Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 15 22
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : t^19 - 93567/667*t^17 + 56576166/7337*t^15 - 1577757510/7337*t^13 + 24226003620/7337*t^11 - 18992429820/667*t^9 + 3930143490/29*t^7 - 224016557310/667*t^5 + 250467132825/667*t^3 - 83438061525/667*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 183040666278697947938063486844166976369695731455646257277091903864412094177731/326915119611802177062684452066802854741902753040441489793534410477626357174*t^39 + 131753893497780254279153508481726236662381456850891290848393839224503603814785005979/938573308405484050346967061883790995964002803979107517197237292481265271446554*t^37 - 112747479420179450388367143698688364382924069088148612921873732945339632985343457254/5394099473594735921534293459102247103241395425167284581593317772880834893371*t^35 + 323383255009501980081327789326410666156083975435118099596820013559770247671105183571350/156428884734247341724494510313965165994000467329851252866206215413544211907759*t^33 - 682226906166276488636253913006635816545639685552578247629919561295143931985114868397465/4740269234371131567408924554968641393757589919086401602006248951925582179023*t^31 + 1503051193658546550001899698718711356117530015698239063021920679300253477913559741321715/206098662363962242061257589346462669293808257351582678348097780518503573001*t^29 - 1300538826657401457510873101229717483504590133387998802388914720914895383434368840347653505/4740269234371131567408924554968641393757589919086401602006248951925582179023*t^27 + 36725778838815430088543712696811316215379267146831925489809306156898828977611381718168711695/4740269234371131567408924554968641393757589919086401602006248951925582179023*t^25 - 782028150279681163677940352124622955278285354135526457904192406883652821309425416460283510000/4740269234371131567408924554968641393757589919086401602006248951925582179023*t^23 + 545521330299475230861223672082552929764555514379312655075928085493960968637858732701343209250/206098662363962242061257589346462669293808257351582678348097780518503573001*t^21 - 6556881556600740928702442739267996011770890793189586987562678284722049345525126824766473614375/206098662363962242061257589346462669293808257351582678348097780518503573001*t^19 + 58398058658121003568500432283802839076448087207902657835331864436011861032223289056343898309375/206098662363962242061257589346462669293808257351582678348097780518503573001*t^17 - 378925477926550738125437459628792575665608415061382580312491795301784023884403020317074591130625/206098662363962242061257589346462669293808257351582678348097780518503573001*t^15 + 1747838337748157610016370956544304929899039075575752672445216150173405648817336528407458688803125/206098662363962242061257589346462669293808257351582678348097780518503573001*t^13 - 5533942295728277665493992681751419002342864186322740056288225082165856518107746774063969133533125/206098662363962242061257589346462669293808257351582678348097780518503573001*t^11 + 11432379870220324654633407571172639519439371601926839113773566167398863182515954289705631759001250/206098662363962242061257589346462669293808257351582678348097780518503573001*t^9 - 28543465795458005955802612900979454740140648881596524852892939456132389313371574105616583629069375/412197324727924484122515178692925338587616514703165356696195561037007146002*t^7 + 18951588781225363003861505836017108751177662967203375203421956878430809593829633306057105914118125/412197324727924484122515178692925338587616514703165356696195561037007146002*t^5 - 2575476936845141656464107290263634995322968591301152525002254573778780524950415447119987537796875/206098662363962242061257589346462669293808257351582678348097780518503573001*t^3 + 113630886351313560313702913668001205548410336746780884618663576403986952880387544198909303221875/206098662363962242061257589346462669293808257351582678348097780518503573001*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:
| (7.568929199072927088 + 7.6144450270279997394e-880j)  +/-  (2.35e-246, 2.35e-246j)
| (-6.2853062854562699857 + 4.611535369001467025e-882j)  +/-  (8.75e-246, 8.75e-246j)
| (-5.2786057891011313054 + 1.3111910257847401762e-881j)  +/-  (9.21e-246, 9.21e-246j)
| (-10.139770284918567833 + 1.361481956450199294e-885j)  +/-  (1.96e-248, 1.96e-248j)
| (-8.3078738580941753327 + 1.3837764295787072423e-883j)  +/-  (8.58e-247, 8.58e-247j)
| (8.3078738580941753327 - 3.8338873725034839292e-885j)  +/-  (8.79e-247, 8.79e-247j)
| (-7.568929199072927088 - 1.8050138915790706148e-886j)  +/-  (2.48e-246, 2.48e-246j)
| (9.138242212579670435 - 6.988437127164810099e-889j)  +/-  (1.85e-247, 1.85e-247j)
| (-1.4697192347651409339 - 1.7047284777945625119e-892j)  +/-  (1.24e-250, 1.24e-250j)
| (2.6696135500101542242 - 2.897808511354555205e-889j)  +/-  (4.04e-248, 4.04e-248j)
| (1.4697192347651409339 + 3.0132371377000537131e-892j)  +/-  (1.11e-250, 1.11e-250j)
| (3.560501704302579101 + 7.0954401597478166498e-887j)  +/-  (9.08e-247, 9.08e-247j)
| (6.8956391981569169575 - 1.1449178258402679231e-892j)  +/-  (5.25e-246, 5.25e-246j)
| (-3.0954420462911432479 - 2.7401826598209276556e-902j)  +/-  (1.62e-247, 1.62e-247j)
| (2.3344142183389772393 - 2.6865142027163232086e-904j)  +/-  (9.2e-249, 9.2e-249j)
| (-9.138242212579670435 - 1.4054318682491776264e-902j)  +/-  (1.95e-247, 1.95e-247j)
| (-5.7525664932724817643 + 2.6027353919069859913e-899j)  +/-  (9.93e-246, 9.93e-246j)
| (-1.9090466889022845717 - 3.676087221954724159e-908j)  +/-  (1e-249, 1e-249j)
| (4.2958427774257090058 - 6.5127203596184357101e-903j)  +/-  (4.25e-246, 4.25e-246j)
| (10.139770284918567833 + 2.9568451997760807319e-917j)  +/-  (2.1e-248, 2.1e-248j)
| (5.7525664932724817643 + 3.7388920200931152063e-933j)  +/-  (9.63e-246, 9.63e-246j)
| (1.9090466889022845717 - 9.7258427023119386798e-949j)  +/-  (9.61e-250, 9.61e-250j)
| (-3.9139822016309083791 - 1.4265626789566134593e-943j)  +/-  (2.51e-246, 2.51e-246j)
| (-0.74196378430272585765 + 1.0077250995835148463e-953j)  +/-  (9.34e-253, 9.34e-253j)
| (-2.6696135500101542242 + 1.4335644736391415505e-948j)  +/-  (4.22e-248, 4.22e-248j)
| (-3.560501704302579101 - 6.5163936649322713264e-947j)  +/-  (9.28e-247, 9.28e-247j)
| (-4.7888356187420432164 + 2.7688910692513737279e-953j)  +/-  (6.67e-246, 6.67e-246j)
| (5.2786057891011313054 - 4.3146281559489117227e-963j)  +/-  (9.25e-246, 9.25e-246j)
| (-6.8956391981569169575 + 1.667262178544025943e-978j)  +/-  (5.31e-246, 5.31e-246j)
| (-1.1443107334192476783 - 5.3630797076311034747e-988j)  +/-  (1.63e-251, 1.63e-251j)
| (4.7888356187420432164 - 5.1691456516553275845e-981j)  +/-  (6.25e-246, 6.25e-246j)
| (-0.23242277671665704555 - 4.007301314769230933e-1000j)  +/-  (4.03e-254, 4.03e-254j)
| (6.2853062854562699857 + 7.3471154660513220493e-992j)  +/-  (8.6e-246, 8.6e-246j)
| (-2.3344142183389772393 - 1.8851070791521113977e-1002j)  +/-  (8.9e-249, 8.9e-249j)
| (3.9139822016309083791 + 9.1106595520737599637e-1000j)  +/-  (2.51e-246, 2.51e-246j)
| (0.23242277671665704555 - 9.6193593942966890155e-1009j)  +/-  (4.03e-254, 4.03e-254j)
| (-4.2958427774257090058 - 2.7372678073885641076e-1003j)  +/-  (4.17e-246, 4.17e-246j)
| (0.74196378430272585765 - 2.6082320607527275378e-1010j)  +/-  (1.05e-252, 1.05e-252j)
| (-5.087265853868856059e-1028 - 8.7348948080648893277e-1027j)  +/-  (3.59e-1025, 3.59e-1025j)
| (3.0954420462911432479 + 4.9845328813301549589e-1007j)  +/-  (1.78e-247, 1.78e-247j)
| (1.1443107334192476783 - 7.5035102886851898031e-1013j)  +/-  (1.67e-251, 1.67e-251j)
-------------------------------------------------
The weights are:
| (1.0194937619669910177e-13 - 4.1292366902634944501e-892j)  +/-  (4.54e-90, 3.44e-212j)
| (6.0503446909374841506e-10 - 6.8874849356552936473e-891j)  +/-  (3.79e-87, 2.88e-209j)
| (1.6797471059505471647e-07 + 9.0753004798538662e-888j)  +/-  (2.17e-84, 1.65e-206j)
| (2.1756453587119668728e-23 + 5.7931585738131419695e-900j)  +/-  (3e-96, 2.28e-218j)
| (3.1927032313474985197e-16 + 2.6219406250466164063e-895j)  +/-  (1.23e-92, 9.37e-215j)
| (3.1927032313474985197e-16 - 2.0566801163583865701e-894j)  +/-  (2.55e-94, 1.94e-216j)
| (1.0194937619669910177e-13 - 1.7096262670756104442e-893j)  +/-  (2.08e-91, 1.58e-213j)
| (2.6229940475051411041e-19 + 1.0003340541924545894e-896j)  +/-  (2.85e-96, 2.16e-218j)
| (0.052339983088626400292 + 1.7697460694527647788e-884j)  +/-  (2.32e-71, 1.76e-193j)
| (0.0040618420207777240529 - 1.1786016975552839322e-884j)  +/-  (2.21e-79, 1.68e-201j)
| (0.052339983088626400292 + 7.0480299070057649857e-884j)  +/-  (9.75e-72, 7.4e-194j)
| (0.00030274350651554091444 - 1.4439594093554707615e-885j)  +/-  (1.32e-83, 1e-205j)
| (1.2130184966941844807e-11 + 3.8571465340013153378e-891j)  +/-  (2.68e-92, 2.04e-214j)
| (0.0015615661395318333159 - 9.5178110230506573082e-886j)  +/-  (8.59e-83, 6.52e-205j)
| (0.0095630127432989992917 + 2.1659541070034371753e-884j)  +/-  (1.52e-78, 1.16e-200j)
| (2.6229940475051411041e-19 - 2.2207006778502952954e-897j)  +/-  (2.02e-96, 1.54e-218j)
| (1.2799719407665237654e-08 + 5.2430387508633697416e-889j)  +/-  (1.96e-89, 1.49e-211j)
| (0.029702054052193898733 - 3.6717886832339863627e-885j)  +/-  (1.74e-78, 1.32e-200j)
| (1.8126086997338958901e-05 - 1.4393510558396880981e-886j)  +/-  (1.01e-87, 7.66e-210j)
| (2.1756453587119668728e-23 - 1.908363523964542996e-899j)  +/-  (3.69e-100, 2.8e-222j)
| (1.2799719407665237654e-08 + 4.8081222873998605582e-889j)  +/-  (1.53e-91, 1.16e-213j)
| (0.029702054052193898733 - 3.4629151415302295365e-884j)  +/-  (4.35e-80, 3.3e-202j)
| (5.8393910497768499845e-05 - 3.3290034047785477742e-886j)  +/-  (6.11e-88, 4.63e-210j)
| (0.14325785010864828727 + 5.7478749822747115282e-884j)  +/-  (3.19e-80, 2.42e-202j)
| (0.0040618420207777240529 + 1.3977471685132393109e-885j)  +/-  (6.95e-85, 5.27e-207j)
| (0.00030274350651554091444 + 5.78759515774631024e-886j)  +/-  (3.75e-87, 2.84e-209j)
| (2.103000748179546721e-06 - 3.1600519759600563003e-887j)  +/-  (3.62e-90, 2.74e-212j)
| (1.6797471059505471647e-07 - 3.2733636268342202218e-888j)  +/-  (6.35e-93, 4.82e-215j)
| (1.2130184966941844807e-11 + 8.2257268032285505069e-892j)  +/-  (4.85e-95, 3.68e-217j)
| (0.0663557103692331689 - 3.7166406433906028707e-884j)  +/-  (7.97e-84, 6.05e-206j)
| (2.103000748179546721e-06 + 2.0447168647333237854e-887j)  +/-  (3.59e-92, 2.72e-214j)
| (0.21834509805315170304 - 1.94704259689391545e-883j)  +/-  (2.78e-85, 2.11e-207j)
| (6.0503446909374841506e-10 - 4.7223047742282266976e-890j)  +/-  (4.34e-95, 3.3e-217j)
| (0.0095630127432989992917 - 4.6811622878117969127e-886j)  +/-  (8.11e-88, 6.15e-210j)
| (5.8393910497768499845e-05 + 6.0280855767285674496e-886j)  +/-  (7.06e-91, 5.36e-213j)
| (0.21834509805315170304 - 2.3335500741040143361e-883j)  +/-  (7.42e-87, 5.65e-209j)
| (1.8126086997338958901e-05 + 1.1430418308741736935e-886j)  +/-  (5.13e-91, 3.88e-213j)
| (0.14325785010864828727 + 1.0472184073279356855e-883j)  +/-  (9e-88, 6.87e-210j)
| (-0.051137328943835537008 + 3.3971203413668749731e-883j)  +/-  (8.84e-87, 6.76e-209j)
| (0.0015615661395318333159 + 3.8900162782868258573e-885j)  +/-  (4.4e-90, 3.35e-212j)
| (0.0663557103692331689 - 9.9675842275115619347e-884j)  +/-  (2.87e-88, 2.12e-210j)
