Hilbert modular form data - 2.2.13.1-1323.1-m

Formats: - HTML - YAML - JSON - 2025-12-21T01:27:27.856153

• 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': 13, 'field_bad_primes': [13], 'field_label': '2.2.13.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.13.1-1323.1-m', 'label_nsuffix': 12, 'label_suffix': 'm', 'level_bad_primes': [3, 7], 'level_ideal': '[1323, 63, 21*w]', 'level_label': '1323.1', 'level_norm': 1323, 'parallel_weight': 2, 'short_label': '1323.1-m', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[3, 3, -w]', -1], ['[3, 3, -w + 1]', 1], ['[49, 7, -7]', -1]], 'hecke_eigenvalues': [0, -1, 3, 2, -6, 6, 0, 0, 6, -2, 2, -4, -4, 1, 6, -6, 2, 2, 16, 16, 14, -14, 8, 8, 4, -4, -14, 14, 6, 0, 0, 4, -4, 12, 12, -2, -2, 10, -10, -4, 4, -26, -26, 8, -8, -24, -24, -4, -4, -6, 6, -20, 20, 26, -26, -16, 16, 6, -6, 22, 22, 20, 20, -24, 24, -26, -26, 14, 14, 28, -28, -22, 0, 0, 10, 10, 6, -6, -12, 12, 14, 14, -24, -24, 36, -36, -36, 36, -20, 20, 24, -24, -18, 18, -20, -20, 4, 4, 4, -4, 10, -10, 4, 4, 48, -48, 6, 6, -16, -16, 18, -18, -40, 40, 18, -18, 12, -12, 34, 34, 18, -18, 30, -30, -48, 48, 40, 40, -32, -32, 10, 10, 26, -26, 42, -42, 24, 24, -14, -14, -14, 14, -44, -44, 6, -6, 28, 28, 8, -8, 4, 4, 24, -24, -8, -8, -42, -42, 26, -26, -62, -12, 12, -16, -16, -26, -26, 34, -34, 0, 0, 32, 32, -2, 2, -24, -24, -46, -46, 60, -60, -38, -38, 34, -34, -2, -2, -14, -14, -28, -28, 28, -28, 18, -18, -30, -30, -24, 24, 32, 32, -14, -14, -58, 58, -36, 36, -28, -28, -18, -18, -18, 18, 56, 56, 64, 64, -38, 38, -38, 38, 38, -20, 20, -10, -10, 14, -14, -8, 8, -8, -8, 46, 46, 4, 4, 10, -10, -36, -36, -36, 36, 8, -8, 36, 36, 72, 72, 40, -40, -24, 24, -58, -58, -22, 22, 10, 10, -18, 18, -32, -32, 52, -52, 78, -34, -34, 28, 28, -70, 70, 50, 50, -16, -16, 62, 62, 68, -68, 64, -64, -40, 40, 24, -24, -82, -82, -6, 6, -2, 2, 52, -52, -50, -50, -26, 26, -80, -80, 14, -14, -52, 52, -54, -54, -80, -80, 20, -20, 60, 60, 12, -12, 30, 30, 26, 26, -48, 48, -18, 18, 12, 12, -26, -26, 66, -66, -28, -28, 6, -6, -34, -34, -56, 56, 94, 6, -6, 30, -30, -32, -32, 16, 16, 22, -22, -8, -8, 28, -28, 74, 74, 34, -34, -96, -96, -22, -22, -2, 2, 46, -46, -62, 62, -24, 24, -28, -28, -86, -86, 90, 90, -12, 12, -36, -36, 90, -90, -56, -56, -2, -2, 40, -40, 90, -90, -54, -54, -70, -70, -48, 48, 28, 28, -58, -58, 18, -18, -12, -12, -94, 94, 8, 8, 50, 50, 86, -86, 28, -28, 52, 52, -54, -54, 6, -6, 88, 88, 72, -72, 66, -66, -100, 100, -28, 28, -24, 24, -12, -12, 102, -102, -36, -36, -104, 104, -30, -30, -98, 98, 92, 92, 62, 62, 94, 94, 38, -38, 28, -28, -26, -26, 76, 76, -20, 20, 58, 58, 24, 24, -14, 14, -100, -100, -12, 12, 62, -62, 112, -112, 26, 26, -66, 66, 18, 18, -14, 14, -60, 60, -26, 56, 56, 104, -104, 6, -6, -44, 44, 72, 72, 12, 12, 62, 62, -106, 106, -112, 112, -80, -80, 22, 22, 44, 44, 20, 20, 114, -114, -62, -62, 80, -80, 0, 0, 18, -18, -112, 112, 70, 70, -60, 60, -34, -34, -78, 78, -118, 118, 64, 64, -40, -40, 20, -20, -58, -58, -94, 94, 36, -36, -122, 122, 120, 120, -2, 2, 76, 76, -8, 8, 78, -78, -26, -26, -52, -52, 38, 38, 82, -82, -16, 16, 52, -52, 12, 12, -48, -48, 18, -18, 54, -54, -96, -96, 98, 98, 4, -4, -90, 90, 6, -6, -58, -58, -34, -34, -10, 10, 100, 100, 112, -112, -78, 78, -10, 10, -56, -56, 112, 112, -56, 56, -78, 78, -118, 116, 116, 84, -84, -12, 12, 90, 90, -8, -8, 12, 12, -42, 42, 100, 100, -114, -114, 88, 88, 8, -8, -16, 16, 100, 100, 38, 38, 2, -2, 56, 56, -96, -96, -100, 100, -94, 94, 30, 30, -46, -46, 78, 78, 72, -72, 114, -114, 108, -108, 26, -26, 104, -104, 66, 66, -128, 128, 54, 54, -2, -2, 78, -78, -78, 78, 142, -48, 48, 36, -36, -102, -102, -32, -32, -36, 36, -60, 60, -82, -82, -90, -90, 132, 132, 98, -98, 88, -88, 62, 62, 16, -16, -110, -114, 114, 44, 44, -98, 98, -48, 48, 0, 0, 30, -30, -72, -72, -14, -14, 44, 44, 18, -18, 68, -68, 0, 0, 114, 114, -28, -28, -102, 102, -50, -50, -120, 120, 96, -96, 58, 58, 132, -132, 28, 28, -66, 66, 94, -94, -48, 48, -78, 78, -86, -86, -80, -80, -42, -42, -34, 34, -88, 88, -94, -94, 20, 20, 90, -90, 4, 4, -60, 60, 88, -88, 24, -24, -8, 8, -110, -110, -106, 106, 72, 72, 30, -30, -52, -52, -54, 54, 66, -66, 106, 106, 116, 116, 150, -150, -20, -20, -54, -54, -138, 138, 8, -8, 18, -18, 62, 62, -90, 90, 24, 24, 94, -94, 86, 86, -112, -112, 58, 58, 100, 100, -130, -130, -86, -86, 50, -50, -12, -12, -34, 34, -92, 92, 62, 62, -40, 40, -38, -38, 2, -2, 82, 82, -38, 38, -112, -112, -86, 86, -68, 68, -146, -146, 56, 56, -76, -76, -74, -74, 94, 94, 42, -42, 110, -110, 124, 124, -12, 12, 18, 18, -6, -6, 16, -16, 22, 60, -60, -60, -60, 6, -6, -88, 88, 104, 104, 92, -92, -102, 102, 96, 96, -22, -22, -44, 44, 12, -12, -46, -46, -34, 34, -112, 112, -40, 40, -40, -40, 118, 118, 150, -150, 132, -132, 20, 20, 54, -54, -54, -54, 42, -42, 20, -20, 82, 82, 44, -44, -14, -14, -164, 164, 6, 6, -2, 2, -98, -98, 108, 108, -62, 62, 156, 156, 24, -24, -82, -82, 138, -138, -108, 108, -46, -46, 22, -22, 98, 98, -24, 24, 90, -90, 8, 8, 86, 86, -28, 28, 150, 150, -58, 58, 136, 136, 68, 68, -76, -76, -82, 82, -126, 126, -56, 56, -162, 162, 102, -102, 86, -86, -136, -136, -90, 90, -60, 60, -18, -168, -168, -34, -34, 74, -74, 20, 20, 18, 18, 44, 44, 18, -18, 144, -144, -90, -90, 96, -96, 36, -36, 110, 110, -40, -40, 80, 80, 124, -124, -42, -42, 84, -84, 46, 46, 92, -92, 102, 102, 42, -42, -104, -104, 98, 98, 70, 70, -132, 132, 34, -34, 38, 38, -160, 160, 128, -128, 44, 44, 174, -174, 112, 112, -6, 6, -140, -140, 58, 58, 54, -54, 26, -26, 96, 96, 22, 22, 34, 34, 54, -54, -66, 66, 148, 148, 38, 38, 64, 64, 98, 98, 26, -26, -122, -122, -148, -148, 136, -136, -50, 50, -56, -56, 94, -94, -96, -96, 76, -76, -158, -158, -114, -114, 54, -54, -116, -116, 48, -48, 118, 118, 86, 86, -76, -76, -16, -16, 106, 106, -72, -72, -16, -16, -142, 142, -130, -130, -60, -60, -44, 44, 138, -138, -12, 12, 120, -120, -78, 78, 122, -122, 76, 76, 40, -40, -6, -6, 16, 16, 98, -98, -60, -60, 130, -46, 46, -30, -30, 178, -178, 16, 16, -138, 138, 40, 40, 4, -4, -14, 14, -92, 92, 42, -42, 132, -132, -160, 160, 100, 100, 120, -120, 14, -14, 188, 188, -30, -30, 154, -154, 30, 30, 138, 138, 154, 154, 162, -162, -96, 96, 12, -12, 148, 148, 134, 134, -116, 116, 18, -18, 96, 96, -52, -52, -132, -132, -84, 84, -162, 162, -100, -100, 38, -38, 66, 66, 48, 48], 'hecke_polynomial': 'x', 'label': '2.2.13.1-1323.1-m'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 13, 'ideals': ['[1, 1, 1]', '[3, 3, -w]', '[3, 3, -w + 1]', '[4, 2, 2]', '[9, 3, 3]', '[9, 9, w + 3]', '[9, 9, -w + 4]', '[12, 6, -2*w]', '[12, 6, -2*w + 2]', '[13, 13, -2*w + 1]', '[16, 4, 4]', '[17, 17, w + 4]', '[17, 17, -w + 5]', '[23, 23, 3*w + 1]', '[23, 23, -3*w + 4]', '[25, 5, 5]', '[27, 9, -3*w]', '[27, 9, -3*w + 3]', '[27, 27, w + 5]', '[27, 27, -w + 6]', '[29, 29, 3*w - 2]', '[29, 29, -3*w + 1]', '[36, 6, 6]', '[36, 18, 2*w + 6]', '[36, 18, -2*w + 8]', '[39, 39, w + 6]', '[39, 39, -w + 7]', '[43, 43, -4*w - 1]', '[43, 43, 4*w - 5]', '[48, 12, -4*w]', '[48, 12, -4*w + 4]', '[49, 7, -7]', '[51, 51, -4*w + 3]', '[51, 51, -2*w + 9]', '[51, 51, 2*w + 7]', '[51, 51, -4*w + 1]', '[52, 26, -4*w + 2]', '[53, 53, -w - 7]', '[53, 53, w - 8]', '[61, 61, -3*w - 8]', '[61, 61, 3*w - 11]', '[64, 8, 8]', '[68, 34, 2*w + 8]', '[68, 34, -2*w + 10]', '[69, 69, -w - 8]', '[69, 69, -5*w - 1]', '[69, 69, 5*w - 6]', '[69, 69, -w + 9]', '[75, 15, -5*w]', '[75, 15, -5*w + 5]', '[79, 79, 5*w - 4]', '[79, 79, 5*w - 1]', '[81, 9, 9]', '[81, 27, 3*w + 9]', '[81, 27, -3*w + 12]', '[81, 81, -5*w + 2]', '[81, 81, -5*w + 3]', '[87, 87, -w - 9]', '[87, 87, 2*w - 11]', '[87, 87, 2*w + 9]', '[87, 87, -w + 10]', '[92, 46, 6*w + 2]', '[92, 46, -6*w + 8]', '[100, 10, 10]', '[101, 101, -6*w - 1]', '[101, 101, 6*w - 7]', '[103, 103, 3*w - 13]', '[103, 103, -3*w - 10]', '[107, 107, -w - 10]', '[107, 107, w - 11]', '[108, 18, -6*w]', '[108, 18, -6*w + 6]', '[108, 54, 2*w + 10]', '[108, 54, -2*w + 12]', '[113, 113, 6*w - 5]', '[113, 113, 6*w - 1]', '[116, 58, 6*w - 4]', '[116, 58, -6*w + 2]', '[117, 39, -6*w + 3]', '[117, 117, -7*w + 10]', '[117, 117, -7*w - 3]', '[121, 11, -11]', '[127, 127, -3*w - 11]', '[127, 127, 3*w - 14]', '[129, 129, w + 11]', '[129, 129, 5*w + 12]', '[129, 129, 5*w - 17]', '[129, 129, w - 12]', '[131, 131, 2*w - 13]', '[131, 131, -2*w - 11]', '[139, 139, -7*w - 1]', '[139, 139, 7*w - 8]', '[144, 12, 12]', '[144, 36, 4*w + 12]', '[144, 36, -4*w + 16]', '[147, 21, 7*w]', '[147, 21, 7*w - 7]', '[153, 51, 3*w + 12]', '[153, 51, -3*w + 15]', '[153, 153, w + 12]', '[153, 153, -7*w + 6]', '[153, 153, -7*w + 1]', '[153, 153, -w + 13]', '[156, 78, 2*w + 12]', '[156, 78, -2*w + 14]', '[157, 157, 7*w - 2]', '[157, 157, 7*w - 5]', '[159, 159, 7*w - 3]', '[159, 159, 8*w + 3]', '[159, 159, 8*w - 11]', '[159, 159, 7*w - 4]', '[169, 13, 13]', '[172, 86, -8*w - 2]', '[172, 86, 8*w - 10]', '[173, 173, 4*w - 17]', '[173, 173, -4*w - 13]', '[179, 179, -w - 13]', '[179, 179, w - 14]', '[181, 181, 3*w - 16]', '[181, 181, -3*w - 13]', '[183, 183, 8*w + 1]', '[183, 183, 11*w + 9]', '[183, 183, 11*w - 20]', '[183, 183, 8*w - 9]', '[191, 191, 9*w - 13]', '[191, 191, -9*w - 4]', '[192, 24, -8*w]', '[192, 24, -8*w + 8]', '[196, 14, -14]', '[199, 199, 8*w - 7]', '[199, 199, 8*w - 1]', '[204, 102, -8*w + 6]', '[204, 102, -4*w + 18]', '[204, 102, 4*w + 14]', '[204, 102, -8*w + 2]', '[207, 69, 9*w + 3]', '[207, 69, -9*w + 12]', '[207, 207, w + 14]', '[207, 207, 8*w - 5]', '[207, 207, -8*w + 3]', '[207, 207, w - 15]', '[208, 52, -8*w + 4]', '[211, 211, -3*w - 14]', '[211, 211, 3*w - 17]', '[212, 106, -2*w - 14]', '[212, 106, 2*w - 16]', '[221, 221, -9*w + 11]', '[221, 221, -9*w - 2]', '[225, 15, 15]', '[225, 45, 5*w + 15]', '[225, 45, -5*w + 20]', '[233, 233, -9*w - 1]', '[233, 233, 9*w - 10]', '[237, 237, -w - 15]', '[237, 237, -4*w - 15]', '[237, 237, 4*w - 19]', '[237, 237, w - 16]', '[243, 27, -9*w]', '[243, 27, -9*w + 9]', '[243, 81, 3*w + 15]', '[243, 81, -3*w + 18]', '[243, 243, -2*w + 17]', '[243, 243, 2*w + 15]', '[244, 122, -6*w - 16]', '[244, 122, 6*w - 22]', '[251, 251, 9*w - 8]', '[251, 251, 9*w - 1]', '[256, 16, 16]', '[257, 257, 9*w - 2]', '[257, 257, 9*w - 7]', '[261, 87, 9*w - 6]', '[261, 87, -9*w + 3]', '[261, 261, -5*w + 21]', '[261, 261, -10*w + 13]', '[261, 261, 10*w + 3]', '[261, 261, -5*w - 16]', '[263, 263, 9*w - 4]', '[263, 263, 9*w - 5]', '[269, 269, -w - 16]', '[269, 269, w - 17]', '[272, 68, 4*w + 16]', '[272, 68, -4*w + 20]', '[276, 138, -2*w - 16]', '[276, 138, -10*w - 2]', '[276, 138, 10*w - 12]', '[276, 138, -2*w + 18]', '[277, 277, 3*w - 19]', '[277, 277, -3*w - 16]', '[283, 283, 11*w - 16]', '[283, 283, -11*w - 5]', '[289, 17, 17]', '[289, 289, -10*w - 1]', '[289, 289, -10*w + 11]', '[299, 299, -5*w - 17]', '[299, 299, -5*w + 22]', '[300, 30, -10*w]', '[300, 30, -10*w + 10]', '[303, 303, w + 17]', '[303, 303, 7*w - 25]', '[303, 303, 7*w + 18]', '[303, 303, w - 18]', '[309, 309, 10*w - 9]', '[309, 309, 13*w + 9]', '[309, 309, 13*w - 22]', '[309, 309, 10*w - 1]', '[311, 311, 2*w - 19]', '[311, 311, -2*w - 17]', '[313, 313, -3*w - 17]', '[313, 313, 3*w - 20]', '[316, 158, 10*w - 8]', '[316, 158, 10*w - 2]', '[321, 321, 10*w - 3]', '[321, 321, 11*w + 3]', '[321, 321, 11*w - 14]', '[321, 321, 10*w - 7]', '[324, 18, 18]', '[324, 54, 6*w + 18]', '[324, 54, -6*w + 24]', '[324, 162, -10*w + 4]', '[324, 162, -10*w + 6]', '[325, 65, -10*w + 5]', '[337, 337, 11*w - 13]', '[337, 337, -11*w - 2]', '[339, 339, -w - 18]', '[339, 339, 5*w - 23]', '[339, 339, -5*w - 18]', '[339, 339, w - 19]', '[347, 347, -12*w - 5]', '[347, 347, 12*w - 17]', '[348, 174, -2*w - 18]', '[348, 174, 4*w - 22]', '[348, 174, 4*w + 18]', '[348, 174, -2*w + 20]', '[351, 117, 3*w + 18]', '[351, 117, -3*w + 21]', '[351, 351, -11*w - 1]', '[351, 351, -11*w + 12]', '[361, 19, -19]', '[363, 33, 11*w]', '[363, 33, 11*w - 11]', '[367, 367, 6*w - 25]', '[367, 367, -6*w - 19]', '[368, 92, 12*w + 4]', '[368, 92, -12*w + 16]', '[373, 373, 11*w - 10]', '[373, 373, 11*w - 1]', '[377, 377, w + 19]', '[377, 377, w - 20]', '[381, 381, 14*w - 23]', '[381, 381, 11*w - 2]', '[381, 381, 11*w - 9]', '[381, 381, 14*w + 9]', '[387, 129, -12*w - 3]', '[387, 129, 12*w - 15]', '[387, 387, -11*w + 8]', '[387, 387, -17*w - 15]', '[387, 387, 17*w - 32]', '[387, 387, 11*w - 3]', '[389, 389, -4*w - 19]', '[389, 389, 4*w - 23]', '[391, 391, -11*w + 7]', '[391, 391, 3*w - 22]', '[391, 391, 3*w + 19]', '[391, 391, 11*w - 4]', '[393, 393, 13*w - 19]', '[393, 393, 11*w - 5]', '[393, 393, 11*w - 6]', '[393, 393, 13*w + 6]', '[400, 20, 20]', '[404, 202, -12*w - 2]', '[404, 202, 12*w - 14]', '[412, 206, 6*w - 26]', '[412, 206, -6*w - 20]', '[417, 417, w + 20]', '[417, 417, 8*w + 21]', '[417, 417, 8*w - 29]', '[417, 417, w - 21]', '[419, 419, -12*w - 1]', '[419, 419, 12*w - 13]', '[425, 85, 5*w + 20]', '[425, 85, -5*w + 25]', '[428, 214, -2*w - 20]', '[428, 214, 2*w - 22]', '[432, 36, -12*w]', '[432, 36, -12*w + 12]', '[432, 108, 4*w + 20]', '[432, 108, -4*w + 24]', '[433, 433, -3*w - 20]', '[433, 433, 3*w - 23]', '[439, 439, 13*w - 17]', '[439, 439, -13*w - 4]', '[441, 21, 21]', '[441, 63, -7*w - 21]', '[441, 63, 7*w - 28]', '[443, 443, 12*w - 11]', '[443, 443, 12*w - 1]', '[452, 226, 12*w - 10]', '[452, 226, 12*w - 2]', '[459, 153, -12*w + 9]', '[459, 153, -6*w + 27]', '[459, 153, 6*w + 21]', '[459, 153, -12*w + 3]', '[459, 459, w + 21]', '[459, 459, -13*w + 16]', '[459, 459, -13*w - 3]', '[459, 459, -w + 22]', '[464, 116, 12*w - 8]', '[464, 116, -12*w + 4]', '[467, 467, 12*w - 7]', '[467, 467, 12*w - 5]', '[468, 78, -12*w + 6]', '[468, 234, -14*w + 20]', '[468, 234, -14*w - 6]', '[471, 471, 5*w - 26]', '[471, 471, 2*w - 23]', '[471, 471, -2*w - 21]', '[471, 471, -5*w - 21]', '[477, 159, -3*w - 21]', '[477, 159, 3*w - 24]', '[477, 477, 4*w - 25]', '[477, 477, -11*w - 24]', '[477, 477, 11*w - 35]', '[477, 477, -4*w - 21]', '[484, 22, -22]', '[491, 491, 7*w - 29]', '[491, 491, -7*w - 22]', '[493, 493, 13*w + 1]', '[493, 493, -14*w - 5]', '[493, 493, 14*w - 19]', '[493, 493, -13*w + 14]', '[503, 503, -w - 22]', '[503, 503, w - 23]', '[507, 39, -13*w]', '[507, 39, -13*w + 13]', '[508, 254, -6*w - 22]', '[508, 254, 6*w - 28]', '[516, 258, 2*w + 22]', '[516, 258, 10*w + 24]', '[516, 258, 10*w - 34]', '[516, 258, 2*w - 24]', '[519, 519, 13*w - 12]', '[519, 519, 17*w - 29]', '[519, 519, 17*w + 12]', '[519, 519, 13*w - 1]', '[521, 521, -15*w + 22]', '[521, 521, 8*w - 31]', '[523, 523, 3*w - 25]', '[523, 523, -3*w - 22]', '[524, 262, 4*w - 26]', '[524, 262, -4*w - 22]', '[529, 23, 23]', '[529, 529, -13*w + 2]', '[529, 529, -13*w + 11]', '[537, 537, 13*w - 3]', '[537, 537, 14*w + 3]', '[537, 537, 14*w - 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68]', '[9013, 9013, 36*w - 133]', '[9013, 9013, -36*w - 97]', '[9049, 9049, -9*w - 92]', '[9049, 9049, 9*w - 101]', '[9091, 9091, 3*w - 97]', '[9091, 9091, -3*w - 94]', '[9103, 9103, 56*w - 61]', '[9103, 9103, -56*w - 5]', '[9109, 9109, 53*w - 22]', '[9109, 9109, 53*w - 31]', '[9127, 9127, 53*w - 28]', '[9127, 9127, 53*w - 25]', '[9151, 9151, -59*w - 17]', '[9151, 9151, 59*w - 76]', '[9161, 9161, 17*w - 109]', '[9161, 9161, -17*w - 92]', '[9181, 9181, 55*w - 2]', '[9181, 9181, 55*w - 53]', '[9187, 9187, -27*w - 94]', '[9187, 9187, 27*w - 121]', '[9203, 9203, 2*w - 97]', '[9203, 9203, -2*w - 95]', '[9221, 9221, 54*w - 43]', '[9221, 9221, 54*w - 11]', '[9227, 9227, 57*w - 65]', '[9227, 9227, -57*w - 8]', '[9239, 9239, -34*w - 97]', '[9239, 9239, 34*w - 131]', '[9257, 9257, 29*w - 124]', '[9257, 9257, -29*w - 95]', '[9281, 9281, 54*w - 41]', '[9281, 9281, 54*w - 13]', '[9283, 9283, -3*w - 95]', '[9283, 9283, 3*w - 98]', '[9311, 9311, 25*w - 119]', '[9311, 9311, -25*w - 94]', '[9337, 9337, -61*w - 22]', '[9337, 9337, 61*w - 83]', '[9343, 9343, 33*w - 130]', '[9343, 9343, -64*w + 95]', '[9377, 9377, 54*w - 17]', '[9377, 9377, 54*w - 37]', '[9403, 9403, 27*w - 122]', '[9403, 9403, -27*w - 95]', '[9409, 97, -97]', '[9413, 9413, 54*w - 19]', '[9413, 9413, 54*w - 35]', '[9421, 9421, 59*w - 73]', '[9421, 9421, -59*w - 14]', '[9437, 9437, -57*w - 5]', '[9437, 9437, 57*w - 62]', '[9439, 9439, -9*w - 94]', '[9439, 9439, 9*w - 103]', '[9461, 9461, 54*w - 23]', '[9461, 9461, 54*w - 31]', '[9463, 9463, 56*w - 55]', '[9463, 9463, 56*w - 1]', '[9467, 9467, -26*w - 95]', '[9467, 9467, 26*w - 121]', '[9473, 9473, 54*w - 29]', '[9473, 9473, 54*w - 25]', '[9491, 9491, 60*w - 77]', '[9491, 9491, -60*w - 17]', '[9533, 9533, 31*w - 128]', '[9533, 9533, 66*w - 101]', '[9539, 9539, -19*w - 94]', '[9539, 9539, 19*w - 113]', '[9551, 9551, -13*w - 94]', '[9551, 9551, 13*w - 107]', '[9619, 9619, 30*w - 127]', '[9619, 9619, -30*w - 97]', '[9623, 9623, 23*w - 118]', '[9623, 9623, -23*w - 95]', '[9629, 9629, 57*w - 59]', '[9629, 9629, -57*w - 2]', '[9643, 9643, 61*w - 80]', '[9643, 9643, -61*w - 19]', '[9649, 9649, 55*w - 41]', '[9649, 9649, 55*w - 14]', '[9689, 9689, -57*w - 1]', '[9689, 9689, 57*w - 58]', '[9697, 9697, 21*w - 116]', '[9697, 9697, -21*w - 95]', '[9721, 9721, 55*w - 38]', '[9721, 9721, 55*w - 17]', '[9733, 9733, -12*w - 95]', '[9733, 9733, 12*w - 107]', '[9749, 9749, 4*w - 101]', '[9749, 9749, -4*w - 97]', '[9767, 9767, -14*w - 95]', '[9767, 9767, 14*w - 109]', '[9803, 9803, 57*w - 56]', '[9803, 9803, 57*w - 1]', '[9811, 9811, 55*w - 32]', '[9811, 9811, 55*w - 23]', '[9829, 9829, 55*w - 26]', '[9829, 9829, 55*w - 29]', '[9851, 9851, 60*w - 73]', '[9851, 9851, -60*w - 13]', '[9857, 9857, 57*w - 2]', '[9857, 9857, 57*w - 55]', '[9871, 9871, -3*w - 98]', '[9871, 9871, 3*w - 101]', '[9883, 9883, 6*w - 103]', '[9883, 9883, -6*w - 97]', '[9907, 9907, 59*w - 67]', '[9907, 9907, -59*w - 8]', '[9923, 9923, 29*w - 127]', '[9923, 9923, -29*w - 98]', '[9929, 9929, -63*w - 23]', '[9929, 9929, 63*w - 86]', '[9931, 9931, 61*w - 77]', '[9931, 9931, -61*w - 16]', '[9941, 9941, -7*w - 97]', '[9941, 9941, 7*w - 104]', '[9949, 9949, 36*w - 137]', '[9949, 9949, -36*w - 101]', '[9967, 9967, 56*w - 43]', '[9967, 9967, 56*w - 13]']}
• 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': [-3, -1, 1], 'conductor': 13, 'degree': 2, 'dirichlet_group': [1, 12], 'disc_abs': 13, 'disc_rad': 13, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[1, 2]]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[2, 1]]], [13, [0]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[1, 2]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [[1, 2]]], [47, [[2, 1]]], [53, [[1, 2]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1], 'galois_label': '2T1', 'galt': 1, 'grd': 3.605551275463989, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.13.1', 'local_algs': ['13.1.2.1a1.1'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 0, 'ramps': [13], 'rd': 3.60555127546, 'regulator': {'__RealLiteral__': 0, 'data': '1.19476321729', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a']}