Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 5 36
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : 16*t^9 - 168*t^7 + 432*t^5 - 270*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^45 - 86706513550052870645640383681667356910534234943690212808/12638783590828860632123548997686844617726134144104027*t^43 + 168668892312937094484233730697008461934828515011701727094553/126387835908288606321235489976868446177261341441040270*t^41 - 39504247626660421809374555974773514280647038606974985352721877/252775671816577212642470979953736892354522682882080540*t^39 + 1558201685052571638808814145407993705584528791596341302674697267/126387835908288606321235489976868446177261341441040270*t^37 - 702447839400381310378862112486571562861096288894133893143265999367/1011102687266308850569883919814947569418090731528322160*t^35 + 1063987169731455985129614828175210448425574877674409215588566771095/36767370446047594566177597084179911615203299328302624*t^33 - 16723859046745210360884037519177044588967894409757271557403618714191/18383685223023797283088798542089955807601649664151312*t^31 + 100416718876349873774826494909626249539410573633414444155657093331529/4595921305755949320772199635522488951900412416037828*t^29 - 29666175209967479975357890408291305891741248312627076475184158310563653/73534740892095189132355194168359823230406598656605248*t^27 + 1686990100445805656694561748568274097187038573591795879482012090288469959/294138963568380756529420776673439292921626394626420992*t^25 - 36834139499552187992644126100677872386607002373232016367900762241507813125/588277927136761513058841553346878585843252789252841984*t^23 + 153389568819856672815122746025743039609012282115401786891223438877882549975/294138963568380756529420776673439292921626394626420992*t^21 - 7714151172102044229479176810052115812310076207867748781890393345095932707775/2353111708547046052235366213387514343373011157011367936*t^19 + 72091049461644401722927997225807653747017881351264912273341742843197387508475/4706223417094092104470732426775028686746022314022735872*t^17 - 245182318077374227500229673517899360328992725210820681133144314469641012844075/4706223417094092104470732426775028686746022314022735872*t^15 + 590050878382222657190250100253772836315672809961835237265348655446525890474375/4706223417094092104470732426775028686746022314022735872*t^13 - 3869653613294121835091421776148233501517444855833855649321511560976590850591875/18824893668376368417882929707100114746984089256090943488*t^11 + 32838876128411029470368901193523982231275865703783988484632546202553667443987875/150599149347010947343063437656800917975872714048727547904*t^9 - 41945074230774563199151579714039962970806053047193096721136498027546467432850875/301198298694021894686126875313601835951745428097455095808*t^7 + 7259944929098067538350357608903378409932022046434444785613003709550752818907125/150599149347010947343063437656800917975872714048727547904*t^5 - 9184715468338858129716731091085340093179946622292368655324726664713514937665625/1204793194776087578744507501254407343806981712389820383232*t^3 + 902485577343800218303044285237121003782607943104032098185641202104703235161875/2409586389552175157489015002508814687613963424779640766464*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:
| (6.0624092977762271075 + 5.7019248088749460252e-943j)  +/-  (4.44e-245, 4.44e-245j)
| (7.5942026358823840287 + 1.6191007445366517264e-954j)  +/-  (1.54e-246, 1.54e-246j)
| (8.2726145892508225517 - 2.5397296406631745423e-964j)  +/-  (1.27e-247, 1.27e-247j)
| (5.2074723138255284558 - 8.5714738096934450004e-963j)  +/-  (7.83e-245, 7.83e-245j)
| (6.5276774636628043999 - 1.0538605855237061386e-976j)  +/-  (2.37e-245, 2.37e-245j)
| (-6.5276774636628043999 - 1.287785568977506326e-986j)  +/-  (2.44e-245, 2.44e-245j)
| (-5.2074723138255284558 - 8.463541800924993667e-985j)  +/-  (8.16e-245, 8.16e-245j)
| (-8.2726145892508225517 - 1.8215828631462049544e-991j)  +/-  (1.33e-247, 1.33e-247j)
| (-7.5942026358823840287 - 2.0834336032042600791e-990j)  +/-  (1.71e-246, 1.71e-246j)
| (-2.3043628301887178094 + 7.4066550866886837163e-992j)  +/-  (8.65e-248, 8.65e-248j)
| (-4.807141128223972877 + 1.6255487929364477229e-988j)  +/-  (7.33e-245, 7.33e-245j)
| (4.807141128223972877 + 1.2857841063511632923e-987j)  +/-  (7.04e-245, 7.04e-245j)
| (-6.0624092977762271075 + 8.9394599093590243203e-1001j)  +/-  (4.47e-245, 4.47e-245j)
| (-4.0458710576940900206 - 1.1681007735991607056e-1001j)  +/-  (3.16e-245, 3.16e-245j)
| (-3.3259475457146620924 + 6.6840610481446518444e-1005j)  +/-  (5.06e-246, 5.06e-246j)
| (2.3043628301887178094 + 1.9582227132034411623e-1004j)  +/-  (9.43e-248, 9.43e-248j)
| (1.018265286491027959 + 1.5817574414305969742e-1013j)  +/-  (5.44e-251, 5.44e-251j)
| (5.6244966541548564557 - 5.5286661901734648168e-1007j)  +/-  (7.16e-245, 7.16e-245j)
| (-1.6506801238857845559 + 3.4669770443651271907e-1026j)  +/-  (2.89e-249, 2.89e-249j)
| (-7.0311887278274531629 + 2.0454877119272299027e-1022j)  +/-  (7.94e-246, 7.94e-246j)
| (1.6506801238857845559 - 9.7512519745399485899e-1026j)  +/-  (2.57e-249, 2.57e-249j)
| (1.3304490401732908555 - 1.3616770045437281375e-1026j)  +/-  (3.78e-250, 3.78e-250j)
| (-4.4206246610929623613 + 2.3340963353132577195e-1020j)  +/-  (5.48e-245, 5.48e-245j)
| (-1.9753784520327327028 + 4.2854763750978544283e-1029j)  +/-  (1.78e-248, 1.78e-248j)
| (7.0311887278274531629 + 7.069270118619744535e-1025j)  +/-  (7.84e-246, 7.84e-246j)
| (4.4206246610929623613 - 2.6399970628369103675e-1029j)  +/-  (5.16e-245, 5.16e-245j)
| (3.6813684069211380037 + 3.5671530804434992088e-1036j)  +/-  (1.51e-245, 1.51e-245j)
| (2.6384291054842239697 + 2.1803796003991696108e-1042j)  +/-  (3.94e-247, 3.94e-247j)
| (-1.018265286491027959 + 3.6470524834856902989e-1047j)  +/-  (5.22e-251, 5.22e-251j)
| (1.9984782860225586619e-1067 + 7.7815108987676665935e-1067j)  +/-  (3.62e-1065, 3.62e-1065j)
| (-2.6384291054842239697 - 5.2496731736566421379e-1043j)  +/-  (4.44e-247, 4.44e-247j)
| (2.9786191409097622466 - 3.1411331621486309378e-1041j)  +/-  (1.56e-246, 1.56e-246j)
| (1.9753784520327327028 + 2.6181063950590533428e-1046j)  +/-  (1.68e-248, 1.68e-248j)
| (4.0458710576940900206 - 9.0305204132539230787e-1044j)  +/-  (2.97e-245, 2.97e-245j)
| (-0.52464762327529031788 - 6.6076327685577962276e-1059j)  +/-  (1.3e-252, 1.3e-252j)
| (-5.6244966541548564557 - 1.9316226889640840234e-1053j)  +/-  (6.99e-245, 6.99e-245j)
| (-0.29140148750908140831 - 1.2926427893489283847e-1062j)  +/-  (1.19e-253, 1.19e-253j)
| (0.73395630342256598469 + 1.7030090688038632691e-1060j)  +/-  (7.46e-252, 7.46e-252j)
| (-3.6813684069211380037 - 1.5399143386958497111e-1055j)  +/-  (1.37e-245, 1.37e-245j)
| (-2.9786191409097622466 - 1.8743855710276078345e-1059j)  +/-  (1.6e-246, 1.6e-246j)
| (-1.3304490401732908555 - 2.9228374774953287908e-1064j)  +/-  (3.92e-250, 3.92e-250j)
| (0.29140148750908140831 + 5.4207093307953549255e-1068j)  +/-  (1.19e-253, 1.19e-253j)
| (-0.73395630342256598469 - 8.7246269180871309057e-1067j)  +/-  (7.3e-252, 7.3e-252j)
| (0.52464762327529031788 - 1.8477485039949443321e-1067j)  +/-  (1.21e-252, 1.21e-252j)
| (3.3259475457146620924 + 5.9588695257394522422e-1072j)  +/-  (5.17e-246, 5.17e-246j)
-------------------------------------------------
The weights are:
| (2.7754659188353521216e-17 - 1.0613055649092211057e-958j)  +/-  (4.4e-79, 5.55e-201j)
| (3.0689006270170984703e-26 - 1.4159579811908519191e-964j)  +/-  (9.61e-84, 1.21e-205j)
| (8.386911011031246573e-31 + 3.654456612150637317e-967j)  +/-  (1.21e-85, 1.53e-207j)
| (3.8468477156104988983e-13 - 3.9255171563870297111e-957j)  +/-  (8.2e-78, 1.03e-199j)
| (8.4909356798573133081e-20 - 1.4083940972632043841e-960j)  +/-  (5.04e-81, 6.36e-203j)
| (8.4909356798573133081e-20 + 5.2047372738218909791e-962j)  +/-  (9.35e-86, 1.18e-207j)
| (3.8468477156104988983e-13 - 2.9779104286892871642e-958j)  +/-  (4.09e-82, 5.16e-204j)
| (8.386911011031246573e-31 - 5.6345210201911853382e-968j)  +/-  (9.37e-91, 1.18e-212j)
| (3.0689006270170984703e-26 + 1.5882087103029510952e-965j)  +/-  (5.07e-89, 6.4e-211j)
| (0.00092380527335367131388 - 3.0224313606968014117e-952j)  +/-  (9.2e-72, 1.16e-193j)
| (2.0412914757154101227e-11 + 3.0500659820503808813e-957j)  +/-  (5.32e-82, 6.71e-204j)
| (2.0412914757154101227e-11 + 2.6410966834560807564e-956j)  +/-  (1.54e-82, 1.94e-204j)
| (2.7754659188353521216e-17 - 1.3052152371664507124e-960j)  +/-  (1.91e-85, 2.4e-207j)
| (1.6215723582146808739e-08 + 1.7505501402584272455e-955j)  +/-  (1.44e-80, 1.82e-202j)
| (3.1107622700987722318e-06 + 5.1644593700244389532e-954j)  +/-  (1.63e-78, 2.06e-200j)
| (0.00092380527335367131388 - 6.7290265528831728087e-952j)  +/-  (2.67e-76, 3.36e-198j)
| (0.060918543410266565919 - 3.1152090287936707443e-950j)  +/-  (1.34e-66, 1.69e-188j)
| (4.3911704853750614409e-15 + 6.0845491959862730189e-958j)  +/-  (1.49e-85, 1.88e-207j)
| (0.011934476496026427072 - 2.7526570307616670342e-951j)  +/-  (2.51e-72, 3.17e-194j)
| (1.0087896404408611453e-22 - 1.2876181427960344465e-963j)  +/-  (6.98e-89, 8.8e-211j)
| (0.011934476496026427072 - 4.8125097866577753287e-951j)  +/-  (1.09e-73, 1.38e-195j)
| (0.030495297716665911069 + 1.2081667508588404394e-950j)  +/-  (1.19e-71, 1.5e-193j)
| (6.9928525977384001303e-10 - 2.5338379233661447891e-956j)  +/-  (4.2e-82, 5.29e-204j)
| (0.0037237192818695304827 + 9.4596511519816106246e-952j)  +/-  (7.07e-75, 8.92e-197j)
| (1.0087896404408611453e-22 + 1.7402882275642623189e-962j)  +/-  (3.26e-90, 4.11e-212j)
| (6.9928525977384001303e-10 - 1.6178924082624559539e-955j)  +/-  (9.96e-85, 1.26e-206j)
| (2.6406216798025905493e-07 - 4.1949206735138057594e-954j)  +/-  (5.39e-84, 6.8e-206j)
| (0.00018019223546565378077 + 2.2264836529506819159e-952j)  +/-  (2.08e-81, 2.62e-203j)
| (0.060918543410266565919 - 2.2192183498173425247e-950j)  +/-  (1.12e-76, 1.41e-198j)
| (0.16847125355879700288 - 1.0034495145236443068e-949j)  +/-  (6.12e-76, 7.72e-198j)
| (0.00018019223546565378077 + 8.7617256784223913144e-953j)  +/-  (1.22e-81, 1.54e-203j)
| (2.7185604886431241106e-05 - 6.644264520190482032e-953j)  +/-  (1.01e-82, 1.28e-204j)
| (0.0037237192818695304827 + 1.8603888988518783526e-951j)  +/-  (4.39e-80, 5.54e-202j)
| (1.6215723582146808739e-08 + 8.7749645617031887491e-955j)  +/-  (6.4e-85, 8.07e-207j)
| (0.082277658142890211968 - 1.05539538896567022e-949j)  +/-  (1.24e-78, 1.56e-200j)
| (4.3911704853750614409e-15 + 2.2799028542010004e-959j)  +/-  (1.39e-89, 1.76e-211j)
| (0.14243967572950795878 + 1.0744871860222402371e-949j)  +/-  (5.4e-79, 6.82e-201j)
| (0.082840427569420197449 + 8.1107444989202759173e-950j)  +/-  (9.01e-80, 1.14e-201j)
| (2.6406216798025905493e-07 - 1.0250929321503820942e-954j)  +/-  (2.16e-85, 2.73e-207j)
| (2.7185604886431241106e-05 - 2.2662817251306435343e-953j)  +/-  (4.31e-84, 5.43e-206j)
| (0.030495297716665911069 + 7.7331348556679721592e-951j)  +/-  (1.48e-81, 1.86e-203j)
| (0.14243967572950795878 + 1.1829975795653859843e-949j)  +/-  (4.1e-81, 5.23e-203j)
| (0.082840427569420197449 + 6.3589458465986833085e-950j)  +/-  (5.24e-81, 6.59e-203j)
| (0.082277658142890211968 - 1.2553717386111034115e-949j)  +/-  (2.61e-81, 3.32e-203j)
| (3.1107622700987722318e-06 + 1.7718423227721677021e-953j)  +/-  (7.21e-86, 8.52e-208j)
