Hilbert modular form data - 4.4.19821.1-27.2-f

Formats: - HTML - YAML - JSON - 2024-05-01T17:58:39.722422

• 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': 19821, 'field_bad_primes': [3, 6607], 'field_label': '4.4.19821.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.19821.1-27.2-f', 'label_nsuffix': 5, 'label_suffix': 'f', 'level_bad_primes': [3], 'level_ideal': '[27, 9, -1/3*w^3 + 2/3*w^2 + 2*w - 1]', 'level_label': '27.2', 'level_norm': 27, 'parallel_weight': 2, 'short_label': '27.2-f', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, w]', -1]], 'hecke_eigenvalues': [0, -1, -2, -4, 5, -3, -1, 6, -7, 8, 6, 0, -10, 6, -7, 0, -12, -6, -4, -6, -1, -6, 9, 17, 0, 2, 0, -6, 12, 14, 14, -22, 11, -15, -12, -21, 3, 23, 14, -18, 12, 15, -6, 2, -6, 2, -18, 24, 30, 2, 20, 23, 30, 18, 5, -10, 11, 30, -37, 35, 24, -12, 29, -22, -1, 20, -15, -34, -22, 11, -25, -9, 15, -30, -22, -34, -12, -12, 21, 24, -40, 26, 30, 15, 14, 12, 9, 24, -36, 18, -16, -43, -10, 32, 24, 39, 12, -18, -36, -4, -30, -9, 18, -13, 14, -10, 6, -27, -24, -24, -34, -31, -12, -16, 14, -30, 3, -39, -31, 21, 8, -16, -16, -13, -22, 35, -48, -4, 11, 5, -21, -51, 3, -39, -27, 44, 11, -42, -48, 38, -52, -27, 23, -24, 41, -49, -30, 12, -52, 23, 18, -6, -18, 5, -39, 2, 18, -24, -12, -24, -42, -46, -13, -10, 30, -57, 36, 50, -52, -46, -28, -39, 33, 12, -39, 35, -46, 51, -6, 14, -10, 47, -27, 33, -55, -24, 54, -42, -34, -22, -42, -15, -15, -3, 33, -66, 6, -42, 5, -24, -25, 20, -10, -6, -30, -55, -52, -25, -40, -45, 36, 42, 68, -13, -6, 6, 15, 24, -49, 47, 48, -42, 6, 12, 26, 14, 11, -10, 65, -40, -34, 36, 51, -63, -12, -63, 57, 30, -73, -49, -18, -24, -75, -43, 15, -48, 59, -42, 32, -3, 39, 68, 41, -15, 47, 62, 8, -28, 78, -6, -46, 68, 48, 27, 14, -52, -22, -55, -25, -40, 50, -46, 38, -16, 72, 66, 24, 0, -33, -73, 20, -72, 2, 75, -18, -58, 44, 42, -54, -57, 21, 62, -7, 30, 5, -48, 2, 38, -52], 'hecke_polynomial': 'x', 'label': '4.4.19821.1-27.2-f'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 19821, 'ideals': ['[1, 1, 1]', '[3, 3, w]', '[7, 7, 1/3*w^3 - 2/3*w^2 - 2*w + 2]', '[9, 3, 1/3*w^3 - 2/3*w^2 - 2*w + 4]', '[9, 3, w + 1]', '[13, 13, 2/3*w^3 - 1/3*w^2 - 5*w]', '[16, 2, 2]', '[17, 17, 1/3*w^3 - 2/3*w^2 - 3*w + 5]', '[19, 19, -1/3*w^3 + 2/3*w^2 + 2*w - 5]', '[21, 21, 2/3*w^3 - 1/3*w^2 - 5*w - 1]', '[23, 23, -1/3*w^3 + 2/3*w^2 + 3*w - 2]', '[25, 5, 1/3*w^3 + 1/3*w^2 - 3*w]', '[25, 5, -2/3*w^3 + 1/3*w^2 + 5*w - 3]', '[27, 3, -w^3 + w^2 + 8*w - 6]', '[27, 9, -1/3*w^3 + 2/3*w^2 + 2*w - 1]', '[29, 29, -2/3*w^3 + 1/3*w^2 + 4*w - 3]', '[29, 29, -1/3*w^3 + 2/3*w^2 + 2*w]', '[37, 37, 1/3*w^3 + 1/3*w^2 - 2*w - 3]', '[39, 39, w^3 - w^2 - 7*w + 6]', '[41, 41, -2/3*w^3 + 1/3*w^2 + 5*w - 4]', '[43, 43, 2/3*w^3 - 1/3*w^2 - 6*w]', '[47, 47, 2/3*w^3 - 1/3*w^2 - 4*w]', '[48, 6, 2*w]', '[49, 49, -w^3 + 7*w + 1]', '[51, 51, -1/3*w^3 - 1/3*w^2 + 3*w - 1]', '[57, 57, 1/3*w^3 - 2/3*w^2 - 3*w + 1]', '[59, 59, 1/3*w^3 + 1/3*w^2 - 2*w - 4]', '[59, 59, 4/3*w^3 - 5/3*w^2 - 10*w + 9]', '[63, 21, 2/3*w^3 - 1/3*w^2 - 4*w + 2]', '[63, 21, -2*w + 1]', '[67, 67, -1/3*w^3 + 2/3*w^2 + 3*w]', '[69, 69, -w^3 + 8*w]', '[71, 71, 2/3*w^3 - 1/3*w^2 - 4*w + 1]', '[73, 73, -1/3*w^3 + 2/3*w^2 + w - 3]', '[75, 15, 1/3*w^3 + 1/3*w^2 - w - 2]', '[75, 15, 2/3*w^3 - 1/3*w^2 - 2*w - 1]', '[81, 3, 3]', '[81, 9, -w^2 + 6]', '[81, 9, -w^2 + w + 2]', '[83, 83, -w^3 + w^2 + 8*w - 4]', '[83, 83, -2/3*w^3 + 1/3*w^2 + 6*w - 1]', '[87, 87, -1/3*w^3 - 4/3*w^2 + w + 2]', '[87, 87, -1/3*w^3 + 2/3*w^2 - 2*w - 1]', '[91, 91, -2/3*w^3 - 2/3*w^2 + 5*w + 3]', '[97, 97, 5/3*w^3 - 4/3*w^2 - 13*w + 6]', '[101, 101, -1/3*w^3 + 2/3*w^2 + 4*w - 2]', '[111, 111, 2/3*w^3 + 2/3*w^2 - 5*w - 1]', '[112, 14, 2/3*w^3 - 4/3*w^2 - 4*w + 4]', '[117, 39, w^3 - 9*w - 2]', '[117, 39, w^2 - 3]', '[119, 119, 1/3*w^3 - 2/3*w^2 - 4*w + 3]', '[123, 123, -1/3*w^3 - 1/3*w^2 + 2]', '[127, 127, w^2 - w - 4]', '[129, 129, 1/3*w^3 - 2/3*w^2 - 4*w - 2]', '[131, 131, 7/3*w^3 - 8/3*w^2 - 18*w + 15]', '[131, 131, 4/3*w^3 - 8/3*w^2 - 10*w + 17]', '[133, 133, -w^3 + 6*w - 2]', '[137, 137, 1/3*w^3 + 1/3*w^2 - 4*w - 3]', '[139, 139, w^2 - 5]', '[141, 141, 1/3*w^3 + 4/3*w^2 - 4*w - 2]', '[144, 6, 2/3*w^3 - 4/3*w^2 - 4*w + 8]', '[144, 6, 2*w + 2]', '[147, 147, -1/3*w^3 + 2/3*w^2 + w + 2]', '[151, 151, 1/3*w^3 - 2/3*w^2 - 4*w + 6]', '[153, 51, 1/3*w^3 - 2/3*w^2 - 2*w + 7]', '[153, 51, -w^2 + 4]', '[161, 161, -2/3*w^3 + 1/3*w^2 + 5*w - 6]', '[163, 163, -2/3*w^3 + 4/3*w^2 + 6*w - 9]', '[163, 163, -2/3*w^3 + 1/3*w^2 + 3*w - 4]', '[169, 169, -w^3 + 6*w + 1]', '[171, 57, -w - 4]', '[171, 57, 4/3*w^3 + 1/3*w^2 - 11*w - 2]', '[175, 35, 1/3*w^3 - 5/3*w^2 + 3]', '[175, 35, w^3 - 2*w^2 - 7*w + 10]', '[177, 177, -1/3*w^3 + 2/3*w^2 + w - 4]', '[177, 177, 2/3*w^3 + 2/3*w^2 - 6*w - 1]', '[179, 179, w^2 - 2*w - 4]', '[179, 179, w^2 - w - 7]', '[189, 21, w^2 + w - 6]', '[189, 63, w^3 - 9*w]', '[191, 191, 1/3*w^3 + 1/3*w^2 - w - 3]', '[191, 191, -2/3*w^3 + 1/3*w^2 + 4*w - 6]', '[193, 193, -w^3 + 9*w + 1]', '[193, 193, 4/3*w^3 - 2/3*w^2 - 9*w]', '[197, 197, 2/3*w^3 - 1/3*w^2 - 5*w - 3]', '[197, 197, w^3 - 8*w + 1]', '[197, 197, w^3 - 7*w + 2]', '[197, 197, -4/3*w^3 + 2/3*w^2 + 11*w - 3]', '[201, 201, 1/3*w^3 + 1/3*w^2 + 2*w + 1]', '[203, 203, -2/3*w^3 + 4/3*w^2 + 7*w - 9]', '[203, 203, -1/3*w^3 + 5/3*w^2 - w + 1]', '[207, 69, -w^3 + w^2 + 6*w - 5]', '[207, 69, -4/3*w^3 + 5/3*w^2 + 11*w - 10]', '[208, 26, 4/3*w^3 - 2/3*w^2 - 10*w]', '[213, 213, 1/3*w^3 + 4/3*w^2 - 3*w - 2]', '[219, 219, 1/3*w^3 - 5/3*w^2 - w + 1]', '[221, 221, -1/3*w^3 - 1/3*w^2 + 2*w - 3]', '[223, 223, 4/3*w^3 - 5/3*w^2 - 10*w + 8]', '[225, 15, 7/3*w^3 - 8/3*w^2 - 17*w + 16]', '[225, 15, w^3 - w^2 - 6*w + 3]', '[225, 15, w^3 - 5*w - 1]', '[225, 15, w^3 - 6*w + 1]', '[233, 233, -4/3*w^3 + 2/3*w^2 + 9*w - 5]', '[241, 241, 1/3*w^3 + 1/3*w^2 - 4*w - 4]', '[243, 9, 3*w]', '[243, 9, -w^3 + w^2 + 8*w - 3]', '[243, 27, -w^3 + 6*w]', '[247, 247, -1/3*w^3 - 4/3*w^2 + w + 4]', '[249, 249, 2*w + 3]', '[249, 249, -1/3*w^3 + 2/3*w^2 + 3*w + 2]', '[256, 4, 4]', '[257, 257, -w^3 - w^2 + 6*w + 5]', '[259, 259, -w^3 + w^2 + 6*w - 4]', '[261, 87, -4*w - 1]', '[261, 87, -2*w^3 + 2*w^2 + 15*w - 15]', '[261, 87, 1/3*w^3 + 1/3*w^2 - 5*w + 1]', '[261, 87, -w^3 - w^2 + 5*w - 1]', '[269, 269, -1/3*w^3 - 1/3*w^2 + 5*w]', '[269, 269, -2/3*w^3 + 4/3*w^2 + 4*w - 3]', '[271, 271, -2/3*w^3 + 4/3*w^2 + 3*w - 6]', '[271, 271, w^3 - 8*w - 5]', '[272, 34, 2/3*w^3 - 4/3*w^2 - 6*w + 10]', '[273, 273, 2/3*w^3 - 1/3*w^2 - 3*w + 5]', '[277, 277, 2*w^3 - 2*w^2 - 16*w + 13]', '[281, 281, 2/3*w^3 + 2/3*w^2 - 5*w]', '[281, 281, -w^3 + w^2 + 7*w - 2]', '[287, 287, -4/3*w^3 + 8/3*w^2 + 9*w - 12]', '[289, 289, -2/3*w^3 - 2/3*w^2 + 7*w]', '[291, 291, 1/3*w^3 + 1/3*w^2 - 4*w - 5]', '[299, 299, 1/3*w^3 + 1/3*w^2 - 3*w - 6]', '[301, 301, 1/3*w^3 - 2/3*w^2 - w + 5]', '[303, 303, 1/3*w^3 + 4/3*w^2 + 1]', '[304, 38, -2/3*w^3 + 4/3*w^2 + 4*w - 10]', '[323, 323, 4/3*w^3 - 2/3*w^2 - 10*w - 1]', '[325, 65, -w^3 - w^2 + 9*w + 5]', '[325, 65, -1/3*w^3 - 4/3*w^2 + 3*w + 9]', '[329, 329, -1/3*w^3 + 2/3*w^2 - w + 3]', '[331, 331, 2/3*w^3 - 4/3*w^2 - 5*w + 4]', '[331, 331, 8/3*w^3 - 7/3*w^2 - 20*w + 15]', '[333, 111, -1/3*w^3 + 5/3*w^2 + 2*w - 10]', '[333, 111, w^3 + w^2 - 7*w - 4]', '[336, 42, 4/3*w^3 - 2/3*w^2 - 10*w - 2]', '[343, 7, -4/3*w^3 + 2/3*w^2 + 11*w - 6]', '[343, 343, 1/3*w^3 + 1/3*w^2 - w - 4]', '[347, 347, 2/3*w^3 + 2/3*w^2 - 4*w - 5]', '[349, 349, -1/3*w^3 + 2/3*w^2 + 3*w - 8]', '[349, 349, -1/3*w^3 + 2/3*w^2 - 3]', '[351, 39, w^3 - 7*w + 3]', '[351, 117, 2/3*w^3 - 1/3*w^2 - 4*w - 4]', '[353, 353, -5/3*w^3 + 1/3*w^2 + 12*w]', '[353, 353, 1/3*w^3 - 5/3*w^2 - 2*w + 14]', '[357, 357, 4/3*w^3 - 2/3*w^2 - 9*w + 1]', '[361, 361, -1/3*w^3 - 1/3*w^2 + 3]', '[367, 367, -1/3*w^3 + 5/3*w^2 + 4*w - 9]', '[367, 367, 1/3*w^3 + 1/3*w^2 + w - 3]', '[368, 46, -2/3*w^3 + 4/3*w^2 + 6*w - 4]', '[369, 123, -w^3 + 5*w - 2]', '[369, 123, -8/3*w^3 + 10/3*w^2 + 19*w - 20]', '[377, 377, -4/3*w^3 + 2/3*w^2 + 9*w + 4]', '[377, 377, w^2 + w - 7]', '[379, 379, 4/3*w^3 + 1/3*w^2 - 12*w]', '[379, 379, -5/3*w^3 + 7/3*w^2 + 13*w - 12]', '[381, 381, w^3 - w^2 - 4*w]', '[383, 383, -5/3*w^3 + 10/3*w^2 + 12*w - 21]', '[387, 129, w^3 - w^2 - 10*w - 2]', '[387, 129, 5/3*w^3 - 4/3*w^2 - 13*w + 5]', '[391, 391, -1/3*w^3 - 1/3*w^2 + 5*w + 3]', '[393, 393, -1/3*w^3 + 2/3*w^2 + w - 7]', '[393, 393, -4/3*w^3 + 2/3*w^2 + 9*w - 4]', '[397, 397, 1/3*w^3 + 4/3*w^2 - 5*w - 6]', '[397, 397, 4/3*w^3 + 1/3*w^2 - 8*w]', '[397, 397, -1/3*w^3 + 2/3*w^2 + w - 6]', '[397, 397, w^3 + w^2 - 8*w - 7]', '[399, 399, 1/3*w^3 + 1/3*w^2 - 3*w + 4]', '[400, 10, 2/3*w^3 + 2/3*w^2 - 6*w]', '[400, 10, -4/3*w^3 + 2/3*w^2 + 10*w - 6]', '[401, 401, 5/3*w^3 - 1/3*w^2 - 14*w + 1]', '[411, 411, 2/3*w^3 - 4/3*w^2 - 5*w - 1]', '[413, 413, 1/3*w^3 - 5/3*w^2 - 3*w + 8]', '[413, 413, -4/3*w^3 + 5/3*w^2 + 8*w - 6]', '[417, 417, w^3 - 5*w]', '[419, 419, 1/3*w^3 + 4/3*w^2 - 4*w - 3]', '[419, 419, 1/3*w^3 - 5/3*w^2 - 3*w + 12]', '[423, 141, w^3 + w^2 - 8*w - 2]', '[423, 141, w^3 - 9*w + 3]', '[425, 85, 8/3*w^3 - 10/3*w^2 - 21*w + 21]', '[425, 85, 2/3*w^3 - 1/3*w^2 - 7*w + 4]', '[432, 6, -2*w^3 + 2*w^2 + 16*w - 12]', '[432, 18, -2/3*w^3 + 4/3*w^2 + 4*w - 2]', '[433, 433, -w^3 + w^2 + 9*w - 4]', '[433, 433, 1/3*w^3 + 4/3*w^2 - 4*w - 9]', '[437, 437, w^2 - 2*w - 5]', '[441, 147, -w^3 + w^2 + 7*w - 1]', '[441, 147, -5/3*w^3 + 1/3*w^2 + 13*w - 2]', '[443, 443, 4/3*w^3 - 2/3*w^2 - 8*w - 1]', '[443, 443, -4/3*w^3 + 8/3*w^2 + 9*w - 17]', '[449, 449, -w^3 + w^2 + 8*w - 2]', '[449, 449, 5/3*w^3 - 7/3*w^2 - 13*w + 18]', '[453, 453, -1/3*w^3 - 4/3*w^2 + 4*w - 1]', '[457, 457, -w^3 + 3*w^2 + 7*w - 20]', '[457, 457, 2/3*w^3 + 2/3*w^2 - 5*w - 9]', '[459, 51, -w^3 + 7*w + 6]', '[459, 153, -1/3*w^3 + 2/3*w^2 + 5*w - 1]', '[461, 461, 4/3*w^3 - 2/3*w^2 - 9*w + 2]', '[461, 461, -2/3*w^3 + 7/3*w^2 + 4*w - 16]', '[463, 463, 4/3*w^3 + 1/3*w^2 - 11*w - 1]', '[464, 58, -4/3*w^3 + 2/3*w^2 + 8*w - 6]', '[464, 58, -2/3*w^3 + 4/3*w^2 + 4*w]', '[467, 467, w^3 - 2*w^2 - 9*w + 8]', '[469, 469, -w^2 + w - 2]', '[475, 95, -4/3*w^3 + 2/3*w^2 + 9*w - 3]', '[475, 95, -3*w^3 + 3*w^2 + 22*w - 19]', '[479, 479, 4/3*w^3 - 8/3*w^2 - 10*w + 15]', '[479, 479, 5/3*w^3 - 1/3*w^2 - 14*w]', '[481, 481, -8/3*w^3 + 1/3*w^2 + 20*w + 3]', '[483, 483, -1/3*w^3 + 5/3*w^2 + w - 7]', '[489, 489, 2/3*w^3 + 2/3*w^2 - 5*w + 2]', '[489, 489, -1/3*w^3 - 7/3*w^2 + 2]', '[491, 491, -1/3*w^3 + 2/3*w^2 + 2*w - 8]', '[493, 493, w^3 - w^2 - 5*w + 2]', '[493, 493, -7/3*w^3 + 11/3*w^2 + 18*w - 20]', '[497, 497, -3*w + 5]', '[507, 507, -1/3*w^3 + 5/3*w^2 + 4*w - 4]', '[509, 509, -11/3*w^3 + 13/3*w^2 + 27*w - 27]', '[511, 511, -1/3*w^3 - 1/3*w^2 + 7*w - 6]', '[513, 57, w^3 - w^2 - 5*w + 3]', '[513, 171, w^3 - w^2 - 9*w + 6]', '[523, 523, -w - 5]', '[523, 523, 4/3*w^3 - 2/3*w^2 - 10*w + 9]', '[525, 105, -4/3*w^3 - 4/3*w^2 + 12*w + 5]', '[525, 105, -w^3 - w^2 + 8*w + 6]', '[529, 529, -2/3*w^3 + 4/3*w^2 + 4*w - 1]', '[531, 177, w^3 - w^2 - 9*w + 5]', '[531, 177, -2/3*w^3 + 7/3*w^2 + 4*w - 14]', '[531, 177, w^3 + w^2 - 8*w - 5]', '[531, 177, 1/3*w^3 - 5/3*w^2 - 2*w + 1]', '[533, 533, -1/3*w^3 + 5/3*w^2 + 2*w - 9]', '[537, 537, w^3 - 2*w^2 - 4*w]', '[537, 537, w^3 - w^2 - 7*w]', '[541, 541, 8/3*w^3 - 7/3*w^2 - 21*w + 13]', '[547, 547, -2/3*w^3 + 1/3*w^2 + 5*w - 7]', '[551, 551, -2/3*w^3 + 1/3*w^2 + 7*w - 1]', '[551, 551, 8/3*w^3 - 7/3*w^2 - 19*w + 18]', '[557, 557, -2/3*w^3 + 1/3*w^2 + 7*w - 3]', '[559, 559, -8/3*w^3 - 2/3*w^2 + 22*w + 11]', '[563, 563, w^2 + w - 8]', '[563, 563, 1/3*w^3 + 1/3*w^2 - w - 6]', '[567, 21, w^3 - 2*w^2 - 6*w + 6]', '[567, 63, 5/3*w^3 - 4/3*w^2 - 13*w + 11]', '[567, 63, w^3 - 6*w - 5]', '[569, 569, 1/3*w^3 + 4/3*w^2 - 4*w - 6]', '[569, 569, -1/3*w^3 + 5/3*w^2 + 2*w - 6]', '[571, 571, 5/3*w^3 - 4/3*w^2 - 11*w + 1]', '[573, 573, 2/3*w^3 + 5/3*w^2 - 5*w - 1]', '[573, 573, -1/3*w^3 - 4/3*w^2 - 2*w + 2]', '[575, 115, -2/3*w^3 + 7/3*w^2 + 6*w - 12]', '[575, 115, 1/3*w^3 + 4/3*w^2 - 2*w - 4]', '[579, 579, -w^3 + w^2 + 7*w + 3]', '[579, 579, 2/3*w^3 + 5/3*w^2 - 8*w - 4]', '[581, 581, -2/3*w^3 + 4/3*w^2 + 3*w - 7]', '[581, 581, 2/3*w^3 + 5/3*w^2 - 3*w - 6]', '[591, 591, -2/3*w^3 + 1/3*w^2 + 5*w + 4]', '[591, 591, w^3 - 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4/3*w^2 + 8*w - 8]', '[1883, 1883, -w^3 + 3*w^2 - 5]', '[1887, 1887, 2/3*w^3 - 1/3*w^2 - 8*w + 2]', '[1893, 1893, 1/3*w^3 + 7/3*w^2 - w + 1]', '[1893, 1893, 5/3*w^3 + 2/3*w^2 - 11*w - 7]', '[1897, 1897, -4/3*w^3 + 5/3*w^2 + 9*w - 3]', '[1897, 1897, w^3 - 14*w + 13]', '[1901, 1901, -2/3*w^3 + 1/3*w^2 + 2*w + 9]', '[1901, 1901, 10/3*w^3 - 11/3*w^2 - 24*w + 21]', '[1904, 238, 2/3*w^3 - 4/3*w^2 - 8*w + 6]', '[1907, 1907, w^3 + w^2 - 10*w - 8]', '[1907, 1907, 5*w^3 - 6*w^2 - 38*w + 35]', '[1909, 1909, 1/3*w^3 - 2/3*w^2 + 9]', '[1909, 1909, -5/3*w^3 + 4/3*w^2 + 12*w - 1]', '[1911, 1911, w^2 - w - 12]', '[1917, 213, -w^3 + 3*w^2 + 7*w - 18]', '[1917, 639, 2/3*w^3 - 1/3*w^2 - w - 4]', '[1919, 1919, 2*w^3 - 3*w^2 - 17*w + 13]', '[1923, 1923, 4/3*w^3 + 7/3*w^2 - 12*w - 5]', '[1927, 1927, -2/3*w^3 + 4/3*w^2 + 2*w - 7]', '[1929, 1929, 2/3*w^3 + 2/3*w^2 - 3*w + 5]', '[1929, 1929, 2/3*w^3 + 2/3*w^2 + w + 2]', '[1933, 1933, 1/3*w^3 + 1/3*w^2 - 7]', '[1933, 1933, 3*w^3 - w^2 - 22*w + 4]', '[1939, 1939, 1/3*w^3 - 5/3*w^2 - 4*w + 12]', '[1943, 1943, -5/3*w^3 + 7/3*w^2 + 9*w - 12]', '[1943, 1943, -w^3 + 3*w^2 + 6*w - 20]', '[1949, 1949, 5/3*w^3 + 2/3*w^2 - 15*w - 9]', '[1951, 1951, w^3 + w^2 - 12*w - 1]', '[1959, 1959, 5/3*w^3 - 1/3*w^2 - 15*w - 1]', '[1959, 1959, -5*w - 3]', '[1963, 1963, 2*w^3 - 2*w^2 - 13*w + 8]', '[1967, 1967, -1/3*w^3 - 1/3*w^2 + 6*w - 9]', '[1967, 1967, 1/3*w^3 - 8/3*w^2 + 5]', '[1968, 246, -2/3*w^3 - 2/3*w^2 + 4]', '[1971, 219, 3*w^3 - 4*w^2 - 22*w + 21]', '[1971, 657, w^2 - 6*w + 3]', '[1977, 1977, 4/3*w^3 - 2/3*w^2 - 6*w + 1]', '[1979, 1979, -7/3*w^3 + 5/3*w^2 + 17*w - 15]', '[1983, 1983, 1/3*w^3 + 7/3*w^2 - w - 5]', '[1989, 663, -5/3*w^3 + 7/3*w^2 + 10*w - 14]', '[1989, 663, 2*w^3 - 16*w + 1]', '[1993, 1993, -5/3*w^3 + 1/3*w^2 + 12*w - 6]', '[1999, 1999, -4/3*w^3 - 1/3*w^2 + 13*w + 7]', '[1999, 1999, 2/3*w^3 + 5/3*w^2 - 6*w - 5]', '[2001, 2001, 2/3*w^3 - 4/3*w^2 - 3*w + 11]', '[2001, 2001, 5/3*w^3 + 5/3*w^2 - 15*w - 7]', '[2003, 2003, -4/3*w^3 - 1/3*w^2 + 14*w + 6]', '[2007, 669, 1/3*w^3 - 8/3*w^2 - 2*w + 1]', '[2007, 669, w^3 - w^2 - 10*w + 4]', '[2009, 2009, 1/3*w^3 - 2/3*w^2 + 8]', '[2021, 2021, -7/3*w^3 - 4/3*w^2 + 18*w + 9]', '[2023, 2023, 2/3*w^3 - 4/3*w^2 - 4*w - 3]', '[2025, 15, w^3 + w^2 - 9*w]', '[2025, 15, 2*w^3 - w^2 - 15*w + 9]', '[2025, 45, 10/3*w^3 - 11/3*w^2 - 26*w + 19]', '[2025, 45, 5/3*w^3 - 4/3*w^2 - 13*w + 2]', '[2025, 45, w^3 - 3*w^2 - 3*w + 1]', '[2025, 45, w^3 - 2*w^2 - 7*w + 5]', '[2027, 2027, 11/3*w^3 - 13/3*w^2 - 29*w + 25]', '[2029, 2029, 5/3*w^3 + 2/3*w^2 - 16*w + 1]', '[2029, 2029, 2/3*w^3 + 2/3*w^2 - 2*w - 5]', '[2032, 254, 2*w^2 - 2*w - 8]', '[2037, 2037, -w^3 + w^2 + 10*w - 6]', '[2039, 2039, 16/3*w^3 - 20/3*w^2 - 39*w + 41]', '[2049, 2049, 2/3*w^3 + 11/3*w^2 - 4]', '[2053, 2053, -4/3*w^3 - 4/3*w^2 + 9*w + 1]', '[2059, 2059, 5/3*w^3 - 7/3*w^2 - 15*w + 15]', '[2059, 2059, 11/3*w^3 - 10/3*w^2 - 27*w + 18]', '[2064, 258, 2/3*w^3 - 4/3*w^2 - 8*w - 4]', '[2069, 2069, -2*w^3 + 3*w^2 + 12*w - 16]', '[2069, 2069, -5/3*w^3 - 2/3*w^2 + 11*w - 1]', '[2075, 415, 2*w^3 - 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5/3*w^2 - 10*w + 8]', '[233, 233, -4/3*w^3 + 2/3*w^2 + 9*w - 5]', '[241, 241, 1/3*w^3 + 1/3*w^2 - 4*w - 4]', '[257, 257, -w^3 - w^2 + 6*w + 5]', '[269, 269, -1/3*w^3 - 1/3*w^2 + 5*w]', '[269, 269, -2/3*w^3 + 4/3*w^2 + 4*w - 3]', '[271, 271, -2/3*w^3 + 4/3*w^2 + 3*w - 6]', '[271, 271, w^3 - 8*w - 5]', '[277, 277, 2*w^3 - 2*w^2 - 16*w + 13]', '[281, 281, 2/3*w^3 + 2/3*w^2 - 5*w]', '[281, 281, -w^3 + w^2 + 7*w - 2]', '[331, 331, 2/3*w^3 - 4/3*w^2 - 5*w + 4]', '[331, 331, 8/3*w^3 - 7/3*w^2 - 20*w + 15]', '[343, 7, -4/3*w^3 + 2/3*w^2 + 11*w - 6]', '[347, 347, 2/3*w^3 + 2/3*w^2 - 4*w - 5]', '[349, 349, -1/3*w^3 + 2/3*w^2 + 3*w - 8]', '[349, 349, -1/3*w^3 + 2/3*w^2 - 3]', '[353, 353, -5/3*w^3 + 1/3*w^2 + 12*w]', '[353, 353, 1/3*w^3 - 5/3*w^2 - 2*w + 14]', '[367, 367, -1/3*w^3 + 5/3*w^2 + 4*w - 9]', '[367, 367, 1/3*w^3 + 1/3*w^2 + w - 3]', '[379, 379, 4/3*w^3 + 1/3*w^2 - 12*w]', '[379, 379, -5/3*w^3 + 7/3*w^2 + 13*w - 12]', '[383, 383, -5/3*w^3 + 10/3*w^2 + 12*w - 21]', '[397, 397, 1/3*w^3 + 4/3*w^2 - 5*w - 6]', '[397, 397, 4/3*w^3 + 1/3*w^2 - 8*w]', '[397, 397, -1/3*w^3 + 2/3*w^2 + w - 6]', '[397, 397, w^3 + w^2 - 8*w - 7]', '[401, 401, 5/3*w^3 - 1/3*w^2 - 14*w + 1]', '[419, 419, 1/3*w^3 + 4/3*w^2 - 4*w - 3]', '[419, 419, 1/3*w^3 - 5/3*w^2 - 3*w + 12]', '[433, 433, -w^3 + w^2 + 9*w - 4]', '[433, 433, 1/3*w^3 + 4/3*w^2 - 4*w - 9]', '[443, 443, 4/3*w^3 - 2/3*w^2 - 8*w - 1]', '[443, 443, -4/3*w^3 + 8/3*w^2 + 9*w - 17]', '[449, 449, -w^3 + w^2 + 8*w - 2]', '[449, 449, 5/3*w^3 - 7/3*w^2 - 13*w + 18]', '[457, 457, -w^3 + 3*w^2 + 7*w - 20]', '[457, 457, 2/3*w^3 + 2/3*w^2 - 5*w - 9]', '[461, 461, 4/3*w^3 - 2/3*w^2 - 9*w + 2]', '[461, 461, -2/3*w^3 + 7/3*w^2 + 4*w - 16]', '[463, 463, 4/3*w^3 + 1/3*w^2 - 11*w - 1]', '[467, 467, w^3 - 2*w^2 - 9*w + 8]', '[479, 479, 4/3*w^3 - 8/3*w^2 - 10*w + 15]', '[479, 479, 5/3*w^3 - 1/3*w^2 - 14*w]', '[491, 491, -1/3*w^3 + 2/3*w^2 + 2*w - 8]', '[509, 509, -11/3*w^3 + 13/3*w^2 + 27*w - 27]', '[523, 523, -w - 5]', '[523, 523, 4/3*w^3 - 2/3*w^2 - 10*w + 9]', '[541, 541, 8/3*w^3 - 7/3*w^2 - 21*w + 13]', '[547, 547, -2/3*w^3 + 1/3*w^2 + 5*w - 7]', '[557, 557, -2/3*w^3 + 1/3*w^2 + 7*w - 3]', '[563, 563, w^2 + w - 8]', '[563, 563, 1/3*w^3 + 1/3*w^2 - w - 6]', '[569, 569, 1/3*w^3 + 4/3*w^2 - 4*w - 6]', '[569, 569, -1/3*w^3 + 5/3*w^2 + 2*w - 6]', '[571, 571, 5/3*w^3 - 4/3*w^2 - 11*w + 1]', '[593, 593, -2/3*w^3 + 1/3*w^2 + 4*w - 7]', '[593, 593, -2*w^3 + w^2 + 15*w - 1]', '[599, 599, -1/3*w^3 + 2/3*w^2 + 5*w - 2]', '[601, 601, w^3 - 10*w - 2]', '[607, 607, 1/3*w^3 + 4/3*w^2 - 4*w - 4]', '[607, 607, 7/3*w^3 - 8/3*w^2 - 18*w + 14]', '[617, 617, -5/3*w^3 + 10/3*w^2 + 13*w - 24]', '[617, 617, 1/3*w^3 + 4/3*w^2 - 2*w - 6]', '[617, 617, w^2 + w - 10]', '[617, 617, 1/3*w^3 + 1/3*w^2 - 6*w - 1]', '[631, 631, 7/3*w^3 - 2/3*w^2 - 18*w + 3]', '[631, 631, -1/3*w^3 + 2/3*w^2 + 5*w - 3]', '[641, 641, 5/3*w^3 - 1/3*w^2 - 11*w - 2]', '[643, 643, -5/3*w^3 + 7/3*w^2 + 14*w - 13]', '[643, 643, -2/3*w^3 + 4/3*w^2 + 6*w - 3]', '[653, 653, w^3 - w^2 - 8*w + 1]', '[653, 653, 1/3*w^3 + 4/3*w^2 - 3*w - 13]', '[659, 659, -1/3*w^3 + 5/3*w^2 + 2*w - 8]', '[661, 661, 5/3*w^3 - 4/3*w^2 - 11*w + 9]', '[683, 683, 4/3*w^3 - 2/3*w^2 - 7*w + 8]', '[709, 709, -2*w^3 + 17*w + 2]', '[709, 709, 1/3*w^3 + 1/3*w^2 - 4]', '[733, 733, 1/3*w^3 - 2/3*w^2 - 2*w - 3]', '[733, 733, 5/3*w^3 - 4/3*w^2 - 14*w + 9]', '[733, 733, 2/3*w^3 - 7/3*w^2 - 2*w + 10]', '[733, 733, 4/3*w^3 - 8/3*w^2 - 9*w + 18]', '[743, 743, w^3 - w^2 - 8*w - 1]', '[751, 751, -4/3*w^3 - 1/3*w^2 + 10*w]', '[757, 757, 5/3*w^3 - 7/3*w^2 - 11*w + 15]', '[757, 757, 2/3*w^3 + 5/3*w^2 - 3*w - 5]', '[761, 761, 7/3*w^3 - 5/3*w^2 - 18*w + 11]', '[761, 761, 1/3*w^3 + 4/3*w^2 - 4*w - 13]', '[773, 773, 1/3*w^3 + 4/3*w^2 - 3*w - 7]', '[773, 773, 1/3*w^3 + 1/3*w^2 - 3*w - 7]', '[809, 809, w^3 - 8*w + 4]', '[811, 811, -2/3*w^3 + 4/3*w^2 + 5*w]', '[823, 823, 7/3*w^3 - 5/3*w^2 - 17*w + 9]', '[827, 827, -5/3*w^3 + 1/3*w^2 + 12*w - 4]', '[827, 827, 1/3*w^3 + 4/3*w^2 - 4*w - 10]', '[829, 829, -1/3*w^3 - 1/3*w^2 - w - 3]', '[841, 29, -1/3*w^3 - 4/3*w^2 + 2*w + 12]', '[857, 857, 4*w^3 - 4*w^2 - 31*w + 26]', '[859, 859, 11/3*w^3 - 10/3*w^2 - 27*w + 21]', '[863, 863, 7/3*w^3 - 5/3*w^2 - 17*w + 8]', '[877, 877, 1/3*w^3 + 4/3*w^2 - 3*w - 6]', '[877, 877, -4/3*w^3 + 5/3*w^2 + 11*w - 6]', '[881, 881, 5/3*w^3 - 4/3*w^2 - 11*w + 4]', '[881, 881, 4/3*w^3 - 11/3*w^2 - 10*w + 24]', '[883, 883, 10/3*w^3 - 17/3*w^2 - 25*w + 36]', '[883, 883, -4/3*w^3 + 2/3*w^2 + 11*w - 8]', '[887, 887, -1/3*w^3 + 2/3*w^2 + 3*w - 9]', '[887, 887, 3*w^3 - 2*w^2 - 23*w + 8]', '[911, 911, 4/3*w^3 + 1/3*w^2 - 7*w]', '[919, 919, -4/3*w^3 + 5/3*w^2 + 7*w - 6]', '[929, 929, 2*w^3 + w^2 - 14*w - 8]', '[937, 937, -7/3*w^3 + 5/3*w^2 + 15*w - 14]', '[941, 941, -1/3*w^3 - 1/3*w^2 + 6*w]', '[941, 941, -7/3*w^3 - 1/3*w^2 + 18*w + 3]', '[971, 971, -4/3*w^3 + 5/3*w^2 + 10*w - 6]', '[977, 977, -7/3*w^3 + 11/3*w^2 + 18*w - 27]', '[977, 977, 7/3*w^3 - 2/3*w^2 - 17*w]', '[997, 997, 7/3*w^3 - 2/3*w^2 - 17*w + 2]', '[1009, 1009, 4/3*w^3 + 1/3*w^2 - 13*w + 3]', '[1009, 1009, 2/3*w^3 - 7/3*w^2 - 6*w + 15]', '[1013, 1013, 4/3*w^3 + 4/3*w^2 - 12*w - 7]', '[1013, 1013, 4/3*w^3 + 1/3*w^2 - 9*w + 2]', '[1019, 1019, -1/3*w^3 + 2/3*w^2 + 6*w]', '[1021, 1021, w^2 - 11]', '[1021, 1021, 10/3*w^3 - 8/3*w^2 - 25*w + 17]', '[1021, 1021, -7/3*w^3 + 2/3*w^2 + 19*w + 4]', '[1021, 1021, -5/3*w^3 + 7/3*w^2 + 10*w - 13]', '[1031, 1031, -w^3 + 2*w^2 + 9*w - 14]', '[1031, 1031, -2/3*w^3 + 4/3*w^2 + 4*w - 13]', '[1031, 1031, -w^3 + 9*w - 5]', '[1031, 1031, w^2 + 2*w - 7]', '[1033, 1033, 4/3*w^3 - 11/3*w^2 - 9*w + 26]', '[1033, 1033, -4/3*w^3 + 2/3*w^2 + 7*w - 9]', '[1061, 1061, -1/3*w^3 + 2/3*w^2 - 5]', '[1061, 1061, -5/3*w^3 + 4/3*w^2 + 14*w - 7]', '[1069, 1069, 4/3*w^3 + 4/3*w^2 - 11*w - 3]', '[1069, 1069, -7/3*w^3 + 14/3*w^2 + 17*w - 30]', '[1087, 1087, 2*w^3 - w^2 - 14*w + 2]', '[1091, 1091, -w^3 + 10*w - 7]', '[1091, 1091, -4/3*w^3 + 5/3*w^2 + 8*w - 2]', '[1093, 1093, 2/3*w^3 + 2/3*w^2 - 7*w + 3]', '[1103, 1103, 1/3*w^3 - 2/3*w^2 - w - 4]', '[1109, 1109, -1/3*w^3 + 2/3*w^2 + 5*w - 9]', '[1109, 1109, w^3 + w^2 - 7*w - 11]', '[1117, 1117, -w^3 + 10*w - 1]', '[1129, 1129, -4/3*w^3 + 8/3*w^2 + 10*w - 11]', '[1163, 1163, -4/3*w^3 + 2/3*w^2 + 12*w - 5]', '[1163, 1163, -1/3*w^3 + 5/3*w^2 + 2*w - 15]', '[1181, 1181, -5/3*w^3 + 4/3*w^2 + 11*w - 7]', '[1187, 1187, 10/3*w^3 - 8/3*w^2 - 26*w + 17]', '[1193, 1193, -2/3*w^3 + 7/3*w^2 + 5*w - 13]', '[1193, 1193, 5/3*w^3 - 1/3*w^2 - 11*w]', '[1193, 1193, 2/3*w^3 - 1/3*w^2 - 6*w - 5]', '[1193, 1193, 4/3*w^3 + 1/3*w^2 - 10*w - 9]', '[1201, 1201, 2/3*w^3 + 5/3*w^2 - 6*w - 11]', '[1229, 1229, -2/3*w^3 + 7/3*w^2 + 7*w - 13]', '[1231, 1231, 5/3*w^3 - 4/3*w^2 - 11*w - 2]', '[1249, 1249, -1/3*w^3 - 1/3*w^2 + 4*w - 6]', '[1249, 1249, -5/3*w^3 + 4/3*w^2 + 11*w - 6]', '[1259, 1259, 5/3*w^3 - 7/3*w^2 - 13*w + 19]', '[1277, 1277, 4/3*w^3 + 1/3*w^2 - 13*w]', '[1291, 1291, 5/3*w^3 - 1/3*w^2 - 9*w - 2]', '[1297, 1297, -1/3*w^3 + 5/3*w^2 + w - 12]', '[1327, 1327, w^3 + 2*w^2 - 7*w - 13]', '[1327, 1327, 2/3*w^3 - 1/3*w^2 - 5*w - 5]', '[1361, 1361, -1/3*w^3 + 5/3*w^2 + 4*w - 11]', '[1367, 1367, 2/3*w^3 - 1/3*w^2 - 8*w]', '[1367, 1367, -3*w - 5]', '[1399, 1399, -2/3*w^3 + 4/3*w^2 + 3*w - 9]', '[1399, 1399, -5/3*w^3 + 4/3*w^2 + 13*w - 3]', '[1433, 1433, -5/3*w^3 + 4/3*w^2 + 13*w - 15]', '[1433, 1433, -7/3*w^3 + 8/3*w^2 + 19*w - 15]', '[1439, 1439, -w^3 + 2*w^2 + 6*w - 14]', '[1439, 1439, -1/3*w^3 + 2/3*w^2 - w + 7]', '[1447, 1447, 1/3*w^3 + 1/3*w^2 - 5*w - 6]', '[1447, 1447, -4/3*w^3 + 2/3*w^2 + 12*w - 3]', '[1451, 1451, 4/3*w^3 - 8/3*w^2 - 10*w + 21]', '[1451, 1451, w^2 - 3*w - 5]', '[1451, 1451, -2/3*w^3 + 4/3*w^2 + 5*w - 13]', '[1451, 1451, 10/3*w^3 - 14/3*w^2 - 25*w + 33]', '[1453, 1453, 2/3*w^3 - 7/3*w^2 - 5*w + 12]', '[1453, 1453, 5/3*w^3 - 1/3*w^2 - 15*w - 2]', '[1453, 1453, -4/3*w^3 - 1/3*w^2 + 9*w - 3]', '[1453, 1453, 4/3*w^3 + 1/3*w^2 - 7*w - 4]', '[1471, 1471, -1/3*w^3 + 2/3*w^2 - 6]', '[1489, 1489, -5/3*w^3 + 1/3*w^2 + 13*w - 4]', '[1489, 1489, -2/3*w^3 + 1/3*w^2 + 2*w - 6]', '[1493, 1493, 7/3*w^3 - 11/3*w^2 - 17*w + 27]', '[1493, 1493, -2*w^3 + 2*w^2 + 15*w - 8]', '[1511, 1511, 17/3*w^3 - 19/3*w^2 - 43*w + 37]', '[1523, 1523, -w^3 + 3*w^2 + 9*w - 11]', '[1523, 1523, 1/3*w^3 + 1/3*w^2 - 5*w - 7]', '[1523, 1523, -w^3 + 3*w^2 + 8*w - 22]', '[1523, 1523, 2/3*w^3 + 5/3*w^2 - 4*w - 5]', '[1543, 1543, 1/3*w^3 + 1/3*w^2 - 6*w - 4]', '[1543, 1543, -4/3*w^3 + 5/3*w^2 + 10*w - 5]', '[1553, 1553, -4/3*w^3 + 5/3*w^2 + 11*w - 5]', '[1559, 1559, 2*w^3 - 15*w + 1]', '[1559, 1559, -4/3*w^3 + 2/3*w^2 + 5*w - 3]', '[1567, 1567, 1/3*w^3 + 1/3*w^2 - 6]', '[1571, 1571, 1/3*w^3 + 1/3*w^2 + 3*w - 1]', '[1571, 1571, -4/3*w^3 + 5/3*w^2 + 8*w - 14]', '[1579, 1579, -10/3*w^3 + 11/3*w^2 + 24*w - 20]', '[1583, 1583, 1/3*w^3 - 2/3*w^2 - 2*w - 4]', '[1597, 1597, 11/3*w^3 - 19/3*w^2 - 28*w + 42]', '[1601, 1601, 10/3*w^3 - 14/3*w^2 - 25*w + 26]', '[1613, 1613, 8/3*w^3 - 16/3*w^2 - 19*w + 36]', '[1627, 1627, -2/3*w^3 + 1/3*w^2 + 3*w - 9]', '[1627, 1627, -2/3*w^3 + 1/3*w^2 + 6*w - 9]', '[1637, 1637, 2*w^3 + w^2 - 16*w - 4]', '[1657, 1657, -2/3*w^3 + 7/3*w^2 + 6*w - 16]', '[1657, 1657, 2/3*w^3 + 2/3*w^2 - 3*w - 6]', '[1663, 1663, -3*w + 10]', '[1663, 1663, 1/3*w^3 + 4/3*w^2 - w - 9]', '[1667, 1667, -2/3*w^3 + 1/3*w^2 + 2*w - 7]', '[1667, 1667, 8/3*w^3 - 4/3*w^2 - 22*w + 3]', '[1669, 1669, 3*w^3 - 2*w^2 - 22*w + 11]', '[1693, 1693, 1/3*w^3 - 2/3*w^2 - 3*w - 4]', '[1697, 1697, -4/3*w^3 + 2/3*w^2 + 7*w - 3]', '[1709, 1709, 3*w^3 - 3*w^2 - 23*w + 23]', '[1741, 1741, -3*w^3 + 2*w^2 + 24*w - 10]', '[1747, 1747, -2/3*w^3 + 7/3*w^2 + 4*w - 10]', '[1747, 1747, 1/3*w^3 - 8/3*w^2 - 4*w + 9]', '[1753, 1753, 4/3*w^3 - 2/3*w^2 - 7*w + 2]', '[1753, 1753, 8/3*w^3 - 16/3*w^2 - 19*w + 37]', '[1759, 1759, 2*w^2 - w - 5]', '[1759, 1759, -5/3*w^3 + 10/3*w^2 + 14*w - 21]', '[1777, 1777, -1/3*w^3 + 2/3*w^2 + 6*w - 2]', '[1783, 1783, 7/3*w^3 - 8/3*w^2 - 17*w + 12]', '[1783, 1783, -5/3*w^3 - 2/3*w^2 + 10*w - 3]', '[1787, 1787, -1/3*w^3 - 1/3*w^2 - 2*w - 3]', '[1787, 1787, 4/3*w^3 + 1/3*w^2 - 12*w + 2]', '[1811, 1811, 5/3*w^3 - 1/3*w^2 - 10*w - 6]', '[1811, 1811, -w^3 + w^2 + 5*w - 10]', '[1847, 1847, w^2 - 2*w - 10]', '[1861, 1861, 2*w^2 - w - 11]', '[1867, 1867, w^3 + 2*w^2 - 7*w - 4]', '[1871, 1871, -1/3*w^3 + 5/3*w^2 - 9]', '[1873, 1873, 2/3*w^3 + 5/3*w^2 - 7*w - 6]', '[1877, 1877, -2/3*w^3 + 1/3*w^2 + 8*w - 3]', '[1877, 1877, -1/3*w^3 + 2/3*w^2 + 6*w - 3]', '[1879, 1879, w^3 + 2*w^2 - 11*w - 8]', '[1879, 1879, 8/3*w^3 - 7/3*w^2 - 20*w + 18]', '[1901, 1901, -2/3*w^3 + 1/3*w^2 + 2*w + 9]', '[1901, 1901, 10/3*w^3 - 11/3*w^2 - 24*w + 21]', '[1907, 1907, w^3 + w^2 - 10*w - 8]', '[1907, 1907, 5*w^3 - 6*w^2 - 38*w + 35]', '[1933, 1933, 1/3*w^3 + 1/3*w^2 - 7]', '[1933, 1933, 3*w^3 - w^2 - 22*w + 4]', '[1949, 1949, 5/3*w^3 + 2/3*w^2 - 15*w - 9]', '[1951, 1951, w^3 + w^2 - 12*w - 1]', '[1979, 1979, -7/3*w^3 + 5/3*w^2 + 17*w - 15]', '[1993, 1993, -5/3*w^3 + 1/3*w^2 + 12*w - 6]', '[1999, 1999, -4/3*w^3 - 1/3*w^2 + 13*w + 7]', '[1999, 1999, 2/3*w^3 + 5/3*w^2 - 6*w - 5]']}
• 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': [3, 6, -8, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 19821, 'disc_rad': 19821, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [0]], [5, [[2, 2]]], [7, [[3, 1], [1, 1]]], [11, [[4, 1]]], [13, [[3, 1], [1, 1]]], [17, [[3, 1], [1, 1]]], [19, [[3, 1], [1, 1]]], [23, [[3, 1], [1, 1]]], [29, [[2, 1], [1, 2]]], [31, [[4, 1]]], [37, [[3, 1], [1, 1]]], [41, [[3, 1], [1, 1]]], [43, [[3, 1], [1, 1]]], [47, [[3, 1], [1, 1]]], [53, [[2, 2]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 140.78707327024026, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.19821.1', 'local_algs': ['3.2.1.2', '3.2.0.1', 'm6607.1.2.0', 'm6607.2.1.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 6607], 'rd': 11.8653728669, 'regulator': {'__RealLiteral__': 0, 'data': '7.78166253878', 'prec': 44}, 'res': {'gal': ['-515421,12353706,-51782880,-36283044,435959287,-236280912,-896279497,439465410,903724106,-216365040,-462063205,33831348,129454804,2146038,-21501279,-1375476,2209714,190698,-141481,-12876,5459,438,-115,-6,1'], 'sib': ['-14414,-6637,4091,143,-133,-1,1', '-163,-1889,-3239,8467,5341,-6442,-3698,1147,729,-59,-51,0,1', '422239,-1174363,-529253,20837,23484,199,-317,-2,1', '662535,4001181,-2931068,-2028121,739383,314103,-79234,-21066,4320,620,-113,-6,1', '9,-46,30,31,-13,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{3} a^{3} - \\frac{2}{3} a^{2} - 2 a + 3 \\)', '\\( a - 1 \\)', '\\( \\frac{1}{3} a^{3} - \\frac{2}{3} a^{2} - 3 a + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/3*a^3 + 1/3*a^2']}