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 34
-------------------------------------------------
Trying to find an order 34 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^42 - 286094818370013242090772500234309316720147/550137279426976141076861937602324405120*t^40 + 22811731046233409795677132680121155810987867903/9136404868083506262933984628730602558030400*t^38 - 4719666458351410015212305935419364832017200013/639098271560521127752032422305293380906560*t^36 + 21534428004518514996795540843888593419568046166996381/1429738247076929904274371268522773317706921694080*t^34 - 717383389665944684068157313640437599463183998992194979/31930820851384767862127624997008604095454584501120*t^32 + 1316237942236569928645802859593554211659879770317982563/51887583883500247775957390620138981655113699814320*t^30 - 77493444286553063613474032748279148718434867319632183/3500661581345593927913167283217772375532408533200*t^28 + 6598145561573480989164818289071523522762015008124587313/436571395433588291632193217631514190477508370851520*t^26 - 22527372048060281737349787117304964883956037643764463899/2773907481754953299139935367412544010264783956333504*t^24 + 29615662175250880720096240622065697679969109962606467/8614619508555755587391103625504795062934111665632*t^22 - 9841340616186557509066199746844853908903923242039321/8614619508555755587391103625504795062934111665632*t^20 + 22124695444238835073703717274415539634693293717090597/74848333434992630513398113467500678415657035783360*t^18 - 2333551657700883815590253447906319625289836792841669/39702159474213482272324216708848185942218079850304*t^16 + 30017590302230539714063936921651752491328706216617/3407274880249664523371108150386224912951551628944*t^14 - 799379653032992909300170560248816493686913449563251/825346815223553352622739966582017096221879698426512*t^12 + 72919559584591226209252145582762132727640429584567197/970607854702898742684342200700452105156930525349578112*t^10 - 502016944460493173790442772363997756031687138329656997/129183283518790570752511259569417315900648610397717658240*t^8 + 1588287830425756719637448341563599377821082892925255/12918328351879057075251125956941731590064861039771765824*t^6 - 345684391748415199391757487212717285704177490751313/167938268574427741978264637440242510670843193517032955712*t^4 + 4595330573920825145463004006581280200651304763931/335876537148855483956529274880485021341686387034065911424*t^2 - 31534952433554567854034276737927190763506085/2086189671732021639481548291183136778519791223814073984
-------------------------------------------------
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:
| (0.97843964888199510446 - 2.6528191867479668211e-883j)  +/-  (4.68e-241, 4.68e-241j)
| (-0.99832037416984394053 + 1.2784374562543429743e-899j)  +/-  (1.26e-241, 1.26e-241j)
| (-0.93697787409570507852 - 3.1926508326254725098e-908j)  +/-  (3.63e-241, 3.63e-241j)
| (0.99832037416984394053 + 7.4117082114402886951e-913j)  +/-  (1.24e-241, 1.24e-241j)
| (0.90877598962425348466 + 9.4622653531343761613e-929j)  +/-  (2.02e-241, 2.02e-241j)
| (0.93697787409570507852 - 2.2537161073931550599e-930j)  +/-  (3.32e-241, 3.32e-241j)
| (-0.32578858192130330182 - 1.5842462051253970456e-952j)  +/-  (6.55e-250, 6.55e-250j)
| (-0.90877598962425348466 + 2.0246516941691453246e-943j)  +/-  (1.99e-241, 1.99e-241j)
| (-0.97843964888199510446 - 1.5638725624578022937e-942j)  +/-  (5e-241, 5e-241j)
| (0.99117777590470037198 + 5.9970415011450801326e-943j)  +/-  (3.41e-241, 3.41e-241j)
| (0.8759146438048195034 + 4.6690272578628356875e-954j)  +/-  (9.44e-242, 9.44e-242j)
| (-0.99117777590470037198 + 9.7910995043317266678e-961j)  +/-  (3.54e-241, 3.54e-241j)
| (-0.96028985649753623168 - 1.011663244416572624e-962j)  +/-  (5.2e-241, 5.2e-241j)
| (-0.79666647741362673959 + 8.6449996479001839238e-965j)  +/-  (1.07e-242, 1.07e-242j)
| (0.96028985649753623168 + 2.9973647746269433676e-963j)  +/-  (4.87e-241, 4.87e-241j)
| (0.83852801286566864936 - 1.7228480534269985737e-974j)  +/-  (3.43e-242, 3.43e-242j)
| (0.79666647741362673959 - 4.5211502834307065769e-978j)  +/-  (1.04e-242, 1.04e-242j)
| (-0.46124311661959894904 - 6.8486035763047854333e-986j)  +/-  (1.24e-247, 1.24e-247j)
| (-0.75038252812253361829 - 8.4282899236583415857e-980j)  +/-  (2.41e-243, 2.41e-243j)
| (-0.8759146438048195034 - 2.6163259938019489594e-980j)  +/-  (9.53e-242, 9.53e-242j)
| (0.64524043728326823552 - 1.7712317106320681721e-982j)  +/-  (8.56e-245, 8.56e-245j)
| (0.75038252812253361829 - 3.7232779075200711882e-983j)  +/-  (2.51e-243, 2.51e-243j)
| (0.18343464249564980494 - 8.5847912852719297197e-996j)  +/-  (1.93e-252, 1.93e-252j)
| (-0.83852801286566864936 - 5.19825280522551936e-989j)  +/-  (3.42e-242, 3.42e-242j)
| (-0.69981930882596395391 - 2.2512491695811043076e-991j)  +/-  (4.96e-244, 4.96e-244j)
| (0.25531276429021805999 - 3.8543747939741594549e-996j)  +/-  (3.92e-251, 3.92e-251j)
| (0.69981930882596395391 + 8.1858499856069077813e-994j)  +/-  (5.36e-244, 5.36e-244j)
| (0.46124311661959894904 - 9.4594615361695979884e-1001j)  +/-  (1.21e-247, 1.21e-247j)
| (-0.11050211792867690275 - 3.4073713980524813953e-1005j)  +/-  (9.11e-254, 9.11e-254j)
| (-0.64524043728326823552 + 6.2149106125999416001e-999j)  +/-  (8.45e-245, 8.45e-245j)
| (-0.25531276429021805999 - 4.2656035697949013822e-1006j)  +/-  (3.95e-251, 3.95e-251j)
| (0.39454119918649796261 - 1.6268906897508059366e-1002j)  +/-  (9.56e-249, 9.56e-249j)
| (0.5870066479770320582 - 6.0110718455378748972e-1001j)  +/-  (1.29e-245, 1.29e-245j)
| (0.036909197537821205694 - 4.3114176736970700127e-1007j)  +/-  (4.85e-255, 4.85e-255j)
| (-0.5870066479770320582 + 5.6667649894251838968e-1004j)  +/-  (1.14e-245, 1.14e-245j)
| (-0.39454119918649796261 + 2.51505957513609015e-1007j)  +/-  (9.42e-249, 9.42e-249j)
| (0.11050211792867690275 - 1.9689014725683981254e-1009j)  +/-  (9.29e-254, 9.29e-254j)
| (0.52553240991632898582 - 3.7652214105880646577e-1007j)  +/-  (1.32e-246, 1.32e-246j)
| (0.32578858192130330182 + 8.6188735522225440768e-1010j)  +/-  (6.37e-250, 6.37e-250j)
| (-0.18343464249564980494 - 1.4965372219706905042e-1014j)  +/-  (2.08e-252, 2.08e-252j)
| (-0.52553240991632898582 + 5.0843834615766553692e-1014j)  +/-  (1.38e-246, 1.38e-246j)
| (-0.036909197537821205694 - 1.889461471303229104e-1029j)  +/-  (6.88e-255, 6.88e-255j)
-------------------------------------------------
The weights are:
| (0.015481112931927699504 + 1.0900775139265145781e-883j)  +/-  (5.34e-76, 3.93e-192j)
| (0.0043073058318009849937 - 2.8512614709833966204e-886j)  +/-  (1.43e-76, 1.05e-192j)
| (0.025801211158868577671 - 5.3369724957294462022e-885j)  +/-  (1.35e-76, 9.89e-193j)
| (0.0043073058318009849937 - 2.8350372581996230925e-884j)  +/-  (1.01e-76, 7.39e-193j)
| (0.0305630692334546578 - 2.0352214621674597132e-883j)  +/-  (5.7e-77, 4.19e-193j)
| (0.025801211158868577671 + 2.4655313697161074466e-883j)  +/-  (8.68e-77, 6.38e-193j)
| (0.069667070322417190698 - 3.9397530659155593412e-884j)  +/-  (1.85e-78, 1.36e-194j)
| (0.0305630692334546578 + 7.5127066330743984592e-885j)  +/-  (2.91e-78, 2.14e-194j)
| (0.015481112931927699504 - 2.0986779033819878668e-885j)  +/-  (1.38e-78, 1.02e-194j)
| (0.0099640248265143818622 + 1.5830026779024211659e-883j)  +/-  (3.68e-78, 2.71e-194j)
| (0.035137430023215382115 + 1.802190804005964513e-883j)  +/-  (1.07e-79, 7.89e-196j)
| (0.0099640248265143818622 + 1.0237769495051483401e-885j)  +/-  (1.23e-78, 9.05e-195j)
| (0.020776216091852425023 + 3.5273560637989206486e-885j)  +/-  (8.08e-79, 5.94e-195j)
| (0.044086883919055377913 - 1.5106498004817559494e-884j)  +/-  (3.14e-81, 2.31e-197j)
| (0.020776216091852425023 - 3.7678608834788030945e-883j)  +/-  (4.15e-79, 3.06e-195j)
| (0.039629088942539748232 - 1.6286037607061397759e-883j)  +/-  (4.19e-81, 3.08e-197j)
| (0.044086883919055377913 + 1.4752252457613438095e-883j)  +/-  (4.51e-82, 3.32e-198j)
| (0.06555952945292333638 - 3.2052636104525121013e-884j)  +/-  (3.3e-84, 2.43e-200j)
| (0.048457612832959680245 + 1.7615484363128254155e-884j)  +/-  (3.54e-83, 2.6e-199j)
| (0.035137430023215382115 - 9.9640948905742095652e-885j)  +/-  (4.35e-82, 3.2e-198j)
| (0.056472448763332761813 - 1.1080485281778128875e-883j)  +/-  (6.67e-85, 4.91e-201j)
| (0.048457612832959680245 - 1.335368960383105485e-883j)  +/-  (1.58e-83, 1.16e-199j)
| (0.07246690464479600703 + 6.8729011747496143063e-884j)  +/-  (2.5e-87, 1.84e-203j)
| (0.039629088942539748232 + 1.2540708422051286838e-884j)  +/-  (2.4e-83, 1.76e-199j)
| (0.052624403514997722875 - 2.0123123406957656562e-884j)  +/-  (5.3e-85, 3.9e-201j)
| (0.071231698288719737798 - 7.369763718741982587e-884j)  +/-  (2.1e-87, 1.55e-203j)
| (0.052624403514997722875 + 1.2121086388738820931e-883j)  +/-  (3.84e-85, 2.82e-201j)
| (0.06555952945292333638 + 8.9222616375098404323e-884j)  +/-  (1.62e-87, 1.19e-203j)
| (0.07333237548230784498 + 5.0934880726441887395e-884j)  +/-  (7.29e-89, 5.36e-205j)
| (0.056472448763332761813 + 2.2738524611331492547e-884j)  +/-  (2.7e-87, 1.99e-203j)
| (0.071231698288719737798 + 4.3195654340475139265e-884j)  +/-  (1.19e-88, 8.77e-205j)
| (0.067784087451071915512 - 8.3845216164920197946e-884j)  +/-  (1.39e-88, 1.02e-204j)
| (0.059925324211799319064 + 1.0224871109455545188e-883j)  +/-  (6.59e-88, 4.85e-204j)
| (0.073780531349535542512 + 5.9316234677794805718e-884j)  +/-  (6.64e-90, 4.89e-206j)
| (0.059925324211799319064 - 2.5566843080283989939e-884j)  +/-  (2.49e-89, 1.83e-205j)
| (0.067784087451071915512 + 3.5657519769451611626e-884j)  +/-  (1.29e-89, 9.47e-206j)
| (0.07333237548230784498 - 6.3904505834217293926e-884j)  +/-  (3.69e-90, 2.71e-206j)
| (0.062951670725909705979 - 9.5206966254295511965e-884j)  +/-  (9.07e-90, 6.67e-206j)
| (0.069667070322417190698 + 7.8730234746868126008e-884j)  +/-  (2.81e-90, 2.07e-206j)
| (0.07246690464479600703 - 4.7027383968069671448e-884j)  +/-  (6.69e-91, 4.98e-207j)
| (0.062951670725909705979 + 2.8670695020081156895e-884j)  +/-  (5.43e-91, 4.2e-207j)
| (0.073780531349535542512 - 5.5003796385000856365e-884j)  +/-  (6.21e-91, 4.5e-207j)
