Hilbert modular form data - 2.2.268.1-16.1-k

Formats: - HTML - YAML - JSON - 2024-05-31T15:19:44.699740

• 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': 4, 'disc': 268, 'field_bad_primes': [2, 67], 'field_label': '2.2.268.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.268.1-16.1-k', 'label_nsuffix': 10, 'label_suffix': 'k', 'level_bad_primes': [2], 'level_ideal': '[16, 4, 4]', 'level_label': '16.1', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.1-k', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, -27*w + 221]', 1]], 'hecke_eigenvalues': [0, '-e', 'e', 'e^3 - 7*e', '-e^3 + 7*e', 'e^3 - 8*e', '-e^3 + 8*e', '4*e^2 - 30', '4*e^2 - 30', '6*e^2 - 45', '-2*e^2 + 21', '-2*e^2 + 21', 'e^3 - 10*e', '-e^3 + 10*e', '3*e^2 - 26', '3*e^2 - 26', '-3*e', '3*e', 0, '6*e^2 - 38', '6*e^2 - 38', '-3*e', '3*e', '-4*e^2 + 33', '-4*e^2 + 33', '-3*e^3 + 24*e', '3*e^3 - 24*e', '-17*e^2 + 123', '-17*e^2 + 123', '3*e^2 - 16', '3*e^2 - 16', '-9*e^2 + 81', '-19*e^2 + 147', '-19*e^2 + 147', '4*e^3 - 32*e', '-4*e^3 + 32*e', '-3*e^2 + 31', '-3*e^2 + 31', 'e^3 - 2*e', '-e^3 + 2*e', '-3*e^2 + 43', '-3*e^2 + 43', '-9*e^3 + 69*e', '9*e^3 - 69*e', '3*e^2 - 28', '3*e^2 - 28', 0, 0, '-2*e^2 + 9', '-2*e^2 + 9', '-15*e^2 + 108', '-15*e^2 + 108', '5*e^3 - 38*e', '-5*e^3 + 38*e', 6, 6, '-6*e^2 + 45', '-6*e^2 + 45', '-6*e', '6*e', '-8*e^2 + 69', '-8*e^2 + 69', '8*e^3 - 62*e', '-8*e^3 + 62*e', '3*e^3 - 24*e', '-3*e^3 + 24*e', -18, -18, '-3*e^2 - 4', 0, 0, '6*e', '-6*e', '-3*e^3 + 27*e', '3*e^3 - 27*e', '-18*e^2 + 132', '-18*e^2 + 132', '21*e^2 - 160', '21*e^2 - 160', '-15*e^2 + 121', '-15*e^2 + 121', '-5*e^3 + 34*e', '5*e^3 - 34*e', '-17*e^2 + 117', '-17*e^2 + 117', '12*e^2 - 91', '12*e^2 - 91', '7*e^2 - 36', '7*e^2 - 36', '-3*e^3 + 27*e', '3*e^3 - 27*e', '-7*e^3 + 46*e', '7*e^3 - 46*e', '-e^3 + 10*e', 'e^3 - 10*e', '-e^3 + 8*e', 'e^3 - 8*e', '-22*e^2 + 168', '-22*e^2 + 168', '24*e^2 - 197', '3*e', '-3*e', '-3*e^2 + 21', '-3*e^2 + 21', '-6*e^3 + 42*e', '6*e^3 - 42*e', '4*e^2 - 54', '4*e^2 - 54', '-3*e^3 + 15*e', '3*e^3 - 15*e', '2*e^3 - 4*e', '-2*e^3 + 4*e', '6*e^2 - 56', '6*e^2 - 56', '12*e^2 - 95', '12*e^2 - 95', '-e^2 - 6', '-e^2 - 6', '-3*e^3 + 27*e', '3*e^3 - 27*e', 0, 0, '9*e^3 - 69*e', '-9*e^3 + 69*e', '18*e^2 - 152', '18*e^2 - 152', '-6*e^3 + 42*e', '6*e^3 - 42*e', '-9*e^3 + 69*e', '9*e^3 - 69*e', '8*e^2 - 24', '8*e^2 - 24', '4*e^2 - 3', '4*e^2 - 3', '3*e^3 - 36*e', '-3*e^3 + 36*e', '3*e^2 - 9', '3*e^2 - 9', '9*e^3 - 60*e', '-9*e^3 + 60*e', '-22*e^2 + 159', '-22*e^2 + 159', '-24*e^2 + 163', '-24*e^2 + 163', '21*e^2 - 157', '21*e^2 - 157', '-6*e^2 + 41', '-6*e^2 + 41', '2*e^2 - 9', '2*e^2 - 9', '9*e^3 - 78*e', '-9*e^3 + 78*e', '-5*e^3 + 26*e', '5*e^3 - 26*e', '20*e^2 - 183', '20*e^2 - 183', '-20*e^2 + 171', '-20*e^2 + 171', '3*e^3 - 6*e', '-3*e^3 + 6*e', '8*e^3 - 59*e', '-8*e^3 + 59*e', '-18*e^2 + 109', '-18*e^2 + 109'], 'hecke_polynomial': 'x^4 - 15*x^2 + 55', 'label': '2.2.268.1-16.1-k'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 268, 'ideals': ['[1, 1, 1]', '[2, 2, -27*w + 221]', '[3, 3, -w + 8]', '[3, 3, -w - 8]', '[4, 2, 2]', '[6, 6, 5*w + 41]', '[6, 6, -5*w + 41]', '[7, 7, -11*w + 90]', '[7, 7, -11*w - 90]', '[8, 4, -54*w + 442]', '[9, 3, 3]', '[9, 9, 16*w + 131]', '[9, 9, -16*w + 131]', '[11, 11, 6*w - 49]', '[11, 11, 6*w + 49]', '[12, 6, -2*w + 16]', '[12, 6, -2*w - 16]', '[14, 14, -w + 9]', '[14, 14, w + 9]', '[16, 4, 4]', '[17, 17, 4*w + 33]', '[17, 17, -4*w + 33]', '[18, 6, -81*w + 663]', '[18, 18, -w - 7]', '[18, 18, -w + 7]', '[21, 21, -2*w + 17]', '[21, 21, -43*w + 352]', '[21, 21, 43*w + 352]', '[21, 21, 2*w + 17]', '[22, 22, -3*w - 25]', '[22, 22, 3*w - 25]', '[24, 12, 10*w + 82]', '[24, 12, -10*w + 82]', '[25, 5, -5]', '[27, 9, -3*w + 24]', '[27, 9, -3*w - 24]', '[27, 27, -38*w + 311]', '[27, 27, -38*w - 311]', '[28, 14, -22*w + 180]', '[28, 14, -22*w - 180]', '[29, 29, -70*w + 573]', '[29, 29, 151*w - 1236]', '[31, 31, -w - 6]', '[31, 31, w - 6]', '[32, 8, -108*w + 884]', '[33, 33, 97*w - 794]', '[33, 33, -w - 10]', '[33, 33, w - 10]', '[33, 33, -97*w - 794]', '[34, 34, -7*w - 57]', '[34, 34, -7*w + 57]', '[36, 6, 6]', '[36, 18, 32*w + 262]', '[36, 18, -32*w + 262]', '[37, 37, -21*w - 172]', '[37, 37, -21*w + 172]', '[42, 42, -w - 5]', '[42, 42, -17*w + 139]', '[42, 42, -17*w - 139]', '[42, 42, -w + 5]', '[43, 43, 2*w - 15]', '[43, 43, 2*w + 15]', '[44, 22, 12*w - 98]', '[44, 22, 12*w + 98]', '[48, 12, -4*w + 32]', '[48, 12, -4*w - 32]', '[49, 7, 7]', '[49, 49, -9*w + 74]', '[49, 49, 9*w + 74]', '[50, 10, 135*w - 1105]', '[51, 51, -w - 4]', '[51, 51, -65*w + 532]', '[51, 51, -65*w - 532]', '[51, 51, -w + 4]', '[54, 18, 15*w + 123]', '[54, 18, -15*w + 123]', '[54, 54, w + 11]', '[54, 54, -w + 11]', '[56, 28, -2*w + 18]', '[56, 28, 2*w + 18]', '[58, 58, -w - 3]', '[58, 58, w - 3]', '[62, 62, 383*w - 3135]', '[62, 62, -59*w + 483]', '[63, 21, -33*w + 270]', '[63, 21, -33*w - 270]', '[63, 63, -w - 2]', '[63, 63, -8*w - 65]', '[63, 63, -8*w + 65]', '[63, 63, -w + 2]', '[64, 8, 8]', '[66, 66, w + 1]', '[66, 66, 49*w + 401]', '[66, 66, 49*w - 401]', '[66, 66, w - 1]', '[67, 67, -w]', '[68, 34, 8*w + 66]', '[68, 34, -8*w + 66]', '[72, 12, -162*w + 1326]', '[72, 36, -2*w - 14]', '[72, 36, -2*w + 14]', '[73, 73, -3*w - 26]', '[73, 73, -3*w + 26]', '[74, 74, 3*w - 23]', '[74, 74, -3*w - 23]', '[75, 15, 5*w - 40]', '[75, 15, 5*w + 40]', '[77, 77, -w - 12]', '[77, 77, -26*w - 213]', '[77, 77, 26*w - 213]', '[77, 77, w - 12]', '[79, 79, 92*w - 753]', '[79, 79, 313*w - 2562]', '[81, 9, 9]', '[81, 27, 48*w + 393]', '[81, 27, -48*w + 393]', '[81, 81, -7*w + 58]', '[81, 81, 7*w + 58]', '[84, 42, -4*w + 34]', '[84, 42, -86*w + 704]', '[84, 42, 86*w + 704]', '[84, 42, 4*w + 34]', '[86, 86, 37*w - 303]', '[86, 86, -37*w - 303]', '[87, 87, 28*w - 229]', '[87, 87, -13*w + 106]', '[87, 87, 13*w + 106]', '[87, 87, -28*w - 229]', '[88, 44, -6*w - 50]', '[88, 44, 6*w - 50]', '[89, 89, -5*w - 42]', '[89, 89, -5*w + 42]', '[93, 93, 14*w - 115]', '[93, 93, -2*w + 19]', '[93, 93, -2*w - 19]', '[93, 93, 14*w + 115]', '[96, 24, 20*w + 164]', '[96, 24, -20*w + 164]', '[98, 14, -189*w + 1547]', '[98, 98, -9*w - 73]', '[98, 98, -9*w + 73]', '[99, 33, 18*w - 147]', '[99, 33, 18*w + 147]', '[99, 99, 23*w + 188]', '[99, 99, 2*w - 13]', '[99, 99, 2*w + 13]', '[99, 99, 23*w - 188]', '[100, 10, -10]', '[102, 102, w + 13]', '[102, 102, 113*w + 925]', '[102, 102, -113*w + 925]', '[102, 102, -w + 13]', '[108, 18, -6*w + 48]', '[108, 18, -6*w - 48]', '[108, 54, -76*w + 622]', '[108, 54, -76*w - 622]', '[111, 111, 119*w - 974]', '[111, 111, -4*w + 31]', '[111, 111, 4*w + 31]', '[111, 111, -119*w - 974]', '[112, 28, -44*w + 360]', '[112, 28, -44*w - 360]', '[116, 58, -140*w + 1146]', '[116, 58, 302*w - 2472]', '[119, 119, -60*w - 491]', '[119, 119, -3*w - 22]', '[119, 119, -3*w + 22]', '[119, 119, -60*w + 491]', '[121, 11, 11]', '[121, 121, 75*w + 614]', '[121, 121, -75*w + 614]', '[124, 62, -2*w - 12]', '[124, 62, 2*w - 12]', '[126, 42, -3*w + 27]', '[126, 42, 3*w + 27]', '[126, 126, 13*w + 107]', '[126, 126, 167*w + 1367]', '[126, 126, -167*w + 1367]', '[126, 126, -13*w + 107]', '[128, 16, -216*w + 1768]', '[129, 129, -w - 14]', '[129, 129, -31*w - 254]', '[129, 129, 31*w - 254]', '[129, 129, w - 14]', '[132, 66, 194*w - 1588]', '[132, 66, -2*w - 20]', '[132, 66, 2*w - 20]', '[132, 66, -194*w - 1588]', '[134, 134, -221*w + 1809]', '[136, 68, -14*w - 114]', '[136, 68, -14*w + 114]', '[139, 139, 10*w + 81]', '[139, 139, 10*w - 81]', '[144, 12, 12]', '[144, 36, 64*w + 524]', '[144, 36, -64*w + 524]', '[146, 146, 39*w - 319]', '[146, 146, -39*w - 319]', '[147, 21, -7*w + 56]', '[147, 21, -7*w - 56]', '[147, 147, -146*w + 1195]', '[147, 147, -2*w + 11]', '[147, 147, -2*w - 11]', '[147, 147, -146*w - 1195]', '[148, 74, -42*w - 344]', '[148, 74, -42*w + 344]', '[149, 149, 19*w - 156]', '[149, 149, -19*w - 156]', '[150, 30, -25*w - 205]', '[150, 30, 25*w - 205]', '[153, 51, 12*w + 99]', '[153, 51, -12*w + 99]', '[153, 153, -53*w + 434]', '[153, 153, 4*w + 35]', '[153, 153, -4*w + 35]', '[153, 153, 53*w + 434]', '[154, 154, 5*w - 39]', '[154, 154, 103*w + 843]', '[154, 154, 103*w - 843]', '[154, 154, 5*w + 39]', '[157, 157, -102*w + 835]', '[157, 157, 561*w - 4592]', '[158, 158, -w - 15]', '[158, 158, w - 15]', '[162, 18, -243*w + 1989]', '[162, 54, -3*w - 21]', '[162, 54, -3*w + 21]', '[162, 162, -19*w + 155]', '[162, 162, -19*w - 155]', '[168, 84, -2*w - 10]', '[168, 84, -34*w + 278]', '[168, 84, -34*w - 278]', '[168, 84, -2*w + 10]', '[169, 13, -13]', '[172, 86, 4*w - 30]', '[172, 86, 4*w + 30]', '[173, 173, 2*w - 21]', '[173, 173, -2*w - 21]', '[174, 174, 11*w - 91]', '[174, 174, -5*w + 43]', '[174, 174, -5*w - 43]', '[174, 174, 11*w + 91]', '[175, 35, 55*w - 450]', '[175, 35, 55*w + 450]', '[176, 44, 24*w - 196]', '[176, 44, 24*w + 196]', '[178, 178, -29*w - 237]', '[178, 178, 29*w - 237]', '[179, 179, 87*w - 712]', '[179, 179, 87*w + 712]', '[181, 181, 3*w - 28]', '[181, 181, 3*w + 28]', '[186, 186, 11*w + 89]', '[186, 186, -71*w - 581]', '[186, 186, 71*w - 581]', '[186, 186, -11*w + 89]', '[187, 187, 173*w - 1416]', '[187, 187, 2*w - 9]', '[187, 187, 2*w + 9]', '[187, 187, 173*w + 1416]', '[189, 63, -6*w + 51]', '[189, 63, -129*w + 1056]', '[189, 63, 129*w + 1056]', '[189, 63, 6*w + 51]', '[189, 189, w + 16]', '[189, 189, 10*w + 83]', '[189, 189, -10*w + 83]', '[189, 189, -w + 16]', '[191, 191, 15*w - 122]', '[191, 191, 15*w + 122]', '[192, 24, -8*w + 64]', '[192, 24, -8*w - 64]', '[193, 193, 36*w + 295]', '[193, 193, -36*w + 295]', '[196, 14, 14]', '[196, 98, -18*w + 148]', '[196, 98, 18*w + 148]', '[198, 66, -9*w - 75]', '[198, 66, 9*w - 75]', '[198, 198, -91*w - 745]', '[198, 198, -7*w - 59]', '[198, 198, 7*w - 59]', '[198, 198, 91*w - 745]', '[200, 20, 270*w - 2210]', '[201, 201, -8*w + 67]', '[201, 201, 8*w + 67]', '[203, 203, 6*w - 47]', '[203, 203, -3*w + 20]', '[203, 203, 3*w + 20]', '[203, 203, -6*w - 47]', '[204, 102, -2*w - 8]', '[204, 102, -130*w + 1064]', '[204, 102, -130*w - 1064]', '[204, 102, -2*w + 8]', '[216, 36, 30*w + 246]', '[216, 36, -30*w + 246]', '[216, 108, 2*w + 22]', '[216, 108, -2*w + 22]', '[217, 217, -24*w + 197]', '[217, 217, 156*w + 1277]', '[217, 217, 156*w - 1277]', '[217, 217, -24*w - 197]', '[219, 219, -50*w + 409]', '[219, 219, 2*w - 7]', '[219, 219, -2*w - 7]', '[219, 219, 50*w + 409]', '[222, 222, -w - 17]', '[222, 222, 47*w - 385]', '[222, 222, 47*w + 385]', '[222, 222, -w + 17]', '[224, 56, -4*w + 36]', '[224, 56, 4*w + 36]', '[225, 15, 15]', '[225, 45, -80*w - 655]', '[225, 45, 80*w - 655]', '[231, 231, 200*w - 1637]', '[231, 231, 4*w + 29]', '[231, 231, 20*w + 163]', '[231, 231, 5*w + 38]', '[231, 231, 5*w - 38]', '[231, 231, 20*w - 163]', '[231, 231, 4*w - 29]', '[231, 231, 200*w + 1637]', '[232, 116, -2*w - 6]', '[232, 116, 2*w - 6]', '[237, 237, -17*w - 140]', '[237, 237, -58*w - 475]', '[237, 237, 58*w - 475]', '[237, 237, 17*w - 140]', '[238, 238, -69*w + 565]', '[238, 238, 3*w + 29]', '[238, 238, -3*w + 29]', '[238, 238, 69*w + 565]', '[239, 239, 12*w + 97]', '[239, 239, 12*w - 97]', '[241, 241, -183*w + 1498]', '[241, 241, 480*w - 3929]', '[242, 22, -297*w + 2431]', '[242, 242, -3*w - 19]', '[242, 242, -3*w + 19]', '[243, 27, -9*w + 72]', '[243, 27, -9*w - 72]', '[243, 81, -114*w + 933]', '[243, 81, -114*w - 933]', '[243, 243, -2*w + 5]', '[243, 243, -2*w - 5]', '[248, 124, 766*w - 6270]', '[248, 124, -118*w + 966]', '[251, 251, 45*w + 368]', '[251, 251, 45*w - 368]', '[252, 42, -66*w + 540]', '[252, 42, -66*w - 540]', '[252, 126, -2*w - 4]', '[252, 126, -16*w - 130]', '[252, 126, -16*w + 130]', '[252, 126, -2*w + 4]', '[256, 16, 16]', '[257, 257, -w - 18]', '[257, 257, w - 18]', '[258, 258, 7*w - 55]', '[258, 258, 599*w - 4903]', '[258, 258, 157*w - 1285]', '[258, 258, 7*w + 55]', '[259, 259, 25*w - 204]', '[259, 259, 2*w - 3]', '[259, 259, -2*w - 3]', '[259, 259, -25*w - 204]', '[261, 87, -210*w + 1719]', '[261, 87, 453*w - 3708]', '[261, 261, 5*w + 44]', '[261, 261, -2*w + 23]', '[261, 261, -2*w - 23]', '[261, 261, 5*w - 44]', '[264, 132, 2*w + 2]', '[264, 132, 98*w + 802]', '[264, 132, 98*w - 802]', '[264, 132, 2*w - 2]', '[267, 267, 82*w + 671]', '[267, 267, 2*w - 1]', '[267, 267, -2*w - 1]', '[267, 267, -82*w + 671]', '[268, 134, -2*w]', '[269, 269, 41*w + 336]', '[269, 269, -41*w + 336]', '[271, 271, 40*w - 327]', '[271, 271, -40*w - 327]', '[272, 68, 16*w + 132]', '[272, 68, -16*w + 132]', '[275, 55, -30*w + 245]', '[275, 55, -30*w - 245]', '[277, 277, 426*w - 3487]', '[277, 277, -237*w + 1940]', '[278, 278, -23*w - 189]', '[278, 278, 23*w - 189]', '[279, 93, -3*w - 18]', '[279, 93, 3*w - 18]', '[279, 279, 227*w - 1858]', '[279, 279, 35*w + 286]', '[279, 279, -35*w + 286]', '[279, 279, -227*w - 1858]', '[288, 24, -324*w + 2652]', '[288, 72, -4*w - 28]', '[288, 72, -4*w + 28]', '[289, 17, 17]', '[289, 289, -264*w + 2161]', '[289, 289, 264*w + 2161]', '[292, 146, -6*w - 52]', '[292, 146, -6*w + 52]', '[293, 293, -998*w + 8169]', '[293, 293, 107*w - 876]', '[294, 42, 35*w + 287]', '[294, 42, -35*w + 287]', '[294, 294, w + 19]', '[294, 294, -145*w + 1187]', '[294, 294, 145*w + 1187]', '[294, 294, -w + 19]', '[296, 148, 6*w - 46]', '[296, 148, -6*w - 46]', '[297, 99, 291*w - 2382]', '[297, 99, -3*w - 30]', '[297, 99, 3*w - 30]', '[297, 99, -291*w - 2382]', '[297, 297, 29*w - 238]', '[297, 297, 4*w - 37]', '[297, 297, -4*w - 37]', '[297, 297, -29*w - 238]', '[298, 298, 13*w + 105]', '[298, 298, 13*w - 105]', '[300, 30, 10*w - 80]', '[300, 30, 10*w + 80]', '[301, 301, 15*w - 124]', '[301, 301, -318*w - 2603]', '[301, 301, 318*w - 2603]', '[301, 301, -15*w - 124]', '[306, 102, -21*w - 171]', '[306, 102, -21*w + 171]', '[306, 306, -61*w + 499]', '[306, 306, -5*w + 37]', '[306, 306, -5*w - 37]', '[306, 306, -61*w - 499]', '[308, 154, -2*w - 24]', '[308, 154, -52*w - 426]', '[308, 154, 52*w - 426]', '[308, 154, 2*w - 24]', '[311, 311, 804*w - 6581]', '[311, 311, 141*w - 1154]', '[314, 314, 3*w - 17]', '[314, 314, -3*w - 17]', '[316, 158, 184*w - 1506]', '[316, 158, 626*w - 5124]', '[317, 317, -7*w + 60]', '[317, 317, -7*w - 60]', '[319, 319, 8*w - 63]', '[319, 319, -17*w + 138]', '[319, 319, 17*w + 138]', '[319, 319, -8*w - 63]', '[324, 18, 18]', '[324, 54, 96*w + 786]', '[324, 54, -96*w + 786]', '[324, 162, -14*w + 116]', '[324, 162, 14*w + 116]', '[331, 331, 254*w - 2079]', '[331, 331, 475*w - 3888]', '[333, 111, -63*w - 516]', '[333, 111, -63*w + 516]', '[333, 333, w + 20]', '[333, 333, 22*w - 181]', '[333, 333, 22*w + 181]', '[333, 333, w - 20]', '[336, 84, -8*w + 68]', '[336, 84, -172*w + 1408]', '[336, 84, 172*w + 1408]', '[336, 84, 8*w + 68]', '[338, 26, 351*w - 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108]', '[9989, 9989, -5*w - 108]', '[9989, 9989, -86*w - 711]', '[9993, 9993, 211*w + 1730]', '[9993, 9993, -13*w - 146]', '[9993, 9993, -13*w + 146]', '[9993, 9993, 211*w - 1730]', '[9996, 714, -14*w - 56]', '[9996, 714, -910*w + 7448]', '[9996, 714, -910*w - 7448]', '[9996, 714, -14*w + 56]', '[9996, 4998, -190*w - 1552]', '[9996, 4998, -220*w - 1798]', '[9996, 4998, -44*w - 346]', '[9996, 4998, -76*w - 614]', '[9996, 4998, -76*w + 614]', '[9996, 4998, -44*w + 346]', '[9996, 4998, -220*w + 1798]', '[9996, 4998, -190*w + 1552]', '[9998, 9998, 103*w - 849]', '[9998, 9998, -103*w - 849]', '[10000, 100, -100]'], 'label': '2.2.268.1', 'narrow_class_no': 2, 'primes': ['[2, 2, -27*w + 221]', '[3, 3, -w + 8]', '[3, 3, -w - 8]', '[7, 7, -11*w + 90]', '[7, 7, -11*w - 90]', '[11, 11, 6*w - 49]', '[11, 11, 6*w + 49]', '[17, 17, 4*w + 33]', '[17, 17, -4*w + 33]', '[25, 5, -5]', '[29, 29, -70*w + 573]', '[29, 29, 151*w - 1236]', '[31, 31, -w - 6]', '[31, 31, w - 6]', '[37, 37, -21*w - 172]', '[37, 37, -21*w + 172]', '[43, 43, 2*w - 15]', '[43, 43, 2*w + 15]', '[67, 67, -w]', '[73, 73, -3*w - 26]', '[73, 73, -3*w + 26]', '[79, 79, 92*w - 753]', '[79, 79, 313*w - 2562]', '[89, 89, -5*w - 42]', '[89, 89, -5*w + 42]', '[139, 139, 10*w + 81]', '[139, 139, 10*w - 81]', '[149, 149, 19*w - 156]', '[149, 149, -19*w - 156]', '[157, 157, -102*w + 835]', '[157, 157, 561*w - 4592]', '[169, 13, -13]', '[173, 173, 2*w - 21]', '[173, 173, -2*w - 21]', '[179, 179, 87*w - 712]', '[179, 179, 87*w + 712]', '[181, 181, 3*w - 28]', '[181, 181, 3*w + 28]', '[191, 191, 15*w - 122]', '[191, 191, 15*w + 122]', '[193, 193, 36*w + 295]', '[193, 193, -36*w + 295]', '[239, 239, 12*w + 97]', '[239, 239, 12*w - 97]', '[241, 241, -183*w + 1498]', '[241, 241, 480*w - 3929]', '[251, 251, 45*w + 368]', '[251, 251, 45*w - 368]', '[257, 257, -w - 18]', '[257, 257, w - 18]', '[269, 269, 41*w + 336]', '[269, 269, -41*w + 336]', '[271, 271, 40*w - 327]', '[271, 271, -40*w - 327]', '[277, 277, 426*w - 3487]', '[277, 277, -237*w + 1940]', '[293, 293, -998*w + 8169]', '[293, 293, 107*w - 876]', '[311, 311, 804*w - 6581]', '[311, 311, 141*w - 1154]', '[317, 317, -7*w + 60]', '[317, 317, -7*w - 60]', '[331, 331, 254*w - 2079]', '[331, 331, 475*w - 3888]', '[347, 347, -3*w - 16]', '[347, 347, 3*w - 16]', '[349, 349, -9*w - 76]', '[349, 349, -9*w + 76]', '[361, 19, -19]', '[367, 367, 7*w + 54]', '[367, 367, 7*w - 54]', '[379, 379, 5*w + 36]', '[379, 379, 5*w - 36]', '[383, 383, 168*w - 1375]', '[383, 383, 831*w - 6802]', '[389, 389, 34*w - 279]', '[389, 389, -34*w - 279]', '[397, 397, -6*w - 53]', '[397, 397, -6*w + 53]', '[421, 421, -3*w - 32]', '[421, 421, 3*w - 32]', '[443, 443, -27*w - 220]', '[443, 443, -27*w + 220]', '[449, 449, -4*w - 39]', '[449, 449, 4*w - 39]', '[457, 457, 51*w + 418]', '[457, 457, -51*w + 418]', '[461, 461, 2*w - 27]', '[461, 461, -2*w - 27]', '[463, 463, 136*w + 1113]', '[463, 463, 136*w - 1113]', '[487, 487, 32*w + 261]', '[487, 487, -32*w + 261]', '[499, 499, -62*w - 507]', '[499, 499, 62*w - 507]', '[503, 503, -3*w - 10]', '[503, 503, 3*w - 10]', '[509, 509, -w - 24]', '[509, 509, w - 24]', '[529, 23, -23]', '[547, 547, 47*w + 384]', '[547, 547, -47*w + 384]', '[557, 557, 14*w - 117]', '[557, 557, 14*w + 117]', '[563, 563, 6*w + 43]', '[563, 563, 6*w - 43]', '[569, 569, -56*w - 459]', '[569, 569, 56*w - 459]', '[587, 587, -3*w - 4]', '[587, 587, 3*w - 4]', '[599, 599, 3*w - 2]', '[599, 599, -3*w - 2]', '[601, 601, 117*w - 958]', '[601, 601, 117*w + 958]', '[613, 613, 6*w - 55]', '[613, 613, -6*w - 55]', '[617, 617, -269*w + 2202]', '[617, 617, 836*w - 6843]', '[631, 631, -4*w - 21]', '[631, 631, 4*w - 21]', '[647, 647, 21*w - 170]', '[647, 647, 21*w + 170]', '[683, 683, 18*w + 145]', '[683, 683, 18*w - 145]', '[709, 709, 30*w - 247]', '[709, 709, 30*w + 247]', '[727, 727, 416*w - 3405]', '[727, 727, 637*w - 5214]', '[739, 739, 158*w - 1293]', '[739, 739, 158*w + 1293]', '[761, 761, -100*w - 819]', '[761, 761, -100*w + 819]', '[773, 773, 122*w + 999]', '[773, 773, 122*w - 999]', '[787, 787, -1322*w + 10821]', '[787, 787, -217*w + 1776]', '[797, 797, 674*w - 5517]', '[797, 797, -431*w + 3528]', '[811, 811, 14*w - 111]', '[811, 811, 14*w + 111]', '[821, 821, 2*w - 33]', '[821, 821, -2*w - 33]', '[829, 829, -66*w - 541]', '[829, 829, 66*w - 541]', '[853, 853, -171*w - 1400]', '[853, 853, 171*w - 1400]', '[877, 877, 54*w - 443]', '[877, 877, -54*w - 443]', '[881, 881, 1300*w - 10641]', '[881, 881, -247*w + 2022]', '[883, 883, 31*w + 252]', '[883, 883, 31*w - 252]', '[919, 919, 13*w + 102]', '[919, 919, 13*w - 102]', '[953, 953, 4*w - 45]', '[953, 953, -4*w - 45]', '[977, 977, -71*w - 582]', '[977, 977, 71*w - 582]', '[983, 983, 36*w - 293]', '[983, 983, 36*w + 293]', '[991, 991, -4*w - 9]', '[991, 991, 4*w - 9]', '[997, 997, 3*w - 40]', '[997, 997, -3*w - 40]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-67, 0, 1], 'conductor': 268, 'degree': 2, 'dirichlet_group': [1, 267], 'disc_abs': 268, 'disc_rad': 134, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[1, 2]]], [5, [[2, 1]]], [7, [[1, 2]]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[1, 2]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[1, 2]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 16.3707055437449, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.268.1', 'local_algs': ['2.2.2.2', '67.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 67], 'rd': 16.3707055437, 'regulator': {'__RealLiteral__': 0, 'data': '11.4894930579', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 5967 a - 48842 \\)'], 'used_grh': False, 'zk': ['1', 'a']}