Hilbert modular form data - 4.4.11344.1-16.1-c

Formats: - HTML - YAML - JSON - 2024-06-01T10:48:13.754558

• 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': 11344, 'field_bad_primes': [2, 709], 'field_label': '4.4.11344.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.11344.1-16.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [2], 'level_ideal': '[16, 2, 2]', 'level_label': '16.1', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.1-c', '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]', -1]], 'hecke_eigenvalues': [0, -1, 0, -5, 5, -10, 4, 6, 6, -10, -3, 10, 4, 12, -6, -4, -7, 13, 1, -11, 1, -9, -9, 17, -14, 9, -4, -18, -9, -17, -6, 4, 20, -15, 12, -18, 16, -16, -9, -12, 19, 22, -14, -26, 11, 21, 29, 1, 11, -16, 8, 9, -19, -8, -6, 0, 32, -10, 17, 18, -15, -12, -29, 1, 9, -16, -10, -14, -9, 4, -16, 2, 22, -26, 10, 0, -28, 10, -36, 24, -19, -23, 9, -19, -25, 21, -10, 28, 0, -30, 2, 31, -29, -11, -5, -2, -15, -19, -40, -12, -4, 4, -38, -23, 17, 10, -46, 20, 16, -10, 18, -38, 31, 36, 40, 35, -4, 16, 34, -38, -20, 36, -4, -4, -44, 16, 30, 22, 18, -42, -12, 16, -21, -8, -46, -2, -21, 4, -12, -20, -30, -20, -6, 6, -14, -52, -7, 22, -51, -12, -16, -14, -46, 19, -48, 21, 17, -29, 32, 18, -21], 'hecke_polynomial': 'x', 'label': '4.4.11344.1-16.1-c'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 11344, 'ideals': ['[1, 1, 1]', '[2, 2, w - 1]', '[3, 3, w]', '[4, 2, -w^3 + 2*w^2 + 3*w - 4]', '[5, 5, -w + 2]', '[6, 6, w^3 - 3*w^2 - 2*w + 6]', '[8, 2, -w^3 + w^2 + 5*w + 1]', '[9, 9, -w^2 + w + 3]', '[10, 10, -w^2 + w + 2]', '[11, 11, w + 2]', '[12, 6, -w^2 + 2*w + 3]', '[15, 15, -w^2 + 2*w]', '[16, 2, 2]', '[18, 18, -w^3 + 2*w^2 + 2*w - 3]', '[20, 10, -w^3 + 2*w^2 + w - 2]', '[22, 22, -w^3 + 2*w^2 + 2*w - 1]', '[24, 6, -w^3 + 3*w^2 + w - 3]', '[25, 25, -w^3 + 2*w^2 + 3*w - 1]', '[27, 3, -w^3 + 2*w^2 + 4*w - 4]', '[27, 27, -w^3 + w^2 + 3*w]', '[29, 29, -w^2 + 3*w + 1]', '[30, 30, -w^3 + 2*w^2 + 4*w - 3]', '[31, 31, w^3 - 2*w^2 - 2*w + 2]', '[31, 31, -w^2 + 2*w + 4]', '[32, 4, 2*w - 2]', '[33, 33, w^3 - 2*w^2 - w + 3]', '[36, 18, -w^3 + 2*w^2 + 3*w]', '[40, 10, -w^3 + w^2 + 5*w - 1]', '[44, 22, w^3 - 4*w^2 + w + 4]', '[45, 45, w^3 - 3*w^2 - w + 6]', '[47, 47, w^3 - w^2 - 4*w + 1]', '[48, 6, 2*w]', '[49, 7, 2*w^3 - 2*w^2 - 8*w - 1]', '[49, 7, w^3 - w^2 - 3*w - 2]', '[50, 50, w^3 - 3*w^2 + 4]', '[53, 53, w^3 - 3*w^2 - w + 2]', '[53, 53, w^3 - 5*w - 5]', '[54, 6, -w^3 + 2*w^2 + 4*w - 1]', '[54, 54, -2*w^2 + w + 3]', '[55, 55, -w^2 + 4]', '[58, 58, -2*w^3 + 2*w^2 + 9*w + 1]', '[60, 30, w^3 - 2*w^2 - 3*w + 6]', '[61, 61, 2*w - 1]', '[61, 61, -w^3 + 4*w^2 - 4]', '[62, 62, w^3 - 4*w - 1]', '[62, 62, -w^3 + 3*w^2 + 2*w - 4]', '[64, 4, -2*w^3 + 4*w^2 + 6*w - 8]', '[66, 66, -w^2 + w + 6]', '[67, 67, 3*w^3 - 3*w^2 - 13*w - 4]', '[72, 18, w^3 - 3*w^2 + w + 3]', '[73, 73, -w^3 + 4*w^2 - 10]', '[73, 73, w^2 - w + 1]', '[75, 75, -w^2 + 3*w + 3]', '[80, 10, -2*w + 4]', '[81, 3, 3]', '[81, 81, -w^2 + 2*w + 6]', '[83, 83, -4*w^3 + 5*w^2 + 17*w + 1]', '[83, 83, 3*w^3 - 3*w^2 - 14*w - 5]', '[87, 87, -2*w^2 + 3*w + 6]', '[88, 22, w^3 - 3*w^2 - w + 7]', '[89, 89, w^3 - w^2 - 4*w + 5]', '[89, 89, w^3 - 3*w^2 - w + 8]', '[90, 90, w + 3]', '[93, 93, -w^3 + 2*w^2 + 4*w]', '[93, 93, 2*w^2 - 2*w - 3]', '[94, 94, w^2 + w - 4]', '[96, 12, 2*w^3 - 6*w^2 - 4*w + 12]', '[97, 97, -w^3 + 7*w + 5]', '[97, 97, 2*w^3 - 3*w^2 - 7*w + 1]', '[98, 14, 2*w^2 - 3*w - 1]', '[98, 14, -w^3 + w^2 + 4*w + 4]', '[99, 99, -2*w^3 + 5*w^2 + 4*w - 6]', '[100, 50, w^2 + 1]', '[103, 103, -3*w^3 + 8*w^2 + 7*w - 19]', '[106, 106, -2*w^3 + 6*w^2 - w - 5]', '[106, 106, w^3 - w^2 - 4*w + 2]', '[108, 6, w^3 - 2*w^2 - w + 4]', '[108, 54, -w^3 + 5*w + 6]', '[110, 110, -w^3 + w^2 + 4*w - 4]', '[113, 113, -w^2 + 2*w - 2]', '[116, 58, -w^2 + 5]', '[120, 30, -w^3 + w^2 + 3*w + 3]', '[121, 121, -w^3 + w^2 + 5*w - 2]', '[122, 122, 2*w^2 - 3*w + 1]', '[122, 122, 3*w^3 - 8*w^2 + 7]', '[124, 62, -2*w^3 + 5*w^2 + 4*w - 11]', '[124, 62, w^2 + 2*w - 1]', '[125, 5, 2*w^3 - 5*w^2 - 3*w + 7]', '[125, 125, -2*w^3 + 5*w^2 + 3*w - 5]', '[127, 127, 2*w^2 - 3*w - 4]', '[128, 4, -2*w^3 + 2*w^2 + 10*w + 2]', '[132, 66, -w^3 + 2*w^2 + 5*w - 6]', '[134, 134, 2*w^2 - 3*w - 5]', '[135, 15, -w^3 - w^2 + 7*w + 8]', '[135, 135, -w^3 + 3*w^2 + 2*w - 3]', '[137, 137, -w^3 + 3*w^2 + 3*w - 4]', '[137, 137, w^3 - w^2 - 6*w - 1]', '[141, 141, w^3 - 3*w - 3]', '[144, 18, -2*w^2 + 2*w + 6]', '[145, 145, -w^3 + 4*w^2 + w - 5]', '[146, 146, 3*w^3 - 8*w^2 - 6*w + 13]', '[146, 146, w^3 - 2*w^2 + 2*w - 1]', '[147, 21, w^3 + w^2 - 6*w - 3]', '[147, 21, -2*w^3 + 5*w^2 + 3*w - 3]', '[149, 149, 2*w^3 - 3*w^2 - 5*w - 1]', '[150, 150, -2*w^3 + 4*w^2 + 7*w - 9]', '[151, 151, -w^3 + 3*w^2 - 5]', '[155, 155, w^3 - w^2 - 5*w - 4]', '[155, 155, w^3 - 4*w^2 + 8]', '[157, 157, -w^3 + 2*w^2 + w - 5]', '[159, 159, -w^3 + 3*w^2 - 2*w - 3]', '[159, 159, -w^3 + 4*w^2 - 6]', '[160, 20, -2*w^2 + 2*w + 4]', '[162, 6, 3*w - 3]', '[162, 162, -2*w^3 + 4*w^2 + 5*w - 3]', '[163, 163, 4*w^3 - 4*w^2 - 18*w - 7]', '[165, 165, -w^3 + 4*w]', '[166, 166, w^3 - 4*w^2 + 11]', '[166, 166, w^2 - 3*w - 4]', '[167, 167, -3*w^3 + 4*w^2 + 13*w - 1]', '[167, 167, 2*w^2 - 4*w - 1]', '[173, 173, w^3 - 5*w - 1]', '[173, 173, 2*w^3 - 3*w^2 - 9*w + 1]', '[174, 174, -2*w^3 + 5*w^2 + 3*w - 6]', '[176, 22, 2*w + 4]', '[178, 178, 3*w + 5]', '[178, 178, w^2 + 5*w - 8]', '[179, 179, -2*w^3 + 3*w^2 + 8*w - 4]', '[180, 90, -2*w^3 + 5*w^2 + 2*w - 3]', '[181, 181, 2*w^2 - 2*w - 5]', '[183, 183, 2*w^2 - w]', '[183, 183, 2*w^3 - 4*w^2 + 3]', '[186, 186, w^3 - 2*w^2 + 3]', '[186, 186, w^2 - 3*w - 6]', '[188, 94, -2*w^3 + 5*w^2 + 4*w - 13]', '[192, 12, -2*w^2 + 4*w + 6]', '[193, 193, 4*w^3 - 9*w^2 - 11*w + 17]', '[194, 194, -w^3 + 3*w^2 + 2*w - 2]', '[194, 194, -w^3 + 4*w^2 - 7]', '[196, 14, -w^2 + 4*w - 1]', '[196, 14, w^3 - 2*w^2 - 5*w + 2]', '[197, 197, w^3 - w^2 - 6*w + 1]', '[197, 197, -w^3 + 5*w^2 - w - 4]', '[198, 198, -w^3 + w^2 + 6*w]', '[199, 199, -3*w^3 + 4*w^2 + 11*w + 5]', '[200, 50, -3*w^3 + 7*w^2 + 7*w - 13]', '[201, 201, 2*w^2 - 5*w]', '[206, 206, 2*w^3 - 11*w - 11]', '[211, 211, -2*w^3 + 5*w^2 + 6*w - 8]', '[212, 106, -w^3 + 4*w^2 + w - 8]', '[212, 106, w^2 + 2*w - 5]', '[216, 6, -w^3 - w^2 + 7*w + 5]', '[216, 54, -w^3 + w^2 + 5*w - 3]', '[219, 219, 2*w^3 - 4*w^2 - 6*w + 3]', '[219, 219, w^3 - w^2 + w]', '[220, 110, -w^2 + 4*w + 1]', '[225, 225, -2*w^3 + 2*w^2 + 9*w]', '[226, 226, -w^3 + 4*w^2 + 2*w - 11]', '[227, 227, w^2 - 3*w - 5]', '[232, 58, -w^3 + w^2 + 5*w - 5]', '[233, 233, 2*w^3 - 6*w^2 - 5*w + 16]', '[233, 233, -5*w^3 + 13*w^2 + 13*w - 26]', '[235, 235, w^3 - 2*w^2 - 5*w + 5]', '[240, 30, -2*w^2 + 4*w]', '[242, 242, -2*w^3 + 2*w^2 + 7*w + 1]', '[243, 9, 3*w]', '[243, 243, 2*w^3 - 5*w^2 - 3*w + 9]', '[244, 122, w^3 - 4*w^2 - 3*w + 10]', '[244, 122, 2*w^3 - 7*w^2 - 4*w + 13]', '[245, 35, -3*w^3 + 2*w^2 + 16*w + 4]', '[245, 35, w^3 - 3*w^2 - 1]', '[248, 62, w^3 + w^2 - 7*w - 7]', '[248, 62, w^3 - 5*w^2 + 3*w + 5]', '[249, 249, w^2 - 4*w]', '[249, 249, -2*w^3 + 4*w^2 + 8*w - 9]', '[250, 10, -3*w^3 + 10*w^2 + 2*w - 13]', '[250, 250, -w^3 + 6*w + 1]', '[251, 251, -2*w^3 + 4*w^2 + 5*w - 4]', '[251, 251, -w^3 + 5*w^2 + w - 8]', '[251, 251, w^2 + w - 5]', '[251, 251, -w^3 + 2*w^2 + 3*w - 7]', '[254, 254, 2*w^3 - 5*w^2 - w + 4]', '[256, 4, 4]', '[257, 257, w^3 - 5*w^2 + 2*w + 11]', '[261, 261, -2*w^3 + 3*w^2 + 6*w]', '[263, 263, -3*w^3 + 8*w^2 + 9*w - 17]', '[264, 66, -w^3 + 3*w^2 + 3*w - 3]', '[265, 265, 3*w^3 - 9*w^2 + 7]', '[265, 265, w^2 - w - 7]', '[267, 267, -w^3 + 3*w^2 + 4*w - 3]', '[267, 267, w^3 + w - 3]', '[268, 134, 2*w^3 - 5*w^2 - 2*w + 5]', '[269, 269, -3*w^3 + 2*w^2 + 13*w + 7]', '[269, 269, 3*w^3 - 4*w^2 - 13*w - 1]', '[270, 30, -2*w^3 + 4*w^2 + 5*w - 5]', '[270, 270, w^2 + 3*w]', '[271, 271, 2*w^3 - 5*w^2 - 5*w + 7]', '[274, 274, 2*w^3 - 4*w^2 - 3*w + 7]', '[274, 274, w^2 - w + 2]', '[275, 275, w^3 - 2*w^2 - 4*w + 8]', '[277, 277, -w^3 + w^2 + 5*w - 4]', '[279, 279, w^3 - 2*w^2 - 5*w + 3]', '[279, 279, -w^3 - w^2 + 6*w + 9]', '[282, 282, 3*w^3 - 8*w^2 - 8*w + 15]', '[283, 283, 3*w - 2]', '[288, 36, -2*w^3 + 4*w^2 + 4*w - 6]', '[290, 290, -2*w^3 + 3*w^2 + 9*w - 4]', '[291, 291, -w^3 + 4*w^2 - 2*w]', '[291, 291, w^3 + w^2 - 7*w - 6]', '[292, 146, 8*w^3 - 19*w^2 - 22*w + 37]', '[292, 146, -2*w^3 + 3*w^2 + 6*w - 7]', '[293, 293, 3*w^3 - 2*w^2 - 15*w - 5]', '[294, 42, -w^3 + 3*w^2 - 6]', '[294, 42, -w^3 + 8*w + 3]', '[297, 33, -2*w^3 + 4*w^2 + 8*w - 5]', '[297, 297, w^3 - 4*w^2 + 2*w + 6]', '[298, 298, -w^3 + 6*w^2 - 4*w - 5]', '[300, 150, -2*w^3 + 3*w^2 + 6*w - 3]', '[302, 302, 2*w^3 - 7*w^2 - w + 8]', '[305, 305, -4*w^3 + 12*w^2 - 11]', '[305, 305, -2*w^2 + 5*w - 2]', '[307, 307, -w - 4]', '[307, 307, -2*w^3 + 11*w + 8]', '[309, 309, 3*w^3 - 5*w^2 - 10*w + 3]', '[310, 310, -3*w + 1]', '[310, 310, -w^3 + 4*w + 5]', '[313, 313, -2*w^3 + 2*w^2 + 7*w - 2]', '[314, 314, w^3 - 5*w^2 - 2*w + 8]', '[318, 318, w^3 - w^2 - 6*w + 6]', '[318, 318, w^3 - 2*w - 3]', '[319, 319, -w^3 + w^2 + 7*w + 2]', '[320, 20, -2*w^3 + 4*w^2 + 2*w - 4]', '[324, 6, -3*w^3 + 6*w^2 + 9*w - 12]', '[324, 162, -2*w^3 + w^2 + 10*w + 3]', '[326, 326, 2*w^2 - 5*w - 5]', '[330, 330, 2*w^3 - 7*w^2 + 3*w + 6]', '[332, 166, -3*w^3 + 8*w^2 + 7*w - 14]', '[332, 166, w^3 - 4*w^2 - w + 4]', '[334, 334, w^3 - 3*w^2 - 2*w + 10]', '[334, 334, 2*w^3 - 3*w^2 - 9*w + 2]', '[335, 335, 3*w^3 - 5*w^2 - 10*w + 1]', '[339, 339, 3*w^3 - 7*w^2 - 7*w + 12]', '[341, 341, -2*w^3 + 5*w^2 + 7*w - 11]', '[341, 341, 2*w^3 - 2*w^2 - 6*w + 1]', '[346, 346, w^3 - w^2 - 2]', '[346, 346, w^3 - 2*w^2 - 2*w + 7]', '[347, 347, -w^3 + 3*w^2 + w - 10]', '[347, 347, 3*w^3 - 3*w^2 - 11*w - 4]', '[348, 174, -w^3 + 5*w]', '[349, 349, -w^3 + w^2 + 4*w + 5]', '[349, 349, 2*w^2 - 2*w - 11]', '[352, 44, -2*w^3 + 4*w^2 + 4*w - 2]', '[353, 353, 2*w^3 - 7*w^2 - 3*w + 17]', '[353, 353, w^3 - w^2 - 6*w - 5]', '[356, 178, -6*w^3 + 13*w^2 + 16*w - 29]', '[356, 178, 3*w^2 + 2*w - 5]', '[358, 358, -3*w^3 + 3*w^2 + 12*w + 2]', '[359, 359, 2*w^2 - 4*w - 7]', '[359, 359, 3*w^2 - 3*w - 13]', '[360, 90, -3*w^3 + 5*w^2 + 11*w - 3]', '[361, 19, 6*w^3 - 6*w^2 - 28*w - 7]', '[361, 19, 2*w^2 - w - 8]', '[362, 362, 2*w^3 - 4*w^2 - 3*w + 5]', '[363, 363, -w^3 + w^2 + 2*w + 3]', '[365, 365, -4*w^3 + 12*w^2 + 6*w - 23]', '[365, 365, -w^3 + 3*w^2 - 3*w + 2]', '[366, 366, -3*w^3 + 7*w^2 + 6*w - 12]', '[366, 366, -2*w^3 + 3*w^2 + 9*w - 12]', '[367, 367, -2*w^3 + w^2 + 9*w + 7]', '[367, 367, -4*w^3 + 5*w^2 + 16*w + 4]', '[372, 186, -3*w^2 + 2*w + 9]', '[372, 186, w^3 - 7*w]', '[373, 373, -2*w^3 + 3*w^2 + 6*w - 2]', '[373, 373, -w^3 + 3*w^2 + 3*w - 2]', '[373, 373, -2*w^3 + 7*w^2 + w - 13]', '[373, 373, 3*w^3 - 9*w^2 - 7*w + 22]', '[375, 15, -w^3 + 5*w^2 - w - 6]', '[375, 375, w^3 - 5*w^2 + 3*w + 6]', '[376, 94, 3*w^3 - w^2 - 15*w - 11]', '[379, 379, -2*w^3 + 6*w^2 + 2*w - 11]', '[379, 379, 2*w^3 - 5*w^2 - 7*w + 7]', '[381, 381, 2*w^3 - 3*w^2 - 4*w]', '[384, 12, -2*w^3 + 6*w^2 + 2*w - 6]', '[386, 386, 4*w^3 - 5*w^2 - 17*w - 2]', '[388, 194, 2*w^3 - 5*w^2 + 5]', '[388, 194, -2*w^3 + 7*w^2 + 2*w - 19]', '[392, 14, -3*w^3 + 5*w^2 + 11*w - 7]', '[392, 14, 5*w^3 - 3*w^2 - 25*w - 11]', '[394, 394, 2*w^3 - 3*w^2 - 9*w - 2]', '[394, 394, 4*w^3 - 10*w^2 + w + 7]', '[396, 198, w^2 - 2*w + 3]', '[398, 398, 2*w^3 - 5*w^2 - 7*w + 10]', '[400, 50, -2*w^3 + 4*w^2 + 6*w - 2]', '[402, 402, 2*w^3 - 3*w^2 - 5*w]', '[405, 15, -3*w + 6]', '[405, 405, w^3 - 4*w^2 - 2*w + 12]', '[409, 409, -w^3 + 4*w^2 + 2*w - 14]', '[411, 411, w^3 - w^2 + 3]', '[411, 411, -2*w^3 + 7*w^2 - 6]', '[412, 206, 2*w^3 - 3*w^2 - 8*w + 5]', '[415, 415, -5*w^3 + 9*w^2 + 17*w - 10]', '[415, 415, 3*w^3 - 4*w^2 - 11*w - 1]', '[422, 422, 3*w^3 - 7*w^2 - 6*w + 14]', '[423, 423, 2*w^3 - 4*w^2 - 8*w + 3]', '[424, 106, w^3 + w^2 - 9*w - 7]', '[424, 106, -3*w^3 + 7*w^2 + 7*w - 17]', '[432, 6, -2*w^3 + 4*w^2 + 8*w - 8]', '[432, 54, -2*w^3 + 2*w^2 + 6*w]', '[433, 433, -2*w^3 + 4*w^2 + 4*w - 5]', '[433, 433, 3*w^2 - 4*w - 10]', '[435, 435, 2*w^3 - 6*w^2 - 6*w + 15]', '[438, 438, -8*w^3 + 21*w^2 + 21*w - 48]', '[438, 438, 2*w^3 - 7*w^2 - 3*w + 12]', '[440, 110, -3*w^3 + 3*w^2 + 13*w + 1]', '[441, 63, w^3 - 8*w - 6]', '[441, 63, w^3 - 5*w^2 + 5*w + 6]', '[443, 443, -w^3 + 3*w^2 - 7]', '[443, 443, -w^3 + 3*w^2 + 4*w - 11]', '[445, 445, w^3 - 2*w^2 - 9*w + 13]', '[445, 445, -4*w^3 + 4*w^2 + 17*w + 2]', '[447, 447, w^3 + 3*w^2 - 9*w - 6]', '[450, 450, -w^2 - w + 6]', '[452, 226, 3*w^3 - 2*w^2 - 15*w - 10]', '[453, 453, w^3 - 4*w^2 - w + 3]', '[454, 454, w^3 - 4*w^2 - 2*w + 5]', '[457, 457, -3*w^3 + 5*w^2 + 10*w - 5]', '[461, 461, -2*w^3 + 3*w^2 + 8*w + 4]', '[463, 463, -5*w^3 + 3*w^2 + 25*w + 16]', '[464, 58, -2*w^2 + 6*w + 2]', '[465, 465, -2*w^3 + 6*w^2 - 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36]', '[1667, 1667, 2*w^3 - 3*w^2 - 4*w - 4]', '[1667, 1667, -4*w^3 + 8*w^2 + 15*w - 16]', '[1669, 1669, -2*w^3 + 3*w^2 + 10*w - 4]', '[1670, 1670, 3*w^3 - 8*w^2 - 10*w + 23]', '[1670, 1670, 3*w^3 - 5*w^2 - 12*w + 10]', '[1674, 186, w^3 + w^2 - 4*w - 8]', '[1674, 186, 4*w^3 - 11*w^2 - 7*w + 22]', '[1674, 1674, 6*w^3 - 14*w^2 - 15*w + 27]', '[1674, 1674, -w^3 - w^2 + 2*w + 6]', '[1675, 1675, 3*w^3 - 7*w^2 - 11*w + 16]', '[1678, 1678, -4*w^3 + 23*w + 19]', '[1682, 1682, -w^2 + 5*w + 8]', '[1688, 422, -w^3 - 3*w^2 + 11*w + 19]', '[1689, 1689, 4*w^3 - 11*w^2 + 6]', '[1692, 846, 2*w^3 + w^2 - 12*w - 9]', '[1695, 1695, 2*w^2 - 3*w - 12]', '[1696, 212, -4*w^3 + 12*w^2 - 2*w - 10]', '[1696, 212, 2*w^3 - 2*w^2 - 8*w + 4]', '[1697, 1697, 3*w^3 - 8*w^2 - 4*w + 2]', '[1697, 1697, -w^3 + w^2 + 8*w - 5]', '[1698, 1698, -5*w^3 + 12*w^2 + 10*w - 21]', '[1699, 1699, 5*w^3 - 13*w^2 - 12*w + 23]', '[1699, 1699, 3*w^2 - w - 11]', '[1705, 1705, -4*w^2 + 4*w + 13]', '[1705, 1705, 2*w^3 - 6*w^2 - 5*w + 8]', '[1706, 1706, w^3 - 8*w + 5]', '[1707, 1707, w^3 + 3*w^2 - 11*w - 12]', '[1713, 1713, -2*w^3 - w^2 + 11*w + 9]', '[1723, 1723, 2*w^3 - w^2 - 8*w - 8]', '[1723, 1723, 3*w^3 - 10*w^2 - 6*w + 20]', '[1726, 1726, -3*w^3 + 8*w^2 + 2*w - 11]', '[1726, 1726, 3*w^3 - 4*w^2 - 8*w - 1]', '[1727, 1727, -2*w^3 + w^2 + w - 7]', '[1728, 12, 2*w^3 - 4*w^2 - 2*w + 8]', '[1728, 108, -2*w^3 + 10*w + 12]', '[1730, 1730, w^3 - 4*w^2 - 4*w + 1]', '[1730, 1730, 2*w^3 - 6*w^2 - 7*w + 17]', '[1731, 1731, 3*w^3 - 7*w^2 - 6*w + 3]', '[1732, 866, 5*w^3 - 12*w^2 - 11*w + 26]', '[1732, 866, 2*w^3 - w^2 - 8*w + 1]', '[1733, 1733, w^3 - 2*w^2 + w - 5]', '[1733, 1733, 2*w^3 + w^2 - 12*w - 10]', '[1733, 1733, w^3 + w^2 - 5*w - 10]', '[1733, 1733, 2*w^3 - 8*w^2 - 2*w + 13]', '[1735, 1735, -2*w^3 + 4*w^2 - 5]', '[1735, 1735, 3*w^3 - 7*w^2 - 6*w + 1]', '[1737, 1737, 2*w^3 - w^2 - 13*w - 3]', '[1740, 870, -w^2 + 6*w - 3]', '[1745, 1745, -w^3 + 2*w^2 - w + 7]', '[1745, 1745, 9*w^3 - 9*w^2 - 40*w - 11]', '[1746, 1746, -2*w^3 + w^2 + 9*w]', '[1746, 1746, -w^3 + 3*w^2 + 2*w - 12]', '[1749, 1749, 4*w^2 - 2*w - 9]', '[1749, 1749, -2*w^3 + 5*w^2 - 4*w]', '[1752, 438, 3*w^3 - 5*w^2 - 15*w + 15]', '[1752, 438, -3*w^3 + 11*w^2 - w - 9]', '[1753, 1753, 3*w^3 - 7*w^2 - 2*w + 5]', '[1758, 1758, w^3 + 2*w^2 - 8*w - 3]', '[1759, 1759, -w^3 + 2*w^2 + 8*w - 10]', '[1759, 1759, -7*w^3 + 3*w^2 + 36*w + 25]', '[1760, 220, -2*w^3 + 2*w^2 + 8*w - 8]', '[1762, 1762, 3*w^3 - 4*w^2 - 8*w + 5]', '[1764, 126, -3*w^3 + 6*w^2 + 7*w - 6]', '[1764, 126, 5*w^3 - 6*w^2 - 17*w - 6]', '[1765, 1765, w^3 - 3*w - 7]', '[1765, 1765, -6*w^3 + 8*w^2 + 26*w - 1]', '[1766, 1766, 4*w^2 - 5*w - 13]', '[1766, 1766, w^3 - 4*w^2 - 6*w + 11]', '[1769, 1769, 5*w^3 - 16*w^2 + 5*w + 11]', '[1769, 1769, -2*w^3 + 7*w^2 - w - 1]', '[1772, 886, 6*w^3 - 13*w^2 - 16*w + 25]', '[1772, 886, 10*w^3 - 25*w^2 - 28*w + 53]', '[1773, 1773, w^2 - 7*w - 3]', '[1773, 1773, -w^3 - 2*w^2 + 6*w]', '[1774, 1774, -2*w^2 + 5*w - 5]', '[1780, 890, -6*w^3 + 11*w^2 + 6*w - 13]', '[1780, 890, -3*w^3 - 2*w^2 + 11*w + 10]', '[1782, 66, -3*w^3 + 6*w^2 + 6*w - 3]', '[1782, 1782, -4*w^3 + 5*w^2 + 15*w]', '[1783, 1783, -2*w^3 + 8*w + 1]', '[1783, 1783, 5*w^3 - 6*w^2 - 20*w - 2]', '[1787, 1787, -3*w^3 + 6*w^2 + 7*w - 7]', '[1787, 1787, -2*w^3 + 7*w^2 + w - 17]', '[1788, 894, 3*w^3 + 2*w^2 - 23*w - 12]', '[1790, 1790, -3*w^3 + 6*w^2 + 10*w - 5]', '[1791, 1791, 2*w^3 - 7*w^2 - 3*w + 9]', '[1793, 1793, w^3 - w^2 - 4*w - 7]', '[1795, 1795, -3*w^3 + 9*w^2 + 7*w - 26]', '[1795, 1795, -2*w^3 + 8*w^2 - w - 14]', '[1798, 1798, w^3 + 2*w^2 - 10*w - 13]', '[1798, 1798, 2*w^3 - 7*w^2 + 3*w + 8]', '[1800, 450, w^3 - 5*w^2 + 7*w + 3]', '[1801, 1801, -w^2 - 4]', '[1801, 1801, 3*w^3 - 6*w^2 - 4*w + 10]', '[1803, 1803, 2*w^3 - 4*w^2 - 9*w + 6]', '[1805, 95, -2*w^3 + 5*w^2 + 6*w - 16]', '[1805, 95, 6*w^3 - 8*w^2 - 25*w + 4]', '[1808, 226, -2*w^2 + 4*w - 4]', '[1809, 201, 4*w^3 - 5*w^2 - 16*w - 8]', '[1809, 1809, 3*w^3 - 7*w^2 - 7*w + 6]', '[1810, 1810, -w^2 - w - 4]', '[1811, 1811, -6*w^3 + 5*w^2 + 28*w + 8]', '[1811, 1811, 2*w^3 - 10*w - 13]', '[1812, 906, w^3 - 2*w^2 - w - 6]', '[1814, 1814, -w^3 + 4*w^2 - 6*w + 1]', '[1814, 1814, 5*w^2 - 7*w - 4]', '[1815, 1815, -w^3 + 4*w^2 - 3*w + 3]', '[1816, 454, 7*w^3 - 7*w^2 - 33*w - 11]', '[1821, 1821, 3*w^3 - 19*w - 15]', '[1825, 1825, 5*w^3 - 7*w^2 - 22*w + 7]', '[1825, 1825, -2*w^3 + 6*w^2 + 3*w - 4]', '[1826, 1826, w^3 - w^2 - 10*w - 8]', '[1826, 1826, -4*w^2 + 7*w + 19]', '[1828, 914, -5*w^3 + 12*w^2 + 9*w - 20]', '[1830, 1830, w^3 - 2*w^2 - 2*w + 9]', '[1830, 1830, 3*w^3 - 7*w^2 - 4*w + 12]', '[1831, 1831, -5*w^3 + 15*w^2 + 9*w - 32]', '[1831, 1831, 3*w^3 - 5*w^2 - 13*w + 8]', '[1831, 1831, 2*w^3 - 8*w^2 + 7]', '[1831, 1831, 8*w^3 - 5*w^2 - 39*w - 23]', '[1835, 1835, -5*w^3 + 10*w^2 + 12*w - 4]', '[1835, 1835, -w^3 + w^2 + 3*w + 8]', '[1837, 1837, -3*w^3 + 11*w^2 - 13]', '[1837, 1837, 5*w^3 - 14*w^2 - 10*w + 32]', '[1838, 1838, 6*w^3 - 19*w^2 - 7*w + 28]', '[1838, 1838, -4*w^2 + 3*w + 7]', '[1839, 1839, -3*w^3 + 7*w^2 + 2*w - 9]', '[1839, 1839, 4*w^2 - 8*w - 3]', '[1842, 1842, -w^3 - 3*w^2 + 6*w + 6]', '[1842, 1842, -3*w^3 + 10*w^2 + 6*w - 21]', '[1844, 922, 3*w^3 - 2*w^2 - 13*w - 2]', '[1849, 43, 5*w^3 - 9*w^2 - 17*w + 14]', '[1849, 43, 5*w^3 - 10*w^2 - 14*w + 22]', '[1852, 926, w^2 - 4*w + 7]', '[1854, 1854, 3*w^3 - 7*w^2 - 4*w + 6]', '[1856, 116, -2*w^2 + 10]', '[1858, 1858, 5*w^2 - w - 10]', '[1860, 930, 4*w^3 - 9*w^2 - 8*w + 15]', '[1860, 930, 3*w^3 - 8*w^2 - 5*w + 18]', '[1861, 1861, 4*w^2 - 6*w - 11]', '[1861, 1861, -3*w^3 - 2*w^2 + 21*w + 23]', '[1864, 466, -3*w^3 + 5*w^2 + 11*w + 1]', '[1864, 466, -5*w^3 + 13*w^2 + 7*w - 19]', '[1865, 1865, -3*w^3 + 8*w^2 + 6*w - 10]', '[1865, 1865, 4*w^3 - 4*w^2 - 20*w - 1]', '[1865, 1865, -3*w^3 + 7*w^2 + 4*w - 7]', '[1865, 1865, -6*w^3 + 10*w^2 + 23*w - 8]', '[1871, 1871, 4*w^2 - 8*w - 11]', '[1874, 1874, -2*w^3 + 8*w^2 + w - 19]', '[1875, 15, -5*w^3 + 15*w^2 - 15]', '[1875, 1875, -2*w^3 + 15*w + 6]', '[1878, 1878, -5*w^3 + 14*w^2 + 14*w - 27]', '[1879, 1879, 8*w^3 - 9*w^2 - 35*w - 7]', '[1880, 470, w^3 + w^2 - 7*w - 13]', '[1884, 942, w^2 - 2*w - 9]', '[1889, 1889, -w^3 - 2*w^2 + 10*w + 14]', '[1891, 1891, -2*w^3 + 5*w^2 + 6*w - 4]', '[1891, 1891, 2*w^3 - 5*w^2 + 4*w - 2]', '[1891, 1891, -w^3 + 6*w^2 - 2*w - 8]', '[1891, 1891, 5*w - 4]', '[1893, 1893, -4*w^3 + 9*w^2 + 9*w - 15]', '[1894, 1894, -3*w^3 + 10*w^2 + 4*w - 17]', '[1895, 1895, -w^3 - 2*w + 2]', '[1895, 1895, 3*w^3 - 3*w^2 - 14*w + 1]', '[1899, 1899, -5*w^3 + 9*w^2 + 16*w - 15]', '[1901, 1901, -3*w^3 + 8*w^2 + 5*w - 19]', '[1901, 1901, 3*w^3 - 2*w^2 - 12*w - 8]', '[1903, 1903, 4*w^3 - w^2 - 15*w - 5]', '[1903, 1903, 4*w^3 - 10*w^2 - 8*w + 23]', '[1905, 1905, 3*w^3 - 10*w^2 + 6]', '[1906, 1906, -5*w^3 + 15*w^2 + 10*w - 28]', '[1906, 1906, 4*w^2 - 5*w + 1]', '[1907, 1907, -w^3 - 3*w^2 + 8*w + 17]', '[1908, 954, 3*w^3 - 8*w^2 - 3*w]', '[1908, 954, -3*w^3 + 6*w^2 + 5*w - 12]', '[1913, 1913, 8*w^3 - 19*w^2 - 21*w + 37]', '[1914, 1914, -3*w^3 + 5*w^2 + 8*w - 6]', '[1916, 958, 5*w^3 - 10*w^2 - 15*w + 14]', '[1920, 60, -2*w^3 + 2*w^2 + 6*w + 6]', '[1922, 62, -w^3 + 2*w^2 - 4*w + 5]', '[1922, 62, w^2 + 3*w - 8]', '[1922, 1922, -2*w^3 + 4*w^2 + 9*w - 7]', '[1922, 1922, w^3 - w^2 + 2*w + 4]', '[1923, 1923, 3*w^3 - w^2 - 12*w - 3]', '[1923, 1923, 3*w^3 - 4*w^2 - 9*w + 3]', '[1929, 1929, w^3 + w^2 - 7*w]', '[1929, 1929, -8*w^3 + 7*w^2 + 36*w + 12]', '[1930, 1930, 5*w^3 - 9*w^2 - 16*w + 8]', '[1931, 1931, 2*w^2 - 6*w - 7]', '[1934, 1934, -5*w^3 + 13*w^2 + 10*w - 26]', '[1934, 1934, 2*w^3 - 7*w + 1]', '[1936, 242, -2*w^3 + 2*w^2 + 10*w - 4]', '[1940, 970, -w^3 - 2*w^2 + 7*w + 2]', '[1940, 970, -w^2 + 2*w - 5]', '[1942, 1942, -w^3 + 6*w^2 - 4*w - 11]', '[1943, 1943, 3*w^3 - 9*w^2 - 4*w + 11]', '[1944, 18, -3*w^3 + 9*w^2 + 3*w - 9]', '[1944, 486, -3*w^3 + 7*w^2 + 9*w - 9]', '[1948, 974, -7*w^3 + 20*w^2 + 19*w - 44]', '[1951, 1951, -w^3 - w^2 + 11*w + 4]', '[1952, 244, 4*w^2 - 6*w + 2]', '[1952, 244, 6*w^3 - 16*w^2 + 14]', '[1956, 978, w^2 + 2*w - 9]', '[1958, 1958, -3*w^3 + 4*w^2 + 12*w - 5]', '[1958, 1958, -4*w^3 + 10*w^2 + 3*w - 11]', '[1960, 70, -3*w^3 + 7*w^2 + 3*w - 5]', '[1960, 70, 3*w^3 - w^2 - 19*w - 7]', '[1964, 982, -2*w^3 + 5*w^2 + 2*w - 11]', '[1969, 1969, -5*w^3 + 6*w^2 + 20*w - 2]', '[1970, 1970, -7*w^2 + 7*w + 4]', '[1970, 1970, 3*w^3 - 5*w^2 - 8*w + 2]', '[1971, 219, 10*w^3 - 23*w^2 - 28*w + 40]', '[1971, 219, -w^3 + 2*w^2 + 7*w - 7]', '[1971, 1971, 4*w^3 - 5*w^2 - 17*w + 3]', '[1971, 1971, -3*w^3 + 2*w^2 + 6*w]', '[1980, 990, -3*w^3 + 4*w^2 + 9*w]', '[1983, 1983, 3*w^3 - 7*w^2 - 3*w + 6]', '[1984, 124, -4*w^3 + 10*w^2 + 8*w - 22]', '[1984, 124, 2*w^2 + 4*w - 2]', '[1987, 1987, -3*w^3 + 6*w^2 + 6*w - 8]', '[1990, 1990, w^3 + 3*w^2 - 8*w - 14]', '[1991, 1991, 2*w^3 + 2*w^2 - 9*w - 10]', '[1992, 498, 3*w^3 - 3*w^2 - 13*w - 9]', '[1992, 498, -w^3 - 3*w^2 + 9*w + 21]', '[1996, 998, -2*w^3 + 5*w^2 - 7]', '[1996, 998, 6*w^3 - 11*w^2 - 20*w + 17]', '[1997, 1997, -w^3 + 3*w^2 + 6*w - 5]', '[2000, 10, 4*w^3 - 10*w^2 - 6*w + 14]', '[2000, 250, -4*w^3 + 10*w^2 + 6*w - 10]', '[2003, 2003, -w^3 + w^2 + 9*w - 8]', '[2003, 2003, -w^3 + 6*w^2 - 2*w - 16]', '[2004, 1002, 10*w^3 - 27*w^2 - 24*w + 57]', '[2004, 1002, -w^2 - 4*w + 3]', '[2008, 502, -3*w^3 + 5*w^2 + 11*w + 5]', '[2008, 502, 3*w^3 - 5*w^2 - 7*w + 7]', '[2008, 502, 3*w^3 - 3*w^2 - 13*w + 1]', '[2008, 502, 3*w^3 - 5*w^2 - 13*w + 5]', '[2010, 2010, 3*w^3 - 9*w^2 - 2*w + 6]', '[2011, 2011, -2*w^3 + 7*w^2 - 14]', '[2011, 2011, 4*w^3 - 4*w^2 - 18*w - 1]', '[2011, 2011, -4*w^3 + 10*w^2 + 6*w - 17]', '[2011, 2011, 2*w^3 + w^2 - 10*w - 4]', '[2013, 2013, 3*w^3 - 5*w^2 + 4*w - 3]', '[2013, 2013, -w^3 + 8*w^2 - w - 9]', '[2017, 2017, 6*w^3 - 15*w^2 - 15*w + 35]', '[2017, 2017, -5*w^3 + 14*w^2 + 13*w - 35]', '[2018, 2018, -3*w^3 + 13*w^2 + 4*w - 20]', '[2025, 75, -3*w^3 + 6*w^2 + 9*w - 3]', '[2025, 2025, 2*w^3 - 9*w^2 + 3*w + 9]', '[2026, 2026, -w^3 + 2*w^2 - 2*w - 5]', '[2027, 2027, 6*w^3 - 13*w^2 - 18*w + 26]', '[2029, 2029, w^3 + w^2 - 8*w - 13]', '[2029, 2029, 7*w^3 - 18*w^2 - 16*w + 40]', '[2032, 254, 4*w^2 - 6*w - 8]', '[2034, 2034, w^3 + 2*w^2 - 12*w - 9]', '[2038, 2038, -3*w^3 + 3*w^2 + 8*w - 10]', '[2042, 2042, -w^3 - 3*w^2 + 10*w + 14]', '[2043, 2043, 2*w^3 + w^2 - 10*w - 12]', '[2045, 2045, 7*w^3 - 9*w^2 - 29*w - 2]', '[2046, 2046, -3*w^3 + 3*w^2 + 10*w + 6]', '[2046, 2046, 4*w^3 - 8*w^2 - 11*w + 9]', '[2048, 8, -4*w^3 + 4*w^2 + 20*w + 4]', '[2053, 2053, -7*w^3 + 4*w^2 + 38*w + 20]', '[2055, 2055, w^3 - 6*w^2 + w + 9]', '[2055, 2055, -2*w^3 + 3*w^2 + 3*w + 3]', '[2056, 514, -3*w^3 - w^2 + 23*w + 11]', '[2060, 1030, 3*w^3 - 6*w^2 - 13*w + 16]', '[2062, 2062, w^3 - 6*w^2 + 5]', '[2063, 2063, 3*w^2 - 2*w - 14]', '[2066, 2066, -3*w^3 + 10*w^2 - 2*w - 11]', '[2068, 1034, 2*w^3 - 7*w^2 - 2*w + 7]', '[2069, 2069, 6*w^3 - 15*w^2 - 13*w + 25]', '[2069, 2069, -3*w^3 + 10*w^2 + 3*w - 23]', '[2073, 2073, -w^3 + w^2 + w + 6]', '[2073, 2073, w^3 - 5*w^2 - 3*w + 6]', '[2075, 2075, -12*w^3 + 29*w^2 + 33*w - 61]', '[2075, 2075, 3*w^3 - 5*w^2 - 10*w + 11]', '[2076, 1038, 4*w^3 - 5*w^2 - 14*w - 3]', '[2076, 1038, 7*w^3 - 20*w^2 - 17*w + 42]', '[2077, 2077, -4*w^3 + 3*w^2 + 19*w + 13]', '[2077, 2077, 3*w^3 - 9*w^2 + 1]', '[2078, 2078, w^3 - 5]', '[2078, 2078, 4*w^3 - 10*w^2 - 9*w + 25]', '[2081, 2081, 2*w^3 - 6*w^2 - 7*w + 8]', '[2082, 2082, -w^3 + 6*w^2 - 4*w - 9]', '[2082, 2082, w^3 - 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18]', '[2250, 2250, -3*w^3 + 5*w^2 + 12*w]', '[2251, 2251, 2*w^3 - 2*w^2 - 10*w + 11]', '[2251, 2251, 5*w^3 - 14*w^2 - 11*w + 35]', '[2252, 1126, 4*w^3 - 11*w^2 - 8*w + 17]', '[2256, 282, 2*w^3 - 6*w - 6]', '[2258, 2258, 7*w^3 - 7*w^2 - 30*w - 10]', '[2259, 2259, -3*w^3 + 4*w^2 + 6*w]', '[2259, 2259, -3*w^3 + 4*w^2 + 8*w - 12]', '[2259, 2259, -2*w^3 + 5*w^2 + 2*w - 12]', '[2259, 2259, -2*w^3 + 8*w^2 + 3*w - 18]', '[2260, 1130, 2*w^3 - w^2 - 8*w - 11]', '[2263, 2263, w^3 - 3*w^2 + 2*w + 7]', '[2263, 2263, -4*w^3 + 7*w^2 + 16*w - 14]', '[2263, 2263, 3*w^3 - 6*w^2 - 3*w + 5]', '[2263, 2263, 6*w^2 - 7*w - 28]', '[2264, 566, -w^3 + w^2 + 5*w + 7]', '[2265, 2265, 4*w^3 - 11*w^2 - w + 9]', '[2266, 2266, 6*w^3 - 13*w^2 - 17*w + 22]', '[2267, 2267, -4*w^3 + 8*w^2 + 9*w - 14]', '[2269, 2269, -3*w^3 + 5*w^2 + 4*w - 5]', '[2270, 2270, 2*w^3 - 7*w - 7]', '[2271, 2271, -2*w^2 + 9*w - 6]', '[2273, 2273, -4*w^3 + 7*w^2 + 12*w - 4]', '[2274, 2274, w^3 + w^2 - 8*w]', '[2274, 2274, -4*w^3 + 11*w^2 + w - 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12*w - 6]', '[2352, 42, -4*w^3 + 10*w^2 + 6*w - 6]', '[2355, 2355, 3*w^3 - 5*w^2 - 5*w + 6]', '[2362, 2362, 2*w^3 - 5*w^2 + w - 2]', '[2362, 2362, 4*w^3 - 8*w^2 - 11*w + 11]', '[2364, 1182, 3*w^3 - 4*w^2 - 11*w + 6]', '[2364, 1182, 2*w^3 - 7*w^2 + 6*w + 3]', '[2367, 2367, -3*w^3 + 6*w^2 + 5*w - 3]', '[2371, 2371, 3*w^3 - 6*w^2 - 9*w + 17]', '[2371, 2371, 2*w^3 - 15*w - 4]', '[2374, 2374, -3*w^3 + 4*w^2 + 6*w - 5]', '[2376, 66, -w^3 - w^2 + 7*w - 1]', '[2376, 594, -3*w^3 + 3*w^2 + 11*w - 3]', '[2377, 2377, -4*w^3 + 7*w^2 + 16*w - 10]', '[2377, 2377, -3*w^3 + 7*w^2 + 8*w - 19]', '[2381, 2381, 8*w^3 - 7*w^2 - 39*w - 11]', '[2381, 2381, 4*w^2 - 9*w - 2]', '[2383, 2383, 3*w^3 - 7*w^2 - 11*w + 14]', '[2384, 298, 4*w^3 - 6*w^2 - 10*w - 2]', '[2385, 2385, 2*w^2 - 8*w + 3]', '[2385, 2385, 5*w^2 - 6*w - 18]', '[2386, 2386, w^3 - 7*w^2 + 8]', '[2388, 1194, -3*w^2 - 4*w + 9]', '[2391, 2391, 2*w^3 - 5*w^2 - w + 9]', '[2391, 2391, w^3 - 5*w^2 + 9*w + 6]', '[2393, 2393, w^3 - w^2 - 8*w + 1]', '[2393, 2393, -w^3 + 5*w^2 + 5*w - 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12*w - 11]', '[5274, 5274, 3*w^2 - 7*w - 12]', '[5275, 5275, w^3 - 5*w^2 + w + 20]', '[5277, 5277, 2*w^3 - 9*w^2 + 2*w + 18]', '[5277, 5277, 4*w^2 - 6*w + 3]', '[5279, 5279, -3*w^3 + 9*w^2 + 11*w - 20]', '[5279, 5279, w^3 - w^2 - 9*w - 10]', '[5280, 660, 4*w^3 - 14*w^2 + 6*w + 12]', '[5281, 5281, -4*w^3 + 14*w^2 + 3*w - 32]', '[5286, 5286, 2*w^3 + 4*w^2 - 7*w - 9]', '[5288, 1322, 3*w^3 - 9*w^2 - 11*w + 17]', '[5292, 42, -7*w^3 + 8*w^2 + 31*w + 8]', '[5292, 42, w^3 + 4*w^2 - 7*w - 8]', '[5292, 378, -5*w^2 + 6*w + 9]', '[5292, 378, 7*w^3 - 6*w^2 - 33*w - 18]', '[5294, 5294, 3*w^3 - 6*w^2 - 10*w + 19]', '[5295, 5295, 2*w^3 + w^2 - 11*w - 3]', '[5295, 5295, -5*w^3 + 13*w^2 + 12*w - 21]', '[5297, 5297, -3*w^3 + 8*w^2 - 10]', '[5297, 5297, -5*w^3 + 12*w^2 + 10*w - 26]', '[5297, 5297, 4*w^3 - 2*w^2 - 17*w - 4]', '[5297, 5297, -3*w^3 + 8*w^2 + 8*w - 10]', '[5298, 5298, -w^2 + 9*w - 12]', '[5298, 5298, -8*w^3 + 23*w^2 + 19*w - 48]', '[5300, 2650, 2*w^3 - 9*w^2 + 5]', '[5300, 2650, 4*w^3 - 9*w^2 - 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8]', '[5335, 5335, 5*w^3 - 9*w^2 - 18*w + 7]', '[5335, 5335, -3*w^3 - w^2 + 17*w + 14]', '[5340, 2670, 8*w^3 - 15*w^2 - 24*w + 39]', '[5340, 2670, -2*w^3 - 3*w^2 + 2*w + 9]', '[5342, 5342, -4*w^3 + 8*w^2 + 9*w - 11]', '[5342, 5342, 3*w^3 - 3*w^2 - 12*w + 4]', '[5342, 5342, 5*w^3 - 15*w^2 - 12*w + 38]', '[5342, 5342, -4*w^3 + 19*w^2 - 5*w - 16]', '[5344, 668, 2*w^3 - 6*w^2 - 4*w + 20]', '[5344, 668, 4*w^3 - 6*w^2 - 18*w + 4]', '[5345, 5345, -4*w^3 + 14*w^2 - 19]', '[5345, 5345, -4*w^3 + 10*w^2 + 7*w - 22]', '[5346, 198, -3*w^2 + 3*w + 18]', '[5346, 5346, -w^3 - w^2 + 10*w - 6]', '[5349, 5349, -5*w^3 + 11*w^2 + 2*w - 9]', '[5349, 5349, w^3 + w^2 - 11*w + 6]', '[5351, 5351, -3*w^3 - 3*w^2 + 20*w + 29]', '[5351, 5351, -6*w^3 + 18*w^2 + 11*w - 38]', '[5354, 5354, 4*w^3 - 14*w^2 - 3*w + 29]', '[5354, 5354, 3*w^3 - 6*w^2 - 14*w + 5]', '[5357, 5357, w^3 - 7*w^2 - 6*w + 13]', '[5360, 670, 6*w^3 - 10*w^2 - 20*w + 2]', '[5361, 5361, 3*w^3 - 7*w^2 - 9*w + 6]', '[5361, 5361, -5*w^2 + 5*w + 9]', '[5363, 5363, w^3 - 7*w^2 + 3*w + 10]', '[5363, 5363, 5*w^3 - 5*w^2 - 19*w - 4]', '[5363, 5363, w^3 + 4*w^2 - 9*w - 17]', '[5363, 5363, w^3 - 3*w^2 + 4*w + 7]', '[5364, 2682, 8*w^3 - 11*w^2 - 24*w - 9]', '[5366, 5366, 5*w^2 - 7*w - 14]', '[5366, 5366, -2*w^3 + 10*w^2 - 3*w - 11]', '[5368, 1342, -w^3 + 3*w^2 + 9*w - 13]', '[5368, 1342, -3*w^3 + 9*w^2 + 7*w - 13]', '[5370, 5370, -2*w^2 + 7*w + 9]', '[5373, 597, 4*w^3 - 5*w^2 - 13*w + 1]', '[5373, 5373, -3*w^3 + 5*w^2 + w - 6]', '[5374, 5374, 4*w^3 - 11*w^2 - 3*w + 16]', '[5379, 5379, w^3 - 11*w - 3]', '[5380, 2690, -w^3 + 6*w^2 + 3*w - 2]', '[5380, 2690, w^3 + 2*w^2 - 3*w - 10]', '[5381, 5381, 5*w^3 - 4*w^2 - 22*w - 4]', '[5381, 5381, -5*w^3 + 9*w^2 + 17*w - 16]', '[5385, 5385, 3*w^3 - 5*w^2 - 14*w + 9]', '[5385, 5385, 4*w^3 - 9*w^2 - 6*w + 6]', '[5387, 5387, 3*w^3 - 3*w^2 - 12*w + 13]', '[5390, 770, -w^3 + w^2 - 4*w + 2]', '[5390, 770, -2*w^3 + 9*w + 13]', '[5393, 5393, 5*w^2 - 4*w - 14]', '[5393, 5393, 5*w^3 - 11*w^2 - 12*w + 17]', '[5394, 5394, 4*w^3 - 6*w^2 - 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7*w - 11]', '[5459, 5459, -6*w^3 + 15*w^2 + 16*w - 26]', '[5462, 5462, 2*w^3 - 4*w^2 - w + 11]', '[5463, 5463, w^3 - 4*w^2 + 4*w - 6]', '[5465, 5465, w^3 - 8*w^2 + w + 7]', '[5465, 5465, w^3 - 5*w^2 + 6*w - 5]', '[5470, 5470, -3*w^3 + 5*w^2 + 18*w - 22]', '[5470, 5470, -2*w^3 - w^2 + 13*w + 4]', '[5471, 5471, -5*w^3 + 8*w^2 + 15*w - 11]', '[5475, 5475, 2*w^3 - 5*w^2 + 4*w + 6]', '[5475, 5475, 3*w^3 - 2*w^2 - 13*w - 15]', '[5478, 5478, -w^3 - 2*w^2 + 4*w - 3]', '[5478, 5478, 4*w^3 - 9*w^2 - 11*w + 24]', '[5480, 1370, w^3 - 7*w^2 + 3*w + 19]', '[5480, 1370, -5*w^3 + 3*w^2 + 23*w + 17]', '[5483, 5483, 6*w^3 - 12*w^2 - 17*w + 20]', '[5484, 2742, 13*w^3 - 32*w^2 - 35*w + 72]', '[5489, 5489, 3*w^3 - 5*w^2 - 14*w + 5]', '[5489, 5489, 4*w^3 - 2*w^2 - 24*w - 19]', '[5490, 5490, -w^3 + 8*w^2 - 9]', '[5490, 5490, 2*w^2 + 5*w - 3]', '[5492, 2746, w^3 - 2*w^2 - 9*w + 10]', '[5493, 5493, -2*w^3 + 10*w^2 - 6*w - 15]', '[5493, 5493, 5*w^3 - 11*w^2 - 12*w + 15]', '[5493, 5493, w^3 - w^2 - 4*w - 9]', '[5493, 5493, -4*w^3 + 8*w^2 - 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11]', '[379, 379, 2*w^3 - 5*w^2 - 7*w + 7]', '[409, 409, -w^3 + 4*w^2 + 2*w - 14]', '[433, 433, -2*w^3 + 4*w^2 + 4*w - 5]', '[433, 433, 3*w^2 - 4*w - 10]', '[443, 443, -w^3 + 3*w^2 - 7]', '[443, 443, -w^3 + 3*w^2 + 4*w - 11]', '[457, 457, -3*w^3 + 5*w^2 + 10*w - 5]', '[461, 461, -2*w^3 + 3*w^2 + 8*w + 4]', '[463, 463, -5*w^3 + 3*w^2 + 25*w + 16]', '[479, 479, 3*w^2 - 6*w - 8]', '[487, 487, w^3 - 3*w^2 - 5*w + 8]', '[491, 491, 2*w^3 - 4*w^2 - 3*w + 2]', '[499, 499, w^3 - w^2 - 7*w + 4]', '[499, 499, w^3 - 6*w - 8]', '[521, 521, 2*w^3 - 4*w^2 - 8*w + 7]', '[521, 521, 3*w^3 - 5*w^2 - 8*w - 1]', '[521, 521, w^3 - 5*w + 1]', '[521, 521, w^3 - 8*w + 2]', '[523, 523, -2*w^3 + 5*w^2 + 4*w - 4]', '[547, 547, -2*w^3 + 4*w^2 + 6*w - 1]', '[547, 547, -w^3 - w^2 + 6*w + 11]', '[563, 563, -2*w^3 + 8*w^2 - 3*w - 8]', '[569, 569, 3*w^3 - 7*w^2 - 10*w + 13]', '[571, 571, -3*w^3 + 4*w^2 + 11*w - 1]', '[577, 577, -w^3 + 5*w^2 - 3*w - 10]', '[601, 601, -2*w^3 + 6*w^2 + 4*w - 17]', '[607, 607, 2*w^3 - 12*w - 5]', '[613, 613, 6*w^3 - 5*w^2 - 27*w - 11]', '[613, 613, 2*w + 5]', '[631, 631, 5*w^3 - 14*w^2 - 11*w + 29]', '[641, 641, w^3 + w^2 - 5*w - 8]', '[641, 641, -w^3 + 5*w^2 - 13]', '[643, 643, w^2 + w - 7]', '[643, 643, -3*w^3 + 3*w^2 + 15*w + 8]', '[661, 661, 3*w^3 - 2*w^2 - 14*w - 4]', '[691, 691, -2*w^3 + 3*w^2 + 9*w - 7]', '[691, 691, 2*w^3 - 5*w^2 - 3*w + 11]', '[709, 709, 7*w^3 - 16*w^2 - 20*w + 32]', '[709, 709, -w^3 + 4*w^2 + 2*w - 4]', '[709, 709, -2*w^3 + 3*w^2 + 4*w - 2]', '[719, 719, -2*w^3 + 3*w^2 + 7*w - 7]', '[719, 719, -w^3 + 4*w^2 - 14]', '[739, 739, 5*w^3 - 3*w^2 - 24*w - 17]', '[739, 739, -4*w^3 + 10*w^2 + 10*w - 17]', '[743, 743, 2*w^3 - 2*w^2 - 11*w - 2]', '[757, 757, -3*w^3 + 5*w^2 + 11*w - 2]', '[761, 761, w^3 - 3*w - 5]', '[761, 761, w^2 - 5*w - 1]', '[769, 769, -w^3 - w^2 + 9*w + 8]', '[773, 773, -2*w^3 + 4*w^2 + 7*w - 2]', '[797, 797, -2*w^3 + w^2 + 12*w + 10]', '[797, 797, -2*w^3 + 5*w^2 + 3*w + 1]', '[809, 809, 3*w^2 - 4*w - 8]', '[821, 821, -3*w^3 + 6*w^2 + 9*w - 5]', '[823, 823, -2*w^3 + 5*w^2 + w - 7]', '[823, 823, -3*w^3 + 6*w^2 + 6*w - 10]', '[827, 827, w^3 + 2*w^2 - 5*w - 7]', '[827, 827, w^3 - 2*w^2 - 6*w - 4]', '[829, 829, 3*w^3 - w^2 - 15*w - 14]', '[829, 829, w^3 + 2*w^2 - 7*w - 13]', '[839, 839, 4*w^3 - 11*w^2 - 8*w + 26]', '[853, 853, w^3 - 4*w - 8]', '[863, 863, 5*w^3 - 2*w^2 - 26*w - 14]', '[863, 863, 2*w^3 - 5*w^2 - 5*w + 5]', '[881, 881, 2*w^3 + w^2 - 11*w - 11]', '[883, 883, -6*w^3 + 15*w^2 + 14*w - 32]', '[883, 883, -w^3 + 2*w^2 + 2*w - 8]', '[887, 887, w^3 - w^2 - 7*w + 2]', '[907, 907, 3*w^3 - 3*w^2 - 10*w - 5]', '[907, 907, w^3 - 2*w^2 - 2*w - 4]', '[919, 919, 3*w^3 - 3*w^2 - 11*w - 2]', '[919, 919, -4*w^3 + 10*w^2 + 7*w - 16]', '[929, 929, 3*w^3 - 3*w^2 - 10*w + 1]', '[937, 937, 6*w^3 - 8*w^2 - 24*w + 1]', '[947, 947, 3*w^3 - 6*w^2 - 8*w + 8]', '[953, 953, 4*w - 1]', '[953, 953, 4*w^3 - 9*w^2 - 10*w + 16]', '[961, 31, -w^3 + 6*w - 2]', '[967, 967, 2*w^3 - 8*w - 7]', '[967, 967, 4*w^3 - 9*w^2 - 12*w + 14]', '[971, 971, 5*w^3 - 6*w^2 - 20*w - 4]']}
• 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, 4, -4, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 11344, 'disc_rad': 1418, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1], [1, 1]]], [5, [[3, 1], [1, 1]]], [7, [[2, 2]]], [11, [[3, 1], [1, 1]]], [13, [[4, 1]]], [17, [[4, 1]]], [19, [[2, 2]]], [23, [[4, 1]]], [29, [[3, 1], [1, 1]]], [31, [[2, 1], [1, 2]]], [37, [[4, 1]]], [41, [[4, 1]]], [43, [[2, 2]]], [47, [[3, 1], [1, 1]]], [53, [[2, 1], [1, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [28, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 59.77571494764291, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.11344.1', 'local_algs': ['2.4.4.5', 'm709.1.1.0', 'm709.1.1.0', 'm709.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 709], 'rd': 10.3202817619, 'regulator': {'__RealLiteral__': 0, 'data': '9.49444200802', 'prec': 44}, 'res': {'gal': ['421875,900000,-4992900,-6127792,20197413,15885472,-38836672,-19437586,41113330,12368482,-25633792,-4304874,9791893,843458,-2361888,-91336,365120,4866,-35926,-72,2163,-2,-72,0,1'], 'sib': ['-1,0,15,0,-11,0,1', '-184,-288,420,104,-50,-2,1', '1156,0,-10180,0,13160,0,-4820,0,700,0,-44,0,1', '124,-2096,5304,-2608,-3592,3544,184,-1092,228,98,-32,-2,1', '753,-854,-1146,616,545,-28,-44,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 2 \\)', '\\( a^{2} - a - 1 \\)', '\\( a^{3} - a^{2} - 5 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}