Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 53
-------------------------------------------------
Trying to find an order 53 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^59 - 205555454997603146883980831008756902906593676180306089029985/132673921194919697215055115424737796685927620643991976099*t^57 + 1777326364994255897795296631019082593947549087727753325721356885/1592087054339036366580661385096853560231131447727903713188*t^55 - 37224627196886482014538055931819498152121908515010358083042214937565/74828091553934709229291085099552117330863178043211474519836*t^53 + 1644114637476432882710895234222688513856393241500402827199264310592625/10689727364847815604184440728507445332980454006173067788548*t^51 - 875092312374712103952413057945755686293467687545391599585538758348777575/24942697184644903076430361699850705776954392681070491506612*t^49 + 1560367811123195124625010778297693348284440535087202397551962157640223375/254517318210662276290105731631129650785248904908882566394*t^47 - 4554949172537596561807301314739707458393132769254609046411404230356165375/5415262089588559070002249609172971293303168189550692902*t^45 + 498984515675288344700031285962222259665151075602238211907810178042285088875/5415262089588559070002249609172971293303168189550692902*t^43 - 44154444737267688213234914497420528703201556286310790765968105023959202805625/5415262089588559070002249609172971293303168189550692902*t^41 + 6362133319743129571162365018346516557507101947860640463779271045987989225912125/10830524179177118140004499218345942586606336379101385804*t^39 - 375078813454556641849392388769930844920660069000498392807025188729362531553666875/10830524179177118140004499218345942586606336379101385804*t^37 + 18146732720442866735398858105163732264141105938663898490031430120159591498969150625/10830524179177118140004499218345942586606336379101385804*t^35 - 721168827062875188321806728870531964851515348222639465197145478752225096361864891875/10830524179177118140004499218345942586606336379101385804*t^33 + 5880845378509273933865961874192785795526761859832353342746303772445507234177959996875/2707631044794279535001124804586485646651584094775346451*t^31 - 157064642256357322715804846414817759799902558849963517998328454389972274231720359393125/2707631044794279535001124804586485646651584094775346451*t^29 + 3420786110653513436959293880274942800526366982971795929873750227224940238334268492000000/2707631044794279535001124804586485646651584094775346451*t^27 - 60400983194118840455415364645266958210991580063787017761096073311190443287665609956250000/2707631044794279535001124804586485646651584094775346451*t^25 + 3431457909645396039132575065909516061104067393029140770887811584292516814069642961254890625/10830524179177118140004499218345942586606336379101385804*t^23 - 38801406986785180507445473313236612391569366694628403355281078690703161884580833043935234375/10830524179177118140004499218345942586606336379101385804*t^21 + 344691856757157634765926268168141132265690213380672046243318160605729639228519168786658703125/10830524179177118140004499218345942586606336379101385804*t^19 - 2364409103389564646557219884219531593832486673925076721793357281947524556678276967387790859375/10830524179177118140004499218345942586606336379101385804*t^17 + 6121061682853995741517331061532676533796367153829051093952690281616109925650488299163024765625/5415262089588559070002249609172971293303168189550692902*t^15 - 23205073605896841086743901186261945939767328316540385423998149339240769502406093569303545234375/5415262089588559070002249609172971293303168189550692902*t^13 + 61764730945655834205926395233275653792885466455244631642122791484667382522438471616466249609375/5415262089588559070002249609172971293303168189550692902*t^11 - 108681405463364877931730936138327601583208730292026741248918364626163405542344729995832848703125/5415262089588559070002249609172971293303168189550692902*t^9 + 230668175568733918641390634649229670502990146788436910545245406229052798030182942144993969296875/10830524179177118140004499218345942586606336379101385804*t^7 - 126457235627289748868856653701483607915443175041492575578772627945047164916971063680196281328125/10830524179177118140004499218345942586606336379101385804*t^5 + 26085629682060700133836439328208572475254833041841586110129529979524912615708701351635455234375/10830524179177118140004499218345942586606336379101385804*t^3 - 626857223464107267939842839050165807456308493211356266943681713189458130045065848652658203125/10830524179177118140004499218345942586606336379101385804*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: 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:
| (12.913032095846633709 - 4.4868883861684441214e-565j)  +/-  (4.02e-244, 4.02e-244j)
| (9.7068895255705413293 + 9.609127869782496198e-600j)  +/-  (1.7e-241, 1.7e-241j)
| (-11.478946195572813755 + 2.8207228463649746772e-617j)  +/-  (1.43e-242, 1.43e-242j)
| (10.854227087299951809 + 3.6288511386870164732e-625j)  +/-  (4.59e-242, 4.59e-242j)
| (-13.827134632431421178 + 1.4205528216352012129e-644j)  +/-  (2.39e-245, 2.39e-245j)
| (4.4366774472578474901 - 6.252145248447875736e-642j)  +/-  (5.84e-244, 5.84e-244j)
| (13.827134632431421178 - 2.6185987843543787034e-639j)  +/-  (2.42e-245, 2.42e-245j)
| (-12.913032095846633709 + 3.6542284965439251804e-648j)  +/-  (3.88e-244, 3.88e-244j)
| (-5.7793358923301358274 + 2.6592662519251072932e-645j)  +/-  (1.54e-242, 1.54e-242j)
| (3.2932147533114480716 - 5.8377518539808835648e-648j)  +/-  (4.76e-244, 4.76e-244j)
| (9.1694390616904185856 + 1.0212474013197271278e-644j)  +/-  (2.37e-241, 2.37e-241j)
| (-4.8808044431679010614 + 9.4574497074159183168e-660j)  +/-  (1.9e-243, 1.9e-243j)
| (-10.266520480782454493 - 3.8879612947962955305e-658j)  +/-  (9.21e-242, 9.21e-242j)
| (12.155573492780389176 - 1.1214636683147792726e-668j)  +/-  (3.29e-243, 3.29e-243j)
| (-9.1694390616904185856 + 1.1320717355653201169e-681j)  +/-  (2.16e-241, 2.16e-241j)
| (-5.3277929669460084364 - 1.2364434666439082043e-686j)  +/-  (5.13e-243, 5.13e-243j)
| (7.1725538586424197033 + 8.8224071674517439358e-700j)  +/-  (1.2e-241, 1.2e-241j)
| (11.478946195572813755 + 9.3968490946499679112e-725j)  +/-  (1.48e-242, 1.48e-242j)
| (-8.1455535128770310818 + 1.3826627034307213919e-737j)  +/-  (1.98e-241, 1.98e-241j)
| (-1.4648883046992263421 + 1.2479315770967714683e-752j)  +/-  (1.98e-250, 1.98e-250j)
| (-12.155573492780389176 - 5.2415063229296677944e-742j)  +/-  (3.28e-243, 3.28e-243j)
| (-3.990914153185582889 + 4.8480171617986718338e-744j)  +/-  (2.11e-244, 2.11e-244j)
| (4.8808044431679010614 + 2.7729384098825199856e-743j)  +/-  (1.95e-243, 1.95e-243j)
| (2.7512593534648085722 + 7.4078387716820778043e-747j)  +/-  (8.35e-247, 8.35e-247j)
| (-10.854227087299951809 + 8.4392578726302571677e-741j)  +/-  (4.37e-242, 4.37e-242j)
| (-4.4366774472578474901 - 2.2692275530844980456e-745j)  +/-  (6.36e-244, 6.36e-244j)
| (3.47860450277707897 + 4.3514734134106644945e-746j)  +/-  (2.06e-244, 2.06e-244j)
| (-9.7068895255705413293 + 2.4802633138827257152e-741j)  +/-  (1.6e-241, 1.6e-241j)
| (10.266520480782454493 - 2.1461452211059256079e-751j)  +/-  (9.3e-242, 9.3e-242j)
| (-0.16590200531301341924 + 2.1044157799455336768e-787j)  +/-  (2.56e-254, 2.56e-254j)
| (6.2365883435788051863 + 2.2769033318556856924e-762j)  +/-  (3.29e-242, 3.29e-242j)
| (1.8891758777537106755 + 2.1198241967670595271e-770j)  +/-  (2.81e-249, 2.81e-249j)
| (1.4648883046992263421 - 8.6333667392903269033e-772j)  +/-  (1.98e-250, 1.98e-250j)
| (2.3164103987921511048 + 4.7304225563258088141e-769j)  +/-  (4.49e-248, 4.49e-248j)
| (-2.3164103987921511048 + 5.3223463203513267066e-769j)  +/-  (4.61e-248, 4.61e-248j)
| (3.990914153185582889 + 3.2874942496385494199e-765j)  +/-  (2.09e-244, 2.09e-244j)
| (-2.7512593534648085722 + 1.4513632416945683936e-769j)  +/-  (7.84e-247, 7.84e-247j)
| (6.7006166698077861898 + 9.8189919277918101478e-762j)  +/-  (6.31e-242, 6.31e-242j)
| (1.0416257711643523236 + 9.2188928095459152168e-775j)  +/-  (1.07e-251, 1.07e-251j)
| (-6.2365883435788051863 + 2.7599032540204139705e-765j)  +/-  (3.18e-242, 3.18e-242j)
| (5.3277929669460084364 - 5.0654580216437540224e-766j)  +/-  (5.09e-243, 5.09e-243j)
| (-6.7006166698077861898 + 8.0103840566171043744e-766j)  +/-  (6.62e-242, 6.62e-242j)
| (8.6500170747569648063 + 6.9996049644711653717e-763j)  +/-  (2.47e-241, 2.47e-241j)
| (0.61670659019259415219 - 1.206810264038751856e-781j)  +/-  (5.51e-253, 5.51e-253j)
| (0.16590200531301341924 + 5.5846002772365555093e-783j)  +/-  (2.56e-254, 2.56e-254j)
| (-8.6500170747569648063 - 1.1340293037571186835e-770j)  +/-  (2.48e-241, 2.48e-241j)
| (5.7793358923301358274 - 6.8041856464375144578e-772j)  +/-  (1.38e-242, 1.38e-242j)
| (-1.0416257711643523236 - 9.4325659520835740388e-781j)  +/-  (1.07e-251, 1.07e-251j)
| (-5.9694899639463729812e-804 - 2.9160187095259685114e-804j)  +/-  (3.92e-802, 3.92e-802j)
| (-3.47860450277707897 + 2.6360561014666228252e-773j)  +/-  (2.14e-244, 2.14e-244j)
| (-7.6536896270622478851 - 8.8364686421976705496e-771j)  +/-  (1.8e-241, 1.8e-241j)
| (-7.1725538586424197033 + 1.5612449333846311537e-770j)  +/-  (1.21e-241, 1.21e-241j)
| (7.6536896270622478851 - 1.2041699193146160823e-769j)  +/-  (1.85e-241, 1.85e-241j)
| (-1.8891758777537106755 - 2.3615453118375241653e-790j)  +/-  (2.87e-249, 2.87e-249j)
| (-3.2932147533114480716 + 1.1173574014547334968e-784j)  +/-  (4.5e-244, 4.5e-244j)
| (8.1455535128770310818 - 1.1965542590304851243e-781j)  +/-  (2.21e-241, 2.21e-241j)
| (-0.61670659019259415219 - 3.7771587222887120145e-809j)  +/-  (5.67e-253, 5.67e-253j)
| (-3.3242574335521189524 + 4.4412093161123858431e-797j)  +/-  (6.36e-244, 6.36e-244j)
| (3.3242574335521189524 - 5.6326497540192551455e-797j)  +/-  (6.23e-244, 6.23e-244j)
-------------------------------------------------
The weights are:
| (2.012199217760703376e-37 + 6.0491961108344012953e-601j)  +/-  (1.09e-73, 6.63e-193j)
| (7.5693945377483495836e-22 - 4.307125628536332754e-594j)  +/-  (7.85e-67, 4.79e-186j)
| (6.3015039213572355411e-30 + 3.0067706767412917146e-599j)  +/-  (1.84e-72, 1.12e-191j)
| (6.2975703299322314294e-27 - 1.3469729801659118522e-596j)  +/-  (8.98e-70, 5.48e-189j)
| (1.2826444587969529168e-42 - 6.8792173042856620894e-606j)  +/-  (1.78e-77, 1.09e-196j)
| (9.4104523985779345094e-06 + 3.9349177020348850486e-585j)  +/-  (5.25e-51, 3.21e-170j)
| (1.2826444587969529168e-42 + 2.0123718107590189585e-604j)  +/-  (2.38e-76, 1.45e-195j)
| (2.012199217760703376e-37 + 3.4958920700474647199e-603j)  +/-  (9.71e-76, 5.93e-195j)
| (1.0122813455487443316e-08 - 1.7028674317253436116e-587j)  +/-  (5.09e-59, 3.11e-178j)
| (0.0069931282770366626181 + 3.7289733947005314127e-582j)  +/-  (2.38e-46, 1.45e-165j)
| (1.1640776052287527008e-19 + 5.5176898590313088249e-593j)  +/-  (4.54e-67, 2.77e-186j)
| (1.1926501619554038867e-06 - 4.0591240181256613245e-586j)  +/-  (6.14e-56, 3.75e-175j)
| (2.9583335206907624028e-24 + 3.1030955390875721671e-596j)  +/-  (1.49e-71, 9.07e-191j)
| (2.3286063370462568797e-33 - 1.5516928977902840613e-599j)  +/-  (5.29e-74, 3.23e-193j)
| (1.1640776052287527008e-19 + 9.3540189291060494945e-594j)  +/-  (9.62e-70, 5.87e-189j)
| (1.2285731395416693411e-07 + 8.5311933990488748606e-587j)  +/-  (9.46e-59, 5.77e-178j)
| (1.2809733001982632576e-12 + 2.766526288337762678e-589j)  +/-  (2.05e-65, 1.25e-184j)
| (6.3015039213572355411e-30 + 5.1141347293315293793e-598j)  +/-  (7.26e-73, 4.43e-192j)
| (7.76696317667851135e-16 + 1.1924162254773602236e-591j)  +/-  (3.71e-68, 2.27e-187j)
| (0.05777940087136020887 + 5.0452488497970943914e-583j)  +/-  (2.01e-40, 1.23e-159j)
| (2.3286063370462568797e-33 - 4.6885062298050764511e-601j)  +/-  (5.76e-76, 3.52e-195j)
| (6.2572427736453022214e-05 - 1.0270211829633854883e-584j)  +/-  (5.04e-57, 3.08e-176j)
| (1.1926501619554038867e-06 - 8.9921989755890686482e-586j)  +/-  (5.05e-61, 3.08e-180j)
| (0.0040165566743031893205 - 2.4662722034406390751e-583j)  +/-  (1.58e-52, 9.64e-172j)
| (6.2975703299322314294e-27 - 1.166796178126033018e-597j)  +/-  (1.76e-73, 1.08e-192j)
| (9.4104523985779345094e-06 + 1.9224389821969046393e-585j)  +/-  (3.88e-59, 2.37e-178j)
| (0.00096718059916686637866 + 5.3390542544110948956e-583j)  +/-  (1.69e-56, 1.03e-175j)
| (7.5693945377483495836e-22 - 6.1049101160909925282e-595j)  +/-  (1.79e-71, 1.09e-190j)
| (2.9583335206907624028e-24 + 2.7178556779861049063e-595j)  +/-  (1.52e-73, 9.27e-193j)
| (0.21834940440027241565 - 8.4133634947456830353e-582j)  +/-  (1.13e-48, 6.91e-168j)
| (6.5788979809023961267e-10 + 9.0199790256702930361e-588j)  +/-  (9.66e-67, 5.89e-186j)
| (0.028489629186780892407 - 4.2419233104823358971e-583j)  +/-  (7.1e-52, 4.34e-171j)
| (0.05777940087136020887 + 6.3364146788077449736e-583j)  +/-  (1.33e-49, 8.11e-169j)
| (0.011719596048657870239 + 3.008764872626179895e-583j)  +/-  (5.74e-54, 3.5e-173j)
| (0.011719596048657870239 + 2.0934937796856066947e-583j)  +/-  (1.02e-56, 6.21e-176j)
| (6.2572427736453022214e-05 - 1.9458060277841004679e-584j)  +/-  (2.75e-60, 1.68e-179j)
| (0.0040165566743031893205 - 1.5999253929432403704e-583j)  +/-  (8.67e-59, 5.29e-178j)
| (3.3221626338579937046e-11 - 1.6651509191181516144e-588j)  +/-  (1.81e-68, 1.1e-187j)
| (0.098188967939569490191 - 1.0047568510475334951e-582j)  +/-  (8.25e-52, 5.04e-171j)
| (6.5788979809023961267e-10 + 3.1447820494415059362e-588j)  +/-  (2.21e-68, 1.35e-187j)
| (1.2285731395416693411e-07 + 2.0515636188183857415e-586j)  +/-  (1.18e-65, 7.19e-185j)
| (3.3221626338579937046e-11 - 5.2741891017885865353e-589j)  +/-  (5.61e-70, 3.42e-189j)
| (1.153962814453724574e-17 - 5.8591900616433371119e-592j)  +/-  (7.64e-74, 4.66e-193j)
| (0.14115914041131724495 + 1.8444413231959792565e-582j)  +/-  (2.45e-55, 1.5e-174j)
| (0.21834940440027241565 - 8.6323608479212291931e-582j)  +/-  (2.72e-55, 1.66e-174j)
| (1.153962814453724574e-17 - 1.1583619295482812117e-592j)  +/-  (7.2e-74, 4.4e-193j)
| (1.0122813455487443316e-08 - 4.4620101222141972455e-587j)  +/-  (1.04e-67, 6.35e-187j)
| (0.098188967939569490191 - 8.5475953262109107059e-583j)  +/-  (8.79e-59, 5.36e-178j)
| (-0.12208972379982657429 + 1.4689958777297820812e-581j)  +/-  (6.52e-57, 3.98e-176j)
| (0.00096718059916686637866 + 3.0729647082915878296e-583j)  +/-  (3.58e-65, 2.18e-184j)
| (3.6938782339654588228e-14 - 1.0434055194783657702e-590j)  +/-  (1.18e-72, 7.18e-192j)
| (1.2809733001982632576e-12 + 7.9067566098597644846e-590j)  +/-  (8.66e-72, 5.29e-191j)
| (3.6938782339654588228e-14 - 4.0802497822924128658e-590j)  +/-  (7.15e-74, 4.37e-193j)
| (0.028489629186780892407 - 3.1591471182092841487e-583j)  +/-  (1.42e-64, 8.66e-184j)
| (0.0069931282770366626181 + 2.2134701060693788454e-582j)  +/-  (2.68e-66, 1.64e-185j)
| (7.76696317667851135e-16 + 5.2670607174086250908e-591j)  +/-  (6.51e-76, 3.94e-195j)
| (0.14115914041131724495 + 1.6762962990186496431e-582j)  +/-  (1.32e-65, 8.21e-185j)
| (-0.0066914517114060743628 - 2.437779890256122514e-582j)  +/-  (2.83e-66, 1.73e-185j)
| (-0.0066914517114060743628 - 4.12804964983531145e-582j)  +/-  (2.19e-66, 1.31e-185j)
