Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 15 22
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : 16*t^19 - 748536/667*t^17 + 226304664/7337*t^15 - 3155515020/7337*t^13 + 24226003620/7337*t^11 - 9496214910/667*t^9 + 1965071745/58*t^7 - 112008278655/2668*t^5 + 250467132825/10672*t^3 - 83438061525/21344*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^41 - 732162665114791791752253947376667905478782925822585029108367615457648376710924/163457559805901088531342226033401427370951376520220744896767205238813178587*t^39 + 263507786995560508558307016963452473324762913701782581696787678449007207629570011958/469286654202742025173483530941895497982001401989553758598618646240632635723277*t^37 - 225494958840358900776734287397376728765848138176297225843747465890679265970686914508/5394099473594735921534293459102247103241395425167284581593317772880834893371*t^35 + 323383255009501980081327789326410666156083975435118099596820013559770247671105183571350/156428884734247341724494510313965165994000467329851252866206215413544211907759*t^33 - 682226906166276488636253913006635816545639685552578247629919561295143931985114868397465/9480538468742263134817849109937282787515179838172803204012497903851164358046*t^31 + 1503051193658546550001899698718711356117530015698239063021920679300253477913559741321715/824394649455848968245030357385850677175233029406330713392391122074014292004*t^29 - 1300538826657401457510873101229717483504590133387998802388914720914895383434368840347653505/37922153874969052539271396439749131150060719352691212816049991615404657432184*t^27 + 36725778838815430088543712696811316215379267146831925489809306156898828977611381718168711695/75844307749938105078542792879498262300121438705382425632099983230809314864368*t^25 - 48876759392480072729871272007788934704892834633470403619012025430228301331839088528767719375/9480538468742263134817849109937282787515179838172803204012497903851164358046*t^23 + 272760665149737615430611836041276464882277757189656327537964042746980484318929366350671604625/6595157195646791745960242859086805417401864235250645707139128976592114336032*t^21 - 6556881556600740928702442739267996011770890793189586987562678284722049345525126824766473614375/26380628782587166983840971436347221669607456941002582828556515906368457344128*t^19 + 58398058658121003568500432283802839076448087207902657835331864436011861032223289056343898309375/52761257565174333967681942872694443339214913882005165657113031812736914688256*t^17 - 378925477926550738125437459628792575665608415061382580312491795301784023884403020317074591130625/105522515130348667935363885745388886678429827764010331314226063625473829376512*t^15 + 1747838337748157610016370956544304929899039075575752672445216150173405648817336528407458688803125/211045030260697335870727771490777773356859655528020662628452127250947658753024*t^13 - 5533942295728277665493992681751419002342864186322740056288225082165856518107746774063969133533125/422090060521394671741455542981555546713719311056041325256904254501895317506048*t^11 + 5716189935110162327316703785586319759719685800963419556886783083699431591257977144852815879500625/422090060521394671741455542981555546713719311056041325256904254501895317506048*t^9 - 28543465795458005955802612900979454740140648881596524852892939456132389313371574105616583629069375/3376720484171157373931644343852444373709754488448330602055234036015162540048384*t^7 + 18951588781225363003861505836017108751177662967203375203421956878430809593829633306057105914118125/6753440968342314747863288687704888747419508976896661204110468072030325080096768*t^5 - 2575476936845141656464107290263634995322968591301152525002254573778780524950415447119987537796875/6753440968342314747863288687704888747419508976896661204110468072030325080096768*t^3 + 113630886351313560313702913668001205548410336746780884618663576403986952880387544198909303221875/13506881936684629495726577375409777494839017953793322408220936144060650160193536*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-6.4617130366402449294 + 1.2826555620607235248e-423j)  +/-  (5.63e-120, 5.63e-120j)
| (5.8745539423008364156 - 2.6052988122968167764e-425j)  +/-  (2.69e-119, 2.69e-119j)
| (-7.1699003281397703922 - 1.3603879031679673417e-426j)  +/-  (5.66e-121, 5.66e-121j)
| (-4.4443826962805585135 - 1.3085662618576475174e-422j)  +/-  (2.57e-118, 2.57e-118j)
| (-5.8745539423008364156 - 1.0148951503681888295e-430j)  +/-  (2.99e-119, 2.99e-119j)
| (-5.3520411629853306619 - 2.7061075673760909471e-433j)  +/-  (7.06e-119, 7.06e-119j)
| (4.4443826962805585135 + 1.6922681396022004346e-440j)  +/-  (2.44e-118, 2.44e-118j)
| (3.3862181400001748776 + 2.7871347105955135754e-440j)  +/-  (1.72e-118, 1.72e-118j)
| (-4.0676787766194897745 - 2.6822003752678722842e-446j)  +/-  (2.76e-118, 2.76e-118j)
| (-3.3862181400001748776 + 2.4556253985809178177e-458j)  +/-  (1.87e-118, 1.87e-118j)
| (2.1888080617024303415 - 1.1910865767826642527e-464j)  +/-  (5.12e-120, 5.12e-120j)
| (7.1699003281397703922 + 2.007227467317909156e-465j)  +/-  (5.51e-121, 5.51e-121j)
| (4.8759532376325231043 + 7.1029997597427052042e-462j)  +/-  (1.5e-118, 1.5e-118j)
| (-1.8877018443596724697 - 2.1065069518452150311e-466j)  +/-  (1.14e-120, 1.14e-120j)
| (0.80914987938530168368 + 2.190117196393199339e-469j)  +/-  (5.39e-124, 5.39e-124j)
| (2.5176548995386133367 + 4.9321893752891539072e-464j)  +/-  (2.52e-119, 2.52e-119j)
| (-1.3498998593245308008 - 5.1527422122463470513e-469j)  +/-  (2.94e-122, 2.94e-122j)
| (4.0676787766194897745 - 7.7484550634360508846e-463j)  +/-  (2.64e-118, 2.64e-118j)
| (-4.8759532376325231043 - 5.3522212255182649143e-464j)  +/-  (1.51e-118, 1.51e-118j)
| (-3.732537948683976683 - 1.0891076160556197043e-469j)  +/-  (2.87e-118, 2.87e-118j)
| (5.3520411629853306619 - 8.6318857680108680158e-475j)  +/-  (6.81e-119, 6.81e-119j)
| (1.3498998593245308008 + 7.9720595355542054267e-477j)  +/-  (3.11e-122, 3.11e-122j)
| (0.16434772151855500617 + 1.1490990510463123184e-480j)  +/-  (8.52e-127, 8.52e-127j)
| (6.4617130366402449294 - 5.3384394913011994475e-475j)  +/-  (5.66e-120, 5.66e-120j)
| (-1.6506801238857845559 - 8.6946174011742820644e-476j)  +/-  (3.35e-121, 3.35e-121j)
| (-2.7676033562166682643 - 2.1884634014466767686e-473j)  +/-  (6.89e-119, 6.89e-119j)
| (1.8877018443596724697 + 6.4971959272349598903e-477j)  +/-  (1.15e-120, 1.15e-120j)
| (1.6506801238857845559 + 1.5681442428527212878e-477j)  +/-  (2.92e-121, 2.92e-121j)
| (-1.0392484373427345816 + 1.2714389922806720329e-479j)  +/-  (3.68e-123, 3.68e-123j)
| (-0.16434772151855500617 - 6.1509977464584799916e-483j)  +/-  (1.06e-126, 1.06e-126j)
| (-2.5176548995386133367 + 2.6119448559398271195e-475j)  +/-  (2.47e-119, 2.47e-119j)
| (3.0376195588289713971 - 4.8842469934552105079e-474j)  +/-  (1.2e-118, 1.2e-118j)
| (2.7676033562166682643 + 1.8787059188074843829e-475j)  +/-  (7.32e-119, 7.32e-119j)
| (3.732537948683976683 + 3.910847766834303854e-479j)  +/-  (2.75e-118, 2.75e-118j)
| (-2.1888080617024303415 + 5.6305852471717362558e-482j)  +/-  (5.46e-120, 5.46e-120j)
| (0.52464762327529031788 + 4.7835409880357184764e-488j)  +/-  (2.93e-125, 2.93e-125j)
| (-3.0376195588289713971 + 1.0102140662602700838e-485j)  +/-  (1.26e-118, 1.26e-118j)
| (1.0392484373427345816 - 2.7603155174844350748e-494j)  +/-  (3.65e-123, 3.65e-123j)
| (-2.400273729375907662e-503 - 1.0573826451580222284e-504j)  +/-  (9.85e-502, 9.85e-502j)
| (-0.80914987938530168368 + 1.822343846344078666e-494j)  +/-  (4.74e-124, 4.74e-124j)
| (-0.52464762327529031788 - 1.8763871436100760534e-495j)  +/-  (2.93e-125, 2.93e-125j)
-------------------------------------------------
The weights are:
| (2.6229940475051411041e-19 + 9.5107700319462137246e-439j)  +/-  (5.24e-31, 1.99e-90j)
| (3.1927032313474985197e-16 + 1.8314063674560706836e-437j)  +/-  (1.29e-30, 4.93e-90j)
| (2.1756453587119668728e-23 - 2.1541462056429443996e-441j)  +/-  (5.12e-33, 1.95e-92j)
| (6.0503446909374841506e-10 - 5.909694719655110388e-431j)  +/-  (5.6e-26, 2.13e-85j)
| (3.1927032313474985197e-16 - 1.3174782042645368194e-436j)  +/-  (4.82e-30, 1.83e-89j)
| (1.0194937619669910177e-13 + 1.0782228413049824418e-434j)  +/-  (7.99e-29, 3.04e-88j)
| (6.0503446909374841506e-10 - 8.908228504210413026e-433j)  +/-  (1.51e-29, 5.73e-89j)
| (2.103000748179546721e-06 + 1.0019659574401231445e-429j)  +/-  (1.09e-25, 4.13e-85j)
| (1.2799719407665237654e-08 + 3.0817870023614864682e-430j)  +/-  (3.63e-26, 1.38e-85j)
| (2.103000748179546721e-06 + 7.4143165990810485347e-429j)  +/-  (1.6e-24, 6.09e-84j)
| (0.0015615661395318333159 + 3.9714645058946583119e-427j)  +/-  (4.57e-21, 1.74e-80j)
| (2.1756453587119668728e-23 + 5.0558321348747253729e-442j)  +/-  (1.32e-38, 5.03e-98j)
| (1.2130184966941844807e-11 + 3.5754171849850544518e-434j)  +/-  (8.31e-32, 3.16e-91j)
| (0.0040618420207777240529 - 3.5275174554065439804e-426j)  +/-  (5e-21, 1.9e-80j)
| (0.0663557103692331689 - 2.2337642973757708258e-425j)  +/-  (3.89e-18, 1.48e-77j)
| (0.00030274350651554091444 - 1.2216027357596221158e-427j)  +/-  (4e-24, 1.52e-83j)
| (0.029702054052193898733 - 1.0590655762209659511e-425j)  +/-  (3.88e-18, 1.48e-77j)
| (1.2799719407665237654e-08 + 1.3639797121870552056e-431j)  +/-  (1.34e-29, 5.11e-89j)
| (1.2130184966941844807e-11 - 7.7198755215037074039e-433j)  +/-  (1.23e-30, 4.68e-90j)
| (1.6797471059505471647e-07 - 1.4246380354676075465e-429j)  +/-  (1.12e-27, 4.28e-87j)
| (1.0194937619669910177e-13 - 9.9953654045927370454e-436j)  +/-  (8.12e-34, 3.09e-93j)
| (0.029702054052193898733 - 5.6561014517299488428e-426j)  +/-  (4.14e-22, 1.58e-81j)
| (0.21834509805315170304 - 7.9951660797888859054e-425j)  +/-  (5.16e-21, 1.96e-80j)
| (2.6229940475051411041e-19 - 1.7524987464455323671e-439j)  +/-  (2.21e-37, 8.41e-97j)
| (0.0095630127432989992917 + 6.5174714717230243571e-426j)  +/-  (4.94e-23, 1.88e-82j)
| (5.8393910497768499845e-05 + 1.8922785895131684012e-427j)  +/-  (2.44e-27, 9.29e-87j)
| (0.0040618420207777240529 - 1.4243210742231526949e-426j)  +/-  (4.81e-25, 1.83e-84j)
| (0.0095630127432989992917 + 2.9873674497544589722e-426j)  +/-  (1.89e-24, 7.19e-84j)
| (0.052339983088626400292 + 2.2171101800761907203e-425j)  +/-  (6.63e-24, 2.52e-83j)
| (0.21834509805315170304 - 8.609160493170424548e-425j)  +/-  (1.61e-23, 6.14e-83j)
| (0.00030274350651554091444 - 4.4140020271087250379e-427j)  +/-  (2.08e-27, 7.92e-87j)
| (1.8126086997338958901e-05 - 8.8910397832346154304e-429j)  +/-  (3.47e-29, 1.32e-88j)
| (5.8393910497768499845e-05 + 4.3996881888691655444e-428j)  +/-  (2.05e-28, 7.81e-88j)
| (1.6797471059505471647e-07 - 1.2403107085456718517e-430j)  +/-  (3.03e-31, 1.15e-90j)
| (0.0015615661395318333159 + 1.1678984022662165239e-426j)  +/-  (3.96e-28, 1.51e-87j)
| (0.14325785010864828727 + 2.8051782060681852441e-425j)  +/-  (2.31e-26, 8.79e-86j)
| (1.8126086997338958901e-05 - 4.7285787731323874985e-428j)  +/-  (7.79e-30, 2.96e-89j)
| (0.052339983088626400292 + 1.3767583366098752618e-425j)  +/-  (6.89e-27, 2.64e-86j)
| (-0.051137328943835537008 + 1.3161905703417756864e-424j)  +/-  (3.56e-26, 1.35e-85j)
| (0.0663557103692331689 - 3.2281458670696954167e-425j)  +/-  (1.27e-27, 4.96e-87j)
| (0.14325785010864828727 + 3.5560938926911048078e-425j)  +/-  (1.66e-27, 6.11e-87j)
