Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 50
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^52 - 8049204161305181715573889735897/3136731024047862700526996136*t^50 + 4765126058686701823976988752962225/6273462048095725401053992272*t^48 - 144136923148651368544502394670876175/1045577008015954233508998712*t^46 + 35957598208624648183886552927537181375/2091154016031908467017997424*t^44 - 13100120041879529600004569290939981694175/8364616064127633868071989696*t^42 + 1807222486251823148956998007913334782693175/16729232128255267736143979392*t^40 - 7433904627831144858485744239614780824023875/1286864009865789825857229184*t^38 + 625895841286842455102028693203507898268641375/2573728019731579651714458368*t^36 - 167590447752846455614094331178242740855331725625/20589824157852637213715666944*t^34 + 527769197819744178538748073256360791644964758625/2422332253865016142790078464*t^32 - 2832215901765081210923732811338206671361341727875/605583063466254035697519616*t^30 + 97502809959797929495076420218049903744419248451875/1211166126932508071395039232*t^28 - 5369797836257109139322357667305223125608025662063125/4844664507730032285580156928*t^26 + 117683248951924290935899152973375132205406634614328125/9689329015460064571160313856*t^24 - 1018536385686210072750983741478486922181768024791584375/9689329015460064571160313856*t^22 + 13778960594649971907123850541502757942815415473208865625/19378658030920129142320627712*t^20 - 1149191719050119679478598084671940508169409631441390140625/310058528494722066277130043392*t^18 + 9064249171918055901722041027880892602340247974864894515625/620117056989444132554260086784*t^16 - 13200582208279096622962102635868880345116601182859957109375/310058528494722066277130043392*t^14 + 55005823781296903975004681338736187971116657681443604359375/620117056989444132554260086784*t^12 - 313965133522378915126199858586833528052274617022639110046875/2480468227957776530217040347136*t^10 + 577185084624226277006471700383165392793000172175352614921875/4960936455915553060434080694272*t^8 - 311754897251827411277629755980878970924021931493586109609375/4960936455915553060434080694272*t^6 + 170112339370785136975009917656416227266386044517663707421875/9921872911831106120868161388544*t^4 - 139562753240811016225441188311791773797048046577762652484375/79374983294648848966945291108352*t^2 + 4454525410987242344418186756670152669937134246868005609375/158749966589297697933890582216704
-------------------------------------------------
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:
| (7.6059911106907851538 + 8.3148343691300014728e-954j)  +/-  (1.11e-243, 1.11e-243j)
| (8.0925945573854805598 + 6.73152782654589649e-954j)  +/-  (3.09e-244, 3.09e-244j)
| (-8.0925945573854805598 + 1.5761891142183273928e-953j)  +/-  (2.93e-244, 2.93e-244j)
| (-5.2048036372563151142 + 2.2727849140989275357e-951j)  +/-  (6.66e-243, 6.66e-243j)
| (5.2048036372563151142 + 1.5303635174185124177e-956j)  +/-  (6.6e-243, 6.6e-243j)
| (3.1730211682573385111 + 3.3158418551757415728e-959j)  +/-  (3.4e-245, 3.4e-245j)
| (-7.6059911106907851538 + 8.1700477157887376871e-957j)  +/-  (1.19e-243, 1.19e-243j)
| (-9.293575958183946578 - 5.0236898526333056741e-960j)  +/-  (2.73e-246, 2.73e-246j)
| (8.6370092635421982069 + 2.4145132839290925024e-959j)  +/-  (4.45e-245, 4.45e-245j)
| (6.7333734174089101566 + 2.8095912421418092539e-957j)  +/-  (5.73e-243, 5.73e-243j)
| (9.293575958183946578 + 1.0476611394968807458e-960j)  +/-  (2.79e-246, 2.79e-246j)
| (-5.9430161946989463536 + 4.1852860977941965028e-957j)  +/-  (9.36e-243, 9.36e-243j)
| (-2.2206512219782252773 + 6.427465339072502122e-963j)  +/-  (2.77e-247, 2.77e-247j)
| (0.13915896192634841885 - 1.23991755868021928e-969j)  +/-  (2.44e-254, 2.44e-254j)
| (-3.8277446600718552457 + 2.6371908490827276085e-959j)  +/-  (4.34e-244, 4.34e-244j)
| (7.1564738531917567101 + 6.1311454937221035598e-959j)  +/-  (2.96e-243, 2.96e-243j)
| (-8.6370092635421982069 - 2.475377919160662544e-960j)  +/-  (4.5e-245, 4.5e-245j)
| (6.330292622254254263 - 1.850326096985247948e-958j)  +/-  (8.19e-243, 8.19e-243j)
| (5.5685810184638831138 + 9.7321985412089321088e-959j)  +/-  (8.82e-243, 8.82e-243j)
| (4.5029112539471756927 + 2.3718621026569825948e-959j)  +/-  (2.56e-243, 2.56e-243j)
| (-6.7333734174089101566 + 3.1587697015329044701e-957j)  +/-  (5.34e-243, 5.34e-243j)
| (1.9100688240359040878 + 8.7397694267034770255e-968j)  +/-  (4.26e-248, 4.26e-248j)
| (-7.1564738531917567101 - 4.1692899810163595939e-960j)  +/-  (3.13e-243, 3.13e-243j)
| (-3.1730211682573385111 + 4.049224877965412216e-966j)  +/-  (3.71e-245, 3.71e-245j)
| (-2.8519559718975106864 + 1.4738465208590175322e-966j)  +/-  (9.37e-246, 9.37e-246j)
| (1.2995201293276029699 - 3.9300012808562004354e-972j)  +/-  (6.34e-250, 6.34e-250j)
| (1.000572545989715646 + 1.7327909808922062363e-972j)  +/-  (5e-251, 5e-251j)
| (-6.330292622254254263 - 7.5144061041122271101e-963j)  +/-  (7.79e-243, 7.79e-243j)
| (4.1624384056186294502 + 1.0891087923395328072e-976j)  +/-  (1.08e-243, 1.08e-243j)
| (-1.6029128843130299667 + 3.3927255569566112262e-982j)  +/-  (5.75e-249, 5.75e-249j)
| (-0.13915896192634841885 - 7.2192009020321082092e-988j)  +/-  (2.44e-254, 2.44e-254j)
| (-5.5685810184638831138 + 2.222289281308927978e-977j)  +/-  (9.13e-243, 9.13e-243j)
| (2.5345794496659032793 + 1.2608614594385649795e-996j)  +/-  (1.64e-246, 1.64e-246j)
| (-3.4981300538950969166 + 3.5893049025807854788e-994j)  +/-  (1.36e-244, 1.36e-244j)
| (3.4981300538950969166 + 1.8213801923458567654e-1000j)  +/-  (1.37e-244, 1.37e-244j)
| (-1.2995201293276029699 - 2.3804748610331003434e-1012j)  +/-  (6.28e-250, 6.28e-250j)
| (2.8519559718975106864 + 2.8990147213687510397e-1004j)  +/-  (9.08e-246, 9.08e-246j)
| (3.8277446600718552457 + 3.2969293828700302311e-1007j)  +/-  (4.16e-244, 4.16e-244j)
| (-1.9100688240359040878 - 5.4366013466654074886e-1013j)  +/-  (4.19e-248, 4.19e-248j)
| (-4.5029112539471756927 - 1.6644190399206657425e-1022j)  +/-  (2.51e-243, 2.51e-243j)
| (-0.7071067811865475244 + 1.0113003808108019459e-1055j)  +/-  (4.25e-252, 4.25e-252j)
| (-2.5345794496659032793 - 7.4636486149858269515e-1049j)  +/-  (1.77e-246, 1.77e-246j)
| (-4.8500166487075076394 - 4.6585237013807983941e-1049j)  +/-  (4.47e-243, 4.47e-243j)
| (0.42010764000127503579 - 1.2213206945341048684e-1072j)  +/-  (2.69e-253, 2.69e-253j)
| (4.8500166487075076394 + 1.7407807183373706814e-1061j)  +/-  (4.57e-243, 4.57e-243j)
| (-1.000572545989715646 + 2.6035095816630282564e-1073j)  +/-  (5.51e-251, 5.51e-251j)
| (5.9430161946989463536 + 8.0294952785132021757e-1070j)  +/-  (9.09e-243, 9.09e-243j)
| (2.2206512219782252773 + 1.0003940745859666679e-1075j)  +/-  (2.9e-247, 2.9e-247j)
| (1.6029128843130299667 + 5.1587957518398493926e-1080j)  +/-  (5.97e-249, 5.97e-249j)
| (0.7071067811865475244 - 2.7399748487549697146e-1083j)  +/-  (4.18e-252, 4.18e-252j)
| (-4.1624384056186294502 + 7.8600734918737559757e-1082j)  +/-  (1.12e-243, 1.12e-243j)
| (-0.42010764000127503579 - 9.8729128717464857293e-1094j)  +/-  (2.69e-253, 2.69e-253j)
-------------------------------------------------
The weights are:
| (1.9731549049855903664e-26 - 1.0140301667083193903e-971j)  +/-  (4.43e-77, 2.34e-198j)
| (1.0412787821401903482e-29 + 2.1110749983251314772e-973j)  +/-  (1.79e-78, 9.46e-200j)
| (1.0412787821401903482e-29 + 9.7221595138248852347e-973j)  +/-  (2.69e-80, 1.42e-201j)
| (3.4796576414310975406e-13 + 4.2635548999383100538e-963j)  +/-  (2.41e-71, 1.28e-192j)
| (3.4796576414310975406e-13 - 7.5985237822409505254e-965j)  +/-  (4.43e-71, 2.34e-192j)
| (7.7294513862677136431e-06 - 7.1264412960164369806e-961j)  +/-  (1.71e-61, 9.08e-183j)
| (1.9731549049855903664e-26 - 5.410847214777964537e-971j)  +/-  (3.18e-79, 1.68e-200j)
| (1.3206966388825494374e-38 + 2.1327028441842215737e-977j)  +/-  (5.18e-84, 2.74e-205j)
| (1.3233546445215437649e-33 - 2.1438825874150978647e-975j)  +/-  (7.3e-82, 3.86e-203j)
| (4.7468260301534046879e-21 - 6.0166057267886917855e-969j)  +/-  (2.4e-77, 1.27e-198j)
| (1.3206966388825494374e-38 + 6.0139037503758970696e-978j)  +/-  (3.28e-84, 1.73e-205j)
| (9.832650185311170121e-17 - 1.5827797979892449634e-965j)  +/-  (3.16e-77, 1.67e-198j)
| (0.0012714428050223593251 - 3.5219681958295727177e-959j)  +/-  (1.7e-61, 8.99e-183j)
| (0.15427774570617988208 - 5.5885151150201243454e-958j)  +/-  (1.7e-61, 9.02e-183j)
| (8.1190497935201022392e-08 + 3.7245067607302817137e-961j)  +/-  (2.24e-70, 1.18e-191j)
| (1.404296801423295829e-23 + 2.976839453355399716e-970j)  +/-  (1.24e-78, 6.57e-200j)
| (1.3233546445215437649e-33 - 8.6471556089095871659e-975j)  +/-  (1.33e-84, 7.03e-206j)
| (8.795739386516851203e-19 + 9.004815067099025159e-968j)  +/-  (2.45e-77, 1.3e-198j)
| (7.0978663130471015862e-15 + 9.8144116380127198768e-966j)  +/-  (5.36e-76, 2.84e-197j)
| (3.0316077853383064311e-10 - 2.764784336698041635e-963j)  +/-  (4.62e-74, 2.45e-195j)
| (4.7468260301534046879e-21 - 4.6998716948539997066e-968j)  +/-  (8.61e-82, 4.56e-203j)
| (0.0045371228635318689104 - 3.1642550758584406803e-959j)  +/-  (8.48e-66, 4.49e-187j)
| (1.404296801423295829e-23 + 1.8857510327167243023e-969j)  +/-  (1.15e-82, 6.09e-204j)
| (7.7294513862677136431e-06 + 2.9348300893706484708e-960j)  +/-  (3.34e-73, 1.77e-194j)
| (5.2850318571938121258e-05 - 7.3057488793317803068e-960j)  +/-  (4.85e-72, 2.57e-193j)
| (0.031407389126915366477 - 1.2121532518887353988e-958j)  +/-  (1.48e-64, 7.81e-186j)
| (0.06144871206794869826 + 2.0812638574882847552e-958j)  +/-  (4.2e-64, 2.22e-185j)
| (8.795739386516851203e-19 + 9.231025447513340768e-967j)  +/-  (2.16e-81, 1.14e-202j)
| (5.6898517501397425297e-09 + 1.3380968816711299134e-962j)  +/-  (3.87e-77, 2.05e-198j)
| (0.013194299507443541572 - 1.2223074037210234015e-958j)  +/-  (2.18e-68, 1.15e-189j)
| (0.15427774570617988208 + 5.8954980328438443371e-958j)  +/-  (5.03e-66, 2.66e-187j)
| (7.0978663130471015862e-15 + 2.9077034528710854994e-964j)  +/-  (4.81e-80, 2.55e-201j)
| (0.0002888319162188930527 - 5.7731887159855975152e-960j)  +/-  (2.4e-73, 1.27e-194j)
| (8.9518905820260330513e-07 - 1.0860442992047208928e-960j)  +/-  (1.36e-75, 7.22e-197j)
| (8.9518905820260330513e-07 + 2.1273334363274768591e-961j)  +/-  (2.81e-76, 1.49e-197j)
| (0.031407389126915366477 + 2.0186255251557860016e-958j)  +/-  (9.49e-70, 5.02e-191j)
| (5.2850318571938121258e-05 + 2.1358283225205817151e-960j)  +/-  (7.05e-75, 3.73e-196j)
| (8.1190497935201022392e-08 - 5.6749481593336771018e-962j)  +/-  (3.7e-77, 1.96e-198j)
| (0.0045371228635318689104 + 6.8315687159398624227e-959j)  +/-  (6.02e-73, 3.19e-194j)
| (3.0316077853383064311e-10 + 3.8246900931477435881e-962j)  +/-  (1.82e-80, 9.61e-202j)
| (0.099355115065793465444 + 4.2755024835054230428e-958j)  +/-  (2.08e-72, 1.1e-193j)
| (0.0002888319162188930527 + 1.6724413047252390671e-959j)  +/-  (1e-75, 5.3e-197j)
| (1.2041026389943619913e-11 - 1.4039549425980656041e-962j)  +/-  (5.11e-81, 2.69e-202j)
| (0.13415777878602286334 + 4.5562651510272365682e-958j)  +/-  (3.23e-73, 1.7e-194j)
| (1.2041026389943619913e-11 + 4.9535418897426966538e-964j)  +/-  (7.02e-82, 3.69e-203j)
| (0.06144871206794869826 - 3.0716521175488306521e-958j)  +/-  (5.73e-75, 2.99e-196j)
| (9.832650185311170121e-17 - 1.0478402285341389866e-966j)  +/-  (1.24e-84, 6.55e-206j)
| (0.0012714428050223593251 + 1.4158721792379907345e-959j)  +/-  (1.43e-77, 7.44e-199j)
| (0.013194299507443541572 + 6.4681491087433045857e-959j)  +/-  (5.56e-77, 2.93e-198j)
| (0.099355115065793465444 - 3.2529253275912959098e-958j)  +/-  (4.73e-76, 2.28e-197j)
| (5.6898517501397425297e-09 - 1.2028790406438708878e-961j)  +/-  (2.84e-81, 1.83e-202j)
| (0.13415777878602286334 - 5.3561923394766692203e-958j)  +/-  (4.96e-76, 2.04e-197j)
