Hilbert modular form data - 3.3.229.1-37.3-c

Formats: - HTML - YAML - JSON - 2024-04-28T11:18:00.651997

• 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': 4, 'disc': 229, 'field_bad_primes': [229], 'field_label': '3.3.229.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.229.1-37.3-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [37], 'level_ideal': '[37, 37, 2*w^2 - w - 10]', 'level_label': '37.3', 'level_norm': 37, 'parallel_weight': 2, 'short_label': '37.3-c', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[37, 37, 2*w^2 - w - 10]', -1]], 'hecke_eigenvalues': ['-1/6*e^3 + 11/6*e', 'e', 0, '1/6*e^3 - 17/6*e', 'e^2 - 5', 4, '-e^2 + 11', '-1/6*e^3 + 5/6*e', '-2*e', '-2*e', 1, '-1/3*e^3 + 11/3*e', '-e^2 + 5', '1/3*e^3 - 11/3*e', '-2*e', '1/2*e^3 - 9/2*e', -2, '-1/6*e^3 + 29/6*e', '-1/6*e^3 + 29/6*e', '2*e^2 - 16', '-e^2 + 5', 'e^2 - 3', '2/3*e^3 - 40/3*e', '-e^2 + 9', '-e^2 + 11', '-1/6*e^3 + 17/6*e', '-2*e^2 + 24', '-2*e^2 + 18', '5/6*e^3 - 49/6*e', '1/3*e^3 - 23/3*e', 4, '-e^3 + 15*e', '3/2*e^3 - 39/2*e', '1/3*e^3 + 1/3*e', '-1/3*e^3 + 11/3*e', '-2/3*e^3 + 28/3*e', '2*e^2 - 28', '-1/6*e^3 + 29/6*e', '2*e^2 - 18', '-2*e^2 + 20', '-3*e^2 + 25', '-e^2 - 1', '2*e^2 - 12', '2/3*e^3 - 46/3*e', 0, '-2*e^2 + 18', 12, '-5/3*e^3 + 67/3*e', '-e^2 + 3', '-e^2 + 13', -6, '1/3*e^3 - 11/3*e', '-11/6*e^3 + 115/6*e', '-2*e^2 + 6', 'e^2 - 27', '-e^2 + 29', '-1/6*e^3 + 41/6*e', '-1/3*e^3 + 23/3*e', '1/3*e^3 - 17/3*e', '-1/6*e^3 + 17/6*e', '-3*e^2 + 37', 4, '3/2*e^3 - 39/2*e', '2*e^2 - 14', '5/3*e^3 - 61/3*e', '2/3*e^3 - 40/3*e', '-e^2 + 15', '-5/6*e^3 + 25/6*e', '1/6*e^3 - 5/6*e', '-2*e^2 - 6', 'e^3 - 17*e', '-1/3*e^3 + 5/3*e', '-4/3*e^3 + 44/3*e', 0, '-3/2*e^3 + 43/2*e', -20, '2*e^3 - 26*e', 8, '5/6*e^3 - 73/6*e', '4*e^2 - 48', '1/6*e^3 - 77/6*e', '-2/3*e^3 + 10/3*e', '5/2*e^3 - 53/2*e', '-2*e^2 + 4', '-1/2*e^3 + 25/2*e', '1/3*e^3 + 13/3*e', '3*e^2 - 41', '5/6*e^3 - 37/6*e', 8, -16, '-5/3*e^3 + 85/3*e', '-2/3*e^3 + 46/3*e', '4/3*e^3 - 56/3*e', -16, '-2*e^2 + 32', '4*e^2 - 38', '2*e^2 - 12', '5/3*e^3 - 55/3*e', '-5/3*e^3 + 61/3*e', '-4*e^2 + 54', '-e^3 + 11*e', '6*e', '-2*e^2 - 8', '8*e', -12, 12, '2*e^2 + 16', 18, '2*e^2 + 8', '-e^2 + 15', '-7/3*e^3 + 83/3*e', '-6*e^2 + 56', '-7/3*e^3 + 83/3*e', '6*e^2 - 46', '-3/2*e^3 + 63/2*e', 14, '-1/6*e^3 + 17/6*e', 18, '10*e', '5/3*e^3 - 85/3*e', '8/3*e^3 - 100/3*e', '4*e^2 - 40', '-1/3*e^3 + 41/3*e', '-4*e^2 + 24', '-5/6*e^3 + 49/6*e', '-2*e^2 + 10', '8*e^2 - 66', '-2/3*e^3 - 2/3*e', '-7/6*e^3 + 71/6*e', '-2*e^3 + 30*e', '-e^3 + 17*e', '4*e^2 - 24', '-17/6*e^3 + 217/6*e', '-7*e^2 + 67', '5*e^2 - 57', '-2*e^3 + 22*e', '-1/3*e^3 - 1/3*e', '5/3*e^3 - 43/3*e', '13/6*e^3 - 173/6*e', '2*e^2 + 8', '3*e^2 - 3', '-e^3 + 5*e', '-3*e^2 + 27', '-6*e^2 + 68', '2*e^2 - 2', '-4*e^2 + 22', '-2*e^2 - 24', '2*e^2 - 48', '6*e^2 - 32', 'e^2 + 21', '-4*e^3 + 44*e', '-12*e', '-e^2 + 33', '2/3*e^3 - 46/3*e', '10/3*e^3 - 140/3*e', '-1/6*e^3 + 17/6*e', '11/6*e^3 - 223/6*e', '-5/2*e^3 + 61/2*e', '-2*e^3 + 34*e', '3*e^2 - 55', 'e^3 - 21*e', '5/3*e^3 - 91/3*e', '-4/3*e^3 + 98/3*e', '4*e^2 - 2', '2*e^2 + 14'], 'hecke_polynomial': 'x^4 - 17*x^2 + 36', 'label': '3.3.229.1-37.3-c'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 229, 'ideals': ['[1, 1, 1]', '[2, 2, w + 1]', '[4, 2, -w^2 + w + 3]', '[4, 4, w - 1]', '[7, 7, w^2 - 2]', '[8, 2, 2]', '[8, 8, w^2 - w - 4]', '[13, 13, -w^2 + 2*w + 2]', '[14, 14, -w + 3]', '[16, 4, w^2 + w - 3]', '[16, 4, 2*w + 2]', '[16, 16, -w - 3]', '[23, 23, -2*w + 1]', '[26, 26, -w^2 - w + 4]', '[27, 3, 3]', '[28, 14, w^2 + w - 5]', '[28, 28, -w^2 + 2*w + 3]', '[29, 29, -2*w + 3]', '[31, 31, -2*w^2 + 2*w + 3]', '[32, 4, -2*w^2 + 2*w + 6]', '[32, 8, 2*w - 2]', '[32, 32, -2*w^2 + w + 5]', '[37, 37, 4*w^2 - 2*w - 13]', '[37, 37, -2*w^2 + 5]', '[37, 37, 2*w^2 - w - 10]', '[41, 41, w^2 - 2*w - 4]', '[46, 46, -w^2 + 2*w + 5]', '[47, 47, w - 4]', '[49, 7, 2*w^2 - w - 4]', '[49, 49, w + 4]', '[52, 26, w^2 - w - 7]', '[52, 52, -2*w^2 - w + 3]', '[53, 53, 2*w^2 - 2*w - 7]', '[53, 53, 3*w^2 - 2*w - 8]', '[53, 53, 2*w + 5]', '[54, 6, 3*w + 3]', '[56, 14, 2*w^2 - 4]', '[56, 56, -2*w^2 - w + 7]', '[58, 58, -2*w^2 + w + 3]', '[59, 59, 2*w^2 - 2*w - 9]', '[62, 62, -w^2 + 7]', '[64, 4, 4]', '[64, 8, w^2 - 3*w - 3]', '[64, 16, 2*w^2 - 2*w - 8]', '[64, 64, -w^2 - 2*w + 3]', '[67, 67, 2*w^2 - 3]', '[73, 73, 2*w^2 + w - 8]', '[74, 74, 2*w^2 + 3*w - 3]', '[74, 74, 2*w^2 + w - 9]', '[74, 74, w^2 - 3*w - 8]', '[79, 79, -2*w^2 - 2*w + 5]', '[82, 82, -w^2 - 2*w - 3]', '[89, 89, w^2 + 2*w - 4]', '[91, 91, 3*w - 2]', '[92, 46, -3*w^2 + 3*w + 5]', '[92, 92, w^2 + 2*w - 7]', '[94, 94, w^2 - 3*w - 4]', '[98, 14, w^2 + 3*w - 2]', '[98, 98, 3*w^2 - 2*w - 7]', '[101, 101, 3*w^2 - 8]', '[104, 26, -2*w^2 + 4*w + 4]', '[104, 104, w - 5]', '[106, 106, -w - 5]', '[106, 106, w^2 + 2*w - 5]', '[106, 106, 2*w^2 + 7*w + 5]', '[107, 107, 3*w^2 + 2*w - 8]', '[108, 6, -3*w^2 + 3*w + 9]', '[108, 12, 3*w - 3]', '[109, 109, w^2 + 2*w - 6]', '[112, 28, -w^2 + 3*w + 7]', '[112, 28, -2*w + 6]', '[112, 112, 3*w^2 - 3*w - 4]', '[113, 113, 2*w^2 - 3*w - 6]', '[116, 58, w^2 - 3*w - 5]', '[116, 116, -w^2 + w + 8]', '[118, 118, -3*w - 7]', '[124, 62, -w^2 - w - 3]', '[124, 124, -w^2 + 3*w + 6]', '[125, 5, -5]', '[127, 127, 4*w - 1]', '[128, 8, 2*w^2 + 2*w - 6]', '[128, 8, 4*w + 4]', '[128, 32, -2*w - 6]', '[128, 128, 3*w^2 - 4*w - 7]', '[131, 131, 4*w^2 - 3*w - 10]', '[134, 134, 2*w^2 + 5*w - 1]', '[137, 137, 3*w^2 - 2*w - 6]', '[139, 139, -w^2 - 2*w + 10]', '[146, 146, 3*w^2 + w - 6]', '[148, 74, -3*w^2 + w + 15]', '[148, 74, 3*w^2 + w - 13]', '[148, 74, 7*w^2 - 3*w - 27]', '[148, 148, -2*w^2 + 3*w + 7]', '[148, 148, 3*w^2 - 7]', '[148, 148, -3*w^2 - w + 12]', '[157, 157, 4*w^2 - 4*w - 11]', '[158, 158, 3*w^2 - 3*w - 10]', '[161, 161, w^2 - 4*w - 4]', '[163, 163, 2*w^2 - 4*w - 5]', '[164, 82, w^2 + w - 9]', '[164, 164, -3*w^2 + 2*w + 5]', '[169, 13, 2*w^2 - 3*w - 10]', '[169, 169, -w^2 - 2*w - 4]', '[173, 173, 3*w^2 - 2*w - 4]', '[173, 173, 2*w^2 - 3*w - 8]', '[173, 173, 2*w^2 + 2*w - 7]', '[178, 178, 3*w^2 + 2*w - 3]', '[179, 179, 4*w^2 - 2*w - 11]', '[182, 182, 2*w^2 - 3*w - 9]', '[184, 46, -4*w + 2]', '[184, 184, 3*w^2 - w - 6]', '[188, 94, -3*w^2 - w + 5]', '[188, 188, -2*w^2 - 3*w - 3]', '[189, 21, 3*w^2 - 6]', '[191, 191, w - 6]', '[193, 193, -w - 6]', '[193, 193, 2*w^2 + 2*w - 11]', '[193, 193, 2*w^2 - w - 12]', '[196, 14, w^2 + 3*w - 9]', '[196, 28, -3*w^2 + 5*w + 6]', '[196, 98, -3*w^2 + 3*w + 11]', '[196, 196, w^2 + 3*w - 4]', '[197, 197, 3*w^2 - 2*w - 16]', '[199, 199, 4*w^2 + w - 10]', '[202, 202, 3*w^2 + 4*w - 5]', '[203, 203, 3*w^2 - 4*w - 8]', '[208, 52, 3*w^2 - w - 5]', '[208, 52, -2*w^2 - 2*w + 8]', '[208, 208, w^2 - 4*w - 5]', '[211, 211, 5*w + 4]', '[212, 106, 3*w^2 + w - 17]', '[212, 106, 3*w^2 + 3*w - 19]', '[212, 106, -3*w^2 + 3*w + 13]', '[212, 212, -5*w^2 + 6*w + 11]', '[212, 212, -4*w^2 + 3*w + 9]', '[212, 212, 2*w^2 + 3*w - 5]', '[214, 214, 5*w^2 + 6*w - 5]', '[216, 6, 6]', '[216, 24, 3*w^2 - 3*w - 12]', '[217, 217, -w^2 + 2*w - 4]', '[218, 218, 3*w^2 - 5]', '[223, 223, -2*w + 7]', '[224, 28, 2*w^2 + 2*w - 10]', '[224, 56, -2*w^2 + 4*w + 6]', '[224, 224, w^2 - 9]', '[226, 226, -w^2 - w - 4]', '[227, 227, -2*w^2 + w - 2]', '[229, 229, 3*w^2 - 4]', '[229, 229, 4*w - 3]', '[232, 58, -4*w + 6]', '[232, 232, 3*w^2 - 6*w - 5]', '[236, 118, 5*w^2 - w - 23]', '[236, 236, -4*w^2 + w + 11]', '[239, 239, -2*w - 7]', '[241, 241, -w^2 + 4*w - 6]', '[241, 241, w^2 - 4*w - 6]', '[241, 241, -w^2 + 4*w + 8]', '[248, 62, -4*w^2 + 4*w + 6]', '[248, 248, w^2 + 3*w - 8]', '[250, 10, -5*w - 5]', '[251, 251, -3*w - 8]', '[254, 254, 4*w^2 + 3*w - 1]', '[256, 8, -4*w^2 + 4*w + 12]', '[256, 16, -w^2 + 3*w - 5]', '[256, 16, 4*w - 4]', '[256, 64, -4*w^2 + 2*w + 10]', '[256, 256, -w^2 + w - 4]', '[257, 257, -w^2 - 4]', '[259, 259, -6*w^2 + 19]', '[259, 259, -5*w^2 + 24]', '[259, 259, -w^2 + 2*w + 10]', '[262, 262, w^2 + 3*w - 6]', '[263, 263, 3*w^2 + 2*w - 10]', '[268, 134, w^2 + 3*w - 7]', '[268, 268, -2*w^2 + 5*w + 5]', '[269, 269, 4*w^2 - 4*w - 5]', '[274, 274, w^2 + 4*w - 3]', '[278, 278, -3*w^2 + 4*w + 9]', '[281, 281, 2*w^2 - 4*w - 7]', '[283, 283, 4*w^2 - 3*w - 8]', '[287, 287, -2*w^2 - 3*w + 6]', '[292, 146, 7*w^2 - 3*w - 23]', '[292, 292, -w^2 - w + 10]', '[296, 74, 8*w^2 - 4*w - 26]', '[296, 74, 4*w^2 - 10]', '[296, 74, 4*w^2 - 2*w - 20]', '[296, 296, -5*w^2 - w + 18]', '[296, 296, -w^2 - 2*w + 11]', '[296, 296, -9*w^2 + 4*w + 37]', '[299, 299, -4*w^2 + 5*w + 10]', '[313, 313, 4*w^2 - w - 10]', '[314, 314, w - 7]', '[316, 158, -w^2 + 5*w + 5]', '[316, 316, -w - 7]', '[317, 317, 5*w - 2]', '[322, 322, 3*w^2 + 3*w - 8]', '[326, 326, -2*w^2 - w - 3]', '[328, 82, 2*w^2 - 4*w - 8]', '[328, 328, -2*w^2 + w + 13]', '[329, 329, -4*w^2 + 2*w + 9]', '[331, 331, -2*w^2 - 2*w + 15]', '[338, 26, -w^2 - 5*w - 8]', '[338, 338, -4*w^2 + 3*w + 7]', '[343, 7, 7]', '[343, 343, 4*w^2 + 2*w - 7]', '[346, 346, w^2 + 6*w - 1]', '[346, 346, -w^2 - 3*w - 6]', '[346, 346, 4*w^2 + 3*w - 5]', '[347, 347, -4*w^2 + 4*w + 13]', '[347, 347, 4*w^2 + 2*w - 13]', '[347, 347, 3*w^2 - 4*w - 10]', '[349, 349, 2*w^2 - 4*w - 11]', '[351, 39, -3*w^2 + 6*w + 6]', '[353, 353, w^2 + 4*w - 4]', '[356, 178, 5*w^2 - 3*w - 13]', '[356, 356, w^2 - 2*w + 5]', '[358, 358, 2*w^2 + 3*w - 7]', '[359, 359, 2*w^2 - 5*w - 6]', '[359, 359, 2*w^2 - 4*w - 9]', '[359, 359, 6*w - 1]', '[364, 182, 5*w^2 - 5*w - 9]', '[364, 364, -w^2 - 4*w - 7]', '[368, 92, -2*w^2 + 4*w + 10]', '[368, 92, -w^2 - w - 5]', '[368, 368, 2*w^2 + 5*w - 3]', '[371, 371, -3*w^2 - 2*w + 12]', '[371, 371, -2*w^2 - w + 14]', '[371, 371, 5*w^2 + 4*w - 8]', '[376, 94, 2*w - 8]', '[376, 376, -4*w^2 + 3*w + 5]', '[377, 377, 4*w^2 - 9]', '[378, 42, -3*w + 9]', '[379, 379, 5*w^2 - 14]', '[382, 382, w^2 - 5*w - 6]', '[383, 383, 5*w^2 - 2*w - 14]', '[383, 383, 4*w^2 + w - 8]', '[383, 383, 3*w^2 + 2*w - 14]', '[386, 386, w^2 - 5*w - 10]', '[386, 386, -w^2 - 7*w - 6]', '[386, 386, 4*w^2 - w - 9]', '[389, 389, 4*w^2 - 4*w - 19]', '[392, 14, 4*w^2 - 2*w - 8]', '[392, 56, -3*w^2 - 2*w + 13]', '[392, 98, 2*w + 8]', '[392, 392, 3*w^2 - 4*w - 15]', '[394, 394, w^2 - 6*w - 13]', '[398, 398, 5*w^2 + 7*w - 6]', '[403, 403, 2*w^2 + 4*w - 5]', '[404, 202, 5*w^2 + w - 21]', '[404, 404, -3*w^2 + 4*w + 11]', '[406, 406, -w^2 - 5]', '[413, 413, -5*w^2 - 2*w + 16]', '[416, 52, 2*w^2 - 2*w - 14]', '[416, 104, -4*w^2 - 2*w + 6]', '[416, 416, 4*w^2 + 3*w - 11]', '[419, 419, 2*w^2 + 3*w - 8]', '[422, 422, -w^2 + 6*w - 3]', '[424, 106, 4*w^2 - 4*w - 14]', '[424, 106, 6*w^2 - 4*w - 16]', '[424, 106, 4*w + 10]', '[424, 424, -6*w^2 - w + 27]', '[424, 424, -5*w^2 + w + 24]', '[424, 424, 3*w^2 - 5*w - 18]', '[428, 214, 7*w^2 - w - 23]', '[428, 428, -w^2 + 2*w + 11]', '[432, 12, 3*w^2 + 3*w - 9]', '[432, 12, 6*w + 6]', '[432, 48, -3*w - 9]', '[434, 434, 5*w^2 - w - 14]', '[436, 218, 7*w^2 - 5*w - 19]', '[436, 436, w^2 - 4*w + 7]', '[439, 439, 4*w^2 - 2*w - 7]', '[439, 439, 4*w^2 + w - 22]', '[439, 439, 9*w^2 - 4*w - 30]', '[443, 443, 2*w^2 + 3*w - 12]', '[443, 443, 3*w^2 - 4*w - 12]', '[443, 443, 3*w^2 - 4*w - 14]', '[446, 446, -2*w^2 + 5*w + 7]', '[448, 28, 4*w^2 - 8]', '[448, 56, -w^2 - 5*w + 3]', '[448, 112, -4*w^2 - 2*w + 14]', '[448, 448, w^2 - 5*w - 8]', '[449, 449, -6*w^2 + 5*w + 14]', '[449, 449, -2*w^2 - 5*w - 6]', '[449, 449, 4*w^2 - w - 8]', '[452, 226, w^2 + 3*w - 13]', '[452, 452, -5*w^2 + 5*w + 8]', '[454, 454, -w^2 - 9*w - 4]', '[458, 458, 3*w^2 + 8*w - 1]', '[458, 458, 4*w^2 + w - 3]', '[461, 461, 5*w^2 - 4*w - 22]', '[461, 461, 5*w - 4]', '[461, 461, 4*w^2 - 2*w - 5]', '[464, 116, -4*w^2 + 2*w + 6]', '[464, 116, w^2 + w - 11]', '[464, 464, 2*w^2 + 3*w - 9]', '[469, 469, w^2 + 2*w + 6]', '[472, 118, 4*w^2 - 4*w - 18]', '[472, 472, -7*w^2 + 3*w + 32]', '[478, 478, -2*w^2 - 9*w - 7]', '[479, 479, w - 8]', '[481, 481, -8*w^2 + 31]', '[481, 481, 4*w^2 - 4*w - 15]', '[481, 481, w^2 + 4*w - 6]', '[482, 482, -3*w^2 - 6*w - 5]', '[482, 482, 3*w^2 - 6*w - 7]', '[482, 482, 3*w^2 + 8*w + 7]', '[487, 487, 2*w^2 + 3*w - 10]', '[496, 124, 3*w^2 - 5*w - 9]', '[496, 124, -2*w^2 + 14]', '[496, 496, 4*w^2 - w - 7]', '[499, 499, 6*w^2 + 2*w - 15]', '[500, 10, 5*w^2 - 5*w - 15]', '[500, 20, -5*w + 5]', '[502, 502, -5*w^2 + 2*w + 13]', '[503, 503, 4*w^2 - 7]', '[503, 503, 4*w^2 + w - 6]', '[503, 503, w^2 + 2*w - 12]', '[508, 254, 5*w^2 - 5*w - 7]', '[508, 508, 4*w^2 - 5*w + 1]', '[509, 509, 4*w^2 - 2*w - 21]', '[509, 509, 2*w^2 - w - 14]', '[509, 509, 6*w^2 - 29]', '[511, 511, -4*w^2 + 4*w + 17]', '[512, 8, 8]', '[512, 16, 2*w^2 - 6*w - 6]', '[512, 32, 4*w^2 - 4*w - 16]', '[512, 128, -2*w^2 - 4*w + 6]', '[512, 512, 5*w^2 - 13]', '[514, 514, -w^2 - 8*w - 5]', '[518, 518, 7*w^2 - w - 32]', '[518, 518, -5*w^2 + 4*w + 19]', '[518, 518, 6*w^2 - 3*w - 17]', '[521, 521, 4*w^2 - w - 6]', '[523, 523, 2*w^2 - 5*w - 8]', '[524, 262, -w^2 + w + 11]', '[524, 524, 4*w^2 + w - 5]', '[526, 526, 5*w^2 + 4*w - 7]', '[529, 23, 4*w^2 + 2*w - 15]', '[529, 529, -w^2 - 4*w + 8]', '[533, 533, -2*w^2 + 3*w - 4]', '[536, 134, 4*w^2 - 6]', '[536, 536, -3*w^2 - 3*w + 10]', '[538, 538, -7*w + 1]', '[541, 541, 6*w^2 - w - 18]', '[541, 541, 4*w^2 - 5]', '[541, 541, -w^2 + 2*w - 6]', '[547, 547, -4*w^2 + 5*w + 12]', '[548, 274, w^2 + 5*w - 13]', '[548, 548, -5*w^2 + 8*w + 9]', '[553, 553, w^2 - 6*w - 12]', '[556, 278, -11*w^2 + 9*w + 31]', '[556, 556, -w^2 + 8*w - 11]', '[562, 562, -2*w^2 - 3*w - 5]', '[563, 563, 4*w^2 - 3*w - 22]', '[566, 566, w^2 + 5*w - 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20]', '[9719, 9719, 16*w^2 - 12*w - 39]', '[9722, 9722, -5*w^2 + 13*w + 22]', '[9731, 9731, 14*w^2 - 17*w - 34]', '[9731, 9731, 14*w^2 - 8*w - 35]', '[9731, 9731, 11*w + 28]', '[9733, 9733, 6*w^2 + 13*w - 12]', '[9734, 9734, 23*w^2 - 16*w - 73]', '[9736, 2434, 22*w^2 - 12*w - 68]', '[9736, 9736, -w^2 - 7*w + 28]', '[9737, 9737, 8*w + 25]', '[9739, 9739, 12*w^2 + 5*w - 22]', '[9739, 9739, 2*w^2 - 27]', '[9739, 9739, 20*w^2 - 13*w - 68]', '[9742, 9742, -3*w^2 - 13*w - 22]', '[9742, 9742, 15*w^2 + 17*w - 14]', '[9742, 9742, 13*w^2 + 26*w - 5]', '[9749, 9749, 4*w^2 - 14*w - 19]', '[9751, 1393, 5*w^2 - 6*w - 38]', '[9751, 9751, 17*w^2 + 10*w - 36]', '[9752, 2438, -8*w^2 - 16*w + 10]', '[9752, 2438, 14*w^2 - 20*w - 28]', '[9752, 2438, 12*w^2 - 8*w - 22]', '[9752, 9752, -7*w^2 - 7*w + 34]', '[9752, 9752, -4*w^2 - 7*w + 39]', '[9752, 9752, 13*w^2 + 7*w - 24]', '[9769, 9769, 16*w^2 - 9*w - 44]', '[9769, 9769, 10*w^2 - 11*w - 38]', '[9769, 9769, 2*w^2 - 6*w - 29]', '[9772, 4886, -17*w^2 + 3*w + 53]', '[9772, 9772, w^2 - 4*w - 25]', '[9776, 2444, -13*w^2 + 11*w + 23]', '[9776, 2444, -8*w^2 + 10*w - 6]', '[9776, 9776, -8*w^2 + 15*w + 21]', '[9778, 9778, -11*w^2 + 21]', '[9778, 9778, 7*w^2 + 7*w - 32]', '[9778, 9778, 2*w^2 - w - 27]', '[9781, 9781, 6*w^2 + 2*w - 41]', '[9782, 9782, -3*w^2 - 11*w - 20]', '[9787, 9787, 12*w^2 - 3*w - 28]', '[9787, 9787, 6*w^2 - 7*w - 42]', '[9787, 9787, -14*w^2 + 14*w + 41]', '[9788, 4894, 17*w^2 + 3*w - 77]', '[9788, 9788, -13*w^2 + 13*w + 40]', '[9793, 9793, -w^2 + 16*w + 24]', '[9793, 9793, -12*w^2 + w + 28]', '[9793, 9793, -8*w^2 + 14*w + 23]', '[9796, 4898, 11*w^2 + 19*w - 11]', '[9796, 9796, 12*w^2 - 9*w - 19]', '[9799, 9799, -3*w^2 + 14*w + 26]', '[9802, 754, 7*w^2 + 9*w - 22]', '[9802, 9802, 9*w^2 - 11*w - 40]', '[9808, 2452, -6*w^2 + 14*w + 20]', '[9808, 2452, -7*w^2 + 5*w - 7]', '[9808, 9808, 3*w^2 - w - 30]', '[9817, 9817, 15*w^2 + 2*w - 76]', '[9826, 34, -17*w - 17]', '[9827, 9827, 14*w^2 - 29*w - 16]', '[9828, 546, 15*w^2 - 15*w - 27]', '[9828, 1092, -3*w^2 - 12*w - 21]', '[9829, 9829, 3*w - 22]', '[9832, 2458, 6*w^2 - 4*w - 40]', '[9832, 9832, -18*w^2 + 11*w + 75]', '[9838, 9838, -w^2 - 18*w - 19]', '[9839, 9839, 15*w^2 - 16*w - 40]', '[9844, 4922, 9*w^2 - 11*w - 37]', '[9844, 9844, -13*w^2 + 5*w + 64]', '[9848, 2462, 6*w^2 - 12*w - 28]', '[9848, 9848, -8*w^2 + 5*w + 47]', '[9851, 9851, 8*w^2 + 10*w - 21]', '[9851, 9851, 6*w^2 + 11*w - 16]', '[9851, 9851, -8*w^2 - 19*w + 6]', '[9854, 9854, 14*w^2 - 11*w - 61]', '[9857, 9857, 6*w^2 - 12*w - 31]', '[9862, 9862, -w^2 + 2*w - 19]', '[9863, 9863, 7*w^2 + 2*w + 8]', '[9866, 9866, -13*w^2 - 17*w - 8]', '[9868, 4934, 7*w^2 - w - 43]', '[9868, 9868, -11*w^2 + 2*w + 21]', '[9871, 9871, -17*w^2 + 12*w + 44]', '[9872, 2468, 2*w^2 - 16*w + 10]', '[9872, 2468, 13*w^2 - 15*w - 35]', '[9872, 2468, -w^2 + 7*w + 27]', '[9872, 2468, -11*w^2 + 5*w + 17]', '[9872, 2468, 12*w^2 + 10*w - 10]', '[9872, 2468, 6*w^2 + 8*w - 26]', '[9872, 9872, -17*w^2 + 4*w + 53]', '[9872, 9872, 13*w^2 - 8*w - 29]', '[9872, 9872, -10*w^2 - 13*w + 19]', '[9874, 9874, 11*w^2 + 5*w - 10]', '[9875, 395, 10*w^2 + 10*w - 25]', '[9881, 9881, -9*w^2 + 12*w + 46]', '[9881, 9881, -2*w^2 - 5*w - 18]', '[9881, 9881, -8*w^2 + 16*w - 9]', '[9883, 9883, -10*w - 27]', '[9883, 9883, 4*w^2 - 6*w - 35]', '[9883, 9883, -3*w - 22]', '[9884, 4942, -w^2 - 3*w + 25]', '[9884, 9884, 11*w^2 - 5*w - 14]', '[9887, 9887, 18*w^2 - 8*w - 55]', '[9893, 9893, -8*w^2 + 19*w - 12]', '[9896, 2474, 12*w^2 - 2*w - 28]', '[9896, 9896, -13*w^2 - 4*w + 49]', '[9898, 1414, 15*w^2 + 17*w - 2]', '[9898, 9898, -9*w^2 + w + 50]', '[9901, 9901, 12*w^2 - 11*w - 44]', '[9902, 9902, -w^2 - 20*w - 13]', '[9904, 2476, -6*w^2 - 4*w - 10]', '[9904, 2476, -11*w^2 + w + 21]', '[9904, 2476, -9*w^2 + 11*w + 39]', '[9904, 2476, 6*w^2 + 12*w - 14]', '[9904, 2476, -w^2 + 11*w + 31]', '[9904, 2476, 14*w^2 + 16*w - 10]', '[9904, 9904, -13*w^2 - 2*w + 31]', '[9904, 9904, -13*w^2 - 16*w + 21]', '[9904, 9904, -3*w^2 + 14*w + 21]', '[9916, 4958, w^2 + w + 19]', '[9916, 4958, 11*w^2 - 11*w - 41]', '[9916, 4958, 31*w^2 - 19*w - 101]', '[9916, 9916, -4*w^2 - 11*w + 15]', '[9916, 9916, -4*w^2 - 13*w + 41]', '[9916, 9916, 11*w^2 + 2*w - 9]', '[9917, 9917, 16*w^2 - 5*w - 48]', '[9919, 9919, 4*w^2 - 10*w + 15]', '[9926, 9926, -30*w^2 + 29*w + 71]', '[9931, 9931, 6*w^2 - 12*w - 29]', '[9932, 4966, -7*w^2 + 3*w + 43]', '[9932, 9932, 11*w^2 + w - 20]', '[9936, 276, -6*w^2 + 12*w + 30]', '[9936, 276, -3*w^2 - 3*w - 15]', '[9936, 1104, 6*w^2 + 15*w - 9]', '[9938, 9938, -5*w^2 - 5*w - 12]', '[9946, 9946, -2*w^2 - 25*w - 11]', '[9947, 203, -14*w + 21]', '[9947, 9947, 8*w^2 - 12*w - 29]', '[9949, 9949, 11*w^2 + 4*w - 16]', '[9953, 9953, -2*w^2 + 4*w - 17]', '[9953, 9953, 14*w^2 - 5*w - 38]', '[9953, 9953, 5*w^2 + 10*w - 18]', '[9958, 9958, 16*w^2 - 11*w - 59]', '[9958, 9958, -w^2 - 13*w + 12]', '[9958, 9958, 7*w^2 - 12*w - 37]', '[9964, 4982, 5*w^2 + w - 37]', '[9964, 4982, 15*w^2 - 11*w - 55]', '[9964, 4982, -9*w^2 - 7*w + 31]', '[9964, 9964, -11*w^2 + 4*w + 19]', '[9964, 9964, -5*w^2 - 9*w + 22]', '[9964, 9964, 2*w^2 - 15*w - 19]', '[9967, 9967, 7*w^2 - 16*w - 18]', '[9968, 2492, 2*w^2 + 12*w - 26]', '[9968, 2492, 13*w^2 + 5*w - 27]', '[9968, 9968, -10*w^2 + 19*w + 19]', '[9971, 767, 6*w^2 + 4*w - 43]', '[9971, 9971, -3*w^2 + 16*w + 34]', '[9982, 9982, 7*w^2 - 13*w - 24]', '[9992, 2498, 4*w^2 + 12*w - 38]', '[9992, 2498, 2*w^2 - 16*w - 16]', '[9992, 2498, -18*w^2 + 16*w + 52]', '[9992, 9992, 5*w + 23]', '[9992, 9992, -25*w^2 + 13*w + 80]', '[9992, 9992, 18*w^2 + w - 87]', '[9998, 9998, -5*w^2 - 2*w - 11]'], 'label': '3.3.229.1', 'narrow_class_no': 2, 'primes': ['[2, 2, w + 1]', '[4, 2, -w^2 + w + 3]', '[7, 7, w^2 - 2]', '[13, 13, -w^2 + 2*w + 2]', '[23, 23, -2*w + 1]', '[27, 3, 3]', '[29, 29, -2*w + 3]', '[31, 31, -2*w^2 + 2*w + 3]', '[37, 37, 4*w^2 - 2*w - 13]', '[37, 37, -2*w^2 + 5]', '[37, 37, 2*w^2 - w - 10]', '[41, 41, w^2 - 2*w - 4]', '[47, 47, w - 4]', '[49, 7, 2*w^2 - w - 4]', '[53, 53, 2*w^2 - 2*w - 7]', '[53, 53, 3*w^2 - 2*w - 8]', '[53, 53, 2*w + 5]', '[59, 59, 2*w^2 - 2*w - 9]', '[67, 67, 2*w^2 - 3]', '[73, 73, 2*w^2 + w - 8]', '[79, 79, -2*w^2 - 2*w + 5]', '[89, 89, w^2 + 2*w - 4]', '[101, 101, 3*w^2 - 8]', '[107, 107, 3*w^2 + 2*w - 8]', '[109, 109, w^2 + 2*w - 6]', '[113, 113, 2*w^2 - 3*w - 6]', '[125, 5, -5]', '[127, 127, 4*w - 1]', '[131, 131, 4*w^2 - 3*w - 10]', '[137, 137, 3*w^2 - 2*w - 6]', '[139, 139, -w^2 - 2*w + 10]', '[157, 157, 4*w^2 - 4*w - 11]', '[163, 163, 2*w^2 - 4*w - 5]', '[169, 13, 2*w^2 - 3*w - 10]', '[173, 173, 3*w^2 - 2*w - 4]', '[173, 173, 2*w^2 - 3*w - 8]', '[173, 173, 2*w^2 + 2*w - 7]', '[179, 179, 4*w^2 - 2*w - 11]', '[191, 191, w - 6]', '[193, 193, -w - 6]', '[193, 193, 2*w^2 + 2*w - 11]', '[193, 193, 2*w^2 - w - 12]', '[197, 197, 3*w^2 - 2*w - 16]', '[199, 199, 4*w^2 + w - 10]', '[211, 211, 5*w + 4]', '[223, 223, -2*w + 7]', '[227, 227, -2*w^2 + w - 2]', '[229, 229, 3*w^2 - 4]', '[229, 229, 4*w - 3]', '[239, 239, -2*w - 7]', '[241, 241, -w^2 + 4*w - 6]', '[241, 241, w^2 - 4*w - 6]', '[241, 241, -w^2 + 4*w + 8]', '[251, 251, -3*w - 8]', '[257, 257, -w^2 - 4]', '[263, 263, 3*w^2 + 2*w - 10]', '[269, 269, 4*w^2 - 4*w - 5]', '[281, 281, 2*w^2 - 4*w - 7]', '[283, 283, 4*w^2 - 3*w - 8]', '[313, 313, 4*w^2 - w - 10]', '[317, 317, 5*w - 2]', '[331, 331, -2*w^2 - 2*w + 15]', '[347, 347, -4*w^2 + 4*w + 13]', '[347, 347, 4*w^2 + 2*w - 13]', '[347, 347, 3*w^2 - 4*w - 10]', '[349, 349, 2*w^2 - 4*w - 11]', '[353, 353, w^2 + 4*w - 4]', '[359, 359, 2*w^2 - 5*w - 6]', '[359, 359, 2*w^2 - 4*w - 9]', '[359, 359, 6*w - 1]', '[379, 379, 5*w^2 - 14]', '[383, 383, 5*w^2 - 2*w - 14]', '[383, 383, 4*w^2 + w - 8]', '[383, 383, 3*w^2 + 2*w - 14]', '[389, 389, 4*w^2 - 4*w - 19]', '[419, 419, 2*w^2 + 3*w - 8]', '[439, 439, 4*w^2 - 2*w - 7]', '[439, 439, 4*w^2 + w - 22]', '[439, 439, 9*w^2 - 4*w - 30]', '[443, 443, 2*w^2 + 3*w - 12]', '[443, 443, 3*w^2 - 4*w - 12]', '[443, 443, 3*w^2 - 4*w - 14]', '[449, 449, -6*w^2 + 5*w + 14]', '[449, 449, -2*w^2 - 5*w - 6]', '[449, 449, 4*w^2 - w - 8]', '[461, 461, 5*w^2 - 4*w - 22]', '[461, 461, 5*w - 4]', '[461, 461, 4*w^2 - 2*w - 5]', '[479, 479, w - 8]', '[487, 487, 2*w^2 + 3*w - 10]', '[499, 499, 6*w^2 + 2*w - 15]', '[503, 503, 4*w^2 - 7]', '[503, 503, 4*w^2 + w - 6]', '[503, 503, w^2 + 2*w - 12]', '[509, 509, 4*w^2 - 2*w - 21]', '[509, 509, 2*w^2 - w - 14]', '[509, 509, 6*w^2 - 29]', '[521, 521, 4*w^2 - w - 6]', '[523, 523, 2*w^2 - 5*w - 8]', '[529, 23, 4*w^2 + 2*w - 15]', '[541, 541, 6*w^2 - w - 18]', '[541, 541, 4*w^2 - 5]', '[541, 541, -w^2 + 2*w - 6]', '[547, 547, -4*w^2 + 5*w + 12]', '[563, 563, 4*w^2 - 3*w - 22]', '[571, 571, 4*w^2 + 3*w - 12]', '[577, 577, 2*w - 9]', '[593, 593, 2*w^2 - 7*w + 8]', '[593, 593, 2*w^2 + 4*w - 15]', '[593, 593, -2*w - 9]', '[599, 599, w^2 + 8*w + 6]', '[601, 601, -w^2 - 6]', '[607, 607, 6*w^2 - 4*w - 15]', '[607, 607, 4*w^2 + 2*w - 17]', '[607, 607, 6*w^2 - 7*w - 8]', '[613, 613, -3*w + 10]', '[617, 617, -7*w - 6]', '[617, 617, 2*w^2 + 4*w - 7]', '[617, 617, 7*w^2 - 4*w - 20]', '[619, 619, 3*w^2 - 6*w - 8]', '[619, 619, 5*w^2 - 2*w - 12]', '[619, 619, 3*w^2 + 4*w - 8]', '[643, 643, -5*w^2 + 12]', '[643, 643, 2*w^2 - 2*w - 15]', '[643, 643, 6*w^2 - 6*w - 17]', '[647, 647, w^2 - 2*w - 12]', '[653, 653, 2*w^2 - 4*w + 5]', '[659, 659, 5*w^2 - 4*w - 8]', '[677, 677, 6*w^2 - 2*w - 17]', '[691, 691, 6*w^2 - 5*w - 20]', '[691, 691, 6*w^2 - 3*w - 16]', '[691, 691, -4*w^2 - 3*w + 22]', '[709, 709, -8*w^2 + 6*w + 21]', '[719, 719, w^2 - 4*w - 14]', '[727, 727, 2*w^2 - 15]', '[739, 739, -4*w^2 + 5*w + 20]', '[761, 761, 5*w^2 - 6*w - 14]', '[773, 773, 10*w^2 - 5*w - 32]', '[797, 797, 6*w^2 - 5*w - 12]', '[809, 809, 2*w^2 + 5*w - 6]', '[811, 811, 6*w - 5]', '[823, 823, 5*w^2 - 2*w - 10]', '[827, 827, -2*w^2 - 4*w + 13]', '[829, 829, 4*w^2 + 4*w - 11]', '[839, 839, -6*w^2 - 2*w + 21]', '[841, 29, 2*w^2 + 3*w - 18]', '[853, 853, -2*w^2 - 5]', '[857, 857, -2*w^2 + 2*w - 5]', '[877, 877, 2*w^2 + 4*w - 11]', '[881, 881, 6*w - 7]', '[887, 887, 3*w^2 - 6*w - 10]', '[907, 907, 4*w^2 - 5*w - 18]', '[907, 907, 3*w^2 + 4*w - 10]', '[907, 907, 7*w^2 - 6*w - 22]', '[929, 929, 4*w^2 - 7*w - 10]', '[937, 937, -8*w - 7]', '[947, 947, 5*w^2 - 2*w - 8]', '[961, 31, 7*w^2 - 8*w - 10]', '[967, 967, 2*w^2 - 6*w - 13]', '[967, 967, 7*w^2 + 2*w - 24]', '[967, 967, 6*w^2 - 5*w - 26]', '[977, 977, 2*w^2 - 6*w - 11]', '[977, 977, 6*w^2 + 6*w - 5]', '[977, 977, -w^2 - 2*w - 8]', '[983, 983, 2*w^2 + 6*w - 5]']}
• 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, -4, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 229, 'disc_rad': 229, 'disc_sign': 1, 'frobs': [[2, [[2, 1], [1, 1]]], [3, [[3, 1]]], [5, [[3, 1]]], [7, [[2, 1], [1, 1]]], [11, [[3, 1]]], [13, [[2, 1], [1, 1]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[2, 1], [1, 1]]], [29, [[2, 1], [1, 1]]], [31, [[2, 1], [1, 1]]], [37, [[1, 3]]], [41, [[2, 1], [1, 1]]], [43, [[3, 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': [3], 'galois_label': '3T2', 'galt': 2, 'grd': 15.132745950421556, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.229.1', 'local_algs': ['m229.1.1.0', 'm229.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [229], 'rd': 6.11803317264, 'regulator': {'__RealLiteral__': 0, 'data': '2.35545459084', 'prec': 44}, 'res': {'gal': ['-1,-2,14,0,-14,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a + 2 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}