Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 56
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 56 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^61 - 531599802575561949837609695594068504860910779049284228655925262175154/155305158738556770794039759038947868295261702838393123027590315211*t^59 + 212179687376320765652573318733372064975260704791327559930903425099918696/155305158738556770794039759038947868295261702838393123027590315211*t^57 - 17512015686543560271780997712410320886841157386735082574677947147616172015/51768386246185590264679919679649289431753900946131041009196771737*t^55 + 1341311773706832769894895112646708357221462581247143304776505661217299623395/23008171664971373450968853190955239747446178198280462670754120772*t^53 - 342241692772272476496952590768018421937418310177734806294397765457804109305565/46016343329942746901937706381910479494892356396560925341508241544*t^51 + 33564290476100833931882072803950715344476063035152827618158283122269152129868675/46016343329942746901937706381910479494892356396560925341508241544*t^49 - 2593944685139722361721947084212374966941940784820698922301301446745149712723786575/46016343329942746901937706381910479494892356396560925341508241544*t^47 + 1285384650236233089409638250858221941421933615931498304461631965597710479816673785625/368130746639541975215501651055283835959138851172487402732065932352*t^45 - 129135441594562647295929616746619721278328068704271431943225376833444874779556890864875/736261493279083950431003302110567671918277702344974805464131864704*t^43 + 2651487285725600837627607299692222179330677990047296558345839945262467676968810797549125/368130746639541975215501651055283835959138851172487402732065932352*t^41 - 380363311074296569628988056982229920079546203942370803055604596660525169951091035131125/1564849082421007333540920939661142767095170461944686090253202688*t^39 + 39824100866926819643654094713136725823738904725641442188607861980473020568170420156246499875/5890091946232671603448026416884541375346221618759798443713054917632*t^37 - 1828085976689548484175854532117484695669825028039610974042338305161496473584310908214683733125/11780183892465343206896052833769082750692443237519596887426109835264*t^35 + 34598648067095023794966659507210776752299331205969857052218636112604179121059203773288229598125/11780183892465343206896052833769082750692443237519596887426109835264*t^33 - 269369089138379618722924515685030523339168247133600661514174077005771647699863057575544886140625/5890091946232671603448026416884541375346221618759798443713054917632*t^31 + 54999045889710372226490209055186983179441375090035664943544193915020235755854967410403316816736875/94241471139722745655168422670152662005539545900156775099408878682112*t^29 - 1143989351046907472336554147515540938250013767293232561591424115475811305430035617642384394747335625/188482942279445491310336845340305324011079091800313550198817757364224*t^27 + 1203100832681531766984073925614648244417065927312938514997599787296930552070280406315483506041071875/23560367784930686413792105667538165501384886475039193774852219670528*t^25 - 129780332582422967896636629421329496990553160233150342922636003166632907299511842165439467302505515625/376965884558890982620673690680610648022158183600627100397635514728448*t^23 + 2771444309825952923763506594739671667890032993000982751365261369373219599031050503522754289936381890625/1507863538235563930482694762722442592088632734402508401590542058913792*t^21 - 23088626633363033443185874407886030979294427018563965226179356301232539289395409150259419587497077859375/3015727076471127860965389525444885184177265468805016803181084117827584*t^19 + 73673697318669602671812619065590824191010754036251271190641371878311717748394014513971827611833135578125/3015727076471127860965389525444885184177265468805016803181084117827584*t^17 - 176022727273423024629757482929225251777726059822095179432716285373762898136013610700975692280008544609375/3015727076471127860965389525444885184177265468805016803181084117827584*t^15 + 2448347587789908879688322577537015224311501253301530126985678617589552938782354886041929981650084399296875/24125816611769022887723116203559081473418123750440134425448672942620672*t^13 - 5976867364098877453437375450927436347772154766208075931272819338580885212160216521727194126571306273640625/48251633223538045775446232407118162946836247500880268850897345885241344*t^11 + 2445865643116913764584425074263797990339962008369775414656104264501482598305079843131071925458343710140625/24125816611769022887723116203559081473418123750440134425448672942620672*t^9 - 5052907990792581499684354565964866361423492955219999243677738216332917819482084190171861402817748341859375/96503266447076091550892464814236325893672495001760537701794691770482688*t^7 + 6031071511372815417376327340330515016459578511185159936830611708016826956808878764931116167234429364765625/386013065788304366203569859256945303574689980007042150807178767081930752*t^5 - 1771927982075684331685202334898220132528574230532615473298769037433890026199164417773882720985101860859375/772026131576608732407139718513890607149379960014084301614357534163861504*t^3 + 84515877519463442811358795544314993892329305257039201253863152174547225633262421122365918536098631171875/772026131576608732407139718513890607149379960014084301614357534163861504*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:
| (7.9842334304345343163 - 8.5071073652302162709e-518j)  +/-  (1.02e-241, 1.02e-241j)
| (-8.8945587707267415753 + 5.5720416413907188149e-522j)  +/-  (5.92e-243, 5.92e-243j)
| (-10.064948015044350536 - 2.752879465274753902e-526j)  +/-  (4.05e-245, 4.05e-245j)
| (6.8070090615989166078 - 1.2373318763086499306e-521j)  +/-  (6.16e-241, 6.16e-241j)
| (8.4211396201643992334 - 1.4953619738624996234e-527j)  +/-  (3e-242, 3e-242j)
| (-7.9842334304345343163 + 1.8313993527325665637e-539j)  +/-  (9.97e-242, 9.97e-242j)
| (-9.4247734386859434191 - 1.4836479621326913437e-553j)  +/-  (7.59e-244, 7.59e-244j)
| (-0.7071067811865475244 + 4.2705126019602151618e-579j)  +/-  (7.06e-251, 7.06e-251j)
| (-6.0924727377126449198 - 1.5760823641262187858e-568j)  +/-  (7.44e-241, 7.44e-241j)
| (8.8945587707267415753 - 5.684395118702402502e-583j)  +/-  (6.38e-243, 6.38e-243j)
| (2.913222971755159525 + 3.4331290367101571483e-588j)  +/-  (1.08e-244, 1.08e-244j)
| (-6.8070090615989166078 + 2.1669554490368496705e-581j)  +/-  (6.34e-241, 6.34e-241j)
| (-2.913222971755159525 - 1.3784785104175450239e-593j)  +/-  (1.03e-244, 1.03e-244j)
| (9.4247734386859434191 - 5.4361728676406290436e-595j)  +/-  (7.46e-244, 7.46e-244j)
| (-3.5163889442477495085 - 3.3652891109469802471e-592j)  +/-  (2.06e-243, 2.06e-243j)
| (2.0250284333418254576 + 3.2731548546410002222e-596j)  +/-  (4.15e-247, 4.15e-247j)
| (4.1317257535431329853 - 4.0523573927586428223e-591j)  +/-  (2.19e-242, 2.19e-242j)
| (10.064948015044350536 - 8.0585955065820667386e-594j)  +/-  (3.57e-245, 3.57e-245j)
| (-1.7320508075688772935 - 9.586213967986949147e-597j)  +/-  (5.32e-248, 5.32e-248j)
| (7.5733961921250561353 - 6.6194811601895003284e-589j)  +/-  (2.31e-241, 2.31e-241j)
| (-8.4211396201643992334 + 7.0792249489632280319e-590j)  +/-  (2.99e-242, 2.99e-242j)
| (1.4399198011991257069 - 5.9801368714332121481e-606j)  +/-  (6.62e-249, 6.62e-249j)
| (-7.5733961921250561353 + 6.4205528503820997554e-595j)  +/-  (2.35e-241, 2.35e-241j)
| (7.1823643206767886415 + 2.0947806463296470606e-606j)  +/-  (4.13e-241, 4.13e-241j)
| (-7.1823643206767886415 + 1.8580825919415453897e-621j)  +/-  (4.28e-241, 4.28e-241j)
| (5.0856229130488359417 + 2.1496118712856188215e-630j)  +/-  (2.54e-241, 2.54e-241j)
| (3.8223329048119757892 + 3.8144673516239469629e-637j)  +/-  (7.42e-243, 7.42e-243j)
| (4.7627957318106879143 - 9.7249810213395448738e-638j)  +/-  (1.39e-241, 1.39e-241j)
| (-5.7495084459855003018 + 1.7197704746644192346e-649j)  +/-  (5.84e-241, 5.84e-241j)
| (-3.213477571399546048 + 1.0349401807977898328e-665j)  +/-  (4.44e-244, 4.44e-244j)
| (2.6152797153978747669 + 4.6519374528194847971e-668j)  +/-  (2e-245, 2e-245j)
| (4.4450355298433336558 + 2.631543842658338297e-664j)  +/-  (6.35e-242, 6.35e-242j)
| (0.59398009070136586473 - 8.388882056302805683e-674j)  +/-  (1.27e-251, 1.27e-251j)
| (1.147586454199604517 + 5.8718140406684181319e-672j)  +/-  (7.58e-250, 7.58e-250j)
| (-2.6152797153978747669 + 5.069476153563846463e-667j)  +/-  (1.86e-245, 1.86e-245j)
| (-4.7627957318106879143 + 3.1038941692504936812e-662j)  +/-  (1.36e-241, 1.36e-241j)
| (-0.84665593850133918546 - 3.2510889685019996342e-680j)  +/-  (1.48e-250, 1.48e-250j)
| (0.29120976359718559587 + 2.61500287012812952e-711j)  +/-  (1.65e-253, 1.65e-253j)
| (1.7320508075688772935 + 3.0595019592456987402e-677j)  +/-  (5.61e-248, 5.61e-248j)
| (-1.4399198011991257069 + 5.2601129099632502044e-678j)  +/-  (6.87e-249, 6.87e-249j)
| (-1.147586454199604517 + 5.5069395926524985834e-679j)  +/-  (7.68e-250, 7.68e-250j)
| (-2.3193220030356720841 - 1.1163550377533785347e-676j)  +/-  (2.93e-246, 2.93e-246j)
| (0.7071067811865475244 + 6.6110677035909686508e-680j)  +/-  (7.22e-251, 7.22e-251j)
| (-3.8223329048119757892 - 1.5328823331106757361e-671j)  +/-  (7.23e-243, 7.23e-243j)
| (5.4142400439527630561 - 9.958615363452978089e-671j)  +/-  (4.03e-241, 4.03e-241j)
| (-4.4450355298433336558 - 7.1103151802058485319e-670j)  +/-  (6.14e-242, 6.14e-242j)
| (-4.1317257535431329853 - 3.434023315555978999e-679j)  +/-  (2.15e-242, 2.15e-242j)
| (3.213477571399546048 + 6.584777944094936857e-692j)  +/-  (4.8e-244, 4.8e-244j)
| (-6.4444261538168287115 + 4.1916140914252767698e-689j)  +/-  (7.28e-241, 7.28e-241j)
| (2.3193220030356720841 + 2.1704837933464649233e-700j)  +/-  (3.19e-246, 3.19e-246j)
| (6.0924727377126449198 - 1.0890963521936670639e-695j)  +/-  (7.67e-241, 7.67e-241j)
| (-0.59398009070136586473 - 5.8830276638800822039e-716j)  +/-  (1.31e-251, 1.31e-251j)
| (6.4444261538168287115 - 1.0266160999535732028e-704j)  +/-  (7.2e-241, 7.2e-241j)
| (5.7495084459855003018 - 1.7309012869907476194e-719j)  +/-  (5.86e-241, 5.86e-241j)
| (3.5163889442477495085 + 1.0984013274003117712e-731j)  +/-  (2e-243, 2e-243j)
| (-2.0250284333418254576 - 7.2065191305717679947e-741j)  +/-  (4.19e-247, 4.19e-247j)
| (-0.29120976359718559587 + 1.9633297594223509371e-752j)  +/-  (1.65e-253, 1.65e-253j)
| (-5.4142400439527630561 + 1.8207403116250336518e-737j)  +/-  (4.5e-241, 4.5e-241j)
| (0.84665593850133918546 + 2.8338199842269020227e-765j)  +/-  (1.41e-250, 1.41e-250j)
| (-2.9630513518053251256e-780 + 4.3422489201713334957e-780j)  +/-  (3.21e-778, 3.21e-778j)
| (-5.0856229130488359417 - 1.7319820350263446152e-754j)  +/-  (2.51e-241, 2.51e-241j)
-------------------------------------------------
The weights are:
| (4.9196569148393822133e-29 + 3.6586389861795406619e-545j)  +/-  (2.09e-68, 1.77e-187j)
| (1.2286321770508674828e-35 + 3.5969016600722819769e-551j)  +/-  (1.32e-71, 1.12e-190j)
| (4.2162619860141298172e-45 + 4.9009151858184606102e-556j)  +/-  (4.7e-75, 3.97e-194j)
| (1.5657995103862716629e-21 + 1.0995812233983441768e-541j)  +/-  (1.06e-65, 8.95e-185j)
| (4.0660734579433605222e-32 + 2.0754381689867841067e-547j)  +/-  (1.1e-70, 9.29e-190j)
| (4.9196569148393822133e-29 + 9.3842217281527257937e-548j)  +/-  (5.01e-70, 4.23e-189j)
| (8.5330048972347180734e-40 - 2.597033028688436755e-553j)  +/-  (1.52e-73, 1.28e-192j)
| (-0.037947810239941639378 - 4.5639021663609269672e-531j)  +/-  (1.02e-43, 8.63e-163j)
| (1.4852101257627975794e-17 - 9.9075512825606973749e-542j)  +/-  (7.28e-65, 6.15e-184j)
| (1.2286321770508674828e-35 - 1.3691433138756604605e-549j)  +/-  (1.05e-73, 8.9e-193j)
| (3.4782379340758728965e-05 - 1.2406643969768466279e-534j)  +/-  (1.28e-50, 1.08e-169j)
| (1.5657995103862716629e-21 - 7.796991700952460408e-544j)  +/-  (1.59e-67, 1.34e-186j)
| (3.4782379340758728965e-05 - 8.5309506316731132854e-535j)  +/-  (4.15e-51, 3.5e-170j)
| (8.5330048972347180734e-40 + 5.8289908834907302269e-552j)  +/-  (6.43e-76, 5.44e-195j)
| (7.3243324277814161758e-07 - 7.9936344090535686053e-536j)  +/-  (1.62e-55, 1.37e-174j)
| (0.0027429114118045306443 + 2.3898897624738834746e-533j)  +/-  (1.75e-45, 1.48e-164j)
| (6.7709632054722701253e-09 - 6.9929932445676689102e-537j)  +/-  (5.88e-60, 4.97e-179j)
| (4.2162619860141298172e-45 - 7.2462769637435744976e-555j)  +/-  (1.91e-78, 1.61e-197j)
| (0.0082149014708145172128 - 4.5662589281752554807e-533j)  +/-  (9.39e-45, 7.93e-164j)
| (2.7801427288771010763e-26 - 3.5526436626636033979e-544j)  +/-  (6.67e-71, 5.63e-190j)
| (4.0660734579433605222e-32 - 2.3676291027227081576e-549j)  +/-  (1.04e-73, 8.79e-193j)
| (0.020714761359055872966 + 1.4570848692030682871e-532j)  +/-  (9.1e-44, 7.69e-163j)
| (2.7801427288771010763e-26 - 2.5375439671811281455e-546j)  +/-  (6.87e-72, 5.8e-191j)
| (8.521799701282078026e-24 + 6.1058379475853166491e-543j)  +/-  (3.8e-71, 3.21e-190j)
| (8.521799701282078026e-24 + 5.0526631620888767427e-545j)  +/-  (4.27e-71, 3.61e-190j)
| (1.0757129169962191327e-12 - 6.7978892200901898942e-541j)  +/-  (4.87e-67, 4.12e-186j)
| (7.8390374227222816687e-08 + 3.0750423398847008944e-536j)  +/-  (1.27e-62, 1.08e-181j)
| (2.5420865138078956235e-11 - 1.6761973745357774714e-538j)  +/-  (4.16e-66, 3.51e-185j)
| (8.4162991091968223772e-16 + 8.5619401911563023895e-541j)  +/-  (8.19e-71, 6.92e-190j)
| (5.5722517806607322213e-06 + 2.7179649587393641444e-535j)  +/-  (2.36e-62, 1.99e-181j)
| (0.00017930500190581014901 + 3.5424776885551071097e-534j)  +/-  (5.28e-59, 4.46e-178j)
| (4.6709279650697458717e-10 + 1.3048011098632242961e-537j)  +/-  (2.97e-65, 2.51e-184j)
| (0.13676770400405860115 + 3.8928368863780912529e-531j)  +/-  (2.28e-50, 1.92e-169j)
| (0.044344091081581346933 - 4.0491371504159670406e-532j)  +/-  (1.57e-50, 1.33e-169j)
| (0.00017930500190581014901 + 2.4921853955368429528e-534j)  +/-  (1.54e-60, 1.3e-179j)
| (2.5420865138078956235e-11 - 2.3210170609039078682e-538j)  +/-  (1.7e-69, 1.44e-188j)
| (0.090538068128618743919 + 1.9946041369259666429e-531j)  +/-  (1.13e-51, 9.51e-171j)
| (0.15165023314383643876 - 1.3634313282136758267e-531j)  +/-  (2.35e-52, 1.98e-171j)
| (0.0082149014708145172128 - 5.8684165245160286981e-533j)  +/-  (4.07e-56, 3.43e-175j)
| (0.020714761359055872966 + 1.179434641842351858e-532j)  +/-  (3.53e-55, 2.98e-174j)
| (0.044344091081581346933 - 3.4155033889456071216e-532j)  +/-  (2.25e-53, 1.9e-172j)
| (0.00076766464822658516063 - 6.8446704596775066786e-534j)  +/-  (3.43e-60, 2.9e-179j)
| (-0.037947810239941639378 - 5.0737657405409106836e-531j)  +/-  (5.03e-54, 4.25e-173j)
| (7.8390374227222816687e-08 + 2.1542118178279718972e-536j)  +/-  (1.92e-66, 1.62e-185j)
| (3.4783746598374422628e-14 + 9.2422089027811173693e-540j)  +/-  (2.64e-72, 2.23e-191j)
| (4.6709279650697458717e-10 + 1.1695953592531291644e-537j)  +/-  (3.03e-69, 2.56e-188j)
| (6.7709632054722701253e-09 - 5.2817245118107202423e-537j)  +/-  (4.14e-68, 3.5e-187j)
| (5.5722517806607322213e-06 + 4.0039267772436948804e-535j)  +/-  (5.08e-67, 4.29e-186j)
| (1.8514886383065978668e-19 + 9.6709273660342159238e-543j)  +/-  (5.24e-75, 4.43e-194j)
| (0.00076766464822658516063 - 9.4463463636667109244e-534j)  +/-  (2.59e-64, 2.19e-183j)
| (1.4852101257627975794e-17 + 1.2058366815169945932e-540j)  +/-  (3.83e-76, 3.24e-195j)
| (0.13676770400405860115 + 3.5609413799893881399e-531j)  +/-  (2.08e-62, 1.76e-181j)
| (1.8514886383065978668e-19 - 3.9205041420111372904e-541j)  +/-  (3.88e-77, 3.28e-196j)
| (8.4162991091968223772e-16 - 3.8613007452283599149e-540j)  +/-  (3.1e-75, 2.62e-194j)
| (7.3243324277814161758e-07 - 1.1742780682276331911e-535j)  +/-  (5.8e-70, 4.9e-189j)
| (0.0027429114118045306443 + 1.7916508836460518294e-533j)  +/-  (3.73e-68, 3.15e-187j)
| (0.15165023314383643876 - 1.304973554898186806e-531j)  +/-  (3.43e-66, 2.82e-185j)
| (3.4783746598374422628e-14 - 6.3471586746870074699e-540j)  +/-  (1.14e-76, 9.6e-196j)
| (0.090538068128618743919 + 2.2635366519740244568e-531j)  +/-  (2.99e-67, 1.75e-186j)
| (0.1639739945414250944 + 1.1513303403504142849e-531j)  +/-  (1.32e-67, 5.82e-187j)
| (1.0757129169962191327e-12 + 4.0921459362724998146e-539j)  +/-  (7.27e-76, 6.24e-195j)
