Hilbert modular form data - 4.4.11197.1-19.1-e

Formats: - HTML - YAML - JSON - 2024-04-30T21:08:43.996523

• 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': 3, 'disc': 11197, 'field_bad_primes': [11197], 'field_label': '4.4.11197.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.11197.1-19.1-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [19], 'level_ideal': '[19, 19, -w^3 + 2*w^2 + 4*w - 1]', 'level_label': '19.1', 'level_norm': 19, 'parallel_weight': 2, 'short_label': '19.1-e', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[19, 19, -w^3 + 2*w^2 + 4*w - 1]', 1]], 'hecke_eigenvalues': ['e', 'e^2 - 2*e - 4', 'e^2 - 4', '-e^2 + 2*e + 5', '-e + 3', 'e^2 - 6', -1, 'e^2 + 3*e - 7', 'e^2 - e - 3', '2*e^2 - 2*e - 5', 'e^2 - 4', '-3*e^2 + e + 8', '-2*e^2 + 3*e + 8', '4*e^2 - 2*e - 8', '-5*e^2 + 4*e + 11', '3*e^2 - 8', '-e^2 - 3*e + 2', 0, '-e^2 + 10', '2*e^2 + 2*e - 3', '4*e^2 - 2*e - 9', '4*e^2 - 4*e - 2', '3*e^2 - 6*e - 17', '2*e^2 - 7', '-4*e^2 + 3*e + 18', '-5*e^2 + e + 22', '-2*e - 10', '-2*e^2 - 3', '2*e^2 - 5*e', '4*e^2 - 6*e - 9', '3*e^2 - 3*e + 1', '-6*e^2 + 3*e + 14', '-2*e + 20', '2*e^2 + e - 12', '5*e^2 - 3*e + 1', '2*e^2 - 6*e - 7', '3*e^2 + 10*e - 18', '-3*e^2 + 7*e + 25', '-e^2 + e + 13', '2*e^2 - 7*e - 18', '6*e^2 - 17*e - 17', '-5*e^2 + 16*e + 18', '-3*e + 12', '-e^2 - 3*e + 5', 'e^2 + 2*e + 5', '-7*e^2 + 6*e + 28', '3*e^2 - 6', '-e^2 - 5*e - 3', '3*e^2 - 2*e - 16', '-3*e^2 + 7*e + 8', '-5*e^2 - 2*e + 25', '-2*e^2 - 7*e + 9', '8*e^2 - 10*e - 20', '9*e + 2', '-6*e - 8', '7*e^2 - 5*e - 9', '-4*e^2 - e + 18', '5*e^2 - 2*e + 6', '5*e^2 - 14*e - 11', '3*e^2 + 2', '2*e^2 - e + 19', '-2*e^2 - 5*e + 20', '-e^2 + 6*e - 5', '-3*e^2 + 9*e + 24', '4*e^2 + 6*e - 23', '-10*e^2 + 10*e + 10', 'e^2 - 6*e - 7', '-6*e^2 + 3*e + 27', '-2*e^2 - 9*e + 14', '-10*e^2 + 16*e + 32', '-7*e^2 + 6*e', '2*e^2 + 6*e - 12', '-6*e^2 - 5*e + 16', '-e^2 - e + 31', '-2*e^2 + 4*e + 8', '5*e^2 + 2*e - 8', '-4*e^2 - 6*e + 36', '-7*e^2 + 28', '8*e^2 - 18*e - 32', '-7*e^2 + 8*e + 40', '-6*e^2 + 13*e + 20', '4*e^2 + e - 22', '9*e^2 - 24*e - 30', '-3*e^2 - 10*e + 22', '4*e^2 + 4*e - 36', '4*e^2 - 5*e - 16', '-4*e^2 - 6*e + 16', '-4*e^2 + 11*e + 12', '-4*e^2 - 11*e + 11', '-11*e^2 + 16*e + 28', '-7*e^2 + 11*e + 6', '-e^2 + e + 2', '7*e^2 + 9*e - 34', '-3*e^2 - 2*e + 7', '-3*e^2 - 4*e + 15', '3*e^2 + 3*e - 20', 'e^2 - e + 17', '-2*e^2 - 13*e + 6', '-3*e^2 + 5*e + 31', '-11*e^2 + 26', '-5*e^2 - 11*e + 19', '5*e^2 - 4*e + 7', '15*e^2 - 15*e - 25', '-3*e^2 + 4*e + 18', '7*e^2 + e - 28', '2*e^2 + 3*e + 1', '4*e^2 - 6*e - 25', '3*e^2 - 4*e + 1', '8*e^2 - 9*e - 5', '17*e^2 - 12*e - 35', '5*e^2 - 9*e - 1', '-6*e^2 + 11*e + 5', '11*e + 7', '5*e^2 - 20*e - 15', '-11*e^2 + 5*e + 7', '6*e^2 - 13*e - 32', '8*e^2 - 4*e - 1', '-8*e^2 + 9*e + 34', '-e^2 - 18*e + 11', '-4*e^2 + 16', '-7*e^2 + 8*e + 44', '3*e^2 - 16*e - 2', '18*e^2 - 15*e - 42', '-9*e^2 + 15*e + 27', '-5*e^2 + 7*e + 19', '-12*e^2 + 5*e + 25', '5*e^2 - 12*e - 33', '-6*e^2 + 3*e + 30', '-3*e^2 + 8*e + 3', 'e^2 - 5*e + 14', '-17*e^2 + 10*e + 48', '-8*e^2 + e + 18', 'e^2 + 8*e - 29', '3*e^2 - 2*e - 43', '13*e^2 - 13*e - 30', '-2*e^2 + 5*e - 21', '-12*e^2 + 3*e + 26', '9*e^2 - 25*e - 20', '5*e^2 - 10*e - 22', '-4*e^2 + 20*e + 20', 'e^2 + 21*e - 4', '-6*e^2 + 2*e + 20', '8*e^2 - 9*e - 41', '9*e^2 - 14*e - 46', '6*e^2 - 7*e - 26', '8*e^2 - 20*e - 52', '15*e^2 - 8*e - 27', '4*e^2 - 6*e - 28', '3*e^2 - 20*e - 19', '-2*e^2 - e - 8', '-15*e^2 + 17*e + 25', '12*e^2 - 12*e - 51', '-9*e^2 - 6*e + 55', '-7*e^2 + 6*e + 37', '-10*e^2 + 9*e + 34', '5*e^2 + 13*e - 37', '-6*e^2 + e - 3', '-11*e^2 + 7*e + 20', '2*e^2 + 16*e - 22', '11*e^2 - 14*e - 27', '8*e^2 - 26*e - 25', '-15*e^2 + 26*e + 49', '9*e^2 - 3*e + 9', '14*e^2 - 4*e - 21', '-3*e^2 + 12*e + 42', '7*e^2 - 23*e - 12', '-12*e^2 + 15*e + 47', '-5*e^2 + 25*e + 31', '-7*e^2 + 2*e - 4', '-5*e^2 - 9*e + 41', '10*e^2 - 12*e - 1', '5*e^2 + 17*e - 21', '15*e^2 + 2*e - 40', '-e^2 - 16', '24*e^2 - 12*e - 54', '-15*e^2 - 4*e + 51', '3*e^2 - 7*e + 27', '-15*e^2 + 9*e + 54', '-8*e^2 + 8*e + 15', '6*e^2 + 15*e - 29', 'e^2 - 5*e - 7', '-8*e^2 + 12*e + 8', '-2*e^2 + 4*e + 32', '-16*e^2 + 11*e + 14', '-10*e^2 + 25*e + 12', '-15*e^2 + 4*e + 51', '5*e^2 + 2*e + 15', '-13*e^2 + 5*e + 36', '12*e^2 + 8*e - 44', '6*e + 33', '-5*e^2 - 17*e + 49', '4*e^2 - 14*e + 7', 'e^2 - 10*e - 27', '6*e^2 + 4*e - 19', '2*e^2 - 10*e - 7', '-3*e^2 - 10*e + 4', '11*e^2 - 22*e - 35', '-9*e^2 + 15*e - 11', '-17*e^2 + 15*e + 17', '-4*e^2 + 10*e', '-10*e^2 + 43', '11*e^2 + 14*e - 44', '-14*e^2 + 18*e + 65', '-6*e^2 + 2*e + 13', '3*e^2 - 25*e + 13', '-4*e^2 + 24*e - 8', '-8*e^2 + 15*e + 23', '11*e - 13', '-9*e^2 + 12*e + 54', '-7*e^2 - 14*e + 32', '-13*e^2 - 2*e + 22', '-14*e^2 + 6*e + 48', '8*e^2 - 15*e - 37', '-14*e^2 + 32', '-13*e^2 - 14*e + 51', '-3*e^2 + 21*e - 6', '-2*e^2 - 18*e - 7', '10*e^2 - 30', '2*e^2 + 15*e + 18', '18*e^2 - 8*e - 61', '4*e^2 - 15*e - 35', '-2*e^2 - 4*e - 17', '-21*e^2 + 33*e + 60', '13*e^2 + e - 28', '-7*e^2 + e + 14', '-14*e^2 + 6*e + 21', '12*e^2 + 12*e - 76', '5*e^2 + 13*e + 9', '8*e^2 - 9*e - 35', '-8*e^2 - 5*e + 13', '13*e^2 - 33*e - 25', '12*e^2 + 4*e - 30', '3*e^2 - 15*e - 35', '-11*e^2 + 28*e + 5', '-9*e^2 + e + 71', '-3*e^2 + 9*e', '12*e^2 + 7*e - 58', '-9*e^2 - 12*e + 61', '9*e^2 - 4*e - 17', '2*e^2 + 15*e - 32', '6*e^2 - 9*e + 10', '14*e^2 + 20*e - 65', '-e + 26', '-6*e^2 + 14*e + 67', '19*e^2 - 39*e - 49', '-e^2 + 18*e + 28', '-24*e^2 + 27*e + 70', '-12*e + 41', '26*e^2 - 24*e - 50', '-16*e^2 + 36*e + 43', '11*e^2 + 18*e - 42', '5*e^2 - 16*e + 4', '14*e^2 - 19*e - 42', '4*e^2 + 7*e - 7', '-14*e^2 - 6*e + 20', '2*e^2 - 15*e + 4', '-2*e^2 + 8*e + 32', '-19*e^2 + 77', '4*e^2 - 8*e - 31', '12*e^2 - 21*e - 22', '22*e^2 - 21*e - 44', '-28*e^2 + 17*e + 71', '-21*e^2 + 9*e + 39', '4*e^2 + 12*e - 8', '-8*e^2 + 56', '-5*e^2 + e - 14', '20*e^2 - 16*e - 50', 'e^2 - 17*e - 19', '-19*e^2 + 40', '4*e^2 - 16*e + 3', '-e^2 - 10*e - 12', '-5*e^2 - 5*e + 41', '10*e^2 - 8*e - 7', '-5*e^2 - 7*e + 35', '12*e^2 - 12*e - 37', '19*e - 14', '4*e^2 + 15*e - 28', '-11*e^2 + 6*e - 7', '-7*e^2 + 3*e + 24', '-17*e^2 - 11*e + 64', '22*e^2 - 17*e - 19', '10*e^2 + 4*e + 5', '7*e^2 - 14*e - 37', '7*e^2 - 2*e + 11', '13*e^2 - 3*e - 45', '-18*e^2 + 9*e + 71', '10*e^2 - 8*e + 17', '-15*e^2 + 6*e + 34', '-e^2 - e - 29', '17*e^2 + 9*e - 65', '12*e^2 - 24*e - 41', '16*e^2 - 11*e - 22', '-12*e^2 + 27*e + 15', '12*e^2 - 16*e - 63', 'e^2 + 6*e + 4', '-3*e^2 - 15*e + 5', '29*e^2 - 34*e - 71', '7*e^2 - 30*e - 34', '-14*e^2 + 29*e + 42', '22*e^2 - 21*e - 37', '4*e^2 + 19*e - 46', '22*e^2 - 5*e - 76', '7*e^2 - 27*e - 26', '6*e^2 - 19*e - 51', '10*e^2 + 15*e - 61', '-17*e^2 + 39*e + 32', '3*e^2 - 2*e + 34', '-21*e^2 + 6*e + 46', '-6*e^2 + 11*e - 14', '-2*e^2 + 30*e - 22', '17*e^2 - 8*e - 18', '13*e^2 - 33*e - 45', '4*e^2 - 10*e + 6', '-13*e^2 + 5*e - 1', '-5*e^2 + 71', '-20*e^2 + 8*e + 39', '6*e^2 - 4*e - 11', '7*e^2 - 15*e - 70', '-13*e^2 - 6*e + 34', '12*e - 59', '18*e^2 - 3*e - 27', '-22*e^2 + 7*e + 58', '7*e^2 + 22*e - 24', '19*e^2 - 29*e - 60', '-7*e^2 - 6*e + 14', '-16*e^2 + 18*e + 23', '-8*e^2 + e + 18', '2*e^2 - 13*e - 2', '7*e^2 - 41*e - 8', '3*e^2 - 5*e + 11', '11*e^2 - 31*e - 75', '-7*e^2 - 10*e + 6', '-3*e^2 - 6*e - 28', '-e^2 - 15*e + 12', '9*e^2 - 3*e + 41', '12*e - 60', '6*e^2 - 2*e - 32', '10*e^2 - 3*e - 16', '-5*e^2 + 6*e - 5', '5*e^2 + e - 18', '-2*e^2 - 24*e - 10', '-12*e^2 + 25*e + 65', '5*e^2 - 12*e + 13', '-9*e^2 + 6*e + 22', '-6*e^2 + 8*e - 34', '9*e^2 - 12*e - 24', '6*e^2 - 12*e - 20', '5*e^2 + 12*e - 51', '-10*e^2 + 30*e + 52', '6*e^2 + 21*e - 15', '6*e^2 - 6*e + 58', '-17*e^2 + 52*e + 63', '-28*e^2 + 14*e + 56', '-23*e^2 - 17*e + 97', '-15*e^2 + 17*e + 85', '-26*e^2 + e + 76', '-14*e^2 + 21*e + 1', '2*e^2 - 7*e + 18', '28*e - 5', '31*e^2 - 20*e - 67', '-7*e^2 + 9*e + 34', '18*e + 39', '18*e^2 + 28*e - 95', 'e^2 + 4*e - 10', '-30*e^2 + 27*e + 74', '-16*e^2 + 38*e + 48', '-21*e^2 + 39*e + 39', '7*e^2 - 30*e - 31', '11*e^2 + 12*e - 101', '-5*e^2 - 7*e - 12', '13*e^2 - 28*e - 24', '13*e^2 + 2*e - 90', '-4*e^2 - 13*e + 50', '5*e^2 - 17*e + 38', '11*e^2 - 50*e - 33', '6*e^2 + 6*e - 49', '5*e^2 - 16*e + 40', '-10*e^2 + 26*e + 7', '-e^2 + 6*e + 49', -43, '-14*e^2 + 21*e + 46', '21*e^2 - 22*e - 57', '-10*e^2 - 16*e + 22', '-e^2 - 11*e + 18', '-5*e^2 + 32*e + 24', '-24*e^2 + 22*e + 68', '-e^2 + 12*e - 26', '-26*e^2 + 30*e + 80', '-2*e^2 - 2*e + 59', '-31*e^2 + 32*e + 78', '8*e^2 + 10*e - 11', '-4*e^2 + 2*e - 54', '8*e^2 + 21*e - 20', '-11*e^2 + 12*e + 42', '12*e^2 + e - 94', '-8*e^2 + 3*e + 30', '-4*e^2 + 29*e + 37', '25*e^2 - 15*e - 82', '-32*e - 7', '-31*e^2 + 8*e + 92', '7*e^2 - 24*e - 18', '-18*e^2 + 38*e + 73', '-e^2 - 17*e + 16', '-35*e^2 + 15*e + 95', '12*e^2 - 3*e + 8', '-15*e^2 - 14*e + 77', '-19*e^2 - 15*e + 105', '-21*e^2 + 7*e + 48', '8*e^2 - 11*e + 27', '8*e^2 + 5*e - 41', '18*e^2 - 39*e - 51', '-13*e^2 - 20*e + 48', '-7*e^2 - 29*e + 43', 'e^2 - 29*e + 45', '-12*e^2 + 35*e + 26', '7*e^2 + 4*e - 42', '-32*e^2 + 15*e + 101', '-10*e^2 - 15*e + 62', '-4*e^2 - 10*e + 7', '2*e^2 - 15*e + 16', '-42*e^2 + 34*e + 83', '19*e^2 + 5*e - 90', '-13*e^2 - 4*e + 8', '-3*e^2 + 20*e + 7', '-4*e^2 + 32*e - 34', '28*e^2 - 18*e - 48', '-7*e^2 - 3*e + 62', '13*e^2 + 14*e - 31', '24*e^2 + 6*e - 61', '18*e^2 + 19*e - 52', '-6*e^2 + 20*e + 25', '-9*e^2 + 33*e + 9', '-12*e^2 + 14*e - 17', '-5*e^2 + 23*e - 33', '-22*e^2 + 2*e + 89', '-2*e^2 - 8*e - 23', '16*e^2 - 38*e - 86', '5*e^2 - 13*e - 62', '9*e^2 - 24*e - 2', '-17*e^2 + 35*e + 66', '2*e^2 - 6*e - 74', '-14*e + 34', '-5*e^2 + 29*e + 1', '34*e^2 - 12*e - 79', '-6*e^2 - 8*e + 50', '13*e^2 - 14*e - 61', '-14*e^2 + 63', '-20*e^2 - 4*e + 69', '27*e^2 - 24*e - 55', '-29*e^2 + 16*e + 104', '-3*e^2 + 24*e - 34', '-34*e^2 + 21*e + 92', '36*e^2 - 15*e - 106', '19*e^2 - 36*e - 44', '-4*e^2 + 20*e - 38', '25*e^2 - 24*e - 94', '-8*e^2 + 9*e + 14', '18*e^2 - 30*e - 27', '-11*e^2 + 25*e + 7', '-2*e^2 - 23*e + 12', '-8*e^2 - 31*e + 72', '28*e^2 + 8*e - 80', '-14*e^2 + 34*e + 87', '-15*e^2 + 38*e + 82', '-24*e^2 + 15*e + 63', '-18*e^2 + 11*e + 21', '3*e^2 + 11*e + 20', '-2*e^2 + 3*e - 30', '-20*e^2 + 39*e + 46', '19*e^2 - 40', '-20*e^2 - 12*e + 95', '-5*e^2 + 3*e + 62', '2*e^2 - 41*e + 12', '7*e^2 + 5*e - 45', '23*e^2 - 22*e - 13', '-24*e^2 - 3*e + 46', '10*e^2 - 15*e - 20', '11*e^2 + 37*e - 60', '-5*e^2 - 26*e - 7', '4*e^2 - 21*e + 23', '14*e^2 - 33*e - 15', '10*e^2 - 36*e - 21', '14*e^2 + 6*e - 70', '-15*e^2 - 15*e + 65', '9*e^2 + 26*e - 95', '29*e^2 - 25*e - 53', '-10*e^2 + 17*e + 72', '13*e^2 - 19*e - 34', '-6*e^2 - 8*e + 80', '2*e^2 - 13*e + 19', '-9*e^2 - 5*e - 44', '18*e - 16', 'e^2 - 9*e - 67', '-13*e^2 + 12*e + 10', '-25*e^2 - 7*e + 120', '-14*e^2 - 5*e + 29', '3*e^2 + 20*e - 41', '-15*e^2 + 16*e + 64', '9*e^2 + 30*e - 29', '-35*e^2 + 28*e + 66', '27*e^2 - 9*e - 80', '-e^2 - 10*e + 38', '5*e^2 + 5*e + 10', '11*e^2 - 3*e - 41', '-18*e^2 + 8*e + 66', '36*e^2 - 15*e - 84', '18*e^2 + 31*e - 103', '-12*e^2 - 37*e + 87', '-e^2 + 14*e + 27', '9*e^2 - 41*e - 33', '-29*e^2 + 39*e + 86', '-3*e^2 - 5*e - 19', '6*e^2 - 12*e - 63', '19*e^2 - 24*e - 75', '-10*e^2 - 18*e + 10', '21*e^2 - 23*e - 105', '-10*e^2 + 17*e + 27', '-27*e^2 + 100', '20*e^2 - 14*e - 85', '19*e^2 - 24*e - 49', '-9*e^2 + 7*e + 35', '9*e^2 - 5*e - 34', '-24*e^2 - 3*e + 81', '29*e^2 - 5*e - 89', '34*e^2 - 26*e - 91', '13*e + 22', '24*e^2 - 15*e - 81', '8*e^2 + 5*e + 18', '-9*e^2 + 46*e + 24', '-24*e^2 + 21*e + 60', '25*e^2 - 39*e - 19', '5*e^2 + 15*e - 62', '-12*e^2 + 34*e + 62', '-8*e^2 + 20*e + 36', '-8*e^2 + e - 29', '2*e^2 + 19*e - 12', '-3*e^2 + 48*e + 21', '-22*e^2 + 17*e + 98', '-13*e^2 + 38*e + 59', '-18*e - 6', '8*e^2 + 7*e + 30', '5*e^2 + 5*e - 41', '7*e^2 + 15*e - 36', '-25*e^2 + 20*e + 93', '-18*e^2 + 33*e + 57', '6*e^2 + 11*e + 16', '20*e^2 - 3*e - 89', '-8*e^2 + 5*e - 9', '-21*e^2 - 18*e + 93', '19*e^2 - 34*e - 1', '-21*e^2 + 21*e + 95', '18*e^2 - 15*e - 54', '9*e^2 + 13*e - 43'], 'hecke_polynomial': 'x^3 - x^2 - 4*x + 1', 'label': '4.4.11197.1-19.1-e'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 11197, 'ideals': ['[1, 1, 1]', '[3, 3, w + 1]', '[7, 7, w^3 - 2*w^2 - 3*w + 1]', '[9, 9, -w + 2]', '[11, 11, -w - 2]', '[11, 11, -w^3 + 2*w^2 + 3*w - 2]', '[13, 13, -w^2 + 2*w + 2]', '[16, 2, 2]', '[19, 19, -w^3 + 2*w^2 + 4*w - 1]', '[21, 21, w^3 - w^2 - 5*w]', '[23, 23, -w^2 + w + 3]', '[23, 23, -w^2 + 3]', '[27, 3, w^3 - 3*w^2 - w + 4]', '[27, 27, -w^2 + w + 2]', '[29, 29, -w^3 + 3*w^2 + 3*w - 5]', '[29, 29, w^3 - 2*w^2 - 4*w]', '[33, 33, -w^3 + w^2 + 4*w - 1]', '[33, 33, w^3 - 2*w^2 - 2*w + 1]', '[39, 39, w^3 - 2*w^2 - 5*w + 4]', '[47, 47, -w^3 + 2*w^2 + 3*w - 5]', '[47, 47, w^2 - 3*w - 2]', '[48, 6, 2*w + 2]', '[49, 49, w^3 - 2*w^2 - 5*w + 2]', '[57, 57, -w^3 + 3*w^2 + 4*w - 6]', '[61, 61, -w^3 + 2*w^2 + 5*w - 3]', '[63, 63, w^3 - 2*w^2 - 2*w + 4]', '[67, 67, -w^3 + w^2 + 5*w - 1]', '[67, 67, -2*w^3 + 3*w^2 + 11*w - 7]', '[69, 69, 2*w^3 - 3*w^2 - 8*w]', '[69, 69, -w^2 + 4*w - 1]', '[77, 77, -2*w^3 + 3*w^2 + 8*w - 1]', '[77, 77, w - 4]', '[81, 3, 3]', '[81, 81, -2*w^3 + 3*w^2 + 8*w - 3]', '[83, 83, -2*w + 3]', '[87, 87, -w^3 + w^2 + 6*w - 2]', '[87, 87, -w^2 - w + 3]', '[89, 89, 3*w^3 - 7*w^2 - 9*w + 9]', '[91, 91, w + 3]', '[97, 97, w^3 - w^2 - 4*w - 3]', '[97, 97, -w^3 + 5*w + 3]', '[99, 99, -2*w^3 + 5*w^2 + 5*w - 5]', '[99, 99, w^2 - 4]', '[103, 103, -w^3 + 3*w^2 + w - 5]', '[103, 103, -w^3 + 2*w^2 + 3*w + 2]', '[112, 14, 2*w^3 - 4*w^2 - 6*w + 2]', '[117, 117, w^3 - 3*w^2 - 4*w + 3]', '[121, 11, 2*w^3 - 3*w^2 - 7*w + 3]', '[121, 11, 2*w^3 - 5*w^2 - 3*w + 2]', '[121, 121, w^3 - 2*w^2 - 4*w + 6]', '[121, 121, -w^3 + w^2 + 5*w - 2]', '[127, 127, -2*w^3 + 4*w^2 + 6*w - 5]', '[131, 131, w^2 - 3*w - 3]', '[133, 133, w^3 - w^2 - 4*w - 4]', '[137, 137, -2*w^3 + 3*w^2 + 9*w - 3]', '[139, 139, 2*w - 5]', '[141, 141, -w^3 + w^2 + w - 4]', '[141, 141, w^3 - 2*w^2 - 5*w - 2]', '[143, 143, -w^3 + w^2 + 7*w - 2]', '[143, 143, w^3 - 6*w - 4]', '[144, 18, -2*w + 4]', '[147, 147, -w^3 + 8*w + 4]', '[149, 149, -2*w^3 + 4*w^2 + 9*w - 4]', '[151, 151, 3*w^3 - 5*w^2 - 12*w + 3]', '[151, 151, w^3 - w^2 - 6*w + 3]', '[161, 161, 2*w^3 - 4*w^2 - 8*w + 3]', '[161, 161, 2*w^3 - 3*w^2 - 10*w + 2]', '[163, 163, -2*w^3 + 5*w^2 + 5*w - 9]', '[167, 167, -w^3 + 2*w^2 + 6*w - 7]', '[169, 169, w^3 - 2*w^2 - 6*w + 1]', '[171, 171, -2*w^3 + 4*w^2 + 6*w - 3]', '[176, 22, -2*w - 4]', '[176, 22, -2*w^3 + 4*w^2 + 6*w - 4]', '[179, 179, -w^3 + 4*w^2 - w - 5]', '[179, 179, -3*w^3 + 8*w^2 + 7*w - 12]', '[181, 181, 2*w^3 - 5*w^2 - 4*w + 2]', '[183, 183, -w^3 + 3*w^2 + 5*w - 2]', '[189, 21, w^3 - 3*w^2 - 4*w + 7]', '[189, 189, w^3 - w^2 - 7*w + 1]', '[199, 199, w^3 - 5*w - 5]', '[201, 201, -3*w^3 + 6*w^2 + 10*w - 5]', '[201, 201, -2*w^3 + 2*w^2 + 7*w]', '[203, 203, -2*w^3 + 3*w^2 + 7*w + 3]', '[203, 203, -2*w^3 + 4*w^2 + 9*w - 7]', '[207, 207, w^3 - 2*w^2 - 3*w + 6]', '[207, 207, w^3 - 3*w^2 - w + 6]', '[208, 26, -2*w^2 + 4*w + 4]', '[209, 209, -w^2 + 5]', '[209, 209, -w^3 + 4*w^2 - w - 4]', '[211, 211, 2*w^2 - 3*w - 7]', '[223, 223, -2*w^3 + 3*w^2 + 8*w - 4]', '[223, 223, -2*w^3 + 3*w^2 + 10*w - 5]', '[223, 223, w^3 - 2*w^2 - 6*w + 8]', '[223, 223, 2*w^3 - 2*w^2 - 9*w]', '[227, 227, 2*w^3 - 3*w^2 - 7*w + 2]', '[229, 229, -w^3 + 3*w^2 + 4*w - 2]', '[229, 229, -2*w^3 + 2*w^2 + 8*w - 1]', '[231, 231, w^2 - 3*w - 4]', '[231, 231, -w^3 + 3*w^2 + 2]', '[233, 233, -2*w^3 + 4*w^2 + 7*w - 1]', '[243, 9, 3*w + 3]', '[243, 243, w^3 - 3*w^2 + 4]', '[247, 247, -2*w^3 + 2*w^2 + 11*w]', '[249, 249, 2*w^2 - w - 3]', '[251, 251, w^2 + w - 4]', '[253, 253, 2*w^3 - 5*w^2 - 4*w + 1]', '[253, 253, -2*w^3 + 4*w^2 + 9*w - 5]', '[253, 253, w^3 - 2*w^2 - 6*w + 4]', '[253, 253, 2*w^3 - 5*w^2 - 5*w + 4]', '[256, 4, 4]', '[257, 257, -2*w^3 + 4*w^2 + 9*w - 2]', '[261, 261, -2*w^3 + 3*w^2 + 7*w - 1]', '[261, 261, 2*w^3 - 4*w^2 - 5*w + 1]', '[263, 263, -w^3 + 2*w^2 + 6*w - 2]', '[263, 263, w^2 - 3*w - 6]', '[263, 263, 2*w^3 - 4*w^2 - 7*w]', '[263, 263, -w^3 + 8*w]', '[267, 267, 2*w^3 - 4*w^2 - 9*w + 6]', '[271, 271, 2*w^2 - w - 5]', '[271, 271, -3*w^3 + 7*w^2 + 8*w - 6]', '[273, 273, -2*w^3 + 5*w^2 + 2*w - 2]', '[277, 277, -w^3 + 2*w^2 + w - 4]', '[283, 283, -2*w^3 + 3*w^2 + 9*w - 4]', '[291, 291, 2*w^3 - w^2 - 10*w - 4]', '[291, 291, -3*w^3 + w^2 + 11*w + 4]', '[297, 33, -w^3 + 3*w^2 + w - 7]', '[297, 33, 2*w^3 - 3*w^2 - 8*w - 4]', '[297, 297, -3*w^3 + 5*w^2 + 11*w]', '[297, 297, -w^3 + 2*w^2 + 6*w - 3]', '[299, 299, -w^2 + 3*w + 5]', '[299, 299, -w^3 + w^2 + 5*w + 5]', '[304, 38, -2*w^3 + 4*w^2 + 8*w - 2]', '[307, 307, -w^3 + 3*w^2 + w - 8]', '[309, 309, -w - 4]', '[309, 309, -w^3 + w^2 + 8*w + 3]', '[311, 311, 2*w^2 - 6*w - 3]', '[313, 313, -w^3 + 2*w^2 + 2*w + 4]', '[313, 313, -4*w^3 + 9*w^2 + 12*w - 12]', '[313, 313, w^2 - 2*w - 7]', '[313, 313, 4*w^3 - 8*w^2 - 14*w + 11]', '[317, 317, 2*w^3 - w^2 - 12*w - 5]', '[317, 317, w^3 - 6*w]', '[319, 319, -w^3 + 4*w + 4]', '[319, 319, -w^3 + 4*w^2 + 3*w - 7]', '[319, 319, 2*w^2 - 3*w - 3]', '[319, 319, w^3 - w^2 - 3*w - 3]', '[329, 329, -w^3 - w^2 + 11*w + 1]', '[329, 329, -3*w^3 + 6*w^2 + 10*w - 7]', '[331, 331, -w^3 + 2*w^2 + 5*w - 8]', '[336, 42, 2*w^3 - 2*w^2 - 10*w]', '[343, 7, -2*w^3 + 3*w^2 + 6*w - 3]', '[343, 343, -2*w^2 + 3*w + 6]', '[347, 347, -3*w^3 + 5*w^2 + 14*w - 8]', '[351, 39, 2*w^3 - 3*w^2 - 8*w + 5]', '[351, 351, -w^3 + 2*w^2 + 3*w + 3]', '[353, 353, -2*w^3 + 5*w^2 + 6*w - 5]', '[359, 359, 2*w^3 - 4*w^2 - 5*w + 2]', '[361, 361, -w^3 + w^2 + 6*w + 5]', '[363, 33, -w^2 + 2*w - 3]', '[363, 33, w^3 - 7*w]', '[363, 363, w^3 - 2*w^2 - w + 5]', '[363, 363, w^3 - 4*w^2 - 2*w + 9]', '[367, 367, 2*w^2 - 7*w + 1]', '[367, 367, -w^3 + 3*w^2 + 4*w - 8]', '[367, 367, 3*w^2 - 6*w - 8]', '[367, 367, -3*w^3 + 6*w^2 + 11*w - 5]', '[368, 46, -2*w^2 + 2*w + 6]', '[368, 46, -2*w^2 + 6]', '[377, 377, w^2 - 4*w + 5]', '[377, 377, -w^3 + 2*w^2 + 4*w - 7]', '[379, 379, 2*w^3 - 4*w^2 - 5*w + 3]', '[379, 379, w^3 - 9*w + 2]', '[381, 381, -2*w^3 + 2*w^2 + 7*w - 3]', '[393, 393, w^3 - 2*w^2 - 6*w - 3]', '[397, 397, -w^3 + 4*w^2 - 2*w - 5]', '[399, 399, -3*w^3 + 7*w^2 + 10*w - 9]', '[409, 409, 2*w^2 - 3*w - 4]', '[411, 411, -3*w^3 + 4*w^2 + 12*w - 1]', '[417, 417, 2*w^2 - 3*w - 5]', '[419, 419, w^3 - w^2 - 8*w + 4]', '[419, 419, 2*w^3 - 3*w^2 - 10*w + 6]', '[423, 423, -2*w^3 + 5*w^2 + 8*w - 11]', '[423, 423, -w^3 + 5*w^2 - 4*w - 4]', '[427, 427, -w^3 + 4*w^2 - 7]', '[429, 429, -2*w^3 + 4*w^2 + 8*w - 1]', '[429, 429, 2*w^2 - 7*w]', '[432, 6, 2*w^3 - 6*w^2 - 2*w + 8]', '[432, 54, -2*w^2 + 2*w + 4]', '[437, 437, 2*w^3 - 6*w^2 - w + 6]', '[437, 437, -3*w^3 + 4*w^2 + 13*w - 2]', '[439, 439, -2*w^3 + 5*w^2 + 5*w - 3]', '[441, 441, 2*w^3 - 3*w^2 - 9*w + 5]', '[447, 447, -2*w^3 + 5*w^2 + 11*w - 2]', '[449, 449, 2*w^2 - 2*w - 5]', '[453, 453, 2*w^3 - 3*w^2 - 6*w + 2]', '[453, 453, 4*w^3 - 5*w^2 - 18*w]', '[457, 457, 2*w^3 - 2*w^2 - 9*w - 6]', '[461, 461, 2*w^3 - 3*w^2 - 6*w + 1]', '[461, 461, -w^3 + 4*w^2 + w - 5]', '[463, 463, -w^3 + 4*w^2 - 12]', '[463, 463, -2*w^3 + 5*w^2 + 4*w - 8]', '[464, 58, -2*w^3 + 6*w^2 + 6*w - 10]', '[464, 58, 2*w^3 - 4*w^2 - 8*w]', '[469, 469, 2*w^2 - 5*w - 5]', '[469, 469, -5*w^3 + 11*w^2 + 17*w - 15]', '[479, 479, w^3 - 5*w - 6]', '[483, 483, w^3 - 3*w^2 + 2*w - 3]', '[483, 483, -2*w^3 + 3*w^2 + 5*w - 3]', '[487, 487, -3*w^3 + 8*w^2 + 8*w - 13]', '[487, 487, -4*w^3 + 6*w^2 + 17*w - 4]', '[489, 489, -w^3 + 2*w^2 + 2*w - 7]', '[491, 491, -w^3 + 4*w^2 - 6]', '[499, 499, -4*w^3 + 10*w^2 + 10*w - 15]', '[499, 499, -2*w^3 + 4*w^2 + 10*w - 3]', '[501, 501, -w^3 + 4*w^2 + 2*w - 6]', '[503, 503, w^2 + w - 5]', '[507, 507, 3*w^3 - 7*w^2 - 7*w + 6]', '[513, 57, -2*w^3 + 3*w^2 + 11*w - 5]', '[513, 513, -2*w^3 + 2*w^2 + 9*w - 1]', '[517, 517, w^3 - 8*w + 1]', '[517, 517, -w^3 + w^2 + 8*w + 4]', '[517, 517, 4*w^3 - 8*w^2 - 13*w + 12]', '[517, 517, 2*w^3 - 3*w^2 - 4*w + 9]', '[528, 66, -2*w^3 + 2*w^2 + 8*w - 2]', '[528, 66, 2*w^3 - 4*w^2 - 4*w + 2]', '[529, 23, -3*w^3 + 7*w^2 + 7*w - 7]', '[529, 23, 3*w^3 - 4*w^2 - 12*w]', '[529, 529, 3*w^3 - 5*w^2 - 14*w + 4]', '[529, 529, -w^3 + 10*w - 5]', '[537, 537, -w^3 + 3*w^2 + 4*w - 9]', '[537, 537, w^3 - w^2 - 3*w - 4]', '[539, 539, -3*w + 5]', '[539, 539, -w^3 + 4*w^2 + 2*w - 8]', '[541, 541, -2*w^3 + 7*w^2 - 10]', '[543, 543, -w^3 + w^2 + 8*w]', '[547, 547, w^3 - 3*w^2 + 2*w - 4]', '[547, 547, -2*w^3 + 2*w^2 + 11*w - 1]', '[549, 549, -2*w^3 + 3*w^2 + 10*w - 7]', '[551, 551, -2*w^3 + 3*w^2 + 9*w - 6]', '[551, 551, 3*w^3 - 5*w^2 - 11*w + 8]', '[557, 557, -w^3 + 10*w - 2]', '[557, 557, 3*w^3 - 4*w^2 - 16*w + 5]', '[563, 563, -2*w^3 + 5*w^2 + 9*w - 11]', '[563, 563, -3*w^3 + 6*w^2 + 13*w - 7]', '[567, 21, 3*w^3 - 6*w^2 - 9*w + 3]', '[567, 567, 2*w^3 - 6*w^2 - 5*w + 9]', '[571, 571, -w^3 + 2*w^2 + 3*w - 7]', '[571, 571, -3*w^3 + 5*w^2 + 13*w + 1]', '[577, 577, -2*w^3 + 5*w^2 + 7*w - 5]', '[577, 577, -2*w^3 + 6*w^2 + 6*w - 7]', '[581, 581, -3*w^3 + 8*w^2 + 5*w - 5]', '[587, 587, 3*w^3 - 6*w^2 - 13*w + 10]', '[587, 587, -w^3 + 4*w^2 + 2*w - 7]', '[597, 597, 3*w^3 - w^2 - 13*w - 6]', '[599, 599, -3*w^3 + 6*w^2 + 8*w - 8]', '[603, 603, -w^3 + w^2 + 8*w - 3]', '[603, 603, -3*w^3 + 4*w^2 + 14*w - 2]', '[609, 609, 2*w^3 - 5*w^2 - 6*w + 4]', '[609, 609, -2*w^3 + 5*w^2 + 8*w - 5]', '[611, 611, -w^3 + 4*w^2 + w - 8]', '[611, 611, 3*w^3 - 6*w^2 - 7*w - 3]', '[617, 617, -4*w^3 + 7*w^2 + 15*w - 3]', '[617, 617, -w^3 + 4*w^2 + w - 6]', '[621, 69, -w^3 + 7*w - 1]', '[621, 69, 2*w^3 - 6*w^2 - 5*w + 11]', '[621, 621, 3*w^3 - 6*w^2 - 10*w + 2]', '[621, 621, 2*w + 5]', '[623, 623, 5*w^3 - 10*w^2 - 18*w + 17]', '[624, 78, 2*w^3 - 4*w^2 - 10*w + 8]', '[625, 5, -5]', '[627, 627, -w^3 - w^2 + 5*w + 5]', '[627, 627, w^3 - w^2 - 2*w - 3]', '[631, 631, w^2 - 4*w - 4]', '[633, 633, 2*w^3 - w^2 - 10*w - 7]', '[637, 637, 3*w^3 - 5*w^2 - 11*w + 2]', '[641, 641, -2*w^3 + 3*w^2 + 11*w - 1]', '[641, 641, -3*w^3 + 5*w^2 + 12*w - 7]', '[643, 643, -w^3 + 4*w^2 - w - 8]', '[647, 647, 3*w^3 - 4*w^2 - 15*w + 3]', '[647, 647, -3*w^3 + 5*w^2 + 10*w - 6]', '[661, 661, 3*w^2 - 5]', '[661, 661, 2*w^3 - 2*w^2 - 10*w + 1]', '[667, 667, 3*w^3 - 6*w^2 - 8*w + 11]', '[667, 667, -w^3 + 3*w^2 + 3]', '[667, 667, w^3 - 3*w^2 + w + 4]', '[667, 667, 2*w^3 - 4*w^2 - 7*w + 10]', '[669, 669, -3*w^3 + 5*w^2 + 11*w - 3]', '[669, 669, -3*w^3 + 3*w^2 + 10*w - 2]', '[669, 669, w^3 - 4*w^2 - w + 7]', '[669, 669, 4*w^3 - 3*w^2 - 15*w - 2]', '[671, 671, 2*w^3 - 6*w^2 - 5*w + 10]', '[671, 671, 2*w^3 - 5*w^2 - 10*w + 5]', '[677, 677, 5*w^3 - 13*w^2 - 9*w + 13]', '[679, 679, -4*w^3 + 7*w^2 + 15*w]', '[679, 679, 3*w^3 - 4*w^2 - 16*w - 1]', '[681, 681, 3*w^3 - 2*w^2 - 11*w]', '[683, 683, w^3 - w^2 - 8*w + 1]', '[683, 683, w^3 - w^2 - 8*w - 7]', '[687, 687, 3*w^2 + 5*w - 1]', '[687, 687, 3*w^3 - 2*w^2 - 17*w - 6]', '[693, 693, -3*w^3 + 6*w^2 + 11*w - 4]', '[693, 693, -3*w^3 + 5*w^2 + 11*w - 9]', '[699, 699, -2*w^3 + 3*w^2 + 12*w + 1]', '[701, 701, -3*w^3 + 10*w^2 + w - 13]', '[701, 701, -w^3 + w^2 - 4]', '[701, 701, w^3 - w^2 - 8*w + 2]', '[701, 701, -4*w^3 + 6*w^2 + 20*w - 7]', '[709, 709, 4*w^3 - 7*w^2 - 18*w + 3]', '[719, 719, w^3 - 3*w^2 - 2*w - 2]', '[721, 721, -2*w^3 + 2*w^2 + 13*w - 5]', '[721, 721, 4*w^3 - 8*w^2 - 11*w]', '[727, 727, 3*w^3 - 6*w^2 - 13*w + 9]', '[729, 9, -w^3 + 4*w + 5]', '[729, 27, -3*w + 6]', '[729, 729, -3*w^3 + 6*w^2 + 13*w - 8]', '[733, 733, 4*w^3 - 5*w^2 - 17*w - 1]', '[737, 737, 3*w^3 - 3*w^2 - 12*w + 1]', '[737, 737, 6*w^3 - 10*w^2 - 23*w]', '[737, 737, w^3 - 3*w^2 + 6]', '[737, 737, 5*w^3 - 9*w^2 - 21*w + 12]', '[739, 739, -3*w^3 + 5*w^2 + 8*w + 1]', '[739, 739, w - 6]', '[741, 741, -2*w^3 + 5*w^2 + 4*w - 9]', '[747, 747, -2*w^2 + 7*w - 6]', '[751, 751, -3*w^3 + 6*w^2 + 9*w - 7]', '[752, 94, -2*w^3 + 4*w^2 + 6*w - 10]', '[752, 94, 2*w^2 - 6*w - 4]', '[753, 753, w^3 + 2*w^2 - 3*w - 4]', '[759, 759, w^3 + w^2 - 10*w - 7]', '[759, 759, w^3 - 2*w^2 - 7*w + 2]', '[759, 759, w^3 - w^2 - 5*w - 6]', '[759, 759, -3*w^3 + 7*w^2 + 8*w - 14]', '[761, 761, -w - 5]', '[761, 761, -3*w^3 + 6*w^2 + 14*w - 17]', '[768, 12, 4*w + 4]', '[771, 771, -2*w^3 + 5*w^2 + 13*w]', '[773, 773, -3*w + 7]', '[783, 87, -2*w^3 + 3*w^2 + 11*w - 2]', '[783, 87, w^3 - 10*w + 1]', '[783, 783, w^3 - 5*w - 7]', '[783, 783, -2*w^3 + 3*w^2 + 6*w - 8]', '[784, 98, 2*w^3 - 4*w^2 - 10*w + 4]', '[787, 787, w^3 - 3*w - 4]', '[789, 789, -3*w^3 + 4*w^2 + 11*w + 1]', '[789, 789, -w^3 + 4*w^2 + 7*w - 1]', '[789, 789, 2*w^3 - 3*w^2 - 13*w - 2]', '[789, 789, w^3 - 2*w^2 - 9*w - 6]', '[793, 793, -3*w^3 + 6*w^2 + 9*w - 4]', '[797, 797, -4*w^3 + 6*w^2 + 16*w + 1]', '[797, 797, -w^3 + 2*w^2 + 7*w - 4]', '[801, 801, 2*w^3 - 5*w^2 - 9*w + 4]', '[809, 809, -3*w^3 + 7*w^2 + 10*w - 8]', '[809, 809, 3*w^2 - 3*w - 13]', '[811, 811, 3*w^3 - 6*w^2 - 7*w]', '[813, 813, -2*w^3 + 4*w^2 + 9*w - 12]', '[813, 813, -2*w^3 + 3*w^2 + 11*w - 3]', '[819, 819, -w^2 - w + 6]', '[821, 821, 3*w^3 - 5*w^2 - 10*w]', '[831, 831, -w^3 - w^2 - 3]', '[839, 839, w^3 - 12*w + 11]', '[839, 839, -3*w^3 + 5*w^2 + 15*w - 12]', '[841, 29, -2*w^3 + 2*w^2 + 8*w - 3]', '[841, 29, 2*w^3 - 2*w^2 - 12*w + 3]', '[841, 841, -w^3 + w^2 + 3*w + 6]', '[841, 841, w^3 - 7*w + 2]', '[847, 77, -w^2 + 2*w + 8]', '[847, 77, w^3 - 2*w^2 - 7*w + 3]', '[847, 847, -w^3 + 4*w^2 - 2*w - 6]', '[847, 847, -w^3 + 5*w^2 - 3*w - 4]', '[849, 849, -3*w^3 + 4*w^2 + 11*w - 2]', '[853, 853, 2*w^2 - 5*w - 6]', '[857, 857, w^3 - 2*w^2 - 3*w - 4]', '[857, 857, -2*w^3 + 2*w^2 + 9*w + 9]', '[859, 859, -2*w^3 + 4*w^2 + 10*w - 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6]', '[1539, 57, -3*w^3 + 6*w^2 + 12*w - 3]', '[1539, 1539, -4*w^3 + 10*w^2 + 9*w - 8]', '[1541, 1541, w^3 - 5*w^2 + 4*w + 8]', '[1541, 1541, -2*w^3 + 5*w^2 + 11*w - 4]', '[1541, 1541, -3*w^3 + 6*w^2 + 13*w - 3]', '[1541, 1541, -7*w^3 + 14*w^2 + 28*w - 22]', '[1549, 1549, w^2 - 3*w - 9]', '[1549, 1549, 5*w^3 - 10*w^2 - 16*w + 6]', '[1551, 1551, -4*w^2 + 9*w + 1]', '[1551, 1551, 4*w^3 - 5*w^2 - 13*w + 8]', '[1551, 1551, 3*w^3 - 4*w^2 - 10*w]', '[1551, 1551, -3*w^3 + 5*w^2 + 8*w - 6]', '[1552, 194, 2*w^3 - 2*w^2 - 8*w - 6]', '[1552, 194, -2*w^3 + 10*w + 6]', '[1553, 1553, 3*w^3 - 3*w^2 - 16*w]', '[1553, 1553, -4*w^3 + 11*w^2 + 5*w - 5]', '[1559, 1559, -5*w^3 + 12*w^2 + 12*w - 13]', '[1561, 1561, -w^3 + 4*w^2 - w - 10]', '[1561, 1561, 4*w^3 - 9*w^2 - 11*w + 16]', '[1561, 1561, -2*w^3 + w^2 + 14*w + 7]', '[1561, 1561, -2*w^3 + 8*w^2 - 2*w - 13]', '[1567, 1567, -w - 6]', '[1571, 1571, -2*w^3 + w^2 + 16*w + 5]', '[1571, 1571, -3*w^3 + 6*w^2 + 15*w - 1]', '[1573, 143, w^2 + 4]', '[1573, 143, 3*w^3 - 5*w^2 - 15*w + 3]', '[1573, 1573, -3*w^3 + 7*w^2 + 8*w - 3]', '[1573, 1573, 2*w^3 - 7*w^2 - w + 10]', '[1577, 1577, 3*w^3 - 6*w^2 - 8*w + 5]', '[1579, 1579, -4*w^3 + 8*w^2 + 16*w - 7]', '[1584, 198, -4*w^3 + 10*w^2 + 10*w - 10]', '[1584, 198, 2*w^2 - 8]', '[1587, 69, 5*w^3 - 4*w^2 - 21*w - 3]', '[1587, 69, -2*w^3 + 2*w^2 + 9*w - 4]', '[1587, 1587, -3*w^3 + 6*w^2 + 8*w - 4]', '[1587, 1587, -3*w^3 + 4*w^2 + 8*w - 5]', '[1589, 1589, -w^3 + w^2 + 5*w + 7]', '[1597, 1597, -w^3 + 2*w^2 + 8*w - 5]', '[1597, 1597, -w^3 + 3*w^2 + 3*w - 12]', '[1601, 1601, 3*w^3 - 6*w^2 - 14*w + 11]', '[1603, 1603, w^3 - 9*w - 7]', '[1603, 1603, w^3 - w^2 - 2*w - 5]', '[1607, 1607, -3*w^3 + 4*w^2 + 13*w - 4]', '[1611, 1611, 3*w^2 - 2*w - 8]', '[1611, 1611, -4*w^3 + 13*w^2 - 11]', '[1617, 1617, -3*w^2 + 2*w + 5]', '[1617, 1617, -3*w^3 + 3*w^2 + 17*w - 1]', '[1619, 1619, 4*w^2 - 3*w - 15]', '[1621, 1621, -2*w^3 + 4*w^2 + 11*w - 3]', '[1621, 1621, -w^2 - w - 4]', '[1623, 1623, w^3 - w^2 - 4*w - 8]', '[1629, 1629, -2*w^3 + 5*w^2 + 11*w + 1]', '[1631, 1631, 3*w^3 - 5*w^2 - 9*w - 6]', '[1637, 1637, -2*w^3 + 3*w^2 + 15*w - 18]', '[1637, 1637, 7*w^3 - 18*w^2 - 14*w + 19]', '[1639, 1639, 2*w^3 - 7*w^2 - 5*w + 15]', '[1639, 1639, 4*w^3 - 9*w^2 - 20*w + 6]', '[1641, 1641, 3*w^2 - 5*w - 5]', '[1641, 1641, -4*w^3 + 5*w^2 + 16*w + 1]', '[1647, 183, -5*w^3 + 12*w^2 + 14*w - 14]', '[1647, 1647, -3*w^3 + 5*w^2 + 9*w - 5]', '[1648, 206, -2*w^3 + 6*w^2 + 2*w - 10]', '[1648, 206, -2*w^3 + 4*w^2 + 6*w + 4]', '[1651, 1651, -2*w^3 + 3*w^2 + 12*w - 6]', '[1653, 1653, -3*w^3 + 4*w^2 + 9*w - 4]', '[1653, 1653, -3*w^2 + 5*w + 8]', '[1657, 1657, -2*w^3 + w^2 + 19*w - 12]', '[1657, 1657, -3*w^3 + 4*w^2 + 10*w - 2]', '[1657, 1657, 3*w^3 - 3*w^2 - 20*w + 8]', '[1657, 1657, -3*w^3 + 6*w^2 + 7*w - 6]', '[1661, 1661, -3*w^3 + 4*w^2 + 12*w - 5]', '[1661, 1661, -3*w^3 + 8*w^2 + 5*w - 11]', '[1661, 1661, -7*w^3 + 10*w^2 + 30*w - 3]', '[1661, 1661, -w^3 + 4*w^2 + w - 15]', '[1667, 1667, -w^3 + 3*w^2 + 6*w - 9]', '[1667, 1667, -w^3 + 3*w^2 - w - 6]', '[1669, 1669, 3*w^2 - 7*w - 8]', '[1669, 1669, 4*w^2 - 14*w + 5]', '[1671, 1671, -3*w^3 + 6*w^2 + 11*w - 1]', '[1671, 1671, 5*w^3 - 8*w^2 - 20*w + 2]', '[1681, 41, -3*w^3 + 5*w^2 + 15*w - 7]', '[1681, 41, -w^3 + 2*w^2 + 8*w - 2]', '[1689, 1689, -w^3 + 6*w^2 + 4*w - 9]', '[1689, 1689, -3*w^3 + 7*w^2 + 15*w - 4]', '[1691, 1691, -3*w^3 + 7*w^2 + 11*w - 18]', '[1693, 1693, w^3 - w^2 - w - 4]', '[1697, 1697, 3*w^3 - 6*w^2 - 11*w]', '[1697, 1697, 5*w^3 - 7*w^2 - 21*w + 1]', '[1699, 1699, 2*w^2 - 5*w - 8]', '[1701, 63, 3*w^3 - 3*w^2 - 15*w]', '[1701, 1701, w^3 + w^2 - 12*w + 3]', '[1703, 1703, 3*w^3 - 5*w^2 - 9*w - 5]', '[1709, 1709, -2*w^3 + 7*w^2 + 6*w - 13]', '[1713, 1713, -4*w^3 + 6*w^2 + 23*w + 4]', '[1713, 1713, -w^3 + w^2 - w - 6]', '[1721, 1721, -2*w^3 + w^2 + 13*w]', '[1723, 1723, 2*w^2 - 5*w - 11]', '[1723, 1723, -2*w^3 + 4*w^2 + 6*w - 11]', '[1729, 1729, -3*w^3 + 6*w^2 + 14*w - 2]', '[1731, 1731, -w^3 + 4*w^2 + 8*w - 3]', '[1731, 1731, 4*w^2 + 5*w - 5]', '[1733, 1733, -4*w^3 + 7*w^2 + 14*w - 2]', '[1733, 1733, -2*w^3 + 2*w^2 + 9*w - 5]', '[1743, 1743, -w^3 + w^2 + 9*w - 2]', '[1747, 1747, w^3 - 2*w^2 - 3*w - 5]', '[1747, 1747, -4*w^3 + 9*w^2 + 10*w - 14]', '[1757, 1757, -3*w^3 + 7*w^2 + 9*w - 5]', '[1759, 1759, 2*w^3 - 3*w^2 - 12*w - 6]', '[1759, 1759, -2*w^3 + 4*w^2 + 3*w - 7]', '[1761, 1761, w^3 + 2*w^2 - 2*w - 6]', '[1761, 1761, 3*w^3 - 7*w^2 - 12*w + 7]', '[1769, 1769, 6*w^3 - 12*w^2 - 19*w + 19]', '[1769, 1769, w^2 - 5*w - 5]', '[1771, 1771, 3*w^3 - 5*w^2 - 9*w + 1]', '[1771, 1771, -w^3 + 4*w^2 + 3*w - 12]', '[1771, 1771, 3*w^3 - 4*w^2 - 11*w + 7]', '[1771, 1771, 2*w^3 - 7*w^2 - w + 9]', '[1777, 1777, -3*w^3 + 4*w^2 + 14*w - 4]', '[1781, 1781, -5*w^3 + 9*w^2 + 19*w - 3]', '[1783, 1783, -2*w^3 + 6*w^2 + w - 8]', '[1787, 1787, -6*w^3 + 10*w^2 + 23*w - 10]', '[1787, 1787, 2*w^3 - w^2 - 18*w + 11]', '[1789, 1789, -w^3 + 2*w^2 + 4*w - 9]', '[1791, 1791, w^2 - 2*w - 9]', '[1792, 28, 4*w^3 - 8*w^2 - 12*w + 4]', '[1793, 1793, 3*w^3 - 7*w^2 - 7*w + 16]', '[1793, 1793, 6*w^3 - 12*w^2 - 23*w + 21]', '[1797, 1797, -3*w^3 + 2*w^2 + 9*w - 5]', '[1799, 1799, 2*w^3 - w^2 - 10*w - 9]', '[1807, 1807, -2*w^3 + 9*w^2 - 6*w - 10]', '[1809, 201, -4*w^3 + 9*w^2 + 10*w - 7]', '[1809, 201, -5*w^3 + 9*w^2 + 20*w - 5]', '[1809, 1809, -2*w^3 + 5*w^2 + 8*w - 2]', '[1809, 1809, -6*w^3 + 14*w^2 + 16*w - 13]', '[1823, 1823, -5*w^3 + 9*w^2 + 22*w - 8]', '[1827, 1827, -2*w^3 + 5*w^2 + 5*w - 14]', '[1827, 1827, 2*w^3 - 3*w^2 - 8*w - 6]', '[1831, 1831, -6*w^3 + 17*w^2 + 9*w - 18]', '[1831, 1831, -4*w^3 + 11*w^2 + 9*w - 16]', '[1833, 1833, -6*w^3 + 14*w^2 + 23*w - 24]', '[1833, 1833, -3*w^3 + 8*w^2 + 6*w - 5]', '[1837, 1837, -3*w^2 + 5*w + 6]', '[1837, 1837, 2*w^3 - 6*w^2 - 8*w + 13]', '[1841, 1841, -4*w^3 + 7*w^2 + 12*w + 5]', '[1841, 1841, 5*w^2 - 13*w - 7]', '[1841, 1841, 3*w^2 - 5*w - 7]', '[1841, 1841, -5*w^3 + 7*w^2 + 23*w - 3]', '[1843, 1843, 5*w^3 - 7*w^2 - 21*w - 1]', '[1843, 1843, -5*w^3 + 5*w^2 + 22*w + 2]', '[1849, 43, -w^3 + 5*w^2 - 2*w - 9]', '[1849, 43, 3*w^2 - 2*w - 6]', '[1851, 1851, -5*w^3 + 6*w^2 + 24*w + 1]', '[1851, 1851, w^3 + w^2 - 2*w - 5]', '[1859, 1859, 3*w^2 - 2*w - 7]', '[1859, 1859, -w^3 + 2*w^2 - w + 4]', '[1861, 1861, -w^2 + 2*w - 5]', '[1863, 69, -3*w^2 + 3*w + 9]', '[1863, 69, -3*w^2 + 9]', '[1863, 1863, 2*w^3 - 5*w^2 - 9*w + 13]', '[1863, 1863, 3*w^3 - 9*w^2 - 5*w + 13]', '[1867, 1867, w^3 - 2*w^2 - 2*w - 6]', '[1867, 1867, 5*w^3 - 7*w^2 - 24*w + 4]', '[1867, 1867, -2*w^3 + 5*w^2 + 2*w - 7]', '[1867, 1867, 6*w^3 - 13*w^2 - 18*w + 12]', '[1869, 1869, 2*w^3 - 7*w^2 - 2*w + 13]', '[1871, 1871, 2*w^2 - w - 11]', '[1872, 234, 2*w^3 - 6*w^2 - 8*w + 6]', '[1873, 1873, -w^3 + 5*w^2 - 2*w - 6]', '[1873, 1873, -w^3 + 2*w^2 + 8*w - 3]', '[1875, 15, -5*w - 5]', '[1877, 1877, -4*w^3 + 4*w^2 + 21*w + 2]', '[1879, 1879, 4*w - 7]', '[1879, 1879, 5*w^3 - 9*w^2 - 22*w + 5]', '[1879, 1879, 3*w^2 - 3*w - 5]', '[1879, 1879, -3*w^3 + 7*w^2 + 12*w - 20]', '[1881, 1881, w^3 - 2*w^2 - 5*w + 10]', '[1881, 1881, 4*w^3 - 6*w^2 - 15*w + 4]', '[1893, 1893, w^3 - 3*w^2 - 8*w - 4]', '[1897, 1897, -3*w^3 + 5*w^2 + 15*w - 4]', '[1897, 1897, -4*w^3 + 7*w^2 + 16*w - 11]', '[1899, 1899, -2*w^3 + 7*w^2 + w - 14]', '[1901, 1901, 3*w^2 - 4*w - 5]', '[1907, 1907, -2*w^3 + 8*w^2 - 2*w - 11]', '[1909, 1909, -2*w^3 + 5*w^2 + 3*w - 9]', '[1909, 1909, -2*w^3 + 3*w^2 + 6*w - 9]', '[1911, 1911, 3*w^3 - 6*w^2 - 10*w + 14]', '[1923, 1923, -4*w^3 + 5*w^2 + 14*w - 4]', '[1923, 1923, -3*w^3 + 6*w^2 + 16*w + 1]', '[1929, 1929, w^3 - w^2 - 6*w - 7]', '[1931, 1931, -w^3 + 4*w - 5]', '[1933, 1933, -w^3 + 4*w^2 - w - 11]', '[1933, 1933, w^3 - 4*w - 7]', '[1933, 1933, 6*w^3 - 16*w^2 - 9*w + 12]', '[1933, 1933, -4*w^2 + 13*w - 6]', '[1936, 22, 4*w^3 - 6*w^2 - 14*w + 6]', '[1936, 22, 4*w^3 - 10*w^2 - 6*w + 4]', '[1936, 242, 2*w^3 - 4*w^2 - 8*w + 12]', '[1936, 242, -2*w^3 + 2*w^2 + 10*w - 4]', '[1937, 1937, -5*w^3 + 8*w^2 + 20*w - 4]', '[1939, 1939, -2*w^3 + 2*w^2 + 11*w - 4]', '[1941, 1941, 5*w^3 - 7*w^2 - 21*w]', '[1941, 1941, 2*w^3 - 2*w^2 - 8*w - 7]', '[1943, 1943, -4*w^2 + 7*w + 13]', '[1943, 1943, 3*w^3 - 8*w^2 - 11*w + 10]', '[1943, 1943, -w^3 + 7*w^2 - 8*w - 11]', '[1943, 1943, 2*w^3 - 12*w - 5]', '[1949, 1949, 2*w^3 - 2*w^2 - 12*w + 5]', '[1949, 1949, -w^3 + 2*w^2 - w - 5]', '[1951, 1951, -3*w^3 + 6*w^2 + 15*w - 4]', '[1951, 1951, 4*w^3 - 8*w^2 - 10*w + 13]', '[1957, 1957, -4*w^3 + 7*w^2 + 16*w + 1]', '[1957, 1957, 3*w^3 - 5*w^2 - 15*w + 6]', '[1963, 1963, 6*w^3 - 8*w^2 - 30*w + 1]', '[1963, 1963, 4*w^3 - 10*w^2 - 8*w + 5]', '[1969, 1969, -2*w^3 + 2*w^2 + 8*w + 9]', '[1969, 1969, 4*w^3 - 11*w^2 - 11*w + 21]', '[1969, 1969, 2*w^3 - 2*w^2 - 15*w + 8]', '[1969, 1969, -3*w^2 + 4*w + 9]', '[1973, 1973, -w^3 - w^2 + 13*w - 1]', '[1979, 1979, 3*w^3 - 6*w^2 - 12*w - 1]', '[1979, 1979, 4*w^3 - 6*w^2 - 20*w + 9]', '[1981, 1981, -w^3 + 5*w^2 - 3*w - 11]', '[1983, 1983, -2*w^3 + w^2 + 12*w]', '[1983, 1983, 4*w^3 - 4*w^2 - 15*w - 1]', '[1991, 1991, 3*w^3 - 6*w^2 - 12*w + 2]', '[1991, 1991, 4*w^3 - 3*w^2 - 26*w - 5]', '[1993, 1993, 2*w^2 - 5*w - 9]', '[2001, 2001, 2*w^3 - 3*w^2 - 12*w + 5]', '[2001, 2001, -3*w^3 + 6*w^2 + 14*w - 7]', '[2001, 2001, 4*w^3 - 9*w^2 - 11*w + 5]', '[2001, 2001, -4*w^3 + 8*w^2 + 15*w - 6]', '[2007, 2007, -3*w^3 + 6*w^2 + 14*w - 10]', '[2007, 2007, -3*w^3 + 4*w^2 + 19*w - 12]', '[2007, 2007, -w^3 - w^2 + 3*w + 6]', '[2007, 2007, 2*w^3 - 3*w^2 - 12*w + 2]', '[2013, 2013, -3*w^2 - w + 8]', '[2013, 2013, -w^3 + 5*w^2 - 6]', '[2027, 2027, -w^3 - w^2 + 13*w - 6]', '[2027, 2027, -7*w^3 + 17*w^2 + 18*w - 19]', '[2027, 2027, -3*w^3 + 8*w^2 + 11*w - 17]', '[2027, 2027, 5*w^3 - 9*w^2 - 18*w + 4]', '[2031, 2031, -3*w^3 + 2*w^2 + 5*w - 9]', '[2032, 254, -4*w^3 + 8*w^2 + 12*w - 10]', '[2037, 2037, 5*w^3 - 8*w^2 - 26*w - 4]', '[2037, 2037, -5*w^3 + 6*w^2 + 27*w + 4]', '[2039, 2039, -3*w^3 + 4*w^2 + 15*w - 5]', '[2043, 2043, 3*w^3 - 7*w^2 - 10*w + 6]', '[2047, 2047, w^2 + 2*w - 7]', '[2047, 2047, 8*w^3 - 17*w^2 - 27*w + 26]', '[2049, 2049, 2*w^3 - 5*w^2 - 10*w]', '[2049, 2049, 2*w^3 - 5*w^2 - 18*w - 8]', '[2061, 2061, -3*w^3 + 6*w^2 + 7*w - 5]', '[2061, 2061, -2*w^3 + 4*w^2 + 11*w - 4]', '[2079, 231, -2*w^3 + 3*w^2 + 5*w + 4]', '[2079, 231, 2*w^3 - 11*w - 7]', '[2079, 2079, -3*w^3 + 5*w^2 + 16*w - 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w^2 - 15*w - 9]', '[4871, 4871, 4*w^2 - 7*w - 10]', '[4871, 4871, 6*w^3 - 11*w^2 - 21*w - 2]', '[4883, 4883, -2*w^3 + 2*w^2 + 14*w + 11]', '[4887, 543, -4*w^3 + 3*w^2 + 19*w + 2]', '[4887, 4887, -w^3 - 2*w^2 + 13*w - 1]', '[4893, 4893, 4*w^3 - 2*w^2 - 24*w - 9]', '[4901, 4901, -2*w^3 + 8*w^2 - w - 12]', '[4901, 4901, 4*w^3 - 7*w^2 - 11*w + 8]', '[4903, 4903, -3*w^3 + 11*w^2 - 2*w - 14]', '[4903, 4903, 4*w^2 - 15*w + 6]', '[4907, 4907, -w^3 + 10*w^2 - 13*w - 23]', '[4907, 4907, w^3 - 7*w^2 + 8*w + 9]', '[4907, 4907, -3*w^3 + 3*w^2 + 14*w - 3]', '[4907, 4907, -3*w^3 + 8*w^2 + 11*w - 22]', '[4911, 4911, -3*w^3 + 10*w^2 + 3*w - 16]', '[4911, 4911, 3*w^3 - 4*w^2 - 16*w + 12]', '[4912, 614, -2*w^3 + 6*w^2 + 2*w - 16]', '[4917, 4917, -w^3 - 4*w^2 + 4*w + 13]', '[4917, 4917, 4*w^2 - 2*w - 9]', '[4919, 4919, -2*w^3 + 3*w^2 + 4*w - 11]', '[4923, 4923, 3*w^3 - 2*w^2 - 10*w - 5]', '[4923, 4923, -2*w^3 + w^2 + 17*w - 4]', '[4927, 4927, 7*w^3 - 17*w^2 - 13*w + 4]', '[4927, 4927, w^3 + w^2 - 14*w + 2]', '[4933, 4933, -w^3 + 3*w^2 + 7*w - 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3]', '[5159, 5159, 3*w^3 - 3*w^2 - 18*w + 5]', '[5159, 5159, 7*w^3 - 10*w^2 - 34*w + 2]', '[5161, 5161, 4*w^3 - 10*w^2 - 3*w - 6]', '[5163, 5163, -5*w^3 + 6*w^2 + 19*w + 2]', '[5167, 5167, 8*w^3 - 15*w^2 - 35*w + 28]', '[5167, 5167, -6*w^3 + 14*w^2 + 15*w - 15]', '[5169, 5169, 2*w^3 - 3*w^2 - 16*w - 11]', '[5169, 5169, -2*w^3 + 2*w^2 + w - 9]', '[5173, 5173, 6*w^3 - 13*w^2 - 15*w - 4]', '[5173, 5173, -6*w^3 + 13*w^2 + 16*w - 7]', '[5179, 5179, -3*w^3 + 7*w^2 + 11*w - 3]', '[5187, 5187, -2*w^3 + 4*w^2 + w + 4]', '[5191, 5191, -2*w^3 - w^2 + 19*w + 1]', '[5191, 5191, -3*w^3 + 3*w^2 + 19*w - 7]', '[5191, 5191, 4*w^3 - 8*w^2 - 17*w + 21]', '[5191, 5191, 5*w^3 - 8*w^2 - 22*w + 10]', '[5193, 5193, -6*w^3 + 14*w^2 + 13*w - 16]', '[5193, 5193, -5*w^3 + 11*w^2 + 13*w - 12]', '[5199, 5199, -4*w^3 + 3*w^2 + 10*w - 3]', '[5199, 5199, -5*w^3 + 5*w^2 + 24*w + 2]', '[5209, 5209, w^3 - 2*w^2 - w - 9]', '[5209, 5209, -4*w^3 + 5*w^2 + 13*w - 3]', '[5221, 5221, 4*w^3 - 8*w^2 - 20*w + 5]', '[5221, 5221, 3*w^3 - 9*w^2 - 16*w + 7]', '[5229, 5229, -3*w^3 + 10*w^2 + 8*w - 14]', '[5233, 5233, 3*w^3 - 2*w^2 - 22*w + 6]', '[5237, 5237, -6*w^3 + 14*w^2 + 17*w - 14]', '[5241, 5241, -3*w^3 + 3*w^2 + 8*w - 10]', '[5241, 5241, w^3 - w^2 - 11*w - 6]', '[5249, 5249, 4*w^3 - 9*w^2 - 9*w - 4]', '[5249, 5249, -3*w^3 + 5*w^2 + 13*w + 6]', '[5257, 5257, -w^3 + 2*w^2 + 6*w - 13]', '[5261, 5261, 5*w^3 - 7*w^2 - 28*w + 15]', '[5261, 5261, -3*w^3 + 3*w^2 + 16*w - 3]', '[5263, 5263, 2*w^3 - 5*w^2 - 12*w + 5]', '[5264, 658, -2*w^3 - 2*w^2 + 22*w + 2]', '[5264, 658, -6*w^3 + 12*w^2 + 20*w - 14]', '[5267, 5267, -5*w^3 + 4*w^2 + 14*w - 5]', '[5267, 5267, -4*w^3 + 4*w^2 + 15*w - 4]', '[5267, 5267, 3*w^3 - 3*w^2 - 16*w - 11]', '[5267, 5267, 4*w^3 - 2*w^2 - 26*w - 13]', '[5269, 5269, 5*w^3 - 10*w^2 - 20*w + 8]', '[5269, 5269, -4*w^3 + w^2 + 19*w + 13]', '[5271, 5271, -2*w^3 + 4*w^2 + 13*w - 2]', '[5273, 5273, 5*w^3 - 13*w^2 - 19*w + 18]', '[5273, 5273, -4*w^3 + 7*w^2 + 20*w - 4]', '[5273, 5273, -4*w^3 + 8*w^2 + 9*w - 8]', '[5273, 5273, 3*w^3 - 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7*w - 12]', '[5349, 5349, -w^2 - w - 6]', '[5357, 5357, 10*w^3 - 13*w^2 - 42*w + 4]', '[5357, 5357, 8*w^3 - 17*w^2 - 32*w + 31]', '[5357, 5357, 4*w^3 - 12*w^2 - 12*w + 23]', '[5357, 5357, 2*w^3 - 7*w^2 - w + 21]', '[5359, 5359, -5*w^3 + 7*w^2 + 19*w - 3]', '[5359, 5359, -5*w^3 + 6*w^2 + 24*w - 1]', '[5361, 5361, -8*w^3 + 9*w^2 + 31*w - 4]', '[5361, 5361, 5*w^3 - 11*w^2 - 13*w + 9]', '[5367, 5367, -w^3 + 2*w^2 - 2*w - 8]', '[5373, 597, -w^3 + 6*w^2 - 2*w - 16]', '[5373, 5373, w^3 - w^2 - 11*w - 9]', '[5376, 84, 4*w^3 - 4*w^2 - 20*w]', '[5377, 5377, -4*w^2 + 5*w + 13]', '[5379, 5379, -3*w^3 + 4*w^2 + 15*w - 10]', '[5379, 5379, 6*w^3 - 11*w^2 - 20*w + 15]', '[5387, 5387, -4*w^3 + 6*w^2 + 21*w - 2]', '[5391, 5391, -6*w^3 + 16*w^2 + 15*w - 19]', '[5397, 5397, 5*w^3 - 3*w^2 - 25*w - 11]', '[5399, 5399, 2*w^3 - 7*w^2 - 2*w + 23]', '[5399, 5399, -2*w^3 + 15*w]', '[5401, 5401, 3*w^3 - 5*w^2 - 17*w + 11]', '[5401, 5401, -4*w^2 + 3*w + 11]', '[5407, 5407, -2*w^3 + 6*w^2 + w - 11]', '[5411, 5411, 3*w^3 - 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17*w + 26]', '[5489, 5489, -w^3 + w^2 + 4*w + 10]', '[5489, 5489, 4*w^3 - 10*w^2 - 23*w + 4]', '[5493, 5493, -w^3 + 2*w^2 + 9*w - 12]', '[5493, 5493, -w^3 + 4*w^2 + 5*w - 12]', '[5499, 5499, -4*w^3 + 13*w^2 + 17*w - 18]', '[5499, 5499, -w^3 + 2*w^2 + 10*w - 2]', '[5507, 5507, -4*w^3 + 7*w^2 + 12*w - 6]', '[5507, 5507, w^3 + 3*w^2 - 18*w + 3]', '[5509, 5509, -4*w^3 + 8*w^2 + 15*w - 2]', '[5511, 5511, 3*w^3 - 7*w^2 - 15*w + 13]', '[5511, 5511, -6*w^2 - w + 11]', '[5519, 5519, w^3 + w^2 - 5*w - 19]', '[5523, 5523, 5*w^3 - 8*w^2 - 20*w - 7]', '[5523, 5523, 3*w^3 - 2*w^2 - 12*w - 7]', '[5523, 5523, -5*w^3 + 3*w^2 + 29*w + 9]', '[5523, 5523, -8*w^3 + 10*w^2 + 35*w + 2]', '[5529, 5529, -3*w^3 + 3*w^2 + 4*w - 11]', '[5529, 5529, 2*w^3 - 4*w^2 - 5*w + 13]', '[5533, 5533, -w^3 - 3*w^2 + 3*w + 10]', '[5533, 5533, 4*w^3 - 10*w^2 - 13*w + 11]', '[5547, 129, 2*w^3 - w^2 - 8*w - 8]', '[5547, 129, 3*w^3 + w^2 - 8*w - 6]', '[5551, 5551, -3*w^3 + 7*w^2 + 15*w - 8]', '[5552, 694, -6*w^3 + 10*w^2 + 28*w - 16]', '[5553, 5553, -7*w^3 + 15*w^2 + 21*w - 10]', '[5553, 5553, -4*w^3 + 11*w^2 + 5*w - 13]', '[5557, 5557, w^2 - 2*w - 11]', '[5557, 5557, -5*w^3 + 6*w^2 + 22*w - 2]', '[5561, 5561, -w^3 + w^2 + 11*w - 5]', '[5561, 5561, -4*w^3 + 5*w^2 + 18*w - 4]', '[5573, 5573, -5*w^3 + 9*w^2 + 23*w - 13]', '[5573, 5573, 4*w^3 - 7*w^2 - 11*w + 1]', '[5573, 5573, 2*w^3 - 6*w^2 + 9]', '[5573, 5573, 3*w^2 - 11]', '[5577, 5577, -4*w^3 + 3*w^2 + 24*w + 2]', '[5577, 5577, -5*w^3 + 9*w^2 + 17*w - 9]', '[5579, 5579, 7*w^3 - 10*w^2 - 29*w - 11]', '[5579, 5579, -2*w^3 + 8*w^2 - w - 10]', '[5581, 5581, 6*w^3 - 10*w^2 - 21*w + 12]', '[5583, 5583, -w^3 + w^2 - 3*w - 5]', '[5589, 207, 6*w^3 - 9*w^2 - 24*w]', '[5589, 207, -3*w^2 + 12*w - 3]', '[5589, 5589, w^3 - 6*w^2 - 2*w + 11]', '[5589, 5589, -2*w^2 - w + 10]', '[5591, 5591, w^3 + w^2 - 3*w - 8]', '[5601, 5601, -w^3 - w^2 + w - 5]', '[5601, 5601, 8*w^3 - 11*w^2 - 35*w - 1]', '[5601, 5601, 5*w^3 - 7*w^2 - 24*w + 6]', '[5601, 5601, w^3 - 11*w - 7]', '[5607, 5607, -w^3 - 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7*w - 12]', '[5701, 5701, -w^3 + 4*w^2 - 4*w - 7]', '[5703, 5703, 3*w^3 - w^2 - 9*w - 5]', '[5707, 5707, -w^3 - 3*w^2 + 17*w - 1]', '[5711, 5711, -3*w^3 + 21*w + 4]', '[5711, 5711, -2*w^3 + 4*w^2 + 6*w - 13]', '[5721, 5721, 2*w^3 - 2*w^2 - 7*w - 9]', '[5727, 5727, -4*w^3 + 9*w^2 + 12*w - 4]', '[5727, 5727, -2*w^3 + 11*w^2 - 14*w + 3]', '[5733, 5733, 5*w^3 - 11*w^2 - 15*w + 7]', '[5737, 5737, -w^3 + 3*w^2 + 6*w - 14]', '[5737, 5737, -4*w^3 + 3*w^2 + 27*w]', '[5741, 5741, -5*w^3 + 11*w^2 + 13*w - 10]', '[5744, 718, 4*w^3 - 8*w^2 - 10*w + 4]', '[5747, 5747, -5*w^3 + 9*w^2 + 16*w + 7]', '[5749, 5749, 3*w^3 - 16*w - 12]', '[5749, 5749, w^3 - 4*w^2 - 7*w + 11]', '[5769, 5769, -3*w^3 + 3*w^2 + 17*w - 4]', '[5769, 5769, -5*w^3 + 10*w^2 + 22*w - 17]', '[5771, 5771, -8*w^3 + 9*w^2 + 35*w + 5]', '[5771, 5771, 4*w^3 - 8*w^2 - 9*w + 19]', '[5773, 5773, -3*w^3 + 3*w^2 + 6*w - 11]', '[5773, 5773, -2*w^3 + 4*w^2 + 2*w - 11]', '[5776, 722, -2*w^3 + 2*w^2 + 12*w + 10]', '[5787, 5787, -4*w^3 + 13*w^2 + 3*w - 17]', '[5793, 5793, -3*w^3 + 2*w - 4]', '[5799, 5799, 3*w^3 - 14*w - 8]', '[5799, 5799, w^3 - w^2 - 9*w - 10]', '[5799, 5799, -2*w^3 + w^2 + 15*w - 6]', '[5799, 5799, -4*w^3 + 9*w^2 + 7*w - 6]', '[5801, 5801, -w^3 + 6*w^2 - 4*w - 10]', '[5808, 66, -2*w^2 + 4*w - 6]', '[5808, 66, 2*w^3 - 14*w]', '[5808, 726, 2*w^3 - 4*w^2 - 2*w + 10]', '[5808, 726, 2*w^3 - 8*w^2 - 4*w + 18]', '[5811, 5811, -6*w^3 + 13*w^2 + 19*w - 27]', '[5817, 5817, -4*w^3 + 5*w^2 + 13*w - 2]', '[5819, 253, 5*w^3 - 9*w^2 - 16*w + 11]', '[5819, 253, -8*w^3 + 8*w^2 + 33*w + 3]', '[5819, 253, 3*w^3 - 2*w^2 - 18*w]', '[5819, 253, w^3 - w^2 - 7*w - 9]', '[5819, 5819, 4*w^3 - 6*w^2 - 13*w + 2]', '[5819, 5819, 4*w^3 - 6*w^2 - 18*w + 9]', '[5819, 5819, -5*w + 12]', '[5819, 5819, 6*w^3 - 11*w^2 - 19*w]', '[5821, 5821, -4*w^3 + 9*w^2 + 15*w - 8]', '[5823, 5823, 4*w^3 - 5*w^2 - 24*w + 9]', '[5823, 5823, -5*w^3 + 12*w^2 + 17*w - 15]', '[5827, 5827, -3*w^2 + 10*w - 9]', '[5827, 5827, 10*w^3 - 23*w^2 - 31*w + 31]', '[5829, 5829, 9*w^3 - 19*w^2 - 35*w + 32]', '[5829, 5829, -w^3 + 2*w^2 + 2*w + 8]', '[5829, 5829, 4*w^3 - 5*w^2 - 16*w - 10]', '[5829, 5829, -w^3 + 4*w^2 + 9*w - 5]', '[5833, 5833, 6*w^3 - 11*w^2 - 27*w + 9]', '[5837, 5837, 2*w^3 - 3*w^2 - 8*w - 8]', '[5839, 5839, -w^3 + 2*w^2 + 5*w - 12]', '[5847, 5847, -2*w^3 + 19*w + 2]', '[5847, 5847, 4*w^3 - 6*w^2 - 13*w + 3]', '[5853, 5853, -3*w^3 + 9*w^2 + 20*w - 1]', '[5853, 5853, 4*w^3 - 2*w^2 - 9*w + 9]', '[5871, 5871, 2*w^2 + 2*w - 9]', '[5871, 5871, 7*w^3 - 18*w^2 - 22*w + 30]', '[5872, 734, 4*w^2 - 14*w + 2]', '[5872, 734, -2*w^3 + 6*w^2 + 8*w - 16]', '[5872, 734, 6*w^2 - 12*w - 16]', '[5872, 734, -6*w^3 + 12*w^2 + 22*w - 10]', '[5873, 5873, 6*w^3 - 16*w^2 - 17*w + 24]', '[5873, 5873, -7*w^3 + 20*w^2 + 10*w - 24]', '[5881, 5881, -w^3 + 4*w^2 + 4*w - 14]', '[5881, 5881, 2*w^3 - 3*w^2 - 7*w - 9]', '[5887, 203, -w^3 + 4*w^2 - 3*w - 9]', '[5887, 203, w^3 - 8*w^2 + 11*w + 13]', '[5887, 5887, 2*w^3 - 8*w^2 + 5*w + 8]', '[5887, 5887, w^3 - 3*w^2 + 2*w + 11]', '[5888, 92, -4*w^2 + 4*w + 12]', '[5888, 92, -4*w^2 + 12]', '[5889, 5889, 5*w^3 - 14*w^2 - 13*w + 27]', '[5889, 5889, 3*w^3 - 6*w^2 - 17*w + 19]', '[5897, 5897, w^3 - w^2 - 6*w - 9]', '[5897, 5897, -w^3 + 6*w^2 - w - 16]', '[5903, 5903, 5*w^3 - 11*w^2 - 11*w + 3]', '[5907, 5907, w^3 - 6*w^2 - 2*w + 17]', '[5907, 5907, w^3 - 7*w^2 + 14*w - 2]', '[5907, 5907, 7*w^3 - 16*w^2 - 23*w + 21]', '[5907, 5907, 4*w^3 - 9*w^2 - 13*w + 6]', '[5909, 5909, 3*w^3 - 2*w^2 - 22*w - 3]', '[5911, 5911, -7*w^3 + 8*w^2 + 25*w - 6]', '[5911, 5911, -7*w^3 + 9*w^2 + 29*w - 4]', '[5917, 5917, -9*w^3 + 22*w^2 + 23*w - 25]', '[5917, 5917, -4*w^3 + 5*w^2 + 19*w - 4]', '[5919, 5919, -4*w^3 + 8*w^2 + 15*w]', '[5923, 5923, -3*w^3 + w^2 + 24*w + 1]', '[5927, 5927, -3*w^3 + 9*w^2 + 3*w - 14]', '[5929, 539, 2*w^3 + w^2 - 15*w - 7]', '[5929, 539, w^3 - 6*w^2 + 4*w + 9]', '[5929, 5929, 5*w^3 - 11*w^2 - 21*w + 17]', '[5929, 5929, 3*w^2 + w - 10]', '[5937, 5937, 6*w^3 - 10*w^2 - 23*w + 5]', '[5937, 5937, 3*w^3 - 6*w^2 - 22*w - 4]', '[5939, 5939, -2*w^3 + 2*w^2 + 5*w - 9]', '[5939, 5939, w^3 - w^2 + 9]', '[5941, 5941, 5*w^3 - 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7*w + 13]', '[2179, 2179, -w^3 + 4*w^2 - 3*w - 6]', '[2197, 13, 5*w^3 - 12*w^2 - 10*w + 6]', '[2203, 2203, 3*w^2 - 4*w - 6]', '[2207, 2207, 2*w^3 - 7*w^2 + w + 9]', '[2209, 47, -w^3 + 4*w^2 - 2*w - 8]', '[2213, 2213, -3*w^3 + 2*w^2 + 18*w + 2]', '[2221, 2221, -2*w^3 + 2*w^2 + 10*w - 5]', '[2237, 2237, 3*w^2 - 4*w - 8]', '[2237, 2237, -3*w^3 + 6*w^2 + 14*w - 8]', '[2243, 2243, -w^3 + 3*w^2 + 5*w - 12]', '[2273, 2273, -3*w^3 + 4*w^2 + 8*w - 4]', '[2287, 2287, 4*w^3 - 8*w^2 - 18*w + 5]', '[2287, 2287, -3*w^3 + 6*w^2 + 14*w - 18]', '[2309, 2309, -2*w^3 + 5*w^2 + 7]', '[2311, 2311, -w^3 + 5*w^2 - w - 11]', '[2311, 2311, 3*w^3 - 5*w^2 - 12*w - 5]', '[2333, 2333, -3*w^3 + 4*w^2 + 13*w - 5]', '[2333, 2333, w^2 - 5*w - 8]', '[2347, 2347, -w^2 + 7*w - 8]', '[2347, 2347, 4*w^3 - 7*w^2 - 16*w + 12]', '[2351, 2351, 5*w^3 - 13*w^2 - 8*w + 6]', '[2351, 2351, -4*w^3 + 7*w^2 + 18*w - 1]', '[2357, 2357, -4*w^3 + 8*w^2 + 12*w - 5]', '[2357, 2357, -w^3 + 4*w^2 - w - 16]', '[2371, 2371, -5*w^3 + 7*w^2 + 20*w - 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6]', '[2903, 2903, 2*w^2 - 6*w - 7]', '[2909, 2909, w^3 + w^2 - 11*w + 3]', '[2927, 2927, -3*w^3 + 2*w^2 + 11*w - 2]', '[2927, 2927, -w^3 + 3*w^2 - w - 9]', '[2939, 2939, w^3 - w^2 - 5*w - 8]', '[2953, 2953, 2*w^2 - 10*w + 13]', '[2953, 2953, 4*w^3 - 9*w^2 - 11*w + 4]', '[2957, 2957, 2*w^3 - w^2 - 16*w + 6]', '[2999, 2999, 6*w^3 - 12*w^2 - 20*w + 17]', '[3001, 3001, 4*w^3 - 7*w^2 - 15*w - 5]', '[3001, 3001, 3*w^2 - 8*w - 7]', '[3011, 3011, 3*w^3 - 2*w^2 - 11*w - 5]', '[3023, 3023, -5*w^3 + 8*w^2 + 26*w - 16]', '[3037, 3037, -w^3 + 4*w^2 - 2*w - 9]', '[3037, 3037, -5*w^3 + 9*w^2 + 18*w - 9]', '[3041, 3041, 5*w^3 - 10*w^2 - 15*w + 4]', '[3061, 3061, -5*w^3 + 7*w^2 + 17*w + 3]', '[3061, 3061, -3*w^3 + 6*w^2 + 15*w - 5]', '[3061, 3061, 5*w^3 - 10*w^2 - 16*w + 13]', '[3061, 3061, 5*w^3 - 9*w^2 - 25*w + 21]', '[3067, 3067, -5*w^3 + 12*w^2 + 13*w - 11]', '[3067, 3067, 7*w^3 - 12*w^2 - 27*w + 12]', '[3079, 3079, 3*w^2 - 2*w - 13]', '[3089, 3089, 3*w^3 - 3*w^2 - 19*w + 6]', '[3089, 3089, -2*w^3 + 8*w^2 - 3*w - 11]', '[3089, 3089, 2*w^3 - 5*w^2 - w - 7]', '[3089, 3089, 5*w^3 - 8*w^2 - 17*w + 10]', '[3109, 3109, -5*w^3 + 11*w^2 + 21*w - 14]', '[3119, 3119, 2*w^2 + 3*w - 7]', '[3121, 3121, -w^3 + 5*w^2 - 10]', '[3121, 3121, -3*w^3 + 10*w^2 + 7*w - 23]', '[3137, 3137, -6*w^3 + 17*w^2 + 6*w - 9]', '[3167, 3167, w^3 - w^2 - 4*w - 9]', '[3187, 3187, -7*w^3 + 18*w^2 + 12*w - 12]', '[3187, 3187, -5*w^3 + 10*w^2 + 23*w - 27]', '[3187, 3187, w^3 + 2*w^2 - 14*w + 1]', '[3187, 3187, -4*w^3 + 8*w^2 + 11*w - 3]', '[3203, 3203, 4*w^3 - 7*w^2 - 20*w + 14]', '[3203, 3203, -5*w^3 + 6*w^2 + 28*w - 6]', '[3203, 3203, 6*w^3 - 9*w^2 - 24*w + 8]', '[3203, 3203, -w^3 + 5*w^2 - 9*w + 10]', '[3221, 3221, -3*w^3 + 9*w^2 + 7*w - 16]', '[3221, 3221, -w^3 + 2*w^2 + 4*w - 10]', '[3229, 3229, -4*w^3 + 10*w^2 + 15*w - 21]', '[3229, 3229, 6*w^3 - 11*w^2 - 21*w + 4]', '[3251, 3251, w^3 + 2*w^2 - 10*w - 10]', '[3271, 3271, 3*w^3 - 8*w^2 - 14*w + 11]', '[3299, 3299, 4*w^3 - 7*w^2 - 17*w - 5]', '[3301, 3301, w^2 - 2*w - 10]', '[3307, 3307, -4*w^3 + 9*w^2 + 13*w - 8]', '[3313, 3313, -4*w^3 + 9*w^2 + 8*w - 3]', '[3313, 3313, w^3 - 10*w - 7]', '[3323, 3323, 5*w^3 - 7*w^2 - 20*w + 2]', '[3331, 3331, -4*w^3 + 6*w^2 + 19*w - 8]', '[3343, 3343, -3*w^3 + 4*w^2 + 14*w - 6]', '[3343, 3343, 3*w^3 - 4*w^2 - 18*w + 8]', '[3347, 3347, 2*w^3 - 7*w^2 - 9*w + 14]', '[3361, 3361, -2*w^3 + 7*w^2 + 3*w - 11]', '[3373, 3373, -2*w^3 + 7*w^2 + 4*w - 13]', '[3391, 3391, -3*w^3 + 8*w^2 + 7*w - 5]', '[3407, 3407, -3*w^3 + 5*w^2 + 16*w - 9]', '[3449, 3449, -w^3 + w^2 + 10*w - 2]', '[3457, 3457, 4*w^2 - 8*w - 7]', '[3457, 3457, w^3 - 2*w^2 - 2*w - 7]', '[3467, 3467, -5*w^3 + 7*w^2 + 20*w + 1]', '[3469, 3469, -w^3 + 2*w^2 + 5*w - 11]', '[3469, 3469, -2*w^3 + 7*w^2 + 4*w - 12]', '[3481, 59, w^3 - 3*w - 7]', '[3481, 59, w^2 + 2*w - 9]', '[3491, 3491, -4*w^3 + 8*w^2 + 20*w - 23]', '[3499, 3499, -5*w^3 + 11*w^2 + 14*w - 21]', '[3527, 3527, w^3 + 2*w^2 - 10*w - 6]', '[3529, 3529, -4*w^3 + 10*w^2 + 11*w - 10]', '[3533, 3533, -4*w^3 + 7*w^2 + 19*w - 6]', '[3539, 3539, 5*w^3 - 11*w^2 - 21*w + 26]', '[3547, 3547, -2*w^3 + 5*w^2 + w - 7]', '[3559, 3559, -w^3 - w^2 + 3*w + 7]', '[3571, 3571, -3*w^3 + 3*w^2 + 14*w - 2]', '[3581, 3581, w^3 - w^2 - 5]', '[3581, 3581, -5*w^3 + 8*w^2 + 17*w + 2]', '[3593, 3593, -4*w^3 + 8*w^2 + 17*w - 5]', '[3607, 3607, -w^3 + 3*w^2 + 6*w - 11]', '[3617, 3617, -6*w^3 + 10*w^2 + 30*w - 21]', '[3631, 3631, 5*w^2 - 10*w - 13]', '[3637, 3637, 2*w^3 + w^2 - 19*w - 8]', '[3643, 3643, -4*w^3 + 7*w^2 + 21*w - 1]', '[3643, 3643, 3*w^2 - 3*w - 19]', '[3659, 3659, 2*w^3 + w^2 - 18*w - 10]', '[3671, 3671, 4*w^3 - 8*w^2 - 14*w - 1]', '[3677, 3677, -3*w^3 + 7*w^2 + 6*w - 12]', '[3677, 3677, -3*w^3 + 4*w^2 + 13*w - 7]', '[3691, 3691, 2*w^3 - 17*w + 1]', '[3691, 3691, -5*w^3 + 10*w^2 + 16*w - 12]', '[3697, 3697, -5*w^3 + 16*w^2 + 2*w - 17]', '[3701, 3701, 2*w^3 - 18*w + 3]', '[3709, 3709, w^3 - 4*w - 10]', '[3727, 3727, 6*w^3 - 11*w^2 - 26*w + 11]', '[3767, 3767, 7*w^3 - 18*w^2 - 15*w + 18]', '[3767, 3767, -w^3 - 2*w^2 + 7*w + 9]', '[3779, 3779, 7*w^3 - 14*w^2 - 28*w + 15]', '[3779, 3779, -3*w^3 + 5*w^2 + 16*w - 3]', '[3797, 3797, -7*w^3 + 19*w^2 + 14*w - 23]', '[3821, 3821, -3*w^3 + 10*w^2 + 2*w - 13]', '[3821, 3821, -6*w^3 + 10*w^2 + 24*w + 1]', '[3851, 3851, -4*w^3 + 8*w^2 + 15*w - 4]', '[3863, 3863, -w^3 + 5*w^2 - 7*w - 5]', '[3863, 3863, -2*w^3 + 8*w^2 - w - 13]', '[3881, 3881, -3*w^3 + 7*w^2 + 12*w - 5]', '[3881, 3881, 4*w^3 - 5*w^2 - 23*w + 9]', '[3889, 3889, 4*w^3 - 8*w^2 - 18*w + 13]', '[3889, 3889, w^3 - w^2 - 11*w - 5]', '[3907, 3907, -7*w^3 + 20*w^2 + 10*w - 21]', '[3911, 3911, 4*w^3 - 7*w^2 - 13*w + 3]', '[3917, 3917, 3*w^3 - 2*w^2 - 22*w + 3]', '[3917, 3917, 6*w^3 - 11*w^2 - 27*w + 22]', '[3923, 3923, -3*w^3 + 8*w^2 + 11*w - 19]', '[3923, 3923, -3*w^3 + 9*w^2 + 9*w - 22]', '[3931, 3931, -5*w^3 + 8*w^2 + 21*w - 9]', '[3943, 3943, -5*w^3 + 10*w^2 + 18*w - 7]', '[3989, 3989, 7*w^3 - 13*w^2 - 30*w + 22]', '[3989, 3989, -w^2 + 4*w - 8]']}
• nf_fields •

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

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 3, -4, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 11197, 'disc_rad': 11197, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[3, 1], [1, 1]]], [5, [[4, 1]]], [7, [[3, 1], [1, 1]]], [11, [[2, 1], [1, 2]]], [13, [[3, 1], [1, 1]]], [17, [[4, 1]]], [19, [[3, 1], [1, 1]]], [23, [[2, 1], [1, 2]]], [29, [[2, 1], [1, 2]]], [31, [[4, 1]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[2, 1], [1, 2]]], [53, [[4, 1]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12], 'galois_label': '4T5', 'galt': 5, 'grd': 105.8158778255891, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.11197.1', 'local_algs': ['m11197.1.1.0', 'm11197.1.1.0', 'm11197.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [11197], 'rd': 10.2866844914, 'regulator': {'__RealLiteral__': 0, 'data': '5.67295698421', 'prec': 44}, 'res': {'gal': ['-96336,80568,6512340,13036642,-37412473,-65538308,91068555,111754924,-124883636,-79806354,97786367,19927508,-40515976,1781916,8764120,-1742086,-932931,314428,36818,-23802,659,748,-68,-8,1'], 'sib': ['-4,0,25,0,-11,0,1', '1,14,-1,-221,162,443,-336,-289,196,61,-29,-3,1', '1259,-2266,935,75,-67,-1,1', '256,0,-5533,0,30401,0,-10234,0,1195,0,-58,0,1', '437703,28333,-91709,-5293,5770,193,-133,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a - 1 \\)', '\\( a^{2} - 3 a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}