Starting with polynomial:
P : t
Extension levels are: 1 32 34
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : t^33 - 528/65*t^31 + 2728/91*t^29 - 158224/2379*t^27 + 356004/3599*t^25 - 7120080/68381*t^23 + 5458728/68381*t^21 - 163761840/3624193*t^19 + 61410690/3242699*t^17 - 54587280/9346603*t^15 + 81880920/62755763*t^13 - 12902448/62755763*t^11 + 59136220/2698497809*t^9 - 163761840/110638410169*t^7 + 81880920/1438299332197*t^5 - 54587280/53217075291289*t^3 + 2047023/372519527039023*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^67 - 75107/4485*t^65 + 316931708/2366217*t^63 - 70736510373716/103862390967*t^61 + 1216737755363236748/492139169631027*t^59 - 4102719886265249598436/601452454682122065*t^57 + 66492194609850925322830602196/4471725085220436355642275*t^55 - 85955960845619029676529141390196/3270619727330227150516759935*t^53 + 16361195055823924875859871304870972376/426568356384022538593366931440155*t^51 - 290032750432150208492903843119635140595776/6193095043777044401049686614678763295*t^49 + 2241933086673416741796340909445642138777779818316/46417062192206108329335818773121606316673425*t^47 - 1284849065567234077827111982318788087661116269768516/30324167970461458643665027987844657913903351375*t^45 + 234084394269332274330946253699882419362554185549092127057748/7367917184033846315801220419883541250641884104381932725*t^43 - 306988805291439370190256796376132103034855103643738657982242868/15026952770292657861615144874496899631163781257446305070925*t^41 + 1816789777578411409123960331968262805557301460507024290529528612/160979233150820605758231073443580159261552184515219988402355*t^39 - 9568289255767762123476109433985838195849137536256047686011757129129671196/1785264638633784593152267492326899492449850128588655353146645450773625*t^37 + 1501562756292629777544448123031206734453905816663349240966047915103754664842958/686680089320469612080617413039514626547346617318153096772027936864936964375*t^35 - 104620603809716511970783001771847364735017698408850808914806905662123669551116046/136727815499267220759709221470639355211670245031148826611550362628907020135125*t^33 + 12996279365379332947657785570642181870823407644901756430878336131270206526148/56757084059471656604279460967471712416633559581215785226878523299670826125*t^31 - 101403969111125973679952286243378916926234824687066641486048992689764920297436/1737499121691567810240684143810666293012427356212057425171216729399600451375*t^29 + 1358942021647535004512582843134317374647374584381176609063665726278795760244/107844773070511105463214877891696528531805835902817357424420348721354510775*t^27 - 214485003125242323639961488985877425091992381406593657241886505582721393068/93711270047025319562052814122414362399432421510995139642302582222259617625*t^25 + 76677560675495430380314137995994802864440689015480648357531794901080169948/221158597310979754166444641328897895262660514765948529555834094044532697595*t^23 - 166236602144284285406425475609412799786197080518758817367351622332952266668/3836620883786127039670061386531750443904415017026672317077295805381241145235*t^21 + 211902782224263466257139402744694767618688094529727250038006687458664416/48077955937169511775314052462803890274491416253467071642572629140115803825*t^19 - 15543240361498185105883206730781083516847276803425543926283078711923684888/43318238299389730109557961268986305137316766044373831549957938855244339246325*t^17 + 9621252068634028857271243033292312223261675537531252740153626158960892772/420441724670547380475121388787220020450427435136569541514297641830312704449625*t^15 - 2836746792230461546116828973110244483406208715788005567205917791475163076/2550679796334654108215736425309134790732593106495188551853405693770563740327725*t^13 + 366201681901305194642781664288214429793902307483839647876426109118977588/9221688494440672545087662460733025781879375077328758610546928277478191984261775*t^11 - 7475228890327402447125636128436526226167807596915366601215793220644028/7545017859087822991435360195145202912446761426905347954083850408845793441668725*t^9 + 4053227927900001465900869528960077799137238674826834795363371568963812/252338930620603857824671490970967341849608354388723303797693219229175980660254025*t^7 - 1116565155317529726388537551746465764510802187630109996695387155334268/7389925825317684407722522235578329297024244664241182468361015705997296576478867875*t^5 + 948080646070657489792821534824587092660878013721175550072862321021/1405888327743364350737455449695389476019246545880029835444290792848266177964272425*t^3 - 640754947652224554503662437292524187649994070518891591848921219533/710910864395561240022906639062635278373732336700001753456329710916939930657267089575*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:
| (0.98645572623064248811 + 7.323278165839802232e-858j)  +/-  (2.91e-231, 2.91e-231j)
| (-0.99742469424645521727 + 1.7609296688842766059e-864j)  +/-  (2.19e-231, 2.19e-231j)
| (-0.95381693154833893871 + 1.8960624160113122103e-865j)  +/-  (1.21e-231, 1.21e-231j)
| (-0.97769776639556024686 - 1.9140397671213061349e-864j)  +/-  (2.52e-231, 2.52e-231j)
| (0.90231676774343358304 + 1.6763770305790487719e-866j)  +/-  (1.33e-232, 1.33e-232j)
| (0.97769776639556024686 + 1.0098112622525891368e-868j)  +/-  (2.76e-231, 2.76e-231j)
| (0.99742469424645521727 - 4.0825829979949236443e-874j)  +/-  (2.28e-231, 2.28e-231j)
| (-0.92151140011766531366 + 4.5896628554812186935e-885j)  +/-  (3.06e-232, 3.06e-232j)
| (-0.99957248040197061237 + 2.316199925717659114e-883j)  +/-  (8.22e-232, 8.22e-232j)
| (-0.18643929882799157234 + 6.3314702482430458007e-908j)  +/-  (2.16e-250, 2.16e-250j)
| (0.88113695736615228092 + 1.1905626666379037544e-887j)  +/-  (5.32e-233, 5.32e-233j)
| (-0.96682290968999276893 - 5.3811368934719222744e-886j)  +/-  (2.04e-231, 2.04e-231j)
| (-0.98645572623064248811 + 7.7357608263528263604e-888j)  +/-  (3.06e-231, 3.06e-231j)
| (-0.85800965267650406464 + 6.1616026606669231112e-893j)  +/-  (1.7e-233, 1.7e-233j)
| (0.68173195996974278627 + 2.7404449838419886416e-896j)  +/-  (2.25e-237, 2.25e-237j)
| (0.85800965267650406464 - 1.626159657720293791e-890j)  +/-  (1.68e-233, 1.68e-233j)
| (0.95381693154833893871 - 1.1086319979301276363e-888j)  +/-  (1.18e-231, 1.18e-231j)
| (0.92151140011766531366 + 2.4662490239377498947e-897j)  +/-  (3.47e-232, 3.47e-232j)
| (-0.77755454123725048431 - 4.7330422098247707253e-911j)  +/-  (3.31e-235, 3.31e-235j)
| (-0.90231676774343358304 - 1.1212347052539446293e-908j)  +/-  (1.4e-232, 1.4e-232j)
| (-0.99306135553260535754 - 7.0660877166435957978e-906j)  +/-  (3.35e-231, 3.35e-231j)
| (0.77755454123725048431 + 6.6054052415610663137e-910j)  +/-  (3.27e-235, 3.27e-235j)
| (-0.36633925774807334107 + 1.0891443161095329545e-920j)  +/-  (2.13e-245, 2.13e-245j)
| (-0.8061623562741665898 + 1.5935545607130988062e-910j)  +/-  (1.38e-234, 1.38e-234j)
| (-0.74723049644956215786 - 1.4978275047449957594e-911j)  +/-  (6.91e-236, 6.91e-236j)
| (0.96682290968999276893 - 9.9934765347423155011e-905j)  +/-  (1.85e-231, 1.85e-231j)
| (0.74723049644956215786 + 4.4086634988947465282e-930j)  +/-  (7.32e-236, 7.32e-236j)
| (0.32233036969708987756 + 2.8415380560209069735e-941j)  +/-  (1.34e-246, 1.34e-246j)
| (0.99957248040197061237 - 1.3458957388167873979e-923j)  +/-  (8.6e-232, 8.6e-232j)
| (-0.64670058297517796966 + 5.680887153880889114e-954j)  +/-  (3.3e-238, 3.3e-238j)
| (-0.046865273381329082262 - 2.6487706635705633155e-968j)  +/-  (2.46e-254, 2.46e-254j)
| (0.57244293169105634518 - 1.439510437145729047e-954j)  +/-  (4.43e-240, 4.43e-240j)
| (0.7152643817222187341 + 2.5592748881387760132e-949j)  +/-  (1.27e-236, 1.27e-236j)
| (0.83299733908667720963 - 1.1122816089286906675e-944j)  +/-  (4.95e-234, 4.95e-234j)
| (-0.7152643817222187341 - 2.9347563356439570115e-955j)  +/-  (1.26e-236, 1.26e-236j)
| (-0.68173195996974278627 + 8.2487678130103180578e-956j)  +/-  (2.07e-237, 2.07e-237j)
| (0.18643929882799157234 + 2.5787070679790056197e-967j)  +/-  (2.03e-250, 2.03e-250j)
| (0.61024234583637902731 + 2.989560299932581482e-955j)  +/-  (4e-239, 4e-239j)
| (0.99306135553260535754 + 4.9473634948413643307e-949j)  +/-  (2.85e-231, 2.85e-231j)
| (-0.93869437261116835036 + 2.5808102513488475194e-964j)  +/-  (6.55e-232, 6.55e-232j)
| (-0.57244293169105634518 - 6.8241026209287038191e-976j)  +/-  (4.63e-240, 4.63e-240j)
| (-0.83299733908667720963 + 4.7303215292901244409e-969j)  +/-  (4.97e-234, 4.97e-234j)
| (0.8061623562741665898 - 3.4657223401359727541e-967j)  +/-  (1.41e-234, 1.41e-234j)
| (0.64670058297517796966 + 2.0099596205256408471e-972j)  +/-  (3.05e-238, 3.05e-238j)
| (-0.14019106034177492404 + 1.281465435164428286e-986j)  +/-  (1.06e-251, 1.06e-251j)
| (-0.61024234583637902731 - 3.3239452255188769636e-975j)  +/-  (4.19e-239, 4.19e-239j)
| (-0.88113695736615228092 + 5.9347733511172627123e-971j)  +/-  (5.29e-233, 5.29e-233j)
| (0.49316417327086815102 - 1.5135252925711457918e-979j)  +/-  (4.38e-242, 4.38e-242j)
| (0.45185001727245069573 + 5.8559694682119689725e-981j)  +/-  (3.64e-243, 3.64e-243j)
| (0.093631065854733385671 + 8.9105748626530595518e-991j)  +/-  (5.2e-253, 5.2e-253j)
| (-0.32233036969708987756 + 3.55483381124296921e-986j)  +/-  (1.35e-246, 1.35e-246j)
| (-0.49316417327086815102 + 1.2846851166084450909e-981j)  +/-  (4.5e-242, 4.5e-242j)
| (-0.2776090971524970294 - 1.51412631631820496e-986j)  +/-  (7.18e-248, 7.18e-248j)
| (0.36633925774807334107 + 1.8394392109888439777e-984j)  +/-  (2.03e-245, 2.03e-245j)
| (0.53338990478634764355 - 1.3956802299472307464e-978j)  +/-  (4.91e-241, 4.91e-241j)
| (-0.093631065854733385671 - 5.0921730917564849246e-991j)  +/-  (4.85e-253, 4.85e-253j)
| (-0.40954274507141799937 + 2.0099943570075891102e-983j)  +/-  (3.32e-244, 3.32e-244j)
| (0.046865273381329082262 + 1.7719524569903047913e-992j)  +/-  (2.46e-254, 2.46e-254j)
| (0.93869437261116835036 - 1.2500779141664792282e-987j)  +/-  (6.92e-232, 6.92e-232j)
| (0.40954274507141799937 + 1.0595558612536081867e-1002j)  +/-  (2.91e-244, 2.91e-244j)
| (-3.0031735411781499688e-1036 - 1.2601702784251302959e-1036j)  +/-  (2.18e-1034, 2.18e-1034j)
| (-0.53338990478634764355 - 1.4356615118582068876e-1003j)  +/-  (4.91e-241, 4.91e-241j)
| (-0.45185001727245069573 - 2.492543104477375633e-1005j)  +/-  (3.49e-243, 3.49e-243j)
| (0.14019106034177492404 - 1.9102815102677188605e-1011j)  +/-  (1.01e-251, 1.01e-251j)
| (0.2776090971524970294 + 8.3493560474832457126e-1008j)  +/-  (7.36e-248, 7.36e-248j)
| (0.23227765539724113496 - 7.9624924692195298502e-1009j)  +/-  (4.11e-249, 4.11e-249j)
| (-0.23227765539724113496 + 1.4251643484277323187e-1009j)  +/-  (4.02e-249, 4.02e-249j)
-------------------------------------------------
The weights are:
| (0.0076946559875423204837 - 1.0607007172519257629e-858j)  +/-  (6.34e-40, 5.92e-149j)
| (0.0032250895286294278165 - 1.2591535157681458711e-860j)  +/-  (2.83e-40, 2.64e-149j)
| (0.014071453862050045343 + 5.3579811864533209703e-860j)  +/-  (1.3e-40, 1.22e-149j)
| (0.0098156348212861590421 + 3.6920537918065908407e-860j)  +/-  (9.69e-41, 9.04e-150j)
| (0.02019127489606300628 - 1.7746523909087452687e-858j)  +/-  (1.42e-41, 1.33e-150j)
| (0.0098156348212861590421 + 8.2804481595645168731e-858j)  +/-  (3.88e-41, 3.62e-150j)
| (0.0032250895286294278165 + 2.27738034878392386e-858j)  +/-  (1.19e-41, 1.11e-150j)
| (0.018194377952554501009 + 7.045293361537712525e-860j)  +/-  (6.04e-42, 5.64e-151j)
| (0.0011516012900481880558 + 4.2850525179215213962e-861j)  +/-  (2.11e-41, 1.97e-150j)
| (0.046059141161662809716 - 2.9016737650177460621e-859j)  +/-  (9.22e-45, 8.6e-154j)
| (0.022162342861295120044 + 1.5547060526003184847e-858j)  +/-  (1.2e-43, 1.12e-152j)
| (0.011938233854576595159 - 4.5300757051018564407e-860j)  +/-  (1.46e-41, 1.36e-150j)
| (0.0076946559875423204837 - 2.8562358056243864504e-860j)  +/-  (1.72e-41, 1.6e-150j)
| (0.024081252653542093192 - 9.6400175716948120325e-860j)  +/-  (1.29e-44, 1.2e-153j)
| (0.034292877334557789045 - 8.3166346761278471966e-859j)  +/-  (1.36e-46, 1.27e-155j)
| (0.024081252653542093192 - 1.3843003027671737869e-858j)  +/-  (1.82e-45, 1.7e-154j)
| (0.014071453862050045343 + 3.1852480229931090131e-858j)  +/-  (7.87e-46, 7.35e-155j)
| (0.018194377952554501009 + 2.0698286178453420322e-858j)  +/-  (1.91e-45, 1.78e-154j)
| (0.029477027569876141163 + 1.234580200980597765e-859j)  +/-  (2.6e-48, 2.43e-157j)
| (0.02019127489606300628 - 7.9054467808803368012e-860j)  +/-  (2.44e-46, 2.27e-155j)
| (0.0054989503006964430296 + 2.0522396897244494824e-860j)  +/-  (5.03e-44, 4.7e-153j)
| (0.029477027569876141163 + 1.0425122388267750106e-858j)  +/-  (1.13e-49, 1.06e-158j)
| (0.043621052300575026201 - 2.3826687799483979386e-859j)  +/-  (1.07e-51, 9.98e-161j)
| (0.027729407633335975496 - 1.1433459224987686603e-859j)  +/-  (1.5e-48, 1.4e-157j)
| (0.031158316608357778794 - 1.3273912351928129453e-859j)  +/-  (1.43e-49, 1.34e-158j)
| (0.011938233854576595159 - 4.5072872197781372234e-858j)  +/-  (2.72e-48, 2.54e-157j)
| (0.031158316608357778794 - 9.6197519368085760017e-859j)  +/-  (1.08e-50, 1.01e-159j)
| (0.044381387035405725596 + 4.9372953632937140313e-859j)  +/-  (2.75e-54, 2.57e-163j)
| (0.0011516012900481880558 - 6.4865558983943683715e-859j)  +/-  (1.47e-49, 1.37e-158j)
| (0.035758063555085939725 + 1.6176467310273982026e-859j)  +/-  (1.1e-52, 1.03e-161j)
| (0.046832686633605091536 + 3.3485130724208762209e-859j)  +/-  (2.12e-54, 1.98e-163j)
| (0.038440190620604196793 + 6.8597789032612854467e-859j)  +/-  (1.64e-53, 1.53e-162j)
| (0.032761061077367768321 + 8.9252523658834794093e-859j)  +/-  (1.73e-51, 1.61e-160j)
| (0.025932719419237453371 + 1.248520901219421073e-858j)  +/-  (1.41e-50, 1.31e-159j)
| (0.032761061077367768321 + 1.422351661395126452e-859j)  +/-  (1.22e-52, 1.14e-161j)
| (0.034292877334557789045 - 1.519175646048295997e-859j)  +/-  (3.64e-53, 3.39e-162j)
| (0.046059141161662809716 - 4.2541125807456504734e-859j)  +/-  (3.53e-57, 3.29e-166j)
| (0.037143847993933005709 - 7.2928842374933201545e-859j)  +/-  (2.21e-54, 2.06e-163j)
| (0.0054989503006964430296 - 6.1504090021727411756e-858j)  +/-  (8.5e-51, 7.93e-160j)
| (0.01616316265339878284 - 6.1929062766767049255e-860j)  +/-  (1.63e-51, 1.52e-160j)
| (0.038440190620604196793 + 1.8218193108587412397e-859j)  +/-  (3.03e-56, 2.83e-165j)
| (0.025932719419237453371 + 1.0530361147278897127e-859j)  +/-  (1.01e-52, 9.42e-162j)
| (0.027729407633335975496 - 1.1368092805370596137e-858j)  +/-  (5.89e-53, 5.5e-162j)
| (0.035758063555085939725 + 7.7758220273336241665e-859j)  +/-  (9.29e-55, 8.67e-164j)
| (0.046421142855270857316 + 3.0441509321552045399e-859j)  +/-  (3.75e-59, 3.5e-168j)
| (0.037143847993933005709 - 1.7183434001050120998e-859j)  +/-  (4.5e-56, 4.2e-165j)
| (0.022162342861295120044 + 8.7673517535662730878e-860j)  +/-  (5e-53, 4.67e-162j)
| (0.040784972888532712117 + 6.108503596059407121e-859j)  +/-  (1.69e-58, 1.58e-167j)
| (0.041827228004862558461 - 5.7795695362532189364e-859j)  +/-  (4.71e-59, 4.4e-168j)
| (0.046681009195083972306 - 3.8624268219896345699e-859j)  +/-  (3.62e-61, 3.38e-170j)
| (0.044381387035405725596 + 2.5053603878970310502e-859j)  +/-  (1.01e-60, 9.42e-170j)
| (0.040784972888532712117 + 2.0365159604765286326e-859j)  +/-  (1.31e-60, 1.22e-169j)
| (0.045043927474426307496 - 2.6323770564815005369e-859j)  +/-  (5.16e-61, 4.82e-170j)
| (0.043621052300575026201 - 5.1978379658300394712e-859j)  +/-  (1.16e-61, 1.08e-170j)
| (0.039652622568141909457 - 6.4673583870439610994e-859j)  +/-  (5.25e-60, 4.9e-169j)
| (0.046681009195083972306 - 3.1927705570224565819e-859j)  +/-  (4.71e-62, 4.4e-171j)
| (0.042770988005077959738 + 2.2636134128213565517e-859j)  +/-  (7.2e-62, 6.72e-171j)
| (0.046832686633605091536 + 3.6825503786174376207e-859j)  +/-  (4.62e-63, 4.31e-172j)
| (0.01616316265339878284 - 2.4962601307700033734e-858j)  +/-  (1.39e-60, 1.3e-169j)
| (0.042770988005077959738 + 5.4774357253185234382e-859j)  +/-  (2.83e-62, 2.64e-171j)
| (0.04688144479057056617 - 3.5116648612285008875e-859j)  +/-  (3.86e-63, 3.61e-172j)
| (0.039652622568141909457 - 1.9279161478459951971e-859j)  +/-  (8.29e-63, 7.74e-172j)
| (0.041827228004862558461 - 2.148213338295701228e-859j)  +/-  (4.73e-63, 4.42e-172j)
| (0.046421142855270857316 + 4.0527318670138136689e-859j)  +/-  (1.62e-64, 1.51e-173j)
| (0.045043927474426307496 - 4.6942412788443755798e-859j)  +/-  (4.02e-65, 3.75e-174j)
| (0.045601577008031056261 + 4.4672909560440487055e-859j)  +/-  (3.54e-65, 3.31e-174j)
| (0.045601577008031056261 + 2.7644531472404689404e-859j)  +/-  (3.05e-65, 2.66e-174j)
