Starting with polynomial:
P : 5/2*t^3 - 3/2*t
Extension levels are: 3 4 36
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 5/2*t^3 - 3/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : 5/2*t^7 - 77/18*t^5 + 3745/1782*t^3 - 155/594*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 5/2*t^43 - 14495289199434918665694985466195943482215240958873245750766923/539900688376186890223246128176265999836811075052218560816016*t^41 + 7174657331243041103879316738737406403354270960443220540358315315/53450168149242502132101366689450333983844296430169637520785584*t^39 - 16797696597640088018863803143262153008841903097805757915410388617/40492551628214016766743459613219949987760830628916392061201200*t^37 + 9617695654473275324085055982283740903402852786423112718944421528189/10838506319151951821231666023138539946723982331673287608381521200*t^35 - 321834241915766474095077365742540159685984610670488918103689194318097/230860184597936573792234486292850900865220823664641026058526401560*t^33 + 134001319469033423615699871575347108617139476900179197397110662014077/80451276450796078745778684617205616968183014307374903020395564180*t^31 - 1666973838157466279744695886807294596785719748897014510618610365890021/1078047104440667455193434373870555267373652391718823700473300560012*t^29 + 1156391324185527844521389964408021296325747553393553314128279251260457/1023462440924684292905159215699894241177518093403946551082247367100*t^27 - 3918627921263837756175439352253201678325476928700193936552018417266051/5989150580225930306630190965947529263186957731771242780407225333400*t^25 + 573482520630237389256843430755527234063633768959097987329287920001661/1906112271619730862805782516118952791588196982459369441416560410456*t^23 - 110944742097492461914243262582536826224277964672285685755001334375618293/1012145616230077088149870516059163932333332597685925173392193577952136*t^21 + 10606489511553055654143262440481748930499846540091722743441594463904115/337381872076692362716623505353054644111110865895308391130731192650712*t^19 - 10856029475904649544991257288738293492847542541519623247533961680158403/1546333580351506662451191066201500452175924802020163459349184632982430*t^17 + 2334198530964041289818042455871929795553616758133748821828405458644681/1943612958702684263476200628664336536727051727440363557600951435922580*t^15 - 85437921457884075629355291337243735698890546829759997558695956382487/555631727177151546507885603448674738747959420386906192172927359647924*t^13 + 467570879255661531253204220828450389397278253922474644955876461541295/32782271903451941243965250603471809586129605802827465338202714219227516*t^11 - 21062771041438966153499205821521565065665061706046034511504755877555/23025157351864128096633127447519427903582936080690772665935654818984208*t^9 + 4193619899563437005958265576095658138426219763348016723922158756841/110789598934110823515814765778553932756411302610480083166601879590404240*t^7 - 845085815265649297926551169432181661009559498219297833406945494039/933798048158934083919010168704954576089752407716903558118501556547692880*t^5 + 51706841639541023723263525591656620972738300298942373789991684573/5042509460058244053162654911006754710884663001671279213839908405357541552*t^3 - 850677994857491343504965022938111357262825372183278198244371/24410488395855953231077859181913750329317179122890010025504397536308984*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 + 1.2961466770101038269e-837j)  +/-  (9.62e-241, 9.62e-241j)
| (-0.99833863072656243624 - 1.2282931971351598537e-853j)  +/-  (3.33e-241, 3.33e-241j)
| (-0.93715617903365820907 - 2.9158409701593306827e-873j)  +/-  (1.17e-240, 1.17e-240j)
| (0.99126301521863110105 + 1.2948196938026362693e-886j)  +/-  (1.03e-240, 1.03e-240j)
| (0.90902512216996588099 + 2.0867144942336575555e-888j)  +/-  (8.43e-241, 8.43e-241j)
| (0.93715617903365820907 - 1.9196154393285829398e-889j)  +/-  (1.34e-240, 1.34e-240j)
| (-0.97860389196370077971 + 1.0610937015116444282e-896j)  +/-  (1.52e-240, 1.52e-240j)
| (-0.8770327226154323114 + 1.6345308355111690722e-919j)  +/-  (4.71e-241, 4.71e-241j)
| (-0.96049126870802028342 - 1.2570703128231657454e-933j)  +/-  (1.47e-240, 1.47e-240j)
| (0.97860389196370077971 + 2.8965024173288240979e-942j)  +/-  (1.36e-240, 1.36e-240j)
| (0.8770327226154323114 - 3.6205680668179325158e-945j)  +/-  (4.95e-241, 4.95e-241j)
| (0.96049126870802028342 + 5.8860178862409598918e-946j)  +/-  (1.41e-240, 1.41e-240j)
| (-0.90902512216996588099 + 1.7263837405599262229e-947j)  +/-  (8.32e-241, 8.32e-241j)
| (-0.84347866900604208363 - 4.5142225802878950235e-955j)  +/-  (2.82e-241, 2.82e-241j)
| (0.99833863072656243624 + 1.4095701505892999853e-956j)  +/-  (3.47e-241, 3.47e-241j)
| (0.84347866900604208363 - 1.1338081955837131285e-957j)  +/-  (2.86e-241, 2.86e-241j)
| (0.81097156249745819336 - 2.7984806631522001224e-958j)  +/-  (1.25e-241, 1.25e-241j)
| (-0.434243749346802558 + 4.5397174373457108107e-965j)  +/-  (5.58e-248, 5.58e-248j)
| (-0.81097156249745819336 - 9.9629957375223503237e-959j)  +/-  (1.16e-241, 1.16e-241j)
| (-0.77459666924148337704 - 1.4049314182582006612e-960j)  +/-  (3.46e-242, 3.46e-242j)
| (0.77459666924148337704 + 1.4293091690294730456e-959j)  +/-  (3.34e-242, 3.34e-242j)
| (0.72998696373915534215 - 2.8901994489239369638e-963j)  +/-  (5.49e-243, 5.49e-243j)
| (0.149183043769156755 + 8.208941261473056709e-974j)  +/-  (4.72e-253, 4.72e-253j)
| (-0.72998696373915534215 + 1.737750194837910893e-964j)  +/-  (5.3e-243, 5.3e-243j)
| (-0.67897899023723841031 - 5.2064106697598096842e-967j)  +/-  (7.76e-244, 7.76e-244j)
| (0.22273491498697249068 + 2.5239164220517987968e-979j)  +/-  (9.11e-252, 9.11e-252j)
| (0.67897899023723841031 - 2.9371169981924012136e-968j)  +/-  (7.87e-244, 7.87e-244j)
| (0.434243749346802558 + 6.325752138233370452e-972j)  +/-  (5.43e-248, 5.43e-248j)
| (-0.149183043769156755 - 9.7975683551069017213e-980j)  +/-  (4.75e-253, 4.75e-253j)
| (-0.62318533741131475204 - 4.3773239046615253026e-970j)  +/-  (8.13e-245, 8.13e-245j)
| (-0.22273491498697249068 - 8.0172925302857370635e-977j)  +/-  (9.11e-252, 9.11e-252j)
| (0.36568112936387440736 + 9.0135429758785534587e-974j)  +/-  (3.44e-249, 3.44e-249j)
| (0.62318533741131475204 + 3.7177757683682065709e-969j)  +/-  (8.18e-245, 8.18e-245j)
| (-1.2688842029525098768e-994 + 1.7828634294009463296e-994j)  +/-  (9.41e-993, 9.41e-993j)
| (-0.56344269758174513499 + 1.7199118590674102178e-974j)  +/-  (8.22e-246, 8.22e-246j)
| (-0.36568112936387440736 - 1.651299788593242116e-975j)  +/-  (3.47e-249, 3.47e-249j)
| (0.074799470671664208137 + 4.0276833708817595921e-980j)  +/-  (2.16e-254, 2.16e-254j)
| (0.56344269758174513499 - 5.4112902390476147271e-974j)  +/-  (8.06e-246, 8.06e-246j)
| (0.29503945542113725115 + 3.2275403014705941199e-979j)  +/-  (1.93e-250, 1.93e-250j)
| (-0.29503945542113725115 + 3.6139808130479141895e-979j)  +/-  (1.84e-250, 1.84e-250j)
| (-0.50030780383937667711 + 2.3358869714896142983e-975j)  +/-  (6.58e-247, 6.58e-247j)
| (-0.074799470671664208137 + 2.081243529090381492e-982j)  +/-  (2.16e-254, 2.16e-254j)
| (0.50030780383937667711 + 1.8307266368021549264e-976j)  +/-  (6.32e-247, 6.32e-247j)
-------------------------------------------------
The weights are:
| (0.0098823841848720258251 + 8.1037385820625196134e-838j)  +/-  (2.45e-67, 7.91e-184j)
| (0.0042617282810384156948 + 4.9704880094390422578e-838j)  +/-  (1.57e-67, 5.05e-184j)
| (0.025829702041106227013 - 1.4915936656401337386e-837j)  +/-  (2.32e-68, 7.47e-185j)
| (0.0098823841848720258251 + 6.4609590116372638885e-840j)  +/-  (7.02e-69, 2.26e-185j)
| (0.03029085637468434676 + 7.0532915204544215172e-839j)  +/-  (3.62e-69, 1.17e-185j)
| (0.025829702041106227013 - 4.1850555295175878043e-839j)  +/-  (3.76e-69, 1.21e-185j)
| (0.015414448071225053581 - 2.1394507259566565611e-837j)  +/-  (3.48e-68, 1.12e-184j)
| (0.033330281991555527969 - 1.9871419453456179094e-837j)  +/-  (3.94e-70, 1.27e-186j)
| (0.020773611782702076096 + 1.5672998480020572642e-837j)  +/-  (1.58e-68, 5.09e-185j)
| (0.015414448071225053581 - 1.3748934173667298194e-839j)  +/-  (3.61e-71, 1.16e-187j)
| (0.033330281991555527969 - 1.2149672092282016656e-838j)  +/-  (5.4e-72, 1.74e-188j)
| (0.020773611782702076096 + 2.4710361353381634269e-839j)  +/-  (3.91e-71, 1.26e-187j)
| (0.03029085637468434676 + 1.6298187744099388314e-837j)  +/-  (5.94e-71, 1.92e-187j)
| (0.033111252368303702242 + 2.4995375239243805202e-837j)  +/-  (3.23e-72, 1.04e-188j)
| (0.0042617282810384156948 - 1.7676534452637080832e-840j)  +/-  (2.53e-72, 8.15e-189j)
| (0.033111252368303702242 + 2.0133216680205114805e-838j)  +/-  (1.3e-73, 4.19e-190j)
| (0.032961060958799136216 - 2.5844652076924301387e-838j)  +/-  (2.22e-74, 7.16e-191j)
| (0.067383786068421179082 + 3.2430979970306389167e-838j)  +/-  (6.27e-78, 2.02e-194j)
| (0.032961060958799136216 - 2.5834905049053896501e-837j)  +/-  (4.56e-75, 1.47e-191j)
| (0.040589374386181409743 + 1.9744290143367076147e-837j)  +/-  (6.03e-76, 1.94e-192j)
| (0.040589374386181409743 + 2.422572550312155986e-838j)  +/-  (1.06e-76, 3.42e-193j)
| (0.048178402802511342229 - 1.9530653254110556448e-838j)  +/-  (1.01e-77, 3.25e-194j)
| (0.074037010175391576441 + 1.4199356688467477294e-838j)  +/-  (3.12e-81, 1.01e-197j)
| (0.048178402802511342229 - 1.286652041483043239e-837j)  +/-  (7.15e-78, 2.3e-194j)
| (0.053581458026994262614 + 8.7009427420116177423e-838j)  +/-  (7.8e-79, 2.52e-195j)
| (0.07299746109952006386 - 1.3528830134138588119e-838j)  +/-  (6.48e-82, 2.09e-198j)
| (0.053581458026994262614 + 1.6268094154813275977e-838j)  +/-  (3.94e-80, 1.27e-196j)
| (0.067383786068421179082 + 1.2672462245432462963e-838j)  +/-  (2.43e-82, 7.83e-199j)
| (0.074037010175391576441 + 1.9230478012261158635e-838j)  +/-  (1.64e-83, 5.29e-200j)
| (0.057874468036516329374 - 6.3159029746164595695e-838j)  +/-  (1.26e-81, 4.05e-198j)
| (0.07299746109952006386 - 2.1370684788229267385e-838j)  +/-  (1.24e-83, 4.01e-200j)
| (0.069671647814244304167 - 1.2753763027204314722e-838j)  +/-  (1.6e-83, 5.16e-200j)
| (0.057874468036516329374 - 1.4399611460881534518e-838j)  +/-  (1.15e-82, 3.7e-199j)
| (0.074868789912908268071 + 1.6164282168612582204e-838j)  +/-  (2.02e-84, 6.52e-201j)
| (0.061520598559472515278 + 4.8576887020461798321e-838j)  +/-  (1.23e-83, 3.97e-200j)
| (0.069671647814244304167 - 2.7664074763788423438e-838j)  +/-  (1.51e-84, 4.86e-201j)
| (0.074660833640091219551 - 1.5069084648501680554e-838j)  +/-  (9.63e-85, 3.1e-201j)
| (0.061520598559472515278 + 1.3367275275184838472e-838j)  +/-  (6.87e-85, 2.2e-201j)
| (0.071542373581916234568 + 1.3045982922576280625e-838j)  +/-  (5.63e-85, 1.82e-201j)
| (0.071542373581916234568 + 2.4103005175686818615e-838j)  +/-  (1.54e-85, 5e-202j)
| (0.064672864797998917661 - 3.9032246824059416422e-838j)  +/-  (2.07e-85, 6.71e-202j)
| (0.074660833640091219551 - 1.7528886921971516693e-838j)  +/-  (9.49e-86, 3.11e-202j)
| (0.064672864797998917661 - 1.284758641377527716e-838j)  +/-  (7e-86, 2.11e-202j)
