Starting with polynomial:
P : 32*t^5 - 160*t^3 + 120*t
Extension levels are: 5 14 32
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P1 : 32*t^5 - 160*t^3 + 120*t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : 32*t^19 - 161072/33*t^17 + 37235888/165*t^15 - 52394888/11*t^13 + 52122616*t^11 - 305527040*t^9 + 935949105*t^7 - 2754381357/2*t^5 + 6473363715/8*t^3 - 1927283085/16*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 32*t^51 - 1459424030363858787147307302990427685031575060979229918753077804509630181627958416817833319215896332551470512/87745432851566710976812014670979861123532323561578632873722248162267583652943548832103083537299186737097*t^49 + 833958955284724527428990177096391926117545380458631823969796511073103244684190539745870055445315562255591463976656/211905220336533607009001015430416364613330561401212398390039229311876214521858670429528946742577535970089255*t^47 - 119462932772966897811096647632741457325298110545660895342497595207001936208086113855380641221255715971931614303435016/211905220336533607009001015430416364613330561401212398390039229311876214521858670429528946742577535970089255*t^45 + 8520862540544831245671399163388202656198869816824602695886976324095070312153520202271105514275264866704452444510533264/155397161580124645139934077982305334049775745027555758819362101495375890649363024981654560944556859711398787*t^43 - 256336294163073537077173873966725087663864481579610285851855486522028677456190817836016188833564844780473417882855885004/66598783534339133631400319135273714592761033583238182351155186355161095992584153563566240404810082733456623*t^41 + 19690671703039150766524543997149857367339812720796388445799900407694829249447652656443232271272893740428194017024608189785/97336683627111041461277389505400044404804587544732728051688349288312371066084532131366043668568582456590449*t^39 - 528935386513286922257188486160114971949941912361000985656312372149045121947154268384036156328446298808343819852680136452111/64891122418074027640851593003600029603203058363155152034458899525541580710723021420910695779045721637726966*t^37 + 199124845866541242925118575943555937344495760290113276778839932383968942131331371385061965978746259042105424864376260954280217/778693469016888331690219116043200355238436700357861824413506794306498968528676257050928349348548659652723592*t^35 - 3530125776103452256869600338891658870547845088648255544017543166182018409755303697972009194368607859312351232466751352718865/559607236088313569306661240419116317095534818798319672593249582685231023017374241502643441860257750379248*t^33 + 2904120330630376794667065641012277055484230842444005443177980704031158638069914680287652904925377140092332304776099287109855455/23596771788390555505764215637672738037528384859329146194348690736560574803899280516694798465107535140991624*t^31 - 89837958676404227821608900280663591393208969594182980613896322634714739708559475247551636748238580900647417649405378296522848475/47193543576781111011528431275345476075056769718658292388697381473121149607798561033389596930215070281983248*t^29 + 1101103308114756643438618116268394826649786472032626874457934170517180878043254396695956252675319006421259508333792200691985936975/47193543576781111011528431275345476075056769718658292388697381473121149607798561033389596930215070281983248*t^27 - 592227917909994481778211978175419151135773235238231094838375540583748318495941825187182719863183643678912227631010146212404921475/2621863532043395056196023959741415337503153873258794021594298970728952755988808946299422051678615015665736*t^25 + 3131888418688050783047008737378545849804490995740278979842194315104878274867729651297140166411830099411393905731621061496762369375/1823905065769318299962451450254897626089150520527856710674294936159271482426997527860467514211210445680512*t^23 - 37060554915740467582237943076054797143642708082372348089935300520053192509962568415041313044651016278690333788642372264848680896875/3647810131538636599924902900509795252178301041055713421348589872318542964853995055720935028422420891361024*t^21 + 70989539468764148941305034038429465822977650016253173774664313699953004517516543743214350635505001985167949227962500662933883939375/1535920055384689094705222273898861158811916227812931966883616788344649669412208444514077906704177217415168*t^19 - 488697517246311774721733036523319972126698854315125143720403800550834581700766303942402006366459125198945303393596079145670993067125/3071840110769378189410444547797722317623832455625863933767233576689299338824416889028155813408354434830336*t^17 + 1246124427031784230670181016379605504398440293203860107247454996930500537308360527904426684116801111479656862620780649365783248955875/3071840110769378189410444547797722317623832455625863933767233576689299338824416889028155813408354434830336*t^15 - 4579348313680312682991676432981670140000983621858811764837965606404898450768081262740742826140465392517815483383026857538455972619375/6143680221538756378820889095595444635247664911251727867534467153378598677648833778056311626816708869660672*t^13 + 132839642686791049206503745922727216278452675269323175751545829048383776981508386430875592139954783635825922123574131315959315713125/139629095944062644973202024899896468982901475255721087898510617122240879037473494955825264245834292492288*t^11 - 896883568509277348118135079023938025677269147355474458335079351809721127523760764030658183166122805107869502170396068236662552953125/1117032767552501159785616199199171751863211802045768703188084936977927032299787959646602113966674339938304*t^9 + 1873003737365984016707975628716387580837481524821005304029515190298488311860535144603136547179752742191332645993386072893248093356875/4468131070210004639142464796796687007452847208183074812752339747911708129199151838586408455866697359753216*t^7 - 1109655324453458106876179965530920983369281226136484414329977169804499417441653956790384405775816374512977916663752474069528612354375/8936262140420009278284929593593374014905694416366149625504679495823416258398303677172816911733394719506432*t^5 + 670507374594183255728158314758949414630309045933833808293058810642897214501074999360767931853605591411520612283255919151341897028125/35745048561680037113139718374373496059622777665464598502018717983293665033593214708691267646933578878025728*t^3 - 79678458941391570434768471026367654053172733616464304519083624029612598960238255597343453992703801589737820348969847674287371771875/71490097123360074226279436748746992119245555330929197004037435966587330067186429417382535293867157756051456*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:
| (-3.5528575550671930628 - 1.7334482146496534475e-890j)  +/-  (2.22e-244, 2.22e-244j)
| (7.4447996622545167016 + 8.2325464159704964659e-893j)  +/-  (1.23e-245, 1.23e-245j)
| (-7.4447996622545167016 - 1.4875123781952726837e-895j)  +/-  (1.3e-245, 1.3e-245j)
| (-3.8879058412990795166 + 2.4632623273606829134e-890j)  +/-  (1.19e-243, 1.19e-243j)
| (-5.9391173299368034216 + 1.2075972273531692213e-899j)  +/-  (2.98e-244, 2.98e-244j)
| (-8.0985567945582748097 + 2.3994612892119472753e-905j)  +/-  (1.55e-246, 1.55e-246j)
| (5.9391173299368034216 + 6.8853153115576484843e-905j)  +/-  (3.09e-244, 3.09e-244j)
| (-9.5373016113985254056 - 2.6205458423175614703e-921j)  +/-  (2.3e-248, 2.3e-248j)
| (-5.0903541712853262333 + 1.8927385493548889304e-914j)  +/-  (6.43e-244, 6.43e-244j)
| (1.7187923623555089224 + 1.2109960105443469621e-921j)  +/-  (4.42e-248, 4.42e-248j)
| (-5.5047468949815531606 - 2.1022578531545068672e-916j)  +/-  (4.68e-244, 4.68e-244j)
| (-0.95857246461381850711 - 8.5603263952494599337e-926j)  +/-  (7.74e-251, 7.74e-251j)
| (-2.594640160845429473 - 1.1584596849792768948e-917j)  +/-  (5.8e-246, 5.8e-246j)
| (5.5047468949815531606 - 1.0601637770026585859e-930j)  +/-  (4.92e-244, 4.92e-244j)
| (9.5373016113985254056 - 1.5749319865066720357e-949j)  +/-  (2.46e-248, 2.46e-248j)
| (2.0201828704560856329 + 8.9363547512361885168e-949j)  +/-  (2.56e-247, 2.56e-247j)
| (8.0985567945582748097 + 7.8219256678146806486e-946j)  +/-  (1.44e-246, 1.44e-246j)
| (-6.3991540093797109807 - 6.6672851682097334188e-947j)  +/-  (1.56e-244, 1.56e-244j)
| (5.0903541712853262333 - 4.3124419600416219413e-946j)  +/-  (6.84e-244, 6.84e-244j)
| (-3.2095060327776332981 - 3.1747629891577461857e-955j)  +/-  (6.07e-245, 6.07e-245j)
| (4.6929196191131403725 + 6.287739405051357042e-954j)  +/-  (8.19e-244, 8.19e-244j)
| (6.3991540093797109807 + 2.0467176346216626908e-961j)  +/-  (1.5e-244, 1.5e-244j)
| (3.5528575550671930628 - 1.606477045516173648e-962j)  +/-  (2.12e-244, 2.12e-244j)
| (2.594640160845429473 + 6.8912045243780455307e-973j)  +/-  (5.7e-246, 5.7e-246j)
| (4.033830770482871939 - 4.7168228227697513569e-974j)  +/-  (1.72e-243, 1.72e-243j)
| (-6.8946902669790913698 + 1.7939452923328967706e-987j)  +/-  (5.34e-245, 5.34e-245j)
| (1.2626423414961939956 - 1.1876929043274022495e-992j)  +/-  (1.47e-249, 1.47e-249j)
| (-2.8861868413382062663 - 7.3984721839214246639e-987j)  +/-  (1.87e-245, 1.87e-245j)
| (6.8946902669790913698 + 1.0062133025704122031e-987j)  +/-  (5.49e-245, 5.49e-245j)
| (-1.2626423414961939956 - 7.7040605498837188279e-992j)  +/-  (1.44e-249, 1.44e-249j)
| (-2.31662704261800368 - 3.9524556547552005617e-988j)  +/-  (1.33e-246, 1.33e-246j)
| (3.2095060327776332981 + 1.6784141932597122209e-986j)  +/-  (5.69e-245, 5.69e-245j)
| (3.8879058412990795166 + 7.0635857564689712992e-991j)  +/-  (1.26e-243, 1.26e-243j)
| (4.3143299182176741975 - 3.3955507866555559358e-1001j)  +/-  (1.14e-243, 1.14e-243j)
| (-2.0201828704560856329 + 6.9190401048433734565e-1005j)  +/-  (2.47e-247, 2.47e-247j)
| (-1.7187923623555089224 + 1.0273652660338755324e-1006j)  +/-  (4.42e-248, 4.42e-248j)
| (-4.3143299182176741975 + 2.4436409125966862971e-1000j)  +/-  (1.17e-243, 1.17e-243j)
| (0.46844531406652970763 - 2.39421165515219418e-1014j)  +/-  (1.84e-251, 1.84e-251j)
| (-4.6929196191131403725 + 1.2316388222840611932e-1008j)  +/-  (8.19e-244, 8.19e-244j)
| (-1.4759224472426343846 - 9.9788488024282089359e-1015j)  +/-  (9.9e-249, 9.9e-249j)
| (-0.55060098022749982601 - 3.8859508210616942651e-1017j)  +/-  (1.36e-251, 1.36e-251j)
| (2.31662704261800368 - 1.7786030300212882275e-1012j)  +/-  (1.28e-246, 1.28e-246j)
| (5.8792244327650477416e-1031 + 2.5415305916354288467e-1030j)  +/-  (1.33e-1028, 1.33e-1028j)
| (0.95857246461381850711 - 3.4586484256074945861e-1017j)  +/-  (7.41e-251, 7.41e-251j)
| (1.4759224472426343846 + 4.2242970914780630176e-1015j)  +/-  (1.04e-248, 1.04e-248j)
| (-0.46844531406652970763 + 8.8096992485173943741e-1017j)  +/-  (1.95e-251, 1.95e-251j)
| (-0.43984473019950202599 - 2.8938887614656622186e-1017j)  +/-  (1.05e-251, 1.05e-251j)
| (-4.033830770482871939 + 9.9110370295956551197e-1016j)  +/-  (1.75e-243, 1.75e-243j)
| (0.43984473019950202599 + 2.6579438622035745823e-1024j)  +/-  (1.15e-251, 1.15e-251j)
| (2.8861868413382062663 + 1.770372774398207348e-1022j)  +/-  (1.81e-245, 1.81e-245j)
| (0.55060098022749982601 + 1.1178671715204877203e-1029j)  +/-  (1.36e-251, 1.36e-251j)
-------------------------------------------------
The weights are:
| (6.4744261851706348721e-07 - 4.9376956142609278779e-896j)  +/-  (4.69e-59, 2.08e-180j)
| (2.8220200211641973062e-25 - 6.5481952132520381774e-910j)  +/-  (8.42e-76, 3.73e-197j)
| (2.8220200211641973062e-25 + 1.8936697059588060587e-909j)  +/-  (1.24e-75, 5.49e-197j)
| (4.3626772630732944057e-08 - 1.3906706982894194445e-896j)  +/-  (1.11e-61, 4.92e-183j)
| (1.2073606619639542245e-16 - 4.5818531379841515786e-904j)  +/-  (3.96e-71, 1.76e-192j)
| (1.3807186620701763181e-29 - 6.1685048082565641028e-912j)  +/-  (6.49e-78, 2.88e-199j)
| (1.2073606619639542245e-16 + 1.1103667906997647489e-904j)  +/-  (1.21e-74, 5.38e-196j)
| (6.366950444489051525e-39 + 7.492518019572336733e-917j)  +/-  (3e-82, 1.33e-203j)
| (1.2771591026282451032e-12 - 3.7615671609517158753e-901j)  +/-  (4.75e-69, 2.11e-190j)
| (0.0084624235657974872881 - 5.894825631428021016e-894j)  +/-  (1.39e-53, 6.15e-175j)
| (1.6533235907327201917e-14 + 1.4106927995293463096e-902j)  +/-  (2.65e-70, 1.18e-191j)
| (0.074824231588132128754 + 7.0577641911450378945e-893j)  +/-  (2.75e-54, 1.22e-175j)
| (0.00018681089838043865055 + 1.026923129324615256e-894j)  +/-  (3.33e-59, 1.48e-180j)
| (1.6533235907327201917e-14 - 2.9063300420005375048e-903j)  +/-  (6.2e-75, 2.75e-196j)
| (6.366950444489051525e-39 - 3.3716738263726704924e-917j)  +/-  (6.36e-87, 2.82e-208j)
| (0.0029040265481560061617 + 1.6162229215746355623e-894j)  +/-  (2.57e-59, 1.14e-180j)
| (1.3807186620701763181e-29 + 2.3586358711118911978e-912j)  +/-  (5.14e-83, 2.28e-204j)
| (4.4127607752859155258e-19 + 1.1557944835820360275e-905j)  +/-  (7.68e-76, 3.41e-197j)
| (1.2771591026282451032e-12 + 6.3134150438974130963e-902j)  +/-  (1.2e-74, 5.33e-196j)
| (6.3663171728239859856e-06 + 1.5461843259939411824e-895j)  +/-  (2.31e-66, 1.02e-187j)
| (5.9826712725258947294e-11 - 1.2636257470793035232e-900j)  +/-  (5.7e-74, 2.53e-195j)
| (4.4127607752859155258e-19 - 3.2049205707251394229e-906j)  +/-  (7.25e-79, 3.22e-200j)
| (6.4744261851706348721e-07 - 1.9288649147563635658e-897j)  +/-  (1.43e-71, 6.34e-193j)
| (0.00018681089838043865055 + 1.6663127224884024196e-895j)  +/-  (4.19e-68, 1.86e-189j)
| (6.0540673341354600682e-09 - 3.5516669158132916917e-898j)  +/-  (3.87e-73, 1.72e-194j)
| (6.6239383250146396002e-22 - 1.9888430429520863996e-907j)  +/-  (1.57e-81, 6.95e-203j)
| (0.030177139354607017545 - 2.5784663968184005091e-893j)  +/-  (3.22e-62, 1.43e-183j)
| (4.1946790102371706182e-05 - 3.7907882499733484142e-895j)  +/-  (8.41e-70, 3.73e-191j)
| (6.6239383250146396002e-22 + 6.1946527101908914551e-908j)  +/-  (1.53e-81, 6.77e-203j)
| (0.030177139354607017545 - 5.3569894345006596235e-893j)  +/-  (2.1e-64, 9.31e-186j)
| (0.00075153343381923663835 - 2.4145072842672241361e-894j)  +/-  (1.04e-68, 4.6e-190j)
| (6.3663171728239859856e-06 + 8.5776819648882285815e-897j)  +/-  (8.4e-72, 3.72e-193j)
| (4.3626772630732944057e-08 + 7.6164026403410641046e-898j)  +/-  (3.53e-73, 1.57e-194j)
| (1.6915511092934892332e-09 + 2.8232275530897902282e-899j)  +/-  (1.48e-74, 6.56e-196j)
| (0.0029040265481560061617 + 5.7397680115368689138e-894j)  +/-  (2.06e-70, 9.12e-192j)
| (0.0084624235657974872881 - 1.6638242650588395937e-893j)  +/-  (7.25e-70, 3.21e-191j)
| (1.6915511092934892332e-09 - 3.3738136677544324464e-898j)  +/-  (8.64e-78, 3.83e-199j)
| (-1.9646922144713575335 + 3.4850618500212256121e-891j)  +/-  (2.16e-70, 9.55e-192j)
| (5.9826712725258947294e-11 + 9.9278573790649785039e-900j)  +/-  (7.69e-79, 3.41e-200j)
| (0.012434556872160757104 + 3.898885182671939073e-893j)  +/-  (1.23e-70, 5.47e-192j)
| (0.57130799583326748052 - 1.1614364032906394775e-891j)  +/-  (2.78e-70, 1.23e-191j)
| (0.00075153343381923663835 - 5.2441052352046423942e-895j)  +/-  (3.58e-74, 1.59e-195j)
| (0.20440494257074916588 + 1.1967224533397992207e-892j)  +/-  (5.03e-71, 2.23e-192j)
| (0.074824231588132128754 + 4.0938449652308781228e-893j)  +/-  (5.69e-72, 2.52e-193j)
| (0.012434556872160757104 + 1.6340521159095441484e-893j)  +/-  (1.79e-72, 7.96e-194j)
| (-1.9646922144713575335 + 4.5253767847447223166e-891j)  +/-  (8.72e-71, 3.86e-192j)
| (1.6613920131082570847 - 3.469665849742220724e-891j)  +/-  (6.39e-71, 2.83e-192j)
| (6.0540673341354600682e-09 + 8.0859676640192465315e-897j)  +/-  (1.03e-78, 4.74e-200j)
| (1.6613920131082570847 - 2.7154510835384078208e-891j)  +/-  (2.92e-72, 1.29e-193j)
| (4.1946790102371706182e-05 - 4.14934310379535304e-896j)  +/-  (1.8e-77, 1.16e-198j)
| (0.57130799583326748052 - 8.5381161199462876883e-892j)  +/-  (7.67e-73, 3.23e-194j)
