Starting with polynomial:
P : t
Extension levels are: 1 4 10 34
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P2 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P3 : t^15 - 1805/21*t^13 + 169685/63*t^11 - 2447225/63*t^9 + 268675*t^7 - 846835*t^5 + 1039225*t^3 - 327525*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^49 - 4175800205808505672520320090786198999805978345308978443685245435150381643997343295853489/4590629804181073661263159751716754087714196155258679218560831995805786188647872427496*t^47 + 1639633442027414667183921517477927533365639865733293557910836978694224563542005361199709720153/4338145164951114609893685965372332612889915366719451861539986236036467948272239443983720*t^45 - 3224001978586333697225100349480918863501361774349694221876997003445050706332371000278738334502641/33837532286618693957170750529904194380541339860411724520011892641084449996523467663073016*t^43 + 236744622419333190661335716380685164876887194671393693222072429147849178429133444756845441862551561/14501799551408011695930321655673226163089145654462167651433668274750478569938628998459864*t^41 - 204913304471979855280122079027876331999195528039473245799213203871201803099814802953850243949393547175/101512596859856081871512251589712583141624019581235173560035677923253349989570402989219048*t^39 + 6316533025430263551483970362931845268601710122239858784069040298489318324671947729402795692387733947005/33837532286618693957170750529904194380541339860411724520011892641084449996523467663073016*t^37 - 9118187731350101871789057357350193072553957422696970314921971475049982440619167281652153329663607361551/690561883400381509330015316936820293480435507355341316734936584511927550949458523736184*t^35 + 3502705545374631251376036636993091822085826256436846332138207398476869859612758763804464314050421287821165/4833933183802670565310107218557742054363048551487389217144556091583492856646209666153288*t^33 - 25067979424138137839153374150874514976438182329410632715812941909067995730721847733387997460237504089338635/805655530633778427551684536426290342393841425247898202857426015263915476107701611025548*t^31 + 845823351087858857131392077188279206277381522984991943535999708992932508774412080795127326786808437148569475/805655530633778427551684536426290342393841425247898202857426015263915476107701611025548*t^29 - 3205634250434898003043614006112402984493730884283728105036220656315531643217682298473803555745498140168579975/115093647233396918221669219489470048913405917892556886122489430751987925158243087289364*t^27 + 1330179635623195626049131204605440707400948836783403659056003712436407028024498971506436915444588391989345275/2295314902090536830631579875858377043857098077629339609280415997902893094323936213748*t^25 - 7195269663505307303147833907171441634427250020847203123040057995535839181800642264815269256739327243315488125/765104967363512276877193291952792347952366025876446536426805332634297698107978737916*t^23 + 12896858368647880770186691960140958643016749497321164262734706386020166701602750824595437156586933435110866875/109300709623358896696741898850398906850338003696635219489543618947756814015425533988*t^21 - 41202187137980680290277682657151375631564035826849532330807614040520678758496402607458993471337691028977991875/36433569874452965565580632950132968950112667898878406496514539649252271338475177996*t^19 + 127221201665247331790886152292500751388320140206688740326828652008171602840322668239284286840539684012099044375/15614387089051270956677414121485558121476857670947888498506231278250973430775076284*t^17 - 9447119284826398906207668212197093454781066672534450982220901963909053216580797983806318632255270726235393354625/218601419246717793393483797700797813700676007393270438979087237895513628030851067976*t^15 + 1709550630279463198340996190013364426054780341225152068435371517453887637624286058829132090403514989993405923125/10409591392700847304451609414323705414317905113965258999004154185500648953850050856*t^13 - 31426373789790618575568913313928035074200404377195029518261909575910999869788663949923167981671865478150059650625/72867139748905931131161265900265937900225335797756812993029079298504542676950355992*t^11 + 54245925137612520539265552783291583499632798397459586738346384885169279236529081016074534150271100401476833053125/72867139748905931131161265900265937900225335797756812993029079298504542676950355992*t^9 - 2716809932920654938137836567477849613175758991348831697247691029853075398392163129876923655640419236839070940625/3469863797566949101483869804774568471439301704655086333001384728500216317950016952*t^7 + 1521983973176400770096156310676939892621577306251042758179112904278014889618301667215480307033748794226530230625/3469863797566949101483869804774568471439301704655086333001384728500216317950016952*t^5 - 331693360783493209857351330325205866213699516361766042363268026742383091397561171168445125333640941475310696875/3469863797566949101483869804774568471439301704655086333001384728500216317950016952*t^3 + 4565967048866500492887700704482738760709333621071055677585247560936990098297633603659688510011099956590334375/3469863797566949101483869804774568471439301704655086333001384728500216317950016952*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:
| (8.6461489004863156859 - 1.0484765987947415535e-736j)  +/-  (2.1e-244, 2.1e-244j)
| (10.024225393010539605 - 1.5127279272030481821e-740j)  +/-  (2.69e-245, 2.69e-245j)
| (11.785572076509104437 + 5.3587701104258127753e-745j)  +/-  (3.5e-247, 3.5e-247j)
| (-8.6461489004863156859 - 3.5312885351126829722e-743j)  +/-  (2.24e-244, 2.24e-244j)
| (10.823512133662207428 + 1.5562290789908051685e-743j)  +/-  (4.16e-246, 4.16e-246j)
| (3.2764024443557768692 - 4.9060130529934947353e-745j)  +/-  (7.55e-247, 7.55e-247j)
| (9.3085100040762066526 + 6.2676320292951476075e-741j)  +/-  (9.29e-245, 9.29e-245j)
| (-2.0639358295654824712 - 5.8270803082534771403e-755j)  +/-  (5.84e-249, 5.84e-249j)
| (-11.785572076509104437 - 6.8659394782873638865e-754j)  +/-  (3.35e-247, 3.35e-247j)
| (8.0215421444315089321 - 4.538433193213027607e-748j)  +/-  (4.6e-244, 4.6e-244j)
| (-9.3085100040762066526 + 9.0522827752871041795e-763j)  +/-  (8.48e-245, 8.48e-245j)
| (-10.823512133662207428 - 1.6894908161120438443e-764j)  +/-  (4.31e-246, 4.31e-246j)
| (7.4252037740830775214 + 1.6439729788915352791e-760j)  +/-  (6.45e-244, 6.45e-244j)
| (-10.024225393010539605 + 3.0213651324768901128e-770j)  +/-  (2.54e-245, 2.54e-245j)
| (-6.8503505181994369174 + 1.1398196105002663507e-767j)  +/-  (8.42e-244, 8.42e-244j)
| (-7.4252037740830775214 - 3.491769103653906707e-768j)  +/-  (6.03e-244, 6.03e-244j)
| (1.6052080826208982934 - 3.4320347530171266864e-775j)  +/-  (1.12e-249, 1.12e-249j)
| (-6.287590974526623999 - 3.0912729395969924821e-767j)  +/-  (1.42e-243, 1.42e-243j)
| (-2.473740787593568232 + 2.9977006045726791249e-775j)  +/-  (3.68e-248, 3.68e-248j)
| (-3.2764024443557768692 - 1.3695510385680126563e-773j)  +/-  (7.54e-247, 7.54e-247j)
| (4.2251281035186893476 - 1.6547281655163497402e-769j)  +/-  (1.03e-245, 1.03e-245j)
| (1.1834670573895621997 + 1.3914262911908478019e-790j)  +/-  (9.36e-251, 9.36e-251j)
| (-5.9074473874552246428 - 8.70996711591292095e-782j)  +/-  (3.52e-243, 3.52e-243j)
| (-2.8569700138728056542 - 5.9019467343694391095e-797j)  +/-  (1.61e-247, 1.61e-247j)
| (4.7272467664021150687 - 1.3829595506061885346e-817j)  +/-  (4.47e-245, 4.47e-245j)
| (5.9074473874552246428 + 3.0046948261251824856e-876j)  +/-  (3.46e-243, 3.46e-243j)
| (2.473740787593568232 - 3.4050604532439414131e-908j)  +/-  (3.77e-248, 3.77e-248j)
| (-1.064304362806788026e-928 + 2.6721135725866370257e-928j)  +/-  (1.41e-926, 1.41e-926j)
| (5.7976321753375833534 - 2.5385856304088778296e-921j)  +/-  (2.71e-243, 2.71e-243j)
| (-1.1834670573895621997 - 7.0717811624363964772e-949j)  +/-  (9.82e-251, 9.82e-251j)
| (-5.2436021027024333864 - 1.2863802467848335591e-940j)  +/-  (1.84e-244, 1.84e-244j)
| (-8.0215421444315089321 + 3.9195513689125761232e-947j)  +/-  (3.97e-244, 3.97e-244j)
| (1.3556261799742658658 - 3.4476516097996020961e-958j)  +/-  (4.38e-250, 4.38e-250j)
| (6.287590974526623999 - 3.0215212393987325859e-958j)  +/-  (1.62e-243, 1.62e-243j)
| (-3.7386519962521728647 + 4.8136780674211887329e-973j)  +/-  (2.58e-246, 2.58e-246j)
| (-4.2251281035186893476 - 2.7390245923477517901e-972j)  +/-  (1.03e-245, 1.03e-245j)
| (6.8503505181994369174 - 2.1576025891106676663e-969j)  +/-  (7.9e-244, 7.9e-244j)
| (0.68573644261161065561 - 9.9003697695208793884e-980j)  +/-  (8.41e-253, 8.41e-253j)
| (2.8569700138728056542 + 5.4758620385923113378e-975j)  +/-  (1.64e-247, 1.64e-247j)
| (-4.7272467664021150687 + 5.1468542358234986346e-971j)  +/-  (4.76e-245, 4.76e-245j)
| (-0.68573644261161065561 + 2.5566106708135072892e-979j)  +/-  (8.41e-253, 8.41e-253j)
| (-1.6052080826208982934 - 4.1866195879448846205e-976j)  +/-  (1.01e-249, 1.01e-249j)
| (3.7386519962521728647 - 1.3800563222749679792e-973j)  +/-  (2.57e-246, 2.57e-246j)
| (0.12139277284397661833 - 5.7036248232290589442e-981j)  +/-  (1.95e-254, 1.95e-254j)
| (-5.7976321753375833534 + 3.6669079487300783338e-969j)  +/-  (2.75e-243, 2.75e-243j)
| (-1.3556261799742658658 + 1.5462133532936931861e-980j)  +/-  (4.31e-250, 4.31e-250j)
| (-0.12139277284397661833 + 8.0928227016909715065e-983j)  +/-  (1.63e-254, 1.63e-254j)
| (5.2436021027024333864 - 8.0370957681947276667e-977j)  +/-  (1.93e-244, 1.93e-244j)
| (2.0639358295654824712 - 8.9728811307112414057e-984j)  +/-  (5.82e-249, 5.82e-249j)
-------------------------------------------------
The weights are:
| (1.4965859962240128032e-17 + 8.4207034308610849951e-753j)  +/-  (4.92e-72, 5.11e-193j)
| (4.530589604758706341e-23 - 5.5574009345670553753e-757j)  +/-  (2.28e-75, 2.36e-196j)
| (3.0502733597216691066e-31 - 5.475227531957766178e-762j)  +/-  (1.73e-79, 1.8e-200j)
| (1.4965859962240128032e-17 + 9.0729714551717022909e-755j)  +/-  (2.65e-76, 2.75e-197j)
| (1.2489663588786341328e-26 + 3.1309169612026518138e-759j)  +/-  (2.04e-77, 2.11e-198j)
| (0.00082725733396639530179 - 1.0013426543153491204e-744j)  +/-  (1.1e-57, 1.15e-178j)
| (4.1837765224601522531e-20 + 6.5491107319380677658e-755j)  +/-  (1.97e-74, 2.04e-195j)
| (0.020588370853858037139 + 1.5477767079161640767e-743j)  +/-  (3e-51, 3.12e-172j)
| (3.0502733597216691066e-31 + 8.4122964507145691703e-763j)  +/-  (5.52e-84, 5.73e-205j)
| (2.5900107144391477366e-15 - 6.6552285542214485372e-752j)  +/-  (2.99e-73, 3.11e-194j)
| (4.1837765224601522531e-20 - 2.4158712875028155028e-756j)  +/-  (2.85e-79, 2.96e-200j)
| (1.2489663588786341328e-26 - 3.5011252368455414632e-760j)  +/-  (1.25e-82, 1.3e-203j)
| (2.4866799910709027194e-13 + 7.3517112221172352211e-751j)  +/-  (1.97e-74, 2.05e-195j)
| (4.530589604758706341e-23 + 4.1016226304920852664e-758j)  +/-  (4.88e-81, 5.06e-202j)
| (1.4582059842458575606e-11 - 1.1628120534524853427e-750j)  +/-  (1.76e-76, 1.82e-197j)
| (2.4866799910709027194e-13 + 5.584347517537508452e-752j)  +/-  (1.35e-77, 1.4e-198j)
| (0.054707230286753891117 - 1.2352436483796031127e-742j)  +/-  (3.31e-58, 3.44e-179j)
| (5.896196922031808051e-10 + 3.3510951025349874798e-749j)  +/-  (7.67e-76, 7.97e-197j)
| (0.0072385614421953669122 - 5.4435000386580319857e-744j)  +/-  (1.46e-64, 1.52e-185j)
| (0.00082725733396639530179 - 4.5155371778417027334e-745j)  +/-  (1.05e-68, 1.09e-189j)
| (2.6245963505469648698e-05 - 5.8503299270269205189e-746j)  +/-  (3.35e-73, 3.47e-194j)
| (0.10860998309139234292 - 2.9113889979711036861e-742j)  +/-  (5.38e-58, 5.59e-179j)
| (-2.3400176278323144142e-09 - 5.9598124707083403769e-748j)  +/-  (6.45e-76, 6.7e-197j)
| (0.0026529744299036493949 + 1.8150254938913656696e-744j)  +/-  (2.86e-67, 2.97e-188j)
| (2.851498307768635382e-06 + 1.4910986324621792931e-746j)  +/-  (5.07e-75, 5.26e-196j)
| (-2.3400176278323144142e-09 - 3.1677027716049429714e-747j)  +/-  (2.78e-78, 2.88e-199j)
| (0.0072385614421953669122 - 9.8024724044971036476e-744j)  +/-  (2.71e-70, 2.81e-191j)
| (-0.64763982279431243907 + 2.1336374718495758023e-741j)  +/-  (4.37e-64, 4.53e-185j)
| (1.4329728326309641296e-08 + 4.158811153165025658e-747j)  +/-  (4.41e-78, 4.58e-199j)
| (0.10860998309139234292 - 2.2105644200491709166e-742j)  +/-  (2.22e-65, 2.3e-186j)
| (2.2402668488413015487e-07 - 1.0800779019019504247e-747j)  +/-  (3.1e-78, 3.22e-199j)
| (2.5900107144391477366e-15 - 2.4936712332534855159e-753j)  +/-  (6.83e-83, 7.09e-204j)
| (-0.021246493800255972969 + 3.2855626781411420102e-742j)  +/-  (2.7e-67, 2.81e-188j)
| (5.896196922031808051e-10 + 2.1221978689400647972e-748j)  +/-  (3.35e-80, 3.48e-201j)
| (0.00017535886446495442451 + 9.5839831977159296022e-746j)  +/-  (1.24e-75, 1.29e-196j)
| (2.6245963505469648698e-05 - 2.0085029916647483239e-746j)  +/-  (4.86e-77, 5.05e-198j)
| (1.4582059842458575606e-11 - 1.0035814055332689449e-749j)  +/-  (5.27e-82, 5.48e-203j)
| (0.15556061556413915484 + 1.5141428145282451904e-742j)  +/-  (2.01e-70, 2.08e-191j)
| (0.0026529744299036493949 + 3.6032198845622563859e-744j)  +/-  (2.37e-75, 2.46e-196j)
| (2.851498307768635382e-06 + 4.3680323523152168776e-747j)  +/-  (2.18e-78, 2.26e-199j)
| (0.15556061556413915484 + 1.2916846420433792108e-742j)  +/-  (3.28e-72, 3.4e-193j)
| (0.054707230286753891117 - 8.4853767089990883937e-743j)  +/-  (1.49e-73, 1.55e-194j)
| (0.00017535886446495442451 + 2.4209193257225714299e-745j)  +/-  (1.21e-77, 1.26e-198j)
| (0.4946767192480765545 - 1.1617674211842439155e-741j)  +/-  (1.56e-72, 1.62e-193j)
| (1.4329728326309641296e-08 + 8.2000734691489711385e-748j)  +/-  (2e-79, 2.07e-200j)
| (-0.021246493800255972969 + 2.3952171627170532299e-742j)  +/-  (1.66e-73, 1.71e-194j)
| (0.4946767192480765545 - 1.129606800598381894e-741j)  +/-  (8.98e-73, 9.36e-194j)
| (2.2402668488413015487e-07 - 4.4101726983640953795e-747j)  +/-  (6.24e-80, 6.57e-201j)
| (0.020588370853858037139 + 2.5177767677111068322e-743j)  +/-  (1.34e-75, 1.32e-196j)
