Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 15 30
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : t^19 - 93567/667*t^17 + 56576166/7337*t^15 - 1577757510/7337*t^13 + 24226003620/7337*t^11 - 18992429820/667*t^9 + 3930143490/29*t^7 - 224016557310/667*t^5 + 250467132825/667*t^3 - 83438061525/667*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^49 - 2148111459170021593366361913152842740141861787821945838966989848894334360795664429649972819736192164353675211589/2274841511059700443437085475174494322943075677920520831443305990337378281299088475741765213332313757357751754*t^47 + 926794012497784810490065521222160874248463832170633147668543808728268621882368157582706323368252223919497321349267/2274841511059700443437085475174494322943075677920520831443305990337378281299088475741765213332313757357751754*t^45 - 1335217129268811949637627203800397097731157872351424654767244851188040589618645794426560835687766495044790647924180680/12511628310828352438903970113459718776186916228562864572938182946855580547144986616579708673327725665467634647*t^43 + 645973171963149764776540274611000448354029431893863672605440174786777155288261147295880984663931689374586067623611652345/33960133986534099477025061736533522392507344048956346697975067998608004342250677959287780684746683949126436899*t^41 - 166446750333940275765704890107801965599547798334590687991146978445545398665651923724869839057527014621207505102708949098705/67920267973068198954050123473067044785014688097912693395950135997216008684501355918575561369493367898252873798*t^39 + 273210773745804578955625398740076707663938395138482095228886040338791425568826310281483633119815062133119231801019962317328535/1154644555542159382218852099042139761345249697664515787731152311952672147636523050615784543281387254270298854566*t^37 - 10115086299084423035282479542008728064312451457649898256446710285777744227915268206538525381429956187687003070334721487391365315/577322277771079691109426049521069880672624848832257893865576155976336073818261525307892271640693627135149427283*t^35 + 25345196538138814330549762568421965773909479784950994510430105820954435838980590381367898591852938477271192652667021488201149575/25100968598742595265627219544394342637940210818793821472416354607666785818185283709038794419160592484136931621*t^33 - 2398896644188816254838542148157557760913185923577980231233935283305228781633115027418068815588639103358844698994214457800944049575/52483843433734517373584186320097261879329531712023444896870559634212370347114684118899297421881238830468129753*t^31 + 2955654381124324765901818457587218363967089796775462186957040182774980547638418024892006541635572415628075386806963461518407393625/1809787704611535081847730562761974547563087300414601548167950332214219667141885659272389566271766856223038957*t^29 - 83479150455246246249782900496660848120648629604263791679465683875341012951424725040910856814395062232414544736799898550064092761250/1809787704611535081847730562761974547563087300414601548167950332214219667141885659272389566271766856223038957*t^27 + 7354463613518300487151950102776405297626479773855142506293266658062331352302921356549414296431166728598929104719993563534539369000/7153311085421087280030555584039425089182163242745460664695455858554227933367136993171500261943742514715569*t^25 - 1416448126282522970684006663864629938821597467281389284353157699248157348656704349759651061737459697543311478841496250126486045659375/78686421939631960080336111424433675981003795670200067311650014444096507267038506924886502881381167661871259*t^23 + 19331858313198078731062017767763864957599010506942246529094989748859605953552775966256501984763150584384037516329794883235864807703125/78686421939631960080336111424433675981003795670200067311650014444096507267038506924886502881381167661871259*t^21 - 10704414146861131147760932199282524345592696653173644069726052700072384570748163185388945845905388885754573742788235859393425880347500/4141390628401682109491374285496509262158094508957898279560527076005079329844131943415079099020061455887961*t^19 + 5029161016706303737884851787711643400947986979315548925689018599024411514532621142855443808740694611095926007543440073167973217520625/243611213435393065264198487382147603656358500526935192915325122117945842932007761377357594060003615052233*t^17 - 59753000415919973478858880827643471098056769887181347067590473370376609741615197584584859086569191162970700013955487439650330210695625/487222426870786130528396974764295207312717001053870385830650244235891685864015522754715188120007230104466*t^15 + 256897599669911717503789602777219416777434396984505723286502101867323928036320383893208320188183028518345020645157290410114268050534375/487222426870786130528396974764295207312717001053870385830650244235891685864015522754715188120007230104466*t^13 - 385143156888045829775285385210017882332381908990299302903004077968966615538812998567082403636653136895487842295797758762278553363518750/243611213435393065264198487382147603656358500526935192915325122117945842932007761377357594060003615052233*t^11 + 69570340687228094119923886110440384623796006755928124357937047013892353545594183043961216880048408847061504672106428795109243674634375/22146473948672096842199862489286145786941681866085017537756829283449622084727978307032508550909419550203*t^9 - 170372374403137084303215068694561738547948379726239041336866949587355289913305173043713943918330983463763185677279607654985444333315625/44292947897344193684399724978572291573883363732170035075513658566899244169455956614065017101818839100406*t^7 + 115398443097450904539018295729776429018940596106809540331967086064043622318724341880459350814353749153556202760417558459133593492384375/44292947897344193684399724978572291573883363732170035075513658566899244169455956614065017101818839100406*t^5 - 18129358188232164699096264494462024647148279258054150092654441852341768620837777004440793542583284927104122337518068016890092634390625/22146473948672096842199862489286145786941681866085017537756829283449622084727978307032508550909419550203*t^3 + 1799858646221399258936722232789998753982341018292155311023827971840575675200939272649617863287288332958701518330910651862082747765625/22146473948672096842199862489286145786941681866085017537756829283449622084727978307032508550909419550203*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: 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
Positive weights:   49 out of 49
Indefinite weights: 0 out of 49
Negative weights:   0 out of 49
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (10.133974707230248323 + 6.4730670873342708095e-574j)  +/-  (2.11e-245, 2.11e-245j)
| (12.193364559095769001 - 1.6615432557073904208e-578j)  +/-  (1.84e-247, 1.84e-247j)
| (-12.193364559095769001 - 4.3184806762786011311e-583j)  +/-  (1.83e-247, 1.83e-247j)
| (-8.0585818256548776952 - 2.7360178743331379177e-579j)  +/-  (4.71e-244, 4.71e-244j)
| (11.002223522560903804 - 1.2818115796015773183e-576j)  +/-  (3.69e-246, 3.69e-246j)
| (4.7888356187420432164 + 3.27879310494514375e-582j)  +/-  (1.12e-244, 1.12e-244j)
| (5.7525664932724817643 + 7.0279578139023537336e-605j)  +/-  (9.81e-244, 9.81e-244j)
| (-1.4697192347651409339 - 2.3887022699037237718e-634j)  +/-  (1.46e-250, 1.46e-250j)
| (-2.3344142183389772393 + 9.1463687133689220966e-628j)  +/-  (2.03e-248, 2.03e-248j)
| (9.3812640502346646327 + 4.6444601946619008889e-635j)  +/-  (8.88e-245, 8.88e-245j)
| (1.9090466889022845717 + 3.8115809173840252701e-661j)  +/-  (1.69e-249, 1.69e-249j)
| (6.8956391981569169575 + 1.104916678543756306e-659j)  +/-  (1.77e-243, 1.77e-243j)
| (-7.4581614450681907169 + 1.8456498846230904299e-675j)  +/-  (9.06e-244, 9.06e-244j)
| (-8.6963366023623516981 + 1.7991718062949400186e-675j)  +/-  (2.55e-244, 2.55e-244j)
| (-6.4413965231702094964 - 1.3514392091695614215e-673j)  +/-  (3.47e-243, 3.47e-243j)
| (8.0585818256548776952 + 4.0972380093693085858e-677j)  +/-  (5.2e-244, 5.2e-244j)
| (3.4944544608095896987 - 1.010936056471453889e-687j)  +/-  (3.03e-246, 3.03e-246j)
| (-11.002223522560903804 + 3.498475480053570553e-694j)  +/-  (3.39e-246, 3.39e-246j)
| (-9.3812640502346646327 - 1.7398644058497259054e-691j)  +/-  (9.97e-245, 9.97e-245j)
| (-4.3426145735928089279 - 1.040992717659648132e-689j)  +/-  (3.82e-245, 3.82e-245j)
| (5.2609328267978718288 + 2.2083651182365659856e-695j)  +/-  (3.12e-244, 3.12e-244j)
| (2.3344142183389772393 - 5.1422643195291921225e-711j)  +/-  (1.85e-248, 1.85e-248j)
| (8.6963366023623516981 - 5.7008007414416912609e-710j)  +/-  (2.6e-244, 2.6e-244j)
| (6.4413965231702094964 + 1.3970926244865978558e-721j)  +/-  (3.47e-243, 3.47e-243j)
| (-3.0954420462911432479 - 1.658851621198966012e-744j)  +/-  (7.67e-247, 7.67e-247j)
| (6.200455928441350252 - 3.1032518671143298846e-743j)  +/-  (3.18e-243, 3.18e-243j)
| (7.4581614450681907169 + 2.264645989709047618e-758j)  +/-  (9.76e-244, 9.76e-244j)
| (4.3426145735928089279 - 2.3045260081288077076e-764j)  +/-  (3.73e-245, 3.73e-245j)
| (-6.8956391981569169575 - 3.9174292169405913795e-763j)  +/-  (1.63e-243, 1.63e-243j)
| (-3.4944544608095896987 - 4.9578647386698448899e-769j)  +/-  (3.27e-246, 3.27e-246j)
| (-4.7888356187420432164 - 7.9833428232785826934e-765j)  +/-  (1.11e-244, 1.11e-244j)
| (-10.133974707230248323 - 1.655425936904242119e-766j)  +/-  (2.43e-245, 2.43e-245j)
| (-5.7525664932724817643 + 2.4055304044666405156e-765j)  +/-  (1.01e-243, 1.01e-243j)
| (-1.9090466889022845717 - 4.4122711516095912718e-771j)  +/-  (1.74e-249, 1.74e-249j)
| (3.9139822016309083791 - 3.0798523793630658629e-767j)  +/-  (1.1e-245, 1.1e-245j)
| (-3.9139822016309083791 - 5.9892474438732516332e-767j)  +/-  (1.1e-245, 1.1e-245j)
| (-6.200455928441350252 - 5.1553220085774397015e-764j)  +/-  (2.99e-243, 2.99e-243j)
| (1.4697192347651409339 + 3.2496197263991175795e-774j)  +/-  (1.43e-250, 1.43e-250j)
| (7.4042074092561855103e-797 - 5.9753957552263200096e-796j)  +/-  (2.95e-794, 2.95e-794j)
| (-5.2609328267978718288 + 1.1035630022503176062e-772j)  +/-  (3.29e-244, 3.29e-244j)
| (-0.41766662710031645289 + 3.3259858874099714033e-783j)  +/-  (1.91e-253, 1.91e-253j)
| (-2.7232926702439711366 + 1.1278535548016206399e-777j)  +/-  (1.45e-247, 1.45e-247j)
| (3.0954420462911432479 + 6.817412889542358504e-776j)  +/-  (7.37e-247, 7.37e-247j)
| (0.74196378430272585765 + 7.9681126501954940392e-782j)  +/-  (2.51e-252, 2.51e-252j)
| (-1.0542766776250694802 + 2.0550632746907228464e-781j)  +/-  (1.6e-251, 1.6e-251j)
| (2.7232926702439711366 - 1.6358600890022871446e-779j)  +/-  (1.37e-247, 1.37e-247j)
| (-0.74196378430272585765 - 1.1142892722233228439e-783j)  +/-  (2.29e-252, 2.29e-252j)
| (1.0542766776250694802 - 3.1490625323375600536e-783j)  +/-  (1.54e-251, 1.54e-251j)
| (0.41766662710031645289 - 3.823118200889833583e-785j)  +/-  (1.91e-253, 1.91e-253j)
-------------------------------------------------
The weights are:
| (1.5946035017535067465e-23 - 6.0544742390765984655e-596j)  +/-  (9.01e-73, 2.62e-195j)
| (3.5760135871354914433e-33 + 2.6767266941305027529e-602j)  +/-  (5.59e-77, 1.63e-199j)
| (3.5760135871354914433e-33 - 2.5450640653244069014e-603j)  +/-  (1.3e-78, 3.78e-201j)
| (1.9510612024955082095e-15 + 2.82839060204061087e-593j)  +/-  (2.97e-70, 8.64e-193j)
| (1.9847316096610543596e-27 - 7.2162803875309780026e-599j)  +/-  (8.9e-75, 2.59e-197j)
| (1.9176696830898245607e-06 - 3.5247779748966129416e-586j)  +/-  (1.26e-60, 3.68e-183j)
| (1.2829236375428639672e-08 - 2.0092945719850368852e-587j)  +/-  (5.24e-64, 1.52e-186j)
| (0.059136595703659589249 - 2.4806347683438088096e-583j)  +/-  (2.59e-41, 7.54e-164j)
| (0.010706994522439346215 - 6.9889353569036236075e-584j)  +/-  (9.1e-50, 2.65e-172j)
| (2.2076695379063066529e-20 + 9.9145801431150775492e-595j)  +/-  (9.3e-73, 2.71e-195j)
| (0.028179867528516411097 + 1.8153871050736300784e-583j)  +/-  (1.6e-47, 4.65e-170j)
| (1.0119626572508382207e-11 + 2.0261499840746703623e-589j)  +/-  (8.88e-68, 2.58e-190j)
| (1.9405194422170844753e-13 - 1.3060707273330914117e-591j)  +/-  (7.7e-72, 2.24e-194j)
| (9.9487669801525543295e-18 - 2.0155544760631024923e-594j)  +/-  (7.86e-75, 2.29e-197j)
| (1.1755821160754055742e-10 - 6.3536820020043364388e-589j)  +/-  (2.25e-70, 6.55e-193j)
| (1.9510612024955082095e-15 + 4.9856238754018095473e-592j)  +/-  (1.26e-72, 3.67e-195j)
| (0.00036732310439957852444 + 1.3193880458973478277e-584j)  +/-  (5e-61, 1.46e-183j)
| (1.9847316096610543596e-27 + 3.0864263943906892013e-600j)  +/-  (1.34e-80, 3.9e-203j)
| (2.2076695379063066529e-20 + 4.1363686410312499607e-596j)  +/-  (6e-77, 1.74e-199j)
| (1.3948841145122088046e-05 + 5.0271781082654882153e-586j)  +/-  (8.24e-67, 2.4e-189j)
| (1.8880199060069557601e-07 + 7.6198354966863525123e-587j)  +/-  (2.67e-67, 7.76e-190j)
| (0.010706994522439346215 - 1.1311703139529915557e-583j)  +/-  (6.95e-59, 2.02e-181j)
| (9.9487669801525543295e-18 - 2.2780934565815404512e-593j)  +/-  (4.92e-75, 1.43e-197j)
| (1.1755821160754055742e-10 - 2.9666686497982622613e-588j)  +/-  (1.56e-70, 4.55e-193j)
| (0.0012673058116489018084 - 1.8015677418011794251e-584j)  +/-  (1.1e-66, 3.19e-189j)
| (5.9648960664489060885e-10 + 7.7422245732889118588e-588j)  +/-  (4.34e-70, 1.26e-192j)
| (1.9405194422170844753e-13 - 1.0005785214057412524e-590j)  +/-  (2.87e-73, 8.35e-196j)
| (1.3948841145122088046e-05 + 1.3305393821695642754e-585j)  +/-  (5.19e-68, 1.51e-190j)
| (1.0119626572508382207e-11 + 3.6062184473363518563e-590j)  +/-  (7.76e-77, 2.26e-199j)
| (0.00036732310439957852444 + 6.2712130444979594533e-585j)  +/-  (2.13e-70, 6.19e-193j)
| (1.9176696830898245607e-06 - 1.1690377879185528043e-586j)  +/-  (6.65e-74, 1.94e-196j)
| (1.5946035017535067465e-23 - 5.3732857497351488731e-598j)  +/-  (2.04e-84, 5.95e-207j)
| (1.2829236375428639672e-08 - 5.4716899602885582651e-588j)  +/-  (3.25e-76, 9.47e-199j)
| (0.028179867528516411097 + 1.2280409507230176941e-583j)  +/-  (8.12e-69, 2.36e-191j)
| (7.9754421648914016928e-05 - 4.3846729838300320113e-585j)  +/-  (1.6e-72, 4.65e-195j)
| (7.9754421648914016928e-05 - 1.876437444020015121e-585j)  +/-  (4.77e-73, 1.39e-195j)
| (5.9648960664489060885e-10 + 1.8103504552347881175e-588j)  +/-  (8.18e-77, 2.38e-199j)
| (0.059136595703659589249 - 3.3457221401458049754e-583j)  +/-  (5.81e-71, 1.69e-193j)
| (0.17174079056733817571 - 8.4115312147042473878e-583j)  +/-  (2.49e-70, 7.26e-193j)
| (1.8880199060069557601e-07 + 2.4509219038192027171e-587j)  +/-  (1.01e-75, 2.93e-198j)
| (0.14200731260910030394 + 9.3572315437577795224e-583j)  +/-  (9.41e-71, 2.74e-193j)
| (0.0036343328836384089585 + 3.9340800420972529912e-584j)  +/-  (2.48e-72, 7.21e-195j)
| (0.0012673058116489018084 - 3.4518202790094875105e-584j)  +/-  (4.96e-74, 1.44e-196j)
| (0.082397605248439985548 - 1.0904375389427580977e-582j)  +/-  (2.68e-72, 7.8e-195j)
| (0.086336444016420826952 + 5.8381160296235461868e-583j)  +/-  (2.64e-72, 7.78e-195j)
| (0.0036343328836384089585 + 6.9319563638097904578e-584j)  +/-  (7.52e-74, 2.18e-196j)
| (0.082397605248439985548 - 9.3845393891152099785e-583j)  +/-  (4.55e-72, 1.34e-194j)
| (0.086336444016420826952 + 7.2293227027964040027e-583j)  +/-  (6.7e-73, 1.96e-195j)
| (0.14200731260910030394 + 1.0181011780524112476e-582j)  +/-  (1.3e-72, 3.64e-195j)
