Starting with polynomial:
P : t
Extension levels are: 1 2 8 44
-------------------------------------------------
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 44 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^55 - 48106547474891507491668710569229085124182174818121116041098367735045002141826423630832330137555103453161796171/3399603140566430159157283133047599304039034599212289203073015362616128898173321488149101500502720497028090435*t^53 + 23218537280159990477645402725921220597057911000296764564710959985817972836359294401014495368192138425679092025783471631/245086334759296780451397283873324482061942930957244456182426962594415775304445840089504047457288943288382720365084485*t^51 - 7819848422076128915963282283894179469266061360038271275914922221956273970127300891507371995112296444238543978913993780059/19594412183285425345343672260099867512928747189903304816435837201617076122085244478057721629457841909099053019933244689*t^49 + 18022968719232518198134738460188888638296329273578937782085450280733243835299055945586950646241839387846244677261608741233266/15185669442046204642641346001577397322519779072175061232737773831253233994616064470494734262829827479551766090448264633975*t^47 - 23540652412299968880175769109457273825019956985073882697678008170993428306590895354317747983795199019285952228872767228729811954/8883616623597029715945187410922777433674070757222410821151597691283141886850397715239419543755449075537783162912234810875375*t^45 + 910466819827349401403023810461331310148499521298298360184213784679853730179283696936507618875290723415335123642971563141125702/197413702746600660354337498020506165192757127938275796025591059806292041930008838116431545416787757234172959175827440241675*t^43 - 3267457298327011655031124872078086216492398756375546934555701236024951210190741896368221496609680899755801542837187116280776131854/509524766788976304374545082390926412362506147208689829542050525360039760221352811178509818720729201421400407632810623263763175*t^41 + 188224061322117237534601166684272961840751491877200935426311074649638664213235892824934610046533870831287122188824231583752299118311/25985763106237791523101799201937247030487813507643181306644576793362027771288993370104000754757189272491420789273341786451921925*t^39 - 528812859031953390899509210045780489190360837933787507199583466853567392710238879103938525825986323497187014454254601428189592933/78667189620226016574295121047554127130265474746849912406590796726448856731844711300238248628400142598270705237979624622515575*t^37 + 18282370789670376806177641508850257521531375701376353945932999562070454738807066339540472712810467943419217915163699963928283709683/3540023532910170745843280447139935720861946363608246058296585852690198552933012008510721188278006416922181735709083108013200875*t^35 - 32570210927174714055230339758400706434119509891036916895843734161808124072001277992933175120511871929074989819862942859916128551043/9870418556467181961939499599672526656991544566766521362544598201030318318177927600200481430845735538947730251330031724695630675*t^33 + 20721648363456199829792316665240825072613551275831972689407395361730586411680561133957988385516302347383064585542563037148320908/11792614762804279524419951731986292302259909876662510588464275031099543988265146475747289642587497657046272701708520579086775*t^31 - 14270238539603465765531065259852560876409609261715217918428060510549000524691612847867234929174839187561056602426671814446117356/18298884976765261330996476825495970813851584291372861257961806082740671705928675565814759790221979123002836950927014691686375*t^29 + 692136001216003399963549796079253681015410985008318828785880771073850039880993601067409701219656719596434515122322361801106398436/2404473485946955338892937054870170564940098175886393969296181319272124262159027969348059436435168056762572775351809730487589675*t^27 - 190573389861325144697492980739641753661754135908446104878830319176174681733494723258884964182050121837345907849718095306685516948/2165368055583889257501249757683689879639104141145788582192147053124312818534893275288079908509600862888669039193030071849554375*t^25 + 140047119960120091028162730849831964665328413748115261317020138698051149668391372294972743730921758887544486078442007998908619457/6322874722304956631903649292436374448546184092145702660001069395122993430121888363841193332848034519634913594443647809800698775*t^23 - 5780688133532986498226070485693904503539350822476109761285790729225032971499507182443414536865558683030063762051219968361516243489/1270897819183296283012633507779711264157783002521286234660214948419721679454499561132079859902454938446617632483173209769940453775*t^21 + 4148966964485409178281925662231514609969783733287870267755886432621014637639146978652312386159736313157275092383635170920949772677/5507223883127617226388078533712082144683726344258907016860931443152127277636164764905679392910638066602009740760417242336408633025*t^19 - 162804407892139703561473239103953390955027222414750868774933157924043468979636236724418036891946721177446801729169524923438540437/1642505368652096365764865527598340288765321892147393320818172535676950240698505280761342976832997318109371326191703388065244680025*t^17 + 897762004782840131016618972032230903397455114175750209965668560361235945374378870110271045268639337145737289481370209683434792378/88405436018627539686755997514851844954133501842050875796978110008494674719948960699801695517776032121769103733259329416452875424875*t^15 - 539383517038721124672572429311336162670296836761879788159667590784601964872969733837201485082201008430345610300498317640992524938/683465474323320496474851539407923573748852796999579529437327319444982968007329551341225521899496082817263208861956608798921885181275*t^13 + 144549311933678682012970030155836994745823872283154313302233505676097098627025101025748695224939666173831139482556181884541134898/3218713473095295671432847847980905035347161462792891630085191051403295857880671647769361218518139672071042975067846935454751784058825*t^11 - 464552326386964513408059810987682129424554680019452139892059544091642814258502137933092921856042865466796219977298003778721676546/260715791320718949386060675686453307863120078486224222036900475163666964488334403469318258699969313437754480980495601771834894508764825*t^9 + 1329531183226440067260743266512565884452845715919381141023552501792945686219556854592271552797118080434483145247882924012033101/28968421257857661042895630631828145318124453165136024670766719462629662720926044829924250966663257048639386775610622419092766056529425*t^7 - 1689126886923769928511713872406929402786972751267496985707088644995265951037495678179745524408817876218668259514154267447996201/2462315806917901188646128603705392352040578519036562097015171154323521331278713810543561332166376849134347875926902905622885114805001125*t^5 + 7196638623708693894664964252216353957025472484475841064075662110529714641925888231800346762838878005225557927629431355386269/1477389484150740713187677162223235411224347111421937258209102692594112798767228286326136799299826109480608725556141743373731068883000675*t^3 - 76317189770530784003588676915963997969687603439154026431541653380119550986931296359986294036140248042318206323469407693/7350196438560899070585458518523559259822622444885259991090063147234392033667802419533018901989184624281635450528068374993686909865675*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:
| (-0.99925539339707464221 + 4.8929105963198738032e-886j)  +/-  (2.07e-235, 2.07e-235j)
| (-0.87255335150671091832 + 4.8993916585208459377e-889j)  +/-  (5.59e-237, 5.59e-237j)
| (-0.94263912812584987797 + 2.328172656333207766e-887j)  +/-  (1.38e-235, 1.38e-235j)
| (0.99079325588510780584 - 4.9047534574888645731e-885j)  +/-  (9.5e-235, 9.5e-235j)
| (0.94263912812584987797 - 4.0926308668436160521e-894j)  +/-  (1.38e-235, 1.38e-235j)
| (0.95943209500616697645 - 1.2593640386094231362e-900j)  +/-  (3.22e-235, 3.22e-235j)
| (0.9961500922510981447 - 3.9005593753031460916e-916j)  +/-  (6.34e-235, 6.34e-235j)
| (-0.9225217132136291628 + 7.1149424829188462103e-939j)  +/-  (5.48e-236, 5.48e-236j)
| (-0.9728975066439420398 + 4.4487547939847477738e-937j)  +/-  (6.03e-235, 6.03e-235j)
| (-0.99079325588510780584 + 3.9111749704018557015e-936j)  +/-  (9.21e-235, 9.21e-235j)
| (0.87255335150671091832 + 1.6027274644219381506e-939j)  +/-  (5.79e-237, 5.79e-237j)
| (0.99925539339707464221 - 3.5160104114504306202e-936j)  +/-  (2.28e-235, 2.28e-235j)
| (-0.95943209500616697645 - 4.5041840597124105023e-949j)  +/-  (2.97e-235, 2.97e-235j)
| (-0.89913471668678478187 + 1.652610416472131371e-953j)  +/-  (1.85e-236, 1.85e-236j)
| (0.69527583331321906591 - 1.3671071994610121446e-955j)  +/-  (1.82e-240, 1.82e-240j)
| (0.84286679618557505573 + 2.0444399238009406566e-951j)  +/-  (1.69e-237, 1.69e-237j)
| (0.9225217132136291628 - 5.2626535671989922807e-949j)  +/-  (5.95e-236, 5.95e-236j)
| (-0.9961500922510981447 - 5.6676026969916732374e-953j)  +/-  (6.42e-235, 6.42e-235j)
| (-0.73625128286813396221 + 1.823581635366327123e-959j)  +/-  (1.19e-239, 1.19e-239j)
| (-0.84286679618557505573 + 9.3919710317025524744e-958j)  +/-  (1.43e-237, 1.43e-237j)
| (-0.9831964995514863944 + 6.6037303912463850972e-955j)  +/-  (8.68e-235, 8.68e-235j)
| (0.73625128286813396221 - 2.6543761755435707782e-958j)  +/-  (1.28e-239, 1.28e-239j)
| (-0.69527583331321906591 + 2.7037644462452266924e-960j)  +/-  (1.71e-240, 1.71e-240j)
| (-0.81017673653030383583 + 1.7743959335891679566e-958j)  +/-  (3.51e-238, 3.51e-238j)
| (-0.77459666924148337704 - 7.874764209161942475e-959j)  +/-  (6.84e-239, 6.84e-239j)
| (0.89913471668678478187 + 1.129975130734699473e-953j)  +/-  (1.84e-236, 1.84e-236j)
| (0.77459666924148337704 + 7.3296013399892746083e-962j)  +/-  (6.97e-239, 6.97e-239j)
| (0.9831964995514863944 - 2.2050244665353791666e-962j)  +/-  (9.06e-235, 9.06e-235j)
| (0.17688645164771626193 - 7.8348037543806137731e-1005j)  +/-  (9.27e-252, 9.27e-252j)
| (-0.65181551174545473569 + 1.4173211777232255331e-995j)  +/-  (2.28e-241, 2.28e-241j)
| (-0.34809060189060850632 - 1.3055223875762911861e-1001j)  +/-  (7.48e-248, 7.48e-248j)
| (0.23486295963167437907 + 8.7803417420218728966e-1004j)  +/-  (2.1e-250, 2.1e-250j)
| (0.65181551174545473569 - 5.3309496618867530289e-993j)  +/-  (2.27e-241, 2.27e-241j)
| (-0.059244517225594210524 - 2.2303095877900258005e-1008j)  +/-  (2.13e-254, 2.13e-254j)
| (-0.55806685067819680295 - 4.921356251564119616e-998j)  +/-  (3.13e-243, 3.13e-243j)
| (-0.60602480562886801376 - 1.8475277416412890356e-996j)  +/-  (2.7e-242, 2.7e-242j)
| (1.773296226637497196e-1020 - 5.5527625280999849964e-1021j)  +/-  (1.02e-1018, 1.02e-1018j)
| (0.60602480562886801376 + 1.1283057834934905292e-994j)  +/-  (2.71e-242, 2.71e-242j)
| (0.81017673653030383583 + 3.4530253306584720812e-995j)  +/-  (3.38e-238, 3.38e-238j)
| (-0.17688645164771626193 - 4.0299228099826274428e-1011j)  +/-  (9.31e-252, 9.31e-252j)
| (-0.5081127709588822868 + 2.2675908477717309736e-1004j)  +/-  (2.5e-244, 2.5e-244j)
| (-0.11827707073203099456 + 1.9286646407121324281e-1012j)  +/-  (4.65e-253, 4.65e-253j)
| (0.5081127709588822868 - 1.2542957508784970667e-1001j)  +/-  (2.6e-244, 2.6e-244j)
| (0.55806685067819680295 - 4.7679829756644607906e-1004j)  +/-  (2.86e-243, 2.86e-243j)
| (0.059244517225594210524 + 3.5902936417713730383e-1016j)  +/-  (2.13e-254, 2.13e-254j)
| (-0.40293661887532529296 - 4.7900243707618394188e-1009j)  +/-  (1.25e-246, 1.25e-246j)
| (-0.23486295963167437907 + 1.203680065718811918e-1012j)  +/-  (2.04e-250, 2.04e-250j)
| (0.11827707073203099456 - 7.4071089256458570429e-1015j)  +/-  (4.87e-253, 4.87e-253j)
| (0.45634100522928665108 - 1.8648434442736362218e-1009j)  +/-  (1.81e-245, 1.81e-245j)
| (0.2919991541426287378 + 3.1598914732409983819e-1011j)  +/-  (4.2e-249, 4.2e-249j)
| (-0.2919991541426287378 - 5.320878074590749744e-1011j)  +/-  (4.16e-249, 4.16e-249j)
| (-0.45634100522928665108 + 6.975125559544674753e-1009j)  +/-  (1.95e-245, 1.95e-245j)
| (0.9728975066439420398 + 9.2888847925950445296e-1012j)  +/-  (5.94e-235, 5.94e-235j)
| (0.34809060189060850632 - 3.4738239104706871286e-1031j)  +/-  (7.36e-248, 7.36e-248j)
| (0.40293661887532529296 + 2.4199763521890504177e-1029j)  +/-  (1.23e-246, 1.23e-246j)
-------------------------------------------------
The weights are:
| (0.0019022057826325816507 + 6.3072125452270243052e-886j)  +/-  (4.98e-49, 2.3e-161j)
| (0.028149892264927714343 - 4.481025258774941187e-887j)  +/-  (2.28e-49, 1.05e-161j)
| (0.0184618768697032951 + 1.117037959056859746e-886j)  +/-  (2.31e-49, 1.06e-161j)
| (0.0064351434508495415018 + 1.039247450609468329e-885j)  +/-  (1.51e-50, 6.98e-163j)
| (0.0184618768697032951 + 6.6711521576268935755e-886j)  +/-  (8.29e-51, 3.82e-163j)
| (0.015121827832568104168 - 1.1775257250123238965e-885j)  +/-  (6.09e-51, 2.81e-163j)
| (0.0042679287638907409519 + 3.3288478026510317499e-885j)  +/-  (5e-51, 2.3e-163j)
| (0.021763428681966138798 - 9.7112985196299349694e-887j)  +/-  (3.6e-51, 1.66e-163j)
| (0.011831975999487576753 + 2.7720771609054271596e-886j)  +/-  (5.3e-52, 2.44e-164j)
| (0.0064351434508495415018 + 6.704393156592258998e-886j)  +/-  (2.2e-52, 1.02e-164j)
| (0.028149892264927714343 - 1.7956749353714234464e-886j)  +/-  (1.05e-54, 4.84e-167j)
| (0.0019022057826325816507 - 6.181285459720272989e-886j)  +/-  (4.73e-53, 2.18e-165j)
| (0.015121827832568104168 - 1.5405075863600344617e-886j)  +/-  (4.47e-52, 2.06e-164j)
| (0.02499795691595909575 + 6.3154165252755959258e-887j)  +/-  (7.05e-53, 3.25e-165j)
| (0.042242880209753900289 + 4.432902112699268949e-887j)  +/-  (5.41e-57, 2.49e-169j)
| (0.031206260050471151073 + 1.2759997344925812653e-886j)  +/-  (7.7e-56, 3.55e-168j)
| (0.021763428681966138798 - 4.0672329660452092628e-886j)  +/-  (7.09e-55, 3.27e-167j)
| (0.0042679287638907409519 - 1.0260861748272813102e-885j)  +/-  (4.71e-53, 2.17e-165j)
| (0.039683809728861196358 - 1.8098618012373191582e-887j)  +/-  (6.22e-58, 2.87e-170j)
| (0.031206260050471151073 + 3.3366313732833387873e-887j)  +/-  (3.83e-56, 1.76e-168j)
| (0.0088482276536203588304 - 4.4990035627570689083e-886j)  +/-  (2.08e-53, 9.59e-166j)
| (0.039683809728861196358 - 5.5570425697388284797e-887j)  +/-  (7.34e-61, 3.38e-173j)
| (0.042242880209753900289 + 1.5576095752375953664e-887j)  +/-  (3.11e-59, 1.43e-171j)
| (0.034154932903472714203 - 2.6416817964392162352e-887j)  +/-  (2.23e-57, 1.03e-169j)
| (0.036984409831104488575 + 2.1560158571774835529e-887j)  +/-  (4.99e-58, 2.3e-170j)
| (0.02499795691595909575 + 2.6353154642896671258e-886j)  +/-  (2.66e-60, 1.23e-172j)
| (0.036984409831104488575 + 7.1304589182962920635e-887j)  +/-  (5.1e-62, 2.35e-174j)
| (0.0088482276536203588304 - 5.2669788147916348856e-885j)  +/-  (4.77e-60, 2.2e-172j)
| (0.058327731179369061339 + 1.1354088086225194086e-887j)  +/-  (1.34e-66, 6.17e-179j)
| (0.044652004221524791089 - 1.3704993003069256712e-887j)  +/-  (3.83e-62, 1.77e-174j)
| (0.055501830378936087354 - 9.1088505526917799144e-888j)  +/-  (4.04e-66, 1.86e-178j)
| (0.057590698903673320801 - 1.2277320128451888235e-887j)  +/-  (8.4e-67, 3.87e-179j)
| (0.044652004221524791089 - 3.6103567093891237917e-887j)  +/-  (1.8e-65, 8.3e-178j)
| (0.059173824899248551709 + 9.2450960202816504778e-888j)  +/-  (2.46e-67, 1.13e-179j)
| (0.048985170265446043909 - 1.123798951427744919e-887j)  +/-  (4.24e-65, 1.95e-177j)
| (0.046902207732156751403 + 1.2299837320767985165e-887j)  +/-  (2.98e-64, 1.37e-176j)
| (0.059279869681883143604 - 9.5795452965321583787e-888j)  +/-  (8.35e-68, 3.85e-180j)
| (0.046902207732156751403 + 2.9959603964365330816e-887j)  +/-  (3.55e-67, 1.64e-179j)
| (0.034154932903472714203 - 9.3946089037406530419e-887j)  +/-  (8.01e-65, 3.69e-177j)
| (0.058327731179369061339 + 8.8894714389099401093e-888j)  +/-  (1.63e-68, 7.5e-181j)
| (0.050893237911152420008 + 1.0436607379094709861e-887j)  +/-  (3.23e-67, 1.49e-179j)
| (0.058856068070695330068 - 9.0171216888607893188e-888j)  +/-  (2.41e-68, 1.11e-180j)
| (0.050893237911152420008 + 2.1681206006540105055e-887j)  +/-  (1.15e-69, 5.32e-182j)
| (0.048985170265446043909 - 2.5288007030163938426e-887j)  +/-  (6.15e-69, 2.84e-181j)
| (0.059173824899248551709 + 1.0031041160380550594e-887j)  +/-  (5.88e-70, 2.71e-182j)
| (0.054157491512282913023 + 9.4053115994042180336e-888j)  +/-  (9.43e-70, 4.34e-182j)
| (0.057590698903673320801 - 8.8600926090476208457e-888j)  +/-  (5.23e-70, 2.41e-182j)
| (0.058856068070695330068 - 1.0615258098946377562e-887j)  +/-  (1.37e-70, 6.33e-183j)
| (0.052619437613637271613 - 1.8860135578121844258e-887j)  +/-  (6.34e-72, 2.92e-184j)
| (0.056647605531667287534 + 1.34250999384258239e-887j)  +/-  (3.34e-72, 1.54e-184j)
| (0.056647605531667287534 + 8.9310420340388994926e-888j)  +/-  (2.42e-71, 1.11e-183j)
| (0.052619437613637271613 - 9.8388343672277810967e-888j)  +/-  (2.77e-71, 1.28e-183j)
| (0.011831975999487576753 + 2.2762669581890847982e-885j)  +/-  (2.68e-71, 1.23e-183j)
| (0.055501830378936087354 - 1.4851509404796325895e-887j)  +/-  (5.09e-73, 2.36e-185j)
| (0.054157491512282913023 + 1.6629800681542128987e-887j)  +/-  (5.01e-73, 2.29e-185j)
