Hilbert modular form data - 2.2.209.1-5.2-c

Formats: - HTML - YAML - JSON - 2024-05-21T07:15:59.277141

• 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': 10, 'disc': 209, 'field_bad_primes': [11, 19], 'field_label': '2.2.209.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.209.1-5.2-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [5], 'level_ideal': '[5,5,-4*w - 27]', 'level_label': '5.2', 'level_norm': 5, 'parallel_weight': 2, 'short_label': '5.2-c', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5,5,-4*w - 27]', -1]], 'hecke_eigenvalues': ['e', '5*e^9 - 64*e^7 + 227*e^5 - 168*e^3 + 24*e', '-e^8 + 13*e^6 - 48*e^4 + 42*e^2 - 9', 1, '3*e^8 - 38*e^6 + 132*e^4 - 90*e^2 + 10', 'e^8 - 13*e^6 + 48*e^4 - 43*e^2 + 10', '-8*e^9 + 102*e^7 - 359*e^5 + 258*e^3 - 35*e', '-10*e^9 + 127*e^7 - 442*e^5 + 299*e^3 - 38*e', '-4*e^9 + 51*e^7 - 179*e^5 + 125*e^3 - 11*e', '6*e^8 - 77*e^6 + 274*e^4 - 204*e^2 + 30', '-4*e^8 + 51*e^6 - 179*e^4 + 125*e^2 - 18', '-2*e^9 + 27*e^7 - 108*e^5 + 123*e^3 - 36*e', '15*e^9 - 192*e^7 + 682*e^5 - 512*e^3 + 85*e', '23*e^9 - 294*e^7 + 1041*e^5 - 772*e^3 + 128*e', '4*e^9 - 50*e^7 + 167*e^5 - 89*e^3 + 6*e', '-2*e^8 + 26*e^6 - 96*e^4 + 85*e^2 - 22', '8*e^8 - 103*e^6 + 370*e^4 - 289*e^2 + 41', '-2*e^8 + 26*e^6 - 97*e^4 + 92*e^2 - 24', '-9*e^9 + 116*e^7 - 419*e^5 + 337*e^3 - 55*e', '-19*e^9 + 243*e^7 - 862*e^5 + 648*e^3 - 122*e', '-31*e^9 + 396*e^7 - 1398*e^5 + 1013*e^3 - 142*e', '14*e^9 - 182*e^7 + 671*e^5 - 590*e^3 + 127*e', '-17*e^9 + 218*e^7 - 777*e^5 + 594*e^3 - 122*e', '-29*e^9 + 372*e^7 - 1327*e^5 + 1011*e^3 - 159*e', '-10*e^9 + 130*e^7 - 479*e^5 + 418*e^3 - 89*e', '-2*e^9 + 24*e^7 - 72*e^5 + 12*e^3 + 4*e', '-9*e^8 + 115*e^6 - 407*e^4 + 305*e^2 - 53', '18*e^8 - 229*e^6 + 800*e^4 - 553*e^2 + 74', '-30*e^9 + 386*e^7 - 1389*e^5 + 1106*e^3 - 201*e', '7*e^9 - 89*e^7 + 311*e^5 - 217*e^3 + 34*e', '-2*e^8 + 25*e^6 - 85*e^4 + 56*e^2 - 7', '-e^6 + 9*e^4 - 14*e^2 - 11', 'e^8 - 14*e^6 + 63*e^4 - 99*e^2 + 25', '-11*e^8 + 139*e^6 - 479*e^4 + 315*e^2 - 40', '-12*e^9 + 155*e^7 - 564*e^5 + 472*e^3 - 89*e', '7*e^9 - 92*e^7 + 349*e^5 - 344*e^3 + 90*e', '43*e^9 - 551*e^7 + 1960*e^5 - 1474*e^3 + 234*e', '-10*e^9 + 126*e^7 - 429*e^5 + 254*e^3 - 17*e', '2*e^6 - 22*e^4 + 60*e^2 - 24', '-9*e^8 + 114*e^6 - 396*e^4 + 268*e^2 - 34', '3*e^9 - 39*e^7 + 144*e^5 - 124*e^3 + 6*e', '3*e^9 - 40*e^7 + 156*e^5 - 163*e^3 + 36*e', '-2*e^8 + 27*e^6 - 106*e^4 + 110*e^2 - 26', '19*e^8 - 242*e^6 + 847*e^4 - 587*e^2 + 82', '-23*e^9 + 297*e^7 - 1077*e^5 + 881*e^3 - 156*e', '37*e^9 - 473*e^7 + 1674*e^5 - 1231*e^3 + 173*e', '38*e^9 - 486*e^7 + 1721*e^5 - 1266*e^3 + 187*e', '16*e^9 - 206*e^7 + 740*e^5 - 574*e^3 + 74*e', '-e^8 + 12*e^6 - 36*e^4 + e^2 + 10', '17*e^8 - 219*e^6 + 791*e^4 - 640*e^2 + 100', '41*e^9 - 525*e^7 + 1865*e^5 - 1394*e^3 + 207*e', '-4*e^7 + 51*e^5 - 174*e^3 + 91*e', '-15*e^8 + 192*e^6 - 681*e^4 + 504*e^2 - 76', '4*e^8 - 53*e^6 + 204*e^4 - 207*e^2 + 45', '42*e^9 - 537*e^7 + 1900*e^5 - 1392*e^3 + 205*e', '23*e^9 - 294*e^7 + 1039*e^5 - 749*e^3 + 71*e', '11*e^8 - 141*e^6 + 504*e^4 - 388*e^2 + 53', '-25*e^9 + 322*e^7 - 1161*e^5 + 928*e^3 - 152*e', '-62*e^9 + 796*e^7 - 2846*e^5 + 2190*e^3 - 350*e', '40*e^9 - 510*e^7 + 1794*e^5 - 1282*e^3 + 166*e', '26*e^9 - 333*e^7 + 1185*e^5 - 900*e^3 + 160*e', '-33*e^8 + 420*e^6 - 1470*e^4 + 1026*e^2 - 150', '15*e^8 - 190*e^6 + 659*e^4 - 446*e^2 + 67', '-25*e^8 + 320*e^6 - 1137*e^4 + 849*e^2 - 118', '-17*e^8 + 217*e^6 - 764*e^4 + 546*e^2 - 81', '-15*e^9 + 190*e^7 - 659*e^5 + 445*e^3 - 59*e', '-18*e^9 + 232*e^7 - 837*e^5 + 668*e^3 - 101*e', '-14*e^8 + 177*e^6 - 609*e^4 + 389*e^2 - 58', '14*e^8 - 179*e^6 + 634*e^4 - 470*e^2 + 66', '24*e^8 - 305*e^6 + 1063*e^4 - 719*e^2 + 88', '-6*e^8 + 79*e^6 - 301*e^4 + 299*e^2 - 70', '-72*e^9 + 919*e^7 - 3241*e^5 + 2351*e^3 - 359*e', '32*e^9 - 407*e^7 + 1423*e^5 - 984*e^3 + 104*e', '28*e^8 - 356*e^6 + 1242*e^4 - 854*e^2 + 126', '-2*e^8 + 25*e^6 - 78*e^4 + 10*e^2 + 4', '3*e^8 - 40*e^6 + 157*e^4 - 176*e^2 + 51', '-33*e^8 + 422*e^6 - 1498*e^4 + 1125*e^2 - 169', '-49*e^9 + 630*e^7 - 2261*e^5 + 1768*e^3 - 284*e', '-4*e^9 + 50*e^7 - 166*e^5 + 76*e^3 + 40*e', '3*e^8 - 37*e^6 + 121*e^4 - 59*e^2', '-35*e^8 + 446*e^6 - 1565*e^4 + 1105*e^2 - 151', '17*e^9 - 213*e^7 + 716*e^5 - 395*e^3 + 17*e', '-7*e^9 + 90*e^7 - 321*e^5 + 238*e^3 - 32*e', '29*e^9 - 375*e^7 + 1365*e^5 - 1141*e^3 + 226*e', '21*e^9 - 268*e^7 + 943*e^5 - 665*e^3 + 55*e', '-14*e^8 + 179*e^6 - 632*e^4 + 452*e^2 - 65', '13*e^8 - 162*e^6 + 538*e^4 - 276*e^2 + 10', '-6*e^8 + 74*e^6 - 243*e^4 + 125*e^2 - 15', '5*e^8 - 64*e^6 + 222*e^4 - 133*e^2 + 10', '34*e^8 - 434*e^6 + 1528*e^4 - 1090*e^2 + 166', '-24*e^8 + 305*e^6 - 1062*e^4 + 716*e^2 - 78', '10*e^8 - 126*e^6 + 431*e^4 - 265*e^2 + 29', '-12*e^8 + 152*e^6 - 526*e^4 + 352*e^2 - 63', '-16*e^9 + 200*e^7 - 667*e^5 + 349*e^3 - 26*e', '98*e^9 - 1250*e^7 + 4400*e^5 - 3162*e^3 + 476*e', '44*e^9 - 565*e^7 + 2021*e^5 - 1557*e^3 + 247*e', '39*e^9 - 497*e^7 + 1746*e^5 - 1244*e^3 + 190*e', '68*e^9 - 871*e^7 + 3098*e^5 - 2336*e^3 + 383*e', '-67*e^9 + 857*e^7 - 3038*e^5 + 2257*e^3 - 347*e', '12*e^9 - 154*e^7 + 548*e^5 - 400*e^3 + 12*e', '8*e^9 - 100*e^7 + 333*e^5 - 174*e^3 + 21*e', '11*e^8 - 137*e^6 + 457*e^4 - 252*e^2 + 31', '23*e^8 - 296*e^6 + 1067*e^4 - 859*e^2 + 134', '37*e^8 - 473*e^6 + 1675*e^4 - 1237*e^2 + 179', '27*e^8 - 344*e^6 + 1213*e^4 - 893*e^2 + 134', '16*e^9 - 202*e^7 + 694*e^5 - 441*e^3 + 45*e', '-92*e^9 + 1177*e^7 - 4171*e^5 + 3078*e^3 - 450*e', '18*e^9 - 227*e^7 + 772*e^5 - 440*e^3 - 23*e', '-84*e^9 + 1072*e^7 - 3779*e^5 + 2736*e^3 - 423*e', '-19*e^8 + 244*e^6 - 869*e^4 + 643*e^2 - 94', 'e^8 - 11*e^6 + 24*e^4 + 29*e^2 - 38', '-10*e^8 + 130*e^6 - 479*e^4 + 419*e^2 - 83', '-13*e^8 + 165*e^6 - 570*e^4 + 368*e^2 - 67', '-25*e^8 + 322*e^6 - 1160*e^4 + 923*e^2 - 159', '-29*e^8 + 373*e^6 - 1339*e^4 + 1048*e^2 - 173', '11*e^8 - 144*e^6 + 531*e^4 - 442*e^2 + 64', '32*e^8 - 406*e^6 + 1407*e^4 - 923*e^2 + 109', '10*e^8 - 125*e^6 + 417*e^4 - 218*e^2 + 16', '6*e^8 - 72*e^6 + 222*e^4 - 74*e^2 + 3', '-14*e^8 + 178*e^6 - 622*e^4 + 431*e^2 - 64', '15*e^8 - 195*e^6 + 717*e^4 - 614*e^2 + 115', '12*e^9 - 155*e^7 + 562*e^5 - 457*e^3 + 64*e', '37*e^9 - 470*e^7 + 1639*e^5 - 1127*e^3 + 149*e', '-2*e^9 + 20*e^7 - 19*e^5 - 179*e^3 + 128*e', '-2*e^9 + 31*e^7 - 159*e^5 + 299*e^3 - 133*e', '-4*e^9 + 49*e^7 - 157*e^5 + 60*e^3 + 34*e', '22*e^9 - 280*e^7 + 981*e^5 - 686*e^3 + 63*e', '21*e^8 - 266*e^6 + 921*e^4 - 611*e^2 + 84', '4*e^8 - 47*e^6 + 131*e^4 + 30*e^2 - 58', '20*e^8 - 254*e^6 + 887*e^4 - 620*e^2 + 78', '13*e^8 - 166*e^6 + 589*e^4 - 445*e^2 + 36', '-19*e^8 + 246*e^6 - 897*e^4 + 746*e^2 - 115', '11*e^8 - 141*e^6 + 499*e^4 - 358*e^2 + 45', '-3*e^8 + 43*e^6 - 195*e^4 + 293*e^2 - 91', '-30*e^8 + 382*e^6 - 1343*e^4 + 974*e^2 - 171', '31*e^9 - 397*e^7 + 1413*e^5 - 1068*e^3 + 155*e', '30*e^9 - 383*e^7 + 1354*e^5 - 1003*e^3 + 168*e', '-21*e^8 + 267*e^6 - 932*e^4 + 636*e^2 - 81', '-4*e^8 + 54*e^6 - 215*e^4 + 238*e^2 - 48', '-101*e^9 + 1292*e^7 - 4579*e^5 + 3396*e^3 - 546*e', '54*e^9 - 692*e^7 + 2466*e^5 - 1887*e^3 + 341*e', '11*e^9 - 140*e^7 + 489*e^5 - 335*e^3 + 41*e', '-58*e^9 + 739*e^7 - 2590*e^5 + 1804*e^3 - 211*e', '6*e^8 - 83*e^6 + 347*e^4 - 432*e^2 + 110', '-33*e^8 + 417*e^6 - 1441*e^4 + 959*e^2 - 109', '-55*e^9 + 707*e^7 - 2536*e^5 + 1984*e^3 - 348*e', '-37*e^9 + 467*e^7 - 1599*e^5 + 985*e^3 - 64*e', '46*e^9 - 584*e^7 + 2030*e^5 - 1362*e^3 + 170*e', '-21*e^9 + 271*e^7 - 982*e^5 + 799*e^3 - 125*e', '32*e^8 - 408*e^6 + 1431*e^4 - 1008*e^2 + 158', '-37*e^8 + 475*e^6 - 1694*e^4 + 1280*e^2 - 176', '-25*e^9 + 318*e^7 - 1111*e^5 + 773*e^3 - 137*e', '-43*e^9 + 547*e^7 - 1914*e^5 + 1341*e^3 - 213*e', '-22*e^8 + 280*e^6 - 983*e^4 + 713*e^2 - 130', '15*e^8 - 192*e^6 + 675*e^4 - 466*e^2 + 51', '43*e^8 - 549*e^6 + 1935*e^4 - 1392*e^2 + 190', '44*e^8 - 563*e^6 + 2004*e^4 - 1526*e^2 + 220', '22*e^9 - 281*e^7 + 991*e^5 - 714*e^3 + 116*e', '-31*e^9 + 398*e^7 - 1423*e^5 + 1089*e^3 - 139*e', '-2*e^8 + 20*e^6 - 27*e^4 - 107*e^2 + 30', '-27*e^8 + 345*e^6 - 1217*e^4 + 875*e^2 - 106', '-16*e^9 + 205*e^7 - 727*e^5 + 529*e^3 - 41*e', '50*e^9 - 640*e^7 + 2275*e^5 - 1724*e^3 + 307*e', '47*e^8 - 604*e^6 + 2165*e^4 - 1678*e^2 + 247', '-11*e^8 + 142*e^6 - 511*e^4 + 391*e^2 - 24', '-77*e^9 + 982*e^7 - 3457*e^5 + 2485*e^3 - 347*e', '68*e^9 - 871*e^7 + 3097*e^5 - 2329*e^3 + 365*e', '-40*e^8 + 508*e^6 - 1773*e^4 + 1229*e^2 - 159'], 'hecke_polynomial': 'x^10 - 13*x^8 + 48*x^6 - 43*x^4 + 12*x^2 - 1', 'label': '2.2.209.1-5.2-c'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 209, 'ideals': ['[1, 1, 1]', '[2, 2, -11*w - 74]', '[2, 2, -11*w + 85]', '[4, 2, 2]', '[4, 4, -w + 8]', '[4, 4, w + 7]', '[5, 5, 4*w - 31]', '[5, 5, -4*w - 27]', '[8, 4, -22*w - 148]', '[8, 4, -22*w + 170]', '[8, 8, -3*w + 23]', '[8, 8, -3*w - 20]', '[9, 3, 3]', '[10, 10, 7*w + 47]', '[10, 10, w - 7]', '[10, 10, w + 6]', '[10, 10, 7*w - 54]', '[11, 11, -70*w - 471]', '[13, 13, -2*w - 13]', '[13, 13, -2*w + 15]', '[16, 4, 4]', '[16, 8, -2*w + 16]', '[16, 8, 2*w + 14]', '[16, 16, -15*w + 116]', '[16, 16, 15*w + 101]', '[18, 6, -33*w - 222]', '[18, 6, -33*w + 255]', '[19, 19, 92*w - 711]', '[20, 10, 8*w - 62]', '[20, 10, -8*w - 54]', '[20, 20, -59*w - 397]', '[20, 20, -w - 8]', '[20, 20, w - 9]', '[20, 20, 59*w - 456]', '[22, 22, w + 5]', '[22, 22, w - 6]', '[23, 23, -26*w + 201]', '[23, 23, -26*w - 175]', '[25, 5, 5]', '[25, 25, 48*w + 323]', '[25, 25, -48*w + 371]', '[26, 26, -37*w + 286]', '[26, 26, 5*w + 34]', '[26, 26, -5*w + 39]', '[26, 26, 37*w + 249]', '[29, 29, 18*w - 139]', '[29, 29, 18*w + 121]', '[32, 8, -44*w - 296]', '[32, 8, -44*w + 340]', '[32, 16, -6*w + 46]', '[32, 16, -6*w - 40]', '[32, 32, -w - 4]', '[32, 32, -w + 5]', '[36, 6, 6]', '[36, 12, -3*w + 24]', '[36, 12, 3*w + 21]', '[38, 38, -w - 9]', '[38, 38, w - 10]', '[40, 20, 14*w + 94]', '[40, 20, 2*w - 14]', '[40, 20, 2*w + 12]', '[40, 20, 14*w - 108]', '[40, 40, w + 3]', '[40, 40, 103*w + 693]', '[40, 40, 103*w - 796]', '[40, 40, w - 4]', '[41, 41, -10*w - 67]', '[41, 41, 10*w - 77]', '[44, 22, -140*w - 942]', '[44, 44, -19*w - 128]', '[44, 44, 19*w - 147]', '[45, 15, 12*w - 93]', '[45, 15, -12*w - 81]', '[46, 46, -w - 2]', '[46, 46, 5*w - 38]', '[46, 46, -5*w - 33]', '[46, 46, w - 3]', '[47, 47, 2*w - 17]', '[47, 47, 2*w + 15]', '[49, 7, -7]', '[50, 10, -55*w - 370]', '[50, 10, -55*w + 425]', '[50, 50, -w - 1]', '[50, 50, -3*w - 19]', '[50, 50, -3*w + 22]', '[50, 50, -w + 2]', '[52, 26, -4*w - 26]', '[52, 26, -4*w + 30]', '[52, 52, -w]', '[52, 52, -29*w + 224]', '[52, 52, -29*w - 195]', '[52, 52, -w + 1]', '[55, 55, 6*w + 41]', '[55, 55, -6*w + 47]', '[58, 58, -w - 10]', '[58, 58, 9*w - 70]', '[58, 58, -9*w - 61]', '[58, 58, w - 11]', '[64, 8, 8]', '[64, 16, -4*w + 32]', '[64, 16, 4*w + 28]', '[64, 32, -30*w + 232]', '[64, 32, 30*w + 202]', '[64, 64, -129*w + 997]', '[64, 64, 129*w + 868]', '[65, 65, 114*w + 767]', '[65, 65, 2*w - 13]', '[65, 65, 2*w + 11]', '[65, 65, 114*w - 881]', '[72, 12, -66*w - 444]', '[72, 12, -66*w + 510]', '[72, 24, -9*w + 69]', '[72, 24, -9*w - 60]', '[76, 38, 184*w - 1422]', '[76, 76, 25*w + 168]', '[76, 76, 25*w - 193]', '[79, 79, 40*w - 309]', '[79, 79, 40*w + 269]', '[80, 20, 16*w - 124]', '[80, 20, -16*w - 108]', '[80, 40, -118*w - 794]', '[80, 40, -2*w - 16]', '[80, 40, 2*w - 18]', '[80, 40, 118*w - 912]', '[80, 80, -w - 11]', '[80, 80, -41*w - 276]', '[80, 80, 41*w - 317]', '[80, 80, w - 12]', '[81, 9, 9]', '[82, 82, -3*w + 25]', '[82, 82, -23*w - 155]', '[82, 82, -23*w + 178]', '[82, 82, -3*w - 22]', '[88, 44, 2*w + 10]', '[88, 44, 2*w - 12]', '[88, 88, 13*w + 87]', '[88, 88, 13*w - 100]', '[90, 30, 21*w + 141]', '[90, 30, 3*w - 21]', '[90, 30, 3*w + 18]', '[90, 30, 21*w - 162]', '[92, 46, -52*w + 402]', '[92, 46, -52*w - 350]', '[92, 92, -7*w - 48]', '[92, 92, 107*w - 827]', '[92, 92, 107*w + 720]', '[92, 92, -7*w + 55]', '[94, 94, 335*w - 2589]', '[94, 94, -17*w + 131]', '[94, 94, 17*w + 114]', '[94, 94, -125*w + 966]', '[95, 95, -8*w + 61]', '[95, 95, -8*w - 53]', '[98, 14, 77*w + 518]', '[98, 14, 77*w - 595]', '[99, 33, -210*w - 1413]', '[100, 10, 10]', '[100, 20, -5*w + 40]', '[100, 20, 5*w + 35]', '[100, 50, 96*w + 646]', '[100, 50, -96*w + 742]', '[100, 100, -13*w + 101]', '[100, 100, 63*w + 424]', '[100, 100, -63*w + 487]', '[100, 100, 13*w + 88]', '[104, 52, -74*w + 572]', '[104, 52, 10*w + 68]', '[104, 52, -10*w + 78]', '[104, 52, 74*w + 498]', '[104, 104, w + 12]', '[104, 104, -85*w + 657]', '[104, 104, 85*w + 572]', '[104, 104, -w + 13]', '[107, 107, 4*w + 25]', '[107, 107, -4*w + 29]', '[109, 109, 2*w - 11]', '[109, 109, -2*w - 9]', '[110, 110, -51*w + 394]', '[110, 110, -7*w - 46]', '[110, 110, -7*w + 53]', '[110, 110, -51*w - 343]', '[115, 115, -34*w + 263]', '[115, 115, 2*w - 19]', '[115, 115, 2*w + 17]', '[115, 115, -34*w - 229]', '[116, 58, 36*w - 278]', '[116, 58, 36*w + 242]', '[116, 116, 5*w - 37]', '[116, 116, 195*w - 1507]', '[116, 116, 195*w + 1312]', '[116, 116, 5*w + 32]', '[117, 39, -6*w - 39]', '[117, 39, -6*w + 45]', '[121, 11, 11]', '[125, 25, 20*w - 155]', '[125, 25, -20*w - 135]', '[125, 125, 4*w - 33]', '[125, 125, -4*w - 29]', '[127, 127, 136*w + 915]', '[127, 127, 136*w - 1051]', '[128, 16, -88*w - 592]', '[128, 16, -88*w + 680]', '[128, 32, -12*w + 92]', '[128, 32, -12*w - 80]', '[128, 64, -2*w - 8]', '[128, 64, -2*w + 10]', '[128, 128, -3*w + 20]', '[128, 128, -3*w - 17]', '[130, 130, -w - 13]', '[130, 130, -27*w - 182]', '[130, 130, 199*w - 1538]', '[130, 130, -3*w - 23]', '[130, 130, 3*w - 26]', '[130, 130, -199*w - 1339]', '[130, 130, 27*w - 209]', '[130, 130, w - 14]', '[137, 137, -8*w - 55]', '[137, 137, 8*w - 63]', '[143, 143, 32*w + 215]', '[143, 143, 32*w - 247]', '[144, 12, 12]', '[144, 24, -6*w + 48]', '[144, 24, 6*w + 42]', '[144, 48, -45*w + 348]', '[144, 48, 45*w + 303]', '[145, 145, -62*w + 479]', '[145, 145, -2*w + 9]', '[145, 145, -2*w - 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324]', '[9848, 9848, w + 99]', '[9848, 9848, -2549*w - 17151]', '[9848, 9848, -2549*w + 19700]', '[9848, 9848, w - 100]', '[9859, 9859, -114*w + 887]', '[9859, 9859, 114*w + 773]', '[9864, 1644, 570*w - 4404]', '[9864, 1644, 78*w + 516]', '[9864, 1644, 78*w - 594]', '[9864, 1644, 570*w + 3834]', '[9864, 3288, 15*w - 51]', '[9864, 3288, 1047*w - 8091]', '[9864, 3288, 1047*w + 7044]', '[9864, 3288, 15*w + 36]', '[9865, 9865, -96*w + 749]', '[9865, 9865, -328*w + 2537]', '[9865, 9865, 328*w + 2209]', '[9865, 9865, 96*w + 653]', '[9868, 4934, 156*w + 1054]', '[9868, 4934, -156*w + 1210]', '[9868, 9868, 19*w + 160]', '[9868, 9868, -1151*w + 8896]', '[9868, 9868, 1151*w + 7745]', '[9868, 9868, -19*w + 179]', '[9872, 2468, -608*w + 4700]', '[9872, 2468, -608*w - 4092]', '[9872, 4936, 982*w + 6608]', '[9872, 4936, -82*w - 560]', '[9872, 4936, -82*w + 642]', '[9872, 4936, 982*w - 7590]', '[9872, 9872, 133*w - 1033]', '[9872, 9872, -7*w - 108]', '[9872, 9872, -7*w + 115]', '[9872, 9872, 133*w + 900]', '[9873, 3291, -18*w - 75]', '[9873, 3291, 18*w - 93]', '[9874, 9874, 1637*w + 11014]', '[9874, 9874, 365*w + 2454]', '[9874, 9874, 365*w - 2819]', '[9874, 9874, 1637*w - 12651]', '[9875, 1975, -20*w + 115]', '[9875, 1975, -380*w + 2935]', '[9875, 1975, -380*w - 2555]', '[9875, 1975, -20*w - 95]', '[9875, 9875, -84*w + 641]', '[9875, 9875, -1836*w - 12353]', '[9875, 9875, -1836*w + 14189]', '[9875, 9875, -84*w - 557]', '[9880, 4940, -14*w + 26]', '[9880, 4940, -518*w - 3484]', '[9880, 4940, -3814*w + 29476]', '[9880, 4940, -62*w - 406]', '[9880, 4940, -62*w + 468]', '[9880, 4940, -1154*w + 8918]', '[9880, 4940, -518*w + 4002]', '[9880, 4940, -14*w - 12]', '[9880, 9880, -157*w - 1052]', '[9880, 9880, -451*w - 3033]', '[9880, 9880, -71*w - 468]', '[9880, 9880, -43*w + 316]', '[9880, 9880, -43*w - 273]', '[9880, 9880, -71*w + 539]', '[9880, 9880, -451*w + 3484]', '[9880, 9880, -157*w + 1209]', '[9881, 9881, -8*w - 111]', '[9881, 9881, 2008*w + 13511]', '[9881, 9881, 2008*w - 15519]', '[9881, 9881, 8*w - 119]', '[9887, 9887, 1618*w + 10887]', '[9887, 9887, 1618*w - 12505]', '[9895, 9895, 544*w - 4203]', '[9895, 9895, -16*w + 67]', '[9895, 9895, 16*w + 51]', '[9895, 9895, -544*w - 3659]', '[9900, 330, -2100*w - 14130]', '[9900, 660, -285*w - 1920]', '[9900, 660, 285*w - 2205]', '[9900, 1650, 12*w - 138]', '[9900, 1650, -12*w - 126]', '[9900, 3300, 21*w - 192]', '[9900, 3300, -111*w - 753]', '[9900, 3300, 111*w - 864]', '[9900, 3300, -21*w - 171]', '[9902, 9902, -29*w - 170]', '[9902, 9902, -201*w + 1550]', '[9902, 9902, -201*w - 1349]', '[9902, 9902, -29*w + 199]', '[9904, 2476, -24*w - 188]', '[9904, 2476, 24*w - 212]', '[9904, 4952, -190*w - 1282]', '[9904, 4952, -10*w - 118]', '[9904, 4952, 10*w - 128]', '[9904, 4952, 190*w - 1472]', '[9904, 9904, -99*w - 673]', '[9904, 9904, -1401*w - 9427]', '[9904, 9904, 1401*w - 10828]', '[9904, 9904, 99*w - 772]', '[9907, 9907, 236*w + 1585]', '[9907, 9907, -236*w + 1821]', '[9913, 9913, 22*w - 135]', '[9913, 9913, 38*w + 237]', '[9913, 9913, -38*w + 275]', '[9913, 9913, -22*w - 113]', '[9917, 9917, 114*w - 875]', '[9917, 9917, 14*w - 25]', '[9917, 9917, -14*w - 11]', '[9917, 9917, -114*w - 761]', '[9918, 3306, 903*w + 6075]', '[9918, 3306, 123*w - 945]', '[9918, 3306, 123*w + 822]', '[9918, 3306, 903*w - 6978]', '[9922, 902, -33*w + 275]', '[9922, 902, -253*w - 1705]', '[9922, 902, -253*w + 1958]', '[9922, 902, -33*w - 242]', '[9923, 9923, -14*w - 135]', '[9923, 9923, 14*w - 149]', '[9925, 1985, -60*w - 415]', '[9925, 1985, 60*w - 475]', '[9925, 9925, -108*w - 733]', '[9925, 9925, -524*w - 3527]', '[9925, 9925, 524*w - 4051]', '[9925, 9925, 108*w - 841]', '[9927, 3309, 102*w + 693]', '[9927, 3309, 102*w - 795]', '[9932, 4966, 136*w - 1046]', '[9932, 4966, 24*w + 130]', '[9932, 4966, 24*w - 154]', '[9932, 4966, 136*w + 910]', '[9932, 9932, 21*w - 125]', '[9932, 9932, 19*w - 104]', '[9932, 9932, 999*w + 6721]', '[9932, 9932, 161*w + 1079]', '[9932, 9932, 161*w - 1240]', '[9932, 9932, 999*w - 7720]', '[9932, 9932, 19*w + 85]', '[9932, 9932, 21*w + 104]', '[9934, 9934, 11*w - 133]', '[9934, 9934, -105*w - 713]', '[9934, 9934, 105*w - 818]', '[9934, 9934, -11*w - 122]', '[9937, 9937, 48*w - 385]', '[9937, 9937, -48*w - 337]', '[9938, 9938, 971*w + 6534]', '[9938, 9938, -619*w - 4166]', '[9938, 9938, -619*w + 4785]', '[9938, 9938, 971*w - 7505]', '[9950, 1990, 35*w + 215]', '[9950, 1990, -15*w - 35]', '[9950, 1990, 15*w - 50]', '[9950, 1990, -35*w + 250]', '[9950, 9950, -197*w - 1322]', '[9950, 9950, 951*w - 7349]', '[9950, 9950, -633*w + 4891]', '[9950, 9950, 1449*w - 11198]', '[9950, 9950, -1449*w - 9749]', '[9950, 9950, 633*w + 4258]', '[9950, 9950, -951*w - 6398]', '[9950, 9950, 197*w - 1519]', '[9952, 2488, -316*w + 2440]', '[9952, 2488, -44*w - 280]', '[9952, 2488, -44*w + 324]', '[9952, 2488, -316*w - 2124]', '[9952, 4976, -2326*w + 17976]', '[9952, 4976, -14*w - 10]', '[9952, 4976, -14*w + 24]', '[9952, 4976, -2326*w - 15650]', '[9952, 9952, -61*w + 460]', '[9952, 9952, -259*w + 1999]', '[9952, 9952, -259*w - 1740]', '[9952, 9952, -61*w - 399]', '[9967, 9967, 18*w - 173]', '[9967, 9967, -18*w - 155]', '[9974, 9974, 1213*w + 8161]', '[9974, 9974, 165*w - 1271]', '[9974, 9974, 165*w + 1106]', '[9974, 9974, 1213*w - 9374]', '[9980, 4990, 1276*w - 9862]', '[9980, 4990, 4*w - 106]', '[9980, 4990, -4*w - 102]', '[9980, 4990, -1276*w - 8586]', '[9980, 9980, 173*w - 1341]', '[9980, 9980, 473*w - 3657]', '[9980, 9980, 67*w - 528]', '[9980, 9980, 37*w - 304]', '[9980, 9980, -37*w - 267]', '[9980, 9980, -67*w - 461]', '[9980, 9980, -473*w - 3184]', '[9980, 9980, -173*w - 1168]', '[9981, 3327, 1140*w + 7671]', '[9981, 3327, 1140*w - 8811]', '[9985, 9985, 818*w + 5503]', '[9985, 9985, 14*w - 23]', '[9985, 9985, -14*w - 9]', '[9985, 9985, -818*w + 6321]', '[9986, 9986, 25*w - 219]', '[9986, 9986, 197*w + 1329]', '[9986, 9986, 197*w - 1526]', '[9986, 9986, 25*w + 194]', '[9988, 4994, -28*w + 190]', '[9988, 4994, -28*w - 162]', '[9988, 9988, -193*w - 1295]', '[9988, 9988, -17*w + 80]', '[9988, 9988, -17*w - 63]', '[9988, 9988, -193*w + 1488]', '[9992, 4996, -2*w - 100]', '[9992, 4996, 58*w - 460]', '[9992, 4996, -58*w - 402]', '[9992, 4996, 2*w - 102]', '[9992, 9992, -433*w - 2915]', '[9992, 9992, 43*w - 348]', '[9992, 9992, -43*w - 305]', '[9992, 9992, 433*w - 3348]', '[10000, 100, 100]', '[10000, 200, -50*w + 400]', '[10000, 200, 50*w + 350]', '[10000, 400, -375*w + 2900]', '[10000, 400, 375*w + 2525]', '[10000, 500, 960*w + 6460]', '[10000, 500, -960*w + 7420]', '[10000, 1000, -130*w + 1010]', '[10000, 1000, 630*w + 4240]', '[10000, 1000, -630*w + 4870]', '[10000, 1000, 130*w + 880]', '[10000, 2000, -15*w + 155]', '[10000, 2000, 85*w + 580]', '[10000, 2000, -85*w + 665]', '[10000, 2000, 15*w + 140]', '[10000, 2500, -32*w + 268]', '[10000, 2500, 32*w + 236]', '[10000, 5000, 6*w + 106]', '[10000, 5000, 246*w + 1658]', '[10000, 5000, -246*w + 1904]', '[10000, 5000, -6*w + 112]', '[10000, 10000, -1813*w + 14012]', '[10000, 10000, -77*w + 604]', '[10000, 10000, 77*w + 527]', '[10000, 10000, 1813*w + 12199]'], 'label': '2.2.209.1', 'narrow_class_no': 2, 'primes': ['[2, 2, -11*w - 74]', '[2, 2, -11*w + 85]', '[5, 5, 4*w - 31]', '[5, 5, -4*w - 27]', '[9, 3, 3]', '[11, 11, -70*w - 471]', '[13, 13, -2*w - 13]', '[13, 13, -2*w + 15]', '[19, 19, 92*w - 711]', '[23, 23, -26*w + 201]', '[23, 23, -26*w - 175]', '[29, 29, 18*w - 139]', '[29, 29, 18*w + 121]', '[41, 41, -10*w - 67]', '[41, 41, 10*w - 77]', '[47, 47, 2*w - 17]', '[47, 47, 2*w + 15]', '[49, 7, -7]', '[79, 79, 40*w - 309]', '[79, 79, 40*w + 269]', '[107, 107, 4*w + 25]', '[107, 107, -4*w + 29]', '[109, 109, 2*w - 11]', '[109, 109, -2*w - 9]', '[127, 127, 136*w + 915]', '[127, 127, 136*w - 1051]', '[137, 137, -8*w - 55]', '[137, 137, 8*w - 63]', '[151, 151, -16*w - 107]', '[151, 151, 16*w - 123]', '[157, 157, 188*w + 1265]', '[157, 157, 188*w - 1453]', '[163, 163, 14*w + 95]', '[163, 163, 14*w - 109]', '[167, 167, -24*w + 185]', '[167, 167, -24*w - 161]', '[173, 173, 2*w - 7]', '[173, 173, -2*w - 5]', '[191, 191, 2*w - 21]', '[191, 191, -2*w - 19]', '[193, 193, 2*w - 5]', '[193, 193, -2*w - 3]', '[199, 199, 166*w - 1283]', '[199, 199, 166*w + 1117]', '[211, 211, 4*w - 27]', '[211, 211, -4*w - 23]', '[227, 227, 84*w - 649]', '[227, 227, 84*w + 565]', '[229, 229, -100*w + 773]', '[229, 229, -100*w - 673]', '[241, 241, 14*w - 107]', '[241, 241, -14*w - 93]', '[251, 251, -10*w - 69]', '[251, 251, 10*w - 79]', '[281, 281, 6*w + 37]', '[281, 281, -6*w + 43]', '[289, 17, -17]', '[293, 293, 298*w + 2005]', '[293, 293, 298*w - 2303]', '[307, 307, -4*w - 21]', '[307, 307, 4*w - 25]', '[311, 311, 22*w + 149]', '[311, 311, -22*w + 171]', '[313, 313, 16*w - 125]', '[313, 313, -16*w - 109]', '[337, 337, 46*w + 309]', '[337, 337, -46*w + 355]', '[353, 353, -64*w + 495]', '[353, 353, -64*w - 431]', '[367, 367, 2*w - 25]', '[367, 367, -2*w - 23]', '[373, 373, -38*w + 293]', '[373, 373, 38*w + 255]', '[389, 389, 4*w - 37]', '[389, 389, -4*w - 33]', '[397, 397, -12*w - 83]', '[397, 397, 12*w - 95]', '[409, 409, 202*w + 1359]', '[409, 409, 202*w - 1561]', '[419, 419, -50*w + 387]', '[419, 419, 50*w + 337]', '[431, 431, 320*w - 2473]', '[431, 431, 320*w + 2153]', '[439, 439, 128*w - 989]', '[439, 439, 128*w + 861]', '[443, 443, -86*w - 579]', '[443, 443, -86*w + 665]', '[463, 463, 306*w + 2059]', '[463, 463, 306*w - 2365]', '[467, 467, 2*w - 27]', '[467, 467, -2*w - 25]', '[499, 499, 30*w + 203]', '[499, 499, -30*w + 233]', '[523, 523, 68*w + 457]', '[523, 523, 68*w - 525]', '[547, 547, 4*w - 19]', '[547, 547, -4*w - 15]', '[563, 563, -28*w - 187]', '[563, 563, 28*w - 215]', '[569, 569, 150*w - 1159]', '[569, 569, 150*w + 1009]', '[577, 577, 72*w + 485]', '[577, 577, 72*w - 557]', '[587, 587, 262*w - 2025]', '[587, 587, 262*w + 1763]', '[601, 601, -10*w + 73]', '[601, 601, 10*w + 63]', '[607, 607, 16*w - 121]', '[607, 607, -16*w - 105]', '[617, 617, -152*w + 1175]', '[617, 617, -152*w - 1023]', '[619, 619, -6*w - 47]', '[619, 619, 6*w - 53]', '[631, 631, -58*w + 449]', '[631, 631, 58*w + 391]', '[643, 643, -174*w + 1345]', '[643, 643, -174*w - 1171]', '[647, 647, 218*w + 1467]', '[647, 647, 218*w - 1685]', '[653, 653, -196*w - 1319]', '[653, 653, 196*w - 1515]', '[659, 659, -52*w + 401]', '[659, 659, 52*w + 349]', '[673, 673, 482*w + 3243]', '[673, 673, 482*w - 3725]', '[677, 677, 246*w + 1655]', '[677, 677, 246*w - 1901]', '[691, 691, 2*w - 31]', '[691, 691, -2*w - 29]', '[709, 709, 20*w + 137]', '[709, 709, 20*w - 157]', '[719, 719, -94*w + 727]', '[719, 719, -94*w - 633]', '[727, 727, 38*w + 257]', '[727, 727, -38*w + 295]', '[743, 743, -8*w + 55]', '[743, 743, 8*w + 47]', '[757, 757, 12*w - 97]', '[757, 757, 12*w + 85]', '[787, 787, -4*w - 5]', '[787, 787, 4*w - 9]', '[811, 811, 4*w - 7]', '[811, 811, -4*w - 3]', '[823, 823, 6*w - 55]', '[823, 823, -6*w - 49]', '[827, 827, -4*w - 1]', '[827, 827, 4*w - 5]', '[857, 857, 6*w - 35]', '[857, 857, -6*w - 29]', '[859, 859, -10*w - 73]', '[859, 859, 10*w - 83]', '[877, 877, 194*w - 1499]', '[877, 877, 194*w + 1305]', '[881, 881, -8*w - 61]', '[881, 881, 8*w - 69]', '[883, 883, -66*w + 511]', '[883, 883, 66*w + 445]', '[887, 887, 504*w + 3391]', '[887, 887, 504*w - 3895]', '[929, 929, 424*w + 2853]', '[929, 929, 424*w - 3277]', '[941, 941, 386*w - 2983]', '[941, 941, 386*w + 2597]', '[947, 947, 2*w - 35]', '[947, 947, -2*w - 33]', '[953, 953, 22*w - 167]', '[953, 953, -22*w - 145]', '[961, 31, -31]']}
• 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': [-52, -1, 1], 'conductor': 209, 'degree': 2, 'dirichlet_group': [1, 208], 'disc_abs': 209, 'disc_rad': 209, 'disc_sign': 1, 'frobs': [[2, [[1, 2]]], [3, [[2, 1]]], [5, [[1, 2]]], [7, [[2, 1]]], [11, [0]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [0]], [23, [[1, 2]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 14.45683229480096, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.209.1', 'local_algs': ['11.2.1.2', '19.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [11, 19], 'rd': 14.4568322948, 'regulator': {'__RealLiteral__': 0, 'data': '11.4414509452', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 6440 a + 43331 \\)'], 'used_grh': False, 'zk': ['1', 'a']}