Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 59
-------------------------------------------------
Trying to find an order 59 Kronrod extension for:
P1 : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 256*t^67 - 244856694290676702757325000745002579655942832313721527863290496641510914273583232/967528771764560602463735145922041574307692450758956315504021178199395590253*t^65 + 6018254093870891682555944735947400269233196808104695186448355129850905975722823032960/51279024903521711930577962733868203438307699890224684721713122444567966283409*t^63 - 2516448666144918674191644830025833135801774725659387640930218235611200049562674336724160/74069702638420250566390390615587404966444455396991211264696732419931506853813*t^61 + 26033156001269420616717703258859486327342359183067637484616949559454304994965685153816839520/3777554834559432778885909921394957653288667225246551774499533353416506849544463*t^59 - 3938042971030209549544698827410874075243293925918518451215193417665755297759716419124673453200/3777554834559432778885909921394957653288667225246551774499533353416506849544463*t^57 + 153873653156581661302629549714865349857229367838826412504229692319671269545132917245792670629000/1259184944853144259628636640464985884429555741748850591499844451138835616514821*t^55 - 4779668607203072389806120734482509049808725411670346119828902182814073697253908797825116683066900/419728314951048086542878880154995294809851913916283530499948150379611872171607*t^53 + 523142414069886404915539339437262501935432680677708549664539413947406982908212555879254172024250/609184782222130749699388795580544694934473024551935457909939260347767593863*t^51 - 1902082805242713541919809381276876459640414490039456059876926308535864104898421255615412188179875/35834398954242985276434635034149687937321942620702085759408191785162799639*t^49 + 194499776237796740997236578795428413537787773609456277776368701435676676495506217186700075775600875/71668797908485970552869270068299375874643885241404171518816383570325599278*t^47 - 16559588436707878021097134404812843172433960697976082418842956136922115354721987749952851275158570125/143337595816971941105738540136598751749287770482808343037632767140651198556*t^45 + 1179152010564490088235108886792719290927010419194814394721430588084686825005613915945447370852695809375/286675191633943882211477080273197503498575540965616686075265534281302397112*t^43 - 70421189267628279525621842798058175926417697311558103528191496719202749228662470737186034136627189173125/573350383267887764422954160546395006997151081931233372150531068562604794224*t^41 + 3532275589668572603952488052583557237825324969841447362869523729566386759028950222117285633029843546189375/1146700766535775528845908321092790013994302163862466744301062137125209588448*t^39 - 148824542377704220888948638039508203266277554341590473957725508894230764334093825386702214040388617118860625/2293401533071551057691816642185580027988604327724933488602124274250419176896*t^37 + 1315334583433163110113137921044540387303855411821731029031663374005323147294838273744556340012920136868605625/1146700766535775528845908321092790013994302163862466744301062137125209588448*t^35 - 77859941255941082697325181461810880140982281633609482895995837794897828845344428111384818922353415097546459375/4586803066143102115383633284371160055977208655449866977204248548500838353792*t^33 + 3845210689856944200297480598359027070258685661904700844382121688260672236199860754759734282523313920333437753125/18347212264572408461534533137484640223908834621799467908816994194003353415168*t^31 - 78843511465190128133454258519751904086512788850671148592408558938887638792018192695428783050636767909713191621875/36694424529144816923069066274969280447817669243598935817633988388006706830336*t^29 + 1334125694817225088018665386634987596094440980239377761954809778594912581014213298522897282694883746518706827665625/73388849058289633846138132549938560895635338487197871635267976776013413660672*t^27 - 18484257403478317185844159693275490541544388804024471445397297265285531989920884359287366979299597863908570119371875/146777698116579267692276265099877121791270676974395743270535953552026827321344*t^25 + 207635757955982359631881210435943194244793595567450425416622985689973274332804234076315602355532235016621740880390625/293555396233158535384552530199754243582541353948791486541071907104053654642688*t^23 - 1867863965070929383809660063666708450899157942891740216418372970358406272265617509315358849673506980862100871014609375/587110792466317070769105060399508487165082707897582973082143814208107309285376*t^21 + 13250077224791126867475550882963046814112280700512485402818566806777637296809728543805747555647200375940277933154921875/1174221584932634141538210120799016974330165415795165946164287628416214618570752*t^19 - 72682862119043872134413310693986107069479960301851126600789101629336896034998856213433422209450138301421680122697453125/2348443169865268283076420241598033948660330831590331892328575256832429237141504*t^17 + 300680444228875707445031888108311819296486604860310582685671949047519037396210648241561214507093945779261747032825015625/4696886339730536566152840483196067897320661663180663784657150513664858474283008*t^15 - 907868315029206661042548682597206998697684374717053661488649532367743472971478378084462599889295418603010239508067109375/9393772679461073132305680966392135794641323326361327569314301027329716948566016*t^13 + 1914760058843938484452194088634129954349998029512712944030844387129198485660377854471847049939464077044319041807638203125/18787545358922146264611361932784271589282646652722655138628602054659433897132032*t^11 - 2653560478292328835004919117283512357811118042240270298818238257855327501379363900033598626169005792724402351651016484375/37575090717844292529222723865568543178565293305445310277257204109318867794264064*t^9 + 2208963638304948000746176425841107099214565792027518268949511166727223731173127349510546881439092042460612018444564453125/75150181435688585058445447731137086357130586610890620554514408218637735588528128*t^7 - 957694958078920007146073257457758432028503215954328869234777099530105109437520862314090935551813774907002878472266796875/150300362871377170116890895462274172714261173221781241109028816437275471177056256*t^5 + 334025730803131573154135982537184279033189628210832061975395917055252619350779745079502954307918708398828356010000390625/601201451485508680467563581849096690857044692887124964436115265749101884708225024*t^3 - 12828104077844948349702218849698732580040544460331326584704725099367152799633996644159474917229124351805342444775390625/1202402902971017360935127163698193381714089385774249928872230531498203769416450048*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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
Positive weights:   67 out of 67
Indefinite weights: 0 out of 67
Negative weights:   0 out of 67
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.2291516694911106514 + 5.1935239482529680406e-818j)  +/-  (7.89e-240, 7.89e-240j)
| (-10.441505650290769424 - 2.2860762875556527537e-824j)  +/-  (1.82e-244, 1.82e-244j)
| (9.285983290689301037 - 1.4558197899495650448e-818j)  +/-  (3.73e-242, 3.73e-242j)
| (6.1899116564300612878 + 1.7384678054127549443e-821j)  +/-  (1.13e-239, 1.13e-239j)
| (-6.8725866063981664112 - 1.3485330581756761912e-831j)  +/-  (9.99e-240, 9.99e-240j)
| (10.441505650290769424 - 2.2919896196832668913e-836j)  +/-  (1.64e-244, 1.64e-244j)
| (7.5985149253800782278 - 7.7337994346577421772e-839j)  +/-  (4.51e-240, 4.51e-240j)
| (-5.222551425506762319 + 5.2746277690634892309e-850j)  +/-  (4.2e-240, 4.2e-240j)
| (8.8190145522998767061 - 3.0062218472649051917e-853j)  +/-  (2.24e-241, 2.24e-241j)
| (-8.8190145522998767061 + 5.5498905403337113983e-863j)  +/-  (2.14e-241, 2.14e-241j)
| (-7.5985149253800782278 - 7.0202707925723142895e-862j)  +/-  (4.52e-240, 4.52e-240j)
| (7.2291516694911106514 - 6.1752017011958844209e-860j)  +/-  (7.57e-240, 7.57e-240j)
| (-1.7046024487737268365 + 5.4282842810334086852e-885j)  +/-  (1.85e-247, 1.85e-247j)
| (9.8092821393430208481 - 4.5000089540125122141e-877j)  +/-  (4.49e-243, 4.49e-243j)
| (-6.5267099129961591023 - 8.2752034332345993164e-884j)  +/-  (1.13e-239, 1.13e-239j)
| (2.2596938866225172446 - 2.1731232065899394709e-894j)  +/-  (2.14e-245, 2.14e-245j)
| (-2.9306374202572440192 + 7.2399411983183331126e-892j)  +/-  (6.85e-243, 6.85e-243j)
| (6.8725866063981664112 - 1.8625670738124030334e-888j)  +/-  (1.01e-239, 1.01e-239j)
| (-2.2596938866225172446 + 4.1807952854670904537e-909j)  +/-  (2.17e-245, 2.17e-245j)
| (7.9835417122685248389 - 1.0287782666393887749e-902j)  +/-  (2.1e-240, 2.1e-240j)
| (-9.8092821393430208481 + 8.7985351390348307061e-913j)  +/-  (4.47e-243, 4.47e-243j)
| (2.9306374202572440192 - 1.8037924103781968185e-912j)  +/-  (6.91e-243, 6.91e-243j)
| (-2.5359458383404441894 - 1.3426201407318134065e-913j)  +/-  (2.33e-244, 2.33e-244j)
| (8.3883107355730035002 - 1.221514935325512363e-908j)  +/-  (8.12e-241, 8.12e-241j)
| (-5.8609289505569174427 - 1.3334328261185894371e-909j)  +/-  (9.34e-240, 9.34e-240j)
| (-8.3883107355730035002 + 1.6137858446987448268e-913j)  +/-  (8.57e-241, 8.57e-241j)
| (0.88919704232086329641 + 4.6096034317191933631e-922j)  +/-  (9.72e-251, 9.72e-251j)
| (5.8609289505569174427 - 8.4846935476221428698e-911j)  +/-  (9.52e-240, 9.52e-240j)
| (4.6055241673845401494 + 1.5226844442730145485e-914j)  +/-  (1.08e-240, 1.08e-240j)
| (-0.88919704232086329641 - 6.6106491487305931897e-925j)  +/-  (9.21e-251, 9.21e-251j)
| (-4.911659102896065842 + 2.2243102853307699399e-914j)  +/-  (2.34e-240, 2.34e-240j)
| (3.4234223346364986262 + 2.8299000811790344247e-916j)  +/-  (2.62e-242, 2.62e-242j)
| (5.222551425506762319 - 1.2648767628185857108e-913j)  +/-  (4.11e-240, 4.11e-240j)
| (1.9816567566958429259 - 4.6383299149130853542e-925j)  +/-  (2.07e-246, 2.07e-246j)
| (-1.1571937124467801947 + 1.4627669765858105697e-927j)  +/-  (1.22e-249, 1.22e-249j)
| (-3.7122591555541882255 + 2.6021566276221350757e-919j)  +/-  (7.3e-242, 7.3e-242j)
| (-4.3037188640611103683 + 5.7802050335372410093e-919j)  +/-  (4.72e-241, 4.72e-241j)
| (4.3037188640611103683 + 2.4662766633412853011e-918j)  +/-  (4.75e-241, 4.75e-241j)
| (-7.9835417122685248389 + 4.8163127314284906916e-918j)  +/-  (2.28e-240, 2.28e-240j)
| (-3.1448867535097233878 + 3.992294229282063201e-920j)  +/-  (1.18e-242, 1.18e-242j)
| (-1.9816567566958429259 - 6.1168639554554764474e-924j)  +/-  (2.22e-246, 2.22e-246j)
| (4.0059650272419882972 - 1.9197487836781171938e-918j)  +/-  (1.91e-241, 1.91e-241j)
| (-9.285983290689301037 - 5.6358262835034804914e-920j)  +/-  (3.72e-242, 3.72e-242j)
| (2.7889913669406716192 + 1.4326545583745216311e-920j)  +/-  (2.57e-243, 2.57e-243j)
| (5.5387499062027964048 + 4.9209946993114928685e-917j)  +/-  (6.85e-240, 6.85e-240j)
| (3.7122591555541882255 + 6.4730012481750403598e-927j)  +/-  (7.66e-242, 7.66e-242j)
| (-4.0059650272419882972 + 1.592519356033051573e-926j)  +/-  (1.89e-241, 1.89e-241j)
| (0.16174609190387186732 + 5.5999740122014125671e-940j)  +/-  (5.63e-254, 5.63e-254j)
| (1.1571937124467801947 + 2.7891631712017720205e-935j)  +/-  (1.33e-249, 1.33e-249j)
| (-6.1899116564300612878 + 1.8606898101099006836e-924j)  +/-  (1.14e-239, 1.14e-239j)
| (6.5267099129961591023 - 1.176897631762258322e-925j)  +/-  (1.12e-239, 1.12e-239j)
| (-0.62845369232965557907 - 7.5965095098266956451e-948j)  +/-  (6.81e-252, 6.81e-252j)
| (4.911659102896065842 + 1.8499307522031089802e-935j)  +/-  (2.23e-240, 2.23e-240j)
| (1.4294867484172030937 - 1.4580639441749204547e-945j)  +/-  (1.52e-248, 1.52e-248j)
| (3.1448867535097233878 + 5.7275149555753032145e-939j)  +/-  (1.23e-242, 1.23e-242j)
| (-4.6055241673845401494 - 5.0046189672612642587e-936j)  +/-  (1.16e-240, 1.16e-240j)
| (-0.16174609190387186732 + 6.6045276983409373443e-952j)  +/-  (5.63e-254, 5.63e-254j)
| (-2.7889913669406716192 + 3.3334989000847729842e-940j)  +/-  (2.7e-243, 2.7e-243j)
| (-4.4790848838665081336e-985 + 7.0024847020892799377e-985j)  +/-  (5.57e-983, 5.57e-983j)
| (0.62845369232965557907 + 1.1514310836208637666e-949j)  +/-  (7.04e-252, 7.04e-252j)
| (-3.4234223346364986262 + 3.8401145006431478023e-940j)  +/-  (2.86e-242, 2.86e-242j)
| (-1.4294867484172030937 + 8.5967879225242832788e-947j)  +/-  (1.5e-248, 1.5e-248j)
| (-0.38118699020732211685 + 3.0208566975376237191e-950j)  +/-  (5.39e-253, 5.39e-253j)
| (2.5359458383404441894 - 1.0302949479410788283e-941j)  +/-  (2.37e-244, 2.37e-244j)
| (0.38118699020732211685 - 1.5202767850835231926e-950j)  +/-  (4.82e-253, 4.82e-253j)
| (1.7046024487737268365 + 1.4426135307644151611e-945j)  +/-  (1.91e-247, 1.91e-247j)
| (-5.5387499062027964048 - 4.0594678566506397227e-948j)  +/-  (6.64e-240, 6.64e-240j)
-------------------------------------------------
The weights are:
| (4.1143438959209028407e-24 + 1.6767920959144704118e-840j)  +/-  (4.61e-64, 1.17e-181j)
| (1.8453523188769239076e-48 + 9.0158730086746889144e-855j)  +/-  (1.07e-74, 2.71e-192j)
| (9.8404270124708174381e-39 - 1.8603764712804470257e-851j)  +/-  (2.16e-72, 5.47e-190j)
| (4.3001790621535585652e-18 - 5.5021842548301554248e-838j)  +/-  (1.16e-61, 2.93e-179j)
| (6.0790937233335262284e-22 - 9.1425517247319386635e-840j)  +/-  (7.58e-64, 1.92e-181j)
| (1.8453523188769239076e-48 - 4.878849116426910366e-856j)  +/-  (3.05e-76, 7.73e-194j)
| (1.7877244887632830941e-26 + 6.1456122544126057892e-844j)  +/-  (1.11e-67, 2.82e-185j)
| (2.5245509703309284599e-13 + 1.2055167561720011693e-835j)  +/-  (4.68e-59, 1.19e-176j)
| (4.2080334263244546801e-35 - 8.3201422094504898514e-850j)  +/-  (1.96e-71, 4.97e-189j)
| (4.2080334263244546801e-35 - 1.7949003852938378728e-847j)  +/-  (7.66e-73, 1.94e-190j)
| (1.7877244887632830941e-26 + 3.0554325928608266539e-842j)  +/-  (4.86e-68, 1.23e-185j)
| (4.1143438959209028407e-24 - 2.0452860521131934383e-842j)  +/-  (2.89e-67, 7.33e-185j)
| (0.0085261756483412707674 - 2.7128302887646474317e-829j)  +/-  (3.36e-36, 8.51e-154j)
| (5.171698424503939891e-43 + 2.3356248137068094109e-853j)  +/-  (2.55e-75, 6.47e-193j)
| (6.0849646066883606784e-20 + 5.8711705930884274102e-839j)  +/-  (1.78e-65, 4.51e-183j)
| (0.00095021402376495152483 - 6.4048321779124394881e-830j)  +/-  (1.06e-44, 2.68e-162j)
| (1.4168085481308646377e-05 + 4.4280458216171288402e-830j)  +/-  (6.04e-50, 1.53e-167j)
| (6.0790937233335262284e-22 + 5.8433643522908573155e-841j)  +/-  (8.62e-67, 2.18e-184j)
| (0.00095021402376495152483 - 9.5225707375613182368e-830j)  +/-  (3.47e-45, 8.79e-163j)
| (4.6388717761734256773e-29 - 1.3903983257019148513e-845j)  +/-  (4.27e-70, 1.08e-187j)
| (5.171698424503939891e-43 - 7.7566698381952569924e-852j)  +/-  (1.55e-78, 3.92e-196j)
| (1.4168085481308646377e-05 + 2.6593860458392571605e-830j)  +/-  (1.81e-53, 4.58e-171j)
| (0.00024771508438413879555 + 6.6912654418935604242e-830j)  +/-  (3.24e-49, 8.2e-167j)
| (6.4923844758681352629e-32 + 1.9651345502470757953e-847j)  +/-  (1.75e-71, 4.43e-189j)
| (2.2164333022168796003e-16 + 2.9989837875291643328e-837j)  +/-  (6.07e-66, 1.54e-183j)
| (6.4923844758681352629e-32 + 1.2018994622190497894e-845j)  +/-  (9.78e-74, 2.48e-191j)
| (0.06782261053657181489 + 1.3999934668890915581e-828j)  +/-  (2.03e-44, 5.14e-162j)
| (2.2164333022168796003e-16 + 2.4039042995431807676e-837j)  +/-  (1.98e-66, 5.02e-184j)
| (1.0529627001504592754e-10 + 1.7458220279643813779e-834j)  +/-  (6.56e-64, 1.66e-181j)
| (0.06782261053657181489 + 1.6379519813190481759e-828j)  +/-  (8.35e-45, 2.12e-162j)
| (5.8008662496468280116e-12 - 6.8198119286155163187e-835j)  +/-  (1.02e-64, 2.59e-182j)
| (1.3098581047828494361e-06 + 1.074023293624768026e-831j)  +/-  (1.46e-59, 3.69e-177j)
| (2.5245509703309284599e-13 + 6.045402944684820774e-836j)  +/-  (1.25e-65, 3.18e-183j)
| (0.0030876395976881602475 + 1.1038288371105246436e-829j)  +/-  (9.91e-52, 2.51e-169j)
| (0.039993453356989639289 - 8.7644971545665075271e-829j)  +/-  (7.23e-45, 1.83e-162j)
| (1.7028306221433823629e-07 - 3.9855281647937237749e-832j)  +/-  (1.15e-61, 2.92e-179j)
| (1.5282072254309544572e-09 - 1.7884859082662488947e-833j)  +/-  (6.87e-64, 1.74e-181j)
| (1.5282072254309544572e-09 - 8.8662570403545783286e-834j)  +/-  (5.37e-64, 1.36e-181j)
| (4.6388717761734256773e-29 - 6.1286167293244749209e-844j)  +/-  (7.01e-75, 1.78e-192j)
| (7.6126183374981264507e-06 - 1.0862931258666804512e-830j)  +/-  (1.61e-59, 4.07e-177j)
| (0.0030876395976881602475 + 1.5641102835071327849e-829j)  +/-  (4.05e-54, 1.03e-171j)
| (1.7902793111258034646e-08 + 4.3587336621752079137e-833j)  +/-  (8.64e-64, 2.19e-181j)
| (9.8404270124708174381e-39 + 1.6980854241819735987e-849j)  +/-  (4.72e-80, 1.2e-197j)
| (4.9361882953985349826e-05 - 3.9793863278091078611e-830j)  +/-  (4.31e-60, 1.09e-177j)
| (8.5531575207242834457e-15 - 1.1127955637873638364e-836j)  +/-  (2.02e-68, 5.13e-186j)
| (1.7028306221433823629e-07 - 2.1213441593274721465e-832j)  +/-  (2.79e-63, 7.07e-181j)
| (1.7902793111258034646e-08 + 8.5125069373787432008e-833j)  +/-  (2.01e-65, 5.09e-183j)
| (0.10747826548598220077 - 1.3620842684765320776e-827j)  +/-  (7.07e-56, 1.79e-173j)
| (0.039993453356989639289 - 7.1457554663280129704e-829j)  +/-  (3.05e-56, 7.72e-174j)
| (4.3001790621535585652e-18 - 4.25844524848177185e-838j)  +/-  (2.04e-71, 5.16e-189j)
| (6.0849646066883606784e-20 - 1.7815608939845385838e-839j)  +/-  (1.26e-71, 3.2e-189j)
| (0.097098014739120635312 - 3.204456422667940103e-828j)  +/-  (2.17e-58, 5.48e-176j)
| (5.8008662496468280116e-12 - 3.3023384581393870977e-835j)  +/-  (3.63e-67, 9.18e-185j)
| (0.020023180094499435276 + 3.751269175475993144e-829j)  +/-  (5.57e-60, 1.41e-177j)
| (7.6126183374981264507e-06 - 6.3010018873606711261e-831j)  +/-  (4.88e-63, 1.24e-180j)
| (1.0529627001504592754e-10 + 3.5979348214503793473e-834j)  +/-  (1.11e-68, 2.81e-186j)
| (0.10747826548598220077 - 1.4015622221653568436e-827j)  +/-  (1.51e-59, 3.79e-177j)
| (4.9361882953985349826e-05 - 6.4723651254825368918e-830j)  +/-  (8.63e-64, 2.17e-181j)
| (0.078172778234497774102 + 1.8811536561399305686e-827j)  +/-  (1.2e-59, 3e-177j)
| (0.097098014739120635312 - 2.8678421241338916166e-828j)  +/-  (5.13e-61, 1.29e-178j)
| (1.3098581047828494361e-06 + 1.9340953364829029805e-831j)  +/-  (8.51e-66, 2.14e-183j)
| (0.020023180094499435276 + 4.8266279977450619632e-829j)  +/-  (2.55e-62, 6.3e-180j)
| (0.11561370004511036955 + 6.6648113460415413151e-828j)  +/-  (9.22e-61, 2.27e-178j)
| (0.00024771508438413879555 + 4.2929079862691286721e-830j)  +/-  (1.69e-64, 4.13e-182j)
| (0.11561370004511036955 + 6.2308517331746539785e-828j)  +/-  (1.14e-61, 2.92e-179j)
| (0.0085261756483412707674 - 2.0092142895673129279e-829j)  +/-  (8.38e-64, 2e-181j)
| (8.5531575207242834457e-15 - 1.9754630351616337208e-836j)  +/-  (3.12e-72, 9e-190j)
