Hilbert modular form data - 2.2.76.1-76.1-b

Formats: - HTML - YAML - JSON - 2025-10-03T05:34:01.214991

• 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': 76, 'field_bad_primes': [2, 19], 'field_label': '2.2.76.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.76.1-76.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2, 19], 'level_ideal': '[76, 38, 2*w]', 'level_label': '76.1', 'level_norm': 76, 'parallel_weight': 2, 'short_label': '76.1-b', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, -3*w - 13]', -1], ['[19, 19, w]', -1]], 'hecke_eigenvalues': [0, -2, -2, -1, -1, -3, -3, 1, -4, -4, -5, -6, -6, -13, -13, 12, 12, -2, -2, 9, 9, -8, -8, -10, -10, 6, 6, -2, -2, 3, -6, -6, -11, -11, -15, -15, -2, -2, -2, -2, 6, 6, -10, -18, -18, 2, 2, -18, -18, -2, -2, -4, -4, 17, 17, 3, 3, 1, 1, -12, -12, -10, -10, 4, 4, -11, -11, -6, -6, 30, 30, -4, -4, -21, -21, 5, 5, -24, -24, -2, -2, -13, -13, -19, -19, 26, 26, -26, -26, 18, 11, 11, -28, -28, 1, 1, -42, -42, -13, -13, 22, 22, 12, 12, -32, -32, -47, -47, 9, 9, -27, -27, 34, 34, 20, 20, -10, -10, -6, -6, -6, -6, 40, 40, 16, 16, -5, -5, 9, 9, 31, 31, -4, -4, 39, 39, 0, 0, 45, 45, 28, 28, 10, 10, -54, 42, 42, -6, -6, -51, -51, -22, -22, 40, 40, 18, 18, 14, 14, -31, -31, -20, -20, 12, 12, 38, 38, 37, 37, -27, -27, -18, -18, 26, 26, 12, 12, -21, -21, 21, 21, 56, 56, 35, 35, 8, 8, 45, 45, -22, -22, 8, 8, 5, 5, -30, -30, 62, 62, 62, 62, -7, -7, -48, -48, -15, -15, -50, -50, 2, 2, 2, 2, 12, 12, -42, -42, -52, -52, 26, -45, -45, 22, 22, 22, 22, 3, 3, 72, 72, 22, 22, -9, -9, -20, -20, -60, -60, -63, -63, 23, 23, -60, -60, -22, -22, 16, 16, 16, 16, 34, 34, -37, -37, -37, -37, -15, -15, -38, -38, 58, 58, 26, 26, -6, -6, 15, 15, 18, 63, 63, -64, -64, -57, -57, -38, -38, -9, -9, 14, 14, 57, 57, -30, -30, -85, -9, -9, 6, 6, -14, -14, -46, -46, -56, -56, 83, 83, -64, -64, -47, -47, 88, 88, 36, 36, -70, -70, -78, -78, 54, 54, 80, 80, 23, 23, 61, 61, 14, 14, -39, -39, 16, 16, 6, 6, -28, -28, 50, 50, 2, 2, -93, 77, 77, -77, -77, -37, -37, -75, -75, 16, 16, -40, -40, 18, 18, -6, -6, 40, 40, 45, 45, 26, 26, 71, 71, 54, 54, -71, -71, 54, 54, 37, 37, 74, 74, -42, -42, -80, -80, 18, 18, -30, -30, -54, -54, -43, -43, -20, -20, -61, -61, -45, -45, -13, -13, 75, 75, 90, 90, 64, 64, 10, 10, 62, 62, -6, -6, -76, -76, 50, 50, -78, -78, -41, -41, 72, 72, -95, -95, 14, 14, -90, -9, -9, 50, 50, -14, -14, -42, -42, 0, 0, 52, 52, 18, 18, -22, -22, 2, 2, -74, -74, 43, 43, -50, -50, -29, -29, -41, -41, -55, -55, 16, 16, -63, -63, 2, 2, 91, 91, 42, 42, -14, -14, -30, -30, -65, -65, -9, -9, -72, -72, 57, 57, 2, 2, 92, 92, 84, 84, 101, 101, 68, 68, 26, 26, -10, -10, 14, 14, -50, -50, 22, 22, -16, -16, -23, -23, 11, 11, -72, -72, 106, 106, 12, 12, -62, -62, -55, -55, -38, -38, -22, -22, 0, 0, 18, 18, -18, -18, 2, 2, 6, 6, 10, 10, -51, -51, 14, 14, 74, 74, -60, -60, -100, -100, 30, 30, 96, 96, 97, 97, 42, 42, 66, 66, -70, -70, -89, -89, 69, 69, -36, -36, 92, 92, -76, -76, 64, 64, -85, -85, 64, 64, -14, -14, -66, -66, -4, -4, 15, 15, 20, 20, -30, -30, -43, -43, -101, -101, -81, -81, -120, -120, -129, -129, 54, 54, -114, -114, -54, -54, -34, -34, -127, -127, -94, -94, 66, 66, -98, -98, -124, -124, 25, 25, -26, -26, 85, 85, -20, -20, -6, -6, -39, -39, 54, 54, 37, 37, 79, 79, -20, -20, 101, 101, 11, 11, -56, -56, 95, 95, -77, -77, 26, 26, 80, 80, 130, 130, -104, -104, -45, -45, 79, 79, 12, 12, -86, -86, -25, -25, 22, 22, 10, 10, -131, -131, -2, -2, 82, 82, 70, 70, -66, -66, -84, -84, -125, -125, -132, -132, -84, -84, 14, 14, -71, -71, -17, -17, 74, 74, -33, -33, 40, 40, -52, -52, 54, 54, -56, -56, 100, 100, 30, 30, 9, 9, 24, 24, 124, 124, 32, 32, -72, -72, 30, 30, -12, -12, -6, -6, -38, -38, -41, -41, 66, 66, 90, 90, 111, 111, -110, -110, -13, -13, -84, -84, 113, 113, -118, -118, -142, -142, -118, -118, -100, -100, 41, 41, 0, 0, 99, 99, -8, -8, 46, 46, 61, 61, 102, 102, -134, -134, -34, -34, -69, -69, 108, 108, -57, -57, -86, -86, 96, 96, -27, -27, 52, 52, 83, 83, -87, -87, 68, 68, 106, 106, 74, 74, 123, 123, -74, -74, 100, 100, 148, 148, -46, -46, 92, 92, -12, -12, -31, -31, -11, -11, -60, -60, -54, -54, 110, 110, 8, 8, 39, 39, -50, -50, -63, -63, -32, -32, 102, 102, -44, -44, 50, 50, -104, -104, 114, 114, -74, -74, 34, 34, -129, -129, -22, -22, 84, 84, 0, 0, 54, 54, 64, 64, 59, 59, -10, -10, 109, 109, 72, 72, -91, -91, 36, 36, -53, -53, -152, -152, -58, -58, 10, 10, -71, -71, 92, 92, -61, -61, -116, -116, -56, -56, -144, -144, 127, 127, 99, 99, 69, 69, -124, -124, -90, -90, 142, 142, 28, 28, 128, 128, -58, -58, 59, 59, 2, 2, -22, -60, -60, 48, 48, -110, -110, -47, -47, -148, -148, -70, -70, -88, -88, 15, 15, -144, -144, 34, 34, 166, 166, 31, 31, -62, -62, -40, -40, -149, -149, 96, 96, 109, 109, 24, 24, -46, -46, -138, -138, 158, 158, -154, -154, -51, -51, -102, -102, -129, -129, -3, -3, 123, 123, 1, 1, -117, -117, 60, 60, -46, -46, -144, -144, -96, -96, 28, 28, -90, -90, -15, -15, 31, 31, -42, -42, -24, -24, 122, 122, 62, 62, 30, 30, -30, -30, -2, -2, 84, 84, -4, -4, -32, -32, -39, -39, -55, -55, -98, -98, 10, 10, 27, 27, -46, -46, -73, -73, 20, 20, 47, 47, -72, -72, -104, -104, -34, 46, 46, -26, -26, 38, 38, 110, 110, 7, 7, 100, 100, -9, -9, 76, 76, 39, 39, -51, -51, -46, -46, -16, -16, 10, 10, 91, 91, 1, 1, -35, -35, 40, 40, 37, 37, 8, 8, -82, -82, 156, 156, -165, -165, -89, -89, 114, 114, 94, 94, 74, 74, 142, 142, -32, -32, 99, 99, -163, -163, -158, -158, 17, 17, 118, 118, 112, 112, 78, 78, 95, 95, -153, -153, 118, 118, 76, 76, -61, -61, 135, 135, -54, -54, -31, -31, 0, 0, -7, -7, 137, 137, 86, 86, -42, -42, -13, -13, 68, 68, 5, 5, -162, -162, 136, 136, 161, 161, 122, 122, -83, -83, -20, -20, 150, 150, 90, 90, 38, 38, -38, -38, 135, 135, -75, -75, -3, -3, 84, 84, -131, -131, 54, 54, 94, 94, 154, 154, 82, 82, 114, 114, -130, -130, 114, 114, 30, 30, 130, 130, 125, 125, 3, 3, -98, -98, 78, 78, -164, -164, -38, -38, -42, -42, 87, 87, -130, -96, -96, -122, -122, -25, -25, 14, 14, 93, 93, -12, -12, 78, 78, -168, -168, 65, 65, -38, -38, 109, 109, -55, -55, 71, 71, 14, 14, -11, -11, 54, 54, 5, 5, -30, -30, -52, -52, 8, 8, 181, 181, 110, 110, -128, -128, 4, 4, -55, -55, 106, 106, -81, -81, 101, 101], 'hecke_polynomial': 'x', 'label': '2.2.76.1-76.1-b'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 76, 'ideals': ['[1, 1, 1]', '[2, 2, -3*w - 13]', '[3, 3, w + 4]', '[3, 3, w - 4]', '[4, 2, 2]', '[5, 5, 2*w + 9]', '[5, 5, -2*w + 9]', '[6, 6, w - 5]', '[6, 6, -w - 5]', '[8, 4, -6*w - 26]', '[9, 3, 3]', '[9, 9, -5*w + 22]', '[9, 9, 5*w + 22]', '[10, 10, -w - 3]', '[10, 10, -w + 3]', '[12, 6, 2*w + 8]', '[12, 6, 2*w - 8]', '[15, 15, w + 2]', '[15, 15, 4*w - 17]', '[15, 15, 4*w + 17]', '[15, 15, w - 2]', '[16, 4, 4]', '[17, 17, w + 6]', '[17, 17, -w + 6]', '[18, 6, -9*w - 39]', '[18, 18, -w - 1]', '[18, 18, -w + 1]', '[19, 19, w]', '[20, 10, 4*w + 18]', '[20, 10, -4*w + 18]', '[24, 12, 2*w - 10]', '[24, 12, -2*w - 10]', '[25, 5, 5]', '[25, 25, -3*w + 14]', '[25, 25, 3*w + 14]', '[27, 9, 3*w + 12]', '[27, 9, 3*w - 12]', '[27, 27, 2*w - 7]', '[27, 27, 2*w + 7]', '[30, 30, -w - 7]', '[30, 30, -7*w - 31]', '[30, 30, 7*w - 31]', '[30, 30, w - 7]', '[31, 31, 20*w + 87]', '[31, 31, 7*w + 30]', '[32, 8, -12*w - 52]', '[34, 34, -5*w - 21]', '[34, 34, -5*w + 21]', '[36, 6, 6]', '[36, 18, -10*w + 44]', '[36, 18, 10*w + 44]', '[38, 38, -13*w - 57]', '[40, 20, -2*w - 6]', '[40, 20, -2*w + 6]', '[45, 15, 6*w + 27]', '[45, 15, -6*w + 27]', '[45, 45, w + 8]', '[45, 45, -2*w + 11]', '[45, 45, 2*w + 11]', '[45, 45, -w + 8]', '[48, 12, 4*w + 16]', '[48, 12, 4*w - 16]', '[49, 7, -7]', '[50, 10, -15*w - 65]', '[50, 50, -3*w + 11]', '[50, 50, -3*w - 11]', '[51, 51, 10*w - 43]', '[51, 51, 2*w - 5]', '[51, 51, 2*w + 5]', '[51, 51, 10*w + 43]', '[54, 18, 3*w - 15]', '[54, 18, -3*w - 15]', '[54, 54, 5*w - 23]', '[54, 54, -5*w - 23]', '[57, 57, 4*w + 19]', '[57, 57, -4*w + 19]', '[59, 59, 6*w + 25]', '[59, 59, -6*w + 25]', '[60, 30, 2*w + 4]', '[60, 30, 8*w - 34]', '[60, 30, 8*w + 34]', '[60, 30, 2*w - 4]', '[61, 61, -9*w - 40]', '[61, 61, 9*w - 40]', '[62, 62, -w - 9]', '[62, 62, w - 9]', '[64, 8, 8]', '[67, 67, 2*w - 3]', '[67, 67, -2*w - 3]', '[68, 34, 2*w + 12]', '[68, 34, -2*w + 12]', '[71, 71, 3*w + 10]', '[71, 71, 3*w - 10]', '[72, 12, -18*w - 78]', '[72, 36, -2*w - 2]', '[72, 36, -2*w + 2]', '[73, 73, 27*w + 118]', '[73, 73, -12*w - 53]', '[75, 15, 5*w + 20]', '[75, 15, 5*w - 20]', '[75, 75, 13*w - 56]', '[75, 75, 2*w - 1]', '[75, 75, 2*w + 1]', '[75, 75, 13*w + 56]', '[76, 38, 2*w]', '[79, 79, 4*w - 15]', '[79, 79, -4*w - 15]', '[80, 20, 8*w + 36]', '[80, 20, -8*w + 36]', '[81, 9, 9]', '[81, 27, -15*w + 66]', '[81, 27, 15*w + 66]', '[81, 81, w + 10]', '[81, 81, -w + 10]', '[85, 85, -3*w + 16]', '[85, 85, 18*w + 79]', '[85, 85, -18*w + 79]', '[85, 85, 3*w + 16]', '[90, 30, -3*w - 9]', '[90, 30, -3*w + 9]', '[90, 90, -7*w - 29]', '[90, 90, -11*w - 47]', '[90, 90, -11*w + 47]', '[90, 90, -7*w + 29]', '[93, 93, -7*w + 32]', '[93, 93, -2*w + 13]', '[93, 93, 2*w + 13]', '[93, 93, 7*w + 32]', '[95, 95, 9*w - 38]', '[95, 95, 9*w + 38]', '[96, 24, 4*w - 20]', '[96, 24, -4*w - 20]', '[98, 14, 21*w + 91]', '[100, 10, 10]', '[100, 50, -6*w + 28]', '[100, 50, 6*w + 28]', '[101, 101, 5*w + 24]', '[101, 101, 5*w - 24]', '[102, 102, -w - 11]', '[102, 102, -11*w - 49]', '[102, 102, 11*w - 49]', '[102, 102, w - 11]', '[103, 103, 29*w + 126]', '[103, 103, 16*w + 69]', '[107, 107, 3*w - 8]', '[107, 107, -3*w - 8]', '[108, 18, 6*w + 24]', '[108, 18, 6*w - 24]', '[108, 54, 4*w - 14]', '[108, 54, 4*w + 14]', '[114, 114, -5*w + 19]', '[114, 114, -5*w - 19]', '[118, 118, 3*w + 17]', '[118, 118, 3*w - 17]', '[120, 60, -2*w - 14]', '[120, 60, -14*w - 62]', '[120, 60, 14*w - 62]', '[120, 60, 2*w - 14]', '[121, 11, -11]', '[122, 122, 3*w + 7]', '[122, 122, 3*w - 7]', '[124, 62, 40*w + 174]', '[124, 62, 14*w + 60]', '[125, 25, 10*w + 45]', '[125, 25, -10*w + 45]', '[125, 125, w + 12]', '[125, 125, -w + 12]', '[127, 127, -8*w - 33]', '[127, 127, -8*w + 33]', '[128, 16, -24*w - 104]', '[134, 134, 35*w + 153]', '[134, 134, -17*w - 75]', '[135, 45, 3*w + 6]', '[135, 45, 12*w - 51]', '[135, 45, 12*w + 51]', '[135, 45, 3*w - 6]', '[135, 135, 19*w - 82]', '[135, 135, 4*w + 13]', '[135, 135, 4*w - 13]', '[135, 135, 19*w + 82]', '[136, 68, -10*w - 42]', '[136, 68, -10*w + 42]', '[137, 137, -4*w + 21]', '[137, 137, 4*w + 21]', '[142, 142, 9*w - 41]', '[142, 142, -9*w - 41]', '[144, 12, 12]', '[144, 36, -20*w + 88]', '[144, 36, 20*w + 88]', '[146, 146, 3*w - 5]', '[146, 146, -3*w - 5]', '[147, 21, -7*w - 28]', '[147, 21, -7*w + 28]', '[149, 149, 2*w - 15]', '[149, 149, -2*w - 15]', '[150, 30, 5*w - 25]', '[150, 30, -5*w - 25]', '[150, 150, -w - 13]', '[150, 150, -23*w - 101]', '[150, 150, 23*w - 101]', '[150, 150, w - 13]', '[151, 151, -5*w - 18]', '[151, 151, 5*w - 18]', '[152, 76, -26*w - 114]', '[153, 51, 3*w + 18]', '[153, 51, -3*w + 18]', '[153, 153, 13*w + 58]', '[153, 153, 8*w + 37]', '[153, 153, -8*w + 37]', '[153, 153, -13*w + 58]', '[155, 155, 6*w - 23]', '[155, 155, 3*w + 4]', '[155, 155, 3*w - 4]', '[155, 155, 6*w + 23]', '[157, 157, 6*w + 29]', '[157, 157, 6*w - 29]', '[158, 158, -7*w + 33]', '[158, 158, -7*w - 33]', '[160, 40, -4*w - 12]', '[160, 40, -4*w + 12]', '[162, 18, -27*w - 117]', '[162, 54, -3*w - 3]', '[162, 54, -3*w + 3]', '[162, 162, -17*w - 73]', '[162, 162, -17*w + 73]', '[167, 167, 3*w - 2]', '[167, 167, -3*w - 2]', '[169, 13, -13]', '[170, 170, -9*w - 37]', '[170, 170, -3*w - 1]', '[170, 170, -3*w + 1]', '[170, 170, -9*w + 37]', '[171, 57, 3*w]', '[171, 171, 22*w - 95]', '[171, 171, 22*w + 95]', '[177, 177, w + 14]', '[177, 177, -16*w + 71]', '[177, 177, -16*w - 71]', '[177, 177, w - 14]', '[179, 179, -15*w - 64]', '[179, 179, -15*w + 64]', '[180, 30, 12*w + 54]', '[180, 30, -12*w + 54]', '[180, 90, 2*w + 16]', '[180, 90, -4*w + 22]', '[180, 90, 4*w + 22]', '[180, 90, -2*w + 16]', '[183, 183, -4*w + 11]', '[183, 183, -11*w + 46]', '[183, 183, -11*w - 46]', '[183, 183, -4*w - 11]', '[186, 186, -13*w + 55]', '[186, 186, -5*w + 17]', '[186, 186, -5*w - 17]', '[186, 186, -13*w - 55]', '[190, 190, 3*w - 19]', '[190, 190, -3*w - 19]', '[192, 24, 8*w + 32]', '[192, 24, 8*w - 32]', '[196, 14, -14]', '[197, 197, -19*w - 84]', '[197, 197, 46*w + 201]', '[200, 20, -30*w - 130]', '[200, 100, -6*w + 22]', '[200, 100, -6*w - 22]', '[201, 201, -11*w + 50]', '[201, 201, 5*w - 26]', '[201, 201, 5*w + 26]', '[201, 201, -11*w - 50]', '[202, 202, -7*w + 27]', '[202, 202, 7*w + 27]', '[204, 102, 20*w - 86]', '[204, 102, 4*w - 10]', '[204, 102, 4*w + 10]', '[204, 102, 20*w + 86]', '[206, 206, -w - 15]', '[206, 206, w - 15]', '[211, 211, 38*w + 165]', '[211, 211, 25*w + 108]', '[213, 213, 43*w + 188]', '[213, 213, -2*w + 17]', '[213, 213, 2*w + 17]', '[213, 213, -43*w + 188]', '[214, 214, -15*w - 67]', '[214, 214, 63*w + 275]', '[216, 36, 6*w - 30]', '[216, 36, -6*w - 30]', '[216, 108, 10*w - 46]', '[216, 108, -10*w - 46]', '[219, 219, 10*w + 41]', '[219, 219, -5*w - 16]', '[219, 219, 5*w - 16]', '[219, 219, -10*w + 41]', '[223, 223, -4*w - 9]', '[223, 223, 4*w - 9]', '[225, 15, 15]', '[225, 45, -25*w + 110]', '[225, 45, 25*w + 110]', '[225, 75, -9*w + 42]', '[225, 75, 9*w + 42]', '[225, 225, 7*w + 34]', '[225, 225, 4*w + 23]', '[225, 225, -4*w + 23]', '[225, 225, -7*w + 34]', '[227, 227, 57*w + 248]', '[227, 227, 18*w + 77]', '[228, 114, 8*w + 38]', '[228, 114, -8*w + 38]', '[229, 229, -3*w - 20]', '[229, 229, 3*w - 20]', '[233, 233, -28*w - 123]', '[233, 233, 37*w + 162]', '[236, 118, 12*w + 50]', '[236, 118, -12*w + 50]', '[237, 237, w + 16]', '[237, 237, 34*w + 149]', '[237, 237, -31*w - 136]', '[237, 237, w - 16]', '[240, 60, 4*w + 8]', '[240, 60, 16*w - 68]', '[240, 60, 16*w + 68]', '[240, 60, 4*w - 8]', '[242, 22, 33*w + 143]', '[243, 27, 9*w + 36]', '[243, 27, 9*w - 36]', '[243, 81, 6*w - 21]', '[243, 81, 6*w + 21]', '[243, 243, 14*w + 59]', '[243, 243, 14*w - 59]', '[244, 122, -18*w - 80]', '[244, 122, 18*w - 80]', '[245, 35, -14*w - 63]', '[245, 35, 14*w - 63]', '[248, 124, -2*w - 18]', '[248, 124, 2*w - 18]', '[250, 50, -5*w - 15]', '[250, 50, -5*w + 15]', '[250, 250, -23*w - 99]', '[250, 250, -23*w + 99]', '[254, 254, 5*w + 27]', '[254, 254, -5*w + 27]', '[255, 255, 28*w - 121]', '[255, 255, 8*w - 31]', '[255, 255, 4*w - 7]', '[255, 255, 7*w + 26]', '[255, 255, 7*w - 26]', '[255, 255, 4*w + 7]', '[255, 255, 8*w + 31]', '[255, 255, 28*w + 121]', '[256, 16, 16]', '[268, 134, 4*w - 6]', '[268, 134, -4*w - 6]', '[270, 90, -3*w - 21]', '[270, 90, -21*w - 93]', '[270, 90, 21*w - 93]', '[270, 90, 3*w - 21]', '[270, 270, -w - 17]', '[270, 270, 13*w - 59]', '[270, 270, -13*w - 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388]', '[6737, 6737, 79*w + 354]', '[6737, 6737, 79*w - 354]', '[6761, 6761, -59*w - 270]', '[6761, 6761, -59*w + 270]', '[6763, 6763, -29*w - 96]', '[6763, 6763, 29*w - 96]', '[6779, 6779, -21*w - 40]', '[6779, 6779, 21*w - 40]', '[6781, 6781, -150*w - 659]', '[6781, 6781, 201*w + 880]', '[6791, 6791, -45*w - 178]', '[6791, 6791, -45*w + 178]', '[6823, 6823, 19*w - 6]', '[6823, 6823, -19*w - 6]', '[6841, 6841, -156*w - 685]', '[6841, 6841, 195*w + 854]', '[6857, 6857, -64*w + 291]', '[6857, 6857, -64*w - 291]', '[6871, 6871, -20*w - 27]', '[6871, 6871, 20*w - 27]', '[6889, 83, -83]', '[6899, 6899, -30*w - 101]', '[6899, 6899, 30*w - 101]', '[6907, 6907, -43*w + 168]', '[6907, 6907, -43*w - 168]', '[6911, 6911, -87*w - 370]', '[6911, 6911, -87*w + 370]', '[6917, 6917, -11*w - 96]', '[6917, 6917, 11*w - 96]', '[6947, 6947, -42*w + 163]', '[6947, 6947, -42*w - 163]', '[6961, 6961, 15*w - 106]', '[6961, 6961, -15*w - 106]', '[6967, 6967, -37*w - 138]', '[6967, 6967, -37*w + 138]', '[6977, 6977, 256*w + 1119]', '[6977, 6977, -121*w - 534]', '[6983, 6983, -51*w + 206]', '[6983, 6983, -51*w - 206]', '[6991, 6991, -40*w - 153]', '[6991, 6991, -40*w + 153]', '[6997, 6997, 21*w - 124]', '[6997, 6997, -21*w - 124]', '[7001, 7001, 35*w + 174]', '[7001, 7001, 35*w - 174]', '[7019, 7019, 426*w + 1855]', '[7019, 7019, 75*w + 316]', '[7043, 7043, 246*w + 1069]', '[7043, 7043, 129*w + 556]', '[7069, 7069, -18*w - 115]', '[7069, 7069, 18*w - 115]', '[7127, 7127, -27*w - 82]', '[7127, 7127, 27*w - 82]', '[7129, 7129, -72*w - 325]', '[7129, 7129, 72*w - 325]', '[7159, 7159, -20*w - 21]', '[7159, 7159, 20*w - 21]', '[7193, 7193, 13*w - 102]', '[7193, 7193, -13*w - 102]', '[7211, 7211, -90*w + 383]', '[7211, 7211, -90*w - 383]', '[7219, 7219, 26*w - 75]', '[7219, 7219, -26*w - 75]', '[7229, 7229, 247*w + 1080]', '[7229, 7229, -130*w - 573]', '[7237, 7237, -6*w - 89]', '[7237, 7237, 6*w - 89]', '[7247, 7247, 108*w + 463]', '[7247, 7247, 303*w + 1318]', '[7297, 7297, -9*w - 94]', '[7297, 7297, 9*w - 94]', '[7321, 7321, 45*w - 214]', '[7321, 7321, 45*w + 214]', '[7369, 7369, 75*w - 338]', '[7369, 7369, -75*w - 338]', '[7417, 7417, 36*w + 179]', '[7417, 7417, 36*w - 179]', '[7433, 7433, -8*w - 93]', '[7433, 7433, 8*w - 93]', '[7451, 7451, 27*w - 80]', '[7451, 7451, -27*w - 80]', '[7457, 7457, -16*w - 111]', '[7457, 7457, 16*w - 111]', '[7499, 7499, -45*w - 176]', '[7499, 7499, -45*w + 176]', '[7507, 7507, 118*w + 507]', '[7507, 7507, 287*w + 1248]', '[7523, 7523, 306*w + 1331]', '[7523, 7523, 111*w + 476]', '[7529, 7529, 20*w - 123]', '[7529, 7529, -20*w - 123]', '[7541, 7541, -19*w - 120]', '[7541, 7541, 19*w - 120]', '[7549, 7549, 30*w - 157]', '[7549, 7549, 30*w + 157]', '[7573, 7573, 3*w - 88]', '[7573, 7573, -3*w - 88]', '[7583, 7583, -39*w + 146]', '[7583, 7583, -39*w - 146]', '[7591, 7591, -20*w - 3]', '[7591, 7591, 20*w - 3]', '[7603, 7603, -41*w - 156]', '[7603, 7603, -41*w + 156]', '[7649, 7649, 73*w - 330]', '[7649, 7649, -73*w - 330]', '[7673, 7673, -52*w + 243]', '[7673, 7673, -52*w - 243]', '[7681, 7681, 324*w + 1415]', '[7681, 7681, -105*w - 466]', '[7691, 7691, -30*w - 97]', '[7691, 7691, 30*w - 97]', '[7703, 7703, 21*w - 26]', '[7703, 7703, -21*w - 26]', '[7727, 7727, 168*w + 727]', '[7727, 7727, 207*w + 898]', '[7753, 7753, -48*w + 227]', '[7753, 7753, -48*w - 227]', '[7757, 7757, 46*w + 219]', '[7757, 7757, 46*w - 219]', '[7823, 7823, -96*w + 409]', '[7823, 7823, -96*w - 409]', '[7829, 7829, -125*w - 552]', '[7829, 7829, 278*w + 1215]', '[7853, 7853, -97*w - 432]', '[7853, 7853, 358*w + 1563]', '[7873, 7873, -12*w - 103]', '[7873, 7873, 12*w - 103]', '[7877, 7877, 211*w + 924]', '[7877, 7877, -166*w - 729]', '[7879, 7879, -29*w - 90]', '[7879, 7879, 29*w - 90]', '[7901, 7901, -10*w - 99]', '[7901, 7901, 10*w - 99]', '[7907, 7907, -57*w + 232]', '[7907, 7907, -57*w - 232]', '[7919, 7919, -24*w - 55]', '[7919, 7919, 24*w - 55]', '[7921, 89, -89]', '[7949, 7949, -175*w - 768]', '[7949, 7949, 202*w + 885]', '[7963, 7963, 274*w + 1191]', '[7963, 7963, 131*w + 564]', '[8011, 8011, -62*w - 255]', '[8011, 8011, -62*w + 255]', '[8039, 8039, -84*w - 355]', '[8039, 8039, -84*w + 355]', '[8053, 8053, 27*w + 148]', '[8053, 8053, -27*w + 148]', '[8059, 8059, 331*w + 1440]', '[8059, 8059, 110*w + 471]', '[8081, 8081, -w - 90]', '[8081, 8081, w - 90]', '[8087, 8087, 117*w + 502]', '[8087, 8087, 312*w + 1357]', '[8101, 8101, 315*w + 1376]', '[8101, 8101, -114*w - 505]', '[8117, 8117, 269*w + 1176]', '[8117, 8117, -134*w - 591]', '[8123, 8123, -21*w - 16]', '[8123, 8123, 21*w - 16]', '[8147, 8147, -33*w + 112]', '[8147, 8147, -33*w - 112]', '[8191, 8191, -55*w + 222]', '[8191, 8191, -55*w - 222]', '[8209, 8209, 33*w + 170]', '[8209, 8209, 33*w - 170]', '[8233, 8233, -117*w - 518]', '[8233, 8233, 312*w + 1363]', '[8269, 8269, -15*w - 112]', '[8269, 8269, 15*w - 112]', '[8287, 8287, 23*w - 42]', '[8287, 8287, -23*w - 42]', '[8293, 8293, -3*w - 92]', '[8293, 8293, 3*w - 92]', '[8311, 8311, 200*w + 867]', '[8311, 8311, 187*w + 810]', '[8329, 8329, -60*w + 277]', '[8329, 8329, -60*w - 277]', '[8363, 8363, 21*w - 4]', '[8363, 8363, -21*w - 4]', '[8369, 8369, 260*w + 1137]', '[8369, 8369, -143*w - 630]', '[8377, 8377, -24*w - 139]', '[8377, 8377, 24*w - 139]', '[8387, 8387, -87*w + 368]', '[8387, 8387, -87*w - 368]', '[8419, 8419, -70*w + 291]', '[8419, 8419, -70*w - 291]', '[8431, 8431, 32*w - 105]', '[8431, 8431, -32*w - 105]', '[8461, 8461, 9*w - 100]', '[8461, 8461, -9*w - 100]', '[8467, 8467, -22*w - 27]', '[8467, 8467, 22*w - 27]', '[8513, 8513, -28*w + 153]', '[8513, 8513, 28*w + 153]', '[8521, 8521, -21*w - 130]', '[8521, 8521, 21*w - 130]', '[8527, 8527, -52*w + 207]', '[8527, 8527, -52*w - 207]', '[8537, 8537, -56*w - 261]', '[8537, 8537, -56*w + 261]', '[8539, 8539, -59*w - 240]', '[8539, 8539, -59*w + 240]', '[8543, 8543, -24*w - 49]', '[8543, 8543, 24*w - 49]', '[8563, 8563, -74*w + 309]', '[8563, 8563, -74*w - 309]', '[8573, 8573, 2*w - 93]', '[8573, 8573, -2*w - 93]', '[8597, 8597, -14*w - 111]', '[8597, 8597, 14*w - 111]', '[8647, 8647, 157*w + 678]', '[8647, 8647, 248*w + 1077]', '[8663, 8663, -69*w - 286]', '[8663, 8663, -69*w + 286]', '[8669, 8669, -50*w + 237]', '[8669, 8669, -50*w - 237]', '[8681, 8681, 101*w - 450]', '[8681, 8681, -101*w - 450]', '[8689, 8689, -63*w + 290]', '[8689, 8689, -63*w - 290]', '[8713, 8713, -12*w - 107]', '[8713, 8713, 12*w - 107]', '[8731, 8731, 82*w + 345]', '[8731, 8731, 485*w + 2112]', '[8737, 8737, 39*w + 194]', '[8737, 8737, 39*w - 194]', '[8741, 8741, 5*w - 96]', '[8741, 8741, -5*w - 96]', '[8807, 8807, -48*w - 187]', '[8807, 8807, -48*w + 187]', '[8819, 8819, -30*w - 91]', '[8819, 8819, 30*w - 91]', '[8821, 8821, -30*w + 161]', '[8821, 8821, 30*w + 161]', '[8831, 8831, -57*w + 230]', '[8831, 8831, -57*w - 230]', '[8861, 8861, 25*w - 144]', '[8861, 8861, -25*w - 144]', '[8867, 8867, -42*w - 157]', '[8867, 8867, -42*w + 157]', '[8887, 8887, -43*w + 162]', '[8887, 8887, -43*w - 162]', '[8893, 8893, 33*w + 172]', '[8893, 8893, 33*w - 172]', '[8923, 8923, 29*w - 84]', '[8923, 8923, -29*w - 84]', '[8941, 8941, 294*w + 1285]', '[8941, 8941, -135*w - 596]', '[8951, 8951, 27*w - 70]', '[8951, 8951, -27*w - 70]', '[8963, 8963, 321*w + 1396]', '[8963, 8963, 126*w + 541]', '[8969, 8969, 43*w - 210]', '[8969, 8969, 43*w + 210]', '[8971, 8971, -22*w - 15]', '[8971, 8971, 22*w - 15]', '[8999, 8999, -36*w - 125]', '[8999, 8999, -36*w + 125]', '[9013, 9013, -78*w - 353]', '[9013, 9013, 78*w - 353]', '[9029, 9029, -22*w - 135]', '[9029, 9029, 22*w - 135]', '[9041, 9041, 20*w - 129]', '[9041, 9041, -20*w - 129]', '[9043, 9043, 31*w - 96]', '[9043, 9043, -31*w - 96]', '[9049, 9049, 45*w + 218]', '[9049, 9049, 45*w - 218]', '[9059, 9059, 510*w + 2221]', '[9059, 9059, 81*w + 340]', '[9103, 9103, 209*w + 906]', '[9103, 9103, 196*w + 849]', '[9137, 9137, 49*w + 234]', '[9137, 9137, 49*w - 234]', '[9151, 9151, -23*w - 30]', '[9151, 9151, 23*w - 30]', '[9181, 9181, -15*w - 116]', '[9181, 9181, 15*w - 116]', '[9187, 9187, 22*w - 3]', '[9187, 9187, -22*w - 3]', '[9199, 9199, 305*w + 1326]', '[9199, 9199, 136*w + 585]', '[9221, 9221, 371*w + 1620]', '[9221, 9221, -110*w - 489]', '[9227, 9227, -27*w - 68]', '[9227, 9227, 27*w - 68]', '[9241, 9241, -144*w - 635]', '[9241, 9241, 285*w + 1246]', '[9257, 9257, -124*w - 549]', '[9257, 9257, 331*w + 1446]', '[9277, 9277, 9*w - 104]', '[9277, 9277, -9*w - 104]', '[9281, 9281, -76*w + 345]', '[9281, 9281, -76*w - 345]', '[9323, 9323, -66*w - 271]', '[9323, 9323, -66*w + 271]', '[9343, 9343, -71*w + 294]', '[9343, 9343, -71*w - 294]', '[9349, 9349, -102*w - 455]', '[9349, 9349, 102*w - 455]', '[9397, 9397, -69*w + 316]', '[9397, 9397, -69*w - 316]', '[9409, 97, -97]', '[9419, 9419, -51*w + 200]', '[9419, 9419, -51*w - 200]', '[9421, 9421, -150*w - 661]', '[9421, 9421, 279*w + 1220]', '[9433, 9433, -3*w - 98]', '[9433, 9433, 3*w - 98]', '[9439, 9439, -41*w + 150]', '[9439, 9439, -41*w - 150]', '[9473, 9473, 7*w - 102]', '[9473, 9473, -7*w - 102]', '[9491, 9491, -42*w + 155]', '[9491, 9491, -42*w - 155]', '[9497, 9497, -4*w - 99]', '[9497, 9497, 4*w - 99]', '[9551, 9551, -48*w + 185]', '[9551, 9551, -48*w - 185]', '[9601, 9601, 36*w + 185]', '[9601, 9601, 36*w - 185]', '[9643, 9643, 34*w - 111]', '[9643, 9643, -34*w - 111]', '[9649, 9649, 15*w - 118]', '[9649, 9649, -15*w - 118]', '[9661, 9661, -159*w - 700]', '[9661, 9661, 270*w + 1181]', '[9677, 9677, 41*w + 204]', '[9677, 9677, 41*w - 204]', '[9679, 9679, -79*w - 330]', '[9679, 9679, -79*w + 330]', '[9697, 9697, 9*w - 106]', '[9697, 9697, -9*w - 106]', '[9719, 9719, -24*w - 35]', '[9719, 9719, 24*w - 35]', '[9733, 9733, 267*w + 1168]', '[9733, 9733, -162*w - 713]', '[9743, 9743, 159*w + 686]', '[9743, 9743, 276*w + 1199]', '[9787, 9787, 83*w + 348]', '[9787, 9787, 538*w + 2343]', '[9803, 9803, -69*w - 284]', '[9803, 9803, -69*w + 284]', '[9829, 9829, 3*w - 100]', '[9829, 9829, -3*w - 100]', '[9871, 9871, -95*w - 402]', '[9871, 9871, -95*w + 402]', '[9883, 9883, 91*w + 384]', '[9883, 9883, 494*w + 2151]', '[9907, 9907, -23*w - 12]', '[9907, 9907, 23*w - 12]', '[9929, 9929, -5*w - 102]', '[9929, 9929, 5*w - 102]', '[9931, 9931, 218*w + 945]', '[9931, 9931, 205*w + 888]', '[9941, 9941, -70*w - 321]', '[9941, 9941, -70*w + 321]', '[9973, 9973, 18*w - 127]', '[9973, 9973, -18*w - 127]']}
• 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': [-19, 0, 1], 'conductor': 76, 'degree': 2, 'dirichlet_group': [1, 75], 'disc_abs': 76, 'disc_rad': 38, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[1, 2]]], [5, [[1, 2]]], [7, [[2, 1]]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [0]], [23, [[2, 1]]], [29, [[2, 1]]], [31, [[1, 2]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[2, 1]]], [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': 8.717797887081348, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.76.1', 'local_algs': ['2.1.2.2a1.2', '19.1.2.1a1.2'], 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [2, 19], 'rd': 8.71779788708, 'regulator': {'__RealLiteral__': 0, 'data': '5.82893696698', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 39 a + 170 \\)'], 'used_grh': False, 'zk': ['1', 'a']}