Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 60
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 60 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^65 - 5357409470929652665147931394320360994814258578580555061871946288541717829049/2727947585273246397408571533222204062597038579454282342044916363740573897*t^63 + 4931223025131748852943846278624313671446288510974284960607364288110649763166817/2727947585273246397408571533222204062597038579454282342044916363740573897*t^61 - 2830355427121285432380954693549533223348081136148103474971923009429542231415387755/2727947585273246397408571533222204062597038579454282342044916363740573897*t^59 + 39207704503642494902854277185268166378285168851180440349530117688402514679797570915/94067158112870565427881777007662209055070295843251115242928150473812893*t^57 - 11730141957395177869917655568004645270364654372348055691555888409608098196638992781565/94067158112870565427881777007662209055070295843251115242928150473812893*t^55 + 2715324346713804349470141135493835372330341455015653848763057029743038773456956383484045/94067158112870565427881777007662209055070295843251115242928150473812893*t^53 - 498802476797967333466534283460661182642914084221967651394264024734325184072786189575322935/94067158112870565427881777007662209055070295843251115242928150473812893*t^51 + 74002929091435187382202476978882981539089665589275207107682890303616884746482304785109341375/94067158112870565427881777007662209055070295843251115242928150473812893*t^49 - 8978071391460160916371958708531074178343942811137875901051638500023927549399211823956578134625/94067158112870565427881777007662209055070295843251115242928150473812893*t^47 + 898595038139385929492646121277745129516740191777378090866430125225413493454962428992802349545625/94067158112870565427881777007662209055070295843251115242928150473812893*t^45 - 74654358220148014867615285993361586505652164869570543296826481306478056283799169174134949241035875/94067158112870565427881777007662209055070295843251115242928150473812893*t^43 + 5168927837507012626939867911157027740948000898488090484840071255916725085186359410604037591821051375/94067158112870565427881777007662209055070295843251115242928150473812893*t^41 - 7291226215571714972222151964343436859761768346109252962545436362925949129100228986315233687072385625/2294320929582208912875165292869809976952934044957344274217759767653973*t^39 + 352491913775524046752419490679924925971115637421979209593122931316100370068440827136865895926870005625/2294320929582208912875165292869809976952934044957344274217759767653973*t^37 - 14236042520247517120914796781999549136003014589955815680223647533094159773876692939133167591255183916875/2294320929582208912875165292869809976952934044957344274217759767653973*t^35 + 479376423190328152411300606390564347027443178427421095267835357182889661116579841653473581032749456033125/2294320929582208912875165292869809976952934044957344274217759767653973*t^33 - 13415206185665824013323109031575585573369129777549684429923780036739655750111892591318810721568131730399375/2294320929582208912875165292869809976952934044957344274217759767653973*t^31 + 310559148854737947441340856959319836319069572573197122009541164591088258010808847253879663875012186233034375/2294320929582208912875165292869809976952934044957344274217759767653973*t^29 - 5911104652764560995118275844454058183412062344467230020307149064682791307356181408612123861182668955078678125/2294320929582208912875165292869809976952934044957344274217759767653973*t^27 + 91791188725583702281241959312750954999468755281915999520404382051603389933554780597270164038417699850620090625/2294320929582208912875165292869809976952934044957344274217759767653973*t^25 - 1151692722781884763509782291668743579637390158073097650604042759508905343385926843065661665161165663788443109375/2294320929582208912875165292869809976952934044957344274217759767653973*t^23 + 11536437300426021400186038005672115574425209388464679165761463477332768673950495831298488004599951358020731359375/2294320929582208912875165292869809976952934044957344274217759767653973*t^21 - 90901640597664178225725166814056240212898359857359016489451451254693130628930970709267362527423250706616676328125/2294320929582208912875165292869809976952934044957344274217759767653973*t^19 + 553146471558995280445845313345969673558178926025970870132706034640688721335940011303388527678976365279331853828125/2294320929582208912875165292869809976952934044957344274217759767653973*t^17 - 2540002649344135975786885071057711196582851585849577403938956782140227219995989269894960246694804083703984599421875/2294320929582208912875165292869809976952934044957344274217759767653973*t^15 + 8545405299395468936304790474360441566644484109692035557312916989624518632734349278461623411241405098072332054546875/2294320929582208912875165292869809976952934044957344274217759767653973*t^13 - 20266449262660205427730189177794810312344812617710716916604202867033586297959062017732186153133067903382345149265625/2294320929582208912875165292869809976952934044957344274217759767653973*t^11 + 32160332224627891204766036029274925211084038948424172968382153924267868704427328275298918364442347417392813866328125/2294320929582208912875165292869809976952934044957344274217759767653973*t^9 - 31711643275388183593791343287891534906645807805753059063532701499333471590581145556619740513256246804283840267421875/2294320929582208912875165292869809976952934044957344274217759767653973*t^7 + 17348524061756964636352580921388042769580847429178424411426162984583450605539976436665075292605200925635007892421875/2294320929582208912875165292869809976952934044957344274217759767653973*t^5 - 4321722913930349286550454303291361072949074665944947559823859146172436865040654706665763025398155784957271677265625/2294320929582208912875165292869809976952934044957344274217759767653973*t^3 + 312840762310073073735345440261177543477900732957052835178113674047986123235835524746880704163305003614807190781250/2294320929582208912875165292869809976952934044957344274217759767653973*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:
| (-12.475508419325284267 - 1.7851840231793105805e-746j)  +/-  (2.39e-241, 2.39e-241j)
| (-14.769551566284901287 + 1.2528000097564944365e-754j)  +/-  (2.02e-244, 2.02e-244j)
| (12.475508419325284267 - 6.4022440088330482793e-760j)  +/-  (2.36e-241, 2.36e-241j)
| (-11.866561544679884094 - 1.9567469548674791295e-763j)  +/-  (8.56e-241, 8.56e-241j)
| (-13.875632875628203532 + 3.5504177458171493263e-781j)  +/-  (4.95e-243, 4.95e-243j)
| (11.866561544679884094 + 1.4689462478050772334e-791j)  +/-  (8.91e-241, 8.91e-241j)
| (-9.7236713598244546876 + 1.0166197765659797859e-805j)  +/-  (1.05e-239, 1.05e-239j)
| (-2.0679249759375977487 + 2.8120996457388293921e-826j)  +/-  (2.23e-248, 2.23e-248j)
| (-5.6697278840973298212 - 2.0952505732405105764e-817j)  +/-  (9.46e-242, 9.46e-242j)
| (6.9513808132081946935 + 2.1802508476978205988e-823j)  +/-  (1.71e-240, 1.71e-240j)
| (4.0278002577422219612 - 6.4029667180209002953e-827j)  +/-  (3.29e-244, 3.29e-244j)
| (2.4494897427831780982 + 7.0685039554845743228e-830j)  +/-  (1.74e-247, 1.74e-247j)
| (13.135741434782918299 - 4.0364641191743905772e-824j)  +/-  (4.83e-242, 4.83e-242j)
| (-4.0278002577422219612 - 4.0124005193830973616e-826j)  +/-  (3.07e-244, 3.07e-244j)
| (-6.0914025032199983431 + 1.5335267288466458561e-821j)  +/-  (2.82e-241, 2.82e-241j)
| (4.4322205211448540368 - 6.842544913243191109e-840j)  +/-  (1.55e-243, 1.55e-243j)
| (-13.135741434782918299 - 8.3476880032580379637e-840j)  +/-  (4.15e-242, 4.15e-242j)
| (-10.227758904339969119 + 1.5138704624253086268e-857j)  +/-  (8.06e-240, 8.06e-240j)
| (8.2934865126982437685 + 6.7349221365939163984e-869j)  +/-  (8.67e-240, 8.67e-240j)
| (9.7236713598244546876 + 2.3995574497487377955e-868j)  +/-  (1.07e-239, 1.07e-239j)
| (-1.3383720361352307327 + 5.7435560476022206921e-879j)  +/-  (2.74e-250, 2.74e-250j)
| (2.0679249759375977487 - 1.2019707990640485557e-877j)  +/-  (2.44e-248, 2.44e-248j)
| (-8.7585699358586324911 - 8.410210367607657449e-868j)  +/-  (1.13e-239, 1.13e-239j)
| (7.3909698876298635089 + 7.5260735430581251198e-878j)  +/-  (3.42e-240, 3.42e-240j)
| (-2.8374504767424985136 - 4.0251465006496897133e-884j)  +/-  (1.34e-246, 1.34e-246j)
| (1.6958230668281439575 + 1.7796020850199775714e-886j)  +/-  (2.49e-249, 2.49e-249j)
| (13.875632875628203532 + 1.5437228614467659724e-881j)  +/-  (4.85e-243, 4.85e-243j)
| (11.294293883109800545 + 2.7381624235607276244e-878j)  +/-  (2.33e-240, 2.33e-240j)
| (6.5184234736714093849 + 4.1409863177535323707e-878j)  +/-  (7.66e-241, 7.66e-241j)
| (-6.9513808132081946935 - 5.2240009730258863885e-876j)  +/-  (1.73e-240, 1.73e-240j)
| (-0.67347005366326006936 - 4.3291145055271652115e-900j)  +/-  (2.38e-252, 2.38e-252j)
| (7.8380123852027619628 - 1.0778381237301473602e-885j)  +/-  (6.31e-240, 6.31e-240j)
| (5.2529012434387684398 + 5.5012802156963451499e-889j)  +/-  (2.88e-242, 2.88e-242j)
| (-4.8405086724532140998 + 6.9502785392884568174e-891j)  +/-  (7.11e-243, 7.11e-243j)
| (10.749948922494310114 + 1.4644770631714539089e-885j)  +/-  (4.79e-240, 4.79e-240j)
| (2.8374504767424985136 - 2.4138216789375081437e-901j)  +/-  (1.4e-246, 1.4e-246j)
| (-8.2934865126982437685 - 4.5796587954750329668e-893j)  +/-  (8.39e-240, 8.39e-240j)
| (-2.4494897427831780982 - 1.7702540793773552052e-926j)  +/-  (1.95e-247, 1.95e-247j)
| (4.8405086724532140998 + 1.176600414833100248e-918j)  +/-  (7.21e-243, 7.21e-243j)
| (-11.294293883109800545 - 5.4369999290410568737e-927j)  +/-  (2.3e-240, 2.3e-240j)
| (-9.2347014265227974714 + 1.1430978977871343611e-955j)  +/-  (1.09e-239, 1.09e-239j)
| (-10.749948922494310114 + 1.7906569515309290936e-971j)  +/-  (4.54e-240, 4.54e-240j)
| (3.6271272938914804898 + 4.851505346702842999e-982j)  +/-  (5.68e-245, 5.68e-245j)
| (1 + 1.8298378672474920882e-988j)  +/-  (3.08e-251, 3.08e-251j)
| (9.2347014265227974714 - 7.569367532649660265e-977j)  +/-  (1.17e-239, 1.17e-239j)
| (-3.2302442089898752902 + 3.8037256013458389035e-982j)  +/-  (1.05e-245, 1.05e-245j)
| (-1.6958230668281439575 - 2.6905102741228606849e-986j)  +/-  (2.42e-249, 2.42e-249j)
| (-6.5184234736714093849 - 5.8620519351205443351e-977j)  +/-  (7.45e-241, 7.45e-241j)
| (5.6697278840973298212 - 1.8920805657045153228e-978j)  +/-  (1.01e-241, 1.01e-241j)
| (-4.4322205211448540368 + 4.2576229940163776776e-980j)  +/-  (1.64e-243, 1.64e-243j)
| (-7.8380123852027619628 + 1.3907600151414238758e-975j)  +/-  (5.68e-240, 5.68e-240j)
| (14.769551566284901287 - 2.4144892633045160102e-984j)  +/-  (2.01e-244, 2.01e-244j)
| (-7.3909698876298635089 + 8.7587444164460231838e-979j)  +/-  (3.56e-240, 3.56e-240j)
| (6.0914025032199983431 - 7.1923901799002200934e-989j)  +/-  (2.88e-241, 2.88e-241j)
| (1.3383720361352307327 + 4.2448897254716916588e-997j)  +/-  (3.21e-250, 3.21e-250j)
| (10.227758904339969119 - 8.934392885102885536e-986j)  +/-  (7.71e-240, 7.71e-240j)
| (-0.34151886142624604045 - 3.7281880906025248882e-1002j)  +/-  (1.58e-253, 1.58e-253j)
| (-3.6271272938914804898 - 1.6996857723103502011e-992j)  +/-  (6.11e-245, 6.11e-245j)
| (8.7585699358586324911 + 1.6012474591331382947e-986j)  +/-  (1.1e-239, 1.1e-239j)
| (0.34151886142624604045 - 3.7619157835144376899e-1002j)  +/-  (1.41e-253, 1.41e-253j)
| (3.2302442089898752902 + 7.490814399160166967e-995j)  +/-  (9.87e-246, 9.87e-246j)
| (-5.2529012434387684398 + 5.0868523092650899457e-988j)  +/-  (3.08e-242, 3.08e-242j)
| (-1 + 5.7159660173201129361e-1001j)  +/-  (3.18e-251, 3.18e-251j)
| (-8.5167316989235919392e-1024 + 2.9096125372545173202e-1023j)  +/-  (1.97e-1021, 1.97e-1021j)
| (0.67347005366326006936 + 3.9796316134914498109e-1003j)  +/-  (2.22e-252, 2.22e-252j)
-------------------------------------------------
The weights are:
| (4.025320988157954849e-35 - 4.5977189889840639935e-780j)  +/-  (1.19e-58, 2.8e-178j)
| (1.7641915841717933019e-48 - 4.6775723246653373165e-788j)  +/-  (8.79e-64, 2.07e-183j)
| (4.025320988157954849e-35 - 2.8800183826798474433e-782j)  +/-  (2.27e-61, 5.34e-181j)
| (6.2119324200359664918e-32 + 5.1241986752251612944e-779j)  +/-  (7.4e-58, 1.74e-177j)
| (4.9451660327423712653e-43 + 4.5977003929005308152e-785j)  +/-  (4.76e-62, 1.12e-181j)
| (6.2119324200359664918e-32 + 1.2818814393969411129e-780j)  +/-  (9.85e-61, 2.31e-180j)
| (5.8244323564410924221e-22 + 1.6360503688942386598e-774j)  +/-  (4.77e-54, 1.12e-173j)
| (0.017752278645761167097 + 5.2417180005263592364e-764j)  +/-  (1.67e-17, 3.92e-137j)
| (1.7495658290835093948e-08 - 1.0690656057294099628e-767j)  +/-  (6.93e-42, 1.63e-161j)
| (5.5926904182269026596e-12 + 4.4492709464678168425e-770j)  +/-  (8.19e-49, 1.92e-168j)
| (4.8183601470296664372e-05 - 4.596105349071991627e-766j)  +/-  (8.64e-36, 2.03e-155j)
| (0.0076493151727574248733 - 1.7275742019261051271e-764j)  +/-  (2.59e-24, 6.08e-144j)
| (9.4111962687315329833e-39 + 3.8693927686984656494e-784j)  +/-  (4.29e-64, 1.01e-183j)
| (4.8183601470296664372e-05 - 8.9788785120443792982e-766j)  +/-  (6.77e-36, 1.59e-155j)
| (1.4833755129899555872e-09 + 2.87365267537419535e-768j)  +/-  (9.56e-45, 2.25e-164j)
| (8.7905450931160922914e-06 + 1.5812801894365666276e-766j)  +/-  (3.9e-39, 9.17e-159j)
| (9.4111962687315329833e-39 - 1.5009849956380582735e-782j)  +/-  (7.14e-62, 1.68e-181j)
| (3.9402934972943115605e-24 - 1.4888381998852111879e-775j)  +/-  (1.94e-56, 4.57e-176j)
| (2.1277652282259374797e-16 - 1.8020077148163556837e-772j)  +/-  (4.04e-55, 9.48e-175j)
| (5.8244323564410924221e-22 + 2.0280677399443670839e-775j)  +/-  (4.63e-59, 1.09e-178j)
| (0.056714856116816174559 + 1.841252379071593334e-763j)  +/-  (5.99e-20, 1.41e-139j)
| (0.017752278645761167097 + 3.7510824297482145196e-764j)  +/-  (2.98e-28, 7e-148j)
| (4.1248277917894110246e-18 + 1.2567505942767749639e-772j)  +/-  (2.58e-55, 6.06e-175j)
| (2.4293921685335091149e-13 - 8.0190000987232793679e-771j)  +/-  (1.04e-52, 2.45e-172j)
| (0.0027816975668563345642 + 1.2058011223417592777e-764j)  +/-  (3.13e-35, 7.34e-155j)
| (0.034648124229226526293 - 7.7483813873504198938e-764j)  +/-  (1.7e-26, 4e-146j)
| (4.9451660327423712653e-43 - 2.4429123167013481689e-786j)  +/-  (1.44e-68, 3.37e-188j)
| (4.4396644955015406768e-29 - 3.8745267304283454667e-779j)  +/-  (1.27e-62, 2.99e-182j)
| (1.0179054077951622322e-10 - 2.2086445335689024943e-769j)  +/-  (1.06e-51, 2.49e-171j)
| (5.5926904182269026596e-12 + 1.5646903910557052033e-769j)  +/-  (1.56e-54, 3.66e-174j)
| (0.10393000346465860939 + 3.8151361877610538699e-763j)  +/-  (7.63e-29, 1.79e-148j)
| (8.2194967241379022926e-15 + 1.2823554546990450429e-771j)  +/-  (9.02e-55, 2.12e-174j)
| (1.6855698824882821707e-07 + 1.4848264875528534635e-767j)  +/-  (4.12e-49, 9.68e-169j)
| (1.3369961907546428561e-06 - 1.1442141127687131398e-766j)  +/-  (2.71e-49, 6.37e-169j)
| (1.7114800181358123702e-26 + 8.5950019798268679559e-778j)  +/-  (4e-62, 9.39e-182j)
| (0.0027816975668563345642 + 7.5893765295387423816e-765j)  +/-  (7.03e-41, 1.65e-160j)
| (2.1277652282259374797e-16 - 8.94923315374977675e-772j)  +/-  (1.49e-58, 3.49e-178j)
| (0.0076493151727574248733 - 2.5717129221972061232e-764j)  +/-  (3.96e-41, 9.3e-161j)
| (1.3369961907546428561e-06 - 5.0450830667658677922e-767j)  +/-  (1.04e-48, 2.43e-168j)
| (4.4396644955015406768e-29 - 7.7967830207134636618e-778j)  +/-  (8.35e-65, 1.96e-184j)
| (5.8330930913139211871e-20 - 1.5416006870602849276e-773j)  +/-  (8.24e-61, 1.94e-180j)
| (1.7114800181358123702e-26 + 1.1568587012040499421e-776j)  +/-  (8.77e-64, 2.06e-183j)
| (0.00022124183323595269069 + 1.245558017666456869e-765j)  +/-  (7.76e-49, 1.82e-168j)
| (0.079786545145283619515 - 2.4793431831717882197e-763j)  +/-  (1.2e-41, 2.81e-161j)
| (5.8330930913139211871e-20 - 2.3012353736822003894e-774j)  +/-  (2.78e-62, 6.53e-182j)
| (0.00085427501005117503396 - 5.3772012736347229582e-765j)  +/-  (2.57e-49, 6.03e-169j)
| (0.034648124229226526293 - 1.0186278869062703492e-763j)  +/-  (9.87e-44, 2.32e-163j)
| (1.0179054077951622322e-10 - 7.0421765392245536335e-769j)  +/-  (6.47e-57, 1.52e-176j)
| (1.7495658290835093948e-08 - 4.0097719140653546243e-768j)  +/-  (1.07e-55, 2.5e-175j)
| (8.7905450931160922914e-06 + 3.3239960026767829868e-766j)  +/-  (3e-53, 7.04e-173j)
| (8.2194967241379022926e-15 + 5.6170730963787865824e-771j)  +/-  (7.56e-60, 1.78e-179j)
| (1.7641915841717933019e-48 + 3.9385315141456448766e-789j)  +/-  (2.49e-78, 5.85e-198j)
| (2.4293921685335091149e-13 - 3.1332104282757181616e-770j)  +/-  (3.64e-59, 8.55e-179j)
| (1.4833755129899555872e-09 + 9.880859084323944416e-769j)  +/-  (6.55e-58, 1.54e-177j)
| (0.056714856116816174559 + 1.4844691126226738543e-763j)  +/-  (1.47e-50, 3.46e-170j)
| (3.9402934972943115605e-24 - 1.4740324791022747956e-776j)  +/-  (1.12e-66, 2.64e-186j)
| (0.12707729378980140999 - 4.2230366762968651061e-763j)  +/-  (1.21e-51, 2.84e-171j)
| (0.00022124183323595269069 + 2.2667159940148901027e-765j)  +/-  (2.73e-55, 6.44e-175j)
| (4.1248277917894110246e-18 + 2.1998904637391995526e-773j)  +/-  (1.57e-63, 3.68e-183j)
| (0.12707729378980140999 - 3.9979850093450073835e-763j)  +/-  (3.45e-53, 8.01e-173j)
| (0.00085427501005117503396 - 3.1653144973948415535e-765j)  +/-  (3.74e-55, 8.8e-175j)
| (1.6855698824882821707e-07 + 3.6446135873685991148e-767j)  +/-  (7.15e-58, 1.69e-177j)
| (0.079786545145283619515 - 2.9114535686248027023e-763j)  +/-  (3.59e-53, 8.58e-173j)
| (0.13705174047828155815 + 4.2344998366950777995e-763j)  +/-  (2.36e-53, 5.7e-173j)
| (0.10393000346465860939 + 3.4243256045081513104e-763j)  +/-  (1.37e-53, 2.88e-173j)
