Hilbert modular form data - 4.4.5125.1-45.2-a

Formats: - HTML - YAML - JSON - 2024-05-06T03:53:03.595055

• 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': 2, 'disc': 5125, 'field_bad_primes': [5, 41], 'field_label': '4.4.5125.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.5125.1-45.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [3, 5], 'level_ideal': '[45,15,w^3 - 5*w - 2]', 'level_label': '45.2', 'level_norm': 45, 'parallel_weight': 2, 'short_label': '45.2-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5,5,-w^2 + 4]', 1], ['[9,3,-w^3 + 5*w + 5]', -1]], 'hecke_eigenvalues': [-1, 'e', 1, 'e - 3', '-2*e + 1', '-e', '3*e - 4', 'e - 7', '-2*e + 4', '-3*e - 3', '-2*e + 3', '2*e - 7', '4*e - 1', '3*e - 4', '-8*e + 5', '-7*e + 1', '-3*e + 1', '-4*e + 1', '6*e - 15', '7*e - 4', '-6*e + 2', '-4*e + 7', '2*e - 10', '-3*e - 6', '-12*e + 12', '6*e - 4', '-5*e + 5', 13, '-5*e - 9', '10*e - 9', '7*e - 16', '4*e + 5', '-6*e - 2', '12*e - 6', 'e - 1', '-12*e + 10', '13*e - 11', 'e + 5', '12*e - 15', '3*e + 14', -14, '-5*e - 2', '-6*e + 12', '12*e - 12', '14*e - 17', '-6*e + 12', '3*e - 10', '-4*e + 17', '-13*e + 5', '-12*e + 18', 'e - 22', '8*e - 23', '7*e - 7', '-8*e + 22', '-e + 7', '7*e - 24', '13*e - 13', '18*e - 14', -13, '-14*e + 26', '-2*e + 15', '13*e - 5', 'e - 11', '4*e + 2', '-5*e + 8', -4, '-12*e + 20', '-16*e + 20', '18*e - 12', '4*e + 12', '10*e - 25', '-11*e - 2', '-16*e + 21', '-4*e - 10', '-12*e + 12', '-2*e - 16', '2*e - 10', '2*e - 25', '9*e - 9', '6*e + 6', '16*e - 16', '-12*e + 25', '-12*e + 8', '5*e - 15', '-8*e + 2', '12*e + 8', '10*e - 12', '-6*e + 1', '27*e - 26', '5*e - 21', '-11*e - 5', '-7*e - 22', '24*e - 29', '18*e - 22', '-4*e - 8', '13*e - 12', '-6*e + 2', '2*e + 7', '-2*e - 18', '-19*e + 33', '-12*e + 20', '-18*e + 27', '-e + 27', '-8*e + 18', '3*e - 8', '18*e - 38', '-3*e - 27', '-18*e + 21', '-20*e + 18', '-7*e - 17', 2, '20*e - 32', '21*e - 34', '-4*e - 31', '9*e - 19', '-2*e - 10', '2*e + 46', '7*e - 21', '-10*e + 13', '-19*e + 12', '-15*e + 16', '3*e - 42', '5*e - 20', '11*e - 5', '15*e - 24', '7*e - 23', '15*e - 12', '-8*e + 30', '-3*e - 24', '6*e + 20', '-11*e + 1', '-4*e + 10', '20*e - 5', '6*e + 38', '12*e - 26', '11*e + 15', '2*e + 32', '4*e + 10', '-15*e + 41', '-7*e + 28', '-30*e + 36', '-10*e - 2', '-22*e + 22', '-14*e + 8', '-15*e - 1', '-20*e + 42', '22*e - 30', '-27*e + 13', '18*e - 35', '-4*e - 9', '3*e + 29', '-7*e - 23', '24*e - 36', 'e - 25', '18*e - 10', '-18*e', '-10*e + 46', '-11*e - 11', '26*e - 38', '-15*e + 29', '-2*e + 38', '7*e - 5', '17*e - 16', '-17*e - 3', '5*e - 4', '6*e + 10', '-8*e + 18', '-7*e + 28', '12*e - 19', '-5*e + 32', '-12*e - 26', '31*e - 21'], 'hecke_polynomial': 'x^2 - 2*x - 1', 'label': '4.4.5125.1-45.2-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 5125, 'ideals': ['[1, 1, 1]', '[5, 5, -w^2 + 2*w + 3]', '[9, 3, w^3 - 3*w^2 - 2*w + 9]', '[9, 3, -w^3 + 5*w + 5]', '[11, 11, w]', '[11, 11, w - 1]', '[16, 2, 2]', '[19, 19, -w^3 + 2*w^2 + 3*w - 2]', '[19, 19, w^3 - w^2 - 4*w + 2]', '[25, 5, -2*w^2 + 2*w + 7]', '[29, 29, w^3 - 4*w^2 - w + 10]', '[29, 29, -w^3 + 3*w^2 + w - 7]', '[41, 41, 3*w^2 - 2*w - 10]', '[45, 15, -w^3 + 3*w^2 + 2*w - 6]', '[45, 15, -w^3 + 5*w + 2]', '[49, 7, -2*w^2 + 3*w + 8]', '[49, 7, w^3 - 2*w^2 - 2*w + 5]', '[55, 55, -3*w^2 + 2*w + 11]', '[55, 55, -3*w^2 + 4*w + 10]', '[71, 71, -w - 3]', '[71, 71, w - 4]', '[79, 79, -w^3 + w^2 + 3*w + 3]', '[79, 79, -w^3 + 2*w^2 + 2*w - 6]', '[80, 10, -2*w^2 + 4*w + 6]', '[81, 3, 3]', '[81, 9, -2*w^2 + 7]', '[81, 9, 2*w^2 - 4*w - 5]', '[89, 89, w^3 - 3*w^2 - 3*w + 7]', '[89, 89, w^3 - 6*w - 2]', '[95, 95, w^3 - 3*w^2 - w + 8]', '[95, 95, w^3 - 4*w - 5]', '[99, 33, -w^3 + 4*w^2 - 11]', '[99, 33, -w^3 + 4*w^2 + 2*w - 11]', '[99, 33, w^3 + w^2 - 5*w - 8]', '[99, 33, -w^3 - w^2 + 7*w + 6]', '[101, 101, 2*w^3 - 5*w^2 - 3*w + 9]', '[101, 101, -w^3 + 3*w^2 + 3*w - 12]', '[109, 109, -w^3 + 4*w^2 + w - 9]', '[109, 109, -w^3 + 2*w^2 + 4*w - 2]', '[121, 11, -3*w^2 + 3*w + 11]', '[121, 11, -3*w^2 + 3*w + 10]', '[121, 121, w^3 - 5*w^2 + 15]', '[121, 121, -w^3 - 2*w^2 + 7*w + 11]', '[125, 5, -2*w^3 + 3*w^2 + 6*w - 1]', '[131, 131, -2*w^3 + 5*w^2 + 4*w - 9]', '[131, 131, -w^3 + w^2 + 3*w + 5]', '[131, 131, -w^3 + 2*w^2 + 2*w - 8]', '[131, 131, -w^3 + 6*w^2 - 18]', '[144, 6, 2*w^3 - 6*w^2 - 4*w + 18]', '[144, 6, -2*w^3 + 10*w + 10]', '[145, 145, 2*w^3 - 7*w^2 + 14]', '[145, 145, -2*w^3 + 7*w^2 + w - 12]', '[149, 149, -w^3 - 2*w^2 + 7*w + 8]', '[149, 149, -2*w^3 + 6*w^2 + 5*w - 16]', '[151, 151, w^2 + w - 5]', '[151, 151, w^2 - 3*w - 3]', '[169, 13, w^3 - 4*w^2 - w + 6]', '[169, 13, 2*w^3 - 5*w^2 - 4*w + 6]', '[171, 57, -2*w^3 + 5*w^2 + 4*w - 10]', '[171, 57, w^2 + w - 4]', '[171, 57, 2*w^3 - w^2 - 8*w - 3]', '[171, 57, w^2 - 3*w - 2]', '[176, 22, 2*w]', '[176, 22, 2*w - 2]', '[179, 179, w^3 - 4*w - 6]', '[179, 179, -w^3 + 3*w^2 + w - 9]', '[181, 181, w^3 + 3*w^2 - 7*w - 15]', '[181, 181, w^3 - 6*w^2 + 2*w + 18]', '[191, 191, 5*w^2 - 7*w - 15]', '[191, 191, -4*w^2 + 5*w + 12]', '[199, 199, -w^3 + 3*w^2 + 3*w - 6]', '[199, 199, w^3 - 6*w - 1]', '[205, 205, 2*w^3 - 3*w^2 - 5*w + 3]', '[209, 209, w^3 + 2*w^2 - 5*w - 11]', '[209, 209, 3*w^2 - w - 13]', '[209, 209, -3*w^2 + 5*w + 11]', '[209, 209, w^3 - 5*w^2 + 2*w + 13]', '[211, 211, w^3 - 7*w - 4]', '[211, 211, -w^3 + 3*w^2 + 4*w - 10]', '[225, 15, w^3 - 5*w^2 - 2*w + 19]', '[225, 15, -w^3 - 2*w^2 + 9*w + 13]', '[229, 229, -w^3 - w^2 + 5*w + 9]', '[229, 229, -w^3 + 4*w^2 - 12]', '[239, 239, 4*w^2 - 5*w - 17]', '[239, 239, 4*w^2 - 3*w - 18]', '[241, 241, -w^3 + 3*w^2 + w - 2]', '[241, 241, -w^3 + 3*w^2 + 4*w - 9]', '[241, 241, w^3 - 7*w - 3]', '[241, 241, -w^3 + 4*w - 1]', '[245, 35, -3*w^3 + 4*w^2 + 11*w + 2]', '[245, 35, -w^3 + 4*w^2 + w - 7]', '[256, 4, 4]', '[261, 87, -3*w^3 + 10*w^2 + 9*w - 35]', '[261, 87, -2*w^3 + 4*w^2 + 5*w - 6]', '[261, 87, -4*w^2 + 5*w + 13]', '[261, 87, 2*w^3 - 5*w^2 - 7*w + 19]', '[271, 271, -w - 4]', '[271, 271, w^3 - 3*w^2 - 2*w + 2]', '[271, 271, -2*w^3 + 6*w^2 + 2*w - 7]', '[271, 271, w - 5]', '[275, 55, -2*w^3 + 2*w^2 + 7*w]', '[275, 55, -2*w^3 + 4*w^2 + 5*w - 7]', '[281, 281, w^3 - 2*w^2 - 3*w - 1]', '[281, 281, -w^3 + w^2 + 4*w - 5]', '[289, 17, -2*w^3 + w^2 + 9*w + 1]', '[289, 17, -2*w^3 + 5*w^2 + 5*w - 9]', '[304, 38, -2*w^3 + 4*w^2 + 6*w - 4]', '[304, 38, 2*w^3 - 2*w^2 - 8*w + 4]', '[311, 311, w^3 - w^2 - 6*w + 1]', '[311, 311, -w^3 + 2*w^2 + 5*w - 5]', '[319, 319, -2*w^3 + 8*w^2 + w - 18]', '[319, 319, 3*w^3 - 9*w^2 - 4*w + 21]', '[319, 319, -w^3 + 5*w^2 - 11]', '[319, 319, 2*w^3 - 5*w^2 - 3*w + 11]', '[331, 331, -3*w^3 + 5*w^2 + 10*w - 5]', '[331, 331, 3*w^3 - 2*w^2 - 12*w - 6]', '[349, 349, -2*w^3 + 2*w^2 + 10*w + 3]', '[349, 349, -2*w^3 - w^2 + 12*w + 10]', '[349, 349, 2*w^3 + w^2 - 10*w - 12]', '[349, 349, -2*w^3 + 4*w^2 + 8*w - 13]', '[355, 355, -w^3 + 6*w^2 - 5*w - 12]', '[355, 355, w^3 + w^2 - 9*w - 9]', '[361, 19, 4*w^2 - 4*w - 15]', '[361, 19, -4*w^2 + 4*w + 13]', '[361, 361, w^3 - 3*w^2 - 3*w + 13]', '[361, 361, -w^3 + 6*w + 8]', '[369, 123, -2*w^3 + 10*w^2 + 4*w - 35]', '[369, 123, -w^3 + 2*w^2 + w - 6]', '[379, 379, w^3 + w^2 - 5*w - 10]', '[379, 379, -3*w^3 + 4*w^2 + 12*w - 7]', '[379, 379, w^3 + 4*w^2 - 8*w - 21]', '[379, 379, w^3 - 3*w - 6]', '[389, 389, 2*w^3 - 6*w^2 - 4*w + 13]', '[389, 389, -5*w^2 + 7*w + 13]', '[389, 389, 2*w^3 - 7*w^2 - 5*w + 20]', '[389, 389, 2*w^3 - 10*w - 5]', '[395, 395, w^3 - 3*w^2 - 3*w + 4]', '[395, 395, -7*w^2 + 11*w + 20]', '[400, 10, -4*w^2 + 4*w + 14]', '[405, 15, -3*w^2 + 6*w + 9]', '[405, 45, w^3 + 3*w^2 - 8*w - 15]', '[405, 45, -w^3 + 6*w^2 - w - 19]', '[419, 419, -w^3 + 5*w^2 + w - 13]', '[419, 419, 4*w^2 - 7*w - 14]', '[419, 419, 2*w^3 - 3*w^2 - 5*w - 1]', '[419, 419, -w^3 - 2*w^2 + 8*w + 8]', '[421, 421, -2*w^2 + 5*w + 7]', '[421, 421, w^3 - 6*w^2 + 5*w + 13]', '[439, 439, 2*w^3 - 2*w^2 - 9*w + 3]', '[439, 439, w^3 + w^2 - 7*w - 4]', '[441, 21, w^3 - 4*w^2 - 2*w + 17]', '[441, 21, 3*w^3 - 7*w^2 - 9*w + 23]', '[441, 21, -4*w^3 - 3*w^2 + 26*w + 29]', '[441, 21, -w^3 - 3*w^2 + 8*w + 14]', '[445, 445, 3*w^3 - 3*w^2 - 11*w - 6]', '[445, 445, 3*w^2 - 5*w - 12]', '[449, 449, 3*w^3 - 6*w^2 - 9*w + 8]', '[449, 449, 5*w^2 - 8*w - 17]', '[449, 449, 2*w^3 - w^2 - 8*w - 7]', '[449, 449, -3*w^3 + 3*w^2 + 12*w - 4]', '[451, 451, 3*w^3 - 2*w^2 - 10*w]', '[451, 451, 3*w^3 - 5*w^2 - 8*w + 10]', '[464, 58, 2*w^3 - 8*w^2 - 2*w + 20]', '[464, 58, -2*w^3 + 6*w^2 + 2*w - 14]', '[475, 95, -w^3 - 2*w^2 + 9*w + 8]', '[475, 95, w^3 - 5*w^2 - 2*w + 14]', '[479, 479, -2*w^3 + 3*w^2 + 5*w + 3]', '[479, 479, 3*w^3 - 7*w^2 - 9*w + 15]', '[495, 165, w^3 - 4*w^2 + w + 11]', '[495, 165, -2*w^3 - w^2 + 9*w + 11]', '[495, 165, -w^3 - w^2 + 4*w + 9]', '[495, 165, 2*w^3 - 7*w^2 - w + 17]', '[499, 499, -w^3 + 4*w^2 + 4*w - 9]', '[499, 499, w^3 + w^2 - 9*w - 2]', '[505, 505, 2*w^2 - 5*w - 3]', '[505, 505, -2*w^2 - w + 6]', '[509, 509, 2*w^3 + 2*w^2 - 11*w - 16]', '[509, 509, -2*w^3 + 8*w^2 + w - 23]', '[521, 521, -3*w^3 + w^2 + 13*w + 6]', '[521, 521, w^3 + 4*w^2 - 10*w - 16]', '[539, 77, 4*w^2 - 2*w - 11]', '[539, 77, -2*w^3 + 3*w^2 + 8*w]', '[539, 77, -2*w^3 + 5*w^2 + 5*w - 8]', '[539, 77, -w^3 + 6*w^2 - 16]', '[541, 541, 3*w^3 - 2*w^2 - 13*w - 3]', '[541, 541, -w^3 + 7*w^2 - w - 25]', '[541, 541, w^3 + 4*w^2 - 10*w - 20]', '[541, 541, -3*w^3 + 7*w^2 + 8*w - 15]', '[545, 545, 2*w^3 - 8*w^2 + 2*w + 17]', '[545, 545, -w^3 - 3*w^2 + 11*w + 16]', '[551, 551, -w^3 + 4*w^2 - 2*w - 2]', '[551, 551, -2*w^3 + 10*w^2 + 2*w - 31]', '[551, 551, w^3 - 5*w^2 + 4*w + 8]', '[551, 551, 3*w^3 - 6*w^2 - 8*w + 14]', '[571, 571, w^3 + 4*w^2 - 9*w - 15]', '[571, 571, w^3 - 7*w^2 + 2*w + 19]', '[601, 601, -3*w^3 + 2*w^2 + 13*w + 5]', '[601, 601, 3*w^3 - 7*w^2 - 8*w + 17]', '[605, 55, -3*w^3 + 4*w^2 + 10*w]', '[605, 55, -3*w^3 + 5*w^2 + 8*w - 3]', '[605, 605, -w^3 + 3*w - 2]', '[605, 605, w^3 - 3*w^2]', '[619, 619, w^3 - 3*w - 7]', '[619, 619, w^3 - 5*w^2 + 3*w + 13]', '[619, 619, 3*w^3 - 4*w^2 - 9*w - 2]', '[619, 619, -w^3 + 3*w^2 - 9]', '[625, 5, 5]', '[639, 213, 5*w^3 + w^2 - 27*w - 26]', '[639, 213, -2*w^3 + 5*w^2 + 4*w - 16]', '[639, 213, -5*w^3 + 16*w^2 + 10*w - 47]', '[639, 213, 2*w^3 - w^2 - 8*w - 9]', '[641, 641, 6*w^2 - 4*w - 23]', '[641, 641, -3*w^3 + w^2 + 12*w + 5]', '[655, 655, 3*w^3 - 7*w^2 - 5*w + 12]', '[655, 655, -9*w^2 + 15*w + 26]', '[655, 655, w^3 - w^2 - 7*w - 2]', '[655, 655, 2*w^3 - 12*w^2 + 7*w + 28]', '[656, 82, 6*w^2 - 4*w - 20]', '[659, 659, -2*w^3 + 6*w^2 + 3*w - 17]', '[659, 659, -2*w^3 + 9*w + 10]', '[661, 661, 3*w^3 - 6*w^2 - 9*w + 14]', '[661, 661, 5*w^2 - 6*w - 18]', '[661, 661, -5*w^2 + 4*w + 19]', '[661, 661, 3*w^3 - 3*w^2 - 12*w - 2]', '[691, 691, -3*w^3 + 5*w^2 + 10*w - 6]', '[691, 691, -3*w^3 + 4*w^2 + 11*w - 6]', '[701, 701, -w^3 - 4*w^2 + 9*w + 20]', '[701, 701, -w^3 + 4*w^2 + 3*w - 19]', '[701, 701, -w^3 + 4*w^2 + 4*w - 15]', '[701, 701, w^3 - 7*w^2 + 2*w + 24]', '[709, 709, 3*w^2 - 5*w - 13]', '[709, 709, 3*w^2 - w - 15]', '[711, 237, 2*w^3 - 9*w^2 - w + 27]', '[711, 237, -4*w^3 + 2*w^2 + 19*w + 15]', '[711, 237, 2*w^3 + 3*w^2 - 13*w - 19]', '[711, 237, -4*w^3 + 10*w^2 + 11*w - 32]', '[719, 719, -w^3 + 3*w^2 + 4*w - 4]', '[719, 719, -w^3 + 7*w - 2]', '[720, 30, -2*w^3 + 6*w^2 + 4*w - 12]', '[720, 30, -2*w^3 + 10*w + 4]', '[725, 145, -w^3 + 7*w - 4]', '[725, 145, -w^3 + w^2 + w + 5]', '[729, 9, 3*w^3 - 9*w^2 - 6*w + 27]', '[729, 9, -3*w^3 + 15*w + 15]', '[729, 27, w^3 + 2*w^2 - 8*w - 7]', '[729, 27, 2*w^3 - 2*w^2 - 9*w + 4]', '[739, 739, -w^3 + 4*w^2 + 3*w - 9]', '[739, 739, -2*w^3 - w^2 + 11*w + 8]', '[739, 739, 2*w^3 - 7*w^2 - 3*w + 16]', '[739, 739, -w^3 - w^2 + 8*w + 3]', '[745, 745, -4*w^3 + 5*w^2 + 12*w + 2]', '[745, 745, w^3 - 6*w^2 + 3*w + 18]', '[751, 751, 3*w^3 - 5*w^2 - 10*w + 10]', '[751, 751, 2*w^2 - 5*w - 5]', '[755, 755, 3*w^3 - 6*w^2 - 8*w + 2]', '[755, 755, -w^3 + 4*w^2 - 4]', '[761, 761, 3*w^3 - 3*w^2 - 11*w + 3]', '[761, 761, w^3 - 2*w^2 - 3*w - 2]', '[761, 761, -w^3 + w^2 + 4*w - 6]', '[761, 761, -3*w^3 + 6*w^2 + 8*w - 8]', '[769, 769, -w^3 - w^2 + 7*w + 1]', '[769, 769, -2*w^3 + 6*w^2 + 6*w - 15]', '[769, 769, -2*w^3 + 5*w^2 + 5*w - 7]', '[769, 769, 2*w^3 + w^2 - 12*w - 9]', '[779, 779, w^3 + w^2 - 7*w - 2]', '[779, 779, 9*w^2 - 4*w - 31]', '[781, 781, w^2 - 4*w]', '[781, 781, w^2 - 5*w + 4]', '[781, 781, -w^2 - 3*w]', '[781, 781, -w^2 - 2*w + 3]', '[784, 14, -4*w^2 + 6*w + 16]', '[784, 14, 2*w^3 - 4*w^2 - 4*w + 10]', '[801, 267, 4*w^3 - 13*w^2 - 11*w + 41]', '[801, 267, 4*w^3 - 2*w^2 - 19*w - 9]', '[801, 267, 4*w^3 + w^2 - 25*w - 21]', '[801, 267, 4*w^3 - 10*w^2 - 11*w + 26]', '[809, 809, -2*w^3 + 8*w^2 + 4*w - 23]', '[809, 809, -3*w^3 + 11*w^2 + 2*w - 28]', '[829, 829, -3*w^3 + 7*w^2 + 7*w - 9]', '[829, 829, w^3 + 2*w^2 - 6*w - 15]', '[829, 829, -w^3 + 5*w^2 - w - 18]', '[829, 829, -3*w^3 + 2*w^2 + 12*w - 2]', '[839, 839, 2*w^3 - 9*w^2 + 20]', '[839, 839, -3*w^3 + 10*w^2 + 5*w - 30]', '[841, 29, 5*w^2 - 5*w - 19]', '[841, 29, 5*w^2 - 5*w - 16]', '[841, 841, -3*w^3 + 6*w^2 + 9*w - 13]', '[841, 841, -3*w^3 + 3*w^2 + 12*w + 1]', '[845, 65, w^3 - 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22]', '[1595, 1595, -5*w^2 + w + 22]', '[1595, 1595, w^3 - 7*w^2 + 7*w + 10]', '[1595, 1595, -3*w^3 + 8*w^2 + 2*w - 7]', '[1611, 537, -2*w^3 + 10*w^2 + w - 32]', '[1611, 537, 4*w^3 - w^2 - 21*w - 19]', '[1611, 537, -4*w^3 + 11*w^2 + 11*w - 37]', '[1611, 537, 2*w^3 + 4*w^2 - 15*w - 23]', '[1616, 202, 4*w^3 - 10*w^2 - 6*w + 18]', '[1616, 202, -2*w^3 + 6*w^2 + 6*w - 24]', '[1621, 1621, -w^3 - 5*w^2 + 11*w + 23]', '[1621, 1621, -w^3 + 8*w^2 - 2*w - 28]', '[1629, 543, -2*w^3 + 13*w^2 + w - 47]', '[1629, 543, 4*w^3 + 2*w^2 - 27*w - 31]', '[1629, 543, -2*w^3 - 7*w^2 + 21*w + 35]', '[1629, 543, 4*w^3 - 14*w^2 - 11*w + 52]', '[1639, 1639, 4*w^3 - 13*w^2 - 7*w + 38]', '[1639, 1639, 2*w^3 - 7*w^2 - 2*w + 22]', '[1639, 1639, -3*w^3 + 3*w^2 + 8*w + 3]', '[1639, 1639, -4*w^3 + w^2 + 15*w + 11]', '[1655, 1655, 3*w^3 + 9*w^2 - 29*w - 40]', '[1655, 1655, -w^3 - 11*w^2 + 22*w + 40]', '[1661, 1661, w^3 - 6*w + 5]', '[1661, 1661, w^3 - 4*w^2 + 3]', '[1661, 1661, w^3 + w^2 - 5*w]', '[1661, 1661, w^3 - 3*w^2 - 3*w]', '[1669, 1669, 5*w^2 - 3*w - 23]', '[1669, 1669, 5*w^2 - 7*w - 21]', '[1681, 41, 6*w^2 - 6*w - 23]', '[1681, 41, 6*w^2 - 6*w - 19]', '[1691, 1691, w^3 + 7*w^2 - 15*w - 29]', '[1691, 1691, w^3 + w^2 - 6*w - 14]', '[1691, 1691, w^3 - 4*w^2 - w + 18]', '[1691, 1691, w^3 - 10*w^2 + 2*w + 36]', '[1699, 1699, 4*w^2 - 6*w - 19]', '[1699, 1699, 3*w^3 - w^2 - 13*w - 12]', '[1699, 1699, 4*w^3 + w^2 - 20*w - 15]', '[1699, 1699, 4*w^2 - 2*w - 21]', '[1709, 1709, -4*w^2 + w + 19]', '[1709, 1709, 4*w^2 - 7*w - 16]', '[1719, 573, -w^3 + 3*w^2 - w - 10]', '[1719, 573, 2*w^3 - 3*w^2 - 4*w - 3]', '[1719, 573, -w^3 + 2*w + 9]', '[1719, 573, 2*w^3 - 3*w^2 - 4*w + 8]', '[1741, 1741, -w^3 + 8*w^2 - 2*w - 25]', '[1741, 1741, w^3 + 5*w^2 - 11*w - 20]', '[1744, 218, -2*w^3 + 8*w^2 + 2*w - 18]', '[1744, 218, -2*w^3 + 4*w^2 + 8*w - 4]', '[1745, 1745, 4*w^3 + 3*w^2 - 25*w - 25]', '[1745, 1745, -4*w^3 - 3*w^2 + 28*w + 31]', '[1745, 1745, -2*w^3 + 3*w^2 + 4*w + 5]', '[1745, 1745, -6*w^3 + 3*w^2 + 27*w + 19]', '[1759, 1759, 2*w^3 + w^2 - 11*w - 6]', '[1759, 1759, -2*w^3 + 7*w^2 - 17]', '[1759, 1759, -2*w^3 - w^2 + 8*w + 12]', '[1759, 1759, 2*w^3 - 7*w^2 - 3*w + 14]', '[1775, 355, 2*w^3 + 4*w^2 - 13*w - 21]', '[1775, 355, -2*w^3 + 10*w^2 - w - 28]', '[1789, 1789, -2*w^3 + 10*w^2 - 4*w - 25]', '[1789, 1789, 2*w^3 + 4*w^2 - 10*w - 21]', '[1791, 597, -5*w^3 + 2*w^2 + 24*w + 14]', '[1791, 597, -3*w^3 + 10*w^2 + 9*w - 32]', '[1791, 597, 5*w^3 - 13*w^2 - 13*w + 35]', '[1791, 597, 3*w^3 + w^2 - 20*w - 16]', '[1801, 1801, w^3 - 10*w^2 + 4*w + 28]', '[1801, 1801, w^3 + 7*w^2 - 13*w - 23]', '[1805, 95, 4*w^3 - 5*w^2 - 14*w - 1]', '[1805, 95, -4*w^3 + 7*w^2 + 10*w - 5]', '[1805, 1805, -3*w^2 + 7*w + 6]', '[1805, 1805, 3*w^2 + w - 10]', '[1811, 1811, -4*w^3 + 4*w^2 + 13*w - 5]', '[1811, 1811, 3*w^3 + 4*w^2 - 17*w - 24]', '[1831, 1831, -4*w^3 + 3*w^2 + 15*w - 1]', '[1831, 1831, -4*w^3 + 9*w^2 + 9*w - 13]', '[1845, 615, 2*w^3 - w^2 - 10*w + 5]', '[1845, 615, -w^3 - 7*w^2 + 7*w + 24]', '[1859, 143, 5*w^2 - 2*w - 22]', '[1859, 143, -2*w^3 + 5*w^2 - w - 11]', '[1859, 143, -3*w^3 + 9*w^2 - 17]', '[1859, 143, 3*w^3 - 5*w^2 - 7*w - 2]', '[1871, 1871, w^3 - 3*w^2 - 3*w + 15]', '[1871, 1871, -w^3 - 5*w^2 + 10*w + 19]', '[1879, 1879, 6*w^2 - 2*w - 25]', '[1879, 1879, -2*w^3 - 2*w^2 + 7*w + 15]', '[1881, 627, w^3 + 5*w^2 - 11*w - 22]', '[1881, 627, -4*w^3 + 9*w^2 + 11*w - 22]', '[1881, 627, w^2 - 2*w - 10]', '[1881, 627, -w^3 + 8*w^2 - 4*w - 25]', '[1881, 627, -w^3 - 5*w^2 + 9*w + 22]', '[1881, 627, -w^2 + 11]', '[1881, 627, w^3 - 8*w^2 + 2*w + 27]', '[1881, 627, 4*w^3 - 3*w^2 - 17*w - 6]', '[1889, 1889, -w^3 + 6*w^2 - 13]', '[1889, 1889, w^3 + 3*w^2 - 9*w - 8]', '[1895, 1895, 2*w^3 + 4*w^2 - 17*w - 19]', '[1895, 1895, -3*w^3 - 2*w^2 + 17*w + 23]', '[1895, 1895, 5*w^3 - 27*w - 19]', '[1895, 1895, 7*w^2 - 10*w - 18]', '[1899, 633, 3*w^3 - 8*w^2 - 9*w + 19]', '[1899, 633, 8*w^3 + 2*w^2 - 47*w - 42]', '[1899, 633, -3*w^3 + w^2 + 16*w + 5]', '[1899, 633, -8*w^3 + 26*w^2 + 19*w - 79]', '[1901, 1901, 3*w^2 - 7*w - 9]', '[1901, 1901, 3*w^2 + w - 13]', '[1919, 1919, 4*w^2 - 9]', '[1919, 1919, -6*w^3 + 15*w^2 + 18*w - 46]', '[1919, 1919, 3*w^3 - w^2 - 13*w - 1]', '[1919, 1919, 4*w^3 - 11*w^2 - 9*w + 24]', '[1931, 1931, -4*w^3 + 2*w^2 + 15*w + 7]', '[1931, 1931, -w^3 - 5*w^2 + 11*w + 21]', '[1931, 1931, -w^3 + 8*w^2 - 2*w - 26]', '[1931, 1931, 4*w^3 - 10*w^2 - 7*w + 20]', '[1936, 22, -6*w^2 + 6*w + 22]', '[1936, 22, -6*w^2 + 6*w + 20]', '[1936, 242, 2*w^3 - 10*w^2 + 30]', '[1936, 242, -2*w^3 - 4*w^2 + 14*w + 22]', '[1945, 1945, 2*w^3 - 5*w^2 - 2*w + 12]', '[1945, 1945, -2*w^3 + 11*w^2 - 6*w - 27]', '[1945, 1945, 4*w^3 - w^2 - 18*w - 15]', '[1945, 1945, -w^3 + 5*w^2 - 2*w - 17]', '[1949, 1949, 4*w^3 - 5*w^2 - 16*w - 2]', '[1949, 1949, 8*w^2 - 11*w - 21]', '[1951, 1951, w^3 + 5*w^2 - 10*w - 23]', '[1951, 1951, w^3 - 8*w^2 + 3*w + 27]', '[1969, 1969, 2*w^3 - 8*w^2 - 3*w + 20]', '[1969, 1969, w^3 - 5*w^2 - 2*w + 11]', '[1969, 1969, w^3 + 2*w^2 - 9*w - 5]', '[1969, 1969, 2*w^3 + 2*w^2 - 13*w - 11]', '[1975, 395, w^3 - 7*w^2 + 5*w + 21]', '[1975, 395, w^3 + 4*w^2 - 6*w - 20]', '[1979, 1979, -w^3 + 7*w^2 + w - 28]', '[1979, 1979, 3*w^3 - 2*w^2 - 11*w - 8]', '[1991, 1991, 5*w^3 - w^2 - 22*w - 11]', '[1991, 1991, -4*w^3 + 8*w^2 + 11*w - 11]', '[1991, 1991, 4*w^3 - 4*w^2 - 15*w + 4]', '[1991, 1991, -5*w^3 + 14*w^2 + 9*w - 29]', '[2000, 10, -4*w^3 + 6*w^2 + 12*w - 2]', '[2009, 287, -2*w^3 - w^2 + 10*w + 16]', '[2009, 287, 2*w^3 - 7*w^2 - 2*w + 23]', '[2011, 2011, 3*w^3 - 4*w^2 - 11*w + 14]', '[2011, 2011, 3*w^3 - 4*w^2 - 11*w - 5]', '[2011, 2011, w^3 + 6*w^2 - 13*w - 26]', '[2011, 2011, 3*w^3 - 5*w^2 - 10*w - 2]', '[2025, 15, -6*w^2 + 6*w + 21]', '[2025, 45, 4*w^3 - 4*w^2 - 14*w + 5]', '[2025, 45, 4*w^3 - 8*w^2 - 10*w + 9]', '[2039, 2039, -3*w^3 + 6*w^2 + 12*w - 20]', '[2039, 2039, -3*w^3 + 3*w^2 + 15*w + 5]', '[2059, 2059, -w^3 + 7*w^2 - 19]', '[2059, 2059, -w^3 + 6*w^2 - 3*w - 20]', '[2059, 2059, 2*w^3 - 4*w^2 - 3*w + 10]', '[2059, 2059, -w^3 - 4*w^2 + 11*w + 13]', '[2061, 687, 2*w^3 - 11*w^2 - w + 37]', '[2061, 687, -4*w^3 + 23*w + 23]', '[2061, 687, 2*w^3 + 5*w^2 - 17*w - 27]', '[2061, 687, -4*w^3 + 12*w^2 + 11*w - 42]', '[2069, 2069, -2*w^3 - 6*w^2 + 17*w + 23]', '[2069, 2069, -3*w^3 + 19*w + 7]', '[2071, 2071, -2*w^3 + 6*w^2 + w - 4]', '[2071, 2071, -w^3 + 9*w^2 - 2*w - 29]', '[2071, 2071, -3*w^3 + w^2 + 15*w + 15]', '[2071, 2071, w^3 + 6*w^2 - 9*w - 26]', '[2095, 2095, 7*w^3 - 12*w^2 - 21*w + 2]', '[2095, 2095, -5*w^3 + 7*w^2 + 15*w + 2]', '[2095, 2095, 2*w^3 - 7*w^2 + w + 16]', '[2095, 2095, -w^3 + 14*w^2 - 16*w - 36]', '[2096, 262, -4*w^3 + 10*w^2 + 8*w - 18]', '[2096, 262, -2*w^3 + 2*w^2 + 6*w + 10]', '[2096, 262, -2*w^3 + 4*w^2 + 4*w - 16]', '[2096, 262, -2*w^3 + 12*w^2 - 36]', '[2101, 2101, -3*w^2 - w + 11]', '[2101, 2101, 6*w^2 - w - 22]', '[2101, 2101, 6*w^2 - 11*w - 17]', '[2101, 2101, -3*w^2 + 7*w + 7]', '[2105, 2105, -w^3 - 5*w^2 + 9*w + 20]', '[2105, 2105, w^3 - 8*w^2 + 4*w + 23]', '[2111, 2111, -w^3 + w^2 + 3*w - 7]', '[2111, 2111, w^3 + 5*w^2 - 9*w - 21]', '[2111, 2111, -w^3 + 8*w^2 - 4*w - 24]', '[2111, 2111, w^3 - 2*w^2 - 2*w - 4]', '[2129, 2129, -3*w^3 + 8*w^2 + 7*w - 15]', '[2129, 2129, -3*w^3 + w^2 + 14*w + 3]', '[2141, 2141, 3*w^2 + w - 12]', '[2141, 2141, 2*w^3 + 5*w^2 - 16*w - 23]', '[2141, 2141, -2*w^3 + 11*w^2 - 32]', '[2141, 2141, 3*w^2 - 7*w - 8]', '[2151, 717, -4*w^3 + 15*w^2 + 8*w - 54]', '[2151, 717, 7*w^3 + 5*w^2 - 45*w - 52]', '[2151, 717, 4*w^3 + 3*w^2 - 26*w - 35]', '[2151, 717, -7*w^3 + 26*w^2 + 14*w - 85]', '[2161, 2161, 2*w^3 - 5*w^2 - 5*w + 2]', '[2161, 2161, -3*w^3 + 9*w^2 + 3*w - 10]', '[2169, 723, -5*w^3 + 4*w^2 + 20*w + 12]', '[2169, 723, 3*w^3 - 10*w^2 - 3*w + 26]', '[2169, 723, -4*w^3 + w^2 + 21*w + 10]', '[2169, 723, -7*w^3 + 23*w^2 + 17*w - 70]', '[2169, 723, 4*w^3 - 11*w^2 - 11*w + 28]', '[2169, 723, 7*w^3 + 2*w^2 - 42*w - 37]', '[2169, 723, -5*w^3 + 11*w^2 + 13*w - 31]', '[2169, 723, 3*w^3 + w^2 - 14*w - 16]', '[2179, 2179, -2*w^3 + 5*w^2 + 6*w - 6]', '[2179, 2179, -2*w^3 + w^2 + 10*w - 3]', '[2189, 2189, 2*w^3 - 6*w^2 - 2*w + 17]', '[2189, 2189, w^3 - 3*w^2 + w + 11]', '[2189, 2189, w^3 - 2*w - 10]', '[2189, 2189, 2*w^3 - 8*w - 11]', '[2195, 2195, 3*w^3 - w^2 - 13*w - 13]', '[2195, 2195, 4*w^3 - 6*w^2 - 11*w - 1]', '[2205, 105, -4*w^3 + 3*w^2 + 17*w + 5]', '[2205, 105, -4*w^3 + 3*w^2 + 14*w - 1]', '[2205, 105, -w^3 - 2*w^2 + 11*w + 7]', '[2205, 105, w^2 + 3*w - 8]', '[2209, 47, -2*w^3 + 5*w^2 + 6*w - 5]', '[2209, 47, -2*w^3 + w^2 + 10*w - 4]', '[2221, 2221, -w^3 - 5*w^2 + 10*w + 20]', '[2221, 2221, -w^3 + 8*w^2 - 3*w - 24]', '[2225, 445, 3*w^3 - 3*w^2 - 13*w + 5]', '[2225, 445, 3*w^3 - 6*w^2 - 10*w + 8]', '[2239, 2239, -4*w^3 - w^2 + 21*w + 16]', '[2239, 2239, -2*w^3 - 3*w^2 + 15*w + 15]', '[2239, 2239, 4*w^3 - 8*w^2 - 11*w + 6]', '[2239, 2239, -4*w^3 + 13*w^2 + 7*w - 32]', '[2245, 2245, 13*w^2 - 20*w - 42]', '[2245, 2245, 2*w^3 - 6*w^2 - 6*w + 13]', '[2245, 2245, 2*w^3 - 12*w - 3]', '[2245, 2245, -3*w^3 - 2*w^2 + 16*w + 21]', '[2251, 2251, 4*w^3 - 6*w^2 - 13*w + 3]', '[2251, 2251, 3*w^3 - 13*w^2 - 2*w + 39]', '[2251, 2251, -3*w^3 - 4*w^2 + 19*w + 27]', '[2251, 2251, -5*w^2 + 10*w + 16]', '[2255, 2255, -2*w^2 + 3*w - 1]', '[2255, 2255, -6*w^3 + 5*w^2 + 21*w - 11]', '[2269, 2269, -4*w^3 + 2*w^2 + 17*w + 13]', '[2269, 2269, -3*w^3 + w^2 + 13*w + 15]', '[2281, 2281, 4*w - 5]', '[2281, 2281, -4*w - 1]', '[2291, 2291, w^3 + 4*w^2 - 14*w - 18]', '[2291, 2291, 2*w^3 - 11*w^2 - w + 36]', '[2291, 2291, -w^3 + 10*w^2 - 2*w - 35]', '[2291, 2291, 2*w^3 + 6*w^2 - 15*w - 32]', '[2299, 209, -w^3 - 4*w^2 + 12*w + 13]', '[2299, 209, -3*w^3 + 8*w^2 + 6*w - 11]', '[2299, 209, w^3 - 7*w^2 - w + 20]', '[2299, 209, 3*w^3 - w^2 - 13*w]', '[2299, 2299, 7*w^2 - 3*w - 22]', '[2299, 2299, 2*w^3 - 9*w^2 + 3*w + 22]', '[2299, 2299, 2*w^3 + 3*w^2 - 9*w - 18]', '[2299, 2299, 7*w^2 - 11*w - 18]', '[2304, 12, 4*w^3 - 12*w^2 - 8*w + 36]', '[2304, 12, -4*w^3 + 20*w + 20]', '[2309, 2309, 4*w^3 - 5*w^2 - 12*w - 3]', '[2309, 2309, 2*w^3 - 9*w^2 + 4*w + 21]', '[2311, 2311, 9*w^2 - 7*w - 37]', '[2311, 2311, 9*w^2 - 11*w - 35]', '[2320, 290, 4*w^3 - 14*w^2 + 28]', '[2320, 290, -4*w^3 + 14*w^2 + 2*w - 24]', '[2321, 2321, 2*w^3 - 5*w^2 - 7*w + 21]', '[2321, 2321, w^3 - 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7*w^2 - 5*w + 20]', '[389, 389, 2*w^3 - 10*w - 5]', '[419, 419, -w^3 + 5*w^2 + w - 13]', '[419, 419, 4*w^2 - 7*w - 14]', '[419, 419, 2*w^3 - 3*w^2 - 5*w - 1]', '[419, 419, -w^3 - 2*w^2 + 8*w + 8]', '[421, 421, -2*w^2 + 5*w + 7]', '[421, 421, w^3 - 6*w^2 + 5*w + 13]', '[439, 439, 2*w^3 - 2*w^2 - 9*w + 3]', '[439, 439, w^3 + w^2 - 7*w - 4]', '[449, 449, 3*w^3 - 6*w^2 - 9*w + 8]', '[449, 449, 5*w^2 - 8*w - 17]', '[449, 449, 2*w^3 - w^2 - 8*w - 7]', '[449, 449, -3*w^3 + 3*w^2 + 12*w - 4]', '[479, 479, -2*w^3 + 3*w^2 + 5*w + 3]', '[479, 479, 3*w^3 - 7*w^2 - 9*w + 15]', '[499, 499, -w^3 + 4*w^2 + 4*w - 9]', '[499, 499, w^3 + w^2 - 9*w - 2]', '[509, 509, 2*w^3 + 2*w^2 - 11*w - 16]', '[509, 509, -2*w^3 + 8*w^2 + w - 23]', '[521, 521, -3*w^3 + w^2 + 13*w + 6]', '[521, 521, w^3 + 4*w^2 - 10*w - 16]', '[541, 541, 3*w^3 - 2*w^2 - 13*w - 3]', '[541, 541, -w^3 + 7*w^2 - w - 25]', '[541, 541, w^3 + 4*w^2 - 10*w - 20]', '[541, 541, -3*w^3 + 7*w^2 + 8*w - 15]', '[571, 571, w^3 + 4*w^2 - 9*w - 15]', '[571, 571, w^3 - 7*w^2 + 2*w + 19]', '[601, 601, -3*w^3 + 2*w^2 + 13*w + 5]', '[601, 601, 3*w^3 - 7*w^2 - 8*w + 17]', '[619, 619, w^3 - 3*w - 7]', '[619, 619, w^3 - 5*w^2 + 3*w + 13]', '[619, 619, 3*w^3 - 4*w^2 - 9*w - 2]', '[619, 619, -w^3 + 3*w^2 - 9]', '[641, 641, 6*w^2 - 4*w - 23]', '[641, 641, -3*w^3 + w^2 + 12*w + 5]', '[659, 659, -2*w^3 + 6*w^2 + 3*w - 17]', '[659, 659, -2*w^3 + 9*w + 10]', '[661, 661, 3*w^3 - 6*w^2 - 9*w + 14]', '[661, 661, 5*w^2 - 6*w - 18]', '[661, 661, -5*w^2 + 4*w + 19]', '[661, 661, 3*w^3 - 3*w^2 - 12*w - 2]', '[691, 691, -3*w^3 + 5*w^2 + 10*w - 6]', '[691, 691, -3*w^3 + 4*w^2 + 11*w - 6]', '[701, 701, -w^3 - 4*w^2 + 9*w + 20]', '[701, 701, -w^3 + 4*w^2 + 3*w - 19]', '[701, 701, -w^3 + 4*w^2 + 4*w - 15]', '[701, 701, w^3 - 7*w^2 + 2*w + 24]', '[709, 709, 3*w^2 - 5*w - 13]', '[709, 709, 3*w^2 - w - 15]', '[719, 719, -w^3 + 3*w^2 + 4*w - 4]', '[719, 719, -w^3 + 7*w - 2]', '[739, 739, -w^3 + 4*w^2 + 3*w - 9]', '[739, 739, -2*w^3 - w^2 + 11*w + 8]', '[739, 739, 2*w^3 - 7*w^2 - 3*w + 16]', '[739, 739, -w^3 - w^2 + 8*w + 3]', '[751, 751, 3*w^3 - 5*w^2 - 10*w + 10]', '[751, 751, 2*w^2 - 5*w - 5]', '[761, 761, 3*w^3 - 3*w^2 - 11*w + 3]', '[761, 761, w^3 - 2*w^2 - 3*w - 2]', '[761, 761, -w^3 + w^2 + 4*w - 6]', '[761, 761, -3*w^3 + 6*w^2 + 8*w - 8]', '[769, 769, -w^3 - w^2 + 7*w + 1]', '[769, 769, -2*w^3 + 6*w^2 + 6*w - 15]', '[769, 769, -2*w^3 + 5*w^2 + 5*w - 7]', '[769, 769, 2*w^3 + w^2 - 12*w - 9]', '[809, 809, -2*w^3 + 8*w^2 + 4*w - 23]', '[809, 809, -3*w^3 + 11*w^2 + 2*w - 28]', '[829, 829, -3*w^3 + 7*w^2 + 7*w - 9]', '[829, 829, w^3 + 2*w^2 - 6*w - 15]', '[829, 829, -w^3 + 5*w^2 - w - 18]', '[829, 829, -3*w^3 + 2*w^2 + 12*w - 2]', '[839, 839, 2*w^3 - 9*w^2 + 20]', '[839, 839, -3*w^3 + 10*w^2 + 5*w - 30]', '[841, 29, 5*w^2 - 5*w - 16]', '[881, 881, -w^3 - 4*w^2 + 8*w + 18]', '[881, 881, 2*w^3 - 7*w^2 - w + 9]', '[881, 881, 2*w^3 - 6*w^2 - 3*w + 6]', '[881, 881, -w^3 + 7*w^2 - 3*w - 21]', '[911, 911, -w^3 - 4*w^2 + 8*w + 16]', '[911, 911, -w^3 - w^2 + 9*w + 5]', '[911, 911, -w^3 + 4*w^2 + 4*w - 12]', '[911, 911, w^3 - 7*w^2 + 3*w + 19]', '[919, 919, -4*w^3 + 7*w^2 + 14*w - 9]', '[919, 919, 4*w^3 - 5*w^2 - 16*w + 8]', '[929, 929, 3*w^2 - w - 16]', '[929, 929, 3*w^2 - 5*w - 14]', '[941, 941, -w^3 - w^2 + 9*w + 7]', '[941, 941, -3*w^3 + 7*w^2 + 7*w - 15]', '[941, 941, 3*w^3 - 2*w^2 - 12*w - 4]', '[941, 941, w^3 + 4*w^2 - 13*w - 16]', '[961, 31, -2*w^2 + 2*w + 13]', '[961, 31, 5*w^2 - 5*w - 18]', '[971, 971, w^3 + 4*w^2 - 9*w - 19]', '[971, 971, w^3 - 7*w^2 + 2*w + 23]', '[991, 991, 3*w^3 - 7*w^2 - 7*w + 14]', '[991, 991, -3*w^3 + 2*w^2 + 12*w + 3]']}
• 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': [11, 7, -6, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 5125, 'disc_rad': 205, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[2, 2]]], [5, [0]], [7, [[2, 2]]], [11, [[2, 1], [1, 2]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[2, 1], [1, 2]]], [23, [[4, 1]]], [29, [[2, 1], [1, 2]]], [31, [[2, 2]]], [37, [[4, 1]]], [41, [0]], [43, [[4, 1]]], [47, [[2, 2]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 21.410136276713814, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.5125.1', 'local_algs': ['5.4.3.2', '41.2.1.2', '41.2.0.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 41], 'rd': 8.46103452991, 'regulator': {'__RealLiteral__': 0, 'data': '3.09100676599', 'prec': 44}, 'res': {'gal': ['1,0,-19,0,41,0,-19,0,1'], 'sib': ['5,0,-15,0,1', '1,0,-19,0,41,0,-19,0,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a - 4 \\)', '\\( a^{3} - 5 a - 4 \\)', '\\( a^{3} - 4 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}