Starting with polynomial:
P : t
Extension levels are: 1 2 4 36
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P3 : t^7 - 77/45*t^5 + 749/891*t^3 - 31/297*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 14495289199434918665694985466195943482215240958873245750766923/1349751720940467225558115320440664999592027687630546402040040*t^41 + 1434931466248608220775863347747481280670854192088644108071663063/26725084074621251066050683344725166991922148215084818760392792*t^39 - 16797696597640088018863803143262153008841903097805757915410388617/101231379070535041916858649033049874969402076572290980153003000*t^37 + 9617695654473275324085055982283740903402852786423112718944421528189/27096265797879879553079165057846349866809955829183219020953803000*t^35 - 321834241915766474095077365742540159685984610670488918103689194318097/577150461494841434480586215732127252163052059161602565146316003900*t^33 + 134001319469033423615699871575347108617139476900179197397110662014077/201128191126990196864446711543014042420457535768437257550988910450*t^31 - 1666973838157466279744695886807294596785719748897014510618610365890021/2695117761101668637983585934676388168434130979297059251183251400030*t^29 + 1156391324185527844521389964408021296325747553393553314128279251260457/2558656102311710732262898039249735602943795233509866377705618417750*t^27 - 3918627921263837756175439352253201678325476928700193936552018417266051/14972876450564825766575477414868823157967394329428106951018063333500*t^25 + 573482520630237389256843430755527234063633768959097987329287920001661/4765280679049327157014456290297381978970492456148423603541401026140*t^23 - 110944742097492461914243262582536826224277964672285685755001334375618293/2530364040575192720374676290147909830833331494214812933480483944880340*t^21 + 2121297902310611130828652488096349786099969308018344548688318892780823/168690936038346181358311752676527322055555432947654195565365596325356*t^19 - 10856029475904649544991257288738293492847542541519623247533961680158403/3865833950878766656127977665503751130439812005050408648372961582456075*t^17 + 2334198530964041289818042455871929795553616758133748821828405458644681/4859032396756710658690501571660841341817629318600908894002378589806450*t^15 - 85437921457884075629355291337243735698890546829759997558695956382487/1389079317942878866269714008621686846869898550967265480432318399119810*t^13 + 93514175851132306250640844165690077879455650784494928991175292308259/16391135951725970621982625301735904793064802901413732669101357109613758*t^11 - 4212554208287793230699841164304313013133012341209206902300951175511/11512578675932064048316563723759713951791468040345386332967827409492104*t^9 + 4193619899563437005958265576095658138426219763348016723922158756841/276973997335277058789536914446384831891028256526200207916504698976010600*t^7 - 845085815265649297926551169432181661009559498219297833406945494039/2334495120397335209797525421762386440224381019292258895296253891369232200*t^5 + 51706841639541023723263525591656620972738300298942373789991684573/12606273650145610132906637277516886777211657504178198034599771013393853880*t^3 - 850677994857491343504965022938111357262825372183278198244371/61026220989639883077694647954784375823292947807225025063760993840772460*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:
| (-0.99126301521863110105 + 5.0666056116613210697e-838j)  +/-  (1.1e-240, 1.1e-240j)
| (-0.99833863072656243624 + 3.8676377168726011228e-852j)  +/-  (3.83e-241, 3.83e-241j)
| (-0.93715617903365820907 - 2.4042421059197209661e-872j)  +/-  (1.39e-240, 1.39e-240j)
| (0.99126301521863110105 + 2.665818315763655236e-886j)  +/-  (1.11e-240, 1.11e-240j)
| (0.90902512216996588099 + 6.6229975154111871091e-888j)  +/-  (8.36e-241, 8.36e-241j)
| (0.93715617903365820907 - 7.004691126763644441e-889j)  +/-  (1.3e-240, 1.3e-240j)
| (-0.97860389196370077971 + 3.9990882941293141244e-895j)  +/-  (1.53e-240, 1.53e-240j)
| (-0.8770327226154323114 - 1.7888446563616984408e-919j)  +/-  (5.34e-241, 5.34e-241j)
| (-0.96049126870802028342 - 1.0917802103763416673e-933j)  +/-  (1.66e-240, 1.66e-240j)
| (0.97860389196370077971 + 2.5917889879267636612e-942j)  +/-  (1.6e-240, 1.6e-240j)
| (0.8770327226154323114 + 1.764625352917780166e-944j)  +/-  (5.52e-241, 5.52e-241j)
| (0.96049126870802028342 + 2.2779049615105404717e-946j)  +/-  (1.65e-240, 1.65e-240j)
| (-0.90902512216996588099 - 3.8027024449650520833e-945j)  +/-  (9.27e-241, 9.27e-241j)
| (-0.84347866900604208363 - 1.8185758178778565779e-951j)  +/-  (3e-241, 3e-241j)
| (0.99833863072656243624 + 5.3515698791412988002e-956j)  +/-  (3.57e-241, 3.57e-241j)
| (0.84347866900604208363 + 1.8644710308374418929e-955j)  +/-  (2.96e-241, 2.96e-241j)
| (0.81097156249745819336 + 1.786201992958353931e-957j)  +/-  (1.29e-241, 1.29e-241j)
| (-0.434243749346802558 + 5.0739400224072374466e-964j)  +/-  (5.25e-248, 5.25e-248j)
| (-0.81097156249745819336 + 1.2902518855980720029e-956j)  +/-  (1.24e-241, 1.24e-241j)
| (-0.77459666924148337704 - 2.0505782459003972024e-959j)  +/-  (3.34e-242, 3.34e-242j)
| (0.77459666924148337704 - 1.6711419859295683993e-959j)  +/-  (3.5e-242, 3.5e-242j)
| (0.72998696373915534215 + 5.3758205059808129907e-963j)  +/-  (5.66e-243, 5.66e-243j)
| (0.149183043769156755 - 1.5120196219854756954e-973j)  +/-  (4.72e-253, 4.72e-253j)
| (-0.72998696373915534215 + 2.7385635229106708421e-963j)  +/-  (6.19e-243, 6.19e-243j)
| (-0.67897899023723841031 - 1.3229298629659141249e-966j)  +/-  (7.16e-244, 7.16e-244j)
| (0.22273491498697249068 - 3.4318374983009216612e-975j)  +/-  (9e-252, 9e-252j)
| (0.67897899023723841031 - 7.2177585861290964852e-967j)  +/-  (8.18e-244, 8.18e-244j)
| (0.434243749346802558 - 1.2715092539726262421e-971j)  +/-  (5.27e-248, 5.27e-248j)
| (-0.149183043769156755 + 6.6766605369876822374e-977j)  +/-  (4.32e-253, 4.32e-253j)
| (-0.62318533741131475204 + 1.8404964293096830201e-967j)  +/-  (8.51e-245, 8.51e-245j)
| (-0.22273491498697249068 - 1.1205121134566187153e-977j)  +/-  (1.01e-251, 1.01e-251j)
| (0.36568112936387440736 - 3.5420861537635940528e-973j)  +/-  (3.49e-249, 3.49e-249j)
| (0.62318533741131475204 + 3.4091235223503083303e-970j)  +/-  (8.95e-245, 8.95e-245j)
| (5.0852985094023667582e-991 - 7.1451695269027533492e-991j)  +/-  (3.77e-989, 3.77e-989j)
| (-0.56344269758174513499 - 3.450517813593666643e-971j)  +/-  (8.91e-246, 8.91e-246j)
| (-0.36568112936387440736 + 3.1914307004331213429e-976j)  +/-  (3.45e-249, 3.45e-249j)
| (0.074799470671664208137 + 4.4972362252597304283e-980j)  +/-  (1.93e-254, 1.93e-254j)
| (0.56344269758174513499 - 1.2289914957318738196e-972j)  +/-  (8.13e-246, 8.13e-246j)
| (0.29503945542113725115 + 7.4897692195829916396e-978j)  +/-  (1.8e-250, 1.8e-250j)
| (-0.29503945542113725115 + 1.756711037374628182e-981j)  +/-  (1.88e-250, 1.88e-250j)
| (-0.50030780383937667711 + 8.3153646029497410098e-975j)  +/-  (7.18e-247, 7.18e-247j)
| (-0.074799470671664208137 - 4.1514204370172413569e-982j)  +/-  (1.93e-254, 1.93e-254j)
| (0.50030780383937667711 + 5.2830415153379069087e-975j)  +/-  (7.18e-247, 7.18e-247j)
-------------------------------------------------
The weights are:
| (0.0098823841848720258251 + 3.1677315618341197529e-838j)  +/-  (2.45e-67, 8.94e-184j)
| (0.0042617282810384156948 + 1.9429515878104212475e-838j)  +/-  (1.57e-67, 5.7e-184j)
| (0.025829702041106227013 - 5.8306031027935808962e-838j)  +/-  (2.32e-68, 8.44e-185j)
| (0.0098823841848720258251 + 2.5255730517001949132e-840j)  +/-  (7.02e-69, 2.56e-185j)
| (0.03029085637468434676 + 2.757114378493953226e-839j)  +/-  (3.62e-69, 1.32e-185j)
| (0.025829702041106227013 - 1.6359279553052084182e-839j)  +/-  (3.76e-69, 1.37e-185j)
| (0.015414448071225053581 - 8.363060482482955901e-838j)  +/-  (3.48e-68, 1.27e-184j)
| (0.033330281991555527969 - 7.7676891898378129328e-838j)  +/-  (3.94e-70, 1.44e-186j)
| (0.020773611782702076096 + 6.1265367152433621139e-838j)  +/-  (1.58e-68, 5.74e-185j)
| (0.015414448071225053581 - 5.3744246908346605454e-840j)  +/-  (3.61e-71, 1.31e-187j)
| (0.033330281991555527969 - 4.7492770605714716036e-839j)  +/-  (5.4e-72, 1.97e-188j)
| (0.020773611782702076096 + 9.6592197256580213075e-840j)  +/-  (3.91e-71, 1.42e-187j)
| (0.03029085637468434676 + 6.3709216671871387353e-838j)  +/-  (5.94e-71, 2.16e-187j)
| (0.033111252368303702242 + 9.7706309555075474293e-838j)  +/-  (3.23e-72, 1.18e-188j)
| (0.0042617282810384156948 - 6.9097140193305825491e-841j)  +/-  (2.53e-72, 9.21e-189j)
| (0.033111252368303702242 + 7.8700250845085598698e-839j)  +/-  (1.3e-73, 4.73e-190j)
| (0.032961060958799136216 - 1.0102611191075618396e-838j)  +/-  (2.22e-74, 8.09e-191j)
| (0.067383786068421179082 + 1.2677190631562094743e-838j)  +/-  (6.27e-78, 2.28e-194j)
| (0.032961060958799136216 - 1.0098801101756169148e-837j)  +/-  (4.56e-75, 1.66e-191j)
| (0.040589374386181409743 + 7.7179946539238744512e-838j)  +/-  (6.03e-76, 2.2e-192j)
| (0.040589374386181409743 + 9.4697767588941002318e-839j)  +/-  (1.06e-76, 3.87e-193j)
| (0.048178402802511342229 - 7.6344845172114278609e-839j)  +/-  (1.01e-77, 3.67e-194j)
| (0.074037010175391576441 + 5.5504937485719722319e-839j)  +/-  (3.12e-81, 1.14e-197j)
| (0.048178402802511342229 - 5.0294913139545761358e-838j)  +/-  (7.15e-78, 2.6e-194j)
| (0.053581458026994262614 + 3.4011772051224209038e-838j)  +/-  (7.8e-79, 2.84e-195j)
| (0.07299746109952006386 - 5.2883865609219315998e-839j)  +/-  (6.48e-82, 2.36e-198j)
| (0.053581458026994262614 + 6.3591581568486454207e-839j)  +/-  (3.94e-80, 1.44e-196j)
| (0.067383786068421179082 + 4.9536344508772798476e-839j)  +/-  (2.43e-82, 8.85e-199j)
| (0.074037010175391576441 + 7.5171467504438420204e-839j)  +/-  (1.64e-83, 5.97e-200j)
| (0.057874468036516329374 - 2.4688710021397024945e-838j)  +/-  (1.26e-81, 4.58e-198j)
| (0.07299746109952006386 - 8.35374833678968622e-839j)  +/-  (1.24e-83, 4.53e-200j)
| (0.069671647814244304167 - 4.9854147273277745596e-839j)  +/-  (1.6e-83, 5.83e-200j)
| (0.057874468036516329374 - 5.6287728485898400418e-839j)  +/-  (1.15e-82, 4.18e-199j)
| (0.074868789912908268071 + 6.3185783057275185354e-839j)  +/-  (2.02e-84, 7.37e-201j)
| (0.061520598559472515278 + 1.8988586148494073969e-838j)  +/-  (1.23e-83, 4.49e-200j)
| (0.069671647814244304167 - 1.0813819062742886578e-838j)  +/-  (1.51e-84, 5.49e-201j)
| (0.074660833640091219551 - 5.8904682777736271009e-839j)  +/-  (9.63e-85, 3.5e-201j)
| (0.061520598559472515278 + 5.2252351622812797875e-839j)  +/-  (6.87e-85, 2.49e-201j)
| (0.071542373581916234568 + 5.0996427686437441947e-839j)  +/-  (5.63e-85, 2.06e-201j)
| (0.071542373581916234568 + 9.4218056835000681613e-839j)  +/-  (1.54e-85, 5.64e-202j)
| (0.064672864797998917661 - 1.5257609675064980889e-838j)  +/-  (2.07e-85, 7.58e-202j)
| (0.074660833640091219551 - 6.8519989612521487811e-839j)  +/-  (9.49e-86, 3.51e-202j)
| (0.064672864797998917661 - 5.0220900593204511876e-839j)  +/-  (7e-86, 2.38e-202j)
