Hilbert modular form data - 4.4.16997.1-25.1-f

Formats: - HTML - YAML - JSON - 2024-05-01T09:37:53.787731

• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 4, 'dimension': 2, 'disc': 16997, 'field_bad_primes': [23, 739], 'field_label': '4.4.16997.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.16997.1-25.1-f', 'label_nsuffix': 5, 'label_suffix': 'f', 'level_bad_primes': [5], 'level_ideal': '[25, 5, -w^3 + 4*w]', 'level_label': '25.1', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.1-f', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5, 5, w]', -1], ['[5, 5, -w^2 + w + 2]', 1]], 'hecke_eigenvalues': [1, -1, 'e', 'e', 'e + 6', '-e - 3', '3*e + 5', '-e - 2', 8, '-e - 7', '-e - 6', '-2*e - 3', -5, '-e - 2', '-2*e - 8', '-3*e - 9', '-2*e - 11', '-2*e - 5', -4, '-e - 15', 10, '-4*e - 13', '2*e + 3', '3*e + 6', '-e - 8', '-4*e - 13', '2*e - 4', '2*e + 11', '-5*e - 3', '-4*e - 11', '6*e + 9', '3*e - 7', '-2*e - 9', '2*e + 10', '-4*e - 18', '-e - 11', '-4*e - 24', 'e + 8', '-2*e + 15', '8*e + 14', '-2*e', 0, '3*e + 24', '-7*e - 11', '-6*e + 2', '-10*e - 25', 'e - 23', '10*e + 26', '6*e + 20', '5*e + 4', '11*e + 19', 8, '-6*e - 20', '4*e - 8', '-4*e - 4', '2*e + 22', '-6*e - 33', '12*e + 28', '4*e + 13', 'e - 4', '12*e + 29', '4*e + 6', 28, '2*e + 1', '-5*e - 23', '2*e + 8', -6, '2*e - 10', '11*e + 18', 'e + 2', '8*e + 34', '-2*e - 22', '-7*e - 5', '-12*e - 30', '-e + 23', 24, '9*e + 33', '9*e + 19', '-5*e - 7', '-7*e - 18', '-4*e - 14', '-6*e - 20', '-4*e - 11', '-6*e - 18', '-5*e - 2', '-2*e - 22', '4*e + 35', '-4*e - 28', '3*e + 34', '14*e + 37', '2*e - 1', '5*e + 31', '-10*e - 14', '-8*e - 9', '2*e + 12', '-7*e - 36', '-e - 12', '6*e + 21', '-4*e + 28', '10*e + 24', '3*e - 9', '-3*e + 15', '-7*e - 24', '-2*e + 16', '-4*e - 20', '-4*e - 34', '5*e + 24', '4*e + 25', '-2*e + 4', -8, '3*e + 40', '-12*e - 22', '-2*e - 16', '-2*e - 8', '-8*e - 30', '-4*e - 42', '5*e + 22', '8*e + 37', '-5*e + 6', '7*e - 7', '-6*e - 7', '-16*e - 34', '2*e + 2', '-12*e - 42', '11*e + 21', '6*e + 28', '2*e + 4', '-6*e - 20', '12*e + 21', '-12*e - 26', 'e - 14', '-6*e - 14', '-3*e - 28', '-12*e - 3', '4*e - 25', '2*e - 14', '-16*e - 26', '-6*e - 32', '6*e - 17', '-13*e - 29', '5*e - 22', '12*e + 37', -35, '16*e + 46', 'e + 3', '9*e + 23', '14*e + 22', '4*e + 21', '4*e + 39', '5*e + 32', '5*e - 3', '3*e + 20', '-8*e - 19', '-4*e - 7', '-2*e + 30', '5*e - 6', '-16*e - 22', '8*e + 22', '-e - 16', '-e + 16', '14*e + 5', '5*e + 10', '-7*e - 28', '12*e + 33', '-8*e - 4', '3*e + 26', '8*e - 17', '10*e - 7', '-3*e - 40', '-10*e - 8'], 'hecke_polynomial': 'x^2 + 4*x - 2', 'label': '4.4.16997.1-25.1-f'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 16997, 'ideals': ['[1, 1, 1]', '[5, 5, w]', '[5, 5, -w^2 + w + 2]', '[7, 7, -w^2 + 2]', '[13, 13, -w^2 + 3]', '[13, 13, w^2 - w - 4]', '[16, 2, 2]', '[19, 19, -w^2 + w + 1]', '[23, 23, -w^3 + 4*w + 2]', '[25, 5, -w^3 + 4*w]', '[25, 5, -w^3 + w^2 + 3*w - 1]', '[25, 25, -w^3 + 5*w + 3]', '[25, 25, w^3 - 5*w]', '[29, 29, w^3 - w^2 - 4*w + 1]', '[29, 29, -w + 3]', '[31, 31, -w^3 + w^2 + 5*w - 2]', '[35, 35, w + 3]', '[35, 35, w^2 - w - 5]', '[37, 37, w^3 - 4*w - 1]', '[37, 37, w^3 - 3*w + 1]', '[49, 49, w^3 + w^2 - 5*w - 4]', '[53, 53, -w^3 + 2*w^2 + 4*w - 6]', '[59, 59, w^2 + w - 4]', '[61, 61, -2*w^2 + w + 8]', '[65, 65, w^3 - w^2 - 4*w]', '[65, 65, -w^3 + 3*w]', '[65, 65, 2*w + 1]', '[65, 65, -w^3 + 2*w^2 + 3*w - 6]', '[73, 73, -w^3 + 5*w - 1]', '[79, 79, 2*w^2 + w - 6]', '[79, 79, 2*w^3 - w^2 - 9*w + 3]', '[80, 10, 2*w]', '[80, 10, -2*w^2 + 2*w + 4]', '[81, 3, -3]', '[83, 83, -w^3 + w^2 + 3*w - 4]', '[91, 91, w^3 - w^2 - 6*w + 4]', '[91, 91, w^3 - 3*w - 3]', '[95, 95, -w^3 + w^2 + 5*w - 1]', '[95, 95, w^3 - 6*w]', '[97, 97, -w^3 + 6*w + 2]', '[97, 97, -2*w^3 + w^2 + 10*w - 1]', '[97, 97, 3*w^3 - 4*w^2 - 15*w + 13]', '[97, 97, w^3 - w^2 - 6*w + 2]', '[103, 103, -2*w^3 + 3*w^2 + 11*w - 9]', '[109, 109, w^2 + 3*w - 3]', '[112, 14, -2*w^2 + 4]', '[115, 115, -2*w^2 + w + 5]', '[115, 115, -w^3 + 5*w - 2]', '[125, 5, -2*w^3 + w^2 + 9*w - 5]', '[125, 5, -w^3 + 6*w + 1]', '[125, 25, -2*w^2 - w + 5]', '[125, 25, -w^2 + 2*w + 5]', '[125, 125, w^2 + w - 5]', '[125, 125, -w^3 + w^2 + 6*w - 3]', '[133, 133, 2*w^2 - w - 7]', '[137, 137, -w^2 + 7]', '[145, 145, w^3 - w^2 - 6*w]', '[145, 145, -w^3 + 2*w^2 + 2*w - 5]', '[145, 145, w^3 - 2*w^2 - 4*w + 3]', '[145, 145, w^2 + 1]', '[149, 149, w^3 - 2*w^2 - 5*w + 4]', '[149, 149, w^3 + 2*w^2 - 6*w - 7]', '[151, 151, w^3 + w^2 - 5*w - 3]', '[155, 155, -2*w^2 + w + 6]', '[155, 155, w^3 - w^2 - 3*w + 5]', '[161, 161, w - 4]', '[163, 163, w^3 - 3*w - 4]', '[163, 163, -w^3 + 6*w - 3]', '[167, 167, w^3 - 2*w^2 - 6*w + 4]', '[169, 13, w^3 + w^2 - 4*w - 7]', '[169, 13, w^2 + 2*w - 4]', '[169, 169, w + 4]', '[169, 169, 2*w^2 - 7]', '[175, 35, w^2 + 3*w]', '[175, 35, w^3 - w^2 - 3*w + 6]', '[175, 175, w^3 - w^2 - 5*w]', '[175, 175, w^2 + w - 6]', '[185, 185, 2*w^2 - 3*w - 7]', '[185, 185, 2*w^2 - 5]', '[185, 185, -w^3 + w^2 + w - 3]', '[185, 185, 3*w^2 + 2*w - 5]', '[191, 191, w^3 - w^2 - 5*w - 2]', '[191, 191, 2*w^3 - 9*w - 2]', '[197, 197, w^3 - 4*w + 4]', '[203, 203, 2*w^2 - 2*w - 3]', '[203, 203, w^3 - 3*w^2 - 2*w + 6]', '[208, 26, -2*w^2 + 6]', '[208, 26, 2*w^2 - 2*w - 8]', '[211, 211, -w^3 + 2*w^2 + 6*w - 8]', '[217, 217, -w^3 - w^2 + 4*w + 1]', '[223, 223, -w^3 + 3*w^2 + 4*w - 6]', '[229, 229, w^3 - w^2 - 5*w - 1]', '[245, 245, 2*w^3 - w^2 - 8*w + 4]', '[245, 245, w^3 + w^2 - 3*w - 5]', '[247, 247, w^2 + 3*w - 2]', '[247, 247, -w^3 + 2*w^2 + 4*w - 2]', '[251, 251, 2*w^3 - 2*w^2 - 7*w + 3]', '[256, 4, 4]', '[257, 257, 3*w^2 - 14]', '[259, 259, -3*w - 2]', '[259, 259, -w^3 - 2*w^2 - w + 2]', '[263, 263, w^2 - 3*w - 1]', '[263, 263, w^2 - 2*w - 7]', '[265, 265, 2*w^3 - 2*w^2 - 7*w + 5]', '[265, 265, 2*w^3 - 3*w^2 - 6*w + 3]', '[269, 269, -w^3 + w^2 + 2*w - 4]', '[269, 269, 2*w^3 - 11*w - 1]', '[271, 271, -w^3 + w^2 + 4*w - 7]', '[277, 277, w^3 - w^2 - 3*w + 8]', '[295, 295, w^2 - 3*w - 3]', '[295, 295, w^3 + w^2 - 4*w]', '[299, 299, -w^3 + w^2 + 6*w + 1]', '[299, 299, -w^3 - w^2 + 7*w + 6]', '[304, 38, -2*w^2 + 2*w + 2]', '[305, 305, -2*w^3 + w^2 + 8*w]', '[305, 305, w^3 + w^2 - 5*w - 2]', '[311, 311, w^3 + 2*w^2 - 7*w - 11]', '[311, 311, -3*w^2 - 2*w + 8]', '[317, 317, -2*w^3 + 2*w^2 + 7*w - 4]', '[325, 65, -w^2 + 3*w + 2]', '[325, 65, 2*w^3 - 3*w^2 - 7*w + 5]', '[325, 65, -w^3 + 2*w^2 + 5*w - 3]', '[325, 65, 2*w^3 + w^2 - 10*w - 5]', '[325, 325, -w^3 + 2*w^2 + w - 5]', '[325, 325, 2*w^2 - 3*w - 2]', '[325, 325, 2*w^3 - w^2 - 10*w]', '[325, 325, 3*w - 1]', '[331, 331, w^2 - w - 8]', '[331, 331, 3*w^3 - 2*w^2 - 12*w + 9]', '[337, 337, -2*w^3 + 2*w^2 + 11*w - 8]', '[343, 7, w^3 - 3*w^2 - 4*w + 11]', '[343, 343, w^3 - 2*w^2 - 3*w + 8]', '[347, 347, -2*w^3 + 2*w^2 + 9*w - 4]', '[349, 349, -w^3 + 2*w^2 + 2*w - 6]', '[353, 353, 2*w^2 - w - 12]', '[353, 353, 2*w^3 - w^2 - 9*w - 1]', '[361, 361, -2*w^3 + 3*w^2 + 10*w - 8]', '[365, 365, -w^2 - 2*w + 5]', '[365, 365, -w^3 + w^2 + 3*w + 3]', '[367, 367, -2*w^3 + w^2 + 10*w - 6]', '[367, 367, 2*w^3 - 11*w - 3]', '[368, 46, -2*w^3 + 8*w + 4]', '[371, 371, -w^2 + w - 2]', '[377, 377, w^3 + w^2 - 6*w - 2]', '[377, 377, 2*w^3 - w^2 - 8*w + 3]', '[377, 377, w^3 - 3*w^2 - 3*w + 9]', '[377, 377, w^3 - 2*w^2 - 6*w + 9]', '[379, 379, -3*w - 1]', '[379, 379, w^3 - 2*w - 3]', '[383, 383, -w^3 + 2*w^2 + 4*w - 11]', '[383, 383, -w^3 - w^2 + 7*w + 4]', '[389, 389, 2*w^3 - w^2 - 11*w + 4]', '[395, 395, -3*w^3 + 6*w^2 + 7*w - 4]', '[395, 395, -w^3 - w^2 + 4*w + 10]', '[395, 395, -2*w^3 + w^2 + 3*w]', '[395, 395, 2*w^2 - 2*w - 9]', '[400, 10, -2*w^3 + 8*w]', '[400, 10, -2*w^3 + 2*w^2 + 6*w - 2]', '[400, 50, -2*w^3 + 10*w + 6]', '[400, 50, 2*w^3 - 10*w]', '[401, 401, w^3 + 2*w^2 - 7*w - 6]', '[401, 401, 2*w^3 - 11*w - 6]', '[403, 403, -2*w^3 + 9*w - 1]', '[403, 403, -w^3 + w + 2]', '[405, 15, -3*w]', '[405, 15, 3*w^2 - 3*w - 6]', '[413, 413, -w^3 + w - 3]', '[415, 415, w^3 - 3*w^2 - 5*w + 5]', '[415, 415, 2*w^3 - 2*w^2 - 5*w + 2]', '[419, 419, -2*w^3 + w^2 + 8*w - 1]', '[421, 421, -w^3 + 3*w^2 + 3*w - 12]', '[421, 421, -w^3 - 2*w^2 + 2*w + 6]', '[427, 427, -w^3 + 4*w + 6]', '[433, 433, w^3 - 2*w^2 - 6*w + 11]', '[433, 433, w^2 - 8]', '[437, 437, -2*w^3 + w^2 + 11*w - 1]', '[439, 439, -w^3 + 3*w^2 + 3*w - 7]', '[443, 443, w^3 - w^2 - 2*w - 4]', '[443, 443, 2*w^3 + w^2 - 7*w - 2]', '[443, 443, 2*w^3 - w^2 - 8*w + 2]', '[443, 443, -w^2 - 2]', '[455, 455, w^3 - w^2 - w - 2]', '[455, 455, -3*w + 5]', '[455, 455, w^3 + 2*w^2 - 4*w - 10]', '[455, 455, -w^3 + 3*w^2 + 4*w - 7]', '[464, 58, 2*w^3 - 2*w^2 - 8*w + 2]', '[464, 58, -2*w + 6]', '[467, 467, 3*w^3 - 5*w^2 - 15*w + 19]', '[467, 467, 2*w^3 - 3*w^2 - 8*w + 13]', '[467, 467, -w^3 + 2*w^2 + 3*w - 9]', '[467, 467, -w^3 + 3*w^2 + 3*w - 8]', '[475, 95, -2*w^3 + 2*w^2 + 11*w - 7]', '[475, 95, w^3 - w^2 - 2*w + 5]', '[475, 475, -3*w^2 + 2*w + 8]', '[475, 475, w - 5]', '[479, 479, -w^3 - 3*w^2 + 5*w + 13]', '[479, 479, -w^3 + w^2 + w - 4]', '[481, 481, -2*w^3 - 2*w^2 + 11*w + 9]', '[481, 481, -2*w^2 - 4*w + 3]', '[481, 481, -w^3 - w^2 + 5*w + 1]', '[481, 481, w^3 - 7*w - 3]', '[485, 485, w + 5]', '[485, 485, w^3 - 2*w^2 - 3*w + 10]', '[485, 485, w^3 - 2*w^2 - 6*w + 10]', '[485, 485, w^3 + w^2 - 3*w - 6]', '[485, 485, -2*w^3 - w^2 + 8*w + 9]', '[485, 485, -w^3 - 3*w^2 + 6*w + 13]', '[485, 485, -w^3 + 3*w^2 + 5*w - 9]', '[485, 485, -w^3 + 3*w - 5]', '[487, 487, 3*w^3 - w^2 - 13*w - 2]', '[491, 491, w^2 + w - 9]', '[496, 62, -2*w^3 + 2*w^2 + 10*w - 4]', '[499, 499, -3*w^3 + 3*w^2 + 13*w - 7]', '[503, 503, 2*w^2 + w - 9]', '[509, 509, -2*w^2 - 3*w + 6]', '[509, 509, -w^3 + w^2 - 4]', '[511, 511, -w^3 + 2*w^2 + 5*w - 2]', '[515, 515, -2*w^2 - 2*w + 7]', '[515, 515, -w^3 + 3*w^2 + 4*w - 10]', '[521, 521, -3*w^2 + w + 12]', '[523, 523, 2*w^3 - 8*w - 3]', '[529, 23, -3*w^3 + 2*w^2 + 13*w - 7]', '[529, 23, 2*w^3 - w^2 - 6*w - 1]', '[541, 541, -w^3 + w^2 + 7*w - 4]', '[545, 545, w^3 + 3*w^2 - 3*w]', '[545, 545, -2*w^3 + 2*w^2 + 2*w - 1]', '[547, 547, 2*w^3 - 3*w^2 - 9*w + 7]', '[551, 551, -w^3 - 2*w^2 + 3*w + 8]', '[551, 551, 2*w^3 - 8*w - 1]', '[553, 553, -w^3 + 5*w^2 + 4*w - 4]', '[553, 553, -3*w^3 + 13*w + 7]', '[557, 557, 3*w^2 - 2*w - 9]', '[557, 557, w^3 - 6*w - 7]', '[560, 70, 2*w + 6]', '[560, 70, 2*w^2 - 2*w - 10]', '[563, 563, -2*w^3 + w^2 + 6*w - 6]', '[567, 21, 3*w^2 - 6]', '[575, 115, 3*w^2 + w - 6]', '[575, 115, -w^2 - 3*w + 5]', '[575, 575, -2*w^3 + 4*w^2 + 7*w - 10]', '[575, 575, -w^3 + 2*w^2 + 2*w + 1]', '[577, 577, -w^3 + 4*w^2 + 2*w - 13]', '[581, 581, w^3 + w^2 - 3]', '[587, 587, w^2 - 2*w + 3]', '[587, 587, w^2 + 2*w - 6]', '[589, 589, w^3 - 3*w^2 - 4*w + 8]', '[592, 74, 2*w^3 - 8*w - 2]', '[592, 74, 2*w^3 - 6*w + 2]', '[593, 593, -2*w^3 + 2*w^2 + 11*w - 3]', '[599, 599, w^3 + 3*w^2 - 6*w - 12]', '[601, 601, -2*w^3 + w^2 + 9*w + 2]', '[607, 607, -w^3 + 3*w^2 + 4*w - 9]', '[617, 617, -2*w^3 + w^2 + 7*w - 3]', '[619, 619, -2*w^3 + 4*w^2 + 9*w - 11]', '[625, 5, 5]', '[625, 25, -w^3 + 3*w^2 + 2*w - 10]', '[625, 25, -2*w^3 + 3*w^2 + 7*w - 10]', '[625, 25, w^2 - 3*w - 7]', '[625, 25, -w^3 + w - 4]', '[625, 125, w^3 - 4*w + 5]', '[625, 125, 2*w^2 - 4*w - 5]', '[625, 625, -w^3 + 2*w + 4]', '[625, 625, w^3 + w^2 - 5*w]', '[631, 631, 3*w^2 - w - 7]', '[631, 631, -w^3 - w^2 + 6*w + 1]', '[637, 637, -2*w^3 + 3*w^2 + 7*w - 4]', '[637, 637, 2*w^3 - w^2 - 6*w + 3]', '[641, 641, -w^3 + 2*w^2 + 5*w - 1]', '[641, 641, -w^3 + 2*w^2 + 2*w - 7]', '[643, 643, -3*w^3 + w^2 + 14*w - 4]', '[647, 647, -3*w^3 + 5*w^2 + 14*w - 18]', '[647, 647, -w^3 + 7*w + 2]', '[647, 647, -2*w^3 + 7*w - 1]', '[647, 647, 2*w^3 - w^2 - 10*w - 1]', '[653, 653, -2*w^3 - w^2 + 11*w + 4]', '[659, 659, -w^3 - w^2 + 5*w - 1]', '[665, 665, 2*w^3 - w^2 - 7*w]', '[665, 665, -w^3 - 2*w^2 + 4*w + 3]', '[667, 667, w^3 - w^2 - 2*w + 6]', '[667, 667, w^3 - w^2 - 7*w + 3]', '[673, 673, -w^3 + w^2 + 7*w - 2]', '[673, 673, -w^3 + w^2 + 2*w - 8]', '[679, 679, -2*w^3 - w^2 + 7*w + 4]', '[679, 679, -2*w^3 - w^2 + 9*w + 3]', '[679, 679, -2*w^3 + 2*w^2 + 9*w - 3]', '[679, 679, 2*w^3 + w^2 - 6*w - 1]', '[683, 683, 2*w^3 - 11*w - 8]', '[683, 683, 2*w^3 - 7*w - 3]', '[685, 685, -w^3 + 7*w]', '[685, 685, w^3 - 2*w^2 - 6*w + 2]', '[689, 689, -w^3 + w^2 + 5*w - 8]', '[689, 689, -w^2 - 2*w + 9]', '[701, 701, 2*w^3 - 4*w^2 - 10*w + 17]', '[703, 703, -2*w^3 + w^2 + 4*w - 4]', '[703, 703, -w^3 + 2*w^2 + w - 6]', '[713, 713, -w^3 - 2*w^2 + 4*w + 11]', '[721, 721, w^3 - 7*w - 1]', '[725, 145, -w^3 - 3*w^2 + 5*w + 12]', '[725, 145, 2*w^2 + w - 10]', '[725, 145, -3*w^3 + 2*w^2 + 13*w - 5]', '[725, 145, 2*w^3 + w^2 - 10*w - 4]', '[725, 725, -3*w^2 - w + 9]', '[725, 725, 2*w^3 - 4*w^2 - 6*w + 5]', '[725, 725, 2*w^3 - 9*w + 2]', '[725, 725, -w^3 + w - 5]', '[727, 727, -w^3 + w^2 + 4*w - 8]', '[727, 727, 3*w^2 - 11]', '[739, 739, 2*w^3 + 3*w^2 - 8*w - 13]', '[743, 743, 2*w^2 + w - 12]', '[743, 743, 3*w^2 - 2*w - 14]', '[745, 745, -w^3 + 4*w^2 + 2*w - 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12]', '[1537, 1537, -2*w^3 + 13*w - 6]', '[1537, 1537, -5*w^3 + 8*w^2 + 19*w - 23]', '[1539, 57, 3*w^2 - 3*w - 3]', '[1552, 194, -2*w^3 + 12*w + 4]', '[1552, 194, -4*w^3 + 2*w^2 + 20*w - 2]', '[1552, 194, 6*w^3 - 8*w^2 - 30*w + 26]', '[1552, 194, 2*w^3 - 2*w^2 - 12*w + 4]', '[1553, 1553, -w^3 - 4*w^2 + 2*w + 9]', '[1553, 1553, 2*w^3 - 2*w^2 - 9*w + 1]', '[1555, 1555, 2*w^3 - w^2 - 10*w - 5]', '[1555, 1555, -w^3 + 2*w^2 + 7*w + 1]', '[1555, 1555, 5*w^3 + w^2 - 21*w - 17]', '[1555, 1555, -3*w^3 - 2*w^2 + 8*w]', '[1559, 1559, -w^3 + 8*w - 2]', '[1561, 1561, -5*w^2 + 3]', '[1577, 1577, 3*w^3 - 3*w^2 - 8*w + 6]', '[1579, 1579, 3*w^3 - 6*w^2 - 11*w + 19]', '[1579, 1579, 3*w^3 - 2*w^2 - 11*w + 7]', '[1579, 1579, -4*w^3 + 2*w^2 + 19*w - 8]', '[1579, 1579, w^3 + 3*w^2 - 5*w - 6]', '[1585, 1585, -3*w^3 + 7*w^2 + 4*w - 12]', '[1585, 1585, -2*w^3 + 5*w^2 + 6*w - 10]', '[1601, 1601, 3*w^3 - 15*w - 8]', '[1603, 1603, w^3 + 4*w^2 - 4*w - 7]', '[1607, 1607, 2*w^3 + w^2 - 6*w - 7]', '[1609, 1609, 3*w^3 - 13*w - 4]', '[1613, 1613, -w^3 + 3*w^2 + 5*w - 17]', '[1613, 1613, 2*w^3 + 3*w^2 - 8*w - 14]', '[1619, 1619, -w^3 + 3*w^2 + 9*w - 8]', '[1625, 65, -w^3 + 3*w^2 + 2*w]', '[1625, 65, -3*w^3 + 13*w + 3]', '[1625, 65, 4*w^3 - 2*w^2 - 18*w + 5]', '[1625, 65, -3*w^3 + 13*w - 2]', '[1625, 325, w^3 + 2*w^2 - 3*w - 10]', '[1625, 325, w^3 + 4*w^2 - 7*w - 15]', '[1625, 325, -w^3 - 4*w^2 + 2*w + 10]', '[1625, 325, 3*w^3 - w^2 - 15*w + 5]', '[1625, 1625, -4*w^2 + 2*w + 15]', '[1625, 1625, -3*w^3 + w^2 + 12*w - 4]', '[1625, 1625, 3*w^3 - 2*w^2 - 14*w + 2]', '[1625, 1625, -w^3 + 2*w^2 + 2*w - 10]', '[1637, 1637, w^3 + w^2 - 8*w - 4]', '[1643, 1643, 5*w^3 - 4*w^2 - 24*w + 17]', '[1648, 206, -4*w^3 + 6*w^2 + 22*w - 18]', '[1655, 1655, w^2 - 3*w + 5]', '[1655, 1655, 2*w^3 + 3*w^2 - 11*w - 11]', '[1655, 1655, -2*w^3 + 2*w^2 + 5*w - 7]', '[1655, 1655, w^3 - w^2 - 8*w]', '[1667, 1667, w^3 + 2*w^2 - 5*w - 2]', '[1667, 1667, 4*w^3 - w^2 - 19*w + 3]', '[1669, 1669, -3*w^3 + 2*w^2 + 13*w - 13]', '[1679, 1679, -3*w^2 + 3*w + 13]', '[1681, 41, 5*w^3 - 7*w^2 - 25*w + 27]', '[1681, 41, -2*w^3 + 4*w^2 + 11*w - 9]', '[1685, 1685, -w^3 + w^2 + 4]', '[1685, 1685, 2*w^3 - w^2 - 10*w + 10]', '[1693, 1693, 2*w^2 - 3*w - 11]', '[1693, 1693, 2*w^3 + 3*w^2 - 9*w - 9]', '[1711, 1711, -3*w^3 + 2*w^2 + 12*w - 4]', '[1711, 1711, -w^3 + 2*w^2 + 7*w - 12]', '[1715, 35, -3*w^3 + 2*w^2 + 12*w - 5]', '[1715, 35, 2*w^3 + w^2 - 8*w + 1]', '[1715, 1715, -2*w^3 + 3*w^2 + 9*w - 5]', '[1715, 1715, -3*w^3 + 2*w^2 + 10*w + 1]', '[1721, 1721, -w^3 + 2*w^2 - 7]', '[1723, 1723, -w^3 + 3*w^2 + 2*w - 12]', '[1723, 1723, 2*w^3 + 3*w^2 - 7*w - 6]', '[1729, 1729, w^3 + w^2 - 5*w - 11]', '[1729, 1729, -w^3 + 2*w^2 + 2*w - 11]', '[1733, 1733, -w^3 + w^2 + w - 7]', '[1733, 1733, -2*w^3 + 5*w^2 + 6*w - 17]', '[1735, 1735, -2*w^3 + 3*w^2 + 6*w - 10]', '[1735, 1735, -w^3 + 5*w^2 - 12]', '[1741, 1741, 2*w^3 + w^2 - 7*w - 9]', '[1744, 218, 2*w^2 + 6*w - 6]', '[1745, 1745, 2*w^3 - 4*w^2 - 7*w + 5]', '[1745, 1745, 4*w^3 - 5*w^2 - 10*w + 3]', '[1747, 1747, -w^3 + w^2 + 8*w - 4]', '[1757, 1757, -w^3 + 3*w^2 - 2*w - 4]', '[1759, 1759, w^3 - 3*w^2 - 6*w + 3]', '[1765, 1765, 3*w^3 + 3*w^2 - 16*w - 14]', '[1765, 1765, -w^3 + 3*w^2 + w - 10]', '[1765, 1765, 6*w^2 - 6*w - 17]', '[1765, 1765, 2*w^3 - w^2 - 12*w]', '[1769, 1769, 3*w^3 + 2*w^2 - 18*w - 7]', '[1769, 1769, -w^3 + 8*w + 3]', '[1777, 1777, 4*w^3 - 7*w^2 - 19*w + 26]', '[1781, 1781, -4*w^2 + w + 16]', '[1781, 1781, w^3 - 4*w^2 - 6*w + 16]', '[1787, 1787, 2*w^3 - 2*w^2 - 13*w + 1]', '[1789, 1789, 2*w^3 + 3*w^2 - 9*w - 17]', '[1789, 1789, -w^3 + 4*w^2 + 3*w - 13]', '[1792, 28, -4*w^2 + 8]', '[1799, 1799, 2*w^2 - 3*w - 13]', '[1801, 1801, 2*w^3 + w^2 - 9*w - 13]', '[1805, 1805, w^3 - 4*w^2 - 3*w + 9]', '[1805, 1805, w^3 - w^2 - 5]', '[1813, 1813, w^3 + 6]', '[1813, 1813, -2*w^3 - 3*w^2 + 13*w + 19]', '[1817, 1817, w^3 - 4*w^2 + 3*w + 11]', '[1817, 1817, w^3 + 3*w^2 - 6*w - 19]', '[1823, 1823, -3*w^3 + 4*w^2 + 12*w - 17]', '[1825, 365, 2*w^3 - 4*w^2 - 5*w + 11]', '[1825, 365, 2*w^3 - 3*w^2 - 7*w + 15]', '[1825, 1825, -w^3 - 4*w^2 + 6*w + 17]', '[1825, 1825, -2*w^3 + 4*w^2 + 9*w - 20]', '[1829, 1829, 4*w^3 - 2*w^2 - 17*w + 8]', '[1831, 1831, 4*w^3 - 3*w^2 - 15*w + 1]', '[1835, 1835, -w^3 + 2*w^2 + w + 3]', '[1835, 1835, w^2 - w - 10]', '[1835, 1835, w^3 - 2*w^2 - 8*w + 10]', '[1835, 1835, 3*w^3 + 2*w^2 - 13*w - 16]', '[1840, 230, -4*w^2 + 2*w + 10]', '[1840, 230, -2*w^3 + 10*w - 4]', '[1841, 1841, 2*w^3 + 3*w^2 - 5*w - 9]', '[1841, 1841, 3*w^3 - 3*w^2 - 7*w + 3]', '[1843, 1843, -w^3 - w^2 + 2*w + 7]', '[1843, 1843, w^3 - 4*w^2 - 4*w + 14]', '[1843, 1843, 2*w^2 + 3*w - 8]', '[1843, 1843, -4*w^3 + 7*w^2 + 20*w - 22]', '[1855, 1855, -w^3 + 4*w^2 + 5*w - 13]', '[1855, 1855, w^3 - 3*w^2 - 6*w + 15]', '[1861, 1861, -w^3 + 2*w^2 + w - 8]', '[1861, 1861, -2*w^3 + 3*w^2 + 7*w - 13]', '[1863, 69, 3*w^3 - 12*w - 6]', '[1871, 1871, 2*w^3 + w^2 - 9*w - 1]', '[1877, 1877, w^3 - 5*w^2 - 2*w + 18]', '[1879, 1879, -2*w^3 + 12*w + 1]', '[1883, 1883, 2*w^3 + w^2 - 2*w - 3]', '[1883, 1883, 3*w^3 - w^2 - 12*w - 2]', '[1885, 1885, -2*w^3 + 10*w - 5]', '[1885, 1885, -w^3 + 3*w^2 - 9]', '[1885, 1885, w^3 + 2*w^2 - 5*w - 1]', '[1885, 1885, -w^3 + 4*w^2 + 5*w - 10]', '[1885, 1885, -3*w^3 + 3*w^2 + 10*w - 5]', '[1885, 1885, -4*w^2 - w + 8]', '[1885, 1885, w^3 - w - 5]', '[1885, 1885, -2*w^2 + 5*w + 3]', '[1889, 1889, 5*w^2 - w - 9]', '[1891, 1891, -w^2 + w - 4]', '[1895, 1895, 3*w^3 - 2*w^2 - 7*w - 2]', '[1895, 1895, -2*w^3 + 6*w^2 - w - 11]', '[1895, 1895, -3*w^2 - w]', '[1895, 1895, 4*w^2 - 2*w - 5]', '[1897, 1897, 4*w^2 + 2*w - 9]', '[1901, 1901, 4*w^3 - 5*w^2 - 18*w + 23]', '[1909, 1909, w^3 + 2*w^2 - 6*w - 3]', '[1915, 1915, 2*w^3 - 2*w^2 - 12*w + 5]', '[1915, 1915, 2*w^3 + 2*w^2 - 11*w - 7]', '[1915, 1915, -w^3 + w^2 + 3*w + 5]', '[1915, 1915, -w^3 + w^2 - 6]', '[1933, 1933, 2*w^3 + 3*w^2 - 12*w - 11]', '[1937, 1937, -w^3 + 8*w - 1]', '[1937, 1937, 3*w^3 - 15*w - 11]', '[1937, 1937, 2*w^3 + w^2 - 8*w + 2]', '[1937, 1937, -6*w^3 - 2*w^2 + 27*w + 23]', '[1939, 1939, 2*w^3 + w^2 - 10*w - 13]', '[1945, 1945, 2*w^3 - 2*w^2 - 6*w + 9]', '[1945, 1945, -w^3 + w^2 + 6*w - 10]', '[1949, 1949, 4*w^2 + w - 17]', '[1957, 1957, 2*w^3 - 5*w^2 - 13*w + 16]', '[1961, 1961, -2*w^3 + 3*w^2 + 13*w - 11]', '[1961, 1961, -2*w^3 + w^2 + 12*w - 4]', '[1963, 1963, 2*w^3 - w^2 - 11*w - 4]', '[1963, 1963, -4*w^3 - w^2 + 18*w + 12]', '[1973, 1973, w^3 + 4*w^2 - 9*w - 17]', '[1975, 395, 4*w^3 - 8*w^2 - 5*w + 12]', '[1975, 395, w^3 + w + 5]', '[1975, 395, -w^3 + 2*w^2 + 5*w - 13]', '[1975, 395, 2*w^3 - 2*w^2 - 9*w]', '[1975, 1975, -w^3 - 5*w^2 + 7*w + 14]', '[1975, 1975, w^3 - w^2 - 4*w - 5]', '[1975, 1975, 4*w^3 - w^2 - 15*w - 8]', '[1975, 1975, -w^3 - 2*w^2 + 9*w + 5]', '[1987, 1987, -2*w^3 + 5*w^2 + 10*w - 17]', '[1987, 1987, -3*w^3 - w^2 + 12*w + 8]', '[1997, 1997, -2*w^3 + 3*w^2 + 8*w - 3]', '[1999, 1999, 2*w^3 + w^2 - 10*w - 2]', '[2000, 10, -4*w^3 + 2*w^2 + 18*w - 10]', '[2000, 10, -2*w^3 + 12*w + 2]', '[2000, 50, -4*w^2 - 2*w + 10]', '[2000, 50, -2*w^2 + 4*w + 10]', '[2000, 250, 2*w^2 + 2*w - 10]', '[2000, 250, -2*w^3 + 2*w^2 + 12*w - 6]', '[2003, 2003, w^3 + 4*w^2 - 8*w - 11]', '[2005, 2005, 2*w^3 - w^2 - 5*w - 5]', '[2005, 2005, w^2 - 4*w - 10]', '[2005, 2005, 5*w^3 - 4*w^2 - 16*w - 7]', '[2005, 2005, 3*w^3 + 5*w^2 - 16*w - 22]', '[2011, 2011, -3*w^3 + 2*w^2 + 15*w - 2]', '[2015, 2015, w^3 - w^2 - w + 8]', '[2015, 2015, -3*w^2 - 3*w + 10]', '[2015, 2015, -w^3 + 5*w + 8]', '[2015, 2015, w^2 - 10]', '[2017, 2017, 2*w^3 - 3*w^2 - 7*w + 14]', '[2025, 15, 3*w^3 - 12*w]', '[2025, 15, 3*w^3 - 3*w^2 - 9*w + 3]', '[2025, 75, 3*w^3 - 15*w - 9]', '[2025, 75, -3*w^3 + 15*w]', '[2027, 2027, 5*w^3 - 4*w^2 - 21*w + 16]', '[2027, 2027, -w^3 + w^2 + 8*w - 3]', '[2029, 2029, -w^3 - 2*w^2 + 7*w + 16]', '[2029, 2029, -w^2 - 4]', '[2039, 2039, -w^3 + w^2 + w - 9]', '[2063, 2063, 4*w^3 - 7*w^2 - 20*w + 23]', '[2063, 2063, -w^3 + 3*w^2 - 2*w - 9]', '[2065, 2065, -4*w^2 + 15]', '[2065, 2065, w^3 + 4*w^2 - w - 12]', '[2069, 2069, w^3 + 2*w^2 - w - 7]', '[2071, 2071, -2*w^3 + w^2 - w + 2]', '[2075, 415, 3*w^2 - 4*w - 1]', '[2075, 415, 3*w^3 - 12*w + 5]', '[2075, 2075, w^3 - 8*w - 2]', '[2075, 2075, -4*w^3 + 3*w^2 + 17*w - 10]', '[2081, 2081, w^3 - 4*w - 8]', '[2081, 2081, w^2 + 3*w - 8]', '[2089, 2089, 5*w^3 - 8*w^2 - 24*w + 29]', '[2089, 2089, -w^3 + 3*w^2 + 6*w - 2]', '[2093, 2093, -w^3 + 3*w^2 + 7*w - 12]', '[2093, 2093, -w^3 + 4*w^2 + 3*w - 12]', '[2095, 2095, w^3 - 5*w^2 + 2*w + 13]', '[2095, 2095, w^3 - 4*w^2 - 3*w + 10]', '[2099, 2099, -w^3 + 4*w^2 + 5*w - 12]', '[2105, 2105, 4*w^3 - 2*w^2 - 15*w - 4]', '[2105, 2105, -2*w^3 - 4*w^2 + 5*w + 5]', '[2105, 2105, 3*w^3 - 3*w^2 - 13*w + 5]', '[2105, 2105, -w^2 + 6*w + 7]', '[2111, 2111, -2*w^3 + 11*w - 4]', '[2111, 2111, -w^3 + 4*w^2 + 5*w - 11]', '[2117, 2117, -2*w^3 + 5*w^2 + 7*w - 16]', '[2117, 2117, -3*w^3 + w^2 + 17*w - 8]', '[2119, 2119, -w^3 - 6*w^2 + 10*w + 21]', '[2119, 2119, -3*w^3 + 4*w^2 + 13*w - 9]', '[2119, 2119, 4*w^3 - 4*w^2 - 15*w + 7]', '[2119, 2119, 3*w^2 - 4*w - 12]', '[2128, 266, 4*w^2 - 2*w - 14]', '[2129, 2129, 3*w^3 - w^2 - 15*w - 3]', '[2131, 2131, 4*w^3 - w^2 - 20*w + 3]', '[2131, 2131, -3*w^2 - 4*w + 9]', '[2135, 2135, -2*w^2 + 5*w + 5]', '[2135, 2135, 2*w^3 - 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8*w - 16]', '[2197, 169, w^2 - 2*w - 11]', '[2197, 2197, -2*w^3 - 3*w^2 + 9*w + 18]', '[2197, 2197, -w^3 - 4*w^2 + 3*w + 12]', '[2213, 2213, w^3 - 8*w - 1]', '[2215, 2215, -w^3 - 2*w]', '[2215, 2215, -w^3 + 4*w^2 - 3*w - 5]', '[2215, 2215, w^3 + 5*w^2 - 10]', '[2215, 2215, -w^3 + 6*w^2 - w - 9]', '[2215, 2215, -3*w^3 + 11*w^2 - w - 18]', '[2215, 2215, w^2 - 5*w - 9]', '[2215, 2215, -w^3 + 4*w^2 + 4*w - 10]', '[2215, 2215, -w^3 + 4*w^2 - w - 11]', '[2219, 2219, -w^3 + 2*w^2 - 2*w - 2]', '[2221, 2221, -w^3 + 4*w^2 + 4*w - 13]', '[2231, 2231, w^3 + 4*w^2 - 5*w - 16]', '[2231, 2231, -2*w^3 + 5*w^2 + 11*w - 19]', '[2231, 2231, -3*w^3 - 5*w^2 + 15*w + 28]', '[2231, 2231, -3*w^3 - 5*w^2 + 16*w + 24]', '[2237, 2237, w^3 + 3*w^2 - 4*w - 16]', '[2237, 2237, w^3 - w - 9]', '[2237, 2237, 3*w^3 - 2*w^2 - 12*w - 3]', '[2237, 2237, 3*w^2 - w - 18]', '[2239, 2239, w^3 - 5*w^2 - 5*w + 19]', '[2239, 2239, 4*w^3 - w^2 - 18*w + 1]', '[2243, 2243, w^3 + 2*w^2 - 3*w - 11]', '[2251, 2251, 2*w^3 - 4*w^2 - 7*w + 16]', '[2257, 2257, -4*w^3 + w^2 + 17*w - 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3]', '[9785, 9785, -2*w^3 + 3*w^2 + 16*w]', '[9787, 9787, -7*w^3 + 2*w^2 + 32*w - 4]', '[9791, 9791, 2*w^2 - 7*w - 6]', '[9793, 9793, 2*w^3 + 7*w^2 - 7*w - 16]', '[9803, 9803, 3*w^3 - 3*w^2 - 19*w - 1]', '[9803, 9803, -2*w^3 + 6*w^2 + 8*w - 17]', '[9805, 9805, 3*w^3 + w^2 - 13*w + 10]', '[9805, 9805, w^3 - 6*w + 10]', '[9805, 9805, -2*w^3 + 2*w^2 + 3]', '[9805, 9805, -3*w^3 + 2*w^2 + 7*w + 7]', '[9815, 9815, 3*w^3 + 3*w^2 - 9*w - 13]', '[9815, 9815, -w^3 + w^2 - 2*w - 10]', '[9815, 9815, -5*w^3 + 3*w^2 + 20*w - 2]', '[9815, 9815, -w^3 - 6*w^2 + 8*w + 20]', '[9817, 9817, -5*w^3 - 3*w^2 + 21*w + 16]', '[9821, 9821, -2*w^3 + 9*w^2 + 4*w - 32]', '[9827, 9827, -3*w^3 + 5*w^2 + 17*w - 23]', '[9829, 9829, -4*w^3 + 3*w^2 + 13*w - 3]', '[9839, 9839, 3*w^3 - 3*w^2 - 15*w + 2]', '[9841, 9841, -4*w^3 + 3*w^2 + 20*w - 3]', '[9841, 9841, 6*w^3 - w^2 - 27*w - 6]', '[9851, 9851, -5*w^3 + 3*w^2 + 21*w - 7]', '[9851, 9851, 3*w^2 + 2*w - 23]', '[9851, 9851, -4*w^3 + 7*w^2 + 13*w - 21]', '[9851, 9851, -w^3 + 3*w^2 - 2*w - 12]', '[9853, 9853, -3*w^3 + 18*w + 2]', '[9857, 9857, w^3 + 7*w^2 - 6*w - 31]', '[9857, 9857, 3*w^3 - 2*w^2 - 7*w - 8]', '[9859, 9859, 3*w^3 - 18*w - 4]', '[9863, 9863, w^3 + w^2 - w + 8]', '[9863, 9863, 2*w^3 - 6*w^2 - 5*w + 2]', '[9865, 9865, -4*w^3 + 3*w^2 + 16*w + 5]', '[9865, 9865, -9*w^3 + 3*w^2 + 33*w + 19]', '[9872, 1234, -4*w^3 + 2*w^2 + 14*w - 6]', '[9875, 395, -3*w^3 + 8*w + 8]', '[9875, 395, w^3 + 2*w^2 - 2*w + 5]', '[9875, 395, 2*w^3 - w^2 - 14*w + 5]', '[9875, 395, w^3 + 5*w^2 - 11*w - 11]', '[9875, 1975, -5*w^3 + w^2 + 13*w + 5]', '[9875, 1975, -7*w^3 + 33*w + 10]', '[9875, 1975, 7*w^2 + 6*w - 5]', '[9875, 1975, 5*w^3 + 2*w^2 - 24*w - 10]', '[9875, 9875, -2*w^3 - w^2 + 2*w + 6]', '[9875, 9875, -w^3 + 2*w^2 - 4*w - 5]', '[9875, 9875, 7*w^3 + 6*w^2 - 39*w - 37]', '[9875, 9875, -2*w^3 + 3*w^2 + 4*w + 5]', '[9883, 9883, -2*w^3 + 2*w^2 + 14*w - 7]', '[9887, 9887, 2*w^3 + 3*w^2 - 9*w - 24]', '[9887, 9887, -3*w^3 + 8*w^2 + 16*w - 31]', '[9893, 9893, -w^3 - 2*w^2 - 6]', '[9893, 9893, -w^3 + 10*w + 2]', '[9893, 9893, -2*w^3 - 2*w^2 + 6*w + 13]', '[9893, 9893, 2*w^3 + 4*w^2 - 14*w - 11]', '[9899, 9899, -4*w^3 + 4*w^2 + 16*w - 3]', '[9901, 9901, -5*w^2 - 4*w + 17]', '[9901, 9901, 5*w^3 - w^2 - 21*w - 6]', '[9904, 1238, -4*w^3 + 8*w^2 + 18*w - 22]', '[9919, 9919, 7*w^2 - 2*w - 6]', '[9919, 9919, -6*w^3 + 2*w^2 + 27*w - 22]', '[9929, 9929, -5*w^3 - w^2 + 26*w + 6]', '[9929, 9929, 8*w^3 - 6*w^2 - 36*w + 21]', '[9931, 9931, 3*w^3 - w^2 - 11*w - 12]', '[9935, 9935, 3*w^3 - 3*w^2 - 14*w + 1]', '[9935, 9935, 5*w^3 - 2*w^2 - 19*w + 10]', '[9935, 9935, -w^3 - 7*w^2 + 15*w + 26]', '[9935, 9935, -w^3 - 6*w^2 + 5*w + 15]', '[9937, 9937, -2*w^3 + 5*w^2 + w - 13]', '[9943, 9943, 6*w^2 - 7*w - 21]', '[9943, 9943, 4*w^2 + 2*w - 19]', '[9947, 203, -4*w^3 - 2*w^2 + 16*w + 19]', '[9947, 203, -w^3 + 3*w^2 + 11*w - 4]', '[9947, 9947, 3*w^3 - 19*w + 3]', '[9947, 9947, 4*w^3 - 3*w^2 - 16*w - 4]', '[9949, 9949, -7*w^3 + 7*w^2 + 30*w - 34]', '[9953, 9953, 2*w^3 + 3*w^2 - 9*w - 4]', '[9953, 9953, -4*w^3 + 5*w^2 + 16*w - 27]', '[9953, 9953, -4*w^3 + 5*w^2 + 17*w - 26]', '[9953, 9953, -3*w^3 + 7*w^2 + 13*w - 24]', '[9959, 9959, -6*w^3 + 3*w^2 + 26*w + 2]', '[9959, 9959, 6*w^3 + w^2 - 27*w - 16]', '[9961, 9961, 7*w^2 + 3*w - 12]', '[9971, 767, 3*w^3 - 11*w + 11]', '[9971, 767, -w^3 - 2*w^2 + 6*w + 18]', '[9971, 9971, 2*w^3 - 3*w^2 - 5*w + 18]', '[9971, 9971, w^3 + 5*w^2 - 16]', '[9973, 9973, -4*w^3 + 2*w^2 + 15*w - 3]', '[9985, 9985, 3*w^3 - 11*w^2 - 2*w + 19]', '[9985, 9985, 3*w^3 - 4*w^2 - 5*w + 10]', '[9989, 9989, 2*w^3 + 4*w^2 - 12*w - 11]', '[9991, 9991, -2*w^3 + 4*w^2 + 11*w - 4]', '[9991, 9991, 6*w^3 - 25*w + 4]', '[9991, 9991, -3*w^3 + 3*w^2 + 18*w - 8]', '[9991, 9991, -2*w^3 + 6*w^2 + 13*w - 11]', '[9995, 9995, w^3 + 2*w^2 - 10]', '[9995, 9995, 3*w^3 - 2*w^2 - 11*w - 9]', '[10000, 10, 10]', '[10000, 50, -2*w^3 + 6*w^2 + 4*w - 20]', '[10000, 50, -4*w^3 + 6*w^2 + 14*w - 20]', '[10000, 50, 2*w^2 - 6*w - 14]', '[10000, 50, -2*w^3 + 2*w - 8]', '[10000, 250, 2*w^3 - 8*w + 10]', '[10000, 250, 4*w^2 - 8*w - 10]', '[10000, 1250, -2*w^3 + 4*w + 8]', '[10000, 1250, 2*w^3 + 2*w^2 - 10*w]'], 'label': '4.4.16997.1', 'narrow_class_no': 1, 'primes': ['[5, 5, w]', '[5, 5, -w^2 + w + 2]', '[7, 7, -w^2 + 2]', '[13, 13, -w^2 + 3]', '[13, 13, w^2 - w - 4]', '[16, 2, 2]', '[19, 19, -w^2 + w + 1]', '[23, 23, -w^3 + 4*w + 2]', '[25, 5, -w^3 + w^2 + 3*w - 1]', '[29, 29, w^3 - w^2 - 4*w + 1]', '[29, 29, -w + 3]', '[31, 31, -w^3 + w^2 + 5*w - 2]', '[37, 37, w^3 - 4*w - 1]', '[37, 37, w^3 - 3*w + 1]', '[53, 53, -w^3 + 2*w^2 + 4*w - 6]', '[59, 59, w^2 + w - 4]', '[61, 61, -2*w^2 + w + 8]', '[73, 73, -w^3 + 5*w - 1]', '[79, 79, 2*w^2 + w - 6]', '[79, 79, 2*w^3 - w^2 - 9*w + 3]', '[81, 3, -3]', '[83, 83, -w^3 + w^2 + 3*w - 4]', '[97, 97, -w^3 + 6*w + 2]', '[97, 97, -2*w^3 + w^2 + 10*w - 1]', '[97, 97, 3*w^3 - 4*w^2 - 15*w + 13]', '[97, 97, w^3 - w^2 - 6*w + 2]', '[103, 103, -2*w^3 + 3*w^2 + 11*w - 9]', '[109, 109, w^2 + 3*w - 3]', '[137, 137, -w^2 + 7]', '[149, 149, w^3 - 2*w^2 - 5*w + 4]', '[149, 149, w^3 + 2*w^2 - 6*w - 7]', '[151, 151, w^3 + w^2 - 5*w - 3]', '[163, 163, w^3 - 3*w - 4]', '[163, 163, -w^3 + 6*w - 3]', '[167, 167, w^3 - 2*w^2 - 6*w + 4]', '[169, 13, w^2 + 2*w - 4]', '[191, 191, w^3 - w^2 - 5*w - 2]', '[191, 191, 2*w^3 - 9*w - 2]', '[197, 197, w^3 - 4*w + 4]', '[211, 211, -w^3 + 2*w^2 + 6*w - 8]', '[223, 223, -w^3 + 3*w^2 + 4*w - 6]', '[229, 229, w^3 - w^2 - 5*w - 1]', '[251, 251, 2*w^3 - 2*w^2 - 7*w + 3]', '[257, 257, 3*w^2 - 14]', '[263, 263, w^2 - 3*w - 1]', '[263, 263, w^2 - 2*w - 7]', '[269, 269, -w^3 + w^2 + 2*w - 4]', '[269, 269, 2*w^3 - 11*w - 1]', '[271, 271, -w^3 + w^2 + 4*w - 7]', '[277, 277, w^3 - w^2 - 3*w + 8]', '[311, 311, w^3 + 2*w^2 - 7*w - 11]', '[311, 311, -3*w^2 - 2*w + 8]', '[317, 317, -2*w^3 + 2*w^2 + 7*w - 4]', '[331, 331, w^2 - w - 8]', '[331, 331, 3*w^3 - 2*w^2 - 12*w + 9]', '[337, 337, -2*w^3 + 2*w^2 + 11*w - 8]', '[343, 7, w^3 - 3*w^2 - 4*w + 11]', '[347, 347, -2*w^3 + 2*w^2 + 9*w - 4]', '[349, 349, -w^3 + 2*w^2 + 2*w - 6]', '[353, 353, 2*w^2 - w - 12]', '[353, 353, 2*w^3 - w^2 - 9*w - 1]', '[367, 367, -2*w^3 + w^2 + 10*w - 6]', '[367, 367, 2*w^3 - 11*w - 3]', '[379, 379, -3*w - 1]', '[379, 379, w^3 - 2*w - 3]', '[383, 383, -w^3 + 2*w^2 + 4*w - 11]', '[383, 383, -w^3 - w^2 + 7*w + 4]', '[389, 389, 2*w^3 - w^2 - 11*w + 4]', '[401, 401, w^3 + 2*w^2 - 7*w - 6]', '[401, 401, 2*w^3 - 11*w - 6]', '[419, 419, -2*w^3 + w^2 + 8*w - 1]', '[421, 421, -w^3 + 3*w^2 + 3*w - 12]', '[421, 421, -w^3 - 2*w^2 + 2*w + 6]', '[433, 433, w^3 - 2*w^2 - 6*w + 11]', '[433, 433, w^2 - 8]', '[439, 439, -w^3 + 3*w^2 + 3*w - 7]', '[443, 443, w^3 - w^2 - 2*w - 4]', '[443, 443, 2*w^3 + w^2 - 7*w - 2]', '[443, 443, 2*w^3 - w^2 - 8*w + 2]', '[443, 443, -w^2 - 2]', '[467, 467, 3*w^3 - 5*w^2 - 15*w + 19]', '[467, 467, 2*w^3 - 3*w^2 - 8*w + 13]', '[467, 467, -w^3 + 2*w^2 + 3*w - 9]', '[467, 467, -w^3 + 3*w^2 + 3*w - 8]', '[479, 479, -w^3 - 3*w^2 + 5*w + 13]', '[479, 479, -w^3 + w^2 + w - 4]', '[487, 487, 3*w^3 - w^2 - 13*w - 2]', '[491, 491, w^2 + w - 9]', '[499, 499, -3*w^3 + 3*w^2 + 13*w - 7]', '[503, 503, 2*w^2 + w - 9]', '[509, 509, -2*w^2 - 3*w + 6]', '[509, 509, -w^3 + w^2 - 4]', '[521, 521, -3*w^2 + w + 12]', '[523, 523, 2*w^3 - 8*w - 3]', '[529, 23, 2*w^3 - w^2 - 6*w - 1]', '[541, 541, -w^3 + w^2 + 7*w - 4]', '[547, 547, 2*w^3 - 3*w^2 - 9*w + 7]', '[557, 557, 3*w^2 - 2*w - 9]', '[557, 557, w^3 - 6*w - 7]', '[563, 563, -2*w^3 + w^2 + 6*w - 6]', '[577, 577, -w^3 + 4*w^2 + 2*w - 13]', '[587, 587, w^2 - 2*w + 3]', '[587, 587, w^2 + 2*w - 6]', '[593, 593, -2*w^3 + 2*w^2 + 11*w - 3]', '[599, 599, w^3 + 3*w^2 - 6*w - 12]', '[601, 601, -2*w^3 + w^2 + 9*w + 2]', '[607, 607, -w^3 + 3*w^2 + 4*w - 9]', '[617, 617, -2*w^3 + w^2 + 7*w - 3]', '[619, 619, -2*w^3 + 4*w^2 + 9*w - 11]', '[631, 631, 3*w^2 - w - 7]', '[631, 631, -w^3 - w^2 + 6*w + 1]', '[641, 641, -w^3 + 2*w^2 + 5*w - 1]', '[641, 641, -w^3 + 2*w^2 + 2*w - 7]', '[643, 643, -3*w^3 + w^2 + 14*w - 4]', '[647, 647, -3*w^3 + 5*w^2 + 14*w - 18]', '[647, 647, -w^3 + 7*w + 2]', '[647, 647, -2*w^3 + 7*w - 1]', '[647, 647, 2*w^3 - w^2 - 10*w - 1]', '[653, 653, -2*w^3 - w^2 + 11*w + 4]', '[659, 659, -w^3 - w^2 + 5*w - 1]', '[673, 673, -w^3 + w^2 + 7*w - 2]', '[673, 673, -w^3 + w^2 + 2*w - 8]', '[683, 683, 2*w^3 - 11*w - 8]', '[683, 683, 2*w^3 - 7*w - 3]', '[701, 701, 2*w^3 - 4*w^2 - 10*w + 17]', '[727, 727, -w^3 + w^2 + 4*w - 8]', '[727, 727, 3*w^2 - 11]', '[739, 739, 2*w^3 + 3*w^2 - 8*w - 13]', '[743, 743, 2*w^2 + w - 12]', '[743, 743, 3*w^2 - 2*w - 14]', '[751, 751, w^3 + w^2 - 3*w - 7]', '[757, 757, -2*w^3 + 10*w - 1]', '[761, 761, -2*w^3 + w^2 + 7*w - 1]', '[761, 761, 3*w^2 + w - 7]', '[773, 773, -2*w^3 + 2*w^2 + 8*w - 1]', '[797, 797, -2*w^3 + w^2 + 9*w + 3]', '[797, 797, 3*w^3 - 14*w - 8]', '[809, 809, 5*w^3 - 5*w^2 - 24*w + 16]', '[821, 821, -4*w^3 + 3*w^2 + 18*w - 9]', '[821, 821, w^3 - w - 3]', '[823, 823, 3*w^2 + w - 8]', '[829, 829, -2*w^3 + 3*w^2 + 10*w - 7]', '[829, 829, 3*w^2 - 2*w - 16]', '[841, 29, 2*w^2 + w - 11]', '[853, 853, 3*w^3 - 2*w^2 - 14*w + 3]', '[853, 853, 3*w^3 - 5*w^2 - 14*w + 17]', '[857, 857, 3*w^2 - w - 8]', '[857, 857, 3*w^3 - w^2 - 13*w + 3]', '[859, 859, w^3 - 3*w^2 - 6*w + 12]', '[877, 877, w^3 + 2*w^2 - 5*w - 4]', '[877, 877, w^2 - w - 9]', '[881, 881, w^3 + 2*w^2 - 4*w - 12]', '[881, 881, w^2 - 4*w - 4]', '[883, 883, -3*w^3 + 2*w^2 + 11*w - 8]', '[887, 887, -2*w^3 + w^2 + 6*w - 1]', '[911, 911, 3*w^2 - w - 17]', '[911, 911, 2*w^3 - 2*w^2 - 12*w + 3]', '[919, 919, 5*w^3 - 6*w^2 - 22*w + 24]', '[919, 919, -2*w^3 + w^2 + 6*w - 7]', '[929, 929, 2*w^3 - 7*w - 1]', '[937, 937, -w^3 - w^2 + 8*w - 2]', '[947, 947, 3*w^3 + w^2 - 15*w - 6]', '[947, 947, -2*w^3 + 9*w + 9]', '[953, 953, w^3 - 2*w^2 - 6*w + 1]', '[977, 977, w^3 - w^2 - 3*w + 9]', '[977, 977, w^3 + w^2 - 3*w - 8]', '[983, 983, w^3 - 5*w - 7]', '[991, 991, -w^3 + 2*w^2 + 2*w - 8]', '[991, 991, w^2 + 4*w - 1]', '[997, 997, 2*w^3 + w^2 - 12*w - 8]']}
• 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': [5, -1, -6, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 16997, 'disc_rad': 16997, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[4, 1]]], [5, [[2, 1], [1, 2]]], [7, [[3, 1], [1, 1]]], [11, [[4, 1]]], [13, [[2, 1], [1, 2]]], [17, [[4, 1]]], [19, [[3, 1], [1, 1]]], [23, [0]], [29, [[2, 1], [1, 2]]], [31, [[3, 1], [1, 1]]], [37, [[2, 1], [1, 2]]], [41, [[2, 2]]], [43, [[4, 1]]], [47, [[4, 1]]], [53, [[3, 1], [1, 1]]], [59, [[3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 130.3725431216251, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.16997.1', 'local_algs': ['23.2.1.2', '23.2.0.1', 'm739.1.2.0', 'm739.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [23, 739], 'rd': 11.41807966, 'regulator': {'__RealLiteral__': 0, 'data': '6.66578568548', 'prec': 44}, 'res': {'gal': ['256,0,-95808,0,1072320,0,-4827252,0,11099977,0,-13977148,0,9763690,0,-3725572,0,760147,0,-81808,0,4450,0,-112,0,1'], 'sib': ['-1,0,16,0,-12,0,1', '-204,-235,190,89,-42,-3,1', '1076311,206186,-195826,-20538,9815,542,-176,-4,1', '16,240,1156,1832,-673,-3822,-2083,572,502,-22,-39,0,1', '41616,0,-211949,0,251268,0,-53880,0,3748,0,-104,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a - 1 \\)', '\\( a^{2} - a - 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}