Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 7 40
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : 16*t^11 - 328*t^9 + 2112*t^7 - 5040*t^5 + 4095*t^3 - 1575/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^51 - 29985319106587111525672911604303195028401136952134327671055037849458613304/3452008873983076440048795220156472902343624860042187456485826643003883*t^49 + 7470648615900572956506989240682655475087837933642463713715895321424869231176/3452008873983076440048795220156472902343624860042187456485826643003883*t^47 - 19290925641496568697801348158916395874647565180154709597569099878363282460952100/58684150857712299480829518742660039339841622620717186760259052931066011*t^45 + 2001898753310817709785174891898277834109774058030504081096443704561401313265247080/58684150857712299480829518742660039339841622620717186760259052931066011*t^43 - 150747932057308705591328633155604430240945622918742499712672334061117470463719095260/58684150857712299480829518742660039339841622620717186760259052931066011*t^41 + 17081371493724236580226029093768517717487585707105482874126975023344469732280336590435/117368301715424598961659037485320078679683245241434373520518105862132022*t^39 - 1490239604761277556284023881300987999248054267630379256607057526788681580114490153999755/234736603430849197923318074970640157359366490482868747041036211724264044*t^37 + 203243452789597030050691503467992173492402919793280337313954326655047117550344679666447475/938946413723396791693272299882560629437465961931474988164144846897056176*t^35 - 643377652424242744387387388894962754374675047510034930117480234163207897415365701165043775/110464283967458446081561447045007132874995995521349998607546452576124256*t^33 + 6869213124055812834343561685388623364622591147412782760583068735507675238122893498577373525/55232141983729223040780723522503566437497997760674999303773226288062128*t^31 - 233382779564287001195766580134886017387360923098171646733217685353903391156081217153335829525/110464283967458446081561447045007132874995995521349998607546452576124256*t^29 + 3153115611443108353380841433058632509533825513515595982122142185013972766602378005167424883725/110464283967458446081561447045007132874995995521349998607546452576124256*t^27 - 67571583060162864207677089986084633165124899988120884574136745745617188530419454489881104815125/220928567934916892163122894090014265749991991042699997215092905152248512*t^25 + 2284673970486593790404958173748174722158550244035608975716902010950813322084743442477730785586875/883714271739667568652491576360057062999967964170799988860371620608994048*t^23 - 30223577579853803707698946911854914734096666835295823598023084276869741367041161525268822107681875/1767428543479335137304983152720114125999935928341599977720743241217988096*t^21 + 1237392422315911944795478818802237878077863954693368415553287163649238015212293309914139623933430625/14139428347834681098439865221760913007999487426732799821765945929743904768*t^19 - 9650442168240241803482983592206329602512174607906942710175573206008188295616586249862587671322923125/28278856695669362196879730443521826015998974853465599643531891859487809536*t^17 + 28093466994279845302929099515982517144915325340773029557003561495924249842408692010397063994461628125/28278856695669362196879730443521826015998974853465599643531891859487809536*t^15 - 118799658055065871346874914364990729170247444497131630419963398218108161899884761330718367574878278125/56557713391338724393759460887043652031997949706931199287063783718975619072*t^13 + 43941906223434071350971640601733118128045668885067289503161440457789728738793312654351426931253959375/14139428347834681098439865221760913007999487426732799821765945929743904768*t^11 - 43208568228616220449626584242930985436339620232064541051883466499350957651399535897248811971550409375/14139428347834681098439865221760913007999487426732799821765945929743904768*t^9 + 839500351766887719327194775399084803230309974577580575530959020713121901483634917912519157719498634375/452461707130709795150075687096349216255983597655449594296510269751804952576*t^7 - 563200925155540506119997726991778912875292526285031084084045356089538958385241299806543029846026859375/904923414261419590300151374192698432511967195310899188593020539503609905152*t^5 + 345717572934617183295563704991174356691094770989938268138052910489820546883088943143102889450063640625/3619693657045678361200605496770793730047868781243596754372082158014439620608*t^3 - 31800727012789693990202343057044898831806179800030850595352023832416349573784452196817352698884453125/7239387314091356722401210993541587460095737562487193508744164316028879241216*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:
| (7.1227667025661533331 + 2.3782320599459781221e-910j)  +/-  (2.43e-244, 2.43e-244j)
| (8.8341781391518277144 + 3.9806016105992474551e-921j)  +/-  (7.9e-247, 7.9e-247j)
| (-6.6664101832998587687 - 2.3309757464908146027e-918j)  +/-  (5.81e-244, 5.81e-244j)
| (-2.5876478632282788277 + 1.0652667185671776386e-921j)  +/-  (1.61e-245, 1.61e-245j)
| (-6.236653988015551996 - 1.5511552145802854263e-917j)  +/-  (1.01e-243, 1.01e-243j)
| (-8.8341781391518277144 - 4.1911908171872617752e-922j)  +/-  (7.7e-247, 7.7e-247j)
| (6.236653988015551996 - 8.0672429700657279114e-920j)  +/-  (1.05e-243, 1.05e-243j)
| (-4.6818779206674662899 + 1.5223248193849244726e-925j)  +/-  (8.95e-244, 8.95e-244j)
| (-8.168663774788812523 + 3.6245485456325410375e-929j)  +/-  (1.17e-245, 1.17e-245j)
| (-3.2759416955673464603 + 1.3312147327511420988e-929j)  +/-  (5.62e-245, 5.62e-245j)
| (7.6165257250749913012 + 8.7530616666366638074e-927j)  +/-  (7.13e-245, 7.13e-245j)
| (1.9733279582902362806 + 1.287406514324556083e-933j)  +/-  (1.9e-247, 1.9e-247j)
| (5.8270165994502692374 + 6.54433081363286206e-936j)  +/-  (1.42e-243, 1.42e-243j)
| (5.0522526177554434564 - 7.3840519497193414665e-951j)  +/-  (1.32e-243, 1.32e-243j)
| (-5.8270165994502692374 + 5.3039727361320110795e-957j)  +/-  (1.45e-243, 1.45e-243j)
| (3.966345354559309351 + 5.423507505122696524e-969j)  +/-  (3.05e-244, 3.05e-244j)
| (4.6818779206674662899 - 7.2642814332777218044e-983j)  +/-  (9.19e-244, 9.19e-244j)
| (4.3203721380334389863 + 2.4976607723933407421e-999j)  +/-  (5.41e-244, 5.41e-244j)
| (8.168663774788812523 + 9.4290745738600313924e-1013j)  +/-  (1.1e-245, 1.1e-245j)
| (-7.6165257250749913012 + 4.0656831971474292564e-1011j)  +/-  (7.08e-245, 7.08e-245j)
| (-7.1227667025661533331 + 5.103146634450793695e-1010j)  +/-  (2.58e-244, 2.58e-244j)
| (3.6186026875452647736 + 3.9268321059475308602e-1011j)  +/-  (1.34e-244, 1.34e-244j)
| (-3.966345354559309351 + 1.3678771533043850419e-1012j)  +/-  (3.02e-244, 3.02e-244j)
| (-5.0522526177554434564 - 8.5004235274991071497e-1012j)  +/-  (1.34e-243, 1.34e-243j)
| (6.6664101832998587687 - 1.7939134809267428217e-1017j)  +/-  (6.76e-244, 6.76e-244j)
| (-4.3203721380334389863 + 3.9699736131519441206e-1024j)  +/-  (5.64e-244, 5.64e-244j)
| (1.0362802085752798674 + 6.2834594966422144495e-1031j)  +/-  (1.29e-250, 1.29e-250j)
| (2.3399106244156159831 + 2.5910140524795567561e-1025j)  +/-  (1.72e-245, 1.72e-245j)
| (-2.3399106244156159831 - 1.3534000403874847018e-1029j)  +/-  (1.83e-245, 1.83e-245j)
| (5.4332210468704205558 + 4.838328137983269303e-1028j)  +/-  (1.56e-243, 1.56e-243j)
| (2.5876478632282788277 - 1.6619304694552754158e-1033j)  +/-  (1.61e-245, 1.61e-245j)
| (-5.4332210468704205558 + 3.4586940503042421902e-1032j)  +/-  (1.67e-243, 1.67e-243j)
| (1.6506801238857845559 + 4.4383084146320407714e-1038j)  +/-  (1.57e-248, 1.57e-248j)
| (-3.6186026875452647736 - 1.9191093738974208924e-1034j)  +/-  (1.38e-244, 1.38e-244j)
| (-1.6506801238857845559 + 5.1235511224143338974e-1039j)  +/-  (1.44e-248, 1.44e-248j)
| (-1.9733279582902362806 + 1.6409060098496792145e-1036j)  +/-  (2e-247, 2e-247j)
| (-1.1555244088435139909e-1061 + 2.5451921140873498553e-1062j)  +/-  (6.03e-1060, 6.03e-1060j)
| (0.7624799995719576139 + 1.215943080869003386e-1040j)  +/-  (1.42e-251, 1.42e-251j)
| (2.9364170609337066713 + 7.6445102229684274273e-1036j)  +/-  (2.31e-245, 2.31e-245j)
| (-0.7624799995719576139 - 8.3630992101514890705e-1042j)  +/-  (1.31e-251, 1.31e-251j)
| (-0.52464762327529031788 - 1.7740658604499608888e-1042j)  +/-  (1.59e-252, 1.59e-252j)
| (3.2759416955673464603 - 1.4183633005038933852e-1033j)  +/-  (6.03e-245, 6.03e-245j)
| (0.2762472984358009721 - 3.1988520813223044034e-1045j)  +/-  (1.04e-253, 1.04e-253j)
| (2.3862793919737297977 + 3.1176890720465769339e-1036j)  +/-  (2.88e-245, 2.88e-245j)
| (-1.0362802085752798674 + 1.2666823469700389021e-1041j)  +/-  (1.31e-250, 1.31e-250j)
| (-1.3371081727648255001 - 1.7386622162863454354e-1040j)  +/-  (1.23e-249, 1.23e-249j)
| (-0.2762472984358009721 - 4.833188007378387115e-1046j)  +/-  (1.04e-253, 1.04e-253j)
| (1.3371081727648255001 + 6.4975166826345390538e-1043j)  +/-  (1.23e-249, 1.23e-249j)
| (0.52464762327529031788 + 3.8000882491056549133e-1044j)  +/-  (1.5e-252, 1.5e-252j)
| (-2.9364170609337066713 - 8.9917534408470329285e-1036j)  +/-  (2.62e-245, 2.62e-245j)
| (-2.3862793919737297977 - 3.3482580792223873302e-1042j)  +/-  (2.68e-245, 2.68e-245j)
-------------------------------------------------
The weights are:
| (2.4695256574207775565e-23 - 4.5768717855683868503e-932j)  +/-  (1.76e-77, 7.55e-199j)
| (5.5372858576481390888e-35 - 1.8391738003468032957e-939j)  +/-  (3.4e-82, 1.46e-203j)
| (1.2476095762525836415e-20 + 1.3131910739931082777e-932j)  +/-  (2.1e-77, 9e-199j)
| (0.00026873367006038457705 - 1.1375162821163244248e-921j)  +/-  (1.3e-58, 5.56e-180j)
| (3.0284636823479302981e-18 - 2.9108954753896915914e-931j)  +/-  (4.04e-76, 1.73e-197j)
| (5.5372858576481390888e-35 + 1.9725284695177764957e-940j)  +/-  (1.82e-84, 7.79e-206j)
| (3.0284636823479302981e-18 - 4.3832280844173510096e-930j)  +/-  (3.79e-78, 1.63e-199j)
| (6.23456336466155266e-11 - 6.0846979174382531272e-927j)  +/-  (3.72e-72, 1.59e-193j)
| (3.5152327296238765484e-30 - 7.5375919586962915501e-938j)  +/-  (1.09e-82, 4.69e-204j)
| (4.1969126094327172161e-06 - 1.3256698527847144144e-923j)  +/-  (5.01e-66, 2.15e-187j)
| (1.8694926425858515398e-26 - 2.3770275460387698743e-934j)  +/-  (2.78e-82, 1.19e-203j)
| (0.0037726443180705676572 + 6.1343368665462906144e-921j)  +/-  (3.11e-60, 1.33e-181j)
| (4.060898080435662142e-16 + 4.8151179763135519942e-929j)  +/-  (9.94e-78, 4.27e-199j)
| (1.7393294197001432959e-12 + 3.9593219910254824001e-927j)  +/-  (3.85e-76, 1.65e-197j)
| (4.060898080435662142e-16 + 4.8203294436707266619e-930j)  +/-  (2.1e-78, 9.02e-200j)
| (2.9112428822913068676e-08 - 1.169807277303970656e-924j)  +/-  (2.05e-73, 8.82e-195j)
| (6.23456336466155266e-11 - 2.9419723519992304186e-926j)  +/-  (1.25e-75, 5.36e-197j)
| (1.5790462361504481796e-09 + 1.9468892454932256676e-925j)  +/-  (1.15e-74, 4.93e-196j)
| (3.5152327296238765484e-30 + 1.1020533563361345715e-936j)  +/-  (2.45e-86, 1.05e-207j)
| (1.8694926425858515398e-26 + 7.9625125124621677653e-936j)  +/-  (2.04e-86, 8.77e-208j)
| (2.4695256574207775565e-23 - 4.122323077111802488e-934j)  +/-  (5.78e-85, 2.48e-206j)
| (4.0035711787673869026e-07 + 6.5551562630674580074e-924j)  +/-  (2.93e-75, 1.26e-196j)
| (2.9112428822913068676e-08 - 3.3306729398682291053e-925j)  +/-  (6.17e-78, 2.65e-199j)
| (1.7393294197001432959e-12 + 6.7350431503943125151e-928j)  +/-  (8.47e-81, 3.64e-202j)
| (1.2476095762525836415e-20 + 3.9691672011523497319e-931j)  +/-  (1.4e-84, 6.01e-206j)
| (1.5790462361504481796e-09 + 4.7690701345322772906e-926j)  +/-  (4.91e-79, 2.11e-200j)
| (0.05605804142976254744 - 3.3184459610649549247e-920j)  +/-  (2.22e-67, 9.52e-189j)
| (0.0018384625596751064814 - 2.2683472974195276218e-920j)  +/-  (2.94e-74, 1.26e-195j)
| (0.0018384625596751064814 - 1.1454453917282515997e-920j)  +/-  (6.74e-75, 2.89e-196j)
| (3.3018783504066663661e-14 - 4.6772827454162522841e-928j)  +/-  (1.64e-81, 7.02e-203j)
| (0.00026873367006038457705 - 2.4416506699615551973e-921j)  +/-  (1.64e-75, 7.06e-197j)
| (3.3018783504066663661e-14 - 6.2957172588340243812e-929j)  +/-  (2.76e-82, 1.18e-203j)
| (0.011764223655187952749 - 9.3529556160552726492e-921j)  +/-  (1.45e-73, 6.21e-195j)
| (4.0035711787673869026e-07 + 2.1391960363985620988e-924j)  +/-  (1.72e-78, 7.39e-200j)
| (0.011764223655187952749 - 5.8323995857847707452e-921j)  +/-  (7.64e-75, 3.28e-196j)
| (0.0037726443180705676572 + 3.4715767608734207086e-921j)  +/-  (1.73e-75, 7.42e-197j)
| (0.15871026955988831862 - 8.3513072806502708555e-920j)  +/-  (4.77e-73, 2.05e-194j)
| (0.079928480360799832414 + 6.203093764267478547e-920j)  +/-  (2.79e-73, 1.2e-194j)
| (3.4467563905259585203e-05 + 2.1177602928792567246e-922j)  +/-  (5.72e-78, 2.46e-199j)
| (0.079928480360799832414 + 5.0031707112879756436e-920j)  +/-  (1.91e-74, 8.2e-196j)
| (0.099844733636181286197 - 7.4782493684269679122e-920j)  +/-  (2.27e-74, 9.74e-196j)
| (4.1969126094327172161e-06 - 3.5819478274424276699e-923j)  +/-  (8.35e-79, 3.58e-200j)
| (0.13902277347417826149 + 8.9310432737715633179e-920j)  +/-  (2.58e-74, 1.11e-195j)
| (-0.0010165142900650483914 + 2.2281952802635241324e-920j)  +/-  (6.73e-76, 2.89e-197j)
| (0.05605804142976254744 - 2.4752871568824353409e-920j)  +/-  (6.49e-76, 2.78e-197j)
| (0.029124190816978930991 + 1.1601999560289877178e-920j)  +/-  (1.17e-76, 5.02e-198j)
| (0.13902277347417826149 + 8.2639955559012801936e-920j)  +/-  (4.87e-75, 2.09e-196j)
| (0.029124190816978930991 + 1.6966739666088582723e-920j)  +/-  (1.64e-76, 7.04e-198j)
| (0.099844733636181286197 - 8.6678292604717327036e-920j)  +/-  (1.57e-75, 6.73e-197j)
| (3.4467563905259585203e-05 + 8.8205408815227330759e-923j)  +/-  (3.05e-80, 1.31e-201j)
| (-0.0010165142900650483914 + 1.1085692846607739533e-920j)  +/-  (4.07e-78, 1.74e-199j)
