Starting with polynomial:
P : 1300075/1024*t^13 - 2028117/512*t^11 + 4849845/1024*t^9 - 692835/256*t^7 + 765765/1024*t^5 - 45045/512*t^3 + 3003/1024*t
Extension levels are: 13 40
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : 1300075/1024*t^13 - 2028117/512*t^11 + 4849845/1024*t^9 - 692835/256*t^7 + 765765/1024*t^5 - 45045/512*t^3 + 3003/1024*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1300075/1024*t^53 - 64335810708197587874858174381297366846628948558242515968462147481277706872638073/3903626987468104258799916984011184288074498728225829314543640431533176355328*t^51 + 1440514589272610718880847074566692312200011391822117399274128682986211033910488673975/14279467520158325378690096327512912125776516347850083632600636698548359107789824*t^49 - 1783518175323133326436515000663413954722403565465478743042470066087458818738025022285775/4606913208691079725299892327663853274578648586725133231967780414869164357150691968*t^47 + 558314357109328950937135792995231530773887685045438656942290113655953415422871780495909025/534401932208165248134787510009006979851123236060115454908262528124823065429480268288*t^45 - 563205704661103668553980874505757388194658954479895814427846615332331928360654847086512225/267200966104082624067393755004503489925561618030057727454131264062411532714740134144*t^43 + 146505908855149869919569550610556141296473529600173678166453549611073384777253867158190275700195/44399715733650993310782550694078326906970871821582572340143175624194674745077509130171904*t^41 - 45579050888604183593525469800729907010031486483824815592194102081113843655561443434297099199225/11099928933412748327695637673519581726742717955395643085035793906048668686269377282542976*t^39 + 76818366614191298756449022603419961651129563495563577040811294171610641507545401487214723887325/18607838424182644411415498699375001727589914450424526338839845487063020184939645736252416*t^37 - 633783243009727279518535352146412986431873168423420052828688132851144143299518186700647906013994575/186980864405399302368108638680669704859687255355090852915832187376752758328366030180732402176*t^35 + 122262723302037338982997639896781806996317315596284334465403307549479332912713726885600102296741375/53423104115828372105173896765905629959910644387168815118809196393357930950961722908780686336*t^33 - 101305364012683425946299768304546330617023956120318304913241264353338110881089953254896865209125/79420955532247294796303650698743706970378727603928875522830550193775027684510544402512832*t^31 + 1371072072467921831172354953111438015820762279927231323194564832360951133374327781422539073339125/2333332900464644660912093461907918563405609514432669032601780302244700813351827028653135616*t^29 - 260735907405364111745142457197917416589328414487224757587308846846413934324551347716670286705625/1166666450232322330456046730953959281702804757216334516300890151122350406675913514326567808*t^27 + 54402125521350975545447927421832057202957146349207852591691473992654113286854352753565658258375/777777633488214886970697820635972854468536504810889677533926767414900271117275676217711872*t^25 - 3482882585174330659929395109918054998115278525634516916139728072343558398976240687457078014275/194444408372053721742674455158993213617134126202722419383481691853725067779318919054427968*t^23 + 7369831215261286220934047229070554820059797796307010022700100893148051874343250654738888683645/1979797612515456075925412634346112720465365648609537360995449953419746144662156266735993856*t^21 - 58912716110956492509766016574105974373517501316701883212108132077040341175574358793319599437675/94888871285562216210425134117588688245161453586928540659139065624617833076307632498560848384*t^19 + 2750620812565742785611081668834574093359946234254197883723783407841167871149648846258309460782025/33590660435089024538490497477626395638787154569772703393335229231114712909012901904490540327936*t^17 - 457279848699245842143810138651065944104727841258830543992708476560445722507426068036741481974275/54584823207019664875047058401142892913029126175880643014169747500561408477145965594797128032896*t^15 + 34765003862598547155432073908937008039186783612830401182009273917939087036262590293437058590676575/53638686271431324017212909388856416102536621322165378535257471877218344063542102191153977813659136*t^13 - 75620362142136080371510806873672338309065404215436132941785893291345523837688004451455345839635/2063026395055050923738958053417554465482177743160206866740671995277628617828542391967460685140736*t^11 + 542430993750741194729351702176037370813737763501846362191032381040239666240523915045604625225/375095708191827440679810555166828084633123226029128521225576726414114294150644071266811033661952*t^9 - 170892827918384981468522512676089326905467139550730375205627075866468313315126056205531692575/4594922425349886148327679300793644036755759518856824385013314898572900103345389873018435162358912*t^7 + 1285156718516799383006934899847784794916089296203286953074739239867094926845361778928675/2292160591307544377790199813328499862445973445834918942452236652028633835927113486571520939008*t^5 - 10749702869922965656839930148094452756559606879015122591987197147698035228161876184170475/2625669957342792084758673886167796592431862582203899648579037084898800059054508498867677235633664*t^3 + 48690295841841970563945896233134046473993733920635500887445824562122968909608299395541/5251339914685584169517347772335593184863725164407799297158074169797600118109016997735354471267328*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (0.99876926125135689411 - 3.7886136190957542381e-822j)  +/-  (5.31e-238, 5.31e-238j)
| (0.99353155713819377503 - 3.0845158450256995903e-835j)  +/-  (1.71e-237, 1.71e-237j)
| (-0.89712307663800694986 + 1.1605983582813033529e-853j)  +/-  (1.33e-237, 1.33e-237j)
| (-0.9708971113963602745 - 2.7327673370572074997e-853j)  +/-  (3.48e-237, 3.48e-237j)
| (0.91759839922297796521 + 1.4495020385047615201e-851j)  +/-  (2.88e-237, 2.88e-237j)
| (0.93539445262475808956 - 1.5418853170559422032e-880j)  +/-  (4.03e-237, 4.03e-237j)
| (-0.95413480065212929242 - 2.2780957025898464099e-900j)  +/-  (3.95e-237, 3.95e-237j)
| (-0.91759839922297796521 - 1.9877426781736132965e-900j)  +/-  (2.92e-237, 2.92e-237j)
| (-0.99353155713819377503 + 8.1075215261513158244e-900j)  +/-  (1.77e-237, 1.77e-237j)
| (0.98418305471858814947 + 2.0040204667374034548e-899j)  +/-  (3.08e-237, 3.08e-237j)
| (0.89712307663800694986 - 1.4931526397699267972e-909j)  +/-  (1.46e-237, 1.46e-237j)
| (-0.99876926125135689411 - 2.6407068384811522182e-914j)  +/-  (5.53e-238, 5.53e-238j)
| (-0.86985557477808483753 + 1.2408764441014675934e-915j)  +/-  (4.25e-238, 4.25e-238j)
| (-0.76256893507052394991 - 2.7466979386076549609e-917j)  +/-  (7.24e-240, 7.24e-240j)
| (0.9708971113963602745 + 2.6476132814369535463e-913j)  +/-  (3.71e-237, 3.71e-237j)
| (0.86985557477808483753 + 7.3114729806040124014e-926j)  +/-  (4.25e-238, 4.25e-238j)
| (0.68085010793338287234 - 6.0570459877538469733e-929j)  +/-  (4.08e-241, 4.08e-241j)
| (-0.98418305471858814947 - 4.2986453202100184965e-925j)  +/-  (2.8e-237, 2.8e-237j)
| (-0.80157809073330991279 + 3.7799698809263597514e-929j)  +/-  (2.84e-239, 2.84e-239j)
| (-0.93539445262475808956 - 2.2386765144337240426e-926j)  +/-  (4.34e-237, 4.34e-237j)
| (0.80157809073330991279 + 1.4428833910890695734e-926j)  +/-  (2.89e-239, 2.89e-239j)
| (0.76256893507052394991 - 1.2169142560406385152e-927j)  +/-  (6.76e-240, 6.76e-240j)
| (0.95413480065212929242 - 4.6720880994863848851e-930j)  +/-  (3.66e-237, 3.66e-237j)
| (-0.72162447029681646909 - 6.968386240721410561e-942j)  +/-  (1.73e-240, 1.73e-240j)
| (-0.68085010793338287234 + 1.6456588094015775507e-943j)  +/-  (4.19e-241, 4.19e-241j)
| (0.23045831595513479407 + 1.5005303908509638217e-953j)  +/-  (2.61e-250, 2.61e-250j)
| (0.72162447029681646909 - 1.5655013524895730632e-940j)  +/-  (1.65e-240, 1.65e-240j)
| (0.83759686470219160165 - 6.9805384644715088581e-943j)  +/-  (1.11e-238, 1.11e-238j)
| (-0.33558225828270120222 - 1.9901274583604741832e-952j)  +/-  (3.85e-248, 3.85e-248j)
| (-0.64234933944034022064 - 2.7400981444893222552e-945j)  +/-  (9.01e-242, 9.01e-242j)
| (-0.83759686470219160165 + 6.122417418392633286e-948j)  +/-  (1.1e-238, 1.1e-238j)
| (0.55496520057099842221 + 3.7575801719689648827e-950j)  +/-  (1.47e-243, 1.47e-243j)
| (0.64234933944034022064 + 7.4493260139550952024e-949j)  +/-  (9.16e-242, 9.16e-242j)
| (0.39214554347268456581 - 1.0812207244143494251e-955j)  +/-  (5.06e-247, 5.06e-247j)
| (-0.60187576503397872036 + 2.0788895331605555155e-952j)  +/-  (1.48e-242, 1.48e-242j)
| (-0.50319540135741869547 - 1.3357035756870911235e-955j)  +/-  (1.08e-244, 1.08e-244j)
| (0.12239993026289953592 + 1.4507634753917636477e-962j)  +/-  (6.62e-253, 6.62e-253j)
| (0.60187576503397872036 - 4.6113708621820319655e-954j)  +/-  (1.46e-242, 1.46e-242j)
| (0.061954273930648668482 - 1.1159694721196175403e-967j)  +/-  (2.89e-254, 2.89e-254j)
| (-0.12239993026289953592 - 2.2432067763206055844e-965j)  +/-  (6.35e-253, 6.35e-253j)
| (-0.55496520057099842221 - 1.1546741997440945813e-957j)  +/-  (1.47e-243, 1.47e-243j)
| (-0.179092246907487661 - 7.2188264396671225087e-966j)  +/-  (1.72e-251, 1.72e-251j)
| (0.33558225828270120222 + 6.6694367953518064499e-961j)  +/-  (3.65e-248, 3.65e-248j)
| (0.50319540135741869547 - 1.2071198563640273673e-958j)  +/-  (1.11e-244, 1.11e-244j)
| (-3.9008709980285378759e-979 - 7.7395503772791120742e-979j)  +/-  (4.59e-977, 4.59e-977j)
| (-0.44849275103644685288 + 2.2255337005922806927e-962j)  +/-  (8.83e-246, 8.83e-246j)
| (-0.28110787734478358222 - 1.6505035094949868632e-965j)  +/-  (3.11e-249, 3.11e-249j)
| (0.179092246907487661 - 1.9357615201017305343e-969j)  +/-  (1.58e-251, 1.58e-251j)
| (0.44849275103644685288 - 4.8131060301314375969e-961j)  +/-  (7.8e-246, 7.8e-246j)
| (0.28110787734478358222 + 9.9915963270624216657e-966j)  +/-  (3.23e-249, 3.23e-249j)
| (-0.23045831595513479407 + 1.2944682018472773144e-966j)  +/-  (2.77e-250, 2.77e-250j)
| (-0.39214554347268456581 - 3.633884057526386394e-963j)  +/-  (5.36e-247, 5.36e-247j)
| (-0.061954273930648668482 + 1.1403519720703262837e-970j)  +/-  (2.32e-254, 2.32e-254j)
-------------------------------------------------
The weights are:
| (0.0031566836220726632449 + 5.0692443935390936311e-822j)  +/-  (1.45e-53, 5.81e-168j)
| (0.0073103354284411229763 - 8.7531494412410375042e-822j)  +/-  (1.15e-53, 4.61e-168j)
| (0.02404260799316715329 - 7.838111772095340195e-823j)  +/-  (1.09e-54, 4.37e-169j)
| (0.015144814069765016527 - 1.1288700688225764606e-823j)  +/-  (6.91e-55, 2.76e-169j)
| (0.017689776619698136763 + 1.7932823836414569268e-821j)  +/-  (3.89e-55, 1.55e-169j)
| (0.018647000060481420652 - 1.5258915604432169123e-821j)  +/-  (4.39e-55, 1.75e-169j)
| (0.018165967145017793053 + 2.3835584199128820849e-823j)  +/-  (1.65e-55, 6.6e-170j)
| (0.017689776619698136763 + 7.5957385392557934024e-823j)  +/-  (1.64e-55, 6.56e-170j)
| (0.0073103354284411229763 - 2.3011789388601380827e-824j)  +/-  (7.86e-57, 3.14e-171j)
| (0.011359871160203387631 + 7.3288547944660196113e-822j)  +/-  (1.97e-56, 7.88e-171j)
| (0.02404260799316715329 - 1.4619551249033541689e-821j)  +/-  (4.83e-57, 1.93e-171j)
| (0.0031566836220726632449 + 5.9870958317121362793e-825j)  +/-  (2.99e-57, 1.2e-171j)
| (0.030058918958884474632 + 7.0099672447060467123e-823j)  +/-  (1.18e-57, 4.73e-172j)
| (0.040211225775731271424 - 1.0420577568008250685e-822j)  +/-  (2.33e-59, 9.32e-174j)
| (0.015144814069765016527 - 7.9774880130020299422e-822j)  +/-  (1.39e-57, 5.54e-172j)
| (0.030058918958884474632 + 1.0161061444725972724e-821j)  +/-  (5.22e-59, 2.09e-173j)
| (0.039686653638260994202 - 1.1673651761296433322e-821j)  +/-  (1.1e-61, 4.41e-176j)
| (0.011359871160203387631 + 5.3909611854921161586e-824j)  +/-  (6.18e-58, 2.47e-172j)
| (0.037644462715733203448 + 8.0731416780058096116e-823j)  +/-  (2.29e-60, 9.16e-175j)
| (0.018647000060481420652 - 4.9997363167482850473e-823j)  +/-  (3.44e-58, 1.38e-172j)
| (0.037644462715733203448 + 7.370745456812730091e-822j)  +/-  (2.44e-61, 9.76e-176j)
| (0.040211225775731271424 - 7.770591004271559559e-822j)  +/-  (7.1e-62, 2.84e-176j)
| (0.018165967145017793053 + 1.0428849945847996281e-821j)  +/-  (3.1e-59, 1.24e-173j)
| (0.041335875335426527395 + 1.4927031316817382766e-822j)  +/-  (6.7e-63, 2.68e-177j)
| (0.039686653638260994202 - 2.209594359394435397e-822j)  +/-  (8.77e-64, 3.51e-178j)
| (0.049702705594195237629 + 9.1575346745579117047e-822j)  +/-  (1.73e-67, 6.91e-182j)
| (0.041335875335426527395 + 9.2660486309801099581e-822j)  +/-  (1.08e-63, 4.33e-178j)
| (0.034275056074659674321 - 8.0207017332310168267e-822j)  +/-  (4.61e-62, 1.84e-176j)
| (0.055995423917920311779 + 3.586399282668145159e-822j)  +/-  (1.37e-68, 5.5e-183j)
| (0.038171497375023867414 + 2.7843639003958558883e-822j)  +/-  (9.52e-66, 3.81e-180j)
| (0.034275056074659674321 - 7.039531507801230554e-823j)  +/-  (3.46e-63, 1.38e-177j)
| (0.049745411225845138567 + 8.4252481811993545785e-822j)  +/-  (5.93e-68, 2.37e-182j)
| (0.038171497375023867414 + 1.2820471327236796894e-821j)  +/-  (1.59e-66, 6.37e-181j)
| (0.056745386270178945349 - 6.3287109728128654251e-822j)  +/-  (1.31e-69, 5.24e-184j)
| (0.043657678791138330423 - 2.743576479641483065e-822j)  +/-  (5.12e-68, 2.05e-182j)
| (0.053479093147317678855 - 2.2472649570719420775e-822j)  +/-  (1.1e-69, 4.39e-184j)
| (0.059022393616072923298 + 6.0736953994990088746e-822j)  +/-  (5.59e-72, 2.24e-186j)
| (0.043657678791138330423 - 1.1064661145181255879e-821j)  +/-  (1.19e-68, 4.77e-183j)
| (0.061492702584397648382 - 4.8612395275803240989e-822j)  +/-  (2.07e-72, 8.3e-187j)
| (0.059022393616072923298 + 4.7475442726869961132e-822j)  +/-  (2.13e-73, 8.53e-188j)
| (0.049745411225845138567 + 2.406562670091302157e-822j)  +/-  (5.65e-71, 2.26e-185j)
| (0.053943123722867948122 - 5.5054636924420399734e-822j)  +/-  (1.61e-73, 6.42e-188j)
| (0.055995423917920311779 + 7.2159395631435092015e-822j)  +/-  (3.46e-73, 1.38e-187j)
| (0.053479093147317678855 - 6.8109172541171985986e-822j)  +/-  (2.19e-72, 8.74e-187j)
| (0.062178437775335697937 + 4.3164963840239421177e-822j)  +/-  (4.52e-74, 1.81e-188j)
| (0.055724972000419218115 + 2.3515502062373602389e-822j)  +/-  (6.56e-74, 2.62e-188j)
| (0.052501144269412063539 - 4.8267685347549103983e-822j)  +/-  (1.65e-74, 6.61e-189j)
| (0.053943123722867948122 - 7.9112548655330532014e-822j)  +/-  (3.01e-74, 1.21e-188j)
| (0.055724972000419218115 + 6.1847257157055845077e-822j)  +/-  (3.17e-74, 1.27e-188j)
| (0.052501144269412063539 - 8.6080578382244706301e-822j)  +/-  (2.19e-74, 8.74e-189j)
| (0.049702705594195237629 + 5.7237848001929488601e-822j)  +/-  (1.38e-75, 5.54e-190j)
| (0.056745386270178945349 - 2.7601591168886212905e-822j)  +/-  (7.1e-76, 2.88e-190j)
| (0.061492702584397648382 - 4.293373245095074939e-822j)  +/-  (9.02e-76, 3.56e-190j)
