Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 53
-------------------------------------------------
Trying to find an order 53 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^59 - 6577774559923300700287386592280220893010997637769794848959520/132673921194919697215055115424737796685927620643991976099*t^57 + 7109305459977023591181186524076330375790196350911013302885427540/398021763584759091645165346274213390057782861931975928297*t^55 - 74449254393772964029076111863638996304243817030020716166084429875130/18707022888483677307322771274888029332715794510802868629959*t^53 + 1644114637476432882710895234222688513856393241500402827199264310592625/2672431841211953901046110182126861333245113501543266947137*t^51 - 875092312374712103952413057945755686293467687545391599585538758348777575/12471348592322451538215180849925352888477196340535245753306*t^49 + 1560367811123195124625010778297693348284440535087202397551962157640223375/254517318210662276290105731631129650785248904908882566394*t^47 - 4554949172537596561807301314739707458393132769254609046411404230356165375/10830524179177118140004499218345942586606336379101385804*t^45 + 498984515675288344700031285962222259665151075602238211907810178042285088875/21661048358354236280008998436691885173212672758202771608*t^43 - 44154444737267688213234914497420528703201556286310790765968105023959202805625/43322096716708472560017996873383770346425345516405543216*t^41 + 6362133319743129571162365018346516557507101947860640463779271045987989225912125/173288386866833890240071987493535081385701382065622172864*t^39 - 375078813454556641849392388769930844920660069000498392807025188729362531553666875/346576773733667780480143974987070162771402764131244345728*t^37 + 18146732720442866735398858105163732264141105938663898490031430120159591498969150625/693153547467335560960287949974140325542805528262488691456*t^35 - 721168827062875188321806728870531964851515348222639465197145478752225096361864891875/1386307094934671121920575899948280651085611056524977382912*t^33 + 5880845378509273933865961874192785795526761859832353342746303772445507234177959996875/693153547467335560960287949974140325542805528262488691456*t^31 - 157064642256357322715804846414817759799902558849963517998328454389972274231720359393125/1386307094934671121920575899948280651085611056524977382912*t^29 + 13362445744740286863122241719823995314556121027233577851069336825097422805993236296875/10830524179177118140004499218345942586606336379101385804*t^27 - 3775061449632427528463460290329184888186973753986688610068504581949402705479100622265625/346576773733667780480143974987070162771402764131244345728*t^25 + 3431457909645396039132575065909516061104067393029140770887811584292516814069642961254890625/44361827037909475901458428798344980834739553808799276253184*t^23 - 38801406986785180507445473313236612391569366694628403355281078690703161884580833043935234375/88723654075818951802916857596689961669479107617598552506368*t^21 + 344691856757157634765926268168141132265690213380672046243318160605729639228519168786658703125/177447308151637903605833715193379923338958215235197105012736*t^19 - 2364409103389564646557219884219531593832486673925076721793357281947524556678276967387790859375/354894616303275807211667430386759846677916430470394210025472*t^17 + 6121061682853995741517331061532676533796367153829051093952690281616109925650488299163024765625/354894616303275807211667430386759846677916430470394210025472*t^15 - 23205073605896841086743901186261945939767328316540385423998149339240769502406093569303545234375/709789232606551614423334860773519693355832860940788420050944*t^13 + 61764730945655834205926395233275653792885466455244631642122791484667382522438471616466249609375/1419578465213103228846669721547039386711665721881576840101888*t^11 - 108681405463364877931730936138327601583208730292026741248918364626163405542344729995832848703125/2839156930426206457693339443094078773423331443763153680203776*t^9 + 230668175568733918641390634649229670502990146788436910545245406229052798030182942144993969296875/11356627721704825830773357772376315093693325775052614720815104*t^7 - 126457235627289748868856653701483607915443175041492575578772627945047164916971063680196281328125/22713255443409651661546715544752630187386651550105229441630208*t^5 + 26085629682060700133836439328208572475254833041841586110129529979524912615708701351635455234375/45426510886819303323093431089505260374773303100210458883260416*t^3 - 626857223464107267939842839050165807456308493211356266943681713189458130045065848652658203125/90853021773638606646186862179010520749546606200420917766520832*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: 0
  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:
| (-7.6750975779685040979 - 1.2961847130270074474e-927j)  +/-  (3.14e-242, 3.14e-242j)
| (6.1164857309400730128 - 7.8729782727093414256e-935j)  +/-  (1.75e-241, 1.75e-241j)
| (-7.2595262511518477377 + 9.2708957775416719386e-935j)  +/-  (6.84e-242, 6.84e-242j)
| (7.2595262511518477377 - 1.0066245441272730446e-943j)  +/-  (7.06e-242, 7.06e-242j)
| (8.116840695765057781 - 9.3291857240713706242e-945j)  +/-  (1.06e-242, 1.06e-242j)
| (-5.7597761254732523398 - 4.8973881585258490976e-942j)  +/-  (1.59e-241, 1.59e-241j)
| (7.6750975779685040979 + 1.3421091735502174957e-955j)  +/-  (3.08e-242, 3.08e-242j)
| (-8.595288445956459873 + 6.6004298048676611859e-954j)  +/-  (2.22e-243, 2.22e-243j)
| (-9.1308925606526908019 - 2.2735973997387518468e-958j)  +/-  (2.84e-244, 2.84e-244j)
| (2.3286544839701081959 + 3.7054447142568402709e-964j)  +/-  (3.21e-244, 3.21e-244j)
| (9.7772606629716181677 + 3.6636755207210144765e-967j)  +/-  (1.58e-245, 1.58e-245j)
| (3.7673185356855180148 + 7.5922579711374201994e-963j)  +/-  (3.72e-243, 3.72e-243j)
| (-9.7772606629716181677 - 8.1821588700185639805e-962j)  +/-  (1.61e-245, 1.61e-245j)
| (5.4119758363928534411 + 2.0680116808161297085e-962j)  +/-  (1.48e-241, 1.48e-241j)
| (6.8638074077595988784 + 5.982479332437331616e-962j)  +/-  (1.19e-241, 1.19e-241j)
| (-5.4119758363928534411 + 6.2949384905577177289e-961j)  +/-  (1.36e-241, 1.36e-241j)
| (-6.1164857309400730128 + 2.3082921354437318457e-990j)  +/-  (1.81e-241, 1.81e-241j)
| (1.9454341456378826077 - 1.1316075172306815404e-1021j)  +/-  (5.45e-247, 5.45e-247j)
| (-1.9454341456378826077 + 3.5659705472675995749e-1018j)  +/-  (5.52e-247, 5.52e-247j)
| (-6.8638074077595988784 - 1.3356394013266390076e-1014j)  +/-  (1.13e-241, 1.13e-241j)
| (8.595288445956459873 + 1.4803899791988643211e-1034j)  +/-  (2.22e-243, 2.22e-243j)
| (2.8220024608508935676 + 1.1899883179642112359e-1035j)  +/-  (1.34e-244, 1.34e-244j)
| (9.1308925606526908019 - 1.516276965575962224e-1035j)  +/-  (2.92e-244, 2.92e-244j)
| (-1.6379495009969648811 + 3.8832902054888283584e-1039j)  +/-  (3.37e-248, 3.37e-248j)
| (-8.116840695765057781 + 6.4523116563792819053e-1032j)  +/-  (1.04e-242, 1.04e-242j)
| (5.0717614718717925924 - 1.1987105330730206642e-1038j)  +/-  (8.08e-242, 8.08e-242j)
| (1.0358324539336883987 - 6.6343214768281933543e-1049j)  +/-  (1.37e-250, 1.37e-250j)
| (3.451249919409453948 - 5.1518804092802642754e-1042j)  +/-  (1.26e-243, 1.26e-243j)
| (3.13720470889344501 - 1.3063537215020193378e-1042j)  +/-  (3.97e-244, 3.97e-244j)
| (-0.73654064624898050245 + 2.1413370735890350493e-1050j)  +/-  (8.78e-252, 8.78e-252j)
| (-6.4837725401981084617 + 1.7330280385179154561e-1039j)  +/-  (1.71e-241, 1.71e-241j)
| (2.4597448329797309294 - 6.0367164642903537288e-1047j)  +/-  (1.45e-244, 1.45e-244j)
| (0.43607741192761650868 + 4.7457575728752584136e-1056j)  +/-  (4.15e-253, 4.15e-253j)
| (2.3506049736744922228 - 3.534661203482656775e-1047j)  +/-  (4.16e-244, 4.16e-244j)
| (-3.13720470889344501 - 2.016370235747314764e-1046j)  +/-  (4.22e-244, 4.22e-244j)
| (-4.0866076002214457376 - 1.3524559779007148548e-1044j)  +/-  (9.07e-243, 9.07e-243j)
| (-3.451249919409453948 - 1.6503758349433266956e-1045j)  +/-  (1.3e-243, 1.3e-243j)
| (-4.7380514853527070331 - 5.3662811629602024715e-1043j)  +/-  (4.83e-242, 4.83e-242j)
| (-4.4099339092135510713 + 3.1516974304684153632e-1044j)  +/-  (2.45e-242, 2.45e-242j)
| (-2.3506049736744922228 + 2.1275535356683978458e-1047j)  +/-  (4.24e-244, 4.24e-244j)
| (-5.0717614718717925924 + 3.8814630370132839925e-1046j)  +/-  (8.04e-242, 8.04e-242j)
| (-2.8220024608508935676 - 1.0432140007213915871e-1049j)  +/-  (1.44e-244, 1.44e-244j)
| (4.7380514853527070331 - 6.9886262958558636044e-1045j)  +/-  (4.83e-242, 4.83e-242j)
| (0.73654064624898050245 + 1.3796569918994688934e-1055j)  +/-  (8.37e-252, 8.37e-252j)
| (-2.3286544839701081959 + 3.4497516448067126736e-1048j)  +/-  (3.19e-244, 3.19e-244j)
| (-0.43607741192761650868 - 1.3645909551940343058e-1056j)  +/-  (3.85e-253, 3.85e-253j)
| (-1.0358324539336883987 + 3.2462942151426152567e-1054j)  +/-  (1.36e-250, 1.36e-250j)
| (1.6379495009969648811 - 8.2140682466717329764e-1052j)  +/-  (3.38e-248, 3.38e-248j)
| (-0.11731043296927842467 + 9.7051506677841462457e-1058j)  +/-  (1.99e-254, 1.99e-254j)
| (-1.3358490740136969497 - 6.5925301663629430021e-1054j)  +/-  (2.17e-249, 2.17e-249j)
| (-3.7673185356855180148 - 6.9772666633223050636e-1048j)  +/-  (3.56e-243, 3.56e-243j)
| (6.4837725401981084617 + 4.8092127281101111364e-1044j)  +/-  (1.57e-241, 1.57e-241j)
| (4.0866076002214457376 - 5.6474958794160525526e-1046j)  +/-  (1.06e-242, 1.06e-242j)
| (1.3358490740136969497 - 1.8317988277995266665e-1054j)  +/-  (2.16e-249, 2.16e-249j)
| (5.7597761254732523398 - 7.9013261035564988155e-1046j)  +/-  (1.55e-241, 1.55e-241j)
| (4.4099339092135510713 + 1.2182997884442903313e-1054j)  +/-  (2.26e-242, 2.26e-242j)
| (-8.6582980474266964169e-1099 - 2.0199293388764398015e-1100j)  +/-  (5.11e-1097, 5.11e-1097j)
| (-2.4597448329797309294 + 2.8942060886906953666e-1059j)  +/-  (1.43e-244, 1.43e-244j)
| (0.11731043296927842467 + 1.1131912378626943201e-1068j)  +/-  (1.99e-254, 1.99e-254j)
-------------------------------------------------
The weights are:
| (6.2975703299322314294e-27 - 6.6066018344459213901e-953j)  +/-  (1.15e-61, 1.34e-181j)
| (1.153962814453724574e-17 - 4.7254382211969247251e-950j)  +/-  (1.06e-56, 1.23e-176j)
| (2.9583335206907624028e-24 + 5.09454696909850888e-952j)  +/-  (1.86e-60, 2.16e-180j)
| (2.9583335206907624028e-24 + 1.4405491000448184984e-953j)  +/-  (2.91e-61, 3.39e-181j)
| (6.3015039213572355411e-30 + 1.3803665029798677149e-956j)  +/-  (1.27e-64, 1.48e-184j)
| (7.76696317667851135e-16 + 3.8582945832176863661e-948j)  +/-  (1.41e-57, 1.64e-177j)
| (6.2975703299322314294e-27 - 5.3824499913518557121e-955j)  +/-  (5.62e-63, 6.55e-183j)
| (2.3286063370462568797e-33 + 3.7599886163414980209e-957j)  +/-  (4.77e-67, 5.56e-187j)
| (2.012199217760703376e-37 - 1.8257172488030908318e-959j)  +/-  (6.34e-69, 7.39e-189j)
| (0.0069931282770366626181 + 1.0520586846993110238e-939j)  +/-  (5.2e-41, 6.06e-161j)
| (1.2826444587969529168e-42 - 3.1208029811306100775e-963j)  +/-  (6.83e-72, 7.96e-192j)
| (1.2285731395416693411e-07 + 3.9790654242389256522e-944j)  +/-  (1.62e-51, 1.88e-171j)
| (1.2826444587969529168e-42 + 2.5761669168891782246e-962j)  +/-  (9.17e-72, 1.07e-191j)
| (3.6938782339654588228e-14 - 4.7158166322973639463e-948j)  +/-  (1.6e-58, 1.86e-178j)
| (7.5693945377483495836e-22 - 2.8630041991436984542e-952j)  +/-  (2.5e-62, 2.92e-182j)
| (3.6938782339654588228e-14 - 2.7904319246630558479e-947j)  +/-  (3.46e-60, 4.03e-180j)
| (1.153962814453724574e-17 - 4.7164440243878797093e-949j)  +/-  (3.04e-62, 3.54e-182j)
| (0.0040165566743031893205 - 7.6460698220497542665e-941j)  +/-  (8.88e-44, 1.04e-163j)
| (0.0040165566743031893205 - 1.286370970690127976e-940j)  +/-  (4.17e-45, 4.86e-165j)
| (7.5693945377483495836e-22 - 5.0098830485657561604e-951j)  +/-  (2.52e-64, 2.94e-184j)
| (2.3286063370462568797e-33 - 2.1435889108282118599e-958j)  +/-  (4.63e-70, 5.4e-190j)
| (6.2572427736453022214e-05 - 4.8489898813880193138e-942j)  +/-  (1.27e-51, 1.48e-171j)
| (2.012199217760703376e-37 + 1.5922096145178460283e-960j)  +/-  (4.63e-72, 5.39e-192j)
| (0.011719596048657870239 + 1.5530029076712373877e-940j)  +/-  (1.26e-45, 1.47e-165j)
| (6.3015039213572355411e-30 - 4.8872021740788813495e-955j)  +/-  (4.07e-69, 4.75e-189j)
| (1.2809733001982632576e-12 + 3.6120056981980080125e-947j)  +/-  (5.26e-61, 6.13e-181j)
| (0.05777940087136020887 + 2.4460169845136112869e-940j)  +/-  (2.3e-41, 2.68e-161j)
| (1.1926501619554038867e-06 - 1.9009451162075839404e-943j)  +/-  (1.59e-55, 1.85e-175j)
| (9.4104523985779345094e-06 + 9.0394293353389074531e-943j)  +/-  (2.93e-54, 3.42e-174j)
| (0.098188967939569490191 - 5.0537844818689111386e-940j)  +/-  (1.53e-43, 1.78e-163j)
| (1.1640776052287527008e-19 + 5.1030707594327527425e-950j)  +/-  (1.57e-66, 1.83e-186j)
| (0.00096718059916686637866 + 1.4579390924554441922e-940j)  +/-  (2.57e-51, 3e-171j)
| (0.14115914041131724495 + 8.215913564265453759e-940j)  +/-  (2.71e-46, 3.16e-166j)
| (-0.0066914517114060743628 - 1.158320005223332127e-939j)  +/-  (3.58e-50, 4.17e-170j)
| (9.4104523985779345094e-06 + 2.1621893615559609309e-942j)  +/-  (1.12e-60, 1.31e-180j)
| (1.0122813455487443316e-08 - 2.6098232493566372412e-944j)  +/-  (3.79e-64, 4.42e-184j)
| (1.1926501619554038867e-06 - 5.0306387973037628157e-943j)  +/-  (2.56e-62, 2.99e-182j)
| (3.3221626338579937046e-11 - 1.0363932394101034234e-945j)  +/-  (4.13e-66, 4.81e-186j)
| (6.5788979809023961267e-10 + 5.4268239988328449894e-945j)  +/-  (2.51e-65, 2.93e-185j)
| (-0.0066914517114060743628 - 2.1865460299332356053e-939j)  +/-  (1.85e-60, 2.16e-180j)
| (1.2809733001982632576e-12 + 1.7951230986805878894e-946j)  +/-  (2.86e-67, 3.33e-187j)
| (6.2572427736453022214e-05 - 1.0522614660423344098e-941j)  +/-  (1.38e-62, 1.61e-182j)
| (3.3221626338579937046e-11 - 2.4257091656548836319e-946j)  +/-  (7.16e-70, 8.35e-190j)
| (0.098188967939569490191 - 4.1659024262242628225e-940j)  +/-  (6.12e-58, 7.13e-178j)
| (0.0069931282770366626181 + 1.9734117766053327926e-939j)  +/-  (1.72e-60, 2.01e-180j)
| (0.14115914041131724495 + 9.2094468665076969384e-940j)  +/-  (2.7e-58, 3.15e-178j)
| (0.05777940087136020887 + 3.2123779206615794412e-940j)  +/-  (5.2e-59, 6.06e-179j)
| (0.011719596048657870239 + 1.0051083753764863523e-940j)  +/-  (1.98e-61, 2.3e-181j)
| (0.21834940440027241565 - 4.2792005725767226953e-939j)  +/-  (8.51e-59, 9.92e-179j)
| (0.028489629186780892407 - 2.169043491445489968e-940j)  +/-  (1.12e-59, 1.3e-179j)
| (1.2285731395416693411e-07 + 1.1715976366430022438e-943j)  +/-  (4.2e-65, 4.9e-185j)
| (1.1640776052287527008e-19 + 4.4987726034369714404e-951j)  +/-  (5.36e-75, 6.25e-195j)
| (1.0122813455487443316e-08 - 7.9089815439815633244e-945j)  +/-  (3.62e-69, 4.22e-189j)
| (0.028489629186780892407 - 1.5239812886983670133e-940j)  +/-  (1.92e-63, 2.24e-183j)
| (7.76696317667851135e-16 + 5.2455647096677685208e-949j)  +/-  (1.22e-73, 1.42e-193j)
| (6.5788979809023961267e-10 + 1.4539593771400216479e-945j)  +/-  (3.64e-70, 4.25e-190j)
| (-0.12208972379982657429 + 7.2636914921784791553e-939j)  +/-  (2.56e-63, 2.65e-183j)
| (0.00096718059916686637866 + 2.8407705913223820435e-940j)  +/-  (2.12e-65, 2.84e-185j)
| (0.21834940440027241565 - 4.1499141132258980641e-939j)  +/-  (1.39e-63, 1.4e-183j)
