Hilbert modular form data - 4.4.5725.1-31.2-c

Formats: - HTML - YAML - JSON - 2024-05-04T15:07:51.201620

• 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': 5725, 'field_bad_primes': [5, 229], 'field_label': '4.4.5725.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.5725.1-31.2-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [31], 'level_ideal': '[31,31,2/3*w^3 - 7/3*w + 2/3]', 'level_label': '31.2', 'level_norm': 31, 'parallel_weight': 2, 'short_label': '31.2-c', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[31,31,2/3*w^3 - 7/3*w + 2/3]', -1]], 'hecke_eigenvalues': ['e', 'e', '2*e + 5', '-3/2*e - 9/2', '-1/2*e + 5/2', '-1/2*e - 5/2', '-1/2*e - 15/2', '-1/2*e - 3/2', '-2*e - 5', '-1/2*e + 1/2', '-2*e - 7', 1, '4*e + 8', '-7/2*e - 19/2', '-2*e - 4', '-1/2*e - 27/2', '5*e + 11', '-9/2*e - 31/2', '-3/2*e + 7/2', '7/2*e + 17/2', '-2*e + 7', '3*e + 2', '-9/2*e - 13/2', '-7/2*e + 1/2', '3/2*e - 21/2', '-5/2*e + 23/2', '-3*e - 8', '9*e + 21', '4*e + 3', '3/2*e - 27/2', '-1/2*e - 35/2', 'e - 8', '-1/2*e - 21/2', '-5*e - 17', '6*e + 8', '-5/2*e + 11/2', '5*e - 2', '-3/2*e - 39/2', '-2*e + 16', '2*e - 16', '-7*e - 8', -24, '5*e + 12', '-3*e - 14', '5*e + 24', '15/2*e + 57/2', '-23/2*e - 49/2', '4*e + 20', '5*e + 17', '11/2*e + 19/2', '5/2*e - 33/2', '9/2*e + 21/2', '3*e + 20', '13/2*e + 51/2', '7*e + 24', '6*e + 31', '-e + 2', '-15/2*e - 25/2', '-11/2*e - 57/2', '11/2*e + 47/2', 1, '2*e - 7', '1/2*e + 5/2', '-e - 4', '19/2*e + 29/2', '-13/2*e - 1/2', '-5*e - 26', '-21/2*e - 47/2', '-4*e - 19', -23, '15/2*e + 11/2', '2*e - 3', '-7*e - 27', '21/2*e + 65/2', '6*e - 14', '7*e + 2', '-e - 21', '-27/2*e - 53/2', '15*e + 36', '7/2*e - 7/2', '5*e - 5', '3*e + 28', '-7*e + 6', '-11/2*e - 29/2', '-9*e - 14', '-6*e - 13', '5*e + 4', '-31/2*e - 61/2', '10*e + 16', 'e + 8', '-13/2*e - 45/2', '9/2*e - 29/2', '8*e + 25', '10*e + 24', '5*e + 24', '31/2*e + 43/2', '-11/2*e - 61/2', '-19/2*e - 17/2', -15, '15/2*e - 25/2', '3*e + 29', '-7*e + 1', 'e - 28', '-5*e - 13', '-10*e - 3', '2*e - 11', '5*e + 40', '-11/2*e - 33/2', '17/2*e + 3/2', '6*e - 10', '3*e + 34', '31/2*e + 65/2', '-7/2*e - 21/2', '-15/2*e - 11/2', '23/2*e + 5/2', '-9*e - 3', '3*e + 11', '-3*e + 6', '-4*e + 12', '5/2*e + 15/2', '-6*e - 5', '-8*e + 11', '-13/2*e - 67/2', '17/2*e + 69/2', '9/2*e + 53/2', '-6*e + 13', '-11/2*e - 33/2', '5*e - 13', '-23/2*e - 21/2', '-13*e - 5', '-3*e - 40', '17/2*e + 9/2', '43/2*e + 91/2', '-5/2*e - 17/2', '5/2*e - 17/2', '-25/2*e - 79/2', '-1/2*e + 19/2', '5*e + 10', '7*e - 13', '27/2*e + 19/2', '-5/2*e + 1/2', '-12*e - 20', '13*e + 10', '-29/2*e - 23/2', '6*e + 22', '-4*e - 23', '-7*e + 10', '-9*e - 19', '4*e + 13', '7/2*e - 67/2', '-10*e + 7', '-15/2*e - 29/2', '27/2*e + 75/2', '-3*e - 26', '-1/2*e - 85/2', '-15*e - 44', '-3/2*e + 1/2', 21, '-21/2*e - 3/2', '11*e + 29', '-13/2*e - 33/2', '18*e + 43', 'e + 36', '19/2*e + 107/2', '12*e + 19', -35, '-3*e - 2', '-27/2*e - 59/2', '11*e + 50', '3/2*e + 87/2', '-16*e - 17'], 'hecke_polynomial': 'x^2 + 4*x - 1', 'label': '4.4.5725.1-31.2-c'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 5725, 'ideals': ['[1, 1, 1]', '[9, 3, 1/3*w^3 - 8/3*w - 2/3]', '[9, 3, -w + 1]', '[11, 11, w]', '[11, 11, -1/3*w^3 + 2/3*w + 5/3]', '[11, 11, 1/3*w^3 - 8/3*w + 1/3]', '[11, 11, -2/3*w^3 + 13/3*w + 4/3]', '[16, 2, 2]', '[25, 5, 2/3*w^3 - 10/3*w - 1/3]', '[29, 29, -w - 3]', '[29, 29, -1/3*w^3 + 8/3*w - 10/3]', '[31, 31, w^3 - 6*w + 1]', '[31, 31, w^3 - 6*w - 2]', '[41, 41, 2/3*w^3 + w^2 - 13/3*w - 10/3]', '[41, 41, 2/3*w^3 - 13/3*w + 5/3]', '[59, 59, 2/3*w^3 - 13/3*w + 8/3]', '[59, 59, w^3 + w^2 - 6*w - 4]', '[79, 79, 2/3*w^3 + w^2 - 10/3*w - 19/3]', '[79, 79, 1/3*w^3 + w^2 - 2/3*w - 17/3]', '[81, 3, 3]', '[81, 9, 2/3*w^3 - w^2 - 10/3*w + 8/3]', '[81, 9, -w^3 - w^2 + 5*w + 6]', '[89, 89, 4/3*w^3 - 23/3*w - 5/3]', '[89, 89, 1/3*w^3 + 2*w^2 - 5/3*w - 32/3]', '[99, 33, 1/3*w^3 - 8/3*w - 11/3]', '[99, 33, w^2 - w - 6]', '[99, 33, -w^2 + w]', '[99, 33, -w^3 - 2*w^2 + 5*w + 7]', '[99, 33, 2/3*w^3 + w^2 - 13/3*w - 7/3]', '[99, 33, -2/3*w^3 - w^2 + 13/3*w + 25/3]', '[99, 33, -1/3*w^3 + 2*w^2 + 5/3*w - 31/3]', '[99, 33, -w + 4]', '[101, 101, 5/3*w^3 + w^2 - 31/3*w - 16/3]', '[101, 101, 2/3*w^3 - w^2 - 4/3*w + 8/3]', '[109, 109, -w^3 - 2*w^2 + 7*w + 7]', '[109, 109, -1/3*w^3 + 2*w^2 + 2/3*w - 16/3]', '[121, 11, -2/3*w^3 + w^2 + 13/3*w - 11/3]', '[121, 11, -w^3 + 5*w]', '[121, 11, 4/3*w^3 + w^2 - 23/3*w - 11/3]', '[121, 11, -1/3*w^3 + w^2 + 5/3*w - 4/3]', '[121, 11, -w^3 + 5*w + 1]', '[121, 11, 2/3*w^3 - w^2 - 7/3*w + 14/3]', '[121, 121, 1/3*w^3 - 11/3*w + 7/3]', '[121, 121, 1/3*w^3 - 11/3*w - 5/3]', '[121, 121, 4/3*w^3 + w^2 - 17/3*w - 11/3]', '[121, 121, 4/3*w^3 - w^2 - 23/3*w + 16/3]', '[131, 131, w^3 - w^2 - 7*w + 5]', '[131, 131, -2/3*w^3 - w^2 + 4/3*w + 13/3]', '[139, 139, -2/3*w^3 - w^2 + 13/3*w + 4/3]', '[139, 139, w^2 - w - 7]', '[144, 6, 2/3*w^3 - 16/3*w - 4/3]', '[144, 6, -2*w + 2]', '[151, 151, -5/3*w^3 + 28/3*w - 5/3]', '[151, 151, -1/3*w^3 + w^2 + 2/3*w - 16/3]', '[151, 151, w^3 + w^2 - 6*w - 3]', '[151, 151, -w^3 + w^2 + 7*w - 6]', '[176, 22, 2*w]', '[176, 22, -2/3*w^3 + 4/3*w + 10/3]', '[176, 22, 2/3*w^3 - 16/3*w + 2/3]', '[176, 22, -4/3*w^3 + 26/3*w + 8/3]', '[179, 179, 5/3*w^3 + w^2 - 28/3*w - 19/3]', '[179, 179, -1/3*w^3 + w^2 + 11/3*w - 4/3]', '[181, 181, -4/3*w^3 - 2*w^2 + 20/3*w + 29/3]', '[181, 181, 1/3*w^3 + w^2 - 2/3*w - 20/3]', '[181, 181, w^3 + w^2 - 5*w - 7]', '[181, 181, 5/3*w^3 + w^2 - 28/3*w - 16/3]', '[191, 191, 2*w - 1]', '[191, 191, 2/3*w^3 - 16/3*w - 1/3]', '[199, 199, 1/3*w^3 - 11/3*w + 4/3]', '[199, 199, 1/3*w^3 - 11/3*w - 2/3]', '[211, 211, -2/3*w^3 - w^2 + 19/3*w + 16/3]', '[211, 211, 2/3*w^3 + w^2 - 19/3*w - 7/3]', '[225, 15, -w^3 - 2*w^2 + 6*w + 10]', '[225, 15, -2*w^2 + w + 7]', '[229, 229, 1/3*w^3 - 11/3*w + 1/3]', '[239, 239, -5/3*w^3 - w^2 + 25/3*w + 19/3]', '[239, 239, -4/3*w^3 + w^2 + 20/3*w - 7/3]', '[251, 251, -2/3*w^3 + w^2 + 16/3*w - 14/3]', '[251, 251, -1/3*w^3 - w^2 - 1/3*w + 14/3]', '[256, 4, 4]', '[261, 87, -4/3*w^3 + 32/3*w + 17/3]', '[261, 87, 4*w - 7]', '[261, 87, w^2 + 2*w - 3]', '[261, 87, -1/3*w^3 + w^2 + 11/3*w - 19/3]', '[269, 269, 2/3*w^3 + w^2 - 7/3*w - 19/3]', '[269, 269, 1/3*w^3 + 2*w^2 - 2/3*w - 32/3]', '[275, 55, 2/3*w^3 + 2*w^2 - 13/3*w - 22/3]', '[275, 55, 1/3*w^3 - 2*w^2 - 2/3*w + 13/3]', '[275, 55, -1/3*w^3 - 2*w^2 + 8/3*w + 29/3]', '[275, 55, 4/3*w^3 + 2*w^2 - 23/3*w - 38/3]', '[279, 93, -2*w^2 - w + 12]', '[279, 93, -2*w^2 + 2*w + 9]', '[279, 93, -4/3*w^3 - 3*w^2 + 23/3*w + 53/3]', '[279, 93, -7/3*w^3 - 3*w^2 + 47/3*w + 59/3]', '[281, 281, w^3 - w^2 - 5*w + 1]', '[281, 281, 4/3*w^3 + w^2 - 20/3*w - 23/3]', '[289, 17, 2/3*w^3 + w^2 - 16/3*w - 4/3]', '[289, 17, 1/3*w^3 + w^2 - 11/3*w - 20/3]', '[319, 319, 4/3*w^3 + 2*w^2 - 17/3*w - 26/3]', '[319, 319, w^3 - 2*w^2 - 6*w + 9]', '[319, 319, -1/3*w^3 - 4/3*w + 11/3]', '[319, 319, -2/3*w^3 + w^2 + 19/3*w - 29/3]', '[319, 319, 8/3*w^3 + w^2 - 55/3*w - 34/3]', '[319, 319, -w^2 - 3*w]', '[319, 319, 2/3*w^3 - w^2 + 5/3*w - 13/3]', '[319, 319, -4/3*w^3 + 29/3*w + 8/3]', '[331, 331, 1/3*w^3 + 2*w^2 - 8/3*w - 23/3]', '[331, 331, 2/3*w^3 + 2*w^2 - 13/3*w - 28/3]', '[341, 341, 5/3*w^3 + 4*w^2 - 31/3*w - 73/3]', '[341, 341, w^3 + 2*w^2 - 8*w - 11]', '[341, 341, 1/3*w^3 - w^2 - 11/3*w + 16/3]', '[341, 341, -4/3*w^3 - 3*w^2 + 29/3*w + 53/3]', '[341, 341, w^3 + 2*w^2 - 5*w - 11]', '[341, 341, -1/3*w^3 - 3*w^2 + 5/3*w + 56/3]', '[341, 341, 11/3*w^3 + 4*w^2 - 70/3*w - 85/3]', '[341, 341, 4/3*w^3 - w^2 - 17/3*w + 1/3]', '[349, 349, 4/3*w^3 - 17/3*w + 1/3]', '[349, 349, -5/3*w^3 + 28/3*w - 2/3]', '[361, 19, -1/3*w^3 + 5/3*w + 14/3]', '[361, 19, 4/3*w^3 - 20/3*w - 5/3]', '[369, 123, -w^3 + 3*w + 4]', '[369, 123, -2*w^3 - 2*w^2 + 11*w + 12]', '[369, 123, w^2 + 2*w - 9]', '[369, 123, 2/3*w^3 + 2*w^2 - 10/3*w - 37/3]', '[379, 379, 4/3*w^3 + 2*w^2 - 23/3*w - 41/3]', '[379, 379, -5/3*w^3 + 31/3*w - 5/3]', '[389, 389, 5/3*w^3 + w^2 - 25/3*w - 16/3]', '[389, 389, -4/3*w^3 + w^2 + 20/3*w - 10/3]', '[400, 10, 4/3*w^3 - 20/3*w - 2/3]', '[401, 401, -1/3*w^3 - 3*w^2 + 5/3*w + 26/3]', '[401, 401, 1/3*w^3 + w^2 - 11/3*w - 23/3]', '[401, 401, -2/3*w^3 - 3*w^2 + 10/3*w + 52/3]', '[401, 401, 2/3*w^3 + w^2 - 16/3*w - 1/3]', '[409, 409, -2*w^3 - w^2 + 11*w + 2]', '[409, 409, -5/3*w^3 - 2*w^2 + 28/3*w + 37/3]', '[409, 409, 1/3*w^3 - 11/3*w - 17/3]', '[409, 409, 5/3*w^3 + 3*w^2 - 25/3*w - 37/3]', '[419, 419, -1/3*w^3 + 3*w^2 - 1/3*w - 37/3]', '[419, 419, 2*w^3 + 3*w^2 - 12*w - 13]', '[421, 421, -1/3*w^3 + 3*w^2 + 2/3*w - 31/3]', '[421, 421, -5/3*w^3 - w^2 + 25/3*w + 13/3]', '[421, 421, -w^3 + 7*w - 4]', '[421, 421, -4/3*w^3 + w^2 + 20/3*w - 13/3]', '[439, 439, -4/3*w^3 + w^2 + 14/3*w - 7/3]', '[439, 439, 4/3*w^3 - 17/3*w - 5/3]', '[439, 439, -7/3*w^3 - w^2 + 41/3*w + 17/3]', '[439, 439, 5/3*w^3 - 28/3*w - 4/3]', '[449, 449, w^3 + 3*w^2 - 6*w - 17]', '[449, 449, 1/3*w^3 + 3*w^2 - 8/3*w - 26/3]', '[449, 449, -4/3*w^3 + 26/3*w + 17/3]', '[449, 449, 7/3*w^3 + w^2 - 38/3*w - 8/3]', '[451, 451, 7/3*w^3 + 3*w^2 - 44/3*w - 50/3]', '[451, 451, 3*w - 4]', '[451, 451, -4/3*w^3 - w^2 + 20/3*w + 26/3]', '[451, 451, -2/3*w^3 - w^2 + 7/3*w + 22/3]', '[451, 451, -2/3*w^3 - 3*w^2 + 13/3*w + 52/3]', '[451, 451, -2/3*w^3 + w^2 - 2/3*w - 2/3]', '[451, 451, 5/3*w^3 + w^2 - 22/3*w - 22/3]', '[451, 451, 2*w^2 + w - 14]', '[461, 461, -5/3*w^3 + w^2 + 28/3*w - 14/3]', '[461, 461, -2/3*w^3 - 2*w^2 + 10/3*w + 43/3]', '[461, 461, -2*w^3 - w^2 + 12*w + 4]', '[461, 461, -w^3 + 8*w - 5]', '[464, 58, -2*w - 6]', '[464, 58, -2/3*w^3 + 16/3*w - 20/3]', '[479, 479, w^3 + w^2 - 7*w - 2]', '[479, 479, -4/3*w^3 - w^2 + 23/3*w + 5/3]', '[496, 62, 2*w^3 - 12*w + 2]', '[496, 62, 2*w^3 - 12*w - 4]', '[499, 499, -4/3*w^3 - 2*w^2 + 23/3*w + 17/3]', '[499, 499, -4/3*w^3 - w^2 + 29/3*w + 8/3]', '[521, 521, 2*w^3 - 11*w + 2]', '[521, 521, 4/3*w^3 - w^2 - 14/3*w + 1/3]', '[531, 177, -w^2 - 3*w + 10]', '[531, 177, -1/3*w^3 - 2*w^2 + 2/3*w + 35/3]', '[531, 177, -8/3*w^3 - 3*w^2 + 46/3*w + 52/3]', '[531, 177, -w^3 - w^2 + 4*w + 7]', '[569, 569, w^3 + 3*w^2 - 6*w - 9]', '[569, 569, 4/3*w^3 + w^2 - 26/3*w - 32/3]', '[569, 569, -w^3 + 6*w - 6]', '[569, 569, -1/3*w^3 - 3*w^2 + 8/3*w + 50/3]', '[571, 571, 2/3*w^3 + 3*w^2 - 10/3*w - 46/3]', '[571, 571, 2*w^2 - 15]', '[599, 599, -w^3 + 2*w^2 + 4*w - 10]', '[599, 599, -w^2 - 3*w + 8]', '[601, 601, 5/3*w^3 + 3*w^2 - 28/3*w - 34/3]', '[601, 601, 1/3*w^3 - 3*w^2 - 2/3*w + 43/3]', '[619, 619, 2/3*w^3 - w^2 - 13/3*w + 2/3]', '[619, 619, 2/3*w^3 + w^2 - 7/3*w - 25/3]', '[619, 619, 2*w^3 + w^2 - 11*w - 6]', '[619, 619, -2/3*w^3 + 13/3*w - 17/3]', '[625, 5, 5]', '[631, 631, 2/3*w^3 + 2*w^2 - 19/3*w - 31/3]', '[631, 631, w^3 + 2*w^2 - 8*w - 6]', '[631, 631, 2/3*w^3 + 2*w^2 - 4/3*w - 31/3]', '[631, 631, -2/3*w^3 + 2*w^2 + 16/3*w - 23/3]', '[649, 649, -1/3*w^3 - 4/3*w + 2/3]', '[649, 649, -1/3*w^3 - 7/3*w + 17/3]', '[649, 649, -5/3*w^3 - 2*w^2 + 28/3*w + 40/3]', '[649, 649, 2*w^3 + 2*w^2 - 10*w - 11]', '[649, 649, 1/3*w^3 - 2*w^2 - 11/3*w + 43/3]', '[649, 649, 10/3*w^3 + 4*w^2 - 62/3*w - 71/3]', '[649, 649, 2/3*w^3 + w^2 - 4/3*w - 22/3]', '[649, 649, 3*w^2 - 16]', '[656, 82, 4/3*w^3 + 2*w^2 - 26/3*w - 20/3]', '[656, 82, 4/3*w^3 - 26/3*w + 10/3]', '[659, 659, -2/3*w^3 + 1/3*w + 16/3]', '[659, 659, 5/3*w^3 - 34/3*w - 13/3]', '[661, 661, w^3 - 8*w + 2]', '[661, 661, 4/3*w^3 + w^2 - 23/3*w + 1/3]', '[661, 661, 5/3*w^3 + w^2 - 31/3*w - 10/3]', '[661, 661, -3*w - 1]', '[691, 691, -4/3*w^3 + 29/3*w + 2/3]', '[691, 691, 1/3*w^3 + 4/3*w - 5/3]', '[691, 691, -5/3*w^3 + w^2 + 25/3*w - 5/3]', '[691, 691, 2*w^3 + w^2 - 10*w - 7]', '[701, 701, -2/3*w^3 - 3*w^2 + 19/3*w + 46/3]', '[701, 701, w^3 - 2*w^2 - 6*w + 8]', '[701, 701, 4/3*w^3 + 2*w^2 - 17/3*w - 29/3]', '[701, 701, 5/3*w^3 + 3*w^2 - 28/3*w - 52/3]', '[709, 709, 1/3*w^3 - 14/3*w + 10/3]', '[709, 709, -2/3*w^3 + 19/3*w + 7/3]', '[711, 237, -w^3 - w^2 + 7*w - 2]', '[711, 237, -8/3*w^3 - 2*w^2 + 49/3*w + 31/3]', '[711, 237, -5/3*w^3 - w^2 + 28/3*w + 4/3]', '[711, 237, -w^3 - w^2 + 7*w + 1]', '[719, 719, 3*w^2 - w - 10]', '[719, 719, -4/3*w^3 - 3*w^2 + 23/3*w + 47/3]', '[725, 145, -8/3*w^3 - 2*w^2 + 43/3*w + 25/3]', '[725, 145, -5/3*w^3 + 2*w^2 + 22/3*w - 26/3]', '[729, 9, w^3 - 8*w - 2]', '[729, 9, -3*w + 3]', '[729, 27, -1/3*w^3 - 2*w^2 + 11/3*w + 35/3]', '[729, 27, w^3 + 2*w^2 - 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29/3*w - 26/3]', '[1441, 1441, 4/3*w^3 + 5*w^2 - 29/3*w - 101/3]', '[1441, 1441, 1/3*w^3 - 4*w^2 - 5/3*w + 82/3]', '[1441, 1441, 5/3*w^3 - 31/3*w + 14/3]', '[1441, 1441, -5/3*w^3 - 4*w^2 + 25/3*w + 22/3]', '[1451, 1451, -1/3*w^3 + 3*w^2 + 5/3*w - 28/3]', '[1451, 1451, 4/3*w^3 + 3*w^2 - 20/3*w - 50/3]', '[1475, 295, 4/3*w^3 - 2*w^2 - 17/3*w + 34/3]', '[1475, 295, -1/3*w^3 - w^2 + 14/3*w + 26/3]', '[1481, 1481, 7/3*w^3 + w^2 - 38/3*w - 17/3]', '[1481, 1481, -w^3 + 6*w - 7]', '[1489, 1489, 7/3*w^3 + 2*w^2 - 41/3*w - 23/3]', '[1489, 1489, -w^3 + 2*w^2 + 3*w - 9]', '[1511, 1511, -1/3*w^3 + w^2 - 1/3*w - 31/3]', '[1511, 1511, 4/3*w^3 + w^2 - 26/3*w + 7/3]', '[1529, 1529, -w^3 - 3*w^2 + 6*w + 14]', '[1529, 1529, 11/3*w^3 + w^2 - 73/3*w - 28/3]', '[1529, 1529, -5/3*w^3 - w^2 + 16/3*w + 22/3]', '[1529, 1529, w^3 - w^2 - 7*w]', '[1529, 1529, 2/3*w^3 + w^2 - 4/3*w - 28/3]', '[1529, 1529, -7/3*w^3 + w^2 + 44/3*w - 7/3]', '[1529, 1529, 4/3*w^3 - w^2 - 2/3*w - 8/3]', '[1529, 1529, 1/3*w^3 + 3*w^2 - 8/3*w - 35/3]', '[1531, 1531, 1/3*w^3 + 3*w^2 - 11/3*w - 35/3]', '[1531, 1531, 4/3*w^3 + 3*w^2 - 26/3*w - 41/3]', '[1549, 1549, -2/3*w^3 + 2*w^2 + 19/3*w - 29/3]', '[1549, 1549, 1/3*w^3 + w^2 - 17/3*w - 8/3]', '[1559, 1559, 3*w^2 - 8]', '[1559, 1559, 2/3*w^3 + w^2 - 22/3*w - 13/3]', '[1559, 1559, w^3 + w^2 - 9*w - 3]', '[1559, 1559, w^3 + 3*w^2 - 5*w - 18]', '[1571, 1571, 2*w^2 + 2*w - 15]', '[1571, 1571, 1/3*w^3 + 4*w^2 - 14/3*w - 56/3]', '[1579, 1579, -2/3*w^3 + 2*w^2 + 7/3*w - 41/3]', '[1579, 1579, 5/3*w^3 + 2*w^2 - 28/3*w - 10/3]', '[1584, 66, 2/3*w^3 - 16/3*w - 22/3]', '[1584, 66, 2*w^2 - 2*w - 12]', '[1584, 66, -2*w^2 + 2*w]', '[1584, 66, -2*w^3 - 4*w^2 + 10*w + 14]', '[1584, 66, 4/3*w^3 + 2*w^2 - 26/3*w - 14/3]', '[1584, 66, -4/3*w^3 - 2*w^2 + 26/3*w + 50/3]', '[1584, 66, -2/3*w^3 + 4*w^2 + 10/3*w - 62/3]', '[1584, 66, -2*w + 8]', '[1601, 1601, -7/3*w^3 + 44/3*w - 7/3]', '[1601, 1601, -1/3*w^3 - 4*w^2 + 2/3*w + 68/3]', '[1609, 1609, -4/3*w^3 - w^2 + 26/3*w - 1/3]', '[1609, 1609, -1/3*w^3 + w^2 - 1/3*w - 25/3]', '[1611, 537, -13/3*w^3 - 5*w^2 + 80/3*w + 86/3]', '[1611, 537, w^3 + w^2 - 10*w - 15]', '[1611, 537, -w^3 - 3*w^2 + 7*w + 12]', '[1611, 537, -w^3 + 3*w - 5]', '[1616, 202, 10/3*w^3 + 2*w^2 - 62/3*w - 32/3]', '[1616, 202, 4/3*w^3 - 2*w^2 - 8/3*w + 16/3]', '[1619, 1619, -w^3 - 3*w^2 + 7*w + 14]', '[1619, 1619, -2/3*w^3 - 3*w^2 + 16/3*w + 34/3]', '[1619, 1619, -2*w^3 + 13*w - 3]', '[1619, 1619, -w^3 + 2*w - 2]', '[1621, 1621, 4/3*w^3 + 2*w^2 - 29/3*w - 17/3]', '[1621, 1621, 1/3*w^3 + 2*w^2 - 14/3*w - 32/3]', '[1629, 543, 13/3*w^3 + 4*w^2 - 74/3*w - 56/3]', '[1629, 543, -2*w^3 - w^2 + 12*w + 2]', '[1629, 543, -w^3 - 2*w^2 + 8*w + 4]', '[1629, 543, 2*w^3 + 2*w^2 - 11*w - 5]', '[1629, 543, -w^3 - 3*w^2 + 6*w + 13]', '[1629, 543, -10/3*w^3 - 3*w^2 + 62/3*w + 47/3]', '[1629, 543, -w^3 - w^2 + 8*w - 3]', '[1629, 543, -4*w^3 - 5*w^2 + 24*w + 28]', '[1661, 1661, -5/3*w^3 - 4*w^2 + 25/3*w + 55/3]', '[1661, 1661, 2*w^3 + 2*w^2 - 9*w - 11]', '[1661, 1661, -7/3*w^3 - 6*w^2 + 41/3*w + 107/3]', '[1661, 1661, 8/3*w^3 + 4*w^2 - 49/3*w - 67/3]', '[1661, 1661, -5/3*w^3 + 2*w^2 + 28/3*w - 20/3]', '[1661, 1661, -2/3*w^3 + 4*w^2 + 13/3*w - 83/3]', '[1661, 1661, 1/3*w^3 + 5*w^2 - 5/3*w - 86/3]', '[1661, 1661, -4/3*w^3 - 2*w^2 + 20/3*w + 41/3]', '[1661, 1661, -1/3*w^3 + 4*w^2 - 4/3*w - 34/3]', '[1661, 1661, -4/3*w^3 + 29/3*w - 19/3]', '[1661, 1661, 2/3*w^3 - 2*w^2 - 10/3*w + 11/3]', '[1661, 1661, -w^2 + 11]', '[1661, 1661, -1/3*w^3 + 3*w^2 + 11/3*w - 34/3]', '[1661, 1661, 2*w^3 - 14*w - 1]', '[1661, 1661, -2/3*w^3 - 2/3*w + 7/3]', '[1661, 1661, -2/3*w^3 - 5*w^2 + 16/3*w + 97/3]', '[1669, 1669, 5/3*w^3 + w^2 - 22/3*w - 28/3]', '[1669, 1669, -5/3*w^3 + w^2 + 28/3*w + 1/3]', '[1681, 41, 2*w^3 - 10*w + 1]', '[1681, 41, 2*w^3 - 10*w - 3]', '[1681, 1681, -w^3 - w^2 + 4*w + 14]', '[1681, 1681, 5/3*w^3 + 5*w^2 - 25/3*w - 76/3]', '[1699, 1699, -w^3 - w^2 + 8*w - 2]', '[1699, 1699, 1/3*w^3 + w^2 - 14/3*w - 29/3]', '[1709, 1709, w^3 + 3*w^2 - 7*w - 13]', '[1709, 1709, 2/3*w^3 + 3*w^2 - 16/3*w - 37/3]', '[1711, 1711, 2/3*w^3 + w^2 - 22/3*w - 10/3]', '[1711, 1711, w^3 + w^2 - 9*w - 4]', '[1711, 1711, -2/3*w^3 + 2*w^2 + 1/3*w - 23/3]', '[1711, 1711, -7/3*w^3 - 2*w^2 + 44/3*w + 26/3]', '[1719, 573, -2*w^2 + 3*w - 1]', '[1719, 573, 1/3*w^3 - 8/3*w - 20/3]', '[1719, 573, -5/3*w^3 - 2*w^2 + 34/3*w + 52/3]', '[1719, 573, -w + 7]', '[1744, 218, -2*w^3 - 4*w^2 + 14*w + 14]', '[1744, 218, -2/3*w^3 + 4*w^2 + 4/3*w - 32/3]', '[1759, 1759, -4/3*w^3 + w^2 + 29/3*w - 1/3]', '[1759, 1759, -2/3*w^3 - w^2 + 1/3*w + 28/3]', '[1791, 597, -2/3*w^3 - w^2 + 13/3*w + 34/3]', '[1791, 597, -4/3*w^3 - w^2 + 29/3*w + 38/3]', '[1791, 597, w^2 - w + 3]', '[1791, 597, w^2 - 3*w + 5]', '[1801, 1801, 1/3*w^3 - 2*w^2 - 14/3*w + 52/3]', '[1801, 1801, 4/3*w^3 + 4*w^2 - 32/3*w - 59/3]', '[1811, 1811, -7/3*w^3 + w^2 + 47/3*w - 28/3]', '[1811, 1811, 2*w^3 + 4*w^2 - 13*w - 13]', '[1829, 1829, 8/3*w^3 + w^2 - 55/3*w - 25/3]', '[1829, 1829, w^3 + 2*w^2 - 8*w - 18]', '[1829, 1829, -5/3*w^3 - w^2 + 40/3*w + 4/3]', '[1829, 1829, -10/3*w^3 - 4*w^2 + 59/3*w + 53/3]', '[1849, 43, 3*w^3 + 2*w^2 - 15*w - 12]', '[1849, 43, -2/3*w^3 + 2*w^2 + 16/3*w - 53/3]', '[1861, 1861, -5/3*w^3 - 2*w^2 + 31/3*w - 2/3]', '[1861, 1861, -2/3*w^3 + 4*w^2 + 7/3*w - 56/3]', '[1871, 1871, -5/3*w^3 + 2*w^2 + 34/3*w - 23/3]', '[1871, 1871, -8/3*w^3 + w^2 + 49/3*w - 26/3]', '[1879, 1879, 2/3*w^3 + w^2 - 4/3*w - 31/3]', '[1879, 1879, w^3 - w^2 - 7*w - 1]', '[1899, 633, 10/3*w^3 + 2*w^2 - 65/3*w - 62/3]', '[1899, 633, -7/3*w^3 - 2*w^2 + 41/3*w + 56/3]', '[1899, 633, w^3 - 2*w^2 - 3*w - 2]', '[1899, 633, -w^3 + 2*w^2 + 5]', '[1901, 1901, -1/3*w^3 + 3*w^2 + 11/3*w - 64/3]', '[1901, 1901, -2/3*w^3 - 3*w^2 + 4/3*w + 16/3]', '[1936, 22, -4/3*w^3 + 2*w^2 + 26/3*w - 22/3]', '[1936, 22, -2*w^3 + 10*w]', '[1936, 22, 8/3*w^3 + 2*w^2 - 46/3*w - 22/3]', '[1936, 22, -2/3*w^3 + 2*w^2 + 10/3*w - 8/3]', '[1936, 22, -2*w^3 + 10*w + 2]', '[1936, 22, 4/3*w^3 - 2*w^2 - 14/3*w + 28/3]', '[1936, 242, 2/3*w^3 - 22/3*w + 14/3]', '[1936, 242, 2/3*w^3 - 22/3*w - 10/3]', '[1936, 242, 8/3*w^3 + 2*w^2 - 34/3*w - 22/3]', '[1936, 242, 8/3*w^3 - 2*w^2 - 46/3*w + 32/3]', '[1949, 1949, 11/3*w^3 + w^2 - 64/3*w - 7/3]', '[1949, 1949, 7/3*w^3 + 4*w^2 - 44/3*w - 50/3]', '[1951, 1951, -4/3*w^3 - w^2 + 17/3*w + 32/3]', '[1951, 1951, 4/3*w^3 + 2*w^2 - 17/3*w - 35/3]', '[1969, 1969, -8/3*w^3 - 4*w^2 + 52/3*w + 67/3]', '[1969, 1969, 2/3*w^3 + 2*w^2 - 19/3*w - 49/3]', '[1969, 1969, 6*w^3 + 6*w^2 - 37*w - 39]', '[1969, 1969, -8/3*w^3 - 3*w^2 + 58/3*w + 79/3]', '[1969, 1969, 8/3*w^3 + 4*w^2 - 49/3*w - 55/3]', '[1969, 1969, 2/3*w^3 + w^2 + 2/3*w + 11/3]', '[1969, 1969, 2/3*w^3 - 2*w^2 - 10/3*w + 5/3]', '[1969, 1969, -8/3*w^3 - 2*w^2 + 37/3*w + 19/3]', '[1975, 395, -4/3*w^3 + w^2 + 26/3*w - 1/3]', '[1975, 395, -1/3*w^3 + 3*w^2 + 8/3*w - 31/3]', '[1979, 1979, -5/3*w^3 - w^2 + 19/3*w + 25/3]', '[1979, 1979, -2/3*w^3 + 3*w^2 + 10/3*w - 29/3]', '[1979, 1979, 5/3*w^3 + 3*w^2 - 25/3*w - 49/3]', '[1979, 1979, 2*w^3 - w^2 - 12*w + 1]', '[1991, 1991, -10/3*w^3 - 4*w^2 + 53/3*w + 44/3]', '[1991, 1991, -7/3*w^3 - 4*w^2 + 44/3*w + 68/3]', '[1991, 1991, 8/3*w^3 - 46/3*w - 1/3]', '[1991, 1991, 1/3*w^3 - 2*w^2 - 8/3*w + 10/3]', '[1991, 1991, -5/3*w^3 + 34/3*w - 14/3]', '[1991, 1991, 8/3*w^3 + 4*w^2 - 46/3*w - 55/3]', '[1991, 1991, 14/3*w^3 + 3*w^2 - 85/3*w - 61/3]', '[1991, 1991, -1/3*w^3 - 2*w^2 + 14/3*w - 4/3]', '[1991, 1991, -16/3*w^3 - 4*w^2 + 95/3*w + 68/3]', '[1991, 1991, 4/3*w^3 + 2*w^2 - 26/3*w - 11/3]', '[1991, 1991, -7/3*w^3 - 2*w^2 + 47/3*w + 26/3]', '[1991, 1991, 3*w^3 + 2*w^2 - 18*w - 9]', '[1991, 1991, 1/3*w^3 - 2*w^2 + 1/3*w - 2/3]', '[1991, 1991, 2*w^3 + 3*w^2 - 13*w - 11]', '[1991, 1991, 16/3*w^3 + 6*w^2 - 98/3*w - 113/3]', '[1991, 1991, w^3 + 2*w^2 - 4*w - 1]', '[1999, 1999, -5/3*w^3 - 2*w^2 + 22/3*w + 34/3]', '[1999, 1999, 4/3*w^3 - 2*w^2 - 23/3*w + 19/3]', '[1999, 1999, 7/3*w^3 + w^2 - 35/3*w - 20/3]', '[1999, 1999, -2*w^3 + w^2 + 10*w - 2]', '[2011, 2011, 7/3*w^3 + 4*w^2 - 38/3*w - 35/3]', '[2011, 2011, -2/3*w^3 + 4*w^2 + 7/3*w - 68/3]', '[2025, 15, 2*w^3 - 10*w - 1]', '[2025, 45, -2/3*w^3 - w^2 + 4/3*w + 34/3]', '[2025, 45, w^3 - 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28/3]', '[9791, 9791, -1/3*w^3 + 3*w^2 - 4/3*w - 52/3]', '[9799, 9799, -4/3*w^3 + 3*w^2 + 14/3*w - 52/3]', '[9799, 9799, -3*w^3 - 3*w^2 + 17*w + 8]', '[9799, 9799, -w^2 - w - 6]', '[9799, 9799, w^2 + w - 15]', '[9801, 33, -2*w^3 + 3*w^2 + 13*w - 11]', '[9801, 33, -3*w^3 + 15*w]', '[9801, 33, 4*w^3 + 3*w^2 - 23*w - 11]', '[9801, 33, -w^3 + 3*w^2 + 5*w - 4]', '[9801, 33, -3*w^3 + 15*w + 3]', '[9801, 33, 2*w^3 - 3*w^2 - 7*w + 14]', '[9801, 99, -4/3*w^3 - 5*w^2 + 26/3*w + 77/3]', '[9801, 99, -2/3*w^3 + 3*w^2 + 16/3*w - 77/3]', '[9801, 99, 2/3*w^3 + 2*w^2 - 1/3*w - 55/3]', '[9801, 99, 11/3*w^3 + 3*w^2 - 70/3*w - 40/3]', '[9801, 99, -8/3*w^3 + 2*w^2 + 34/3*w - 17/3]', '[9801, 99, -2*w^3 + 4*w^2 + 11*w - 15]', '[9801, 99, -w^3 - 5*w^2 + 7*w + 17]', '[9801, 99, 3*w^3 + 4*w^2 - 14*w - 20]', '[9801, 99, -w^3 + 2*w^2 + 8*w]', '[9801, 99, -w^3 - 3*w^2 + 3*w + 1]', '[9801, 99, 2*w^3 + 2*w^2 - 13*w]', '[9801, 99, -4*w^3 - 2*w^2 + 22*w + 11]', '[9801, 363, w^3 - 11*w + 7]', '[9801, 363, w^3 - 11*w - 5]', '[9801, 363, 4*w^3 + 3*w^2 - 17*w - 11]', '[9801, 363, 4*w^3 - 3*w^2 - 23*w + 16]', '[9801, 1089, w^3 - 2*w^2 - 2*w + 12]', '[9801, 1089, 1/3*w^3 + 3*w^2 - 8/3*w - 2/3]', '[9801, 1089, 8/3*w^3 + 2*w^2 - 49/3*w - 13/3]', '[9801, 1089, 3*w^3 - w^2 - 19*w - 1]', '[9801, 1089, -2*w^3 - w^2 + 6*w + 11]', '[9801, 1089, -w^3 - 3*w^2 + 6*w + 25]', '[9801, 1089, -5*w^2 + w + 22]', '[9801, 1089, -2*w^3 - 5*w^2 + 11*w + 21]', '[9819, 3273, 2*w^3 + w^2 - 15*w + 3]', '[9819, 3273, 16/3*w^3 + 3*w^2 - 101/3*w - 50/3]', '[9819, 3273, w^2 - 5*w - 10]', '[9819, 3273, -2*w^3 + 3*w^2 + 3*w - 7]', '[9829, 9829, 2*w^3 + 5*w^2 - 13*w - 19]', '[9829, 9829, 2/3*w^3 + 5*w^2 - 19/3*w - 70/3]', '[9839, 9839, 14/3*w^3 + 3*w^2 - 76/3*w - 58/3]', '[9839, 9839, -10/3*w^3 - 6*w^2 + 56/3*w + 53/3]', '[9859, 9859, 4*w^3 + 3*w^2 - 18*w - 18]', '[9859, 9859, 13/3*w^3 + 4*w^2 - 77/3*w - 53/3]', '[9859, 9859, 13/3*w^3 + 6*w^2 - 80/3*w - 95/3]', '[9859, 9859, 11/3*w^3 - 3*w^2 - 61/3*w + 26/3]', '[9871, 9871, 1/3*w^3 + 5*w^2 - 8/3*w - 59/3]', '[9871, 9871, -2*w^3 - w^2 + 16*w + 7]', '[9889, 9889, 17/3*w^3 + 3*w^2 - 115/3*w - 52/3]', '[9889, 9889, -1/3*w^3 + 6*w^2 + 2/3*w - 67/3]', '[9889, 9889, w^3 + 8*w^2 - 6*w - 47]', '[9889, 9889, 11/3*w^3 - 8*w^2 - 25/3*w + 32/3]', '[9889, 9889, 4/3*w^3 + 7*w^2 - 47/3*w - 77/3]', '[9889, 9889, 20/3*w^3 + 7*w^2 - 121/3*w - 157/3]', '[9889, 9889, -13/3*w^3 + 3*w^2 + 68/3*w - 13/3]', '[9889, 9889, 1/3*w^3 + 10*w^2 - 20/3*w - 71/3]', '[9889, 9889, -w^3 + 4*w^2 + 8*w - 15]', '[9889, 9889, -2*w^3 - 8*w^2 + 11*w + 22]', '[9889, 9889, -8/3*w^3 - 6*w^2 + 43/3*w + 88/3]', '[9889, 9889, -4/3*w^3 - 4*w^2 + 11/3*w + 62/3]', '[9889, 9889, -14/3*w^3 - 10*w^2 + 85/3*w + 184/3]', '[9889, 9889, -5/3*w^3 - 8*w^2 + 49/3*w + 112/3]', '[9889, 9889, -5/3*w^3 + 9*w^2 - 8/3*w - 65/3]', '[9889, 9889, 3*w^3 - 3*w^2 - 13*w]', '[9901, 9901, 8/3*w^3 + 4*w^2 - 55/3*w - 43/3]', '[9901, 9901, 1/3*w^3 + 4*w^2 - 20/3*w - 56/3]', '[9904, 1238, 4/3*w^3 - 2*w^2 - 26/3*w + 4/3]', '[9904, 1238, 4/3*w^3 + 2*w^2 - 14/3*w - 50/3]', '[9904, 1238, 4*w^3 + 2*w^2 - 22*w - 12]', '[9904, 1238, -4/3*w^3 + 26/3*w - 34/3]', '[9931, 9931, -13/3*w^3 - 6*w^2 + 80/3*w + 92/3]', '[9931, 9931, -14/3*w^3 - 4*w^2 + 85/3*w + 58/3]', '[9949, 9949, 13/3*w^3 + 3*w^2 - 68/3*w - 68/3]', '[9949, 9949, -7/3*w^3 + 5*w^2 + 41/3*w - 67/3]', '[9981, 3327, -5*w^3 - w^2 + 36*w + 20]', '[9981, 3327, -10/3*w^3 - 5*w^2 + 56/3*w + 89/3]', '[9981, 3327, -w^3 + 5*w^2 + 3*w - 13]', '[9981, 3327, -2/3*w^3 - 3*w^2 - 2/3*w + 58/3]', '[9981, 3327, -w^3 + w^2 - 6*w + 15]', '[9981, 3327, -4/3*w^3 + 2*w^2 + 29/3*w - 7/3]', '[9981, 3327, -w^3 + 3*w^2 + 9*w - 8]', '[9981, 3327, -w^3 - 2*w^2 + 2*w + 16]', '[9999, 3333, -w^2 - 5*w + 3]', '[9999, 3333, -28/3*w^3 - 8*w^2 + 173/3*w + 143/3]', '[9999, 3333, 2/3*w^3 - 3*w^2 + 2/3*w + 41/3]', '[9999, 3333, -2*w^2 + 4*w - 5]', '[9999, 3333, -5/3*w^3 + w^2 + 7/3*w - 11/3]', '[9999, 3333, -3*w^3 - 3*w^2 + 19*w + 11]', '[9999, 3333, -2*w^3 - 2*w^2 + 14*w + 21]', '[9999, 3333, 2*w^3 - w^2 - 17*w - 8]', '[9999, 3333, -16/3*w^3 + 3*w^2 + 101/3*w - 40/3]', '[9999, 3333, -1/3*w^3 - 5*w^2 + 11/3*w + 71/3]', '[9999, 3333, 4*w^3 + w^2 - 26*w - 3]', '[9999, 3333, w^3 + w^2 - 7*w - 15]', '[9999, 3333, -2*w^3 + 4*w^2 + 9*w - 11]', '[9999, 3333, -7*w^3 - 3*w^2 + 43*w + 21]', '[9999, 3333, -w^3 - 3*w^2 + 10*w + 18]', '[9999, 3333, 12*w^3 + 8*w^2 - 76*w - 53]', '[10000, 10, 10]'], 'label': '4.4.5725.1', 'narrow_class_no': 1, 'primes': ['[9, 3, 1/3*w^3 - 8/3*w - 2/3]', '[9, 3, -w + 1]', '[11, 11, w]', '[11, 11, -1/3*w^3 + 2/3*w + 5/3]', '[11, 11, 1/3*w^3 - 8/3*w + 1/3]', '[11, 11, -2/3*w^3 + 13/3*w + 4/3]', '[16, 2, 2]', '[25, 5, 2/3*w^3 - 10/3*w - 1/3]', '[29, 29, -w - 3]', '[29, 29, -1/3*w^3 + 8/3*w - 10/3]', '[31, 31, w^3 - 6*w + 1]', '[31, 31, w^3 - 6*w - 2]', '[41, 41, 2/3*w^3 + w^2 - 13/3*w - 10/3]', '[41, 41, 2/3*w^3 - 13/3*w + 5/3]', '[59, 59, 2/3*w^3 - 13/3*w + 8/3]', '[59, 59, w^3 + w^2 - 6*w - 4]', '[79, 79, 2/3*w^3 + w^2 - 10/3*w - 19/3]', '[79, 79, 1/3*w^3 + w^2 - 2/3*w - 17/3]', '[89, 89, 4/3*w^3 - 23/3*w - 5/3]', '[89, 89, 1/3*w^3 + 2*w^2 - 5/3*w - 32/3]', '[101, 101, 5/3*w^3 + w^2 - 31/3*w - 16/3]', '[101, 101, 2/3*w^3 - w^2 - 4/3*w + 8/3]', '[109, 109, -w^3 - 2*w^2 + 7*w + 7]', '[109, 109, -1/3*w^3 + 2*w^2 + 2/3*w - 16/3]', '[131, 131, w^3 - w^2 - 7*w + 5]', '[131, 131, -2/3*w^3 - w^2 + 4/3*w + 13/3]', '[139, 139, -2/3*w^3 - w^2 + 13/3*w + 4/3]', '[139, 139, w^2 - w - 7]', '[151, 151, -5/3*w^3 + 28/3*w - 5/3]', '[151, 151, -1/3*w^3 + w^2 + 2/3*w - 16/3]', '[151, 151, w^3 + w^2 - 6*w - 3]', '[151, 151, -w^3 + w^2 + 7*w - 6]', '[179, 179, 5/3*w^3 + w^2 - 28/3*w - 19/3]', '[179, 179, -1/3*w^3 + w^2 + 11/3*w - 4/3]', '[181, 181, -4/3*w^3 - 2*w^2 + 20/3*w + 29/3]', '[181, 181, 1/3*w^3 + w^2 - 2/3*w - 20/3]', '[181, 181, w^3 + w^2 - 5*w - 7]', '[181, 181, 5/3*w^3 + w^2 - 28/3*w - 16/3]', '[191, 191, 2*w - 1]', '[191, 191, 2/3*w^3 - 16/3*w - 1/3]', '[199, 199, 1/3*w^3 - 11/3*w + 4/3]', '[199, 199, 1/3*w^3 - 11/3*w - 2/3]', '[211, 211, -2/3*w^3 - w^2 + 19/3*w + 16/3]', '[211, 211, 2/3*w^3 + w^2 - 19/3*w - 7/3]', '[229, 229, 1/3*w^3 - 11/3*w + 1/3]', '[239, 239, -5/3*w^3 - w^2 + 25/3*w + 19/3]', '[239, 239, -4/3*w^3 + w^2 + 20/3*w - 7/3]', '[251, 251, -2/3*w^3 + w^2 + 16/3*w - 14/3]', '[251, 251, -1/3*w^3 - w^2 - 1/3*w + 14/3]', '[269, 269, 2/3*w^3 + w^2 - 7/3*w - 19/3]', '[269, 269, 1/3*w^3 + 2*w^2 - 2/3*w - 32/3]', '[281, 281, w^3 - w^2 - 5*w + 1]', '[281, 281, 4/3*w^3 + w^2 - 20/3*w - 23/3]', '[289, 17, 2/3*w^3 + w^2 - 16/3*w - 4/3]', '[289, 17, 1/3*w^3 + w^2 - 11/3*w - 20/3]', '[331, 331, 1/3*w^3 + 2*w^2 - 8/3*w - 23/3]', '[331, 331, 2/3*w^3 + 2*w^2 - 13/3*w - 28/3]', '[349, 349, 4/3*w^3 - 17/3*w + 1/3]', '[349, 349, -5/3*w^3 + 28/3*w - 2/3]', '[361, 19, -1/3*w^3 + 5/3*w + 14/3]', '[361, 19, 4/3*w^3 - 20/3*w - 5/3]', '[379, 379, 4/3*w^3 + 2*w^2 - 23/3*w - 41/3]', '[379, 379, -5/3*w^3 + 31/3*w - 5/3]', '[389, 389, 5/3*w^3 + w^2 - 25/3*w - 16/3]', '[389, 389, -4/3*w^3 + w^2 + 20/3*w - 10/3]', '[401, 401, -1/3*w^3 - 3*w^2 + 5/3*w + 26/3]', '[401, 401, 1/3*w^3 + w^2 - 11/3*w - 23/3]', '[401, 401, -2/3*w^3 - 3*w^2 + 10/3*w + 52/3]', '[401, 401, 2/3*w^3 + w^2 - 16/3*w - 1/3]', '[409, 409, -2*w^3 - w^2 + 11*w + 2]', '[409, 409, -5/3*w^3 - 2*w^2 + 28/3*w + 37/3]', '[409, 409, 1/3*w^3 - 11/3*w - 17/3]', '[409, 409, 5/3*w^3 + 3*w^2 - 25/3*w - 37/3]', '[419, 419, -1/3*w^3 + 3*w^2 - 1/3*w - 37/3]', '[419, 419, 2*w^3 + 3*w^2 - 12*w - 13]', '[421, 421, -1/3*w^3 + 3*w^2 + 2/3*w - 31/3]', '[421, 421, -5/3*w^3 - w^2 + 25/3*w + 13/3]', '[421, 421, -w^3 + 7*w - 4]', '[421, 421, -4/3*w^3 + w^2 + 20/3*w - 13/3]', '[439, 439, -4/3*w^3 + w^2 + 14/3*w - 7/3]', '[439, 439, 4/3*w^3 - 17/3*w - 5/3]', '[439, 439, -7/3*w^3 - w^2 + 41/3*w + 17/3]', '[439, 439, 5/3*w^3 - 28/3*w - 4/3]', '[449, 449, w^3 + 3*w^2 - 6*w - 17]', '[449, 449, 1/3*w^3 + 3*w^2 - 8/3*w - 26/3]', '[449, 449, -4/3*w^3 + 26/3*w + 17/3]', '[449, 449, 7/3*w^3 + w^2 - 38/3*w - 8/3]', '[461, 461, -5/3*w^3 + w^2 + 28/3*w - 14/3]', '[461, 461, -2/3*w^3 - 2*w^2 + 10/3*w + 43/3]', '[461, 461, -2*w^3 - w^2 + 12*w + 4]', '[461, 461, -w^3 + 8*w - 5]', '[479, 479, w^3 + w^2 - 7*w - 2]', '[479, 479, -4/3*w^3 - w^2 + 23/3*w + 5/3]', '[499, 499, -4/3*w^3 - 2*w^2 + 23/3*w + 17/3]', '[499, 499, -4/3*w^3 - w^2 + 29/3*w + 8/3]', '[521, 521, 2*w^3 - 11*w + 2]', '[521, 521, 4/3*w^3 - w^2 - 14/3*w + 1/3]', '[569, 569, w^3 + 3*w^2 - 6*w - 9]', '[569, 569, 4/3*w^3 + w^2 - 26/3*w - 32/3]', '[569, 569, -w^3 + 6*w - 6]', '[569, 569, -1/3*w^3 - 3*w^2 + 8/3*w + 50/3]', '[571, 571, 2/3*w^3 + 3*w^2 - 10/3*w - 46/3]', '[571, 571, 2*w^2 - 15]', '[599, 599, -w^3 + 2*w^2 + 4*w - 10]', '[599, 599, -w^2 - 3*w + 8]', '[601, 601, 5/3*w^3 + 3*w^2 - 28/3*w - 34/3]', '[601, 601, 1/3*w^3 - 3*w^2 - 2/3*w + 43/3]', '[619, 619, 2/3*w^3 - w^2 - 13/3*w + 2/3]', '[619, 619, 2/3*w^3 + w^2 - 7/3*w - 25/3]', '[619, 619, 2*w^3 + w^2 - 11*w - 6]', '[619, 619, -2/3*w^3 + 13/3*w - 17/3]', '[631, 631, 2/3*w^3 + 2*w^2 - 19/3*w - 31/3]', '[631, 631, w^3 + 2*w^2 - 8*w - 6]', '[631, 631, 2/3*w^3 + 2*w^2 - 4/3*w - 31/3]', '[631, 631, -2/3*w^3 + 2*w^2 + 16/3*w - 23/3]', '[659, 659, -2/3*w^3 + 1/3*w + 16/3]', '[659, 659, 5/3*w^3 - 34/3*w - 13/3]', '[661, 661, w^3 - 8*w + 2]', '[661, 661, 4/3*w^3 + w^2 - 23/3*w + 1/3]', '[661, 661, 5/3*w^3 + w^2 - 31/3*w - 10/3]', '[661, 661, -3*w - 1]', '[691, 691, -4/3*w^3 + 29/3*w + 2/3]', '[691, 691, 1/3*w^3 + 4/3*w - 5/3]', '[691, 691, -5/3*w^3 + w^2 + 25/3*w - 5/3]', '[691, 691, 2*w^3 + w^2 - 10*w - 7]', '[701, 701, -2/3*w^3 - 3*w^2 + 19/3*w + 46/3]', '[701, 701, w^3 - 2*w^2 - 6*w + 8]', '[701, 701, 4/3*w^3 + 2*w^2 - 17/3*w - 29/3]', '[701, 701, 5/3*w^3 + 3*w^2 - 28/3*w - 52/3]', '[709, 709, 1/3*w^3 - 14/3*w + 10/3]', '[709, 709, -2/3*w^3 + 19/3*w + 7/3]', '[719, 719, 3*w^2 - w - 10]', '[719, 719, -4/3*w^3 - 3*w^2 + 23/3*w + 47/3]', '[739, 739, 5/3*w^3 + w^2 - 34/3*w - 10/3]', '[739, 739, 4/3*w^3 + 2*w^2 - 23/3*w - 14/3]', '[761, 761, 7/3*w^3 + 2*w^2 - 41/3*w - 26/3]', '[761, 761, 2*w^3 + 3*w^2 - 12*w - 15]', '[769, 769, -2/3*w^3 + 19/3*w - 8/3]', '[769, 769, -4/3*w^3 + 2*w^2 + 17/3*w - 31/3]', '[769, 769, 1/3*w^3 - 14/3*w - 5/3]', '[769, 769, -1/3*w^3 + 3*w^2 + 2/3*w - 34/3]', '[809, 809, -4/3*w^3 + w^2 + 26/3*w - 7/3]', '[809, 809, w^3 + w^2 - 3*w - 7]', '[811, 811, 4/3*w^3 + w^2 - 17/3*w - 23/3]', '[811, 811, -1/3*w^3 - 2*w^2 + 2/3*w + 38/3]', '[821, 821, 8/3*w^3 + 3*w^2 - 43/3*w - 34/3]', '[821, 821, 2/3*w^3 + 2*w^2 - 7/3*w - 34/3]', '[821, 821, -w^3 - w^2 + 4*w + 8]', '[821, 821, 2/3*w^3 + 4*w^2 - 7/3*w - 58/3]', '[829, 829, 4/3*w^3 + 3*w^2 - 26/3*w - 50/3]', '[829, 829, 7/3*w^3 - 41/3*w - 5/3]', '[839, 839, 2*w^3 + w^2 - 10*w - 3]', '[839, 839, 5/3*w^3 - w^2 - 25/3*w + 17/3]', '[841, 29, 5/3*w^3 - 25/3*w - 7/3]', '[859, 859, -7/3*w^3 - w^2 + 32/3*w + 29/3]', '[859, 859, 2*w^3 + w^2 - 14*w - 6]', '[859, 859, 1/3*w^3 + 2*w^2 - 2/3*w - 47/3]', '[859, 859, -5/3*w^3 - 2*w^2 + 31/3*w + 49/3]', '[881, 881, w^3 + 4*w^2 - 4*w - 20]', '[881, 881, 8/3*w^3 + 2*w^2 - 43/3*w - 34/3]', '[919, 919, -w^3 + 3*w - 7]', '[919, 919, 1/3*w^3 + 3*w^2 - 5/3*w - 35/3]', '[919, 919, -5/3*w^3 + 31/3*w - 23/3]', '[919, 919, 2/3*w^3 + 3*w^2 - 10/3*w - 43/3]', '[929, 929, w^2 - 2*w - 9]', '[929, 929, w^3 + w^2 - 7*w + 1]', '[961, 31, 2/3*w^3 - 10/3*w - 19/3]', '[971, 971, -w^3 - 3*w^2 + 7*w + 16]', '[971, 971, -5/3*w^3 + w^2 + 25/3*w - 8/3]', '[971, 971, 2*w^3 + w^2 - 10*w - 6]', '[971, 971, 1/3*w^3 + 2*w^2 - 8/3*w - 47/3]']}
• 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, 6, -8, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 5725, 'disc_rad': 1145, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[2, 2]]], [5, [0]], [7, [[4, 1]]], [11, [[1, 4]]], [13, [[4, 1]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[4, 1]]], [29, [[2, 1], [1, 2]]], [31, [[2, 1], [1, 2]]], [37, [[2, 2]]], [41, [[2, 1], [1, 2]]], [43, [[2, 2]]], [47, [[4, 1]]], [53, [[2, 2]]], [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': 33.83784863137726, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.5725.1', 'local_algs': ['5.4.2.1', 'm229.1.2.0', 'm229.2.1.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 229], 'rd': 8.69849008461, 'regulator': {'__RealLiteral__': 0, 'data': '3.06647090016', 'prec': 44}, 'res': {'gal': ['16,0,-140,0,257,0,-35,0,1'], 'sib': ['-1,15,-14,-2,1', '16,0,-140,0,257,0,-35,0,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{3} a^{3} - \\frac{5}{3} a + \\frac{1}{3} \\)', '\\( \\frac{1}{3} a^{3} - \\frac{2}{3} a - \\frac{2}{3} \\)', '\\( \\frac{1}{3} a^{3} - \\frac{8}{3} a - \\frac{5}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/3*a^3 + 1/3*a + 1/3']}