^2 - 26*w + 10]', '[839, 839, w^3 + 2*w^2 - 5*w - 7]', '[839, 839, 3*w^3 - w^2 - 15*w + 2]', '[841, 29, 3*w^3 + w^2 - 14*w - 2]', '[841, 29, 4*w^3 - 2*w^2 - 21*w + 10]', '[857, 857, -8*w^3 + 4*w^2 + 44*w - 11]', '[857, 857, -3*w^3 + 3*w^2 + 20*w - 9]', '[859, 859, w^3 + 2*w^2 - 6*w - 6]', '[877, 877, w^3 - 3*w^2 - 4*w + 14]', '[883, 883, 2*w^3 + w^2 - 10*w - 11]', '[887, 887, 3*w^3 + w^2 - 20*w - 2]', '[919, 919, 7*w^3 - 3*w^2 - 39*w + 9]', '[929, 929, 3*w^3 - 17*w + 2]', '[929, 929, -6*w^3 + 2*w^2 + 35*w - 10]', '[937, 937, w^3 + w^2 - 3*w - 5]', '[937, 937, -2*w^3 + 3*w^2 + 12*w - 12]', '[937, 937, -3*w^3 - 2*w^2 + 19*w + 8]', '[937, 937, 3*w^3 - 2*w^2 - 13*w + 3]', '[941, 941, w^3 + 2*w^2 - 6*w - 8]', '[941, 941, 5*w^3 - w^2 - 28*w - 3]', '[947, 947, -4*w^3 + 2*w^2 + 25*w - 6]', '[953, 953, w^3 - 7*w - 7]', '[953, 953, -3*w^3 + 2*w^2 + 18*w - 3]', '[967, 967, w^3 - 2*w^2 - 5*w - 3]', '[971, 971, w^2 + 2*w - 6]', '[977, 977, 2*w^3 - 11*w - 8]', '[997, 997, -3*w^3 + w^2 + 17*w + 2]', '[997, 997, -2*w^3 + 2*w^2 + 14*w - 7]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, -6, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 16357, 'disc_rad': 16357, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[3, 1], [1, 1]]], [5, [[2, 1], [1, 2]]], [7, [[4, 1]]], [11, [0]], [13, [[3, 1], [1, 1]]], [17, [[4, 1]]], [19, [[3, 1], [1, 1]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[3, 1], [1, 1]]], [37, [[3, 1], [1, 1]]], [41, [[3, 1], [1, 1]]], [43, [[3, 1], [1, 1]]], [47, [[3, 1], [1, 1]]], [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': 127.89448776237387, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.16357.1', 'local_algs': ['11.2.0.1', '11.2.1.1', 'm1487.1.2.0', 'm1487.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [11, 1487], 'rd': 11.3090445115, 'regulator': {'__RealLiteral__': 0, 'data': '8.07607772386', 'prec': 44}, 'res': {'gal': ['68970256,439608080,576419360,-911718078,-1649468937,845703912,1785466394,-502354106,-1050821872,225965568,378151812,-78353774,-86923755,19633294,12781328,-3330484,-1154124,362580,56664,-23752,-905,836,-30,-12,1'], 'sib': ['-1,0,32,0,-12,0,1', '1,16,29,-289,186,529,-400,-317,186,63,-29,-3,1', '224,-1895,1802,185,-90,-3,1', '50176,0,-121189,0,69092,0,-15424,0,1492,0,-64,0,1', '947511,-48775,-135945,3500,6851,-50,-140,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} - 6 a - 1 \\)', '\\( a^{3} - 5 a + 1 \\)', '\\( a^{3} - 6 a - 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}