Starting with polynomial:
P : 6435/128*t^8 - 3003/32*t^6 + 3465/64*t^4 - 315/32*t^2 + 35/128
Extension levels are: 8 35
-------------------------------------------------
Trying to find an order 35 Kronrod extension for:
P1 : 6435/128*t^8 - 3003/32*t^6 + 3465/64*t^4 - 315/32*t^2 + 35/128
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 6435/128*t^43 - 4551063707455968531535762993585220095987269/8751425059818267299241136484562151497344*t^41 + 182174829642923145261524541548448432304471106873/72965006436234803607422975440036938109105600*t^39 - 1376689504394098359254053280901204504296045504526813/186425591444579923216965702249294376868764808000*t^37 + 375923686475138604070977095984529740694108436543498819/24959723471694329148420036592576955714486625436800*t^35 - 38691004119249956405488216397983129865592827047937675077/1722220919546908711240982524887809944299577155139200*t^33 + 11086853690762471190179390782509586182169915495215779431/437078793975920013837673595331376008591180565887600*t^31 - 312097426617274144068576855627781229967614129387554927/14099315934707097220570115978431484148102598899600*t^29 + 1322575022233661199776759825131226402489678270235855259/87512995456802672403538650900609211953740269032000*t^27 - 64225960694316017903705147216481455986552693378568927/7908581811651797061653122525832832487671342831040*t^25 + 119461638486196804923174553004931520065758859934016809/34747279661831831770880208544350636355407070098080*t^23 - 34770839482775206648804103627397592614250062426629659/30430847405703653911143536675487203267778862632480*t^21 + 5999590371399934423133774857420430425753338309122413/20287231603802435940762357783658135511852575088320*t^19 - 316307184733766059444836389828888960229511981435460183/5376116375007645524302024812669405910640932398404800*t^17 + 7118885667442210488534199456028128396265505488209709/806417456251146828645303721900410886596139859760720*t^15 - 410759443533015565735231448865514193760323434410613/422409143750600719766587663852596178693216117017520*t^13 + 589267456296748046928073029554726503936796825006459347/7782466064461067660979611118820231996243813739930788480*t^11 - 175906930102702738447706378576109853124055823840353877/44572305641913387512883227316879510523941842328694515840*t^9 + 224417583784585967960881321147781640560074348864373/1768742287377515377495366163368234544600866759075179200*t^7 - 779704580947747686025891339303553559201924298159/353748457475503075499073232673646908920173351815035840*t^5 + 1496430139451585323496515853932117636101192541/92282206297957324043236495480081802327001743951748480*t^3 - 327545684950348067168617942764749552687071/11598310081164035262264696153234324882628634485738880*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:
| (-0.978460248776049536 - 4.5862398055355548426e-833j)  +/-  (5.05e-241, 5.05e-241j)
| (0.99832397355928228077 + 1.1841951871419762032e-830j)  +/-  (1.37e-241, 1.37e-241j)
| (-0.90862539153057721853 + 1.0287014122403171455e-837j)  +/-  (1.98e-241, 1.98e-241j)
| (0.99119280195449504198 + 3.0906518612341475982e-835j)  +/-  (3.64e-241, 3.64e-241j)
| (0.93691683603734449638 - 6.7812175810669819959e-853j)  +/-  (3.52e-241, 3.52e-241j)
| (0.90862539153057721853 + 8.6408499769643127462e-882j)  +/-  (2e-241, 2e-241j)
| (-0.93691683603734449638 + 5.9011201362144285043e-892j)  +/-  (3.56e-241, 3.56e-241j)
| (-0.87569974508523913001 + 5.189763924895487005e-901j)  +/-  (9.89e-242, 9.89e-242j)
| (0.79666647741362673959 + 1.5257070362386225707e-921j)  +/-  (1.13e-242, 1.13e-242j)
| (-0.99832397355928228077 + 1.9747184776770339322e-927j)  +/-  (1.23e-241, 1.23e-241j)
| (0.83835094269229437072 - 1.1854705514636886227e-935j)  +/-  (3.45e-242, 3.45e-242j)
| (-0.99119280195449504198 + 5.6749942145482949122e-942j)  +/-  (3.53e-241, 3.53e-241j)
| (-0.83835094269229437072 + 1.4106384509330387693e-943j)  +/-  (3.66e-242, 3.66e-242j)
| (-0.79666647741362673959 - 5.3236845162961807406e-945j)  +/-  (1.06e-242, 1.06e-242j)
| (0.978460248776049536 - 2.7093637256353100305e-942j)  +/-  (5.1e-241, 5.1e-241j)
| (0.87569974508523913001 + 8.29390359711229848e-948j)  +/-  (1.02e-241, 1.02e-241j)
| (0.70031447707532616426 + 3.5243655863475982167e-952j)  +/-  (5.46e-244, 5.46e-244j)
| (-0.18343464249564980494 + 1.2088429201939420677e-960j)  +/-  (2.58e-252, 2.58e-252j)
| (-0.75064644474108548674 + 3.2653859077015728114e-950j)  +/-  (2.72e-243, 2.72e-243j)
| (-0.96028985649753623168 + 5.0490933177729931569e-951j)  +/-  (4.65e-241, 4.65e-241j)
| (0.25389411395571308906 + 8.2226294824255458038e-962j)  +/-  (4.27e-251, 4.27e-251j)
| (0.75064644474108548674 - 2.1892482429533262439e-952j)  +/-  (2.78e-243, 2.78e-243j)
| (0.96028985649753623168 + 6.4896125137867985347e-957j)  +/-  (4.92e-241, 4.92e-241j)
| (-0.58741846170462652534 - 3.9485665391834003203e-961j)  +/-  (1.13e-245, 1.13e-245j)
| (-0.70031447707532616426 - 1.5147058118429941974e-960j)  +/-  (5.29e-244, 5.29e-244j)
| (0.11407648763037290535 - 1.4698309403221847774e-970j)  +/-  (1.46e-253, 1.46e-253j)
| (0.64581153588388988362 - 8.3809028373537793177e-962j)  +/-  (9.47e-245, 9.47e-245j)
| (0.39329631639210070388 + 1.2555489617552393378e-967j)  +/-  (9.27e-249, 9.27e-249j)
| (-0.049513866174485501414 - 6.0299406483932286407e-974j)  +/-  (9.17e-255, 9.17e-255j)
| (-0.64581153588388988362 + 6.9545362834576574117e-965j)  +/-  (8.58e-245, 8.58e-245j)
| (-0.25389411395571308906 - 3.2427984109130781487e-971j)  +/-  (4.31e-251, 4.31e-251j)
| (0.46063866562494127476 + 3.0220521923905592546e-966j)  +/-  (1.25e-247, 1.25e-247j)
| (0.52553240991632898582 + 3.5210070473060732952e-964j)  +/-  (1.34e-246, 1.34e-246j)
| (0.049513866174485501414 + 2.4610611326766476116e-974j)  +/-  (8.27e-255, 8.27e-255j)
| (-0.46063866562494127476 + 1.8079333306932083666e-967j)  +/-  (1.27e-247, 1.27e-247j)
| (-0.39329631639210070388 - 8.9119268541359305996e-969j)  +/-  (8.8e-249, 8.8e-249j)
| (-2.7375004584621288388e-982 - 6.9304235623976564084e-982j)  +/-  (3.2e-980, 3.2e-980j)
| (0.58741846170462652534 + 7.7625920722419302796e-969j)  +/-  (1.07e-245, 1.07e-245j)
| (0.18343464249564980494 - 5.3510404103076586278e-975j)  +/-  (2.58e-252, 2.58e-252j)
| (-0.32413947210566669299 + 4.7149906671715731753e-972j)  +/-  (7.44e-250, 7.44e-250j)
| (-0.52553240991632898582 - 8.8008109455629154338e-970j)  +/-  (1.42e-246, 1.42e-246j)
| (-0.11407648763037290535 - 1.5130354469529739478e-976j)  +/-  (1.57e-253, 1.57e-253j)
| (0.32413947210566669299 - 1.2993927995271563746e-972j)  +/-  (6.79e-250, 6.79e-250j)
-------------------------------------------------
The weights are:
| (0.015485187061149591868 - 2.0985181363946423508e-832j)  +/-  (9.97e-74, 3.27e-190j)
| (0.0042985269299030642689 - 1.5403621889178760921e-830j)  +/-  (3.94e-74, 1.3e-190j)
| (0.030652394462819030005 + 7.7475472178255022305e-832j)  +/-  (1.98e-74, 6.51e-191j)
| (0.0099523864433399816852 + 2.5664680060573436342e-830j)  +/-  (3.16e-74, 1.04e-190j)
| (0.025881787014848824476 - 1.591761014245085072e-830j)  +/-  (4.57e-75, 1.5e-191j)
| (0.030652394462819030005 + 1.5665420549378611645e-830j)  +/-  (2.88e-75, 9.46e-192j)
| (0.025881787014848824476 - 5.4943333498046446556e-832j)  +/-  (8.62e-76, 2.83e-192j)
| (0.035162678901393705224 - 1.0580936313010194821e-831j)  +/-  (3.55e-76, 1.17e-192j)
| (0.043850091495680304671 - 1.5378561462599857385e-830j)  +/-  (4.67e-77, 1.54e-193j)
| (0.0042985269299030642689 - 2.0659717464870712765e-833j)  +/-  (4.06e-77, 1.33e-193j)
| (0.0395209647133179562 + 1.5581682643256303083e-830j)  +/-  (1.53e-77, 5.02e-194j)
| (0.0099523864433399816852 + 6.4875239445677639147e-833j)  +/-  (9.1e-77, 2.99e-193j)
| (0.0395209647133179562 + 1.3904845026296094524e-831j)  +/-  (6.24e-78, 2.05e-194j)
| (0.043850091495680304671 - 1.7595030094601016492e-831j)  +/-  (1.1e-78, 3.62e-195j)
| (0.015485187061149591868 - 1.8953140248126837699e-830j)  +/-  (8.85e-79, 2.91e-195j)
| (0.035162678901393705224 - 1.5634598679053704712e-830j)  +/-  (7.83e-79, 2.57e-195j)
| (0.052452974991629596165 - 1.4684942552597057213e-830j)  +/-  (4.37e-81, 1.44e-197j)
| (0.070202385691531277425 - 2.5648115355574735946e-830j)  +/-  (2.41e-83, 7.92e-200j)
| (0.048187742644386586101 + 2.1598617552522960639e-831j)  +/-  (9.68e-81, 3.18e-197j)
| (0.020816078227291746082 + 3.9162070972547407685e-832j)  +/-  (7.88e-79, 2.59e-195j)
| (0.070516703334230376928 + 2.7388645187444310857e-830j)  +/-  (3.6e-84, 1.18e-200j)
| (0.048187742644386586101 + 1.5038148687731638915e-830j)  +/-  (6.08e-81, 2e-197j)
| (0.020816078227291746082 + 1.6759766078140854298e-830j)  +/-  (1.13e-79, 3.71e-196j)
| (0.060213853790248235966 - 3.8066774938730669526e-831j)  +/-  (1.23e-83, 4.05e-200j)
| (0.052452974991629596165 - 2.6051385739766918892e-831j)  +/-  (2.69e-82, 8.85e-199j)
| (0.068030033021119321397 + 5.5862670355167669853e-830j)  +/-  (3.29e-85, 1.08e-201j)
| (0.056505594627315272149 + 1.4482980776062472229e-830j)  +/-  (1.53e-83, 5.04e-200j)
| (0.068362066474660738942 + 1.8370364822183481605e-830j)  +/-  (2.45e-85, 8.04e-202j)
| (0.058946048820933253303 - 8.4621801547919011041e-830j)  +/-  (4.04e-86, 1.33e-202j)
| (0.056505594627315272149 + 3.1329081625914330487e-831j)  +/-  (1.29e-84, 4.24e-201j)
| (0.070516703334230376928 + 1.6316738657481408593e-830j)  +/-  (1.95e-86, 6.41e-203j)
| (0.066217201053795912913 - 1.6313165937982064197e-830j)  +/-  (4.94e-86, 1.62e-202j)
| (0.063477132109330708485 + 1.5138987082045057305e-830j)  +/-  (4.99e-86, 1.64e-202j)
| (0.058946048820933253303 - 9.3417752704465300965e-830j)  +/-  (5.23e-87, 1.72e-203j)
| (0.066217201053795912913 - 6.0397435423978305498e-831j)  +/-  (6.5e-88, 2.14e-204j)
| (0.068362066474660738942 + 8.0159520700984555167e-831j)  +/-  (4.62e-88, 1.52e-204j)
| (0.042873703433375806446 + 1.1527645505112758097e-829j)  +/-  (2.33e-87, 7.66e-204j)
| (0.060213853790248235966 - 1.4586193458305536062e-830j)  +/-  (1.02e-87, 3.34e-204j)
| (0.070202385691531277425 - 3.7140154382497777027e-830j)  +/-  (4.44e-88, 1.46e-204j)
| (0.069831316474386612524 - 1.1128928000905545206e-830j)  +/-  (7.78e-89, 2.56e-205j)
| (0.063477132109330708485 + 4.7240315711951359805e-831j)  +/-  (4.91e-89, 1.61e-205j)
| (0.068030033021119321397 + 4.4445200367864309242e-830j)  +/-  (1.48e-88, 4.93e-205j)
| (0.069831316474386612524 - 2.1768541572427217909e-830j)  +/-  (3.64e-89, 1.14e-205j)
