Hilbert modular form data - 2.2.56.1-81.1-a

Formats: - HTML - YAML - JSON - 2025-12-16T12:56:31.106632

• 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': 2, 'dimension': 1, 'disc': 56, 'field_bad_primes': [2, 7], 'field_label': '2.2.56.1', 'is_CM': 'yes', 'is_base_change': 'yes', 'label': '2.2.56.1-81.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [3], 'level_ideal': '[81, 9, 9]', 'level_label': '81.1', 'level_norm': 81, 'parallel_weight': 2, 'short_label': '81.1-a', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[9, 3, 3]', 1]], 'hecke_eigenvalues': [-1, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 12, 12, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 20, 20, 2, 2, -10, -10, 0, 0, 20, 20, 0, 0, 0, 0, -4, -4, 0, 0, -18, -18, 0, 0, -12, -12, 0, 0, 0, 0, 22, 22, 0, 0, 0, 0, -26, -26, 34, 0, 0, 0, 0, -36, -36, 30, 30, 4, 4, 0, 0, 38, 0, 0, 12, 12, 0, 0, 0, 0, 34, 34, 0, 0, 20, 20, -2, -2, 6, 6, 0, 0, 0, 0, -44, -44, 36, 36, 0, 0, 0, 0, 18, -44, -44, -22, -22, -4, -4, 0, 0, 26, 26, -46, -46, 0, 0, 44, 44, 0, 0, -30, -30, 0, 0, 52, 52, 0, 0, 0, 0, 0, 0, 52, 52, 0, 0, 0, 0, -38, -38, -44, -44, 0, 0, 0, 0, -54, 0, 0, -12, -12, 0, 0, 60, 60, 0, 0, -20, -20, -58, -58, 46, 46, 0, 0, 0, 0, -2, -2, 0, 0, 52, 52, 0, 0, 10, 10, 0, 0, 44, 44, 0, 0, 0, 0, 0, 0, -22, -22, 0, 0, 68, 68, 36, 36, 0, 0, -4, -4, -66, -66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, -20, 58, 58, -34, -34, 0, 0, 0, 0, -38, 0, 0, 62, 62, 0, 0, -76, -76, -74, -74, 0, 0, 68, 68, 0, 0, -52, -52, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 76, 76, 0, 0, 44, 44, 0, 0, 82, 0, 0, -68, -68, 0, 0, -60, -60, 0, 0, -76, -76, 6, 6, 0, 0, 0, 0, 0, 0, 18, 18, 0, 0, -22, -22, 0, 0, 0, 0, 0, 0, -68, -68, 76, 76, -30, -30, 4, 4, 0, 0, 0, 0, -34, -34, -60, -60, -82, -82, 90, 90, 0, 0, -38, -38, -92, -92, 0, 0, -52, -52, 0, 0, -86, -86, 0, 0, -68, -68, 0, 0, -36, -36, 0, 0, 0, 0, 74, 74, 0, 0, 0, 0, -50, -50, -92, -92, -90, -90, 0, 0, 54, 54, -4, -4, 0, 0, 0, 0, 58, 58, 94, 94, 0, 0, 0, 0, 92, 92, 0, 0, -82, -82, 0, 0, 52, 52, -102, -102, 0, 0, -68, -68, 0, 0, 62, 62, 0, 0, 0, 0, 2, 2, -6, 100, 100, 36, 36, -86, -86, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 92, -26, -26, 0, 0, 44, 44, 76, 76, 0, 0, 0, 0, 102, 102, -100, -100, 0, 0, 34, 34, -110, -110, 0, 0, 0, 0, 20, 20, 0, 0, -52, -52, 94, 94, 0, 0, 106, 106, 108, 108, 92, 92, -78, -78, -46, -46, -100, -100, 0, 0, -114, -114, 116, 116, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -76, -76, 118, 0, 0, 0, 0, -54, -54, 0, 0, -116, -116, 0, 0, 0, 0, -44, -44, 0, 0, 118, 118, 0, 0, 0, 0, 92, 92, 114, 114, 0, 0, 0, 0, 0, 0, 12, 12, -62, -62, 0, 0, 20, 20, 0, 0, -122, -122, -124, -124, 0, 0, 0, 0, 0, 0, -66, -66, -124, -124, 0, 0, 0, 0, -118, -118, -116, -116, 0, 0, 0, 0, 94, 94, 0, 0, 124, 124, 0, 0, -36, -36, -10, -10, 0, 0, 0, 0, -108, -108, 0, 0, -92, -92, 22, 22, 0, 0, -26, -26, -116, -116, 0, 0, 68, 68, 0, 0, 130, 130, 0, 0, -132, -132, 0, 0, 0, 0, 82, 82, 0, 0, 100, 100, -116, -116, 0, 0, -46, -46, 0, 0, 0, 0, 0, 0, 0, 0, 60, 60, 0, 0, 0, 0, 92, 92, 86, 86, 50, 50, -130, -130, 0, 0, 124, 124, 0, 0, 122, 122, 0, 0, 0, 0, 110, 110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -134, -134, 0, 0, -62, -62, -94, -94, 0, 0, 114, 52, 52, 0, 0, 0, 0, 4, 4, -76, -76, -142, -142, 0, 0, -138, -138, -130, -130, -118, -118, 0, 0, 146, 0, 0, 0, 0, 0, 0, 116, 116, 0, 0, 124, 124, 0, 0, 0, 0, 146, 146, -108, -108, 0, 0, 0, 0, 148, 148, 0, 0, 0, 0, 68, 68, 0, 0, -18, -18, 0, 0, 0, 0, -148, -148, -26, -26, 0, 0, 0, 0, 0, 0, 0, 0, -150, -150, 0, 0, 52, 52, 0, 0, 38, 38, -124, -124, 0, 0, 0, 0, 86, 86, -12, -12, 0, 0, 0, 0, -20, -20, 0, 0, -148, -148, 0, 0, 0, 0, 150, 150, 0, 0, 156, 156, 50, 50, 0, 0, 0, 0, 100, 100, 36, 36, -54, -54, 0, 0, 0, 0, -94, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -148, -148, -58, -58, -146, -146, -158, -158, 0, 0, 0, 0, -132, -132, 0, 0, 0, 0, 156, 156, -62, -62, 116, 116, -92, -92, -122, -122, -76, -76, 0, 0, -138, -138, -52, -52, -66, -66, 0, 0, 0, 0, 108, 108, 0, 0, -148, -148, -162, -162, 158, 158, 0, 0, 0, 0, 0, 0, 12, 12, 0, 0, 0, 0, 20, 20, 142, 142, -106, -106, -74, -74, 0, 0, 132, 132, 166, -164, -164, 0, 0, 0, 0, 166, 166, 0, 0, -68, -68, -110, -110, 0, 0, 0, 0, -146, -146, 0, 0, 6, 6, 10, 10, -44, -44, 0, 0, -92, -92, 0, 0, 0, 0, 76, 76, 0, 0, -30, -30, 150, 150, -34, -34, -172, -172, 148, 148, 0, 0, -38, -38, -124, -124, 0, 0, 0, 0, 138, 138, 0, 0, 0, 0, 100, 100, 0, 0, 0, 0, 170, 170, 174, 174, 0, 0, 0, 0, -20, -20, 0, 0, 0, 0, -122, -122, 0, 0, 0, 0, -50, -50, 0, 0, -142, -142, 0, 0, 68, 68, 0, 0, -164, -164, 178, 0, 0, 0, 0, 172, 172, 58, 58, -174, -174, 0, 0, 0, 0, -132, -132, 0, 0, -102, -102, 0, 0, 0, 0, -76, -76, -124, -124, 0, 0, 0, 0, 170, 170, 0, 0, 172, 172, 0, 0, 0, 0, 0, 0, -106, -106, 162, 162, -178, -178, -100, -100, 0, 0, 0, 0, -180, -180, 0, 0, 0, 0, 116, 116, 0, 0, -110, -110, 134, 134, 74, 74, 0, 0, 148, 148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -166, -166, -78, -78, 0, 0, -132, -132, -114, -114, 0, 0, 164, 164, 186, 186, -68, -68, 0, 0, -108, -108, 0, 0, 0, 0, -82, -82, 0, 0, 0, 0, -178, -178, 0, 0, 118, 118, 172, 172, 0, 0, 188, 188, 0, 0, -158, -158, 44, 44, 76, 76, 0, 0, 0, 0, 0, 0, -190, -190, 0, 0, -122, -122, 100, 100, 0, 0, 26, 26, 180, 180, 0, 0, 0, 0, 94, 94, 0, 0, 188, 188, 194, 0, 0, -172, -172, 0, 0, -38, -38, 0, 0, 0, 0, 190, 190, 0, 0, 194, 194, 0, 0, 0, 0, -4, -4, 46, 46, -12, -12, 0, 0, 0, 0, 108, 108, 0, 0, 0, 0, 166, 166, -50, -50, 0, 0, 0, 0, 92, 92, 0, 0, 0, 0, 102, 102, 156, 156, 0, 0, 164, 164, 148, 148, -194, -194, 0, 0, 0, 0, 36, 36, 172, 172, 0, 0, 0, 0], 'hecke_polynomial': 'x', 'label': '2.2.56.1-81.1-a'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 56, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 4]', '[4, 2, 2]', '[5, 5, -w + 3]', '[5, 5, w + 3]', '[7, 7, -2*w - 7]', '[8, 4, -2*w - 8]', '[9, 3, 3]', '[10, 10, w + 2]', '[10, 10, -w + 2]', '[11, 11, w + 5]', '[11, 11, -w + 5]', '[13, 13, -w - 1]', '[13, 13, -w + 1]', '[14, 14, w]', '[16, 4, 4]', '[18, 6, -3*w - 12]', '[20, 10, -2*w + 6]', '[20, 10, 2*w + 6]', '[22, 22, -w - 6]', '[22, 22, w - 6]', '[25, 5, 5]', '[25, 25, -2*w + 9]', '[25, 25, 2*w + 9]', '[26, 26, 3*w + 10]', '[26, 26, 3*w - 10]', '[28, 14, -4*w - 14]', '[31, 31, 2*w - 5]', '[31, 31, -2*w - 5]', '[32, 8, -4*w - 16]', '[35, 35, w + 7]', '[35, 35, w - 7]', '[36, 6, 6]', '[40, 20, 2*w + 4]', '[40, 20, -2*w + 4]', '[43, 43, 7*w + 27]', '[43, 43, 3*w + 13]', '[44, 22, 2*w + 10]', '[44, 22, -2*w + 10]', '[45, 15, -3*w + 9]', '[45, 15, 3*w + 9]', '[47, 47, 2*w - 3]', '[47, 47, -2*w - 3]', '[49, 7, 7]', '[50, 10, 5*w + 20]', '[50, 50, -w - 8]', '[50, 50, w - 8]', '[52, 26, -2*w - 2]', '[52, 26, -2*w + 2]', '[55, 55, -4*w - 13]', '[55, 55, -2*w + 1]', '[55, 55, 2*w + 1]', '[55, 55, 4*w - 13]', '[56, 28, 2*w]', '[61, 61, 7*w + 25]', '[61, 61, -5*w - 17]', '[62, 62, 13*w + 48]', '[62, 62, -3*w - 8]', '[63, 21, -6*w - 21]', '[64, 8, 8]', '[65, 65, -4*w + 17]', '[65, 65, -2*w + 11]', '[65, 65, -2*w - 11]', '[65, 65, -4*w - 17]', '[67, 67, -w - 9]', '[67, 67, w - 9]', '[70, 70, 3*w + 14]', '[70, 70, 3*w - 14]', '[72, 12, -6*w - 24]', '[77, 77, -3*w - 7]', '[77, 77, -3*w + 7]', '[80, 20, -4*w + 12]', '[80, 20, 4*w + 12]', '[81, 9, 9]', '[86, 86, -w - 10]', '[86, 86, w - 10]', '[88, 44, -2*w - 12]', '[88, 44, 2*w - 12]', '[90, 30, 3*w + 6]', '[90, 30, -3*w + 6]', '[91, 91, -5*w + 21]', '[91, 91, 5*w + 21]', '[94, 94, -5*w - 16]', '[94, 94, 11*w + 40]', '[98, 14, -7*w - 28]', '[99, 33, 3*w + 15]', '[99, 33, -3*w + 15]', '[100, 10, 10]', '[100, 50, -4*w + 18]', '[100, 50, 4*w + 18]', '[101, 101, 3*w - 5]', '[101, 101, -3*w - 5]', '[103, 103, 4*w - 11]', '[103, 103, -4*w - 11]', '[104, 52, 6*w + 20]', '[104, 52, 6*w - 20]', '[107, 107, -w - 11]', '[107, 107, w - 11]', '[110, 110, -7*w + 24]', '[110, 110, -3*w - 4]', '[110, 110, 3*w - 4]', '[110, 110, 7*w + 24]', '[112, 28, -8*w - 28]', '[113, 113, 2*w - 13]', '[113, 113, -2*w - 13]', '[117, 39, -3*w - 3]', '[117, 39, -3*w + 3]', '[121, 11, 11]', '[121, 121, -6*w + 25]', '[121, 121, 6*w + 25]', '[122, 122, 3*w - 2]', '[122, 122, -3*w - 2]', '[124, 62, 4*w - 10]', '[124, 62, -4*w - 10]', '[125, 25, 5*w - 15]', '[125, 25, -5*w - 15]', '[125, 125, -3*w - 1]', '[125, 125, 3*w - 1]', '[126, 42, 3*w]', '[128, 16, -8*w - 32]', '[130, 130, -w - 12]', '[130, 130, -3*w + 16]', '[130, 130, -3*w - 16]', '[130, 130, -w + 12]', '[134, 134, 5*w + 22]', '[134, 134, 13*w + 50]', '[137, 137, 4*w + 19]', '[137, 137, 16*w + 61]', '[140, 70, 2*w + 14]', '[140, 70, 2*w - 14]', '[143, 143, -6*w - 19]', '[143, 143, -4*w - 9]', '[143, 143, -4*w + 9]', '[143, 143, -6*w + 19]', '[144, 12, 12]', '[154, 154, 5*w - 14]', '[154, 154, 5*w + 14]', '[155, 155, w + 13]', '[155, 155, -11*w - 43]', '[155, 155, 11*w - 43]', '[155, 155, -w + 13]', '[157, 157, 13*w + 47]', '[157, 157, -7*w - 23]', '[160, 40, 4*w + 8]', '[160, 40, -4*w + 8]', '[162, 18, -9*w - 36]', '[163, 163, -3*w - 17]', '[163, 163, 3*w - 17]', '[167, 167, -8*w - 27]', '[167, 167, 12*w + 43]', '[169, 13, 13]', '[169, 169, -2*w + 15]', '[169, 169, 2*w + 15]', '[172, 86, 14*w + 54]', '[172, 86, 6*w + 26]', '[173, 173, 11*w + 39]', '[173, 173, -9*w - 31]', '[175, 35, 10*w + 35]', '[175, 175, -4*w + 7]', '[175, 175, -4*w - 7]', '[176, 44, 4*w + 20]', '[176, 44, -4*w + 20]', '[179, 179, 17*w + 65]', '[179, 179, 5*w + 23]', '[180, 30, -6*w + 18]', '[180, 30, 6*w + 18]', '[181, 181, -5*w - 13]', '[181, 181, 5*w - 13]', '[182, 182, -w - 14]', '[182, 182, w - 14]', '[188, 94, 4*w - 6]', '[188, 94, -4*w - 6]', '[193, 193, 12*w + 47]', '[193, 193, 8*w + 33]', '[196, 14, 14]', '[198, 66, -3*w - 18]', '[198, 66, 3*w - 18]', '[199, 199, -4*w - 5]', '[199, 199, 4*w - 5]', '[200, 20, 10*w + 40]', '[200, 100, -2*w - 16]', '[200, 100, 2*w - 16]', '[202, 202, -7*w - 22]', '[202, 202, 17*w + 62]', '[206, 206, 27*w + 100]', '[206, 206, -5*w - 12]', '[208, 52, -4*w - 4]', '[208, 52, -4*w + 4]', '[211, 211, -w - 15]', '[211, 211, w - 15]', '[214, 214, 7*w + 30]', '[214, 214, 15*w + 58]', '[215, 215, 6*w - 17]', '[215, 215, 4*w - 3]', '[215, 215, -4*w - 3]', '[215, 215, -6*w - 17]', '[217, 217, 24*w + 91]', '[217, 217, -4*w - 21]', '[220, 110, -8*w - 26]', '[220, 110, -4*w + 2]', '[220, 110, 4*w + 2]', '[220, 110, 8*w - 26]', '[223, 223, -4*w - 1]', '[223, 223, 4*w - 1]', '[224, 56, 4*w]', '[225, 15, 15]', '[225, 75, -6*w + 27]', '[225, 75, 6*w + 27]', '[226, 226, 5*w + 24]', '[226, 226, 21*w + 80]', '[229, 229, -5*w - 11]', '[229, 229, 5*w - 11]', '[233, 233, 2*w - 17]', '[233, 233, -2*w - 17]', '[234, 78, 9*w + 30]', '[234, 78, 9*w - 30]', '[235, 235, 9*w - 37]', '[235, 235, -3*w + 19]', '[235, 235, 3*w + 19]', '[235, 235, -9*w - 37]', '[242, 22, -11*w - 44]', '[242, 242, -w - 16]', '[242, 242, w - 16]', '[244, 122, 14*w + 50]', '[244, 122, -10*w - 34]', '[245, 35, -7*w + 21]', '[245, 35, 7*w + 21]', '[248, 124, 26*w + 96]', '[248, 124, -6*w - 16]', '[250, 50, -5*w - 10]', '[250, 50, 5*w - 10]', '[250, 250, 11*w - 38]', '[250, 250, -11*w - 38]', '[252, 42, -12*w - 42]', '[256, 16, 16]', '[260, 130, -8*w + 34]', '[260, 130, -4*w + 22]', '[260, 130, -4*w - 22]', '[260, 130, -8*w - 34]', '[268, 134, -2*w - 18]', '[268, 134, 2*w - 18]', '[269, 269, 5*w - 9]', '[269, 269, -5*w - 9]', '[271, 271, -8*w - 25]', '[271, 271, 20*w + 73]', '[274, 274, -3*w - 20]', '[274, 274, 3*w - 20]', '[275, 55, -5*w - 25]', '[275, 55, 5*w - 25]', '[275, 275, w + 17]', '[275, 275, 7*w + 31]', '[275, 275, -7*w + 31]', '[275, 275, -w + 17]', '[279, 93, 6*w - 15]', '[279, 93, -6*w - 15]', '[280, 140, 6*w + 28]', '[280, 140, 6*w - 28]', '[281, 281, 14*w + 55]', '[281, 281, 10*w + 41]', '[286, 286, 7*w - 20]', '[286, 286, 5*w + 8]', '[286, 286, 5*w - 8]', '[286, 286, 7*w + 20]', '[288, 24, -12*w - 48]', '[289, 17, -17]', '[293, 293, 19*w + 69]', '[293, 293, -9*w - 29]', '[301, 301, -5*w + 7]', '[301, 301, -5*w - 7]', '[305, 305, -4*w - 23]', '[305, 305, -2*w + 19]', '[305, 305, 2*w + 19]', '[305, 305, 4*w - 23]', '[308, 154, -6*w - 14]', '[308, 154, -6*w + 14]', '[310, 310, w + 18]', '[310, 310, -9*w - 38]', '[310, 310, 9*w - 38]', '[310, 310, -w + 18]', '[311, 311, 18*w + 65]', '[311, 311, -10*w - 33]', '[314, 314, -5*w - 6]', '[314, 314, 5*w - 6]', '[315, 105, 3*w + 21]', '[315, 105, 3*w - 21]', '[320, 40, -8*w + 24]', '[320, 40, 8*w + 24]', '[324, 18, 18]', '[325, 65, 5*w + 5]', '[325, 65, 5*w - 5]', '[325, 325, -11*w - 37]', '[325, 325, -7*w - 19]', '[325, 325, -7*w + 19]', '[325, 325, -11*w + 37]', '[326, 326, 29*w + 110]', '[326, 326, 5*w + 26]', '[329, 329, 20*w + 77]', '[329, 329, -8*w - 35]', '[331, 331, 15*w + 59]', '[331, 331, 11*w + 45]', '[334, 334, 5*w - 4]', '[334, 334, -5*w - 4]', '[335, 335, -6*w - 13]', '[335, 335, -12*w - 41]', '[335, 335, 12*w - 41]', '[335, 335, 6*w - 13]', '[337, 337, 6*w + 29]', '[337, 337, 26*w + 99]', '[338, 26, -13*w - 52]', '[338, 338, 7*w - 32]', '[338, 338, -7*w - 32]', '[341, 341, -15*w - 53]', '[341, 341, 5*w + 3]', '[341, 341, -5*w + 3]', '[341, 341, 15*w - 53]', '[343, 49, -14*w - 49]', '[344, 172, -2*w - 20]', '[344, 172, 2*w - 20]', '[346, 346, 5*w - 2]', '[346, 346, -5*w - 2]', '[347, 347, -w - 19]', '[347, 347, w - 19]', '[349, 349, -5*w - 1]', '[349, 349, 5*w - 1]', '[350, 70, -5*w]', '[350, 350, 9*w + 28]', '[350, 350, 9*w - 28]', '[352, 88, -4*w - 24]', '[352, 88, 4*w - 24]', '[358, 358, 3*w - 22]', '[358, 358, -3*w - 22]', '[360, 60, 6*w + 12]', '[360, 60, -6*w + 12]', '[361, 19, -19]', '[362, 362, -7*w - 18]', '[362, 362, 33*w + 122]', '[364, 182, -10*w + 42]', '[364, 182, 10*w + 42]', '[367, 367, 8*w - 23]', '[367, 367, -8*w - 23]', '[376, 188, -10*w - 32]', '[376, 188, 22*w + 80]', '[379, 379, -5*w - 27]', '[379, 379, 5*w - 27]', '[383, 383, 6*w - 11]', '[383, 383, -6*w - 11]', '[385, 385, 12*w - 49]', '[385, 385, -2*w + 21]', '[385, 385, -2*w - 21]', '[385, 385, 12*w + 49]', '[386, 386, -w - 20]', '[386, 386, w - 20]', '[387, 129, 21*w + 81]', '[387, 129, 9*w + 39]', '[392, 28, -14*w - 56]', '[396, 66, 6*w + 30]', '[396, 66, -6*w + 30]', '[397, 397, 7*w - 17]', '[397, 397, -7*w - 17]', '[398, 398, -11*w - 36]', '[398, 398, 21*w + 76]', '[400, 20, 20]', '[400, 100, -8*w + 36]', '[400, 100, 8*w + 36]', '[401, 401, 4*w - 25]', '[401, 401, -4*w - 25]', '[403, 403, 3*w + 23]', '[403, 403, 7*w - 33]', '[403, 403, 7*w + 33]', '[403, 403, 3*w - 23]', '[404, 202, 6*w - 10]', '[404, 202, -6*w - 10]', '[405, 45, -9*w + 27]', '[405, 45, 9*w + 27]', '[412, 206, 8*w - 22]', '[412, 206, -8*w - 22]', '[416, 104, 12*w + 40]', '[416, 104, 12*w - 40]', '[422, 422, 11*w + 46]', '[422, 422, 19*w + 74]', '[423, 141, 6*w - 9]', '[423, 141, -6*w - 9]', '[427, 427, -w - 21]', '[427, 427, -w + 21]', '[428, 214, -2*w - 22]', '[428, 214, 2*w - 22]', '[430, 430, 13*w - 44]', '[430, 430, 7*w - 16]', '[430, 430, -7*w - 16]', '[430, 430, -13*w - 44]', '[434, 434, -5*w + 28]', '[434, 434, -5*w - 28]', '[439, 439, -10*w - 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109]', '[8731, 8731, -15*w - 109]', '[8737, 8737, -16*w - 111]', '[8737, 8737, 16*w - 111]', '[8741, 8741, 25*w - 3]', '[8741, 8741, -25*w - 3]', '[8747, 8747, 131*w + 499]', '[8747, 8747, 31*w + 149]', '[8761, 8761, -26*w - 135]', '[8761, 8761, 26*w - 135]', '[8779, 8779, 33*w + 155]', '[8779, 8779, 125*w + 477]', '[8783, 8783, 94*w + 339]', '[8783, 8783, -54*w - 179]', '[8803, 8803, 77*w + 303]', '[8803, 8803, 57*w + 233]', '[8837, 8837, 27*w - 37]', '[8837, 8837, -27*w - 37]', '[8839, 8839, 26*w - 25]', '[8839, 8839, -26*w - 25]', '[8849, 8849, 22*w - 125]', '[8849, 8849, -22*w - 125]', '[8861, 8861, 93*w + 335]', '[8861, 8861, -55*w - 183]', '[8893, 8893, -41*w - 121]', '[8893, 8893, 131*w + 481]', '[8929, 8929, 40*w + 177]', '[8929, 8929, 108*w + 415]', '[8951, 8951, -28*w - 45]', '[8951, 8951, 28*w - 45]', '[8969, 8969, 2*w - 95]', '[8969, 8969, -2*w - 95]', '[8971, 8971, 69*w + 275]', '[8971, 8971, 65*w + 261]', '[9007, 9007, 32*w - 73]', '[9007, 9007, -32*w - 73]', '[9011, 9011, -w - 95]', '[9011, 9011, w - 95]', '[9029, 9029, 119*w + 435]', '[9029, 9029, -45*w - 139]', '[9041, 9041, 20*w - 121]', '[9041, 9041, -20*w - 121]', '[9059, 9059, -5*w - 97]', '[9059, 9059, 5*w - 97]', '[9067, 9067, -9*w - 101]', '[9067, 9067, 9*w - 101]', '[9103, 9103, -26*w - 19]', '[9103, 9103, 26*w - 19]', '[9127, 9127, 28*w - 43]', '[9127, 9127, -28*w - 43]', '[9133, 9133, 89*w + 319]', '[9133, 9133, -59*w - 199]', '[9137, 9137, -14*w - 109]', '[9137, 9137, 14*w - 109]', '[9173, 9173, -29*w - 51]', '[9173, 9173, 29*w - 51]', '[9209, 9209, -10*w - 103]', '[9209, 9209, 10*w - 103]', '[9227, 9227, 41*w + 181]', '[9227, 9227, 109*w + 419]', '[9239, 9239, -26*w - 15]', '[9239, 9239, 26*w - 15]', '[9241, 9241, 70*w + 279]', '[9241, 9241, 66*w + 265]', '[9283, 9283, 3*w - 97]', '[9283, 9283, -3*w - 97]', '[9341, 9341, -63*w - 215]', '[9341, 9341, 85*w + 303]', '[9343, 9343, 26*w - 11]', '[9343, 9343, -26*w - 11]', '[9377, 9377, 104*w + 401]', '[9377, 9377, 44*w + 191]', '[9397, 9397, -53*w - 173]', '[9397, 9397, 103*w + 373]', '[9403, 9403, 133*w + 507]', '[9403, 9403, 33*w + 157]', '[9409, 97, -97]', '[9413, 9413, 39*w - 109]', '[9413, 9413, -39*w - 109]', '[9419, 9419, 35*w + 163]', '[9419, 9419, 127*w + 485]', '[9421, 9421, -65*w - 223]', '[9421, 9421, 83*w + 295]', '[9433, 9433, -12*w - 107]', '[9433, 9433, 12*w - 107]', '[9439, 9439, 26*w - 5]', '[9439, 9439, -26*w - 5]', '[9463, 9463, -26*w - 1]', '[9463, 9463, 26*w - 1]', '[9473, 9473, -28*w - 143]', '[9473, 9473, 28*w - 143]', '[9511, 9511, -68*w - 235]', '[9511, 9511, 80*w + 283]', '[9521, 9521, 50*w + 211]', '[9521, 9521, 94*w + 365]', '[9533, 9533, 79*w + 279]', '[9533, 9533, -69*w - 239]', '[9551, 9551, -70*w - 243]', '[9551, 9551, 78*w + 275]', '[9587, 9587, -19*w - 121]', '[9587, 9587, 19*w - 121]', '[9601, 9601, -30*w - 149]', '[9601, 9601, 30*w - 149]', '[9619, 9619, 15*w - 113]', '[9619, 9619, -15*w - 113]', '[9623, 9623, 34*w - 81]', '[9623, 9623, -34*w - 81]', '[9631, 9631, -40*w - 113]', '[9631, 9631, 40*w - 113]', '[9643, 9643, 17*w - 117]', '[9643, 9643, -17*w - 117]', '[9677, 9677, 27*w - 23]', '[9677, 9677, -27*w - 23]', '[9679, 9679, 100*w + 361]', '[9679, 9679, -56*w - 185]', '[9689, 9689, -32*w - 155]', '[9689, 9689, 32*w - 155]', '[9697, 9697, -6*w - 101]', '[9697, 9697, 6*w - 101]', '[9719, 9719, 114*w + 415]', '[9719, 9719, -50*w - 159]', '[9733, 9733, 31*w - 61]', '[9733, 9733, -31*w - 61]', '[9739, 9739, 57*w + 235]', '[9739, 9739, 85*w + 333]', '[9743, 9743, 126*w + 461]', '[9743, 9743, -46*w - 141]', '[9749, 9749, 29*w - 45]', '[9749, 9749, -29*w - 45]', '[9769, 9769, 48*w + 205]', '[9769, 9769, 100*w + 387]', '[9787, 9787, -w - 99]', '[9787, 9787, w - 99]', '[9791, 9791, 30*w - 53]', '[9791, 9791, -30*w - 53]', '[9811, 9811, 95*w + 369]', '[9811, 9811, 51*w + 215]', '[9851, 9851, 5*w - 101]', '[9851, 9851, -5*w - 101]', '[9857, 9857, 26*w - 139]', '[9857, 9857, -26*w - 139]', '[9887, 9887, 28*w - 33]', '[9887, 9887, -28*w - 33]', '[9901, 9901, -47*w - 145]', '[9901, 9901, 125*w + 457]', '[9907, 9907, 61*w + 249]', '[9907, 9907, 81*w + 319]', '[9923, 9923, 7*w - 103]', '[9923, 9923, -7*w - 103]', '[9967, 9967, -52*w - 167]', '[9967, 9967, 112*w + 407]', '[9973, 9973, -31*w - 59]', '[9973, 9973, 31*w - 59]']}
• 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[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	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': [-14, 0, 1], 'conductor': 56, 'degree': 2, 'dirichlet_group': [1, 27], 'disc_abs': 56, 'disc_rad': 14, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 1]]], [5, [[1, 2]]], [7, [0]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [[2, 1]]], [31, [[1, 2]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [[1, 2]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 7.483314773547883, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.56.1', 'local_algs': ['2.1.2.3a1.1', '7.1.2.1a1.2'], 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [2, 7], 'rd': 7.48331477355, 'regulator': {'__RealLiteral__': 0, 'data': '3.40008441411', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 4 a - 15 \\)'], 'used_grh': False, 'zk': ['1', 'a']}