Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 50
-------------------------------------------------
Trying to find an order 50 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^58 - 2226177299100671417968274674909530562368058572971486391253888/11998724209199654391509790114482532688358698626274742307*t^56 + 8233972862800846933664161697010241380223050356291394294371198080/131985966301196198306607691259307859571945684889022165377*t^54 - 8159832327165502092356267212129736757800443582668650806257650944960/630599616772381836353792302683359773510407161136439234579*t^52 + 3512984755660176736263411418624664963335702082758028062708262378395760/1891798850317145509061376908050079320531221483409317703737*t^50 - 370844479393649106991570295030695209085923165141256376261920248542320600/1891798850317145509061376908050079320531221483409317703737*t^48 + 9963887746025659834013994174623872448642839542488623991079966418612538800/630599616772381836353792302683359773510407161136439234579*t^46 - 628362309932722822363508780993077289371747453478833125927877668340296507000/630599616772381836353792302683359773510407161136439234579*t^44 + 66636522948988214590611002978426139819228939897579989538855223480685620875/1333191578799961599056643346053614743150966514030526923*t^42 - 5377390885873434245767995059054142182597521202866440505208295005055634545375/2666383157599923198113286692107229486301933028061053846*t^40 + 175843200348641874910293540618877703687295822880290977579736544118696940607125/2666383157599923198113286692107229486301933028061053846*t^38 - 9363905480005422122038349300366656263946144204270304418990163767221197164632625/5332766315199846396226573384214458972603866056122107692*t^36 + 813939975701605990445592001924320648114817392855071683149695266666669265228038125/21331065260799385584906293536857835890415464224488430768*t^34 - 28883406325853818945081525578502062224197983488492915396048542728371261264711735625/42662130521598771169812587073715671780830928448976861536*t^32 + 104466200347068532404409988927574175145244182371582570084895253211399897386462988125/10665532630399692792453146768428917945207732112244215384*t^30 - 2457170196202565466638129332904721343817238794453564948656884980180850508632576155625/21331065260799385584906293536857835890415464224488430768*t^28 + 374086928643544282641895543344996431144184946216076574138335687366870284114445550725625/341297044172790169358500696589725374246647427591814892288*t^26 - 5722317121751329112713433691832682566977476670677909304354242336946411964747346024203125/682594088345580338717001393179450748493294855183629784576*t^24 + 34880270354099632727165410017548922494281966351061338985126541090726856214853909184828125/682594088345580338717001393179450748493294855183629784576*t^22 - 335198793512056905655920858124998448145441167711795594832697451731613448321630208008765625/1365188176691160677434002786358901496986589710367259569152*t^20 + 5008260872676358522594146072793203305685298871235664655208135424330093515730241728502484375/5460752706764642709736011145435605987946358841469038276608*t^18 - 28570441701518965220123992454394398768480593178541301439016301573606454134906394077749796875/10921505413529285419472022290871211975892717682938076553216*t^16 + 30399701915360120061605828845481625220701953475796200681420860087003362143092093475908671875/5460752706764642709736011145435605987946358841469038276608*t^14 - 93590328818478788341949941421564042866199461135208874957164025536117732150635652626436484375/10921505413529285419472022290871211975892717682938076553216*t^12 + 799086745330153294035019062385132015234617843617258012336957057788978005113125654103971640625/87372043308234283355776178326969695807141741463504612425728*t^10 - 1113366501459433878685099928897545333556077967023342638749207092071416909409460631496502078125/174744086616468566711552356653939391614283482927009224851456*t^8 + 462427333510355425981821385777764230693635801848701204689908470846681593950432702538149796875/174744086616468566711552356653939391614283482927009224851456*t^6 - 197408423550751962430261779232691165042539492816375464789934292208145838427136919620865859375/349488173232937133423104713307878783228566965854018449702912*t^4 + 64945822705011873162067838694306759161249913484825142399511844723149137271651972818880234375/1397952692931748533692418853231515132914267863416073798811648*t^2 - 1738573502600879937515969716334431816807563020346735078396880856652599805394380357183046875/2795905385863497067384837706463030265828535726832147597623296
-------------------------------------------------
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:
| (-6.2836843314275991555 - 1.5158342928784735842e-839j)  +/-  (6.49e-242, 6.49e-242j)
| (6.6657610600968855424 + 7.9591281360709077273e-846j)  +/-  (4.46e-242, 4.46e-242j)
| (-6.6657610600968855424 + 6.8819944587320865437e-846j)  +/-  (4.5e-242, 4.5e-242j)
| (6.2836843314275991555 - 4.2151394053807371644e-849j)  +/-  (6.07e-242, 6.07e-242j)
| (-7.9255985949233037028 - 2.1112703064049423857e-850j)  +/-  (4.63e-243, 4.63e-243j)
| (8.4066140031428638592 - 1.5069467564797466132e-859j)  +/-  (1.07e-243, 1.07e-243j)
| (7.0636282537612243816 + 2.406876068594646101e-856j)  +/-  (3.03e-242, 3.03e-242j)
| (7.9255985949233037028 - 1.649917562147935184e-858j)  +/-  (4.59e-243, 4.59e-243j)
| (-4.8647438193915534628 - 2.0135431339137218839e-855j)  +/-  (2.8e-242, 2.8e-242j)
| (1.439965414920350086 - 4.9982741891943409031e-873j)  +/-  (1.34e-248, 1.34e-248j)
| (0.88705462188948304557 - 1.1664493458929042585e-875j)  +/-  (7.53e-251, 7.53e-251j)
| (3.8766681916875499569 - 2.621741395573726566e-867j)  +/-  (2.91e-243, 2.91e-243j)
| (-3.8766681916875499569 + 8.0341752395634376852e-865j)  +/-  (3.06e-243, 3.06e-243j)
| (-5.91446441070021838 + 1.3836637062143681039e-878j)  +/-  (6.44e-242, 6.44e-242j)
| (-5.5559408646617745498 - 4.3311771956849149091e-902j)  +/-  (5.62e-242, 5.62e-242j)
| (4.2006138082961084329 + 8.4618772631360623414e-916j)  +/-  (7.32e-243, 7.32e-243j)
| (4.5297411446610644798 - 1.79530372151094782e-913j)  +/-  (1.49e-242, 1.49e-242j)
| (5.2064650501911400587 + 2.2827618686832262264e-912j)  +/-  (4.45e-242, 4.45e-242j)
| (-0.88705462188948304557 + 1.1194830230817560047e-922j)  +/-  (6.77e-251, 6.77e-251j)
| (1.97273637254978903 + 1.2077264004240125333e-916j)  +/-  (4.51e-245, 4.51e-245j)
| (7.4814612320037019593 - 2.3159279399020937883e-915j)  +/-  (1.34e-242, 1.34e-242j)
| (-1.97273637254978903 - 1.3227233723631412673e-916j)  +/-  (3.82e-245, 3.82e-245j)
| (-8.9450479857473076844 + 7.2801740379136745427e-915j)  +/-  (1.58e-244, 1.58e-244j)
| (-8.4066140031428638592 + 9.5380442817777221076e-913j)  +/-  (1.07e-243, 1.07e-243j)
| (-1.9816567566958429259 + 3.9029395770548855123e-923j)  +/-  (4.18e-245, 4.18e-245j)
| (-9.594754945819264912 + 2.3870370686875430455e-919j)  +/-  (8.08e-246, 8.08e-246j)
| (-7.4814612320037019593 + 1.0315525992864071711e-920j)  +/-  (1.42e-242, 1.42e-242j)
| (3.5573303622037405342 - 2.9036105088199994602e-937j)  +/-  (1.04e-243, 1.04e-243j)
| (-5.2064650501911400587 + 2.0842046382144507061e-938j)  +/-  (4.3e-242, 4.3e-242j)
| (-1.734853841305404828 + 9.4990411188619637992e-953j)  +/-  (3.02e-247, 3.02e-247j)
| (9.594754945819264912 + 1.2287009348556157154e-951j)  +/-  (8.67e-246, 8.67e-246j)
| (-1.1571937124467801947 + 4.6767289918202263509e-955j)  +/-  (9.95e-250, 9.95e-250j)
| (2.6224496666018081837 + 6.5523337822366692407e-952j)  +/-  (2.45e-245, 2.45e-245j)
| (-3.5573303622037405342 + 2.5876698917476301258e-949j)  +/-  (9.09e-244, 9.09e-244j)
| (-4.5297411446610644798 + 1.2513302863740021173e-948j)  +/-  (1.52e-242, 1.52e-242j)
| (-2.3165884765267447646 - 2.5692838654624793885e-960j)  +/-  (7.34e-246, 7.34e-246j)
| (-7.0636282537612243816 + 2.0795098002720862882e-956j)  +/-  (2.8e-242, 2.8e-242j)
| (1.1571937124467801947 + 2.7621766454016034183e-965j)  +/-  (9.66e-250, 9.66e-250j)
| (8.9450479857473076844 + 2.0874112207712180224e-959j)  +/-  (1.46e-244, 1.46e-244j)
| (-2.6224496666018081837 + 8.5610053285302763024e-961j)  +/-  (2.32e-245, 2.32e-245j)
| (2.9306374202572440192 - 1.6567977158716809453e-961j)  +/-  (8.54e-245, 8.54e-245j)
| (-4.2006138082961084329 - 4.8403257440155643804e-956j)  +/-  (7.12e-243, 7.12e-243j)
| (1.9816567566958429259 + 1.7174511662355856293e-961j)  +/-  (4.32e-245, 4.32e-245j)
| (-0.12814327744003912572 + 1.7081031928040913331e-971j)  +/-  (2.38e-254, 2.38e-254j)
| (5.91446441070021838 - 2.1319740379939759756e-956j)  +/-  (6.53e-242, 6.53e-242j)
| (-1.439965414920350086 - 3.4411724423468332593e-966j)  +/-  (1.5e-248, 1.5e-248j)
| (2.3165884765267447646 - 1.6734800812184169238e-963j)  +/-  (7.98e-246, 7.98e-246j)
| (3.2421230268092057462 - 2.4991647508042636681e-962j)  +/-  (2.98e-244, 2.98e-244j)
| (0.63077121168096945774 - 7.1046730848675310826e-970j)  +/-  (6.3e-252, 6.3e-252j)
| (5.5559408646617745498 + 6.1247896382222231466e-959j)  +/-  (6.34e-242, 6.34e-242j)
| (1.734853841305404828 + 3.5023191868045454256e-965j)  +/-  (3.02e-247, 3.02e-247j)
| (-0.63077121168096945774 - 3.2144422965694807895e-970j)  +/-  (6.3e-252, 6.3e-252j)
| (4.8647438193915534628 - 8.5599709473730060652e-964j)  +/-  (2.75e-242, 2.75e-242j)
| (0.12814327744003912572 + 1.6471977372590615662e-975j)  +/-  (2.38e-254, 2.38e-254j)
| (0.38118699020732211685 + 3.55169989400532718e-974j)  +/-  (3.92e-253, 3.92e-253j)
| (-2.9306374202572440192 + 1.8005754748929930158e-963j)  +/-  (8.82e-245, 8.82e-245j)
| (-0.38118699020732211685 + 2.0602499026935962944e-974j)  +/-  (4.19e-253, 4.19e-253j)
| (-3.2421230268092057462 - 8.1408727774928925156e-971j)  +/-  (3.43e-244, 3.43e-244j)
-------------------------------------------------
The weights are:
| (1.5057258260359772167e-18 - 1.5870421903801030874e-856j)  +/-  (1.72e-63, 1.22e-182j)
| (1.1093991506920737571e-20 - 1.1810994946954735592e-859j)  +/-  (1.4e-65, 9.87e-185j)
| (1.1093991506920737571e-20 - 4.002991053563980122e-858j)  +/-  (2.93e-65, 2.07e-184j)
| (1.5057258260359772167e-18 + 1.8161600922605330977e-858j)  +/-  (2.4e-64, 1.69e-183j)
| (1.3620514989991616151e-28 + 5.0300213373403513466e-863j)  +/-  (1.82e-70, 1.29e-189j)
| (5.7882271486948986452e-32 - 9.0925721635621951173e-866j)  +/-  (2.15e-72, 1.52e-191j)
| (4.9201821779961246988e-23 + 5.9918411958189703496e-861j)  +/-  (7.22e-68, 5.1e-187j)
| (1.3620514989991616151e-28 + 5.8122977371888174778e-864j)  +/-  (6.76e-71, 4.78e-190j)
| (1.0062612432273087793e-11 - 1.2438768112444752827e-853j)  +/-  (2.24e-62, 1.59e-181j)
| (0.020445948876973041982 + 1.3024203098521889489e-847j)  +/-  (7.36e-38, 5.2e-157j)
| (0.067531986943573770257 + 3.0172663011685521954e-847j)  +/-  (7.36e-38, 5.2e-157j)
| (5.393380524844564032e-08 - 3.5319841577415553968e-852j)  +/-  (4.79e-58, 3.39e-177j)
| (5.393380524844564032e-08 + 1.4908997186069778091e-851j)  +/-  (1.73e-58, 1.22e-177j)
| (1.318241409625811616e-16 + 7.4692557206853908953e-856j)  +/-  (3.36e-66, 2.38e-185j)
| (7.8364968102670899525e-15 - 3.8124740672422802e-855j)  +/-  (3.67e-65, 2.59e-184j)
| (3.9996622848979714424e-09 + 6.4472367924727150274e-853j)  +/-  (3.35e-61, 2.37e-180j)
| (2.2981958577452108152e-10 - 1.0681990279071112708e-853j)  +/-  (6.39e-63, 4.52e-182j)
| (3.2901433935625336853e-13 - 2.0681763309663304677e-855j)  +/-  (6.11e-66, 4.32e-185j)
| (0.067531986943573770257 - 4.0091741485158120243e-847j)  +/-  (4.69e-46, 3.32e-165j)
| (-0.016808756205717618075 + 1.510301786728176249e-846j)  +/-  (9.44e-51, 6.67e-170j)
| (1.1915754694447739407e-25 - 2.2523420705440825977e-862j)  +/-  (9.44e-73, 6.67e-192j)
| (-0.016808756205717618075 - 2.8925624073653140547e-846j)  +/-  (6.86e-53, 4.85e-172j)
| (5.8192885613576560983e-36 + 3.9005532105700632875e-867j)  +/-  (4.4e-81, 3.11e-200j)
| (5.7882271486948986452e-32 - 6.2919024291027341308e-865j)  +/-  (3.05e-79, 2.16e-198j)
| (0.019257098841532638309 + 2.7723359417876909895e-846j)  +/-  (1.92e-54, 1.36e-173j)
| (4.4234721322582721269e-41 - 6.4885439834572888935e-870j)  +/-  (1.04e-83, 7.37e-203j)
| (1.1915754694447739407e-25 - 2.5884492649373293017e-861j)  +/-  (1.35e-76, 9.55e-196j)
| (5.7139383476995771554e-07 + 1.7842061840859576508e-851j)  +/-  (1.49e-65, 1.05e-184j)
| (3.2901433935625336853e-13 + 2.2060173248122169019e-854j)  +/-  (5.14e-70, 3.64e-189j)
| (0.008511882563820627109 + 2.311153787919620221e-847j)  +/-  (4.99e-57, 3.53e-176j)
| (4.4234721322582721269e-41 - 1.3530310047997529009e-870j)  +/-  (3e-86, 2.12e-205j)
| (0.040955047756978039924 + 2.7949244493532676736e-847j)  +/-  (7.36e-54, 5.2e-173j)
| (0.00017842170883243359792 - 1.8199276606204764119e-849j)  +/-  (1.19e-63, 8.44e-183j)
| (5.7139383476995771554e-07 - 6.4402482003864958453e-851j)  +/-  (6.99e-67, 4.94e-186j)
| (2.2981958577452108152e-10 + 6.5856678225819741039e-853j)  +/-  (2.69e-69, 1.9e-188j)
| (0.0008055232360509586963 - 2.1559122622602873303e-848j)  +/-  (1.11e-62, 7.87e-182j)
| (4.9201821779961246988e-23 + 1.0253959812385480996e-859j)  +/-  (3.58e-76, 2.53e-195j)
| (0.040955047756978039924 - 1.9255999734021601043e-847j)  +/-  (1.93e-59, 1.37e-178j)
| (5.8192885613576560983e-36 + 6.8165795501419405307e-868j)  +/-  (5.69e-85, 4.02e-204j)
| (0.00017842170883243359792 + 4.4270633683570861952e-849j)  +/-  (2.63e-65, 1.86e-184j)
| (3.2542181809428117844e-05 + 3.8918400448416329229e-850j)  +/-  (1.15e-67, 8.1e-187j)
| (3.9996622848979714424e-09 - 3.2449566932587012552e-852j)  +/-  (5.49e-69, 3.88e-188j)
| (0.019257098841532638309 - 1.4429733074739498811e-846j)  +/-  (2.45e-63, 1.73e-182j)
| (0.14187632568697585161 + 6.5129812861198484286e-847j)  +/-  (7.27e-62, 5.14e-181j)
| (1.318241409625811616e-16 - 2.2608354225459972521e-857j)  +/-  (2.11e-76, 1.49e-195j)
| (0.020445948876973041982 - 2.0768004795839513753e-847j)  +/-  (5.18e-64, 3.66e-183j)
| (0.0008055232360509586963 + 9.9446977693105377602e-849j)  +/-  (1.96e-66, 1.38e-185j)
| (4.8120918874980161354e-06 - 8.4738160433145782652e-851j)  +/-  (3.57e-69, 2.52e-188j)
| (0.095099012638221406326 - 4.3936968566207165474e-847j)  +/-  (3.46e-64, 2.45e-183j)
| (7.8364968102670899525e-15 + 2.3434059810226024049e-856j)  +/-  (6.96e-76, 4.92e-195j)
| (0.008511882563820627109 - 1.3110927790097654823e-847j)  +/-  (2.15e-66, 1.52e-185j)
| (0.095099012638221406326 + 5.3742239214985475861e-847j)  +/-  (3.5e-66, 2.5e-185j)
| (1.0062612432273087793e-11 + 1.5831719174682866894e-854j)  +/-  (4.62e-74, 3.26e-193j)
| (0.14187632568697585161 - 6.2526515549765669903e-847j)  +/-  (2.19e-66, 1.56e-185j)
| (0.12210952411154043844 + 5.5708017927523829129e-847j)  +/-  (2.2e-66, 1.56e-185j)
| (3.2542181809428117844e-05 - 1.0694947851824505035e-849j)  +/-  (2.7e-71, 1.89e-190j)
| (0.12210952411154043844 - 6.2903334754948087275e-847j)  +/-  (1.03e-67, 9.31e-187j)
| (4.8120918874980161354e-06 + 2.6538977597507632914e-850j)  +/-  (5.39e-72, 3.74e-191j)
