Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 6 40
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : 3/2*t^8 - 161/52*t^6 + 105/52*t^4 - 245/572*t^2 + 25/1716
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^48 - 1748741060645123232402649784228044173776349845625822583131818688560717177/98444697432338868075210732044940888518502977496663299119441435214487604*t^46 + 1154558256638138372815834781467726515234915200798176403834832845612279737335/11714918994448325300950077113347965733701854322102932595213530790524024876*t^44 - 1498995442510175690342255285055293474034081412415391228707777226719497310043945/4404120429030543941080702519494520529652267704268226012706451487190531940148*t^42 + 1547691796730430787918839097105024790271655700887038391377907791098533727942225/1887480183870233117606015365497651655565257587543525434017050637367370831492*t^40 - 95130844639133607553163844642837584725256436635277556882463049046143373128431403/64997074024044181460125093227265286498054895899255247638074333486778949402404*t^38 + 30128519714123408107782980892369683928987613002723157247887602564615274391606636981/15014324099554205917288896535498281181050680952727962204395171035445937311955324*t^36 - 4637162806510898554790304526586849036855851350807999681245555805291491776188494675/2144903442793457988184128076499754454435811564675423172056453005063705330279332*t^34 + 518376311636222650099873198634556784520690046803206272344059807546362418353103565/279105082573836779211125400328845053785765141214449004563495667325580194492676*t^32 - 38154757512977265515352907647375928755826833474403253766752775129452629363718574485/29724691294113616985984855135021998228183987539338818986012288570174290713469994*t^30 + 77161662009985527703178559910009090175939981435988597401699509431449145263425515017/107623882271790682190634820316458959102045472125192275639010010340286224997046530*t^28 - 37079610654545429141380337315620548961572558320696138704918795394992869281608761501/114457144638253582647183062876234131108524549720442578854185249092050429758763770*t^26 + 2704700009965451831245165971509395864564752763995119471642256923823900044578672005/22891428927650716529436612575246826221704909944088515770837049818410085951752754*t^24 - 503906254229264386728519266979724212234446202184030071316940547385325279636882615/14567272953959546882368753456975253050175851782601782763259940793533691060206298*t^22 + 146260206875360053995481199944563193435590914563592025997850748733006472999194429275/18152903139627018207843233772170733193811993585662193006273780505999198159739933922*t^20 - 1578486588505369661081211485513006582204404723146630184724295955879537742112795008953/1071021285237994074262750792558073258434907621554069387370153049853952691424656101398*t^18 + 92265319846143415785832466567499725516989782169450616196339607028766571950284584/443670789245233667880178455906409800511560738009142248289210045507022655933991757*t^16 - 214310262917987143302885680797041160522699917385714118636867279242335892866522416655/9702192819214769849203742473761369517586810218783922685588445275147571439964531742076*t^14 + 3095589607456071154902326936256853429864752474266954260405700495828938407083777365/1812497559633528433367732110482893206582151359553040501703335930522073785487879556212*t^12 - 40844381625889307482253798155774648718553073058718995359162057411683804185076544025/445380082153584305035725444966841848853777738624715316009465183654651403833976221858276*t^10 + 1365776405825990380794766899415548208145246928014131272089802418958844754009270623/427914196578933940132363662811279423408531552796295107538505764687802329173820291589324*t^8 - 47592989987378495171312026709539717600389442063144955557847157475560854887761/736513247123810568214051054752632398293513860234587104197083932337009172416213927004*t^6 + 653993072564087525803268283671609686465695793551964719490965476739214834111755/1039220191691696711750026038255964313992148056791002404022085428527519942279277851002644*t^4 - 2020791115246856314738534439216138317275313024075731857640856756878769315995/1039220191691696711750026038255964313992148056791002404022085428527519942279277851002644*t^2 + 207431966103342539127447049204081341141450529623452107466044770387830725/661321940167443362022743842526522745267730581594274257104963454517512690541358632456228
-------------------------------------------------
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: 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:
| (0.99272416408425730518 - 3.2892700458026145497e-832j)  +/-  (4.89e-239, 4.89e-239j)
| (-0.99861620325747322197 - 1.710516116906726884e-843j)  +/-  (1.74e-239, 1.74e-239j)
| (-0.90155493418853085911 - 7.2782155365273738498e-844j)  +/-  (5.59e-239, 5.59e-239j)
| (0.99861620325747322197 + 3.1527718486938619208e-842j)  +/-  (1.67e-239, 1.67e-239j)
| (0.92529062229914575602 - 3.7905167870281509052e-856j)  +/-  (7.29e-239, 7.29e-239j)
| (0.90155493418853085911 + 8.8102252878293866723e-870j)  +/-  (5.23e-239, 5.23e-239j)
| (-0.96715706910802284963 + 1.3371150471065892563e-874j)  +/-  (9.34e-239, 9.34e-239j)
| (-0.92529062229914575602 - 7.1076633661538423205e-876j)  +/-  (7.25e-239, 7.25e-239j)
| (-0.94792656918455258157 - 2.249022739816448199e-876j)  +/-  (8.39e-239, 8.39e-239j)
| (-0.33529190314801829774 + 3.3457046888478475896e-890j)  +/-  (3.91e-249, 3.91e-249j)
| (0.85110112875893547946 + 4.4644611863840508312e-878j)  +/-  (8.66e-240, 8.66e-240j)
| (0.96715706910802284963 + 2.3370970827684046443e-893j)  +/-  (9.14e-239, 9.14e-239j)
| (-0.87881491138714150739 + 1.5418075055471773232e-912j)  +/-  (2.58e-239, 2.58e-239j)
| (-0.85110112875893547946 - 7.0093226309241076193e-913j)  +/-  (8.62e-240, 8.62e-240j)
| (0.98219129046748981137 + 3.3896319645996490055e-911j)  +/-  (7.99e-239, 7.99e-239j)
| (0.81611494119817089799 + 7.7407872559398736989e-921j)  +/-  (1.87e-240, 1.87e-240j)
| (0.68329786959932057014 + 5.3485273395764312735e-928j)  +/-  (8.5e-243, 8.5e-243j)
| (0.013059715838004799788 + 2.4325027890964536686e-940j)  +/-  (1.72e-255, 1.72e-255j)
| (-0.81611494119817089799 - 8.0309178681958152136e-924j)  +/-  (1.86e-240, 1.86e-240j)
| (-0.98219129046748981137 + 1.9461910029449342018e-923j)  +/-  (7.59e-239, 7.59e-239j)
| (0.87881491138714150739 - 1.4804232569054305838e-929j)  +/-  (2.74e-239, 2.74e-239j)
| (0.77587412671791236132 + 9.0772158481318499961e-940j)  +/-  (3.51e-241, 3.51e-241j)
| (0.94792656918455258157 - 6.6533155864857091234e-942j)  +/-  (8.28e-239, 8.28e-239j)
| (-0.73143071434642501443 + 1.3609471021985422065e-951j)  +/-  (5.74e-242, 5.74e-242j)
| (-0.77587412671791236132 - 2.3038394548665545445e-950j)  +/-  (3.54e-241, 3.54e-241j)
| (0.13741302819147009672 - 8.2535975175236759268e-964j)  +/-  (6.17e-253, 6.17e-253j)
| (0.73143071434642501443 - 1.4947704673050155477e-952j)  +/-  (6.02e-242, 6.02e-242j)
| (0.33529190314801829774 + 2.4771913154463231939e-961j)  +/-  (3.81e-249, 3.81e-249j)
| (-0.99272416408425730518 - 7.8487454516103018976e-954j)  +/-  (5.56e-239, 5.56e-239j)
| (-0.63183344183498684674 + 5.0890328248104838651e-960j)  +/-  (1.08e-243, 1.08e-243j)
| (-0.39881073144539894915 - 3.2728246301975097598e-965j)  +/-  (6.17e-248, 6.17e-248j)
| (0.52015000639158534905 + 1.3892770396785296886e-963j)  +/-  (1.03e-245, 1.03e-245j)
| (0.57735026918962576451 + 6.2936271177846669066e-962j)  +/-  (1.16e-244, 1.16e-244j)
| (0.070881187428353018448 + 4.2253856517450469944e-972j)  +/-  (2.56e-254, 2.56e-254j)
| (-0.57735026918962576451 - 4.4371856816695341711e-961j)  +/-  (1.17e-244, 1.17e-244j)
| (-0.68329786959932057014 + 2.4593939954534369652e-963j)  +/-  (9.07e-243, 9.07e-243j)
| (-0.013059715838004799788 + 1.0397540552231625108e-974j)  +/-  (1.72e-255, 1.72e-255j)
| (0.63183344183498684674 - 6.8355745348037239909e-967j)  +/-  (1.05e-243, 1.05e-243j)
| (0.2041968861768067152 - 2.8311569736547571329e-977j)  +/-  (1.14e-251, 1.14e-251j)
| (-0.2041968861768067152 - 7.0536102442504978961e-976j)  +/-  (1.08e-251, 1.08e-251j)
| (-0.52015000639158534905 + 1.4339639696233702738e-971j)  +/-  (1.04e-245, 1.04e-245j)
| (-0.13741302819147009672 - 1.5378611565517789781e-978j)  +/-  (6.37e-253, 6.37e-253j)
| (0.39881073144539894915 + 3.355995620261096532e-972j)  +/-  (6.14e-248, 6.14e-248j)
| (0.46053463661286728241 + 2.6246515600738384512e-971j)  +/-  (8.76e-247, 8.76e-247j)
| (-0.070881187428353018448 - 9.8868205688899323888e-980j)  +/-  (2.7e-254, 2.7e-254j)
| (-0.46053463661286728241 + 1.1435840379262112208e-973j)  +/-  (9.36e-247, 9.36e-247j)
| (-0.27030335398072387767 + 2.9619217493186902443e-976j)  +/-  (2.12e-250, 2.12e-250j)
| (0.27030335398072387767 - 2.2043249289560061053e-975j)  +/-  (1.99e-250, 1.99e-250j)
-------------------------------------------------
The weights are:
| (0.0082273971860488925349 + 2.1490038076926350831e-832j)  +/-  (5.91e-66, 6.13e-181j)
| (0.0035495623329905470244 + 3.6598169778774386325e-835j)  +/-  (1.27e-66, 1.32e-181j)
| (0.023026648006035193838 + 3.538224549849203218e-833j)  +/-  (1.23e-66, 1.28e-181j)
| (0.0035495623329905470244 + 1.236913250608428017e-832j)  +/-  (2.55e-66, 2.64e-181j)
| (0.023773659014444614192 + 5.710073677329568438e-832j)  +/-  (4.53e-67, 4.7e-182j)
| (0.023026648006035193838 - 7.3515865150244434526e-832j)  +/-  (3.45e-67, 3.58e-182j)
| (0.017205599847836325632 - 5.7325057017110663017e-834j)  +/-  (2.09e-68, 2.16e-183j)
| (0.023773659014444614192 - 2.0075470459269741948e-833j)  +/-  (1.91e-68, 1.98e-183j)
| (0.021139997581780590914 + 1.0610728273067974296e-833j)  +/-  (1.84e-68, 1.91e-183j)
| (0.064309283818350983909 + 5.2687988557116072171e-833j)  +/-  (2.31e-71, 2.39e-186j)
| (0.031705831068663350307 - 5.0580008789596694656e-832j)  +/-  (4.8e-70, 4.98e-185j)
| (0.017205599847836325632 + 4.3943319958026733942e-832j)  +/-  (1.36e-69, 1.41e-184j)
| (0.023930289135546614613 - 4.4009094151314708388e-833j)  +/-  (9.49e-70, 9.83e-185j)
| (0.031705831068663350307 + 3.8850179562034592501e-833j)  +/-  (1.78e-70, 1.85e-185j)
| (0.012816064154976099734 - 5.6392438961911472313e-832j)  +/-  (4.8e-70, 4.97e-185j)
| (0.037871533101105145449 + 3.2052188715934195301e-832j)  +/-  (5.89e-72, 6.1e-187j)
| (0.049852763591948999939 - 1.3762186458921828692e-832j)  +/-  (7.42e-74, 7.69e-189j)
| (0.038410295163122264756 + 8.4263828282727904691e-832j)  +/-  (2.63e-75, 2.73e-190j)
| (0.037871533101105145449 - 3.1294724466762727656e-833j)  +/-  (8.79e-73, 9.11e-188j)
| (0.012816064154976099734 + 3.0075942268780609982e-834j)  +/-  (3.35e-72, 3.47e-187j)
| (0.023930289135546614613 + 7.2307330126273434705e-832j)  +/-  (2.08e-71, 2.15e-186j)
| (0.042451743360424087953 - 2.2219276700751003503e-832j)  +/-  (3.05e-73, 3.16e-188j)
| (0.021139997581780590914 - 4.5966123082584130621e-832j)  +/-  (2.05e-71, 2.13e-186j)
| (0.046354749094833875817 - 2.5581237644528032316e-833j)  +/-  (8.44e-76, 8.75e-191j)
| (0.042451743360424087953 + 2.7243331668674935052e-833j)  +/-  (5.13e-75, 5.32e-190j)
| (0.066910929585609453345 + 1.9531345104886092712e-832j)  +/-  (3.79e-78, 3.92e-193j)
| (0.046354749094833875817 + 1.6879878055749420347e-832j)  +/-  (7.75e-75, 8.03e-190j)
| (0.064309283818350983909 - 1.0642996931002448798e-832j)  +/-  (2.85e-78, 2.95e-193j)
| (0.0082273971860488925349 - 1.3630236890765002161e-834j)  +/-  (1.98e-74, 2.05e-189j)
| (0.053024421441060605019 - 2.6350084954232914791e-833j)  +/-  (7.25e-78, 7.52e-193j)
| (0.062674368522387317902 - 4.2754087609714982746e-833j)  +/-  (5.4e-79, 5.6e-194j)
| (0.058458443328020429849 + 1.0071478586365663963e-832j)  +/-  (9.05e-79, 9.38e-194j)
| (0.055891812085500869976 - 1.0707874780799798846e-832j)  +/-  (2.44e-78, 2.53e-193j)
| (0.06555027457252363006 - 3.3966981527151624426e-832j)  +/-  (7.34e-80, 7.61e-195j)
| (0.055891812085500869976 + 2.8328412713173151111e-833j)  +/-  (1.69e-79, 1.75e-194j)
| (0.049852763591948999939 + 2.5407675282500644332e-833j)  +/-  (2.33e-78, 2.41e-193j)
| (0.038410295163122264756 - 8.2075561648552972269e-832j)  +/-  (2.51e-80, 2.6e-195j)
| (0.053024421441060605019 + 1.1861549297720857598e-832j)  +/-  (2.25e-79, 2.33e-194j)
| (0.066533187617291340757 - 1.4377032972756507814e-832j)  +/-  (5.57e-81, 5.77e-196j)
| (0.066533187617291340757 + 9.4715375519896080774e-833j)  +/-  (3.15e-82, 3.26e-197j)
| (0.058458443328020429849 - 3.146012141950530802e-833j)  +/-  (1.12e-81, 1.16e-196j)
| (0.066910929585609453345 - 1.478172480409978626e-832j)  +/-  (3.41e-82, 3.53e-197j)
| (0.062674368522387317902 + 1.0017251937211086216e-832j)  +/-  (1.17e-82, 1.21e-197j)
| (0.060721234174614289857 - 9.8480678804093834048e-833j)  +/-  (1.61e-82, 1.67e-197j)
| (0.06555027457252363006 + 2.9439700838663511425e-832j)  +/-  (1.47e-82, 1.52e-197j)
| (0.060721234174614289857 + 3.6064041650165033896e-833j)  +/-  (1.39e-83, 1.44e-198j)
| (0.065609912214884476623 - 6.8206061088950205109e-833j)  +/-  (1.53e-83, 1.6e-198j)
| (0.065609912214884476623 + 1.192464708244485648e-832j)  +/-  (1.38e-83, 1.39e-198j)
