Hilbert modular form data - 4.4.5225.1-44.4-f

Formats: - HTML - YAML - JSON - 2024-05-04T02:35:13.215364

• 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': 3, 'disc': 5225, 'field_bad_primes': [5, 11, 19], 'field_label': '4.4.5225.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.5225.1-44.4-f', 'label_nsuffix': 5, 'label_suffix': 'f', 'level_bad_primes': [2, 11], 'level_ideal': '[44, 22, -w^2 + w + 2]', 'level_label': '44.4', 'level_norm': 44, 'parallel_weight': 2, 'short_label': '44.4-f', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4, 2, w + 1]', -1], ['[11, 11, -w + 2]', -1]], 'hecke_eigenvalues': ['e', 1, '-1/2*e^2 + 5/2', '1/2*e^2 + e - 11/2', 1, '-1/2*e^2 + e + 11/2', 4, '-2*e - 2', '-1/2*e^2 + 1/2', '-e^2 - 2*e + 7', 'e^2 - 9', '-2*e + 6', '1/2*e^2 + 2*e - 9/2', '-e^2 + 9', 6, '-1/2*e^2 + 9/2', 'e^2 - 4*e - 13', '-1/2*e^2 + 3*e + 23/2', '-e^2 + 2*e + 7', 'e^2 - 9', 2, '1/2*e^2 - e - 11/2', 'e^2 + 2*e + 1', -8, '-2*e^2 - 2*e + 16', '-e^2 + 2*e + 15', '3/2*e^2 - 2*e - 39/2', '-2*e^2 + 14', '-3*e^2 - 2*e + 15', '-3/2*e^2 + e + 13/2', '3/2*e^2 - 35/2', '1/2*e^2 - e - 19/2', -2, '-3/2*e^2 + 4*e + 31/2', '-2*e^2 - 4*e + 20', '-6*e + 2', 'e^2 - 2*e - 11', '1/2*e^2 - 5*e - 11/2', '-1/2*e^2 + 4*e - 3/2', '-1/2*e^2 + 3*e + 7/2', '-1/2*e^2 + 2*e + 9/2', 2, '2*e^2 - 2*e - 16', '-1/2*e^2 - 2*e + 5/2', '-e^2 - 2*e + 27', '-3*e^2 + 23', '-5/2*e^2 + e + 55/2', 'e^2 + 4*e - 9', '-1/2*e^2 - 5*e + 27/2', '2*e^2 + 4*e - 6', 22, '-4*e - 2', '3*e^2 - 2*e - 21', '-5/2*e^2 - 6*e + 53/2', '-3/2*e^2 + 7/2', '-e^2 + 13', '-2*e - 2', '4*e^2 - 24', '-e^2 + 2*e + 21', '3*e^2 - 4*e - 27', '3*e^2 - 2*e - 13', '5/2*e^2 + e - 31/2', '8*e', 'e^2 + 2*e + 5', '3/2*e^2 - 39/2', '-3*e^2 - 4*e + 25', '7/2*e^2 - 2*e - 63/2', 'e^2 - 1', '4*e^2 - 2*e - 26', '5/2*e^2 - 41/2', '-1/2*e^2 - 2*e + 61/2', 'e^2 + 6*e - 3', '-1/2*e^2 - 4*e - 3/2', 'e^2 - 2*e - 9', '-e^2 - 8*e + 5', '-9/2*e^2 - 3*e + 67/2', '5/2*e^2 - 3*e - 19/2', '-5*e^2 + 31', '-5/2*e^2 + 4*e + 73/2', '3*e^2 - 3', '-5/2*e^2 + 2*e + 29/2', '3*e^2 + 4*e - 25', '-2*e^2 + 4*e + 12', 'e^2 - 4*e + 5', '2*e^2 + 4*e - 38', '-3/2*e^2 + e + 21/2', 'e^2 - 4*e - 5', '4*e^2 - 38', '2*e^2 - 10', '-2*e^2 + 4*e + 38', '9/2*e^2 + 5*e - 83/2', 'e^2 + 1', '-1/2*e^2 - 11*e + 11/2', '4*e^2 - 6*e - 32', '-5/2*e^2 - 12*e + 57/2', '4*e^2 - 2*e - 44', 'e^2 + 21', '-5*e^2 - 4*e + 27', '-7/2*e^2 - e + 37/2', '-11/2*e^2 - 6*e + 67/2', '-4*e^2 - 4*e + 30', '-13/2*e^2 - e + 67/2', '-3*e^2 + 12*e + 35', '-e^2 - 8*e + 21', '-4*e^2 + 4*e + 36', '-e^2 - 6*e - 5', '11/2*e^2 + e - 53/2', '2*e - 6', 'e^2 + 10*e - 5', '3*e^2 + 4*e - 47', '-3*e^2 - 2*e + 1', '9/2*e^2 - e - 75/2', '7/2*e^2 + 2*e - 55/2', '-2*e^2 - 6*e - 6', '-e^2 - 2*e + 15', '-5/2*e^2 - 3*e - 25/2', '4*e^2 + 4*e - 12', '3/2*e^2 - 3*e - 57/2', '5*e^2 + 2*e - 31', '-3/2*e^2 + 7*e + 37/2', '-3/2*e^2 + 10*e + 7/2', '3*e^2 + 2*e - 27', '3*e^2 - 4*e - 19', '5/2*e^2 + 9*e - 75/2', '-5/2*e^2 - e + 55/2', '-5*e^2 + 4*e + 31', '3*e^2 - 4*e - 41', '-2*e^2 - 2*e + 16', '5*e^2 - 4*e - 39', '-2*e^2 - 4*e + 22', 'e^2 + 8*e - 25', 'e^2 + 10*e - 11', '1/2*e^2 + 4*e + 19/2', '5/2*e^2 + 10*e - 53/2', '-7*e^2 - 6*e + 49', '7/2*e^2 + 3*e - 57/2', '5/2*e^2 - e - 55/2', '-2*e + 4', '7/2*e^2 - 2*e - 79/2', '-4*e^2 - 8*e + 12', '-1/2*e^2 + 6*e - 27/2', '-4*e^2 - 14*e + 44', '-7/2*e^2 - 2*e + 31/2', 'e^2 - 6*e + 15', '7/2*e^2 - 6*e - 95/2', '-6*e^2 - 4*e + 34', '3*e^2 + 2*e - 45', 'e^2 + 4*e - 39', '2*e^2 - 6*e + 8', '-1/2*e^2 + 8*e + 45/2', '8*e^2 - 62', '-3*e^2 + 2*e + 39', '-3/2*e^2 - 4*e - 25/2', '-5*e^2 - 4*e + 31', '-6*e - 18', '-e^2 + 4*e - 1', 'e^2 - 6*e - 13', '-5*e^2 - 10*e + 47', '2*e^2 + 12*e + 2', '-e^2 - 6*e - 9'], 'hecke_polynomial': 'x^3 + x^2 - 11*x - 7', 'label': '4.4.5225.1-44.4-f'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 5225, 'ideals': ['[1, 1, 1]', '[4, 2, -1/2*w^3 + w^2 + 3*w - 7/2]', '[4, 2, w + 1]', '[11, 11, w]', '[11, 11, 1/2*w^3 - w^2 - 3*w + 5/2]', '[11, 11, -w + 2]', '[16, 2, 2]', '[16, 4, -1/2*w^3 + w^2 + w - 7/2]', '[16, 4, w^3 - 2*w^2 - 5*w + 6]', '[19, 19, -1/2*w^3 + 3*w + 3/2]', '[25, 5, -w^3 + 2*w^2 + 4*w - 4]', '[31, 31, w^3 - 2*w^2 - 5*w + 3]', '[31, 31, -1/2*w^3 + w^2 + w - 1/2]', '[44, 22, 1/2*w^3 - w^2 - 3*w + 11/2]', '[44, 22, -w - 3]', '[44, 22, -3/2*w^3 + 4*w^2 + 4*w - 19/2]', '[44, 22, -w^2 + w + 2]', '[44, 22, -w^3 + w^2 + 6*w]', '[44, 22, -w^3 + 3*w^2 + 3*w - 10]', '[59, 59, 1/2*w^3 - w^2 - 4*w + 15/2]', '[59, 59, 1/2*w^3 - w^2 - 4*w - 5/2]', '[61, 61, -2*w^3 + 5*w^2 + 8*w - 12]', '[61, 61, 1/2*w^3 - 2*w - 5/2]', '[64, 4, -w^3 + 2*w^2 + 6*w - 7]', '[64, 4, 2*w + 2]', '[64, 8, 1/2*w^3 - w^2 - w - 1/2]', '[64, 8, w^3 - 2*w^2 - 5*w + 2]', '[71, 71, -1/2*w^3 + 2*w^2 - 15/2]', '[71, 71, 3/2*w^3 - 4*w^2 - 5*w + 23/2]', '[76, 38, w^3 - 3*w^2 - 4*w + 6]', '[76, 38, 1/2*w^3 - 2*w^2 - 2*w + 17/2]', '[79, 79, -5/2*w^3 + 6*w^2 + 9*w - 31/2]', '[79, 79, -4*w^3 + 10*w^2 + 17*w - 28]', '[79, 79, -w^3 + w^2 + 4*w + 1]', '[79, 79, 5/2*w^3 - 6*w^2 - 9*w + 23/2]', '[81, 3, -3]', '[89, 89, 2*w^3 - 4*w^2 - 9*w + 6]', '[89, 89, -1/2*w^3 + w + 3/2]', '[100, 10, 5/2*w^3 - 7*w^2 - 9*w + 39/2]', '[100, 10, -2*w^2 + w + 7]', '[101, 101, 1/2*w^3 - 5*w - 9/2]', '[101, 101, -5/2*w^3 + 7*w^2 + 9*w - 37/2]', '[121, 11, 3/2*w^3 - 3*w^2 - 6*w + 11/2]', '[121, 11, 5/2*w^3 - 7*w^2 - 7*w + 33/2]', '[121, 11, 3/2*w^3 - 3*w^2 - 6*w + 13/2]', '[121, 11, 1/2*w^3 - 2*w^2 + 19/2]', '[121, 121, -3/2*w^3 + 3*w^2 + 5*w - 11/2]', '[121, 121, -2*w^3 + 4*w^2 + 9*w - 8]', '[124, 62, -w^2 + 2*w + 1]', '[124, 62, -2*w^3 + 4*w^2 + 9*w - 9]', '[124, 62, 3/2*w^3 - 3*w^2 - 5*w + 13/2]', '[124, 62, -1/2*w^3 + 2*w^2 - 17/2]', '[131, 131, 1/2*w^3 - 4*w - 1/2]', '[131, 131, -w^3 + 3*w^2 + 2*w - 9]', '[139, 139, -w^3 + 2*w^2 + 6*w - 6]', '[139, 139, -2*w - 1]', '[149, 149, w^2 - 6]', '[149, 149, -3/2*w^3 + 4*w^2 + 6*w - 17/2]', '[151, 151, w^3 - w^2 - 6*w + 1]', '[151, 151, 2*w - 1]', '[151, 151, -w^3 + 2*w^2 + 6*w - 4]', '[151, 151, 3/2*w^3 - 4*w^2 - 4*w + 21/2]', '[169, 13, 7/2*w^3 - 9*w^2 - 13*w + 43/2]', '[169, 13, -1/2*w^3 + 2*w^2 + 4*w - 3/2]', '[176, 22, 2*w]', '[176, 22, w^3 - 2*w^2 - 6*w + 5]', '[176, 22, -2*w + 4]', '[176, 44, -3/2*w^3 + 5*w^2 + 5*w - 33/2]', '[176, 44, w^3 - 4*w^2 - 3*w + 10]', '[176, 44, -1/2*w^3 + 2*w + 7/2]', '[176, 44, -w^3 + w^2 + 7*w + 1]', '[176, 44, 2*w^3 - 5*w^2 - 8*w + 11]', '[176, 44, -w^3 + 3*w^2 + w - 6]', '[179, 179, -1/2*w^3 + w^2 + 4*w - 7/2]', '[179, 179, -1/2*w^3 + w^2 + 4*w - 3/2]', '[181, 181, -1/2*w^3 + 3*w^2 + w - 17/2]', '[181, 181, -2*w^3 + 6*w^2 + 7*w - 18]', '[199, 199, 3/2*w^3 - 2*w^2 - 7*w + 1/2]', '[199, 199, -1/2*w^3 + 2*w^2 - w - 17/2]', '[199, 199, 5/2*w^3 - 6*w^2 - 9*w + 25/2]', '[199, 199, -3*w^3 + 8*w^2 + 11*w - 23]', '[209, 209, -1/2*w^3 + w^2 + 4*w - 5/2]', '[209, 209, 3/2*w^3 - 2*w^2 - 9*w - 3/2]', '[209, 209, 3/2*w^3 - 4*w^2 - 3*w + 11/2]', '[211, 211, -2*w^3 + 6*w^2 + 7*w - 16]', '[211, 211, -1/2*w^3 + 3*w^2 + w - 21/2]', '[211, 211, 1/2*w^3 - 4*w - 13/2]', '[211, 211, -w^3 + 3*w^2 + 2*w - 3]', '[236, 118, -w^2 + 7]', '[236, 118, 3/2*w^3 - 4*w^2 - 6*w + 15/2]', '[236, 118, w^2 - 3*w - 5]', '[236, 118, -w^2 + 3*w + 2]', '[239, 239, 3/2*w^3 - 2*w^2 - 9*w + 7/2]', '[239, 239, 5/2*w^3 - 5*w^2 - 11*w + 17/2]', '[241, 241, -2*w^3 + 4*w^2 + 10*w - 7]', '[241, 241, -2*w^3 + 3*w^2 + 10*w - 4]', '[241, 241, -w^3 + 2*w^2 + 2*w - 2]', '[241, 241, -5/2*w^3 + 6*w^2 + 8*w - 27/2]', '[244, 122, 13/2*w^3 - 17*w^2 - 25*w + 95/2]', '[244, 122, w^3 + 2*w^2 - 5*w - 8]', '[244, 122, 1/2*w^3 - 4*w + 1/2]', '[244, 122, w^3 - 3*w^2 - 2*w + 10]', '[251, 251, -1/2*w^3 + w^2 + w - 13/2]', '[251, 251, 5/2*w^3 - 5*w^2 - 11*w + 25/2]', '[251, 251, -2*w^3 + 4*w^2 + 7*w - 10]', '[251, 251, -w^3 + 2*w^2 + 5*w - 9]', '[256, 4, 4]', '[256, 8, -w^3 + 2*w^2 + 2*w - 7]', '[256, 8, 2*w^3 - 4*w^2 - 10*w + 12]', '[256, 16, 1/2*w^3 - 3*w^2 + w + 27/2]', '[256, 16, 2*w^3 - 5*w^2 - 6*w + 13]', '[269, 269, 1/2*w^3 - 3*w^2 + 13/2]', '[269, 269, -3/2*w^3 + 5*w^2 + 4*w - 35/2]', '[271, 271, -3/2*w^3 + 4*w^2 + 6*w - 13/2]', '[271, 271, -5/2*w^3 + 6*w^2 + 11*w - 29/2]', '[275, 55, w^3 - 4*w^2 - 3*w + 11]', '[275, 55, -3/2*w^3 + 5*w^2 + 5*w - 31/2]', '[275, 55, -3*w^3 + 8*w^2 + 11*w - 19]', '[281, 281, 7/2*w^3 - 10*w^2 - 11*w + 53/2]', '[281, 281, 1/2*w^3 - 5*w - 5/2]', '[281, 281, -1/2*w^3 - 2*w^2 + 5*w + 19/2]', '[281, 281, 3/2*w^3 - 5*w^2 - 5*w + 27/2]', '[284, 142, 5/2*w^3 - 6*w^2 - 10*w + 25/2]', '[284, 142, -11/2*w^3 + 14*w^2 + 22*w - 75/2]', '[284, 142, w^3 - 2*w^2 - 7*w - 2]', '[284, 142, -w^3 + 3*w^2 + 5*w - 5]', '[304, 38, -w^3 + 6*w + 3]', '[304, 76, 2*w^3 - 3*w^2 - 10*w + 3]', '[304, 76, -5/2*w^3 + 6*w^2 + 8*w - 25/2]', '[316, 158, w^3 - 5*w^2 - 4*w + 12]', '[316, 158, 8*w^3 - 21*w^2 - 31*w + 57]', '[316, 158, -w^3 + 5*w^2 - 16]', '[316, 158, -w^3 + w^2 + 3*w - 6]', '[316, 158, 2*w^3 - 5*w^2 - 7*w + 16]', '[316, 158, 1/2*w^3 - 3*w^2 + w + 15/2]', '[316, 158, -6*w^3 + 17*w^2 + 19*w - 43]', '[316, 158, -w^3 - 3*w^2 + 6*w + 12]', '[324, 6, 3/2*w^3 - 3*w^2 - 9*w + 21/2]', '[324, 6, -3*w - 3]', '[331, 331, 3/2*w^3 - 4*w^2 - 7*w + 17/2]', '[331, 331, 1/2*w^3 - 2*w^2 - 3*w + 17/2]', '[341, 341, 1/2*w^3 - 3*w^2 + 11/2]', '[341, 341, 3/2*w^3 - 2*w^2 - 6*w + 5/2]', '[341, 341, 3/2*w^3 - 5*w^2 - 4*w + 37/2]', '[341, 341, 1/2*w^3 - 4*w + 3/2]', '[341, 341, -w^3 + 3*w^2 + 2*w - 11]', '[341, 341, 3*w^3 - 7*w^2 - 12*w + 17]', '[349, 349, 1/2*w^3 + w^2 - 4*w - 9/2]', '[349, 349, 5/2*w^3 - 7*w^2 - 8*w + 39/2]', '[356, 178, -9/2*w^3 + 13*w^2 + 15*w - 75/2]', '[356, 178, 11/2*w^3 - 14*w^2 - 24*w + 91/2]', '[356, 178, 3*w^2 - 5*w - 16]', '[356, 178, -w^2 + 2*w + 9]', '[359, 359, 1/2*w^3 - w^2 - 3/2]', '[359, 359, 3/2*w^3 - 3*w^2 - 8*w + 7/2]', '[361, 19, -1/2*w^3 + w^2 + 2*w - 13/2]', '[361, 19, 2*w^3 - 4*w^2 - 8*w + 9]', '[379, 379, 5/2*w^3 - 4*w^2 - 12*w + 15/2]', '[379, 379, -3*w^3 + 7*w^2 + 10*w - 17]', '[389, 389, -7/2*w^3 + 9*w^2 + 13*w - 51/2]', '[389, 389, w^3 - 5*w - 1]', '[389, 389, -9/2*w^3 + 11*w^2 + 18*w - 59/2]', '[389, 389, -7/2*w^3 + 8*w^2 + 13*w - 43/2]', '[400, 10, -2*w^3 + 4*w^2 + 8*w - 8]', '[400, 20, 1/2*w^3 + w^2 - 3*w - 5/2]', '[400, 20, -3*w^3 + 8*w^2 + 11*w - 24]', '[401, 401, -1/2*w^3 + 3*w^2 + 4*w - 9/2]', '[401, 401, 1/2*w^3 + 3*w^2 - 4*w - 23/2]', '[404, 202, w^2 - w - 9]', '[404, 202, -1/2*w^3 - 2*w^2 + 2*w + 7/2]', '[404, 202, -3*w^3 + 6*w^2 + 15*w - 16]', '[404, 202, 2*w^3 - 4*w^2 - 7*w + 9]', '[421, 421, -7/2*w^3 + 9*w^2 + 16*w - 61/2]', '[421, 421, 1/2*w^3 - 4*w^2 + w + 35/2]', '[449, 449, -7/2*w^3 + 8*w^2 + 17*w - 47/2]', '[449, 449, 3*w^3 - 7*w^2 - 14*w + 17]', '[461, 461, -5/2*w^3 + 5*w^2 + 11*w - 21/2]', '[461, 461, 2*w^3 - 4*w^2 - 7*w + 8]', '[475, 95, 1/2*w^3 - 2*w^2 + w + 21/2]', '[479, 479, 3/2*w^3 - 2*w^2 - 10*w + 9/2]', '[479, 479, 5/2*w^3 - 5*w^2 - 12*w + 17/2]', '[484, 22, 1/2*w^3 - w^2 + w + 7/2]', '[484, 22, -7/2*w^3 + 10*w^2 + 12*w - 55/2]', '[484, 22, 1/2*w^3 - 2*w - 11/2]', '[484, 22, -4*w^3 + 11*w^2 + 15*w - 31]', '[484, 22, 3*w^2 - 2*w - 11]', '[484, 22, -2*w^3 + 4*w^2 + 11*w - 11]', '[484, 22, 3*w^2 - w - 10]', '[484, 22, 2*w^3 - 5*w^2 - 8*w + 9]', '[484, 242, -2*w^2 + w + 11]', '[484, 242, 3*w^3 - 9*w^2 - 9*w + 22]', '[484, 242, -3*w^2 + 3*w + 14]', '[484, 242, -5/2*w^3 + 7*w^2 + 9*w - 31/2]', '[491, 491, 2*w^2 - 2*w - 5]', '[491, 491, 2*w^3 - 6*w^2 - 6*w + 19]', '[496, 62, 2*w^3 - 4*w^2 - 10*w + 6]', '[496, 62, -w^3 + 2*w^2 + 2*w - 1]', '[496, 124, -w^3 + w^2 + 3*w + 1]', '[496, 124, w^3 - 2*w^2 - 7*w + 8]', '[496, 124, -1/2*w^3 + w^2 + 5*w + 1/2]', '[496, 124, 3*w^3 - 7*w^2 - 13*w + 16]', '[509, 509, 3/2*w^3 - 4*w^2 - 4*w + 25/2]', '[509, 509, w^3 - w^2 - 6*w + 3]', '[521, 521, 3/2*w^3 - 3*w^2 - 8*w + 5/2]', '[521, 521, 3*w^3 - 8*w^2 - 12*w + 20]', '[524, 262, -3/2*w^3 + 4*w^2 + 8*w - 35/2]', '[524, 262, w^3 - 5*w - 6]', '[524, 262, 7/2*w^3 - 9*w^2 - 13*w + 41/2]', '[524, 262, w^3 - 3*w^2 - 6*w + 2]', '[529, 23, 3/2*w^3 - 2*w^2 - 8*w + 9/2]', '[529, 23, -2*w^3 + 5*w^2 + 6*w - 14]', '[541, 541, w^3 - w^2 - 4*w - 3]', '[541, 541, 5/2*w^3 - 6*w^2 - 10*w + 23/2]', '[556, 278, w + 5]', '[556, 278, -w^3 + w^2 + w - 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25/2]', '[1796, 898, -w^3 + 3*w^2 - 16]', '[1796, 898, w^3 - 3*w^2 - 3*w + 15]', '[1796, 898, -21/2*w^3 + 27*w^2 + 43*w - 163/2]', '[1811, 1811, -5*w^3 + 14*w^2 + 18*w - 38]', '[1811, 1811, -1/2*w^3 - w^2 + 8*w + 21/2]', '[1829, 1829, 3*w^3 - 6*w^2 - 14*w + 8]', '[1829, 1829, 2*w^3 - 4*w^2 - 6*w + 3]', '[1829, 1829, -1/2*w^3 + 5*w^2 - 2*w - 43/2]', '[1829, 1829, -7/2*w^3 + 11*w^2 + 10*w - 53/2]', '[1831, 1831, 3/2*w^3 - 7*w^2 - 6*w + 49/2]', '[1831, 1831, 9/2*w^3 - 13*w^2 - 18*w + 67/2]', '[1831, 1831, -9/2*w^3 + 13*w^2 + 15*w - 69/2]', '[1831, 1831, 3/2*w^3 - 5*w^2 + 15/2]', '[1844, 922, 4*w^2 - 3*w - 17]', '[1844, 922, -7*w^3 + 19*w^2 + 27*w - 56]', '[1844, 922, 5*w^2 - w - 14]', '[1844, 922, -9/2*w^3 + 13*w^2 + 15*w - 67/2]', '[1859, 143, -7/2*w^3 + 5*w^2 + 18*w - 11/2]', '[1859, 143, -11/2*w^3 + 15*w^2 + 18*w - 77/2]', '[1859, 143, -4*w^3 + 12*w^2 + 10*w - 21]', '[1859, 143, -w^3 + 2*w^2 - 12]', '[1859, 143, -5/2*w^3 + 4*w^2 + 9*w - 17/2]', '[1859, 143, 1/2*w^3 - 2*w^2 - 2*w + 27/2]', '[1871, 1871, -5/2*w^3 + 5*w^2 + 12*w - 9/2]', '[1871, 1871, 3/2*w^3 - 3*w^2 - 4*w - 1/2]', '[1871, 1871, -3*w^3 + 10*w^2 + 10*w - 34]', '[1871, 1871, -9/2*w^3 + 12*w^2 + 20*w - 79/2]', '[1889, 1889, -1/2*w^3 + 9*w + 21/2]', '[1889, 1889, w^3 - 5*w^2 - 6*w + 7]', '[1889, 1889, -4*w^3 + 10*w^2 + 18*w - 35]', '[1889, 1889, -7/2*w^3 + 10*w^2 + 12*w - 69/2]', '[1891, 1891, -11/2*w^3 + 14*w^2 + 19*w - 65/2]', '[1891, 1891, -2*w^3 + 6*w^2 + 8*w - 25]', '[1891, 1891, w^3 - 4*w^2 - 4*w + 4]', '[1891, 1891, -5/2*w^3 + 2*w^2 + 13*w + 7/2]', '[1900, 190, w^3 - w^2 - 2*w - 2]', '[1900, 190, -7/2*w^3 + 8*w^2 + 16*w - 35/2]', '[1901, 1901, -4*w^3 + 12*w^2 + 11*w - 32]', '[1901, 1901, 5/2*w^3 - 6*w^2 - 8*w + 39/2]', '[1901, 1901, 2*w^3 - 3*w^2 - 10*w + 10]', '[1901, 1901, 1/2*w^3 + 3*w^2 - 7*w - 27/2]', '[1916, 958, -11/2*w^3 + 14*w^2 + 26*w - 103/2]', '[1916, 958, -13/2*w^3 + 18*w^2 + 24*w - 109/2]', '[1916, 958, w^3 - 7*w - 12]', '[1916, 958, 3*w^2 - 6*w - 19]', '[1919, 1919, -5/2*w^3 + 6*w^2 + 11*w - 21/2]', '[1919, 1919, 3*w^3 - 8*w^2 - 13*w + 19]', '[1931, 1931, -3*w^3 + 10*w^2 + 12*w - 24]', '[1931, 1931, 15/2*w^3 - 19*w^2 - 29*w + 95/2]', '[1931, 1931, -5/2*w^3 + 4*w^2 + 9*w - 13/2]', '[1931, 1931, -5/2*w^3 + 5*w^2 + 6*w - 27/2]', '[1936, 22, 3*w^3 - 6*w^2 - 12*w + 11]', '[1936, 22, 5*w^3 - 14*w^2 - 14*w + 33]', '[1936, 22, 3*w^3 - 6*w^2 - 12*w + 13]', '[1936, 22, w^3 - 4*w^2 + 19]', '[1936, 44, -1/2*w^3 + 2*w^2 + 3/2]', '[1936, 44, -1/2*w^3 - 2*w^2 + 4*w + 11/2]', '[1936, 44, 2*w^3 - 7*w^2 - 5*w + 11]', '[1936, 44, 3/2*w^3 - 4*w^2 - 2*w + 27/2]', '[1936, 44, -w^2 + 2*w + 11]', '[1936, 44, -w^3 + 5*w^2 + w - 25]', '[1936, 44, 4*w^3 - 11*w^2 - 14*w + 33]', '[1936, 44, -2*w^3 + 3*w^2 + 12*w - 9]', '[1936, 242, -3*w^3 + 6*w^2 + 10*w - 11]', '[1936, 242, -4*w^3 + 8*w^2 + 18*w - 16]', '[1936, 484, -3*w^3 + 8*w^2 + 9*w - 22]', '[1936, 484, w^2 - w - 11]', '[1936, 484, w^3 - 3*w^2 - 3*w + 1]', '[1936, 484, 3/2*w^3 - w^2 - 9*w + 1/2]', '[1949, 1949, -1/2*w^3 + w^2 - 2*w - 7/2]', '[1949, 1949, 5/2*w^3 - 8*w^2 - 9*w + 29/2]', '[1951, 1951, -6*w^3 + 15*w^2 + 22*w - 38]', '[1951, 1951, 9/2*w^3 - 11*w^2 - 16*w + 49/2]', '[1964, 982, 2*w^3 - 7*w - 5]', '[1964, 982, 1/2*w^3 - w^2 + w - 9/2]', '[1964, 982, -2*w^3 + 4*w^2 + 11*w - 3]', '[1964, 982, -17/2*w^3 + 21*w^2 + 35*w - 111/2]', '[1969, 1969, -3/2*w^3 + 2*w^2 + 9*w - 17/2]', '[1969, 1969, 1/2*w^3 - 3*w + 11/2]', '[1969, 1969, -5/2*w^3 + 6*w^2 + 11*w - 45/2]', '[1969, 1969, -3/2*w^3 + 2*w^2 + 11*w - 25/2]', '[1969, 1969, 1/2*w^3 - w + 11/2]', '[1969, 1969, -3/2*w^3 + 4*w^2 + 5*w - 35/2]', '[1975, 395, 3/2*w^3 - 2*w^2 - 9*w + 25/2]', '[1975, 395, 7*w^3 - 18*w^2 - 31*w + 57]', '[1975, 395, -2*w^3 + 5*w^2 + 10*w - 4]', '[1975, 395, 5/2*w^3 - 6*w^2 - 7*w + 7/2]', '[1979, 1979, -3/2*w^3 + 4*w^2 + 9*w - 9/2]', '[1979, 1979, 5/2*w^3 - 3*w^2 - 12*w + 3/2]', '[1979, 1979, -9/2*w^3 + 11*w^2 + 16*w - 51/2]', '[1979, 1979, 3/2*w^3 - 4*w^2 - 9*w + 35/2]', '[1984, 124, -2*w^2 + 4*w + 2]', '[1984, 124, -4*w^3 + 8*w^2 + 18*w - 18]', '[1984, 124, 3*w^3 - 6*w^2 - 10*w + 13]', '[1984, 124, -w^3 + 4*w^2 - 17]', '[1984, 248, -3*w^3 + 4*w^2 + 15*w - 4]', '[1984, 248, -w^2 - 3]', '[1984, 248, 3/2*w^3 - 4*w^2 - 6*w + 35/2]', '[1984, 248, 9/2*w^3 - 11*w^2 - 15*w + 51/2]', '[1991, 1991, 4*w^3 - 9*w^2 - 16*w + 22]', '[1991, 1991, 5/2*w^3 - 3*w^2 - 8*w + 11/2]', '[1991, 1991, -5/2*w^3 + 3*w^2 + 14*w - 7/2]', '[1991, 1991, -7/2*w^3 + 9*w^2 + 10*w - 45/2]', '[1991, 1991, 1/2*w^3 - 4*w^2 + w + 17/2]', '[1991, 1991, -5/2*w^3 + 4*w^2 + 10*w - 15/2]', '[1999, 1999, 4*w^3 - 7*w^2 - 20*w + 8]', '[1999, 1999, 7/2*w^3 - 8*w^2 - 10*w + 25/2]', '[2025, 15, 3*w^3 - 6*w^2 - 12*w + 12]', '[2029, 2029, w^2 - 12]', '[2029, 2029, 3/2*w^3 - 4*w^2 - 6*w + 5/2]', '[2036, 1018, -11/2*w^3 + 14*w^2 + 22*w - 71/2]', '[2036, 1018, -7/2*w^3 + 9*w^2 + 17*w - 65/2]', '[2036, 1018, -w^3 + 4*w^2 + 7*w - 4]', '[2036, 1018, w^3 + w^2 - 4*w - 8]', '[2084, 1042, w^2 - 7*w - 14]', '[2084, 1042, -3*w^3 + 9*w^2 + 9*w - 28]', '[2084, 1042, -21/2*w^3 + 27*w^2 + 41*w - 151/2]', '[2084, 1042, -2*w^3 + 4*w^2 + 5*w - 13]', '[2089, 2089, 1/2*w^3 + 2*w^2 - 7*w - 17/2]', '[2089, 2089, 5/2*w^3 - 8*w^2 - 5*w + 45/2]', '[2089, 2089, 13/2*w^3 - 17*w^2 - 24*w + 83/2]', '[2089, 2089, w^3 - 4*w^2 - 8*w + 4]', '[2096, 262, w^3 - 8*w - 1]', '[2096, 262, -2*w^3 + 6*w^2 + 4*w - 18]', '[2096, 524, -5/2*w^3 + 4*w^2 + 10*w - 13/2]', '[2096, 524, 3*w^3 - 8*w^2 - 13*w + 30]', '[2096, 524, -1/2*w^3 + 3*w^2 + 3*w - 3/2]', '[2096, 524, -4*w^3 + 9*w^2 + 16*w - 21]', '[2099, 2099, -3/2*w^3 + 2*w^2 + 11*w - 13/2]', '[2099, 2099, w^3 - 2*w^2 - w - 1]', '[2099, 2099, 9/2*w^3 - 9*w^2 - 22*w + 35/2]', '[2099, 2099, 5/2*w^3 - 5*w^2 - 13*w + 13/2]', '[2111, 2111, -4*w^3 + 12*w^2 + 14*w - 37]', '[2111, 2111, 4*w^3 - 8*w^2 - 19*w + 14]', '[2111, 2111, 5/2*w^3 - 8*w^2 - 3*w + 45/2]', '[2111, 2111, -3/2*w^3 + 13*w + 7/2]', '[2116, 46, -9/2*w^3 + 12*w^2 + 20*w - 81/2]', '[2116, 46, 13/2*w^3 - 17*w^2 - 25*w + 87/2]', '[2116, 46, w^3 - 5*w^2 - 6*w + 8]', '[2116, 46, w^3 + 2*w^2 - 5*w - 12]', '[2129, 2129, -9/2*w^3 + 14*w^2 + 13*w - 83/2]', '[2129, 2129, -19/2*w^3 + 24*w^2 + 37*w - 127/2]', '[2141, 2141, 5/2*w^3 - 3*w^2 - 12*w + 13/2]', '[2141, 2141, -7/2*w^3 + 11*w^2 + 10*w - 59/2]', '[2141, 2141, -1/2*w^3 + 2*w^2 - 3*w - 27/2]', '[2141, 2141, -1/2*w^3 + 5*w^2 - 2*w - 37/2]', '[2161, 2161, -3/2*w^3 + 5*w^2 + 7*w - 39/2]', '[2161, 2161, -2*w^3 + 6*w^2 + 9*w - 12]', '[2164, 1082, w^3 + 3*w^2 - 8*w - 14]', '[2164, 1082, 1/2*w^3 + w^2 - 7*w - 1/2]', '[2164, 1082, -13/2*w^3 + 18*w^2 + 22*w - 97/2]', '[2164, 1082, -w^3 + 4*w^2 - w - 16]', '[2179, 2179, -2*w^3 + 5*w^2 + 10*w - 8]', '[2179, 2179, -1/2*w^3 + 2*w^2 + 4*w - 23/2]', '[2189, 2189, 5*w^3 - 13*w^2 - 20*w + 33]', '[2189, 2189, -5/2*w^3 + 9*w^2 + 6*w - 45/2]', '[2189, 2189, 4*w^3 - 12*w^2 - 13*w + 34]', '[2189, 2189, 3/2*w^3 - 4*w^2 - w + 15/2]', '[2189, 2189, 3/2*w^3 - 5*w^2 - 8*w + 11/2]', '[2189, 2189, 7/2*w^3 - 9*w^2 - 13*w + 35/2]', '[2189, 2189, -1/2*w^3 + 5*w^2 - w - 33/2]', '[2189, 2189, -2*w^3 + 4*w^2 + 11*w - 2]', '[2189, 2189, 17/2*w^3 - 23*w^2 - 28*w + 105/2]', '[2189, 2189, -5/2*w^3 + 5*w^2 + 14*w - 23/2]', '[2189, 2189, 1/2*w^3 - 5*w^2 + 2*w + 41/2]', '[2189, 2189, -7/2*w^3 + 11*w^2 + 10*w - 55/2]', '[2201, 2201, 4*w^3 - 12*w^2 - 13*w + 30]', '[2201, 2201, -3/2*w^3 + 13*w + 21/2]', '[2201, 2201, 5/2*w^3 - 5*w^2 - 14*w + 25/2]', '[2201, 2201, -2*w^3 + 8*w^2 + 4*w - 21]', '[2209, 47, 1/2*w^3 - 2*w^2 - 3*w - 3/2]', '[2209, 47, -9/2*w^3 + 10*w^2 + 18*w - 39/2]', '[2221, 2221, -4*w^3 + 12*w^2 + 15*w - 38]', '[2221, 2221, 11/2*w^3 - 13*w^2 - 24*w + 65/2]', '[2224, 278, -2*w^3 + 4*w^2 + 12*w - 12]', '[2224, 278, 4*w + 2]', '[2224, 556, w^2 + 6*w + 5]', '[2224, 556, w^3 - w^2 - 3*w - 4]', '[2224, 556, -9/2*w^3 + 10*w^2 + 24*w - 69/2]', '[2224, 556, 3*w^3 - 7*w^2 - 13*w + 13]', '[2225, 445, w^3 - 5*w - 13]', '[2225, 445, 7/2*w^3 - 11*w^2 - 12*w + 71/2]', '[2239, 2239, -13/2*w^3 + 15*w^2 + 31*w - 89/2]', '[2239, 2239, 17/2*w^3 - 22*w^2 - 32*w + 111/2]', '[2251, 2251, -1/2*w^3 + 6*w^2 - 3*w - 41/2]', '[2251, 2251, -9/2*w^3 + 14*w^2 + 13*w - 79/2]', '[2269, 2269, 1/2*w^3 - 3*w - 19/2]', '[2269, 2269, -3*w^3 + 6*w^2 + 11*w - 13]', '[2276, 1138, w^3 + 3*w^2 - 5*w - 9]', '[2276, 1138, 3/2*w^3 - 2*w^2 - 10*w + 19/2]', '[2276, 1138, 5*w^2 - 6*w - 25]', '[2276, 1138, -w^3 + 3*w^2 - 14]', '[2276, 1138, -19/2*w^3 + 26*w^2 + 36*w - 155/2]', '[2276, 1138, -8*w^3 + 21*w^2 + 31*w - 61]', '[2276, 1138, 9/2*w^3 - 14*w^2 - 12*w + 65/2]', '[2276, 1138, -7*w^2 + 2*w + 19]', '[2284, 1142, -6*w^3 + 14*w^2 + 25*w - 35]', '[2284, 1142, -5/2*w^3 + 8*w^2 + 6*w - 49/2]', '[2284, 1142, -12*w^3 + 31*w^2 + 47*w - 87]', '[2284, 1142, -2*w^3 + 5*w^2 + 5*w - 16]', '[2299, 209, -3*w^3 + 6*w^2 + 11*w - 11]', '[2299, 209, 3/2*w^3 + w^2 - 11*w - 21/2]', '[2299, 209, -2*w^2 + 5*w]', '[2299, 209, 7/2*w^3 - 7*w^2 - 15*w + 27/2]', '[2299, 2299, 1/2*w^3 - 5*w^2 + 4*w + 53/2]', '[2299, 2299, -5/2*w^3 + 9*w^2 + 4*w - 33/2]', '[2309, 2309, -w^3 + 4*w^2 + 6*w - 2]', '[2309, 2309, w^3 - 2*w^2 - 8*w + 2]', '[2309, 2309, -7/2*w^3 + 8*w^2 + 11*w - 43/2]', '[2309, 2309, -w^3 + 2*w^2 + 8*w - 8]', '[2311, 2311, 5/2*w^3 - 7*w^2 - 10*w + 27/2]', '[2311, 2311, -1/2*w^3 + 3*w^2 + 2*w - 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w - 39/2]', '[5381, 5381, 9/2*w^3 - 11*w^2 - 15*w + 61/2]', '[5381, 5381, -3/2*w^3 + 6*w^2 + w - 49/2]', '[5396, 2698, -5*w + 3]', '[5396, 2698, 6*w^3 - 17*w^2 - 23*w + 51]', '[5396, 2698, -w^3 + 7*w^2 - w - 28]', '[5396, 2698, w^3 - 3*w^2 + 2*w + 10]', '[5399, 5399, -3/2*w^3 + 5*w^2 + 4*w - 9/2]', '[5399, 5399, -1/2*w^3 + 3*w^2 - 39/2]', '[5401, 5401, 8*w^3 - 22*w^2 - 29*w + 60]', '[5401, 5401, 2*w^3 - 2*w^2 - 5*w]', '[5401, 5401, -4*w^3 + 10*w^2 + 17*w - 22]', '[5401, 5401, -1/2*w^3 - w^2 + w + 19/2]', '[5401, 5401, 13/2*w^3 - 15*w^2 - 29*w + 73/2]', '[5401, 5401, -2*w^3 + 6*w^2 + w - 10]', '[5419, 5419, 9/2*w^3 - 13*w^2 - 19*w + 89/2]', '[5419, 5419, -5*w^3 + 15*w^2 + 18*w - 47]', '[5429, 5429, 5/2*w^3 - 2*w^2 - 15*w - 1/2]', '[5429, 5429, 1/2*w^3 + w^2 - 5*w - 31/2]', '[5429, 5429, 9/2*w^3 - 10*w^2 - 16*w + 47/2]', '[5429, 5429, -9/2*w^3 + 12*w^2 + 13*w - 61/2]', '[5431, 5431, 5/2*w^3 - 4*w^2 - 14*w + 27/2]', '[5431, 5431, -2*w^3 + 5*w^2 + 4*w - 18]', '[5441, 5441, 3/2*w^3 - 5*w^2 - 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5]', '[5584, 1396, 11*w^3 - 27*w^2 - 45*w + 73]', '[5591, 5591, -7/2*w^3 + 8*w^2 + 15*w - 21/2]', '[5591, 5591, 9/2*w^3 - 11*w^2 - 19*w + 49/2]', '[5591, 5591, -w^3 + 8*w^2 - w - 35]', '[5591, 5591, -6*w^2 + 4*w + 21]', '[5599, 5599, -5/2*w^3 + 8*w^2 + 11*w - 33/2]', '[5599, 5599, 4*w^3 - 10*w^2 - 18*w + 23]', '[5599, 5599, 2*w^2 + 2*w - 11]', '[5599, 5599, 11/2*w^3 - 16*w^2 - 19*w + 83/2]', '[5599, 5599, 5/2*w^3 - 8*w^2 - 11*w + 59/2]', '[5599, 5599, 2*w^3 - 4*w^2 - 14*w + 17]', '[5609, 5609, 3/2*w^3 - w^2 - 11*w + 7/2]', '[5609, 5609, -2*w^3 + 6*w^2 + 3*w - 20]', '[5609, 5609, 4*w^3 - 6*w^2 - 23*w + 2]', '[5609, 5609, 3/2*w^3 - w^2 + 21/2]', '[5609, 5609, 3*w^3 - 2*w^2 - 14*w - 8]', '[5609, 5609, 9/2*w^3 - 10*w^2 - 13*w + 31/2]', '[5609, 5609, 3*w^3 - 2*w^2 - 19*w - 5]', '[5609, 5609, 11/2*w^3 - 10*w^2 - 27*w + 27/2]', '[5611, 5611, -5/2*w^3 + 16*w + 21/2]', '[5611, 5611, 2*w^2 + w + 2]', '[5611, 5611, -7/2*w^3 + 8*w^2 + 8*w - 41/2]', '[5611, 5611, -3/2*w^3 - w^2 + 10*w + 15/2]', '[5636, 2818, 11/2*w^3 - 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45/2]', '[5764, 2882, 4*w^3 - 5*w^2 - 21*w]', '[5764, 2882, -11/2*w^3 + 15*w^2 + 17*w - 77/2]', '[5764, 2882, 4*w^3 - 8*w^2 - 13*w + 15]', '[5764, 2882, -w^2 + w + 13]', '[5764, 2882, 5*w^2 - 6*w - 33]', '[5764, 2882, w^3 - 3*w^2 + 2*w + 16]', '[5764, 2882, w^3 - 3*w^2 - 3*w - 1]', '[5764, 2882, -6*w^3 + 15*w^2 + 19*w - 31]', '[5764, 2882, -2*w^3 + 13*w + 7]', '[5764, 2882, 5/2*w^3 - 4*w^2 - 16*w + 33/2]', '[5764, 2882, -9/2*w^3 + 14*w^2 + 12*w - 49/2]', '[5776, 38, -w^3 + 2*w^2 + 4*w - 13]', '[5776, 38, 4*w^3 - 8*w^2 - 16*w + 18]', '[5776, 76, 5/2*w^3 - 4*w^2 - 6*w + 29/2]', '[5776, 76, 2*w^3 - 5*w^2 - 3*w + 17]', '[5776, 76, -6*w^3 + 13*w^2 + 28*w - 39]', '[5776, 76, -3*w^3 + 5*w^2 + 17*w - 15]', '[5779, 5779, -2*w^3 + 4*w^2 + 4*w - 3]', '[5779, 5779, 4*w^3 - 8*w^2 - 20*w + 13]', '[5791, 5791, -1/2*w^3 + 2*w^2 - 7*w - 31/2]', '[5791, 5791, 7/2*w^3 - 6*w^2 - 23*w + 47/2]', '[5801, 5801, 9/2*w^3 - 13*w^2 - 17*w + 61/2]', '[5801, 5801, -5/2*w^3 + 7*w^2 + 12*w - 15/2]', '[5801, 5801, w^3 - 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3*w^2 - 13*w + 27/2]', '[9796, 4898, 5/2*w^3 - 11*w^2 - 11*w + 35/2]', '[9796, 4898, -1/2*w^3 - 5*w^2 + 13*w + 41/2]', '[9796, 4898, -3*w^3 + 9*w^2 + 17*w - 18]', '[9796, 4898, 4*w^3 - 13*w^2 - 15*w + 36]', '[9796, 4898, 12*w^3 - 31*w^2 - 41*w + 78]', '[9796, 4898, -w^3 + 5*w^2 + 4*w - 32]', '[9796, 4898, 5*w^3 - 11*w^2 - 26*w + 26]', '[9796, 4898, 3/2*w^3 + 6*w^2 - 14*w - 61/2]', '[9796, 4898, 17/2*w^3 - 20*w^2 - 40*w + 113/2]', '[9796, 4898, -5*w^2 + 5*w + 1]', '[9796, 4898, -3*w^3 + 5*w^2 + 18*w + 2]', '[9796, 4898, -6*w^3 + 17*w^2 + 15*w - 27]', '[9796, 4898, -12*w^3 + 35*w^2 + 33*w - 82]', '[9801, 33, -9/2*w^3 + 9*w^2 + 18*w - 33/2]', '[9801, 33, -15/2*w^3 + 21*w^2 + 21*w - 99/2]', '[9801, 33, -9/2*w^3 + 9*w^2 + 18*w - 39/2]', '[9801, 33, -3/2*w^3 + 6*w^2 - 57/2]', '[9801, 363, 9/2*w^3 - 9*w^2 - 15*w + 33/2]', '[9801, 363, 6*w^3 - 12*w^2 - 27*w + 24]', '[9811, 9811, 7/2*w^3 - 2*w^2 - 22*w - 15/2]', '[9811, 9811, 7*w^3 - 19*w^2 - 20*w + 45]', '[9829, 9829, -7/2*w^3 + 10*w^2 + 16*w - 45/2]', '[9829, 9829, -2*w^3 + 7*w^2 + 10*w - 26]', '[9839, 9839, 17/2*w^3 - 19*w^2 - 37*w + 93/2]', '[9839, 9839, 4*w^3 - 6*w^2 - 13*w + 10]', '[9839, 9839, 17/2*w^3 - 21*w^2 - 31*w + 93/2]', '[9839, 9839, 7/2*w^3 - 2*w^2 - 13*w + 5/2]', '[9851, 9851, -3/2*w^3 + 3*w^2 - 35/2]', '[9851, 9851, 8*w^3 - 22*w^2 - 26*w + 57]', '[9859, 9859, -1/2*w^3 + 5*w^2 - 53/2]', '[9859, 9859, -3*w^3 - w^2 + 10*w + 9]', '[9859, 9859, -2*w^2 - 7*w - 2]', '[9859, 9859, -9/2*w^3 + 13*w^2 + 16*w - 53/2]', '[9869, 9869, -7/2*w^3 + 10*w^2 + 15*w - 43/2]', '[9869, 9869, 9/2*w^3 - 11*w^2 - 24*w + 45/2]', '[9869, 9869, -5/2*w^3 + 6*w^2 + 14*w - 7/2]', '[9869, 9869, -3/2*w^3 + 6*w^2 + 7*w - 49/2]', '[9871, 9871, 5/2*w^3 - 6*w^2 - 11*w + 51/2]', '[9871, 9871, -4*w^3 + 7*w^2 + 16*w - 10]', '[9899, 9899, 2*w^3 + 5*w^2 - 16*w - 32]', '[9899, 9899, -5/2*w^3 + 10*w^2 + 9*w - 61/2]', '[9901, 9901, 5*w^3 - 11*w^2 - 18*w + 21]', '[9901, 9901, -9/2*w^3 + 8*w^2 + 20*w - 23/2]', '[9904, 1238, -3*w^3 + 12*w^2 + 6*w - 31]', '[9904, 1238, -3*w^3 + 8*w^2 + 14*w - 9]', '[9904, 1238, w^3 - 4*w^2 - 6*w + 25]', '[9904, 1238, -3*w^3 + 12*w^2 + 6*w - 41]', '[9904, 2476, -5*w^3 + 13*w^2 + 19*w - 27]', '[9904, 2476, -2*w^3 + 9*w^2 + 4*w - 27]', '[9904, 2476, 11*w^3 - 25*w^2 - 53*w + 75]', '[9904, 2476, -7/2*w^3 + 4*w^2 + 10*w - 7/2]', '[9904, 2476, -2*w^3 + w^2 - w - 9]', '[9904, 2476, -10*w^3 + 23*w^2 + 44*w - 57]', '[9904, 2476, -7/2*w^3 + 12*w^2 + 10*w - 71/2]', '[9904, 2476, -w^3 - w^2 + 5*w + 14]', '[9929, 9929, -5*w^3 + 11*w^2 + 18*w - 25]', '[9929, 9929, -9/2*w^3 + 8*w^2 + 20*w - 31/2]', '[9931, 9931, 13/2*w^3 - 14*w^2 - 31*w + 85/2]', '[9931, 9931, 15/2*w^3 - 15*w^2 - 35*w + 67/2]', '[9941, 9941, -17/2*w^3 + 20*w^2 + 35*w - 107/2]', '[9941, 9941, -7/2*w^3 + 4*w^2 + 13*w - 15/2]', '[9949, 9949, 5/2*w^3 - 6*w^2 - 15*w + 29/2]', '[9949, 9949, -7/2*w^3 + 12*w^2 + 10*w - 65/2]', '[9956, 4978, 4*w^3 - 7*w^2 - 23*w + 15]', '[9956, 4978, 3*w^3 - 11*w^2 - 8*w + 30]', '[9956, 4978, -5/2*w^3 + 10*w^2 + 6*w - 65/2]', '[9956, 4978, 2*w^3 - 5*w^2 - w + 12]', '[9971, 767, -5*w^3 + 12*w^2 + 21*w - 25]', '[9971, 767, -7/2*w^3 + 12*w^2 + 11*w - 63/2]', '[9971, 767, 3/2*w^3 - w^2 - 5*w - 13/2]', '[9971, 767, 5/2*w^3 - 10*w^2 - 7*w + 67/2]', '[10000, 10, 10]', '[10000, 20, -5/2*w^3 + 5*w^2 + 5*w - 35/2]', '[10000, 20, 5*w^3 - 10*w^2 - 25*w + 30]'], 'label': '4.4.5225.1', 'narrow_class_no': 2, 'primes': ['[4, 2, -1/2*w^3 + w^2 + 3*w - 7/2]', '[4, 2, w + 1]', '[11, 11, w]', '[11, 11, 1/2*w^3 - w^2 - 3*w + 5/2]', '[11, 11, -w + 2]', '[19, 19, -1/2*w^3 + 3*w + 3/2]', '[25, 5, -w^3 + 2*w^2 + 4*w - 4]', '[31, 31, w^3 - 2*w^2 - 5*w + 3]', '[31, 31, -1/2*w^3 + w^2 + w - 1/2]', '[59, 59, 1/2*w^3 - w^2 - 4*w + 15/2]', '[59, 59, 1/2*w^3 - w^2 - 4*w - 5/2]', '[61, 61, -2*w^3 + 5*w^2 + 8*w - 12]', '[61, 61, 1/2*w^3 - 2*w - 5/2]', '[71, 71, -1/2*w^3 + 2*w^2 - 15/2]', '[71, 71, 3/2*w^3 - 4*w^2 - 5*w + 23/2]', '[79, 79, -5/2*w^3 + 6*w^2 + 9*w - 31/2]', '[79, 79, -4*w^3 + 10*w^2 + 17*w - 28]', '[79, 79, -w^3 + w^2 + 4*w + 1]', '[79, 79, 5/2*w^3 - 6*w^2 - 9*w + 23/2]', '[81, 3, -3]', '[89, 89, 2*w^3 - 4*w^2 - 9*w + 6]', '[89, 89, -1/2*w^3 + w + 3/2]', '[101, 101, 1/2*w^3 - 5*w - 9/2]', '[101, 101, -5/2*w^3 + 7*w^2 + 9*w - 37/2]', '[131, 131, 1/2*w^3 - 4*w - 1/2]', '[131, 131, -w^3 + 3*w^2 + 2*w - 9]', '[139, 139, -w^3 + 2*w^2 + 6*w - 6]', '[139, 139, -2*w - 1]', '[149, 149, w^2 - 6]', '[149, 149, -3/2*w^3 + 4*w^2 + 6*w - 17/2]', '[151, 151, w^3 - w^2 - 6*w + 1]', '[151, 151, 2*w - 1]', '[151, 151, -w^3 + 2*w^2 + 6*w - 4]', '[151, 151, 3/2*w^3 - 4*w^2 - 4*w + 21/2]', '[169, 13, 7/2*w^3 - 9*w^2 - 13*w + 43/2]', '[169, 13, -1/2*w^3 + 2*w^2 + 4*w - 3/2]', '[179, 179, -1/2*w^3 + w^2 + 4*w - 7/2]', '[179, 179, -1/2*w^3 + w^2 + 4*w - 3/2]', '[181, 181, -1/2*w^3 + 3*w^2 + w - 17/2]', '[181, 181, -2*w^3 + 6*w^2 + 7*w - 18]', '[199, 199, 3/2*w^3 - 2*w^2 - 7*w + 1/2]', '[199, 199, -1/2*w^3 + 2*w^2 - w - 17/2]', '[199, 199, 5/2*w^3 - 6*w^2 - 9*w + 25/2]', '[199, 199, -3*w^3 + 8*w^2 + 11*w - 23]', '[211, 211, -2*w^3 + 6*w^2 + 7*w - 16]', '[211, 211, -1/2*w^3 + 3*w^2 + w - 21/2]', '[211, 211, 1/2*w^3 - 4*w - 13/2]', '[211, 211, -w^3 + 3*w^2 + 2*w - 3]', '[239, 239, 3/2*w^3 - 2*w^2 - 9*w + 7/2]', '[239, 239, 5/2*w^3 - 5*w^2 - 11*w + 17/2]', '[241, 241, -2*w^3 + 4*w^2 + 10*w - 7]', '[241, 241, -2*w^3 + 3*w^2 + 10*w - 4]', '[241, 241, -w^3 + 2*w^2 + 2*w - 2]', '[241, 241, -5/2*w^3 + 6*w^2 + 8*w - 27/2]', '[251, 251, -1/2*w^3 + w^2 + w - 13/2]', '[251, 251, 5/2*w^3 - 5*w^2 - 11*w + 25/2]', '[251, 251, -2*w^3 + 4*w^2 + 7*w - 10]', '[251, 251, -w^3 + 2*w^2 + 5*w - 9]', '[269, 269, 1/2*w^3 - 3*w^2 + 13/2]', '[269, 269, -3/2*w^3 + 5*w^2 + 4*w - 35/2]', '[271, 271, -3/2*w^3 + 4*w^2 + 6*w - 13/2]', '[271, 271, -5/2*w^3 + 6*w^2 + 11*w - 29/2]', '[281, 281, 7/2*w^3 - 10*w^2 - 11*w + 53/2]', '[281, 281, 1/2*w^3 - 5*w - 5/2]', '[281, 281, -1/2*w^3 - 2*w^2 + 5*w + 19/2]', '[281, 281, 3/2*w^3 - 5*w^2 - 5*w + 27/2]', '[331, 331, 3/2*w^3 - 4*w^2 - 7*w + 17/2]', '[331, 331, 1/2*w^3 - 2*w^2 - 3*w + 17/2]', '[349, 349, 1/2*w^3 + w^2 - 4*w - 9/2]', '[349, 349, 5/2*w^3 - 7*w^2 - 8*w + 39/2]', '[359, 359, 1/2*w^3 - w^2 - 3/2]', '[359, 359, 3/2*w^3 - 3*w^2 - 8*w + 7/2]', '[361, 19, -1/2*w^3 + w^2 + 2*w - 13/2]', '[379, 379, 5/2*w^3 - 4*w^2 - 12*w + 15/2]', '[379, 379, -3*w^3 + 7*w^2 + 10*w - 17]', '[389, 389, -7/2*w^3 + 9*w^2 + 13*w - 51/2]', '[389, 389, w^3 - 5*w - 1]', '[389, 389, -9/2*w^3 + 11*w^2 + 18*w - 59/2]', '[389, 389, -7/2*w^3 + 8*w^2 + 13*w - 43/2]', '[401, 401, -1/2*w^3 + 3*w^2 + 4*w - 9/2]', '[401, 401, 1/2*w^3 + 3*w^2 - 4*w - 23/2]', '[421, 421, -7/2*w^3 + 9*w^2 + 16*w - 61/2]', '[421, 421, 1/2*w^3 - 4*w^2 + w + 35/2]', '[449, 449, -7/2*w^3 + 8*w^2 + 17*w - 47/2]', '[449, 449, 3*w^3 - 7*w^2 - 14*w + 17]', '[461, 461, -5/2*w^3 + 5*w^2 + 11*w - 21/2]', '[461, 461, 2*w^3 - 4*w^2 - 7*w + 8]', '[479, 479, 3/2*w^3 - 2*w^2 - 10*w + 9/2]', '[479, 479, 5/2*w^3 - 5*w^2 - 12*w + 17/2]', '[491, 491, 2*w^2 - 2*w - 5]', '[491, 491, 2*w^3 - 6*w^2 - 6*w + 19]', '[509, 509, 3/2*w^3 - 4*w^2 - 4*w + 25/2]', '[509, 509, w^3 - w^2 - 6*w + 3]', '[521, 521, 3/2*w^3 - 3*w^2 - 8*w + 5/2]', '[521, 521, 3*w^3 - 8*w^2 - 12*w + 20]', '[529, 23, 3/2*w^3 - 2*w^2 - 8*w + 9/2]', '[529, 23, -2*w^3 + 5*w^2 + 6*w - 14]', '[541, 541, w^3 - w^2 - 4*w - 3]', '[541, 541, 5/2*w^3 - 6*w^2 - 10*w + 23/2]', '[569, 569, 1/2*w^3 - w - 7/2]', '[569, 569, 7/2*w^3 - 7*w^2 - 16*w + 27/2]', '[569, 569, 5/2*w^3 - 6*w^2 - 11*w + 27/2]', '[569, 569, -5/2*w^3 + 5*w^2 + 8*w - 17/2]', '[571, 571, 3/2*w^3 - 3*w^2 - 8*w + 3/2]', '[571, 571, 7/2*w^3 - 9*w^2 - 14*w + 45/2]', '[599, 599, -7/2*w^3 + 10*w^2 + 13*w - 53/2]', '[599, 599, -1/2*w^3 + 4*w^2 + w - 29/2]', '[619, 619, -3/2*w^3 + 6*w^2 + 3*w - 31/2]', '[619, 619, -3/2*w^3 + 4*w^2 + 7*w - 9/2]', '[619, 619, 1/2*w^3 - 2*w^2 - 3*w + 25/2]', '[619, 619, -3/2*w^3 + 6*w^2 + 3*w - 41/2]', '[641, 641, -3/2*w^3 + 5*w^2 + 6*w - 39/2]', '[641, 641, -7/2*w^3 + 8*w^2 + 17*w - 45/2]', '[661, 661, 5/2*w^3 - 7*w^2 - 8*w + 41/2]', '[661, 661, -w^3 + 4*w^2 - 14]', '[701, 701, -1/2*w^3 + 3*w^2 + 5*w - 5/2]', '[701, 701, 11/2*w^3 - 14*w^2 - 21*w + 69/2]', '[719, 719, -3/2*w^3 + 4*w^2 + 7*w - 13/2]', '[719, 719, -3*w^3 + 7*w^2 + 12*w - 13]', '[719, 719, -w^2 - 4*w - 2]', '[719, 719, 5*w^3 - 14*w^2 - 17*w + 37]', '[739, 739, w^3 - 7*w - 3]', '[739, 739, -5/2*w^3 + 7*w^2 + 7*w - 37/2]', '[751, 751, 5*w^3 - 14*w^2 - 16*w + 36]', '[751, 751, w^3 + 2*w^2 - 8*w - 12]', '[761, 761, 1/2*w^3 - 2*w^2 + 2*w + 15/2]', '[761, 761, w^3 - w^2 - 8*w + 3]', '[769, 769, -1/2*w^3 + 4*w^2 - w - 29/2]', '[769, 769, -5/2*w^3 + 8*w^2 + 7*w - 43/2]', '[809, 809, 1/2*w^3 - w^2 - 3*w - 7/2]', '[809, 809, w - 6]', '[811, 811, -5*w^3 + 12*w^2 + 24*w - 38]', '[811, 811, -2*w^3 + 6*w^2 + 6*w - 21]', '[811, 811, 2*w^2 - 2*w - 3]', '[811, 811, 2*w^2 + 4*w - 1]', '[821, 821, -1/2*w^3 + 5*w + 17/2]', '[821, 821, 2*w^3 - 2*w^2 - 10*w - 1]', '[829, 829, -3*w^3 + 9*w^2 + 10*w - 23]', '[829, 829, 1/2*w^3 - 4*w^2 + 31/2]', '[839, 839, -3*w^3 + 8*w^2 + 12*w - 28]', '[839, 839, -3*w^3 + 6*w^2 + 15*w - 17]', '[841, 29, -5/2*w^3 + 5*w^2 + 10*w - 17/2]', '[841, 29, 5/2*w^3 - 5*w^2 - 10*w + 23/2]', '[911, 911, -1/2*w^3 + 6*w - 3/2]', '[911, 911, w^2 - 4*w - 6]', '[919, 919, 7/2*w^3 - 8*w^2 - 14*w + 37/2]', '[919, 919, 2*w^3 - 3*w^2 - 8*w + 4]', '[929, 929, 1/2*w^3 - 2*w^2 - 1/2]', '[929, 929, 1/2*w^3 - 2*w^2 - 3*w + 29/2]', '[929, 929, 2*w^3 - 2*w^2 - 7*w + 2]', '[929, 929, w^2 - 2*w - 10]', '[941, 941, 5/2*w^3 - 6*w^2 - 13*w + 25/2]', '[941, 941, -3/2*w^3 + 8*w + 7/2]', '[941, 941, 7/2*w^3 - 10*w^2 - 12*w + 45/2]', '[941, 941, 1/2*w^3 - 3*w^2 + 2*w + 29/2]', '[961, 31, 5/2*w^3 - 5*w^2 - 10*w + 21/2]', '[971, 971, w^3 - w^2 - 4*w - 5]', '[971, 971, 5/2*w^3 - 6*w^2 - 10*w + 19/2]', '[991, 991, -1/2*w^3 + 4*w^2 - 27/2]', '[991, 991, 3*w^3 - 9*w^2 - 10*w + 25]']}
• 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, 1, -8, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 5225, 'disc_rad': 1045, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[4, 1]]], [5, [0]], [7, [[4, 1]]], [11, [0]], [13, [[2, 2]]], [17, [[4, 1]]], [19, [0]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[2, 1], [1, 2]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[4, 1]]], [47, [[2, 2]]], [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, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 32.32645975048923, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.5225.1', 'local_algs': ['5.4.2.1', '11.1.0.1', '11.1.0.1', '11.2.1.2', '19.2.1.2', '19.2.0.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [5, 11, 19], 'rd': 8.50200926099, 'regulator': {'__RealLiteral__': 0, 'data': '3.62009337972', 'prec': 44}, 'res': {'gal': ['4,66,-55,-216,172,66,-32,-2,1'], 'sib': ['4,15,-14,-2,1', '4,66,-55,-216,172,66,-32,-2,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{3} - a^{2} - 2 a + \\frac{5}{2} \\)', '\\( a^{3} - 2 a^{2} - 5 a + 5 \\)', '\\( \\frac{1}{2} a^{3} - 3 a - \\frac{5}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2']}