Starting with polynomial:
P : 32*t^5 - 160*t^3 + 120*t
Extension levels are: 5 64
-------------------------------------------------
Trying to find an order 64 Kronrod extension for:
P1 : 32*t^5 - 160*t^3 + 120*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 32*t^69 - 2938268861021159386158183368143984784683912408900166562272/81336797374064149466377530038708517437375496175393683*t^67 + 23424600351932188850252535345870305073365085481737041272517144/1220051960610962241995662950580627761560632442630905245*t^65 - 1560118097822252975366555192663269234036644821385590732826207872/244010392122192448399132590116125552312126488526181049*t^63 + 665732280170886784025337785250056698396774086024328622829619856/444463373628765844078565737916439985996587410794501*t^61 - 116784786368560746311674962114760786884558868494559463141805030640/444463373628765844078565737916439985996587410794501*t^59 + 15943946014681729597716385613162652216647891955394902914483293931180/444463373628765844078565737916439985996587410794501*t^57 - 1738264205628734868911634969171998955396929346685294692598359151581336/444463373628765844078565737916439985996587410794501*t^55 + 308182307998855405853743402971311536561340326511828931362523411151902135/888926747257531688157131475832879971993174821589002*t^53 - 22503112985575670655919379167036681267782383287021804477363594978133614095/888926747257531688157131475832879971993174821589002*t^51 + 5465148864176195521818330352134609633300686712202546612143383751363399584625/3555706989030126752628525903331519887972699286356008*t^49 - 69448111348953232441624503492543727555833167493216712759124741474244538367625/888926747257531688157131475832879971993174821589002*t^47 + 23755342398423672583271537864851670339650641970007785188187186000319246928175275/7111413978060253505257051806663039775945398572712016*t^45 - 857084805983517261506996257843220057913564455101408862157857530613981269032773625/7111413978060253505257051806663039775945398572712016*t^43 + 104556845343582622346260135467051182792075010869331298710491434811669316984187109625/28445655912241014021028207226652159103781594290848064*t^41 - 1348396118776092620727110194230775295120850003195558238019789148990987526399996396875/14222827956120507010514103613326079551890797145424032*t^39 + 940624073751035477013931078460530845564914725431315590566919391609724444073445319284375/455130494595856224336451315626434545660505508653569024*t^37 - 17301011513456969370869365917959313282209055215875979053986073398098495115644604312658875/455130494595856224336451315626434545660505508653569024*t^35 + 1070956930576470695409933307408982285273260968331183150434022289311762074773315999050145625/1820521978383424897345805262505738182642022034614276096*t^33 - 1736167661223433443338618007287175078695326329904532670921402971144808894112791284169991875/227565247297928112168225657813217272830252754326784512*t^31 + 150179633860563515315857794381008950528779863022309536456148331286970141670668325586703084375/1820521978383424897345805262505738182642022034614276096*t^29 - 1344979897500539638040175451969552454788154239446094602907285123461007966937707861440588215625/1820521978383424897345805262505738182642022034614276096*t^27 + 39584664393889583278931439591009948760609792409790384095528650634195056258915515352585951033125/7282087913533699589383221050022952730568088138457104384*t^25 - 118455412238887356763380904717634271744766841093194065855766459678068722741319147407336133890625/3641043956766849794691610525011476365284044069228552192*t^23 + 9114069772046830379819470822011085814688985509640511923209204483710810349826830612313793864109375/58256703308269596715065768400183621844544705107656835072*t^21 - 34686845457690826176122595731997994927596282309150329484434127923335675601939759912355200258859375/58256703308269596715065768400183621844544705107656835072*t^19 + 410139083731590022608282083886807846109183971555651450410260748241622432061459537057225684453765625/233026813233078386860263073600734487378178820430627340288*t^17 - 229901871089319261386591770063992134907935882634477932944396888000581234807426588465170832307096875/58256703308269596715065768400183621844544705107656835072*t^15 + 3034150320022061066016175130484969544538030083137109383747737472374067383346641309833368580300453125/466053626466156773720526147201468974756357640861254680576*t^13 - 3537437914550396528200270162163544710266832479075792292489015681462416525534286206099107136896609375/466053626466156773720526147201468974756357640861254680576*t^11 + 11032128308231107270661599915151101977442314600355620063515446603423541822470972761547982448960234375/1864214505864627094882104588805875899025430563445018722304*t^9 - 2655309982802181482122218566102260054484650724860189782958808449329766545665142758995638520970390625/932107252932313547441052294402937949512715281722509361152*t^7 + 44582197433195077618140417099560501593988561137091552541941372408172274275427180430563136411744203125/59654864187668067036227346841788028768813778030240599113728*t^5 - 5109463417058460694317733698069262148431137730033117948613949855650228975453166293531076919308515625/59654864187668067036227346841788028768813778030240599113728*t^3 + 619847406337382353412739727573191093613596493728477625638156881103818404990886343827120928006796875/238619456750672268144909387367152115075255112120962396454912*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: 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:
| (8.0408933923728945294 + 1.2640603653559091907e-549j)  +/-  (3.45e-239, 3.45e-239j)
| (10.21647018624352243 + 1.3456965319838440926e-557j)  +/-  (1.81e-242, 1.81e-242j)
| (9.2411127016754006463 - 5.6002956035990360248e-554j)  +/-  (1.3e-240, 1.3e-240j)
| (-9.70088963274890604 - 4.2175172865876546599e-559j)  +/-  (2.05e-241, 2.05e-241j)
| (-3.9485046320600344064 - 8.4658384629221068453e-559j)  +/-  (2.42e-241, 2.42e-241j)
| (-8.419278800272294802 - 2.6987128888519810076e-557j)  +/-  (1.36e-239, 1.36e-239j)
| (-9.2411127016754006463 - 3.170961689921584698e-558j)  +/-  (1.14e-240, 1.14e-240j)
| (-7.6781246218076124825 - 9.9230681731340365131e-557j)  +/-  (5.91e-239, 5.91e-239j)
| (-3.3869421113991380205 - 5.0884488059067560843e-560j)  +/-  (1.67e-242, 1.67e-242j)
| (-4.8126501686887789915 - 3.336041910241220729e-557j)  +/-  (6.29e-240, 6.29e-240j)
| (-10.21647018624352243 - 3.420607050954242105e-560j)  +/-  (1.83e-242, 1.83e-242j)
| (5.7113770488317617633 + 6.1531613026335206148e-555j)  +/-  (4.87e-239, 4.87e-239j)
| (-2.2899624644106420239 - 9.1984258556772361145e-568j)  +/-  (1.61e-245, 1.61e-245j)
| (-2.0201828704560856329 - 3.9442410444758776113e-569j)  +/-  (1.9e-246, 1.9e-246j)
| (-7.3281401300614532399 + 1.2144757214273259585e-561j)  +/-  (8.59e-239, 8.59e-239j)
| (-10.839818130269039692 + 2.5719306901064311047e-568j)  +/-  (7.32e-244, 7.32e-244j)
| (3.1097275393245868866 - 7.8286180155656636661e-565j)  +/-  (3.52e-243, 3.52e-243j)
| (-5.407228157561544521 + 7.1268883973892009696e-562j)  +/-  (2.89e-239, 2.89e-239j)
| (9.70088963274890604 + 1.3159854719901418943e-560j)  +/-  (1.97e-241, 1.97e-241j)
| (4.5212865022486704125 - 1.7358904331892764588e-561j)  +/-  (2.39e-240, 2.39e-240j)
| (10.839818130269039692 + 1.1802975719121073208e-567j)  +/-  (7.88e-244, 7.88e-244j)
| (2.2899624644106420239 + 6.4758344834716717992e-573j)  +/-  (1.68e-245, 1.68e-245j)
| (-8.8173119330270088128 + 2.1643530601620674516e-568j)  +/-  (4.83e-240, 4.83e-240j)
| (8.419278800272294802 - 1.3057528309276893188e-565j)  +/-  (1.39e-239, 1.39e-239j)
| (-5.107819467774274894 + 3.5470675781224678317e-577j)  +/-  (1.39e-239, 1.39e-239j)
| (6.6586708257198167337 + 4.8164080783171480387e-578j)  +/-  (1.19e-238, 1.19e-238j)
| (2.0201828704560856329 + 8.7001153839387670208e-591j)  +/-  (1.92e-246, 1.92e-246j)
| (4.2333493133044081902 + 2.8877157645315727988e-585j)  +/-  (7.96e-241, 7.96e-241j)
| (5.107819467774274894 + 3.3871310101692565788e-583j)  +/-  (1.41e-239, 1.41e-239j)
| (8.8173119330270088128 - 2.372229905762355492e-590j)  +/-  (4.4e-240, 4.4e-240j)
| (-4.5212865022486704125 - 8.0493372592507565823e-606j)  +/-  (2.34e-240, 2.34e-240j)
| (2.5614008179199744666 + 3.0976395102136604136e-610j)  +/-  (1e-244, 1e-244j)
| (1.2208138713105050498 + 3.9497438776556346935e-614j)  +/-  (2.49e-249, 2.49e-249j)
| (-0.95857246461381850711 + 3.1318913828816918472e-616j)  +/-  (2.07e-250, 2.07e-250j)
| (-8.0408933923728945294 + 5.3013619882915681158e-603j)  +/-  (3.42e-239, 3.42e-239j)
| (1.7520096051576400658 - 7.0589619918253672531e-615j)  +/-  (2.5e-247, 2.5e-247j)
| (-3.1097275393245868866 + 3.1494246677694834667e-610j)  +/-  (3.25e-243, 3.25e-243j)
| (7.6781246218076124825 + 3.5863379910289608926e-605j)  +/-  (5.61e-239, 5.61e-239j)
| (6.0208505954551711262 + 1.5538180484323862792e-626j)  +/-  (7.93e-239, 7.93e-239j)
| (-6.0208505954551711262 + 9.2664403302698601566e-641j)  +/-  (7.96e-239, 7.96e-239j)
| (-2.8346066214253134418 + 3.5801098213044252594e-649j)  +/-  (6.98e-244, 6.98e-244j)
| (3.3869421113991380205 + 1.4325476804374489751e-648j)  +/-  (1.67e-242, 1.67e-242j)
| (-6.3363393315677726153 + 5.0315680544905556232e-643j)  +/-  (9.79e-239, 9.79e-239j)
| (3.6664565726394729607 - 4.6330585438909592424e-646j)  +/-  (6.42e-242, 6.42e-242j)
| (6.3363393315677726153 - 2.7977548311008035012e-657j)  +/-  (1e-238, 1e-238j)
| (-1.2208138713105050498 + 1.8751596003389903922e-703j)  +/-  (2.36e-249, 2.36e-249j)
| (0.95857246461381850711 - 2.9903722802175251389e-703j)  +/-  (2.01e-250, 2.01e-250j)
| (1.4854827209802735384 + 4.690802695541186078e-702j)  +/-  (2.63e-248, 2.63e-248j)
| (-2.5614008179199744666 - 8.6336233817606101941e-698j)  +/-  (1.04e-244, 1.04e-244j)
| (-9.1024525954206720041e-731 - 1.2774911979378913348e-730j)  +/-  (1.08e-728, 1.08e-728j)
| (5.407228157561544521 + 1.1032877490506517825e-692j)  +/-  (2.78e-239, 2.78e-239j)
| (-1.7520096051576400658 + 5.0480846101180966485e-723j)  +/-  (2.47e-247, 2.47e-247j)
| (-6.9888534490232163542 - 4.2878781061545256851e-714j)  +/-  (1.06e-238, 1.06e-238j)
| (6.9888534490232163542 + 9.6152741310553677139e-739j)  +/-  (1.06e-238, 1.06e-238j)
| (0.70016431100239854366 + 1.6250722495768496993e-782j)  +/-  (1.63e-251, 1.63e-251j)
| (0.21354131430258726897 + 2.9566744773174589603e-782j)  +/-  (6.86e-254, 6.86e-254j)
| (7.3281401300614532399 + 1.3828853669528349054e-767j)  +/-  (8.86e-239, 8.86e-239j)
| (3.9485046320600344064 + 1.7636392259524887226e-783j)  +/-  (2.47e-241, 2.47e-241j)
| (4.8126501686887789915 + 4.2056370513170837507e-781j)  +/-  (6.3e-240, 6.3e-240j)
| (2.8346066214253134418 - 6.9669845164698174596e-793j)  +/-  (7.04e-244, 7.04e-244j)
| (-6.6586708257198167337 + 5.8215714248650180809e-786j)  +/-  (1.14e-238, 1.14e-238j)
| (-4.2333493133044081902 - 9.9020159367759762394e-791j)  +/-  (7.78e-241, 7.78e-241j)
| (-0.70016431100239854366 - 2.8912923659276025607e-802j)  +/-  (1.69e-251, 1.69e-251j)
| (-0.4491186950852895545 - 5.8148388045538467527e-803j)  +/-  (1.08e-252, 1.08e-252j)
| (-5.7113770488317617633 - 4.1882091010589457661e-788j)  +/-  (5.46e-239, 5.46e-239j)
| (-3.6664565726394729607 - 2.9516335475191045215e-794j)  +/-  (6.43e-242, 6.43e-242j)
| (0.4491186950852895545 - 1.4357607738714423849e-805j)  +/-  (1.18e-252, 1.18e-252j)
| (-1.4854827209802735384 - 5.7346536446601780222e-801j)  +/-  (2.7e-248, 2.7e-248j)
| (-0.21354131430258726897 + 1.1175434133153343553e-805j)  +/-  (6.86e-254, 6.86e-254j)
-------------------------------------------------
The weights are:
| (1.7375074252692974154e-29 - 3.9998918230764582976e-577j)  +/-  (2.18e-47, 1.04e-164j)
| (1.4654840246536476259e-46 + 1.9803189531256835018e-586j)  +/-  (7.21e-55, 3.43e-172j)
| (2.0253820654346503849e-38 + 3.3966437507278776087e-582j)  +/-  (1.03e-51, 4.92e-169j)
| (3.6739905011994433421e-42 + 1.1452925697339292224e-584j)  +/-  (7.19e-56, 3.42e-173j)
| (2.7094097540799415553e-08 - 5.6577875012489097024e-566j)  +/-  (3.27e-31, 1.55e-148j)
| (3.5887914871142754371e-32 - 1.7379986608724200944e-579j)  +/-  (2.74e-52, 1.3e-169j)
| (2.0253820654346503849e-38 - 9.7951910810664069566e-583j)  +/-  (9.22e-55, 4.38e-172j)
| (5.0075517726035753851e-27 - 8.921209478118702838e-577j)  +/-  (2.42e-50, 1.15e-167j)
| (1.6369149355972640978e-06 - 5.7457644933134138423e-565j)  +/-  (4.92e-30, 2.34e-147j)
| (1.4442151844149670784e-11 - 2.9443599115784588987e-567j)  +/-  (3.95e-39, 1.88e-156j)
| (1.4654840246536476259e-46 - 6.2472011635155870787e-587j)  +/-  (1.09e-58, 5.17e-176j)
| (1.1790599628547794949e-15 - 4.3232951286903157464e-569j)  +/-  (1.89e-47, 8.99e-165j)
| (0.00080600067411799364626 - 5.9161530404528510982e-564j)  +/-  (8.97e-23, 4.26e-140j)
| (0.0025628243994496831301 + 1.0574883295626203401e-563j)  +/-  (4.25e-20, 2.02e-137j)
| (9.2487181526601158067e-25 + 1.4524341549660461776e-575j)  +/-  (5.34e-50, 2.54e-167j)
| (3.7910046786348584272e-52 + 8.529551923969155148e-590j)  +/-  (2.36e-61, 1.12e-178j)
| (9.8343084609574973406e-06 + 5.7964665259279309921e-565j)  +/-  (3.38e-35, 1.61e-152j)
| (3.4121799743844756226e-14 + 2.2367579610252826316e-569j)  +/-  (1.32e-43, 6.28e-161j)
| (3.6739905011994433421e-42 - 3.8178448841442646448e-584j)  +/-  (8.97e-62, 4.26e-179j)
| (2.1644571572448000895e-10 - 3.6247921751720613856e-567j)  +/-  (5.1e-45, 2.43e-162j)
| (3.7910046786348584272e-52 - 2.5462345375767166453e-589j)  +/-  (6.89e-66, 3.27e-183j)
| (0.00080600067411799364626 - 5.798216797339586303e-564j)  +/-  (1.46e-31, 6.93e-149j)
| (3.9775998852554765649e-35 + 5.0014854011949063134e-581j)  +/-  (2.93e-56, 1.39e-173j)
| (3.5887914871142754371e-32 + 5.4756658432476817753e-579j)  +/-  (1.01e-58, 4.78e-176j)
| (7.8311594312127229401e-13 - 2.7453896942265397808e-568j)  +/-  (3.02e-45, 1.44e-162j)
| (1.021017968651673164e-20 - 1.8274951840467339635e-572j)  +/-  (1.3e-54, 6.17e-172j)
| (0.0025628243994496831301 + 1.1093739892139413121e-563j)  +/-  (4.81e-32, 2.28e-149j)
| (2.6619911854005568441e-09 + 1.1201078140779286054e-566j)  +/-  (1.76e-45, 8.38e-163j)
| (7.8311594312127229401e-13 - 3.6285064001037471065e-568j)  +/-  (2.83e-49, 1.35e-166j)
| (3.9775998852554765649e-35 - 1.7578337433655783311e-580j)  +/-  (2.94e-60, 1.39e-177j)
| (2.1644571572448000895e-10 + 1.0143999182680138709e-566j)  +/-  (2.55e-46, 1.21e-163j)
| (0.00021735279496326291713 + 2.8604476565358769192e-564j)  +/-  (5.35e-38, 2.54e-155j)
| (0.033504016779221465512 - 5.7332381631954990765e-563j)  +/-  (2.68e-28, 1.27e-145j)
| (0.058676253954308771004 + 8.4160869394607968342e-563j)  +/-  (2.68e-28, 1.27e-145j)
| (1.7375074252692974154e-29 + 4.4575049177652361579e-578j)  +/-  (1.91e-57, 9.1e-175j)
| (0.0070056771623579347022 - 2.0106606449897085945e-563j)  +/-  (5.19e-33, 2.47e-150j)
| (9.8343084609574973406e-06 + 1.267968800905169472e-564j)  +/-  (7.93e-42, 3.77e-159j)
| (5.0075517726035753851e-27 + 5.8613367043448949929e-576j)  +/-  (4.35e-58, 2.07e-175j)
| (3.1814196133162415578e-17 - 3.57510861856491484e-570j)  +/-  (2.06e-53, 9.79e-171j)
| (3.1814196133162415578e-17 + 2.4412908126508780583e-571j)  +/-  (1.07e-53, 5.1e-171j)
| (5.009994960451203709e-05 - 1.8881735750599682744e-564j)  +/-  (2.12e-42, 1.01e-159j)
| (1.6369149355972640978e-06 - 2.3734266679382104215e-565j)  +/-  (2.09e-45, 9.92e-163j)
| (6.5813195988878086845e-19 - 2.5006963042241273846e-572j)  +/-  (5.81e-55, 2.76e-172j)
| (2.2990602458147907086e-07 + 9.1195096375908629798e-566j)  +/-  (8.66e-47, 4.11e-164j)
| (6.5813195988878086845e-19 + 2.3731937970643614984e-571j)  +/-  (2.02e-55, 9.58e-173j)
| (0.033504016779221465512 - 5.2084973585853748913e-563j)  +/-  (3.03e-39, 1.44e-156j)
| (0.058676253954308771004 + 9.1598190600859529822e-563j)  +/-  (3.94e-38, 1.87e-155j)
| (0.016496867735336810906 + 3.4686870389978166662e-563j)  +/-  (2e-39, 9.5e-157j)
| (0.00021735279496326291713 + 3.2897653177446420285e-564j)  +/-  (2.61e-44, 1.24e-161j)
| (0.11693664652830460019 + 3.592167982434746042e-562j)  +/-  (1.15e-39, 5.47e-157j)
| (3.4121799743844756226e-14 + 1.38666274442172775e-568j)  +/-  (7.26e-53, 3.45e-170j)
| (0.0070056771623579347022 - 1.8498400327424746302e-563j)  +/-  (8.43e-43, 4.01e-160j)
| (1.1564097887400033e-22 - 1.9893490152506300489e-574j)  +/-  (1.68e-58, 7.99e-176j)
| (1.1564097887400033e-22 + 1.3641587361185022695e-573j)  +/-  (4.07e-58, 1.93e-175j)
| (0.088326385255909256842 - 1.4296174011973975333e-562j)  +/-  (2.92e-42, 1.39e-159j)
| (0.1208317996013088921 - 3.1250703923090637904e-562j)  +/-  (1.59e-42, 7.56e-160j)
| (9.2487181526601158067e-25 - 9.3105877675404802333e-575j)  +/-  (3.32e-59, 1.58e-176j)
| (2.7094097540799415553e-08 - 3.291647714267106273e-566j)  +/-  (1.02e-50, 4.85e-168j)
| (1.4442151844149670784e-11 + 1.137811269490422314e-567j)  +/-  (1.08e-52, 5.12e-170j)
| (5.009994960451203709e-05 - 1.3284374372541915252e-564j)  +/-  (1.38e-48, 6.54e-166j)
| (1.021017968651673164e-20 + 2.3612966696376752046e-573j)  +/-  (1.42e-60, 6.76e-178j)
| (2.6619911854005568441e-09 - 3.7875540197396997933e-566j)  +/-  (5.72e-55, 2.72e-172j)
| (0.088326385255909256842 - 1.3374585212441451671e-562j)  +/-  (3.66e-49, 1.74e-166j)
| (0.11304266731205293781 + 2.0915484211842275117e-562j)  +/-  (3.54e-49, 1.68e-166j)
| (1.1790599628547794949e-15 - 2.2946849744981977185e-570j)  +/-  (1.62e-58, 7.7e-176j)
| (2.2990602458147907086e-07 + 1.0202537754839240474e-565j)  +/-  (4.06e-54, 1.93e-171j)
| (0.11304266731205293781 + 2.1871973236048263605e-562j)  +/-  (5.86e-50, 2.82e-167j)
| (0.016496867735336810906 + 3.1476848519879894071e-563j)  +/-  (2.51e-51, 1.15e-168j)
| (0.1208317996013088921 - 3.0578194910802345284e-562j)  +/-  (5.1e-50, 2.48e-167j)
