Integer Points on A^4+B^4+C^4=20402*D^4
[2025.12.05]A^4+B^4+C^4=20402*D^4の整点
■整点を求める方法は、 "A^4+B^4+C^4=3362*D^4の整点" と同様なので、詳細はそちらを参照すること。ただし、参照する数式のみ記載する。
自然数nを固定したとき、不定方程式
A^4+B^4+C^4=2*n^2*D^4 ----------(1)
を満たす自明でない整数の組(A,B,C,D) (ただし C!=0かつgcd(A,B,C,D)=1)を探す。
以下では、Elkiesの論文(参考文献[1])の方法およびTom Womackの文書(参考文献[5])を参考にして、(1)を満たす整数の組(A,B,C,D)を探す。
ここで、整数A,B,C,Dは0以上として良い。
■x=A/C,y=B/C.t=D/Cとすると、
x^4+y^4+1=2*n^2*t^4 ----------(2)
つまり、(2)を満たす有理数の組(x,y,t)を見つければ良い。
そのためには、nある有理数uに対して、
±(u^2-2)*y^2=(-u^2+4*u-2)*x^2-2*(u^2-2*u+2)*x+(-u^2+4*u-2) ----------(3a±)
±n*(u^2-2)*t^2=(u^2-2*u+2)*x^2+(-u^2+4*u-2)*x+(u^2-2*u+2) ----------(3b±)
の両方を満たす有理数の組(x,y,t)を見つければ良い。
■任意の有理数uについて、２次曲線(3b+)および(3b-)は、non-singularである。
また、u^2 > 2のとき、(3b+)のみ、u^2 < 2のとき、(3b-)のみが成立する。
■２次曲線(3a)がsingularであるのは、u=0,1,2のときであり。そのときに限る。
u=1のとき、(3a+)はsingularであるが、有理点を持たない。
u-0,2のとき、(3a+)はsingularであり、
x^2 - x + 1=n*t^2 --------(**)
が有理点をもつかどうかを議論する必要がある。
20402=2*101^2であるので、以下では、n=101とする。
■n=101のとき、２次曲線(**)は、有理点を持たないことが確認できる。
{MAGMAでの計算]
> P2 := ProjectiveSpace(Rationals(), 2);
> N:=101;
> C := Conic(P2,-N*y^2+x^2+x*z+z^2);
> HasRationalPoint(C);
false
>
■有理数u(u!=0,1,2)の高さが小さいものから、順に調べる。
例えば、有理数uの高さが600以下の範囲で、２次曲線(3a+)と２つの２次曲線の和集合(3b±)が共に有理点を持つようなuを選択すると、以下のように718個のuが抽出される。
これらのuについて、(3a+),(3b±)を共に満たす有理数の組(x,y,t)を見つければ良い。
[MAGMAによる計算]
> PP(101,1,600);
** u= 1/53 ; tau(u)= 105/52 ; -5407*x^2 + 5617*y^2 + 11026*x*z - 5407*z^2
(-523/244295 : -240208/244295 : 1) C1b (-631148/249093 : 77281/249093 : 1)
** u= 1/293 ; tau(u)= 585/292 ; -170527*x^2 + 171697*y^2 + 342226*x*z - 170527*z^2
(85301/103855 : -16776/103855 : 1) C1b (-264204/143489 : -35563/143489 : 1)
** u= -1/441 ; tau(u)= 883/442 ; -390727*x^2 + 388961*y^2 + 779690*x*z - 390727*z^2
(8893/10573 : 1806/10573 : 1) C2b (2764048/8910409 : 786599/8910409 : 1)
** u= 1/545 ; tau(u)= 1089/544 ; -591871*x^2 + 594049*y^2 + 1185922*x*z - 591871*z^2
(-458591/8827831 : -9270184/8827831 : 1) C1b (-235200955/23669916 : 24640823/23669916 : 1)
** u= 4/17 ; tau(u)= 30/13 ; -322*x^2 + 562*y^2 + 916*x*z - 322*z^2
(9/22 : -1/22 : 1) C1b (1421/824 : -123/824 : 1)
** u= 4/29 ; tau(u)= 54/25 ; -1234*x^2 + 1666*y^2 + 2932*x*z - 1234*z^2
(2 : -3/7 : 1) C1b (5960/3063 : 3551/21441 : 1)
** u= 4/53 ; tau(u)= 102/49 ; -4786*x^2 + 5602*y^2 + 10420*x*z - 4786*z^2
(-4507/888 : -5047/888 : 1) C1b (620687/26336 : 58443/26336 : 1)
** u= -4/81 ; tau(u)= 166/85 ; -14434*x^2 + 13106*y^2 + 27572*x*z - 14434*z^2
(112/157 : 63/157 : 1) C2b (-7952008/120875 : -818047/120875 : 1)
** u= -4/117 ; tau(u)= 238/121 ; -29266*x^2 + 27362*y^2 + 56660*x*z - 29266*z^2
(17717/15866 : 4785/15866 : 1) C2b (209797/218049 : 21311/218049 : 1)
** u= 4/245 ; tau(u)= 486/241 ; -116146*x^2 + 120034*y^2 + 236212*x*z - 116146*z^2
(2246/2799 : 301/2799 : 1) C1b (-12662147616/241680449 : 1261671397/241680449 : 1)
** u= 4/425 ; tau(u)= 846/421 ; -354466*x^2 + 361234*y^2 + 715732*x*z - 354466*z^2
(639176/111181 : -74535/15883 : 1) C1b (45077757/696232 : -4430701/696232 : 1)
** u= -5/269 ; tau(u)= 543/274 ; -150127*x^2 + 144697*y^2 + 294874*x*z - 150127*z^2
(13225/19761 : -51458/138327 : 1) C2b (-4199435/208072 : 3029679/1456504 : 1)
** u= -5/477 ; tau(u)= 959/482 ; -464623*x^2 + 455033*y^2 + 919706*x*z - 464623*z^2
(5663/135467 : -131226/135467 : 1) C2b (498080/6768717 : -653317/6768717 : 1)
** u= -7/13 ; tau(u)= 33/20 ; -751*x^2 + 289*y^2 + 1138*x*z - 751*z^2
(5/3 : 92/51 : 1) C2b (781/415 : 1413/7055 : 1)
** u= -7/25 ; tau(u)= 57/32 ; -1999*x^2 + 1201*y^2 + 3298*x*z - 1999*z^2
(1/7 : 8/7 : 1) C2b (124620/252341 : 23633/252341 : 1)
** u= -7/61 ; tau(u)= 129/68 ; -9199*x^2 + 7393*y^2 + 16690*x*z - 9199*z^2
(-209/789 : -1096/789 : 1) C2b (11036/30987 : 2807/30987 : 1)
** u= 7/89 ; tau(u)= 171/82 ; -13399*x^2 + 15793*y^2 + 29290*x*z - 13399*z^2
(17377/26853 : 1598/26853 : 1) C1b (1666197/337096 : 5093/11624 : 1)
** u= 7/257 ; tau(u)= 507/250 ; -124951*x^2 + 132049*y^2 + 257098*x*z - 124951*z^2
(28753/313173 : -275782/313173 : 1) C1b (77804369/3040931 : 7497981/3040931 : 1)
** u= -7/333 ; tau(u)= 673/340 ; -231151*x^2 + 221729*y^2 + 452978*x*z - 231151*z^2
(-3266659/4173995 : -7559268/4173995 : 1) C2b (287580/176977 : 25057/176977 : 1)
** u= -8/41 ; tau(u)= 90/49 ; -4738*x^2 + 3298*y^2 + 8164*x*z - 4738*z^2
(1123/1460 : -903/1460 : 1) C2b (204740/200701 : 20563/200701 : 1)
** u= -8/197 ; tau(u)= 402/205 ; -83986*x^2 + 77554*y^2 + 161668*x*z - 83986*z^2
(327/784 : 71/112 : 1) C2b (-3126700/1638753 : 428417/1638753 : 1)
** u= 8/205 ; tau(u)= 402/197 ; -77554*x^2 + 83986*y^2 + 161668*x*z - 77554*z^2
(6585/92941 : 578864/650587 : 1) C1b (150645/12017 : -99263/84119 : 1)
** u= -8/305 ; tau(u)= 618/313 ; -195874*x^2 + 185986*y^2 + 381988*x*z - 195874*z^2
(1288/3165 : 1981/3165 : 1) C2b (1289613/568553 : 112031/568553 : 1)
** u= 8/493 ; tau(u)= 978/485 ; -470386*x^2 + 486034*y^2 + 956548*x*z - 470386*z^2
(23379/46895 : 22352/46895 : 1) C1b (-8417651/1305961 : -901281/1305961 : 1)
** u= -11/221 ; tau(u)= 453/232 ; -107527*x^2 + 97561*y^2 + 205330*x*z - 107527*z^2
(168907/244689 : -102220/244689 : 1) C2b (5612711/14785093 : -1303933/14785093 : 1)
** u= 11/373 ; tau(u)= 735/362 ; -261967*x^2 + 278137*y^2 + 540346*x*z - 261967*z^2
(48248953/62688153 : -4230254/62688153 : 1) C1b (1600424/5329811 : -467217/5329811 : 1)
** u= -11/389 ; tau(u)= 789/400 ; -319879*x^2 + 302521*y^2 + 622642*x*z - 319879*z^2
(-17081/5001 : -22600/5001 : 1) C2b (282500817/42187148 : 26580347/42187148 : 1)
** u= -11/533 ; tau(u)= 1077/544 ; -591751*x^2 + 568057*y^2 + 1160050*x*z - 591751*z^2
(70163/196997 : -921464/1378979 : 1) C2b (-4851796/349867 : 3546757/2449069 : 1)
** u= 12/13 ; tau(u)= 14 ; 142*x^2 + 194*y^2 + 340*x*z + 142*z^2
(-144/119 : -67/119 : 1) C1b (-683/9056 : 819/9056 : 1)
** u= 12/49 ; tau(u)= 86/37 ; -2594*x^2 + 4658*y^2 + 7540*x*z - 2594*z^2
(3036/1153 : -455/1153 : 1) C1b (41152/44771 : 4413/44771 : 1)
** u= 12/121 ; tau(u)= 230/109 ; -23618*x^2 + 29138*y^2 + 53044*x*z - 23618*z^2
(6784/79263 : 64427/79263 : 1) C1b (1082368/615287 : 92871/615287 : 1)
** u= -12/185 ; tau(u)= 382/197 ; -77474*x^2 + 68306*y^2 + 146068*x*z - 77474*z^2
(311/402 : -1121/2814 : 1) C2b (69893125/4164857 : 48814317/29153999 : 1)
** u= 13/81 ; tau(u)= 149/68 ; -9079*x^2 + 12953*y^2 + 22370*x*z - 9079*z^2
(1183/4297 : -2268/4297 : 1) C1b (17005/13327 : -1555/13327 : 1)
** u= 13/245 ; tau(u)= 477/232 ; -107479*x^2 + 119881*y^2 + 227698*x*z - 107479*z^2
(39223/10901 : 25956/10901 : 1) C1b (-2178005/79289 : -214933/79289 : 1)
** u= 14 ; tau(u)= 12/13 ; -142*x^2 - 194*y^2 + 340*x*z - 142*z^2
(2/3 : -1/3 : 1) C1a (-9064/3185 : -201/637 : 1)
** u= 16/41 ; tau(u)= 66/25 ; -994*x^2 + 3106*y^2 + 4612*x*z - 994*z^2
(-451/1316 : -175/188 : 1) C1b (-82220/16027 : 7467/16027 : 1)
** u= -16/49 ; tau(u)= 114/65 ; -8194*x^2 + 4546*y^2 + 13252*x*z - 8194*z^2
(285/691 : 658/691 : 1) C2b (-27377/2307 : 3467/2307 : 1)
** u= 17/25 ; tau(u)= 33/8 ; 161*x^2 + 961*y^2 + 1378*x*z + 161*z^2
(-3/7 : 20/31 : 1) C1b (28/43 : -141/1333 : 1)
** u= -17/65 ; tau(u)= 147/82 ; -13159*x^2 + 8161*y^2 + 21898*x*z - 13159*z^2
(-103/1389 : 1874/1389 : 1) C2b (535688/83753 : -56469/83753 : 1)
** u= 17/229 ; tau(u)= 441/212 ; -89599*x^2 + 104593*y^2 + 194770*x*z - 89599*z^2
(88583/191473 : -80892/191473 : 1) C1b (-4722197/1018836 : -505909/1018836 : 1)
** u= -17/233 ; tau(u)= 483/250 ; -124711*x^2 + 108289*y^2 + 233578*x*z - 124711*z^2
(21313/38577 : -21530/38577 : 1) C2b (32974279/532176 : 3378361/532176 : 1)
** u= 19/29 ; tau(u)= 39/10 ; 161*x^2 + 1321*y^2 + 1882*x*z + 161*z^2
(-1097/2523 : -1738/2523 : 1) C1b (327722440/653413 : 27527313/653413 : 1)
** u= -19/49 ; tau(u)= 117/68 ; -8887*x^2 + 4441*y^2 + 14050*x*z - 8887*z^2
(153/223 : 196/223 : 1) C2b (-165747/49244 : -25099/49244 : 1)
** u= 19/149 ; tau(u)= 279/130 ; -33439*x^2 + 44041*y^2 + 78202*x*z - 33439*z^2
(7299/4079 : 466/4079 : 1) C1b (353681/210064 : 30479/210064 : 1)
** u= -20/153 ; tau(u)= 326/173 ; -59458*x^2 + 46418*y^2 + 106676*x*z - 59458*z^2
(-29/4504 : 5127/4504 : 1) C2b (1728890415/32133211 : 182520761/32133211 : 1)
** u= -20/521 ; tau(u)= 1062/541 ; -584962*x^2 + 542482*y^2 + 1128244*x*z - 584962*z^2
(-466/1213 : -1731/1213 : 1) C2b (-31694280/107971517 : -12919223/107971517 : 1)
** u= 21/37 ; tau(u)= 53/16 ; -71*x^2 + 2297*y^2 + 3250*x*z - 71*z^2
(9/431 : 16/431 : 1) C1b (282700/26459 : -23715/26459 : 1)
** u= -21/149 ; tau(u)= 319/170 ; -57359*x^2 + 43961*y^2 + 102202*x*z - 57359*z^2
(-14759/26981 : 46474/26981 : 1) C2b (-76448/760505 : -86457/760505 : 1)
** u= 21/169 ; tau(u)= 317/148 ; -43367*x^2 + 56681*y^2 + 100930*x*z - 43367*z^2
(7779/3521 : -2648/3521 : 1) C1b (-172106716/1693717 : 16227927/1693717 : 1)
** u= 21/313 ; tau(u)= 605/292 ; -170087*x^2 + 195497*y^2 + 366466*x*z - 170087*z^2
(-6499/26823 : 31456/26823 : 1) C1b (926140/1311197 : -115989/1311197 : 1)
** u= -23/113 ; tau(u)= 249/136 ; -36463*x^2 + 25009*y^2 + 62530*x*z - 36463*z^2
(8223/10453 : 6556/10453 : 1) C2b (821329/495195 : 14851/99039 : 1)
** u= -24/241 ; tau(u)= 506/265 ; -139874*x^2 + 115586*y^2 + 256612*x*z - 139874*z^2
(-9855/2053 : -12944/2053 : 1) C2b (27764324/1375231 : 2834691/1375231 : 1)
** u= 24/389 ; tau(u)= 754/365 ; -265874*x^2 + 302066*y^2 + 569092*x*z - 265874*z^2
(16259/29427 : 9668/29427 : 1) C1b (1370903/1926052 : 170637/1926052 : 1)
** u= -24/541 ; tau(u)= 1106/565 ; -637874*x^2 + 584786*y^2 + 1223812*x*z - 637874*z^2
(12212887/37445339 : 1594856/2202667 : 1) C2b (116694295/54645563 : -10156197/54645563 : 1)
** u= -25/81 ; tau(u)= 187/106 ; -21847*x^2 + 12497*y^2 + 35594*x*z - 21847*z^2
(19367/7091 : 2682/1013 : 1) C2b (486313/1377040 : 135943/1377040 : 1)
** u= -25/121 ; tau(u)= 267/146 ; -42007*x^2 + 28657*y^2 + 71914*x*z - 42007*z^2
(-8087/164833 : 208010/164833 : 1) C2b (-13264/186905 : -21729/186905 : 1)
** u= 25/173 ; tau(u)= 321/148 ; -43183*x^2 + 59233*y^2 + 103666*x*z - 43183*z^2
(-98039/193251 : 259600/193251 : 1) C1b (-2050540/1464777 : -276947/1464777 : 1)
** u= 25/257 ; tau(u)= 489/232 ; -107023*x^2 + 131473*y^2 + 239746*x*z - 107023*z^2
(-827/3487 : -3964/3487 : 1) C1b (682293/136495 : -60167/136495 : 1)
** u= -28/85 ; tau(u)= 198/113 ; -24754*x^2 + 13666*y^2 + 39988*x*z - 24754*z^2
(479/22 : -621/22 : 1) C2b (-2874568/1148655 : 445001/1148655 : 1)
** u= 28/405 ; tau(u)= 782/377 ; -283474*x^2 + 327266*y^2 + 612308*x*z - 283474*z^2
(137831/222134 : 43731/222134 : 1) C1b (-294837320/74568427 : -32329769/74568427 : 1)
** u= 29/109 ; tau(u)= 189/80 ; -11959*x^2 + 22921*y^2 + 36562*x*z - 11959*z^2
(-643/17539 : -13368/17539 : 1) C1b (6132/2525 : 517/2525 : 1)
** u= -29/557 ; tau(u)= 1143/586 ; -685951*x^2 + 619657*y^2 + 1307290*x*z - 685951*z^2
(-497309/738711 : -1285646/738711 : 1) C2b (-5874300353/203529269 : -611501351/203529269 : 1)
** u= 30/13 ; tau(u)= 4/17 ; 322*x^2 - 562*y^2 + 916*x*z + 322*z^2
(-324/107 : 101/107 : 1) C1a (-824/1421 : -123/1421 : 1)
** u= 31/65 ; tau(u)= 99/34 ; -1351*x^2 + 7489*y^2 + 10762*x*z - 1351*z^2
(1553/18425 : -4534/18425 : 1) C1b (2619528/342355 : 219199/342355 : 1)
** u= -31/361 ; tau(u)= 753/392 ; -306367*x^2 + 259681*y^2 + 567970*x*z - 306367*z^2
(6174737/22747107 : -18660964/22747107 : 1) C2b (-32112357/2358449 : 3479999/2358449 : 1)
** u= 31/569 ; tau(u)= 1107/538 ; -577927*x^2 + 646561*y^2 + 1226410*x*z - 577927*z^2
(286151/201751 : -8202/201751 : 1) C1b (142417679/309928 : -13786579/309928 : 1)
** u= 32/37 ; tau(u)= 42/5 ; 974*x^2 + 1714*y^2 + 2788*x*z + 974*z^2
(-9/22 : 1/22 : 1) C1b (-925/71 : 81/71 : 1)
** u= 32/49 ; tau(u)= 66/17 ; 446*x^2 + 3778*y^2 + 5380*x*z + 446*z^2
(-178/291 : -245/291 : 1) C1b (-16406940/7113541 : 1455335/7113541 : 1)
** u= 32/145 ; tau(u)= 258/113 ; -24514*x^2 + 41026*y^2 + 67588*x*z - 24514*z^2
(417/12094 : 8899/12094 : 1) C1b (1531452/170125 : -133501/170125 : 1)
** u= 32/565 ; tau(u)= 1098/533 ; -567154*x^2 + 637426*y^2 + 1206628*x*z - 567154*z^2
(8849/14020 : 3117/14020 : 1) C1b (-183860/2183597 : -220309/2183597 : 1)
** u= 33/8 ; tau(u)= 17/25 ; -161*x^2 - 961*y^2 + 1378*x*z - 161*z^2
(9/61 : 380/1891 : 1) C1a (-1835/1364 : 6297/42284 : 1)
** u= 33/20 ; tau(u)= -7/13 ; 751*x^2 - 289*y^2 + 1138*x*z + 751*z^2
(-1/583 : 15956/9911 : 1) C1a (12644/65 : 30113/1105 : 1)
** u= 35/37 ; tau(u)= 39/2 ; 1217*x^2 + 1513*y^2 + 2746*x*z + 1217*z^2
(-5/7 : -2/7 : 1) C1b (119373/19048 : 12223/19048 : 1)
** u= 35/117 ; tau(u)= 199/82 ; -12223*x^2 + 26153*y^2 + 40826*x*z - 12223*z^2
(6697/23029 : 5298/23029 : 1) C1b (378848/15273 : 32927/15273 : 1)
** u= -35/221 ; tau(u)= 477/256 ; -129847*x^2 + 96457*y^2 + 228754*x*z - 129847*z^2
(-14435/80643 : -108608/80643 : 1) C2b (2313973/2482460 : -242183/2482460 : 1)
** u= -35/257 ; tau(u)= 549/292 ; -169303*x^2 + 130873*y^2 + 302626*x*z - 169303*z^2
(79559/343981 : -313008/343981 : 1) C2b (325617/4688875 : -483047/4688875 : 1)
** u= 37/233 ; tau(u)= 429/196 ; -75463*x^2 + 107209*y^2 + 185410*x*z - 75463*z^2
(253997/2439407 : 1778336/2439407 : 1) C1b (86696860/37224171 : -7329625/37224171 : 1)
** u= -37/261 ; tau(u)= 559/298 ; -176239*x^2 + 134873*y^2 + 313850*x*z - 176239*z^2
(481369/365329 : -260694/365329 : 1) C2b (-7672231/981675 : 35477/39267 : 1)
** u= 39/2 ; tau(u)= 35/37 ; -1217*x^2 - 1513*y^2 + 2746*x*z - 1217*z^2
(7/5 : -2/5 : 1) C1a (44760/61151 : -5459/61151 : 1)
** u= 39/10 ; tau(u)= 19/29 ; -161*x^2 - 1321*y^2 + 1882*x*z - 161*z^2
(3113/23499 : -854/3357 : 1) C1a (-9845/7856 : -1101/7856 : 1)
** u= -40/117 ; tau(u)= 274/157 ; -47698*x^2 + 25778*y^2 + 76676*x*z - 47698*z^2
(27635/42419 : 35436/42419 : 1) C2b (-606162300/60414851 : -78327161/60414851 : 1)
** u= -41/401 ; tau(u)= 843/442 ; -389047*x^2 + 319921*y^2 + 712330*x*z - 389047*z^2
(1501/2169 : 7706/15183 : 1) C2b (-8709441/284533 : 6517327/1991731 : 1)
** u= -41/521 ; tau(u)= 1083/562 ; -630007*x^2 + 541201*y^2 + 1174570*x*z - 630007*z^2
(284407/685011 : -466450/685011 : 1) C2b (4926248/6844139 : -612711/6844139 : 1)
** u= 42/5 ; tau(u)= 32/37 ; -974*x^2 - 1714*y^2 + 2788*x*z - 974*z^2
(141/59 : 16/59 : 1) C1a (-596/769 : 101/769 : 1)
** u= -43/117 ; tau(u)= 277/160 ; -49351*x^2 + 25529*y^2 + 78578*x*z - 49351*z^2
(2869/1363 : 19128/9541 : 1) C2b (867140/406121 : 595223/2842847 : 1)
** u= -43/313 ; tau(u)= 669/356 ; -251623*x^2 + 194089*y^2 + 449410*x*z - 251623*z^2
(-73/177 : 1948/1239 : 1) C2b (5868948/811061 : -4089289/5677427 : 1)
** u= -44/113 ; tau(u)= 270/157 ; -47362*x^2 + 23602*y^2 + 74836*x*z - 47362*z^2
(10997/5944 : -10311/5944 : 1) C2b (371792/64605 : -41929/64605 : 1)
** u= 44/117 ; tau(u)= 190/73 ; -8722*x^2 + 25442*y^2 + 38036*x*z - 8722*z^2
(25621/118498 : 22359/118498 : 1) C1b (15463/136032 : 11471/136032 : 1)
** u= -44/125 ; tau(u)= 294/169 ; -55186*x^2 + 29314*y^2 + 88372*x*z - 55186*z^2
(2/11 : 13/11 : 1) C2b (308961/341320 : 34607/341320 : 1)
** u= -44/245 ; tau(u)= 534/289 ; -165106*x^2 + 118114*y^2 + 287092*x*z - 165106*z^2
(11588/11651 : 7021/11651 : 1) C2b (-9295839/4015336 : 101771/308872 : 1)
** u= -44/405 ; tau(u)= 854/449 ; -401266*x^2 + 326114*y^2 + 731252*x*z - 401266*z^2
(1873/1216 : -41589/49856 : 1) C2b (201552/198095 : -820141/8121895 : 1)
** u= -47/245 ; tau(u)= 537/292 ; -168319*x^2 + 117841*y^2 + 290578*x*z - 168319*z^2
(92163/249817 : 210952/249817 : 1) C2b (-131335689/12846685 : 15376537/12846685 : 1)
** u= 47/457 ; tau(u)= 867/410 ; -333991*x^2 + 415489*y^2 + 753898*x*z - 333991*z^2
(109559/262299 : 113186/262299 : 1) C1b (-115895/317048 : -36277/317048 : 1)
** u= -48/305 ; tau(u)= 658/353 ; -246914*x^2 + 183746*y^2 + 435268*x*z - 246914*z^2
(-3642/9041 : -14341/9041 : 1) C2b (-7253044/2187655 : 940293/2187655 : 1)
** u= -49/529 ; tau(u)= 1107/578 ; -665767*x^2 + 557281*y^2 + 1227850*x*z - 665767*z^2
(-815257/15997651 : 18310530/15997651 : 1) C2b (7198888/3105189 : -637199/3105189 : 1)
** u= -52/565 ; tau(u)= 1182/617 ; -758674*x^2 + 635746*y^2 + 1399828*x*z - 758674*z^2
(12451/9412 : -5717/9412 : 1) C2b (55482800/9454819 : 5322707/9454819 : 1)
** u= 53/16 ; tau(u)= 21/37 ; 71*x^2 - 2297*y^2 + 3250*x*z + 71*z^2
(-43/4101 : -520/4101 : 1) C1a (962021/35012 : -80631/35012 : 1)
** u= -53/45 ; tau(u)= 143/98 ; -16399*x^2 + 1241*y^2 + 23258*x*z - 16399*z^2
(7499/8195 : -21882/8195 : 1) C2b (3632/915 : -931/915 : 1)
** u= -53/557 ; tau(u)= 1167/610 ; -741391*x^2 + 617689*y^2 + 1364698*x*z - 741391*z^2
(1021263/1123783 : -481682/1123783 : 1) C2b (-13956057/12608165 : -2441323/12608165 : 1)
** u= 54/25 ; tau(u)= 4/29 ; 1234*x^2 - 1666*y^2 + 2932*x*z + 1234*z^2
(-83/152 : -25/1064 : 1) C1a (-8795/3624 : 5213/25368 : 1)
** u= 55/353 ; tau(u)= 651/298 ; -174583*x^2 + 246193*y^2 + 426826*x*z - 174583*z^2
(82751/571839 : 393322/571839 : 1) C1b (516829/1029695 : -87499/1029695 : 1)
** u= -56/65 ; tau(u)= 186/121 ; -26146*x^2 + 5314*y^2 + 37732*x*z - 26146*z^2
(4/7 : -11/7 : 1) C2b (-22233/30187 : -9061/30187 : 1)
** u= -56/221 ; tau(u)= 498/277 ; -150322*x^2 + 94546*y^2 + 251140*x*z - 150322*z^2
(78139/725511 : 834272/725511 : 1) C2b (45707660/1377491 : 5148435/1377491 : 1)
** u= -56/225 ; tau(u)= 506/281 ; -154786*x^2 + 98114*y^2 + 259172*x*z - 154786*z^2
(20356/21331 : -14985/21331 : 1) C2b (-19594663/26412 : -2242541/26412 : 1)
** u= -56/233 ; tau(u)= 522/289 ; -163906*x^2 + 105442*y^2 + 275620*x*z - 163906*z^2
(-1301/383 : 2040/383 : 1) C2b (-293508/452591 : -76223/452591 : 1)
** u= 56/313 ; tau(u)= 570/257 ; -128962*x^2 + 192802*y^2 + 328036*x*z - 128962*z^2
(633589/12279957 : 9375316/12279957 : 1) C1b (-69843884/131885 : -6414763/131885 : 1)
** u= 57/32 ; tau(u)= -7/25 ; 1999*x^2 - 1201*y^2 + 3298*x*z + 1999*z^2
(-957/5627 : 6280/5627 : 1) C1a (1000764/55331 : -120703/55331 : 1)
** u= 57/97 ; tau(u)= 137/40 ; 49*x^2 + 15569*y^2 + 22018*x*z + 49*z^2
(-4611/113023 : 26396/113023 : 1) C1b (166996/220685 : 23181/220685 : 1)
** u= -57/185 ; tau(u)= 427/242 ; -113879*x^2 + 65201*y^2 + 185578*x*z - 113879*z^2
(-110835/1557577 : 2179474/1557577 : 1) C2b (279208/267263 : 28539/267263 : 1)
** u= 59/549 ; tau(u)= 1039/490 ; -476719*x^2 + 599321*y^2 + 1083002*x*z - 476719*z^2
(-1131355/1376957 : -2311134/1376957 : 1) C1b (-1028723/8212335 : -824213/8212335 : 1)
** u= -60/121 ; tau(u)= 302/181 ; -61922*x^2 + 25682*y^2 + 94804*x*z - 61922*z^2
(-2016/10337 : -18557/10337 : 1) C2b (8681069/3439864 : -938379/3439864 : 1)
** u= 60/509 ; tau(u)= 958/449 ; -399602*x^2 + 514562*y^2 + 921364*x*z - 399602*z^2
(27134/764323 : 92263/109189 : 1) C1b (8115056/8345761 : -824871/8345761 : 1)
** u= 61/65 ; tau(u)= 69/4 ; 3689*x^2 + 4729*y^2 + 8482*x*z + 3689*z^2
(-9063/8731 : 4288/8731 : 1) C1b (-825980/276941 : -70513/276941 : 1)
** u= 61/225 ; tau(u)= 389/164 ; -50071*x^2 + 97529*y^2 + 155042*x*z - 50071*z^2
(14335/292681 : 193428/292681 : 1) C1b (-15151044/10397825 : -1859617/10397825 : 1)
** u= 61/317 ; tau(u)= 573/256 ; -127351*x^2 + 197257*y^2 + 332050*x*z - 127351*z^2
(379749/1682651 : 919456/1682651 : 1) C1b (-4363175/929532 : -437915/929532 : 1)
** u= 64/221 ; tau(u)= 378/157 ; -45202*x^2 + 93586*y^2 + 146980*x*z - 45202*z^2
(5047/51803 : -29964/51803 : 1) C1b (-221040028/15577321 : -19955579/15577321 : 1)
** u= 64/585 ; tau(u)= 1106/521 ; -538786*x^2 + 680354*y^2 + 1227332*x*z - 538786*z^2
(210919/356203 : 13332/356203 : 1) C1b (100218004/45420879 : 8510447/45420879 : 1)
** u= -65/281 ; tau(u)= 627/346 ; -235207*x^2 + 153697*y^2 + 397354*x*z - 235207*z^2
(-2240887/1061549 : 3944506/1061549 : 1) C2b (24893917/4650767 : 2540467/4650767 : 1)
** u= 65/421 ; tau(u)= 777/356 ; -249247*x^2 + 350257*y^2 + 607954*x*z - 249247*z^2
(225277/72231 : -107624/72231 : 1) C1b (-52268060/5567723 : 5078557/5567723 : 1)
** u= 66/17 ; tau(u)= 32/49 ; -446*x^2 - 3778*y^2 + 5380*x*z - 446*z^2
(5951/20649 : -10976/20649 : 1) C1a (959884/206353 : -81019/206353 : 1)
** u= 66/25 ; tau(u)= 16/41 ; 994*x^2 - 3106*y^2 + 4612*x*z + 994*z^2
(1015/2603 : -2534/2603 : 1) C1a (91773/24575 : 8573/24575 : 1)
** u= -68/125 ; tau(u)= 318/193 ; -69874*x^2 + 26626*y^2 + 105748*x*z - 69874*z^2
(-64/71 : 205/71 : 1) C2b (-20035/132064 : 20483/132064 : 1)
** u= 68/225 ; tau(u)= 382/157 ; -44674*x^2 + 96626*y^2 + 150548*x*z - 44674*z^2
(496/2293 : 879/2293 : 1) C1b (4009757/43440 : 351041/43440 : 1)
** u= 68/433 ; tau(u)= 798/365 ; -261826*x^2 + 370354*y^2 + 641428*x*z - 261826*z^2
(315097/4831732 : 3733343/4831732 : 1) C1b (-4368567/327197 : -417793/327197 : 1)
** u= -68/569 ; tau(u)= 1206/637 ; -806914*x^2 + 642898*y^2 + 1459060*x*z - 806914*z^2
(-32728/526669 : 623385/526669 : 1) C2b (-20564392/16167771 : 3437999/16167771 : 1)
** u= 69/4 ; tau(u)= 61/65 ; -3689*x^2 - 4729*y^2 + 8482*x*z - 3689*z^2
(565/333 : -44/333 : 1) C1a (2154268/281005 : -192959/281005 : 1)
** u= -69/157 ; tau(u)= 383/226 ; -97391*x^2 + 44537*y^2 + 151450*x*z - 97391*z^2
(358093/1558749 : -1922350/1558749 : 1) C2b (14885896/510053 : -1889529/510053 : 1)
** u= 69/557 ; tau(u)= 1045/488 ; -471527*x^2 + 615737*y^2 + 1096786*x*z - 471527*z^2
(140117/31207 : 89396/31207 : 1) C1b (-1019783725/14634316 : 96361347/14634316 : 1)
** u= 71/153 ; tau(u)= 235/82 ; -8407*x^2 + 41777*y^2 + 60266*x*z - 8407*z^2
(10799/88427 : 14814/88427 : 1) C1b (428032/506593 : 52049/506593 : 1)
** u= -71/269 ; tau(u)= 609/340 ; -226159*x^2 + 139681*y^2 + 375922*x*z - 226159*z^2
(28997/933731 : -50332/40597 : 1) C2b (-313578692/142568267 : -47933033/142568267 : 1)
** u= 73/221 ; tau(u)= 369/148 ; -38479*x^2 + 92353*y^2 + 141490*x*z - 38479*z^2
(459/25369 : -688/1103 : 1) C1b (62089661/455767 : -5396647/455767 : 1)
** u= -73/369 ; tau(u)= 811/442 ; -385399*x^2 + 266993*y^2 + 663050*x*z - 385399*z^2
(164159/207287 : -128130/207287 : 1) C2b (4496304/2617043 : -405677/2617043 : 1)
** u= -73/577 ; tau(u)= 1227/650 ; -839671*x^2 + 660529*y^2 + 1510858*x*z - 839671*z^2
(-1119611/788281 : 2098130/788281 : 1) C2b (-108899255/9081608 : 12151843/9081608 : 1)
** u= 75/541 ; tau(u)= 1007/466 ; -428687*x^2 + 579737*y^2 + 1019674*x*z - 428687*z^2
(319123/5343623 : -4265030/5343623 : 1) C1b (128699915/4014121 : -11856699/4014121 : 1)
** u= -76/97 ; tau(u)= 270/173 ; -54082*x^2 + 13042*y^2 + 78676*x*z - 54082*z^2
(24/35 : 7/5 : 1) C2b (-133207/39637 : 2167/3049 : 1)
** u= 76/245 ; tau(u)= 414/169 ; -51346*x^2 + 114274*y^2 + 177172*x*z - 51346*z^2
(52086/215389 : 68341/215389 : 1) C1b (837289/256880 : 70217/256880 : 1)
** u= -76/277 ; tau(u)= 630/353 ; -243442*x^2 + 147682*y^2 + 402676*x*z - 243442*z^2
(1961/2608 : -1899/2608 : 1) C2b (-12906405/15373519 : 2945687/15373519 : 1)
** u= -76/405 ; tau(u)= 886/481 ; -456946*x^2 + 322274*y^2 + 790772*x*z - 456946*z^2
(45046/67537 : 43353/67537 : 1) C2b (5361120/1631777 : -508589/1631777 : 1)
** u= 76/449 ; tau(u)= 822/373 ; -272482*x^2 + 397426*y^2 + 681460*x*z - 272482*z^2
(390523/1101768 : -446159/1101768 : 1) C1b (278281/101608 : 1809/7816 : 1)
** u= 77/81 ; tau(u)= 85/4 ; 5897*x^2 + 7193*y^2 + 13154*x*z + 5897*z^2
(-2063/3319 : 36/3319 : 1) C1b (-94588/31533 : 8111/31533 : 1)
** u= 77/109 ; tau(u)= 141/32 ; 3881*x^2 + 17833*y^2 + 25810*x*z + 3881*z^2
(-14779/36579 : 21064/36579 : 1) C1b (-324052/139399 : 28183/139399 : 1)
** u= 77/241 ; tau(u)= 405/164 ; -47863*x^2 + 110233*y^2 + 169954*x*z - 47863*z^2
(79/393 : -148/393 : 1) C1b (3769939/2406281 : 337153/2406281 : 1)
** u= 77/337 ; tau(u)= 597/260 ; -129271*x^2 + 221209*y^2 + 362338*x*z - 129271*z^2
(10889/42447 : -19108/42447 : 1) C1b (11491255/3035933 : -971417/3035933 : 1)
** u= 77/349 ; tau(u)= 621/272 ; -142039*x^2 + 237673*y^2 + 391570*x*z - 142039*z^2
(4533527/1778617 : -942792/1778617 : 1) C1b (81484/1213907 : -107179/1213907 : 1)
** u= 77/373 ; tau(u)= 669/296 ; -169303*x^2 + 272329*y^2 + 453490*x*z - 169303*z^2
(-64789/1206513 : -1018700/1206513 : 1) C1b (58631284/84391863 : -7522891/84391863 : 1)
** u= -77/477 ; tau(u)= 1031/554 ; -607903*x^2 + 449129*y^2 + 1068890*x*z - 607903*z^2
(228373/216877 : 127986/216877 : 1) C2b (-6428904/14951815 : -419953/2990363 : 1)
** u= -79/85 ; tau(u)= 249/164 ; -47551*x^2 + 8209*y^2 + 68242*x*z - 47551*z^2
(55/813 : 1864/813 : 1) C2b (731371/388996 : -109197/388996 : 1)
** u= -79/433 ; tau(u)= 945/512 ; -518047*x^2 + 368737*y^2 + 899266*x*z - 518047*z^2
(31757/29971 : -18912/29971 : 1) C2b (-6305780/1456187 : 795859/1456187 : 1)
** u= 80/109 ; tau(u)= 138/29 ; 4718*x^2 + 17362*y^2 + 25444*x*z + 4718*z^2
(-609/205 : -266/205 : 1) C1b (-339759/256796 : 32881/256796 : 1)
** u= -80/149 ; tau(u)= 378/229 ; -98482*x^2 + 38002*y^2 + 149284*x*z - 98482*z^2
(56954/352381 : -501357/352381 : 1) C2b (-7290335/51156 : 1021379/51156 : 1)
** u= -80/257 ; tau(u)= 594/337 ; -220738*x^2 + 125698*y^2 + 359236*x*z - 220738*z^2
(-85823/287159 : -477678/287159 : 1) C2b (-1163415/573484 : 188159/573484 : 1)
** u= 80/277 ; tau(u)= 474/197 ; -71218*x^2 + 147058*y^2 + 231076*x*z - 71218*z^2
(44156/245625 : -114541/245625 : 1) C1b (-33214148/1263957 : 2965667/1263957 : 1)
** u= 80/369 ; tau(u)= 658/289 ; -160642*x^2 + 265922*y^2 + 439364*x*z - 160642*z^2
(163/20422 : 15699/20422 : 1) C1b (579081/306965 : 49501/306965 : 1)
** u= -80/441 ; tau(u)= 962/521 ; -536482*x^2 + 382562*y^2 + 931844*x*z - 536482*z^2
(-18226/292973 : 365841/292973 : 1) C2b (-81220/775719 : 90611/775719 : 1)
** u= -83/353 ; tau(u)= 789/436 ; -373303*x^2 + 242329*y^2 + 629410*x*z - 373303*z^2
(-335167/8622911 : -11055380/8622911 : 1) C2b (-77313457/3383956 : -8999737/3383956 : 1)
** u= -84/197 ; tau(u)= 478/281 ; -150866*x^2 + 70562*y^2 + 235540*x*z - 150866*z^2
(9561/17276 : 16799/17276 : 1) C2b (64446581/22163992 : -6820167/22163992 : 1)
** u= 85/4 ; tau(u)= 77/81 ; -5897*x^2 - 7193*y^2 + 13154*x*z - 5897*z^2
(4403/3067 : -1044/3067 : 1) C1a (31533/94588 : 8111/94588 : 1)
** u= 86/37 ; tau(u)= 12/49 ; 2594*x^2 - 4658*y^2 + 7540*x*z + 2594*z^2
(-1679/76 : 1169/76 : 1) C1a (2128/15871 : -1497/15871 : 1)
** u= -87/337 ; tau(u)= 761/424 ; -351983*x^2 + 219569*y^2 + 586690*x*z - 351983*z^2
(-8129/13293 : 182260/93051 : 1) C2b (-18311/114443 : -101667/801101 : 1)
** u= -87/349 ; tau(u)= 785/436 ; -372623*x^2 + 236033*y^2 + 623794*x*z - 372623*z^2
(-58057/4821 : 546608/33747 : 1) C2b (1260401/406819 : -855459/2847733 : 1)
** u= -88/81 ; tau(u)= 250/169 ; -49378*x^2 + 5378*y^2 + 70244*x*z - 49378*z^2
(7019/8711 : 18720/8711 : 1) C2b (-459852/34187 : 7247/2011 : 1)
** u= 88/137 ; tau(u)= 186/49 ; 2942*x^2 + 29794*y^2 + 42340*x*z + 2942*z^2
(-2279/32337 : -980/32337 : 1) C1b (19997/15769 : 2207/15769 : 1)
** u= -88/193 ; tau(u)= 474/281 ; -150178*x^2 + 66754*y^2 + 232420*x*z - 150178*z^2
(6401/1788 : -7715/1788 : 1) C2b (229661/1504337 : 179499/1504337 : 1)
** u= -88/277 ; tau(u)= 642/365 ; -258706*x^2 + 145714*y^2 + 419908*x*z - 258706*z^2
(77653/235425 : -237544/235425 : 1) C2b (43724499/53363356 : -5184859/53363356 : 1)
** u= 90/49 ; tau(u)= -8/41 ; 4738*x^2 - 3298*y^2 + 8164*x*z + 4738*z^2
(-1613/1789 : 1092/1789 : 1) C1a (26405/4836 : 251/372 : 1)
** u= 91/461 ; tau(u)= 831/370 ; -265519*x^2 + 416761*y^2 + 698842*x*z - 265519*z^2
(522179/1136199 : 36266/1136199 : 1) C1b (53310317/105754328 : 8992743/105754328 : 1)
** u= 91/477 ; tau(u)= 863/386 ; -289711*x^2 + 446777*y^2 + 753050*x*z - 289711*z^2
(1006769/3136829 : 1309506/3136829 : 1) C1b (-18902697/14578925 : 510853/2915785 : 1)
** u= -92/225 ; tau(u)= 542/317 ; -192514*x^2 + 92786*y^2 + 302228*x*z - 192514*z^2
(29261/75506 : 80055/75506 : 1) C2b (1653762280/80269593 : 203660921/80269593 : 1)
** u= 92/241 ; tau(u)= 390/149 ; -35938*x^2 + 107698*y^2 + 160564*x*z - 35938*z^2
(-1795/1046 : 2059/1046 : 1) C1b (1640239/865875 : 143867/865875 : 1)
** u= 92/361 ; tau(u)= 630/269 ; -136258*x^2 + 252178*y^2 + 405364*x*z - 136258*z^2
(-3284/75661 : -59147/75661 : 1) C1b (1556240/63774957 : -5643949/63774957 : 1)
** u= -97/73 ; tau(u)= 243/170 ; -48391*x^2 + 1249*y^2 + 68458*x*z - 48391*z^2
(12763/27719 : 129186/27719 : 1) C2b (32096/10875 : -13331/10875 : 1)
** u= 97/293 ; tau(u)= 489/196 ; -67423*x^2 + 162289*y^2 + 248530*x*z - 67423*z^2
(-6700891/261172731 : 176173508/261172731 : 1) C1b (223357713/41872436 : -18789307/41872436 : 1)
** u= 99/34 ; tau(u)= 31/65 ; 1351*x^2 - 7489*y^2 + 10762*x*z + 1351*z^2
(333/2783 : 1658/2783 : 1) C1a (-20240/163759 : -13703/163759 : 1)
** u= 102/49 ; tau(u)= 4/53 ; 4786*x^2 - 5602*y^2 + 10420*x*z + 4786*z^2
(-977/6072 : 4613/6072 : 1) C1a (-497432/87329 : 44511/87329 : 1)
** u= -103/225 ; tau(u)= 553/328 ; -204559*x^2 + 90641*y^2 + 316418*x*z - 204559*z^2
(253/7 : -372/7 : 1) C2b (-3013924/2622585 : -672653/2622585 : 1)
** u= 104/409 ; tau(u)= 714/305 ; -175234*x^2 + 323746*y^2 + 520612*x*z - 175234*z^2
(-154/381 : 431/381 : 1) C1b (114791143/273983115 : -23107253/273983115 : 1)
** u= 105/52 ; tau(u)= 1/53 ; 5407*x^2 - 5617*y^2 + 11026*x*z + 5407*z^2
(-1583/473 : 1076/473 : 1) C1a (2055780/136667 : -209591/136667 : 1)
** u= 107/117 ; tau(u)= 127/10 ; 11249*x^2 + 15929*y^2 + 27578*x*z + 11249*z^2
(-13739/17245 : -8178/17245 : 1) C1b (393981/231824 : -49291/231824 : 1)
** u= -109/349 ; tau(u)= 807/458 ; -407647*x^2 + 231721*y^2 + 663130*x*z - 407647*z^2
(-59297/109783 : 1501622/768481 : 1) C2b (-488920/1392779 : 1446975/9749453 : 1)
** u= -109/541 ; tau(u)= 1191/650 ; -833119*x^2 + 573481*y^2 + 1430362*x*z - 833119*z^2
(-337351/77961 : 489650/77961 : 1) C2b (2343568/3435515 : 312637/3435515 : 1)
** u= 111/241 ; tau(u)= 371/130 ; -21479*x^2 + 103841*y^2 + 149962*x*z - 21479*z^2
(8879/286687 : 115502/286687 : 1) C1b (108766289/2033491 : -9173499/2033491 : 1)
** u= -111/545 ; tau(u)= 1201/656 ; -848351*x^2 + 581729*y^2 + 1454722*x*z - 848351*z^2
(760833/694727 : 475648/694727 : 1) C2b (169544285/273288772 : -24727149/273288772 : 1)
** u= 112/153 ; tau(u)= 194/41 ; 9182*x^2 + 34274*y^2 + 50180*x*z + 9182*z^2
(-48007/111323 : -62346/111323 : 1) C1b (-3239268/899929 : -272377/899929 : 1)
** u= 112/257 ; tau(u)= 402/145 ; -29506*x^2 + 119554*y^2 + 174148*x*z - 29506*z^2
(-1437/21748 : 293431/500204 : 1) C1b (-16188/9535 : 39319/219305 : 1)
** u= 112/401 ; tau(u)= 690/289 ; -154498*x^2 + 309058*y^2 + 488644*x*z - 154498*z^2
(868/2481 : -221/2481 : 1) C1b (8839/72291 : -6193/72291 : 1)
** u= 112/461 ; tau(u)= 810/349 ; -231058*x^2 + 412498*y^2 + 668644*x*z - 231058*z^2
(-43375/10664527 : 8028522/10664527 : 1) C1b (2065263836/195446455 : -179708717/195446455 : 1)
** u= -112/493 ; tau(u)= 1098/605 ; -719506*x^2 + 473554*y^2 + 1218148*x*z - 719506*z^2
(591583/628493 : 418902/628493 : 1) C2b (1563708/3401785 : 313817/3401785 : 1)
** u= -112/585 ; tau(u)= 1282/697 ; -959074*x^2 + 671906*y^2 + 1656068*x*z - 959074*z^2
(359/557 : 366/557 : 1) C2b (-88290100/24265971 : 11514193/24265971 : 1)
** u= 114/65 ; tau(u)= -16/49 ; 8194*x^2 - 4546*y^2 + 13252*x*z + 8194*z^2
(29/153 : -14/9 : 1) C1a (606489/80099 : 79169/80099 : 1)
** u= 115/221 ; tau(u)= 327/106 ; -9247*x^2 + 84457*y^2 + 120154*x*z - 9247*z^2
(165787/2148355 : -40402/2148355 : 1) C1b (6590264/4718849 : -654981/4718849 : 1)
** u= -115/577 ; tau(u)= 1269/692 ; -944503*x^2 + 652633*y^2 + 1623586*x*z - 944503*z^2
(49453/238607 : 237864/238607 : 1) C2b (23743911/22517621 : -2350891/22517621 : 1)
** u= 116/157 ; tau(u)= 198/41 ; 10094*x^2 + 35842*y^2 + 52660*x*z + 10094*z^2
(-15994/66679 : -15579/66679 : 1) C1b (-306040/106927 : -25945/106927 : 1)
** u= 116/397 ; tau(u)= 678/281 ; -144466*x^2 + 301762*y^2 + 473140*x*z - 144466*z^2
(712441/2845408 : -969835/2845408 : 1) C1b (-172822456/210029247 : -27318199/210029247 : 1)
** u= 117/68 ; tau(u)= -19/49 ; 8887*x^2 - 4441*y^2 + 14050*x*z + 8887*z^2
(-3097/1263 : -3164/1263 : 1) C1a (2834604/204763 : 371483/204763 : 1)
** u= 119/145 ; tau(u)= 171/26 ; 12809*x^2 + 27889*y^2 + 43402*x*z + 12809*z^2
(-1399/613 : 85662/102371 : 1) C1b (-668533/4537 : 9780037/757679 : 1)
** u= 119/337 ; tau(u)= 555/218 ; -80887*x^2 + 212977*y^2 + 322186*x*z - 80887*z^2
(-22785/385867 : 264662/385867 : 1) C1b (-219536080/978941 : 19019853/978941 : 1)
** u= 119/529 ; tau(u)= 939/410 ; -322039*x^2 + 545521*y^2 + 895882*x*z - 322039*z^2
(-24021/2659 : -21206/2659 : 1) C1b (121722129504/901848721 : -10946259929/901848721 : 1)
** u= -120/269 ; tau(u)= 658/389 ; -288242*x^2 + 130322*y^2 + 447364*x*z - 288242*z^2
(-81/206 : 407/206 : 1) C2b (-181195/878428 : -130983/878428 : 1)
** u= 120/409 ; tau(u)= 698/289 ; -152642*x^2 + 320162*y^2 + 501604*x*z - 152642*z^2
(25441619/86125267 : -20299972/86125267 : 1) C1b (118820/1182199 : 101421/1182199 : 1)
** u= -121/97 ; tau(u)= 315/218 ; -80407*x^2 + 4177*y^2 + 113866*x*z - 80407*z^2
(1713/3253 : 10406/3253 : 1) C2b (6936/19309 : 5593/19309 : 1)
** u= -121/225 ; tau(u)= 571/346 ; -224791*x^2 + 86609*y^2 + 340682*x*z - 224791*z^2
(-1531/581 : -462/83 : 1) C2b (12915219/1526344 : 1669417/1526344 : 1)
** u= -121/441 ; tau(u)= 1003/562 ; -617047*x^2 + 374321*y^2 + 1020650*x*z - 617047*z^2
(-71989/2943023 : 3855390/2943023 : 1) C2b (-1405328/7411719 : 968593/7411719 : 1)
** u= 125/333 ; tau(u)= 541/208 ; -70903*x^2 + 206153*y^2 + 308306*x*z - 70903*z^2
(-126353/21817 : -98880/21817 : 1) C1b (-1313428/1277877 : 174863/1277877 : 1)
** u= 127/10 ; tau(u)= 107/117 ; -11249*x^2 - 15929*y^2 + 27578*x*z - 11249*z^2
(38993/25867 : 14142/25867 : 1) C1a (-17655/13664 : -2441/13664 : 1)
** u= 127/185 ; tau(u)= 243/58 ; 9401*x^2 + 52321*y^2 + 75178*x*z + 9401*z^2
(-3791/29205 : 1802/29205 : 1) C1b (449000/135753 : 40909/135753 : 1)
** u= 129/68 ; tau(u)= -7/61 ; 9199*x^2 - 7393*y^2 + 16690*x*z + 9199*z^2
(-23459/19257 : -11240/19257 : 1) C1a (-21424247/421549 : -2240639/421549 : 1)
** u= -131/593 ; tau(u)= 1317/724 ; -1031191*x^2 + 686137*y^2 + 1751650*x*z - 1031191*z^2
(300269/388599 : -254104/388599 : 1) C2b (-322271236/13839223 : 37166827/13839223 : 1)
** u= -132/109 ; tau(u)= 350/241 ; -98738*x^2 + 6338*y^2 + 139924*x*z - 98738*z^2
(116/1119 : 4105/1119 : 1) C2b (528865/551504 : -137193/551504 : 1)
** u= 132/197 ; tau(u)= 262/65 ; 8974*x^2 + 60194*y^2 + 86068*x*z + 8974*z^2
(-213/100 : 149/100 : 1) C1b (3027491/365104 : 259719/365104 : 1)
** u= 132/245 ; tau(u)= 358/113 ; -8114*x^2 + 102626*y^2 + 145588*x*z - 8114*z^2
(29/666 : -2023/15318 : 1) C1b (1565144/610195 : -3176259/14034485 : 1)
** u= -132/493 ; tau(u)= 1118/625 ; -763826*x^2 + 468674*y^2 + 1267348*x*z - 763826*z^2
(407266/1033809 : -133525/147687 : 1) C2b (7488847/473915 : -834567/473915 : 1)
** u= 133/269 ; tau(u)= 405/136 ; -19303*x^2 + 127033*y^2 + 181714*x*z - 19303*z^2
(-126199/1545067 : -802548/1545067 : 1) C1b (-25418601/13510916 : 2526797/13510916 : 1)
** u= 133/281 ; tau(u)= 429/148 ; -26119*x^2 + 140233*y^2 + 201730*x*z - 26119*z^2
(9519921/406000763 : 158613800/406000763 : 1) C1b (-3822537/2078149 : -386603/2078149 : 1)
** u= 133/365 ; tau(u)= 597/232 ; -89959*x^2 + 248761*y^2 + 374098*x*z - 89959*z^2
(2701/18679 : -7276/18679 : 1) C1b (-2172844/3512095 : 392813/3512095 : 1)
** u= -133/421 ; tau(u)= 975/554 ; -596143*x^2 + 336793*y^2 + 968314*x*z - 596143*z^2
(-1187375/22668433 : -31455358/22668433 : 1) C2b (-151535/4520483 : 550621/4520483 : 1)
** u= 133/533 ; tau(u)= 933/400 ; -302311*x^2 + 550489*y^2 + 888178*x*z - 302311*z^2
(66689/15567 : 30008/15567 : 1) C1b (82005150811/296995700 : -7319947439/296995700 : 1)
** u= 133/549 ; tau(u)= 965/416 ; -328423*x^2 + 585113*y^2 + 948914*x*z - 328423*z^2
(-344813/1122085 : -69624/66005 : 1) C1b (6976245/1179799 : 596797/1179799 : 1)
** u= 136/149 ; tau(u)= 162/13 ; 18158*x^2 + 25906*y^2 + 44740*x*z + 18158*z^2
(-3364/4237 : -2025/4237 : 1) C1b (-105695/118373 : -11335/118373 : 1)
** u= 136/509 ; tau(u)= 882/373 ; -259762*x^2 + 499666*y^2 + 796420*x*z - 259762*z^2
(-205271/127109 : -268128/127109 : 1) C1b (93257159/7817283 : -8084161/7817283 : 1)
** u= 136/557 ; tau(u)= 978/421 ; -335986*x^2 + 602002*y^2 + 974980*x*z - 335986*z^2
(2679/9211 : 77632/211853 : 1) C1b (1248548/330795 : 484499/1521657 : 1)
** u= 137/40 ; tau(u)= 57/97 ; -49*x^2 - 15569*y^2 + 22018*x*z - 49*z^2
(2551/3427 : -3508/3427 : 1) C1a (-854564/712555 : 93201/712555 : 1)
** u= 137/241 ; tau(u)= 345/104 ; -2863*x^2 + 97393*y^2 + 137794*x*z - 2863*z^2
(-221927/193995 : 4282724/3297915 : 1) C1b (6156/42679 : 61169/725543 : 1)
** u= -137/257 ; tau(u)= 651/394 ; -291703*x^2 + 113329*y^2 + 442570*x*z - 291703*z^2
(34681/36037 : 39470/36037 : 1) C2b (-1631993/617784 : 290797/617784 : 1)
** u= 137/397 ; tau(u)= 657/260 ; -116431*x^2 + 296449*y^2 + 450418*x*z - 116431*z^2
(5119775/38421357 : -17064616/38421357 : 1) C1b (8682453/501335 : 742957/501335 : 1)
** u= 138/29 ; tau(u)= 80/109 ; -4718*x^2 - 17362*y^2 + 25444*x*z - 4718*z^2
(4807/24126 : -2347/24126 : 1) C1a (8417572/6059683 : -802007/6059683 : 1)
** u= 139/197 ; tau(u)= 255/58 ; 12593*x^2 + 58297*y^2 + 84346*x*z + 12593*z^2
(-14107/72105 : -17482/72105 : 1) C1b (-169386728/116089055 : 16123811/116089055 : 1)
** u= -140/117 ; tau(u)= 374/257 ; -112498*x^2 + 7778*y^2 + 159476*x*z - 112498*z^2
(4045/39874 : 141159/39874 : 1) C2b (860416/547741 : -195209/547741 : 1)
** u= 140/181 ; tau(u)= 222/41 ; 16238*x^2 + 45922*y^2 + 68884*x*z + 16238*z^2
(-12728/48349 : 6263/48349 : 1) C1b (5510671/123280 : -477489/123280 : 1)
** u= -140/197 ; tau(u)= 534/337 ; -207538*x^2 + 58018*y^2 + 304756*x*z - 207538*z^2
(692/269 : 997/269 : 1) C2b (34687337/10589045 : -4603803/10589045 : 1)
** u= -140/261 ; tau(u)= 662/401 ; -302002*x^2 + 116642*y^2 + 457844*x*z - 302002*z^2
(14239/869098 : -1381161/869098 : 1) C2b (295453/548808 : -58243/548808 : 1)
** u= 140/369 ; tau(u)= 598/229 ; -85282*x^2 + 252722*y^2 + 377204*x*z - 85282*z^2
(-28466/132805 : -108939/132805 : 1) C1b (4431040/569293 : 372883/569293 : 1)
** u= 141/32 ; tau(u)= 77/109 ; -3881*x^2 - 17833*y^2 + 25810*x*z - 3881*z^2
(683/163 : 232/163 : 1) C1a (-55213/134935 : 2595/26987 : 1)
** u= 141/557 ; tau(u)= 973/416 ; -326231*x^2 + 600617*y^2 + 966610*x*z - 326231*z^2
(1121731/4136741 : 1584424/4136741 : 1) C1b (2462104141/72524180 : 43533009/14504836 : 1)
** u= 143/98 ; tau(u)= -53/45 ; 16399*x^2 - 1241*y^2 + 23258*x*z + 16399*z^2
(991/8201 : -32466/8201 : 1) C1a (-8807/7040 : 1919/7040 : 1)
** u= -143/549 ; tau(u)= 1241/692 ; -937279*x^2 + 582353*y^2 + 1560530*x*z - 937279*z^2
(41869/8059 : 44964/8059 : 1) C2b (1800811797/406977620 : -36627011/81395524 : 1)
** u= -143/569 ; tau(u)= 1281/712 ; -993439*x^2 + 627073*y^2 + 1661410*x*z - 993439*z^2
(-3892013/37674177 : 51585628/37674177 : 1) C2b (289765468/23271571 : -31664139/23271571 : 1)
** u= 147/82 ; tau(u)= -17/65 ; 13159*x^2 - 8161*y^2 + 21898*x*z + 13159*z^2
(-10103/8111 : -7126/8111 : 1) C1a (-124731157/648760 : -14330919/648760 : 1)
** u= -147/305 ; tau(u)= 757/452 ; -386999*x^2 + 164441*y^2 + 594658*x*z - 386999*z^2
(-11597/9 : 302624/153 : 1) C2b (12271757/1038292 : -26437047/17650964 : 1)
** u= 148/153 ; tau(u)= 158/5 ; 21854*x^2 + 24914*y^2 + 46868*x*z + 21854*z^2
(-14902/10691 : 2157/10691 : 1) C1b (-120833/31200 : 10597/31200 : 1)
** u= -148/169 ; tau(u)= 486/317 ; -179074*x^2 + 35218*y^2 + 258100*x*z - 179074*z^2
(33172/34121 : -56745/34121 : 1) C2b (-35694408/676775 : 275557/27071 : 1)
** u= -148/225 ; tau(u)= 598/373 ; -256354*x^2 + 79346*y^2 + 379508*x*z - 256354*z^2
(6613/14818 : -19545/14818 : 1) C2b (-182901120/3931277 : -28556291/3931277 : 1)
** u= -148/397 ; tau(u)= 942/545 ; -572146*x^2 + 293314*y^2 + 909268*x*z - 572146*z^2
(-34678/343727 : -3635689/2406089 : 1) C2b (9737147/63200 : -8409339/442400 : 1)
** u= -148/529 ; tau(u)= 1206/677 ; -894754*x^2 + 537778*y^2 + 1476340*x*z - 894754*z^2
(-15908/491 : -21045/491 : 1) C2b (18118557/67917121 : -6846827/67917121 : 1)
** u= 149/68 ; tau(u)= 13/81 ; 9079*x^2 - 12953*y^2 + 22370*x*z + 9079*z^2
(586189/1429001 : -252288/204143 : 1) C1a (-105695/118373 : -11335/118373 : 1)
** u= 149/181 ; tau(u)= 213/32 ; 20153*x^2 + 43321*y^2 + 67570*x*z + 20153*z^2
(-63077/63853 : -50344/63853 : 1) C1b (74124332/124709 : -6516753/124709 : 1)
** u= -149/293 ; tau(u)= 735/442 ; -368527*x^2 + 149497*y^2 + 562426*x*z - 368527*z^2
(-575249/950967 : 2258998/950967 : 1) C2b (61029184/10215171 : 7489667/10215171 : 1)
** u= -149/333 ; tau(u)= 815/482 ; -442447*x^2 + 199577*y^2 + 686426*x*z - 442447*z^2
(3773/11645 : 94194/81515 : 1) C2b (99625/22944 : 79129/160608 : 1)
** u= -151/121 ; tau(u)= 393/272 ; -125167*x^2 + 6481*y^2 + 177250*x*z - 125167*z^2
(40129/72447 : -230120/72447 : 1) C2b (-67677431/335467 : 24989667/335467 : 1)
** u= -152/113 ; tau(u)= 378/265 ; -117346*x^2 + 2434*y^2 + 165988*x*z - 117346*z^2
(-3373/4375 : -49776/4375 : 1) C2b (15692/8113 : 6677/8113 : 1)
** u= -152/125 ; tau(u)= 402/277 ; -130354*x^2 + 8146*y^2 + 184708*x*z - 130354*z^2
(41303/37923 : -121640/37923 : 1) C2b (271604/556309 : 138133/556309 : 1)
** u= -152/245 ; tau(u)= 642/397 ; -292114*x^2 + 96946*y^2 + 435268*x*z - 292114*z^2
(-15117/24160 : -63931/24160 : 1) C2b (38525/44401 : 5077/44401 : 1)
** u= 152/433 ; tau(u)= 714/281 ; -134818*x^2 + 351874*y^2 + 532900*x*z - 134818*z^2
(-986939/13758349 : -9667652/13758349 : 1) C1b (3821924547/135085079 : -328165703/135085079 : 1)
** u= 152/457 ; tau(u)= 762/305 ; -162946*x^2 + 394594*y^2 + 603748*x*z - 162946*z^2
(121556/505485 : -132673/505485 : 1) C1b (-69196364/245399 : -6028069/245399 : 1)
** u= -155/281 ; tau(u)= 717/436 ; -356167*x^2 + 133897*y^2 + 538114*x*z - 356167*z^2
(35453/409967 : 626104/409967 : 1) C2b (-90011500/7164183 : -13386497/7164183 : 1)
** u= 156/265 ; tau(u)= 374/109 ; 574*x^2 + 116114*y^2 + 164212*x*z + 574*z^2
(-5143/418326 : 46663/418326 : 1) C1b (1586416/1593875 : 188493/1593875 : 1)
** u= 156/433 ; tau(u)= 710/277 ; -129122*x^2 + 350642*y^2 + 528436*x*z - 129122*z^2
(123110/472653 : 12427/472653 : 1) C1b (-2381663/4263968 : -463671/4263968 : 1)
** u= -156/485 ; tau(u)= 1126/641 ; -797426*x^2 + 446114*y^2 + 1292212*x*z - 797426*z^2
(-45159/4108268 : -5541671/4108268 : 1) C2b (21008939/1165495 : -2432133/1165495 : 1)
** u= -157/229 ; tau(u)= 615/386 ; -273343*x^2 + 80233*y^2 + 402874*x*z - 273343*z^2
(-30317/34603 : -111706/34603 : 1) C2b (33994189/8725511 : 4540177/8725511 : 1)
** u= 158/5 ; tau(u)= 148/153 ; -21854*x^2 - 24914*y^2 + 46868*x*z - 21854*z^2
(1889/2668 : -327/2668 : 1) C1a (-198561496/1445299 : -19227211/1445299 : 1)
** u= -159/181 ; tau(u)= 521/340 ; -205919*x^2 + 40241*y^2 + 296722*x*z - 205919*z^2
(8013/153559 : 47792/21937 : 1) C2b (20163481/1120580 : 3707019/1120580 : 1)
** u= 159/305 ; tau(u)= 451/146 ; -17351*x^2 + 160769*y^2 + 228682*x*z - 17351*z^2
(1189/26913 : 40094/188391 : 1) C1b (5277862792/256384487 : 3092461227/1794691409 : 1)
** u= 159/377 ; tau(u)= 595/218 ; -69767*x^2 + 258977*y^2 + 379306*x*z - 69767*z^2
(729/6685 : -2246/6685 : 1) C1b (406724383/2251040 : 34598151/2251040 : 1)
** u= 161/265 ; tau(u)= 369/104 ; 4289*x^2 + 114529*y^2 + 162082*x*z + 4289*z^2
(-1133995/14181439 : 3896052/14181439 : 1) C1b (-19411159/1851571 : -1628033/1851571 : 1)
** u= -161/377 ; tau(u)= 915/538 ; -552967*x^2 + 258337*y^2 + 863146*x*z - 552967*z^2
(2648833/1555053 : 2536126/1555053 : 1) C2b (-84222648/32880853 : -13924841/32880853 : 1)
** u= 161/481 ; tau(u)= 801/320 ; -178879*x^2 + 436801*y^2 + 667522*x*z - 178879*z^2
(-95569/24001 : -86496/24001 : 1) C1b (-562556476/3454015 : 49012061/3454015 : 1)
** u= 162/13 ; tau(u)= 136/149 ; -18158*x^2 - 25906*y^2 + 44740*x*z - 18158*z^2
(3364/4237 : 2025/4237 : 1) C1a (17005/13327 : -1555/13327 : 1)
** u= 163/261 ; tau(u)= 359/98 ; 7361*x^2 + 109673*y^2 + 155450*x*z + 7361*z^2
(-28871/517261 : -56154/517261 : 1) C1b (-3908248/2478279 : 379259/2478279 : 1)
** u= 163/293 ; tau(u)= 423/130 ; -7231*x^2 + 145129*y^2 + 205498*x*z - 7231*z^2
(5815/165867 : -2594/165867 : 1) C1b (125141880/5517569 : 10471331/5517569 : 1)
** u= -164/117 ; tau(u)= 398/281 ; -131026*x^2 + 482*y^2 + 185300*x*z - 131026*z^2
(-193/98 : 639/14 : 1) C2b (131112/99469 : -128239/99469 : 1)
** u= 164/313 ; tau(u)= 462/149 ; -17506*x^2 + 169042*y^2 + 240340*x*z - 17506*z^2
(20802/286817 : 9013/286817 : 1) C1b (272837/1017361 : 86743/1017361 : 1)
** u= 164/457 ; tau(u)= 750/293 ; -144802*x^2 + 390802*y^2 + 589396*x*z - 144802*z^2
(-29201/392716 : -273415/392716 : 1) C1b (-552360/1231931 : 126907/1231931 : 1)
** u= -164/569 ; tau(u)= 1302/733 ; -1047682*x^2 + 620626*y^2 + 1722100*x*z - 1047682*z^2
(-1314/179 : 1903/179 : 1) C2b (99009832/26478501 : -10023551/26478501 : 1)
** u= -165/389 ; tau(u)= 943/554 ; -586607*x^2 + 275417*y^2 + 916474*x*z - 586607*z^2
(1253/3709 : 70462/63053 : 1) C2b (5118352/1297547 : -9605229/22058299 : 1)
** u= 166/85 ; tau(u)= -4/81 ; 14434*x^2 - 13106*y^2 + 27572*x*z + 14434*z^2
(5875/922232 : -973719/922232 : 1) C1a (-17031/8720 : 1481/8720 : 1)
** u= 167/361 ; tau(u)= 555/194 ; -47383*x^2 + 232753*y^2 + 335914*x*z - 47383*z^2
(-12517/13931 : 17974/13931 : 1) C1b (-2101931/2896351 : 322137/2896351 : 1)
** u= 167/409 ; tau(u)= 651/242 ; -89239*x^2 + 306673*y^2 + 451690*x*z - 89239*z^2
(-11793/146807 : -94138/146807 : 1) C1b (-16320235/12139023 : -1894015/12139023 : 1)
** u= -168/529 ; tau(u)= 1226/697 ; -943394*x^2 + 531458*y^2 + 1531300*x*z - 943394*z^2
(-461741/3083019 : 4620884/3083019 : 1) C2b (-433036/201907 : -69231/201907 : 1)
** u= -169/225 ; tau(u)= 619/394 ; -281911*x^2 + 72689*y^2 + 411722*x*z - 281911*z^2
(219571/15280591 : 29778450/15280591 : 1) C2b (40008/215113 : 31811/215113 : 1)
** u= 169/305 ; tau(u)= 441/136 ; -8431*x^2 + 157489*y^2 + 223042*x*z - 8431*z^2
(19681/629667 : 60788/629667 : 1) C1b (-16033234401/168275060 : -1343104477/168275060 : 1)
** u= -169/361 ; tau(u)= 891/530 ; -533239*x^2 + 232081*y^2 + 822442*x*z - 533239*z^2
(30707/242139 : 332462/242139 : 1) C2b (682189/4320576 : -518269/4320576 : 1)
** u= 171/26 ; tau(u)= 119/145 ; -12809*x^2 - 27889*y^2 + 43402*x*z - 12809*z^2
(9/7 : 1034/1169 : 1) C1a (-11811/545 : -175651/91015 : 1)
** u= 171/82 ; tau(u)= 7/89 ; 13399*x^2 - 15793*y^2 + 29290*x*z + 13399*z^2
(65479/50449 : 109194/50449 : 1) C1a (-53686496/5065857 : -4941023/5065857 : 1)
** u= -172/261 ; tau(u)= 694/433 ; -345394*x^2 + 106658*y^2 + 511220*x*z - 345394*z^2
(42702788/503368787 : 850532637/503368787 : 1) C2b (13271113/2758720 : 356975/551744 : 1)
** u= -172/277 ; tau(u)= 726/449 ; -373618*x^2 + 123874*y^2 + 556660*x*z - 373618*z^2
(-80334/5147539 : -9044123/5147539 : 1) C2b (50164931/4593407 : 541593/353339 : 1)
** u= 172/317 ; tau(u)= 462/145 ; -12466*x^2 + 171394*y^2 + 243028*x*z - 12466*z^2
(-2 : -127/71 : 1) C1b (-22495/10253 : 149877/727963 : 1)
** u= -172/373 ; tau(u)= 918/545 ; -564466*x^2 + 248674*y^2 + 872308*x*z - 564466*z^2
(-15471/32174 : 68111/32174 : 1) C2b (69707616/11707175 : -8271701/11707175 : 1)
** u= 173/205 ; tau(u)= 237/32 ; 27881*x^2 + 54121*y^2 + 86098*x*z + 27881*z^2
(-17161/29361 : -14344/29361 : 1) C1b (1183485884/31157509 : 105954713/31157509 : 1)
** u= 173/565 ; tau(u)= 957/392 ; -277399*x^2 + 608521*y^2 + 945778*x*z - 277399*z^2
(1746727/5389381 : -17612/5389381 : 1) C1b (-2994251/8216420 : -836333/8216420 : 1)
** u= -175/313 ; tau(u)= 801/488 ; -445663*x^2 + 165313*y^2 + 672226*x*z - 445663*z^2
(31917/90343 : 114124/90343 : 1) C2b (3591100/2523317 : -381983/2523317 : 1)
** u= -175/373 ; tau(u)= 921/548 ; -569983*x^2 + 247633*y^2 + 878866*x*z - 569983*z^2
(78643/81153 : 82120/81153 : 1) C2b (-1455148/2749155 : -30061/161715 : 1)
** u= -176/197 ; tau(u)= 570/373 ; -247282*x^2 + 46642*y^2 + 355876*x*z - 247282*z^2
(21039/1523209 : 3472558/1523209 : 1) C2b (-2044228/77305 : 407879/77305 : 1)
** u= -176/245 ; tau(u)= 666/421 ; -323506*x^2 + 89074*y^2 + 474532*x*z - 323506*z^2
(-2945/4041 : -12418/4041 : 1) C2b (-2182324/722431 : -442787/722431 : 1)
** u= -176/333 ; tau(u)= 842/509 ; -487186*x^2 + 190802*y^2 + 739940*x*z - 487186*z^2
(-23113/35381 : 87930/35381 : 1) C2b (56061655/67849324 : 7249595/67849324 : 1)
** u= 176/529 ; tau(u)= 882/353 ; -218242*x^2 + 528706*y^2 + 808900*x*z - 218242*z^2
(-29147/8987 : -28014/8987 : 1) C1b (-6343523/3122300 : -135583/624460 : 1)
** u= -177/289 ; tau(u)= 755/466 ; -402983*x^2 + 135713*y^2 + 601354*x*z - 402983*z^2
(151039/151719 : -185878/151719 : 1) C2b (2170840/2197457 : 262779/2197457 : 1)
** u= 177/593 ; tau(u)= 1009/416 ; -314783*x^2 + 671969*y^2 + 1049410*x*z - 314783*z^2
(-1156669/22988709 : 17021128/22988709 : 1) C1b (-75736031/6096707 : 6839187/6096707 : 1)
** u= -179/221 ; tau(u)= 621/400 ; -287959*x^2 + 65641*y^2 + 417682*x*z - 287959*z^2
(7249/10151 : -14640/10151 : 1) C2b (-50625295/19546836 : -11651201/19546836 : 1)
** u= -184/261 ; tau(u)= 706/445 ; -362194*x^2 + 102386*y^2 + 532292*x*z - 362194*z^2
(-2228/3967 : -10917/3967 : 1) C2b (3984340/4657779 : -562969/4657779 : 1)
** u= 184/293 ; tau(u)= 402/109 ; 10094*x^2 + 137842*y^2 + 195460*x*z + 10094*z^2
(-227/517 : 15508/21197 : 1) C1b (-158868/4699 : -545141/192659 : 1)
** u= -184/373 ; tau(u)= 930/557 ; -586642*x^2 + 244402*y^2 + 898756*x*z - 586642*z^2
(14034/573439 : 871883/573439 : 1) C2b (1452797/2342988 : 239719/2342988 : 1)
** u= 185/349 ; tau(u)= 513/164 ; -19567*x^2 + 209377*y^2 + 297394*x*z - 19567*z^2
(-5797/536917 : 1239708/3758419 : 1) C1b (446698012/27408065 : -261637639/191856455 : 1)
** u= 186/49 ; tau(u)= 88/137 ; -2942*x^2 - 29794*y^2 + 42340*x*z - 2942*z^2
(4/11 : 7/11 : 1) C1a (29100116/415335 : 487723/83067 : 1)
** u= 186/121 ; tau(u)= -56/65 ; 26146*x^2 - 5314*y^2 + 37732*x*z + 26146*z^2
(-26113/330661 : -692824/330661 : 1) C1a (-187815/30428 : 31529/30428 : 1)
** u= 187/106 ; tau(u)= -25/81 ; 21847*x^2 - 12497*y^2 + 35594*x*z + 21847*z^2
(-2281/1021 : -2070/1021 : 1) C1a (5570464/207525 : 676861/207525 : 1)
** u= 187/261 ; tau(u)= 335/74 ; 24017*x^2 + 101273*y^2 + 147194*x*z + 24017*z^2
(-23135/110941 : -26166/110941 : 1) C1b (-1016243936/66930751 : 85460033/66930751 : 1)
** u= 188/193 ; tau(u)= 198/5 ; 35294*x^2 + 39154*y^2 + 74548*x*z + 35294*z^2
(-5918/7661 : -1359/7661 : 1) C1b (245286233/39619680 : 25857743/39619680 : 1)
** u= -188/269 ; tau(u)= 726/457 ; -382354*x^2 + 109378*y^2 + 562420*x*z - 382354*z^2
(-124/483 : -155/69 : 1) C2b (-59710024/104860383 : 24235559/104860383 : 1)
** u= -188/377 ; tau(u)= 942/565 ; -603106*x^2 + 248914*y^2 + 922708*x*z - 603106*z^2
(90570/767621 : -1090807/767621 : 1) C2b (47224240/2377089 : 6191621/2377089 : 1)
** u= 188/409 ; tau(u)= 630/221 ; -62338*x^2 + 299218*y^2 + 432244*x*z - 62338*z^2
(268/4171 : 58339/171011 : 1) C1b (36583/123680 : 429289/5070880 : 1)
** u= 189/80 ; tau(u)= 29/109 ; 11959*x^2 - 22921*y^2 + 36562*x*z + 11959*z^2
(643/17539 : -13368/17539 : 1) C1a (-4672428/164327 : -410663/164327 : 1)
** u= 190/73 ; tau(u)= 44/117 ; 8722*x^2 - 25442*y^2 + 38036*x*z + 8722*z^2
(-4217/18476 : -2577/18476 : 1) C1a (89867336/6439161 : 7876723/6439161 : 1)
** u= -191/233 ; tau(u)= 657/424 ; -323071*x^2 + 72097*y^2 + 468130*x*z - 323071*z^2
(63613/90007 : -131372/90007 : 1) C2b (1527548/1514521 : 214691/1514521 : 1)
** u= 191/433 ; tau(u)= 675/242 ; -80647*x^2 + 338497*y^2 + 492106*x*z - 80647*z^2
(-132767/7466357 : -3837570/7466357 : 1) C1b (60359280/17203231 : 5089303/17203231 : 1)
** u= -192/353 ; tau(u)= 898/545 ; -557186*x^2 + 212354*y^2 + 843268*x*z - 557186*z^2
(-60343/732166 : 1261571/732166 : 1) C2b (-168403/45748 : -28263/45748 : 1)
** u= -193/289 ; tau(u)= 771/482 ; -427399*x^2 + 129793*y^2 + 631690*x*z - 427399*z^2
(30417/276713 : 462842/276713 : 1) C2b (181696/805187 : -107917/805187 : 1)
** u= 193/549 ; tau(u)= 905/356 ; -216223*x^2 + 565553*y^2 + 856274*x*z - 216223*z^2
(-885137/405853 : 136008/57979 : 1) C1b (-168653/1243300 : -112219/1243300 : 1)
** u= 194/41 ; tau(u)= 112/153 ; -9182*x^2 - 34274*y^2 + 50180*x*z - 9182*z^2
(137/181 : 150/181 : 1) C1a (-176291852/1347279 : -15029987/1347279 : 1)
** u= 196/233 ; tau(u)= 270/37 ; 35678*x^2 + 70162*y^2 + 111316*x*z + 35678*z^2
(-13250/36527 : -357/36527 : 1) C1b (-1706389/227064 : 146027/227064 : 1)
** u= 196/305 ; tau(u)= 414/109 ; 14654*x^2 + 147634*y^2 + 209812*x*z + 14654*z^2
(-2706/791 : -1501/791 : 1) C1b (-13161560/7364601 : -1226807/7364601 : 1)
** u= 196/389 ; tau(u)= 582/193 ; -36082*x^2 + 264226*y^2 + 377140*x*z - 36082*z^2
(-12216/110011 : -59927/110011 : 1) C1b (-30744061/14042368 : -2942081/14042368 : 1)
** u= -196/445 ; tau(u)= 1086/641 ; -783346*x^2 + 357634*y^2 + 1217812*x*z - 783346*z^2
(301779/1917260 : 2506147/1917260 : 1) C2b (-45140608/863375 : -5933601/863375 : 1)
** u= -196/493 ; tau(u)= 1182/689 ; -911026*x^2 + 447682*y^2 + 1435540*x*z - 911026*z^2
(248/477 : -457/477 : 1) C2b (-1507883/1504649 : 343141/1504649 : 1)
** u= -197/293 ; tau(u)= 783/490 ; -441391*x^2 + 132889*y^2 + 651898*x*z - 441391*z^2
(16487/107791 : 175434/107791 : 1) C2b (-308652851/27732336 : 51124619/27732336 : 1)
** u= 197/493 ; tau(u)= 789/296 ; -136423*x^2 + 447289*y^2 + 661330*x*z - 136423*z^2
(1433181/10153391 : 3248732/10153391 : 1) C1b (240956/2427853 : 204457/2427853 : 1)
** u= -197/557 ; tau(u)= 1311/754 ; -1098223*x^2 + 581689*y^2 + 1757530*x*z - 1098223*z^2
(849957/5913497 : 7224926/5913497 : 1) C2b (102170336/40752697 : -10156159/40752697 : 1)
** u= 198/5 ; tau(u)= 188/193 ; -35294*x^2 - 39154*y^2 + 74548*x*z - 35294*z^2
(1048/945 : 43/135 : 1) C1a (-274205/41113 : 28727/41113 : 1)
** u= 198/41 ; tau(u)= 116/157 ; -10094*x^2 - 35842*y^2 + 52660*x*z - 10094*z^2
(61541/289924 : 38411/289924 : 1) C1a (451408/200719 : 39019/200719 : 1)
** u= 198/113 ; tau(u)= -28/85 ; 24754*x^2 - 13666*y^2 + 39988*x*z + 24754*z^2
(-15/16 : -13/16 : 1) C1a (-454795/503336 : -50603/503336 : 1)
** u= 199/82 ; tau(u)= 35/117 ; 12223*x^2 - 26153*y^2 + 40826*x*z + 12223*z^2
(-953/209 : 366/209 : 1) C1a (-795045/453232 : 69317/453232 : 1)
** u= -199/493 ; tau(u)= 1185/692 ; -918127*x^2 + 446497*y^2 + 1443826*x*z - 918127*z^2
(19317301/5930967 : -3094336/847281 : 1) C2b (11061779/8174321 : -1089747/8174321 : 1)
** u= 200/289 ; tau(u)= 378/89 ; 24158*x^2 + 127042*y^2 + 182884*x*z + 24158*z^2
(-15884/16331 : -16575/16331 : 1) C1b (-84423660/24953851 : 550763/1919527 : 1)
** u= -200/441 ; tau(u)= 1082/641 ; -781762*x^2 + 348962*y^2 + 1210724*x*z - 781762*z^2
(8720/1139 : 693/67 : 1) C2b (6448981/3116356 : -659819/3116356 : 1)
** u= -203/185 ; tau(u)= 573/388 ; -259879*x^2 + 27241*y^2 + 369538*x*z - 259879*z^2
(38897/31059 : 5008/1827 : 1) C2b (1559245/565359 : -318547/565359 : 1)
** u= 203/541 ; tau(u)= 879/338 ; -187279*x^2 + 544153*y^2 + 813850*x*z - 187279*z^2
(3591/25519 : -9566/25519 : 1) C1b (-189454663/18794624 : 16748271/18794624 : 1)
** u= -204/361 ; tau(u)= 926/565 ; -596834*x^2 + 219026*y^2 + 899092*x*z - 596834*z^2
(829066/7383021 : 11192881/7383021 : 1) C2b (160881727/6148280 : 22362087/6148280 : 1)
** u= 205/477 ; tau(u)= 749/272 ; -105943*x^2 + 413033*y^2 + 603026*x*z - 105943*z^2
(84181/780667 : -249384/780667 : 1) C1b (-4645459/1672175 : 442621/1672175 : 1)
** u= 208/449 ; tau(u)= 690/241 ; -72898*x^2 + 359938*y^2 + 519364*x*z - 72898*z^2
(7857/88127 : 24214/88127 : 1) C1b (559547755/3111968564 : 260618507/3111968564 : 1)
** u= 209/421 ; tau(u)= 633/212 ; -46207*x^2 + 310801*y^2 + 444370*x*z - 46207*z^2
(52963/745749 : 3980/18189 : 1) C1b (-2356737561/6579317 : -198332747/6579317 : 1)
** u= 211/461 ; tau(u)= 711/250 ; -80479*x^2 + 380521*y^2 + 550042*x*z - 80479*z^2
(8455/57127 : -382/8161 : 1) C1b (-4636881/4563965 : -589261/4563965 : 1)
** u= 212/325 ; tau(u)= 438/113 ; 19406*x^2 + 166306*y^2 + 236788*x*z + 19406*z^2
(-3066/859 : 11215/6013 : 1) C1b (-195785/61776 : -117781/432432 : 1)
** u= -212/441 ; tau(u)= 1094/653 ; -807874*x^2 + 344018*y^2 + 1241780*x*z - 807874*z^2
(2449942/2124547 : 2430393/2124547 : 1) C2b (-103396263/11753189 : 14891701/11753189 : 1)
** u= 213/32 ; tau(u)= 149/181 ; -20153*x^2 - 43321*y^2 + 67570*x*z - 20153*z^2
(109311/184631 : -100312/184631 : 1) C1a (2480804/597367 : -208449/597367 : 1)
** u= 213/425 ; tau(u)= 637/212 ; -44519*x^2 + 315881*y^2 + 451138*x*z - 44519*z^2
(180687/10411937 : 3549140/10411937 : 1) C1b (-67467764/2939081 : 5702703/2939081 : 1)
** u= -213/541 ; tau(u)= 1295/754 ; -1091663*x^2 + 539993*y^2 + 1722394*x*z - 1091663*z^2
(-400793/3552359 : 5511574/3552359 : 1) C2b (5549495/8489848 : 825459/8489848 : 1)
** u= -215/441 ; tau(u)= 1097/656 ; -814447*x^2 + 342737*y^2 + 1249634*x*z - 814447*z^2
(1652387/751613 : -1817256/751613 : 1) C2b (2608195/9323257 : -1058113/9323257 : 1)
** u= -215/569 ; tau(u)= 1353/784 ; -1183087*x^2 + 601297*y^2 + 1876834*x*z - 1183087*z^2
(4877/136859 : 186592/136859 : 1) C2b (-50235812/3301583 : 6511127/3301583 : 1)
** u= 217/281 ; tau(u)= 345/64 ; 38897*x^2 + 110833*y^2 + 166114*x*z + 38897*z^2
(-73081/59817 : 58496/59817 : 1) C1b (-14540/22247 : -2029/22247 : 1)
** u= -217/433 ; tau(u)= 1083/650 ; -797911*x^2 + 327889*y^2 + 1219978*x*z - 797911*z^2
(77/24053 : -37430/24053 : 1) C2b (-5975/19976 : 3299/19976 : 1)
** u= 217/449 ; tau(u)= 681/232 ; -60559*x^2 + 356113*y^2 + 510850*x*z - 60559*z^2
(-194331/1254871 : -789956/1254871 : 1) C1b (-145139852/44718539 : -13218473/44718539 : 1)
** u= -219/233 ; tau(u)= 685/452 ; -360647*x^2 + 60617*y^2 + 517186*x*z - 360647*z^2
(570711/411461 : -970352/411461 : 1) C2b (-1164184756/23560351 : -242662587/23560351 : 1)
** u= 220/401 ; tau(u)= 582/181 ; -17122*x^2 + 273202*y^2 + 387124*x*z - 17122*z^2
(-298577/3332346 : 1453057/3332346 : 1) C1b (25544587/4360175 : -2154433/4360175 : 1)
** u= 222/41 ; tau(u)= 140/181 ; -16238*x^2 - 45922*y^2 + 68884*x*z - 16238*z^2
(1414/5249 : -827/5249 : 1) C1a (-3454840/550927 : 312333/550927 : 1)
** u= 223/233 ; tau(u)= 243/10 ; 49529*x^2 + 58849*y^2 + 108778*x*z + 49529*z^2
(-9619/13381 : 21402/93667 : 1) C1b (-83789/52409 : 50857/366863 : 1)
** u= -224/225 ; tau(u)= 674/449 ; -353026*x^2 + 51074*y^2 + 504452*x*z - 353026*z^2
(-37751/576769 : -1588800/576769 : 1) C2b (-32299/279665 : -67033/279665 : 1)
** u= 224/409 ; tau(u)= 594/185 ; -18274*x^2 + 284386*y^2 + 403012*x*z - 18274*z^2
(-626753/6431 : -175944/6431 : 1) C1b (108556113380/7795620093 : -9086339263/7795620093 : 1)
** u= 228/229 ; tau(u)= 230 ; 51982*x^2 + 52898*y^2 + 104884*x*z + 51982*z^2
(-28810/27793 : 3593/27793 : 1) C1b (-13841477/187232 : -1362231/187232 : 1)
** u= 230 ; tau(u)= 228/229 ; -51982*x^2 - 52898*y^2 + 104884*x*z - 51982*z^2
(22833/21986 : -2833/21986 : 1) C1a (1265072/853127 : -111141/853127 : 1)
** u= 230/109 ; tau(u)= 12/121 ; 23618*x^2 - 29138*y^2 + 53044*x*z + 23618*z^2
(-2180/4479 : -1529/4479 : 1) C1a (-27227/4015 : -2439/4015 : 1)
** u= -231/361 ; tau(u)= 953/592 ; -647567*x^2 + 207281*y^2 + 961570*x*z - 647567*z^2
(-12917/11213 : 39824/11213 : 1) C2b (3682804/26747495 : 740121/5349499 : 1)
** u= -232/441 ; tau(u)= 1114/673 ; -852034*x^2 + 335138*y^2 + 1294820*x*z - 852034*z^2
(-251051/51517 : 465780/51517 : 1) C2b (-5347910365/870782004 : -823858655/870782004 : 1)
** u= 232/545 ; tau(u)= 858/313 ; -142114*x^2 + 540226*y^2 + 789988*x*z - 142114*z^2
(29452/191229 : -40151/191229 : 1) C1b (41050643/1754343 : 3469001/1754343 : 1)
** u= 235/82 ; tau(u)= 71/153 ; 8407*x^2 - 41777*y^2 + 60266*x*z + 8407*z^2
(21961/233015 : -135666/233015 : 1) C1a (348155/922488 : -87079/922488 : 1)
** u= 235/293 ; tau(u)= 351/58 ; 48497*x^2 + 116473*y^2 + 178426*x*z + 48497*z^2
(-761/2407 : -2734/16849 : 1) C1b (1486296/953825 : -1202227/6676775 : 1)
** u= -235/441 ; tau(u)= 1117/676 ; -858727*x^2 + 333737*y^2 + 1302914*x*z - 858727*z^2
(79379/61697 : 82992/61697 : 1) C2b (85622012/5143575 : -11444603/5143575 : 1)
** u= 236/241 ; tau(u)= 246/5 ; 55646*x^2 + 60466*y^2 + 116212*x*z + 55646*z^2
(-11235/11138 : -22327/77966 : 1) C1b (79232/61285 : -4867/25235 : 1)
** u= -236/377 ; tau(u)= 990/613 ; -695842*x^2 + 228562*y^2 + 1035796*x*z - 695842*z^2
(-1354/7045 : 14139/7045 : 1) C2b (40409976/1688375 : 5885777/1688375 : 1)
** u= -236/405 ; tau(u)= 1046/641 ; -766066*x^2 + 272354*y^2 + 1149812*x*z - 766066*z^2
(115813/126604 : 144603/126604 : 1) C2b (-154928/196747 : -46471/196747 : 1)
** u= 237/32 ; tau(u)= 173/205 ; -27881*x^2 - 54121*y^2 + 86098*x*z - 27881*z^2
(3091/2715 : -2152/2715 : 1) C1a (-1768027/674172 : -185141/674172 : 1)
** u= 238/121 ; tau(u)= -4/117 ; 29266*x^2 - 27362*y^2 + 56660*x*z + 29266*z^2
(-62356/42463 : 24585/42463 : 1) C1a (-1355091656/58192853 : 134252551/58192853 : 1)
** u= 243/10 ; tau(u)= 223/233 ; -49529*x^2 - 58849*y^2 + 108778*x*z - 49529*z^2
(281/303 : 818/2121 : 1) C1a (2319240/1843691 : 1479857/12905837 : 1)
** u= 243/58 ; tau(u)= 127/185 ; -9401*x^2 - 52321*y^2 + 75178*x*z - 9401*z^2
(1969/5839 : -3114/5839 : 1) C1a (-28738040/910669 : -2434553/910669 : 1)
** u= 243/170 ; tau(u)= -97/73 ; 48391*x^2 - 1249*y^2 + 68458*x*z + 48391*z^2
(-13681/8765 : 60462/8765 : 1) C1a (-17364008/356757 : -8914537/356757 : 1)
** u= -244/349 ; tau(u)= 942/593 ; -643762*x^2 + 184066*y^2 + 946900*x*z - 643762*z^2
(-92203/387762 : -859961/387762 : 1) C2b (-66472/147369 : 31699/147369 : 1)
** u= -245/389 ; tau(u)= 1023/634 ; -743887*x^2 + 242617*y^2 + 1106554*x*z - 743887*z^2
(17123/174935 : 284722/174935 : 1) C2b (-10804480/956953 : -1723463/956953 : 1)
** u= 246/5 ; tau(u)= 236/241 ; -55646*x^2 - 60466*y^2 + 116212*x*z - 55646*z^2
(103/126 : 167/882 : 1) C1a (46249/100659 : -60353/704613 : 1)
** u= -247/265 ; tau(u)= 777/512 ; -463279*x^2 + 79441*y^2 + 664738*x*z - 463279*z^2
(-100235/635691 : -1717088/635691 : 1) C2b (20703343/511133 : 4141909/511133 : 1)
** u= 247/545 ; tau(u)= 843/298 ; -116599*x^2 + 533041*y^2 + 771658*x*z - 116599*z^2
(-4048767/116920469 : 60656282/116920469 : 1) C1b (-2120865/873536 : 204247/873536 : 1)
** u= -248/233 ; tau(u)= 714/481 ; -401218*x^2 + 47074*y^2 + 571300*x*z - 401218*z^2
(13721/29597 : 64360/29597 : 1) C2b (694412/105779 : -153117/105779 : 1)
** u= -248/353 ; tau(u)= 954/601 ; -660898*x^2 + 187714*y^2 + 971620*x*z - 660898*z^2
(-7609/20558 : 50015/20558 : 1) C2b (605596/492497 : 72221/492497 : 1)
** u= -248/425 ; tau(u)= 1098/673 ; -844354*x^2 + 299746*y^2 + 1267108*x*z - 844354*z^2
(-167679/166181 : 524200/166181 : 1) C2b (-47901996/29234579 : 10245097/29234579 : 1)
** u= 249/136 ; tau(u)= -23/113 ; 36463*x^2 - 25009*y^2 + 62530*x*z + 36463*z^2
(-190897/628867 : 574084/628867 : 1) C1a (-133848527/3736821 : 14652809/3736821 : 1)
** u= 249/164 ; tau(u)= -79/85 ; 47551*x^2 - 8209*y^2 + 68242*x*z + 47551*z^2
(-13011/8029 : 3148/1147 : 1) C1a (1121259/3631 : 227977/3631 : 1)
** u= -249/193 ; tau(u)= 635/442 ; -328727*x^2 + 12497*y^2 + 465226*x*z - 328727*z^2
(-2713/3099 : -27554/3099 : 1) C2b (-307120/1672333 : 816429/1672333 : 1)
** u= 249/317 ; tau(u)= 385/68 ; 52753*x^2 + 138977*y^2 + 210226*x*z + 52753*z^2
(-637863/2308247 : -224324/2308247 : 1) C1b (-12064484/120005 : -1041453/120005 : 1)
** u= 249/509 ; tau(u)= 769/260 ; -73199*x^2 + 456161*y^2 + 653362*x*z - 73199*z^2
(1071317/18482779 : 737356/2640397 : 1) C1b (147835763/348172 : 12445383/348172 : 1)
** u= 250/169 ; tau(u)= -88/81 ; 49378*x^2 - 5378*y^2 + 70244*x*z + 49378*z^2
(-17081/33749 : 74880/33749 : 1) C1a (1084340/1493557 : -606209/1493557 : 1)
** u= 251/349 ; tau(u)= 447/98 ; 43793*x^2 + 180601*y^2 + 262810*x*z + 43793*z^2
(-489259/745053 : 581210/745053 : 1) C1b (-4448611/1758383 : 382179/1758383 : 1)
** u= 253/293 ; tau(u)= 333/40 ; 60809*x^2 + 107689*y^2 + 174898*x*z + 60809*z^2
(-85249/195661 : 36996/195661 : 1) C1b (17276/386905 : 35261/386905 : 1)
** u= 255/58 ; tau(u)= 139/197 ; -12593*x^2 - 58297*y^2 + 84346*x*z - 12593*z^2
(19549/8943 : -12374/8943 : 1) C1a (348947176/300259295 : -35969373/300259295 : 1)
** u= 256/261 ; tau(u)= 266/5 ; 65486*x^2 + 70706*y^2 + 136292*x*z + 65486*z^2
(-89/115 : -12/115 : 1) C1b (271871140/500617 : 2044729/38509 : 1)
** u= -256/445 ; tau(u)= 1146/701 ; -917266*x^2 + 330514*y^2 + 1378852*x*z - 917266*z^2
(-31859/92533 : -28168/13219 : 1) C2b (431068/1808513 : 223529/1808513 : 1)
** u= 257/421 ; tau(u)= 585/164 ; 12257*x^2 + 288433*y^2 + 408274*x*z + 12257*z^2
(-7551407/1684991 : -561828/240713 : 1) C1b (-53479665/2245253 : -4475089/2245253 : 1)
** u= 258/113 ; tau(u)= 32/145 ; 24514*x^2 - 41026*y^2 + 67588*x*z + 24514*z^2
(-981/412 : 1/4 : 1) C1a (6689996/68415 : -606433/68415 : 1)
** u= 259/317 ; tau(u)= 375/58 ; 60353*x^2 + 133897*y^2 + 207706*x*z + 60353*z^2
(-6069/2659 : -2290/2659 : 1) C1b (-16118456/2479425 : -1365283/2479425 : 1)
** u= -260/369 ; tau(u)= 998/629 ; -723682*x^2 + 204722*y^2 + 1063604*x*z - 723682*z^2
(13078/58585 : -655041/410095 : 1) C2b (251184/887269 : 830323/6210883 : 1)
** u= 260/441 ; tau(u)= 622/181 ; 2078*x^2 + 321362*y^2 + 454484*x*z + 2078*z^2
(-8083/590774 : -67053/590774 : 1) C1b (-15978805/714039 : -1338059/714039 : 1)
** u= 260/529 ; tau(u)= 798/269 ; -77122*x^2 + 492082*y^2 + 704404*x*z - 77122*z^2
(36246/1060459 : -348473/1060459 : 1) C1b (-1591855/39288 : 134407/39288 : 1)
** u= 262/65 ; tau(u)= 132/197 ; -8974*x^2 - 60194*y^2 + 86068*x*z - 8974*z^2
(200/1083 : 359/1083 : 1) C1a (522629/327320 : -49389/327320 : 1)
** u= -263/221 ; tau(u)= 705/484 ; -399343*x^2 + 28513*y^2 + 566194*x*z - 399343*z^2
(-26425/245369 : -990836/245369 : 1) C2b (90117884/823095 : 28073653/823095 : 1)
** u= 263/313 ; tau(u)= 363/50 ; 64169*x^2 + 126769*y^2 + 200938*x*z + 64169*z^2
(-301885/480371 : -258698/480371 : 1) C1b (-333939448/1228392003 : 103245937/1228392003 : 1)
** u= -263/449 ; tau(u)= 1161/712 ; -944719*x^2 + 334033*y^2 + 1417090*x*z - 944719*z^2
(18049/320579 : 3617268/2244053 : 1) C2b (-4929772739/351961767 : -5245741271/2463732369 : 1)
** u= 265/557 ; tau(u)= 849/292 ; -100303*x^2 + 550273*y^2 + 791026*x*z - 100303*z^2
(-4946853/40801289 : -24455128/40801289 : 1) C1b (17654020/1632117 : 1478137/1632117 : 1)
** u= 266/5 ; tau(u)= 256/261 ; -65486*x^2 - 70706*y^2 + 136292*x*z - 65486*z^2
(115/89 : 12/89 : 1) C1a (386252/552715 : 48797/552715 : 1)
** u= 267/146 ; tau(u)= -25/121 ; 42007*x^2 - 28657*y^2 + 71914*x*z + 42007*z^2
(-19087/102907 : 15070/14701 : 1) C1a (-42979072/1039995 : 4723637/1039995 : 1)
** u= 268/317 ; tau(u)= 366/49 ; 67022*x^2 + 129154*y^2 + 205780*x*z + 67022*z^2
(-145904/62233 : -37555/62233 : 1) C1b (430553891/68561832 : -40631521/68561832 : 1)
** u= 269/481 ; tau(u)= 693/212 ; -17527*x^2 + 390361*y^2 + 552610*x*z - 17527*z^2
(-14551/325511 : 107108/325511 : 1) C1b (-21737797/611289 : -1822109/611289 : 1)
** u= -269/509 ; tau(u)= 1287/778 ; -1138207*x^2 + 445801*y^2 + 1728730*x*z - 1138207*z^2
(-478081/1974611 : 3768202/1974611 : 1) C2b (-5074222560/26274887 : -705453335/26274887 : 1)
** u= 270/37 ; tau(u)= 196/233 ; -35678*x^2 - 70162*y^2 + 111316*x*z - 35678*z^2
(14138/5189 : -1029/5189 : 1) C1a (4702584/1973935 : 396937/1973935 : 1)
** u= 270/157 ; tau(u)= -44/113 ; 47362*x^2 - 23602*y^2 + 74836*x*z + 47362*z^2
(-4141/11360 : -12009/11360 : 1) C1a (-540173/358672 : -52441/358672 : 1)
** u= 270/173 ; tau(u)= -76/97 ; 54082*x^2 - 13042*y^2 + 78676*x*z + 54082*z^2
(-5599/10174 : 14683/10174 : 1) C1a (-2316184/373761 : 358943/373761 : 1)
** u= 271/401 ; tau(u)= 531/130 ; 39641*x^2 + 248161*y^2 + 355402*x*z + 39641*z^2
(-22067689/19328887 : 21757806/19328887 : 1) C1b (1859200/5109939 : 473981/5109939 : 1)
** u= -271/405 ; tau(u)= 1081/676 ; -840511*x^2 + 254609*y^2 + 1242002*x*z - 840511*z^2
(19927/4825 : 515268/82025 : 1) C2b (-33732/22783 : 137197/387311 : 1)
** u= -271/409 ; tau(u)= 1089/680 ; -851359*x^2 + 261121*y^2 + 1259362*x*z - 851359*z^2
(-1499/1367 : -2466684/698537 : 1) C2b (340/10383 : 801923/5305713 : 1)
** u= 272/441 ; tau(u)= 610/169 ; 16862*x^2 + 314978*y^2 + 446084*x*z + 16862*z^2
(-16771/638 : -273/638 : 1) C1b (1535461/1217220 : 167057/1217220 : 1)
** u= 272/477 ; tau(u)= 682/205 ; -10066*x^2 + 381074*y^2 + 539108*x*z - 10066*z^2
(-81505/40724 : 70107/40724 : 1) C1b (178502705/41052917 : 15265673/41052917 : 1)
** u= -273/521 ; tau(u)= 1315/794 ; -1186343*x^2 + 468353*y^2 + 1803754*x*z - 1186343*z^2
(158319/555503 : 711638/555503 : 1) C2b (3208929328/60082955 : -437672571/60082955 : 1)
** u= 274/157 ; tau(u)= -40/117 ; 47698*x^2 - 25778*y^2 + 76676*x*z + 47698*z^2
(189025/3247151 : -4626204/3247151 : 1) C1a (2314177/133380 : -291163/133380 : 1)
** u= 277/160 ; tau(u)= -43/117 ; 49351*x^2 - 25529*y^2 + 78578*x*z + 49351*z^2
(-8149/4915 : -50376/34405 : 1) C1a (-75851/204620 : 144917/1432340 : 1)
** u= 279/130 ; tau(u)= 19/149 ; 33439*x^2 - 44041*y^2 + 78202*x*z + 33439*z^2
(-3151/10691 : 5874/10691 : 1) C1a (-43177768/11344697 : -3719827/11344697 : 1)
** u= 280/389 ; tau(u)= 498/109 ; 54638*x^2 + 224242*y^2 + 326404*x*z + 54638*z^2
(-74661/322027 : -91492/322027 : 1) C1b (3665537/100357 : -312697/100357 : 1)
** u= -280/421 ; tau(u)= 1122/701 ; -904402*x^2 + 276082*y^2 + 1337284*x*z - 904402*z^2
(-666076/3359061 : 7018057/3359061 : 1) C2b (-344724901/4704484 : 53876729/4704484 : 1)
** u= 280/509 ; tau(u)= 738/229 ; -26482*x^2 + 439762*y^2 + 623044*x*z - 26482*z^2
(-287273/11801351 : 3632484/11801351 : 1) C1b (-139938493/7344367 : -11761787/7344367 : 1)
** u= -289/433 ; tau(u)= 1155/722 ; -959047*x^2 + 291457*y^2 + 1417546*x*z - 959047*z^2
(-53919/2657 : -101422/2657 : 1) C2b (1209240/1832533 : 209449/1832533 : 1)
** u= 289/533 ; tau(u)= 777/244 ; -35551*x^2 + 484657*y^2 + 687250*x*z - 35551*z^2
(505607/19347693 : 3688592/19347693 : 1) C1b (-1365592900/42536873 : 114655335/42536873 : 1)
** u= -292/313 ; tau(u)= 918/605 ; -646786*x^2 + 110674*y^2 + 927988*x*z - 646786*z^2
(9161/1652 : 2783/236 : 1) C2b (10830275/9609544 : 1637071/9609544 : 1)
** u= -292/481 ; tau(u)= 1254/773 ; -1109794*x^2 + 377458*y^2 + 1657780*x*z - 1109794*z^2
(136868/283179 : 347315/283179 : 1) C2b (-141894264/62676047 : 27965387/62676047 : 1)
** u= -293/333 ; tau(u)= 959/626 ; -697903*x^2 + 135929*y^2 + 1005530*x*z - 697903*z^2
(10877/187073 : 406494/187073 : 1) C2b (-2887763/2039335 : 174019/407867 : 1)
** u= 294/169 ; tau(u)= -44/125 ; 55186*x^2 - 29314*y^2 + 88372*x*z + 55186*z^2
(-3364/4609 : -3815/4609 : 1) C1a (-2177987/465855 : 234779/465855 : 1)
** u= -295/361 ; tau(u)= 1017/656 ; -773647*x^2 + 173617*y^2 + 1121314*x*z - 773647*z^2
(864035/3387349 : 851808/483907 : 1) C2b (-230280500/152010417 : -63076987/152010417 : 1)
** u= -296/281 ; tau(u)= 858/577 ; -578242*x^2 + 70306*y^2 + 823780*x*z - 578242*z^2
(58398/388163 : -1000829/388163 : 1) C2b (7867565/2896652 : 1490415/2896652 : 1)
** u= 296/369 ; tau(u)= 442/73 ; 76958*x^2 + 184706*y^2 + 282980*x*z + 76958*z^2
(-1843471/3318494 : 1835253/3318494 : 1) C1b (-18957003/664169 : 1636157/664169 : 1)
** u= -296/401 ; tau(u)= 1098/697 ; -884002*x^2 + 233986*y^2 + 1293220*x*z - 884002*z^2
(30677/30813 : -43796/30813 : 1) C2b (604316/817573 : -98993/817573 : 1)
** u= 296/529 ; tau(u)= 762/233 ; -20962*x^2 + 472066*y^2 + 668260*x*z - 20962*z^2
(-10613/29407 : 154192/205849 : 1) C1b (6224459/724535 : 731775/1014349 : 1)
** u= 299/397 ; tau(u)= 495/98 ; 70193*x^2 + 225817*y^2 + 334426*x*z + 70193*z^2
(-38599/93437 : -46522/93437 : 1) C1b (-312399/319544 : 34013/319544 : 1)
** u= -299/425 ; tau(u)= 1149/724 ; -958951*x^2 + 271849*y^2 + 1409602*x*z - 958951*z^2
(133251/197741 : 252860/197741 : 1) C2b (137068711892/1091773327 : 21842120921/1091773327 : 1)
** u= -301/445 ; tau(u)= 1191/746 ; -1022431*x^2 + 305449*y^2 + 1509082*x*z - 1022431*z^2
(-3095/27441 : -54518/27441 : 1) C2b (30670272/15520145 : 3622511/15520145 : 1)
** u= 301/545 ; tau(u)= 789/244 ; -28471*x^2 + 503449*y^2 + 713122*x*z - 28471*z^2
(-58794093/501031321 : 236892088/501031321 : 1) C1b (217512299/457609 : 18212803/457609 : 1)
** u= 302/181 ; tau(u)= -60/121 ; 61922*x^2 - 25682*y^2 + 94804*x*z + 61922*z^2
(75968/225729 : -63899/32247 : 1) C1a (5860955/792368 : -866073/792368 : 1)
** u= 304/425 ; tau(u)= 546/121 ; 63134*x^2 + 268834*y^2 + 390532*x*z + 63134*z^2
(-14698/84009 : 9251/84009 : 1) C1b (68572484/1196299 : 5832403/1196299 : 1)
** u= -304/481 ; tau(u)= 1266/785 ; -1140034*x^2 + 370306*y^2 + 1695172*x*z - 1140034*z^2
(2516/2171 : -2999/2171 : 1) C2b (-203579060/13409491 : -32039151/13409491 : 1)
** u= -304/493 ; tau(u)= 1290/797 ; -1178002*x^2 + 393682*y^2 + 1756516*x*z - 1178002*z^2
(60908/120411 : 147521/120411 : 1) C2b (-91529973/298794220 : -54472519/298794220 : 1)
** u= -304/541 ; tau(u)= 1386/845 ; -1335634*x^2 + 492946*y^2 + 2013412*x*z - 1335634*z^2
(-1810/5411 : 11323/5411 : 1) C2b (995093/2432500 : 273367/2432500 : 1)
** u= 304/569 ; tau(u)= 834/265 ; -48034*x^2 + 555106*y^2 + 787972*x*z - 48034*z^2
(1211/89597 : 23254/89597 : 1) C1b (-85833612/21919967 : 7533977/21919967 : 1)
** u= 305/577 ; tau(u)= 849/272 ; -54943*x^2 + 572833*y^2 + 813826*x*z - 54943*z^2
(-771/452987 : -142048/452987 : 1) C1b (-903173/6974660 : -594857/6974660 : 1)
** u= -307/405 ; tau(u)= 1117/712 ; -919639*x^2 + 233801*y^2 + 1341938*x*z - 919639*z^2
(-209/132469 : -4471452/2251973 : 1) C2b (58869539/33202449 : 124546939/564441633 : 1)
** u= -308/233 ; tau(u)= 774/541 ; -490498*x^2 + 13714*y^2 + 693940*x*z - 490498*z^2
(258919/433052 : -1852425/433052 : 1) C2b (287192/388851 : -137809/388851 : 1)
** u= 308/325 ; tau(u)= 342/17 ; 94286*x^2 + 116386*y^2 + 211828*x*z + 94286*z^2
(-581/694 : 265/694 : 1) C1b (1766855/61176 : -170377/61176 : 1)
** u= 308/369 ; tau(u)= 430/61 ; 87422*x^2 + 177458*y^2 + 279764*x*z + 87422*z^2
(-79787/210178 : 39231/210178 : 1) C1b (-31721835/522184 : -2788333/522184 : 1)
** u= 308/397 ; tau(u)= 486/89 ; 79022*x^2 + 220354*y^2 + 331060*x*z + 79022*z^2
(-44713/24508 : 26721/24508 : 1) C1b (18936816/16653985 : 483727/3330797 : 1)
** u= -308/521 ; tau(u)= 1350/829 ; -1279618*x^2 + 448018*y^2 + 1917364*x*z - 1279618*z^2
(-2149/22054 : 40065/22054 : 1) C2b (177485400/25689071 : 23504053/25689071 : 1)
** u= 309/361 ; tau(u)= 413/52 ; 90073*x^2 + 165161*y^2 + 266050*x*z + 90073*z^2
(-79219/127767 : -63080/127767 : 1) C1b (-5991476/1106225 : -102027/221245 : 1)
** u= -311/401 ; tau(u)= 1113/712 ; -917167*x^2 + 224881*y^2 + 1335490*x*z - 917167*z^2
(-17787093/8602817 : -50009116/8602817 : 1) C2b (71691236/44497683 : 8971897/44497683 : 1)
** u= 312/449 ; tau(u)= 586/137 ; 59806*x^2 + 305858*y^2 + 440740*x*z + 59806*z^2
(-10043/46517 : -106244/325619 : 1) C1b (3245/1009 : 2085/7063 : 1)
** u= -312/541 ; tau(u)= 1394/853 ; -1357874*x^2 + 488018*y^2 + 2040580*x*z - 1357874*z^2
(39859/69951 : 11408/9993 : 1) C2b (5041636/6104885 : 134121/1220977 : 1)
** u= -313/481 ; tau(u)= 1275/794 ; -1162903*x^2 + 364753*y^2 + 1723594*x*z - 1162903*z^2
(1445667/3398363 : -4501990/3398363 : 1) C2b (25207536/6082409 : -3299993/6082409 : 1)
** u= 315/218 ; tau(u)= -121/97 ; 80407*x^2 - 4177*y^2 + 113866*x*z + 80407*z^2
(-11731/32675 : -112926/32675 : 1) C1a (-255785/425904 : 112007/425904 : 1)
** u= 317/148 ; tau(u)= 21/169 ; 43367*x^2 - 56681*y^2 + 100930*x*z + 43367*z^2
(-6047/31969 : -21580/31969 : 1) C1a (6865244/805913 : -680523/805913 : 1)
** u= -317/533 ; tau(u)= 1383/850 ; -1344511*x^2 + 467689*y^2 + 2013178*x*z - 1344511*z^2
(285291/317179 : -365630/317179 : 1) C2b (-692593/5220168 : 832957/5220168 : 1)
** u= 318/193 ; tau(u)= -68/125 ; 69874*x^2 - 26626*y^2 + 105748*x*z + 69874*z^2
(-931/4786 : -6685/4786 : 1) C1a (-201763/279775 : 29541/279775 : 1)
** u= 319/170 ; tau(u)= -21/149 ; 57359*x^2 - 43961*y^2 + 102202*x*z + 57359*z^2
(358201/228039 : -652046/228039 : 1) C1a (760505/76448 : -86457/76448 : 1)
** u= 321/148 ; tau(u)= 25/173 ; 43183*x^2 - 59233*y^2 + 103666*x*z + 43183*z^2
(13357/103173 : 14500/14739 : 1) C1a (318977/146228 : 37463/146228 : 1)
** u= 325/569 ; tau(u)= 813/244 ; -13447*x^2 + 541897*y^2 + 766594*x*z - 13447*z^2
(128361/7401911 : 126020/7401911 : 1) C1b (-6412465/773373 : 541643/773373 : 1)
** u= 326/173 ; tau(u)= -20/153 ; 59458*x^2 - 46418*y^2 + 106676*x*z + 59458*z^2
(1909/2192 : -33/16 : 1) C1a (2143424/28441 : 230329/28441 : 1)
** u= 327/106 ; tau(u)= 115/221 ; 9247*x^2 - 84457*y^2 + 120154*x*z + 9247*z^2
(-434753/6495245 : 788938/6495245 : 1) C1a (27074525/2438968 : -2296983/2438968 : 1)
** u= 328/389 ; tau(u)= 450/61 ; 100142*x^2 + 195058*y^2 + 310084*x*z + 100142*z^2
(-91349/72999 : -59840/72999 : 1) C1b (229666340/16423621 : 20890237/16423621 : 1)
** u= -328/493 ; tau(u)= 1314/821 ; -1240498*x^2 + 378514*y^2 + 1834180*x*z - 1240498*z^2
(204437/889773 : 1360196/889773 : 1) C2b (2836733/2572569 : 339119/2572569 : 1)
** u= 328/585 ; tau(u)= 842/257 ; -24514*x^2 + 576866*y^2 + 816548*x*z - 24514*z^2
(283165/9456193 : 114456/9456193 : 1) C1b (-273174327/993925 : -22870091/993925 : 1)
** u= -329/281 ; tau(u)= 891/610 ; -635959*x^2 + 49681*y^2 + 902122*x*z - 635959*z^2
(25783/39899 : 101034/39899 : 1) C2b (-2520320/546039 : -67597/42003 : 1)
** u= 329/333 ; tau(u)= 337/4 ; 108209*x^2 + 113537*y^2 + 221810*x*z + 108209*z^2
(-153977/161893 : -33528/161893 : 1) C1b (95073268/588415 : 1875643/117683 : 1)
** u= 332/441 ; tau(u)= 550/109 ; 86462*x^2 + 278738*y^2 + 412724*x*z + 86462*z^2
(-28276/66581 : -34125/66581 : 1) C1b (37941/592744 : 51527/592744 : 1)
** u= 333/40 ; tau(u)= 253/293 ; -60809*x^2 - 107689*y^2 + 174898*x*z - 60809*z^2
(20339/47591 : -7716/47591 : 1) C1a (-7333420/342209 : -668851/342209 : 1)
** u= 335/74 ; tau(u)= 187/261 ; -24017*x^2 - 101273*y^2 + 147194*x*z - 24017*z^2
(68701/400835 : -28326/400835 : 1) C1a (-428757/157768 : 40751/157768 : 1)
** u= 336/433 ; tau(u)= 530/97 ; 94078*x^2 + 262082*y^2 + 393796*x*z + 94078*z^2
(-4731/17315 : -2726/17315 : 1) C1b (155535916/4281959 : -13507413/4281959 : 1)
** u= 337/4 ; tau(u)= 329/333 ; -108209*x^2 - 113537*y^2 + 221810*x*z - 108209*z^2
(97727/108223 : -19932/108223 : 1) C1a (-47580732/12299335 : 1074817/2459867 : 1)
** u= 337/405 ; tau(u)= 473/68 ; 104321*x^2 + 214481*y^2 + 337298*x*z + 104321*z^2
(-27565/60797 : -21636/60797 : 1) C1b (-21545539/2607836 : 1842923/2607836 : 1)
** u= 337/569 ; tau(u)= 801/232 ; 5921*x^2 + 533953*y^2 + 755170*x*z + 5921*z^2
(-140069/3329 : 147132/23303 : 1) C1b (-32859676/10293907 : -1547989/5542873 : 1)
** u= -340/261 ; tau(u)= 862/601 ; -606802*x^2 + 20642*y^2 + 858644*x*z - 606802*z^2
(-1786/11813 : -71229/11813 : 1) C2b (-10121535407/129757248 : -4634851783/129757248 : 1)
** u= 340/389 ; tau(u)= 438/49 ; 110798*x^2 + 187042*y^2 + 307444*x*z + 110798*z^2
(-97914/64265 : -47089/64265 : 1) C1b (-64888864/31959175 : -5514581/31959175 : 1)
** u= -340/541 ; tau(u)= 1422/881 ; -1436722*x^2 + 469762*y^2 + 2137684*x*z - 1436722*z^2
(-171680/1396751 : -2673579/1396751 : 1) C2b (32490960/88234483 : -10599763/88234483 : 1)
** u= -341/245 ; tau(u)= 831/586 ; -570511*x^2 + 3769*y^2 + 806842*x*z - 570511*z^2
(45079/8175 : 488698/8175 : 1) C2b (-1025104/573095 : -1530417/573095 : 1)
** u= 341/421 ; tau(u)= 501/80 ; 103481*x^2 + 238201*y^2 + 367282*x*z + 103481*z^2
(-152457/167393 : 130688/167393 : 1) C1b (-2685868/14331323 : -1207167/14331323 : 1)
** u= -341/461 ; tau(u)= 1263/802 ; -1170127*x^2 + 308761*y^2 + 1711450*x*z - 1170127*z^2
(127631/1108851 : 1984178/1108851 : 1) C2b (-1144879/24285368 : -4154877/24285368 : 1)
** u= 341/477 ; tau(u)= 613/136 ; 79289*x^2 + 338777*y^2 + 492050*x*z + 79289*z^2
(-253783/413819 : 44580/59117 : 1) C1b (-8365292/3963429 : -734357/3963429 : 1)
** u= 342/17 ; tau(u)= 308/325 ; -94286*x^2 - 116386*y^2 + 211828*x*z - 94286*z^2
(1024/1123 : -471/1123 : 1) C1a (5396999/848640 : -481867/848640 : 1)
** u= 343/353 ; tau(u)= 363/10 ; 117449*x^2 + 131569*y^2 + 249418*x*z + 117449*z^2
(-25639/33693 : -6118/33693 : 1) C1b (69826600/14958757 : 7555767/14958757 : 1)
** u= 343/377 ; tau(u)= 411/34 ; 115337*x^2 + 166609*y^2 + 286570*x*z + 115337*z^2
(-170679/315373 : 59710/315373 : 1) C1b (830719/388517 : -96817/388517 : 1)
** u= 343/401 ; tau(u)= 459/58 ; 110921*x^2 + 203953*y^2 + 328330*x*z + 110921*z^2
(-34007/14237 : 6342/14237 : 1) C1b (-529849433/49508520 : 9199201/9901704 : 1)
** u= 345/64 ; tau(u)= 217/281 ; -38897*x^2 - 110833*y^2 + 166114*x*z - 38897*z^2
(16097/58641 : 10816/58641 : 1) C1a (7545161/1662676 : -631917/1662676 : 1)
** u= 345/104 ; tau(u)= 137/241 ; 2863*x^2 - 97393*y^2 + 137794*x*z + 2863*z^2
(29677/61025 : -882964/1037425 : 1) C1a (251159164/48436189 : -365320741/823415213 : 1)
** u= -347/425 ; tau(u)= 1197/772 ; -1071559*x^2 + 240841*y^2 + 1553218*x*z - 1071559*z^2
(18656621/57033703 : 95703024/57033703 : 1) C2b (-276626252/18329895 : 51741391/18329895 : 1)
** u= -348/421 ; tau(u)= 1190/769 ; -1061618*x^2 + 233378*y^2 + 1537204*x*z - 1061618*z^2
(-1750807/2069724 : -7569593/2069724 : 1) C2b (1190333200/16476407 : 212901771/16476407 : 1)
** u= 350/241 ; tau(u)= -132/109 ; 98738*x^2 - 6338*y^2 + 139924*x*z + 98738*z^2
(2182/1827 : 14635/1827 : 1) C1a (3622423/1317493 : 1536219/1317493 : 1)
** u= 351/58 ; tau(u)= 235/293 ; -48497*x^2 - 116473*y^2 + 178426*x*z - 48497*z^2
(201/107 : -746/749 : 1) C1a (3523335/2763907 : 2341919/19347349 : 1)
** u= -352/289 ; tau(u)= 930/641 ; -697858*x^2 + 43138*y^2 + 988804*x*z - 697858*z^2
(-7887/953 : 34544/953 : 1) C2b (-196361620/3794383 : -67054571/3794383 : 1)
** u= -352/457 ; tau(u)= 1266/809 ; -1185058*x^2 + 293794*y^2 + 1726660*x*z - 1185058*z^2
(9671/2801 : -15802/2801 : 1) C2b (-71924020/1201163 : -12409695/1201163 : 1)
** u= -352/481 ; tau(u)= 1314/833 ; -1263874*x^2 + 338818*y^2 + 1850500*x*z - 1263874*z^2
(3163/7484 : -10815/7484 : 1) C2b (-232327132/41885091 : -43199779/41885091 : 1)
** u= -355/337 ; tau(u)= 1029/692 ; -831703*x^2 + 101113*y^2 + 1184866*x*z - 831703*z^2
(-433305/3329849 : -10471636/3329849 : 1) C2b (-46546436/14865725 : -13959131/14865725 : 1)
** u= -355/421 ; tau(u)= 1197/776 ; -1078327*x^2 + 228457*y^2 + 1558834*x*z - 1078327*z^2
(-166571/1300271 : -3096612/1300271 : 1) C2b (229775/20469 : 39721/20469 : 1)
** u= -356/333 ; tau(u)= 1022/689 ; -822706*x^2 + 95042*y^2 + 1171220*x*z - 822706*z^2
(-107906/780559 : -2532339/780559 : 1) C2b (70005/17033 : -14645/17033 : 1)
** u= 358/113 ; tau(u)= 132/245 ; 8114*x^2 - 102626*y^2 + 145588*x*z + 8114*z^2
(870/1993 : -38717/45839 : 1) C1a (-802105/24656 : 1544109/567088 : 1)
** u= 359/98 ; tau(u)= 163/261 ; -7361*x^2 - 109673*y^2 + 155450*x*z - 7361*z^2
(32971/517553 : -78330/517553 : 1) C1a (21247392/12726451 : 2030891/12726451 : 1)
** u= 359/361 ; tau(u)= 363/2 ; 128873*x^2 + 131761*y^2 + 260650*x*z + 128873*z^2
(-21139/24461 : 5434/171227 : 1) C1b (736168/153069 : -569887/1071483 : 1)
** u= -359/569 ; tau(u)= 1497/928 ; -1593487*x^2 + 518641*y^2 + 2369890*x*z - 1593487*z^2
(4510447/7474041 : -8949560/7474041 : 1) C2b (458349484/350700077 : 51425993/350700077 : 1)
** u= -361/529 ; tau(u)= 1419/890 ; -1453879*x^2 + 429361*y^2 + 2143882*x*z - 1453879*z^2
(5930747/19145627 : 28166398/19145627 : 1) C2b (3915305/346731 : 579989/346731 : 1)
** u= 363/2 ; tau(u)= 359/361 ; -128873*x^2 - 131761*y^2 + 260650*x*z - 128873*z^2
(60711/69401 : -30514/485807 : 1) C1a (-46534789/16222023 : 39033523/113554161 : 1)
** u= 363/10 ; tau(u)= 343/353 ; -117449*x^2 - 131569*y^2 + 249418*x*z - 117449*z^2
(300579/242873 : -71302/242873 : 1) C1a (2455139/273360 : -226579/273360 : 1)
** u= 363/50 ; tau(u)= 263/313 ; -64169*x^2 - 126769*y^2 + 200938*x*z - 64169*z^2
(899/1449 : 110/207 : 1) C1a (8372816/1638285 : 708811/1638285 : 1)
** u= -364/361 ; tau(u)= 1086/725 ; -918754*x^2 + 128146*y^2 + 1311892*x*z - 918754*z^2
(6906/19123 : 40147/19123 : 1) C2b (-21770843/1195753 : 5093277/1195753 : 1)
** u= 364/405 ; tau(u)= 446/41 ; 129134*x^2 + 195554*y^2 + 331412*x*z + 129134*z^2
(-29764/17099 : 9189/17099 : 1) C1b (-418309208/2800647 : 38216099/2800647 : 1)
** u= 365/433 ; tau(u)= 501/68 ; 123977*x^2 + 241753*y^2 + 384226*x*z + 123977*z^2
(-3149/8065 : 31888/185495 : 1) C1b (-261909/21140 : 522013/486220 : 1)
** u= 366/49 ; tau(u)= 268/317 ; -67022*x^2 - 129154*y^2 + 205780*x*z - 67022*z^2
(161612/101853 : 85379/101853 : 1) C1a (47644381/414168 : -4219559/414168 : 1)
** u= 367/401 ; tau(u)= 435/34 ; 132377*x^2 + 186913*y^2 + 323914*x*z + 132377*z^2
(-327641/211279 : -110998/211279 : 1) C1b (-125399872/1340225 : 11564751/1340225 : 1)
** u= 367/593 ; tau(u)= 819/226 ; 32537*x^2 + 568609*y^2 + 805450*x*z + 32537*z^2
(-293639/6454769 : 543882/6454769 : 1) C1b (603241661/3334912 : 50527949/3334912 : 1)
** u= 368/457 ; tau(u)= 546/89 ; 119582*x^2 + 282274*y^2 + 433540*x*z + 119582*z^2
(-46601/89929 : 45722/89929 : 1) C1b (-347640643/4815929 : -30200223/4815929 : 1)
** u= -368/593 ; tau(u)= 1554/961 ; -1711618*x^2 + 567874*y^2 + 2550340*x*z - 1711618*z^2
(8/23 : 31/23 : 1) C2b (125957473/6106229 : 18182591/6106229 : 1)
** u= 369/104 ; tau(u)= 161/265 ; -4289*x^2 - 114529*y^2 + 162082*x*z - 4289*z^2
(3097/28549 : -9708/28549 : 1) C1a (651956/270125 : 58513/270125 : 1)
** u= 369/148 ; tau(u)= 73/221 ; 38479*x^2 - 92353*y^2 + 141490*x*z + 38479*z^2
(-33769/150959 : 46476/150959 : 1) C1a (-18957003/664169 : 1636157/664169 : 1)
** u= 371/130 ; tau(u)= 111/241 ; 21479*x^2 - 103841*y^2 + 149962*x*z + 21479*z^2
(3787/1149 : 3086/1149 : 1) C1a (-2725171/184265 : -228711/184265 : 1)
** u= 373/441 ; tau(u)= 509/68 ; 129881*x^2 + 249833*y^2 + 398210*x*z + 129881*z^2
(-362057/880093 : -192528/880093 : 1) C1b (-9310911/959923 : 803323/959923 : 1)
** u= 374/109 ; tau(u)= 156/265 ; -574*x^2 - 116114*y^2 + 164212*x*z - 574*z^2
(72131/469892 : -216371/469892 : 1) C1a (-14760328/3336455 : -1267149/3336455 : 1)
** u= 374/257 ; tau(u)= -140/117 ; 112498*x^2 - 7778*y^2 + 159476*x*z + 112498*z^2
(4946/46453 : -190461/46453 : 1) C1a (1370857/28008 : 443087/28008 : 1)
** u= 375/58 ; tau(u)= 259/317 ; -60353*x^2 - 133897*y^2 + 207706*x*z - 60353*z^2
(12991/36701 : 7510/36701 : 1) C1a (-2111624/3367405 : -391223/3367405 : 1)
** u= -377/369 ; tau(u)= 1115/746 ; -970903*x^2 + 130193*y^2 + 1385354*x*z - 970903*z^2
(-260513/2042791 : -42745074/14299537 : 1) C2b (-1302648/321425 : -2482237/2249975 : 1)
** u= 378/89 ; tau(u)= 200/289 ; -24158*x^2 - 127042*y^2 + 182884*x*z - 24158*z^2
(981/6244 : -1105/6244 : 1) C1a (-543747/890372 : -93103/890372 : 1)
** u= 378/157 ; tau(u)= 64/221 ; 45202*x^2 - 93586*y^2 + 146980*x*z + 45202*z^2
(-877/51 : -550/51 : 1) C1a (-408180/112999 : -34265/112999 : 1)
** u= 378/229 ; tau(u)= -80/149 ; 98482*x^2 - 38002*y^2 + 149284*x*z + 98482*z^2
(-1741/2027 : 2154/2027 : 1) C1a (3526620/294697 : -519827/294697 : 1)
** u= 378/265 ; tau(u)= -152/113 ; 117346*x^2 - 2434*y^2 + 165988*x*z + 117346*z^2
(-335/643 : 3264/643 : 1) C1a (-8113/15692 : 6677/15692 : 1)
** u= -380/281 ; tau(u)= 942/661 ; -729442*x^2 + 13522*y^2 + 1031764*x*z - 729442*z^2
(1635/6508 : -40213/6508 : 1) C2b (379308968/9288915 : 229123493/9288915 : 1)
** u= -380/461 ; tau(u)= 1302/841 ; -1270162*x^2 + 280642*y^2 + 1839604*x*z - 1270162*z^2
(-222787375/99610194 : 644216411/99610194 : 1) C2b (-14843424/6681295 : -3611419/6681295 : 1)
** u= 382/157 ; tau(u)= 68/225 ; 44674*x^2 - 96626*y^2 + 150548*x*z + 44674*z^2
(-18428/85463 : 4695/12209 : 1) C1a (-6674880/138587 : -582721/138587 : 1)
** u= 382/197 ; tau(u)= -12/185 ; 77474*x^2 - 68306*y^2 + 146068*x*z + 77474*z^2
(-1315/2664 : 11111/18648 : 1) C1a (-32529616/1027181 : 23044911/7190267 : 1)
** u= 383/226 ; tau(u)= -69/157 ; 97391*x^2 - 44537*y^2 + 151450*x*z + 97391*z^2
(-43951/135807 : 22250/19401 : 1) C1a (242024/751775 : -24033/150355 : 1)
** u= -384/445 ; tau(u)= 1274/829 ; -1227026*x^2 + 248594*y^2 + 1770532*x*z - 1227026*z^2
(89723/123021 : -189266/123021 : 1) C2b (4334177/6217372 : 841641/6217372 : 1)
** u= 384/533 ; tau(u)= 682/149 ; 103054*x^2 + 420722*y^2 + 612580*x*z + 103054*z^2
(-231863/1092489 : 251600/1092489 : 1) C1b (58112797/4054841 : -5003217/4054841 : 1)
** u= 385/68 ; tau(u)= 249/317 ; -52753*x^2 - 138977*y^2 + 210226*x*z - 52753*z^2
(278189/1033697 : 4328/1033697 : 1) C1a (301595/507644 : -45117/507644 : 1)
** u= 385/549 ; tau(u)= 713/164 ; 94433*x^2 + 454577*y^2 + 656594*x*z + 94433*z^2
(-8502991/4165295 : 5703804/4165295 : 1) C1b (-2785804284/107702125 : 234433279/107702125 : 1)
** u= 388/425 ; tau(u)= 462/37 ; 147806*x^2 + 210706*y^2 + 363988*x*z + 147806*z^2
(-2828/1461 : 173/1461 : 1) C1b (-53717525/1161791 : -4924937/1161791 : 1)
** u= 389/164 ; tau(u)= 61/225 ; 50071*x^2 - 97529*y^2 + 155042*x*z + 50071*z^2
(953/961 : -1548/961 : 1) C1a (229666340/16423621 : 20890237/16423621 : 1)
** u= 389/493 ; tau(u)= 597/104 ; 129689*x^2 + 334777*y^2 + 507730*x*z + 129689*z^2
(-116109/389377 : 67900/389377 : 1) C1b (-26027203/9285156 : -2192357/9285156 : 1)
** u= 389/549 ; tau(u)= 709/160 ; 100121*x^2 + 451481*y^2 + 654002*x*z + 100121*z^2
(-309293/1670197 : 329352/1670197 : 1) C1b (715020/1487731 : -147899/1487731 : 1)
** u= 390/149 ; tau(u)= 92/241 ; 35938*x^2 - 107698*y^2 + 160564*x*z + 35938*z^2
(-36634/155079 : -1753/155079 : 1) C1a (-9828886967/12406560 : -844163441/12406560 : 1)
** u= -391/397 ; tau(u)= 1185/788 ; -1089007*x^2 + 162337*y^2 + 1557106*x*z - 1089007*z^2
(-490045/9077 : 9003044/63539 : 1) C2b (3357044/520691 : 4600389/3644837 : 1)
** u= -391/577 ; tau(u)= 1545/968 ; -1721167*x^2 + 512977*y^2 + 2539906*x*z - 1721167*z^2
(-405591/146035 : 957484/146035 : 1) C2b (-61517100/3406889 : 10000337/3406889 : 1)
** u= -392/333 ; tau(u)= 1058/725 ; -897586*x^2 + 68114*y^2 + 1273028*x*z - 897586*z^2
(-983/592 : 5313/592 : 1) C2b (-3302721/1306171 : 1315271/1306171 : 1)
** u= 393/272 ; tau(u)= -151/121 ; 125167*x^2 - 6481*y^2 + 177250*x*z + 125167*z^2
(-40129/72447 : 230120/72447 : 1) C1a (-249551/256877 : 71469/256877 : 1)
** u= -395/317 ; tau(u)= 1029/712 ; -857863*x^2 + 44953*y^2 + 1214866*x*z - 857863*z^2
(-2973/7589041 : 33161716/7589041 : 1) C2b (-36198125/33096148 : -23413887/33096148 : 1)
** u= 395/397 ; tau(u)= 399/2 ; 156017*x^2 + 159193*y^2 + 315226*x*z + 156017*z^2
(-17065/19631 : -514/19631 : 1) C1b (-767808/2402497 : -210857/2402497 : 1)
** u= 397/461 ; tau(u)= 525/64 ; 149417*x^2 + 267433*y^2 + 433234*x*z + 149417*z^2
(-139369/58713 : -21856/58713 : 1) C1b (-74942572/3643547 : -6605871/3643547 : 1)
** u= 398/281 ; tau(u)= -164/117 ; 131026*x^2 - 482*y^2 + 185300*x*z + 131026*z^2
(673/1982 : -41277/1982 : 1) C1a (-183424/211083 : 211237/211083 : 1)
** u= 399/2 ; tau(u)= 395/397 ; -156017*x^2 - 159193*y^2 + 315226*x*z - 156017*z^2
(250391/217405 : -5014/217405 : 1) C1a (-18788763/10288505 : -2524667/10288505 : 1)
** u= -399/485 ; tau(u)= 1369/884 ; -1403711*x^2 + 311249*y^2 + 2033362*x*z - 1403711*z^2
(-1837/505 : -4736/505 : 1) C2b (-8405362684/293620375 : 1548514233/293620375 : 1)
** u= -400/409 ; tau(u)= 1218/809 ; -1148962*x^2 + 174562*y^2 + 1643524*x*z - 1148962*z^2
(-19519/44051 : 152890/44051 : 1) C2b (1330740/5077753 : -918667/5077753 : 1)
** u= 402/109 ; tau(u)= 184/293 ; -10094*x^2 - 137842*y^2 + 195460*x*z - 10094*z^2
(59/54 : 2609/2214 : 1) C1a (143524/40293 : -505159/1652013 : 1)
** u= 402/145 ; tau(u)= 112/257 ; 29506*x^2 - 119554*y^2 + 174148*x*z + 29506*z^2
(-211/2956 : -25807/67988 : 1) C1a (-811371/191204 : 120409/338284 : 1)
** u= 402/197 ; tau(u)= 8/205 ; 77554*x^2 - 83986*y^2 + 161668*x*z + 77554*z^2
(-9935/16763 : 38368/117341 : 1) C1a (42179/22985 : 38881/160895 : 1)
** u= 402/205 ; tau(u)= -8/197 ; 83986*x^2 - 77554*y^2 + 161668*x*z + 83986*z^2
(-2745/7921 : 5548/7921 : 1) C1a (-442789/405345 : -42361/405345 : 1)
** u= 402/277 ; tau(u)= -152/125 ; 130354*x^2 - 8146*y^2 + 184708*x*z + 130354*z^2
(-862/699 : -2459/699 : 1) C1a (35275/243828 : 90421/243828 : 1)
** u= 405/136 ; tau(u)= 133/269 ; 19303*x^2 - 127033*y^2 + 181714*x*z + 19303*z^2
(-889/10915 : 2084/10915 : 1) C1a (-155105/702091 : 4549/54007 : 1)
** u= 405/164 ; tau(u)= 77/241 ; 47863*x^2 - 110233*y^2 + 169954*x*z + 47863*z^2
(180763/102787 : -9468/4469 : 1) C1a (1472585/497213 : 146921/497213 : 1)
** u= 407/577 ; tau(u)= 747/170 ; 107849*x^2 + 500209*y^2 + 723658*x*z + 107849*z^2
(-179061/460987 : 258238/460987 : 1) C1b (-4640017/11933392 : -1027567/11933392 : 1)
** u= -408/317 ; tau(u)= 1042/725 ; -884786*x^2 + 34514*y^2 + 1252228*x*z - 884786*z^2
(15648/33697 : 127495/33697 : 1) C2b (-2904508/3067603 : -2338143/3067603 : 1)
** u= -408/449 ; tau(u)= 1306/857 ; -1302434*x^2 + 236738*y^2 + 1872100*x*z - 1302434*z^2
(18793/20682 : -34967/20682 : 1) C2b (-40074388/6593389 : -8886201/6593389 : 1)
** u= 411/34 ; tau(u)= 343/377 ; -115337*x^2 - 166609*y^2 + 286570*x*z - 115337*z^2
(1837/3203 : 826/3203 : 1) C1a (2388479/1090107 : 202111/1090107 : 1)
** u= -412/349 ; tau(u)= 1110/761 ; -988498*x^2 + 73858*y^2 + 1401844*x*z - 988498*z^2
(-8393/80526 : -317107/80526 : 1) C2b (2438608/51195 : 736529/51195 : 1)
** u= -412/421 ; tau(u)= 1254/833 ; -1218034*x^2 + 184738*y^2 + 1742260*x*z - 1218034*z^2
(4162723/12541552 : -25670057/12541552 : 1) C2b (1019488/1589519 : 246373/1589519 : 1)
** u= 413/52 ; tau(u)= 309/361 ; -90073*x^2 - 165161*y^2 + 266050*x*z - 90073*z^2
(746321/1887953 : -148580/1887953 : 1) C1a (94821611/420500 : -1690989/84100 : 1)
** u= 414/109 ; tau(u)= 196/305 ; -14654*x^2 - 147634*y^2 + 209812*x*z - 14654*z^2
(3058/5695 : 267/335 : 1) C1a (4538787/3071465 : -444529/3071465 : 1)
** u= 414/169 ; tau(u)= 76/245 ; 51346*x^2 - 114274*y^2 + 177172*x*z + 51346*z^2
(3715/84562 : 60879/84562 : 1) C1a (-52424/463639 : 39533/463639 : 1)
** u= -416/353 ; tau(u)= 1122/769 ; -1009666*x^2 + 76162*y^2 + 1431940*x*z - 1009666*z^2
(-108103/189507 : 1008058/189507 : 1) C2b (4283164/4823847 : 1077691/4823847 : 1)
** u= 416/541 ; tau(u)= 666/125 ; 141806*x^2 + 412306*y^2 + 616612*x*z + 141806*z^2
(-183979/358669 : 206880/358669 : 1) C1b (-8911315323/41853500 : -765944827/41853500 : 1)
** u= -419/549 ; tau(u)= 1517/968 ; -1698487*x^2 + 427241*y^2 + 2476850*x*z - 1698487*z^2
(-164009/383437 : -1027620/383437 : 1) C2b (21453844/6481725 : 119611/259269 : 1)
** u= -420/541 ; tau(u)= 1502/961 ; -1670642*x^2 + 408962*y^2 + 2432404*x*z - 1670642*z^2
(-142772/967961 : 2175487/967961 : 1) C2b (35314760/27743809 : 4444869/27743809 : 1)
** u= 420/593 ; tau(u)= 766/173 ; 116542*x^2 + 526898*y^2 + 763156*x*z + 116542*z^2
(-3404/2229 : 2707/2229 : 1) C1b (107885191/11456531 : 9332961/11456531 : 1)
** u= 423/130 ; tau(u)= 163/293 ; 7231*x^2 - 145129*y^2 + 205498*x*z + 7231*z^2
(-81295/2530499 : 167598/2530499 : 1) C1a (19271760/3651013 : 1652747/3651013 : 1)
** u= -424/333 ; tau(u)= 1090/757 ; -966322*x^2 + 42002*y^2 + 1367876*x*z - 966322*z^2
(-404899/5829170 : -29366349/5829170 : 1) C2b (2586175/761548 : 850399/761548 : 1)
** u= -424/409 ; tau(u)= 1242/833 ; -1208002*x^2 + 154786*y^2 + 1722340*x*z - 1208002*z^2
(-54962/12353 : 179781/12353 : 1) C2b (-392409/109843 : -111703/109843 : 1)
** u= 424/441 ; tau(u)= 458/17 ; 179198*x^2 + 209186*y^2 + 389540*x*z + 179198*z^2
(-13061/13063 : -5040/13063 : 1) C1b (-72166572/37888981 : -6168757/37888981 : 1)
** u= 424/521 ; tau(u)= 618/97 ; 160958*x^2 + 363106*y^2 + 561700*x*z + 160958*z^2
(-262107/333953 : -235616/333953 : 1) C1b (33605500/2791481 : -3019915/2791481 : 1)
** u= 427/242 ; tau(u)= -57/185 ; 113879*x^2 - 65201*y^2 + 185578*x*z + 113879*z^2
(-3/19 : 22/19 : 1) C1a (2231915/273767 : 286029/273767 : 1)
** u= -427/541 ; tau(u)= 1509/968 ; -1691719*x^2 + 403033*y^2 + 2459410*x*z - 1691719*z^2
(425339/246057 : 612260/246057 : 1) C2b (361847788/37624981 : 58586361/37624981 : 1)
** u= -428/585 ; tau(u)= 1598/1013 ; -1869154*x^2 + 501266*y^2 + 2736788*x*z - 1869154*z^2
(-8696/343 : 2469/49 : 1) C2b (-31271817/2455643 : -5424941/2455643 : 1)
** u= 429/148 ; tau(u)= 133/281 ; 26119*x^2 - 140233*y^2 + 201730*x*z + 26119*z^2
(-4831/95989 : 32456/95989 : 1) C1a (403074073/25681461 : 34362773/25681461 : 1)
** u= 429/196 ; tau(u)= 37/233 ; 75463*x^2 - 107209*y^2 + 185410*x*z + 75463*z^2
(-1021/351 : 448/351 : 1) C1a (-12623943/1764380 : 222335/352876 : 1)
** u= 430/61 ; tau(u)= 308/369 ; -87422*x^2 - 177458*y^2 + 279764*x*z - 87422*z^2
(16772/40909 : -10893/40909 : 1) C1a (-8248672/188905 : 734099/188905 : 1)
** u= -431/485 ; tau(u)= 1401/916 ; -1492351*x^2 + 284689*y^2 + 2148562*x*z - 1492351*z^2
(-77995955/380863863 : -1008204704/380863863 : 1) C2b (5134333804/15983685 : -990280027/15983685 : 1)
** u= 435/34 ; tau(u)= 367/401 ; -132377*x^2 - 186913*y^2 + 323914*x*z - 132377*z^2
(128875/74661 : 31046/74661 : 1) C1a (869776/1116021 : 101827/1116021 : 1)
** u= 437/457 ; tau(u)= 477/20 ; 190169*x^2 + 226729*y^2 + 418498*x*z + 190169*z^2
(-8409/6125 : 296/875 : 1) C1b (-32824381/19393921 : -2827651/19393921 : 1)
** u= 438/49 ; tau(u)= 340/389 ; -110798*x^2 - 187042*y^2 + 307444*x*z - 110798*z^2
(17/10 : -7/10 : 1) C1a (-226768/169175 : -29603/169175 : 1)
** u= 438/113 ; tau(u)= 212/325 ; -19406*x^2 - 166306*y^2 + 236788*x*z - 19406*z^2
(613/252 : 2875/1764 : 1) C1a (-12211240/2679727 : 7472193/18758089 : 1)
** u= 441/136 ; tau(u)= 169/305 ; 8431*x^2 - 157489*y^2 + 223042*x*z + 8431*z^2
(-841/673539 : -153244/673539 : 1) C1a (1535461/1217220 : 167057/1217220 : 1)
** u= 441/212 ; tau(u)= 17/229 ; 89599*x^2 - 104593*y^2 + 194770*x*z + 89599*z^2
(192341/1110461 : 1218924/1110461 : 1) C1a (-72166572/37888981 : -6168757/37888981 : 1)
** u= 442/73 ; tau(u)= 296/369 ; -76958*x^2 - 184706*y^2 + 282980*x*z - 76958*z^2
(30947/47689 : 30240/47689 : 1) C1a (62089661/455767 : -5396647/455767 : 1)
** u= -443/333 ; tau(u)= 1109/776 ; -1008103*x^2 + 25529*y^2 + 1426130*x*z - 1008103*z^2
(61067/38297 : -1911012/268079 : 1) C2b (5451977/101996 : -19805987/713972 : 1)
** u= 446/41 ; tau(u)= 364/405 ; -129134*x^2 - 195554*y^2 + 331412*x*z - 129134*z^2
(25168/52421 : -1737/52421 : 1) C1a (673135619/39623665 : -60334813/39623665 : 1)
** u= 447/98 ; tau(u)= 251/349 ; -43793*x^2 - 180601*y^2 + 262810*x*z - 43793*z^2
(13493/15831 : 14350/15831 : 1) C1a (2044160/54051 : -172795/54051 : 1)
** u= -448/373 ; tau(u)= 1194/821 ; -1147378*x^2 + 77554*y^2 + 1626340*x*z - 1147378*z^2
(916/3889 : 12707/3889 : 1) C2b (9003/50119 : -14251/50119 : 1)
** u= -448/577 ; tau(u)= 1602/1025 ; -1900546*x^2 + 465154*y^2 + 2767108*x*z - 1900546*z^2
(174011/459559 : 714780/459559 : 1) C2b (-43453532/502995 : -7516547/502995 : 1)
** u= -449/521 ; tau(u)= 1491/970 ; -1680199*x^2 + 341281*y^2 + 2424682*x*z - 1680199*z^2
(-155085269/319479067 : -986365966/319479067 : 1) C2b (43815368/16899447 : -6439973/16899447 : 1)
** u= 450/61 ; tau(u)= 328/389 ; -100142*x^2 - 195058*y^2 + 310084*x*z - 100142*z^2
(91549/222199 : 51840/222199 : 1) C1a (-15151044/10397825 : -1859617/10397825 : 1)
** u= 451/146 ; tau(u)= 159/305 ; 17351*x^2 - 160769*y^2 + 228682*x*z + 17351*z^2
(2653/6231 : -37346/43617 : 1) C1a (-54642965/3073207 : -32011197/21512449 : 1)
** u= 451/485 ; tau(u)= 519/34 ; 201089*x^2 + 267049*y^2 + 472762*x*z + 201089*z^2
(-4197/6707 : 1642/6707 : 1) C1b (4586083/1111800 : 482879/1111800 : 1)
** u= 453/232 ; tau(u)= -11/221 ; 107527*x^2 - 97561*y^2 + 205330*x*z + 107527*z^2
(42991/46931 : -93332/46931 : 1) C1a (-3181117/13933999 : 1282437/13933999 : 1)
** u= -455/333 ; tau(u)= 1121/788 ; -1034863*x^2 + 14753*y^2 + 1463666*x*z - 1034863*z^2
(439/9313 : 75444/9313 : 1) C2b (-653003/74887 : 496133/74887 : 1)
** u= 456/545 ; tau(u)= 634/89 ; 192094*x^2 + 386114*y^2 + 609892*x*z + 192094*z^2
(-76135/98662 : 64331/98662 : 1) C1b (171421460/9378973 : -15439869/9378973 : 1)
** u= 458/17 ; tau(u)= 424/441 ; -179198*x^2 - 209186*y^2 + 389540*x*z - 179198*z^2
(31763/36298 : -12411/36298 : 1) C1a (-4722197/1018836 : -505909/1018836 : 1)
** u= 459/58 ; tau(u)= 343/401 ; -110921*x^2 - 203953*y^2 + 328330*x*z - 110921*z^2
(369021/143743 : 9730/143743 : 1) C1a (-912410088/18013105 : -16401953/3602621 : 1)
** u= 462/37 ; tau(u)= 388/425 ; -147806*x^2 - 210706*y^2 + 363988*x*z - 147806*z^2
(43161/60614 : 25205/60614 : 1) C1a (-9865271/21560 : 913113/21560 : 1)
** u= 462/145 ; tau(u)= 172/317 ; 12466*x^2 - 171394*y^2 + 243028*x*z + 12466*z^2
(2 : 127/71 : 1) C1a (3560/11081 : -70261/786751 : 1)
** u= 462/149 ; tau(u)= 164/313 ; 17506*x^2 - 169042*y^2 + 240340*x*z + 17506*z^2
(-3253/53722 : -7177/53722 : 1) C1a (-602072/240549 : -53011/240549 : 1)
** u= 464/477 ; tau(u)= 490/13 ; 214958*x^2 + 239762*y^2 + 455396*x*z + 214958*z^2
(-219809/191641 : 61362/191641 : 1) C1b (14544740/860429 : -1451623/860429 : 1)
** u= -467/449 ; tau(u)= 1365/916 ; -1460023*x^2 + 185113*y^2 + 2081314*x*z - 1460023*z^2
(16574469/34911899 : 72622028/34911899 : 1) C2b (1198892/1136713 : 213311/1136713 : 1)
** u= -469/421 ; tau(u)= 1311/890 ; -1364239*x^2 + 134521*y^2 + 1938682*x*z - 1364239*z^2
(472581/940577 : -2197934/940577 : 1) C2b (10487560/20380729 : 4002501/20380729 : 1)
** u= -471/509 ; tau(u)= 1489/980 ; -1698959*x^2 + 296321*y^2 + 2438962*x*z - 1698959*z^2
(-1402885/658029 : -4622212/658029 : 1) C2b (2872108/1750715 : -419007/1750715 : 1)
** u= -472/577 ; tau(u)= 1626/1049 ; -1978018*x^2 + 443074*y^2 + 2866660*x*z - 1978018*z^2
(736384/5110531 : -9729803/5110531 : 1) C2b (7865797/4668449 : -1027927/4668449 : 1)
** u= 473/68 ; tau(u)= 337/405 ; -104321*x^2 - 214481*y^2 + 337298*x*z - 104321*z^2
(89239/244679 : -36684/244679 : 1) C1a (-24592780/846337 : -2194169/846337 : 1)
** u= 473/493 ; tau(u)= 513/20 ; 222929*x^2 + 262369*y^2 + 486898*x*z + 222929*z^2
(-59027/48203 : 18588/48203 : 1) C1b (145183796/4814385 : 14132939/4814385 : 1)
** u= 474/197 ; tau(u)= 80/277 ; 71218*x^2 - 147058*y^2 + 231076*x*z + 71218*z^2
(665/7153 : -5698/7153 : 1) C1a (-188268/112343 : 16507/112343 : 1)
** u= 474/281 ; tau(u)= -88/193 ; 150178*x^2 - 66754*y^2 + 232420*x*z + 150178*z^2
(31983/44242 : -107849/44242 : 1) C1a (89593/122139 : -25283/122139 : 1)
** u= -476/369 ; tau(u)= 1214/845 ; -1201474*x^2 + 45746*y^2 + 1700372*x*z - 1201474*z^2
(2251/4378 : -16437/4378 : 1) C2b (2080104/1372421 : 632779/1372421 : 1)
** u= -476/389 ; tau(u)= 1254/865 ; -1269874*x^2 + 76066*y^2 + 1799092*x*z - 1269874*z^2
(702340/12917493 : -50786861/12917493 : 1) C2b (5560872/569713 : -1770617/569713 : 1)
** u= -476/401 ; tau(u)= 1278/877 ; -1311682*x^2 + 95026*y^2 + 1859860*x*z - 1311682*z^2
(-514641679/2080570044 : -9185014607/2080570044 : 1) C2b (732360/17521919 : -5295815/17521919 : 1)
** u= -476/557 ; tau(u)= 1590/1033 ; -1907602*x^2 + 393922*y^2 + 2754676*x*z - 1907602*z^2
(-374189/415210 : 1612259/415210 : 1) C2b (49226760/2903011 : 8793757/2903011 : 1)
** u= 477/20 ; tau(u)= 437/457 ; -190169*x^2 - 226729*y^2 + 418498*x*z - 190169*z^2
(17309/23177 : -888/3311 : 1) C1a (33558828/21299935 : 2915543/21299935 : 1)
** u= 477/232 ; tau(u)= 13/245 ; 107479*x^2 - 119881*y^2 + 227698*x*z + 107479*z^2
(-24009/16771 : -2044/16771 : 1) C1a (14544740/860429 : -1451623/860429 : 1)
** u= 477/256 ; tau(u)= -35/221 ; 129847*x^2 - 96457*y^2 + 228754*x*z + 129847*z^2
(154075/98459 : -284576/98459 : 1) C1a (512521/1827804 : -234079/1827804 : 1)
** u= 478/281 ; tau(u)= -84/197 ; 150866*x^2 - 70562*y^2 + 235540*x*z + 150866*z^2
(-243176/385027 : 361735/385027 : 1) C1a (-930616/569195 : 18387/113839 : 1)
** u= 480/481 ; tau(u)= 482 ; 230398*x^2 + 232322*y^2 + 462724*x*z + 230398*z^2
(-268133/287675 : -16168/287675 : 1) C1b (15785108/764815 : 1606593/764815 : 1)
** u= 480/493 ; tau(u)= 506/13 ; 230062*x^2 + 255698*y^2 + 486436*x*z + 230062*z^2
(-1243/955 : 218/955 : 1) C1b (-349756/523285 : -45831/523285 : 1)
** u= 482 ; tau(u)= 480/481 ; -230398*x^2 - 232322*y^2 + 462724*x*z - 230398*z^2
(18559/16972 : -341/16972 : 1) C1a (61983260/7919213 : 5803473/7919213 : 1)
** u= 483/250 ; tau(u)= -17/233 ; 124711*x^2 - 108289*y^2 + 233578*x*z + 124711*z^2
(17081/991 : -19330/991 : 1) C1a (5153155/5767023 : -988717/5767023 : 1)
** u= 484/569 ; tau(u)= 654/85 ; 219806*x^2 + 413266*y^2 + 661972*x*z + 219806*z^2
(-42799/109628 : -85481/767396 : 1) C1b (670848/587297 : 640741/4111079 : 1)
** u= 486/89 ; tau(u)= 308/397 ; -79022*x^2 - 220354*y^2 + 331060*x*z - 79022*z^2
(7586/22013 : -7515/22013 : 1) C1a (241363/385464 : 34757/385464 : 1)
** u= 486/241 ; tau(u)= 4/245 ; 116146*x^2 - 120034*y^2 + 236212*x*z + 116146*z^2
(1670/311 : 1953/311 : 1) C1a (-3046225177/95111957 : 296163469/95111957 : 1)
** u= 486/317 ; tau(u)= -148/169 ; 179074*x^2 - 35218*y^2 + 258100*x*z + 179074*z^2
(-8807/22288 : -5499/3184 : 1) C1a (-163824675/644718152 : -103618135/644718152 : 1)
** u= 489/196 ; tau(u)= 97/293 ; 67423*x^2 - 162289*y^2 + 248530*x*z + 67423*z^2
(224407/4969091 : -3462200/4969091 : 1) C1a (-844868/1912011 : 162733/1912011 : 1)
** u= 489/232 ; tau(u)= 25/257 ; 107023*x^2 - 131473*y^2 + 239746*x*z + 107023*z^2
(11483/649407 : -597500/649407 : 1) C1a (-4567132/5796415 : 527487/5796415 : 1)
** u= 490/13 ; tau(u)= 464/477 ; -214958*x^2 - 239762*y^2 + 455396*x*z - 214958*z^2
(139/167 : 42/167 : 1) C1a (-2178005/79289 : -214933/79289 : 1)
** u= 493/557 ; tau(u)= 621/64 ; 234857*x^2 + 377449*y^2 + 628690*x*z + 234857*z^2
(-782383/418447 : 235536/418447 : 1) C1b (-51022141/7167508 : -4431289/7167508 : 1)
** u= 495/98 ; tau(u)= 299/397 ; -70193*x^2 - 225817*y^2 + 334426*x*z - 70193*z^2
(1559/7005 : -406/7005 : 1) C1a (-8086896/1752419 : 738643/1752419 : 1)
** u= 497/529 ; tau(u)= 561/32 ; 244961*x^2 + 312673*y^2 + 561730*x*z + 244961*z^2
(-108529/101369 : -49864/101369 : 1) C1b (239556/53297 : -25193/53297 : 1)
** u= 498/109 ; tau(u)= 280/389 ; -54638*x^2 - 224242*y^2 + 326404*x*z - 54638*z^2
(147533/568195 : 195068/568195 : 1) C1a (-107311517/631340 : -9118527/631340 : 1)
** u= 498/277 ; tau(u)= -56/221 ; 150322*x^2 - 94546*y^2 + 251140*x*z + 150322*z^2
(-3679/4254 : -2953/4254 : 1) C1a (-104645/158057 : 14565/158057 : 1)
** u= 500/541 ; tau(u)= 582/41 ; 246638*x^2 + 335362*y^2 + 588724*x*z + 246638*z^2
(-27476/25489 : -14015/25489 : 1) C1b (88040927/7101072 : -8506037/7101072 : 1)
** u= 501/68 ; tau(u)= 365/433 ; -123977*x^2 - 241753*y^2 + 384226*x*z - 123977*z^2
(3875/5851 : -75508/134573 : 1) C1a (-1113884/311719 : 2549747/7169537 : 1)
** u= 501/80 ; tau(u)= 341/421 ; -103481*x^2 - 238201*y^2 + 367282*x*z - 103481*z^2
(905663/403735 : 369664/403735 : 1) C1a (346679/773515 : -65811/773515 : 1)
** u= 506/13 ; tau(u)= 480/493 ; -230062*x^2 - 255698*y^2 + 486436*x*z - 230062*z^2
(904/775 : -239/775 : 1) C1a (5751005/934919 : 521361/934919 : 1)
** u= 506/265 ; tau(u)= -24/241 ; 139874*x^2 - 115586*y^2 + 256612*x*z + 139874*z^2
(-82577/495997 : -463712/495997 : 1) C1a (405361/940315 : 126849/940315 : 1)
** u= 506/281 ; tau(u)= -56/225 ; 154786*x^2 - 98114*y^2 + 259172*x*z + 154786*z^2
(-20639/21179 : 15000/21179 : 1) C1a (2014244/1311195 : -341747/1311195 : 1)
** u= 507/250 ; tau(u)= 7/257 ; 124951*x^2 - 132049*y^2 + 257098*x*z + 124951*z^2
(-76829/58761 : 7930/58761 : 1) C1a (-956080/608569 : -83241/608569 : 1)
** u= -508/369 ; tau(u)= 1246/877 ; -1280194*x^2 + 14258*y^2 + 1810580*x*z - 1280194*z^2
(467/1238 : -9153/1238 : 1) C2b (1124160/554671 : 658435/554671 : 1)
** u= -508/397 ; tau(u)= 1302/905 ; -1379986*x^2 + 57154*y^2 + 1953268*x*z - 1379986*z^2
(11/56 : 9839/2296 : 1) C2b (-3368960/130321 : 58388259/5343161 : 1)
** u= 509/68 ; tau(u)= 373/441 ; -129881*x^2 - 249833*y^2 + 398210*x*z - 129881*z^2
(548069/953389 : 451836/953389 : 1) C1a (93257159/7817283 : -8084161/7817283 : 1)
** u= -511/565 ; tau(u)= 1641/1076 ; -2054431*x^2 + 377329*y^2 + 2954002*x*z - 2054431*z^2
(-56621/2270001 : 5392544/2270001 : 1) C2b (4190908/9236975 : 1378621/9236975 : 1)
** u= 513/20 ; tau(u)= 473/493 ; -222929*x^2 - 262369*y^2 + 486898*x*z - 222929*z^2
(16625/19337 : -6636/19337 : 1) C1a (-7026629/1167180 : -731509/1167180 : 1)
** u= 513/164 ; tau(u)= 185/349 ; 19567*x^2 - 209377*y^2 + 297394*x*z + 19567*z^2
(319/52399 : 117204/366793 : 1) C1a (746049/409021 : 513077/2863147 : 1)
** u= 517/521 ; tau(u)= 525/4 ; 267257*x^2 + 275593*y^2 + 542914*x*z + 267257*z^2
(-5143/4323 : 160/4323 : 1) C1b (268715/311972 : 49581/311972 : 1)
** u= 519/34 ; tau(u)= 451/485 ; -201089*x^2 - 267049*y^2 + 472762*x*z - 201089*z^2
(481825/275867 : -56486/275867 : 1) C1a (274655328/3791737 : 25563169/3791737 : 1)
** u= -520/421 ; tau(u)= 1362/941 ; -1500562*x^2 + 84082*y^2 + 2125444*x*z - 1500562*z^2
(2587/128803 : -536444/128803 : 1) C2b (-243476219164/4035294915 : 862808101/39953415 : 1)
** u= 520/569 ; tau(u)= 618/49 ; 265598*x^2 + 377122*y^2 + 652324*x*z + 265598*z^2
(-106545/65539 : -32536/65539 : 1) C1b (-14582340/5710459 : 1232669/5710459 : 1)
** u= 521/340 ; tau(u)= -159/181 ; 205919*x^2 - 40241*y^2 + 296722*x*z + 205919*z^2
(64235/46359 : 232528/46359 : 1) C1a (-12214564/11540981 : -1779321/11540981 : 1)
** u= 522/289 ; tau(u)= -56/233 ; 163906*x^2 - 105442*y^2 + 275620*x*z + 163906*z^2
(1301/383 : 2040/383 : 1) C1a (1908469/4031652 : 613097/4031652 : 1)
** u= -524/545 ; tau(u)= 1614/1069 ; -2010946*x^2 + 319474*y^2 + 2879572*x*z - 2010946*z^2
(111842/90723 : 197707/90723 : 1) C2b (45509960/18111723 : -7462219/18111723 : 1)
** u= 525/4 ; tau(u)= 517/521 ; -267257*x^2 - 275593*y^2 + 542914*x*z - 267257*z^2
(4585/4497 : 788/4497 : 1) C1a (20865523/9368668 : -1795819/9368668 : 1)
** u= 525/64 ; tau(u)= 397/461 ; -149417*x^2 - 267433*y^2 + 433234*x*z - 149417*z^2
(88207/218927 : 12560/218927 : 1) C1a (2510235956/18498445 : 224232153/18498445 : 1)
** u= -528/397 ; tau(u)= 1322/925 ; -1432466*x^2 + 36434*y^2 + 2026468*x*z - 1432466*z^2
(-5937/181717 : 1166050/181717 : 1) C2b (2592943/700187 : -1131153/700187 : 1)
** u= 528/545 ; tau(u)= 562/17 ; 278206*x^2 + 315266*y^2 + 594628*x*z + 278206*z^2
(-235/163 : -58/1141 : 1) C1b (-113615/70181 : 68889/491267 : 1)
** u= 530/97 ; tau(u)= 336/433 ; -94078*x^2 - 262082*y^2 + 393796*x*z - 94078*z^2
(1213/4509 : -626/4509 : 1) C1a (6252868/2625403 : 532689/2625403 : 1)
** u= 531/130 ; tau(u)= 271/401 ; -39641*x^2 - 248161*y^2 + 355402*x*z - 39641*z^2
(404727/86161 : -150298/86161 : 1) C1a (-50351272/4536293 : 4299023/4536293 : 1)
** u= 533/549 ; tau(u)= 565/16 ; 283577*x^2 + 318713*y^2 + 603314*x*z + 283577*z^2
(-821225/704569 : 231384/704569 : 1) C1b (31013692/4202253 : -3213599/4202253 : 1)
** u= 534/289 ; tau(u)= -44/245 ; 165106*x^2 - 118114*y^2 + 287092*x*z + 165106*z^2
(-457/1626 : 1477/1626 : 1) C1a (1474760/477217 : 15123/36709 : 1)
** u= 534/337 ; tau(u)= -140/197 ; 207538*x^2 - 58018*y^2 + 304756*x*z + 207538*z^2
(9592/273287 : -530339/273287 : 1) C1a (-43424/433395 : -65321/433395 : 1)
** u= 537/292 ; tau(u)= -47/245 ; 168319*x^2 - 117841*y^2 + 290578*x*z + 168319*z^2
(-24295/24253 : -15176/24253 : 1) C1a (672816011/12951615 : -75174737/12951615 : 1)
** u= 541/208 ; tau(u)= 125/333 ; 70903*x^2 - 206153*y^2 + 308306*x*z + 70903*z^2
(350173/4300637 : 2942040/4300637 : 1) C1a (-8911315323/41853500 : -765944827/41853500 : 1)
** u= 542/317 ; tau(u)= -92/225 ; 192514*x^2 - 92786*y^2 + 302228*x*z + 192514*z^2
(4921/32384 : -52395/32384 : 1) C1a (-158555312/30017435 : -17948201/30017435 : 1)
** u= 543/274 ; tau(u)= -5/269 ; 150127*x^2 - 144697*y^2 + 294874*x*z + 150127*z^2
(-1577/1533 : -2122/10731 : 1) C1a (114999/16475 : 87323/115325 : 1)
** u= -544/433 ; tau(u)= 1410/977 ; -1613122*x^2 + 79042*y^2 + 2284036*x*z - 1613122*z^2
(6319835/29676219 : 115623784/29676219 : 1) C2b (2133917/4079708 : 1128381/4079708 : 1)
** u= 544/545 ; tau(u)= 546 ; 295934*x^2 + 298114*y^2 + 594052*x*z + 295934*z^2
(-5743849/5422767 : -354752/5422767 : 1) C1b (412302340/4295067 : -41164859/4295067 : 1)
** u= 544/593 ; tau(u)= 642/49 ; 291134*x^2 + 407362*y^2 + 708100*x*z + 291134*z^2
(-482851/254693 : -28000/254693 : 1) C1b (-3238703/385709 : -287581/385709 : 1)
** u= 546 ; tau(u)= 544/545 ; -295934*x^2 - 298114*y^2 + 594052*x*z - 295934*z^2
(28718601/27150415 : -1808608/27150415 : 1) C1a (14065/5628 : -1219/5628 : 1)
** u= 546/89 ; tau(u)= 368/457 ; -119582*x^2 - 282274*y^2 + 433540*x*z - 119582*z^2
(378/883 : 349/883 : 1) C1a (-384727/417755 : -11183/83551 : 1)
** u= 546/121 ; tau(u)= 304/425 ; -63134*x^2 - 268834*y^2 + 390532*x*z - 63134*z^2
(264239/812391 : 374770/812391 : 1) C1a (-44321053/17362260 : 4252511/17362260 : 1)
** u= 549/292 ; tau(u)= -35/257 ; 169303*x^2 - 130873*y^2 + 302626*x*z + 169303*z^2
(-26635/66589 : -2972/3917 : 1) C1a (-361519/415964 : -39379/415964 : 1)
** u= 550/109 ; tau(u)= 332/441 ; -86462*x^2 - 278738*y^2 + 412724*x*z - 86462*z^2
(155791/93416 : -106365/93416 : 1) C1a (280080/317009 : -32233/317009 : 1)
** u= 553/328 ; tau(u)= -103/225 ; 204559*x^2 - 90641*y^2 + 316418*x*z + 204559*z^2
(-7327207/10933477 : -10549020/10933477 : 1) C1a (-2437876/2999905 : 307927/2999905 : 1)
** u= 555/194 ; tau(u)= 167/361 ; 47383*x^2 - 232753*y^2 + 335914*x*z + 47383*z^2
(40561/267543 : -174838/267543 : 1) C1a (428179/472960 : 57587/472960 : 1)
** u= 555/218 ; tau(u)= 119/337 ; 80887*x^2 - 212977*y^2 + 322186*x*z + 80887*z^2
(-88591/391791 : 93658/391791 : 1) C1a (-207398720/12036251 : 17715267/12036251 : 1)
** u= -556/405 ; tau(u)= 1366/961 ; -1537906*x^2 + 18914*y^2 + 2175092*x*z - 1537906*z^2
(178/907 : -49941/6349 : 1) C2b (1606425/2035733 : -7654427/14250131 : 1)
** u= -556/549 ; tau(u)= 1654/1105 ; -2132914*x^2 + 293666*y^2 + 3044852*x*z - 2132914*z^2
(5701039/10977094 : -21502851/10977094 : 1) C2b (9183944/5425005 : 1502371/5425005 : 1)
** u= -557/485 ; tau(u)= 1527/1042 ; -1861279*x^2 + 160201*y^2 + 2641978*x*z - 1861279*z^2
(52739/142791 : -380806/142791 : 1) C2b (40680400/2031137 : -11222321/2031137 : 1)
** u= 559/298 ; tau(u)= -37/261 ; 176239*x^2 - 134873*y^2 + 313850*x*z + 176239*z^2
(-8167/4231 : -5490/4231 : 1) C1a (-2349529/613267 : -221999/613267 : 1)
** u= 561/32 ; tau(u)= 497/529 ; -244961*x^2 - 312673*y^2 + 561730*x*z - 244961*z^2
(282571/254387 : -126040/254387 : 1) C1a (2675340/1093031 : 227155/1093031 : 1)
** u= 562/17 ; tau(u)= 528/545 ; -278206*x^2 - 315266*y^2 + 594628*x*z - 278206*z^2
(13837/10857 : 22546/75999 : 1) C1a (369425/221051 : -223239/1547357 : 1)
** u= 565/16 ; tau(u)= 533/549 ; -283577*x^2 - 318713*y^2 + 603314*x*z - 283577*z^2
(174661/146525 : -46896/146525 : 1) C1a (-183860/2183597 : -220309/2183597 : 1)
** u= 570/257 ; tau(u)= 56/313 ; 128962*x^2 - 192802*y^2 + 328036*x*z + 128962*z^2
(1884/121201 : 101077/121201 : 1) C1a (2113473/356203 : 208991/356203 : 1)
** u= 570/373 ; tau(u)= -176/197 ; 247282*x^2 - 46642*y^2 + 355876*x*z + 247282*z^2
(-253625/614247 : 1073642/614247 : 1) C1a (-996373/704740 : -139281/704740 : 1)
** u= 571/346 ; tau(u)= -121/225 ; 224791*x^2 - 86609*y^2 + 340682*x*z + 224791*z^2
(-260701/277201 : -302610/277201 : 1) C1a (-76174376/2618981 : -10392313/2618981 : 1)
** u= -572/461 ; tau(u)= 1494/1033 ; -1806994*x^2 + 97858*y^2 + 2559220*x*z - 1806994*z^2
(73442/1420423 : -5884503/1420423 : 1) C2b (11555861/82697737 : -26981243/82697737 : 1)
** u= 573/256 ; tau(u)= 61/317 ; 127351*x^2 - 197257*y^2 + 332050*x*z + 127351*z^2
(431519/5744319 : -31424/35679 : 1) C1a (-4992572/5350075 : -104977/1070015 : 1)
** u= 573/388 ; tau(u)= -203/185 ; 259879*x^2 - 27241*y^2 + 369538*x*z + 259879*z^2
(-15221/83955 : 228292/83955 : 1) C1a (110105/82644 : 46177/82644 : 1)
** u= -579/449 ; tau(u)= 1477/1028 ; -1778327*x^2 + 67961*y^2 + 2516770*x*z - 1778327*z^2
(240121/908927 : 3878660/908927 : 1) C2b (-79849/901372 : -410811/901372 : 1)
** u= -580/481 ; tau(u)= 1542/1061 ; -1915042*x^2 + 126322*y^2 + 2714164*x*z - 1915042*z^2
(4853/36314 : -900857/254198 : 1) C2b (-109215960/6061427 : -259286441/42429989 : 1)
** u= 582/41 ; tau(u)= 500/541 ; -246638*x^2 - 335362*y^2 + 588724*x*z - 246638*z^2
(21225/23248 : -11723/23248 : 1) C1a (-264854960/6200183 : -24938253/6200183 : 1)
** u= 582/181 ; tau(u)= 220/401 ; 17122*x^2 - 273202*y^2 + 387124*x*z + 17122*z^2
(24337/168804 : 87431/168804 : 1) C1a (-54650837/13897360 : 4672763/13897360 : 1)
** u= 582/193 ; tau(u)= 196/389 ; 36082*x^2 - 264226*y^2 + 377140*x*z + 36082*z^2
(-151478/3434583 : -933499/3434583 : 1) C1a (250343/3273069 : -277937/3273069 : 1)
** u= 583/593 ; tau(u)= 603/10 ; 339689*x^2 + 363409*y^2 + 703498*x*z + 339689*z^2
(-512081/394235 : 20442/394235 : 1) C1b (20369968/14933307 : 2988107/14933307 : 1)
** u= 584/585 ; tau(u)= 586 ; 341054*x^2 + 343394*y^2 + 684452*x*z + 341054*z^2
(-253433/266443 : -17112/266443 : 1) C1b (-48837607/2516453 : -4731661/2516453 : 1)
** u= 585/164 ; tau(u)= 257/421 ; -12257*x^2 - 288433*y^2 + 408274*x*z - 12257*z^2
(123165/166001 : -164696/166001 : 1) C1a (-273174327/993925 : -22870091/993925 : 1)
** u= 585/292 ; tau(u)= 1/293 ; 170527*x^2 - 171697*y^2 + 342226*x*z + 170527*z^2
(-1087/1197 : -8/171 : 1) C1a (-48837607/2516453 : -4731661/2516453 : 1)
** u= 586 ; tau(u)= 584/585 ; -341054*x^2 - 343394*y^2 + 684452*x*z - 341054*z^2
(253433/266443 : 17112/266443 : 1) C1a (-264204/143489 : -35563/143489 : 1)
** u= 586/137 ; tau(u)= 312/449 ; -59806*x^2 - 305858*y^2 + 440740*x*z - 59806*z^2
(55297/7647 : -116/53529 : 1) C1a (-4474756/323903 : -2678307/2267321 : 1)
** u= 594/185 ; tau(u)= 224/409 ; 18274*x^2 - 284386*y^2 + 403012*x*z + 18274*z^2
(-2362/916715 : 225681/916715 : 1) C1a (72187700/1113303 : 6051283/1113303 : 1)
** u= 594/337 ; tau(u)= -80/257 ; 220738*x^2 - 125698*y^2 + 359236*x*z + 220738*z^2
(8105/41642 : -64227/41642 : 1) C1a (19226724/2401571 : 2472761/2401571 : 1)
** u= 595/218 ; tau(u)= 159/377 ; 69767*x^2 - 258977*y^2 + 379306*x*z + 69767*z^2
(120731/70893 : 133478/70893 : 1) C1a (-4615288/242957 : 389721/242957 : 1)
** u= 597/104 ; tau(u)= 389/493 ; -129689*x^2 - 334777*y^2 + 507730*x*z - 129689*z^2
(32661/18337 : 19100/18337 : 1) C1a (-7726545885/67379884 : 671011535/67379884 : 1)
** u= 597/232 ; tau(u)= 133/365 ; 89959*x^2 - 248761*y^2 + 374098*x*z + 89959*z^2
(1603743/7599499 : -6335876/7599499 : 1) C1a (626933060/34532821 : 54886497/34532821 : 1)
** u= 597/260 ; tau(u)= 77/337 ; 129271*x^2 - 221209*y^2 + 362338*x*z + 129271*z^2
(73611/285527 : 1136/1111 : 1) C1a (-3949420/3258141 : 371629/3258141 : 1)
** u= 598/229 ; tau(u)= 140/369 ; 85282*x^2 - 252722*y^2 + 377204*x*z + 85282*z^2
(-99883/564280 : 163377/564280 : 1) C1a (-2522560/144703 : 214367/144703 : 1)
** u= 598/373 ; tau(u)= -148/225 ; 256354*x^2 - 79346*y^2 + 379508*x*z + 256354*z^2
(88663/177842 : -64365/25406 : 1) C1a (-3957551/1262915 : -498733/1262915 : 1)
718
>
ここからは、 "A^4+B^4+C^4=3362*D^4の整点" と同様なので、最終的に得られた(1)の整点のみを記述する。
ここで、対応する整点が見つかった各有理数uについて、0 <= A <= B <=C を満たすように、A,B,Cを交換して、Dの小さい順に(1)の等式を並べ替えると、以下のようになる。
- u=-380/461のとき
4295871272152466746761976654307690460850681558116960^4+5169308675927745227653369081559493536138890498803277^4+18709046623091823208347464671193295234961314573378103^4=20402*1568787235259872750692717840566404947094690664091313^4
19247294083848865784165893014234872401151261232027640160424710514272166362346200795604713732641505077530348167095333351807105955893238882246953151584407135817064461388898616265476555480181748521811713182489589662075886617417833350329675477400072712714620017678508319578944733092615841507094208597049539637609207928815961392496881328120905667061189501411271634701142478974086087125691572518701891695601555367294917152678352141736704231986392201448574709161148885800761348990655^4+34063415156631116354556690882817658804189705813672468131183190313384409220493906689506194699733373572130642291104145084097330778627587390763915622077612369336050620588401784352659033324211645216102544948323984635272472339968147854990463270178960362238831199269273954814427214974828177950939775647496670480449543958677735031151022158391832774634880618359588567730878781921253588029824894796186882686096260454248407601436717791330006206289213216026091928852830641161172509107496^4+105951836834569633753503000265429021877848565627615541905519400522262925493134066831247086354315465323981276880294952510005854993519897009802073162527430225701535510428437097708260585910116771311048792183316971523732970687319290260354930928876132112045973992758910816648000444929213773236156293809558106447113128472912663306670947797817040545550371900366392392667476310725556374115164267411358345120113876689903057893534960431178064193388407973234691550243169793946422108453669^4=20402*8891213535582817838216805212154948452468654266128206674630946520438059751271626150747566070055166691405164993800491298123653154093814161235978298208190888306269368386655411078168737820637162943986525710170530268558881696757805047670402854280898879604715876798631145088036363461940019099497429015046150822657544278716100609536332819898925789469334184212869888406142839234384320613859046021046014512460176861546543743774942841940491926814004482488102630439222830667160413032151^4
...
- u=64/585のとき
11566524698278008178175494709128636544635230699^4+55533467549319684604321403836601861318197410455^4+96201694481007146665176733936502346101197249772^4=20402*8264519317562045735851914877899065409532634189^4
201235769999025040616108512421530821638831162107243560734114828447424583688096507521490798146880684757758688644666148211712268337309645733499404039775261411478202713850680787144500799524672656548217186771393860840067856953653724116779260833364758917364967848328666362316851330766376143326162664461023546309349641946198920374909979886285763532784690124820162805405495541266029605868098942462395490333147006415654571427760812573^4+228991895296943476846069358448285662572777807118153357453285756551756577519546163310269929208192303786610452779818706360037955911373235156110117650605347292265442021710207693409663364208395033823034314939178256202861056410103338435415013393002525195185499447996413583908881130446501609770338239929712181978813206748210293224248617810024968355097728615975554195642496907049228732704008144538771590265557224812367372811850690439^4+519127799174570159436770936780434763788832033523673104480473483896927444545599366641204876740109713023404406669537640877873019793816391887234477991734277351140126883156972148383912386326463828604173163839474506843368060498612202563168561993407416177158921818781034346507607173846414655178714774639055971065734805835660403534853012430204095252129383053797419893217223439936129567197662044815496947487394990790636804111194014180^4=20402*44078585303199400579121350174470014663054541805938193817685611397527261915640980400243271457196865266495006106221800155421464113302849997206452644326299405370763233816671426823395729056576092348227581208363070526604546895649037793549187956994042490411128508419757707441620852444444661751623291752299605081331907732676863887101136006878397008719692818251708891572360477590288262342510798667746579753789405312363010677481612273^4
...
■これまでの結果より、平方因子を持たない正整数 n <=200 で、
2*n^2≡1,2,3 (mod 5), 2*n^2≡1,2,3 (mod 16), n!≡0 (mod 29)
を満たすものについて、不定方程式(1)は、gcd(A,B,C,D)=1である整数解を持つことが確認できた。
さらに、
n=1,33,41,47,51,59,69,77,89,119,123,137,141,149,159,161,173,179,187,197
について、不定方程式(1)は、gcd(A,B,C,D)=1である整数解を無数に持つことが確認できた。
[2025.12.06追記] u=-380/461のときの整点を追加した。
[参考文献]
- [1]Noam Elkies, "On A^4+B^4+C^4=D^4", Math Comp. 51(184), p824-835, 1988.
- [2]StarkExchange MATHEMATICS, "Distribution of Primitive Pytagorean Triples (PPT) and of solutions of A^4+B^4+C^4=D^4", 2016/07/08.
- [3]StarkExchange MATHEMATICS, "More elliptic curves fpr x^4+y^4+z^4=1?", 2017/07/28.
- [4]Tom Womack, "The quartic surfaces x^4+y^4+z^4=N", 2013/05/17.
- [5]Tom Womack, "elk18.mag", 2013/06/07.
- [6]Tom Womack, "elk18.pts", 2013/06/07.
- [7]Tom Womack, "Integer points on x^4+y^4+z^4=Nt^4", 2013/06/07.
- [8]StarkExchange MATHEMATICS, "a^4+b^4+c^4=2*d^2 such that a,b,c,d are all nonzero Integers & a+b+c!=0", 2024/04/26.
| Last Update: 2025.12.06 |
| H.Nakao |