Starting with polynomial:
P : t
Extension levels are: 1 12 40
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : t^13 - 78/25*t^11 + 429/115*t^9 - 1716/805*t^7 + 1287/2185*t^5 - 2574/37145*t^3 + 429/185725*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 2474311509266680302092501370355455140919906488404227293366234543440867137382/190606786497466028261714696484921107816137633214151821999201192945955876725*t^51 + 25484557085760472691390483406752628256523863632412514803611299124037346906864019/320730227503556136435422085481247049700058472656788987841615863346301034647623*t^49 - 76824043088356799631132696219180571478149029606804845574584792185756740072172298712/251940566100293422477337861669116975953519844586530723623237991438157425781678467*t^47 + 114233116544108225255679957646083177651946329421061617788703859571550570930510850229342/138819251921261675785013161779683453750389434367178428716404133282424741605704835317*t^45 - 3917952728077242911679866953083529657006323161599275230802411237094482979900207631906172/2359927282661448488345223750254618713756620384242033288178870265801220607296982200389*t^43 + 2547928849654780346427296532357498109503887471307368315938322601931711039604415081012004794786/980349192126805623785931124212022432975206456919904258408825391467814058580275860774596435*t^41 - 634143316711014728257745666792763923617829377166258303891396202867670868251289647781524858424/196069838425361124757186224842404486595041291383980851681765078293562811716055172154919287*t^39 + 7031429438369912929652084448825625780423758672362798813804237452779006087647176337502491889/2162434348122787778279730805884399614827343573828631478830021106406737697273259611927771*t^37 - 116024392312993552314606014122913132527574035409321748801590504869774671542245892302178106364118/43458443094223665980087750005858779059185123803234006830046934175456207502100698420912413787*t^35 + 658299762024699631083578623754377746648632739783466600971346386051847262957134079340961649195/365197000791795512437712184923183017304076670615411822101234740970220231110089902696742973*t^33 - 8727343245136275757925945849361912988948086137704094110172891262099393049387208249176738960/8686667011339547868345711795175092949885173331679720760309591427444143652993340794024841*t^31 + 29529079498568783549276725332861769084846138751966215064090775767633891686618985735308419940/63802071497080127446815055599044648218122135160268293860204930139503537865089020314734177*t^29 - 258314211670948965196425963787410443679830008160718026092689879228645383850948703620230624600/1467447644432842931276746278778026909016809108686170758784713393208581370897047467238886071*t^27 + 26948421310885932158735815441155198614467936272053425432416829222367362618875221178236858580/489149214810947643758915426259342303005603036228723586261571131069527123632349155746295357*t^25 - 6901067661026537530510256564543514547349158688563748688326396180494976394256328297128575632/489149214810947643758915426259342303005603036228723586261571131069527123632349155746295357*t^23 + 198407086155910249587671213597268941178080436029263966151570894956200077381700111851901701/67668863709024377595106877150501899625281052442708796518399168329776479553882294273202915*t^21 - 634408034577536599916715752581569248873522695562814733741910158320531335852193929662884366/1297308787107295924751906130513907847101816748258788641824166912836571936590143413066261599*t^19 + 14810180711082206410612904395394126226194353125611511017492439939917447145778160432135196989/229623655317991378681087385100961688937021564441805589602877543572073232776455384112728303023*t^17 - 19697072497477274126533752102347705224594549630209419043971828307893744945803788096884812792/2985107519133887922854136006312501956181280337743472664837408066436952026093919993465467939299*t^15 + 374370750976966452070879783647188133414314536145703606752018025768626593471666068579211830294/733341413867225133047832745550771313901867869638979784661723248321344547743739678394683290421121*t^13 - 8143261504066343289434465674914237534964641724639777406572717005394591340712128625812932652/282054389948932743479935671365681274577641488322684532562201249354363287593746030151801265546585*t^11 + 99300868421188319401254316187832928295421100869903224199731328336885980089798428383634714/87180447802397393439252843876665121233089187299738855519225840709530470710794227501465845714399*t^9 - 2377639344951443220431617567667329765641281941575379133295681055533472185253927738511745288/81164996904031973291944397649175227868006033376056874488399257700572868231749425803864702360105469*t^7 + 2235055162637911970446843304083103991158416167310064266216937808464512916252803093789/5061108493111677576351212673765369325185884727571046610238776435778067483428909758924032073337*t^5 - 859976229593837252547194411847556220524768550321209807358975771815842818252950094733638/266684989827533626530674449418718605852019823949901159033311846730453709904319541926984022040346541*t^3 + 2116969384427911763649821575353654194521466692201543516845470633135781256939491278067/289874988942971333185515705889911528100021547771631694601425920359188815113390806442373937000376675*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (0.99876926125135689411 + 2.3363282115438738923e-820j)  +/-  (5.32e-238, 5.32e-238j)
| (0.99353155713819377503 + 1.1806008165738377365e-834j)  +/-  (1.71e-237, 1.71e-237j)
| (-0.89712307663800694986 - 3.089462437260132995e-853j)  +/-  (1.39e-237, 1.39e-237j)
| (-0.9708971113963602745 - 7.3032706529969957249e-853j)  +/-  (3.78e-237, 3.78e-237j)
| (0.91759839922297796521 - 1.0024955654372471387e-851j)  +/-  (3.05e-237, 3.05e-237j)
| (0.93539445262475808956 - 6.2217055043075115676e-880j)  +/-  (3.95e-237, 3.95e-237j)
| (-0.95413480065212929242 + 3.3228251732055581742e-900j)  +/-  (4.15e-237, 4.15e-237j)
| (-0.91759839922297796521 + 6.9621525366459433183e-902j)  +/-  (3.18e-237, 3.18e-237j)
| (-0.99353155713819377503 + 5.5864665504234348698e-901j)  +/-  (1.69e-237, 1.69e-237j)
| (0.98418305471858814947 - 2.0827318041715644105e-898j)  +/-  (2.84e-237, 2.84e-237j)
| (0.89712307663800694986 + 2.8594665976705598478e-909j)  +/-  (1.39e-237, 1.39e-237j)
| (-0.99876926125135689411 + 3.2106778558352981506e-914j)  +/-  (6.21e-238, 6.21e-238j)
| (-0.86985557477808483753 - 1.0240472005559510738e-914j)  +/-  (3.82e-238, 3.82e-238j)
| (-0.76256893507052394991 - 9.8505137311595956991e-917j)  +/-  (6.67e-240, 6.67e-240j)
| (0.9708971113963602745 - 4.8042137306748731934e-913j)  +/-  (3.68e-237, 3.68e-237j)
| (0.86985557477808483753 + 1.8370820540985370285e-924j)  +/-  (3.9e-238, 3.9e-238j)
| (0.68085010793338287234 + 2.811376707966814869e-928j)  +/-  (3.77e-241, 3.77e-241j)
| (-0.98418305471858814947 + 1.0440151229176701184e-922j)  +/-  (3e-237, 3e-237j)
| (-0.80157809073330991279 + 1.7357321395150237559e-925j)  +/-  (2.74e-239, 2.74e-239j)
| (-0.93539445262475808956 - 1.5780843459447182859e-926j)  +/-  (3.86e-237, 3.86e-237j)
| (0.80157809073330991279 - 1.5040242612655239236e-926j)  +/-  (2.66e-239, 2.66e-239j)
| (0.76256893507052394991 - 1.7579461452271823992e-928j)  +/-  (6.47e-240, 6.47e-240j)
| (0.95413480065212929242 + 1.2794345700552881698e-929j)  +/-  (3.94e-237, 3.94e-237j)
| (-0.72162447029681646909 + 4.6705145391629450455e-944j)  +/-  (1.53e-240, 1.53e-240j)
| (-0.68085010793338287234 - 7.8971323249816895735e-943j)  +/-  (4.01e-241, 4.01e-241j)
| (0.23045831595513479407 - 4.1536725798391797561e-953j)  +/-  (2.23e-250, 2.23e-250j)
| (0.72162447029681646909 + 6.2708231941604775402e-941j)  +/-  (1.76e-240, 1.76e-240j)
| (0.83759686470219160165 + 6.6395902959397890496e-943j)  +/-  (1.03e-238, 1.03e-238j)
| (-0.33558225828270120222 + 5.0179800699506908354e-951j)  +/-  (3.68e-248, 3.68e-248j)
| (-0.64234933944034022064 - 8.0094134565341952396e-944j)  +/-  (8.25e-242, 8.25e-242j)
| (-0.83759686470219160165 + 1.1481570118099667629e-947j)  +/-  (1.05e-238, 1.05e-238j)
| (0.55496520057099842221 + 3.4742544830289057483e-953j)  +/-  (1.29e-243, 1.29e-243j)
| (0.64234933944034022064 + 2.1627383472008860528e-951j)  +/-  (8.56e-242, 8.56e-242j)
| (0.39214554347268456581 + 5.204804462545963657e-957j)  +/-  (5.18e-247, 5.18e-247j)
| (-0.60187576503397872036 - 1.4252791003514299092e-955j)  +/-  (1.26e-242, 1.26e-242j)
| (-0.50319540135741869547 + 5.3572690892131676669e-956j)  +/-  (8.8e-245, 8.8e-245j)
| (0.12239993026289953592 + 2.1104672110718630831e-963j)  +/-  (5.85e-253, 5.85e-253j)
| (0.60187576503397872036 - 3.628150355298051839e-956j)  +/-  (1.37e-242, 1.37e-242j)
| (0.061954273930648668482 - 1.7801912596325824708e-968j)  +/-  (2.52e-254, 2.52e-254j)
| (-0.12239993026289953592 + 2.7237188524680977723e-968j)  +/-  (5.57e-253, 5.57e-253j)
| (-0.55496520057099842221 + 3.621998717272843999e-959j)  +/-  (1.21e-243, 1.21e-243j)
| (-0.179092246907487661 + 1.5444558796831852365e-966j)  +/-  (1.42e-251, 1.42e-251j)
| (0.33558225828270120222 - 4.5272849717791218159e-962j)  +/-  (3.53e-248, 3.53e-248j)
| (0.50319540135741869547 + 5.3209441855404324355e-960j)  +/-  (9.2e-245, 9.2e-245j)
| (-5.5964969322799984487e-981 - 1.1103768867404154681e-980j)  +/-  (6.59e-979, 6.59e-979j)
| (-0.44849275103644685288 + 5.7519979235088137112e-962j)  +/-  (6.83e-246, 6.83e-246j)
| (-0.28110787734478358222 - 4.183059010504655317e-965j)  +/-  (3.28e-249, 3.28e-249j)
| (0.179092246907487661 - 3.095990565782737758e-968j)  +/-  (1.56e-251, 1.56e-251j)
| (0.44849275103644685288 - 3.923665840930023241e-961j)  +/-  (7.26e-246, 7.26e-246j)
| (0.28110787734478358222 - 1.105759930757598557e-964j)  +/-  (3.42e-249, 3.42e-249j)
| (-0.23045831595513479407 + 9.2363907481555334443e-966j)  +/-  (2.55e-250, 2.55e-250j)
| (-0.39214554347268456581 - 4.2615422059947003771e-962j)  +/-  (5.03e-247, 5.03e-247j)
| (-0.061954273930648668482 + 1.605058111436893275e-969j)  +/-  (2.3e-254, 2.3e-254j)
-------------------------------------------------
The weights are:
| (0.0031566836220726632449 - 3.1260560929574225476e-820j)  +/-  (1.45e-53, 5.82e-168j)
| (0.0073103354284411229763 + 5.3978135633457272575e-820j)  +/-  (1.15e-53, 4.62e-168j)
| (0.02404260799316715329 + 4.8335363537947799768e-821j)  +/-  (1.09e-54, 4.38e-169j)
| (0.015144814069765016527 + 6.9614145281652258996e-822j)  +/-  (6.91e-55, 2.77e-169j)
| (0.017689776619698136763 - 1.1058652703588076069e-819j)  +/-  (3.89e-55, 1.56e-169j)
| (0.018647000060481420652 + 9.4097309961928557048e-820j)  +/-  (4.39e-55, 1.76e-169j)
| (0.018165967145017793053 - 1.469871393651060235e-821j)  +/-  (1.65e-55, 6.61e-170j)
| (0.017689776619698136763 - 4.6840718059316742679e-821j)  +/-  (1.64e-55, 6.57e-170j)
| (0.0073103354284411229763 + 1.4190703553330341862e-822j)  +/-  (7.86e-57, 3.15e-171j)
| (0.011359871160203387631 - 4.5194923357498528178e-820j)  +/-  (1.97e-56, 7.9e-171j)
| (0.02404260799316715329 + 9.015453529247036035e-820j)  +/-  (4.83e-57, 1.93e-171j)
| (0.0031566836220726632449 - 3.6920684723149418884e-823j)  +/-  (2.99e-57, 1.2e-171j)
| (0.030058918958884474632 - 4.322843626295913007e-821j)  +/-  (1.18e-57, 4.74e-172j)
| (0.040211225775731271424 + 6.4260681611894745239e-821j)  +/-  (2.33e-59, 9.34e-174j)
| (0.015144814069765016527 + 4.9194856419481508377e-820j)  +/-  (1.39e-57, 5.56e-172j)
| (0.030058918958884474632 - 6.2660320896516276952e-820j)  +/-  (5.22e-59, 2.09e-173j)
| (0.039686653638260994202 + 7.1988026976914197907e-820j)  +/-  (1.1e-61, 4.42e-176j)
| (0.011359871160203387631 - 3.3244495140705163501e-822j)  +/-  (6.18e-58, 2.48e-172j)
| (0.037644462715733203448 - 4.9784724847761745322e-821j)  +/-  (2.29e-60, 9.18e-175j)
| (0.018647000060481420652 + 3.0831924765893599466e-821j)  +/-  (3.44e-58, 1.38e-172j)
| (0.037644462715733203448 - 4.5453250930801770432e-820j)  +/-  (2.44e-61, 9.78e-176j)
| (0.040211225775731271424 + 4.7918982532672724342e-820j)  +/-  (7.1e-62, 2.85e-176j)
| (0.018165967145017793053 - 6.4311694968406692316e-820j)  +/-  (3.1e-59, 1.24e-173j)
| (0.041335875335426527395 - 9.2050675751951210465e-821j)  +/-  (6.7e-63, 2.69e-177j)
| (0.039686653638260994202 + 1.3625927996198753651e-820j)  +/-  (8.77e-64, 3.51e-178j)
| (0.049702705594195237629 - 5.6471862162255371507e-820j)  +/-  (1.73e-67, 6.92e-182j)
| (0.041335875335426527395 - 5.7141036280348623407e-820j)  +/-  (1.08e-63, 4.34e-178j)
| (0.034275056074659674321 + 4.9461342907276687436e-820j)  +/-  (4.61e-62, 1.85e-176j)
| (0.055995423917920311779 - 2.2116284911520070939e-820j)  +/-  (1.37e-68, 5.51e-183j)
| (0.038171497375023867414 - 1.7170365167119097921e-820j)  +/-  (9.52e-66, 3.81e-180j)
| (0.034275056074659674321 + 4.3410750504703508161e-821j)  +/-  (3.46e-63, 1.39e-177j)
| (0.049745411225845138567 - 5.1956063600103375966e-820j)  +/-  (5.93e-68, 2.38e-182j)
| (0.038171497375023867414 - 7.9060130851409023025e-820j)  +/-  (1.59e-66, 6.38e-181j)
| (0.056745386270178945349 + 3.9027326286230501523e-820j)  +/-  (1.31e-69, 5.25e-184j)
| (0.043657678791138330423 + 1.6918840964956461718e-820j)  +/-  (5.12e-68, 2.05e-182j)
| (0.053479093147317678855 + 1.3858231653811345232e-820j)  +/-  (1.1e-69, 4.4e-184j)
| (0.059022393616072923298 - 3.7454719158089443024e-820j)  +/-  (5.59e-72, 2.24e-186j)
| (0.043657678791138330423 + 6.8232558354238888509e-820j)  +/-  (1.19e-68, 4.78e-183j)
| (0.061492702584397648382 + 2.9977855208337098122e-820j)  +/-  (2.07e-72, 8.31e-187j)
| (0.059022393616072923298 - 2.9276729524295014042e-820j)  +/-  (2.13e-73, 8.55e-188j)
| (0.049745411225845138567 - 1.4840574479919846479e-820j)  +/-  (5.65e-71, 2.26e-185j)
| (0.053943123722867948122 + 3.3950598914210227561e-820j)  +/-  (1.61e-73, 6.43e-188j)
| (0.055995423917920311779 - 4.4498607852738250944e-820j)  +/-  (3.46e-73, 1.39e-187j)
| (0.053479093147317678855 + 4.2000952662688277265e-820j)  +/-  (2.19e-72, 8.76e-187j)
| (0.062178437775335697937 - 2.6618582127753890712e-820j)  +/-  (4.52e-74, 1.81e-188j)
| (0.055724972000419218115 - 1.450132855988014556e-820j)  +/-  (6.56e-74, 2.63e-188j)
| (0.052501144269412063539 + 2.9765282586489302485e-820j)  +/-  (1.65e-74, 6.62e-189j)
| (0.053943123722867948122 + 4.8786415795736272066e-820j)  +/-  (3.01e-74, 1.21e-188j)
| (0.055724972000419218115 - 3.813941093764332386e-820j)  +/-  (3.17e-74, 1.27e-188j)
| (0.052501144269412063539 + 5.3083397770306757011e-820j)  +/-  (2.19e-74, 8.76e-189j)
| (0.049702705594195237629 - 3.5296921908571744292e-820j)  +/-  (1.38e-75, 5.56e-190j)
| (0.056745386270178945349 + 1.7021101282627853254e-820j)  +/-  (7.1e-76, 2.89e-190j)
| (0.061492702584397648382 + 2.6475988431878782164e-820j)  +/-  (9.02e-76, 3.57e-190j)
