Hilbert modular form data - 4.4.7056.1-12.1-a

Formats: - HTML - YAML - JSON - 2024-04-30T15:30:44.089507

• 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': 7056, 'field_bad_primes': [2, 3, 7], 'field_label': '4.4.7056.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '4.4.7056.1-12.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2, 3], 'level_ideal': '[12, 6, -w^3 - w^2 + 5*w + 2]', 'level_label': '12.1', 'level_norm': 12, 'parallel_weight': 2, 'short_label': '12.1-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^3+5*w+1]', -1], ['[4,2,-w^3+4*w-1]', -1]], 'hecke_eigenvalues': [1, 2, 1, 2, 2, 2, -10, 2, -10, -6, -6, 6, 6, -10, 6, 6, 12, 12, -6, -6, 12, 12, -10, 2, -10, 2, 2, 2, 6, 0, 6, 0, 12, 12, 0, 0, -22, -22, 2, 2, -10, -10, 0, -18, 0, -18, -24, -6, -24, -6, 14, -10, 14, -10, 2, 2, -6, -6, -6, -6, -22, -22, 26, 26, 26, -34, 14, 26, 14, 26, 6, -6, 6, -6, 36, 36, -30, -30, -10, -10, 2, 2, -22, 2, -22, 2, -6, -12, -6, -12, -18, -18, 18, 18, -18, -18, -18, -18, -10, -10, 2, 38, 2, 38, 24, 24, -42, -42, 18, 18, -48, -48, -10, 38, -10, 38, -36, -36, 0, 0, 2, 2, -46, -46, -46, 14, -46, 14, -6, 30, -6, 30, 14, -10, 14, -10, 12, 12, 0, 0, -22, -22, 38, 38, 14, 14, 36, 48, 36, 48, 38, -58, 24, 24, 42, 42, 0, 0, -12, -12], 'hecke_polynomial': 'x', 'label': '4.4.7056.1-12.1-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 7056, 'ideals': ['[1, 1, 1]', '[3, 3, -w^3 + 5*w + 1]', '[3, 3, w - 1]', '[4, 2, -w^3 + 4*w - 1]', '[9, 3, w^3 - w^2 - 5*w + 3]', '[9, 3, -w^3 - w^2 + 5*w + 3]', '[9, 3, w^3 - 4*w]', '[12, 6, -w^3 - w^2 + 5*w + 2]', '[12, 6, w^3 - w^2 - 3*w]', '[16, 2, 2]', '[25, 5, w^2 - 3]', '[25, 5, w^2 - 2]', '[27, 3, -w^3 + w^2 + 4*w - 1]', '[27, 3, w^3 + w^2 - 4*w - 4]', '[27, 9, -w^3 + 3*w + 2]', '[27, 9, -w^3 + 3*w - 2]', '[36, 6, -w^3 + 6*w - 1]', '[36, 6, -w^3 + 6*w + 1]', '[36, 6, -w^3 + 4*w - 3]', '[37, 37, w + 3]', '[37, 37, w^3 - 5*w + 3]', '[37, 37, -w^3 + 5*w + 3]', '[37, 37, -w + 3]', '[47, 47, w^3 - 3*w - 3]', '[47, 47, w^3 + w^2 - 6*w - 1]', '[47, 47, w^3 - w^2 - 6*w + 1]', '[47, 47, -w^3 - w^2 + 6*w + 4]', '[48, 6, -2*w^3 + 10*w + 2]', '[48, 6, 2*w - 2]', '[49, 7, w^3 - 6*w]', '[59, 59, -w^3 + w^2 + 4*w - 5]', '[59, 59, -w^3 + w^2 + 4*w]', '[59, 59, w^3 + w^2 - 4*w]', '[59, 59, w^3 + w^2 - 4*w - 5]', '[64, 4, -2*w^3 + 8*w - 2]', '[75, 15, w^3 + w^2 - 3*w - 3]', '[75, 15, 2*w^3 + w^2 - 9*w - 2]', '[75, 15, w^3 - w^2 - 3*w + 3]', '[75, 15, -2*w^3 + w^2 + 9*w - 2]', '[81, 3, 3]', '[81, 9, w^3 - 6*w + 4]', '[81, 9, -w^3 + 6*w + 4]', '[81, 9, 2*w^3 - w^2 - 11*w + 4]', '[81, 9, w^3 - w^2 - 7*w + 1]', '[83, 83, -3*w + 2]', '[83, 83, -w^3 + w^2 + 7*w + 1]', '[83, 83, w^3 - w^2 - 6*w + 7]', '[83, 83, -2*w^3 + w^2 + 11*w - 6]', '[100, 10, w^3 + w^2 - 7*w - 2]', '[100, 10, 2*w^3 + w^2 - 11*w - 3]', '[108, 6, -w^3 + w^2 + w + 2]', '[108, 6, w^3 + w^2 - 7*w - 4]', '[108, 18, -w^3 + w^2 + 5*w]', '[108, 18, w^3 + w^2 - 5*w]', '[109, 109, 2*w^3 - 2*w^2 - 9*w + 5]', '[109, 109, 2*w^3 - 11*w + 2]', '[109, 109, w^2 + 2*w + 2]', '[109, 109, 5*w^3 + 2*w^2 - 23*w - 9]', '[111, 111, w^3 - w^2 - 6*w + 5]', '[111, 111, -w^2 + 2*w + 3]', '[111, 111, -w^3 - w^2 + 6*w]', '[111, 111, -2*w^3 + w^2 + 10*w - 2]', '[111, 111, 2*w^3 + w^2 - 10*w - 2]', '[111, 111, w^3 - w^2 - 6*w]', '[111, 111, w^2 + 2*w - 3]', '[111, 111, w^3 + w^2 - 6*w - 5]', '[121, 11, -2*w^3 + 8*w + 1]', '[121, 11, 2*w^3 - 8*w + 1]', '[131, 131, 2*w^3 - 2*w^2 - 5*w + 3]', '[131, 131, -5*w^3 - 2*w^2 + 23*w + 7]', '[131, 131, -3*w^3 - 2*w^2 + 15*w + 6]', '[131, 131, -3*w^3 - 2*w^2 + 13*w + 5]', '[141, 141, -2*w^3 + 7*w - 2]', '[141, 141, 2*w^2 - 2*w - 3]', '[141, 141, -w^3 + 2*w^2 + 2]', '[141, 141, -2*w^2 + 5*w]', '[141, 141, -2*w - 5]', '[141, 141, -2*w^3 + 10*w + 5]', '[141, 141, w^3 + 2*w^2 - 6*w - 4]', '[141, 141, 2*w^3 + 2*w^2 - 10*w - 7]', '[144, 6, 2*w^3 - 2*w^2 - 10*w + 6]', '[144, 6, -2*w^3 - 2*w^2 + 10*w + 6]', '[144, 6, 2*w^3 - 8*w]', '[147, 21, w^3 + w^2 - 6*w - 6]', '[147, 21, -w^3 - w^2 + 6*w - 1]', '[148, 74, -3*w^3 - w^2 + 13*w + 4]', '[148, 74, -2*w^3 + w^2 + 7*w - 1]', '[148, 74, -2*w^3 - w^2 + 7*w + 1]', '[148, 74, -3*w^3 + w^2 + 13*w - 4]', '[167, 167, w^3 - 2*w^2 - w + 3]', '[167, 167, 2*w^3 - w^2 - 7*w + 4]', '[167, 167, 2*w^3 - 2*w^2 - 8*w + 3]', '[167, 167, -3*w^3 - w^2 + 13*w + 1]', '[169, 13, 2*w^3 - 8*w - 5]', '[169, 13, w^3 - 4*w - 4]', '[177, 177, 4*w^3 - 20*w - 1]', '[177, 177, 4*w - 1]', '[177, 177, 6*w^3 + 2*w^2 - 28*w - 9]', '[177, 177, 2*w^3 - 2*w^2 - 4*w + 1]', '[177, 177, w^3 + 2*w^2 - 3*w - 4]', '[177, 177, 2*w^3 - 2*w^2 - 9*w + 6]', '[177, 177, -w^3 + 5*w + 4]', '[177, 177, -w + 4]', '[188, 94, 2*w^3 - w^2 - 9*w + 1]', '[188, 94, -w^3 + w^2 + 3*w - 4]', '[188, 94, -w^3 + 3*w^2 + 9*w - 6]', '[188, 94, -2*w^3 - w^2 + 9*w + 1]', '[192, 12, -2*w^3 - 2*w^2 + 10*w + 4]', '[192, 12, 2*w^3 - 2*w^2 - 6*w]', '[193, 193, w^3 - 7*w - 1]', '[193, 193, 2*w^3 - 11*w - 1]', '[193, 193, -2*w^3 + 11*w - 1]', '[193, 193, w^3 - 7*w + 1]', '[196, 14, -w^3 + 2*w^2 + 6*w - 5]', '[225, 15, -2*w^3 + 11*w]', '[225, 15, 3*w^3 + w^2 - 14*w - 8]', '[225, 15, -3*w^3 + w^2 + 14*w - 8]', '[225, 15, -w^3 + 7*w]', '[225, 15, 2*w^3 - 9*w - 5]', '[225, 15, w^3 - w^2 - 2*w - 3]', '[227, 227, -2*w^3 - w^2 + 8*w + 6]', '[227, 227, 2*w^3 - w^2 - 8*w - 1]', '[227, 227, -2*w^3 - w^2 + 8*w - 1]', '[227, 227, w^3 + 2*w^2 - 7*w - 6]', '[236, 118, 5*w^3 - w^2 - 23*w + 8]', '[236, 118, -w^2 - 3*w + 3]', '[236, 118, -2*w^3 - w^2 + 5*w - 3]', '[236, 118, 3*w^3 - w^2 - 15*w + 2]', '[243, 9, 2*w^3 - w^2 - 8*w - 2]', '[243, 9, -2*w^3 - w^2 + 8*w - 2]', '[243, 9, -3*w^3 + 15*w + 3]', '[243, 9, 3*w - 3]', '[243, 27, -3*w^3 + w^2 + 14*w - 2]', '[243, 27, 3*w^3 + w^2 - 14*w - 2]', '[249, 249, -2*w^3 + 13*w + 8]', '[249, 249, 2*w^2 - w - 6]', '[249, 249, 3*w^3 - 17*w + 8]', '[249, 249, -w^3 - 2*w^2 + 5*w + 4]', '[249, 249, 4*w^3 - w^2 - 18*w + 5]', '[249, 249, 8*w^3 + 3*w^2 - 40*w - 17]', '[249, 249, 2*w^3 + w^2 - 6*w]', '[249, 249, -3*w^2 + 8*w - 2]', '[251, 251, w^2 + 2*w - 4]', '[251, 251, 2*w^3 - w^2 - 10*w + 1]', '[251, 251, -2*w^3 - w^2 + 10*w + 1]', '[251, 251, w^2 - 2*w - 4]', '[256, 4, 4]', '[277, 277, w^3 - 2*w^2 - 4*w + 6]', '[277, 277, -4*w^3 - w^2 + 18*w + 4]', '[277, 277, w^3 - 2*w^2 - 4*w + 4]', '[277, 277, w^3 + 2*w^2 - 4*w - 6]', '[289, 17, 2*w^3 - 7*w]', '[289, 17, 3*w^3 - 13*w]', '[300, 30, w^3 - 2*w^2 - 8*w + 1]', '[300, 30, -w^3 + 2*w - 5]', '[300, 30, 3*w^3 - 2*w^2 - 16*w + 9]', '[300, 30, -3*w^3 + 14*w - 5]', '[311, 311, 2*w^3 + w^2 - 11*w]', '[311, 311, w^3 - w^2 - 7*w + 5]', '[311, 311, w^3 + w^2 - 7*w - 5]', '[311, 311, -2*w^3 + w^2 + 11*w]', '[324, 6, -3*w^3 + 12*w - 3]', '[324, 18, w^3 - 6*w + 5]', '[324, 18, -w^3 + 6*w + 5]', '[324, 18, -w^3 + 2*w^2 + 4*w - 5]', '[324, 18, w^3 + 2*w^2 - 4*w - 5]', '[327, 327, w^3 + w^2 - 3*w - 5]', '[327, 327, -2*w^3 - w^2 + 13*w - 4]', '[327, 327, 2*w^3 + w^2 - 9*w]', '[327, 327, -3*w^3 + 14*w + 4]', '[327, 327, -3*w^3 + 14*w - 4]', '[327, 327, 2*w^2 - w - 9]', '[327, 327, -4*w^3 - 2*w^2 + 21*w + 13]', '[327, 327, -w^3 + w^2 + 3*w - 5]', '[332, 166, 3*w^3 + 2*w^2 - 12*w - 3]', '[332, 166, -w^3 - 4*w^2 - 2*w + 5]', '[332, 166, -3*w^3 + 2*w^2 + 12*w - 7]', '[332, 166, 7*w^3 - 4*w^2 - 34*w + 15]', '[333, 111, -3*w^3 + w^2 + 16*w - 5]', '[333, 111, -w^3 - 2*w^2 + 5*w + 6]', '[333, 111, 3*w^3 + w^2 - 12*w - 1]', '[333, 111, -2*w^2 + w + 4]', '[333, 111, -w^3 + w^2 + 8*w]', '[333, 111, 3*w^3 - w^2 - 12*w + 4]', '[333, 111, 3*w^3 + w^2 - 12*w - 4]', '[333, 111, -2*w^2 - w + 4]', '[333, 111, -w^3 - w^2 + 8*w]', '[333, 111, -3*w^3 - w^2 + 16*w + 5]', '[333, 111, w^3 - 2*w^2 - 5*w + 6]', '[333, 111, 3*w^3 - w^2 - 12*w + 1]', '[337, 337, 2*w^2 + w - 5]', '[337, 337, w^3 + 2*w^2 - 5*w - 5]', '[337, 337, w^3 - 2*w^2 - 5*w + 5]', '[337, 337, 2*w^2 - w - 5]', '[361, 19, 5*w^3 - w^2 - 22*w + 1]', '[361, 19, -3*w^3 - w^2 + 10*w + 4]', '[363, 33, -3*w^3 - 2*w^2 + 13*w + 9]', '[363, 33, w^3 + 2*w^2 - 3*w - 7]', '[363, 33, 2*w^3 - 2*w^2 - 7*w + 1]', '[363, 33, -2*w^3 + 2*w^2 + 9*w - 3]', '[373, 373, 2*w^3 - w^2 - 12*w + 1]', '[373, 373, 2*w^3 + w^2 - 8*w - 9]', '[373, 373, -2*w^3 + w^2 + 8*w - 9]', '[373, 373, w^3 - 2*w^2 - w - 2]', '[383, 383, -4*w^3 - 2*w^2 + 21*w + 11]', '[383, 383, -3*w - 4]', '[383, 383, -w^3 - w^2 + 7*w + 9]', '[383, 383, 2*w^3 + w^2 - 11*w + 4]', '[393, 393, 3*w^3 - 16*w - 2]', '[393, 393, w^3 - 8*w - 2]', '[393, 393, w^3 - w^2 - 3*w - 3]', '[393, 393, 3*w^3 - w^2 - 13*w + 9]', '[393, 393, w^3 + 2*w^2 - 9*w - 3]', '[393, 393, w^3 + w^2 - 3*w + 3]', '[393, 393, -w^3 + 8*w - 2]', '[393, 393, -5*w^3 - 2*w^2 + 21*w + 9]', '[400, 10, 2*w^2 - 6]', '[400, 10, 2*w^2 - 4]', '[419, 419, 3*w - 5]', '[419, 419, 5*w - 3]', '[419, 419, 3*w^3 - 15*w - 5]', '[419, 419, 5*w^3 - 25*w - 3]', '[421, 421, -2*w^3 - 2*w^2 + 13*w + 5]', '[421, 421, 3*w^3 + w^2 - 16*w - 4]', '[421, 421, 3*w^3 + 2*w^2 - 17*w - 5]', '[421, 421, -w^3 - w^2 + 8*w + 1]', '[423, 141, w^2 - 2*w - 5]', '[423, 141, -2*w^3 + 2*w^2 + 7*w - 6]', '[423, 141, -3*w^3 + 2*w^2 + 15*w - 5]', '[423, 141, -2*w^2 + 3*w + 5]', '[423, 141, 5*w^3 - 21*w - 8]', '[423, 141, 3*w^3 - 2*w^2 - 13*w + 4]', '[423, 141, -2*w^2 - 3*w + 5]', '[423, 141, 5*w^3 - 21*w + 8]', '[423, 141, 3*w^3 + 2*w^2 - 13*w - 4]', '[423, 141, -2*w^3 - 2*w^2 + 7*w + 6]', '[423, 141, 3*w^3 + w^2 - 12*w + 2]', '[423, 141, -w^2 - 2*w + 5]', '[432, 6, -2*w^3 + 2*w^2 + 8*w - 2]', '[432, 6, 2*w^3 + 2*w^2 - 8*w - 8]', '[432, 18, -2*w^3 + 6*w + 4]', '[432, 18, -2*w^3 + 6*w - 4]', '[436, 218, -w^3 - w^2 + 9*w - 2]', '[436, 218, -4*w^3 + 3*w^2 + 19*w - 11]', '[436, 218, -3*w^2 - 3*w + 7]', '[436, 218, 5*w^3 + 3*w^2 - 27*w - 12]', '[441, 21, 4*w^3 - w^2 - 17*w + 6]', '[441, 21, 4*w^3 + w^2 - 17*w - 6]', '[441, 21, -2*w^2 + 5]', '[444, 222, -3*w^3 + w^2 + 13*w]', '[444, 222, -2*w^3 - w^2 + 9*w - 1]', '[444, 222, 2*w^3 - w^2 - 7*w + 5]', '[444, 222, -w^3 - w^2 + 3*w + 6]', '[444, 222, -w^3 + w^2 + 3*w - 6]', '[444, 222, 2*w^3 + w^2 - 7*w - 5]', '[444, 222, 2*w^3 - w^2 - 9*w - 1]', '[444, 222, 3*w^3 + w^2 - 13*w]', '[457, 457, -3*w^3 - w^2 + 12*w + 2]', '[457, 457, w^3 - 3*w^2 - 3*w + 3]', '[457, 457, -3*w^3 - w^2 + 12*w + 3]', '[457, 457, w^3 - 3*w^2 - 2*w + 3]', '[467, 467, -w^3 - 2*w^2 + 7*w + 1]', '[467, 467, 2*w^3 + 2*w^2 - 11*w - 9]', '[467, 467, -2*w^3 + 2*w^2 + 11*w - 9]', '[467, 467, w^3 - 2*w^2 - 7*w + 1]', '[479, 479, -3*w^3 + 3*w^2 + 12*w - 5]', '[479, 479, 3*w^3 - 3*w^2 - 10*w + 3]', '[479, 479, -3*w^3 - 3*w^2 + 12*w + 10]', '[479, 479, 5*w^3 + 3*w^2 - 22*w - 12]', '[484, 22, w^3 - 4*w + 5]', '[484, 22, -3*w^3 + 12*w - 7]', '[501, 501, 5*w^3 + w^2 - 22*w - 11]', '[501, 501, -2*w^3 + w^2 + 12*w - 3]', '[501, 501, w^3 - 5*w + 5]', '[501, 501, -2*w^3 - w^2 + 12*w + 2]', '[501, 501, 2*w^3 - w^2 - 12*w + 2]', '[501, 501, w^3 - 5*w - 5]', '[501, 501, 2*w^3 + w^2 - 12*w - 3]', '[501, 501, 5*w^3 - w^2 - 22*w + 11]', '[503, 503, -3*w^3 - w^2 + 14*w + 1]', '[503, 503, -w^3 + w^2 + 2*w - 4]', '[503, 503, w^3 + w^2 - 2*w - 4]', '[503, 503, 3*w^3 - w^2 - 14*w + 1]', '[507, 39, 2*w^3 + 2*w^2 - 13*w - 7]', '[507, 39, w^3 + w^2 - 8*w - 5]', '[507, 39, -2*w^3 + 2*w^2 + 3*w + 3]', '[507, 39, -w^3 + w^2 + 3]', '[524, 262, w^3 - 5*w^2 + 5*w]', '[524, 262, -5*w^3 - w^2 + 25*w + 10]', '[524, 262, -w^3 - w^2 + 7*w + 6]', '[524, 262, -3*w^3 + w^2 + 15*w + 6]', '[529, 23, -3*w^3 + 12*w + 2]', '[529, 23, 3*w^3 - 12*w + 2]', '[531, 177, 3*w^3 + 2*w^2 - 13*w - 10]', '[531, 177, -4*w^3 + 19*w - 3]', '[531, 177, -7*w^3 + 4*w^2 + 35*w - 18]', '[531, 177, w^3 - w - 3]', '[531, 177, -2*w^3 - 3*w^2 + 12*w + 5]', '[531, 177, -2*w^3 - w^2 + 10*w - 3]', '[531, 177, w^3 - w + 3]', '[531, 177, 2*w^3 - 3*w^2 - 12*w + 5]', '[531, 177, 2*w^3 - w^2 - 10*w - 3]', '[531, 177, -3*w^3 + 2*w^2 + 13*w - 10]', '[531, 177, 7*w^3 + 4*w^2 - 35*w - 18]', '[531, 177, -4*w^3 + 19*w + 3]', '[541, 541, -w^3 + 9*w + 3]', '[541, 541, 4*w^3 - 21*w + 3]', '[541, 541, 3*w^3 - 2*w^2 - 10*w + 2]', '[541, 541, w^3 - 9*w + 3]', '[563, 563, 3*w^3 + w^2 - 12*w - 8]', '[563, 563, -3*w^3 - w^2 + 12*w - 3]', '[563, 563, 3*w^3 - w^2 - 12*w - 3]', '[563, 563, -3*w^3 + w^2 + 12*w - 8]', '[564, 282, w^2 - w + 3]', '[564, 282, w^3 - 8*w + 1]', '[564, 282, -3*w^3 + 2*w^2 + 10*w - 3]', '[564, 282, 2*w^3 - 7*w^2 + 3*w + 5]', '[564, 282, 2*w^3 + 3*w^2 - 7*w - 5]', '[564, 282, -3*w^3 - 3*w^2 + 13*w + 10]', '[564, 282, w^3 + w^2 - 5*w - 8]', '[564, 282, 4*w^3 - w^2 - 15*w - 7]', '[576, 12, -2*w^3 + 12*w - 2]', '[576, 12, -2*w^3 + 12*w + 2]', '[576, 12, -2*w^3 + 8*w - 6]', '[579, 579, -2*w^3 - w^2 + 10*w - 1]', '[579, 579, 2*w^3 + w^2 - 12*w + 3]', '[579, 579, w^2 - 2*w - 6]', '[579, 579, 2*w^3 + w^2 - 12*w - 8]', '[579, 579, -w^3 - 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3*w^2 + 4*w + 9]', '[1737, 579, 8*w^3 + 3*w^2 - 36*w - 14]', '[1737, 579, -8*w^3 + 3*w^2 + 36*w - 14]', '[1737, 579, -w^3 + 3*w^2 + 4*w - 9]', '[1737, 579, -6*w^3 - w^2 + 26*w + 8]', '[1737, 579, 4*w^3 - 15*w - 4]', '[1737, 579, w^3 - 3*w^2 - 4*w + 6]', '[1737, 579, 6*w^3 - 2*w^2 - 25*w + 10]', '[1739, 1739, -w^2 + 6*w - 6]', '[1739, 1739, 2*w^3 + 4*w^2 - 17*w - 2]', '[1739, 1739, 4*w^3 - 4*w^2 - 22*w + 9]', '[1739, 1739, 3*w^3 - 2*w^2 - 12*w + 10]', '[1739, 1739, w^3 + 2*w^2 - w - 6]', '[1739, 1739, 2*w^3 - 2*w^2 - 14*w - 3]', '[1739, 1739, 4*w^3 + 2*w^2 - 19*w - 4]', '[1739, 1739, -4*w^3 - 2*w^2 + 22*w + 13]', '[1739, 1739, -4*w^3 + 2*w^2 + 22*w - 13]', '[1739, 1739, 4*w^3 - 2*w^2 - 19*w + 4]', '[1739, 1739, 2*w^3 + 2*w^2 - 14*w + 3]', '[1739, 1739, w^3 - 2*w^2 - w + 6]', '[1739, 1739, 3*w^3 + 2*w^2 - 12*w - 10]', '[1739, 1739, 4*w^3 + 4*w^2 - 22*w - 9]', '[1739, 1739, 2*w^3 - 4*w^2 - 17*w + 2]', '[1739, 1739, w^2 + 6*w + 6]', '[1744, 218, 4*w^3 - 4*w^2 - 18*w + 10]', '[1744, 218, 4*w^3 - 22*w + 4]', '[1744, 218, -4*w^3 + 22*w + 4]', '[1744, 218, 10*w^3 + 4*w^2 - 46*w - 18]', '[1761, 1761, -4*w^3 - w^2 + 18*w + 11]', '[1761, 1761, 6*w^3 - 4*w^2 - 23*w + 9]', '[1761, 1761, 3*w^3 - 17*w + 1]', '[1761, 1761, w^3 - 2*w^2 - 5*w + 13]', '[1761, 1761, -2*w^3 + 13*w + 1]', '[1761, 1761, -3*w^3 + 17*w + 1]', '[1761, 1761, 9*w^3 + 6*w^2 - 41*w - 23]', '[1761, 1761, -4*w^3 + w^2 + 18*w - 11]', '[1764, 42, -w^3 + 6*w - 7]', '[1764, 42, w^3 - 6*w - 7]', '[1764, 42, -3*w^3 + 2*w^2 + 18*w - 5]', '[1776, 222, 2*w^3 - 2*w^2 - 12*w + 10]', '[1776, 222, -2*w^2 + 4*w + 6]', '[1776, 222, -2*w^3 - 2*w^2 + 12*w]', '[1776, 222, -4*w^3 + 2*w^2 + 20*w - 4]', '[1776, 222, 4*w^3 + 2*w^2 - 20*w - 4]', '[1776, 222, 2*w^3 - 2*w^2 - 12*w]', '[1776, 222, 2*w^2 + 4*w - 6]', '[1776, 222, 2*w^3 + 2*w^2 - 12*w - 10]', '[1789, 1789, w^3 - w^2 - 6*w + 10]', '[1789, 1789, -w^3 - w^2 + 6*w - 5]', '[1789, 1789, w^3 - w^2 - 6*w - 5]', '[1789, 1789, -w^3 - w^2 + 6*w + 10]', '[1801, 1801, 4*w^3 + w^2 - 16*w - 3]', '[1801, 1801, 4*w^3 + w^2 - 16*w - 2]', '[1801, 1801, -4*w^3 + w^2 + 16*w - 2]', '[1801, 1801, -4*w^3 + w^2 + 16*w - 3]', '[1811, 1811, w^3 - 2*w^2 + 5*w - 3]', '[1811, 1811, 2*w^3 - w^2 - 13*w + 10]', '[1811, 1811, -10*w^3 - 2*w^2 + 49*w + 13]', '[1811, 1811, 3*w^3 - w^2 - 17*w - 5]', '[1813, 259, 3*w^3 - w^2 - 18*w - 1]', '[1813, 259, 3*w^3 - w^2 - 18*w + 6]', '[1813, 259, 3*w^3 + w^2 - 18*w - 6]', '[1813, 259, 3*w^3 + w^2 - 18*w + 1]', '[1823, 1823, 3*w^3 + 2*w^2 - 11*w - 8]', '[1823, 1823, 4*w^3 - 2*w^2 - 17*w + 2]', '[1823, 1823, -4*w^3 - 2*w^2 + 17*w + 2]', '[1823, 1823, -3*w^3 + 2*w^2 + 11*w - 8]', '[1828, 914, -w^3 - w^2 + 11*w + 4]', '[1828, 914, w^3 - 4*w^2 + 6*w + 1]', '[1828, 914, -w^3 - 2*w^2 + 12*w + 5]', '[1828, 914, w^3 - 5*w^2 + 7*w + 2]', '[1839, 1839, -4*w^3 + 3*w^2 + 14*w - 1]', '[1839, 1839, -3*w^3 + 4*w^2 + 8*w]', '[1839, 1839, -4*w^3 + 6*w^2 + 8*w - 1]', '[1839, 1839, -4*w^3 + 3*w^2 + 20*w - 7]', '[1839, 1839, 7*w^3 + 4*w^2 - 32*w - 20]', '[1839, 1839, 3*w^3 + 4*w^2 - 14*w - 6]', '[1839, 1839, 2*w^3 + 4*w^2 - 12*w - 5]', '[1839, 1839, w^3 + 4*w^2 - 2*w - 14]', '[1847, 1847, 4*w^3 - w^2 - 22*w - 3]', '[1847, 1847, 5*w^3 + 3*w^2 - 26*w - 16]', '[1847, 1847, -3*w^3 - w^2 + 16*w - 5]', '[1847, 1847, w^3 - 2*w^2 + 3*w - 4]', '[1849, 43, 2*w^3 - 13*w]', '[1849, 43, 3*w^3 - 17*w]', '[1868, 934, 2*w^3 - w^2 - 5*w + 5]', '[1868, 934, 5*w^3 + w^2 - 23*w]', '[1868, 934, 9*w^3 - 5*w^2 - 45*w + 18]', '[1868, 934, 5*w^2 + 9*w - 7]', '[1873, 1873, 3*w^2 + w - 6]', '[1873, 1873, w^3 + 3*w^2 - 5*w - 9]', '[1873, 1873, -w^3 + 3*w^2 + 5*w - 9]', '[1873, 1873, 3*w^2 - w - 6]', '[1875, 15, -5*w^3 + 25*w + 5]', '[1875, 15, 5*w - 5]', '[1875, 75, -w^3 - w^2 + 8*w + 8]', '[1875, 75, -3*w^3 + w^2 + 16*w + 3]', '[1875, 75, -w^3 + w^2 + 8*w - 8]', '[1875, 75, 3*w^3 + w^2 - 16*w + 3]', '[1907, 1907, 2*w^2 + 2*w - 11]', '[1907, 1907, -2*w^3 + 2*w^2 + 10*w + 1]', '[1907, 1907, 2*w^3 + 2*w^2 - 10*w + 1]', '[1907, 1907, 2*w^2 - 2*w - 11]', '[1916, 958, -w^3 + 3*w^2 - 5*w + 4]', '[1916, 958, 3*w^3 - 5*w^2 - w - 4]', '[1916, 958, -3*w^3 - w^2 + 19*w + 10]', '[1916, 958, 5*w^3 + 3*w^2 - 29*w - 14]', '[1931, 1931, w^2 - 3*w - 8]', '[1931, 1931, 3*w^3 - w^2 - 15*w - 3]', '[1931, 1931, 3*w^3 + w^2 - 15*w + 3]', '[1931, 1931, w^2 + 3*w - 8]', '[1933, 1933, w^3 - 3*w^2 - 4*w + 8]', '[1933, 1933, -w^3 + 3*w^2 + 4*w - 7]', '[1933, 1933, w^3 + 3*w^2 - 4*w - 7]', '[1933, 1933, w^3 + 3*w^2 - 4*w - 8]', '[1936, 22, -4*w^3 + 16*w + 2]', '[1936, 22, 4*w^3 - 16*w + 2]', '[1941, 1941, -w^3 - 3*w^2 + 5*w + 7]', '[1941, 1941, 3*w^2 - w - 8]', '[1941, 1941, 7*w^3 - 2*w^2 - 30*w + 12]', '[1941, 1941, -6*w^3 - 2*w^2 + 26*w + 9]', '[1941, 1941, -6*w^3 + 2*w^2 + 26*w - 9]', '[1941, 1941, 7*w^3 + 2*w^2 - 30*w - 12]', '[1941, 1941, 3*w^2 + w - 8]', '[1941, 1941, w^3 - 3*w^2 - 5*w + 7]', '[1979, 1979, -3*w^3 - 2*w^2 + 14*w + 2]', '[1979, 1979, -w^3 + 2*w^2 + 2*w - 8]', '[1979, 1979, w^3 + 2*w^2 - 2*w - 8]', '[1979, 1979, 3*w^3 - 2*w^2 - 14*w + 2]', '[2004, 1002, 5*w^3 + w^2 - 21*w - 6]', '[2004, 1002, 4*w^3 - 5*w^2 - 23*w + 13]', '[2004, 1002, -4*w^3 + w^2 + 15*w + 1]', '[2004, 1002, w^3 - 3*w^2 - 5*w + 8]', '[2004, 1002, -3*w^3 + 5*w^2 + 19*w - 12]', '[2004, 1002, 4*w^3 + w^2 - 15*w + 1]', '[2004, 1002, 3*w^2 + w - 7]', '[2004, 1002, -5*w^3 + w^2 + 21*w - 6]', '[2012, 1006, 3*w^3 - w^2 - 11*w + 10]', '[2012, 1006, 4*w^3 + w^2 - 17*w + 5]', '[2012, 1006, 2*w^3 - 3*w^2 - 13*w + 3]', '[2012, 1006, -3*w^3 + 3*w^2 + 17*w - 12]', '[2017, 2017, -w^2 + 2*w - 5]', '[2017, 2017, -2*w^3 + w^2 + 10*w - 10]', '[2017, 2017, 2*w^3 + w^2 - 10*w - 10]', '[2017, 2017, -w^2 - 2*w - 5]', '[2019, 2019, -2*w^3 - 3*w^2 + 13*w + 10]', '[2019, 2019, 8*w^3 + 5*w^2 - 37*w - 16]', '[2019, 2019, 4*w^3 + 2*w^2 - 18*w - 3]', '[2019, 2019, -4*w^3 + w^2 + 17*w + 4]', '[2019, 2019, -3*w^3 - 3*w^2 + 17*w + 5]', '[2019, 2019, 4*w^3 - 2*w^2 - 18*w + 3]', '[2019, 2019, 7*w^3 + 2*w^2 - 33*w - 6]', '[2019, 2019, 2*w^3 - 3*w^2 - 13*w + 10]', '[2025, 15, 3*w^2 - 9]', '[2025, 15, 3*w^2 - 6]', '[2025, 45, 3*w^3 + 4*w^2 - 11*w - 8]', '[2025, 45, -3*w^3 + 4*w^2 + 11*w - 8]', '[2025, 45, 4*w^3 + 4*w^2 - 17*w - 12]', '[2025, 45, -4*w^3 + 4*w^2 + 17*w - 12]', '[2025, 45, -7*w^3 + 2*w^2 + 31*w - 11]', '[2025, 45, -4*w^3 + 2*w^2 + 13*w + 1]', '[2025, 45, -7*w^3 - 2*w^2 + 31*w + 11]', '[2025, 45, -5*w^3 - w^2 + 20*w + 7]', '[2028, 78, 4*w^3 + 3*w^2 - 17*w - 13]', '[2028, 78, 2*w^3 + 3*w^2 - 7*w - 11]', '[2028, 78, -3*w^3 + 3*w^2 + 11*w - 2]', '[2028, 78, -3*w^3 + 3*w^2 + 13*w - 4]', '[2043, 681, 2*w^3 - 2*w^2 - 7*w + 9]', '[2043, 681, -w^3 - w^2 + 8*w + 9]', '[2043, 681, 4*w^3 - 3*w^2 - 22*w + 6]', '[2043, 681, 3*w^3 + w^2 - 16*w + 4]', '[2043, 681, -2*w^3 + 5*w + 6]', '[2043, 681, 5*w^3 + 5*w^2 - 28*w - 12]', '[2043, 681, -2*w^3 + 5*w - 6]', '[2043, 681, -3*w^3 + w^2 + 16*w + 4]', '[2043, 681, -5*w^3 + 5*w^2 + 28*w - 12]', '[2043, 681, -w^3 + w^2 + 8*w - 9]', '[2043, 681, 2*w^3 + 2*w^2 - 7*w - 9]', '[2043, 681, -5*w^3 + 23*w - 6]', '[2053, 2053, w^3 - w^2 - 3*w - 5]', '[2053, 2053, 2*w^3 - w^2 - 9*w + 10]', '[2053, 2053, 2*w^3 + w^2 - 9*w - 10]', '[2053, 2053, -w^3 - w^2 + 3*w - 5]', '[2063, 2063, 2*w^3 + 4*w^2 - 13*w - 13]', '[2063, 2063, 3*w^3 + 4*w^2 - 17*w - 7]', '[2063, 2063, -3*w^3 + 4*w^2 + 17*w - 7]', '[2063, 2063, -2*w^3 + 4*w^2 + 13*w - 13]', '[2075, 415, -5*w^3 - 3*w^2 + 20*w + 11]', '[2075, 415, -7*w^3 - 4*w^2 + 31*w + 17]', '[2075, 415, 4*w^3 + 4*w^2 - 13*w - 3]', '[2075, 415, 5*w^3 + 3*w^2 - 20*w - 4]', '[2075, 415, -4*w^3 + 4*w^2 + 13*w - 3]', '[2075, 415, -5*w^3 + 3*w^2 + 20*w - 4]', '[2075, 415, 5*w^3 - 3*w^2 - 20*w + 11]', '[2075, 415, 7*w^3 - 4*w^2 - 31*w + 17]', '[2096, 262, 4*w^3 - 4*w^2 - 10*w + 6]', '[2096, 262, -10*w^3 - 4*w^2 + 46*w + 14]', '[2096, 262, -4*w^3 - 2*w^2 + 16*w]', '[2096, 262, -6*w^3 - 4*w^2 + 26*w + 10]', '[2099, 2099, -w^3 + 2*w^2 + 8*w - 8]', '[2099, 2099, -3*w^3 - 2*w^2 + 16*w + 2]', '[2099, 2099, 3*w^3 - 2*w^2 - 16*w + 2]', '[2099, 2099, w^3 + 2*w^2 - 8*w - 8]', '[2116, 46, w^3 - 4*w + 7]', '[2116, 46, -5*w^3 + 20*w - 11]', '[2124, 354, 7*w^3 - 3*w^2 - 31*w + 18]', '[2124, 354, 7*w^3 - 3*w^2 - 33*w + 10]', '[2124, 354, 5*w^3 - w^2 - 25*w]', '[2124, 354, -w^2 + 5*w + 5]', '[2124, 354, 2*w^3 - 3*w^2 - 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24*w - 2]', '[5328, 222, -4*w^2 + 2*w + 8]', '[5328, 222, -2*w^3 + 2*w^2 + 16*w]', '[5328, 222, 6*w^3 - 2*w^2 - 24*w + 8]', '[5328, 222, 6*w^3 + 2*w^2 - 24*w - 8]', '[5328, 222, -4*w^2 - 2*w + 8]', '[5328, 222, -2*w^3 - 2*w^2 + 16*w]', '[5328, 222, -6*w^3 - 2*w^2 + 32*w + 10]', '[5328, 222, 2*w^3 - 4*w^2 - 10*w + 12]', '[5328, 222, 6*w^3 - 2*w^2 - 24*w + 2]', '[5329, 73, 3*w^3 - 12*w - 10]', '[5329, 73, 3*w^3 - 12*w + 10]', '[5341, 763, 7*w^3 - 3*w^2 - 28*w + 11]', '[5341, 763, -7*w^3 - 3*w^2 + 28*w + 4]', '[5341, 763, 3*w^3 - 7*w^2 - 4*w + 7]', '[5341, 763, -11*w^3 - 7*w^2 + 52*w + 28]', '[5351, 5351, -9*w^3 - 2*w^2 + 45*w + 4]', '[5351, 5351, 6*w^3 - 28*w + 9]', '[5351, 5351, -6*w^3 + 28*w + 9]', '[5351, 5351, 9*w^3 - 2*w^2 - 45*w + 4]', '[5367, 5367, -2*w^3 + 16*w - 11]', '[5367, 5367, 4*w^3 - 2*w^2 - 20*w + 1]', '[5367, 5367, 2*w^2 + 4*w - 9]', '[5367, 5367, 2*w^2 - 11*w + 6]', '[5367, 5367, 6*w^3 - 32*w - 11]', '[5367, 5367, -9*w^3 + 43*w + 4]', '[5367, 5367, -2*w^3 + w + 4]', '[5367, 5367, -11*w^3 - 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16]', '[5625, 75, -10*w^3 - 3*w^2 + 45*w + 16]', '[5625, 75, 4*w^2 - 13]', '[5625, 75, -5*w^3 + 3*w^2 + 15*w + 1]', '[5625, 75, -6*w^3 - w^2 + 23*w + 8]', '[5653, 5653, -2*w^3 + 4*w^2 + 9*w - 10]', '[5653, 5653, w^3 + 4*w^2 - 3*w - 10]', '[5653, 5653, -w^3 + 4*w^2 + 3*w - 10]', '[5653, 5653, 2*w^3 + 4*w^2 - 9*w - 10]', '[5675, 1135, 2*w^3 + 3*w^2 - 14*w - 11]', '[5675, 1135, 4*w^3 + 4*w^2 - 22*w - 17]', '[5675, 1135, -2*w^3 - 4*w^2 + 14*w + 3]', '[5675, 1135, -4*w^3 - 3*w^2 + 22*w + 4]', '[5675, 1135, 2*w^3 - 4*w^2 - 14*w + 3]', '[5675, 1135, 4*w^3 - 3*w^2 - 22*w + 4]', '[5675, 1135, -4*w^3 + 13*w + 10]', '[5675, 1135, -5*w^3 - 2*w^2 + 20*w + 16]', '[5687, 517, -5*w^3 + 2*w^2 + 21*w + 1]', '[5687, 517, 5*w^3 - 3*w^2 - 24*w + 6]', '[5687, 517, -4*w^3 + 2*w^2 + 15*w - 11]', '[5687, 517, -w^3 + 3*w^2 - 9]', '[5687, 517, w^3 + 3*w^2 - 9]', '[5687, 517, 4*w^3 + 2*w^2 - 15*w - 11]', '[5687, 517, 5*w^3 + 2*w^2 - 21*w + 1]', '[5687, 517, -5*w^3 - 3*w^2 + 24*w + 6]', '[5708, 2854, 8*w^3 - w^2 - 37*w + 13]', '[5708, 2854, 3*w^3 + w^2 - 7*w + 8]', '[5708, 2854, -3*w^3 + 3*w^2 + 19*w - 12]', '[5708, 2854, 4*w^3 - 3*w^2 - 23*w + 3]', '[5711, 5711, -5*w^3 + 3*w^2 + 20*w - 13]', '[5711, 5711, 3*w^3 - 5*w^2 - 2*w + 5]', '[5711, 5711, -5*w^3 - 3*w^2 + 20*w + 2]', '[5711, 5711, 5*w^3 - 4*w^2 - 14*w + 8]', '[5716, 2858, 3*w^3 - w^2 - 19*w + 4]', '[5716, 2858, 4*w^3 - w^2 - 23*w + 1]', '[5716, 2858, -8*w^3 + 5*w^2 + 43*w - 17]', '[5716, 2858, 3*w^3 - 5*w^2 - 23*w + 8]', '[5721, 5721, 2*w^3 - 13*w + 11]', '[5721, 5721, -3*w^3 + 17*w + 11]', '[5721, 5721, w^3 + 4*w^2 - 3*w - 9]', '[5721, 5721, 11*w^3 + 2*w^2 - 51*w - 9]', '[5721, 5721, 2*w^3 - 4*w^2 - 9*w + 11]', '[5721, 5721, 4*w^3 - 2*w^2 - 9*w + 1]', '[5721, 5721, -2*w^2 + 11*w - 3]', '[5721, 5721, 11*w^3 + 2*w^2 - 55*w - 13]', '[5737, 5737, -5*w^3 + 29*w + 8]', '[5737, 5737, -4*w^3 + 25*w - 8]', '[5737, 5737, 4*w^3 - 25*w - 8]', '[5737, 5737, 5*w^3 - 29*w + 8]', '[5748, 2874, -9*w^3 + 2*w^2 + 38*w - 15]', '[5748, 2874, -w^3 - 4*w^2 + 6*w + 11]', '[5748, 2874, w^3 + 4*w^2 - 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10]', '[9323, 9323, -5*w^3 + 2*w^2 + 26*w]', '[9323, 9323, 5*w^3 + 2*w^2 - 26*w]', '[9323, 9323, w^3 + 2*w^2 - 10*w - 10]', '[9325, 1865, -6*w^3 - 2*w^2 + 22*w - 1]', '[9325, 1865, -w^3 - 6*w^2 - 2*w + 8]', '[9325, 1865, -2*w^3 - 6*w^2 + 14*w + 17]', '[9325, 1865, -4*w^3 - 7*w^2 + 22*w + 26]', '[9325, 1865, 2*w^3 - 6*w^2 - 14*w + 17]', '[9325, 1865, 4*w^3 - 7*w^2 - 22*w + 26]', '[9325, 1865, -6*w^3 + 2*w^2 + 22*w + 1]', '[9325, 1865, w^3 - 6*w^2 + 2*w + 8]', '[9327, 9327, -2*w^3 + 4*w^2 + 12*w - 21]', '[9327, 9327, 6*w^3 - 4*w^2 - 31*w + 9]', '[9327, 9327, -10*w^3 + 8*w^2 + 39*w - 16]', '[9327, 9327, -w^3 + 2*w^2 + 9*w - 12]', '[9327, 9327, -w^3 - 2*w^2 + 9*w + 12]', '[9327, 9327, -16*w^3 - 10*w^2 + 72*w + 39]', '[9327, 9327, -6*w^3 - 4*w^2 + 31*w + 9]', '[9327, 9327, 4*w^3 - 2*w^2 - 21*w - 2]', '[9349, 9349, 5*w^3 - w^2 - 29*w - 3]', '[9349, 9349, 4*w^3 - w^2 - 25*w + 8]', '[9349, 9349, -8*w^3 - 4*w^2 + 39*w + 25]', '[9349, 9349, w^3 - 4*w^2 + 3*w - 5]', '[9371, 9371, 5*w^3 + 2*w^2 - 27*w + 1]', '[9371, 9371, 2*w^3 - 2*w^2 - 15*w + 11]', '[9371, 9371, 2*w^3 + 2*w^2 - 15*w - 11]', '[9371, 9371, -5*w^3 + 2*w^2 + 27*w + 1]', '[9392, 1174, -4*w^3 + 4*w^2 + 12*w - 10]', '[9392, 1174, -8*w^3 + 4*w^2 + 36*w - 10]', '[9392, 1174, 8*w^3 + 4*w^2 - 36*w - 10]', '[9392, 1174, 10*w^3 + 4*w^2 - 46*w - 12]', '[9404, 4702, w^3 + 6*w^2 - 14*w - 3]', '[9404, 4702, 2*w^3 + 5*w^2 - 17*w - 3]', '[9404, 4702, 6*w^3 - w^2 - 27*w - 9]', '[9404, 4702, 5*w^3 - 2*w^2 - 22*w - 7]', '[9408, 84, 6*w^3 + 2*w^2 - 22*w - 12]', '[9408, 84, 2*w^3 - 6*w^2 + 2*w + 8]', '[9409, 97, -w^3 + 4*w - 10]', '[9409, 97, w^3 - 4*w - 10]', '[9433, 9433, -9*w^3 - 3*w^2 + 46*w + 12]', '[9433, 9433, -3*w^3 - w^2 + 12*w + 14]', '[9433, 9433, 7*w^3 + 2*w^2 - 31*w - 19]', '[9433, 9433, -9*w^3 - 4*w^2 + 47*w + 13]', '[9457, 1351, w^3 - w^2 - 6*w - 8]', '[9457, 1351, w^3 + w^2 - 6*w - 13]', '[9457, 1351, -w^3 + w^2 + 6*w - 13]', '[9457, 1351, -w^3 - w^2 + 6*w - 8]', '[9467, 9467, -9*w^3 - w^2 + 47*w - 5]', '[9467, 9467, -2*w^3 - w^2 + 19*w + 10]', '[9467, 9467, 2*w^3 - w^2 - 19*w + 10]', '[9467, 9467, 9*w^3 - w^2 - 47*w - 5]', '[9472, 148, 4*w + 12]', '[9472, 148, 4*w^3 - 20*w + 12]', '[9472, 148, -4*w^3 + 20*w + 12]', '[9472, 148, -4*w + 12]', '[9491, 9491, -3*w^3 + 3*w^2 + 15*w + 1]', '[9491, 9491, -3*w^3 - 3*w^2 + 16*w]', '[9491, 9491, 3*w^3 - 3*w^2 - 16*w]', '[9491, 9491, 3*w^3 + 3*w^2 - 15*w + 1]', '[9501, 9501, -w - 10]', '[9501, 9501, w^3 - 5*w + 10]', '[9501, 9501, -6*w^3 - 6*w^2 + 25*w + 16]', '[9501, 9501, 14*w^3 + 5*w^2 - 64*w - 19]', '[9501, 9501, 5*w^3 - 6*w^2 - 19*w + 14]', '[9501, 9501, -6*w^3 + 5*w^2 + 16*w - 6]', '[9501, 9501, 10*w^3 + w^2 - 50*w - 5]', '[9501, 9501, w^2 - 10*w]', '[9508, 4754, -w^3 - 4*w^2 + 16*w - 1]', '[9508, 4754, 8*w^3 - 9*w^2 - 17*w - 1]', '[9508, 4754, 6*w^3 + 3*w^2 - 21*w - 7]', '[9508, 4754, -7*w^3 - 4*w^2 + 40*w + 17]', '[9539, 9539, 4*w^3 + 2*w^2 - 14*w - 11]', '[9539, 9539, 6*w^3 + 2*w^2 - 26*w + 1]', '[9539, 9539, -6*w^3 + 2*w^2 + 26*w + 1]', '[9539, 9539, -4*w^3 + 2*w^2 + 14*w - 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38*w + 20]', '[9596, 4798, 4*w^3 + 5*w^2 - 19*w - 7]', '[9596, 4798, 7*w^3 + 6*w^2 - 36*w - 15]', '[9596, 4798, 5*w^3 - 4*w^2 - 18*w + 1]', '[9596, 4798, 6*w^3 - 7*w^2 - 15*w - 1]', '[9601, 9601, -w^3 - 4*w^2 + 15*w + 4]', '[9601, 9601, -8*w^3 - 3*w^2 + 42*w + 9]', '[9601, 9601, -10*w^3 - 4*w^2 + 51*w + 16]', '[9601, 9601, -2*w^3 - 3*w^2 + 18*w + 6]', '[9604, 14, 7*w^3 - 28*w + 7]', '[9613, 9613, 2*w^3 + w^2 - 10*w - 13]', '[9613, 9613, -w^2 + 2*w - 8]', '[9613, 9613, -w^2 - 2*w - 8]', '[9613, 9613, -2*w^3 + w^2 + 10*w - 13]', '[9623, 9623, -8*w^3 + w^2 + 37*w + 2]', '[9623, 9623, -7*w^3 - 3*w^2 + 34*w + 7]', '[9623, 9623, 7*w^3 - 3*w^2 - 34*w + 7]', '[9623, 9623, 8*w^3 + w^2 - 37*w + 2]', '[9644, 4822, -8*w^3 + w^2 + 31*w - 19]', '[9644, 4822, 9*w^3 + w^2 - 37*w + 14]', '[9644, 4822, 3*w^3 - 3*w^2 - 17*w]', '[9644, 4822, 2*w^3 - 3*w^2 - 13*w + 15]', '[9651, 9651, 2*w^3 - 5*w^2 + 3*w + 6]', '[9651, 9651, 3*w^3 - 6*w^2 - 5*w + 11]', '[9651, 9651, w^3 + 5*w^2 - 12*w - 12]', '[9651, 9651, 5*w^3 - 11*w^2 - w + 7]', '[9651, 9651, 6*w^3 + 3*w^2 - 19*w - 10]', '[9651, 9651, 5*w^3 + 2*w^2 - 19*w - 13]', '[9651, 9651, -11*w^3 - 5*w^2 + 48*w + 24]', '[9651, 9651, 5*w^3 - w^2 - 13*w - 7]', '[9661, 9661, 5*w^3 - w^2 - 28*w + 1]', '[9661, 9661, 3*w^3 - w^2 - 20*w + 4]', '[9661, 9661, -3*w^3 - w^2 + 20*w + 4]', '[9661, 9661, 5*w^3 + w^2 - 28*w - 1]', '[9687, 9687, -4*w^3 + 6*w^2 + 17*w - 7]', '[9687, 9687, 3*w^3 + 6*w^2 - 11*w - 23]', '[9687, 9687, 4*w^3 - 6*w^2 - 11*w + 1]', '[9687, 9687, -6*w^3 + 4*w^2 + 29*w - 9]', '[9687, 9687, -9*w^3 - 6*w^2 + 41*w + 29]', '[9687, 9687, w^3 + 4*w^2 + w - 11]', '[9687, 9687, 6*w^3 - 4*w^2 - 23*w + 3]', '[9687, 9687, -7*w^3 - 4*w^2 + 29*w + 17]', '[9697, 9697, 6*w^3 + 2*w^2 - 23*w - 2]', '[9697, 9697, 7*w^3 - 2*w^2 - 29*w + 8]', '[9697, 9697, -7*w^3 - 2*w^2 + 29*w + 8]', '[9697, 9697, -6*w^3 + 2*w^2 + 23*w - 2]', '[9719, 9719, 2*w^3 - 3*w^2 + 2*w - 6]', '[9719, 9719, 7*w^3 + 4*w^2 - 37*w - 23]', '[9719, 9719, -4*w^3 - 2*w^2 + 23*w - 7]', '[9719, 9719, 6*w^3 - 2*w^2 - 33*w - 2]', '[9743, 9743, -3*w^3 + 3*w^2 + 8*w - 9]', '[9743, 9743, -7*w^3 - 3*w^2 + 32*w + 6]', '[9743, 9743, 7*w^3 - 3*w^2 - 32*w + 6]', '[9743, 9743, 3*w^3 + 3*w^2 - 8*w - 9]', '[9747, 57, -2*w^3 - w^2 + 20*w - 17]', '[9747, 57, -5*w^3 + 2*w^2 + 8*w + 4]', '[9747, 57, -17*w^3 - 2*w^2 + 80*w + 14]', '[9747, 57, 10*w^3 + w^2 - 52*w - 22]', '[9747, 171, -8*w^3 + 5*w^2 + 31*w + 12]', '[9747, 171, 11*w^3 - 3*w^2 - 42*w - 10]', '[9747, 171, -9*w^3 + w^2 + 46*w - 14]', '[9747, 171, 4*w^3 + 9*w^2 - 9*w - 4]', '[9748, 4874, -7*w^3 - w^2 + 27*w - 14]', '[9748, 4874, 2*w^3 - w^2 - 9*w + 13]', '[9748, 4874, -8*w^3 + w^2 + 33*w - 19]', '[9748, 4874, w^3 + w^2 - 3*w + 8]', '[9753, 9753, -w^3 + 3*w^2 - 10*w - 4]', '[9753, 9753, 15*w^3 + 3*w^2 - 74*w - 11]', '[9753, 9753, -19*w^3 - 7*w^2 + 86*w + 23]', '[9753, 9753, -12*w^3 - 9*w^2 + 53*w + 26]', '[9753, 9753, -9*w^3 + 7*w^2 + 26*w - 12]', '[9753, 9753, 7*w^3 - 9*w^2 - 23*w + 19]', '[9753, 9753, -3*w^3 + w^2 + 11*w - 15]', '[9753, 9753, -4*w^3 - w^2 + 17*w - 10]', '[9769, 9769, -3*w^3 + 17*w - 12]', '[9769, 9769, 12*w^3 + 2*w^2 - 60*w - 13]', '[9769, 9769, -2*w^3 + 13*w - 12]', '[9769, 9769, 12*w^3 + 3*w^2 - 60*w - 17]', '[9781, 9781, -4*w^3 - 5*w^2 + 19*w + 16]', '[9781, 9781, -w^3 + 5*w^2 + w - 9]', '[9781, 9781, -6*w^3 - 7*w^2 + 33*w + 18]', '[9781, 9781, 3*w^3 + 7*w^2 - 21*w - 17]', '[9791, 9791, -8*w^3 - w^2 + 42*w - 5]', '[9791, 9791, -2*w^3 - w^2 + 18*w + 10]', '[9791, 9791, 2*w^3 - w^2 - 18*w + 10]', '[9791, 9791, 8*w^3 - w^2 - 42*w - 5]', '[9801, 33, -6*w^3 + 24*w + 3]', '[9801, 33, 6*w^3 - 24*w + 3]', '[9801, 99, -9*w^3 - 4*w^2 + 38*w + 14]', '[9801, 99, -7*w^3 + 4*w^2 + 26*w - 6]', '[9801, 99, 7*w^3 + 4*w^2 - 26*w - 6]', '[9801, 99, 9*w^3 - 4*w^2 - 38*w + 14]', '[9801, 99, -4*w^3 + 5*w^2 + 19*w - 14]', '[9801, 99, 8*w^3 - 7*w^2 - 41*w + 22]', '[9801, 99, w^3 + 5*w^2 - w - 11]', '[9801, 99, w^3 - 7*w^2 - 13*w + 13]', '[9803, 9803, 2*w^3 + 2*w^2 - 14*w - 13]', '[9803, 9803, 4*w^3 + 2*w^2 - 22*w + 3]', '[9803, 9803, 4*w^3 - 2*w^2 - 22*w - 3]', '[9803, 9803, 2*w^3 - 2*w^2 - 14*w + 13]', '[9808, 1226, 8*w^3 - 34*w - 6]', '[9808, 1226, 6*w^3 + 2*w^2 - 20*w + 4]', '[9808, 1226, 6*w^3 - 22*w + 6]', '[9808, 1226, 8*w^3 - 34*w + 6]', '[9819, 3273, -2*w^3 + 6*w^2 + 17*w - 15]', '[9819, 3273, -7*w^3 - 4*w^2 + 29*w + 6]', '[9819, 3273, -6*w^3 - w^2 + 28*w - 4]', '[9819, 3273, 2*w^3 - w^2 - 4*w + 9]', '[9819, 3273, 6*w^3 - 4*w^2 - 23*w + 14]', '[9819, 3273, 7*w^3 - 6*w^2 - 37*w + 15]', '[9819, 3273, 2*w^3 + w^2 - 4*w - 9]', '[9819, 3273, 6*w^3 + 4*w^2 - 23*w - 14]', '[9819, 3273, -5*w^3 - 3*w^2 + 20*w]', '[9819, 3273, -5*w^3 + 3*w^2 + 20*w - 15]', '[9819, 3273, -7*w^3 + 4*w^2 + 29*w - 6]', '[9819, 3273, -6*w^3 + w^2 + 28*w + 4]', '[9825, 1965, -7*w^3 - 2*w^2 + 29*w + 4]', '[9825, 1965, -10*w^3 - 2*w^2 + 45*w + 6]', '[9825, 1965, -5*w^3 - 2*w^2 + 15*w + 4]', '[9825, 1965, -6*w^3 - 2*w^2 + 23*w + 6]', '[9825, 1965, -6*w^2 + 5*w + 7]', '[9825, 1965, -w^3 - 5*w^2 + 8*w + 10]', '[9825, 1965, 3*w^3 + 5*w^2 - 16*w - 15]', '[9825, 1965, -7*w^3 + 7*w^2 + 36*w - 26]', '[9825, 1965, 3*w^3 - 5*w^2 - 16*w + 15]', '[9825, 1965, -6*w^3 + 23*w - 5]', '[9825, 1965, w^3 + 7*w^2 - 12*w - 9]', '[9825, 1965, -w^3 + 5*w^2 + 8*w - 10]', '[9825, 1965, 5*w^3 - 2*w^2 - 15*w + 4]', '[9825, 1965, 6*w^3 - 2*w^2 - 23*w + 6]', '[9825, 1965, w^3 - w^2 - 12*w - 13]', '[9825, 1965, 2*w^3 - 4*w^2 - 21*w - 3]', '[9829, 9829, -2*w^3 - 2*w^2 + 17*w]', '[9829, 9829, -12*w^3 - 8*w^2 + 55*w + 29]', '[9829, 9829, 8*w^3 - 5*w^2 - 29*w + 12]', '[9829, 9829, -6*w^3 - 5*w^2 + 36*w + 15]', '[9837, 3279, 3*w^3 - 5*w^2 - 15*w + 17]', '[9837, 3279, 8*w^3 - 2*w^2 - 34*w + 3]', '[9837, 3279, 9*w^3 + 2*w^2 - 40*w - 10]', '[9837, 3279, 11*w^3 + 8*w^2 - 55*w - 30]', '[9837, 3279, -8*w^3 + 35*w + 3]', '[9837, 3279, -7*w^3 + 6*w^2 + 33*w - 22]', '[9837, 3279, 7*w^3 + 6*w^2 - 33*w - 22]', '[9837, 3279, -8*w^3 + 35*w - 3]', '[9837, 3279, -11*w^3 + 8*w^2 + 55*w - 30]', '[9837, 3279, 8*w^3 + 2*w^2 - 34*w - 3]', '[9837, 3279, 6*w^3 - 7*w^2 - 33*w + 22]', '[9837, 3279, 9*w^3 - 2*w^2 - 40*w + 10]', '[9853, 9853, 7*w^3 - 3*w^2 - 28*w + 8]', '[9853, 9853, 2*w^3 - 5*w^2 - 6*w + 11]', '[9853, 9853, -7*w^3 - 6*w^2 + 34*w + 20]', '[9853, 9853, 2*w^3 - 14*w + 13]', '[9853, 9853, 4*w^3 - 5*w^2 - 18*w + 14]', '[9853, 9853, 4*w^3 - 22*w + 13]', '[9853, 9853, 10*w^3 - w^2 - 44*w - 2]', '[9853, 9853, -7*w^3 - 3*w^2 + 28*w + 7]', '[9853, 9853, 7*w^3 - 3*w^2 - 28*w + 7]', '[9853, 9853, -10*w^3 - w^2 + 44*w - 2]', '[9853, 9853, -13*w^3 - 4*w^2 + 65*w + 22]', '[9853, 9853, -5*w^3 - 2*w^2 + 14*w + 4]', '[9853, 9853, -2*w^3 + 14*w + 13]', '[9853, 9853, 6*w^2 - 6*w - 13]', '[9853, 9853, -11*w^3 - 2*w^2 + 50*w + 6]', '[9853, 9853, -7*w^3 - 3*w^2 + 28*w + 8]', '[9887, 9887, -7*w^3 + 34*w + 8]', '[9887, 9887, 6*w^3 + 6*w^2 - 36*w - 19]', '[9887, 9887, -w^3 - 2*w + 8]', '[9887, 9887, -6*w^3 - 6*w^2 + 36*w + 11]', '[9892, 4946, -3*w^3 + 3*w^2 + 15*w - 20]', '[9892, 4946, 5*w^3 - 28*w - 3]', '[9892, 4946, 5*w^3 - 28*w + 3]', '[9892, 4946, -9*w^3 - 8*w^2 + 52*w + 23]', '[9903, 9903, 2*w^3 + 4*w^2 - 15*w]', '[9903, 9903, w^3 + 2*w^2 - 9*w - 16]', '[9903, 9903, -4*w^3 - 2*w^2 + 21*w - 6]', '[9903, 9903, -4*w^3 - 2*w^2 + 20*w - 5]', '[9903, 9903, -5*w^3 - 4*w^2 + 27*w + 20]', '[9903, 9903, -6*w^3 - 4*w^2 + 32*w + 21]', '[9903, 9903, 2*w^3 + 4*w^2 - 16*w + 1]', '[9903, 9903, 2*w^2 - 4*w - 15]', '[9939, 9939, -5*w^3 - 2*w^2 + 22*w - 2]', '[9939, 9939, 2*w^3 + 5*w^2 - 12*w - 3]', '[9939, 9939, 5*w^3 + 3*w^2 - 19*w - 13]', '[9939, 9939, -6*w^3 + 9*w^2 + 14*w - 5]', '[9939, 9939, 8*w^3 + 8*w^2 - 39*w - 18]', '[9939, 9939, -5*w^3 + 3*w^2 + 19*w - 13]', '[9939, 9939, -6*w^3 + 6*w^2 + 17*w + 4]', '[9939, 9939, -5*w^3 + 2*w^2 + 22*w + 2]', '[9949, 9949, -2*w^3 + 5*w^2 + 12*w - 11]', '[9949, 9949, -2*w^3 + 5*w^2 + 12*w - 14]', '[9949, 9949, 2*w^3 + 5*w^2 - 12*w - 14]', '[9949, 9949, 2*w^3 + 5*w^2 - 12*w - 11]', '[9969, 9969, -10*w^3 + 7*w^2 + 38*w - 14]', '[9969, 9969, 7*w^3 - 10*w^2 - 21*w + 12]', '[9969, 9969, 4*w^2 + w - 24]', '[9969, 9969, 4*w^3 - w^2 - 24*w + 5]', '[9969, 9969, -w^3 + 4*w^2 + 5*w + 4]', '[9969, 9969, 4*w^3 - w^2 - 24*w]', '[9969, 9969, 12*w^3 + 7*w^2 - 50*w - 21]', '[9969, 9969, -14*w^3 - 10*w^2 + 63*w + 38]', '[9971, 767, -4*w^3 + 3*w^2 + 17*w]', '[9971, 767, 3*w^3 + 5*w^2 - 18*w - 19]', '[9971, 767, 3*w^3 - 4*w^2 - 15*w + 3]', '[9971, 767, 3*w^3 + 5*w^2 - 19*w - 17]', '[9971, 767, -3*w^3 + 5*w^2 + 19*w - 17]', '[9971, 767, -3*w^3 - 4*w^2 + 15*w + 3]', '[9971, 767, 4*w^3 + 3*w^2 - 17*w]', '[9971, 767, -8*w^3 - 4*w^2 + 35*w + 23]', '[9972, 1662, -7*w^3 + 30*w + 1]', '[9972, 1662, -7*w^3 + 6*w^2 + 34*w - 21]', '[9972, 1662, -9*w^3 + 4*w^2 + 38*w - 11]', '[9972, 1662, 5*w^3 + 6*w^2 - 26*w - 15]', '[9972, 1662, -3*w^3 + 4*w^2 + 4*w + 7]', '[9972, 1662, -5*w^3 + 18*w + 1]', '[9972, 1662, -5*w^3 + 24*w + 13]', '[9972, 1662, -5*w^3 + 18*w - 1]', '[9972, 1662, -w^3 + 6*w^2 - 2*w - 9]', '[9972, 1662, 7*w^3 - 30*w + 1]', '[9972, 1662, w^3 - 6*w^2 - 10*w + 15]', '[9972, 1662, 9*w^3 + 4*w^2 - 38*w - 11]', '[10000, 10, 10]', '[10000, 50, -6*w^3 + 32*w]', '[10000, 50, -2*w^3 + 16*w]'], 'label': '4.4.7056.1', 'narrow_class_no': 2, 'primes': ['[3, 3, -w^3 + 5*w + 1]', '[3, 3, w - 1]', '[4, 2, -w^3 + 4*w - 1]', '[25, 5, w^2 - 3]', '[25, 5, w^2 - 2]', '[37, 37, w + 3]', '[37, 37, w^3 - 5*w + 3]', '[37, 37, -w^3 + 5*w + 3]', '[37, 37, -w + 3]', '[47, 47, w^3 - 3*w - 3]', '[47, 47, w^3 + w^2 - 6*w - 1]', '[47, 47, w^3 - w^2 - 6*w + 1]', '[47, 47, -w^3 - w^2 + 6*w + 4]', '[49, 7, w^3 - 6*w]', '[59, 59, -w^3 + w^2 + 4*w - 5]', '[59, 59, -w^3 + w^2 + 4*w]', '[59, 59, w^3 + w^2 - 4*w]', '[59, 59, w^3 + w^2 - 4*w - 5]', '[83, 83, -3*w + 2]', '[83, 83, -w^3 + w^2 + 7*w + 1]', '[83, 83, w^3 - w^2 - 6*w + 7]', '[83, 83, -2*w^3 + w^2 + 11*w - 6]', '[109, 109, 2*w^3 - 2*w^2 - 9*w + 5]', '[109, 109, 2*w^3 - 11*w + 2]', '[109, 109, w^2 + 2*w + 2]', '[109, 109, 5*w^3 + 2*w^2 - 23*w - 9]', '[121, 11, -2*w^3 + 8*w + 1]', '[121, 11, 2*w^3 - 8*w + 1]', '[131, 131, 2*w^3 - 2*w^2 - 5*w + 3]', '[131, 131, -5*w^3 - 2*w^2 + 23*w + 7]', '[131, 131, -3*w^3 - 2*w^2 + 15*w + 6]', '[131, 131, -3*w^3 - 2*w^2 + 13*w + 5]', '[167, 167, w^3 - 2*w^2 - w + 3]', '[167, 167, 2*w^3 - w^2 - 7*w + 4]', '[167, 167, 2*w^3 - 2*w^2 - 8*w + 3]', '[167, 167, -3*w^3 - w^2 + 13*w + 1]', '[169, 13, 2*w^3 - 8*w - 5]', '[169, 13, w^3 - 4*w - 4]', '[193, 193, w^3 - 7*w - 1]', '[193, 193, 2*w^3 - 11*w - 1]', '[193, 193, -2*w^3 + 11*w - 1]', '[193, 193, w^3 - 7*w + 1]', '[227, 227, -2*w^3 - w^2 + 8*w + 6]', '[227, 227, 2*w^3 - w^2 - 8*w - 1]', '[227, 227, -2*w^3 - w^2 + 8*w - 1]', '[227, 227, w^3 + 2*w^2 - 7*w - 6]', '[251, 251, w^2 + 2*w - 4]', '[251, 251, 2*w^3 - w^2 - 10*w + 1]', '[251, 251, -2*w^3 - w^2 + 10*w + 1]', '[251, 251, w^2 - 2*w - 4]', '[277, 277, w^3 - 2*w^2 - 4*w + 6]', '[277, 277, -4*w^3 - w^2 + 18*w + 4]', '[277, 277, w^3 - 2*w^2 - 4*w + 4]', '[277, 277, w^3 + 2*w^2 - 4*w - 6]', '[289, 17, 2*w^3 - 7*w]', '[289, 17, 3*w^3 - 13*w]', '[311, 311, 2*w^3 + w^2 - 11*w]', '[311, 311, w^3 - w^2 - 7*w + 5]', '[311, 311, w^3 + w^2 - 7*w - 5]', '[311, 311, -2*w^3 + w^2 + 11*w]', '[337, 337, 2*w^2 + w - 5]', '[337, 337, w^3 + 2*w^2 - 5*w - 5]', '[337, 337, w^3 - 2*w^2 - 5*w + 5]', '[337, 337, 2*w^2 - w - 5]', '[361, 19, 5*w^3 - w^2 - 22*w + 1]', '[361, 19, -3*w^3 - w^2 + 10*w + 4]', '[373, 373, 2*w^3 - w^2 - 12*w + 1]', '[373, 373, 2*w^3 + w^2 - 8*w - 9]', '[373, 373, -2*w^3 + w^2 + 8*w - 9]', '[373, 373, w^3 - 2*w^2 - w - 2]', '[383, 383, -4*w^3 - 2*w^2 + 21*w + 11]', '[383, 383, -3*w - 4]', '[383, 383, -w^3 - w^2 + 7*w + 9]', '[383, 383, 2*w^3 + w^2 - 11*w + 4]', '[419, 419, 3*w - 5]', '[419, 419, 5*w - 3]', '[419, 419, 3*w^3 - 15*w - 5]', '[419, 419, 5*w^3 - 25*w - 3]', '[421, 421, -2*w^3 - 2*w^2 + 13*w + 5]', '[421, 421, 3*w^3 + w^2 - 16*w - 4]', '[421, 421, 3*w^3 + 2*w^2 - 17*w - 5]', '[421, 421, -w^3 - w^2 + 8*w + 1]', '[457, 457, -3*w^3 - w^2 + 12*w + 2]', '[457, 457, w^3 - 3*w^2 - 3*w + 3]', '[457, 457, -3*w^3 - w^2 + 12*w + 3]', '[457, 457, w^3 - 3*w^2 - 2*w + 3]', '[467, 467, -w^3 - 2*w^2 + 7*w + 1]', '[467, 467, 2*w^3 + 2*w^2 - 11*w - 9]', '[467, 467, -2*w^3 + 2*w^2 + 11*w - 9]', '[467, 467, w^3 - 2*w^2 - 7*w + 1]', '[479, 479, -3*w^3 + 3*w^2 + 12*w - 5]', '[479, 479, 3*w^3 - 3*w^2 - 10*w + 3]', '[479, 479, -3*w^3 - 3*w^2 + 12*w + 10]', '[479, 479, 5*w^3 + 3*w^2 - 22*w - 12]', '[503, 503, -3*w^3 - w^2 + 14*w + 1]', '[503, 503, -w^3 + w^2 + 2*w - 4]', '[503, 503, w^3 + w^2 - 2*w - 4]', '[503, 503, 3*w^3 - w^2 - 14*w + 1]', '[529, 23, -3*w^3 + 12*w + 2]', '[529, 23, 3*w^3 - 12*w + 2]', '[541, 541, -w^3 + 9*w + 3]', '[541, 541, 4*w^3 - 21*w + 3]', '[541, 541, 3*w^3 - 2*w^2 - 10*w + 2]', '[541, 541, w^3 - 9*w + 3]', '[563, 563, 3*w^3 + w^2 - 12*w - 8]', '[563, 563, -3*w^3 - w^2 + 12*w - 3]', '[563, 563, 3*w^3 - w^2 - 12*w - 3]', '[563, 563, -3*w^3 + w^2 + 12*w - 8]', '[587, 587, -2*w^3 + 2*w^2 + 6*w - 5]', '[587, 587, -4*w^3 + 2*w^2 + 18*w - 5]', '[587, 587, 4*w^3 + 2*w^2 - 18*w - 5]', '[587, 587, 5*w^3 + 2*w^2 - 23*w - 6]', '[613, 613, -4*w^3 + 17*w + 3]', '[613, 613, 3*w^3 - 11*w - 3]', '[613, 613, 3*w^3 - w^2 - 10*w - 2]', '[613, 613, -4*w^3 + 17*w - 3]', '[647, 647, -w^3 - 2*w^2 + 7*w]', '[647, 647, 2*w^3 + w^2 - 10*w + 2]', '[647, 647, -2*w^3 - 2*w^2 + 11*w + 10]', '[647, 647, w^2 - 2*w - 7]', '[673, 673, 4*w^3 + w^2 - 16*w - 6]', '[673, 673, 6*w^3 + 2*w^2 - 27*w - 10]', '[673, 673, -6*w^3 + 2*w^2 + 27*w - 10]', '[673, 673, w^3 - w^2 - 8*w - 5]', '[709, 709, 2*w^3 - 9*w - 6]', '[709, 709, w^3 - 3*w - 6]', '[709, 709, -w^3 + 3*w - 6]', '[709, 709, -2*w^3 + 9*w - 6]', '[719, 719, 2*w^3 - 2*w^2 - 9*w + 2]', '[719, 719, -2*w^3 - 2*w^2 + 8*w + 1]', '[719, 719, 2*w^3 - 2*w^2 - 8*w + 1]', '[719, 719, -2*w^3 - 2*w^2 + 9*w + 2]', '[757, 757, 3*w^3 - 3*w^2 - 6*w + 2]', '[757, 757, 3*w^3 + 3*w^2 - 13*w - 9]', '[757, 757, -3*w^3 + 3*w^2 + 13*w - 9]', '[757, 757, -2*w^3 - 3*w^2 + 7*w + 6]', '[839, 839, -4*w^3 + w^2 + 20*w - 1]', '[839, 839, w^2 - 4*w - 4]', '[839, 839, w^2 + 4*w - 4]', '[839, 839, 4*w^3 + w^2 - 20*w - 1]', '[841, 29, -w^3 + 6*w - 6]', '[841, 29, w^3 - 6*w - 6]', '[877, 877, 3*w^3 + w^2 - 11*w - 1]', '[877, 877, -4*w^3 - w^2 + 17*w + 4]', '[877, 877, 4*w^3 - w^2 - 17*w + 4]', '[877, 877, -3*w^3 + w^2 + 11*w - 1]', '[887, 887, -3*w^3 - 2*w^2 + 15*w + 4]', '[887, 887, 2*w^2 - 3*w - 6]', '[887, 887, 2*w^2 + 3*w - 6]', '[887, 887, 3*w^3 - 2*w^2 - 15*w + 4]', '[961, 31, -2*w^3 - 3*w^2 + 11*w + 8]', '[961, 31, -2*w^3 + 3*w^2 + 11*w - 8]', '[971, 971, -4*w^3 + 21*w - 6]', '[971, 971, -w^3 + 9*w - 6]', '[971, 971, 6*w^3 + w^2 - 30*w - 9]', '[971, 971, 4*w^3 - 21*w - 6]', '[983, 983, 5*w^3 - 23*w + 4]', '[983, 983, -5*w^3 + 22*w - 6]', '[983, 983, 5*w^3 - 22*w - 6]', '[983, 983, -5*w^3 + 23*w + 4]']}
• 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, 0, -5, 0, 1], 'conductor': 84, 'degree': 4, 'dirichlet_group': [1, 55, 41, 71], 'disc_abs': 7056, 'disc_rad': 42, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 2]]], [7, [0]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[1, 4]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[1, 4]]], [53, [[2, 2]]], [59, [[1, 4]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 2, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 9.16515138991168, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.7056.1', 'local_algs': ['2.4.4.1', '3.2.1.1', '3.2.1.1', '7.4.2.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 7], 'rd': 9.16515138991, 'regulator': {'__RealLiteral__': 0, 'data': '5.7128756596', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-3.0.1', '-7.0.1', '-5.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} - 5 a \\)', '\\( a^{3} - 4 a + 2 \\)', '\\( a^{3} + a^{2} - 3 a - 1 \\)'], 'unitsGmodule': [[1, 1], [4, 1]], 'unitsType': 'Type II (ii)', 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}