Trigonometry Angles π/23

Author

Eric W. Weisstein
October 9, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Trigonometry/TrigonometryAnglesPi23.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TrigonometryAnglesPi23.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Optimzed Cos[Pi/23] code by Michael Trott
May 23, 2003

cos((π/23))

Polynomial Root

RootReduce[Simplify[TrigToExp[Cos[Pi/23]]]]

With[{n=23},If[n==1,1,EulerPhi[n]/{1,2}[[Mod[n,2]+1]]]]

Numerical

N[Cos[Pi/23],20]

Minimal Representation

The following is the value of cos(π/23) expressed through minimal radicals of lowest possible order. cos(π/23) can be trivially expressed in radicals as - (((-1))^(22/23)) (1+(((-1))^(2/23)))/2. But this requires roots of order 23. The following expression needs roots of order 2, 5, and 11 only. The fully backsubstituted form of the expression has a ByteCount of about 500 MB. So one probably does not want to format it.

Off[General::"spell1",General::"spell"]

The Complicated Expression

expr=(c1 = 1/2; c2 = 1/11; c3 = 1; c4 = -I; c5 = 23; c6 = c5^c1; c7 = c4*c6; c8 = -1; c9 = I; c10 = 11; 
   c11 = c10^c1; c12 = c11*c9; c13 = c12 + c8; c14 = c1*c13; c15 = c11*c4; c16 = c15 + c8; c17 = 1/4; 
   c18 = 5; c19 = c18^c1; c20 = c19 + c8; c21 = c1*c20; c22 = 2; c23 = c19 + c3; c24 = c1*c23; 
   c25 = c22 + c24; c26 = c25^c1; c27 = c26*c9; c28 = c21 + c27; c29 = c28^c22; c30 = c17*c29; c31 = 1/8; 
   c32 = 3; c33 = c28^c32; c34 = c31*c33; c35 = c3 + c30 + c34; c36 = c1*c16*c35; c37 = c1*c28; c38 = 1/16; 
   c39 = 4; c40 = c28^c39; c41 = c38*c40; c42 = c37 + c41; c43 = c1*c13*c42; c44 = c36 + c43; c45 = 129; 
   c46 = 109/2; c47 = c28*c46; c48 = 59/4; c49 = c29*c48; c50 = 9/8; c51 = c33*c50; c52 = 9/16; 
   c53 = c40*c52; c54 = 13; c55 = 21; c56 = c28*c55; c57 = 67/4; c58 = c29*c57; c59 = 21/4; c60 = c33*c59; 
   c61 = c22*c40; c62 = c54 + c56 + c58 + c60 + c61; c63 = c1*c13*c62; c64 = 79; c65 = 27; c66 = c28*c65; 
   c67 = 39/4; c68 = c29*c67; c69 = 37/4; c70 = c33*c69; c71 = c40*c59; c72 = c64 + c66 + c68 + c70 + c71; 
   c73 = c1*c16*c72; c74 = c45 + c47 + c49 + c51 + c53 + c63 + c73; c75 = -(1/5); c76 = c74^c75; 
   c77 = c44*c76; c78 = 1/5; c79 = c74^c78; c80 = -(2/5); c81 = c74^c80; c82 = c17*c33; c83 = c22 + c37; 
   c84 = c31*c33*c83; c85 = c21 + c27 + c30; c86 = c17*c29*c85; c87 = c1*c29; c88 = c34 + c87; 
   c89 = c1*c28*c88; c90 = c31*c40; c91 = c3 + c90; c92 = c38*c40*c91; c93 = c1*c28*c83; c94 = c31*c33*c85; 
   c95 = c22 + c90 + c93 + c94; c96 = c1*c13*c95; c97 = c1*c28*c85; c98 = c41 + c82; c99 = c17*c29*c98; 
   c100 = c21 + c27 + c82 + c87 + c97 + c99; c101 = c1*c100*c16; 
   c102 = c101 + c41 + c82 + c84 + c86 + c89 + c92 + c96; c103 = c102*c81; c104 = -(3/5); c105 = c74^c104; 
   c106 = 3/4; c107 = c106*c33; c108 = 3/16; c109 = c108*c40; c110 = 6; c111 = 3/2; c112 = c111*c28; 
   c113 = c106*c29; c114 = c110 + c112 + c113; c115 = c114*c31*c33; c116 = c28*c32; c117 = 3/8; 
   c118 = c117*c33; c119 = c113 + c116 + c118; c120 = c119*c17*c29; c121 = c111*c29; 
   c122 = c109 + c118 + c121; c123 = c1*c122*c28; c124 = c117*c40; c125 = c112 + c124 + c32; 
   c126 = c125*c38*c40; c127 = 9/4; c128 = c127*c29; c129 = 7/8; c130 = c129*c33; c131 = c22*c28; 
   c132 = c110 + c131; c133 = c1*c132*c28; c134 = c114*c38*c40; c135 = c116 + c29; c136 = c135*c17*c29; 
   c137 = c107 + c109 + c32; c138 = c137*c31*c33; c139 = c109 + c112 + c128 + c130 + c133 + c134 + c136 + 
     c138 + c32; c140 = c1*c139*c16; c141 = c114*c17*c29; c142 = c135*c31*c33; c143 = c119*c38*c40; 
   c144 = c124 + c39; c145 = c1*c144*c28; c146 = c141 + c142 + c143 + c145; c147 = c1*c13*c146; 
   c148 = c107 + c109 + c115 + c120 + c123 + c126 + c140 + c147 + c32; c149 = c105*c148; 
   c150 = c103 + c14 + c149 + c77 + c79; c151 = 8; c152 = c150^c151; c153 = c7 + c8; c154 = 1/25; 
   c155 = c150^c22; c156 = c154*c155; c157 = 1/625; c158 = c150^c39; c159 = c157*c158; c160 = 1/3125; 
   c161 = c150^c18; c162 = c160*c161; c163 = 1/15625; c164 = c150^c110; c165 = c163*c164; c166 = 1/78125; 
   c167 = 7; c168 = c150^c167; c169 = c166*c168; c170 = 1/1953125; c171 = 9; c172 = c150^c171; 
   c173 = c170*c172; c174 = c156 + c159 + c162 + c165 + c169 + c173; c175 = c6*c9; c176 = c175 + c8; 
   c177 = c150*c78; c178 = 1/125; c179 = c150^c32; c180 = c178*c179; c181 = 1/390625; c182 = c152*c181; 
   c183 = 1/9765625; c184 = 10; c185 = c150^c184; c186 = c183*c185; c187 = c177 + c180 + c182 + c186 + c3; 
   c188 = 1176332296; c189 = 1178385556/5; c190 = c150*c189; c191 = 1178478726/25; c192 = c155*c191; 
   c193 = 1179150276/125; c194 = c179*c193; c195 = 1183767273/625; c196 = c158*c195; 
   c197 = 1177534926/3125; c198 = c161*c197; c199 = 1174396791/15625; c200 = c164*c199; 
   c201 = 1179350047/78125; c202 = c168*c201; c203 = 1180393188/390625; c204 = c152*c203; 
   c205 = 1181869146/1953125; c206 = c172*c205; c207 = 1179054081/9765625; c208 = c185*c207; 
   c209 = 982734584; c210 = 982687482/5; c211 = c150*c210; c212 = 981745211/25; c213 = c155*c212; 
   c214 = 196457632/25; c215 = c179*c214; c216 = 39303391/25; c217 = c158*c216; c218 = 983147953/3125; 
   c219 = c161*c218; c220 = 983022179/15625; c221 = c164*c220; c222 = 196319417/15625; c223 = c168*c222; 
   c224 = 196348732/78125; c225 = c152*c224; c226 = 196623963/390625; c227 = c172*c226; 
   c228 = 982599471/9765625; c229 = c185*c228; c230 = c209 + c211 + c213 + c215 + c217 + c219 + c221 + 
     c223 + c225 + c227 + c229; c231 = c1*c176*c230; c232 = 1221675211; c233 = 1221535653/5; 
   c234 = c150*c233; c235 = 1222469454/25; c236 = c155*c235; c237 = 244373091/25; c238 = c179*c237; 
   c239 = 1221149113/625; c240 = c158*c239; c241 = 1221152512/3125; c242 = c161*c241; 
   c243 = 1221563571/15625; c244 = c164*c243; c245 = 1222538369/78125; c246 = c168*c245; 
   c247 = 1222296963/390625; c248 = c152*c247; c249 = 244157326/390625; c250 = c172*c249; 
   c251 = 1221562889/9765625; c252 = c185*c251; c253 = c232 + c234 + c236 + c238 + c240 + c242 + c244 + 
     c246 + c248 + c250 + c252; c254 = c1*c153*c253; 
   c255 = c188 + c190 + c192 + c194 + c196 + c198 + c200 + c202 + c204 + c206 + c208 + c231 + c254; 
   c256 = -(1/11); c257 = -(2/11); c258 = 2/5; c259 = c150*c258; c260 = 2/25; c261 = c155*c260; 
   c262 = 2/390625; c263 = c152*c262; c264 = 2/625; c265 = c158*c264; c266 = 2/3125; c267 = c161*c266; 
   c268 = c22 + c265 + c267; c269 = c152*c181*c268; c270 = 2/15625; c271 = c164*c270; 
   c272 = c259 + c267 + c271; c273 = c166*c168*c272; c274 = 2/78125; c275 = c168*c274; 
   c276 = c22 + c259 + c275; c277 = c150*c276*c78; c278 = c261 + c271 + c275; c279 = c163*c164*c278; 
   c280 = 2/125; c281 = c179*c280; c282 = c263 + c275 + c281; c283 = c160*c161*c282; c284 = 2/1953125; 
   c285 = c172*c284; c286 = c261 + c281 + c285; c287 = c183*c185*c286; c288 = c263 + c265 + c285; 
   c289 = c157*c158*c288; c290 = 2/9765625; c291 = c185*c290; c292 = c265 + c281 + c291; 
   c293 = c170*c172*c292; c294 = c22 + c271 + c291; c295 = c154*c155*c294; c296 = c267 + c285 + c291; 
   c297 = c178*c179*c296; c298 = c183*c185*c268; c299 = c165 + c259 + c265; c300 = c154*c155*c299; 
   c301 = c150*c272*c78; c302 = c169 + c261 + c267; c303 = c178*c179*c302; c304 = c160*c161*c278; 
   c305 = c259 + c261 + c263; c306 = c157*c158*c305; c307 = c152*c181*c282; c308 = c173 + c265 + c275; 
   c309 = c166*c168*c308; c310 = c180 + c259 + c285; c311 = c170*c172*c310; c312 = c271 + c285 + c3; 
   c313 = c163*c164*c312; c314 = c156 + c22 + c263 + c298 + c300 + c301 + c303 + c304 + c306 + c307 + 
     c309 + c311 + c313; c315 = c162 + c22 + c281; c316 = c183*c185*c315; c317 = c160*c161*c299; 
   c318 = c154*c155*c302; c319 = c166*c168*c278; c320 = c170*c172*c305; c321 = c150*c282*c78; 
   c322 = c186 + c263 + c267; c323 = c157*c158*c322; c324 = c159 + c261 + c291; c325 = c178*c179*c324; 
   c326 = c163*c164*c292; c327 = c152*c181*c294; c328 = c316 + c317 + c318 + c319 + c320 + c321 + c323 + 
     c325 + c326 + c327; c329 = -(3/11); c330 = 3/5; c331 = c150*c330; c332 = 6/25; c333 = c155*c332; 
   c334 = 12/125; c335 = c179*c334; c336 = 12/625; c337 = c158*c336; c338 = 3/15625; c339 = c164*c338; 
   c340 = 6/78125; c341 = c168*c340; c342 = 3/390625; c343 = c152*c342; c344 = 3/1953125; c345 = c172*c344; 
   c346 = 12/9765625; c347 = c185*c346; c348 = 6/5; c349 = c150*c348; c350 = 12/25; c351 = c155*c350; 
   c352 = 3/3125; c353 = c161*c352; c354 = 6/15625; c355 = c164*c354; c356 = 3/78125; c357 = c168*c356; 
   c358 = 12/1953125; c359 = c172*c358; c360 = c32 + c335 + c343 + c349 + c351 + c353 + c355 + c357 + c359; 
   c361 = c150*c360*c78; c362 = 3/25; c363 = c155*c362; c364 = 3/125; c365 = c179*c364; c366 = 12/390625; 
   c367 = c152*c366; c368 = c32 + c337 + c339 + c341 + c349 + c359 + c363 + c365 + c367; 
   c369 = c163*c164*c368; c370 = 12/5; c371 = c150*c370; c372 = 3/625; c373 = c158*c372; c374 = 6/3125; 
   c375 = c161*c374; c376 = 3/9765625; c377 = c185*c376; 
   c378 = c110 + c339 + c351 + c357 + c367 + c371 + c373 + c375 + c377; c379 = c154*c155*c378; 
   c380 = 12/78125; c381 = c168*c380; c382 = c110 + c331 + c335 + c353 + c355 + c363 + c367 + c377 + c381; 
   c383 = c166*c168*c382; c384 = 12; c385 = 6/125; c386 = c179*c385; c387 = 12/3125; c388 = c161*c387; 
   c389 = 6/390625; c390 = c152*c389; c391 = c337 + c345 + c357 + c363 + c377 + c384 + c386 + c388 + c390; 
   c392 = c183*c185*c391; c393 = 6/625; c394 = c158*c393; c395 = 12/15625; c396 = c164*c395; 
   c397 = 6/1953125; c398 = c172*c397; c399 = c32 + c343 + c365 + c371 + c377 + c388 + c394 + c396 + c398; 
   c400 = c170*c172*c399; c401 = 6/9765625; c402 = c185*c401; 
   c403 = c339 + c345 + c353 + c365 + c371 + c381 + c384 + c394 + c402; c404 = c178*c179*c403; 
   c405 = c32 + c331 + c345 + c351 + c373 + c375 + c381 + c396 + c402; c406 = c152*c181*c405; 
   c407 = c343 + c347 + c353 + c363 + c373 + c384 + c386 + c396 + c398; c408 = c157*c158*c407; 
   c409 = c331 + c333 + c347 + c357 + c359 + c365 + c373 + c388 + c390; c410 = c160*c161*c409; 
   c411 = 7/125; c412 = c179*c411; c413 = c171 + c333 + c341 + c349 + c353 + c355 + c390 + c398 + c412; 
   c414 = c157*c158*c413; c415 = c166*c168*c378; c416 = c160*c161*c399; c417 = 9/625; c418 = c158*c417; 
   c419 = 7/78125; c420 = c168*c419; c421 = c110 + c333 + c345 + c349 + c355 + c375 + c402 + c418 + c420; 
   c422 = c183*c185*c421; c423 = c150*c403*c78; c424 = c170*c172*c405; c425 = 9/125; c426 = c179*c425; 
   c427 = 7/15625; c428 = c164*c427; c429 = c110 + c343 + c349 + c375 + c394 + c398 + c402 + c426 + c428; 
   c430 = c178*c179*c429; c431 = 9/25; c432 = c155*c431; c433 = 7/3125; c434 = c161*c433; 
   c435 = c110 + c357 + c386 + c390 + c394 + c398 + c402 + c432 + c434; c436 = c163*c164*c435; 
   c437 = 9/78125; c438 = c168*c437; c439 = 7/9765625; c440 = c185*c439; 
   c441 = c331 + c333 + c375 + c386 + c390 + c394 + c398 + c438 + c440; c442 = c154*c155*c441; 
   c443 = c331 + c333 + c335 + c337 + c339 + c341 + c343 + c345 + c347; c444 = c152*c181*c443; 
   c445 = c414 + c415 + c416 + c422 + c423 + c424 + c430 + c436 + c442 + c444; c446 = 9/5; 
   c447 = c150*c446; c448 = 7/625; c449 = c158*c448; c450 = 9/15625; c451 = c164*c450; c452 = 7/1953125; 
   c453 = c172*c452; c454 = c32 + c333 + c341 + c349 + c386 + c390 + c394 + c451 + c453; 
   c455 = c160*c161*c454; c456 = c157*c158*c360; c457 = c150*c378*c78; c458 = c154*c155*c399; 
   c459 = c183*c185*c429; c460 = c110 + c333 + c341 + c349 + c355 + c375 + c386 + c390 + c394 + c398 + 
     c402; c461 = c160*c161*c460; c462 = 9/390625; c463 = c152*c462; 
   c464 = c167 + c355 + c363 + c375 + c386 + c394 + c398 + c402 + c463; c465 = c152*c181*c464; c466 = 7/5; 
   c467 = c150*c466; c468 = 9/1953125; c469 = c172*c468; 
   c470 = c110 + c341 + c355 + c365 + c375 + c394 + c402 + c467 + c469; c471 = c170*c172*c470; 
   c472 = c178*c179*c441; c473 = c163*c164*c443; c474 = c166*c168*c409; 
   c475 = c333 + c339 + c341 + c386 + c390 + c398 + c402 + c447 + c449 + c455 + c456 + c457 + c458 + c459 + 
     c461 + c465 + c471 + c472 + c473 + c474; c476 = -(4/11); c477 = 54; c478 = 54/5; c479 = c150*c478; 
   c480 = 88/25; c481 = c155*c480; c482 = 24/125; c483 = c179*c482; c484 = 48/625; c485 = c158*c484; 
   c486 = c161*c336; c487 = 84/15625; c488 = c164*c487; c489 = 16/15625; c490 = c168*c489; c491 = 8/78125; 
   c492 = c152*c491; c493 = 34/1953125; c494 = c172*c493; c495 = 64/9765625; c496 = c185*c495; c497 = 48; 
   c498 = c150*c384; c499 = 84/25; c500 = c155*c499; c501 = 16/25; c502 = c179*c501; c503 = 8/125; 
   c504 = c158*c503; c505 = 34/3125; c506 = c161*c505; c507 = 64/15625; c508 = c164*c507; c509 = 54/78125; 
   c510 = c168*c509; c511 = 54/390625; c512 = c152*c511; c513 = 88/1953125; c514 = c172*c513; 
   c515 = 24/9765625; c516 = c185*c515; c517 = c497 + c498 + c500 + c502 + c504 + c506 + c508 + c510 + 
     c512 + c514 + c516; c518 = c157*c158*c517; c519 = 64; c520 = 54/25; c521 = c155*c520; c522 = 88/125; 
   c523 = c179*c522; c524 = 24/625; c525 = c158*c524; c526 = 48/3125; c527 = c161*c526; c528 = c164*c387; 
   c529 = 84/78125; c530 = c168*c529; c531 = 16/78125; c532 = c152*c531; c533 = 8/390625; c534 = c172*c533; 
   c535 = 34/9765625; c536 = c185*c535; c537 = c479 + c519 + c521 + c523 + c525 + c527 + c528 + c530 + 
     c532 + c534 + c536; c538 = c183*c185*c537; c539 = 40; c540 = 14; c541 = c150*c540; c542 = c155*c370; 
   c543 = c179*c350; c544 = 94/625; c545 = c158*c544; c546 = c161*c393; c547 = 54/15625; c548 = c164*c547; 
   c549 = 66/78125; c550 = c168*c549; c551 = 18/78125; c552 = c152*c551; c553 = 86/1953125; 
   c554 = c172*c553; c555 = 46/9765625; c556 = c185*c555; 
   c557 = c539 + c541 + c542 + c543 + c545 + c546 + c548 + c550 + c552 + c554 + c556; 
   c558 = c170*c172*c557; c559 = 66; c560 = 18; c561 = c150*c560; c562 = 86/25; c563 = c155*c562; 
   c564 = 46/125; c565 = c179*c564; c566 = 14/625; c567 = c161*c566; c568 = c168*c395; c569 = 94/390625; 
   c570 = c152*c569; c571 = c172*c389; c572 = 54/9765625; c573 = c185*c572; 
   c574 = c504 + c528 + c559 + c561 + c563 + c565 + c567 + c568 + c570 + c571 + c573; 
   c575 = c160*c161*c574; c576 = 88/5; c577 = c150*c576; c578 = 24/25; c579 = c155*c578; c580 = 48/125; 
   c581 = c179*c580; c582 = c158*c334; c583 = 84/3125; c584 = c161*c583; c585 = 16/3125; c586 = c164*c585; 
   c587 = 8/15625; c588 = c168*c587; c589 = 34/390625; c590 = c152*c589; c591 = 64/1953125; 
   c592 = c172*c591; c593 = c477 + c573 + c577 + c579 + c581 + c582 + c584 + c586 + c588 + c590 + c592; 
   c594 = c150*c593*c78; c595 = 94; c596 = c110*c150; c597 = 66/125; c598 = c179*c597; c599 = 18/125; 
   c600 = c158*c599; c601 = 86/3125; c602 = c161*c601; c603 = 46/15625; c604 = c164*c603; c605 = 14/78125; 
   c606 = c152*c605; c607 = c172*c366; c608 = c185*c358; 
   c609 = c521 + c588 + c595 + c596 + c598 + c600 + c602 + c604 + c606 + c607 + c608; 
   c610 = c154*c155*c609; c611 = 90; c612 = 86/5; c613 = c150*c612; c614 = 46/25; c615 = c155*c614; 
   c616 = 8/25; c617 = c179*c616; c618 = 14/125; c619 = c158*c618; c620 = 94/78125; c621 = c168*c620; 
   c622 = c152*c340; c623 = 54/1953125; c624 = c172*c623; c625 = 66/9765625; c626 = c185*c625; 
   c627 = c486 + c528 + c611 + c613 + c615 + c617 + c619 + c621 + c622 + c624 + c626; 
   c628 = c163*c164*c627; c629 = 80; c630 = c150*c151; c631 = 34/25; c632 = c155*c631; c633 = 64/125; 
   c634 = c179*c633; c635 = 54/625; c636 = c158*c635; c637 = 54/3125; c638 = c161*c637; c639 = 88/15625; 
   c640 = c164*c639; c641 = 24/78125; c642 = c168*c641; c643 = 48/390625; c644 = c152*c643; 
   c645 = 84/9765625; c646 = c185*c645; c647 = c607 + c629 + c630 + c632 + c634 + c636 + c638 + c640 + 
     c642 + c644 + c646; c648 = c166*c168*c647; c649 = 46; c650 = 14/5; c651 = c155*c650; c652 = 94/3125; 
   c653 = c161*c652; c654 = c164*c374; c655 = 66/390625; c656 = c152*c655; c657 = 18/390625; 
   c658 = c172*c657; c659 = 86/9765625; c660 = c185*c659; 
   c661 = c510 + c543 + c582 + c630 + c649 + c651 + c653 + c654 + c656 + c658 + c660; 
   c662 = c152*c181*c661; c663 = 30; c664 = 66/25; c665 = c155*c664; c666 = 18/25; c667 = c179*c666; 
   c668 = 86/625; c669 = c158*c668; c670 = 46/3125; c671 = c161*c670; c672 = 8/3125; c673 = c164*c672; 
   c674 = 14/15625; c675 = c168*c674; c676 = c152*c380; c677 = 94/9765625; c678 = c185*c677; 
   c679 = c479 + c607 + c663 + c665 + c667 + c669 + c671 + c673 + c675 + c676 + c678; 
   c680 = c178*c179*c679; c681 = c160*c161*c517; c682 = c154*c155*c537; c683 = 58/5; c684 = c150*c683; 
   c685 = c155*c348; c686 = 58/125; c687 = c179*c686; c688 = 67/625; c689 = c158*c688; c690 = 66/1953125; 
   c691 = c172*c690; c692 = c497 + c510 + c527 + c536 + c604 + c656 + c684 + c685 + c687 + c689 + c691; 
   c693 = c163*c164*c692; c694 = 66/5; c695 = c150*c694; c696 = 34/125; c697 = c179*c696; c698 = 58/3125; 
   c699 = c161*c698; c700 = 58/78125; c701 = c168*c700; c702 = 67/390625; c703 = c152*c702; 
   c704 = 48/1953125; c705 = c172*c704; c706 = c477 + c485 + c556 + c654 + c665 + c695 + c697 + c699 + 
     c701 + c703 + c705; c707 = c183*c185*c706; c708 = c178*c179*c593; 
   c709 = c477 + c479 + c481 + c483 + c485 + c486 + c488 + c490 + c492 + c494 + c496; 
   c710 = c166*c168*c709; c711 = 34/5; c712 = c150*c711; c713 = 48/25; c714 = c155*c713; c715 = c158*c385; 
   c716 = 67/15625; c717 = c164*c716; c718 = 48/78125; c719 = c168*c718; c720 = 46/390625; 
   c721 = c152*c720; c722 = c559 + c624 + c626 + c687 + c699 + c712 + c714 + c715 + c717 + c719 + c721; 
   c723 = c170*c172*c722; c724 = 34; c725 = 48/5; c726 = c150*c725; c727 = 58/25; c728 = c155*c727; 
   c729 = c179*c332; c730 = 58/625; c731 = c158*c730; c732 = 67/3125; c733 = c161*c732; c734 = 48/15625; 
   c735 = c164*c734; c736 = 46/78125; c737 = c168*c736; 
   c738 = c512 + c626 + c691 + c724 + c726 + c728 + c729 + c731 + c733 + c735 + c737; 
   c739 = c152*c181*c738; c740 = 46/5; c741 = c150*c740; c742 = 66/625; c743 = c158*c742; 
   c744 = 58/1953125; c745 = c172*c744; c746 = 67/9765625; c747 = c185*c746; 
   c748 = c497 + c506 + c521 + c598 + c622 + c701 + c735 + c741 + c743 + c745 + c747; 
   c749 = c157*c158*c748; c750 = c150*c647*c78; c751 = c681 + c682 + c693 + c707 + c708 + c710 + c723 + 
     c739 + c749 + c750; c752 = 73; c753 = 52/25; c754 = c155*c753; c755 = 72/625; c756 = c158*c755; 
   c757 = 72/3125; c758 = c161*c757; c759 = 64/390625; c760 = c152*c759; c761 = 36/1953125; 
   c762 = c172*c761; c763 = c160*c161*c537; c764 = c157*c158*c706; c765 = 58; c766 = 67/125; 
   c767 = c179*c766; c768 = 48/9765625; c769 = c185*c768; 
   c770 = c485 + c494 + c548 + c550 + c596 + c656 + c671 + c728 + c765 + c767 + c769; 
   c771 = c178*c179*c770; c772 = c170*c172*c574; c773 = c183*c185*c593; c774 = 72; c775 = 72/5; 
   c776 = c150*c775; c777 = 8/5; c778 = c155*c777; c779 = 54/125; c780 = c179*c779; c781 = 64/625; 
   c782 = c158*c781; c783 = 36/3125; c784 = c161*c783; c785 = 73/78125; c786 = c168*c785; 
   c787 = 52/1953125; c788 = c172*c787; c789 = c508 + c512 + c608 + c774 + c776 + c778 + c780 + c782 + 
     c784 + c786 + c788; c790 = c150*c78*c789; c791 = 60; 
   c792 = c486 + c498 + c528 + c542 + c543 + c568 + c582 + c607 + c608 + c676 + c791; 
   c793 = c178*c179*c792; c794 = c152*c181*c709; c795 = 36; c796 = 64/5; c797 = c150*c796; c798 = 73/25; 
   c799 = c155*c798; c800 = 52/625; c801 = c158*c800; c802 = 72/15625; c803 = c164*c802; c804 = 72/78125; 
   c805 = c168*c804; c806 = c486 + c492 + c496 + c624 + c780 + c795 + c797 + c799 + c801 + c803 + c805; 
   c807 = c166*c168*c806; c808 = c163*c164*c748; c809 = c154*c155*c679; 
   c810 = c479 + c496 + c510 + c543 + c673 + c752 + c754 + c756 + c758 + c760 + c762 + c763 + c764 + c771 + 
     c772 + c773 + c790 + c793 + c794 + c807 + c808 + c809; c811 = -(5/11); c812 = 760; c813 = 124; 
   c814 = c150*c813; c815 = 24; c816 = c155*c815; c817 = 611/125; c818 = c179*c817; c819 = 114/125; 
   c820 = c158*c819; c821 = 118/625; c822 = c161*c821; c823 = 28/625; c824 = c164*c823; c825 = 149/15625; 
   c826 = c168*c825; c827 = 111/78125; c828 = c152*c827; c829 = 112/390625; c830 = c172*c829; 
   c831 = 137/1953125; c832 = c185*c831; c833 = 590; c834 = 140; c835 = c150*c834; c836 = 149/5; 
   c837 = c155*c836; c838 = 111/25; c839 = c179*c838; c840 = 112/125; c841 = c158*c840; c842 = 137/625; 
   c843 = c161*c842; c844 = 152/3125; c845 = c164*c844; c846 = 124/15625; c847 = c168*c846; 
   c848 = 24/15625; c849 = c152*c848; c850 = 611/1953125; c851 = c172*c850; c852 = 114/1953125; 
   c853 = c185*c852; c854 = c833 + c835 + c837 + c839 + c841 + c843 + c845 + c847 + c849 + c851 + c853; 
   c855 = c160*c161*c854; c856 = 700; c857 = 149; c858 = c150*c857; c859 = 111/5; c860 = c155*c859; 
   c861 = 112/25; c862 = c179*c861; c863 = 137/125; c864 = c158*c863; c865 = 152/625; c866 = c161*c865; 
   c867 = 124/3125; c868 = c164*c867; c869 = 24/3125; c870 = c168*c869; c871 = 611/390625; 
   c872 = c152*c871; c873 = 114/390625; c874 = c172*c873; c875 = 118/1953125; c876 = c185*c875; 
   c877 = c856 + c858 + c860 + c862 + c864 + c866 + c868 + c870 + c872 + c874 + c876; 
   c878 = c163*c164*c877; c879 = 614; c880 = 739/5; c881 = c150*c880; c882 = 814/25; c883 = c155*c882; 
   c884 = 674/125; c885 = c179*c884; c886 = 654/625; c887 = c158*c886; c888 = 133/625; c889 = c161*c888; 
   c890 = 624/15625; c891 = c164*c890; c892 = 644/78125; c893 = c168*c892; c894 = 754/390625; 
   c895 = c152*c894; c896 = 799/1953125; c897 = c172*c896; c898 = 609/9765625; c899 = c185*c898; 
   c900 = c879 + c881 + c883 + c885 + c887 + c889 + c891 + c893 + c895 + c897 + c899; 
   c901 = c170*c172*c900; c902 = 570; c903 = 118; c904 = c150*c903; c905 = 28; c906 = c155*c905; 
   c907 = 149/25; c908 = c179*c907; c909 = 111/125; c910 = c158*c909; c911 = 112/625; c912 = c161*c911; 
   c913 = 137/3125; c914 = c164*c913; c915 = 152/15625; c916 = c168*c915; c917 = 124/78125; 
   c918 = c152*c917; c919 = c172*c641; c920 = 611/9765625; c921 = c185*c920; 
   c922 = c902 + c904 + c906 + c908 + c910 + c912 + c914 + c916 + c918 + c919 + c921; 
   c923 = c157*c158*c922; c924 = 739; c925 = 814/5; c926 = c150*c925; c927 = 674/25; c928 = c155*c927; 
   c929 = 654/125; c930 = c179*c929; c931 = 133/125; c932 = c158*c931; c933 = 624/3125; c934 = c161*c933; 
   c935 = 644/15625; c936 = c164*c935; c937 = 754/78125; c938 = c168*c937; c939 = 799/390625; 
   c940 = c152*c939; c941 = 609/1953125; c942 = c172*c941; c943 = 614/9765625; c944 = c185*c943; 
   c945 = c924 + c926 + c928 + c930 + c932 + c934 + c936 + c938 + c940 + c942 + c944; 
   c946 = c183*c185*c945; c947 = 665; c948 = 624/5; c949 = c150*c948; c950 = 644/25; c951 = c155*c950; 
   c952 = 754/125; c953 = c179*c952; c954 = 799/625; c955 = c158*c954; c956 = 609/3125; c957 = c161*c956; 
   c958 = 614/15625; c959 = c164*c958; c960 = 739/78125; c961 = c168*c960; c962 = 814/390625; 
   c963 = c152*c962; c964 = 674/1953125; c965 = c172*c964; c966 = 654/9765625; c967 = c185*c966; 
   c968 = c947 + c949 + c951 + c953 + c955 + c957 + c959 + c961 + c963 + c965 + c967; 
   c969 = c178*c179*c968; c970 = 654; c971 = 133; c972 = c150*c971; c973 = 624/25; c974 = c155*c973; 
   c975 = 644/125; c976 = c179*c975; c977 = 754/625; c978 = c158*c977; c979 = 799/3125; c980 = c161*c979; 
   c981 = 609/15625; c982 = c164*c981; c983 = 614/78125; c984 = c168*c983; c985 = 739/390625; 
   c986 = c152*c985; c987 = 814/1953125; c988 = c172*c987; c989 = 674/9765625; c990 = c185*c989; 
   c991 = c970 + c972 + c974 + c976 + c978 + c980 + c982 + c984 + c986 + c988 + c990; 
   c992 = c154*c155*c991; c993 = 745; c994 = 111; c995 = c150*c994; c996 = 112/5; c997 = c155*c996; 
   c998 = 137/25; c999 = c179*c998; c1000 = 152/125; c1001 = c1000*c158; c1002 = 124/625; 
   c1003 = c1002*c161; c1004 = c164*c524; c1005 = 611/78125; c1006 = c1005*c168; c1007 = 114/78125; 
   c1008 = c1007*c152; c1009 = 118/390625; c1010 = c1009*c172; c1011 = 28/390625; c1012 = c1011*c185; 
   c1013 = c1001 + c1003 + c1004 + c1006 + c1008 + c1010 + c1012 + c993 + c995 + c997 + c999; 
   c1014 = c1013*c166*c168; c1015 = 609; c1016 = 614/5; c1017 = c1016*c150; c1018 = 739/25; 
   c1019 = c1018*c155; c1020 = 814/125; c1021 = c1020*c179; c1022 = 674/625; c1023 = c1022*c158; 
   c1024 = 654/3125; c1025 = c1024*c161; c1026 = 133/3125; c1027 = c1026*c164; c1028 = 624/78125; 
   c1029 = c1028*c168; c1030 = 644/390625; c1031 = c1030*c152; c1032 = 754/1953125; c1033 = c1032*c172; 
   c1034 = 799/9765625; c1035 = c1034*c185; c1036 = c1015 + c1017 + c1019 + c1021 + c1023 + c1025 + c1027 + 
     c1029 + c1031 + c1033 + c1035; c1037 = c1036*c152*c181; c1038 = 674; c1039 = 654/5; 
   c1040 = c1039*c150; c1041 = 133/5; c1042 = c1041*c155; c1043 = 624/125; c1044 = c1043*c179; 
   c1045 = 644/625; c1046 = c1045*c158; c1047 = 754/3125; c1048 = c1047*c161; c1049 = 799/15625; 
   c1050 = c1049*c164; c1051 = 609/78125; c1052 = c1051*c168; c1053 = 614/390625; c1054 = c1053*c152; 
   c1055 = 739/1953125; c1056 = c1055*c172; c1057 = 814/9765625; c1058 = c1057*c185; 
   c1059 = c1038 + c1040 + c1042 + c1044 + c1046 + c1048 + c1050 + c1052 + c1054 + c1056 + c1058; 
   c1060 = c1059*c150*c78; c1061 = 616; c1062 = 536/5; c1063 = c1062*c150; c1064 = 626/25; 
   c1065 = c1064*c155; c1066 = 721/125; c1067 = c1066*c179; c1068 = 501/625; c1069 = c1068*c158; 
   c1070 = 496/3125; c1071 = c1070*c161; c1072 = 611/15625; c1073 = c1072*c164; c1074 = 581/78125; 
   c1075 = c1074*c168; c1076 = 626/390625; c1077 = c1076*c152; c1078 = 661/1953125; c1079 = c1078*c172; 
   c1080 = 446/9765625; c1081 = c1080*c185; c1082 = c1061 + c1063 + c1065 + c1067 + c1069 + c1071 + c1073 + 
     c1075 + c1077 + c1079 + c1081; c1083 = c1082*c160*c161; c1084 = 496; c1085 = 611/5; 
   c1086 = c1085*c150; c1087 = 581/25; c1088 = c1087*c155; c1089 = 626/125; c1090 = c1089*c179; 
   c1091 = 661/625; c1092 = c1091*c158; c1093 = 446/3125; c1094 = c1093*c161; c1095 = 616/15625; 
   c1096 = c1095*c164; c1097 = 536/78125; c1098 = c1097*c168; c1099 = 721/1953125; c1100 = c1099*c172; 
   c1101 = 501/9765625; c1102 = c1101*c185; c1103 = c1077 + c1084 + c1086 + c1088 + c1090 + c1092 + c1094 + 
     c1096 + c1098 + c1100 + c1102; c1104 = c1103*c178*c179; c1105 = 626; c1106 = 721/5; 
   c1107 = c1106*c150; c1108 = 501/25; c1109 = c1108*c155; c1110 = 496/125; c1111 = c1110*c179; 
   c1112 = 611/625; c1113 = c1112*c158; c1114 = 581/3125; c1115 = c1114*c161; c1116 = 626/15625; 
   c1117 = c1116*c164; c1118 = 661/78125; c1119 = c1118*c168; c1120 = 446/390625; c1121 = c1120*c152; 
   c1122 = 616/1953125; c1123 = c1122*c172; c1124 = 536/9765625; c1125 = c1124*c185; 
   c1126 = c1105 + c1107 + c1109 + c1111 + c1113 + c1115 + c1117 + c1119 + c1121 + c1123 + c1125; 
   c1127 = c1126*c154*c155; c1128 = c170*c172*c854; c1129 = 661/5; c1130 = c1129*c150; c1131 = 446/25; 
   c1132 = c1131*c155; c1133 = 616/125; c1134 = c1133*c179; c1135 = 536/625; c1136 = c1135*c158; 
   c1137 = 626/3125; c1138 = c1137*c161; c1139 = 721/15625; c1140 = c1139*c164; c1141 = 501/78125; 
   c1142 = c1141*c168; c1143 = 496/390625; c1144 = c1143*c152; c1145 = 581/9765625; c1146 = c1145*c185; 
   c1147 = c1105 + c1130 + c1132 + c1134 + c1136 + c1138 + c1140 + c1142 + c1144 + c1146 + c851; 
   c1148 = c1147*c166*c168; c1149 = c157*c158*c877; c1150 = c150*c78*c922; c1151 = 661; c1152 = 446/5; 
   c1153 = c1152*c150; c1154 = 616/25; c1155 = c1154*c155; c1156 = 536/125; c1157 = c1156*c179; 
   c1158 = 626/625; c1159 = c1158*c158; c1160 = 721/3125; c1161 = c1160*c161; c1162 = 501/15625; 
   c1163 = c1162*c164; c1164 = 496/78125; c1165 = c1164*c168; c1166 = 581/1953125; c1167 = c1166*c172; 
   c1168 = 626/9765625; c1169 = c1168*c185; c1170 = c1151 + c1153 + c1155 + c1157 + c1159 + c1161 + c1163 + 
     c1165 + c1167 + c1169 + c872; c1171 = c1170*c183*c185; 
   c1172 = c812 + c814 + c816 + c818 + c820 + c822 + c824 + c826 + c828 + c830 + c832; 
   c1173 = c1172*c163*c164; c1174 = c1013*c152*c181; 
   c1175 = c1083 + c1104 + c1127 + c1128 + c1148 + c1149 + c1150 + c1171 + c1173 + c1174; c1176 = 635; 
   c1177 = 136; c1178 = c1177*c150; c1179 = 143/5; c1180 = c1179*c155; c1181 = c179*c39; c1182 = 134/125; 
   c1183 = c1182*c158; c1184 = 136/3125; c1185 = c1184*c164; c1186 = 31/3125; c1187 = c1186*c168; 
   c1188 = 22/78125; c1189 = c1188*c172; c1190 = 133/1953125; c1191 = c1190*c185; c1192 = c1082*c154*c155; 
   c1193 = 575; c1194 = 109; c1195 = c1194*c150; c1196 = 118/5; c1197 = c1196*c155; c1198 = c179*c18; 
   c1199 = 82/125; c1200 = c1199*c158; c1201 = 116/625; c1202 = c1201*c161; c1203 = 4/125; 
   c1204 = c1203*c164; c1205 = 118/15625; c1206 = c1205*c168; c1207 = 137/78125; c1208 = c1207*c152; 
   c1209 = 93/390625; c1210 = c1209*c172; c1211 = 92/1953125; c1212 = c1211*c185; 
   c1213 = c1193 + c1195 + c1197 + c1198 + c1200 + c1202 + c1204 + c1206 + c1208 + c1210 + c1212; 
   c1214 = c1213*c150*c78; c1215 = c1147*c160*c161; c1216 = c178*c179*c900; c1217 = c166*c168*c922; 
   c1218 = 666; c1219 = 666/5; c1220 = c1219*c150; c1221 = 666/25; c1222 = c1221*c155; c1223 = 666/125; 
   c1224 = c1223*c179; c1225 = 666/625; c1226 = c1225*c158; c1227 = 666/3125; c1228 = c1227*c161; 
   c1229 = 666/15625; c1230 = c1229*c164; c1231 = 666/78125; c1232 = c1231*c168; c1233 = 666/390625; 
   c1234 = c1233*c152; c1235 = 666/1953125; c1236 = c1235*c172; c1237 = 666/9765625; c1238 = c1237*c185; 
   c1239 = c1218 + c1220 + c1222 + c1224 + c1226 + c1228 + c1230 + c1232 + c1234 + c1236 + c1238; 
   c1240 = c1239*c150*c78; c1241 = 31; c1242 = c1241*c155; c1243 = 22/25; c1244 = c1243*c158; 
   c1245 = 127/3125; c1246 = c1245*c164; c1247 = 136/15625; c1248 = c1247*c168; c1249 = 143/78125; 
   c1250 = c1249*c152; c1251 = 4/15625; c1252 = c1251*c172; c1253 = 134/1953125; c1254 = c1253*c185; 
   c1255 = c1178 + c1242 + c1244 + c1246 + c1248 + c1250 + c1252 + c1254 + c833 + c839 + c889; 
   c1256 = c1255*c157*c158; c1257 = c1172*c183*c185; c1258 = c1013*c170*c172; c1259 = 500; c1260 = 134; 
   c1261 = c1260*c150; c1262 = 136/25; c1263 = c1262*c179; c1264 = 31/25; c1265 = c1264*c158; 
   c1266 = 111/625; c1267 = c1266*c161; c1268 = 22/625; c1269 = c1268*c164; c1270 = 133/15625; 
   c1271 = c1270*c168; c1272 = 127/78125; c1273 = c1272*c152; c1274 = 136/390625; c1275 = c1274*c172; 
   c1276 = 143/1953125; c1277 = c1276*c185; c1278 = c1197 + c1259 + c1261 + c1263 + c1265 + c1267 + c1269 + 
     c1271 + c1273 + c1275 + c1277; c1279 = c1278*c163*c164; c1280 = c1059*c152*c181; 
   c1281 = c1176 + c1178 + c1180 + c1181 + c1183 + c1185 + c1187 + c1189 + c1191 + c1192 + c1214 + c1215 + 
     c1216 + c1217 + c1240 + c1256 + c1257 + c1258 + c1279 + c1280 + c822 + c828; c1282 = -(6/11); 
   c1283 = 6606; c1284 = 1485; c1285 = c1284*c150; c1286 = 1474/5; c1287 = c1286*c155; c1288 = 1326/25; 
   c1289 = c1288*c179; c1290 = 7146/625; c1291 = c1290*c158; c1292 = c161*c520; c1293 = 1389/3125; 
   c1294 = c1293*c164; c1295 = 1521/15625; c1296 = c1295*c168; c1297 = 7146/390625; c1298 = c1297*c152; 
   c1299 = 6416/1953125; c1300 = c1299*c172; c1301 = 7031/9765625; c1302 = c1301*c185; c1303 = 7146; 
   c1304 = 1350; c1305 = c1304*c150; c1306 = 1389/5; c1307 = c1306*c155; c1308 = 1521/25; 
   c1309 = c1308*c179; c1310 = 6416/3125; c1311 = c1310*c161; c1312 = 7031/15625; c1313 = c1312*c164; 
   c1314 = 6606/78125; c1315 = c1314*c168; c1316 = 297/15625; c1317 = c1316*c152; c1318 = 1474/390625; 
   c1319 = c1318*c172; c1320 = 1326/1953125; c1321 = c1320*c185; 
   c1322 = c1291 + c1303 + c1305 + c1307 + c1309 + c1311 + c1313 + c1315 + c1317 + c1319 + c1321; 
   c1323 = c1322*c157*c158; c1324 = 6945; c1325 = 1521; c1326 = c1325*c150; c1327 = 7146/25; 
   c1328 = c1327*c155; c1329 = 6416/125; c1330 = c1329*c179; c1331 = 7031/625; c1332 = c1331*c158; 
   c1333 = 6606/3125; c1334 = c1333*c161; c1335 = 297/625; c1336 = c1335*c164; c1337 = 1474/15625; 
   c1338 = c1337*c168; c1339 = 1326/78125; c1340 = c1339*c152; c1341 = 7146/1953125; c1342 = c1341*c172; 
   c1343 = c185*c509; c1344 = c1324 + c1326 + c1328 + c1330 + c1332 + c1334 + c1336 + c1338 + c1340 + 
     c1342 + c1343; c1345 = c1344*c163*c164; c1346 = 7605; c1347 = 7146/5; c1348 = c1347*c150; 
   c1349 = 6416/25; c1350 = c1349*c155; c1351 = 7031/125; c1352 = c1351*c179; c1353 = 6606/625; 
   c1354 = c1353*c158; c1355 = 297/125; c1356 = c1355*c161; c1357 = 1474/3125; c1358 = c1357*c164; 
   c1359 = 1326/15625; c1360 = c1359*c168; c1361 = c172*c547; c1362 = 1389/1953125; c1363 = c1362*c185; 
   c1364 = c1298 + c1346 + c1348 + c1350 + c1352 + c1354 + c1356 + c1358 + c1360 + c1361 + c1363; 
   c1365 = c1364*c166*c168; c1366 = 7607; c1367 = 7182/5; c1368 = c1367*c150; c1369 = 8001/25; 
   c1370 = c1369*c155; c1371 = 7946/125; c1372 = c1371*c179; c1373 = 7206/625; c1374 = c1373*c158; 
   c1375 = 7722/3125; c1376 = c1375*c161; c1377 = 7326/15625; c1378 = c1377*c164; c1379 = 7521/78125; 
   c1380 = c1379*c168; c1381 = 8181/390625; c1382 = c1381*c152; c1383 = 7722/1953125; c1384 = c1383*c172; 
   c1385 = 6992/9765625; c1386 = c1385*c185; c1387 = c1366 + c1368 + c1370 + c1372 + c1374 + c1376 + 
     c1378 + c1380 + c1382 + c1384 + c1386; c1388 = c1387*c183*c185; c1389 = 6750; c1390 = 1389; 
   c1391 = c1390*c150; c1392 = 1521/5; c1393 = c1392*c155; c1394 = 7146/125; c1395 = c1394*c179; 
   c1396 = 6416/625; c1397 = c1396*c158; c1398 = 7031/3125; c1399 = c1398*c161; c1400 = 6606/15625; 
   c1401 = c1400*c164; c1402 = 297/3125; c1403 = c1402*c168; c1404 = 1474/78125; c1405 = c1404*c152; 
   c1406 = 1326/390625; c1407 = c1406*c172; c1408 = 7146/9765625; c1409 = c1408*c185; 
   c1410 = c1389 + c1391 + c1393 + c1395 + c1397 + c1399 + c1401 + c1403 + c1405 + c1407 + c1409; 
   c1411 = c1410*c160*c161; c1412 = 8001; c1413 = 7946/5; c1414 = c1413*c150; c1415 = 7206/25; 
   c1416 = c1415*c155; c1417 = 7722/125; c1418 = c1417*c179; c1419 = 7326/625; c1420 = c1419*c158; 
   c1421 = 7521/3125; c1422 = c1421*c161; c1423 = 8181/15625; c1424 = c1423*c164; c1425 = 7722/78125; 
   c1426 = c1425*c168; c1427 = 6992/390625; c1428 = c1427*c152; c1429 = 7607/1953125; c1430 = c1429*c172; 
   c1431 = 7182/9765625; c1432 = c1431*c185; c1433 = c1412 + c1414 + c1416 + c1418 + c1420 + c1422 + 
     c1424 + c1426 + c1428 + c1430 + c1432; c1434 = c1433*c150*c78; c1435 = 6992; c1436 = 7607/5; 
   c1437 = c1436*c150; c1438 = 7182/25; c1439 = c1438*c155; c1440 = 8001/125; c1441 = c1440*c179; 
   c1442 = 7946/625; c1443 = c1442*c158; c1444 = 7206/3125; c1445 = c1444*c161; c1446 = 7722/15625; 
   c1447 = c1446*c164; c1448 = 7326/78125; c1449 = c1448*c168; c1450 = 7521/390625; c1451 = c1450*c152; 
   c1452 = 8181/1953125; c1453 = c1452*c172; c1454 = 7722/9765625; c1455 = c1454*c185; 
   c1456 = c1435 + c1437 + c1439 + c1441 + c1443 + c1445 + c1447 + c1449 + c1451 + c1453 + c1455; 
   c1457 = c1456*c170*c172; c1458 = 7206; c1459 = 7722/5; c1460 = c1459*c150; c1461 = 7326/25; 
   c1462 = c1461*c155; c1463 = 7521/125; c1464 = c1463*c179; c1465 = 8181/625; c1466 = c1465*c158; 
   c1467 = 6992/15625; c1468 = c1467*c164; c1469 = 7607/78125; c1470 = c1469*c168; c1471 = 7182/390625; 
   c1472 = c1471*c152; c1473 = 8001/1953125; c1474 = c1473*c172; c1475 = 7946/9765625; c1476 = c1475*c185; 
   c1477 = c1376 + c1458 + c1460 + c1462 + c1464 + c1466 + c1468 + c1470 + c1472 + c1474 + c1476; 
   c1478 = c1477*c178*c179; c1479 = 7946; c1480 = 7206/5; c1481 = c1480*c150; c1482 = 7722/25; 
   c1483 = c1482*c155; c1484 = 7326/125; c1485 = c1484*c179; c1486 = 7521/625; c1487 = c1486*c158; 
   c1488 = 8181/3125; c1489 = c1488*c161; c1490 = 6992/78125; c1491 = c1490*c168; c1492 = 7607/390625; 
   c1493 = c1492*c152; c1494 = 7182/1953125; c1495 = c1494*c172; c1496 = 8001/9765625; c1497 = c1496*c185; 
   c1498 = c1447 + c1479 + c1481 + c1483 + c1485 + c1487 + c1489 + c1491 + c1493 + c1495 + c1497; 
   c1499 = c1498*c154*c155; c1500 = 7722; c1501 = 6992/5; c1502 = c150*c1501; c1503 = 7607/25; 
   c1504 = c1503*c155; c1505 = 7182/125; c1506 = c1505*c179; c1507 = 8001/625; c1508 = c1507*c158; 
   c1509 = 7946/3125; c1510 = c1509*c161; c1511 = 7206/15625; c1512 = c1511*c164; c1513 = 7326/390625; 
   c1514 = c1513*c152; c1515 = 7521/1953125; c1516 = c1515*c172; c1517 = 8181/9765625; c1518 = c1517*c185; 
   c1519 = c1426 + c1500 + c1502 + c1504 + c1506 + c1508 + c1510 + c1512 + c1514 + c1516 + c1518; 
   c1520 = c1519*c152*c181; c1521 = 6511; c1522 = 6684/5; c1523 = c150*c1522; c1524 = 6354/25; 
   c1525 = c1524*c155; c1526 = 1308/25; c1527 = c1526*c179; c1528 = 6381/625; c1529 = c1528*c158; 
   c1530 = 5969/3125; c1531 = c1530*c161; c1532 = 6174/15625; c1533 = c1532*c164; c1534 = 6944/78125; 
   c1535 = c1534*c168; c1536 = 6924/390625; c1537 = c152*c1536; c1538 = 6084/1953125; c1539 = c1538*c172; 
   c1540 = 6084/9765625; c1541 = c1540*c185; c1542 = c1521 + c1523 + c1525 + c1527 + c1529 + c1531 + 
     c1533 + c1535 + c1537 + c1539 + c1541; c1543 = c152*c1542*c181; c1544 = 6944; c1545 = 6924/5; 
   c1546 = c150*c1545; c1547 = 6084/25; c1548 = c1547*c155; c1549 = 6084/125; c1550 = c1549*c179; 
   c1551 = 6511/625; c1552 = c1551*c158; c1553 = 6684/3125; c1554 = c1553*c161; c1555 = 6354/15625; 
   c1556 = c1555*c164; c1557 = 1308/15625; c1558 = c1557*c168; c1559 = 6381/390625; c1560 = c152*c1559; 
   c1561 = 5969/1953125; c1562 = c1561*c172; c1563 = 6174/9765625; c1564 = c1563*c185; 
   c1565 = c1544 + c1546 + c1548 + c1550 + c1552 + c1554 + c1556 + c1558 + c1560 + c1562 + c1564; 
   c1566 = c150*c1565*c78; c1567 = 6540; c1568 = 6381/5; c1569 = c150*c1568; c1570 = 5969/25; 
   c1571 = c155*c1570; c1572 = 6174/125; c1573 = c1572*c179; c1574 = 6944/625; c1575 = c1574*c158; 
   c1576 = 6924/3125; c1577 = c1576*c161; c1578 = 6084/15625; c1579 = c1578*c164; c1580 = 6084/78125; 
   c1581 = c1580*c168; c1582 = 6511/390625; c1583 = c152*c1582; c1584 = 6684/1953125; c1585 = c1584*c172; 
   c1586 = 6354/9765625; c1587 = c1586*c185; c1588 = c1567 + c1569 + c1571 + c1573 + c1575 + c1577 + 
     c1579 + c1581 + c1583 + c1585 + c1587; c1589 = c1588*c170*c172; c1590 = 5969; c1591 = 6174/5; 
   c1592 = c150*c1591; c1593 = 6944/25; c1594 = c155*c1593; c1595 = 6924/125; c1596 = c1595*c179; 
   c1597 = 6084/625; c1598 = c158*c1597; c1599 = 6084/3125; c1600 = c1599*c161; c1601 = 6511/15625; 
   c1602 = c1601*c164; c1603 = 6684/78125; c1604 = c1603*c168; c1605 = 6354/390625; c1606 = c152*c1605; 
   c1607 = 1308/390625; c1608 = c1607*c172; c1609 = 6381/9765625; c1610 = c1609*c185; 
   c1611 = c1590 + c1592 + c1594 + c1596 + c1598 + c1600 + c1602 + c1604 + c1606 + c1608 + c1610; 
   c1612 = c1611*c163*c164; c1613 = c1322*c178*c179; c1614 = c1344*c154*c155; c1615 = 6924; c1616 = 6084/5; 
   c1617 = c150*c1616; c1618 = 6511/125; c1619 = c1618*c179; c1620 = 6684/625; c1621 = c158*c1620; 
   c1622 = 6354/3125; c1623 = c161*c1622; c1624 = 1308/3125; c1625 = c1624*c164; c1626 = 6381/78125; 
   c1627 = c1626*c168; c1628 = 5969/390625; c1629 = c152*c1628; c1630 = 6174/1953125; c1631 = c1630*c172; 
   c1632 = 6944/9765625; c1633 = c1632*c185; c1634 = c1548 + c1615 + c1617 + c1619 + c1621 + c1623 + 
     c1625 + c1627 + c1629 + c1631 + c1633; c1635 = c157*c158*c1634; c1636 = c1364*c183*c185; 
   c1637 = c1283 + c1285 + c1287 + c1289 + c1291 + c1292 + c1294 + c1296 + c1298 + c1300 + c1302; 
   c1638 = c160*c161*c1637; c1639 = c1410*c166*c168; 
   c1640 = c1543 + c1566 + c1589 + c1612 + c1613 + c1614 + c1635 + c1636 + c1638 + c1639; c1641 = 6660; 
   c1642 = 1332; c1643 = c150*c1642; c1644 = 7087/25; c1645 = c155*c1644; c1646 = 1452/25; 
   c1647 = c1646*c179; c1648 = 1386/125; c1649 = c158*c1648; c1650 = 7116/3125; c1651 = c161*c1650; 
   c1652 = 6957/15625; c1653 = c164*c1652; c1654 = 1309/15625; c1655 = c1654*c168; c1656 = c152*c637; 
   c1657 = 1504/390625; c1658 = c1657*c172; c1659 = c185*c395; c1660 = 5760; c1661 = 6187/5; 
   c1662 = c150*c1661; c1663 = 1272/5; c1664 = c155*c1663; c1665 = 1206/25; c1666 = c1665*c179; 
   c1667 = 6216/625; c1668 = c158*c1667; c1669 = 6057/3125; c1670 = c161*c1669; c1671 = 1129/3125; 
   c1672 = c164*c1671; c1673 = 234/3125; c1674 = c1673*c168; c1675 = 1324/78125; c1676 = c152*c1675; 
   c1677 = 264/78125; c1678 = c1677*c172; c1679 = 1152/1953125; c1680 = c1679*c185; 
   c1681 = c1660 + c1662 + c1664 + c1666 + c1668 + c1670 + c1672 + c1674 + c1676 + c1678 + c1680; 
   c1682 = c1681*c183*c185; c1683 = c1611*c170*c172; c1684 = 1504; c1685 = c150*c1684; c1686 = 300; 
   c1687 = c155*c1686; c1688 = 1332/25; c1689 = c1688*c179; c1690 = 1332/125; c1691 = c158*c1690; 
   c1692 = 7087/3125; c1693 = c161*c1692; c1694 = 1452/3125; c1695 = c164*c1694; c1696 = 1386/15625; 
   c1697 = c168*c1696; c1698 = 7116/390625; c1699 = c152*c1698; c1700 = 6957/1953125; c1701 = c1700*c172; 
   c1702 = 1309/1953125; c1703 = c1702*c185; c1704 = c1389 + c1685 + c1687 + c1689 + c1691 + c1693 + 
     c1695 + c1697 + c1699 + c1701 + c1703; c1705 = c160*c161*c1704; c1706 = c1322*c154*c155; 
   c1707 = c163*c1634*c164; c1708 = c1364*c157*c158; c1709 = c1387*c178*c179; c1710 = c150*c1637*c78; 
   c1711 = 6957; c1712 = 1309; c1713 = c150*c1712; c1714 = 270; c1715 = c155*c1714; c1716 = 1504/25; 
   c1717 = c1716*c179; c1718 = c158*c384; c1719 = 1332/625; c1720 = c161*c1719; c1721 = 1332/3125; 
   c1722 = c164*c1721; c1723 = 7087/78125; c1724 = c168*c1723; c1725 = 1452/78125; c1726 = c152*c1725; 
   c1727 = 1386/390625; c1728 = c172*c1727; c1729 = 7116/9765625; c1730 = c1729*c185; 
   c1731 = c1711 + c1713 + c1715 + c1717 + c1718 + c1720 + c1722 + c1724 + c1726 + c1728 + c1730; 
   c1732 = c166*c168*c1731; c1733 = 7320; c1734 = 1464; c1735 = c150*c1734; c1736 = 1464/5; 
   c1737 = c155*c1736; c1738 = 1464/25; c1739 = c1738*c179; c1740 = 1464/125; c1741 = c158*c1740; 
   c1742 = 1464/625; c1743 = c161*c1742; c1744 = 1464/3125; c1745 = c164*c1744; c1746 = 1464/15625; 
   c1747 = c168*c1746; c1748 = 1464/78125; c1749 = c152*c1748; c1750 = 1464/390625; c1751 = c172*c1750; 
   c1752 = 1464/1953125; c1753 = c1752*c185; c1754 = c1733 + c1735 + c1737 + c1739 + c1741 + c1743 + 
     c1745 + c1747 + c1749 + c1751 + c1753; c1755 = c1754*c183*c185; c1756 = c1498*c152*c181; 
   c1757 = c1641 + c1643 + c1645 + c1647 + c1649 + c1651 + c1653 + c1655 + c1656 + c1658 + c1659 + c1682 + 
     c1683 + c1705 + c1706 + c1707 + c1708 + c1709 + c1710 + c1732 + c1755 + c1756; c1758 = -(7/11); 
   c1759 = 76412; c1760 = 15813; c1761 = c150*c1760; c1762 = 78162/25; c1763 = c155*c1762; 
   c1764 = 75047/125; c1765 = c1764*c179; c1766 = 77273/625; c1767 = c158*c1766; c1768 = 77862/3125; 
   c1769 = c161*c1768; c1770 = 3038/625; c1771 = c164*c1770; c1772 = 77679/78125; c1773 = c168*c1772; 
   c1774 = 3094/15625; c1775 = c152*c1774; c1776 = 76146/1953125; c1777 = c172*c1776; 
   c1778 = 76314/9765625; c1779 = c1778*c185; c1780 = 77273; c1781 = 77862/5; c1782 = c150*c1781; 
   c1783 = 3038; c1784 = c155*c1783; c1785 = 77679/125; c1786 = c1785*c179; c1787 = 3094/25; 
   c1788 = c158*c1787; c1789 = 76146/3125; c1790 = c161*c1789; c1791 = 76314/15625; c1792 = c164*c1791; 
   c1793 = 76412/78125; c1794 = c168*c1793; c1795 = 15813/78125; c1796 = c152*c1795; c1797 = 78162/1953125; 
   c1798 = c172*c1797; c1799 = 75047/9765625; c1800 = c1799*c185; 
   c1801 = c1780 + c1782 + c1784 + c1786 + c1788 + c1790 + c1792 + c1794 + c1796 + c1798 + c1800; 
   c1802 = c157*c158*c1801; c1803 = 77679; c1804 = 15470; c1805 = c150*c1804; c1806 = 76146/25; 
   c1807 = c155*c1806; c1808 = 76314/125; c1809 = c179*c1808; c1810 = 76412/625; c1811 = c158*c1810; 
   c1812 = 15813/625; c1813 = c161*c1812; c1814 = 78162/15625; c1815 = c164*c1814; c1816 = 75047/78125; 
   c1817 = c168*c1816; c1818 = 77273/390625; c1819 = c152*c1818; c1820 = 77862/1953125; c1821 = c172*c1820; 
   c1822 = 3038/390625; c1823 = c1822*c185; c1824 = c1803 + c1805 + c1807 + c1809 + c1811 + c1813 + c1815 + 
     c1817 + c1819 + c1821 + c1823; c1825 = c166*c168*c1824; c1826 = 76314; c1827 = 76412/5; 
   c1828 = c150*c1827; c1829 = 15813/5; c1830 = c155*c1829; c1831 = 78162/125; c1832 = c179*c1831; 
   c1833 = 75047/625; c1834 = c158*c1833; c1835 = 77273/3125; c1836 = c161*c1835; c1837 = 77862/15625; 
   c1838 = c164*c1837; c1839 = 3038/3125; c1840 = c168*c1839; c1841 = 77679/390625; c1842 = c152*c1841; 
   c1843 = 3094/78125; c1844 = c172*c1843; c1845 = 76146/9765625; c1846 = c1845*c185; 
   c1847 = c1826 + c1828 + c1830 + c1832 + c1834 + c1836 + c1838 + c1840 + c1842 + c1844 + c1846; 
   c1848 = c183*c1847*c185; c1849 = 79065; c1850 = 78162/5; c1851 = c150*c1850; c1852 = 75047/25; 
   c1853 = c155*c1852; c1854 = 77273/125; c1855 = c179*c1854; c1856 = 77862/625; c1857 = c158*c1856; 
   c1858 = 3038/125; c1859 = c161*c1858; c1860 = 77679/15625; c1861 = c164*c1860; c1862 = 3094/3125; 
   c1863 = c168*c1862; c1864 = 76146/390625; c1865 = c152*c1864; c1866 = 76314/1953125; c1867 = c172*c1866; 
   c1868 = 76412/9765625; c1869 = c185*c1868; c1870 = c1849 + c1851 + c1853 + c1855 + c1857 + c1859 + 
     c1861 + c1863 + c1865 + c1867 + c1869; c1871 = c150*c1870*c78; c1872 = 84282; c1873 = 16474; 
   c1874 = c150*c1873; c1875 = 84099/25; c1876 = c155*c1875; c1877 = 16754/25; c1878 = c179*c1877; 
   c1879 = 82566/625; c1880 = c158*c1879; c1881 = 82734/3125; c1882 = c161*c1881; c1883 = 82832/15625; 
   c1884 = c164*c1883; c1885 = 17097/15625; c1886 = c168*c1885; c1887 = 84582/390625; c1888 = c152*c1887; 
   c1889 = 81467/1953125; c1890 = c172*c1889; c1891 = 83693/9765625; c1892 = c185*c1891; 
   c1893 = c1872 + c1874 + c1876 + c1878 + c1880 + c1882 + c1884 + c1886 + c1888 + c1890 + c1892; 
   c1894 = c160*c161*c1893; c1895 = 82566; c1896 = 82734/5; c1897 = c150*c1896; c1898 = 82832/25; 
   c1899 = c155*c1898; c1900 = 17097/25; c1901 = c179*c1900; c1902 = 84582/625; c1903 = c158*c1902; 
   c1904 = 81467/3125; c1905 = c161*c1904; c1906 = 83693/15625; c1907 = c164*c1906; c1908 = 84282/78125; 
   c1909 = c168*c1908; c1910 = 16474/78125; c1911 = c152*c1910; c1912 = 84099/1953125; c1913 = c172*c1912; 
   c1914 = 16754/1953125; c1915 = c185*c1914; c1916 = c1895 + c1897 + c1899 + c1901 + c1903 + c1905 + 
     c1907 + c1909 + c1911 + c1913 + c1915; c1917 = c170*c172*c1916; c1918 = 83770; c1919 = 82566/5; 
   c1920 = c150*c1919; c1921 = 82734/25; c1922 = c155*c1921; c1923 = 82832/125; c1924 = c179*c1923; 
   c1925 = 17097/125; c1926 = c158*c1925; c1927 = 84582/3125; c1928 = c161*c1927; c1929 = 81467/15625; 
   c1930 = c164*c1929; c1931 = 83693/78125; c1932 = c168*c1931; c1933 = 84282/390625; c1934 = c152*c1933; 
   c1935 = 16474/390625; c1936 = c172*c1935; c1937 = 84099/9765625; c1938 = c185*c1937; 
   c1939 = c1918 + c1920 + c1922 + c1924 + c1926 + c1928 + c1930 + c1932 + c1934 + c1936 + c1938; 
   c1940 = c152*c181*c1939; c1941 = 82370; c1942 = 84099/5; c1943 = c150*c1942; c1944 = 16754/5; 
   c1945 = c155*c1944; c1946 = 82566/125; c1947 = c179*c1946; c1948 = 82734/625; c1949 = c158*c1948; 
   c1950 = 82832/3125; c1951 = c161*c1950; c1952 = 17097/3125; c1953 = c164*c1952; c1954 = 84582/78125; 
   c1955 = c168*c1954; c1956 = 81467/390625; c1957 = c152*c1956; c1958 = 83693/1953125; c1959 = c172*c1958; 
   c1960 = 84282/9765625; c1961 = c185*c1960; c1962 = c1941 + c1943 + c1945 + c1947 + c1949 + c1951 + 
     c1953 + c1955 + c1957 + c1959 + c1961; c1963 = c163*c164*c1962; c1964 = 81467; c1965 = 83693/5; 
   c1966 = c150*c1965; c1967 = 84282/25; c1968 = c155*c1967; c1969 = 16474/25; c1970 = c179*c1969; 
   c1971 = 84099/625; c1972 = c158*c1971; c1973 = 16754/625; c1974 = c161*c1973; c1975 = 82566/15625; 
   c1976 = c164*c1975; c1977 = 82734/78125; c1978 = c168*c1977; c1979 = 82832/390625; c1980 = c152*c1979; 
   c1981 = 17097/390625; c1982 = c172*c1981; c1983 = 84582/9765625; c1984 = c185*c1983; 
   c1985 = c1964 + c1966 + c1968 + c1970 + c1972 + c1974 + c1976 + c1978 + c1980 + c1982 + c1984; 
   c1986 = c178*c179*c1985; c1987 = 84582; c1988 = 81467/5; c1989 = c150*c1988; c1990 = 83693/25; 
   c1991 = c155*c1990; c1992 = 84282/125; c1993 = c179*c1992; c1994 = 16474/125; c1995 = c158*c1994; 
   c1996 = 84099/3125; c1997 = c161*c1996; c1998 = 16754/3125; c1999 = c164*c1998; c2000 = 82566/78125; 
   c2001 = c168*c2000; c2002 = 82734/390625; c2003 = c152*c2002; c2004 = 82832/1953125; c2005 = c172*c2004; 
   c2006 = 17097/1953125; c2007 = c185*c2006; c2008 = c1987 + c1989 + c1991 + c1993 + c1995 + c1997 + 
     c1999 + c2001 + c2003 + c2005 + c2007; c2009 = c154*c155*c2008; c2010 = 70895; c2011 = 68998/5; 
   c2012 = c150*c2011; c2013 = 70727/25; c2014 = c155*c2013; c2015 = 72757/125; c2016 = c179*c2015; 
   c2017 = 71798/625; c2018 = c158*c2017; c2019 = 69194/3125; c2020 = c161*c2019; c2021 = 2749/625; 
   c2022 = c164*c2021; c2023 = 68522/78125; c2024 = c168*c2023; c2025 = 74374/390625; c2026 = c152*c2025; 
   c2027 = 72288/1953125; c2028 = c172*c2027; c2029 = 68333/9765625; c2030 = c185*c2029; 
   c2031 = c2010 + c2012 + c2014 + c2016 + c2018 + c2020 + c2022 + c2024 + c2026 + c2028 + c2030; 
   c2032 = c150*c2031*c78; c2033 = 74374; c2034 = 72288/5; c2035 = c150*c2034; c2036 = 68333/25; 
   c2037 = c155*c2036; c2038 = 14179/25; c2039 = c179*c2038; c2040 = 68998/625; c2041 = c158*c2040; 
   c2042 = 70727/3125; c2043 = c161*c2042; c2044 = 72757/15625; c2045 = c164*c2044; c2046 = 71798/78125; 
   c2047 = c168*c2046; c2048 = 69194/390625; c2049 = c152*c2048; c2050 = 2749/78125; c2051 = c172*c2050; 
   c2052 = 68522/9765625; c2053 = c185*c2052; c2054 = c2033 + c2035 + c2037 + c2039 + c2041 + c2043 + 
     c2045 + c2047 + c2049 + c2051 + c2053; c2055 = c178*c179*c2054; c2056 = 68522; c2057 = 74374/5; 
   c2058 = c150*c2057; c2059 = 72288/25; c2060 = c155*c2059; c2061 = 68333/125; c2062 = c179*c2061; 
   c2063 = 14179/125; c2064 = c158*c2063; c2065 = 68998/3125; c2066 = c161*c2065; c2067 = 70727/15625; 
   c2068 = c164*c2067; c2069 = 72757/78125; c2070 = c168*c2069; c2071 = 71798/390625; c2072 = c152*c2071; 
   c2073 = 69194/1953125; c2074 = c172*c2073; c2075 = 2749/390625; c2076 = c185*c2075; 
   c2077 = c2056 + c2058 + c2060 + c2062 + c2064 + c2066 + c2068 + c2070 + c2072 + c2074 + c2076; 
   c2078 = c160*c161*c2077; c2079 = 70727; c2080 = 72757/5; c2081 = c150*c2080; c2082 = 71798/25; 
   c2083 = c155*c2082; c2084 = 69194/125; c2085 = c179*c2084; c2086 = 2749/25; c2087 = c158*c2086; 
   c2088 = 68522/3125; c2089 = c161*c2088; c2090 = 74374/15625; c2091 = c164*c2090; c2092 = 72288/78125; 
   c2093 = c168*c2092; c2094 = 68333/390625; c2095 = c152*c2094; c2096 = 14179/390625; c2097 = c172*c2096; 
   c2098 = 68998/9765625; c2099 = c185*c2098; c2100 = c2079 + c2081 + c2083 + c2085 + c2087 + c2089 + 
     c2091 + c2093 + c2095 + c2097 + c2099; c2101 = c166*c168*c2100; c2102 = 72288; c2103 = 68333/5; 
   c2104 = c150*c2103; c2105 = 14179/5; c2106 = c155*c2105; c2107 = 68998/125; c2108 = c179*c2107; 
   c2109 = 70727/625; c2110 = c158*c2109; c2111 = 72757/3125; c2112 = c161*c2111; c2113 = 71798/15625; 
   c2114 = c164*c2113; c2115 = 69194/78125; c2116 = c168*c2115; c2117 = 2749/15625; c2118 = c152*c2117; 
   c2119 = 68522/1953125; c2120 = c172*c2119; c2121 = 74374/9765625; c2122 = c185*c2121; 
   c2123 = c2102 + c2104 + c2106 + c2108 + c2110 + c2112 + c2114 + c2116 + c2118 + c2120 + c2122; 
   c2124 = c154*c155*c2123; c2125 = c1801*c183*c185; c2126 = c163*c164*c1824; c2127 = c152*c181*c1847; 
   c2128 = c1759 + c1761 + c1763 + c1765 + c1767 + c1769 + c1771 + c1773 + c1775 + c1777 + c1779; 
   c2129 = c157*c158*c2128; c2130 = c170*c172*c1870; 
   c2131 = c2032 + c2055 + c2078 + c2101 + c2124 + c2125 + c2126 + c2127 + c2129 + c2130; c2132 = 79177; 
   c2133 = 78218/5; c2134 = c150*c2133; c2135 = 75614/25; c2136 = c155*c2135; c2137 = 15029/25; 
   c2138 = c179*c2137; c2139 = 74942/625; c2140 = c158*c2139; c2141 = 80794/3125; c2142 = c161*c2141; 
   c2143 = 78708/15625; c2144 = c164*c2143; c2145 = 74753/78125; c2146 = c168*c2145; c2147 = 15463/78125; 
   c2148 = c152*c2147; c2149 = 75418/1953125; c2150 = c172*c2149; c2151 = 77147/9765625; 
   c2152 = c185*c2151; c2153 = 65269; c2154 = 65066/5; c2155 = c150*c2154; c2156 = 70918/25; 
   c2157 = c155*c2156; c2158 = 68832/125; c2159 = c179*c2158; c2160 = 64877/625; c2161 = c158*c2160; 
   c2162 = 67439/3125; c2163 = c161*c2162; c2164 = 65542/15625; c2165 = c164*c2164; c2166 = 67271/78125; 
   c2167 = c168*c2166; c2168 = 69301/390625; c2169 = c152*c2168; c2170 = 68342/1953125; c2171 = c172*c2170; 
   c2172 = 65738/9765625; c2173 = c185*c2172; c2174 = c2153 + c2155 + c2157 + c2159 + c2161 + c2163 + 
     c2165 + c2167 + c2169 + c2171 + c2173; c2175 = c152*c181*c2174; c2176 = c166*c168*c2031; 
   c2177 = c160*c161*c2100; c2178 = c150*c1847*c78; c2179 = c178*c179*c2128; c2180 = c163*c164*c1870; 
   c2181 = 75614; c2182 = 15029; c2183 = c150*c2182; c2184 = 74942/25; c2185 = c155*c2184; 
   c2186 = 80794/125; c2187 = c179*c2186; c2188 = 78708/625; c2189 = c158*c2188; c2190 = 74753/3125; 
   c2191 = c161*c2190; c2192 = 15463/3125; c2193 = c164*c2192; c2194 = 75418/78125; c2195 = c168*c2194; 
   c2196 = 77147/390625; c2197 = c152*c2196; c2198 = 79177/1953125; c2199 = c172*c2198; 
   c2200 = 78218/9765625; c2201 = c185*c2200; c2202 = c2181 + c2183 + c2185 + c2187 + c2189 + c2191 + 
     c2193 + c2195 + c2197 + c2199 + c2201; c2203 = c157*c158*c2202; c2204 = 74753; c2205 = 15463; 
   c2206 = c150*c2205; c2207 = 75418/25; c2208 = c155*c2207; c2209 = 77147/125; c2210 = c179*c2209; 
   c2211 = 79177/625; c2212 = c158*c2211; c2213 = 78218/3125; c2214 = c161*c2213; c2215 = 75614/15625; 
   c2216 = c164*c2215; c2217 = 15029/15625; c2218 = c168*c2217; c2219 = 74942/390625; c2220 = c152*c2219; 
   c2221 = 80794/1953125; c2222 = c172*c2221; c2223 = 78708/9765625; c2224 = c185*c2223; 
   c2225 = c2204 + c2206 + c2208 + c2210 + c2212 + c2214 + c2216 + c2218 + c2220 + c2222 + c2224; 
   c2226 = c183*c185*c2225; c2227 = 80526; c2228 = 80526/5; c2229 = c150*c2228; c2230 = 80526/25; 
   c2231 = c155*c2230; c2232 = 80526/125; c2233 = c179*c2232; c2234 = 80526/625; c2235 = c158*c2234; 
   c2236 = 80526/3125; c2237 = c161*c2236; c2238 = 80526/15625; c2239 = c164*c2238; c2240 = 80526/78125; 
   c2241 = c168*c2240; c2242 = 80526/390625; c2243 = c152*c2242; c2244 = 80526/1953125; c2245 = c172*c2244; 
   c2246 = 80526/9765625; c2247 = c185*c2246; c2248 = c2227 + c2229 + c2231 + c2233 + c2235 + c2237 + 
     c2239 + c2241 + c2243 + c2245 + c2247; c2249 = c152*c181*c2248; c2250 = c170*c172*c1939; 
   c2251 = c154*c155*c1962; c2252 = c2132 + c2134 + c2136 + c2138 + c2140 + c2142 + c2144 + c2146 + c2148 + 
     c2150 + c2152 + c2175 + c2176 + c2177 + c2178 + c2179 + c2180 + c2203 + c2226 + c2249 + c2250 + c2251; 
   c2253 = -(8/11); c2254 = 847896; c2255 = 855744/5; c2256 = c150*c2255; c2257 = 846188/25; 
   c2258 = c155*c2257; c2259 = 6790; c2260 = c179*c2259; c2261 = 842268/625; c2262 = c158*c2261; 
   c2263 = 841254/3125; c2264 = c161*c2263; c2265 = 855792/15625; c2266 = c164*c2265; c2267 = 852048/78125; 
   c2268 = c168*c2267; c2269 = 845208/390625; c2270 = c152*c2269; c2271 = 847736/1953125; 
   c2272 = c172*c2271; c2273 = 836802/9765625; c2274 = c185*c2273; c2275 = 847736; c2276 = 836802/5; 
   c2277 = c150*c2276; c2278 = 847896/25; c2279 = c155*c2278; c2280 = 855744/125; c2281 = c179*c2280; 
   c2282 = 846188/625; c2283 = c158*c2282; c2284 = 1358/5; c2285 = c161*c2284; c2286 = 842268/15625; 
   c2287 = c164*c2286; c2288 = 841254/78125; c2289 = c168*c2288; c2290 = 855792/390625; c2291 = c152*c2290; 
   c2292 = 852048/1953125; c2293 = c172*c2292; c2294 = 845208/9765625; c2295 = c185*c2294; 
   c2296 = c2275 + c2277 + c2279 + c2281 + c2283 + c2285 + c2287 + c2289 + c2291 + c2293 + c2295; 
   c2297 = c170*c172*c2296; c2298 = 848750; c2299 = 842268/5; c2300 = c150*c2299; c2301 = 841254/25; 
   c2302 = c155*c2301; c2303 = 855792/125; c2304 = c179*c2303; c2305 = 852048/625; c2306 = c158*c2305; 
   c2307 = 845208/3125; c2308 = c161*c2307; c2309 = 847736/15625; c2310 = c164*c2309; c2311 = 836802/78125; 
   c2312 = c168*c2311; c2313 = 847896/390625; c2314 = c152*c2313; c2315 = 855744/1953125; 
   c2316 = c172*c2315; c2317 = 846188/9765625; c2318 = c185*c2317; 
   c2319 = c2298 + c2300 + c2302 + c2304 + c2306 + c2308 + c2310 + c2312 + c2314 + c2316 + c2318; 
   c2320 = c178*c179*c2319; c2321 = 845208; c2322 = 847736/5; c2323 = c150*c2322; c2324 = 836802/25; 
   c2325 = c155*c2324; c2326 = 847896/125; c2327 = c179*c2326; c2328 = 855744/625; c2329 = c158*c2328; 
   c2330 = 846188/3125; c2331 = c161*c2330; c2332 = 1358/25; c2333 = c164*c2332; c2334 = 842268/78125; 
   c2335 = c168*c2334; c2336 = 841254/390625; c2337 = c152*c2336; c2338 = 855792/1953125; 
   c2339 = c172*c2338; c2340 = 852048/9765625; c2341 = c185*c2340; 
   c2342 = c2321 + c2323 + c2325 + c2327 + c2329 + c2331 + c2333 + c2335 + c2337 + c2339 + c2341; 
   c2343 = c152*c181*c2342; c2344 = 846188; c2345 = 169750; c2346 = c150*c2345; c2347 = 842268/25; 
   c2348 = c155*c2347; c2349 = 841254/125; c2350 = c179*c2349; c2351 = 855792/625; c2352 = c158*c2351; 
   c2353 = 852048/3125; c2354 = c161*c2353; c2355 = 845208/15625; c2356 = c164*c2355; c2357 = 847736/78125; 
   c2358 = c168*c2357; c2359 = 836802/390625; c2360 = c152*c2359; c2361 = 847896/1953125; 
   c2362 = c172*c2361; c2363 = 855744/9765625; c2364 = c185*c2363; 
   c2365 = c2344 + c2346 + c2348 + c2350 + c2352 + c2354 + c2356 + c2358 + c2360 + c2362 + c2364; 
   c2366 = c154*c155*c2365; c2367 = 926442; c2368 = 922698/5; c2369 = c150*c2368; c2370 = 915858/25; 
   c2371 = c155*c2370; c2372 = 918386/125; c2373 = c179*c2372; c2374 = 907452/625; c2375 = c158*c2374; 
   c2376 = 918546/3125; c2377 = c161*c2376; c2378 = 926394/15625; c2379 = c164*c2378; c2380 = 916838/78125; 
   c2381 = c168*c2380; c2382 = 36776/15625; c2383 = c152*c2382; c2384 = 912918/1953125; c2385 = c172*c2384; 
   c2386 = 911904/9765625; c2387 = c185*c2386; c2388 = c2367 + c2369 + c2371 + c2373 + c2375 + c2377 + 
     c2379 + c2381 + c2383 + c2385 + c2387; c2389 = c163*c164*c2388; c2390 = 911904; c2391 = 926442/5; 
   c2392 = c150*c2391; c2393 = 922698/25; c2394 = c155*c2393; c2395 = 915858/125; c2396 = c179*c2395; 
   c2397 = 918386/625; c2398 = c158*c2397; c2399 = 907452/3125; c2400 = c161*c2399; c2401 = 918546/15625; 
   c2402 = c164*c2401; c2403 = 926394/78125; c2404 = c168*c2403; c2405 = 916838/390625; c2406 = c152*c2405; 
   c2407 = 36776/78125; c2408 = c172*c2407; c2409 = 912918/9765625; c2410 = c185*c2409; 
   c2411 = c2390 + c2392 + c2394 + c2396 + c2398 + c2400 + c2402 + c2404 + c2406 + c2408 + c2410; 
   c2412 = c160*c161*c2411; c2413 = 907452; c2414 = 918546/5; c2415 = c150*c2414; c2416 = 926394/25; 
   c2417 = c155*c2416; c2418 = 916838/125; c2419 = c179*c2418; c2420 = 36776/25; c2421 = c158*c2420; 
   c2422 = 912918/3125; c2423 = c161*c2422; c2424 = 911904/15625; c2425 = c164*c2424; c2426 = 926442/78125; 
   c2427 = c168*c2426; c2428 = 922698/390625; c2429 = c152*c2428; c2430 = 915858/1953125; 
   c2431 = c172*c2430; c2432 = 918386/9765625; c2433 = c185*c2432; 
   c2434 = c2413 + c2415 + c2417 + c2419 + c2421 + c2423 + c2425 + c2427 + c2429 + c2431 + c2433; 
   c2435 = c183*c185*c2434; c2436 = 926394; c2437 = 916838/5; c2438 = c150*c2437; c2439 = 36776; 
   c2440 = c155*c2439; c2441 = 912918/125; c2442 = c179*c2441; c2443 = 911904/625; c2444 = c158*c2443; 
   c2445 = 926442/3125; c2446 = c161*c2445; c2447 = 922698/15625; c2448 = c164*c2447; c2449 = 915858/78125; 
   c2450 = c168*c2449; c2451 = 918386/390625; c2452 = c152*c2451; c2453 = 907452/1953125; 
   c2454 = c172*c2453; c2455 = 918546/9765625; c2456 = c185*c2455; 
   c2457 = c2436 + c2438 + c2440 + c2442 + c2444 + c2446 + c2448 + c2450 + c2452 + c2454 + c2456; 
   c2458 = c150*c2457*c78; c2459 = 912918; c2460 = 911904/5; c2461 = c150*c2460; c2462 = 926442/25; 
   c2463 = c155*c2462; c2464 = 922698/125; c2465 = c179*c2464; c2466 = 915858/625; c2467 = c158*c2466; 
   c2468 = 918386/3125; c2469 = c161*c2468; c2470 = 907452/15625; c2471 = c164*c2470; c2472 = 918546/78125; 
   c2473 = c168*c2472; c2474 = 926394/390625; c2475 = c152*c2474; c2476 = 916838/1953125; 
   c2477 = c172*c2476; c2478 = 36776/390625; c2479 = c185*c2478; 
   c2480 = c2459 + c2461 + c2463 + c2465 + c2467 + c2469 + c2471 + c2473 + c2475 + c2477 + c2479; 
   c2481 = c157*c158*c2480; c2482 = 922698; c2483 = 915858/5; c2484 = c150*c2483; c2485 = 918386/25; 
   c2486 = c155*c2485; c2487 = 907452/125; c2488 = c179*c2487; c2489 = 918546/625; c2490 = c158*c2489; 
   c2491 = 926394/3125; c2492 = c161*c2491; c2493 = 916838/15625; c2494 = c164*c2493; c2495 = 36776/3125; 
   c2496 = c168*c2495; c2497 = 912918/390625; c2498 = c152*c2497; c2499 = 911904/1953125; 
   c2500 = c172*c2499; c2501 = 926442/9765625; c2502 = c185*c2501; 
   c2503 = c2482 + c2484 + c2486 + c2488 + c2490 + c2492 + c2494 + c2496 + c2498 + c2500 + c2502; 
   c2504 = c166*c168*c2503; c2505 = 776358; c2506 = 773783/5; c2507 = c150*c2506; c2508 = 30942; 
   c2509 = c155*c2508; c2510 = 784932/125; c2511 = c179*c2510; c2512 = 156684/125; c2513 = c158*c2512; 
   c2514 = 769266/3125; c2515 = c161*c2514; c2516 = 768566/15625; c2517 = c164*c2516; c2518 = 30802/3125; 
   c2519 = c168*c2518; c2520 = 795594/390625; c2521 = c152*c2520; c2522 = 782518/1953125; 
   c2523 = c172*c2522; c2524 = 765038/9765625; c2525 = c185*c2524; 
   c2526 = c2505 + c2507 + c2509 + c2511 + c2513 + c2515 + c2517 + c2519 + c2521 + c2523 + c2525; 
   c2527 = c152*c181*c2526; c2528 = 795594; c2529 = 782518/5; c2530 = c150*c2529; c2531 = 765038/25; 
   c2532 = c155*c2531; c2533 = 776358/125; c2534 = c179*c2533; c2535 = 773783/625; c2536 = c158*c2535; 
   c2537 = 30942/125; c2538 = c161*c2537; c2539 = 784932/15625; c2540 = c164*c2539; c2541 = 156684/15625; 
   c2542 = c168*c2541; c2543 = 769266/390625; c2544 = c152*c2543; c2545 = 768566/1953125; 
   c2546 = c172*c2545; c2547 = 30802/390625; c2548 = c185*c2547; 
   c2549 = c2528 + c2530 + c2532 + c2534 + c2536 + c2538 + c2540 + c2542 + c2544 + c2546 + c2548; 
   c2550 = c166*c168*c2549; c2551 = 773783; c2552 = 154710; c2553 = c150*c2552; c2554 = 784932/25; 
   c2555 = c155*c2554; c2556 = 156684/25; c2557 = c179*c2556; c2558 = 769266/625; c2559 = c158*c2558; 
   c2560 = 768566/3125; c2561 = c161*c2560; c2562 = 30802/625; c2563 = c164*c2562; c2564 = 795594/78125; 
   c2565 = c168*c2564; c2566 = 782518/390625; c2567 = c152*c2566; c2568 = 765038/1953125; 
   c2569 = c172*c2568; c2570 = 776358/9765625; c2571 = c185*c2570; 
   c2572 = c2551 + c2553 + c2555 + c2557 + c2559 + c2561 + c2563 + c2565 + c2567 + c2569 + c2571; 
   c2573 = c150*c2572*c78; c2574 = 765038; c2575 = 776358/5; c2576 = c150*c2575; c2577 = 773783/25; 
   c2578 = c155*c2577; c2579 = 30942/5; c2580 = c179*c2579; c2581 = 784932/625; c2582 = c158*c2581; 
   c2583 = 156684/625; c2584 = c161*c2583; c2585 = 769266/15625; c2586 = c164*c2585; c2587 = 768566/78125; 
   c2588 = c168*c2587; c2589 = 30802/15625; c2590 = c152*c2589; c2591 = 795594/1953125; c2592 = c172*c2591; 
   c2593 = 782518/9765625; c2594 = c185*c2593; c2595 = c2574 + c2576 + c2578 + c2580 + c2582 + c2584 + 
     c2586 + c2588 + c2590 + c2592 + c2594; c2596 = c160*c161*c2595; c2597 = 783420; c2598 = 769266/5; 
   c2599 = c150*c2598; c2600 = 768566/25; c2601 = c155*c2600; c2602 = 30802/5; c2603 = c179*c2602; 
   c2604 = 795594/625; c2605 = c158*c2604; c2606 = 782518/3125; c2607 = c161*c2606; c2608 = 765038/15625; 
   c2609 = c164*c2608; c2610 = 776358/78125; c2611 = c168*c2610; c2612 = 773783/390625; c2613 = c152*c2612; 
   c2614 = 30942/78125; c2615 = c172*c2614; c2616 = 784932/9765625; c2617 = c185*c2616; 
   c2618 = c2597 + c2599 + c2601 + c2603 + c2605 + c2607 + c2609 + c2611 + c2613 + c2615 + c2617; 
   c2619 = c170*c172*c2618; c2620 = c2254 + c2256 + c2258 + c2260 + c2262 + c2264 + c2266 + c2268 + c2270 + 
     c2272 + c2274; c2621 = c178*c179*c2620; c2622 = c157*c158*c2296; c2623 = c154*c155*c2319; 
   c2624 = c183*c185*c2342; c2625 = c163*c164*c2365; 
   c2626 = c2527 + c2550 + c2573 + c2596 + c2619 + c2621 + c2622 + c2623 + c2624 + c2625; c2627 = 853168; 
   c2628 = 835688/5; c2629 = c150*c2628; c2630 = 847008/25; c2631 = c155*c2630; c2632 = 844433/125; 
   c2633 = c179*c2632; c2634 = 33768/25; c2635 = c158*c2634; c2636 = 855582/3125; c2637 = c161*c2636; 
   c2638 = 170814/3125; c2639 = c164*c2638; c2640 = 839916/78125; c2641 = c168*c2640; 
   c2642 = 839216/390625; c2643 = c152*c2642; c2644 = 33628/78125; c2645 = c172*c2644; 
   c2646 = 866244/9765625; c2647 = c185*c2646; c2648 = 746412; c2649 = 148980; c2650 = c150*c2649; 
   c2651 = 730746/25; c2652 = c155*c2651; c2653 = 730046/125; c2654 = c179*c2653; c2655 = 146306/125; 
   c2656 = c158*c2655; c2657 = 757074/3125; c2658 = c161*c2657; c2659 = 743998/15625; c2660 = c164*c2659; 
   c2661 = 726518/78125; c2662 = c168*c2661; c2663 = 737838/390625; c2664 = c152*c2663; 
   c2665 = 735263/1953125; c2666 = c172*c2665; c2667 = 147006/1953125; c2668 = c185*c2667; 
   c2669 = c2648 + c2650 + c2652 + c2654 + c2656 + c2658 + c2660 + c2662 + c2664 + c2666 + c2668; 
   c2670 = c163*c164*c2669; c2671 = c150*c2526*c78; c2672 = c152*c181*c2618; c2673 = c160*c161*c2620; 
   c2674 = 839216; c2675 = 168140; c2676 = c150*c2675; c2677 = 866244/25; c2678 = c155*c2677; 
   c2679 = 853168/125; c2680 = c179*c2679; c2681 = 835688/625; c2682 = c158*c2681; c2683 = 847008/3125; 
   c2684 = c161*c2683; c2685 = 844433/15625; c2686 = c164*c2685; c2687 = 33768/3125; c2688 = c168*c2687; 
   c2689 = 855582/390625; c2690 = c152*c2689; c2691 = 170814/390625; c2692 = c172*c2691; 
   c2693 = 839916/9765625; c2694 = c185*c2693; c2695 = c2674 + c2676 + c2678 + c2680 + c2682 + c2684 + 
     c2686 + c2688 + c2690 + c2692 + c2694; c2696 = c154*c155*c2695; c2697 = c183*c185*c2296; 
   c2698 = 839916; c2699 = 839216/5; c2700 = c150*c2699; c2701 = 33628; c2702 = c155*c2701; 
   c2703 = 866244/125; c2704 = c179*c2703; c2705 = 853168/625; c2706 = c158*c2705; c2707 = 835688/3125; 
   c2708 = c161*c2707; c2709 = 847008/15625; c2710 = c164*c2709; c2711 = 844433/78125; c2712 = c168*c2711; 
   c2713 = 33768/15625; c2714 = c152*c2713; c2715 = 855582/1953125; c2716 = c172*c2715; 
   c2717 = 170814/1953125; c2718 = c185*c2717; c2719 = c2698 + c2700 + c2702 + c2704 + c2706 + c2708 + 
     c2710 + c2712 + c2714 + c2716 + c2718; c2720 = c178*c179*c2719; c2721 = c170*c172*c2365; 
   c2722 = 885780; c2723 = 177156; c2724 = c150*c2723; c2725 = 177156/5; c2726 = c155*c2725; 
   c2727 = 177156/25; c2728 = c179*c2727; c2729 = 177156/125; c2730 = c158*c2729; c2731 = 177156/625; 
   c2732 = c161*c2731; c2733 = 177156/3125; c2734 = c164*c2733; c2735 = 177156/15625; c2736 = c168*c2735; 
   c2737 = 177156/78125; c2738 = c152*c2737; c2739 = 177156/390625; c2740 = c172*c2739; 
   c2741 = 177156/1953125; c2742 = c185*c2741; c2743 = c2722 + c2724 + c2726 + c2728 + c2730 + c2732 + 
     c2734 + c2736 + c2738 + c2740 + c2742; c2744 = c163*c164*c2743; c2745 = c157*c158*c2388; 
   c2746 = c166*c168*c2434; c2747 = c2627 + c2629 + c2631 + c2633 + c2635 + c2637 + c2639 + c2641 + c2643 + 
     c2645 + c2647 + c2670 + c2671 + c2672 + c2673 + c2696 + c2697 + c2720 + c2721 + c2744 + c2745 + c2746; 
   c2748 = -(9/11); c2749 = 9384234; c2750 = 1862529; c2751 = c150*c2750; c2752 = 1858758/5; 
   c2753 = c155*c2752; c2754 = 9327504/125; c2755 = c179*c2754; c2756 = 1861716/125; c2757 = c158*c2756; 
   c2758 = 9341532/3125; c2759 = c161*c2758; c2760 = 9333561/15625; c2761 = c164*c2760; 
   c2762 = 9296256/78125; c2763 = c168*c2762; c2764 = 9337467/390625; c2765 = c152*c2764; 
   c2766 = 1860687/390625; c2767 = c172*c2766; c2768 = 9280776/9765625; c2769 = c185*c2768; 
   c2770 = 9341532; c2771 = 9333561/5; c2772 = c150*c2771; c2773 = 9296256/25; c2774 = c155*c2773; 
   c2775 = 9337467/125; c2776 = c179*c2775; c2777 = 1860687/125; c2778 = c158*c2777; c2779 = 9280776/3125; 
   c2780 = c161*c2779; c2781 = 9384234/15625; c2782 = c164*c2781; c2783 = 1862529/15625; 
   c2784 = c168*c2783; c2785 = 1858758/78125; c2786 = c152*c2785; c2787 = 9327504/1953125; 
   c2788 = c172*c2787; c2789 = 1861716/1953125; c2790 = c185*c2789; 
   c2791 = c2770 + c2772 + c2774 + c2776 + c2778 + c2780 + c2782 + c2784 + c2786 + c2788 + c2790; 
   c2792 = c160*c161*c2791; c2793 = 9293790; c2794 = 9327504/5; c2795 = c150*c2794; c2796 = 1861716/5; 
   c2797 = c155*c2796; c2798 = 9341532/125; c2799 = c179*c2798; c2800 = 9333561/625; c2801 = c158*c2800; 
   c2802 = 9296256/3125; c2803 = c161*c2802; c2804 = 9337467/15625; c2805 = c164*c2804; 
   c2806 = 1860687/15625; c2807 = c168*c2806; c2808 = 9280776/390625; c2809 = c152*c2808; 
   c2810 = 9384234/1953125; c2811 = c172*c2810; c2812 = 1862529/1953125; c2813 = c185*c2812; 
   c2814 = c2793 + c2795 + c2797 + c2799 + c2801 + c2803 + c2805 + c2807 + c2809 + c2811 + c2813; 
   c2815 = c154*c155*c2814; c2816 = 9303435; c2817 = 9280776/5; c2818 = c150*c2817; c2819 = 9384234/25; 
   c2820 = c155*c2819; c2821 = 1862529/25; c2822 = c179*c2821; c2823 = 1858758/125; c2824 = c158*c2823; 
   c2825 = 9327504/3125; c2826 = c161*c2825; c2827 = 1861716/3125; c2828 = c164*c2827; 
   c2829 = 9341532/78125; c2830 = c168*c2829; c2831 = 9333561/390625; c2832 = c152*c2831; 
   c2833 = 9296256/1953125; c2834 = c172*c2833; c2835 = 9337467/9765625; c2836 = c185*c2835; 
   c2837 = c2816 + c2818 + c2820 + c2822 + c2824 + c2826 + c2828 + c2830 + c2832 + c2834 + c2836; 
   c2838 = c170*c172*c2837; c2839 = 9333561; c2840 = 9296256/5; c2841 = c150*c2840; c2842 = 9337467/25; 
   c2843 = c155*c2842; c2844 = 1860687/25; c2845 = c179*c2844; c2846 = 9280776/625; c2847 = c158*c2846; 
   c2848 = 9384234/3125; c2849 = c161*c2848; c2850 = 1862529/3125; c2851 = c164*c2850; 
   c2852 = 1858758/15625; c2853 = c168*c2852; c2854 = 9327504/390625; c2855 = c152*c2854; 
   c2856 = 1861716/390625; c2857 = c172*c2856; c2858 = 9341532/9765625; c2859 = c185*c2858; 
   c2860 = c2839 + c2841 + c2843 + c2845 + c2847 + c2849 + c2851 + c2853 + c2855 + c2857 + c2859; 
   c2861 = c163*c164*c2860; c2862 = 10104114; c2863 = 2017038; c2864 = c150*c2863; c2865 = 10118142/25; 
   c2866 = c155*c2865; c2867 = 10110171/125; c2868 = c179*c2867; c2869 = 10072866/625; c2870 = c158*c2869; 
   c2871 = 10114077/3125; c2872 = c161*c2871; c2873 = 2016009/3125; c2874 = c164*c2873; 
   c2875 = 10057386/78125; c2876 = c168*c2875; c2877 = 10160844/390625; c2878 = c152*c2877; 
   c2879 = 2017851/390625; c2880 = c172*c2879; c2881 = 402816/390625; c2882 = c185*c2881; 
   c2883 = c2862 + c2864 + c2866 + c2868 + c2870 + c2872 + c2874 + c2876 + c2878 + c2880 + c2882; 
   c2884 = c178*c179*c2883; c2885 = 10114077; c2886 = 2016009; c2887 = c150*c2886; c2888 = 10057386/25; 
   c2889 = c155*c2888; c2890 = 10160844/125; c2891 = c179*c2890; c2892 = 2017851/125; c2893 = c158*c2892; 
   c2894 = 402816/125; c2895 = c161*c2894; c2896 = 10104114/15625; c2897 = c164*c2896; 
   c2898 = 2017038/15625; c2899 = c168*c2898; c2900 = 10118142/390625; c2901 = c152*c2900; 
   c2902 = 10110171/1953125; c2903 = c172*c2902; c2904 = 10072866/9765625; c2905 = c185*c2904; 
   c2906 = c2885 + c2887 + c2889 + c2891 + c2893 + c2895 + c2897 + c2899 + c2901 + c2903 + c2905; 
   c2907 = c152*c181*c2906; c2908 = 10057386; c2909 = 10160844/5; c2910 = c150*c2909; c2911 = 2017851/5; 
   c2912 = c155*c2911; c2913 = 402816/5; c2914 = c179*c2913; c2915 = 10104114/625; c2916 = c158*c2915; 
   c2917 = 2017038/625; c2918 = c161*c2917; c2919 = 10118142/15625; c2920 = c164*c2919; 
   c2921 = 10110171/78125; c2922 = c168*c2921; c2923 = 10072866/390625; c2924 = c152*c2923; 
   c2925 = 10114077/1953125; c2926 = c172*c2925; c2927 = 2016009/1953125; c2928 = c185*c2927; 
   c2929 = c2908 + c2910 + c2912 + c2914 + c2916 + c2918 + c2920 + c2922 + c2924 + c2926 + c2928; 
   c2930 = c183*c185*c2929; c2931 = 10085190; c2932 = 10118142/5; c2933 = c150*c2932; c2934 = 10110171/25; 
   c2935 = c155*c2934; c2936 = 10072866/125; c2937 = c179*c2936; c2938 = 10114077/625; c2939 = c158*c2938; 
   c2940 = 2016009/625; c2941 = c161*c2940; c2942 = 10057386/15625; c2943 = c164*c2942; 
   c2944 = 10160844/78125; c2945 = c168*c2944; c2946 = 2017851/78125; c2947 = c152*c2946; 
   c2948 = 402816/78125; c2949 = c172*c2948; c2950 = 10104114/9765625; c2951 = c185*c2950; 
   c2952 = c2931 + c2933 + c2935 + c2937 + c2939 + c2941 + c2943 + c2945 + c2947 + c2949 + c2951; 
   c2953 = c157*c158*c2952; c2954 = 10072866; c2955 = 10114077/5; c2956 = c150*c2955; c2957 = 2016009/5; 
   c2958 = c155*c2957; c2959 = 10057386/125; c2960 = c179*c2959; c2961 = 10160844/625; c2962 = c158*c2961; 
   c2963 = 2017851/625; c2964 = c161*c2963; c2965 = 402816/625; c2966 = c164*c2965; c2967 = 10104114/78125; 
   c2968 = c168*c2967; c2969 = 2017038/78125; c2970 = c152*c2969; c2971 = 10118142/1953125; 
   c2972 = c172*c2971; c2973 = 10110171/9765625; c2974 = c185*c2973; 
   c2975 = c2954 + c2956 + c2958 + c2960 + c2962 + c2964 + c2966 + c2968 + c2970 + c2972 + c2974; 
   c2976 = c166*c168*c2975; c2977 = 10089255; c2978 = 2014080; c2979 = c150*c2978; c2980 = 10104114/25; 
   c2981 = c155*c2980; c2982 = 2017038/25; c2983 = c179*c2982; c2984 = 10118142/625; c2985 = c158*c2984; 
   c2986 = 10110171/3125; c2987 = c161*c2986; c2988 = 10072866/15625; c2989 = c164*c2988; 
   c2990 = 10114077/78125; c2991 = c168*c2990; c2992 = 2016009/78125; c2993 = c152*c2992; 
   c2994 = 10057386/1953125; c2995 = c172*c2994; c2996 = 10160844/9765625; c2997 = c185*c2996; 
   c2998 = c2977 + c2979 + c2981 + c2983 + c2985 + c2987 + c2989 + c2991 + c2993 + c2995 + c2997; 
   c2999 = c150*c2998*c78; c3000 = 8556216; c3001 = 8623752/5; c3002 = c150*c3001; c3003 = 8555244/25; 
   c3004 = c155*c3003; c3005 = 1696428/25; c3006 = c179*c3005; c3007 = 1703849/125; c3008 = c158*c3007; 
   c3009 = 1710579/625; c3010 = c161*c3009; c3011 = 1711026/3125; c3012 = c164*c3011; 
   c3013 = 8578836/78125; c3014 = c168*c3013; c3015 = 8556774/390625; c3016 = c152*c3015; 
   c3017 = 8488329/1953125; c3018 = c172*c3017; c3019 = 8508144/9765625; c3020 = c185*c3019; 
   c3021 = c3000 + c3002 + c3004 + c3006 + c3008 + c3010 + c3012 + c3014 + c3016 + c3018 + c3020; 
   c3022 = c152*c181*c3021; c3023 = 8555130; c3024 = 8578836/5; c3025 = c150*c3024; c3026 = 8556774/25; 
   c3027 = c155*c3026; c3028 = 8488329/125; c3029 = c179*c3028; c3030 = 8508144/625; c3031 = c158*c3030; 
   c3032 = 8556216/3125; c3033 = c161*c3032; c3034 = 8623752/15625; c3035 = c164*c3034; 
   c3036 = 8555244/78125; c3037 = c168*c3036; c3038 = 1696428/78125; c3039 = c152*c3038; 
   c3040 = 1703849/390625; c3041 = c172*c3040; c3042 = 1710579/1953125; c3043 = c185*c3042; 
   c3044 = c3023 + c3025 + c3027 + c3029 + c3031 + c3033 + c3035 + c3037 + c3039 + c3041 + c3043; 
   c3045 = c166*c168*c3044; c3046 = 8482140; c3047 = 1703849; c3048 = c150*c3047; c3049 = 1710579/5; 
   c3050 = c155*c3049; c3051 = 1711026/25; c3052 = c179*c3051; c3053 = 8578836/625; c3054 = c158*c3053; 
   c3055 = 8556774/3125; c3056 = c161*c3055; c3057 = 8488329/15625; c3058 = c164*c3057; 
   c3059 = 8508144/78125; c3060 = c168*c3059; c3061 = 8556216/390625; c3062 = c152*c3061; 
   c3063 = 8623752/1953125; c3064 = c172*c3063; c3065 = 8555244/9765625; c3066 = c185*c3065; 
   c3067 = c3046 + c3048 + c3050 + c3052 + c3054 + c3056 + c3058 + c3060 + c3062 + c3064 + c3066; 
   c3068 = c170*c172*c3067; c3069 = 8623752; c3070 = 8555244/5; c3071 = c150*c3070; c3072 = 1696428/5; 
   c3073 = c155*c3072; c3074 = 1703849/25; c3075 = c179*c3074; c3076 = 1710579/125; c3077 = c158*c3076; 
   c3078 = 1711026/625; c3079 = c161*c3078; c3080 = 8578836/15625; c3081 = c164*c3080; 
   c3082 = 8556774/78125; c3083 = c168*c3082; c3084 = 8488329/390625; c3085 = c152*c3084; 
   c3086 = 8508144/1953125; c3087 = c172*c3086; c3088 = 8556216/9765625; c3089 = c185*c3088; 
   c3090 = c3069 + c3071 + c3073 + c3075 + c3077 + c3079 + c3081 + c3083 + c3085 + c3087 + c3089; 
   c3091 = c150*c3090*c78; c3092 = 8555244; c3093 = 1696428; c3094 = c150*c3093; c3095 = 1703849/5; 
   c3096 = c155*c3095; c3097 = 1710579/25; c3098 = c179*c3097; c3099 = 1711026/125; c3100 = c158*c3099; 
   c3101 = 8578836/3125; c3102 = c161*c3101; c3103 = 8556774/15625; c3104 = c164*c3103; 
   c3105 = 8488329/78125; c3106 = c168*c3105; c3107 = 8508144/390625; c3108 = c152*c3107; 
   c3109 = 8556216/1953125; c3110 = c172*c3109; c3111 = 8623752/9765625; c3112 = c185*c3111; 
   c3113 = c3092 + c3094 + c3096 + c3098 + c3100 + c3102 + c3104 + c3106 + c3108 + c3110 + c3112; 
   c3114 = c163*c164*c3113; c3115 = c2749 + c2751 + c2753 + c2755 + c2757 + c2759 + c2761 + c2763 + c2765 + 
     c2767 + c2769; c3116 = c154*c155*c3115; c3117 = c157*c158*c2791; c3118 = c160*c161*c2814; 
   c3119 = c178*c179*c2837; c3120 = c183*c185*c2860; 
   c3121 = c3022 + c3045 + c3068 + c3091 + c3114 + c3116 + c3117 + c3118 + c3119 + c3120; c3122 = 9264939; 
   c3123 = 9284754/5; c3124 = c150*c3123; c3125 = 9332826/25; c3126 = c155*c3125; c3127 = 9400362/125; 
   c3128 = c179*c3127; c3129 = 9331854/625; c3130 = c158*c3129; c3131 = 14814/5; c3132 = c161*c3131; 
   c3133 = 1859171/3125; c3134 = c164*c3133; c3135 = 1865901/15625; c3136 = c168*c3135; 
   c3137 = 1866348/78125; c3138 = c152*c3137; c3139 = 9355446/1953125; c3140 = c172*c3139; 
   c3141 = 9333384/9765625; c3142 = c185*c3141; c3143 = 8128995; c3144 = 1626246; c3145 = c150*c3144; 
   c3146 = 8154936/25; c3147 = c155*c3146; c3148 = 8132874/125; c3149 = c179*c3148; c3150 = 8064429/625; 
   c3151 = c158*c3150; c3152 = 8084244/3125; c3153 = c161*c3152; c3154 = 8132316/15625; c3155 = c164*c3154; 
   c3156 = 8199852/78125; c3157 = c168*c3156; c3158 = 8131344/390625; c3159 = c152*c3158; 
   c3160 = 1611648/390625; c3161 = c172*c3160; c3162 = 1619069/1953125; c3163 = c185*c3162; 
   c3164 = c3143 + c3145 + c3147 + c3149 + c3151 + c3153 + c3155 + c3157 + c3159 + c3161 + c3163; 
   c3165 = c157*c158*c3164; c3166 = c152*c181*c3067; c3167 = c170*c172*c3113; c3168 = 9284754; 
   c3169 = 9332826/5; c3170 = c150*c3169; c3171 = 9400362/25; c3172 = c155*c3171; c3173 = 9331854/125; 
   c3174 = c179*c3173; c3175 = 14814; c3176 = c158*c3175; c3177 = 1859171/625; c3178 = c161*c3177; 
   c3179 = 1865901/3125; c3180 = c164*c3179; c3181 = 1866348/15625; c3182 = c168*c3181; 
   c3183 = 9355446/390625; c3184 = c152*c3183; c3185 = 9333384/1953125; c3186 = c172*c3185; 
   c3187 = 9264939/9765625; c3188 = c185*c3187; c3189 = c3168 + c3170 + c3172 + c3174 + c3176 + c3178 + 
     c3180 + c3182 + c3184 + c3186 + c3188; c3190 = c154*c155*c3189; c3191 = c166*c168*c3115; 
   c3192 = c163*c164*c2791; c3193 = 9355446; c3194 = 9333384/5; c3195 = c150*c3194; c3196 = 9264939/25; 
   c3197 = c155*c3196; c3198 = 9284754/125; c3199 = c179*c3198; c3200 = 9332826/625; c3201 = c158*c3200; 
   c3202 = 9400362/3125; c3203 = c161*c3202; c3204 = 9331854/15625; c3205 = c164*c3204; c3206 = 14814/125; 
   c3207 = c168*c3206; c3208 = 1859171/78125; c3209 = c152*c3208; c3210 = 1865901/390625; 
   c3211 = c172*c3210; c3212 = 1866348/1953125; c3213 = c185*c3212; 
   c3214 = c3193 + c3195 + c3197 + c3199 + c3201 + c3203 + c3205 + c3207 + c3209 + c3211 + c3213; 
   c3215 = c160*c161*c3214; c3216 = c178*c179*c2860; c3217 = 9743586; c3218 = 9743586/5; 
   c3219 = c150*c3218; c3220 = 9743586/25; c3221 = c155*c3220; c3222 = 9743586/125; c3223 = c179*c3222; 
   c3224 = 9743586/625; c3225 = c158*c3224; c3226 = 9743586/3125; c3227 = c161*c3226; 
   c3228 = 9743586/15625; c3229 = c164*c3228; c3230 = 9743586/78125; c3231 = c168*c3230; 
   c3232 = 9743586/390625; c3233 = c152*c3232; c3234 = 9743586/1953125; c3235 = c172*c3234; 
   c3236 = 9743586/9765625; c3237 = c185*c3236; c3238 = c3217 + c3219 + c3221 + c3223 + c3225 + c3227 + 
     c3229 + c3231 + c3233 + c3235 + c3237; c3239 = c157*c158*c3238; c3240 = c150*c2883*c78; 
   c3241 = c183*c185*c2952; c3242 = c3122 + c3124 + c3126 + c3128 + c3130 + c3132 + c3134 + c3136 + c3138 + 
     c3140 + c3142 + c3165 + c3166 + c3167 + c3190 + c3191 + c3192 + c3215 + c3216 + c3239 + c3240 + c3241; 
   c3243 = c1*c153*c230; c3244 = c1*c176*c253; c3245 = c188 + c190 + c192 + c194 + c196 + c198 + c200 + 
     c202 + c204 + c206 + c208 + c3243 + c3244; 
   c1*(c2*(-(1/625)*c158*(c1283 + c1285 + c1287 + c1289 + c1291 + c1292 + c1294 + c1296 + c1298 + c1300 + 
         c1302 + c1323 + c1345 + c1365 + c1388 + c1411 + c1434 + c1457 + c1478 + c1499 + c1520 + 
         c1*c153*c1757 + c1*c1640*c176)*c255^c1282 - (c179*c255^c2)/125 - 
       (c152*(c1*c153*c174 + c1*c176*c187)*c255^c256)/390625 - 
       1/1953125*c172*c255^c2253*(c2254 + c2256 + c2258 + c2260 + c2262 + c2264 + c2266 + c2268 + c2270 + 
          c2272 + c2274 + c2297 + c2320 + c2343 + c2366 + c2389 + c2412 + c2435 + c2458 + c2481 + c2504 + 
          c1*c176*c2626 + c1*c153*c2747) - 1/15625*c164*c255^c2748*(c2749 + c2751 + c2753 + c2755 + c2757 + 
          c2759 + c2761 + c2763 + c2765 + c2767 + c2769 + c2792 + c2815 + c2838 + c2861 + c2884 + c2907 + 
          c2930 + c2953 + c2976 + c2999 + c1*c176*c3121 + c1*c153*c3242) - 
       1/3125*c161*c255^c257*(c259 + c261 + c263 + c269 + c273 + c277 + c279 + c283 + c287 + c289 + c293 + 
          c295 + c297 + c1*c153*c314 + c1*c176*c328) - 1/25*c155*c255^c329*(c331 + c333 + c335 + c337 + 
         c339 + c341 + c343 + c345 + c347 + c361 + c369 + c379 + c383 + c392 + c400 + c404 + c406 + c408 + 
         c410 + c1*c176*c445 + c1*c153*c475) + c1*(c3 + c7) + c150*(c1759 + c1761 + c1763 + c1765 + c1767 + 
         c1769 + c1771 + c1773 + c1775 + c1777 + c1779 + c1802 + c1825 + c1848 + c1871 + c1894 + c1917 + 
         c1940 + c1963 + c1986 + c2009 + c1*c176*c2131 + c1*c153*c2252)*c255^c1758*c75 - 
       1/9765625*c185*c255^c476*(c477 + c479 + c481 + c483 + c485 + c486 + c488 + c490 + c492 + c494 + 
          c496 + c518 + c538 + c558 + c575 + c594 + c610 + c628 + c648 + c662 + c680 + c1*c176*c751 + 
          c1*c153*c810) - 1/78125*c168*c255^c811*(c1014 + c1037 + c1060 + c1*c1281*c153 + c1*c1175*c176 + 
          c812 + c814 + c816 + c818 + c820 + c822 + c824 + c826 + c828 + c830 + c832 + c855 + c878 + c901 + 
          c923 + c946 + c969 + c992)) + 
     c2*(c1*(c175 + c3) + (c1283 + c1285 + c1287 + c1289 + c1291 + c1292 + c1294 + c1296 + c1298 + c1300 + 
         c1302 + c1323 + c1345 + c1365 + c1388 + c1411 + c1434 + c1457 + c1478 + c1499 + c1520 + 
         c1*c153*c1640 + c1*c1757*c176)*c3245^c1282*c8 + (c1759 + c1761 + c1763 + c1765 + c1767 + c1769 + 
         c1771 + c1773 + c1775 + c1777 + c1779 + c1802 + c1825 + c1848 + c1871 + c1894 + c1917 + c1940 + 
         c1963 + c1986 + c2009 + c1*c153*c2131 + c1*c176*c2252)*c3245^c1758*c8 + c3245^c2*c8 + 
       (c2254 + c2256 + c2258 + c2260 + c2262 + c2264 + c2266 + c2268 + c2270 + c2272 + c2274 + c2297 + 
         c2320 + c2343 + c2366 + c2389 + c2412 + c2435 + c2458 + c2481 + c2504 + c1*c153*c2626 + 
         c1*c176*c2747)*c3245^c2253*c8 + (c1*c174*c176 + c1*c153*c187)*c3245^c256*c8 + 
       (c2749 + c2751 + c2753 + c2755 + c2757 + c2759 + c2761 + c2763 + c2765 + c2767 + c2769 + c2792 + 
         c2815 + c2838 + c2861 + c2884 + c2907 + c2930 + c2953 + c2976 + c2999 + c1*c153*c3121 + 
         c1*c176*c3242)*c3245^c2748*c8 + c3245^c257*(c259 + c261 + c263 + c269 + c273 + c277 + c279 + 
         c283 + c287 + c289 + c293 + c295 + c297 + c1*c176*c314 + c1*c153*c328)*c8 + 
       c3245^c329*(c331 + c333 + c335 + c337 + c339 + c341 + c343 + c345 + c347 + c361 + c369 + c379 + 
         c383 + c392 + c400 + c404 + c406 + c408 + c410 + c1*c153*c445 + c1*c176*c475)*c8 + 
       c3245^c476*c8*(c477 + c479 + c481 + c483 + c485 + c486 + c488 + c490 + c492 + c494 + c496 + c518 + 
         c538 + c558 + c575 + c594 + c610 + c628 + c648 + c662 + c680 + c1*c153*c751 + c1*c176*c810) + 
       c3245^c811*c8*(c1014 + c1037 + c1060 + c1*c1175*c153 + c1*c1281*c176 + c812 + c814 + c816 + c818 + 
         c820 + c822 + c824 + c826 + c828 + c830 + c832 + c855 + c878 + c901 + c923 + c946 + c969 + c992))));

v4.2

ByteCount[expr] Megabyte/1024.^2

N[expr,20]//Timing

v5.0

ByteCount[expr] Megabyte/1024.^2

N[expr,20]//Timing

sin((π/23))

Polynomial Root

RootReduce[Simplify[TrigToExp[Sin[Pi/23]]]]

N[%,20]

N[Sin[Pi/23],20]

With[{n=23},If[n==2,1,EulerPhi[n]/{1,1,2,1}[[Mod[n,4]+1]]]]