Starting with polynomial:
P : 676039/1024*t^12 - 969969/512*t^10 + 2078505/1024*t^8 - 255255/256*t^6 + 225225/1024*t^4 - 9009/512*t^2 + 231/1024
Extension levels are: 12 37
-------------------------------------------------
Trying to find an order 37 Kronrod extension for:
P1 : 676039/1024*t^12 - 969969/512*t^10 + 2078505/1024*t^8 - 255255/256*t^6 + 225225/1024*t^4 - 9009/512*t^2 + 231/1024
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 676039/1024*t^49 - 11861487707756676301329398743689009270130349558154828078780469967830479/1499758685835304192919911116029448956784757994635710812328171001600*t^47 + 160474790481950740988592037845792558596095966989484053313718141650247619051/3609919156805577192358226056282883638980912493088155925273907600851200*t^45 - 17885019782484572074916069688213193418648642828783109889621498590281312747161/114795429186417354716991588589795699719593017280203358423710261707068160*t^43 + 3697518744650198318034186486341893716212283114441643531994063764757229395340379/9687996582021583502099844347895449132158745643077081822955210600451125760*t^41 - 10440114452794927597922664625113585428312675187819073432454136129524533784280498975/15036739494955699753609168412368526598023589112619938697408782372960192292096*t^39 + 3368138633886957856256134605797562577684612221637304142367673173219405399773409997891/3462407120549009811686321673900647571913326440405906936903338046405307435680000*t^37 - 38794526358897459130312145261038190467154389747349203199714058896977360223489607425583/36107959971439673750443068884963896107096118592804458056277668198226777543520000*t^35 + 10416084112968752770458133940321673065352745631186788234883568781849713953600573889167/10967551477956007855749552474149461491353259551183386190355997613151235104128000*t^33 - 8369801300583067075255570072284880241630764666651283107358905255702895853839590303939/12338495412700508837718246533418144177772416995081309464150497314795139492144000*t^31 + 21694110902843953413473415278673303045110327615064884918298768590294548560703567044721/55111946176728939475141501182601043994050129244696515606538888006084956398243200*t^29 - 38284408858487904206223085257573520612842195798544341204618358342152398638559140471303/205877959855596612981850435452245279288118298902601926116380903471007021027920000*t^27 + 323290205159967184277148006120064577569533305133653166809357554128797842802112114647/4524790326496628856743965614335061083255347228628613760799580296066088374240000*t^25 - 98632345232087786853857480513469586308770411318644470404624275313224163019596946009/4434294519966696279609086302048359861590240284056041485583588690144766606755200*t^23 + 3530274067595792776781666803525265860060563198196561313855081119178978998676555163/633470645709528039944155186006908551655748612008005926511941241449252372393600*t^21 - 2677952361989870165006089621061723737893660267605169771674253664351148245098987763/2407188453696206551787789706826252496291844725630422520745376717507159015095680*t^19 + 48634687833575099150308078984462649830152254525891607230519283149137514748278134563/278727084112192337575428281843039762728529389283522607665254146237671043853184000*t^17 - 4597854597981739293158941659032340933374051265046467081788827562607307904015546567673/217894898004706359899591059330796334513027850072393798542312428821299338532226592000*t^15 + 15297077844324961053865084442715239464779371879038100710510504143180195248968195787297/7974953266972252772325032771507145843176819312649613026648634894859555790279493267200*t^13 - 214173596594777447306963548535532315270056124846954680979005333248678049874595278647/1691656753600174830493188769713636997037507126925675490501225583758087591877468268800*t^11 + 27383217407918852046757648923963556969008255235008445302377009330833354631112914841/4736638910080489525380928555198183591705019955391891373403431634522645257256911152640*t^9 - 27154935910958350767699518167713305898099296194909539318260082780150014221299759/159590259773601399103131016010720471418632747823176933066153356958310150177119648000*t^7 + 415325050137329968923164011430355184603828502621541965935514659648605023067915603/143790824056014860591921045425659144748188105788682416692604174619437445309584802848000*t^5 - 12676790411979285315181030437759794037674285018450665272891668215409692344367887/546405131412856470249299972617504750043114801996993183431895863553862292176422250822400*t^3 + 1590093335502797523550518658884767676554105687132358329075495578135962864228961/28413066833468536452963598576110247002241969703843645538458584904800839193173957042764800*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:
| (-0.99856304572754737291 - 5.0997206432732955761e-875j)  +/-  (2.14e-239, 2.14e-239j)
| (-0.9924515837450457095 + 1.1100397229846541402e-880j)  +/-  (6.53e-239, 6.53e-239j)
| (-0.90411725637047485668 - 1.4354005984648282894e-885j)  +/-  (8.15e-239, 8.15e-239j)
| (0.99856304572754737291 - 4.3072987114348925395e-895j)  +/-  (2.01e-239, 2.01e-239j)
| (0.92521231161653272788 - 2.6595841556111114895e-906j)  +/-  (1.22e-238, 1.22e-238j)
| (0.90411725637047485668 - 2.7924123104434287044e-915j)  +/-  (8.35e-239, 8.35e-239j)
| (-0.87963515307003802062 - 9.9459102774957005077e-915j)  +/-  (3.45e-239, 3.45e-239j)
| (-0.92521231161653272788 - 9.2854029750859473597e-924j)  +/-  (1.17e-238, 1.17e-238j)
| (0.98156063424671925069 + 3.0185873544672528172e-937j)  +/-  (9.91e-239, 9.91e-239j)
| (-0.98156063424671925069 + 1.0694987995957333882e-945j)  +/-  (1.12e-238, 1.12e-238j)
| (0.84803719064273879626 - 1.9466352978509981343e-953j)  +/-  (1.05e-239, 1.05e-239j)
| (0.9924515837450457095 + 9.7316355141150670521e-965j)  +/-  (6.71e-239, 6.71e-239j)
| (-0.81099539420829629268 + 1.3153165692617261491e-970j)  +/-  (2.42e-240, 2.42e-240j)
| (-0.84803719064273879626 + 2.7756887879891122909e-973j)  +/-  (1.03e-239, 1.03e-239j)
| (0.96612852479198944797 - 1.12457269577669112e-977j)  +/-  (1.17e-238, 1.17e-238j)
| (0.81099539420829629268 + 8.9967496812047938553e-985j)  +/-  (2.35e-240, 2.35e-240j)
| (0.72577177772649978484 + 5.10952817845592838e-986j)  +/-  (1.16e-241, 1.16e-241j)
| (-0.94676177129349449379 + 4.1264173342060351737e-981j)  +/-  (1.38e-238, 1.38e-238j)
| (-0.72577177772649978484 + 6.987747922903778628e-990j)  +/-  (1.14e-241, 1.14e-241j)
| (-0.96612852479198944797 + 1.9697784611212318177e-987j)  +/-  (1.27e-238, 1.27e-238j)
| (0.87963515307003802062 - 2.3883235287574871509e-987j)  +/-  (3.36e-239, 3.36e-239j)
| (0.76990267419430468704 + 3.5627655756312630453e-995j)  +/-  (5.46e-241, 5.46e-241j)
| (0.94676177129349449379 - 1.1733303857456957351e-997j)  +/-  (1.34e-238, 1.34e-238j)
| (-0.67983764035350074008 - 3.6108274346314814507e-999j)  +/-  (2.39e-242, 2.39e-242j)
| (-0.76990267419430468704 - 1.8504698769465016394e-1002j)  +/-  (5.7e-241, 5.7e-241j)
| (0.18624725689726962492 - 1.1873954901599255702e-1013j)  +/-  (8.54e-252, 8.54e-252j)
| (0.67983764035350074008 + 1.2190332932707919582e-1006j)  +/-  (2.27e-242, 2.27e-242j)
| (0.36783149899818019375 + 1.0221966319470586813e-1011j)  +/-  (4.13e-248, 4.13e-248j)
| (-0.18624725689726962492 + 7.4809121151175784614e-1015j)  +/-  (8.72e-252, 8.72e-252j)
| (-0.63362206781073487614 + 2.3418797956867593309e-1006j)  +/-  (4.85e-243, 4.85e-243j)
| (-0.42736005101730244945 + 1.6898353599395224901e-1011j)  +/-  (6.1e-247, 6.1e-247j)
| (0.5382545933574250513 - 2.4443051529894953237e-1009j)  +/-  (9.67e-245, 9.67e-245j)
| (0.5873179542866174473 - 1.7407908326997361734e-1008j)  +/-  (8.03e-244, 8.03e-244j)
| (3.6813452767785597091e-1023 + 1.6050921921161877779e-1023j)  +/-  (1.97e-1021, 1.97e-1021j)
| (-0.5382545933574250513 + 1.4161185996742420582e-1008j)  +/-  (9.1e-245, 9.1e-245j)
| (-0.5873179542866174473 - 2.6845528363444871034e-1010j)  +/-  (7.45e-244, 7.45e-244j)
| (0.12523340851146891547 + 2.1473335069832274234e-1019j)  +/-  (4.08e-253, 4.08e-253j)
| (0.63362206781073487614 + 1.0474118753137088805e-1014j)  +/-  (4.5e-243, 4.5e-243j)
| (-0.063068594834620926918 - 3.587583779924602287e-1022j)  +/-  (1.96e-254, 1.96e-254j)
| (-0.24672762075948266676 - 3.3447583072534862922e-1018j)  +/-  (1.58e-250, 1.58e-250j)
| (-0.48465262972833320316 - 8.5766038007254998863e-1015j)  +/-  (8.33e-246, 8.33e-246j)
| (-0.12523340851146891547 - 1.8171811735484050324e-1022j)  +/-  (4.22e-253, 4.22e-253j)
| (0.24672762075948266676 + 9.8165405533231711742e-1019j)  +/-  (1.53e-250, 1.53e-250j)
| (0.48465262972833320316 + 6.4143436695498682135e-1015j)  +/-  (8.04e-246, 8.04e-246j)
| (0.063068594834620926918 + 1.6504093385061659692e-1023j)  +/-  (1.95e-254, 1.95e-254j)
| (-0.36783149899818019375 - 2.3274348215266301646e-1017j)  +/-  (3.88e-248, 3.88e-248j)
| (-0.30731935151460113602 + 1.426383330318095651e-1018j)  +/-  (2.59e-249, 2.59e-249j)
| (0.30731935151460113602 - 1.2721385181516351382e-1018j)  +/-  (2.62e-249, 2.62e-249j)
| (0.42736005101730244945 - 3.6573544299461009654e-1016j)  +/-  (6.32e-247, 6.32e-247j)
-------------------------------------------------
The weights are:
| (0.0036851721075401698062 - 6.8294745514446667589e-875j)  +/-  (1.52e-60, 3.54e-176j)
| (0.0085253402863480219349 + 1.1803832077613343068e-874j)  +/-  (1.19e-60, 2.77e-176j)
| (0.021477192453860969608 - 2.2438424194290205514e-874j)  +/-  (2.02e-61, 4.68e-177j)
| (0.0036851721075401698062 - 9.4102085396129576849e-878j)  +/-  (1.21e-62, 2.81e-178j)
| (0.021544314232302611323 + 7.4859051646377569287e-876j)  +/-  (1.54e-62, 3.58e-178j)
| (0.021477192453860969608 - 1.1138048253512125436e-875j)  +/-  (1.14e-62, 2.65e-178j)
| (0.028170604922418707289 + 1.8630409779723930571e-874j)  +/-  (3.18e-62, 7.4e-178j)
| (0.021544314232302611323 + 1.9633343434810137266e-874j)  +/-  (3.16e-62, 7.35e-178j)
| (0.013219537429207685992 - 8.5076470170322231235e-877j)  +/-  (2.48e-63, 5.76e-179j)
| (0.013219537429207685992 - 9.9081272506621164332e-875j)  +/-  (1.94e-62, 4.51e-178j)
| (0.034626618503068275286 - 1.1101640634977155426e-875j)  +/-  (3.18e-64, 7.4e-180j)
| (0.0085253402863480219349 + 3.6232138746251462236e-877j)  +/-  (2.14e-63, 4.96e-179j)
| (0.039241299403816260156 + 1.108914268974701358e-874j)  +/-  (1.44e-64, 3.35e-180j)
| (0.034626618503068275286 - 1.3619117631276354798e-874j)  +/-  (6.79e-64, 1.58e-179j)
| (0.017554846034831281479 + 1.7817745066197298064e-876j)  +/-  (1.07e-63, 2.49e-179j)
| (0.039241299403816260156 + 1.1494319957392750444e-875j)  +/-  (1.75e-65, 4.06e-181j)
| (0.045275460087205220929 + 1.7044718219177567815e-875j)  +/-  (1.21e-66, 2.81e-182j)
| (0.020915318166722408449 - 1.3970481525224937425e-874j)  +/-  (3.46e-64, 8.03e-180j)
| (0.045275460087205220929 + 1.0774099238265691818e-874j)  +/-  (1.04e-67, 2.41e-183j)
| (0.017554846034831281479 + 1.0792940066966362836e-874j)  +/-  (2.71e-64, 6.29e-180j)
| (0.028170604922418707289 + 1.179681264675260673e-875j)  +/-  (2.91e-66, 6.76e-182j)
| (0.042784875663364073584 - 1.3349152445102801227e-875j)  +/-  (6.26e-68, 1.46e-183j)
| (0.020915318166722408449 - 3.7201428632343872478e-876j)  +/-  (4.45e-66, 1.03e-181j)
| (0.046314683666786836562 - 1.2173118299269773186e-874j)  +/-  (5.81e-70, 1.35e-185j)
| (0.042784875663364073584 - 1.0324272226954879335e-874j)  +/-  (2.4e-68, 5.57e-184j)
| (0.060599343683459502348 + 6.1522192051712051774e-875j)  +/-  (7.23e-74, 1.68e-189j)
| (0.046314683666786836562 - 2.3116541931092127134e-875j)  +/-  (6.76e-71, 1.57e-186j)
| (0.060207226917607732833 - 4.1947497961167211549e-875j)  +/-  (9.84e-74, 2.29e-189j)
| (0.060599343683459502348 + 8.9733731898742612485e-875j)  +/-  (5.59e-75, 1.3e-190j)
| (0.046026156581035049589 + 1.3801936902322706184e-874j)  +/-  (2.68e-72, 6.23e-188j)
| (0.058640686700400337792 + 9.6719025076324382025e-875j)  +/-  (1.52e-74, 3.53e-190j)
| (0.051318361678025718469 + 3.8360010490558232006e-875j)  +/-  (3.39e-74, 7.88e-190j)
| (0.047129963432932569806 - 3.6758833401572586818e-875j)  +/-  (9.74e-74, 2.26e-189j)
| (0.063241875083501187916 - 7.3832959424643848927e-875j)  +/-  (9.26e-77, 2.15e-192j)
| (0.051318361678025718469 + 1.2807138601447615175e-874j)  +/-  (2.86e-75, 6.64e-191j)
| (0.047129963432932569806 - 1.4175278330441195884e-874j)  +/-  (1.04e-74, 2.42e-190j)
| (0.061548781837556214334 - 6.6384460653005381104e-875j)  +/-  (4.42e-77, 1.03e-192j)
| (0.046026156581035049589 + 3.0859810084005625591e-875j)  +/-  (6.91e-75, 1.61e-190j)
| (0.062733133805942974165 + 7.930446642172382757e-875j)  +/-  (2.11e-77, 4.91e-193j)
| (0.060486957843609075872 - 9.0703588800766981545e-875j)  +/-  (6.96e-78, 1.62e-193j)
| (0.055694033083653089322 - 1.0954497437144375776e-874j)  +/-  (8.06e-77, 1.87e-192j)
| (0.061548781837556214334 - 8.5423210748677657727e-875j)  +/-  (8.86e-78, 2.06e-193j)
| (0.060486957843609075872 - 5.4761649448937338971e-875j)  +/-  (4.47e-79, 1.04e-194j)
| (0.055694033083653089322 - 3.7955574295877652136e-875j)  +/-  (4.09e-79, 9.5e-195j)
| (0.062733133805942974165 + 6.9881949027800350855e-875j)  +/-  (1.38e-78, 3.2e-194j)
| (0.060207226917607732833 - 9.087357858367243265e-875j)  +/-  (3.94e-79, 9.16e-195j)
| (0.060659153936554619114 + 8.9921708914364418578e-875j)  +/-  (3.45e-79, 8.02e-195j)
| (0.060659153936554619114 + 4.7598324356935623892e-875j)  +/-  (3.1e-80, 7.27e-196j)
| (0.058640686700400337792 + 3.874416258724603478e-875j)  +/-  (2.46e-80, 5.63e-196j)
