Hilbert modular form data - 3.3.837.1-16.3-c

Formats: - HTML - YAML - JSON - 2024-05-04T22:45:48.341653

• 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': 3, 'disc': 837, 'field_bad_primes': [3, 31], 'field_label': '3.3.837.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.837.1-16.3-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [2], 'level_ideal': '[16, 16, -w^2 - w + 4]', 'level_label': '16.3', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.3-c', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [], 'hecke_eigenvalues': [0, 'e', 'e^2 + e - 7', 'e^2 - 6', '-e - 2', '2*e - 2', 'e^2 + 2*e - 8', '-2*e^2 - 4*e + 16', '2*e^2 + 2*e - 14', 6, '2*e^2 + e - 16', '-e^2', -6, '2*e^2 - 6', '-e^2 + 6', '4*e^2 + 3*e - 24', '2*e^2 - 14', '-2*e^2 - 3*e + 12', '-2*e + 2', '-3*e^2 - 4*e + 16', 'e^2 - 2', '-4*e^2 - 2*e + 26', '-4*e - 2', '-3*e - 6', '-5*e^2 - 6*e + 36', '-2*e^2 + 18', '2*e^2 + 4*e - 16', '-2*e^2 - 6*e + 12', '4*e^2 + 6*e - 30', 6, '3*e^2 + 6*e - 18', '-2*e^2 - 6*e + 20', '2*e^2 - 6', '2*e^2 - 2*e - 16', '2*e^2 + 3*e - 12', '2*e^2 + 3*e - 12', '-2*e^2 + 24', '-2*e^2 - 4*e + 22', '6*e + 6', '-2*e^2 + 12', 12, '-2*e^2 - 3*e', '-5*e + 2', '2*e^2', '-2*e^2 + 3*e + 18', '-3*e^2 - 6*e + 30', 6, 'e^2 - 2*e - 16', '-2*e^2 - 8*e + 20', '6*e + 4', '4*e^2 + 4*e - 28', '4*e^2 + 4*e - 16', '-4*e^2 - 6*e + 36', '-6*e^2 - 8*e + 38', '6*e^2 + 6*e - 30', '-2*e^2 - 2', '3*e - 6', '2*e^2 + 2*e - 8', '-6*e^2 - 3*e + 46', '4*e^2 - 3*e - 18', '-3*e^2 + 6*e + 18', '-6*e^2 - 6*e + 48', '2*e^2 + 4*e - 22', '-6*e^2 + 30', '5*e^2 + 2*e - 20', '-4*e^2 - 4*e + 46', '4*e^2 + 6*e - 32', '-8*e^2 - 6*e + 54', 'e^2 - 6*e - 6', '4*e^2 - 18', '4*e^2 + 12*e - 24', '2*e^2 + 2*e - 8', '7*e^2 + 6*e - 34', '-4*e^2 + 2*e + 34', '-2*e^2 - e + 22', 18, '-6*e - 6', 18, '-2*e^2 - 3*e + 10', '-6*e + 12', 'e^2', '3*e^2 + 10*e - 22', '-4*e^2 - 6*e + 36', '5*e^2 + 6*e - 50', '-4*e^2 + 4*e + 32', '-5*e^2 - 6*e + 36', '-12*e^2 - 6*e + 72', '-5*e^2 + 2*e + 16', '-7*e^2 - 8*e + 68', '-4*e^2 - 3*e + 12', '4*e^2 + 12*e - 42', 'e^2 + 4', '-2*e^2 - 3*e + 16', '6*e^2 + 8*e - 68', '2*e^2 + 2*e + 4', '8*e^2 + 9*e - 72', '2*e^2 - 6*e - 20', '-8*e^2 + 30', '8*e^2 + 12*e - 72', '6*e^2 + 6*e - 46', '-4*e^2 - 6*e + 8', '6*e^2 - 32', '-10*e^2 - 12*e + 80', '-4*e^2 - 6*e + 14', '-2*e^2 + 3*e + 18', '-7*e^2 + 4*e + 44', '-9*e^2 - 14*e + 80', '4*e^2 - 18', '-6*e^2 - 6*e + 54', '8*e^2 + 12*e - 78', '-4*e^2 + 8*e + 28', '-6*e^2 - 9*e + 30', '6*e^2 + 6*e - 60', '-e^2 - 2*e - 34', '9*e^2 - 58', '-4*e^2 + 4*e + 38', '-8*e^2 + 4*e + 50', '-12*e^2 - 6*e + 84', '3*e + 30', '4*e^2 - 12*e - 38', '4*e^2 - 5*e - 16', '-4*e^2 - 4*e + 10', '18*e^2 + 9*e - 102', '-8*e^2 + 3*e + 66', '8*e^2 + 9*e - 66', '4*e^2 - 10*e - 26', '4*e^2 + 5*e - 62', '-4*e^2 + 6*e + 26', '6*e^2 + 12*e - 42', '2*e^2 + 12*e - 6', '-6*e + 18', '-3*e^2 + 4*e + 20', '3*e^2 - 42', '-4*e^2 + 42', '-2*e^2 + 3*e + 18', '-8*e^2 - 12*e + 42', '-9*e^2 - 18*e + 66', '6*e^2 + 6*e - 18', '-10*e^2 - 3*e + 44', '2*e^2 + 6*e - 12', '9*e^2 + 6*e - 60', '8*e^2 - 60', '8*e^2 + 12*e - 62', '8*e^2 + 12*e - 72', '2*e^2 - 6*e - 30', '-e^2 + 10*e + 20', '-14*e^2 - 4*e + 82', '7*e^2 + 2*e - 38', '-4*e^2 + 3*e + 26', '-8*e^2 - 4*e + 28', '-3*e^2 + 6*e + 48', '6*e^2 + 12*e - 66', '-12*e^2 - 18*e + 102', '10*e^2 + 12*e - 66', '4*e^2 - 9*e - 24', '-12*e^2 - 3*e + 72', '4*e^2 - 12', '-2*e^2 - 12*e + 6', '-6*e^2 + 54', '-7*e^2 + 42', '-2*e^2 + 5*e - 20', '3*e^2 - 12*e - 12', '-4*e^2 + 18', '-12*e - 16'], 'hecke_polynomial': 'x^3 - x^2 - 9*x + 12', 'label': '3.3.837.1-16.3-c'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 837, 'ideals': ['[1, 1, 1]', '[2, 2, w^2 - 2*w - 1]', '[3, 3, w + 2]', '[4, 2, w^2 + w - 3]', '[4, 4, w + 1]', '[5, 5, -w + 2]', '[6, 6, w - 1]', '[8, 2, 2]', '[8, 8, w - 3]', '[9, 3, -w^2 + 2*w + 2]', '[10, 10, -w - 3]', '[12, 6, w^2 - w - 3]', '[12, 12, w^2 + 3*w + 2]', '[13, 13, -2*w - 5]', '[15, 15, -w^2 + 4]', '[16, 4, -w^2 + w + 5]', '[16, 4, 2*w^2 - 4*w - 2]', '[16, 16, -w^2 - w + 4]', '[18, 6, w^2 + w - 2]', '[20, 10, w^2 + w - 1]', '[20, 20, -w^2 + w + 2]', '[24, 6, 2*w + 4]', '[24, 24, w^2 - w - 6]', '[25, 5, -w^2 - 2*w + 2]', '[25, 25, -2*w^2 - 4*w + 1]', '[26, 26, -w^2 + 3]', '[27, 3, 3]', '[30, 30, -w^2 + 3*w - 2]', '[31, 31, -w^2 + 2]', '[31, 31, -2*w + 1]', '[32, 4, 2*w^2 + 2*w - 6]', '[32, 8, 2*w + 2]', '[32, 32, w^2 - 2*w - 3]', '[36, 6, w^2 + w - 5]', '[36, 12, w^2 - 2*w + 1]', '[37, 37, 2*w + 3]', '[39, 39, w - 4]', '[40, 10, -2*w + 4]', '[40, 40, -w^2 - 4*w - 3]', '[41, 41, -w - 4]', '[43, 43, 2*w^2 - 2*w - 7]', '[45, 15, -2*w^2 - 2*w + 7]', '[47, 47, -2*w^2 - w + 8]', '[48, 12, -w^2 + w + 9]', '[48, 12, 2*w - 2]', '[48, 48, w^2 - 4*w + 3]', '[50, 10, 2*w^2 - w - 9]', '[50, 50, w^2 + w - 6]', '[52, 26, -w^2 - w + 7]', '[52, 52, -2*w^2 + 5*w - 1]', '[53, 53, 3*w^2 - 6*w - 2]', '[53, 53, -2*w^2 + 3*w + 18]', '[53, 53, 2*w - 3]', '[54, 6, 3*w^2 - 6*w - 3]', '[59, 59, 2*w^2 - 3*w - 4]', '[60, 30, 3*w^2 - 5*w - 7]', '[60, 60, -w^2 - 2*w + 3]', '[61, 61, w^2 - 2*w - 4]', '[62, 62, 3*w^2 - 5*w - 6]', '[62, 62, 3*w - 7]', '[64, 4, 4]', '[64, 8, -w^2 - 3*w - 3]', '[64, 16, 2*w - 6]', '[64, 64, -2*w^2 - 3*w + 3]', '[65, 65, -w^2 - 2*w - 2]', '[71, 71, 4*w + 9]', '[72, 6, -2*w^2 + 4*w + 4]', '[72, 24, 2*w^2 + 5*w - 1]', '[73, 73, 2*w^2 - 9]', '[74, 74, w^2 + w - 10]', '[75, 15, 2*w^2 - 6*w + 1]', '[75, 75, -2*w^2 + 2*w + 9]', '[78, 78, -2*w^2 - 3*w + 5]', '[79, 79, w^2 - 4*w + 2]', '[80, 20, -2*w - 6]', '[80, 20, -3*w^2 + 7*w + 3]', '[80, 80, -w^2 + 9]', '[81, 9, 3*w + 6]', '[82, 82, -2*w^2 + 3*w + 3]', '[86, 86, -w^2 + 2*w + 9]', '[90, 30, w^2 - 2*w - 5]', '[93, 93, -2*w^2 - 4*w + 3]', '[93, 93, -2*w^2 - 3*w + 2]', '[94, 94, w - 5]', '[96, 12, 2*w^2 - 2*w - 6]', '[96, 24, 2*w^2 + 6*w + 4]', '[96, 96, -w - 5]', '[97, 97, 2*w^2 - w - 8]', '[97, 97, -w^2 + 2*w - 2]', '[97, 97, -2*w^2 - 2*w + 5]', '[100, 10, -w^2 + 3*w - 3]', '[100, 20, -w^2 + 3*w + 12]', '[100, 50, w^2 - 3*w - 3]', '[100, 100, -3*w^2 + 6*w + 5]', '[101, 101, w^2 + 2*w - 4]', '[104, 26, -4*w - 10]', '[104, 104, -w^2 - 3*w + 2]', '[106, 106, w^2 + 5*w + 2]', '[106, 106, 2*w^2 + w - 11]', '[106, 106, -7*w^2 + 16*w + 5]', '[107, 107, 3*w + 8]', '[108, 6, 3*w^2 + 3*w - 9]', '[108, 12, 3*w + 3]', '[111, 111, -4*w^2 + 9*w + 4]', '[113, 113, w^2 - 2*w - 6]', '[117, 39, w^2 - 2*w - 8]', '[118, 118, 3*w + 5]', '[120, 30, -2*w^2 + 8]', '[120, 120, 2*w^2 - 5*w - 3]', '[122, 122, 5*w^2 - 13*w]', '[123, 123, -w^2 - 6*w - 8]', '[124, 62, -w^2 - 5*w - 7]', '[124, 62, -w^2 - 5*w - 5]', '[124, 124, -w^2 + 2*w + 7]', '[124, 124, -w^2 + w + 10]', '[125, 5, 5]', '[125, 125, 3*w + 4]', '[127, 127, 3*w - 2]', '[128, 8, -2*w^2 + 2*w + 10]', '[128, 8, 4*w^2 - 8*w - 4]', '[128, 32, -2*w^2 - 2*w + 8]', '[128, 128, -w^2 + w - 2]', '[129, 129, 2*w^2 + w - 12]', '[130, 130, -2*w^2 + 3*w + 7]', '[131, 131, -3*w^2 - 4*w + 8]', '[135, 15, -3*w + 6]', '[137, 137, 4*w^2 + 2*w - 17]', '[137, 137, -w^2 - 2*w + 10]', '[137, 137, 2*w^2 - 2*w - 5]', '[139, 139, -w^2 + 6*w + 20]', '[141, 141, -3*w^2 + 4*w + 8]', '[142, 142, w^2 + 2*w - 5]', '[144, 12, w^2 - 5*w + 7]', '[144, 12, 2*w^2 + 2*w - 4]', '[144, 48, -2*w^2 + w + 7]', '[146, 146, w^2 - 4*w + 5]', '[148, 74, 3*w^2 - 5*w - 5]', '[148, 148, -3*w^2 - 2*w + 13]', '[149, 149, 2*w^2 - 4*w - 21]', '[150, 30, -w^2 - 2*w - 3]', '[150, 150, 3*w^2 + 2*w - 11]', '[151, 151, -2*w^2 + 7*w - 4]', '[155, 155, -2*w^2 + 4*w + 5]', '[155, 155, 2*w^2 - 5*w + 2]', '[156, 78, -3*w^2 - w + 13]', '[156, 156, w^2 - 3*w - 4]', '[158, 158, -w^2 - 3*w - 4]', '[159, 159, -3*w^2 + 2*w + 16]', '[159, 159, 4*w - 1]', '[159, 159, 2*w^2 + w - 6]', '[160, 20, 2*w^2 + 2*w - 2]', '[160, 40, -2*w^2 + 2*w + 4]', '[160, 160, 4*w^2 - 7*w - 7]', '[162, 18, 3*w - 3]', '[164, 82, -5*w^2 - 7*w + 11]', '[164, 164, -w^2 - 5*w - 4]', '[167, 167, 2*w - 7]', '[167, 167, 2*w^2 + 2*w - 3]', '[167, 167, 2*w^2 - 7]', '[169, 13, 4*w^2 - 10*w + 1]', '[169, 169, -2*w^2 + 2*w + 11]', '[172, 86, -3*w^2 + w + 21]', '[172, 172, 3*w - 5]', '[173, 173, 2*w^2 - 2*w - 17]', '[177, 177, w^2 + 2*w - 6]', '[179, 179, 2*w^2 + 3*w - 6]', '[179, 179, 3*w - 4]', '[179, 179, w - 6]', '[180, 30, w^2 + w - 11]', '[180, 60, 4*w^2 - 11*w + 1]', '[181, 181, -w - 6]', '[183, 183, -2*w - 7]', '[185, 185, -2*w^2 + w + 6]', '[186, 186, w^2 + 2*w - 9]', '[186, 186, 3*w^2 - w - 14]', '[188, 94, 3*w^2 - 3*w - 13]', '[188, 188, -7*w^2 + 15*w + 6]', '[191, 191, 2*w^2 - 2*w - 13]', '[192, 12, 4*w + 8]', '[192, 24, w^2 + 3*w - 13]', '[192, 48, 2*w^2 - 2*w - 12]', '[192, 192, -3*w^2 + 5*w + 4]', '[194, 194, 4*w^2 - 11*w + 3]', '[194, 194, 3*w^2 + w - 20]', '[194, 194, -11*w^2 + 25*w + 6]', '[195, 195, -w^2 + 6*w - 8]', '[197, 197, 5*w^2 - 12*w]', '[197, 197, 3*w^2 - 14]', '[197, 197, -3*w^2 - 4*w + 6]', '[199, 199, 4*w - 9]', '[200, 10, -2*w^2 - 4*w + 4]', '[200, 40, w^2 + 2*w - 7]', '[200, 50, -4*w^2 - 8*w + 2]', '[200, 200, 2*w^2 + w - 5]', '[202, 202, -3*w^2 + 7*w + 4]', '[205, 205, w^2 + 2*w - 8]', '[208, 52, -2*w^2 + 6]', '[208, 52, 3*w^2 + 5*w - 3]', '[208, 208, 3*w^2 - 3*w - 10]', '[211, 211, 2*w^2 + 2*w - 9]', '[211, 211, 4*w - 11]', '[211, 211, w^2 - 2*w - 12]', '[212, 106, w^2 + w + 3]', '[212, 106, 5*w^2 - w - 27]', '[212, 106, -w^2 + 3*w + 11]', '[212, 212, -3*w^2 + 10*w + 1]', '[212, 212, 2*w^2 - w - 3]', '[212, 212, -3*w^2 + 5*w + 8]', '[213, 213, -2*w^2 + 3*w + 8]', '[214, 214, 2*w^2 - w - 5]', '[215, 215, 4*w^2 - 3*w - 30]', '[216, 6, 6]', '[216, 24, 3*w - 9]', '[219, 219, 4*w^2 + 3*w - 16]', '[222, 222, 2*w^2 + w - 3]', '[223, 223, 2*w^2 + w - 4]', '[225, 15, -2*w^2 + w + 4]', '[225, 75, -w^2 - 4*w + 2]', '[226, 226, 3*w^2 - 9*w + 2]', '[227, 227, 4*w^2 - 2*w - 19]', '[229, 229, -6*w^2 - 5*w + 22]', '[233, 233, -3*w^2 + 2*w + 12]', '[234, 78, w^2 - 5*w + 4]', '[235, 235, -2*w^2 + 3]', '[236, 118, -w^2 + w + 11]', '[236, 236, -w^2 + 5*w - 2]', '[237, 237, -2*w^2 + 5]', '[240, 60, w^2 - w + 3]', '[240, 60, -2*w^2 + 6*w - 4]', '[240, 240, -3*w^2 - 5*w + 2]', '[241, 241, -w^2 + 4*w + 14]', '[243, 9, -3*w^2 + 6*w + 6]', '[244, 122, -3*w^2 - 3*w + 11]', '[244, 244, -w^2 - 3]', '[246, 246, -w^2 - 3*w + 4]', '[248, 62, -2*w^2 + 4]', '[248, 62, -4*w + 2]', '[248, 248, -2*w^2 + 7*w - 3]', '[248, 248, 3*w^2 - 4*w - 7]', '[250, 10, 5*w^2 - 10*w - 5]', '[250, 250, w^2 + 2*w - 13]', '[254, 254, -8*w^2 + 19*w + 5]', '[256, 8, 4*w^2 + 4*w - 12]', '[256, 16, w^2 - 5*w + 3]', '[256, 16, 4*w + 4]', '[256, 64, 2*w^2 - 4*w - 6]', '[256, 256, -5*w^2 + 9*w + 10]', '[257, 257, -w^2 - 4*w - 6]', '[258, 258, -4*w^2 + 7*w + 9]', '[260, 130, 3*w^2 - 9*w + 1]', '[260, 260, 3*w^2 + 3*w - 8]', '[262, 262, w^2 - 3*w - 6]', '[265, 265, -2*w^2 - 6*w - 5]', '[265, 265, 4*w + 7]', '[265, 265, -2*w^2 + 7*w - 6]', '[270, 30, -3*w - 9]', '[271, 271, -6*w^2 + 12*w + 7]', '[274, 274, w^2 - 3*w - 14]', '[274, 274, 9*w^2 - 22*w - 1]', '[274, 274, -w^2 + 11]', '[277, 277, -w^2 - 2*w - 4]', '[278, 278, 3*w^2 + w - 12]', '[279, 93, 2*w^2 - 7*w + 2]', '[279, 93, -4*w^2 + 5*w + 14]', '[281, 281, w^2 - 4*w - 4]', '[282, 282, w^2 - 3*w - 10]', '[284, 142, 3*w^2 - w - 13]', '[284, 284, -4*w^2 + 9*w + 5]', '[288, 12, 2*w^2 + 2*w - 10]', '[288, 24, 2*w^2 - 4*w + 2]', '[288, 96, -w^2 - 7*w - 10]', '[291, 291, 3*w^2 + 2*w - 14]', '[291, 291, -4*w - 5]', '[291, 291, -6*w^2 + 4*w + 29]', '[292, 146, -3*w^2 + 5*w + 29]', '[292, 292, 2*w^2 + 3*w - 7]', '[293, 293, 3*w^2 + 2*w - 10]', '[295, 295, w^2 - 4*w - 16]', '[296, 74, 4*w + 6]', '[296, 296, 2*w^2 - 3*w - 9]', '[298, 298, 3*w^2 - 13]', '[300, 30, w^2 - 3*w - 7]', '[300, 60, -3*w^2 + 4*w + 11]', '[300, 150, -w^2 - 3*w - 5]', '[300, 300, -w + 7]', '[302, 302, w + 7]', '[303, 303, 4*w^2 + 6*w - 7]', '[305, 305, 4*w^2 - 6*w - 9]', '[310, 310, 3*w^2 + 4*w - 5]', '[310, 310, 2*w^2 + 5*w - 3]', '[311, 311, -6*w^2 + 14*w + 5]', '[312, 78, 2*w - 8]', '[312, 312, -5*w^2 - 10*w + 3]', '[313, 313, -2*w^2 - 10*w - 13]', '[316, 158, w^2 - 3*w - 9]', '[316, 316, -3*w^2 + 3*w + 14]', '[317, 317, -4*w^2 - 2*w + 19]', '[318, 318, -9*w^2 + 22*w + 5]', '[318, 318, 2*w^2 - 5*w + 3]', '[318, 318, 5*w^2 + 3*w - 20]', '[320, 20, -4*w + 8]', '[320, 40, w^2 + 3*w - 5]', '[320, 80, -2*w^2 - 8*w - 6]', '[320, 320, -w^2 + 3*w + 8]', '[321, 321, w^2 - 4*w + 6]', '[324, 18, 3*w^2 - 3*w - 9]', '[324, 36, 3*w^2 + 9*w + 6]', '[325, 65, 3*w^2 - 4*w - 6]', '[325, 325, 4*w - 3]', '[328, 82, -2*w - 8]', '[328, 328, -w^2 - w + 12]', '[331, 331, 2*w^2 + 4*w - 5]', '[333, 111, w^2 - 2*w + 4]', '[334, 334, -3*w^2 - 4*w + 9]', '[334, 334, 3*w^2 - 6*w + 1]', '[334, 334, 3*w^2 - 8*w + 3]', '[337, 337, -4*w^2 - 3*w + 14]', '[338, 26, w^2 + 4*w - 3]', '[338, 338, -3*w^2 + 10*w - 5]', '[339, 339, -4*w - 11]', '[343, 7, -7]', '[344, 86, 4*w^2 - 4*w - 14]', '[344, 344, w^2 + 5*w + 8]', '[346, 346, -3*w^2 + 2*w + 11]', '[351, 39, -6*w - 15]', '[353, 353, w^2 + 8*w + 14]', '[353, 353, -4*w^2 + 4*w + 31]', '[353, 353, 2*w^2 + 2*w - 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35]', '[1860, 930, -5*w^2 + 17*w - 9]', '[1860, 930, 7*w^2 + 11*w - 15]', '[1860, 1860, w^2 + 9*w + 8]', '[1860, 1860, -5*w^2 - 3*w + 26]', '[1861, 1861, 10*w^2 + 16*w - 19]', '[1861, 1861, 4*w^2 - w - 10]', '[1861, 1861, w^2 + 10*w + 20]', '[1864, 466, -6*w^2 + 4*w + 24]', '[1864, 1864, 12*w^2 - 27*w - 11]', '[1865, 1865, -7*w^2 + 20*w - 2]', '[1865, 1865, -2*w^2 + 8*w + 7]', '[1865, 1865, 7*w^2 - 8*w - 22]', '[1866, 1866, 8*w^2 + 19*w - 3]', '[1867, 1867, 4*w^2 + w - 6]', '[1867, 1867, 8*w^2 + 3*w - 40]', '[1867, 1867, 6*w^2 - 13*w - 10]', '[1868, 934, -3*w^2 - 7*w - 7]', '[1868, 1868, w^2 - 2*w + 9]', '[1871, 1871, 6*w^2 - 2*w - 27]', '[1871, 1871, 4*w - 15]', '[1871, 1871, -3*w^2 + 6*w + 28]', '[1872, 156, 2*w^2 - 10*w + 8]', '[1872, 156, w^2 + 7*w - 5]', '[1872, 624, -5*w^2 - 17*w - 8]', '[1873, 1873, -8*w - 15]', '[1875, 75, -5*w^2 + 20]', '[1875, 75, -4*w^2 - 3*w + 28]', '[1875, 1875, -4*w^2 - 6*w + 13]', '[1877, 1877, 2*w - 13]', '[1877, 1877, 13*w^2 - 32*w]', '[1877, 1877, -4*w^2 - 21*w - 28]', '[1878, 1878, -8*w^2 - 15*w + 11]', '[1880, 470, -4*w^2 + 6]', '[1880, 1880, 6*w^2 - 9*w - 11]', '[1882, 1882, 3*w^2 + 10*w - 3]', '[1882, 1882, -8*w^2 + 15*w + 9]', '[1882, 1882, -5*w^2 + 3*w + 18]', '[1888, 236, -2*w^2 + 2*w + 22]', '[1888, 472, -2*w^2 + 10*w - 4]', '[1888, 1888, -8*w^2 - 11*w + 17]', '[1891, 1891, 5*w^2 - 6*w - 6]', '[1891, 1891, 7*w - 6]', '[1893, 1893, 2*w + 13]', '[1894, 1894, w^2 + 9*w + 10]', '[1894, 1894, w^2 + 10*w + 15]', '[1894, 1894, 4*w^2 + w - 9]', '[1896, 474, -4*w^2 + 10]', '[1896, 1896, 6*w^2 - 7*w - 17]', '[1898, 1898, 3*w^2 - 2*w - 27]', '[1899, 633, 5*w^2 - 4*w - 16]', '[1899, 633, 19*w^2 - 38*w - 26]', '[1899, 633, 4*w^2 - 5*w - 20]', '[1901, 1901, 5*w^2 - 8*w - 16]', '[1902, 1902, 2*w^2 - 3*w - 23]', '[1905, 1905, 2*w^2 - 6*w - 11]', '[1906, 1906, 5*w^2 - w - 20]', '[1906, 1906, 5*w^2 - 16*w + 1]', '[1906, 1906, 4*w^2 - w - 7]', '[1907, 1907, -11*w^2 + 24*w + 12]', '[1908, 318, -5*w^2 + 13*w + 7]', '[1908, 318, 5*w^2 + 5*w - 43]', '[1908, 318, -w^2 - w + 17]', '[1908, 636, 11*w^2 + 29*w + 2]', '[1908, 636, -7*w^2 + 20*w - 1]', '[1908, 636, -2*w^2 + 7*w + 25]', '[1910, 1910, -4*w^2 + 7*w + 37]', '[1916, 958, -w^2 - 9*w - 9]', '[1916, 1916, -3*w^2 + 6*w + 13]', '[1917, 213, 12*w + 27]', '[1920, 120, 2*w^2 - 2*w + 6]', '[1920, 120, -4*w^2 + 12*w - 8]', '[1920, 480, -6*w^2 - 10*w + 4]', '[1920, 1920, 4*w^2 - w - 9]', '[1922, 62, 7*w^2 - 12*w - 17]', '[1922, 62, -6*w^2 + 17*w - 7]', '[1922, 1922, -3*w^2 - 13*w - 16]', '[1923, 1923, 3*w^2 + 4*w - 16]', '[1923, 1923, 8*w^2 + 13*w - 12]', '[1923, 1923, -2*w^2 - 12*w - 19]', '[1924, 962, -5*w^2 - w + 19]', '[1924, 1924, 7*w^2 - 4*w - 31]', '[1926, 642, -5*w^2 + 16*w - 5]', '[1927, 1927, -9*w^2 - 8*w + 30]', '[1928, 482, -2*w^2 + 8*w + 28]', '[1928, 1928, 4*w^2 + w - 7]', '[1929, 1929, 7*w^2 + 8*w - 18]', '[1931, 1931, 5*w^2 - 6*w - 10]', '[1933, 1933, 4*w^2 - 7*w - 14]', '[1934, 1934, 9*w^2 - 24*w + 5]', '[1935, 645, 8*w^2 - 4*w - 49]', '[1937, 1937, 8*w^2 - 4*w - 47]', '[1940, 970, w^2 + w + 9]', '[1940, 970, -5*w^2 + w + 3]', '[1940, 970, 9*w^2 + 7*w - 35]', '[1940, 1940, w^2 + 3*w + 10]', '[1940, 1940, 8*w^2 - 15*w - 7]', '[1940, 1940, -w^2 + 6*w - 13]', '[1942, 1942, 2*w^2 + 11*w + 7]', '[1944, 18, -6*w^2 + 12*w + 12]', '[1944, 72, 6*w^2 + 15*w - 3]', '[1948, 974, -13*w^2 - 19*w + 27]', '[1948, 1948, -3*w^2 - 13*w - 10]', '[1950, 390, -7*w^2 + 16*w + 9]', '[1950, 1950, -3*w^2 - 4*w + 25]', '[1951, 1951, 2*w^2 + w - 22]', '[1952, 244, -6*w^2 - 6*w + 22]', '[1952, 488, -2*w^2 - 6]', '[1952, 1952, 3*w^2 - 9*w + 8]', '[1954, 1954, 7*w^2 + 6*w - 27]', '[1959, 1959, 4*w^2 - 7]', '[1961, 1961, 4*w^2 - 9]', '[1961, 1961, 3*w - 14]', '[1961, 1961, -6*w^2 + 7*w + 24]', '[1963, 1963, -4*w^2 - 3*w + 24]', '[1965, 1965, 4*w^2 - 15*w + 14]', '[1968, 492, 3*w^2 - 7*w - 35]', '[1968, 492, -2*w^2 - 6*w + 8]', '[1968, 1968, 7*w - 13]', '[1970, 1970, -3*w^2 + 6*w - 5]', '[1970, 1970, -9*w^2 - 4*w + 39]', '[1970, 1970, -3*w^2 + 12*w - 7]', '[1971, 219, 6*w^2 - 27]', '[1973, 1973, 2*w^2 - 5*w - 26]', '[1975, 395, -6*w^2 - 2*w + 37]', '[1975, 1975, -6*w^2 - w + 26]', '[1977, 1977, 7*w^2 - 12*w - 10]', '[1979, 1979, 3*w^2 + 8*w - 6]', '[1979, 1979, 3*w^2 + 6*w - 10]', '[1979, 1979, w^2 + 6*w - 24]', '[1982, 1982, 2*w^2 + 5*w - 11]', '[1983, 1983, -8*w^2 + 15*w + 8]', '[1983, 1983, -6*w^2 + 2*w + 43]', '[1983, 1983, 5*w^2 + 6*w - 8]', '[1984, 124, -4*w^2 + 8]', '[1984, 124, -8*w + 4]', '[1984, 248, 3*w^2 - 7*w - 31]', '[1984, 248, w^2 - 5*w - 21]', '[1984, 496, -4*w^2 + 14*w - 6]', '[1984, 496, 6*w^2 - 8*w - 14]', '[1984, 1984, 5*w^2 + 14*w + 9]', '[1984, 1984, -7*w^2 - 4*w + 27]', '[1986, 1986, 2*w^2 + 3*w + 7]', '[1987, 1987, 2*w^2 + 2*w - 23]', '[1990, 1990, -4*w^2 - 3*w + 27]', '[1996, 998, -5*w^2 - 5*w + 11]', '[1996, 1996, 2*w^2 - 11*w - 5]', '[1998, 222, 3*w^2 + 3*w - 30]', '[1999, 1999, 4*w + 15]', '[2000, 20, -5*w^2 + 5*w + 25]', '[2000, 20, 10*w^2 - 20*w - 10]', '[2000, 80, -5*w^2 - 5*w + 20]', '[2000, 500, 2*w^2 + 4*w - 26]', '[2000, 500, -w^2 + w + 17]', '[2000, 2000, -7*w^2 - 10*w + 13]', '[2003, 2003, 7*w^2 - 18*w + 4]', '[2004, 1002, -11*w^2 - 9*w + 41]', '[2004, 1002, -w^2 - 3*w + 19]', '[2004, 1002, w^2 - w + 9]', '[2004, 2004, -w^2 - 5*w - 12]', '[2004, 2004, 19*w^2 + 45*w + 2]', '[2004, 2004, 9*w^2 + 17*w - 8]', '[2005, 2005, 4*w^2 + 5*w + 4]', '[2005, 2005, 10*w^2 + 2*w - 49]', '[2005, 2005, -2*w^2 + 10*w - 7]', '[2007, 669, -2*w^2 + 10*w - 5]', '[2011, 2011, -4*w^2 + 15*w - 10]', '[2012, 1006, -3*w^2 + 5*w + 23]', '[2012, 2012, 5*w^2 - 6*w - 7]', '[2015, 2015, -3*w - 14]', '[2015, 2015, 2*w^2 - 6*w - 21]', '[2018, 2018, 11*w^2 - 29*w - 2]', '[2019, 2019, -4*w^2 + 9*w + 10]', '[2020, 1010, 3*w^2 + 13*w + 7]', '[2020, 2020, 2*w^2 - 7*w - 9]', '[2021, 2021, w^2 + 6*w - 8]', '[2022, 2022, w^2 - 7*w - 18]', '[2025, 45, 6*w^2 - 18*w + 3]', '[2025, 225, -6*w^2 + 6*w + 27]', '[2026, 2026, -9*w^2 + 3*w + 46]', '[2026, 2026, 9*w^2 - 5*w - 48]', '[2026, 2026, -w^2 - 9]', '[2028, 78, 5*w^2 + 7*w - 15]', '[2028, 156, -4*w^2 - 3*w + 25]', '[2028, 1014, 3*w^2 + 5*w - 29]', '[2028, 2028, w^2 + 11*w + 18]', '[2032, 508, 5*w^2 - 5*w - 13]', '[2032, 508, -16*w^2 + 38*w + 10]', '[2032, 2032, -w^2 - 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7]', '[9930, 9930, w^2 - 13*w + 12]', '[9931, 9931, -13*w - 16]', '[9932, 4966, 17*w^2 - 3*w - 91]', '[9932, 9932, -10*w^2 + 17*w + 27]', '[9934, 9934, 4*w^2 + 7*w - 31]', '[9935, 9935, 2*w^2 + 15*w - 48]', '[9939, 9939, 11*w^2 + 10*w - 42]', '[9942, 9942, 10*w^2 + 15*w - 13]', '[9942, 9942, -27*w^2 + 58*w + 23]', '[9942, 9942, -w^2 - 11*w + 12]', '[9948, 4974, 5*w^2 + 7*w - 27]', '[9948, 9948, -4*w^2 - 9*w + 43]', '[9949, 9949, -9*w^2 + 10*w + 40]', '[9950, 1990, -22*w^2 + 21*w + 89]', '[9950, 9950, -5*w^2 - 9*w + 58]', '[9951, 9951, 9*w^2 - 28*w + 4]', '[9951, 9951, -10*w^2 + 15*w + 16]', '[9952, 1244, 2*w^2 + 10*w - 14]', '[9952, 2488, 2*w^2 - 16*w + 22]', '[9952, 9952, -5*w^2 - 22*w - 17]', '[9957, 9957, 13*w^2 - 30*w + 2]', '[9957, 9957, 12*w^2 + 7*w - 46]', '[9957, 9957, 8*w^2 - 29]', '[9963, 369, 6*w^2 - 12*w - 21]', '[9964, 4982, -9*w^2 - 9*w + 35]', '[9964, 4982, -21*w^2 - 15*w + 83]', '[9964, 4982, -11*w^2 - 15*w + 21]', '[9964, 9964, -17*w - 9]', '[9964, 9964, -4*w^2 + 3*w - 9]', '[9964, 9964, -w^2 - 9*w - 24]', '[9969, 9969, 4*w^2 - 10*w - 39]', '[9969, 9969, -6*w^2 + w + 50]', '[9969, 9969, -10*w^2 + 9*w + 34]', '[9971, 767, 6*w^2 + 11*w - 18]', '[9971, 9971, 15*w - 34]', '[9972, 1662, -7*w^2 - 13*w + 17]', '[9972, 3324, -7*w^2 + 5*w - 4]', '[9973, 9973, 4*w^2 + 9*w - 18]', '[9974, 9974, -w^2 + 13*w - 16]', '[9978, 9978, -10*w^2 - 33*w - 17]', '[9978, 9978, -5*w^2 - 15*w + 8]', '[9978, 9978, -2*w^2 - 15*w + 5]', '[9980, 4990, -5*w^2 + 9*w + 27]', '[9980, 9980, 15*w^2 - 29*w - 12]', '[9984, 312, -12*w^2 - 4*w + 52]', '[9984, 624, 4*w^2 - 12*w - 16]', '[9984, 624, -9*w^2 + 29*w - 11]', '[9984, 2496, -12*w^2 + 22*w + 26]', '[9984, 9984, 8*w^2 + 19*w - 9]', '[9990, 1110, -18*w^2 + 45*w - 3]', '[9992, 2498, -8*w^2 + 26*w - 4]', '[9992, 2498, 8*w^2 + 10*w - 28]', '[9992, 2498, 4*w^2 - 2*w - 40]', '[9992, 9992, 13*w^2 + 40*w + 11]', '[9992, 9992, -7*w^2 - 5*w + 46]', '[9992, 9992, -7*w^2 - 5*w + 62]', '[9993, 9993, 7*w^2 - 10*w - 66]', '[9993, 9993, -17*w^2 + 38*w + 18]', '[9993, 9993, w^2 - 12*w - 16]', '[9995, 9995, -4*w^2 - 7*w + 30]', '[9997, 9997, 10*w^2 + 53*w + 70]', '[9997, 9997, 16*w^2 - 7*w - 98]', '[9997, 9997, -20*w^2 - 14*w + 77]', '[9998, 9998, -19*w^2 + 39*w + 12]', '[9998, 9998, -6*w^2 - 3*w + 53]', '[9998, 9998, -3*w^2 - 18*w - 13]', '[10000, 100, 3*w^2 + 21*w + 29]', '[10000, 100, -10*w - 30]', '[10000, 100, 6*w^2 - 8*w - 42]', '[10000, 100, -15*w^2 + 35*w + 15]', '[10000, 400, -9*w^2 + 12*w + 13]', '[10000, 400, -5*w^2 + 45]', '[10000, 2500, -3*w^2 - 9*w + 35]', '[10000, 2500, -6*w^2 - 26*w - 24]', '[10000, 10000, -4*w^2 + 9*w + 33]'], 'label': '3.3.837.1', 'narrow_class_no': 1, 'primes': ['[2, 2, w^2 - 2*w - 1]', '[3, 3, w + 2]', '[4, 2, w^2 + w - 3]', '[5, 5, -w + 2]', '[13, 13, -2*w - 5]', '[25, 5, -w^2 - 2*w + 2]', '[31, 31, -w^2 + 2]', '[31, 31, -2*w + 1]', '[37, 37, 2*w + 3]', '[41, 41, -w - 4]', '[43, 43, 2*w^2 - 2*w - 7]', '[47, 47, -2*w^2 - w + 8]', '[53, 53, 3*w^2 - 6*w - 2]', '[53, 53, -2*w^2 + 3*w + 18]', '[53, 53, 2*w - 3]', '[59, 59, 2*w^2 - 3*w - 4]', '[61, 61, w^2 - 2*w - 4]', '[71, 71, 4*w + 9]', '[73, 73, 2*w^2 - 9]', '[79, 79, w^2 - 4*w + 2]', '[97, 97, 2*w^2 - w - 8]', '[97, 97, -w^2 + 2*w - 2]', '[97, 97, -2*w^2 - 2*w + 5]', '[101, 101, w^2 + 2*w - 4]', '[107, 107, 3*w + 8]', '[113, 113, w^2 - 2*w - 6]', '[127, 127, 3*w - 2]', '[131, 131, -3*w^2 - 4*w + 8]', '[137, 137, 4*w^2 + 2*w - 17]', '[137, 137, -w^2 - 2*w + 10]', '[137, 137, 2*w^2 - 2*w - 5]', '[139, 139, -w^2 + 6*w + 20]', '[149, 149, 2*w^2 - 4*w - 21]', '[151, 151, -2*w^2 + 7*w - 4]', '[167, 167, 2*w - 7]', '[167, 167, 2*w^2 + 2*w - 3]', '[167, 167, 2*w^2 - 7]', '[169, 13, 4*w^2 - 10*w + 1]', '[173, 173, 2*w^2 - 2*w - 17]', '[179, 179, 2*w^2 + 3*w - 6]', '[179, 179, 3*w - 4]', '[179, 179, w - 6]', '[181, 181, -w - 6]', '[191, 191, 2*w^2 - 2*w - 13]', '[197, 197, 5*w^2 - 12*w]', '[197, 197, 3*w^2 - 14]', '[197, 197, -3*w^2 - 4*w + 6]', '[199, 199, 4*w - 9]', '[211, 211, 2*w^2 + 2*w - 9]', '[211, 211, 4*w - 11]', '[211, 211, w^2 - 2*w - 12]', '[223, 223, 2*w^2 + w - 4]', '[227, 227, 4*w^2 - 2*w - 19]', '[229, 229, -6*w^2 - 5*w + 22]', '[233, 233, -3*w^2 + 2*w + 12]', '[241, 241, -w^2 + 4*w + 14]', '[257, 257, -w^2 - 4*w - 6]', '[271, 271, -6*w^2 + 12*w + 7]', '[277, 277, -w^2 - 2*w - 4]', '[281, 281, w^2 - 4*w - 4]', '[293, 293, 3*w^2 + 2*w - 10]', '[311, 311, -6*w^2 + 14*w + 5]', '[313, 313, -2*w^2 - 10*w - 13]', '[317, 317, -4*w^2 - 2*w + 19]', '[331, 331, 2*w^2 + 4*w - 5]', '[337, 337, -4*w^2 - 3*w + 14]', '[343, 7, -7]', '[353, 353, w^2 + 8*w + 14]', '[353, 353, -4*w^2 + 4*w + 31]', '[353, 353, 2*w^2 + 2*w - 11]', '[359, 359, 6*w^2 + w - 30]', '[367, 367, -4*w^2 + 4*w + 17]', '[373, 373, -2*w^2 + 3*w + 16]', '[373, 373, 2*w^2 - 3*w - 10]', '[373, 373, -2*w^2 + 3*w - 2]', '[401, 401, -w^2 + 6*w - 10]', '[401, 401, w^2 + 6*w + 10]', '[401, 401, -w^2 - 4]', '[409, 409, -8*w^2 + 18*w + 7]', '[419, 419, 4*w - 5]', '[431, 431, w^2 - 12]', '[433, 433, 3*w - 10]', '[443, 443, -2*w^2 + 5*w + 22]', '[457, 457, w^2 + 4*w - 4]', '[463, 463, w - 8]', '[467, 467, -3*w^2 + 4*w + 12]', '[479, 479, -w^2 - 2*w + 14]', '[487, 487, -3*w - 10]', '[499, 499, -2*w^2 + 4*w - 3]', '[503, 503, -w^2 + 6*w - 6]', '[521, 521, -2*w - 9]', '[523, 523, 4*w^2 - 9*w - 6]', '[547, 547, 8*w^2 + 14*w - 11]', '[547, 547, 7*w^2 + 10*w - 16]', '[547, 547, -2*w^2 + 5*w - 4]', '[563, 563, 5*w + 8]', '[571, 571, -w^2 + 6*w - 4]', '[593, 593, 3*w^2 - 2*w - 24]', '[599, 599, 8*w^2 + 2*w - 39]', '[601, 601, w^2 - 4*w - 8]', '[607, 607, 2*w^2 - 4*w - 9]', '[607, 607, -6*w^2 - 4*w + 23]', '[607, 607, 4*w^2 - 12*w + 1]', '[613, 613, 3*w^2 - 10]', '[617, 617, 2*w^2 - w - 18]', '[619, 619, -5*w^2 + 4*w + 20]', '[631, 631, -3*w^2 + 6*w + 8]', '[641, 641, w^2 - 4*w - 10]', '[641, 641, 4*w^2 - 5*w - 10]', '[641, 641, 2*w^2 + 4*w - 7]', '[643, 643, 2*w^2 + 3*w - 10]', '[653, 653, -3*w^2 + 10*w - 2]', '[659, 659, 4*w^2 + 5*w - 8]', '[661, 661, -5*w^2 + 4*w + 24]', '[661, 661, 5*w - 4]', '[661, 661, -4*w^2 - 6*w + 5]', '[673, 673, 8*w^2 - 20*w + 1]', '[683, 683, 3*w^2 + 2*w - 18]', '[701, 701, 3*w^2 - 2*w - 6]', '[709, 709, -5*w^2 - 4*w + 20]', '[739, 739, 5*w^2 - 24]', '[757, 757, 3*w^2 - 4]', '[761, 761, -8*w^2 + 16*w + 9]', '[761, 761, 8*w^2 + 11*w - 18]', '[761, 761, -w^2 + 2*w - 6]', '[769, 769, 4*w^2 - 17]', '[769, 769, -4*w^2 + 9*w + 44]', '[769, 769, -5*w - 14]', '[773, 773, -7*w^2 - 6*w + 24]', '[773, 773, 9*w^2 - 22*w]', '[773, 773, 3*w^2 - 8]', '[787, 787, -6*w^2 + 11*w + 8]', '[809, 809, 6*w^2 - 15*w + 2]', '[809, 809, 6*w^2 - 9*w - 14]', '[809, 809, 5*w - 6]', '[821, 821, 5*w^2 + 2*w - 26]', '[821, 821, 2*w^2 - 4*w - 11]', '[821, 821, -4*w^2 + 4*w + 19]', '[823, 823, 4*w^2 - 3*w - 14]', '[827, 827, 2*w^2 + 3*w - 12]', '[827, 827, 3*w^2 + 8*w + 6]', '[827, 827, -6*w + 13]', '[829, 829, 6*w + 11]', '[839, 839, 2*w^2 - 4*w - 17]', '[857, 857, -w^2 + 4*w - 8]', '[859, 859, 2*w^2 + 3*w - 16]', '[877, 877, 6*w^2 + 2*w - 31]', '[877, 877, 5*w^2 - 12*w + 2]', '[877, 877, 2*w^2 + 5*w - 6]', '[883, 883, 7*w + 18]', '[887, 887, 4*w^2 - 8*w - 9]', '[941, 941, -w - 10]', '[941, 941, 3*w^2 - 4*w - 28]', '[941, 941, 6*w^2 - 14*w + 1]', '[947, 947, -8*w^2 + 17*w + 10]', '[947, 947, 5*w^2 - 8*w - 8]', '[947, 947, 4*w^2 - 4*w - 11]', '[953, 953, -3*w^2 + 6*w + 32]', '[953, 953, -6*w - 7]', '[953, 953, 2*w^2 + 9*w + 12]', '[967, 967, 4*w^2 - 2*w - 15]', '[971, 971, 6*w^2 - 11*w - 6]', '[977, 977, -2*w^2 - 2*w + 21]', '[991, 991, 9*w + 20]']}
• 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, -6, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 837, 'disc_rad': 93, 'disc_sign': 1, 'frobs': [[2, [[2, 1], [1, 1]]], [3, [0]], [5, [[2, 1], [1, 1]]], [7, [[3, 1]]], [11, [[3, 1]]], [13, [[2, 1], [1, 1]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [0]], [37, [[2, 1], [1, 1]]], [41, [[2, 1], [1, 1]]], [43, [[2, 1], [1, 1]]], [47, [[2, 1], [1, 1]]], [53, [[1, 3]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [7, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 20.05960194310363, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.837.1', 'local_algs': ['3.3.3.1', '31.1.0.1', '31.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 31], 'rd': 9.42414195717, 'regulator': {'__RealLiteral__': 0, 'data': '6.80136952587', 'prec': 44}, 'res': {'gal': ['4,-18,3,29,-12,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( 2 a^{2} + 6 a + 3 \\)'], 'unitsGmodule': [[4, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}