Starting with polynomial:
P : 32*t^5 - 160*t^3 + 120*t
Extension levels are: 5 60
-------------------------------------------------
Trying to find an order 60 Kronrod extension for:
P1 : 32*t^5 - 160*t^3 + 120*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 32*t^65 - 8655296520517891654795166862986953258392398387569269760/274964871045848058956059254065666169824960138389627*t^63 + 27935579333661626399594049416769451697075921845073497393740/1924754097320936412692414778459663188774720968727389*t^61 - 8032806743202586904099023813551128135559083023965983892881700/1924754097320936412692414778459663188774720968727389*t^59 + 85097094277150605756633799213601040470231807659950307615399725/101302847227417705931179725182087536251301103617231*t^57 - 1822529959603467853656731379724853392496772948807116239930604430/14471835318202529418739960740298219464471586231033*t^55 + 845741398043641797795961083682512292432262420987900635278247400475/57887341272810117674959842961192877857886344924132*t^53 - 77874029140105640864836754106527501753747665556734964975071426906575/57887341272810117674959842961192877857886344924132*t^51 + 23168120513827813516300943433791615722865423195363918490054141954129375/231549365091240470699839371844771511431545379696528*t^49 - 352337806089264350560381207630793160959144561153696277977623498082431875/57887341272810117674959842961192877857886344924132*t^47 + 6580668998367972128146697657780441805729066900077058729427711448713016625/21539475822440974018589709008815954551771663227584*t^45 - 11792355456179989254407530747869721845292527344198369644992410947670651338125/926197460364961882799357487379086045726181518786112*t^43 + 38107513131742953590085825957237766269272464468267595775492973771130839738125/86157903289763896074358836035263818207086652910336*t^41 - 553033039910857176273434042754757586162840167973524322409007333892170382896875/43078951644881948037179418017631909103543326455168*t^39 + 107374694902202107225004924821102333325285311008393377531826924122189610645928125/344631613159055584297435344141055272828346611641344*t^37 - 2177681343212744969340659359861483257442659483652051169864058436557483510663748125/344631613159055584297435344141055272828346611641344*t^35 + 147349982747406991232557299848507337914547278161622354274673712817988396879090753125/1378526452636222337189741376564221091313386446565376*t^33 - 259038045571946960075233923545008706898187342883135871402132199194987712090587684375/172315806579527792148717672070527636414173305820672*t^31 + 96480234546382193524797164860196558914391561487107767222655241937935815003400038109375/5514105810544889348758965506256884365253545786261504*t^29 - 923759183759587325986172109917649701647197772025002281472195246428095069752712446453125/5514105810544889348758965506256884365253545786261504*t^27 + 28879595696569997440970318832828229330643321227342515436526212337342453089797520018621875/22056423242179557395035862025027537461014183145046016*t^25 - 91244844167297092961844148860399596803352428671464340062435802458684977952619011463046875/11028211621089778697517931012513768730507091572523008*t^23 + 3685064823556891863317955006102078504044017990013155905131816247618326147570965558591171875/88225692968718229580143448100110149844056732580184064*t^21 - 14644811008787761555859656947880501175951576807664531038778456660547161815235299790343359375/88225692968718229580143448100110149844056732580184064*t^19 + 179927400416269950615733274610954397617806149036948193059381631465711986084992255617471484375/352902771874872918320573792400440599376226930320736256*t^17 - 104343293203206976319988405816615574735394210755648373747169073117479759333453989058212015625/88225692968718229580143448100110149844056732580184064*t^15 + 2839400354072702188897134883750304613349855719160988271521185631176715864475021899002844296875/1411611087499491673282295169601762397504907721282945024*t^13 - 3405703325742365899961810262912759079299233740012666178405844603830529464471957339123738203125/1411611087499491673282295169601762397504907721282945024*t^11 + 10930839303456732692465603882102092170726411545825133857772552752603675920989855733986887109375/5646444349997966693129180678407049590019630885131780096*t^9 - 2720588845175403106823057805149289178128985959613788023258604507603953415007264720776664453125/2823222174998983346564590339203524795009815442565890048*t^7 + 5983745537651497564410911857786614639169945074441123947598954680507157560402081691897823359375/22585777399991866772516722713628198360078523540527120384*t^5 - 741421410111578170922055996229373484526528435312860924311353328795396490924114492271327734375/22585777399991866772516722713628198360078523540527120384*t^3 + 104541846218104535837360921701346146979176039125436929874548402077539464072660051372819140625/90343109599967467090066890854512793440314094162108481536*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:   65 out of 65
Indefinite weights: 0 out of 65
Negative weights:   0 out of 65
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-9.8148530019225276126 + 1.1006383453210443737e-755j)  +/-  (3.68e-243, 3.68e-243j)
| (-7.9903126312841058773 - 1.2391231794683478917e-764j)  +/-  (1.96e-240, 1.96e-240j)
| (-6.8803529564621038107 - 7.0532962131601533683e-783j)  +/-  (7.88e-240, 7.88e-240j)
| (8.3947753061955544072 + 1.5534657123659240236e-794j)  +/-  (7.11e-241, 7.11e-241j)
| (10.446751420613133568 + 3.4403461366101193887e-799j)  +/-  (1.64e-244, 1.64e-244j)
| (-9.2918542136491147256 + 5.1398327679056914439e-793j)  +/-  (3.61e-242, 3.61e-242j)
| (-7.2365712098269646682 - 4.3769575436621680481e-794j)  +/-  (6.07e-240, 6.07e-240j)
| (7.6056033303326738152 + 4.4409852073196433153e-801j)  +/-  (3.69e-240, 3.69e-240j)
| (-8.3947753061955544072 + 8.2124033959265016876e-800j)  +/-  (6.85e-241, 6.85e-241j)
| (4.616097117209236838 - 4.3917982334309129527e-804j)  +/-  (5.36e-241, 5.36e-241j)
| (-8.8251806746631198681 + 8.9679554291928642667e-802j)  +/-  (1.97e-241, 1.97e-241j)
| (-3.7227649590078695824 + 2.6306423671056995827e-809j)  +/-  (2.4e-242, 2.4e-242j)
| (4.921837522262650305 + 4.7857723676394891234e-809j)  +/-  (1.43e-240, 1.43e-240j)
| (9.2918542136491147256 - 2.8170038558676234964e-809j)  +/-  (3.5e-242, 3.5e-242j)
| (9.8148530019225276126 - 5.8597319710833292104e-811j)  +/-  (3.87e-243, 3.87e-243j)
| (-7.6056033303326738152 + 7.5541197759933499513e-808j)  +/-  (3.98e-240, 3.98e-240j)
| (3.7227649590078695824 + 1.7117025818179386905e-812j)  +/-  (2.36e-242, 2.36e-242j)
| (5.8698416091625426805 + 1.5433266081890478771e-808j)  +/-  (6.86e-240, 6.86e-240j)
| (-1.747019592423810543 - 3.7650462945932824259e-820j)  +/-  (1.38e-247, 1.38e-247j)
| (-3.1438316502319580113 - 1.0472361393206831488e-815j)  +/-  (1.43e-243, 1.43e-243j)
| (3.4318031784406349446 - 7.2671061090245266654e-814j)  +/-  (6.44e-243, 6.44e-243j)
| (8.8251806746631198681 - 9.9736551575796705818e-813j)  +/-  (1.91e-241, 1.91e-241j)
| (7.9903126312841058773 - 9.3837261010379925087e-811j)  +/-  (1.79e-240, 1.79e-240j)
| (6.5348402979992875848 + 1.6406105887594900982e-809j)  +/-  (9.12e-240, 9.12e-240j)
| (-2.8586975815913342769 - 5.6396180412374658173e-822j)  +/-  (2.85e-244, 2.85e-244j)
| (-5.8698416091625426805 - 6.6397694291983454631e-817j)  +/-  (6.86e-240, 6.86e-240j)
| (2.0201828704560856329 + 6.6767427862714834607e-834j)  +/-  (1.1e-246, 1.1e-246j)
| (-6.1984242025187054007 - 2.26852774381946847e-826j)  +/-  (8.57e-240, 8.57e-240j)
| (5.5480785284622506835 + 2.0944182007194038205e-832j)  +/-  (4.61e-240, 4.61e-240j)
| (-2.5763289493239540324 - 3.9099361513699781621e-838j)  +/-  (5.4e-245, 5.4e-245j)
| (-10.446751420613133568 + 5.0035660021259816445e-838j)  +/-  (1.74e-244, 1.74e-244j)
| (1.747019592423810543 - 4.5008499206556390276e-840j)  +/-  (1.55e-247, 1.55e-247j)
| (1.4780609094482323726 - 1.634314492305985951e-840j)  +/-  (1.72e-248, 1.72e-248j)
| (-4.921837522262650305 + 5.5733259422044176018e-831j)  +/-  (1.29e-240, 1.29e-240j)
| (-1.4780609094482323726 - 5.2037045129767052067e-842j)  +/-  (1.67e-248, 1.67e-248j)
| (-4.616097117209236838 + 2.4409059128828863007e-831j)  +/-  (6.11e-241, 6.11e-241j)
| (5.2323061748455350386 + 8.1235884665445015938e-832j)  +/-  (2.56e-240, 2.56e-240j)
| (1.2146258642290308564 + 1.0179204209284751906e-841j)  +/-  (1.73e-249, 1.73e-249j)
| (0.95857246461381850711 - 2.1590554424400629579e-842j)  +/-  (1.88e-250, 1.88e-250j)
| (6.1984242025187054007 + 1.1658790582477115533e-830j)  +/-  (7.85e-240, 7.85e-240j)
| (-0.47224010822839132869 - 9.2176809570772651484e-846j)  +/-  (1.23e-252, 1.23e-252j)
| (-5.2323061748455350386 + 2.5471389997743406648e-831j)  +/-  (2.84e-240, 2.84e-240j)
| (2.5763289493239540324 - 9.6989533085489367629e-850j)  +/-  (4.89e-245, 4.89e-245j)
| (0.7114642490837205436 - 1.217721822291447461e-856j)  +/-  (1.64e-251, 1.64e-251j)
| (0.47224010822839132869 - 1.5924395704938645215e-857j)  +/-  (1.26e-252, 1.26e-252j)
| (-5.5480785284622506835 + 5.0101954256830126643e-844j)  +/-  (4.42e-240, 4.42e-240j)
| (-3.4318031784406349446 + 2.5554378914692207585e-859j)  +/-  (5.85e-243, 5.85e-243j)
| (-2.0201828704560856329 + 1.2565895262349696571e-864j)  +/-  (1.23e-246, 1.23e-246j)
| (2.296760897435954448 + 1.4143350121595151684e-863j)  +/-  (8.51e-246, 8.51e-246j)
| (3.1438316502319580113 + 3.3680360681861981464e-862j)  +/-  (1.44e-243, 1.44e-243j)
| (-0.7114642490837205436 - 9.5753383566431940993e-871j)  +/-  (1.72e-251, 1.72e-251j)
| (0.23630259832672347293 + 6.2675134669265894777e-872j)  +/-  (7.16e-254, 7.16e-254j)
| (2.8586975815913342769 - 1.7269167394717580612e-862j)  +/-  (3.01e-244, 3.01e-244j)
| (-6.5348402979992875848 - 2.8992645307558639006e-858j)  +/-  (9.42e-240, 9.42e-240j)
| (6.8803529564621038107 + 1.2715538061606307926e-865j)  +/-  (8.52e-240, 8.52e-240j)
| (-1.2146258642290308564 - 1.0759088845088117919e-881j)  +/-  (1.75e-249, 1.75e-249j)
| (-2.296760897435954448 + 1.866762245200484586e-878j)  +/-  (7.73e-246, 7.73e-246j)
| (-4.0169368065832636354 + 1.2426722195634593683e-874j)  +/-  (7.66e-242, 7.66e-242j)
| (1.2637834713683747882e-919 - 2.0182025113791243059e-919j)  +/-  (1.55e-917, 1.55e-917j)
| (7.2365712098269646682 + 1.4584586501131542708e-876j)  +/-  (6.41e-240, 6.41e-240j)
| (4.3145999378355841798 + 1.6153801870445255398e-878j)  +/-  (2.25e-241, 2.25e-241j)
| (-0.23630259832672347293 + 5.2354794818504752846e-891j)  +/-  (7.16e-254, 7.16e-254j)
| (-4.3145999378355841798 - 9.28758299584313741e-881j)  +/-  (2.36e-241, 2.36e-241j)
| (-0.95857246461381850711 - 1.3816609798606597069e-888j)  +/-  (1.91e-250, 1.91e-250j)
| (4.0169368065832636354 + 1.5819716118717150309e-887j)  +/-  (8.27e-242, 8.27e-242j)
-------------------------------------------------
The weights are:
| (4.6335928954583178051e-43 + 5.1110876963076104118e-797j)  +/-  (9.69e-66, 4.31e-185j)
| (4.1600324754827625384e-29 + 3.5654966234308381773e-791j)  +/-  (2.54e-60, 1.13e-179j)
| (5.4577288470855385906e-22 - 1.1874266108271887473e-787j)  +/-  (1.22e-56, 5.41e-176j)
| (5.8206360224199763278e-32 - 1.3447589675189875046e-793j)  +/-  (1.99e-64, 8.84e-184j)
| (1.653030201868352104e-48 - 4.1651425636298612981e-802j)  +/-  (2.02e-70, 8.96e-190j)
| (8.8182792603266295947e-39 - 1.5046867554043141431e-795j)  +/-  (5.32e-65, 2.36e-184j)
| (3.6921753742686330517e-24 + 9.9978944880386108498e-789j)  +/-  (9.37e-59, 4.16e-178j)
| (1.6036947442328976406e-26 - 8.9808578144231001389e-791j)  +/-  (1.27e-63, 5.66e-183j)
| (5.8206360224199763278e-32 - 1.7812657355468821772e-792j)  +/-  (1.45e-62, 6.45e-182j)
| (9.5399856854037978801e-11 + 2.2503234481973894392e-782j)  +/-  (8.15e-53, 3.62e-172j)
| (3.7717400075732407966e-35 + 5.7947611812465499235e-794j)  +/-  (5.22e-64, 2.32e-183j)
| (1.5801923162172825651e-07 - 3.3041734560481293532e-780j)  +/-  (1.74e-47, 7.74e-167j)
| (5.2413045354221722672e-12 - 4.5509638831856679472e-783j)  +/-  (1.61e-54, 7.13e-174j)
| (8.8182792603266295947e-39 - 4.0748727465789974336e-797j)  +/-  (6.17e-70, 2.74e-189j)
| (4.6335928954583178051e-43 + 2.57777685229004594e-799j)  +/-  (1.63e-71, 7.26e-191j)
| (1.6036947442328976406e-26 - 6.8478349200389612579e-790j)  +/-  (1.83e-62, 8.11e-182j)
| (1.5801923162172825651e-07 - 1.4898075017777926152e-780j)  +/-  (3.01e-51, 1.34e-170j)
| (1.9938960360419648706e-16 + 1.860881394148440027e-785j)  +/-  (1.47e-60, 6.55e-180j)
| (0.0072321013930817554206 + 2.2286617227180145176e-777j)  +/-  (7.5e-38, 3.33e-157j)
| (8.2446798770875195697e-06 - 3.0304940260375339016e-779j)  +/-  (6.34e-49, 2.82e-168j)
| (1.2536371884284981704e-06 + 5.026936701393115038e-780j)  +/-  (2.08e-50, 9.23e-170j)
| (3.7717400075732407966e-35 + 3.0271101632372574465e-795j)  +/-  (4.45e-69, 1.98e-188j)
| (4.1600324754827625384e-29 + 4.0566296629571078673e-792j)  +/-  (6.33e-67, 2.81e-186j)
| (5.4659137733721240543e-20 + 2.3886818047483481811e-787j)  +/-  (9.95e-64, 4.42e-183j)
| (4.5210163232542788093e-05 + 8.1781003246133826218e-779j)  +/-  (1.41e-50, 6.27e-170j)
| (1.9938960360419648706e-16 + 7.3600614244306775163e-785j)  +/-  (8.76e-64, 3.89e-183j)
| (0.0026199256565097379224 - 7.0454754071753970851e-778j)  +/-  (1.54e-47, 6.83e-167j)
| (3.8652393377887425567e-18 - 1.0022014802330378956e-785j)  +/-  (1.82e-64, 8.07e-184j)
| (7.702545649889950912e-15 - 1.3204282213349394585e-784j)  +/-  (3.5e-62, 1.55e-181j)
| (0.00020772620605829973371 - 2.0558154313726927442e-778j)  +/-  (2.97e-51, 1.32e-170j)
| (1.653030201868352104e-48 + 1.3435604485469641238e-800j)  +/-  (7.55e-78, 3.36e-197j)
| (0.0072321013930817554206 + 1.5563175313286715248e-777j)  +/-  (2.84e-47, 1.26e-166j)
| (0.016915405628762023625 - 3.245327281192678474e-777j)  +/-  (2.28e-45, 1.01e-164j)
| (5.2413045354221722672e-12 - 1.3662155384261765305e-782j)  +/-  (1.82e-62, 8.07e-182j)
| (0.016915405628762023625 - 4.3933337364735598803e-777j)  +/-  (1.82e-47, 8.09e-167j)
| (9.5399856854037978801e-11 + 6.2288957452145451537e-782j)  +/-  (1.13e-61, 5.02e-181j)
| (2.2766676123526305897e-13 + 8.2310025486746371552e-784j)  +/-  (2.89e-63, 1.29e-182j)
| (0.033559354697555924464 + 6.3707600719903487496e-777j)  +/-  (3.72e-47, 1.65e-166j)
| (0.056661286127818332429 - 1.1617649929682441123e-776j)  +/-  (3.74e-47, 1.66e-166j)
| (3.8652393377887425567e-18 - 2.2778293154944704618e-786j)  +/-  (2.81e-66, 1.25e-185j)
| (0.10683870198238544383 - 3.0310142363512972666e-776j)  +/-  (6.46e-49, 2.87e-168j)
| (2.2766676123526305897e-13 + 2.6926151637237856872e-783j)  +/-  (5.13e-64, 2.28e-183j)
| (0.00020772620605829973371 - 1.2023510020689267213e-778j)  +/-  (1.04e-57, 4.64e-177j)
| (0.082518527615233659237 + 1.9130746737701971892e-776j)  +/-  (1.09e-49, 4.84e-169j)
| (0.10683870198238544383 - 2.753262877942398648e-776j)  +/-  (5.75e-50, 2.56e-169j)
| (7.702545649889950912e-15 - 4.7335497071055669684e-784j)  +/-  (7.84e-65, 3.48e-184j)
| (1.2536371884284981704e-06 + 1.0414420513747434009e-779j)  +/-  (1.46e-59, 6.48e-179j)
| (0.0026199256565097379224 - 1.0688074539423965266e-777j)  +/-  (2.38e-55, 1.06e-174j)
| (0.00080298438588784493178 + 3.0045978363718397884e-778j)  +/-  (7.58e-57, 3.37e-176j)
| (8.2446798770875195697e-06 - 1.5624441862999910967e-779j)  +/-  (1.66e-60, 7.37e-180j)
| (0.082518527615233659237 + 2.2114551703437831526e-776j)  +/-  (4.1e-54, 1.82e-173j)
| (0.12585261940985229888 + 3.4233459184425638426e-776j)  +/-  (1.8e-53, 8.01e-173j)
| (4.5210163232542788093e-05 + 4.4947420640581078255e-779j)  +/-  (1.5e-59, 6.65e-179j)
| (5.4659137733721240543e-20 + 1.1810870244040419131e-786j)  +/-  (2.24e-69, 9.94e-189j)
| (5.4577288470855385906e-22 - 2.1100353854831038556e-788j)  +/-  (6.34e-72, 2.82e-191j)
| (0.033559354697555924464 + 8.1661221655663471372e-777j)  +/-  (3.51e-57, 1.55e-176j)
| (0.00080298438588784493178 + 4.8354487429034812369e-778j)  +/-  (6.42e-60, 2.83e-179j)
| (1.6399806418659690911e-08 + 9.6334075812909646739e-781j)  +/-  (2.29e-64, 1.01e-183j)
| (0.13347296501260846195 - 3.7271018740971387857e-776j)  +/-  (2.57e-57, 1.15e-176j)
| (3.6921753742686330517e-24 + 1.5369828959772782162e-789j)  +/-  (3.98e-73, 1.77e-192j)
| (1.3903376153531519541e-09 - 1.0022993203255940315e-781j)  +/-  (4.31e-66, 1.91e-185j)
| (0.12585261940985229888 + 3.5919068137952477014e-776j)  +/-  (1.36e-59, 5.81e-179j)
| (1.3903376153531519541e-09 - 2.5683818293785830764e-781j)  +/-  (5.65e-66, 2.37e-185j)
| (0.056661286127818332429 - 1.4126946399316428846e-776j)  +/-  (1.93e-60, 7.67e-180j)
| (1.6399806418659690911e-08 + 4.046942741208390796e-781j)  +/-  (1.6e-65, 7.2e-185j)
