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Integer Points on A^4+20007*B^4=C^4+20007*D^4


[2026.06.24]A^4+20007*B^4=C^4+20007*D^4の整点


■Diophantine Equation
       A^4+n*B^4=C^4+n*D^4 ----------(1)
を満たす自明でない整数の組(A,B,C,D) (ただし 0 < A < C, 0 < D < Bかつgcd(A,B,C,D)=1)を探す。

以下では、Elkiesの論文(参考文献[1])の方法によって、(1)を満たす整数の組(A,B,C,D)を探す。

■(1)およびD!=0より、A/D=y,B/D=x.C/D=tとすると、
       y^4+n*x^4 = t^4+n ----------(2)
       y^4-t^4= y n(1-x^4)
       (y^2+t^2)*(x^2-t^2) = n*(1+x^2)*(1-x^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。

ここで、ある有理数u > 0に対して、
       y^2+t^2 = (n/u)*(1+x^2) ----------(2a)
       y^2-t^2 = u*(1-x^2) ----------(2b)
よって、
       2*u*y^2 = (n+u^2)*x^2+(n-u^2) ----------(3a)
       2*u*t^2 = (n-u^2)*x^2+(n+u^2) ----------(3b)
を満たす有理数の組(x,y,t)が存在すれば、(x,y,t)が(2)を満たすことが分かる。

[pari/gpによる計算]
gp > YY2(n,u,x)
%1 = (1/(2*u)*n - 1/2*u)*x^2 + (1/(2*u)*n + 1/2*u)
gp > TT2(n,u,x)
%2 = (1/(2*u)*n + 1/2*u)*x^2 + (1/(2*u)*n - 1/2*u)
gp > YY2(n,u,x)^2+n*x^4-TT2(n,u,x)^2-n
%3 = 0

■2次曲線(3a),(3b)は、n=u^2のときはsoncularであり、それ以外のときはnon-singularである。
2次曲線(3a)の右辺の判別式は
    -4*(n+u^2)*(n-u^2)
となる。ここで、nが平方数でなければ、任意の有理数uについて、判別式は0にならないので、2次曲線(3a)は常にnon-singularである。
nが平方数であるならば、n=u^2のときに限り、2次曲線(3a)はsingularであり。それ以外のuにつては、non-singularである。

同様に、2次曲線(3b)の右辺の判別式は
    -4*(n-u^2)*(n+u^2)
となる。nが平方数でなければ、任意の有理数uについて、判別式は0にならないので、2次曲線(3b)は常にnon-singularである。
nが平方数であるならば、n=u^2のときに限り、2次曲線(3b)はsingularであり。それ以外のuにつては、non-singularである。

■以下では、n=20007とする。

Pari/GPで簡単なプログラム("a45s.gp")を作成して、max{A,B,C,D} <= 100000の範囲で、小さい整数解を探すと、19個の整数解
    732^4+20007*199^4=2346^4+20007*91^4
    1164^4+20007*789^4=8298^4+20007*623^4
    1902^4+20007*649^4=7716^4+20007*173^4
    2037^4+20007*419^4=5001^4+20007*143^4
    3519^4+20007*371^4=4803^4+20007*57^4
    4422^4+20007*457^4=5952^4+20007*19^4
    5349^4+20007*8149^4=42987^4+20007*8069^4
    6069^4+20007*1214^4=12171^4+20007*1034^4
    8433^4+20007*1202^4=14709^4+20007*156^4
    9141^4+20007*1802^4=15753^4+20007*1672^4
    9189^4+20007*1771^4=12153^4+20007*1737^4
    15891^4+20007*3554^4=25377^4+20007*3452^4
    17901^4+20007*5723^4=66573^4+20007*3131^4
    20211^4+20007*6509^4=77097^4+20007*2473^4
    21678^4+20007*5307^4=63252^4+20007*1433^4
    33138^4+20007*3659^4=46704^4+20007*1143^4
    37863^4+20007*1144^4=37977^4+20007*828^4
    41817^4+20007*1424^4=42087^4+20007*596^4
    56783^4+20007*7546^4=92747^4+20007*2824^4
が見つかった。
これらの整数解から、(3a),(3b)を満たす有理数uをいくつか求めると、
    u = 1157/6, 1368/101, 1469/2, 6840/493, 7011/5, 7785/4, 9918/97, 11115/146, 17295/92, 36569/80, 38415/238, 49725/166, 91143/674, 113886/1037, 154071/1009, 452205/1666
となる。
[gp2cによる計算]
gp > sss(20007,100000)
1:732^4+20007*199^4=2346^4+20007*91^4
2:1164^4+20007*789^4=8298^4+20007*623^4
3:1902^4+20007*649^4=7716^4+20007*173^4
4:2037^4+20007*419^4=5001^4+20007*143^4
5:3519^4+20007*371^4=4803^4+20007*57^4
6:4422^4+20007*457^4=5952^4+20007*19^4
7:5349^4+20007*8149^4=42987^4+20007*8069^4
8:6069^4+20007*1214^4=12171^4+20007*1034^4
9:8433^4+20007*1202^4=14709^4+20007*156^4
10:9141^4+20007*1802^4=15753^4+20007*1672^4
11:9189^4+20007*1771^4=12153^4+20007*1737^4
12:15891^4+20007*3554^4=25377^4+20007*3452^4
13:17901^4+20007*5723^4=66573^4+20007*3131^4
14:20211^4+20007*6509^4=77097^4+20007*2473^4
15:21678^4+20007*5307^4=63252^4+20007*1433^4
16:33138^4+20007*3659^4=46704^4+20007*1143^4
17:37863^4+20007*1144^4=37977^4+20007*828^4
18:41817^4+20007*1424^4=42087^4+20007*596^4
19:56783^4+20007*7546^4=92747^4+20007*2824^4
19 solutions,
time = 86h, 3min, 25,375 ms.
%1 = 19
{Pari/GPによる計算]
gp > uu(20007,732,199,2346,91)
[u, -1; 6*u + 1157, 1; 290*u - 45999, 1]
[u, -1; 6*u - 1157, 1; 290*u - 45999, 1]
[u, -1; 6*u + 1157, 1; 290*u + 45999, 1]
time = 1 ms.
%1 = [-1157/6, 45999/290]
gp > uu(20007,1164,789,8298,623)
[u, -1; 166*u + 49725, 1; 706*u - 203319, 1]
[u, -1; 166*u - 49725, 1; 706*u - 203319, 1]
[u, -1; 166*u + 49725, 1; 706*u + 203319, 1]
time = 1 ms.
%2 = [-49725/166, 203319/706]
gp > uu(20007,1902,649,7716,173)
[u, -1; 238*u + 38415, 1; 274*u - 39159, 1]
[u, -1; 238*u - 38415, 1; 274*u - 39159, 1]
[u, -1; 238*u + 38415, 1; 274*u + 39159, 1]
time = 1 ms.
%3 = [-38415/238, 39159/274]
gp > uu(20007,2037,419,5001,143)
[u, -1; 92*u + 17295, 1; 281*u - 37791, 1]
[u, -1; 92*u - 17295, 1; 281*u - 37791, 1]
[u, -1; 92*u + 17295, 1; 281*u + 37791, 1]
time = 1 ms.
%4 = [-17295/92, 37791/281]
gp > uu(20007,3519,371,4803,57)
[u, -1; 157*u - 12483, 1; 428*u + 112905, 1]
[u, -1; 157*u - 12483, 1; 428*u - 112905, 1]
[u, -1; 157*u + 12483, 1; 428*u + 112905, 1]
time = 1 ms.
%5 = [12483/157, -112905/428]
(20:38) gp > uu(20007,4422,457,5952,19)
[u, -1; 146*u - 11115, 1; 238*u + 62763, 1]
[u, -1; 146*u - 11115, 1; 238*u - 62763, 1]
[u, -1; 146*u + 11115, 1; 238*u + 62763, 1]
time = 1 ms.
%6 = [11115/146, -62763/238]
gp > uu(20007,5349,8149,42987,8069)
[u, -1; 5*u - 7011, 1; 14416*u + 20849933, 1]
[u, -1; 5*u - 7011, 1; 14416*u - 20849933, 1]
[u, -1; 5*u + 7011, 1; 14416*u + 20849933, 1]
%7 = [7011/5, -20849933/14416]
gp > uu(20007,6069,1214,12171,1034)
[u, -1; 80*u + 36569, 1; 281*u - 77292, 1]
[u, -1; 80*u - 36569, 1; 281*u - 77292, 1]
[u, -1; 80*u + 36569, 1; 281*u + 77292, 1]
%8 = [-36569/80, 77292/281]
gp > uu(20007,8433,1202,14709,156)
[u, -1; 97*u - 9918, 1; 7322*u + 1481805, 1]
[u, -1; 97*u - 9918, 1; 7322*u - 1481805, 1]
[u, -1; 97*u + 9918, 1; 7322*u + 1481805, 1]
time = 2 ms.
%9 = [9918/97, -1481805/7322]
gp > uu(20007,9141,1802,15753,1672)
[u, -1; 2*u + 1469, 1; 12545*u - 4572198, 1]
[u, -1; 2*u - 1469, 1; 12545*u - 4572198, 1]
[u, -1; 2*u + 1469, 1; 12545*u + 4572198, 1]
time = 1 ms.
%10 = [-1469/2, 4572198/12545]
gp > uu(20007,9189,1771,12153,1737)
[u, -1; 4*u + 7785, 1; 14909*u - 7907211, 1]
[u, -1; 4*u - 7785, 1; 14909*u - 7907211, 1]
[u, -1; 4*u + 7785, 1; 14909*u + 7907211, 1]
time = 1 ms.
%12 = [-7785/4, 7907211/14909]
gp > uu(20007,15891,3554,25377,3452)
[u, -1; 113*u - 61902, 1; 1054*u + 1322295, 1]
[u, -1; 113*u - 61902, 1; 1054*u - 1322295, 1]
[u, -1; 113*u + 61902, 1; 1054*u + 1322295, 1]
time = 1 ms.
%13 = [61902/113, -1322295/1054]
gp > uu(20007,17901,5723,66573,3131)
[u, -1; 233*u - 41743, 1; 608*u + 125905, 1]
[u, -1; 233*u - 41743, 1; 608*u - 125905, 1]
[u, -1; 233*u + 41743, 1; 608*u + 125905, 1]
time = 2 ms.
%15 = [41743/233, -125905/608]
gp > uu(20007,20211,6509,77097,2473)
[u, -1; 1009*u - 154071, 1; 1996*u + 349765, 1]
[u, -1; 1009*u - 154071, 1; 1996*u - 349765, 1]
[u, -1; 1009*u + 154071, 1; 1996*u + 349765, 1]
time = 1 ms.
%16 = [154071/1009, -349765/1996]
gp > uu(20007,21678,5307,63252,1433)
[u, -1; 674*u - 91143, 1; 19370*u + 3316581, 1]
[u, -1; 674*u - 91143, 1; 19370*u - 3316581, 1]
[u, -1; 674*u + 91143, 1; 19370*u + 3316581, 1]
time = 1 ms.
%17 = [91143/674, -3316581/19370]
gp > uu(20007,33138,3659,46704,1143)
[u, -1; 1666*u + 452205, 1; 3626*u - 325071, 1]
[u, -1; 1666*u - 452205, 1; 3626*u - 325071, 1]
[u, -1; 1666*u + 452205, 1; 3626*u + 325071, 1]
time = 1 ms.
%18 = [325071/3626, -452205/1666]
gp > uu(20007,37863,1144, 37977,828)
[u, -1; 493*u - 6840, 1; 632*u + 2916693, 1]
[u, -1; 493*u - 6840, 1; 632*u - 2916693, 1]
[u, -1; 493*u + 6840, 1; 632*u + 2916693, 1]
time = 1 ms.
%19 = [6840/493, -2916693/632]
gp > uu(20007,41817,1424,42087,596)
[u, -1; 101*u - 1368, 1; 920*u + 1936181, 1]
[u, -1; 101*u - 1368, 1; 920*u - 1936181, 1]
[u, -1; 101*u + 1368, 1; 920*u + 1936181, 1]
%20 = [1368/101, -1936181/920]
gp > uu(20007,56783,7546,92747,2824)
[u, -1; 1037*u - 113886, 1; 23610*u + 5702177, 1]
[u, -1; 1037*u - 113886, 1; 23610*u - 5702177, 1]
[u, -1; 1037*u + 113886, 1; 23610*u + 5702177, 1]
time = 1 ms.
%21 = [113886/1037, -5702177/23610]

■有理数u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200以下の範囲で、2つの2次曲線(3a)と(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1198個のuが抽出される。
[MAGMAによる計算]
> PP(20007,1,200);
**u= 1 , ht= 57 ; ( -100 , -10002 ), ( 57/44 , -3601/22 )
**u= 1/4 , ht= 775 ; ( 199/777 , 160444/777 ), ( 201/775 , 160156/775 )
**u= 1/8 , ht= 101 ; ( 5064/6311 , 9156121/25244 ), ( 101/99 , 40009/99 )
**u= 1/16 , ht= 2981 ; ( -1165/2983 , 2562387/5966 ), ( -1163/2981 , 1280157/2981 )
**u= 1/17 , ht= 134 ; ( 134/19 , 55812/19 ), ( 3217/21118 , -4404582/10559 )
**u= 1/28 , ht= 80559 ; ( 90623/93423 , 68883728/93423 ), ( -80559/27311 , 45018766/27311 )
**u= 1/32 , ht= 2556 ; ( -2923/4043 , -2822679/4043 ), ( -1361/2556 , -13107031/20448 )
**u= 1/33 , ht= 6937 ; ( 2402/6937 , 4217872/6937 ), ( -15977/16450 , 6587808/8225 )
**u= 1/44 , ht= 31397 ; ( 95355/42313 , 69211133/42313 ), ( 31397/15381 , 23195276/15381 )
**u= 1/49 , ht= 3669 ; ( 3670/3247 , 24015156/22729 ), ( 3669/3248 , 12007367/11368 )
**u= 1/64 , ht= 9335 ; ( -9335/8759 , -10242489/8759 ), ( -9337/8761 , -10244751/8761 )
**u= 1/68 , ht= 2681 ; ( 2681/2341 , 2935521/2341 ), ( 373807/45333 , -310561973/45333 )
**u= 1/79 , ht= 180455 ; ( 348601/188547 , -352322021/188547 ), ( 84549/180455 , 177154981/180455 )
**u= 1/113 , ht= 119683 ; ( -157264/49349 , 175242066/49349 ), ( 119683/19000 , -64420263/9500 )
**u= 1/116 , ht= 192831 ; ( -192831/68227 , 220340417/68227 ), ( 68227/192831 , 12961201/11343 )
**u= 1/140 , ht= 114263 ; ( -2538507/926773 , -3198073606/926773 ), ( 114263/62043 , -153869417/62043 )
**u= 1/143 , ht= 102775 ; ( -147981/173171 , 272440391/173171 ), ( -56443/102775 , 140239989/102775 )
**u= 1/144 , ht= 28589 ; ( 3505/28589 , -69139427/57178 ), ( 3507/28591 , 207434329/171546 )
**u= 1/177 , ht= 368663 ; ( 208888/368663 , -563833946/368663 ), ( 1353619/148226 , 905977466/74113 )
**u= 1/196 , ht= 39199 ; ( -785/39201 , 54902008/39201 ), ( -783/39199 , 54899152/39199 )
**u= 1/200 , ht= 43272 ; ( 43272/17095 , -1316195321/341900 ), ( -55091/484 , 311708319/1936 )
**u= 3/29 , ht= 2921 ; ( 2921/1819 , -1070061/1819 ), ( -54803/14957 , -17665233/14957 )
**u= 3/35 , ht= 1397 ; ( 7148/17683 , 6515838/17683 ), ( -1397/332 , 245271/166 )
**u= 3/37 , ht= 55 ; ( -55/19 , 20439/19 ), ( -5429/18860 , 3446787/9430 )
**u= 3/40 , ht= 3704 ; ( 2609/3704 , 6618549/14816 ), ( 5632/6667 , -12749481/26668 )
**u= 3/44 , ht= 12545 ; ( 12545/863 , 4816566/863 ), ( -154711/7385 , -59327652/7385 )
**u= 3/67 , ht= 3946 ; ( -3946/7 , 266448 ), ( 55937/84010 , -23852724/42005 )
**u= 3/68 , ht= 7409 ; ( -10243/161 , 4878099/161 ), ( -2383/7409 , -3706002/7409 )
**u= 3/101 , ht= 2231 ; ( 216097/119137 , 143203791/119137 ), ( -2231/716 , 679881/358 )
**u= 3/112 , ht= 12755 ; ( -12755/979 , -7817724/979 ), ( 66029/25793 , -86641719/51586 )
**u= 3/115 , ht= 3791 ; ( -464/3791 , 2365086/3791 ), ( 95603/77962 , -38195586/38981 )
**u= 3/125 , ht= 1634 ; ( 1634/899 , 6020256/4495 ), ( -2521/1261 , 9099189/6305 )
**u= 3/133 , ht= 1801 ; ( -68860/153733 , -112179426/153733 ), ( -1801/460 , -618939/230 )
**u= 3/136 , ht= 175835 ; ( -175835/24901 , 119591946/24901 ), ( -706969/39161 , 476815602/39161 )
**u= 3/140 , ht= 15377 ; ( -9067/15377 , 12196773/15377 ), ( 25757/125297 , 87399243/125297 )
**u= 3/148 , ht= 29695 ; ( 29695/8827 , 21762861/8827 ), ( -281629/13853 , 198083526/13853 )
**u= 3/181 , ht= 54983 ; ( 16792/54983 , -44662914/54983 ), ( -49759/73651 , -69052587/73651 )
**u= 3/184 , ht= 2213930 ; ( 2213930/328367 , -7012506159/1313468 ), ( -4424593/139343 , 3467471202/139343 )
**u= 4/7 , ht= 997 ; ( 13177/17 , -3486891/34 ), ( -277/997 , -273819/1994 )
**u= 4/11 , ht= 1609 ; ( -4217/491 , 1408311/982 ), ( 1609/3 , -533741/6 )
**u= 4/15 , ht= 23263 ; ( 23263/13543 , 10427121/27086 ), ( 45359/9449 , 17947761/18898 )
**u= 4/27 , ht= 22381 ; ( 87637/5287 , 45628271/10574 ), ( 22381/175 , 34895717/1050 )
**u= 4/51 , ht= 192503 ; ( 152947/367759 , -284489829/735518 ), ( 179651/192503 , -188073489/385006 )
**u= 4/91 , ht= 119361 ; ( 1456591/1683 , 1389743257/3366 ), ( -119361/110323 , 155077361/220646 )
**u= 4/95 , ht= 277019 ; ( 559731/213931 , -584150125/427862 ), ( -277019/218501 , 343946937/437002 )
**u= 4/111 , ht= 413539 ; ( 413539/93563 , 446780603/187126 ), ( -1282799/211705 , 1370033673/423410 )
**u= 4/123 , ht= 173747 ; ( -411883/487487 , -101130699/139282 ), ( 173747/115855 , -231645351/231710 )
**u= 4/147 , ht= 3871 ; ( 163853/2057 , 1390981343/28798 ), ( 3871/1181 , -34354349/16534 )
**u= 5/17 , ht= 993 ; ( -40456/3277 , -7485444/3277 ), ( -993/724 , -56660/181 )
**u= 5/47 , ht= 16899 ; ( 308/16899 , -5182904/16899 ), ( -439399/537308 , 53210874/134327 )
**u= 5/73 , ht= 534 ; ( 534/23 , 204266/23 ), ( 433373/77206 , 84114141/38603 )
**u= 5/81 , ht= 4816 ; ( 4816/3763 , 2460380/3763 ), ( -3763/4816 , -615095/1204 )
**u= 5/106 , ht= 4223 ; ( -3674/4223 , -5155467/8446 ), ( 18991867/16213554 , -22999407337/32427108 )
**u= 5/118 , ht= 28201 ; ( 13333/28201 , -15156642/28201 ), ( 251353/55709 , -125091912/55709 )
**u= 5/122 , ht= 31862 ; ( 271321/39643 , -135469416/39643 ), ( -16389/31862 , 35403587/63724 )
**u= 5/126 , ht= 315569 ; ( 315569/62813 , 161550316/62813 ), ( 863788/233851 , -898612881/467702 )
**u= 5/137 , ht= 437949 ; ( 377258/437949 , -302624726/437949 ), ( -483181/63002 , -127553373/31501 )
**u= 5/143 , ht= 217696 ; ( -217696/193 , -116441988/193 ), ( 258987/214096 , 44933251/53524 )
**u= 5/154 , ht= 184182 ; ( -184182/31561 , -207449737/63122 ), ( 1870411/251618 , 2095139787/503236 )
**u= 5/186 , ht= 224723 ; ( -68351/224723 , -143287384/224723 ), ( -4986233/453554 , 6108566463/907108 )
**u= 8/15 , ht= 752 ; ( -89317/21248 , -50294673/84992 ), ( -752/23 , 412155/92 )
**u= 8/19 , ht= 651 ; ( 1985/446 , 1254357/1784 ), ( 394/651 , -469159/2604 )
**u= 8/39 , ht= 11437 ; ( 106492/9577 , 94447177/38308 ), ( 11437/3572 , 10583923/14288 )
**u= 8/43 , ht= 37687 ; ( 233453/78266 , -228377811/313064 ), ( 37687/5566 , -35334807/22264 )
**u= 8/51 , ht= 1310 ; ( -42614/991 , -43057173/3964 ), ( -1087/1310 , -1719493/5240 )
**u= 8/59 , ht= 5017 ; ( 238/5017 , 5456943/20068 ), ( 209193/68950 , 239308879/275800 )
**u= 8/71 , ht= 4267 ; ( -7348/23963 , -29872779/95852 ), ( -2052/4267 , 5643109/17068 )
**u= 8/99 , ht= 52101 ; ( 37670/52101 , 38778683/89316 ), ( 524314/118295 , 756452347/473180 )
**u= 8/103 , ht= 165032 ; ( -76915/165032 , -261373221/660128 ), ( 396604/317397 , -729204629/1269588 )
**u= 8/107 , ht= 258974 ; ( -63845/258974 , -390257451/1035896 ), ( 1542587/756886 , -2514052059/3027544 )
**u= 8/119 , ht= 151407 ; ( -128600/151407 , 306516769/605628 ), ( 228916/127171 , 404061429/508684 )
**u= 8/123 , ht= 1587337 ; ( -1587337/604646 , 2664613009/2418584 ), ( 11638706/8981045 , 23061612637/35924180 )
**u= 8/135 , ht= 27091 ; ( -27091/22604 , 173956201/271248 ), ( 79439/25084 , 410725283/301008 )
**u= 8/191 , ht= 254873 ; ( -587740/991257 , 2252741797/3965028 ), ( 18988/254873 , 499612581/1019492 )
**u= 9/16 , ht= 109 ; ( -45/109 , -15726/109 ), ( -137/329 , -47526/329 )
**u= 9/31 , ht= 2643 ; ( -8632/231 , -534294/77 ), ( 2643/736 , -254637/368 )
**u= 9/55 , ht= 181 ; ( 303/643 , 175749/643 ), ( -181/126 , -9088/21 )
**u= 9/73 , ht= 1963 ; ( 1890/1963 , 776208/1963 ), ( 243619/28780 , 34938723/14390 )
**u= 9/76 , ht= 491 ; ( -491/263 , 161889/263 ), ( 19449/19957 , -8099253/19957 )
**u= 9/100 , ht= 697 ; ( -253/697 , 247209/697 ), ( -761/2089 , -741228/2089 )
**u= 9/103 , ht= 343 ; ( -137/343 , -17853/49 ), ( 7343/1103 , -2512419/1103 )
**u= 9/112 , ht= 4471 ; ( 4471/1671 , 561357/557 ), ( 14011/3791 , 602499/446 )
**u= 9/121 , ht= 382 ; ( 382/261 , 18852/29 ), ( 981/1790 , -4117122/9845 )
**u= 9/148 , ht= 1473 ; ( 86227/6643 , -35076306/6643 ), ( -1473/437 , -623169/437 )
**u= 9/169 , ht= 1769 ; ( 628/1769 , 10576542/22997 ), ( 629/1770 , -1763956/3835 )
**u= 9/184 , ht= 19543 ; ( -45041/84348 , 1747187/3408 ), ( 11484/19543 , 41003919/78172 )
**u= 9/196 , ht= 1447 ; ( -365/4339 , -2032374/4339 ), ( -121/1447 , 677742/1447 )
**u= 10/7 , ht= 151 ; ( 151/52 , -26727/104 ), ( 52/151 , -177/2 )
**u= 10/19 , ht= 6994 ; ( -1423/6994 , 1967973/13988 ), ( 9711/2 , -2677625/4 )
**u= 10/31 , ht= 6557 ; ( -6557/4944 , 2892257/9888 ), ( -38733/46424 , -21293941/92848 )
**u= 10/51 , ht= 4037 ; ( 39389938/4229291 , -1626942825/768962 ), ( -4037/434 , 1834195/868 )
**u= 10/63 , ht= 388 ; ( 388/249 , -694421/1494 ), ( 249/388 , -694421/2328 )
**u= 10/71 , ht= 57211 ; ( -8268132/6752131 , -5689820033/13504262 ), ( 57211/2612 , -30525801/5224 )
**u= 10/83 , ht= 39139 ; ( -39139/7922 , -23013009/15844 ), ( 87469/140838 , -95543701/281676 )
**u= 10/87 , ht= 129308 ; ( -9176/176743 , -14917445/50498 ), ( 129308/36479 , 79271977/72958 )
**u= 10/91 , ht= 28593 ; ( 18106/30027 , -21158351/60054 ), ( -28593/13774 , 19151485/27548 )
**u= 10/143 , ht= 364492 ; ( -364492/68941 , -280604517/137882 ), ( 24626431/2957212 , 18762227961/5914424 )
**u= 10/159 , ht= 46639 ; ( 145471/146372 , -164604195/292744 ), ( 46639/45208 , 51809241/90416 )
**u= 10/167 , ht= 502611 ; ( -502611/34628 , 411836147/69256 ), ( -26885252/1402711 , -22007396535/2805422 )
**u= 12 , ht= 127 ; ( 115/127 , -9897/254 ), ( -37/137 , -8169/274 )
**u= 12/5 , ht= 191 ; ( -169/191 , -32931/382 ), ( -71/289 , -38421/578 )
**u= 12/61 , ht= 5479 ; ( -1841/5479 , 2606817/10958 ), ( -3254441/54199 , -1467970467/108398 )
**u= 12/101 , ht= 217447 ; ( -2917919/541129 , -1722232083/1082258 ), ( -217447/217055 , -178300683/434110 )
**u= 12/137 , ht= 18583 ; ( -632729/917563 , -753326589/1835126 ), ( 18583/9541 , 14118789/19082 )
**u= 12/157 , ht= 61871 ; ( -441065/273913 , 375662853/547826 ), ( -10663/61871 , -45426369/123742 )
**u= 12/181 , ht= 81883 ; ( 5168651/151331 , -4017148407/302662 ), ( -49523/81883 , -74342919/163766 )
**u= 12/197 , ht= 574837 ; ( -1908283/31379 , 1546856127/62758 ), ( -574837/91811 , -471805551/183622 )
**u= 13/9 , ht= 273 ; ( -664/731 , -82184/731 ), ( -273/40 , -8611/15 )
**u= 13/10 , ht= 609 ; ( 229/609 , 57076/609 ), ( 3477/577 , 309190/577 )
**u= 13/11 , ht= 509 ; ( -399/509 , 59503/509 ), ( 1543/580 , 75831/290 )
**u= 13/17 , ht= 679 ; ( 338/2399 , -277098/2399 ), ( 679/662 , -54231/331 )
**u= 13/19 , ht= 1 ; ( -1 , 171 ), ( -72717/69430 , -6078412/34715 )
**u= 13/28 , ht= 9651 ; ( -389887/122961 , -60008156/122961 ), ( -9651/653 , -1419874/653 )
**u= 13/30 , ht= 77 ; ( 4363/7568 , 241321/1376 ), ( -77/23 , 12210/23 )
**u= 13/44 , ht= 8225 ; ( 8225/3077 , -1615881/3077 ), ( 16391/25081 , 5513166/25081 )
**u= 13/49 , ht= 14878 ; ( -33050/29253 , 59992822/204771 ), ( -13537/14878 , 13670553/52073 )
**u= 13/55 , ht= 1124 ; ( -1124/559 , -258252/559 ), ( -29649/38416 , 1247893/4802 )
**u= 13/59 , ht= 10927 ; ( 16027/493 , -3416547/493 ), ( 10927/8720 , -1489377/4360 )
**u= 13/62 , ht= 9235 ; ( -9235/5428 , 4679541/10856 ), ( 17953/7661 , 4263474/7661 )
**u= 13/76 , ht= 24455 ; ( 928843/169527 , 228333029/169527 ), ( 19933/24455 , 7629633/24455 )
**u= 13/83 , ht= 3301 ; ( 1098/3301 , 879176/3301 ), ( 19667/7225 , -5295069/7225 )
**u= 13/84 , ht= 769 ; ( 769/659 , 257479/659 ), ( -26941/28205 , -9916468/28205 )
**u= 13/94 , ht= 7121 ; ( -45253/11852 , 25162389/23704 ), ( -5616/7121 , -4878217/14242 )
**u= 13/115 , ht= 5107 ; ( -5107/4783 , 2081457/4783 ), ( -22887/4598 , 3472196/2299 )
**u= 13/118 , ht= 2919 ; ( -1565/2919 , 142576/417 ), ( 85442/2075 , -51508023/4150 )
**u= 13/126 , ht= 7317 ; ( -491179/68324 , 308830931/136648 ), ( -5143/7317 , 8354602/21951 )
**u= 13/128 , ht= 227 ; ( -26935/55447 , 38692197/110894 ), ( -227/90 , 1226191/1440 )
**u= 13/136 , ht= 6183 ; ( 7981/909 , 2598542/909 ), ( 6183/1433 , -2053216/1433 )
**u= 13/142 , ht= 25367 ; ( -21217/49144 , -35388579/98288 ), ( -5589/25367 , -8586392/25367 )
**u= 13/163 , ht= 31619 ; ( 1589389/235233 , -569027737/235233 ), ( -21513/31619 , 13544297/31619 )
**u= 13/166 , ht= 24193 ; ( 24193/10747 , -9461394/10747 ), ( 55206/143435 , -109860157/286870 )
**u= 13/170 , ht= 1647 ; ( -493917/72863 , 180575006/72863 ), ( -253/1647 , 9880/27 )
**u= 13/171 , ht= 1 ; ( 106864859/106879479 , -164476268479/320638437 ), ( -1 , -513 )
**u= 13/176 , ht= 30793 ; ( 271163/11977 , 28539489/3422 ), ( -30793/1445 , -22689261/2890 )
**u= 13/178 , ht= 36796 ; ( -36796/9573 , 28142749/19146 ), ( 13929/58963 , 22422596/58963 )
**u= 13/180 , ht= 14471 ; ( -10503/31877 , -37473047/95631 ), ( 5381/14471 , -5745949/14471 )
**u= 13/185 , ht= 7536 ; ( -69372/11837 , 26552552/11837 ), ( -4391/7536 , -822703/1884 )
**u= 13/189 , ht= 11591 ; ( 4304/11591 , -14145742/34773 ), ( 108029/15664 , -62443171/23496 )
**u= 13/194 , ht= 21261 ; ( 1030415/85829 , 399501762/85829 ), ( -8809/21261 , -8891824/21261 )
**u= 13/200 , ht= 23286 ; ( 23286/10627 , 200829073/212540 ), ( -21907/53018 , -90018477/212072 )
**u= 15/2 , ht= 106 ; ( 67/106 , 9165/212 ), ( -454/17 , -33231/34 )
**u= 15/22 , ht= 2623 ; ( 10601/107 , -1284120/107 ), ( 2623/1336 , 713115/2672 )
**u= 15/26 , ht= 289 ; ( 133/289 , 41892/289 ), ( -16312/22571 , -7334079/45142 )
**u= 15/38 , ht= 1301 ; ( 1301/313 , -213018/313 ), ( 8411/4832 , 3088389/9664 )
**u= 15/59 , ht= 6842 ; ( 6842/6551 , 1878978/6551 ), ( -69787/102886 , -12330231/51443 )
**u= 15/67 , ht= 63236 ; ( 63236/19753 , -14003892/19753 ), ( 66269/127172 , 7578171/31793 )
**u= 15/77 , ht= 377 ; ( 146/377 , 91614/377 ), ( -2237051/868898 , -271915479/434449 )
**u= 15/82 , ht= 13447 ; ( -145073/9374 , 67992069/18748 ), ( -13447/2461 , 3196812/2461 )
**u= 15/98 , ht= 6191 ; ( -23849/17587 , -53028306/123109 ), ( -6191/4213 , 13401000/29491 )
**u= 15/166 , ht= 196049 ; ( -196049/14107 , 65398890/14107 ), ( -299819/166807 , -114156912/166807 )
**u= 15/179 , ht= 17437 ; ( 239524/134407 , 94896240/134407 ), ( -17437/1864 , 6501/2 )
**u= 16/15 , ht= 5507 ; ( -373/5507 , 2138173/22028 ), ( -5507/373 , -2138173/1492 )
**u= 16/23 , ht= 8095 ; ( 8095/4369 , -4412313/17476 ), ( 6871/9401 , -5585361/37604 )
**u= 16/67 , ht= 224221 ; ( -1119079/74861 , -918212247/299444 ), ( 54711/224221 , 188950247/896884 )
**u= 16/111 , ht= 168127 ; ( -1407377/358559 , -1530396059/1434236 ), ( 168127/156065 , -241727011/624260 )
**u= 16/119 , ht= 322213 ; ( 1391403/119701 , 1523713787/478804 ), ( 111821/322213 , 372122673/1288852 )
**u= 17/8 , ht= 329 ; ( -29536/4907 , -8216259/19628 ), ( 177/329 , 25631/329 )
**u= 17/23 , ht= 22331 ; ( 83984/78303 , 13358254/78303 ), ( -17827/22331 , -3324189/22331 )
**u= 17/40 , ht= 53959 ; ( -591/53959 , -8278915/53959 ), ( 303481/82326 , -192971723/329304 )
**u= 17/55 , ht= 34176 ; ( -34176/28159 , 7966426/28159 ), ( -77633/157328 , -15780813/78664 )
**u= 17/71 , ht= 35443 ; ( 34315/150329 , -31517637/150329 ), ( 35443/3493 , -7279653/3493 )
**u= 17/79 , ht= 628947 ; ( 1110702/407207 , 255063016/407207 ), ( -366137/628947 , -156910271/628947 )
**u= 17/80 , ht= 176743 ; ( 182473/204343 , -59440032/204343 ), ( 7813/176743 , -76770111/353486 )
**u= 17/92 , ht= 276167 ; ( 12265/276167 , 64319916/276167 ), ( -435348609/52758035 , 102034911443/52758035 )
**u= 17/103 , ht= 473692 ; ( 473692/177989 , -2650614/3787 ), ( -2224087/1829700 , 354512681/914850 )
**u= 17/120 , ht= 98791 ; ( 35801/98791 , -27922472/98791 ), ( -98791/35801 , 27922472/35801 )
**u= 17/128 , ht= 1988 ; ( -1988/531 , -9035603/8496 ), ( 82871/92105 , -34003521/92105 )
**u= 17/148 , ht= 1739985 ; ( -1739985/335567 , 522946978/335567 ), ( 30021569/2007537 , -8879422852/2007537 )
**u= 17/161 , ht= 2637 ; ( 14871866/19223811 , -7480971836/19223811 ), ( 2637/2032 , 512341/1016 )
**u= 17/167 , ht= 358780 ; ( 1153051/102287 , 362877723/102287 ), ( -88947/358780 , 57937547/179390 )
**u= 17/168 , ht= 474458 ; ( 474458/257479 , 678914707/1029916 ), ( 4937207/563894 , -6249739229/2255576 )
**u= 17/176 , ht= 3881803 ; ( -3881803/296283 , -1252860197/296283 ), ( -37657791/10289075 , -25126197209/20578150 )
**u= 17/177 , ht= 624820 ; ( 624820/139171 , 206589102/139171 ), ( -22349297/6263006 , 3745314716/3131503 )
**u= 17/180 , ht= 951509 ; ( -951509/125791 , 312365415/125791 ), ( 117172437/5111557 , 114511063544/15334671 )
**u= 17/183 , ht= 779939 ; ( -1851488/254171 , -613270498/254171 ), ( -779939/25552 , -128038551/12776 )
**u= 17/184 , ht= 659953 ; ( -659953/337672 , 975726429/1350688 ), ( -4046404/1055939 , 5504215857/4223756 )
**u= 17/188 , ht= 299329 ; ( -373/899959 , 299332107/899959 ), ( 299329/142913 , 110324058/142913 )
**u= 17/192 , ht= 437849 ; ( 437849/278873 , 24926934/39839 ), ( 755471/168383 , 520328943/336766 )
**u= 17/199 , ht= 1607 ; ( 270124/21971 , 92741262/21971 ), ( 1607/15 , -549937/15 )
**u= 19/3 , ht= 13 ; ( -302/97 , -12596/97 ), ( 13/10 , -326/5 )
**u= 19/12 , ht= 649 ; ( 20255/6259 , 153183/569 ), ( 649/115 , 52393/115 )
**u= 19/13 , ht= 289210 ; ( -289910/289149 , -33874976/289149 ), ( 287691/289210 , -16874408/144605 )
**u= 19/21 , ht= 244 ; ( -244/113 , -28274/113 ), ( 2887/1004 , 160703/502 )
**u= 19/25 , ht= 399 ; ( 1438/2063 , -288510/2063 ), ( -399/226 , 26305/113 )
**u= 19/29 , ht= 497 ; ( 497/439 , -81939/439 ), ( 1649/555 , 214993/555 )
**u= 19/42 , ht= 1051 ; ( 1165/4567 , -700884/4567 ), ( 274/1051 , -323023/2102 )
**u= 19/47 , ht= 15797 ; ( -11766/18079 , 3393206/18079 ), ( -15797/42 , -1242499/21 )
**u= 19/52 , ht= 1 ; ( 1 , -234 ), ( -52929/22835 , -9538093/22835 )
**u= 19/53 , ht= 16676 ; ( -16676/1079 , 2791482/1079 ), ( -8507/19743 , -3591121/19743 )
**u= 19/54 , ht= 1783 ; ( -3163/1921 , 623984/1921 ), ( -1783/539 , -314078/539 )
**u= 19/60 , ht= 14783 ; ( -728087/51193 , 129726256/51193 ), ( 14783/5663 , -2813662/5663 )
**u= 19/69 , ht= 27728 ; ( 27728/10961 , 5682906/10961 ), ( 644141/195112 , 64141183/97556 )
**u= 19/82 , ht= 1779 ; ( 32219/1729 , 957732/247 ), ( -1779/599 , -390034/599 )
**u= 19/116 , ht= 9389 ; ( -2733/9389 , -58942/229 ), ( 63427/45671 , 19315551/45671 )
**u= 19/117 , ht= 1 ; ( -1 , -351 ), ( 3328643/3346220 , 585721257/1673110 )
**u= 19/124 , ht= 6163 ; ( -3571/6163 , -1819962/6163 ), ( 161599/61717 , 44199201/61717 )
**u= 19/138 , ht= 54107 ; ( 54107/37202 , 35398567/74404 ), ( -37138/59255 , 37699901/118510 )
**u= 19/169 , ht= 2697 ; ( 1316/2697 , -11637076/35061 ), ( 159/4712 , -2285326/7657 )
**u= 19/175 , ht= 4310 ; ( -4310/1153 , 6771342/5765 ), ( -21641/2110 , 16500237/5275 )
**u= 19/181 , ht= 3549 ; ( -29665/28979 , -12801969/28979 ), ( -3549/1700 , 35729/50 )
**u= 19/182 , ht= 18570 ; ( 130841/269 , -40502286/269 ), ( -13189/18570 , 14101411/37140 )
**u= 24/5 , ht= 187 ; ( 32/1307 , 238875/5228 ), ( -28/187 , 34509/748 )
**u= 24/37 , ht= 21196 ; ( -21196/19541 , -14320659/78164 ), ( -622376/103379 , -313399581/413516 )
**u= 24/65 , ht= 1089562 ; ( 1257383/26738 , 828039993/106952 ), ( 1089562/460817 , 778886463/1843268 )
**u= 24/85 , ht= 563 ; ( 308/563 , 483171/2252 ), ( -1973/628 , -1558917/2512 )
**u= 24/97 , ht= 19046 ; ( 2071/19046 , -15408951/76184 ), ( -103126/50231 , -92260041/200924 )
**u= 24/161 , ht= 11009 ; ( -2822206/27977 , 2924509959/111908 ), ( -11009/4930 , -12499119/19720 )
**u= 24/185 , ht= 170911 ; ( -209398/78647 , 248452749/314588 ), ( 170911/15326 , 190601163/61304 )
**u= 25/9 , ht= 531 ; ( 136/915 , 832846/13725 ), ( -531/8 , -47813/12 )
**u= 25/16 , ht= 3035 ; ( -853/3035 , -1261323/15175 ), ( -803/3085 , 1275273/15425 )
**u= 25/39 , ht= 24170 ; ( -120530/84701 , -92014032/423505 ), ( -2759/24170 , 7597344/60425 )
**u= 25/56 , ht= 1513 ; ( -1455/1513 , -1571093/7565 ), ( -1513/1455 , -1571093/7275 )
**u= 25/64 , ht= 12163 ; ( -52469/36417 , -40882981/145668 ), ( -3945/12163 , 40924711/243260 )
**u= 25/68 , ht= 27607 ; ( -20877/27607 , 28546867/138035 ), ( -64091/65109 , 75351416/325545 )
**u= 25/71 , ht= 7373 ; ( -7373/11 , 1242735/11 ), ( -11/7373 , -1242735/7373 )
**u= 25/124 , ht= 1300085 ; ( 1300085/465751 , 1538077953/2328755 ), ( 2699297/78929 , -601524780/78929 )
**u= 25/127 , ht= 40756 ; ( 2627644/366917 , 598091010/366917 ), ( 7101/40756 , 23314861/101890 )
**u= 25/132 , ht= 29431 ; ( -652411/9569 , -749774297/47845 ), ( -29419/29431 , 47818333/147155 )
**u= 25/151 , ht= 92350 ; ( 92350/18813 , -115832548/94065 ), ( 93609/71563 , -28963457/71563 )
**u= 25/196 , ht= 32475 ; ( -32525/21943 , 384568431/768005 ), ( -32475/21893 , 383888206/766255 )
**u= 26/15 , ht= 91 ; ( -5444/221 , -827767/442 ), ( -44/91 , -15357/182 )
**u= 26/59 , ht= 12235 ; ( 12235/1202 , 3704529/2404 ), ( -1021214/33293 , -307889481/66586 )
**u= 26/71 , ht= 2587 ; ( -2587/324 , 861833/648 ), ( -324/2587 , -861833/5174 )
**u= 26/115 , ht= 10151 ; ( -774/10151 , 4282885/20302 ), ( 122174/19709 , -52062651/39418 )
**u= 26/167 , ht= 755815 ; ( 755815/276692 , -408040029/553384 ), ( -6831392/1250573 , 3520827513/2501146 )
**u= 26/175 , ht= 2533 ; ( -38804/128965 , -349461957/1289650 ), ( 2533/1308 , 13573/24 )
**u= 26/187 , ht= 286118 ; ( -192585/286118 , 26431933/81748 ), ( 730159/2694 , 391706449/5388 )
**u= 29 , ht= 762 ; ( -762/629 , -494/17 ), ( -2183/426 , 21053/213 )
**u= 29/10 , ht= 26843 ; ( 408194/75259 , 48746901/150518 ), ( -26843/7727 , 1640862/7727 )
**u= 29/18 , ht= 2703 ; ( 3713/2163 , 1015768/6489 ), ( -2703/1493 , -729988/4479 )
**u= 29/23 , ht= 55400 ; ( 55400/15403 , 5121588/15403 ), ( -68101/646 , 3033201/323 )
**u= 29/54 , ht= 78658 ; ( -19049/78658 , 66274543/471948 ), ( 78658/19049 , 66274543/114294 )
**u= 29/74 , ht= 30431 ; ( -23515/30431 , -6144372/30431 ), ( -445979/113942 , -147085323/227884 )
**u= 29/78 , ht= 421868 ; ( -1535825/2610197 , -496768858/2610197 ), ( 421868/54257 , -6066901/4718 )
**u= 29/102 , ht= 174991 ; ( -174991/7861 , 32857134/7861 ), ( 712951/148619 , -136607394/148619 )
**u= 29/103 , ht= 391356 ; ( 391356/230161 , -85579468/230161 ), ( -3954979/465884 , -187660587/116471 )
**u= 29/114 , ht= 435880 ; ( -435880/169973 , -185551347/339946 ), ( 53051839/2588827 , 10532877284/2588827 )
**u= 29/119 , ht= 101 ; ( -52/101 , 23016/101 ), ( -101/52 , -5754/13 )
**u= 29/129 , ht= 3164398 ; ( -454130/3269899 , -696394302/3269899 ), ( -2587639/3164398 , 431142407/1582199 )
**u= 29/154 , ht= 19849 ; ( -33885/1845223 , 425363096/1845223 ), ( 19849/4658 , -9398253/9316 )
**u= 29/166 , ht= 6778037 ; ( 6778037/1762679 , -1675888182/1762679 ), ( -15417274/19117283 , -11753798739/38234566 )
**u= 29/198 , ht= 61571 ; ( 2934675/1269902 , -5014084673/7619412 ), ( -61571/25945 , -17461366/25945 )
**u= 30/17 , ht= 37969 ; ( -103007/70546 , -18799287/141092 ), ( -37969/9002 , -5876307/18004 )
**u= 30/41 , ht= 38033 ; ( -2273977/687986 , 555568155/1375972 ), ( -38033/14734 , -9538191/29468 )
**u= 30/49 , ht= 3287 ; ( -4981/1438 , 1325379/2876 ), ( -3287/1966 , -6854115/27524 )
**u= 30/77 , ht= 54916 ; ( 168316/10697 , 54049263/21394 ), ( 42673/54916 , 22287801/109832 )
**u= 30/101 , ht= 7427 ; ( -66796/31073 , 27039261/62146 ), ( -7427/4996 , -3285321/9992 )
**u= 30/121 , ht= 6113 ; ( 6113/5906 , -37561977/129932 ), ( -11474/2887 , 52284849/63514 )
**u= 30/149 , ht= 27376 ; ( 664376/642473 , -412012011/1284946 ), ( -9427/27376 , 12907479/54752 )
**u= 30/193 , ht= 589951 ; ( 203758/589951 , 316673061/1179902 ), ( 27985889/732938 , 14204052501/1465876 )
**u= 32/43 , ht= 24726 ; ( 24726/17287 , 27983063/138296 ), ( 1139/46418 , 43066179/371344 )
**u= 32/51 , ht= 13967 ; ( 8047/15578 , -17711301/124624 ), ( -11822/13967 , 18483829/111736 )
**u= 32/67 , ht= 18169 ; ( 18169/7382 , -22705701/59056 ), ( 20609/12770 , 28070211/102160 )
**u= 32/123 , ht= 5662 ; ( 474167/249446 , -840480591/1995568 ), ( -4301/5662 , 11154069/45296 )
**u= 32/127 , ht= 165183 ; ( -165183/48304 , -274331237/386432 ), ( -112736/194223 , 357969077/1553784 )
**u= 32/135 , ht= 244 ; ( -19811/784 , 97751791/18816 ), ( -244 , 401007/8 )
**u= 32/155 , ht= 74306 ; ( 100634/52119 , -199572097/416952 ), ( 74306/6509 , -131353317/52072 )
**u= 32/167 , ht= 323192 ; ( -323192/243439 , 739595337/1947512 ), ( 814017/152864 , 1513940569/1222912 )
**u= 32/175 , ht= 907672 ; ( 274851/907672 , -8872776509/36306880 ), ( 2240317/1053264 , 23160785149/42130560 )
**u= 32/183 , ht= 26393 ; ( 26393/9496 , 53670871/75968 ), ( -1834337/242164 , -3540364153/1937312 )
**u= 36/19 , ht= 889 ; ( -6983/4949 , 1243761/9898 ), ( 889/243 , 44647/162 )
**u= 36/47 , ht= 3377 ; ( 3805/6531 , -575871/4354 ), ( -3297/3377 , -1078713/6754 )
**u= 36/103 , ht= 154279 ; ( 168489/169519 , -80869983/339038 ), ( 154279/48601 , -54730203/97202 )
**u= 36/115 , ht= 6629 ; ( -6629/5239 , 3020817/10478 ), ( -5239/6629 , -3020817/13258 )
**u= 36/119 , ht= 14571 ; ( -6955/14571 , 652447/3238 ), ( -182811/4325 , -66504807/8650 )
**u= 36/151 , ht= 7743 ; ( 2609/7743 , 12537/58 ), ( 7743/2609 , 3347379/5218 )
**u= 36/155 , ht= 9687 ; ( -148841/13371 , 20676009/8914 ), ( -9687/1627 , 4077099/3254 )
**u= 37/3 , ht= 3169 ; ( -7120/3937 , 231242/3937 ), ( 3169/3112 , -63251/1556 )
**u= 37/4 , ht= 4343 ; ( 4343/27 , 142519/27 ), ( -6383/965 , -212727/965 )
**u= 37/16 , ht= 4243 ; ( 40699/2559 , -5363497/5118 ), ( -4243/3073 , 689169/6146 )
**u= 37/24 , ht= 53837 ; ( 53837/45683 , 5687544/45683 ), ( 181357/15605 , -14663657/15605 )
**u= 37/43 , ht= 113509 ; ( -323510/74669 , -35798124/74669 ), ( 10503/113509 , -722993/6677 )
**u= 37/48 , ht= 57863 ; ( -202691/62227 , 24153689/62227 ), ( 57863/25301 , -14388723/50602 )
**u= 37/51 , ht= 676 ; ( -676/421 , -93514/421 ), ( 60631/8101 , 7182949/8101 )
**u= 37/64 , ht= 35133 ; ( -23375/35133 , -22203637/140532 ), ( 62307/42223 , 39602651/168892 )
**u= 37/75 , ht= 1766 ; ( 1766/791 , 39364/113 ), ( -260617/26389 , 186507419/131945 )
**u= 37/88 , ht= 13751 ; ( 13751/892 , -8501991/3568 ), ( 610677/308221 , 105513119/308221 )
**u= 37/92 , ht= 541901 ; ( -534485149/43869953 , 84578689923/43869953 ), ( -541901/460163 , -112121736/460163 )
**u= 37/99 , ht= 58319 ; ( -285073/60937 , -47692439/60937 ), ( -58319/43480 , -5950553/21740 )
**u= 37/100 , ht= 121447 ; ( -121447/19125 , 5945671/5625 ), ( -19125/121447 , 101076407/607235 )
**u= 37/107 , ht= 30209 ; ( 517213/270521 , 99276519/270521 ), ( 30209/10665 , 5448923/10665 )
**u= 37/115 , ht= 1037159 ; ( -1037159/369521 , 194141463/369521 ), ( -4268929/984524 , -386248647/492262 )
**u= 37/132 , ht= 8747 ; ( 222325/129067 , -48564474/129067 ), ( 7009/8747 , 2117479/8747 )
**u= 37/136 , ht= 152306 ; ( 50370713/128807 , 9658802712/128807 ), ( -126069/152306 , -6593443/26488 )
**u= 37/164 , ht= 99215 ; ( -436359/1559029 , -340901903/1559029 ), ( -91763/99215 , -28457433/99215 )
**u= 37/176 , ht= 97807 ; ( 49935/97807 , -23955224/97807 ), ( -437269/17889 , -190929817/35778 )
**u= 37/184 , ht= 16937413 ; ( -16937413/317923 , 3778393371/317923 ), ( 59721993/1633975 , 13325430652/1633975 )
**u= 37/188 , ht= 631601 ; ( 3745/631601 , 203136/901 ), ( -2871997/3042889 , -943336401/3042889 )
**u= 37/192 , ht= 195689 ; ( -189511/207737 , 64066223/207737 ), ( 195689/104105 , 50501973/104105 )
**u= 38/41 , ht= 3303 ; ( 30040/38527 , -10151031/77054 ), ( -3303/2888 , -911647/5776 )
**u= 38/117 , ht= 565 ; ( 1556027/737326 , 604378761/1474652 ), ( -254/565 , -217433/1130 )
**u= 38/145 , ht= 14897 ; ( 14897/13552 , 715389/2464 ), ( 36421/128496 , 52187575/256992 )
**u= 39/14 , ht= 529 ; ( 235/529 , 34692/529 ), ( -3049/2747 , -245934/2747 )
**u= 39/22 , ht= 200 ; ( 200/53 , -31083/106 ), ( 353/320 , 71583/640 )
**u= 39/38 , ht= 329 ; ( 101/329 , -4854/47 ), ( 20111/3980 , 4048107/7960 )
**u= 39/41 , ht= 449 ; ( -3997/799 , 417993/799 ), ( 367/449 , -59469/449 )
**u= 39/43 , ht= 9571 ; ( 8188/15283 , -107112/899 ), ( 9571/3680 , -269229/920 )
**u= 39/44 , ht= 1685 ; ( -1685/1087 , 213021/1087 ), ( 5297/1249 , -578172/1249 )
**u= 39/71 , ht= 6914 ; ( -6914/6647 , -1294296/6647 ), ( -14767/2060 , 1006059/1030 )
**u= 39/74 , ht= 13319 ; ( -15317/5329 , -2234304/5329 ), ( 13319/3995 , -1915758/3995 )
**u= 39/89 , ht= 11227 ; ( 7934/11227 , 2077128/11227 ), ( 62299577/4109686 , 4716705276/2054843 )
**u= 39/137 , ht= 1642 ; ( 32125/67 , 6022089/67 ), ( -683/1642 , -166686/821 )
**u= 39/142 , ht= 11893 ; ( 5858/11893 , -5060319/23786 ), ( -1802837/364225 , 351020094/364225 )
**u= 39/146 , ht= 28819 ; ( 46445/30239 , -10725006/30239 ), ( 2977/28819 , 5606646/28819 )
**u= 39/167 , ht= 75037 ; ( -277028/19397 , 57476058/19397 ), ( 75037/722 , -7765476/361 )
**u= 39/170 , ht= 70583 ; ( -276803/144712 , 130447863/289424 ), ( -70583/58957 , 19204332/58957 )
**u= 39/188 , ht= 1165 ; ( 1165/413 , -271428/413 ), ( -104743/243527 , -58213986/243527 )
**u= 39/193 , ht= 383428 ; ( 383428/128987 , 90009054/128987 ), ( 2197211/74404 , -244575759/37202 )
**u= 39/200 , ht= 2779 ; ( 2779/340 , 12682449/6800 ), ( 17608/3715 , 81518511/74300 )
**u= 41/9 , ht= 4546 ; ( -4546/3817 , 278136/3817 ), ( -14059/17430 , 1573864/26145 )
**u= 41/25 , ht= 40696 ; ( -40696/3679 , -3191130/3679 ), ( 735137/22938 , -28723198/11469 )
**u= 41/28 , ht= 435 ; ( 435/307 , -44006/307 ), ( -307/435 , 44006/435 )
**u= 41/31 , ht= 90203 ; ( 90203/55049 , -9190179/55049 ), ( 135893/25905 , 12031799/25905 )
**u= 41/32 , ht= 68 ; ( -68/3 , -48113/24 ), ( 48731/34565 , -5279169/34565 )
**u= 41/40 , ht= 52242 ; ( -52242/15713 , -21557089/62852 ), ( 911041/5601 , 90006026/5601 )
**u= 41/68 , ht= 8119257 ; ( 10774429/4012611 , -1480927486/4012611 ), ( -8119257/1423523 , 1061776157/1423523 )
**u= 41/88 , ht= 147945 ; ( -195203/259922 , -190523637/1039688 ), ( -122743/147945 , 28167814/147945 )
**u= 41/95 , ht= 220763 ; ( -220763/33613 , 33997485/33613 ), ( 921153/4907 , 140244493/4907 )
**u= 41/103 , ht= 12952178 ; ( -12952178/10090673 , -153107916/593569 ), ( -23858803/33283 , -3782278167/33283 )
**u= 41/105 , ht= 815588 ; ( -815588/189563 , 134020970/189563 ), ( 267372353/11676262 , 21418082576/5838131 )
**u= 41/116 , ht= 121357 ; ( -115921/121357 , 28233813/121357 ), ( -26928597/14785525 , 5168265494/14785525 )
**u= 41/128 , ht= 6493 ; ( 6493/1283 , -2339271/2566 ), ( -1283/6493 , 2339271/12986 )
**u= 41/151 , ht= 364999 ; ( 54090/364999 , -70824272/364999 ), ( 2957323/1010631 , -599869453/1010631 )
**u= 41/160 , ht= 16551 ; ( 383513/482233 , -121737669/482233 ), ( -11609/16551 , 3994372/16551 )
**u= 41/168 , ht= 1430686 ; ( 1430686/366049 , -1195945671/1464196 ), ( -17188709/13315 , -3480027987/13315 )
**u= 41/175 , ht= 2983163 ; ( -2506485/4486711 , 5309854457/22433555 ), ( 2983163/707715 , 3167673169/3538575 )
**u= 41/180 , ht= 48239 ; ( 34561/48239 , -12436040/48239 ), ( -2253009/38911 , -1416673652/116733 )
**u= 41/192 , ht= 624551 ; ( -624551/251389 , 582865283/1005556 ), ( 7398749/257465 , 6409383309/1029860 )
**u= 45/2 , ht= 187 ; ( -509/153 , -1232/17 ), ( 41/187 , 3990/187 )
**u= 45/14 , ht= 508 ; ( -171/508 , 471/8 ), ( 40132/9661 , 4606671/19322 )
**u= 45/17 , ht= 142 ; ( 142/11 , -8754/11 ), ( 227/6 , 2327 )
**u= 45/23 , ht= 487 ; ( -364/487 , 43476/487 ), ( 51167/52156 , -1306095/13039 )
**u= 45/26 , ht= 18913 ; ( 22131/24913 , -2533422/24913 ), ( -18913/6749 , 1526754/6749 )
**u= 45/34 , ht= 723 ; ( -604/723 , 54603/482 ), ( 723/604 , 163809/1208 )
**u= 45/74 , ht= 12747 ; ( -45509/23457 , -312696/1117 ), ( -12747/10231 , -2096388/10231 )
**u= 45/134 , ht= 69839 ; ( 69839/43843 , 14232012/43843 ), ( 74453/101521 , -21728670/101521 )
**u= 45/142 , ht= 72 ; ( -3727/4509 , 115484/501 ), ( 72 , 25587/2 )
**u= 45/167 , ht= 4673 ; ( 4506/4673 , 1250778/4673 ), ( -2009221/161612 , 97094994/40403 )
**u= 45/194 , ht= 155917 ; ( -155917/140591 , 3963498/12781 ), ( -79871/250608 , 1583263/7264 )
**u= 48/13 , ht= 2593 ; ( 2815/1567 , -670659/6268 ), ( -761/2593 , -562479/10372 )
**u= 48/109 , ht= 705617 ; ( 705617/198113 , -441847317/792452 ), ( 2764357/73147 , -1667158257/292588 )
**u= 48/137 , ht= 150833 ; ( -644081/306973 , 482241669/1227892 ), ( -150833/51379 , -107698941/205516 )
**u= 48/157 , ht= 17963 ; ( 61349/7027 , 44678859/28108 ), ( 17963/379 , -12999951/1516 )
**u= 48/173 , ht= 42283 ; ( 18755/42283 , 35132211/169132 ), ( -89839/214295 , -176485137/857180 )
**u= 49 , ht= 49 ; ( -40/49 , 6402/343 ), ( 9/98 , -4622/343 )
**u= 49/4 , ht= 599 ; ( 599/437 , -148149/3059 ), ( 697/535 , 175932/3745 )
**u= 49/8 , ht= 12 ; ( 1261/1331 , 518706/9317 ), ( -7/12 , -15713/336 )
**u= 49/32 , ht= 3163 ; ( -8112/1357 , -37225277/75992 ), ( 3163/1120 , 15188331/62720 )
**u= 49/36 , ht= 7843 ; ( -7843/2489 , -4937761/17423 ), ( -112291/25715 , 69133648/180005 )
**u= 49/52 , ht= 35149 ; ( 35149/26361 , -31687903/184527 ), ( -80973/61507 , -73339004/430549 )
**u= 49/55 , ht= 11621 ; ( -12728/13707 , -13874582/95949 ), ( 5429/11621 , 9514005/81347 )
**u= 49/65 , ht= 39191 ; ( -19662/66983 , 56292452/468881 ), ( -39191/1426 , -15811842/4991 )
**u= 49/72 , ht= 2232 ; ( 2232/83 , -22746403/6972 ), ( 4033/7833 , 22431077/164493 )
**u= 49/81 , ht= 7993 ; ( -980/7993 , 21746702/167853 ), ( -1029/8042 , 32841092/253323 )
**u= 49/88 , ht= 26705 ; ( 26705/23658 , -133895779/662424 ), ( -34097/17735 , -36060309/124145 )
**u= 49/97 , ht= 102341 ; ( 91186/102341 , 135023388/716387 ), ( -134991/67576 , -74352739/236516 )
**u= 49/100 , ht= 18279 ; ( 14429/18279 , 23291827/127953 ), ( 78569/4717 , -393623553/165095 )
**u= 49/103 , ht= 18380 ; ( -18380/8091 , 20384542/56637 ), ( -37461/26605 , 46639643/186235 )
**u= 49/120 , ht= 18347 ; ( -18347/1843 , -20202731/12901 ), ( 185936/58361 , -854073585/1634108 )
**u= 49/124 , ht= 11007 ; ( -8461/11007 , 15462371/77049 ), ( 24049/1853 , -26864013/12971 )
**u= 49/136 , ht= 64851 ; ( 28148/64851 , -329839661/1815828 ), ( -990259/17467 , 1155216009/122269 )
**u= 49/144 , ht= 22143 ; ( 22241/18403 , 69294083/257642 ), ( 22143/18305 , -103444436/384405 )
**u= 49/172 , ht= 299361 ; ( 238781/657601 , -917693103/4603207 ), ( -299361/66655 , -402293726/466585 )
**u= 49/183 , ht= 29729 ; ( 56536/4887431 , 6613205294/34212017 ), ( -29729/18871 , 47643111/132097 )
**u= 49/192 , ht= 9455 ; ( 77429/2699 , 107372542/18893 ), ( -1973/9455 , -53543027/264740 )
**u= 49/199 , ht= 168940 ; ( -814244/221153 , 1190452434/1548071 ), ( 149239/168940 , 159022977/591290 )
**u= 51/4 , ht= 41 ; ( 41/23 , -1314/23 ), ( -5903/1121 , -168936/1121 )
**u= 51/8 , ht= 4583 ; ( -4583/2233 , -201822/2233 ), ( -36127/3935 , 1440984/3935 )
**u= 51/13 , ht= 8087 ; ( -9898/1087 , -502632/1087 ), ( 8087/1210 , 206532/605 )
**u= 51/29 , ht= 11681 ; ( -11681/4037 , 932061/4037 ), ( -69203/2126 , 2611098/1063 )
**u= 51/35 , ht= 46 ; ( -46/31 , -4596/31 ), ( 3737/4738 , 249990/2369 )
**u= 51/37 , ht= 6433 ; ( -2743/6433 , 85113/919 ), ( 9611/6521 , 989457/6521 )
**u= 51/44 , ht= 853 ; ( -24133/4511 , 2280723/4511 ), ( 853/5 , -79248/5 )
**u= 51/53 , ht= 40609 ; ( -31789/40609 , -5258259/40609 ), ( 69977/1255 , 7136151/1255 )
**u= 51/61 , ht= 2386 ; ( 2386/7 , 37284 ), ( 235207/78254 , -13557474/39127 )
**u= 51/64 , ht= 40187 ; ( 87379/12397 , -9888009/12397 ), ( -40187/13205 , -9479079/26410 )
**u= 51/76 , ht= 1489 ; ( -94165/23179 , -11840142/23179 ), ( -1247/1489 , -237132/1489 )
**u= 51/83 , ht= 22607 ; ( -62158/112207 , -16366968/112207 ), ( 22607/10178 , 1581696/5089 )
**u= 51/101 , ht= 222073 ; ( 222073/30779 , -31555599/30779 ), ( -541423/328111 , -89107527/328111 )
**u= 51/149 , ht= 159100 ; ( -159100/118189 , -33882654/118189 ), ( -446849/5660 , -38198907/2830 )
**u= 51/163 , ht= 21251 ; ( 2384/21251 , 3823674/21251 ), ( -13147313/10497422 , 1504127886/5248711 )
**u= 51/197 , ht= 33317 ; ( 535768/1992977 , -405675426/1992977 ), ( -15193/33317 , -7198029/33317 )
**u= 51/200 , ht= 20495 ; ( 1961551/133426 , 1557640305/533704 ), ( 20495/11911 , 23475363/59555 )
**u= 52/19 , ht= 1 ; ( 1 , 171/2 ), ( 66831/4625 , 8101717/9250 )
**u= 52/47 , ht= 13933 ; ( -15377/10661 , -3558363/21322 ), ( -13933/10601 , -3329499/21202 )
**u= 52/59 , ht= 30549 ; ( -27253/39653 , -10252197/79306 ), ( -131/30549 , 6509129/61098 )
**u= 52/83 , ht= 60261 ; ( 60261/29717 , 16980287/59434 ), ( 106511/36625 , -28464843/73250 )
**u= 52/163 , ht= 139517 ; ( -320815/25071 , -113965603/50142 ), ( -22179/139517 , 50031511/279034 )
**u= 52/171 , ht= 90120365 ; ( 90120365/90003363 , 138605237521/540020178 ), ( 90121197/90004195 ,
-138606518801/540025170 )
**u= 53 , ht= 31 ; ( -3324/1511 , 47792/1511 ), ( 31/24 , 137/6 )
**u= 53/25 , ht= 222 ; ( -11470/14917 , -923298/10655 ), ( -35/222 , -1043/15 )
**u= 53/46 , ht= 228028 ; ( -714075/594268 , 1588319/10904 ), ( 228028/144825 , 50341759/289650 )
**u= 53/65 , ht= 39159 ; ( -32464/39159 , 5634076/39159 ), ( -50547/10468 , 1429406/2617 )
**u= 53/70 , ht= 121497 ; ( 121497/16742 , -28194293/33484 ), ( 169342/70117 , 42135345/140234 )
**u= 53/81 , ht= 1991 ; ( 1960/1991 , 1036352/5973 ), ( -81281/4776 , 11325964/5373 )
**u= 53/86 , ht= 31469 ; ( 277765/446497 , -66995688/446497 ), ( -20174/31469 , 9524859/62938 )
**u= 53/111 , ht= 117320 ; ( -289096/363991 , -67281128/363991 ), ( -101683/117320 , 2808979/14665 )
**u= 53/122 , ht= 118078 ; ( 118078/52661 , 5605437/15046 ), ( -2717701/5494970 , -43267329/255580 )
**u= 53/134 , ht= 173189 ; ( -173189/167506 , -76635777/335012 ), ( 763999/620485 , -156525312/620485 )
**u= 53/138 , ht= 75701 ; ( 75701/72113 , 16873532/72113 ), ( 15949267/1687519 , -2588435228/1687519 )
**u= 53/170 , ht= 1162791 ; ( -941894/1162791 , -536097461/2325582 ), ( -11900441/1897099 , 2158618806/1897099 )
**u= 53/174 , ht= 548801 ; ( 5133047/917 , -930222668/917 ), ( -339469/548801 , 116944264/548801 )
**u= 53/190 , ht= 5771 ; ( 13530127/25694212 , 10998292629/51388424 ), ( 5771/3159 , 1245884/3159 )
**u= 53/191 , ht= 2774981 ; ( 19510460/1760257 , -3719476488/1760257 ), ( -2774981/671614 , -271048191/335807 )
**u= 57/2 , ht= 10 ; ( 10 , 369/2 ), ( -139/38 , 5493/76 )
**u= 57/7 , ht= 86 ; ( 86/583 , 20688/583 ), ( -47/86 , 1716/43 )
**u= 57/10 , ht= 17 ; ( 8/17 , 1575/34 ), ( 673/112 , 57207/224 )
**u= 57/22 , ht= 29 ; ( 1171/247 , 74352/247 ), ( -29/7 , -1854/7 )
**u= 57/23 , ht= 170 ; ( -170/37 , -11052/37 ), ( 2693/1819 , 206481/1819 )
**u= 57/46 , ht= 1142 ; ( -19337/10678 , 3969369/21356 ), ( 1142/475 , -222267/950 )
**u= 57/68 , ht= 4853 ; ( 4853/1861 , 567792/1861 ), ( -7777/59 , -849621/59 )
**u= 57/73 , ht= 5123 ; ( 5216/2077 , -635466/2077 ), ( 5123/1984 , 310917/992 )
**u= 57/92 , ht= 787 ; ( -419/787 , 113292/787 ), ( 2867/2729 , 502953/2729 )
**u= 57/94 , ht= 6757 ; ( 2527/6757 , -926586/6757 ), ( -10621/281 , -1364658/281 )
**u= 57/107 , ht= 4136 ; ( 12662/2711 , 1774446/2711 ), ( 3173/4136 , -178587/1034 )
**u= 57/110 , ht= 29401 ; ( -29401/794 , 8173017/1588 ), ( -24852361/3829259 , -3493818402/3829259 )
**u= 57/122 , ht= 110861 ; ( -74665/120413 , 20731854/120413 ), ( -110861/14860 , -32733801/29720 )
**u= 57/170 , ht= 10211 ; ( -7996/10211 , 4480299/20422 ), ( -176789/144001 , 39384546/144001 )
**u= 57/172 , ht= 333119 ; ( -1954415/40699 , 339635067/40699 ), ( 333119/136867 , 62571279/136867 )
**u= 57/173 , ht= 3529 ; ( -3218/3529 , 832182/3529 ), ( -112369/8050 , 9815013/4025 )
**u= 57/175 , ht= 863 ; ( -256/1543 , -1370538/7715 ), ( -863/313 , 160881/313 )
**u= 57/196 , ht= 859 ; ( 859/709 , -206574/709 ), ( -25957/2855 , -4843209/2855 )
**u= 58/15 , ht= 36167 ; ( 177487/147352 , 23465063/294704 ), ( -15148/36167 , 3987799/72334 )
**u= 58/59 , ht= 14143 ; ( -14143/8302 , -3308619/16604 ), ( 83441/1683934 , -340145817/3367868 )
**u= 58/79 , ht= 8020 ; ( 116432197/8343528 , -27251164499/16687056 ), ( -591/8020 , -1877371/16040 )
**u= 58/91 , ht= 70271 ; ( -70271/31194 , 19263851/62388 ), ( 911811/151870 , 231613403/303740 )
**u= 58/99 , ht= 19373 ; ( 30574/3239 , 8034923/6478 ), ( -19373/5058 , 15698213/30348 )
**u= 58/139 , ht= 1520601 ; ( -75128233930/5584912611 , -23329068220099/11169825222 ), ( -1520601/20770 ,
-470930759/41540 )
**u= 58/143 , ht= 1872705 ; ( -74658660/35665697 , -25988186923/71331394 ), ( -896204/1872705 , -652090511/3745410 )
**u= 58/167 , ht= 38588 ; ( -8339/38588 , -13400313/77176 ), ( 48658249/6712692 , 16672542521/13425384 )
**u= 61/12 , ht= 5827 ; ( 17281/13649 , -976732/13649 ), ( 5827/2393 , 279569/2393 )
**u= 61/27 , ht= 7453 ; ( -7453/2807 , 529891/2807 ), ( -437981/100844 , 44864863/151266 )
**u= 61/45 , ht= 32821 ; ( -27666/32821 , 11062684/98463 ), ( 93977/70048 , -5034555/35024 )
**u= 61/59 , ht= 662489 ; ( -344420/662489 , -73446774/662489 ), ( 748891/224668 , 38454639/112334 )
**u= 61/88 , ht= 40835 ; ( 782345/248416 , -394425813/993664 ), ( 35544/40835 , 26014183/163340 )
**u= 61/92 , ht= 95919 ; ( 17163145/3414941 , 2149454469/3414941 ), ( 81061/95919 , -15425473/95919 )
**u= 61/104 , ht= 29343 ; ( 373183/2327681 , 307868832/2327681 ), ( -12361/29343 , 4158173/29343 )
**u= 61/112 , ht= 3878531 ; ( 3878531/3427759 , -1402996479/6855518 ), ( 27824133/1885717 , -3779549321/1885717 )
**u= 61/124 , ht= 163397 ; ( 424603/1183049 , -25605879/169007 ), ( -1771/163397 , -23301768/163397 )
**u= 61/136 , ht= 166091 ; ( 166091/162453 , -34696498/162453 ), ( 755271/606742 , -578727811/2426968 )
**u= 61/160 , ht= 88324 ; ( 88324/53541 , 133843441/428328 ), ( -53541/88324 , -133843441/706592 )
**u= 61/171 , ht= 15997 ; ( 26916760/2391747 , -798565706/422073 ), ( 15997/13280 , 1740817/6640 )
**u= 64/11 , ht= 33711 ; ( 33711/403 , 11173967/3224 ), ( -83767/7731 , 27928523/61848 )
**u= 64/43 , ht= 22609 ; ( 22609/18309 , -53149/408 ), ( -533833/138085 , 361659831/1104680 )
**u= 64/47 , ht= 221265 ; ( -221265/202769 , 205788739/1622152 ), ( 327421/156435 , 248823599/1251480 )
**u= 64/51 , ht= 314255 ; ( -25857865/758117 , 18476650861/6064936 ), ( -294923/314255 , -307827759/2514040 )
**u= 64/127 , ht= 83567 ; ( -1697351/195711 , 1925815897/1565688 ), ( 69343/83567 , 122396541/668536 )
**u= 64/159 , ht= 17213 ; ( -17213/7379 , -23619143/59032 ), ( 8488913/302321 , -10712815541/2418568 )
**u= 64/187 , ht= 1224545 ; ( 1224545/224843 , 1702827027/1798744 ), ( -20427169/188635 , -27939894459/1509080 )
**u= 64/191 , ht= 466139 ; ( 466139/108587 , -661579503/868696 ), ( 1802551/636687 , -2642476871/5093496 )
**u= 65/3 , ht= 49 ; ( -2/49 , -1066/49 ), ( 931/88 , 5081/22 )
**u= 65/7 , ht= 743 ; ( 1152/571 , 42146/571 ), ( -743/176 , 12555/88 )
**u= 65/29 , ht= 187 ; ( 16/187 , 1140/17 ), ( -13655631/1173248 , -228939557/293312 )
**u= 65/31 , ht= 143 ; ( 143/19 , 9963/19 ), ( -32227/4291 , 2245857/4291 )
**u= 65/47 , ht= 13957 ; ( 13957/7189 , -190743/1027 ), ( -17997/3811 , 1564633/3811 )
**u= 65/97 , ht= 20101 ; ( 20244/39547 , 5428226/39547 ), ( 20101/16662 , 1595012/8331 )
**u= 65/118 , ht= 64052 ; ( -9639/64052 , -17457775/128104 ), ( -100801/28173 , -14104594/28173 )
**u= 65/119 , ht= 57772 ; ( 342689/818717 , 120111519/818717 ), ( -2799/57772 , -3913687/28886 )
**u= 65/146 , ht= 10409 ; ( -10409/2147 , 1593126/2147 ), ( 795909/135478 , 242043493/270956 )
**u= 65/177 , ht= 3629854 ; ( 3629854/857627 , -615587076/857627 ), ( -9326969/708662 , -771912194/354331 )
**u= 65/194 , ht= 218129 ; ( 467326/176617 , 24663933/50462 ), ( 178213/218129 , -48670566/218129 )
**u= 65/198 , ht= 1624 ; ( -1437/1624 , 324461/1392 ), ( -2591/3493 , 759184/3493 )
**u= 68/7 , ht= 57397 ; ( 57397/6899 , -3701751/13798 ), ( -77891/203733 , 13974031/407466 )
**u= 68/19 , ht= 109363 ; ( -225825/9661 , -23892349/19322 ), ( -109363/107465 , -16212417/214930 )
**u= 68/31 , ht= 398507 ; ( 212693/398507 , -61013457/797014 ), ( -894587/505683 , -138800653/1011366 )
**u= 68/35 , ht= 4397 ; ( -4397/2407 , -719343/4814 ), ( -226999/67771 , 34000419/135542 )
**u= 68/39 , ht= 223 ; ( -145/223 , -40297/446 ), ( -10816099/6464411 , 1908941927/12928822 )
**u= 68/55 , ht= 661619 ; ( -866157/304243 , 165150565/608486 ), ( 661619/208419 , -124795645/416838 )
**u= 68/59 , ht= 520529 ; ( 395137/930267 , 188327219/1860534 ), ( -520529/45635 , 97364199/91270 )
**u= 68/67 , ht= 12693 ; ( 12693/11159 , 3355781/22318 ), ( 908711/312947 , -190836399/625894 )
**u= 68/75 , ht= 10207 ; ( -124093/101207 , -33639979/202414 ), ( 10207/6619 , -12778441/66190 )
**u= 68/83 , ht= 265461 ; ( 24795115/4548593 , -5571052407/9097186 ), ( 265461/14137 , 58750763/28274 )
**u= 68/95 , ht= 3679651 ; ( 36635549/1535709 , 8669453497/3071418 ), ( -3679651/405539 , -875280153/811078 )
**u= 68/99 , ht= 411627 ; ( 179153/411627 , 325062227/2469762 ), ( 576003/561593 , -582503323/3369558 )
**u= 68/103 , ht= 308003 ; ( 210771/308003 , -91882379/616006 ), ( 8238793/742041 , 2036539231/1484082 )
**u= 68/115 , ht= 2114193 ; ( -2114193/571747 , -569729557/1143494 ), ( -8107627/624783 , 2115356921/1249566 )
**u= 68/139 , ht= 13882313 ; ( -13882313/62723 , 3970293339/125446 ), ( 85761089/53307091 , 28879388223/106614182 )
**u= 68/155 , ht= 56467 ; ( 56467/50887 , -22956531/101774 ), ( -20656491/1650799 , -6258329539/3301598 )
**u= 68/159 , ht= 71473 ; ( 71473/983 , -21864079/1966 ), ( -193559419/11997371 , 59319710687/23994742 )
**u= 72/11 , ht= 45 ; ( 45/34 , 8817/136 ), ( -989/34 , 154911/136 )
**u= 72/23 , ht= 408 ; ( 13736/13897 , 4418301/55588 ), ( -408/29 , -92511/116 )
**u= 72/59 , ht= 2046 ; ( -1081/2046 , 279351/2728 ), ( 13427/5462 , 5249751/21848 )
**u= 72/155 , ht= 72667 ; ( -348721/48854 , -206695965/195416 ), ( -72667/63578 , 56676849/254312 )
**u= 73/30 , ht= 14729 ; ( 57899/58159 , 5261828/58159 ), ( -14729/5131 , -1000162/5131 )
**u= 73/50 , ht= 43 ; ( -43/7 , 3606/7 ), ( -37703/5406 , 31529473/54060 )
**u= 73/61 , ht= 42346 ; ( -338678/29823 , 31083394/29823 ), ( -23741/42346 , 2219241/21173 )
**u= 73/86 , ht= 739759 ; ( 1358821/583316 , 321054111/1166632 ), ( -739759/494685 , 96608974/494685 )
**u= 73/106 , ht= 5418189 ; ( 15715516/2867521 , 3850641681/5735042 ), ( 5418189/882184 , 1323238459/1764368 )
**u= 73/114 , ht= 909346 ; ( -909346/258679 , -236330317/517358 ), ( -4232297/1471598 , -1120108339/2943196 )
**u= 73/122 , ht= 1957421 ; ( 729735/1957421 , -270109766/1957421 ), ( -5402161/2189960 , 1507419987/4379920 )
**u= 73/133 , ht= 339273 ; ( 6620144/1505363 , -916541652/1505363 ), ( 339273/46540 , -11557954/11635 )
**u= 73/150 , ht= 46508 ; ( 1637557/19985 , 167709764/14275 ), ( -46508/39085 , -87098557/390850 )
**u= 73/154 , ht= 840467 ; ( 840467/270513 , -128262082/270513 ), ( -2057271/2259536 , 887827363/4519072 )
**u= 73/174 , ht= 598883 ; ( 4654835/549566 , -1447529829/1099132 ), ( 598883/264455 , 101091626/264455 )
**u= 73/182 , ht= 3581024 ; ( 1221485/3581024 , -1195057527/7162048 ), ( 11549303/2145909 , -1855144634/2145909 )
**u= 75/43 , ht= 32899 ; ( 360484/275615 , -171823326/1378075 ), ( 32899/23732 , -1536087/11866 )
**u= 75/59 , ht= 54374 ; ( 54374/46693 , 6357900/46693 ), ( 75167/8672 , -16781349/21680 )
**u= 75/77 , ht= 2949857 ; ( -118985/2949857 , 1495977141/14749285 ), ( -5456878633/126865120 , 1382937791127/317162800
)
**u= 75/92 , ht= 324655 ; ( -414751/103715 , 236789007/518575 ), ( -324655/246527 , 225785436/1232635 )
**u= 75/104 , ht= 29971 ; ( 120623/94423 , -2200203/11515 ), ( -29971/9419 , 18500799/47095 )
**u= 75/109 , ht= 32767 ; ( 45488/253 , 27423762/1265 ), ( 24131/32767 , -4906647/32767 )
**u= 75/133 , ht= 20593 ; ( -3949/20593 , 2792775/20593 ), ( 819205/41666 , -273129258/104165 )
**u= 75/148 , ht= 231229 ; ( -3025393/1250549 , 459947577/1250549 ), ( -231229/36947 , -32899980/36947 )
**u= 75/172 , ht= 80255 ; ( -172459/49937 , 27194253/49937 ), ( -80255/9787 , 61229289/48935 )
**u= 75/176 , ht= 27911 ; ( -27911/491 , -42770301/4910 ), ( -51389/1939 , -39396057/9695 )
**u= 75/181 , ht= 144823 ; ( -34186/144823 , 23120568/144823 ), ( 381113/55459 , -59839839/55459 )
**u= 75/197 , ht= 15190 ; ( -15190/3919 , 12714468/19595 ), ( -30865/34411 , -37465083/172055 )
**u= 76/13 , ht= 112985 ; ( 349235/355293 , 41217017/710586 ), ( -105831/112985 , 12806861/225970 )
**u= 76/33 , ht= 2003 ; ( -2003/1297 , 314521/2594 ), ( -1609/4925 , -682869/9850 )
**u= 76/89 , ht= 76633 ; ( 76633/65419 , 21810939/130838 ), ( 146519/67843 , 34952151/135686 )
**u= 76/97 , ht= 27533 ; ( 27533/20743 , 7790283/41486 ), ( 29517/8953 , -6970667/17906 )
**u= 76/105 , ht= 18401 ; ( 36277/4687 , -8600319/9374 ), ( -16669/18401 , 5837717/36802 )
**u= 76/117 , ht= 1 ; ( -1 , 351/2 ), ( -2763/1475 , 39527/150 )
**u= 76/185 , ht= 56859 ; ( -287991/331019 , 136935059/662038 ), ( -16919/56859 , 18514219/113718 )
**u= 76/189 , ht= 1511 ; ( -433/1511 , -495831/3022 ), ( -518177/49271 , 492590069/295626 )
**u= 78/5 , ht= 296 ; ( -296/181 , 17523/362 ), ( -448/347 , -28743/694 )
**u= 78/37 , ht= 667 ; ( 11303/3644 , 1636011/7288 ), ( 556/667 , 119631/1334 )
**u= 78/109 , ht= 3484 ; ( -3484/331 , 827553/662 ), ( -29572/23075 , 8869803/46150 )
**u= 78/125 , ht= 317 ; ( 317/28 , 57561/40 ), ( 1456/59 , 1845039/590 )
**u= 81 , ht= 10 ; ( -8/19 , -254/19 ), ( -1/10 , 46/5 )
**u= 81/4 , ht= 145 ; ( -145/49 , -482/7 ), ( 49/145 , -3374/145 )
**u= 81/7 , ht= 85 ; ( 85 , -2491 ), ( 1/85 , -2491/85 )
**u= 81/8 , ht= 128 ; ( 128/93 , -19877/372 ), ( 149/120 , -24067/480 )
**u= 81/16 , ht= 161 ; ( 53/161 , -15077/322 ), ( -161/53 , 15077/106 )
**u= 81/32 , ht= 1 ; ( 0 , 503/8 ), ( 126423/503 , -15803 )
**u= 81/44 , ht= 951 ; ( 313/951 , -73808/951 ), ( -973/39 , -71789/39 )
**u= 81/47 , ht= 1629 ; ( 1629/1441 , -165697/1441 ), ( -2181/1955 , 223151/1955 )
**u= 81/100 , ht= 1769 ; ( -27857/7439 , -16020998/37195 ), ( -1769/1369 , -248584/1369 )
**u= 81/113 , ht= 2610 ; ( -60/9439 , -1115098/9439 ), ( 1367/2610 , 174028/1305 )
**u= 81/140 , ht= 1977 ; ( -125319/87481 , 20096110/87481 ), ( 1907/1977 , -361187/1977 )
**u= 81/145 , ht= 245281 ; ( -552214/20681 , 73947904/20681 ), ( 245281/18764 , -16459697/9382 )
**u= 81/151 , ht= 3703 ; ( 3545/3703 , -100007/529 ), ( -1326661/7072 , 90586027/3536 )
**u= 81/176 , ht= 1877 ; ( -8133/57031 , 16986533/114062 ), ( 939/1877 , -309424/1877 )
**u= 81/188 , ht= 20963 ; ( 15417/20963 , 3965057/20963 ), ( 10523/45867 , 7170508/45867 )
**u= 81/196 , ht= 4235 ; ( -38797/22921 , -7010849/22921 ), ( -1003/4235 , 4739822/29645 )
**u= 85/22 , ht= 7109 ; ( 7109/4238 , 842115/8476 ), ( -511458/63479 , 52467983/126958 )
**u= 85/26 , ht= 21882 ; ( 490537/130229 , -28068144/130229 ), ( -13231/21882 , 2828647/43764 )
**u= 85/33 , ht= 81451 ; ( 327772/116011 , 21665472/116011 ), ( -81451/1412 , -1269396/353 )
**u= 85/38 , ht= 7342 ; ( -89271/38827 , 6509584/38827 ), ( 7342/3409 , -1082757/6818 )
**u= 85/54 , ht= 4679 ; ( -4679/322 , 2243195/1932 ), ( 6803/6601 , 2267014/19803 )
**u= 85/57 , ht= 449182 ; ( -449182/4639 , -36789622/4639 ), ( -1625783/362834 , -68220221/181417 )
**u= 85/63 , ht= 810689 ; ( 346568/810689 , -75919276/810689 ), ( 3297913/1541144 , -78364547/385286 )
**u= 85/66 , ht= 10639 ; ( -4559681/94573 , 401928092/94573 ), ( 3133/10639 , -977424/10639 )
**u= 85/98 , ht= 249156 ; ( 249156/127637 , 420898637/1786918 ), ( -456151/160763 , 363593598/1125341 )
**u= 85/106 , ht= 32594 ; ( 32594/10917 , 7678385/21834 ), ( 10917/32594 , 7678385/65188 )
**u= 85/126 , ht= 4171 ; ( -10005879/423512 , 7317151519/2541072 ), ( 2353/4171 , 583160/4171 )
**u= 85/138 , ht= 103223 ; ( 28726/103223 , 27309501/206446 ), ( -26800747/14205746 , 7731289575/28411492 )
**u= 85/178 , ht= 700463 ; ( -471364/1348953 , 413638781/2697906 ), ( -700463/555149 , 129361986/555149 )
**u= 85/186 , ht= 835909 ; ( 835909/470977 , 141954324/470977 ), ( -9952439/18587 , -1472500822/18587 )
**u= 87/5 , ht= 32 ; ( -32/7 , -780/7 ), ( -113/442 , -5433/221 )
**u= 87/14 , ht= 181 ; ( -59755/209009 , -8728944/209009 ), ( -181/55 , -7596/55 )
**u= 87/22 , ht= 18703 ; ( 74033/1411 , -3722736/1411 ), ( 18703/14611 , 1193802/14611 )
**u= 87/35 , ht= 169846 ; ( 169846/22391 , -10866318/22391 ), ( 1078141/3859514 , -127090167/1929757 )
**u= 87/98 , ht= 3085 ; ( 3085/1666 , -5210481/23324 ), ( -1666/3085 , 5210481/43190 )
**u= 87/118 , ht= 237641 ; ( 237641/15683 , -27740646/15683 ), ( -6170537/1194964 , -1464233823/2389928 )
**u= 87/133 , ht= 80089 ; ( 23830/80089 , -10333314/80089 ), ( -132541/121958 , -11136759/60979 )
**u= 87/134 , ht= 1248269 ; ( -134209/1248269 , -155839368/1248269 ), ( 1818523/503983 , 234239526/503983 )
**u= 87/139 , ht= 7496 ; ( -7496/1241 , 960552/1241 ), ( -1241/7496 , -120069/937 )
**u= 87/155 , ht= 1445584 ; ( -1445584/156899 , 194117772/156899 ), ( 30852343/3189152 , -1035193713/797288 )
**u= 87/170 , ht= 1410869 ; ( 2819593/574573 , 402308898/574573 ), ( 1410869/1112009 , 251158992/1112009 )
**u= 87/178 , ht= 28622 ; ( -8927903/519091 , 1279399248/519091 ), ( 28622/4681 , 8298327/9362 )
**u= 89/8 , ht= 1964 ; ( -1964/1539 , 299063/6156 ), ( 124469/8459 , -3752448/8459 )
**u= 89/24 , ht= 52639 ; ( -21335/52639 , 2950727/52639 ), ( -241694/55495 , 51535107/221980 )
**u= 89/36 , ht= 3255 ; ( -63727033/9395879 , 4096965138/9395879 ), ( -491/3255 , 628097/9765 )
**u= 89/41 , ht= 178339 ; ( -102038/178339 , -13948908/178339 ), ( 11022209/1598482 , 378076986/799241 )
**u= 89/44 , ht= 21091 ; ( -167905/168609 , 2390554/24087 ), ( -21091/18355 , -1966272/18355 )
**u= 89/52 , ht= 32119 ; ( -32119/22889 , 3015174/22889 ), ( -83029/1419 , -6349034/1419 )
**u= 89/55 , ht= 161691 ; ( -161691/117889 , 15732959/117889 ), ( -297443/131178 , 12780502/65589 )
**u= 89/57 , ht= 197786 ; ( -1901494/41869 , -152227176/41869 ), ( -94901/197786 , 8779292/98893 )
**u= 89/68 , ht= 5135 ; ( 75959/504359 , 44592648/504359 ), ( 239/5135 , -449394/5135 )
**u= 89/87 , ht= 1023626 ; ( -2566502/861737 , 267712972/861737 ), ( -793601/1023626 , 955826/7639 )
**u= 89/92 , ht= 28969 ; ( 91273/45687 , 10379162/45687 ), ( 28141/28969 , 69609/491 )
**u= 89/104 , ht= 1782303 ; ( 83598758/2009159 , -36163871739/8036636 ), ( -1782303/186170 , 775002989/744680 )
**u= 89/111 , ht= 575005 ; ( 575005/425969 , 79929941/425969 ), ( -4895087/577631 , 550569929/577631 )
**u= 89/112 , ht= 307387 ; ( 20625/307387 , 69133367/614774 ), ( 1211887/11475 , 271962133/22950 )
**u= 89/144 , ht= 172447 ; ( 56459/172447 , -46170261/344894 ), ( 1188031/331573 , -7298659/15422 )
**u= 89/152 , ht= 5377849 ; ( -5377849/701246 , 405070707/400712 ), ( -11409174/1162531 , 193420199/150004 )
**u= 89/153 , ht= 84580 ; ( 84580/35559 , 36095702/106677 ), ( 5050253/378772 , -332071437/189386 )
**u= 89/159 , ht= 85247 ; ( -11276804/315197 , 1508105642/315197 ), ( 38561/85247 , -12507791/85247 )
**u= 89/164 , ht= 2690339 ; ( 1705679/6359343 , -893929262/6359343 ), ( 2690339/162607 , 365935809/162607 )
**u= 89/176 , ht= 141069 ; ( -668557/671309 , -133255338/671309 ), ( 141069/77027 , -22606403/77027 )
**u= 89/185 , ht= 1240809 ; ( 20418518/3282523 , -2982149664/3282523 ), ( -1240809/180574 , -90405548/90287 )
**u= 89/196 , ht= 155821 ; ( -155821/58217 , -172824483/407519 ), ( -1066937/129309 , 1116643127/905163 )
**u= 90/7 , ht= 303 ; ( -303/44 , 17013/88 ), ( 587/524 , 43917/1048 )
**u= 90/31 , ht= 621 ; ( 22373/18144 , 375733/4032 ), ( -621/32 , -73017/64 )
**u= 90/167 , ht= 188523 ; ( -52124/188523 , 5921931/41894 ), ( -34164/261593 , -71885043/523186 )
**u= 90/199 , ht= 2272 ; ( 87708/7511 , -26183937/15022 ), ( -2272/1509 , -270427/1006 )
**u= 95 , ht= 17 ; ( -9/17 , -13 ), ( -17/46 , 204/23 )
**u= 95/28 , ht= 3629 ; ( 3629/1613 , 215598/1613 ), ( -51407/3851 , -2799975/3851 )
**u= 95/34 , ht= 749 ; ( -749/407 , -51000/407 ), ( -4081/747 , -248288/747 )
**u= 95/36 , ht= 1619 ; ( 1367/1619 , -130465/1619 ), ( 20569/6213 , 3969379/18639 )
**u= 95/44 , ht= 6911 ; ( -7859/8157 , -771004/8157 ), ( 6911/2357 , -497067/2357 )
**u= 95/63 , ht= 4244 ; ( 4244/1507 , 366798/1507 ), ( 65801/10942 , 2716648/5471 )
**u= 95/68 , ht= 79371 ; ( 8753/79371 , -6757345/79371 ), ( 637163/8911 , 53924091/8911 )
**u= 95/92 , ht= 299913 ; ( 425291/168197 , -45013392/168197 ), ( 299913/44521 , -29843354/44521 )
**u= 95/121 , ht= 1411 ; ( -48/1411 , 1753010/15521 ), ( 1199329/40147 , -1490005095/441617 )
**u= 95/141 , ht= 6917 ; ( -375128/18779 , 45765880/18779 ), ( -6917/4504 , 125721/563 )
**u= 95/144 , ht= 6891 ; ( 14263/8291 , 4062995/16582 ), ( -6137/6891 , -6817655/41346 )
**u= 95/153 , ht= 61232 ; ( 61232/51529 , -10157926/51529 ), ( 316993/207904 , -270323/1168 )
**u= 95/156 , ht= 27203 ; ( -27203/9379 , 3687910/9379 ), ( -989383/45209 , -126939814/45209 )
**u= 95/161 , ht= 2662 ; ( 2662/569 , 354432/569 ), ( -65171/9533 , 8575953/9533 )
**u= 95/179 , ht= 149288 ; ( -149288/7699 , 20522928/7699 ), ( 444351/296888 , 9171146/37111 )
**u= 95/189 , ht= 71287 ; ( 101998/69679 , -17426238/69679 ), ( -71287/33524 , -8334956/25143 )
**u= 95/196 , ht= 171 ; ( 171/73 , -26711/73 ), ( -4343/459 , -627403/459 )
**u= 95/198 , ht= 16937 ; ( -98324/52057 , 32128655/104114 ), ( 16541/16937 , 3418390/16937 )
**u= 96/5 , ht= 4 ; ( 9236/34091 , -6500733/272728 ), ( 4 , -759/8 )
**u= 96/37 , ht= 2084 ; ( 67532/7777 , 4823169/8888 ), ( -469/2084 , -1060941/16672 )
**u= 96/53 , ht= 11063 ; ( 4429844/45419 , -2633564427/363352 ), ( -11063/4360 , 7069983/34880 )
**u= 96/61 , ht= 3352 ; ( 7489/26488 , -2508237/30272 ), ( 3352/1339 , 2302329/10712 )
**u= 96/73 , ht= 284146 ; ( 284146/38209 , -200035293/305672 ), ( -1173097/134990 , 823949253/1079920 )
**u= 96/85 , ht= 150083 ; ( -150083/141892 , -155503635/1135136 ), ( -257723/48532 , -197457099/388256 )
**u= 96/109 , ht= 98443 ; ( -465347/230836 , -442880049/1846688 ), ( -98443/6524 , 84117897/52192 )
**u= 96/113 , ht= 94 ; ( 5111230/72673 , 4437425433/581384 ), ( 94/19 , -83253/152 )
**u= 96/125 , ht= 21607 ; ( 80999/34844 , -402531207/1393760 ), ( -4268/21607 , -20108763/172856 )
**u= 96/185 , ht= 10502 ; ( -10502/1153 , 11735109/9224 ), ( -1153/10502 , -11735109/84016 )
**u= 96/193 , ht= 469502 ; ( 38147/469502 , -534414099/3756016 ), ( -135289/534614 , 625641783/4276912 )
**u= 97/12 , ht= 38879 ; ( 38879/4373 , -1374147/4373 ), ( -44053/2561 , 1554863/2561 )
**u= 97/16 , ht= 127599 ; ( -424253/12157 , 17224818/12157 ), ( 127599/9605 , 10405151/19210 )
**u= 97/20 , ht= 7297 ; ( -7297/3103 , -359970/3103 ), ( 10397/10177 , 660753/10177 )
**u= 97/33 , ht= 73069 ; ( 163580/54163 , 10050598/54163 ), ( 73069/41870 , -2456712/20935 )
**u= 97/44 , ht= 196921 ; ( -196921/2861 , -13264827/2861 ), ( 778513/85073 , -52760814/85073 )
**u= 97/47 , ht= 15214 ; ( 15214/11407 , -120348/1037 ), ( -11407/15214 , 661914/7607 )
**u= 97/55 , ht= 135356 ; ( 135356/131891 , 14233278/131891 ), ( 418481/372556 , 21098805/186278 )
**u= 97/56 , ht= 135795 ; ( -1444719/1126871 , -139237171/1126871 ), ( -6221/135795 , 10329772/135795 )
**u= 97/72 , ht= 54253 ; ( 46040/116491 , -43175753/465964 ), ( 54253/1765 , 4677669/1765 )
**u= 97/79 , ht= 5914 ; ( 83165/730491 , -66363751/730491 ), ( 2359/5914 , -287346/2957 )
**u= 97/80 , ht= 17287 ; ( -179553/398317 , 79373177/796634 ), ( 2887/17287 , 1591890/17287 )
**u= 97/81 , ht= 7891 ; ( -14822/802257 , 660052252/7220313 ), ( -7891/1330 , 365706/665 )
**u= 97/108 , ht= 42809 ; ( -34507/42809 , -17408801/128427 ), ( -7273903/1159169 , 777362436/1159169 )
**u= 97/116 , ht= 145035 ; ( 145035/42143 , -16519109/42143 ), ( 3107329/1091829 , 360239681/1091829 )
**u= 97/135 , ht= 153632 ; ( -153632/44753 , -56642342/134259 ), ( -1140643/1174528 , -96592061/587264 )
**u= 97/145 , ht= 305542 ; ( 5314102/5083697 , 52900284/299041 ), ( -155703/305542 , 20967358/152771 )
**u= 97/188 , ht= 22111 ; ( 87719181/5084063 , 12234576961/5084063 ), ( -22111/1953 , 3090778/1953 )
**u= 97/191 , ht= 1229205 ; ( -1229205/240731 , 175792903/240731 ), ( 18172423/6216587 , 2695586583/6216587 )
**u= 97/199 , ht= 28585 ; ( -6674096/3551121 , -1083025298/3551121 ), ( 3511/28585 , 4125759/28585 )
**u= 97/200 , ht= 94543 ; ( 135459/118373 , -129177779/591865 ), ( -94543/90864 , -376644671/1817280 )
**u= 100/3 , ht= 3529 ; ( 3529/581 , -603061/5810 ), ( -2297/10507 , -1815547/105070 )
**u= 100/39 , ht= 1909 ; ( -1909/1445 , -1495387/14450 ), ( -86795/14293 , 54951651/142930 )
**u= 100/83 , ht= 598689 ; ( 598689/10219 , 545586761/102190 ), ( 779027/11111 , 141989901/22222 )
**u= 100/199 , ht= 231 ; ( 165601/221255 , -389929347/2212550 ), ( -231/167 , -80435/334 )
**u= 101/19 , ht= 71071 ; ( -57543/71071 , -360683/6461 ), ( -452969/157215 , -20811329/157215 )
**u= 101/27 , ht= 11597 ; ( -11597/11233 , 2504723/33699 ), ( -595363/44962 , -46329256/67443 )
**u= 101/44 , ht= 818737 ; ( 818737/535509 , 64579907/535509 ), ( -30565743/10544381 , 2134705679/10544381 )
**u= 101/51 , ht= 568199 ; ( -568199/182843 , 42419207/182843 ), ( -986269/172468 , -35583323/86234 )
**u= 101/64 , ht= 383089 ; ( 949347/227629 , 155444249/455258 ), ( 6403/383089 , 122010891/1532356 )
**u= 101/67 , ht= 387989 ; ( 2566545/650881 , 30811777/92983 ), ( -387989/10125 , 31618741/10125 )
**u= 101/72 , ht= 168958 ; ( 563459/165541 , 49591107/165541 ), ( -166197/168958 , 240163987/2027496 )
**u= 101/75 , ht= 31001 ; ( -4783525/1728043 , -2191715973/8640215 ), ( -31001/21674 , 1630106/10837 )
**u= 101/83 , ht= 29101 ; ( 29101/779 , -2639379/779 ), ( -1082973/4917988 , 228286151/2458994 )
**u= 101/96 , ht= 171125 ; ( -171125/130384 , -167823201/1043072 ), ( -225464/5437 , 175936663/43496 )
**u= 101/112 , ht= 61501 ; ( -91465/35053 , -20632899/70106 ), ( -61501/4019 , 6491433/4019 )
**u= 101/115 , ht= 300163 ; ( 388641/176719 , 45563599/176719 ), ( 300163/96567 , 33652279/96567 )
**u= 101/120 , ht= 1737002 ; ( 4304429/628229 , -474232195/628229 ), ( 1737002/659267 , -810205229/2637068 )
**u= 101/132 , ht= 220753 ; ( 220753/43807 , -25732984/43807 ), ( 18214523/663077 , -2084078086/663077 )
**u= 101/133 , ht= 751573 ; ( 1743146/460531 , 206928624/460531 ), ( 751573/509932 , 3065937/14998 )
**u= 101/148 , ht= 514735 ; ( -514735/10591 , -3666636/623 ), ( -9750707/4636863 , -1307240177/4636863 )
**u= 101/181 , ht= 1864543 ; ( -23199000/27938387 , 4862235206/27938387 ), ( -1864543/987960 , -141264367/493980 )
**u= 101/188 , ht= 4766259 ; ( -9699209/1822371 , 1346669981/1822371 ), ( 4766259/975239 , 663866549/975239 )
**u= 101/195 , ht= 1304792 ; ( 1304792/192473 , -183292854/192473 ), ( 4760053/1782587 , -706390899/1782587 )
**u= 104/55 , ht= 13914 ; ( -13914/4819 , -4283729/19276 ), ( 34462/6687 , -10214165/26748 )
**u= 104/103 , ht= 6858 ; ( 6858/163 , -2731159/652 ), ( 163/6858 , -2731159/27432 )
**u= 104/183 , ht= 50393 ; ( -714001/23786 , -54160541/13592 ), ( 50393/9218 , 27187251/36872 )
**u= 106/19 , ht= 187706 ; ( 187706/44503 , 16326057/89006 ), ( 3214/254413 , -21531081/508826 )
**u= 106/23 , ht= 52592 ; ( -865436/72481 , -80880213/144962 ), ( -52592/23423 , -5366409/46846 )
**u= 106/43 , ht= 5165 ; ( -5165/4854 , -903029/9708 ), ( 7045127/8157322 , -1373204949/16314644 )
**u= 106/47 , ht= 228200 ; ( -228200/156307 , -36841131/312614 ), ( -4804172/730783 , -647352003/1461566 )
**u= 106/75 , ht= 5161 ; ( 1414/5161 , -900437/10322 ), ( -292390/115817 , 264593813/1158170 )
**u= 106/79 , ht= 185680 ; ( 746852/1011739 , -217166949/2023478 ), ( 141993/185680 , -40365761/371360 )
**u= 106/87 , ht= 864929 ; ( -864929/368644 , -170383601/737288 ), ( -2202848/1559467 , 489122013/3118934 )
**u= 106/123 , ht= 674906 ; ( 12658699/3922706 , 2855608453/7845412 ), ( 674906/412301 , 170419603/824602 )
**u= 106/127 , ht= 12014740 ; ( 12014740/665639 , -2634676257/1331278 ), ( 25835641/526700 , -5658117183/1053400 )
**u= 106/151 , ht= 551225 ; ( 264853/1622796 , -392571653/3245592 ), ( -205436/551225 , -140445801/1102450 )
**u= 106/163 , ht= 467563 ; ( 80438/467563 , 117686019/935126 ), ( -219301298/19351403 , -54610586871/38702806 )
**u= 106/179 , ht= 2498170 ; ( 7404142/1359491 , 1956819789/2718982 ), ( 1291531/2498170 , 731030613/4996340 )
**u= 106/191 , ht= 2353313 ; ( 3709355/4188956 , -1502410311/8377912 ), ( 2353313/137904 , 632990431/275808 )
**u= 106/195 , ht= 6667 ; ( 6667/518 , 259183/148 ), ( -11737754/605191 , 3188856979/1210382 )
**u= 109/8 , ht= 110219 ; ( -585989/1691 , -15804282/1691 ), ( -110219/28346 , -12384807/113384 )
**u= 109/11 , ht= 17603 ; ( -327621/64963 , 10588091/64963 ), ( -289/17603 , 558003/17603 )
**u= 109/12 , ht= 7691 ; ( -2129/7691 , 265299/7691 ), ( -9227/6703 , -378717/6703 )
**u= 109/20 , ht= 28241 ; ( -249633/25393 , 10742344/25393 ), ( 28241/23541 , -1575365/23541 )
**u= 109/29 , ht= 5280 ; ( 5280/4091 , 344558/4091 ), ( 2289703/89834 , -59128614/44917 )
**u= 109/43 , ht= 11308 ; ( 11308/2237 , -724026/2237 ), ( 246993/47557 , 15803419/47557 )
**u= 109/44 , ht= 281055 ; ( -2933585/159967 , -186666444/159967 ), ( -153467/281055 , 20347369/281055 )
**u= 109/51 , ht= 9067 ; ( -9067/4681 , -698057/4681 ), ( -196949/52730 , 6975052/26365 )
**u= 109/56 , ht= 1755 ; ( -1755/254 , 508459/1016 ), ( -586966/7663 , -168347937/30652 )
**u= 109/68 , ht= 296917 ; ( 1462785/506467 , -122281633/506467 ), ( -296917/73717 , 24169386/73717 )
**u= 109/77 , ht= 131729 ; ( -98564/131729 , 13830486/131729 ), ( -50105021/6174090 , 2122036324/3087045 )
**u= 109/88 , ht= 48579 ; ( -2628133/1172763 , 258626204/1172763 ), ( 48579/9221 , -4443797/9221 )
**u= 109/93 , ht= 2065519 ; ( -2332958/615917 , -222909764/615917 ), ( 2065519/1367120 , -114419747/683560 )
**u= 109/99 , ht= 172559 ; ( 116125/172559 , 19826073/172559 ), ( -3660967/526814 , -176282574/263407 )
**u= 109/107 , ht= 2278620 ; ( 2278620/1055821 , 248859478/1055821 ), ( 11509169/3119764 , 590846727/1559882 )
**u= 109/124 , ht= 282801 ; ( 63073/282801 , -30910316/282801 ), ( 714983/456629 , 90501567/456629 )
**u= 109/131 , ht= 6723431 ; ( -6909642/8439329 , -1195942372/8439329 ), ( 6723431/494407 , -739209957/494407 )
**u= 109/156 , ht= 962713 ; ( -11198657/1031041 , 1345608362/1031041 ), ( -962713/402599 , 124859966/402599 )
**u= 109/164 , ht= 2778433 ; ( 5231823/171521 , -91741988/24503 ), ( 2778433/948849 , -360198748/948849 )
**u= 109/168 , ht= 7137607 ; ( 84463/7137607 , -886349461/7137607 ), ( 7772683/1326355 , -979096417/1326355 )
**u= 109/172 , ht= 33577 ; ( -467551/1797861 , 233398181/1797861 ), ( -2887/33577 , -4234128/33577 )
**u= 109/184 , ht= 12042 ; ( 708053/70500909 , -9162037751/70500909 ), ( -12042/355 , -6262139/1420 )
**u= 109/189 , ht= 397463 ; ( 5000290/428399 , -1982871676/1285197 ), ( 397463/39694 , -26303826/19847 )
**u= 109/195 , ht= 225133 ; ( 1366511/2557831 , -387950307/2557831 ), ( -164423/225133 , -37294503/225133 )
**u= 111/49 , ht= 9530 ; ( 9530/1939 , 4523352/13573 ), ( 10523/2389 , -717159/2389 )
**u= 111/52 , ht= 30151 ; ( 175439/88261 , 13443273/88261 ), ( -23149/30151 , 2602143/30151 )
**u= 111/56 , ht= 22763 ; ( 172829/97187 , 14085312/97187 ), ( 4451/22763 , 1647579/22763 )
**u= 111/65 , ht= 11663 ; ( 11663/7633 , 1066797/7633 ), ( 23827/59243 , 4887009/59243 )
**u= 111/76 , ht= 3229 ; ( -2243/3229 , 325386/3229 ), ( 4749271/104227 , 393165981/104227 )
**u= 111/89 , ht= 8579 ; ( 7333/8579 , 1010763/8579 ), ( -999199/111343 , 90044607/111343 )
**u= 111/100 , ht= 27463 ; ( 27463/26179 , -18009357/130895 ), ( -2121089/275923 , -1015313583/1379615 )
**u= 111/124 , ht= 2344361 ; ( -2344361/331063 , 250281786/331063 ), ( -408525763/152555885 , -46099798512/152555885 )
**u= 111/127 , ht= 2243339 ; ( 6002800/1473563 , 94465026/210509 ), ( 2243339/494146 , -122878854/247073 )
**u= 111/136 , ht= 35561 ; ( -252935/404761 , 52841022/404761 ), ( -35561/7313 , -4019379/7313 )
**u= 111/140 , ht= 11177183 ; ( 12156973/707143 , -1367825403/707143 ), ( 11177183/999253 , 1260509889/999253 )
**u= 111/145 , ht= 66134 ; ( -203134/46411 , -23819064/46411 ), ( -28289/66134 , 4111272/33067 )
**u= 111/160 , ht= 168403 ; ( 262871/52106 , 257436933/416848 ), ( 168403/115277 , -1441539/6781 )
**u= 111/191 , ht= 264128 ; ( -264128/159269 , -3678714/14479 ), ( -1616351/1431272 , -141627387/715636 )
**u= 111/200 , ht= 119339 ; ( -119339/4339 , 16032285/4339 ), ( -154681/15481 , -20870556/15481 )
**u= 113/5 , ht= 218 ; ( -218/7 , 4530/7 ), ( -7/218 , -2265/109 )
**u= 113/19 , ht= 189720 ; ( 189720/88697 , -8584316/88697 ), ( -290531/56846 , 6075603/28423 )
**u= 113/22 , ht= 197429 ; ( 135895/197429 , 10579836/197429 ), ( 205724/81303 , 19533761/162606 )
**u= 113/26 , ht= 504469 ; ( -504469/2609 , 24191268/2609 ), ( 617889/204944 , 62487409/409888 )
**u= 113/29 , ht= 21391 ; ( -736/21391 , 1084896/21391 ), ( -223889/174560 , 449559/5455 )
**u= 113/70 , ht= 152828 ; ( -145533/152828 , 33225689/305656 ), ( 2578364/611749 , -417231969/1223498 )
**u= 113/74 , ht= 322472 ; ( -322472/109947 , 55148639/219894 ), ( 7428279/2609140 , 1274537069/5218280 )
**u= 113/77 , ht= 441236 ; ( 704920/217587 , 60906628/217587 ), ( 58777/441236 , 9187344/110309 )
**u= 113/82 , ht= 1243950 ; ( 6968850/122219 , -1187629523/244438 ), ( -337543/1243950 , 219627169/2487900 )
**u= 113/94 , ht= 436426 ; ( 10842315/1951889 , -1004925608/1951889 ), ( -436426/45465 , -80057231/90930 )
**u= 113/110 , ht= 3208747 ; ( -3208747/237993 , -317503526/237993 ), ( 316702/9784567 , -1932060237/19569134 )
**u= 113/122 , ht= 590720 ; ( 34596881/3854467 , -3617622684/3854467 ), ( 504527/590720 , -161466711/1181440 )
**u= 113/130 , ht= 240349 ; ( -6035173/3763447 , 762998418/3763447 ), ( 240349/20649 , -25879490/20649 )
**u= 113/133 , ht= 328259 ; ( -320830/328259 , -49805862/328259 ), ( 6730457/31884250 , -1767942537/15942125 )
**u= 113/138 , ht= 6658243 ; ( 781444/6658243 , 1481984671/13316486 ), ( -25053503/1239131 , 2772570212/1239131 )
**u= 113/141 , ht= 776944 ; ( 776944/172759 , 88921972/172759 ), ( -15180509/2132176 , 428175137/533044 )
**u= 113/163 , ht= 2667787 ; ( -3279548/1150931 , 417504684/1150931 ), ( -2667787/2149936 , 51447351/268742 )
**u= 113/165 , ht= 167693 ; ( 160558/167693 , 28059026/167693 ), ( -7968803/2550038 , -505610301/1275019 )
**u= 113/178 , ht= 1288174 ; ( 1074486/5054477 , -1297342819/10108954 ), ( 1102253/1288174 , -425643699/2576348 )
**u= 113/179 , ht= 8254127 ; ( -54526838/1133033 , -6865355238/1133033 ), ( -8254127/1017178 , -523457589/508589 )
**u= 113/190 , ht= 1052822 ; ( -6016929/1659926 , 1618985617/3319852 ), ( 1052822/897687 , 358877689/1795374 )
**u= 114/7 , ht= 874 ; ( -4174/2021 , 228927/4042 ), ( 874/265 , 45519/530 )
**u= 114/11 , ht= 80 ; ( -80/41 , 5577/82 ), ( 41/80 , -5577/160 )
**u= 114/35 , ht= 173 ; ( 68/173 , 20607/346 ), ( -292204/110681 , 34639623/221362 )
**u= 114/55 , ht= 466 ; ( -359/466 , 81735/932 ), ( 323/2138 , 300399/4276 )
**u= 114/163 , ht= 16537 ; ( -3512/16537 , -4043787/33074 ), ( -3628451/224380 , 869566287/448760 )
**u= 114/175 , ht= 1226 ; ( -23587/9950 , -31723107/99500 ), ( -1226/349 , -315927/698 )
**u= 117 , ht= 1 ; ( 0 , 12 ), ( 1/4 , -6 )
**u= 117/11 , ht= 34 ; ( -85/3 , 867 ), ( -21/34 , 36 )
**u= 117/19 , ht= 1 ; ( -1 , 57 ), ( 407/752 , 17223/376 )
**u= 117/22 , ht= 26 ; ( 2393/61 , -103746/61 ), ( -26/7 , -2337/14 )
**u= 117/25 , ht= 22 ; ( -22/3 , 342 ), ( -3/22 , -513/11 )
**u= 117/76 , ht= 1 ; ( -367/203 , 33807/203 ), ( 1 , -114 )
**u= 117/83 , ht= 1509 ; ( -1177/1509 , -53739/503 ), ( 12297/2809 , -1062639/2809 )
**u= 117/85 , ht= 524 ; ( 524/479 , 60522/479 ), ( 1439/9956 , 3273/38 )
**u= 117/94 , ht= 7684 ; ( 42261/3439 , 3801048/3439 ), ( 7684/775 , -1384773/1550 )
**u= 117/124 , ht= 2997 ; ( -18725/1179 , -214646/131 ), ( -2997/1013 , 325746/1013 )
**u= 117/127 , ht= 284 ; ( -700/697 , 102936/697 ), ( -97/284 , -7818/71 )
**u= 117/136 , ht= 379 ; ( -29/379 , -40989/379 ), ( 3643/5 , -392844/5 )
**u= 117/178 , ht= 1557 ; ( -311/1557 , -21764/173 ), ( 85023/1096 , 20979747/2192 )
**u= 117/187 , ht= 230 ; ( 230/111 , 10764/37 ), ( 19443/10994 , -61398/239 )
**u= 121/4 , ht= 485 ; ( -485/417 , -127507/4587 ), ( 901/485 , 207246/5335 )
**u= 121/16 , ht= 1015 ; ( 1015/537 , 459031/5907 ), ( -23033/4201 , -9379347/46211 )
**u= 121/20 , ht= 1213 ; ( 14433/1123 , 6469421/12353 ), ( 1213/223 , -552129/2453 )
**u= 121/25 , ht= 2099 ; ( -12062/2711 , 30896304/149105 ), ( 2099/1532 , -3249423/42130 )
**u= 121/31 , ht= 44013 ; ( 69785/29547 , 42190051/325017 ), ( -44013/16220 , 13064323/89210 )
**u= 121/36 , ht= 6451 ; ( 6451/2963 , -4259318/32593 ), ( 61317/18379 , 115269296/606507 )
**u= 121/39 , ht= 3806 ; ( 38035/21083 , -27159163/231913 ), ( 3617/3806 , -1639752/20933 )
**u= 121/52 , ht= 857 ; ( 25867/1323 , -18678094/14553 ), ( -313/857 , 657966/9427 )
**u= 121/56 , ht= 9697 ; ( -8265/9697 , -9536599/106667 ), ( -9697/8265 , 9536599/90915 )
**u= 121/60 , ht= 39433 ; ( -35909/43751 , 43851029/481261 ), ( 39433/3463 , -30670664/38093 )
**u= 121/64 , ht= 12799 ; ( -24655/12303 , -22046017/135333 ), ( 577/12799 , 10250481/140789 )
**u= 121/71 , ht= 53170 ; ( -53170/3701 , -44914872/40711 ), ( -264817/65546 , 114963636/360503 )
**u= 121/73 , ht= 37587 ; ( 44432/26693 , -44292942/293623 ), ( -37587/35048 , -21958649/192764 )
**u= 121/76 , ht= 13847 ; ( -859/13847 , -12097617/152317 ), ( -14713/20779 , 22199403/228569 )
**u= 121/84 , ht= 431897 ; ( -489035/42433 , -449947797/466763 ), ( 431897/275405 , -469561977/3029455 )
**u= 121/100 , ht= 17209 ; ( 15439/38993 , 209733534/2144615 ), ( 9957/17209 , -99425281/946495 )
**u= 121/105 , ht= 155227 ; ( 123608/155227 , -203367062/1707497 ), ( -291883/5848 , 149606683/32164 )
**u= 121/116 , ht= 51923 ; ( 215385/258827 , 362726599/2847097 ), ( 51923/48675 , -76666624/535425 )
**u= 121/136 , ht= 22340 ; ( 22340/3381 , 105413923/148764 ), ( 121899/41132 , -600243011/1809808 )
**u= 121/151 , ht= 90987 ; ( 1137874/881023 , 1768676652/9691253 ), ( 90987/19715 , -114422941/216865 )
**u= 121/167 , ht= 280979 ; ( -392798/142103 , -539892216/1563133 ), ( 280979/125001 , 397488847/1375011 )
**u= 121/168 , ht= 20543 ; ( -1180691/48341 , -1531880809/531751 ), ( -20543/11482 , -122036603/505208 )
**u= 121/183 , ht= 294130 ; ( 1095914/9199 , 1482820436/101189 ), ( -68491/294130 , 204302166/1617715 )
**u= 121/188 , ht= 16653 ; ( -1654027/281527 , -2300883933/3096797 ), ( -12863/16653 , -28856747/183183 )
**u= 121/191 , ht= 45327 ; ( 45327/2161 , -62724661/23771 ), ( -52331/43933 , 94447119/483263 )
**u= 121/192 , ht= 3901 ; ( 829/3901 , 5527108/42911 ), ( 3901/829 , 5527108/9119 )
**u= 121/199 , ht= 400486 ; ( -1515296698/65856409 , -2139961600632/724420499 ), ( 333423/400486 , -367624672/2202673 )
**u= 123/8 , ht= 206 ; ( 157865/3866 , 16016463/15464 ), ( -206/73 , 22401/292 )
**u= 123/13 , ht= 1732 ; ( -1732/49 , -56214/49 ), ( -285659/26348 , -4674183/13174 )
**u= 123/16 , ht= 715 ; ( -715/617 , -68121/1234 ), ( 2243/2393 , -236607/4786 )
**u= 123/28 , ht= 34267 ; ( -34267/901 , 1635006/901 ), ( -5028061/106817 , -240109929/106817 )
**u= 123/32 , ht= 23503 ; ( -18925/90107 , 9397389/180214 ), ( 16474/23503 , -11712249/188024 )
**u= 123/40 , ht= 31411 ; ( -31411/6884 , 7334811/27536 ), ( -353657/140383 , -21706179/140383 )
**u= 123/52 , ht= 56609 ; ( -22483/56609 , 565929/8087 ), ( 5567233/386611 , -362968809/386611 )
**u= 123/68 , ht= 39301 ; ( -101857/83851 , -9811119/83851 ), ( -39301/2417 , -2928441/2417 )
**u= 123/76 , ht= 484181 ; ( -484181/127771 , 39366948/127771 ), ( 697703/8052413 , -635407569/8052413 )
**u= 123/85 , ht= 32807 ; ( -9339178/1962487 , -793420788/1962487 ), ( 1867/32807 , -2731989/32807 )
**u= 123/100 , ht= 39673 ; ( -147659/85159 , -15371895/85159 ), ( 13255/39673 , 18860574/198365 )
**u= 123/101 , ht= 53995 ; ( 39334/78421 , 1135944/11203 ), ( 8141/53995 , 4948839/53995 )
**u= 123/109 , ht= 8900 ; ( -7004252/3242947 , 726715338/3242947 ), ( -5303/8900 , -487713/4450 )
**u= 123/125 , ht= 7679 ; ( 1696/7679 , -792930/7679 ), ( 7679/1696 , -396465/848 )
**u= 123/140 , ht= 34009 ; ( 377623/469813 , 64318503/469813 ), ( 34009/24329 , -4461948/24329 )
**u= 123/160 , ht= 45184 ; ( -364693/185707 , -46684380/185707 ), ( -45184/9371 , 42112293/74968 )
**u= 123/181 , ht= 408361 ; ( 526286/152159 , -66468012/152159 ), ( -207451/408361 , -55572117/408361 )
**u= 123/187 , ht= 2048260 ; ( -2048260/428653 , -258067302/428653 ), ( 3718243/444740 , 230909181/222370 )
**u= 123/188 , ht= 12533005 ; ( 12533005/3423559 , -1606499817/3423559 ), ( 67606819/10739263 , -8464641189/10739263 )
**u= 125/2 , ht= 196 ; ( 251/417 , 32164/2085 ), ( 47/196 , -4635/392 )
**u= 125/23 , ht= 268 ; ( -279218/166131 , 69671654/830655 ), ( -169/268 , -16986/335 )
**u= 125/34 , ht= 1431 ; ( -948/2401 , 192407/3430 ), ( 1187/1431 , 484882/7155 )
**u= 125/46 , ht= 37439 ; ( 20557/37439 , -12958578/187195 ), ( 37439/20557 , -12958578/102785 )
**u= 125/58 , ht= 250337 ; ( -608173/128369 , -211714698/641845 ), ( 250337/203589 , -109919888/1017945 )
**u= 125/82 , ht= 65251 ; ( 2007377/41509 , -813194598/207545 ), ( 65251/24497 , 28231668/122485 )
**u= 125/87 , ht= 2074 ; ( -2074/653 , -907122/3265 ), ( -63749/35068 , 1517792/8767 )
**u= 125/97 , ht= 91746 ; ( 77462/96571 , 54538062/482855 ), ( -10363/91746 , -20336179/229365 )
**u= 125/119 , ht= 30878 ; ( 30878/21239 , 18286398/106195 ), ( -51253/3296 , 1253031/824 )
**u= 125/126 , ht= 108 ; ( -51301/21313 , -27891332/106565 ), ( -108/31 , 67699/186 )
**u= 125/146 , ht= 62776 ; ( -62776/47673 , -85204957/476730 ), ( -798711/55973 , -86548346/55973 )
**u= 125/158 , ht= 190152 ; ( 256727/234844 , 391246149/2348440 ), ( -190152/151681 , -273516251/1516810 )
**u= 125/178 , ht= 4077499 ; ( -7782417/998501 , -4682262538/4992505 ), ( -4077499/605592 , -4920030641/6055920 )
**u= 128/3 , ht= 170 ; ( -170/7 , 39749/112 ), ( -377/166 , 103973/2656 )
**u= 128/15 , ht= 4993 ; ( 19496/71 , 10660885/1136 ), ( -4993/3292 , -3278619/52672 )
**u= 128/39 , ht= 32335 ; ( -32335/5924 , -29030577/94784 ), ( -5924/32335 , 29030577/517360 )
**u= 128/43 , ht= 2834 ; ( 2834/2017 , -3226143/32272 ), ( -490847/559170 , 690099199/8946720 )
**u= 128/51 , ht= 9257 ; ( -29639/63334 , 70641427/1013344 ), ( -6298/9257 , 11309021/148112 )
**u= 128/55 , ht= 60164 ; ( -88273/48952 , -105875295/783232 ), ( 60164/7089 , 63556535/113424 )
**u= 128/67 , ht= 72817 ; ( 212137/121754 , -283174347/1948064 ), ( 72817/2266 , -84355011/36256 )
**u= 128/111 , ht= 176356 ; ( -290372/53173 , 439901959/850768 ), ( 176356/126665 , -323576541/2026640 )
**u= 128/135 , ht= 664 ; ( -239/664 , 3479435/31872 ), ( 4818544/302389 , -7934816259/4838224 )
**u= 128/151 , ht= 1527359 ; ( 999456/1717159 , -3453400793/27474544 ), ( 1527359/432760 , -2759278689/6924160 )
**u= 128/155 , ht= 6798 ; ( -162086/5477899 , -9650910243/87646384 ), ( 6798/443 , 11996803/7088 )
**u= 128/167 , ht= 159184 ; ( -1994207/182304 , -3660330937/2916864 ), ( -28023/159184 , -295440481/2546944 )
**u= 128/199 , ht= 967321 ; ( -1115200/734903 , 2664913809/11758448 ), ( 967321/55304 , 1933308801/884864 )
**u= 130/47 , ht= 7531 ; ( -5582/7531 , 66327/886 ), ( 47158/3589 , 5689509/7178 )
**u= 130/63 , ht= 4483 ; ( -4483/3014 , -68383/548 ), ( 291709/12178 , -40661049/24356 )
**u= 130/163 , ht= 364119 ; ( 32444/508893 , -114220027/1017786 ), ( 364119/165748 , -89612239/331496 )
**u= 130/187 , ht= 35296 ; ( 687737/340104 , -184069391/680208 ), ( -3413/35296 , 8507391/70592 )
**u= 136/7 , ht= 1340 ; ( -1150525/58816 , 103577181/235264 ), ( 73/1340 , 120657/5360 )
**u= 136/15 , ht= 12404 ; ( 12404/3271 , -1701355/13084 ), ( 25637/1492 , 3418991/5968 )
**u= 136/19 , ht= 567282 ; ( 1588910/1133727 , -291758323/4534908 ), ( 567282/111569 , 86556029/446276 )
**u= 136/35 , ht= 100129 ; ( 100129/82454 , -26323275/329816 ), ( -202246/331539 , 78805631/1326156 )
**u= 136/59 , ht= 353166 ; ( 353166/66013 , -94661821/264052 ), ( 1081267/40566 , -285159869/162264 )
**u= 136/75 , ht= 91405 ; ( -585142/160505 , -901261141/3210100 ), ( -91405/69446 , 170527817/1388920 )
**u= 136/99 , ht= 71342 ; ( 64929/71342 , -98781617/856104 ), ( 56284939/4630578 , -57833912149/55566936 )
**u= 136/107 , ht= 180882 ; ( -200202/421147 , -165479741/1684588 ), ( -9257/180882 , 64269409/723528 )
**u= 136/143 , ht= 134159 ; ( -17564/134159 , -55507821/536636 ), ( 3702389/2244504 , 1776181721/8978016 )
**u= 136/155 , ht= 2356619 ; ( 7085543/12689878 , 6207585399/50759512 ), ( 220874/2356619 , 1010910507/9426476 )
**u= 136/159 , ht= 7455307 ; ( -35848387/1295444 , -15517085983/5181776 ), ( -7455307/394364 , 3229574201/1577456 )
**u= 136/195 , ht= 7330378 ; ( 7330378/1025443 , -3545793599/4101772 ), ( 52353478/1218043 , -25087197687/4872172 )
**u= 136/199 , ht= 52648 ; ( -2731969/217808 , 1326293631/871232 ), ( 36529/52648 , 31010607/210592 )
**u= 137/21 , ht= 1280 ; ( 1506208/930353 , 69292008/930353 ), ( -643/1280 , 7007/160 )
**u= 137/26 , ht= 169089 ; ( -2408425/508619 , -107185092/508619 ), ( -169089/13340 , -14790829/26680 )
**u= 137/58 , ht= 2000556 ; ( 2000556/650867 , 273784703/1301734 ), ( -48815281/4571283 , 3191103698/4571283 )
**u= 137/61 , ht= 129641 ; ( -23774/129641 , 8797446/129641 ), ( -349297/12150 , 11664407/6075 )
**u= 137/62 , ht= 3702 ; ( -722183/364026 , -108822797/728052 ), ( 3702/385 , -500917/770 )
**u= 137/69 , ht= 53011 ; ( -27821024/41912929 , -3570898068/41912929 ), ( -53011/40300 , -1181686/10075 )
**u= 137/98 , ht= 24290 ; ( 533191/606843 , 68334296/606843 ), ( 21519/24290 , -38431129/340060 )
**u= 137/114 , ht= 217913 ; ( -217913/19397 , -1174088/1141 ), ( 490399/177754 , 95184139/355508 )
**u= 137/146 , ht= 1034194 ; ( 5243801/3665979 , 660611404/3665979 ), ( 953091/1034194 , -290420903/2068388 )
**u= 137/155 , ht= 9787 ; ( -81866/365681 , 39866754/365681 ), ( 9787/2768 , -270513/692 )
**u= 137/170 , ht= 1802433 ; ( 1753021/3111321 , 397884320/3111321 ), ( -1802433/64592 , -401897225/129184 )
**u= 137/174 , ht= 142235 ; ( 142235/85511 , -18706486/85511 ), ( 937723/595175 , 125190948/595175 )
**u= 137/187 , ht= 274003 ; ( -44700124/26359997 , -6063841992/26359997 ), ( 274003/154510 , 18378903/77255 )
**u= 137/197 , ht= 159556629 ; ( 330347804/34799773 , 39839285688/34799773 ), ( 159556629/18868832 , -209457877/205096 )
**u= 137/198 , ht= 196737 ; ( 294429/12697 , 106303708/38091 ), ( 121156/196737 , 166687747/1180422 )
**u= 144/31 , ht= 917 ; ( -75/917 , -24411/524 ), ( 19411/4717 , -3709797/18868 )
**u= 144/67 , ht= 2239 ; ( -1435/2239 , 725763/8956 ), ( -39907/9087 , 3723419/12116 )
**u= 144/103 , ht= 1107 ; ( 1107/283 , 386589/1132 ), ( 5609/665 , -1911219/2660 )
**u= 144/151 , ht= 3435 ; ( 403331/41837 , 166118919/167348 ), ( 3133/3435 , -634889/4580 )
**u= 144/175 , ht= 9139 ; ( -607119/282119 , 295255155/1128476 ), ( 9139/3035 , -21235659/60700 )
**u= 144/179 , ht= 16625 ; ( 16625/7317 , -900211/3252 ), ( -19137/120125 , -54256311/480500 )
**u= 145 , ht= 662 ; ( 662/201 , -2044/201 ), ( -123/664 , 385/332 )
**u= 145/8 , ht= 2352 ; ( 2352/181 , 219869/724 ), ( 110723/6484 , -10507293/25936 )
**u= 145/17 , ht= 69991 ; ( 13462/69991 , 2445000/69991 ), ( 3489161/102812 , 59880129/51406 )
**u= 145/33 , ht= 90854 ; ( -90854/7837 , -4349068/7837 ), ( -236381/46598 , -5750478/23299 )
**u= 145/39 , ht= 198919 ; ( 20428/269989 , -14049414/269989 ), ( -198919/81412 , -5575793/40706 )
**u= 145/48 , ht= 256711 ; ( 120763/256711 , 32655863/513422 ), ( 401521/60157 , -46737547/120314 )
**u= 145/63 , ht= 7463 ; ( -7463/489 , 1479007/1467 ), ( 470143/90946 , -15786758/45473 )
**u= 145/76 , ht= 671381 ; ( 671381/314713 , -53687673/314713 ), ( 19058289/19470323 , 1972836695/19470323 )
**u= 145/97 , ht= 711297 ; ( 1381624/863547 , 133280506/863547 ), ( -711297/573266 , -37366834/286633 )
**u= 145/103 , ht= 26517 ; ( 1622636/3245813 , 305905674/3245813 ), ( 26517/21676 , -1443557/10838 )
**u= 145/104 , ht= 183493 ; ( 7390482/798559 , 2518496639/3194236 ), ( -60461/183493 , -16364127/183493 )
**u= 145/108 , ht= 787907 ; ( 787907/9469 , -12002258/1671 ), ( -16817947/902959 , 1453855861/902959 )
**u= 145/111 , ht= 175273 ; ( -93199/175273 , 17371957/175273 ), ( -391643/1774 , -17137080/887 )
**u= 145/119 , ht= 4895101 ; ( 2265537/4895101 , -488745337/4895101 ), ( -5858191/2752768 , -293246427/1376384 )
**u= 145/144 , ht= 206073 ; ( 706667/423141 , 246286559/1269423 ), ( -206073/27799 , -62178787/83397 )
**u= 145/161 , ht= 208163 ; ( 1216038/1109341 , -3690980/23603 ), ( 208163/12134 , 10988130/6067 )
**u= 145/199 , ht= 564779 ; ( -808316/1550033 , -204831558/1550033 ), ( 256727/564779 , -72690843/564779 )
**u= 146/3 , ht= 524 ; ( -652/2033 , -64099/4066 ), ( 524/205 , 16821/410 )
**u= 146/7 , ht= 7305 ; ( 7305/2398 , -333799/4796 ), ( -123401/58074 , 6014899/116148 )
**u= 146/11 , ht= 18163 ; ( 147665/122992 , -10543413/245984 ), ( 18163/1520 , 1005093/3040 )
**u= 146/23 , ht= 218 ; ( 173/218 , -22101/436 ), ( 6569826/207221 , -522395347/414442 )
**u= 146/27 , ht= 83576 ; ( -114124/25021 , 30131167/150126 ), ( 83576/26621 , 22649413/159726 )
**u= 146/31 , ht= 97838 ; ( -21729/97838 , -9242531/195676 ), ( -712622/102089 , -66391419/204178 )
**u= 146/51 , ht= 529588 ; ( 529588/169069 , 65713553/338138 ), ( -721069/1266860 , -172320081/2533720 )
**u= 146/95 , ht= 1839597 ; ( 1302182/1839597 , -363682979/3679194 ), ( -3093983402/259392623 , -501020565315/518785246
)
**u= 146/107 , ht= 688340 ; ( -688340/91797 , -118913989/183594 ), ( -1479633/1568 , 253393753/3136 )
**u= 146/111 , ht= 845566 ; ( -845566/132233 , 149268209/264466 ), ( -1116197/17594 , 194717331/35188 )
**u= 146/147 , ht= 333080 ; ( -10793741/33858964 , -49932736933/474025496 ), ( 659/333080 , -66853927/666160 )
**u= 146/151 , ht= 1024794 ; ( 1024794/81497 , -209128661/162994 ), ( -1456571/1096990 , -370950321/2193980 )
**u= 146/159 , ht= 756709 ; ( 932462/227191 , 200342759/454382 ), ( -756709/70250 , -158646133/140500 )
**u= 146/175 , ht= 296263 ; ( 8541154/3520495 , 919623543/3200450 ), ( 296263/134738 , -71277921/269476 )
**u= 146/195 , ht= 1063984 ; ( -862811/1063984 , -316681691/2127968 ), ( 6096928/1306493 , -1441492861/2612986 )
**u= 147/5 , ht= 2531 ; ( 14707/827 , -1860723/5789 ), ( -2531/791 , 348423/5537 )
**u= 147/8 , ht= 55 ; ( 55/46 , 46773/1288 ), ( 6194/1817 , -4246971/50876 )
**u= 147/19 , ht= 977 ; ( 220/977 , -252414/6839 ), ( -405797/103868 , 52786149/363538 )
**u= 147/20 , ht= 3181 ; ( -119/3181 , 823155/22267 ), ( -8893/1337 , 2325369/9359 )
**u= 147/40 , ht= 667 ; ( 667/152 , 999063/4256 ), ( -152/667 , -999063/18676 )
**u= 147/44 , ht= 6173 ; ( -6173/493 , 2371368/3451 ), ( -493/6173 , -2371368/43211 )
**u= 147/61 , ht= 99479 ; ( 99479/7271 , -4088967/4627 ), ( 223531/210850 , 69293862/737975 )
**u= 147/80 , ht= 5333 ; ( -2113/5333 , -5925873/74662 ), ( 21031/13591 , 12933483/95137 )
**u= 147/131 , ht= 77890 ; ( -77890/8329 , 51771204/58303 ), ( 324307/48650 , -108373434/170275 )
**u= 147/136 , ht= 23942 ; ( 12715/114562 , -310496217/3207736 ), ( -23942/20785 , 85404453/581980 )
**u= 147/164 , ht= 4277 ; ( -16235/28537 , 24279411/199759 ), ( 4277/3457 , -4066827/24199 )
**u= 147/173 , ht= 268127 ; ( 14176454/1115473 , 10800368352/7808311 ), ( 268127/91021 , 215064777/637147 )
**u= 147/176 , ht= 2529817 ; ( 4126819/565591 , 6381911079/7918274 ), ( 2529817/186355 , -3886631871/2608970 )
**u= 147/181 , ht= 145607 ; ( -88037/153197 , -12479031/97489 ), ( -145607/54217 , 120708159/379519 )
**u= 148/7 , ht= 11503 ; ( -61211/18393 , -2754473/36786 ), ( -11503/3491 , 527793/6982 )
**u= 148/23 , ht= 110543 ; ( -11955/110543 , 8776753/221086 ), ( -117841/122187 , -13385693/244374 )
**u= 148/31 , ht= 2463 ; ( 355/2463 , 227941/4926 ), ( 2463/355 , 227941/710 )
**u= 148/39 , ht= 64283 ; ( 465613/1487 , -47794551/2974 ), ( -64283/16993 , 6829781/33986 )
**u= 148/51 , ht= 28957 ; ( 28957/397 , -3399877/794 ), ( -19249/817865 , 96044117/1635730 )
**u= 148/63 , ht= 1037539 ; ( -1037539/180433 , -137424211/360866 ), ( -2808151/139003 , -366992227/278006 )
**u= 148/115 , ht= 3514441 ; ( 3514441/2855721 , -798482647/5711442 ), ( -12615741/816029 , -2229262819/1632058 )
**u= 148/131 , ht= 254975 ; ( -63133651/5781781 , 11930857359/11563562 ), ( 235849/254975 , -65365707/509950 )
**u= 148/147 , ht= 244595 ; ( 244595/199613 , -62938779/399226 ), ( -1422661/449357 , -2082055497/6290998 )
**u= 148/159 , ht= 1339919 ; ( -468229/1339919 , -294291527/2679838 ), ( 5282336887/802840805 , 1107816285517/1605681610
)
**u= 148/171 , ht= 526443 ; ( -1468201/151169 , -317351561/302338 ), ( 526443/69037 , 342496591/414222 )
**u= 148/175 , ht= 3419161 ; ( 11401577/515877 , -2482535317/1031754 ), ( 3419161/866261 , 767237541/1732522 )
**u= 149/2 , ht= 7360 ; ( -7360/5427 , 203053/10854 ), ( -4093/40628 , 807531/81256 )
**u= 149/6 , ht= 27614 ; ( 5285/27614 , -1144623/55228 ), ( -43174/55 , -1759557/110 )
**u= 149/10 , ht= 102973 ; ( -33207/102973 , 2816026/102973 ), ( 146503/53397 , -4057430/53397 )
**u= 149/57 , ht= 2223409 ; ( -789574/2223409 , 145978014/2223409 ), ( -2944627/280162 , 91506139/140081 )
**u= 149/66 , ht= 2668781 ; ( -10370797/937841 , -693076358/937841 ), ( -2668781/1524628 , 409220299/3049256 )
**u= 149/78 , ht= 162056 ; ( -856171/139616 , -125539971/279232 ), ( -162056/116885 , 28919517/233770 )
**u= 149/79 , ht= 82704 ; ( -82704/6803 , 6042952/6803 ), ( 964321/1297780 , -29436783/324445 )
**u= 149/94 , ht= 915559 ; ( -2076165/1164391 , 189095458/1164391 ), ( 915559/103493 , -73200954/103493 )
**u= 149/95 , ht= 767348 ; ( 767348/212833 , -63592776/212833 ), ( 707307/1960718 , 83228855/980359 )
**u= 149/102 , ht= 237583 ; ( 72899137/7922638 , 12135633381/15845276 ), ( -154403/237583 , 23447328/237583 )
**u= 149/110 , ht= 45444 ; ( -3979/45444 , -1120123/12984 ), ( 108276/1615589 , 12099451/140486 )
**u= 149/126 , ht= 528412 ; ( 434573/571969 , 66069038/571969 ), ( -528412/78691 , -98276207/157382 )
**u= 149/127 , ht= 1965282 ; ( 1965282/109177 , -181745578/109177 ), ( -5415017/1560712 , -130096473/390178 )
**u= 149/153 , ht= 236287 ; ( 28480070/414371 , -2886724214/414371 ), ( 236287/70622 , -12497607/35311 )
**u= 149/170 , ht= 1272279 ; ( 2473199/27171 , -264231292/27171 ), ( -1272279/255766 , -277287467/511532 )
**u= 152 , ht= 7 ; ( 7/2 , -33/8 ), ( -53/42 , -2467/168 )
**u= 152/45 , ht= 309 ; ( 176/309 , -232261/3708 ), ( -18712/5543 , -4249219/22172 )
**u= 152/77 , ht= 5483 ; ( -5483/2536 , -1720071/10144 ), ( -98068/10579 , -28089273/42316 )
**u= 152/81 , ht= 210 ; ( -210/187 , 739091/6732 ), ( -187/210 , 739091/7560 )
**u= 152/101 , ht= 42303 ; ( 68344/1179 , -22290269/4716 ), ( -42303/13348 , -14466913/53392 )
**u= 152/125 , ht= 7423 ; ( 7423/6048 , 3473773/24192 ), ( 6048/7423 , 3473773/29692 )
**u= 152/137 , ht= 14875 ; ( -14875/1154 , -5666583/4616 ), ( -1154/14875 , -5666583/59500 )
**u= 152/161 , ht= 9383 ; ( -26063/22398 , 14149513/89592 ), ( 2138/9383 , -3962337/37532 )
**u= 152/169 , ht= 882 ; ( 882/37 , -372391/148 ), ( -3982/16725 , 94282699/869700 )
**u= 152/197 , ht= 4079 ; ( -233657/5304 , 106446529/21216 ), ( -452/4079 , -1869153/16316 )
**u= 153/20 , ht= 16437 ; ( -16437/9733 , 690288/9733 ), ( 2175671/133661 , 78937977/133661 )
**u= 153/23 , ht= 47 ; ( -47 , -1821 ), ( 1/47 , -1821/47 )
**u= 153/31 , ht= 1433 ; ( -1433/813 , -24717/271 ), ( 2643/2348 , 79587/1174 )
**u= 153/44 , ht= 727 ; ( 727/67 , -39147/67 ), ( 22819/3635 , -1239708/3635 )
**u= 153/56 , ht= 508 ; ( 5485/1061 , -337989/1061 ), ( -508/417 , 53027/556 )
**u= 153/112 , ht= 2811 ; ( 367/2811 , -161733/1874 ), ( 58413/4909 , -5016456/4909 )
**u= 153/116 , ht= 11483 ; ( 10555/11483 , -1358322/11483 ), ( 16927/39953 , -3778716/39953 )
**u= 153/121 , ht= 1143 ; ( 220/1143 , -126542/1397 ), ( 26709/9716 , 13904109/53438 )
**u= 153/128 , ht= 4339 ; ( -77009/10927 , -7115253/10927 ), ( 4339/1157 , -1643289/4628 )
**u= 153/164 , ht= 91323 ; ( 160619/432859 , -47809884/432859 ), ( 18917/91323 , 3219034/30441 )
**u= 153/167 , ht= 16111 ; ( -2927/16111 , 1711083/16111 ), ( -16773/1931 , 1764279/1931 )
**u= 153/175 , ht= 148509 ; ( -156664/2433 , 27932598/4055 ), ( -148509/43712 , 41399109/109280 )
**u= 153/185 , ht= 3955174 ; ( 3955174/837621 , -49403696/93069 ), ( 4318713/949012 , 243157365/474506 )
**u= 153/188 , ht= 32953 ; ( -933499/122873 , 104386917/122873 ), ( -32953/15175 , 4022274/15175 )
**u= 153/200 , ht= 12931 ; ( -12931/6331 , -1646391/6331 ), ( 17729/14204 , -155091/848 )
**u= 156/5 , ht= 53 ; ( 253/7 , -1263/2 ), ( -7/53 , 1869/106 )
**u= 156/125 , ht= 47 ; ( -43/47 , 57033/470 ), ( 684779/621409 , 827887887/6214090 )
**u= 157/8 , ht= 63422 ; ( -63422/3151 , -5679453/12604 ), ( -2591503/464425 , -59975277/464425 )
**u= 157/11 , ht= 15827 ; ( -12505/15827 , 10911/323 ), ( -15827/12505 , -534639/12505 )
**u= 157/13 , ht= 1507 ; ( -257072/55929 , -7546582/55929 ), ( -1507/194 , 21942/97 )
**u= 157/16 , ht= 6667 ; ( 8527/9693 , -824651/19386 ), ( -6667/1253 , 217083/1253 )
**u= 157/24 , ht= 1105 ; ( -1105/617 , 49463/617 ), ( 126416/17039 , 19973343/68156 )
**u= 157/35 , ht= 64053 ; ( -64053/1957 , -3024713/1957 ), ( -213697/271207 , -16303581/271207 )
**u= 157/45 , ht= 150917 ; ( -2531894/139891 , -135740196/139891 ), ( 150917/8928 , -391823/432 )
**u= 157/72 , ht= 3937 ; ( 1389237/2067221 , 506112922/6201663 ), ( 3937/2534 , -1268543/10136 )
**u= 157/84 , ht= 1232699 ; ( 48069535/4281343 , 3530320778/4281343 ), ( 1051679/1232699 , -118541957/1232699 )
**u= 157/93 , ht= 518947 ; ( 155596/518947 , -41707046/518947 ), ( -3242539/776332 , -128337669/388166 )
**u= 157/99 , ht= 12733 ; ( -6617/12733 , -67043/749 ), ( 2965021/384894 , -356219632/577341 )
**u= 157/100 , ht= 91227 ; ( -569471/214979 , 48585639/214979 ), ( -91227/9925 , 36626954/49625 )
**u= 157/104 , ht= 55332 ; ( -371480/649319 , -243589791/2597276 ), ( -6457/55332 , -18138119/221328 )
**u= 157/112 , ht= 97827 ; ( -17561/97827 , 16793101/195654 ), ( 443889/233917 , -84774637/467834 )
**u= 157/115 , ht= 8365971 ; ( 19244471/7283551 , 1761307707/7283551 ), ( 8365971/51701 , 716176319/51701 )
**u= 157/136 , ht= 160018 ; ( -160018/8673 , 8524109/4956 ), ( 42679/531530 , -198547587/2126120 )
**u= 157/147 , ht= 31843 ; ( -31843/22609 , -26456607/158263 ), ( -6302507/177569 , -4271504501/1242983 )
**u= 157/152 , ht= 5330145 ; ( 5330145/1161032 , -2147348359/4644128 ), ( 6098743/3227121 , -679045523/3227121 )
**u= 157/176 , ht= 590889 ; ( 590889/6041 , -62575231/6041 ), ( 3483229/1034915 , 384805608/1034915 )
**u= 157/180 , ht= 2381243 ; ( -5567831/3576779 , -708707021/3576779 ), ( 2381243/62373 , 765322646/187119 )
**u= 157/189 , ht= 24867506 ; ( -24867506/2065841 , -8214792704/6197523 ), ( 1836803557/466418422 ,
103983670548/233209211 )
**u= 157/196 , ht= 624775 ; ( 624775/196853 , 512416623/1377971 ), ( -1040151/173699 , 824950523/1215893 )
**u= 159/10 , ht= 112744 ; ( -46871/112744 , 6152409/225488 ), ( -333748/797 , 16848219/1594 )
**u= 159/11 , ht= 9763 ; ( -94/9763 , -258186/9763 ), ( -9763/94 , 129093/47 )
**u= 159/19 , ht= 239 ; ( -68/239 , -36 ), ( 1776487/470180 , -15908079/117545 )
**u= 159/34 , ht= 3317 ; ( 26195/1889 , -1214022/1889 ), ( -559/3317 , 5016/107 )
**u= 159/61 , ht= 159013 ; ( -333846362/6237139 , 20681930298/6237139 ), ( -159013/7916 , 2466186/1979 )
**u= 159/82 , ht= 123893 ; ( -342103/69578 , -50145861/139156 ), ( 39638/123893 , 18684849/247786 )
**u= 159/122 , ht= 187564 ; ( -70771/187564 , -35128017/375128 ), ( -180508/448097 , 84644811/896194 )
**u= 159/131 , ht= 244001 ; ( 254968/82441 , 24326412/82441 ), ( -244001/51928 , 5662107/12982 )
**u= 159/146 , ht= 727625 ; ( -727625/75302 , -140214261/150604 ), ( 84737/3428429 , 328676586/3428429 )
**u= 159/182 , ht= 1259177 ; ( -10189505/1898389 , -1109092998/1898389 ), ( 1259177/1039685 , -174736314/1039685 )
**u= 164/3 , ht= 18517 ; ( -3386927/570893 , -86119423/1141786 ), ( 11287/18517 , -566273/37034 )
**u= 164/7 , ht= 5323 ; ( -38163/51773 , 2668849/103546 ), ( -347/5323 , 217431/10646 )
**u= 164/19 , ht= 69935 ; ( -69935/48397 , -5786823/96794 ), ( -4320911/680573 , 298349727/1361146 )
**u= 164/31 , ht= 155075 ; ( -604251/2198893 , -198443993/4397786 ), ( -66947/155075 , 14682789/310150 )
**u= 164/51 , ht= 188977 ; ( 379/188977 , 21085853/377954 ), ( -2018251/462287 , 231019829/924574 )
**u= 164/79 , ht= 1160759 ; ( -263927/1160759 , -165282777/2321518 ), ( 17807617/3000015 , -2507406377/6000030 )
**u= 164/99 , ht= 558335 ; ( 6475819/369543 , -3024085003/2217258 ), ( -436131/558335 , 330327827/3350010 )
**u= 164/107 , ht= 206671 ; ( 206671/53661 , -34498477/107322 ), ( 718029/165481 , 119063497/330962 )
**u= 164/127 , ht= 405263 ; ( -15820167/1782287 , 2802322069/3564574 ), ( 405263/212223 , 80529809/424446 )
**u= 164/131 , ht= 106007 ; ( 106007/41499 , 20351849/82998 ), ( -367849/405053 , -4253067/35222 )
**u= 164/143 , ht= 2423337 ; ( -4553117/2841517 , 143212989/811862 ), ( -2423337/1823023 , -566441323/3646046 )
**u= 164/195 , ht= 1549279 ; ( 62610437/3131927 , 13673608423/6263854 ), ( 784099/1549279 , 378744207/3098558 )
**u= 164/199 , ht= 2086387 ; ( -66395/2086387 , -459973293/4172774 ), ( -14709557/4449765 , -3386339177/8899530 )
**u= 169/4 , ht= 835 ; ( -2521/343 , -37428/343 ), ( 349/835 , 13482/835 )
**u= 169/9 , ht= 842 ; ( 908/179 , 21186/179 ), ( 509/842 , 11308/421 )
**u= 169/16 , ht= 3209 ; ( -3509/19323 , 605959/19323 ), ( 283/3209 , -197733/6418 )
**u= 169/21 , ht= 1460 ; ( -1460/1333 , 69692/1333 ), ( -4717/484 , -41861/121 )
**u= 169/25 , ht= 2438 ; ( 11918/2979 , -2360468/14895 ), ( -737/2438 , -48942/1219 )
**u= 169/34 , ht= 3507 ; ( 1025/3507 , -23428/501 ), ( 27279/8098 , 2554433/16196 )
**u= 169/40 , ht= 109 ; ( 109/51 , 5854/51 ), ( 6189/6349 , -431426/6349 )
**u= 169/59 , ht= 28680 ; ( 28680/9623 , 1787444/9623 ), ( 94177/3966 , -2785781/1983 )
**u= 169/79 , ht= 7887 ; ( -2620/7887 , 568366/7887 ), ( -7887/2620 , -284183/1310 )
**u= 169/86 , ht= 1142749 ; ( -508623/1142749 , -89249908/1142749 ), ( 296092/1452835 , 211556631/2905670 )
**u= 169/87 , ht= 21923 ; ( 73711/11071 , 5348469/11071 ), ( -21923/14702 , 947156/7351 )
**u= 169/100 , ht= 7079 ; ( 7079/633 , -2733842/3165 ), ( -74499/86483 , -43909696/432415 )
**u= 169/103 , ht= 163922 ; ( -163922/80703 , 14265884/80703 ), ( 2673147/4632413 , -417596969/4632413 )
**u= 169/106 , ht= 72161 ; ( 8720/72161 , -11515767/144322 ), ( -114663/16300 , 18348889/32600 )
**u= 169/108 , ht= 768685 ; ( -768685/160913 , -188366171/482739 ), ( -959221/252965 , -237962032/758895 )
**u= 169/123 , ht= 24704 ; ( 1614560/58609 , 137849404/58609 ), ( 839/24704 , 527257/6176 )
**u= 169/152 , ht= 332867 ; ( -332867/82397 , 32525742/82397 ), ( 354986/483445 , -227562777/1933780 )
**u= 169/162 , ht= 26747 ; ( -17898/41377 , 11352113/106398 ), ( 26747/4047 , 23841538/36423 )
**u= 169/183 , ht= 212678 ; ( 311965/76849 , 903747/2077 ), ( 44437/212678 , -11306312/106339 )
**u= 170/3 , ht= 3446 ; ( -3446/2513 , -110519/5026 ), ( 4502/1559 , 134349/3118 )
**u= 170/7 , ht= 939 ; ( -939/188 , 38339/376 ), ( 22481/21732 , 1269827/43464 )
**u= 170/31 , ht= 52 ; ( 21/52 , -4793/104 ), ( -52/21 , -4793/42 )
**u= 170/39 , ht= 15553 ; ( 688504/154633 , 67580253/309266 ), ( -15553/944 , -1493589/1888 )
**u= 170/67 , ht= 567229 ; ( -2743754/12100297 , -1558350975/24200594 ), ( 567229/150422 , -73704795/300844 )
**u= 170/111 , ht= 1138516 ; ( 1138516/524057 , 202579001/1048114 ), ( 4330016/848057 , -713230531/1696114 )
**u= 170/171 , ht= 759318 ; ( 759318/601561 , -583044241/3609366 ), ( -284473/1188654 , 735598561/7131924 )
**u= 170/191 , ht= 497447 ; ( -9398848/188779 , -1993204347/377558 ), ( -497447/13096 , 105512535/26192 )
**u= 170/199 , ht= 501337 ; ( -445381/1845308 , -410845875/3690616 ), ( 133784/501337 , -112297095/1002674 )
**u= 171 , ht= 1 ; ( 0 , 12 ), ( -1/2 , 3 )
**u= 171/7 , ht= 34 ; ( -86/19 , -1758/19 ), ( -1/34 , 339/17 )
**u= 171/13 , ht= 24 ; ( -24/11 , 66 ), ( 99/31 , -2871/31 )
**u= 171/40 , ht= 52 ; ( -3/52 , 10083/208 ), ( -79/39 , -1421/13 )
**u= 171/49 , ht= 21 ; ( 8/21 , 2808/49 ), ( -49/32 , -1371/14 )
**u= 171/52 , ht= 1127 ; ( -40815/43477 , 469869/6211 ), ( 1127/485 , 67683/485 )
**u= 171/58 , ht= 878 ; ( 1973/1362 , -93093/908 ), ( 878/37 , 102399/74 )
**u= 171/59 , ht= 56 ; ( 850/2277 , 15868/253 ), ( 3/56 , -1647/28 )
**u= 171/118 , ht= 1562 ; ( 6350/1807 , 1097013/3614 ), ( -1447/1562 , -353811/3124 )
**u= 171/136 , ht= 131 ; ( -131/107 , -141 ), ( 34133/30869 , -4104948/30869 )
**u= 171/142 , ht= 911 ; ( 911/59 , 83202/59 ), ( 1469/49 , 133968/49 )
**u= 171/160 , ht= 921 ; ( -921/844 , 966873/6752 ), ( -446983/92447 , 88321389/184894 )
**u= 171/178 , ht= 4835 ; ( -4835/2641 , 562182/2641 ), ( 64019/30911 , 7254516/30911 )
**u= 171/181 , ht= 2119 ; ( 1395/2119 , -261057/2119 ), ( 5099/150 , 87488/25 )
**u= 171/184 , ht= 401 ; ( -102/401 , -171717/1604 ), ( 4143/2159 , 28512/127 )
**u= 173/7 , ht= 5216 ; ( -5216/1553 , -108084/1553 ), ( 295787/143264 , 1668609/35816 )
**u= 173/10 , ht= 349 ; ( -279/349 , 10762/349 ), ( -62861/104089 , -2913810/104089 )
**u= 173/39 , ht= 18514 ; ( -18514/11351 , 1031054/11351 ), ( 75871/17794 , -1851183/8897 )
**u= 173/46 , ht= 312113 ; ( -208515/312113 , -19361338/312113 ), ( 47431492/4636933 , -4917503103/9273866 )
**u= 173/71 , ht= 12646 ; ( -12646/2619 , -827362/2619 ), ( 807441/481480 , -15060029/120370 )
**u= 173/102 , ht= 6158186 ; ( 19103627/9804746 , -3298023261/19609492 ), ( 6158186/101885 , 946076933/203770 )
**u= 173/103 , ht= 1099790 ; ( 742270/1186303 , -107999634/1186303 ), ( 1041389/1099790 , -58443921/549895 )
**u= 173/106 , ht= 15681015 ; ( -15681015/10730051 , 1487530834/10730051 ), ( -20819441/1342509 , 1633445518/1342509 )
**u= 173/122 , ht= 2466629 ; ( 964625/3175997 , -25345392/288727 ), ( 2466629/1070578 , 451709049/2141156 )
**u= 173/130 , ht= 4845732 ; ( 15598356/1844941 , 2723525897/3689882 ), ( 1115837/4845732 , 862216057/9691464 )
**u= 173/153 , ht= 401564 ; ( 401564/329623 , -48865392/329623 ), ( -7174521/958840 , 510634859/719130 )
**u= 173/169 , ht= 2075987 ; ( 9317280/85153 , -11973897968/1106989 ), ( 2075987/236320 , 167822883/192010 )
**u= 174/25 , ht= 787 ; ( 5803/3734 , 2614791/37340 ), ( 454/787 , -344241/7870 )
**u= 174/49 , ht= 1054 ; ( -8578/2219 , -6582021/31066 ), ( 613/1054 , 129411/2108 )
**u= 174/53 , ht= 1456 ; ( -5573144/1651621 , 641580339/3303242 ), ( -131/1456 , 161349/2912 )
**u= 174/61 , ht= 6361 ; ( 3128/6361 , -839661/12722 ), ( -131833/636364 , 3345939/55336 )
**u= 174/89 , ht= 55966 ; ( -8240086/4700603 , 1357105719/9401206 ), ( 51427/55966 , 10873551/111932 )
**u= 174/113 , ht= 85162 ; ( 88658/16093 , 188631/418 ), ( -85162/5497 , -13757667/10994 )
**u= 174/121 , ht= 125242 ; ( -125242/66331 , 260042259/1459282 ), ( -424826/78505 , 792757293/1727110 )
**u= 174/137 , ht= 1903907 ; ( 196202/1903907 , 339741351/3807814 ), ( 2881754/527135 , 520010151/1054270 )
**u= 174/193 , ht= 74938 ; ( 2878151/1819546 , 717351909/3639092 ), ( -44143/74938 , -18322737/149876 )
**u= 181/10 , ht= 15487 ; ( -14533/15487 , 499548/15487 ), ( 73693/118423 , -3267174/118423 )
**u= 181/14 , ht= 11509 ; ( -11509/5272 , -702333/10544 ), ( -176537/12219 , -4942694/12219 )
**u= 181/25 , ht= 30047 ; ( 334738/63937 , 12652122/63937 ), ( 30047/18986 , -3304779/47465 )
**u= 181/26 , ht= 214 ; ( 214/97 , -17799/194 ), ( 2810783/5731805 , -241816914/5731805 )
**u= 181/31 , ht= 3434 ; ( -260378/32851 , -10854066/32851 ), ( -1543/3434 , 771/17 )
**u= 181/54 , ht= 647366 ; ( 936575/212222 , -314695043/1273332 ), ( -647366/152863 , -218085043/917178 )
**u= 181/63 , ht= 4694 ; ( -4694/409 , 277974/409 ), ( 27513/38210 , -4167251/57315 )
**u= 181/70 , ht= 1137427 ; ( -1137427/637738 , 162203337/1275476 ), ( -44426638/5537647 , -5570284131/11075294 )
**u= 181/74 , ht= 138451 ; ( -54023/138451 , 9505398/138451 ), ( -19158359/665982 , 2452267661/1331964 )
**u= 181/95 , ht= 162881 ; ( -87786/162881 , -13408046/162881 ), ( -4156127/1726102 , 163056855/863051 )
**u= 181/110 , ht= 1338793 ; ( 1338793/547112 , -225523383/1094224 ), ( -7647688/349507 , -1193920803/699014 )
**u= 181/114 , ht= 1304981 ; ( 10787680/1086109 , 1721117063/2172218 ), ( -1304981/895580 , 251267433/1791160 )
**u= 181/150 , ht= 606953 ; ( -144467/1973089 , -900690654/9865445 ), ( -606953/498347 , -71505106/498347 )
**u= 181/159 , ht= 8338949 ; ( 13075690/62851 , 1225718754/62851 ), ( 8338949/265760 , -195533451/66440 )
**u= 181/175 , ht= 1611465 ; ( -5779504/310825 , -2845980456/1554125 ), ( 1611465/742156 , 218104229/927695 )
**u= 181/177 , ht= 45283 ; ( 31772/45283 , 5471276/45283 ), ( -137519/262324 , -7323513/65581 )
**u= 181/178 , ht= 1135739 ; ( -1771313/914243 , -17973312/83113 ), ( -1135739/126479 , 113347674/126479 )
**u= 181/185 , ht= 7264142 ; ( -7264142/2904913 , -71915142/264083 ), ( -31203667/3176178 , 1585793561/1588089 )
**u= 183 , ht= 88 ; ( 88/53 , -354/53 ), ( 53/88 , -177/44 )
**u= 183/4 , ht= 1315 ; ( 1759/49 , 24624/49 ), ( -419/1315 , 19518/1315 )
**u= 183/7 , ht= 22646 ; ( 22646/5167 , 447324/5167 ), ( -149039/13718 , -1488246/6859 )
**u= 183/8 , ht= 18668 ; ( 29995/4 , -2475993/16 ), ( -18668/2401 , 1594197/9604 )
**u= 183/17 , ht= 1493 ; ( -1359380/196121 , 41752206/196121 ), ( -1493/1295 , 1629/35 )
**u= 183/23 , ht= 980921 ; ( -275042/996329 , 36698976/996329 ), ( 980921/125758 , 17559912/62879 )
**u= 183/25 , ht= 31 ; ( -2375/6449 , 1271577/32245 ), ( -25/31 , 7359/155 )
**u= 183/32 , ht= 31733 ; ( -47657/63616 , -26601819/508928 ), ( 5816/31733 , 10786209/253864 )
**u= 183/52 , ht= 32369 ; ( -10063/32369 , -1807698/32369 ), ( -2528129/147505 , -135058764/147505 )
**u= 183/89 , ht= 269 ; ( 4523485/191321 , -315762807/191321 ), ( 269/91 , 19809/91 )
**u= 183/92 , ht= 39695 ; ( -39695/739 , 2815221/739 ), ( -22991641/2307485 , 1638825399/2307485 )
**u= 183/100 , ht= 19151 ; ( -19151/3505 , -7196682/17525 ), ( 5935/29021 , -10949553/145105 )
**u= 183/112 , ht= 387047 ; ( -53009335/9622409 , 4215260814/9622409 ), ( -387047/22775 , -30339087/22775 )
**u= 183/121 , ht= 6551 ; ( -3314/6551 , 6568068/72061 ), ( 479/6809 , 6106137/74899 )
**u= 183/128 , ht= 296 ; ( 122291/59443 , -11373477/59443 ), ( -296/23 , -17277/16 )
**u= 183/136 , ht= 7748 ; ( -98575/87524 , -45464349/350096 ), ( 7748/5113 , 3201669/20452 )
**u= 183/140 , ht= 41081 ; ( -303581/37949 , 26763198/37949 ), ( 24281/41081 , -4174530/41081 )
**u= 183/145 , ht= 1099921 ; ( -593924/2026661 , -188027478/2026661 ), ( 1099921/515669 , -108155979/515669 )
**u= 183/161 , ht= 762331 ; ( -594416/762331 , -90688362/762331 ), ( 1205717/63905 , -113274423/63905 )
**u= 183/164 , ht= 585187 ; ( 1025065/1339207 , 159682944/1339207 ), ( -585187/500903 , 72933837/500903 )
**u= 185/43 , ht= 125743 ; ( 257502/5479 , 12413734/5479 ), ( 125743/73584 , 1756693/18396 )
**u= 185/54 , ht= 21701 ; ( 78131/31232 , 9091551/62464 ), ( 12953/21701 , -1365462/21701 )
**u= 185/66 , ht= 43 ; ( 1/43 , -2570/43 ), ( 43 , -2570 )
**u= 185/98 , ht= 64021 ; ( -64021/29703 , -35961070/207921 ), ( -106972499/23575687 , 55822274442/165029809 )
**u= 185/114 , ht= 2141641 ; ( 1541203/2141641 , -207165076/2141641 ), ( 1605701/3409922 , 591817569/6819844 )
**u= 185/138 , ht= 113197 ; ( 10111/113197 , -9817692/113197 ), ( -532123/413039 , -58189650/413039 )
**u= 185/139 , ht= 260881 ; ( 93942/260881 , 24039770/260881 ), ( 564533/872974 , 45063873/436487 )
**u= 185/154 , ht= 336752 ; ( 750159/982853 , -112829126/982853 ), ( 62731/336752 , -62514897/673504 )
**u= 185/166 , ht= 348968 ; ( -143471/348968 , -71495991/697936 ), ( 93143/4062701 , -384999060/4062701 )
**u= 185/178 , ht= 283674 ; ( -283674/201287 , 68249003/402574 ), ( -795049/885627 , 116760962/885627 )
**u= 190 , ht= 33 ; ( 14/33 , -71/6 ), ( 143/206 , 2211/412 )
**u= 190/17 , ht= 378 ; ( -378/89 , 23171/178 ), ( 89/378 , -23171/756 )
**u= 190/61 , ht= 2483 ; ( -2483/1324 , 318897/2648 ), ( 5012/71 , -568269/142 )
**u= 190/137 , ht= 21974 ; ( -45497/94106 , -17755437/188212 ), ( 21974/10877 , -4164849/21754 )
**u= 190/177 , ht= 14813 ; ( -14813/1766 , 2880125/3532 ), ( -108133/152234 , -36051623/304468 )
**u= 192/5 , ht= 233 ; ( -233/97 , -31731/776 ), ( -97/233 , 31731/1864 )
**u= 192/17 , ht= 37 ; ( 31/37 , 11499/296 ), ( -37/31 , 11499/248 )
**u= 192/65 , ht= 2143 ; ( 2143/947 , 1090599/7576 ), ( 947/2143 , 1090599/17144 )
**u= 192/85 , ht= 56483 ; ( -56483/56227 , -42430011/449816 ), ( -72803/72547 , -54717435/580376 )
**u= 192/97 , ht= 190565 ; ( 190565/157391 , 140561829/1259128 ), ( 513581/59233 , 294049863/473864 )
**u= 192/133 , ht= 230653 ; ( -133621/517547 , -355978107/4140376 ), ( 230653/176389 , 193373367/1411112 )
**u= 192/149 , ht= 248791 ; ( 6230195/11531 , 4391297457/92248 ), ( -248791/51295 , 179060427/410360 )
**u= 192/157 , ht= 199183 ; ( 6086323/602941 , -4425118743/4823528 ), ( 199183/19889 , -144839739/159112 )
**u= 192/181 , ht= 25171 ; ( 6709/25171 , 20238063/201368 ), ( 25171/6709 , 20238063/53672 )
**u= 193/20 , ht= 428197 ; ( -814899/1062611 , -3921898/96601 ), ( -428197/24777 , 13841509/24777 )
**u= 193/23 , ht= 3467 ; ( 63401/14917 , -2245287/14917 ), ( 3467/3076 , 80031/1538 )
**u= 193/44 , ht= 4110121 ; ( 4110121/652931 , -198651399/652931 ), ( 8602559/592975 , -411990672/592975 )
**u= 193/65 , ht= 174053 ; ( 99038/174053 , 11624952/174053 ), ( -622937/12522 , -18086372/6261 )
**u= 193/68 , ht= 68805 ; ( -139745811/21600883 , -8393332862/21600883 ), ( 13759/68805 , 4164907/68805 )
**u= 193/76 , ht= 175379 ; ( -732607/2314613 , -152395389/2314613 ), ( -40271/175379 , 11292147/175379 )
**u= 193/79 , ht= 1780253 ; ( -116590/2098017 , -134478796/2098017 ), ( -1780253/999125 , -130642689/999125 )
**u= 193/92 , ht= 38233 ; ( 2048379/3001223 , 250927459/3001223 ), ( 38233/15049 , 2837544/15049 )
**u= 193/95 , ht= 25169 ; ( 16821/25169 , 2124343/25169 ), ( -7755793/73713 , 544314299/73713 )
**u= 193/113 , ht= 348994 ; ( 7732272/2269019 , 616672066/2269019 ), ( -71027/348994 , 13627254/174497 )
**u= 193/116 , ht= 233947 ; ( -230633/233947 , -3639027/33421 ), ( -3090941/328159 , -241035123/328159 )
**u= 193/124 , ht= 137817 ; ( -120103/137817 , 14655602/137817 ), ( -19958391/2600185 , 1613666632/2600185 )
**u= 193/129 , ht= 536809 ; ( 392203250/1113133 , -4581237328/159019 ), ( 536809/507956 , 30215703/253978 )
**u= 193/135 , ht= 253603 ; ( -251753/253603 , 89674915/760809 ), ( 9028549/2262496 , -68701981/199632 )
**u= 193/145 , ht= 303691 ; ( 728518/9624123 , -836762524/9624123 ), ( -303691/27176 , 13217037/13588 )
**u= 193/148 , ht= 4273 ; ( -548633/343289 , 56682246/343289 ), ( 129/4273 , -374404/4273 )
**u= 193/151 , ht= 60967 ; ( -60967/32653 , 6118359/32653 ), ( 411219/107860 , 18805817/53930 )
**u= 193/161 , ht= 3706757 ; ( -689670/3706757 , 344436232/3706757 ), ( 8528627/5067610 , -453132624/2533805 )
**u= 193/168 , ht= 314054 ; ( -314054/20063 , -117459053/80252 ), ( 321409/36257 , -30183514/36257 )
**u= 193/172 , ht= 7590925 ; ( 7590925/227089 , 717029241/227089 ), ( 27248351/5981153 , 2634102342/5981153 )
**u= 193/175 , ht= 1039903 ; ( 1288262/258129 , 625642108/1290645 ), ( -1039903/236806 , -253944762/592015 )
**u= 193/176 , ht= 9576563 ; ( -16463849/1088851 , 3151735911/2177702 ), ( -9576563/853197 , 918317726/853197 )
**u= 193/177 , ht= 1962457 ; ( 646499368/198824489 , 64783638198/198824489 ), ( 1962457/48086 , -94015042/24043 )
**u= 195/19 , ht= 538 ; ( -538/481 , -22524/481 ), ( -481/538 , 11262/269 )
**u= 195/38 , ht= 71 ; ( -21491/3703 , -962256/3703 ), ( -71/43 , 3666/43 )
**u= 195/76 , ht= 1417 ; ( 1417/809 , 101874/809 ), ( -14639/12607 , -1206336/12607 )
**u= 195/83 , ht= 1019 ; ( -1581854/1320653 , 134461140/1320653 ), ( 1019/392 , -35625/196 )
**u= 195/118 , ht= 2563 ; ( 12842/4169 , -2100855/8338 ), ( 2563/911 , 211644/911 )
**u= 195/184 , ht= 766 ; ( 766/637 , 387165/2548 ), ( 13849/118 , -5382375/472 )
**u= 195/191 , ht= 20522 ; ( -20522/12139 , 2360142/12139 ), ( -364283/45794 , -18171885/22897 )
**u= 196/47 , ht= 7115 ; ( 584051/66299 , -402876477/928186 ), ( -1157/7115 , 4940697/99610 )
**u= 196/51 , ht= 78865 ; ( -78865/21469 , -58362083/300566 ), ( -2280463/318395 , -1645244409/4457530 )
**u= 196/71 , ht= 205583 ; ( -37095/205583 , 176086901/2878162 ), ( -248249/131033 , 236595921/1834462 )
**u= 196/139 , ht= 371555 ; ( 371555/302889 , 565261229/4240446 ), ( -3183877/12237895 , 14910528897/171330530 )
**u= 196/155 , ht= 921 ; ( -1040493/16297 , -1295737171/228158 ), ( 301/921 , -1206491/12894 )
**u= 196/167 , ht= 3791 ; ( -551/3791 , -4951557/53074 ), ( -24408007/535113 , -31556281721/7491582 )
**u= 196/171 , ht= 174471 ; ( 544469/129433 , -731933737/1812062 ), ( 174471/85475 , 762324911/3589950 )
**u= 196/187 , ht= 116653 ; ( 71095/116653 , -186847053/1633142 ), ( 55366369/35102675 , 89663672031/491437450 )
**u= 197/2 , ht= 3891 ; ( -4124/803 , 62829/1606 ), ( 3891/95 , 47788/95 )
**u= 197/6 , ht= 4241 ; ( 4241/4214 , 29811/1204 ), ( 28406/33431 , -1524803/66862 )
**u= 197/9 , ht= 1219 ; ( 5818/1273 , -125926/1273 ), ( 1219/270 , -40469/405 )
**u= 197/14 , ht= 603835 ; ( -603835/223 , 16020108/223 ), ( 23325613/698015 , -625272048/698015 )
**u= 197/73 , ht= 4807 ; ( -326190/574849 , -3658634/52259 ), ( -4807/1106 , -150183/553 )
**u= 197/79 , ht= 281497 ; ( 1165474/266849 , -75717018/266849 ), ( 281497/59270 , -9111321/29635 )
**u= 197/82 , ht= 827969 ; ( 7274800/2491289 , -992273589/4982578 ), ( 827969/172092 , -109152907/344184 )
**u= 197/110 , ht= 14819 ; ( -775271/6222324 , 937347577/12444648 ), ( -3324/14819 , 2269949/29638 )
**u= 197/122 , ht= 197381 ; ( 3106082/839261 , 506457093/1678522 ), ( -91393/197381 , 17119452/197381 )
**u= 197/126 , ht= 269417 ; ( -269417/87347 , -22653458/87347 ), ( 1619032/113647 , 259661259/227294 )
**u= 197/134 , ht= 74943 ; ( -7088887/3331422 , 1292171117/6662844 ), ( -74943/30515 , -6675038/30515 )
**u= 197/138 , ht= 1207769 ; ( 1051645/1207769 , 134060436/1207769 ), ( -50994863/764245 , -4269526572/764245 )
**u= 197/145 , ht= 388501 ; ( 7884804/1014629 , -682126120/1014629 ), ( -388501/165636 , 9060238/41409 )
**u= 197/161 , ht= 521761 ; ( -163616/521761 , -49443384/521761 ), ( 814753/10880 , -9209727/1360 )
**u= 197/178 , ht= 4588068 ; ( 4588068/1490779 , 917268209/2981558 ), ( 2034283/11274441 , 1089161476/11274441 )
**u= 197/190 , ht= 964443 ; ( 964443/339647 , 14347516/48521 ), ( -23991004/1120251 , -4718268607/2240502 )
**u= 197/198 , ht= 948701 ; ( 4645889/983483 , 476160746/983483 ), ( 178162/948701 , -193575793/1897402 )
**u= 200/23 , ht= 7897 ; ( 7897/1004 , -1078035/4016 ), ( -39136/178835 , -123970509/3576700 )
**u= 200/111 , ht= 12416 ; ( -571/12416 , -18523713/248320 ), ( -12416/571 , 18523713/11420 )
**u= 200/147 , ht= 3557 ; ( -2626/3557 , -1516485/14228 ), ( 552791/491390 , -8878925099/68794600 )
**u= 200/159 , ht= 181147 ; ( -2977072/84367 , 5311730843/1687340 ), ( 181147/36404 , 65911907/145616 )
**u= 200/163 , ht= 217130 ; ( 214033/217130 , -550582893/4342600 ), ( 829715/80078 , -1505369337/1601560 )
**u= 200/171 , ht= 40922 ; ( 516114/208789 , -441325447/1789620 ), ( 40922/6627 , -230039593/397620 )
1198
>
また、小さい整点から求めたuについても調べる。

■これらのuについて、(2),(3a),(3b)を満たす有理数解(x,y,t)を持たないものもあれば、有理数解(x,y,t)を持つものもある。
これらのuを順に調べれば良い。

ここからは、A^4+B^4=C^4+D^4と同様なので、最終的に得られた整点のみ記述する。
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, 0 < C < D, 0 < A < Cを満たすように、
A,B,C,Dの符号を変更したり、A,B,C,Dを交換して、Dの小さい順に並び替えると、以下のようになる。

[2026.06.25追記]u=247/4,247/9のときの整数解を追加した。

[参考文献]


Last Update: 2026.06.26
H.Nakao

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