Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 47
-------------------------------------------------
Trying to find an order 47 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^51 - 3014525145094298207101964693489854303256/317748388298858572428944674243562367*t^49 + 11783793547728040261636497203629411895721224/4554393565616972871481540330824393927*t^47 - 1963721031222598294440174360825801831879620420/4554393565616972871481540330824393927*t^45 + 6790190608767327850241624561592601349173503520/138011926230817359741864858509830119*t^43 - 4368095018512056958028749384082758395645002960/1069859893262150075518332236510311*t^41 + 546619172824827397902853550243110762188469529035/2139719786524300151036664473020622*t^39 - 52773327954335769299301087908427187600802843542355/4279439573048600302073328946041244*t^37 + 7979213950661897191165809599013906222401489040541575/17117758292194401208293315784164976*t^35 - 476769836949434110547906499296541061656270694625979675/34235516584388802416586631568329952*t^33 + 5658415198801776874644156613931181482550273562911590925/17117758292194401208293315784164976*t^31 - 213830423070971844518420188688304005891578480652749574925/34235516584388802416586631568329952*t^29 + 110797697935337355277698673490419859386170714804949311675/1180535054634096635054711433390688*t^27 - 2638473161952043704514160637317870730341614325301546288375/2361070109268193270109422866781376*t^25 + 98941504991211938023457457045873928865887549156480732479375/9444280437072773080437691467125504*t^23 - 1447177137340147784488980797632061301007186787114311106814375/18888560874145546160875382934251008*t^21 + 65222347617998821284012137170898757092865908281506615135635625/151108486993164369287003063474008064*t^19 - 556749307831863080848805347709430861476545790676800025452713125/302216973986328738574006126948016128*t^17 + 1761596249302844119964593661167053750323476390538363487762965625/302216973986328738574006126948016128*t^15 - 8032016274015480447472477200278170894491607692494940144620615625/604433947972657477148012253896032256*t^13 + 6351150061328809054864871602428965793122499768977043273785615625/302216973986328738574006126948016128*t^11 - 13230279648957581797547498833892946551325189634450519190607178125/604433947972657477148012253896032256*t^9 + 67413422480775365669142920103706968649990736914040021014723996875/4835471583781259817184098031168258048*t^7 - 46859713574576368507136286430629360705128931164866683315417421875/9670943167562519634368196062336516096*t^5 + 29160749845685108583966455882163671562427420289832882376140140625/38683772670250078537472784249346064384*t^3 - 2595094446405392360052261328293793297238694020944356318651328125/77367545340500157074945568498692128768*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
-------------------------------------------------
The nodes are:
| (-7.3904287793485429616 - 2.8478403251328846715e-972j)  +/-  (4.77e-244, 4.77e-244j)
| (-6.510714400738752897 + 9.4244729081824962607e-989j)  +/-  (2.34e-243, 2.34e-243j)
| (8.429222547274105924 - 8.8342338412557081576e-1001j)  +/-  (1.93e-245, 1.93e-245j)
| (-3.2455755843691540389 + 7.1554589014356879049e-1000j)  +/-  (2.92e-245, 2.92e-245j)
| (7.8807813849671529634 + 7.7081877063138390099e-1000j)  +/-  (1.17e-244, 1.17e-244j)
| (-8.429222547274105924 - 7.7365399149600876042e-1000j)  +/-  (2.01e-245, 2.01e-245j)
| (7.3904287793485429616 + 4.6599481404002525055e-1000j)  +/-  (4.99e-244, 4.99e-244j)
| (-9.0904211727197229022 + 4.0657898632188744149e-1003j)  +/-  (1.3e-246, 1.3e-246j)
| (-3.5782822159072722414 - 4.9210399965018943704e-999j)  +/-  (9.82e-245, 9.82e-245j)
| (4.6103899308327623637 - 4.300519510646247512e-1004j)  +/-  (1.37e-243, 1.37e-243j)
| (1.3486411374553316129 + 1.0955420912855329948e-1011j)  +/-  (9.55e-250, 9.55e-250j)
| (9.0904211727197229022 + 3.1264615445110452119e-1009j)  +/-  (1.36e-246, 1.36e-246j)
| (-1.3486411374553316129 - 1.0699762773433644711e-1011j)  +/-  (1.06e-249, 1.06e-249j)
| (-4.6103899308327623637 + 7.7581352860364713841e-1004j)  +/-  (1.29e-243, 1.29e-243j)
| (-6.9373168436895023286 + 8.6454423925895363583e-1015j)  +/-  (1.25e-243, 1.25e-243j)
| (0.78349118720866437668 - 1.1841751874798529815e-1031j)  +/-  (1.16e-251, 1.16e-251j)
| (6.9373168436895023286 + 2.7357430110530581191e-1022j)  +/-  (1.09e-243, 1.09e-243j)
| (-7.8807813849671529634 - 7.7998057520180907317e-1025j)  +/-  (1.16e-244, 1.16e-244j)
| (6.510714400738752897 + 3.3124377579458391835e-1027j)  +/-  (2.16e-243, 2.16e-243j)
| (-6.1041886003377185205 - 1.368101243284726826e-1027j)  +/-  (3.02e-243, 3.02e-243j)
| (-2.9175871801944237294 - 1.9044229358088993233e-1039j)  +/-  (8.04e-246, 8.04e-246j)
| (-5.7135024145822619273 + 1.8858029224969829092e-1036j)  +/-  (3.22e-243, 3.22e-243j)
| (3.5782822159072722414 - 6.3930600895269758068e-1045j)  +/-  (9.78e-245, 9.78e-245j)
| (2.2747352094415623406 - 1.8300132777957693312e-1047j)  +/-  (3.39e-247, 3.39e-247j)
| (-1.9600196942258714251 - 4.1464707098972037853e-1048j)  +/-  (5.02e-248, 5.02e-248j)
| (6.1041886003377185205 + 4.0654523945332892391e-1042j)  +/-  (3.09e-243, 3.09e-243j)
| (3.2455755843691540389 - 3.7437816224825276727e-1046j)  +/-  (3.03e-245, 3.03e-245j)
| (2.5940045461779365993 - 2.4928297641950615873e-1048j)  +/-  (1.7e-246, 1.7e-246j)
| (3.9161926068782674229 - 6.9814822427945992375e-1045j)  +/-  (2.93e-244, 2.93e-244j)
| (-2.2747352094415623406 - 3.8380803785791994359e-1048j)  +/-  (3.37e-247, 3.37e-247j)
| (1.6506801238857845559 + 1.883159287954125016e-1050j)  +/-  (7.45e-249, 7.45e-249j)
| (5.3356798436058161552 - 2.8911290841066255551e-1043j)  +/-  (2.98e-243, 2.98e-243j)
| (1.9600196942258714251 - 1.3994662557687831227e-1049j)  +/-  (5.35e-248, 5.35e-248j)
| (1.226174902402299113e-1073 + 6.023230758025729407e-1073j)  +/-  (3.13e-1071, 3.13e-1071j)
| (-1.0577797832063331739 + 4.2836981209198976591e-1052j)  +/-  (1.14e-250, 1.14e-250j)
| (-3.9161926068782674229 - 2.8968309146292042303e-1044j)  +/-  (3.03e-244, 3.03e-244j)
| (-5.3356798436058161552 + 3.6712651674052412547e-1047j)  +/-  (3.07e-243, 3.07e-243j)
| (0.52464762327529031788 + 1.5404891134027084455e-1067j)  +/-  (1.18e-252, 1.18e-252j)
| (5.7135024145822619273 + 2.3706670597759914857e-1057j)  +/-  (3.54e-243, 3.54e-243j)
| (4.9685313686562811147 + 8.187104509390885532e-1059j)  +/-  (2.33e-243, 2.33e-243j)
| (-1.6506801238857845559 - 3.7961141822136551431e-1066j)  +/-  (6.75e-249, 6.75e-249j)
| (-2.5940045461779365993 + 1.0247555814885231941e-1062j)  +/-  (1.68e-246, 1.68e-246j)
| (-4.9685313686562811147 + 1.7548592955048589435e-1061j)  +/-  (2.12e-243, 2.12e-243j)
| (0.26628283679330702554 + 7.0564106203854773814e-1085j)  +/-  (8.53e-254, 8.53e-254j)
| (-4.2599543267468891547 + 3.983387969669817315e-1075j)  +/-  (6.96e-244, 6.96e-244j)
| (-0.78349118720866437668 - 2.8217074205304176684e-1093j)  +/-  (1.29e-251, 1.29e-251j)
| (-0.26628283679330702554 - 1.9047200278961733603e-1094j)  +/-  (8.53e-254, 8.53e-254j)
| (2.9175871801944237294 + 1.0433274796056104703e-1091j)  +/-  (7.18e-246, 7.18e-246j)
| (1.0577797832063331739 - 1.5807580424471042952e-1098j)  +/-  (1.28e-250, 1.28e-250j)
| (4.2599543267468891547 + 1.3466876187358028547e-1098j)  +/-  (7.74e-244, 7.74e-244j)
| (-0.52464762327529031788 - 1.4690796853780123992e-1111j)  +/-  (1.04e-252, 1.04e-252j)
-------------------------------------------------
The weights are:
| (5.0406549914652865442e-25 - 1.0997531781252884994e-995j)  +/-  (6.72e-79, 8.88e-199j)
| (9.1356668809122989735e-20 - 8.9516476836876952811e-994j)  +/-  (3.32e-76, 4.38e-196j)
| (4.6224874069092227697e-32 - 2.1121960157655903647e-1001j)  +/-  (2.76e-83, 3.64e-203j)
| (4.9608187306766727643e-06 + 5.6340552835455666994e-987j)  +/-  (1.28e-63, 1.69e-183j)
| (3.0918330597268383597e-28 + 2.047288626232732985e-999j)  +/-  (5.25e-82, 6.94e-202j)
| (4.6224874069092227697e-32 + 3.2166350564097484911e-1000j)  +/-  (3.72e-83, 4.91e-203j)
| (5.0406549914652865442e-25 - 9.7118725978997975837e-998j)  +/-  (2.97e-81, 3.92e-201j)
| (5.5690438658536513791e-37 - 5.8658183342075666403e-1003j)  +/-  (3.57e-85, 4.72e-205j)
| (5.1999105739924506002e-07 - 1.6318864361601174992e-987j)  +/-  (1.34e-67, 1.77e-187j)
| (1.1730475600976656707e-10 + 4.69026005969898821e-990j)  +/-  (3.02e-74, 3.99e-194j)
| (0.027208957752314274887 + 1.0978553956963132179e-984j)  +/-  (5.97e-53, 7.89e-173j)
| (5.5690438658536513791e-37 + 6.050565703863233037e-1004j)  +/-  (4.8e-86, 6.34e-206j)
| (0.027208957752314274887 + 1.5879795236437800003e-984j)  +/-  (1.59e-53, 2.1e-173j)
| (1.1730475600976656707e-10 + 2.0246825223360529043e-989j)  +/-  (2.25e-73, 2.97e-193j)
| (3.1074787396106424831e-22 + 8.9275053069767129643e-995j)  +/-  (9.34e-80, 1.23e-199j)
| (0.080947564761231225677 + 4.5125395157306568046e-984j)  +/-  (1.79e-56, 2.36e-176j)
| (3.1074787396106424831e-22 + 2.8233047380085669766e-996j)  +/-  (9.95e-82, 1.31e-201j)
| (3.0918330597268383597e-28 - 6.375937339778440442e-998j)  +/-  (1.58e-82, 2.09e-202j)
| (9.1356668809122989735e-20 - 5.6649248752936443573e-995j)  +/-  (2.32e-81, 3.07e-201j)
| (1.4758360778158692953e-17 + 8.8530156583333497975e-993j)  +/-  (1.45e-78, 1.92e-198j)
| (3.6936632781150751362e-05 - 1.7622329216870323294e-986j)  +/-  (7.79e-70, 1.03e-189j)
| (1.4401677491096192118e-15 - 7.6569719198483223024e-992j)  +/-  (4.83e-78, 6.38e-198j)
| (5.1999105739924506002e-07 - 5.6715782485516580073e-988j)  +/-  (4.63e-76, 6.11e-196j)
| (0.0010124118828583632721 - 7.0047631948190710535e-986j)  +/-  (9.22e-71, 1.22e-190j)
| (0.0037799354816876385794 + 3.2311982982662428081e-985j)  +/-  (4.7e-68, 6.21e-188j)
| (1.4758360778158692953e-17 + 8.4382566209708429606e-994j)  +/-  (9.59e-83, 1.27e-202j)
| (4.9608187306766727643e-06 + 2.1955925593971688493e-987j)  +/-  (2.43e-75, 3.21e-195j)
| (0.00021687471903402849967 + 2.4178704184053313637e-986j)  +/-  (3.69e-73, 4.88e-193j)
| (4.1998145335218049325e-08 + 1.3055396234403221656e-988j)  +/-  (9.64e-78, 1.27e-197j)
| (0.0010124118828583632721 - 1.3234214296732900902e-985j)  +/-  (1.62e-72, 2.13e-192j)
| (0.011324142113317128083 - 4.6893276897458751616e-985j)  +/-  (3.73e-70, 4.93e-190j)
| (9.0788204304049869292e-14 + 9.1860454486473379582e-992j)  +/-  (2.51e-82, 3.32e-202j)
| (0.0037799354816876385794 + 1.87656545505034106e-985j)  +/-  (7.1e-72, 9.38e-192j)
| (0.15134519716875011177 - 9.4791642916766635181e-984j)  +/-  (6.07e-69, 8.02e-189j)
| (0.052227135045083344473 - 3.1719011174320629742e-984j)  +/-  (2.68e-69, 3.54e-189j)
| (4.1998145335218049325e-08 + 4.2487733977109452666e-988j)  +/-  (4.25e-79, 5.61e-199j)
| (9.0788204304049869292e-14 + 5.6893866769481532749e-991j)  +/-  (9.57e-83, 1.26e-202j)
| (0.10952560042968894515 - 6.9646813897044475698e-984j)  +/-  (6.85e-71, 9.05e-191j)
| (1.4401677491096192118e-15 - 9.7987221518805893898e-993j)  +/-  (2.23e-83, 2.94e-203j)
| (3.885881721843316001e-12 - 7.1369896749671029749e-991j)  +/-  (9.53e-82, 1.26e-201j)
| (0.011324142113317128083 - 7.3865120009382166618e-985j)  +/-  (9e-75, 1.19e-194j)
| (0.00021687471903402849967 + 5.0331381897744915461e-986j)  +/-  (4.05e-77, 5.35e-197j)
| (3.885881721843316001e-12 - 3.6420110356543797217e-990j)  +/-  (5.82e-83, 7.67e-203j)
| (0.13804231709533451991 + 8.7167680756228191995e-984j)  +/-  (5.47e-75, 6.77e-195j)
| (2.5730780327457904226e-09 - 9.8637737675834477126e-989j)  +/-  (2.35e-81, 3.11e-201j)
| (0.080947564761231225677 + 5.582788747905018955e-984j)  +/-  (3.31e-76, 4.07e-196j)
| (0.13804231709533451991 + 9.3683902488804467332e-984j)  +/-  (4.5e-76, 5.79e-196j)
| (3.6936632781150751362e-05 - 7.6466594060940436099e-987j)  +/-  (3.99e-80, 5.57e-200j)
| (0.052227135045083344473 - 2.3776089662604187134e-984j)  +/-  (3.66e-77, 4.56e-197j)
| (2.5730780327457904226e-09 - 2.6504099911965174928e-989j)  +/-  (8.96e-83, 1.31e-202j)
| (0.10952560042968894515 - 8.0290915288903905992e-984j)  +/-  (1.08e-76, 1.11e-196j)
