Starting with polynomial:
P : 32*t^5 - 160*t^3 + 120*t
Extension levels are: 5 58
-------------------------------------------------
Trying to find an order 58 Kronrod extension for:
P1 : 32*t^5 - 160*t^3 + 120*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 32*t^63 - 10386226931623322076655036100418944253766785230463920/353429722047178973897232293879307462896964020043*t^61 + 120426240177749823363225211280438699428440984823740707896/9542602495273832295225271934741301498218028541161*t^59 - 32170159144405461233347102339047256082524853210547504322988/9542602495273832295225271934741301498218028541161*t^57 + 181796092121388282887000595570269106716331425192994386757154/289169772584055524097735513173978833279334198217*t^55 - 2797555997741546110578111450094738369517132702477494814692145/32129974731561724899748390352664314808814910913*t^53 + 597761427540893388947509622635488748301273118114172654885595495/64259949463123449799496780705328629617629821826*t^51 - 33677272684417316104023143596358381784060352099194273289829543825/42839966308748966532997853803552419745086547884*t^49 + 4580975376691293591614884577546777472381008223458508620038600965575/85679932617497933065995707607104839490173095768*t^47 - 507621939558803512971383935838903666934126111519736612130162431739975/171359865234995866131991415214209678980346191536*t^45 + 5134853279038428223376145987051103491438245649691078226928622945378625/38079970052221303584886981158713261995632487008*t^43 - 1158841809771094211249163551869824997287036691621652887446669817764626375/228479820313327821509321886952279571973794922048*t^41 + 72293270503811687272428466036233225070828501432079263250708139411358197125/456959640626655643018643773904559143947589844096*t^39 - 1248866563316560964516133258938355958561873579162972279011034887539790157375/304639760417770428679095849269706095965059896064*t^37 + 17925647217422785437912953698992106951713323730508396599688720040319419889875/203093173611846952452730566179804063976706597376*t^35 - 640517689686014401662490628162406306269101500664749779978347826115568753769375/406186347223693904905461132359608127953413194752*t^33 + 18939957910858003290363781067919674953131636158789570366310882347770369012261875/812372694447387809810922264719216255906826389504*t^31 - 461534236322837044929456749680151933554362900783188113175409838685369605176511875/1624745388894775619621844529438432511813652779008*t^29 + 9215601236307726379449116873318046697612466139246672433961591913596014944791068125/3249490777789551239243689058876865023627305558016*t^27 - 149665137729423753565474777534072071669813876195906769790215066062848945780142935625/6498981555579102478487378117753730047254611116032*t^25 + 1958566813983962337141040530833658766218438303189821129281912242187782107988629296875/12997963111158204956974756235507460094509222232064*t^23 - 20414218810375807008793403203980777939101522805603186417294368746242706265680757671875/25995926222316409913949512471014920189018444464128*t^21 + 167055804965005260202232463495384326632065874906996681144745461318761647277345698953125/51991852444632819827899024942029840378036888928256*t^19 - 1054353326338231825103578301775936946678204299331513015465827321637386123615526140515625/103983704889265639655798049884059680756073777856512*t^17 + 5019268276982009321712994465357408878906208092410675132729696608137631113377008712484375/207967409778531279311596099768119361512147555713024*t^15 - 17522114313187843748625008209462981382576247935430350973476935996542006806286157500984375/415934819557062558623192199536238723024295111426048*t^13 + 43251515449320393689269373841458674813355352498019668048369962946184974397073054609765625/831869639114125117246384399072477446048590222852096*t^11 - 910176455723588730945697508039939012147394581423262711247838873545056618835289772796875/21059990863648737145478086052467783444268106907648*t^9 + 75184188224446359481676096412775253459648841604772417710360547863034650068913392056109375/3327478556456500468985537596289909784194360891408384*t^7 - 44524760954396483135651423494396494619353223516009861004763500882639284215639394722234375/6654957112913000937971075192579819568388721782816768*t^5 + 12396054309779174121416696030538436515359150195034654652337360674598167130974215249140625/13309914225826001875942150385159639136777443565633536*t^3 - 1046255755876800847612104387793456308428958207687884014197105744609823744016489513203125/26619828451652003751884300770319278273554887131267072*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: 0
  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
Positive weights:   63 out of 63
Indefinite weights: 0 out of 63
Negative weights:   0 out of 63
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (7.3947432330096874262 + 8.5376249352899650652e-758j)  +/-  (1.31e-240, 1.31e-240j)
| (-9.6204537335220689657 + 2.0888506534517393413e-773j)  +/-  (1.75e-243, 1.75e-243j)
| (9.6204537335220689657 - 3.4256601590433489702e-770j)  +/-  (1.85e-243, 1.85e-243j)
| (7.0225753108026810498 - 2.3543411498044855091e-784j)  +/-  (2.04e-240, 2.04e-240j)
| (-9.0938713285570916815 + 4.6938590638726401569e-798j)  +/-  (1.57e-242, 1.57e-242j)
| (8.1902157501482229185 - 5.809372940228026649e-810j)  +/-  (2.69e-241, 2.69e-241j)
| (7.7825893806722442791 + 5.3675276643462272963e-828j)  +/-  (6.64e-241, 6.64e-241j)
| (9.0938713285570916815 + 5.9390010863478693804e-847j)  +/-  (1.52e-242, 1.52e-242j)
| (-4.6845160354495095346 - 4.0420961857755301815e-858j)  +/-  (3.33e-241, 3.33e-241j)
| (2.8818669109600130395 - 7.5056021009400956677e-864j)  +/-  (1.76e-244, 1.76e-244j)
| (0.95857246461381850711 + 3.5218838702293329576e-869j)  +/-  (2.74e-250, 2.74e-250j)
| (-2.0201828704560856329 + 8.7943358193734005491e-866j)  +/-  (9.04e-247, 9.04e-247j)
| (-1.4635412852940053839 - 2.9839188474547713766e-867j)  +/-  (1.41e-248, 1.41e-248j)
| (-2.8818669109600130395 - 4.2295619869753997725e-863j)  +/-  (2.07e-244, 2.07e-244j)
| (-5.317810775335332942 + 2.268227137568537127e-857j)  +/-  (1.13e-240, 1.13e-240j)
| (1.1987013514168031852 + 7.6724901036712954333e-870j)  +/-  (2.02e-249, 2.02e-249j)
| (8.6238483313208265355 + 3.1940236644952126574e-861j)  +/-  (8.1e-242, 8.1e-242j)
| (-3.7680770576428719751 + 2.5697693058763805074e-866j)  +/-  (1.39e-242, 1.39e-242j)
| (-2.3046683862059262502 - 3.7291934712311089681e-870j)  +/-  (5.79e-246, 5.79e-246j)
| (5.317810775335332942 + 2.3773969303204765789e-862j)  +/-  (1.14e-240, 1.14e-240j)
| (10.256463004682147608 + 4.5590433611608962679e-868j)  +/-  (8.7e-245, 8.7e-245j)
| (-10.256463004682147608 + 1.404315101202936683e-869j)  +/-  (8.36e-245, 8.36e-245j)
| (-4.3750739789259050502 + 2.3472511746754576582e-864j)  +/-  (1.23e-241, 1.23e-241j)
| (-8.6238483313208265355 + 4.1292954741929651393e-867j)  +/-  (7.86e-242, 7.86e-242j)
| (-7.0225753108026810498 - 1.5556103786492313496e-863j)  +/-  (2.06e-240, 2.06e-240j)
| (3.4697336862959418068 - 5.9044089323337141321e-868j)  +/-  (3.6e-243, 3.6e-243j)
| (0.7471336316916944499 + 3.1770890313282684976e-874j)  +/-  (3.87e-251, 3.87e-251j)
| (4.6845160354495095346 + 1.1199790638221754117e-863j)  +/-  (2.97e-241, 2.97e-241j)
| (-6.6632023825400190192 + 9.4789509382221413423e-863j)  +/-  (2.46e-240, 2.46e-240j)
| (-1.7391790692012749877 - 9.9723253161453484115e-871j)  +/-  (1.11e-247, 1.11e-247j)
| (4.9985646339905355082 - 1.0566322724398971608e-863j)  +/-  (6.3e-241, 6.3e-241j)
| (4.3750739789259050502 - 4.8148385808048840948e-865j)  +/-  (1.2e-241, 1.2e-241j)
| (1.7391790692012749877 + 7.8803214232312710322e-871j)  +/-  (1.09e-247, 1.09e-247j)
| (-1.1987013514168031852 + 1.0886848958495831432e-872j)  +/-  (2.01e-249, 2.01e-249j)
| (-3.4697336862959418068 + 4.6409375636328441957e-866j)  +/-  (3.73e-243, 3.73e-243j)
| (4.0697366925086459501 - 2.1648885259942114927e-866j)  +/-  (4.23e-242, 4.23e-242j)
| (-3.1744077026966014215 - 6.7405508166911975458e-867j)  +/-  (8.55e-244, 8.55e-244j)
| (2.5919621807434523794 + 2.1848136982087028976e-869j)  +/-  (3.39e-245, 3.39e-245j)
| (3.7680770576428719751 + 1.7551502622011839754e-866j)  +/-  (1.32e-242, 1.32e-242j)
| (-6.3144995771862026085 - 7.3145007475032739579e-863j)  +/-  (2.72e-240, 2.72e-240j)
| (-4.0697366925086459501 - 1.4768692415264921376e-865j)  +/-  (4.38e-242, 4.38e-242j)
| (6.6632023825400190192 - 7.1017940763960117327e-864j)  +/-  (2.5e-240, 2.5e-240j)
| (2.0201828704560856329 - 3.3227074807084407176e-873j)  +/-  (8.51e-247, 8.51e-247j)
| (3.1744077026966014215 - 7.5798907345567438329e-870j)  +/-  (8.47e-244, 8.47e-244j)
| (-7.3947432330096874262 - 1.6520242591420807131e-866j)  +/-  (1.33e-240, 1.33e-240j)
| (-0.7471336316916944499 - 2.7003904965318421339e-877j)  +/-  (3.58e-251, 3.58e-251j)
| (-2.5919621807434523794 + 2.205481855479846224e-871j)  +/-  (3.34e-245, 3.34e-245j)
| (6.3144995771862026085 - 5.5631138522037686213e-866j)  +/-  (2.64e-240, 2.64e-240j)
| (2.3046683862059262502 + 6.0414109804516061211e-874j)  +/-  (5.41e-246, 5.41e-246j)
| (0.51997424892678164635 + 3.5875834475318489026e-880j)  +/-  (2.88e-252, 2.88e-252j)
| (-4.9985646339905355082 - 5.4876262443431584061e-868j)  +/-  (5.8e-241, 5.8e-241j)
| (-0.26525515695122017217 + 1.389317898710737088e-881j)  +/-  (1.07e-253, 1.07e-253j)
| (-8.1902157501482229185 - 1.1070142739936640434e-869j)  +/-  (2.69e-241, 2.69e-241j)
| (0.26525515695122017217 - 1.3429134285338804403e-881j)  +/-  (1.07e-253, 1.07e-253j)
| (-5.6429560410933153009 + 9.2676887363131234526e-868j)  +/-  (1.75e-240, 1.75e-240j)
| (-7.7825893806722442791 - 2.7354212568339568752e-869j)  +/-  (6.8e-241, 6.8e-241j)
| (-0.51997424892678164635 + 2.2908532614718877153e-881j)  +/-  (2.85e-252, 2.85e-252j)
| (-2.113060736416677366e-915 - 3.1794853924559214008e-916j)  +/-  (1.35e-913, 1.35e-913j)
| (5.6429560410933153009 - 1.0427358834532043995e-868j)  +/-  (1.86e-240, 1.86e-240j)
| (1.4635412852940053839 + 1.8244752774942600801e-878j)  +/-  (1.39e-248, 1.39e-248j)
| (5.9748431040921622839 + 2.4250423037416518258e-878j)  +/-  (2.38e-240, 2.38e-240j)
| (-5.9748431040921622839 - 8.8811762089831009615e-886j)  +/-  (2.36e-240, 2.36e-240j)
| (-0.95857246461381850711 - 7.7346489505907905709e-898j)  +/-  (3.03e-250, 3.03e-250j)
-------------------------------------------------
The weights are:
| (3.8228250845857101017e-25 - 2.5026979336064795684e-781j)  +/-  (1.36e-62, 3.3e-180j)
| (2.040182398545316494e-41 + 8.2431095248060426709e-792j)  +/-  (7.16e-71, 1.74e-188j)
| (2.040182398545316494e-41 - 6.3017239730405160438e-791j)  +/-  (2.69e-70, 6.55e-188j)
| (7.8747949393735381479e-23 + 1.3972256356089351917e-780j)  +/-  (9.42e-62, 2.29e-179j)
| (3.3828221538127396145e-37 - 1.2267826596955598094e-789j)  +/-  (1.54e-70, 3.75e-188j)
| (1.7445371388952683368e-30 + 7.1309170312903049735e-785j)  +/-  (3.69e-66, 8.98e-184j)
| (1.1103852676686801402e-27 - 4.0903011737145550914e-783j)  +/-  (1.13e-64, 2.75e-182j)
| (3.3828221538127396145e-37 + 1.1904897858814487046e-788j)  +/-  (1.84e-69, 4.48e-187j)
| (5.1837132325659957037e-11 - 7.9659973173586154041e-776j)  +/-  (6.68e-58, 1.63e-175j)
| (4.0620192460984478973e-05 - 5.2114479251474507439e-772j)  +/-  (1.14e-45, 2.77e-163j)
| (0.050000507453921284536 + 1.6957600837172620164e-769j)  +/-  (1.5e-30, 3.65e-148j)
| (0.0026957011305184801246 + 4.4576555769474461648e-771j)  +/-  (1.21e-38, 2.95e-156j)
| (0.017997903441584214552 + 2.64878270211362589e-770j)  +/-  (1.26e-31, 3.07e-149j)
| (4.0620192460984478973e-05 - 2.28855815444098806e-772j)  +/-  (4.14e-47, 1.01e-164j)
| (9.5040974388116047291e-14 - 2.5000914406522648203e-777j)  +/-  (1.64e-61, 4e-179j)
| (0.034282561755713656588 - 8.7037379519725015575e-770j)  +/-  (1.37e-30, 3.34e-148j)
| (1.2747283871710930947e-33 - 1.1242669574451923055e-786j)  +/-  (5.92e-69, 1.44e-186j)
| (1.153931481766658471e-07 + 6.3781040288545098629e-774j)  +/-  (6.99e-54, 1.7e-171j)
| (0.00079608756382887537911 - 1.7471250582624626021e-771j)  +/-  (3.75e-43, 9.13e-161j)
| (9.5040974388116047291e-14 - 1.5302638921961641129e-776j)  +/-  (1.32e-61, 3.21e-179j)
| (8.5498561862400235027e-47 + 8.8209200161360942188e-794j)  +/-  (2.5e-75, 6.09e-193j)
| (8.5498561862400235027e-47 - 1.4301006330442675464e-794j)  +/-  (8.02e-79, 1.95e-196j)
| (8.4344459164425584804e-10 + 3.7955359546543430491e-775j)  +/-  (3.37e-58, 8.2e-176j)
| (1.2747283871710930947e-33 + 8.6264903110187483345e-788j)  +/-  (2.17e-74, 5.27e-192j)
| (7.8747949393735381479e-23 + 3.6067910969624526579e-782j)  +/-  (2.45e-70, 5.95e-188j)
| (9.8942010259366986349e-07 - 6.3109487494294425436e-773j)  +/-  (2.18e-57, 5.31e-175j)
| (0.068200915950434148342 - 2.3485230290672410943e-769j)  +/-  (1.11e-39, 2.71e-157j)
| (5.1837132325659957037e-11 - 3.550379356197447012e-775j)  +/-  (1.24e-62, 3.01e-180j)
| (1.0427431526009219406e-20 - 4.7342124787853006024e-781j)  +/-  (5.58e-70, 1.36e-187j)
| (0.007640080757991689716 - 1.0973526933544710216e-770j)  +/-  (2.29e-46, 5.58e-164j)
| (2.5160838868697432886e-12 + 7.7452274288355891163e-776j)  +/-  (1.07e-63, 2.61e-181j)
| (8.4344459164425584804e-10 + 1.4793926304079793423e-774j)  +/-  (4.56e-62, 1.11e-179j)
| (0.007640080757991689716 - 1.772260723936720478e-770j)  +/-  (7.51e-51, 1.83e-168j)
| (0.034282561755713656588 - 6.2755655601205219208e-770j)  +/-  (1.56e-45, 3.8e-163j)
| (9.8942010259366986349e-07 - 2.2799564373242620098e-773j)  +/-  (3.03e-59, 7.38e-177j)
| (1.0974227420646946497e-08 - 5.6275084554963254255e-774j)  +/-  (1.41e-61, 3.43e-179j)
| (6.9710671269822142587e-06 + 7.5033275760314433109e-773j)  +/-  (2.22e-58, 5.4e-176j)
| (0.00019680130988026096746 + 1.3550215114708475364e-771j)  +/-  (3.12e-57, 7.59e-175j)
| (1.153931481766658471e-07 + 1.9631701851353536373e-773j)  +/-  (7.82e-61, 1.9e-178j)
| (9.361114422353682542e-19 + 5.1293974069361009249e-780j)  +/-  (5.59e-72, 1.36e-189j)
| (1.0974227420646946497e-08 - 1.632128325298123765e-774j)  +/-  (7.2e-63, 1.75e-180j)
| (1.0427431526009219406e-20 - 9.0976876433478129915e-780j)  +/-  (2.12e-71, 5.16e-189j)
| (0.0026957011305184801246 + 7.8087313232299248977e-771j)  +/-  (8.37e-57, 2.03e-174j)
| (6.9710671269822142587e-06 + 1.8790876010097796407e-772j)  +/-  (4.58e-60, 1.11e-177j)
| (3.8228250845857101017e-25 - 2.2068275893419497366e-783j)  +/-  (2.79e-76, 6.77e-194j)
| (0.068200915950434148342 - 1.9175018851769884408e-769j)  +/-  (2.45e-55, 5.99e-173j)
| (0.00019680130988026096746 + 6.5165351045030922608e-772j)  +/-  (8.75e-60, 2.14e-177j)
| (9.361114422353682542e-19 + 6.5096567929454904501e-779j)  +/-  (2.06e-71, 5.04e-189j)
| (0.00079608756382887537911 - 3.3292408462273859526e-771j)  +/-  (2.88e-59, 7.04e-177j)
| (0.10499754428413684274 + 2.3656618286204075461e-769j)  +/-  (8.77e-56, 2.14e-173j)
| (2.5160838868697432886e-12 + 1.497497553411793756e-776j)  +/-  (1.3e-68, 3.18e-186j)
| (0.13792006702557535376 - 1.9825875547516425305e-769j)  +/-  (2.04e-58, 4.96e-176j)
| (1.7445371388952683368e-30 - 3.6396942247435860448e-786j)  +/-  (1.99e-79, 4.84e-197j)
| (0.13792006702557535376 - 2.1301133146364732974e-769j)  +/-  (7.88e-60, 1.93e-177j)
| (2.7451070921968287985e-15 + 3.670803418961887957e-778j)  +/-  (6.84e-72, 1.7e-189j)
| (1.1103852676686801402e-27 + 1.0452479321529290734e-784j)  +/-  (3.94e-78, 9.48e-196j)
| (0.10499754428413684274 + 2.0548274279335765479e-769j)  +/-  (9.01e-61, 2.15e-178j)
| (0.15044624276290676277 + 1.993881659784920768e-769j)  +/-  (7.19e-61, 1.71e-178j)
| (2.7451070921968287985e-15 + 2.7320002847160296506e-777j)  +/-  (1.89e-72, 4.53e-190j)
| (0.017997903441584214552 + 3.9559723323061783454e-770j)  +/-  (5.6e-64, 1.25e-181j)
| (5.9354538011904709645e-17 - 4.4121737635935183858e-778j)  +/-  (2.25e-73, 5.38e-191j)
| (5.9354538011904709645e-17 - 4.6858937425366903961e-779j)  +/-  (7.92e-74, 2.42e-191j)
| (0.050000507453921284536 + 1.3065711719884634453e-769j)  +/-  (2.16e-63, 3.94e-181j)
