Starting with polynomial:
P : t^3 - 3*t
Extension levels are: 3 6 10 16
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P2 : t^9 - 117/4*t^7 + 945/4*t^5 - 2205/4*t^3 + 945/4*t
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P3 : t^19 - 23713751/205892*t^17 + 2134183615/411784*t^15 - 48885080515/411784*t^13 + 623352876985/411784*t^11 - 4536269518165/411784*t^9 + 18427952550645/411784*t^7 - 38805894891225/411784*t^5 + 36681698574675/411784*t^3 - 11110847880825/411784*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 148158172019154347566494279532305444494687200256542484844439972024607051000023761563231/385760606209899831860610471660979420398054611050129842754406267835781132157028090276*t^33 + 2249942320220592204173182865179529289145984970438942004160704874997340053778177337020913259/34718454558890984867454942449488147835824914994511685847896564105220301894132528124840*t^31 - 220849158772970079249588044514404572697676391214019057797593782286207915104784526104267559039/34718454558890984867454942449488147835824914994511685847896564105220301894132528124840*t^29 + 14076452535407047075509904706929932084194209883569653124917820365324652269134990345424626592113/34718454558890984867454942449488147835824914994511685847896564105220301894132528124840*t^27 - 3079461704370215575368823985946098203044130613330964437033194113796741253296061531689893628203229/173592272794454924337274712247440739179124574972558429239482820526101509470662640624200*t^25 + 13621590005974628394299390435466707875960413189403142442133883552507558252569258603353414031836829/24798896113493560619610673178205819882732082138936918462783260075157358495808948660600*t^23 - 7555344735732247770778736796311822778855080357658901316591419468071013675725945354433109059803407/617766095353932115079269438602991954374108807731524659215241354185414624450756728200*t^21 + 3219710580700670279502708780755276042659877667713327453155485017016560499238619994520958078064961/16343018395606669711091784090026242179209227717765202624741834766809910699755469000*t^19 - 94703184350745630527408004926675491861812450062856179314573920985767025554447829325616105822169860877/41331493522489267699351121963676366471220136898228197437972100125262264159681581101000*t^17 + 157484513545995039812258087014296855688128394169414274752888698243122811598842273074780125572399172993/8266298704497853539870224392735273294244027379645639487594420025052452831936316220200*t^15 - 23549631437656828001609343706484598645025341463453683544660303514393391646415889277922730696464830187/211956377038406501022313445967571110108821214862708704810113333975703918767597851800*t^13 + 93354849639900358921608632783963512574570620469839157037326776142611274152386412728501470282091552853/211956377038406501022313445967571110108821214862708704810113333975703918767597851800*t^11 - 4883263925242950190669085624551426689401578018559150322810148516683487563072259572222768280960294573/4325640347722581653516600938113696124669820711483851118573741509708243240155058200*t^9 + 13537565622105100537332391567346142747089590000147244485599043633820513434062805161738407228679234793/7850236186607648186011609109910041115141526476396618696670864221322367361762883400*t^7 - 916695994687218333091656821821092731491782773637716223198067748233865557741850872806864840043001917/672877387423512701658137923706574952726416555119710174000359790399060059579675720*t^5 + 281593491909388686402915463907712078147402844378914597860805998856747021879331968381790179022242211/672877387423512701658137923706574952726416555119710174000359790399060059579675720*t^3 - 4733364936815051007936085288803863817032716310637460684423752827270817573558587806396618867308523/224292462474504233886045974568858317575472185039903391333453263466353353193225240*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:   35 out of 35
Indefinite weights: 0 out of 35
Negative weights:   0 out of 35
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-2.5960831150492021594 - 1.1050426515170833845e-880j)  +/-  (2.37e-248, 2.37e-248j)
| (7.1221067008046166582 - 1.0078721674574952557e-886j)  +/-  (8.1e-248, 8.1e-248j)
| (-5.187016039913656066 + 6.3538749882774392838e-895j)  +/-  (5.63e-247, 5.63e-247j)
| (-9.0169397898903025175 + 1.024878682336718366e-907j)  +/-  (1.99e-249, 1.99e-249j)
| (7.9807717985905608802 - 1.4023593429629088391e-908j)  +/-  (2.08e-248, 2.08e-248j)
| (4.7364330859522970841 + 4.5118425197133036698e-907j)  +/-  (4.86e-247, 4.86e-247j)
| (2.5960831150492021594 + 4.5107992376296398827e-909j)  +/-  (2.4e-248, 2.4e-248j)
| (5.6981777684881095893 + 3.3844543937855370188e-907j)  +/-  (4.38e-247, 4.38e-247j)
| (9.0169397898903025175 - 1.3963702665371202271e-910j)  +/-  (2.3e-249, 2.3e-249j)
| (4.1849560176727318607 - 1.3244477880706830725e-908j)  +/-  (2.53e-247, 2.53e-247j)
| (6.3633944943363699876 + 3.151518602847243427e-908j)  +/-  (2.12e-247, 2.12e-247j)
| (-2.8612795760570581173 + 3.9199419889863288836e-908j)  +/-  (6.76e-248, 6.76e-248j)
| (-4.7364330859522970841 - 7.9813963351308504826e-917j)  +/-  (4.61e-247, 4.61e-247j)
| (-3.2053337944991945187 - 7.1781376106672341268e-927j)  +/-  (1.07e-247, 1.07e-247j)
| (0.74109534999454084186 - 1.6488169806214670495e-940j)  +/-  (5.29e-253, 5.29e-253j)
| (-6.3633944943363699876 - 1.5734574478847017967e-933j)  +/-  (2.15e-247, 2.15e-247j)
| (5.187016039913656066 - 5.7085884871292100698e-945j)  +/-  (5.49e-247, 5.49e-247j)
| (-7.9807717985905608802 + 1.9063274463662008856e-947j)  +/-  (1.91e-248, 1.91e-248j)
| (2.8612795760570581173 - 4.8332969220261599415e-957j)  +/-  (6.83e-248, 6.83e-248j)
| (-7.1221067008046166582 + 2.6237837031918426267e-966j)  +/-  (7.67e-248, 7.67e-248j)
| (1.2304236340273060078 + 7.5155445173661806883e-983j)  +/-  (8.05e-252, 8.05e-252j)
| (2.233626061676941652 - 1.4695077981660744504e-980j)  +/-  (2.52e-249, 2.52e-249j)
| (-5.6981777684881095893 - 2.777484299053905248e-978j)  +/-  (4.62e-247, 4.62e-247j)
| (-2.233626061676941652 + 2.0097012656704749893e-988j)  +/-  (2.8e-249, 2.8e-249j)
| (-1.7320508075688772935 - 1.4303117504608810517e-991j)  +/-  (1.31e-250, 1.31e-250j)
| (3.2053337944991945187 + 9.5235418465119135952e-989j)  +/-  (1.05e-247, 1.05e-247j)
| (-1.0186092831219181674e-997 - 3.5677227739371699213e-997j)  +/-  (1.3e-995, 1.3e-995j)
| (3.6353185190372782452 - 4.9934474267624454849e-989j)  +/-  (1.63e-247, 1.63e-247j)
| (-4.1849560176727318607 - 9.1595014604086556701e-992j)  +/-  (2.64e-247, 2.64e-247j)
| (-0.74109534999454084186 - 1.1782461115042818907e-1006j)  +/-  (5.1e-253, 5.1e-253j)
| (-0.24899229757996061181 - 1.864347661025932158e-1008j)  +/-  (3.03e-254, 3.03e-254j)
| (1.7320508075688772935 - 6.4556776768647385379e-1006j)  +/-  (1.28e-250, 1.28e-250j)
| (0.24899229757996061181 + 9.7736286126372698211e-1010j)  +/-  (3.03e-254, 3.03e-254j)
| (-3.6353185190372782452 - 1.3078644323556745816e-1007j)  +/-  (1.55e-247, 1.55e-247j)
| (-1.2304236340273060078 + 4.6153158242607664529e-1014j)  +/-  (8.29e-252, 8.29e-252j)
-------------------------------------------------
The weights are:
| (0.0031554462691875638051 + 7.2960453903813094283e-885j)  +/-  (3.33e-79, 2.59e-202j)
| (3.0972223576063161713e-12 + 9.614650826440623516e-893j)  +/-  (1.66e-94, 1.3e-217j)
| (2.4676421345798078671e-07 + 7.1374028743203234035e-888j)  +/-  (4.02e-90, 3.13e-213j)
| (1.0541326582333341189e-18 - 6.4475540051731132355e-897j)  +/-  (2.06e-98, 1.61e-221j)
| (5.4500412650636899171e-15 - 1.0273691196235303667e-894j)  +/-  (1.66e-96, 1.3e-219j)
| (2.7342206801187829817e-06 + 1.5527380069053769786e-887j)  +/-  (3.27e-90, 2.55e-213j)
| (0.0031554462691875638051 - 6.7157018745160263035e-884j)  +/-  (1.62e-83, 1.26e-206j)
| (2.1394194479561106307e-08 + 1.7511343719436448115e-889j)  +/-  (1.37e-92, 1.07e-215j)
| (1.0541326582333341189e-18 + 3.5648548396619924778e-897j)  +/-  (1.22e-99, 9.51e-223j)
| (3.5729348198975100228e-05 - 1.2258045356029958129e-886j)  +/-  (7.09e-90, 5.53e-213j)
| (4.6011760348656187011e-10 - 5.0850360972474168304e-891j)  +/-  (4.89e-94, 3.81e-217j)
| (0.0023113452403522101207 - 7.9805412190751042735e-883j)  +/-  (1.74e-88, 1.36e-211j)
| (2.7342206801187829817e-06 - 5.3194404506635037492e-887j)  +/-  (1.04e-94, 8.15e-218j)
| (0.00081895392750226490906 + 8.8938391099467907078e-884j)  +/-  (2.44e-90, 1.9e-213j)
| (0.14807083115521600615 - 3.4944260058370955247e-883j)  +/-  (2.94e-88, 2.29e-211j)
| (4.6011760348656187011e-10 + 1.2093261872025562905e-890j)  +/-  (3.46e-99, 2.7e-222j)
| (2.4676421345798078671e-07 - 2.3759890355549144433e-888j)  +/-  (1.22e-94, 9.51e-218j)
| (5.4500412650636899171e-15 + 2.0180140735021657292e-894j)  +/-  (8.26e-103, 6.45e-226j)
| (0.0023113452403522101207 + 3.8780860507897175091e-884j)  +/-  (7.11e-92, 5.54e-215j)
| (3.0972223576063161713e-12 - 2.0644040237515765071e-892j)  +/-  (3.5e-101, 2.73e-224j)
| (0.092364726716986305928 + 1.623739494697436321e-883j)  +/-  (1.22e-88, 9.49e-212j)
| (0.015673473751851151542 + 7.1737105217779572089e-884j)  +/-  (3e-91, 2.34e-214j)
| (2.1394194479561106307e-08 - 4.6821059659134287576e-889j)  +/-  (2.46e-98, 1.92e-221j)
| (0.015673473751851151542 + 9.5589047662887791763e-883j)  +/-  (2.51e-92, 1.96e-215j)
| (0.045273685465150515865 - 4.5320415784308976105e-883j)  +/-  (6.53e-92, 5.09e-215j)
| (0.00081895392750226490906 - 9.3400981058693533522e-885j)  +/-  (5.05e-94, 3.94e-217j)
| (0.0005148945080687842938 - 2.22303988917018525e-882j)  +/-  (1.81e-91, 1.41e-214j)
| (0.000275242141167851575 + 1.2830593254643448407e-885j)  +/-  (5.29e-95, 4.12e-218j)
| (3.5729348198975100228e-05 + 5.2315208533210619349e-886j)  +/-  (6.9e-97, 5.38e-220j)
| (0.14807083115521600615 - 6.2865762866963132937e-883j)  +/-  (1.67e-92, 1.29e-215j)
| (0.19176011588804442959 + 1.5591698907242102216e-882j)  +/-  (5.22e-92, 4.04e-215j)
| (0.045273685465150515865 - 9.0473893263405744139e-884j)  +/-  (1.93e-93, 1.51e-216j)
| (0.19176011588804442959 + 1.2862623724976601824e-882j)  +/-  (2.63e-92, 2.05e-215j)
| (0.000275242141167851575 - 7.6933993153595162785e-885j)  +/-  (5.66e-96, 4.43e-219j)
| (0.092364726716986305928 + 4.5496327691950569808e-883j)  +/-  (7.47e-94, 5.47e-217j)
