Hilbert modular form data - 4.4.14656.1-17.1-a

Formats: - HTML - YAML - JSON - 2024-05-02T01:17:12.500068

• 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': 6, 'disc': 14656, 'field_bad_primes': [2, 229], 'field_label': '4.4.14656.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.14656.1-17.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [17], 'level_ideal': '[17, 17, -w^2 + w + 3]', 'level_label': '17.1', 'level_norm': 17, 'parallel_weight': 2, 'short_label': '17.1-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[17, 17, -w^2 + w + 3]', -1]], 'hecke_eigenvalues': ['e^4 - 5*e^2 + 4', 'e', '-e^2 + 1', '-e^5 + 3*e^3 + 2*e', 1, '-e^3 + 4*e', '3*e^5 - 13*e^3 + 9*e', '2*e^4 - 8*e^2 - 2', 'e^4 - 9', 'e^5 - 2*e^3 - 9*e', '-3*e^5 + 13*e^3 - 9*e', '-e^5 + 3*e^3 - 2*e', '-3*e^4 + 16*e^2 - 13', '-6*e^5 + 34*e^3 - 40*e', '3*e^5 - 12*e^3 + 3*e', '5*e^5 - 25*e^3 + 23*e', '-8*e^5 + 43*e^3 - 48*e', '4*e^2 - 6', '12*e^4 - 51*e^2 + 35', '8*e^4 - 46*e^2 + 47', '-6*e^4 + 23*e^2 - 7', '-5*e^4 + 20*e^2 - 4', '4*e^5 - 23*e^3 + 33*e', '6*e^3 - 19*e', '3*e^5 - 18*e^3 + 24*e', '-e^2 - 9', '3*e^5 - 19*e^3 + 25*e', '-8*e^5 + 42*e^3 - 43*e', '-4*e^5 + 28*e^3 - 39*e', '-4*e^5 + 15*e^3 - 10*e', '-3*e^2 + 6', '-e^5 + 9*e^3 - 20*e', '-13*e^4 + 51*e^2 - 25', '-2*e^4 + 11*e^2 - 28', '-2*e^5 + 5*e^3 + 8*e', '-6*e^5 + 35*e^3 - 47*e', '-5*e^5 + 27*e^3 - 31*e', '7*e^4 - 32*e^2 + 16', '6*e^5 - 26*e^3 + 19*e', '9*e^5 - 42*e^3 + 41*e', '-3*e^4 + 15*e^2 - 9', '5*e^4 - 24*e^2 + 13', '8*e^5 - 43*e^3 + 48*e', '7*e^5 - 29*e^3 + 20*e', '-4*e^3 + e', '7*e^5 - 30*e^3 + 13*e', '6*e^4 - 30*e^2 + 21', '-9*e^4 + 37*e^2 - 15', '-4*e^4 + 34*e^2 - 50', '7*e^4 - 29*e^2 + 11', '3*e^5 - 26*e^3 + 47*e', '-9*e^5 + 44*e^3 - 43*e', '-17*e^4 + 76*e^2 - 64', '-13*e^4 + 68*e^2 - 69', '-e^4 + 3*e^2 + 11', '2*e^4 - 7*e^2 + 10', '16*e^5 - 78*e^3 + 75*e', '-10*e^4 + 43*e^2 - 47', '5*e^4 - 31*e^2 + 34', '15*e^4 - 66*e^2 + 57', '-4*e^5 + 11*e^3 + 17*e', '-2*e^5 + 10*e^3 - 11*e', '19*e^4 - 88*e^2 + 70', '2*e^5 - 3*e^3 - 3*e', '-7*e^5 + 39*e^3 - 55*e', '14*e^4 - 64*e^2 + 49', '-19*e^2 + 42', '-3*e^2 + 11', '-9*e^4 + 39*e^2 - 25', '-3*e^4 + e^2 + 13', '-4*e^4 + 16*e^2 - 16', '-13*e^4 + 72*e^2 - 82', '5*e^4 - 17*e^2 - 11', '-4*e^4 + 23*e^2 - 25', '-10*e^5 + 46*e^3 - 37*e', '3*e^4 - 14*e^2 + 1', '15*e^4 - 57*e^2 + 18', '-12*e^4 + 57*e^2 - 51', '-2*e^4 + 4*e^2 + 1', '-7*e^4 + 37*e^2 - 38', '7*e^4 - 29*e^2 + 21', '-2*e^4 + 4*e^2 + 15', '6*e^5 - 18*e^3 - 7*e', '-20*e^4 + 91*e^2 - 75', '4*e^4 - 22*e^2 + 17', '10*e^5 - 55*e^3 + 56*e', '-2*e^3 + 6*e', '4*e^5 - 15*e^3 + 12*e', '2*e^5 - e^3 - 23*e', '5*e^5 - 35*e^3 + 68*e', '2*e^5 - 17*e^3 + 40*e', '7*e^5 - 38*e^3 + 29*e', '6*e^5 - 32*e^3 + 39*e', '14*e^5 - 75*e^3 + 86*e', '11*e^4 - 42*e^2 + 4', '2*e^4 + 11*e^2 - 45', '13*e^5 - 65*e^3 + 71*e', '-5*e^5 + 28*e^3 - 46*e', '-3*e^4 + 9*e^2 - 32', '-7*e^5 + 37*e^3 - 33*e', '-6*e^5 + 19*e^3 - 6*e', '-17*e^4 + 73*e^2 - 52', '3*e^5 - 19*e^3 + 10*e', '-14*e^5 + 82*e^3 - 100*e', '-e^5 + 14*e^3 - 31*e', '18*e^4 - 86*e^2 + 73', '-19*e^4 + 86*e^2 - 101', '20*e^4 - 85*e^2 + 50', '8*e^4 - 42*e^2 + 26', '17*e^4 - 92*e^2 + 92', '-19*e^4 + 106*e^2 - 104', '-3*e^5 - 5*e^3 + 40*e', '-12*e^5 + 51*e^3 - 43*e', '14*e^5 - 61*e^3 + 37*e', '-6*e^5 + 45*e^3 - 76*e', '4*e^5 - 16*e^3 - 5*e', '-9*e^4 + 61*e^2 - 87', '-2*e^5 + 16*e^3 - 9*e', '-2*e^5 + 24*e^3 - 50*e', '-31*e^4 + 142*e^2 - 115', '14*e^4 - 58*e^2 + 31', '-9*e^3 + 19*e', '4*e^5 - 23*e^3 + 44*e', '-21*e^4 + 106*e^2 - 109', '7*e^4 - 60*e^2 + 83', '-6*e^5 + 36*e^3 - 25*e', '-2*e^4 + 16*e^2 - 2', '-3*e^5 + 8*e^3 - 5*e', '7*e^5 - 45*e^3 + 65*e', '-17*e^4 + 57*e^2 - 1', '-3*e^5 + 20*e', '-6*e^5 + 18*e^3 + 3*e', '10*e^5 - 38*e^3 + 6*e', '-12*e^5 + 57*e^3 - 44*e', '9*e^4 - 28*e^2 - 22', '12*e^4 - 49*e^2 + 47', '5*e^5 - 24*e^3 + 28*e', '5*e^4 - 7*e^2 - 25', '2*e^5 - 23*e^3 + 57*e', '13*e^5 - 66*e^3 + 61*e', '6*e^4 - 14*e^2 + 4', '-9*e^4 + 52*e^2 - 67', '16*e^4 - 78*e^2 + 54', '14*e^4 - 78*e^2 + 89', '-9*e^5 + 65*e^3 - 103*e', '7*e^5 - 58*e^3 + 94*e', '-24*e^4 + 109*e^2 - 88', '-14*e^4 + 88*e^2 - 87', '-8*e^5 + 46*e^3 - 69*e', '-2*e^5 + e^3 + 34*e', '7*e^5 - 9*e^3 - 56*e', '-18*e^4 + 94*e^2 - 106', '18*e^4 - 108*e^2 + 118', '-13*e^4 + 51*e^2 - 33', '-28*e^4 + 110*e^2 - 63', '38*e^4 - 176*e^2 + 158', '-5*e^5 + 22*e^3 + 7*e', '-23*e^5 + 121*e^3 - 139*e', '4*e^4 - 18*e^2 + 20', '4*e^5 - 7*e^3 - 30*e', 'e^5 - 6*e^3 + 13*e', '31*e^4 - 153*e^2 + 151'], 'hecke_polynomial': 'x^6 - 7*x^4 + 14*x^2 - 7', 'label': '4.4.14656.1-17.1-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 14656, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[3, 3, w + 1]', '[4, 2, -w^2 + 2]', '[5, 5, -w^2 + w + 1]', '[6, 6, -w + 2]', '[8, 2, -w^3 + 2*w^2 + 4*w - 4]', '[9, 9, -w^3 + 2*w^2 + 3*w - 3]', '[10, 10, w + 2]', '[11, 11, w^2 - 3]', '[12, 6, -w^2 + 2*w]', '[15, 15, -w^2 + 2*w + 3]', '[16, 2, 2]', '[17, 17, -w^2 + w + 3]', '[18, 18, -w^2 + w + 2]', '[19, 19, -w^3 + 2*w^2 + 3*w - 1]', '[20, 10, w^3 - 3*w^2 - 2*w + 6]', '[22, 22, 2*w^3 - 4*w^2 - 7*w + 6]', '[24, 6, -w^3 + 2*w^2 + 4*w - 2]', '[25, 25, -w^3 + w^2 + 3*w - 1]', '[27, 3, w^3 - 3*w^2 - w + 5]', '[27, 27, -w^3 + w^2 + 4*w - 1]', '[30, 30, -w^3 + 2*w^2 + 3*w]', '[32, 4, 2*w]', '[33, 33, w^3 - 2*w^2 - 2*w + 1]', '[34, 34, -w^3 + w^2 + 3*w]', '[36, 18, -w^3 + w^2 + 2*w]', '[38, 38, w^3 - 3*w^2 - 3*w + 8]', '[40, 10, -w^3 + 2*w^2 + 2*w - 2]', '[41, 41, -w^3 + 2*w^2 + w - 1]', '[41, 41, -w^3 + w^2 + 2*w - 1]', '[43, 43, w^3 - w^2 - 5*w + 1]', '[44, 22, w^2 - 2*w - 4]', '[45, 45, 2*w - 1]', '[47, 47, w^2 - 2*w - 5]', '[47, 47, -2*w^3 + 6*w^2 + w - 5]', '[48, 6, 2*w + 2]', '[50, 50, -w^2 + w + 6]', '[51, 51, -w^3 + 4*w + 3]', '[54, 6, -w^3 + 3*w^2 + w - 2]', '[54, 54, -2*w^3 + 5*w^2 + 5*w - 8]', '[55, 55, -w^3 + 3*w^2 + 3*w - 9]', '[57, 57, -w^3 + w^2 + 6*w + 1]', '[60, 30, -w^2 + 4]', '[61, 61, -2*w^3 + 5*w^2 + 4*w - 7]', '[64, 4, -2*w^2 + 4]', '[66, 66, -w^3 + 2*w^2 + 3*w - 6]', '[67, 67, -2*w^2 + 2*w + 9]', '[67, 67, -w^3 + 2*w^2 + 4*w - 1]', '[68, 34, -w^2 + 4*w - 2]', '[71, 71, w^3 - w^2 - 6*w + 3]', '[72, 18, -w^3 + 2*w^2 + 2*w + 2]', '[75, 75, -w^3 + 2*w^2 + w + 1]', '[76, 38, -w^3 + w^2 + 4*w - 2]', '[80, 10, -2*w^2 + 2*w + 2]', '[81, 3, 3]', '[81, 81, -2*w^2 + 4*w + 3]', '[82, 82, -w^3 + 2*w^2 + 5*w - 2]', '[82, 82, -w + 4]', '[83, 83, -w^3 + 2*w^2 + 5*w + 1]', '[85, 85, w^2 + 1]', '[86, 86, w^3 - w^2 - 3*w - 2]', '[88, 22, w^3 - 2*w^2 - 4*w]', '[89, 89, -w - 3]', '[89, 89, -w^2 - 2*w + 1]', '[90, 90, -2*w^3 + 3*w^2 + 7*w - 4]', '[94, 94, -3*w^3 + 6*w^2 + 11*w - 12]', '[94, 94, w^3 - 2*w^2 - 5*w]', '[95, 95, -2*w^3 + 5*w^2 + 6*w - 9]', '[96, 12, -2*w + 4]', '[97, 97, w^3 - w^2 - 6*w + 1]', '[99, 99, w^3 - 5*w - 1]', '[100, 50, -w^3 + w^2 + 6*w]', '[101, 101, 2*w^3 - 3*w^2 - 9*w + 3]', '[101, 101, -2*w^3 + 4*w^2 + 6*w - 7]', '[102, 102, w^3 - 3*w^2 - w + 6]', '[103, 103, -w^3 + 4*w^2 - w - 7]', '[107, 107, -2*w^3 + 5*w^2 + 7*w - 13]', '[107, 107, -w^3 + w^2 + 4*w - 3]', '[108, 6, -2*w^3 + 3*w^2 + 8*w - 4]', '[108, 54, w^3 - 3*w^2 + 4]', '[110, 110, w^3 - w^2 - 5*w + 2]', '[114, 114, -2*w^2 + w + 6]', '[120, 30, -w^3 + 4*w]', '[121, 121, -w^3 + 2*w^2 + 5*w - 5]', '[122, 122, w^3 - 4*w^2 + w + 4]', '[123, 123, -2*w^3 + 4*w^2 + 6*w - 3]', '[123, 123, -2*w^3 + 4*w^2 + 7*w - 5]', '[125, 5, 3*w^3 - 7*w^2 - 8*w + 13]', '[125, 125, -2*w^3 + 4*w^2 + 6*w - 5]', '[127, 127, -w^3 + 3*w^2 + 2*w - 3]', '[127, 127, 2*w^3 - 2*w^2 - 8*w + 1]', '[128, 4, -2*w^3 + 4*w^2 + 8*w - 8]', '[129, 129, 2*w^3 - 2*w^2 - 8*w - 1]', '[131, 131, w^2 - 3*w - 3]', '[131, 131, w^2 - 5]', '[132, 66, -w^2 - 2*w + 2]', '[134, 134, -2*w^3 + 2*w^2 + 9*w]', '[134, 134, 3*w + 2]', '[135, 15, -w^3 + 7*w + 1]', '[135, 135, -2*w^3 + 3*w^2 + 9*w - 5]', '[136, 34, -w^3 + 8*w + 2]', '[141, 141, -w^2 + 4*w - 1]', '[141, 141, w^3 - w^2 - 7*w - 5]', '[142, 142, w^3 - 2*w^2 - w - 2]', '[144, 18, -2*w^3 + 4*w^2 + 6*w - 6]', '[149, 149, -w^3 + 2*w^2 + 5*w - 3]', '[150, 150, -w^3 + 3*w^2 + 3*w - 4]', '[151, 151, -2*w^3 + 6*w^2 + 4*w - 15]', '[152, 38, -w^3 + 2*w + 2]', '[153, 153, -2*w^3 + 4*w^2 + 8*w - 7]', '[157, 157, w^3 - 4*w^2 + w + 5]', '[157, 157, 3*w^3 - 8*w^2 - 8*w + 17]', '[160, 20, 2*w + 4]', '[162, 6, 3*w]', '[162, 162, -w^3 + 2*w^2 + 5*w - 4]', '[163, 163, -4*w^3 + 8*w^2 + 14*w - 15]', '[163, 163, 3*w^3 - 6*w^2 - 11*w + 9]', '[164, 82, -3*w^3 + 7*w^2 + 8*w - 12]', '[164, 82, -w^2 + 4*w]', '[165, 165, 2*w^2 - 2*w - 7]', '[166, 166, w^2 + 5*w + 2]', '[167, 167, w^3 - 6*w - 1]', '[170, 170, -2*w^3 + 4*w^2 + 5*w - 2]', '[171, 171, -w^2 + 7]', '[172, 86, w^3 + w^2 - 6*w - 2]', '[176, 22, 2*w^2 - 6]', '[178, 178, 2*w^2 - 3*w - 6]', '[178, 178, -w^2 - 3*w]', '[180, 90, -2*w^3 + 5*w^2 + 2*w - 2]', '[181, 181, 2*w^2 - 3*w - 3]', '[183, 183, -w^3 + w^2 + 5*w - 3]', '[187, 187, 2*w^3 - 5*w^2 - 4*w + 5]', '[188, 94, 3*w^2 - 8]', '[188, 94, -w^2 + 6]', '[190, 190, w^3 - 2*w^2 - w + 4]', '[191, 191, 3*w^3 - 8*w^2 - 9*w + 21]', '[191, 191, -w^3 + w^2 + 3*w + 3]', '[192, 12, -2*w^2 + 4*w]', '[194, 194, w^3 - 2*w^2 - 3*w - 2]', '[197, 197, -2*w^3 + 4*w^2 + 9*w - 11]', '[197, 197, 2*w^2 - 2*w - 3]', '[198, 198, 2*w^3 - 6*w^2 - w + 4]', '[199, 199, -w^3 + 4*w^2 - 2*w - 5]', '[199, 199, -w^3 + 3*w^2 + w - 7]', '[200, 50, w^3 - 4*w^2 - 2*w + 10]', '[201, 201, -2*w^3 + 11*w + 9]', '[201, 201, -w^3 + 2*w^2 + 7*w + 1]', '[202, 202, w^3 - w^2 - 5*w - 4]', '[202, 202, -2*w^2 + w + 4]', '[204, 102, -w^3 + 3*w^2 + 2*w - 2]', '[205, 205, -2*w^3 + 5*w^2 + 3*w - 5]', '[205, 205, -2*w^2 + w + 5]', '[206, 206, 2*w^3 - 5*w^2 - 3*w + 2]', '[209, 209, 2*w^3 - 3*w^2 - 7*w + 3]', '[211, 211, 2*w^3 - 5*w^2 - 5*w + 7]', '[211, 211, 4*w^3 - 9*w^2 - 12*w + 15]', '[213, 213, 2*w^3 - 3*w^2 - 7*w + 1]', '[214, 214, w^3 - w^2 - 5*w + 4]', '[214, 214, -w^3 + w + 2]', '[215, 215, w^3 - 3*w^2 - 2*w + 1]', '[216, 6, -w^3 + 4*w + 4]', '[216, 54, -w^3 + 8*w + 4]', '[220, 110, w^3 - w^2 - 2*w - 2]', '[225, 225, w^3 - 2*w^2 - 2*w + 7]', '[228, 114, w^3 - 5*w^2 + 4*w + 4]', '[229, 229, 3*w - 1]', '[229, 229, 4*w^3 - 9*w^2 - 12*w + 17]', '[229, 229, 5*w^3 - 12*w^2 - 16*w + 29]', '[233, 233, w^2 - w - 7]', '[235, 235, 3*w^3 - 8*w^2 - 7*w + 17]', '[235, 235, w^3 - 3*w - 3]', '[240, 30, -2*w^2 + 4*w + 6]', '[242, 242, w^2 - w + 2]', '[243, 9, 3*w + 3]', '[243, 243, w^3 - 3*w^2 - w + 9]', '[244, 122, w^3 - 3*w^2 - 2*w + 10]', '[246, 246, -2*w^2 + 5*w + 4]', '[246, 246, -w^2 + 3*w + 4]', '[249, 249, -w^3 + 3*w^2 + 10*w + 3]', '[250, 10, -w^3 + 4*w^2 + w - 6]', '[250, 250, -2*w^2 + 3*w + 4]', '[251, 251, -2*w^3 + 2*w^2 + 6*w - 5]', '[251, 251, w^3 - w^2 - 3*w - 5]', '[254, 254, w^3 - 2*w^2 + w + 2]', '[254, 254, 2*w^3 - 7*w - 4]', '[255, 255, -w^3 + w^2 + 6*w - 5]', '[256, 4, 4]', '[257, 257, -w^3 + 2*w^2 + 5*w - 9]', '[257, 257, -w^3 + 2*w^2 + 3*w - 7]', '[258, 258, 2*w^3 - 9*w - 4]', '[262, 262, w^3 - 5*w]', '[262, 262, w^3 - 3*w^2 - 3*w]', '[264, 66, -w^3 + 4*w^2 - 8]', '[267, 267, -w^3 + 4*w^2 - 4*w - 3]', '[267, 267, -w^2 - 4*w - 3]', '[268, 134, -2*w^3 + w^2 + 8*w + 4]', '[268, 134, -2*w^3 + w^2 + 6*w - 2]', '[269, 269, -2*w^3 + 2*w^2 + 11*w - 1]', '[269, 269, w^3 - 5*w - 9]', '[270, 30, w^3 - 3*w^2 - w + 8]', '[270, 270, -w^3 + w^2 + 3*w + 4]', '[271, 271, -4*w^3 + 11*w^2 + 10*w - 27]', '[272, 34, -2*w^2 + 2*w + 6]', '[275, 275, -w^3 + 3*w^2 - 5]', '[277, 277, w^3 - 3*w^2 - 3*w + 11]', '[281, 281, -2*w^3 + 2*w^2 + 7*w + 1]', '[281, 281, -5*w^3 + 13*w^2 + 13*w - 27]', '[282, 282, 2*w^3 - 6*w^2 - 5*w + 12]', '[282, 282, -w^3 + 4*w^2 + w - 10]', '[283, 283, -w^3 + 3*w^2 + 3*w - 3]', '[283, 283, -2*w^3 + 3*w^2 + 8*w - 5]', '[284, 142, w^3 + w^2 - 8*w - 10]', '[285, 285, -w^3 + 3*w^2 + 5*w - 5]', '[288, 36, -2*w^2 + 2*w + 4]', '[289, 289, -w^2 + 2*w + 7]', '[291, 291, 2*w^3 - 3*w^2 - 9*w - 1]', '[293, 293, -3*w^3 + 9*w^2 + 4*w - 15]', '[297, 33, -2*w^3 + 6*w^2 + 5*w - 13]', '[297, 297, w - 5]', '[298, 298, w^2 + w + 2]', '[300, 150, w^3 - w^2 + 2]', '[302, 302, 2*w^3 - 4*w^2 - 7*w + 4]', '[303, 303, -2*w^3 + 2*w^2 + 7*w - 3]', '[303, 303, 3*w^3 - 4*w^2 - 14*w - 1]', '[304, 38, -2*w^3 + 4*w^2 + 6*w - 2]', '[305, 305, -w^3 + 2*w^2 + 2*w + 3]', '[306, 306, w + 4]', '[307, 307, w^2 - 4*w - 3]', '[309, 309, w^3 - w^2 - 4*w - 5]', '[311, 311, w^2 + w - 5]', '[313, 313, -3*w^3 + 5*w^2 + 11*w - 5]', '[313, 313, 2*w^3 - 5*w^2 - 2*w + 3]', '[314, 314, -2*w^3 + 5*w^2 + w - 2]', '[314, 314, -2*w^3 + 4*w^2 + 5*w - 6]', '[317, 317, -2*w^3 + 4*w^2 + 5*w - 3]', '[317, 317, 2*w^2 - 2*w - 5]', '[320, 20, 2*w^3 - 6*w^2 - 4*w + 12]', '[321, 321, -w^3 + 4*w^2 + 2*w - 9]', '[321, 321, -2*w^3 + w^2 + 5*w - 1]', '[323, 323, -2*w^3 + 2*w^2 + 10*w - 1]', '[324, 6, -3*w^2 + 6]', '[324, 162, w^2 + 2]', '[326, 326, -2*w^2 + w + 8]', '[326, 326, w^2 - 3*w - 6]', '[328, 82, w^3 - 4*w^2 + 6]', '[328, 82, w^3 - 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9]', '[1819, 1819, -6*w^3 + 15*w^2 + 16*w - 33]', '[1822, 1822, w^3 - 2*w^2 + 3*w - 4]', '[1823, 1823, -4*w^2 - 3*w + 3]', '[1824, 228, -4*w^2 + 2*w + 12]', '[1826, 1826, 4*w^3 - 3*w^2 - 21*w - 12]', '[1828, 914, 6*w^3 - 9*w^2 - 26*w + 8]', '[1830, 1830, -3*w^3 + 3*w^2 + 11*w - 4]', '[1831, 1831, -3*w^2 - w + 9]', '[1832, 458, w^3 - 2*w^2 - 4*w + 10]', '[1832, 458, -3*w^3 + 4*w^2 + 8*w - 12]', '[1832, 458, -5*w^3 + 10*w^2 + 14*w - 20]', '[1835, 1835, -2*w^3 + 8*w^2 + 2*w - 9]', '[1836, 102, -2*w^3 + 3*w^2 + 2*w + 2]', '[1836, 918, -w^2 - 2*w + 8]', '[1837, 1837, -w^3 + 3*w^2 + 8*w - 1]', '[1838, 1838, -2*w^3 + 2*w^2 + w + 2]', '[1839, 1839, -5*w^3 + 13*w^2 + 13*w - 23]', '[1839, 1839, 3*w^3 - 14*w - 11]', '[1842, 1842, -w^3 + 6*w^2 - 5*w - 6]', '[1843, 1843, w^3 + 3*w^2 - 13*w - 11]', '[1845, 1845, -3*w^3 + 2*w^2 + 9*w + 1]', '[1845, 1845, -3*w^3 + 7*w^2 + 12*w - 13]', '[1847, 1847, w^3 - 9*w - 7]', '[1849, 1849, 2*w^3 - w^2 - 10*w - 11]', '[1851, 1851, -w^3 + 4*w^2 + 5*w - 3]', '[1851, 1851, -3*w^3 + 5*w^2 + 12*w - 11]', '[1851, 1851, -2*w^3 + 2*w^2 + 11*w - 5]', '[1851, 1851, 4*w^3 - w^2 - 15*w - 7]', '[1852, 926, -3*w^2 + 8*w + 6]', '[1854, 1854, w^3 - 2*w^2 + w - 8]', '[1857, 1857, 5*w^3 - 2*w^2 - 18*w - 5]', '[1857, 1857, -3*w^3 + 3*w^2 + 10*w + 1]', '[1857, 1857, 3*w^2 + 7*w + 1]', '[1857, 1857, w^3 + 3*w^2 - 10*w - 21]', '[1858, 1858, w^3 + 2*w^2 - 9*w - 6]', '[1858, 1858, w^3 - 5*w^2 + w + 8]', '[1864, 466, 3*w^3 - 2*w^2 - 8*w + 2]', '[1865, 1865, -2*w^3 - w^2 + 14*w + 11]', '[1866, 1866, -w^3 + w^2 + 7*w - 10]', '[1867, 1867, w^3 - 3*w^2 + 4*w - 9]', '[1867, 1867, w^3 - 5*w^2 - 4*w + 13]', '[1868, 934, 2*w^3 + w^2 - 6*w - 6]', '[1870, 1870, 3*w^3 - 6*w^2 - 11*w + 6]', '[1873, 1873, -w^2 + 2*w - 5]', '[1873, 1873, -2*w^3 + 5*w^2 + 9*w - 21]', '[1874, 1874, -3*w^3 + 5*w^2 + 7*w - 8]', '[1874, 1874, -2*w^3 + 7*w^2 + w]', '[1875, 15, -5*w^2 + 5]', '[1875, 1875, -w^3 + 4*w^2 + 4*w - 1]', '[1877, 1877, -4*w^3 + 8*w^2 + 19*w - 25]', '[1878, 1878, -2*w^3 - w^2 + 7*w]', '[1878, 1878, -4*w^3 + 6*w^2 + 19*w]', '[1879, 1879, -w^3 + 5*w^2 - 3*w - 11]', '[1879, 1879, w^3 + 2*w^2 - 7*w - 1]', '[1880, 470, -3*w^3 + 4*w^2 + 10*w - 10]', '[1880, 470, 3*w^3 - 4*w^2 - 12*w + 6]', '[1881, 1881, -2*w^3 + 6*w^2 + 4*w - 19]', '[1882, 1882, 3*w^3 - 4*w^2 - 15*w + 2]', '[1884, 942, -4*w^3 + 11*w^2 + 8*w - 16]', '[1884, 942, -5*w^3 + 17*w^2 - 4*w - 8]', '[1889, 1889, 7*w^3 - 15*w^2 - 22*w + 25]', '[1892, 946, -5*w^3 + 7*w^2 + 20*w - 2]', '[1893, 1893, 4*w^3 - 4*w^2 - 21*w - 1]', '[1894, 1894, -w^2 + 7*w + 4]', '[1894, 1894, 5*w^2 + w - 6]', '[1899, 1899, -w^3 + 8*w^2 - 11*w - 11]', '[1899, 1899, w^3 - 4*w^2 - 7*w + 1]', '[1900, 950, -3*w^3 + 9*w^2 + 2*w - 6]', '[1902, 1902, -4*w^3 + 11*w^2 + 5*w - 10]', '[1902, 1902, -2*w^3 + 6*w^2 + w - 10]', '[1905, 1905, -w^3 + 10*w - 3]', '[1905, 1905, 6*w^3 - 7*w^2 - 26*w - 1]', '[1906, 1906, 3*w^3 - 2*w^2 - 9*w]', '[1907, 1907, -4*w^3 + 10*w^2 + 10*w - 15]', '[1910, 1910, 2*w^3 - 6*w^2 - 3*w + 4]', '[1910, 1910, -3*w^3 + w^2 + 13*w + 8]', '[1913, 1913, -2*w^2 + 8*w - 9]', '[1916, 958, -3*w^3 + 3*w^2 + 10*w - 10]', '[1916, 958, -2*w^3 + 5*w^2 - 2*w - 4]', '[1917, 213, 2*w^3 - 3*w^2 - 8*w - 5]', '[1917, 1917, 2*w^2 - 2*w - 13]', '[1919, 1919, w^3 - 4*w^2 - 3*w + 15]', '[1919, 1919, 3*w^3 - w^2 - 10*w - 5]', '[1920, 60, -2*w^3 + 8*w]', '[1923, 1923, 2*w^3 - 9*w - 1]', '[1926, 1926, -4*w^3 + 10*w^2 + 9*w - 20]', '[1926, 1926, -w^3 + 5*w^2 + 3*w - 6]', '[1927, 1927, -8*w^3 + 19*w^2 + 23*w - 35]', '[1927, 1927, 2*w^3 - w^2 - 9*w + 1]', '[1927, 1927, -w^3 - w^2 + 10*w - 1]', '[1927, 1927, 3*w^3 - 2*w^2 - 10*w + 3]', '[1931, 1931, -4*w^3 + 7*w^2 + 15*w - 13]', '[1935, 1935, w^3 - w^2 - w - 5]', '[1936, 242, -2*w^3 + 4*w^2 + 10*w - 10]', '[1938, 1938, -2*w^3 + 2*w^2 + 13*w - 6]', '[1940, 970, 5*w^3 - 11*w^2 - 14*w + 16]', '[1941, 1941, 2*w^3 - 4*w^2 - 10*w + 5]', '[1941, 1941, -w^3 + 3*w^2 + w + 3]', '[1942, 1942, 3*w^3 - 5*w^2 - 13*w + 12]', '[1944, 18, -3*w^3 + 6*w^2 + 12*w - 6]', '[1944, 486, -3*w^3 + 2*w^2 + 16*w + 2]', '[1945, 1945, -3*w^3 + 3*w^2 + 10*w - 1]', '[1945, 1945, -6*w^3 + 16*w^2 + 16*w - 35]', '[1951, 1951, -4*w^2 + 7*w + 1]', '[1951, 1951, w^3 + 2*w^2 - 10*w - 13]', '[1952, 244, 2*w^3 - 8*w^2 + 2*w + 8]', '[1956, 978, -w^3 + 5*w^2 - 12]', '[1956, 978, 2*w^3 - 5*w^2 - 6*w + 16]', '[1957, 1957, 2*w^3 + w^2 - 20*w + 3]', '[1958, 1958, -4*w^3 + 4*w^2 + 15*w + 6]', '[1958, 1958, -6*w^3 + 11*w^2 + 23*w - 14]', '[1959, 1959, 2*w^3 - 2*w^2 - 4*w - 3]', '[1959, 1959, -w^3 - 2*w - 3]', '[1964, 982, 2*w^3 - 9*w^2 - 6*w + 22]', '[1965, 1965, 3*w^3 - 4*w^2 - 11*w - 7]', '[1965, 1965, 4*w^2 - 6*w - 13]', '[1968, 246, -4*w^3 + 8*w^2 + 12*w - 6]', '[1968, 246, -4*w^3 + 8*w^2 + 14*w - 10]', '[1970, 1970, 2*w^3 + 2*w^2 - 7*w - 6]', '[1970, 1970, -4*w^3 + 9*w^2 + 15*w - 18]', '[1977, 1977, -3*w^3 + 4*w^2 + 10*w - 3]', '[1977, 1977, -4*w^3 + 7*w^2 + 17*w - 9]', '[1979, 1979, -3*w^3 + 2*w^2 + 9*w - 7]', '[1980, 990, 2*w^3 - 5*w^2 - 6*w + 4]', '[1982, 1982, -w^3 + w^2 - w + 4]', '[1983, 1983, -4*w^3 + 2*w^2 + 12*w - 3]', '[1985, 1985, 2*w^2 + 4*w - 5]', '[1990, 1990, w^3 + 4*w^2 - 7*w - 2]', '[1990, 1990, 2*w^2 - 5*w - 8]', '[1991, 1991, w^3 - w^2 + w + 5]', '[1992, 498, -3*w^3 + 4*w^2 + 18*w + 8]', '[1994, 1994, -2*w^3 + 3*w^2 + 11*w - 2]', '[1999, 1999, -w^3 - w^2 + 7*w - 1]', '[2000, 10, 6*w^3 - 14*w^2 - 16*w + 26]', '[2000, 250, -4*w^3 + 8*w^2 + 12*w - 10]', '[2004, 1002, 2*w^3 - 7*w^2]', '[2005, 2005, w^3 - 2*w^2 + 4*w - 1]', '[2008, 502, w^3 - 2*w^2 + 2*w + 4]', '[2008, 502, 5*w^3 - 8*w^2 - 22*w + 14]', '[2010, 2010, -7*w^3 + 8*w^2 + 31*w + 4]', '[2010, 2010, -3*w^3 + 4*w^2 + 13*w + 6]', '[2011, 2011, 4*w^2 + 2*w - 3]', '[2011, 2011, -2*w^3 + 5*w^2 + 7*w - 5]', '[2012, 1006, -3*w^3 + 7*w^2 + 6*w - 14]', '[2012, 1006, -3*w^3 + 7*w^2 + 10*w - 10]', '[2012, 1006, -4*w^3 + 7*w^2 + 14*w - 14]', '[2012, 1006, -4*w^3 + 3*w^2 + 8*w - 10]', '[2013, 2013, 2*w^3 - 6*w^2 - 9*w + 11]', '[2017, 2017, 3*w^3 - 4*w^2 - 15*w + 3]', '[2019, 2019, -3*w^3 + 5*w^2 + 13*w - 1]', '[2020, 1010, 3*w^3 - 3*w^2 - 18*w - 10]', '[2020, 1010, -9*w^3 + 21*w^2 + 30*w - 46]', '[2021, 2021, w^3 - 11*w - 3]', '[2021, 2021, 2*w^3 - 7*w^2 - 4*w + 15]', '[2022, 2022, 6*w^2 + w - 8]', '[2025, 75, -3*w^3 + 3*w^2 + 9*w - 3]', '[2025, 2025, -w^3 + w^2 + 9*w + 1]', '[2026, 2026, 4*w^3 - 10*w^2 - 7*w + 12]', '[2027, 2027, -2*w^3 + 6*w^2 + 7*w - 17]', '[2027, 2027, -6*w^3 + 15*w^2 + 15*w - 25]', '[2029, 2029, -w^3 + w^2 + 3*w - 7]', '[2029, 2029, 4*w^2 - 6*w - 5]', '[2032, 254, -2*w^3 + 6*w^2 + 4*w - 6]', '[2032, 254, 4*w^3 - 4*w^2 - 16*w + 2]', '[2033, 2033, -4*w^3 + 13*w^2 + 11*w - 31]', '[2033, 2033, w^3 - 5*w^2 + w + 9]', '[2039, 2039, -2*w^3 + 5*w^2 + 2*w - 9]', '[2039, 2039, -2*w^3 + 5*w^2 + 9*w - 17]', '[2040, 510, -w^3 + 4*w^2 + 6*w - 2]', '[2045, 2045, 2*w^2 - 2*w + 3]', '[2048, 8, -4*w^3 + 8*w^2 + 16*w - 16]', '[2049, 2049, 2*w^3 - 7*w^2 - 3*w + 15]', '[2050, 2050, -3*w^3 + 6*w^2 + 7*w - 4]', '[2050, 2050, -3*w^3 + 5*w^2 + 9*w - 6]', '[2052, 114, -4*w^3 + 9*w^2 + 10*w - 14]', '[2052, 1026, -3*w^2 + 10*w - 2]', '[2053, 2053, 3*w^3 - 4*w^2 - 16*w - 1]', '[2053, 2053, -w^3 + w^2 + 9*w - 13]', '[2056, 514, w^3 + 2*w^2 - 6*w - 8]', '[2056, 514, 7*w^3 - 16*w^2 - 24*w + 34]', '[2057, 2057, -4*w^3 + 8*w^2 + 12*w - 13]', '[2060, 1030, -4*w^3 + 9*w^2 + 18*w - 32]', '[2061, 2061, w^3 - 5*w^2 + 9]', '[2061, 2061, -w^3 + 6*w^2 - 5*w - 9]', '[2061, 2061, -w^3 - w^2 + 13*w - 5]', '[2063, 2063, 3*w^3 - 7*w^2 - 7*w + 5]', '[2063, 2063, 3*w^3 - 9*w^2 - 9*w + 23]', '[2064, 258, 4*w^3 - 4*w^2 - 16*w - 2]', '[2068, 1034, w^3 + w^2 - 14*w + 8]', '[2068, 1034, -2*w^3 - w^2 + 14*w + 18]', '[2074, 2074, w^2 - 3*w + 6]', '[2075, 2075, -5*w^3 + 16*w + 7]', '[2078, 2078, -3*w^3 + 9*w^2 - w - 8]', '[2078, 2078, w^3 + 2*w^2 - 9*w - 2]', '[2081, 2081, 4*w^3 - 5*w^2 - 14*w - 3]', '[2084, 1042, 3*w^3 - 3*w^2 - 10*w]', '[2084, 1042, 5*w^2 + 4*w - 8]', '[2089, 2089, -3*w^3 + 5*w^2 + 9*w - 3]', '[2089, 2089, -3*w^3 + 4*w^2 + 10*w - 1]', '[2090, 2090, 4*w^2 - 7*w - 10]', '[2091, 2091, w^3 - 2*w^2 - 8*w + 13]', '[2091, 2091, 3*w^3 - 8*w^2 - 11*w + 21]', '[2094, 2094, -4*w^3 + 12*w^2 + 3*w - 16]', '[2094, 2094, 2*w^3 - 6*w^2 - 3*w + 2]', '[2096, 262, 2*w^2 - 6*w - 6]', '[2096, 262, 2*w^2 - 10]', '[2097, 2097, 2*w^3 + w^2 - 18*w - 5]', '[2099, 2099, 3*w^3 - 8*w^2 - 5*w + 7]', '[2099, 2099, -6*w^3 + 14*w^2 + 18*w - 25]', '[2101, 2101, -3*w - 7]', '[2101, 2101, -w^3 - 2*w^2 + 9*w + 9]', '[2103, 2103, w^3 - 2*w^2 - 11*w - 5]', '[2105, 2105, 4*w^3 - 9*w^2 - 10*w + 13]', '[2110, 2110, 2*w^3 - 5*w^2 + w - 2]', '[2110, 2110, 3*w^3 - 7*w^2 - 11*w + 10]', '[2112, 132, -2*w^2 - 4*w + 4]', '[2113, 2113, -3*w^3 + 4*w^2 + 9*w - 5]', '[2113, 2113, 3*w^3 - 5*w^2 - 14*w + 5]', '[2115, 2115, -4*w^3 + 10*w^2 + 6*w - 5]', '[2115, 2115, 2*w^3 - 5*w^2 - 8*w + 5]', '[2118, 2118, -w^3 + 4*w^2 - w - 12]', '[2118, 2118, 3*w^3 - 3*w^2 - 13*w + 2]', '[2125, 85, 3*w^3 - 7*w^2 - 3*w + 3]', '[2125, 2125, -4*w^3 + 7*w^2 + 17*w - 11]', '[2126, 2126, 3*w^3 - 10*w^2 + 3*w + 8]', '[2126, 2126, -3*w^3 + 5*w^2 + 5*w + 2]', '[2126, 2126, -2*w^3 + 5*w^2 + 3*w - 14]', '[2126, 2126, 2*w^3 - 7*w^2 - w + 4]', '[2129, 2129, -w^3 + w^2 + 2*w - 7]', '[2130, 2130, 5*w^3 - 5*w^2 - 21*w - 2]', '[2131, 2131, -4*w^3 + 11*w^2 + 12*w - 29]', '[2134, 2134, w^3 - 8*w^2 + 5*w + 28]', '[2136, 534, 3*w^3 - 8*w^2 - 4*w + 4]', '[2136, 534, 3*w^3 - 6*w^2 - 14*w + 4]', '[2138, 2138, w^3 - 4*w^2 + w - 2]', '[2140, 1070, 3*w^3 - 3*w^2 - 10*w + 6]', '[2140, 1070, -5*w^3 + 13*w^2 + 14*w - 24]', '[2141, 2141, -4*w^2 + w + 9]', '[2144, 268, -4*w^3 + 4*w^2 + 18*w]', '[2144, 268, 6*w + 4]', '[2150, 2150, w^3 - 4*w^2 - 7*w]', '[2152, 538, -w^3 - 2*w^2 + 6*w + 6]', '[2152, 538, 9*w^3 - 16*w^2 - 36*w + 26]', '[2155, 2155, -6*w^2 + 2*w + 3]', '[2159, 2159, 4*w^3 - 7*w^2 - 19*w + 3]', '[2159, 2159, -2*w^3 + 2*w^2 + 9*w - 5]', '[2160, 30, -2*w^3 + 14*w + 2]', '[2160, 270, -4*w^3 + 6*w^2 + 18*w - 10]', '[2161, 2161, 2*w^2 - 4*w - 13]', '[2165, 2165, -2*w^3 + 7*w^2 + 3*w - 13]', '[2166, 2166, w^3 - 4*w^2 - 5*w + 12]', '[2167, 2167, 2*w^3 - w^2 - 2*w + 5]', '[2167, 2167, 7*w^3 - 15*w^2 - 23*w + 33]', '[2168, 542, 5*w^3 - 8*w^2 - 16*w + 16]', '[2172, 1086, 3*w^3 - 11*w^2 + 2*w + 4]', '[2174, 2174, 5*w - 8]', '[2176, 68, -2*w^3 + 16*w + 4]', '[2178, 2178, -3*w^3 + 6*w^2 + 7*w - 8]', '[2179, 2179, 8*w^3 - 20*w^2 - 25*w + 47]', '[2181, 2181, 6*w^3 - 6*w^2 - 25*w - 1]', '[2181, 2181, 2*w^3 - 4*w^2 - 13*w - 1]', '[2187, 9, 3*w^3 - 9*w^2 - 3*w + 15]', '[2187, 81, -3*w^3 + 3*w^2 + 12*w - 3]', '[2187, 2187, -3*w^3 + 5*w^2 + 12*w + 1]', '[2188, 1094, -2*w^3 + w^2 - 2]', '[2188, 1094, w^3 + w^2 - 4*w - 8]', '[2189, 2189, -w^3 + 3*w^2 + 5*w + 3]', '[2189, 2189, w^3 - 5*w^2 + 11]', '[2193, 2193, -w^3 + 2*w - 5]', '[2196, 1098, -w^3 + 5*w^2 - 4*w + 2]', '[2199, 2199, 3*w^3 - 9*w^2 - w + 11]', '[2200, 550, 5*w^3 - 12*w^2 - 14*w + 20]', '[2202, 2202, -w^3 - 4*w^2 + 3*w + 6]', '[2203, 2203, w^3 - 6*w^2 + 21]', '[2203, 2203, -9*w^3 + 18*w^2 + 32*w - 33]', '[2206, 2206, 3*w^3 - 5*w^2 - 7*w - 4]', '[2207, 2207, -6*w^3 + 17*w^2 + 14*w - 41]', '[2209, 47, 6*w^3 - 11*w^2 - 21*w + 13]', '[2209, 47, -3*w^3 + 5*w^2 + 15*w - 13]', '[2209, 2209, 3*w^3 - 3*w^2 - 9*w - 1]', '[2209, 2209, -w^3 + 4*w^2 + 2*w - 17]', '[2211, 2211, 2*w^3 - 2*w^2 - 6*w - 5]', '[2211, 2211, 5*w^3 - 8*w^2 - 20*w + 5]', '[2213, 2213, w^3 - 2*w^2 - 9*w - 1]', '[2213, 2213, -w^3 + 8*w^2 + 4*w - 15]', '[2214, 246, -4*w^3 + 9*w^2 + 13*w - 14]', '[2214, 246, -2*w^3 + 11*w + 2]', '[2214, 2214, -2*w^3 + w^2 + 13*w - 2]', '[2214, 2214, -3*w^3 + 4*w^2 + 13*w - 6]', '[2216, 554, -3*w^3 + 4*w^2 + 8*w - 6]', '[2217, 2217, w^3 + 2*w^2 - 9*w - 7]', '[2217, 2217, -6*w^3 + 12*w^2 + 23*w - 19]', '[2221, 2221, -3*w^3 + 5*w^2 + 8*w - 1]', '[2221, 2221, -5*w^2 + 9]', '[2222, 2222, -2*w^3 - w^2 + 9*w + 10]', '[2222, 2222, -10*w^3 + 26*w^2 + 29*w - 62]', '[2225, 2225, 4*w^3 - 2*w^2 - 12*w + 1]', '[2225, 2225, 3*w^3 - 19*w - 9]', '[2227, 2227, 2*w^3 - w^2 - 8*w - 7]', '[2227, 2227, -w^3 + 4*w^2 - w - 13]', '[2228, 1114, -w^3 + 5*w^2 - 10]', '[2229, 2229, -w^3 - w^2 + 12*w + 3]', '[2234, 2234, 5*w^3 - 12*w^2 - 15*w + 30]', '[2234, 2234, 2*w^3 - 7*w^2 - 3*w + 14]', '[2235, 2235, -4*w^3 + 7*w^2 + 15*w - 5]', '[2237, 2237, -2*w^3 + 4*w^2 + 6*w - 13]', '[2238, 2238, -w^2 + 5*w + 6]', '[2239, 2239, 4*w^3 - 8*w^2 - 11*w + 3]', '[2241, 249, -w^3 + 10*w + 1]', '[2241, 2241, -5*w^3 + w^2 + 21*w + 9]', '[2244, 1122, 3*w^3 - 3*w^2 - 8*w + 4]', '[2246, 2246, w^3 - 4*w^2 - 5*w + 2]', '[2246, 2246, -4*w^2 - 3*w + 2]', '[2248, 562, -w^3 - 2*w^2 + 8*w + 10]', '[2248, 562, 3*w^3 - 8*w^2 - 12*w + 18]', '[2250, 90, 3*w^3 - 7*w^2 - 13*w + 18]', '[2250, 2250, -2*w^3 + 3*w^2 + 11*w - 6]', '[2252, 1126, 3*w^3 - 5*w^2 - 12*w + 12]', '[2252, 1126, -2*w^3 + 3*w^2 + 4*w + 4]', '[2253, 2253, -3*w^3 + 5*w^2 + 9*w - 5]', '[2255, 2255, 3*w^3 - 8*w^2 - 9*w + 13]', '[2255, 2255, 3*w^3 - 8*w^2 - 6*w + 9]', '[2256, 282, -2*w^2 + 8*w - 2]', '[2256, 282, 2*w^3 - 2*w^2 - 14*w - 10]', '[2258, 2258, 4*w^3 - 7*w^2 - 17*w + 10]', '[2259, 2259, 5*w^3 - 10*w^2 - 16*w + 11]', '[2259, 2259, -2*w^3 + w^2 + 3*w + 3]', '[2264, 566, 3*w^3 - 8*w^2 - 6*w + 18]', '[2264, 566, 5*w^3 - 14*w^2 - 14*w + 36]', '[2265, 2265, w^3 + 2*w^2 - 6*w - 7]', '[2266, 2266, -10*w^3 + 19*w^2 + 39*w - 36]', '[2267, 2267, -6*w^3 + 14*w^2 + 17*w - 23]', '[2267, 2267, 3*w^3 - 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19*w + 15]', '[2297, 2297, 4*w^3 - 8*w^2 - 12*w + 11]', '[2299, 2299, 2*w^3 - 7*w^2 + 13]', '[2302, 2302, w^3 - 2*w^2 + w - 6]', '[2302, 2302, 4*w^3 - 6*w^2 - 7*w - 2]', '[2304, 36, -4*w^3 + 8*w^2 + 12*w - 12]', '[2306, 2306, 4*w^3 - 5*w^2 - 15*w - 2]', '[2306, 2306, 2*w^3 - 8*w^2 - w + 20]', '[2307, 2307, 2*w^3 - 5*w^2 - 3*w + 13]', '[2309, 2309, -2*w^3 + 5*w^2 + 8*w - 19]', '[2311, 2311, w^2 + 2*w - 9]', '[2311, 2311, 2*w^2 - 5*w - 11]', '[2312, 578, w^3 - 6*w^2 + 4*w + 6]', '[2313, 2313, -w^2 - 3*w - 5]', '[2313, 2313, 6*w^3 - 13*w^2 - 18*w + 25]', '[2315, 2315, -w^3 + 2*w^2 - w + 7]', '[2318, 2318, -w^3 - 2*w^2 + 3*w + 8]', '[2321, 2321, -2*w^3 + w^2 + 14*w + 1]', '[2321, 2321, -5*w^3 + 10*w^2 + 15*w - 19]', '[2322, 258, -w^3 + 6*w^2 - 5*w - 8]', '[2322, 2322, 2*w^3 - 3*w^2 - 13*w - 2]', '[2328, 582, w^3 + 2*w^2 - 10*w - 14]', '[2330, 2330, 3*w^3 - 4*w^2 - 5*w]', '[2334, 2334, 5*w^3 - 10*w^2 - 19*w + 14]', '[2334, 2334, -5*w^3 + 9*w^2 + 19*w - 16]', '[2335, 2335, 3*w^3 - 3*w^2 - 7*w - 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39]', '[557, 557, -2*w^3 + 2*w^2 + 5*w - 7]', '[563, 563, 3*w^3 - 7*w^2 - 7*w + 7]', '[563, 563, 2*w^3 - 6*w^2 - 6*w + 19]', '[569, 569, w^3 - w^2 - 5*w - 5]', '[571, 571, -2*w^3 + 5*w^2 + 8*w - 7]', '[571, 571, 5*w^3 - 13*w^2 - 15*w + 31]', '[587, 587, -2*w^3 + 6*w^2 + 3*w - 13]', '[613, 613, 3*w^2 - 3*w - 11]', '[613, 613, -3*w^2 + w + 5]', '[617, 617, w^2 + 2*w + 3]', '[617, 617, -w^3 + 2*w^2 + 6*w - 5]', '[617, 617, -4*w^3 + 10*w^2 + 8*w - 13]', '[617, 617, w^3 + w^2 - 6*w - 5]', '[619, 619, 2*w^3 - w^2 - 9*w - 1]', '[619, 619, -w^3 + 7*w - 1]', '[619, 619, -w^3 + 3*w^2 + 4*w - 1]', '[619, 619, -3*w^3 + 10*w^2 + 5*w - 27]', '[631, 631, 4*w^3 - 8*w^2 - 12*w + 7]', '[641, 641, 2*w^3 - 4*w^2 - 4*w + 3]', '[647, 647, 3*w^3 - 7*w^2 - 9*w + 11]', '[647, 647, -w^3 + 4*w^2 + 5*w - 5]', '[653, 653, -w^3 + 5*w^2 - 3*w - 5]', '[653, 653, -w^2 + w - 3]', '[659, 659, -2*w^3 + 3*w^2 + 9*w - 7]', '[659, 659, -5*w^3 + 11*w^2 + 16*w - 19]', '[661, 661, -3*w^3 + 5*w^2 + 9*w - 9]', '[673, 673, -2*w^3 + 3*w^2 + 10*w - 5]', '[683, 683, 3*w^3 - 7*w^2 - 12*w + 21]', '[701, 701, w^3 - 2*w^2 - 4*w - 3]', '[727, 727, 2*w^3 - 6*w^2 - 7*w + 15]', '[727, 727, 2*w^3 - 4*w^2 - 8*w + 3]', '[733, 733, -w^3 + 4*w^2 - 15]', '[739, 739, -8*w^3 + 18*w^2 + 26*w - 35]', '[739, 739, w^3 - 2*w^2 - 5]', '[743, 743, -3*w^3 + 8*w^2 + 3*w - 3]', '[751, 751, -2*w^3 + 3*w^2 + 10*w - 9]', '[757, 757, -w - 5]', '[769, 769, 3*w^3 - 7*w^2 - 10*w + 19]', '[787, 787, -3*w^3 + 7*w^2 + 8*w - 9]', '[821, 821, -2*w^3 + 11*w + 7]', '[827, 827, 2*w^3 - 5*w^2 - 4*w + 1]', '[827, 827, 3*w^3 - 5*w^2 - 12*w + 9]', '[829, 829, -w^2 - 3]', '[829, 829, -8*w^3 + 18*w^2 + 25*w - 35]', '[853, 853, w^3 - 9*w - 1]', '[853, 853, -2*w^2 + 7*w - 1]', '[859, 859, -w^3 + 2*w^2 - 5]', '[863, 863, -2*w^3 + 6*w^2 - 7]', '[877, 877, -4*w^3 + 12*w^2 + 5*w - 19]', '[877, 877, -3*w^3 + 9*w^2 + 5*w - 17]', '[883, 883, 8*w^3 - 17*w^2 - 28*w + 35]', '[911, 911, 2*w^3 - 3*w^2 - 10*w + 11]', '[919, 919, -w^3 + 6*w - 3]', '[929, 929, -4*w^3 + 9*w^2 + 11*w - 15]', '[929, 929, 3*w^3 - 5*w^2 - 10*w + 3]', '[937, 937, 4*w^3 - 11*w^2 - 11*w + 23]', '[937, 937, -2*w^2 + 7*w + 1]', '[941, 941, -w^3 + 5*w^2 - 19]', '[947, 947, -2*w^3 + 4*w^2 + 7*w - 1]', '[947, 947, 3*w^3 - 6*w^2 - 7*w + 13]', '[953, 953, 3*w^2 - 2*w - 9]', '[971, 971, 2*w^3 - 4*w^2 - 10*w + 1]', '[991, 991, -2*w^3 + 3*w^2 + 9*w - 9]', '[997, 997, w^3 - 4*w^2 - w + 15]']}
• 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': [2, 4, -4, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 14656, 'disc_rad': 458, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1], [1, 1]]], [5, [[3, 1], [1, 1]]], [7, [[4, 1]]], [11, [[3, 1], [1, 1]]], [13, [[4, 1]]], [17, [[3, 1], [1, 1]]], [19, [[3, 1], [1, 1]]], [23, [[4, 1]]], [29, [[4, 1]]], [31, [[4, 1]]], [37, [[2, 2]]], [41, [[2, 1], [1, 2]]], [43, [[3, 1], [1, 1]]], [47, [[2, 1], [1, 2]]], [53, [[2, 2]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 42.80186911806539, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.14656.1', 'local_algs': ['2.4.6.8', 'm229.1.1.0', 'm229.1.1.0', 'm229.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 229], 'rd': 11.0028163487, 'regulator': {'__RealLiteral__': 0, 'data': '11.1614390382', 'prec': 44}, 'res': {'gal': ['-27,-828,852,24512,-21680,-146184,119160,379392,-299932,-519040,421708,399348,-356534,-170204,184996,33568,-58036,768,10384,-1568,-908,248,20,-12,1'], 'sib': ['-1,0,8,0,-6,0,1', '-229,0,323,0,-39,0,1', '1,-12,38,0,-148,102,182,-156,-68,72,-4,-6,1', '16,0,-244,0,515,0,-427,0,160,0,-25,0,1', '33,590,-210,-722,267,110,-32,-4,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a^{2} - 2 a - 1 \\)', '\\( a^{2} + a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}