Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 14 25
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P2 : 4*t^16 - 935281/4314*t^14 + 38001691/8628*t^12 - 245286041/5752*t^10 + 2383796415/11504*t^8 - 11245499265/23008*t^6 + 22854346515/46016*t^4 - 15081381315/92032*t^2 + 1321665345/184064
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^41 - 36536974694389094843212509710635785995330102214740239325090121926765779672113742201/32150743854912056419033642393750760042974640151649777114354423296475175400730794*t^39 + 9259868215363355243689200919527550291020978495319500146757339170835263350661422092211/64301487709824112838067284787501520085949280303299554228708846592950350801461588*t^37 - 462447457979799083176873521359164470440448877604339894829759851482460578030562407789761/42867658473216075225378189858334346723966186868866369485805897728633567200974392*t^35 + 45776370905664007030888923307200637701903101647584989044325966540055022169509708078786815/85735316946432150450756379716668693447932373737732738971611795457267134401948784*t^33 - 1585060310564307642449504145356768830143045303709391703025508134739337644151986286839537745/85735316946432150450756379716668693447932373737732738971611795457267134401948784*t^31 + 79344071084585707551349204790445447298870654935203233221698944389279793299512748223447250595/171470633892864300901512759433337386895864747475465477943223590914534268803897568*t^29 - 2925793443979718949426878216714613608478811977771785032966552336865135452340379067292746590495/342941267785728601803025518866674773791729494950930955886447181829068537607795136*t^27 + 80281085711114562781916785777749715513638845987368173667567923015839624344272543221373847982685/685882535571457203606051037733349547583458989901861911772894363658137075215590272*t^25 - 411258558565986546787726921990764449704867563072561107404289580827497606081088872343995105282125/342941267785728601803025518866674773791729494950930955886447181829068537607795136*t^23 + 6281500670342710996702938352542903865120309229832848447210152043592644973290568129154887429000375/685882535571457203606051037733349547583458989901861911772894363658137075215590272*t^21 - 64095839865757365706766139166854327996365117697530269326592590843346573431863103540385508025375/1238055118360031053440525338868861999248120920400472764933022317072449594251968*t^19 + 293502141673042590436376580419950077954086477364112898812658344314814430524029047194532893952380875/1371765071142914407212102075466699095166917979803723823545788727316274150431180544*t^17 - 13923079053948846574541063772965381323253813158842071921198789895356176603125019422978502097706015375/21948241138286630515393633207467185522670687676859581176732619637060386406898888704*t^15 + 57622461937705910509286910269435145645319700012068398739825145576742213945310441671822355955342038125/43896482276573261030787266414934371045341375353719162353465239274120772813797777408*t^13 - 159851360409156031359691484202767240696102148670238048347000480298567777184255792734375894116842440625/87792964553146522061574532829868742090682750707438324706930478548241545627595554816*t^11 + 279115522286207473254642472688860495358158390460184385152389053203937935276283302125512878363975493125/175585929106293044123149065659737484181365501414876649413860957096483091255191109632*t^9 - 549813201564225037357668732207353973154889250840852886075156979588195840435793169846466307860055733125/702343716425172176492596262638949936725462005659506597655443828385932365020764438528*t^7 + 242433021364848837771831353767583860301010189797732276229929339664139216885174211745279768171974724375/1404687432850344352985192525277899873450924011319013195310887656771864730041528877056*t^5 - 23068971148632182727388035650359331397703705095394716608431201336821784563630846612371768430774909375/2809374865700688705970385050555799746901848022638026390621775313543729460083057754112*t^3 + 347056281150675885231842479960558287667080986292315542772540052936826878495315072540110649501040625/5618749731401377411940770101111599493803696045276052781243550627087458920166115508224*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:
| (-5.4668733830932886602 + 5.1841126999919392719e-608j)  +/-  (9.69e-247, 9.69e-247j)
| (7.2869246827826277308 + 4.0058602016269476797e-620j)  +/-  (1.06e-248, 1.06e-248j)
| (-7.2869246827826277308 + 2.4585320578220504614e-618j)  +/-  (1.09e-248, 1.09e-248j)
| (-5.9924631839661411334 + 5.762247749492915614e-617j)  +/-  (4.18e-247, 4.18e-247j)
| (-6.5799986155008037743 - 1.675099974413277942e-623j)  +/-  (1.14e-247, 1.14e-247j)
| (5.9924631839661411334 - 2.5266080990980913366e-625j)  +/-  (4.72e-247, 4.72e-247j)
| (3.0091043993715327196 - 6.2016889162607857749e-624j)  +/-  (9.84e-247, 9.84e-247j)
| (-1.2306846131070304577 + 3.8627400359434440079e-628j)  +/-  (1.06e-249, 1.06e-249j)
| (4.5281459663671905541 + 1.312383251711991309e-638j)  +/-  (2.36e-246, 2.36e-246j)
| (-3.3414165773772030467 + 2.3093769449741287433e-679j)  +/-  (1.54e-246, 1.54e-246j)
| (0.7071067811865475244 - 1.6303312650764680332e-711j)  +/-  (2.07e-252, 2.07e-252j)
| (-4.5281459663671905541 - 2.5385840019099900766e-729j)  +/-  (2.47e-246, 2.47e-246j)
| (-1.7883518963075274379 + 2.4174285665242971467e-746j)  +/-  (9.18e-249, 9.18e-249j)
| (3.7042296813249592447 + 8.0631157198124265022e-756j)  +/-  (2.42e-246, 2.42e-246j)
| (2.0971653372354515085 - 7.2014058936646734402e-762j)  +/-  (4.55e-248, 4.55e-248j)
| (-3.7042296813249592447 - 6.7530019348314890076e-780j)  +/-  (2.28e-246, 2.28e-246j)
| (6.5799986155008037743 - 9.8005056877054954569e-801j)  +/-  (1.05e-247, 1.05e-247j)
| (4.9820149281042827006 - 4.2600651847579988429e-798j)  +/-  (1.67e-246, 1.67e-246j)
| (-1.1241963452296225958 + 3.2381489669768862867e-803j)  +/-  (3.48e-250, 3.48e-250j)
| (-4.1016479573062841729 + 1.8237712483216504477e-801j)  +/-  (2.33e-246, 2.33e-246j)
| (5.4668733830932886602 - 2.7540146312367463185e-813j)  +/-  (1.11e-246, 1.11e-246j)
| (1.1241963452296225958 + 1.6681254344361100833e-815j)  +/-  (3.54e-250, 3.54e-250j)
| (-2.3782295662273317563 + 1.13277678465106193e-810j)  +/-  (1.7e-247, 1.7e-247j)
| (-3.0091043993715327196 - 1.2452767449627970319e-820j)  +/-  (9.23e-247, 9.23e-247j)
| (-0.096147910590510889955 + 2.8151442645236666955e-837j)  +/-  (1.1e-254, 1.1e-254j)
| (-2.0971653372354515085 - 2.7730818043028458429e-829j)  +/-  (4.76e-248, 4.76e-248j)
| (1.2306846131070304577 + 4.4623275924589291066e-835j)  +/-  (1.26e-249, 1.26e-249j)
| (0.096147910590510889955 + 1.7564946474281522618e-846j)  +/-  (1.56e-254, 1.56e-254j)
| (-0.7071067811865475244 - 9.6003476601045881811e-838j)  +/-  (2.07e-252, 2.07e-252j)
| (-0.22680478892243133872 + 8.8000417316407669073e-840j)  +/-  (4.51e-254, 4.51e-254j)
| (2.6866294303993381143 - 1.8980471836263135601e-832j)  +/-  (4.93e-247, 4.93e-247j)
| (1.419949258843231818 - 1.472580607483743173e-836j)  +/-  (2.1e-249, 2.1e-249j)
| (3.3414165773772030467 + 4.9967435061045920749e-832j)  +/-  (1.77e-246, 1.77e-246j)
| (4.1016479573062841729 + 2.6306853448446763632e-832j)  +/-  (2.26e-246, 2.26e-246j)
| (-1.419949258843231818 - 7.8157933581540117523e-836j)  +/-  (2.1e-249, 2.1e-249j)
| (2.3782295662273317563 + 8.6456648327082434427e-834j)  +/-  (1.75e-247, 1.75e-247j)
| (-4.9820149281042827006 + 8.2178008773549159277e-831j)  +/-  (1.87e-246, 1.87e-246j)
| (0.22680478892243133872 + 8.4162206472842612958e-851j)  +/-  (4.51e-254, 4.51e-254j)
| (1.7883518963075274379 - 8.1108676733209491549e-847j)  +/-  (9.36e-249, 9.36e-249j)
| (-4.0956316915564932831e-853 - 2.6754526734147694426e-852j)  +/-  (1.11e-850, 1.11e-850j)
| (-2.6866294303993381143 + 1.5937249818374217796e-842j)  +/-  (4.63e-247, 4.63e-247j)
-------------------------------------------------
The weights are:
| (2.9738471652862228044e-14 + 1.1030238107032872513e-620j)  +/-  (2.27e-95, 1.76e-217j)
| (3.9973512683931943787e-24 - 1.0864591720638491933e-628j)  +/-  (2.08e-101, 1.62e-223j)
| (3.9973512683931943787e-24 + 7.6132364449683527093e-628j)  +/-  (7.53e-101, 5.84e-223j)
| (7.8998105726106707675e-17 + 6.5539030310334552581e-623j)  +/-  (1.65e-97, 1.28e-219j)
| (5.6037118534230192748e-20 - 3.5873744097748487567e-625j)  +/-  (4.1e-99, 3.18e-221j)
| (7.8998105726106707675e-17 - 3.0059895410478109486e-624j)  +/-  (1.75e-100, 1.36e-222j)
| (2.137867598649383275e-05 + 1.7082421556914407052e-615j)  +/-  (1.46e-90, 1.13e-212j)
| (-0.034892465180015623787 + 2.8616286736589238431e-611j)  +/-  (8.46e-78, 6.57e-200j)
| (3.0908042592430573608e-10 + 9.4864324809194659949e-620j)  +/-  (1.31e-96, 1.02e-218j)
| (2.7553712295180985679e-06 - 9.5877164463208460361e-616j)  +/-  (4.44e-92, 3.44e-214j)
| (0.13790527431104653446 + 1.1476760394666332439e-611j)  +/-  (2.22e-79, 1.72e-201j)
| (3.0908042592430573608e-10 + 1.0100597310633753867e-618j)  +/-  (7.53e-96, 5.84e-218j)
| (0.0077543868508825780875 + 1.1785958534244873986e-612j)  +/-  (1.11e-84, 8.62e-207j)
| (2.3619008353003960801e-07 + 2.2536151153865931198e-617j)  +/-  (1.09e-94, 8.49e-217j)
| (0.0019680208917356157187 - 1.809211530781825506e-613j)  +/-  (2.71e-88, 2.1e-210j)
| (2.3619008353003960801e-07 + 1.1725646238368174236e-616j)  +/-  (6.2e-94, 4.81e-216j)
| (5.6037118534230192748e-20 + 3.3147168614171023383e-626j)  +/-  (2.97e-103, 2.31e-225j)
| (4.3911040230351340374e-12 - 4.2804481435513419213e-621j)  +/-  (3.1e-99, 2.41e-221j)
| (0.08875978463075811655 - 2.6821115877855511046e-611j)  +/-  (2.77e-84, 2.15e-206j)
| (1.1500137251158809738e-08 - 1.1509865232121518247e-617j)  +/-  (2.66e-96, 2.06e-218j)
| (2.9738471652862228044e-14 + 1.4100160891898683152e-622j)  +/-  (1.35e-100, 1.05e-222j)
| (0.08875978463075811655 - 1.7671705634004614912e-611j)  +/-  (2.32e-86, 1.8e-208j)
| (0.00057552495047236780741 + 1.308517627808012515e-613j)  +/-  (5.28e-92, 4.09e-214j)
| (2.137867598649383275e-05 + 5.8911242898851291959e-615j)  +/-  (6.69e-94, 5.19e-216j)
| (-1.723705936969717124 + 1.1570909334598043444e-609j)  +/-  (8.75e-87, 6.79e-209j)
| (0.0019680208917356157187 - 4.0611666904040980598e-613j)  +/-  (5.13e-91, 3.98e-213j)
| (-0.034892465180015623787 + 1.8099730167386339245e-611j)  +/-  (4.9e-89, 3.8e-211j)
| (-1.723705936969717124 + 1.1170940074214843633e-609j)  +/-  (1.98e-87, 1.53e-209j)
| (0.13790527431104653446 + 1.4886715453373893771e-611j)  +/-  (2.65e-88, 2.05e-210j)
| (0.66322112383268938438 - 2.6886810681216945047e-610j)  +/-  (1.42e-87, 1.1e-209j)
| (0.00013235558257958567268 - 1.0284312892673142931e-614j)  +/-  (3.43e-95, 2.66e-217j)
| (0.032556954856817928255 - 4.7849917702559936603e-612j)  +/-  (6.4e-91, 4.97e-213j)
| (2.7553712295180985679e-06 - 2.3135338712933199701e-616j)  +/-  (4.57e-97, 3.54e-219j)
| (1.1500137251158809738e-08 - 1.6422141000468875223e-618j)  +/-  (3.31e-99, 2.56e-221j)
| (0.032556954856817928255 - 8.1428236985234585934e-612j)  +/-  (4.19e-92, 3.25e-214j)
| (0.00057552495047236780741 + 5.1516785776477584276e-614j)  +/-  (4.94e-95, 3.85e-217j)
| (4.3911040230351340374e-12 - 9.2245322560475456752e-620j)  +/-  (1.53e-102, 1.21e-224j)
| (0.66322112383268938438 - 2.4744765684229162869e-610j)  +/-  (8.13e-92, 8.7e-214j)
| (0.0077543868508825780875 + 5.9756796020314729396e-613j)  +/-  (3.14e-94, 2.53e-216j)
| (2.6514011883836249926 - 1.7748656197613443496e-609j)  +/-  (3.24e-91, 4.08e-213j)
| (0.00013235558257958567268 - 3.0160365612906097194e-614j)  +/-  (3.56e-96, 2.42e-218j)
