Starting with polynomial:
P : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Extension levels are: 6 8 26
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : 231/16*t^14 - 3731/80*t^12 + 1182181/20400*t^10 - 200960617/5814000*t^8 + 14859361517/1482570000*t^6 - 123220867/98838000*t^4 + 4422019/98838000*t^2 - 22771/889542000
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 231/16*t^40 - 1188679641939255157663064435774016002609900591237855264493337500903767036061725563779091012539510957737593571111/8498062580836962605514962553601883044646250258256244404582346687380663435423055272048289936880742088574445840*t^38 + 58284910561017626792621425631505145147774956133560881995926599097719574604950688408288069442585283509975199642075697/93181256198877294969471564400244647584546134081779719896245431427128974569413801058009499157897337001218798635600*t^36 - 2773867391502034552932835647347026694547337567246578572354415603618541911991817804196193604423129433866584294408609727269/1619956139017481773044263147098253198257334541011740430396226825360637222889258931393495142860045203766188814279906000*t^34 + 400830538120296902114609110723102804650379217212080460250294642524264184979919160040027442475369700061095479795986965194256817/124907730571529818036686062621477749259880690618798378223470067011197783469140615691927563924688072964644342393061077071250*t^32 - 961485369844559161177744774857873295502903720667842839969047238593328246515501425098162389399582992810886864598848557215145849/220425406890934973005916581096725439870377689327291255688476588843290206122012851221048642220037775819960604223048959537500*t^30 + 332101057507639557742801070392359926842042606411536365817011502238080515387639579440048158238817656949730502979686141066835903297/74713327730748391158980737456920950020261968647910881789223762304846081593578553460171487310507865865889115912886533137062500*t^28 - 44413048000619054215752792749091337543602195810100385267148744268503182997219483224551743769065900968455406777531062808093598576857/12829772637924113729820172236102465537479385256219256620845504462988169131249309200180647800960410726490478984560875470296372500*t^26 + 2723835132849780028081389449006635277979219717723204022296370954800451543939656851508052277760563897623173919269061123634359562168047/1308636809068259600441657568082451484822897296134364175326241455224793251387429538418426075697961894102028856425209297970229995000*t^24 - 20723902985653052392101530056081925015162405108245056548824733792747175852650509136389406523247651203593735377452361157558803830329581/21374401214781573473880406945346707585440655836861281530328610435338289772661349127500959236400044270333137988278418533513756585000*t^22 + 1065971816624394181393023995680946778075124307136991069146171186715896766944351158909832844803518478548037288724261688395111239111217/3053485887825939067697200992192386797920093690980183075761230062191184253237335589642994176628577752904733998325488361930536655000*t^20 - 36694251934780532189490497262587828886855722101129089903346873041090076505738896709566458063551178447144299513341360646010695457361/380628434770546421181091536422873700571756831285618388945305686422723798880000281257436947225168971968734154915919601902698475000*t^18 + 192388253796305681365636278583685536879813488978856602794618290932144035073741633040160791789516175432219516001428089741612559501761/9552778605721707207145577717060083155722150695775464390268492191468085721041261960787138128430891081455831904978037119909620092500*t^16 - 1220797531342982892600533114645046724159802187569267836320878645973859116984627320469119117334904394400016151625789823487377845723287/391663922834589995492968686399463409384608178526794040001008179850191514562691740392272663265666534339689108104099521916294423792500*t^14 + 9936512864466965767754644255001851018404081071356791198178418194568764059195514058927187723598170486931435411342001226918163904371/28658335817165121621436733151180249467166452087326393170805476574404257163123785882361414385292673244367495714934111359728860277500*t^12 - 10392729094760187472773706680967368998353289170970742390525272833890578663114680607758706079383742717703065314522670257188775951797/391663922834589995492968686399463409384608178526794040001008179850191514562691740392272663265666534339689108104099521916294423792500*t^10 + 71808933556781906531751539463705734303397606655159907678082598637533251432323976345503306148175351364731054892130974679633537027449/54832949196842599369015616095924877313845144993751165600141145179026812038776843654918172857193314807556475134573933068281219330950000*t^8 - 177085592308900202843109770150114270281877816808934086512633865474794594451032745837442693156264709101342102225486517382662858873/4699967074015079945915624236793560912615298142321528480012098158202298174752300884707271959187998412076269297249194262995533085510000*t^6 + 20295629118985905723246972325965948508836398919092858704167297624347432852078722658906287876776745183468409974084474148878297/38211114422886828828582310868240332622888602783101857561073968765872342884165047843148552513723564325823327619912148479638480370000*t^4 - 4013564280159674239751042282008068393641921821091670285237595358459917694709444614872681197955349193310768347564983796815597/1566655691338359981971874745597853637538432714107176160004032719400766058250766961569090653062666137358756432416398087665177695170000*t^2 + 1725339343189928990092671131629461451579444978522761937668694469087848631279552469299318900714723342592830391291305311/1309588348796771501957913874029165579366491742442531155421327660180206921757607057658372991724210083860260794899156296190705813300
-------------------------------------------------
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:
| (0.93246951420315202781 - 3.3188662946031301226e-859j)  +/-  (7.28e-242, 7.28e-242j)
| (0.97280484429821866348 + 5.3903640768930610771e-886j)  +/-  (7.57e-242, 7.57e-242j)
| (-0.86616921466037025174 + 6.2600482080282011778e-910j)  +/-  (1.01e-242, 1.01e-242j)
| (0.98851944675836295466 - 4.7008345276968560351e-910j)  +/-  (4.48e-242, 4.48e-242j)
| (0.9535263841219116597 - 1.4905096793725591528e-927j)  +/-  (1e-241, 1e-241j)
| (0.82190330787833020415 - 1.7347164476595018945e-936j)  +/-  (2.74e-243, 2.74e-243j)
| (0.99778892484414950241 - 4.4162856142597050246e-937j)  +/-  (1.42e-242, 1.42e-242j)
| (-0.90372031405463366803 - 1.111918809022157801e-941j)  +/-  (2.91e-242, 2.91e-242j)
| (-0.93246951420315202781 - 3.8306321241374431293e-940j)  +/-  (6.93e-242, 6.93e-242j)
| (-0.02411517758027983534 + 1.2665739049101735432e-947j)  +/-  (2.76e-255, 2.76e-255j)
| (0.90372031405463366803 - 4.1286290930563321315e-942j)  +/-  (2.79e-242, 2.79e-242j)
| (-0.97280484429821866348 + 3.0558222152278157087e-949j)  +/-  (8.37e-242, 8.37e-242j)
| (-0.98851944675836295466 + 2.835038548116838738e-951j)  +/-  (4.97e-242, 4.97e-242j)
| (-0.77244165097321173678 + 6.7275110524111836288e-956j)  +/-  (6.36e-244, 6.36e-244j)
| (-0.99778892484414950241 - 9.9302702513795263125e-954j)  +/-  (1.39e-242, 1.39e-242j)
| (0.86616921466037025174 - 2.2020853381472755793e-955j)  +/-  (9.79e-243, 9.79e-243j)
| (0.59920627834642048211 - 9.1348178883568129936e-964j)  +/-  (3.02e-246, 3.02e-246j)
| (-0.9535263841219116597 - 1.3146996012186197238e-959j)  +/-  (1.01e-241, 1.01e-241j)
| (-0.82190330787833020415 + 9.7980049443742193308e-963j)  +/-  (2.77e-243, 2.77e-243j)
| (-0.46194088448213480754 - 1.8535237152320518243e-968j)  +/-  (2.96e-248, 2.96e-248j)
| (0.53257188365324649169 + 1.6707433603817437504e-965j)  +/-  (3.32e-247, 3.32e-247j)
| (0.71879967573286822574 - 2.2970638127730285796e-962j)  +/-  (1.33e-244, 1.33e-244j)
| (-0.53257188365324649169 + 4.3621536556295804603e-970j)  +/-  (3.34e-247, 3.34e-247j)
| (-0.71879967573286822574 + 4.9466944192479346832e-968j)  +/-  (1.34e-244, 1.34e-244j)
| (-0.59920627834642048211 - 1.5910725357324934264e-968j)  +/-  (2.7e-246, 2.7e-246j)
| (0.088796399489429533958 + 1.2020323461629288845e-967j)  +/-  (3.71e-254, 3.71e-254j)
| (0.66120938646626451366 + 1.2588724976328042424e-967j)  +/-  (2.02e-245, 2.02e-245j)
| (0.31382128214859103935 - 1.3808264065995015004e-969j)  +/-  (1.61e-250, 1.61e-250j)
| (-0.088796399489429533958 + 4.4507740141779317635e-971j)  +/-  (3.71e-254, 3.71e-254j)
| (-0.66120938646626451366 + 1.505173339377307766e-969j)  +/-  (2.13e-245, 2.13e-245j)
| (-0.16321357943108126031 + 9.6997355039000926332e-977j)  +/-  (6.25e-253, 6.25e-253j)
| (0.38856703034965661823 - 3.5872825124065954094e-972j)  +/-  (2.17e-249, 2.17e-249j)
| (0.46194088448213480754 - 3.2617865676752050596e-972j)  +/-  (2.78e-248, 2.78e-248j)
| (0.02411517758027983534 - 1.7521543288293252443e-973j)  +/-  (2.76e-255, 2.76e-255j)
| (-0.38856703034965661823 + 6.7426277023570086454e-976j)  +/-  (2.09e-249, 2.09e-249j)
| (-0.31382128214859103935 - 6.6573166440086124503e-978j)  +/-  (1.81e-250, 1.81e-250j)
| (0.23861918608319690863 - 1.4931029694860692426e-978j)  +/-  (1.05e-251, 1.05e-251j)
| (0.77244165097321173678 - 1.4681768821219663821e-981j)  +/-  (6.57e-244, 6.57e-244j)
| (0.16321357943108126031 - 2.8911597394888622712e-991j)  +/-  (6.47e-253, 6.47e-253j)
| (-0.23861918608319690863 - 3.4035476991966246404e-999j)  +/-  (9.02e-252, 9.02e-252j)
-------------------------------------------------
The weights are:
| (0.023937983092018416762 - 1.8072061577967931743e-860j)  +/-  (6.74e-75, 1.27e-191j)
| (0.01820821464452647425 - 6.9537487078899493314e-860j)  +/-  (3.46e-75, 6.51e-192j)
| (0.041207007512317227593 - 4.5236833495734001783e-861j)  +/-  (2.2e-77, 4.13e-194j)
| (0.012753553803853666871 + 1.8474029718915024122e-860j)  +/-  (1.17e-75, 2.2e-192j)
| (0.01970260162404126097 + 2.7714923260924167921e-859j)  +/-  (1.64e-75, 3.09e-192j)
| (0.047077814592151262524 - 8.1663000182192375427e-860j)  +/-  (1.16e-77, 2.18e-194j)
| (0.0056569092321986798128 - 3.756516107092517609e-861j)  +/-  (3.34e-76, 6.27e-193j)
| (0.0335213183560389201 + 4.3974861430643597052e-861j)  +/-  (2.45e-78, 4.6e-195j)
| (0.023937983092018416762 - 4.2600301690705390261e-861j)  +/-  (9.55e-79, 1.79e-195j)
| (0.053256561462736143564 + 2.7459736060872709969e-859j)  +/-  (2.89e-80, 5.44e-197j)
| (0.0335213183560389201 - 2.8086413827466009238e-859j)  +/-  (9.18e-77, 1.73e-193j)
| (0.01820821464452647425 - 1.472133124971578317e-861j)  +/-  (7.22e-80, 1.36e-196j)
| (0.012753553803853666871 + 5.3902866742652453294e-862j)  +/-  (1.63e-80, 3.06e-197j)
| (0.051668639220949068534 - 6.276493005407874807e-861j)  +/-  (6.88e-82, 1.29e-198j)
| (0.0056569092321986798128 - 1.2711946401322504898e-862j)  +/-  (4.74e-81, 8.91e-198j)
| (0.041207007512317227593 + 1.2272149787811346999e-859j)  +/-  (1.13e-80, 2.12e-197j)
| (0.064350902555104766514 - 5.3725747855381568748e-860j)  +/-  (8.18e-84, 1.54e-200j)
| (0.01970260162404126097 + 3.0943308754380984091e-861j)  +/-  (2.52e-80, 4.73e-197j)
| (0.047077814592151262524 + 5.1466643883228616593e-861j)  +/-  (1.18e-81, 2.21e-198j)
| (0.072238889502367613326 + 1.8492175789408851092e-860j)  +/-  (5.12e-85, 9.63e-202j)
| (0.068805833041694668921 + 5.2681202905420905876e-860j)  +/-  (1.08e-84, 2.03e-201j)
| (0.055575651624767740026 - 6.0462687542818401948e-860j)  +/-  (6.73e-84, 1.26e-200j)
| (0.068805833041694668921 - 1.4379858649196743402e-860j)  +/-  (3.79e-85, 7.12e-202j)
| (0.055575651624767740026 + 7.82371085192584961e-861j)  +/-  (2.26e-84, 4.24e-201j)
| (0.064350902555104766514 + 1.1689690903388635651e-860j)  +/-  (2.79e-85, 5.24e-202j)
| (0.072305835503200603387 + 1.8609860512182612151e-859j)  +/-  (1.4e-87, 2.62e-204j)
| (0.059702915972848991182 + 5.6582554981144326704e-860j)  +/-  (9.37e-86, 1.76e-202j)
| (0.075060995304186219072 - 7.2976176041041793246e-860j)  +/-  (4.63e-88, 8.7e-205j)
| (0.072305835503200603387 - 1.5373703138619757355e-859j)  +/-  (4.52e-88, 8.48e-205j)
| (0.059702915972848991182 - 9.6309181764391653893e-861j)  +/-  (2.2e-86, 4.14e-203j)
| (0.075374457593177245843 + 8.5924170688643230081e-860j)  +/-  (1.39e-88, 2.61e-205j)
| (0.074270305731869096241 + 6.1233655337106264378e-860j)  +/-  (8.47e-89, 1.59e-205j)
| (0.072238889502367613326 - 5.4801515968022358424e-860j)  +/-  (1.16e-88, 2.18e-205j)
| (0.053256561462736143564 - 2.8917749491793308963e-859j)  +/-  (1.24e-88, 2.33e-205j)
| (0.074270305731869096241 - 2.5211367066726566861e-860j)  +/-  (1.26e-89, 2.37e-206j)
| (0.075060995304186219072 + 3.6224757835049525392e-860j)  +/-  (5.46e-90, 1.03e-206j)
| (0.075323609629951934507 + 9.1534649063456821326e-860j)  +/-  (1.74e-90, 3.33e-207j)
| (0.051668639220949068534 + 6.6868748898405382626e-860j)  +/-  (5.9e-91, 1.11e-207j)
| (0.075374457593177245843 - 1.2238535564367628024e-859j)  +/-  (1.95e-90, 3.75e-207j)
| (0.075323609629951934507 - 5.4232737683742462268e-860j)  +/-  (1.13e-90, 1.98e-207j)
