{{1, -1, 9/32, 1/16, -3/4, -3/8, 15/32, -3/32, -3/16, 3/16, -3/32, -1/4, 1/4, 
  1/8, -3/8, 1/8, -3/8, 3/8, 1/8, -1/2, 1/8, 1/8, 47/48, -37/48, 3/16, 43/48, 
  17/64, -3/64, -5/32, -17/32, 11/48, 9/32, -1/16, -3/16, -15/64, 5/32, 
  -3/32, -1/32, 3/64, 17/64, 7/32, -3/64, -5/32, -5/32, -3/64, 7/64, -17/32, 
  -29/96, -7/192, 9/32, 13/16, 17/64, 1/16, -3/64, -11/192, -19/192, -9/16, 
  23/64, 5/24, -17/32, -83/96, -7/192, 9/32, 13/16, -23/24, -3/32, 107/96, 
  3/8, -49/192, 19/16, 181/48, -1/4, -7/6, -215/64, -11/64, -45/16, -9/16, 
  47/12, 13/8, 41/96, 57/32, -3/32, 23/192, -33/32, -35/12, -25/32, 529/192, 
  239/96, -15/16, 15/16, 9/64, -3/64, -1/32, -1/8, -17/32, 11/48, 9/32, 
  65/128, -15/128, -27/64, 15/64, -1/4, 37/96, -17/16, -67/64, 35/96, 53/32, 
  25/128, -3/64, -11/64, -73/48, -97/64, -13/48, 763/192, 9/32, -9/128, 
  101/64, 17/128, 31/128, -3/64, 7/128, -23/128, -5/64, -5/64, 19/384, 7/128, 
  1/192, -35/64, -17/32, 1/6, 7/48, 9/32, 17/64, -43/192, 9/128, 197/384, 
  -3/32, -15/64, -35/192, 227/384, -9/128, 35/64, -125/384, -23/96, 19/32, 
  221/192, -1/8, -169/192, -203/192, -11/96, -45/32, -1/64, 457/192, 13/16, 
  19/384, -39/128, -1/192, 17/128, -1/12, -9/128, -5/96, -5/192, -145/192, 
  -5/192, 47/24, 161/192, 1/24, -1/128, 3/64, -19/192, -3/128, 11/192, -9/8, 
  9/8, 5/8, -23/16, 15/16, -5/16, -1/2, 3/8, -7/8, -3/64, 7/64, -9/8, 3/8, 
  -187/128, -3/64, -9/8, 211/128, 9/32, -6, 41/8, 6, -269/128, -3/8, 381/128, 
  269/128, 9/8, 1223/384, 21/4, 1789/128, -1/4, -53/24, -535/384, -45/8, 
  -13/8, -43/24, 4, -4, -7/12, -15/8, 9/8, -9/32, -227/64, -7/96, -15/64, 
  9/8, 6, -139/32, -9/32, -7/16, 127/16, 7/16, 259/48, -211/8, -107/24, 
  -43/24, -309/16, 131/48, -1507/192, 2695/96, 307/192, 541/192, -917/32, 
  -901/192, 1507/192, -91/32, -3259/96, -1195/192, 91/32, -11/16, -1/8, 
  -5/16, -3/32, 3/16, -3/32, -17/64, 17/64, -5/32, 17/128, -1/4, 1/4, 61/512, 
  75/512, -57/256, -81/512, 93/512, 171/512, -73/256, -7/512, 109/512, 
  75/256, -17/256, -13/256, 15/32, -21/16, 1/4, 5/16, -3/32, -67/128, 9/128, 
  23/64, -19/512, -17/256, 31/128, 21/32, -9/8, 9/8, -17/8, 5/8, 3/32, 5/32, 
  -7/8, 3/2, -15/128, -157/128, 141/256, -3/16, 515/256, -443/256, 3/32, 
  -103/32, -141/256, 45/32, 1181/256, 203/256, -15/128, 927/256, 1/16, 61/48, 
  -9/32, -9/64, -2983/768, 9/32, 865/256, -7/48, -9/8, 3/8, 377/128, 
  -193/128, -3/32, -3/64, 51/16, 75/256, -4415/768, 439/256, 6211/768, -19/8, 
  -127/24, 3/16, 7/3, 4703/768, 7/8, 45/8, -427/48, -13/4, -1, -1245/256, 
  3/16, -787/384, -69/256, 1/32, 113/24, 533/256, -4241/768, -185/48, 
  533/256, 21/256, -533/256, -61/256, -3/32, 117/256, 1273/256, 483/128, 
  365/32, 31/16, -8/3, -9/8, -117/32, -21/4, -793/128, 1625/768, 171/32, 
  -325/96, -877/128, 485/256, 189/32, 3/8, -577/128, 7/48, 15/32, -179/128, 
  129/64, -9/4, 167/128, -61/32, -61/64, 29/64, 15/8, -9/32, 137/48, -271/64, 
  7/64, -9/64, -7/64, -113/384, 1393/384, -2951/192, 21/32, 537/256, -35/16, 
  979/192, -595/48, 2465/768, -77/256, 255/128, 17/32, 17/32, 75/128, -3/32, 
  553/384, 1045/768, 3/16, -955/192, -1309/768, 1205/96, -1025/384, 
  -5021/768, 3/16, 103/16, 2309/256, -101/8, 45/8, 319/256, -2843/384, 
  -295/256, -985/384, -1945/384, 3/16, 649/96, 2005/768, -595/48, 2119/256, 
  955/768, -2819/384, -19/6, 2197/768, 17/32, -1339/768, -3/32, -859/768, 
  3/16, 2203/384, -439/384, 541/768, -193/192, -397/256, 259/384, -1985/384, 
  -761/256, -1681/768, -81/128, -5995/384, 6221/768, 2515/256, -5189/384, 
  -10243/768, -17/192, 129/128, -5/2, -854627/86528, 9/32, -3/32, -1/16, 
  -7249/10608, 26587921/8825856, -7/32, 1/16, -985/2176, -3/32, -6593/42432, 
  1/8, 70165/84864, 709/4352, 5660555/2206464, -3/8, 70405/169728, 
  -3988469/2206464, 16157/28288, -11848123/17651712, -311/256, 
  -3936617/1470976, 11593249/2206464, -3473/8704, -99/128, 9/32, 
  202693/169728, 39/128, -418451/339456, 1321/4352, -514069/1038336, 399/256, 
  120959/339456, 74609861/17651712, -33/512, -11848123/17651712, 
  -11249285/2941952, -583949/678912, 11593249/2206464, 7877/13056, -45/256, 
  110265/113152, 115/64, 446513/339456, 152873/275808, 563/256, 
  137076827/17651712, 25881581/4412928, 25/32, -3/32, -9/16, -23573/17408, 
  -381/1024, 2625/28288, 12047/17408, 16673509/5883904, 33443/169728, 
  -683441/1103232, 327/1024, -1103/1024, -651/512, 10687/17408, 1777/1024, 
  17179/169728, -13467241/5883904, 11/16, -293/1024, -1351/1024, -5999/4352, 
  -6925/84864, 220111/169728, 1025711/1103232, -488245/2206464, 
  -195359/169728, 2024351/2206464, 2024351/2206464, 15551/4352, -1487/544, 
  -175549/169728, -120655/17408, 12403541/8825856, 1397899/339456, 3327/1088, 
  7245869/1103232, -126071/42432, -13679843/2941952, -34727/8704, 
  179611/28288, -55743743/4412928, 33121/17408, -603/1024, -12049/4352, 
  1006781/678912, -596467/678912, 8393/21216, -28505/17408, -5370939/735488, 
  -7842997/8825856, -795881/339456, 5445325/8825856, 156493/113152, 3/64, 
  39110087/4412928, 6677015/1103232, 10487/4352, 9241189/2941952, 
  -419975/339456, -13812001/2941952, -6936167/2206464, 116285/52224, 
  -179611/56576, 55743743/8825856, 15585/8704, -5999/4352, -167593/339456, 
  -16503/8704, 209017/137904, 240041/84864, -109/1024, 2954089/4412928, 
  -1245/544, 13/512, -1/16, -3/8, -3/32, -33129/17408, -12478499/2941952, 
  128771/113152, 57099799/8825856, -53359/17408, 1/32, 190219/56576, 83/96, 
  -55743743/8825856, -3/4, 7/24, 3/16, 1/192, -5/64, -3/4, 37/192, -5/64, 
  -9/16, 3/16, 3/16, -13/32, 3/32, 3/16, 91/144, -3/16, -3/32, 301/192, 
  -361/288, -221/576, 5/96, 71/48, -71/96, 9/32, -3/4, 11/24, 3/16, 1/192, 
  -1/64, 143/192, -5/32, -49/64, 3/16, -1/192, 5/64, -43/192, 1/64, 7/32, 
  -149/576, 47/288, 8/9, 135/256, -19/36, -259/256, -81/64, 1/4, 83/96, 
  -25/96, 55/192, -5/48, -17/96, 1057/768, 61/64, -9/128, -533/384, -13/16, 
  17/256, 73/64, 85/512, 81/512, 875/1536, 769/256, 10253/1536, -57/32, 
  -105/32, 9/64, 229/64, 5759/1536, -5/32, 135/32, -9/32, -489/64, -39/16, 
  -591/256, -311/256, 3/32, -77/384, -215/64, -363/128, -11/32, -713/512, 
  675/512, 29/768, 11095/1536, -51/32, 163/64, 565/512, -1717/256, -141/64, 
  5/48, 191/256, -15/128, 341/256, 933/256, 955/768, -23/256, -375/128, 
  -923/768, -35/192, 23/64, -3/64, 187/384, -35/128, -1/32, 19/32, 227/192, 
  -3/64, -61/192, -79/96, -9/16, -45/32, 25/12, 13/16, 19/192, -3/8, -79/384, 
  -3/4, -13/64, -19/32, -123/64, 3/32, 175/192, 479/192, 41/96, 45/32, 79/96, 
  -227/96, -13/16, 1/12, 1/64, 3/64, -9/32, 131/128, 15/64, 71/96, -3/64, 
  -101/64, -79/96, 107/512, -15/128, 1331/768, 9/64, 5/16, 245/512, -103/192, 
  3/32, 97/256, 373/512, -25/64, -19/32, -391/384, 179/256, 169/192, 
  2837/1536, 11/96, 45/32, 185/256, -457/192, -13/16, -1529/1536, -7/256, 
  -181/256, -5/32, -595/96, 1/12, 563/256, -21/128, 5/96, 4337/1536, 145/192, 
  89/768, -101/48, -251/192, -1/24, 161/256, -3/64, 17/64, 19/192, -5/128, 
  -11/192, -3/64, -15501/8704, -1, 3/32, 160999/169728, 53/64, 245413/339456, 
  -525/1088, 13903937/5883904, 75/512, 37939/113152, -13467241/5883904, 
  -9005/4992, 3/64, -168149/519168, 35/64, 6077/4352, 69417337/17651712, 
  3685/339456, 13642183/8825856, -1403247/1470976, 52537/26112, 15/16, 
  -87/512, -39769/113152, 285/256, 222943/113152, -85043/52224, 
  -7328497/2206464, -399/512, 320581/226304, -81018499/35303424, 
  171503/113152, 204051823/35303424, 38390623/5883904, -47136237/11767808, 
  -7623679/1103232, -66971/52224, -5557/2873, 2049/512, -372709/678912, 
  160290667/11767808, 298515547/35303424, -654725/1103232, 99026035/35303424, 
  -59688065/5883904, 135/64, 26226341/2941952, -11007739/8825856, 12117/8704, 
  4555/2176, -3025/1088, 293483/169728, -188843/84864, -53507/113152, 
  -10961/8704, -67252643/8825856, 12403541/8825856, -2252035/678912, 
  13140919/2941952, 827569/339456, 45398915/8825856, 28337051/4412928, 
  20209/17408, 661979/2206464, -74099/42432, -12777721/2941952, 
  -14294665/8825856, 10171/104448, 20293005/2941952, -4736687/5883904, 
  8355571/1357824, 648613/367744, -102977/52224, 291215/104448, 
  -4074947/4412928, -67084271/8825856, -8651731/1357824, -89367801/5883904, 
  990235/678912, -1073/256, 8930681/17651712, 56470443/5883904, 2577/1024, 
  -91805/52224, 15091/104448, -9/128, 559165/169728, 65559731/17651712, 
  63382819/17651712, 26002447/17651712, -35128915/17651712, 1246283/5883904, 
  -64017983/8825856, -55743743/17651712, 72292223/17651712, -17/128, -31/128, 
  3/64, -37/384, 23/128, 23/192, -31/216, 5/64, 637/3456, -7/128, -79/576, 
  45/64, 335/864, -31/96, -1/18, -9/32, -7/64, 397/3456, -17/128, 311/576, 
  -605/3456, -1249/1152, -87/128, 99/128, -721/384, 1543/1728, -49/36, 
  -95/864, -973/3456, -49/128, 781/1152, 25/72, 3/32, 325/1152, -25/384, 
  -301/1152, 7/384, 17/192, 91/1728, -17/192, -115/1152, 7/128, 341/1728, 
  -1/192, 103/768, 359/864, 37/128, -155/432, 5/64, -229/384, 89/128, 
  -35/192, -1109/1152, 17/96, 227/576, -97/288, -439/1152, 17/144, 127/1152, 
  1/288, 9/64, -3/8, 7/8, -4151497/22984, -4469/1536, 5639/1536, -2101/768, 
  1719/512, 5549/1536, -57/256, -3199/1536, 57/256, -6319/1536, 29/192, 
  -671/256, -155/64, 2101/1536, -57/256, -377/1536, 1931/768, 3/32, -29/128, 
  -111/256, -11371/1536, -131/256, -5851/384, 29/192, 465/128, -761/256, 
  -155/64, 2449/1536, -107/16, 9883/1536, -859/768, 365/384, 163/32, 117/64, 
  589/48, 195/128, 325/384, 1473/256, 255/128, -145/256, -1909/256, 
  11419/1536, -1241/96, 2521/1536, 6, -9/32, -171/32, 5/2, 45/4, 275/128, 
  -31/16, 3/8, -7/8, 1087/384, -39/8, -2671/128, -1535/384, 137/16, -91/48, 
  -185/48, -5115923/2941952, 14289817/735488, 4151497/91936, 
  115142119/8825856, 116285/52224, -21282977/8825856, 1073917789/14709760, 
  -5150399/735488, 1788741/22984, 72953/104448, -2091577/367744, 
  -720911281/8825856, 709373/1470976, 229121/104448, 69785465/2206464, 
  -1281891457/8825856, 699823559/7354880, -34209/8704, -5046031/86528, 
  -5115923/2941952, 142802859/1470976, 114362161/1470976, 2394243/56576, 
  593847271/14709760, 5014597/86528, -2315721809/22064640, -43919623/1379040, 
  -1575111491/14709760, -93/256, 2565256849/22064640, 47924523/865280, 
  55743743/2941952, -63/128, -5598587/1470976, 7376185/183872, 118475/52224, 
  -1423167/173056, -4420999/339456, -7115315/2941952, 538415/52224, 
  35583635/519168, -604973047/4412928, -22559479/367744, 151008667/1131520, 
  -27/32, -87/512, -9/128, 603/512, 27/128, 9/32, -355/256, 51/128, 117/256, 
  283/256, -3/16, -2065/512, 15/64, -33/64, 1439/128, 957/128, -19/8, 45/8, 
  -13/4, -19/8, 45/8, -13/4, 1099/768, 275/128, -25051/3072, -19/8, 45/8, 
  -13/4, 2461/384, 839/192, -24691/1536, 3/16, 139/32, 19/128, -11/32, 1/4, 
  273/1024, 273/512, 49/128, -11/16, -273/1024, 5/16, -1967/1024, 1923/512, 
  9/32, 29/64, -3/8, -819/512, -109/1024, 1169/256, -1079/512, -1/256, 
  -969/256, 1099/768, 275/128, -25051/3072, 7/2, 19/4, -45/4, 13/2, 
  -1099/768, -275/128, 25051/3072, -63/8, 123221315/2206464, -471645/14144, 
  109654367/2206464, 21919/1632, -2611627/84864, -15899/544, -477313/84864, 
  -4593342733/44129280, -9/8, 1884106559/22064640, 29124967/399360, 
  2022697631/14709760, -403357933/2263040, -3516426703/44129280, 
  -173937487/2206464, 1697370547/5516160, 452991293/7354880, 
  111156691/551616, 58817/2176, 113618159/29419520, -1965/512, 
  -3697855/339456, 1798685011/22064640, 3/8, -496620535/8825856, 
  -744976469/17651712, -1982626561/22064640, 45419447/452608, 
  1930436063/88258560, 85947073/1103232, -29105607/216320, 
  -1636539501/29419520, -110570599/1103232, 1697/768, 447/256, -6077/384, 
  -1085/256, -1485570871/88258560, 280465/10608, 4164884731/88258560, 
  143783/6528, 1519/256, 1029383/21216, -47087017/2941952, -1223/128, 
  -707/64, 49/96, 105/64, 11/16, 6, -139/32, -9/32, -93/16, 1537/192, 
  -3259/96, -1741/192, 91/32, 2939/192, -9/16, 27/32, 1257/128, 7/64, 
  163/384, 15/64, -63/128, -133/64, 51/64, 9/128, -123/128, -119/192, 
  -255/128, -9/32, -95/16, -65/16, 9/128, 91/16, -9/16, -35/8, 1123/128, 
  -43/128, -471/64, -321/128, 89/256, -1607/256, -77/64, 113/16, 3207/256, 
  -1137/256, 1043/128, -199/256, -1411/128, -219/16, 113/16, 1557/128, 
  -1137/256, -172123/26112, -2101253/169728, -6325601/735488, 
  58882749/1470976, 4151/1536, -7/512, -129/512, 919/384, 183/128, 557/256, 
  -77/128, -197/96, 9/256, 425/768, 4487/1536, -331/384, 1553/384, 149/256, 
  -16433/1536, -323/64, 561/512, -12557/1536, 3/128, -17977/1536, 3739/1536, 
  7609/512, -753/512, -3959/1536, 649/192, -2441/768, 1639/512, 1259/384, 
  -3063/512, -9329/1536, 9/64, -741/1024, 3381/1024, -99/256, 119851/9216, 
  -4625/1024, -85079/4608, -25/32, 32615/2304, 3061/512, -67817/28288, 
  8453/512, 34343/21216, 1419655/2941952, 17329/2304, -13397237/8825856, 
  5005159/2941952, -357229/52224, -11508113/519168, -1112313/1470976, 
  82300069/2941952, 563021309/8825856, 94933745/1470976, -101417/34816, 
  135578501/17651712, 22905113/1038336, 2035509/226304, -96922387/4412928, 
  -156113687/4412928, -1304993/367744, 2404163/1038336, -97560557/17651712, 
  4591799/1470976, 41797/13056, 23990269/1357824, 555347311/17651712, 
  -517194401/5883904, -191698649/1470976, 210819/226304, -19248769/565760, 
  -901256549/17651712, 252118409/3394560, 1751321723/88258560, 
  2472699211/29419520, 418906999/7354880, -114274319/5883904, 
  -653868717/14709760, 55743743/5883904, -17/768, 3/32, 15/128, 2713/768, 
  -5/32, -1537/384, -447/128, 387/512, -153/512, 20455/4608, -603/256, 
  -16141/4608, 7669/1152, -63/128, -26401/4608, -93/128, 233/768, 47/32, 
  -3/16, -3559/1536, -93/256, -4757/768, 5633/1536, -249/512, -5593/1536, 
  -1077/512, -173/128, 3/128, -601/512, 19/64, 9/128, -751/768, -141/128, 
  1/128, -101/128, 359/384, 541/256, 607/768, -221/256, 1/32, 1291/768, 
  1079/384, 3133/768, 1137/256, -9/128, -2989/768, -3/16, -19/8, 1069/384, 
  257/64, 45/8, -22849/3072, -13/4, -19/16, -17567/4608, 8275/2304, 1547/768, 
  10123/4608, -431/256, -301/128, -397/384, 174409/34816, 44792105/2941952, 
  -46197277/17651712, 12283897/1357824, 14607431/11767808, 120883/52224, 
  19/8, -100401825/11767808, -103918543/5883904, -12241/1632, 
  -5207209/159744, 87883/42432, -45/8, 51195691/2941952, 95283463/8825856, 
  13/4, -536239/104448, 11516705/5883904, 54195061/17651712, 6869737/1357824, 
  99312779/11767808, -256901/39936, -14855315/11767808, -1194379/259584, 
  193722461/35303424, 716015/4412928, -1422385/104448, -20848655/5883904, 
  -249482459/17651712, 96934265/17651712, -7585241/452608, 733/192, 203/144, 
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  -48491/6144, -25/16, 1087/384, 23/192, 3/8, -84509/2176, -223161/29419520, 
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  71/64, 21589/36864, -91/2048, -31/32, -1675/36864, -9/64, -311/768, 
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  -3701/2048, -7381/3072, 6953/8192, 8079/8192, 33571/18432, 1445/2048, 
  -11039/9216, 37/24, -2699/8192, 1949/9216, -15311/8192, -31901/18432, 
  19805/12288, 16381/6912, -27427/18432, -4247/4096, 45091/9216, 21459/4096, 
  439/1152, -573/1024, -3347/768, -5917/4608, -13153/12288, -71783/18432, 
  -323533/73728, 28195/27648, 103469/73728, 1541/1024, -9/512, 21/512, 
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  25189/12288, -3367/6144, -21367/4096, 37/3072, -5763/4096, -23461/6144, 
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  773/1152, 125/256, -27/256, -27/512, 13/144, 19/512, -1229/1152, -189/512, 
  27/256, 7/128, 155/4608, -3/256, -61/512, 3/256, -219/256, 95/512, 163/256, 
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  2677/768, 2405/2304, 1031/768, 4277/4608, -269/2304, 1415/768, -541/256, 
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  -631/1152, 11/48, -2299/2304, -53/64, -135/64, 6185/2304, 238847/313344, 
  3345/2048, -2483231/905216, -21091/12288, -3644687/4073472, -46505/52224, 
  -374878115/211820544, -3459/1024, -1539787/1018368, -1038609167/423641088, 
  5017685/4073472, 193694983/70606848, -17614791/23535616, 
  1832687999/423641088, 62368191/11767808, -108473/104448, -8053/3072, 
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