Starting with polynomial:
P : 5/2*t^3 - 3/2*t
Extension levels are: 3 8 32
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 5/2*t^3 - 3/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : 5/2*t^11 - 10483/1482*t^9 + 1617/221*t^7 - 69993/20995*t^5 + 68299/109174*t^3 - 3633/109174*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 5/2*t^43 - 12727778157039849914003985210140813638737349291101238720773909854918193735284226667345/471392179847737987580323517716601698284400113345928641200500528901562748118558096718*t^41 + 27984916838032362406529428573502659670539618617957016648782302244855311179134216930598722407/206211687554842602011981473633921704418756540583459848914761957619310878071333535804530895*t^39 - 2489861030408042278939870691173044494317595094743207388461715268876075663860164372810697129161/5907783961001017001501153446389370935365428610048946197856250470040959015622590595943841255*t^37 + 219105140824583331644262067363353220793332697246202598263901426620587227599637151472233734303669/241976356758808778554636284995948206804693582795155467556029985005787225434404738107836785650*t^35 - 2451240863933983211551289143092499334193837821189164418050890591998559594254847516405686893077041/1716608742653666981981713880618314925920355652064455846309248011276349375728777142106183314670*t^33 + 3249573244888654691686384911747899606018104834420333778116357168622941374571587394621547423949476/1898673306268449843707047170986924084730090342434928436069319770048083400427283808693202757135*t^31 - 117937130500737314199759348638862048644249225463083557273469812065203415024812113279759160817200516/74048258944469543904574839668490039304473523354962209006703471031875252616664068539034907528265*t^29 + 3159024327966184439343153764809942758329700162417400228586684634506175700426326050299315486170131983/2710166277367585306907439131866735438543730954791616849645347039766634245769904908528677615534499*t^27 - 7692082764938413115259274121758375668837742882444702915275131657131941207921010176067077953664896593/11388875382100251645836104613969899634905991904038845735689136420671753596896324045811394538214775*t^25 + 6148843151995131909270393043979914609395337221623735197329165504087280369220056949164490726289718/19806739794956959384062790632991129799836507659197992583807193775081310603297954862280686153417*t^23 - 2089969749590631446379039662061413624568403173724634984295977222203857557524438123019673494290802/18507937185451584998222607640663842599847228468430911102901804019338273842425957822131132963029*t^21 + 133684289592841967645710412491888213404291709185509934919400982692883602599138090444123075200453449/4139608617146004511269123242295146128165830100772380450015703498991993916089272566216663406064153*t^19 - 985079004341805068235531363162847936349994399231578833677785685272547737875413847295206077670491/137180012653961163141471920309975602687756553047037948635997971701489077141359909601721789284777*t^17 + 27938650736565062078079335173391529189670590177984492237495656802912296876259719446898722292354836/22876784463175288088592523181104754918811166346373681434297308810218913746809137865934192507196635*t^15 - 11124491251679504916296949678953652854105513171529362280877063990001891326579419160757621567109676/71680591317949236010923239300794898745608321218637535160798234272019263073335298646593803189216123*t^13 + 25004946509767669789190505161809275368810256755393924735156482900512497776896478721636794828322057/1753417541469835157805660776742521369315649703655902783164141422961701973640048074585909954936209778*t^11 - 802987936330933173503827209758725300889867738231357889742037012256526385461682051568381784098361/888094598926280144862607406402056277965069330423119591472746954487095804830673700114941405746911446*t^9 + 1341512351803297791755061363198079392748657640709640283049629300967282775519336336313825959/36358576882268080932719536821503982558137612806972881006826617312990084534130586265247744442271*t^7 - 3638118997885312690122469711137186823348946174759673961335923038209253151568473705936684336273/4193780050485211795184534974676376868168382949220286959732416173966841300589292472765001082693748495*t^5 + 11972974087960658737695634254822190901481371973757364037175367452450269440329198174599085309903/1243036406963816776092696166494078103725108706148893054864688153963771761494666288927546320910427053918*t^3 - 13229526470654654444993786528808421155004757073394751660114606304263425241824510878574291247/414345468987938925364232055498026034575036235382964351621562717987923920498222096309182106970142351306*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-0.99079325588510780584 - 4.0474235129057349614e-879j)  +/-  (1.55e-240, 1.55e-240j)
| (-0.99824211202414544095 - 6.7503018133399998366e-899j)  +/-  (5.09e-241, 5.09e-241j)
| (-0.94118636068750354611 - 3.2837071837444243673e-915j)  +/-  (3.88e-240, 3.88e-240j)
| (0.99824211202414544095 - 4.8074364547977174945e-928j)  +/-  (4.63e-241, 4.63e-241j)
| (0.89517743961337165704 + 3.737004780198566399e-929j)  +/-  (8.91e-241, 8.91e-241j)
| (0.95991152576398518645 - 7.8240519124696055664e-929j)  +/-  (3.94e-240, 3.94e-240j)
| (-0.95991152576398518645 - 1.0416085251713794562e-930j)  +/-  (3.63e-240, 3.63e-240j)
| (-0.89517743961337165704 - 1.2704111268339706223e-945j)  +/-  (8.12e-241, 8.12e-241j)
| (-0.97768378973450271003 + 5.7181999826473514728e-962j)  +/-  (2.65e-240, 2.65e-240j)
| (0.94118636068750354611 + 8.5341193405935427574e-968j)  +/-  (3.89e-240, 3.89e-240j)
| (0.86018069830952675564 + 2.3942836303656656606e-976j)  +/-  (2.35e-241, 2.35e-241j)
| (0.99079325588510780584 - 5.6508370396405114911e-974j)  +/-  (1.52e-240, 1.52e-240j)
| (-0.9225217132136291628 - 2.2424879486889809574e-985j)  +/-  (2.54e-240, 2.54e-240j)
| (-0.77459666924148337704 - 3.2869082009546489614e-996j)  +/-  (1.2e-242, 1.2e-242j)
| (0.97768378973450271003 - 1.2379134217437689446e-993j)  +/-  (2.64e-240, 2.64e-240j)
| (0.81967893274042111351 - 9.7577285256886152732e-997j)  +/-  (5.93e-242, 5.93e-242j)
| (0.9225217132136291628 - 1.1416853716392465891e-997j)  +/-  (2.52e-240, 2.52e-240j)
| (-0.36226816275891688475 + 8.3434341165615561645e-1007j)  +/-  (3.1e-249, 3.1e-249j)
| (-0.81967893274042111351 + 1.6080473766463914384e-996j)  +/-  (5.96e-242, 5.96e-242j)
| (-0.86018069830952675564 + 4.7133789886214134289e-1001j)  +/-  (2.32e-241, 2.32e-241j)
| (0.61714901545025722939 - 1.3578206715377232894e-1005j)  +/-  (5.36e-245, 5.36e-245j)
| (0.77459666924148337704 - 9.1581769427375927519e-1004j)  +/-  (1.27e-242, 1.27e-242j)
| (0.2201334945764722168 - 5.2408970907110855521e-1015j)  +/-  (8.31e-252, 8.31e-252j)
| (-0.72555082087673657936 + 1.0483060779234058595e-1006j)  +/-  (2.44e-243, 2.44e-243j)
| (-0.67298995551131638023 - 1.7454341485415799344e-1007j)  +/-  (3.91e-244, 3.91e-244j)
| (0.14722522284027688619 + 4.0376511018657479683e-1018j)  +/-  (4.38e-253, 4.38e-253j)
| (0.72555082087673657936 + 8.2895494320690401221e-1007j)  +/-  (2.51e-243, 2.51e-243j)
| (0.49575008981926662358 - 5.4030619727046682554e-1011j)  +/-  (6.62e-247, 6.62e-247j)
| (-0.073735173888883940603 - 2.4484542731731128023e-1018j)  +/-  (2.07e-254, 2.07e-254j)
| (-0.61714901545025722939 + 3.9689423376507565009e-1010j)  +/-  (5.15e-245, 5.15e-245j)
| (-0.2919991541426287378 - 5.1921767715278466955e-1016j)  +/-  (1.62e-250, 1.62e-250j)
| (0.2919991541426287378 + 3.2790380368770832166e-1016j)  +/-  (1.61e-250, 1.61e-250j)
| (0.67298995551131638023 + 3.8201199241344257914e-1012j)  +/-  (4.02e-244, 4.02e-244j)
| (0.073735173888883940603 + 7.0203917270837896878e-1021j)  +/-  (2.07e-254, 2.07e-254j)
| (-0.55806685067819680295 - 2.3659129008799813915e-1012j)  +/-  (6.18e-246, 6.18e-246j)
| (-0.49575008981926662358 + 5.0807031972065595102e-1015j)  +/-  (7.21e-247, 7.21e-247j)
| (1.6364146537014938077e-1031 + 6.9513414853571948257e-1032j)  +/-  (7.65e-1030, 7.65e-1030j)
| (0.55806685067819680295 - 3.75769476367970175e-1016j)  +/-  (6.28e-246, 6.28e-246j)
| (0.36226816275891688475 - 3.455751651458835948e-1020j)  +/-  (3.06e-249, 3.06e-249j)
| (-0.2201334945764722168 + 4.0397788054921227583e-1021j)  +/-  (8.61e-252, 8.61e-252j)
| (-0.43035965396280641142 + 4.4268880380503674021e-1017j)  +/-  (4.68e-248, 4.68e-248j)
| (-0.14722522284027688619 - 2.3970237587175056493e-1022j)  +/-  (5.05e-253, 5.05e-253j)
| (0.43035965396280641142 - 1.8993695771269912829e-1018j)  +/-  (4.44e-248, 4.44e-248j)
-------------------------------------------------
The weights are:
| (0.010354952257525082105 - 3.1166832157759001649e-879j)  +/-  (5.65e-71, 1.11e-186j)
| (0.0045054235995968554658 - 1.405547040198744646e-879j)  +/-  (3.63e-71, 7.12e-187j)
| (0.017422303765155584499 + 9.7599028303834884189e-879j)  +/-  (5.72e-72, 1.12e-187j)
| (0.0045054235995968554658 + 5.2637162053562146146e-882j)  +/-  (6.47e-73, 1.27e-188j)
| (0.031720560400367783546 + 2.3050640324046381706e-880j)  +/-  (3.26e-73, 6.39e-189j)
| (0.019243120211514815753 - 1.3092356085762224233e-880j)  +/-  (3.14e-73, 6.16e-189j)
| (0.019243120211514815753 - 8.2700423581774901026e-879j)  +/-  (5.84e-72, 1.15e-187j)
| (0.031720560400367783546 + 4.5466151792376148982e-879j)  +/-  (2.1e-73, 4.12e-189j)
| (0.015728129282725815745 + 8.1654055822834343405e-879j)  +/-  (7.04e-72, 1.38e-187j)
| (0.017422303765155584499 + 2.5060226965776495499e-880j)  +/-  (2.43e-74, 4.77e-190j)
| (0.037952592412385341116 - 1.9532941748523778404e-880j)  +/-  (2.78e-75, 5.46e-191j)
| (0.010354952257525082105 - 2.1150162757558836137e-881j)  +/-  (5.34e-75, 1.05e-190j)
| (0.022319262213550395791 - 8.0266225867054957357e-879j)  +/-  (1.88e-74, 3.69e-190j)
| (0.047153592395734648911 - 1.5433459448548333848e-879j)  +/-  (1.1e-77, 2.15e-193j)
| (0.015728129282725815745 + 5.437914977221016152e-881j)  +/-  (6.42e-75, 1.26e-190j)
| (0.042909255276749185001 + 1.8550471658838135269e-880j)  +/-  (2.44e-77, 4.78e-193j)
| (0.022319262213550395791 - 2.8640862340310233429e-880j)  +/-  (2.82e-75, 5.52e-191j)
| (0.069275342681017897568 + 5.625909505282580532e-880j)  +/-  (8.02e-81, 1.57e-196j)
| (0.042909255276749185001 + 1.9627295019490823589e-879j)  +/-  (4.49e-78, 8.81e-194j)
| (0.037952592412385341116 - 2.7681079902594255861e-879j)  +/-  (1.76e-77, 3.45e-193j)
| (0.057458006953587082653 + 2.2610580892248439452e-880j)  +/-  (1.87e-81, 3.66e-197j)
| (0.047153592395734648911 - 1.8900420838414387648e-880j)  +/-  (1.4e-79, 2.74e-195j)
| (0.072473369690097810926 + 2.9250464474526356441e-880j)  +/-  (3.7e-83, 7.26e-199j)
| (0.050862061548672017572 + 1.2920338442018155584e-879j)  +/-  (1.78e-80, 3.49e-196j)
| (0.054220527963362451246 - 1.1162544189086792126e-879j)  +/-  (2.03e-81, 3.99e-197j)
| (0.073265761260978328993 - 3.1445371084462671418e-880j)  +/-  (4.09e-84, 8.01e-200j)
| (0.050862061548672017572 + 1.9966987248610326244e-880j)  +/-  (1.01e-81, 1.98e-197j)
| (0.063898757553783398446 + 2.4418804821174278913e-880j)  +/-  (1.03e-83, 2.02e-199j)
| (0.073658767897356463228 + 3.9400861481225490644e-880j)  +/-  (3.67e-85, 7.19e-201j)
| (0.057458006953587082653 + 9.7302473480607980476e-880j)  +/-  (1.83e-83, 3.59e-199j)
| (0.071164462778544280858 - 5.0426041753924735249e-880j)  +/-  (3.88e-85, 7.61e-201j)
| (0.071164462778544280858 - 2.7469308577449936268e-880j)  +/-  (4.13e-85, 8.1e-201j)
| (0.054220527963362451246 - 2.1321848661296656034e-880j)  +/-  (1.17e-83, 2.3e-199j)
| (0.073658767897356463228 + 3.3942614822079346058e-880j)  +/-  (2.05e-85, 4.03e-201j)
| (0.060708800251963958253 - 8.4588043390426081978e-880j)  +/-  (2.98e-85, 5.84e-201j)
| (0.063898757553783398446 + 7.3326154778475702448e-880j)  +/-  (8e-86, 1.57e-201j)
| (0.073772421377020722576 - 3.6611658411664694153e-880j)  +/-  (1.95e-86, 3.81e-202j)
| (0.060708800251963958253 - 2.3632528066749092694e-880j)  +/-  (2.25e-86, 4.39e-202j)
| (0.069275342681017897568 + 2.6133516535198357363e-880j)  +/-  (4.9e-87, 9.65e-203j)
| (0.072473369690097810926 + 4.5960839885404290308e-880j)  +/-  (9.38e-88, 1.85e-203j)
| (0.066818738916820441035 - 6.383503557134060932e-880j)  +/-  (1.3e-87, 2.56e-203j)
| (0.073265761260978328993 - 4.2421490576556277778e-880j)  +/-  (7.84e-88, 1.55e-203j)
| (0.066818738916820441035 - 2.5173433953643435741e-880j)  +/-  (5.73e-88, 1.06e-203j)
