Hilbert modular form data - 2.2.12.1-49.1-a

Formats: - HTML - YAML - JSON - 2024-05-16T14:57:59.403574

• 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': 2, 'dimension': 6, 'disc': 12, 'field_bad_primes': [2, 3], 'field_label': '2.2.12.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.12.1-49.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [7], 'level_ideal': '[49, 7, -7]', 'level_label': '49.1', 'level_norm': 49, 'parallel_weight': 2, 'short_label': '49.1-a', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[49, 7, -7]', 1]], 'hecke_eigenvalues': ['e', '-1/2*e^5 + 9/2*e^3 - 7*e', '1/2*e^5 - 5*e^3 + 17/2*e', '1/2*e^5 - 5*e^3 + 17/2*e', '-1/2*e^4 + 7/2*e^2 - 2', '-1/2*e^4 + 7/2*e^2 - 2', '1/2*e^5 - 4*e^3 + 7/2*e', '1/2*e^5 - 4*e^3 + 7/2*e', 'e^4 - 7*e^2 + 8', '-e^4 + 9*e^2 - 12', '-e^4 + 9*e^2 - 12', 'e^5 - 8*e^3 + 7*e', 'e^5 - 8*e^3 + 7*e', -1, '-1/2*e^5 + 7/2*e^3 + 4*e', '-1/2*e^5 + 7/2*e^3 + 4*e', '1/2*e^4 - 15/2*e^2 + 14', '1/2*e^4 - 15/2*e^2 + 14', '-3/2*e^5 + 12*e^3 - 25/2*e', '-3/2*e^5 + 12*e^3 - 25/2*e', 'e^4 - 7*e^2 + 6', 'e^4 - 7*e^2 + 6', '1/2*e^5 - 9/2*e^3 + 3*e', '1/2*e^5 - 9/2*e^3 + 3*e', -2, -2, '-3/2*e^5 + 14*e^3 - 37/2*e', '-3/2*e^5 + 14*e^3 - 37/2*e', '-3*e^4 + 25*e^2 - 22', '-3*e^4 + 25*e^2 - 22', '-5/2*e^5 + 45/2*e^3 - 31*e', '-5/2*e^5 + 45/2*e^3 - 31*e', '-3/2*e^4 + 29/2*e^2 - 26', '-3/2*e^4 + 29/2*e^2 - 26', 'e^3 - 3*e', 'e^3 - 3*e', '1/2*e^5 - 2*e^3 - 25/2*e', '1/2*e^5 - 2*e^3 - 25/2*e', '7/2*e^4 - 57/2*e^2 + 30', '7/2*e^4 - 57/2*e^2 + 30', '3/2*e^5 - 16*e^3 + 73/2*e', '3/2*e^5 - 16*e^3 + 73/2*e', 'e^4 - 11*e^2 + 12', 'e^4 - 11*e^2 + 12', '7/2*e^5 - 61/2*e^3 + 42*e', '7/2*e^5 - 61/2*e^3 + 42*e', '5/2*e^4 - 35/2*e^2 + 10', '5/2*e^4 - 35/2*e^2 + 10', '-3/2*e^5 + 16*e^3 - 85/2*e', '-3/2*e^5 + 16*e^3 - 85/2*e', '-2*e^4 + 10*e^2 + 14', '-2*e^4 + 10*e^2 + 14', '-5/2*e^5 + 43/2*e^3 - 32*e', '-5/2*e^5 + 43/2*e^3 - 32*e', '7/2*e^5 - 32*e^3 + 85/2*e', '7/2*e^5 - 32*e^3 + 85/2*e', '4*e^4 - 30*e^2 + 24', '4*e^4 - 30*e^2 + 24', '-2*e^4 + 16*e^2 + 8', '-4*e^5 + 37*e^3 - 55*e', '-4*e^5 + 37*e^3 - 55*e', '3*e^4 - 21*e^2 + 10', '3*e^4 - 21*e^2 + 10', '-3*e^4 + 23*e^2 - 26', '-3*e^4 + 23*e^2 - 26', '3/2*e^5 - 17*e^3 + 95/2*e', '3/2*e^5 - 17*e^3 + 95/2*e', '-7/2*e^4 + 65/2*e^2 - 34', '-7/2*e^4 + 65/2*e^2 - 34', '1/2*e^5 - 2*e^3 - 5/2*e', '1/2*e^5 - 2*e^3 - 5/2*e', '-3*e^4 + 23*e^2 - 2', '-2*e^4 + 18*e^2 - 26', '-2*e^4 + 18*e^2 - 26', '2*e^5 - 16*e^3 + 10*e', '2*e^5 - 16*e^3 + 10*e', '1/2*e^4 + 1/2*e^2 - 22', '1/2*e^4 + 1/2*e^2 - 22', 'e^4 - 3*e^2 + 6', 'e^4 - 3*e^2 + 6', '-7/2*e^5 + 61/2*e^3 - 26*e', '-7/2*e^5 + 61/2*e^3 - 26*e', '-2*e^4 + 24*e^2 - 32', '-2*e^4 + 24*e^2 - 32', '-9/2*e^5 + 42*e^3 - 139/2*e', '-9/2*e^5 + 42*e^3 - 139/2*e', '4*e^4 - 36*e^2 + 34', '4*e^4 - 36*e^2 + 34', '-1/2*e^5 + 6*e^3 - 31/2*e', '-1/2*e^5 + 6*e^3 - 31/2*e', '-e^4 + e^2 + 30', '-e^4 + e^2 + 30', '-9/2*e^5 + 75/2*e^3 - 42*e', '-9/2*e^5 + 75/2*e^3 - 42*e', '-e^5 + 2*e^3 + 23*e', '-e^5 + 2*e^3 + 23*e', '3/2*e^5 - 16*e^3 + 73/2*e', '3/2*e^5 - 16*e^3 + 73/2*e', '3*e^5 - 31*e^3 + 54*e', '3*e^5 - 31*e^3 + 54*e', '4*e^4 - 34*e^2 + 24', '4*e^4 - 34*e^2 + 24', '11/2*e^5 - 101/2*e^3 + 72*e', '11/2*e^5 - 101/2*e^3 + 72*e', '2*e^4 - 10*e^2 + 6', '2*e^4 - 10*e^2 + 6', '-5/2*e^5 + 51/2*e^3 - 56*e', '-5/2*e^5 + 51/2*e^3 - 56*e', '5/2*e^5 - 20*e^3 + 55/2*e', '5/2*e^5 - 20*e^3 + 55/2*e', 'e^4 + e^2 - 38', 'e^4 + e^2 - 38', '-e^4 + 3*e^2 + 18', '-e^4 + 3*e^2 + 18', '-2*e^5 + 19*e^3 - 43*e', '-2*e^5 + 19*e^3 - 43*e', '3/2*e^5 - 17*e^3 + 103/2*e', '3/2*e^5 - 17*e^3 + 103/2*e', '-3/2*e^4 + 37/2*e^2 - 58', '-3/2*e^4 + 37/2*e^2 - 58', '2*e^4 - 8*e^2 - 16', '2*e^4 - 8*e^2 - 16', '11/2*e^5 - 48*e^3 + 129/2*e', '11/2*e^5 - 48*e^3 + 129/2*e', 'e^4 - 15*e^2 + 14', 'e^4 - 15*e^2 + 14', '4*e^5 - 38*e^3 + 58*e', '4*e^5 - 38*e^3 + 58*e', '-9/2*e^4 + 71/2*e^2 - 46', '-9/2*e^4 + 71/2*e^2 - 46', '-5/2*e^5 + 18*e^3 - 23/2*e', '-5/2*e^5 + 18*e^3 - 23/2*e', '-5*e^4 + 35*e^2 - 2', '-5*e^4 + 35*e^2 - 2', '6*e^4 - 54*e^2 + 70', '6*e^4 - 54*e^2 + 70', '3/2*e^5 - 12*e^3 + 25/2*e', '3/2*e^5 - 12*e^3 + 25/2*e', '-7/2*e^4 + 65/2*e^2 - 54', '-7/2*e^4 + 65/2*e^2 - 54', '-6*e^5 + 57*e^3 - 97*e', '-6*e^5 + 57*e^3 - 97*e', '-12*e^2 + 50', '1/2*e^4 - 23/2*e^2 + 42', '1/2*e^4 - 23/2*e^2 + 42', '5/2*e^5 - 22*e^3 + 67/2*e', '5/2*e^5 - 22*e^3 + 67/2*e', 'e^4 - 7*e^2 + 10', 'e^4 - 7*e^2 + 10', '6*e^5 - 59*e^3 + 91*e', '6*e^5 - 59*e^3 + 91*e', '-3/2*e^5 + 16*e^3 - 37/2*e', '-3/2*e^5 + 16*e^3 - 37/2*e', '-11*e^4 + 85*e^2 - 86', '-11*e^4 + 85*e^2 - 86', '-15/2*e^5 + 67*e^3 - 159/2*e', '-15/2*e^5 + 67*e^3 - 159/2*e', '4*e^2 + 26', '-3/2*e^5 + 27/2*e^3 - e', '-3/2*e^5 + 27/2*e^3 - e', '-3*e^5 + 35*e^3 - 94*e', '-3*e^5 + 35*e^3 - 94*e', '13/2*e^4 - 123/2*e^2 + 50', '13/2*e^4 - 123/2*e^2 + 50', '-5*e^4 + 39*e^2 - 36', '-5*e^4 + 39*e^2 - 36', '9/2*e^5 - 32*e^3 + 27/2*e', '9/2*e^5 - 32*e^3 + 27/2*e', '7/2*e^4 - 41/2*e^2 - 2', '7/2*e^4 - 41/2*e^2 - 2', '3/2*e^5 - 16*e^3 + 33/2*e', '3/2*e^5 - 16*e^3 + 33/2*e', '-4*e^4 + 34*e^2 - 48', '-4*e^4 + 34*e^2 - 48', '5/2*e^4 - 51/2*e^2 + 22', '5/2*e^4 - 51/2*e^2 + 22', '3/2*e^5 - 47/2*e^3 + 79*e', '3/2*e^5 - 47/2*e^3 + 79*e', '-5*e^4 + 41*e^2 - 20', '-5*e^4 + 41*e^2 - 20', '-7/2*e^5 + 34*e^3 - 109/2*e', '-7/2*e^5 + 34*e^3 - 109/2*e', '6*e^4 - 50*e^2 + 82', '6*e^4 - 50*e^2 + 82', '-4*e^4 + 30*e^2 - 16', '-4*e^4 + 30*e^2 - 16', '6*e^5 - 50*e^3 + 48*e', '6*e^5 - 50*e^3 + 48*e', '4*e^2 + 18', '4*e^2 + 18', '-9/2*e^5 + 40*e^3 - 115/2*e', '-9/2*e^5 + 40*e^3 - 115/2*e', '-19/2*e^5 + 78*e^3 - 173/2*e', '-19/2*e^5 + 78*e^3 - 173/2*e', '-3*e^4 + 17*e^2 - 8', '-3*e^4 + 17*e^2 - 8', '-3*e^4 + 27*e^2 - 36', '-3*e^4 + 27*e^2 - 36', '2*e^5 - 9*e^3 - 23*e', '2*e^5 - 9*e^3 - 23*e', '-1/2*e^4 + 7/2*e^2 + 22', '-1/2*e^4 + 7/2*e^2 + 22', '4*e^4 - 36*e^2 + 50', '4*e^4 - 36*e^2 + 50', '5/2*e^5 - 57/2*e^3 + 49*e', '5/2*e^5 - 57/2*e^3 + 49*e', '3/2*e^5 - 7*e^3 - 61/2*e', '3/2*e^5 - 7*e^3 - 61/2*e', '3*e^4 - 35*e^2 + 70', '3*e^4 - 35*e^2 + 70', '5/2*e^5 - 61/2*e^3 + 83*e', '5/2*e^5 - 61/2*e^3 + 83*e', '-7*e^3 + 53*e', '-7*e^3 + 53*e', '-13*e^4 + 103*e^2 - 102', '-13*e^4 + 103*e^2 - 102', '-1/2*e^5 + 2*e^3 + 57/2*e', '-1/2*e^5 + 2*e^3 + 57/2*e', '3*e^4 - 25*e^2 + 14', '3*e^4 - 25*e^2 + 14', '27/2*e^5 - 231/2*e^3 + 147*e', '27/2*e^5 - 231/2*e^3 + 147*e', '11*e^4 - 91*e^2 + 108', '11*e^4 - 91*e^2 + 108', '-3/2*e^5 + 20*e^3 - 157/2*e', '-3/2*e^5 + 20*e^3 - 157/2*e', '9/2*e^5 - 35*e^3 + 69/2*e', '9/2*e^5 - 35*e^3 + 69/2*e', '-7*e^4 + 57*e^2 - 42', '-7*e^4 + 57*e^2 - 42', '6*e^5 - 54*e^3 + 96*e', '6*e^5 - 54*e^3 + 96*e', '-6*e^4 + 62*e^2 - 82', '-6*e^4 + 62*e^2 - 82', '-21/2*e^5 + 94*e^3 - 291/2*e', '-21/2*e^5 + 94*e^3 - 291/2*e', '-3*e^5 + 31*e^3 - 82*e', '-3*e^5 + 31*e^3 - 82*e', '-11/2*e^5 + 47*e^3 - 139/2*e', '-11/2*e^5 + 47*e^3 - 139/2*e', '4*e^4 - 34*e^2 + 32', '4*e^4 - 34*e^2 + 32', '6*e^5 - 53*e^3 + 61*e', '6*e^5 - 53*e^3 + 61*e', '-5/2*e^5 + 59/2*e^3 - 64*e', '-5/2*e^5 + 59/2*e^3 - 64*e', '15/2*e^5 - 72*e^3 + 237/2*e', '15/2*e^5 - 72*e^3 + 237/2*e', '4*e^4 - 28*e^2 + 26', '4*e^4 - 28*e^2 + 26', '11/2*e^5 - 54*e^3 + 253/2*e', '11/2*e^5 - 54*e^3 + 253/2*e', '7*e^4 - 61*e^2 + 42', '7*e^4 - 61*e^2 + 42', '-1/2*e^5 - 2*e^3 + 97/2*e', '-1/2*e^5 - 2*e^3 + 97/2*e', '5*e^4 - 41*e^2 + 36', '5*e^4 - 41*e^2 + 36', '-e^4 + 15*e^2 - 46', '-e^4 + 15*e^2 - 46', '-3/2*e^5 + 9*e^3 - 7/2*e', '-3/2*e^5 + 9*e^3 - 7/2*e', '3/2*e^4 - 45/2*e^2 + 26', '3/2*e^4 - 45/2*e^2 + 26', '-2*e^4 + 8*e^2 + 72', '-9/2*e^4 + 39/2*e^2 + 58', '-9/2*e^4 + 39/2*e^2 + 58', '9/2*e^4 - 71/2*e^2 + 22', '9/2*e^4 - 71/2*e^2 + 22', '11*e^4 - 89*e^2 + 114', '11*e^4 - 89*e^2 + 114', '-8*e^4 + 80*e^2 - 94', '-8*e^4 + 80*e^2 - 94', '15/2*e^5 - 63*e^3 + 111/2*e', '15/2*e^5 - 63*e^3 + 111/2*e', '-2*e^4 + 16*e^2 + 8', '-2*e^4 + 16*e^2 + 8', '-e^4 + 7*e^2 + 20', '-e^4 + 7*e^2 + 20', '11/2*e^5 - 101/2*e^3 + 88*e', '11/2*e^5 - 101/2*e^3 + 88*e', '-10*e^5 + 92*e^3 - 110*e', '-10*e^5 + 92*e^3 - 110*e', '-3*e^5 + 35*e^3 - 106*e', '-3*e^5 + 35*e^3 - 106*e', '-4*e^4 + 48*e^2 - 58', '-17/2*e^4 + 151/2*e^2 - 54', '-17/2*e^4 + 151/2*e^2 - 54', '-23/2*e^5 + 98*e^3 - 253/2*e', '-23/2*e^5 + 98*e^3 - 253/2*e', '8*e^4 - 68*e^2 + 38', '8*e^4 - 68*e^2 + 38', '3/2*e^5 - 7/2*e^3 - 29*e', '3/2*e^5 - 7/2*e^3 - 29*e', '-11/2*e^5 + 113/2*e^3 - 94*e', '-11/2*e^5 + 113/2*e^3 - 94*e', '-6*e^4 + 54*e^2 - 66', '-6*e^4 + 54*e^2 - 66', '3/2*e^5 - 25/2*e^3 + 26*e', '3/2*e^5 - 25/2*e^3 + 26*e', '3*e^4 - 21*e^2 - 10', '3*e^4 - 21*e^2 - 10', '-15/2*e^5 + 61*e^3 - 147/2*e', '-15/2*e^5 + 61*e^3 - 147/2*e', '8*e^4 - 68*e^2 + 82', '8*e^4 - 68*e^2 + 82', '-7/2*e^5 + 37*e^3 - 147/2*e', '-7/2*e^5 + 37*e^3 - 147/2*e', '-11/2*e^4 + 85/2*e^2 - 82', '-11/2*e^4 + 85/2*e^2 - 82', '-7/2*e^5 + 34*e^3 - 85/2*e', '-7/2*e^5 + 34*e^3 - 85/2*e', '2*e^4 - 24*e^2 + 8', '2*e^4 - 24*e^2 + 8', '-2*e^5 + 20*e^3 - 30*e', '-2*e^5 + 20*e^3 - 30*e', '-1/2*e^5 + 18*e^3 - 151/2*e', '-1/2*e^5 + 18*e^3 - 151/2*e', '7*e^4 - 53*e^2 + 50', '7*e^4 - 53*e^2 + 50', '29/2*e^5 - 261/2*e^3 + 175*e', '29/2*e^5 - 261/2*e^3 + 175*e', '-19/2*e^5 + 84*e^3 - 265/2*e', '-19/2*e^5 + 84*e^3 - 265/2*e', '-4*e^4 + 28*e^2 - 14', '-4*e^4 + 28*e^2 - 14', '6*e^2 - 16', '6*e^2 - 16', '6*e^4 - 58*e^2 + 98', '6*e^4 - 58*e^2 + 98', '19/2*e^5 - 86*e^3 + 281/2*e', '19/2*e^5 - 86*e^3 + 281/2*e', '-10*e^4 + 74*e^2 - 34', '-10*e^4 + 74*e^2 - 34', '-3/2*e^5 + 17/2*e^3 + 18*e', '-3/2*e^5 + 17/2*e^3 + 18*e', '1/2*e^5 - 23/2*e^3 + 44*e', '1/2*e^5 - 23/2*e^3 + 44*e', '-7*e^4 + 49*e^2 - 54', '-7*e^4 + 49*e^2 - 54', '7*e^4 - 57*e^2 + 78', '7*e^4 - 57*e^2 + 78', '-20*e^2 + 74', '-20*e^2 + 74', '15/2*e^5 - 67*e^3 + 151/2*e', '15/2*e^5 - 67*e^3 + 151/2*e', '31/2*e^4 - 257/2*e^2 + 118', '31/2*e^4 - 257/2*e^2 + 118', '2*e^5 - 30*e^3 + 92*e', '2*e^5 - 30*e^3 + 92*e', '-10*e^4 + 84*e^2 - 68', '-10*e^4 + 84*e^2 - 68', '8*e^4 - 56*e^2 + 46', '8*e^4 - 56*e^2 + 46', '-8*e^5 + 78*e^3 - 154*e', '-8*e^5 + 78*e^3 - 154*e', '-5/2*e^5 + 29/2*e^3 + e', '-5/2*e^5 + 29/2*e^3 + e', '17/2*e^5 - 74*e^3 + 171/2*e', '17/2*e^5 - 74*e^3 + 171/2*e', '-4*e^4 + 32*e^2 - 26', '-4*e^4 + 32*e^2 - 26', '1/2*e^5 - 10*e^3 + 131/2*e', '1/2*e^5 - 10*e^3 + 131/2*e', '11/2*e^5 - 48*e^3 + 113/2*e', '11/2*e^5 - 48*e^3 + 113/2*e', '3*e^4 - 5*e^2 - 24', '3*e^4 - 5*e^2 - 24', '-e^4 - e^2 + 12', '-e^4 - e^2 + 12', '17/2*e^5 - 78*e^3 + 215/2*e', '17/2*e^5 - 78*e^3 + 215/2*e', '-29/2*e^5 + 130*e^3 - 395/2*e', '-29/2*e^5 + 130*e^3 - 395/2*e', '-2*e^4 + 36*e^2 - 104', '-2*e^4 + 36*e^2 - 104', '-5/2*e^5 + 49/2*e^3 - 33*e', '-5/2*e^5 + 49/2*e^3 - 33*e', '19/2*e^5 - 76*e^3 + 157/2*e', '19/2*e^5 - 76*e^3 + 157/2*e', '-10*e^4 + 74*e^2 - 62', '-10*e^4 + 74*e^2 - 62', '-5*e^4 + 35*e^2 - 42', '-5*e^4 + 35*e^2 - 42', '3*e^5 - 25*e^3 + 20*e', '3*e^5 - 25*e^3 + 20*e', '-23/2*e^4 + 185/2*e^2 - 98', '-23/2*e^4 + 185/2*e^2 - 98', 'e^5 - 16*e^3 + 59*e', 'e^5 - 16*e^3 + 59*e', '-5*e^4 + 31*e^2 + 16', '-5*e^4 + 31*e^2 + 16', '9/2*e^5 - 42*e^3 + 127/2*e', '9/2*e^5 - 42*e^3 + 127/2*e', '13/2*e^5 - 48*e^3 + 19/2*e', '13/2*e^5 - 48*e^3 + 19/2*e', '2*e^4 - 6*e^2 + 6', '2*e^4 - 6*e^2 + 6', '-23/2*e^4 + 177/2*e^2 - 90', '-23/2*e^4 + 177/2*e^2 - 90', '12*e^4 - 114*e^2 + 152', '12*e^4 - 114*e^2 + 152', '4*e^2 + 74', '-13/2*e^5 + 111/2*e^3 - 58*e', '-13/2*e^5 + 111/2*e^3 - 58*e', 34, 34, '-15/2*e^5 + 77*e^3 - 275/2*e', '-15/2*e^5 + 77*e^3 - 275/2*e', '4*e^4 - 46*e^2 + 48', '4*e^4 - 46*e^2 + 48', '31/2*e^5 - 138*e^3 + 393/2*e', '31/2*e^5 - 138*e^3 + 393/2*e', '-6*e^5 + 57*e^3 - 109*e', '-6*e^5 + 57*e^3 - 109*e', '-11/2*e^4 + 85/2*e^2 + 6', '-11/2*e^4 + 85/2*e^2 + 6', '-7/2*e^5 + 22*e^3 + 23/2*e', '-7/2*e^5 + 22*e^3 + 23/2*e', '-17/2*e^5 + 157/2*e^3 - 113*e', '-17/2*e^5 + 157/2*e^3 - 113*e', '11*e^4 - 97*e^2 + 86', '11*e^4 - 97*e^2 + 86', '1/2*e^5 - 7*e^3 + 21/2*e', '1/2*e^5 - 7*e^3 + 21/2*e', '-10*e^5 + 87*e^3 - 123*e', '-10*e^5 + 87*e^3 - 123*e', '3*e^4 - 29*e^2 - 30', '3*e^4 - 29*e^2 - 30', '-15/2*e^5 + 63*e^3 - 111/2*e', '-15/2*e^5 + 63*e^3 - 111/2*e', '-8*e^5 + 72*e^3 - 92*e', '-8*e^5 + 72*e^3 - 92*e', '29/2*e^4 - 251/2*e^2 + 118', '29/2*e^4 - 251/2*e^2 + 118', '19*e^4 - 163*e^2 + 178', '19*e^4 - 163*e^2 + 178', '-3*e^4 + e^2 + 46', '-3*e^4 + e^2 + 46', '-13/2*e^5 + 115/2*e^3 - 88*e', '-13/2*e^5 + 115/2*e^3 - 88*e', '3*e^4 - 9*e^2 - 2', '3*e^4 - 9*e^2 - 2', '-3/2*e^5 + 6*e^3 + 115/2*e', '-3/2*e^5 + 6*e^3 + 115/2*e', '-8*e^4 + 56*e^2 - 34', '-8*e^4 + 56*e^2 - 34', '-16*e^5 + 136*e^3 - 172*e', '-16*e^5 + 136*e^3 - 172*e', '-2*e^4 + 10*e^2 + 42', '-2*e^4 + 10*e^2 + 42', '11/2*e^4 - 93/2*e^2 + 30', '11/2*e^4 - 93/2*e^2 + 30', '4*e^5 - 21*e^3 - 21*e', '4*e^5 - 21*e^3 - 21*e', '-9/2*e^5 + 47*e^3 - 181/2*e', '-9/2*e^5 + 47*e^3 - 181/2*e', '-3*e^4 + 33*e^2 - 36', '-3*e^4 + 33*e^2 - 36', '-e^4 + 9*e^2 - 20', '-e^4 + 9*e^2 - 20', '-1/2*e^5 + 3/2*e^3 - 14*e', '-1/2*e^5 + 3/2*e^3 - 14*e', '7/2*e^4 - 41/2*e^2 + 30', '7/2*e^4 - 41/2*e^2 + 30', '-5/2*e^5 + 29*e^3 - 117/2*e', '-5/2*e^5 + 29*e^3 - 117/2*e', '2*e^2 - 16', '2*e^2 - 16', '-12*e^4 + 116*e^2 - 158', '-12*e^4 + 116*e^2 - 158', '-13/2*e^5 + 141/2*e^3 - 175*e', '-13/2*e^5 + 141/2*e^3 - 175*e', '3/2*e^5 - 28*e^3 + 193/2*e', '3/2*e^5 - 28*e^3 + 193/2*e', '9*e^5 - 80*e^3 + 111*e', '9*e^5 - 80*e^3 + 111*e', '-3*e^4 + 47*e^2 - 118', '-3*e^4 + 47*e^2 - 118', '15/2*e^5 - 63*e^3 + 167/2*e', '15/2*e^5 - 63*e^3 + 167/2*e', '-21/2*e^4 + 155/2*e^2 - 98', '-21/2*e^4 + 155/2*e^2 - 98', '16*e^5 - 134*e^3 + 146*e', '16*e^5 - 134*e^3 + 146*e', '11*e^4 - 105*e^2 + 138', '11*e^4 - 105*e^2 + 138', '-2*e^4 + 38*e^2 - 122', '-2*e^4 + 38*e^2 - 122', '1/2*e^5 - 15*e^3 + 101/2*e', '1/2*e^5 - 15*e^3 + 101/2*e', '-3*e^4 + e^2 + 54', '-3*e^4 + e^2 + 54', '9/2*e^5 - 105/2*e^3 + 147*e', '9/2*e^5 - 105/2*e^3 + 147*e', '-1/2*e^4 + 23/2*e^2 + 30', '-1/2*e^4 + 23/2*e^2 + 30', '4*e^5 - 43*e^3 + 89*e', '4*e^5 - 43*e^3 + 89*e', '10*e^4 - 72*e^2 + 68', '10*e^4 - 72*e^2 + 68', '-9/2*e^5 + 36*e^3 - 59/2*e', '-9/2*e^5 + 36*e^3 - 59/2*e', '-9/2*e^4 + 87/2*e^2 - 110', '-9/2*e^4 + 87/2*e^2 - 110', '8*e^4 - 62*e^2 + 24', '8*e^4 - 62*e^2 + 24', '7/2*e^5 - 26*e^3 + 17/2*e', '7/2*e^5 - 26*e^3 + 17/2*e', '-13*e^4 + 89*e^2 - 60', '-13*e^4 + 89*e^2 - 60', '-5/2*e^5 + 49/2*e^3 - 73*e', '-5/2*e^5 + 49/2*e^3 - 73*e', '8*e^5 - 75*e^3 + 101*e', '8*e^5 - 75*e^3 + 101*e', '-7*e^4 + 65*e^2 - 94', '-7*e^4 + 65*e^2 - 94', '18*e^4 - 148*e^2 + 172', '18*e^4 - 148*e^2 + 172', '-7/2*e^4 + 73/2*e^2 - 10', '-7/2*e^4 + 73/2*e^2 - 10', '-1/2*e^5 - 10*e^3 + 141/2*e', '-1/2*e^5 - 10*e^3 + 141/2*e', '-3*e^4 + 31*e^2 - 52', '-3*e^4 + 31*e^2 - 52', '7/2*e^5 - 32*e^3 + 21/2*e', '7/2*e^5 - 32*e^3 + 21/2*e', '-e^4 + 15*e^2 - 34', '-e^4 + 15*e^2 - 34', '11/2*e^5 - 99/2*e^3 + 85*e', '11/2*e^5 - 99/2*e^3 + 85*e', '8*e^4 - 64*e^2 + 122', '8*e^4 - 64*e^2 + 122', '5/2*e^5 - 32*e^3 + 207/2*e', '5/2*e^5 - 32*e^3 + 207/2*e', '15/2*e^5 - 73*e^3 + 267/2*e', '15/2*e^5 - 73*e^3 + 267/2*e', '5/2*e^4 - 75/2*e^2 + 114', '5/2*e^4 - 75/2*e^2 + 114', '9*e^3 - 43*e', '9*e^3 - 43*e', '3/2*e^4 - 61/2*e^2 + 106', '3/2*e^4 - 61/2*e^2 + 106', '-3*e^4 + 33*e^2 - 64', '-3*e^4 + 33*e^2 - 64', '2*e^5 - 19*e^3 + 63*e', '2*e^5 - 19*e^3 + 63*e', '25/2*e^5 - 231/2*e^3 + 160*e', '25/2*e^5 - 231/2*e^3 + 160*e', '17/2*e^5 - 187/2*e^3 + 194*e', '17/2*e^5 - 187/2*e^3 + 194*e', '-19*e^5 + 173*e^3 - 232*e', '-19*e^5 + 173*e^3 - 232*e', '9/2*e^5 - 42*e^3 + 207/2*e', '9/2*e^5 - 42*e^3 + 207/2*e', '-11/2*e^4 + 109/2*e^2 - 98', '-11/2*e^4 + 109/2*e^2 - 98', '-5*e^4 + 29*e^2 + 2', '-5*e^4 + 29*e^2 + 2', '14*e^5 - 126*e^3 + 160*e', '14*e^5 - 126*e^3 + 160*e', '3/2*e^5 - 9/2*e^3 - 42*e', '3/2*e^5 - 9/2*e^3 - 42*e', '11/2*e^4 - 77/2*e^2 - 30', '11/2*e^4 - 77/2*e^2 - 30', '31/2*e^5 - 138*e^3 + 325/2*e', '31/2*e^5 - 138*e^3 + 325/2*e', '-2*e^4 + 6*e^2 + 38', '-2*e^4 + 6*e^2 + 38', '-13/2*e^5 + 68*e^3 - 311/2*e', '-13/2*e^5 + 68*e^3 - 311/2*e', '7*e^4 - 75*e^2 + 62', '7*e^4 - 75*e^2 + 62', '-6*e^4 + 74*e^2 - 102', '-6*e^4 + 74*e^2 - 102', '-e^4 + 31*e^2 - 96', '-e^4 + 31*e^2 - 96', '35/2*e^5 - 150*e^3 + 373/2*e', '35/2*e^5 - 150*e^3 + 373/2*e', '13/2*e^5 - 105/2*e^3 + 41*e', '13/2*e^5 - 105/2*e^3 + 41*e', '11/2*e^4 - 93/2*e^2 + 110', '11/2*e^4 - 93/2*e^2 + 110', '-21/2*e^5 + 108*e^3 - 395/2*e', '-21/2*e^5 + 108*e^3 - 395/2*e', '2*e^4 + 2*e^2 - 106', '2*e^4 + 2*e^2 - 106', '7/2*e^5 - 81/2*e^3 + 84*e', '7/2*e^5 - 81/2*e^3 + 84*e', '-9*e^4 + 75*e^2 + 2', '-9*e^4 + 75*e^2 + 2', '7/2*e^4 - 73/2*e^2 + 78', '7/2*e^4 - 73/2*e^2 + 78', '-23/2*e^5 + 104*e^3 - 281/2*e', '-23/2*e^5 + 104*e^3 - 281/2*e', '-13*e^4 + 87*e^2 - 38', '-13*e^4 + 87*e^2 - 38', '-11/2*e^5 + 109/2*e^3 - 136*e', '-11/2*e^5 + 109/2*e^3 - 136*e', '19/2*e^5 - 84*e^3 + 249/2*e', '19/2*e^5 - 84*e^3 + 249/2*e', '-4*e^4 + 40*e^2 + 54', '-16*e^4 + 136*e^2 - 114', '-16*e^4 + 136*e^2 - 114', '31/2*e^5 - 131*e^3 + 263/2*e', '31/2*e^5 - 131*e^3 + 263/2*e', '7/2*e^5 - 22*e^3 - 39/2*e', '7/2*e^5 - 22*e^3 - 39/2*e', '-15/2*e^4 + 97/2*e^2 - 54', '-15/2*e^4 + 97/2*e^2 - 54', '4*e^4 - 36*e^2 + 62', '4*e^4 - 36*e^2 + 62', '3*e^5 - 47*e^3 + 158*e', '3*e^5 - 47*e^3 + 158*e', '-9/2*e^4 + 39/2*e^2 + 62', '-9/2*e^4 + 39/2*e^2 + 62', '9*e^4 - 73*e^2 + 100', '9*e^4 - 73*e^2 + 100', '-13/2*e^5 + 45*e^3 - 61/2*e', '-13/2*e^5 + 45*e^3 - 61/2*e', '6*e^4 - 28*e^2 - 76', '6*e^4 - 28*e^2 - 76', '10*e^5 - 69*e^3 + 21*e', '10*e^5 - 69*e^3 + 21*e', '-3/2*e^5 + 32*e^3 - 305/2*e', '-3/2*e^5 + 32*e^3 - 305/2*e', '15*e^5 - 138*e^3 + 195*e', '15*e^5 - 138*e^3 + 195*e', '-10*e^2 + 120', '-10*e^2 + 120', '12*e^5 - 110*e^3 + 202*e', '12*e^5 - 110*e^3 + 202*e', '-37/2*e^5 + 327/2*e^3 - 202*e', '-37/2*e^5 + 327/2*e^3 - 202*e', '12*e^4 - 106*e^2 + 72', '12*e^4 - 106*e^2 + 72', '-31/2*e^5 + 140*e^3 - 309/2*e', '-31/2*e^5 + 140*e^3 - 309/2*e', '10*e^4 - 66*e^2 + 86', '10*e^4 - 66*e^2 + 86', '-e^4 + 41*e^2 - 124', '-e^4 + 41*e^2 - 124', '5/2*e^4 - 3/2*e^2 - 2', '5/2*e^4 - 3/2*e^2 - 2', '7*e^5 - 75*e^3 + 182*e', '7*e^5 - 75*e^3 + 182*e', '8*e^4 - 64*e^2 + 138', '8*e^4 - 64*e^2 + 138', '-13*e^5 + 125*e^3 - 182*e', '-13*e^5 + 125*e^3 - 182*e', '-11/2*e^5 + 117/2*e^3 - 112*e', '-11/2*e^5 + 117/2*e^3 - 112*e', '3/2*e^4 - 29/2*e^2 + 18', '3/2*e^4 - 29/2*e^2 + 18', '-17/2*e^5 + 78*e^3 - 331/2*e', '-17/2*e^5 + 78*e^3 - 331/2*e', '-6*e^4 + 54*e^2 - 142', '-6*e^4 + 54*e^2 - 142', '21/2*e^5 - 82*e^3 + 87/2*e', '21/2*e^5 - 82*e^3 + 87/2*e', '-e^4 + 23*e^2 - 106', '-e^4 + 23*e^2 - 106', '-22*e^4 + 172*e^2 - 172', '-22*e^4 + 172*e^2 - 172', '-5/2*e^5 + 35/2*e^3 - 12*e', '-5/2*e^5 + 35/2*e^3 - 12*e', '-10*e^5 + 92*e^3 - 138*e', '-10*e^5 + 92*e^3 - 138*e', '23/2*e^5 - 106*e^3 + 313/2*e', '23/2*e^5 - 106*e^3 + 313/2*e', '-9*e^4 + 71*e^2 - 82', '-9*e^4 + 71*e^2 - 82', '7*e^5 - 62*e^3 + 87*e', '7*e^5 - 62*e^3 + 87*e', '7/2*e^5 - 61/2*e^3 + 66*e', '7/2*e^5 - 61/2*e^3 + 66*e', '-9/2*e^4 + 47/2*e^2 + 30', '-9/2*e^4 + 47/2*e^2 + 30', '-3*e^4 + 21*e^2 - 82', '-3*e^4 + 21*e^2 - 82', '-23/2*e^5 + 111*e^3 - 303/2*e', '-23/2*e^5 + 111*e^3 - 303/2*e', '9/2*e^5 - 87/2*e^3 + 76*e', '9/2*e^5 - 87/2*e^3 + 76*e', '33/2*e^4 - 207/2*e^2 + 18', '33/2*e^4 - 207/2*e^2 + 18', '5*e^4 - 51*e^2 + 64', '5*e^4 - 51*e^2 + 64', '-31/2*e^5 + 146*e^3 - 529/2*e', '-31/2*e^5 + 146*e^3 - 529/2*e', '-3*e^4 + 23*e^2 - 30', '-3*e^4 + 23*e^2 - 30', '-15/2*e^5 + 52*e^3 - 1/2*e', '-15/2*e^5 + 52*e^3 - 1/2*e', '8*e^4 - 80*e^2 + 54', '8*e^4 - 80*e^2 + 54', '-5/2*e^5 + 20*e^3 - 119/2*e', '-5/2*e^5 + 20*e^3 - 119/2*e', '6*e^5 - 65*e^3 + 133*e', '6*e^5 - 65*e^3 + 133*e', '-19/2*e^5 + 95*e^3 - 379/2*e', '-19/2*e^5 + 95*e^3 - 379/2*e', '11/2*e^5 - 50*e^3 + 109/2*e', '11/2*e^5 - 50*e^3 + 109/2*e', '2*e^4 - 14*e^2 + 78', '2*e^4 - 14*e^2 + 78', '15/2*e^4 - 137/2*e^2 + 22', '15/2*e^4 - 137/2*e^2 + 22', '9*e^4 - 55*e^2 - 34', '9*e^4 - 55*e^2 - 34', '-39/2*e^5 + 180*e^3 - 533/2*e', '-39/2*e^5 + 180*e^3 - 533/2*e', '23/2*e^5 - 105*e^3 + 283/2*e', '23/2*e^5 - 105*e^3 + 283/2*e', '1/2*e^5 - 9/2*e^3 + 11*e', '1/2*e^5 - 9/2*e^3 + 11*e', '-e^5 + 30*e^3 - 149*e', '-e^5 + 30*e^3 - 149*e', '-16*e^4 + 124*e^2 - 98', '-16*e^4 + 124*e^2 - 98', '-25/2*e^5 + 98*e^3 - 151/2*e', '-25/2*e^5 + 98*e^3 - 151/2*e', '5/2*e^4 - 59/2*e^2 - 54', '5/2*e^4 - 59/2*e^2 - 54', '3*e^4 - 3*e^2 - 46', '3*e^4 - 3*e^2 - 46', '6*e^4 - 34*e^2 + 2', '6*e^4 - 34*e^2 + 2', '-5*e^5 + 47*e^3 - 104*e', '-5*e^5 + 47*e^3 - 104*e', '-15/2*e^5 + 60*e^3 - 105/2*e', '-15/2*e^5 + 60*e^3 - 105/2*e', '9*e^4 - 75*e^2 + 38', '9*e^4 - 75*e^2 + 38', '17/2*e^5 - 100*e^3 + 491/2*e', '17/2*e^5 - 100*e^3 + 491/2*e', '19*e^4 - 151*e^2 + 124', '19*e^4 - 151*e^2 + 124', '-3*e^4 + 9*e^2 + 2', '-3*e^4 + 9*e^2 + 2', '-17/2*e^4 + 95/2*e^2 + 38', '-17/2*e^4 + 95/2*e^2 + 38', '-4*e^5 + 32*e^3 - 60*e', '-4*e^5 + 32*e^3 - 60*e', '-4*e^4 + 40*e^2 + 2', '-4*e^4 + 40*e^2 + 2', '-9*e^4 + 69*e^2 - 92', '-9*e^4 + 69*e^2 - 92', '-19/2*e^5 + 88*e^3 - 189/2*e', '-19/2*e^5 + 88*e^3 - 189/2*e', '51/2*e^5 - 216*e^3 + 529/2*e', '51/2*e^5 - 216*e^3 + 529/2*e', '2*e^4 - 38*e^2 + 102', '2*e^4 - 38*e^2 + 102', '41/2*e^5 - 345/2*e^3 + 215*e', '41/2*e^5 - 345/2*e^3 + 215*e', '6*e^4 - 18*e^2 - 66', '6*e^4 - 18*e^2 - 66', '5/2*e^5 - 15*e^3 - 23/2*e', '5/2*e^5 - 15*e^3 - 23/2*e', '-37/2*e^4 + 299/2*e^2 - 102', '-37/2*e^4 + 299/2*e^2 - 102', '12*e^5 - 97*e^3 + 111*e', '12*e^5 - 97*e^3 + 111*e', '13*e^4 - 123*e^2 + 136', '13*e^4 - 123*e^2 + 136', '-9/2*e^5 + 46*e^3 - 263/2*e', '-9/2*e^5 + 46*e^3 - 263/2*e', '19*e^5 - 167*e^3 + 190*e', '19*e^5 - 167*e^3 + 190*e', '-7/2*e^5 + 43/2*e^3 + 45*e', '-7/2*e^5 + 43/2*e^3 + 45*e', '-24*e^4 + 204*e^2 - 238', '-24*e^4 + 204*e^2 - 238', '-13/2*e^5 + 55*e^3 - 145/2*e', '-13/2*e^5 + 55*e^3 - 145/2*e', '-39/2*e^5 + 349/2*e^3 - 262*e', '-39/2*e^5 + 349/2*e^3 - 262*e', '23/2*e^4 - 241/2*e^2 + 166', '23/2*e^4 - 241/2*e^2 + 166', '-17*e^5 + 156*e^3 - 211*e', '-17*e^5 + 156*e^3 - 211*e', '-13*e^4 + 123*e^2 - 180', '-13*e^4 + 123*e^2 - 180', 'e^4 + 5*e^2 - 54', 'e^4 + 5*e^2 - 54', '-15/2*e^5 + 91/2*e^3 + 17*e', '-15/2*e^5 + 91/2*e^3 + 17*e', '-6*e^4 + 52*e^2 - 48', '-6*e^4 + 52*e^2 - 48', '19/2*e^5 - 106*e^3 + 465/2*e', '19/2*e^5 - 106*e^3 + 465/2*e', '29/2*e^5 - 141*e^3 + 525/2*e', '29/2*e^5 - 141*e^3 + 525/2*e', '16*e^4 - 136*e^2 + 146', '16*e^4 - 136*e^2 + 146', '-11/2*e^4 + 61/2*e^2 + 26', '-11/2*e^4 + 61/2*e^2 + 26', 142, '9*e^3 - 43*e', '9*e^3 - 43*e', '-35/2*e^4 + 293/2*e^2 - 98', '-35/2*e^4 + 293/2*e^2 - 98', '-43/2*e^5 + 198*e^3 - 589/2*e', '-43/2*e^5 + 198*e^3 - 589/2*e', '33/2*e^5 - 299/2*e^3 + 234*e', '33/2*e^5 - 299/2*e^3 + 234*e', '-7*e^4 + 43*e^2 - 68', '-7*e^4 + 43*e^2 - 68', '-43/2*e^5 + 184*e^3 - 421/2*e', '-43/2*e^5 + 184*e^3 - 421/2*e', '-27/2*e^5 + 120*e^3 - 257/2*e', '-27/2*e^5 + 120*e^3 - 257/2*e', '9*e^4 - 77*e^2 + 102', '9*e^4 - 77*e^2 + 102', '-5*e^5 + 59*e^3 - 156*e', '-5*e^5 + 59*e^3 - 156*e', '11*e^4 - 73*e^2 - 22', '11*e^4 - 73*e^2 - 22', '-33/2*e^4 + 327/2*e^2 - 186', '-33/2*e^4 + 327/2*e^2 - 186', '-5/2*e^4 + 59/2*e^2 + 10', '-5/2*e^4 + 59/2*e^2 + 10', '20*e^4 - 170*e^2 + 232', '20*e^4 - 170*e^2 + 232', '14*e^2 - 56', '14*e^2 - 56', '4*e^4 - 44*e^2 + 54', '4*e^4 - 44*e^2 + 54', '25/2*e^5 - 110*e^3 + 183/2*e', '25/2*e^5 - 110*e^3 + 183/2*e', '12*e^4 - 88*e^2 + 50', '12*e^4 - 88*e^2 + 50', '14*e^5 - 123*e^3 + 207*e', '14*e^5 - 123*e^3 + 207*e', '-11*e^4 + 101*e^2 - 64', '-11*e^4 + 101*e^2 - 64', '25/2*e^5 - 111*e^3 + 349/2*e', '25/2*e^5 - 111*e^3 + 349/2*e', '-3*e^4 + 27*e^2 - 22', '-3*e^4 + 27*e^2 - 22', '13*e^5 - 127*e^3 + 240*e', '13*e^5 - 127*e^3 + 240*e', '-9*e^4 + 49*e^2 + 76', '-9*e^4 + 49*e^2 + 76', '-9/2*e^5 + 38*e^3 - 15/2*e', '-9/2*e^5 + 38*e^3 - 15/2*e', '-e^4 - 23*e^2 + 100', '-e^4 - 23*e^2 + 100', '-13*e^4 + 97*e^2 - 146', '-13*e^4 + 97*e^2 - 146', '51/2*e^4 - 421/2*e^2 + 214', '51/2*e^4 - 421/2*e^2 + 214', '-13*e^5 + 92*e^3 - 35*e', '-13*e^5 + 92*e^3 - 35*e', '5/2*e^4 + 13/2*e^2 - 102', '5/2*e^4 + 13/2*e^2 - 102', '51/2*e^5 - 445/2*e^3 + 272*e', '51/2*e^5 - 445/2*e^3 + 272*e', '-25/2*e^4 + 207/2*e^2 - 62', '-25/2*e^4 + 207/2*e^2 - 62', '31/2*e^5 - 146*e^3 + 545/2*e', '31/2*e^5 - 146*e^3 + 545/2*e', '3*e^4 - 61*e^2 + 150', '3*e^4 - 61*e^2 + 150', '7/2*e^5 - 75/2*e^3 + 147*e', '7/2*e^5 - 75/2*e^3 + 147*e', '-11/2*e^5 + 74*e^3 - 389/2*e', '-11/2*e^5 + 74*e^3 - 389/2*e', '-10*e^4 + 70*e^2 - 90', '-10*e^4 + 70*e^2 - 90', '3*e^4 + 3*e^2 - 28', '3*e^4 + 3*e^2 - 28', '20*e^5 - 190*e^3 + 278*e', '20*e^5 - 190*e^3 + 278*e', '-19/2*e^5 + 77*e^3 - 47/2*e', '-19/2*e^5 + 77*e^3 - 47/2*e', '57/2*e^5 - 262*e^3 + 707/2*e', '57/2*e^5 - 262*e^3 + 707/2*e', '21/2*e^5 - 213/2*e^3 + 199*e', '21/2*e^5 - 213/2*e^3 + 199*e', '9/2*e^4 - 47/2*e^2 + 22', '9/2*e^4 - 47/2*e^2 + 22', '19/2*e^5 - 70*e^3 + 61/2*e', '19/2*e^5 - 70*e^3 + 61/2*e', '2*e^4 + 2*e^2 - 18', '2*e^4 + 2*e^2 - 18', '-27/2*e^5 + 251/2*e^3 - 237*e', '-27/2*e^5 + 251/2*e^3 - 237*e', '-25/2*e^5 + 116*e^3 - 307/2*e', '-25/2*e^5 + 116*e^3 - 307/2*e', 'e^4 - 19*e^2 - 62', 'e^4 - 19*e^2 - 62', '9/2*e^5 - 61/2*e^3 + 25*e', '9/2*e^5 - 61/2*e^3 + 25*e', '-27/2*e^5 + 129*e^3 - 439/2*e', '-27/2*e^5 + 129*e^3 - 439/2*e', '24*e^2 - 58', '24*e^2 - 58', '-29/2*e^4 + 275/2*e^2 - 218', '-29/2*e^4 + 275/2*e^2 - 218', '-57/2*e^5 + 240*e^3 - 583/2*e', '-57/2*e^5 + 240*e^3 - 583/2*e', '3*e^5 - 44*e^3 + 121*e', '3*e^5 - 44*e^3 + 121*e', '3/2*e^5 + 2*e^3 - 127/2*e', '3/2*e^5 + 2*e^3 - 127/2*e', '5*e^4 - 35*e^2 - 10', '5*e^4 - 35*e^2 - 10', '-3/2*e^5 + 26*e^3 - 157/2*e', '-3/2*e^5 + 26*e^3 - 157/2*e', '-13*e^4 + 115*e^2 - 204', '-13*e^4 + 115*e^2 - 204', '17/2*e^5 - 125/2*e^3 + 45*e', '17/2*e^5 - 125/2*e^3 + 45*e', '3/2*e^5 - 135/2*e', '3/2*e^5 - 135/2*e', '31/2*e^4 - 257/2*e^2 + 90', '31/2*e^4 - 257/2*e^2 + 90', '7/2*e^4 - 65/2*e^2 + 122', '7/2*e^4 - 65/2*e^2 + 122', '-25/2*e^5 + 118*e^3 - 467/2*e', '-25/2*e^5 + 118*e^3 - 467/2*e', '21/2*e^5 - 157/2*e^3 + 59*e', '21/2*e^5 - 157/2*e^3 + 59*e', '12*e^4 - 116*e^2 + 70', '12*e^4 - 116*e^2 + 70', '13/2*e^5 - 133/2*e^3 + 183*e', '13/2*e^5 - 133/2*e^3 + 183*e', '-14*e^4 + 86*e^2 - 30', '-14*e^4 + 86*e^2 - 30', '7*e^4 - 57*e^2 + 118', '7*e^4 - 57*e^2 + 118', '3/2*e^5 - 30*e^3 + 285/2*e', '3/2*e^5 - 30*e^3 + 285/2*e', '18*e^4 - 126*e^2 + 110', '18*e^4 - 126*e^2 + 110', '27*e^4 - 237*e^2 + 266', '27*e^4 - 237*e^2 + 266', '-22*e^4 + 156*e^2 - 128', '-22*e^4 + 156*e^2 - 128', '-3*e^4 + 13*e^2 + 44', '-3*e^4 + 13*e^2 + 44', '-17/2*e^5 + 163/2*e^3 - 186*e', '-17/2*e^5 + 163/2*e^3 - 186*e', '-7*e^4 + 91*e^2 - 124', '-7*e^4 + 91*e^2 - 124', '25/2*e^5 - 116*e^3 + 455/2*e', '25/2*e^5 - 116*e^3 + 455/2*e', '-6*e^4 + 34*e^2 - 30', '-6*e^4 + 34*e^2 - 30', '-17/2*e^5 + 77*e^3 - 209/2*e', '-17/2*e^5 + 77*e^3 - 209/2*e', '9/2*e^5 - 75/2*e^3 + 6*e', '9/2*e^5 - 75/2*e^3 + 6*e', '18*e^4 - 166*e^2 + 174', '18*e^4 - 166*e^2 + 174', '11/2*e^5 - 43*e^3 + 115/2*e', '11/2*e^5 - 43*e^3 + 115/2*e', '7/2*e^4 - 89/2*e^2 + 142', '7/2*e^4 - 89/2*e^2 + 142', 'e^5 + 9*e^3 - 92*e', 'e^5 + 9*e^3 - 92*e', '22*e^4 - 198*e^2 + 262', '22*e^4 - 198*e^2 + 262', '11/2*e^4 - 101/2*e^2 - 42', '11/2*e^4 - 101/2*e^2 - 42', '-5/2*e^5 + 28*e^3 - 43/2*e', '-5/2*e^5 + 28*e^3 - 43/2*e', '-10*e^5 + 75*e^3 - 79*e', '-10*e^5 + 75*e^3 - 79*e', '11/2*e^4 - 117/2*e^2 + 78', '11/2*e^4 - 117/2*e^2 + 78', '33/2*e^5 - 293/2*e^3 + 205*e', '33/2*e^5 - 293/2*e^3 + 205*e', '-3*e^4 + 43*e^2 - 124', '-3*e^4 + 43*e^2 - 124', '-5*e^4 + 63*e^2 - 180', '-5*e^4 + 63*e^2 - 180', '-3/2*e^5 + 29/2*e^3 - 20*e', '-3/2*e^5 + 29/2*e^3 - 20*e', '3*e^5 - 21*e^3 - 36*e', '3*e^5 - 21*e^3 - 36*e', '-31/2*e^4 + 305/2*e^2 - 174', '-31/2*e^4 + 305/2*e^2 - 174', '-26*e^5 + 236*e^3 - 342*e', '-26*e^5 + 236*e^3 - 342*e', '-3/2*e^4 - 11/2*e^2 + 138', '-3/2*e^4 - 11/2*e^2 + 138', '-7*e^4 + 57*e^2 + 8', '-7*e^4 + 57*e^2 + 8', '21/2*e^4 - 115/2*e^2 - 18', '21/2*e^4 - 115/2*e^2 - 18', '29/2*e^5 - 118*e^3 + 291/2*e', '29/2*e^5 - 118*e^3 + 291/2*e', '-14*e^4 + 70*e^2 + 78', '-14*e^4 + 70*e^2 + 78', '-1/2*e^5 + 4*e^3 - 35/2*e', '-1/2*e^5 + 4*e^3 - 35/2*e', '15/2*e^5 - 73*e^3 + 171/2*e', '15/2*e^5 - 73*e^3 + 171/2*e', '-27/2*e^5 + 122*e^3 - 329/2*e', '-27/2*e^5 + 122*e^3 - 329/2*e', '-18*e^4 + 152*e^2 - 88', '13*e^4 - 113*e^2 + 148', '13*e^4 - 113*e^2 + 148', '9*e^4 - 47*e^2 - 62', '9*e^4 - 47*e^2 - 62', '-10*e^4 + 72*e^2 - 20', '-10*e^4 + 72*e^2 - 20', '11*e^5 - 105*e^3 + 184*e', '11*e^5 - 105*e^3 + 184*e', '1/2*e^4 - 15/2*e^2 + 6', '1/2*e^4 - 15/2*e^2 + 6', '21/2*e^5 - 94*e^3 + 283/2*e', '21/2*e^5 - 94*e^3 + 283/2*e', '12*e^4 - 74*e^2 - 16', '12*e^4 - 74*e^2 - 16', '5*e^4 - 9*e^2 - 172', '5*e^4 - 9*e^2 - 172', '-3*e^5 + 30*e^3 - 23*e', '-3*e^5 + 30*e^3 - 23*e', '-3/2*e^5 + 23/2*e^3 + e', '-3/2*e^5 + 23/2*e^3 + e', '-19/2*e^5 + 197/2*e^3 - 176*e', '-19/2*e^5 + 197/2*e^3 - 176*e', '16*e^2 - 82', '16*e^2 - 82', '9/2*e^5 - 57*e^3 + 345/2*e', '9/2*e^5 - 57*e^3 + 345/2*e', '-24*e^4 + 192*e^2 - 174', '-24*e^4 + 192*e^2 - 174', '-45/2*e^5 + 209*e^3 - 637/2*e', '-45/2*e^5 + 209*e^3 - 637/2*e', '-51/2*e^4 + 437/2*e^2 - 254', '-51/2*e^4 + 437/2*e^2 - 254', '18*e^5 - 145*e^3 + 141*e', '18*e^5 - 145*e^3 + 141*e', '-24*e^4 + 180*e^2 - 142', '-24*e^4 + 180*e^2 - 142', '13/2*e^5 - 75*e^3 + 393/2*e', '13/2*e^5 - 75*e^3 + 393/2*e', '-11*e^4 + 87*e^2 + 28', '-11*e^4 + 87*e^2 + 28', '-5/2*e^5 + 57/2*e^3 - 65*e', '-5/2*e^5 + 57/2*e^3 - 65*e', '21/2*e^4 - 155/2*e^2 + 66', '21/2*e^4 - 155/2*e^2 + 66', '10*e^4 - 96*e^2 + 72', '10*e^4 - 96*e^2 + 72', '13*e^4 - 123*e^2 + 234', '13*e^4 - 123*e^2 + 234', '8*e^4 - 92*e^2 + 134', '8*e^4 - 92*e^2 + 134', '-11/2*e^5 + 101/2*e^3 - 96*e', '-11/2*e^5 + 101/2*e^3 - 96*e', 'e^4 - 23*e^2 + 54', 'e^4 - 23*e^2 + 54', '-49/2*e^5 + 214*e^3 - 591/2*e', '-49/2*e^5 + 214*e^3 - 591/2*e', '-7/2*e^4 + 65/2*e^2 + 6', '-7/2*e^4 + 65/2*e^2 + 6', '-3/2*e^5 + 18*e^3 - 165/2*e', '-3/2*e^5 + 18*e^3 - 165/2*e', '-8*e^5 + 74*e^3 - 102*e', '-8*e^5 + 74*e^3 - 102*e', '-17/2*e^4 + 119/2*e^2 - 10', '-17/2*e^4 + 119/2*e^2 - 10', '17*e^4 - 117*e^2 + 98', '17*e^4 - 117*e^2 + 98', '-11*e^5 + 94*e^3 - 107*e', '-11*e^5 + 94*e^3 - 107*e', '29/2*e^4 - 227/2*e^2 + 54', '29/2*e^4 - 227/2*e^2 + 54', '21/2*e^5 - 245/2*e^3 + 303*e', '21/2*e^5 - 245/2*e^3 + 303*e', '13/2*e^4 - 139/2*e^2 + 154', '13/2*e^4 - 139/2*e^2 + 154', '10*e^4 - 86*e^2 + 106', '10*e^4 - 86*e^2 + 106', '-23/2*e^5 + 82*e^3 - 37/2*e', '-23/2*e^5 + 82*e^3 - 37/2*e', '-15*e^4 + 97*e^2 - 30', '-15*e^4 + 97*e^2 - 30', '-36*e^2 + 114', '-36*e^2 + 114', '-13/2*e^5 + 135/2*e^3 - 106*e', '-13/2*e^5 + 135/2*e^3 - 106*e', '-9*e^4 + 47*e^2 + 70', '-9*e^4 + 47*e^2 + 70', '-9*e^4 + 91*e^2 - 52', '-9*e^4 + 91*e^2 - 52', '-29/2*e^5 + 130*e^3 - 459/2*e', '-29/2*e^5 + 130*e^3 - 459/2*e', '4*e^4 - 48*e^2 + 170', '4*e^4 - 48*e^2 + 170', '10*e^5 - 86*e^3 + 92*e', '10*e^5 - 86*e^3 + 92*e', '9/2*e^5 - 54*e^3 + 315/2*e', '9/2*e^5 - 54*e^3 + 315/2*e', '11/2*e^5 - 101/2*e^3 + 24*e', '11/2*e^5 - 101/2*e^3 + 24*e', '-13*e^4 + 121*e^2 - 164', '-13*e^4 + 121*e^2 - 164', '-13/2*e^5 + 40*e^3 + 21/2*e', '-13/2*e^5 + 40*e^3 + 21/2*e', '-1/2*e^5 + 19/2*e^3 - 14*e', '-1/2*e^5 + 19/2*e^3 - 14*e', '49/2*e^4 - 359/2*e^2 + 150', '49/2*e^4 - 359/2*e^2 + 150', '-11*e^4 + 75*e^2 - 54', '-11*e^4 + 75*e^2 - 54', '-e^4 + 37*e^2 - 60', '-e^4 + 37*e^2 - 60', '-6*e^5 + 67*e^3 - 183*e', '-6*e^5 + 67*e^3 - 183*e', '-23/2*e^5 + 219/2*e^3 - 191*e', '-23/2*e^5 + 219/2*e^3 - 191*e', '19/2*e^5 - 86*e^3 + 209/2*e', '19/2*e^5 - 86*e^3 + 209/2*e', '9*e^4 - 75*e^2 - 2', '9*e^4 - 75*e^2 - 2', '-21/2*e^5 + 114*e^3 - 443/2*e', '-21/2*e^5 + 114*e^3 - 443/2*e', '-9*e^4 + 75*e^2 - 82', '-9*e^4 + 75*e^2 - 82', '-11*e^4 + 113*e^2 - 226', '-11*e^4 + 113*e^2 - 226', '25/2*e^5 - 113*e^3 + 249/2*e', '25/2*e^5 - 113*e^3 + 249/2*e', 'e^4 + 21*e^2 - 110', 'e^4 + 21*e^2 - 110', '39/2*e^4 - 361/2*e^2 + 154', '39/2*e^4 - 361/2*e^2 + 154', '11*e^4 - 125*e^2 + 242', '11*e^4 - 125*e^2 + 242', '-16*e^4 + 134*e^2 - 128', '-16*e^4 + 134*e^2 - 128', '-33/2*e^5 + 293/2*e^3 - 189*e', '-33/2*e^5 + 293/2*e^3 - 189*e', '27/2*e^5 - 137*e^3 + 431/2*e', '27/2*e^5 - 137*e^3 + 431/2*e', '7*e^5 - 69*e^3 + 84*e', '7*e^5 - 69*e^3 + 84*e', '-2*e^4 + 38*e^2 - 138', '-2*e^4 + 38*e^2 - 138', '-28*e^4 + 238*e^2 - 296', '-28*e^4 + 238*e^2 - 296', '47/2*e^5 - 214*e^3 + 553/2*e', '47/2*e^5 - 214*e^3 + 553/2*e', '19/2*e^5 - 175/2*e^3 + 151*e', '19/2*e^5 - 175/2*e^3 + 151*e', '23*e^4 - 181*e^2 + 254', '23*e^4 - 181*e^2 + 254', '7*e^4 - 59*e^2 + 164', '7*e^4 - 59*e^2 + 164', '49/2*e^5 - 419/2*e^3 + 250*e', '49/2*e^5 - 419/2*e^3 + 250*e', '43/2*e^4 - 397/2*e^2 + 218', '43/2*e^4 - 397/2*e^2 + 218', '-37/2*e^5 + 176*e^3 - 591/2*e', '-37/2*e^5 + 176*e^3 - 591/2*e', '23/2*e^4 - 233/2*e^2 + 114', '23/2*e^4 - 233/2*e^2 + 114', '11/2*e^5 - 58*e^3 + 241/2*e', '11/2*e^5 - 58*e^3 + 241/2*e', '-6*e^4 + 76*e^2 - 164', '-6*e^4 + 76*e^2 - 164', '35/2*e^5 - 323/2*e^3 + 317*e', '35/2*e^5 - 323/2*e^3 + 317*e', '-5/2*e^5 + 16*e^3 + 37/2*e', '-5/2*e^5 + 16*e^3 + 37/2*e', '-1/2*e^5 + 47/2*e^3 - 132*e', '-1/2*e^5 + 47/2*e^3 - 132*e', '-7/2*e^5 + 59/2*e^3 - 27*e', '-7/2*e^5 + 59/2*e^3 - 27*e', '17*e^5 - 146*e^3 + 221*e', '17*e^5 - 146*e^3 + 221*e', '-11/2*e^5 + 58*e^3 - 261/2*e', '-11/2*e^5 + 58*e^3 - 261/2*e', '23*e^4 - 199*e^2 + 230', '23*e^4 - 199*e^2 + 230', '-22*e^4 + 150*e^2 - 54', '-22*e^4 + 150*e^2 - 54', '-33*e^5 + 305*e^3 - 414*e', '-33*e^5 + 305*e^3 - 414*e', '4*e^4 - 4*e^2 - 38', '4*e^4 - 4*e^2 - 38', '-18*e^4 + 168*e^2 - 192', '-18*e^4 + 168*e^2 - 192', '25*e^4 - 187*e^2 + 156', '25*e^4 - 187*e^2 + 156', '17*e^5 - 167*e^3 + 316*e', '17*e^5 - 167*e^3 + 316*e', '3*e^4 - 29*e^2 - 10', '3*e^4 - 29*e^2 - 10', '-39/2*e^4 + 369/2*e^2 - 222', '-39/2*e^4 + 369/2*e^2 - 222', '-30*e^5 + 260*e^3 - 362*e', '-30*e^5 + 260*e^3 - 362*e', '-33/2*e^5 + 138*e^3 - 199/2*e', '-33/2*e^5 + 138*e^3 - 199/2*e', '5*e^4 - 53*e^2 + 142', '5*e^4 - 53*e^2 + 142', '11*e^4 - 121*e^2 + 130', '11*e^4 - 121*e^2 + 130', '3*e^5 - 30*e^3 - 9*e', '3*e^5 - 30*e^3 - 9*e', '-31/2*e^5 + 283/2*e^3 - 175*e', '-31/2*e^5 + 283/2*e^3 - 175*e', '3*e^4 - 21*e^2 + 114', '3*e^4 - 21*e^2 + 114', '14*e^4 - 146*e^2 + 210', '14*e^4 - 146*e^2 + 210', '21/2*e^5 - 114*e^3 + 511/2*e', '21/2*e^5 - 114*e^3 + 511/2*e', '21/2*e^5 - 113*e^3 + 501/2*e', '21/2*e^5 - 113*e^3 + 501/2*e', '-12*e^5 + 126*e^3 - 266*e', '-12*e^5 + 126*e^3 - 266*e', '-59/2*e^4 + 485/2*e^2 - 266', '-59/2*e^4 + 485/2*e^2 - 266', '21/2*e^5 - 107*e^3 + 441/2*e', '21/2*e^5 - 107*e^3 + 441/2*e', '-9*e^4 + 61*e^2 - 20', '-9*e^4 + 61*e^2 - 20', '-5/2*e^4 + 27/2*e^2 - 70', '-5/2*e^4 + 27/2*e^2 - 70'], 'hecke_polynomial': 'x^6 - 10*x^4 + 21*x^2 - 8', 'label': '2.2.12.1-49.1-a'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 12, 'ideals': ['[1, 1, 1]', '[2, 2, -w + 1]', '[3, 3, w]', '[4, 2, 2]', '[6, 6, w - 3]', '[8, 4, -2*w + 2]', '[9, 3, 3]', '[11, 11, -2*w + 1]', '[11, 11, 2*w + 1]', '[12, 6, 2*w]', '[13, 13, w + 4]', '[13, 13, -w + 4]', '[16, 4, 4]', '[18, 6, -3*w + 3]', '[22, 22, w + 5]', '[22, 22, w - 5]', '[23, 23, -3*w + 2]', '[23, 23, 3*w + 2]', '[24, 12, 2*w - 6]', '[25, 5, 5]', '[26, 26, -3*w - 1]', '[26, 26, -3*w + 1]', '[27, 9, 3*w]', '[32, 8, -4*w + 4]', '[33, 33, w + 6]', '[33, 33, w - 6]', '[36, 6, 6]', '[37, 37, 2*w - 7]', '[37, 37, -2*w - 7]', '[39, 39, 4*w - 3]', '[39, 39, 4*w + 3]', '[44, 22, -4*w + 2]', '[44, 22, 4*w + 2]', '[46, 46, w + 7]', '[46, 46, w - 7]', '[47, 47, -4*w - 1]', '[47, 47, 4*w - 1]', '[48, 12, 4*w]', '[49, 7, -7]', '[50, 10, -5*w + 5]', '[52, 26, 2*w + 8]', '[52, 26, -2*w + 8]', '[54, 18, 3*w - 9]', '[59, 59, 5*w - 4]', '[59, 59, -5*w - 4]', '[61, 61, -w - 8]', '[61, 61, w - 8]', '[64, 8, 8]', '[66, 66, 5*w + 3]', '[66, 66, -5*w + 3]', '[69, 69, 2*w - 9]', '[69, 69, 2*w + 9]', '[71, 71, 5*w - 2]', '[71, 71, -5*w - 2]', '[72, 12, -6*w + 6]', '[73, 73, 3*w - 10]', '[73, 73, -3*w - 10]', '[74, 74, 9*w - 13]', '[74, 74, 5*w - 1]', '[75, 15, 5*w]', '[78, 78, -w - 9]', '[78, 78, w - 9]', '[81, 9, 9]', '[83, 83, 6*w - 5]', '[83, 83, -6*w - 5]', '[88, 44, 2*w + 10]', '[88, 44, 2*w - 10]', '[92, 46, -6*w + 4]', '[92, 46, 6*w + 4]', '[94, 94, 5*w - 13]', '[94, 94, -3*w + 11]', '[96, 24, 4*w - 12]', '[97, 97, -w - 10]', '[97, 97, w - 10]', '[98, 14, 7*w - 7]', '[99, 33, -6*w + 3]', '[99, 33, 6*w + 3]', '[100, 10, 10]', '[104, 52, -6*w - 2]', '[104, 52, -6*w + 2]', '[107, 107, -6*w - 1]', '[107, 107, 6*w - 1]', '[108, 18, 6*w]', '[109, 109, 2*w - 11]', '[109, 109, -2*w - 11]', '[111, 111, -7*w + 6]', '[111, 111, -7*w - 6]', '[117, 39, 3*w + 12]', '[117, 39, -3*w + 12]', '[118, 118, 9*w - 19]', '[118, 118, -w + 11]', '[121, 11, 11]', '[121, 121, -4*w + 13]', '[121, 121, 4*w + 13]', '[122, 122, 9*w - 11]', '[122, 122, 7*w - 5]', '[128, 16, -8*w + 8]', '[131, 131, -7*w - 4]', '[131, 131, 7*w - 4]', '[132, 66, 2*w + 12]', '[132, 66, 2*w - 12]', '[138, 138, -7*w + 3]', '[138, 138, 7*w + 3]', '[141, 141, -w - 12]', '[141, 141, -w + 12]', '[142, 142, -3*w + 13]', '[142, 142, 7*w - 17]', '[143, 143, 8*w - 7]', '[143, 143, 7*w - 2]', '[143, 143, -7*w - 2]', '[143, 143, -8*w - 7]', '[144, 12, 12]', '[146, 146, 13*w - 19]', '[146, 146, 7*w - 1]', '[147, 21, -7*w]', '[148, 74, 4*w - 14]', '[148, 74, -4*w - 14]', '[150, 30, 5*w - 15]', '[156, 78, 8*w - 6]', '[156, 78, 8*w + 6]', '[157, 157, 2*w - 13]', '[157, 157, -2*w - 13]', '[162, 18, -9*w + 9]', '[166, 166, 11*w - 23]', '[166, 166, -w + 13]', '[167, 167, 8*w - 5]', '[167, 167, -8*w - 5]', '[169, 13, 13]', '[169, 169, 3*w + 14]', '[169, 169, -3*w + 14]', '[176, 44, -8*w + 4]', '[176, 44, 8*w + 4]', '[177, 177, -4*w - 15]', '[177, 177, -4*w + 15]', '[179, 179, 9*w - 8]', '[179, 179, -9*w - 8]', '[181, 181, 5*w - 16]', '[181, 181, -5*w - 16]', '[183, 183, -8*w - 3]', '[183, 183, -8*w + 3]', '[184, 92, 2*w + 14]', '[184, 92, 2*w - 14]', '[188, 94, -8*w - 2]', '[188, 94, 8*w - 2]', '[191, 191, -8*w - 1]', '[191, 191, 8*w - 1]', '[192, 24, 8*w]', '[193, 193, -w - 14]', '[193, 193, w - 14]', '[194, 194, 11*w - 13]', '[194, 194, 9*w - 7]', '[196, 14, -14]', '[198, 66, 3*w + 15]', '[198, 66, 3*w - 15]', '[200, 20, -10*w + 10]', '[207, 69, -9*w + 6]', '[207, 69, 9*w + 6]', '[208, 52, 4*w + 16]', '[208, 52, -4*w + 16]', '[213, 213, -2*w + 15]', '[213, 213, -2*w - 15]', '[214, 214, 7*w - 19]', '[214, 214, -5*w + 17]', '[216, 36, 6*w - 18]', '[218, 218, 13*w - 17]', '[218, 218, 9*w - 5]', '[219, 219, -10*w + 9]', '[219, 219, -10*w - 9]', '[222, 222, -13*w + 27]', '[222, 222, -w + 15]', '[225, 15, 15]', '[227, 227, 9*w - 4]', '[227, 227, -9*w - 4]', '[229, 229, 3*w - 16]', '[229, 229, -3*w - 16]', '[234, 78, -9*w - 3]', '[234, 78, -9*w + 3]', '[236, 118, 10*w - 8]', '[236, 118, -10*w - 8]', '[239, 239, 9*w - 2]', '[239, 239, -9*w - 2]', '[241, 241, 4*w - 17]', '[241, 241, -4*w - 17]', '[242, 22, 11*w - 11]', '[242, 242, -9*w - 1]', '[242, 242, -9*w + 1]', '[243, 27, 9*w]', '[244, 122, -2*w - 16]', '[244, 122, 2*w - 16]', '[249, 249, -5*w + 18]', '[249, 249, -5*w - 18]', '[251, 251, -10*w - 7]', '[251, 251, 10*w - 7]', '[253, 253, -w - 16]', '[253, 253, -6*w + 19]', '[253, 253, 6*w + 19]', '[253, 253, w - 16]', '[256, 16, 16]', '[262, 262, 11*w - 25]', '[262, 262, -3*w + 17]', '[263, 263, 11*w - 10]', '[263, 263, -11*w - 10]', '[264, 132, 10*w + 6]', '[264, 132, -10*w + 6]', '[275, 55, -10*w + 5]', '[275, 55, 10*w + 5]', '[276, 138, 4*w - 18]', '[276, 138, 4*w + 18]', '[277, 277, 2*w - 17]', '[277, 277, -2*w - 17]', '[282, 282, -13*w + 15]', '[282, 282, 11*w - 9]', '[284, 142, 10*w - 4]', '[284, 142, -10*w - 4]', '[286, 286, -w - 17]', '[286, 286, -5*w - 19]', '[286, 286, -5*w + 19]', '[286, 286, -w + 17]', '[288, 24, -12*w + 12]', '[289, 17, -17]', '[291, 291, -10*w + 3]', '[291, 291, -10*w - 3]', '[292, 146, 6*w - 20]', '[292, 146, -6*w - 20]', '[294, 42, -7*w + 21]', '[296, 148, 18*w - 26]', '[296, 148, 10*w - 2]', '[297, 99, 3*w + 18]', '[297, 99, 3*w - 18]', '[299, 299, -10*w - 1]', '[299, 299, 11*w - 8]', '[299, 299, -11*w - 8]', '[299, 299, 10*w - 1]', '[300, 30, 10*w]', '[311, 311, 12*w - 11]', '[311, 311, -12*w - 11]', '[312, 156, -2*w - 18]', '[312, 156, 2*w - 18]', '[313, 313, -4*w - 19]', '[313, 313, 4*w - 19]', '[314, 314, 11*w - 7]', '[314, 314, 15*w - 19]', '[321, 321, -w - 18]', '[321, 321, -w + 18]', '[324, 18, 18]', '[325, 65, 5*w + 20]', '[325, 65, -5*w + 20]', '[327, 327, -11*w - 6]', '[327, 327, -11*w + 6]', '[332, 166, 12*w - 10]', '[332, 166, -12*w - 10]', '[333, 111, 6*w - 21]', '[333, 111, -6*w - 21]', '[334, 334, -3*w + 19]', '[334, 334, 13*w - 29]', '[337, 337, 7*w - 22]', '[337, 337, -7*w - 22]', '[338, 26, -13*w + 13]', '[338, 338, -11*w + 5]', '[338, 338, -11*w - 5]', '[347, 347, -11*w - 4]', '[347, 347, 11*w - 4]', '[349, 349, 2*w - 19]', '[349, 349, -2*w - 19]', '[351, 117, 12*w - 9]', '[351, 117, 12*w + 9]', '[352, 88, 4*w + 20]', '[352, 88, 4*w - 20]', '[354, 354, -19*w + 27]', '[354, 354, 11*w - 3]', '[358, 358, 17*w - 35]', '[358, 358, -w + 19]', '[359, 359, 11*w - 2]', '[359, 359, -11*w - 2]', '[361, 19, -19]', '[362, 362, 21*w - 31]', '[362, 362, 11*w - 1]', '[363, 33, -11*w]', '[363, 363, 13*w - 12]', '[363, 363, 13*w + 12]', '[366, 366, -5*w + 21]', '[366, 366, -11*w + 27]', '[368, 92, -12*w + 8]', '[368, 92, 12*w + 8]', '[373, 373, -3*w - 20]', '[373, 373, 3*w - 20]', '[376, 188, 10*w - 26]', '[376, 188, -6*w + 22]', '[382, 382, 9*w - 25]', '[382, 382, -7*w + 23]', '[383, 383, 12*w - 7]', '[383, 383, -12*w - 7]', '[384, 48, 8*w - 24]', '[386, 386, 15*w - 17]', '[386, 386, 13*w - 11]', '[388, 194, -2*w - 20]', '[388, 194, 2*w - 20]', '[392, 28, 14*w - 14]', '[393, 393, -4*w + 21]', '[393, 393, -4*w - 21]', '[396, 66, -12*w + 6]', '[396, 66, 12*w + 6]', '[397, 397, -w - 20]', '[397, 397, w - 20]', '[400, 20, 20]', '[407, 407, 16*w - 19]', '[407, 407, 12*w + 5]', '[407, 407, -12*w + 5]', '[407, 407, -16*w - 19]', '[409, 409, -5*w - 22]', '[409, 409, 5*w - 22]', '[414, 138, 3*w + 21]', '[414, 138, 3*w - 21]', '[416, 104, -12*w - 4]', '[416, 104, -12*w + 4]', '[419, 419, 14*w - 13]', '[419, 419, -14*w - 13]', '[421, 421, -6*w - 23]', '[421, 421, 6*w - 23]', '[423, 141, -12*w - 3]', '[423, 141, 12*w - 3]', '[426, 426, -17*w + 21]', '[426, 426, 13*w - 9]', '[428, 214, -12*w - 2]', '[428, 214, 12*w - 2]', '[429, 429, -7*w - 24]', '[429, 429, -2*w + 21]', '[429, 429, -2*w - 21]', '[429, 429, -7*w + 24]', '[431, 431, -12*w - 1]', '[431, 431, 12*w - 1]', '[432, 36, 12*w]', '[433, 433, -9*w - 26]', '[433, 433, 9*w - 26]', '[436, 218, 4*w - 22]', '[436, 218, -4*w - 22]', '[438, 438, -19*w + 39]', '[438, 438, -w + 21]', '[441, 21, -21]', '[443, 443, -13*w - 8]', '[443, 443, 13*w - 8]', '[444, 222, -14*w + 12]', '[444, 222, -14*w - 12]', '[450, 30, -15*w + 15]', '[454, 454, -5*w + 23]', '[454, 454, 13*w - 31]', '[457, 457, 3*w - 22]', '[457, 457, -3*w - 22]', '[458, 458, 19*w - 25]', '[458, 458, 13*w - 7]', '[467, 467, 14*w - 11]', '[467, 467, -14*w - 11]', '[468, 78, 6*w + 24]', '[468, 78, -6*w + 24]', '[471, 471, -13*w + 6]', '[471, 471, -13*w - 6]', '[472, 236, 18*w - 38]', '[472, 236, -2*w + 22]', '[478, 478, -7*w + 25]', '[478, 478, 11*w - 29]', '[479, 479, 15*w - 14]', '[479, 479, -15*w - 14]', '[481, 481, -w - 22]', '[481, 481, 15*w - 34]', '[481, 481, -15*w - 34]', '[481, 481, w - 22]', '[482, 482, 13*w - 5]', '[482, 482, 21*w - 29]', '[484, 22, 22]', '[484, 242, -8*w + 26]', '[484, 242, 8*w + 26]', '[486, 54, 9*w - 27]', '[488, 244, 18*w - 22]', '[488, 244, 14*w - 10]', '[491, 491, 13*w - 4]', '[491, 491, -13*w - 4]', '[498, 498, 13*w - 3]', '[498, 498, -23*w + 33]', '[501, 501, -5*w - 24]', '[501, 501, -5*w + 24]', '[502, 502, 17*w - 37]', '[502, 502, -3*w + 23]', '[503, 503, 13*w - 2]', '[503, 503, -13*w - 2]', '[506, 506, -13*w - 1]', '[506, 506, 15*w + 13]', '[506, 506, 15*w - 13]', '[506, 506, -13*w + 1]', '[507, 39, 13*w]', '[507, 507, 14*w - 9]', '[507, 507, 14*w + 9]', '[512, 32, -16*w + 16]', '[517, 517, 6*w - 25]', '[517, 517, -2*w + 23]', '[517, 517, 2*w + 23]', '[517, 517, -6*w - 25]', '[524, 262, -14*w - 8]', '[524, 262, 14*w - 8]', '[526, 526, 21*w - 43]', '[526, 526, -w + 23]', '[528, 132, 4*w + 24]', '[528, 132, 4*w - 24]', '[529, 23, 23]', '[529, 529, -7*w + 26]', '[529, 529, 7*w + 26]', '[531, 177, 15*w - 12]', '[531, 177, -15*w - 12]', '[537, 537, -8*w + 27]', '[537, 537, -8*w - 27]', '[539, 77, 14*w - 7]', '[539, 77, -14*w - 7]', '[541, 541, 9*w - 28]', '[541, 541, -9*w - 28]', '[543, 543, -16*w + 15]', '[543, 543, -16*w - 15]', '[549, 183, -3*w - 24]', '[549, 183, 3*w - 24]', '[550, 110, 5*w + 25]', '[550, 110, 5*w - 25]', '[552, 276, -14*w + 6]', '[552, 276, 14*w + 6]', '[554, 554, 15*w - 11]', '[554, 554, 19*w - 23]', '[563, 563, -14*w - 5]', '[563, 563, 14*w - 5]', '[564, 282, -2*w - 24]', '[564, 282, -2*w + 24]', '[568, 284, -6*w + 26]', '[568, 284, 14*w - 34]', '[572, 286, 16*w - 14]', '[572, 286, 14*w - 4]', '[572, 286, -14*w - 4]', '[572, 286, -16*w - 14]', '[573, 573, -w - 24]', '[573, 573, -w + 24]', '[575, 115, -15*w + 10]', '[575, 115, 15*w + 10]', '[576, 24, 24]', '[577, 577, 4*w - 25]', '[577, 577, -4*w - 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95]', '[7583, 7583, 52*w - 23]', '[7583, 7583, -52*w - 23]', '[7607, 7607, -51*w - 14]', '[7607, 7607, 51*w - 14]', '[7621, 7621, -10*w - 89]', '[7621, 7621, 10*w - 89]', '[7643, 7643, 53*w - 28]', '[7643, 7643, -53*w - 28]', '[7669, 7669, 5*w - 88]', '[7669, 7669, -5*w - 88]', '[7681, 7681, 24*w - 97]', '[7681, 7681, -24*w - 97]', '[7691, 7691, 58*w - 49]', '[7691, 7691, -58*w - 49]', '[7703, 7703, 51*w - 10]', '[7703, 7703, -51*w - 10]', '[7717, 7717, 3*w - 88]', '[7717, 7717, -3*w - 88]', '[7727, 7727, 56*w - 41]', '[7727, 7727, -56*w - 41]', '[7741, 7741, -w - 88]', '[7741, 7741, w - 88]', '[7753, 7753, -19*w - 94]', '[7753, 7753, 19*w - 94]', '[7789, 7789, -15*w - 92]', '[7789, 7789, 15*w - 92]', '[7823, 7823, 52*w - 17]', '[7823, 7823, -52*w - 17]', '[7873, 7873, 4*w - 89]', '[7873, 7873, -4*w - 89]', '[7883, 7883, -58*w - 47]', '[7883, 7883, 58*w - 47]', '[7907, 7907, 54*w - 29]', '[7907, 7907, -54*w - 29]', '[7919, 7919, 55*w - 34]', '[7919, 7919, -55*w - 34]', '[7921, 89, -89]', '[7933, 7933, -31*w - 104]', '[7933, 7933, 31*w - 104]', '[7993, 7993, 36*w - 109]', '[7993, 7993, -36*w - 109]', '[8017, 8017, 23*w - 98]', '[8017, 8017, -23*w - 98]', '[8039, 8039, 56*w - 37]', '[8039, 8039, -56*w - 37]', '[8053, 8053, -18*w - 95]', '[8053, 8053, 18*w - 95]', '[8087, 8087, -52*w - 5]', '[8087, 8087, 52*w - 5]', '[8089, 8089, 8*w - 91]', '[8089, 8089, -8*w - 91]', '[8101, 8101, 11*w - 92]', '[8101, 8101, -11*w - 92]', '[8111, 8111, -52*w - 1]', '[8111, 8111, 52*w - 1]', '[8123, 8123, -54*w - 25]', '[8123, 8123, 54*w - 25]', '[8147, 8147, -57*w - 40]', '[8147, 8147, 57*w - 40]', '[8161, 8161, 15*w - 94]', '[8161, 8161, -15*w - 94]', '[8171, 8171, -53*w - 16]', '[8171, 8171, 53*w - 16]', '[8209, 8209, -20*w - 97]', '[8209, 8209, 20*w - 97]', '[8219, 8219, 54*w - 23]', '[8219, 8219, -54*w - 23]', '[8221, 8221, -9*w - 92]', '[8221, 8221, 9*w - 92]', '[8231, 8231, -53*w - 14]', '[8231, 8231, 53*w - 14]', '[8233, 8233, -4*w - 91]', '[8233, 8233, 4*w - 91]', '[8243, 8243, -58*w - 43]', '[8243, 8243, 58*w - 43]', '[8269, 8269, 2*w - 91]', '[8269, 8269, -2*w - 91]', '[8291, 8291, -55*w - 28]', '[8291, 8291, 55*w - 28]', '[8293, 8293, 29*w - 104]', '[8293, 8293, -29*w - 104]', '[8317, 8317, 7*w - 92]', '[8317, 8317, -7*w - 92]', '[8329, 8329, -13*w - 94]', '[8329, 8329, 13*w - 94]', '[8353, 8353, 31*w - 106]', '[8353, 8353, -31*w - 106]', '[8363, 8363, -53*w - 8]', '[8363, 8363, 53*w - 8]', '[8377, 8377, 32*w - 107]', '[8377, 8377, -32*w - 107]', '[8387, 8387, 54*w - 19]', '[8387, 8387, -54*w - 19]', '[8389, 8389, -5*w - 92]', '[8389, 8389, 5*w - 92]', '[8423, 8423, 53*w - 2]', '[8423, 8423, -53*w - 2]', '[8447, 8447, 56*w - 31]', '[8447, 8447, -56*w - 31]', '[8461, 8461, -w - 92]', '[8461, 8461, w - 92]', '[8521, 8521, -19*w - 98]', '[8521, 8521, 19*w - 98]', '[8543, 8543, -63*w - 58]', '[8543, 8543, 63*w - 58]', '[8581, 8581, -26*w - 103]', '[8581, 8581, 26*w - 103]', '[8627, 8627, -54*w - 11]', '[8627, 8627, 54*w - 11]', '[8629, 8629, -27*w - 104]', '[8629, 8629, 27*w - 104]', '[8641, 8641, 16*w - 97]', '[8641, 8641, -16*w - 97]', '[8663, 8663, -61*w - 50]', '[8663, 8663, 61*w - 50]', '[8677, 8677, 21*w - 100]', '[8677, 8677, -21*w - 100]', '[8689, 8689, -7*w - 94]', '[8689, 8689, 7*w - 94]', '[8699, 8699, 54*w - 7]', '[8699, 8699, -54*w - 7]', '[8713, 8713, -29*w - 106]', '[8713, 8713, 29*w - 106]', '[8737, 8737, 17*w - 98]', '[8737, 8737, -17*w - 98]', '[8747, 8747, -54*w - 1]', '[8747, 8747, 54*w - 1]', '[8761, 8761, -5*w - 94]', '[8761, 8761, 5*w - 94]', '[8783, 8783, -56*w - 25]', '[8783, 8783, 56*w - 25]', '[8807, 8807, 64*w - 59]', '[8807, 8807, -64*w - 59]', '[8819, 8819, 55*w - 16]', '[8819, 8819, -55*w - 16]', '[8821, 8821, -14*w - 97]', '[8821, 8821, 14*w - 97]', '[8831, 8831, 65*w - 62]', '[8831, 8831, -65*w - 62]', '[8867, 8867, -58*w - 35]', '[8867, 8867, 58*w - 35]', '[8893, 8893, 38*w - 115]', '[8893, 8893, -38*w - 115]', '[8929, 8929, 15*w - 98]', '[8929, 8929, -15*w - 98]', '[8941, 8941, -25*w - 104]', '[8941, 8941, 25*w - 104]', '[8951, 8951, -60*w - 43]', '[8951, 8951, 60*w - 43]', '[8963, 8963, 57*w - 28]', '[8963, 8963, -57*w - 28]', '[8999, 8999, -59*w - 38]', '[8999, 8999, 59*w - 38]', '[9001, 9001, 20*w - 101]', '[9001, 9001, -20*w - 101]', '[9011, 9011, -55*w - 8]', '[9011, 9011, 55*w - 8]', '[9013, 9013, 2*w - 95]', '[9013, 9013, -2*w - 95]', '[9049, 9049, 27*w - 106]', '[9049, 9049, -27*w - 106]', '[9059, 9059, -55*w - 4]', '[9059, 9059, 55*w - 4]', '[9109, 9109, 10*w - 97]', '[9109, 9109, -10*w - 97]', '[9133, 9133, 17*w - 100]', '[9133, 9133, -17*w - 100]', '[9157, 9157, 22*w - 103]', '[9157, 9157, -22*w - 103]', '[9181, 9181, -30*w - 109]', '[9181, 9181, 30*w - 109]', '[9203, 9203, 63*w - 52]', '[9203, 9203, -63*w - 52]', '[9227, 9227, 61*w - 44]', '[9227, 9227, -61*w - 44]', '[9239, 9239, -56*w - 13]', '[9239, 9239, 56*w - 13]', '[9241, 9241, -11*w - 98]', '[9241, 9241, 11*w - 98]', '[9277, 9277, -33*w - 112]', '[9277, 9277, 33*w - 112]', '[9311, 9311, 65*w - 58]', '[9311, 9311, -65*w - 58]', '[9323, 9323, 62*w - 47]', '[9323, 9323, -62*w - 47]', '[9337, 9337, -36*w - 115]', '[9337, 9337, 36*w - 115]', '[9349, 9349, 37*w - 116]', '[9349, 9349, -37*w - 116]', '[9371, 9371, -67*w - 64]', '[9371, 9371, 67*w - 64]', '[9397, 9397, 2*w - 97]', '[9397, 9397, -2*w - 97]', '[9419, 9419, -59*w - 32]', '[9419, 9419, 59*w - 32]', '[9421, 9421, 26*w - 107]', '[9421, 9421, -26*w - 107]', '[9431, 9431, -60*w - 37]', '[9431, 9431, 60*w - 37]', '[9433, 9433, -16*w - 101]', '[9433, 9433, 16*w - 101]', '[9467, 9467, -58*w - 25]', '[9467, 9467, 58*w - 25]', '[9479, 9479, -64*w - 53]', '[9479, 9479, 64*w - 53]', '[9491, 9491, -57*w - 16]', '[9491, 9491, 57*w - 16]', '[9539, 9539, 65*w - 56]', '[9539, 9539, -65*w - 56]', '[9551, 9551, 57*w - 14]', '[9551, 9551, -57*w - 14]', '[9587, 9587, 66*w - 59]', '[9587, 9587, -66*w - 59]', '[9601, 9601, -w - 98]', '[9601, 9601, w - 98]', '[9613, 9613, 14*w - 101]', '[9613, 9613, -14*w - 101]', '[9623, 9623, 67*w - 62]', '[9623, 9623, -67*w - 62]', '[9649, 9649, 23*w - 106]', '[9649, 9649, -23*w - 106]', '[9661, 9661, -31*w - 112]', '[9661, 9661, 31*w - 112]', '[9697, 9697, -32*w - 113]', '[9697, 9697, 32*w - 113]', '[9719, 9719, 61*w - 38]', '[9719, 9719, -61*w - 38]', '[9721, 9721, 24*w - 107]', '[9721, 9721, -24*w - 107]', '[9733, 9733, -19*w - 104]', '[9733, 9733, 19*w - 104]', '[9743, 9743, 57*w - 2]', '[9743, 9743, -57*w - 2]', '[9767, 9767, -59*w - 26]', '[9767, 9767, 59*w - 26]', '[9769, 9769, 12*w - 101]', '[9769, 9769, -12*w - 101]', '[9781, 9781, 35*w - 116]', '[9781, 9781, -35*w - 116]', '[9791, 9791, 63*w - 46]', '[9791, 9791, -63*w - 46]', '[9803, 9803, 58*w - 17]', '[9803, 9803, -58*w - 17]', '[9817, 9817, 37*w - 118]', '[9817, 9817, -37*w - 118]', '[9829, 9829, -38*w - 119]', '[9829, 9829, 38*w - 119]', '[9839, 9839, 60*w - 31]', '[9839, 9839, -60*w - 31]', '[9851, 9851, 62*w - 41]', '[9851, 9851, -62*w - 41]', '[9887, 9887, -64*w - 49]', '[9887, 9887, 64*w - 49]', '[9901, 9901, 10*w - 101]', '[9901, 9901, -10*w - 101]', '[9923, 9923, -58*w - 13]', '[9923, 9923, 58*w - 13]', '[9949, 9949, -17*w - 104]', '[9949, 9949, 17*w - 104]', '[9973, 9973, 3*w - 100]', '[9973, 9973, -3*w - 100]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-3, 0, 1], 'conductor': 12, 'degree': 2, 'dirichlet_group': [1, 11], 'disc_abs': 12, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [[2, 1]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 3.4641016151377544, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.12.1', 'local_algs': ['2.2.2.2', '3.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 3], 'rd': 3.46410161514, 'regulator': {'__RealLiteral__': 0, 'data': '1.31695789692', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a']}