Hilbert modular form data - 4.4.6809.1-31.1-a

Formats: - HTML - YAML - JSON - 2024-05-06T05:33:26.203189

• 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': 5, 'disc': 6809, 'field_bad_primes': [11, 619], 'field_label': '4.4.6809.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.6809.1-31.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [31], 'level_ideal': '[31, 31, -w^3 + 6*w + 2]', 'level_label': '31.1', 'level_norm': 31, 'parallel_weight': 2, 'short_label': '31.1-a', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[31, 31, -w^3 + 6*w + 2]', -1]], 'hecke_eigenvalues': ['e', '-e^3 + 5*e', '-e^3 + 4*e', 'e^4 + 2*e^3 - 5*e^2 - 10*e - 3', 'e^4 + 2*e^3 - 6*e^2 - 9*e + 2', '-e^3 + 5*e - 2', '-e^4 + 4*e^2 - e + 1', 1, '-2*e^4 - 3*e^3 + 8*e^2 + 14*e + 5', '-3*e^4 - 2*e^3 + 17*e^2 + 10*e - 7', '2*e^4 + 5*e^3 - 10*e^2 - 25*e + 1', '3*e^4 + 2*e^3 - 18*e^2 - 12*e + 7', 'e^4 + 3*e^3 - 4*e^2 - 18*e - 7', '-5*e^4 - 6*e^3 + 25*e^2 + 27*e - 5', '3*e^4 + 2*e^3 - 14*e^2 - 10*e - 8', 'e^4 + 4*e^3 - 4*e^2 - 16*e - 4', '2*e^4 + 3*e^3 - 10*e^2 - 10*e + 4', '2*e^4 + 5*e^3 - 8*e^2 - 22*e - 5', '-5*e^4 - 3*e^3 + 22*e^2 + 13*e + 6', '2*e^4 + 2*e^3 - 10*e^2 - 7*e', '-2*e^4 - 9*e^3 + 11*e^2 + 43*e - 5', '4*e^4 + 6*e^3 - 21*e^2 - 25*e + 10', '4*e^2 - 10', '-5*e^4 - 9*e^3 + 27*e^2 + 43*e - 4', '2*e^3 - 2*e^2 - 15*e + 1', '-e^4 + 5*e^3 + 8*e^2 - 23*e - 8', '-2*e^4 - 2*e^3 + 13*e^2 + 11*e - 6', '3*e^4 + 3*e^3 - 16*e^2 - 14*e + 2', '-2*e^4 - 3*e^3 + 12*e^2 + 14*e - 4', '-2*e^4 + 14*e^2 + 5*e - 9', '-e^4 + 5*e^3 + 4*e^2 - 27*e - 7', '-4*e^4 - 4*e^3 + 19*e^2 + 20*e - 3', '-4*e^4 - 7*e^3 + 19*e^2 + 38*e - 6', '-4*e^4 - 4*e^3 + 19*e^2 + 20*e - 8', '3*e^4 + 5*e^3 - 14*e^2 - 25*e - 11', '-8*e^4 - 8*e^3 + 42*e^2 + 43*e - 9', '5*e^4 + 9*e^3 - 24*e^2 - 35*e - 6', 'e^4 + 2*e^3 - 2*e^2 - 6*e - 2', '-e^4 - 2*e^3 + 5*e^2 + 5*e - 6', 'e^4 - 4*e^3 - 9*e^2 + 15*e + 8', '-7*e^4 - 12*e^3 + 35*e^2 + 59*e + 1', 'e^4 - 2*e^3 - 9*e^2 + 10*e + 7', '4*e^4 + 8*e^3 - 20*e^2 - 30*e + 5', '-5*e^4 - 7*e^3 + 25*e^2 + 30*e - 2', '-2*e^3 - e^2 + 6*e - 7', '-2*e^4 - 11*e^3 + 8*e^2 + 51*e + 7', '2*e^4 + 5*e^3 - 13*e^2 - 24*e + 15', '5*e^4 + 9*e^3 - 28*e^2 - 51*e + 9', '5*e^4 + 5*e^3 - 26*e^2 - 25*e + 2', '-3*e^4 + 16*e^2 + 5*e + 5', '7*e^4 + 12*e^3 - 40*e^2 - 56*e + 16', '-10*e^4 - 15*e^3 + 53*e^2 + 77*e - 2', '-4*e^4 - 2*e^3 + 24*e^2 + 12*e - 21', '4*e^3 + 2*e^2 - 29*e - 15', '-4*e^3 - e^2 + 26*e + 14', '3*e^4 + 4*e^3 - 14*e^2 - 22*e - 16', '2*e^4 + 2*e^3 - 7*e^2 - 7*e - 10', '13*e^4 + 14*e^3 - 68*e^2 - 70*e + 7', '-8*e^4 - 17*e^3 + 40*e^2 + 75*e - 3', '4*e^4 + 7*e^3 - 23*e^2 - 40*e + 20', '2*e^4 + e^3 - 10*e^2 + 2*e', '3*e^4 + 4*e^3 - 7*e^2 - 19*e - 18', '-2*e^4 + e^3 + 10*e^2 - 8*e + 6', '-2*e^4 - 8*e^3 + 8*e^2 + 37*e - 2', '11*e^4 + 12*e^3 - 53*e^2 - 53*e + 12', '-3*e^4 - 4*e^3 + 15*e^2 + 24*e', '-3*e^4 - 8*e^3 + 11*e^2 + 44*e + 7', '-15*e^4 - 18*e^3 + 75*e^2 + 79*e - 13', '3*e^4 + 8*e^3 - 13*e^2 - 36*e - 11', '3*e^4 + 8*e^3 - 14*e^2 - 33*e - 8', '8*e^4 + 10*e^3 - 39*e^2 - 50*e - 2', '-6*e^4 - 3*e^3 + 31*e^2 + 14*e - 1', '5*e^4 - 28*e^2 + 5*e + 21', '4*e^4 + 4*e^3 - 26*e^2 - 17*e + 5', '-6*e^4 + e^3 + 32*e^2 - 3*e - 8', '6*e^4 + 15*e^3 - 27*e^2 - 82*e - 9', '-5*e^4 - 3*e^3 + 29*e^2 + 9*e - 13', '-3*e^4 - 9*e^3 + 15*e^2 + 38*e - 1', '10*e^4 + 13*e^3 - 49*e^2 - 75*e - 9', '-8*e^4 - 8*e^3 + 40*e^2 + 31*e - 10', '4*e^4 + 3*e^3 - 17*e^2 - 15*e', '-7*e^4 - 4*e^3 + 38*e^2 + 13*e - 11', '6*e^4 + 2*e^3 - 33*e^2 - 13*e + 7', '4*e^4 - 4*e^3 - 20*e^2 + 14*e - 3', '-4*e^4 - 2*e^3 + 32*e^2 + 16*e - 32', '-2*e^4 + 2*e^3 + 8*e^2 - 11*e - 3', '20*e^4 + 24*e^3 - 102*e^2 - 122*e + 9', '11*e^4 + 16*e^3 - 54*e^2 - 73*e + 9', '-3*e^4 - 7*e^3 + 12*e^2 + 32*e + 4', '-10*e^4 - 14*e^3 + 53*e^2 + 74*e - 10', '3*e^4 + 9*e^3 - 18*e^2 - 36*e + 17', '4*e^4 + 11*e^3 - 18*e^2 - 48*e - 6', '2*e^4 + 13*e^3 - 9*e^2 - 63*e + 6', '-e^4 + 6*e^3 + 2*e^2 - 37*e + 4', '-4*e^4 + 4*e^3 + 28*e^2 - 17*e - 28', '19*e^4 + 19*e^3 - 100*e^2 - 102*e + 5', '4*e^4 - 29*e^2 + 7*e + 36', '11*e^4 + 11*e^3 - 51*e^2 - 55*e - 6', '4*e^4 + 12*e^3 - 28*e^2 - 57*e + 32', '-5*e^4 - 15*e^3 + 32*e^2 + 80*e - 19', '-9*e^4 - 13*e^3 + 48*e^2 + 65*e - 27', '-3*e^4 - 9*e^3 + 3*e^2 + 33*e + 36', '-4*e^4 - 4*e^3 + 23*e^2 + 18*e - 15', '-e^4 - 2*e^3 + 6*e^2 + 2*e - 31', '4*e^4 + 13*e^3 - 25*e^2 - 69*e + 21', '-6*e^4 - 24*e^3 + 36*e^2 + 125*e - 4', '11*e^4 + 17*e^3 - 52*e^2 - 80*e + 21', '-2*e^4 - 6*e^3 + 14*e^2 + 29*e + 13', '4*e^4 - e^3 - 28*e^2 + 22', '16*e^4 + 31*e^3 - 81*e^2 - 150*e + 9', '-3*e^4 - 3*e^3 + 12*e^2 + 31*e + 28', '-10*e^4 - 10*e^3 + 48*e^2 + 47*e + 2', '12*e^4 + 18*e^3 - 56*e^2 - 88*e - 16', '3*e^4 + 2*e^3 - 23*e^2 - 12*e + 32', '4*e^4 + 14*e^3 - 13*e^2 - 73*e - 6', '-7*e^4 - 32*e^3 + 33*e^2 + 146*e', '-16*e^4 - 19*e^3 + 86*e^2 + 98*e - 28', '5*e^4 - e^3 - 11*e^2 + 13*e - 40', '-3*e^3 + e^2 - 3*e - 3', '-11*e^4 - 26*e^3 + 49*e^2 + 133*e + 1', '3*e^4 + 2*e^3 - 23*e^2 + 7*e + 51', '-2*e^4 + 3*e^3 + e^2 - 15*e + 33', '-8*e^4 - 7*e^3 + 46*e^2 + 30*e - 31', '17*e^4 + 13*e^3 - 88*e^2 - 73*e + 5', 'e^4 + 14*e^3 - 2*e^2 - 68*e - 19', '15*e^4 + 14*e^3 - 76*e^2 - 73*e + 4', 'e^4 + 10*e^3 - 15*e^2 - 59*e + 22', '-11*e^4 - 16*e^3 + 53*e^2 + 79*e - 13', '-12*e^4 - 23*e^3 + 61*e^2 + 113*e - 3', '12*e^4 + 20*e^3 - 66*e^2 - 109*e + 14', '-4*e^4 - 9*e^3 + 16*e^2 + 46*e - 2', '12*e^4 + 13*e^3 - 61*e^2 - 73*e - 12', '-9*e^4 - 17*e^3 + 40*e^2 + 75*e - 6', '-2*e^3 - 6*e^2 + 28*e + 32', '-9*e^4 - 22*e^3 + 46*e^2 + 113*e + 4', '-8*e^4 - e^3 + 51*e^2 + 16*e - 46', '6*e^4 + 10*e^3 - 37*e^2 - 46*e + 34', '7*e^4 + 9*e^3 - 33*e^2 - 44*e - 6', '-7*e^4 - 6*e^3 + 47*e^2 + 35*e - 48', '17*e^4 + 38*e^3 - 85*e^2 - 172*e + 2', '-e^4 + 6*e^3 - 7*e^2 - 37*e + 17', 'e^3 + 14*e^2 - 8*e - 28', '6*e^4 + 12*e^3 - 36*e^2 - 67*e + 23', '-6*e^4 - 2*e^3 + 34*e^2 + 17*e - 25', '-7*e^4 + e^3 + 43*e^2 + 2*e - 33', '-7*e^4 - 18*e^3 + 42*e^2 + 92*e - 3', '2*e^4 - 7*e^3 - 11*e^2 + 28*e - 11', '-10*e^4 - 15*e^3 + 41*e^2 + 68*e + 9', '-8*e^4 - e^3 + 49*e^2 + 12*e - 20', '-5*e^4 - 16*e^3 + 28*e^2 + 77*e', '9*e^4 + 4*e^3 - 48*e^2 - 16*e + 16', '-18*e^4 - 15*e^3 + 87*e^2 + 68*e - 12', '-12*e^4 - 20*e^3 + 64*e^2 + 91*e - 14', '7*e^4 + 15*e^3 - 35*e^2 - 84*e - 7', '-8*e^4 - 13*e^3 + 45*e^2 + 57*e - 8', '2*e^4 - 2*e^3 + 2*e^2 + 21*e - 32', 'e^4 + 10*e^3 - 3*e^2 - 49*e - 5', '-17*e^4 - 19*e^3 + 89*e^2 + 102*e - 5', '9*e^4 + 14*e^3 - 44*e^2 - 61*e + 4', '4*e^4 + 19*e^3 - 11*e^2 - 96*e - 31'], 'hecke_polynomial': 'x^5 + 2*x^4 - 5*x^3 - 10*x^2 + 1', 'label': '4.4.6809.1-31.1-a'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 6809, 'ideals': ['[1, 1, 1]', '[2, 2, w + 1]', '[4, 4, -w + 1]', '[5, 5, w^3 - 4*w]', '[8, 2, w^3 - w^2 - 4*w + 3]', '[8, 8, w^3 - 4*w - 1]', '[10, 10, -w^2 + w + 2]', '[11, 11, w^3 - 5*w + 1]', '[16, 2, 2]', '[16, 16, w^3 - 6*w + 1]', '[17, 17, -w^3 - w^2 + 5*w + 4]', '[20, 20, w^3 - w^2 - 5*w + 1]', '[22, 22, -w^2 + 3]', '[23, 23, -w^2 + 2]', '[25, 25, w^3 - w^2 - 3*w + 2]', '[29, 29, -w^2 - w + 3]', '[31, 31, -w^3 + 6*w + 2]', '[32, 4, 2*w + 2]', '[32, 32, w^3 - w^2 - 4*w]', '[34, 34, -w + 3]', '[40, 10, -w^3 - w^2 + 6*w + 5]', '[40, 40, w + 3]', '[43, 43, w^3 - 6*w]', '[44, 44, -w^3 - w^2 + 3*w + 3]', '[46, 46, 2*w^3 + w^2 - 9*w - 4]', '[47, 47, 2*w^3 - 9*w]', '[47, 47, -2*w^3 + w^2 + 8*w - 2]', '[50, 50, w^3 - 6*w - 1]', '[53, 53, -4*w^3 + 2*w^2 + 18*w - 5]', '[55, 55, w^3 + w^2 - 5*w - 2]', '[58, 58, w^3 + w^2 - 6*w - 2]', '[59, 59, w^2 - w - 5]', '[59, 59, 3*w^3 - 15*w - 5]', '[62, 62, -2*w^3 + w^2 + 8*w - 1]', '[64, 4, -w^3 - w^2 + 4*w + 5]', '[64, 8, -2*w + 2]', '[64, 64, -w^3 + 5*w + 4]', '[68, 68, -w^2 + 2*w + 3]', '[71, 71, w^3 - 3*w - 3]', '[80, 10, 2*w^3 - 8*w]', '[80, 80, 2*w^3 - 2*w^2 - 9*w + 5]', '[81, 3, -3]', '[83, 83, -2*w^3 + 8*w + 3]', '[85, 85, 2*w^3 - 11*w - 4]', '[86, 86, w^3 - w^2 - 5*w - 1]', '[88, 22, w^3 - w^2 - 6*w - 1]', '[88, 88, w^3 - w^2 - 3*w + 3]', '[89, 89, -2*w^3 + 11*w - 2]', '[92, 92, 2*w^3 - w^2 - 9*w]', '[94, 94, 2*w^3 + w^2 - 7*w - 2]', '[94, 94, -w^3 - w^2 + 4*w]', '[100, 100, w^3 - w^2 - 6*w - 2]', '[101, 101, 2*w^3 - w^2 - 10*w]', '[101, 101, 2*w^3 - 2*w^2 - 10*w + 3]', '[106, 106, -2*w^3 + 9*w - 1]', '[107, 107, 3*w^3 - 15*w - 1]', '[107, 107, 4*w^3 - 2*w^2 - 18*w + 3]', '[109, 109, 2*w^3 - 10*w + 3]', '[109, 109, 3*w^3 - 2*w^2 - 13*w + 3]', '[110, 110, 2*w^3 - 2*w^2 - 7*w + 1]', '[113, 113, 3*w^3 - w^2 - 15*w + 2]', '[113, 113, 3*w^3 - 13*w - 5]', '[115, 115, w^3 - w^2 - 7*w]', '[116, 116, w^3 - 4*w + 3]', '[118, 118, w^3 - 6*w - 5]', '[118, 118, 3*w^3 - 17*w - 8]', '[121, 11, 2*w^3 + w^2 - 8*w - 2]', '[121, 11, 3*w^3 - 13*w - 1]', '[124, 124, -w^3 - w^2 + 5*w + 1]', '[125, 5, -2*w^3 + w^2 + 7*w + 1]', '[125, 125, 2*w^3 - 9*w + 2]', '[127, 127, 2*w^3 - 8*w - 1]', '[127, 127, -w^3 + 2*w^2 + 3*w - 3]', '[128, 4, 2*w^3 - 2*w^2 - 8*w + 6]', '[128, 16, 2*w^3 - 8*w - 2]', '[128, 128, w^3 - 2*w^2 - 3*w + 4]', '[136, 34, w^3 + w^2 - 6*w - 1]', '[136, 136, 2*w^3 - 7*w + 1]', '[137, 137, 2*w^3 - 10*w + 1]', '[137, 137, 2*w^3 - 11*w]', '[139, 139, 2*w^3 - 9*w - 6]', '[142, 142, w^3 + 2*w^2 - 5*w - 4]', '[145, 145, w^3 - 7*w + 1]', '[155, 155, -2*w^3 - w^2 + 11*w + 3]', '[157, 157, -4*w^3 - w^2 + 19*w + 7]', '[160, 20, -2*w^2 + 2*w + 4]', '[160, 160, -w^2 - 2*w + 3]', '[162, 6, -3*w - 3]', '[163, 163, 5*w^3 - 2*w^2 - 25*w + 7]', '[166, 166, -2*w^3 - 2*w^2 + 9*w + 5]', '[167, 167, w^2 + w - 5]', '[167, 167, -w^3 + 2*w^2 + 4*w - 6]', '[169, 13, -w^3 + w^2 + 3*w - 4]', '[169, 13, w^2 - 2*w - 4]', '[170, 170, 3*w^3 - w^2 - 13*w + 1]', '[172, 172, w^3 + w^2 - 7*w + 1]', '[173, 173, -2*w^3 + w^2 + 11*w - 7]', '[173, 173, w - 4]', '[176, 22, 2*w^3 - 10*w + 2]', '[176, 176, 2*w^3 - 11*w - 3]', '[178, 178, -2*w^3 + w^2 + 7*w]', '[181, 181, w + 4]', '[181, 181, -2*w - 5]', '[184, 46, w^3 - w^2 - 6*w + 5]', '[184, 184, w^3 - 7*w - 2]', '[187, 187, 2*w^3 - w^2 - 9*w - 1]', '[188, 188, -3*w^3 + 3*w^2 + 12*w - 4]', '[188, 188, 2*w^3 - w^2 - 11*w + 2]', '[191, 191, -w^3 + 2*w^2 + 6*w - 6]', '[191, 191, 2*w^3 - w^2 - 11*w + 1]', '[193, 193, -3*w^3 + 16*w]', '[200, 50, -w^3 - w^2 + 2*w + 3]', '[200, 200, w^3 + w^2 - 6*w]', '[202, 202, -2*w^2 - 5*w + 1]', '[202, 202, w^3 - w^2 - 8*w - 2]', '[212, 212, -2*w^3 - w^2 + 6*w + 1]', '[214, 214, 2*w^3 + 3*w^2 - 5*w - 6]', '[214, 214, 2*w^3 - 11*w - 1]', '[215, 215, w^3 - 2*w^2 - 5*w + 5]', '[218, 218, 2*w^3 - 5*w + 1]', '[218, 218, w^3 - 7*w]', '[220, 220, -w^3 + 4*w + 5]', '[226, 226, 2*w^3 - w^2 - 10*w - 1]', '[226, 226, 3*w^3 + 2*w^2 - 15*w - 8]', '[227, 227, 6*w^3 - 3*w^2 - 27*w + 5]', '[227, 227, 2*w^3 - 11*w - 2]', '[229, 229, -2*w^3 + w^2 + 10*w - 6]', '[230, 230, -w^3 + w^2 + 3*w + 3]', '[232, 58, -w^3 + w^2 + 4*w + 3]', '[232, 232, 2*w^3 - w^2 - 11*w - 2]', '[233, 233, 4*w^3 - 3*w^2 - 17*w + 5]', '[233, 233, 2*w^3 + w^2 - 7*w - 5]', '[233, 233, w^3 - 7*w - 1]', '[233, 233, 2*w^3 - 7*w]', '[235, 235, 2*w^3 - w^2 - 7*w + 7]', '[235, 235, -3*w^3 + w^2 + 13*w - 6]', '[236, 236, 3*w^3 - 13*w - 2]', '[236, 236, -w^3 + 2*w^2 + 4*w - 5]', '[239, 239, 2*w^2 - 2*w - 7]', '[239, 239, -4*w^3 + w^2 + 18*w]', '[241, 241, w^3 - 5*w - 5]', '[242, 22, 3*w^3 - 2*w^2 - 14*w + 3]', '[242, 22, 3*w^3 + 2*w^2 - 11*w - 4]', '[248, 62, -w^3 + w^2 + 2*w - 3]', '[248, 248, 2*w^3 + 2*w^2 - 9*w - 7]', '[250, 10, -4*w^3 - 3*w^2 + 14*w + 7]', '[250, 250, -2*w^2 - w + 5]', '[253, 253, 2*w^3 - 2*w^2 - 9*w + 2]', '[254, 254, 2*w^3 + 2*w^2 - 7*w - 3]', '[254, 254, -3*w^3 + 3*w^2 + 15*w - 5]', '[256, 4, 4]', '[256, 32, 2*w^3 - 12*w + 2]', '[256, 256, -w^3 + 2*w + 3]', '[263, 263, -4*w^3 + w^2 + 20*w - 4]', '[265, 265, -3*w^3 + 13*w + 3]', '[269, 269, w^3 + 2*w^2 - 6*w - 6]', '[271, 271, 2*w^3 + w^2 - 12*w - 8]', '[272, 34, -2*w^3 - 2*w^2 + 10*w + 8]', '[272, 272, 3*w^3 - w^2 - 12*w - 2]', '[274, 274, 2*w^3 - 7*w - 1]', '[274, 274, 2*w^3 - w^2 - 9*w - 2]', '[275, 275, 3*w + 4]', '[277, 277, w^3 + w^2 - 7*w - 6]', '[278, 278, 2*w^3 + w^2 - 13*w - 8]', '[283, 283, 6*w^3 - 3*w^2 - 27*w + 7]', '[283, 283, -3*w^3 + 3*w^2 + 13*w - 8]', '[284, 284, w^3 - 2*w^2 - w - 2]', '[289, 289, -2*w^2 - w + 4]', '[290, 290, -w^2 + 2*w + 5]', '[293, 293, -2*w^3 + w^2 + 9*w + 3]', '[293, 293, 4*w^3 - w^2 - 19*w + 3]', '[295, 295, -4*w^3 + 18*w + 1]', '[295, 295, -2*w^3 - 3*w^2 + 8*w + 12]', '[310, 310, -2*w^3 + w^2 + 9*w - 6]', '[313, 313, 2*w^2 - w - 4]', '[313, 313, -2*w^3 + 2*w^2 + 8*w - 1]', '[314, 314, -5*w^3 + 2*w^2 + 23*w - 2]', '[317, 317, 3*w^3 + w^2 - 13*w - 10]', '[319, 319, -w^3 - 2*w^2 + 5*w + 5]', '[320, 20, w^3 + w^2 - 8*w - 1]', '[320, 40, 2*w^3 - 2*w^2 - 10*w + 2]', '[320, 320, 3*w^3 + w^2 - 12*w - 4]', '[324, 12, 3*w - 3]', '[326, 326, 3*w^3 - 2*w^2 - 13*w + 2]', '[331, 331, w^3 + 2*w^2 - 4*w - 6]', '[332, 332, -2*w^3 + 2*w^2 + 7*w + 1]', '[334, 334, w^3 + 2*w^2 - 4*w - 5]', '[334, 334, w^3 + w^2 - 3*w - 5]', '[338, 26, -w^2 - 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2*w^2 - 14*w]', '[1840, 1840, 3*w^3 - w^2 - 14*w + 8]', '[1847, 1847, -w^3 + 11*w - 5]', '[1847, 1847, -2*w^3 + w^2 + 11*w - 9]', '[1849, 1849, 7*w^3 - w^2 - 35*w]', '[1853, 1853, 3*w^3 - 3*w^2 - 13*w + 2]', '[1853, 1853, -w^3 + w^2 - w + 4]', '[1856, 116, w^3 - 3*w^2 + 7]', '[1856, 232, 2*w^3 - 8*w + 6]', '[1856, 1856, -3*w^3 - 3*w^2 + 11*w + 11]', '[1859, 143, -6*w^3 + 3*w^2 + 25*w - 7]', '[1859, 143, -4*w^3 + 2*w^2 + 15*w - 2]', '[1861, 1861, 5*w^3 - 2*w^2 - 24*w]', '[1861, 1861, 2*w^3 + 3*w^2 - 10*w - 10]', '[1863, 69, 3*w^2 - 6]', '[1864, 466, 3*w^3 + w^2 - 14*w - 1]', '[1864, 466, w^3 + 3*w^2 - 6*w - 9]', '[1864, 466, 5*w^3 - 3*w^2 - 22*w + 3]', '[1864, 466, 5*w^3 - w^2 - 24*w + 5]', '[1864, 1864, -w^3 - 3*w^2 + 5*w + 7]', '[1864, 1864, w^2 + 2*w + 5]', '[1864, 1864, -4*w^3 + w^2 + 21*w + 10]', '[1864, 1864, w^3 + 3*w^2 - 10*w + 2]', '[1865, 1865, -5*w^3 + 19*w - 3]', '[1867, 1867, 4*w^3 - 2*w^2 - 19*w]', '[1868, 1868, w^3 + w^2 - 10*w]', '[1868, 1868, -3*w^3 - w^2 + 21*w - 5]', '[1870, 1870, 2*w^3 + 3*w^2 - 14*w - 5]', '[1871, 1871, 2*w^3 - 8*w - 9]', '[1871, 1871, 7*w^3 - 2*w^2 - 35*w + 5]', '[1873, 1873, 3*w^3 - 17*w - 3]', '[1874, 1874, w^3 - 2*w^2 - 11*w - 2]', '[1874, 1874, 3*w^3 - 2*w^2 - 13*w - 2]', '[1880, 470, 7*w^3 + w^2 - 32*w - 11]', '[1880, 470, -3*w^3 - w^2 + 16*w + 1]', '[1880, 1880, 6*w^3 + w^2 - 25*w - 2]', '[1880, 1880, -5*w^3 + w^2 + 20*w - 4]', '[1882, 1882, 3*w^3 + 3*w^2 - 16*w - 8]', '[1888, 236, 2*w^3 - 12*w - 10]', '[1888, 236, 6*w^3 - 34*w - 16]', '[1888, 1888, -2*w^3 - w^2 + 11*w + 12]', '[1888, 1888, -3*w^3 + 17*w + 2]', '[1892, 1892, 3*w^3 + 2*w^2 - 13*w - 4]', '[1895, 1895, -4*w^3 + w^2 + 22*w + 4]', '[1901, 1901, 2*w^3 + w^2 - 7*w - 9]', '[1901, 1901, 9*w^3 - 3*w^2 - 43*w + 8]', '[1903, 1903, -2*w^3 + 13*w + 2]', '[1903, 1903, -w^3 + w^2 + 11*w + 4]', '[1906, 1906, 5*w^2 + 5*w - 4]', '[1909, 1909, -2*w^3 - w^2 + 14*w + 6]', '[1910, 1910, 4*w^3 - w^2 - 16*w - 1]', '[1910, 1910, -w^3 + 2*w^2 + 2*w - 9]', '[1912, 478, -3*w^3 + 3*w^2 + 16*w - 17]', '[1912, 478, -13*w^3 + 5*w^2 + 62*w - 13]', '[1912, 1912, -5*w^3 - 2*w^2 + 26*w + 9]', '[1912, 1912, w^3 + 2*w^2 - 5*w - 14]', '[1913, 1913, -7*w^3 + 2*w^2 + 30*w + 4]', '[1915, 1915, -5*w^3 - w^2 + 21*w + 2]', '[1916, 1916, 4*w^3 - w^2 - 15*w - 4]', '[1921, 1921, 12*w^3 + 5*w^2 - 61*w - 33]', '[1921, 1921, -3*w^2 + w + 7]', '[1922, 1922, -3*w^2 + w + 8]', '[1928, 482, -w^3 + 3*w^2 + 2*w - 11]', '[1928, 1928, -5*w^3 - w^2 + 21*w + 9]', '[1930, 1930, w^3 + 2*w^2 - 3*w - 10]', '[1931, 1931, 3*w^3 - w^2 - 17*w]', '[1933, 1933, -4*w^3 + 2*w^2 + 17*w + 2]', '[1936, 22, 4*w^3 + 2*w^2 - 16*w - 4]', '[1936, 22, 6*w^3 - 26*w - 2]', '[1936, 176, w^3 - 2*w^2 - 7*w + 8]', '[1936, 176, 5*w^3 - 5*w^2 - 23*w + 15]', '[1942, 1942, -3*w^3 - 4*w^2 + 17*w + 12]', '[1945, 1945, -7*w^3 + 2*w^2 + 30*w - 12]', '[1949, 1949, -5*w^3 + w^2 + 21*w - 2]', '[1949, 1949, -5*w^3 + 4*w^2 + 22*w - 6]', '[1951, 1951, 8*w^3 + 3*w^2 - 38*w - 18]', '[1954, 1954, 4*w^3 - 3*w^2 - 15*w + 8]', '[1955, 1955, 5*w^3 + 2*w^2 - 20*w - 8]', '[1958, 1958, -7*w^3 + 4*w^2 + 31*w - 6]', '[1964, 1964, 3*w^3 + 2*w^2 - 5*w - 4]', '[1964, 1964, 3*w^3 - 16*w - 11]', '[1966, 1966, 3*w^3 - 2*w^2 - 14*w - 1]', '[1966, 1966, -w^3 - 2*w^2 + 5]', '[1972, 1972, -w^3 - 3*w^2 + 4*w + 8]', '[1978, 1978, -3*w^3 - 2*w^2 + 12*w + 11]', '[1984, 124, -3*w^3 + w^2 + 16*w - 9]', '[1984, 248, -2*w^3 - 2*w^2 + 10*w + 2]', '[1984, 1984, -w^2 + 6*w - 5]', '[1985, 1985, 8*w^3 + w^2 - 40*w - 18]', '[1985, 1985, -5*w^3 + w^2 + 21*w + 4]', '[1987, 1987, -8*w^3 - w^2 + 39*w + 17]', '[1987, 1987, 6*w^3 + w^2 - 26*w - 12]', '[1991, 1991, -5*w^3 + 21*w - 3]', '[1991, 1991, -4*w^3 + 18*w - 3]', '[1993, 1993, -2*w^3 + 13*w - 8]', '[1993, 1993, 3*w^2 - 8]', '[1994, 1994, 4*w^3 + w^2 - 24*w - 15]', '[1994, 1994, -5*w^3 + w^2 + 24*w - 6]', '[1999, 1999, 2*w^3 - 9*w + 6]', '[2000, 10, -6*w^3 - 2*w^2 + 26*w + 8]', '[2000, 80, -w^3 + 3*w^2 + 6*w - 12]', '[2000, 250, 4*w^3 - 18*w + 4]', '[2000, 2000, 3*w^3 - w^2 - 18*w - 4]', '[2005, 2005, -3*w^3 + 2*w^2 + 18*w]', '[2006, 2006, 9*w^3 - 43*w - 12]', '[2006, 2006, -w^3 + 4*w^2 + 2*w - 15]', '[2011, 2011, 11*w^3 - 4*w^2 - 52*w + 10]', '[2018, 2018, -7*w^3 + 2*w^2 + 33*w - 6]', '[2020, 2020, 7*w^3 - w^2 - 29*w + 11]', '[2020, 2020, 4*w^3 - w^2 - 16*w + 9]', '[2021, 2021, 5*w^3 - 5*w^2 - 21*w + 10]', '[2021, 2021, -2*w^2 + 7*w + 6]', '[2024, 506, 3*w^3 + 3*w^2 - 10*w - 3]', '[2024, 2024, -w^2 - 4*w + 5]', '[2025, 75, -3*w^3 + 3*w^2 + 9*w - 6]', '[2032, 254, 4*w^3 - 16*w - 2]', '[2032, 254, -2*w^3 + 4*w^2 + 6*w - 6]', '[2032, 2032, -2*w^3 + 3*w^2 + 14*w - 7]', '[2032, 2032, 3*w^3 - 4*w^2 - 12*w + 9]', '[2036, 2036, 5*w^3 - 22*w + 1]', '[2036, 2036, -3*w^3 - 3*w^2 + 9*w + 1]', '[2047, 2047, -5*w^3 + 4*w^2 + 20*w - 4]', '[2048, 8, 4*w^3 - 4*w^2 - 16*w + 12]', '[2048, 32, 4*w^3 - 16*w - 4]', '[2048, 256, 2*w^3 - 4*w^2 - 6*w + 8]', '[2048, 2048, 3*w^3 - 2*w^2 - 13*w - 4]', '[2053, 2053, 6*w^3 - w^2 - 27*w - 7]', '[2053, 2053, -2*w^3 + 2*w^2 + 6*w - 7]', '[2057, 187, 3*w^3 - 4*w^2 - 12*w + 8]', '[2057, 187, 8*w^3 + w^2 - 41*w - 17]', '[2059, 2059, w^3 - 6*w - 8]', '[2062, 2062, 3*w^3 + 4*w^2 - 12*w - 9]', '[2066, 2066, 3*w^3 + 4*w^2 - 11*w - 6]', '[2066, 2066, -4*w^3 + 3*w^2 + 14*w - 7]', '[2066, 2066, 5*w^2 + 6*w - 5]', '[2066, 2066, -4*w^3 + 3*w^2 + 18*w - 3]', '[2068, 2068, -2*w^3 + 3*w^2 + 12*w - 1]', '[2068, 2068, 3*w^3 - 2*w^2 - 20*w - 5]', '[2069, 2069, 3*w^3 + 3*w^2 - 17*w - 8]', '[2075, 2075, -w^3 - 3*w^2 + 9*w + 2]', '[2078, 2078, -3*w^3 + 3*w^2 + 11*w - 9]', '[2078, 2078, 2*w^3 - w^2 - 16*w - 7]', '[2083, 2083, -13*w^3 + 7*w^2 + 59*w - 18]', '[2087, 2087, 4*w^3 + w^2 - 23*w - 11]', '[2092, 2092, w^3 - 3*w^2 + 5*w + 1]', '[2095, 2095, 4*w^3 + 4*w^2 - 15*w - 8]', '[2101, 2101, -8*w^3 + 5*w^2 + 40*w - 12]', '[2101, 2101, 5*w^3 - 4*w^2 - 26*w + 12]', '[2102, 2102, -4*w^3 - w^2 + 13*w + 6]', '[2104, 526, -5*w^3 + w^2 + 24*w + 5]', '[2104, 2104, -4*w^3 + 4*w^2 + 15*w - 3]', '[2108, 2108, -2*w^3 + 3*w^2 + 12*w - 9]', '[2111, 2111, 2*w^2 + 2*w - 9]', '[2113, 2113, -2*w^3 + 3*w^2 + 5*w - 7]', '[2116, 2116, 3*w^3 + w^2 - 15*w - 1]', '[2120, 530, -w^3 + w^2 + 8*w - 7]', '[2120, 2120, -4*w^3 + 5*w^2 + 21*w - 10]', '[2123, 2123, 2*w^3 - 10*w - 9]', '[2125, 85, -11*w^3 - 2*w^2 + 56*w + 28]', '[2125, 2125, 3*w^3 - 2*w^2 - 15*w - 1]', '[2126, 2126, 3*w^3 - 8*w - 1]', '[2129, 2129, -2*w^2 - 3*w - 4]', '[2131, 2131, -w^3 + 2*w^2 + 2*w - 10]', '[2131, 2131, -8*w^3 + 4*w^2 + 38*w - 7]', '[2138, 2138, -5*w^3 - 3*w^2 + 17*w + 5]', '[2140, 2140, -7*w^3 + 28*w - 5]', '[2140, 2140, 5*w^3 - 2*w^2 - 19*w - 4]', '[2141, 2141, 4*w^3 - 16*w - 3]', '[2141, 2141, 14*w^3 - 8*w^2 - 64*w + 19]', '[2143, 2143, 13*w^3 - 8*w^2 - 59*w + 19]', '[2143, 2143, -4*w^3 + 4*w^2 + 19*w - 18]', '[2150, 2150, -w + 7]', '[2152, 538, w^3 + w^2 - 2*w - 11]', '[2152, 2152, -4*w^3 - 2*w^2 + 23*w + 11]', '[2159, 2159, -8*w^3 + 4*w^2 + 35*w - 10]', '[2159, 2159, 5*w^3 + w^2 - 27*w - 12]', '[2162, 2162, -w^3 + w^2 + w - 7]', '[2162, 2162, -3*w^3 - w^2 + 18*w + 16]', '[2164, 2164, w^2 + 7*w]', '[2164, 2164, w^3 - 10*w + 1]', '[2168, 542, 3*w^3 + w^2 - 14*w - 13]', '[2168, 2168, -7*w^3 - 4*w^2 + 33*w + 18]', '[2174, 2174, -3*w^3 - 3*w^2 + 9*w - 1]', '[2174, 2174, -5*w^3 + 21*w - 6]', '[2176, 68, 2*w^3 + 2*w^2 - 12*w - 2]', '[2176, 272, 4*w^3 - 14*w + 2]', '[2176, 2176, -3*w^3 + 12*w + 11]', '[2179, 2179, -5*w^3 + w^2 + 27*w + 6]', '[2179, 2179, -w^3 - 2*w^2 + 11*w + 1]', '[2180, 2180, 4*w^3 - 3*w^2 - 12*w - 1]', '[2180, 2180, 7*w^3 - 7*w^2 - 33*w + 13]', '[2182, 2182, 5*w^3 - 4*w^2 - 25*w + 14]', '[2182, 2182, 2*w^3 + w^2 - 6*w - 7]', '[2186, 2186, -w^2 + 4*w + 7]', '[2192, 274, 4*w^3 - 20*w + 2]', '[2192, 274, 4*w^3 - 22*w]', '[2192, 2192, 4*w^3 - w^2 - 24*w + 13]', '[2192, 2192, 5*w^3 - 2*w^2 - 28*w + 13]', '[2194, 2194, -5*w^3 + w^2 + 23*w + 11]', '[2195, 2195, -4*w^2 - 3*w + 12]', '[2200, 550, w^3 - w^2 - 4*w + 9]', '[2200, 2200, 4*w^3 + 3*w^2 - 16*w - 7]', '[2201, 2201, 4*w^3 + 3*w^2 - 20*w - 10]', '[2203, 2203, -w^3 - 2*w^2 + 11*w + 5]', '[2203, 2203, 4*w^3 - 2*w^2 - 18*w - 1]', '[2206, 2206, -2*w^3 + 3*w^2 + 16*w + 1]', '[2207, 2207, w^3 + 2*w^2 - 2*w - 8]', '[2207, 2207, -4*w^3 - w^2 + 22*w + 8]', '[2207, 2207, 6*w^3 - 31*w]', '[2207, 2207, 2*w^3 - 2*w^2 - 14*w + 1]', '[2209, 47, -3*w^3 - 2*w^2 + 15*w + 5]', '[2209, 47, 4*w^3 - 19*w + 2]', '[2209, 2209, w^3 - 4*w^2 - w + 9]', '[2209, 2209, 10*w^3 - 4*w^2 - 46*w + 5]', '[2216, 554, -w^3 - w^2 + 4*w + 11]', '[2216, 2216, 5*w^3 + 3*w^2 - 24*w - 12]', '[2218, 2218, -w^3 + 3*w^2 + 10*w - 6]', '[2218, 2218, 3*w^3 + 4*w^2 - 9*w - 4]', '[2221, 2221, w^2 + 3*w - 7]', '[2222, 2222, 6*w^3 - w^2 - 26*w + 7]', '[2222, 2222, 6*w^3 - 27*w - 1]', '[2224, 278, 4*w^3 - 18*w - 12]', '[2224, 2224, -2*w^3 - 3*w^2 + 16*w + 5]', '[2225, 2225, -9*w^3 + 8*w^2 + 33*w - 11]', '[2234, 2234, 4*w^3 + 3*w^2 - 17*w - 8]', '[2237, 2237, 4*w^3 + w^2 - 22*w - 6]', '[2237, 2237, w^2 + 3*w - 13]', '[2239, 2239, -6*w^3 + 3*w^2 + 25*w - 3]', '[2239, 2239, -5*w^3 + 4*w^2 + 21*w - 5]', '[2243, 2243, 6*w^3 - w^2 - 32*w + 8]', '[2243, 2243, 2*w^3 + 3*w^2 - 13*w - 13]', '[2245, 2245, -2*w^3 - 2*w^2 + 8*w + 13]', '[2245, 2245, w^3 - 2*w^2 - w + 7]', '[2246, 2246, 2*w^3 - w^2 - 14*w + 3]', '[2246, 2246, -w^2 - 7*w - 6]', '[2251, 2251, -3*w^3 + 2*w^2 + 12*w - 12]', '[2258, 2258, -2*w^3 + 4*w^2 + 7*w - 15]', '[2260, 2260, -w^3 - w^2 + 2*w + 8]', '[2260, 2260, 3*w^3 + 2*w^2 - 16*w - 5]', '[2264, 566, 5*w^3 - w^2 - 26*w - 3]', '[2264, 566, w^3 + w^2 - 6*w - 11]', '[2264, 2264, -w^3 - w^2 + 7*w - 5]', '[2264, 2264, 3*w^3 - w^2 - 18*w + 4]', '[2269, 2269, -3*w^3 + 10*w + 8]', '[2269, 2269, -9*w^3 + 7*w^2 + 41*w - 20]', '[2270, 2270, 5*w^3 - w^2 - 20*w - 6]', '[2270, 2270, 2*w^3 - 4*w^2 - 9*w + 13]', '[2272, 284, 2*w^3 + 4*w^2 - 10*w - 8]', '[2272, 2272, -4*w^3 + 3*w^2 + 11*w + 2]', '[2279, 2279, 3*w^3 + 2*w^2 - 19*w - 5]', '[2284, 2284, 2*w^3 - 9*w - 9]', '[2284, 2284, -2*w^3 - w^2 + 14*w + 1]', '[2290, 2290, -4*w^3 - w^2 + 16*w - 1]', '[2293, 2293, 4*w^3 + w^2 - 14*w - 6]', '[2300, 2300, 3*w^3 - 19*w + 4]', '[2302, 2302, -2*w^3 - 2*w^2 + 13*w + 1]', '[2309, 2309, -10*w^3 + 6*w^2 + 44*w - 11]', '[2312, 578, 3*w^3 - 3*w^2 - 16*w + 11]', '[2312, 2312, 2*w^3 - w^2 - 14*w - 3]', '[2320, 290, 2*w^3 - 14*w + 2]', '[2320, 2320, 4*w^3 + 2*w^2 - 19*w - 7]', '[2323, 2323, 4*w^3 + w^2 - 17*w - 1]', '[2323, 2323, 4*w^3 + w^2 - 16*w + 4]', '[2329, 2329, 7*w^3 - 31*w - 11]', '[2329, 2329, 5*w^3 - w^2 - 23*w - 6]', '[2330, 2330, 2*w^3 + 3*w^2 - 16*w - 11]', '[2330, 2330, 4*w^3 - 2*w^2 - 13*w - 3]', '[2330, 2330, w^3 + w^2 - 10*w - 2]', '[2330, 2330, 2*w^3 - 4*w^2 - 11*w + 7]', '[2332, 2332, -5*w^3 + 3*w^2 + 25*w - 3]', '[2333, 2333, -12*w^3 + 7*w^2 + 53*w - 15]', '[2333, 2333, -5*w^3 + 4*w^2 + 25*w - 19]', '[2335, 2335, w^3 - w^2 - w + 8]', '[2335, 2335, -5*w^3 + 4*w^2 + 21*w - 13]', '[2341, 2341, -3*w^3 + 4*w^2 + 10*w - 10]', '[2344, 586, -3*w^3 - w^2 + 18*w + 3]', '[2344, 586, 5*w^3 - w^2 - 26*w - 7]', '[2344, 2344, 3*w^3 - 3*w^2 - 14*w + 2]', '[2344, 2344, 4*w^3 + w^2 - 15*w - 10]', '[2349, 87, 3*w^2 + 3*w - 9]', '[2350, 2350, -3*w^2 - 2*w + 11]', '[2350, 2350, -3*w^3 + 4*w^2 + 13*w - 8]', '[2351, 2351, 6*w^3 - 6*w^2 - 28*w + 19]', '[2354, 2354, -w^3 + 2*w^2 + w - 16]', '[2354, 2354, 3*w^3 - 2*w^2 - 17*w + 10]', '[2357, 2357, -2*w^3 + w^2 + 4*w + 6]', '[2360, 590, 7*w^3 + 3*w^2 - 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14*w - 15]', '[5303, 5303, -6*w^3 + 3*w^2 + 24*w + 4]', '[5303, 5303, 5*w^3 - 2*w^2 - 27*w + 5]', '[5303, 5303, 6*w^3 - 3*w^2 - 27*w + 1]', '[5303, 5303, -4*w^2 + 8*w + 9]', '[5308, 5308, 4*w^3 + w^2 - 18*w + 1]', '[5308, 5308, -2*w^3 + w^2 + 4*w - 7]', '[5311, 5311, -8*w^3 + w^2 + 41*w + 11]', '[5311, 5311, 3*w - 10]', '[5311, 5311, w^3 + 2*w^2 - 10*w - 10]', '[5311, 5311, -4*w^3 + 2*w^2 + 19*w + 4]', '[5312, 332, -9*w^3 - w^2 + 44*w + 21]', '[5312, 664, -4*w^3 + 4*w^2 + 14*w + 2]', '[5312, 5312, -9*w^3 - 2*w^2 + 39*w + 20]', '[5314, 5314, 5*w^3 + 3*w^2 - 12*w - 6]', '[5315, 5315, 4*w^3 - 2*w^2 - 14*w + 9]', '[5318, 5318, -2*w^3 - w^2 + 15*w + 2]', '[5321, 5321, 6*w^3 + 3*w^2 - 27*w - 23]', '[5321, 5321, 5*w^3 - 23*w - 15]', '[5323, 5323, 5*w^3 - 4*w^2 - 20*w + 2]', '[5323, 5323, -w^3 + w^2 + 7*w - 12]', '[5324, 44, 5*w^3 - 3*w^2 - 32*w - 10]', '[5324, 484, -3*w^3 - 3*w^2 + 19*w + 15]', '[5326, 5326, 3*w^3 + 3*w^2 - 11*w - 1]', '[5332, 5332, w^3 + w - 6]', '[5336, 1334, 7*w^3 + w^2 - 30*w - 13]', '[5336, 5336, -5*w^2 + 5*w + 12]', '[5338, 5338, 2*w^3 + w^2 - 6*w - 11]', '[5342, 5342, 2*w^3 - 5*w^2 - 14*w + 3]', '[5344, 668, 2*w^3 + 4*w^2 - 8*w - 10]', '[5344, 668, 2*w^3 + 2*w^2 - 6*w - 10]', '[5344, 5344, -4*w^3 - w^2 + 22*w - 1]', '[5344, 5344, -5*w^3 + 2*w^2 + 19*w]', '[5345, 5345, -5*w^3 + 2*w^2 + 17*w - 17]', '[5347, 5347, -w^3 + 6*w^2 - 3*w - 9]', '[5350, 5350, 6*w^3 - 5*w^2 - 24*w + 5]', '[5350, 5350, -8*w^3 - w^2 + 34*w + 5]', '[5353, 5353, -w^3 + 2*w^2 - w - 7]', '[5353, 5353, -5*w^3 + 4*w^2 + 22*w - 4]', '[5354, 5354, -5*w^3 + 2*w^2 + 17*w - 4]', '[5354, 5354, 3*w^3 - 3*w^2 - 19*w - 3]', '[5354, 5354, 4*w^3 + w^2 - 15*w - 12]', '[5354, 5354, 3*w^3 - 7*w - 6]', '[5359, 5359, 5*w^3 - 27*w + 7]', '[5359, 5359, 4*w^3 - 13*w - 2]', '[5359, 5359, w^3 - 2*w^2 - 12*w]', '[5359, 5359, w^3 - 13*w - 9]', '[5363, 5363, -w^3 + 3*w^2 + 3*w + 4]', '[5363, 5363, 2*w^2 - 5*w + 6]', '[5374, 5374, 2*w^3 + w^2 - 5*w - 8]', '[5375, 215, 2*w^3 - 6*w^2 - 2*w + 9]', '[5375, 5375, 4*w^3 - 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14*w - 13]', '[5800, 1450, 5*w^3 - 3*w^2 - 20*w - 3]', '[5800, 5800, 3*w^3 - 2*w^2 - 19*w + 2]', '[5804, 5804, -3*w^3 + 3*w^2 + 15*w + 5]', '[5807, 5807, 3*w^3 + 2*w^2 - 21*w - 1]', '[5818, 5818, 3*w^3 + 2*w^2 - 11*w - 12]', '[5818, 5818, -w^3 + 5*w^2 + 13*w + 1]', '[5819, 5819, 2*w^3 - 3*w^2 - 12*w + 12]', '[5825, 5825, 2*w^3 + 4*w^2 - 8*w - 1]', '[5825, 5825, 3*w^3 + 2*w^2 - 15*w + 3]', '[5825, 5825, 4*w^3 - 5*w^2 - 15*w + 3]', '[5825, 5825, 5*w^2 - 2*w - 6]', '[5827, 5827, 10*w^3 - w^2 - 49*w - 1]', '[5827, 5827, -6*w^3 + 2*w^2 + 24*w + 3]', '[5828, 5828, -w^3 + 2*w - 9]', '[5828, 5828, 4*w^3 - 3*w^2 - 12*w + 7]', '[5830, 5830, -w^2 - 2*w - 7]', '[5836, 5836, -2*w^3 + 5*w^2 + 5*w - 8]', '[5836, 5836, 5*w^3 - 3*w^2 - 23*w + 1]', '[5839, 5839, -w^3 - 6*w^2 + 12*w + 12]', '[5839, 5839, 5*w^3 - 25*w + 3]', '[5842, 5842, -7*w^3 + 6*w^2 + 36*w - 17]', '[5842, 5842, -4*w^3 - w^2 + 25*w + 18]', '[5843, 5843, -3*w^3 - 2*w^2 + 6*w + 6]', '[5843, 5843, -2*w^3 + w^2 + 3*w + 9]', '[5843, 5843, 4*w^3 - 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11]', '[9890, 9890, w^3 + 4*w^2 - 15*w - 4]', '[9892, 9892, w^3 - w^2 - 13*w + 1]', '[9896, 2474, -3*w^3 - 3*w^2 + 22*w + 5]', '[9896, 2474, 9*w^3 - 5*w^2 - 38*w + 3]', '[9896, 9896, 6*w^3 - 21*w - 13]', '[9896, 9896, -2*w^3 - 5*w^2 + 13*w + 14]', '[9904, 1238, 12*w^3 - 6*w^2 - 52*w + 8]', '[9904, 9904, -w^3 - 4*w^2 + 10*w + 15]', '[9907, 9907, 6*w^3 + 2*w^2 - 34*w - 7]', '[9908, 9908, -4*w^3 + w^2 + 18*w - 11]', '[9908, 9908, -5*w^3 - w^2 + 25*w - 7]', '[9911, 9911, -7*w^3 + w^2 + 35*w - 10]', '[9914, 9914, -2*w^3 + 4*w^2 + 19*w + 1]', '[9914, 9914, 2*w^3 - 5*w^2 - 20*w - 7]', '[9920, 620, 3*w^3 - w^2 - 12*w - 11]', '[9920, 1240, -2*w^3 + 2*w - 8]', '[9920, 9920, -6*w^3 + 5*w^2 + 27*w - 6]', '[9925, 9925, 7*w^3 + 6*w^2 - 23*w - 9]', '[9925, 9925, 2*w^2 - w - 16]', '[9931, 9931, 5*w^2 - 2*w - 8]', '[9931, 9931, 13*w^3 - 5*w^2 - 61*w + 6]', '[9934, 9934, -2*w^3 + 9*w - 9]', '[9935, 9935, w^3 + 6*w^2 - 11*w - 15]', '[9935, 9935, -5*w^3 - w^2 + 27*w + 20]', '[9938, 9938, 2*w^3 - w^2 - 16*w + 9]', '[9941, 9941, -6*w^3 + 4*w^2 + 22*w + 7]', '[9941, 9941, -3*w^3 + 4*w^2 + 10*w - 14]', '[9944, 2486, 3*w^3 - 3*w^2 - 10*w + 15]', '[9944, 2486, -7*w^3 - 3*w^2 + 30*w + 21]', '[9944, 9944, 7*w^3 + 4*w^2 - 25*w - 10]', '[9944, 9944, 5*w^3 + 3*w^2 - 28*w - 8]', '[9955, 9955, -7*w^3 - 5*w^2 + 27*w + 12]', '[9955, 9955, -5*w^3 - 4*w^2 + 21*w + 9]', '[9962, 9962, 7*w^3 + w^2 - 38*w - 16]', '[9962, 9962, -7*w^3 + 4*w^2 + 26*w + 7]', '[9964, 9964, -7*w^3 + 8*w^2 + 26*w - 19]', '[9964, 9964, -3*w^2 + 4*w - 5]', '[9965, 9965, -10*w^3 + 5*w^2 + 43*w - 11]', '[9965, 9965, -5*w^3 + 3*w^2 + 29*w]', '[9967, 9967, -8*w^3 + 41*w]', '[9970, 9970, 7*w^3 + 6*w^2 - 37*w - 26]', '[9970, 9970, -4*w^3 - 3*w^2 + 19*w + 6]', '[9971, 767, 3*w^3 - 2*w^2 - 20*w + 2]', '[9971, 767, 2*w^3 - 16*w - 3]', '[9971, 767, 7*w^3 - 4*w^2 - 28*w - 2]', '[9971, 767, 2*w^3 - w^2 - 14*w - 12]', '[9973, 9973, 2*w^3 + 4*w^2 - 17*w - 14]', '[9976, 2494, w^3 + 3*w^2 - 14*w - 5]', '[9976, 9976, w^3 - 2*w^2 + 13]', '[9977, 9977, -3*w^3 + 4*w^2 + 18*w]', '[9977, 9977, -15*w^3 + 6*w^2 + 69*w - 19]', '[9986, 9986, 5*w^3 - 14*w - 5]', '[9986, 9986, 5*w^3 + 2*w^2 - 32*w - 17]', '[9988, 9988, 7*w^3 + 4*w^2 - 30*w - 13]', '[9988, 9988, 10*w^3 - 2*w^2 - 45*w - 3]', '[9992, 2498, -21*w^3 + 11*w^2 + 96*w - 29]', '[9992, 9992, -3*w^3 + 3*w^2 + 10*w - 14]', '[9995, 9995, 8*w^3 - w^2 - 31*w + 7]', '[9998, 9998, -w^3 - 5*w^2 - w + 13]', '[9998, 9998, 4*w^3 + w^2 - 24*w - 7]', '[10000, 10, 10]', '[10000, 80, -10*w^3 + 5*w^2 + 50*w - 5]', '[10000, 1250, 4*w^3 + 4*w^2 - 16*w - 6]', '[10000, 10000, -w^3 - 2*w + 7]'], 'label': '4.4.6809.1', 'narrow_class_no': 1, 'primes': ['[2, 2, w + 1]', '[5, 5, w^3 - 4*w]', '[8, 2, w^3 - w^2 - 4*w + 3]', '[11, 11, w^3 - 5*w + 1]', '[17, 17, -w^3 - w^2 + 5*w + 4]', '[23, 23, -w^2 + 2]', '[29, 29, -w^2 - w + 3]', '[31, 31, -w^3 + 6*w + 2]', '[43, 43, w^3 - 6*w]', '[47, 47, 2*w^3 - 9*w]', '[47, 47, -2*w^3 + w^2 + 8*w - 2]', '[53, 53, -4*w^3 + 2*w^2 + 18*w - 5]', '[59, 59, w^2 - w - 5]', '[59, 59, 3*w^3 - 15*w - 5]', '[71, 71, w^3 - 3*w - 3]', '[81, 3, -3]', '[83, 83, -2*w^3 + 8*w + 3]', '[89, 89, -2*w^3 + 11*w - 2]', '[101, 101, 2*w^3 - w^2 - 10*w]', '[101, 101, 2*w^3 - 2*w^2 - 10*w + 3]', '[107, 107, 3*w^3 - 15*w - 1]', '[107, 107, 4*w^3 - 2*w^2 - 18*w + 3]', '[109, 109, 2*w^3 - 10*w + 3]', '[109, 109, 3*w^3 - 2*w^2 - 13*w + 3]', '[113, 113, 3*w^3 - w^2 - 15*w + 2]', '[113, 113, 3*w^3 - 13*w - 5]', '[121, 11, 3*w^3 - 13*w - 1]', '[125, 5, -2*w^3 + w^2 + 7*w + 1]', '[127, 127, 2*w^3 - 8*w - 1]', '[127, 127, -w^3 + 2*w^2 + 3*w - 3]', '[137, 137, 2*w^3 - 10*w + 1]', '[137, 137, 2*w^3 - 11*w]', '[139, 139, 2*w^3 - 9*w - 6]', '[157, 157, -4*w^3 - w^2 + 19*w + 7]', '[163, 163, 5*w^3 - 2*w^2 - 25*w + 7]', '[167, 167, w^2 + w - 5]', '[167, 167, -w^3 + 2*w^2 + 4*w - 6]', '[169, 13, -w^3 + w^2 + 3*w - 4]', '[169, 13, w^2 - 2*w - 4]', '[173, 173, -2*w^3 + w^2 + 11*w - 7]', '[173, 173, w - 4]', '[181, 181, w + 4]', '[181, 181, -2*w - 5]', '[191, 191, -w^3 + 2*w^2 + 6*w - 6]', '[191, 191, 2*w^3 - w^2 - 11*w + 1]', '[193, 193, -3*w^3 + 16*w]', '[227, 227, 6*w^3 - 3*w^2 - 27*w + 5]', '[227, 227, 2*w^3 - 11*w - 2]', '[229, 229, -2*w^3 + w^2 + 10*w - 6]', '[233, 233, 4*w^3 - 3*w^2 - 17*w + 5]', '[233, 233, 2*w^3 + w^2 - 7*w - 5]', '[233, 233, w^3 - 7*w - 1]', '[233, 233, 2*w^3 - 7*w]', '[239, 239, 2*w^2 - 2*w - 7]', '[239, 239, -4*w^3 + w^2 + 18*w]', '[241, 241, w^3 - 5*w - 5]', '[263, 263, -4*w^3 + w^2 + 20*w - 4]', '[269, 269, w^3 + 2*w^2 - 6*w - 6]', '[271, 271, 2*w^3 + w^2 - 12*w - 8]', '[277, 277, w^3 + w^2 - 7*w - 6]', '[283, 283, 6*w^3 - 3*w^2 - 27*w + 7]', '[283, 283, -3*w^3 + 3*w^2 + 13*w - 8]', '[293, 293, -2*w^3 + w^2 + 9*w + 3]', '[293, 293, 4*w^3 - w^2 - 19*w + 3]', '[313, 313, 2*w^2 - w - 4]', '[313, 313, -2*w^3 + 2*w^2 + 8*w - 1]', '[317, 317, 3*w^3 + w^2 - 13*w - 10]', '[331, 331, w^3 + 2*w^2 - 4*w - 6]', '[349, 349, -w^3 + 3*w^2 + w - 4]', '[353, 353, 3*w^3 - 14*w]', '[353, 353, -2*w^3 + w^2 + 7*w + 5]', '[361, 19, -5*w^3 + w^2 + 23*w - 2]', '[361, 19, -2*w^3 + 7*w + 6]', '[373, 373, -w^3 + 4*w - 4]', '[379, 379, -w^3 - 2*w^2 + 5*w + 7]', '[383, 383, w^2 - 2*w - 6]', '[389, 389, -4*w^3 + 2*w^2 + 16*w - 5]', '[397, 397, 5*w^3 - 2*w^2 - 24*w + 2]', '[397, 397, 3*w^3 + 2*w^2 - 16*w - 14]', '[401, 401, 2*w^2 - 5]', '[419, 419, -w^3 - w^2 + 9*w + 6]', '[439, 439, 3*w^3 - w^2 - 15*w - 2]', '[449, 449, 4*w^3 + w^2 - 17*w - 5]', '[449, 449, 4*w^3 - w^2 - 17*w - 5]', '[467, 467, -3*w^3 + 16*w - 2]', '[467, 467, 2*w^3 + w^2 - 10*w - 2]', '[479, 479, 4*w^3 - 19*w - 8]', '[491, 491, 3*w - 4]', '[491, 491, -w^3 + 2*w^2 + 5*w - 11]', '[509, 509, -7*w^3 + 3*w^2 + 33*w - 10]', '[509, 509, 4*w^3 - w^2 - 21*w - 3]', '[523, 523, -w^3 - 2*w^2 + 6*w + 2]', '[541, 541, -5*w^3 + 2*w^2 + 26*w - 8]', '[541, 541, 2*w^3 + w^2 - 9*w - 1]', '[571, 571, -4*w^3 + 3*w^2 + 20*w - 14]', '[571, 571, -3*w^3 - w^2 + 15*w + 4]', '[593, 593, w^3 - 4*w - 6]', '[613, 613, 4*w^3 - 2*w^2 - 19*w + 2]', '[617, 617, -w^3 + 3*w - 5]', '[617, 617, -w^3 + 2*w^2 + 3*w - 9]', '[617, 617, 8*w^3 - 3*w^2 - 38*w + 8]', '[617, 617, w^3 - 8*w]', '[619, 619, 6*w^3 - 3*w^2 - 26*w + 4]', '[631, 631, 3*w^3 + w^2 - 17*w - 8]', '[631, 631, w^2 - 3*w - 5]', '[641, 641, -3*w^3 + 2*w^2 + 16*w - 10]', '[643, 643, -2*w^3 + 3*w^2 + 7*w - 9]', '[647, 647, w^3 - w^2 - 3*w - 4]', '[653, 653, 2*w^3 + w^2 - 11*w - 1]', '[653, 653, w^3 + 2*w^2 - 7*w - 9]', '[653, 653, -4*w^3 - w^2 + 17*w + 3]', '[653, 653, 3*w^3 - 2*w^2 - 13*w + 1]', '[661, 661, 2*w^3 - 3*w^2 - 8*w + 8]', '[673, 673, 3*w^3 - 12*w - 2]', '[673, 673, 2*w^3 - w^2 - 12*w]', '[683, 683, -w^3 + 2*w^2 + 2*w - 6]', '[691, 691, -5*w^3 + 22*w + 8]', '[691, 691, 2*w^3 - 12*w - 3]', '[719, 719, 6*w^3 + w^2 - 28*w - 8]', '[733, 733, -3*w^2 + 3*w + 7]', '[733, 733, 3*w^3 - 14*w + 2]', '[733, 733, -w^3 + w^2 + 7*w - 8]', '[733, 733, 2*w^3 - 6*w - 5]', '[751, 751, 3*w^3 + 3*w^2 - 13*w - 12]', '[751, 751, 5*w^3 - 2*w^2 - 25*w + 5]', '[751, 751, -4*w^3 + 3*w^2 + 20*w - 12]', '[751, 751, 2*w^3 + w^2 - 9*w + 1]', '[757, 757, -3*w^3 + w^2 + 11*w + 2]', '[773, 773, w^3 - w^2 - 7*w + 6]', '[787, 787, -9*w^3 + 4*w^2 + 43*w - 13]', '[787, 787, w^2 + 2*w - 6]', '[797, 797, -w^3 + 4*w^2 - 2*w - 6]', '[797, 797, 2*w^3 - w^2 - 9*w + 7]', '[821, 821, -6*w^3 + 27*w + 2]', '[823, 823, 8*w^3 - 4*w^2 - 37*w + 8]', '[827, 827, -3*w^3 + 3*w^2 + 15*w - 4]', '[829, 829, w^3 + w^2 - 3*w - 8]', '[839, 839, 2*w^3 - 3*w^2 - 8*w + 6]', '[839, 839, 8*w^3 - 2*w^2 - 38*w + 3]', '[859, 859, 4*w^3 - 2*w^2 - 18*w + 1]', '[859, 859, -4*w^3 + 4*w^2 + 17*w - 10]', '[863, 863, -4*w^3 + w^2 + 19*w + 3]', '[877, 877, -4*w^3 + w^2 + 18*w + 4]', '[883, 883, -6*w^3 + 3*w^2 + 31*w - 13]', '[883, 883, 4*w^3 - w^2 - 17*w - 1]', '[887, 887, 3*w^3 - 4*w^2 - 11*w + 11]', '[907, 907, 5*w^3 - 4*w^2 - 21*w + 11]', '[907, 907, -2*w^3 + 2*w^2 + 8*w - 11]', '[911, 911, 2*w^3 - 2*w^2 - 11*w]', '[919, 919, 4*w^3 - 17*w - 2]', '[937, 937, 3*w^3 - 2*w^2 - 15*w + 1]', '[937, 937, 3*w^3 - 17*w + 1]', '[941, 941, 4*w^3 - w^2 - 16*w - 4]', '[953, 953, -2*w^3 + 2*w^2 + 13*w - 6]', '[971, 971, -3*w^3 + 11*w + 9]', '[977, 977, 8*w^3 - 4*w^2 - 39*w + 16]', '[983, 983, 4*w^3 - w^2 - 21*w + 3]', '[983, 983, 2*w^3 - 3*w^2 - 9*w + 7]', '[997, 997, w^3 - w^2 - w - 6]', '[997, 997, w^3 - 9*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, -1, -5, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 6809, 'disc_rad': 6809, 'disc_sign': 1, 'frobs': [[2, [[3, 1], [1, 1]]], [3, [[4, 1]]], [5, [[3, 1], [1, 1]]], [7, [[4, 1]]], [11, [0]], [13, [[2, 2]]], [17, [[3, 1], [1, 1]]], [19, [[2, 2]]], [23, [[3, 1], [1, 1]]], [29, [[3, 1], [1, 1]]], [31, [[3, 1], [1, 1]]], [37, [[2, 2]]], [41, [[4, 1]]], [43, [[3, 1], [1, 1]]], [47, [[2, 1], [1, 2]]], [53, [[3, 1], [1, 1]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 82.516664983505, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.6809.1', 'local_algs': ['11.2.0.1', '11.2.1.2', 'm619.1.2.0', 'm619.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [11, 619], 'rd': 9.08386839312, 'regulator': {'__RealLiteral__': 0, 'data': '5.75333674058', 'prec': 44}, 'res': {'gal': ['653,-22846,-14913,1832186,-3437485,-9964284,20484764,16284890,-38346842,-6394096,32302837,-4621088,-13217906,4423678,2623257,-1382210,-199179,203176,-7307,-14218,1830,416,-78,-4,1'], 'sib': ['-1,0,21,0,-10,0,1', '-1672,5676,4680,-15985,-3090,11287,-546,-2486,290,210,-31,-6,1', '1,12,10,-165,103,303,-208,-205,116,50,-23,-3,1', '158698,-16821,-37206,1974,3010,-42,-94,0,1', '291,580,242,-105,-70,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{3} - 4 a - 2 \\)', '\\( a^{3} - a^{2} - 3 a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}