Hilbert modular form data - 3.3.1708.1-4.1-a

Formats: - HTML - YAML - JSON - 2024-05-04T23:44:21.643960

• 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': 1708, 'field_bad_primes': [2, 7, 61], 'field_label': '3.3.1708.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1708.1-4.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2], 'level_ideal': '[4, 2, w^2 + 2*w]', 'level_label': '4.1', 'level_norm': 4, 'parallel_weight': 2, 'short_label': '4.1-a', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, -w]', -1]], 'hecke_eigenvalues': [0, 'e', 1, '-2*e + 2', '2*e', '-e + 4', -5, '-2*e + 4', '-2*e + 9', '2*e - 6', '-e - 2', '-2*e + 10', '-e - 4', 10, '6*e - 3', '-5*e + 4', '5*e', '-7*e + 16', '2*e - 10', '7*e', -3, '6*e - 2', '-8*e + 2', '2*e', 10, '-12*e + 16', '-2*e + 12', '-5*e + 8', '12*e - 10', '-5*e - 6', '4*e - 6', '-2*e + 18', '-6*e - 6', '-10*e + 16', '-7*e - 8', '-9*e + 10', '-5*e - 8', '12*e - 11', '-2*e + 10', '-6*e + 14', '2*e - 3', '-9*e + 8', '-2*e + 8', -4, '-2*e + 16', '5*e - 20', '10*e - 10', -2, '10*e - 6', '-2*e - 9', '-2*e - 2', '16*e - 14', '14*e - 22', '-4*e - 5', '-4*e + 6', '-8*e - 10', '2*e + 20', '-6*e + 28', '-16*e + 6', '2*e + 1', '5*e - 22', '-8*e - 4', '-12*e + 4', '-4*e + 6', '-16*e + 10', '14*e - 24', '4*e - 28', '2*e - 6', '-13*e + 22', '-4*e - 7', '6*e - 6', '10*e - 8', '-12*e + 10', '-4*e - 17', '-16*e + 26', '-3*e + 10', '-6*e + 6', '8*e - 10', '-4*e + 4', '-9*e + 10', '-2*e + 3', '14*e - 30', '10*e - 9', '17*e - 6', '4*e - 12', '7*e - 34', 38, '-6*e + 8', '-4*e - 6', '-2*e - 3', '4*e - 28', '2*e - 24', '12*e - 22', '-2*e - 12', '18*e - 24', '-18*e + 16', '-16*e + 14', '-18*e + 7', '10*e + 3', '12*e + 2', '18*e - 22', '10*e + 2', '16*e - 30', '-20*e + 26', '12*e - 16', '16*e - 2', '-2*e + 34', '26*e - 18', '12*e + 18', '4*e - 26', '16*e - 6', '-16*e + 14', 'e - 10', '-2*e - 22', '6*e - 28', '4*e + 26', '14*e - 30', '-10*e - 6', '-26*e + 28', '15*e - 14', '4*e - 6', '13*e - 20', '8*e + 6', '-4*e + 9', '-14*e + 46', '-26*e + 38', '-20*e - 4', '6*e + 32', '-12*e - 2', '20*e - 12', '32*e - 27', '-21*e + 30', '10*e - 6', '-25*e + 38', '2*e + 28', '-16*e + 14', '-14*e + 36', '24*e - 27', '-14*e + 2', '-4*e + 6', '6*e - 12', '-6*e + 44', '6*e + 1', '6*e - 1', '-24*e + 33', '-26*e + 23', '-4*e + 12', '-16*e + 18', '-23*e + 42', '-6*e + 46', '14*e - 30', '4*e', '25*e - 42', '24*e - 17', '28*e - 38', '24*e - 46', '-16*e + 18', '-6*e + 15', '-10*e + 19', '10*e + 24', '40*e - 42', '-14*e - 10', '22*e - 35', 37, '-18*e + 17'], 'hecke_polynomial': 'x^2 - 2*x - 1', 'label': '3.3.1708.1-4.1-a'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 1708, 'ideals': ['[1, 1, 1]', '[2, 2, -w]', '[2, 2, w^2 - 2*w - 5]', '[4, 2, w^2 + 2*w]', '[4, 2, -w^2 + w + 8]', '[4, 4, -w - 1]', '[5, 5, w^2 + 3*w + 1]', '[7, 7, -2*w^2 + 2*w + 17]', '[7, 7, -w^2 + w + 9]', '[8, 2, 2]', '[8, 4, 3*w^2 - 4*w - 22]', '[8, 4, w^2 + w]', '[8, 8, -w + 3]', '[10, 10, -2*w^2 + 3*w + 14]', '[10, 10, w - 1]', '[13, 13, 2*w + 1]', '[14, 14, w + 3]', '[14, 14, -w^2 - 2*w + 1]', '[14, 14, -w + 4]', '[14, 14, -w + 2]', '[16, 4, -2*w]', '[16, 4, w^2 - 2*w - 6]', '[16, 4, 2*w^2 - 4*w - 10]', '[16, 8, w^2 - w - 6]', '[16, 16, w^2 + 2*w + 1]', '[20, 10, -w^2 + 2*w + 4]', '[20, 10, -w^2 - w + 2]', '[20, 20, -2*w^2 + 5*w + 7]', '[25, 5, -3*w^2 + 5*w + 19]', '[25, 25, w^2 - 3*w - 3]', '[26, 26, -2*w^2 + 3*w + 15]', '[26, 26, -2*w^2 - 5*w - 2]', '[27, 3, 3]', '[28, 14, -w^2 - 3*w]', '[28, 14, w^2 - 2*w - 8]', '[28, 14, 3*w^2 - 7*w - 12]', '[28, 14, w^2 - 4]', '[28, 28, w^2 - 2*w - 7]', '[28, 28, 2*w^2 - 3*w - 13]', '[29, 29, w^2 + w - 1]', '[31, 31, w^2 - w - 1]', '[32, 4, 2*w^2 + 4*w]', '[32, 4, -2*w^2 + 2*w + 16]', '[32, 8, w^2 - 2*w - 2]', '[32, 8, -2*w - 2]', '[32, 16, -3*w^2 + 3*w + 26]', '[32, 32, w^2 - 2*w - 3]', '[35, 35, 2*w + 3]', '[35, 35, -w^2 + w + 5]', '[37, 37, 2*w^2 + 6*w + 3]', '[40, 10, 2*w^2 + 6*w + 2]', '[40, 20, w^2 - 6]', '[40, 20, w^2 - w - 10]', '[40, 40, -w^2 + 1]', '[41, 41, -6*w^2 - 14*w - 3]', '[49, 7, w^2 + w + 1]', '[49, 7, -2*w^2 - 6*w - 1]', '[49, 49, -2*w + 1]', '[50, 10, -2*w^2 + 5*w + 6]', '[50, 10, -w^2 + 3]', '[50, 50, w + 4]', '[50, 50, 3*w^2 + 6*w + 1]', '[52, 26, -w^2 + w + 4]', '[52, 26, -3*w^2 + 8*w + 8]', '[52, 52, -2*w^2 - 3*w - 1]', '[53, 53, -4*w^2 + 6*w + 27]', '[54, 6, -3*w]', '[54, 6, 3*w^2 - 6*w - 15]', '[56, 14, -4*w^2 + 4*w + 34]', '[56, 14, -2*w^2 + 2*w + 18]', '[56, 28, w^2 - 3*w - 4]', '[56, 28, w^2 - w - 2]', '[56, 28, w^2 - 2]', '[56, 28, -w^2 - 4*w - 2]', '[56, 56, -3*w^2 + 2*w + 29]', '[56, 56, -w^2 - 4*w - 3]', '[58, 58, -2*w^2 - 7*w - 2]', '[58, 58, -w + 5]', '[59, 59, 2*w^2 - 4*w - 11]', '[61, 61, w^2 - w - 3]', '[61, 61, -2*w^2 + 2*w + 13]', '[62, 62, -2*w^2 - 5*w]', '[62, 62, 3*w^2 - 4*w - 21]', '[64, 4, 4]', '[64, 8, 6*w^2 - 8*w - 44]', '[64, 8, -w^2 - 2*w + 2]', '[64, 8, 2*w^2 + 2*w]', '[64, 16, -2*w + 6]', '[64, 32, -w^2 - w + 4]', '[64, 64, w^2 - 6*w + 9]', '[65, 65, -3*w^2 + 3*w + 25]', '[70, 70, w^2 - 11]', '[70, 70, 3*w + 2]', '[70, 70, -2*w^2 - 3*w]', '[70, 70, 2*w^2 - w - 21]', '[73, 73, w^2 + 3*w + 3]', '[74, 74, w^2 - 7]', '[74, 74, -10*w^2 + 13*w + 76]', '[80, 20, -4*w^2 + 6*w + 28]', '[80, 20, -w^2 - 2*w - 2]', '[80, 20, 2*w - 2]', '[80, 40, 3*w^2 + 7*w]', '[80, 80, -w^2 + 4*w - 3]', '[82, 82, -2*w^2 + 3*w + 12]', '[82, 82, -w^2 - 1]', '[91, 91, -w^2 + 3*w + 5]', '[91, 91, -2*w^2 + 4*w + 9]', '[97, 97, w^2 + w - 15]', '[98, 14, -2*w^2 + w + 20]', '[98, 14, -4*w^2 - 11*w - 4]', '[98, 14, w^2 - 4*w - 3]', '[98, 14, 2*w^2 - 5*w - 5]', '[98, 98, 2*w^2 + 3*w - 2]', '[98, 98, 3*w^2 - 8*w - 9]', '[100, 10, w^2 - 8]', '[100, 10, w^2 + 5*w + 2]', '[100, 20, w^2 - 13]', '[100, 50, -w^2 - 4*w]', '[100, 50, 3*w^2 - 5*w - 18]', '[100, 100, w^2 - 2*w + 1]', '[101, 101, w^2 + 3*w - 1]', '[101, 101, w^2 - w - 11]', '[101, 101, 2*w - 5]', '[103, 103, 3*w^2 - 3*w - 23]', '[103, 103, -w^2 + w - 1]', '[103, 103, 2*w - 3]', '[104, 26, 4*w + 2]', '[104, 52, w^2 + w - 16]', '[104, 52, w^2 - 10]', '[104, 104, w^2 - 2*w - 11]', '[106, 106, -w^2 + 6*w + 1]', '[106, 106, -2*w^2 + 5*w + 8]', '[107, 107, 5*w^2 - 7*w - 37]', '[108, 6, 3*w^2 + 6*w]', '[108, 6, -3*w^2 + 3*w + 24]', '[108, 12, -3*w - 3]', '[112, 28, 2*w + 6]', '[112, 28, -2*w^2 - 4*w + 2]', '[112, 28, -w^2 - 6*w - 2]', '[112, 28, 7*w^2 - 10*w - 50]', '[112, 28, -2*w + 8]', '[112, 28, -2*w + 4]', '[112, 56, w^2 - 5*w + 6]', '[112, 56, w^2 - 7*w + 12]', '[112, 112, w + 5]', '[112, 112, -w^2 + 9]', '[116, 58, 3*w^2 - 6*w - 16]', '[116, 58, w^2 - 3*w - 10]', '[116, 116, -3*w^2 - 8*w - 1]', '[118, 118, 2*w^2 - 5*w - 4]', '[118, 118, -3*w^2 - 2*w + 43]', '[122, 122, -3*w + 11]', '[122, 122, 3*w + 4]', '[122, 122, -5*w - 2]', '[122, 122, 7*w^2 - 8*w - 57]', '[124, 62, w^2 - 3*w - 6]', '[124, 62, -7*w^2 + 8*w + 56]', '[124, 124, -w^2 - 6*w - 1]', '[125, 5, 5]', '[125, 125, -2*w^2 - 2*w - 1]', '[127, 127, w^2 + w - 5]', '[128, 8, -4*w]', '[128, 8, 2*w^2 - 4*w - 12]', '[128, 8, 4*w^2 - 8*w - 20]', '[128, 16, 3*w^2 + 6*w + 2]', '[128, 16, 2*w^2 - 2*w - 12]', '[128, 32, 2*w^2 + 4*w + 2]', '[128, 64, 3*w^2 - 5*w - 20]', '[128, 128, -3*w + 1]', '[130, 130, w^2 + 4*w + 5]', '[130, 130, -w + 6]', '[135, 15, 3*w^2 + 9*w + 3]', '[139, 139, -4*w^2 + 10*w + 13]', '[140, 70, -w^2 + 3*w - 2]', '[140, 70, -5*w^2 + 8*w + 32]', '[140, 70, -w^2 + 5*w - 4]', '[140, 70, -3*w^2 - 8*w - 4]', '[140, 140, -2*w^2 - 5*w - 3]', '[140, 140, w^2 + 2*w - 3]', '[145, 145, -3*w^2 + 7*w + 11]', '[146, 146, -14*w^2 + 17*w + 110]', '[146, 146, 2*w^2 - 3*w - 11]', '[148, 74, -w^2 - w - 2]', '[148, 74, -3*w^2 + 4*w + 20]', '[148, 148, -5*w^2 + 8*w + 33]', '[149, 149, 5*w^2 + 13*w + 5]', '[149, 149, w^2 - 3*w - 7]', '[149, 149, 5*w^2 + 11*w + 3]', '[151, 151, w^2 - 3*w - 9]', '[151, 151, 5*w^2 - 7*w - 35]', '[151, 151, 6*w + 1]', '[155, 155, 4*w^2 - 4*w - 35]', '[160, 20, -2*w^2 + 4*w + 8]', '[160, 20, -2*w^2 - 2*w + 4]', '[160, 40, 3*w^2 + 10*w + 2]', '[160, 40, -4*w^2 + 10*w + 14]', '[160, 80, -w^2 + 3*w + 8]', '[160, 160, 2*w^2 + 7*w + 1]', '[163, 163, -2*w^2 + 2*w + 19]', '[164, 82, -w^2 + 4*w + 4]', '[164, 82, w^2 + 9*w + 2]', '[164, 164, -3*w^2 + 8*w + 7]', '[169, 13, 4*w^2 - 6*w - 29]', '[169, 169, 5*w^2 + 11*w + 1]', '[173, 173, 3*w^2 - w - 33]', '[173, 173, 2*w^2 - 4*w - 17]', '[173, 173, -6*w^2 - 14*w - 1]', '[175, 35, -w^2 + 5*w + 3]', '[175, 35, -2*w^2 + 1]', '[175, 175, 4*w^2 - 8*w - 21]', '[175, 175, -4*w^2 - 10*w - 1]', '[179, 179, -4*w^2 - 8*w - 1]', '[181, 181, -2*w^2 - 2*w + 1]', '[181, 181, w^2 + 5*w + 3]', '[181, 181, -4*w^2 - 8*w + 1]', '[182, 182, 5*w - 17]', '[182, 182, 2*w^2 + 7*w + 3]', '[182, 182, -3*w - 8]', '[182, 182, 2*w^2 - w - 14]', '[185, 185, 2*w^2 - 4*w - 13]', '[189, 21, -6*w^2 + 6*w + 51]', '[189, 21, -3*w^2 + 3*w + 27]', '[191, 191, 3*w^2 + 7*w + 3]', '[191, 191, 4*w^2 - 6*w - 31]', '[191, 191, 4*w^2 - 4*w - 33]', '[193, 193, -4*w - 3]', '[194, 194, -4*w^2 + 5*w + 28]', '[194, 194, -w^2 - 2*w - 3]', '[196, 14, w^2 + 3*w + 4]', '[196, 14, w^2 - 4*w + 4]', '[196, 14, -w^2 - w + 6]', '[196, 14, w^2 - 6*w + 8]', '[196, 28, -3*w^2 - 10*w - 3]', '[196, 28, 8*w^2 - 11*w - 59]', '[196, 98, -5*w^2 - 14*w - 4]', '[196, 98, -w^2 + w + 12]', '[196, 196, 2*w^2 + w - 1]', '[200, 10, -6*w^2 + 10*w + 38]', '[200, 20, -w^2 - 2]', '[200, 20, -w^2 + 5*w - 2]', '[200, 40, 2*w^2 + 5*w - 1]', '[200, 50, 2*w^2 - 6*w - 6]', '[200, 100, -5*w^2 + 4*w + 46]', '[200, 100, -w^2 - 5*w - 4]', '[200, 200, -6*w^2 + 7*w + 49]', '[202, 202, -2*w^2 + 5*w + 9]', '[202, 202, -8*w^2 + 13*w + 51]', '[202, 202, -2*w^2 + 5*w]', '[202, 202, -6*w^2 - 13*w]', '[202, 202, 3*w - 2]', '[202, 202, -7*w^2 + 16*w + 29]', '[203, 203, 3*w^2 - 5*w - 21]', '[203, 203, 2*w^2 - 2*w - 11]', '[205, 205, 2*w^2 - 4*w - 3]', '[206, 206, -w - 6]', '[206, 206, 2*w^2 + 7*w + 4]', '[206, 206, -2*w^2 + 3*w]', '[206, 206, -4*w^2 - 7*w - 1]', '[206, 206, 5*w^2 - 6*w - 41]', '[206, 206, -5*w^2 + 12*w + 19]', '[208, 52, -4*w^2 + 6*w + 30]', '[208, 52, -w^2 + 2*w - 2]', '[208, 52, -4*w^2 - 10*w - 4]', '[208, 104, w^2 + 3*w - 2]', '[208, 208, -7*w^2 + 10*w + 49]', '[212, 106, -w^2 + 11*w - 26]', '[212, 106, -3*w^2 + 8*w + 4]', '[212, 212, 2*w^2 - w - 19]', '[214, 214, 2*w^2 + w + 1]', '[214, 214, 2*w^2 - 3*w - 10]', '[216, 6, 6]', '[216, 12, 9*w^2 - 12*w - 66]', '[216, 12, 3*w^2 + 3*w]', '[216, 24, -3*w + 9]', '[217, 217, 3*w^2 - 7*w - 13]', '[217, 217, 2*w^2 - 4*w - 7]', '[223, 223, -2*w^2 - 2*w + 3]', '[224, 28, -2*w^2 - 6*w]', '[224, 28, 2*w^2 - 4*w - 16]', '[224, 28, 6*w^2 - 14*w - 24]', '[224, 28, 2*w^2 - 8]', '[224, 56, 2*w^2 - 4*w - 14]', '[224, 56, 4*w^2 - 6*w - 26]', '[224, 56, 5*w^2 - 10*w - 26]', '[224, 56, 3*w^2 - 6*w - 14]', '[224, 112, -w^2 - 5*w]', '[224, 112, w^2 - w + 2]', '[224, 224, 4*w^2 - 7*w - 23]', '[224, 224, 7*w^2 - 12*w - 43]', '[227, 227, 7*w^2 + 19*w + 5]', '[229, 229, -w^2 + 7*w + 1]', '[232, 58, 2*w^2 + 2*w - 2]', '[232, 116, -3*w^2 + 4*w + 26]', '[232, 116, -5*w^2 + 5*w + 42]', '[232, 232, w^2 - 4*w - 5]', '[233, 233, -2*w - 7]', '[236, 118, -w^2 - 2*w + 4]', '[236, 118, 11*w^2 - 15*w - 80]', '[236, 236, -w + 7]', '[239, 239, 2*w^2 - 4*w - 15]', '[241, 241, -3*w^2 + 5*w + 17]', '[244, 122, 3*w^2 - 5*w - 22]', '[244, 122, 5*w^2 + 12*w + 4]', '[244, 122, -3*w^2 - 10*w - 8]', '[244, 122, -13*w^2 + 17*w + 100]', '[244, 244, -w^2 - 4*w + 1]', '[244, 244, 2*w^2 + w - 9]', '[245, 35, -6*w^2 + 8*w + 43]', '[245, 35, -3*w^2 + 5*w + 23]', '[245, 245, -11*w^2 + 15*w + 81]', '[248, 62, 2*w^2 - 2*w - 2]', '[248, 124, -w^2 + 14]', '[248, 124, -w^2 - 3*w + 22]', '[248, 248, -2*w^2 + w + 15]', '[250, 10, -5*w]', '[250, 10, 5*w^2 - 10*w - 25]', '[250, 250, 2*w^2 - 3*w - 19]', '[250, 250, 2*w^2 + w - 28]', '[251, 251, -6*w^2 + 12*w + 31]', '[254, 254, -2*w^2 - 3*w - 2]', '[254, 254, -4*w^2 + 7*w + 25]', '[256, 8, 4*w^2 + 8*w]', '[256, 8, -4*w^2 + 4*w + 32]', '[256, 16, -3*w^2 + 2*w + 30]', '[256, 16, 2*w^2 - 4*w - 4]', '[256, 16, -4*w - 4]', '[256, 32, -6*w^2 + 6*w + 52]', '[256, 64, 2*w^2 - 4*w - 6]', '[256, 128, 3*w^2 + 5*w - 2]', '[256, 256, 4*w^2 - 11*w - 11]', '[257, 257, 4*w^2 - 4*w - 31]', '[259, 259, -4*w^2 + 4*w + 27]', '[259, 259, -w^2 + 5*w + 15]', '[260, 130, -5*w^2 - 13*w - 2]', '[260, 130, w^2 - 4*w - 12]', '[260, 260, 3*w^2 - 4*w - 19]', '[263, 263, 9*w^2 - 11*w - 67]', '[265, 265, -w^2 - w + 7]', '[269, 269, 2*w^2 + 6*w + 5]', '[270, 30, -6*w^2 + 9*w + 42]', '[270, 30, 3*w - 3]', '[271, 271, 2*w^2 - 4*w - 5]', '[271, 271, -4*w + 13]', '[271, 271, -2*w^2 - 8*w - 7]', '[277, 277, -3*w^2 + 3*w + 19]', '[278, 278, 2*w^2 - w - 18]', '[278, 278, 5*w + 3]', '[280, 70, 4*w + 6]', '[280, 70, -2*w^2 + 2*w + 10]', '[280, 140, 11*w^2 - 13*w - 88]', '[280, 140, -5*w^2 + 12*w + 18]', '[280, 140, -3*w^2 + 8*w + 10]', '[280, 140, -3*w^2 - 5*w - 2]', '[280, 280, -2*w^2 + 3*w + 9]', '[280, 280, -3*w^2 + 6*w + 17]', '[281, 281, -6*w^2 + 10*w + 37]', '[283, 283, 2*w^2 + 4*w - 3]', '[283, 283, 2*w^2 + 8*w + 3]', '[283, 283, -3*w^2 - 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9*w - 36]', '[1940, 1940, -2*w^2 - 9*w + 1]', '[1945, 1945, -12*w^2 - 34*w - 9]', '[1946, 1946, -14*w^2 + 39*w + 34]', '[1946, 1946, 4*w^2 + 15*w + 2]', '[1946, 1946, -3*w^2 + 8*w + 17]', '[1946, 1946, -6*w^2 + 11*w + 31]', '[1948, 974, -7*w^2 - 5*w]', '[1948, 974, -w^2 + 2*w - 8]', '[1948, 1948, -2*w^2 + 11*w - 11]', '[1949, 1949, -14*w^2 + 26*w + 79]', '[1952, 244, 6*w^2 - 10*w - 44]', '[1952, 244, 10*w^2 + 24*w + 8]', '[1952, 244, -6*w^2 - 20*w - 16]', '[1952, 244, -26*w^2 + 34*w + 200]', '[1952, 488, -2*w^2 - 8*w + 2]', '[1952, 488, w^2 - 2*w - 18]', '[1952, 488, 3*w^2 - 6*w + 2]', '[1952, 488, 4*w^2 + 2*w - 18]', '[1952, 976, 11*w^2 - 17*w - 72]', '[1952, 976, -43*w^2 + 55*w + 326]', '[1952, 1952, 3*w^2 - 4*w - 31]', '[1952, 1952, 2*w^2 - 5*w + 5]', '[1960, 70, -12*w^2 + 16*w + 86]', '[1960, 70, -6*w^2 + 10*w + 46]', '[1960, 140, -13*w^2 + 24*w + 74]', '[1960, 140, 5*w^2 + 12*w - 2]', '[1960, 140, -w^2 - w - 8]', '[1960, 140, 3*w^2 + 9*w - 2]', '[1960, 280, -11*w^2 + 16*w + 75]', '[1960, 280, -20*w^2 + 29*w + 141]', '[1960, 490, -22*w^2 + 30*w + 162]', '[1960, 980, -w^2 - 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27]', '[9970, 9970, -5*w^2 + 24*w + 11]', '[9970, 9970, -10*w^2 - 7*w - 3]', '[9970, 9970, 6*w^2 + 11*w - 12]', '[9970, 9970, 2*w^2 + 7*w - 44]', '[9970, 9970, -6*w^2 + 9*w + 22]', '[9971, 767, -23*w^2 - 63*w - 25]', '[9971, 9971, -5*w^2 - 9*w + 13]', '[9973, 9973, -28*w^2 - 66*w - 7]', '[9973, 9973, -w^2 - 13*w + 55]', '[9973, 9973, 20*w^2 - 24*w - 145]', '[9986, 9986, 28*w^2 + 69*w + 20]', '[9986, 9986, 4*w^2 - 19*w - 12]', '[9986, 9986, -10*w^2 - 7*w + 1]', '[9986, 9986, 6*w^2 - 25*w + 3]', '[9986, 9986, -7*w^2 - 8*w + 113]', '[9986, 9986, w - 22]', '[9989, 9989, 13*w^2 - 11*w - 121]', '[9989, 9989, 26*w^2 - 24*w - 229]', '[9990, 1110, 18*w^2 + 39*w + 3]', '[9990, 1110, -6*w^2 + 15*w + 66]', '[9991, 9991, -25*w^2 - 69*w - 29]', '[9991, 9991, w^2 - 17*w + 49]', '[9991, 9991, 19*w^2 - 27*w - 143]', '[9995, 9995, -7*w^2 - 21*w - 17]', '[9998, 9998, -8*w^2 + 25*w + 20]', '[9998, 9998, 4*w^2 + 19*w + 13]', '[10000, 100, 8*w^2 + 10*w - 4]', '[10000, 100, -7*w^2 + 10*w + 66]', '[10000, 100, -20*w^2 + 30*w + 140]', '[10000, 100, -12*w^2 + 10*w + 106]', '[10000, 100, -5*w^2 - 10*w - 10]', '[10000, 100, 10*w - 10]', '[10000, 200, 3*w^2 - 15*w - 14]', '[10000, 200, 15*w^2 + 35*w]', '[10000, 400, -16*w^2 - 45*w - 17]', '[10000, 400, -5*w^2 + 20*w - 15]', '[10000, 2500, -10*w^2 - 32*w - 18]', '[10000, 2500, -21*w^2 + 22*w + 174]', '[10000, 2500, 4*w^2 - 14*w - 20]', '[10000, 5000, 11*w^2 - 27*w - 34]', '[10000, 10000, 6*w^2 + w - 17]'], 'label': '3.3.1708.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -w]', '[2, 2, w^2 - 2*w - 5]', '[5, 5, w^2 + 3*w + 1]', '[7, 7, -2*w^2 + 2*w + 17]', '[7, 7, -w^2 + w + 9]', '[13, 13, 2*w + 1]', '[25, 5, -3*w^2 + 5*w + 19]', '[27, 3, 3]', '[29, 29, w^2 + w - 1]', '[31, 31, w^2 - w - 1]', '[37, 37, 2*w^2 + 6*w + 3]', '[41, 41, -6*w^2 - 14*w - 3]', '[53, 53, -4*w^2 + 6*w + 27]', '[59, 59, 2*w^2 - 4*w - 11]', '[61, 61, w^2 - w - 3]', '[61, 61, -2*w^2 + 2*w + 13]', '[73, 73, w^2 + 3*w + 3]', '[97, 97, w^2 + w - 15]', '[101, 101, w^2 + 3*w - 1]', '[101, 101, w^2 - w - 11]', '[101, 101, 2*w - 5]', '[103, 103, 3*w^2 - 3*w - 23]', '[103, 103, -w^2 + w - 1]', '[103, 103, 2*w - 3]', '[107, 107, 5*w^2 - 7*w - 37]', '[127, 127, w^2 + w - 5]', '[139, 139, -4*w^2 + 10*w + 13]', '[149, 149, 5*w^2 + 13*w + 5]', '[149, 149, w^2 - 3*w - 7]', '[149, 149, 5*w^2 + 11*w + 3]', '[151, 151, w^2 - 3*w - 9]', '[151, 151, 5*w^2 - 7*w - 35]', '[151, 151, 6*w + 1]', '[163, 163, -2*w^2 + 2*w + 19]', '[169, 13, 4*w^2 - 6*w - 29]', '[173, 173, 3*w^2 - w - 33]', '[173, 173, 2*w^2 - 4*w - 17]', '[173, 173, -6*w^2 - 14*w - 1]', '[179, 179, -4*w^2 - 8*w - 1]', '[181, 181, -2*w^2 - 2*w + 1]', '[181, 181, w^2 + 5*w + 3]', '[181, 181, -4*w^2 - 8*w + 1]', '[191, 191, 3*w^2 + 7*w + 3]', '[191, 191, 4*w^2 - 6*w - 31]', '[191, 191, 4*w^2 - 4*w - 33]', '[193, 193, -4*w - 3]', '[223, 223, -2*w^2 - 2*w + 3]', '[227, 227, 7*w^2 + 19*w + 5]', '[229, 229, -w^2 + 7*w + 1]', '[233, 233, -2*w - 7]', '[239, 239, 2*w^2 - 4*w - 15]', '[241, 241, -3*w^2 + 5*w + 17]', '[251, 251, -6*w^2 + 12*w + 31]', '[257, 257, 4*w^2 - 4*w - 31]', '[263, 263, 9*w^2 - 11*w - 67]', '[269, 269, 2*w^2 + 6*w + 5]', '[271, 271, 2*w^2 - 4*w - 5]', '[271, 271, -4*w + 13]', '[271, 271, -2*w^2 - 8*w - 7]', '[277, 277, -3*w^2 + 3*w + 19]', '[281, 281, -6*w^2 + 10*w + 37]', '[283, 283, 2*w^2 + 4*w - 3]', '[283, 283, 2*w^2 + 8*w + 3]', '[283, 283, -3*w^2 - 7*w + 1]', '[293, 293, w^2 - 7*w - 3]', '[307, 307, -2*w^2 - 1]', '[311, 311, 7*w^2 - 9*w - 51]', '[317, 317, -w^2 - 3*w + 23]', '[317, 317, 2*w^2 - 6*w - 7]', '[317, 317, 7*w^2 + 19*w + 7]', '[331, 331, -3*w^2 - 9*w - 1]', '[331, 331, w^2 - w - 13]', '[331, 331, 2*w^2 - 23]', '[337, 337, 2*w^2 + 4*w + 3]', '[347, 347, 2*w^2 + 8*w + 1]', '[353, 353, 2*w^2 - 2*w - 9]', '[373, 373, w^2 - 7*w + 13]', '[379, 379, w^2 + w - 9]', '[383, 383, w^2 + 3*w + 5]', '[389, 389, -w^2 + w - 3]', '[401, 401, -4*w^2 - 8*w + 3]', '[409, 409, 2*w^2 - 3]', '[409, 409, w^2 - 5*w - 5]', '[409, 409, 5*w^2 - 5*w - 41]', '[419, 419, 6*w^2 - 8*w - 49]', '[421, 421, w^2 + w - 11]', '[431, 431, 4*w^2 - 8*w - 19]', '[443, 443, 2*w^2 - 5]', '[457, 457, -2*w^2 + 2*w - 1]', '[461, 461, 2*w^2 - 13]', '[463, 463, 2*w^2 - 2*w - 7]', '[467, 467, 2*w^2 + 8*w + 9]', '[479, 479, -2*w^2 - 6*w + 1]', '[479, 479, 3*w^2 - w - 15]', '[479, 479, 12*w^2 - 14*w - 95]', '[487, 487, -6*w^2 + 14*w + 23]', '[491, 491, 11*w^2 - 13*w - 85]', '[521, 521, -5*w^2 + 11*w + 21]', '[521, 521, 4*w - 3]', '[521, 521, 8*w + 1]', '[523, 523, -10*w^2 + 14*w + 73]', '[541, 541, 3*w^2 - w - 19]', '[547, 547, 11*w^2 + 25*w + 1]', '[547, 547, 3*w^2 - 5*w - 15]', '[547, 547, 7*w^2 - 7*w - 59]', '[557, 557, -3*w^2 + 7*w + 7]', '[571, 571, 4*w^2 + 10*w + 5]', '[587, 587, 2*w^2 - 6*w - 9]', '[599, 599, -9*w^2 + 17*w + 49]', '[599, 599, -3*w^2 + 3*w + 17]', '[599, 599, 8*w^2 + 18*w + 5]', '[601, 601, 19*w^2 - 25*w - 143]', '[617, 617, 7*w^2 - 9*w - 57]', '[619, 619, 3*w^2 - 7*w - 15]', '[619, 619, w^2 - 5*w - 7]', '[619, 619, -2*w - 9]', '[641, 641, -w^2 + 3*w - 5]', '[643, 643, 7*w^2 - 7*w - 61]', '[647, 647, -7*w^2 + 11*w + 45]', '[653, 653, -8*w^2 - 16*w - 3]', '[659, 659, w^2 - 3*w - 15]', '[673, 673, w^2 + 3*w - 5]', '[683, 683, -7*w^2 - 15*w - 1]', '[701, 701, 3*w^2 + 3*w - 5]', '[709, 709, -3*w^2 - 5*w - 3]', '[733, 733, -6*w - 5]', '[743, 743, -2*w^2 - 2*w - 3]', '[743, 743, 4*w - 5]', '[743, 743, 6*w^2 - 6*w - 49]', '[751, 751, -6*w^2 - 12*w + 1]', '[757, 757, w^2 - 5*w - 9]', '[757, 757, -w^2 - w - 5]', '[757, 757, 4*w^2 - 8*w - 23]', '[773, 773, -8*w^2 + 14*w + 47]', '[787, 787, 8*w^2 - 10*w - 65]', '[797, 797, 9*w^2 - 13*w - 65]', '[811, 811, 6*w^2 - 8*w - 41]', '[821, 821, 6*w^2 - 6*w - 53]', '[823, 823, -4*w^2 - 6*w + 1]', '[823, 823, 9*w^2 + 19*w + 5]', '[823, 823, w^2 - 7*w - 5]', '[827, 827, -3*w^2 - 3*w + 47]', '[829, 829, -4*w^2 + 4*w + 37]', '[841, 29, 5*w^2 - 9*w - 27]', '[853, 853, 11*w^2 - 15*w - 79]', '[857, 857, -9*w^2 + 21*w + 35]', '[863, 863, 3*w^2 + 11*w + 5]', '[877, 877, 4*w - 7]', '[881, 881, -3*w^2 + w - 1]', '[887, 887, 2*w^2 - 19]', '[911, 911, -8*w^2 + 6*w + 75]', '[919, 919, 10*w^2 + 22*w - 1]', '[929, 929, -4*w^2 - 6*w + 3]', '[937, 937, 3*w^2 + 11*w + 7]', '[947, 947, -6*w - 7]', '[947, 947, 10*w^2 - 12*w - 81]', '[947, 947, 2*w^2 - 10*w - 5]', '[953, 953, 3*w^2 - w - 13]', '[961, 31, 7*w^2 - 9*w - 49]', '[967, 967, 6*w^2 - 14*w - 25]', '[983, 983, -10*w^2 - 22*w - 1]', '[991, 991, 3*w^2 - w - 21]', '[997, 997, 3*w^2 - 5*w - 5]', '[997, 997, -2*w^2 - 10*w - 1]', '[997, 997, -8*w + 27]']}
• 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, -8, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1708, 'disc_rad': 854, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1]]], [5, [[2, 1], [1, 1]]], [7, [0]], [11, [[3, 1]]], [13, [[2, 1], [1, 1]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[3, 1]]], [29, [[2, 1], [1, 1]]], [31, [[2, 1], [1, 1]]], [37, [[2, 1], [1, 1]]], [41, [[2, 1], [1, 1]]], [43, [[3, 1]]], [47, [[3, 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': [6, 3, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 41.32795663954365, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1708.1', 'local_algs': ['2.1.0.1', '2.2.2.2', '7.1.0.1', '7.2.1.2', '61.1.0.1', '61.2.1.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 7, 61], 'rd': 11.953523934, 'regulator': {'__RealLiteral__': 0, 'data': '12.8730037743', 'prec': 44}, 'res': {'gal': ['56,224,186,-38,-45,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a - 7 \\)', '\\( 5 a^{2} - 9 a - 29 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}