Hilbert modular form data - 4.4.6125.1-16.1-b

Formats: - HTML - YAML - JSON - 2024-05-05T01:34:43.267536

• 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': 6125, 'field_bad_primes': [5, 7], 'field_label': '4.4.6125.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '4.4.6125.1-16.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2], 'level_ideal': '[16, 2, 2]', 'level_label': '16.1', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.1-b', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[16, 2, 2]', 1]], 'hecke_eigenvalues': [-4, 'e', 'e', '-e + 1', '-e + 1', -1, '-e + 3', 'e + 2', '-e + 3', 'e + 2', 14, '-e - 7', 'e - 8', 'e - 8', '-e - 7', 6, 6, 6, 6, 2, '-e', 'e - 1', 'e - 1', '-e', 0, 0, 0, 0, '2*e + 8', '-2*e + 10', '2*e + 8', '-2*e + 10', -18, -18, -18, -18, '2*e + 2', '-2*e + 4', '2*e + 2', '-2*e + 4', '-3*e + 2', '-3*e + 2', '3*e - 1', '3*e - 1', '-4*e + 4', '4*e', '-4*e + 4', '4*e', '-2*e + 10', '-2*e + 10', '2*e + 8', '2*e + 8', '-e - 16', 'e - 17', 'e - 17', '-e - 16', 'e - 2', '-e - 1', 'e - 2', '-e - 1', 2, 2, 2, 2, '-3*e + 17', '-3*e + 17', '3*e + 14', '3*e + 14', '-3*e + 25', '-3*e + 25', '3*e + 22', '3*e + 22', '-4*e', '4*e - 4', '4*e - 4', '-4*e', '-4*e - 12', '4*e - 16', '-4*e - 12', '4*e - 16', '-2*e + 2', '-2*e + 2', '2*e', '2*e', '2*e + 16', '-2*e + 18', '2*e + 16', '-2*e + 18', 22, 22, 22, 22, '-3*e - 2', '3*e - 5', '-3*e - 2', '3*e - 5', '-2*e - 14', '2*e - 16', '-2*e - 14', '2*e - 16', '2*e - 4', '2*e - 4', '-2*e - 2', '-2*e - 2', '-e + 27', '-e + 27', 'e + 26', 'e + 26', '3*e + 1', '-3*e + 4', '3*e + 1', '-3*e + 4', '-4*e + 22', '-4*e + 22', '4*e + 18', '4*e + 18', '-7*e + 7', '7*e', '7*e', '-7*e + 7', -34, -34, -34, -34, '2*e + 12', '-2*e + 14', '-2*e + 14', '2*e + 12', '-2*e - 10', '2*e - 12', '-2*e - 10', '2*e - 12', 'e - 33', 'e - 33', '-e - 32', '-e - 32', '-2*e + 20', '-2*e + 20', '2*e + 18', '2*e + 18', '-4*e - 16', '4*e - 20', '-4*e - 16', '4*e - 20', '-4*e + 36', '-4*e + 36', '4*e + 32', '4*e + 32', '-3*e + 34', '3*e + 31', '5*e - 24', '-5*e - 19', '5*e - 24', '-5*e - 19', '-4*e + 32', '4*e + 28', '4*e + 28', '-4*e + 32', '4*e + 2', '-4*e + 6', '-4*e + 6', '4*e + 2', '-11*e + 14', '11*e + 3', '4*e - 28', '-4*e - 24', '-4*e - 24', '4*e - 28'], 'hecke_polynomial': 'x^2 - x - 23', 'label': '4.4.6125.1-16.1-b'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 6125, 'ideals': ['[1, 1, 1]', '[5, 5, -2*w^3 - 2*w^2 + 13*w + 8]', '[11, 11, 2*w^3 + 3*w^2 - 12*w - 11]', '[11, 11, -w^3 - 2*w^2 + 6*w + 9]', '[11, 11, w^3 + w^2 - 7*w - 4]', '[11, 11, w - 1]', '[16, 2, 2]', '[19, 19, -w^2 + 4]', '[19, 19, 2*w^3 + 2*w^2 - 13*w - 6]', '[19, 19, 3*w^3 + 4*w^2 - 18*w - 16]', '[19, 19, -w^3 - w^2 + 5*w + 3]', '[25, 5, -2*w^3 - 2*w^2 + 12*w + 7]', '[49, 7, 2*w^3 + 3*w^2 - 13*w - 15]', '[55, 55, -w^3 - 2*w^2 + 5*w + 11]', '[55, 55, -2*w^3 - 3*w^2 + 13*w + 14]', '[55, 55, -w^3 - 2*w^2 + 5*w + 6]', '[55, 55, 2*w^3 + 3*w^2 - 13*w - 9]', '[59, 59, -3*w^3 - 4*w^2 + 19*w + 14]', '[59, 59, 3*w^3 + 4*w^2 - 18*w - 17]', '[59, 59, 2*w^3 + 3*w^2 - 11*w - 13]', '[59, 59, -w^3 - 2*w^2 + 7*w + 9]', '[71, 71, 3*w^3 + 3*w^2 - 17*w - 10]', '[71, 71, -2*w^3 - w^2 + 14*w + 2]', '[71, 71, 5*w^3 + 7*w^2 - 30*w - 25]', '[71, 71, -3*w^3 - 4*w^2 + 16*w + 16]', '[80, 10, -4*w^3 - 4*w^2 + 26*w + 16]', '[81, 3, -3]', '[89, 89, -2*w^3 - 2*w^2 + 13*w + 4]', '[89, 89, 3*w^3 + 4*w^2 - 17*w - 16]', '[89, 89, 3*w^3 + 4*w^2 - 18*w - 18]', '[89, 89, -4*w^3 - 5*w^2 + 25*w + 18]', '[95, 95, w^3 + 2*w^2 - 6*w - 12]', '[95, 95, -2*w^3 - 3*w^2 + 12*w + 8]', '[95, 95, -w^3 - w^2 + 7*w + 7]', '[95, 95, -w + 4]', '[121, 11, -3*w^3 - 3*w^2 + 18*w + 11]', '[121, 11, -5*w^3 - 6*w^2 + 30*w + 22]', '[121, 11, 3*w^3 + 3*w^2 - 17*w - 11]', '[121, 11, 4*w^3 + 4*w^2 - 25*w - 14]', '[121, 11, -3*w^3 - 3*w^2 + 18*w + 10]', '[121, 11, -2*w^3 - w^2 + 12*w + 2]', '[121, 121, -w^3 - 3*w^2 + 6*w + 14]', '[121, 121, -5*w^3 - 7*w^2 + 30*w + 26]', '[121, 121, -3*w^3 - 3*w^2 + 20*w + 11]', '[121, 121, w^3 + w^2 - 4*w - 5]', '[125, 5, -6*w^3 - 8*w^2 + 37*w + 34]', '[139, 139, -w^3 + 6*w + 1]', '[139, 139, -3*w^3 - 3*w^2 + 19*w + 8]', '[139, 139, 4*w^3 + 5*w^2 - 24*w - 21]', '[139, 139, -2*w^3 - 2*w^2 + 11*w + 5]', '[151, 151, -6*w^3 - 7*w^2 + 37*w + 27]', '[151, 151, 3*w^3 + 5*w^2 - 19*w - 17]', '[151, 151, -6*w^3 - 8*w^2 + 37*w + 31]', '[151, 151, 4*w^3 + 6*w^2 - 25*w - 26]', '[176, 22, 4*w^3 + 6*w^2 - 24*w - 22]', '[176, 22, -2*w^3 - 4*w^2 + 12*w + 18]', '[176, 22, 2*w^3 + 2*w^2 - 14*w - 8]', '[176, 22, 2*w - 2]', '[191, 191, 5*w^3 + 7*w^2 - 31*w - 26]', '[191, 191, -2*w^3 - 3*w^2 + 10*w + 13]', '[191, 191, -5*w^3 - 7*w^2 + 31*w + 29]', '[191, 191, 2*w^3 + 4*w^2 - 13*w - 17]', '[199, 199, 2*w^3 + 4*w^2 - 11*w - 20]', '[199, 199, -2*w^3 - 2*w^2 + 11*w + 3]', '[199, 199, 3*w^3 + 5*w^2 - 17*w - 17]', '[199, 199, 3*w^3 + 3*w^2 - 19*w - 6]', '[209, 209, -6*w^3 - 8*w^2 + 36*w + 27]', '[209, 209, w^2 + w - 2]', '[209, 209, -w^3 + w^2 + 7*w - 7]', '[209, 209, -6*w^3 - 7*w^2 + 38*w + 26]', '[209, 209, -2*w^3 - 2*w^2 + 10*w + 11]', '[209, 209, 3*w^3 + 4*w^2 - 17*w - 17]', '[209, 209, 2*w^3 + 3*w^2 - 11*w - 15]', '[209, 209, w^3 + 2*w^2 - 7*w - 11]', '[209, 209, 6*w^3 + 8*w^2 - 35*w - 30]', '[209, 209, 4*w^3 + 4*w^2 - 26*w - 17]', '[209, 209, -w^3 + 4*w]', '[209, 209, 4*w^3 + 5*w^2 - 25*w - 17]', '[209, 209, -w^2 + w + 6]', '[209, 209, -3*w^3 - 4*w^2 + 19*w + 12]', '[209, 209, 2*w^2 - 13]', '[209, 209, -w^3 + 7*w]', '[211, 211, 3*w^3 + 5*w^2 - 18*w - 19]', '[211, 211, -3*w^3 - 5*w^2 + 18*w + 21]', '[211, 211, 2*w^3 + 4*w^2 - 12*w - 17]', '[211, 211, -4*w^3 - 6*w^2 + 24*w + 23]', '[229, 229, 2*w^3 + 4*w^2 - 13*w - 19]', '[229, 229, -2*w^3 - 3*w^2 + 10*w + 15]', '[229, 229, -5*w^3 - 7*w^2 + 31*w + 24]', '[229, 229, 2*w^3 + 2*w^2 - 14*w - 3]', '[245, 35, 17*w^3 + 19*w^2 - 109*w - 76]', '[256, 4, 4]', '[269, 269, 2*w^3 + w^2 - 11*w - 1]', '[269, 269, -6*w^3 - 7*w^2 + 37*w + 24]', '[269, 269, 5*w^3 + 6*w^2 - 29*w - 24]', '[269, 269, 3*w^3 + 2*w^2 - 19*w - 7]', '[275, 55, -2*w^3 - 3*w^2 + 10*w + 11]', '[275, 55, -w^3 + 8*w - 3]', '[275, 55, 5*w^3 + 7*w^2 - 31*w - 28]', '[275, 55, -2*w^3 - 4*w^2 + 13*w + 15]', '[281, 281, -4*w^3 - 6*w^2 + 25*w + 25]', '[281, 281, -5*w^3 - 7*w^2 + 31*w + 27]', '[281, 281, w^2 + 2*w - 7]', '[281, 281, 3*w^3 + 5*w^2 - 19*w - 18]', '[295, 295, 5*w^3 + 5*w^2 - 31*w - 16]', '[295, 295, 13*w^3 + 15*w^2 - 82*w - 59]', '[295, 295, -9*w^3 - 10*w^2 + 58*w + 39]', '[295, 295, -11*w^3 - 14*w^2 + 69*w + 57]', '[304, 38, -2*w^2 + 8]', '[304, 38, 4*w^3 + 4*w^2 - 26*w - 12]', '[304, 38, 6*w^3 + 8*w^2 - 36*w - 32]', '[304, 38, -2*w^3 - 2*w^2 + 10*w + 6]', '[331, 331, -2*w^3 - 3*w^2 + 12*w + 7]', '[331, 331, w^3 + w^2 - 7*w - 8]', '[331, 331, w^3 + 2*w^2 - 6*w - 13]', '[331, 331, w - 5]', '[349, 349, 2*w^3 + 5*w^2 - 16*w - 12]', '[349, 349, 2*w^3 + 4*w^2 - 15*w - 10]', '[349, 349, 8*w^3 + 9*w^2 - 50*w - 32]', '[349, 349, 2*w^3 + 4*w^2 - 15*w - 9]', '[355, 355, 4*w^3 + 6*w^2 - 23*w - 25]', '[355, 355, 12*w^3 + 15*w^2 - 74*w - 57]', '[355, 355, -13*w^3 - 18*w^2 + 82*w + 82]', '[355, 355, -3*w^3 - 3*w^2 + 17*w + 7]', '[361, 19, -5*w^3 - 5*w^2 + 33*w + 19]', '[361, 19, -4*w^3 - 4*w^2 + 24*w + 13]', '[361, 19, -4*w^3 - 4*w^2 + 24*w + 15]', '[361, 19, -8*w^3 - 11*w^2 + 48*w + 40]', '[361, 19, 2*w^3 + 2*w^2 - 9*w - 10]', '[361, 19, -w^3 - 4*w^2 + 6*w + 20]', '[361, 361, 3*w^3 + 5*w^2 - 19*w - 19]', '[361, 361, 4*w^3 + 6*w^2 - 25*w - 24]', '[361, 361, -w^2 - 2*w + 6]', '[361, 361, -w^3 - 2*w^2 + 4*w + 8]', '[400, 10, -4*w^3 - 4*w^2 + 24*w + 14]', '[401, 401, 4*w^3 + 3*w^2 - 21*w - 12]', '[401, 401, 3*w^3 + 2*w^2 - 16*w - 9]', '[401, 401, -3*w^3 - 6*w^2 + 20*w + 19]', '[401, 401, -4*w^3 - 3*w^2 + 27*w + 9]', '[405, 15, 6*w^3 + 6*w^2 - 39*w - 24]', '[409, 409, -5*w^3 - 6*w^2 + 31*w + 20]', '[409, 409, 3*w^3 + 4*w^2 - 20*w - 12]', '[409, 409, -3*w^3 - 5*w^2 + 17*w + 23]', '[409, 409, 4*w^3 + 5*w^2 - 23*w - 21]', '[419, 419, -4*w^3 - 4*w^2 + 21*w + 18]', '[419, 419, -4*w^3 - 4*w^2 + 20*w + 19]', '[419, 419, -3*w^3 - 4*w^2 + 16*w + 18]', '[419, 419, -2*w^3 - w^2 + 8*w + 10]', '[421, 421, -6*w^3 - 7*w^2 + 36*w + 26]', '[421, 421, 5*w^3 + 5*w^2 - 31*w - 17]', '[421, 421, 3*w^3 + 2*w^2 - 18*w - 6]', '[421, 421, 4*w^3 + 4*w^2 - 23*w - 14]', '[431, 431, 6*w^3 + 7*w^2 - 36*w - 25]', '[431, 431, -3*w^3 - 2*w^2 + 18*w + 5]', '[431, 431, 4*w^3 + 4*w^2 - 23*w - 15]', '[431, 431, -5*w^3 - 5*w^2 + 31*w + 18]', '[439, 439, w^3 + w^2 - 4*w - 1]', '[439, 439, w^3 + 3*w^2 - 6*w - 10]', '[439, 439, 3*w^3 + 3*w^2 - 20*w - 7]', '[439, 439, 5*w^3 + 7*w^2 - 30*w - 30]', '[445, 445, -4*w^3 - 7*w^2 + 24*w + 32]', '[445, 445, -15*w^3 - 19*w^2 + 94*w + 78]', '[445, 445, 15*w^3 + 17*w^2 - 95*w - 67]', '[445, 445, 7*w^3 + 8*w^2 - 43*w - 29]', '[475, 95, 2*w^3 + 3*w^2 - 10*w - 16]', '[475, 95, 2*w^3 + 4*w^2 - 13*w - 20]', '[475, 95, w^3 - 8*w - 2]', '[475, 95, 5*w^3 + 7*w^2 - 31*w - 23]', '[479, 479, -4*w^3 - 5*w^2 + 25*w + 15]', '[479, 479, -5*w^3 - 6*w^2 + 32*w + 21]', '[479, 479, 5*w^3 + 7*w^2 - 29*w - 28]', '[479, 479, 2*w^2 + w - 9]', '[491, 491, 7*w^3 + 8*w^2 - 43*w - 31]', '[491, 491, 6*w^3 + 6*w^2 - 37*w - 24]', '[491, 491, 4*w^3 + 3*w^2 - 24*w - 6]', '[491, 491, 5*w^3 + 5*w^2 - 29*w - 21]', '[509, 509, -4*w^3 - 5*w^2 + 25*w + 14]', '[509, 509, -3*w^3 - 4*w^2 + 17*w + 20]', '[509, 509, -6*w^3 - 7*w^2 + 38*w + 25]', '[509, 509, -6*w^3 - 8*w^2 + 35*w + 31]', '[539, 77, -8*w^3 - 11*w^2 + 48*w + 44]', '[539, 77, 6*w^3 + 10*w^2 - 36*w - 47]', '[539, 77, -11*w^3 - 12*w^2 + 71*w + 49]', '[539, 77, 3*w^3 + 2*w^2 - 20*w - 7]', '[541, 541, 9*w^3 + 12*w^2 - 55*w - 46]', '[541, 541, w^3 + 4*w^2 - 7*w - 17]', '[541, 541, -4*w^3 - 5*w^2 + 21*w + 19]', '[541, 541, -4*w^3 - 3*w^2 + 27*w + 8]', '[571, 571, -3*w^3 - 6*w^2 + 18*w + 23]', '[571, 571, 6*w^3 + 9*w^2 - 36*w - 37]', '[571, 571, 7*w^3 + 10*w^2 - 42*w - 36]', '[571, 571, 2*w^3 + 5*w^2 - 12*w - 24]', '[605, 55, -10*w^3 - 13*w^2 + 62*w + 55]', '[605, 55, 4*w^3 + 4*w^2 - 26*w - 11]', '[605, 55, -2*w^2 + 7]', '[605, 55, -8*w^3 - 11*w^2 + 49*w + 47]', '[605, 55, -2*w^3 - 2*w^2 + 10*w + 5]', '[605, 55, 6*w^3 + 8*w^2 - 36*w - 33]', '[605, 605, -2*w^3 - 4*w^2 + 11*w + 13]', '[605, 605, -3*w^3 - 4*w^2 + 20*w + 11]', '[605, 605, 3*w^3 + 5*w^2 - 17*w - 24]', '[605, 605, -2*w^3 - 3*w^2 + 14*w + 15]', '[619, 619, -9*w^3 - 11*w^2 + 55*w + 39]', '[619, 619, -5*w^3 - 4*w^2 + 32*w + 14]', '[619, 619, 7*w^3 + 9*w^2 - 42*w - 36]', '[619, 619, 4*w^3 + 6*w^2 - 26*w - 27]', '[625, 5, 5]', '[631, 631, 2*w^3 + 5*w^2 - 12*w - 21]', '[631, 631, -7*w^3 - 10*w^2 + 42*w + 39]', '[631, 631, 4*w^3 + 4*w^2 - 27*w - 13]', '[631, 631, w^3 + w^2 - 3*w - 4]', '[641, 641, -9*w^3 - 10*w^2 + 56*w + 36]', '[641, 641, -5*w^3 - 9*w^2 + 30*w + 32]', '[641, 641, -3*w^3 - 6*w^2 + 19*w + 21]', '[641, 641, 4*w^3 + 3*w^2 - 22*w - 10]', '[649, 649, w^3 + w^2 - 4*w]', '[649, 649, -5*w^3 - 6*w^2 + 31*w + 19]', '[649, 649, -4*w^3 - 4*w^2 + 22*w + 19]', '[649, 649, -10*w^3 - 12*w^2 + 63*w + 46]', '[649, 649, -2*w^3 - w^2 + 13*w + 5]', '[649, 649, -2*w^3 + 11*w + 2]', '[649, 649, -2*w^3 - 4*w^2 + 11*w + 11]', '[649, 649, -3*w^3 - 5*w^2 + 17*w + 26]', '[649, 649, 9*w^3 + 11*w^2 - 55*w - 45]', '[649, 649, 3*w^3 + 4*w^2 - 20*w - 9]', '[649, 649, 4*w^3 + 5*w^2 - 23*w - 22]', '[649, 649, 4*w^3 + 5*w^2 - 26*w - 16]', '[649, 649, -2*w^3 + 12*w - 7]', '[649, 649, 2*w^3 + 4*w^2 - 13*w - 21]', '[649, 649, 6*w^3 + 6*w^2 - 38*w - 25]', '[649, 649, 6*w^3 + 7*w^2 - 34*w - 22]', '[695, 695, -7*w^3 - 9*w^2 + 44*w + 41]', '[695, 695, 17*w^3 + 20*w^2 - 107*w - 80]', '[695, 695, -2*w^3 - w^2 + 15*w + 4]', '[695, 695, -8*w^3 - 12*w^2 + 49*w + 53]', '[701, 701, -2*w^3 - 5*w^2 + 14*w + 20]', '[701, 701, -6*w^3 - 7*w^2 + 36*w + 34]', '[701, 701, 4*w^3 + 6*w^2 - 23*w - 17]', '[701, 701, -9*w^3 - 12*w^2 + 56*w + 46]', '[719, 719, 3*w^3 + 5*w^2 - 17*w - 25]', '[719, 719, -3*w^3 - 2*w^2 + 17*w + 3]', '[719, 719, 7*w^3 + 8*w^2 - 43*w - 26]', '[719, 719, -6*w^3 - 7*w^2 + 35*w + 29]', '[751, 751, 2*w^3 + 2*w^2 - 15*w - 4]', '[751, 751, 5*w^3 + 8*w^2 - 30*w - 34]', '[751, 751, w^3 + w^2 - 9*w - 5]', '[751, 751, -4*w^3 - 7*w^2 + 24*w + 26]', '[755, 755, 8*w^3 + 10*w^2 - 50*w - 37]', '[755, 755, -25*w^3 - 31*w^2 + 157*w + 128]', '[755, 755, -24*w^3 - 29*w^2 + 151*w + 116]', '[755, 755, 22*w^3 + 25*w^2 - 140*w - 98]', '[769, 769, 6*w^3 + 8*w^2 - 37*w - 27]', '[769, 769, -w^3 - 3*w^2 + 7*w + 16]', '[769, 769, 2*w^3 + w^2 - 14*w - 5]', '[769, 769, -3*w^3 - 4*w^2 + 16*w + 19]', '[781, 781, 8*w^3 + 11*w^2 - 51*w - 52]', '[781, 781, -2*w^3 - 3*w^2 + 11*w + 6]', '[781, 781, -12*w^3 - 15*w^2 + 72*w + 56]', '[781, 781, -4*w^3 - 7*w^2 + 27*w + 17]', '[781, 781, 6*w^3 + 8*w^2 - 34*w - 23]', '[781, 781, -5*w^3 - 8*w^2 + 30*w + 29]', '[781, 781, 5*w^3 + 4*w^2 - 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6*w^2 + 24*w + 16]', '[1520, 190, -2*w^3 - 2*w^2 + 14*w + 14]', '[1520, 190, -2*w + 8]', '[1529, 1529, 7*w^3 + 10*w^2 - 42*w - 43]', '[1529, 1529, -w^3 - 3*w^2 + 4*w + 9]', '[1529, 1529, -3*w^3 - 6*w^2 + 16*w + 22]', '[1529, 1529, 11*w^3 + 15*w^2 - 63*w - 55]', '[1529, 1529, -13*w^3 - 16*w^2 + 82*w + 62]', '[1529, 1529, -2*w^3 + 2*w^2 + 15*w - 16]', '[1529, 1529, -4*w^3 - 7*w^2 + 22*w + 32]', '[1529, 1529, 4*w^3 + 6*w^2 - 27*w - 26]', '[1529, 1529, -3*w^3 - 5*w^2 + 16*w + 25]', '[1529, 1529, w^3 + w^2 - 3*w]', '[1529, 1529, 2*w^3 + 5*w^2 - 12*w - 17]', '[1529, 1529, 5*w^3 + 7*w^2 - 32*w - 22]', '[1529, 1529, 3*w^3 + 5*w^2 - 20*w - 24]', '[1529, 1529, 5*w^3 + 7*w^2 - 33*w - 23]', '[1529, 1529, -4*w^3 - 4*w^2 + 27*w + 9]', '[1529, 1529, -3*w^2 + 4*w + 10]', '[1539, 57, 3*w^2 - 12]', '[1539, 57, -6*w^3 - 6*w^2 + 39*w + 18]', '[1539, 57, -9*w^3 - 12*w^2 + 54*w + 48]', '[1539, 57, 3*w^3 + 3*w^2 - 15*w - 9]', '[1559, 1559, 6*w^3 + 8*w^2 - 38*w - 27]', '[1559, 1559, 4*w^3 + 6*w^2 - 22*w - 27]', '[1559, 1559, -7*w^3 - 9*w^2 + 42*w + 38]', '[1559, 1559, 5*w^3 + 5*w^2 - 32*w - 13]', '[1609, 1609, -w^3 + w^2 + 5*w - 9]', '[1609, 1609, -3*w^3 - 6*w^2 + 17*w + 21]', '[1609, 1609, -8*w^3 - 10*w^2 + 49*w + 34]', '[1609, 1609, 5*w^3 + 8*w^2 - 29*w - 36]', '[1621, 1621, 3*w^3 + 5*w^2 - 15*w - 19]', '[1621, 1621, 2*w^2 + 3*w - 12]', '[1621, 1621, -4*w^3 - 7*w^2 + 26*w + 26]', '[1621, 1621, 7*w^3 + 10*w^2 - 44*w - 40]', '[1655, 1655, 6*w^3 + 5*w^2 - 39*w - 18]', '[1655, 1655, 3*w^3 + 2*w^2 - 21*w - 10]', '[1655, 1655, 16*w^3 + 18*w^2 - 103*w - 75]', '[1655, 1655, 13*w^3 + 13*w^2 - 84*w - 49]', '[1661, 1661, -16*w^3 - 18*w^2 + 101*w + 71]', '[1661, 1661, 5*w^3 + 3*w^2 - 25*w - 16]', '[1661, 1661, -4*w^3 - 5*w^2 + 26*w + 26]', '[1661, 1661, 6*w^3 + 5*w^2 - 37*w - 18]', '[1661, 1661, -6*w^3 - 6*w^2 + 40*w + 23]', '[1661, 1661, -3*w^3 - 5*w^2 + 15*w + 11]', '[1661, 1661, -w^2 - 4*w]', '[1661, 1661, 19*w^3 + 23*w^2 - 118*w - 91]', '[1661, 1661, 19*w^3 + 24*w^2 - 119*w - 97]', '[1661, 1661, -w^3 - 2*w^2 + 7*w + 1]', '[1661, 1661, -8*w^3 - 9*w^2 + 48*w + 35]', '[1661, 1661, -7*w^3 - 10*w^2 + 44*w + 39]', '[1661, 1661, 7*w^3 + 11*w^2 - 42*w - 33]', '[1661, 1661, 5*w^3 + 9*w^2 - 30*w - 47]', '[1661, 1661, -8*w^3 - 9*w^2 + 47*w + 35]', '[1661, 1661, -3*w^3 - 4*w^2 + 19*w + 22]', '[1669, 1669, -5*w^3 - 7*w^2 + 27*w + 30]', '[1669, 1669, 3*w^3 + w^2 - 12*w - 13]', '[1669, 1669, 6*w^3 + 7*w^2 - 31*w - 31]', '[1669, 1669, -5*w^3 - 4*w^2 + 25*w + 21]', '[1681, 41, -6*w^3 - 6*w^2 + 36*w + 19]', '[1681, 41, -6*w^3 - 6*w^2 + 36*w + 23]', '[1691, 1691, -w^3 + 9*w - 3]', '[1691, 1691, 7*w^3 + 9*w^2 - 44*w - 42]', '[1691, 1691, -w^3 - 3*w^2 + 3*w + 13]', '[1691, 1691, -5*w^3 - 4*w^2 + 28*w + 13]', '[1691, 1691, -8*w^3 - 10*w^2 + 51*w + 46]', '[1691, 1691, 4*w^3 + 7*w^2 - 25*w - 27]', '[1691, 1691, -10*w^3 - 15*w^2 + 60*w + 51]', '[1691, 1691, 10*w^3 + 12*w^2 - 59*w - 45]', '[1691, 1691, 3*w^2 + 2*w - 24]', '[1691, 1691, -9*w^3 - 9*w^2 + 59*w + 31]', '[1691, 1691, w^3 + 6*w^2 - 6*w - 28]', '[1691, 1691, -4*w^3 - 2*w^2 + 24*w + 5]', '[1691, 1691, 6*w^3 + 6*w^2 - 34*w - 21]', '[1691, 1691, -6*w^3 - 9*w^2 + 38*w + 34]', '[1691, 1691, 5*w^3 + 7*w^2 - 28*w - 19]', '[1691, 1691, 5*w^3 + 5*w^2 - 35*w - 24]', '[1699, 1699, 4*w^3 + 5*w^2 - 28*w - 13]', '[1699, 1699, -11*w^3 - 15*w^2 + 66*w + 51]', '[1699, 1699, -w^3 - 5*w^2 + 6*w + 29]', '[1699, 1699, 3*w^3 + 3*w^2 - 14*w - 18]', '[1745, 1745, 5*w^3 + 8*w^2 - 32*w - 30]', '[1745, 1745, 31*w^3 + 40*w^2 - 194*w - 168]', '[1745, 1745, 6*w^3 + 9*w^2 - 38*w - 36]', '[1745, 1745, 4*w^3 + 7*w^2 - 25*w - 28]', '[1775, 355, 12*w^3 + 13*w^2 - 75*w - 46]', '[1775, 355, -8*w^3 - 13*w^2 + 48*w + 58]', '[1775, 355, -5*w^3 - 7*w^2 + 26*w + 23]', '[1775, 355, 7*w^3 + 12*w^2 - 42*w - 42]', '[1801, 1801, -3*w^3 - 7*w^2 + 19*w + 26]', '[1801, 1801, 5*w^3 + 4*w^2 - 27*w - 17]', '[1801, 1801, -11*w^3 - 12*w^2 + 69*w + 46]', '[1801, 1801, -4*w^3 - 9*w^2 + 28*w + 27]', '[1805, 95, -w^2 + 2*w + 8]', '[1805, 95, -5*w^3 - 6*w^2 + 32*w + 18]', '[1805, 95, -10*w^3 - 14*w^2 + 61*w + 60]', '[1805, 95, 5*w^3 + 7*w^2 - 29*w - 31]', '[1805, 95, -2*w^2 - w + 6]', '[1805, 95, w^3 + 5*w^2 - 9*w - 13]', '[1805, 1805, -12*w^3 - 16*w^2 + 70*w + 59]', '[1805, 1805, -2*w^3 + 8*w + 1]', '[1805, 1805, -2*w^3 + 2*w^2 + 14*w - 15]', '[1805, 1805, 12*w^3 + 14*w^2 - 76*w - 53]', '[1831, 1831, 5*w^3 + 8*w^2 - 32*w - 31]', '[1831, 1831, 6*w^3 + 9*w^2 - 38*w - 35]', '[1831, 1831, 5*w^3 + 8*w^2 - 31*w - 32]', '[1831, 1831, 5*w^3 + 8*w^2 - 31*w - 31]', '[1871, 1871, 7*w^3 + 11*w^2 - 45*w - 38]', '[1871, 1871, -2*w^3 - 5*w^2 + 8*w + 27]', '[1871, 1871, -8*w^3 - 12*w^2 + 51*w + 51]', '[1871, 1871, 11*w^3 + 15*w^2 - 67*w - 59]', '[1879, 1879, 3*w^3 + 7*w^2 - 16*w - 37]', '[1879, 1879, -7*w^3 - 9*w^2 + 46*w + 40]', '[1879, 1879, 12*w^3 + 15*w^2 - 73*w - 60]', '[1879, 1879, 5*w^3 + 8*w^2 - 32*w - 38]', '[1889, 1889, -3*w^3 - 5*w^2 + 16*w + 26]', '[1889, 1889, w^3 + 3*w^2 - 4*w - 8]', '[1889, 1889, -5*w^3 - 7*w^2 + 32*w + 21]', '[1889, 1889, 3*w^3 + 5*w^2 - 20*w - 25]', '[1901, 1901, 6*w^3 + 7*w^2 - 39*w - 34]', '[1901, 1901, 10*w^3 + 14*w^2 - 60*w - 53]', '[1901, 1901, -5*w^3 - 9*w^2 + 30*w + 41]', '[1901, 1901, -8*w^3 - 10*w^2 + 49*w + 47]', '[1936, 22, -6*w^3 - 6*w^2 + 36*w + 22]', '[1936, 22, -10*w^3 - 12*w^2 + 60*w + 44]', '[1936, 22, 6*w^3 + 6*w^2 - 34*w - 22]', '[1936, 22, 8*w^3 + 8*w^2 - 50*w - 28]', '[1936, 22, -6*w^3 - 6*w^2 + 36*w + 20]', '[1936, 22, -4*w^3 - 2*w^2 + 24*w + 4]', '[1936, 242, -2*w^3 - 6*w^2 + 12*w + 28]', '[1936, 242, -10*w^3 - 14*w^2 + 60*w + 52]', '[1936, 242, -6*w^3 - 6*w^2 + 40*w + 22]', '[1936, 242, 2*w^3 + 2*w^2 - 8*w - 10]', '[1949, 1949, -7*w^3 - 10*w^2 + 41*w + 41]', '[1949, 1949, 6*w^3 + 7*w^2 - 39*w - 23]', '[1949, 1949, -4*w^3 - 5*w^2 + 22*w + 24]', '[1949, 1949, -7*w^3 - 9*w^2 + 43*w + 29]', '[1979, 1979, -3*w^3 - 2*w^2 + 16*w + 4]', '[1979, 1979, 8*w^3 + 10*w^2 - 47*w - 40]', '[1979, 1979, 3*w^3 + w^2 - 19*w - 3]', '[1979, 1979, -8*w^3 - 9*w^2 + 50*w + 30]', '[2000, 10, -12*w^3 - 16*w^2 + 74*w + 68]', '[2005, 2005, -7*w^3 - 9*w^2 + 44*w + 31]', '[2005, 2005, 5*w^3 + 5*w^2 - 32*w - 12]', '[2005, 2005, 5*w^3 + 7*w^2 - 28*w - 30]', '[2005, 2005, 7*w^3 + 9*w^2 - 42*w - 39]', '[2011, 2011, -5*w^3 - 9*w^2 + 32*w + 30]', '[2011, 2011, 7*w^3 + 6*w^2 - 37*w - 24]', '[2011, 2011, 9*w^3 + 13*w^2 - 56*w - 56]', '[2011, 2011, -12*w^3 - 16*w^2 + 74*w + 61]', '[2025, 15, 6*w^3 + 6*w^2 - 36*w - 21]', '[2029, 2029, 11*w^3 + 13*w^2 - 70*w - 49]', '[2029, 2029, 5*w^3 + 7*w^2 - 32*w - 20]', '[2029, 2029, 11*w^3 + 15*w^2 - 64*w - 56]', '[2029, 2029, -w^3 + 3*w^2 + 8*w - 18]', '[2045, 2045, 13*w^3 + 15*w^2 - 81*w - 58]', '[2045, 2045, -12*w^3 - 12*w^2 + 76*w + 41]', '[2045, 2045, 11*w^3 + 15*w^2 - 69*w - 63]', '[2045, 2045, -15*w^3 - 20*w^2 + 93*w + 83]', '[2081, 2081, 5*w^3 + 7*w^2 - 31*w - 35]', '[2081, 2081, 11*w^3 + 13*w^2 - 67*w - 50]', '[2081, 2081, -11*w^3 - 16*w^2 + 65*w + 62]', '[2081, 2081, 8*w^3 + 9*w^2 - 53*w - 32]', '[2089, 2089, -8*w^3 - 7*w^2 + 51*w + 18]', '[2089, 2089, 8*w^3 + 9*w^2 - 45*w - 29]', '[2089, 2089, -11*w^3 - 13*w^2 + 69*w + 48]', '[2089, 2089, 13*w^3 + 16*w^2 - 79*w - 64]', '[2095, 2095, -8*w^3 - 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112*w - 103]', '[2105, 2105, -19*w^3 - 24*w^2 + 118*w + 98]', '[2105, 2105, 9*w^3 + 13*w^2 - 55*w - 59]', '[2105, 2105, 8*w^3 + 11*w^2 - 48*w - 46]', '[2111, 2111, -4*w^3 - 8*w^2 + 26*w + 27]', '[2111, 2111, 10*w^3 + 14*w^2 - 62*w - 59]', '[2111, 2111, 2*w^3 - 16*w + 9]', '[2111, 2111, -11*w^3 - 15*w^2 + 68*w + 56]', '[2155, 2155, 17*w^3 + 22*w^2 - 105*w - 90]', '[2155, 2155, 10*w^3 + 13*w^2 - 61*w - 54]', '[2155, 2155, -7*w^3 - 11*w^2 + 42*w + 51]', '[2155, 2155, -20*w^3 - 26*w^2 + 125*w + 111]', '[2189, 2189, 6*w^3 + 11*w^2 - 34*w - 50]', '[2189, 2189, -w^3 + 5*w^2 + 8*w - 37]', '[2189, 2189, -4*w^3 - 5*w^2 + 21*w + 13]', '[2189, 2189, -5*w^3 - 8*w^2 + 28*w + 35]', '[2189, 2189, -w^3 + w^2 + 10*w - 1]', '[2189, 2189, 5*w^3 + 5*w^2 - 27*w - 16]', '[2189, 2189, 3*w^3 + 5*w^2 - 14*w - 27]', '[2189, 2189, -8*w^3 - 8*w^2 + 51*w + 25]', '[2189, 2189, -2*w^3 - 5*w^2 + 10*w + 19]', '[2189, 2189, 17*w^3 + 23*w^2 - 100*w - 77]', '[2189, 2189, 7*w^3 + 12*w^2 - 40*w - 44]', '[2189, 2189, -15*w^3 - 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w^2 + 16*w]', '[4895, 4895, -19*w^3 - 22*w^2 + 119*w + 87]', '[4895, 4895, -3*w^3 - 3*w^2 + 20*w]', '[4895, 4895, 9*w^3 + 14*w^2 - 53*w - 53]', '[4895, 4895, 2*w^3 + 5*w^2 - 10*w - 33]', '[4895, 4895, -3*w^3 - 5*w^2 + 21*w + 8]', '[4895, 4895, 8*w^3 + 12*w^2 - 49*w - 48]', '[4895, 4895, 18*w^3 + 24*w^2 - 109*w - 90]', '[4895, 4895, 17*w^3 + 23*w^2 - 107*w - 98]', '[4895, 4895, -w^3 - 3*w^2 + 6*w + 3]', '[4895, 4895, -18*w^3 - 23*w^2 + 105*w + 80]', '[4895, 4895, -13*w^3 - 15*w^2 + 80*w + 57]', '[4895, 4895, 7*w^3 + 8*w^2 - 36*w - 32]', '[4895, 4895, -w^3 + 4*w^2 + 12*w - 33]', '[4895, 4895, -2*w^3 - 3*w^2 + 17*w + 8]', '[4919, 4919, 16*w^3 + 19*w^2 - 100*w - 71]', '[4919, 4919, -7*w^3 - 5*w^2 + 37*w + 17]', '[4919, 4919, -7*w^3 - 10*w^2 + 41*w + 50]', '[4919, 4919, -13*w^3 - 16*w^2 + 78*w + 64]', '[4951, 4951, 6*w^3 + 5*w^2 - 34*w - 19]', '[4951, 4951, -11*w^3 - 12*w^2 + 68*w + 45]', '[4951, 4951, 11*w^3 + 13*w^2 - 65*w - 46]', '[4951, 4951, -6*w^3 - 4*w^2 + 37*w + 9]', '[4955, 4955, 36*w^3 + 45*w^2 - 225*w - 184]', '[4955, 4955, 38*w^3 + 43*w^2 - 242*w - 172]', '[4955, 4955, -33*w^3 - 38*w^2 + 210*w + 150]', '[4955, 4955, -31*w^3 - 37*w^2 + 195*w + 146]', '[4969, 4969, w^3 + 3*w^2 - 9*w - 15]', '[4969, 4969, -7*w^3 - 10*w^2 + 40*w + 42]', '[4969, 4969, 7*w^3 + 9*w^2 - 41*w - 40]', '[4969, 4969, 8*w^3 + 10*w^2 - 51*w - 34]', '[4975, 995, 2*w^3 - 2*w^2 - 15*w + 14]', '[4975, 995, 12*w^3 + 14*w^2 - 73*w - 45]', '[4975, 995, -11*w^3 - 15*w^2 + 63*w + 57]', '[4975, 995, -5*w^3 - 3*w^2 + 29*w + 2]', '[5021, 5021, -6*w^3 - 10*w^2 + 39*w + 37]', '[5021, 5021, 4*w^3 + 5*w^2 - 29*w - 19]', '[5021, 5021, -7*w^3 - 12*w^2 + 41*w + 50]', '[5021, 5021, w^3 + 4*w^2 - 2*w - 21]', '[5039, 5039, -8*w^3 - 11*w^2 + 50*w + 31]', '[5039, 5039, 5*w^3 + w^2 - 30*w - 2]', '[5039, 5039, -9*w^3 - 9*w^2 + 50*w + 29]', '[5039, 5039, -7*w^3 - 6*w^2 + 39*w + 17]', '[5041, 71, -8*w^3 - 8*w^2 + 48*w + 25]', '[5041, 71, -6*w^3 - 10*w^2 + 39*w + 39]', '[5041, 71, -8*w^3 - 8*w^2 + 48*w + 31]', '[5041, 71, 2*w^3 + 3*w^2 - 17*w - 9]', '[5041, 71, 9*w^3 + 14*w^2 - 53*w - 54]', '[5041, 71, -6*w^3 - 7*w^2 + 41*w + 26]', '[5041, 5041, 9*w^3 + 10*w^2 - 53*w - 35]', '[5041, 5041, -10*w^3 - 11*w^2 + 61*w + 41]', '[5041, 5041, 4*w^3 + 5*w^2 - 24*w - 28]', '[5041, 5041, 6*w^3 + 5*w^2 - 35*w - 18]', '[5051, 5051, -2*w^3 - 5*w^2 + 11*w + 32]', '[5051, 5051, 11*w^3 + 12*w^2 - 72*w - 45]', '[5051, 5051, 16*w^3 + 21*w^2 - 100*w - 82]', '[5051, 5051, -3*w^3 - 8*w^2 + 22*w + 30]', '[5059, 5059, -9*w^3 - 13*w^2 + 53*w + 54]', '[5059, 5059, -5*w^3 - 6*w^2 + 27*w + 29]', '[5059, 5059, 7*w^3 + 8*w^2 - 46*w - 25]', '[5059, 5059, -10*w^3 - 13*w^2 + 61*w + 43]', '[5099, 5099, -13*w^3 - 19*w^2 + 78*w + 80]', '[5099, 5099, 9*w^3 + 14*w^2 - 49*w - 58]', '[5099, 5099, -9*w^3 - 15*w^2 + 53*w + 68]', '[5099, 5099, 5*w^3 + 6*w^2 - 36*w - 13]', '[5111, 5111, -14*w^3 - 21*w^2 + 86*w + 71]', '[5111, 5111, -7*w^3 - 6*w^2 + 38*w + 25]', '[5111, 5111, 3*w^3 + w^2 - 25*w - 10]', '[5111, 5111, 16*w^3 + 20*w^2 - 95*w - 71]', '[5111, 5111, -5*w^3 - 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173]', '[5245, 5245, -39*w^3 - 50*w^2 + 245*w + 211]', '[5251, 5251, -14*w^3 - 17*w^2 + 84*w + 61]', '[5251, 5251, 15*w^3 + 20*w^2 - 93*w - 81]', '[5251, 5251, 13*w^3 + 19*w^2 - 77*w - 67]', '[5251, 5251, 9*w^3 + 13*w^2 - 56*w - 52]', '[5251, 5251, -3*w^3 - 8*w^2 + 21*w + 28]', '[5251, 5251, -8*w^3 - 8*w^2 + 47*w + 25]', '[5251, 5251, -10*w^3 - 11*w^2 + 60*w + 43]', '[5251, 5251, -8*w^3 - 11*w^2 + 43*w + 38]', '[5251, 5251, -9*w^3 - 10*w^2 + 60*w + 42]', '[5251, 5251, 10*w^3 + 12*w^2 - 67*w - 42]', '[5251, 5251, -7*w^3 - 6*w^2 + 42*w + 23]', '[5251, 5251, 5*w^3 + 9*w^2 - 32*w - 34]', '[5251, 5251, -10*w^3 - 15*w^2 + 64*w + 63]', '[5251, 5251, 8*w^3 + 12*w^2 - 50*w - 45]', '[5251, 5251, -9*w^3 - 9*w^2 + 55*w + 28]', '[5251, 5251, 6*w^3 + 10*w^2 - 38*w - 41]', '[5255, 5255, 13*w^3 + 15*w^2 - 81*w - 53]', '[5255, 5255, -19*w^3 - 22*w^2 + 119*w + 82]', '[5255, 5255, 11*w^3 + 11*w^2 - 70*w - 35]', '[5255, 5255, 17*w^3 + 18*w^2 - 108*w - 64]', '[5261, 5261, -9*w^3 - 13*w^2 + 53*w + 39]', '[5261, 5261, 12*w^3 + 17*w^2 - 72*w - 65]', '[5261, 5261, 7*w^3 + 8*w^2 - 46*w - 40]', '[5261, 5261, 2*w^3 + 6*w^2 - 11*w - 38]', '[5269, 5269, -5*w^3 - 6*w^2 + 26*w + 29]', '[5269, 5269, -6*w^3 - 7*w^2 + 34*w + 34]', '[5269, 5269, 11*w^3 + 14*w^2 - 62*w - 44]', '[5269, 5269, 2*w^3 - w^2 - 10*w + 9]', '[5269, 5269, -8*w^3 - 13*w^2 + 46*w + 44]', '[5269, 5269, w^3 - w^2 - 8*w]', '[5269, 5269, 9*w^3 + 11*w^2 - 55*w - 33]', '[5269, 5269, -13*w^3 - 16*w^2 + 80*w + 57]', '[5269, 5269, -2*w^3 + 11*w - 10]', '[5269, 5269, 9*w^3 + 12*w^2 - 53*w - 49]', '[5269, 5269, 16*w^3 + 20*w^2 - 99*w - 84]', '[5269, 5269, 4*w^2 + 2*w - 19]', '[5269, 5269, -6*w^3 - 4*w^2 + 39*w + 13]', '[5269, 5269, w^3 + 3*w^2 - 8*w - 19]', '[5269, 5269, 7*w^3 + 9*w^2 - 44*w - 27]', '[5269, 5269, -6*w^3 - 3*w^2 + 40*w - 4]', '[5275, 1055, -3*w^3 - 5*w^2 + 14*w + 21]', '[5275, 1055, -w^3 + w^2 + 10*w - 7]', '[5275, 1055, -2*w^2 - 4*w + 13]', '[5275, 1055, 2*w^3 + 4*w^2 - 8*w - 15]', '[5296, 662, -4*w^3 - 6*w^2 + 24*w + 14]', '[5296, 662, 2*w^3 + 2*w^2 - 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59*w - 43]', '[5651, 5651, -7*w^3 - 6*w^2 + 41*w + 17]', '[5659, 5659, -7*w^3 - 5*w^2 + 34*w + 28]', '[5659, 5659, -7*w^3 - 5*w^2 + 47*w + 7]', '[5659, 5659, -8*w^3 - 10*w^2 + 43*w + 32]', '[5659, 5659, 4*w^3 + 2*w^2 - 17*w - 19]', '[5669, 5669, -6*w^3 - 7*w^2 + 33*w + 32]', '[5669, 5669, 8*w^3 + 12*w^2 - 47*w - 52]', '[5669, 5669, -11*w^3 - 14*w^2 + 67*w + 47]', '[5669, 5669, 6*w^3 + 7*w^2 - 40*w - 20]', '[5680, 710, 8*w^3 + 12*w^2 - 46*w - 50]', '[5680, 710, 24*w^3 + 30*w^2 - 148*w - 114]', '[5680, 710, -26*w^3 - 36*w^2 + 164*w + 164]', '[5680, 710, -6*w^3 - 6*w^2 + 34*w + 14]', '[5689, 5689, -9*w^3 - 8*w^2 + 58*w + 30]', '[5689, 5689, 15*w^3 + 19*w^2 - 92*w - 78]', '[5689, 5689, -11*w^3 - 13*w^2 + 72*w + 46]', '[5689, 5689, -15*w^3 - 19*w^2 + 91*w + 67]', '[5725, 1145, 8*w^3 + 8*w^2 - 53*w - 23]', '[5725, 1145, -2*w^3 - 7*w^2 + 12*w + 27]', '[5725, 1145, 3*w^3 + 3*w^2 - 13*w - 8]', '[5725, 1145, 4*w^2 - 2*w - 21]', '[5741, 5741, 4*w^3 + 9*w^2 - 24*w - 37]', '[5741, 5741, -11*w^3 - 16*w^2 + 66*w + 63]', '[5741, 5741, -6*w^3 - 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111*w - 83]', '[9781, 9781, 17*w^3 + 24*w^2 - 101*w - 91]', '[9801, 33, 9*w^3 + 9*w^2 - 54*w - 33]', '[9801, 33, 15*w^3 + 18*w^2 - 90*w - 66]', '[9801, 33, -9*w^3 - 9*w^2 + 51*w + 33]', '[9801, 33, -12*w^3 - 12*w^2 + 75*w + 42]', '[9801, 33, 9*w^3 + 9*w^2 - 54*w - 30]', '[9801, 33, 6*w^3 + 3*w^2 - 36*w - 6]', '[9801, 363, 3*w^3 + 9*w^2 - 18*w - 42]', '[9801, 363, 15*w^3 + 21*w^2 - 90*w - 78]', '[9801, 363, 9*w^3 + 9*w^2 - 60*w - 33]', '[9801, 363, -3*w^3 - 3*w^2 + 12*w + 15]', '[9811, 9811, 11*w^3 + 12*w^2 - 66*w - 46]', '[9811, 9811, 8*w^3 + 7*w^2 - 48*w - 26]', '[9811, 9811, -9*w^3 - 9*w^2 + 53*w + 29]', '[9811, 9811, -10*w^3 - 10*w^2 + 61*w + 32]', '[9851, 9851, 2*w^3 + 4*w^2 - 7*w - 13]', '[9851, 9851, -10*w^3 - 15*w^2 + 62*w + 63]', '[9851, 9851, -w^3 + w^2 + 11*w - 12]', '[9851, 9851, 7*w^3 + 12*w^2 - 44*w - 43]', '[9859, 9859, 17*w^3 + 21*w^2 - 102*w - 83]', '[9859, 9859, 18*w^3 + 21*w^2 - 113*w - 78]', '[9859, 9859, 7*w^3 + 11*w^2 - 46*w - 31]', '[9859, 9859, 5*w^3 + 10*w^2 - 37*w - 23]', '[9869, 9869, -17*w^3 - 22*w^2 + 104*w + 90]', '[9869, 9869, w^3 + 7*w^2 - 11*w - 16]', '[9869, 9869, 10*w^3 + 13*w^2 - 59*w - 64]', '[9869, 9869, 6*w^3 + 6*w^2 - 30*w - 31]', '[9869, 9869, -6*w^3 - 6*w^2 + 29*w + 32]', '[9869, 9869, -13*w^3 - 18*w^2 + 73*w + 69]', '[9869, 9869, -9*w^3 - 15*w^2 + 59*w + 41]', '[9869, 9869, -7*w^3 - 14*w^2 + 43*w + 47]', '[9869, 9869, 4*w^3 + 11*w^2 - 34*w - 24]', '[9869, 9869, 9*w^3 + 10*w^2 - 57*w - 21]', '[9869, 9869, -18*w^3 - 23*w^2 + 108*w + 79]', '[9869, 9869, 11*w^3 + 16*w^2 - 68*w - 49]', '[9869, 9869, 7*w^3 + 13*w^2 - 48*w - 36]', '[9869, 9869, -9*w^3 - 11*w^2 + 49*w + 35]', '[9869, 9869, 5*w^3 + 8*w^2 - 36*w - 15]', '[9869, 9869, 7*w^3 + 9*w^2 - 45*w - 23]', '[9871, 9871, -15*w^3 - 21*w^2 + 90*w + 79]', '[9871, 9871, -9*w^3 - 9*w^2 + 60*w + 32]', '[9871, 9871, -11*w^3 - 14*w^2 + 67*w + 67]', '[9871, 9871, 6*w^3 + 7*w^2 - 33*w - 12]', '[9895, 9895, 16*w^3 + 22*w^2 - 100*w - 101]', '[9895, 9895, -27*w^3 - 36*w^2 + 168*w + 152]', '[9895, 9895, 3*w^3 + w^2 - 23*w - 1]', '[9895, 9895, 26*w^3 + 31*w^2 - 162*w - 122]', '[9904, 1238, -18*w^3 - 22*w^2 + 110*w + 78]', '[9904, 1238, -10*w^3 - 8*w^2 + 64*w + 28]', '[9904, 1238, 14*w^3 + 18*w^2 - 84*w - 72]', '[9904, 1238, 8*w^3 + 12*w^2 - 52*w - 54]', '[9929, 9929, 10*w^3 + 11*w^2 - 64*w - 36]', '[9929, 9929, 3*w^3 + 2*w^2 - 14*w - 4]', '[9929, 9929, -w^3 + 3*w^2 + 7*w - 13]', '[9929, 9929, -12*w^3 - 16*w^2 + 71*w + 64]', '[9941, 9941, 16*w^3 + 17*w^2 - 100*w - 67]', '[9941, 9941, -18*w^3 - 22*w^2 + 107*w + 75]', '[9941, 9941, -16*w^3 - 23*w^2 + 95*w + 89]', '[9941, 9941, -11*w^3 - 12*w^2 + 73*w + 42]', '[10000, 10, 10]'], 'label': '4.4.6125.1', 'narrow_class_no': 2, 'primes': ['[5, 5, -2*w^3 - 2*w^2 + 13*w + 8]', '[11, 11, 2*w^3 + 3*w^2 - 12*w - 11]', '[11, 11, -w^3 - 2*w^2 + 6*w + 9]', '[11, 11, w^3 + w^2 - 7*w - 4]', '[11, 11, w - 1]', '[16, 2, 2]', '[19, 19, -w^2 + 4]', '[19, 19, 2*w^3 + 2*w^2 - 13*w - 6]', '[19, 19, 3*w^3 + 4*w^2 - 18*w - 16]', '[19, 19, -w^3 - w^2 + 5*w + 3]', '[49, 7, 2*w^3 + 3*w^2 - 13*w - 15]', '[59, 59, -3*w^3 - 4*w^2 + 19*w + 14]', '[59, 59, 3*w^3 + 4*w^2 - 18*w - 17]', '[59, 59, 2*w^3 + 3*w^2 - 11*w - 13]', '[59, 59, -w^3 - 2*w^2 + 7*w + 9]', '[71, 71, 3*w^3 + 3*w^2 - 17*w - 10]', '[71, 71, -2*w^3 - w^2 + 14*w + 2]', '[71, 71, 5*w^3 + 7*w^2 - 30*w - 25]', '[71, 71, -3*w^3 - 4*w^2 + 16*w + 16]', '[81, 3, -3]', '[89, 89, -2*w^3 - 2*w^2 + 13*w + 4]', '[89, 89, 3*w^3 + 4*w^2 - 17*w - 16]', '[89, 89, 3*w^3 + 4*w^2 - 18*w - 18]', '[89, 89, -4*w^3 - 5*w^2 + 25*w + 18]', '[139, 139, -w^3 + 6*w + 1]', '[139, 139, -3*w^3 - 3*w^2 + 19*w + 8]', '[139, 139, 4*w^3 + 5*w^2 - 24*w - 21]', '[139, 139, -2*w^3 - 2*w^2 + 11*w + 5]', '[151, 151, -6*w^3 - 7*w^2 + 37*w + 27]', '[151, 151, 3*w^3 + 5*w^2 - 19*w - 17]', '[151, 151, -6*w^3 - 8*w^2 + 37*w + 31]', '[151, 151, 4*w^3 + 6*w^2 - 25*w - 26]', '[191, 191, 5*w^3 + 7*w^2 - 31*w - 26]', '[191, 191, -2*w^3 - 3*w^2 + 10*w + 13]', '[191, 191, -5*w^3 - 7*w^2 + 31*w + 29]', '[191, 191, 2*w^3 + 4*w^2 - 13*w - 17]', '[199, 199, 2*w^3 + 4*w^2 - 11*w - 20]', '[199, 199, -2*w^3 - 2*w^2 + 11*w + 3]', '[199, 199, 3*w^3 + 5*w^2 - 17*w - 17]', '[199, 199, 3*w^3 + 3*w^2 - 19*w - 6]', '[211, 211, 3*w^3 + 5*w^2 - 18*w - 19]', '[211, 211, -3*w^3 - 5*w^2 + 18*w + 21]', '[211, 211, 2*w^3 + 4*w^2 - 12*w - 17]', '[211, 211, -4*w^3 - 6*w^2 + 24*w + 23]', '[229, 229, 2*w^3 + 4*w^2 - 13*w - 19]', '[229, 229, -2*w^3 - 3*w^2 + 10*w + 15]', '[229, 229, -5*w^3 - 7*w^2 + 31*w + 24]', '[229, 229, 2*w^3 + 2*w^2 - 14*w - 3]', '[269, 269, 2*w^3 + w^2 - 11*w - 1]', '[269, 269, -6*w^3 - 7*w^2 + 37*w + 24]', '[269, 269, 5*w^3 + 6*w^2 - 29*w - 24]', '[269, 269, 3*w^3 + 2*w^2 - 19*w - 7]', '[281, 281, -4*w^3 - 6*w^2 + 25*w + 25]', '[281, 281, -5*w^3 - 7*w^2 + 31*w + 27]', '[281, 281, w^2 + 2*w - 7]', '[281, 281, 3*w^3 + 5*w^2 - 19*w - 18]', '[331, 331, -2*w^3 - 3*w^2 + 12*w + 7]', '[331, 331, w^3 + w^2 - 7*w - 8]', '[331, 331, w^3 + 2*w^2 - 6*w - 13]', '[331, 331, w - 5]', '[349, 349, 2*w^3 + 5*w^2 - 16*w - 12]', '[349, 349, 2*w^3 + 4*w^2 - 15*w - 10]', '[349, 349, 8*w^3 + 9*w^2 - 50*w - 32]', '[349, 349, 2*w^3 + 4*w^2 - 15*w - 9]', '[401, 401, 4*w^3 + 3*w^2 - 21*w - 12]', '[401, 401, 3*w^3 + 2*w^2 - 16*w - 9]', '[401, 401, -3*w^3 - 6*w^2 + 20*w + 19]', '[401, 401, -4*w^3 - 3*w^2 + 27*w + 9]', '[409, 409, -5*w^3 - 6*w^2 + 31*w + 20]', '[409, 409, 3*w^3 + 4*w^2 - 20*w - 12]', '[409, 409, -3*w^3 - 5*w^2 + 17*w + 23]', '[409, 409, 4*w^3 + 5*w^2 - 23*w - 21]', '[419, 419, -4*w^3 - 4*w^2 + 21*w + 18]', '[419, 419, -4*w^3 - 4*w^2 + 20*w + 19]', '[419, 419, -3*w^3 - 4*w^2 + 16*w + 18]', '[419, 419, -2*w^3 - w^2 + 8*w + 10]', '[421, 421, -6*w^3 - 7*w^2 + 36*w + 26]', '[421, 421, 5*w^3 + 5*w^2 - 31*w - 17]', '[421, 421, 3*w^3 + 2*w^2 - 18*w - 6]', '[421, 421, 4*w^3 + 4*w^2 - 23*w - 14]', '[431, 431, 6*w^3 + 7*w^2 - 36*w - 25]', '[431, 431, -3*w^3 - 2*w^2 + 18*w + 5]', '[431, 431, 4*w^3 + 4*w^2 - 23*w - 15]', '[431, 431, -5*w^3 - 5*w^2 + 31*w + 18]', '[439, 439, w^3 + w^2 - 4*w - 1]', '[439, 439, w^3 + 3*w^2 - 6*w - 10]', '[439, 439, 3*w^3 + 3*w^2 - 20*w - 7]', '[439, 439, 5*w^3 + 7*w^2 - 30*w - 30]', '[479, 479, -4*w^3 - 5*w^2 + 25*w + 15]', '[479, 479, -5*w^3 - 6*w^2 + 32*w + 21]', '[479, 479, 5*w^3 + 7*w^2 - 29*w - 28]', '[479, 479, 2*w^2 + w - 9]', '[491, 491, 7*w^3 + 8*w^2 - 43*w - 31]', '[491, 491, 6*w^3 + 6*w^2 - 37*w - 24]', '[491, 491, 4*w^3 + 3*w^2 - 24*w - 6]', '[491, 491, 5*w^3 + 5*w^2 - 29*w - 21]', '[509, 509, -4*w^3 - 5*w^2 + 25*w + 14]', '[509, 509, -3*w^3 - 4*w^2 + 17*w + 20]', '[509, 509, -6*w^3 - 7*w^2 + 38*w + 25]', '[509, 509, -6*w^3 - 8*w^2 + 35*w + 31]', '[541, 541, 9*w^3 + 12*w^2 - 55*w - 46]', '[541, 541, w^3 + 4*w^2 - 7*w - 17]', '[541, 541, -4*w^3 - 5*w^2 + 21*w + 19]', '[541, 541, -4*w^3 - 3*w^2 + 27*w + 8]', '[571, 571, -3*w^3 - 6*w^2 + 18*w + 23]', '[571, 571, 6*w^3 + 9*w^2 - 36*w - 37]', '[571, 571, 7*w^3 + 10*w^2 - 42*w - 36]', '[571, 571, 2*w^3 + 5*w^2 - 12*w - 24]', '[619, 619, -9*w^3 - 11*w^2 + 55*w + 39]', '[619, 619, -5*w^3 - 4*w^2 + 32*w + 14]', '[619, 619, 7*w^3 + 9*w^2 - 42*w - 36]', '[619, 619, 4*w^3 + 6*w^2 - 26*w - 27]', '[631, 631, 2*w^3 + 5*w^2 - 12*w - 21]', '[631, 631, -7*w^3 - 10*w^2 + 42*w + 39]', '[631, 631, 4*w^3 + 4*w^2 - 27*w - 13]', '[631, 631, w^3 + w^2 - 3*w - 4]', '[641, 641, -9*w^3 - 10*w^2 + 56*w + 36]', '[641, 641, -5*w^3 - 9*w^2 + 30*w + 32]', '[641, 641, -3*w^3 - 6*w^2 + 19*w + 21]', '[641, 641, 4*w^3 + 3*w^2 - 22*w - 10]', '[701, 701, -2*w^3 - 5*w^2 + 14*w + 20]', '[701, 701, -6*w^3 - 7*w^2 + 36*w + 34]', '[701, 701, 4*w^3 + 6*w^2 - 23*w - 17]', '[701, 701, -9*w^3 - 12*w^2 + 56*w + 46]', '[719, 719, 3*w^3 + 5*w^2 - 17*w - 25]', '[719, 719, -3*w^3 - 2*w^2 + 17*w + 3]', '[719, 719, 7*w^3 + 8*w^2 - 43*w - 26]', '[719, 719, -6*w^3 - 7*w^2 + 35*w + 29]', '[751, 751, 2*w^3 + 2*w^2 - 15*w - 4]', '[751, 751, 5*w^3 + 8*w^2 - 30*w - 34]', '[751, 751, w^3 + w^2 - 9*w - 5]', '[751, 751, -4*w^3 - 7*w^2 + 24*w + 26]', '[769, 769, 6*w^3 + 8*w^2 - 37*w - 27]', '[769, 769, -w^3 - 3*w^2 + 7*w + 16]', '[769, 769, 2*w^3 + w^2 - 14*w - 5]', '[769, 769, -3*w^3 - 4*w^2 + 16*w + 19]', '[821, 821, 6*w^3 + 6*w^2 - 37*w - 23]', '[821, 821, 5*w^3 + 5*w^2 - 29*w - 20]', '[821, 821, -7*w^3 - 8*w^2 + 42*w + 27]', '[821, 821, 4*w^3 + 3*w^2 - 24*w - 7]', '[829, 829, 7*w^3 + 8*w^2 - 44*w - 28]', '[829, 829, 7*w^3 + 9*w^2 - 41*w - 35]', '[829, 829, -2*w^3 - w^2 + 10*w + 2]', '[829, 829, 2*w^3 - 13*w + 2]', '[839, 839, 4*w^3 + 8*w^2 - 25*w - 26]', '[839, 839, -3*w^3 - 3*w^2 + 15*w + 16]', '[839, 839, -w^3 - 4*w^2 + 8*w + 10]', '[839, 839, -3*w^3 - 7*w^2 + 18*w + 26]', '[841, 29, -5*w^3 - 5*w^2 + 30*w + 16]', '[841, 29, -5*w^3 - 5*w^2 + 30*w + 19]', '[859, 859, 5*w^3 + 6*w^2 - 32*w - 20]', '[859, 859, -4*w^3 - 5*w^2 + 23*w + 23]', '[859, 859, -5*w^3 - 6*w^2 + 31*w + 18]', '[859, 859, -2*w^3 - w^2 + 13*w + 6]', '[911, 911, 9*w^3 + 12*w^2 - 56*w - 48]', '[911, 911, 6*w^3 + 5*w^2 - 38*w - 14]', '[911, 911, 7*w^3 + 8*w^2 - 40*w - 28]', '[911, 911, 10*w^3 + 12*w^2 - 61*w - 46]', '[929, 929, -7*w^3 - 10*w^2 + 39*w + 39]', '[929, 929, -10*w^3 - 13*w^2 + 60*w + 45]', '[929, 929, -6*w^3 - 7*w^2 + 32*w + 29]', '[929, 929, -3*w^3 - w^2 + 12*w + 12]', '[961, 31, -5*w^3 - 5*w^2 + 30*w + 17]', '[961, 31, -5*w^3 - 5*w^2 + 30*w + 18]', '[991, 991, 10*w^3 + 12*w^2 - 61*w - 45]', '[991, 991, -6*w^3 - 9*w^2 + 38*w + 38]', '[991, 991, 6*w^3 + 8*w^2 - 37*w - 38]', '[991, 991, -8*w^3 - 11*w^2 + 49*w + 43]']}
• 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': [11, 9, -9, -1, 1], 'conductor': 35, 'degree': 4, 'dirichlet_group': [1, 27, 13, 29], 'disc_abs': 6125, 'disc_rad': 35, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[4, 1]]], [5, [0]], [7, [0]], [11, [[1, 4]]], [13, [[4, 1]]], [17, [[4, 1]]], [19, [[1, 4]]], [23, [[4, 1]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[4, 1]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[1, 4]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 2], 'galois_label': '4T1', 'galt': 1, 'grd': 8.846602693265513, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.6125.1', 'local_algs': ['5.4.3.1', '7.4.2.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 7], 'rd': 8.84660269327, 'regulator': {'__RealLiteral__': 0, 'data': '3.36611485007', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} + a^{2} - 6 a - 4 \\)', '\\( a^{3} + a^{2} - 7 a - 5 \\)', '\\( a^{3} + 2 a^{2} - 6 a - 10 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}