Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 51
-------------------------------------------------
Trying to find an order 51 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^55 - 9191112662685498731875117957543214298418689/6555076147722879249220403680783482721244*t^53 + 140273187096353747160246291588685529771765986527/154044289471487662356679486498411843949234*t^51 - 112181796988658283776776485689443088587415752906425/308088578942975324713358972996823687898468*t^49 + 7742782489315119499774373269800136236747000019938900/77022144735743831178339743249205921974617*t^47 - 66753623081276346979498684393308292572703540280463675/3277538073861439624610201840391741360622*t^45 + 5149435802153154124352817870923009062153076073528162525/1638769036930719812305100920195870680311*t^43 - 1239317861634305486558009862598510270028767354206265103025/3277538073861439624610201840391741360622*t^41 + 59098483492718788410283375216900301173728071874605425401375/1638769036930719812305100920195870680311*t^39 - 1389248185028250086072551503886305732990700510186338355221375/504236626747913788401569513906421747788*t^37 + 42800739749777854448495006643825952784858718842794559677549875/252118313373956894200784756953210873894*t^35 - 4270131765906186371200463111926680140160453693007352810492246625/504236626747913788401569513906421747788*t^33 + 43167445196311676029285107419624430464571834717620094699748512000/126059156686978447100392378476605436947*t^31 - 1413631033966456457988948486478635747755163044887890217439836393125/126059156686978447100392378476605436947*t^29 + 37375976884228273507137877942621138065964363755317583383884331598750/126059156686978447100392378476605436947*t^27 - 793726915573986055286015115195341037617289552941320007531656780884375/126059156686978447100392378476605436947*t^25 + 13437697295601950963405001692595401982146699352404774448768060764915625/126059156686978447100392378476605436947*t^23 - 718202276273469634647823504759869204105431670913740622583274807368221875/504236626747913788401569513906421747788*t^21 + 3737600356108367425899747691375342954047741997467155180264832881148796875/252118313373956894200784756953210873894*t^19 - 59590214829042041929899352502861921085538166418723456145633772253982453125/504236626747913788401569513906421747788*t^17 + 88997489252180613929526355295975967287481486626107481925535133121078562500/126059156686978447100392378476605436947*t^15 - 774529430253434711786246474794175987200607162653277679499770470310783609375/252118313373956894200784756953210873894*t^13 + 1181872424829791671862194207455643747992250136977335730597828649049551390625/126059156686978447100392378476605436947*t^11 - 4802751632057571412267230153605331327638097998750562536726575593071597578125/252118313373956894200784756953210873894*t^9 + 3013213086442204712942375697497926378490367829195342546933875112375796015625/126059156686978447100392378476605436947*t^7 - 8308517580061238040162375517640377707954179802957298552906554062889165515625/504236626747913788401569513906421747788*t^5 + 1279865181082955879411807597928359648909161278352742380418686836626903578125/252118313373956894200784756953210873894*t^3 - 220715386972487411701857022151893591061880873484069933055968924798926234375/504236626747913788401569513906421747788*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
Positive weights:   55 out of 55
Indefinite weights: 0 out of 55
Negative weights:   0 out of 55
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (9.3053475436877500958 + 3.4142067103788361881e-537j)  +/-  (4.49e-242, 4.49e-242j)
| (13.453017827565657873 + 3.7784394200135810999e-550j)  +/-  (8.64e-246, 8.64e-246j)
| (-11.770191258769988478 - 1.0072724133889221412e-550j)  +/-  (1.03e-243, 1.03e-243j)
| (-8.2422143496089295292 - 5.7061788672869165519e-548j)  +/-  (6.08e-242, 6.08e-242j)
| (-13.453017827565657873 + 2.7460979378331011412e-552j)  +/-  (8.76e-246, 8.76e-246j)
| (12.532771430880271241 + 2.5843957336782917503e-547j)  +/-  (1.49e-244, 1.49e-244j)
| (7.2409582084610319574 + 1.3251024474995433831e-553j)  +/-  (3.34e-242, 3.34e-242j)
| (-11.088998173360694755 + 4.8042147452084013632e-570j)  +/-  (4.48e-243, 4.48e-243j)
| (10.460104690176451931 + 6.7022293019665048683e-567j)  +/-  (1.3e-242, 1.3e-242j)
| (-5.3631288226557599902 - 5.9069794212848052281e-581j)  +/-  (1.54e-243, 1.54e-243j)
| (-12.532771430880271241 - 8.1425454764431021299e-582j)  +/-  (1.5e-244, 1.5e-244j)
| (-7.2409582084610319574 + 1.4360554008159335612e-579j)  +/-  (3.36e-242, 3.36e-242j)
| (-4.4692563797074340503 + 5.778641951480300912e-584j)  +/-  (1.29e-244, 1.29e-244j)
| (-9.3053475436877500958 + 6.26608720985499867e-579j)  +/-  (4.21e-242, 4.21e-242j)
| (-2.3344142183389772393 + 7.657010068302925519e-586j)  +/-  (2.24e-248, 2.24e-248j)
| (5.3631288226557599902 - 7.6958889513054669157e-580j)  +/-  (1.62e-243, 1.62e-243j)
| (2.3344142183389772393 - 2.714873252740127924e-593j)  +/-  (2.41e-248, 2.41e-248j)
| (7.7350983930442160532 + 7.3783222582514112717e-605j)  +/-  (4.8e-242, 4.8e-242j)
| (-1.5216468817952859617 - 1.7680652948967039146e-637j)  +/-  (2.56e-250, 2.56e-250j)
| (11.088998173360694755 + 3.60497029033328983e-637j)  +/-  (4.45e-243, 4.45e-243j)
| (3.5989520149633452071 - 7.5619726319516854157e-652j)  +/-  (6.32e-246, 6.32e-246j)
| (-10.460104690176451931 - 1.6596104919343515319e-656j)  +/-  (1.34e-242, 1.34e-242j)
| (-4.0313299730623968988 - 3.5784467389769127475e-670j)  +/-  (3e-245, 3e-245j)
| (8.7646173831062649121 + 5.8289783833931172346e-695j)  +/-  (5.67e-242, 5.67e-242j)
| (9.8685433225409811177 + 3.6664371835957272133e-725j)  +/-  (2.65e-242, 2.65e-242j)
| (-7.7350983930442160532 - 1.5575024174828124133e-739j)  +/-  (4.83e-242, 4.83e-242j)
| (-6.7579906120647499397 + 1.4452625592964174691e-740j)  +/-  (2.11e-242, 2.11e-242j)
| (11.770191258769988478 + 3.0712455443279008219e-739j)  +/-  (1.13e-243, 1.13e-243j)
| (-6.2847621483050841053 - 7.0295328295440694201e-747j)  +/-  (1.01e-242, 1.01e-242j)
| (4.9130393321959841345 + 3.9901066670163360963e-747j)  +/-  (4.97e-244, 4.97e-244j)
| (-8.7646173831062649121 - 4.9664958883559231265e-749j)  +/-  (5.28e-242, 5.28e-242j)
| (1.9245570492171148258 + 1.1017845713704360224e-757j)  +/-  (2.48e-249, 2.48e-249j)
| (3.1719642685210842305 + 1.6938122997854278438e-755j)  +/-  (1.11e-246, 1.11e-246j)
| (-3.5989520149633452071 + 1.4173149522040096979e-755j)  +/-  (6.66e-246, 6.66e-246j)
| (-9.8685433225409811177 - 7.6386080186650567101e-749j)  +/-  (2.7e-242, 2.7e-242j)
| (-1.1269481594888072442 - 2.3529314076095269979e-762j)  +/-  (2.23e-251, 2.23e-251j)
| (8.2422143496089295292 - 1.6087777334124538412e-751j)  +/-  (5.74e-242, 5.74e-242j)
| (-2.7347858162973228943e-801 - 7.1679533537500968932e-801j)  +/-  (4.22e-799, 4.22e-799j)
| (4.0313299730623968988 + 3.9280376416563560228e-765j)  +/-  (3.17e-245, 3.17e-245j)
| (6.7579906120647499397 - 1.41835228112699732e-761j)  +/-  (1.98e-242, 1.98e-242j)
| (-1.9245570492171148258 + 6.5478898449421329784e-775j)  +/-  (2.4e-249, 2.4e-249j)
| (-3.1719642685210842305 + 2.5972949334337769688e-772j)  +/-  (1.05e-246, 1.05e-246j)
| (2.750378675500735572 - 4.4501095096430137214e-773j)  +/-  (1.76e-247, 1.76e-247j)
| (1.5216468817952859617 - 2.0727204503587932323e-776j)  +/-  (2.43e-250, 2.43e-250j)
| (-2.750378675500735572 + 2.0053813566259730692e-773j)  +/-  (1.64e-247, 1.64e-247j)
| (-0.74196378430272585765 - 7.117650807858623152e-779j)  +/-  (1.61e-252, 1.61e-252j)
| (-5.8201192414516842273 + 7.3280749649511585875e-769j)  +/-  (4.57e-243, 4.57e-243j)
| (4.4692563797074340503 - 7.2837028946267924982e-770j)  +/-  (1.33e-244, 1.33e-244j)
| (1.1269481594888072442 + 5.6382968017476427007e-777j)  +/-  (2.21e-251, 2.21e-251j)
| (0.74196378430272585765 - 6.8929490498267879254e-778j)  +/-  (1.61e-252, 1.61e-252j)
| (-4.9130393321959841345 + 7.9028230727109977197e-770j)  +/-  (4.65e-244, 4.65e-244j)
| (-0.36728191276458026973 + 4.2503505181235838438e-779j)  +/-  (8.94e-254, 8.94e-254j)
| (6.2847621483050841053 - 6.5687007091287203071e-767j)  +/-  (9.65e-243, 9.65e-243j)
| (0.36728191276458026973 - 3.672466606195145211e-784j)  +/-  (8.94e-254, 8.94e-254j)
| (5.8201192414516842273 + 6.0030896050853161604e-772j)  +/-  (4.46e-243, 4.46e-243j)
-------------------------------------------------
The weights are:
| (3.4634968105756981277e-20 - 5.7430803993635162144e-556j)  +/-  (2.94e-70, 9.25e-191j)
| (2.1242008979154163023e-40 + 1.0974947244014759584e-567j)  +/-  (5.55e-79, 1.75e-199j)
| (2.3563702597871332709e-31 - 9.3256228126041909077e-564j)  +/-  (6.38e-77, 2.01e-197j)
| (3.6344941673094908271e-16 - 8.678306493946121455e-556j)  +/-  (1.84e-69, 5.78e-190j)
| (2.1242008979154163023e-40 - 2.0001639638724730984e-568j)  +/-  (1.9e-80, 5.98e-201j)
| (2.5569268492224240251e-35 - 5.6168070155502675882e-565j)  +/-  (6.9e-79, 2.17e-199j)
| (8.0211315907274814488e-13 - 4.4077639684575655148e-553j)  +/-  (7.42e-68, 2.33e-188j)
| (5.1679791707848623859e-28 + 5.0638024616162528068e-562j)  +/-  (2.97e-76, 9.34e-197j)
| (4.2284251423534780272e-25 + 2.862044600216325684e-559j)  +/-  (2.35e-75, 7.4e-196j)
| (1.0270224795096818556e-07 - 3.7998251369506037473e-551j)  +/-  (2.03e-63, 6.38e-184j)
| (2.5569268492224240251e-35 + 8.3009974581732347754e-566j)  +/-  (5.66e-79, 1.78e-199j)
| (8.0211315907274814488e-13 - 5.4993188619318552848e-554j)  +/-  (3.91e-69, 1.23e-189j)
| (8.087035693122302921e-06 - 4.8878708942169384363e-550j)  +/-  (2.77e-61, 8.73e-182j)
| (3.4634968105756981277e-20 - 6.3539237597589669746e-558j)  +/-  (1.32e-73, 4.14e-194j)
| (0.010802827483325837587 + 5.3803115765345681209e-548j)  +/-  (1.81e-51, 5.68e-172j)
| (1.0270224795096818556e-07 - 1.4138648511686302488e-550j)  +/-  (5.6e-67, 1.76e-187j)
| (0.010802827483325837587 + 8.9838106207075946981e-548j)  +/-  (1.59e-53, 4.99e-174j)
| (2.0315794925915575742e-14 + 8.1625857131906400291e-554j)  +/-  (1.22e-72, 3.82e-193j)
| (0.050021063071589869888 + 1.9309623397947451285e-547j)  +/-  (2.25e-47, 7.06e-168j)
| (5.1679791707848623859e-28 - 5.789975756551281203e-561j)  +/-  (1.15e-79, 3.63e-200j)
| (0.00026390939093280138295 - 9.4995262464535098039e-549j)  +/-  (2.05e-62, 6.44e-183j)
| (4.2284251423534780272e-25 - 1.6720924857834849953e-560j)  +/-  (1.01e-77, 3.17e-198j)
| (5.1347258120871911598e-05 + 1.5030546784733124122e-549j)  +/-  (2.09e-63, 6.58e-184j)
| (4.4163390840273052538e-18 + 2.7657003425303852487e-555j)  +/-  (2.15e-75, 6.75e-196j)
| (1.63649770516564983e-22 - 1.2905071524891948529e-557j)  +/-  (2.94e-77, 9.25e-198j)
| (2.0315794925915575742e-14 + 7.5216892302145934597e-555j)  +/-  (2.46e-73, 7.74e-194j)
| (2.3068741671991718083e-11 + 3.4468950745025600301e-553j)  +/-  (5.46e-72, 1.72e-192j)
| (2.3563702597871332709e-31 + 7.9738332214536322751e-563j)  +/-  (8.98e-83, 2.82e-203j)
| (4.9537141027212688695e-10 - 1.876565540266323491e-552j)  +/-  (1.73e-71, 5.44e-192j)
| (1.0223058583117620957e-06 + 4.6528256819900955458e-550j)  +/-  (1.69e-71, 5.33e-192j)
| (4.4163390840273052538e-18 + 8.2761506504403405906e-557j)  +/-  (3.99e-76, 1.26e-196j)
| (0.025452857441524140212 - 1.6175704511283222015e-547j)  +/-  (9.36e-63, 2.95e-183j)
| (0.001106092811178334554 + 2.1802683326529708914e-548j)  +/-  (1.88e-67, 5.93e-188j)
| (0.00026390939093280138295 - 4.2007746349170288417e-549j)  +/-  (4.74e-68, 1.49e-188j)
| (1.63649770516564983e-22 + 3.7906138837116482377e-559j)  +/-  (1.51e-78, 4.75e-199j)
| (0.08246779985803168488 - 3.2059001688885772738e-547j)  +/-  (8.52e-61, 2.68e-181j)
| (3.6344941673094908271e-16 - 1.4323991139436075427e-554j)  +/-  (1.97e-77, 6.2e-198j)
| (0.14594142450756708733 + 7.1463345789857138989e-547j)  +/-  (1.53e-62, 4.81e-183j)
| (5.1347258120871911598e-05 + 3.8008510957107870235e-549j)  +/-  (4.18e-71, 1.31e-191j)
| (2.3068741671991718083e-11 + 2.1735721319036990601e-552j)  +/-  (5.94e-76, 1.87e-196j)
| (0.025452857441524140212 - 1.0631389187816662844e-547j)  +/-  (2.99e-66, 9.41e-187j)
| (0.001106092811178334554 + 1.0717389741606656932e-548j)  +/-  (1.26e-69, 3.97e-190j)
| (0.0038047044037198630931 - 4.607543926755437405e-548j)  +/-  (2.45e-69, 7.7e-190j)
| (0.050021063071589869888 + 2.6859355689201497051e-547j)  +/-  (3.28e-67, 1.03e-187j)
| (0.0038047044037198630931 - 2.5052250287817052779e-548j)  +/-  (4.05e-69, 1.28e-189j)
| (0.1150418971539559788 + 4.7992454629545963314e-547j)  +/-  (6.07e-67, 1.91e-187j)
| (8.1041464419636617817e-09 + 8.970632956205720907e-552j)  +/-  (3.67e-74, 1.16e-194j)
| (8.087035693122302921e-06 - 1.392208769721466262e-549j)  +/-  (2.19e-73, 6.89e-194j)
| (0.08246779985803168488 - 4.0894185962970025134e-547j)  +/-  (3.72e-69, 1.17e-189j)
| (0.1150418971539559788 + 5.6308948232675104397e-547j)  +/-  (2.48e-69, 7.82e-190j)
| (1.0223058583117620957e-06 + 1.4373391818364877577e-550j)  +/-  (3.02e-73, 9.49e-194j)
| (0.13800756820662829823 - 6.3248920457065223448e-547j)  +/-  (1.24e-69, 3.91e-190j)
| (4.9537141027212688695e-10 - 9.6854941934931522019e-552j)  +/-  (5.9e-77, 1.86e-197j)
| (0.13800756820662829823 - 6.8446954431261286118e-547j)  +/-  (1.14e-70, 3.63e-191j)
| (8.1041464419636617817e-09 + 3.893145525806197831e-551j)  +/-  (2.85e-76, 8.95e-197j)
