Starting with polynomial:
P : 2*t
Extension levels are: 1 4 66
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 66 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^71 - 35003326546863776213822690402642956169134214640016055072321/14086253957141200492463318535504016865612632846361736941*t^69 + 67358154343367023570870051065698733261498461346619718749445199939/46287430503165984818234464707666199420403111533144667588126*t^67 - 49494610376843732165384002904859605204576724697827214524285514958475/92574861006331969636468929415332398840806223066289335176252*t^65 + 457533206249080368848876762466449447607171170500673043660858075609705/3306245035940427487016747479119014244314507966653190542009*t^63 - 5730373244817283027930310234970203763150390699445760480402129653162155/213306131350995321743015966394775112536419868816334873678*t^61 + 1734606355459834980419261814181955773544851486132575469501044480232263255/426612262701990643486031932789550225072839737632669747356*t^59 - 420130589218085369004185727633451004972898454832747127366218364825058698615/853224525403981286972063865579100450145679475265339494712*t^57 + 165837617198679232660774881839281464807707544662821486138792729723362821489925/3412898101615925147888255462316401800582717901061357978848*t^55 - 27024935904601938174244506621233978462516865882883442737552123297187348215170825/6825796203231850295776510924632803601165435802122715957696*t^53 + 69275659808243836022505353903215228772327945317615759230683282289563487321427125/257577215216296237576472110363502022685488143476328904064*t^51 - 7902312896592179175258972847787937587056363079686474855743076537044412753548784125/515154430432592475152944220727004045370976286952657808128*t^49 + 380349534353951689746281779325738374288681914398642562636365429550727792600107089625/515154430432592475152944220727004045370976286952657808128*t^47 - 31004981398952219802024238449132823417922826630775224091885862352129991137221928283125/1030308860865184950305888441454008090741952573905315616256*t^45 + 2144809686836119545903217372076466666012568424789095096877988237048666334457753423780625/2060617721730369900611776882908016181483905147810631232512*t^43 - 126026393006745844979482214231706237269578926405450812362043500736463293832658791989210625/4121235443460739801223553765816032362967810295621262465024*t^41 + 25156524855559658652336267517093788549477700906663658267570408239440713322042270548493395625/32969883547685918409788430126528258903742482364970099720192*t^39 - 1064966909215655939086386186658534076235367582589533077226685995748339462941489945592313418125/65939767095371836819576860253056517807484964729940199440384*t^37 + 38163099017283834927188558090133178285479856661788033510558993594803491244490822526002565653125/131879534190743673639153720506113035614969929459880398880768*t^35 - 1153971983972337868029464269531076536723828765826096888746344888002698070616345650486934735028125/263759068381487347278307441012226071229939858919760797761536*t^33 + 7329653567889380998357309572264755919852045513364704912970510095919634707392547428366640457803125/131879534190743673639153720506113035614969929459880398880768*t^31 - 155620562708474426770500049108460362734488342095278807547225119920132394828994899348236757782240625/263759068381487347278307441012226071229939858919760797761536*t^29 + 2742493743179997333746938800840052267371308598551324040299143925478218007513138004049811972726253125/527518136762974694556614882024452142459879717839521595523072*t^27 - 39783926607599824300429745153548632663902527776912569522578447158471710103512298630425123013481453125/1055036273525949389113229764048904284919759435679043191046144*t^25 + 940526405393407693469745498076898518266862541993236638637795333412551612281771810557668971284804765625/4220145094103797556452919056195617139679037742716172764184576*t^23 - 8947149714993560635312227460114668627000550691244686201001419625396438707316983341674485627670313078125/8440290188207595112905838112391234279358075485432345528369152*t^21 + 67461699649288914417031779320815611360818438982286062002552282070165164774832445234536093762121753078125/16880580376415190225811676224782468558716150970864691056738304*t^19 - 395617748844520268390126843251584903345260564207507098025939734881899255278469241306216690384175194703125/33761160752830380451623352449564937117432301941729382113476608*t^17 + 880993606423681200964202056530685358704091806016255045547275392078927680728815012349831516905184640234375/33761160752830380451623352449564937117432301941729382113476608*t^15 - 2890208727275971371337342631821401699323667801129979292816199547018138974238005460162653486450543756796875/67522321505660760903246704899129874234864603883458764226953216*t^13 + 6707793721818853743085500555005880914698973157167780680103580539640016265702153343458685241878445914609375/135044643011321521806493409798259748469729207766917528453906432*t^11 - 10420272728937072928068670024495352943816211246411376731103041523681768608490473002223534019786981308359375/270089286022643043612986819596519496939458415533835056907812864*t^9 + 80012684813661528620086079144291007828250133384079076252705724869953581631714232743686626691421322158046875/4321428576362288697807789113544311951031334648541360910525005824*t^7 - 41872097187547428345785804318212758263353657272426927945858103146454415618059371059227719992059156402734375/8642857152724577395615578227088623902062669297082721821050011648*t^5 + 9571925348267610397258023850644842079086609557442373127432855549623580841306421296181236429537011187109375/17285714305449154791231156454177247804125338594165443642100023296*t^3 - 578180925704029300615785991332392620429177622712373972009753390965114881025105088654300277683842052734375/34571428610898309582462312908354495608250677188330887284200046592*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
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-7.292853923550291761 - 5.2010073401745885333e-1908j)  +/-  (1.24e-493, 1.24e-493j)
| (10.081159315304530212 - 1.8344786704022893681e-1933j)  +/-  (1.41e-496, 1.41e-496j)
| (11.410549687014360798 - 2.496501978643926659e-1939j)  +/-  (2.78e-499, 2.78e-499j)
| (-6.6329065139552740162 + 7.5673041816511623179e-1932j)  +/-  (1.39e-493, 1.39e-493j)
| (9.1581897373181535137 - 2.4728383624086359124e-1943j)  +/-  (4e-495, 4e-495j)
| (-8.3619604093570891907 - 3.1342995027024341985e-1941j)  +/-  (2.98e-494, 2.98e-494j)
| (9.5975858609643152171 - 4.4148289510645501641e-1948j)  +/-  (9.06e-496, 9.06e-496j)
| (-2.8335314484022087939 - 3.3136846956764737481e-1950j)  +/-  (3.98e-499, 3.98e-499j)
| (-8.7489232740829963174 + 2.422419401007262007e-1945j)  +/-  (1.28e-494, 1.28e-494j)
| (-7.9923749858810845151 + 1.1277348525134381061e-1946j)  +/-  (5.98e-494, 5.98e-494j)
| (-10.640380874893844313 - 3.6612130673119626188e-1956j)  +/-  (1.12e-497, 1.12e-497j)
| (6.6329065139552740162 + 1.4513207288693963539e-1951j)  +/-  (1.37e-493, 1.37e-493j)
| (-9.1581897373181535137 - 7.6971199025199338233e-1953j)  +/-  (3.89e-495, 3.89e-495j)
| (-6.0022284071015326538 + 4.3938151738148041789e-1959j)  +/-  (7.98e-494, 7.98e-494j)
| (-9.5975858609643152171 + 2.3716120306638933739e-1972j)  +/-  (8.96e-496, 8.96e-496j)
| (-6.9586878265079796087 + 1.1532631443478067637e-1971j)  +/-  (1.56e-493, 1.56e-493j)
| (7.9923749858810845151 + 1.0749645349562925372e-1979j)  +/-  (5.87e-494, 5.87e-494j)
| (2.5608051508215372269 - 1.8218947059258214291e-1985j)  +/-  (7.4e-500, 7.4e-500j)
| (8.7489232740829963174 + 1.1137667698508271185e-1980j)  +/-  (1.23e-494, 1.23e-494j)
| (5.0969044231060009487 - 1.1417623533107720083e-1981j)  +/-  (1.35e-494, 1.35e-494j)
| (2.8335314484022087939 + 1.423404879862110242e-1985j)  +/-  (4.11e-499, 4.11e-499j)
| (-4.8036977352635894175 + 4.3038832644746074733e-1979j)  +/-  (5.71e-495, 5.71e-495j)
| (5.6956670981309602172 - 9.7025487799390699316e-1991j)  +/-  (5.33e-494, 5.33e-494j)
| (-7.6368116126511338988 + 5.9108363470956576559e-1991j)  +/-  (9.61e-494, 9.61e-494j)
| (8.3619604093570891907 + 1.6577116813432060842e-2000j)  +/-  (3.15e-494, 3.15e-494j)
| (3.1080373432225145929 - 1.4654810135701586185e-2006j)  +/-  (2.45e-498, 2.45e-498j)
| (1.485659962860629954 - 4.3125108930025412501e-2012j)  +/-  (1.56e-503, 1.56e-503j)
| (-3.3844898176730036825 + 4.1567802590507934844e-2002j)  +/-  (1.26e-497, 1.26e-497j)
| (-11.410549687014360798 + 1.6092720853495802704e-2017j)  +/-  (2.72e-499, 2.72e-499j)
| (-0.21298427405534033551 + 1.7908931525557097e-2027j)  +/-  (3.92e-509, 3.92e-509j)
| (3.3844898176730036825 - 1.7426884925817744302e-2014j)  +/-  (1.12e-497, 1.12e-497j)
| (4.5140474499465628104 + 3.3351490875173390976e-2011j)  +/-  (2.04e-495, 2.04e-495j)
| (1.2209439255733494899 - 1.7034538504310976213e-2022j)  +/-  (1.42e-504, 1.42e-504j)
| (4.8036977352635894175 - 7.7459832455794815105e-2012j)  +/-  (5.71e-495, 5.71e-495j)
| (-6.3143902351681779556 + 1.0220457974936420306e-2021j)  +/-  (1.16e-493, 1.16e-493j)
| (-5.3940724382217361343 + 1.0052448532912925317e-2054j)  +/-  (2.79e-494, 2.79e-494j)
| (10.640380874893844313 + 1.4049031542452840988e-2080j)  +/-  (1.12e-497, 1.12e-497j)
| (-2.0201828704560856329 + 1.808950807465943852e-2085j)  +/-  (1.42e-501, 1.42e-501j)
| (-5.0969044231060009487 - 3.8295880383797407264e-2083j)  +/-  (1.3e-494, 1.3e-494j)
| (3.9440362221447470592 + 3.0243595115420404844e-2103j)  +/-  (1.91e-496, 1.91e-496j)
| (-5.6956670981309602172 + 8.4522238739421844189e-2100j)  +/-  (5.33e-494, 5.33e-494j)
| (6.3143902351681779556 - 2.0076367033801456788e-2103j)  +/-  (1.16e-493, 1.16e-493j)
| (2.0201828704560856329 - 1.1928007915116949276e-2112j)  +/-  (1.3e-501, 1.3e-501j)
| (-10.081159315304530212 + 5.0500523829070818282e-2108j)  +/-  (1.24e-496, 1.24e-496j)
| (-3.6630827188449554528 + 1.2599774876073547744e-2105j)  +/-  (5.31e-497, 5.31e-497j)
| (0.69995621544326107342 + 1.2965999444808297852e-2117j)  +/-  (8.05e-507, 8.05e-507j)
| (-4.2275982466791879405 - 1.0704143657610149377e-2104j)  +/-  (6.59e-496, 6.59e-496j)
| (6.0022284071015326538 + 5.5498401334457220411e-2109j)  +/-  (7.92e-494, 7.92e-494j)
| (4.2275982466791879405 + 4.3856055560245579652e-2113j)  +/-  (6.37e-496, 6.37e-496j)
| (5.3940724382217361343 - 1.0084312972953192593e-2110j)  +/-  (2.67e-494, 2.67e-494j)
| (-1.752145965821050241 + 2.3717042781275378956e-2119j)  +/-  (1.43e-502, 1.43e-502j)
| (-0.69995621544326107342 + 3.2188158666931438781e-2124j)  +/-  (7.21e-507, 7.21e-507j)
| (0.21298427405534033551 + 4.2460448991827728568e-2126j)  +/-  (3.92e-509, 3.92e-509j)
| (-4.5140474499465628104 - 1.1900033803133442789e-2111j)  +/-  (2.21e-495, 2.21e-495j)
| (-2.5608051508215372269 - 6.8926392397003384069e-2124j)  +/-  (6.77e-500, 6.77e-500j)
| (-3.9440362221447470592 + 5.7135996778321775452e-2120j)  +/-  (1.92e-496, 1.92e-496j)
| (-1.2209439255733494899 + 3.0227310605506688023e-2133j)  +/-  (1.35e-504, 1.35e-504j)
| (-1.485659962860629954 - 2.9023499492151101548e-2132j)  +/-  (1.58e-503, 1.58e-503j)
| (2.2897217212947825758 + 1.9634640789505044413e-2129j)  +/-  (9.78e-501, 9.78e-501j)
| (1.752145965821050241 + 1.6411337074842925983e-2131j)  +/-  (1.55e-502, 1.55e-502j)
| (3.6630827188449554528 + 2.6264674321654212212e-2125j)  +/-  (5.05e-497, 5.05e-497j)
| (-0.44865433154886803076 - 1.8644708337790382337e-2137j)  +/-  (6.43e-508, 6.43e-508j)
| (7.6368116126511338988 - 3.301881879498810824e-2121j)  +/-  (9.32e-494, 9.32e-494j)
| (6.9586878265079796087 - 8.3146235373137684894e-2128j)  +/-  (1.49e-493, 1.49e-493j)
| (7.292853923550291761 + 2.0300365833274838453e-2141j)  +/-  (1.26e-493, 1.26e-493j)
| (0.95857246461381850711 - 5.947637355369564771e-2155j)  +/-  (1.16e-505, 1.16e-505j)
| (-7.7492993111351480343e-2163 - 2.6037358381305308817e-2163j)  +/-  (5.8e-2161, 5.8e-2161j)
| (-0.95857246461381850711 + 2.7015970883611585709e-2154j)  +/-  (1.18e-505, 1.18e-505j)
| (-2.2897217212947825758 + 5.6718379312840178746e-2153j)  +/-  (1.1e-500, 1.1e-500j)
| (-3.1080373432225145929 + 1.0095511041241424542e-2160j)  +/-  (2.66e-498, 2.66e-498j)
| (0.44865433154886803076 + 1.5563078007511480926e-2181j)  +/-  (5.88e-508, 5.88e-508j)
-------------------------------------------------
The weights are:
| (1.5244123336969071042e-24 - 5.8233250465030960588e-1931j)  +/-  (1.16e-163, 2.09e-408j)
| (2.111966371546776709e-45 + 1.8613545582807562939e-1943j)  +/-  (7.76e-174, 1.4e-418j)
| (1.8000423401646286702e-57 + 2.8925409217579457867e-1949j)  +/-  (6.87e-178, 1.24e-422j)
| (1.4199582785518555272e-20 - 1.2114414802572693566e-1929j)  +/-  (3.21e-162, 5.8e-407j)
| (8.9556084384445394368e-38 + 1.16059551883047212e-1939j)  +/-  (1.36e-171, 2.45e-416j)
| (9.1530669787249930516e-32 - 1.7666054430296681338e-1935j)  +/-  (1.16e-169, 2.09e-414j)
| (2.5594230282843422452e-41 - 1.977028458538514369e-1941j)  +/-  (6.66e-173, 1.2e-417j)
| (5.0305918977133438477e-05 + 2.1160836282528990366e-1922j)  +/-  (1.6e-141, 2.89e-386j)
| (1.2818947967116811626e-34 + 4.8791827182953122379e-1937j)  +/-  (1.97e-171, 3.56e-416j)
| (3.7014773692765949979e-29 + 5.4472563192743746067e-1934j)  +/-  (1.11e-168, 2.01e-413j)
| (2.3628822581394312969e-50 + 3.6835575870294735414e-1945j)  +/-  (1.96e-179, 3.53e-424j)
| (1.4199582785518555272e-20 - 5.7410700863309261394e-1931j)  +/-  (6.88e-169, 1.24e-413j)
| (8.9556084384445394368e-38 - 1.023569451246512059e-1938j)  +/-  (1.05e-173, 1.89e-418j)
| (3.9401571478796883984e-17 - 3.4628371734613639972e-1928j)  +/-  (2.27e-164, 4.09e-409j)
| (2.5594230282843422452e-41 + 1.4488834726994019525e-1940j)  +/-  (7.92e-176, 1.43e-420j)
| (1.736375307315185762e-22 + 2.5829194257903875845e-1930j)  +/-  (1.28e-166, 2.31e-411j)
| (3.7014773692765949979e-29 - 2.4929103448989088844e-1935j)  +/-  (7.58e-176, 1.37e-420j)
| (0.00021768435955135942294 - 2.1886619663045970589e-1922j)  +/-  (3.36e-151, 6.06e-396j)
| (1.2818947967116811626e-34 - 4.4287040794998685918e-1938j)  +/-  (1.18e-177, 2.12e-422j)
| (8.6921230408280974367e-13 + 6.0190626602996779921e-1927j)  +/-  (1.97e-167, 3.55e-412j)
| (5.0305918977133438477e-05 + 9.3185267360031457479e-1923j)  +/-  (1.23e-154, 2.21e-399j)
| (1.5642119793531810207e-11 - 1.331185480868487054e-1925j)  +/-  (3.38e-165, 6.1e-410j)
| (1.3979366779213187905e-15 + 2.1228966598838935313e-1928j)  +/-  (7.46e-170, 1.35e-414j)
| (9.2539401448533548086e-27 - 1.768898656795899864e-1932j)  +/-  (4.51e-172, 8.14e-417j)
| (9.1530669787249930516e-32 + 1.2064591101757547043e-1936j)  +/-  (3.9e-177, 7.04e-422j)
| (9.9134945736105559169e-06 - 3.6990633524129087479e-1923j)  +/-  (5.19e-158, 9.37e-403j)
| (0.016488444730237162296 - 3.5688300602160368992e-1921j)  +/-  (1.05e-145, 1.9e-390j)
| (1.6593026712846493502e-06 + 3.7275637964510013726e-1923j)  +/-  (8.29e-161, 1.5e-405j)
| (1.8000423401646286702e-57 - 1.3138503529022476429e-1948j)  +/-  (1.88e-187, 3.4e-432j)
| (0.12076751004531813688 + 4.5885930854538869219e-1920j)  +/-  (2.61e-146, 4.71e-391j)
| (1.6593026712846493502e-06 + 1.3644476470463097451e-1923j)  +/-  (2.43e-160, 4.38e-405j)
| (2.2980173037296650262e-10 + 1.131264127509874725e-1925j)  +/-  (1.54e-166, 2.77e-411j)
| (0.033504724164203737587 + 6.2947296985577903087e-1921j)  +/-  (1.31e-146, 2.36e-391j)
| (1.5642119793531810207e-11 - 2.7392340155443190692e-1926j)  +/-  (1.86e-167, 3.35e-412j)
| (8.5907453840765746261e-19 + 6.53498915877316436e-1929j)  +/-  (8.68e-172, 1.57e-416j)
| (3.9020173943024086706e-14 - 7.9754284109320803171e-1927j)  +/-  (7.79e-171, 1.41e-415j)
| (2.3628822581394312969e-50 - 6.8759531885887040699e-1946j)  +/-  (8.57e-189, 1.55e-433j)
| (0.0025610428329401276126 - 1.7532466301968903153e-1921j)  +/-  (2.4e-159, 4.33e-404j)
| (8.6921230408280974367e-13 + 3.3960130603826267951e-1926j)  +/-  (2.05e-170, 3.7e-415j)
| (2.7949227688979776568e-08 + 1.4695466186914966303e-1924j)  +/-  (4.72e-168, 8.52e-413j)
| (1.3979366779213187905e-15 + 1.726365848686465939e-1927j)  +/-  (1.61e-171, 2.91e-416j)
| (8.5907453840765746261e-19 + 4.69915107074298869e-1930j)  +/-  (8.42e-177, 1.52e-421j)
| (0.0025610428329401276126 - 9.9261851536155066042e-1922j)  +/-  (8.03e-161, 1.45e-405j)
| (2.111966371546776709e-45 - 1.1598155221235181594e-1942j)  +/-  (3.56e-186, 6.42e-431j)
| (2.3481799482671772494e-07 - 1.4068844194657430176e-1923j)  +/-  (6.91e-169, 1.25e-413j)
| (0.08843608114371952357 + 1.7729059677400221827e-1920j)  +/-  (7.51e-158, 1.36e-402j)
| (2.7812345198693520178e-09 - 1.6012261903281562715e-1924j)  +/-  (2.58e-170, 4.66e-415j)
| (3.9401571478796883984e-17 - 3.3615632488959692163e-1929j)  +/-  (2.32e-176, 4.19e-421j)
| (2.7812345198693520178e-09 - 4.2603949891320143804e-1925j)  +/-  (3.66e-171, 6.6e-416j)
| (3.9020173943024086706e-14 - 1.1936378735413435449e-1927j)  +/-  (2.05e-174, 3.69e-419j)
| (0.0070000457415972392568 + 3.1548701951569788965e-1921j)  +/-  (6.81e-166, 1.23e-410j)
| (0.08843608114371952357 + 2.1493585099932174893e-1920j)  +/-  (1.29e-162, 2.34e-407j)
| (0.12076751004531813688 + 4.3281829509661732962e-1920j)  +/-  (2.87e-162, 5.18e-407j)
| (2.2980173037296650262e-10 + 4.8066405875189396956e-1925j)  +/-  (3.29e-172, 5.94e-417j)
| (0.00021768435955135942294 - 4.5575035002383279919e-1922j)  +/-  (2.87e-169, 5.18e-414j)
| (2.7949227688979776568e-08 + 4.931033991872162682e-1924j)  +/-  (2.27e-171, 4.1e-416j)
| (0.033504724164203737587 + 8.8262270333802689109e-1921j)  +/-  (6.77e-166, 1.22e-410j)
| (0.016488444730237162296 - 5.3948644481174818354e-1921j)  +/-  (1.22e-166, 2.21e-411j)
| (0.00080600672410154282209 + 4.8095374988454341572e-1922j)  +/-  (1.2e-169, 2.17e-414j)
| (0.0070000457415972392568 + 1.9325831519854238525e-1921j)  +/-  (1.68e-168, 3.02e-413j)
| (2.3481799482671772494e-07 - 4.6610971939765523558e-1924j)  +/-  (4.69e-173, 8.47e-418j)
| (0.11320155830699864296 - 3.2485101916261600037e-1920j)  +/-  (2.37e-168, 4.29e-413j)
| (9.2539401448533548086e-27 + 4.075284156699896723e-1934j)  +/-  (4.43e-186, 8e-431j)
| (1.736375307315185762e-22 + 6.0563559973264978002e-1932j)  +/-  (2.52e-184, 4.55e-429j)
| (1.5244123336969071042e-24 - 5.4357867442040867859e-1933j)  +/-  (2.15e-185, 3.88e-430j)
| (0.058714575300523863019 - 1.0702029882606920387e-1920j)  +/-  (5.84e-173, 1.05e-417j)
| (0.11648036427955215901 - 5.198161596887601822e-1920j)  +/-  (3.14e-172, 5.68e-417j)
| (0.058714575300523863019 - 1.3941125343535075212e-1920j)  +/-  (3.04e-173, 5.53e-418j)
| (0.00080600672410154282209 + 9.2117807477939711645e-1922j)  +/-  (7.21e-176, 1.3e-420j)
| (9.9134945736105559169e-06 - 9.1936062139997801466e-1923j)  +/-  (4.01e-177, 7.37e-422j)
| (0.11320155830699864296 - 2.871979386380625417e-1920j)  +/-  (9.34e-174, 1.44e-418j)
