Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 11 30
-------------------------------------------------
Trying to find an order 11 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 35/8*t^15 - 638415/40664*t^13 + 11181153/503608*t^11 - 55088825/3525256*t^9 + 19993545/3525256*t^7 - 160318323/162665384*t^5 + 10517265/162665384*t^3 - 64053/91941304*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^45 - 2318628329995223185105424119053523735140406707655895428122450887876862763564531561547793761181568765414134517227659136212625/45044511504360117760749531328627860078623959050837258902349047551930734233248254728604483232169516592757205390727865420628*t^43 + 143167116842019729631321577884861973134103166288810901700521955843271241884166769950632794023908743142301394308065104941151037165/506390398332016443866346231196434403003890547649512464580207992578805314250176879658971600496049705535776503002562663058699976*t^41 - 32042845317715890416662832399912641255615662399865487377985984940787353485133387209234380495499291524242606567195718134786001350014463/33284154699166359826558171670637039549240468888544067650044055988217860396364188490444800100304479057881901933478189358187996697522*t^39 + 2680881375480103173761714567594143816402026726555718840931127161868987721203354403822877318042652397940967105465047552231233513998911343/1177747012432040424632058382191772168665431976056174701463097365736939675563655900431123695856927720509667299184612854212806036989240*t^37 - 475180664173265534108750627524283678558956507965984619738082077866000654107693968522440533095408989537932548521656426523428580539488253001189/119791828551396398098473164610357065059816482951008880557505583431991624138703463503780755139586932157883637101774771856690876598475471348*t^35 + 10625036176182701588898021213993149456782772183510591339593448648456911445228453533176953831172504350539536985029558857329951306415127920277/2013308042880611732747448144711883446383470301697628244663959385411623935104259890819844624194738355594682976500416333725897085688663384*t^33 - 8147535219658511473761656918162210753673363608991451828462593073388150200910114693050501272568074610906833778155141815261624044945214421258/1487102531673179120779365106889459363805972381935748135263151818769949497520191964810112506507477194473345380369625701047537620110944545*t^31 + 326449573482136696446596814327649083900307022304535559841490529936133762008332525073901340671286653443968212565150957132963410883916427688911/72570603545651141094033017216205616953731452238464509000841808755973535478985367882733490317564887090299254562037734211119835861414093796*t^29 - 1369614029844221982853348948850663888568425437024448695090703207244412984911375110732452538530558659176408649710631577315808081731124703634013/465398435781893187450863914756101239159799530659718046853224643108960716658710511421877818340905254166049567300024599832181556067764297170*t^27 + 2929887367823633114395192022559496538525175371987079835271989234624570500102165266523773642332307038054671046851278440573939495004026181927229/1904553598738209044029689251155737378715487310084384622507042385645900778941799939049530764287396886279525921566254516236312214061927739188*t^25 - 305565274123526594951291231578169783246122334010084486260305678309067478303554482984473513904569319848992074127734295059041127406832313677585/476138399684552261007422312788934344678871827521096155626760596411475194735449984762382691071849221569881480391563629059078053515481934797*t^23 + 404837984418085339998916996103285054735831418609784353725697922036018009790651398196351254941846651183800221085522648794014735428430360003453/1904553598738209044029689251155737378715487310084384622507042385645900778941799939049530764287396886279525921566254516236312214061927739188*t^21 - 74676805624506350571779609803863281504391390999414471484168418745190789310586162420263776387152239097611851687049237092561008256402764166333665/1348287908363884988241303583443179511460656766446166856690521220295465901435155656851421386060885038565455814903082036458435025254840415935162*t^19 + 20656535682156790381017310593709841994409504587793854823623423165295265598942525050116933423801320903259005147431298245267048412519331294704981/1845025558813737352330204903659087752525109259347386224944923775141163865121791951480892423030684789615886904604217523574700560875044779700748*t^17 - 2194899062172886257122342911574981698750341493659443647767911249270410637792538189807207633398572176123407919072968829445385107039701928161570/1275238253885965522934112212823193005421766693960693420182520844582863259716532672347087410035914486940392419358797406000160681781280950675517*t^15 + 13977827082336139378070545329576956341322789569251757100276541568686038062342728268576554303019418267075926588250814811830887443621488247510485/71413342217614069284310283918098808303618934861798831530221167296640342544125829651436894962011211268661975484092654736008998179751733237828952*t^13 - 16023190811354630683917551274489427228029681393511614456531825578527229653373723923620577862374256091693960833862582222704172636296895355347/1011929950452021224676461513009497283654519319904032025731878888818790278965345764291615920514328904616667668802932354558831958012676381912556*t^11 + 3010057424694938291388149848899753728703275227225010137735256277056588660118685104514981839110260298754976258312015104635875295929916874795/3495758010652436957973230681305536070806521286941201543437399797737639145516649003916491361776772579584851946773766315748692218589245682970648*t^9 - 25222663016714627886084709520563926539118198916648745139279157161030603779591243727466729770188573207123952543483505174717945517612744901/873939502663109239493307670326384017701630321735300385859349949434409786379162250979122840444193144896212986693441578937173054647311420742662*t^7 + 176135802034926047437033781244307824398743911414410507441272871816763811424093893052576068174508119497566410883292235920184800540983415/341690632620163010929714277120089991883344185941621203493881183237513600689597271059506674459383785974459212842548587253631570238046570515928*t^5 - 11914708944638421040801363824430529477121118635736441137294637454189449989697114761989876247115208134311952781842692389139096781639725/3246061009891548603832285632640854922891769766445401433191871240756379206551174075065313407364145966757362522004211578909499917261442419901316*t^3 + 20377815229069518321355931699862728112369426862461092523192757804793087060184064912952752344452055286133226700736629518298127626821/4798524971144028370882509196077785538187833567788854292544505312422473609684344284879158950016563603032622858614921464474912921169088794636728*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: 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:
| (0.26652429579318568293 + 7.4850267218635145933e-927j)  +/-  (5.63e-251, 5.63e-251j)
| (0.99847746609942163118 - 9.8483718009392183501e-911j)  +/-  (2.2e-237, 2.2e-237j)
| (-0.92770035119641786425 - 2.2817416761345047247e-919j)  +/-  (1.26e-239, 1.26e-239j)
| (0.99980047526083274195 - 3.3439664422049575137e-914j)  +/-  (1.26e-237, 1.26e-237j)
| (0.95275482203958774276 - 3.582988675415761448e-924j)  +/-  (4.97e-239, 4.97e-239j)
| (0.97216638465276785034 + 5.9067723049743605807e-923j)  +/-  (1.61e-238, 1.61e-238j)
| (-0.99847746609942163118 + 5.1403088399535971613e-927j)  +/-  (2.15e-237, 2.15e-237j)
| (-0.89710604644228456132 - 2.6153933089320185398e-956j)  +/-  (3.44e-240, 3.44e-240j)
| (-0.99440647375811783848 - 5.3914383756479419429e-966j)  +/-  (1.1e-237, 1.1e-237j)
| (-0.99980047526083274195 + 8.054225734006313588e-998j)  +/-  (1.14e-237, 1.14e-237j)
| (0.86113631159405257522 + 4.1761869395835833351e-1019j)  +/-  (7.67e-241, 7.67e-241j)
| (-0.19144170808558539966 - 6.2673342839714951271e-1031j)  +/-  (2.53e-252, 2.53e-252j)
| (-0.95275482203958774276 + 2.7959857511504330426e-1015j)  +/-  (4.67e-239, 4.67e-239j)
| (-0.86113631159405257522 + 2.4291387748063742156e-1019j)  +/-  (7.81e-241, 7.81e-241j)
| (0.99440647375811783848 + 1.7766064920183867766e-1014j)  +/-  (1.17e-237, 1.17e-237j)
| (0.72322064929065662618 + 1.2008747600402291871e-1022j)  +/-  (3.73e-243, 3.73e-243j)
| (0.92770035119641786425 - 3.3624515926989163355e-1018j)  +/-  (1.35e-239, 1.35e-239j)
| (-0.9859491905566242687 + 5.1455683589379376559e-1017j)  +/-  (4.73e-238, 4.73e-238j)
| (-0.72322064929065662618 + 9.7797363838855494667e-1035j)  +/-  (3.86e-243, 3.86e-243j)
| (-0.97216638465276785034 - 2.9035266870508738357e-1031j)  +/-  (1.6e-238, 1.6e-238j)
| (0.89710604644228456132 + 4.4934799770703482847e-1030j)  +/-  (3.46e-240, 3.46e-240j)
| (0.77393504704850814801 + 4.1054937678520052345e-1034j)  +/-  (2.6e-242, 2.6e-242j)
| (0.11513928820520961921 + 2.6426567231197324923e-1046j)  +/-  (9.99e-254, 9.99e-254j)
| (-0.81999839724789285472 - 6.1349684318630016961e-1037j)  +/-  (1.55e-241, 1.55e-241j)
| (-0.77393504704850814801 + 4.5312060054353178005e-1038j)  +/-  (2.45e-242, 2.45e-242j)
| (0.19144170808558539966 - 3.3919043007847456988e-1047j)  +/-  (2.59e-252, 2.59e-252j)
| (0.81999839724789285472 + 3.9354070990529506874e-1032j)  +/-  (1.52e-241, 1.52e-241j)
| (0.9859491905566242687 - 3.2228300047456513061e-1040j)  +/-  (4.36e-238, 4.36e-238j)
| (-0.41138270978771086891 + 1.6541150436798369255e-1053j)  +/-  (1.96e-248, 1.96e-248j)
| (-0.66815854448971766693 - 1.5904038727755390193e-1051j)  +/-  (4.59e-244, 4.59e-244j)
| (-0.3399810435848562648 - 1.0293986904913701877e-1056j)  +/-  (9.7e-250, 9.7e-250j)
| (0.54633537010580514983 - 1.3490652955807612227e-1049j)  +/-  (3.61e-246, 3.61e-246j)
| (0.60907868895332483421 - 5.0636400992260343587e-1048j)  +/-  (4.35e-245, 4.35e-245j)
| (0.037653510379929317429 - 1.5053706013870685043e-1060j)  +/-  (5.77e-255, 5.77e-255j)
| (-0.60907868895332483421 + 8.1557546043711857874e-1052j)  +/-  (4.56e-245, 4.56e-245j)
| (-0.48030483331819931702 - 2.8900473157336884051e-1054j)  +/-  (2.68e-247, 2.68e-247j)
| (5.3683183537894083658e-1083 - 9.6082000184165263134e-1082j)  +/-  (4.33e-1080, 4.33e-1080j)
| (0.66815854448971766693 + 1.3797206751481721437e-1051j)  +/-  (4.31e-244, 4.31e-244j)
| (0.41138270978771086891 - 5.2103025423313963664e-1056j)  +/-  (1.71e-248, 1.71e-248j)
| (-0.26652429579318568293 - 7.210668621303411336e-1060j)  +/-  (5.97e-251, 5.97e-251j)
| (-0.54633537010580514983 + 2.3067786244752102113e-1055j)  +/-  (3.58e-246, 3.58e-246j)
| (-0.037653510379929317429 - 1.4359510737126950254e-1063j)  +/-  (5.77e-255, 5.77e-255j)
| (0.3399810435848562648 + 1.10876906319337698e-1057j)  +/-  (1.01e-249, 1.01e-249j)
| (0.48030483331819931702 + 7.8110893345571353343e-1055j)  +/-  (2.71e-247, 2.71e-247j)
| (-0.11513928820520961921 + 6.7212559742412046394e-1062j)  +/-  (1.08e-253, 1.08e-253j)
-------------------------------------------------
The weights are:
| (0.07434093348613523091 - 7.4433581890566803522e-915j)  +/-  (4.1e-65, 4.16e-178j)
| (0.0023888366711430664048 - 6.8958748050666576663e-911j)  +/-  (2.04e-65, 2.07e-178j)
| (0.027847614620025593735 - 8.0223125065810253157e-915j)  +/-  (1.38e-67, 1.41e-180j)
| (0.00055841095876644447263 + 1.0144167752459802598e-910j)  +/-  (1.88e-65, 1.91e-178j)
| (0.022243384969180958595 + 5.2606700128658513142e-913j)  +/-  (5.4e-67, 5.49e-180j)
| (0.016579619205041573101 - 1.5678890807667984347e-912j)  +/-  (1.08e-66, 1.1e-179j)
| (0.0023888366711430664048 + 1.1779237770818282115e-913j)  +/-  (1.62e-69, 1.65e-182j)
| (0.033313334722996151044 + 5.6829008527379637991e-915j)  +/-  (5.51e-70, 5.6e-183j)
| (0.0060379210883931202653 - 7.6656174992934911756e-914j)  +/-  (4.96e-70, 5.04e-183j)
| (0.00055841095876644447263 - 6.7137669197106823119e-914j)  +/-  (1.06e-69, 1.08e-182j)
| (0.038591484767842426788 - 5.8495506146135772213e-914j)  +/-  (4.18e-73, 4.25e-186j)
| (0.075754794509296327952 + 6.0970740682405229175e-915j)  +/-  (4.14e-74, 4.21e-187j)
| (0.022243384969180958595 + 1.232672911469692639e-914j)  +/-  (2.45e-71, 2.49e-184j)
| (0.038591484767842426788 - 4.3202102539754566286e-915j)  +/-  (2.1e-72, 2.13e-185j)
| (0.0060379210883931202653 - 3.7527444227918224706e-911j)  +/-  (2.84e-71, 2.89e-184j)
| (0.052941101726882445542 + 1.6545851899172088329e-914j)  +/-  (3.31e-75, 3.36e-188j)
| (0.027847614620025593735 - 2.1832844947923546353e-913j)  +/-  (5.38e-73, 5.47e-186j)
| (0.01102979779760801782 + 3.9363819043603430404e-914j)  +/-  (1.06e-71, 1.08e-184j)
| (0.052941101726882445542 + 2.645278748384711431e-915j)  +/-  (2.25e-76, 2.28e-189j)
| (0.016579619205041573101 - 2.0933175850703107246e-914j)  +/-  (2.98e-72, 3.03e-185j)
| (0.033313334722996151044 + 1.0626424357549079111e-913j)  +/-  (1.61e-74, 1.64e-187j)
| (0.048437098715977653446 - 2.3414950167504742535e-914j)  +/-  (3.59e-76, 3.64e-189j)
| (0.076805483646532708517 - 1.3278146631004223539e-914j)  +/-  (1.13e-78, 1.15e-191j)
| (0.043643827012926478727 + 3.4873232276863726832e-915j)  +/-  (7.57e-76, 7.69e-189j)
| (0.048437098715977653446 - 2.9663920829980398022e-915j)  +/-  (1.32e-76, 1.34e-189j)
| (0.075754794509296327952 + 8.9897171584021601056e-915j)  +/-  (2.89e-79, 2.94e-192j)
| (0.043643827012926478727 + 3.5531198413835698215e-914j)  +/-  (5.11e-77, 5.19e-190j)
| (0.01102979779760801782 + 6.2352346340994134247e-912j)  +/-  (9.59e-75, 9.74e-188j)
| (0.07023176515449808 - 2.8730795417103432863e-915j)  +/-  (8.75e-81, 8.9e-194j)
| (0.057128077369657144128 - 2.465038796299837774e-915j)  +/-  (2.75e-79, 2.79e-192j)
| (0.072500716870771042869 + 3.3900844579903207611e-915j)  +/-  (5.56e-81, 5.65e-194j)
| (0.064451341183005049623 - 8.3077795387670464606e-915j)  +/-  (1.23e-81, 1.25e-194j)
| (0.060972546471611828448 + 9.8943277883944037071e-915j)  +/-  (2.83e-81, 2.88e-194j)
| (0.078961736026550120148 + 3.7564575151391647682e-914j)  +/-  (4.1e-82, 4.16e-195j)
| (0.060972546471611828448 + 2.396709655445162084e-915j)  +/-  (1.27e-81, 1.29e-194j)
| (0.067543745422594657224 + 2.5791647774709432878e-915j)  +/-  (2.43e-82, 2.47e-195j)
| (-0.004607144794872239522 - 5.7284739139912432642e-914j)  +/-  (1.25e-82, 1.27e-195j)
| (0.057128077369657144128 - 1.2437415739404386688e-914j)  +/-  (1.97e-82, 2e-195j)
| (0.07023176515449808 - 6.8994609569232120049e-915j)  +/-  (5.68e-84, 5.77e-197j)
| (0.07434093348613523091 - 4.3068651171661066514e-915j)  +/-  (1.43e-83, 1.45e-196j)
| (0.064451341183005049623 - 2.431557707600424824e-915j)  +/-  (3.94e-83, 4.01e-196j)
| (0.078961736026550120148 + 3.4834346733529602485e-914j)  +/-  (1.47e-83, 1.5e-196j)
| (0.072500716870771042869 + 6.8906748752464993003e-915j)  +/-  (9.22e-85, 9.42e-198j)
| (0.067543745422594657224 + 7.3605189655294951826e-915j)  +/-  (7.49e-85, 7.66e-198j)
| (0.076805483646532708517 - 1.0532434812836254413e-914j)  +/-  (2.02e-84, 2.03e-197j)
