Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 53
-------------------------------------------------
Trying to find an order 53 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^57 - 29908483841498755012015840173067704877477849464/2452070369646233148101113457952700592074375*t^55 + 519118801831427020314611944071262819854683860089408/120151448112665424256954559439682329011644375*t^53 - 113609340376506383730068481524194193836704397909366002/120151448112665424256954559439682329011644375*t^51 + 689204639176661967004010848285006854123489954569297433/4806057924506616970278182377587293160465775*t^49 - 1571736236545774555902249715963546275271769424827212797/98082814785849325924044538318108023682975*t^47 + 134328502563941957969341685914251687817983856554439369752/98082814785849325924044538318108023682975*t^45 - 35987866979363248933512035779656260794006247621094141806439/392331259143397303696178153272432094731900*t^43 + 7681196484177677448722115021066351333179038919597442061684119/1569325036573589214784712613089728378927600*t^41 - 132081100422742762228970186490994270666206014855685257194833633/627730014629435685913885045235891351571040*t^39 + 144008698214986407107840439975998076184204288494437619227548449/19616562957169865184808907663621604736595*t^37 - 524305775818059519489424649759267118515056145279269577097941063343/2510920058517742743655540180943565406284160*t^35 + 24366565754024542399946839304530554594169843944638856386298259261893/5021840117035485487311080361887130812568320*t^33 - 231281619097837737850771304625028479755159025171287683570713678278811/2510920058517742743655540180943565406284160*t^31 + 11187483260321822900924011285475898759924953695587775920855360369213/7846625182867946073923563065448641894638*t^29 - 36010022594623905745059170083367044795545482725720897595255343625097253/2008736046814194194924432144754852325027328*t^27 + 2925258296499224360798384470215148186776443200636796944688276230106444685/16069888374513553559395457158038818600218624*t^25 - 47598962689173461933335731958732894101587545362888563745629576150575766985/32139776749027107118790914316077637200437248*t^23 + 38382956331864949961790342455889413069281024043967920525060752547202822405/4017472093628388389848864289509704650054656*t^21 - 6199101455615213327568631954207019595541967780606181462066659171582072237775/128559106996108428475163657264310548801748992*t^19 + 48125184607085459638407602219682641533826405637366801795466718718970412967675/257118213992216856950327314528621097603497984*t^17 - 140545092341828827407684707058671485166070681675911027468723334547129487460525/257118213992216856950327314528621097603497984*t^15 + 37513646931597548140587902131491560872300657147784106055396521309048441245025/32139776749027107118790914316077637200437248*t^13 - 1804369658899207402070554705931071440467154459831057087510169402742738840845575/1028472855968867427801309258114484390413991936*t^11 + 7247947264735037025073328547528886088855061820657379766651998153267808462274125/4113891423875469711205237032457937561655967744*t^9 - 9019065417719865757945641029483907669254906708187912205195715531218103545108875/8227782847750939422410474064915875123311935488*t^7 + 193212716566128761734257092869846320710186925935559481761502746661572768011475/514236427984433713900654629057242195206995968*t^5 - 1897945078608167609349683393488942288554765156353235921551811985119140078546325/32911131391003757689641896259663500493247741952*t^3 + 163077940747771505123925641765563019736507960416332684540919985583616370623475/65822262782007515379283792519327000986495483904*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:   57 out of 57
Indefinite weights: 0 out of 57
Negative weights:   0 out of 57
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-9.0868904186079847678 - 1.0126892102371130697e-913j)  +/-  (2.84e-244, 2.84e-244j)
| (-9.7321208404724955281 - 6.9435186974639558622e-915j)  +/-  (1.35e-245, 1.35e-245j)
| (9.7321208404724955281 - 1.7932419057510587167e-914j)  +/-  (1.32e-245, 1.32e-245j)
| (4.3897318095398553986 - 4.4996890524624473703e-910j)  +/-  (1.71e-242, 1.71e-242j)
| (-7.2207128507614612564 + 9.4174276868196371888e-911j)  +/-  (6.28e-242, 6.28e-242j)
| (-8.0752356863878501813 - 2.4759222907519071068e-911j)  +/-  (9.25e-243, 9.25e-243j)
| (8.0752356863878501813 - 9.7798195389707898613e-910j)  +/-  (9.32e-243, 9.32e-243j)
| (-5.0453107274267405798 + 1.4239153779448706013e-910j)  +/-  (6.7e-242, 6.7e-242j)
| (-5.7283511795239745039 + 6.1118466170172135856e-911j)  +/-  (1.41e-241, 1.41e-241j)
| (7.6348288196389166024 + 3.4251652699827938145e-915j)  +/-  (2.7e-242, 2.7e-242j)
| (1.9422393696986837808 + 1.2483001845275985704e-936j)  +/-  (1.7e-247, 1.7e-247j)
| (5.0453107274267405798 - 2.3493482022225853855e-930j)  +/-  (6.67e-242, 6.67e-242j)
| (6.0829363240936066213 - 2.1693576511243264165e-944j)  +/-  (1.5e-241, 1.5e-241j)
| (-3.4446932488389714861 - 9.1610616539368995328e-964j)  +/-  (6.62e-244, 6.62e-244j)
| (7.2207128507614612564 + 7.3522557598689052963e-969j)  +/-  (6.26e-242, 6.26e-242j)
| (6.4482991162994960794 - 3.1112831495220102084e-985j)  +/-  (1.32e-241, 1.32e-241j)
| (4.7145348468258753067 - 1.2894036378004293477e-995j)  +/-  (3.52e-242, 3.52e-242j)
| (4.0702002215444284392 + 1.6139920402377774942e-1001j)  +/-  (7.61e-243, 7.61e-243j)
| (-1.3622903316554831734 + 9.781321871446709909e-1009j)  +/-  (1.86e-249, 1.86e-249j)
| (3.1378070987687300728 - 1.5208174671121061516e-1003j)  +/-  (1.6e-244, 1.6e-244j)
| (5.7283511795239745039 + 3.1796495552729099788e-1000j)  +/-  (1.3e-241, 1.3e-241j)
| (1.3622903316554831734 + 3.8142361100261054399e-1015j)  +/-  (2.01e-249, 2.01e-249j)
| (2.2367104820103970935 - 5.8242786989095137947e-1012j)  +/-  (1.22e-246, 1.22e-246j)
| (-1.077665307016189271 - 7.9760468663942476769e-1016j)  +/-  (2.09e-250, 2.09e-250j)
| (8.5524473432484271769 - 8.7066529012019299764e-1009j)  +/-  (1.97e-243, 1.97e-243j)
| (-8.5524473432484271769 - 3.0376098663216037406e-1008j)  +/-  (2.02e-243, 2.02e-243j)
| (-7.6348288196389166024 - 4.5162468378058914102e-1007j)  +/-  (2.77e-242, 2.77e-242j)
| (-5.3829049413354622481 - 4.0617919241604670313e-1005j)  +/-  (1.03e-241, 1.03e-241j)
| (-4.7145348468258753067 + 1.2557704506003829188e-1007j)  +/-  (3.62e-242, 3.62e-242j)
| (-2.2367104820103970935 + 4.6039533427627629873e-1015j)  +/-  (1.12e-246, 1.12e-246j)
| (9.0868904186079847678 + 2.5497077427543100448e-1013j)  +/-  (2.73e-244, 2.73e-244j)
| (-6.8265862439085002405 + 2.9902806199345179825e-1009j)  +/-  (1e-241, 1e-241j)
| (-6.0829363240936066213 + 1.9180578846534693521e-1009j)  +/-  (1.43e-241, 1.43e-241j)
| (3.4446932488389714861 + 2.2086515060864308408e-1015j)  +/-  (6.32e-244, 6.32e-244j)
| (-4.0702002215444284392 - 3.0824004737857327093e-1012j)  +/-  (6.93e-243, 6.93e-243j)
| (-0.79790553000156896681 + 2.2759963169018524173e-1025j)  +/-  (1.72e-251, 1.72e-251j)
| (0.52464762327529031788 + 1.822975501420348749e-1026j)  +/-  (1.35e-252, 1.35e-252j)
| (-3.1378070987687300728 - 1.9800845862197369384e-1019j)  +/-  (1.53e-244, 1.53e-244j)
| (1.6506801238857845559 - 2.8763159174853579292e-1022j)  +/-  (1.88e-248, 1.88e-248j)
| (2.8343499544489162306 + 2.2620706667607626724e-1019j)  +/-  (3.7e-245, 3.7e-245j)
| (-0.52464762327529031788 + 1.6543274107886385051e-1026j)  +/-  (1.32e-252, 1.32e-252j)
| (-1.6506801238857845559 - 7.9570621636401713923e-1023j)  +/-  (2.21e-248, 2.21e-248j)
| (3.7553523537378572103 - 2.9936747365006001286e-1017j)  +/-  (2.38e-243, 2.38e-243j)
| (6.8265862439085002405 - 5.5520393194871751471e-1016j)  +/-  (1.01e-241, 1.01e-241j)
| (-4.3897318095398553986 - 1.9772744617017667913e-1024j)  +/-  (1.67e-242, 1.67e-242j)
| (5.3829049413354622481 + 2.5077845967297917486e-1025j)  +/-  (1.03e-241, 1.03e-241j)
| (-2.8343499544489162306 + 1.3818643224125875223e-1031j)  +/-  (3.61e-245, 3.61e-245j)
| (2.5340490458594469902 - 2.3392878596737133049e-1035j)  +/-  (6.58e-246, 6.58e-246j)
| (-2.3053717552032630366e-1056 - 4.8459744079712318305e-1057j)  +/-  (1.34e-1054, 1.34e-1054j)
| (-6.4482991162994960794 + 1.2000375537465652662e-1031j)  +/-  (1.43e-241, 1.43e-241j)
| (-2.5340490458594469902 - 1.7761563255449367135e-1036j)  +/-  (6.68e-246, 6.68e-246j)
| (-1.9422393696986837808 + 5.4634149777152498584e-1038j)  +/-  (1.66e-247, 1.66e-247j)
| (0.79790553000156896681 - 2.303637138201229426e-1043j)  +/-  (1.63e-251, 1.63e-251j)
| (0.25922110100080471862 - 8.9005354506190357226e-1045j)  +/-  (7.9e-254, 7.9e-254j)
| (1.077665307016189271 + 3.3598110223480845387e-1042j)  +/-  (2.19e-250, 2.19e-250j)
| (-3.7553523537378572103 + 3.8966050990802430652e-1041j)  +/-  (2.34e-243, 2.34e-243j)
| (-0.25922110100080471862 - 1.4682341050333112881e-1051j)  +/-  (7.9e-254, 7.9e-254j)
-------------------------------------------------
The weights are:
| (4.4766595546569932974e-37 + 1.8309624160428798077e-934j)  +/-  (7.65e-70, 1.51e-190j)
| (3.0895015136782014074e-42 - 4.0895160359457432826e-937j)  +/-  (1.3e-71, 2.58e-192j)
| (3.0895015136782014074e-42 + 1.1361218848355044328e-936j)  +/-  (1.21e-73, 2.4e-194j)
| (7.7735383434797329816e-10 + 1.6483903160582770574e-918j)  +/-  (6.49e-55, 1.29e-175j)
| (5.170087054759359143e-24 + 1.0296990601122783439e-927j)  +/-  (1.41e-65, 2.79e-186j)
| (1.2325298607190500084e-29 + 1.2560802373185008785e-930j)  +/-  (8.5e-68, 1.68e-188j)
| (1.2325298607190500084e-29 - 4.5686807990105189095e-930j)  +/-  (2.65e-70, 5.25e-191j)
| (1.6602562684423833192e-12 + 2.6677600944490174203e-921j)  +/-  (2.92e-59, 5.78e-180j)
| (1.1073188368278708339e-15 + 2.0852489261732079777e-923j)  +/-  (1.22e-61, 2.41e-182j)
| (1.1627943026525208923e-26 + 1.7543344581362051815e-928j)  +/-  (1.82e-69, 3.6e-190j)
| (0.0038024314271254897604 + 8.4488256555800306414e-916j)  +/-  (6.43e-43, 1.27e-163j)
| (1.6602562684423833192e-12 - 2.0136341283533373578e-920j)  +/-  (1.38e-61, 2.73e-182j)
| (1.7278624818979163764e-17 + 1.8845861542231776645e-923j)  +/-  (1.01e-65, 1.99e-186j)
| (1.2237003144079373502e-06 - 2.6699744120868613957e-918j)  +/-  (8.39e-57, 1.66e-177j)
| (5.170087054759359143e-24 - 4.6588171189855582912e-927j)  +/-  (2.66e-69, 5.26e-190j)
| (1.8326317123556569466e-19 - 1.4535842261129135491e-924j)  +/-  (3.9e-67, 7.73e-188j)
| (4.1101471245989587671e-11 + 2.2349050390839554251e-919j)  +/-  (8.84e-62, 1.75e-182j)
| (1.1425333978325444654e-08 - 4.6639094202841455595e-918j)  +/-  (3.39e-60, 6.71e-181j)
| (0.025280605372138695183 + 1.3127383558906854368e-915j)  +/-  (2.82e-46, 5.59e-167j)
| (9.1181104944258696506e-06 + 4.7237992244199006244e-917j)  +/-  (1.69e-57, 3.34e-178j)
| (1.1073188368278708339e-15 - 2.0978514801573861819e-922j)  +/-  (1.56e-65, 3.09e-186j)
| (0.025280605372138695183 + 2.4463711334264607803e-915j)  +/-  (3.48e-47, 6.9e-168j)
| (0.001121625463896485243 - 4.5032705933569096412e-916j)  +/-  (2.41e-53, 4.77e-174j)
| (0.049883396640429460269 - 2.3206146759732712678e-915j)  +/-  (3e-46, 5.94e-167j)
| (4.8429249603369553784e-33 + 7.2575244059187637442e-932j)  +/-  (2.71e-75, 5.38e-196j)
| (4.8429249603369553784e-33 - 2.1897945176857784359e-932j)  +/-  (1.12e-78, 2.22e-199j)
| (1.1627943026525208923e-26 - 4.3542203737577698018e-929j)  +/-  (2.15e-76, 4.25e-197j)
| (5.0191150037018741073e-14 - 1.043248259411747105e-922j)  +/-  (3.73e-71, 7.39e-192j)
| (4.1101471245989587671e-11 - 1.1923067216769160281e-920j)  +/-  (6.44e-70, 1.28e-190j)
| (0.001121625463896485243 - 1.5174666703994220873e-916j)  +/-  (8.91e-62, 1.76e-182j)
| (4.4766595546569932974e-37 - 5.5584830116888129834e-934j)  +/-  (8.55e-81, 1.69e-201j)
| (1.2545634343126444147e-21 - 1.7860598888160800784e-926j)  +/-  (1.25e-75, 2.47e-196j)
| (1.7278624818979163764e-17 - 2.4820903712026177088e-924j)  +/-  (9.68e-74, 1.92e-194j)
| (1.2237003144079373502e-06 - 2.0377939108612034707e-917j)  +/-  (2e-66, 3.97e-187j)
| (1.1425333978325444654e-08 - 2.0357982046828230374e-919j)  +/-  (6.15e-70, 1.22e-190j)
| (0.082625337333766145046 + 3.8017948861427876939e-915j)  +/-  (1.49e-58, 2.94e-179j)
| (0.11543492009590669254 - 7.1987087279450170589e-915j)  +/-  (3.45e-59, 6.82e-180j)
| (9.1181104944258696506e-06 + 8.3930686450641853838e-918j)  +/-  (1.29e-67, 2.56e-188j)
| (0.0107285734248013407 - 1.4851830278162896649e-915j)  +/-  (3.41e-61, 6.74e-182j)
| (5.52432852290791807e-05 - 1.0586933406910126114e-916j)  +/-  (1.28e-65, 2.53e-186j)
| (0.11543492009590669254 - 5.7014365707258392042e-915j)  +/-  (5.9e-60, 1.17e-180j)
| (0.0107285734248013407 - 6.900276267957063924e-916j)  +/-  (1.37e-63, 2.7e-184j)
| (1.3237621925036499563e-07 + 8.9172343095498792564e-918j)  +/-  (8.9e-68, 1.76e-188j)
| (1.2545634343126444147e-21 + 9.2554639612236613728e-926j)  +/-  (2.89e-76, 5.74e-197j)
| (7.7735383434797329816e-10 + 4.9447856377451020713e-920j)  +/-  (5.37e-72, 1.07e-192j)
| (5.0191150037018741073e-14 + 2.0956095600070352019e-921j)  +/-  (2.48e-72, 4.89e-193j)
| (5.52432852290791807e-05 - 2.4054110413773894898e-917j)  +/-  (1.56e-69, 3.07e-190j)
| (0.00027416842478606973034 + 2.2509692265697019666e-916j)  +/-  (4.12e-67, 8.15e-188j)
| (0.14552617103538865478 - 8.7583463934504807389e-915j)  +/-  (2.63e-65, 5.18e-186j)
| (1.8326317123556569466e-19 + 2.377147322788853581e-925j)  +/-  (3.28e-77, 6.49e-198j)
| (0.00027416842478606973034 + 6.3056678130775423014e-917j)  +/-  (3.34e-69, 6.53e-190j)
| (0.0038024314271254897604 + 3.3648899015824467803e-916j)  +/-  (2.12e-68, 4.11e-189j)
| (0.082625337333766145046 + 5.4319481368443468448e-915j)  +/-  (2.38e-67, 4.57e-188j)
| (0.13802012658169727467 + 8.5426976082727185492e-915j)  +/-  (4.29e-67, 8.3e-188j)
| (0.049883396640429460269 - 3.7741755696329047083e-915j)  +/-  (9.3e-68, 1.78e-188j)
| (1.3237621925036499563e-07 + 7.7264068999204444355e-919j)  +/-  (8.05e-72, 1.7e-192j)
| (0.13802012658169727467 + 7.6161151983905620953e-915j)  +/-  (1.8e-67, 3.05e-188j)
