Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 49
-------------------------------------------------
Trying to find an order 49 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 120467144407256828403785304449623849061606/93327259163492604202079550460405149381*t^51 + 1076718766733956729741760849481357034492832773/1399908887452389063031193256906077240715*t^49 - 131194567176661181120967832125057609974609347016/466636295817463021010397752302025746905*t^47 + 1433895292408893970637290030137358993710092919626/20288534600759261783060771839218510735*t^45 - 17558634686228814329288774985579084433579496561372/1352568973383950785537384789281234049*t^43 + 2444410141183355836845008454147088004760548328260754/1352568973383950785537384789281234049*t^41 - 264049752215165516343132962980715930132639680398641256/1352568973383950785537384789281234049*t^39 + 22477533112029903206427642275988625403708835410237449491/1352568973383950785537384789281234049*t^37 - 1523104813132377180735010299510172050779366368779073863858/1352568973383950785537384789281234049*t^35 + 82655323607513830610994298773911001871169798890895230693845/1352568973383950785537384789281234049*t^33 - 3602896318592631786704854406416570185692280103531031879604240/1352568973383950785537384789281234049*t^31 + 126182000975826452987034727434293634505352560257067173245502660/1352568973383950785537384789281234049*t^29 - 3543074797479309639184952833094631358564662579780798637397316360/1352568973383950785537384789281234049*t^27 + 79404697758976140421939469961862928448461993683780200004740264780/1352568973383950785537384789281234049*t^25 - 1410495198326134893290824410406175708163555433925082554481310218000/1352568973383950785537384789281234049*t^23 + 19667629618245547729502461417084662909692641806501983691280709820375/1352568973383950785537384789281234049*t^21 - 212523193858090173838651430481796337407531041487521793288126929035250/1352568973383950785537384789281234049*t^19 + 1750124560558320119063288391842716850775534581480939435399423876339625/1352568973383950785537384789281234049*t^17 - 10747699474791370344319368607424057440185387140545288345843425965217000/1352568973383950785537384789281234049*t^15 + 47843530687095869981662103863293381644713951720308715302181275611463750/1352568973383950785537384789281234049*t^13 - 148653752307266744655167490086512092495493953181180900614682553189377500/1352568973383950785537384789281234049*t^11 + 306069422560052082567309644783305005251067902608982492337793486976741250/1352568973383950785537384789281234049*t^9 - 387495362748258153911235144302964237279219937176902210265379102840485000/1352568973383950785537384789281234049*t^7 + 268606742965148712233673923894868265805527640153244406185088255580683125/1352568973383950785537384789281234049*t^5 - 83130774770622881784398829950061777047950302533936375489379498101568750/1352568973383950785537384789281234049*t^3 + 7233185736413139754813855578736257141339775088057493766028685415621875/1352568973383950785537384789281234049*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:   53 out of 53
Indefinite weights: 0 out of 53
Negative weights:   0 out of 53
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.9132415327499114814 - 5.1245585894851818455e-599j)  +/-  (2.02e-243, 2.02e-243j)
| (-13.155037475355857736 - 3.3513586792412305848e-612j)  +/-  (4.19e-246, 4.19e-246j)
| (-11.458366036789685275 - 2.1384913755044952465e-609j)  +/-  (4.43e-244, 4.43e-244j)
| (9.5389069500683207821 + 1.3840111707875332405e-622j)  +/-  (8.61e-243, 8.61e-243j)
| (-9.5389069500683207821 + 1.1989148066698047988e-638j)  +/-  (8.45e-243, 8.45e-243j)
| (10.13628624100512027 + 1.1480362901781853295e-651j)  +/-  (4.65e-243, 4.65e-243j)
| (7.3820271665338938738 + 3.0775900070318861045e-678j)  +/-  (1.22e-242, 1.22e-242j)
| (-10.771082614163123056 - 9.2126540122726270899e-692j)  +/-  (1.75e-243, 1.75e-243j)
| (-10.13628624100512027 - 3.7270070950692330185e-693j)  +/-  (4.65e-243, 4.65e-243j)
| (7.8950920360891041956 - 2.8792464175498937991e-700j)  +/-  (1.41e-242, 1.41e-242j)
| (11.458366036789685275 + 7.447899718633149542e-715j)  +/-  (4.58e-244, 4.58e-244j)
| (2.3344142183389772393 - 3.2878787546600756737e-729j)  +/-  (1.52e-248, 1.52e-248j)
| (13.155037475355857736 - 4.9724669864748604222e-722j)  +/-  (4.38e-246, 4.38e-246j)
| (-2.3344142183389772393 - 3.7096518743257744309e-736j)  +/-  (1.54e-248, 1.54e-248j)
| (-5.9132415327499114814 - 2.3031852490934935928e-733j)  +/-  (2.13e-243, 2.13e-243j)
| (12.227419960634609719 + 4.8032970137090648356e-730j)  +/-  (6.84e-245, 6.84e-245j)
| (-8.9699148885910922794 + 1.6254756922944829438e-736j)  +/-  (1.36e-242, 1.36e-242j)
| (-6.3927269277602555412 + 7.8941899658451836664e-739j)  +/-  (4.43e-243, 4.43e-243j)
| (8.9699148885910922794 + 9.9494962177329633137e-740j)  +/-  (1.34e-242, 1.34e-242j)
| (8.4233666613184450901 + 1.8989387868341048698e-755j)  +/-  (1.64e-242, 1.64e-242j)
| (4.072134513854930507 - 1.1726229372113847965e-768j)  +/-  (1.73e-245, 1.73e-245j)
| (1.1220169521668657743 - 8.431438059553697982e-776j)  +/-  (1.95e-251, 1.95e-251j)
| (-3.1901530240696168749 + 5.5442129892584115864e-772j)  +/-  (6.93e-247, 6.93e-247j)
| (-4.5222853282761992104 - 1.4947150056300389787e-769j)  +/-  (6.8e-245, 6.8e-245j)
| (6.8818434387756842801 + 1.7357887356044305098e-766j)  +/-  (8e-243, 8e-243j)
| (-6.8818434387756842801 + 3.2590632773461243228e-778j)  +/-  (7.61e-243, 7.61e-243j)
| (3.1901530240696168749 - 4.5012332149108160602e-782j)  +/-  (6.7e-247, 6.7e-247j)
| (6.3927269277602555412 - 1.1933771806125833975e-780j)  +/-  (4.39e-243, 4.39e-243j)
| (-8.4233666613184450901 - 2.648089369244101981e-789j)  +/-  (1.43e-242, 1.43e-242j)
| (-5.7834354724525954318e-820 - 1.8329928546536318376e-819j)  +/-  (1.02e-817, 1.02e-817j)
| (-12.227419960634609719 + 1.4181936595495294383e-794j)  +/-  (7.13e-245, 7.13e-245j)
| (-4.9788229160457512258 + 1.3818973482825735983e-797j)  +/-  (2.6e-244, 2.6e-244j)
| (-2.7586513552596905778 + 1.0719789277843072261e-808j)  +/-  (1.09e-247, 1.09e-247j)
| (5.4422424692112487433 + 1.8419913613565548897e-802j)  +/-  (8.03e-244, 8.03e-244j)
| (10.771082614163123056 + 9.7326189609476582517e-823j)  +/-  (1.79e-243, 1.79e-243j)
| (-7.8950920360891041956 - 6.8738531365006564394e-832j)  +/-  (1.46e-242, 1.46e-242j)
| (1.5141558530288918005 + 7.548679482433400967e-840j)  +/-  (2e-250, 2e-250j)
| (3.6280941494067609147 - 1.2984436730154764949e-834j)  +/-  (3.7e-246, 3.7e-246j)
| (-7.3820271665338938738 + 5.4534982700740308694e-832j)  +/-  (1.15e-242, 1.15e-242j)
| (-5.4422424692112487433 - 5.4912838645495386869e-834j)  +/-  (7.73e-244, 7.73e-244j)
| (-0.36967578027363698777 + 1.3041362450439214677e-842j)  +/-  (1.33e-253, 1.33e-253j)
| (-3.6280941494067609147 - 2.6582616349636731422e-837j)  +/-  (3.51e-246, 3.51e-246j)
| (2.7586513552596905778 - 4.7159110665425764933e-838j)  +/-  (1.05e-247, 1.05e-247j)
| (0.74196378430272585765 + 1.3849773025068244083e-841j)  +/-  (1.57e-252, 1.57e-252j)
| (-4.072134513854930507 - 3.4927138436472975906e-835j)  +/-  (1.72e-245, 1.72e-245j)
| (-1.5141558530288918005 + 1.6510661640285275134e-840j)  +/-  (2.12e-250, 2.12e-250j)
| (-1.1220169521668657743 - 1.6791637847396211025e-841j)  +/-  (1.95e-251, 1.95e-251j)
| (1.9188988433929954878 - 1.9714286111616179041e-838j)  +/-  (1.82e-249, 1.82e-249j)
| (0.36967578027363698777 - 1.4937389002720288783e-842j)  +/-  (1.08e-253, 1.08e-253j)
| (4.5222853282761992104 - 1.6292255345830073573e-831j)  +/-  (7.36e-245, 7.36e-245j)
| (-1.9188988433929954878 - 1.7643589333085641097e-840j)  +/-  (1.62e-249, 1.62e-249j)
| (-0.74196378430272585765 + 3.0114299841007415579e-844j)  +/-  (1.88e-252, 1.88e-252j)
| (4.9788229160457512258 + 4.9493353786501554648e-833j)  +/-  (2.62e-244, 2.62e-244j)
-------------------------------------------------
The weights are:
| (4.8395751078947051434e-09 + 8.1428600843936701971e-607j)  +/-  (2.83e-59, 1.61e-179j)
| (1.127833771588814999e-38 + 4.1215212403076345136e-624j)  +/-  (1.24e-77, 7.02e-198j)
| (8.889276916224599652e-30 + 1.6704823106456880616e-619j)  +/-  (1.18e-74, 6.7e-195j)
| (4.0498801509509240194e-21 + 2.4553161123021270389e-614j)  +/-  (9.37e-72, 5.32e-192j)
| (4.0498801509509240194e-21 - 5.7611112958544977518e-615j)  +/-  (1.45e-71, 8.22e-192j)
| (1.1983803510927702682e-23 - 1.0170159284672134801e-615j)  +/-  (2.79e-73, 1.59e-193j)
| (2.9649170716322031498e-13 + 8.5840837699090143208e-610j)  +/-  (7.03e-67, 3.99e-187j)
| (1.684158526834451477e-26 - 8.5574919442983796425e-618j)  +/-  (3.42e-74, 1.94e-194j)
| (1.1983803510927702682e-23 + 2.6760312175339883053e-616j)  +/-  (4.97e-73, 2.82e-193j)
| (6.0503352079870415511e-15 - 7.9668585161316731621e-611j)  +/-  (4.52e-69, 2.57e-189j)
| (8.889276916224599652e-30 - 5.2332392412926938109e-619j)  +/-  (7.56e-78, 4.29e-198j)
| (0.010990070087489034092 + 5.5573344201761518373e-604j)  +/-  (1.11e-50, 6.29e-171j)
| (1.127833771588814999e-38 - 1.0852324143193069214e-623j)  +/-  (6.5e-82, 3.69e-202j)
| (0.010990070087489034092 + 2.4114416045573522308e-604j)  +/-  (1.13e-52, 6.41e-173j)
| (4.8395751078947051434e-09 + 2.0970466072850487681e-608j)  +/-  (1.42e-68, 8.09e-189j)
| (1.1299197638726436439e-33 + 4.5551680982403185119e-621j)  +/-  (5.52e-80, 3.13e-200j)
| (7.5024064930293209532e-19 + 9.1910244786548738836e-614j)  +/-  (9.99e-75, 5.67e-195j)
| (2.580402254499405033e-10 - 4.0012975561925118542e-609j)  +/-  (5.23e-70, 2.97e-190j)
| (7.5024064930293209532e-19 - 4.4751741211337359996e-613j)  +/-  (8.12e-74, 4.61e-194j)
| (8.3843837751171032332e-17 + 6.5200538593298587563e-612j)  +/-  (7.41e-73, 4.21e-193j)
| (4.4718669054625459203e-05 + 2.6284644746298240476e-605j)  +/-  (2.02e-65, 1.15e-185j)
| (0.081991672940440443451 - 2.6751183877668420325e-603j)  +/-  (3.29e-49, 1.87e-169j)
| (0.0010697661331335677863 + 4.0459123568547854938e-605j)  +/-  (2.65e-63, 1.51e-183j)
| (6.5521426164229547694e-06 - 1.4592008602869912491e-606j)  +/-  (4.07e-68, 2.31e-188j)
| (1.0254872399369458009e-11 - 8.779810265862077239e-609j)  +/-  (2.89e-71, 1.64e-191j)
| (1.0254872399369458009e-11 + 6.6464122567250768267e-610j)  +/-  (1.23e-73, 6.96e-194j)
| (0.0010697661331335677863 + 1.3525647957954401567e-604j)  +/-  (1.6e-64, 9.09e-185j)
| (2.580402254499405033e-10 + 1.0269309981080694869e-607j)  +/-  (7.8e-71, 4.43e-191j)
| (8.3843837751171032332e-17 - 1.1415636676669084171e-612j)  +/-  (6.44e-77, 3.66e-197j)
| (0.14737236555565977292 + 4.3082857592296712045e-603j)  +/-  (8.47e-57, 4.81e-177j)
| (1.1299197638726436439e-33 - 1.5855069095350504363e-621j)  +/-  (1.35e-84, 7.67e-205j)
| (7.5990750103930677834e-07 + 3.9685622543131998365e-607j)  +/-  (3.33e-71, 1.89e-191j)
| (0.0038008901901530805617 - 1.0283935003404263295e-604j)  +/-  (6.36e-66, 3.61e-186j)
| (6.8996990869409669225e-08 - 2.3327840422875119131e-606j)  +/-  (6.49e-72, 3.69e-192j)
| (1.684158526834451477e-26 + 2.9390827548795764751e-617j)  +/-  (5.85e-81, 3.32e-201j)
| (6.0503352079870415511e-15 + 1.143448808034206301e-611j)  +/-  (1.02e-76, 5.79e-197j)
| (0.050541147840053932189 + 1.7375587096268590451e-603j)  +/-  (6.79e-65, 3.85e-185j)
| (0.00024380310063717123851 - 6.1121863479099489069e-605j)  +/-  (3.51e-70, 1.99e-190j)
| (2.9649170716322031498e-13 - 9.4832073014965020681e-611j)  +/-  (5.75e-76, 3.26e-196j)
| (6.8996990869409669225e-08 - 9.6758456016986637638e-608j)  +/-  (2.11e-73, 1.2e-193j)
| (0.13797640494089063252 - 3.7589396825511460518e-603j)  +/-  (7.18e-66, 4.07e-186j)
| (0.00024380310063717123851 - 1.4638670207937874247e-605j)  +/-  (9.13e-72, 5.18e-192j)
| (0.0038008901901530805617 - 2.8270291162741976018e-604j)  +/-  (2.41e-71, 1.37e-191j)
| (0.11366726450293089425 + 3.6300324957496297858e-603j)  +/-  (3.16e-68, 1.79e-188j)
| (4.4718669054625459203e-05 + 4.8463717045513748828e-606j)  +/-  (2.34e-72, 1.33e-192j)
| (0.050541147840053932189 + 1.0291181742650987125e-603j)  +/-  (5e-70, 2.84e-190j)
| (0.081991672940440443451 - 1.8218368241788630468e-603j)  +/-  (2.46e-69, 1.39e-189j)
| (0.025980692662105567938 - 1.0218560569353825758e-603j)  +/-  (1.22e-70, 6.93e-191j)
| (0.13797640494089063252 - 4.2602736694450191717e-603j)  +/-  (4.28e-69, 2.43e-189j)
| (6.5521426164229547694e-06 - 1.0947526402471352361e-605j)  +/-  (4.87e-75, 2.76e-195j)
| (0.025980692662105567938 - 5.211402087515975006e-604j)  +/-  (3.74e-72, 2.43e-192j)
| (0.11366726450293089425 + 2.8206351836074830907e-603j)  +/-  (2.72e-71, 1.92e-191j)
| (7.5990750103930677834e-07 + 4.6259604710682476927e-606j)  +/-  (1.17e-75, 6.54e-196j)
