Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 54
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^63 - 810818431327004532740032471608140029095142862794736333940273405610573948167776039936609425931544240192/470622712839540463687115737495650644131780814390962820980432319183756725308041894180151503120829959*t^61 + 3260027769103118625460988235443007257049640700752736434743353717244265029061038980608195709247976600718778/2353113564197702318435578687478253220658904071954814104902161595918783626540209470900757515604149795*t^59 - 1627503372835707821363739137728039846000681604831951368602924132297566495834038332776445728837937838483634433/2353113564197702318435578687478253220658904071954814104902161595918783626540209470900757515604149795*t^57 + 566020401165708604352961298106450054074005474380524543190383164409024338771414056726143453799677495732788921699/2353113564197702318435578687478253220658904071954814104902161595918783626540209470900757515604149795*t^55 - 29175210894363036148022871936719247953895746799408840545958133702456024881423047378310075423907587372088872901176/470622712839540463687115737495650644131780814390962820980432319183756725308041894180151503120829959*t^53 + 340409354326315643847200279383860610682578515524711940590095817355003384606680048376869375321672080098213597618966/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^51 - 53280880836235542023659932865602114618396063624701541232788897917131235913850871989988889461613310277375279878060305/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^49 + 6694735115600754970323491541210107950153884243215808814775305492420168281835043905053621450661627385974474319970832155/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^47 - 683449891134089883470482259650156065775909914630529734759464691241491475645732614317784026401279631665442847512232119640/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^45 + 57164556141343460457892795134825657833892667701493030189322729095429002277671686882740174792317136290798355375796878527450/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^43 - 3939511469298036090475287689009089018422921279134185560755714183965190043705763717763335350842346120415056904827432058871025/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^41 + 224472720245486092601261514682688241828563417523707489669028585308439089808537446609613000402857559651330388101128650529583675/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^39 - 10593055460177093401624133581433707885032144890312046039336901615925164154036059299045227723836822608813040022382625226297980800/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^37 + 414063172829292277055678738068408800641577935530656638748421701428787733559565746039053498212139558772316012721925202940926057150/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^35 - 13388439376893509901796753787730297473539238410417180727062245671749466933683475485524051086398397044536367874373706391903589979125/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^33 + 357147969527614615630642480187493466282643905212096882452215252816240852283821534854091070052471760948879387994993916323334793375125/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^31 - 7828275718080125257529019809450939422661784901847202148799878025334772054484745421694330440445797044524714716993983959392910141382000/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^29 + 140221070676731229773658841160566340330649610944682896651098660108699204963852515021132564864858105047195514683970027976186098816905750/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^27 - 2038235893890536501826615012600949752032858769556500599797699542391772570592790132617857533331473355766526716075495640418716132722780375/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^25 + 23834624613953909094132833695337633163954642693107495104149726279678374125822380101068587081923373475521938186208311589595672760791303125/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^23 - 221831681843467718160052231452587761139713126455948788985975208692311214953076729365936284641929681533159998274000108617409396959297075000/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^21 + 1621784026331241912954328913649881308013987824387018487448216456112475733187511133017869088812273231280184003076400322866228251697816381250/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^19 - 9163749590263379018174348214008757048532679308419587396441606222079287774372386167679556625818665957432554044732886585952774849299200521875/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^17 + 39215237498045520141125131455991964153485531574989100058544731859490079382341815415163685421020594694856270864388882819659723102651090565625/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^15 - 123848778192187537851888002828082398185508935427661079149508511987413073508593546238702002709435323242957688807429150708833943294563282875000/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^13 + 279014284832407121065918700352616752635664980272677061992489730635585676498690758150769831065020605126496125182918500832170512837779409218750/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^11 - 428150296753489096160139032359316803728831241984745328785582479016170094254416075400406159144557234317603005534987359017313562124690200746875/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^9 + 418960196725862426969084465824035461791746986211214470944858063705459522351979740805960845479796083873542124639751587244531502123611924465625/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^7 - 236172923040973868440128590837305278837425483445369683282729517010009856548919029145479815641124096849561478835343160101072858697036907850000/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^5 + 64024514077599341103245108678636140089027219559571148981805568687447713174112996010075696441522202537896137691341769725164602896457538406250/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*t^3 - 5436766249572597188864102231726128969643685940676195302611074907739317028420691769391622014409626562999686702635384650633076755307586734375/27683688990561203746300925735038273184222400846527224763554842304926866194590699657655970771813527*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:
| (-10.167352165902392533 - 1.4033024674001820393e-721j)  +/-  (7.18e-241, 7.18e-241j)
| (-5.8612794788723646857 - 3.7603510803089489913e-725j)  +/-  (4.62e-242, 4.62e-242j)
| (9.1249492126776519484 + 6.7057423093223426956e-727j)  +/-  (1.3e-240, 1.3e-240j)
| (-7.6703238745241109304 - 1.5023966315498470704e-726j)  +/-  (7.52e-241, 7.52e-241j)
| (-14.241015207527531358 - 5.6228469687720584648e-736j)  +/-  (5.91e-245, 5.91e-245j)
| (-13.336160551833826455 + 1.1588506307566900232e-734j)  +/-  (1.19e-243, 1.19e-243j)
| (9.6370947485717167994 - 2.9552862185590046478e-732j)  +/-  (1.09e-240, 1.09e-240j)
| (-12.586784106634895871 + 1.3573717367590865215e-734j)  +/-  (1.09e-242, 1.09e-242j)
| (13.336160551833826455 - 8.6208490261995271335e-736j)  +/-  (1.22e-243, 1.22e-243j)
| (-10.719820059200567111 + 1.4083261526781278248e-731j)  +/-  (3.99e-241, 3.99e-241j)
| (-9.1249492126776519484 + 9.5731781485929990243e-740j)  +/-  (1.23e-240, 1.23e-240j)
| (11.300329462119762999 - 1.5234025820686338204e-747j)  +/-  (1.79e-241, 1.79e-241j)
| (-11.300329462119762999 - 7.083284887812559227e-747j)  +/-  (1.56e-241, 1.56e-241j)
| (-11.917730514071422739 - 3.9730416656298776011e-753j)  +/-  (4.68e-242, 4.68e-242j)
| (-3.32007434189318759 - 8.0266738462161105598e-756j)  +/-  (1.84e-245, 1.84e-245j)
| (12.586784106634895871 - 1.5138522523451894213e-752j)  +/-  (9.82e-243, 9.82e-243j)
| (11.917730514071422739 + 2.1890973397366337884e-751j)  +/-  (4.62e-242, 4.62e-242j)
| (-9.6370947485717167994 - 6.2127857559409639999e-750j)  +/-  (1.14e-240, 1.14e-240j)
| (8.6278951112360324523 - 1.6226787922004518434e-757j)  +/-  (1.28e-240, 1.28e-240j)
| (7.2065344072349472974 - 2.7137738965220231093e-758j)  +/-  (4.96e-241, 4.96e-241j)
| (14.241015207527531358 - 1.9133481336658169966e-770j)  +/-  (6.23e-245, 6.23e-245j)
| (4.1479107601386304007 - 2.7033346107924118003e-768j)  +/-  (3.19e-244, 3.19e-244j)
| (3.7313022243357029508 - 1.3277347604256552925e-769j)  +/-  (9.42e-245, 9.42e-245j)
| (-7.2065344072349472974 - 7.4973629665619619584e-766j)  +/-  (4.66e-241, 4.66e-241j)
| (-6.7510628900316699097 - 2.6276502357071616813e-788j)  +/-  (2.53e-241, 2.53e-241j)
| (7.6703238745241109304 + 1.8420744858001629536e-794j)  +/-  (7.51e-241, 7.51e-241j)
| (2.9179120910478034996 + 1.0093740409769106269e-808j)  +/-  (4.58e-246, 4.58e-246j)
| (6.7510628900316699097 - 7.4510680413104437673e-803j)  +/-  (2.68e-241, 2.68e-241j)
| (-8.6278951112360324523 + 6.903350264867740034e-816j)  +/-  (1.4e-240, 1.4e-240j)
| (-8.1436246607500640865 + 7.5675887180541283554e-832j)  +/-  (9.98e-241, 9.98e-241j)
| (1.6786752234026707639 + 3.6843531353434123858e-846j)  +/-  (4.81e-249, 4.81e-249j)
| (-4.9948748519975038707 + 1.1539500651609712401e-839j)  +/-  (5.01e-243, 5.01e-243j)
| (-5.4254523382977396881 + 2.9495544723566205571e-839j)  +/-  (1.64e-242, 1.64e-242j)
| (-6.3029199918086190765 + 2.7950868522540480145e-838j)  +/-  (1.09e-241, 1.09e-241j)
| (10.167352165902392533 - 5.2724046216114527659e-838j)  +/-  (7.66e-241, 7.66e-241j)
| (-2.9179120910478034996 + 1.7004515098791036957e-844j)  +/-  (4.8e-246, 4.8e-246j)
| (6.3029199918086190765 - 1.7931180654482001342e-838j)  +/-  (1.12e-241, 1.12e-241j)
| (-4.5691146656272691921 - 1.8458791538987676442e-844j)  +/-  (1.36e-243, 1.36e-243j)
| (1.0379709584894152952 - 4.2519268023443815352e-850j)  +/-  (6.51e-251, 6.51e-251j)
| (4.5691146656272691921 + 1.2901362688949137028e-841j)  +/-  (1.41e-243, 1.41e-243j)
| (-2.3344142183389772393 - 2.3581044049259317146e-846j)  +/-  (6.29e-247, 6.29e-247j)
| (5.8612794788723646857 + 8.8861207543953917678e-840j)  +/-  (4.73e-242, 4.73e-242j)
| (3.32007434189318759 + 2.0764213918116784087e-843j)  +/-  (1.88e-245, 1.88e-245j)
| (0.74196378430272585765 - 6.1338312592703048845e-851j)  +/-  (4.44e-252, 4.44e-252j)
| (-2.0498787073206508617 - 3.1335142597642987881e-849j)  +/-  (7.5e-248, 7.5e-248j)
| (2.5509998446397081563 + 1.0677124034057210234e-844j)  +/-  (1.68e-246, 1.68e-246j)
| (-1.6786752234026707639 - 5.3624812373958478068e-848j)  +/-  (4.92e-249, 4.92e-249j)
| (5.4254523382977396881 - 7.3292267668197326791e-841j)  +/-  (1.67e-242, 1.67e-242j)
| (1.3252480603660961493 - 1.6030297950083722422e-848j)  +/-  (4.86e-250, 4.86e-250j)
| (2.3344142183389772393 + 9.2107844867406262777e-846j)  +/-  (6.03e-247, 6.03e-247j)
| (-2.5509998446397081563 - 4.9327536917395406211e-846j)  +/-  (1.74e-246, 1.74e-246j)
| (-0.74196378430272585765 + 7.3393862541586696968e-851j)  +/-  (4.63e-252, 4.63e-252j)
| (8.1436246607500640865 - 4.0558276157342892076e-840j)  +/-  (1e-240, 1e-240j)
| (4.9948748519975038707 + 3.2890356150599272873e-845j)  +/-  (5.15e-243, 5.15e-243j)
| (10.719820059200567111 - 1.8977572822725950522e-847j)  +/-  (4.05e-241, 4.05e-241j)
| (2.0498787073206508617 - 2.3811133540766882884e-853j)  +/-  (8.38e-248, 8.38e-248j)
| (-0.38185219332030882229 - 5.1661229712955691818e-858j)  +/-  (2.01e-253, 2.01e-253j)
| (-4.1479107601386304007 - 1.6436315672826309647e-849j)  +/-  (3.17e-244, 3.17e-244j)
| (-6.5655245394353285475e-896 - 4.2528030636909354042e-895j)  +/-  (2.71e-893, 2.71e-893j)
| (0.38185219332030882229 + 2.1302981113786787123e-860j)  +/-  (2.01e-253, 2.01e-253j)
| (-3.7313022243357029508 - 2.2808423920779276248e-855j)  +/-  (7.6e-245, 7.6e-245j)
| (-1.3252480603660961493 + 4.6457062483723059765e-861j)  +/-  (4.95e-250, 4.95e-250j)
| (-1.0379709584894152952 + 2.232280134226033378e-861j)  +/-  (6.59e-251, 6.59e-251j)
-------------------------------------------------
The weights are:
| (7.6939653740689034312e-24 - 1.8678737274834817038e-742j)  +/-  (9.05e-45, 7.14e-165j)
| (6.0673913062276805317e-09 - 8.4178298745177450015e-733j)  +/-  (1.94e-30, 1.53e-150j)
| (1.6702566214264138001e-19 + 1.1979909193266689936e-740j)  +/-  (1.44e-43, 1.13e-163j)
| (3.1321798711568256266e-14 + 8.9151069848245297022e-737j)  +/-  (1.33e-37, 1.05e-157j)
| (3.8128073806057621643e-45 - 5.1876363175266876937e-754j)  +/-  (8.34e-55, 6.57e-175j)
| (7.7147076616490497324e-40 + 3.4161635498592723162e-751j)  +/-  (4.53e-53, 3.58e-173j)
| (1.4131527949918201671e-21 - 8.4907071894117689246e-742j)  +/-  (8.91e-48, 7.03e-168j)
| (1.1105528178349798299e-35 - 5.7648208581418736939e-749j)  +/-  (8.52e-52, 6.72e-172j)
| (7.7147076616490497324e-40 - 1.3328462902778293316e-751j)  +/-  (1.04e-57, 8.22e-178j)
| (2.5109137625440582411e-26 + 7.270616995604810263e-744j)  +/-  (3.33e-48, 2.62e-168j)
| (1.6702566214264138001e-19 - 5.5332443595372817268e-740j)  +/-  (2.49e-45, 1.96e-165j)
| (4.4445627087664845738e-29 + 7.0478165145667852019e-746j)  +/-  (1.17e-54, 9.25e-175j)
| (4.4445627087664845738e-29 - 2.2117905090971765003e-745j)  +/-  (7.44e-50, 5.87e-170j)
| (3.6743960128347836856e-32 + 4.6000461757283067347e-747j)  +/-  (2.97e-51, 2.34e-171j)
| (0.00065734459483153543994 - 5.1733139122894044113e-730j)  +/-  (1.06e-28, 8.32e-149j)
| (1.1105528178349798299e-35 + 2.1071331136866775338e-749j)  +/-  (1.8e-58, 1.42e-178j)
| (3.6743960128347836856e-32 - 1.5725784014565465181e-747j)  +/-  (4.85e-57, 3.83e-177j)
| (1.4131527949918201671e-21 + 3.5243442212392576259e-741j)  +/-  (2.23e-48, 1.76e-168j)
| (1.339147233791653279e-17 - 1.4021847590708603262e-739j)  +/-  (5.51e-51, 4.34e-171j)
| (9.6781810912410871447e-13 + 8.9544342641549710019e-737j)  +/-  (7.89e-49, 6.22e-169j)
| (3.8128073806057621643e-45 + 2.1659782676457122281e-754j)  +/-  (4.04e-63, 3.19e-183j)
| (3.069153705489193619e-05 - 8.2519143941757815613e-732j)  +/-  (3.24e-40, 2.55e-160j)
| (0.00015660990560237293181 + 3.3954443085457193948e-731j)  +/-  (1.83e-38, 1.44e-158j)
| (9.6781810912410871447e-13 - 8.7033620020210307759e-736j)  +/-  (1.12e-47, 8.8e-168j)
| (2.2847124783187012793e-11 + 8.46935873181124185e-735j)  +/-  (5.35e-47, 4.22e-167j)
| (3.1321798711568256266e-14 - 1.1924692024562211918e-737j)  +/-  (4.96e-51, 3.91e-171j)
| (0.0022256904222636279536 + 6.7037109073318704793e-730j)  +/-  (1.14e-37, 8.98e-158j)
| (2.2847124783187012793e-11 - 5.9698676013073670577e-736j)  +/-  (1.72e-49, 1.36e-169j)
| (1.339147233791653279e-17 + 7.3740458675925068182e-739j)  +/-  (2.05e-51, 1.62e-171j)
| (7.5840488938145504833e-16 - 8.5719871449210074712e-738j)  +/-  (1.29e-50, 1.02e-170j)
| (0.036217891505096806667 + 1.2919310735244137347e-728j)  +/-  (1.09e-33, 8.56e-154j)
| (6.5299023956258755851e-07 - 5.652457079819161613e-732j)  +/-  (5.38e-47, 4.24e-167j)
| (7.0092609468004387758e-08 + 2.5174996255461729245e-732j)  +/-  (1.41e-47, 1.11e-167j)
| (4.1925341794970999236e-10 - 9.8558105107120466365e-734j)  +/-  (1.06e-48, 8.39e-169j)
| (7.6939653740689034312e-24 + 4.8523364420522957074e-743j)  +/-  (1.68e-60, 1.33e-180j)
| (0.0022256904222636279536 + 2.0001324065865144416e-729j)  +/-  (8.94e-44, 7.05e-164j)
| (4.1925341794970999236e-10 + 3.5753100566100557024e-735j)  +/-  (1.46e-53, 1.15e-173j)
| (4.9474079111794774839e-06 + 1.5913661216010900308e-731j)  +/-  (8.06e-48, 6.35e-168j)
| (0.061967048932178079737 + 3.3980632118310862727e-728j)  +/-  (1.66e-36, 1.31e-156j)
| (4.9474079111794774839e-06 + 1.9703999332532373914e-732j)  +/-  (1.33e-50, 1.05e-170j)
| (0.0048630607482471554421 + 1.7503590268338007415e-728j)  +/-  (3.17e-44, 2.5e-164j)
| (6.0673913062276805317e-09 - 1.9448044773412271298e-734j)  +/-  (1.93e-53, 1.52e-173j)
| (0.00065734459483153543994 - 1.4313527206492592407e-730j)  +/-  (4.73e-48, 3.73e-168j)
| (0.10149331840266486036 - 3.3134500388009714166e-728j)  +/-  (1.81e-40, 1.43e-160j)
| (0.017506684342991856288 - 1.9203436696321109304e-728j)  +/-  (8.11e-45, 6.39e-165j)
| (0.0048148123167316097969 - 3.6827025141314586707e-729j)  +/-  (1.22e-46, 9.58e-167j)
| (0.036217891505096806667 + 2.3293481305961234783e-728j)  +/-  (7.62e-45, 6.01e-165j)
| (7.0092609468004387758e-08 + 9.7144533809402895374e-734j)  +/-  (3.33e-53, 2.62e-173j)
| (0.0538249046489510537 - 2.3645947437564140804e-728j)  +/-  (3.5e-44, 2.76e-164j)
| (0.0048630607482471554421 + 7.5305437624061271717e-729j)  +/-  (1.29e-46, 1.01e-166j)
| (0.0048148123167316097969 - 9.3611730617797385298e-729j)  +/-  (1.55e-47, 1.22e-167j)
| (0.10149331840266486036 - 4.2742262628738116474e-728j)  +/-  (1.46e-45, 1.15e-165j)
| (7.5840488938145504833e-16 + 1.3916892474032118969e-738j)  +/-  (1.43e-58, 1.12e-178j)
| (6.5299023956258755851e-07 - 4.5083569954128871256e-733j)  +/-  (8.47e-53, 6.68e-173j)
| (2.5109137625440582411e-26 - 2.1539141480399728178e-744j)  +/-  (1.56e-64, 1.23e-184j)
| (0.017506684342991856288 - 9.2498181388855538657e-729j)  +/-  (4.77e-48, 3.76e-168j)
| (0.13955901652385102465 + 3.1928515877288994475e-728j)  +/-  (3.98e-48, 3.14e-168j)
| (3.069153705489193619e-05 - 4.8228920115586709738e-731j)  +/-  (1.49e-53, 1.17e-173j)
| (0.1533544982365663084 - 2.7455031024375761106e-728j)  +/-  (3.37e-49, 2.66e-169j)
| (0.13955901652385102465 + 2.8021743108045191746e-728j)  +/-  (2.69e-49, 2.12e-169j)
| (0.00015660990560237293181 + 1.5298048755994132441e-730j)  +/-  (5.34e-53, 4.21e-173j)
| (0.0538249046489510537 - 3.7467692803829375568e-728j)  +/-  (1.35e-50, 1.07e-170j)
| (0.061967048932178079737 + 4.8610810226994388504e-728j)  +/-  (1.83e-50, 1.43e-170j)
