Starting with polynomial:
P : 16*t^5 - 20*t^3 + 5*t
Extension levels are: 5 6 10 20
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 16*t^5 - 20*t^3 + 5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P2 : 16*t^11 - 48*t^9 + 53*t^7 - 26*t^5 + 85/16*t^3 - 5/16*t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P3 : 16*t^21 - 88*t^19 + 208*t^17 - 276*t^15 + 3605/16*t^13 - 3731/32*t^11 + 2431/64*t^9 - 957/128*t^7 + 3333/4096*t^5 - 335/8192*t^3 + 5/8192*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^41 - 168*t^39 + 818*t^37 - 2451*t^35 + 10115/2*t^33 - 30481/4*t^31 + 138787/16*t^29 - 243629/32*t^27 + 21352149/4096*t^25 - 22931025/8192*t^23 + 38629305/32768*t^21 - 25398555/65536*t^19 + 25820145/262144*t^17 - 9992005/524288*t^15 + 5757475/2097152*t^13 - 1196069/4194304*t^11 + 5475173/268435456*t^9 - 503481/536870912*t^7 + 53333/2147483648*t^5 - 1335/4294967296*t^3 + 5/4294967296*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:   41 out of 41
Indefinite weights: 0 out of 41
Negative weights:   0 out of 41
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (1 + 2.1809922667671097918e-925j)  +/-  (7.54e-241, 7.54e-241j)
| (-1 + 4.9273570764501872813e-945j)  +/-  (7.33e-241, 7.33e-241j)
| (-0.95105651629515357212 + 4.8142557904197821158e-948j)  +/-  (3.35e-241, 3.35e-241j)
| (0.9969173337331279762 - 9.0973949279836429914e-949j)  +/-  (1.26e-240, 1.26e-240j)
| (0.92387953251128675613 - 3.3205959594794965263e-961j)  +/-  (1.53e-241, 1.53e-241j)
| (0.98768834059513772619 - 1.0356296191537541366e-964j)  +/-  (1.17e-240, 1.17e-240j)
| (-0.89100652418836786236 + 4.3269604226821276906e-975j)  +/-  (5.34e-242, 5.34e-242j)
| (-0.92387953251128675613 - 1.1991750123919355651e-975j)  +/-  (1.43e-241, 1.43e-241j)
| (-0.98768834059513772619 + 1.1284119941749195445e-973j)  +/-  (1.06e-240, 1.06e-240j)
| (0.95105651629515357212 + 3.1061827743411280297e-973j)  +/-  (3.91e-241, 3.91e-241j)
| (0.89100652418836786236 - 3.740641901757969423e-980j)  +/-  (5.47e-242, 5.47e-242j)
| (-0.9969173337331279762 + 4.836948898588749786e-986j)  +/-  (1.34e-240, 1.34e-240j)
| (-0.85264016435409222152 - 2.054931338154056525e-991j)  +/-  (1.85e-242, 1.85e-242j)
| (-0.8090169943749474241 - 1.9949912636202206277e-992j)  +/-  (4.08e-243, 4.08e-243j)
| (0.97236992039767660183 + 7.0496852288160985386e-991j)  +/-  (7.02e-241, 7.02e-241j)
| (0.85264016435409222152 + 1.1151225202924882268e-1001j)  +/-  (1.55e-242, 1.55e-242j)
| (0.8090169943749474241 - 2.3753223141076538686e-1011j)  +/-  (4.37e-243, 4.37e-243j)
| (-0.97236992039767660183 + 1.4473300228042625846e-1019j)  +/-  (5.7e-241, 5.7e-241j)
| (-0.76040596560003093817 + 1.6359375449659768453e-1023j)  +/-  (8.24e-244, 8.24e-244j)
| (-0.23344536385590541177 - 2.2532021639922871498e-1033j)  +/-  (5.32e-252, 5.32e-252j)
| (0.64944804833018365573 - 6.4570467453491019739e-1023j)  +/-  (2.28e-245, 2.28e-245j)
| (0.7071067811865475244 + 2.2103642898833600119e-1025j)  +/-  (1.54e-244, 1.54e-244j)
| (0.15643446504023086901 + 2.7589474540496508556e-1038j)  +/-  (2.2e-253, 2.2e-253j)
| (-0.64944804833018365573 - 6.8971110097962607198e-1037j)  +/-  (1.99e-245, 1.99e-245j)
| (-0.7071067811865475244 - 1.8721856345024204636e-1038j)  +/-  (1.6e-244, 1.6e-244j)
| (0.078459095727844945033 + 4.5022999653566202696e-1041j)  +/-  (1.12e-254, 1.12e-254j)
| (0.76040596560003093817 - 2.2889200108261952359e-1042j)  +/-  (7.55e-244, 7.55e-244j)
| (0.45399049973954679156 - 1.7143958696928861735e-1050j)  +/-  (1.79e-248, 1.79e-248j)
| (-0.15643446504023086901 - 4.4945275039101217468e-1058j)  +/-  (2.57e-253, 2.57e-253j)
| (-0.58778525229247312917 + 1.3569707051887394647e-1050j)  +/-  (2.32e-246, 2.32e-246j)
| (-0.078459095727844945033 + 2.2121150680501925063e-1058j)  +/-  (1.22e-254, 1.22e-254j)
| (0.38268343236508977173 + 3.0632853136584339947e-1052j)  +/-  (1.43e-249, 1.43e-249j)
| (0.58778525229247312917 + 5.8202933400214859332e-1051j)  +/-  (2.51e-246, 2.51e-246j)
| (1.0365231442263043835e-1060 + 6.6894687388937882119e-1061j)  +/-  (5.06e-1059, 5.06e-1059j)
| (-0.45399049973954679156 + 1.9169443885904797237e-1059j)  +/-  (1.94e-248, 1.94e-248j)
| (-0.38268343236508977173 - 2.1008728199856203579e-1062j)  +/-  (1.47e-249, 1.47e-249j)
| (0.23344536385590541177 + 1.9997646531091659247e-1059j)  +/-  (5.06e-252, 5.06e-252j)
| (0.52249856471594886499 + 3.3234337798507429469e-1059j)  +/-  (2.51e-247, 2.51e-247j)
| (0.3090169943749474241 - 3.6227014560417852624e-1066j)  +/-  (1.09e-250, 1.09e-250j)
| (-0.3090169943749474241 + 1.5957753073933759025e-1067j)  +/-  (9.72e-251, 9.72e-251j)
| (-0.52249856471594886499 + 2.9826059127455562164e-1064j)  +/-  (2.82e-247, 2.82e-247j)
-------------------------------------------------
The weights are:
| (0.0125 - 1.4544492179003163424e-924j)  +/-  (7.48e-73, 7e-189j)
| (0.0125 - 1.363120166729443587e-927j)  +/-  (1.28e-73, 1.2e-189j)
| (0.025 - 2.7946297923093733225e-927j)  +/-  (1.17e-73, 1.09e-189j)
| (0.025 + 1.7687547709958228151e-924j)  +/-  (3.91e-73, 3.66e-189j)
| (0.025 + 7.1629626653649238388e-926j)  +/-  (1.09e-74, 1.02e-190j)
| (0.025 - 4.4287130496514652868e-925j)  +/-  (8.58e-74, 8.04e-190j)
| (0.025 - 2.8833748573437704962e-927j)  +/-  (3.67e-75, 3.43e-191j)
| (0.025 + 2.8341071126218172398e-927j)  +/-  (5.82e-75, 5.45e-191j)
| (0.025 - 2.743126553373672434e-927j)  +/-  (1.67e-75, 1.56e-191j)
| (0.025 - 1.1140360787963005028e-925j)  +/-  (1.15e-75, 1.08e-191j)
| (0.025 - 5.0025752700473729075e-926j)  +/-  (1.22e-76, 1.14e-192j)
| (0.025 + 2.730448864763299618e-927j)  +/-  (1.93e-75, 1.81e-191j)
| (0.025 + 2.9430867212245380008e-927j)  +/-  (3e-77, 2.81e-193j)
| (0.025 - 3.0140571834714679863e-927j)  +/-  (3.17e-78, 2.97e-194j)
| (0.025 + 1.9733857974333444863e-925j)  +/-  (6.13e-76, 5.74e-192j)
| (0.025 + 3.7001131570339066854e-926j)  +/-  (3.2e-78, 2.99e-194j)
| (0.025 - 2.8549559417984855901e-926j)  +/-  (3.75e-79, 3.51e-195j)
| (0.025 + 2.7644310585604676639e-927j)  +/-  (4.7e-77, 4.4e-193j)
| (0.025 + 3.0972859519135446028e-927j)  +/-  (5.37e-80, 5.03e-196j)
| (0.025 + 4.4205287292763692663e-927j)  +/-  (2.76e-83, 2.59e-199j)
| (0.025 + 1.5553987478733100668e-926j)  +/-  (1.52e-82, 1.42e-198j)
| (0.025 - 1.8615933441567763907e-926j)  +/-  (5.83e-82, 5.46e-198j)
| (0.025 - 6.4636124177095632812e-927j)  +/-  (4.88e-85, 4.57e-201j)
| (0.025 + 3.3056395273786194054e-927j)  +/-  (2.87e-83, 2.68e-199j)
| (0.025 - 3.1939892261033340103e-927j)  +/-  (2e-82, 1.87e-198j)
| (0.025 + 5.9166995644368215523e-927j)  +/-  (8.68e-86, 8.12e-202j)
| (0.025 + 2.2757163718924708522e-926j)  +/-  (5.19e-83, 4.86e-199j)
| (0.025 - 9.9860545728909012138e-927j)  +/-  (3.96e-86, 3.71e-202j)
| (0.025 - 4.7149067515279300184e-927j)  +/-  (3.11e-86, 2.91e-202j)
| (0.025 - 3.4340164446327890088e-927j)  +/-  (1.21e-85, 1.13e-201j)
| (0.025 + 5.0558066490578682233e-927j)  +/-  (1.78e-86, 1.67e-202j)
| (0.025 + 8.832551972171349308e-927j)  +/-  (4.84e-87, 4.53e-203j)
| (0.025 - 1.3227281889454374893e-926j)  +/-  (2.71e-86, 2.54e-202j)
| (0.025 - 5.4524806669177744794e-927j)  +/-  (4.84e-87, 4.53e-203j)
| (0.025 - 3.7500112056402548224e-927j)  +/-  (5.31e-88, 4.97e-204j)
| (0.025 + 3.9434049322419867346e-927j)  +/-  (3.99e-88, 3.73e-204j)
| (0.025 + 7.1129707000987127228e-927j)  +/-  (3.46e-88, 3.24e-204j)
| (0.025 + 1.1418773356512025869e-926j)  +/-  (4.18e-88, 3.92e-204j)
| (0.025 - 7.890904150364080972e-927j)  +/-  (2.11e-88, 1.97e-204j)
| (0.025 - 4.1653245835217909754e-927j)  +/-  (3.81e-89, 3.61e-205j)
| (0.025 + 3.5812714660489934214e-927j)  +/-  (3.04e-89, 2.79e-205j)
