Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 7 50
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P2 : t^11 - 41*t^9 + 528*t^7 - 2520*t^5 + 4095*t^3 - 1575*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^61 - 159780808144946850849720776913993034898630070509315114892399548236809303183552022919486788037287/100371175104610794176270587397583032050826432384911432142286510164079626087515255181457820082*t^59 + 16920872504903924219997027400238389018654191869090700529397517223501415952918326013961477470525003/14338739300658684882324369628226147435832347483558776020326644309154232298216465025922545726*t^57 - 2093600716791832125925342625322359603721497240126883928791982580491329339905329298486982427488820675590/3864290241527515575786417614806946733956817646819090137478030641317065604369337324486126073157*t^55 + 667871905674191422322863550857891194654301058903291637280162276441507526401459045441546735476009828546315/3864290241527515575786417614806946733956817646819090137478030641317065604369337324486126073157*t^53 - 28627075379380359541565710940045635397828854479955867115186947807498032407436045623173727424543101022138825/702598225732275559233894111783081224355785026694380024996005571148557382612606786270204740574*t^51 + 56967521442231230933736363665681892900373349583112222123144510072101301641687628101512295517078974701931602025/7728580483055031151572835229613893467913635293638180274956061282634131208738674648972252146314*t^49 - 82724225890473480051623940317632977237508693303252070045991350323989372021090702176347223237066714206217822400/78863066153622766852784032955243810897077911159573268111796543700348277640190557642574001493*t^47 + 409518761565027971451951619385282387877725576972404418737068891675014947187814427063182369196226432138228499375/3428828963200989863164523171967122212916430919981446439643327986971664245225676419242347891*t^45 - 6863287206773352659221944723911884862094451688670495298600320503945434678636242815098472382151148357211492532875/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^43 + 516327969467520883350800159317927691247669367382949087029806823853024947118871288352265915658183810319906464637625/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^41 - 15936118585274951401972355308513498079650972602666867566836438748918575478646648021221558943375494233174855851834750/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^39 + 809714338457269421062330249411447523797033880381290110396192980476660439859102028350988344474412997607166841796694875/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^37 - 67818338497390518085729472641532272570863036777524860771469105805170867187811695413879850542054000336443496598444181875/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^35 + 2340152978353774612886293491772624917167116549480248454438471417398294145578977980012267179996126805553389951607219345625/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^33 - 33209040528286985412165288509882572289126686451407684975188887340150559047921168543941385010538740277954330174455258590000/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^31 + 772781589551746179614393733869947633571187692273581920907845017098874111533973979212856669463074516638557722256072912786875/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^29 - 29351705821549109945130204832188445620551177113720889836275291919487656822974525638057637712540236785163949600043021118193125/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^27 + 452119767326125705215553912363776054402515741773757581795471423254466867005331716671499050427906840929897106069517195250784375/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^25 - 2802304948338281798772379582349043271609327954873932778184413845648151567906232922254667376898546070074395441169401296276656250/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^23 + 27684275245083867525152899473931061589996571329917085988949202208337612114017526527813168726053692562358036812341463671018953125/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^21 - 430659646488430189711865624051208912312658952708388453302982847923401240983636462900423442312850835991624236367252446226160328125/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^19 + 2597587219698270978352310555292548320324132965764685092579536249681553965794764649569804318126344523810624873329283683687185984375/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^17 - 5959035681127417363221114155333294806103510376983194431170828005656551296221434468152505799122819832006245033987102749909736250000/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^15 + 20282628310618264616260192516998968006283198590280859540938420932034999832354366282421162762872700516658636388860755387947344609375/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^13 - 99031694638442722576733108535488769125703640039515760609322609337074044874343407437706952754854627166842850596400590795598934015625/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^11 + 165411921160853798955631429309157981130339679849914337920417516469335835787531409780824743540613107172873002252329133018919389171875/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^9 - 88163620056482861324495796113300036236002567439004925546999855016289482266728841514717837973421670349596512994219007479414093406250/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^7 + 53715951728280908639906399173428096683880089826235484661751897627190437405315563344903103650338456678878038272959463275378783515625/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^5 - 30705653516209711921362997898995933601514035403032128828846563247689347693802819923755101415679317940194753343983125275883297890625/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^3 + 2611712053686638207598833125877332311503732718409969748444503409908438723489136389598145915786783089688252659346461790427988671875/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*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:
| (-10.367350044414017961 - 2.3657750952555887807e-945j)  +/-  (1.64e-241, 1.64e-241j)
| (12.242631159393501613 + 7.6047836523543494624e-952j)  +/-  (4.61e-243, 4.61e-243j)
| (9.8126281613036578462 - 2.2753385962412029801e-947j)  +/-  (3e-241, 3e-241j)
| (5.9388805343429787612 - 8.4139595966424600164e-954j)  +/-  (3.28e-242, 3.28e-242j)
| (-12.995530651104013326 - 4.3853225583345677891e-954j)  +/-  (6.19e-244, 6.19e-244j)
| (-12.242631159393501613 + 2.0121434951982287204e-953j)  +/-  (4.68e-243, 4.68e-243j)
| (-8.766384299957083385 + 1.601019163150517137e-952j)  +/-  (4.97e-241, 4.97e-241j)
| (-13.904706783445003456 + 2.9503306066183064562e-960j)  +/-  (3.24e-245, 3.24e-245j)
| (13.904706783445003456 - 7.1469559044885944011e-960j)  +/-  (3.36e-245, 3.36e-245j)
| (5.4974742997799397604 - 9.2844174627767359661e-956j)  +/-  (1.29e-242, 1.29e-242j)
| (8.2677470728660210541 + 4.69666359043954245e-957j)  +/-  (4.84e-241, 4.84e-241j)
| (-9.8126281613036578462 + 6.0812390536938177992e-965j)  +/-  (2.87e-241, 2.87e-241j)
| (-6.3871764613008377069 - 2.367814279357924184e-968j)  +/-  (7.91e-242, 7.91e-242j)
| (12.995530651104013326 + 2.3491655338861135625e-969j)  +/-  (6.54e-244, 6.54e-244j)
| (8.766384299957083385 + 5.5999078888679507435e-967j)  +/-  (5.33e-241, 5.33e-241j)
| (-10.950348680748157319 + 2.1758790091174922356e-973j)  +/-  (6.58e-242, 6.58e-242j)
| (3.7895512460677696538 + 1.6265396555370758279e-976j)  +/-  (9.94e-245, 9.94e-245j)
| (10.950348680748157319 + 4.097718732945696453e-971j)  +/-  (6.54e-242, 6.54e-242j)
| (-2.3344142183389772393 - 7.1917260323909495343e-978j)  +/-  (7.93e-246, 7.93e-246j)
| (-8.2677470728660210541 - 7.9178375531698154772e-972j)  +/-  (4.58e-241, 4.58e-241j)
| (11.57050266908651828 + 1.2474638781282443781e-973j)  +/-  (2.26e-242, 2.26e-242j)
| (3.3747086797406716539 - 1.7080270657565454293e-977j)  +/-  (2.34e-245, 2.34e-245j)
| (2.3013955541771823955 - 3.3819703631930977081e-979j)  +/-  (6.13e-246, 6.13e-246j)
| (-6.8431463168447814523 - 2.61642649524048357e-973j)  +/-  (1.51e-241, 1.51e-241j)
| (-9.2803397444522850917 - 8.8653017519105408552e-973j)  +/-  (4.5e-241, 4.5e-241j)
| (5.0623149520260404652 + 1.2432270708907895824e-973j)  +/-  (4.6e-243, 4.6e-243j)
| (2.9619421584142826705 + 5.3728643763558729755e-983j)  +/-  (5.8e-246, 5.8e-246j)
| (10.367350044414017961 + 2.2796000982411095652e-977j)  +/-  (1.64e-241, 1.64e-241j)
| (-7.7821322586958336012 - 2.7896311061141594757e-981j)  +/-  (4.01e-241, 4.01e-241j)
| (-2.3013955541771823955 + 5.0941279844016859442e-993j)  +/-  (6.29e-246, 6.29e-246j)
| (2.3344142183389772393 + 1.1119095823662516399e-993j)  +/-  (7.76e-246, 7.76e-246j)
| (-3.7895512460677696538 + 3.5587636440528666893e-989j)  +/-  (9.15e-245, 9.15e-245j)
| (7.3077436237221767307 - 6.5124330754460293398e-989j)  +/-  (2.61e-241, 2.61e-241j)
| (-11.57050266908651828 - 1.3359140944593949488e-1001j)  +/-  (2.26e-242, 2.26e-242j)
| (9.2803397444522850917 - 2.6499707085050317659e-1004j)  +/-  (4.02e-241, 4.02e-241j)
| (-1.1044256274198961776 - 3.1525192702603368098e-1031j)  +/-  (5.23e-251, 5.23e-251j)
| (6.8431463168447814523 + 3.6138381495314629485e-1022j)  +/-  (1.64e-241, 1.64e-241j)
| (-7.3077436237221767307 - 5.3489145930230347348e-1029j)  +/-  (2.56e-241, 2.56e-241j)
| (1.1044256274198961776 - 9.0454553955317357185e-1041j)  +/-  (5.31e-251, 5.31e-251j)
| (-1.837597716535811529 - 3.4821789414189673558e-1038j)  +/-  (1.37e-248, 1.37e-248j)
| (-3.3747086797406716539 - 7.0918192359948746759e-1035j)  +/-  (2.58e-245, 2.58e-245j)
| (-2.5135563360455431336 - 8.5965379841458051188e-1036j)  +/-  (3.64e-246, 3.64e-246j)
| (1.4655215253859805014 - 3.9188150106179437855e-1040j)  +/-  (8.14e-250, 8.14e-250j)
| (-5.0623149520260404652 - 1.0200728902226487052e-1032j)  +/-  (4.61e-243, 4.61e-243j)
| (-2.9619421584142826705 - 1.1444439670845656817e-1036j)  +/-  (5.72e-246, 5.72e-246j)
| (4.6328811754148542753 + 1.6028240162072890238e-1031j)  +/-  (1.33e-243, 1.33e-243j)
| (-5.4974742997799397604 + 7.8521204948790759834e-1034j)  +/-  (1.33e-242, 1.33e-242j)
| (-4.6328811754148542753 - 6.6235570417881805753e-1035j)  +/-  (1.29e-243, 1.29e-243j)
| (0.37320482172801912193 + 1.8356233881845408131e-1051j)  +/-  (1.77e-253, 1.77e-253j)
| (-5.9388805343429787612 + 4.9958808681999506645e-1039j)  +/-  (3.41e-242, 3.41e-242j)
| (6.3871764613008377069 - 4.1387297038371659468e-1051j)  +/-  (7.45e-242, 7.45e-242j)
| (-1.4655215253859805014 + 7.4418400422470206849e-1067j)  +/-  (8.18e-250, 8.18e-250j)
| (-4.2087518096017645116 + 3.1783791217574410927e-1061j)  +/-  (3.61e-244, 3.61e-244j)
| (1.837597716535811529 + 4.9242068583335711444e-1072j)  +/-  (1.39e-248, 1.39e-248j)
| (0.74196378430272585765 + 9.435148407834292022e-1075j)  +/-  (3.16e-252, 3.16e-252j)
| (-0.74196378430272585765 - 1.4118113105410061164e-1074j)  +/-  (3.16e-252, 3.16e-252j)
| (-0.37320482172801912193 + 2.3777448754888619256e-1076j)  +/-  (1.77e-253, 1.77e-253j)
| (7.7821322586958336012 + 8.3722297683699615238e-1069j)  +/-  (3.81e-241, 3.81e-241j)
| (4.2087518096017645116 - 5.5559235892704777248e-1077j)  +/-  (3.97e-244, 3.97e-244j)
| (-7.7246840271931348645e-1104 - 7.3813865262353980054e-1104j)  +/-  (6.52e-1102, 6.52e-1102j)
| (2.5135563360455431336 + 2.9738065468161830007e-1082j)  +/-  (3.63e-246, 3.63e-246j)
-------------------------------------------------
The weights are:
| (1.0366091916415821056e-24 - 1.3870651006710258941e-968j)  +/-  (2.36e-65, 5.16e-185j)
| (8.0002518091883128189e-34 - 2.0794004975067588494e-976j)  +/-  (5.19e-70, 1.14e-189j)
| (2.6722187085015550242e-22 + 3.5167351857498117612e-968j)  +/-  (2.25e-64, 4.93e-184j)
| (3.8918901504528354364e-09 + 3.2717893384206970776e-961j)  +/-  (3.49e-52, 7.65e-172j)
| (6.8714185857065334609e-38 + 7.9111516615560637789e-977j)  +/-  (1.9e-72, 4.16e-192j)
| (8.0002518091883128189e-34 - 1.6056720391539649208e-974j)  +/-  (4.91e-71, 1.08e-190j)
| (4.1427371941989149493e-18 + 6.951106180023662825e-966j)  +/-  (4.47e-64, 9.78e-184j)
| (4.3527454385648689903e-43 - 1.0591441294945725131e-979j)  +/-  (1.1e-74, 2.41e-194j)
| (4.3527454385648689903e-43 + 3.9870317921490118503e-981j)  +/-  (9.78e-77, 2.14e-196j)
| (4.7851597921205155529e-08 - 1.3739986948308887507e-960j)  +/-  (5.93e-55, 1.3e-174j)
| (2.8148246950188220041e-16 - 1.4892165980595696518e-965j)  +/-  (2.3e-64, 5.04e-184j)
| (2.6722187085015550242e-22 + 9.289106623154526862e-968j)  +/-  (1.9e-67, 4.16e-187j)
| (2.4962854505146472581e-10 - 1.0137576447893384685e-961j)  +/-  (4.24e-60, 9.28e-180j)
| (6.8714185857065334609e-38 - 7.447199392207707558e-979j)  +/-  (3.76e-75, 8.23e-195j)
| (4.1427371941989149493e-18 + 1.7624205927740797891e-966j)  +/-  (3.13e-66, 6.85e-186j)
| (2.1913879272700536767e-27 - 1.4791672040024534023e-970j)  +/-  (7.97e-71, 1.75e-190j)
| (0.00012662999527792034264 - 3.7547239704311878143e-958j)  +/-  (4.56e-52, 9.98e-172j)
| (2.1913879272700536767e-27 - 5.2033108766701248844e-972j)  +/-  (1.32e-71, 2.89e-191j)
| (-0.057892907945988112882 - 1.4286458184583491958e-954j)  +/-  (8.06e-46, 1.77e-165j)
| (2.8148246950188220041e-16 - 5.8096685796101667338e-965j)  +/-  (9.08e-67, 1.99e-186j)
| (2.1784738365119294583e-30 + 5.0976003092438716689e-974j)  +/-  (7.64e-73, 1.67e-192j)
| (0.00055452268172165878693 + 1.5387934252815317132e-957j)  +/-  (4.02e-52, 8.79e-172j)
| (0.064439767325835695765 + 9.6759754776737406497e-955j)  +/-  (9.75e-47, 2.13e-166j)
| (1.2446811278523158235e-11 + 1.8265166125029832401e-962j)  +/-  (8.77e-65, 1.92e-184j)
| (4.1427737069762344119e-20 - 7.7496810166971097238e-967j)  +/-  (1.07e-68, 2.35e-188j)
| (4.6965006725234194915e-07 + 5.5620955655208471173e-960j)  +/-  (1.91e-59, 4.18e-179j)
| (0.0020571385630529171204 - 7.2359093009497685663e-957j)  +/-  (7.1e-52, 1.55e-171j)
| (1.0366091916415821056e-24 + 4.1344897055634529633e-970j)  +/-  (2.56e-71, 5.6e-191j)
| (1.3524833579655723462e-14 + 4.3904584585244034616e-964j)  +/-  (5.11e-67, 1.12e-186j)
| (0.064439767325835695765 + 1.3286999223656414568e-954j)  +/-  (3.18e-51, 6.97e-171j)
| (-0.057892907945988112882 - 1.0356972366244178338e-954j)  +/-  (1.21e-49, 2.64e-169j)
| (0.00012662999527792034264 - 6.2780328566560462745e-958j)  +/-  (1.34e-59, 2.93e-179j)
| (4.7424367380062215562e-13 - 8.297982610278078902e-964j)  +/-  (1.06e-66, 2.31e-186j)
| (2.1784738365119294583e-30 + 1.7242192464314063911e-972j)  +/-  (2.06e-75, 4.51e-195j)
| (4.1427737069762344119e-20 - 2.2493058542530122131e-967j)  +/-  (4.67e-70, 1.02e-189j)
| (0.078096541309374226152 - 1.3046500504961535694e-955j)  +/-  (1.07e-48, 2.35e-168j)
| (1.2446811278523158235e-11 + 5.1133770456585307443e-963j)  +/-  (7.12e-66, 1.56e-185j)
| (4.7424367380062215562e-13 - 2.9829130724678325784e-963j)  +/-  (1.61e-67, 3.52e-187j)
| (0.078096541309374226152 - 1.1201228341116342986e-955j)  +/-  (8.8e-50, 1.93e-169j)
| (0.028282880232825848127 - 1.1532967951611321123e-955j)  +/-  (2.17e-54, 4.74e-174j)
| (0.00055452268172165878693 + 2.4406733267549839511e-957j)  +/-  (6.34e-61, 1.39e-180j)
| (0.011067271512401275079 + 1.6743626141676856478e-955j)  +/-  (3.86e-57, 8.44e-177j)
| (0.049626599054940172238 + 9.7878456873268428988e-956j)  +/-  (1.78e-54, 3.89e-174j)
| (4.6965006725234194915e-07 + 1.0389406811903762091e-959j)  +/-  (3.07e-66, 6.72e-186j)
| (0.0020571385630529171204 - 1.0866950376409626358e-956j)  +/-  (3.3e-60, 7.23e-180j)
| (3.717853533724866243e-06 - 2.3144750189836806078e-959j)  +/-  (3.02e-65, 6.61e-185j)
| (4.7851597921205155529e-08 - 2.396283769781344908e-960j)  +/-  (3.31e-67, 7.25e-187j)
| (3.717853533724866243e-06 - 4.2356656113523715233e-959j)  +/-  (5.67e-66, 1.24e-185j)
| (0.13828505732722496449 - 1.2838684497308678517e-955j)  +/-  (6.31e-60, 1.38e-179j)
| (3.8918901504528354364e-09 + 5.13694974292943927e-961j)  +/-  (4.63e-68, 1.01e-187j)
| (2.4962854505146472581e-10 - 2.3946094605432193656e-962j)  +/-  (1.07e-70, 2.33e-190j)
| (0.049626599054940172238 + 1.1982425659216053807e-955j)  +/-  (1.56e-61, 3.41e-181j)
| (2.3952647107262769137e-05 + 1.6491558598173943243e-958j)  +/-  (2e-65, 4.37e-185j)
| (0.028282880232825848127 - 8.9502359668667151906e-956j)  +/-  (3.69e-63, 8.08e-183j)
| (0.11072522224720034095 + 1.2235851189198396547e-955j)  +/-  (9.7e-62, 2.13e-181j)
| (0.11072522224720034095 + 1.3556060275727596697e-955j)  +/-  (5.01e-62, 1.1e-181j)
| (0.13828505732722496449 - 1.3517768499540556587e-955j)  +/-  (2.74e-62, 6e-182j)
| (1.3524833579655723462e-14 + 1.1736025445739201148e-964j)  +/-  (1.64e-73, 3.59e-193j)
| (2.3952647107262769137e-05 + 9.3895260714396100685e-959j)  +/-  (1.01e-67, 2.22e-187j)
| (0.14920617107874674338 + 1.3232801542185320162e-955j)  +/-  (3.09e-64, 7.5e-184j)
| (0.011067271512401275079 + 1.1845377994909214388e-955j)  +/-  (1.84e-64, 4.03e-184j)
