Hilbert modular form data - 2.2.12.1-768.1-m

Formats: - HTML - YAML - JSON - 2026-02-08T19:53:10.960671

• 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': 12, 'field_bad_primes': [2, 3], 'field_label': '2.2.12.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.12.1-768.1-m', 'label_nsuffix': 12, 'label_suffix': 'm', 'level_bad_primes': [2, 3], 'level_ideal': '[768, 48, 16*w]', 'level_label': '768.1', 'level_norm': 768, 'parallel_weight': 2, 'short_label': '768.1-m', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, -w + 1]', -1], ['[3, 3, w]', 1]], 'hecke_eigenvalues': [0, -1, -4, 0, -2, 2, 0, -4, 6, -6, -6, -12, 0, -6, -4, 12, -14, 10, 8, -12, -10, 14, 0, -4, 10, 2, 4, -20, -10, 2, -12, 20, -14, 2, 16, -16, -20, -4, 18, 6, -24, -24, 10, -22, 24, 12, 14, -14, 8, 0, -26, 6, 8, -12, 0, -16, 2, -10, -6, 32, 8, -6, 10, -18, 6, 28, 16, 26, 18, 0, 12, 10, -14, -22, -16, -16, 10, -14, 18, -6, 4, -16, 18, 6, -28, 24, 2, 2, -24, 4, 2, -38, -40, 28, 24, 4, 36, 12, 16, 44, -38, -18, 4, 24, -14, 2, 12, 4, 12, -24, -14, 2, 26, 34, 40, 36, 12, -12, -22, -38, -14, -46, 8, -36, 14, 50, -36, 8, -26, -22, 16, -24, 34, -34, 50, -14, 20, -36, -10, 34, 40, 28, -18, 10, 10, -56, -24, -30, -6, 48, -32, 56, 0, -38, 42, -44, -28, 26, -24, 12, 16, -16, 42, 18, 34, 58, 28, 4, -30, 50, 0, 56, -30, 18, 2, -14, 8, 36, 42, 6, 16, -16, -26, -38, -50, 46, 8, -40, 34, -14, -12, -12, 36, 36, 2, -14, -26, -38, -8, 64, 58, -34, 38, 46, -56, -68, 12, 0, 18, 18, 20, -12, -72, 44, 10, -22, 8, 56, 10, -34, -28, -8, -22, -22, 12, 0, 12, 20, 50, 6, -32, 60, 74, -14, 0, 52, 24, -44, 8, 52, 50, -46, 48, 20, 12, -60, -48, -56, 18, -58, 8, -12, 34, 34, -52, 4, 14, -22, 74, -70, 12, -36, -70, 14, -6, -30, 34, -30, 42, -14, 2, 74, -38, 36, -48, 2, 10, 10, -22, -60, -68, 48, 28, 16, -60, 74, -70, 50, -24, -64, 46, -82, -60, 36, -12, -12, 66, -46, 4, -32, 2, -46, 4, 84, -58, -58, -24, 84, -86, -74, 48, 68, -38, 34, -16, -64, -48, 56, -22, -38, 60, -12, -32, 4, 62, 22, -46, 2, 34, 42, -72, 8, 38, 2, -36, 36, -48, -12, 34, 2, 46, 70, 26, -22, -68, 48, 70, -6, 12, 24, 74, -14, 10, -70, -48, 40, -44, -84, -16, 40, 26, -70, 32, -16, -64, -60, -54, 42, 10, 26, -40, -36, -40, -72, 58, -10, -60, 24, -56, 8, -46, -62, 86, -10, -48, 96, 18, -90, -56, 20, -94, -14, -60, -60, -8, -64, -46, -86, 34, 26, 86, -62, -66, -72, -12, -14, 34, 0, -20, -58, -18, -40, 88, -84, -40, 26, -70, 8, 96, -84, -8, -62, 50, -84, 8, -8, 84, 22, 38, 20, -44, -40, -12, 2, 34, 38, 46, -70, 98, -76, 80, -70, -86, 40, -68, -86, -22, -88, -84, -6, 90, -30, 6, 72, -68, -68, -60, -46, 98, 110, 50, -24, 60, -46, 62, -4, 60, 58, -22, -58, -98, -12, 52, -20, -84, -56, 12, 58, -102, -44, -68, 46, -54, 20, -72, 86, 54, -70, -46, 72, -60, 46, -86, 64, 12, -46, 34, -72, 28, 58, -70, -40, -4, 106, 10, 114, -6, -28, -24, -102, 54, -20, 16, -40, -44, -22, 10, -62, -94, -38, -110, 104, -40, 94, 34, -64, -48, -22, 10, 12, 84, -2, 14, -92, 68, 60, -24, -82, 26, -84, -72, -6, 82, -30, -78, 104, 88, -84, -116, -20, -12, 48, -32, -60, 76, 78, 18, -54, 42, 24, 64, 12, 60, 74, 94, -16, 8, -94, 34, 20, -36, -14, 34, -42, -2, 54, -18, -12, -8, -56, 60, -30, -102, 112, 80, -34, 86, 4, -52, -102, -22, -70, -6, -24, 24, -94, 18, -76, 60, 64, -4, -70, 66, -14, -84, -20, 68, 12, 2, -70, -30, 114, -104, -24, -14, 106, 34, 82, 12, -16, 70, -98, -48, -124, -100, 116, 32, 24, 18, -22, 64, 108, -36, 12, -118, 82, 40, -16, 18, 50, 122, -14, -110, -42, -84, 56, 86, 74, 120, -104, 116, 108, -14, -10, -36, 40, -38, 46, -12, -96, -38, -118, 130, -62, 116, -24, 8, -8, 12, 80, -22, -38, -48, -72, -60, 24, -2, 34, 18, 66, -36, 56, 36, 84, 114, -6, 26, 58, -12, -8, -94, -46, 84, 32, -70, -38, 0, 44, -48, 96, -28, 76, 64, -84, 14, 106, -2, 98, 34, 50, -88, -60, -84, 20, 88, 12, 48, 40, 10, 106, 132, 32, 70, -22, -66, 102, 50, 82, -28, -48, -120, 24, -50, 62, 12, 20, 106, -38, -2, 6, -74, 10, 92, -72, -18, 150, 18, 46, 56, -116, -76, 72, -82, -38, -52, -148, -46, 138, -84, -8, 54, 66, -120, 144, 58, -102, 116, 128, -88, 68, 8, -36, 38, -26, -56, 4, 32, -60, 2, -70, 96, -44, -54, 90, -94, -46, 76, -52, -46, -38, -48, 16, 12, 84, -58, 22, -86, -134, -38, 84, -72, 74, -46, -80, -48, -44, 60, 6, -70, 16, -84, -96, -52, 130, 34, -24, 0, 142, 22, 154, -14, -126, 114, 14, -14, -10, -6, -118, 26, -92, -116, 106, -86, -40, -96, 74, 26, -24, -76, 10, 98, 0, 136, 146, -14, 52, -20, -98, 122, -86, 130, -70, -86, 0, 72, -54, -66, 84, 12, -18, -150, -12, -80, 154, -38, -60, -24, -52, 16, 10, 50, 158, -10, -124, -112, 92, -8, 72, 120, -100, 20, -114, -38, -24, -48, 22, 70, -40, 60, -32, 152, 38, 58, -48, -84, 104, -124, 2, -62, 82, -26, -104, 24, 56, -60, 44, 96, -18, -90, 96, 72, -118, -38, -8, -12, -84, 144, -94, -14, 18, -18, -72, 88, -20, -124, -26, -106, 52, -108, 98, -14, -118, 26, 20, 116, 142, -38, -6, -54, 130, 82, -46, -62, -60, -56, -122, -62, -108, -88, -74, -34, 64, -84, -156, -160, 154, 58, 108, -68, -62, 34, -64, -120, 70, -122, 74, 118, -44, 16, 16, -96, 22, 2, 44, -36, -110, -122, 2, 34, 84, 144, -8, -80, 46, -38, 148, 24, -158, -98, -94, 34, 114, -94, -56, -104, 86, -26, -68, 80, 40, 12, 44, -64, 34, 74, 130, 74, -38, -62, 114, 128, 76, 70, -70, -120, -20, -134, 10, -38, 154, 20, 120, -60, 108, 148, 44, 22, 14, -140, 160, 122, 58, -84, -20, -94, 2, 32, -40, 2, 82, 156, 124, -30, -46, 52, 28, 26, 10, 26, -62, -30, 58, 58, -158, -120, -84, 98, 10, -116, 144, -38, 146, 144, -36, 176, -92, -70, -62, 170, -134, -112, -76, -62, 74, 12, 56, 74, -86, 18, -126, 132, -24, 62, 130, 46, 94, 44, -164, 46, -106, -94, 34, 52, -124, 50, -46, 128, -104, 92, -168, -40, -100, 186, -30, -8, -60, 52, -68, 66, -70, -78, 34, 130, -86, -148, -32, 56, 20, -72, 72, -86, 106, 80, 28, -70, 94, 14, 110, 92, 116, -102, 34, 98, 142, 2, -22, 122, -158, 12, -156, 12, -44, 108, 120, -78, -62, -6, 118, 108, 56, -36, 44, -118, 10, -86, -70, 68, 140, 42, 42, -180, 100, -146, 170, 48, 136, -138, 70, -152, -60, 104, 24, 140, -84, -28, 164, -40, -84, 108, -68, 66, 82, 50, -34, -120, 104, 10, 58, 62, 2, -158, -110, -24, 72, 74, -86, 122, 42, -168, 104, 36, -8, -166, 170, -22, -14, -96, -48, 160, -60, 42, 18, -134, 38, -72, 80, 180, -4, -24, -144, 142, -70, -140, -68, -158, 10, -174, -74], 'hecke_polynomial': 'x', 'label': '2.2.12.1-768.1-m'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 12, 'ideals': ['[1, 1, 1]', '[2, 2, -w + 1]', '[3, 3, w]', '[4, 2, 2]', '[6, 6, w - 3]', '[8, 4, -2*w + 2]', '[9, 3, 3]', '[11, 11, -2*w + 1]', '[11, 11, 2*w + 1]', '[12, 6, 2*w]', '[13, 13, w + 4]', '[13, 13, -w + 4]', '[16, 4, 4]', '[18, 6, -3*w + 3]', '[22, 22, w + 5]', '[22, 22, w - 5]', '[23, 23, -3*w + 2]', '[23, 23, 3*w + 2]', '[24, 12, 2*w - 6]', '[25, 5, 5]', '[26, 26, -3*w - 1]', '[26, 26, -3*w + 1]', '[27, 9, 3*w]', '[32, 8, -4*w + 4]', '[33, 33, w + 6]', '[33, 33, w - 6]', '[36, 6, 6]', '[37, 37, 2*w - 7]', '[37, 37, -2*w - 7]', '[39, 39, 4*w - 3]', '[39, 39, 4*w + 3]', '[44, 22, -4*w + 2]', '[44, 22, 4*w + 2]', '[46, 46, w + 7]', '[46, 46, w - 7]', '[47, 47, -4*w - 1]', '[47, 47, 4*w - 1]', '[48, 12, 4*w]', '[49, 7, -7]', '[50, 10, -5*w + 5]', '[52, 26, 2*w + 8]', '[52, 26, -2*w + 8]', '[54, 18, 3*w - 9]', '[59, 59, 5*w - 4]', '[59, 59, -5*w - 4]', '[61, 61, -w - 8]', '[61, 61, w - 8]', '[64, 8, 8]', '[66, 66, 5*w + 3]', '[66, 66, -5*w + 3]', '[69, 69, 2*w - 9]', '[69, 69, 2*w + 9]', '[71, 71, 5*w - 2]', '[71, 71, -5*w - 2]', '[72, 12, -6*w + 6]', '[73, 73, 3*w - 10]', '[73, 73, -3*w - 10]', '[74, 74, 9*w - 13]', '[74, 74, 5*w - 1]', '[75, 15, 5*w]', '[78, 78, -w - 9]', '[78, 78, w - 9]', '[81, 9, 9]', '[83, 83, 6*w - 5]', '[83, 83, -6*w - 5]', '[88, 44, 2*w + 10]', '[88, 44, 2*w - 10]', '[92, 46, -6*w + 4]', '[92, 46, 6*w + 4]', '[94, 94, 5*w - 13]', '[94, 94, -3*w + 11]', '[96, 24, 4*w - 12]', '[97, 97, -w - 10]', '[97, 97, w - 10]', '[98, 14, 7*w - 7]', '[99, 33, -6*w + 3]', '[99, 33, 6*w + 3]', '[100, 10, 10]', '[104, 52, -6*w - 2]', '[104, 52, -6*w + 2]', '[107, 107, -6*w - 1]', '[107, 107, 6*w - 1]', '[108, 18, 6*w]', '[109, 109, 2*w - 11]', '[109, 109, -2*w - 11]', '[111, 111, -7*w + 6]', '[111, 111, -7*w - 6]', '[117, 39, 3*w + 12]', '[117, 39, -3*w + 12]', '[118, 118, 9*w - 19]', '[118, 118, -w + 11]', '[121, 11, 11]', '[121, 121, -4*w + 13]', '[121, 121, 4*w + 13]', '[122, 122, 9*w - 11]', '[122, 122, 7*w - 5]', '[128, 16, -8*w + 8]', '[131, 131, -7*w - 4]', '[131, 131, 7*w - 4]', '[132, 66, 2*w + 12]', '[132, 66, 2*w - 12]', '[138, 138, -7*w + 3]', '[138, 138, 7*w + 3]', '[141, 141, -w - 12]', '[141, 141, -w + 12]', '[142, 142, -3*w + 13]', '[142, 142, 7*w - 17]', '[143, 143, 8*w - 7]', '[143, 143, 7*w - 2]', '[143, 143, -7*w - 2]', '[143, 143, -8*w - 7]', '[144, 12, 12]', '[146, 146, 13*w - 19]', '[146, 146, 7*w - 1]', '[147, 21, -7*w]', '[148, 74, 4*w - 14]', '[148, 74, -4*w - 14]', '[150, 30, 5*w - 15]', '[156, 78, 8*w - 6]', '[156, 78, 8*w + 6]', '[157, 157, 2*w - 13]', '[157, 157, -2*w - 13]', '[162, 18, -9*w + 9]', '[166, 166, 11*w - 23]', '[166, 166, -w + 13]', '[167, 167, 8*w - 5]', '[167, 167, -8*w - 5]', '[169, 13, 13]', '[169, 169, 3*w + 14]', '[169, 169, -3*w + 14]', '[176, 44, -8*w + 4]', '[176, 44, 8*w + 4]', '[177, 177, -4*w - 15]', '[177, 177, -4*w + 15]', '[179, 179, 9*w - 8]', '[179, 179, -9*w - 8]', '[181, 181, 5*w - 16]', '[181, 181, -5*w - 16]', '[183, 183, -8*w - 3]', '[183, 183, -8*w + 3]', '[184, 92, 2*w + 14]', '[184, 92, 2*w - 14]', '[188, 94, -8*w - 2]', '[188, 94, 8*w - 2]', '[191, 191, -8*w - 1]', '[191, 191, 8*w - 1]', '[192, 24, 8*w]', '[193, 193, -w - 14]', '[193, 193, w - 14]', '[194, 194, 11*w - 13]', '[194, 194, 9*w - 7]', '[196, 14, -14]', '[198, 66, 3*w + 15]', '[198, 66, 3*w - 15]', '[200, 20, -10*w + 10]', '[207, 69, -9*w + 6]', '[207, 69, 9*w + 6]', '[208, 52, 4*w + 16]', '[208, 52, -4*w + 16]', '[213, 213, -2*w + 15]', '[213, 213, -2*w - 15]', '[214, 214, 7*w - 19]', '[214, 214, -5*w + 17]', '[216, 36, 6*w - 18]', '[218, 218, 13*w - 17]', '[218, 218, 9*w - 5]', '[219, 219, -10*w + 9]', '[219, 219, -10*w - 9]', '[222, 222, -13*w + 27]', '[222, 222, -w + 15]', '[225, 15, 15]', '[227, 227, 9*w - 4]', '[227, 227, -9*w - 4]', '[229, 229, 3*w - 16]', '[229, 229, -3*w - 16]', '[234, 78, -9*w - 3]', '[234, 78, -9*w + 3]', '[236, 118, 10*w - 8]', '[236, 118, -10*w - 8]', '[239, 239, 9*w - 2]', '[239, 239, -9*w - 2]', '[241, 241, 4*w - 17]', '[241, 241, -4*w - 17]', '[242, 22, 11*w - 11]', '[242, 242, -9*w - 1]', '[242, 242, -9*w + 1]', '[243, 27, 9*w]', '[244, 122, -2*w - 16]', '[244, 122, 2*w - 16]', '[249, 249, -5*w + 18]', '[249, 249, -5*w - 18]', '[251, 251, -10*w - 7]', '[251, 251, 10*w - 7]', '[253, 253, -w - 16]', '[253, 253, -6*w + 19]', '[253, 253, 6*w + 19]', '[253, 253, w - 16]', '[256, 16, 16]', '[262, 262, 11*w - 25]', '[262, 262, -3*w + 17]', '[263, 263, 11*w - 10]', '[263, 263, -11*w - 10]', '[264, 132, 10*w + 6]', '[264, 132, -10*w + 6]', '[275, 55, -10*w + 5]', '[275, 55, 10*w + 5]', '[276, 138, 4*w - 18]', '[276, 138, 4*w + 18]', '[277, 277, 2*w - 17]', '[277, 277, -2*w - 17]', '[282, 282, -13*w + 15]', '[282, 282, 11*w - 9]', '[284, 142, 10*w - 4]', '[284, 142, -10*w - 4]', '[286, 286, -w - 17]', '[286, 286, -5*w - 19]', '[286, 286, -5*w + 19]', '[286, 286, -w + 17]', '[288, 24, -12*w + 12]', '[289, 17, -17]', '[291, 291, -10*w + 3]', '[291, 291, -10*w - 3]', '[292, 146, 6*w - 20]', '[292, 146, -6*w - 20]', '[294, 42, -7*w + 21]', '[296, 148, 18*w - 26]', '[296, 148, 10*w - 2]', '[297, 99, 3*w + 18]', '[297, 99, 3*w - 18]', '[299, 299, -10*w - 1]', '[299, 299, 11*w - 8]', '[299, 299, -11*w - 8]', '[299, 299, 10*w - 1]', '[300, 30, 10*w]', '[311, 311, 12*w - 11]', '[311, 311, -12*w - 11]', '[312, 156, -2*w - 18]', '[312, 156, 2*w - 18]', '[313, 313, -4*w - 19]', '[313, 313, 4*w - 19]', '[314, 314, 11*w - 7]', '[314, 314, 15*w - 19]', '[321, 321, -w - 18]', '[321, 321, -w + 18]', '[324, 18, 18]', '[325, 65, 5*w + 20]', '[325, 65, -5*w + 20]', '[327, 327, -11*w - 6]', '[327, 327, -11*w + 6]', '[332, 166, 12*w - 10]', '[332, 166, -12*w - 10]', '[333, 111, 6*w - 21]', '[333, 111, -6*w - 21]', '[334, 334, -3*w + 19]', '[334, 334, 13*w - 29]', '[337, 337, 7*w - 22]', '[337, 337, -7*w - 22]', '[338, 26, -13*w + 13]', '[338, 338, -11*w + 5]', '[338, 338, -11*w - 5]', '[347, 347, -11*w - 4]', '[347, 347, 11*w - 4]', '[349, 349, 2*w - 19]', '[349, 349, -2*w - 19]', '[351, 117, 12*w - 9]', '[351, 117, 12*w + 9]', '[352, 88, 4*w + 20]', '[352, 88, 4*w - 20]', '[354, 354, -19*w + 27]', '[354, 354, 11*w - 3]', '[358, 358, 17*w - 35]', '[358, 358, -w + 19]', '[359, 359, 11*w - 2]', '[359, 359, -11*w - 2]', '[361, 19, -19]', '[362, 362, 21*w - 31]', '[362, 362, 11*w - 1]', '[363, 33, -11*w]', '[363, 363, 13*w - 12]', '[363, 363, 13*w + 12]', '[366, 366, -5*w + 21]', '[366, 366, -11*w + 27]', '[368, 92, -12*w + 8]', '[368, 92, 12*w + 8]', '[373, 373, -3*w - 20]', '[373, 373, 3*w - 20]', '[376, 188, 10*w - 26]', '[376, 188, -6*w + 22]', '[382, 382, 9*w - 25]', '[382, 382, -7*w + 23]', '[383, 383, 12*w - 7]', '[383, 383, -12*w - 7]', '[384, 48, 8*w - 24]', '[386, 386, 15*w - 17]', '[386, 386, 13*w - 11]', '[388, 194, -2*w - 20]', '[388, 194, 2*w - 20]', '[392, 28, 14*w - 14]', '[393, 393, -4*w + 21]', '[393, 393, -4*w - 21]', '[396, 66, -12*w + 6]', '[396, 66, 12*w + 6]', '[397, 397, -w - 20]', '[397, 397, w - 20]', '[400, 20, 20]', '[407, 407, 16*w - 19]', '[407, 407, 12*w + 5]', '[407, 407, -12*w + 5]', '[407, 407, -16*w - 19]', '[409, 409, -5*w - 22]', '[409, 409, 5*w - 22]', '[414, 138, 3*w + 21]', '[414, 138, 3*w - 21]', '[416, 104, -12*w - 4]', '[416, 104, -12*w + 4]', '[419, 419, 14*w - 13]', '[419, 419, -14*w - 13]', '[421, 421, -6*w - 23]', '[421, 421, 6*w - 23]', '[423, 141, -12*w - 3]', '[423, 141, 12*w - 3]', '[426, 426, -17*w + 21]', '[426, 426, 13*w - 9]', '[428, 214, -12*w - 2]', '[428, 214, 12*w - 2]', '[429, 429, -7*w - 24]', '[429, 429, -2*w + 21]', '[429, 429, -2*w - 21]', '[429, 429, -7*w + 24]', '[431, 431, -12*w - 1]', '[431, 431, 12*w - 1]', '[432, 36, 12*w]', '[433, 433, -9*w - 26]', '[433, 433, 9*w - 26]', '[436, 218, 4*w - 22]', '[436, 218, -4*w - 22]', '[438, 438, -19*w + 39]', '[438, 438, -w + 21]', '[441, 21, -21]', '[443, 443, -13*w - 8]', '[443, 443, 13*w - 8]', '[444, 222, -14*w + 12]', '[444, 222, -14*w - 12]', '[450, 30, -15*w + 15]', '[454, 454, -5*w + 23]', '[454, 454, 13*w - 31]', '[457, 457, 3*w - 22]', '[457, 457, -3*w - 22]', '[458, 458, 19*w - 25]', '[458, 458, 13*w - 7]', '[467, 467, 14*w - 11]', '[467, 467, -14*w - 11]', '[468, 78, 6*w + 24]', '[468, 78, -6*w + 24]', '[471, 471, -13*w + 6]', '[471, 471, -13*w - 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91]', '[7309, 7309, -18*w - 91]', '[7321, 7321, 5*w - 86]', '[7321, 7321, -5*w - 86]', '[7331, 7331, 50*w - 13]', '[7331, 7331, -50*w - 13]', '[7333, 7333, 14*w - 89]', '[7333, 7333, -14*w - 89]', '[7369, 7369, -3*w - 86]', '[7369, 7369, 3*w - 86]', '[7393, 7393, -w - 86]', '[7393, 7393, w - 86]', '[7417, 7417, 27*w - 98]', '[7417, 7417, -27*w - 98]', '[7451, 7451, 50*w - 7]', '[7451, 7451, -50*w - 7]', '[7477, 7477, 29*w - 100]', '[7477, 7477, -29*w - 100]', '[7487, 7487, -52*w - 25]', '[7487, 7487, 52*w - 25]', '[7489, 7489, 12*w - 89]', '[7489, 7489, -12*w - 89]', '[7499, 7499, -50*w - 1]', '[7499, 7499, 50*w - 1]', '[7523, 7523, -54*w - 35]', '[7523, 7523, 54*w - 35]', '[7537, 7537, -32*w - 103]', '[7537, 7537, 32*w - 103]', '[7547, 7547, -51*w - 16]', '[7547, 7547, 51*w - 16]', '[7549, 7549, -33*w - 104]', '[7549, 7549, 33*w - 104]', '[7559, 7559, 56*w - 43]', '[7559, 7559, -56*w - 43]', '[7561, 7561, -36*w - 107]', '[7561, 7561, 36*w - 107]', '[7573, 7573, -22*w - 95]', '[7573, 7573, 22*w - 95]', '[7583, 7583, 52*w - 23]', '[7583, 7583, -52*w - 23]', '[7607, 7607, -51*w - 14]', '[7607, 7607, 51*w - 14]', '[7621, 7621, -10*w - 89]', '[7621, 7621, 10*w - 89]', '[7643, 7643, 53*w - 28]', '[7643, 7643, -53*w - 28]', '[7669, 7669, 5*w - 88]', '[7669, 7669, -5*w - 88]', '[7681, 7681, 24*w - 97]', '[7681, 7681, -24*w - 97]', '[7691, 7691, 58*w - 49]', '[7691, 7691, -58*w - 49]', '[7703, 7703, 51*w - 10]', '[7703, 7703, -51*w - 10]', '[7717, 7717, 3*w - 88]', '[7717, 7717, -3*w - 88]', '[7727, 7727, 56*w - 41]', '[7727, 7727, -56*w - 41]', '[7741, 7741, -w - 88]', '[7741, 7741, w - 88]', '[7753, 7753, -19*w - 94]', '[7753, 7753, 19*w - 94]', '[7789, 7789, -15*w - 92]', '[7789, 7789, 15*w - 92]', '[7823, 7823, 52*w - 17]', '[7823, 7823, -52*w - 17]', '[7873, 7873, 4*w - 89]', '[7873, 7873, -4*w - 89]', '[7883, 7883, -58*w - 47]', '[7883, 7883, 58*w - 47]', '[7907, 7907, 54*w - 29]', '[7907, 7907, -54*w - 29]', '[7919, 7919, 55*w - 34]', '[7919, 7919, -55*w - 34]', '[7921, 89, -89]', '[7933, 7933, -31*w - 104]', '[7933, 7933, 31*w - 104]', '[7993, 7993, 36*w - 109]', '[7993, 7993, -36*w - 109]', '[8017, 8017, 23*w - 98]', '[8017, 8017, -23*w - 98]', '[8039, 8039, 56*w - 37]', '[8039, 8039, -56*w - 37]', '[8053, 8053, -18*w - 95]', '[8053, 8053, 18*w - 95]', '[8087, 8087, -52*w - 5]', '[8087, 8087, 52*w - 5]', '[8089, 8089, 8*w - 91]', '[8089, 8089, -8*w - 91]', '[8101, 8101, 11*w - 92]', '[8101, 8101, -11*w - 92]', '[8111, 8111, -52*w - 1]', '[8111, 8111, 52*w - 1]', '[8123, 8123, -54*w - 25]', '[8123, 8123, 54*w - 25]', '[8147, 8147, -57*w - 40]', '[8147, 8147, 57*w - 40]', '[8161, 8161, 15*w - 94]', '[8161, 8161, -15*w - 94]', '[8171, 8171, -53*w - 16]', '[8171, 8171, 53*w - 16]', '[8209, 8209, -20*w - 97]', '[8209, 8209, 20*w - 97]', '[8219, 8219, 54*w - 23]', '[8219, 8219, -54*w - 23]', '[8221, 8221, -9*w - 92]', '[8221, 8221, 9*w - 92]', '[8231, 8231, -53*w - 14]', '[8231, 8231, 53*w - 14]', '[8233, 8233, -4*w - 91]', '[8233, 8233, 4*w - 91]', '[8243, 8243, -58*w - 43]', '[8243, 8243, 58*w - 43]', '[8269, 8269, 2*w - 91]', '[8269, 8269, -2*w - 91]', '[8291, 8291, -55*w - 28]', '[8291, 8291, 55*w - 28]', '[8293, 8293, 29*w - 104]', '[8293, 8293, -29*w - 104]', '[8317, 8317, 7*w - 92]', '[8317, 8317, -7*w - 92]', '[8329, 8329, -13*w - 94]', '[8329, 8329, 13*w - 94]', '[8353, 8353, 31*w - 106]', '[8353, 8353, -31*w - 106]', '[8363, 8363, -53*w - 8]', '[8363, 8363, 53*w - 8]', '[8377, 8377, 32*w - 107]', '[8377, 8377, -32*w - 107]', '[8387, 8387, 54*w - 19]', '[8387, 8387, -54*w - 19]', '[8389, 8389, -5*w - 92]', '[8389, 8389, 5*w - 92]', '[8423, 8423, 53*w - 2]', '[8423, 8423, -53*w - 2]', '[8447, 8447, 56*w - 31]', '[8447, 8447, -56*w - 31]', '[8461, 8461, -w - 92]', '[8461, 8461, w - 92]', '[8521, 8521, -19*w - 98]', '[8521, 8521, 19*w - 98]', '[8543, 8543, -63*w - 58]', '[8543, 8543, 63*w - 58]', '[8581, 8581, -26*w - 103]', '[8581, 8581, 26*w - 103]', '[8627, 8627, -54*w - 11]', '[8627, 8627, 54*w - 11]', '[8629, 8629, -27*w - 104]', '[8629, 8629, 27*w - 104]', '[8641, 8641, 16*w - 97]', '[8641, 8641, -16*w - 97]', '[8663, 8663, -61*w - 50]', '[8663, 8663, 61*w - 50]', '[8677, 8677, 21*w - 100]', '[8677, 8677, -21*w - 100]', '[8689, 8689, -7*w - 94]', '[8689, 8689, 7*w - 94]', '[8699, 8699, 54*w - 7]', '[8699, 8699, -54*w - 7]', '[8713, 8713, -29*w - 106]', '[8713, 8713, 29*w - 106]', '[8737, 8737, 17*w - 98]', '[8737, 8737, -17*w - 98]', '[8747, 8747, -54*w - 1]', '[8747, 8747, 54*w - 1]', '[8761, 8761, -5*w - 94]', '[8761, 8761, 5*w - 94]', '[8783, 8783, -56*w - 25]', '[8783, 8783, 56*w - 25]', '[8807, 8807, 64*w - 59]', '[8807, 8807, -64*w - 59]', '[8819, 8819, 55*w - 16]', '[8819, 8819, -55*w - 16]', '[8821, 8821, -14*w - 97]', '[8821, 8821, 14*w - 97]', '[8831, 8831, 65*w - 62]', '[8831, 8831, -65*w - 62]', '[8867, 8867, -58*w - 35]', '[8867, 8867, 58*w - 35]', '[8893, 8893, 38*w - 115]', '[8893, 8893, -38*w - 115]', '[8929, 8929, 15*w - 98]', '[8929, 8929, -15*w - 98]', '[8941, 8941, -25*w - 104]', '[8941, 8941, 25*w - 104]', '[8951, 8951, -60*w - 43]', '[8951, 8951, 60*w - 43]', '[8963, 8963, 57*w - 28]', '[8963, 8963, -57*w - 28]', '[8999, 8999, -59*w - 38]', '[8999, 8999, 59*w - 38]', '[9001, 9001, 20*w - 101]', '[9001, 9001, -20*w - 101]', '[9011, 9011, -55*w - 8]', '[9011, 9011, 55*w - 8]', '[9013, 9013, 2*w - 95]', '[9013, 9013, -2*w - 95]', '[9049, 9049, 27*w - 106]', '[9049, 9049, -27*w - 106]', '[9059, 9059, -55*w - 4]', '[9059, 9059, 55*w - 4]', '[9109, 9109, 10*w - 97]', '[9109, 9109, -10*w - 97]', '[9133, 9133, 17*w - 100]', '[9133, 9133, -17*w - 100]', '[9157, 9157, 22*w - 103]', '[9157, 9157, -22*w - 103]', '[9181, 9181, -30*w - 109]', '[9181, 9181, 30*w - 109]', '[9203, 9203, 63*w - 52]', '[9203, 9203, -63*w - 52]', '[9227, 9227, 61*w - 44]', '[9227, 9227, -61*w - 44]', '[9239, 9239, -56*w - 13]', '[9239, 9239, 56*w - 13]', '[9241, 9241, -11*w - 98]', '[9241, 9241, 11*w - 98]', '[9277, 9277, -33*w - 112]', '[9277, 9277, 33*w - 112]', '[9311, 9311, 65*w - 58]', '[9311, 9311, -65*w - 58]', '[9323, 9323, 62*w - 47]', '[9323, 9323, -62*w - 47]', '[9337, 9337, -36*w - 115]', '[9337, 9337, 36*w - 115]', '[9349, 9349, 37*w - 116]', '[9349, 9349, -37*w - 116]', '[9371, 9371, -67*w - 64]', '[9371, 9371, 67*w - 64]', '[9397, 9397, 2*w - 97]', '[9397, 9397, -2*w - 97]', '[9419, 9419, -59*w - 32]', '[9419, 9419, 59*w - 32]', '[9421, 9421, 26*w - 107]', '[9421, 9421, -26*w - 107]', '[9431, 9431, -60*w - 37]', '[9431, 9431, 60*w - 37]', '[9433, 9433, -16*w - 101]', '[9433, 9433, 16*w - 101]', '[9467, 9467, -58*w - 25]', '[9467, 9467, 58*w - 25]', '[9479, 9479, -64*w - 53]', '[9479, 9479, 64*w - 53]', '[9491, 9491, -57*w - 16]', '[9491, 9491, 57*w - 16]', '[9539, 9539, 65*w - 56]', '[9539, 9539, -65*w - 56]', '[9551, 9551, 57*w - 14]', '[9551, 9551, -57*w - 14]', '[9587, 9587, 66*w - 59]', '[9587, 9587, -66*w - 59]', '[9601, 9601, -w - 98]', '[9601, 9601, w - 98]', '[9613, 9613, 14*w - 101]', '[9613, 9613, -14*w - 101]', '[9623, 9623, 67*w - 62]', '[9623, 9623, -67*w - 62]', '[9649, 9649, 23*w - 106]', '[9649, 9649, -23*w - 106]', '[9661, 9661, -31*w - 112]', '[9661, 9661, 31*w - 112]', '[9697, 9697, -32*w - 113]', '[9697, 9697, 32*w - 113]', '[9719, 9719, 61*w - 38]', '[9719, 9719, -61*w - 38]', '[9721, 9721, 24*w - 107]', '[9721, 9721, -24*w - 107]', '[9733, 9733, -19*w - 104]', '[9733, 9733, 19*w - 104]', '[9743, 9743, 57*w - 2]', '[9743, 9743, -57*w - 2]', '[9767, 9767, -59*w - 26]', '[9767, 9767, 59*w - 26]', '[9769, 9769, 12*w - 101]', '[9769, 9769, -12*w - 101]', '[9781, 9781, 35*w - 116]', '[9781, 9781, -35*w - 116]', '[9791, 9791, 63*w - 46]', '[9791, 9791, -63*w - 46]', '[9803, 9803, 58*w - 17]', '[9803, 9803, -58*w - 17]', '[9817, 9817, 37*w - 118]', '[9817, 9817, -37*w - 118]', '[9829, 9829, -38*w - 119]', '[9829, 9829, 38*w - 119]', '[9839, 9839, 60*w - 31]', '[9839, 9839, -60*w - 31]', '[9851, 9851, 62*w - 41]', '[9851, 9851, -62*w - 41]', '[9887, 9887, -64*w - 49]', '[9887, 9887, 64*w - 49]', '[9901, 9901, 10*w - 101]', '[9901, 9901, -10*w - 101]', '[9923, 9923, -58*w - 13]', '[9923, 9923, 58*w - 13]', '[9949, 9949, -17*w - 104]', '[9949, 9949, 17*w - 104]', '[9973, 9973, 3*w - 100]', '[9973, 9973, -3*w - 100]']}
• 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
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-3, 0, 1], 'conductor': 12, 'degree': 2, 'dirichlet_group': [1, 11], 'disc_abs': 12, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [[2, 1]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 3.4641016151377544, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.12.1', 'local_algs': ['2.1.2.2a1.2', '3.1.2.1a1.2'], 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [2, 3], 'rd': 3.46410161514, 'regulator': {'__RealLiteral__': 0, 'data': '1.31695789692', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a']}