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 43
-------------------------------------------------
Trying to find an order 43 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^69 - 9521246181320200151638248650514295561705681470331969993/5456123242652626621680000822168059176059192909996139*t^67 + 7805148858705022256579461867250010064230471088747125087930/5456123242652626621680000822168059176059192909996139*t^65 - 12001059850960930731742936147195642121954353105121923490647780/16368369727957879865040002466504177528177578729988417*t^63 + 4317969777298430106331156273166376066739856056267455206364849280/16368369727957879865040002466504177528177578729988417*t^61 - 386983584169138048178086389489255650780752390801236679535951444800/5456123242652626621680000822168059176059192909996139*t^59 + 80810664187746350247369169167604198282380206903342192153668713846500/5456123242652626621680000822168059176059192909996139*t^57 - 13449003712708120770887264436989626450890111267648675674942435056166900/5456123242652626621680000822168059176059192909996139*t^55 + 1816366295743303312386927740621060440068869450071035259989192029613742500/5456123242652626621680000822168059176059192909996139*t^53 - 201676176303146050203385877421656870508365984839187282527976549378156125500/5456123242652626621680000822168059176059192909996139*t^51 + 18584497562750676871584644489740891883231059176914351523420055939903092839700/5456123242652626621680000822168059176059192909996139*t^49 - 1431081020438922162509034724923391630449092177801388077769779139119462525181900/5456123242652626621680000822168059176059192909996139*t^47 + 92531386603084310628740830466577718863052145731602254259592223126319309824400000/5456123242652626621680000822168059176059192909996139*t^45 - 5039766103387320487160281894610755011232763598342550575805810626386594132723844000/5456123242652626621680000822168059176059192909996139*t^43 + 231640960698324270688783432178315555527856596109637610986357269647887656818376566500/5456123242652626621680000822168059176059192909996139*t^41 - 8990127088823542074586195808723141313304029681083265644679768054570465726770545756500/5456123242652626621680000822168059176059192909996139*t^39 + 294470824772110496082964790616101943775715881641937142356190486566215177991206495689250/5456123242652626621680000822168059176059192909996139*t^37 - 8127659119480336040690297750329797460450113991403866507308571382497915851085134428643750/5456123242652626621680000822168059176059192909996139*t^35 + 188538117763454294619200662857340499857898056452686618501333688136188292103492319622215000/5456123242652626621680000822168059176059192909996139*t^33 - 3662136609069552276511473773610895127982150896796231130894315271018894911337665085812402500/5456123242652626621680000822168059176059192909996139*t^31 + 59272902074768357327335332305174664301282628110955305191715040316709718198448758652652440000/5456123242652626621680000822168059176059192909996139*t^29 - 27396099535627022036097686148392256428069155995711085237724589877335505751872330093591320000/188142180781125055920000028350622730208937686551591*t^27 + 301791797704570895797639223920571214731938038279769055485417286650047045569824929184379437500/188142180781125055920000028350622730208937686551591*t^25 - 2706667543691075641753502933322179046843514029912022481697794598091219429486377144337266187500/188142180781125055920000028350622730208937686551591*t^23 + 19537609571452590527930600089236375117323880337636906534153766331489833713815003144099559312500/188142180781125055920000028350622730208937686551591*t^21 - 111909880339473062346401708880090615585836772333764726454709138399803029080648259974841632687500/188142180781125055920000028350622730208937686551591*t^19 + 499804945936989897120987604123015155533355597539736760049529203761300078648892422185394491937500/188142180781125055920000028350622730208937686551591*t^17 - 1702478239193822841017164238748649770839402877090506733910359921154144119330413872101615925312500/188142180781125055920000028350622730208937686551591*t^15 + 4299561689834717806903296610718205063645581888038741996300769082195627585644593011558631395000000/188142180781125055920000028350622730208937686551591*t^13 - 7756271982136547457884960101487343071747804577011682403386771019912984943032064805537648157500000/188142180781125055920000028350622730208937686551591*t^11 + 9499026743016008285880701683653682734530374057690505713542704215658264282856553598098993995937500/188142180781125055920000028350622730208937686551591*t^9 - 7340619869099020717068320172069253722896878371690991470390523204977790795962542185278293787187500/188142180781125055920000028350622730208937686551591*t^7 + 3194582858534957773411621037043702409614369591663427391880052078524191540235982727054357077734375/188142180781125055920000028350622730208937686551591*t^5 - 640072548490537307175118535407861600165787086283020152195539603297666576239776839647306817578125/188142180781125055920000028350622730208937686551591*t^3 + 37167013185898177933379786171792107450239562923352688136639843392198776912272560925178202343750/188142180781125055920000028350622730208937686551591*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:
| (10.971831651496466375 + 6.8439751767239594096e-687j)  +/-  (1.46e-240, 1.46e-240j)
| (-8.9230517278282476137 + 4.7652673376526634143e-701j)  +/-  (5.98e-238, 5.98e-238j)
| (-9.3095760967782511081 + 1.1270348530951705571e-717j)  +/-  (6.87e-239, 6.87e-239j)
| (-12.257535971518112013 + 8.8475386570810518771e-727j)  +/-  (4.93e-242, 4.93e-242j)
| (-13.91442902172140231 + 2.7238573988749614312e-729j)  +/-  (1.84e-244, 1.84e-244j)
| (-10.971831651496466375 + 6.537182131758440323e-725j)  +/-  (1.47e-240, 1.47e-240j)
| (10.392828444505264639 - 1.9557239683548819975e-725j)  +/-  (5.03e-240, 5.03e-240j)
| (-11.588465547451243497 + 4.8924030686319774383e-727j)  +/-  (3.01e-241, 3.01e-241j)
| (13.91442902172140231 + 6.6384617247378640003e-731j)  +/-  (1.96e-244, 1.96e-244j)
| (7.4184299630621771347 + 7.7560586768034602283e-725j)  +/-  (2.48e-239, 2.48e-239j)
| (11.588465547451243497 + 2.333041018230073961e-727j)  +/-  (3.04e-241, 3.04e-241j)
| (-13.007742155799174398 - 3.2415093745517462687e-728j)  +/-  (4.8e-243, 4.8e-243j)
| (-4.0754272144122266022 - 1.0537395858367516511e-727j)  +/-  (1.59e-242, 1.59e-242j)
| (8.9230517278282476137 - 3.2243217730094091148e-723j)  +/-  (6.44e-238, 6.44e-238j)
| (-4.4137123132374714757 - 6.6876130862056567782e-727j)  +/-  (6.43e-242, 6.43e-242j)
| (9.3095760967782511081 - 4.1915538781130678402e-725j)  +/-  (6.42e-239, 6.42e-239j)
| (5.4536153838578314707 - 4.1855020466732725051e-726j)  +/-  (1.44e-240, 1.44e-240j)
| (6.9880887706234122698 - 1.0505826015831721857e-724j)  +/-  (1.72e-239, 1.72e-239j)
| (-9.8421777377581850778 - 1.7780767348630223036e-722j)  +/-  (1.58e-239, 1.58e-239j)
| (-4.7509474830853766697 - 1.2700675206817749765e-728j)  +/-  (1.92e-241, 1.92e-241j)
| (-3.7413352660055678012 + 3.5632721672088060166e-730j)  +/-  (3.53e-243, 3.53e-243j)
| (13.007742155799174398 + 2.1928848630860946941e-731j)  +/-  (4.7e-243, 4.7e-243j)
| (-10.392828444505264639 + 1.0158057824962621888e-724j)  +/-  (5.23e-240, 5.23e-240j)
| (12.257535971518112013 + 4.4262482587304756529e-732j)  +/-  (4.84e-242, 4.84e-242j)
| (-2.780138499509748897 + 2.8190668298766149338e-735j)  +/-  (2.61e-245, 2.61e-245j)
| (-5.0956166313813410952 + 3.3250642107542718207e-730j)  +/-  (5.38e-241, 5.38e-241j)
| (1.8456782079349223725 + 1.8323061175192361114e-737j)  +/-  (6.17e-248, 6.17e-248j)
| (-6.9880887706234122698 + 7.6076474507718080686e-727j)  +/-  (1.76e-239, 1.76e-239j)
| (8.8661085132598740463 + 1.7047026075382695934e-732j)  +/-  (6.28e-238, 6.28e-238j)
| (-1.2192326334033848114 + 6.9136665387427107248e-745j)  +/-  (5.04e-250, 5.04e-250j)
| (6.5803023915404980124 - 6.5942146139788748436e-736j)  +/-  (1.08e-239, 1.08e-239j)
| (1.5312157086954012062 + 1.1118353409414447948e-744j)  +/-  (6.02e-249, 6.02e-249j)
| (8.3405802162746059332 - 5.3546350510429178441e-735j)  +/-  (5.82e-239, 5.82e-239j)
| (-6.1936934837963133401 + 6.7156141527956088545e-733j)  +/-  (7.02e-240, 7.02e-240j)
| (-7.869426697637737727 - 9.9344845477023586856e-741j)  +/-  (3.72e-239, 3.72e-239j)
| (-0.91654504133862789419 + 1.8290231493502365268e-770j)  +/-  (4.11e-251, 4.11e-251j)
| (-7.4184299630621771347 + 9.0388014032290486115e-757j)  +/-  (2.43e-239, 2.43e-239j)
| (4.7509474830853766697 + 7.1414852760344661812e-776j)  +/-  (2.06e-241, 2.06e-241j)
| (4.4137123132374714757 + 4.2694375415378510229e-776j)  +/-  (5.88e-242, 5.88e-242j)
| (-6.5803023915404980124 - 4.9786065034746364179e-771j)  +/-  (1.09e-239, 1.09e-239j)
| (-1.8456782079349223725 - 2.9221068655831003358e-796j)  +/-  (6.03e-248, 6.03e-248j)
| (-5.8204310449201016959 - 6.55941517448090956e-786j)  +/-  (3.22e-240, 3.22e-240j)
| (0.91654504133862789419 - 2.7459583543564944978e-818j)  +/-  (3.82e-251, 3.82e-251j)
| (7.869426697637737727 - 7.1536415115001764871e-804j)  +/-  (3.77e-239, 3.77e-239j)
| (-8.8661085132598740463 - 4.3698065505177035108e-837j)  +/-  (5.81e-238, 5.81e-238j)
| (9.8421777377581850778 + 1.7973624841620350761e-859j)  +/-  (1.62e-239, 1.62e-239j)
| (-3.4201563739999792806 + 2.7925700495957394185e-873j)  +/-  (8.98e-244, 8.98e-244j)
| (6.1936934837963133401 + 3.1752151437214521616e-869j)  +/-  (6.39e-240, 6.39e-240j)
| (2.780138499509748897 + 2.1209164318579116142e-885j)  +/-  (2.51e-245, 2.51e-245j)
| (-1.5312157086954012062 - 2.2173573997079760669e-889j)  +/-  (5.8e-249, 5.8e-249j)
| (4.0754272144122266022 - 1.9527027656261605889e-878j)  +/-  (1.58e-242, 1.58e-242j)
| (-3.1035133815383188794 - 2.3816517601199496818e-882j)  +/-  (1.78e-244, 1.78e-244j)
| (-8.3405802162746059332 - 5.0470217073151586194e-891j)  +/-  (6.24e-239, 6.24e-239j)
| (3.1035133815383188794 - 4.1560373154815943559e-919j)  +/-  (1.57e-244, 1.57e-244j)
| (1.2192326334033848114 + 1.5218771218497772739e-925j)  +/-  (4.99e-250, 4.99e-250j)
| (2.4592049810635398901 + 4.053128279411208454e-921j)  +/-  (3.78e-246, 3.78e-246j)
| (5.0956166313813410952 - 2.1909566307129254691e-912j)  +/-  (5.94e-241, 5.94e-241j)
| (3.4201563739999792806 + 6.4271428433492577653e-921j)  +/-  (8.24e-244, 8.24e-244j)
| (9.0741981745640977167e-949 + 3.2667105560476795756e-948j)  +/-  (2.34e-946, 2.34e-946j)
| (0.61287276024439986103 + 8.0639646072094773504e-929j)  +/-  (2.51e-252, 2.51e-252j)
| (0.30515597075929801293 + 2.55388491908338568e-930j)  +/-  (1.42e-253, 1.42e-253j)
| (-0.61287276024439986103 - 2.7393035024013737383e-929j)  +/-  (2.16e-252, 2.16e-252j)
| (-2.1515300901216484795 + 4.3873139982387556884e-924j)  +/-  (4.88e-247, 4.88e-247j)
| (2.1515300901216484795 - 1.946100374197738749e-924j)  +/-  (4.86e-247, 4.86e-247j)
| (-5.4536153838578314707 + 1.1128421186066958231e-914j)  +/-  (1.44e-240, 1.44e-240j)
| (-2.4592049810635398901 + 2.620104713522706471e-929j)  +/-  (3.76e-246, 3.76e-246j)
| (3.7413352660055678012 - 1.031287755831746879e-926j)  +/-  (3.63e-243, 3.63e-243j)
| (5.8204310449201016959 - 8.28624513528126858e-921j)  +/-  (3.19e-240, 3.19e-240j)
| (-0.30515597075929801293 - 3.601981568887218542e-944j)  +/-  (1.59e-253, 1.59e-253j)
-------------------------------------------------
The weights are:
| (1.7207392012996497446e-27 - 8.4440824290299787239e-713j)  +/-  (4.58e-49, 8.73e-167j)
| (-9.811713029286027219e-19 - 9.4178045200897943537e-708j)  +/-  (2.85e-43, 5.43e-161j)
| (3.2265640372853333979e-20 + 1.3169562831213156746e-709j)  +/-  (1.4e-44, 2.67e-162j)
| (6.6381482628833896749e-34 - 4.6212091625117204758e-719j)  +/-  (8.8e-54, 1.68e-171j)
| (3.7931716741103665854e-43 - 1.3936633742999937109e-724j)  +/-  (3.75e-58, 7.15e-176j)
| (1.7207392012996497446e-27 - 5.3667868562642847326e-715j)  +/-  (7.79e-51, 1.49e-168j)
| (7.8985986277545048526e-25 + 1.246405412569687396e-711j)  +/-  (1.02e-52, 1.94e-170j)
| (1.760352557091305223e-30 + 6.2989209803397194212e-717j)  +/-  (2.08e-52, 3.97e-170j)
| (3.7931716741103665854e-43 + 1.178654965661743453e-723j)  +/-  (4.58e-62, 8.73e-180j)
| (1.972677017380013248e-13 - 1.0896769386907779719e-704j)  +/-  (1.79e-45, 3.41e-163j)
| (1.760352557091305223e-30 - 2.30453645642392632e-715j)  +/-  (3.29e-56, 6.28e-174j)
| (5.8441668994155985409e-38 + 1.6148206757588139272e-721j)  +/-  (1.1e-57, 2.1e-175j)
| (3.3373225181155045107e-05 + 7.5396038923328022552e-699j)  +/-  (9.19e-32, 1.75e-149j)
| (-9.811713029286027219e-19 - 9.1452537401114174178e-707j)  +/-  (2.6e-50, 4.96e-168j)
| (7.9199781534313603897e-06 - 2.2831173974871261416e-699j)  +/-  (2.43e-34, 4.64e-152j)
| (3.2265640372853333979e-20 + 1.6068364030531924225e-708j)  +/-  (3.17e-51, 6.04e-169j)
| (5.0467050762875597621e-08 + 9.6726765825285059792e-701j)  +/-  (2.61e-41, 4.97e-159j)
| (4.162915925012694627e-12 + 8.640564594510362741e-704j)  +/-  (1.02e-45, 1.95e-163j)
| (1.9855131791123464186e-22 - 1.8473976011214069661e-711j)  +/-  (8.38e-53, 1.6e-170j)
| (1.6973198876803865071e-06 + 6.3655692009173691381e-700j)  +/-  (3.81e-38, 7.28e-156j)
| (0.00011949822529725110522 - 2.3353724735105557761e-698j)  +/-  (2.1e-33, 4e-151j)
| (5.8441668994155985409e-38 - 1.9019849594628286235e-720j)  +/-  (1.2e-62, 2.29e-180j)
| (7.8985986277545048526e-25 + 3.3778807050689963006e-713j)  +/-  (1.25e-54, 2.39e-172j)
| (6.6381482628833896749e-34 + 8.3493354441871825662e-718j)  +/-  (1.56e-60, 2.98e-178j)
| (0.002718671837167651656 + 3.3918854624153662764e-697j)  +/-  (4.68e-31, 8.92e-149j)
| (3.2248554286971860138e-07 - 1.5418634387156849788e-700j)  +/-  (2.88e-41, 5.49e-159j)
| (0.02256512938514546062 - 3.2927440902865332791e-696j)  +/-  (5.22e-27, 9.95e-145j)
| (4.162915925012694627e-12 + 1.9165890984565434541e-704j)  +/-  (1.12e-48, 2.14e-166j)
| (3.1792249114530625591e-18 + 1.178594012148872233e-706j)  +/-  (2.73e-52, 5.21e-170j)
| (0.058184539572035278121 - 5.5741803349730505746e-696j)  +/-  (7.6e-22, 1.45e-139j)
| (6.2588848500271646386e-11 - 6.1803000808944864171e-703j)  +/-  (3.05e-49, 5.82e-167j)
| (0.039012428848077837833 + 4.8809316785155595753e-696j)  +/-  (3.87e-27, 7.39e-145j)
| (1.5084301040448373678e-16 - 1.8035983907606834654e-706j)  +/-  (1.89e-52, 3.61e-170j)
| (7.0556706179408378204e-10 + 1.0575444349234055965e-702j)  +/-  (2.48e-48, 4.73e-166j)
| (6.5613682276792349587e-15 + 2.1947639473459642883e-706j)  +/-  (4.83e-53, 9.21e-171j)
| (0.078921208733939316977 + 7.6801128506808558823e-696j)  +/-  (8.82e-28, 1.68e-145j)
| (1.972677017380013248e-13 - 2.1054947204981591703e-705j)  +/-  (7.72e-52, 1.47e-169j)
| (1.6973198876803865071e-06 + 1.6088458794981998097e-699j)  +/-  (1.26e-48, 2.41e-166j)
| (7.9199781534313603897e-06 - 5.3562616481734823391e-699j)  +/-  (7.06e-48, 1.35e-165j)
| (6.2588848500271646386e-11 - 1.5463059120934746015e-703j)  +/-  (2.31e-50, 4.4e-168j)
| (0.02256512938514546062 - 2.3444559940190815626e-696j)  +/-  (2.71e-37, 5.17e-155j)
| (6.4903371202669338041e-09 - 6.1931221526638460864e-702j)  +/-  (8.31e-49, 1.59e-166j)
| (0.078921208733939316977 + 9.0802060798676556595e-696j)  +/-  (2.54e-34, 4.84e-152j)
| (6.5613682276792349587e-15 + 1.3329051223856214794e-705j)  +/-  (1.09e-55, 2.09e-173j)
| (3.1792249114530625591e-18 + 1.2510334548713687557e-707j)  +/-  (1.4e-55, 2.66e-173j)
| (1.9855131791123464186e-22 - 3.4038523257445969292e-710j)  +/-  (2.6e-60, 4.96e-178j)
| (0.00036347292861954187947 + 6.3901980436648592328e-698j)  +/-  (6.08e-45, 1.16e-162j)
| (7.0556706179408378204e-10 + 3.799242496178660368e-702j)  +/-  (1.73e-53, 3.29e-171j)
| (0.002718671837167651656 + 5.6941961532625720271e-697j)  +/-  (1.63e-47, 3.1e-165j)
| (0.039012428848077837833 + 3.6854216490161889492e-696j)  +/-  (5.19e-41, 9.89e-159j)
| (3.3373225181155045107e-05 + 1.6450655200007057408e-698j)  +/-  (1.18e-50, 2.25e-168j)
| (0.0010334414546141332028 - 1.5219538379144780878e-697j)  +/-  (1.52e-45, 2.9e-163j)
| (1.5084301040448373678e-16 - 2.457342400724024404e-707j)  +/-  (2.49e-56, 4.76e-174j)
| (0.0010334414546141332028 - 2.7225672193230043554e-697j)  +/-  (4.43e-49, 8.45e-167j)
| (0.058184539572035278121 - 6.9679057524255462387e-696j)  +/-  (1.78e-43, 3.4e-161j)
| (0.0060999437134813475324 - 1.1475682393488694534e-696j)  +/-  (1.14e-47, 2.18e-165j)
| (3.2248554286971860138e-07 - 4.2159469958122262999e-700j)  +/-  (5.54e-53, 1.06e-170j)
| (0.00036347292861954187947 + 1.2178443900916563003e-697j)  +/-  (3.47e-50, 6.63e-168j)
| (0.12125129589579295699 - 1.1678469794276649499e-695j)  +/-  (1.04e-44, 1.98e-162j)
| (0.10142325712829896446 - 1.0610109492258784754e-695j)  +/-  (7.97e-45, 1.52e-162j)
| (0.11693300201893567938 + 1.1518001519148992221e-695j)  +/-  (6.83e-45, 1.31e-162j)
| (0.10142325712829896446 - 9.4874831636281765314e-696j)  +/-  (1.09e-45, 2.08e-163j)
| (0.011956387467815230719 + 1.3963151458394489255e-696j)  +/-  (2.81e-48, 5.38e-166j)
| (0.011956387467815230719 + 2.0775195311224610114e-696j)  +/-  (2.01e-48, 3.84e-166j)
| (5.0467050762875597621e-08 + 3.2495871287087135937e-701j)  +/-  (9.63e-54, 1.84e-171j)
| (0.0060999437134813475324 - 7.2733179632197983199e-697j)  +/-  (5.33e-49, 1.02e-166j)
| (0.00011949822529725110522 - 4.7521944808977465972e-698j)  +/-  (1.12e-51, 2.12e-169j)
| (6.4903371202669338041e-09 - 2.0188011385803127601e-701j)  +/-  (1.8e-55, 3.48e-173j)
| (0.11693300201893567938 + 1.0894645876221086299e-695j)  +/-  (2.07e-48, 3.39e-166j)
