Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 54
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P1 : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 256*t^62 - 27821523064529912692435739254262507415791646844411979987405951493208192/128651022320933044139814050041098820260134650050172833883069711283*t^60 + 10971054632015224571667441014053265681931077124430343723243721195148613760/128651022320933044139814050041098820260134650050172833883069711283*t^58 - 126264731659353187834577761585484759035290662617056603376121994960447514677120/6046598049083853074571260351931644552226328552358123192504276430301*t^56 + 495551700460590171259335390075768006561499357916309133006550894917703483722252240/139071755128928620715138988094427824701205556704236833427598357896923*t^54 - 62688528258234849252191444866253152556053598199832713491468448314646480475800845400/139071755128928620715138988094427824701205556704236833427598357896923*t^52 + 469740987722443042562038132380886526987462306726759316624117721620873511126150636800/10697827317609893901164537545725217284708119746479756417507565992071*t^50 - 36132312981476066532479275186190946225139346312172860864741248986007834565509815604500/10697827317609893901164537545725217284708119746479756417507565992071*t^48 + 47510117192017816202489784329422219833326856488714420268945019551684677097648987461625/227613347183189231939671011611174835844853611627228859946969489193*t^46 - 207646533664692037985182965925831426494343021408030772884032228005828547302243858800125/19792464972451237559971392314015203116943792315411205212779955582*t^44 + 8561163447713139347776178791273768675187089569705630444640169527535348033848862806677375/19792464972451237559971392314015203116943792315411205212779955582*t^42 - 145622449868847300452542808590056405307117386890089969442223810272444351922248048613939750/9896232486225618779985696157007601558471896157705602606389977791*t^40 + 65645812970220694529720329535799273031430146036049989618665397963998532464624489736068830625/158339719779609900479771138512121624935550338523289641702239644656*t^38 - 3069521616610752263809841717743576174639468893974529067410303406417734882234582683104551039375/316679439559219800959542277024243249871100677046579283404479289312*t^36 + 29785999235022868124130534124817207738367826830604017462442065854456125061995170547005362311875/158339719779609900479771138512121624935550338523289641702239644656*t^34 - 1917414549401239020330081382082389508646921337515070829268157384913421199870667669178691808754375/633358879118439601919084554048486499742201354093158566808958578624*t^32 + 102097097934195139183591073831271253662991363224199921422847792289839722388456105509317014013023125/2533435516473758407676338216193945998968805416372634267235834314496*t^30 - 2239568736258893179473295850093611397654462311922945465041844530958013470876157971583169246613784375/5066871032947516815352676432387891997937610832745268534471668628992*t^28 + 20126909555686204283871454935614617015580736844977046672886475757826787117511704270562014181652221875/5066871032947516815352676432387891997937610832745268534471668628992*t^26 - 147135949576739816531304405350498824632745868591175252723612509760504276079629989544068681910271265625/5066871032947516815352676432387891997937610832745268534471668628992*t^24 + 6934424032572255809631750698117930572909268481867333069268273947664582795638464976211143152064103171875/40534968263580134522821411459103135983500886661962148275773349031936*t^22 - 65062211031221197641682211049459672726634608902446192953748873061792566792695904020387003315024265453125/81069936527160269045642822918206271967001773323924296551546698063872*t^20 + 59852546422244988588671107992886692705268546881819977321549034080023476537002996453579027024709851953125/20267484131790067261410705729551567991750443330981074137886674515968*t^18 - 1355655997725256677316989268826276413279706777011381663723454855156179810163027687543165823153967285546875/162139873054320538091285645836412543934003546647848593103093396127744*t^16 + 11523200647363883831740943317286412153088780279599966820656992646707087072651876861849328104966076816328125/648559492217282152365142583345650175736014186591394372412373584510976*t^14 - 35580745727882271718734286757843723690876420476319880146157621959682260914055976066608949712799909345484375/1297118984434564304730285166691300351472028373182788744824747169021952*t^12 + 38196531112873247811261224452083809605956634668964227929617181535806694428503987446541419115168477055765625/1297118984434564304730285166691300351472028373182788744824747169021952*t^10 - 13405939065491022162910554882191053679608227136044839888142489981655252651604315915754959164237979106796875/648559492217282152365142583345650175736014186591394372412373584510976*t^8 + 89843674993350492632313634505403994482656789015279847898721680777329624315524813672548207878504525428671875/10376951875476514437842281333530402811776226985462309958597977352175616*t^6 - 38663080496159861154478027386840729783237464272374073602852077881140616277395141614981375867209659731328125/20753903750953028875684562667060805623552453970924619917195954704351232*t^4 + 1595859287606451215642036817876142523570850015220038188755428531743414322825199552021355768896715232421875/10376951875476514437842281333530402811776226985462309958597977352175616*t^2 - 84372965019351699469082569383443729271191791909111685313376792093631767913216852755690697141377981640625/41507807501906057751369125334121611247104907941849239834391909408702464
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (-6.7288787683894446059 - 7.6366429741082566281e-809j)  +/-  (7.18e-241, 7.18e-241j)
| (-8.343531983253122346 - 2.424916345804422208e-820j)  +/-  (3.13e-242, 3.13e-242j)
| (-9.3480670915359134835 + 4.9697428296235051405e-827j)  +/-  (8.91e-244, 8.91e-244j)
| (6.014792341806203692 - 4.633845337467393419e-825j)  +/-  (9.26e-241, 9.26e-241j)
| (7.4953186646073363962 - 4.8534921487089250327e-826j)  +/-  (2.71e-241, 2.71e-241j)
| (9.9889393179176368256 - 1.2357355326590929049e-830j)  +/-  (3.71e-245, 3.71e-245j)
| (-7.1042047681456731885 - 1.0324813471481285943e-824j)  +/-  (4.79e-241, 4.79e-241j)
| (8.8173402894045455675 + 7.7035734940264225499e-833j)  +/-  (7.09e-243, 7.09e-243j)
| (-3.4533776105810735507 + 1.5011150343592653931e-831j)  +/-  (8.93e-243, 8.93e-243j)
| (1.1571937124467801947 - 3.7837954376819935341e-839j)  +/-  (9.36e-250, 9.36e-250j)
| (8.343531983253122346 + 2.6133037473067158688e-831j)  +/-  (3.19e-242, 3.19e-242j)
| (-4.6883651257248000451 - 2.3172693429518547351e-829j)  +/-  (2.31e-241, 2.31e-241j)
| (-9.9889393179176368256 + 1.0282319028826730497e-833j)  +/-  (4.04e-245, 4.04e-245j)
| (-1.9816567566958429259 + 6.4336922548021949376e-835j)  +/-  (1.18e-246, 1.18e-246j)
| (-5.6722914676737676866 - 5.1305393053692172146e-829j)  +/-  (7.94e-241, 7.94e-241j)
| (-5.3376864522649776199 + 1.4435005726503874875e-832j)  +/-  (6.44e-241, 6.44e-241j)
| (6.3664494952160148069 - 2.0657596405803545922e-835j)  +/-  (9.26e-241, 9.26e-241j)
| (-4.3722201808218105292 - 7.5547476085832766594e-837j)  +/-  (1.1e-241, 1.1e-241j)
| (-2.2651834909201651958 - 8.4591496077105245706e-849j)  +/-  (1.13e-245, 1.13e-245j)
| (-0.89396922582288789311 + 5.3656171355447526385e-853j)  +/-  (7.98e-251, 7.98e-251j)
| (9.3480670915359134835 + 7.9920789367339227724e-846j)  +/-  (7.87e-244, 7.87e-244j)
| (3.754699469151045748 + 1.1787187942945898963e-844j)  +/-  (2.13e-242, 2.13e-242j)
| (5.6722914676737676866 + 1.4114230191851660356e-842j)  +/-  (7.9e-241, 7.9e-241j)
| (4.6883651257248000451 + 3.6057287434883422915e-843j)  +/-  (2.14e-241, 2.14e-241j)
| (-7.4953186646073363962 + 1.1105124346157557262e-843j)  +/-  (2.62e-241, 2.62e-241j)
| (5.3376864522649776199 - 4.3276128685612715777e-853j)  +/-  (5.89e-241, 5.89e-241j)
| (7.1042047681456731885 + 3.7912755334517573449e-852j)  +/-  (5.17e-241, 5.17e-241j)
| (1.4265978530975164435 - 1.915141067322847165e-861j)  +/-  (1.08e-248, 1.08e-248j)
| (0.89396922582288789311 - 2.5900667591382592221e-862j)  +/-  (7.5e-251, 7.5e-251j)
| (-1.7017410578955989388 + 1.8431996359484865214e-859j)  +/-  (1.25e-247, 1.25e-247j)
| (3.1602517692489874271 - 6.5965640834761825319e-856j)  +/-  (4.88e-243, 4.88e-243j)
| (-6.3664494952160148069 - 3.4122139166803007683e-852j)  +/-  (8.95e-241, 8.95e-241j)
| (-8.8173402894045455675 - 1.4399935118951756369e-865j)  +/-  (6.64e-243, 6.64e-243j)
| (-3.1602517692489874271 + 2.1440437467539901149e-864j)  +/-  (4.56e-243, 4.56e-243j)
| (5.0099772487479511599 + 1.5480206365346068023e-862j)  +/-  (4e-241, 4e-241j)
| (-2.5500160204537708063 + 1.0316919098837562669e-866j)  +/-  (1.21e-244, 1.21e-244j)
| (-5.0099772487479511599 - 1.1252208322737318097e-862j)  +/-  (4.04e-241, 4.04e-241j)
| (7.9063408947581415529 + 3.9053103209675834911e-869j)  +/-  (1.08e-241, 1.08e-241j)
| (-7.9063408947581415529 - 2.9824364044134534125e-868j)  +/-  (1.11e-241, 1.11e-241j)
| (2.8153593611779900474 + 1.1560807376006070764e-881j)  +/-  (1.64e-243, 1.64e-243j)
| (-0.63606291564586530806 - 5.8690763594697154881e-889j)  +/-  (5.59e-252, 5.59e-252j)
| (4.3722201808218105292 + 2.8857272987193367606e-879j)  +/-  (1.11e-241, 1.11e-241j)
| (1.9816567566958429259 - 3.6244951101688666961e-885j)  +/-  (1.24e-246, 1.24e-246j)
| (1.7017410578955989388 - 1.4807952867686026796e-887j)  +/-  (1.29e-247, 1.29e-247j)
| (2.2651834909201651958 + 1.0410945825932449932e-883j)  +/-  (1.16e-245, 1.16e-245j)
| (-2.8153593611779900474 - 2.1864951674243080762e-879j)  +/-  (1.56e-243, 1.56e-243j)
| (2.9306374202572440192 - 1.4266323817558505358e-880j)  +/-  (3.27e-243, 3.27e-243j)
| (3.4533776105810735507 - 7.7093135613728901638e-881j)  +/-  (9.74e-243, 9.74e-243j)
| (2.5500160204537708063 - 3.5373054281415049104e-882j)  +/-  (1.37e-244, 1.37e-244j)
| (4.0610781730290349198 + 7.9844211523466425941e-880j)  +/-  (5.2e-242, 5.2e-242j)
| (-4.0610781730290349198 + 1.9571973837623771788e-878j)  +/-  (5.62e-242, 5.62e-242j)
| (-0.38118699020732211685 + 5.5573069044392153315e-909j)  +/-  (3.81e-253, 3.81e-253j)
| (-6.014792341806203692 - 2.0014260793647635056e-898j)  +/-  (9.43e-241, 9.43e-241j)
| (6.7288787683894446059 - 3.7641453880552572763e-913j)  +/-  (7.38e-241, 7.38e-241j)
| (0.63606291564586530806 + 3.822470316290797322e-925j)  +/-  (4.99e-252, 4.99e-252j)
| (-3.754699469151045748 + 3.4250844183580933405e-921j)  +/-  (2.09e-242, 2.09e-242j)
| (-1.4265978530975164435 - 7.7358878070940450896e-937j)  +/-  (1.13e-248, 1.13e-248j)
| (-1.1571937124467801947 + 3.2760371654461156029e-939j)  +/-  (9.69e-250, 9.69e-250j)
| (-2.9306374202572440192 + 1.5373254819790661362e-940j)  +/-  (3.56e-243, 3.56e-243j)
| (0.38118699020732211685 + 6.3371867984203693984e-952j)  +/-  (3.81e-253, 3.81e-253j)
| (0.12707517889449802622 - 7.5216952734622244751e-952j)  +/-  (2.43e-254, 2.43e-254j)
| (-0.12707517889449802622 + 8.5941793045991874484e-952j)  +/-  (2.43e-254, 2.43e-254j)
-------------------------------------------------
The weights are:
| (4.5073902096639290124e-21 - 2.542660896628193927e-828j)  +/-  (5.33e-53, 1.42e-171j)
| (1.4946614040251793683e-31 + 4.8335029714775114212e-835j)  +/-  (6.42e-59, 1.71e-177j)
| (3.6052126588346237668e-39 + 2.8623148699916872525e-839j)  +/-  (4.11e-62, 1.1e-180j)
| (3.7998910122211915135e-17 + 4.1061257586763438553e-828j)  +/-  (5.39e-53, 1.44e-171j)
| (9.0192965693504788049e-26 + 6.7518649760190608089e-833j)  +/-  (7.14e-59, 1.91e-177j)
| (1.9382331282946387881e-44 - 7.8783650772237559847e-843j)  +/-  (4.72e-67, 1.26e-185j)
| (2.6032168094152403174e-23 - 5.4888970939878580139e-830j)  +/-  (1.94e-57, 5.17e-176j)
| (4.8282474887804431082e-35 - 7.1385111018058340796e-838j)  +/-  (9.75e-64, 2.6e-182j)
| (1.1138121695402613937e-06 - 6.2681378654802321703e-821j)  +/-  (4.23e-43, 1.13e-161j)
| (0.03937701258044938415 - 1.3602632751311497096e-818j)  +/-  (3.54e-19, 9.44e-138j)
| (1.4946614040251793683e-31 + 5.1779580855030954862e-836j)  +/-  (2.52e-62, 6.73e-181j)
| (5.1144554528620926908e-11 - 9.8992131361021644415e-824j)  +/-  (3.86e-50, 1.03e-168j)
| (1.9382331282946387881e-44 - 4.0400806113127127661e-842j)  +/-  (5.09e-68, 1.36e-186j)
| (0.0031341832080148735005 - 4.8616051938937553564e-819j)  +/-  (1.17e-33, 3.13e-152j)
| (2.0297180480804042851e-15 + 4.7445637078456747403e-826j)  +/-  (1.69e-54, 4.51e-173j)
| (7.9036058855072815728e-14 - 2.9971498875094316216e-825j)  +/-  (2.89e-53, 7.7e-172j)
| (5.0244637752155698854e-19 - 3.5522450529348529577e-829j)  +/-  (5.37e-60, 1.43e-178j)
| (8.8240375766635575735e-10 + 5.1639751337467387767e-823j)  +/-  (5.92e-50, 1.58e-168j)
| (0.00094971096661561528344 + 3.1029850442638927844e-819j)  +/-  (5.93e-39, 1.58e-157j)
| (0.066037017217495376741 - 2.7498482342614385024e-818j)  +/-  (9.02e-29, 2.41e-147j)
| (3.6052126588346237668e-39 + 4.66316286063889214e-840j)  +/-  (1.37e-68, 3.66e-187j)
| (1.2932686691580068676e-07 - 3.5353585500622182533e-822j)  +/-  (4.55e-52, 1.22e-170j)
| (2.0297180480804042851e-15 - 4.0423973429286952984e-827j)  +/-  (1.55e-58, 4.12e-177j)
| (5.1144554528620926908e-11 + 1.76920801930798836e-824j)  +/-  (1.93e-56, 5.16e-175j)
| (9.0192965693504788049e-26 + 1.2530644729450647453e-831j)  +/-  (1.84e-64, 4.9e-183j)
| (7.9036058855072815728e-14 + 3.455508520883414137e-826j)  +/-  (4.07e-58, 1.09e-176j)
| (2.6032168094152403174e-23 - 1.4892744512956067299e-831j)  +/-  (1.63e-63, 4.34e-182j)
| (0.020081022672658773288 + 8.178743273615107284e-819j)  +/-  (5.36e-40, 1.43e-158j)
| (0.066037017217495376741 + 2.1048715276605535181e-818j)  +/-  (7.69e-37, 2.05e-155j)
| (0.0086561835353844719744 + 7.8735101589329567117e-819j)  +/-  (3.5e-42, 9.34e-161j)
| (7.381140173852636389e-06 - 1.3721795100390206171e-820j)  +/-  (4.92e-52, 1.31e-170j)
| (5.0244637752155698854e-19 + 1.2835004919345065521e-827j)  +/-  (9.88e-62, 2.64e-180j)
| (4.8282474887804431082e-35 - 5.3138090512306561036e-837j)  +/-  (7.17e-70, 1.91e-188j)
| (7.381140173852636389e-06 + 3.8024882676494015314e-820j)  +/-  (1.77e-52, 4.72e-171j)
| (2.301232103932819892e-12 - 2.609211966287411029e-825j)  +/-  (5.47e-59, 1.46e-177j)
| (0.00023973255299135317563 - 2.2990730574367369323e-819j)  +/-  (4.86e-50, 1.3e-168j)
| (2.301232103932819892e-12 + 1.7819033400370087117e-824j)  +/-  (3.72e-58, 9.92e-177j)
| (1.697177660365806986e-28 - 2.2615948287565143811e-834j)  +/-  (6.41e-68, 1.71e-186j)
| (1.697177660365806986e-28 - 2.811040488407765751e-833j)  +/-  (5.97e-67, 1.59e-185j)
| (4.3140616385799828079e-05 - 1.1284735906862717825e-819j)  +/-  (6.79e-55, 1.81e-173j)
| (0.096352213390754007097 + 3.583669865261743445e-818j)  +/-  (1.72e-46, 4.59e-165j)
| (8.8240375766635575735e-10 - 1.0962632078687046062e-823j)  +/-  (8.32e-59, 2.22e-177j)
| (0.0031341832080148735005 + 2.6495637520966912582e-819j)  +/-  (2.17e-52, 5.79e-171j)
| (0.0086561835353844719744 - 4.6949359180592911103e-819j)  +/-  (3.82e-51, 1.02e-169j)
| (0.00094971096661561528344 - 1.5399915287223976514e-819j)  +/-  (7.27e-54, 1.94e-172j)
| (4.3140616385799828079e-05 + 2.7521061100632359928e-819j)  +/-  (4.58e-56, 1.22e-174j)
| (1.2338960076860204463e-05 + 7.9530730321907255288e-820j)  +/-  (9.8e-56, 2.61e-174j)
| (1.1138121695402613937e-06 + 2.0163794812794794659e-821j)  +/-  (6.27e-58, 1.67e-176j)
| (0.00023973255299135317563 + 1.0354154210323551926e-819j)  +/-  (1.34e-55, 3.57e-174j)
| (1.1980851033746589469e-08 + 6.3418447395173821684e-823j)  +/-  (8.33e-60, 2.22e-178j)
| (1.1980851033746589469e-08 - 2.5649680035140803934e-822j)  +/-  (1.27e-62, 3.39e-181j)
| (0.12403024229520260339 - 4.2109230072652635808e-818j)  +/-  (1.43e-56, 3.81e-175j)
| (3.7998910122211915135e-17 - 7.3278407567601277605e-827j)  +/-  (2.01e-67, 5.36e-186j)
| (4.5073902096639290124e-21 + 2.5577314557883572691e-830j)  +/-  (7.6e-69, 2.03e-187j)
| (0.096352213390754007097 - 2.9646725667083432971e-818j)  +/-  (3.91e-57, 1.04e-175j)
| (1.2932686691580068676e-07 + 1.2461658907660763379e-821j)  +/-  (4.55e-62, 1.21e-180j)
| (0.020081022672658773288 - 1.2579784177172195541e-818j)  +/-  (7.76e-59, 2.07e-177j)
| (0.03937701258044938415 + 1.9252945335204300875e-818j)  +/-  (1.45e-58, 3.88e-177j)
| (1.2338960076860204463e-05 - 2.0225896846105616356e-819j)  +/-  (3.42e-60, 9.12e-179j)
| (0.12403024229520260339 + 3.7594084582771851801e-818j)  +/-  (7.06e-59, 1.89e-177j)
| (0.14107856480797889034 - 4.3005874173967038459e-818j)  +/-  (3.05e-59, 8.09e-178j)
| (0.14107856480797889034 + 4.466147603490915512e-818j)  +/-  (2.62e-59, 7.04e-178j)
