Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 15 28
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : 16*t^19 - 748536/667*t^17 + 226304664/7337*t^15 - 3155515020/7337*t^13 + 24226003620/7337*t^11 - 9496214910/667*t^9 + 1965071745/58*t^7 - 112008278655/2668*t^5 + 250467132825/10672*t^3 - 83438061525/21344*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^47 - 94932843271577860536816831937884374924758489807924975718694466041829082469880363737466213619435339112/14754889366344037615700338574737211355293216469316160972180519915290685398042078456273183160004613*t^45 + 3636560291880333784589999564173884250210037011272095120051451442492443619477530036664562607709170138662736/3083771877565903861681370762120077173256282242087077643185728662295753248190794397361095280440964117*t^43 - 403519736826478926550391447566258040088697261730752656257229063961047915738419282948235912922433376869278152/3083771877565903861681370762120077173256282242087077643185728662295753248190794397361095280440964117*t^41 + 2581293196915339056044739773280580240902681928897981018703829281073465235498138580127778376358686244927032559747/262120609593101828242916514780206559726783990577401599670786936295139026096217523775693098837481949945*t^39 - 12164494761016507090641731502623072010122583985859303602746780191233368092868730872783074220547964199768499484289/22793096486356680716775349111322309541459477441513182580068429243055567486627610763103747724998430430*t^37 + 11315493584872569462014679900243364528047789940972694819308609664567854774772622424203565028507626843379750140556763/524241219186203656485833029560413119453567981154803199341573872590278052192435047551386197674963899890*t^35 - 139705554458983526859491207968476335310795663457705221436392778602456129474297242350054618367289014609317101308894349/209696487674481462594333211824165247781427192461921279736629549036111220876974019020554479069985559956*t^33 + 606857505887720008311126076310539764538418046598232481432185936092840171297790583871957451576106974523925926951518313/38126634122632993198969674877120954142077671356712959952114463461111131068540730731009905285451919992*t^31 - 22632230798777927505645240239117288819558322897711130748460231560474034746523454581461516938472705147618143874725406577/76253268245265986397939349754241908284155342713425919904228926922222262137081461462019810570903839984*t^29 + 11402870015143964615568100107657756397784823245747847501121707433785425613588815290982529713510875563369165763373058129/2629423042940206427515149991525583044281218714256066203594100928352491797830395222828269330031166896*t^27 - 261150605504618511933022192730612109333143084126697219005022109551683588773976257523468848637270124066780698055564712317/5258846085880412855030299983051166088562437428512132407188201856704983595660790445656538660062333792*t^25 + 406294943604888418303159200507445561568131458882561303556502480909067764084303254386574702737071547079056466855682257425/914581927979202235657443475313246276271728248436892592554469888122605842723615729679398027836927616*t^23 - 5641468406399544596148144459189846733055134142857288018501146397021555216767464691166711809358977411039756386713820470725/1829163855958404471314886950626492552543456496873785185108939776245211685447231459358796055673855232*t^21 + 395851406317132883335620903461931121511807159676467271269458022018725309484765124334053167945009731059317622765672985875/24067945473136900938353775666138059901887585485181384014591312845331732703253045517878895469392832*t^19 - 376006744882606218785537038036533762756837417512819981016942302808615379091458386132402501803405803753242607957116670125/5663045993679270809024417803797190565150020114160325650492073610666290047824246004206798933974784*t^17 + 18022516655210669951330109398412552871866798892271721356473260593834872351320131498477830521365131057843379164533452391375/90608735898868332944390684860755049042400321826565210407873177770660640765187936067308782943596544*t^15 - 77999337704345324190501741330068380552148430734547654087801644279610505749458475984447090640144257640714923887710807854375/181217471797736665888781369721510098084800643653130420815746355541321281530375872134617565887193088*t^13 + 14691352913887472570985208391830761106365427644769193761775773887771896674824657783751743327754134554360956479651175756875/22652183974717083236097671215188762260600080456641302601968294442665160191296984016827195735899136*t^11 - 29301438927436612985835956918512151852674148898608340604193732011068763053418551430459279207000138020286234941201221893875/45304367949434166472195342430377524521200160913282605203936588885330320382593968033654391471798272*t^9 + 575572768197928025319726407988411201588964327447776593133407586587772657705336521022110586434553759762784689447551974585125/1449739774381893327110250957772080784678405149225043366525970844330570252243006977076940527097544704*t^7 - 390485071174229944782350442403708885168390392726693491194042322275163018241707301540380945269098783390893073768818366426625/2899479548763786654220501915544161569356810298450086733051941688661140504486013954153881054195089408*t^5 + 61377059974335649538786716424772026272267550598300523016735845723055455102056334996985533278099176734601947882725129256875/2899479548763786654220501915544161569356810298450086733051941688661140504486013954153881054195089408*t^3 - 6085504241581199406127636527446717241699389593565109704127320270593620837109964962976850129974421175561173350318346223125/5798959097527573308441003831088323138713620596900173466103883377322281008972027908307762108390178816*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:
| (6.7090352551820100335 - 1.7774909573848445035e-930j)  +/-  (9.61e-246, 9.61e-246j)
| (4.1786518665495062111 - 1.4790622572914213263e-941j)  +/-  (1.46e-243, 1.46e-243j)
| (-4.8759532376325231043 - 5.771943453527747603e-953j)  +/-  (3.22e-244, 3.22e-244j)
| (-4.0676787766194897745 + 2.7422874103412832918e-951j)  +/-  (1.29e-243, 1.29e-243j)
| (5.7328622775120893487 + 2.7199196356356443182e-957j)  +/-  (8.43e-245, 8.43e-245j)
| (-6.7090352551820100335 + 2.9260231832046472236e-969j)  +/-  (9.52e-246, 9.52e-246j)
| (-5.2929320473750482627 + 4.3849816995888430603e-967j)  +/-  (1.7e-244, 1.7e-244j)
| (-4.4806942696926895069 + 1.2943379328292564775e-965j)  +/-  (5.84e-244, 5.84e-244j)
| (-7.2770499724885627841 + 9.514479538914072178e-975j)  +/-  (1.84e-246, 1.84e-246j)
| (1.0392484373427345816 + 2.8508723131968371049e-979j)  +/-  (9.74e-251, 9.74e-251j)
| (4.8759532376325231043 + 8.1844157003457988417e-972j)  +/-  (3.09e-244, 3.09e-244j)
| (4.0676787766194897745 - 6.7855597070170644573e-981j)  +/-  (1.26e-243, 1.26e-243j)
| (7.2770499724885627841 - 8.24529820753293997e-992j)  +/-  (1.75e-246, 1.75e-246j)
| (-0.74580391741535655811 - 2.1777168424160921781e-996j)  +/-  (1.19e-251, 1.19e-251j)
| (-2.7676033562166682643 - 7.6431199895529102562e-990j)  +/-  (7.36e-246, 7.36e-246j)
| (-7.9616646982578355848 + 9.212592958807548485e-994j)  +/-  (1.44e-247, 1.44e-247j)
| (2.7676033562166682643 + 3.048435922815269071e-990j)  +/-  (7.11e-246, 7.11e-246j)
| (-5.7328622775120893487 + 2.3374530901571294121e-989j)  +/-  (8.99e-245, 8.99e-245j)
| (-1.0392484373427345816 + 7.2235893203328195638e-995j)  +/-  (1.04e-250, 1.04e-250j)
| (7.9616646982578355848 + 5.0154495341615679561e-994j)  +/-  (1.34e-247, 1.34e-247j)
| (1.6506801238857845559 - 7.3827290345197383498e-993j)  +/-  (1.1e-248, 1.1e-248j)
| (4.5367733829384092666e-1007 - 8.2438481699574185396e-1007j)  +/-  (4.42e-1005, 4.42e-1005j)
| (-6.2013764260981098774 - 6.8042298137496342932e-990j)  +/-  (3.43e-245, 3.43e-245j)
| (3.7247592685574827416 - 7.9962585551936137593e-989j)  +/-  (2.09e-244, 2.09e-244j)
| (3.0693510888631658653 - 2.0388926416703027681e-991j)  +/-  (2.53e-245, 2.53e-245j)
| (6.2013764260981098774 + 2.1258554732141685552e-993j)  +/-  (3.68e-245, 3.68e-245j)
| (2.4716737797307611118 + 1.6256040736991530399e-998j)  +/-  (2.1e-246, 2.1e-246j)
| (2.1888080617024303415 - 5.5761534598779643732e-999j)  +/-  (4.45e-247, 4.45e-247j)
| (-3.0693510888631658653 - 3.3216482804463018522e-1001j)  +/-  (2.32e-245, 2.32e-245j)
| (-2.4716737797307611118 - 4.9304202694928973649e-1003j)  +/-  (1.8e-246, 1.8e-246j)
| (5.2929320473750482627 - 4.6801175825648228853e-1001j)  +/-  (1.77e-244, 1.77e-244j)
| (-1.3498998593245308008 + 1.6371702356808525401e-1018j)  +/-  (1.17e-249, 1.17e-249j)
| (3.3862181400001748776 + 8.185876266903409026e-1014j)  +/-  (6.45e-245, 6.45e-245j)
| (-1.6506801238857845559 - 9.2222138466979113926e-1024j)  +/-  (1.18e-248, 1.18e-248j)
| (-3.3862181400001748776 - 5.0918116740588630711e-1018j)  +/-  (6.76e-245, 6.76e-245j)
| (0.29485451031649697135 - 1.3539967107014976676e-1032j)  +/-  (1.13e-253, 1.13e-253j)
| (-1.925324614085472264 + 7.0047009282430751914e-1027j)  +/-  (8.39e-248, 8.39e-248j)
| (0.74580391741535655811 + 2.1071036611209898946e-1031j)  +/-  (1.18e-251, 1.18e-251j)
| (-4.1786518665495062111 + 6.7457050690647662433e-1024j)  +/-  (1.52e-243, 1.52e-243j)
| (-0.29485451031649697135 - 9.0242924024445840511e-1046j)  +/-  (1.13e-253, 1.13e-253j)
| (-0.52464762327529031788 + 3.2516180602386630787e-1045j)  +/-  (1.3e-252, 1.3e-252j)
| (4.4806942696926895069 - 4.8086862070585366037e-1041j)  +/-  (6.07e-244, 6.07e-244j)
| (1.3498998593245308008 - 8.2022307676597166959e-1056j)  +/-  (1.2e-249, 1.2e-249j)
| (1.925324614085472264 - 3.3383462185182219177e-1053j)  +/-  (8.46e-248, 8.46e-248j)
| (-3.7247592685574827416 + 1.5625093034791024833e-1058j)  +/-  (2.24e-244, 2.24e-244j)
| (-2.1888080617024303415 + 5.7006970910684153254e-1065j)  +/-  (4.28e-247, 4.28e-247j)
| (0.52464762327529031788 - 7.1605654864114388486e-1070j)  +/-  (1.4e-252, 1.4e-252j)
-------------------------------------------------
The weights are:
| (8.5098278923977914525e-21 + 1.2522684312783205735e-949j)  +/-  (1.38e-88, 1.06e-208j)
| (1.4595760102130602227e-09 + 5.4925813378039840772e-942j)  +/-  (2.97e-79, 2.28e-199j)
| (1.0842495357397273447e-11 + 2.1623783346588086974e-945j)  +/-  (3.08e-83, 2.36e-203j)
| (1.0787656158545588984e-08 - 2.3742951312491283804e-942j)  +/-  (4.77e-80, 3.66e-200j)
| (1.3617290716235642728e-15 + 3.5117577497894435329e-947j)  +/-  (1.27e-86, 9.74e-207j)
| (8.5098278923977914525e-21 + 1.1272963683497347422e-951j)  +/-  (1.97e-90, 1.51e-210j)
| (1.6438767302054146989e-13 - 8.3032991602666739372e-947j)  +/-  (1.76e-85, 1.35e-205j)
| (4.1139022621273859927e-10 - 6.1536273524060321787e-944j)  +/-  (2.16e-82, 1.66e-202j)
| (3.4612404346293112488e-24 - 9.4034760443135162269e-954j)  +/-  (1.73e-92, 1.33e-212j)
| (0.059109215631114557888 - 6.4689258845127399333e-938j)  +/-  (3.74e-62, 2.86e-182j)
| (1.0842495357397273447e-11 + 1.3666124991802489142e-944j)  +/-  (1.2e-86, 9.19e-207j)
| (1.0787656158545588984e-08 - 9.6871061359099416889e-942j)  +/-  (2.43e-83, 1.87e-203j)
| (3.4612404346293112488e-24 + 2.3153945342087209609e-952j)  +/-  (1.36e-94, 1.05e-214j)
| (0.086173394249004628042 + 1.1177955937680063416e-937j)  +/-  (7.05e-66, 5.41e-186j)
| (7.9353306406220496015e-05 - 3.4552887742994464241e-940j)  +/-  (2.87e-79, 2.2e-199j)
| (1.3179749310774598101e-28 + 2.2413130966004255812e-956j)  +/-  (4.67e-96, 3.58e-216j)
| (7.9353306406220496015e-05 - 8.3077733991381464226e-940j)  +/-  (8.77e-81, 6.73e-201j)
| (1.3617290716235642728e-15 + 2.7552734785733841323e-948j)  +/-  (4.41e-89, 3.39e-209j)
| (0.059109215631114557888 - 4.733620004477047187e-938j)  +/-  (7.94e-70, 6.09e-190j)
| (1.3179749310774598101e-28 - 2.6250087030040770939e-955j)  +/-  (1.03e-97, 7.88e-218j)
| (0.010700230333840230299 - 2.1696888375519281253e-938j)  +/-  (6.69e-76, 5.13e-196j)
| (0.17142868511252497273 - 1.6325473394183172632e-937j)  +/-  (1.63e-70, 1.25e-190j)
| (5.4468259851929367945e-18 - 6.9060449084156519226e-950j)  +/-  (9.68e-91, 7.43e-211j)
| (1.8525238359832227166e-07 + 1.8068524184805808017e-941j)  +/-  (1.01e-84, 7.74e-205j)
| (1.4042106365233763143e-05 + 2.5020772390519572656e-940j)  +/-  (4.94e-83, 3.79e-203j)
| (5.4468259851929367945e-18 - 1.7562953216225910592e-948j)  +/-  (1.13e-92, 8.7e-213j)
| (0.0003662447246266273934 + 2.4904936903894741535e-939j)  +/-  (1.48e-81, 1.14e-201j)
| (0.0012713967147094986114 - 6.5362929630328084682e-939j)  +/-  (6.23e-81, 4.78e-201j)
| (1.4042106365233763143e-05 + 9.3131632992818579736e-941j)  +/-  (4.49e-86, 3.44e-206j)
| (0.0003662447246266273934 + 1.1494887769906269641e-939j)  +/-  (1.53e-84, 1.18e-204j)
| (1.6438767302054146989e-13 - 7.0373348554397610187e-946j)  +/-  (8.01e-91, 6.15e-211j)
| (0.028187639015623028386 + 2.3250252267931721615e-938j)  +/-  (7.49e-81, 5.75e-201j)
| (1.9369603897192351198e-06 - 6.682578447605189135e-941j)  +/-  (3.48e-85, 2.67e-205j)
| (0.010700230333840230299 - 1.3128505167250133546e-938j)  +/-  (1.15e-82, 8.84e-203j)
| (1.9369603897192351198e-06 - 2.1995471605741845833e-941j)  +/-  (1.33e-87, 1.02e-207j)
| (0.14191227121175667912 + 1.9717210120442778978e-937j)  +/-  (1.32e-81, 1.03e-201j)
| (0.0036355401766956980026 + 7.3264394351668310672e-939j)  +/-  (2.66e-84, 2.05e-204j)
| (0.086173394249004628042 + 1.3973944511415196224e-937j)  +/-  (2.18e-82, 1.7e-202j)
| (1.4595760102130602227e-09 + 1.2765186700267542581e-942j)  +/-  (4.13e-89, 3.2e-209j)
| (0.14191227121175667912 + 1.8057073100027340317e-937j)  +/-  (3.89e-82, 3.05e-202j)
| (0.082834195091191148888 - 1.8011919011115189343e-937j)  +/-  (2.82e-82, 2.21e-202j)
| (4.1139022621273859927e-10 - 3.0900757644995848106e-943j)  +/-  (3.43e-90, 2.7e-210j)
| (0.028187639015623028386 + 3.4963153701087963229e-938j)  +/-  (1.3e-84, 1.02e-204j)
| (0.0036355401766956980026 + 1.3223858936988367495e-938j)  +/-  (1.56e-85, 1.26e-205j)
| (1.8525238359832227166e-07 + 5.1679628418662114088e-942j)  +/-  (6.68e-89, 5.06e-209j)
| (0.0012713967147094986114 - 3.3205270202795129694e-939j)  +/-  (5.47e-86, 4.06e-206j)
| (0.082834195091191148888 - 2.1067972763854629819e-937j)  +/-  (4.24e-84, 3.71e-204j)
