Hilbert modular form data - 4.4.11324.1-16.2-b

Formats: - HTML - YAML - JSON - 2025-11-09T02:27:10.498145

• 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': 11324, 'field_bad_primes': [2, 19, 149], 'field_label': '4.4.11324.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.11324.1-16.2-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2], 'level_ideal': '[16, 4, -w^3 + w^2 + 4*w - 2]', 'level_label': '16.2', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.2-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]', -1]], 'hecke_eigenvalues': [0, 3, -1, -3, -3, -4, -2, -10, 3, -10, -3, 5, 11, -2, -13, -2, -14, -3, 3, 1, 6, 14, -4, -1, -6, -11, -6, 2, 7, -6, -23, 3, 16, -9, 22, -4, -6, 4, -7, 7, -10, 17, -11, 10, 2, -26, 2, 18, 2, -18, 15, -4, 17, -6, 2, -12, 2, -22, -19, 16, -10, 2, 26, 10, 0, 18, 17, -5, 34, -31, -33, -26, -24, -1, -22, -20, 1, -11, -15, 14, 5, 34, -14, 26, -19, -16, 3, 1, -18, 10, -10, -16, -4, 10, 0, -22, 15, -34, 38, 25, -2, 10, 18, 18, 12, -14, -27, 29, -16, 34, 34, -28, -7, -14, 27, -10, -20, 30, 36, 32, 32, 29, 35, -50, -46, 38, -17, 5, -14, 22, -13, 17, 12, 10, 5, -30, -56, 48, 14, 39, -14, -38, 44, 18, 2, 34, 38, 10, -18, 18, 28, 16, -22, -24, -50, 58, -28, -40, -14, 28, 5, 18, -8, -7, -48, 44, 18, -54, 9, -15, 6, -1, -46, -45, -44, 48, 16, 16, 61, -54, -60, -5, 37, 23, -5, -34, 18, -3, 14, 2, -47, 5, 11, -25, 17, -7, -62, 42, 40, -50, 46, -52, 68, -62, -30, 42, -60, -55, -2, -42, 61, -10, 18, 72, -24, 38, -42, -65, 42, 12, 60, 22, -28, -64, 20, -26, 29, -39, 50, 20, 0, 24, 16, -4, -54, -52, 40, 6, -54, -78, -10, 18, -36, -59, -78, 53, 18, -7, 55, 69, 42, -47, -44, 16, -33, 47, 45, -32, 18, -17, -49, -61, -25, -33, 62, 62, -73, 12, -36, 41, 59, -79, -74, -58, -18, -18, 48, -61, -34, 45, 12, 6, -41, 73, -79, 65, 76, 36, 69, 42, -74, 86, -53, -42, -8, 84, -36, -52, -73, -70, -42, 21, 35, 27, 9, 64, -16, 86, -15, 70, 6, 15, 49, -21, 14, 46, 44, 53, -2, 58, -26, -35, 46, -81, -68, -32, 56, 68, 74, 58, -21, -66, 29, -56, -8, 54, 44, 70, 23, -7, 42, -41, 28, -89, 41, 79, -56, -4, 24, 14, -16, 58, -37, 14, -76, 86, -26, 34, 19, 12, -51, 20, -93, 98, 62, -7, 36, 22, -82, -82, -26, 89, -28, 14, 64, 27, 5, -50, -17, -84, -78, -35, 61, -49, -42, -94, -18, -56, 76, 56, 2, -82, -52, -9, -2, -44, 54, -57, -49, 10, 98, -98, 18, 15, 20, -10, 58, -26, 94, -102, 68, -74, -30, -47, -6, -18, 43, -90, 96, 38, -42, 56, -84, -29, 36, -82, -93, -29, 90, 47, 101, -98, -19, 22, 34, -96, 40, -100, 4, -26, 90, -57, -58, 86, -20, 2, 90, 108, -50, -57, -2, -72, -10, -28, 66, 15, 35, 27, 42, 80, -76, -54, -12, -46, -17, -4, -38, -23, -90, -32, -36, 14, -71, -78, 113, 10, -98, -39, -91, 33, -9, -48, 16, 22, 50, 60, 4, 58, -6, -52, 53, -42, -51, 9, 70, 76, -54, -28, 29, -8, -3, 18, -75, -12, -38, -57, -15, -60, 20, 68, -65, 66, 88, 18, 112, -14, 94, 99, 71, -62, 84, -97, -31, -41, 65, 4, 104, -64, -106, -72, 122, 54, 17, 78, 59, 43, 31, 62, 106, 48, 34, -83, 18, -9, -92, -8, 0, -122, 48, 26, -42], 'hecke_polynomial': 'x', 'label': '4.4.11324.1-16.2-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 11324, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[4, 2, -w^3 + w^2 + 4*w - 4]', '[4, 2, -w^3 + 4*w + 1]', '[5, 5, w + 1]', '[8, 2, -w^3 + w^2 + 5*w - 4]', '[8, 4, w^3 - 4*w]', '[10, 10, w^2 - w - 2]', '[13, 13, -w^2 + 3]', '[16, 2, 2]', '[16, 4, -w^3 + w^2 + 4*w - 2]', '[16, 4, w^2 + w - 1]', '[17, 17, -w^3 + w^2 + 3*w - 1]', '[19, 19, -w^3 + 3*w - 1]', '[20, 10, -w^3 + 4*w - 2]', '[20, 10, w^3 - 4*w - 3]', '[23, 23, -w + 3]', '[25, 25, w^3 - 5*w + 1]', '[26, 26, -w^3 + 3*w]', '[31, 31, -w^2 - 2*w + 1]', '[32, 4, 2*w]', '[32, 4, w^3 - w^2 - 3*w + 2]', '[32, 8, -w^2 + 2*w + 2]', '[34, 34, w^2 + w - 4]', '[38, 38, -w^2 + w + 4]', '[40, 10, -w^3 + w^2 + 5*w - 2]', '[40, 20, -w^2 + 6]', '[41, 41, w^3 + w^2 - 5*w - 3]', '[43, 43, 2*w - 1]', '[46, 46, w^3 - 2*w^2 - 5*w + 6]', '[50, 50, w^3 - 3*w - 2]', '[52, 26, -w^3 - w^2 + 6*w + 4]', '[52, 26, -w^3 + 6*w + 1]', '[53, 53, -w - 3]', '[53, 53, w^3 - w^2 - 4*w + 1]', '[61, 61, w^3 - 3*w - 5]', '[62, 62, -w^3 + 5*w - 2]', '[64, 4, -2*w^3 + 2*w^2 + 8*w - 8]', '[64, 4, -2*w^3 + 8*w + 2]', '[64, 8, w^3 - 6*w + 1]', '[64, 8, -w^2 - 2*w + 2]', '[65, 65, -w^3 - w^2 + 3*w + 3]', '[67, 67, w^3 + w^2 - 5*w - 1]', '[68, 34, w^3 + w^2 - 4*w]', '[68, 34, w^2 - w - 5]', '[76, 38, w^3 - 6*w + 3]', '[76, 38, -w^3 + w^2 + 4*w]', '[80, 10, 2*w + 2]', '[80, 20, -w^3 + 6*w]', '[80, 20, w^2 + w - 5]', '[81, 3, -3]', '[82, 82, 2*w^3 - 7*w - 2]', '[83, 83, -w^3 + 5*w - 3]', '[85, 85, -w^3 - w^2 + 6*w + 1]', '[86, 86, 2*w^2 - w]', '[89, 89, w^2 + 1]', '[92, 46, 2*w^3 - w^2 - 9*w + 5]', '[92, 46, -w^3 + 2*w - 2]', '[95, 95, -w^3 + w^2 + 5*w - 7]', '[97, 97, w^3 - w^2 - 5*w + 1]', '[97, 97, 3*w^3 - 5*w^2 - 14*w + 21]', '[97, 97, w^3 - 3*w - 3]', '[97, 97, w^3 - 7*w - 3]', '[100, 50, -2*w^3 + 3*w^2 + 8*w - 12]', '[100, 50, w^3 - 2*w^2 - 6*w + 7]', '[103, 103, w^3 - w^2 - 3*w + 5]', '[104, 26, w^3 + w^2 - 7*w]', '[104, 52, w^3 - w^2 - 6*w + 2]', '[106, 106, -w^2 - 3*w]', '[106, 106, w^2 - 3*w - 2]', '[107, 107, -2*w^3 + 2*w^2 + 8*w - 7]', '[109, 109, 3*w^3 - 3*w^2 - 13*w + 11]', '[113, 113, 2*w^3 - 2*w^2 - 10*w + 7]', '[113, 113, w^3 + w^2 - 5*w - 7]', '[115, 115, -w^2 + 2*w + 3]', '[121, 11, 2*w^2 - w - 9]', '[121, 11, 2*w^2 - w - 7]', '[122, 122, w^3 + 2*w^2 - 9*w - 2]', '[124, 62, -w^3 + 2*w + 2]', '[124, 62, -2*w^3 + w^2 + 9*w - 1]', '[125, 5, -w^3 + 2*w^2 + 3*w - 7]', '[125, 125, 2*w^3 - 8*w - 1]', '[128, 4, -2*w^3 + 2*w^2 + 10*w - 8]', '[128, 8, 2*w^3 - 8*w]', '[128, 8, w^3 - w^2 - 3*w + 6]', '[128, 16, w^3 + w^2 - 4*w - 6]', '[130, 130, w - 4]', '[131, 131, 4*w^3 - 5*w^2 - 18*w + 19]', '[134, 134, 2*w^3 - 5*w - 2]', '[136, 34, w^3 - w^2 - 5*w]', '[136, 68, w^3 - 4*w - 4]', '[137, 137, w^3 + w^2 - 6*w - 5]', '[137, 137, 3*w^3 - 13*w - 3]', '[139, 139, 3*w^3 - 5*w^2 - 13*w + 19]', '[149, 149, 2*w^3 - 9*w + 1]', '[152, 38, w^3 - w^2 - w - 2]', '[152, 76, -w^3 - w^2 + 2*w - 2]', '[155, 155, -2*w^2 + 7]', '[160, 20, w^3 + w^2 - 5*w]', '[160, 20, 2*w^2 - 2*w - 4]', '[160, 40, -w^3 + 2*w - 4]', '[162, 6, -3*w]', '[163, 163, -2*w^2 + 11]', '[163, 163, -w^3 + w^2 + 6*w - 3]', '[163, 163, w^3 - 2*w^2 - 5*w + 5]', '[163, 163, 3*w^3 - 3*w^2 - 14*w + 15]', '[164, 82, w^3 - w^2 - 6*w + 4]', '[164, 82, 4*w^3 + w^2 - 21*w - 7]', '[166, 166, -w^3 + w + 2]', '[169, 169, w^3 - w^2 - 4*w + 7]', '[170, 170, w^3 + 2*w^2 - 3*w - 4]', '[172, 86, w^3 - 3*w^2 - 4*w + 8]', '[172, 86, -w^3 - 2*w^2 + 6*w + 3]', '[173, 173, 2*w^3 - 10*w + 1]', '[173, 173, 2*w^3 - 3*w^2 - 8*w + 13]', '[178, 178, 2*w^3 - 4*w^2 - 9*w + 14]', '[179, 179, 2*w^3 + w^2 - 8*w - 1]', '[181, 181, 2*w^3 - 4*w^2 - 9*w + 15]', '[184, 46, w^3 + w^2 - 3*w - 4]', '[184, 92, 2*w^3 - w^2 - 8*w + 2]', '[190, 190, -w^3 + 5*w + 4]', '[193, 193, w^2 - 7]', '[194, 194, -2*w^3 + w^2 + 9*w - 6]', '[194, 194, 2*w^2 + w - 8]', '[194, 194, 3*w + 2]', '[194, 194, w^3 + 2*w^2 - 7*w - 2]', '[199, 199, 2*w^2 - 5]', '[200, 50, -w^3 - w^2 + 3*w - 2]', '[200, 100, w^3 - 2*w^2 - 4*w + 4]', '[205, 205, 3*w^3 + w^2 - 12*w - 5]', '[206, 206, 2*w^2 + w - 2]', '[208, 26, -2*w^2 + 6]', '[208, 52, -2*w^3 + w^2 + 10*w - 6]', '[208, 52, -2*w^3 - w^2 + 7*w - 1]', '[211, 211, -2*w^3 + 8*w - 3]', '[211, 211, -2*w^3 + w^2 + 8*w - 3]', '[212, 106, 3*w^3 - 2*w^2 - 12*w + 10]', '[212, 106, 4*w^3 + w^2 - 17*w - 5]', '[212, 106, 3*w^3 - 12*w - 5]', '[212, 106, -w^3 + 2*w^2 + 6*w - 10]', '[214, 214, -3*w^3 + 13*w + 2]', '[215, 215, 2*w^2 + w - 1]', '[218, 218, -2*w^3 - w^2 + 3*w]', '[221, 221, -w^3 + 7*w - 3]', '[223, 223, 3*w - 1]', '[223, 223, -2*w^3 - w^2 + 8*w + 5]', '[226, 226, -w - 4]', '[226, 226, 2*w^3 - 11*w - 2]', '[229, 229, -w^3 + 3*w^2 + 4*w - 11]', '[230, 230, -2*w^2 - 3*w + 4]', '[233, 233, -w^3 + 3*w^2 - 5]', '[233, 233, w^3 + 2*w^2 - 5*w - 3]', '[239, 239, 2*w^3 - 7*w - 1]', '[241, 241, w^3 - 2*w^2 - 3*w + 11]', '[242, 22, 2*w^3 - w^2 - 7*w]', '[242, 22, 2*w^3 - w^2 - 9*w]', '[244, 122, 4*w^3 - 5*w^2 - 16*w + 16]', '[244, 122, 6*w^3 - w^2 - 25*w - 7]', '[247, 247, 2*w^2 + 3*w - 5]', '[248, 62, -w^3 - w^2 + 7*w + 4]', '[248, 124, 3*w^3 - 3*w^2 - 14*w + 10]', '[250, 10, w^3 - 2*w^2 - 3*w + 2]', '[250, 250, -2*w^3 + 2*w^2 + 7*w - 2]', '[251, 251, 2*w^2 - w - 5]', '[251, 251, 2*w^2 + 2*w - 7]', '[256, 4, 4]', '[256, 8, -2*w^3 + 2*w^2 + 8*w - 4]', '[256, 8, 2*w^2 + 2*w - 2]', '[256, 16, 2*w^3 + w^2 - 10*w - 2]', '[256, 16, 2*w^3 - w^2 - 9*w + 7]', '[260, 130, w^3 + 2*w^2 - 6*w - 7]', '[260, 130, w^2 - 4*w]', '[262, 262, -w^3 + 2*w^2 + 3*w - 8]', '[265, 265, w^3 - 7*w - 1]', '[265, 265, -w^2 - 4*w - 3]', '[268, 134, -w^3 + w^2 + 2*w - 4]', '[268, 134, 2*w^3 + w^2 - 13*w - 5]', '[271, 271, -2*w^3 + 2*w^2 + 7*w - 9]', '[272, 34, -2*w^3 + 2*w^2 + 6*w - 2]', '[272, 68, -w^3 + 2*w^2 + 6*w - 4]', '[272, 68, -w^3 + 2*w + 3]', '[274, 274, 2*w^3 - w^2 - 9*w - 2]', '[274, 274, 4*w^3 - 4*w^2 - 19*w + 16]', '[278, 278, w^3 + 2*w^2 - 5*w - 8]', '[283, 283, 6*w^3 - 6*w^2 - 28*w + 23]', '[289, 289, -2*w^3 + 7*w - 1]', '[293, 293, 4*w^3 - 4*w^2 - 17*w + 17]', '[293, 293, 2*w^3 - 2*w^2 - 7*w + 5]', '[298, 298, 2*w^3 + w^2 - 7*w - 4]', '[299, 299, w^3 - 3*w^2 - 3*w + 9]', '[304, 38, -2*w^3 + 6*w - 2]', '[304, 76, w^3 - 2*w^2 - 4*w + 11]', '[304, 76, -w^2 - 2*w + 6]', '[305, 305, 2*w^3 + 2*w^2 - 12*w - 7]', '[307, 307, 6*w^3 - 7*w^2 - 28*w + 29]', '[310, 310, -2*w^3 + 7*w]', '[311, 311, w^3 - 2*w^2 - 3*w + 1]', '[311, 311, 2*w^2 - 2*w - 7]', '[311, 311, 2*w^3 - 4*w^2 - 8*w + 17]', '[311, 311, -w^3 + 3*w^2 + 4*w - 9]', '[320, 20, -2*w^3 + 8*w - 4]', '[320, 20, 2*w^3 - 8*w - 6]', '[320, 40, w^3 - 3*w^2 - 4*w + 10]', '[320, 40, 2*w^3 - w^2 - 9*w - 1]', '[323, 323, 2*w^3 - 11*w - 1]', '[324, 6, 3*w^3 - 3*w^2 - 12*w + 12]', '[324, 6, 3*w^3 - 12*w - 3]', '[325, 325, 2*w^3 - 2*w^2 - 9*w + 5]', '[326, 326, -2*w^3 + 11*w]', '[326, 326, w^2 + w + 2]', '[326, 326, -w^3 + w - 2]', '[326, 326, -2*w^3 + 9*w - 2]', '[328, 82, 3*w^3 - w^2 - 13*w + 2]', '[328, 164, -3*w^3 + 16*w + 4]', '[332, 166, 4*w^3 - 5*w^2 - 16*w + 20]', '[332, 166, -w^2 + 3*w + 3]', '[335, 335, 3*w^3 + w^2 - 10*w - 3]', '[338, 338, w^2 + 3*w - 2]', '[340, 170, w^3 - 2*w^2 - 2*w + 6]', '[340, 170, w^2 + 3*w - 3]', '[344, 86, w^3 - w^2 - 5*w + 8]', '[344, 172, w^3 + 2*w^2 - 4*w - 4]', '[346, 346, 2*w^3 - 7*w - 4]', '[346, 346, -w^3 + 2*w^2 + 5*w - 4]', '[347, 347, -w^3 - w^2 + 6*w - 1]', '[347, 347, -3*w^3 + 5*w^2 + 15*w - 21]', '[349, 349, 2*w^3 + 2*w^2 - 11*w - 7]', '[349, 349, 3*w^3 - w^2 - 15*w + 3]', '[353, 353, w^3 + w^2 - 3*w - 5]', '[353, 353, -4*w^3 + 16*w + 5]', '[356, 178, -2*w^3 + w^2 + 6*w - 4]', '[356, 178, -2*w^3 - 3*w^2 + 3*w + 5]', '[358, 358, 3*w^3 + 2*w^2 - 9*w - 4]', '[361, 19, 2*w^3 - 4*w^2 - 10*w + 17]', '[361, 19, 6*w^3 - 8*w^2 - 27*w + 31]', '[362, 362, 2*w^3 + 2*w^2 - 9*w - 8]', '[367, 367, 3*w^3 - 3*w^2 - 13*w + 9]', '[367, 367, -2*w^2 - w + 9]', '[368, 46, -2*w + 6]', '[368, 92, -w^3 + 2*w^2 + 4*w - 3]', '[368, 92, w^3 + 2*w^2 - 6*w - 4]', '[373, 373, -2*w^3 + w^2 + 10*w - 7]', '[379, 379, w^3 + 2*w^2 - 7*w - 7]', '[380, 190, w^3 - 2*w - 6]', '[380, 190, 2*w^3 - w^2 - 7*w + 1]', '[383, 383, -w^3 + 2*w^2 + 3*w - 9]', '[386, 386, -w^3 + 7*w]', '[388, 194, -4*w^3 - w^2 + 17*w + 7]', '[388, 194, w^3 - 3*w^2 - 6*w + 12]', '[388, 194, -2*w^3 + 3*w^2 + 7*w - 11]', '[388, 194, -w^3 - w^2 + 2*w + 4]', '[388, 194, 4*w^3 - w^2 - 17*w - 5]', '[388, 194, 2*w^3 - 3*w^2 - 8*w + 8]', '[388, 194, 3*w^3 + 4*w^2 - 8*w - 5]', '[388, 194, 2*w^3 + w^2 - 8*w]', '[389, 389, -2*w^3 + 3*w^2 + 10*w - 9]', '[389, 389, w^2 - 2*w - 5]', '[391, 391, w^3 - 3*w + 5]', '[397, 397, 2*w^3 - w^2 - 10*w - 1]', '[397, 397, w - 5]', '[398, 398, 2*w^3 - 5*w]', '[400, 50, 2*w^3 - 10*w + 2]', '[400, 100, w^3 + 2*w^2 - 4*w - 5]', '[400, 100, -w^3 + w^2 - 2]', '[403, 403, 3*w^3 + w^2 - 10*w + 1]', '[405, 15, -3*w - 3]', '[409, 409, w^3 - w^2 - 6*w - 3]', '[410, 410, -2*w^3 + w^2 + 7*w + 4]', '[412, 206, -5*w^3 + 5*w^2 + 22*w - 24]', '[412, 206, -2*w^3 - w^2 + 9*w + 1]', '[415, 415, -2*w^3 + 6*w - 1]', '[416, 52, w^3 - w^2 - 7*w + 6]', '[416, 52, -2*w^3 + 6*w]', '[416, 104, -w^3 + 2*w + 4]', '[419, 419, w^3 - 7*w + 1]', '[419, 419, -3*w^3 + 2*w^2 + 13*w - 11]', '[421, 421, w^3 + w^2 - 4*w + 3]', '[421, 421, 3*w^3 + w^2 - 14*w - 3]', '[422, 422, -2*w^3 - 2*w^2 + 5*w + 4]', '[422, 422, -w^3 - 2*w^2 + 5*w + 4]', '[424, 106, 3*w^3 - 3*w^2 - 15*w + 10]', '[424, 106, -w^3 + 3*w^2 + 3*w - 12]', '[424, 212, -4*w^3 - w^2 + 16*w + 2]', '[424, 212, -2*w^3 - w^2 + 8*w + 6]', '[425, 425, 3*w^3 + w^2 - 11*w + 1]', '[428, 214, w^3 - 4*w - 5]', '[428, 214, 3*w^3 - 2*w^2 - 12*w + 2]', '[430, 430, 2*w^3 - 3*w^2 - 3*w + 2]', '[431, 431, w^2 + 2*w - 7]', '[436, 218, 2*w^3 + w^2 - 5*w - 3]', '[436, 218, -w^3 + 4*w^2 + 8*w - 14]', '[437, 437, w^3 + 2*w^2 - 5*w - 7]', '[442, 442, -2*w^3 + 2*w^2 + 7*w - 10]', '[445, 445, 2*w^3 - 2*w^2 - 6*w + 3]', '[446, 446, 3*w^2 - w]', '[446, 446, -3*w^3 - 2*w^2 + 13*w + 4]', '[449, 449, w^3 + w^2 - 3*w - 9]', '[452, 226, 3*w^3 + 2*w^2 - 14*w - 9]', '[452, 226, -7*w^3 + 11*w^2 + 32*w - 44]', '[452, 226, 8*w^3 + w^2 - 37*w - 11]', '[452, 226, 5*w^3 - 5*w^2 - 22*w + 20]', '[457, 457, -2*w^3 + w^2 + 8*w - 9]', '[457, 457, 2*w^3 - 2*w^2 - 7*w + 11]', '[458, 458, 2*w^3 - w^2 - 7*w + 2]', '[460, 230, -2*w^3 + w^2 + 10*w - 8]', '[460, 230, -3*w^2 - w + 7]', '[463, 463, -w^3 - w^2 + 8*w - 3]', '[463, 463, 3*w^3 - 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5]', '[1814, 1814, -w^3 - 2*w^2 + 9*w + 6]', '[1814, 1814, 2*w^3 + 2*w^2 - 9*w]', '[1819, 1819, -2*w^3 - 2*w^2 + 10*w + 1]', '[1822, 1822, -2*w^3 + 15*w + 6]', '[1823, 1823, -w^3 + 3*w^2 + 6*w - 5]', '[1828, 914, 10*w^3 - 11*w^2 - 42*w + 48]', '[1828, 914, 3*w^3 - 10*w + 1]', '[1828, 914, -4*w^3 - w^2 + 17*w + 1]', '[1828, 914, -11*w^3 + 12*w^2 + 48*w - 54]', '[1831, 1831, 5*w^3 - 4*w^2 - 21*w + 17]', '[1832, 458, 3*w^3 - w^2 - 13*w - 6]', '[1832, 916, -3*w^3 + 3*w^2 + 14*w - 18]', '[1835, 1835, -2*w^3 - 3*w^2 + 8*w + 9]', '[1835, 1835, 3*w^3 - w^2 - 16*w + 3]', '[1838, 1838, 3*w^3 - 7*w]', '[1838, 1838, 2*w^3 + 3*w^2 - w - 4]', '[1840, 230, -2*w^2 + 4*w + 6]', '[1840, 460, -2*w^3 - w^2 + 14*w - 2]', '[1840, 460, w^2 + 5*w - 1]', '[1843, 1843, w^3 - 9*w + 5]', '[1843, 1843, w^3 - 3*w^2 - 4*w + 3]', '[1843, 1843, -2*w^3 - 3*w^2 + 4*w + 7]', '[1843, 1843, -w + 7]', '[1849, 1849, w^3 - 9*w - 1]', '[1852, 926, 3*w^3 - 8*w + 2]', '[1852, 926, -w^3 + 2*w^2 + 4*w - 13]', '[1852, 926, -3*w^3 + 4*w^2 + 8*w - 7]', '[1852, 926, w^2 - 6*w]', '[1853, 1853, w^3 - w^2 + 2*w - 5]', '[1863, 69, 3*w - 9]', '[1864, 466, -w^3 - 3*w^2 + 5*w + 6]', '[1864, 466, 3*w^3 - w^2 - 11*w + 2]', '[1864, 932, -2*w^3 - w^2 + 12*w - 2]', '[1864, 932, -w^3 + w^2 + 10*w + 2]', '[1865, 1865, -3*w^3 + w^2 + 11*w - 3]', '[1867, 1867, 3*w^3 - w^2 - 10*w + 5]', '[1871, 1871, 2*w^3 + 2*w^2 - 6*w - 7]', '[1873, 1873, -3*w^3 + 3*w^2 + 10*w - 7]', '[1874, 1874, 2*w^3 + 2*w^2 - 5*w - 6]', '[1874, 1874, 2*w^2 - 3*w - 8]', '[1879, 1879, 2*w^3 - 4*w^2 - 7*w + 17]', '[1886, 1886, -3*w^3 + 13*w - 4]', '[1889, 1889, 3*w^3 - 17*w - 3]', '[1891, 1891, -4*w^3 + 21*w + 1]', '[1895, 1895, -w^3 + 3*w^2 + 2*w - 17]', '[1900, 950, 3*w^3 + 2*w^2 - 14*w - 3]', '[1900, 950, 2*w^3 + 3*w^2 - 12*w - 8]', '[1907, 1907, -4*w^3 - 2*w^2 + 19*w + 5]', '[1907, 1907, 6*w^3 - 8*w^2 - 29*w + 33]', '[1909, 1909, -2*w^3 + 14*w - 11]', '[1912, 478, w^3 + 3*w^2 - 5*w - 10]', '[1912, 956, -2*w^3 + w^2 + 12*w + 6]', '[1913, 1913, -w^3 + w^2 + 8*w - 3]', '[1913, 1913, w^3 + 2*w^2 - 9*w + 3]', '[1915, 1915, -2*w - 7]', '[1921, 1921, -w^3 + 5*w^2 + 3*w - 19]', '[1921, 1921, 6*w^3 - 2*w^2 - 26*w + 1]', '[1922, 1922, 2*w^3 + 3*w^2 - 5*w - 8]', '[1928, 482, -7*w^3 - 3*w^2 + 29*w + 12]', '[1928, 964, w^3 - 6*w^2 - 8*w + 20]', '[1930, 1930, -2*w^3 + 2*w^2 + 11*w + 2]', '[1933, 1933, w^2 + 4*w - 9]', '[1933, 1933, 6*w^3 - 6*w^2 - 26*w + 23]', '[1936, 22, 4*w^2 - 2*w - 18]', '[1936, 22, 4*w^2 - 2*w - 14]', '[1936, 44, 5*w^3 - 2*w^2 - 26*w + 12]', '[1936, 44, 3*w^3 - 2*w^2 - 16*w + 5]', '[1936, 44, -5*w^3 - 2*w^2 + 22*w + 12]', '[1936, 44, 3*w^3 - 14*w + 3]', '[1937, 1937, -3*w^3 - 2*w^2 + 19*w + 5]', '[1940, 970, -6*w^3 + w^2 + 23*w + 11]', '[1940, 970, w^3 - w^2 - 8*w + 4]', '[1940, 970, -w^3 + 2*w^2 + 8*w - 5]', '[1940, 970, 5*w^3 + 3*w^2 - 16*w - 4]', '[1940, 970, 6*w^3 - w^2 - 27*w - 5]', '[1940, 970, -w^3 - 4*w^2 + 2*w + 10]', '[1940, 970, -w^3 + 4*w - 7]', '[1940, 970, 3*w^3 - 4*w^2 - 12*w + 10]', '[1945, 1945, -w^3 + 3*w^2 + 9*w - 5]', '[1945, 1945, w^3 - w^2 - 7*w - 5]', '[1948, 974, -w^3 + 2*w^2 + 8*w - 14]', '[1948, 974, 6*w^3 - w^2 - 23*w - 9]', '[1948, 974, 7*w^3 + 2*w^2 - 32*w - 9]', '[1948, 974, 6*w^3 - 5*w^2 - 26*w + 24]', '[1951, 1951, w^3 + 2*w^2 - 3*w - 11]', '[1951, 1951, -2*w^3 + 2*w^2 + 10*w - 1]', '[1952, 244, -5*w^3 + 7*w^2 + 13*w - 8]', '[1952, 244, 2*w^3 + 4*w^2 - 18*w - 4]', '[1952, 488, w^3 + 8*w^2 - 18*w - 12]', '[1954, 1954, -2*w^3 - w^2 + 7*w + 8]', '[1955, 1955, 5*w^3 - 5*w^2 - 21*w + 19]', '[1957, 1957, -4*w^3 - w^2 + 14*w - 7]', '[1966, 1966, 3*w^3 - 9*w + 2]', '[1966, 1966, -w^2 + 5*w + 4]', '[1973, 1973, -5*w^3 + 7*w^2 + 23*w - 25]', '[1976, 494, -w^3 + 3*w^2 - w - 6]', '[1976, 988, -3*w^3 + 8*w + 4]', '[1978, 1978, -3*w^3 + 2*w^2 + 9*w - 10]', '[1979, 1979, -3*w^3 + 5*w^2 + 11*w - 19]', '[1982, 1982, 2*w^2 - 7*w]', '[1982, 1982, 3*w^3 - 2*w^2 - 15*w + 2]', '[1984, 124, -2*w^3 + 4*w + 4]', '[1984, 124, -4*w^3 + 2*w^2 + 18*w - 2]', '[1984, 248, -3*w^3 + 3*w^2 + 8*w - 2]', '[1984, 248, -w^3 + 6*w + 7]', '[1985, 1985, -2*w^3 - 2*w^2 + 8*w + 13]', '[1985, 1985, w^2 - 4*w - 5]', '[1987, 1987, 2*w^3 - 2*w^2 - 6*w + 11]', '[1990, 1990, w^2 - 3*w + 6]', '[1993, 1993, -w^3 + 3*w - 7]', '[1993, 1993, w^3 + w^2 - 2*w - 9]', '[1996, 998, -11*w^3 + 14*w^2 + 50*w - 62]', '[1996, 998, w^3 - 4*w - 7]', '[1997, 1997, 5*w^3 - w^2 - 19*w - 5]', '[1999, 1999, -3*w^3 + 3*w^2 + 15*w - 19]', '[2000, 10, -2*w^3 + 4*w^2 + 6*w - 14]', '[2000, 20, 4*w^3 - 3*w^2 - 22*w + 18]', '[2000, 20, w^3 - 2*w^2 - 8*w + 7]', '[2000, 250, 4*w^3 - 16*w - 2]', '[2000, 500, 3*w^3 + w^2 - 12*w - 10]', '[2000, 500, -3*w^3 + 2*w^2 + 16*w - 9]', '[2008, 502, 5*w^3 - 5*w^2 - 21*w + 18]', '[2008, 502, 7*w^3 - 7*w^2 - 31*w + 32]', '[2008, 1004, -w^3 + 4*w^2 + 8*w - 8]', '[2008, 1004, -2*w^3 + w^2 + 12*w - 2]', '[2011, 2011, 5*w^3 - 6*w^2 - 23*w + 21]', '[2012, 1006, -3*w^3 + w^2 + 10*w]', '[2012, 1006, -3*w^3 - 2*w^2 + 8*w + 5]', '[2014, 2014, w^3 + 2*w^2 - 7*w - 12]', '[2014, 2014, 3*w^3 - 17*w + 2]', '[2015, 2015, 2*w^3 - 3*w^2 - 8*w + 17]', '[2025, 75, -3*w^3 + 15*w - 3]', '[2033, 2033, 4*w^3 - 2*w^2 - 16*w - 3]', '[2036, 1018, -w^3 - 4*w^2 + 2*w + 9]', '[2036, 1018, -3*w^3 + w^2 + 14*w - 8]', '[2038, 2038, -5*w^3 + 23*w]', '[2039, 2039, -2*w^3 + 4*w^2 + 8*w - 9]', '[2039, 2039, -3*w^3 + 4*w^2 + 11*w - 17]', '[2045, 2045, w^3 - 2*w^2 - 13*w - 5]', '[2047, 2047, -4*w^3 + 4*w^2 + 15*w - 19]', '[2048, 8, -4*w^3 + 4*w^2 + 20*w - 16]', '[2048, 16, 4*w^3 - 16*w]', '[2048, 16, 2*w^3 - 2*w^2 - 6*w + 12]', '[2048, 32, 2*w^3 + 2*w^2 - 8*w - 12]', '[2048, 32, w^3 - 5*w^2 + w + 10]', '[2048, 64, w^3 - 3*w^2 - 4*w + 2]', '[2050, 2050, -3*w^3 - 2*w^2 + 19*w + 8]', '[2053, 2053, -2*w^3 + 3*w^2 + 8*w - 5]', '[2057, 187, -4*w^3 + 19*w + 9]', '[2057, 187, 3*w^3 + w^2 - 20*w + 5]', '[2060, 1030, -5*w^3 + 2*w^2 + 18*w - 14]', '[2060, 1030, 3*w^2 - 3*w - 11]', '[2062, 2062, 4*w^3 - 5*w^2 - 15*w + 20]', '[2069, 2069, 5*w^3 - 6*w^2 - 21*w + 19]', '[2069, 2069, w^3 - 2*w^2 - 5*w - 3]', '[2069, 2069, 5*w^3 - 10*w^2 - 23*w + 43]', '[2069, 2069, 3*w^3 - 2*w^2 - 13*w + 1]', '[2071, 2071, 4*w^3 + 6*w^2 - 6*w - 9]', '[2074, 2074, -2*w^2 - 3*w + 16]', '[2075, 2075, -w^3 + w^2 + 6*w - 11]', '[2077, 2077, -5*w^3 - 4*w^2 + 15*w + 7]', '[2078, 2078, -2*w^3 - 3*w^2 + 9*w + 6]', '[2080, 260, w^3 - 3*w^2 - 5*w + 4]', '[2080, 260, 2*w - 8]', '[2080, 520, -2*w^3 - 3*w^2 + 10*w + 6]', '[2081, 2081, 7*w^3 - 10*w^2 - 31*w + 37]', '[2081, 2081, -3*w^3 + 2*w^2 + 11*w - 15]', '[2084, 1042, w^3 - 2*w^2 - 8*w + 6]', '[2084, 1042, 6*w^3 + w^2 - 33*w - 11]', '[2092, 1046, 3*w^3 - w^2 - 8*w + 4]', '[2092, 1046, 5*w^3 - 16*w - 5]', '[2095, 2095, -4*w^3 + 14*w - 5]', '[2095, 2095, -2*w^3 + 2*w^2 + 10*w + 1]', '[2096, 262, 8*w^3 - 10*w^2 - 36*w + 38]', '[2096, 524, -4*w^3 + w^2 + 18*w - 6]', '[2096, 524, -4*w^3 + 5*w^2 + 17*w - 25]', '[2099, 2099, -4*w^3 + 5*w^2 + 14*w - 13]', '[2102, 2102, -w^3 - 2*w^2 + 3*w + 12]', '[2102, 2102, -2*w^3 + 7*w - 8]', '[2102, 2102, -5*w^3 + 21*w]', '[2102, 2102, 4*w^3 + 2*w^2 - 11*w]', '[2105, 2105, 7*w^3 + 2*w^2 - 29*w - 9]', '[2105, 2105, 3*w^3 + 2*w^2 - 5*w + 1]', '[2106, 78, 3*w^3 - 9*w]', '[2108, 1054, 2*w^3 - 3*w^2 - 12*w + 12]', '[2108, 1054, -3*w^3 + 8*w - 7]', '[2110, 2110, 2*w^3 - 13*w + 4]', '[2110, 2110, 2*w^3 - 3*w^2 - 9*w + 6]', '[2111, 2111, w^3 + 3*w^2 - 6*w - 9]', '[2116, 1058, w^2 + 3*w + 5]', '[2116, 1058, -3*w^3 + 2*w^2 + 14*w - 2]', '[2119, 2119, -4*w^3 + 2*w^2 + 16*w - 9]', '[2119, 2119, 5*w^3 - w^2 - 18*w - 11]', '[2119, 2119, 2*w^3 - 7*w - 9]', '[2119, 2119, 4*w^3 - 2*w^2 - 17*w + 13]', '[2120, 530, w^3 + w^2 - 5*w - 10]', '[2120, 530, 3*w^3 - 3*w^2 - 17*w + 4]', '[2120, 1060, w^3 + 3*w^2 - 6*w - 18]', '[2120, 1060, 5*w^3 - 3*w^2 - 22*w + 6]', '[2122, 2122, 2*w^3 + 3*w^2 - 3*w + 2]', '[2122, 2122, 2*w^3 + w^2 - 7*w - 10]', '[2125, 85, 2*w^3 + w^2 - 16*w + 9]', '[2125, 2125, 2*w^3 - 4*w^2 - 7*w + 19]', '[2126, 2126, 3*w^3 - 6*w^2 - 15*w + 26]', '[2129, 2129, 4*w^3 - 4*w^2 - 20*w + 15]', '[2129, 2129, 4*w^2 - 3*w - 15]', '[2132, 1066, 9*w^3 + w^2 - 40*w - 16]', '[2132, 1066, 8*w^3 + w^2 - 35*w - 11]', '[2138, 2138, 2*w^3 - 4*w^2 - 5*w]', '[2140, 1070, 4*w^3 + w^2 - 22*w - 4]', '[2140, 1070, 2*w^3 + w^2 - 13*w - 7]', '[2141, 2141, -w^3 + w^2 + w - 7]', '[2144, 268, w^3 - 3*w^2 + 3*w + 4]', '[2144, 268, 4*w^3 - 10*w - 4]', '[2144, 536, 4*w^3 - 3*w^2 - 10*w - 2]', '[2147, 2147, 4*w^3 - w^2 - 16*w + 5]', '[2147, 2147, -w^3 + 6*w^2 + 7*w - 19]', '[2150, 2150, w^3 + 4*w^2 - 9*w - 2]', '[2153, 2153, 7*w^3 - 11*w^2 - 30*w + 45]', '[2153, 2153, -4*w^3 + 8*w^2 + 17*w - 37]', '[2153, 2153, 4*w^3 + w^2 - 14*w - 3]', '[2153, 2153, -3*w^3 + 4*w^2 + 13*w - 11]', '[2155, 2155, w^3 + 3*w^2 - 5*w - 7]', '[2158, 2158, 2*w^3 - w^2 - 3*w + 4]', '[2161, 2161, 3*w^3 - 7*w^2 - 11*w + 27]', '[2164, 1082, 5*w^3 - 20*w - 9]', '[2164, 1082, -3*w^3 + 5*w^2 + 16*w - 24]', '[2164, 1082, -4*w^3 + 9*w^2 + 20*w - 32]', '[2164, 1082, 4*w^3 + 3*w^2 - 17*w - 9]', '[2168, 542, 3*w^3 + w^2 - 7*w - 4]', '[2168, 1084, -w^3 + 5*w^2 + 10*w - 18]', '[2173, 2173, 4*w^3 + 2*w^2 - 21*w - 5]', '[2173, 2173, 6*w^3 - 4*w^2 - 27*w + 11]', '[2174, 2174, -5*w - 4]', '[2176, 68, 2*w^3 - 2*w^2 - 10*w]', '[2176, 136, -3*w^3 + w^2 + 15*w - 8]', '[2176, 136, 2*w^3 - 8*w - 8]', '[2176, 272, -4*w^3 - w^2 + 14*w - 6]', '[2179, 2179, w^3 + 3*w^2 - 5*w - 9]', '[2179, 2179, -2*w^3 + 14*w - 7]', '[2180, 1090, 2*w^3 + 7*w^2 - 2*w - 12]', '[2180, 1090, -2*w^3 + 3*w^2 + 7*w - 3]', '[2182, 2182, 3*w^3 - 2*w^2 - 9*w - 6]', '[2182, 2182, -5*w^3 + 8*w^2 + 21*w - 34]', '[2185, 2185, -2*w^3 - 2*w^2 + 9*w - 1]', '[2186, 2186, -2*w^3 + 4*w^2 + 5*w - 12]', '[2186, 2186, 4*w^2 + w - 12]', '[2186, 2186, 2*w^3 + w^2 - 11*w + 2]', '[2186, 2186, -2*w^3 + 4*w^2 + 5*w - 4]', '[2188, 1094, 2*w^3 + w^2 - 7*w - 9]', '[2188, 1094, 5*w^2 + 6*w - 12]', '[2192, 274, 2*w^3 + 2*w^2 - 12*w - 10]', '[2192, 274, 6*w^3 - 26*w - 6]', '[2192, 548, 2*w^3 - w^2 - 13*w - 1]', '[2192, 548, 5*w^3 - 26*w]', '[2192, 548, -4*w^3 + w^2 + 21*w - 5]', '[2192, 548, 7*w^3 - 8*w^2 - 30*w + 32]', '[2197, 13, w^3 + 3*w^2 - 6*w - 7]', '[2197, 2197, 2*w^3 - w^2 - 4*w - 5]', '[2203, 2203, 6*w^3 - 9*w^2 - 28*w + 33]', '[2203, 2203, 3*w^3 + 3*w^2 - 13*w - 7]', '[2207, 2207, -4*w^3 + 16*w - 5]', '[2210, 2210, -2*w^3 - w^2 + 5*w - 6]', '[2221, 2221, 5*w^3 - 3*w^2 - 21*w + 13]', '[2221, 2221, -3*w^3 + 3*w^2 + 16*w - 13]', '[2224, 278, 8*w^3 - 6*w^2 - 36*w + 22]', '[2224, 556, -6*w^3 + w^2 + 30*w + 2]', '[2224, 556, 5*w^2 + w - 21]', '[2225, 2225, -2*w^3 + 8*w^2 + 12*w - 23]', '[2227, 2227, -2*w^3 + w^2 + 12*w - 3]', '[2230, 2230, 3*w^3 - 4*w^2 - 5*w + 2]', '[2230, 2230, 2*w^3 + 2*w^2 - 13*w - 8]', '[2231, 2231, 2*w^3 - 2*w^2 - 2*w - 7]', '[2231, 2231, -3*w^3 + 3*w^2 + 12*w - 5]', '[2231, 2231, w^3 - w^2 - 2*w + 11]', '[2231, 2231, 2*w^3 - 3*w^2 - 12*w + 9]', '[2234, 2234, 3*w^3 - 2*w^2 - 15*w - 4]', '[2236, 1118, -3*w^3 + 3*w^2 + 10*w]', '[2236, 1118, -w^3 + 2*w^2 + 4*w + 3]', '[2237, 2237, w^3 - w^2 - 3*w - 5]', '[2239, 2239, 3*w^3 - w^2 - 16*w + 9]', '[2239, 2239, -4*w^3 + 8*w^2 + 18*w - 31]', '[2243, 2243, -2*w^3 + 2*w^2 + 12*w - 5]', '[2245, 2245, 3*w^3 + 3*w^2 - 16*w - 11]', '[2249, 2249, 4*w^2 - 4*w - 9]', '[2249, 2249, 4*w^3 - 3*w^2 - 18*w + 7]', '[2251, 2251, 3*w^3 + 3*w^2 - 14*w - 7]', '[2251, 2251, 4*w^3 + 2*w^2 - 15*w - 1]', '[2252, 1126, 7*w^3 - 11*w^2 - 34*w + 40]', '[2252, 1126, 6*w^3 - w^2 - 31*w - 7]', '[2258, 2258, 2*w^3 - 3*w^2 + 3*w]', '[2258, 2258, 2*w^3 + 2*w^2 - 9*w + 2]', '[2260, 1130, -10*w^3 - 3*w^2 + 47*w + 25]', '[2260, 1130, 5*w^3 - 2*w^2 - 22*w + 10]', '[2260, 1130, -7*w^3 + 2*w^2 + 34*w - 5]', '[2260, 1130, -3*w^3 + 8*w^2 + 16*w - 30]', '[2264, 566, 9*w^3 + w^2 - 41*w - 10]', '[2264, 1132, 10*w^3 - 11*w^2 - 44*w + 46]', '[2267, 2267, w^3 - 5*w^2 + 15]', '[2269, 2269, 3*w^3 - 3*w^2 - 11*w + 3]', '[2273, 2273, -w^3 + 5*w^2 + 2*w - 17]', '[2278, 2278, w^2 + 5*w - 2]', '[2279, 2279, -3*w^3 + 5*w^2 + 16*w - 25]', '[2279, 2279, 5*w^3 - w^2 - 23*w - 5]', '[2281, 2281, -3*w^3 - w^2 + 11*w + 7]', '[2284, 1142, 4*w^3 + 3*w^2 - 17*w - 5]', '[2284, 1142, 4*w^3 - w^2 - 16*w + 12]', '[2284, 1142, -2*w^3 + 3*w^2 + 6*w - 12]', '[2284, 1142, 5*w^3 + 2*w^2 - 28*w - 11]', '[2285, 2285, 2*w^3 + w^2 - 4*w + 7]', '[2285, 2285, -3*w^3 - w^2 + 7*w - 5]', '[2287, 2287, -3*w^3 + 4*w^2 + 17*w - 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17]', '[5617, 5617, -2*w^3 + 2*w^2 + 5*w - 13]', '[5617, 5617, 6*w^3 - 4*w^2 - 24*w + 19]', '[5618, 106, 2*w^3 - 3*w^2 + w + 4]', '[5618, 106, w^3 - 11*w - 6]', '[5618, 5618, -4*w^3 + 3*w^2 + 11*w - 12]', '[5618, 5618, -4*w^3 - 5*w^2 + 25*w + 12]', '[5630, 5630, -3*w^2 + 3*w + 16]', '[5633, 5633, 6*w^3 - 9*w^2 - 24*w + 35]', '[5638, 5638, 4*w^3 - 2*w^2 - 13*w]', '[5641, 5641, 2*w^2 + 6*w - 5]', '[5641, 5641, -9*w^3 + 15*w^2 + 41*w - 59]', '[5644, 2822, 5*w^3 - 4*w^2 - 20*w + 15]', '[5644, 2822, -2*w^3 - 3*w^2 + 8*w - 4]', '[5645, 5645, w^3 + 5*w^2 - 2*w - 11]', '[5645, 5645, 2*w^3 - w^2 + 3]', '[5648, 706, 2*w^3 + 2*w^2 - 6*w - 10]', '[5648, 706, -8*w^3 + 32*w + 10]', '[5648, 1412, 5*w^3 - 3*w^2 - 20*w + 6]', '[5648, 1412, 5*w^3 + 2*w^2 - 16*w - 1]', '[5648, 1412, -4*w^3 + 3*w^2 + 14*w - 10]', '[5648, 1412, 3*w^3 + 2*w^2 - 20*w - 3]', '[5650, 5650, -5*w^3 + 23*w - 2]', '[5650, 5650, -7*w^3 - 2*w^2 + 31*w + 16]', '[5651, 5651, 5*w^3 - 4*w^2 - 17*w + 19]', '[5651, 5651, -3*w^3 + 2*w^2 + 17*w - 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7]', '[1451, 1451, -w^3 + 5*w^2 + 5*w - 19]', '[1459, 1459, -5*w + 9]', '[1471, 1471, -4*w^3 + 8*w^2 + 19*w - 29]', '[1483, 1483, w^3 + 3*w^2 - 6*w - 5]', '[1483, 1483, -3*w^3 - w^2 + 12*w - 1]', '[1487, 1487, -2*w^3 + 2*w^2 + 11*w - 15]', '[1489, 1489, 2*w^3 - 5*w^2 - 10*w + 23]', '[1493, 1493, 3*w^3 - 5*w^2 - 12*w + 25]', '[1493, 1493, 3*w^3 - 6*w^2 - 15*w + 25]', '[1499, 1499, 2*w^2 + 2*w - 13]', '[1499, 1499, w^3 + 3*w^2 - 5*w - 11]', '[1523, 1523, -w^3 + 3*w^2 + 5*w - 5]', '[1523, 1523, 4*w^3 - w^2 - 14*w + 9]', '[1523, 1523, -3*w^3 + w^2 + 14*w - 7]', '[1523, 1523, -2*w^3 + 3*w^2 + 6*w - 11]', '[1543, 1543, -w^3 + 3*w^2 + w - 9]', '[1543, 1543, -4*w^3 + 7*w^2 + 20*w - 29]', '[1559, 1559, 2*w^2 - 13]', '[1559, 1559, -4*w^2 - w + 17]', '[1571, 1571, 5*w - 3]', '[1579, 1579, 2*w^2 + 2*w - 11]', '[1579, 1579, w^3 + w^2 - 7*w - 11]', '[1583, 1583, 2*w^3 - 3*w^2 - 10*w + 7]', '[1597, 1597, -3*w^3 + w^2 + 7*w + 1]', '[1601, 1601, -5*w^3 + 3*w^2 + 23*w - 13]', '[1601, 1601, 5*w^3 - w^2 - 20*w + 9]', '[1607, 1607, 2*w^3 - w^2 - 10*w - 5]', '[1609, 1609, 3*w^3 - 8*w^2 - 13*w + 37]', '[1609, 1609, 3*w^3 - 2*w^2 - 11*w + 7]', '[1613, 1613, 2*w^3 - 4*w^2 - 12*w + 13]', '[1621, 1621, 5*w - 1]', '[1621, 1621, -2*w^3 + 5*w^2 + 8*w - 17]', '[1627, 1627, 3*w^3 + w^2 - 14*w - 1]', '[1627, 1627, -2*w^3 + 2*w^2 + 9*w + 1]', '[1637, 1637, 7*w^3 - 12*w^2 - 31*w + 49]', '[1657, 1657, -2*w^3 + 2*w^2 + 9*w - 1]', '[1657, 1657, -5*w^3 + w^2 + 21*w - 7]', '[1663, 1663, 9*w^3 - 11*w^2 - 39*w + 45]', '[1667, 1667, -4*w^3 + 3*w^2 + 16*w - 7]', '[1669, 1669, -w^3 - w^2 - w - 3]', '[1693, 1693, -3*w^3 + w^2 + 11*w - 1]', '[1693, 1693, w^3 + 2*w^2 - 11*w - 5]', '[1709, 1709, 3*w^3 + 3*w^2 - 16*w - 5]', '[1721, 1721, w^3 - 4*w^2 - 3*w + 11]', '[1747, 1747, 2*w^3 - 2*w^2 - 11*w + 1]', '[1747, 1747, w^3 + 3*w^2 - 4*w - 7]', '[1753, 1753, -6*w^3 + 6*w^2 + 28*w - 21]', '[1787, 1787, w^3 + 3*w^2 - 7*w - 13]', '[1787, 1787, -w^3 + w^2 + 8*w - 5]', '[1789, 1789, 2*w^3 + 3*w^2 - 12*w - 7]', '[1789, 1789, 4*w^2 - 15]', '[1801, 1801, w^3 + 3*w^2 - 7*w - 7]', '[1811, 1811, -3*w^3 + 2*w^2 + 11*w - 5]', '[1823, 1823, -w^3 + 3*w^2 + 6*w - 5]', '[1831, 1831, 5*w^3 - 4*w^2 - 21*w + 17]', '[1867, 1867, 3*w^3 - w^2 - 10*w + 5]', '[1871, 1871, 2*w^3 + 2*w^2 - 6*w - 7]', '[1873, 1873, -3*w^3 + 3*w^2 + 10*w - 7]', '[1879, 1879, 2*w^3 - 4*w^2 - 7*w + 17]', '[1889, 1889, 3*w^3 - 17*w - 3]', '[1907, 1907, -4*w^3 - 2*w^2 + 19*w + 5]', '[1907, 1907, 6*w^3 - 8*w^2 - 29*w + 33]', '[1913, 1913, -w^3 + w^2 + 8*w - 3]', '[1913, 1913, w^3 + 2*w^2 - 9*w + 3]', '[1933, 1933, w^2 + 4*w - 9]', '[1933, 1933, 6*w^3 - 6*w^2 - 26*w + 23]', '[1951, 1951, w^3 + 2*w^2 - 3*w - 11]', '[1951, 1951, -2*w^3 + 2*w^2 + 10*w - 1]', '[1973, 1973, -5*w^3 + 7*w^2 + 23*w - 25]', '[1979, 1979, -3*w^3 + 5*w^2 + 11*w - 19]', '[1987, 1987, 2*w^3 - 2*w^2 - 6*w + 11]', '[1993, 1993, -w^3 + 3*w - 7]', '[1993, 1993, w^3 + w^2 - 2*w - 9]', '[1997, 1997, 5*w^3 - w^2 - 19*w - 5]', '[1999, 1999, -3*w^3 + 3*w^2 + 15*w - 19]', '[2011, 2011, 5*w^3 - 6*w^2 - 23*w + 21]', '[2039, 2039, -2*w^3 + 4*w^2 + 8*w - 9]', '[2039, 2039, -3*w^3 + 4*w^2 + 11*w - 17]', '[2053, 2053, -2*w^3 + 3*w^2 + 8*w - 5]', '[2069, 2069, 5*w^3 - 6*w^2 - 21*w + 19]', '[2069, 2069, w^3 - 2*w^2 - 5*w - 3]', '[2069, 2069, 5*w^3 - 10*w^2 - 23*w + 43]', '[2069, 2069, 3*w^3 - 2*w^2 - 13*w + 1]', '[2081, 2081, 7*w^3 - 10*w^2 - 31*w + 37]', '[2081, 2081, -3*w^3 + 2*w^2 + 11*w - 15]', '[2099, 2099, -4*w^3 + 5*w^2 + 14*w - 13]', '[2111, 2111, w^3 + 3*w^2 - 6*w - 9]', '[2129, 2129, 4*w^3 - 4*w^2 - 20*w + 15]', '[2129, 2129, 4*w^2 - 3*w - 15]', '[2141, 2141, -w^3 + w^2 + w - 7]', '[2153, 2153, 7*w^3 - 11*w^2 - 30*w + 45]', '[2153, 2153, -4*w^3 + 8*w^2 + 17*w - 37]', '[2153, 2153, 4*w^3 + w^2 - 14*w - 3]', '[2153, 2153, -3*w^3 + 4*w^2 + 13*w - 11]', '[2161, 2161, 3*w^3 - 7*w^2 - 11*w + 27]', '[2179, 2179, w^3 + 3*w^2 - 5*w - 9]', '[2179, 2179, -2*w^3 + 14*w - 7]', '[2197, 13, w^3 + 3*w^2 - 6*w - 7]', '[2203, 2203, 6*w^3 - 9*w^2 - 28*w + 33]', '[2203, 2203, 3*w^3 + 3*w^2 - 13*w - 7]', '[2207, 2207, -4*w^3 + 16*w - 5]', '[2221, 2221, 5*w^3 - 3*w^2 - 21*w + 13]', '[2221, 2221, -3*w^3 + 3*w^2 + 16*w - 13]', '[2237, 2237, w^3 - w^2 - 3*w - 5]', '[2239, 2239, 3*w^3 - w^2 - 16*w + 9]', '[2239, 2239, -4*w^3 + 8*w^2 + 18*w - 31]', '[2243, 2243, -2*w^3 + 2*w^2 + 12*w - 5]', '[2251, 2251, 3*w^3 + 3*w^2 - 14*w - 7]', '[2251, 2251, 4*w^3 + 2*w^2 - 15*w - 1]', '[2267, 2267, w^3 - 5*w^2 + 15]', '[2269, 2269, 3*w^3 - 3*w^2 - 11*w + 3]', '[2273, 2273, -w^3 + 5*w^2 + 2*w - 17]', '[2281, 2281, -3*w^3 - w^2 + 11*w + 7]', '[2287, 2287, -3*w^3 + 4*w^2 + 17*w - 19]', '[2287, 2287, 4*w^2 + w - 11]', '[2287, 2287, w^3 - 5*w - 7]', '[2287, 2287, -5*w^3 + 21*w - 3]', '[2293, 2293, w^3 + w^2 - 8*w - 7]', '[2293, 2293, -2*w^3 - 2*w^2 + 7*w + 9]', '[2293, 2293, -4*w^3 + 6*w^2 + 16*w - 25]', '[2293, 2293, -5*w^3 + w^2 + 20*w - 7]', '[2309, 2309, 2*w^3 + 2*w^2 - 12*w - 1]', '[2311, 2311, -2*w^3 - w^2 + 10*w - 3]', '[2333, 2333, -5*w^3 + 7*w^2 + 25*w - 29]', '[2341, 2341, 6*w^3 - 7*w^2 - 24*w + 27]', '[2341, 2341, -w^3 + 5*w^2 + 6*w - 11]', '[2347, 2347, -5*w^3 + 7*w^2 + 23*w - 33]', '[2347, 2347, 4*w^3 - 2*w^2 - 16*w + 3]', '[2347, 2347, -6*w^3 + 8*w^2 + 26*w - 37]', '[2347, 2347, -w^3 - w^2 + 4*w - 5]', '[2351, 2351, -3*w^2 - 2*w + 13]', '[2357, 2357, 6*w^3 - 4*w^2 - 29*w + 15]', '[2357, 2357, 3*w^3 - 4*w^2 - 13*w + 21]', '[2371, 2371, 3*w^3 - 13*w + 9]', '[2371, 2371, -7*w^3 + 29*w + 9]', '[2377, 2377, w^3 - 3*w^2 - 7*w + 15]', '[2377, 2377, 4*w^3 - 6*w^2 - 21*w + 25]', '[2399, 2399, -3*w^3 + w^2 + 10*w - 1]', '[2401, 7, -7]', '[2411, 2411, 4*w^3 + w^2 - 16*w + 1]', '[2417, 2417, 3*w^3 + 2*w^2 - 15*w - 3]', '[2423, 2423, 5*w^3 + w^2 - 20*w - 3]', '[2437, 2437, -2*w^3 + 3*w^2 + 12*w - 11]', '[2437, 2437, 7*w^3 - 13*w^2 - 32*w + 55]', '[2437, 2437, -3*w^3 + w^2 + 14*w - 9]', '[2437, 2437, 3*w^3 - 3*w^2 - 9*w + 5]', '[2459, 2459, 5*w^2 - 2*w - 23]', '[2459, 2459, 5*w^3 - 4*w^2 - 23*w + 19]', '[2467, 2467, 4*w^3 + 4*w^2 - 15*w - 11]', '[2473, 2473, -w - 7]', '[2503, 2503, -4*w^3 + w^2 + 16*w - 11]', '[2521, 2521, 3*w^3 - 7*w^2 - 16*w + 27]', '[2531, 2531, -2*w^2 + w - 3]', '[2539, 2539, w^3 - 3*w^2 - 2*w + 13]', '[2543, 2543, -w^3 + 3*w^2 + 5*w - 3]', '[2549, 2549, 3*w^3 - 9*w - 5]', '[2549, 2549, -3*w^3 + w^2 + 10*w - 3]', '[2551, 2551, 2*w^3 - 4*w^2 - 9*w + 21]', '[2557, 2557, 3*w^3 - 4*w^2 - 15*w + 11]', '[2579, 2579, 6*w^3 - 8*w^2 - 27*w + 29]', '[2591, 2591, 2*w^3 - 6*w^2 - 8*w + 23]', '[2609, 2609, 6*w^3 - 5*w^2 - 26*w + 17]', '[2617, 2617, 7*w^3 - 7*w^2 - 32*w + 31]', '[2633, 2633, -5*w^3 + 3*w^2 + 22*w - 15]', '[2659, 2659, -6*w^3 - w^2 + 26*w + 13]', '[2659, 2659, w^3 + 3*w^2 - 7*w - 17]', '[2663, 2663, 2*w^3 - 2*w^2 - 12*w - 5]', '[2683, 2683, 4*w^3 - 3*w^2 - 22*w + 21]', '[2683, 2683, -w^3 + 3*w^2 + 5*w - 1]', '[2687, 2687, -w^3 - w^2 + 3*w - 5]', '[2687, 2687, -2*w^3 - w^2 + 12*w - 3]', '[2687, 2687, -3*w^3 + 5*w^2 + 15*w - 15]', '[2687, 2687, 3*w^3 + 3*w^2 - 16*w - 9]', '[2693, 2693, 2*w^3 + 3*w^2 - 10*w - 7]', '[2711, 2711, 6*w^3 - 8*w^2 - 28*w + 29]', '[2719, 2719, w^3 - 5*w^2 + w + 13]', '[2729, 2729, 4*w^3 - 3*w^2 - 16*w + 9]', '[2729, 2729, 2*w^2 + 5*w - 5]', '[2741, 2741, 3*w^3 + w^2 - 12*w + 3]', '[2741, 2741, w^3 - 9*w + 3]', '[2749, 2749, w^3 - w^2 - 4*w - 5]', '[2749, 2749, -2*w^3 + 13*w - 3]', '[2789, 2789, -3*w^3 + 4*w^2 + 11*w - 19]', '[2789, 2789, 3*w^3 - w^2 - 17*w + 11]', '[2791, 2791, 2*w^3 + 2*w^2 - 9*w - 15]', '[2791, 2791, w^3 - 9*w + 1]', '[2791, 2791, 7*w^3 - 11*w^2 - 33*w + 47]', '[2791, 2791, 3*w^3 - 17*w - 1]', '[2801, 2801, 2*w^2 - 4*w - 7]', '[2801, 2801, 3*w^3 - w^2 - 7*w + 1]', '[2803, 2803, -w^3 + 2*w^2 - w - 5]', '[2809, 53, -2*w^3 + 4*w^2 + 7*w - 7]', '[2819, 2819, 4*w^2 - 2*w - 13]', '[2833, 2833, 2*w^3 + w^2 - 6*w - 7]', '[2843, 2843, 6*w^3 - 8*w^2 - 25*w + 35]', '[2843, 2843, 4*w^3 - 2*w^2 - 19*w + 11]', '[2861, 2861, 8*w^3 - 11*w^2 - 36*w + 49]', '[2879, 2879, w^3 - w^2 - 5*w - 5]', '[2879, 2879, w^3 + w^2 - w - 13]', '[2887, 2887, 7*w^3 + 2*w^2 - 35*w - 9]', '[2887, 2887, -4*w^3 + 5*w^2 + 20*w - 15]', '[2939, 2939, 4*w^3 - 2*w^2 - 18*w + 1]', '[2939, 2939, -w^3 + w^2 + 9*w - 7]', '[2953, 2953, -5*w^3 + 9*w^2 + 22*w - 33]', '[2963, 2963, w^3 - 5*w^2 - 5*w + 17]', '[3001, 3001, 4*w^2 + w - 19]', '[3037, 3037, w^3 + w^2 - 7]', '[3037, 3037, w^3 + 4*w^2 - 9*w - 9]', '[3041, 3041, -5*w^3 + 7*w^2 + 22*w - 33]', '[3041, 3041, -4*w^3 - w^2 + 16*w + 9]', '[3041, 3041, -2*w^3 - 4*w^2 + 14*w + 13]', '[3041, 3041, -2*w^3 + 3*w^2 + 6*w - 13]', '[3049, 3049, -w^3 + 3*w^2 + 7*w - 3]', '[3067, 3067, w^3 + w^2 - 4*w - 11]', '[3067, 3067, -3*w^3 + 6*w^2 + 13*w - 29]', '[3079, 3079, 2*w^3 + 5*w^2 - 6*w - 17]', '[3079, 3079, 2*w^3 + 3*w^2 - 10*w - 9]', '[3079, 3079, w^3 + 3*w^2 - 7*w - 15]', '[3079, 3079, -5*w^3 + w^2 + 21*w + 9]', '[3089, 3089, -4*w^3 + w^2 + 16*w - 3]', '[3089, 3089, 5*w^3 - 2*w^2 - 25*w + 5]', '[3109, 3109, -w^2 - 5]', '[3109, 3109, w^2 - 2*w - 11]', '[3119, 3119, 5*w^3 - 9*w^2 - 24*w + 31]', '[3119, 3119, 2*w^3 - 4*w - 5]', '[3137, 3137, -w^3 + 3*w^2 + 2*w - 15]', '[3167, 3167, -2*w^3 - 2*w^2 + 15*w + 7]', '[3167, 3167, 4*w^3 - 4*w^2 - 21*w + 19]', '[3169, 3169, -5*w^2 - 4*w + 9]', '[3181, 3181, -3*w^3 + 2*w^2 + 9*w - 3]', '[3187, 3187, -4*w^3 + 2*w^2 + 16*w - 7]', '[3187, 3187, 2*w^3 + 2*w^2 - 10*w + 1]', '[3191, 3191, -5*w^3 + 4*w^2 + 23*w - 23]', '[3191, 3191, 5*w^3 + w^2 - 18*w - 5]', '[3203, 3203, -2*w^3 + 6*w^2 + 10*w - 27]', '[3229, 3229, 4*w^3 + w^2 - 18*w - 1]', '[3229, 3229, 7*w^3 - 5*w^2 - 31*w + 17]', '[3257, 3257, 5*w^3 - 11*w^2 - 23*w + 47]', '[3271, 3271, 6*w^3 - 11*w^2 - 30*w + 43]', '[3271, 3271, 6*w - 1]', '[3271, 3271, -5*w^3 - w^2 + 21*w + 11]', '[3271, 3271, 2*w^3 - 13*w + 1]', '[3299, 3299, -w^3 + 3*w^2 + 8*w - 15]', '[3299, 3299, -2*w^2 + 6*w + 5]', '[3301, 3301, -8*w^3 - w^2 + 34*w + 13]', '[3307, 3307, -w^3 + 2*w^2 + 9*w - 3]', '[3307, 3307, -8*w^3 + 6*w^2 + 35*w - 25]', '[3313, 3313, 6*w^3 - 6*w^2 - 25*w + 31]', '[3323, 3323, -6*w^3 + w^2 + 26*w - 3]', '[3323, 3323, -2*w^2 - 3*w + 15]', '[3347, 3347, 2*w^3 - 6*w^2 - 5*w + 17]', '[3373, 3373, 4*w^3 - 4*w^2 - 18*w + 11]', '[3373, 3373, 4*w^3 - 6*w^2 - 20*w + 19]', '[3389, 3389, 4*w^2 - 11]', '[3389, 3389, 3*w^3 - 7*w^2 - 15*w + 21]', '[3391, 3391, 4*w^3 - 15*w + 1]', '[3391, 3391, 4*w^3 - 7*w^2 - 16*w + 29]', '[3433, 3433, -5*w^2 + 2*w + 19]', '[3433, 3433, -w^3 + 4*w^2 + 7*w - 17]', '[3449, 3449, 2*w^2 - 3*w - 11]', '[3449, 3449, 3*w^3 - w^2 - 15*w - 7]', '[3463, 3463, 4*w^2 - w - 13]', '[3463, 3463, -5*w^3 - 3*w^2 + 23*w + 7]', '[3467, 3467, 3*w^3 + 2*w^2 - 13*w - 1]', '[3469, 3469, 4*w^2 - 3*w - 9]', '[3491, 3491, w^3 - 5*w^2 - 7*w + 11]', '[3499, 3499, 5*w^3 - 2*w^2 - 23*w + 1]', '[3499, 3499, -8*w^3 + 9*w^2 + 34*w - 37]', '[3511, 3511, w^3 - 5*w^2 - 8*w + 11]', '[3511, 3511, -2*w^3 + 6*w^2 + 4*w - 13]', '[3517, 3517, w^3 + 4*w^2 - 3*w - 9]', '[3527, 3527, w^2 - 4*w - 7]', '[3529, 3529, -8*w^3 + 10*w^2 + 38*w - 39]', '[3529, 3529, 2*w^3 - 5*w - 7]', '[3539, 3539, 6*w^3 - 4*w^2 - 28*w + 11]', '[3539, 3539, 4*w^2 - w - 9]', '[3541, 3541, 6*w^3 - 23*w - 9]', '[3547, 3547, -3*w^3 - 2*w^2 + 11*w + 9]', '[3557, 3557, -3*w^3 + 2*w^2 + 15*w + 3]', '[3571, 3571, 3*w^3 - w^2 - 15*w + 11]', '[3581, 3581, 6*w^3 - 2*w^2 - 28*w + 1]', '[3593, 3593, 5*w^3 - w^2 - 24*w + 5]', '[3593, 3593, -2*w^3 + 3*w^2 + 4*w - 9]', '[3607, 3607, 3*w^3 - 4*w^2 - 17*w + 11]', '[3607, 3607, -w^3 - 5*w^2 + 6*w + 21]', '[3617, 3617, 2*w^3 + 4*w^2 - 7*w - 7]', '[3617, 3617, 2*w^2 + 4*w - 11]', '[3623, 3623, -5*w^3 + 4*w^2 + 25*w - 17]', '[3631, 3631, 8*w^3 - 14*w^2 - 36*w + 57]', '[3631, 3631, -2*w^3 + 4*w^2 + 13*w - 7]', '[3637, 3637, 6*w^3 - 3*w^2 - 26*w + 7]', '[3637, 3637, w^3 + 2*w^2 - w - 9]', '[3659, 3659, 4*w^3 - 4*w^2 - 14*w + 13]', '[3677, 3677, -w^3 + w^2 + 3*w - 11]', '[3691, 3691, -4*w^3 + 5*w^2 + 14*w - 19]', '[3697, 3697, -4*w^3 + 18*w - 3]', '[3719, 3719, w^3 + 5*w^2 - 2*w - 9]', '[3733, 3733, 3*w^2 + 2*w - 15]', '[3733, 3733, -5*w^3 + 5*w^2 + 22*w - 15]', '[3767, 3767, w^3 + w^2 - w - 9]', '[3767, 3767, -3*w^3 + 3*w^2 + 13*w - 5]', '[3793, 3793, 2*w^2 + 3*w - 13]', '[3793, 3793, 5*w^3 - 3*w^2 - 25*w + 9]', '[3797, 3797, -9*w^3 - w^2 + 39*w + 15]', '[3797, 3797, 4*w^3 - 6*w^2 - 21*w + 21]', '[3803, 3803, -6*w^3 + 4*w^2 + 26*w - 15]', '[3803, 3803, 2*w - 9]', '[3823, 3823, -5*w^3 + 10*w^2 + 23*w - 39]', '[3833, 3833, w^3 + w^2 - 5*w - 11]', '[3847, 3847, 3*w^3 - 5*w^2 - 11*w + 21]', '[3851, 3851, 4*w^2 - 2*w - 9]', '[3851, 3851, -2*w^3 + 6*w^2 + 9*w - 21]', '[3853, 3853, -w^3 + w^2 + 7*w - 13]', '[3863, 3863, 4*w^3 - 6*w^2 - 18*w + 19]', '[3881, 3881, -4*w^3 + 14*w + 7]', '[3889, 3889, -3*w^3 + w^2 + 12*w - 13]', '[3889, 3889, -4*w^3 + 2*w^2 + 21*w - 9]', '[3889, 3889, 5*w^3 - 6*w^2 - 25*w + 25]', '[3889, 3889, 3*w^3 - 7*w^2 - 12*w + 21]', '[3907, 3907, -3*w^3 + 9*w^2 + 14*w - 39]', '[3917, 3917, 3*w^3 + 3*w^2 - 13*w - 17]', '[3917, 3917, 9*w^3 - 11*w^2 - 40*w + 41]', '[3917, 3917, -w^3 + w^2 + 4*w - 11]', '[3917, 3917, 3*w^3 - 3*w^2 - 11*w - 1]', '[3923, 3923, -2*w^3 + 4*w^2 + 12*w - 21]', '[3923, 3923, w^3 + 3*w^2 - 11*w - 7]', '[3931, 3931, -3*w^3 + 19*w - 7]', '[3947, 3947, -4*w^3 + 4*w^2 + 22*w - 9]', '[3947, 3947, -5*w^3 - w^2 + 17*w + 7]', '[3947, 3947, -w^3 - 4*w^2 + 3*w + 17]', '[3947, 3947, -2*w^3 - 4*w^2 + 12*w + 3]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	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': [2, 4, -5, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 11324, 'disc_rad': 5662, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [[3, 1], [1, 1]]], [7, [[4, 1]]], [11, [[2, 2]]], [13, [[3, 1], [1, 1]]], [17, [[3, 1], [1, 1]]], [19, [0]], [23, [[3, 1], [1, 1]]], [29, [[4, 1]]], [31, [[3, 1], [1, 1]]], [37, [[4, 1]]], [41, [[3, 1], [1, 1]]], [43, [[3, 1], [1, 1]]], [47, [[4, 1]]], [53, [[2, 1], [1, 2]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 106.41428475538423, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.11324.1', 'local_algs': ['2.1.2.2a1.2', '2.2.1.0a1.1', '19.1.2.1a1.1', '19.2.1.0a1.1', '149.1.2.1a1.2', '149.2.1.0a1.1'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 19, 149], 'rd': 10.3157299672, 'regulator': {'__RealLiteral__': 0, 'data': '8.65208837325', 'prec': 44}, 'res': {'gal': ['16,-1312,-18784,594592,491388,-11086944,-22633912,14199812,51786361,-241732,-46643816,-7502448,21039062,4372276,-5224280,-1081892,750931,136284,-64240,-9088,3230,304,-88,-4,1'], 'sib': ['-293,-911,277,3060,1853,-1839,-1550,353,407,-14,-39,-1,1', '-45296,0,4248,0,-119,0,1', '-9208,25424,17920,-71228,-1308,39540,-5451,-6198,1023,340,-57,-6,1', '170105,-341502,-145559,18440,10112,-32,-183,-2,1', '2,-13,3,19,-7,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a^{3} - a^{2} - 5 a + 5 \\)', '\\( a^{3} - a^{2} - 4 a + 5 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}