Hilbert modular form data - 4.4.7488.1-18.1-b

Formats: - HTML - YAML - JSON - 2024-05-06T10:35:04.714393

• 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': 7488, 'field_bad_primes': [2, 3, 13], 'field_label': '4.4.7488.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.7488.1-18.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2, 3], 'level_ideal': '[18, 6, w^2 - w - 4]', 'level_label': '18.1', 'level_norm': 18, 'parallel_weight': 2, 'short_label': '18.1-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, -w^3 + 2*w^2 + 4*w - 1]', 1], ['[9, 3, w^3 - 2*w^2 - 3*w + 1]', -1]], 'hecke_eigenvalues': [-1, 1, 'e', '-e - 6', '3*e + 8', '-3*e - 10', 2, -4, -4, '3*e + 6', '-3*e - 12', '-4*e - 18', '4*e + 6', '-6*e - 18', '6*e + 18', '3*e + 2', '-3*e - 16', '2*e + 12', '-2*e', 8, 8, '-2*e - 6', 0, '2*e + 6', 0, '-3*e - 16', '3*e + 2', -4, '-4*e', '-2*e - 12', '4*e + 24', '2*e', '-4*e - 18', '4*e + 6', '4*e + 12', '-2*e - 6', '2*e + 6', '-4*e - 12', '6*e + 14', '-6*e - 22', '9*e + 24', '-9*e - 30', '6*e + 8', '-6*e - 28', '-14*e - 48', '14*e + 36', '-3*e - 28', '3*e - 10', '-4*e - 6', '-8*e - 36', '4*e + 18', '8*e + 12', '-3*e - 10', '3*e + 8', '-6*e - 10', '6*e + 26', '6*e + 2', '-6*e - 34', '6*e + 26', '-12*e - 34', '-6*e - 10', '12*e + 38', '3*e + 20', '-3*e - 4', '-3*e + 2', '3*e + 14', '12*e + 26', '-12*e - 46', '-9*e - 36', '9*e + 18', '-12*e - 34', '6*e + 20', '12*e + 38', '-6*e - 16', '-2*e - 30', '2*e - 18', 2, 2, '12*e + 44', '-12*e - 28', '12*e + 48', 'e - 12', '-e - 18', '-12*e - 24', '-9*e - 28', '9*e + 26', '5*e + 24', '-5*e - 6', '-4*e + 12', '4*e + 36', '21*e + 60', '-21*e - 66', '12*e + 26', '-12*e - 46', -12, -12, '-16*e - 48', '16*e + 48', '-11*e - 42', '11*e + 24', 26, -10, '-18*e - 52', '18*e + 56', '2*e + 36', '-3*e - 42', '-2*e + 24', '3*e - 24', -34, -34, '-14*e - 18', '14*e + 66', -24, -24, '5*e + 18', '-5*e - 12', '-12*e - 22', '6*e + 2', '12*e + 50', '-6*e - 34', -22, -22, 2, '6*e + 18', '-19*e - 66', '-6*e - 18', '19*e + 48', '6*e - 4', '-6*e - 40', '3*e + 36', '-3*e + 18', '3*e + 20', '-3*e + 2', '3*e + 20', '-3*e + 2', '10*e + 60', '-10*e', '18*e + 50', '-18*e - 58', '14*e + 24', '-14*e - 60', '8*e + 48', '-8*e', '-9*e - 34', '9*e + 20', '-24*e - 70', '24*e + 74', '-18*e - 36', '18*e + 72', '-6*e - 58', '6*e - 22', '-28*e - 78', '28*e + 90', '10*e + 36', '-10*e - 24', '12*e + 26', '6*e + 32', '-12*e - 46', '-6*e - 4'], 'hecke_polynomial': 'x^2 + 6*x + 6', 'label': '4.4.7488.1-18.1-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 7488, 'ideals': ['[1, 1, 1]', '[2, 2, -w^3 + 2*w^2 + 4*w - 1]', '[4, 2, w^3 - 2*w^2 - 3*w]', '[8, 2, w^3 - w^2 - 5*w - 3]', '[9, 3, w^3 - 2*w^2 - 3*w + 1]', '[11, 11, -w^3 + 2*w^2 + 4*w]', '[11, 11, -w + 2]', '[13, 13, w + 2]', '[13, 13, w^3 - 2*w^2 - 4*w + 4]', '[13, 13, -w^2 + 2*w + 2]', '[16, 2, 2]', '[18, 6, w^2 - w - 4]', '[22, 22, w^2 - w - 2]', '[22, 22, w^3 - 3*w^2 - 2*w + 4]', '[26, 26, -w^3 + w^2 + 6*w]', '[26, 26, w^2 - 3*w - 2]', '[26, 26, -2*w^3 + 3*w^2 + 9*w]', '[32, 4, -2*w^3 + 4*w^2 + 8*w - 2]', '[36, 6, -w^3 + 2*w^2 + 3*w + 2]', '[37, 37, -w^3 + 2*w^2 + 5*w - 3]', '[37, 37, w^3 - 2*w^2 - 5*w + 1]', '[44, 22, w^2 - 3]', '[44, 22, 2*w^3 - 5*w^2 - 6*w + 5]', '[47, 47, -2*w^3 + 2*w^2 + 10*w + 5]', '[47, 47, w^2 - w - 5]', '[52, 26, 2*w^3 - 3*w^2 - 8*w - 1]', '[52, 26, 2*w^3 - 5*w^2 - 4*w + 3]', '[52, 26, w^3 - 2*w^2 - 5*w + 2]', '[59, 59, -w^3 + 3*w^2 + 3*w - 6]', '[59, 59, w^3 - 3*w^2 - 3*w + 2]', '[64, 4, 2*w^3 - 4*w^2 - 6*w]', '[71, 71, -2*w^3 + 4*w^2 + 7*w]', '[71, 71, w^3 - 2*w^2 - 2*w - 2]', '[72, 6, -3*w^3 + 5*w^2 + 13*w + 1]', '[73, 73, w^3 - 2*w^2 - 4*w - 2]', '[73, 73, w - 4]', '[74, 74, -2*w^3 + 5*w^2 + 7*w - 8]', '[74, 74, w^3 - 3*w^2 - 4*w + 2]', '[81, 3, 3]', '[83, 83, w^3 - w^2 - 6*w + 1]', '[83, 83, w^2 - 3*w - 3]', '[88, 22, w^3 - w^2 - 7*w + 1]', '[88, 22, -w^3 + w^2 + 7*w + 1]', '[94, 94, -w - 3]', '[94, 94, 5*w^3 - 9*w^2 - 20*w + 4]', '[97, 97, -3*w^3 + 5*w^2 + 12*w + 1]', '[97, 97, -2*w^3 + 5*w^2 + 3*w - 1]', '[99, 33, w^3 - w^2 - 4*w - 3]', '[99, 33, 2*w^3 - 5*w^2 - 5*w + 3]', '[104, 26, -w^3 + 3*w^2 + w - 5]', '[104, 26, -w^3 + w^2 + 5*w - 1]', '[104, 26, -w^3 + 3*w^2 + w - 7]', '[107, 107, -2*w^3 + 3*w^2 + 9*w - 1]', '[107, 107, 2*w - 3]', '[107, 107, -w^3 + 3*w^2 - 3]', '[107, 107, 2*w^3 - 4*w^2 - 8*w + 1]', '[109, 109, -3*w^3 + 5*w^2 + 12*w - 1]', '[109, 109, 2*w^3 - 5*w^2 - 3*w + 3]', '[117, 39, 2*w^3 - 3*w^2 - 7*w + 1]', '[117, 39, 3*w^3 - 7*w^2 - 8*w + 7]', '[117, 39, w^3 - w^2 - 7*w]', '[118, 118, 5*w^3 - 10*w^2 - 18*w + 9]', '[118, 118, -w^3 + 2*w^2 + 2*w - 5]', '[121, 11, -2*w^3 + 4*w^2 + 6*w - 1]', '[121, 11, -2*w^3 + 4*w^2 + 6*w - 3]', '[121, 121, w^3 - 4*w^2 + w + 3]', '[121, 121, -w^3 + 7*w + 5]', '[128, 4, 2*w^3 - 2*w^2 - 10*w - 6]', '[131, 131, 2*w^2 - 6*w - 3]', '[131, 131, -3*w^3 + 5*w^2 + 13*w + 2]', '[131, 131, 2*w^3 - 4*w^2 - 5*w - 2]', '[131, 131, -2*w^3 + 2*w^2 + 12*w + 5]', '[142, 142, -2*w^3 + 2*w^2 + 11*w + 7]', '[142, 142, 3*w^3 - 5*w^2 - 12*w]', '[143, 143, -2*w^3 + 5*w^2 + 6*w - 4]', '[143, 143, -w^3 + w^2 + 5*w - 2]', '[143, 143, w^3 - 4*w^2 + 2*w + 4]', '[143, 143, w^3 - 3*w^2 - w + 6]', '[143, 143, -w^2 + 4]', '[143, 143, -2*w^3 + 2*w^2 + 11*w + 2]', '[144, 6, 2*w^3 - 4*w^2 - 6*w + 2]', '[146, 146, 3*w^3 - 5*w^2 - 14*w - 2]', '[146, 146, 4*w^3 - 8*w^2 - 15*w + 5]', '[148, 74, -w^3 + 4*w^2 - w - 4]', '[148, 74, -w^3 + 7*w + 4]', '[162, 6, -3*w^3 + 6*w^2 + 12*w - 3]', '[166, 166, -3*w^3 + 5*w^2 + 14*w]', '[166, 166, 2*w^2 - 3*w - 7]', '[167, 167, -2*w^2 + 4*w + 9]', '[167, 167, -w^2 + 3*w + 5]', '[169, 13, -w^3 + 6*w + 4]', '[169, 13, 2*w^3 - 6*w^2 - 3*w + 6]', '[169, 13, w^3 - 2*w^2 - 3*w + 5]', '[169, 13, -w^3 + 2*w^2 + 3*w + 3]', '[169, 169, -2*w^2 + 4*w + 3]', '[169, 169, -2*w^2 + 4*w + 5]', '[176, 22, -2*w^3 + 4*w^2 + 8*w]', '[176, 22, -2*w + 4]', '[179, 179, -2*w^3 + 5*w^2 + 4*w - 6]', '[179, 179, 2*w^3 - 4*w^2 - 8*w - 1]', '[179, 179, -3*w^3 + 3*w^2 + 17*w + 8]', '[179, 179, -2*w^3 + 3*w^2 + 8*w - 2]', '[188, 94, 3*w^3 - 6*w^2 - 13*w + 2]', '[188, 94, -4*w^3 + 7*w^2 + 16*w + 1]', '[193, 193, 6*w^3 - 8*w^2 - 30*w - 7]', '[193, 193, -2*w^3 + w^2 + 13*w + 7]', '[194, 194, -4*w^3 + 4*w^2 + 21*w + 11]', '[194, 194, -w^3 + w^2 + 4*w + 4]', '[198, 66, -w^3 + 2*w^2 + 6*w - 1]', '[198, 66, 2*w^3 - 4*w^2 - 9*w + 5]', '[208, 26, 2*w + 4]', '[208, 26, 2*w^3 - 4*w^2 - 8*w + 8]', '[208, 26, -2*w^2 + 4*w + 4]', '[214, 214, -w^3 - w^2 + 8*w + 10]', '[214, 214, 2*w^3 - 4*w^2 - 9*w + 3]', '[214, 214, 3*w^3 - 6*w^2 - 10*w + 5]', '[214, 214, w^3 - 8*w - 9]', '[218, 218, 3*w^3 - 6*w^2 - 10*w - 1]', '[218, 218, -w^3 + 3*w^2 + 4*w - 6]', '[227, 227, 3*w^3 - 4*w^2 - 15*w - 1]', '[227, 227, -3*w^3 + 7*w^2 + 8*w - 3]', '[229, 229, -3*w^3 + w^2 + 20*w + 15]', '[229, 229, -w^3 + 5*w^2 - 4*w - 5]', '[234, 78, 2*w^2 - 5*w - 5]', '[234, 78, -w^3 + 8*w + 1]', '[234, 78, w^3 - 8*w - 7]', '[236, 118, -3*w^3 + 6*w^2 + 11*w - 2]', '[236, 118, -w^3 + 2*w^2 + w + 2]', '[239, 239, -4*w^3 + 5*w^2 + 20*w + 4]', '[239, 239, -5*w^3 + 7*w^2 + 24*w + 3]', '[241, 241, -2*w^3 + 4*w^2 + 9*w - 4]', '[241, 241, -w^3 + 2*w^2 + 6*w - 2]', '[242, 22, w^3 - 4*w^2 - 2*w + 9]', '[242, 22, -w^3 + 6*w + 7]', '[242, 242, -2*w^3 + 3*w^2 + 9*w - 2]', '[242, 242, -w^3 + 3*w^2 - 4]', '[256, 4, 4]', '[262, 262, 3*w^3 - 4*w^2 - 16*w - 3]', '[262, 262, 2*w^3 - 4*w^2 - 5*w + 1]', '[262, 262, 4*w^3 - 6*w^2 - 17*w - 3]', '[262, 262, 2*w^2 - 3*w - 3]', '[263, 263, -w^3 + 4*w^2 - w - 7]', '[263, 263, -2*w^3 + 5*w^2 + 3*w - 5]', '[263, 263, -w^3 + 7*w + 1]', '[263, 263, -3*w^3 + 5*w^2 + 12*w - 3]', '[277, 277, -2*w^3 + w^2 + 12*w + 8]', '[277, 277, 3*w^3 - 5*w^2 - 14*w + 1]', '[277, 277, 2*w^2 - 2*w - 3]', '[277, 277, -2*w^3 + 6*w^2 + 4*w - 9]', '[284, 142, 4*w^3 - 7*w^2 - 14*w - 5]', '[284, 142, -4*w^3 + 9*w^2 + 10*w + 1]', '[286, 286, -2*w^3 + 6*w^2 + 5*w - 7]', '[286, 286, -4*w^3 + 9*w^2 + 15*w - 12]', '[286, 286, w^3 - 3*w^2 - 6*w + 2]', '[286, 286, w^3 - 4*w^2 - 2*w + 7]', '[286, 286, w^3 - 2*w^2 - 4*w - 3]', '[286, 286, -w + 5]', '[288, 12, 2*w^2 - 2*w - 8]', '[289, 17, -w^3 + 4*w^2 - 4]', '[289, 17, 2*w^2 - 3*w - 6]', '[292, 146, -4*w^3 + 7*w^2 + 14*w + 3]', '[292, 146, -4*w^3 + 9*w^2 + 10*w - 1]', '[296, 74, -w^3 + w^2 + 3*w + 3]', '[296, 74, -3*w^3 + 7*w^2 + 9*w - 5]', '[313, 313, -w - 4]', '[313, 313, -2*w^3 + 3*w^2 + 11*w + 1]', '[313, 313, -w^3 + 2*w^2 + 4*w - 6]', '[313, 313, -2*w^3 + 14*w + 13]', '[324, 6, 3*w^3 - 6*w^2 - 9*w]', '[332, 166, -3*w^2 + 8*w + 5]', '[332, 166, 2*w^3 - w^2 - 14*w - 3]', '[333, 111, -2*w^3 + 6*w^2 + 4*w - 7]', '[333, 111, -2*w^2 + 2*w + 5]', '[334, 334, -2*w^3 + 6*w^2 + 5*w - 9]', '[334, 334, -w^3 + 4*w^2 + 2*w - 5]', '[337, 337, 2*w^3 - 3*w^2 - 11*w + 3]', '[337, 337, -5*w^3 + 6*w^2 + 27*w + 7]', '[337, 337, w^3 - w^2 - 8*w - 1]', '[337, 337, -6*w^3 + 6*w^2 + 33*w + 14]', '[338, 26, -3*w^3 + 7*w^2 + 10*w - 6]', '[338, 26, -5*w^3 + 8*w^2 + 22*w + 3]', '[338, 26, w^2 + w - 4]', '[338, 26, -4*w^3 + 7*w^2 + 17*w]', '[338, 338, -3*w^3 + 4*w^2 + 14*w + 1]', '[338, 338, -2*w^3 + 6*w^2 + w - 5]', '[349, 349, -w^3 + 4*w^2 - 6]', '[349, 349, 2*w^2 - 3*w - 4]', '[352, 44, 2*w^2 - 2*w - 4]', '[352, 44, 2*w^3 - 6*w^2 - 4*w + 8]', '[358, 358, 4*w^3 - 9*w^2 - 15*w + 10]', '[358, 358, 2*w^2 - 3*w - 5]', '[358, 358, 3*w^3 - 4*w^2 - 16*w - 7]', '[358, 358, -3*w^2 + 3*w + 10]', '[359, 359, -4*w^3 + 7*w^2 + 16*w + 2]', '[359, 359, -9*w^3 + 13*w^2 + 42*w + 9]', '[373, 373, w^3 + w^2 - 10*w - 5]', '[373, 373, 2*w^2 - 7*w]', '[373, 373, 3*w^2 - 7*w - 5]', '[373, 373, 3*w^3 - 4*w^2 - 16*w - 2]', '[376, 94, -3*w^3 + 5*w^2 + 11*w + 1]', '[376, 94, -5*w^3 + 5*w^2 + 27*w + 15]', '[383, 383, 2*w^3 - 6*w^2 - 3*w + 2]', '[383, 383, w^3 - 6*w - 8]', '[386, 386, -2*w^3 + 2*w^2 + 11*w + 1]', '[386, 386, -w^3 + 4*w^2 - 2*w - 5]', '[388, 194, w^2 - 2*w - 7]', '[388, 194, -w^2 + 2*w - 3]', '[396, 66, -2*w^3 + 5*w^2 + 8*w - 3]', '[396, 66, 2*w^3 - 5*w^2 - 8*w + 9]', '[397, 397, -3*w^3 + 7*w^2 + 9*w - 12]', '[397, 397, -2*w^3 + 2*w^2 + 13*w]', '[407, 407, 2*w^3 - 3*w^2 - 9*w + 3]', '[407, 407, 3*w - 4]', '[407, 407, -3*w^3 + 6*w^2 + 12*w - 2]', '[407, 407, w^3 - 3*w^2 + 5]', '[409, 409, -2*w^3 + 4*w^2 + 5*w - 8]', '[409, 409, -3*w^3 + 6*w^2 + 10*w - 10]', '[416, 52, -2*w^3 + 2*w^2 + 12*w]', '[416, 52, 2*w^2 - 6*w - 4]', '[416, 52, -4*w^3 + 6*w^2 + 18*w]', '[419, 419, -w^3 + 3*w^2 + 4*w - 7]', '[419, 419, w^3 - 2*w^2 - w - 3]', '[419, 419, 3*w^3 - 6*w^2 - 11*w + 1]', '[419, 419, 2*w^3 - 5*w^2 - 7*w + 3]', '[421, 421, -w^3 + 4*w^2 + w - 7]', '[421, 421, -w^3 + 4*w^2 + w - 5]', '[423, 141, 5*w^3 - 8*w^2 - 23*w - 3]', '[423, 141, -4*w^3 + 8*w^2 + 15*w - 4]', '[428, 214, 2*w^3 - w^2 - 14*w - 7]', '[428, 214, -3*w^3 + 8*w^2 + 5*w - 2]', '[428, 214, -3*w^2 + 8*w + 1]', '[428, 214, -3*w^3 + 4*w^2 + 13*w + 6]', '[431, 431, w^2 - 6]', '[431, 431, -2*w^3 + 5*w^2 + 6*w - 2]', '[436, 218, 4*w^3 - 5*w^2 - 20*w - 9]', '[436, 218, -2*w^3 + 7*w^2 - 2*w + 1]', '[443, 443, 2*w^3 - 5*w^2 - 7*w - 1]', '[443, 443, 6*w^3 - 6*w^2 - 33*w - 16]', '[443, 443, w^3 + w^2 - 11*w - 6]', '[443, 443, w^3 + w^2 - 11*w - 2]', '[454, 454, -w^3 + w^2 + 8*w - 2]', '[454, 454, -2*w^2 + 3*w + 11]', '[457, 457, 2*w^3 - 5*w^2 - 3*w - 3]', '[457, 457, -3*w^3 + 5*w^2 + 12*w + 5]', '[458, 458, -2*w^3 + 7*w^2 + w - 12]', '[458, 458, 4*w^3 - 6*w^2 - 19*w + 1]', '[468, 78, -2*w^3 + 3*w^2 + 10*w + 5]', '[468, 78, w^2 - 4*w + 5]', '[468, 78, w^3 - 4*w^2 - w + 6]', '[472, 118, -w^3 - w^2 + 9*w + 13]', '[472, 118, -3*w^3 + 5*w^2 + 11*w - 1]', '[478, 478, w^3 - w^2 - 8*w]', '[478, 478, 2*w^3 - 3*w^2 - 11*w + 2]', '[479, 479, -2*w^2 + 5*w + 6]', '[479, 479, -w^3 + 8*w]', '[481, 481, -3*w^3 + 7*w^2 + 7*w - 4]', '[481, 481, -4*w^3 + 7*w^2 + 15*w + 1]', '[481, 481, -2*w^3 + 2*w^2 + 13*w + 2]', '[481, 481, 3*w^3 - 5*w^2 - 11*w]', '[481, 481, w^3 - 10*w]', '[481, 481, 3*w^3 - 7*w^2 - 6*w + 1]', '[482, 482, 2*w^3 - 6*w^2 - 3*w + 13]', '[482, 482, w^3 - 3*w^2 + 8]', '[484, 22, -w^3 + 2*w^2 + 3*w - 6]', '[484, 22, w^3 - 2*w^2 - 3*w - 4]', '[484, 242, w^3 - 2*w^2 - 7*w + 4]', '[484, 242, 3*w^3 - 6*w^2 - 13*w + 4]', '[503, 503, -2*w^3 + 5*w^2 + 9*w - 9]', '[503, 503, -3*w^3 + 7*w^2 + 12*w - 5]', '[503, 503, -w^3 + 5*w^2 - 4*w - 7]', '[503, 503, -2*w^3 + 6*w^2 + 6*w - 11]', '[512, 8, -4*w^3 + 8*w^2 + 16*w - 4]', '[517, 517, -w^3 + 3*w^2 + 3*w - 10]', '[517, 517, -2*w^3 + 3*w^2 + 11*w - 1]', '[517, 517, 2*w^3 - 3*w^2 - 12*w - 2]', '[517, 517, 5*w^3 - 8*w^2 - 21*w - 1]', '[524, 262, -w^3 + 7*w]', '[524, 262, w^3 - 5*w - 6]', '[524, 262, -2*w^3 + 5*w^2 + 6*w - 1]', '[524, 262, 3*w^3 - 4*w^2 - 13*w]', '[526, 526, 6*w^3 - 11*w^2 - 25*w + 6]', '[526, 526, 3*w^3 - 7*w^2 - 12*w + 8]', '[526, 526, -2*w^3 + w^2 + 11*w + 6]', '[526, 526, -4*w^2 + 5*w + 15]', '[529, 23, 3*w^3 - 6*w^2 - 9*w + 1]', '[529, 23, -3*w^3 + 6*w^2 + 9*w - 5]', '[531, 177, -4*w^3 + 9*w^2 + 14*w - 8]', '[531, 177, -w^2 - 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13]', '[1573, 143, -4*w^3 + 6*w^2 + 13*w - 4]', '[1573, 143, -4*w^3 + 6*w^2 + 15*w]', '[1573, 143, -7*w^3 + 16*w^2 + 20*w - 18]', '[1573, 143, -5*w^3 + 12*w^2 + 12*w - 10]', '[1573, 143, -2*w^3 + 3*w^2 + 12*w - 2]', '[1573, 143, -3*w^3 + 7*w^2 + 13*w - 8]', '[1573, 1573, w + 6]', '[1573, 1573, w^3 - 2*w^2 - 4*w + 8]', '[1573, 1573, 3*w^3 - 6*w^2 - 7*w + 3]', '[1573, 1573, 2*w^3 - 3*w^2 - 8*w + 8]', '[1573, 1573, 2*w^3 - 5*w^2 - 4*w + 12]', '[1573, 1573, 5*w^3 - 10*w^2 - 17*w + 7]', '[1584, 66, 2*w^3 - 2*w^2 - 8*w - 6]', '[1584, 66, 4*w^3 - 10*w^2 - 10*w + 6]', '[1588, 794, -5*w^3 + 10*w^2 + 17*w - 6]', '[1588, 794, -2*w^3 + 7*w^2 + 2*w - 11]', '[1597, 1597, -6*w^3 + 12*w^2 + 20*w - 3]', '[1597, 1597, -4*w^3 + 8*w^2 + 10*w + 1]', '[1606, 1606, -5*w^3 + 14*w^2 + 10*w - 17]', '[1606, 1606, 3*w^2 - 5*w - 6]', '[1606, 1606, w^3 - 5*w^2 + 2*w + 8]', '[1606, 1606, -2*w^3 + 11*w + 5]', '[1607, 1607, -7*w^3 + 12*w^2 + 30*w]', '[1607, 1607, -5*w^3 + 9*w^2 + 21*w]', '[1609, 1609, -5*w^3 + 10*w^2 + 14*w + 2]', '[1609, 1609, w^3 - 11*w + 1]', '[1609, 1609, 3*w^3 - 4*w^2 - 17*w - 1]', '[1609, 1609, -5*w^2 + 12*w + 6]', '[1611, 537, -3*w^3 + 5*w^2 + 13*w - 8]', '[1611, 537, -3*w^3 + 4*w^2 + 11*w + 5]', '[1611, 537, 8*w^3 - 11*w^2 - 38*w - 6]', '[1611, 537, -w^3 + 3*w^2 - w - 8]', '[1619, 1619, -w^3 - w^2 + 11*w]', '[1619, 1619, -w^3 - w^2 + 11*w + 8]', '[1621, 1621, 2*w^3 - 4*w^2 - 11*w + 6]', '[1621, 1621, 4*w^3 - 7*w^2 - 14*w]', '[1621, 1621, -3*w^3 + 6*w^2 + 14*w - 4]', '[1621, 1621, -4*w^3 + 9*w^2 + 10*w - 4]', '[1628, 814, -3*w^2 + 8*w + 7]', '[1628, 814, -4*w^3 + 11*w^2 + 6*w - 3]', '[1628, 814, 4*w^3 - 5*w^2 - 18*w - 9]', '[1628, 814, 2*w^3 - w^2 - 14*w - 1]', '[1636, 818, -4*w^3 + 7*w^2 + 14*w - 3]', '[1636, 818, -4*w^3 + 9*w^2 + 10*w - 7]', '[1654, 1654, 5*w^3 - 8*w^2 - 24*w - 1]', '[1654, 1654, w^3 + 2*w^2 - 10*w - 13]', '[1657, 1657, 3*w^2 - 5*w - 7]', '[1657, 1657, -w^3 + 5*w^2 - 2*w - 7]', '[1664, 52, -2*w^3 + 6*w^2 + 2*w - 10]', '[1664, 52, -2*w^3 + 2*w^2 + 10*w - 2]', '[1664, 52, -2*w^3 + 6*w^2 + 2*w - 14]', '[1669, 1669, -w^3 + 2*w^2 + 5*w - 9]', '[1669, 1669, w^3 - 2*w^2 - 5*w - 5]', '[1676, 838, -4*w^3 + 9*w^2 + 12*w - 3]', '[1676, 838, -5*w^3 + 12*w^2 + 11*w]', '[1676, 838, -5*w^3 + 8*w^2 + 19*w + 8]', '[1676, 838, -2*w^3 + 3*w^2 + 6*w + 5]', '[1678, 1678, 10*w^3 - 22*w^2 - 33*w + 25]', '[1678, 1678, -4*w^2 + 9*w + 7]', '[1682, 58, -5*w^3 + 4*w^2 + 26*w + 15]', '[1682, 58, -3*w^3 + 8*w^2 + 10*w - 15]', '[1684, 842, -3*w^3 + 4*w^2 + 17*w]', '[1684, 842, -w^3 + 11*w]', '[1692, 282, -w^3 - 2*w^2 + 7*w + 12]', '[1692, 282, 4*w^3 - 5*w^2 - 18*w - 11]', '[1693, 1693, -2*w^3 + 7*w^2 + 4*w - 12]', '[1693, 1693, -6*w^3 + 9*w^2 + 29*w + 1]', '[1693, 1693, -6*w^3 + 6*w^2 + 32*w + 13]', '[1693, 1693, -2*w^3 + 7*w^2 + 4*w - 8]', '[1703, 1703, -2*w^3 + 2*w^2 + 11*w - 2]', '[1703, 1703, w^3 - w^2 - w - 4]', '[1703, 1703, -w^3 + 3*w^2 - 2*w - 5]', '[1703, 1703, -w^3 + 3*w^2 - 3*w - 4]', '[1703, 1703, -w^3 + w^2 + 2*w + 5]', '[1703, 1703, -4*w^3 + 6*w^2 + 16*w - 3]', '[1703, 1703, 2*w^3 - 2*w^2 - 15*w - 6]', '[1703, 1703, 4*w^3 - 5*w^2 - 16*w - 6]', '[1703, 1703, 2*w^3 - 6*w^2 - 6*w + 1]', '[1703, 1703, -w^3 - w^2 + 5*w + 8]', '[1703, 1703, -3*w^3 + 10*w^2 - 2*w - 6]', '[1703, 1703, 2*w^3 - 6*w^2 + 2*w - 3]', '[1706, 1706, 2*w^2 - w - 9]', '[1706, 1706, -3*w^3 + w^2 + 18*w + 16]', '[1712, 214, -4*w^3 + 6*w^2 + 18*w - 2]', '[1712, 214, 4*w - 6]', '[1712, 214, -2*w^3 + 6*w^2 - 6]', '[1712, 214, 4*w^3 - 8*w^2 - 16*w + 2]', '[1724, 862, -5*w^3 + 10*w^2 + 17*w]', '[1724, 862, 3*w^3 - 6*w^2 - 7*w - 4]', '[1726, 1726, -3*w^3 + 5*w^2 + 14*w + 6]', '[1726, 1726, 12*w^3 - 20*w^2 - 51*w + 1]', '[1737, 579, -9*w^3 + 10*w^2 + 47*w + 17]', '[1737, 579, 6*w^3 - 8*w^2 - 31*w - 4]', '[1739, 1739, 6*w^3 - 12*w^2 - 23*w + 14]', '[1739, 1739, 4*w^3 - 9*w^2 - 14*w + 6]', '[1739, 1739, 2*w^3 - w^2 - 7*w - 5]', '[1739, 1739, -6*w^3 + 10*w^2 + 25*w - 4]', '[1744, 218, -6*w^3 + 10*w^2 + 24*w - 2]', '[1744, 218, 4*w^3 - 10*w^2 - 6*w + 6]', '[1746, 582, 11*w^3 - 17*w^2 - 50*w - 6]', '[1746, 582, 4*w^3 - 8*w^2 - 15*w + 1]', '[1753, 1753, 2*w^3 - 2*w^2 - 14*w - 1]', '[1753, 1753, 2*w^3 - 2*w^2 - 14*w + 1]', '[1754, 1754, -5*w^3 + 9*w^2 + 20*w + 2]', '[1754, 1754, -6*w^3 + 7*w^2 + 33*w + 12]', '[1772, 886, 6*w^3 - 11*w^2 - 18*w - 5]', '[1772, 886, -10*w^3 + 17*w^2 + 42*w - 5]', '[1772, 886, -3*w^3 + 4*w^2 + 15*w - 2]', '[1772, 886, w^3 - 4*w^2 + 3*w + 6]', '[1777, 1777, 3*w^2 - 3*w - 7]', '[1777, 1777, w^3 - w^2 - 5*w - 8]', '[1777, 1777, w^3 - 3*w^2 - w - 4]', '[1777, 1777, 3*w^3 - 9*w^2 - 6*w + 11]', '[1782, 66, 3*w^2 - 3*w - 6]', '[1782, 66, 3*w^3 - 9*w^2 - 6*w + 12]', '[1787, 1787, 3*w^3 - w^2 - 22*w - 11]', '[1787, 1787, 5*w^2 - 13*w - 3]', '[1789, 1789, -4*w^3 + 8*w^2 + 19*w - 2]', '[1789, 1789, 6*w^3 - 10*w^2 - 23*w - 4]', '[1801, 1801, 3*w^2 - 4*w - 8]', '[1801, 1801, -2*w^3 + 7*w^2 + 2*w - 8]', '[1816, 454, -w^3 + 7*w^2 - 9*w - 7]', '[1816, 454, 9*w^3 - 15*w^2 - 37*w - 3]', '[1826, 1826, -w^2 - w + 8]', '[1826, 1826, -3*w^3 + 7*w^2 + 10*w - 2]', '[1826, 1826, 2*w^3 - 2*w^2 - 7*w - 5]', '[1826, 1826, 5*w^3 - 12*w^2 - 14*w + 9]', '[1828, 914, -4*w^3 + 9*w^2 + 10*w - 5]', '[1828, 914, 4*w^3 - 7*w^2 - 14*w + 1]', '[1832, 458, -5*w^3 + 5*w^2 + 31*w + 1]', '[1832, 458, 3*w^3 - 9*w^2 - 5*w + 17]', '[1837, 1837, -6*w^3 + 13*w^2 + 19*w - 11]', '[1837, 1837, 3*w^3 - 5*w^2 - 8*w + 1]', '[1837, 1837, 4*w^3 - 7*w^2 - 14*w + 2]', '[1837, 1837, -4*w^3 + 9*w^2 + 10*w - 6]', '[1846, 1846, -3*w^3 + 24*w + 11]', '[1846, 1846, 6*w^3 - 8*w^2 - 31*w - 5]', '[1846, 1846, -6*w^2 + 15*w + 7]', '[1846, 1846, -7*w^3 + 7*w^2 + 38*w + 16]', '[1846, 1846, 2*w^3 + w^2 - 21*w - 4]', '[1846, 1846, 3*w^3 - w^2 - 24*w - 6]', '[1849, 43, 2*w^3 - 7*w^2 - 2*w + 10]', '[1849, 43, 3*w^2 - 4*w - 6]', '[1859, 143, -5*w^3 + 9*w^2 + 20*w + 3]', '[1859, 143, -3*w^3 + 8*w^2 + 7*w - 3]', '[1859, 143, -3*w^3 + 7*w^2 + 12*w - 3]', '[1859, 143, -2*w^3 + 2*w^2 + 12*w - 3]', '[1859, 143, 2*w^3 - 5*w^2 - 9*w + 11]', '[1859, 143, -2*w^2 + 6*w + 7]', '[1859, 143, -2*w^3 + 5*w^2 + w + 5]', '[1859, 143, -w^3 + 5*w + 9]', '[1859, 1859, 4*w^3 - 11*w^2 - 6*w + 2]', '[1859, 1859, 2*w^3 - 8*w^2 + 5*w + 6]', '[1859, 1859, -5*w^3 + 6*w^2 + 26*w + 4]', '[1859, 1859, 4*w^3 - 5*w^2 - 18*w - 10]', '[1861, 1861, -8*w^3 + 12*w^2 + 35*w + 6]', '[1861, 1861, -5*w^3 + 6*w^2 + 25*w + 13]', '[1871, 1871, -5*w^3 + 12*w^2 + 11*w - 13]', '[1871, 1871, 7*w^3 - 14*w^2 - 25*w + 15]', '[1871, 1871, 5*w^3 - 12*w^2 - 12*w + 4]', '[1871, 1871, 5*w^3 - 8*w^2 - 19*w + 5]', '[1872, 78, 4*w^3 - 6*w^2 - 14*w + 2]', '[1872, 78, 6*w^3 - 14*w^2 - 16*w + 14]', '[1872, 78, 2*w^3 - 2*w^2 - 14*w]', '[1888, 236, 10*w^3 - 20*w^2 - 36*w + 18]', '[1888, 236, -2*w^3 + 4*w^2 + 4*w - 10]', '[1894, 1894, -9*w^3 + 12*w^2 + 40*w + 7]', '[1894, 1894, 5*w^3 - 12*w^2 - 16*w + 21]', '[1898, 1898, -2*w^3 + 19*w + 7]', '[1898, 1898, 4*w^3 - 3*w^2 - 25*w - 6]', '[1898, 1898, w^3 - 7*w^2 + 10*w + 8]', '[1898, 1898, 8*w^3 - 10*w^2 - 39*w - 9]', '[1898, 1898, 3*w^3 - 2*w^2 - 22*w + 1]', '[1898, 1898, 7*w^3 - 11*w^2 - 32*w + 2]', '[1912, 478, -w^3 - 3*w^2 + 15*w + 7]', '[1912, 478, -w^3 - 3*w^2 + 15*w + 9]', '[1916, 958, 4*w^3 - 3*w^2 - 26*w - 5]', '[1916, 958, 5*w^2 - 14*w - 7]', '[1924, 962, -3*w^3 + 6*w^2 + 11*w - 12]', '[1924, 962, w^2 - 2*w - 9]', '[1924, 962, 3*w^2 - 4*w - 7]', '[1924, 962, w^3 - 2*w^2 - w + 8]', '[1924, 962, 2*w^3 - 7*w^2 - 2*w + 9]', '[1924, 962, w^2 - 2*w + 5]', '[1926, 642, 8*w^3 - 14*w^2 - 35*w + 3]', '[1926, 642, w^3 - 5*w^2 + 10]', '[1926, 642, 2*w^3 - 5*w^2 - 5*w + 12]', '[1926, 642, -8*w^3 + 13*w^2 + 33*w - 2]', '[1928, 482, 7*w^3 - 11*w^2 - 31*w + 1]', '[1928, 482, 5*w^3 - 7*w^2 - 23*w - 1]', '[1931, 1931, 5*w^3 - 9*w^2 - 19*w + 8]', '[1931, 1931, -7*w^3 + 12*w^2 + 28*w - 6]', '[1936, 22, -4*w^3 + 8*w^2 + 12*w - 2]', '[1936, 22, -4*w^3 + 8*w^2 + 12*w - 6]', '[1936, 242, 2*w^3 - 8*w^2 + 2*w + 6]', '[1936, 242, -2*w^3 + 14*w + 10]', '[1962, 654, -4*w^3 + 7*w^2 + 13*w + 6]', '[1962, 654, -4*w^3 + 10*w^2 + 13*w - 9]', '[1966, 1966, -9*w^3 + 15*w^2 + 40*w - 4]', '[1966, 1966, -11*w^3 + 16*w^2 + 50*w + 9]', '[1969, 1969, 5*w^3 - 8*w^2 - 24*w - 8]', '[1969, 1969, 4*w^3 - 8*w^2 - 11*w]', '[1969, 1969, -2*w^3 + 11*w + 8]', '[1969, 1969, -3*w^3 + 6*w^2 + 14*w - 6]', '[1969, 1969, 2*w^3 - 4*w^2 - 11*w + 4]', '[1969, 1969, -5*w^3 + 10*w^2 + 16*w - 2]', '[1969, 1969, -5*w^3 + 14*w^2 + 10*w - 14]', '[1969, 1969, 5*w^3 - 8*w^2 - 19*w - 3]', '[1993, 1993, 3*w^3 - 9*w^2 - 7*w + 12]', '[1993, 1993, -w^3 + 5*w^2 + w - 8]', '[1993, 1993, 4*w^3 - 7*w^2 - 13*w - 1]', '[1993, 1993, 10*w^3 - 14*w^2 - 49*w - 10]', '[1994, 1994, -9*w^3 + 19*w^2 + 30*w - 24]', '[1994, 1994, -8*w^3 + 14*w^2 + 29*w - 11]', '[1994, 1994, 8*w^3 - 14*w^2 - 33*w + 1]', '[1994, 1994, 6*w^3 - 5*w^2 - 35*w - 20]', '[2012, 1006, -4*w^3 + 11*w^2 + 8*w - 7]', '[2012, 1006, 2*w^3 - w^2 - 10*w - 9]', '[2012, 1006, -2*w^3 - 3*w^2 + 26*w + 5]', '[2012, 1006, -5*w^3 + 10*w^2 + 19*w - 4]', '[2017, 2017, -8*w^3 + 12*w^2 + 35*w + 4]', '[2017, 2017, -w^3 + 7*w + 11]', '[2018, 2018, 7*w^3 - 13*w^2 - 28*w + 4]', '[2018, 2018, 6*w^3 - 10*w^2 - 27*w - 3]', '[2027, 2027, -4*w^3 + 11*w^2 + 7*w - 13]', '[2027, 2027, 2*w^3 - 6*w^2 - w + 8]', '[2027, 2027, -3*w^3 + 4*w^2 + 14*w - 2]', '[2027, 2027, w^3 + w^2 - 7*w - 12]', '[2029, 2029, -4*w^2 + 5*w + 14]', '[2029, 2029, -6*w^3 + 10*w^2 + 24*w + 1]', '[2029, 2029, 5*w^3 - 10*w^2 - 21*w + 7]', '[2029, 2029, -6*w^3 + 7*w^2 + 31*w + 15]', '[2038, 2038, 4*w^3 - 9*w^2 - 9*w + 2]', '[2038, 2038, 5*w^3 - 9*w^2 - 18*w]', '[2039, 2039, -7*w^3 + 13*w^2 + 27*w - 10]', '[2039, 2039, -6*w^3 + 15*w^2 + 17*w - 15]', '[2042, 2042, 7*w^3 - 16*w^2 - 20*w + 23]', '[2042, 2042, -w^3 - w^2 + 10*w]', '[2043, 681, -2*w^3 + 16*w + 11]', '[2043, 681, w^3 - 2*w^2 - 8]', '[2048, 8, 4*w^3 - 4*w^2 - 20*w - 12]', '[2053, 2053, w^3 - 3*w^2 - 5]', '[2053, 2053, -5*w^3 + 9*w^2 + 18*w - 5]', '[2053, 2053, -4*w^3 + 9*w^2 + 9*w - 7]', '[2053, 2053, 2*w^3 - 3*w^2 - 9*w - 7]', '[2061, 687, 13*w^3 - 20*w^2 - 60*w - 2]', '[2061, 687, -w^3 - 2*w^2 + 16*w]', '[2063, 2063, -3*w^3 + 7*w^2 + 10*w - 1]', '[2063, 2063, -2*w^3 + 6*w^2 + 2*w - 11]', '[2063, 2063, w^2 + w - 9]', '[2063, 2063, -2*w^3 + 2*w^2 + 10*w - 3]', '[2066, 2066, -4*w^2 + 11*w + 7]', '[2066, 2066, -8*w^3 + 20*w^2 + 25*w - 31]', '[2068, 1034, -9*w^3 + 20*w^2 + 29*w - 22]', '[2068, 1034, -2*w^3 + 7*w^2 + 4*w - 11]', '[2068, 1034, -w^3 - 2*w^2 + 5*w + 6]', '[2068, 1034, w^3 - 4*w^2 + w + 14]', '[2087, 2087, 4*w^3 - 7*w^2 - 15*w + 11]', '[2087, 2087, -3*w^3 + 7*w^2 + 6*w - 13]', '[2089, 2089, 5*w^3 - 6*w^2 - 28*w - 6]', '[2089, 2089, -4*w^3 + 3*w^2 + 23*w + 9]', '[2089, 2089, 9*w^3 - 9*w^2 - 49*w - 22]', '[2089, 2089, -12*w^3 + 18*w^2 + 56*w + 5]', '[2096, 262, 4*w^2 - 12*w - 6]', '[2096, 262, -6*w^3 + 10*w^2 + 26*w + 4]', '[2096, 262, 4*w^3 - 8*w^2 - 10*w - 4]', '[2096, 262, -4*w^3 + 4*w^2 + 24*w + 10]', '[2099, 2099, -2*w^3 + w^2 + 13*w + 1]', '[2099, 2099, -w^3 + 5*w^2 - 4*w - 9]', '[2104, 526, -5*w^3 + 3*w^2 + 31*w + 19]', '[2104, 526, w^3 - 5*w^2 + w + 9]', '[2104, 526, 7*w^3 - 9*w^2 - 37*w - 9]', '[2104, 526, 11*w^3 - 17*w^2 - 51*w - 5]', '[2106, 78, -3*w^3 + 3*w^2 + 18*w]', '[2106, 78, 3*w^2 - 9*w - 6]', '[2106, 78, -6*w^3 + 9*w^2 + 27*w]', '[2111, 2111, 4*w^3 - 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30*w + 7]', '[4274, 4274, -2*w^3 + 6*w^2 - 3*w - 5]', '[4276, 2138, -4*w^3 + 3*w^2 + 28*w + 7]', '[4276, 2138, 2*w^3 - 3*w^2 - 8*w - 9]', '[4276, 2138, 2*w^3 - 5*w^2 - 4*w - 5]', '[4276, 2138, -5*w^3 + 14*w^2 + 5*w + 2]', '[4283, 4283, 2*w^2 - 7*w - 8]', '[4283, 4283, -3*w^3 + 4*w^2 + 16*w - 6]', '[4297, 4297, -6*w^3 + 10*w^2 + 23*w - 2]', '[4297, 4297, -5*w^3 + 12*w^2 + 10*w - 8]', '[4302, 1434, -4*w^2 + 7*w + 7]', '[4302, 1434, w^3 - 6*w^2 + 4*w + 11]', '[4307, 4307, 5*w^3 - 13*w^2 - 12*w + 9]', '[4307, 4307, -w^3 + 4*w^2 - 3*w - 9]', '[4307, 4307, -3*w^3 + 4*w^2 + 15*w - 5]', '[4307, 4307, 2*w^3 - w^2 - 9*w - 9]', '[4311, 1437, 4*w^3 - 5*w^2 - 21*w + 1]', '[4311, 1437, -w^3 + 5*w^2 - 6*w - 7]', '[4316, 2158, -w^2 - 2*w + 9]', '[4316, 2158, w^3 + 2*w^2 - 15*w + 2]', '[4316, 2158, -3*w^3 + 2*w^2 + 21*w + 10]', '[4316, 2158, 4*w^3 - 9*w^2 - 14*w + 3]', '[4316, 2158, 7*w^3 - 8*w^2 - 35*w - 8]', '[4316, 2158, 5*w^3 - 16*w^2 - w + 12]', '[4328, 1082, 17*w^3 - 21*w^2 - 87*w - 29]', '[4328, 1082, w^3 + 3*w^2 - 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8]', '[5186, 5186, 5*w^3 - 11*w^2 - 18*w + 6]', '[5192, 1298, -7*w^3 + 13*w^2 + 29*w - 13]', '[5192, 1298, -w^3 + 3*w^2 - 5*w - 5]', '[5192, 1298, 3*w^3 - 9*w^2 - w + 9]', '[5192, 1298, 5*w^3 - 7*w^2 - 23*w + 1]', '[5193, 1731, 5*w^3 - 5*w^2 - 29*w - 18]', '[5193, 1731, 7*w^3 - 14*w^2 - 24*w + 10]', '[5202, 102, 2*w^3 - 6*w^2 - w + 13]', '[5202, 102, -w^3 - 3*w^2 + 14*w + 22]', '[5228, 2614, 9*w^3 - 16*w^2 - 31*w - 10]', '[5228, 2614, -9*w^3 + 20*w^2 + 23*w + 2]', '[5231, 5231, -5*w^3 + 8*w^2 + 24*w - 8]', '[5231, 5231, 6*w^3 - 12*w^2 - 22*w + 3]', '[5233, 5233, 6*w^3 - 7*w^2 - 34*w - 6]', '[5233, 5233, 5*w^2 - 16*w - 2]', '[5254, 5254, 7*w^3 - 15*w^2 - 22*w + 12]', '[5254, 5254, -4*w^3 + 7*w^2 + 11*w - 2]', '[5254, 5254, 2*w^3 - 4*w^2 - 9*w + 13]', '[5254, 5254, w^3 - 2*w^2 - 6*w - 7]', '[5256, 438, 13*w^3 - 19*w^2 - 61*w - 15]', '[5256, 438, 11*w^3 - 19*w^2 - 45*w - 1]', '[5258, 5258, 2*w^3 - w^2 - 17*w - 8]', '[5258, 5258, 2*w^3 - 17*w - 11]', '[5258, 5258, w^3 + 2*w^2 - 14*w + 1]', '[5258, 5258, 3*w^3 - 3*w^2 - 20*w + 6]', '[5269, 5269, -2*w^3 - w^2 + 16*w + 8]', '[5269, 5269, 2*w^3 - 9*w^2 + 4*w + 12]', '[5269, 5269, -4*w^2 + 14*w - 1]', '[5269, 5269, -6*w^3 + 8*w^2 + 32*w + 5]', '[5276, 2638, 3*w^3 - 2*w^2 - 15*w - 12]', '[5276, 2638, 2*w^3 + w^2 - 14*w - 19]', '[5279, 5279, -4*w^3 + 6*w^2 + 20*w - 7]', '[5279, 5279, -3*w^3 + 8*w^2 + 2*w - 8]', '[5279, 5279, -6*w^3 + 10*w^2 + 25*w - 6]', '[5279, 5279, -7*w^3 + 14*w^2 + 26*w - 6]', '[5283, 1761, -2*w^3 + w^2 + 12*w - 2]', '[5283, 1761, -2*w^3 + 7*w^2 - 14]', '[5284, 2642, -w^3 + 8*w^2 - 11*w - 8]', '[5284, 2642, 3*w^3 - 23*w - 12]', '[5288, 1322, w^3 - 5*w^2 - w + 17]', '[5288, 1322, -7*w^3 + 7*w^2 + 35*w + 17]', '[5291, 5291, -5*w^3 + 9*w^2 + 19*w - 12]', '[5291, 5291, -8*w^3 + 19*w^2 + 26*w - 20]', '[5291, 5291, 2*w^3 - 5*w^2 - 12*w + 12]', '[5291, 5291, 7*w^3 - 17*w^2 - 17*w + 20]', '[5291, 5291, 5*w^3 - 11*w^2 - 16*w + 3]', '[5291, 5291, -3*w^3 + 10*w^2 - 2*w - 8]', '[5291, 5291, 5*w^3 - 7*w^2 - 19*w + 4]', '[5291, 5291, -6*w^3 + 8*w^2 + 29*w + 2]', '[5291, 5291, 6*w^3 - 13*w^2 - 24*w + 8]', '[5291, 5291, 3*w^2 + 2*w - 8]', '[5291, 5291, -2*w^3 + 3*w^2 + 5*w + 7]', '[5291, 5291, -3*w^3 + 7*w^2 + 5*w - 12]', '[5302, 5302, -6*w^3 + 13*w^2 + 17*w - 12]', '[5302, 5302, -9*w^3 + 20*w^2 + 28*w - 21]', '[5302, 5302, 4*w^3 - 6*w^2 - 11*w + 3]', '[5302, 5302, 5*w^3 - 9*w^2 - 16*w + 6]', '[5303, 5303, 9*w^3 - 12*w^2 - 43*w - 7]', '[5303, 5303, -2*w^3 + 5*w^2 + w - 9]', '[5303, 5303, 5*w^3 - 9*w^2 - 20*w + 11]', '[5303, 5303, 8*w^3 - 12*w^2 - 37*w]', '[5312, 332, -6*w^2 + 16*w + 10]', '[5312, 332, 4*w^3 - 2*w^2 - 28*w - 6]', '[5317, 5317, -12*w^3 + 26*w^2 + 38*w - 37]', '[5317, 5317, -6*w^3 + 10*w^2 + 16*w - 17]', '[5317, 5317, -4*w^3 + 12*w^2 + 9*w - 14]', '[5317, 5317, -16*w^3 + 35*w^2 + 54*w - 50]', '[5317, 5317, -4*w^3 + 5*w^2 + 6*w - 14]', '[5317, 5317, -w^3 + 6*w^2 - 12]', '[5324, 22, -6*w^3 + 15*w^2 + 22*w - 23]', '[5324, 22, 4*w^3 - 11*w^2 - 16*w + 9]', '[5324, 242, 4*w^3 - 9*w^2 - 16*w + 3]', '[5324, 242, -2*w^3 + 5*w^2 + 10*w - 13]', '[5324, 2662, 6*w^3 - 11*w^2 - 24*w + 11]', '[5324, 2662, -2*w^3 + 5*w^2 - 7]', '[5326, 5326, 7*w^3 - 14*w^2 - 24*w + 9]', '[5326, 5326, 7*w^3 - 8*w^2 - 38*w - 19]', '[5328, 222, -4*w^3 + 12*w^2 + 8*w - 14]', '[5328, 222, -4*w^2 + 4*w + 10]', '[5329, 73, -3*w^3 + 6*w^2 + 9*w + 7]', '[5329, 73, -3*w^3 + 6*w^2 + 9*w - 13]', '[5329, 5329, -5*w^3 + 11*w^2 + 22*w - 17]', '[5329, 5329, 8*w^3 - 10*w^2 - 43*w - 10]', '[5344, 668, -4*w^3 + 12*w^2 + 10*w - 18]', '[5344, 668, -2*w^3 + 8*w^2 + 4*w - 10]', '[5351, 5351, -8*w^3 + 16*w^2 + 28*w - 19]', '[5351, 5351, -7*w^3 + 15*w^2 + 22*w - 5]', '[5374, 5374, 4*w^3 - 5*w^2 - 21*w - 12]', '[5374, 5374, 7*w^3 - 11*w^2 - 28*w - 4]', '[5374, 5374, 10*w^3 - 17*w^2 - 41*w + 2]', '[5374, 5374, 8*w^3 - 8*w^2 - 43*w - 25]', '[5378, 5378, -w^3 + 5*w^2 - 4*w - 12]', '[5378, 5378, 2*w^3 - w^2 - 13*w + 2]', '[5387, 5387, -2*w^3 + w^2 + 11*w - 3]', '[5387, 5387, -3*w^3 + 9*w^2 + 4*w - 17]', '[5391, 1797, -6*w^3 + 16*w^2 + 14*w - 13]', '[5391, 1797, -2*w^3 + 10*w + 11]', '[5391, 1797, 5*w^3 - 4*w^2 - 27*w - 19]', '[5391, 1797, 4*w^3 - 4*w^2 - 19*w - 12]', '[5392, 674, 4*w^3 - 6*w^2 - 22*w + 6]', '[5392, 674, -10*w^3 + 12*w^2 + 54*w + 14]', '[5392, 674, 2*w^3 - 2*w^2 - 16*w - 2]', '[5392, 674, -12*w^3 + 12*w^2 + 66*w + 28]', '[5398, 5398, 5*w^3 - 10*w^2 - 22*w + 7]', '[5398, 5398, -w^3 - 4*w^2 + 12*w + 21]', '[5399, 5399, 8*w^3 - 19*w^2 - 28*w + 20]', '[5399, 5399, -9*w^3 + 16*w^2 + 35*w + 3]', '[5399, 5399, -2*w^3 + 7*w^2 + 10*w - 12]', '[5399, 5399, 5*w^3 - 12*w^2 - 7*w - 3]', '[5402, 5402, -2*w^3 + 7*w^2 + 11*w]', '[5402, 5402, -5*w^3 + 12*w^2 + 16*w - 9]', '[5402, 5402, -2*w^2 - w + 9]', '[5402, 5402, 9*w^3 - 21*w^2 - 32*w + 34]', '[5408, 52, -6*w^3 + 14*w^2 + 20*w - 12]', '[5408, 52, -10*w^3 + 16*w^2 + 44*w + 6]', '[5408, 52, 2*w^2 + 2*w - 8]', '[5408, 52, -8*w^3 + 14*w^2 + 34*w]', '[5408, 676, -6*w^3 + 8*w^2 + 28*w + 2]', '[5408, 676, -4*w^3 + 12*w^2 + 2*w - 10]', '[5409, 1803, -6*w^3 + 17*w^2 + 13*w - 17]', '[5409, 1803, -6*w^3 + 5*w^2 + 34*w + 16]', '[5409, 1803, -4*w^3 + 8*w^2 + 15*w - 16]', '[5409, 1803, -9*w^3 + 13*w^2 + 44*w + 5]', '[5413, 5413, -3*w^3 + 4*w^2 + 10*w - 10]', '[5413, 5413, 4*w^3 - 5*w^2 - 19*w - 13]', '[5422, 5422, 4*w^2 - 5*w - 11]', '[5422, 5422, 3*w^3 - 4*w^2 - 18*w - 11]', '[5447, 5447, -w^3 + 6*w^2 + 3*w - 13]', '[5447, 5447, -2*w^3 + 7*w^2 - w - 11]', '[5447, 5447, 7*w^3 - 18*w^2 - 21*w + 19]', '[5447, 5447, 7*w^3 - 17*w^2 - 20*w + 15]', '[5447, 5447, 3*w^3 - 9*w^2 - 15*w + 4]', '[5447, 5447, -w^3 + w^2 + 12*w - 11]', '[5447, 5447, 6*w^3 - 11*w^2 - 27*w - 1]', '[5447, 5447, 3*w^3 - 3*w^2 - 16*w + 1]', '[5447, 5447, 5*w^3 - 5*w^2 - 29*w - 4]', '[5447, 5447, -9*w^3 + 21*w^2 + 33*w - 32]', '[5447, 5447, 2*w^3 - w^2 - 7*w - 7]', '[5447, 5447, -w^3 + 7*w^2 - 11*w - 8]', '[5449, 5449, 7*w^3 - 15*w^2 - 28*w + 13]', '[5449, 5449, 2*w^3 - 9*w^2 - 2*w + 20]', '[5464, 1366, 9*w^3 - 13*w^2 - 39*w - 5]', '[5464, 1366, w^3 - 5*w^2 + w + 19]', '[5468, 2734, -7*w^3 + 14*w^2 + 25*w - 4]', '[5468, 2734, -3*w^3 + 6*w^2 + 5*w + 4]', '[5471, 5471, -6*w^3 + 13*w^2 + 15*w - 17]', '[5471, 5471, 5*w^3 - 6*w^2 - 26*w - 2]', '[5473, 5473, 5*w^2 - 3*w - 13]', '[5473, 5473, w^3 - 3*w^2 - w - 6]', '[5473, 5473, -9*w^3 + 23*w^2 + 26*w - 29]', '[5473, 5473, 5*w^2 - w - 9]', '[5473, 5473, w^3 - w^2 - 5*w - 10]', '[5473, 5473, -7*w^3 + 19*w^2 + 18*w - 21]', '[5476, 74, 9*w^3 - 18*w^2 - 27*w - 4]', '[5476, 74, -5*w^3 + 10*w^2 + 15*w - 4]', '[5476, 2738, 5*w^3 - 8*w^2 - 25*w]', '[5476, 2738, w^3 - 13*w + 4]', '[5483, 5483, w^3 + 3*w^2 - 16*w - 11]', '[5483, 5483, 3*w^3 - 4*w^2 - 11*w - 13]', '[5483, 5483, -7*w^3 + 7*w^2 + 40*w + 17]', '[5483, 5483, -6*w^3 + 5*w^2 + 36*w + 18]', '[5498, 5498, w^3 - w^2 - 6]', '[5498, 5498, -6*w^3 + 13*w^2 + 21*w - 8]', '[5499, 1833, w^3 - 2*w^2 + 3*w + 7]', '[5499, 1833, -7*w^3 + 10*w^2 + 34*w]', '[5499, 1833, -12*w^3 + 28*w^2 + 38*w - 31]', '[5499, 1833, 5*w^3 - 8*w^2 - 20*w + 6]', '[5499, 1833, -8*w^3 + 15*w^2 + 34*w - 4]', '[5499, 1833, 8*w^3 - 13*w^2 - 30*w + 8]', '[5507, 5507, -3*w^3 + 4*w^2 + 15*w - 7]', '[5507, 5507, -w^3 + 4*w^2 - 3*w - 11]', '[5517, 1839, 2*w^2 - 11*w + 4]', '[5517, 1839, 7*w^3 - 12*w^2 - 32*w + 2]', '[5519, 5519, 4*w^3 - 11*w^2 - w + 7]', '[5519, 5519, 9*w^3 - 15*w^2 - 38*w + 5]', '[5524, 2762, -2*w^3 - w^2 + 22*w + 5]', '[5524, 2762, -6*w^3 + 9*w^2 + 30*w - 1]', '[5524, 2762, w^3 - 2*w^2 - w - 10]', '[5524, 2762, -5*w^3 + 12*w^2 + 11*w + 4]', '[5531, 5531, -12*w^3 + 12*w^2 + 66*w + 31]', '[5531, 5531, -4*w^3 + 3*w^2 + 27*w + 11]', '[5533, 5533, -6*w^3 + 14*w^2 + 19*w - 24]', '[5533, 5533, 7*w^3 - 12*w^2 - 26*w + 6]', '[5533, 5533, -7*w^3 + 14*w^2 + 23*w - 13]', '[5533, 5533, -w^3 + w^2 + 11*w + 12]', '[5533, 5533, -5*w^3 + 18*w^2 - 3*w - 15]', '[5533, 5533, -5*w^3 + 9*w^2 + 23*w - 20]', '[5533, 5533, 5*w^3 - 5*w^2 - 31*w - 4]', '[5533, 5533, 5*w^3 - 10*w^2 - 13*w + 9]', '[5546, 5546, 2*w^3 - 8*w^2 - 5*w + 17]', '[5546, 5546, 5*w^3 - 12*w^2 - 12*w + 19]', '[5546, 5546, w^3 - 6*w^2 + 6*w + 23]', '[5546, 5546, 3*w^3 - 11*w^2 - 6*w + 24]', '[5557, 5557, -5*w^3 + 11*w^2 + 12*w - 3]', '[5557, 5557, 6*w^3 - 11*w^2 - 21*w + 1]', '[5564, 2782, -3*w^3 + 10*w^2 + w - 14]', '[5564, 2782, -8*w^3 + 23*w^2 + 10*w - 13]', '[5564, 2782, 7*w^3 - 8*w^2 - 39*w - 16]', '[5564, 2782, w^3 - 8*w^2 + 15*w - 4]', '[5564, 2782, -w^2 - 2*w + 11]', '[5564, 2782, -4*w^3 + 9*w^2 + 14*w - 1]', '[5564, 2782, 3*w^2 - 2*w - 13]', '[5564, 2782, -3*w^3 + 4*w^2 + 15*w - 8]', '[5564, 2782, -3*w^3 + 2*w^2 + 17*w + 2]', '[5564, 2782, -8*w^3 + 9*w^2 + 38*w + 15]', '[5564, 2782, -4*w^3 + 11*w^2 + 10*w - 7]', '[5564, 2782, w^3 - 4*w^2 + 3*w + 12]', '[5569, 5569, 3*w^3 - 10*w^2 - 5*w + 11]', '[5569, 5569, -w^3 + 6*w^2 - w - 13]', '[5581, 5581, -7*w^3 + 15*w^2 + 17*w + 2]', '[5581, 5581, w^3 - w^2 - 4*w - 11]', '[5581, 5581, w^3 + 5*w^2 - 20*w - 9]', '[5581, 5581, -5*w^3 + 8*w^2 + 25*w - 5]', '[5584, 698, -2*w^3 + 8*w^2 - 12]', '[5584, 698, 4*w^2 - 6*w - 8]', '[5591, 5591, 2*w^3 + w^2 - 10*w - 12]', '[5591, 5591, 3*w^3 - 11*w^2 + 4*w + 9]', '[5591, 5591, 5*w^3 - 7*w^2 - 17*w - 6]', '[5591, 5591, -8*w^3 + 21*w^2 + 20*w - 20]', '[5594, 5594, 3*w^3 - 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10]', '[5651, 5651, w^2 + 2*w - 12]', '[5653, 5653, 5*w^3 - 10*w^2 - 22*w + 12]', '[5653, 5653, -2*w^3 + 6*w^2 + 4*w - 17]', '[5666, 5666, -4*w^3 + w^2 + 23*w + 20]', '[5666, 5666, 7*w^3 - 13*w^2 - 30*w + 2]', '[5666, 5666, 8*w^3 - 16*w^2 - 31*w + 9]', '[5666, 5666, 4*w^3 - 11*w^2 - 13*w + 20]', '[5668, 2834, -w^3 + 4*w^2 + w + 4]', '[5668, 2834, -w^3 + 6*w^2 - 3*w - 12]', '[5668, 2834, -3*w^3 + 14*w^2 - 15*w + 6]', '[5668, 2834, -2*w^3 + 3*w^2 + 14*w - 1]', '[5668, 2834, 4*w^3 - 13*w^2 - 6*w + 11]', '[5668, 2834, 5*w^2 - 6*w - 17]', '[5672, 1418, 11*w^3 - 17*w^2 - 49*w - 11]', '[5672, 1418, -7*w^3 + 7*w^2 + 41*w + 15]', '[5687, 517, 5*w^3 - 9*w^2 - 21*w + 12]', '[5687, 517, 3*w^3 - 7*w^2 - 2*w - 3]', '[5687, 517, -w^3 + 3*w^2 - 3*w - 8]', '[5687, 517, 8*w^3 - 15*w^2 - 31*w + 3]', '[5687, 5687, 3*w^3 - 2*w^2 - 18*w - 2]', '[5687, 5687, -3*w^3 + 2*w^2 + 21*w + 11]', '[5687, 5687, 6*w^3 - 4*w^2 - 37*w - 24]', '[5687, 5687, -2*w^3 + 8*w^2 - 3*w - 12]', '[5689, 5689, 4*w^2 - 4*w - 9]', '[5689, 5689, 4*w^3 - 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7]', '[9698, 9698, -11*w^3 + 21*w^2 + 34*w + 10]', '[9698, 9698, -12*w^3 + 20*w^2 + 49*w + 11]', '[9698, 9698, -4*w^3 + 12*w^2 + 13*w - 21]', '[9698, 9698, -w^3 + w^2 + 8]', '[9698, 9698, 17*w^3 - 25*w^2 - 78*w - 18]', '[9698, 9698, 18*w^3 - 22*w^2 - 89*w - 33]', '[9698, 9698, 9*w^3 - 19*w^2 - 34*w + 14]', '[9698, 9698, -2*w^3 + 5*w^2 + 11*w - 14]', '[9698, 9698, 13*w^3 - 24*w^2 - 46*w - 9]', '[9698, 9698, 12*w^3 - 17*w^2 - 53*w - 20]', '[9698, 9698, 7*w^3 - 16*w^2 - 22*w + 11]', '[9704, 2426, -5*w^3 + 13*w^2 + 11*w - 3]', '[9704, 2426, 21*w^3 - 25*w^2 - 105*w - 39]', '[9704, 2426, -w^3 + w^2 + w + 11]', '[9704, 2426, 3*w^3 - 3*w^2 - 13*w - 13]', '[9711, 3237, -4*w^3 + 8*w^2 + 9*w + 8]', '[9711, 3237, 4*w^3 - 6*w^2 - 20*w + 11]', '[9711, 3237, -2*w^2 + 8*w + 11]', '[9711, 3237, 7*w^3 - 14*w^2 - 24*w - 2]', '[9711, 3237, 6*w^3 - 7*w^2 - 26*w - 2]', '[9711, 3237, 8*w^3 - 21*w^2 - 16*w + 22]', '[9719, 9719, 4*w^2 - 12*w - 9]', '[9719, 9719, 4*w^3 - 4*w^2 - 24*w + 1]', '[9731, 9731, 5*w^3 - 14*w^2 - 16*w + 24]', '[9731, 9731, 10*w^3 - 24*w^2 - 28*w + 21]', '[9731, 9731, -2*w^3 + 4*w^2 + 5]', '[9731, 9731, -4*w^3 + 12*w^2 + 13*w - 10]', '[9731, 9731, 8*w^3 - 22*w^2 - 19*w + 20]', '[9731, 9731, w^3 + 4*w^2 - 8*w - 18]', '[9731, 9731, -8*w^3 + 16*w^2 + 30*w - 7]', '[9731, 9731, 4*w^3 - 4*w^2 - 14*w - 7]', '[9733, 9733, -17*w^3 + 23*w^2 + 84*w + 17]', '[9733, 9733, -2*w^3 - 2*w^2 + 17*w + 8]', '[9733, 9733, 6*w^3 - 14*w^2 - 12*w + 3]', '[9733, 9733, -6*w^3 + 12*w^2 + 24*w - 23]', '[9738, 3246, -3*w^3 + 10*w^2 + 2*w - 19]', '[9738, 3246, 9*w^3 - 10*w^2 - 50*w - 23]', '[9743, 9743, -2*w^3 + 6*w^2 - w - 18]', '[9743, 9743, 8*w^3 - 14*w^2 - 33*w - 6]', '[9746, 9746, 4*w^3 - 19*w - 5]', '[9746, 9746, 7*w^3 - 17*w^2 - 16*w + 4]', '[9746, 9746, 3*w^3 - 5*w^2 - 8*w - 12]', '[9746, 9746, 3*w^3 - 11*w^2 + 20]', '[9746, 9746, -2*w^3 - w^2 + 15*w + 2]', '[9746, 9746, -6*w^3 + 13*w^2 + 19*w + 2]', '[9746, 9746, -10*w^3 + 14*w^2 + 47*w + 5]', '[9746, 9746, -6*w^3 + 9*w^2 + 23*w + 10]', '[9748, 4874, -5*w^3 + 8*w^2 + 23*w + 10]', '[9748, 4874, -w^3 + 4*w^2 - 5*w + 10]', '[9767, 9767, -8*w^3 + 16*w^2 + 28*w - 3]', '[9767, 9767, -2*w^3 + 2*w^2 + 6*w + 19]', '[9767, 9767, 3*w^3 - 26*w - 12]', '[9767, 9767, 4*w^3 - 8*w^2 - 8*w - 5]', '[9769, 9769, -7*w^3 + 12*w^2 + 33*w - 1]', '[9769, 9769, -6*w^3 + 9*w^2 + 22*w]', '[9776, 1222, 4*w^3 - 4*w^2 - 16*w + 2]', '[9776, 1222, 2*w^3 + 2*w^2 - 20*w - 18]', '[9776, 1222, -10*w^3 + 24*w^2 + 34*w - 38]', '[9776, 1222, 2*w^3 - 6*w^2 + 14]', '[9776, 1222, 2*w^3 + 2*w^2 - 14*w - 20]', '[9776, 1222, 2*w^3 - 6*w^2 + 2*w + 20]', '[9781, 9781, -7*w^3 + 5*w^2 + 41*w + 24]', '[9781, 9781, -7*w^3 + 10*w^2 + 36*w + 4]', '[9788, 4894, 7*w^3 - 10*w^2 - 29*w - 16]', '[9788, 4894, -7*w^3 + 18*w^2 + 13*w]', '[9788, 4894, -7*w^3 + 14*w^2 + 25*w - 2]', '[9788, 4894, 3*w^3 - 6*w^2 - 5*w - 6]', '[9791, 9791, 6*w^3 - 12*w^2 - 22*w - 1]', '[9791, 9791, 2*w^3 - 4*w^2 - 2*w - 9]', '[9794, 9794, 13*w^3 - 23*w^2 - 52*w + 12]', '[9794, 9794, 6*w^3 - 10*w^2 - 23*w + 9]', '[9794, 9794, 12*w^3 - 25*w^2 - 45*w + 20]', '[9794, 9794, -6*w^3 + 18*w^2 + 11*w - 37]', '[9801, 33, -6*w^3 + 12*w^2 + 18*w - 3]', '[9801, 33, -6*w^3 + 12*w^2 + 18*w - 9]', '[9801, 363, 3*w^3 - 12*w^2 + 3*w + 9]', '[9801, 363, -3*w^3 + 21*w + 15]', '[9808, 1226, 4*w^3 - 14*w^2 - 2*w + 10]', '[9808, 1226, -2*w^3 - 2*w^2 + 16*w + 18]', '[9817, 9817, 8*w^3 - 16*w^2 - 33*w + 12]', '[9817, 9817, -6*w^3 + 13*w^2 + 22*w - 24]', '[9818, 9818, -2*w^3 + w^2 + 9*w + 12]', '[9818, 9818, -6*w^3 + 17*w^2 + 11*w - 24]', '[9819, 3273, w^3 - 3*w^2 - 8*w + 11]', '[9819, 3273, -2*w^3 + 16*w - 1]', '[9819, 3273, -6*w^3 + 13*w^2 + 23*w - 7]', '[9819, 3273, 4*w^2 - 10*w - 13]', '[9836, 4918, 2*w^3 - 7*w^2 + 2*w + 11]', '[9836, 4918, 4*w^3 - 5*w^2 - 20*w + 3]', '[9838, 9838, 12*w^3 - 24*w^2 - 49*w + 15]', '[9838, 9838, 5*w^3 - 15*w^2 - 14*w + 22]', '[9839, 9839, -3*w^3 + 3*w^2 + 15*w - 4]', '[9839, 9839, -3*w^3 + 9*w^2 + 3*w - 16]', '[9851, 9851, -5*w^3 + 13*w^2 + 14*w - 9]', '[9851, 9851, 7*w^3 - 14*w^2 - 26*w + 4]', '[9851, 9851, 3*w^2 - w - 13]', '[9851, 9851, 2*w^3 - 4*w^2 - w - 6]', '[9853, 9853, -10*w^3 + 10*w^2 + 53*w + 32]', '[9853, 9853, -11*w^3 + 16*w^2 + 47*w + 11]', '[9853, 9853, 5*w^3 - 5*w^2 - 32*w - 7]', '[9853, 9853, -2*w^3 - w^2 + 23*w - 1]', '[9866, 9866, 6*w^3 - 9*w^2 - 25*w + 4]', '[9866, 9866, 12*w^3 - 21*w^2 - 49*w + 10]', '[9886, 9886, -5*w^2 + 15*w + 32]', '[9886, 9886, 14*w^3 - 31*w^2 - 43*w + 38]', '[9886, 9886, 13*w^3 - 19*w^2 - 58*w - 10]', '[9886, 9886, -17*w^3 + 30*w^2 + 72*w - 13]', '[9887, 9887, 9*w^3 - 19*w^2 - 33*w + 14]', '[9887, 9887, -9*w^3 + 16*w^2 + 40*w]', '[9896, 2474, -3*w^3 - 3*w^2 + 35*w + 13]', '[9896, 2474, 7*w^3 - 13*w^2 - 29*w + 15]', '[9901, 9901, -5*w^3 + 10*w^2 + 13*w - 5]', '[9901, 9901, -7*w^3 + 14*w^2 + 23*w - 9]', '[9927, 3309, w^3 - w^2 - w - 12]', '[9927, 3309, 5*w^3 - 11*w^2 - 17*w]', '[9934, 9934, w^2 - 3*w - 12]', '[9934, 9934, 11*w^3 - 18*w^2 - 44*w + 5]', '[9934, 9934, -5*w^3 + 12*w^2 + 14*w - 23]', '[9934, 9934, 14*w^3 - 23*w^2 - 59*w + 2]', '[9958, 9958, 20*w^3 - 30*w^2 - 93*w - 11]', '[9958, 9958, -3*w^3 + 14*w^2 - 10*w - 9]', '[9958, 9958, -6*w^3 + 4*w^2 + 37*w + 17]', '[9958, 9958, 12*w^3 - 17*w^2 - 59*w - 6]', '[9958, 9958, w^3 + 3*w^2 - 12*w - 10]', '[9958, 9958, 3*w^3 - 13*w^2 + 14*w + 4]', '[9971, 767, -8*w^3 + 21*w^2 + 26*w - 32]', '[9971, 767, 3*w^2 - 2*w - 16]', '[9971, 767, 3*w^2 - 9*w - 17]', '[9971, 767, -11*w^3 + 27*w^2 + 30*w - 35]', '[9971, 767, 4*w^3 - 13*w^2 - 14*w + 12]', '[9971, 767, 4*w^3 - 3*w^2 - 15*w + 1]', '[9971, 767, 4*w^3 - 11*w^2 - 10*w + 4]', '[9971, 767, 3*w^3 - 3*w^2 - 18*w + 11]', '[9971, 9971, -3*w^3 + 11*w^2 + w - 24]', '[9971, 9971, 3*w^3 - 3*w^2 - 17*w + 4]', '[9971, 9971, -w^3 + 5*w^2 - 5*w - 12]', '[9971, 9971, w^3 + 3*w^2 - 11*w]', '[9972, 1662, w^3 - 8*w^2 + 3*w + 22]', '[9972, 1662, 8*w^3 - 17*w^2 - 32*w + 15]', '[9972, 1662, w^3 + 4*w^2 - 15*w - 8]', '[9972, 1662, -w^3 + 8*w^2 - 9*w - 16]', '[9973, 9973, 3*w^3 - 6*w^2 - 7*w - 11]', '[9973, 9973, 7*w^3 - 9*w^2 - 38*w - 3]', '[9986, 9986, -5*w^3 + 3*w^2 + 26*w + 18]', '[9986, 9986, -4*w^3 + 12*w^2 + 11*w - 25]', '[9986, 9986, 4*w^3 - 11*w^2 - 7*w + 20]', '[9986, 9986, -2*w^3 - w^2 + 19*w + 22]', '[9988, 4994, -8*w^3 + 19*w^2 + 20*w - 15]', '[9988, 4994, 7*w^3 - 14*w^2 - 23*w + 8]', '[9988, 4994, 5*w^3 - 10*w^2 - 13*w + 4]', '[9988, 4994, -5*w^3 + 10*w^2 + 23*w - 24]', '[9997, 9997, -6*w^3 + 11*w^2 + 20*w - 2]', '[9997, 9997, -4*w^3 + 10*w^2 + 19*w - 8]', '[9997, 9997, -9*w^3 + 20*w^2 + 36*w - 30]', '[9997, 9997, -6*w^3 + 13*w^2 + 16*w - 6]', '[9997, 9997, -4*w^3 + 10*w^2 + 21*w - 4]', '[9997, 9997, -7*w^3 + 16*w^2 + 28*w - 22]', '[10000, 10, -10]'], 'label': '4.4.7488.1', 'narrow_class_no': 2, 'primes': ['[2, 2, -w^3 + 2*w^2 + 4*w - 1]', '[9, 3, w^3 - 2*w^2 - 3*w + 1]', '[11, 11, -w^3 + 2*w^2 + 4*w]', '[11, 11, -w + 2]', '[13, 13, w + 2]', '[13, 13, w^3 - 2*w^2 - 4*w + 4]', '[13, 13, -w^2 + 2*w + 2]', '[37, 37, -w^3 + 2*w^2 + 5*w - 3]', '[37, 37, w^3 - 2*w^2 - 5*w + 1]', '[47, 47, -2*w^3 + 2*w^2 + 10*w + 5]', '[47, 47, w^2 - w - 5]', '[59, 59, -w^3 + 3*w^2 + 3*w - 6]', '[59, 59, w^3 - 3*w^2 - 3*w + 2]', '[71, 71, -2*w^3 + 4*w^2 + 7*w]', '[71, 71, w^3 - 2*w^2 - 2*w - 2]', '[73, 73, w^3 - 2*w^2 - 4*w - 2]', '[73, 73, w - 4]', '[83, 83, w^3 - w^2 - 6*w + 1]', '[83, 83, w^2 - 3*w - 3]', '[97, 97, -3*w^3 + 5*w^2 + 12*w + 1]', '[97, 97, -2*w^3 + 5*w^2 + 3*w - 1]', '[107, 107, -2*w^3 + 3*w^2 + 9*w - 1]', '[107, 107, 2*w - 3]', '[107, 107, -w^3 + 3*w^2 - 3]', '[107, 107, 2*w^3 - 4*w^2 - 8*w + 1]', '[109, 109, -3*w^3 + 5*w^2 + 12*w - 1]', '[109, 109, 2*w^3 - 5*w^2 - 3*w + 3]', '[121, 11, -2*w^3 + 4*w^2 + 6*w - 3]', '[131, 131, 2*w^2 - 6*w - 3]', '[131, 131, -3*w^3 + 5*w^2 + 13*w + 2]', '[131, 131, 2*w^3 - 4*w^2 - 5*w - 2]', '[131, 131, -2*w^3 + 2*w^2 + 12*w + 5]', '[167, 167, -2*w^2 + 4*w + 9]', '[167, 167, -w^2 + 3*w + 5]', '[179, 179, -2*w^3 + 5*w^2 + 4*w - 6]', '[179, 179, 2*w^3 - 4*w^2 - 8*w - 1]', '[179, 179, -3*w^3 + 3*w^2 + 17*w + 8]', '[179, 179, -2*w^3 + 3*w^2 + 8*w - 2]', '[193, 193, 6*w^3 - 8*w^2 - 30*w - 7]', '[193, 193, -2*w^3 + w^2 + 13*w + 7]', '[227, 227, 3*w^3 - 4*w^2 - 15*w - 1]', '[227, 227, -3*w^3 + 7*w^2 + 8*w - 3]', '[229, 229, -3*w^3 + w^2 + 20*w + 15]', '[229, 229, -w^3 + 5*w^2 - 4*w - 5]', '[239, 239, -4*w^3 + 5*w^2 + 20*w + 4]', '[239, 239, -5*w^3 + 7*w^2 + 24*w + 3]', '[241, 241, -2*w^3 + 4*w^2 + 9*w - 4]', '[241, 241, -w^3 + 2*w^2 + 6*w - 2]', '[263, 263, -w^3 + 4*w^2 - w - 7]', '[263, 263, -2*w^3 + 5*w^2 + 3*w - 5]', '[263, 263, -w^3 + 7*w + 1]', '[263, 263, -3*w^3 + 5*w^2 + 12*w - 3]', '[277, 277, -2*w^3 + w^2 + 12*w + 8]', '[277, 277, 3*w^3 - 5*w^2 - 14*w + 1]', '[277, 277, 2*w^2 - 2*w - 3]', '[277, 277, -2*w^3 + 6*w^2 + 4*w - 9]', '[289, 17, -w^3 + 4*w^2 - 4]', '[289, 17, 2*w^2 - 3*w - 6]', '[313, 313, -w - 4]', '[313, 313, -2*w^3 + 3*w^2 + 11*w + 1]', '[313, 313, -w^3 + 2*w^2 + 4*w - 6]', '[313, 313, -2*w^3 + 14*w + 13]', '[337, 337, 2*w^3 - 3*w^2 - 11*w + 3]', '[337, 337, -5*w^3 + 6*w^2 + 27*w + 7]', '[337, 337, w^3 - w^2 - 8*w - 1]', '[337, 337, -6*w^3 + 6*w^2 + 33*w + 14]', '[349, 349, -w^3 + 4*w^2 - 6]', '[349, 349, 2*w^2 - 3*w - 4]', '[359, 359, -4*w^3 + 7*w^2 + 16*w + 2]', '[359, 359, -9*w^3 + 13*w^2 + 42*w + 9]', '[373, 373, w^3 + w^2 - 10*w - 5]', '[373, 373, 2*w^2 - 7*w]', '[373, 373, 3*w^2 - 7*w - 5]', '[373, 373, 3*w^3 - 4*w^2 - 16*w - 2]', '[383, 383, 2*w^3 - 6*w^2 - 3*w + 2]', '[383, 383, w^3 - 6*w - 8]', '[397, 397, -3*w^3 + 7*w^2 + 9*w - 12]', '[397, 397, -2*w^3 + 2*w^2 + 13*w]', '[409, 409, -2*w^3 + 4*w^2 + 5*w - 8]', '[409, 409, -3*w^3 + 6*w^2 + 10*w - 10]', '[419, 419, -w^3 + 3*w^2 + 4*w - 7]', '[419, 419, w^3 - 2*w^2 - w - 3]', '[419, 419, 3*w^3 - 6*w^2 - 11*w + 1]', '[419, 419, 2*w^3 - 5*w^2 - 7*w + 3]', '[421, 421, -w^3 + 4*w^2 + w - 7]', '[421, 421, -w^3 + 4*w^2 + w - 5]', '[431, 431, w^2 - 6]', '[431, 431, -2*w^3 + 5*w^2 + 6*w - 2]', '[443, 443, 2*w^3 - 5*w^2 - 7*w - 1]', '[443, 443, 6*w^3 - 6*w^2 - 33*w - 16]', '[443, 443, w^3 + w^2 - 11*w - 6]', '[443, 443, w^3 + w^2 - 11*w - 2]', '[457, 457, 2*w^3 - 5*w^2 - 3*w - 3]', '[457, 457, -3*w^3 + 5*w^2 + 12*w + 5]', '[479, 479, -2*w^2 + 5*w + 6]', '[479, 479, -w^3 + 8*w]', '[503, 503, -2*w^3 + 5*w^2 + 9*w - 9]', '[503, 503, -3*w^3 + 7*w^2 + 12*w - 5]', '[503, 503, -w^3 + 5*w^2 - 4*w - 7]', '[503, 503, -2*w^3 + 6*w^2 + 6*w - 11]', '[529, 23, 3*w^3 - 6*w^2 - 9*w + 1]', '[529, 23, -3*w^3 + 6*w^2 + 9*w - 5]', '[541, 541, -2*w^3 + w^2 + 12*w + 6]', '[541, 541, 2*w^3 - 7*w^2 + 6]', '[563, 563, -3*w^3 + 7*w^2 + 9*w - 4]', '[563, 563, 2*w^2 - 2*w - 9]', '[563, 563, w^3 - w^2 - 3*w - 4]', '[563, 563, -3*w^3 + 8*w^2 + 6*w - 10]', '[577, 577, -6*w^3 + 9*w^2 + 26*w + 2]', '[577, 577, w^3 - 3*w^2 - 2*w + 9]', '[587, 587, -w^3 + 3*w^2 - w - 4]', '[587, 587, -3*w^3 + 5*w^2 + 13*w - 4]', '[599, 599, -w^3 + 2*w^2 + 7*w - 7]', '[599, 599, 3*w^3 - 6*w^2 - 13*w + 1]', '[599, 599, -6*w^3 + 10*w^2 + 26*w + 1]', '[599, 599, -4*w^3 + 7*w^2 + 17*w + 1]', '[601, 601, -2*w^3 + 4*w^2 + 11*w - 8]', '[601, 601, 5*w^3 - 7*w^2 - 25*w - 4]', '[601, 601, -4*w^3 + 9*w^2 + 11*w - 9]', '[601, 601, -3*w^3 + 2*w^2 + 18*w + 10]', '[613, 613, -4*w^3 + 7*w^2 + 18*w - 2]', '[613, 613, -w^3 - w^2 + 8*w + 9]', '[625, 5, -5]', '[647, 647, 3*w^3 - 2*w^2 - 17*w - 13]', '[647, 647, w^2 + w - 5]', '[647, 647, -2*w^3 + 2*w^2 + 9*w + 6]', '[647, 647, -3*w^3 + 7*w^2 + 10*w - 5]', '[661, 661, -2*w^3 + 4*w^2 + 8*w - 9]', '[661, 661, -2*w - 5]', '[683, 683, -2*w^3 + 5*w^2 + 8*w - 2]', '[683, 683, -2*w^3 + 5*w^2 + 8*w - 10]', '[709, 709, -3*w^3 + 6*w^2 + 8*w]', '[709, 709, 3*w^2 - 6*w - 4]', '[733, 733, w^3 - 2*w^2 - 4*w - 4]', '[733, 733, w - 6]', '[743, 743, -3*w^3 + 4*w^2 + 14*w]', '[743, 743, -2*w^3 + 6*w^2 + w - 6]', '[769, 769, -2*w^3 + 4*w^2 + 10*w - 3]', '[769, 769, -2*w^3 + 4*w^2 + 10*w - 5]', '[827, 827, 2*w^2 - 6*w - 5]', '[827, 827, 2*w^3 - 2*w^2 - 12*w + 1]', '[839, 839, -3*w^3 + 7*w^2 + 12*w - 13]', '[839, 839, -w^3 + 4*w^2 - w - 11]', '[841, 29, -4*w^3 + 6*w^2 + 16*w + 1]', '[841, 29, -3*w^2 + 5*w + 15]', '[853, 853, -3*w^3 + 7*w^2 + 6*w - 3]', '[853, 853, -4*w^3 + 7*w^2 + 15*w - 1]', '[863, 863, -3*w^3 + 8*w^2 + 6*w]', '[863, 863, 2*w^3 - 2*w^2 - 9*w - 10]', '[877, 877, -3*w^3 + 8*w^2 + 4*w + 2]', '[877, 877, -2*w^3 + w^2 + 16*w + 4]', '[947, 947, -3*w^3 + 3*w^2 + 13*w + 6]', '[947, 947, -5*w^3 + 13*w^2 + 11*w - 10]', '[983, 983, w^3 - 6*w^2 + 6*w + 10]', '[983, 983, -4*w^3 + 6*w^2 + 16*w + 7]', '[997, 997, w^3 - 5*w^2 - 2*w + 9]', '[997, 997, -4*w^3 + 9*w^2 + 13*w - 15]', '[997, 997, 4*w^3 - 11*w^2 - 11*w + 13]', '[997, 997, 4*w^3 - 5*w^2 - 22*w - 2]']}
• 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': [1, 2, -4, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 7488, 'disc_rad': 78, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 1]]], [7, [[4, 1]]], [11, [[2, 1], [1, 2]]], [13, [0]], [17, [[2, 2]]], [19, [[4, 1]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[4, 1]]], [37, [[2, 1], [1, 2]]], [41, [[4, 1]]], [43, [[2, 2]]], [47, [[2, 1], [1, 2]]], [53, [[2, 2]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 17.663521732655695, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.7488.1', 'local_algs': ['2.4.6.9', '3.4.2.1', '13.1.0.1', '13.1.0.1', '13.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 13], 'rd': 9.30232393605, 'regulator': {'__RealLiteral__': 0, 'data': '5.73562486991', 'prec': 44}, 'res': {'gal': ['1,6,-14,-26,35,26,-12,-4,1'], 'sib': ['3,0,-5,0,1', '1,6,-14,-26,35,26,-12,-4,1']}, 'subfield_mults': [1], 'subfields': ['-3.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{3} - 3 a^{2} - a + 2 \\)', '\\( a^{3} - 2 a^{2} - 3 a + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}