Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 256*t^60 - 1473581004404202414899914318723652556988991685672352073434272298240/7325079701492144457860066035142819399915536933854848280742289*t^58 + 12398302016446704198343457930783408141744702390346348776704317353239488/168476833134319322530781518808284846198057349478661510457072647*t^56 - 2808001636188806674245154430787337556027086820325444260691798269458821760/168476833134319322530781518808284846198057349478661510457072647*t^54 + 4859283159160525182261144551865270664114056132884555267265754675544185357840/1853245164477512547838596706891133308178630844265276615027799117*t^52 - 564759965997788725762871002504244174864750114207240233510946976716180510934960/1853245164477512547838596706891133308178630844265276615027799117*t^50 + 50353802796829691088713380927183131638015982972287196175232126354206538974666500/1853245164477512547838596706891133308178630844265276615027799117*t^48 - 75118328827304828001111344087476593569768602455437182393986559750110102934981200/39430748180372607400821206529598581025077252005644183298463811*t^46 + 183164117362646837566659851854300700934107034239798733411838900268044207710332625/1714380355668374234818313327373851348916402261114964491237557*t^44 - 755786176455459458775295346290590978045511654885230700942541295216146576928889875/155852759606215839528937575215804668083309296464996771930687*t^42 + 111959464735239724879696508359054585594091757196807886908738660221099309891410176875/623411038424863358115750300863218672333237185859987087722748*t^40 - 1700597362307049249246911085796104821484977168007031790429909917707200834899415791875/311705519212431679057875150431609336166618592929993543861374*t^38 + 340086319794443832287674309310733438936957841327502074730424141594617959356974881731375/2493644153699453432463001203452874689332948743439948350890992*t^36 - 7004273650877085970956366243898870724517835309156414051064645180319560951793640358645625/2493644153699453432463001203452874689332948743439948350890992*t^34 + 475228416854933251091486505357214673468134916964991862723299167741735588243246126934989375/9974576614797813729852004813811498757331794973759793403563968*t^32 - 828225146537016529099452647096889712772530365407135157076908154399041151085293644042279375/1246822076849726716231500601726437344666474371719974175445496*t^30 + 302669267545397513385187093305640352725708143339084463363717577363684431751588620690382578125/39898306459191254919408019255245995029327179895039173614255872*t^28 - 2816708941253275464591540395278386205238571868289369512166662584901535692964613645951139805625/39898306459191254919408019255245995029327179895039173614255872*t^26 + 84853117487165995289771516358200351370425468928060151446441567562667102692114783487934025453125/159593225836765019677632077020983980117308719580156694457023488*t^24 - 256259533792049486401549152839623053639086560161599510729858290374232067584908145257893555671875/79796612918382509838816038510491990058654359790078347228511744*t^22 + 9817043081187371480996957239025888481469113174899073256896718755166141116900962431899872055890625/638372903347060078710528308083935920469234878320626777828093952*t^20 - 36726635151161669212731227963253830394845828214628019581088467010334069678061898621297074489921875/638372903347060078710528308083935920469234878320626777828093952*t^18 + 421375745228031192504512129171797388191384912544280244703762160436519523408875218758208711141890625/2553491613388240314842113232335743681876939513282507111312375808*t^16 - 226100341270559575766066379368071454768090435794543431665553336201935970642220870266932617901015625/638372903347060078710528308083935920469234878320626777828093952*t^14 + 5626614761059941758480048865013894378912319708868391855931952237199398507946560270796042668965390625/10213966453552961259368452929342974727507758053130028445249503232*t^12 - 6072201530082497837665135428754728208127536196690121308510948754764177949021252272059803999466265625/10213966453552961259368452929342974727507758053130028445249503232*t^10 + 17109300873389728060545719601904215555991158014284945842641828315980802073353672654918555277026015625/40855865814211845037473811717371898910031032212520113780998012928*t^8 - 3590505489056996545729446091320405639183224317947797038426199024707611003614626144449798707654578125/20427932907105922518736905858685949455015516106260056890499006464*t^6 + 6186136961756321005682642729949457955223740295102790141549654489435140960378190292219997899378203125/163423463256847380149895246869487595640124128850080455123992051712*t^4 - 510966722017059019889951667810344058796231377953931104363416489288951206587059258802623064553046875/163423463256847380149895246869487595640124128850080455123992051712*t^2 + 27077472360149925476280981184928082352346914965155478086889387508274663917451207444473888069453125/653693853027389520599580987477950382560496515400321820495968206848
-------------------------------------------------
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
Positive weights:   60 out of 60
Indefinite weights: 0 out of 60
Negative weights:   0 out of 60
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-5.4510129178808723774 + 9.7990569202389356108e-937j)  +/-  (2.5e-241, 2.5e-241j)
| (9.7980257046341028445 - 1.0073955661220835786e-945j)  +/-  (2.11e-245, 2.11e-245j)
| (8.1420321122987225934 - 2.1733859884316407591e-943j)  +/-  (1.26e-242, 1.26e-242j)
| (6.5157523939136897752 - 2.9700691692622094393e-941j)  +/-  (2.52e-241, 2.52e-241j)
| (-8.1420321122987225934 + 9.4877273143001582251e-941j)  +/-  (1.43e-242, 1.43e-242j)
| (7.2878620070704774388 - 6.702181084844918975e-946j)  +/-  (9.36e-242, 9.36e-242j)
| (-8.6190177803165666573 - 4.3529566874375751046e-945j)  +/-  (2.91e-243, 2.91e-243j)
| (4.4596482103205981912 - 8.878083742320113224e-950j)  +/-  (5.43e-242, 5.43e-242j)
| (-7.7018137855281839894 - 2.3305251330104194833e-951j)  +/-  (4.32e-242, 4.32e-242j)
| (-9.7980257046341028445 + 1.1080272994201519116e-961j)  +/-  (2.06e-245, 2.06e-245j)
| (9.1531781455371981935 + 4.9290925698115842331e-961j)  +/-  (3.57e-244, 3.57e-244j)
| (-3.5213810453825141163 + 6.3164839562783822502e-959j)  +/-  (3.51e-243, 3.51e-243j)
| (-0.89280795760828243268 + 1.548314575602979541e-975j)  +/-  (6.9e-251, 6.9e-251j)
| (-1.7048666507395020204 + 8.9039239680832153034e-972j)  +/-  (1.09e-247, 1.09e-247j)
| (-6.5157523939136897752 - 2.2363863713727106713e-965j)  +/-  (2.61e-241, 2.61e-241j)
| (5.1138088241961862721 - 1.0504172176841081272e-977j)  +/-  (1.53e-241, 1.53e-241j)
| (-7.2878620070704774388 + 7.1733445139430646521e-983j)  +/-  (9.54e-242, 9.54e-242j)
| (5.4510129178808723774 - 4.391798020402490423e-991j)  +/-  (2.51e-241, 2.51e-241j)
| (-3.2207147698668776614 - 4.7914527345208867946e-995j)  +/-  (1.13e-243, 1.13e-243j)
| (6.8938871296406277655 + 1.0445220103708273085e-991j)  +/-  (1.78e-241, 1.78e-241j)
| (3.8286233299284196978 - 1.8297215967113660979e-999j)  +/-  (9.31e-243, 9.31e-243j)
| (2.4639525936596353521 + 2.6581227145316143326e-1002j)  +/-  (5.71e-245, 5.71e-245j)
| (5.7961819502524092624 - 8.7205136669888163975e-998j)  +/-  (2.95e-241, 2.95e-241j)
| (-6.1505589760945873323 + 1.0997949084248650661e-1005j)  +/-  (3.01e-241, 3.01e-241j)
| (-9.1531781455371981935 + 1.8107483151942014025e-1023j)  +/-  (3.86e-244, 3.86e-244j)
| (8.6190177803165666573 + 1.1713718539712240177e-1022j)  +/-  (2.91e-243, 2.91e-243j)
| (3.2207147698668776614 - 1.8223221077799563337e-1022j)  +/-  (1.12e-243, 1.12e-243j)
| (7.7018137855281839894 + 3.9897560079447863468e-1021j)  +/-  (4.17e-242, 4.17e-242j)
| (6.1505589760945873323 - 7.3846779804954561357e-1021j)  +/-  (3e-241, 3e-241j)
| (-0.63520047361450412632 - 1.9795896472981313724e-1030j)  +/-  (5.87e-252, 5.87e-252j)
| (-4.4596482103205981912 - 3.0112002962885218102e-1019j)  +/-  (5.12e-242, 5.12e-242j)
| (-2.6679307998580831053 + 9.7089252768583476999e-1027j)  +/-  (1.49e-244, 1.49e-244j)
| (1.9816567566958429259 - 4.3862991612126810413e-1029j)  +/-  (1.17e-246, 1.17e-246j)
| (3.5213810453825141163 + 1.0490765545165710241e-1026j)  +/-  (3.33e-243, 3.33e-243j)
| (-2.2465154758305637263 - 2.988692223207495022e-1028j)  +/-  (1.04e-245, 1.04e-245j)
| (-3.8286233299284196978 - 2.4107978121629562729e-1023j)  +/-  (9.11e-243, 9.11e-243j)
| (-5.7961819502524092624 - 9.6884390734821822888e-1025j)  +/-  (2.93e-241, 2.93e-241j)
| (1.4285943295727714646 + 5.3171770115428176647e-1043j)  +/-  (1.05e-248, 1.05e-248j)
| (1.7048666507395020204 - 3.3753488246072112412e-1042j)  +/-  (1.11e-247, 1.11e-247j)
| (-2.9306374202572440192 + 9.7927491468279591268e-1038j)  +/-  (3.99e-244, 3.99e-244j)
| (-1.9816567566958429259 - 1.427896671196133924e-1040j)  +/-  (1.18e-246, 1.18e-246j)
| (4.7836015815857536733 - 2.5579039444082656721e-1036j)  +/-  (1.05e-241, 1.05e-241j)
| (1.1571937124467801947 - 1.9075715560007965639e-1043j)  +/-  (9.33e-250, 9.33e-250j)
| (-6.8938871296406277655 + 8.6260735156274515883e-1035j)  +/-  (1.7e-241, 1.7e-241j)
| (-4.1414168694371171923 - 2.6972994597717803088e-1042j)  +/-  (2.36e-242, 2.36e-242j)
| (-1.4285943295727714646 + 6.9927733549735768729e-1051j)  +/-  (1.09e-248, 1.09e-248j)
| (-5.1138088241961862721 + 3.1962098550750089053e-1045j)  +/-  (1.57e-241, 1.57e-241j)
| (2.6679307998580831053 + 1.2362679125703503133e-1056j)  +/-  (1.55e-244, 1.55e-244j)
| (0.89280795760828243268 - 3.0060215682643447802e-1060j)  +/-  (7.14e-251, 7.14e-251j)
| (-0.38118699020732211685 + 1.4163319060408531434e-1062j)  +/-  (4.15e-253, 4.15e-253j)
| (2.9306374202572440192 + 5.4845881665619516673e-1054j)  +/-  (4.05e-244, 4.05e-244j)
| (-1.1571937124467801947 - 3.1899925028813917958e-1059j)  +/-  (8.22e-250, 8.22e-250j)
| (4.1414168694371171923 + 2.9769547605446225313e-1056j)  +/-  (2.24e-242, 2.24e-242j)
| (0.12725180284799686188 - 6.63293066505610748e-1067j)  +/-  (3.6e-254, 3.6e-254j)
| (0.63520047361450412632 - 3.9291461827963074296e-1064j)  +/-  (6.17e-252, 6.17e-252j)
| (-4.7836015815857536733 - 3.1625969649682292873e-1061j)  +/-  (9.78e-242, 9.78e-242j)
| (-2.4639525936596353521 - 2.3918254523701588474e-1069j)  +/-  (5.31e-245, 5.31e-245j)
| (-0.12725180284799686188 - 1.8104445572277651341e-1077j)  +/-  (3.6e-254, 3.6e-254j)
| (2.2465154758305637263 + 2.0445671919351717771e-1071j)  +/-  (1.07e-245, 1.07e-245j)
| (0.38118699020732211685 + 4.9139615887601274887e-1078j)  +/-  (4.1e-253, 4.1e-253j)
-------------------------------------------------
The weights are:
| (2.3974965342998674911e-14 + 1.474180529791071496e-949j)  +/-  (7.85e-63, 1.72e-181j)
| (8.5235748689056227706e-43 - 7.5291660222409250313e-967j)  +/-  (3.85e-78, 8.44e-197j)
| (4.1701403537072118646e-30 + 4.0345564425011607014e-960j)  +/-  (1.38e-73, 3.03e-192j)
| (7.640365306068588782e-20 + 1.5990845971274912851e-954j)  +/-  (1.66e-68, 3.65e-187j)
| (4.1701403537072118646e-30 + 2.0379624451897621648e-959j)  +/-  (2.04e-75, 4.47e-194j)
| (1.9508481346456885178e-24 + 4.6995542980534750228e-957j)  +/-  (1.58e-71, 3.46e-190j)
| (1.5432760992827672547e-33 - 2.6248182186795635982e-961j)  +/-  (4.08e-77, 8.95e-196j)
| (4.1735965535032309015e-10 + 7.947787878218657449e-949j)  +/-  (2.12e-62, 4.65e-181j)
| (4.1606742013130332042e-27 - 9.7227083028843507973e-958j)  +/-  (1.64e-74, 3.6e-193j)
| (8.5235748689056227706e-43 - 2.6411839285412494372e-966j)  +/-  (1.98e-81, 4.35e-200j)
| (1.3353930502268506186e-37 + 4.1245234808548887513e-964j)  +/-  (3.84e-79, 8.42e-198j)
| (7.0689596107556725273e-07 + 5.7897724426793401497e-946j)  +/-  (4.64e-60, 1.02e-178j)
| (0.066278572057202030574 + 7.3513785813189687228e-943j)  +/-  (9.41e-46, 2.06e-164j)
| (0.0085596763744523780018 - 2.2832728373422415006e-943j)  +/-  (9.41e-46, 2.06e-164j)
| (7.640365306068588782e-20 + 1.7972166332904680452e-953j)  +/-  (6.22e-72, 1.36e-190j)
| (8.2670731329247478633e-13 + 1.744205067003090546e-950j)  +/-  (8.46e-68, 1.85e-186j)
| (1.9508481346456885178e-24 + 3.2592307636183003666e-956j)  +/-  (4.16e-74, 9.11e-193j)
| (2.3974965342998674911e-14 - 2.1549420157682380827e-951j)  +/-  (3.44e-69, 7.54e-188j)
| (5.2305827863317608608e-06 - 2.3588785785052412431e-945j)  +/-  (9.94e-61, 2.18e-179j)
| (4.9807702145699538839e-22 - 9.8202717858167326984e-956j)  +/-  (8.34e-74, 1.83e-192j)
| (7.5311641707398751104e-08 + 2.4692316070329698279e-947j)  +/-  (5.11e-65, 1.12e-183j)
| (0.00024698749017601060177 - 3.1895233567323494766e-944j)  +/-  (6.64e-59, 1.46e-177j)
| (5.0638742503276099353e-16 + 2.3091814708461905214e-952j)  +/-  (9e-71, 1.97e-189j)
| (7.5511176715073129113e-18 - 3.4932821997960614351e-952j)  +/-  (4.03e-74, 8.85e-193j)
| (1.3353930502268506186e-37 + 1.6270307542036012448e-963j)  +/-  (1.17e-82, 2.57e-201j)
| (1.5432760992827672547e-33 - 5.9100300974036734393e-962j)  +/-  (1.65e-80, 3.62e-199j)
| (5.2305827863317608608e-06 + 6.0668464389414721414e-946j)  +/-  (4.12e-65, 9.03e-184j)
| (4.1606742013130332042e-27 - 1.6638135974990758409e-958j)  +/-  (1.78e-77, 3.89e-196j)
| (7.5511176715073129113e-18 - 2.1063706173121779577e-953j)  +/-  (1.02e-72, 2.23e-191j)
| (0.096142673529808278921 - 9.5820191488099513093e-943j)  +/-  (6.45e-59, 1.41e-177j)
| (4.1735965535032309015e-10 - 7.9453895805398014982e-948j)  +/-  (6.45e-73, 1.41e-191j)
| (0.00010770622180695934874 - 3.7832431546863395348e-944j)  +/-  (3.18e-66, 6.98e-185j)
| (0.0030496814938923475186 - 7.3993001091998520051e-944j)  +/-  (1.98e-62, 4.35e-181j)
| (7.0689596107556725273e-07 - 1.2451674771828228122e-946j)  +/-  (1.84e-67, 4.04e-186j)
| (0.00090207862961407231417 - 1.2135824081904739525e-943j)  +/-  (7.52e-65, 1.65e-183j)
| (7.5311641707398751104e-08 - 1.4123341481001797483e-946j)  +/-  (6.05e-71, 1.33e-189j)
| (5.0638742503276099353e-16 + 7.5243614945821684894e-951j)  +/-  (1.17e-76, 2.56e-195j)
| (0.0201077444050912083 - 2.0135353052151860381e-943j)  +/-  (4.04e-62, 8.87e-181j)
| (0.0085596763744523780018 + 1.1953072967540452313e-943j)  +/-  (2.17e-63, 4.75e-182j)
| (2.9558819239900576782e-05 + 9.765531110646259153e-945j)  +/-  (2.49e-68, 5.47e-187j)
| (0.0030496814938923475186 + 1.5852089826073730234e-943j)  +/-  (1.11e-65, 2.44e-184j)
| (2.1283606655000543129e-11 - 1.2445838490610382265e-949j)  +/-  (3.71e-73, 8.15e-192j)
| (0.039641898621365187041 + 3.3528194404548748044e-943j)  +/-  (2.26e-63, 4.97e-182j)
| (4.9807702145699538839e-22 - 8.40203119913325879e-955j)  +/-  (4.97e-80, 1.09e-198j)
| (6.334047154110054112e-09 + 3.3770242320408659076e-947j)  +/-  (5.02e-73, 1.1e-191j)
| (0.0201077444050912083 + 3.443781492350834258e-943j)  +/-  (1.19e-66, 2.61e-185j)
| (8.2670731329247478633e-13 - 5.4647021068170898301e-949j)  +/-  (5.71e-76, 1.25e-194j)
| (0.00010770622180695934874 + 1.2968532600265790847e-944j)  +/-  (1.78e-70, 3.9e-189j)
| (0.066278572057202030574 - 5.2821624396903177994e-943j)  +/-  (3.4e-67, 7.46e-186j)
| (0.12371820585046101429 + 1.1187405359202209735e-942j)  +/-  (3.45e-67, 7.48e-186j)
| (2.9558819239900576782e-05 - 2.9365113533943957938e-945j)  +/-  (3.08e-71, 6.75e-190j)
| (0.039641898621365187041 - 5.1600034437207437157e-943j)  +/-  (1e-67, 2.15e-186j)
| (6.334047154110054112e-09 - 4.610447762269389582e-948j)  +/-  (3.85e-74, 8.46e-193j)
| (0.14120919694295988538 + 1.1200906053737189716e-942j)  +/-  (3.25e-68, 6.88e-187j)
| (0.096142673529808278921 + 7.5819242718262053514e-943j)  +/-  (1.37e-68, 2.95e-187j)
| (2.1283606655000543129e-11 + 1.9085422108773255107e-948j)  +/-  (4.59e-76, 1e-194j)
| (0.00024698749017601060177 + 8.4514404712492972625e-944j)  +/-  (1.33e-70, 2.94e-189j)
| (0.14120919694295988538 - 1.1736367804250281493e-942j)  +/-  (6.53e-69, 1.34e-187j)
| (0.00090207862961407231417 + 5.0521702379695922534e-944j)  +/-  (8.38e-71, 2.08e-189j)
| (0.12371820585046101429 - 9.725009447160695941e-943j)  +/-  (3.4e-69, 6.25e-188j)
