Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^60 - 11512351596907831366405580615028535601476497544315250573705252330/7325079701492144457860066035142819399915536933854848280742289*t^58 + 193723469006979753099116530168490752214760974849161699636004958644367/168476833134319322530781518808284846198057349478661510457072647*t^56 - 87750051130900208570161075962104298625846463135170133146618695920588180/168476833134319322530781518808284846198057349478661510457072647*t^54 + 303705197447532823891321534491579416507128508305284704204109667221511584865/1853245164477512547838596706891133308178630844265276615027799117*t^52 - 70594995749723590720358875313030521858093764275905029188868372089522563866870/1853245164477512547838596706891133308178630844265276615027799117*t^50 + 12588450699207422772178345231795782909503995743071799043808031588551634743666625/1853245164477512547838596706891133308178630844265276615027799117*t^48 - 37559164413652414000555672043738296784884301227718591196993279875055051467490600/39430748180372607400821206529598581025077252005644183298463811*t^46 + 183164117362646837566659851854300700934107034239798733411838900268044207710332625/1714380355668374234818313327373851348916402261114964491237557*t^44 - 1511572352910918917550590692581181956091023309770461401885082590432293153857779750/155852759606215839528937575215804668083309296464996771930687*t^42 + 111959464735239724879696508359054585594091757196807886908738660221099309891410176875/155852759606215839528937575215804668083309296464996771930687*t^40 - 6802389449228196996987644343184419285939908672028127161719639670828803339597663167500/155852759606215839528937575215804668083309296464996771930687*t^38 + 340086319794443832287674309310733438936957841327502074730424141594617959356974881731375/155852759606215839528937575215804668083309296464996771930687*t^36 - 14008547301754171941912732487797741449035670618312828102129290360639121903587280717291250/155852759606215839528937575215804668083309296464996771930687*t^34 + 475228416854933251091486505357214673468134916964991862723299167741735588243246126934989375/155852759606215839528937575215804668083309296464996771930687*t^32 - 13251602344592264465591242353550235404360485846514162513230530470384658417364698304676470000/155852759606215839528937575215804668083309296464996771930687*t^30 + 302669267545397513385187093305640352725708143339084463363717577363684431751588620690382578125/155852759606215839528937575215804668083309296464996771930687*t^28 - 5633417882506550929183080790556772410477143736578739024333325169803071385929227291902279611250/155852759606215839528937575215804668083309296464996771930687*t^26 + 84853117487165995289771516358200351370425468928060151446441567562667102692114783487934025453125/155852759606215839528937575215804668083309296464996771930687*t^24 - 1025038135168197945606196611358492214556346240646398042919433161496928270339632581031574222687500/155852759606215839528937575215804668083309296464996771930687*t^22 + 9817043081187371480996957239025888481469113174899073256896718755166141116900962431899872055890625/155852759606215839528937575215804668083309296464996771930687*t^20 - 73453270302323338425462455926507660789691656429256039162176934020668139356123797242594148979843750/155852759606215839528937575215804668083309296464996771930687*t^18 + 421375745228031192504512129171797388191384912544280244703762160436519523408875218758208711141890625/155852759606215839528937575215804668083309296464996771930687*t^16 - 1808802730164476606128531034944571638144723486356347453324426689615487765137766962135460943208125000/155852759606215839528937575215804668083309296464996771930687*t^14 + 5626614761059941758480048865013894378912319708868391855931952237199398507946560270796042668965390625/155852759606215839528937575215804668083309296464996771930687*t^12 - 12144403060164995675330270857509456416255072393380242617021897509528355898042504544119607998932531250/155852759606215839528937575215804668083309296464996771930687*t^10 + 17109300873389728060545719601904215555991158014284945842641828315980802073353672654918555277026015625/155852759606215839528937575215804668083309296464996771930687*t^8 - 14362021956227986182917784365281622556732897271791188153704796098830444014458504577799194830618312500/155852759606215839528937575215804668083309296464996771930687*t^6 + 6186136961756321005682642729949457955223740295102790141549654489435140960378190292219997899378203125/155852759606215839528937575215804668083309296464996771930687*t^4 - 1021933444034118039779903335620688117592462755907862208726832978577902413174118517605246129106093750/155852759606215839528937575215804668083309296464996771930687*t^2 + 27077472360149925476280981184928082352346914965155478086889387508274663917451207444473888069453125/155852759606215839528937575215804668083309296464996771930687
-------------------------------------------------
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: 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
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:
| (-12.189131839258538079 - 1.0346597810907493734e-635j)  +/-  (4.27e-243, 4.27e-243j)
| (-12.944548672235720908 + 5.9004721519871225727e-640j)  +/-  (5.7e-244, 5.7e-244j)
| (11.514572238490112355 + 1.9694520154481423986e-647j)  +/-  (1.97e-242, 1.97e-242j)
| (10.892009510366025721 + 6.6411917734849235972e-647j)  +/-  (6.12e-242, 6.12e-242j)
| (13.856500835973749369 + 5.8481488611128545736e-650j)  +/-  (2.93e-245, 2.93e-245j)
| (12.189131839258538079 - 2.3755199236467784755e-648j)  +/-  (3.79e-243, 3.79e-243j)
| (-13.856500835973749369 - 2.5556660346588661973e-645j)  +/-  (2.75e-245, 2.75e-245j)
| (-10.306593291102674315 + 1.1655278309881113627e-650j)  +/-  (1.36e-241, 1.36e-241j)
| (7.7088963971380679471 - 1.8744845836227601828e-667j)  +/-  (3.55e-241, 3.55e-241j)
| (9.7494286762071031272 + 2.2104330430335958843e-668j)  +/-  (2.43e-241, 2.43e-241j)
| (10.306593291102674315 - 1.4201851981333560629e-669j)  +/-  (1.39e-241, 1.39e-241j)
| (9.2146654045377012949 - 2.5370370962027425289e-668j)  +/-  (3.68e-241, 3.68e-241j)
| (12.944548672235720908 - 3.403025499875359398e-678j)  +/-  (5.21e-244, 5.21e-244j)
| (-10.892009510366025721 - 7.7857779351484974813e-674j)  +/-  (5.99e-242, 5.99e-242j)
| (8.6982039201685423015 + 2.1469746105852710716e-686j)  +/-  (4.32e-241, 4.32e-241j)
| (-5.4144910384028120339 + 4.08362309973756811e-689j)  +/-  (1.29e-242, 1.29e-242j)
| (3.1770526540006302369 - 2.2869397916527615129e-700j)  +/-  (1.45e-245, 1.45e-245j)
| (8.1970391240290932896 - 1.5929200437322733096e-694j)  +/-  (4.06e-241, 4.06e-241j)
| (-11.514572238490112355 + 4.1323622011666960535e-708j)  +/-  (1.89e-242, 1.89e-242j)
| (4.1445471861258943321 + 6.0738463860288366359e-727j)  +/-  (5.48e-244, 5.48e-244j)
| (7.2320177945614571275 - 3.50751691283258607e-725j)  +/-  (2.48e-241, 2.48e-241j)
| (2.0203374760111125422 + 1.9635582103119845389e-742j)  +/-  (1.49e-248, 1.49e-248j)
| (-8.1970391240290932896 - 4.40158136066533589e-733j)  +/-  (3.99e-241, 3.99e-241j)
| (-6.3068949824482909966 - 2.6651445145472705915e-755j)  +/-  (7.05e-242, 7.05e-242j)
| (-3.1770526540006302369 + 3.4420647895104686919e-772j)  +/-  (1.45e-245, 1.45e-245j)
| (-9.2146654045377012949 + 1.7411408967439921733e-771j)  +/-  (3.6e-241, 3.6e-241j)
| (0.89830912461144504704 - 1.5403077229488267937e-799j)  +/-  (8.61e-252, 8.61e-252j)
| (2.8024858612875416991 + 6.1572361993744120383e-795j)  +/-  (1.63e-246, 1.63e-246j)
| (4.979984832663498774 + 3.5648438030728621539e-792j)  +/-  (4.79e-243, 4.79e-243j)
| (-2.8024858612875416991 + 1.1430236325184954754e-793j)  +/-  (1.84e-246, 1.84e-246j)
| (6.3068949824482909966 - 2.051259082820802997e-790j)  +/-  (6.81e-242, 6.81e-242j)
| (1.2626211222442563283 + 1.2042239053031314264e-798j)  +/-  (1.01e-250, 1.01e-250j)
| (1.6365190424351079992 + 1.2910773854986772908e-797j)  +/-  (1.24e-249, 1.24e-249j)
| (2.4110455395133983927 - 4.139447610446179757e-796j)  +/-  (1.58e-247, 1.58e-247j)
| (-2.0203374760111125422 - 2.6162798161064739677e-796j)  +/-  (1.52e-248, 1.52e-248j)
| (-4.979984832663498774 - 3.1780549448673630763e-791j)  +/-  (4.39e-243, 4.39e-243j)
| (-7.7088963971380679471 - 4.5481925074098759588e-788j)  +/-  (3.44e-241, 3.44e-241j)
| (4.5547785080810800576 + 7.2906094311565940094e-812j)  +/-  (1.56e-243, 1.56e-243j)
| (3.7730239206322005748 + 2.9409452313296504141e-812j)  +/-  (1.95e-244, 1.95e-244j)
| (-7.2320177945614571275 - 3.8335588603848895566e-807j)  +/-  (2.41e-241, 2.41e-241j)
| (-0.89830912461144504704 - 1.3980703449544846891e-833j)  +/-  (8.18e-252, 8.18e-252j)
| (-3.4845551749978200401 + 1.3574543030138727433e-826j)  +/-  (7.16e-245, 7.16e-245j)
| (5.4144910384028120339 - 1.1905336091975619974e-822j)  +/-  (1.35e-242, 1.35e-242j)
| (-1.2626211222442563283 + 7.3953107160020079718e-832j)  +/-  (1.09e-250, 1.09e-250j)
| (6.7650342336679603763 - 6.369371135705827212e-822j)  +/-  (1.45e-241, 1.45e-241j)
| (-3.7730239206322005748 - 5.4466336124428371426e-827j)  +/-  (2.02e-244, 2.02e-244j)
| (-1.6365190424351079992 + 1.0566729820181158425e-846j)  +/-  (1.45e-249, 1.45e-249j)
| (-2.4110455395133983927 + 8.5942718558507999021e-840j)  +/-  (1.51e-247, 1.51e-247j)
| (-8.6982039201685423015 - 3.3553894996069247574e-839j)  +/-  (4.25e-241, 4.25e-241j)
| (-9.7494286762071031272 + 1.7404866387556969073e-865j)  +/-  (2.77e-241, 2.77e-241j)
| (0.1799612254240644042 + 8.7634663085291450015e-890j)  +/-  (4.91e-254, 4.91e-254j)
| (-6.7650342336679603763 - 3.0134566037473082227e-876j)  +/-  (1.35e-241, 1.35e-241j)
| (-0.53907981135137510807 - 1.1928512275816325125e-892j)  +/-  (5.94e-253, 5.94e-253j)
| (-4.1445471861258943321 + 3.1313995365948877353e-882j)  +/-  (5.15e-244, 5.15e-244j)
| (5.8568479041986965685 + 2.2219008681927123998e-881j)  +/-  (3.08e-242, 3.08e-242j)
| (-4.5547785080810800576 - 4.6509678783404626903e-882j)  +/-  (1.53e-243, 1.53e-243j)
| (-0.1799612254240644042 - 2.5541868213845113406e-892j)  +/-  (3.13e-254, 3.13e-254j)
| (-5.8568479041986965685 - 1.94336906154929898e-879j)  +/-  (3.14e-242, 3.14e-242j)
| (3.4845551749978200401 - 1.7361549214946403834e-884j)  +/-  (7.89e-245, 7.89e-245j)
| (0.53907981135137510807 - 4.7868664332616412094e-892j)  +/-  (5.3e-253, 5.3e-253j)
-------------------------------------------------
The weights are:
| (1.5432760992827672547e-33 - 1.0277852205866798627e-667j)  +/-  (1.64e-59, 1.84e-181j)
| (1.3353930502268506186e-37 - 1.5311562503392762654e-670j)  +/-  (4.59e-61, 5.15e-183j)
| (4.1701403537072118646e-30 - 4.4427643796427264089e-668j)  +/-  (6.49e-60, 7.29e-182j)
| (4.1606742013130332042e-27 + 1.8206357947659077485e-666j)  +/-  (9.24e-59, 1.04e-180j)
| (8.5235748689056227706e-43 + 8.4646907103731128354e-675j)  +/-  (9.2e-66, 1.03e-187j)
| (1.5432760992827672547e-33 + 6.5499618023738548236e-670j)  +/-  (8.45e-62, 9.49e-184j)
| (8.5235748689056227706e-43 + 1.322252852107095933e-673j)  +/-  (1.15e-66, 1.29e-188j)
| (1.9508481346456885178e-24 + 6.1066220850636974675e-664j)  +/-  (3.64e-60, 4.08e-182j)
| (2.3974965342998674911e-14 + 2.267193610114553194e-659j)  +/-  (9.26e-54, 1.04e-175j)
| (4.9807702145699538839e-22 + 1.061111413976574615e-663j)  +/-  (3.16e-58, 3.55e-180j)
| (1.9508481346456885178e-24 - 5.1102822923809834516e-665j)  +/-  (3.47e-59, 3.89e-181j)
| (7.640365306068588782e-20 - 1.7167589768860271544e-662j)  +/-  (1.03e-57, 1.15e-179j)
| (1.3353930502268506186e-37 - 4.6020562107010939406e-672j)  +/-  (6.18e-66, 6.93e-188j)
| (4.1606742013130332042e-27 - 3.239662029008491404e-665j)  +/-  (3.01e-66, 3.38e-188j)
| (7.5511176715073129113e-18 + 2.2465873753857188263e-661j)  +/-  (2.52e-57, 2.82e-179j)
| (7.5311641707398751104e-08 + 6.4947540553883376304e-655j)  +/-  (4.87e-55, 5.46e-177j)
| (0.00090207862961407231417 - 4.8598127027567701741e-652j)  +/-  (9.88e-44, 1.11e-165j)
| (5.0638742503276099353e-16 - 2.4463703058368231581e-660j)  +/-  (7.97e-57, 8.94e-179j)
| (4.1701403537072118646e-30 + 1.561165370090687831e-666j)  +/-  (4.18e-68, 4.69e-190j)
| (2.9558819239900576782e-05 + 2.8935665676129994163e-653j)  +/-  (3.22e-49, 3.62e-171j)
| (8.2670731329247478633e-13 - 1.8219681499406914901e-658j)  +/-  (4.07e-56, 4.56e-178j)
| (0.0201077444050912083 + 1.8719806633761385975e-651j)  +/-  (4.02e-39, 4.51e-161j)
| (5.0638742503276099353e-16 + 1.2492726259034699368e-659j)  +/-  (5.19e-64, 5.83e-186j)
| (4.1735965535032309015e-10 + 2.5713578167105524396e-656j)  +/-  (4.33e-60, 4.86e-182j)
| (0.00090207862961407231417 + 8.2862984405643243936e-652j)  +/-  (2.97e-50, 3.33e-172j)
| (7.640365306068588782e-20 + 1.2353529841444480098e-661j)  +/-  (1.15e-65, 1.29e-187j)
| (0.096142673529808278921 - 6.7706165840271944052e-651j)  +/-  (3.22e-39, 3.61e-161j)
| (0.0030496814938923475186 + 7.0443882428051681509e-652j)  +/-  (3.37e-46, 3.78e-168j)
| (7.0689596107556725273e-07 + 1.2495233841025533521e-654j)  +/-  (1.78e-54, 2e-176j)
| (0.0030496814938923475186 - 1.1250746498086160384e-651j)  +/-  (1.15e-49, 1.29e-171j)
| (4.1735965535032309015e-10 - 8.1776136421890110291e-657j)  +/-  (2.24e-57, 2.52e-179j)
| (0.066278572057202030574 + 4.783437627178135874e-651j)  +/-  (3.21e-39, 3.6e-161j)
| (0.039641898621365187041 - 3.0772623473872024596e-651j)  +/-  (7.6e-42, 8.53e-164j)
| (0.0085596763744523780018 - 1.1249695754665567013e-651j)  +/-  (1.74e-45, 1.95e-167j)
| (0.0201077444050912083 - 2.6158314002017238073e-651j)  +/-  (2.51e-47, 2.82e-169j)
| (7.0689596107556725273e-07 - 2.975832275042370863e-654j)  +/-  (1e-58, 1.13e-180j)
| (2.3974965342998674911e-14 - 1.0069265669186341277e-658j)  +/-  (6.27e-65, 7.03e-187j)
| (5.2305827863317608608e-06 - 6.0334817024283831223e-654j)  +/-  (1.07e-54, 1.2e-176j)
| (0.00010770622180695934874 - 1.2666455681419489366e-652j)  +/-  (1.22e-52, 1.37e-174j)
| (8.2670731329247478633e-13 + 7.1381684228851424381e-658j)  +/-  (1.93e-64, 2.16e-186j)
| (0.096142673529808278921 + 7.8479705849149815651e-651j)  +/-  (2.51e-46, 2.81e-168j)
| (0.00024698749017601060177 - 5.5690798493183698546e-652j)  +/-  (4.26e-56, 4.78e-178j)
| (7.5311641707398751104e-08 - 2.4994642917128034185e-655j)  +/-  (1.05e-57, 1.18e-179j)
| (0.066278572057202030574 - 5.8889450290843863385e-651j)  +/-  (1.72e-49, 1.93e-171j)
| (2.1283606655000543129e-11 + 1.2904674409209339175e-657j)  +/-  (4.13e-60, 4.63e-182j)
| (0.00010770622180695934874 + 2.4023448551451168574e-652j)  +/-  (1.41e-57, 1.58e-179j)
| (0.039641898621365187041 + 4.03171758987267253e-651j)  +/-  (1.03e-51, 1.15e-173j)
| (0.0085596763744523780018 + 1.6797515073469690535e-651j)  +/-  (5.97e-54, 6.69e-176j)
| (7.5511176715073129113e-18 - 1.3442048703489935121e-660j)  +/-  (2.94e-68, 3.3e-190j)
| (4.9807702145699538839e-22 - 9.5418397616588959073e-663j)  +/-  (1.91e-70, 2.15e-192j)
| (0.14120919694295988538 - 9.6999783334985197736e-651j)  +/-  (3.92e-55, 4.4e-177j)
| (2.1283606655000543129e-11 - 4.5094567335653117633e-657j)  +/-  (3.57e-65, 4e-187j)
| (0.12371820585046101429 - 9.3486932653482948564e-651j)  +/-  (7.07e-56, 7.92e-178j)
| (2.9558819239900576782e-05 - 5.8750810428578338274e-653j)  +/-  (5.45e-61, 6.11e-183j)
| (6.334047154110054112e-09 + 4.7059515415043522748e-656j)  +/-  (1.12e-63, 1.26e-185j)
| (5.2305827863317608608e-06 + 1.3232826738772110829e-653j)  +/-  (4.69e-62, 5.24e-184j)
| (0.14120919694295988538 + 9.9906928223881087277e-651j)  +/-  (3.75e-58, 3.46e-180j)
| (6.334047154110054112e-09 - 1.3411196496097086127e-655j)  +/-  (2.49e-64, 2.81e-186j)
| (0.00024698749017601060177 + 3.0928576726006629631e-652j)  +/-  (1.45e-60, 1.79e-182j)
| (0.12371820585046101429 + 8.5568001331361263259e-651j)  +/-  (1.75e-58, 1.38e-180j)
