Hilbert modular form data - 4.4.8069.1-17.1-b

Formats: - HTML - YAML - JSON - 2024-06-03T23:56:33.675868

• 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': 4, 'disc': 8069, 'field_bad_primes': [8069], 'field_label': '4.4.8069.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.8069.1-17.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [17], 'level_ideal': '[17, 17, w^3 + w^2 - 4*w - 2]', 'level_label': '17.1', 'level_norm': 17, 'parallel_weight': 2, 'short_label': '17.1-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[17, 17, w^3 + w^2 - 4*w - 2]', -1]], 'hecke_eigenvalues': ['e', 'e^2 + 2*e - 2', '-e^3 - 4*e^2 + 1', '-e^3 - 5*e^2 - 4*e + 1', '2*e^3 + 8*e^2 + 2*e - 4', 1, '-2*e^3 - 8*e^2 + 9', 'e^2 + 4*e - 1', '2*e^3 + 7*e^2 - 3*e - 8', 'e^2 + 4*e - 3', 'e^3 + 4*e^2 - 2*e - 6', '2*e^3 + 7*e^2 - 3*e - 8', 'e^3 + 4*e^2 - 3*e - 7', '-4*e^2 - 11*e + 6', '-2*e^3 - 9*e^2 - 7*e + 2', '3*e^3 + 14*e^2 + 5*e - 12', '-6*e^3 - 24*e^2 + 22', '3*e^3 + 7*e^2 - 13*e - 8', '-3*e^3 - 12*e^2 + 13', '-e^3 - 3*e^2 + 2*e - 4', '3*e^3 + 14*e^2 + 10*e - 6', '5*e^3 + 18*e^2 - e - 17', '-3*e^3 - 11*e^2 + 2*e + 3', '-e^3 - 4*e^2 - e - 1', '3*e^3 + 13*e^2 + e - 12', '-e^3 - 6*e^2 - e + 10', '-10*e^3 - 40*e^2 - e + 33', 'e^3 + 2*e^2 - 3*e + 3', '-7*e^3 - 26*e^2 + 2*e + 26', '-e^3 - 4*e^2 - 4*e + 4', '-6*e - 9', '-7*e^3 - 26*e^2 + 14*e + 33', '3*e^3 + 10*e^2 - 4*e - 9', '2*e^3 + 13*e^2 + 21*e - 14', '11*e^3 + 43*e^2 + e - 37', '8*e^3 + 32*e^2 - e - 33', 'e^3 + 10*e^2 + 13*e - 21', '5*e^3 + 20*e^2 + 6*e - 25', '-5*e^2 - 12*e + 4', '2*e^3 + 10*e^2 + 5*e - 6', '8*e^3 + 31*e^2 + 3*e - 27', '-e^3 - 3*e^2 - 11', '-6*e - 11', 'e^3 + 3*e^2 - 3*e + 12', '-5*e^3 - 16*e^2 + 7*e + 6', '-3*e^2 - 16*e - 14', '-9*e^3 - 35*e^2 - 9*e + 15', '5*e^3 + 24*e^2 + 17*e - 21', '-4*e^3 - 11*e^2 + 17*e + 18', '5*e^3 + 22*e^2 + 11*e - 18', '-e^3 - 10*e^2 - 15*e + 8', '-2*e^3 - 11*e^2 - 11*e - 1', '-12*e^3 - 52*e^2 - 15*e + 35', '-6*e^3 - 25*e^2 - 11*e + 9', '13*e^3 + 53*e^2 + 5*e - 43', '-3*e^3 - 11*e^2 + 2*e + 20', '11*e^3 + 47*e^2 + 21*e - 29', '-e^3 - 3*e^2 + e', 'e^3 - 3*e^2 - 16*e + 7', '6*e^3 + 29*e^2 + 12*e - 33', '-4*e^3 - 16*e^2 + 2*e + 31', '-4*e^2 - 9*e + 2', '-5*e^3 - 25*e^2 - 14*e + 27', '2*e^3 + 11*e^2 + 10*e - 23', '9*e^3 + 32*e^2 - 6*e - 38', '-4*e^3 - 10*e^2 + 16*e + 10', '-7*e^3 - 27*e^2 - 9*e', '-2*e^3 - 4*e^2 + 13*e + 15', '-4*e^3 - 19*e^2 - 14*e + 31', '6*e^3 + 23*e^2 + 5*e - 15', '9*e^3 + 34*e^2 - 5*e - 21', '-5*e^3 - 14*e^2 + 9*e + 6', '2*e^3 + 3*e^2 - 8*e + 10', '-2*e^3 - e^2 + 28*e + 7', '8*e^3 + 31*e^2 + 6*e - 4', '2*e^3 + 7*e^2 - 7*e - 16', '-9*e^3 - 36*e^2 - 10*e + 12', '5*e^3 + 24*e^2 + 15*e - 34', '-12*e^3 - 51*e^2 - 11*e + 24', '-e^3 - 4*e^2 + 3*e + 13', '8*e^3 + 33*e^2 + 4*e - 35', '-3*e^3 - 9*e^2 + 13*e + 22', '4*e^3 + 16*e^2 - 23', '6*e^3 + 29*e^2 + 19*e - 28', '-5*e^3 - 16*e^2 + 8*e + 9', '-3*e^3 - 17*e^2 - 26*e - 3', '12*e^3 + 47*e^2 + 3*e - 48', '-15*e^3 - 63*e^2 - 13*e + 42', '-7*e^3 - 22*e^2 + 14*e + 12', '9*e^3 + 41*e^2 + 22*e - 30', '2*e^3 + 10*e^2 - 7*e - 27', '13*e^3 + 49*e^2 + e - 27', '16*e^3 + 62*e^2 + 11*e - 40', '-18*e^3 - 71*e^2 - 16*e + 42', '3*e^3 + 4*e^2 - 17*e - 3', '-9*e^3 - 40*e^2 + 54', '14*e^3 + 54*e^2 + 2*e - 47', '6*e^3 + 34*e^2 + 30*e - 22', '-8*e^3 - 25*e^2 + 27*e + 30', 'e^3 + 5*e^2 - 3', '-6*e^3 - 20*e^2 + 19*e + 36', '7*e^3 + 32*e^2 + 3*e - 30', '-7*e^3 - 37*e^2 - 25*e + 26', '4*e^3 + 18*e^2 + 13*e - 3', '-6*e^3 - 16*e^2 + 32*e + 21', '-11*e^3 - 45*e^2 - 11*e + 20', '-3*e^3 - 11*e^2 - 8*e + 10', '-13*e^3 - 56*e^2 - 14*e + 46', '-6*e^3 - 27*e^2 - 27*e + 15', '2*e^3 + 11*e^2 + 15*e - 15', '3*e^3 + 16*e^2 + 18*e - 17', '-5*e^3 - 20*e^2 + 11*e + 37', '-e^2 - 3*e + 14', '-10*e^3 - 48*e^2 - 35*e + 24', '6*e^3 + 26*e^2 + 6*e - 6', '-6*e^3 - 16*e^2 + 6*e - 14', '-10*e^3 - 40*e^2 + 3*e + 52', '-2*e^3 - e^2 + 12*e - 3', '11*e^3 + 45*e^2 + 5*e - 35', '10*e^3 + 40*e^2 - 11*e - 58', '-7*e^3 - 23*e^2 + 9*e + 24', '-5*e^3 - 19*e^2 + 7*e + 33', '-24*e^3 - 96*e^2 - 15*e + 73', '4*e^3 + 17*e^2 + 8*e - 21', '2*e^3 + 10*e^2 + 4*e - 27', '21*e^3 + 83*e^2 + 15*e - 66', '-2*e^3 - 12*e^2 - 22*e + 2', '-8*e^3 - 36*e^2 - 17*e + 22', '11*e^3 + 42*e^2 + 5*e - 45', '-14*e^3 - 52*e^2 + 13*e + 39', '10*e^3 + 35*e^2 - 10*e - 61', '-8*e^3 - 27*e^2 + 22*e + 33', '6*e^2 + 9*e - 21', '4*e^3 + 23*e^2 + 28*e - 3', '-7*e^3 - 35*e^2 - 23*e + 12', '-2*e^3 - 13*e^2 - 20*e - 15', '-e^3 - 4*e^2 + 6*e - 9', '-13*e^3 - 63*e^2 - 36*e + 33', '-2*e^3 + 2*e^2 + 35*e - 9', '-3*e^3 - 12*e^2 - 6*e + 24', '9*e^3 + 38*e^2 + 9*e - 16', '14*e^3 + 49*e^2 - 27*e - 54', '-11*e^3 - 35*e^2 + 18*e + 28', '2*e^3 + 17*e^2 + 19*e - 41', '3*e^3 + 13*e^2 + 9*e + 22', '-15*e^3 - 58*e^2 + 18*e + 77', '-7*e^3 - 36*e^2 - 22*e + 36', '-e^3 - 5*e^2 + e + 12', '6*e^3 + 18*e^2 - 15*e + 1', '-4*e^3 - 6*e^2 + 25*e + 3', '-2*e^3 - 12*e^2 - 25*e - 19', '6*e^3 + 19*e^2 - 11*e - 33', '-9*e^3 - 30*e^2 - e - 9', '-6*e^3 - 10*e^2 + 40*e + 33', '-3*e^3 - 6*e^2 + 12*e - 15', '-15*e^3 - 65*e^2 - 18*e + 42', '3*e^3 + 5*e^2 - 3*e + 21', '6*e^3 + 19*e^2 - 3*e - 21', '17*e^3 + 76*e^2 + 28*e - 65', '13*e^3 + 47*e^2 - 10*e - 38', '-7*e^3 - 24*e^2 + 13', '-13*e^2 - 37*e + 5', '4*e^3 + 12*e^2 - 6*e + 3', '17*e^3 + 71*e^2 + 4*e - 57', '-9*e^3 - 45*e^2 - 20*e + 59'], 'hecke_polynomial': 'x^4 + 5*x^3 + 4*x^2 - 4*x - 3', 'label': '4.4.8069.1-17.1-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 8069, 'ideals': ['[1, 1, 1]', '[5, 5, w^3 - 4*w]', '[7, 7, w + 1]', '[7, 7, -w^3 + 4*w - 1]', '[13, 13, -w^2 + 3]', '[16, 2, 2]', '[17, 17, w^3 + w^2 - 4*w - 2]', '[17, 17, -w^3 + 5*w - 2]', '[19, 19, -w^2 - w + 4]', '[19, 19, -w^2 - w + 1]', '[25, 25, -w^3 - w^2 + 3*w + 2]', '[29, 29, 2*w^3 - w^2 - 9*w + 5]', '[35, 35, 2*w - 1]', '[35, 35, -w^3 + 5*w - 3]', '[41, 41, -w^3 + w^2 + 5*w - 3]', '[43, 43, w^3 - w^2 - 4*w + 2]', '[43, 43, w^3 - 6*w]', '[47, 47, -w^3 - w^2 + 5*w]', '[49, 7, w^3 - 6*w + 2]', '[49, 7, w^2 + 2*w - 2]', '[49, 49, -w^2 - 2*w + 3]', '[49, 49, w^3 - 3*w - 2]', '[59, 59, 2*w^3 - 8*w + 3]', '[65, 65, w^3 - 6*w + 1]', '[67, 67, w^2 - w - 4]', '[79, 79, w^3 - w^2 - 4*w + 1]', '[80, 10, 2*w^3 - 8*w]', '[81, 3, -3]', '[85, 85, w^3 + w^2 - 6*w - 3]', '[85, 85, w^3 - w^2 - 6*w + 5]', '[91, 91, -w^3 + w^2 + 6*w - 4]', '[91, 91, -w^3 - w^2 + 3*w + 3]', '[95, 95, w^3 - w^2 - 5*w + 2]', '[95, 95, -2*w^3 + 9*w - 3]', '[97, 97, w^3 + w^2 - 5*w + 1]', '[107, 107, -2*w^3 + 3*w^2 + 10*w - 12]', '[109, 109, 2*w^3 - w^2 - 9*w + 3]', '[112, 14, 2*w + 2]', '[112, 14, -2*w^3 + 8*w - 2]', '[119, 119, -w^2 + w + 5]', '[119, 119, -2*w^3 + 10*w - 3]', '[119, 119, -2*w^3 + 8*w - 1]', '[119, 119, -w^3 + 4*w + 3]', '[125, 5, -3*w^3 - w^2 + 12*w + 1]', '[125, 125, -w^3 + 2*w^2 + 5*w - 6]', '[127, 127, -2*w^3 + w^2 + 10*w - 8]', '[133, 133, -w^3 - w^2 + 6*w - 1]', '[133, 133, 2*w^2 - 2*w - 3]', '[133, 133, -w^3 - 2*w^2 + 3*w + 4]', '[133, 133, -w + 4]', '[137, 137, -w^3 + w^2 + 3*w - 5]', '[139, 139, w^3 - w^2 - 5*w + 1]', '[145, 145, 2*w^3 + w^2 - 9*w - 6]', '[149, 149, 2*w^2 - w - 6]', '[149, 149, 2*w^3 + w^2 - 9*w]', '[163, 163, w^3 - 5*w - 3]', '[163, 163, 2*w^3 - 7*w]', '[169, 169, w^3 - w^2 - 5*w + 8]', '[173, 173, -2*w^3 + 11*w - 3]', '[173, 173, -w^3 + w^2 + 4*w - 8]', '[175, 175, w^2 - 2*w - 3]', '[175, 175, 2*w^3 - w^2 - 8*w + 4]', '[179, 179, 2*w^3 - w^2 - 8*w + 5]', '[181, 181, 2*w^3 - w^2 - 8*w]', '[181, 181, 2*w^3 - 9*w - 3]', '[191, 191, 2*w^2 - 5]', '[191, 191, -2*w^2 - w + 10]', '[193, 193, w^3 + w^2 - 3*w - 4]', '[193, 193, -w^3 + 2*w^2 + 3*w - 3]', '[197, 197, -2*w^3 + 9*w - 4]', '[197, 197, w^2 - 7]', '[199, 199, 3*w^3 - 13*w + 1]', '[199, 199, w^3 + 2*w^2 - 5*w - 7]', '[203, 203, -3*w^3 + 14*w - 3]', '[203, 203, -2*w^2 + 11]', '[205, 205, 2*w^3 + w^2 - 8*w - 4]', '[208, 26, -2*w^2 + 6]', '[215, 215, -4*w^3 - 2*w^2 + 19*w + 4]', '[215, 215, -2*w^3 + 7*w + 3]', '[221, 221, -w - 4]', '[221, 221, -2*w^3 + 2*w^2 + 9*w - 7]', '[227, 227, -3*w^3 + w^2 + 13*w - 4]', '[227, 227, -w^3 + 2*w^2 + 7*w - 6]', '[235, 235, w^3 + w^2 - 8*w - 2]', '[241, 241, -2*w^3 + 7*w - 1]', '[245, 35, 2*w^3 + 2*w^2 - 8*w - 3]', '[245, 35, w^3 - w^2 - 3*w + 6]', '[245, 245, -w^3 - 2*w^2 + 4*w + 3]', '[245, 245, -2*w^3 + 7*w - 2]', '[247, 247, 2*w^2 + w - 2]', '[247, 247, 2*w^3 + w^2 - 8*w + 2]', '[256, 4, 4]', '[257, 257, -2*w^3 + w^2 + 7*w - 5]', '[257, 257, 2*w^3 - w^2 - 7*w + 2]', '[263, 263, -w^3 + 7*w - 3]', '[269, 269, -2*w^3 + 2*w^2 + 11*w - 8]', '[271, 271, w^2 + 3*w - 2]', '[271, 271, w^2 + 2*w - 7]', '[272, 34, 2*w^3 + 2*w^2 - 8*w - 4]', '[272, 34, -2*w^3 + 10*w - 4]', '[277, 277, -2*w^3 + 11*w - 2]', '[281, 281, 2*w^3 - 11*w + 1]', '[283, 283, 2*w^3 - 9*w + 5]', '[283, 283, -2*w^3 + w^2 + 11*w - 7]', '[287, 287, -w^3 - 2*w^2 + 3*w + 7]', '[287, 287, -w^3 + w^2 + 7*w - 2]', '[289, 17, 2*w^3 - w^2 - 10*w + 2]', '[289, 17, -w^3 + 2*w^2 + 4*w - 4]', '[289, 289, 2*w^3 + w^2 - 8*w - 5]', '[289, 289, -2*w^3 - w^2 + 8*w - 3]', '[293, 293, -2*w^3 - w^2 + 7*w + 3]', '[295, 295, -w^3 + 6*w + 4]', '[301, 301, 2*w^3 - w^2 - 11*w - 1]', '[301, 301, w^3 + w^2 - 3*w - 5]', '[301, 301, 3*w^3 + 2*w^2 - 13*w - 4]', '[301, 301, w^3 - 7*w + 1]', '[304, 38, -2*w^2 - 2*w + 8]', '[304, 38, -2*w^2 - 2*w + 2]', '[307, 307, -3*w^3 + 2*w^2 + 13*w - 9]', '[311, 311, -w^3 + w^2 + 3*w - 7]', '[313, 313, -w^3 + 2*w^2 + 3*w - 2]', '[313, 313, w^2 - w - 8]', '[317, 317, -2*w^3 - w^2 + 9*w - 1]', '[323, 323, w^3 - 7*w + 2]', '[323, 323, -2*w^3 + w^2 + 6*w - 1]', '[323, 323, w^3 + 2*w^2 - 4*w - 4]', '[323, 323, w^2 + 2]', '[325, 325, w^3 - 2*w + 4]', '[329, 329, 3*w + 2]', '[329, 329, -3*w^3 - w^2 + 10*w + 1]', '[331, 331, w^3 + 2*w^2 - 5*w - 3]', '[335, 335, -3*w^3 - w^2 + 15*w]', '[337, 337, w^3 + 2*w^2 - 6*w - 4]', '[337, 337, w^3 - 2*w^2 - 6*w + 5]', '[343, 7, -2*w^3 - 3*w^2 + 6*w + 5]', '[343, 7, w^3 + 3*w^2 - 2]', '[343, 49, 2*w^3 - w^2 - 9*w + 1]', '[343, 49, w^3 + 2*w^2 - 5*w - 6]', '[343, 343, w^3 + w^2 - 7*w - 3]', '[343, 343, 3*w^3 - w^2 - 13*w + 5]', '[347, 347, 2*w^3 + 2*w^2 - 9*w - 3]', '[347, 347, -2*w^3 + w^2 + 7*w - 4]', '[349, 349, w^2 - 2*w - 4]', '[353, 353, -w^3 + 2*w^2 + 2*w - 6]', '[359, 359, -w^3 + w^2 + 7*w - 6]', '[359, 359, -w^2 - w - 2]', '[361, 19, 2*w^3 - w^2 - 11*w]', '[361, 19, 2*w^2 - w - 9]', '[361, 361, -w^3 - w^2 + 3*w + 6]', '[361, 361, -3*w^3 - w^2 + 14*w]', '[367, 367, -2*w^3 + 2*w^2 + 8*w - 5]', '[373, 373, w^3 + w^2 - 2*w - 4]', '[377, 377, -4*w^3 + 3*w^2 + 20*w - 16]', '[379, 379, 2*w^3 - w^2 - 11*w + 4]', '[389, 389, 3*w^2 + w - 11]', '[395, 395, -3*w^3 + 11*w + 3]', '[397, 397, 3*w^3 - 13*w + 5]', '[400, 50, -2*w^3 - 2*w^2 + 6*w + 4]', '[401, 401, w - 5]', '[405, 15, -3*w^3 + 12*w]', '[409, 409, 3*w^3 - 12*w + 4]', '[409, 409, 3*w^3 + 2*w^2 - 14*w - 4]', '[413, 413, 4*w^3 + 2*w^2 - 15*w + 1]', '[413, 413, -w^3 + 2*w - 7]', '[421, 421, 2*w^3 - w^2 - 10*w + 1]', '[421, 421, w^3 + 2*w^2 - 5*w - 4]', '[425, 425, -w^3 - 2*w^2 + 5*w + 5]', '[425, 425, -w^3 + w^2 + 7*w - 3]', '[439, 439, -2*w^3 + 10*w - 5]', '[443, 443, -2*w^3 + 12*w - 5]', '[443, 443, -4*w^3 + w^2 + 18*w - 9]', '[443, 443, -2*w^3 + w^2 + 7*w - 9]', '[443, 443, 3*w^3 + 2*w^2 - 14*w - 5]', '[449, 449, w^3 + 2*w^2 - 2*w - 6]', '[449, 449, -2*w^3 + w^2 + 11*w - 5]', '[455, 455, 2*w^3 + 2*w^2 - 9*w - 5]', '[455, 455, 2*w^3 - w^2 - 10*w]', '[461, 461, 2*w^3 + 2*w^2 - 9*w - 4]', '[464, 58, 4*w^3 - 2*w^2 - 18*w + 10]', '[467, 467, -w^3 + w^2 + 7*w - 5]', '[469, 469, 3*w^3 - 14*w + 4]', '[469, 469, w^3 - 5*w - 4]', '[475, 475, -w^3 + 2*w^2 + 4*w - 3]', '[475, 475, -3*w^3 - w^2 + 12*w + 4]', '[485, 485, -w^2 + 4*w + 2]', '[487, 487, 2*w^2 + 4*w - 7]', '[491, 491, -w^3 + w^2 + 7*w - 4]', '[493, 493, w^3 - 4*w^2 - 4*w + 18]', '[493, 493, 4*w^3 - w^2 - 20*w + 5]', '[503, 503, 2*w^3 + w^2 - 9*w + 2]', '[521, 521, w^2 - 3*w - 3]', '[523, 523, -w^3 + 2*w^2 + 5*w - 4]', '[523, 523, -w^3 + 8*w - 5]', '[533, 533, -3*w^3 + w^2 + 14*w - 9]', '[535, 535, 2*w^2 + 2*w - 9]', '[545, 545, -4*w^3 - w^2 + 17*w + 6]', '[551, 551, -5*w^3 + 5*w^2 + 24*w - 23]', '[551, 551, w^3 + 2*w^2 - 3*w - 8]', '[553, 553, w^3 - 8*w]', '[553, 553, 2*w^3 + w^2 - 7*w - 4]', '[559, 559, 2*w^3 - 11*w + 6]', '[559, 559, 3*w^3 - 12*w + 1]', '[560, 70, 4*w - 2]', '[560, 70, -2*w^3 + 10*w - 6]', '[563, 563, w^3 + 3*w^2 - w - 8]', '[563, 563, w^3 - 2*w^2 - 8*w + 4]', '[563, 563, -w^3 + w^2 + 2*w - 5]', '[563, 563, -3*w^3 - w^2 + 10*w - 2]', '[567, 21, -3*w - 3]', '[567, 21, 3*w^3 - 12*w + 3]', '[577, 577, 3*w^3 - 16*w]', '[587, 587, w^3 + 2*w^2 - 6]', '[587, 587, -w^3 + 4*w - 6]', '[595, 595, w^3 - 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15*w - 8]', '[1393, 1393, 5*w^3 - w^2 - 25*w + 6]', '[1399, 1399, -3*w^3 + 2*w^2 + 11*w - 7]', '[1405, 1405, -6*w^3 - 3*w^2 + 29*w + 7]', '[1409, 1409, -w^3 + w^2 + 8*w - 4]', '[1415, 1415, -w^2 + 3*w + 5]', '[1415, 1415, 2*w^3 + 3*w^2 - 11*w - 8]', '[1417, 1417, 4*w^3 - w^2 - 20*w + 10]', '[1421, 203, 5*w^2 - w - 20]', '[1421, 203, -4*w^3 - w^2 + 15*w]', '[1421, 1421, 5*w^3 - 2*w^2 - 22*w + 6]', '[1421, 1421, -2*w^3 + 5*w^2 + 10*w - 20]', '[1423, 1423, -w^3 + 3*w^2 + 7*w - 17]', '[1423, 1423, w^3 + w^2 - 8*w - 4]', '[1427, 1427, -2*w^3 + w^2 + 12*w - 4]', '[1427, 1427, 4*w^3 - w^2 - 16*w + 2]', '[1435, 1435, w^3 - 4*w^2 - 5*w + 14]', '[1435, 1435, w^3 - w^2 - w + 5]', '[1445, 85, 2*w^3 + 2*w^2 - 11*w + 1]', '[1445, 85, 2*w^3 - 5*w - 4]', '[1445, 1445, -w^3 - 3]', '[1445, 1445, -4*w^3 + 16*w - 5]', '[1447, 1447, 3*w^2 + 5*w - 6]', '[1451, 1451, -3*w^3 + w^2 + 10*w - 6]', '[1456, 182, -2*w^3 + 2*w^2 + 12*w - 8]', '[1456, 182, -2*w^3 - 2*w^2 + 6*w + 6]', '[1459, 1459, -4*w^3 + w^2 + 17*w - 6]', '[1465, 1465, 4*w^3 - w^2 - 19*w - 2]', '[1475, 1475, -w^3 - 5*w^2 - 3*w + 6]', '[1481, 1481, -2*w^3 + 3*w^2 + 7*w - 13]', '[1483, 1483, -4*w^3 + 2*w^2 + 17*w - 9]', '[1487, 1487, -2*w^3 + 2*w^2 + 7*w - 12]', '[1487, 1487, 2*w^3 + 3*w^2 - 9*w - 16]', '[1489, 1489, -2*w^3 + 13*w - 6]', '[1489, 1489, -2*w^3 + 5*w^2 + 11*w - 16]', '[1493, 1493, -3*w^3 + w^2 + 11*w - 4]', '[1493, 1493, -2*w^3 - 4*w^2 + 4*w + 9]', '[1499, 1499, w^3 + 3*w^2 - 5*w - 5]', '[1501, 1501, 3*w^3 - w^2 - 11*w + 5]', '[1501, 1501, 2*w^2 + w + 2]', '[1505, 1505, w^3 - 2*w^2 - 4*w - 2]', '[1505, 1505, 2*w^3 + w^2 - 6*w - 5]', '[1505, 1505, -w^3 + 3*w^2 - 2*w - 4]', '[1505, 1505, -w^3 + 4*w^2 + 2*w - 10]', '[1520, 190, 2*w^3 - 2*w^2 - 10*w + 4]', '[1520, 190, -4*w^3 + 18*w - 6]', '[1523, 1523, 3*w^3 - 4*w^2 - 12*w + 12]', '[1523, 1523, 2*w^3 + 3*w^2 - 8*w - 5]', '[1523, 1523, 4*w^3 + w^2 - 15*w + 1]', '[1523, 1523, 2*w^2 - 2*w - 9]', '[1535, 1535, 2*w^3 + w^2 - 8*w - 9]', '[1539, 57, 3*w^2 + 3*w - 12]', '[1539, 57, 3*w^2 + 3*w - 3]', '[1543, 1543, -3*w^3 + 9*w - 2]', '[1547, 1547, -w^3 - 3*w^2 + 6*w + 8]', '[1547, 1547, -3*w^2 - 2*w + 14]', '[1547, 1547, -2*w^3 + w^2 + 12*w - 5]', '[1547, 1547, -w^3 - 4*w^2 + 2*w + 8]', '[1549, 1549, w^3 + 3*w^2 - 4*w - 8]', '[1552, 194, 2*w^3 + 2*w^2 - 10*w + 2]', '[1555, 1555, -4*w^3 - w^2 + 18*w - 2]', '[1565, 1565, -2*w^3 - 2*w^2 + 7*w - 4]', '[1565, 1565, -7*w^3 - w^2 + 31*w]', '[1571, 1571, -3*w^3 - w^2 + 11*w + 5]', '[1571, 1571, 4*w^3 - w^2 - 18*w + 11]', '[1585, 1585, 2*w^3 + w^2 - 13*w - 4]', '[1589, 1589, -2*w^3 - 2*w^2 + 9*w + 12]', '[1589, 1589, 4*w^2 + 6*w - 5]', '[1589, 1589, -5*w^3 - w^2 + 24*w - 1]', '[1589, 1589, -2*w^3 - 5*w^2 + 5*w + 13]', '[1601, 1601, -4*w^3 - 2*w^2 + 21*w + 7]', '[1607, 1607, w^3 - 4*w^2 - 4*w + 14]', '[1613, 1613, w^3 + 3*w^2 - 6*w - 5]', '[1615, 1615, 2*w^3 - 5*w + 6]', '[1615, 1615, -2*w^2 + 13]', '[1615, 1615, 2*w^3 + 2*w^2 - 4*w - 5]', '[1615, 1615, w^3 + 3*w^2 - 5*w - 9]', '[1621, 1621, -2*w^3 + 3*w^2 + 9*w - 8]', '[1625, 65, -2*w^3 + w^2 + 13*w - 1]', '[1625, 1625, 4*w^3 + 2*w^2 - 17*w]', '[1627, 1627, -3*w^3 + w^2 + 10*w - 2]', '[1627, 1627, 3*w^3 - 14*w + 7]', '[1645, 1645, 2*w^2 - 2*w + 3]', '[1645, 1645, -3*w^3 + w^2 + 5*w + 2]', '[1649, 1649, -w^2 + 2*w - 5]', '[1649, 1649, 3*w^2 + 3*w - 2]', '[1651, 1651, -5*w^3 + 6*w^2 + 23*w - 25]', '[1655, 1655, -2*w^3 - w^2 + 14*w + 1]', '[1657, 1657, -4*w^3 + 2*w^2 + 19*w - 16]', '[1663, 1663, 2*w^3 + 2*w^2 - 7*w - 8]', '[1669, 1669, -4*w^3 + w^2 + 19*w - 10]', '[1669, 1669, -4*w^3 + 16*w - 1]', '[1669, 1669, -3*w^3 - 4*w^2 + 10*w + 5]', '[1669, 1669, -w^2 - 4*w + 10]', '[1675, 1675, 2*w^3 + 3*w^2 - 8*w - 7]', '[1681, 1681, -w^3 - 3*w^2 + 5*w - 2]', '[1685, 1685, -4*w^3 - 2*w^2 + 23*w + 2]', '[1685, 1685, -3*w^3 - 2*w^2 + 11*w + 6]', '[1687, 1687, w^2 + 2*w + 4]', '[1687, 1687, -4*w^3 - 3*w^2 + 16*w + 1]', '[1693, 1693, 3*w^3 - w^2 - 16*w + 13]', '[1693, 1693, -w^2 - 4]', '[1697, 1697, 4*w^3 + 2*w^2 - 17*w - 9]', '[1697, 1697, 2*w^3 + 3*w^2 - 8*w - 6]', '[1709, 1709, -w^3 + 4*w^2 + 4*w - 12]', '[1711, 1711, -w^3 - w^2 + 4*w - 5]', '[1712, 214, -4*w^3 + 6*w^2 + 20*w - 24]', '[1715, 35, 2*w^3 + 3*w^2 - 6*w + 2]', '[1715, 35, -w^3 - 3*w^2 + 9]', '[1715, 245, -4*w^3 + 17*w - 8]', '[1715, 245, w^3 + w^2 - 2*w + 5]', '[1715, 1715, w^3 + w^2 - 10*w + 4]', '[1715, 1715, 2*w^2 + 5*w - 3]', '[1729, 1729, -4*w^3 + 21*w - 3]', '[1729, 1729, -2*w^3 + 3*w^2 + 7*w - 5]', '[1729, 1729, w^3 - 4*w^2 - 3*w + 12]', '[1729, 1729, 2*w^3 - 7*w + 9]', '[1735, 1735, -4*w^3 - w^2 + 23*w + 3]', '[1735, 1735, w^3 - w^2 - 3*w - 4]', '[1741, 1741, -2*w^3 + w^2 + 6*w - 9]', '[1741, 1741, 2*w^2 - 4*w - 5]', '[1744, 218, 4*w^3 - 2*w^2 - 18*w + 6]', '[1745, 1745, -4*w^3 - 2*w^2 + 20*w + 1]', '[1747, 1747, w^2 + 5*w - 2]', '[1747, 1747, w^3 - 4*w^2 - 3*w + 11]', '[1753, 1753, 3*w^3 + 2*w^2 - 16*w]', '[1759, 1759, -2*w^3 - 3*w^2 + 10*w + 9]', '[1763, 1763, -w^3 + 3*w^2 + 4*w - 4]', '[1763, 1763, w^2 + w - 10]', '[1765, 1765, -w^3 + 3*w^2 + 9*w - 12]', '[1777, 1777, w^3 + 3*w^2 - 5*w - 6]', '[1777, 1777, w^2 + 2*w - 11]', '[1777, 1777, w^3 + 3*w^2 - 6*w - 7]', '[1777, 1777, 2*w^2 + 3*w - 11]', '[1781, 1781, -w^3 + 3*w^2 + 8*w - 15]', '[1787, 1787, -w^3 + 9*w - 1]', '[1787, 1787, -w^3 + 4*w^2 + 4*w - 13]', '[1789, 1789, -3*w^3 - 2*w^2 + 13*w - 1]', '[1792, 28, 4*w + 4]', '[1792, 28, -4*w^3 + 16*w - 4]', '[1795, 1795, -5*w^3 - w^2 + 19*w + 2]', '[1795, 1795, w^3 + 3*w^2 - 6*w - 6]', '[1799, 1799, 3*w^3 + 2*w^2 - 15*w]', '[1799, 1799, 2*w^3 - 8*w + 9]', '[1799, 1799, -3*w^3 - 2*w^2 + 12*w - 3]', '[1799, 1799, w^3 - 4*w - 6]', '[1801, 1801, w^3 - 6*w - 6]', '[1801, 1801, -4*w^3 + w^2 + 13*w - 11]', '[1805, 95, -9*w^3 - 3*w^2 + 39*w + 8]', '[1805, 95, w^3 - 7]', '[1805, 1805, 4*w^3 - w^2 - 16*w + 9]', '[1805, 1805, w^3 - 3*w^2 - 2*w + 11]', '[1807, 1807, 3*w^3 + w^2 - 14*w + 3]', '[1819, 1819, 5*w^3 - w^2 - 21*w + 14]', '[1819, 1819, -3*w^3 + w^2 + 10*w - 5]', '[1823, 1823, 4*w^3 + 3*w^2 - 19*w - 9]', '[1835, 1835, 3*w^3 - 10*w - 6]', '[1841, 1841, -w^3 - 3*w^2 + 5*w + 8]', '[1841, 1841, -2*w^3 + 2*w^2 + 9*w - 2]', '[1843, 1843, -2*w^2 - 5*w + 7]', '[1843, 1843, -3*w^3 - 5*w^2 + 10*w + 4]', '[1847, 1847, -w^3 + w^2 - 4]', '[1849, 43, -5*w^3 + 3*w^2 + 23*w - 12]', '[1849, 43, -4*w^3 + 3*w^2 + 21*w - 10]', '[1849, 1849, 3*w^3 + 2*w^2 - 10*w - 5]', '[1849, 1849, w - 7]', '[1853, 1853, w^3 + 4*w^2 - 6*w - 14]', '[1853, 1853, -6*w^3 - w^2 + 28*w - 1]', '[1861, 1861, -2*w^3 + 2*w^2 + 11*w - 3]', '[1861, 1861, 2*w^2 - 2*w - 15]', '[1861, 1861, -w^2 - w - 4]', '[1861, 1861, -3*w^3 - 3*w^2 + 13*w + 5]', '[1865, 1865, -2*w^3 + 2*w^2 + 9*w - 1]', '[1871, 1871, -3*w^3 + 3*w^2 + 13*w - 9]', '[1873, 1873, -2*w^3 - 4*w^2 + 6*w + 9]', '[1877, 1877, 6*w^3 - 3*w^2 - 28*w + 13]', '[1877, 1877, -w^3 + 2*w^2 + 2*w - 9]', '[1879, 1879, w^2 - 4*w - 4]', '[1879, 1879, -3*w^3 + 12*w - 11]', '[1883, 1883, -2*w^3 + 3*w^2 + 13*w - 6]', '[1883, 1883, -w^3 - 5*w^2 + 2*w + 17]', '[1885, 1885, 2*w^3 + 4*w^2 - 10*w - 15]', '[1895, 1895, -5*w^3 - 3*w^2 + 23*w + 8]', '[1897, 1897, -3*w^3 - 4*w^2 + 10*w + 6]', '[1897, 1897, w^3 + 4*w^2 + w - 2]', '[1897, 1897, 3*w^3 - 3*w^2 - 14*w + 10]', '[1897, 1897, w^3 + 3*w^2 - 5*w - 7]', '[1904, 238, -2*w^2 + 2*w + 10]', '[1904, 238, -4*w^3 + 20*w - 6]', '[1904, 238, -4*w^3 + 16*w - 2]', '[1904, 238, -2*w^3 + 8*w + 6]', '[1913, 1913, 3*w^3 - 14*w + 8]', '[1913, 1913, w^2 - 3*w - 6]', '[1927, 1927, -2*w^3 - 3*w^2 + 9*w + 5]', '[1933, 1933, -w^3 + 2*w^2 - 2*w - 3]', '[1933, 1933, w^3 + w^2 - 5*w - 9]', '[1937, 1937, 3*w^3 + w^2 - 13*w + 7]', '[1937, 1937, 2*w^3 - 2*w^2 - 10*w + 3]', '[1939, 1939, 4*w^3 - w^2 - 19*w]', '[1939, 1939, 3*w^3 + 3*w^2 - 14*w - 9]', '[1943, 1943, 2*w^3 - w^2 - 8*w + 12]', '[1945, 1945, -4*w^3 + w^2 + 21*w - 4]', '[1949, 1949, 3*w^3 - 15*w + 7]', '[1949, 1949, -w^3 - w^2 + 3*w - 5]', '[1949, 1949, 4*w^3 - 16*w + 3]', '[1949, 1949, 2*w^2 - 3*w - 7]', '[1951, 1951, 4*w^3 + 3*w^2 - 20*w - 6]', '[1967, 1967, 4*w^3 - w^2 - 20*w - 1]', '[1967, 1967, 4*w^3 + 3*w^2 - 18*w - 8]', '[1975, 1975, 4*w^3 + w^2 - 14*w]', '[1979, 1979, 3*w^3 - 2*w^2 - 14*w + 17]', '[1979, 1979, 3*w^3 - 14*w + 9]', '[1981, 1981, 4*w^3 + w^2 - 14*w + 3]', '[1981, 1981, -3*w^3 + 2*w^2 + 14*w - 5]', '[1981, 1981, -2*w^3 + w^2 + 6*w - 10]', '[1981, 1981, -4*w^2 + 15]', '[1985, 1985, -2*w^3 - w^2 + 12*w + 7]', '[1993, 1993, 5*w^3 + 2*w^2 - 21*w - 7]', '[2000, 10, -6*w^3 - 2*w^2 + 24*w + 2]', '[2000, 250, -2*w^3 + 4*w^2 + 10*w - 12]', '[2003, 2003, w^3 + 4*w^2 - 6*w - 4]', '[2005, 2005, -4*w^3 + w^2 + 15*w - 1]', '[2009, 287, 3*w^2 - 2*w - 12]', '[2009, 287, -2*w^3 + 5*w^2 + 8*w - 18]', '[2009, 2009, 4*w^3 - w^2 - 16*w + 3]', '[2009, 2009, -3*w^3 + w^2 + 10*w - 11]', '[2021, 2021, 4*w^3 + w^2 - 19*w + 2]', '[2021, 2021, -4*w^3 + 3*w^2 + 16*w - 11]', '[2023, 119, w^3 + 2*w^2 - 3*w + 3]', '[2023, 119, w^2 + 5*w - 3]', '[2023, 119, -3*w^3 - w^2 + 13*w - 5]', '[2023, 119, -w^3 - 2*w^2 + w + 8]', '[2023, 2023, -w^3 - 2*w^2 + 7*w + 8]', '[2023, 2023, -5*w^3 + 2*w^2 + 22*w - 10]', '[2023, 2023, -3*w^3 + w^2 + 9*w - 2]', '[2023, 2023, w^3 - 2*w^2 - w + 7]', '[2025, 75, 3*w^3 + 3*w^2 - 9*w - 6]', '[2029, 2029, -3*w^3 + w^2 + 12*w + 4]', '[2032, 254, -4*w^3 + 2*w^2 + 20*w - 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7*w - 11]', '[9725, 9725, -3*w^3 + 7*w - 15]', '[9737, 9737, -6*w^2 + w + 22]', '[9737, 9737, -8*w^3 + 4*w^2 + 33*w - 28]', '[9745, 9745, -2*w^3 - 3*w^2 + 14*w + 9]', '[9745, 9745, -5*w^3 + 24*w + 8]', '[9745, 9745, -6*w^3 - w^2 + 22*w]', '[9745, 9745, -6*w^3 - 3*w^2 + 31*w + 1]', '[9751, 1393, 5*w^3 + 5*w^2 - 20*w - 11]', '[9751, 1393, -6*w^3 - 5*w^2 + 30*w + 15]', '[9751, 1393, -10*w^3 + 3*w^2 + 44*w - 11]', '[9751, 1393, -w^3 + 6*w^2 + 4*w - 16]', '[9751, 9751, -9*w^3 + w^2 + 40*w + 2]', '[9751, 9751, -2*w^3 - 5*w^2 + 7*w + 12]', '[9751, 9751, -5*w^3 - 5*w^2 + 28*w + 14]', '[9751, 9751, -6*w^3 + 3*w^2 + 25*w - 16]', '[9755, 9755, -12*w^3 - 4*w^2 + 62*w + 9]', '[9761, 9761, 2*w^3 + 3*w^2 - 6*w - 17]', '[9761, 9761, 3*w^3 - 7*w^2 - 15*w + 21]', '[9761, 9761, -2*w^3 + 3*w^2 + 6*w - 18]', '[9761, 9761, -w^3 + w^2 + 11*w - 7]', '[9767, 9767, 4*w^3 - 3*w^2 - 18*w + 6]', '[9767, 9767, -9*w^3 + 3*w^2 + 43*w - 21]', '[9773, 9773, 2*w^3 + 3*w^2 - 4*w - 11]', '[9773, 9773, 6*w^3 + 2*w^2 - 27*w + 2]', '[9776, 1222, -2*w^3 + 4*w^2 + 8*w - 4]', '[9781, 9781, -6*w^3 + 2*w^2 + 25*w - 12]', '[9787, 9787, 7*w^3 + w^2 - 25*w + 11]', '[9791, 9791, -w^3 + w^2 + 11*w - 4]', '[9791, 9791, -4*w^3 + 21*w - 12]', '[9793, 9793, w^3 - w^2 - 5*w + 14]', '[9793, 9793, -4*w^3 - 2*w^2 + 19*w - 4]', '[9803, 9803, w^3 + 5*w^2 - 7*w - 8]', '[9808, 1226, 8*w^3 - 34*w]', '[9809, 9809, 7*w^3 + 3*w^2 - 30*w - 13]', '[9809, 9809, -14*w^3 - 4*w^2 + 61*w + 7]', '[9811, 9811, -4*w^3 + 4*w^2 + 19*w - 12]', '[9811, 9811, 4*w^3 - 5*w^2 - 16*w + 13]', '[9817, 9817, -4*w^3 + 4*w^2 + 17*w - 10]', '[9833, 9833, -3*w^3 - 2*w^2 + 17*w - 6]', '[9835, 9835, 2*w^3 - 2*w^2 - 7*w - 5]', '[9835, 9835, 2*w^3 + 2*w^2 - 5*w - 12]', '[9857, 9857, -2*w^3 + 4*w^2 + 11*w - 26]', '[9863, 9863, -w^3 + 4*w^2 + 9*w - 3]', '[9863, 9863, -3*w^3 - 5*w^2 + 11*w + 11]', '[9871, 9871, 3*w^3 - 3*w^2 - 14*w + 1]', '[9872, 1234, -6*w^3 + 2*w^2 + 28*w - 4]', '[9872, 1234, -8*w^3 + 34*w - 8]', '[9875, 395, w^3 + 2*w^2 + w - 12]', '[9875, 9875, -w^3 - w^2 + 7*w - 10]', '[9881, 9881, 3*w^3 + 3*w^2 - 9*w - 10]', '[9883, 9883, -4*w^3 + 3*w^2 + 20*w - 7]', '[9893, 9893, 3*w^3 + 3*w^2 - 19*w + 3]', '[9893, 9893, 7*w^3 - 3*w^2 - 34*w + 22]', '[9895, 9895, -5*w^3 + 2*w^2 + 19*w - 10]', '[9895, 9895, w^3 - 2*w^2 + w + 8]', '[9899, 9899, w^3 + 2*w^2 + 5*w - 2]', '[9899, 9899, w^3 + 5*w^2 - 4*w - 11]', '[9901, 9901, -6*w^3 + 2*w^2 + 24*w - 15]', '[9901, 9901, -2*w^3 + 3*w - 8]', '[9901, 9901, 3*w^3 - 19*w + 4]', '[9901, 9901, 3*w^3 + w^2 - 9*w - 10]', '[9904, 1238, -6*w^3 + 24*w - 4]', '[9905, 9905, -4*w^3 + 2*w^2 + 19*w - 22]', '[9905, 9905, 2*w^3 + 2*w^2 - w - 9]', '[9905, 9905, 3*w^3 - 5*w^2 - 19*w + 31]', '[9905, 9905, w^2 - 5*w + 11]', '[9907, 9907, 4*w^3 + 3*w^2 - 20*w + 1]', '[9907, 9907, -2*w^3 + 4*w^2 + 9*w - 6]', '[9919, 9919, 5*w^2 - 2*w - 23]', '[9919, 9919, 7*w^3 - w^2 - 30*w + 6]', '[9925, 9925, -6*w^2 - 10*w + 9]', '[9929, 9929, -7*w^3 + 5*w^2 + 37*w - 19]', '[9929, 9929, 5*w^3 - 2*w^2 - 19*w + 8]', '[9931, 9931, 2*w^3 + 3*w^2 - 6*w - 16]', '[9937, 9937, -6*w^3 + 2*w^2 + 23*w - 16]', '[9937, 9937, -5*w^3 + 2*w^2 + 26*w - 22]', '[9937, 9937, -3*w^3 - 4*w^2 + 8*w - 4]', '[9937, 9937, -2*w^3 + 2*w^2 + 2*w - 7]', '[9941, 9941, -8*w^3 + 5*w^2 + 37*w - 34]', '[9947, 203, -9*w^3 - 6*w^2 + 35*w + 4]', '[9947, 203, -w^3 + 2*w^2 + 10*w + 6]', '[9947, 1421, 5*w^3 + 4*w^2 - 21*w - 20]', '[9947, 1421, 11*w^3 - 4*w^2 - 54*w + 24]', '[9947, 9947, -w^3 + 9*w^2 + 6*w - 46]', '[9947, 9947, 9*w^3 + w^2 - 44*w + 4]', '[9949, 9949, -6*w^3 + w^2 + 26*w - 19]', '[9949, 9949, w^2 + 2*w - 14]', '[9961, 9961, 3*w^3 - 2*w^2 - 17*w - 5]', '[9961, 9961, 7*w^3 + 3*w^2 - 31*w - 1]', '[9961, 9961, w^3 + 5*w^2 - 5*w - 16]', '[9961, 9961, 7*w^3 - 6*w^2 - 33*w + 25]', '[9965, 9965, -14*w^3 - w^2 + 66*w + 9]', '[9967, 9967, -w^3 + 3*w^2 + 11*w - 12]', '[9971, 9971, 9*w^3 - 5*w^2 - 39*w + 32]', '[9979, 9979, w^3 - 3*w^2 - 12*w + 15]', '[9979, 9979, -4*w^3 - 6*w^2 + 13*w + 11]', '[9979, 9979, 5*w^3 - w^2 - 24*w + 15]', '[9979, 9979, 6*w^3 + 4*w^2 - 15*w + 5]', '[9983, 9983, -w^3 + 2*w^2 + 11*w - 10]', '[9983, 9983, -w^3 + 7*w^2 + 11*w - 17]', '[9989, 9989, 4*w^3 + w^2 - 18*w - 11]', '[9989, 9989, -4*w^3 - 5*w^2 + 16*w + 13]', '[9989, 9989, 7*w^3 + 3*w^2 - 34*w - 2]', '[9989, 9989, -3*w^3 + 3*w^2 + 18*w - 2]', '[9997, 9997, 2*w^3 + 2*w^2 - 5*w - 15]', '[9997, 9997, -10*w^3 + 7*w^2 + 45*w - 39]', '[10000, 10, 10]', '[10000, 1250, 2*w^3 + 2*w^2 - 4*w - 10]'], 'label': '4.4.8069.1', 'narrow_class_no': 2, 'primes': ['[5, 5, w^3 - 4*w]', '[7, 7, w + 1]', '[7, 7, -w^3 + 4*w - 1]', '[13, 13, -w^2 + 3]', '[16, 2, 2]', '[17, 17, w^3 + w^2 - 4*w - 2]', '[17, 17, -w^3 + 5*w - 2]', '[19, 19, -w^2 - w + 4]', '[19, 19, -w^2 - w + 1]', '[29, 29, 2*w^3 - w^2 - 9*w + 5]', '[41, 41, -w^3 + w^2 + 5*w - 3]', '[43, 43, w^3 - w^2 - 4*w + 2]', '[43, 43, w^3 - 6*w]', '[47, 47, -w^3 - w^2 + 5*w]', '[49, 7, w^2 + 2*w - 2]', '[59, 59, 2*w^3 - 8*w + 3]', '[67, 67, w^2 - w - 4]', '[79, 79, w^3 - w^2 - 4*w + 1]', '[81, 3, -3]', '[97, 97, w^3 + w^2 - 5*w + 1]', '[107, 107, -2*w^3 + 3*w^2 + 10*w - 12]', '[109, 109, 2*w^3 - w^2 - 9*w + 3]', '[125, 5, -3*w^3 - w^2 + 12*w + 1]', '[127, 127, -2*w^3 + w^2 + 10*w - 8]', '[137, 137, -w^3 + w^2 + 3*w - 5]', '[139, 139, w^3 - w^2 - 5*w + 1]', '[149, 149, 2*w^2 - w - 6]', '[149, 149, 2*w^3 + w^2 - 9*w]', '[163, 163, w^3 - 5*w - 3]', '[163, 163, 2*w^3 - 7*w]', '[173, 173, -2*w^3 + 11*w - 3]', '[173, 173, -w^3 + w^2 + 4*w - 8]', '[179, 179, 2*w^3 - w^2 - 8*w + 5]', '[181, 181, 2*w^3 - w^2 - 8*w]', '[181, 181, 2*w^3 - 9*w - 3]', '[191, 191, 2*w^2 - 5]', '[191, 191, -2*w^2 - w + 10]', '[193, 193, w^3 + w^2 - 3*w - 4]', '[193, 193, -w^3 + 2*w^2 + 3*w - 3]', '[197, 197, -2*w^3 + 9*w - 4]', '[197, 197, w^2 - 7]', '[199, 199, 3*w^3 - 13*w + 1]', '[199, 199, w^3 + 2*w^2 - 5*w - 7]', '[227, 227, -3*w^3 + w^2 + 13*w - 4]', '[227, 227, -w^3 + 2*w^2 + 7*w - 6]', '[241, 241, -2*w^3 + 7*w - 1]', '[257, 257, -2*w^3 + w^2 + 7*w - 5]', '[257, 257, 2*w^3 - w^2 - 7*w + 2]', '[263, 263, -w^3 + 7*w - 3]', '[269, 269, -2*w^3 + 2*w^2 + 11*w - 8]', '[271, 271, w^2 + 3*w - 2]', '[271, 271, w^2 + 2*w - 7]', '[277, 277, -2*w^3 + 11*w - 2]', '[281, 281, 2*w^3 - 11*w + 1]', '[283, 283, 2*w^3 - 9*w + 5]', '[283, 283, -2*w^3 + w^2 + 11*w - 7]', '[289, 17, -w^3 + 2*w^2 + 4*w - 4]', '[293, 293, -2*w^3 - w^2 + 7*w + 3]', '[307, 307, -3*w^3 + 2*w^2 + 13*w - 9]', '[311, 311, -w^3 + w^2 + 3*w - 7]', '[313, 313, -w^3 + 2*w^2 + 3*w - 2]', '[313, 313, w^2 - w - 8]', '[317, 317, -2*w^3 - w^2 + 9*w - 1]', '[331, 331, w^3 + 2*w^2 - 5*w - 3]', '[337, 337, w^3 + 2*w^2 - 6*w - 4]', '[337, 337, w^3 - 2*w^2 - 6*w + 5]', '[347, 347, 2*w^3 + 2*w^2 - 9*w - 3]', '[347, 347, -2*w^3 + w^2 + 7*w - 4]', '[349, 349, w^2 - 2*w - 4]', '[353, 353, -w^3 + 2*w^2 + 2*w - 6]', '[359, 359, -w^3 + w^2 + 7*w - 6]', '[359, 359, -w^2 - w - 2]', '[361, 19, 2*w^3 - w^2 - 11*w]', '[367, 367, -2*w^3 + 2*w^2 + 8*w - 5]', '[373, 373, w^3 + w^2 - 2*w - 4]', '[379, 379, 2*w^3 - w^2 - 11*w + 4]', '[389, 389, 3*w^2 + w - 11]', '[397, 397, 3*w^3 - 13*w + 5]', '[401, 401, w - 5]', '[409, 409, 3*w^3 - 12*w + 4]', '[409, 409, 3*w^3 + 2*w^2 - 14*w - 4]', '[421, 421, 2*w^3 - w^2 - 10*w + 1]', '[421, 421, w^3 + 2*w^2 - 5*w - 4]', '[439, 439, -2*w^3 + 10*w - 5]', '[443, 443, -2*w^3 + 12*w - 5]', '[443, 443, -4*w^3 + w^2 + 18*w - 9]', '[443, 443, -2*w^3 + w^2 + 7*w - 9]', '[443, 443, 3*w^3 + 2*w^2 - 14*w - 5]', '[449, 449, w^3 + 2*w^2 - 2*w - 6]', '[449, 449, -2*w^3 + w^2 + 11*w - 5]', '[461, 461, 2*w^3 + 2*w^2 - 9*w - 4]', '[467, 467, -w^3 + w^2 + 7*w - 5]', '[487, 487, 2*w^2 + 4*w - 7]', '[491, 491, -w^3 + w^2 + 7*w - 4]', '[503, 503, 2*w^3 + w^2 - 9*w + 2]', '[521, 521, w^2 - 3*w - 3]', '[523, 523, -w^3 + 2*w^2 + 5*w - 4]', '[523, 523, -w^3 + 8*w - 5]', '[563, 563, w^3 + 3*w^2 - w - 8]', '[563, 563, w^3 - 2*w^2 - 8*w + 4]', '[563, 563, -w^3 + w^2 + 2*w - 5]', '[563, 563, -3*w^3 - w^2 + 10*w - 2]', '[577, 577, 3*w^3 - 16*w]', '[587, 587, w^3 + 2*w^2 - 6]', '[587, 587, -w^3 + 4*w - 6]', '[601, 601, -w - 5]', '[607, 607, w^3 - 2*w^2 - 4*w + 1]', '[613, 613, 4*w^3 - 17*w]', '[617, 617, -3*w^3 + w^2 + 14*w - 2]', '[617, 617, -4*w^3 + 17*w - 4]', '[619, 619, -3*w^3 + 12*w - 2]', '[643, 643, 3*w^3 - w^2 - 12*w + 3]', '[643, 643, -2*w^3 - w^2 + 11*w - 2]', '[647, 647, 2*w^3 + w^2 - 9*w + 3]', '[653, 653, w^3 + w^2 - 7*w - 4]', '[661, 661, -w^3 + 4*w^2 + 6*w - 15]', '[661, 661, 3*w^3 - 2*w^2 - 12*w + 10]', '[677, 677, -3*w^2 - 2*w + 12]', '[691, 691, -2*w^3 + 3*w^2 + 11*w - 10]', '[691, 691, -3*w^3 + 16*w - 3]', '[701, 701, 3*w^3 - 13*w + 6]', '[719, 719, -3*w^2 + w + 10]', '[727, 727, w^3 - 3*w^2 - 4*w + 6]', '[743, 743, -w^3 + 2*w^2 + 5*w - 3]', '[761, 761, -w^3 + 3*w^2 + 3*w - 12]', '[761, 761, 3*w^3 - 2*w^2 - 14*w + 7]', '[769, 769, -3*w^3 + 3*w^2 + 16*w - 13]', '[769, 769, w^3 + 2*w^2 - 7*w - 6]', '[773, 773, w^3 - 8*w + 4]', '[773, 773, 4*w^2 + w - 16]', '[787, 787, w^2 + 4*w - 2]', '[797, 797, -2*w^3 + 3*w^2 + 10*w - 10]', '[797, 797, -w^3 - w^2 + 4*w - 4]', '[797, 797, w^3 + 2*w^2 - 3*w - 9]', '[797, 797, -3*w^3 + 3*w^2 + 11*w - 10]', '[821, 821, w^2 + w - 9]', '[827, 827, w^3 - 8*w + 1]', '[827, 827, -2*w^3 + w^2 + 9*w - 11]', '[827, 827, 3*w^3 - 14*w + 5]', '[827, 827, 2*w^3 + w^2 - 7*w - 5]', '[829, 829, -2*w^3 - 2*w^2 + 9*w - 1]', '[839, 839, -3*w^3 + 15*w - 5]', '[853, 853, -4*w^3 + 15*w - 8]', '[853, 853, -w^3 + 2*w^2 + 6*w - 3]', '[859, 859, -w^3 + w^2 + w - 4]', '[859, 859, w^3 + w^2 - w - 5]', '[881, 881, -w^3 + w^2 + 2*w - 6]', '[881, 881, w^3 + w^2 - 2*w - 6]', '[883, 883, w^3 + 3*w^2 - 3*w - 6]', '[887, 887, w^3 + 3*w^2 - 3*w - 8]', '[919, 919, 2*w^3 - w^2 - 13*w]', '[929, 929, -w^3 - 3*w^2 + 2*w + 10]', '[929, 929, w^3 + w^2 - 5*w - 8]', '[941, 941, w^3 + 2*w^2 - 3*w - 10]', '[953, 953, -w^3 + 5*w - 7]', '[953, 953, -2*w^3 + 3*w^2 + 9*w - 9]', '[953, 953, -2*w^3 - w^2 + 10*w - 3]', '[953, 953, -3*w^3 + 11*w - 1]', '[961, 31, -w^3 + 3*w^2 + 2*w - 10]', '[961, 31, -3*w^2 + 2*w + 7]', '[967, 967, w^3 + 3*w^2 - 3*w - 7]', '[967, 967, 4*w^3 + w^2 - 20*w + 1]', '[983, 983, 2*w^3 - w^2 - 12*w + 8]', '[983, 983, 2*w^3 + w^2 - 6*w - 4]', '[991, 991, 2*w^3 - 12*w + 3]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  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': [1, 5, -5, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 8069, 'disc_rad': 8069, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[4, 1]]], [5, [[3, 1], [1, 1]]], [7, [[2, 1], [1, 2]]], [11, [[4, 1]]], [13, [[3, 1], [1, 1]]], [17, [[2, 1], [1, 2]]], [19, [[2, 1], [1, 2]]], [23, [[4, 1]]], [29, [[3, 1], [1, 1]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[3, 1], [1, 1]]], [43, [[2, 1], [1, 2]]], [47, [[3, 1], [1, 1]]], [53, [[2, 2]]], [59, [[3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12], 'galois_label': '4T5', 'galt': 5, 'grd': 89.8276126811795, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.8069.1', 'local_algs': ['m8069.1.1.0', 'm8069.1.1.0', 'm8069.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [8069], 'rd': 9.4777430162, 'regulator': {'__RealLiteral__': 0, 'data': '4.14172005586', 'prec': 44}, 'res': {'gal': ['1,35,-1833,-102092,-1441761,-4815654,85769,21047197,23020382,-13730864,-28751072,103147,14369451,2154116,-3770276,-720434,572943,104867,-52186,-7748,2807,282,-82,-4,1'], 'sib': ['-1,-16,6,19,-7,-3,1', '-112,-96,1232,-1086,-1287,1669,251,-707,44,113,-15,-6,1', '-9746,-1843,1754,177,-86,-3,1', '176255,-58581,-73103,-1850,4901,244,-120,-4,1', '49284,0,-115517,0,72772,0,-15932,0,1508,0,-64,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a \\)', '\\( a^{3} - 5 a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}