Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 36
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 10838314193756608830705047960208419613816779367961276601/12638783590828860632123548997686844617726134144104027*t^43 + 168668892312937094484233730697008461934828515011701727094553/505551343633154425284941959907473784709045365764161080*t^41 - 39504247626660421809374555974773514280647038606974985352721877/505551343633154425284941959907473784709045365764161080*t^39 + 1558201685052571638808814145407993705584528791596341302674697267/126387835908288606321235489976868446177261341441040270*t^37 - 702447839400381310378862112486571562861096288894133893143265999367/505551343633154425284941959907473784709045365764161080*t^35 + 1063987169731455985129614828175210448425574877674409215588566771095/9191842611511898641544399271044977903800824832075656*t^33 - 16723859046745210360884037519177044588967894409757271557403618714191/2297960652877974660386099817761244475950206208018914*t^31 + 401666875505399495099305979638504998157642294533657776622628373326116/1148980326438987330193049908880622237975103104009457*t^29 - 29666175209967479975357890408291305891741248312627076475184158310563653/2297960652877974660386099817761244475950206208018914*t^27 + 1686990100445805656694561748568274097187038573591795879482012090288469959/4595921305755949320772199635522488951900412416037828*t^25 - 36834139499552187992644126100677872386607002373232016367900762241507813125/4595921305755949320772199635522488951900412416037828*t^23 + 153389568819856672815122746025743039609012282115401786891223438877882549975/1148980326438987330193049908880622237975103104009457*t^21 - 7714151172102044229479176810052115812310076207867748781890393345095932707775/4595921305755949320772199635522488951900412416037828*t^19 + 72091049461644401722927997225807653747017881351264912273341742843197387508475/4595921305755949320772199635522488951900412416037828*t^17 - 245182318077374227500229673517899360328992725210820681133144314469641012844075/2297960652877974660386099817761244475950206208018914*t^15 + 590050878382222657190250100253772836315672809961835237265348655446525890474375/1148980326438987330193049908880622237975103104009457*t^13 - 3869653613294121835091421776148233501517444855833855649321511560976590850591875/2297960652877974660386099817761244475950206208018914*t^11 + 32838876128411029470368901193523982231275865703783988484632546202553667443987875/9191842611511898641544399271044977903800824832075656*t^9 - 41945074230774563199151579714039962970806053047193096721136498027546467432850875/9191842611511898641544399271044977903800824832075656*t^7 + 7259944929098067538350357608903378409932022046434444785613003709550752818907125/2297960652877974660386099817761244475950206208018914*t^5 - 9184715468338858129716731091085340093179946622292368655324726664713514937665625/9191842611511898641544399271044977903800824832075656*t^3 + 902485577343800218303044285237121003782607943104032098185641202104703235161875/9191842611511898641544399271044977903800824832075656*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:
| (-7.364477971894464581 + 1.2932930865025164649e-741j)  +/-  (1.07e-244, 1.07e-244j)
| (11.699243748404044216 + 4.503949719258487342e-758j)  +/-  (1.82e-247, 1.82e-247j)
| (7.9542394498278935014 + 2.7237530373318567047e-755j)  +/-  (8.74e-245, 8.74e-245j)
| (-11.699243748404044216 + 4.7048869362586752211e-757j)  +/-  (1.82e-247, 1.82e-247j)
| (10.739824363074374733 + 6.8939745879457149812e-757j)  +/-  (2.15e-246, 2.15e-246j)
| (-9.9436024584984127604 - 5.5058109630852837216e-754j)  +/-  (1.11e-245, 1.11e-245j)
| (7.364477971894464581 + 1.4028641875460781963e-757j)  +/-  (1e-244, 1e-244j)
| (9.9436024584984127604 - 8.7012194565236923352e-760j)  +/-  (1.04e-245, 1.04e-245j)
| (6.79832417977584397 - 2.9373448423273213803e-758j)  +/-  (9.37e-245, 9.37e-245j)
| (-10.739824363074374733 + 2.049505879655437853e-758j)  +/-  (2.18e-246, 2.18e-246j)
| (-8.5735414495718917094 + 9.5069243824522192096e-766j)  +/-  (6.2e-245, 6.2e-245j)
| (9.2315299999091443191 - 7.2670413799268198233e-784j)  +/-  (3.34e-245, 3.34e-245j)
| (-5.7217257214037610141 + 1.7418115450884514763e-802j)  +/-  (3.77e-245, 3.77e-245j)
| (-9.2315299999091443191 - 2.1987127320024177876e-822j)  +/-  (3.24e-245, 3.24e-245j)
| (-3.7313022243357029508 + 1.8347970406968883359e-835j)  +/-  (5.27e-247, 5.27e-247j)
| (8.5735414495718917094 - 5.2286051130630980176e-839j)  +/-  (6.53e-245, 6.53e-245j)
| (2.3344142183389772393 + 5.6190470929086797483e-847j)  +/-  (4.06e-249, 4.06e-249j)
| (3.7313022243357029508 - 4.4299947727461483485e-844j)  +/-  (5.39e-247, 5.39e-247j)
| (6.2517073498786342877 - 3.0666068937614928124e-854j)  +/-  (6.56e-245, 6.56e-245j)
| (-6.79832417977584397 - 2.6411953092233238832e-887j)  +/-  (9.84e-245, 9.84e-245j)
| (-6.2517073498786342877 - 8.1916331181370311292e-918j)  +/-  (6.59e-245, 6.59e-245j)
| (-7.9542394498278935014 + 1.0216936078245715426e-927j)  +/-  (8.6e-245, 8.6e-245j)
| (5.7217257214037610141 - 1.7928629899754809709e-935j)  +/-  (4.01e-245, 4.01e-245j)
| (-1.0379709584894152952 - 6.9722744956752201402e-942j)  +/-  (9.07e-252, 9.07e-252j)
| (-0.74196378430272585765 - 4.4315932045294679767e-942j)  +/-  (1.88e-252, 1.88e-252j)
| (-1.4400445782493368677 - 4.9147832840092142932e-940j)  +/-  (7.68e-251, 7.68e-251j)
| (1.8815390766593347076 - 2.8584561609827350035e-940j)  +/-  (5.82e-250, 5.82e-250j)
| (0.74196378430272585765 - 1.1930844609135688838e-943j)  +/-  (1.98e-252, 1.98e-252j)
| (-3.2588611670813341081 - 7.6130718026246275465e-935j)  +/-  (1.33e-247, 1.33e-247j)
| (-4.2124035862186828411 + 2.8767515930313463973e-935j)  +/-  (2.18e-246, 2.18e-246j)
| (3.2588611670813341081 + 6.3266612576584791019e-948j)  +/-  (1.44e-247, 1.44e-247j)
| (5.2062411291597083548 + 2.8172950671727026125e-945j)  +/-  (1.84e-245, 1.84e-245j)
| (-5.2062411291597083548 + 9.7968921206468556843e-952j)  +/-  (1.82e-245, 1.82e-245j)
| (-2.7936069976842609762 - 2.9641324887689600757e-966j)  +/-  (2.82e-248, 2.82e-248j)
| (-2.3344142183389772393 - 3.9387133316657349217e-967j)  +/-  (3.84e-249, 3.84e-249j)
| (-4.7036001268911846752 + 4.1157937022570799007e-969j)  +/-  (6.89e-246, 6.89e-246j)
| (-2.1147472790243401332e-996 + 2.6953850443216035631e-996j)  +/-  (1.54e-994, 1.54e-994j)
| (1.0379709584894152952 - 1.4870683145019435466e-982j)  +/-  (9.08e-252, 9.08e-252j)
| (1.4400445782493368677 + 1.3965728229245261138e-981j)  +/-  (7.35e-251, 7.35e-251j)
| (4.7036001268911846752 - 7.6845463267750468304e-976j)  +/-  (6.81e-246, 6.81e-246j)
| (-1.8815390766593347076 + 1.6467788657674959925e-981j)  +/-  (5.37e-250, 5.37e-250j)
| (2.7936069976842609762 - 7.0283125401763054572e-979j)  +/-  (2.49e-248, 2.49e-248j)
| (-0.412103935731036978 - 4.8057081888378584336e-985j)  +/-  (1.42e-253, 1.42e-253j)
| (0.412103935731036978 + 1.9495318153920892631e-984j)  +/-  (1.42e-253, 1.42e-253j)
| (4.2124035862186828411 + 7.7797796325183015215e-984j)  +/-  (2.08e-246, 2.08e-246j)
-------------------------------------------------
The weights are:
| (3.8468477156104988983e-13 + 2.0909259934558926658e-753j)  +/-  (7.71e-82, 5.77e-203j)
| (8.386911011031246573e-31 + 6.2808540301499167897e-765j)  +/-  (5.57e-91, 4.17e-212j)
| (4.3911704853750614409e-15 - 2.5784840674404060853e-756j)  +/-  (3.24e-84, 2.43e-205j)
| (8.386911011031246573e-31 - 2.7622358293372125291e-764j)  +/-  (2.76e-92, 2.07e-213j)
| (3.0689006270170984703e-26 - 1.7759867216765034039e-762j)  +/-  (1.12e-89, 8.41e-211j)
| (1.0087896404408611453e-22 - 9.6904680125700895451e-760j)  +/-  (1.81e-89, 1.35e-210j)
| (3.8468477156104988983e-13 + 3.3777693235109252864e-755j)  +/-  (1.49e-83, 1.11e-204j)
| (1.0087896404408611453e-22 + 1.4440031890528877391e-760j)  +/-  (9.66e-89, 7.23e-210j)
| (2.0412914757154101227e-11 - 3.4701048212888626872e-754j)  +/-  (8.87e-83, 6.64e-204j)
| (3.0689006270170984703e-26 + 9.5258372995852790252e-762j)  +/-  (6.41e-92, 4.8e-213j)
| (2.7754659188353521216e-17 - 1.9403463052614424689e-756j)  +/-  (7.95e-89, 5.95e-210j)
| (8.4909356798573133081e-20 - 5.853220243290669465e-759j)  +/-  (1.08e-88, 8.11e-210j)
| (1.6215723582146808739e-08 - 1.5968007510866556407e-751j)  +/-  (1.45e-84, 1.08e-205j)
| (8.4909356798573133081e-20 + 5.2028592862337775715e-758j)  +/-  (8.18e-90, 6.12e-211j)
| (0.00018019223546565378077 - 3.1105365852944425527e-749j)  +/-  (8.96e-80, 6.7e-201j)
| (2.7754659188353521216e-17 + 1.4719531892262739892e-757j)  +/-  (6.39e-88, 4.78e-209j)
| (0.011934476496026427072 + 3.2451091115016171765e-748j)  +/-  (2.41e-75, 1.8e-196j)
| (0.00018019223546565378077 - 1.0185066650316022741e-749j)  +/-  (8.22e-81, 6.15e-202j)
| (6.9928525977384001303e-10 + 2.891887117274312352e-753j)  +/-  (2.84e-85, 2.13e-206j)
| (2.0412914757154101227e-11 - 8.6807522467628206702e-753j)  +/-  (1.05e-87, 7.83e-209j)
| (6.9928525977384001303e-10 + 3.5385972759707048693e-752j)  +/-  (4.6e-87, 3.44e-208j)
| (4.3911704853750614409e-15 + 6.6974650402621064204e-755j)  +/-  (1.51e-89, 1.13e-210j)
| (1.6215723582146808739e-08 - 2.0045141348183881434e-752j)  +/-  (8.37e-87, 6.26e-208j)
| (0.082840427569420197449 - 1.0126720687969226052e-746j)  +/-  (2.49e-73, 1.86e-194j)
| (0.082277658142890211968 + 1.5561615381989200796e-746j)  +/-  (2.49e-73, 1.86e-194j)
| (0.060918543410266565919 + 3.9318669623302419555e-747j)  +/-  (1.59e-76, 1.19e-197j)
| (0.030495297716665911069 - 9.1660926762610798077e-748j)  +/-  (1.56e-78, 1.16e-199j)
| (0.082277658142890211968 + 1.2712978363199201634e-746j)  +/-  (5.35e-76, 4e-197j)
| (0.00092380527335367131388 + 9.1307602876584944841e-749j)  +/-  (2.26e-83, 1.69e-204j)
| (2.7185604886431241106e-05 + 9.6362096468024992549e-750j)  +/-  (2.46e-85, 1.84e-206j)
| (0.00092380527335367131388 + 3.5287777587928404683e-749j)  +/-  (2.75e-84, 2.06e-205j)
| (2.6406216798025905493e-07 + 1.1778810920606663713e-751j)  +/-  (1.39e-87, 1.04e-208j)
| (2.6406216798025905493e-07 + 6.8606058656543497183e-751j)  +/-  (2.75e-87, 2.06e-208j)
| (0.0037237192818695304827 - 2.46594654659497378e-748j)  +/-  (2.78e-84, 2.08e-205j)
| (0.011934476496026427072 + 6.2571698809485313425e-748j)  +/-  (7.51e-84, 5.62e-205j)
| (3.1107622700987722318e-06 - 2.7012232663566101561e-750j)  +/-  (7.87e-87, 5.89e-208j)
| (0.16847125355879700288 + 1.2245309869465616067e-746j)  +/-  (2.45e-82, 1.83e-203j)
| (0.082840427569420197449 - 7.6247734423664515239e-747j)  +/-  (1.44e-82, 1.08e-203j)
| (0.060918543410266565919 + 2.6456953001521821523e-747j)  +/-  (1.65e-83, 1.24e-204j)
| (3.1107622700987722318e-06 - 5.9558987645091728093e-751j)  +/-  (3.03e-89, 2.27e-210j)
| (0.030495297716665911069 - 1.5457011426296304684e-747j)  +/-  (6.59e-85, 5.13e-206j)
| (0.0037237192818695304827 - 1.1096110662138272554e-748j)  +/-  (5.59e-87, 4.3e-208j)
| (0.14243967572950795878 - 1.4557049369433739105e-746j)  +/-  (1.76e-84, 1.63e-205j)
| (0.14243967572950795878 - 1.3014207691937317357e-746j)  +/-  (7.99e-85, 7.56e-206j)
| (2.7185604886431241106e-05 + 2.6236814681240259259e-750j)  +/-  (9.95e-89, 7.39e-210j)
