Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 44
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^52 - 115226258175118286568144571127163584880271861633382/96463059700968922754665093508150590981130145789*t^50 + 52313244508889740714213761393081251988921042644370655/79686875405148240536462468550211357767020555217*t^48 - 4985361614078026584433216046880202029094095344476713399400/22604510323260384232176520245409955153244830829889*t^46 + 3442028043612710504524894831460119273706191583137117661693690/67813530969781152696529560736229865459734492489667*t^44 - 44339261517591703883266270923022479155803289382605588329215380/5216425459213934822809966210479220419979576345359*t^42 + 24275945864007914471289486091178107912714800342410894113193504090/22604510323260384232176520245409955153244830829889*t^40 - 182171441631947708156090720725683204599215730728207371942960320200/1738808486404644940936655403493073473326525448453*t^38 + 19814295124022451031281895361015854909360071327900900849707458825/2473411787204331352683720346362835666182824251*t^36 - 1198893748227299119977481321707258649861315307961234507227699770950/2473411787204331352683720346362835666182824251*t^34 + 57718816390549484217613344471506469256565877316485796880038193356575/2473411787204331352683720346362835666182824251*t^32 - 2216040924268906519354236413652315974441041904177941514398361909919600/2473411787204331352683720346362835666182824251*t^30 + 67819407524336399299224440707132046522140350902148275030692633712497500/2473411787204331352683720346362835666182824251*t^28 - 1649443244741609665397110751734187340851609951403847886037417302374899000/2473411787204331352683720346362835666182824251*t^26 + 31705556123174987710230940052077892533122186030999361367676645496626592500/2473411787204331352683720346362835666182824251*t^24 - 20772621283230309396769417783466212301200099081500838981442201770775010000/107539642921927450116683493320123289834035837*t^22 + 242700615335770043078164873449080812154894313735079048675367602262491576875/107539642921927450116683493320123289834035837*t^20 - 2167115602536693453189596298084818625549394429235486845500619789374141956250/107539642921927450116683493320123289834035837*t^18 + 14516117195517555526899294246948703395260283277237680915763660054383019003125/107539642921927450116683493320123289834035837*t^16 - 71213835114955415637824474230271298233033697408354921386061727986382466025000/107539642921927450116683493320123289834035837*t^14 + 247982562217042085024324498038267770547178087060159640680905971064215279993750/107539642921927450116683493320123289834035837*t^12 - 587705386775209998094691789551363854446723949734295841293262388391853266637500/107539642921927450116683493320123289834035837*t^10 + 893567440350813158290548122920199520170914440342163764840933926969321164781250/107539642921927450116683493320123289834035837*t^8 - 797348770364747306866596767523524480984278769123583778270223118947850701625000/107539642921927450116683493320123289834035837*t^6 + 359536782402768037026341710124257477019255355903710296381842369480696379265625/107539642921927450116683493320123289834035837*t^4 - 60670719183040424379603193921048673655768498875330789548030588475801293593750/107539642921927450116683493320123289834035837*t^2 + 1543883273673835963592062164167340794728377833051342048147041636825187109375/107539642921927450116683493320123289834035837
-------------------------------------------------
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
Positive weights:   52 out of 52
Indefinite weights: 0 out of 52
Negative weights:   0 out of 52
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.0460673307624772126 - 2.021470598639332303e-897j)  +/-  (3.45e-243, 3.45e-243j)
| (-4.1445471861258943321 - 2.5793275992579178268e-912j)  +/-  (1.61e-245, 1.61e-245j)
| (10.478711818302085571 + 1.178319740917313466e-911j)  +/-  (6.56e-244, 6.56e-244j)
| (12.890244172527732393 + 1.5649250885863594788e-922j)  +/-  (1.97e-246, 1.97e-246j)
| (9.8362430789539376359 - 8.5605123587954865685e-927j)  +/-  (1.78e-243, 1.78e-243j)
| (-8.6552423135600781644 + 5.9585515836964823982e-929j)  +/-  (4.69e-243, 4.69e-243j)
| (6.0425995426704560193 + 4.1346256372688846344e-934j)  +/-  (1.08e-243, 1.08e-243j)
| (-11.17411517235156663 + 6.3613098164166456806e-936j)  +/-  (1.82e-244, 1.82e-244j)
| (11.952071020271616574 + 4.568902266908952521e-937j)  +/-  (2.96e-245, 2.96e-245j)
| (-11.952071020271616574 - 5.7833634866858134916e-942j)  +/-  (2.95e-245, 2.95e-245j)
| (-9.8362430789539376359 + 2.2083166880521906871e-941j)  +/-  (1.85e-243, 1.85e-243j)
| (5.0779719724882498198 + 4.2928122688788499679e-943j)  +/-  (1.73e-244, 1.73e-244j)
| (11.17411517235156663 + 2.5413091840811012235e-944j)  +/-  (2.02e-244, 2.02e-244j)
| (-2.8024858612875416991 + 2.7990241278463652617e-951j)  +/-  (1.31e-247, 1.31e-247j)
| (-3.2405384431626786683 + 7.4471520828527005859e-951j)  +/-  (6.91e-247, 6.91e-247j)
| (-12.890244172527732393 + 2.0661528177772872045e-950j)  +/-  (2.18e-246, 2.18e-246j)
| (2.8024858612875416991 - 6.8842344696569905652e-952j)  +/-  (1.21e-247, 1.21e-247j)
| (-8.101561103046887054 - 4.0225242947153591675e-946j)  +/-  (4.65e-243, 4.65e-243j)
| (-2.3803103671869800362 + 1.21673947846085241e-957j)  +/-  (2.7e-248, 2.7e-248j)
| (5.5560216373246025445 - 8.6523012063591206323e-952j)  +/-  (4.89e-244, 4.89e-244j)
| (4.6076435131950352837 - 4.8897472182017456292e-956j)  +/-  (5.39e-245, 5.39e-245j)
| (4.1445471861258943321 + 5.8391908041869046694e-957j)  +/-  (1.48e-245, 1.48e-245j)
| (-10.478711818302085571 - 2.2332811485711861559e-954j)  +/-  (6.44e-244, 6.44e-244j)
| (-5.5560216373246025445 - 8.2625003174468907226e-958j)  +/-  (4.8e-244, 4.8e-244j)
| (-3.6886225633360935158 - 4.2355127859204741954e-961j)  +/-  (3.3e-246, 3.3e-246j)
| (8.101561103046887054 - 8.5134222485953722672e-957j)  +/-  (4.6e-243, 4.6e-243j)
| (0.91932953204219724211 - 3.2022198965976948399e-971j)  +/-  (6.01e-252, 6.01e-252j)
| (9.2314650714595515657 - 1.2428939034455085468e-962j)  +/-  (3.36e-243, 3.36e-243j)
| (7.5662021145134790134 + 6.6933752314222609369e-963j)  +/-  (4.33e-243, 4.33e-243j)
| (-1.9876699765986020361 - 1.7685316670364373863e-974j)  +/-  (4.6e-249, 4.6e-249j)
| (7.0460673307624772126 + 5.6142993605250668887e-967j)  +/-  (3.56e-243, 3.56e-243j)
| (3.6886225633360935158 + 7.8795267417760713896e-972j)  +/-  (3.34e-246, 3.34e-246j)
| (6.5388068346823967991 + 2.9135801314136988939e-969j)  +/-  (2.08e-243, 2.08e-243j)
| (-7.5662021145134790134 + 8.874510585713312345e-968j)  +/-  (4.36e-243, 4.36e-243j)
| (-5.0779719724882498198 - 9.8414971557956999819e-983j)  +/-  (1.64e-244, 1.64e-244j)
| (-1.6365190424351079992 - 9.857260991301839706e-990j)  +/-  (7.33e-250, 7.33e-250j)
| (-4.6076435131950352837 - 5.1906554880419823153e-984j)  +/-  (5.74e-245, 5.74e-245j)
| (0.53907981135137510807 - 3.6716278569765965581e-992j)  +/-  (4.59e-253, 4.59e-253j)
| (-1.2916566964103788244 - 4.3988383037005456389e-990j)  +/-  (9.38e-251, 9.38e-251j)
| (-9.2314650714595515657 - 4.0149764326071177804e-981j)  +/-  (3.18e-243, 3.18e-243j)
| (-0.91932953204219724211 - 2.637421009191849996e-998j)  +/-  (6.83e-252, 6.83e-252j)
| (8.6552423135600781644 - 1.059588223034520831e-988j)  +/-  (4.62e-243, 4.62e-243j)
| (2.3803103671869800362 + 3.9056558882298568198e-1000j)  +/-  (2.3e-248, 2.3e-248j)
| (3.2405384431626786683 + 1.3890269884870143798e-998j)  +/-  (6.84e-247, 6.84e-247j)
| (1.2916566964103788244 + 5.6438195161259523847e-1003j)  +/-  (9.46e-251, 9.46e-251j)
| (-6.5388068346823967991 + 6.2955507582534116626e-1001j)  +/-  (2.28e-243, 2.28e-243j)
| (-0.17506421868172469175 - 7.4397908404475684211e-1025j)  +/-  (3.1e-254, 3.1e-254j)
| (1.6365190424351079992 - 5.1990953560921224555e-1019j)  +/-  (7.32e-250, 7.32e-250j)
| (1.9876699765986020361 + 3.5090197342713214025e-1021j)  +/-  (4.65e-249, 4.65e-249j)
| (0.17506421868172469175 + 3.7830247064608667165e-1027j)  +/-  (3.1e-254, 3.1e-254j)
| (-0.53907981135137510807 + 1.1243882210187741577e-1025j)  +/-  (3.78e-253, 3.78e-253j)
| (-6.0425995426704560193 + 6.1054857946508611408e-1028j)  +/-  (1.15e-243, 1.15e-243j)
-------------------------------------------------
The weights are:
| (3.3931668633249807455e-12 - 2.7069912872157798157e-908j)  +/-  (6.57e-63, 8.42e-185j)
| (3.413832649897968401e-05 - 3.8760668732556102955e-905j)  +/-  (2.61e-51, 3.35e-173j)
| (3.8074784520247755569e-25 + 4.1612226050935713022e-917j)  +/-  (1.55e-72, 1.99e-194j)
| (3.5868142860352101021e-37 - 2.0356084025895091789e-923j)  +/-  (1.35e-77, 1.73e-199j)
| (2.427483592436574065e-22 - 1.3021414557929048982e-915j)  +/-  (2.25e-71, 2.89e-193j)
| (1.2164365276946802752e-17 - 4.4082130268845858314e-912j)  +/-  (5.63e-70, 7.22e-192j)
| (2.3091649695354606894e-09 + 2.1724207209049869879e-908j)  +/-  (2.82e-63, 3.62e-185j)
| (2.243304259125175216e-28 - 3.5926571791352597218e-918j)  +/-  (3.54e-76, 4.53e-198j)
| (3.1895065215868745821e-32 + 7.7637093869688773382e-921j)  +/-  (1.39e-76, 1.78e-198j)
| (3.1895065215868745821e-32 + 3.0064393421919851226e-920j)  +/-  (5.9e-78, 7.56e-200j)
| (2.427483592436574065e-22 - 7.8787711735694672531e-915j)  +/-  (9.56e-74, 1.23e-195j)
| (4.7582338456961772205e-07 + 5.7533953287124682471e-907j)  +/-  (5.51e-63, 7.06e-185j)
| (2.243304259125175216e-28 - 8.1396883436107805163e-919j)  +/-  (1.93e-75, 2.47e-197j)
| (0.0033924475360978049269 + 9.8412736130307955678e-904j)  +/-  (1.07e-53, 1.37e-175j)
| (0.00092821727060842069296 - 3.475522777387158899e-904j)  +/-  (5.87e-56, 7.53e-178j)
| (3.5868142860352101021e-37 - 6.9440956890115915002e-923j)  +/-  (1.17e-80, 1.5e-202j)
| (0.0033924475360978049269 - 4.2404448172087400848e-904j)  +/-  (2.08e-56, 2.67e-178j)
| (1.2131862529036080619e-15 + 8.13488422045110951e-911j)  +/-  (6.15e-71, 7.89e-193j)
| (0.0096363234230398311481 - 2.6958946591127544749e-903j)  +/-  (6.57e-53, 8.43e-175j)
| (3.8097526979784468894e-08 - 1.1851334515018187023e-907j)  +/-  (5.02e-66, 6.44e-188j)
| (4.5687067649120417317e-06 - 2.5170975488935121259e-906j)  +/-  (7.55e-64, 9.67e-186j)
| (3.413832649897968401e-05 + 1.0049927193610382979e-905j)  +/-  (7.29e-63, 9.35e-185j)
| (3.8074784520247755569e-25 + 2.1244410077721746712e-916j)  +/-  (9.08e-77, 1.16e-198j)
| (3.8097526979784468894e-08 + 1.0023288051251428524e-906j)  +/-  (4.19e-68, 5.37e-190j)
| (0.00020033272976268151998 + 1.1864973013620166146e-904j)  +/-  (8.52e-62, 1.09e-183j)
| (1.2131862529036080619e-15 + 5.6684250412314047768e-912j)  +/-  (7.35e-75, 9.42e-197j)
| (0.099671454979258490807 + 1.7890603418857235625e-902j)  +/-  (2.18e-59, 2.8e-181j)
| (7.3446165172080550517e-20 + 2.8131865325716205242e-914j)  +/-  (9.36e-77, 1.2e-198j)
| (7.7956347142935141052e-14 - 5.7588227173670048364e-911j)  +/-  (4.36e-74, 5.59e-196j)
| (0.020557963800139121903 + 6.7285262614232478862e-903j)  +/-  (4.78e-61, 6.13e-183j)
| (3.3931668633249807455e-12 + 4.8673868191330516189e-910j)  +/-  (2.24e-73, 2.87e-195j)
| (0.00020033272976268151998 - 3.7109587657438805629e-905j)  +/-  (7.5e-68, 9.62e-190j)
| (1.0394555655659256404e-10 - 3.4964388528714394609e-909j)  +/-  (2.1e-72, 2.69e-194j)
| (7.7956347142935141052e-14 - 1.6178396804539544538e-909j)  +/-  (3.48e-77, 4.46e-199j)
| (4.7582338456961772205e-07 - 3.5442587067238448859e-906j)  +/-  (5.96e-73, 7.63e-195j)
| (0.035311937291844305446 - 1.2978830912827000022e-902j)  +/-  (6.29e-65, 8.03e-187j)
| (4.5687067649120417317e-06 + 1.2029708203043493329e-905j)  +/-  (7.27e-72, 9.29e-194j)
| (0.12933565816941122441 - 2.4209264694174265715e-902j)  +/-  (1.4e-64, 1.77e-186j)
| (0.062166401597662357787 + 1.872161972482456392e-902j)  +/-  (2.81e-65, 3.56e-187j)
| (7.3446165172080550517e-20 + 2.095350154557898205e-913j)  +/-  (1.09e-80, 1.39e-202j)
| (0.099671454979258490807 - 2.3259646655035619355e-902j)  +/-  (1.09e-65, 1.37e-187j)
| (1.2164365276946802752e-17 - 4.5178308576794221912e-913j)  +/-  (8.17e-79, 1.03e-200j)
| (0.0096363234230398311481 + 1.3343820587144217145e-903j)  +/-  (3.3e-70, 4.15e-192j)
| (0.00092821727060842069296 + 1.2857693411713107432e-904j)  +/-  (5.59e-71, 7.07e-193j)
| (0.062166401597662357787 - 1.2921018647976921636e-902j)  +/-  (9.05e-69, 1.17e-190j)
| (1.0394555655659256404e-10 + 9.3637652075073511548e-908j)  +/-  (3.42e-77, 4.55e-199j)
| (0.1387600398314174455 - 3.1985119753667117298e-902j)  +/-  (1.09e-68, 1.3e-190j)
| (0.035311937291844305446 + 8.0862555845881148937e-903j)  +/-  (4.06e-70, 4.91e-192j)
| (0.020557963800139121903 - 3.7676056188227462674e-903j)  +/-  (1.36e-70, 1.66e-192j)
| (0.1387600398314174455 + 3.0434268627141604873e-902j)  +/-  (2.18e-69, 2.5e-191j)
| (0.12933565816941122441 + 2.8220560491306948081e-902j)  +/-  (1.12e-69, 1.19e-191j)
| (2.3091649695354606894e-09 - 2.8335828476260490836e-907j)  +/-  (1.36e-76, 1.93e-198j)
