Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 10 28
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : 35/8*t^14 - 436215/27784*t^12 + 12954799/583464*t^10 - 3039465/194488*t^8 + 2679105/472328*t^6 - 8846695/8974232*t^4 + 1485/22952*t^2 - 273/390184
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^42 - 5897514933563278719248070870019895061181879123589638214796321316131851476496857260020350854916463/125199979520452898815527663841304356123642327278854720506671177078723754504560141028220283839258*t^40 + 36284869084215859101759990752921491885476421620854398147466835552842174299384921300768329139897682714551/153960668415932297825633047723601110203653195416698669192022666534894017941838687504940991002244669244*t^38 - 2455705785604648703958141699923416549823453014759340576687777545119064910476817752624609644260949627567/3376330447717813548807742274640375223764324460892514675263654967870482849601725603178530504435190115*t^36 + 183001714746325921420363228651302009181609091732927042151721691853432320386853805415299099701445813354719/118075099085902965249733615547423407825358089718069656072077533733527743083214632522586323926533505736*t^34 - 209317012876074734853716931863905188590883069939683418241126303375032707809684150466699421027120415323253387/86536892840355089399279032324072652585181928195285844848001883068791501941737759426884332728333093020074*t^32 + 2435127789378980252400166501988968703408189651839030817720749533268967129610961797067352345431269290777893903/850946112930158379092910484520047750420955627253644141005351850176449769093754634364362605161942081364061*t^30 - 16580738870462665762619678074079123422712083121636230072145588428022738807845940912727493699736825542564924252/6326599361350307948908160558822963709651452706972745570083268103485778718044871412013304586204004170141497*t^28 + 463941985942361304344727704159334746277138775462849751556751972586046493877505987739987368284513188364656623/246651047226132863505191444788419637803175544131491055363870101500420222925725980975177566713606400395380*t^26 - 1745840225991843763308106257949747107279939871179835188072920948372378678503959850271286626008763889002541815/1640229464053783542309523107842990591391117368474415518169736174977794482456077773484930818645482562629277*t^24 + 79535630172927338513395521034579966517852835033696124789669526214125982175076477565603998177521535774870948285/167303405333485921315571356999985040321893971584390382853313089847735037210519932895462943501839221388186254*t^22 - 665296334020597593246089537353520768724120574409755387410400367963079339306158142672347993907796714117293290/3983414412702045745608841833332977150521285037723580544126502139231786600250474592749117702424743366385387*t^20 + 1804714080771948005437979206345992646619057022348567643834313009259293025021636219431196655688303356655450605/39414837346736031588129592877189458120947451952212270647146442219767151623531011759833375160834302783181724*t^18 - 91875781665198014046367725087143612067473205863549420667246669698464575451968298464808518341242675408089/9502130507892003757986883528734199161269877519819737378772044893868647932384525496584709537327459687363*t^16 + 6114661611646307022427249756134093547776522355189563885200305303250228068291155989847789425098230997996779985/3962930043229915411294735683843298899601731308783460211978532727302176700736493050029129205509178354832550691*t^14 - 1674473754395300524987006084568986749100756138949058706786442969539629357849718792941522120001202451919311780/9246836767536469293021049928967697432404039720494740494616576363705078968385150450067968146188082827942618279*t^12 + 70086459170907682381503950005174990420009258289673318971517411863078275260976235948400032593156925822586741775/4660405730838380523682609164199719505931636019129349209286754487307359800066115826834255945678793745283079612616*t^10 - 108153408332742375418670218514817357540917367022819091596908046644924623296459132547137280594221705071418815/129455714745510570102294699005547764053656556086926366924632069091871105557392106300951554046633159591196655906*t^8 + 8041908160832601560073454943702580150479535029591806199964088865442919859704625802604107698956548903557/282346160840808222687665646686036562821497396045640931133330575990994777660615280918105897593529246654736436*t^6 - 752889440435853396522931414844920437182129830531113256059042728397965239504545127465225446142984296115/1460026858032074098898060515100162752484848376920222183360512057427117731850286913168626549398118341254097623*t^4 + 11965238891908756382254146602913433085345044663943937124410189996964525371036540097736816204868098115/3216291049577902362789930410075720846053579033215561911170983083027853554220921895675815007369767940153954184*t^2 - 8744109359232478852283715970356137819847354047008444179035978570950643709438743027530373185242925/1952748137243726434551029177545973370818244413023734017496668300409768229348416865231744825903073392236329326
-------------------------------------------------
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: 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:
| (0.98589151893178956383 - 4.1850451472742025113e-895j)  +/-  (5.93e-240, 5.93e-240j)
| (-0.99444997880691468328 - 1.3516899316179966232e-903j)  +/-  (4.87e-240, 4.87e-240j)
| (-0.92774640944973865635 + 1.4335250237688394208e-923j)  +/-  (9.98e-241, 9.98e-241j)
| (0.99893473998376008044 + 6.4484647186877667163e-923j)  +/-  (2.04e-240, 2.04e-240j)
| (0.92774640944973865635 - 1.3339505467984357332e-926j)  +/-  (9.28e-241, 9.28e-241j)
| (0.95280406968027788258 + 7.6444474055230469595e-926j)  +/-  (2.21e-240, 2.21e-240j)
| (-0.41135298760164655679 - 2.3537958894482369031e-938j)  +/-  (1.22e-248, 1.22e-248j)
| (-0.86113631159405257522 + 1.0981130061576475748e-928j)  +/-  (1.05e-241, 1.05e-241j)
| (-0.99893473998376008044 + 1.3919486870935348512e-937j)  +/-  (2.01e-240, 2.01e-240j)
| (0.99444997880691468328 - 1.9578800852022233609e-954j)  +/-  (5.24e-240, 5.24e-240j)
| (0.86113631159405257522 - 4.6709480638279791847e-960j)  +/-  (1.05e-241, 1.05e-241j)
| (-0.26656878205867566829 + 1.6115999586880613601e-968j)  +/-  (4.18e-251, 4.18e-251j)
| (-0.98589151893178956383 - 2.5431352912945701364e-955j)  +/-  (5.73e-240, 5.73e-240j)
| (-0.89713036291094040417 + 9.9319650630366042559e-966j)  +/-  (3.65e-241, 3.65e-241j)
| (0.97217703813435809847 - 4.3613819170396884811e-972j)  +/-  (3.85e-240, 3.85e-240j)
| (0.81997795564277018721 + 2.5544012787152510654e-974j)  +/-  (2.77e-242, 2.77e-242j)
| (0.77389887876922281619 - 2.569942183329569851e-975j)  +/-  (5.72e-243, 5.72e-243j)
| (0.41135298760164655679 - 8.0575987010099116772e-981j)  +/-  (1.2e-248, 1.2e-248j)
| (-0.81997795564277018721 - 2.2262682577216461501e-971j)  +/-  (2.87e-242, 2.87e-242j)
| (-0.97217703813435809847 + 4.7145640432928375769e-978j)  +/-  (4.36e-240, 4.36e-240j)
| (0.48025621629700212987 - 2.1982035492790192672e-1001j)  +/-  (1.69e-247, 1.69e-247j)
| (0.72317255923281838433 + 1.6895643662114037461e-996j)  +/-  (1.04e-243, 1.04e-243j)
| (0.89713036291094040417 - 4.2144787013370721803e-994j)  +/-  (3.66e-241, 3.66e-241j)
| (-0.77389887876922281619 - 1.3212923507890952383e-994j)  +/-  (5.83e-243, 5.83e-243j)
| (-0.72317255923281838433 - 3.9344403059359751739e-998j)  +/-  (1.03e-243, 1.03e-243j)
| (0.11539569344883949077 - 4.8162187107869702389e-1009j)  +/-  (9.22e-254, 9.22e-254j)
| (0.6681020309825705898 + 1.1143858433454367071e-1009j)  +/-  (1.64e-244, 1.64e-244j)
| (0.3399810435848562648 + 1.813244061531401884e-1010j)  +/-  (7.31e-250, 7.31e-250j)
| (-0.95280406968027788258 - 2.1933547054854049838e-1012j)  +/-  (2.11e-240, 2.11e-240j)
| (-0.6681020309825705898 - 3.0260404578439879013e-1028j)  +/-  (1.44e-244, 1.44e-244j)
| (-0.3399810435848562648 - 2.8754886169708490111e-1035j)  +/-  (7.37e-250, 7.37e-250j)
| (0.19155689100580920842 + 3.2103182096274953096e-1037j)  +/-  (2.18e-252, 2.18e-252j)
| (0.60901818032859988091 + 2.0100189573688570961e-1030j)  +/-  (1.79e-245, 1.79e-245j)
| (0.038542286252860243122 - 4.6616367864718067725e-1040j)  +/-  (5.42e-255, 5.42e-255j)
| (-0.54627694908708365616 - 4.1242851151468711423e-1030j)  +/-  (2.1e-246, 2.1e-246j)
| (-0.48025621629700212987 + 6.611906196483126489e-1032j)  +/-  (1.67e-247, 1.67e-247j)
| (-0.038542286252860243122 - 4.2943349091662338781e-1040j)  +/-  (5.42e-255, 5.42e-255j)
| (0.54627694908708365616 - 8.7342440192113708693e-1033j)  +/-  (1.88e-246, 1.88e-246j)
| (0.26656878205867566829 + 3.0914072287592779261e-1037j)  +/-  (3.83e-251, 3.83e-251j)
| (-0.11539569344883949077 - 4.3452699391479459887e-1039j)  +/-  (1.02e-253, 1.02e-253j)
| (-0.60901818032859988091 + 7.09264823358347634e-1034j)  +/-  (1.95e-245, 1.95e-245j)
| (-0.19155689100580920842 - 2.9147203461903996477e-1040j)  +/-  (1.99e-252, 1.99e-252j)
-------------------------------------------------
The weights are:
| (0.010988613854389802018 - 3.5569672561445942333e-896j)  +/-  (8.18e-77, 1.36e-191j)
| (0.0063393817512851897921 + 1.6630493168423331183e-897j)  +/-  (2.08e-77, 3.46e-192j)
| (0.027863657831451917405 + 2.3303337035556550285e-897j)  +/-  (2.08e-77, 3.46e-192j)
| (0.0027123310839677062402 - 8.8205203112446382045e-896j)  +/-  (1.97e-77, 3.29e-192j)
| (0.027863657831451917405 - 7.6694589332571131674e-896j)  +/-  (5.05e-78, 8.41e-193j)
| (0.022229409069941195787 + 1.4244785500802032787e-895j)  +/-  (8.44e-78, 1.41e-192j)
| (0.070207840423800394377 + 2.2405896894230702303e-897j)  +/-  (5.46e-80, 9.1e-195j)
| (0.038614325355301219436 + 2.1663419784976124186e-897j)  +/-  (5.49e-80, 9.15e-195j)
| (0.0027123310839677062402 - 5.7963828406316094469e-898j)  +/-  (1.08e-79, 1.8e-194j)
| (0.0063393817512851897921 + 3.8481295862681506112e-895j)  +/-  (5.88e-78, 9.8e-193j)
| (0.038614325355301219436 - 3.2073162745236657904e-896j)  +/-  (2.03e-80, 3.39e-195j)
| (0.074286420834759499808 + 2.4388870238169900602e-897j)  +/-  (1.54e-81, 2.56e-196j)
| (0.010988613854389802018 - 2.3322960303828519122e-897j)  +/-  (4.16e-80, 6.93e-195j)
| (0.033338126447048051585 - 2.2384456061036152024e-897j)  +/-  (1.75e-80, 2.92e-195j)
| (0.016515610603630766635 - 3.5544429681003907769e-895j)  +/-  (8.58e-79, 1.43e-193j)
| (0.043661796830009391622 + 2.3016161259772298825e-896j)  +/-  (2.14e-81, 3.57e-196j)
| (0.048450773591858021274 - 1.7281532340153034566e-896j)  +/-  (3.45e-82, 5.75e-197j)
| (0.070207840423800394377 - 5.44898467276580056e-897j)  +/-  (6.89e-85, 1.15e-199j)
| (0.043661796830009391622 - 2.1146009053691833893e-897j)  +/-  (6.19e-84, 1.03e-198j)
| (0.016515610603630766635 + 2.4895618953900498465e-897j)  +/-  (1.11e-82, 1.85e-197j)
| (0.067529618577155568262 + 6.2969180420874901861e-897j)  +/-  (4.26e-85, 7.1e-200j)
| (0.052951330485941582817 + 1.3444182506537065537e-896j)  +/-  (6.92e-84, 1.15e-198j)
| (0.033338126447048051585 + 4.7487464767790462073e-896j)  +/-  (5.01e-82, 8.34e-197j)
| (0.048450773591858021274 + 2.081814741526379866e-897j)  +/-  (2.44e-85, 4.06e-200j)
| (0.052951330485941582817 - 2.0666525209652634594e-897j)  +/-  (3.81e-86, 6.34e-201j)
| (0.07658390577660166423 - 3.4627205139054242717e-897j)  +/-  (3.5e-88, 5.83e-203j)
| (0.057134529568095771206 - 1.0764567281597459004e-896j)  +/-  (9.84e-86, 1.64e-200j)
| (0.072464609598754551849 + 4.7806143352122363046e-897j)  +/-  (1.92e-87, 3.2e-202j)
| (0.022229409069941195787 - 2.4311375290640188156e-897j)  +/-  (9e-85, 1.5e-199j)
| (0.057134529568095771206 + 2.0682464458115459761e-897j)  +/-  (2.56e-87, 4.27e-202j)
| (0.072464609598754551849 - 2.3289182932174135861e-897j)  +/-  (1.53e-88, 2.55e-203j)
| (0.075662259065624830824 + 3.8148289941782729768e-897j)  +/-  (1.31e-88, 2.18e-203j)
| (0.060973794494137979049 + 8.8286478351045562842e-897j)  +/-  (1.17e-87, 1.94e-202j)
| (0.077046023774957557964 + 3.1734682710094703111e-897j)  +/-  (2.73e-89, 4.55e-204j)
| (0.064445640981287337819 + 2.1204973190738591645e-897j)  +/-  (1.61e-89, 2.69e-204j)
| (0.067529618577155568262 - 2.1716392984094891823e-897j)  +/-  (1.97e-89, 3.29e-204j)
| (0.077046023774957557964 - 2.9346773945248797838e-897j)  +/-  (2.07e-90, 3.45e-205j)
| (0.064445640981287337819 - 7.3904719682933266965e-897j)  +/-  (2.99e-89, 4.98e-204j)
| (0.074286420834759499808 - 4.2465072053077459912e-897j)  +/-  (7.62e-90, 1.27e-204j)
| (0.07658390577660166423 + 2.7370550702926004286e-897j)  +/-  (3.79e-91, 6.33e-206j)
| (0.060973794494137979049 - 2.0861882981354864767e-897j)  +/-  (2.38e-91, 4.31e-206j)
| (0.075662259065624830824 - 2.573574126759992138e-897j)  +/-  (2.68e-91, 4.4e-206j)
