Hilbert modular form data - 4.4.12725.1-16.1-c

Formats: - HTML - YAML - JSON - 2024-05-02T04:38:43.296748

• 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': 4, 'disc': 12725, 'field_bad_primes': [5, 509], 'field_label': '4.4.12725.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.12725.1-16.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [2], 'level_ideal': '[16, 2, 2]', 'level_label': '16.1', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.1-c', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[16, 2, 2]', -1]], 'hecke_eigenvalues': ['1/16*e^3 + 1/4*e^2 - 3/4*e - 4', 'e', '-e', '-1/16*e^3 + 1/4*e^2 + 3/4*e - 4', 1, '-1/4*e^2 - e + 4', '-1/4*e^2 + e + 4', '1/4*e^2 - 8', '1/16*e^3 - 3/4*e - 1', '3/16*e^3 - 1/2*e^2 - 17/4*e + 5', '-3/16*e^3 - 1/2*e^2 + 17/4*e + 5', '-1/16*e^3 + 3/4*e - 1', '-3/16*e^3 - 1/2*e^2 + 17/4*e + 2', '3/16*e^3 - 1/2*e^2 - 17/4*e + 2', '1/4*e^2 - e - 1', '1/4*e^2 + e - 1', '-1/16*e^3 + 1/2*e^2 + 11/4*e - 4', '1/16*e^3 + 1/2*e^2 - 11/4*e - 4', '1/16*e^3 + 3/4*e^2 - 3/4*e - 13', '-1/16*e^3 + 3/4*e^2 + 3/4*e - 13', '1/16*e^3 - 3/4*e - 10', '1/8*e^3 + 1/4*e^2 - 3/2*e', '-1/8*e^3 + 1/4*e^2 + 3/2*e', '-1/16*e^3 + 3/4*e - 10', '1/16*e^3 - 5/4*e^2 - 7/4*e + 18', '-1/16*e^3 - 5/4*e^2 + 7/4*e + 18', '1/4*e^2 - 12', '1/8*e^3 - 7/2*e - 4', '-1/8*e^3 + 7/2*e - 4', '-7/16*e^3 - 3/4*e^2 + 37/4*e + 4', '7/16*e^3 - 3/4*e^2 - 37/4*e + 4', '-1/16*e^3 + 3/4*e^2 + 7/4*e - 11', '1/16*e^3 + 3/4*e^2 - 7/4*e - 11', '3/8*e^3 + 1/2*e^2 - 13/2*e - 8', '-3/8*e^3 + 1/2*e^2 + 13/2*e - 8', '2*e + 4', '7/16*e^3 - 1/2*e^2 - 29/4*e', '-7/16*e^3 - 1/2*e^2 + 29/4*e', '-2*e + 4', '-1/8*e^3 + e^2 - 3/2*e - 16', '1/8*e^3 + e^2 + 3/2*e - 16', '-1/16*e^3 - 1/2*e^2 + 7/4*e + 2', 'e^2 + e - 20', 'e^2 - e - 20', '1/16*e^3 - 1/2*e^2 - 7/4*e + 2', '7/16*e^3 - 1/4*e^2 - 25/4*e + 10', '-7/16*e^3 - e^2 + 33/4*e + 10', '7/16*e^3 - e^2 - 33/4*e + 10', '-7/16*e^3 - 1/4*e^2 + 25/4*e + 10', '5/4*e^2 - 3*e - 15', '1/2*e^3 - 7/4*e^2 - 10*e + 15', '-1/2*e^3 - 7/4*e^2 + 10*e + 15', '5/4*e^2 + 3*e - 15', '-9/16*e^3 + 3/4*e^2 + 39/4*e - 19', '9/16*e^3 + 3/4*e^2 - 39/4*e - 19', '5/8*e^3 - 5/4*e^2 - 23/2*e + 12', '-1/4*e^3 - e^2 + 6*e + 12', '1/4*e^3 - e^2 - 6*e + 12', '-5/8*e^3 - 5/4*e^2 + 23/2*e + 12', '-1/4*e^3 + 5/4*e^2 + 9*e - 13', '1/4*e^3 + 5/4*e^2 - 9*e - 13', '-5/16*e^3 - e^2 + 15/4*e + 22', '5/16*e^3 - e^2 - 15/4*e + 22', '-7/16*e^3 + 1/2*e^2 + 37/4*e - 12', '7/16*e^3 + 1/2*e^2 - 37/4*e - 12', '-3/16*e^3 - 3/2*e^2 + 25/4*e + 19', '3/16*e^3 - 3/2*e^2 - 25/4*e + 19', '-3/4*e^2 + 7', '1/4*e^3', '-5/16*e^3 - 1/4*e^2 + 23/4*e + 20', '5/16*e^3 - 1/4*e^2 - 23/4*e + 20', '-1/4*e^3', '-1/8*e^3 + 1/2*e^2 - 5/2*e - 5', '1/8*e^3 + 1/2*e^2 + 5/2*e - 5', '3*e^2 + e - 48', '3*e^2 - e - 48', '-5/16*e^3 - 9/4*e^2 + 11/4*e + 35', '5/16*e^3 - 9/4*e^2 - 11/4*e + 35', '-13/16*e^3 + 1/4*e^2 + 51/4*e + 2', '13/16*e^3 + 1/4*e^2 - 51/4*e + 2', '1/2*e^3 + 5/4*e^2 - 10*e - 7', '-1/2*e^3 + 5/4*e^2 + 10*e - 7', '-11/16*e^3 - 3/4*e^2 + 37/4*e + 27', '11/16*e^3 - 3/4*e^2 - 37/4*e + 27', '1/8*e^3 - 5/2*e^2 - 3/2*e + 32', '-1/8*e^3 - 5/2*e^2 + 3/2*e + 32', '-3/8*e^3 - 7/4*e^2 + 19/2*e + 20', '3/8*e^3 - 7/4*e^2 - 19/2*e + 20', '2*e^2 - 34', '-1/8*e^3 - 1/4*e^2 - 5/2*e + 17', '1/8*e^3 - 1/4*e^2 + 5/2*e + 17', '-3/8*e^3 + 9/4*e^2 + 15/2*e - 27', '3/8*e^3 + 9/4*e^2 - 15/2*e - 27', '5/16*e^3 - 23/4*e + 1', '-5/16*e^3 + 23/4*e + 1', '1/4*e^3 + e^2 - 8*e - 24', '-1/4*e^3 + e^2 + 8*e - 24', '1/16*e^3 + e^2 + 25/4*e - 22', '-1/16*e^3 + e^2 - 25/4*e - 22', '-9/8*e^3 + 1/4*e^2 + 43/2*e - 5', '1/8*e^3 - 9/4*e^2 - 1/2*e + 31', '-1/8*e^3 - 9/4*e^2 + 1/2*e + 31', '9/8*e^3 + 1/4*e^2 - 43/2*e - 5', '9/16*e^3 + 1/2*e^2 - 35/4*e - 12', '-9/16*e^3 + 1/2*e^2 + 35/4*e - 12', '5/2*e^2 - e - 36', '5/2*e^2 + e - 36', '1/8*e^3 - 1/4*e^2 + 3/2*e - 24', '-1/2*e^2 - 4*e + 16', '-1/2*e^2 + 4*e + 16', '-1/8*e^3 - 1/4*e^2 - 3/2*e - 24', '1/2*e^2 - 3*e - 32', '1/2*e^2 + 3*e - 32', '3/4*e^3 + 5/2*e^2 - 10*e - 38', '-3/4*e^3 + 5/2*e^2 + 10*e - 38', '7/4*e^2 + 5*e - 38', '7/4*e^2 - 5*e - 38', '13/16*e^3 - 7/2*e^2 - 51/4*e + 50', '-13/16*e^3 - 7/2*e^2 + 51/4*e + 50', '-1/16*e^3 - 3/4*e^2 + 11/4*e + 40', '1/16*e^3 - 3/4*e^2 - 11/4*e + 40', '11/16*e^3 + 7/4*e^2 - 69/4*e - 6', '-11/16*e^3 + 7/4*e^2 + 69/4*e - 6', '1/2*e^3 + 3/4*e^2 - 6*e - 12', '-1/2*e^3 + 3/4*e^2 + 6*e - 12', '1/8*e^3 + 2*e^2 - 7/2*e - 5', '-1/8*e^3 + 2*e^2 + 7/2*e - 5', '5/8*e^3 + 5/2*e^2 - 27/2*e - 37', '-5/8*e^3 + 5/2*e^2 + 27/2*e - 37', '3/4*e^3 - 5/4*e^2 - 16*e + 16', '7/16*e^3 - 1/2*e^2 - 21/4*e + 24', '-7/16*e^3 - 1/2*e^2 + 21/4*e + 24', '-3/4*e^3 - 5/4*e^2 + 16*e + 16', '-19/16*e^3 - 13/4*e^2 + 101/4*e + 31', '19/16*e^3 - 13/4*e^2 - 101/4*e + 31', '-19/16*e^3 - 1/4*e^2 + 89/4*e + 21', '3/8*e^3 - e^2 - 15/2*e + 4', '-3/8*e^3 - e^2 + 15/2*e + 4', '19/16*e^3 - 1/4*e^2 - 89/4*e + 21', '3/16*e^3 + 5/4*e^2 - 1/4*e - 4', '11/16*e^3 + e^2 - 49/4*e - 4', '-11/16*e^3 + e^2 + 49/4*e - 4', '-3/16*e^3 + 5/4*e^2 + 1/4*e - 4', '1/2*e^3 - 13/4*e^2 - 8*e + 53', '1/4*e^3 + 5/2*e^2 - 12*e - 28', '-1/4*e^3 + 5/2*e^2 + 12*e - 28', '-1/2*e^3 - 13/4*e^2 + 8*e + 53', '15/16*e^3 + 9/4*e^2 - 49/4*e - 53', '-15/16*e^3 + 9/4*e^2 + 49/4*e - 53', '3/4*e^2 - 23', '-3/8*e^3 - 5/4*e^2 + 15/2*e + 32', '3/8*e^3 - 5/4*e^2 - 15/2*e + 32', '23/16*e^3 - 1/2*e^2 - 97/4*e + 10', '-23/16*e^3 - 1/2*e^2 + 97/4*e + 10'], 'hecke_polynomial': 'x^4 - 28*x^2 + 128', 'label': '4.4.12725.1-16.1-c'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 12725, 'ideals': ['[1, 1, 1]', '[11, 11, -w - 1]', '[11, 11, w^2 - 5]', '[11, 11, -w^2 + 2*w + 4]', '[11, 11, w - 2]', '[16, 2, 2]', '[19, 19, w^2 - 2*w - 5]', '[19, 19, -w^2 + 6]', '[25, 5, -2*w^2 + 2*w + 11]', '[29, 29, w]', '[29, 29, 2*w^2 - w - 10]', '[29, 29, -2*w^2 + 3*w + 9]', '[29, 29, w - 1]', '[31, 31, w^3 - 6*w - 6]', '[31, 31, -w^3 + 3*w^2 + 3*w - 11]', '[41, 41, w^3 - 4*w^2 - 2*w + 16]', '[41, 41, w^3 - 5*w^2 - 2*w + 24]', '[59, 59, w^3 - w^2 - 5*w - 2]', '[59, 59, 2*w^2 - w - 13]', '[61, 61, w^3 - w^2 - 6*w + 3]', '[61, 61, -w^3 + 2*w^2 + 5*w - 3]', '[71, 71, 2*w^2 - w - 16]', '[71, 71, -w^3 + 3*w^2 + 4*w - 10]', '[71, 71, -w^3 + 7*w + 4]', '[71, 71, w^3 - 5*w^2 - 2*w + 23]', '[79, 79, -w^3 + 4*w^2 + 3*w - 16]', '[79, 79, w^3 + w^2 - 8*w - 10]', '[81, 3, -3]', '[121, 11, -3*w^2 + 3*w + 16]', '[121, 11, w^3 - 2*w^2 - 5*w + 10]', '[121, 11, -2*w^2 + w + 14]', '[121, 11, w^3 - w^2 - 6*w - 4]', '[121, 11, 3*w^2 - 3*w - 17]', '[121, 11, 2*w^2 - 3*w - 13]', '[121, 121, w^3 - 2*w^2 - 6*w + 10]', '[121, 121, -w^3 + 2*w^2 + 4*w - 8]', '[121, 121, w^3 - w^2 - 5*w - 3]', '[121, 121, w^3 - w^2 - 7*w - 3]', '[131, 131, 4*w^2 - 5*w - 24]', '[131, 131, 4*w^2 - 3*w - 25]', '[139, 139, w^2 + w - 9]', '[139, 139, -w^3 + w^2 + 6*w - 5]', '[149, 149, w^3 - w^2 - 4*w + 2]', '[149, 149, w^3 - 2*w^2 - 3*w + 2]', '[151, 151, -w^3 + 7*w + 3]', '[151, 151, -w^3 + 3*w^2 + 4*w - 9]', '[176, 22, -2*w - 2]', '[176, 22, 2*w^2 - 10]', '[176, 22, -2*w^2 + 4*w + 8]', '[176, 22, 2*w - 4]', '[179, 179, -w^3 - 2*w^2 + 10*w + 16]', '[179, 179, -w^3 + 3*w^2 + 3*w - 6]', '[179, 179, w^3 - 6*w - 1]', '[179, 179, w^3 - 5*w^2 - 3*w + 23]', '[191, 191, w^3 - 6*w^2 - w + 27]', '[191, 191, w^3 + 3*w^2 - 10*w - 21]', '[199, 199, -w^3 + 2*w^2 + 6*w - 4]', '[199, 199, -4*w^2 + 3*w + 22]', '[199, 199, 4*w^2 - 5*w - 21]', '[199, 199, 3*w^2 - 4*w - 12]', '[209, 209, -w - 4]', '[209, 209, -2*w^3 + 5*w^2 + 9*w - 20]', '[209, 209, -w^3 + 6*w^2 - 27]', '[209, 209, -w^3 + 7*w + 2]', '[209, 209, -w^3 + 3*w^2 + 4*w - 8]', '[209, 209, -w^3 - 3*w^2 + 9*w + 22]', '[209, 209, 2*w^3 - w^2 - 13*w - 8]', '[209, 209, w - 5]', '[239, 239, -w^3 + w^2 + 4*w - 6]', '[239, 239, 2*w^3 - 5*w^2 - 9*w + 17]', '[239, 239, 2*w^3 - w^2 - 13*w - 5]', '[239, 239, w^3 - 8*w^2 + 2*w + 41]', '[241, 241, -w^3 + 5*w^2 + 4*w - 25]', '[241, 241, w^3 - 6*w - 8]', '[241, 241, -w^3 + 3*w^2 + 3*w - 13]', '[241, 241, w^3 - 5*w^2 + w + 19]', '[256, 4, 4]', '[269, 269, w^2 - 2*w - 10]', '[269, 269, w^2 - 11]', '[271, 271, w^3 + 2*w^2 - 8*w - 18]', '[271, 271, 2*w^3 - 13*w - 10]', '[271, 271, 2*w^3 + w^2 - 15*w - 16]', '[271, 271, w^3 - 5*w^2 - w + 23]', '[275, 55, 2*w^3 - 13*w - 11]', '[275, 55, -2*w^3 + w^2 + 12*w + 3]', '[275, 55, -2*w^3 + 5*w^2 + 8*w - 14]', '[275, 55, -2*w^3 + 6*w^2 + 7*w - 22]', '[289, 17, 2*w^2 - 11]', '[289, 17, -2*w^2 + 4*w + 9]', '[304, 38, 2*w^2 - 4*w - 10]', '[304, 38, -2*w^2 + 12]', '[311, 311, w^3 - 4*w^2 - 3*w + 10]', '[311, 311, w^3 - 7*w^2 - w + 34]', '[319, 319, w^3 - 6*w^2 - w + 28]', '[319, 319, 2*w^3 + w^2 - 14*w - 18]', '[319, 319, 2*w^3 - 8*w^2 - 7*w + 36]', '[319, 319, w^2 - 3*w - 6]', '[319, 319, -w^3 + w^2 + 4*w - 4]', '[319, 319, -w^3 - w^2 + 7*w + 13]', '[319, 319, -w^3 + 2*w^2 + 4*w]', '[319, 319, w^3 + 3*w^2 - 10*w - 23]', '[319, 319, w^3 - 6*w^2 - w + 29]', '[319, 319, w^3 - w^2 - 5*w + 5]', '[319, 319, w^3 - 4*w^2 - 2*w + 18]', '[319, 319, -w^3 + 2*w^2 + 3*w]', '[319, 319, -w^2 - w + 8]', '[319, 319, -2*w^3 - 2*w^2 + 17*w + 23]', '[319, 319, -2*w^3 + 7*w^2 + 6*w - 29]', '[319, 319, w^3 + 3*w^2 - 10*w - 22]', '[331, 331, w^3 - w^2 - 7*w + 4]', '[331, 331, w^3 - 2*w^2 - 6*w + 3]', '[341, 341, -3*w^3 - 4*w^2 + 23*w + 35]', '[341, 341, 4*w^2 - 3*w - 18]', '[341, 341, 5*w^2 - 7*w - 24]', '[341, 341, 3*w^3 + 3*w^2 - 21*w - 28]', '[341, 341, 3*w^3 - 12*w^2 - 6*w + 43]', '[341, 341, -5*w^2 + 3*w + 26]', '[341, 341, 4*w^2 - 5*w - 17]', '[341, 341, 3*w^3 - 13*w^2 - 6*w + 51]', '[349, 349, w^3 + w^2 - 6*w - 12]', '[349, 349, -w^3 + 4*w^2 + w - 16]', '[361, 19, 4*w^2 - 4*w - 21]', '[361, 19, -4*w^2 + 4*w + 23]', '[361, 361, -3*w^2 + w + 14]', '[361, 361, 3*w^2 - 5*w - 12]', '[379, 379, w^3 - 3*w^2 - 3*w + 15]', '[379, 379, 2*w^3 - 2*w^2 - 12*w + 1]', '[379, 379, -2*w^3 + 4*w^2 + 10*w - 11]', '[379, 379, w^3 - 6*w - 10]', '[400, 10, -4*w^2 + 4*w + 22]', '[401, 401, -2*w^3 + 7*w^2 + 8*w - 30]', '[401, 401, -w^3 + 2*w^2 + 6*w - 2]', '[419, 419, 5*w^2 - 4*w - 26]', '[419, 419, 5*w^2 - 6*w - 25]', '[421, 421, 3*w^2 - w - 20]', '[421, 421, -2*w^3 + 2*w^2 + 10*w + 3]', '[431, 431, w^2 - 3*w - 5]', '[431, 431, w^2 + w - 7]', '[449, 449, 2*w^3 - 13*w - 7]', '[449, 449, -2*w^3 + 6*w^2 + 7*w - 18]', '[451, 451, -w^3 + 4*w^2 + 5*w - 20]', '[451, 451, 2*w^3 - 3*w^2 - 11*w + 5]', '[451, 451, 2*w^3 - 3*w^2 - 12*w + 9]', '[451, 451, 2*w^3 - 2*w^2 - 13*w - 3]', '[451, 451, -w^3 - w^2 + 8*w + 6]', '[451, 451, w^3 - 4*w^2 - 3*w + 13]', '[451, 451, -w^2 - w + 6]', '[451, 451, 2*w^3 - 2*w^2 - 11*w - 2]', '[461, 461, w^3 - w^2 - 8*w + 3]', '[461, 461, -w^3 + 2*w^2 + 7*w - 5]', '[464, 58, 2*w]', '[464, 58, 4*w^2 - 2*w - 20]', '[464, 58, -4*w^2 + 6*w + 18]', '[464, 58, 2*w - 2]', '[475, 95, 2*w^3 - 3*w^2 - 10*w + 3]', '[475, 95, 2*w^3 - 3*w^2 - 10*w + 8]', '[491, 491, w^3 - 3*w^2 - 6*w + 15]', '[491, 491, w^3 - 9*w - 7]', '[496, 62, 2*w^3 - 12*w - 12]', '[496, 62, -2*w^3 + 6*w^2 + 6*w - 22]', '[499, 499, 4*w^2 - 6*w - 23]', '[499, 499, -4*w^2 + 2*w + 25]', '[509, 509, 2*w^3 - 3*w^2 - 11*w + 6]', '[521, 521, -w^3 + 3*w^2 + 2*w - 12]', '[521, 521, -w^3 + 4*w^2 + 2*w - 19]', '[529, 23, w^3 - 7*w^2 - w + 35]', '[529, 23, -w^3 + 3*w^2 + 4*w - 5]', '[541, 541, 2*w^3 - w^2 - 12*w - 5]', '[541, 541, w^3 - 2*w^2 - 7*w + 9]', '[551, 551, w^3 + 2*w^2 - 8*w - 19]', '[551, 551, -2*w^3 + 4*w^2 + 9*w - 9]', '[551, 551, w^3 - 2*w^2 - 5*w]', '[551, 551, -w^3 + 6*w]', '[551, 551, w^3 - 3*w^2 - 3*w + 5]', '[551, 551, -w^3 + w^2 + 6*w - 6]', '[551, 551, -2*w^3 + 2*w^2 + 11*w - 2]', '[551, 551, -w^3 + 5*w^2 + w - 24]', '[569, 569, w^3 - 8*w - 2]', '[569, 569, -w^3 + 3*w^2 + 5*w - 9]', '[589, 589, -2*w^3 - 3*w^2 + 15*w + 22]', '[589, 589, -w^3 + 8*w^2 - 37]', '[589, 589, -w^3 - 5*w^2 + 13*w + 30]', '[589, 589, -2*w^3 + 9*w^2 + 3*w - 32]', '[599, 599, -w^3 - 4*w^2 + 10*w + 25]', '[599, 599, -w^3 + 7*w^2 - 36]', '[601, 601, 5*w^2 - 6*w - 26]', '[601, 601, -2*w^3 + 8*w^2 + 6*w - 33]', '[601, 601, -2*w^3 - 2*w^2 + 16*w + 21]', '[601, 601, 5*w^2 - 4*w - 27]', '[619, 619, w^3 + 4*w^2 - 11*w - 26]', '[619, 619, w^3 - 3*w^2 - 5*w + 18]', '[625, 5, 5]', '[641, 641, -w^3 + 3*w^2 + 6*w - 14]', '[641, 641, -w^3 + 9*w + 6]', '[649, 649, -w^3 + 7*w^2 - 3*w - 25]', '[649, 649, 2*w^3 - 5*w^2 - 11*w + 26]', '[649, 649, -w^3 + 9*w^2 - 6*w - 37]', '[649, 649, w^3 - w^2 - 8*w + 6]', '[649, 649, 2*w^3 + 2*w^2 - 15*w - 19]', '[649, 649, 3*w^3 - 3*w^2 - 17*w + 7]', '[649, 649, -2*w^3 - 4*w^2 + 18*w + 31]', '[649, 649, -2*w^3 - w^2 + 14*w + 13]', '[656, 82, 2*w^3 - 8*w^2 - 4*w + 32]', '[656, 82, 2*w^3 - 10*w^2 - 4*w + 48]', '[659, 659, -w^3 - 4*w^2 + 10*w + 28]', '[659, 659, -w^3 + 6*w^2 - w - 27]', '[659, 659, -w^3 - 3*w^2 + 8*w + 23]', '[659, 659, -w^3 + 7*w^2 - w - 33]', '[671, 671, w^3 - 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6*w^2 - 6*w + 39]', '[1529, 1529, -w^3 - 2*w^2 + 8*w + 9]', '[1529, 1529, 2*w^3 + 3*w^2 - 12*w - 24]', '[1529, 1529, 3*w^3 - 4*w^2 - 16*w + 16]', '[1529, 1529, -w^3 - 9*w^2 + 10*w + 54]', '[1531, 1531, w^3 + 5*w^2 - 11*w - 34]', '[1531, 1531, -w^3 + w^2 + 9*w - 10]', '[1531, 1531, w^3 - 5*w^2 + 2*w + 15]', '[1531, 1531, -w^3 + 8*w^2 - 2*w - 39]', '[1539, 57, -3*w^2 + 6*w + 15]', '[1539, 57, 3*w^2 - 18]', '[1549, 1549, 3*w^2 - 17]', '[1549, 1549, 3*w^2 - 6*w - 14]', '[1559, 1559, w^3 - 9*w^2 + 5*w + 43]', '[1559, 1559, 2*w^3 - 7*w^2 - 6*w + 37]', '[1579, 1579, -w^3 + 7*w^2 + w - 31]', '[1579, 1579, w^3 + 4*w^2 - 12*w - 24]', '[1601, 1601, -w^3 + 4*w^2 + 4*w - 11]', '[1601, 1601, w^3 + w^2 - 9*w - 4]', '[1639, 1639, -3*w^3 + 15*w^2 - w - 50]', '[1639, 1639, -2*w^3 + 7*w^2 + 6*w - 21]', '[1639, 1639, -w^3 - 5*w^2 + 12*w + 27]', '[1639, 1639, -2*w^3 - 5*w^2 + 13*w + 27]', '[1639, 1639, -2*w^3 + 11*w^2 - 3*w - 33]', '[1639, 1639, -w^3 + 8*w^2 - w - 33]', '[1639, 1639, 2*w^3 + w^2 - 14*w - 10]', '[1639, 1639, 3*w^3 + 6*w^2 - 20*w - 39]', '[1661, 1661, w^3 - 3*w^2 - 2*w + 16]', '[1661, 1661, -2*w^3 - 6*w^2 + 16*w + 43]', '[1661, 1661, 3*w^2 - 6*w - 20]', '[1661, 1661, 3*w^3 + 3*w^2 - 21*w - 32]', '[1661, 1661, 3*w^3 - 12*w^2 - 6*w + 47]', '[1661, 1661, -3*w^2 + 23]', '[1661, 1661, 2*w^3 - 12*w^2 + 2*w + 51]', '[1661, 1661, -w^3 + 5*w + 12]', '[1669, 1669, -w^3 + 9*w - 1]', '[1669, 1669, -w^3 + 3*w^2 + 6*w - 7]', '[1681, 41, 6*w^2 - 6*w - 35]', '[1681, 41, 6*w^2 - 6*w - 31]', '[1681, 1681, w^3 + 3*w^2 - 9*w - 27]', '[1681, 1681, 2*w^3 - 5*w^2 - 6*w + 17]', '[1699, 1699, 2*w^2 - 5*w - 11]', '[1699, 1699, w^3 - 8*w^2 + 2*w + 36]', '[1699, 1699, w^3 + 5*w^2 - 11*w - 31]', '[1699, 1699, 2*w^2 + w - 14]', '[1709, 1709, 2*w^3 - 6*w^2 - 11*w + 24]', '[1709, 1709, -3*w^3 + 5*w^2 + 14*w - 19]', '[1711, 1711, 3*w^3 - w^2 - 17*w - 9]', '[1711, 1711, -2*w^3 + 12*w^2 - 4*w - 47]', '[1711, 1711, 2*w^3 - 3*w^2 - 12*w + 13]', '[1711, 1711, 2*w^3 - w^2 - 13*w]', '[1711, 1711, 6*w^2 - 8*w - 27]', '[1711, 1711, w^3 + 5*w^2 - 13*w - 29]', '[1711, 1711, 4*w^3 - 5*w^2 - 21*w + 14]', '[1711, 1711, w^2 - 4*w - 1]', '[1721, 1721, 2*w^3 - 4*w^2 - 12*w + 19]', '[1721, 1721, -5*w^2 + 3*w + 20]', '[1741, 1741, -2*w^3 + 11*w^2 + 3*w - 47]', '[1741, 1741, -3*w^3 + 8*w^2 + 12*w - 34]', '[1759, 1759, 2*w^3 - 13*w - 17]', '[1759, 1759, 2*w^3 - 6*w^2 - 7*w + 28]', '[1769, 1769, -w^2 + 2*w - 2]', '[1769, 1769, 5*w^2 - 2*w - 32]', '[1769, 1769, w^3 - 13*w^2 + 11*w + 60]', '[1769, 1769, w^3 - 7*w^2 + 3*w + 32]', '[1769, 1769, w^3 + 4*w^2 - 8*w - 29]', '[1769, 1769, w^3 + 10*w^2 - 12*w - 59]', '[1769, 1769, -5*w^2 + 8*w + 29]', '[1769, 1769, w^2 + 1]', '[1775, 355, -2*w^3 + 12*w^2 + w - 60]', '[1775, 355, -w^3 - w^2 + 10*w + 6]', '[1775, 355, -w^3 + 4*w^2 + 5*w - 14]', '[1775, 355, w^3 - 3*w^2 - 6*w + 21]', '[1801, 1801, -w^3 - 2*w^2 + 8*w + 26]', '[1801, 1801, w^3 - 5*w^2 - w + 31]', '[1811, 1811, -3*w^3 + 11*w^2 + 7*w - 42]', '[1811, 1811, 8*w^2 - 11*w - 45]', '[1811, 1811, -8*w^2 + 5*w + 48]', '[1811, 1811, 3*w^3 + 2*w^2 - 20*w - 27]', '[1829, 1829, -w^3 + 8*w^2 - 2*w - 38]', '[1829, 1829, 2*w^3 - 12*w^2 - 3*w + 56]', '[1829, 1829, 2*w^3 + 6*w^2 - 21*w - 43]', '[1829, 1829, w^3 + 5*w^2 - 11*w - 33]', '[1831, 1831, w^3 - 5*w^2 - 3*w + 19]', '[1831, 1831, 2*w^3 - 5*w^2 - 10*w + 15]', '[1849, 43, w^3 - 2*w^2 - 4*w - 2]', '[1849, 43, -w^3 + w^2 + 5*w - 7]', '[1861, 1861, 2*w^3 - 3*w^2 - 10*w - 3]', '[1861, 1861, w^3 + 4*w^2 - 14*w - 24]', '[1871, 1871, w^3 - 8*w^2 + w + 38]', '[1871, 1871, -w^3 - 5*w^2 + 12*w + 32]', '[1879, 1879, -w^3 - 5*w^2 + 11*w + 32]', '[1879, 1879, w^3 - 8*w^2 + 2*w + 37]', '[1889, 1889, w^3 + 6*w^2 - 11*w - 42]', '[1889, 1889, -2*w^3 + 4*w^2 + 7*w - 2]', '[1891, 1891, -4*w^3 + 8*w^2 + 21*w - 23]', '[1891, 1891, w^3 - 9*w^2 + 2*w + 41]', '[1891, 1891, -w^3 - 6*w^2 + 13*w + 35]', '[1891, 1891, -w^3 + 3*w^2 + 7*w - 10]', '[1901, 1901, -5*w^2 + w + 26]', '[1901, 1901, -5*w^2 + 9*w + 22]', '[1931, 1931, 2*w^3 - 2*w^2 - 13*w + 5]', '[1931, 1931, -2*w^3 + 9*w^2 + 7*w - 41]', '[1931, 1931, -8*w^2 + 10*w + 37]', '[1931, 1931, -2*w^3 + 4*w^2 + 11*w - 8]', '[1936, 22, -6*w^2 + 6*w + 32]', '[1936, 22, 2*w^3 - 4*w^2 - 10*w + 20]', '[1936, 22, -4*w^2 + 2*w + 28]', '[1936, 22, 2*w^3 - 2*w^2 - 12*w - 8]', '[1936, 22, 6*w^2 - 6*w - 34]', '[1936, 22, 4*w^2 - 6*w - 26]', '[1936, 242, 2*w^3 - 4*w^2 - 12*w + 20]', '[1936, 242, -2*w^3 + 4*w^2 + 8*w - 16]', '[1936, 242, 2*w^3 - 2*w^2 - 10*w - 6]', '[1936, 242, 2*w^3 - 2*w^2 - 14*w - 6]', '[1949, 1949, 2*w^3 + 3*w^2 - 16*w - 31]', '[1949, 1949, -2*w^3 + 9*w^2 + 4*w - 42]', '[1951, 1951, w^3 + 2*w^2 - 12*w - 11]', '[1951, 1951, w^2 + 2*w - 9]', '[1951, 1951, w^2 - 4*w - 6]', '[1951, 1951, -w^3 + 5*w^2 + 5*w - 20]', '[1969, 1969, -3*w^3 + 12*w^2 + 8*w - 53]', '[1969, 1969, -5*w^3 + 17*w^2 + 18*w - 75]', '[1969, 1969, 3*w - 4]', '[1969, 1969, 2*w^3 - 2*w^2 - 9*w + 6]', '[1969, 1969, 3*w^3 - 17*w^2 + 4*w + 63]', '[1969, 1969, 4*w^2 - 27]', '[1969, 1969, -4*w^3 + 7*w^2 + 19*w - 28]', '[1969, 1969, 3*w^3 - 13*w^2 - w + 41]', '[1969, 1969, -3*w^3 - 4*w^2 + 18*w + 30]', '[1969, 1969, -4*w^3 + 5*w^2 + 21*w + 6]', '[1969, 1969, 4*w^2 - 8*w - 23]', '[1969, 1969, 3*w^3 + 8*w^2 - 21*w - 53]', '[1969, 1969, -2*w^3 + 4*w^2 + 7*w - 3]', '[1969, 1969, 3*w + 1]', '[1969, 1969, 5*w^3 + 2*w^2 - 37*w - 45]', '[1969, 1969, -3*w^3 - 3*w^2 + 23*w + 36]', '[1975, 395, -w^3 + 9*w - 2]', '[1975, 395, w^3 - 3*w^2 - 6*w + 6]', '[1999, 1999, -2*w^3 + 2*w^2 + 9*w + 4]', '[1999, 1999, 3*w^3 + 3*w^2 - 22*w - 34]', '[1999, 1999, 3*w^3 - 12*w^2 - 7*w + 50]', '[1999, 1999, -w^3 + 6*w^2 - 33]', '[2011, 2011, 2*w^3 - 2*w^2 - 15*w - 2]', '[2011, 2011, 2*w^2 - 5*w - 10]', '[2011, 2011, 2*w^2 + w - 13]', '[2011, 2011, -w^3 + 4*w^2 - w - 10]', '[2025, 15, 6*w^2 - 6*w - 33]', '[2029, 2029, w^3 + 5*w^2 - 12*w - 34]', '[2029, 2029, -w^3 + 8*w^2 - w - 40]', '[2039, 2039, 2*w^3 + 6*w^2 - 18*w - 45]', '[2039, 2039, 2*w^3 - 12*w^2 + 55]', '[2059, 2059, 4*w^3 - 11*w^2 - 18*w + 44]', '[2059, 2059, -3*w^3 + 8*w^2 + 12*w - 29]', '[2059, 2059, 7*w^2 - 13*w - 28]', '[2059, 2059, 2*w^3 - w^2 - 16*w]', '[2059, 2059, -w^3 - 3*w^2 + 8*w + 25]', '[2059, 2059, 2*w^3 - 9*w^2 - 3*w + 39]', '[2059, 2059, -2*w^3 - 7*w^2 + 17*w + 47]', '[2059, 2059, w^3 - 2*w^2 - 5*w + 13]', '[2059, 2059, -w^3 + w^2 + 6*w + 7]', '[2059, 2059, 2*w^3 - 13*w^2 + 3*w + 55]', '[2059, 2059, -2*w^3 - 3*w^2 + 15*w + 29]', '[2059, 2059, w^3 - 6*w^2 + w + 29]', '[2059, 2059, -w^3 - 5*w^2 + 8*w + 27]', '[2059, 2059, -3*w^3 - w^2 + 21*w + 26]', '[2059, 2059, 2*w^3 - 3*w^2 - 15*w + 16]', '[2059, 2059, 3*w^3 - w^2 - 18*w - 11]', '[2069, 2069, -w^3 + 8*w^2 - w - 39]', '[2069, 2069, w^3 + 5*w^2 - 12*w - 33]', '[2081, 2081, w^3 + 2*w^2 - 12*w - 15]', '[2081, 2081, 5*w^2 - 2*w - 24]', '[2081, 2081, 5*w^2 - 8*w - 21]', '[2081, 2081, -w^3 + 5*w^2 + 5*w - 24]', '[2089, 2089, -w^3 + 5*w^2 - 2*w - 16]', '[2089, 2089, -2*w^3 + 4*w^2 + 13*w - 11]', '[2096, 262, 8*w^2 - 10*w - 48]', '[2096, 262, 8*w^2 - 6*w - 50]', '[2099, 2099, w^3 - 10*w^2 + 3*w + 45]', '[2099, 2099, 2*w^3 + 5*w^2 - 20*w - 41]', '[2101, 2101, -6*w^3 - 3*w^2 + 42*w + 50]', '[2101, 2101, -5*w^3 + 18*w^2 + 13*w - 66]', '[2101, 2101, 3*w^3 - 6*w^2 - 12*w + 13]', '[2101, 2101, 4*w^3 - 6*w^2 - 20*w + 3]', '[2101, 2101, -4*w^3 + 6*w^2 + 20*w - 19]', '[2101, 2101, 3*w^3 - 3*w^2 - 15*w + 2]', '[2101, 2101, 5*w^3 + 3*w^2 - 34*w - 40]', '[2101, 2101, -6*w^3 + 21*w^2 + 18*w - 83]', '[2111, 2111, -7*w^2 + 4*w + 36]', '[2111, 2111, 2*w^3 - 5*w^2 - 8*w + 26]', '[2129, 2129, 3*w^3 - 7*w^2 - 13*w + 25]', '[2129, 2129, w^3 - 4*w^2 - 6*w + 22]', '[2129, 2129, w^3 + w^2 - 11*w - 13]', '[2129, 2129, -3*w^3 + 2*w^2 + 18*w + 8]', '[2131, 2131, -3*w^3 + 6*w^2 + 15*w - 17]', '[2131, 2131, 3*w^3 - 3*w^2 - 18*w + 1]', '[2141, 2141, -3*w^3 + 8*w^2 + 11*w - 31]', '[2141, 2141, 2*w^3 + 2*w^2 - 16*w - 19]', '[2141, 2141, -2*w^3 + 8*w^2 + 6*w - 31]', '[2141, 2141, 3*w^3 - w^2 - 18*w - 15]', '[2179, 2179, 3*w^3 - 2*w^2 - 17*w - 2]', '[2179, 2179, 4*w^3 - 6*w^2 - 23*w + 10]', '[2189, 2189, 2*w^3 + 3*w^2 - 13*w - 27]', '[2189, 2189, -5*w^3 + 2*w^2 + 29*w + 6]', '[2189, 2189, 4*w^3 - 13*w^2 - 11*w + 42]', '[2189, 2189, 3*w^3 - 8*w^2 - 9*w + 26]', '[2189, 2189, 4*w^3 - 14*w^2 - 7*w + 39]', '[2189, 2189, -3*w^3 + 8*w^2 + 12*w - 28]', '[2189, 2189, -4*w^3 + w^2 + 26*w + 21]', '[2189, 2189, -3*w^3 - w^2 + 15*w + 13]', '[2189, 2189, 3*w^3 - 10*w^2 - 4*w + 24]', '[2189, 2189, -4*w^3 + 11*w^2 + 16*w - 44]', '[2189, 2189, 3*w^3 - w^2 - 19*w - 11]', '[2189, 2189, 4*w^3 + 2*w^2 - 23*w - 22]', '[2189, 2189, -3*w^3 + w^2 + 16*w + 12]', '[2189, 2189, 4*w^3 + w^2 - 25*w - 22]', '[2189, 2189, 5*w^3 - 13*w^2 - 18*w + 32]', '[2189, 2189, 2*w^3 - 9*w^2 - w + 35]', '[2201, 2201, -w^3 - 2*w^2 + 12*w + 17]', '[2201, 2201, w^3 + w^2 - 6*w - 16]', '[2201, 2201, -3*w^3 + 2*w^2 + 18*w - 2]', '[2201, 2201, -3*w^3 + 21*w + 14]', '[2201, 2201, -3*w^3 + 9*w^2 + 12*w - 32]', '[2201, 2201, 3*w^3 - 7*w^2 - 13*w + 15]', '[2201, 2201, -w^3 + 4*w^2 + w - 20]', '[2201, 2201, -w^3 + 5*w^2 + 5*w - 26]', '[2221, 2221, -w^3 + 2*w^2 + 7*w - 16]', '[2221, 2221, 5*w^2 - 9*w - 27]', '[2221, 2221, 5*w^2 - w - 31]', '[2221, 2221, w^3 - w^2 - 8*w - 8]', '[2224, 278, 2*w^2 + 2*w - 18]', '[2224, 278, -2*w^3 + 2*w^2 + 12*w - 10]', '[2239, 2239, 3*w^3 - 8*w^2 - 11*w + 25]', '[2239, 2239, 3*w^3 - w^2 - 18*w - 9]', '[2269, 2269, -w^3 + 2*w^2 + 4*w - 13]', '[2269, 2269, w^3 - w^2 - 5*w - 8]', '[2291, 2291, 3*w^3 - 15*w^2 - 2*w + 59]', '[2291, 2291, 2*w^3 - 7*w^2 - 5*w + 29]', '[2291, 2291, 3*w^3 - 11*w^2 - 8*w + 45]', '[2291, 2291, 2*w^3 - 3*w^2 - 11*w - 3]', '[2291, 2291, 2*w^3 - 3*w^2 - 11*w + 15]', '[2291, 2291, 3*w^3 + 2*w^2 - 21*w - 29]', '[2291, 2291, 2*w^3 + w^2 - 13*w - 19]', '[2291, 2291, 3*w^3 + 6*w^2 - 23*w - 45]', '[2299, 209, w^3 + 2*w^2 - 11*w - 12]', '[2299, 209, w^3 + 2*w^2 - 12*w - 16]', '[2299, 209, -w^3 + 2*w^2 + 2*w - 12]', '[2299, 209, -3*w^3 + 3*w^2 + 19*w + 7]', '[2299, 209, -3*w^3 + 4*w^2 + 16*w - 2]', '[2299, 209, -w^2 - 2*w + 8]', '[2299, 209, -w^3 + w^2 + 3*w + 9]', '[2299, 209, -3*w^3 + 5*w^2 + 15*w - 15]', '[2299, 209, 3*w^3 - 6*w^2 - 16*w + 26]', '[2299, 209, w^3 - 5*w^2 - 5*w + 25]', '[2299, 209, -w^2 + 4*w + 5]', '[2299, 209, -w^3 + 5*w^2 + 4*w - 20]', '[2299, 2299, w^3 + 6*w^2 - 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10*w - 24]', '[5791, 5791, -2*w^3 - w^2 + 14*w + 5]', '[5791, 5791, 2*w^3 - 7*w^2 - 6*w + 16]', '[5801, 5801, -3*w^3 + 10*w^2 + 9*w - 42]', '[5801, 5801, 3*w^3 + w^2 - 20*w - 26]', '[5819, 253, 4*w^3 - 2*w^2 - 23*w - 6]', '[5819, 253, 3*w^2 - 10*w - 24]', '[5819, 253, -6*w^3 + 9*w^2 + 31*w - 30]', '[5819, 253, w^3 + w^2 - 2*w - 4]', '[5819, 253, -5*w^3 + 16*w^2 + 18*w - 63]', '[5819, 253, 2*w^3 - 16*w^2 + 10*w + 67]', '[5819, 253, 3*w^3 - 12*w^2 - 2*w + 39]', '[5819, 253, -7*w^3 + 23*w^2 + 26*w - 99]', '[5839, 5839, 5*w^3 - 4*w^2 - 29*w - 13]', '[5839, 5839, 2*w^3 + 7*w^2 - 21*w - 47]', '[5849, 5849, 8*w^2 - 11*w - 47]', '[5849, 5849, -8*w^2 + 5*w + 50]', '[5851, 5851, -4*w^3 + 7*w^2 + 18*w - 20]', '[5851, 5851, -4*w^3 + 5*w^2 + 20*w - 1]', '[5879, 5879, 3*w^3 - 3*w^2 - 22*w + 5]', '[5879, 5879, 2*w^3 - 17*w - 5]', '[5879, 5879, -2*w^3 + 6*w^2 + 11*w - 20]', '[5879, 5879, 3*w^3 - 6*w^2 - 19*w + 17]', '[5881, 5881, -4*w^3 + 11*w^2 + 16*w - 40]', '[5881, 5881, -4*w^3 + w^2 + 26*w + 17]', '[5909, 5909, 3*w^3 - 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5*w - 21]', '[199, 199, 3*w^2 - 4*w - 12]', '[239, 239, -w^3 + w^2 + 4*w - 6]', '[239, 239, 2*w^3 - 5*w^2 - 9*w + 17]', '[239, 239, 2*w^3 - w^2 - 13*w - 5]', '[239, 239, w^3 - 8*w^2 + 2*w + 41]', '[241, 241, -w^3 + 5*w^2 + 4*w - 25]', '[241, 241, w^3 - 6*w - 8]', '[241, 241, -w^3 + 3*w^2 + 3*w - 13]', '[241, 241, w^3 - 5*w^2 + w + 19]', '[269, 269, w^2 - 2*w - 10]', '[269, 269, w^2 - 11]', '[271, 271, w^3 + 2*w^2 - 8*w - 18]', '[271, 271, 2*w^3 - 13*w - 10]', '[271, 271, 2*w^3 + w^2 - 15*w - 16]', '[271, 271, w^3 - 5*w^2 - w + 23]', '[289, 17, 2*w^2 - 11]', '[289, 17, -2*w^2 + 4*w + 9]', '[311, 311, w^3 - 4*w^2 - 3*w + 10]', '[311, 311, w^3 - 7*w^2 - w + 34]', '[331, 331, w^3 - w^2 - 7*w + 4]', '[331, 331, w^3 - 2*w^2 - 6*w + 3]', '[349, 349, w^3 + w^2 - 6*w - 12]', '[349, 349, -w^3 + 4*w^2 + w - 16]', '[361, 19, 4*w^2 - 4*w - 21]', '[379, 379, w^3 - 3*w^2 - 3*w + 15]', '[379, 379, 2*w^3 - 2*w^2 - 12*w + 1]', '[379, 379, -2*w^3 + 4*w^2 + 10*w - 11]', '[379, 379, w^3 - 6*w - 10]', '[401, 401, -2*w^3 + 7*w^2 + 8*w - 30]', '[401, 401, -w^3 + 2*w^2 + 6*w - 2]', '[419, 419, 5*w^2 - 4*w - 26]', '[419, 419, 5*w^2 - 6*w - 25]', '[421, 421, 3*w^2 - w - 20]', '[421, 421, -2*w^3 + 2*w^2 + 10*w + 3]', '[431, 431, w^2 - 3*w - 5]', '[431, 431, w^2 + w - 7]', '[449, 449, 2*w^3 - 13*w - 7]', '[449, 449, -2*w^3 + 6*w^2 + 7*w - 18]', '[461, 461, w^3 - w^2 - 8*w + 3]', '[461, 461, -w^3 + 2*w^2 + 7*w - 5]', '[491, 491, w^3 - 3*w^2 - 6*w + 15]', '[491, 491, w^3 - 9*w - 7]', '[499, 499, 4*w^2 - 6*w - 23]', '[499, 499, -4*w^2 + 2*w + 25]', '[509, 509, 2*w^3 - 3*w^2 - 11*w + 6]', '[521, 521, -w^3 + 3*w^2 + 2*w - 12]', '[521, 521, -w^3 + 4*w^2 + 2*w - 19]', '[529, 23, w^3 - 7*w^2 - w + 35]', '[529, 23, -w^3 + 3*w^2 + 4*w - 5]', '[541, 541, 2*w^3 - w^2 - 12*w - 5]', '[541, 541, w^3 - 2*w^2 - 7*w + 9]', '[569, 569, w^3 - 8*w - 2]', '[569, 569, -w^3 + 3*w^2 + 5*w - 9]', '[599, 599, -w^3 - 4*w^2 + 10*w + 25]', '[599, 599, -w^3 + 7*w^2 - 36]', '[601, 601, 5*w^2 - 6*w - 26]', '[601, 601, -2*w^3 + 8*w^2 + 6*w - 33]', '[601, 601, -2*w^3 - 2*w^2 + 16*w + 21]', '[601, 601, 5*w^2 - 4*w - 27]', '[619, 619, w^3 + 4*w^2 - 11*w - 26]', '[619, 619, w^3 - 3*w^2 - 5*w + 18]', '[641, 641, -w^3 + 3*w^2 + 6*w - 14]', '[641, 641, -w^3 + 9*w + 6]', '[659, 659, -w^3 - 4*w^2 + 10*w + 28]', '[659, 659, -w^3 + 6*w^2 - w - 27]', '[659, 659, -w^3 - 3*w^2 + 8*w + 23]', '[659, 659, -w^3 + 7*w^2 - w - 33]', '[691, 691, w^3 - w^2 - 8*w + 2]', '[691, 691, 2*w^3 - 2*w^2 - 11*w + 1]', '[701, 701, -w^3 - w^2 + 7*w + 15]', '[701, 701, -w^3 + 4*w^2 + 2*w - 20]', '[709, 709, -2*w^3 - w^2 + 15*w + 15]', '[709, 709, 2*w^3 - 7*w^2 - 7*w + 27]', '[719, 719, -w^3 - 4*w^2 + 13*w + 26]', '[719, 719, w^3 - 7*w^2 - 2*w + 34]', '[739, 739, 2*w^3 + 2*w^2 - 15*w - 24]', '[739, 739, -2*w^3 + 8*w^2 + 5*w - 35]', '[751, 751, -w^3 - 3*w^2 + 9*w + 25]', '[751, 751, -w^3 + 6*w^2 - 30]', '[761, 761, 3*w^3 - 2*w^2 - 16*w - 8]', '[761, 761, -3*w^3 + 7*w^2 + 11*w - 23]', '[769, 769, -2*w^3 + 4*w^2 + 11*w - 10]', '[769, 769, w^3 + 2*w^2 - 9*w - 12]', '[809, 809, -3*w^3 + 3*w^2 + 16*w + 4]', '[809, 809, w^3 + 5*w^2 - 12*w - 30]', '[811, 811, -w^3 - 4*w^2 + 10*w + 27]', '[811, 811, -2*w^3 + 5*w^2 + 9*w - 14]', '[811, 811, -2*w^3 + w^2 + 13*w + 2]', '[811, 811, -w^3 + 7*w^2 - w - 32]', '[821, 821, 2*w^3 - 8*w^2 - 7*w + 35]', '[821, 821, -2*w^3 - 2*w^2 + 17*w + 22]', '[829, 829, -3*w^3 + 20*w + 13]', '[829, 829, -w^3 + 7*w^2 - w - 36]', '[829, 829, w^3 + 4*w^2 - 10*w - 31]', '[829, 829, 2*w^3 - 3*w^2 - 11*w + 14]', '[859, 859, -w^3 + 7*w^2 - 3*w - 31]', '[859, 859, 7*w^2 - 9*w - 39]', '[859, 859, 7*w^2 - 5*w - 41]', '[859, 859, 3*w^3 - 4*w^2 - 17*w + 2]', '[929, 929, w^3 + 5*w^2 - 14*w - 31]', '[929, 929, -2*w^3 + 4*w^2 + 10*w - 5]', '[929, 929, w^3 - 9*w^2 + 4*w + 44]', '[929, 929, -w^3 + 8*w^2 + w - 39]', '[941, 941, -w^3 + 7*w^2 - 34]', '[941, 941, w^3 + 4*w^2 - 11*w - 28]', '[961, 31, -5*w^2 + 5*w + 28]', '[971, 971, -3*w^3 + w^2 + 19*w + 14]', '[971, 971, -3*w^3 + 8*w^2 + 12*w - 31]', '[991, 991, -w^3 - 5*w^2 + 11*w + 35]', '[991, 991, w^3 - 8*w^2 + 2*w + 40]']}
• 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': [29, 11, -10, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 12725, 'disc_rad': 2545, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[4, 1]]], [5, [0]], [7, [[4, 1]]], [11, [[1, 4]]], [13, [[4, 1]]], [17, [[2, 2]]], [19, [[2, 1], [1, 2]]], [23, [[2, 2]]], [29, [[1, 4]]], [31, [[2, 1], [1, 2]]], [37, [[2, 2]]], [41, [[2, 1], [1, 2]]], [43, [[2, 2]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 50.44799302251776, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.12725.1', 'local_algs': ['5.4.2.1', 'm509.1.2.0', 'm509.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 509], 'rd': 10.6209764959, 'regulator': {'__RealLiteral__': 0, 'data': '4.4100184951', 'prec': 40}, 'res': {'gal': ['176,1120,-552,-1086,419,146,-44,-4,1'], 'sib': ['5,0,-23,0,1', '176,1120,-552,-1086,419,146,-44,-4,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a - 6 \\)', '\\( 2 a^{2} - 3 a - 10 \\)', '\\( a - 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}