Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 7 52
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 52 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^63 - 234671598234143765633661789270223013302353924635939486545100389690767199270999544833856297210419221356/16497646471044866892978592775626964551478161310849288120924829533477545433268323305220391248855399*t^61 + 4574667135287898190214941695862048755339967304762765718180526352181988199987801715260886377876746450060445/775389384139108743969993860454467333919473581609916541683466988073444635363611195345358388696203753*t^59 - 536296205051839814721396949100727466692630301364785409426203490105792640467434527933319514882533078889574901/353147640300980220025937797830747498616789948059961989281579024271073794324020940454321642376488838*t^57 + 4854884773237187882696127795885902349352258911715673381726188654988580920930022119413894532326338168163844905290/17833955835199501111309858790452748680147892377028080458719740725689226613363057492943242940012686319*t^55 - 18053306741074739255031695565910896520222911412311985955590165221616488333553908888419515770324888881847348709293615/499350763385586031116676046132676963044140986556786252844152740319298345174165609802410802320355216932*t^53 + 7379868445984555547756610904636527230611480649593084075347681621813056276317248419994478616295776764616427287953971525/1997403053542344124466704184530707852176563946227145011376610961277193380696662439209643209281420867728*t^51 - 1190162027183663618838766206594063675304210595453796372684963030796342800487535116270621120497832712888544422271788523375/3994806107084688248933408369061415704353127892454290022753221922554386761393324878419286418562841735456*t^49 + 117084461164805971766159624687674731845704643101895350449307425810521177952604717361742915868641353761653292449382115325/6071133901344511016616122141430722954943963362392538028500337268319736719442742976321103979578786832*t^47 - 1071031886163076370654113792919518202907950968013861010647488468979733837375698774139936527320104750876406060289873118375/1055849374146871481150629937640125731294602323894354439739189090142562907729172691534105039926745536*t^45 + 184657442462855434676963858419712603769063651260725821597003076577408859902255521772439087027087951944412017748811554786375/4223397496587485924602519750560502925178409295577417758956756360570251630916690766136420159706982144*t^43 - 13120040120656522259400624963525120473997285431557390253659589064422242992807884611374438440301850250059371583831805606686125/8446794993174971849205039501121005850356818591154835517913512721140503261833381532272840319413964288*t^41 + 96386758896902156194808617869441129238079423590319078924769183714444670631021521654219909719032528538329290750511717272794375/2111698748293742962301259875280251462589204647788708879478378180285125815458345383068210079853491072*t^39 - 18778179868026802511597923676537027121870049943036272850744631905100743949041080300729707142083023142519131213045921339064736125/16893589986349943698410079002242011700713637182309671035827025442281006523666763064545680638827928576*t^37 + 1516338289580052273594195492251714062225207393187060183802734039449690290258140988601943363072736644155918984935592841259152409375/67574359945399774793640316008968046802854548729238684143308101769124026094667052258182722555311714304*t^35 - 50695803677344274507970732414815115488428324273925173295529533717301921966886206967869460013047319085405904130488917437999404048125/135148719890799549587280632017936093605709097458477368286616203538248052189334104516365445110623428608*t^33 + 350028618836774656728541178178256275766633991653589450996174087758495981224695582351068520667610903513340898433942003730932442008125/67574359945399774793640316008968046802854548729238684143308101769124026094667052258182722555311714304*t^31 - 15911988731236101878439240350261709550252957996177656666886458615904159331678636164915386959925999407999075811078563040840737981690625/270297439781599099174561264035872187211418194916954736573232407076496104378668209032730890221246857216*t^29 + 592300460375891718982852082248787020687580894377484465901076276020416139924067374362581524685382101442883113600235827355978580962755625/1081189759126396396698245056143488748845672779667818946292929628305984417514672836130923560884987428864*t^27 - 8967959840084428790486347584160871246692619488195101394137552211334794647028072873633054345504825071365197886671201849996662859606471875/2162379518252792793396490112286977497691345559335637892585859256611968835029345672261847121769974857728*t^25 + 13695593591010606476395072011680291835540722262311165723010533633552672716865293939573579827620438877114418182425083530327801681690234375/540594879563198198349122528071744374422836389833909473146464814152992208757336418065461780442493714432*t^23 - 534662287879981179593999847236373894475537953477398898867767260507100496564189187725495150670483740972911498888235204512373724116094171875/4324759036505585586792980224573954995382691118671275785171718513223937670058691344523694243539949715456*t^21 + 8234415687080176403258234748847438177711032005514337950246584000737268513917735759663690708297168934408726681016608233889354867814144140625/17299036146022342347171920898295819981530764474685103140686874052895750680234765378094776974159798861824*t^19 - 46434654191827294809407220014255533187200153778962453229082453404441761871111699770213587492609023637292196092478010390477999101288484375/32608927702209881898533309893111819003828019744929506391492693784911876871319067630715884965428461568*t^17 + 56152581006122021217435979201437889291309960204524069859684892642015248935526268609309652840098179602933093937024959008204790506585364140625/17299036146022342347171920898295819981530764474685103140686874052895750680234765378094776974159798861824*t^15 - 380402275679775498306617296478544055651993414664021899564657847166221808531487969162292068244508173541615190509319061987028515819969328328125/69196144584089369388687683593183279926123057898740412562747496211583002720939061512379107896639195447296*t^13 + 1850778233272863631662084339099328762996213262780884586456581426293256159339710054250371689472652772288889846366341738231900834368080040828125/276784578336357477554750734372733119704492231594961650250989984846332010883756246049516431586556781789184*t^11 - 3083716811583990434953242603970440917079125755115167303884995092050052915035676362746098185532779703321796314778455317156028012292368764609375/553569156672714955109501468745466239408984463189923300501979969692664021767512492099032863173113563578368*t^9 + 410229609701060994664964233293945964360239344361474346273271327931411151657299562717553442461476225994513636862248815155793117718507594953125/138392289168178738777375367186366559852246115797480825125494992423166005441878123024758215793278390894592*t^7 - 998767035297252618256928099005450864397940237261339353779707537266480069324184565461056192757588275707244949341243084727500382102374507109375/1107138313345429910219002937490932478817968926379846601003959939385328043535024984198065726346227127156736*t^5 + 570676999298825140041405168061796982172043357377171750171128328530162246614863611665301079320197274120118448517678998610128697063045161953125/4428553253381719640876011749963729915271875705519386404015839757541312174140099936792262905384908508626944*t^3 - 48560977569682808836047547183542374777029412953274914215891947443935936781656424066790158221483019252767155733087933479024742062843668359375/8857106506763439281752023499927459830543751411038772808031679515082624348280199873584525810769817017253888*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: 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:
| (7.2780117042105427298 + 8.3224868838475547594e-755j)  +/-  (5.12e-241, 5.12e-241j)
| (-8.0989516839269624384 - 1.6706763830158463767e-752j)  +/-  (1.1e-241, 1.1e-241j)
| (-8.5502706972694894074 + 1.8014484364699675158e-760j)  +/-  (3.34e-242, 3.34e-242j)
| (6.8959044902228494456 - 8.3585272955671607315e-768j)  +/-  (8.07e-241, 8.07e-241j)
| (9.0447778072925853208 - 2.2645956805512247025e-771j)  +/-  (6.43e-243, 6.43e-243j)
| (-10.350178094571875931 + 6.2029372999380332469e-772j)  +/-  (2.45e-245, 2.45e-245j)
| (8.0989516839269624384 + 2.1824818375035712656e-769j)  +/-  (1.1e-241, 1.1e-241j)
| (-9.0447778072925853208 + 5.8951631544334230656e-768j)  +/-  (6.07e-243, 6.07e-243j)
| (-3.8848386817262651495 + 2.736264196066271616e-770j)  +/-  (1.58e-242, 1.58e-242j)
| (2.9765979220329603023 - 5.2578276789492711673e-774j)  +/-  (3.62e-244, 3.62e-244j)
| (2.6802341817068396865 - 4.0821233413015594484e-775j)  +/-  (7.98e-245, 7.98e-245j)
| (-2.6802341817068396865 + 7.3906730596171391705e-773j)  +/-  (7.67e-245, 7.67e-245j)
| (-0.52464762327529031788 + 6.1161784331467145614e-781j)  +/-  (2.48e-252, 2.48e-252j)
| (-2.3862793919737297977 - 2.172652200133187668e-773j)  +/-  (1.85e-245, 1.85e-245j)
| (-4.8292373566078450047 + 9.9106557671498143184e-769j)  +/-  (2.15e-241, 2.15e-241j)
| (10.350178094571875931 + 2.0714571563736823343e-776j)  +/-  (2.45e-245, 2.45e-245j)
| (9.6112032262101860862 - 2.3824239245527839377e-775j)  +/-  (6.38e-244, 6.38e-244j)
| (-2.9765979220329603023 + 9.8336508807391295223e-776j)  +/-  (3.27e-244, 3.27e-244j)
| (-1.6666030423147692618 - 8.9454347947472843123e-777j)  +/-  (1.6e-245, 1.6e-245j)
| (5.4856946720993761942 - 7.1328029706037217195e-771j)  +/-  (6.67e-241, 6.67e-241j)
| (8.5502706972694894074 - 3.1617923006398007923e-778j)  +/-  (3.27e-242, 3.27e-242j)
| (-9.6112032262101860862 + 9.3909723917788831109e-776j)  +/-  (6.56e-244, 6.56e-244j)
| (5.1543230437011021146 + 3.9998721032566422596e-779j)  +/-  (3.83e-241, 3.83e-241j)
| (-7.6774080157103982747 + 5.0466966787110561727e-796j)  +/-  (2.79e-241, 2.79e-241j)
| (-6.8959044902228494456 + 2.5059082088793665955e-816j)  +/-  (7.83e-241, 7.83e-241j)
| (3.2759416955673464603 + 6.7539842984119068385e-831j)  +/-  (1.39e-243, 1.39e-243j)
| (0.78060364912981625476 + 3.2400057784602645769e-836j)  +/-  (4.63e-251, 4.63e-251j)
| (4.1950634747509614711 - 6.9667074579792795804e-828j)  +/-  (4.69e-242, 4.69e-242j)
| (-5.1543230437011021146 - 6.6896443840538226513e-826j)  +/-  (3.96e-241, 3.96e-241j)
| (-6.5277525851203312439 - 1.4438364170129846314e-827j)  +/-  (9.59e-241, 9.59e-241j)
| (-5.4856946720993761942 - 1.6671975942434150265e-835j)  +/-  (6.31e-241, 6.31e-241j)
| (3.8848386817262651495 + 2.9362622559731260762e-845j)  +/-  (1.54e-242, 1.54e-242j)
| (1.0362802085752798674 + 1.6990857968664164477e-851j)  +/-  (6.62e-250, 6.62e-250j)
| (6.5277525851203312439 + 1.0375152597395964804e-841j)  +/-  (9.74e-241, 9.74e-241j)
| (-4.5096907495075977972 - 1.8722658405674514543e-842j)  +/-  (9.77e-242, 9.77e-242j)
| (-2.0924222005998321563 - 5.2692761320951545896e-853j)  +/-  (4.52e-246, 4.52e-246j)
| (-6.1711435668798802429 - 2.1439301503639938877e-847j)  +/-  (1.04e-240, 1.04e-240j)
| (4.5096907495075977972 + 1.4202944757003870768e-860j)  +/-  (1.03e-241, 1.03e-241j)
| (3.5785849804381544919 + 4.5870579496100761882e-862j)  +/-  (5.21e-243, 5.21e-243j)
| (2.3862793919737297977 + 2.4574546003339236573e-864j)  +/-  (1.83e-245, 1.83e-245j)
| (-7.2780117042105427298 + 4.5940129804928932893e-859j)  +/-  (5.57e-241, 5.57e-241j)
| (6.1711435668798802429 + 3.3131659181084506792e-867j)  +/-  (9.78e-241, 9.78e-241j)
| (1.6506801238857845559 + 1.0356799316317863763e-872j)  +/-  (1.32e-245, 1.32e-245j)
| (7.6774080157103982747 - 5.4994725991520157849e-868j)  +/-  (2.6e-241, 2.6e-241j)
| (1.747794337201247626 + 1.7156804596877657347e-874j)  +/-  (5.18e-246, 5.18e-246j)
| (-1.3014263152045485896 + 5.3591355075521045216e-876j)  +/-  (1.19e-248, 1.19e-248j)
| (3.3281649244476611966e-909 - 5.5127558002270313244e-909j)  +/-  (4.06e-907, 4.06e-907j)
| (-3.2759416955673464603 + 9.4159762157888143678e-870j)  +/-  (1.34e-243, 1.34e-243j)
| (1.3014263152045485896 + 9.1545525090449712877e-876j)  +/-  (1.24e-248, 1.24e-248j)
| (0.52464762327529031788 + 2.4454783421603208505e-879j)  +/-  (2.16e-252, 2.16e-252j)
| (-1.747794337201247626 + 1.246645473779345657e-873j)  +/-  (5.15e-246, 5.15e-246j)
| (-0.2640494271951554294 - 5.6500764058620845122e-880j)  +/-  (1.29e-253, 1.29e-253j)
| (-1.0362802085752798674 - 3.9292701381758009593e-877j)  +/-  (7.73e-250, 7.73e-250j)
| (2.0924222005998321563 + 5.9239134448612150564e-874j)  +/-  (4.53e-246, 4.53e-246j)
| (1.6666030423147692618 - 1.9671168281533593681e-873j)  +/-  (1.7e-245, 1.7e-245j)
| (-4.1950634747509614711 + 2.9580351080696252273e-868j)  +/-  (4.42e-242, 4.42e-242j)
| (-1.6506801238857845559 - 1.6760194773326783904e-872j)  +/-  (1.2e-245, 1.2e-245j)
| (-3.5785849804381544919 + 1.9517416297042360979e-869j)  +/-  (5.08e-243, 5.08e-243j)
| (5.824261010323148922 + 7.5781765450833983199e-867j)  +/-  (8.68e-241, 8.68e-241j)
| (0.2640494271951554294 - 4.4114108262815878823e-881j)  +/-  (1.29e-253, 1.29e-253j)
| (4.8292373566078450047 - 1.420042807812482269e-871j)  +/-  (2.12e-241, 2.12e-241j)
| (-5.824261010323148922 - 1.3265459471232642256e-881j)  +/-  (9.19e-241, 9.19e-241j)
| (-0.78060364912981625476 - 2.2947620942405316724e-893j)  +/-  (4.27e-251, 4.27e-251j)
-------------------------------------------------
The weights are:
| (2.1789878916982558517e-24 - 1.4087169860704135871e-777j)  +/-  (3.79e-64, 2.27e-183j)
| (7.9993875296203901662e-30 - 1.1457299795911589751e-780j)  +/-  (2.13e-67, 1.28e-186j)
| (4.714442027733152169e-33 - 5.8861034448998830467e-783j)  +/-  (6.54e-69, 3.92e-188j)
| (4.7081010882094353492e-22 + 8.4912161891909850953e-777j)  +/-  (1.05e-63, 6.29e-183j)
| (8.7394883670540732732e-37 + 3.3689300563480854402e-785j)  +/-  (1.09e-71, 6.51e-191j)
| (1.6073764534985807459e-47 + 5.0944416184822305507e-791j)  +/-  (1.2e-75, 7.21e-195j)
| (7.9993875296203901662e-30 + 2.9538424312653694044e-781j)  +/-  (1.26e-68, 7.56e-188j)
| (8.7394883670540732732e-37 + 3.1853563097369476196e-785j)  +/-  (2.45e-71, 1.47e-190j)
| (4.8513288384521820741e-08 - 6.7679649986647754032e-770j)  +/-  (5.67e-53, 3.39e-172j)
| (2.3846952252359372429e-05 + 6.5813037197664507292e-768j)  +/-  (5.25e-47, 3.15e-166j)
| (0.00012631269840983313736 - 2.4486964130514795e-767j)  +/-  (1.17e-44, 7e-164j)
| (0.00012631269840983313736 - 1.8267773007177593821e-767j)  +/-  (1.08e-45, 6.48e-165j)
| (0.11058288396937128583 + 4.8568439243516459778e-765j)  +/-  (3.74e-40, 2.24e-159j)
| (0.00055657993002033724312 + 7.2425861831838545299e-767j)  +/-  (2.75e-43, 1.65e-162j)
| (1.3525136266590064113e-11 + 5.1644369490732846048e-772j)  +/-  (2.69e-59, 1.61e-178j)
| (1.6073764534985807459e-47 + 8.3238428959905976554e-791j)  +/-  (2.94e-78, 1.76e-197j)
| (2.6721523595019922704e-41 - 1.2843715756448814776e-787j)  +/-  (8.58e-76, 5.14e-195j)
| (2.3846952252359372429e-05 + 4.7372462447780413056e-768j)  +/-  (2.51e-50, 1.51e-169j)
| (-0.15378425114845131854 - 9.8709004075298425528e-764j)  +/-  (3.74e-40, 2.24e-159j)
| (1.6108529661433476759e-14 + 2.6045920300997651325e-773j)  +/-  (1.22e-64, 7.33e-184j)
| (4.714442027733152169e-33 - 3.9447150937770134732e-783j)  +/-  (1.45e-72, 8.67e-192j)
| (2.6721523595019922704e-41 - 9.5226705838314924706e-788j)  +/-  (2.25e-77, 1.35e-196j)
| (5.3641300522642576971e-13 - 1.6427977209255472938e-772j)  +/-  (7.31e-64, 4.38e-183j)
| (5.8240165518323478581e-27 + 1.0567380583838837287e-779j)  +/-  (2.47e-72, 1.48e-191j)
| (4.7081010882094353492e-22 + 1.6523028032300252236e-777j)  +/-  (5.64e-71, 3.38e-190j)
| (3.7081053783337843868e-06 - 1.7398077574345451679e-768j)  +/-  (1.07e-57, 6.41e-177j)
| (0.078079534881557114265 - 4.8780134604331450589e-765j)  +/-  (2.87e-47, 1.72e-166j)
| (4.0096520044006173484e-09 + 2.3763379072040429998e-770j)  +/-  (2.35e-62, 1.41e-181j)
| (5.3641300522642576971e-13 - 8.4339371496571027088e-773j)  +/-  (4.57e-66, 2.74e-185j)
| (6.371096185872804084e-20 - 1.86952050342399523e-776j)  +/-  (1.05e-70, 6.28e-190j)
| (1.6108529661433476759e-14 + 1.2360709282132734496e-773j)  +/-  (9.89e-68, 5.93e-187j)
| (4.8513288384521820741e-08 - 1.0596277733873782569e-769j)  +/-  (1.99e-63, 1.19e-182j)
| (0.049828329298084158702 + 4.4030959783938827511e-765j)  +/-  (1.68e-47, 1.01e-166j)
| (6.371096185872804084e-20 - 6.1893901944090550814e-776j)  +/-  (3.1e-72, 1.86e-191j)
| (2.6308300629101310362e-10 - 2.8630585415158302286e-771j)  +/-  (2.48e-65, 1.48e-184j)
| (0.0020988155616850048528 - 3.3465137590637455508e-766j)  +/-  (5.69e-56, 3.41e-175j)
| (5.7290873594814024191e-18 + 1.8539781048022432343e-775j)  +/-  (2.47e-70, 1.48e-189j)
| (2.6308300629101310362e-10 - 4.9355919960304585528e-771j)  +/-  (8.45e-67, 5.06e-186j)
| (4.7115934834039231843e-07 + 4.4160365703064193646e-769j)  +/-  (1.86e-63, 1.12e-182j)
| (0.00055657993002033724312 + 9.3799819687735259092e-767j)  +/-  (2.1e-60, 1.26e-179j)
| (2.1789878916982558517e-24 - 1.3089413638803889474e-778j)  +/-  (1.77e-74, 1.06e-193j)
| (5.7290873594814024191e-18 + 4.9497687025378578102e-775j)  +/-  (2.04e-72, 1.22e-191j)
| (0.14634228587878529306 + 1.0444222592219361905e-763j)  +/-  (6.13e-59, 3.67e-178j)
| (5.8240165518323478581e-27 - 1.9495429256213598945e-779j)  +/-  (5.27e-77, 3.16e-196j)
| (0.024707260622980625853 + 1.5906915089790640737e-764j)  +/-  (9.37e-60, 5.61e-179j)
| (0.028478431334842262642 - 3.6235251951298093664e-765j)  +/-  (1.25e-59, 7.5e-179j)
| (0.14932796700559463638 + 5.1110817148377409944e-765j)  +/-  (9.98e-58, 5.98e-177j)
| (3.7081053783337843868e-06 - 1.2062231696811248443e-768j)  +/-  (3.76e-66, 2.25e-185j)
| (0.028478431334842262642 - 4.1597810697590832252e-765j)  +/-  (2.45e-59, 1.47e-178j)
| (0.11058288396937128583 + 5.1327073885668740949e-765j)  +/-  (4.78e-58, 2.86e-177j)
| (0.024707260622980625853 + 1.3198244199731356699e-764j)  +/-  (8.8e-61, 5.27e-180j)
| (0.13829175445283763433 - 5.0252213050015280158e-765j)  +/-  (4.47e-58, 2.68e-177j)
| (0.049828329298084158702 + 3.9462106192120203261e-765j)  +/-  (9.54e-61, 5.72e-180j)
| (0.0020988155616850048528 - 4.1912630387066930746e-766j)  +/-  (3.94e-62, 2.36e-181j)
| (-0.15378425114845131854 - 1.1790911846729684713e-763j)  +/-  (3.27e-59, 1.96e-178j)
| (4.0096520044006173484e-09 + 1.4497786229742524587e-770j)  +/-  (2.19e-69, 1.31e-188j)
| (0.14634228587878529306 + 8.7587923284887410792e-764j)  +/-  (4.25e-61, 2.55e-180j)
| (4.7115934834039231843e-07 + 2.9426379334005182969e-769j)  +/-  (6.95e-68, 4.17e-187j)
| (3.5806519699527982995e-16 - 3.7518713295541912158e-774j)  +/-  (1.98e-74, 1.19e-193j)
| (0.13829175445283763433 - 5.1667581176379472372e-765j)  +/-  (1.44e-63, 8.55e-183j)
| (1.3525136266590064113e-11 + 9.4219425039638779839e-772j)  +/-  (9.34e-72, 5.59e-191j)
| (3.5806519699527982995e-16 - 1.6116513973175026434e-774j)  +/-  (1.28e-74, 7.69e-194j)
| (0.078079534881557114265 - 4.4924861462587700431e-765j)  +/-  (1.96e-64, 1.14e-183j)
