Starting with polynomial:
P : t
Extension levels are: 1 2 8 46
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P3 : t^11 - 10483/3705*t^9 + 3234/1105*t^7 - 139986/104975*t^5 + 68299/272935*t^3 - 3633/272935*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^57 - 29599400781930309069033617671812265285251286101140319525683154561950220900831923906802121014366404220372124908204124383/1953998444679039915316568714345502480583542680305432599243833810155894310791109097972797349372443441702258881001483080*t^55 + 2071765202987821233583152404832765247384373901105148971357534783244765590948363373423612230557950424794224053322902291929493563/19033001964332420135777565541399655077725701402764958755671132225009704925927540604277049466253609614081962423009067001546280*t^53 - 422747137334139118108832549952364664886517449874894617166957257407224489607200031752146954778105118113563744478684248593258856949/856485088394958906109990449362984478497656563124423144005200950125436721666739327192467225981412432633688309035408015069582600*t^51 + 80914422981030893688091252515377261835535645587101939737687045565023830523007101286676245095858350509217393749014449085328574867691/51052542599132802254179481737338265321492551640648753629602191198788318214226904696270504481131392280614031354610208616912318840*t^49 - 12969105676530159585009670248982447864718948619547538514054546206708921401852933244598675727295061424646667733263052063890049766585529019/3382869103975037309367567908620376805865400203088488037381515194309710935670210272436624303180968880994187252634858948478152527135500*t^47 + 120133925188590749335159097699278550172342529682541370315606940342519009966613084934331981677299041457180232634907314109182725380777242461/16558254035246235251114937657983949628709590467748915130341100687937006158806818701926634747148952943813653394475888537287799211768500*t^45 - 1000948626807254203116671656884536822215261049546567038943776805928160114539720637245432351129022616001499906007385452169036851564993917577/90886416593462669045008657811600790184250418789644045270983374887120900471672982652797306278795363936043830854123210415779697895707100*t^43 + 2691048923705932237238238977360494978837070107278990370373510750181986505497360054784418923227713083915855062704578604470119916515594754637/197290026263857988902579769395913910399958226153129756807744399145213661999485255026803908751531399763607340146755261634253490554095900*t^41 - 95758565191616241316225240532985540078278370453217539489086006482773662028921043008976647381127773239263051665292714589461684683763228636441/6865692913982258013809775974977804081918546270128915536909505090253435437582086874932776024553292711773535437107083104872021471282537320*t^39 + 46741207997718022087332408749275211555275264629536962861664400486044634070806758146124352099474661949182920729180951087779740875193785720469/3937813074821133138824770296039901126606453663704168830211254606420661350839928369563333077510323080301960270945358056100687078670821000*t^37 - 15605829592552316251376088768817658425138193412318609989767345977770825181899689464979627507837788811652744600856783410634602387312992854877/1846545114181661302386756692493286968973647763205909677443695662897824249263921212846082742561337941610523742872682026307101850450159000*t^35 + 524154587086355471646946422366778984041858494759376148775621390272661373775201581174735221073541733327206182278206768710391503517255971782723/103819283537343051342427179216769628526177207768953439394157900858690612790967993837546228549419223799490505496335851808489879332956586600*t^33 - 55838598002291775800659414714088221891633232561010235874070790302615320797043823159926276810323507188456436761158467590735163687754766221869/22047643546908873806590718167002152294537632832654090624028156365152038737866858906360623804849781398278897672608957776534141041138629950*t^31 + 2819680064131434255100480996238468719187768835641972952894470135524313372238461835072938211017496592907678779472028296181835813488976982935/2645717225629064856790886180040258275344515939918490874883378763818244648544023068763274856581973767793467720713074933184096924936635594*t^29 - 64172287668487227774543730423774819872361400378520909686754230183662947809007699109501900109575120168278547068563784468656785162884361411439/171059303381189538154583158192258078147274737494730013462287420074455472966208388066591046761765545331474206080586741369661439112282473750*t^27 + 3911271999141785326844513227867939805088575025385509440897945153987837339970259958306917384003298888204567107688456822272466907560578671919/35576436315745972322748064239415497734333492413433877443723594488419514320607442532367938500310213131617142575164763874601951724206896250*t^25 - 139978799863233627430945216820876409351823079592475000959181726811718293801507870344737638949132920769202690700573243190427346979498656465143/5253928115109365192623434126876880705406370159615915020889100434049793874867307113180097157725812275277219615500332329001216230630874438200*t^23 + 83388775960805403173091249873201813297221470552715338521267482680965982512479928459850990476149367592591695283428523275105329344189324744781/15761784345328095577870302380630642116219110478847745062667301302149381624601921339540291473177436825831658846500996987003648691892623314600*t^21 - 15194846225869506699353498199886455349586278037099572808578156233768600335556462214759160723939787173200847282065106219524187887571080456897/17863355591371841654919676031381394398381658542694111071022941475769299174548844184812330336267761735942546692701129918604135184144973089880*t^19 + 3701603167346297956296210809577735755772568235782990183141052869075789164504325181061278015714421075939035526287885801985026749116273484927/33950822030385079168706986609350603388737070329681790047265824442251591998411545965286592744368553006908348977355948675709613654076703241000*t^17 - 98129088795492547559657898601952815984950051540096433921548479802638909020536864492589689822040152584187470847067714610661628542911635229/8986982302160756250540084690710453838195106851974591483099777058243068470167762167281745138215205207711033552829515825923133026079127328500*t^15 + 91236710172063179215892810821646666225673192103037618245613090970200556364797528163572628910096557353713144479000954492051550994668753597/109641184086361226256589033226667536825980303594090016093817280110565435336046698440837290686225503534074609344520093076262222918165353407700*t^13 - 39114841655364783270718165805578963614674847529407706650970809220240827689746343576340848388997571884152875822050903515760580368570132817/839745104847989321913079899237430098411458852650462507776437111111618833249035593983068737030864974397539856967150885211478307561233746734300*t^11 + 39500025630945020942892062130341962553887642731537986822672472194221170568343131350209219377499340102037170152411907488837173284144417126247/21663912163889398124578017856507069164838497772447161868118079879879764983925270060694003891669660782502612738009951966862759674126220445000818260*t^9 - 294350879716994347743366352361758443949611603312224219060382016072921703735324062854485532609825849355397909498962747262964879216365183437/6334477240903332784964332706581014375683771278493322183660257274818644732141891830612281839669491456872108987722208177445251366703573229532403000*t^7 + 82944152529876435564646666177984296062682542137482540935292640047064354855830256742467915762058313358176666160791803125129874621172509231/120355067577163322914322321425039273137991654291373121489544888221554249910695944781633354953720337680570070766721955371459775967367891361115657000*t^5 - 5977907946747981089742371859223699412756140388187377532779945581214552534254352409436364682299412691548389588113398591407485118325777211/1227621689287065893726087678535400586007514873772005839193357859859853349089098636772660220527947444341814721820563944788889714867152491883379701400*t^3 + 58058768999637711255341359983973541229572650126131057432318581244572061492135597055092095254133339495644867846625472420147869555489/5605578489895278053543779354042925050262624994392720726910309862373759584881728935034978175926700659095044391874721209081688195740422337367030600*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:
| (0.99836332464896938352 + 3.1876514959011891158e-881j)  +/-  (2.66e-232, 2.66e-232j)
| (0.9997147729255778128 + 1.4603645889288196729e-897j)  +/-  (1.04e-232, 1.04e-232j)
| (-0.9225217132136291628 - 7.7492203518778830953e-908j)  +/-  (7.61e-235, 7.61e-235j)
| (-0.99556621253798272378 + 3.4658270623563251687e-904j)  +/-  (2.36e-232, 2.36e-232j)
| (0.95951363374730336604 + 1.5118524105055732146e-907j)  +/-  (8.02e-234, 8.02e-234j)
| (0.94266274130900158154 + 1.3401912468945200313e-907j)  +/-  (2.71e-234, 2.71e-234j)
| (-0.99836332464896938352 + 1.4181746424834861007e-904j)  +/-  (2.38e-232, 2.38e-232j)
| (-0.94266274130900158154 + 2.6258453275954891647e-909j)  +/-  (2.55e-234, 2.55e-234j)
| (-0.98343625153405642542 - 1.3155174467970621983e-908j)  +/-  (6.42e-233, 6.42e-233j)
| (-0.9997147729255778128 - 1.4413185367448337715e-907j)  +/-  (1.1e-232, 1.1e-232j)
| (0.8725474065000954693 - 2.7908782352035804079e-910j)  +/-  (4.4e-236, 4.4e-236j)
| (0.98343625153405642542 + 6.7111697283453674644e-905j)  +/-  (6.28e-233, 6.28e-233j)
| (-0.89912833067026404231 + 1.2796698716792914324e-921j)  +/-  (1.85e-235, 1.85e-235j)
| (-0.8725474065000954693 + 5.6250545706701909555e-922j)  +/-  (4.41e-236, 4.41e-236j)
| (0.9225217132136291628 + 6.274469338659957641e-919j)  +/-  (7.3e-235, 7.3e-235j)
| (0.84286316957253506752 + 3.838390567288869994e-922j)  +/-  (9.9e-237, 9.9e-237j)
| (0.89912833067026404231 - 2.6354519749536604881e-920j)  +/-  (1.88e-235, 1.88e-235j)
| (-0.99079325588510780584 + 1.8341931695566774669e-919j)  +/-  (1.43e-232, 1.43e-232j)
| (-0.77459666924148337704 + 4.6714128665498981614e-924j)  +/-  (3.15e-238, 3.15e-238j)
| (-0.95951363374730336604 - 1.1819642715415162264e-919j)  +/-  (8.6e-234, 8.6e-234j)
| (0.97307894116257979188 - 4.3144661140719928148e-916j)  +/-  (2.38e-233, 2.38e-233j)
| (0.81017529650645141929 - 8.4726666885912165662e-939j)  +/-  (1.81e-237, 1.81e-237j)
| (-0.05924460241488947031 + 1.8967898162181153854e-961j)  +/-  (2.23e-254, 2.23e-254j)
| (-0.84286316957253506752 - 7.4408148805956853157e-943j)  +/-  (9.2e-237, 9.2e-237j)
| (-0.81017529650645141929 + 1.3195556810824978874e-943j)  +/-  (1.78e-237, 1.78e-237j)
| (0.77459666924148337704 - 4.9213269254046169563e-942j)  +/-  (2.87e-238, 2.87e-238j)
| (0.69527663239541975566 + 7.8525328399846319675e-946j)  +/-  (5.67e-240, 5.67e-240j)
| (0.73625196187499019361 - 9.1735597226332517548e-945j)  +/-  (4.29e-239, 4.29e-239j)
| (-0.97307894116257979188 - 4.5998306708500286496e-939j)  +/-  (2.42e-233, 2.42e-233j)
| (-0.65181611277473117012 - 3.4776768764851192145e-956j)  +/-  (6.43e-241, 6.43e-241j)
| (-0.4029363989030375033 + 4.472759298209163526e-960j)  +/-  (1.7e-246, 1.7e-246j)
| (0.60602509373521855488 + 4.5520884159273853433e-950j)  +/-  (6.2e-242, 6.2e-242j)
| (0.65181611277473117012 + 1.2633603420207500929e-949j)  +/-  (6.57e-241, 6.57e-241j)
| (0.05924460241488947031 - 1.074943709058927865e-964j)  +/-  (2.23e-254, 2.23e-254j)
| (-0.73625196187499019361 - 9.1768164275798044447e-955j)  +/-  (4.44e-239, 4.44e-239j)
| (-0.69527663239541975566 - 7.3154047477812257266e-954j)  +/-  (6.12e-240, 6.12e-240j)
| (0.99079325588510780584 + 2.8343781114046962335e-953j)  +/-  (1.38e-232, 1.38e-232j)
| (0.55806685067819680295 + 4.2891271320944748199e-993j)  +/-  (5.66e-243, 5.66e-243j)
| (0.2919991541426287378 - 7.9270812361170219209e-999j)  +/-  (5.53e-249, 5.53e-249j)
| (-0.60602509373521855488 + 1.8546561142333787261e-992j)  +/-  (6.34e-242, 6.34e-242j)
| (-0.55806685067819680295 - 1.4800582327689957274e-995j)  +/-  (5.48e-243, 5.48e-243j)
| (-0.11827721255658732086 - 2.4291643312498150329e-1005j)  +/-  (4.63e-253, 4.63e-253j)
| (0.23486305796025252237 + 9.2262828843605155203e-1002j)  +/-  (2.29e-250, 2.29e-250j)
| (0.5081125826269585003 - 6.0925316626940383461e-996j)  +/-  (4.1e-244, 4.1e-244j)
| (0.99556621253798272378 + 2.52567126097256616e-1001j)  +/-  (2.31e-232, 2.31e-232j)
| (-0.5081125826269585003 - 1.4060102628616003537e-1026j)  +/-  (4.12e-244, 4.12e-244j)
| (-0.23486305796025252237 + 1.6421117069803802325e-1033j)  +/-  (2.23e-250, 2.23e-250j)
| (0.11827721255658732086 - 4.0074096930721422352e-1036j)  +/-  (5.43e-253, 5.43e-253j)
| (0.45634074933163137426 - 6.443170270930653199e-1028j)  +/-  (2.83e-245, 2.83e-245j)
| (0.17688660040263332025 + 1.6703319702140264823e-1034j)  +/-  (1.1e-251, 1.1e-251j)
| (-0.2919991541426287378 - 1.0823907471117506741e-1031j)  +/-  (5.58e-249, 5.58e-249j)
| (-0.45634074933163137426 + 8.9012860850627986188e-1028j)  +/-  (2.72e-245, 2.72e-245j)
| (7.4845087659356674782e-1061 - 1.0676720044508901996e-1060j)  +/-  (7.43e-1059, 7.43e-1059j)
| (0.34809048239910185032 - 4.2302913391038626057e-1031j)  +/-  (9.82e-248, 9.82e-248j)
| (0.4029363989030375033 + 3.3472655353950538716e-1029j)  +/-  (1.71e-246, 1.71e-246j)
| (-0.17688660040263332025 - 1.5614430626522594924e-1034j)  +/-  (1.04e-251, 1.04e-251j)
| (-0.34809048239910185032 + 8.0119580951914952017e-1031j)  +/-  (9.87e-248, 9.87e-248j)
-------------------------------------------------
The weights are:
| (0.0020065483768573918484 + 3.9648693714522961633e-883j)  +/-  (2.04e-46, 1.86e-154j)
| (0.00075187905743797148252 - 1.9595852680702283013e-881j)  +/-  (1.83e-46, 1.66e-154j)
| (0.021776097370118953496 + 2.0431734811002948281e-885j)  +/-  (7.45e-48, 6.78e-156j)
| (0.0036782398753135872479 + 3.3902061007514862979e-884j)  +/-  (3.78e-48, 3.44e-156j)
| (0.015202636231876497363 + 2.5646149637363394193e-883j)  +/-  (4.55e-48, 4.14e-156j)
| (0.018499424854799048968 - 1.0957698277151190606e-883j)  +/-  (2.29e-48, 2.09e-156j)
| (0.0020065483768573918484 - 3.2033312808924058425e-884j)  +/-  (1.99e-48, 1.82e-156j)
| (0.018499424854799048968 - 3.1444718687971365203e-885j)  +/-  (7.93e-50, 7.22e-158j)
| (0.0088077634598753038564 + 1.4882125985161166064e-884j)  +/-  (9.88e-50, 8.99e-158j)
| (0.00075187905743797148252 + 1.3254127236645567722e-884j)  +/-  (1.06e-48, 9.63e-157j)
| (0.02814800066397623377 + 1.4763015080826282227e-884j)  +/-  (1.38e-52, 1.25e-160j)
| (0.0088077634598753038564 + 1.9758321502846591119e-882j)  +/-  (1.46e-51, 1.33e-159j)
| (0.024999747550328211968 - 1.3932610970057591615e-885j)  +/-  (9.53e-52, 8.67e-160j)
| (0.02814800066397623377 + 9.9279044484343201697e-886j)  +/-  (1.16e-52, 1.06e-160j)
| (0.021776097370118953496 + 5.1748654799473158693e-884j)  +/-  (3.6e-52, 3.28e-160j)
| (0.031203824982861242979 - 8.7124628753305230494e-885j)  +/-  (4.96e-54, 4.51e-162j)
| (0.024999747550328211968 - 2.6640816905946062901e-884j)  +/-  (9.65e-53, 8.78e-161j)
| (0.0059750146207443615759 - 2.4559349254655247457e-884j)  +/-  (5.54e-51, 5.05e-159j)
| (0.036983374300105651876 - 4.4737060941126541305e-886j)  +/-  (1.23e-56, 1.12e-164j)
| (0.015202636231876497363 + 5.0889050098713223091e-885j)  +/-  (1.38e-52, 1.26e-160j)
| (0.011939978027182554678 - 6.7163652984627003008e-883j)  +/-  (9.95e-54, 9.06e-162j)
| (0.034153084860263928243 + 5.4279703536692267886e-885j)  +/-  (1.54e-56, 1.41e-164j)
| (0.059173900187669547665 - 1.5923722749932524907e-886j)  +/-  (2.14e-61, 1.95e-169j)
| (0.031203824982861242979 - 7.3580807818236205873e-886j)  +/-  (7.05e-56, 6.41e-164j)
| (0.034153084860263928243 + 5.6480908161113279159e-886j)  +/-  (1.09e-56, 9.95e-165j)
| (0.036983374300105651876 - 3.5446308632721786909e-885j)  +/-  (4.32e-58, 3.94e-166j)
| (0.042242957663960479425 - 1.7028123049661911899e-885j)  +/-  (3.51e-60, 3.2e-168j)
| (0.039683450831160022679 + 2.4122912052042154875e-885j)  +/-  (2.42e-59, 2.2e-167j)
| (0.011939978027182554678 - 8.6139553151511599925e-885j)  +/-  (7.91e-55, 7.2e-163j)
| (0.044652288618503858116 + 2.6081734339658809323e-886j)  +/-  (3.66e-62, 3.33e-170j)
| (0.05415741581048101012 - 1.6186612165252745503e-886j)  +/-  (3.93e-64, 3.58e-172j)
| (0.046902525909167802028 - 9.3296030163992461548e-886j)  +/-  (1.26e-62, 1.15e-170j)
| (0.044652288618503858116 + 1.2419531949739538316e-885j)  +/-  (1.2e-61, 1.09e-169j)
| (0.059173900187669547665 - 1.7932828949072993453e-886j)  +/-  (4.42e-66, 4.02e-174j)
| (0.039683450831160022679 + 3.6451248880137667182e-886j)  +/-  (8.88e-62, 8.09e-170j)
| (0.042242957663960479425 - 3.0472813710743060016e-886j)  +/-  (1.16e-62, 1.05e-170j)
| (0.0059750146207443615759 - 6.4533616149890839933e-882j)  +/-  (6.66e-60, 6.06e-168j)
| (0.048985416003086934214 + 7.1993854440105474972e-886j)  +/-  (7.52e-65, 6.85e-173j)
| (0.056647490846673666022 - 2.761512971776020965e-886j)  +/-  (1.5e-67, 1.36e-175j)
| (0.046902525909167802028 - 2.2814674430697376319e-886j)  +/-  (7.87e-65, 7.17e-173j)
| (0.048985416003086934214 + 2.0366246273065441634e-886j)  +/-  (7.84e-66, 7.14e-174j)
| (0.058856102423194344444 + 1.5358253109991294478e-886j)  +/-  (1.05e-68, 9.57e-177j)
| (0.057590621451776523021 + 2.4168218827592933569e-886j)  +/-  (6.55e-69, 5.96e-177j)
| (0.050893365609485714701 - 5.6944065585630541173e-886j)  +/-  (1.62e-67, 1.47e-175j)
| (0.0036782398753135872479 + 2.4167183199014908366e-881j)  +/-  (6.21e-62, 5.65e-170j)
| (0.050893365609485714701 - 1.8531242532504796299e-886j)  +/-  (7.73e-68, 7.03e-176j)
| (0.057590621451776523021 + 1.4962736591166151217e-886j)  +/-  (6.14e-70, 5.59e-178j)
| (0.058856102423194344444 + 1.9486329539397848956e-886j)  +/-  (8.46e-70, 7.7e-178j)
| (0.052619448208361126567 + 4.6081368051850674613e-886j)  +/-  (2.26e-69, 2.06e-177j)
| (0.058327709349894825514 - 2.152085273874620114e-886j)  +/-  (7.11e-70, 6.47e-178j)
| (0.056647490846673666022 - 1.5116944670289879864e-886j)  +/-  (4.88e-71, 4.44e-179j)
| (0.052619448208361126567 + 1.7169912583845069414e-886j)  +/-  (3.51e-70, 3.2e-178j)
| (0.059279959886497591378 + 1.6767088083963768516e-886j)  +/-  (8.57e-71, 7.8e-179j)
| (0.055501712911594410441 + 3.2128353113685548571e-886j)  +/-  (3.58e-71, 3.26e-179j)
| (0.05415741581048101012 - 3.8094171042057876806e-886j)  +/-  (4.11e-71, 3.74e-179j)
| (0.058327709349894825514 - 1.5042655382459843707e-886j)  +/-  (4.64e-72, 4.25e-180j)
| (0.055501712911594410441 + 1.551645915120338604e-886j)  +/-  (4.89e-72, 4.41e-180j)
