Hilbert modular form data - 4.4.13824.1-12.1-d

Formats: - HTML - YAML - JSON - 2024-05-02T21:23:27.437669

• 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': 1, 'disc': 13824, 'field_bad_primes': [2, 3], 'field_label': '4.4.13824.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.13824.1-12.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [2, 3], 'level_ideal': '[12, 6, -w^3 + w^2 + 4*w - 6]', 'level_label': '12.1', 'level_norm': 12, 'parallel_weight': 2, 'short_label': '12.1-d', '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^2+w+2]', -1], ['[3,3,w^2-w-3]', 1]], 'hecke_eigenvalues': [0, -1, -6, -2, 4, -4, -6, 2, 10, -6, 8, 0, -2, -2, 6, -6, 2, -2, 2, -10, 8, 16, 16, -8, 6, 0, 8, -2, 14, 4, -8, -8, 12, -2, -20, -4, -8, 16, 8, 4, -20, -8, 18, 6, 0, 24, -4, 24, -24, -12, -10, -26, -2, -18, -30, -10, -16, -16, -16, -16, 0, 8, -24, -16, -16, 8, -14, -18, 6, 10, 30, -22, -14, -14, 34, 2, -26, 6, 24, -20, 4, -8, 34, 2, 18, 6, 12, 20, -2, -34, -34, -34, -18, -6, -34, -6, -32, 40, -2, -2, 28, 20, 18, -42, -36, -4, 2, 2, 28, 12, -42, -26, 10, -30, 2, -22, 46, -6, -4, -28, -20, -44, 20, -16, -48, 28, -24, 32, 20, -12, -24, -32, 22, -18, -50, 30, -44, 8, 24, 28, -6, -38, 24, 0, 0, 8, 36, 48, 0, -52, 54, -26, -26, -10, 48, -24, 18, 22, -8, -24, 24, -56, -2, -34], 'hecke_polynomial': 'x', 'label': '4.4.13824.1-12.1-d'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 13824, 'ideals': ['[1, 1, 1]', '[2, 2, -w^2 + w + 2]', '[3, 3, w^2 - w - 3]', '[4, 2, -w^2 + 4]', '[6, 6, -w]', '[8, 2, -w^3 + 4*w - 2]', '[9, 3, -w^2 + 3]', '[11, 11, -w^2 + w + 1]', '[11, 11, -w^2 - w + 1]', '[12, 6, -w^3 + w^2 + 4*w - 6]', '[13, 13, w^3 - 4*w + 1]', '[13, 13, -w^3 + 4*w + 1]', '[16, 2, 2]', '[18, 6, -w^3 + w^2 + 3*w]', '[22, 22, -w^3 + w^2 + 3*w - 2]', '[22, 22, w^3 + w^2 - 3*w - 2]', '[24, 6, w^3 - 4*w]', '[25, 5, -w^2 - 2*w + 1]', '[25, 5, w^2 - 2*w - 1]', '[26, 26, -w^2 - w + 4]', '[26, 26, w^2 - w - 4]', '[27, 3, w^3 - 3*w - 3]', '[32, 4, -2*w^2 + 2*w + 4]', '[33, 33, w + 3]', '[33, 33, w - 3]', '[36, 6, -w^2 + 6]', '[37, 37, w^3 - 3*w - 1]', '[37, 37, w^3 - 3*w + 1]', '[39, 39, -w^3 - w^2 + 5*w + 3]', '[39, 39, w^3 - w^2 - 5*w + 3]', '[44, 22, -w^3 + w^2 + 4*w - 2]', '[44, 22, w^3 + w^2 - 4*w - 2]', '[48, 6, 2*w^2 + 2*w - 6]', '[50, 10, -w^3 + 5*w - 2]', '[50, 10, -w^3 + 5*w + 2]', '[52, 26, -w^2 - 2*w + 2]', '[52, 26, -w^2 + 2*w + 2]', '[54, 6, w^3 - 3*w]', '[59, 59, w^2 - w - 5]', '[59, 59, -w^2 - w + 5]', '[61, 61, -w^3 + w^2 + 4*w - 7]', '[61, 61, w^3 - 3*w^2 - 6*w + 11]', '[64, 4, -2*w^2 + 8]', '[66, 66, -w^2 + w + 6]', '[66, 66, w^2 + w - 6]', '[72, 6, -w^3 + 2*w^2 + 6*w - 6]', '[73, 73, 2*w^2 - w - 5]', '[73, 73, 2*w - 1]', '[73, 73, -2*w - 1]', '[73, 73, 2*w^2 + w - 5]', '[74, 74, w^3 - 2*w^2 - w + 4]', '[74, 74, -w^3 + 4*w^2 - w - 8]', '[75, 15, -w^3 + 5*w - 3]', '[75, 15, -w^3 + 5*w + 3]', '[78, 78, -2*w^2 - w + 6]', '[78, 78, 2*w^2 - w - 6]', '[81, 3, 3]', '[83, 83, 2*w^3 + w^2 - 9*w - 7]', '[83, 83, -2*w^3 + w^2 + 7*w + 1]', '[88, 22, w^3 - 4*w + 4]', '[88, 22, w^3 - 4*w - 4]', '[96, 12, -2*w]', '[99, 33, -w^3 + 2*w^2 + 3*w - 3]', '[99, 33, w^3 + 2*w^2 - 3*w - 3]', '[100, 10, -w^3 + w^2 + 2*w + 2]', '[100, 10, w^3 + w^2 - 2*w + 2]', '[104, 26, w^3 - 2*w - 2]', '[104, 26, w^3 - 2*w + 2]', '[107, 107, w^3 + w^2 - 4*w - 1]', '[107, 107, -w^3 + w^2 + 4*w - 1]', '[108, 6, -w^3 + 3*w^2 + 6*w - 12]', '[109, 109, -w^3 + 2*w^2 + 5*w - 11]', '[109, 109, w^3 + 2*w^2 - 5*w - 11]', '[111, 111, -4*w^2 + 4*w + 9]', '[111, 111, 2*w^2 - 2*w - 3]', '[117, 39, w^3 - w^2 - 6*w + 3]', '[117, 39, -w^3 - w^2 + 6*w + 3]', '[118, 118, -2*w^2 + 3*w + 4]', '[118, 118, 2*w^3 - 7*w - 4]', '[121, 11, 2*w^2 - 7]', '[121, 11, 2*w^2 - 5]', '[121, 121, 2*w^2 - 3*w - 5]', '[121, 121, -2*w^2 - 3*w + 5]', '[122, 122, -w^3 + w^2 + 5*w - 2]', '[122, 122, w^3 + w^2 - 5*w - 2]', '[128, 4, -2*w^3 + 8*w - 4]', '[131, 131, 3*w^3 - 2*w^2 - 14*w + 11]', '[131, 131, 3*w^3 - 12*w + 5]', '[132, 66, 2*w^3 - w^2 - 8*w + 6]', '[132, 66, -2*w^3 - w^2 + 8*w + 6]', '[143, 143, w^3 + w^2 - 3*w - 5]', '[143, 143, w^3 - 3*w^2 - w + 7]', '[143, 143, -w^3 - 3*w^2 + w + 7]', '[143, 143, -w^3 + w^2 + 3*w - 5]', '[144, 6, -2*w^2 + 6]', '[146, 146, 3*w^3 - 4*w^2 - 7*w + 2]', '[146, 146, -2*w^3 + 3*w^2 + 3*w - 2]', '[146, 146, 2*w^3 - w^2 - 5*w - 2]', '[146, 146, w^3 - 2*w^2 - 3*w + 2]', '[148, 74, w^3 + w^2 - 6*w - 4]', '[148, 74, -w^3 + w^2 + 6*w - 4]', '[150, 30, w^3 + 2*w^2 - w]', '[150, 30, -w^3 + 2*w^2 + w]', '[156, 78, -w^3 + w^2 + 4*w]', '[156, 78, w^3 + w^2 - 4*w]', '[157, 157, -3*w^3 + 2*w^2 + 13*w - 11]', '[157, 157, -w^3 + 2*w^2 + 7*w - 5]', '[162, 6, -3*w^2 + 3*w + 6]', '[166, 166, -w - 4]', '[166, 166, -w + 4]', '[167, 167, w^2 + 2*w - 5]', '[167, 167, -w^3 + w^2 + w + 1]', '[167, 167, 3*w^3 - w^2 - 9*w - 5]', '[167, 167, w^2 - 2*w - 5]', '[169, 13, -w^2 - 1]', '[169, 13, -w^2 + 7]', '[169, 169, -3*w^2 - 2*w + 7]', '[169, 169, -3*w^2 + 2*w + 7]', '[176, 22, -2*w^2 + 2*w + 2]', '[176, 22, -2*w^2 - 2*w + 2]', '[177, 177, -2*w^3 - w^2 + 8*w + 9]', '[177, 177, 3*w^2 - 2*w - 9]', '[179, 179, -w^3 + w^2 + 6*w - 1]', '[179, 179, w^3 + w^2 - 6*w - 1]', '[181, 181, -w^3 + 5*w - 5]', '[181, 181, w^3 - 5*w - 5]', '[183, 183, 2*w^2 + w - 9]', '[183, 183, -2*w^2 + w + 9]', '[191, 191, -2*w^3 + 2*w^2 + 6*w - 1]', '[191, 191, -2*w^2 + 2*w + 7]', '[191, 191, -4*w^2 + 4*w + 11]', '[191, 191, -2*w^3 + 8*w + 5]', '[192, 12, -2*w^3 + 2*w^2 + 8*w - 12]', '[198, 66, -w^2 + 3*w]', '[198, 66, -w^2 - 3*w]', '[200, 10, -w^3 + 2*w^2 + 4*w - 4]', '[200, 10, -w^3 - 2*w^2 + 4*w + 4]', '[208, 26, 2*w^3 - 8*w + 2]', '[208, 26, -2*w^3 + 8*w + 2]', '[214, 214, w^3 - 5*w^2 + w + 10]', '[214, 214, w^3 - w^2 - 3*w - 2]', '[216, 6, w^3 - 6*w]', '[218, 218, w^3 - 2*w^2 - 7*w + 4]', '[218, 218, 3*w^3 - 4*w^2 - 15*w + 16]', '[219, 219, -3*w^3 + 2*w^2 + 8*w + 3]', '[219, 219, 2*w^3 - 3*w^2 - 5*w + 3]', '[219, 219, -2*w^3 + w^2 + 7*w + 3]', '[219, 219, -w^3 + 2*w + 3]', '[222, 222, -3*w^2 + w + 6]', '[222, 222, 3*w^2 + w - 6]', '[225, 15, 2*w^3 - 2*w^2 - 6*w + 3]', '[225, 15, 2*w^3 + 2*w^2 - 6*w - 3]', '[227, 227, -w^3 + 2*w^2 + 5*w - 5]', '[227, 227, w^3 + 2*w^2 - 5*w - 5]', '[229, 229, -w^3 + 3*w + 5]', '[229, 229, -w^3 - 4*w^2 + 7*w + 13]', '[234, 78, w^3 - w^2 - 3*w + 6]', '[234, 78, w^3 + w^2 - 3*w - 6]', '[236, 118, w^3 + 3*w^2 - 4*w - 14]', '[236, 118, w^3 - 3*w^2 - 4*w + 14]', '[239, 239, -w^3 + w^2 + 5*w - 1]', '[239, 239, 2*w^3 - 4*w^2 - 12*w + 13]', '[239, 239, 2*w^3 - 2*w^2 - 10*w + 7]', '[239, 239, w^3 + w^2 - 5*w - 1]', '[241, 241, 2*w^3 - w^2 - 8*w + 5]', '[241, 241, -3*w^2 + 4*w + 7]', '[241, 241, -2*w^3 + w^2 + 6*w + 1]', '[241, 241, -2*w^3 - w^2 + 8*w + 5]', '[242, 22, 2*w^3 - w^2 - 7*w - 2]', '[242, 22, 2*w^3 - 3*w^2 - 5*w + 2]', '[242, 242, 2*w^2 - w - 10]', '[242, 242, 2*w^2 + w - 10]', '[243, 9, 3*w^2 - 3*w - 9]', '[244, 122, 2*w^3 - w^2 - 6*w - 4]', '[244, 122, -3*w^2 + 2*w + 8]', '[249, 249, -2*w^3 - w^2 + 8*w + 3]', '[249, 249, 2*w^3 - w^2 - 8*w + 3]', '[251, 251, -w^3 + 2*w - 5]', '[251, 251, 3*w^3 - 2*w^2 - 12*w + 13]', '[256, 4, 4]', '[262, 262, w^2 - w - 8]', '[262, 262, w^2 + w - 8]', '[263, 263, 2*w^3 - 2*w^2 - 8*w + 11]', '[263, 263, -w^3 + w^2 + 3*w - 7]', '[263, 263, 3*w^3 - w^2 - 11*w + 11]', '[263, 263, -2*w^3 + 6*w - 7]', '[264, 66, -w^3 + 2*w^2 + 2*w - 6]', '[264, 66, -w^3 - 2*w^2 + 2*w + 6]', '[275, 55, w^3 + 2*w^2 - w - 5]', '[275, 55, -w^3 + 2*w^2 + 6*w - 5]', '[275, 55, w^3 - 2*w^2 - w + 5]', '[275, 55, w^3 + 2*w^2 - 6*w - 5]', '[277, 277, -3*w^2 - w + 11]', '[277, 277, 3*w^2 - w - 11]', '[286, 286, 2*w^3 + 2*w^2 - 5*w - 2]', '[286, 286, -w^3 + w^2 + 5*w - 8]', '[286, 286, w^3 + w^2 - 5*w - 8]', '[286, 286, 2*w^3 - 2*w^2 - 5*w + 2]', '[288, 12, -2*w^3 + 2*w^2 + 6*w]', '[292, 146, w^3 + w^2 - 4*w - 8]', '[292, 146, -2*w^3 + w^2 + 8*w - 4]', '[292, 146, 2*w^3 + w^2 - 8*w - 4]', '[292, 146, -w^3 + w^2 + 4*w - 8]', '[296, 74, -w^3 + 2*w - 4]', '[296, 74, 3*w^3 - 10*w + 8]', '[297, 33, -w^3 - 3*w^2 + 3*w + 9]', '[297, 33, -w^3 + 3*w^2 + 3*w - 9]', '[300, 30, w^2 + 2*w - 6]', '[300, 30, w^2 - 2*w - 6]', '[311, 311, -w^3 + 5*w^2 + 7*w - 19]', '[311, 311, 2*w^3 - 3*w^2 - 8*w + 17]', '[311, 311, -2*w^3 + 6*w - 5]', '[311, 311, -2*w^3 - 2*w^2 + 8*w + 5]', '[312, 78, w^3 + 2*w^2 - 2*w]', '[312, 78, w^3 - 2*w^2 - 2*w]', '[314, 314, w^3 - 2*w^2 - 3*w + 8]', '[314, 314, -w^3 - 2*w^2 + 3*w + 8]', '[321, 321, 4*w^2 - 5*w - 9]', '[321, 321, -2*w^3 + 7*w + 3]', '[324, 6, -3*w^2 + 12]', '[325, 65, w^2 - 3*w - 1]', '[325, 65, w^3 - 3*w^2 - 4*w + 11]', '[325, 65, w^3 + 3*w^2 - 4*w - 11]', '[325, 65, w^2 + 3*w - 1]', '[327, 327, 4*w^3 - 6*w^2 - 20*w + 27]', '[327, 327, -4*w^2 - 2*w + 15]', '[332, 166, 3*w^3 - 3*w^2 - 16*w + 10]', '[332, 166, -5*w^3 + 5*w^2 + 24*w - 22]', '[333, 111, w^2 - 3*w - 3]', '[333, 111, w^2 + 3*w - 3]', '[334, 334, -w^3 + 3*w^2 - w - 4]', '[334, 334, -3*w^3 + 2*w^2 + 13*w - 10]', '[334, 334, 3*w^3 + 2*w^2 - 13*w - 10]', '[334, 334, 3*w^3 - w^2 - 9*w - 4]', '[337, 337, -2*w^3 + 8*w + 1]', '[337, 337, -w^3 + 3*w^2 + 5*w - 11]', '[337, 337, w^3 + 3*w^2 - 5*w - 11]', '[337, 337, 2*w^3 - 8*w + 1]', '[338, 26, -w^3 - 3*w^2 + 7*w + 8]', '[338, 26, 2*w^3 + 3*w^2 - 11*w - 10]', '[338, 338, -2*w^3 + w^2 + 9*w - 2]', '[338, 338, -2*w^3 - w^2 + 9*w + 2]', '[347, 347, w^3 - 3*w^2 - 6*w + 13]', '[347, 347, -w^3 - 3*w^2 + 6*w + 13]', '[349, 349, -w^3 + 4*w - 5]', '[349, 349, w^3 - 4*w - 5]', '[351, 39, -2*w^3 + 9*w + 3]', '[351, 39, 2*w^3 - 9*w + 3]', '[352, 44, -2*w^3 + 2*w^2 + 6*w - 4]', '[352, 44, 2*w^3 + 2*w^2 - 6*w - 4]', '[354, 354, -w^3 + w^2 + 5*w]', '[354, 354, w^3 + w^2 - 5*w]', '[358, 358, 3*w^3 - 3*w^2 - 7*w - 2]', '[358, 358, -w^3 - 3*w^2 + 5*w + 10]', '[361, 19, 4*w^3 - 2*w^2 - 17*w + 13]', '[361, 19, 2*w^3 - 2*w^2 - 11*w + 7]', '[362, 362, -w^3 + 4*w^2 - w - 4]', '[362, 362, w^3 + 6*w^2 - 9*w - 16]', '[363, 33, -2*w^3 + w^2 + 5*w + 3]', '[363, 33, 2*w^3 - w^2 - 7*w + 9]', '[363, 363, -w^3 + 2*w^2 + 4*w - 3]', '[363, 363, -w^3 - 2*w^2 + 4*w + 3]', '[366, 366, w^3 + 2*w^2 - 7*w - 6]', '[366, 366, -3*w^3 + 11*w + 6]', '[373, 373, -2*w^3 - 5*w^2 + 13*w + 17]', '[373, 373, 2*w^3 - w^2 - 7*w + 1]', '[382, 382, w^2 + 3*w - 2]', '[382, 382, -w^2 - w - 2]', '[382, 382, w^2 - w + 2]', '[382, 382, -w^2 + 3*w + 2]', '[383, 383, 4*w^3 - w^2 - 16*w + 13]', '[383, 383, w^2 + 2*w - 7]', '[383, 383, w^2 - 2*w - 7]', '[383, 383, 2*w^3 + 3*w^2 - 6*w - 5]', '[384, 12, 2*w^3 - 8*w]', '[393, 393, -3*w^3 + w^2 + 13*w - 3]', '[393, 393, -3*w^3 - w^2 + 13*w + 3]', '[396, 66, -w^3 - w^2 + 6*w]', '[396, 66, w^3 - w^2 - 6*w]', '[397, 397, -w^3 + 2*w^2 + 7*w - 7]', '[397, 397, w^3 + 2*w^2 - 7*w - 7]', '[400, 10, -2*w^2 - 4*w + 2]', '[400, 10, 2*w^2 - 4*w - 2]', '[407, 407, 2*w^3 - 2*w^2 - 4*w + 5]', '[407, 407, -2*w^3 + 4*w^2 + 2*w - 7]', '[407, 407, 2*w^3 + 4*w^2 - 2*w - 7]', '[407, 407, -2*w^3 - 2*w^2 + 4*w + 5]', '[416, 52, -2*w^2 - 2*w + 8]', '[416, 52, 2*w^2 - 2*w - 8]', '[419, 419, 5*w^2 - 5*w - 11]', '[419, 419, 3*w^2 - 3*w - 5]', '[421, 421, w^3 + 4*w^2 - 5*w - 17]', '[421, 421, -w^3 + 4*w^2 + 5*w - 17]', '[428, 214, 2*w^3 - w^2 - 10*w + 2]', '[428, 214, -2*w^3 - w^2 + 10*w + 2]', '[429, 429, w^3 + 3*w^2 - 4*w - 9]', '[429, 429, -w^3 + w^2 + 2*w + 3]', '[429, 429, w^3 + w^2 - 2*w + 3]', '[429, 429, -w^3 + 3*w^2 + 4*w - 9]', '[432, 6, -2*w^3 + 6*w - 6]', '[433, 433, w^3 - w^2 - 7*w + 1]', '[433, 433, 3*w - 1]', '[433, 433, -3*w - 1]', '[433, 433, 5*w^3 - 3*w^2 - 21*w + 19]', '[436, 218, -w^3 + 3*w^2 + 4*w - 10]', '[436, 218, w^3 + 3*w^2 - 4*w - 10]', '[438, 438, -2*w^3 + w^2 + 5*w]', '[438, 438, -2*w^2 + w]', '[438, 438, 2*w^2 + w]', '[438, 438, -2*w^3 - w^2 + 5*w]', '[443, 443, w^3 - 4*w^2 - 6*w + 17]', '[443, 443, -3*w^3 + 6*w^2 + 16*w - 25]', '[444, 222, -2*w^3 - w^2 + 8*w]', '[444, 222, 4*w^3 - w^2 - 16*w + 12]', '[450, 30, -2*w^3 + 2*w^2 + 9*w - 6]', '[450, 30, -2*w^3 - 2*w^2 + 9*w + 6]', '[454, 454, 3*w^3 - 2*w^2 - 9*w - 4]', '[454, 454, w^3 - 4*w^2 - w + 8]', '[458, 458, -w^3 + 2*w^2 + 5*w - 4]', '[458, 458, -w^3 - 2*w^2 + 5*w + 4]', '[467, 467, -w^3 + w^2 + 2*w - 5]', '[467, 467, w^3 + w^2 - 2*w - 5]', '[468, 78, 2*w^3 + w^2 - 6*w]', '[468, 78, -2*w^3 + w^2 + 6*w]', '[471, 471, 2*w^3 - 10*w - 3]', '[471, 471, 2*w^3 - 10*w + 3]', '[472, 118, 3*w^3 - 12*w + 4]', '[472, 118, -3*w^3 + 4*w^2 + 16*w - 16]', '[478, 478, 3*w^2 + w - 10]', '[478, 478, 2*w^3 - 2*w^2 - 5*w - 2]', '[478, 478, -4*w^2 + 3*w + 10]', '[478, 478, 3*w^2 - w - 10]', '[481, 481, w + 5]', '[481, 481, 2*w^3 - 7*w - 7]', '[481, 481, -2*w^3 + 7*w - 7]', '[481, 481, -w + 5]', '[482, 482, -w^3 + 3*w^2 + w - 8]', '[482, 482, w^3 - w^2 - w + 4]', '[482, 482, -w^3 - w^2 + w + 4]', '[482, 482, -w^3 - 5*w^2 + 9*w + 16]', '[484, 22, -w^2 - 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7]', '[1789, 1789, 3*w^3 - 2*w^2 - 9*w + 1]', '[1789, 1789, -w^3 - 6*w^2 + 11*w + 17]', '[1800, 30, -w^3 - 2*w^2 + 6*w]', '[1800, 30, -w^3 + 2*w^2 + 6*w]', '[1811, 1811, -3*w^3 + w^2 + 14*w - 1]', '[1811, 1811, -3*w^3 - w^2 + 14*w + 1]', '[1816, 454, 3*w^3 - 8*w^2 - 18*w + 28]', '[1816, 454, -w^3 + 2*w - 8]', '[1822, 1822, -3*w^3 + 4*w^2 + 5*w + 2]', '[1822, 1822, 4*w^3 - 4*w^2 - 9*w + 2]', '[1822, 1822, -2*w^3 + 6*w^2 - w - 10]', '[1822, 1822, 3*w^3 + 6*w^2 - 15*w - 22]', '[1825, 365, -3*w^3 - 3*w^2 + 9*w + 7]', '[1825, 365, -5*w^3 + 7*w^2 + 11*w - 7]', '[1825, 365, 2*w^3 - 5*w^2 + 1]', '[1825, 365, -2*w^3 - 3*w^2 + 4*w - 1]', '[1825, 365, 2*w^3 + 5*w^2 - 1]', '[1825, 365, -2*w^3 + 3*w^2 + 4*w + 1]', '[1825, 365, -3*w^3 + 3*w^2 + 9*w - 7]', '[1825, 365, -5*w^3 - 7*w^2 + 11*w + 7]', '[1826, 1826, 4*w^3 - w^2 - 19*w + 2]', '[1826, 1826, -4*w^3 - w^2 + 21*w + 10]', '[1826, 1826, -4*w^3 + w^2 + 21*w - 10]', '[1826, 1826, 4*w^3 + w^2 - 19*w - 2]', '[1832, 458, -3*w^3 + 14*w - 4]', '[1832, 458, -3*w^3 + 14*w + 4]', '[1837, 1837, -3*w^3 - 2*w^2 + 7*w + 1]', '[1837, 1837, -w^3 + 6*w^2 - w - 13]', '[1837, 1837, -w^3 + 2*w^2 - 3*w + 1]', '[1837, 1837, -3*w^3 - 6*w^2 + 11*w + 17]', '[1837, 1837, 3*w^3 - 6*w^2 - 11*w + 17]', '[1837, 1837, w^3 + 2*w^2 + 3*w + 1]', '[1837, 1837, w^3 + 6*w^2 + w - 13]', '[1837, 1837, 3*w^3 - 2*w^2 - 7*w + 1]', '[1839, 1839, -4*w^3 - 4*w^2 + 20*w + 15]', '[1839, 1839, -4*w^3 + 4*w^2 + 20*w - 15]', '[1849, 43, -4*w^3 + 2*w^2 + 17*w - 7]', '[1849, 43, 4*w^3 + 2*w^2 - 17*w - 7]', '[1850, 370, -w^3 - 3*w^2 + w + 10]', '[1850, 370, 3*w^3 - 3*w^2 - 11*w + 14]', '[1850, 370, 3*w^3 + 3*w^2 - 11*w - 14]', '[1850, 370, -w^3 + 3*w^2 + w - 10]', '[1859, 143, 2*w^3 + w^2 - 11*w + 1]', '[1859, 143, -w^3 - 2*w^2 + 7*w + 1]', '[1859, 143, -2*w^3 + w^2 + 11*w + 1]', '[1859, 143, w^3 - 2*w^2 - 7*w + 1]', '[1859, 1859, 4*w^3 + w^2 - 17*w - 11]', '[1859, 1859, -w^3 + 5]', '[1859, 1859, -w^3 - 5]', '[1859, 1859, -4*w^3 + w^2 + 17*w - 11]', '[1861, 1861, -w^3 - 5*w^2 + 6*w + 19]', '[1861, 1861, -w^3 + 5*w^2 + 6*w - 19]', '[1866, 1866, 2*w^3 + 4*w^2 - 5*w - 12]', '[1866, 1866, 5*w^3 + 6*w^2 - 25*w - 24]', '[1866, 1866, 6*w^2 + 5*w - 12]', '[1866, 1866, -5*w^3 - 3*w^2 + 23*w + 18]', '[1868, 934, 3*w^2 + 2*w - 14]', '[1868, 934, 3*w^2 - 2*w - 14]', '[1871, 1871, 3*w^2 + 2*w - 17]', '[1871, 1871, -4*w^3 + 13*w + 11]', '[1871, 1871, -2*w^3 + 5*w + 7]', '[1871, 1871, 3*w^2 - 2*w - 17]', '[1872, 78, 2*w^3 - 2*w^2 - 12*w + 6]', '[1872, 78, -2*w^3 - 2*w^2 + 12*w + 6]', '[1873, 1873, 8*w^3 - 5*w^2 - 34*w + 31]', '[1873, 1873, 4*w^2 - w - 13]', '[1873, 1873, 4*w^2 + w - 13]', '[1873, 1873, 2*w^3 - w^2 - 12*w + 1]', '[1874, 1874, -2*w^3 + w^2 + 9*w + 2]', '[1874, 1874, -2*w^2 + 3*w + 10]', '[1874, 1874, 2*w^2 + 3*w - 10]', '[1874, 1874, -2*w^3 - w^2 + 9*w - 2]', '[1875, 15, 5*w^2 - 5*w - 15]', '[1875, 75, -3*w^3 + 3*w^2 + 16*w - 9]', '[1875, 75, -3*w^3 - 3*w^2 + 16*w + 9]', '[1884, 942, 2*w^3 + 3*w^2 - 8*w - 6]', '[1884, 942, 2*w^3 - 3*w^2 - 8*w + 6]', '[1888, 236, -4*w^2 + 6*w + 8]', '[1888, 236, 4*w^3 - 14*w - 8]', '[1894, 1894, -w^2 - w - 4]', '[1894, 1894, w^2 - w + 4]', '[1898, 1898, -w^3 - 2*w^2 + w + 8]', '[1898, 1898, -3*w^3 + 9*w - 8]', '[1898, 1898, -2*w^3 + w^2 + 9*w + 4]', '[1898, 1898, 2*w^3 + 3*w^2 - 7*w - 4]', '[1898, 1898, 2*w^3 - 3*w^2 - 7*w + 4]', '[1898, 1898, -2*w^3 - w^2 + 9*w - 4]', '[1898, 1898, -3*w^3 + 9*w + 8]', '[1898, 1898, -w^3 + 2*w^2 + w - 8]', '[1907, 1907, w^3 + 3*w^2 - 8*w - 5]', '[1907, 1907, -3*w^3 - 7*w^2 + 18*w + 23]', '[1912, 478, w^3 - 6*w^2 - 8*w + 20]', '[1912, 478, -w^3 + 4*w^2 + 4*w - 22]', '[1912, 478, w^3 + 4*w^2 - 4*w - 22]', '[1912, 478, -3*w^3 + 2*w^2 + 12*w - 16]', '[1924, 962, -w^3 - 5*w^2 + 2*w + 10]', '[1924, 962, -w^3 + 7*w^2 - 2*w - 14]', '[1924, 962, w^3 + 7*w^2 + 2*w - 14]', '[1924, 962, w^3 - 5*w^2 - 2*w + 10]', '[1926, 642, -4*w^3 + 5*w^2 + 9*w]', '[1926, 642, 5*w^2 - 3*w - 12]', '[1928, 482, -7*w^3 + 6*w^2 + 30*w - 34]', '[1928, 482, -w^3 - 2*w^2 + 2*w + 10]', '[1928, 482, w^3 - 2*w^2 - 2*w + 10]', '[1928, 482, w^3 - 2*w^2 - 2*w + 14]', '[1931, 1931, -w^3 - 4*w^2 + w + 13]', '[1931, 1931, w^3 - 4*w^2 - w + 13]', '[1933, 1933, 3*w^3 + 2*w^2 - 11*w - 7]', '[1933, 1933, -3*w^3 + 2*w^2 + 11*w - 7]', '[1936, 22, 4*w^2 - 14]', '[1936, 22, 4*w^2 - 10]', '[1936, 242, 4*w^2 - 6*w - 10]', '[1936, 242, -4*w^2 - 6*w + 10]', '[1942, 1942, -w^3 + 7*w^2 - 5*w - 14]', '[1942, 1942, 3*w^3 - w^2 - 9*w - 2]', '[1944, 18, 3*w^3 - 12*w]', '[1947, 1947, w^3 - 4*w^2 - 2*w + 15]', '[1947, 1947, -w^3 + 2*w^2 + 8*w - 15]', '[1947, 1947, w^3 + 2*w^2 - 8*w - 15]', '[1947, 1947, -w^3 - 4*w^2 + 2*w + 15]', '[1950, 390, -w^3 + 3*w^2 + w]', '[1950, 390, 3*w^3 - 2*w^2 - 11*w + 6]', '[1950, 390, -3*w^3 - 2*w^2 + 11*w + 6]', '[1950, 390, -w^3 - 3*w^2 + w]', '[1952, 244, -2*w^3 + 2*w^2 + 10*w - 4]', '[1952, 244, 2*w^3 + 2*w^2 - 10*w - 4]', '[1962, 654, 4*w^3 + 2*w^2 - 15*w]', '[1962, 654, 6*w^3 - 4*w^2 - 27*w + 24]', '[1964, 982, 2*w^3 - 3*w^2 - 10*w + 8]', '[1964, 982, -2*w^3 - 3*w^2 + 10*w + 8]', '[1966, 1966, -3*w^3 + 12*w^2 - w - 22]', '[1966, 1966, 2*w^2 - 5*w - 2]', '[1966, 1966, -2*w^2 - 5*w + 2]', '[1966, 1966, -w^3 + 2*w^2 + 3*w + 2]', '[1969, 1969, 2*w^3 - 4*w^2 - w - 1]', '[1969, 1969, -4*w^2 - w + 11]', '[1969, 1969, -4*w^2 + w + 11]', '[1969, 1969, -2*w^3 - 4*w^2 + w - 1]', '[1971, 219, w^3 - 9*w^2 + 6*w + 21]', '[1971, 219, -w^3 + 6*w^2 - 3*w - 9]', '[1971, 219, -w^3 - 6*w^2 + 9*w + 15]', '[1971, 219, w^3 - 3*w^2 + 9]', '[1977, 1977, -2*w^3 + 6*w^2 - w - 9]', '[1977, 1977, -4*w^3 + 2*w^2 + 11*w + 3]', '[1979, 1979, 4*w^3 - 9*w^2 - 25*w + 29]', '[1979, 1979, 4*w^3 - 3*w^2 - 19*w + 11]', '[1983, 1983, -2*w^3 - 4*w^2 + 8*w + 9]', '[1983, 1983, 2*w^3 - 4*w^2 - 8*w + 9]', '[1991, 1991, 6*w^2 - 4*w - 11]', '[1991, 1991, 4*w^2 + 6*w + 1]', '[1991, 1991, 4*w^2 - 6*w + 1]', '[1991, 1991, 6*w^2 + 4*w - 11]', '[1992, 498, 3*w^3 - 2*w^2 - 10*w + 18]', '[1992, 498, -5*w^3 + 6*w^2 + 22*w - 30]', '[1994, 1994, 2*w^3 + 3*w^2 - 11*w - 8]', '[1994, 1994, -2*w^3 + 3*w^2 + 11*w - 8]', '[1998, 222, -w^3 - 3*w^2 + 3*w]', '[1998, 222, -w^3 + 3*w^2 + 3*w]', '[2003, 2003, -2*w^3 + 5*w^2 + 11*w - 23]', '[2003, 2003, 2*w^3 + 5*w^2 - 11*w - 23]', '[2004, 1002, 5*w^3 - 9*w^2 - 26*w + 36]', '[2004, 1002, -2*w^3 - 5*w^2 + 10*w + 18]', '[2004, 1002, -2*w^3 + 5*w^2 + 10*w - 18]', '[2004, 1002, w^3 - w^2 - 2*w + 12]', '[2008, 502, 3*w^3 + 2*w^2 - 16*w - 10]', '[2008, 502, -3*w^3 + 2*w^2 + 16*w - 10]', '[2013, 2013, -3*w^3 - 2*w^2 + 10*w + 3]', '[2013, 2013, w^3 - 8*w - 3]', '[2013, 2013, w^3 - 8*w + 3]', '[2013, 2013, -3*w^3 + 2*w^2 + 10*w - 3]', '[2017, 2017, 3*w^3 + 3*w^2 - 13*w - 19]', '[2017, 2017, -w^3 + 3*w^2 + 3*w - 19]', '[2017, 2017, w^3 + 3*w^2 - 3*w - 19]', '[2017, 2017, w^3 + 7*w^2 - 9*w - 23]', '[2019, 2019, 3*w^3 - 3*w^2 - 10*w + 3]', '[2019, 2019, -w^3 - 4*w^2 + 8*w + 9]', '[2019, 2019, w^3 + 6*w^2 - 10*w - 15]', '[2019, 2019, -5*w^3 - w^2 + 20*w + 15]', '[2022, 2022, -3*w^3 + w^2 + 11*w - 6]', '[2022, 2022, -4*w^2 - w + 12]', '[2022, 2022, 4*w^2 - w - 12]', '[2022, 2022, -3*w^3 - w^2 + 11*w + 6]', '[2025, 15, -3*w^2 - 6*w + 3]', '[2025, 15, 3*w^2 - 6*w - 3]', '[2027, 2027, 3*w^3 + w^2 - 10*w - 11]', '[2027, 2027, -3*w^3 + w^2 + 10*w - 11]', '[2028, 78, 3*w^3 - w^2 - 8*w - 6]', '[2028, 78, 3*w^3 - w^2 - 10*w + 12]', '[2028, 1014, -w^3 + 3*w^2 + 2*w - 12]', '[2028, 1014, w^3 + 3*w^2 - 2*w - 12]', '[2029, 2029, -3*w^3 + 2*w^2 + 7*w + 7]', '[2029, 2029, -3*w^3 - 6*w^2 + 15*w + 23]', '[2038, 2038, -3*w^3 + 9*w - 4]', '[2038, 2038, 3*w^3 - 9*w - 4]', '[2041, 2041, w^3 + w^2 - 5*w + 5]', '[2041, 2041, -w^3 - 5*w^2 + w + 11]', '[2041, 2041, -w^3 + 5*w^2 + w - 11]', '[2041, 2041, w^3 - w^2 - 5*w - 5]', '[2042, 2042, -7*w^3 + 7*w^2 + 19*w - 2]', '[2042, 2042, -3*w^3 - w^2 + 15*w + 10]', '[2043, 681, -2*w^3 - w^2 + 9*w - 3]', '[2043, 681, 2*w^3 - w^2 - 9*w - 3]', '[2048, 8, -4*w^3 + 16*w - 8]', '[2049, 2049, 4*w^3 + w^2 - 16*w - 9]', '[2049, 2049, -2*w^3 - 5*w^2 + 14*w + 15]', '[2053, 2053, 5*w^3 - 4*w^2 - 22*w + 25]', '[2053, 2053, w^3 + 6*w^2 - 17]', '[2061, 687, -5*w^2 + 3*w + 15]', '[2061, 687, -4*w^3 - w^2 + 15*w + 15]', '[2062, 2062, 6*w^3 - 9*w^2 - 13*w + 10]', '[2062, 2062, 2*w^3 - 4*w^2 - 13*w + 14]', '[2062, 2062, 4*w^3 + 2*w^2 - 13*w + 2]', '[2062, 2062, 2*w^3 + 3*w^2 - 13*w - 14]', '[2063, 2063, -2*w^3 + w^2 + 10*w + 1]', '[2063, 2063, 3*w^2 - 4*w - 11]', '[2063, 2063, 3*w^2 + 4*w - 11]', '[2063, 2063, 2*w^3 + w^2 - 10*w + 1]', '[2075, 415, w^3 - 4*w^2 - 7*w + 17]', '[2075, 415, -3*w^3 - 4*w^2 + 17*w + 23]', '[2075, 415, w^3 + 4*w^2 - 7*w - 17]', '[2075, 415, -3*w^3 + 4*w^2 + 17*w - 23]', '[2082, 2082, 3*w^3 - 13*w + 6]', '[2082, 2082, 3*w^3 - 13*w - 6]', '[2087, 2087, -4*w^2 - 2*w + 17]', '[2087, 2087, 4*w^3 - w^2 - 18*w + 1]', '[2087, 2087, -4*w^3 - w^2 + 18*w + 1]', '[2087, 2087, -4*w^3 + 10*w^2 + 24*w - 37]', '[2094, 2094, 2*w^2 + 5*w - 6]', '[2094, 2094, -2*w^2 + 5*w + 6]', '[2096, 262, 6*w^3 - 4*w^2 - 28*w + 22]', '[2096, 262, 6*w^3 - 24*w + 10]', '[2099, 2099, -3*w^3 - 6*w^2 + 17*w + 25]', '[2099, 2099, w^3 - 6*w^2 + w + 17]', '[2101, 2101, -w^3 - w^2 + 10*w - 5]', '[2101, 2101, -w^3 - w^2 - 7]', '[2101, 2101, w^3 + w^2 - 8*w - 1]', '[2101, 2101, w^3 + w^2 - 6*w - 11]', '[2101, 2101, w^3 - w^2 - 6*w + 11]', '[2101, 2101, w^3 - w^2 - 8*w + 1]', '[2101, 2101, -w^3 + w^2 + 7]', '[2101, 2101, -w^3 + w^2 + 10*w + 5]', '[2104, 526, 3*w^3 - 16*w + 2]', '[2104, 526, 3*w^3 + 2*w^2 - 16*w - 8]', '[2104, 526, 3*w^3 - 2*w^2 - 16*w + 8]', '[2104, 526, 3*w^3 - 16*w - 2]', '[2106, 78, -3*w^2 - 3*w + 12]', '[2106, 78, 3*w^2 - 3*w - 12]', '[2112, 132, 4*w^3 - 2*w^2 - 16*w + 12]', '[2112, 132, -4*w^3 - 2*w^2 + 16*w + 12]', '[2113, 2113, -w - 7]', '[2113, 2113, -w^3 + 5*w^2 + w - 13]', '[2113, 2113, -5*w^3 - w^2 + 19*w + 17]', '[2113, 2113, w - 7]', '[2116, 46, 5*w^2 - 26]', '[2116, 46, w^2 - 10]', '[2124, 354, w^3 + 5*w^2 - 6*w - 24]', '[2124, 354, w^3 - 5*w^2 - 6*w + 24]', '[2127, 2127, w^3 - 3*w^2 - 5*w + 3]', '[2127, 2127, -w^3 - 3*w^2 + 5*w + 3]', '[2138, 2138, -w^3 - 3*w^2 + 5*w + 2]', '[2138, 2138, -w^3 + 3*w^2 + 5*w - 2]', '[2148, 1074, -7*w^3 + 5*w^2 + 32*w - 24]', '[2148, 1074, 5*w^3 - 7*w^2 - 28*w + 24]', '[2151, 717, -2*w^3 - 2*w^2 + 9*w + 3]', '[2151, 717, 6*w^3 - w^2 - 24*w + 15]', '[2151, 717, 4*w^3 - w^2 - 18*w + 9]', '[2151, 717, 2*w^3 - 2*w^2 - 9*w + 3]', '[2158, 2158, 4*w^3 + 2*w^2 - 17*w - 10]', '[2158, 2158, -4*w^3 - 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9]', '[9838, 9838, w^3 - 3*w^2 - 11*w + 4]', '[9838, 9838, 3*w^3 - 7*w^2 - 5*w + 4]', '[9838, 9838, 3*w^3 - 15*w^2 + 3*w + 28]', '[9838, 9838, w^3 + 3*w^2 - 11*w - 4]', '[9839, 9839, -8*w^3 - 3*w^2 + 30*w + 29]', '[9839, 9839, 4*w^3 - 4*w^2 - 15*w + 25]', '[9839, 9839, -6*w^3 + 4*w^2 + 23*w - 29]', '[9839, 9839, -2*w^3 - w^2 + 4*w + 13]', '[9841, 9841, -6*w^3 + 8*w^2 + 11*w - 11]', '[9841, 9841, -2*w^3 - 3*w - 5]', '[9841, 9841, -2*w^3 - 3*w + 5]', '[9841, 9841, -6*w^3 - 8*w^2 + 11*w + 11]', '[9851, 9851, 5*w^3 + 6*w^2 - 20*w - 17]', '[9851, 9851, -4*w^3 + 13*w^2 + 25*w - 49]', '[9853, 9853, -5*w^3 - 6*w^2 + 27*w + 25]', '[9853, 9853, w^3 + 6*w^2 - 5*w - 19]', '[9853, 9853, -3*w^3 + 2*w^2 + 15*w - 19]', '[9853, 9853, -w^3 - 7*w^2 + 17]', '[9853, 9853, -7*w^3 - 3*w^2 + 22*w - 13]', '[9853, 9853, 3*w^3 + 2*w^2 - 15*w - 19]', '[9853, 9853, -w^3 + 6*w^2 + 5*w - 19]', '[9853, 9853, 7*w^3 - 2*w^2 - 25*w - 7]', '[9862, 9862, 8*w^3 - 11*w^2 - 17*w + 4]', '[9862, 9862, -7*w^2 + 3*w + 16]', '[9866, 9866, -5*w^3 - 8*w^2 + 27*w + 28]', '[9866, 9866, 3*w^3 + 6*w^2 - 19*w - 16]', '[9882, 366, -3*w^3 + 3*w^2 + 15*w - 6]', '[9882, 366, 3*w^3 + 3*w^2 - 15*w - 6]', '[9887, 9887, 6*w^3 - 8*w^2 - 15*w + 5]', '[9887, 9887, -w^3 + 3*w^2 + w - 19]', '[9887, 9887, w^3 + 3*w^2 - w - 19]', '[9887, 9887, 4*w^3 - 4*w^2 - 13*w - 1]', '[9896, 2474, -w^3 - 2*w - 10]', '[9896, 2474, 11*w^3 - 4*w^2 - 42*w + 38]', '[9897, 9897, 4*w^3 - 2*w^2 - 8*w - 15]', '[9897, 9897, 8*w^3 + 12*w^2 - 38*w - 51]', '[9900, 330, 7*w^2 + 6*w - 12]', '[9900, 330, w^3 + 5*w^2 - 18]', '[9900, 330, 7*w^2 - 6*w - 12]', '[9900, 330, w^3 - 5*w^2 + 18]', '[9901, 9901, -5*w^3 - 4*w^2 + 16*w + 5]', '[9901, 9901, 5*w^3 - 4*w^2 - 16*w + 5]', '[9903, 9903, -6*w^3 + 7*w^2 + 16*w - 3]', '[9903, 9903, 4*w^3 - 3*w^2 - 14*w - 3]', '[9914, 9914, 6*w^3 + 2*w^2 - 27*w - 16]', '[9914, 9914, 8*w^3 - 31*w - 16]', '[9923, 9923, 3*w^3 + 5*w^2 - 14*w - 13]', '[9923, 9923, 3*w^3 - 5*w^2 - 14*w + 13]', '[9924, 4962, -2*w^3 + 7*w^2 + 8*w - 18]', '[9924, 4962, -2*w^3 - 7*w^2 + 8*w + 18]', '[9925, 1985, -2*w^3 + w^2 + 13*w - 17]', '[9925, 1985, -6*w^3 - 5*w^2 + 15*w - 7]', '[9925, 1985, -2*w^3 - w^2 + 13*w + 17]', '[9925, 1985, -6*w^3 + 5*w^2 + 15*w + 7]', '[9927, 3309, -6*w^3 + 5*w^2 + 18*w + 3]', '[9927, 3309, 2*w^3 + 5*w^2 - 6*w - 21]', '[9927, 3309, -2*w^3 + 5*w^2 + 6*w - 21]', '[9927, 3309, 4*w^3 - 5*w^2 - 12*w + 3]', '[9932, 4966, 2*w^3 + 5*w^2 - 2*w - 14]', '[9932, 4966, -4*w^3 - 3*w^2 + 14*w - 2]', '[9932, 4966, -2*w^3 - 3*w^2 + 10*w + 2]', '[9932, 4966, -3*w^2 - 6*w + 14]', '[9932, 4966, -3*w^2 + 6*w + 14]', '[9932, 4966, 2*w^3 - 3*w^2 - 10*w + 2]', '[9932, 4966, 4*w^3 - 3*w^2 - 14*w - 2]', '[9932, 4966, -2*w^3 + 5*w^2 + 2*w - 14]', '[9939, 9939, -6*w^3 - w^2 + 25*w + 15]', '[9939, 9939, -5*w^3 - 5*w^2 + 20*w + 27]', '[9939, 9939, -5*w^3 + w^2 + 14*w + 15]', '[9939, 9939, -6*w^3 + w^2 + 23*w + 9]', '[9942, 9942, 7*w^3 - 6*w^2 - 19*w]', '[9942, 9942, 6*w^3 - 3*w^2 - 17*w - 12]', '[9942, 9942, -2*w^3 - 7*w^2 + 11*w + 24]', '[9942, 9942, w^3 + 4*w^2 - 11*w - 12]', '[9948, 4974, 2*w^3 + w^2 - 4*w - 12]', '[9948, 4974, 8*w^3 + w^2 - 28*w - 24]', '[9949, 9949, 4*w^3 - w^2 - 13*w - 1]', '[9949, 9949, -4*w^3 - w^2 + 13*w - 1]', '[9952, 1244, 4*w^3 - 2*w^2 - 10*w + 4]', '[9952, 1244, -4*w^3 - 2*w^2 + 18*w + 20]', '[9952, 1244, 4*w^3 - 22*w - 4]', '[9952, 1244, -6*w^3 - 2*w^2 + 26*w + 8]', '[9958, 9958, -7*w^3 + 3*w^2 + 27*w - 22]', '[9958, 9958, w^3 - 7*w^2 - w + 22]', '[9958, 9958, -3*w^3 - 3*w^2 + 15*w + 22]', '[9958, 9958, -5*w^3 - 5*w^2 + 17*w + 14]', '[9958, 9958, 5*w^3 - 5*w^2 - 17*w + 14]', '[9958, 9958, -3*w^3 + 3*w^2 + 15*w - 22]', '[9958, 9958, w^3 + 7*w^2 - w - 22]', '[9958, 9958, 7*w^3 + 3*w^2 - 27*w - 22]', '[9969, 9969, -7*w^3 + 5*w^2 + 19*w + 3]', '[9969, 9969, -w^3 + 5*w^2 - 5*w - 9]', '[9971, 767, 5*w^3 - 7*w^2 - 22*w + 23]', '[9971, 767, w^3 - 2*w^2 + w + 11]', '[9971, 767, -5*w^3 - 7*w^2 + 22*w + 23]', '[9971, 767, w^3 + 2*w^2 + w - 11]', '[9971, 9971, w^3 - 6*w^2 + 3*w + 17]', '[9971, 9971, 5*w^3 - 2*w^2 - 17*w + 17]', '[9971, 9971, 5*w^3 + 2*w^2 - 17*w - 17]', '[9971, 9971, w^3 + 6*w^2 + 3*w - 17]', '[9972, 1662, w^3 - 11*w^2 - 6*w + 48]', '[9972, 1662, w^3 + 11*w^2 - 6*w - 48]', '[9973, 9973, 2*w^3 + 7*w^2 - 5*w - 19]', '[9973, 9973, 10*w^3 - 3*w^2 - 39*w + 35]', '[9984, 156, -4*w^3 - 4*w^2 + 20*w + 12]', '[9984, 156, 4*w^3 - 4*w^2 - 20*w + 12]', '[9988, 4994, 7*w^2 + 4*w - 20]', '[9988, 4994, -2*w^3 - w^2 + 12*w + 16]', '[9988, 4994, 2*w^3 - w^2 - 12*w + 16]', '[9988, 4994, 7*w^2 - 4*w - 20]', '[9992, 2498, -w^3 + 6*w^2 + 2*w - 26]', '[9992, 2498, -w^3 - 10*w^2 - 6*w + 26]', '[9992, 2498, -w^3 + 6*w^2 + 10*w - 22]', '[9992, 2498, w^3 + 6*w^2 - 2*w - 26]', '[10000, 10, 10]', '[10000, 50, 6*w^3 + 2*w^2 - 26*w - 10]', '[10000, 50, 6*w^3 - 2*w^2 - 26*w + 10]'], 'label': '4.4.13824.1', 'narrow_class_no': 2, 'primes': ['[2, 2, -w^2 + w + 2]', '[3, 3, w^2 - w - 3]', '[11, 11, -w^2 + w + 1]', '[11, 11, -w^2 - w + 1]', '[13, 13, w^3 - 4*w + 1]', '[13, 13, -w^3 + 4*w + 1]', '[25, 5, -w^2 - 2*w + 1]', '[25, 5, w^2 - 2*w - 1]', '[37, 37, w^3 - 3*w - 1]', '[37, 37, w^3 - 3*w + 1]', '[59, 59, w^2 - w - 5]', '[59, 59, -w^2 - w + 5]', '[61, 61, -w^3 + w^2 + 4*w - 7]', '[61, 61, w^3 - 3*w^2 - 6*w + 11]', '[73, 73, 2*w^2 - w - 5]', '[73, 73, 2*w - 1]', '[73, 73, -2*w - 1]', '[73, 73, 2*w^2 + w - 5]', '[83, 83, 2*w^3 + w^2 - 9*w - 7]', '[83, 83, -2*w^3 + w^2 + 7*w + 1]', '[107, 107, w^3 + w^2 - 4*w - 1]', '[107, 107, -w^3 + w^2 + 4*w - 1]', '[109, 109, -w^3 + 2*w^2 + 5*w - 11]', '[109, 109, w^3 + 2*w^2 - 5*w - 11]', '[121, 11, 2*w^2 - 5]', '[131, 131, 3*w^3 - 2*w^2 - 14*w + 11]', '[131, 131, 3*w^3 - 12*w + 5]', '[157, 157, -3*w^3 + 2*w^2 + 13*w - 11]', '[157, 157, -w^3 + 2*w^2 + 7*w - 5]', '[167, 167, w^2 + 2*w - 5]', '[167, 167, -w^3 + w^2 + w + 1]', '[167, 167, 3*w^3 - w^2 - 9*w - 5]', '[167, 167, w^2 - 2*w - 5]', '[169, 13, -w^2 + 7]', '[179, 179, -w^3 + w^2 + 6*w - 1]', '[179, 179, w^3 + w^2 - 6*w - 1]', '[181, 181, -w^3 + 5*w - 5]', '[181, 181, w^3 - 5*w - 5]', '[191, 191, -2*w^3 + 2*w^2 + 6*w - 1]', '[191, 191, -2*w^2 + 2*w + 7]', '[191, 191, -4*w^2 + 4*w + 11]', '[191, 191, -2*w^3 + 8*w + 5]', '[227, 227, -w^3 + 2*w^2 + 5*w - 5]', '[227, 227, w^3 + 2*w^2 - 5*w - 5]', '[229, 229, -w^3 + 3*w + 5]', '[229, 229, -w^3 - 4*w^2 + 7*w + 13]', '[239, 239, -w^3 + w^2 + 5*w - 1]', '[239, 239, 2*w^3 - 4*w^2 - 12*w + 13]', '[239, 239, 2*w^3 - 2*w^2 - 10*w + 7]', '[239, 239, w^3 + w^2 - 5*w - 1]', '[241, 241, 2*w^3 - w^2 - 8*w + 5]', '[241, 241, -3*w^2 + 4*w + 7]', '[241, 241, -2*w^3 + w^2 + 6*w + 1]', '[241, 241, -2*w^3 - w^2 + 8*w + 5]', '[251, 251, -w^3 + 2*w - 5]', '[251, 251, 3*w^3 - 2*w^2 - 12*w + 13]', '[263, 263, 2*w^3 - 2*w^2 - 8*w + 11]', '[263, 263, -w^3 + w^2 + 3*w - 7]', '[263, 263, 3*w^3 - w^2 - 11*w + 11]', '[263, 263, -2*w^3 + 6*w - 7]', '[277, 277, -3*w^2 - w + 11]', '[277, 277, 3*w^2 - w - 11]', '[311, 311, -w^3 + 5*w^2 + 7*w - 19]', '[311, 311, 2*w^3 - 3*w^2 - 8*w + 17]', '[311, 311, -2*w^3 + 6*w - 5]', '[311, 311, -2*w^3 - 2*w^2 + 8*w + 5]', '[337, 337, -2*w^3 + 8*w + 1]', '[337, 337, -w^3 + 3*w^2 + 5*w - 11]', '[337, 337, w^3 + 3*w^2 - 5*w - 11]', '[337, 337, 2*w^3 - 8*w + 1]', '[347, 347, w^3 - 3*w^2 - 6*w + 13]', '[347, 347, -w^3 - 3*w^2 + 6*w + 13]', '[349, 349, -w^3 + 4*w - 5]', '[349, 349, w^3 - 4*w - 5]', '[361, 19, 4*w^3 - 2*w^2 - 17*w + 13]', '[361, 19, 2*w^3 - 2*w^2 - 11*w + 7]', '[373, 373, -2*w^3 - 5*w^2 + 13*w + 17]', '[373, 373, 2*w^3 - w^2 - 7*w + 1]', '[383, 383, 4*w^3 - w^2 - 16*w + 13]', '[383, 383, w^2 + 2*w - 7]', '[383, 383, w^2 - 2*w - 7]', '[383, 383, 2*w^3 + 3*w^2 - 6*w - 5]', '[397, 397, -w^3 + 2*w^2 + 7*w - 7]', '[397, 397, w^3 + 2*w^2 - 7*w - 7]', '[419, 419, 5*w^2 - 5*w - 11]', '[419, 419, 3*w^2 - 3*w - 5]', '[421, 421, w^3 + 4*w^2 - 5*w - 17]', '[421, 421, -w^3 + 4*w^2 + 5*w - 17]', '[433, 433, w^3 - w^2 - 7*w + 1]', '[433, 433, 3*w - 1]', '[433, 433, -3*w - 1]', '[433, 433, 5*w^3 - 3*w^2 - 21*w + 19]', '[443, 443, w^3 - 4*w^2 - 6*w + 17]', '[443, 443, -3*w^3 + 6*w^2 + 16*w - 25]', '[467, 467, -w^3 + w^2 + 2*w - 5]', '[467, 467, w^3 + w^2 - 2*w - 5]', '[491, 491, 3*w^3 - w^2 - 14*w + 7]', '[491, 491, -3*w^3 - w^2 + 14*w + 7]', '[529, 23, 3*w^2 - 11]', '[529, 23, 3*w^2 - 7]', '[541, 541, 3*w^3 + 2*w^2 - 10*w - 1]', '[541, 541, 3*w^3 - 4*w^2 - 16*w + 17]', '[563, 563, w^3 + 2*w^2 - 2*w - 7]', '[563, 563, -w^3 + 2*w^2 + 2*w - 7]', '[587, 587, -2*w^3 + w^2 + 5*w - 5]', '[587, 587, 2*w^3 + w^2 - 5*w - 5]', '[613, 613, 3*w^3 - 13*w - 1]', '[613, 613, 3*w^3 - 13*w + 1]', '[659, 659, w^3 + 3*w^2 - 4*w - 5]', '[659, 659, -w^3 + 3*w^2 + 4*w - 5]', '[661, 661, w^3 + 4*w^2 - 9*w - 13]', '[661, 661, -3*w^3 + 4*w^2 + 7*w - 5]', '[673, 673, -2*w^3 + 7*w + 1]', '[673, 673, w^3 + w^2 - 7*w - 5]', '[673, 673, -w^3 + w^2 + 7*w - 5]', '[673, 673, 2*w^3 - 7*w + 1]', '[683, 683, -2*w^3 - w^2 + 9*w + 1]', '[683, 683, 2*w^3 - w^2 - 9*w + 1]', '[709, 709, -3*w^3 + 2*w^2 + 8*w + 1]', '[709, 709, -w^3 + 4*w^2 - 2*w - 7]', '[733, 733, 2*w^3 - 5*w^2 - 11*w + 19]', '[733, 733, -2*w^3 + w^2 + 7*w - 11]', '[743, 743, 2*w^3 + 2*w^2 - 11*w - 5]', '[743, 743, 2*w^3 - w^2 - 8*w - 1]', '[743, 743, -2*w^3 - w^2 + 8*w - 1]', '[743, 743, -2*w^3 + 2*w^2 + 11*w - 5]', '[757, 757, 2*w^3 + 3*w^2 - 3*w + 1]', '[757, 757, -2*w^3 + 5*w^2 + 11*w - 17]', '[827, 827, -5*w^3 + 4*w^2 + 21*w - 23]', '[827, 827, -w^3 + w - 7]', '[829, 829, 2*w^3 - 3*w^2 - 9*w + 17]', '[829, 829, -2*w^3 - 3*w^2 + 9*w + 17]', '[841, 29, 2*w^2 - w - 13]', '[841, 29, 2*w^2 + w - 13]', '[853, 853, -w^3 + 6*w - 7]', '[853, 853, -2*w^3 + w^2 + 11*w - 5]', '[863, 863, w^3 - 5*w^2 - 9*w + 13]', '[863, 863, 2*w^3 + 4*w^2 - 5*w - 11]', '[863, 863, -2*w^3 + 4*w^2 + 5*w - 11]', '[863, 863, w^3 - 3*w^2 - 7*w + 7]', '[877, 877, -w^3 - 3*w^2 + 4*w + 17]', '[877, 877, w^3 - 3*w^2 - 4*w + 17]', '[887, 887, -2*w^3 - w^2 + 10*w + 1]', '[887, 887, 2*w^3 + 2*w^2 - 9*w - 5]', '[887, 887, -2*w^3 + 2*w^2 + 9*w - 5]', '[887, 887, 2*w^3 - w^2 - 10*w + 1]', '[911, 911, -2*w^3 + 11*w - 5]', '[911, 911, -w^3 + w^2 + w - 5]', '[911, 911, w^3 + w^2 - w - 5]', '[911, 911, 2*w^3 - 11*w - 5]', '[937, 937, -4*w^3 - 2*w^2 + 16*w + 17]', '[937, 937, 3*w^3 - w^2 - 11*w - 1]', '[937, 937, -3*w^3 - 5*w^2 + 17*w + 19]', '[937, 937, -4*w^2 + 2*w + 13]', '[947, 947, -3*w^3 + 2*w^2 + 10*w + 1]', '[947, 947, 3*w^3 - 12*w - 7]', '[971, 971, w^3 + w^2 - 2*w - 7]', '[971, 971, -w^3 + w^2 + 2*w - 7]', '[983, 983, -w^3 - 3*w^2 + 7*w + 13]', '[983, 983, 2*w^3 - 2*w^2 - 7*w + 1]', '[983, 983, -2*w^3 - 2*w^2 + 7*w + 1]', '[983, 983, w^3 - 7*w^2 + 3*w + 17]', '[997, 997, -w^3 + 2*w^2 + 4*w - 13]', '[997, 997, 3*w^3 - 8*w^2 - 18*w + 29]']}
• 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': [6, 0, -6, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 13824, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 2]]], [7, [[4, 1]]], [11, [[2, 1], [1, 2]]], [13, [[2, 1], [1, 2]]], [17, [[4, 1]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[4, 1]]], [37, [[2, 1], [1, 2]]], [41, [[4, 1]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[2, 2]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [22, 6], 'galois_label': '4T3', 'galt': 3, 'grd': 15.33463450191054, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.13824.1', 'local_algs': ['2.4.9.8', '3.4.3.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 3], 'rd': 10.8432240433, 'regulator': {'__RealLiteral__': 0, 'data': '10.1286120835', 'prec': 44}, 'res': {'gal': ['1,4,-4,-20,4,20,-4,-4,1'], 'sib': ['3,0,-6,0,1', '1,4,-4,-20,4,20,-4,-4,1']}, 'subfield_mults': [1], 'subfields': ['-3.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a + 1 \\)', '\\( 2 a^{2} - 2 a - 5 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}