Starting with polynomial:
P : 1024*t^10 - 23040*t^8 + 161280*t^6 - 403200*t^4 + 302400*t^2 - 30240
Extension levels are: 10 50
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P1 : 1024*t^10 - 23040*t^8 + 161280*t^6 - 403200*t^4 + 302400*t^2 - 30240
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1024*t^60 - 1215016009095548025831063958431217220466357605738142901498460807040/1555036687794148292920053245610087130846944934883434495670771*t^58 + 18532445545745995003927608469504949366234843131036477822408435334111040/66866577575148376595562289561233746626418632199987683313843153*t^56 - 28446520386590174965927073231829716839318582948561396179552324539409163200/468066043026038636168936026928636226384930425399913783196902071*t^54 + 177349666601422841017861438948274117097378996444670996213703500811966384762400/19190707764067584082926377104074085281782147441396465111072984911*t^52 - 2840874651809428411353644758195604469154790685018211644055649840831478044642520/2741529680581083440418053872010583611683163920199495015867569273*t^50 + 243865772397481510916507350916713403569783139332933817594571963882449283024163500/2741529680581083440418053872010583611683163920199495015867569273*t^48 - 16424477500117034439362893165326317039145350328976592233487081311278298023913677000/2741529680581083440418053872010583611683163920199495015867569273*t^46 + 882517332839913523265525128009377847695988517834665437622945637453660226538179945000/2741529680581083440418053872010583611683163920199495015867569273*t^44 - 161806840260447656030313538886419870869025034425079452090135602086207837078037763125/11592091672647287274494942376366104066313589514585602604091202*t^42 + 278347227111725076345589360732686897076634993163499849612007620598253322625627989125/565467886470599379243655725676395320307979976321248907516644*t^40 - 8022505071050841186752934233240525043231844333859878143026519027205289755014565624375/565467886470599379243655725676395320307979976321248907516644*t^38 + 378963633366278168606792729676396804029606790710339744988421399727883563088238058488125/1130935772941198758487311451352790640615959952642497815033288*t^36 - 29360840282070420475070114379777809346899341524712047615322268367381755806428189366121875/4523743091764795033949245805411162562463839810569991260133152*t^34 + 931820708516374283770996874732518598346194617807415403178109133981549769266677454869221875/9047486183529590067898491610822325124927679621139982520266304*t^32 - 3020581817029515096977537299870800670961133676547937620979987557911469166258715062842574375/2261871545882397516974622902705581281231919905284995630066576*t^30 + 127470764937521247835001761339776314630236345009719362595319040793633515967255190163557940625/9047486183529590067898491610822325124927679621139982520266304*t^28 - 8702112542181446307115650910398999491918983261784683452722468016115544211262068281082491409375/72379889468236720543187932886578600999421436969119860162130432*t^26 + 119195852961911610261236922206512921804877238225972308271295762575622301848499354087652228984375/144759778936473441086375865773157201998842873938239720324260864*t^24 - 648705870199984056527684484837810503148136610357443937072556122139140385945947711597096852109375/144759778936473441086375865773157201998842873938239720324260864*t^22 + 5541682051001726042978710648722706228280734199605255402561774963005718083223226889670865477390625/289519557872946882172751731546314403997685747876479440648521728*t^20 - 73158146107495777283165409886560894765897068012710116076579816701768799620776246176513184819765625/1158078231491787528691006926185257615990742991505917762594086912*t^18 + 365824213267915985670125997764403343233518020381655162585091005731340775577037968031316943106015625/2316156462983575057382013852370515231981485983011835525188173824*t^16 - 337759620152323044340686035432792911562880570895605146716783696288875996344319601976384709566015625/1158078231491787528691006926185257615990742991505917762594086912*t^14 + 222743373741858991225774008490774132265841722593286689099615888285270872541106285937816199983984375/579039115745893764345503463092628807995371495752958881297043456*t^12 - 6417382648111294718092783436413837505144315807783471194103484156121964730167335512325953303617484375/18529251703868600459056110818964121855851887864094684201505390592*t^10 + 7401941780673681563614877313638509127866991507254489097356668557302084069848092434054322529857109375/37058503407737200918112221637928243711703775728189368403010781184*t^8 - 2491486312349906606203601953419755331068570423456215044507572632218895056199136103649176482531015625/37058503407737200918112221637928243711703775728189368403010781184*t^6 + 847335992218394425614318893353462619561250434339540355625401298438747375623858005051074110010546875/74117006815474401836224443275856487423407551456378736806021562368*t^4 - 225265444131559660069100055029893479128732840061620884403503547992388035225307910268641281422265625/296468027261897607344897773103425949693630205825514947224086249472*t^2 + 5484937826469426761090580883942370416771820459429497666030730388927646928323064709801822892265625/592936054523795214689795546206851899387260411651029894448172498944
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (-7.2113824104943957821 - 1.4077241225410653917e-900j)  +/-  (6.62e-242, 6.62e-242j)
| (-9.0786308301243584313 + 1.0227810288182111103e-907j)  +/-  (2.64e-244, 2.64e-244j)
| (4.379707689141260863 - 8.8131609948055719535e-905j)  +/-  (2.35e-242, 2.35e-242j)
| (-6.073020897319213434 + 1.4386475839044931793e-903j)  +/-  (1.69e-241, 1.69e-241j)
| (-7.625735723871997144 + 2.2889881036441219101e-908j)  +/-  (2.96e-242, 2.96e-242j)
| (5.7182985991186237305 + 1.6344254159554810118e-912j)  +/-  (1.61e-241, 1.61e-241j)
| (7.2113824104943957821 - 5.0053281656578568867e-915j)  +/-  (6.32e-242, 6.32e-242j)
| (7.625735723871997144 + 1.7897568650169194399e-918j)  +/-  (2.98e-242, 2.98e-242j)
| (8.5438853205710457872 - 9.3766424042081715089e-923j)  +/-  (2.16e-243, 2.16e-243j)
| (9.0786308301243584313 + 1.6975123073445336257e-927j)  +/-  (3.07e-244, 3.07e-244j)
| (6.4385538408540415245 - 1.1156585671911436356e-925j)  +/-  (1.51e-241, 1.51e-241j)
| (6.073020897319213434 + 9.1533148660686952281e-937j)  +/-  (1.69e-241, 1.69e-241j)
| (-6.8170374902396307582 + 3.0817086805021262311e-938j)  +/-  (1.16e-241, 1.16e-241j)
| (-8.5438853205710457872 - 1.6420138905413408403e-946j)  +/-  (2.03e-243, 2.03e-243j)
| (-8.0663981291509522185 + 1.334567309003611874e-944j)  +/-  (1.02e-242, 1.02e-242j)
| (-9.7242133159595808853 + 9.284040414348363612e-948j)  +/-  (1.5e-245, 1.5e-245j)
| (1.3090271005551811654 + 1.2719370418767176808e-951j)  +/-  (5.16e-249, 5.16e-249j)
| (3.1305146972852094382 - 2.8772645252181038163e-946j)  +/-  (3.3e-244, 3.3e-244j)
| (-1.5617288207830784516 + 1.4489058206839247913e-950j)  +/-  (6.59e-248, 6.59e-248j)
| (-6.4385538408540415245 - 6.4530771713753541695e-944j)  +/-  (1.62e-241, 1.62e-241j)
| (-5.0351231607936525592 - 1.1279788520112577684e-943j)  +/-  (8.09e-242, 8.09e-242j)
| (3.4361591188377376033 + 1.110731796971407665e-945j)  +/-  (1.02e-243, 1.02e-243j)
| (9.7242133159595808853 - 4.3066377257533786264e-947j)  +/-  (1.55e-245, 1.55e-245j)
| (-1.7566836492998817735 + 1.7413073934305627043e-949j)  +/-  (3.62e-247, 3.62e-247j)
| (4.0604431170209128394 + 2.0550388252571339581e-944j)  +/-  (9.53e-243, 9.53e-243j)
| (-3.4361591188377376033 - 7.7138565929174225001e-947j)  +/-  (1.08e-243, 1.08e-243j)
| (8.0663981291509522185 - 1.317431553824083391e-943j)  +/-  (1.02e-242, 1.02e-242j)
| (6.8170374902396307582 + 6.4419076054685949268e-949j)  +/-  (1.13e-241, 1.13e-241j)
| (-1.3090271005551811654 - 9.3911686839084953104e-961j)  +/-  (5.59e-249, 5.59e-249j)
| (-3.7460583222870681676 + 8.2523102258212020021e-954j)  +/-  (3.25e-243, 3.25e-243j)
| (-4.379707689141260863 - 2.0994449925805549126e-953j)  +/-  (2.34e-242, 2.34e-242j)
| (-2.5327316742327897964 - 1.672205152551344798e-961j)  +/-  (1.74e-245, 1.74e-245j)
| (1.9727794553775812407 + 2.6052218935485203829e-964j)  +/-  (9.72e-247, 9.72e-247j)
| (2.8291608806921292996 + 4.5587866225480670816e-961j)  +/-  (8.48e-245, 8.48e-245j)
| (-2.8291608806921292996 + 6.2149603605741990795e-961j)  +/-  (7.7e-245, 7.7e-245j)
| (-1.0366108297895136542 + 1.9032644468948456696e-966j)  +/-  (3.97e-250, 3.97e-250j)
| (2.2437240344607359123 + 2.3024865804835351513e-963j)  +/-  (4.02e-246, 4.02e-246j)
| (1.0366108297895136542 - 8.1375083340477678424e-967j)  +/-  (4.57e-250, 4.57e-250j)
| (-2.2437240344607359123 - 3.2581036454919485405e-963j)  +/-  (4.16e-246, 4.16e-246j)
| (-4.7043799198217429386 + 3.6440889739779199651e-957j)  +/-  (4.54e-242, 4.54e-242j)
| (5.0351231607936525592 + 6.4447467153420492502e-970j)  +/-  (7.82e-242, 7.82e-242j)
| (1.7566836492998817735 - 4.7005560269285650141e-993j)  +/-  (3.23e-247, 3.23e-247j)
| (5.3727574113657315911 - 4.4583635427839990049e-987j)  +/-  (1.2e-241, 1.2e-241j)
| (4.7043799198217429386 + 7.0179726731089452486e-995j)  +/-  (4.41e-242, 4.41e-242j)
| (3.7460583222870681676 - 1.8924499102493676866e-1002j)  +/-  (3.3e-243, 3.3e-243j)
| (-0.34290132722370460879 - 1.0077683203566775287e-1013j)  +/-  (4.66e-253, 4.66e-253j)
| (-1.9727794553775812407 + 1.2369136440431334654e-1006j)  +/-  (1.08e-246, 1.08e-246j)
| (0.76774588087055153574 - 4.0042120002160294536e-1011j)  +/-  (3.22e-251, 3.22e-251j)
| (-5.3727574113657315911 - 2.8420207475668809449e-1000j)  +/-  (1.28e-241, 1.28e-241j)
| (-4.0604431170209128394 + 5.7119221727179438791e-1015j)  +/-  (9.48e-243, 9.48e-243j)
| (-0.76774588087055153574 + 1.1647354668688139401e-1029j)  +/-  (3.63e-251, 3.63e-251j)
| (-0.52876956886891532202 - 4.1249413999671009579e-1030j)  +/-  (3.39e-252, 3.39e-252j)
| (-5.7182985991186237305 + 1.2885349727264197979e-1026j)  +/-  (1.57e-241, 1.57e-241j)
| (1.5617288207830784516 - 7.2121256609722390002e-1033j)  +/-  (6.5e-248, 6.5e-248j)
| (0.34290132722370460879 + 2.1240707061923782968e-1039j)  +/-  (4.66e-253, 4.66e-253j)
| (-0.12432625453723180285 + 1.5416439028732512799e-1040j)  +/-  (2.19e-254, 2.19e-254j)
| (-3.1305146972852094382 - 8.2988910773598011052e-1033j)  +/-  (2.93e-244, 2.93e-244j)
| (0.12432625453723180285 - 1.5882127639265250273e-1040j)  +/-  (2.19e-254, 2.19e-254j)
| (2.5327316742327897964 + 1.6149000689911307191e-1034j)  +/-  (1.79e-245, 1.79e-245j)
| (0.52876956886891532202 + 1.0596043736384101804e-1041j)  +/-  (3.24e-252, 3.24e-252j)
-------------------------------------------------
The weights are:
| (5.9186765099051558177e-24 - 1.0706811891484172818e-922j)  +/-  (6.71e-56, 3.47e-176j)
| (5.20424345248916579e-37 - 3.2600953739231630824e-930j)  +/-  (2.31e-62, 1.19e-182j)
| (8.4827747116981941085e-10 + 4.114967933641437234e-913j)  +/-  (8.5e-46, 4.4e-166j)
| (1.9500349785160435621e-17 + 4.4336196120189994595e-919j)  +/-  (1.24e-52, 6.44e-173j)
| (1.3366547759284405239e-26 + 7.6543346962058098622e-925j)  +/-  (1.62e-57, 8.36e-178j)
| (1.2427750714944909315e-15 - 1.8313882567325109401e-917j)  +/-  (2.1e-53, 1.08e-173j)
| (5.9186765099051558177e-24 - 1.9216082654553096271e-922j)  +/-  (1.3e-59, 6.73e-180j)
| (1.3366547759284405239e-26 + 6.0580460693203629576e-924j)  +/-  (3.11e-61, 1.61e-181j)
| (5.6095528750638312207e-33 + 1.7504851888797253013e-927j)  +/-  (6.59e-65, 3.41e-185j)
| (5.20424345248916579e-37 - 1.1083476865969582602e-929j)  +/-  (7.54e-67, 3.91e-187j)
| (2.0788917410413362019e-19 - 8.6255394479912973063e-920j)  +/-  (1.94e-58, 1e-178j)
| (1.9500349785160435621e-17 + 1.3515488982115796241e-918j)  +/-  (3.52e-57, 1.82e-177j)
| (1.4299029017898560622e-21 + 1.2481875623560497282e-921j)  +/-  (1.28e-62, 6.62e-183j)
| (5.6095528750638312207e-33 + 4.4806896548907089995e-928j)  +/-  (1.83e-68, 9.49e-189j)
| (1.4223374980994953027e-29 - 2.765675242613148079e-926j)  +/-  (6.93e-67, 3.59e-187j)
| (3.6052600440202927013e-42 + 6.0632382124406109343e-933j)  +/-  (5.4e-73, 2.8e-193j)
| (0.027289043534765728291 - 2.7374068293827947209e-908j)  +/-  (2.77e-36, 1.43e-156j)
| (9.4950644721908657554e-06 + 3.44507052403434595e-911j)  +/-  (7.15e-52, 3.7e-172j)
| (0.011172212168569619533 - 1.0520022937162546654e-908j)  +/-  (1.18e-40, 6.09e-161j)
| (2.0788917410413362019e-19 - 1.4041054140133552333e-920j)  +/-  (5.18e-63, 2.68e-183j)
| (1.8398583417528953495e-12 - 2.1987421709718057149e-916j)  +/-  (7.6e-61, 3.94e-181j)
| (1.2936776964684078923e-06 - 1.0400998702542306242e-911j)  +/-  (2.87e-54, 1.49e-174j)
| (3.6052600440202927013e-42 + 1.8282658534549773866e-932j)  +/-  (2.98e-75, 1.54e-195j)
| (0.004702101760960172488 + 6.2894270657205722694e-909j)  +/-  (3.66e-46, 1.9e-166j)
| (1.2354894564439568017e-08 - 1.2989539609511217964e-912j)  +/-  (2.11e-57, 1.09e-177j)
| (1.2936776964684078923e-06 + 1.3372444702877912287e-912j)  +/-  (1.79e-57, 9.29e-178j)
| (1.4223374980994953027e-29 - 1.3207233421766805778e-925j)  +/-  (2.11e-69, 1.09e-189j)
| (1.4299029017898560622e-21 + 4.5698570772389981926e-921j)  +/-  (1.8e-65, 9.32e-186j)
| (0.027289043534765728291 + 1.5049350998130810655e-908j)  +/-  (8.8e-45, 4.56e-165j)
| (1.4166688762467908876e-07 - 2.7804722999466400226e-913j)  +/-  (1.34e-59, 6.93e-180j)
| (8.4827747116981941085e-10 - 9.4760523977195167206e-915j)  +/-  (5.94e-62, 3.07e-182j)
| (0.00027104987811853176207 - 1.1156097459008861167e-910j)  +/-  (2.64e-55, 1.37e-175j)
| (0.0029020956417171514321 + 5.4866463705269526385e-909j)  +/-  (1.67e-53, 8.67e-174j)
| (5.6370779062322567676e-05 - 1.162943978310949683e-910j)  +/-  (3.77e-57, 1.95e-177j)
| (5.6370779062322567676e-05 + 2.6201737912495783508e-911j)  +/-  (2.59e-57, 1.34e-177j)
| (0.052663240435384405684 - 2.605660481196760951e-908j)  +/-  (6.36e-49, 3.29e-169j)
| (0.0010402834055984889795 - 1.4507246583209485249e-909j)  +/-  (2.7e-55, 1.4e-175j)
| (0.052663240435384405684 + 4.1616141188854180123e-908j)  +/-  (2.46e-50, 1.28e-170j)
| (0.0010402834055984889795 + 4.8404070567277600004e-910j)  +/-  (7.07e-55, 3.66e-175j)
| (4.5216333461882884417e-11 + 1.520434359887891645e-915j)  +/-  (1.33e-63, 6.9e-184j)
| (1.8398583417528953495e-12 - 2.68010049704252903e-915j)  +/-  (3.98e-65, 2.06e-185j)
| (0.004702101760960172488 - 1.4344640804886234937e-908j)  +/-  (3.39e-55, 1.75e-175j)
| (5.5990782862712460918e-14 + 2.2467768575168941989e-916j)  +/-  (5.62e-66, 2.91e-186j)
| (4.5216333461882884417e-11 + 3.7410581491483234757e-914j)  +/-  (1.95e-64, 1.01e-184j)
| (1.4166688762467908876e-07 + 3.3120480732737596386e-912j)  +/-  (3.58e-62, 1.86e-182j)
| (0.094045566337302498881 + 1.708793923469134738e-907j)  +/-  (1.57e-56, 8.13e-177j)
| (0.0029020956417171514321 - 2.1402262662996901681e-909j)  +/-  (1.3e-58, 6.71e-179j)
| (0.081571626616788455788 - 7.7756078848847477002e-908j)  +/-  (1.28e-56, 6.65e-177j)
| (5.5990782862712460918e-14 + 2.8681949408594418736e-917j)  +/-  (2.49e-69, 1.29e-189j)
| (1.2354894564439568017e-08 + 5.3612363027500744339e-914j)  +/-  (5.34e-66, 2.77e-186j)
| (0.081571626616788455788 + 5.5135972622337320982e-908j)  +/-  (2.11e-58, 1.09e-178j)
| (0.08878508756801837802 - 1.2125379957429196211e-907j)  +/-  (2.36e-58, 1.22e-178j)
| (1.2427750714944909315e-15 - 3.5322311875883263166e-918j)  +/-  (2.44e-70, 1.26e-190j)
| (0.011172212168569619533 + 2.1692628116968301677e-908j)  +/-  (1.51e-60, 7.85e-181j)
| (0.094045566337302498881 - 1.9898619538672208757e-907j)  +/-  (4.35e-60, 2.26e-180j)
| (0.13549037821437248194 - 1.6905374695177961122e-907j)  +/-  (6.99e-60, 3.63e-180j)
| (9.4950644721908657554e-06 - 6.0483190257375073124e-912j)  +/-  (7.55e-65, 3.87e-185j)
| (0.13549037821437248194 + 1.7863253042613902883e-907j)  +/-  (2.8e-60, 1.46e-180j)
| (0.00027104987811853176207 + 4.0123007695889678938e-910j)  +/-  (6.26e-64, 3.02e-184j)
| (0.08878508756801837802 + 1.5344883667416901707e-907j)  +/-  (1.26e-60, 6.57e-181j)
