Starting with polynomial:
P : t^26 - 325*t^24 + 44850*t^22 - 3453450*t^20 + 164038875*t^18 - 5019589575*t^16 + 100391791500*t^14 - 1305093289500*t^12 + 10767019638375*t^10 - 53835098191875*t^8 + 150738274937250*t^6 - 205552193096250*t^4 + 102776096548125*t^2 - 7905853580625
Extension levels are: 26 41
-------------------------------------------------
Trying to find an order 41 Kronrod extension for:
P1 : t^26 - 325*t^24 + 44850*t^22 - 3453450*t^20 + 164038875*t^18 - 5019589575*t^16 + 100391791500*t^14 - 1305093289500*t^12 + 10767019638375*t^10 - 53835098191875*t^8 + 150738274937250*t^6 - 205552193096250*t^4 + 102776096548125*t^2 - 7905853580625
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^67 - 550640152744133860060576276506040808990097967633341732665/347370223533358277498175832229340565547938809983077593*t^65 + 408858505985911643539987903870285705290751067551033581802880/347370223533358277498175832229340565547938809983077593*t^63 - 21027884176011781087081609428500043842656930496715612148431440/38596691503706475277575092469926729505326534442564177*t^61 + 20437741220947824061203594381571318740989138015704219351680265300/115790074511119425832725277409780188515979603327692531*t^59 - 4932968861037107827297576813451477896559958780440130998760484386100/115790074511119425832725277409780188515979603327692531*t^57 + 307301335069634428906882472994751130004049798713141151979318865482600/38596691503706475277575092469926729505326534442564177*t^55 - 15208854811435065078834371645666060783676647605865792474481588099501000/12865563834568825092525030823308909835108844814188059*t^53 + 1826574405257639351310103862093132799780491894335228578252881267804673000/12865563834568825092525030823308909835108844814188059*t^51 - 179749907223957047089963190452558809598245981999795873875322252577135257000/12865563834568825092525030823308909835108844814188059*t^49 + 14629993850785326144737514636003866780623411351809658578512746235485689049200/12865563834568825092525030823308909835108844814188059*t^47 - 991446100154526902951541344680906951809825122399688973390628957979095013612000/12865563834568825092525030823308909835108844814188059*t^45 + 56202373342415893433554400381916774358196825508353346561248018437559171444158500/12865563834568825092525030823308909835108844814188059*t^43 - 2672899304851391749857656274923682704234077851730029300341428671885932355975154500/12865563834568825092525030823308909835108844814188059*t^41 + 106810216195500526369720958109643202512580905224513738617184797590592021026058205000/12865563834568825092525030823308909835108844814188059*t^39 - 3587159610050525818131538057405873972696021838119863377720631705705601418817884079000/12865563834568825092525030823308909835108844814188059*t^37 + 101154564482678031684915789508759762709591161318969520999139063237581913934608252813750/12865563834568825092525030823308909835108844814188059*t^35 - 2390035775068797575353896836482154589483337188145559429182323843339735245270874679653750/12865563834568825092525030823308909835108844814188059*t^33 + 47161335939508999728159661582141197360708069210524417371381284260208240513942624799620000/12865563834568825092525030823308909835108844814188059*t^31 - 773700909003251651097582238951720403388245279902471697026944618300062537374582836496950000/12865563834568825092525030823308909835108844814188059*t^29 + 10491114369531941474186365072132741429858674474458994075250587060384335451335186711623177500/12865563834568825092525030823308909835108844814188059*t^27 - 116714334753220583245949750351650112408446139841852156295154612072446449985036808939633437500/12865563834568825092525030823308909835108844814188059*t^25 + 1055596079186636749677284517049004050370004577188654925900493620784864201563362961995517125000/12865563834568825092525030823308909835108844814188059*t^23 - 7674049011859333052432970413038914193417069970035073126044377348158650202046298446686224875000/12865563834568825092525030823308909835108844814188059*t^21 + 44220739824930198567564101048950270018777679326696054055527808906859045579494591830627908750000/12865563834568825092525030823308909835108844814188059*t^19 - 198489065343557236239824367619931951936775001051752779995668352474912646209789169013559335750000/12865563834568825092525030823308909835108844814188059*t^17 + 678926403410531940237153644047194727796097567339265523943253327053686766197725834589941443750000/12865563834568825092525030823308909835108844814188059*t^15 - 1720483588199148355355856858544547169780073940148143618078035526972643551245547107447315995000000/12865563834568825092525030823308909835108844814188059*t^13 + 3112658294144529498210048567373648237814994438640686166419134273559044921324534784140164444687500/12865563834568825092525030823308909835108844814188059*t^11 - 3823058324670123598217903817626733199946279857415093664284863392272760952027254945444464292187500/12865563834568825092525030823308909835108844814188059*t^9 + 2967725427944932187754581602608479502612093089912301055105503969256782997725782640932732911875000/12865563834568825092525030823308909835108844814188059*t^7 - 1304682295573968489570578110411471899549046351602887910879118401849087727704797356645434665625000/12865563834568825092525030823308909835108844814188059*t^5 + 266855148052301404998026147698827551689093317914562088399632586549891165138766978628262196484375/12865563834568825092525030823308909835108844814188059*t^3 - 15665842203543451257435272427605365494450235123019359800244599736175521790675037906326058984375/12865563834568825092525030823308909835108844814188059*t
-------------------------------------------------
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: 0
  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:
| (10.018115167254202534 - 1.1969901717684351633e-555j)  +/-  (9.45e-241, 9.45e-241j)
| (-13.585915608911291405 + 8.8332740541183124466e-559j)  +/-  (6.52e-245, 6.52e-245j)
| (-11.231539249207662897 + 1.9840943855446840329e-555j)  +/-  (6.85e-242, 6.85e-242j)
| (-8.9230517278282476137 - 1.0089939600113215258e-552j)  +/-  (5.11e-240, 5.11e-240j)
| (13.585915608911291405 + 2.0777487979040750011e-563j)  +/-  (7.08e-245, 7.08e-245j)
| (-10.018115167254202534 - 1.2476577159240425332e-556j)  +/-  (8.59e-241, 8.59e-241j)
| (-6.9880887706234122698 + 1.1958339323788947696e-565j)  +/-  (1.23e-239, 1.23e-239j)
| (7.8198835907687802425 + 1.6590635581163823491e-574j)  +/-  (2.17e-238, 2.17e-238j)
| (11.909569267579933041 + 1.263103549136908701e-589j)  +/-  (1.32e-242, 1.32e-242j)
| (4.7509474830853766697 + 4.5350700175416357423e-590j)  +/-  (1.86e-241, 1.86e-241j)
| (10.60599746618319043 - 2.9654084791585537293e-586j)  +/-  (2.79e-241, 2.79e-241j)
| (6.5664953174443462937 + 2.5014900136317207741e-587j)  +/-  (7.3e-240, 7.3e-240j)
| (-8.4052883162286463906 + 2.44136025473191703e-604j)  +/-  (1.32e-239, 1.32e-239j)
| (8.4052883162286463906 - 7.352084503593943908e-619j)  +/-  (1.25e-239, 1.25e-239j)
| (-3.7010923469598245399 - 3.0944038187931799931e-632j)  +/-  (2.98e-243, 2.98e-243j)
| (6.1936934837963133401 + 2.6638240220681307969e-626j)  +/-  (4.78e-240, 4.78e-240j)
| (8.9230517278282476137 - 4.8099670359868433423e-645j)  +/-  (5.59e-240, 5.59e-240j)
| (-7.869426697637737727 + 1.3960759890996705019e-672j)  +/-  (2.31e-238, 2.31e-238j)
| (5.0749120784837952317 - 5.5441436328541164066e-694j)  +/-  (3.89e-241, 3.89e-241j)
| (-1.5312157086954012062 - 1.6641508122227358449e-701j)  +/-  (4.26e-249, 4.26e-249j)
| (12.669023089131370006 - 7.1552168429075939994e-696j)  +/-  (1.55e-243, 1.55e-243j)
| (4.0754272144122266022 - 6.7906447848696449858e-695j)  +/-  (1.22e-242, 1.22e-242j)
| (-5.4536153838578314707 + 1.4342110219025826967e-692j)  +/-  (9.6e-241, 9.6e-241j)
| (9.459070704504997147 - 4.67627888404828433e-693j)  +/-  (2.23e-240, 2.23e-240j)
| (-11.909569267579933041 - 1.0410665840916765848e-693j)  +/-  (1.3e-242, 1.3e-242j)
| (-5.0749120784837952317 - 3.4520958613015233001e-693j)  +/-  (4.09e-241, 4.09e-241j)
| (-10.60599746618319043 - 5.5927886926223383064e-690j)  +/-  (2.93e-241, 2.93e-241j)
| (11.231539249207662897 + 2.74476376836963183e-695j)  +/-  (7.6e-242, 7.6e-242j)
| (3.4201563739999792806 + 2.3208512956563362169e-697j)  +/-  (9.59e-244, 9.59e-244j)
| (-4.7509474830853766697 + 8.6938026593881590901e-695j)  +/-  (1.95e-241, 1.95e-241j)
| (-3.4201563739999792806 + 1.4287876884146608222e-696j)  +/-  (1.01e-243, 1.01e-243j)
| (-9.459070704504997147 - 5.3451752313862495752e-693j)  +/-  (2.39e-240, 2.39e-240j)
| (0.91654504133862789419 + 4.7385772033522023201e-715j)  +/-  (4.03e-251, 4.03e-251j)
| (3.7010923469598245399 - 2.3213173565947357685e-706j)  +/-  (3.17e-243, 3.17e-243j)
| (-12.669023089131370006 - 3.066083589490912142e-704j)  +/-  (1.45e-243, 1.45e-243j)
| (-2.4011492632680598159 - 8.7462502384315103058e-710j)  +/-  (2.82e-246, 2.82e-246j)
| (-2.1515300901216484795 - 9.9519276693834331946e-711j)  +/-  (7.77e-247, 7.77e-247j)
| (-3.1527492028807548318 - 4.1062795771029536961e-708j)  +/-  (2.15e-244, 2.15e-244j)
| (2.4011492632680598159 + 9.6972505016633984236e-710j)  +/-  (2.89e-246, 2.89e-246j)
| (-7.4501876767429220968 + 1.6382746192540432107e-700j)  +/-  (3.05e-239, 3.05e-239j)
| (-1.9035905970347043881 + 1.7817190979936841421e-735j)  +/-  (1.05e-247, 1.05e-247j)
| (-7.8198835907687802425 + 4.6816920206768615831e-725j)  +/-  (2.19e-238, 2.19e-238j)
| (1.9035905970347043881 + 4.9138167404449059682e-746j)  +/-  (1.01e-247, 1.01e-247j)
| (4.4420052918351518803 + 2.1356012272718112115e-740j)  +/-  (6.15e-242, 6.15e-242j)
| (5.8354607191871418625 - 4.6588334169758729093e-739j)  +/-  (2.36e-240, 2.36e-240j)
| (-1.1738851349007555168 + 1.6695751864960088686e-749j)  +/-  (3.13e-250, 3.13e-250j)
| (7.869426697637737727 + 1.037155246054584029e-736j)  +/-  (2.05e-238, 2.05e-238j)
| (3.1527492028807548318 + 7.3219930813465598453e-745j)  +/-  (2.13e-244, 2.13e-244j)
| (0.64041358544475626386 - 4.8974412289327027986e-752j)  +/-  (3.48e-252, 3.48e-252j)
| (-6.5664953174443462937 - 1.6379926295834490778e-738j)  +/-  (7.87e-240, 7.87e-240j)
| (-5.8354607191871418625 - 7.8960478734167407278e-740j)  +/-  (2.53e-240, 2.53e-240j)
| (-0.64041358544475626386 - 9.3039389786611309092e-754j)  +/-  (3.32e-252, 3.32e-252j)
| (7.4501876767429220968 - 1.9372585058715339587e-740j)  +/-  (3.27e-239, 3.27e-239j)
| (1.5312157086954012062 + 3.9946518902781548354e-751j)  +/-  (4.24e-249, 4.24e-249j)
| (-0.91654504133862789419 - 4.8834256387744081573e-753j)  +/-  (3.83e-251, 3.83e-251j)
| (-3.3121189921339484709e-793 + 1.738450805452074335e-792j)  +/-  (1.19e-790, 1.19e-790j)
| (-4.4420052918351518803 - 1.2704542831221093186e-742j)  +/-  (5.82e-242, 5.82e-242j)
| (-2.780138499509748897 + 5.66065840704627664e-746j)  +/-  (1.98e-245, 1.98e-245j)
| (2.780138499509748897 - 1.4378133025782541064e-746j)  +/-  (1.74e-245, 1.74e-245j)
| (0.30515597075929801293 - 1.0746733618411858924e-754j)  +/-  (1.12e-253, 1.12e-253j)
| (2.1515300901216484795 + 1.9342969426569119056e-748j)  +/-  (7.23e-247, 7.23e-247j)
| (-4.0754272144122266022 + 6.7542844464025293126e-743j)  +/-  (1.23e-242, 1.23e-242j)
| (-0.30515597075929801293 + 1.199541201791965346e-754j)  +/-  (1.12e-253, 1.12e-253j)
| (-6.1936934837963133401 + 2.5804251851589181384e-741j)  +/-  (4.62e-240, 4.62e-240j)
| (1.1738851349007555168 + 8.1742214153879579744e-752j)  +/-  (2.92e-250, 2.92e-250j)
| (5.4536153838578314707 - 5.3163597099988122884e-742j)  +/-  (9.32e-241, 9.32e-241j)
| (6.9880887706234122698 + 2.3559672498020825198e-751j)  +/-  (1.28e-239, 1.28e-239j)
-------------------------------------------------
The weights are:
| (3.6734283785529069838e-23 - 3.3423245665055702199e-575j)  +/-  (4.23e-58, 2.4e-177j)
| (3.5107278432350040897e-41 - 9.7122465864401668404e-586j)  +/-  (4.12e-67, 2.34e-186j)
| (1.0478183288710564193e-28 + 6.5670606267894137439e-578j)  +/-  (7.2e-62, 4.09e-181j)
| (1.0776624108885105822e-18 - 7.5677247912802181007e-570j)  +/-  (4.07e-56, 2.31e-175j)
| (3.5107278432350040897e-41 + 2.0127927985220651306e-586j)  +/-  (1.38e-69, 7.85e-189j)
| (3.6734283785529069838e-23 + 5.8327188268111645461e-574j)  +/-  (4.24e-59, 2.41e-178j)
| (4.3996890908517191322e-12 + 8.1878867457657866774e-566j)  +/-  (1.45e-50, 8.23e-170j)
| (-1.0890505542454649047e-14 + 1.2265728320211735947e-567j)  +/-  (2.99e-55, 1.7e-174j)
| (4.5047018418065301671e-32 + 5.8796363530385127835e-581j)  +/-  (2.7e-66, 1.53e-185j)
| (1.4768352989674612069e-06 + 3.5271436090580692589e-562j)  +/-  (3.29e-44, 1.87e-163j)
| (9.04274478871871038e-26 + 5.9635280014427442576e-577j)  +/-  (5.13e-63, 2.91e-182j)
| (6.866572286895032855e-11 - 8.3304812267276632149e-566j)  +/-  (2.81e-52, 1.6e-171j)
| (9.2899536873372078447e-17 + 8.6406058246293494307e-569j)  +/-  (9.55e-59, 5.42e-178j)
| (9.2899536873372078447e-17 + 2.5798806770838410619e-570j)  +/-  (7.5e-58, 4.25e-177j)
| (0.00014780700266958799107 - 3.5092518065930253045e-560j)  +/-  (9.62e-43, 5.46e-162j)
| (6.6181137457360048554e-10 + 5.4453097305061793456e-565j)  +/-  (1.15e-51, 6.52e-171j)
| (1.0776624108885105822e-18 - 6.0861523496664910299e-572j)  +/-  (1.51e-59, 8.55e-179j)
| (1.3823440669145412306e-14 - 1.3768583084189501129e-566j)  +/-  (2.37e-59, 1.34e-178j)
| (3.6588640807014480368e-07 - 8.3690300645336645342e-563j)  +/-  (9.87e-49, 5.6e-168j)
| (0.046727984286878313186 + 2.2897500635200465653e-558j)  +/-  (8.71e-28, 4.94e-147j)
| (4.5750704837277921178e-36 - 2.1821242859947866322e-583j)  +/-  (2.91e-70, 1.65e-189j)
| (3.7732144560743529427e-05 + 3.2921771190872541086e-561j)  +/-  (6.13e-46, 3.48e-165j)
| (5.3911612629644785843e-08 + 6.042554582911525894e-563j)  +/-  (3.57e-54, 2.02e-173j)
| (8.12160769220243253e-21 + 1.5200177552510869942e-573j)  +/-  (2.79e-61, 1.58e-180j)
| (4.5047018418065301671e-32 - 4.0983033601503112291e-580j)  +/-  (1.19e-71, 6.74e-191j)
| (3.6588640807014480368e-07 - 3.0448499035256021138e-562j)  +/-  (1.35e-53, 7.68e-173j)
| (9.04274478871871038e-26 - 6.9045090473889313549e-576j)  +/-  (4.18e-68, 2.37e-187j)
| (1.0478183288710564193e-28 - 7.5301627924346835517e-579j)  +/-  (9.04e-68, 5.13e-187j)
| (0.00025548497947431684612 + 4.2533005745682523259e-560j)  +/-  (1.23e-47, 6.98e-167j)
| (1.4768352989674612069e-06 + 1.1561985624035551253e-561j)  +/-  (3.06e-53, 1.73e-172j)
| (0.00025548497947431684612 + 9.5412742701000865347e-560j)  +/-  (8.7e-49, 4.94e-168j)
| (8.12160769220243253e-21 - 5.2244898109562866766e-572j)  +/-  (1.89e-65, 1.07e-184j)
| (0.059223434739918117887 + 5.3738847132862666412e-558j)  +/-  (3.35e-39, 1.9e-158j)
| (0.00014780700266958799107 - 1.4514360658712750506e-560j)  +/-  (3.52e-50, 2e-169j)
| (4.5750704837277921178e-36 + 1.2571043437176096917e-582j)  +/-  (2.13e-74, 1.21e-193j)
| (0.0078198539436506110963 - 8.588089950652889241e-559j)  +/-  (4.26e-46, 2.42e-165j)
| (0.0065880117086956122423 + 1.7679952831288115015e-558j)  +/-  (7.82e-45, 4.44e-164j)
| (0.00093644931642366187555 - 1.5416733068468032009e-559j)  +/-  (2.03e-49, 1.15e-168j)
| (0.0078198539436506110963 - 4.9457787552067448608e-559j)  +/-  (1.04e-48, 5.91e-168j)
| (1.7154672637002831708e-13 - 1.6782568847846677803e-566j)  +/-  (6.17e-62, 3.5e-181j)
| (0.022587564448326102702 - 2.0039349798962020745e-558j)  +/-  (1.17e-45, 6.67e-165j)
| (-1.0890505542454649047e-14 + 1.8625507526149149383e-566j)  +/-  (9.16e-62, 5.2e-181j)
| (0.022587564448326102702 - 1.299186248310606685e-558j)  +/-  (1.68e-48, 9.54e-168j)
| (7.040355550918640789e-06 - 1.0290888978695959521e-561j)  +/-  (3.02e-56, 1.71e-175j)
| (5.9496174777208396721e-09 - 2.7759048983986067475e-564j)  +/-  (1.16e-60, 6.6e-180j)
| (0.063750774375524368848 - 4.4393506140300096998e-558j)  +/-  (1.59e-46, 9.05e-166j)
| (1.3823440669145412306e-14 - 8.6343499119962997272e-568j)  +/-  (1.05e-64, 5.94e-184j)
| (0.00093644931642366187555 - 7.3660669785292799197e-560j)  +/-  (3.21e-54, 1.82e-173j)
| (0.10622809530028313184 - 5.6406396489655805501e-558j)  +/-  (1.95e-47, 1.11e-166j)
| (6.866572286895032855e-11 - 5.4772219107451554419e-565j)  +/-  (5.13e-63, 2.91e-182j)
| (5.9496174777208396721e-09 - 1.3271702979462933713e-563j)  +/-  (8.9e-62, 5.05e-181j)
| (0.10622809530028313184 - 6.5130165515546922235e-558j)  +/-  (3.23e-50, 1.83e-169j)
| (1.7154672637002831708e-13 - 1.5090345799608791261e-567j)  +/-  (1.79e-65, 1.01e-184j)
| (0.046727984286878313186 + 1.6189341236463937902e-558j)  +/-  (4.87e-53, 2.76e-172j)
| (0.059223434739918117887 + 6.6043938392544013097e-558j)  +/-  (2.82e-50, 1.6e-169j)
| (0.11608080741802857998 - 6.4395778252336726249e-558j)  +/-  (1.5e-50, 8.52e-170j)
| (7.040355550918640789e-06 - 3.0697739794117435997e-561j)  +/-  (2.87e-59, 1.63e-178j)
| (0.003250860550789596021 + 2.7271088361004298379e-559j)  +/-  (8.26e-56, 4.69e-175j)
| (0.003250860550789596021 + 1.4313265760749419106e-559j)  +/-  (6.63e-57, 3.76e-176j)
| (0.12439659982025212215 + 5.8308076113476027534e-558j)  +/-  (4.14e-53, 2.35e-172j)
| (0.0065880117086956122423 + 1.0809726027280072757e-558j)  +/-  (1.09e-55, 6.18e-175j)
| (3.7732144560743529427e-05 + 8.8287991673232129803e-561j)  +/-  (5.89e-59, 3.34e-178j)
| (0.12439659982025212215 + 6.243789727768895164e-558j)  +/-  (3.61e-54, 2.05e-173j)
| (6.6181137457360048554e-10 + 3.0167061056834619436e-564j)  +/-  (4.07e-63, 2.31e-182j)
| (0.063750774375524368848 - 3.406994453821950949e-558j)  +/-  (4.71e-56, 2.68e-175j)
| (5.3911612629644785843e-08 + 1.4579216717728712396e-563j)  +/-  (2.96e-63, 1.68e-182j)
| (4.3996890908517191322e-12 + 9.9538303237779349361e-567j)  +/-  (1.71e-66, 9.72e-186j)
