Starting with polynomial:
P : t
Extension levels are: 1 16 36
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : t^17 - 136/33*t^15 + 2380/341*t^13 - 61880/9889*t^11 + 77350/24273*t^9 - 12376/13485*t^7 + 43316/310155*t^5 - 1768/186093*t^3 + 221/1178589*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 1741459732289057171770264982980751745245011648855015452358382665481939115597503302/130302818179898099765389921488278699490390907148459289744658619797341315073157019*t^51 + 2609340843897827668848405352816249162318658950192360577569422394126361149847404314565439/30964597066725538203148277586148100939198703480828888957998447554621068301619716981411*t^49 - 1290143235825280707842009019144787345872143628600842265375641161375099012200555793032384568/3870574633340692275393534698268512617399837935103611119749805944327633537702464622676375*t^47 + 474756904606496288537236123216959674989590384751798701999050826511243685723793929797171386384814/511763507445672991960257764270364469759989171941464358642199592153055378721482169945647626125*t^45 - 212335160046743803995398634405835262290843588871941238789894920871273101051846980754902694444892/109934383080922346421092408621041256466960636935573825189805838314360044317948021692028008575*t^43 + 61746120873466215978122028363349614284979030819988265230715821141699164796993444402613633264165052974/19775326631745554441265365739978764337046280253881826396617843613502027852045443986027074266496725*t^41 - 524048404207509926836412066924158891408984682049778710362832483194179164545946717377870167495810899176/130517155769520659312351413883859844624505449675620054217677767849113383823499930307778690158878385*t^39 + 33178081114753032447355221625058687918552113849074327255866623165910226060883067530127388649666470412883/7948160126990040150431656614722234127774370332810195609409864067734468886687495755922420234034260625*t^37 - 6173760162289972382140573326416781968515982433309405981575382679497952186390048484237517904035804566467834/1740647067810818792944532798624169273982587102885432838460760230833848686184561570547010031253503076875*t^35 + 83556169098451041541796314236860909004852435928806236887677072973774127644780698913531252478780560333669/33689943247951331476345796102403276270630718120363216228272778661300297151959256204135678024261349875*t^33 - 1462743415397606971710373993406323727988511230188101742535998684012805031950117849413085072563727079472/1020907371150040347768054427345553826382749033950400491765841777615160519756341097095020546189737875*t^31 + 110880289707295425361894583790632787431877961553435825706233834993753839880481730145898834732340836724/161937031285868468956312081578949917288298122626615250418030075069990978995833415401279121119751525*t^29 - 9852158392018737513399042308640772351385908638057275234016328684460113828805586357702218788929497570008/36435832039320405515170218355263731389867077590988431344056766890747970274062518465287802251944093125*t^27 + 118684538020004785101926362382488740598828491984952420314704081647125373814596686559840725360645720668/1349475260715570574635934013157915977402484355221793753483583958916591491631945128343992675997929375*t^25 - 43601920806816833221322362304689131581832236413732599236725517031018106536393750516932440356890627728/1861102403039039070758775082494308469704643641201534689586925355514534004981099977003106420984970425*t^23 + 10171273171957089817371210064522149913077054283642178733562849572889996686829562915095570648739854693543/2006437581603633121829846700300000376566124449182636353073758890095168978642805875207258095132796751825*t^21 - 24630783682839499526818296157045375890425658651296262695644575685339845155113425289792016251066193302706/27956363637010621497495864024180005246821333991944733186161040535326021102423095194554462792183634742095*t^19 + 696234054709759373746565094607216513954893366114580117111426074768353303605279675311805636881677984194607/5745768421185604049880071000759101078359858380976009636418887541602532231840115091301851431761952298309525*t^17 - 222905772623254746994758258968193987028863745290742708142556142383724409395229698958775860041403220888472/17237305263556812149640213002277303235079575142928028909256662624807596695520345273905554295285856894928575*t^15 + 19655299675880337967379351325925805159453264202176384324547250728104163311812988677412471292352386542/18838584987493783770098593445111806814294617642544293889897991939680433547016770791153611251678532125605*t^13 - 5431672927550057516287789074918491687291151114201578759381923431715287408665930828531814215433500276/88396437249009293075078015396293862743997821245784763637213654486192803566771001404643868180953112281685*t^11 + 36387774036058462404841002254676942458586593404289947716337056248268833628621116616183303162739714/14464871549837884321376402519393541176290552567492052231544052552286095129107982048032632975065054737003*t^9 - 13392963726545124315604760981403565924295197990095123205605516330507549362836944930487959557803192/200900993747748393352450034991576960781813230104056280993667396559529099015388639556008791320347982458375*t^7 + 205371442610088581232293365653129293896676435650561290324847319377515316456814443740759379047139/200900993747748393352450034991576960781813230104056280993667396559529099015388639556008791320347982458375*t^5 - 15172801718662442107424294856560911851598640990164269467199776050889766131082775901591295958/2043060953366932813753729169405867397781151492583623196545770134503685752698867520908563979528962533475*t^3 + 648928115361990566194875977201477075887663072535332753400091746138004898808142354984375211/40180198749549678670490006998315392156362646020811256198733479311905819803077727911201758264069596491675*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:
| (-0.95067552176876776122 + 9.2386340540307181998e-828j)  +/-  (1.09e-236, 1.09e-236j)
| (0.99684411881397497219 + 8.0735599773320272121e-825j)  +/-  (2.84e-236, 2.84e-236j)
| (-0.90699172118503431294 + 5.5513222793236129766e-839j)  +/-  (2.21e-237, 2.21e-237j)
| (-0.99963141862069477912 - 2.5433472141058198922e-837j)  +/-  (1.22e-236, 1.22e-236j)
| (0.88023915372698590212 - 2.3554266755452916043e-839j)  +/-  (8.95e-238, 8.95e-238j)
| (0.95067552176876776122 - 2.3663454902973090625e-841j)  +/-  (1.11e-236, 1.11e-236j)
| (-0.99057547531441733568 - 1.7710139221127267941e-856j)  +/-  (3.13e-236, 3.13e-236j)
| (-0.93049824112387455909 - 3.2291108607790507782e-858j)  +/-  (5.4e-237, 5.4e-237j)
| (-0.99684411881397497219 + 1.5099391354110447231e-856j)  +/-  (2.93e-236, 2.93e-236j)
| (0.99963141862069477912 - 9.8570663949109524048e-855j)  +/-  (1.24e-236, 1.24e-236j)
| (0.90699172118503431294 + 6.6699803291543110413e-875j)  +/-  (2.22e-237, 2.22e-237j)
| (-0.0597797342226052646 - 1.424785768403459296e-909j)  +/-  (2.8e-254, 2.8e-254j)
| (-0.88023915372698590212 - 3.8844469896121606854e-890j)  +/-  (9.26e-238, 9.26e-238j)
| (-0.85033559588970862209 + 4.5409207968233936126e-891j)  +/-  (2.73e-238, 2.73e-238j)
| (0.99057547531441733568 + 2.7510006326885966003e-886j)  +/-  (2.97e-236, 2.97e-236j)
| (0.81738785386835341895 + 3.8068480179511288851e-902j)  +/-  (7.2e-239, 7.2e-239j)
| (0.85033559588970862209 + 2.0860252457762492071e-900j)  +/-  (2.6e-238, 2.6e-238j)
| (-0.96745206434753148027 + 6.3963020488034913833e-902j)  +/-  (1.72e-236, 1.72e-236j)
| (-0.74284269582772626432 - 5.0510352168204358251e-908j)  +/-  (3.82e-240, 3.82e-240j)
| (-0.98076794512515279159 - 1.1247126871930883476e-903j)  +/-  (2.6e-236, 2.6e-236j)
| (0.93049824112387455909 - 3.6884623395674452725e-902j)  +/-  (4.91e-237, 4.91e-237j)
| (0.78151400389680140693 - 1.0485363383141259057e-914j)  +/-  (1.88e-239, 1.88e-239j)
| (0.98076794512515279159 - 3.2078625960707408998e-916j)  +/-  (2.81e-236, 2.81e-236j)
| (-0.81738785386835341895 - 2.2941436772916975135e-934j)  +/-  (6.96e-239, 6.96e-239j)
| (-0.78151400389680140693 + 2.6874337036303076754e-936j)  +/-  (1.81e-239, 1.81e-239j)
| (0.3512317634538763153 + 1.3920988074194147882e-944j)  +/-  (5.31e-248, 5.31e-248j)
| (0.70151246030998184816 + 7.9826226313733447684e-936j)  +/-  (6.6e-241, 6.6e-241j)
| (0.56309094649797788674 - 2.765001501028528668e-939j)  +/-  (1.46e-243, 1.46e-243j)
| (-0.51269053708647696789 - 7.4338327494342270417e-942j)  +/-  (1.35e-244, 1.35e-244j)
| (-0.61147556514249119878 - 2.0420138100677650615e-939j)  +/-  (1.38e-242, 1.38e-242j)
| (-0.3512317634538763153 + 1.899425260853710747e-945j)  +/-  (5.97e-248, 5.97e-248j)
| (0.74284269582772626432 - 2.0862968392995330868e-938j)  +/-  (3.64e-240, 3.64e-240j)
| (0.65767115921669076585 + 1.389634709204344455e-939j)  +/-  (1.06e-241, 1.06e-241j)
| (0.96745206434753148027 + 2.9784957208898901304e-942j)  +/-  (1.81e-236, 1.81e-236j)
| (-0.65767115921669076585 - 2.3731938302536753964e-954j)  +/-  (9.99e-242, 9.99e-242j)
| (-0.70151246030998184816 - 4.9334119280549927033e-961j)  +/-  (6.47e-241, 6.47e-241j)
| (0.11934553688226467039 + 2.9387730494178569636e-972j)  +/-  (4.45e-253, 4.45e-253j)
| (0.61147556514249119878 + 1.0348114465855606013e-963j)  +/-  (1.33e-242, 1.33e-242j)
| (0.29463522780140236947 - 5.9417387087533028021e-970j)  +/-  (3.89e-249, 3.89e-249j)
| (-0.29463522780140236947 - 4.9454632768332114927e-969j)  +/-  (3.81e-249, 3.81e-249j)
| (-0.56309094649797788674 - 1.281562744285879871e-965j)  +/-  (1.45e-243, 1.45e-243j)
| (-0.11934553688226467039 + 3.1682105004222877037e-975j)  +/-  (4.45e-253, 4.45e-253j)
| (0.40657097956722711618 - 1.2652328517374112397e-968j)  +/-  (8.74e-247, 8.74e-247j)
| (0.46045486074953136229 + 8.4877406136130387076e-966j)  +/-  (1.16e-245, 1.16e-245j)
| (0.0597797342226052646 - 1.2048211031559098333e-976j)  +/-  (2.51e-254, 2.51e-254j)
| (-0.40657097956722711618 + 3.4067890612936026552e-969j)  +/-  (8.72e-247, 8.72e-247j)
| (-0.23698390581906360017 - 8.4900203957842659603e-973j)  +/-  (2.06e-250, 2.06e-250j)
| (0.23698390581906360017 - 8.8026201477999543805e-972j)  +/-  (2e-250, 2e-250j)
| (0.51269053708647696789 + 2.1568257672388806048e-967j)  +/-  (1.41e-244, 1.41e-244j)
| (0.17848418149584785585 + 4.8405484064544889218e-975j)  +/-  (1.01e-251, 1.01e-251j)
| (-0.17848418149584785585 + 1.3552870423200270411e-974j)  +/-  (9.58e-252, 9.58e-252j)
| (-0.46045486074953136229 + 1.1519238218364584816e-967j)  +/-  (1.23e-245, 1.23e-245j)
| (-3.7406533924682409535e-1095 - 2.3274722973174127291e-1095j)  +/-  (2.33e-1093, 2.33e-1093j)
-------------------------------------------------
The weights are:
| (0.018487865296097172368 - 3.9913025877230312777e-827j)  +/-  (1.01e-57, 4.55e-170j)
| (0.0044981745880599818381 - 5.9387991067575244216e-826j)  +/-  (2.55e-59, 1.15e-171j)
| (0.025144395344301257648 - 4.321458251144150087e-827j)  +/-  (6.28e-58, 2.82e-170j)
| (0.001201033257616028512 + 7.687779780751162021e-828j)  +/-  (1.35e-58, 6.05e-171j)
| (0.028344894936539648017 + 8.2894407429801702125e-826j)  +/-  (2.07e-60, 9.31e-173j)
| (0.018487865296097172368 - 1.6844637259890744611e-825j)  +/-  (1.16e-60, 5.22e-173j)
| (0.0080410618575698653918 + 2.8101566581396959123e-827j)  +/-  (6.4e-59, 2.88e-171j)
| (0.021854782939519203081 + 3.4735402832350044702e-827j)  +/-  (4.05e-59, 1.82e-171j)
| (0.0044981745880599818381 - 1.9943126251747149235e-827j)  +/-  (1.1e-58, 4.94e-171j)
| (0.001201033257616028512 - 5.0539483968460792027e-825j)  +/-  (2.49e-61, 1.12e-173j)
| (0.025144395344301257648 - 1.0124599491394857827e-825j)  +/-  (1.57e-61, 7.08e-174j)
| (0.05970838908875516038 - 1.3273148507130486736e-826j)  +/-  (2.87e-63, 1.29e-175j)
| (0.028344894936539648017 + 4.8487273633960578656e-827j)  +/-  (2.77e-60, 1.24e-172j)
| (0.031444411311016878662 - 5.2920287897406352002e-827j)  +/-  (4.84e-61, 2.18e-173j)
| (0.0080410618575698653918 + 8.0308024835003909145e-825j)  +/-  (8.77e-62, 3.94e-174j)
| (0.034431381155660733692 + 5.9409920936662567077e-826j)  +/-  (1.43e-63, 6.44e-176j)
| (0.031444411311016878662 - 6.9520674590727903789e-826j)  +/-  (5.76e-63, 2.59e-175j)
| (0.015055225454166731593 + 4.4783602960524355151e-827j)  +/-  (9.38e-61, 4.22e-173j)
| (0.040024653358462485469 + 6.4907095233550381474e-827j)  +/-  (5.77e-65, 2.6e-177j)
| (0.011568540987585356003 - 3.5315278218495035165e-827j)  +/-  (1.11e-60, 5e-173j)
| (0.021854782939519203081 + 1.276833672292069574e-825j)  +/-  (1.38e-63, 6.23e-176j)
| (0.03729486523442550333 - 5.1541792848036126451e-826j)  +/-  (1.2e-65, 5.39e-178j)
| (0.011568540987585356003 - 3.7963219717676935102e-825j)  +/-  (1.28e-63, 5.74e-176j)
| (0.034431381155660733692 + 5.7021856205474327739e-827j)  +/-  (1.45e-64, 6.53e-177j)
| (0.03729486523442550333 - 6.0984466522959609507e-827j)  +/-  (2.77e-65, 1.24e-177j)
| (0.056001275976449086031 + 2.1068090054965305163e-826j)  +/-  (6.75e-71, 3.03e-183j)
| (0.042611167368985636794 - 4.0180724061691610872e-826j)  +/-  (5.59e-69, 2.52e-181j)
| (0.04942201835796133078 + 2.9465937691056314959e-826j)  +/-  (8.89e-71, 4e-183j)
| (0.051348700357825559884 - 8.5709211653640557516e-827j)  +/-  (4.97e-71, 2.23e-183j)
| (0.047318335178928409813 - 7.6990583755966103585e-827j)  +/-  (2.34e-70, 1.05e-182j)
| (0.056001275976449086031 + 1.0050916129550589066e-826j)  +/-  (4.02e-72, 1.81e-184j)
| (0.040024653358462485469 + 4.5273285897330081415e-826j)  +/-  (6.37e-69, 2.86e-181j)
| (0.045045299465600547823 + 3.5974850444717553557e-826j)  +/-  (2.96e-70, 1.33e-182j)
| (0.015055225454166731593 + 2.3806646793015728106e-825j)  +/-  (2.52e-67, 1.13e-179j)
| (0.045045299465600547823 + 7.2867055789485184609e-827j)  +/-  (9.17e-71, 4.12e-183j)
| (0.042611167368985636794 - 6.8852398135215041134e-827j)  +/-  (3.1e-70, 1.39e-182j)
| (0.05938766584024510435 + 1.595231280053675334e-826j)  +/-  (1.8e-75, 8.09e-188j)
| (0.047318335178928409813 - 3.2452220830569348201e-826j)  +/-  (2.91e-72, 1.31e-184j)
| (0.057158028804596518936 - 1.9566696975876363203e-826j)  +/-  (4.98e-75, 2.24e-187j)
| (0.057158028804596518936 - 1.0606030072362281743e-826j)  +/-  (1.66e-75, 7.47e-188j)
| (0.04942201835796133078 + 8.125947200702715218e-827j)  +/-  (2.07e-73, 9.29e-186j)
| (0.05938766584024510435 + 1.2526578823163137856e-826j)  +/-  (3.63e-76, 1.63e-188j)
| (0.054644143432507686306 - 2.2764487587572264e-826j)  +/-  (1.2e-75, 5.4e-188j)
| (0.053091463005500384232 + 2.4694565387219170537e-826j)  +/-  (1.25e-75, 5.61e-188j)
| (0.05970838908875516038 - 1.4975185341892080128e-826j)  +/-  (2.49e-77, 1.12e-189j)
| (0.054644143432507686306 - 9.529556109513155809e-827j)  +/-  (6.87e-77, 3.09e-189j)
| (0.058110205224484040948 + 1.1199830908061411686e-826j)  +/-  (2.07e-77, 9.3e-190j)
| (0.058110205224484040948 + 1.8229458374911574885e-826j)  +/-  (1.06e-77, 4.78e-190j)
| (0.051348700357825559884 - 2.690738608737367307e-826j)  +/-  (4.43e-77, 1.99e-189j)
| (0.058854315928301863197 - 1.7031456395976321192e-826j)  +/-  (5.79e-78, 2.61e-190j)
| (0.058854315928301863197 - 1.1837898417899033355e-826j)  +/-  (9.21e-79, 4.18e-191j)
| (0.053091463005500384232 + 9.0375531079338955273e-827j)  +/-  (9.26e-79, 4.31e-191j)
| (0.059815412497675649841 + 1.4086047353073952946e-826j)  +/-  (8.25e-79, 3.64e-191j)
