Starting with polynomial:
P : t^3 - 3*t
Extension levels are: 3 6 44
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : t^9 - 117/4*t^7 + 945/4*t^5 - 2205/4*t^3 + 945/4*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 21387140945855829472998079268690365449394403568032506463415670307351/17835692609090827687195820508779203504644822889964979983105555100*t^51 + 25583416799738950832710544304540211040155121491070006004616244924570569/38644000653030126655590944435688274260063782928257456630062036050*t^49 - 3367734385487531873785904925313610687563941288494301219931894976240876763/15061251536565587824743137318524660737255628218192649763511357640*t^47 + 18249963121032385511805600172461688016712419056479805040221313107720202167055/352433285955634755098989413253477061251781700305708004466165768776*t^45 - 1710246991080873164445882005960835538855071866505279626322622630903462799412749/195796269975352641721660785140820589584323166836504446925647649320*t^43 + 217910584324680059688403825649731542683415519680976012837238736302519277443783929/195796269975352641721660785140820589584323166836504446925647649320*t^41 - 1651248509435287176667071299789526735657203319097765273116036923728965503118795829/15061251536565587824743137318524660737255628218192649763511357640*t^39 + 1344120687891077844440448744398167684712445466673130227212962786107152796356626255/158539489858585134997296182300259586707953981244133155405382712*t^37 - 82396994660766238957838528636637941668050697911805439302279716706212671951963061879/158539489858585134997296182300259586707953981244133155405382712*t^35 + 4027441745451077220451790327357744673977259008094282332151570544653894793669247585289/158539489858585134997296182300259586707953981244133155405382712*t^33 - 78689876251919795701126065722810185399752243430926356333260400571204722091019267500297/79269744929292567498648091150129793353976990622066577702691356*t^31 + 2458350515653663949720892405553714984165184806103490879164484764197161739866911335497381/79269744929292567498648091150129793353976990622066577702691356*t^29 - 61254070012419105101847174931111060012999353756941975999142252650457859130013783993026835/79269744929292567498648091150129793353976990622066577702691356*t^27 + 1211568441495969153917230388098502162867689675379044467632959105529631528456369029151127215/79269744929292567498648091150129793353976990622066577702691356*t^25 - 18889062005374854056003472173342078562986877763269002621233402265495281824209597010118473675/79269744929292567498648091150129793353976990622066577702691356*t^23 + 9995678490668658159150081791791558810062679940498718904769513231963125451261711838352405725/3446510649099676847767308310875208406694651766176807726203972*t^21 - 46896298486860040823579204043782879503354620767509096055982630596561065279985845992413771025/1723255324549838423883654155437604203347325883088403863101986*t^19 + 667750327947768950272578831525539029974427334535439232689211021611809570239677382470230326625/3446510649099676847767308310875208406694651766176807726203972*t^17 - 7069230255910502493059551944651182587513455087352086890307576402100015030375445949096719775375/6893021298199353695534616621750416813389303532353615452407944*t^15 + 27108476322713882504337471550424276643478499623731491767756808162543712505273682330280816919875/6893021298199353695534616621750416813389303532353615452407944*t^13 - 72789580885123300648053809414523441670913041167511762404932674096295525880110722523034958006125/6893021298199353695534616621750416813389303532353615452407944*t^11 + 130651573221769208772288426103446639640838503378659091338860807415628036283949182037618653219625/6893021298199353695534616621750416813389303532353615452407944*t^9 - 146549061453340025332571041723481608957766102213267742411409360158847399217074953267743411735625/6893021298199353695534616621750416813389303532353615452407944*t^7 + 92286468725354381498804525099405365226876050398074235777201454593416121279082721528382175273125/6893021298199353695534616621750416813389303532353615452407944*t^5 - 26843873072432791996538703194732703399998216867299523842605458162179458723497844532914583355625/6893021298199353695534616621750416813389303532353615452407944*t^3 + 2286182671409517585669369075399265517499855929125919277204159158991536848674906872071844296875/6893021298199353695534616621750416813389303532353615452407944*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
Positive weights:   53 out of 53
Indefinite weights: 0 out of 53
Negative weights:   0 out of 53
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-11.941069601189669619 - 1.4774259207765793395e-957j)  +/-  (3.36e-245, 3.36e-245j)
| (-10.474851502604059147 - 3.3503982178301200077e-953j)  +/-  (8.6e-244, 8.6e-244j)
| (8.1101246138709963267 + 1.4039684950048563241e-957j)  +/-  (5.68e-243, 5.68e-243j)
| (9.8355690391401045875 + 9.7091295038715199859e-957j)  +/-  (2.05e-243, 2.05e-243j)
| (-9.8355690391401045875 + 1.635165907603682735e-956j)  +/-  (1.91e-243, 1.91e-243j)
| (11.941069601189669619 - 1.6534951741735761828e-959j)  +/-  (3.2e-245, 3.2e-245j)
| (-12.874666425496603005 + 1.9612272344483939081e-960j)  +/-  (2.14e-246, 2.14e-246j)
| (-11.166871831970257332 + 1.9328967261019625853e-957j)  +/-  (2.12e-244, 2.12e-244j)
| (-7.5779262653075268093 + 4.0315594961189584411e-956j)  +/-  (5.39e-243, 5.39e-243j)
| (12.874666425496603005 + 1.572310544810157253e-965j)  +/-  (2.28e-246, 2.28e-246j)
| (11.166871831970257332 + 1.2784916660664555016e-963j)  +/-  (2.22e-244, 2.22e-244j)
| (2.444306962537157354 - 2.0325465046912368089e-967j)  +/-  (5.47e-248, 5.47e-248j)
| (8.6607189809952929716 - 5.3457644086934964309e-962j)  +/-  (5.98e-243, 5.98e-243j)
| (-2.444306962537157354 - 4.6889254546857312139e-967j)  +/-  (5.52e-248, 5.52e-248j)
| (-6.5572638495247355908 - 5.1227240795300800071e-962j)  +/-  (2.63e-243, 2.63e-243j)
| (9.2338805793769651725 - 6.7425288851906793464e-969j)  +/-  (4.33e-243, 4.33e-243j)
| (-2.0562296712672554715 - 1.7763776569967883972e-974j)  +/-  (1.12e-248, 1.12e-248j)
| (-5.5821152281100459404 + 1.0975946094831268951e-968j)  +/-  (6.29e-244, 6.29e-244j)
| (-6.0647321545101271124 + 2.5555815624717181707e-970j)  +/-  (1.49e-243, 1.49e-243j)
| (3.7348310182211559025 - 1.2817817865724706395e-986j)  +/-  (5.57e-246, 5.57e-246j)
| (-7.0610729066994078851 - 1.2476698928377909928e-982j)  +/-  (4.35e-243, 4.35e-243j)
| (-9.2338805793769651725 + 3.7627070756473686881e-1002j)  +/-  (3.8e-243, 3.8e-243j)
| (7.0610729066994078851 - 2.545384742578939213e-1008j)  +/-  (4.34e-243, 4.34e-243j)
| (10.474851502604059147 + 1.4211601860775254299e-1014j)  +/-  (7.22e-244, 7.22e-244j)
| (-2.8612795760570581173 + 7.6810424463736892239e-1019j)  +/-  (2.55e-247, 2.55e-247j)
| (4.6428000147151890778 + 1.0870361183940901819e-1017j)  +/-  (7.9e-245, 7.9e-245j)
| (3.293016963519965758 + 8.544901249042449112e-1019j)  +/-  (1.26e-246, 1.26e-246j)
| (-5.1083814254335441109 - 7.4437740678241670037e-1015j)  +/-  (2.28e-244, 2.28e-244j)
| (-4.6428000147151890778 + 4.2201330607928068799e-1023j)  +/-  (7.85e-245, 7.85e-245j)
| (-8.1101246138709963267 - 2.2198936446351134139e-1031j)  +/-  (6.24e-243, 6.24e-243j)
| (-1.7320508075688772935 - 4.0866227475178839785e-1045j)  +/-  (2.83e-249, 2.83e-249j)
| (2.8612795760570581173 - 2.2326771268783154554e-1043j)  +/-  (2.77e-247, 2.77e-247j)
| (1.4446265900208259987 + 8.6780908344236957661e-1046j)  +/-  (5.13e-250, 5.13e-250j)
| (2.0562296712672554715 + 6.9809007521622383848e-1045j)  +/-  (1.09e-248, 1.09e-248j)
| (-1.4446265900208259987 + 5.5123568069061808076e-1046j)  +/-  (5.16e-250, 5.16e-250j)
| (5.1083814254335441109 + 2.4007530550959893337e-1038j)  +/-  (2.45e-244, 2.45e-244j)
| (1.1061247494075292876 - 5.2416751962686822681e-1049j)  +/-  (4.76e-251, 4.76e-251j)
| (0.74109534999454084186 + 4.9470285182931011177e-1050j)  +/-  (2.38e-252, 2.38e-252j)
| (6.0647321545101271124 - 2.511903813510310029e-1040j)  +/-  (1.45e-243, 1.45e-243j)
| (-4.1849560176727318607 + 2.6086490138767730723e-1050j)  +/-  (2.23e-245, 2.23e-245j)
| (-0.37116879133751642977 + 3.2145974679590157601e-1059j)  +/-  (1.7e-253, 1.7e-253j)
| (-8.6607189809952929716 + 3.3016737340694885454e-1048j)  +/-  (5.83e-243, 5.83e-243j)
| (5.5821152281100459404 + 7.7066121350833928321e-1054j)  +/-  (6.39e-244, 6.39e-244j)
| (1.7320508075688772935 + 8.132464855518676448e-1075j)  +/-  (2.86e-249, 2.86e-249j)
| (7.5779262653075268093 - 3.2241857320494676318e-1070j)  +/-  (5.43e-243, 5.43e-243j)
| (-3.293016963519965758 - 2.7769985262654396997e-1079j)  +/-  (1.32e-246, 1.32e-246j)
| (-3.7348310182211559025 + 1.2517937773231859746e-1079j)  +/-  (5.4e-246, 5.4e-246j)
| (6.5572638495247355908 + 2.0057280316229603465e-1081j)  +/-  (2.76e-243, 2.76e-243j)
| (0.37116879133751642977 + 2.8525760487702396918e-1092j)  +/-  (1.5e-253, 1.5e-253j)
| (4.1849560176727318607 + 6.702029056791310228e-1087j)  +/-  (2.37e-245, 2.37e-245j)
| (-0.74109534999454084186 + 2.8947063453603064577e-1094j)  +/-  (2.33e-252, 2.33e-252j)
| (-1.1061247494075292876 - 2.7241476585590257148e-1092j)  +/-  (4.91e-251, 4.91e-251j)
| (4.0868405437247478317e-1230 - 1.3104652037147678201e-1230j)  +/-  (2.27e-1228, 2.27e-1228j)
-------------------------------------------------
The weights are:
| (3.6199010874508916857e-32 + 7.6415521076271223849e-980j)  +/-  (3.97e-75, 2.57e-197j)
| (3.9451829484957811788e-25 + 5.55871658848707837e-976j)  +/-  (2.33e-72, 1.51e-194j)
| (1.1253460684842212021e-15 - 2.4739820834136901501e-971j)  +/-  (2.24e-68, 1.45e-190j)
| (2.4313496180947575837e-22 + 3.1683426624779967438e-975j)  +/-  (9.57e-73, 6.21e-195j)
| (2.4313496180947575837e-22 - 2.5179630478654920929e-974j)  +/-  (9.42e-72, 6.11e-194j)
| (3.6199010874508916857e-32 - 1.6359758527286503336e-980j)  +/-  (9e-78, 5.84e-200j)
| (4.3622791287769727541e-37 - 1.6057924351170575089e-982j)  +/-  (3.45e-78, 2.24e-200j)
| (2.4205935152297247253e-28 - 1.0103909361239632929e-977j)  +/-  (2.44e-74, 1.58e-196j)
| (7.0899321307363612528e-14 + 1.2364944940182644194e-968j)  +/-  (1.05e-68, 6.79e-191j)
| (4.3622791287769727541e-37 + 4.024361659692878232e-983j)  +/-  (1.06e-80, 6.88e-203j)
| (2.4205935152297247253e-28 + 1.8129402383666371641e-978j)  +/-  (2.49e-77, 1.62e-199j)
| (0.0081741407518737941915 - 1.1860240566319979896e-962j)  +/-  (3e-52, 1.95e-174j)
| (1.1537986082285965017e-17 + 1.0934549102852455736e-972j)  +/-  (8.33e-73, 5.4e-195j)
| (0.0081741407518737941915 - 2.2963779363418845008e-962j)  +/-  (2.55e-53, 1.66e-175j)
| (9.1459633162164623203e-11 + 1.8123346747143716299e-967j)  +/-  (3.09e-69, 2e-191j)
| (7.1452689203298737777e-20 - 7.0590515994733380754e-974j)  +/-  (2.97e-74, 1.92e-196j)
| (0.01749750991557392718 + 7.2501398197031872079e-962j)  +/-  (7.23e-52, 4.69e-174j)
| (3.2662833129674392666e-08 + 3.3816733048219406207e-966j)  +/-  (1.59e-67, 1.03e-189j)
| (2.0039512280211952451e-09 - 7.8690126147617721107e-967j)  +/-  (1.62e-68, 1.05e-190j)
| (0.00016649455644287775945 + 2.2958143173058209314e-964j)  +/-  (5.54e-65, 3.59e-187j)
| (3.0324116193836960631e-12 - 4.8213177349362448597e-968j)  +/-  (6.3e-71, 4.09e-193j)
| (7.1452689203298737777e-20 + 7.7195298401709012268e-973j)  +/-  (8.26e-76, 5.36e-198j)
| (3.0324116193836960631e-12 - 1.8468932312062009244e-969j)  +/-  (1.28e-74, 8.31e-197j)
| (3.9451829484957811788e-25 - 9.7475863643472643875e-977j)  +/-  (1.69e-79, 1.09e-201j)
| (0.0028320479537871291516 + 7.1239111579699569175e-963j)  +/-  (2.86e-62, 1.86e-184j)
| (3.8415515864601963621e-06 + 1.3063252950219324922e-965j)  +/-  (5.94e-70, 3.86e-192j)
| (0.00077067864098288468579 - 8.7916834630302001971e-964j)  +/-  (1.77e-65, 1.15e-187j)
| (4.0366663820581156418e-07 - 1.3830065082129290239e-965j)  +/-  (2.6e-69, 1.69e-191j)
| (3.8415515864601963621e-06 + 5.3268209087833530959e-965j)  +/-  (7.43e-69, 4.82e-191j)
| (1.1253460684842212021e-15 + 5.1329551957521193482e-970j)  +/-  (2.48e-75, 1.61e-197j)
| (0.025503766746266454577 - 1.7108285765938450345e-961j)  +/-  (1.46e-60, 9.48e-183j)
| (0.0028320479537871291516 + 3.2511755335639483892e-963j)  +/-  (4.63e-66, 3.01e-188j)
| (0.043586679804249692702 + 1.6920070051169522724e-961j)  +/-  (2.47e-61, 1.61e-183j)
| (0.01749750991557392718 + 4.1835538881142724616e-962j)  +/-  (7.08e-64, 4.59e-186j)
| (0.043586679804249692702 + 2.4776339025460076655e-961j)  +/-  (2.24e-61, 1.45e-183j)
| (4.0366663820581156418e-07 - 2.761392078577998971e-966j)  +/-  (1.65e-73, 1.07e-195j)
| (0.077508868200876677527 - 1.9996519259516968522e-961j)  +/-  (7.46e-62, 4.84e-184j)
| (0.11178654883999354684 + 2.2771621669387165501e-961j)  +/-  (7.04e-62, 4.57e-184j)
| (2.0039512280211952451e-09 - 9.087522970332632874e-968j)  +/-  (4.13e-76, 2.68e-198j)
| (2.8503690041935876723e-05 - 1.9336479047883404709e-964j)  +/-  (1.51e-71, 9.79e-194j)
| (0.13805647113490656507 - 2.8162527916808638564e-961j)  +/-  (2.11e-64, 1.37e-186j)
| (1.1537986082285965017e-17 - 1.9537087140517881194e-971j)  +/-  (6.13e-79, 3.98e-201j)
| (3.2662833129674392666e-08 + 5.2926553123505523858e-967j)  +/-  (2.8e-75, 1.82e-197j)
| (0.025503766746266454577 - 1.0802853706136640341e-961j)  +/-  (1.89e-67, 1.22e-189j)
| (7.0899321307363612528e-14 + 2.207033787687152122e-970j)  +/-  (5.52e-79, 3.58e-201j)
| (0.00077067864098288468579 - 2.203723365837898021e-963j)  +/-  (9.75e-72, 6.33e-194j)
| (0.00016649455644287775945 + 6.6611153058795338186e-964j)  +/-  (1.97e-72, 1.28e-194j)
| (9.1459633162164623203e-11 + 1.3820295537280014418e-968j)  +/-  (1.43e-77, 9.3e-200j)
| (0.13805647113490656507 - 2.5561915632425941869e-961j)  +/-  (1.12e-69, 7.41e-192j)
| (2.8503690041935876723e-05 - 5.6749638975509524299e-965j)  +/-  (7.68e-74, 4.99e-196j)
| (0.11178654883999354684 + 2.7644454710319787654e-961j)  +/-  (2.16e-70, 1.42e-192j)
| (0.077508868200876677527 - 2.6738639463462881114e-961j)  +/-  (1.58e-70, 1e-192j)
| (0.14816801957086281936 + 2.7507894100148189323e-961j)  +/-  (2.13e-70, 1.5e-192j)
