Starting with polynomial:
P : 7391536347803839/67108864*t^30 - 54496920530418135/67108864*t^28 + 180700315442965395/67108864*t^26 - 355924863751295475/67108864*t^24 + 463373879223384675/67108864*t^22 - 419762220002360235/67108864*t^20 + 271274904083157975/67108864*t^18 - 126155198555389575/67108864*t^16 + 42051732851796525/67108864*t^14 - 9888133564634325/67108864*t^12 + 1591748329916745/67108864*t^10 - 166966608033225/67108864*t^8 + 10529425731825/67108864*t^6 - 347123925225/67108864*t^4 + 4508102925/67108864*t^2 - 9694845/67108864
Extension levels are: 30 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : 7391536347803839/67108864*t^30 - 54496920530418135/67108864*t^28 + 180700315442965395/67108864*t^26 - 355924863751295475/67108864*t^24 + 463373879223384675/67108864*t^22 - 419762220002360235/67108864*t^20 + 271274904083157975/67108864*t^18 - 126155198555389575/67108864*t^16 + 42051732851796525/67108864*t^14 - 9888133564634325/67108864*t^12 + 1591748329916745/67108864*t^10 - 166966608033225/67108864*t^8 + 10529425731825/67108864*t^6 - 347123925225/67108864*t^4 + 4508102925/67108864*t^2 - 9694845/67108864
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 7391536347803839/67108864*t^61 - 1014215431703863807/603979776*t^59 + 30102688622807786158877/2473297182720*t^57 - 582582527912478931894605113/10439787408261120*t^55 + 178642174672327350198623068490237/983271377047073587200*t^53 - 1965745486886597486165216118200452381/4398172869531560155545600*t^51 + 76037585863691175375069293933854077716162717/88089443052478934651567603712000*t^49 - 104925071461404497532222865640266980976566853/78163872004312294127447310336000*t^47 + 894195427499707921176638058003530029435009383308411/522692364215556892989947369603727360000*t^45 - 63059058097357603979368075152232499236911025041492369637/34859294615791077195906971984137864347648000*t^43 + 81133568422029970212425339039794374925158408156314929229548013/50675828065340883696619862847640816848784588800000*t^41 - 316172182479208779707251872049497534771680244765192266139567113689/264983904953667480849625262830313831302294614835200000*t^39 + 91748131482672813964102532722538654534865900579536641305120124528016363647/122067176949707190705573183761981172212101570096756948992000000*t^37 - 89429068780155120404514959550329930415872140099294023444724535824880516086661/223016732287115037419082206733139601631509568566774945808384000000*t^35 + 14732179277003821828770790651240304075808721388879102166316860558520673695939619687/81279563165700510962571605654926393512611819812003962874594590720000000*t^33 - 21377245576010556837719121536498839762408493581839392296634435329309551923711177227843/308338652717619643428911988232032225293520872041509868833545917562880000000*t^31 + 626661997426210722063491972615662465372162061034127486429413766239006779535748461607/27998567315737875667682812724517868733549596426757792687184054583296000000*t^29 - 2698799176573110699239593994255899893118211069547814767721466256129770814882123961/444421703424410724883854170230442360849993594075520518844191342592000000*t^27 + 28235660623850722177169694115910654357925073041391026338467397258114477212920563/20511770927280494994639423241405032039230473572716331638962677350400000*t^25 - 384494884902078451667390910127375713437843397064421805392898575569387017037067/1486360212121774999611552408797466089799309679182342872388599808000000*t^23 + 1210192611128070922737205315099629534205099851385863447283681835341221001273/30333881880036224481868416506070736526516524064945772905889792000000*t^21 - 4446263354279054180256465003834665799708548376863309328929298665101038333151/891816127273064999766931445278479653879585807509405723433159884800000*t^19 + 104853538323052110000405022019778615258072710876966260459833384849028408697/211106233025991231828887153713263299710626592115753045643598233600000*t^17 - 562746770374975001227769425981203584770955983461301651833553588366820949989/14566330078793394996193213606215167680033234855986960149408278118400000*t^15 + 8224013728312290215667876862409230822142974109081723981423627255798395417/3601565129371993268289530836701552448359865761095676960018530304000000*t^13 - 1543872287051530723760955704943278026747421198266770661509025206047814947/15606782227278637495921300292373393942892751631414600160080297984000000*t^11 + 3109529984681243611735562228024159585344243160990799924192313057689307/1040452148485242499728086686158226262859516775427640010672019865600000*t^9 - 67921054464376595533266008599527956160453872786141335746416473052819/1159360965454984499697010878862023550043461549762227440463107850240000*t^7 + 4501131366518148162070921693376844471803957839627266382259919725057/6762938965154076248232563460028470708586859040279660069368129126400000*t^5 - 848583642060299175746702639617271348460327311386428317432289861197/236702863780392668688139721100996474800540066409788102427884519424000000*t^3 + 2052472381438583398985303596069590219151222536533041455914747063/355054295670589003032209581651494712200810099614682153641826779136000000*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: 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:
| (-0.99163099687040459486 + 4.1765630279687350418e-800j)  +/-  (1.53e-233, 1.53e-233j)
| (-0.99948441005049063757 - 1.4653844485083043596e-815j)  +/-  (4.64e-234, 4.64e-234j)
| (-0.94437444474855997942 + 2.6501440452723041182e-824j)  +/-  (5.25e-234, 5.25e-234j)
| (0.99689348407464954027 + 1.7354367849163124269e-828j)  +/-  (1.31e-233, 1.31e-233j)
| (0.92620004742927432588 - 2.1635137122214328997e-831j)  +/-  (2.58e-234, 2.58e-234j)
| (0.94437444474855997942 - 9.9701742600687665133e-831j)  +/-  (4.97e-234, 4.97e-234j)
| (0.99163099687040459486 + 2.9625378232779859933e-831j)  +/-  (1.59e-233, 1.59e-233j)
| (-0.92620004742927432588 + 3.3806097612843628995e-828j)  +/-  (2.72e-234, 2.72e-234j)
| (-0.97311632250112626837 + 4.8233304478539802198e-830j)  +/-  (1.25e-233, 1.25e-233j)
| (0.99948441005049063757 - 3.43210571760305185e-843j)  +/-  (4.87e-234, 4.87e-234j)
| (0.85720523354606109896 + 7.4973350100495565096e-846j)  +/-  (1.52e-235, 1.52e-235j)
| (0.20452511668230989144 - 1.6044355552705787001e-860j)  +/-  (2.2e-250, 2.2e-250j)
| (-0.88256053579205268154 + 4.7747106498673276108e-842j)  +/-  (4.78e-235, 4.78e-235j)
| (-0.85720523354606109896 + 2.6499057006481172212e-847j)  +/-  (1.61e-235, 1.61e-235j)
| (0.69785049479331579693 + 1.4375799355506126991e-855j)  +/-  (1.07e-238, 1.07e-238j)
| (0.88256053579205268154 + 7.1636363735684698916e-852j)  +/-  (4.53e-235, 4.53e-235j)
| (0.90557330769990779855 + 7.6422114462392436064e-853j)  +/-  (1.17e-234, 1.17e-234j)
| (-0.98366812327974720997 - 1.8961432243390121512e-847j)  +/-  (1.49e-233, 1.49e-233j)
| (-0.79972783582183908301 - 1.4060733323923583836e-866j)  +/-  (1.24e-236, 1.24e-236j)
| (-0.30407320227362507737 - 4.4916802585936471221e-885j)  +/-  (6.78e-248, 6.78e-248j)
| (0.82956576238276839744 - 1.621566814397464548e-873j)  +/-  (4.63e-236, 4.63e-236j)
| (0.73379006245322680473 - 2.4876777471424569889e-875j)  +/-  (6.31e-238, 6.31e-238j)
| (-0.96002186496830751222 + 2.4692485300473698809e-869j)  +/-  (8.28e-234, 8.28e-234j)
| (-0.82956576238276839744 - 1.2519657019872263633e-883j)  +/-  (4.74e-236, 4.74e-236j)
| (-0.76777743210482619492 + 1.3537558402937120507e-886j)  +/-  (3.2e-237, 3.2e-237j)
| (0.96002186496830751222 + 1.9562189469163857848e-880j)  +/-  (9.24e-234, 9.24e-234j)
| (0.76777743210482619492 - 2.8751620058681464406e-891j)  +/-  (3e-237, 3e-237j)
| (-0.99689348407464954027 - 3.8163590669194769433e-887j)  +/-  (1.21e-233, 1.21e-233j)
| (0.44703376953808917678 - 4.1087939240095161399e-914j)  +/-  (2.26e-244, 2.26e-244j)
| (-0.66006106412662696137 + 1.3047883318403886371e-907j)  +/-  (1.67e-239, 1.67e-239j)
| (0.35270472553087811347 + 2.0534153224484895767e-916j)  +/-  (1.22e-246, 1.22e-246j)
| (0.98366812327974720997 - 6.2810254974607487403e-902j)  +/-  (1.63e-233, 1.63e-233j)
| (0.66006106412662696137 - 2.1139626038287182614e-909j)  +/-  (1.7e-239, 1.7e-239j)
| (-0.62052618298924286114 - 8.7202667933267829481e-910j)  +/-  (2.55e-240, 2.55e-240j)
| (-0.73379006245322680473 + 6.3868072705722527055e-907j)  +/-  (6.22e-238, 6.22e-238j)
| (-0.57934523582636169176 + 1.6397419574733049277e-910j)  +/-  (2.84e-241, 2.84e-241j)
| (-0.90557330769990779855 + 5.234158056244065635e-906j)  +/-  (1.18e-234, 1.18e-234j)
| (0.62052618298924286114 - 3.1582872472763974676e-920j)  +/-  (2.3e-240, 2.3e-240j)
| (0.97311632250112626837 - 1.4791471990267885944e-919j)  +/-  (1.25e-233, 1.25e-233j)
| (0.10280693796673703015 - 6.6466760327150472738e-941j)  +/-  (4.5e-253, 4.5e-253j)
| (-0.53662414814201989926 - 2.85797614637353317e-930j)  +/-  (2.85e-242, 2.85e-242j)
| (-0.69785049479331579693 - 7.3401025488056778473e-927j)  +/-  (1.1e-238, 1.1e-238j)
| (0.25463692616788984644 - 4.3069982019805171803e-936j)  +/-  (3.85e-249, 3.85e-249j)
| (0.57934523582636169176 + 1.493005502777533921e-927j)  +/-  (2.82e-241, 2.82e-241j)
| (-0.051471842555317695833 - 9.224630706827626117e-942j)  +/-  (2.04e-254, 2.04e-254j)
| (-0.49248046786177857499 - 2.2325452780652777284e-931j)  +/-  (2.7e-243, 2.7e-243j)
| (-0.35270472553087811347 + 1.2503923790376688087e-934j)  +/-  (1.09e-246, 1.09e-246j)
| (0.15386991360858354696 + 8.2222234310273386812e-940j)  +/-  (9.13e-252, 9.13e-252j)
| (0.49248046786177857499 + 3.5413483247827796436e-930j)  +/-  (2.6e-243, 2.6e-243j)
| (0.79972783582183908301 - 2.5060784447857708881e-933j)  +/-  (1.3e-236, 1.3e-236j)
| (-0.25463692616788984644 + 4.8137843170963419845e-946j)  +/-  (3.77e-249, 3.77e-249j)
| (-0.44703376953808917678 - 1.7884228831609878029e-942j)  +/-  (2.31e-244, 2.31e-244j)
| (-0.10280693796673703015 + 1.9752442088286811453e-950j)  +/-  (4.8e-253, 4.8e-253j)
| (0.53662414814201989926 + 1.8361113902688300906e-941j)  +/-  (2.92e-242, 2.92e-242j)
| (0.30407320227362507737 - 8.300671858183268755e-947j)  +/-  (7.82e-248, 7.82e-248j)
| (-0.15386991360858354696 + 4.959728747814119736e-951j)  +/-  (9.26e-252, 9.26e-252j)
| (-0.40040125483039439254 + 1.1402131868348232096e-944j)  +/-  (1.63e-245, 1.63e-245j)
| (-0.20452511668230989144 + 1.6358567753336862338e-949j)  +/-  (2e-250, 2e-250j)
| (1.0053226928648889017e-969 - 4.9258290523145025049e-970j)  +/-  (6.83e-968, 6.83e-968j)
| (0.40040125483039439254 - 6.429539072487542411e-945j)  +/-  (1.67e-245, 1.67e-245j)
| (0.051471842555317695833 - 1.1606052287479054427e-953j)  +/-  (2.04e-254, 2.04e-254j)
-------------------------------------------------
The weights are:
| (0.0066307039159312921733 + 7.3679459410163400225e-801j)  +/-  (1.83e-51, 2.13e-161j)
| (0.0013890136986770076246 - 7.3869833742440986856e-801j)  +/-  (1.09e-51, 1.27e-161j)
| (0.016920889189053272628 + 1.4954785530086862755e-800j)  +/-  (6e-52, 7e-162j)
| (0.0038904611270998840513 - 8.5645926098623600729e-803j)  +/-  (4.2e-53, 4.89e-163j)
| (0.019414141193942381173 - 4.2215861043444356476e-802j)  +/-  (3.03e-53, 3.54e-163j)
| (0.016920889189053272628 + 3.6503595841268770757e-802j)  +/-  (3.09e-53, 3.6e-163j)
| (0.0066307039159312921733 + 1.3963638143667963319e-802j)  +/-  (1.67e-53, 1.95e-163j)
| (0.019414141193942381173 - 1.2373790929597193223e-800j)  +/-  (3.91e-54, 4.56e-164j)
| (0.011823015253496341742 + 2.6670503300235979251e-800j)  +/-  (7.02e-54, 8.18e-164j)
| (0.0013890136986770076246 + 2.9135946811881468735e-803j)  +/-  (1.01e-53, 1.17e-163j)
| (0.026509954882333101611 + 5.9886590068462116284e-802j)  +/-  (1.49e-55, 1.73e-165j)
| (0.050405921402782346841 + 1.7600002653188870965e-801j)  +/-  (4.96e-58, 5.78e-168j)
| (0.024191162078080601366 - 9.2711536799660058141e-801j)  +/-  (1.55e-55, 1.81e-165j)
| (0.026509954882333101611 + 8.2365533731450273941e-801j)  +/-  (6.34e-56, 7.38e-166j)
| (0.036882364651821229224 - 9.1155160534360940622e-802j)  +/-  (1.14e-57, 1.33e-167j)
| (0.024191162078080601366 - 5.3954411221015291756e-802j)  +/-  (5.75e-56, 6.7e-166j)
| (0.021828035821609192297 + 4.8052899292971932623e-802j)  +/-  (8.9e-56, 1.04e-165j)
| (0.0092732796595177634284 - 4.8218688133328169686e-800j)  +/-  (3.3e-56, 3.84e-166j)
| (0.030907257562387762473 + 6.7266275618204935907e-801j)  +/-  (6.64e-59, 7.74e-169j)
| (0.049055434555029778888 + 2.9798675237713155565e-801j)  +/-  (1.76e-61, 2.05e-171j)
| (0.028754048765041292844 - 6.5907592374850586567e-802j)  +/-  (6.61e-58, 7.7e-168j)
| (0.034979338028060024137 + 8.4671164271105605771e-802j)  +/-  (2.94e-59, 3.42e-169j)
| (0.014369729507045804812 - 1.9046731786814869988e-800j)  +/-  (1.23e-56, 1.43e-166j)
| (0.028754048765041292844 - 7.4063196849546441716e-801j)  +/-  (1.51e-58, 1.75e-168j)
| (0.032981447057483726032 - 6.1556507746361831152e-801j)  +/-  (5.48e-60, 6.39e-170j)
| (0.014369729507045804812 - 3.0848245050407479699e-802j)  +/-  (6.7e-59, 7.81e-169j)
| (0.032981447057483726032 - 7.8319754905170051043e-802j)  +/-  (6.71e-60, 7.81e-170j)
| (0.0038904611270998840513 + 3.2362837975728598683e-800j)  +/-  (1.78e-57, 2.07e-167j)
| (0.046059238271006988116 - 1.3372553026564401096e-801j)  +/-  (6.41e-64, 7.47e-174j)
| (0.03867894562472759295 + 4.8721261581304190726e-801j)  +/-  (4.63e-63, 5.4e-173j)
| (0.048185861757087129141 - 1.4969386939352869938e-801j)  +/-  (2.21e-64, 2.57e-174j)
| (0.0092732796595177634284 - 1.9438034189163051549e-802j)  +/-  (5.7e-60, 6.65e-170j)
| (0.03867894562472759295 + 9.780579447692859393e-802j)  +/-  (1.38e-62, 1.61e-172j)
| (0.040374538951535959112 - 4.5446804606380744496e-801j)  +/-  (9.2e-64, 1.07e-173j)
| (0.034979338028060024137 + 5.6660285645118753159e-801j)  +/-  (2.15e-62, 2.5e-172j)
| (0.041969810215164246147 + 4.2516519899117728935e-801j)  +/-  (9.54e-65, 1.11e-174j)
| (0.021828035821609192297 + 1.0593610898044496887e-800j)  +/-  (1.64e-60, 1.91e-170j)
| (0.040374538951535959112 - 1.0461466273662437334e-801j)  +/-  (6.47e-65, 7.54e-175j)
| (0.011823015253496341742 + 2.5132783182856502825e-802j)  +/-  (1.12e-61, 1.31e-171j)
| (0.051221547849258772171 + 1.9547021916266046939e-801j)  +/-  (1.71e-68, 1.99e-178j)
| (0.043452539701356069317 - 3.9880755219728274937e-801j)  +/-  (3.82e-66, 4.45e-176j)
| (0.036882364651821229224 - 5.242177595299592135e-801j)  +/-  (8.34e-64, 9.72e-174j)
| (0.049795683427074206358 - 1.6688497236673638552e-801j)  +/-  (4.95e-68, 5.77e-178j)
| (0.041969810215164246147 + 1.115800188361947633e-801j)  +/-  (1.7e-66, 1.98e-176j)
| (0.051426128537459025934 - 2.2845719184545237127e-801j)  +/-  (6.3e-70, 7.34e-180j)
| (0.044814800133162663192 + 3.7498074521471831783e-801j)  +/-  (1.24e-67, 1.44e-177j)
| (0.048185861757087129141 - 3.1496406561635032068e-801j)  +/-  (3.64e-69, 4.24e-179j)
| (0.050881795898749606492 - 1.8551360821241717073e-801j)  +/-  (4.21e-69, 4.91e-179j)
| (0.044814800133162663192 + 1.261171022459231121e-801j)  +/-  (9.78e-69, 1.14e-178j)
| (0.030907257562387762473 + 7.2060441981337431755e-802j)  +/-  (1.88e-66, 2.19e-176j)
| (0.049795683427074206358 - 2.8220496767299981761e-801j)  +/-  (1.22e-70, 1.43e-180j)
| (0.046059238271006988116 - 3.5326329093680799713e-801j)  +/-  (1.81e-69, 2.11e-179j)
| (0.051221547849258772171 + 2.4068883019033098907e-801j)  +/-  (1.4e-71, 1.63e-181j)
| (0.043452539701356069317 - 1.1873682752947065635e-801j)  +/-  (8.54e-70, 9.95e-180j)
| (0.049055434555029778888 + 1.5812491340139782855e-801j)  +/-  (9.93e-71, 1.16e-180j)
| (0.050881795898749606492 - 2.536594398562588526e-801j)  +/-  (5.25e-72, 6.12e-182j)
| (0.047185546569299153945 + 3.3332796921859733567e-801j)  +/-  (2.57e-71, 2.99e-181j)
| (0.050405921402782346841 + 2.6746529662724642375e-801j)  +/-  (4.95e-72, 5.77e-182j)
| (0.051494729429451567558 + 2.1688610354967386967e-801j)  +/-  (3.95e-73, 4.61e-183j)
| (0.047185546569299153945 + 1.4157244490208146572e-801j)  +/-  (2.66e-73, 3.38e-183j)
| (0.051426128537459025934 - 2.0591078095508784139e-801j)  +/-  (2.99e-73, 3.45e-183j)
