Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 18 28
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : 8*t^21 - 12952203/17084*t^19 + 987853833/34168*t^17 - 9840668841/17084*t^15 + 222748598835/34168*t^13 - 5840004786525/136672*t^11 + 43360655152815/273344*t^9 - 85340399389245/273344*t^7 + 155352674512035/546688*t^5 - 385274669454675/4373504*t^3 + 24027902323425/8747008*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^49 - 209029691852685078034292233620043534153065287958186851362291556873898641262954292649377863802117162509551620439383/63417672409610829192717012208567897768901600258736263781984569216687467240428249301082718453871972629058763692*t^47 + 78539174037031200625375315632883296767140089912302362843876231696152132222252894098117418987114212154705411398405335/126835344819221658385434024417135795537803200517472527563969138433374934480856498602165436907743945258117527384*t^45 - 17873772629538376068187021905340031664213934145396042069017682343298386743975378205442736832431584987654641990411876753/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^43 + 13802436797786342284624219472017495644854596920257571068284853140584662738906180554501315954199157544112363432518452312249/2536706896384433167708680488342715910756064010349450551279382768667498689617129972043308738154878905162350547680*t^41 - 1536282712923465139573903028042646795356817643980241403364711358983204549013272249391132088922582830033458659261623895100557/5073413792768866335417360976685431821512128020698901102558765537334997379234259944086617476309757810324701095360*t^39 + 127748014165744251934444257707450307486973655182136453211490287742286611784867210799131999440323828935462565677624382252042837/10146827585537732670834721953370863643024256041397802205117531074669994758468519888173234952619515620649402190720*t^37 - 8119239091754559312852466094059471538039857204573280892573784581407835383491572926849030685949413814778669038995234962788757571/20293655171075465341669443906741727286048512082795604410235062149339989516937039776346469905239031241298804381440*t^35 + 80049452031295777147582271725983857905996025906854492174384531497468348084629721992513990572377787865470429218119551448486069883/8117462068430186136667777562696690914419404833118241764094024859735995806774815910538587962095612496519521752576*t^33 - 1544344668845216703605692301288960666021737393801154594841712030913634542505296984589530255906130682508646757420453472132152950243/8117462068430186136667777562696690914419404833118241764094024859735995806774815910538587962095612496519521752576*t^31 + 46870456604043510427337781365094872145483230940220922941287889727171736721352249020393570109250355529035319165518564895096153912787/16234924136860372273335555125393381828838809666236483528188049719471991613549631821077175924191224993039043505152*t^29 - 1120595366996537792904749385091152140418615160801083126187135813595127946464843885737844054952533534203144187216200418520928482460757/32469848273720744546671110250786763657677619332472967056376099438943983227099263642154351848382449986078087010304*t^27 + 21073378337517597799093133612080849150852317149250080009312186600231946847773332000148557768416245516116208311106949229931812399442441/64939696547441489093342220501573527315355238664945934112752198877887966454198527284308703696764899972156174020608*t^25 - 310333366072546968741932827070798449785059467740161593366707536785496575329802840592976330595835504613649843320056903207942059793853225/129879393094882978186684441003147054630710477329891868225504397755775932908397054568617407393529799944312348041216*t^23 + 3552079152765859509921049471717414151252155668199606457707203524755320346651600518104243524390361529345319514013518510431297722039672225/259758786189765956373368882006294109261420954659783736451008795511551865816794109137234814787059599888624696082432*t^21 - 31258280386101701357533702891606783288848248141720095775889939324087375312711893727249351721574254210784460664638419699593266394078896375/519517572379531912746737764012588218522841909319567472902017591023103731633588218274469629574119199777249392164864*t^19 + 208338682983905540018647959488559237110788520959199209463129961323144555710669207706646798769963914395590152816981587362409070819685657875/1039035144759063825493475528025176437045683818639134945804035182046207463267176436548939259148238399554498784329728*t^17 - 2061408193478679097126969047921258757751233936681972031805194446989801274851771907626832842094848594431971520287120503218978122583039773875/4156140579036255301973902112100705748182735274556539783216140728184829853068705746195757036592953598217995137318912*t^15 + 7366670386867589818013719607572721873563357567577853440432518404724579324798371233915920990679747308999089421250402525320070498308661401875/8312281158072510603947804224201411496365470549113079566432281456369659706137411492391514073185907196435990274637824*t^13 - 18318221633220581618145501257165529916213894402371429850720897897163255977168521790260399205704624324944054517967988319007179331200819667125/16624562316145021207895608448402822992730941098226159132864562912739319412274822984783028146371814392871980549275648*t^11 + 30046879367004143161021907144002955783685578377769250938303514909511624790311884417074889454928970325151480968970739325207866408139967837625/33249124632290042415791216896805645985461882196452318265729125825478638824549645969566056292743628785743961098551296*t^9 - 29969941108026587513899181179444863646151457360252542703968219075648129870129061818526934060754750522589742065734891256572907027063447355125/66498249264580084831582433793611291970923764392904636531458251650957277649099291939132112585487257571487922197102592*t^7 + 15866679447394958265681328554603097519397139463373046330676490867583126902591356549176288264252983842429309107019270772566512390448757284125/132996498529160169663164867587222583941847528785809273062916503301914555298198583878264225170974515142975844394205184*t^5 - 3446892634364763186423430350661686974852850588203105864916585556020146848936572174155526686570131278441454253812648212274007474007519466875/265992997058320339326329735174445167883695057571618546125833006603829110596397167756528450341949030285951688788410368*t^3 + 173062571740404057416726132494134604500392201631009462106263720853821522066728509795998794387665212830463845524279411963073988063059229375/531985994116640678652659470348890335767390115143237092251666013207658221192794335513056900683898060571903377576820736*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
-------------------------------------------------
The nodes are:
| (4.6011958858009393032 + 3.63024070134425198e-513j)  +/-  (3.46e-244, 3.46e-244j)
| (8.0372358378264645588 + 1.7826309223161146037e-516j)  +/-  (1.71e-247, 1.71e-247j)
| (4.9791543116692221306 - 1.5568032991323939649e-513j)  +/-  (2.79e-244, 2.79e-244j)
| (5.8188025650390135672 + 3.9363335810709438606e-514j)  +/-  (1.01e-244, 1.01e-244j)
| (5.3853563457510686316 + 2.1418962719186479426e-514j)  +/-  (1.88e-244, 1.88e-244j)
| (7.3542148974633408976 - 1.3595204918528290388e-515j)  +/-  (2.2e-246, 2.2e-246j)
| (0.18703245774372996923 + 2.3176022861070034906e-533j)  +/-  (4.65e-254, 4.65e-254j)
| (0.72167284382081647552 - 1.9012188640836883194e-520j)  +/-  (8.12e-252, 8.12e-252j)
| (3.6403255507135839419 + 2.0021705293721429435e-513j)  +/-  (2.46e-244, 2.46e-244j)
| (3.3444338676496712713 + 4.2697100850176288812e-514j)  +/-  (1.2e-244, 1.2e-244j)
| (1.0192195488067864917 + 3.522068255834585648e-519j)  +/-  (2.06e-250, 2.06e-250j)
| (6.2832343835578092994 - 5.6204365619996729155e-515j)  +/-  (4.33e-245, 4.33e-245j)
| (1.2247448713915890491 - 7.8226714293103567956e-519j)  +/-  (1.84e-249, 1.84e-249j)
| (1.7319350879389337601 - 1.896032004279530976e-517j)  +/-  (5.57e-248, 5.57e-248j)
| (3.941861650961138182 - 1.6702649938077370029e-513j)  +/-  (3.46e-244, 3.46e-244j)
| (4.2560757575409848653 - 1.4910787203704312227e-513j)  +/-  (3.86e-244, 3.86e-244j)
| (6.7881652692243661271 + 8.5588304855242807036e-515j)  +/-  (1.22e-245, 1.22e-245j)
| (2.2498901573507839375 - 1.8206634119585318167e-515j)  +/-  (2e-246, 2e-246j)
| (2.5017123937686716397 - 5.6777427847297139277e-515j)  +/-  (7.05e-246, 7.05e-246j)
| (1.4354648217352355091 - 1.4806867300367415607e-517j)  +/-  (8.47e-249, 8.47e-249j)
| (2.784698074503156652 + 3.7739127114010255756e-514j)  +/-  (2.08e-245, 2.08e-245j)
| (3.0631196171779235313 - 1.6104031548990412096e-513j)  +/-  (6.05e-245, 6.05e-245j)
| (2.0157584139577802696 - 4.1342231494517815033e-516j)  +/-  (4.27e-247, 4.27e-247j)
| (0.42550602701632622123 - 8.1814886937998388785e-522j)  +/-  (4.9e-253, 4.9e-253j)
| (-6.2832343835578092994 + 3.5628960248673316181e-512j)  +/-  (4.1e-245, 4.1e-245j)
| (-8.0372358378264645588 - 1.547017631555189624e-520j)  +/-  (1.72e-247, 1.72e-247j)
| (-7.3542148974633408976 + 2.7023099293346707323e-517j)  +/-  (2.14e-246, 2.14e-246j)
| (-4.9791543116692221306 + 1.1445949083314589727e-525j)  +/-  (2.84e-244, 2.84e-244j)
| (-5.8188025650390135672 - 5.3928308023337407006e-538j)  +/-  (9.95e-245, 9.95e-245j)
| (-1.7319350879389337601 + 4.1786690528628210115e-550j)  +/-  (5.39e-248, 5.39e-248j)
| (-6.7881652692243661271 + 1.4204310650774026728e-545j)  +/-  (1.18e-245, 1.18e-245j)
| (-3.6403255507135839419 + 7.0929143680357054075e-556j)  +/-  (2.15e-244, 2.15e-244j)
| (-2.5017123937686716397 - 6.6189954872798205064e-565j)  +/-  (6.47e-246, 6.47e-246j)
| (-2.784698074503156652 - 7.77252539278969215e-572j)  +/-  (2.03e-245, 2.03e-245j)
| (-3.0631196171779235313 - 3.0218073380324142159e-593j)  +/-  (5.68e-245, 5.68e-245j)
| (-2.2498901573507839375 + 1.2631330611226922468e-620j)  +/-  (1.94e-246, 1.94e-246j)
| (-0.18703245774372996923 + 1.1033108271342920814e-636j)  +/-  (3.63e-254, 3.63e-254j)
| (-0.72167284382081647552 + 4.2835817847215933464e-643j)  +/-  (8.94e-252, 8.94e-252j)
| (-4.6011958858009393032 - 8.1278917937503272889e-675j)  +/-  (3.52e-244, 3.52e-244j)
| (-4.2560757575409848653 - 1.5418495761379907988e-711j)  +/-  (3.64e-244, 3.64e-244j)
| (1.0586071126168902284e-748 - 3.9722727233764726055e-749j)  +/-  (5.54e-747, 5.54e-747j)
| (-0.42550602701632622123 - 4.5135858996004236223e-738j)  +/-  (4.52e-253, 4.52e-253j)
| (-3.3444338676496712713 - 3.4627498542080455746e-729j)  +/-  (1.26e-244, 1.26e-244j)
| (-1.2247448713915890491 + 1.0408122225804256974e-743j)  +/-  (1.73e-249, 1.73e-249j)
| (-2.0157584139577802696 - 1.4105015118111674569e-741j)  +/-  (4.64e-247, 4.64e-247j)
| (-3.941861650961138182 - 8.6078933670577506018e-738j)  +/-  (3.61e-244, 3.61e-244j)
| (-1.4354648217352355091 - 2.0853342163914347794e-753j)  +/-  (7.96e-249, 7.96e-249j)
| (-1.0192195488067864917 + 2.7007306077434507411e-756j)  +/-  (2.08e-250, 2.08e-250j)
| (-5.3853563457510686316 - 3.7053547382115721184e-749j)  +/-  (1.88e-244, 1.88e-244j)
-------------------------------------------------
The weights are:
| (1.306522850401533586e-10 - 3.5963824717245536353e-522j)  +/-  (2.62e-52, 4.54e-173j)
| (3.9262183874518687473e-29 - 1.4007829798081387732e-535j)  +/-  (1.35e-64, 2.33e-185j)
| (3.7879655010963945353e-12 - 3.4017294839814877646e-524j)  +/-  (2.83e-54, 4.89e-175j)
| (4.9896618340942612516e-16 - 5.6547846158402609782e-527j)  +/-  (3.73e-58, 6.44e-179j)
| (6.009248140659015698e-14 + 2.4030644846264478507e-525j)  +/-  (2.29e-56, 3.95e-177j)
| (1.1160408446740455685e-24 + 7.7424312020698270961e-533j)  +/-  (7.97e-64, 1.38e-184j)
| (0.10784141634270339713 - 7.3245979910027098436e-515j)  +/-  (1.3e-33, 2.25e-154j)
| (0.10255873813385394478 - 2.3681286610523991112e-515j)  +/-  (7.91e-34, 1.37e-154j)
| (2.9737392093782296455e-07 - 6.1448760373192175085e-519j)  +/-  (2.62e-51, 4.52e-172j)
| (2.2648666001269540758e-06 + 2.4207597613264864737e-518j)  +/-  (2.37e-50, 4.09e-171j)
| (0.054557246393840920568 + 2.3359017241409382349e-515j)  +/-  (5.08e-34, 8.78e-155j)
| (1.9470101081005090722e-18 + 9.8324659172112459502e-529j)  +/-  (7.29e-61, 1.26e-181j)
| (0.019575756450692364201 - 2.1859361380163922442e-515j)  +/-  (2.64e-37, 4.57e-158j)
| (0.0084463112484661029573 - 4.8048239470729638123e-516j)  +/-  (2.39e-42, 4.13e-163j)
| (3.066645715924690037e-08 + 4.8503083792726215966e-521j)  +/-  (6.3e-53, 1.09e-173j)
| (2.5128432658393458849e-09 + 6.5739303805083790292e-521j)  +/-  (4.91e-54, 8.49e-175j)
| (2.9122203008380525809e-21 - 1.2117347706931699046e-530j)  +/-  (1.59e-63, 2.75e-184j)
| (0.00081321410069666649114 - 1.8679879368528031124e-516j)  +/-  (4.16e-48, 7.2e-169j)
| (0.00029759088981702077197 + 9.9239616648661853835e-517j)  +/-  (1.96e-49, 3.4e-170j)
| (0.019883420850007722102 + 1.1861659305585667756e-515j)  +/-  (2.69e-44, 4.64e-165j)
| (6.8507287321471633042e-05 - 3.8880280779119281747e-517j)  +/-  (6.54e-51, 1.13e-171j)
| (1.3101182982283476426e-05 + 7.7730785836358163437e-518j)  +/-  (6.83e-52, 1.18e-172j)
| (0.0025026763179032799717 + 2.8880088985243791963e-516j)  +/-  (3.04e-48, 5.26e-169j)
| (0.13055166995745470443 + 3.9861133748060079523e-515j)  +/-  (1.5e-44, 2.59e-165j)
| (1.9470101081005090722e-18 + 3.3553815486299500844e-529j)  +/-  (1.31e-76, 2.26e-197j)
| (3.9262183874518687473e-29 + 6.2324639322486266836e-536j)  +/-  (1.61e-81, 2.79e-202j)
| (1.1160408446740455685e-24 - 3.3066503816659919326e-533j)  +/-  (7.78e-80, 1.35e-200j)
| (3.7879655010963945353e-12 + 5.9303900555137292092e-525j)  +/-  (1.64e-74, 2.83e-195j)
| (4.9896618340942612516e-16 + 3.9267375995009780304e-528j)  +/-  (1.84e-76, 3.18e-197j)
| (0.0084463112484661029573 - 1.2432262490681505046e-516j)  +/-  (6.03e-62, 1.04e-182j)
| (2.9122203008380525809e-21 + 5.5552321258470781635e-531j)  +/-  (8.89e-79, 1.54e-199j)
| (2.9737392093782296455e-07 + 1.1987829950926280642e-520j)  +/-  (1.14e-71, 1.97e-192j)
| (0.00029759088981702077197 + 7.1665358934378503104e-518j)  +/-  (1.46e-67, 2.53e-188j)
| (6.8507287321471633042e-05 - 1.67327212286305302e-518j)  +/-  (6.14e-69, 1.06e-189j)
| (1.3101182982283476426e-05 + 3.8596244071293180921e-519j)  +/-  (2.85e-70, 4.93e-191j)
| (0.00081321410069666649114 - 2.4075206750177037438e-517j)  +/-  (1.69e-67, 2.93e-188j)
| (0.10784141634270339713 - 6.4600221294324956806e-515j)  +/-  (3.32e-62, 5.75e-183j)
| (0.10255873813385394478 - 1.4437863175395150969e-515j)  +/-  (2.39e-63, 4.13e-184j)
| (1.306522850401533586e-10 - 1.1678226878082801423e-523j)  +/-  (5.2e-76, 9e-197j)
| (2.5128432658393458849e-09 + 1.6496926724289198058e-522j)  +/-  (2.95e-75, 5.1e-196j)
| (0.10577551057987557538 + 9.0353922187757580305e-515j)  +/-  (5.4e-64, 9.24e-185j)
| (0.13055166995745470443 + 2.990092159280442497e-515j)  +/-  (3.34e-65, 5.7e-186j)
| (2.2648666001269540758e-06 - 7.5878314266783335032e-520j)  +/-  (1.56e-72, 2.7e-193j)
| (0.019575756450692364201 - 9.0698270482193491775e-516j)  +/-  (4.23e-68, 7.14e-189j)
| (0.0025026763179032799717 + 5.4274012765508173933e-517j)  +/-  (1.54e-69, 2.66e-190j)
| (3.066645715924690037e-08 - 1.6046597459351255408e-521j)  +/-  (1.39e-74, 2.4e-195j)
| (0.019883420850007722102 + 4.1060345194922339096e-516j)  +/-  (4.23e-69, 6.88e-190j)
| (0.054557246393840920568 + 1.1420255668118563511e-515j)  +/-  (1.22e-68, 1.9e-189j)
| (6.009248140659015698e-14 - 2.1760600640549087122e-526j)  +/-  (1.69e-79, 3.04e-200j)
