Hilbert modular form data - 3.3.1304.1-9.2-a

Formats: - HTML - YAML - JSON - 2024-05-06T09:18:14.175217

• 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': 3, 'dimension': 2, 'disc': 1304, 'field_bad_primes': [2, 163], 'field_label': '3.3.1304.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1304.1-9.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [3], 'level_ideal': '[9, 9, 1/2*w^2 - 1/2*w - 6]', 'level_label': '9.2', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.2-a', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [], 'hecke_eigenvalues': ['e', 'e', 0, '-2*e + 3', '-3*e + 3', -1, '-4*e + 6', '3*e - 10', 'e + 3', 0, '-2*e + 3', '-3*e + 7', '3*e + 6', '-6*e + 15', '-7*e + 6', '-12*e + 17', -2, '9*e - 15', '-e + 12', '3*e - 6', '7*e - 12', 7, '10*e - 15', '3*e - 3', 'e + 9', '-3*e - 9', '6*e - 20', '3*e - 10', '-5*e + 15', '-8*e + 21', -18, '-6*e + 21', '-10*e + 9', '5*e - 9', '9*e - 18', '2*e + 6', -13, '-e - 9', '-9*e + 24', '6*e - 8', '-6*e + 13', '9*e - 14', '6*e + 2', '-2*e + 9', 8, '3*e - 19', '3*e + 6', '6*e + 3', '-18*e + 24', '-9*e - 6', '3*e - 8', 25, 14, '-3*e + 21', '11*e - 3', '-12*e + 9', '6*e + 11', '-6*e + 27', '4*e - 6', '-18*e + 36', '-12*e + 35', '-3*e + 15', '-6*e - 4', '-9*e + 1', '9*e - 34', '6*e - 18', '4*e - 15', '-21*e + 24', '-21*e + 40', '10*e - 39', '-18*e + 21', '12*e - 3', '18*e - 34', '-18*e + 35', '23*e - 30', -1, '18*e - 19', '-6*e + 9', '5*e - 15', '-6*e + 31', 4, '3*e - 13', '-15*e + 15', '-14*e + 27', '-e + 3', '17*e - 12', 27, '-18*e + 11', '-12*e - 9', '-27*e + 45', '4*e - 39', '-27*e + 50', '-6*e + 7', '-12*e + 27', '9*e - 5', '22*e - 39', '8*e + 15', '6*e + 21', '22*e - 45', '30*e - 46', '-23*e + 45', '3*e - 27', '-6*e + 38', '-18*e + 16', '-16*e + 9', '23*e - 36', '30*e - 36', '18*e - 5', '9*e - 9', '30*e - 54', '-9*e + 44', 16, '-12*e + 15', '-24*e + 42', '15*e - 51', '-7*e + 48', '-36*e + 61', '6*e - 3', '34*e - 48', '3*e - 4', '-4*e + 39', '-12*e + 15', 31, '29*e - 30', -21, '9*e - 21', '-16*e + 33', '-3*e + 39', '18*e - 13', '26*e - 45', '-18*e + 3', '-9*e + 23', '30*e - 57', '12*e - 45', '6*e + 10', '-10*e - 24', '-14*e + 30', '6*e - 21', '15*e - 9', '-9*e + 35', '24*e - 33', '21*e - 3', '12*e - 50', '5*e - 27', '6*e - 12', '15*e - 40', '12*e - 44', '-34*e + 69', '-8*e + 63', '-11*e + 6', '-5*e - 3', '-17*e + 33', '10*e - 12', '9*e - 31', '41*e - 57', '-21*e + 9', '-3*e + 33', '6*e - 43', '18*e - 37', '16*e - 51', '-5*e + 57'], 'hecke_polynomial': 'x^2 - 3*x + 1', 'label': '3.3.1304.1-9.2-a'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 1304, 'ideals': ['[1, 1, 1]', '[2, 2, -w]', '[2, 2, -1/2*w^2 + 3/2*w]', '[3, 3, -w^2 + 3*w + 1]', '[4, 2, 1/2*w^2 - 1/2*w - 7]', '[4, 2, -w^2 + 11]', '[4, 4, 3/2*w^2 - 1/2*w - 17]', '[6, 6, -w^2 + 10]', '[6, 6, -1/2*w^2 - 1/2*w + 4]', '[8, 2, 2]', '[8, 4, -1/2*w^2 + 1/2*w + 5]', '[8, 4, w + 1]', '[8, 8, 1/2*w^2 + 1/2*w - 3]', '[9, 3, w^2 + w - 7]', '[9, 9, 1/2*w^2 - 1/2*w - 6]', '[11, 11, 2*w^2 - 21]', '[12, 6, 1/2*w^2 - 1/2*w - 3]', '[12, 6, w - 1]', '[12, 12, w + 2]', '[16, 4, -2*w]', '[16, 4, -w^2 + 3*w]', '[16, 4, w^2 - 4*w - 1]', '[16, 8, -1/2*w^2 + 1/2*w + 1]', '[16, 16, -w + 2]', '[17, 17, -1/2*w^2 + 5/2*w]', '[18, 6, -1/2*w^2 - 1/2*w + 5]', '[18, 6, -1/2*w^2 - 1/2*w + 2]', '[18, 18, -1/2*w^2 + 3/2*w + 2]', '[18, 18, 1/2*w^2 + 1/2*w - 1]', '[19, 19, -1/2*w^2 + 1/2*w + 2]', '[22, 22, -w - 4]', '[22, 22, -1/2*w^2 - 1/2*w + 6]', '[24, 6, -2*w^2 + 6*w + 2]', '[24, 12, 1/2*w^2 - 5/2*w - 1]', '[24, 12, 2*w^2 - 7*w - 1]', '[24, 24, -1/2*w^2 + 3/2*w - 1]', '[27, 3, 3]', '[27, 27, 2*w + 1]', '[32, 4, w^2 - w - 14]', '[32, 4, -2*w^2 + 22]', '[32, 8, -w^2 + 9]', '[32, 8, 3*w^2 - w - 34]', '[32, 16, -5/2*w^2 + 17/2*w + 1]', '[32, 32, w^2 - 2*w]', '[33, 33, -1/2*w^2 - 3/2*w + 2]', '[34, 34, 3/2*w^2 + 3/2*w - 11]', '[34, 34, -3/2*w^2 + 1/2*w + 18]', '[36, 6, -1/2*w^2 + 5/2*w - 1]', '[36, 6, w^2 - 2*w - 1]', '[36, 12, 1/2*w^2 + 1/2*w + 1]', '[36, 18, -w^2 + 2*w + 17]', '[36, 18, -3/2*w^2 + 7/2*w + 1]', '[36, 36, w^2 - 4*w]', '[37, 37, w^2 - w - 13]', '[37, 37, -1/2*w^2 + 1/2*w + 8]', '[37, 37, 5/2*w^2 - 17/2*w - 2]', '[38, 38, -1/2*w^2 + 7/2*w + 1]', '[38, 38, 5/2*w^2 - 15/2*w - 2]', '[44, 22, 1/2*w^2 - 1/2*w + 1]', '[44, 22, -w^2 + 4*w - 1]', '[44, 44, -1/2*w^2 + 3/2*w + 3]', '[47, 47, -3/2*w^2 + 11/2*w]', '[48, 12, -2*w^2 + 20]', '[48, 12, -w^2 - w + 8]', '[48, 12, w^2 - 13]', '[48, 24, -9/2*w^2 + 1/2*w + 49]', '[48, 48, 5/2*w^2 - 3/2*w - 31]', '[51, 51, 2*w + 7]', '[53, 53, w^2 - w - 7]', '[54, 6, 3*w]', '[54, 6, 3/2*w^2 - 9/2*w]', '[54, 54, -5/2*w^2 + 15/2*w + 1]', '[54, 54, 5/2*w^2 + 1/2*w - 24]', '[57, 57, 2*w^2 - 2*w - 27]', '[59, 59, 2*w - 1]', '[61, 61, -3/2*w^2 + 3/2*w + 20]', '[64, 4, 4]', '[64, 8, -w^2 + w + 10]', '[64, 8, 2*w + 2]', '[64, 8, w^2 - 2*w - 3]', '[64, 16, w^2 + w - 6]', '[64, 32, 3/2*w^2 + 1/2*w - 15]', '[64, 64, 7/2*w^2 - 1/2*w - 37]', '[66, 66, w^2 - 2*w - 2]', '[66, 66, -1/2*w^2 + 7/2*w]', '[67, 67, w^2 - 3*w - 3]', '[68, 34, -1/2*w^2 - 3/2*w + 3]', '[68, 34, w - 5]', '[68, 68, -w^2 + 8]', '[71, 71, w^2 - w - 1]', '[72, 6, 2*w^2 + 2*w - 14]', '[72, 12, 7/2*w^2 + 1/2*w - 35]', '[72, 12, -2*w^2 + w + 23]', '[72, 18, w^2 - w - 12]', '[72, 24, 2*w^2 - 7*w - 2]', '[72, 36, -w - 5]', '[72, 36, 5/2*w^2 - 1/2*w - 29]', '[72, 72, -2*w^2 - w + 18]', '[73, 73, 3*w^2 - w - 33]', '[74, 74, -1/2*w^2 - 1/2*w + 9]', '[74, 74, -1/2*w^2 + 3/2*w - 2]', '[74, 74, -3/2*w^2 + 1/2*w + 14]', '[74, 74, -1/2*w^2 + 3/2*w + 4]', '[74, 74, -1/2*w^2 - 5/2*w + 1]', '[74, 74, 1/2*w^2 - 3/2*w - 9]', '[76, 38, 3/2*w^2 + 1/2*w - 13]', '[76, 38, w^2 + 2*w - 5]', '[76, 76, 3*w^2 - 32]', '[79, 79, w^2 - w - 11]', '[79, 79, w^2 - 3*w + 1]', '[79, 79, -2*w - 5]', '[81, 9, 1/2*w^2 - 5/2*w - 2]', '[81, 9, 3*w^2 - 9*w - 3]', '[81, 81, -3*w^2 + w + 35]', '[88, 22, 4*w^2 - 42]', '[88, 44, 7/2*w^2 - 23/2*w - 3]', '[88, 44, 2*w^2 + w - 17]', '[88, 88, -3/2*w^2 + 5/2*w + 1]', '[89, 89, -2*w - 3]', '[94, 94, 5/2*w^2 + 1/2*w - 25]', '[94, 94, 3/2*w^2 + 3/2*w - 10]', '[96, 12, w^2 - w - 6]', '[96, 12, 2*w - 2]', '[96, 24, 2*w + 4]', '[96, 24, w^2 - 1]', '[96, 48, -1/2*w^2 + 1/2*w + 9]', '[96, 96, -2*w^2 + w + 22]', '[99, 33, -w^2 - w + 1]', '[99, 99, -3/2*w^2 + 11/2*w + 2]', '[101, 101, w^2 + w - 9]', '[101, 101, 3/2*w^2 + 1/2*w - 16]', '[101, 101, -3/2*w^2 + 7/2*w]', '[102, 102, -1/2*w^2 - 1/2*w - 2]', '[102, 102, 1/2*w^2 - 3/2*w - 5]', '[106, 106, w^2 - 4*w - 2]', '[106, 106, -7/2*w^2 + 21/2*w + 4]', '[107, 107, 1/2*w^2 + 3/2*w - 4]', '[108, 6, -3/2*w^2 + 3/2*w + 21]', '[108, 6, 3*w^2 - 33]', '[108, 12, -9/2*w^2 + 3/2*w + 51]', '[108, 54, -3/2*w^2 - 1/2*w + 17]', '[108, 54, -w^2 + 7]', '[108, 108, 1/2*w^2 - 3/2*w - 11]', '[111, 111, 2*w - 5]', '[111, 111, -w^2 - w + 5]', '[111, 111, -3/2*w^2 + 7/2*w + 4]', '[113, 113, -1/2*w^2 + 1/2*w - 2]', '[113, 113, -4*w^2 + 41]', '[113, 113, 3/2*w^2 - 7/2*w - 2]', '[114, 114, -3/2*w^2 + 1/2*w + 19]', '[114, 114, -1/2*w^2 + 3/2*w + 8]', '[118, 118, 7/2*w^2 - 25/2*w - 2]', '[118, 118, -2*w^2 + w]', '[121, 11, 2*w^2 - 8*w - 1]', '[121, 121, -2*w + 3]', '[122, 122, w^2 - 14]', '[122, 122, 1/2*w^2 - 3/2*w - 6]', '[125, 5, -5]', '[128, 8, -4*w]', '[128, 8, -2*w^2 + 6*w]', '[128, 8, 2*w^2 - 8*w - 2]', '[128, 16, 3*w^2 + 2*w - 25]', '[128, 16, -w^2 + w + 2]', '[128, 32, -2*w + 4]', '[128, 64, -1/2*w^2 - 3/2*w - 3]', '[128, 128, 1/2*w^2 - 3/2*w - 7]', '[131, 131, 7/2*w^2 + 9/2*w - 22]', '[131, 131, -3*w^2 + 3*w + 41]', '[131, 131, w^2 - w - 5]', '[132, 66, -11/2*w^2 + 3/2*w + 61]', '[132, 66, -2*w^2 + w + 25]', '[132, 132, 4*w^2 + w - 38]', '[134, 134, 3/2*w^2 - 5/2*w - 24]', '[134, 134, 5*w^2 - 2*w - 58]', '[136, 34, -w^2 + 5*w]', '[136, 68, 3/2*w^2 - 7/2*w - 3]', '[136, 68, 2*w^2 - 3*w - 1]', '[136, 136, 3*w + 2]', '[137, 137, 3*w^2 - 9*w - 1]', '[139, 139, 2*w^2 - 19]', '[141, 141, -w^2 + w + 15]', '[142, 142, -13/2*w^2 + 3/2*w + 73]', '[142, 142, -5/2*w^2 + 3/2*w + 30]', '[144, 12, -w^2 - w + 10]', '[144, 12, -w^2 - w + 4]', '[144, 12, w^2 - 2*w - 7]', '[144, 24, -5/2*w^2 + 1/2*w + 25]', '[144, 36, -w^2 + 3*w + 4]', '[144, 36, w^2 - 2*w + 1]', '[144, 36, w^2 + w - 2]', '[144, 48, w^2 - 2*w - 16]', '[144, 72, 1/2*w^2 + 3/2*w - 5]', '[144, 144, 3/2*w^2 - 1/2*w - 13]', '[146, 146, 1/2*w^2 + 5/2*w - 2]', '[146, 146, w^2 - 6]', '[148, 74, -8*w^2 + w + 87]', '[148, 74, w^2 + 1]', '[148, 74, -3/2*w^2 + 3/2*w + 1]', '[148, 74, 3*w^2 - 10*w - 3]', '[148, 74, -3/2*w^2 + 15/2*w + 1]', '[148, 74, -1/2*w^2 + 5/2*w + 3]', '[148, 148, 1/2*w^2 - 7/2*w + 1]', '[148, 148, 2*w^2 - 5*w - 2]', '[148, 148, -w + 6]', '[151, 151, 3/2*w^2 - 3/2*w - 14]', '[152, 38, -w^2 + w + 4]', '[152, 76, -1/2*w^2 - 3/2*w + 9]', '[152, 76, -3*w + 1]', '[152, 152, -w - 6]', '[153, 51, w^2 + w - 13]', '[153, 153, -w^2 + w + 3]', '[157, 157, 1/2*w^2 + 3/2*w - 12]', '[157, 157, 11/2*w^2 - 3/2*w - 60]', '[157, 157, -1/2*w^2 + 9/2*w]', '[158, 158, -3/2*w^2 + 9/2*w + 4]', '[158, 158, -3*w^2 + 2*w + 38]', '[158, 158, 2*w^2 + 5*w]', '[158, 158, w^2 - 2]', '[158, 158, 11/2*w^2 - 1/2*w - 60]', '[158, 158, -1/2*w^2 + 7/2*w + 2]', '[159, 159, -6*w^2 + 20*w + 1]', '[162, 18, 5*w^2 - 16*w - 2]', '[162, 18, 3*w^2 - 30]', '[162, 18, -11/2*w^2 + 1/2*w + 58]', '[162, 18, 3/2*w^2 + 3/2*w - 12]', '[162, 162, -w^2 - 2*w + 6]', '[162, 162, 1/2*w^2 + 1/2*w - 10]', '[163, 163, -w^2 + w - 1]', '[163, 163, 7/2*w^2 + 5/2*w - 28]', '[167, 167, 3/2*w^2 + 1/2*w - 12]', '[171, 57, 1/2*w^2 - 5/2*w - 14]', '[171, 171, w^2 + w - 11]', '[173, 173, 1/2*w^2 + 3/2*w - 6]', '[176, 44, -2*w - 8]', '[176, 44, -w^2 + 5]', '[176, 44, -w^2 - w + 12]', '[176, 88, 3/2*w^2 - 3/2*w - 19]', '[176, 176, 4*w^2 - w - 46]', '[177, 177, 7*w^2 - 23*w - 5]', '[178, 178, 2*w^2 + 3*w]', '[178, 178, -3/2*w^2 + 13/2*w + 2]', '[183, 183, -1/2*w^2 - 3/2*w + 8]', '[187, 187, -1/2*w^2 + 1/2*w + 10]', '[188, 94, -1/2*w^2 - 3/2*w + 7]', '[188, 94, -w^2 + 3]', '[188, 188, -1/2*w^2 - 5/2*w - 5]', '[192, 12, -4*w^2 + 12*w + 4]', '[192, 24, w^2 - 5*w - 2]', '[192, 24, 4*w^2 - 14*w - 2]', '[192, 24, -3*w^2 + 2*w + 37]', '[192, 48, -w^2 + 3*w - 2]', '[192, 96, -1/2*w^2 - 7/2*w + 1]', '[192, 192, -w^2 + 4]', '[193, 193, 2*w^2 - 25]', '[197, 197, -5*w^2 - w + 49]', '[198, 66, -5/2*w^2 + 19/2*w + 1]', '[198, 66, 7/2*w^2 - 5/2*w - 44]', '[198, 198, 7/2*w^2 - 1/2*w - 36]', '[198, 198, -3/2*w^2 + 5/2*w + 23]', '[199, 199, 5/2*w^2 - 1/2*w - 30]', '[201, 201, -7/2*w^2 - 1/2*w + 34]', '[202, 202, 1/2*w^2 - 7/2*w + 2]', '[202, 202, -1/2*w^2 - 9/2*w - 2]', '[202, 202, -5/2*w^2 - 1/2*w + 26]', '[202, 202, -w^2 - 2*w - 2]', '[202, 202, -1/2*w^2 - 1/2*w - 3]', '[202, 202, -6*w^2 + w + 64]', '[204, 102, 3*w^2 - 8*w - 1]', '[204, 102, -5/2*w^2 + 17/2*w + 3]', '[204, 204, 3/2*w^2 - 1/2*w - 1]', '[209, 209, 7/2*w^2 - 3/2*w - 40]', '[211, 211, 4*w^2 - 45]', '[212, 106, -9/2*w^2 + 1/2*w + 47]', '[212, 106, 7*w^2 - 2*w - 75]', '[212, 212, -21/2*w^2 + 3/2*w + 115]', '[213, 213, 4*w^2 - 43]', '[214, 214, 3/2*w^2 - 13/2*w]', '[214, 214, -3/2*w^2 - 3/2*w - 1]', '[216, 6, 6]', '[216, 12, 3/2*w^2 - 3/2*w - 15]', '[216, 12, -3*w - 3]', '[216, 24, -3/2*w^2 - 3/2*w + 9]', '[216, 54, 4*w + 2]', '[216, 108, 1/2*w^2 - 1/2*w + 3]', '[216, 108, 2*w^2 - 5*w - 3]', '[216, 216, -w^2 + 2*w + 8]', '[219, 219, -1/2*w^2 + 5/2*w + 4]', '[222, 222, 3/2*w^2 - 17/2*w - 2]', '[222, 222, -1/2*w^2 + 7/2*w - 3]', '[222, 222, -7/2*w^2 - 3/2*w + 32]', '[222, 222, -2*w^2 + 5*w]', '[222, 222, 3/2*w^2 - 5/2*w - 2]', '[222, 222, -7/2*w^2 + 25/2*w + 3]', '[223, 223, -3/2*w^2 + 15/2*w + 2]', '[226, 226, 9/2*w^2 - 27/2*w - 2]', '[226, 226, 5/2*w^2 + 1/2*w - 29]', '[226, 226, 5/2*w^2 + 9/2*w - 12]', '[226, 226, -1/2*w^2 + 15/2*w + 1]', '[226, 226, 3/2*w^2 - 1/2*w - 12]', '[226, 226, 7/2*w^2 + 3/2*w - 31]', '[228, 114, -1/2*w^2 + 5/2*w - 5]', '[228, 114, w^2 - 4*w - 3]', '[228, 228, -1/2*w^2 - 5/2*w + 3]', '[229, 229, -7/2*w^2 + 3/2*w + 42]', '[229, 229, 3/2*w^2 - 3/2*w - 10]', '[229, 229, 2*w^2 - 2*w - 1]', '[233, 233, 13/2*w^2 - 1/2*w - 70]', '[236, 118, w^2 - 15]', '[236, 118, -3/2*w^2 - 5/2*w + 9]', '[236, 236, -5/2*w^2 - 1/2*w + 23]', '[237, 237, 5/2*w^2 + 3/2*w - 22]', '[237, 237, -2*w^2 + 8*w - 3]', '[237, 237, -w^2 + 5*w - 1]', '[241, 241, w^2 - 3*w - 5]', '[242, 22, 9/2*w^2 - 3/2*w - 49]', '[242, 22, 3/2*w^2 - 1/2*w - 20]', '[242, 242, -9/2*w^2 + 31/2*w + 2]', '[242, 242, 2*w^2 - 3*w]', '[243, 9, -3*w^2 - 3*w + 21]', '[243, 27, -3/2*w^2 + 3/2*w + 18]', '[243, 243, -1/2*w^2 - 3/2*w - 4]', '[244, 122, 3/2*w^2 + 1/2*w - 1]', '[244, 122, -2*w^2 + 7*w + 3]', '[244, 244, 3*w - 2]', '[250, 10, 5*w]', '[250, 10, 5/2*w^2 - 15/2*w]', '[256, 8, 2*w^2 - 2*w - 28]', '[256, 8, -4*w^2 + 44]', '[256, 16, -2*w^2 + 18]', '[256, 16, 6*w^2 - 2*w - 68]', '[256, 16, -w^2 - 2*w + 7]', '[256, 32, -5*w^2 + 17*w + 2]', '[256, 64, 2*w^2 - 4*w]', '[256, 128, -3/2*w^2 + 11/2*w + 3]', '[256, 256, w^2 - 4*w + 4]', '[257, 257, 3/2*w^2 - 3/2*w - 16]', '[262, 262, -2*w^2 - 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5/2*w - 13]', '[1952, 1952, 1/2*w^2 + 13/2*w + 9]', '[1954, 1954, 13/2*w^2 - 51/2*w - 4]', '[1954, 1954, -11/2*w^2 - 7/2*w - 1]', '[1956, 978, -7/2*w^2 + 15/2*w + 5]', '[1956, 978, -w^2 + 8*w + 35]', '[1956, 978, -13/2*w^2 + 9/2*w + 83]', '[1956, 978, 9*w^2 - 28*w - 11]', '[1956, 1956, -18*w^2 + 5*w + 202]', '[1956, 1956, 3/2*w^2 - 17/2*w + 7]', '[1958, 1958, 2*w^2 + 11*w + 12]', '[1958, 1958, 5/2*w^2 + 1/2*w - 16]', '[1959, 1959, 1/2*w^2 - 13/2*w - 24]', '[1961, 1961, -8*w^2 + 87]', '[1961, 1961, 11/2*w^2 - 3/2*w - 54]', '[1961, 1961, 33/2*w^2 - 109/2*w - 8]', '[1964, 982, 2*w^2 - 5*w - 13]', '[1964, 982, -5/2*w^2 - 7/2*w + 7]', '[1964, 1964, -2*w^2 - 3*w + 18]', '[1966, 1966, -3/2*w^2 - 7/2*w - 6]', '[1966, 1966, 21/2*w^2 - 71/2*w - 4]', '[1966, 1966, 15/2*w^2 - 41/2*w - 3]', '[1966, 1966, w^2 - 4*w - 14]', '[1966, 1966, -4*w^2 + 9*w]', '[1966, 1966, -13/2*w^2 - 9/2*w + 52]', '[1971, 219, -9*w^2 + 3*w + 99]', '[1971, 1971, w^2 - w - 21]', '[1973, 1973, 5*w^2 - 11*w - 1]', '[1973, 1973, 3/2*w^2 - 3/2*w - 26]', '[1973, 1973, 11/2*w^2 - 3/2*w - 66]', '[1977, 1977, 19/2*w^2 - 7/2*w - 108]', '[1979, 1979, -9*w^2 + 33*w + 7]', '[1982, 1982, -27/2*w^2 + 89/2*w + 10]', '[1982, 1982, 3*w^2 + 4*w - 2]', '[1982, 1982, 1/2*w^2 + 17/2*w - 1]', '[1982, 1982, 11/2*w^2 - 21/2*w - 3]', '[1982, 1982, -5/2*w^2 + 19/2*w + 6]', '[1982, 1982, 7/2*w^2 - 21/2*w + 2]', '[1983, 1983, -w^2 - 3*w + 25]', '[1986, 1986, -3/2*w^2 + 17/2*w - 4]', '[1986, 1986, 2*w^2 + 3*w + 4]', '[1987, 1987, -8*w^2 + 6*w + 103]', '[1993, 1993, -15/2*w^2 + 43/2*w + 6]', '[1996, 998, 7/2*w^2 - 7/2*w - 25]', '[1996, 998, 2*w^2 - w + 3]', '[1996, 998, -7/2*w^2 - 5/2*w + 25]', '[1996, 998, -3/2*w^2 + 11/2*w + 9]', '[1996, 998, 5*w - 9]', '[1996, 998, 4*w^2 - 3*w - 41]', '[1996, 1996, -w^2 + 4*w + 16]', '[1996, 1996, -6*w^2 - w + 62]', '[1996, 1996, -1/2*w^2 - 5/2*w + 19]', '[1997, 1997, 1/2*w^2 + 11/2*w - 22]', '[1998, 222, 3/2*w^2 + 3/2*w - 27]', '[1998, 222, 3/2*w^2 - 9/2*w + 6]', '[1998, 222, 9/2*w^2 - 3/2*w - 42]', '[1998, 222, 3/2*w^2 - 9/2*w - 12]', '[1998, 222, 3/2*w^2 + 15/2*w - 3]', '[1998, 222, -3/2*w^2 + 9/2*w + 27]', '[1998, 1998, -3*w^2 + 2*w + 22]', '[1998, 1998, -3/2*w^2 + 13/2*w + 7]', '[1998, 1998, -3*w^2 + 8*w - 2]', '[1998, 1998, -1/2*w^2 - 9/2*w + 8]', '[1998, 1998, 5/2*w^2 - 3/2*w + 2]', '[1998, 1998, 5/2*w^2 - 27/2*w - 4]', '[1999, 1999, -1/2*w^2 - 7/2*w - 12]', '[2000, 20, 10*w]', '[2000, 20, 5*w^2 - 15*w]', '[2000, 20, -5*w^2 + 20*w + 5]', '[2000, 40, 5/2*w^2 - 5/2*w - 5]', '[2000, 80, 5*w - 10]', '[2004, 1002, -w^2 + 4*w + 15]', '[2004, 1002, -5/2*w^2 + 1/2*w + 35]', '[2004, 2004, 7/2*w^2 + 11/2*w - 21]', '[2006, 2006, 5/2*w^2 + 5/2*w - 24]', '[2006, 2006, 3/2*w^2 + 19/2*w + 17]', '[2007, 669, -2*w^2 + 4*w + 17]', '[2007, 2007, -2*w^2 + 2*w - 3]', '[2012, 1006, -19/2*w^2 + 11/2*w + 117]', '[2012, 1006, 17*w^2 - 2*w - 185]', '[2012, 2012, -51/2*w^2 + 13/2*w + 285]', '[2013, 2013, 31/2*w^2 - 7/2*w - 174]', '[2014, 2014, -9/2*w^2 + 35/2*w + 1]', '[2014, 2014, 31/2*w^2 - 101/2*w - 6]', '[2018, 2018, -3*w^2 - 2*w - 2]', '[2018, 2018, 7/2*w^2 - 29/2*w]', '[2022, 2022, 31/2*w^2 - 97/2*w - 12]', '[2022, 2022, -9/2*w^2 + 35/2*w + 5]', '[2026, 2026, 11/2*w^2 - 1/2*w - 54]', '[2026, 2026, 12*w^2 - w - 132]', '[2027, 2027, 5/2*w^2 + 3/2*w - 14]', '[2027, 2027, -6*w^2 + 59]', '[2027, 2027, 9/2*w^2 - 25/2*w]', '[2031, 2031, 4*w^2 - 2*w - 35]', '[2033, 2033, w^2 - 5*w - 9]', '[2034, 678, 5/2*w^2 + 5/2*w - 4]', '[2034, 678, -37/2*w^2 + 11/2*w + 209]', '[2034, 678, -5/2*w^2 + 7/2*w - 2]', '[2034, 678, w^2 + 4*w - 10]', '[2034, 678, -13/2*w^2 + 11/2*w + 86]', '[2034, 678, 2*w^2 - 7*w - 8]', '[2034, 2034, 7/2*w^2 - 25/2*w - 6]', '[2034, 2034, -19/2*w^2 + 65/2*w + 4]', '[2034, 2034, -13/2*w^2 - 1/2*w + 70]', '[2034, 2034, -3*w^2 - 2*w + 2]', '[2034, 2034, 4*w^2 - 7*w]', '[2034, 2034, -16*w^2 + 3*w + 172]', '[2039, 2039, 9/2*w^2 - 37/2*w - 2]', '[2042, 2042, -9*w - 4]', '[2042, 2042, -9/2*w^2 + 23/2*w + 6]', '[2048, 16, 4*w^2 - 4*w - 56]', '[2048, 16, -8*w^2 + 88]', '[2048, 32, -4*w^2 + 36]', '[2048, 32, 12*w^2 - 4*w - 136]', '[2048, 32, -2*w^2 - 4*w + 14]', '[2048, 64, w^2 + 2*w - 23]', '[2048, 64, -10*w^2 + 34*w + 4]', '[2048, 128, 4*w^2 - 8*w]', '[2048, 256, -3*w^2 + 11*w + 6]', '[2048, 512, 2*w^2 - 8*w + 8]', '[2048, 1024, 1/2*w^2 + 11/2*w - 5]', '[2048, 2048, 5/2*w^2 - 3/2*w - 15]', '[2049, 2049, -13/2*w^2 + 5/2*w + 64]', '[2052, 114, -9/2*w^2 - 3/2*w + 39]', '[2052, 114, -3*w^2 - 6*w + 15]', '[2052, 228, -9*w^2 + 96]', '[2052, 1026, -7/2*w^2 + 7/2*w + 33]', '[2052, 1026, -w + 13]', '[2052, 2052, 3*w^2 + 2*w - 20]', '[2053, 2053, -5/2*w^2 + 5/2*w - 2]', '[2056, 514, 3*w^2 - 3*w - 32]', '[2056, 1028, -w - 13]', '[2056, 1028, 13/2*w^2 - 1/2*w - 77]', '[2056, 2056, -5*w^2 - 2*w + 48]', '[2057, 187, 7/2*w^2 + 5/2*w - 32]', '[2057, 2057, -13/2*w^2 + 37/2*w + 2]', '[2058, 42, 7*w^2 - 70]', '[2058, 42, 7/2*w^2 + 7/2*w - 28]', '[2061, 687, 2*w^2 - 10*w + 7]', '[2061, 687, -11/2*w^2 + 7/2*w + 70]', '[2061, 687, 5/2*w^2 - 1/2*w - 16]', '[2061, 2061, -5*w^2 - w + 57]', '[2061, 2061, 6*w^2 - 16*w - 5]', '[2061, 2061, -1/2*w^2 - 15/2*w + 2]', '[2062, 2062, 29/2*w^2 - 3/2*w - 158]', '[2062, 2062, -8*w^2 + 5*w + 100]', '[2066, 2066, 13*w^2 - 134]', '[2066, 2066, 3/2*w^2 - 17/2*w + 6]', '[2066, 2066, 11/2*w^2 - 41/2*w + 4]', '[2066, 2066, 13/2*w^2 + 9/2*w - 54]', '[2066, 2066, -3/2*w^2 - 3/2*w - 5]', '[2066, 2066, -2*w^2 + 5*w - 4]', '[2068, 1034, 5*w^2 - 4*w - 63]', '[2068, 1034, 27/2*w^2 - 7/2*w - 153]', '[2068, 2068, -21/2*w^2 - 9/2*w + 95]', '[2069, 2069, 8*w^2 - 24*w - 3]', '[2074, 2074, 3/2*w^2 - 17/2*w + 5]', '[2074, 2074, -7/2*w^2 + 13/2*w + 4]', '[2076, 1038, -5/2*w^2 + 9/2*w + 19]', '[2076, 1038, w^2 - 2*w + 7]', '[2076, 2076, 5/2*w^2 + 5/2*w - 11]', '[2078, 2078, -17/2*w^2 - 1/2*w + 85]', '[2078, 2078, 25/2*w^2 - 7/2*w - 136]', '[2081, 2081, 9*w^2 - 29*w - 9]', '[2083, 2083, 3*w^2 - 3*w - 35]', '[2084, 1042, 1/2*w^2 + 15/2*w + 21]', '[2084, 1042, 3*w^2 + 2*w - 31]', '[2084, 2084, -7/2*w^2 + 9/2*w + 49]', '[2087, 2087, w^2 + 7*w - 3]', '[2094, 2094, 11/2*w^2 + 15/2*w - 34]', '[2094, 2094, 13/2*w^2 + 1/2*w - 73]', '[2094, 2094, 11/2*w^2 + 3/2*w - 55]', '[2094, 2094, 9*w^2 + 2*w - 86]', '[2094, 2094, 7/2*w^2 - 1/2*w - 30]', '[2094, 2094, 7/2*w^2 + 7/2*w - 22]', '[2096, 524, -4*w^2 - 2*w + 32]', '[2096, 524, w^2 - 3*w - 24]', '[2096, 524, -w^2 - 8*w - 11]', '[2096, 524, 2*w^2 - 12*w - 4]', '[2096, 524, -3*w^2 - 7*w + 12]', '[2096, 524, w^2 - 21]', '[2096, 524, 5*w^2 - 3*w - 58]', '[2096, 524, -9*w^2 + 27*w + 8]', '[2096, 524, 9*w^2 - 32*w - 5]', '[2096, 1048, -15/2*w^2 - 1/2*w + 79]', '[2096, 1048, -5/2*w^2 + 13/2*w - 3]', '[2096, 1048, -11/2*w^2 - 13/2*w + 35]', '[2096, 2096, 3*w^2 - 8*w - 12]', '[2096, 2096, -9*w^2 - 2*w + 88]', '[2096, 2096, 5/2*w^2 - 15/2*w - 51]', '[2097, 699, -5/2*w^2 + 1/2*w + 4]', '[2097, 2097, 13/2*w^2 - 25/2*w - 108]', '[2102, 2102, -19*w - 4]', '[2102, 2102, -19/2*w^2 + 53/2*w + 6]', '[2103, 2103, 7*w^2 - 3*w - 79]', '[2104, 526, -10*w^2 + 2*w + 114]', '[2104, 1052, 15/2*w^2 + 5/2*w - 71]', '[2104, 1052, -4*w^2 + 3*w + 47]', '[2104, 2104, 33/2*w^2 - 3/2*w - 175]', '[2109, 2109, 7/2*w^2 - 3/2*w - 2]', '[2109, 2109, 7/2*w^2 - 19/2*w - 12]', '[2109, 2109, 1/2*w^2 + 3/2*w + 10]', '[2111, 2111, 6*w^2 - 2*w - 59]', '[2112, 132, -2*w^2 - 6*w + 8]', '[2112, 264, -3*w^2 - w + 22]', '[2112, 264, w^2 - 6*w - 7]', '[2112, 264, 2*w - 14]', '[2112, 528, -5*w^2 - w + 54]', '[2112, 1056, 3/2*w^2 - 11/2*w - 35]', '[2112, 2112, 7*w^2 - 4*w - 84]', '[2113, 2113, -w^2 - 5*w - 11]', '[2118, 2118, 1/2*w^2 - 7/2*w + 12]', '[2118, 2118, 3/2*w^2 + 11/2*w - 7]', '[2122, 2122, -13/2*w^2 - 5/2*w + 58]', '[2122, 2122, -27/2*w^2 + 1/2*w + 143]', '[2123, 2123, 8*w^2 - 26*w - 1]', '[2124, 354, -5*w^2 + 22*w + 5]', '[2124, 354, 11/2*w^2 - 31/2*w - 1]', '[2124, 708, 1/2*w^2 + 25/2*w + 1]', '[2124, 1062, 5*w^2 + 10*w - 21]', '[2124, 1062, 17/2*w^2 - 69/2*w - 7]', '[2124, 2124, -9*w^2 + 26*w + 4]', '[2125, 85, 5/2*w^2 - 25/2*w]', '[2126, 2126, -23/2*w^2 + 1/2*w + 123]', '[2126, 2126, -11/2*w^2 - 3/2*w + 50]', '[2127, 2127, -10*w^2 + 34*w + 3]', '[2131, 2131, -5/2*w^2 + 29/2*w + 4]', '[2133, 237, -3*w^2 + 3*w + 33]', '[2133, 237, -3*w^2 + 9*w - 3]', '[2133, 237, 6*w + 15]', '[2133, 2133, -13*w^2 - w + 131]', '[2133, 2133, -w^2 - w - 7]', '[2133, 2133, -4*w^2 - 12*w - 5]', '[2136, 534, -6*w^2 + 22*w + 2]', '[2136, 1068, 7/2*w^2 - 3/2*w + 1]', '[2136, 1068, 8*w^2 - 21*w - 5]', '[2136, 2136, -3/2*w^2 + 17/2*w + 5]', '[2137, 2137, 5/2*w^2 - 13/2*w - 48]', '[2138, 2138, 9/2*w^2 + 1/2*w - 57]', '[2138, 2138, 5/2*w^2 - 7/2*w - 24]', '[2141, 2141, 9/2*w^2 + 3/2*w - 46]', '[2143, 2143, 3*w^2 - 7*w - 15]', '[2144, 268, 2*w + 14]', '[2144, 268, -3*w^2 + 3*w + 34]', '[2144, 536, -7*w^2 + w + 82]', '[2144, 536, w^2 + 4*w - 21]', '[2144, 1072, 11/2*w^2 + 5/2*w - 51]', '[2144, 2144, 12*w^2 - w - 126]', '[2147, 2147, -6*w^2 + 18*w + 1]', '[2147, 2147, 3*w^2 - 5*w - 5]', '[2147, 2147, -13/2*w^2 + 5/2*w + 78]', '[2153, 2153, -2*w^2 + 6*w - 5]', '[2153, 2153, 8*w^2 + 4*w - 71]', '[2153, 2153, -2*w^2 + 10*w - 3]', '[2154, 2154, 9/2*w^2 + 1/2*w - 41]', '[2154, 2154, 5/2*w^2 + 9/2*w - 16]', '[2157, 2157, 3*w^2 - w - 23]', '[2157, 2157, -1/2*w^2 + 13/2*w + 6]', '[2157, 2157, -5/2*w^2 - 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5/2*w - 6]', '[9901, 9901, 25/2*w^2 - 97/2*w - 8]', '[9902, 9902, -5/2*w^2 + 11/2*w + 49]', '[9902, 9902, 3/2*w^2 + 27/2*w + 22]', '[9903, 9903, 25/2*w^2 + 3/2*w - 122]', '[9904, 2476, 25*w^2 - 83*w - 12]', '[9904, 2476, -29*w^2 + 90*w + 19]', '[9904, 2476, -9*w^2 + 23*w + 2]', '[9904, 4952, 15/2*w^2 - 51/2*w - 11]', '[9904, 9904, -11/2*w^2 + 41/2*w - 11]', '[9907, 9907, 5*w^2 - 11*w - 89]', '[9909, 1101, -6*w^2 + 24*w - 3]', '[9909, 9909, -18*w^2 + 8*w + 211]', '[9911, 9911, 15/2*w^2 - 7/2*w - 68]', '[9916, 4958, 6*w^2 - 9*w - 89]', '[9916, 4958, 37/2*w^2 - 13/2*w - 215]', '[9916, 4958, -23/2*w^2 + 11/2*w + 133]', '[9916, 4958, -17/2*w^2 + 53/2*w - 1]', '[9916, 4958, -3*w^2 + 6*w + 55]', '[9916, 4958, 9*w^2 - 34*w - 9]', '[9916, 9916, -29*w^2 + 6*w + 324]', '[9916, 9916, 31/2*w^2 - 93/2*w - 13]', '[9916, 9916, 1/2*w^2 - 31/2*w + 1]', '[9917, 9917, 4*w^2 - 4*w - 13]', '[9921, 9921, -1/2*w^2 + 1/2*w - 18]', '[9921, 9921, 7/2*w^2 - 11/2*w - 40]', '[9921, 9921, 17/2*w^2 - 45/2*w - 16]', '[9923, 9923, 9/2*w^2 - 5/2*w - 30]', '[9923, 9923, 6*w^2 - 28*w - 3]', '[9923, 9923, -25/2*w^2 + 13/2*w + 148]', '[9924, 4962, 13*w^2 - 38*w - 17]', '[9924, 4962, -7/2*w^2 + 31/2*w + 9]', '[9924, 9924, 5/2*w^2 - 19/2*w + 13]', '[9928, 2482, -5*w^2 + 5*w + 32]', '[9928, 4964, 1/2*w^2 - 17/2*w - 21]', '[9928, 4964, -9*w + 11]', '[9928, 9928, 3*w^2 - 2*w - 48]', '[9929, 9929, -10*w^2 + 4*w + 97]', '[9931, 9931, 8*w^2 - 99]', '[9931, 9931, 7/2*w^2 - 11/2*w - 42]', '[9931, 9931, -1/2*w^2 - 39/2*w - 6]', '[9934, 9934, 9/2*w^2 - 43/2*w]', '[9934, 9934, -6*w^2 - 9*w - 4]', '[9938, 9938, 9/2*w^2 + 5/2*w - 5]', '[9938, 9938, -11/2*w^2 + 37/2*w + 12]', '[9941, 9941, 11/2*w^2 - 23/2*w - 14]', '[9942, 9942, -11/2*w^2 - 19/2*w + 3]', '[9942, 9942, 7/2*w^2 - 29/2*w - 10]', '[9943, 9943, 9/2*w^2 - 13/2*w - 18]', '[9943, 9943, 8*w^2 + 2*w - 93]', '[9944, 2486, 4*w^2 - 4*w - 14]', '[9944, 2486, -5*w^2 + 5*w + 56]', '[9944, 2486, -9*w^2 - 3*w + 88]', '[9944, 4972, 13/2*w^2 + 19/2*w - 33]', '[9944, 4972, 3*w + 23]', '[9944, 4972, -61/2*w^2 + 201/2*w + 21]', '[9944, 4972, -6*w^2 - 7*w + 35]', '[9944, 4972, -8*w^2 + 21*w + 25]', '[9944, 4972, 3/2*w^2 + 13/2*w - 31]', '[9944, 9944, 9*w^2 + 4*w - 84]', '[9944, 9944, 12*w^2 - 25*w - 6]', '[9944, 9944, 1/2*w^2 + 9/2*w + 21]', '[9946, 9946, 3/2*w^2 - 17/2*w - 15]', '[9946, 9946, -7/2*w^2 - 7/2*w - 6]', '[9948, 4974, -21/2*w^2 - 7/2*w + 95]', '[9948, 4974, -7*w^2 - 12*w + 37]', '[9948, 9948, -22*w^2 + w + 234]', '[9949, 9949, 3/2*w^2 - 3/2*w - 34]', '[9956, 4978, -3/2*w^2 - 33/2*w - 7]', '[9956, 4978, -w^2 + 8*w + 27]', '[9956, 4978, -6*w^2 + 13*w + 9]', '[9956, 4978, -7/2*w^2 + 19/2*w - 7]', '[9956, 4978, 3*w^2 - 18*w - 7]', '[9956, 4978, -9/2*w^2 + 5/2*w + 63]', '[9956, 9956, -2*w^2 - w - 10]', '[9956, 9956, -14*w^2 + 5*w + 154]', '[9956, 9956, -5/2*w^2 - 29/2*w + 3]', '[9964, 4982, -w^2 + 6*w - 19]', '[9964, 4982, -5/2*w^2 - 19/2*w + 11]', '[9964, 9964, -9/2*w^2 - 1/2*w + 31]', '[9966, 9966, -13/2*w^2 + 31/2*w + 12]', '[9966, 9966, 5/2*w^2 - 31/2*w + 19]', '[9967, 9967, 11/2*w^2 - 31/2*w - 108]', '[9969, 9969, 25/2*w^2 - 73/2*w - 12]', '[9972, 1662, -w^2 - 4*w - 17]', '[9972, 1662, 2*w^2 - 7*w + 13]', '[9972, 1662, 7/2*w^2 - 11/2*w - 41]', '[9972, 1662, 5/2*w^2 + 23/2*w - 7]', '[9972, 1662, -13/2*w^2 + 5/2*w + 83]', '[9972, 1662, -2*w^2 + 7*w + 35]', '[9972, 3324, 8*w^2 + 11*w - 50]', '[9972, 3324, 8*w^2 - w - 98]', '[9972, 3324, 4*w^2 + w - 22]', '[9972, 4986, 5/2*w^2 + 7/2*w + 9]', '[9972, 4986, -5*w^2 + 6*w + 29]', '[9972, 4986, -2*w^2 + 13*w - 11]', '[9972, 4986, 1/2*w^2 - 17/2*w - 19]', '[9972, 4986, -9/2*w^2 + 25/2*w - 5]', '[9972, 4986, 4*w^2 - 21*w - 7]', '[9972, 9972, -2*w^2 + 7*w + 22]', '[9972, 9972, -2*w^2 - 15*w + 2]', '[9972, 9972, 5/2*w^2 - 3/2*w - 43]', '[9974, 9974, -29/2*w^2 - 1/2*w + 146]', '[9974, 9974, -23/2*w^2 + 65/2*w + 10]', '[9974, 9974, -1/2*w^2 - 5/2*w - 19]', '[9974, 9974, -33*w^2 + 4*w + 358]', '[9974, 9974, w^2 - 20*w - 6]', '[9974, 9974, -3/2*w^2 - 27/2*w - 10]', '[9977, 9977, -21*w^2 + w + 219]', '[9978, 9978, -1/2*w^2 - 21/2*w - 19]', '[9978, 9978, -9/2*w^2 + 7/2*w + 28]', '[9979, 9979, 13/2*w^2 - 1/2*w - 58]', '[9981, 3327, 4*w^2 + 4*w - 13]', '[9981, 9981, 9/2*w^2 - 29/2*w - 14]', '[9986, 9986, -9/2*w^2 + 7/2*w - 3]', '[9986, 9986, 17/2*w^2 - 63/2*w]', '[9992, 2498, 6*w^2 + 6*w - 38]', '[9992, 4996, 19/2*w^2 + 5/2*w - 95]', '[9992, 4996, 6*w^2 + 17*w - 13]', '[9992, 9992, -1/2*w^2 + 35/2*w + 63]', '[9994, 9994, -5/2*w^2 + 15/2*w + 21]', '[9994, 9994, 5/2*w^2 + 1/2*w + 8]', '[9999, 3333, -2*w^2 - 14*w - 13]', '[9999, 3333, 1/2*w^2 - 17/2*w - 20]', '[9999, 3333, 23*w^2 - 73*w - 11]', '[9999, 9999, 11/2*w^2 + 25/2*w + 6]', '[9999, 9999, 9/2*w^2 - 13/2*w - 10]', '[9999, 9999, 9*w^2 + w - 85]'], 'label': '3.3.1304.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -w]', '[2, 2, -1/2*w^2 + 3/2*w]', '[3, 3, -w^2 + 3*w + 1]', '[9, 3, w^2 + w - 7]', '[11, 11, 2*w^2 - 21]', '[17, 17, -1/2*w^2 + 5/2*w]', '[19, 19, -1/2*w^2 + 1/2*w + 2]', '[37, 37, w^2 - w - 13]', '[37, 37, -1/2*w^2 + 1/2*w + 8]', '[37, 37, 5/2*w^2 - 17/2*w - 2]', '[47, 47, -3/2*w^2 + 11/2*w]', '[53, 53, w^2 - w - 7]', '[59, 59, 2*w - 1]', '[61, 61, -3/2*w^2 + 3/2*w + 20]', '[67, 67, w^2 - 3*w - 3]', '[71, 71, w^2 - w - 1]', '[73, 73, 3*w^2 - w - 33]', '[79, 79, w^2 - w - 11]', '[79, 79, w^2 - 3*w + 1]', '[79, 79, -2*w - 5]', '[89, 89, -2*w - 3]', '[101, 101, w^2 + w - 9]', '[101, 101, 3/2*w^2 + 1/2*w - 16]', '[101, 101, -3/2*w^2 + 7/2*w]', '[107, 107, 1/2*w^2 + 3/2*w - 4]', '[113, 113, -1/2*w^2 + 1/2*w - 2]', '[113, 113, -4*w^2 + 41]', '[113, 113, 3/2*w^2 - 7/2*w - 2]', '[121, 11, 2*w^2 - 8*w - 1]', '[125, 5, -5]', '[131, 131, 7/2*w^2 + 9/2*w - 22]', '[131, 131, -3*w^2 + 3*w + 41]', '[131, 131, w^2 - w - 5]', '[137, 137, 3*w^2 - 9*w - 1]', '[139, 139, 2*w^2 - 19]', '[151, 151, 3/2*w^2 - 3/2*w - 14]', '[157, 157, 1/2*w^2 + 3/2*w - 12]', '[157, 157, 11/2*w^2 - 3/2*w - 60]', '[157, 157, -1/2*w^2 + 9/2*w]', '[163, 163, -w^2 + w - 1]', '[163, 163, 7/2*w^2 + 5/2*w - 28]', '[167, 167, 3/2*w^2 + 1/2*w - 12]', '[173, 173, 1/2*w^2 + 3/2*w - 6]', '[193, 193, 2*w^2 - 25]', '[197, 197, -5*w^2 - w + 49]', '[199, 199, 5/2*w^2 - 1/2*w - 30]', '[211, 211, 4*w^2 - 45]', '[223, 223, -3/2*w^2 + 15/2*w + 2]', '[229, 229, -7/2*w^2 + 3/2*w + 42]', '[229, 229, 3/2*w^2 - 3/2*w - 10]', '[229, 229, 2*w^2 - 2*w - 1]', '[233, 233, 13/2*w^2 - 1/2*w - 70]', '[241, 241, w^2 - 3*w - 5]', '[257, 257, 3/2*w^2 - 3/2*w - 16]', '[263, 263, -5*w^2 + w + 57]', '[277, 277, -3*w^2 - w + 27]', '[277, 277, 5/2*w^2 - 1/2*w - 24]', '[277, 277, -9/2*w^2 + 25/2*w + 2]', '[283, 283, -1/2*w^2 - 11/2*w - 2]', '[289, 17, -7/2*w^2 - 1/2*w + 36]', '[317, 317, 7*w^2 - w - 79]', '[317, 317, 3/2*w^2 - 3/2*w - 2]', '[317, 317, 2*w - 9]', '[331, 331, -3*w^2 + 5*w + 47]', '[337, 337, -3/2*w^2 + 3/2*w + 22]', '[343, 7, -7]', '[349, 349, -2*w - 9]', '[349, 349, 1/2*w^2 - 5/2*w - 6]', '[349, 349, 3/2*w^2 - 7/2*w - 8]', '[353, 353, 1/2*w^2 - 13/2*w - 2]', '[359, 359, -1/2*w^2 + 1/2*w - 4]', '[361, 19, 3/2*w^2 + 1/2*w - 10]', '[367, 367, 2*w^2 - 8*w + 1]', '[373, 373, -4*w - 3]', '[383, 383, 15/2*w^2 - 3/2*w - 80]', '[397, 397, w^2 + 3*w - 5]', '[401, 401, 2*w^2 - 2*w - 19]', '[409, 409, 2*w^2 - 1]', '[409, 409, -13/2*w^2 + 1/2*w + 68]', '[409, 409, -1/2*w^2 + 5/2*w - 6]', '[421, 421, -9/2*w^2 + 5/2*w + 54]', '[433, 433, w^2 - 5*w - 27]', '[439, 439, 9*w^2 - w - 99]', '[443, 443, 2*w^2 - 4*w - 3]', '[449, 449, -5*w^2 + 3*w + 61]', '[461, 461, 3/2*w^2 - 11/2*w - 4]', '[463, 463, -7*w^2 - w + 69]', '[463, 463, -1/2*w^2 + 9/2*w - 2]', '[463, 463, -5/2*w^2 + 17/2*w + 4]', '[467, 467, -2*w^2 + 2*w + 25]', '[487, 487, 2*w^2 - 4*w - 33]', '[491, 491, 5/2*w^2 - 9/2*w - 2]', '[499, 499, -6*w^2 + 18*w + 7]', '[499, 499, 3/2*w^2 - 3/2*w - 4]', '[499, 499, 6*w^2 - 20*w - 5]', '[503, 503, w^2 - w - 17]', '[521, 521, -w^2 - w - 3]', '[547, 547, -21/2*w^2 + 5/2*w + 118]', '[547, 547, 3*w^2 - w - 37]', '[547, 547, 6*w^2 - 2*w - 65]', '[569, 569, -13/2*w^2 - 11/2*w + 50]', '[571, 571, -7/2*w^2 + 19/2*w + 4]', '[587, 587, 11/2*w^2 + 17/2*w - 30]', '[601, 601, 2*w^2 - 2*w - 13]', '[607, 607, 3/2*w^2 + 1/2*w - 4]', '[617, 617, -1/2*w^2 - 3/2*w - 6]', '[619, 619, -1/2*w^2 + 9/2*w - 6]', '[643, 643, 2*w^2 - 27]', '[647, 647, -9/2*w^2 + 33/2*w + 4]', '[653, 653, -3*w^2 + 7*w + 3]', '[659, 659, -3/2*w^2 - 1/2*w - 2]', '[661, 661, -6*w^2 + 61]', '[677, 677, 7*w^2 - 3*w - 83]', '[683, 683, 9/2*w^2 - 33/2*w - 2]', '[701, 701, -2*w^2 + 2*w - 1]', '[709, 709, w^2 - 3*w - 9]', '[719, 719, 4*w^2 - 4*w - 55]', '[719, 719, 4*w^2 - 2*w - 45]', '[719, 719, 4*w^2 - 39]', '[727, 727, -4*w - 9]', '[727, 727, -5/2*w^2 + 5/2*w + 32]', '[727, 727, 9/2*w^2 - 29/2*w]', '[733, 733, 4*w - 11]', '[743, 743, -3/2*w^2 + 3/2*w - 2]', '[761, 761, 3/2*w^2 + 5/2*w - 24]', '[769, 769, -2*w^2 + 10*w + 3]', '[773, 773, 3/2*w^2 + 5/2*w - 12]', '[787, 787, 17/2*w^2 - 5/2*w - 92]', '[787, 787, 3*w^2 + w - 35]', '[787, 787, 4*w^2 - 10*w - 1]', '[797, 797, 6*w^2 - 67]', '[809, 809, 5/2*w^2 - 21/2*w]', '[811, 811, w^2 - 9*w - 39]', '[821, 821, -2*w^2 + 6*w + 7]', '[827, 827, 6*w - 1]', '[829, 829, 3/2*w^2 - 11/2*w - 34]', '[839, 839, 5*w^2 + 3*w - 43]', '[853, 853, -4*w^2 - 6*w + 23]', '[857, 857, 3*w^2 - w - 27]', '[859, 859, 3*w^2 - 9*w + 1]', '[863, 863, -2*w - 11]', '[863, 863, 5/2*w^2 - 5/2*w - 2]', '[863, 863, 4*w + 15]', '[877, 877, -3/2*w^2 + 15/2*w - 2]', '[881, 881, -w^2 + 7*w - 1]', '[883, 883, 4*w - 5]', '[907, 907, w^2 - 3*w - 11]', '[911, 911, 5/2*w^2 + 3/2*w - 18]', '[919, 919, 2*w^2 - 2*w - 11]', '[929, 929, 11/2*w^2 + 9/2*w - 42]', '[937, 937, 1/2*w^2 + 7/2*w - 6]', '[941, 941, -9/2*w^2 + 5/2*w + 46]', '[953, 953, 11/2*w^2 - 39/2*w - 2]', '[967, 967, -13*w^2 + w + 139]', '[977, 977, 1/2*w^2 + 11/2*w - 2]', '[983, 983, 1/2*w^2 + 15/2*w + 20]', '[983, 983, 4*w - 9]', '[983, 983, 3/2*w^2 - 15/2*w + 4]', '[991, 991, 3/2*w^2 - 11/2*w - 6]', '[991, 991, w^2 - 3*w - 15]', '[991, 991, 1/2*w^2 - 1/2*w - 14]']}
• 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': [-2, -11, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1304, 'disc_rad': 326, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 1], [1, 1]]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[2, 1], [1, 1]]], [13, [[3, 1]]], [17, [[2, 1], [1, 1]]], [19, [[2, 1], [1, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [[3, 1]]], [37, [[1, 3]]], [41, [[3, 1]]], [43, [[3, 1]]], [47, [[2, 1], [1, 1]]], [53, [[2, 1], [1, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [9, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 36.11094017053558, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1304.1', 'local_algs': ['2.1.0.1', '2.2.3.4', '163.1.0.1', '163.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 163], 'rd': 10.9251111426, 'regulator': {'__RealLiteral__': 0, 'data': '11.9265379008', 'prec': 44}, 'res': {'gal': ['-8,-8,70,-36,-35,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{2} - \\frac{1}{2} a - 4 \\)', '\\( 12 a^{2} - 2 a - 131 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2*a']}