Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 5 44
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : t^7 - 53/3*t^5 + 215/3*t^3 - 55*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^51 - 502801104113177632431699760962800039726305523197440897060431638973/441205073237585111427986598071543479440417793326604661306488215*t^49 + 1578648344836693772765510286824389712465748760765073651756033524771339/2647230439425510668567919588429260876642506759959627967838929290*t^47 - 503867042966654807842557410376747824396673842085911962738813493936065801/2647230439425510668567919588429260876642506759959627967838929290*t^45 + 2442320492300985512437979835094949247982001421045204714070626175476797009/58827343098344681523731546409539130592055705776880621507531762*t^43 - 9429091354233355031527991495031583927646842827348282245342427198885465751/1434813246301089793261745034379003185172090384801966378232482*t^41 + 1122695456505320414296696019614199303262168053123764658509494574071168080233/1434813246301089793261745034379003185172090384801966378232482*t^39 - 102864654767907028028524881724921997713096609682385776580269122840769024019099/1434813246301089793261745034379003185172090384801966378232482*t^37 + 7358912885180672359380219917173250546849355472340251618576003897967460566361081/1434813246301089793261745034379003185172090384801966378232482*t^35 - 414777971664272962311676291438951672762847650279877540245713829824128710409224215/1434813246301089793261745034379003185172090384801966378232482*t^33 + 9254435879929143477638519776476018511091857215662559690204510782845868693610380955/717406623150544896630872517189501592586045192400983189116241*t^31 - 327436308925677321056070661482031501009178932193023187407841986871272754205504433065/717406623150544896630872517189501592586045192400983189116241*t^29 + 9172624170635292761088268343119128239022270991648846358983400634191291698626662741445/717406623150544896630872517189501592586045192400983189116241*t^27 - 202595193177776064810482061291945960611090434717381661527632653783114151947108185282155/717406623150544896630872517189501592586045192400983189116241*t^25 + 3503515113744404513682514953241690798866056186857441444231891709555390205693523507133625/717406623150544896630872517189501592586045192400983189116241*t^23 - 46967162539282914228537165325081273169099960985083571215453007008186421343621787408278875/717406623150544896630872517189501592586045192400983189116241*t^21 + 481634704474466940522161036216038796615078573836684115280559627769417733149372809060592250/717406623150544896630872517189501592586045192400983189116241*t^19 - 3713480797100681575184408829932408495297879590227556073709524867083501707511478311778039250/717406623150544896630872517189501592586045192400983189116241*t^17 + 42116610256241757962203702323850437178982826588543882906261416564058781201408511564071870875/1434813246301089793261745034379003185172090384801966378232482*t^15 - 170829067366143724909574776874798516776125015505559465161527695580501543283320396940118105625/1434813246301089793261745034379003185172090384801966378232482*t^13 + 478443700645597413324555951381348023304569186064074054638290237438917310499473830846786488125/1434813246301089793261745034379003185172090384801966378232482*t^11 - 884839217779094461151583205591670638725305015574576249854656083853450494439105826414928451875/1434813246301089793261745034379003185172090384801966378232482*t^9 + 1019735435000173567567120060098283728257090768966904321912110976940879198724858053717858543125/1434813246301089793261745034379003185172090384801966378232482*t^7 - 673858582897466298140717704369352787723460028257109961088543289073291498794044050963328269375/1434813246301089793261745034379003185172090384801966378232482*t^5 + 218723989830113167227044348670347886187337668236811373747945748063243474216680227475279090625/1434813246301089793261745034379003185172090384801966378232482*t^3 - 22941860727408634407145518307317406655924897303854607634057799027572598365988321418988909375/1434813246301089793261745034379003185172090384801966378232482*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:
| (12.712879724738890577 - 9.7106210475022393819e-901j)  +/-  (1.52e-246, 1.52e-246j)
| (-7.9189731295411585048 + 6.1380107795808244612e-896j)  +/-  (2.89e-243, 2.89e-243j)
| (9.0511467848318936105 - 2.4008446976645252079e-911j)  +/-  (2.09e-243, 2.09e-243j)
| (-6.3518085899720816413 - 3.702082092990677052e-911j)  +/-  (9.61e-244, 9.61e-244j)
| (7.3822899914078990519 + 5.0578051755587670793e-922j)  +/-  (2.8e-243, 2.8e-243j)
| (-9.0511467848318936105 + 5.0680639708846049904e-921j)  +/-  (1.93e-243, 1.93e-243j)
| (-12.712879724738890577 + 8.4647756404728941935e-933j)  +/-  (1.54e-246, 1.54e-246j)
| (8.4738509678410123943 - 4.2502779700581926487e-930j)  +/-  (2.6e-243, 2.6e-243j)
| (-10.996201535184048353 + 1.0696596831450469968e-929j)  +/-  (1.38e-244, 1.38e-244j)
| (-9.6568714081519030355 - 2.3845735813504460456e-936j)  +/-  (1.15e-243, 1.15e-243j)
| (10.300149426745722418 - 2.0683114446573326909e-946j)  +/-  (5.01e-244, 5.01e-244j)
| (3.0274707482915725452 - 3.4536885060640334594e-950j)  +/-  (1.8e-247, 1.8e-247j)
| (-4.4113778947149506932 - 8.7425780246736200038e-947j)  +/-  (1.82e-245, 1.82e-245j)
| (-5.365131646616242809 + 3.1755078789777380863e-945j)  +/-  (1.86e-244, 1.86e-244j)
| (6.3518085899720816413 + 1.1158431254060429673e-949j)  +/-  (9.94e-244, 9.94e-244j)
| (7.9189731295411585048 + 1.2781054062429450179e-948j)  +/-  (3.27e-243, 3.27e-243j)
| (10.996201535184048353 + 1.1083745786941323622e-952j)  +/-  (1.26e-244, 1.26e-244j)
| (-10.300149426745722418 + 3.9497578902630871511e-950j)  +/-  (5.36e-244, 5.36e-244j)
| (9.6568714081519030355 + 2.1223188687000123718e-954j)  +/-  (1.21e-243, 1.21e-243j)
| (-11.77459750870834944 - 1.7061068952213938749e-956j)  +/-  (2.12e-245, 2.12e-245j)
| (2.5762745832756714499 - 3.5396902925701579811e-960j)  +/-  (3.04e-248, 3.04e-248j)
| (11.77459750870834944 - 2.6902976357787575679e-956j)  +/-  (2.3e-245, 2.3e-245j)
| (4.4113778947149506932 - 2.682489295841278843e-956j)  +/-  (1.79e-245, 1.79e-245j)
| (5.8537826361843551087 + 8.0985077418734109133e-955j)  +/-  (4.9e-244, 4.9e-244j)
| (-1.6832095142665958347 - 4.471781602973725677e-960j)  +/-  (5.82e-250, 5.82e-250j)
| (-3.9445010422474016127 + 2.6492623984395331409e-956j)  +/-  (4.53e-246, 4.53e-246j)
| (4.8846558752183204534 + 4.2357059944216783543e-956j)  +/-  (6.37e-245, 6.37e-245j)
| (-3.0274707482915725452 + 1.5345221849698490156e-957j)  +/-  (1.8e-247, 1.8e-247j)
| (-4.8846558752183204534 - 1.243094041183358677e-954j)  +/-  (6.4e-245, 6.4e-245j)
| (-0.9242023674438440386 - 5.2062311429192365103e-967j)  +/-  (6.92e-251, 6.92e-251j)
| (3.4833773961004847262 + 8.1057969127451483249e-964j)  +/-  (9.17e-247, 9.17e-247j)
| (-8.4738509678410123943 + 2.2027974169596723762e-958j)  +/-  (2.82e-243, 2.82e-243j)
| (-7.3822899914078990519 - 3.1213567435400579732e-974j)  +/-  (2.71e-243, 2.71e-243j)
| (-5.8537826361843551087 - 2.3268152111180772099e-986j)  +/-  (4.6e-244, 4.6e-244j)
| (-1.2084377146808692985 - 2.7975077743923438586e-999j)  +/-  (1.3e-250, 1.3e-250j)
| (0.9242023674438440386 - 1.3222240097125622751e-1000j)  +/-  (5.71e-251, 5.71e-251j)
| (5.365131646616242809 - 7.2818737347909244588e-992j)  +/-  (2.09e-244, 2.09e-244j)
| (1.2084377146808692985 - 1.0906398205472141176e-999j)  +/-  (1.43e-250, 1.43e-250j)
| (3.9445010422474016127 + 1.0010670243862148573e-993j)  +/-  (4.58e-246, 4.58e-246j)
| (6.8606921567421002078 + 4.6725060970774116352e-992j)  +/-  (1.7e-243, 1.7e-243j)
| (-0.43061976784138997042 - 1.3411484373991900084e-1002j)  +/-  (1.55e-253, 1.55e-253j)
| (-3.4833773961004847262 - 4.6079178165585160075e-999j)  +/-  (9.36e-247, 9.36e-247j)
| (-6.8606921567421002078 + 2.460357046015464195e-1011j)  +/-  (1.7e-243, 1.7e-243j)
| (2.1290252659381178426 - 2.0956875096675976478e-1027j)  +/-  (4.01e-249, 4.01e-249j)
| (1.6832095142665958347 + 1.6916744487209388225e-1028j)  +/-  (5.45e-250, 5.45e-250j)
| (-2.1290252659381178426 + 1.353437094216195037e-1027j)  +/-  (4.21e-249, 4.21e-249j)
| (-2.5762745832756714499 + 6.9829885226444639434e-1030j)  +/-  (2.76e-248, 2.76e-248j)
| (0.43061976784138997042 + 9.059893091757182587e-1037j)  +/-  (1.55e-253, 1.55e-253j)
| (1 + 4.3372914585216367586e-1034j)  +/-  (1.41e-250, 1.41e-250j)
| (1.1238530453027118076e-1042 - 2.0409710013870135649e-1043j)  +/-  (5.83e-1041, 5.83e-1041j)
| (-1 - 5.1188727381323867109e-1034j)  +/-  (1.36e-250, 1.36e-250j)
-------------------------------------------------
The weights are:
| (3.4732107730485473174e-36 - 9.7906342199447872779e-923j)  +/-  (2.26e-85, 8.1e-206j)
| (5.249542191488816307e-15 + 1.396829552499672728e-909j)  +/-  (1.41e-75, 5.05e-196j)
| (3.8245511072502248842e-19 + 1.0887659129735727539e-913j)  +/-  (1.76e-78, 6.31e-199j)
| (3.4811727517602764377e-10 - 1.0189973111734582452e-907j)  +/-  (2.25e-71, 8.04e-192j)
| (3.0901442671504362662e-13 - 1.9904287458823533899e-910j)  +/-  (1.04e-74, 3.72e-195j)
| (3.8245511072502248842e-19 - 1.631948245350918144e-912j)  +/-  (6.39e-79, 2.29e-199j)
| (3.4732107730485473174e-36 + 4.2136599986819018144e-922j)  +/-  (2.63e-87, 9.4e-208j)
| (5.7630671792696565868e-17 - 1.683626059319582544e-912j)  +/-  (1.47e-78, 5.26e-199j)
| (1.6133728721842963634e-27 + 2.1821867008885139189e-917j)  +/-  (4.93e-84, 1.76e-204j)
| (1.3964616309796177438e-21 + 5.2962529892945031242e-914j)  +/-  (6.31e-81, 2.26e-201j)
| (2.4367037046626328612e-24 + 1.7410745493629673571e-916j)  +/-  (8.81e-84, 3.15e-204j)
| (0.0018499946344094857399 + 2.9908967489350557745e-904j)  +/-  (1.05e-63, 3.77e-184j)
| (1.1148809273077487745e-05 - 2.3912224125893167982e-905j)  +/-  (1.47e-69, 5.25e-190j)
| (1.0854125757326133001e-07 - 1.8194895065112084855e-906j)  +/-  (2.7e-72, 9.67e-193j)
| (3.4811727517602764377e-10 - 1.1190252106533888457e-908j)  +/-  (2.96e-76, 1.06e-196j)
| (5.249542191488816307e-15 + 2.0344649509558572882e-911j)  +/-  (8.05e-79, 2.88e-199j)
| (1.6133728721842963634e-27 - 3.550105680447831286e-918j)  +/-  (3.82e-86, 1.37e-206j)
| (2.4367037046626328612e-24 - 1.3321504431114327816e-915j)  +/-  (3.59e-85, 1.29e-205j)
| (1.3964616309796177438e-21 - 5.2369312515496275575e-915j)  +/-  (3.69e-83, 1.32e-203j)
| (2.6197411328884315762e-31 - 1.8093147853190842638e-919j)  +/-  (1.21e-88, 4.32e-209j)
| (0.0064855983493854003701 - 9.4461006101704038866e-904j)  +/-  (5.03e-68, 1.8e-188j)
| (2.6197411328884315762e-31 + 3.5422922150616937958e-920j)  +/-  (3.19e-88, 1.14e-208j)
| (1.1148809273077487745e-05 - 6.8022721521129319632e-906j)  +/-  (2.64e-75, 9.46e-196j)
| (7.1273084294098130997e-09 + 6.6814353643075787053e-908j)  +/-  (5.8e-78, 2.08e-198j)
| (0.043319507797358984234 - 1.6204199063034268156e-902j)  +/-  (3.61e-67, 1.29e-187j)
| (7.7397015020520008677e-05 + 7.7277531389406619037e-905j)  +/-  (4.53e-76, 1.62e-196j)
| (1.2533700065926849335e-06 + 1.6267157863455226251e-906j)  +/-  (6.57e-77, 2.35e-197j)
| (0.0018499946344094857399 + 6.6931753998752241842e-904j)  +/-  (3.47e-74, 1.24e-194j)
| (1.2533700065926849335e-06 + 6.8641027548727358901e-906j)  +/-  (3.19e-78, 1.14e-198j)
| (0.28295942920690418467 + 4.7082485852632501096e-901j)  +/-  (4.87e-70, 1.74e-190j)
| (0.00042397336924751144921 - 9.0882135662694669034e-905j)  +/-  (3.92e-75, 1.4e-195j)
| (5.7630671792696565868e-17 + 4.9739571363595040999e-911j)  +/-  (2.2e-85, 7.88e-206j)
| (3.0901442671504362662e-13 - 5.6748706639410684173e-909j)  +/-  (5.02e-84, 1.8e-204j)
| (7.1273084294098130997e-09 + 4.4558493627160831186e-907j)  +/-  (3.13e-81, 1.12e-201j)
| (0.1163725398627228025 + 1.3245981526517147208e-901j)  +/-  (6.99e-72, 2.5e-192j)
| (0.28295942920690418467 + 3.7241282338130070876e-901j)  +/-  (1.15e-72, 4.1e-193j)
| (1.0854125757326133001e-07 - 3.4979306906810349676e-907j)  +/-  (1.09e-80, 3.89e-201j)
| (0.1163725398627228025 + 9.7385369909744692395e-902j)  +/-  (1.59e-73, 5.7e-194j)
| (7.7397015020520008677e-05 + 2.5889329469147079391e-905j)  +/-  (1.07e-78, 3.83e-199j)
| (1.2351039099896948869e-11 + 1.6194212557392681827e-909j)  +/-  (3.52e-83, 1.26e-203j)
| (0.15858633864307392257 - 6.6403972509840504516e-902j)  +/-  (1.69e-74, 6.04e-195j)
| (0.00042397336924751144921 - 2.336258824338721378e-904j)  +/-  (1.41e-79, 5.06e-200j)
| (1.2351039099896948869e-11 + 2.2616398416394285321e-908j)  +/-  (4.03e-84, 1.44e-204j)
| (0.01843947159596942475 + 2.9858785745651360765e-903j)  +/-  (7.12e-78, 2.55e-198j)
| (0.043319507797358984234 - 1.05231861005160303e-902j)  +/-  (2.25e-77, 8.04e-198j)
| (0.01843947159596942475 + 5.1817570439497591252e-903j)  +/-  (5.99e-79, 2.14e-199j)
| (0.0064855983493854003701 - 1.8556009657933682426e-903j)  +/-  (1.84e-79, 6.59e-200j)
| (0.15858633864307392257 - 5.9554569532385575025e-902j)  +/-  (7.16e-78, 2.55e-198j)
| (-0.21395377658162094653 - 4.2871518623095223626e-901j)  +/-  (5.81e-77, 2.09e-197j)
| (0.17085401579780080227 + 5.4867428316484182144e-902j)  +/-  (3.94e-78, 1.38e-198j)
| (-0.21395377658162094653 - 5.5263969878629907215e-901j)  +/-  (1.43e-77, 5.19e-198j)
