Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 49
-------------------------------------------------
Trying to find an order 49 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^53 - 963737155258054627230282435596990792492848/93327259163492604202079550460405149381*t^51 + 4306875066935826918967043397925428137971331092/1399908887452389063031193256906077240715*t^49 - 262389134353322362241935664250115219949218694032/466636295817463021010397752302025746905*t^47 + 1433895292408893970637290030137358993710092919626/20288534600759261783060771839218510735*t^45 - 8779317343114407164644387492789542216789748280686/1352568973383950785537384789281234049*t^43 + 1222205070591677918422504227073544002380274164130377/2705137946767901571074769578562468098*t^41 - 33006219026895689542891620372589491266579960049830157/1352568973383950785537384789281234049*t^39 + 22477533112029903206427642275988625403708835410237449491/21641103574143212568598156628499744784*t^37 - 761552406566188590367505149755086025389683184389536931929/21641103574143212568598156628499744784*t^35 + 82655323607513830610994298773911001871169798890895230693845/86564414296572850274392626513998979136*t^33 - 225181019912039486669053400401035636605767506470689492475265/10820551787071606284299078314249872392*t^31 + 31545500243956613246758681858573408626338140064266793311375665/86564414296572850274392626513998979136*t^29 - 442884349684913704898119104136828919820582822472599829674664545/86564414296572850274392626513998979136*t^27 + 19851174439744035105484867490465732112115498420945050001185066195/346257657186291401097570506055995916544*t^25 - 88155949895383430830676525650385981760222214620317659655081888625/173128828593145700548785253027997958272*t^23 + 19667629618245547729502461417084662909692641806501983691280709820375/5540122514980662417561128096895934664704*t^21 - 106261596929045086919325715240898168703765520743760896644063464517625/5540122514980662417561128096895934664704*t^19 + 1750124560558320119063288391842716850775534581480939435399423876339625/22160490059922649670244512387583738658816*t^17 - 1343462434348921293039921075928007180023173392568161043230428245652125/5540122514980662417561128096895934664704*t^15 + 23921765343547934990831051931646690822356975860154357651090637805731875/44320980119845299340489024775167477317632*t^13 - 37163438076816686163791872521628023123873488295295225153670638297344375/44320980119845299340489024775167477317632*t^11 + 153034711280026041283654822391652502625533951304491246168896743488370625/177283920479381197361956099100669909270528*t^9 - 48436920343532269238904393037870529659902492147112776283172387855060625/88641960239690598680978049550334954635264*t^7 + 268606742965148712233673923894868265805527640153244406185088255580683125/1418271363835049578895648792805359274164224*t^5 - 41565387385311440892199414975030888523975151266968187744689749050784375/1418271363835049578895648792805359274164224*t^3 + 7233185736413139754813855578736257141339775088057493766028685415621875/5673085455340198315582595171221437096656896*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:
| (6.7450257895007975153 + 1.1176867589195784648e-911j)  +/-  (6.58e-243, 6.58e-243j)
| (8.6460915705804805192 - 1.6201339281981247746e-921j)  +/-  (4.64e-245, 4.64e-245j)
| (9.3020162055872870676 + 4.099674114097696787e-923j)  +/-  (2.87e-246, 2.87e-246j)
| (-7.1674367370626199036 - 1.7100108339326398999e-921j)  +/-  (3.09e-243, 3.09e-243j)
| (4.520340560893121218 - 2.2189846585888728129e-918j)  +/-  (3.31e-243, 3.31e-243j)
| (3.8482465548406945677 + 1.0904690478724294745e-923j)  +/-  (5.99e-244, 5.99e-244j)
| (-9.3020162055872870676 + 5.5396869058074135367e-940j)  +/-  (3.07e-246, 3.07e-246j)
| (-2.2557788363423974574 + 3.5043147424214115728e-938j)  +/-  (4.43e-247, 4.43e-247j)
| (7.1674367370626199036 - 3.4575280348363076971e-934j)  +/-  (3.17e-243, 3.17e-243j)
| (6.3426876443889363035 - 2.0927285392699369974e-945j)  +/-  (9.44e-243, 9.44e-243j)
| (-7.61630555719526975 - 1.8257654832805239942e-954j)  +/-  (1.19e-243, 1.19e-243j)
| (-4.8661981626224355492 + 7.9459470738770063911e-954j)  +/-  (5.93e-243, 5.93e-243j)
| (-8.6460915705804805192 + 1.2190350256096409417e-957j)  +/-  (4.99e-245, 4.99e-245j)
| (-1.9506610802335868045 - 1.3550833874077656864e-959j)  +/-  (6.96e-248, 6.96e-248j)
| (2.8794339286506064243 - 6.2598388955500745216e-955j)  +/-  (1.18e-245, 1.18e-245j)
| (-5.2198814683594315175 - 2.135825159209306234e-957j)  +/-  (8.91e-243, 8.91e-243j)
| (3.1977386220845326352 + 2.0990155209305166367e-958j)  +/-  (5.57e-245, 5.57e-245j)
| (-3.1977386220845326352 + 5.5909665690646977007e-966j)  +/-  (5.36e-245, 5.36e-245j)
| (7.61630555719526975 + 7.1715603698191830463e-963j)  +/-  (1.25e-243, 1.25e-243j)
| (-5.9562196866389611214 + 1.7090804809825839566e-971j)  +/-  (1.04e-242, 1.04e-242j)
| (5.5826731168105121712 - 6.5286396567144563518e-977j)  +/-  (1.06e-242, 1.06e-242j)
| (-8.1022883259316117464 + 2.7711595535265256427e-992j)  +/-  (3.02e-244, 3.02e-244j)
| (-4.1812931866013965548 + 1.0551943015551378044e-990j)  +/-  (1.44e-243, 1.44e-243j)
| (-6.3426876443889363035 - 5.6149145008257245721e-990j)  +/-  (9.51e-243, 9.51e-243j)
| (-4.520340560893121218 + 3.7233039053402796757e-991j)  +/-  (3.02e-243, 3.02e-243j)
| (-5.5826731168105121712 + 1.7771613827827943784e-990j)  +/-  (1.02e-242, 1.02e-242j)
| (8.1022883259316117464 + 4.3946571020860969895e-990j)  +/-  (3.24e-244, 3.24e-244j)
| (2.2557788363423974574 - 3.4323813032175578036e-997j)  +/-  (4.92e-247, 4.92e-247j)
| (5.2198814683594315175 + 1.9026574423792108394e-996j)  +/-  (8.52e-243, 8.52e-243j)
| (5.9562196866389611214 - 1.0546635462102221618e-1005j)  +/-  (1.12e-242, 1.12e-242j)
| (-3.5205594462629314874 + 5.4192635521528002849e-1011j)  +/-  (1.97e-244, 1.97e-244j)
| (1.9506610802335868045 + 5.5091495436808552371e-1014j)  +/-  (7.26e-248, 7.26e-248j)
| (1.070669871450030807 + 1.2848942414655505968e-1017j)  +/-  (1.47e-250, 1.47e-250j)
| (-6.7450257895007975153 + 3.5013464809387436552e-1010j)  +/-  (6.46e-243, 6.46e-243j)
| (3.5205594462629314874 - 9.3322112054103863111e-1009j)  +/-  (1.96e-244, 1.96e-244j)
| (-2.5654499758287597519 + 5.3728773281260765496e-1020j)  +/-  (2.52e-246, 2.52e-246j)
| (2.5654499758287597519 - 2.2157830487861180191e-1017j)  +/-  (2.51e-246, 2.51e-246j)
| (0.79338579548345291729 - 1.1157486647325631665e-1023j)  +/-  (1.31e-251, 1.31e-251j)
| (4.1812931866013965548 + 5.3188239716998233629e-1016j)  +/-  (1.46e-243, 1.46e-243j)
| (-2.8794339286506064243 + 1.9020706073167900345e-1027j)  +/-  (1.24e-245, 1.24e-245j)
| (-0.52464762327529031788 - 3.3176398752848269885e-1034j)  +/-  (1.25e-252, 1.25e-252j)
| (-1.3568663845742099862 - 6.6336314680612697485e-1031j)  +/-  (1.26e-249, 1.26e-249j)
| (1.3568663845742099862 + 3.0951902608220902688e-1031j)  +/-  (1.41e-249, 1.41e-249j)
| (1.1195725066524466191e-1047 + 1.0157324280404139335e-1047j)  +/-  (8.01e-1046, 8.01e-1046j)
| (-3.8482465548406945677 - 8.6979086927164018736e-1031j)  +/-  (6.04e-244, 6.04e-244j)
| (-1.070669871450030807 - 2.3087219487809365168e-1035j)  +/-  (1.52e-250, 1.52e-250j)
| (-1.6506801238857845559 - 9.650860373121571154e-1034j)  +/-  (1.03e-248, 1.03e-248j)
| (-0.26140025107191685123 - 3.3473170362325469827e-1038j)  +/-  (9.29e-254, 9.29e-254j)
| (0.52464762327529031788 - 7.4337637651417358421e-1037j)  +/-  (1.28e-252, 1.28e-252j)
| (1.6506801238857845559 - 1.4539706317143291446e-1036j)  +/-  (9.69e-249, 9.69e-249j)
| (-0.79338579548345291729 - 5.8746207172413449355e-1041j)  +/-  (1.35e-251, 1.35e-251j)
| (4.8661981626224355492 + 1.7512082871466383965e-1040j)  +/-  (5.61e-243, 5.61e-243j)
| (0.26140025107191685123 + 3.4064157948170090045e-1052j)  +/-  (9.29e-254, 9.29e-254j)
-------------------------------------------------
The weights are:
| (4.0498801509509240194e-21 - 3.1902677966105355246e-931j)  +/-  (3.25e-74, 3.16e-194j)
| (1.1299197638726436439e-33 + 7.6118579050961543185e-939j)  +/-  (4.19e-80, 4.07e-200j)
| (1.127833771588814999e-38 - 1.5437018716109048232e-941j)  +/-  (6.84e-82, 6.65e-202j)
| (1.1983803510927702682e-23 + 1.5269709880562435725e-934j)  +/-  (7.6e-79, 7.39e-199j)
| (2.580402254499405033e-10 - 8.4199046446645999383e-927j)  +/-  (1.58e-67, 1.54e-187j)
| (6.8996990869409669225e-08 - 1.7385478839859049406e-925j)  +/-  (1.69e-64, 1.64e-184j)
| (1.127833771588814999e-38 + 2.4241271819747166112e-942j)  +/-  (2.13e-85, 2.07e-205j)
| (0.0010697661331335677863 + 2.0174789953345497646e-923j)  +/-  (1.19e-56, 1.15e-176j)
| (1.1983803510927702682e-23 - 5.1510725000656085894e-933j)  +/-  (8.75e-77, 8.51e-197j)
| (7.5024064930293209532e-19 + 1.7374891626167048795e-930j)  +/-  (2.05e-74, 1.99e-194j)
| (1.684158526834451477e-26 - 4.9182844113644116278e-936j)  +/-  (2.31e-81, 2.25e-201j)
| (1.0254872399369458009e-11 + 3.618737946248889302e-928j)  +/-  (6.87e-74, 6.68e-194j)
| (1.1299197638726436439e-33 - 9.2480602260490667412e-940j)  +/-  (1.63e-84, 1.58e-204j)
| (0.0038008901901530805617 - 5.0545357312730953645e-923j)  +/-  (2.12e-58, 2.06e-178j)
| (4.4718669054625459203e-05 + 6.0225874298377338967e-924j)  +/-  (3.59e-65, 3.49e-185j)
| (2.9649170716322031498e-13 - 5.2075765360205949339e-929j)  +/-  (2.04e-75, 1.98e-195j)
| (6.5521426164229547694e-06 - 2.0488642124019167014e-924j)  +/-  (6.38e-67, 6.21e-187j)
| (6.5521426164229547694e-06 - 7.5579329652066390917e-925j)  +/-  (2.4e-68, 2.34e-188j)
| (1.684158526834451477e-26 + 8.2786703299344662008e-935j)  +/-  (1.53e-81, 1.49e-201j)
| (8.3843837751171032332e-17 - 6.3702559785004070195e-931j)  +/-  (2.59e-78, 2.52e-198j)
| (6.0503352079870415511e-15 + 7.0797895195201838065e-929j)  +/-  (5.6e-77, 5.45e-197j)
| (8.889276916224599652e-30 + 9.670729811799523394e-938j)  +/-  (6.49e-84, 6.31e-204j)
| (4.8395751078947051434e-09 + 1.1209953390507723673e-926j)  +/-  (5.64e-74, 5.49e-194j)
| (7.5024064930293209532e-19 + 5.1680771736423343507e-932j)  +/-  (7.87e-80, 7.66e-200j)
| (2.580402254499405033e-10 - 2.159152592459778988e-927j)  +/-  (4.45e-75, 4.33e-195j)
| (6.0503352079870415511e-15 + 6.3307098893970819831e-930j)  +/-  (1.29e-77, 1.26e-197j)
| (8.889276916224599652e-30 - 1.0777189006715634739e-936j)  +/-  (1.06e-86, 1.03e-206j)
| (0.0010697661331335677863 + 3.9825896404273133898e-923j)  +/-  (1.26e-71, 1.23e-191j)
| (2.9649170716322031498e-13 - 4.413056578586577663e-928j)  +/-  (5.23e-80, 5.08e-200j)
| (8.3843837751171032332e-17 - 1.068231744800070249e-929j)  +/-  (2.57e-81, 2.5e-201j)
| (7.5990750103930677834e-07 + 2.0785420378906258292e-925j)  +/-  (4.89e-76, 4.75e-196j)
| (0.0038008901901530805617 - 9.0546793110695650733e-923j)  +/-  (3.25e-72, 3.16e-192j)
| (0.050541147840053932189 + 6.5917565961095135055e-922j)  +/-  (1.21e-68, 1.18e-188j)
| (4.0498801509509240194e-21 - 3.2635480884865394242e-933j)  +/-  (2.51e-83, 2.44e-203j)
| (7.5990750103930677834e-07 + 6.3136897608167881651e-925j)  +/-  (1.66e-76, 1.61e-196j)
| (0.00024380310063717123851 - 7.3987164324836839269e-924j)  +/-  (5.22e-75, 5.07e-195j)
| (0.00024380310063717123851 - 1.616129048778646693e-923j)  +/-  (1.06e-74, 1.03e-194j)
| (0.081991672940440443451 - 1.0550269166129592532e-921j)  +/-  (3.31e-72, 3.21e-192j)
| (4.8395751078947051434e-09 + 4.0681311917648644604e-926j)  +/-  (2.44e-78, 2.37e-198j)
| (4.4718669054625459203e-05 + 2.4806107484178366618e-924j)  +/-  (5.33e-76, 5.17e-196j)
| (0.11366726450293089425 + 1.2697218678252658574e-921j)  +/-  (3.57e-73, 3.43e-193j)
| (0.025980692662105567938 - 2.4808727230972513592e-922j)  +/-  (2.77e-74, 2.68e-194j)
| (0.025980692662105567938 - 3.7017575423989439048e-922j)  +/-  (7.15e-74, 6.94e-194j)
| (0.14737236555565977292 + 1.8549649659327516991e-921j)  +/-  (1.86e-73, 1.78e-193j)
| (6.8996990869409669225e-08 - 5.1212311622797604498e-926j)  +/-  (6.65e-78, 6.45e-198j)
| (0.050541147840053932189 + 4.8138375235936161801e-922j)  +/-  (2.19e-74, 2.12e-194j)
| (0.010990070087489034092 + 1.1670533922659359456e-922j)  +/-  (8.42e-75, 8.16e-195j)
| (0.13797640494089063252 - 1.6565170208113550567e-921j)  +/-  (4.47e-74, 4.22e-194j)
| (0.11366726450293089425 + 1.479843744234226881e-921j)  +/-  (1.84e-74, 1.79e-194j)
| (0.010990070087489034092 + 1.9045288859182683931e-922j)  +/-  (6.17e-76, 6.12e-196j)
| (0.081991672940440443451 - 8.3647656848977672138e-922j)  +/-  (7.69e-75, 7.44e-195j)
| (1.0254872399369458009e-11 + 2.5874215339838424191e-927j)  +/-  (5.04e-82, 6.19e-202j)
| (0.13797640494089063252 - 1.7876697464735680876e-921j)  +/-  (1.1e-74, 9.05e-195j)
