Starting with polynomial:
P : 2*t
Extension levels are: 1 4 56
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 56 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^61 - 1488698946934398188033760927573771790176396393566/869747000783558979970315732869543405757899861*t^59 + 15451323782868840253307478774649100978278280505809309/22613422020372533479228209054608128549705396386*t^57 - 637764541794905109587346243185576843305970796426316315/3768903670062088913204701509101354758284232731*t^55 + 1843875909873810047181407122422860823642772935906228635/63210124445485767936347195121196725505815224*t^53 - 18101850990628666941810309864986501435770194895611774475/4862317265037366764334399624707440423524248*t^51 + 7104524789780551725113958878990540526441162683011418771475/19449269060149467057337598498829761694096992*t^49 - 137347881935704000828805383558205225443770814301122881048975/4862317265037366764334399624707440423524248*t^47 + 136225030077824242056945151147516656506629406165660079899778375/77797076240597868229350393995319046776387968*t^45 - 6849464950283612590715736629139007614306416598201452469381974625/77797076240597868229350393995319046776387968*t^43 + 1126453347454579727886235855371893835374113352402793144211343692875/311188304962391472917401575981276187105551872*t^41 - 464292343665048217436617112180204604441578834430151844712443557125/3794979328809652108748799707088733989092096*t^39 + 103513522988254305850290077338888588004066961206115386106502186759875/30359834630477216869990397656709871912736768*t^37 - 2381460560036095679805441828518829360041754545334523307170372343731875/30359834630477216869990397656709871912736768*t^35 + 180824174189963282809991480176352741258971989798260184560678669785299375/121439338521908867479961590626839487650947072*t^33 - 353277913165937519375353473054859533910502658987081274180823233574330625/15179917315238608434995198828354935956368384*t^31 + 144953201275424224422236436449157293883796939085681345240525300414312630625/485757354087635469919846362507357950603788288*t^29 - 52302371534873876727587499446733047239951510278576517018488963951750324375/16750253589228809307580909051977860365647872*t^27 + 1774094695596567023909655387331844164806036522237100173451113743929573640625/67001014356915237230323636207911441462591488*t^25 - 6042175644137366255919063971747359754285032444364030281786917643997881265625/33500507178457618615161818103955720731295744*t^23 + 261567756972267595430364504113390202302167792060319371858439842308384210890625/268004057427660948921294544831645765850365952*t^21 - 1109265401154535010512145953177330298250942677182437688275847316045248115953125/268004057427660948921294544831645765850365952*t^19 + 14503136277338632222152035048984599922482415036399307940868990512953374522203125/1072016229710643795685178179326583063401463808*t^17 - 8949578006759614029767647715845808758609377886595710455874554713393671118671875/268004057427660948921294544831645765850365952*t^15 + 260231886104716472977789104310904195217620818212022764565102776326036103089765625/4288064918842575182740712717306332253605855232*t^13 - 337240483924836073225395744165901448003822272137708192914802713505153556330734375/4288064918842575182740712717306332253605855232*t^11 + 1195121162964850220699971417571689444132233699107239286990483146642295248356703125/17152259675370300730962850869225329014423420928*t^9 - 340844649636304612989817760199941778210212963206462399009543928191617321447234375/8576129837685150365481425434612664507211710464*t^7 + 909025020591112703069735275940144566896002107503670700138611240165627501661953125/68609038701481202923851403476901316057693683712*t^5 - 147343858277835657413934035102180541539366095303463757986279571278383079365078125/68609038701481202923851403476901316057693683712*t^3 + 29629035212755729957334471157149415749227676737539465019795262217994311734765625/274436154805924811695405613907605264230774734848*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:
| (7.5724780651726492201 + 4.7172466793099312374e-711j)  +/-  (2.26e-241, 2.26e-241j)
| (-7.1813936570385322974 - 3.3404446343348001634e-709j)  +/-  (4.24e-241, 4.24e-241j)
| (-7.5724780651726492201 - 4.1547200079286789513e-715j)  +/-  (2.36e-241, 2.36e-241j)
| (6.8059818266610194006 - 2.2543078464622682032e-720j)  +/-  (6.17e-241, 6.17e-241j)
| (2.9104710990182913531 - 4.9568081267936227304e-725j)  +/-  (1.15e-244, 1.15e-244j)
| (5.7482778585481604526 + 1.4106986364085453641e-720j)  +/-  (5.75e-241, 5.75e-241j)
| (-7.9833645948463412845 - 1.2093578268118332787e-719j)  +/-  (9.33e-242, 9.33e-242j)
| (-1.7253754822478942611 - 9.1689558985229852173e-732j)  +/-  (6.65e-248, 6.65e-248j)
| (-9.4240417660825499824 - 9.3047783873232858417e-727j)  +/-  (7.57e-244, 7.57e-244j)
| (8.8937820439165306553 + 1.90729555901270915e-726j)  +/-  (6.36e-243, 6.36e-243j)
| (3.8203808807057694504 + 4.7405456642611642186e-726j)  +/-  (7.84e-243, 7.84e-243j)
| (-10.064264151098148381 + 4.7685474480920013729e-728j)  +/-  (3.85e-245, 3.85e-245j)
| (-8.4203176160983802342 - 1.1272780960847071448e-723j)  +/-  (3.22e-242, 3.22e-242j)
| (7.1813936570385322974 - 7.8896497980983272134e-725j)  +/-  (4.34e-241, 4.34e-241j)
| (-4.1299448593226348143 - 7.7679305432664071386e-727j)  +/-  (2.16e-242, 2.16e-242j)
| (2.6120796483740357234 - 2.1010315077067896593e-736j)  +/-  (2.08e-245, 2.08e-245j)
| (4.7612816963999478708 + 1.285626663501461661e-731j)  +/-  (1.34e-241, 1.34e-241j)
| (-5.084215548505982204 - 1.1892539992823271016e-731j)  +/-  (2.75e-241, 2.75e-241j)
| (-8.8937820439165306553 - 3.8521294377030711597e-741j)  +/-  (6.31e-243, 6.31e-243j)
| (9.4240417660825499824 - 6.823043176479702037e-747j)  +/-  (7.48e-244, 7.48e-244j)
| (10.064264151098148381 + 2.8041787752487961858e-751j)  +/-  (3.9e-245, 3.9e-245j)
| (4.1299448593226348143 + 3.3344366423350718489e-747j)  +/-  (2.29e-242, 2.29e-242j)
| (8.4203176160983802342 + 1.0117453788748282028e-746j)  +/-  (3.24e-242, 3.24e-242j)
| (-0.95857246461381850711 - 8.7040016022951631078e-770j)  +/-  (6.95e-249, 6.95e-249j)
| (-1.1041955934114367217 - 3.645720125303487288e-770j)  +/-  (2.9e-249, 2.9e-249j)
| (-6.8059818266610194006 + 5.2180478712217077036e-761j)  +/-  (6.12e-241, 6.12e-241j)
| (2.0201828704560856329 - 6.6927960231087980657e-792j)  +/-  (5.18e-247, 5.18e-247j)
| (-6.0913166500326997866 + 1.6783119965283247006e-783j)  +/-  (7.76e-241, 7.76e-241j)
| (7.9833645948463412845 - 1.0734176886241065726e-794j)  +/-  (9.8e-242, 9.8e-242j)
| (-0.94296350312030691567 - 1.1792313472291544364e-811j)  +/-  (5.26e-249, 5.26e-249j)
| (-4.7612816963999478708 + 2.8684042499438195268e-802j)  +/-  (1.48e-241, 1.48e-241j)
| (3.2110589153590040702 - 6.7325242838999998798e-821j)  +/-  (5.39e-244, 5.39e-244j)
| (0.58651312239865651402 + 2.125950732358481514e-828j)  +/-  (4.14e-252, 4.14e-252j)
| (-6.4433374462095986317 - 3.3694466996141916315e-816j)  +/-  (7.48e-241, 7.48e-241j)
| (-1.4287670917573502169 - 3.8268327408726030033e-835j)  +/-  (9.74e-249, 9.74e-249j)
| (-2.6120796483740357234 + 4.1609977830899382423e-832j)  +/-  (1.97e-245, 1.97e-245j)
| (4.4433984961954856622 - 7.3744756242000861823e-827j)  +/-  (6.11e-242, 6.11e-242j)
| (1.7253754822478942611 - 3.5953374840795174599e-853j)  +/-  (6.82e-248, 6.82e-248j)
| (2.3154809570220413311 + 5.0117412668024215252e-848j)  +/-  (3.25e-246, 3.25e-246j)
| (5.41292633409138493 - 8.2584195643387553195e-849j)  +/-  (4.46e-241, 4.46e-241j)
| (-5.7482778585481604526 - 8.8029615002808681513e-871j)  +/-  (6.39e-241, 6.39e-241j)
| (-3.2110589153590040702 - 1.2407876204819121287e-882j)  +/-  (5.23e-244, 5.23e-244j)
| (-3.5142291303131801247 - 7.4036271529801423037e-894j)  +/-  (1.88e-243, 1.88e-243j)
| (0.94296350312030691567 + 1.4699516524911516555e-922j)  +/-  (5.13e-249, 5.13e-249j)
| (6.0913166500326997866 - 1.5096441344627700489e-912j)  +/-  (7.45e-241, 7.45e-241j)
| (-2.9104710990182913531 + 2.9637213806195431036e-934j)  +/-  (1.06e-244, 1.06e-244j)
| (-2.0201828704560856329 - 1.9922544834761167611e-935j)  +/-  (5.22e-247, 5.22e-247j)
| (5.084215548505982204 - 1.2981329040480334785e-928j)  +/-  (2.54e-241, 2.54e-241j)
| (1.4287670917573502169 + 3.1924020986103423779e-949j)  +/-  (1.06e-248, 1.06e-248j)
| (3.5142291303131801247 + 9.4529078912439800333e-943j)  +/-  (1.98e-243, 1.98e-243j)
| (-2.3154809570220413311 - 2.7475933805266480973e-947j)  +/-  (3.26e-246, 3.26e-246j)
| (6.4433374462095986317 + 5.2289745681743639006e-940j)  +/-  (7.64e-241, 7.64e-241j)
| (-5.41292633409138493 - 1.8787873114867055618e-947j)  +/-  (4.19e-241, 4.19e-241j)
| (0.95857246461381850711 + 2.253960246170006147e-962j)  +/-  (6.95e-249, 6.95e-249j)
| (0.29168283952520758984 + 1.0891044887601950472e-965j)  +/-  (1.38e-253, 1.38e-253j)
| (-3.8203808807057694504 + 3.2871699139035575569e-955j)  +/-  (7.38e-243, 7.38e-243j)
| (-4.4433984961954856622 - 2.8681710040316021686e-953j)  +/-  (5.66e-242, 5.66e-242j)
| (-0.29168283952520758984 + 9.7531190731652218766e-966j)  +/-  (1.38e-253, 1.38e-253j)
| (-1.0021999506786414731e-989 + 7.8999544938437792148e-990j)  +/-  (7.78e-988, 7.78e-988j)
| (1.1041955934114367217 - 1.3838639429742332027e-961j)  +/-  (3.26e-249, 3.26e-249j)
| (-0.58651312239865651402 + 3.8348782127738625717e-964j)  +/-  (4.35e-252, 4.35e-252j)
-------------------------------------------------
The weights are:
| (2.8194308102890327294e-26 + 8.9891675192309271669e-735j)  +/-  (1.31e-65, 5.35e-184j)
| (8.6426749926993868086e-24 - 2.155255229482709812e-731j)  +/-  (1.43e-64, 5.84e-183j)
| (2.8194308102890327294e-26 - 3.7847348763463202608e-733j)  +/-  (5.28e-66, 2.16e-184j)
| (1.5881026699670310521e-21 + 3.0708004401214942789e-732j)  +/-  (5.42e-64, 2.22e-182j)
| (3.5389422012292138641e-05 + 3.9069152142642149003e-723j)  +/-  (2.77e-44, 1.13e-162j)
| (8.5382059355773701718e-16 - 3.4800607927607066604e-729j)  +/-  (3.28e-60, 1.34e-178j)
| (4.9889497660827002865e-29 + 6.9730127429947267558e-735j)  +/-  (2.61e-68, 1.07e-186j)
| (0.0084812240207512204673 + 4.2219483594502264522e-721j)  +/-  (1.06e-34, 4.34e-153j)
| (8.6521920705909377807e-40 - 7.4194924342555528783e-741j)  +/-  (8.01e-74, 3.28e-192j)
| (1.2458380862045055333e-35 - 1.4116302523870400764e-739j)  +/-  (1.36e-73, 5.55e-192j)
| (7.9617148457003354412e-08 - 9.339549010867727527e-725j)  +/-  (8.09e-54, 3.31e-172j)
| (4.2750009758820610062e-45 + 1.123401750580472251e-743j)  +/-  (4.4e-76, 1.8e-194j)
| (4.123172263280304206e-32 - 1.1646041823358937591e-736j)  +/-  (8.16e-71, 3.34e-189j)
| (8.6426749926993868086e-24 - 1.9437467919367820367e-733j)  +/-  (4.21e-68, 1.73e-186j)
| (6.8747707044377466167e-09 + 8.3992006792635991098e-725j)  +/-  (1.09e-58, 4.47e-177j)
| (0.00018265312686793268409 - 1.1732822081869467165e-722j)  +/-  (1.11e-48, 4.56e-167j)
| (2.5799282664435708988e-11 + 9.707744985230494617e-727j)  +/-  (1.72e-60, 7.06e-179j)
| (1.0915540614731644668e-12 - 9.953274278513791933e-727j)  +/-  (4.03e-63, 1.65e-181j)
| (1.2458380862045055333e-35 + 1.3109709301796838041e-738j)  +/-  (1.13e-72, 4.64e-191j)
| (8.6521920705909377807e-40 + 1.0099952122823421252e-741j)  +/-  (5.76e-77, 2.36e-195j)
| (4.2750009758820610062e-45 - 1.8893357013388244149e-744j)  +/-  (2.13e-79, 8.74e-198j)
| (6.8747707044377466167e-09 + 2.2596831361914102879e-725j)  +/-  (2.53e-60, 1.03e-178j)
| (4.123172263280304206e-32 + 9.4003258033556215554e-738j)  +/-  (7.1e-74, 2.91e-192j)
| (-0.54513595196131236075 - 1.2219103037534472027e-718j)  +/-  (2.19e-42, 8.97e-161j)
| (0.075278589349119457919 + 1.0556594202593977755e-719j)  +/-  (2.19e-42, 8.96e-161j)
| (1.5881026699670310521e-21 + 1.1631891649507659836e-730j)  +/-  (1.29e-70, 5.27e-189j)
| (0.0028095382869178892783 - 9.2471239385805408622e-722j)  +/-  (1.86e-52, 7.61e-171j)
| (1.5065849032786993981e-17 + 4.897340468416097766e-729j)  +/-  (6.59e-70, 2.7e-188j)
| (4.9889497660827002865e-29 - 3.80971667077013152e-736j)  +/-  (6.57e-74, 2.69e-192j)
| (0.58225040593013791305 + 1.1495180305453368e-718j)  +/-  (7.96e-46, 3.26e-164j)
| (2.5799282664435708988e-11 + 4.8080500908418152752e-726j)  +/-  (5.97e-67, 2.44e-185j)
| (5.6649775612264422493e-06 - 1.217989756491794209e-723j)  +/-  (5.36e-60, 2.19e-178j)
| (0.1196318658443353352 - 3.4502906668769541577e-720j)  +/-  (3.25e-49, 1.33e-167j)
| (1.8779879239320761563e-19 - 7.1965586209212735682e-730j)  +/-  (1.83e-70, 7.48e-189j)
| (0.021955803791022037686 - 1.2205459739578826606e-720j)  +/-  (2.45e-52, 1e-170j)
| (0.00018265312686793268409 - 2.5181617146336674257e-722j)  +/-  (7.5e-61, 3.07e-179j)
| (4.7413813989858832936e-10 - 4.9449296323367943766e-726j)  +/-  (8.27e-65, 3.39e-183j)
| (0.0084812240207512204673 + 2.5840616239169596769e-721j)  +/-  (2.15e-55, 8.82e-174j)
| (0.00078352223064289502284 + 3.3445685863480881243e-722j)  +/-  (1.38e-57, 5.64e-176j)
| (3.5291398482801939177e-14 + 2.6035875141015295175e-728j)  +/-  (1.45e-68, 5.93e-187j)
| (8.5382059355773701718e-16 - 3.1595489550388716132e-728j)  +/-  (2.29e-70, 9.37e-189j)
| (5.6649775612264422493e-06 - 3.1939078004992391283e-723j)  +/-  (2.81e-65, 1.15e-183j)
| (7.4420279683984473577e-07 + 1.028394512693388045e-723j)  +/-  (2.62e-66, 1.07e-184j)
| (0.58225040593013791305 + 8.8228651232642476775e-719j)  +/-  (2.45e-57, 1e-175j)
| (1.5065849032786993981e-17 + 3.99004042297809617e-730j)  +/-  (4.93e-72, 2.02e-190j)
| (3.5389422012292138641e-05 + 9.2463331903029112419e-723j)  +/-  (1.32e-64, 5.42e-183j)
| (0.0028095382869178892783 - 1.6502674235411624602e-721j)  +/-  (5.08e-62, 2.08e-180j)
| (1.0915540614731644668e-12 - 1.6945288854945446805e-727j)  +/-  (2.79e-69, 1.14e-187j)
| (0.021955803791022037686 - 8.1491325468512398872e-721j)  +/-  (2.55e-61, 1.05e-179j)
| (7.4420279683984473577e-07 + 3.5187073350286150386e-724j)  +/-  (1.44e-65, 5.9e-184j)
| (0.00078352223064289502284 + 6.5353621490875709313e-722j)  +/-  (2.94e-64, 1.2e-182j)
| (1.8779879239320761563e-19 - 3.8563105140374479996e-731j)  +/-  (2.34e-73, 9.57e-192j)
| (3.5291398482801939177e-14 + 1.8637096471970313549e-727j)  +/-  (3.19e-72, 1.31e-190j)
| (-0.54513595196131236075 - 9.3370203612092610545e-719j)  +/-  (5.52e-62, 2.26e-180j)
| (0.15153699201162397882 + 2.8692571076839112814e-720j)  +/-  (2.13e-63, 8.71e-182j)
| (7.9617148457003354412e-08 - 3.0644270940049519588e-724j)  +/-  (2.78e-69, 1.14e-187j)
| (4.7413813989858832936e-10 - 2.1060854410406890738e-725j)  +/-  (1.33e-70, 5.44e-189j)
| (0.15153699201162397882 + 3.1126235290793586468e-720j)  +/-  (2.34e-65, 9.69e-184j)
| (0.16436694354907808731 - 2.8405019760452120087e-720j)  +/-  (2.22e-65, 9.46e-184j)
| (0.075278589349119457919 + 7.7388624696467496539e-720j)  +/-  (4.85e-65, 2.27e-183j)
| (0.1196318658443353352 - 4.0651007788599406752e-720j)  +/-  (1.94e-65, 7.31e-184j)
