Starting with polynomial:
P : 16*t^4 - 12*t^2 + 1
Extension levels are: 4 5 40
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 12*t^2 + 1
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : 16*t^9 - 32*t^7 + 21*t^5 - 5*t^3 + 5/16*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^49 - 192*t^47 + 1081*t^45 - 3795*t^43 + 148995/16*t^41 - 135751/8*t^39 + 3048227/128*t^37 - 3372291/128*t^35 + 95548245/4096*t^33 - 8544965/512*t^31 + 158936349/16384*t^29 - 75207643/16384*t^27 + 463120749/262144*t^25 - 72212175/131072*t^23 + 289994925/2097152*t^21 - 57998985/2097152*t^19 + 583401555/134217728*t^17 - 17678835/33554432*t^15 + 206253075/4294967296*t^13 - 13656825/4294967296*t^11 + 10015005/68719476736*t^9 - 148005/34359738368*t^7 + 40365/549755813888*t^5 - 325/549755813888*t^3 + 25/17592186044416*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (-0.99211470131447783105 - 6.2932995964011863005e-918j)  +/-  (5.08e-239, 5.08e-239j)
| (-0.99802672842827156195 + 7.4560851684871748997e-919j)  +/-  (1.35e-239, 1.35e-239j)
| (-0.87630668004386358731 + 4.5388156994556361097e-918j)  +/-  (1.08e-239, 1.08e-239j)
| (0.99802672842827156195 - 1.0476318092012283194e-914j)  +/-  (1.36e-239, 1.36e-239j)
| (0.92977648588825140366 + 3.0170079310305588048e-925j)  +/-  (4.52e-239, 4.52e-239j)
| (0.90482705246601952771 - 5.9631125357778940769e-942j)  +/-  (2.53e-239, 2.53e-239j)
| (-0.92977648588825140366 - 1.2040512486651974758e-953j)  +/-  (4.37e-239, 4.37e-239j)
| (-0.90482705246601952771 + 5.2424913451512160728e-953j)  +/-  (2.61e-239, 2.61e-239j)
| (0.98228725072868868109 + 3.9607226315621269891e-952j)  +/-  (7.56e-239, 7.56e-239j)
| (-0.98228725072868868109 - 3.4629490016630110161e-970j)  +/-  (8.45e-239, 8.45e-239j)
| (0.87630668004386358731 - 3.9414802257131496403e-971j)  +/-  (1.08e-239, 1.08e-239j)
| (0.99211470131447783105 + 2.1802811521119824037e-986j)  +/-  (4.49e-239, 4.49e-239j)
| (-0.84432792550201507855 + 1.4189732045989508801e-1011j)  +/-  (3.86e-240, 3.86e-240j)
| (-0.8090169943749474241 - 3.0298188301972310873e-1013j)  +/-  (1.47e-240, 1.47e-240j)
| (0.96858316112863111949 - 3.4539991957122211689e-1009j)  +/-  (9.05e-239, 9.05e-239j)
| (0.68454710592868867373 - 4.8201581906300570702e-1023j)  +/-  (1.52e-242, 1.52e-242j)
| (0.72896862742141152315 - 7.4012823102944707854e-1024j)  +/-  (8.37e-242, 8.37e-242j)
| (-0.96858316112863111949 + 4.5884271401758455222e-1019j)  +/-  (8.26e-239, 8.26e-239j)
| (-0.7705132427757892308 + 2.7778442557558595042e-1025j)  +/-  (4.02e-241, 4.02e-241j)
| (-0.95105651629515357212 + 9.6503359939233237834e-1023j)  +/-  (6.83e-239, 6.83e-239j)
| (0.84432792550201507855 - 3.485500337161320443e-1022j)  +/-  (3.79e-240, 3.79e-240j)
| (0.8090169943749474241 - 8.3635801276929990079e-1029j)  +/-  (1.31e-240, 1.31e-240j)
| (0.95105651629515357212 - 2.2002251525361910385e-1033j)  +/-  (7.3e-239, 7.3e-239j)
| (-0.68454710592868867373 + 2.703387318461350473e-1040j)  +/-  (1.63e-242, 1.63e-242j)
| (-0.72896862742141152315 + 2.5058966025481071277e-1041j)  +/-  (7.46e-242, 7.46e-242j)
| (0.12533323356430424537 + 1.1966592272669885019e-1052j)  +/-  (2.7e-253, 2.7e-253j)
| (0.7705132427757892308 + 1.9340138916474030999e-1043j)  +/-  (3.64e-241, 3.64e-241j)
| (0.36812455268467795916 - 1.5365190072984096741e-1050j)  +/-  (2.47e-248, 2.47e-248j)
| (-0.062790519529313376076 - 9.6288908699272955305e-1057j)  +/-  (1.49e-254, 1.49e-254j)
| (-0.63742398974868971018 - 2.9501087390978414632e-1045j)  +/-  (2.34e-243, 2.34e-243j)
| (-0.42577929156507264886 + 1.659855137544120238e-1052j)  +/-  (3.46e-247, 3.46e-247j)
| (0.53582679497899661827 + 2.2665217926772328373e-1046j)  +/-  (4.78e-245, 4.78e-245j)
| (0.58778525229247312917 - 2.8882514049573633759e-1046j)  +/-  (3.96e-244, 3.96e-244j)
| (0.062790519529313376076 + 7.2895951711726305507e-1059j)  +/-  (8.65e-255, 8.65e-255j)
| (-0.53582679497899661827 + 2.4119253852968025676e-1048j)  +/-  (5.18e-245, 5.18e-245j)
| (-0.58778525229247312917 - 1.9003714404969491998e-1049j)  +/-  (3.01e-244, 3.01e-244j)
| (-0.3090169943749474241 - 1.5911639661414821413e-1054j)  +/-  (1.53e-249, 1.53e-249j)
| (0.63742398974868971018 - 6.0850260328343100322e-1051j)  +/-  (2.58e-243, 2.58e-243j)
| (0.24868988716485478824 - 2.7527023072974807103e-1058j)  +/-  (8.18e-251, 8.18e-251j)
| (-0.12533323356430424537 + 1.7119531850506146433e-1062j)  +/-  (2.45e-253, 2.45e-253j)
| (-0.48175367410171527499 + 8.4042232172957967063e-1055j)  +/-  (4.41e-246, 4.41e-246j)
| (-0.18738131458572463054 - 6.0542425581961319309e-1060j)  +/-  (5.55e-252, 5.55e-252j)
| (0.3090169943749474241 - 7.4039275608410116359e-1057j)  +/-  (1.47e-249, 1.47e-249j)
| (0.48175367410171527499 + 1.2971245767861453036e-1053j)  +/-  (4.09e-246, 4.09e-246j)
| (-1.6988062455881805639e-1070 - 1.7343440154733517506e-1070j)  +/-  (1.19e-1068, 1.19e-1068j)
| (-0.36812455268467795916 + 3.0045621336636564536e-1059j)  +/-  (2.57e-248, 2.57e-248j)
| (-0.24868988716485478824 + 1.195643164729282741e-1059j)  +/-  (8.25e-251, 8.25e-251j)
| (0.18738131458572463054 + 1.1852832409248456725e-1060j)  +/-  (5.21e-252, 5.21e-252j)
| (0.42577929156507264886 - 1.3662796930680398373e-1056j)  +/-  (3.42e-247, 3.42e-247j)
-------------------------------------------------
The weights are:
| (0.0003141683887136888051 - 1.893061489991187137e-918j)  +/-  (3.41e-65, 6.32e-180j)
| (7.8852986855221689502e-05 + 3.5518731661770146077e-919j)  +/-  (2.5e-65, 4.64e-180j)
| (0.0046417320502100338173 - 2.6105651353931807376e-917j)  +/-  (5.69e-66, 1.05e-180j)
| (7.8852986855221689502e-05 + 3.1366945199926806431e-916j)  +/-  (5.23e-67, 9.69e-182j)
| (0.0027103137257858847685 - 4.1603253063006834811e-916j)  +/-  (5.41e-67, 1e-181j)
| (0.0036257601025131028982 + 4.0756588638514313887e-916j)  +/-  (3.58e-67, 6.63e-182j)
| (0.0027103137257858847685 - 1.5262031202505162395e-917j)  +/-  (6.84e-67, 1.27e-181j)
| (0.0036257601025131028982 + 2.0829352738829712621e-917j)  +/-  (6.21e-67, 1.15e-181j)
| (0.00070223514111748596339 + 4.674139291084891948e-916j)  +/-  (1.06e-67, 1.97e-182j)
| (0.00070223514111748596339 + 4.2280238364707800865e-918j)  +/-  (3.12e-67, 5.78e-182j)
| (0.0046417320502100338173 - 3.9951451470451240988e-916j)  +/-  (2.51e-68, 4.65e-183j)
| (0.0003141683887136888051 - 5.5671768517004667801e-916j)  +/-  (8.73e-68, 1.62e-182j)
| (0.0057422070843492735114 + 3.2109714518220898284e-917j)  +/-  (3.13e-68, 5.8e-183j)
| (0.006909830056250525759 - 3.9858347919570999005e-917j)  +/-  (4.66e-69, 8.64e-184j)
| (0.0012369331995613641269 - 4.4011469908146093515e-916j)  +/-  (5.1e-68, 9.45e-183j)
| (0.010627905195293133761 + 3.5519249406738623813e-916j)  +/-  (2.89e-71, 5.36e-186j)
| (0.0093720948047068662392 - 3.6493317061227273149e-916j)  +/-  (5.44e-71, 1.01e-185j)
| (0.0012369331995613641269 - 7.0122320455363757258e-918j)  +/-  (1.39e-68, 2.57e-183j)
| (0.0081261868541427536946 + 4.8045948668959292104e-917j)  +/-  (5.7e-71, 1.06e-185j)
| (0.001909830056250525759 + 1.0704348242199918483e-917j)  +/-  (9.55e-69, 1.77e-183j)
| (0.0057422070843492735114 + 3.9140344864460787822e-916j)  +/-  (4.11e-71, 7.61e-186j)
| (0.006909830056250525759 - 3.83002298401748499e-916j)  +/-  (9.48e-72, 1.76e-186j)
| (0.001909830056250525759 + 4.2597400123864951472e-916j)  +/-  (2.86e-70, 5.29e-185j)
| (0.010627905195293133761 + 6.6164398578851794553e-917j)  +/-  (3.43e-74, 6.35e-189j)
| (0.0093720948047068662392 - 5.6814503392595030392e-917j)  +/-  (3.05e-73, 5.65e-188j)
| (0.019685831611286311195 + 2.3635485247410444086e-916j)  +/-  (1.92e-78, 3.55e-193j)
| (0.0081261868541427536946 + 3.7419673413841644831e-916j)  +/-  (2.96e-73, 5.49e-188j)
| (0.017289686274214115231 + 2.8758253186330345338e-916j)  +/-  (5.21e-78, 9.66e-193j)
| (0.01992114701314477831 - 1.9677501011270938076e-916j)  +/-  (7.38e-79, 1.37e-193j)
| (0.011873813145857246305 - 7.6070518167003740019e-917j)  +/-  (2.23e-76, 4.13e-191j)
| (0.016374239897486897102 - 1.2051945030769861841e-916j)  +/-  (8.28e-79, 1.53e-193j)
| (0.014257792915650726489 - 3.2318987538103386023e-916j)  +/-  (3.18e-78, 5.9e-193j)
| (0.013090169943749474241 + 3.3430079680792380199e-916j)  +/-  (9.19e-78, 1.7e-192j)
| (0.01992114701314477831 - 2.2318903712941509741e-916j)  +/-  (7.26e-80, 1.35e-194j)
| (0.014257792915650726489 - 9.7411225216163900186e-917j)  +/-  (3.17e-79, 5.87e-194j)
| (0.013090169943749474241 + 8.6498940413871547689e-917j)  +/-  (1.41e-78, 2.61e-193j)
| (0.018090169943749474241 - 1.4503923299168746805e-916j)  +/-  (2.17e-81, 4.03e-196j)
| (0.011873813145857246305 - 3.4497656237099659268e-916j)  +/-  (1.69e-79, 3.14e-194j)
| (0.018763066800438635873 + 2.6235311032973364701e-916j)  +/-  (5.57e-82, 1.03e-196j)
| (0.019685831611286311195 + 1.8362843577179291763e-916j)  +/-  (3.41e-82, 6.32e-197j)
| (0.015358267949789966183 + 1.0876595364303710736e-916j)  +/-  (4.59e-81, 8.5e-196j)
| (0.019297764858882514037 - 1.7058999213131348204e-916j)  +/-  (1.47e-82, 2.72e-197j)
| (0.018090169943749474241 - 2.7508761456846962144e-916j)  +/-  (8.54e-83, 1.58e-197j)
| (0.015358267949789966183 + 3.1167509267239429921e-916j)  +/-  (9.25e-83, 1.71e-197j)
| (0.02 + 2.0997885008913296363e-916j)  +/-  (8.26e-83, 1.53e-197j)
| (0.017289686274214115231 + 1.3262621424005728657e-916j)  +/-  (6.39e-83, 1.18e-197j)
| (0.018763066800438635873 + 1.5771024690586260016e-916j)  +/-  (4.05e-83, 7.5e-198j)
| (0.019297764858882514037 - 2.4942604378325333953e-916j)  +/-  (1.01e-83, 1.91e-198j)
| (0.016374239897486897102 - 2.9979265652933937602e-916j)  +/-  (6.87e-84, 1.22e-198j)
