Starting with polynomial:
P : 1024*t^11 - 2816*t^9 + 2816*t^7 - 1232*t^5 + 220*t^3 - 11*t
Extension levels are: 11 22 34
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P1 : 1024*t^11 - 2816*t^9 + 2816*t^7 - 1232*t^5 + 220*t^3 - 11*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : 1024*t^33 - 8448*t^31 + 31680*t^29 - 71456*t^27 + 108108*t^25 - 115830*t^23 + 180895/2*t^21 - 208725/4*t^19 + 1427679/64*t^17 - 898909/128*t^15 + 820743/512*t^13 - 264537/1024*t^11 + 230945/8192*t^9 - 31977/16384*t^7 + 5049/65536*t^5 - 187/131072*t^3 + 33/4194304*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1024*t^67 - 17408*t^65 + 141376*t^63 - 730112*t^61 + 2692540*t^59 - 7548932*t^57 + 33451761/2*t^55 - 30056499*t^53 + 2855107827/64*t^51 - 3546403575/64*t^49 + 29776261515/512*t^47 - 6647420325/128*t^45 + 324837273215/8192*t^43 - 212768262805/8192*t^41 + 958190103325/65536*t^39 - 231926696085/32768*t^37 + 12351427293471/4194304*t^35 - 4409214364119/4194304*t^33 + 10773167031869/33554432*t^31 - 350450612105/4194304*t^29 + 9893428758983/536870912*t^27 - 1836512465073/536870912*t^25 + 2275628770545/4294967296*t^23 - 145467913695/2147483648*t^21 + 969342861825/137438953472*t^19 - 80820408357/137438953472*t^17 + 42255951417/1099511627776*t^15 - 526453501/274877906944*t^13 + 1234423193/17592186044416*t^11 - 31622635/17592186044416*t^9 + 4214419/140737488355328*t^7 - 20383/70368744177664*t^5 + 23969/18014398509481984*t^3 - 33/18014398509481984*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: 0
  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:   67 out of 67
Indefinite weights: 0 out of 67
Negative weights:   0 out of 67
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99547192257308460473 + 2.7109301712610745506e-802j)  +/-  (8.72e-231, 8.72e-231j)
| (-0.99547192257308460473 + 1.6552716201254924592e-807j)  +/-  (8.17e-231, 8.17e-231j)
| (-0.94500081871466848739 + 8.0973475716548767539e-833j)  +/-  (7.52e-232, 7.52e-232j)
| (-0.99886733918300797666 + 5.3021404843891895743e-842j)  +/-  (1.02e-230, 1.02e-230j)
| (0.88883544865492346631 - 3.9397739145471693898e-865j)  +/-  (4.96e-233, 4.96e-233j)
| (0.94500081871466848739 - 2.2976022547234467552e-864j)  +/-  (7.26e-232, 7.26e-232j)
| (1 - 2.0503969540075000606e-861j)  +/-  (5.89e-231, 5.89e-231j)
| (-0.9283679330160726102 - 1.3576551371078226329e-862j)  +/-  (3.56e-232, 3.56e-232j)
| (-1 - 2.5113908378992538035e-859j)  +/-  (5.53e-231, 5.53e-231j)
| (-0.98982144188093273238 + 2.9547139305179471482e-873j)  +/-  (7.36e-231, 7.36e-231j)
| (0.86602540378443864676 - 1.0116547177321448089e-884j)  +/-  (1.82e-233, 1.82e-233j)
| (0.98982144188093273238 - 6.612586709154871251e-881j)  +/-  (6.92e-231, 6.92e-231j)
| (-0.88883544865492346631 + 7.7436328667826264153e-884j)  +/-  (4.64e-233, 4.64e-233j)
| (-0.86602540378443864676 + 1.0898105141866078452e-885j)  +/-  (1.61e-233, 1.61e-233j)
| (0.65486073394528506406 - 7.4012280059045892895e-891j)  +/-  (2.3e-238, 2.3e-238j)
| (0.84125353283118116886 - 4.7081027640910686375e-886j)  +/-  (5.56e-234, 5.56e-234j)
| (0.90963199535451837141 + 1.1393296413232867727e-884j)  +/-  (1.35e-232, 1.35e-232j)
| (-0.9819286972627067004 + 5.7382071324713732492e-882j)  +/-  (5.26e-231, 5.26e-231j)
| (-0.78605309474278746976 - 8.2911925566835424971e-892j)  +/-  (2.69e-235, 2.69e-235j)
| (-0.97181156832354168738 - 1.7370446456850153766e-886j)  +/-  (2.8e-231, 2.8e-231j)
| (0.95949297361449738989 - 3.9356838842040808055e-897j)  +/-  (1.56e-231, 1.56e-231j)
| (0.81457595205033570778 - 2.5021632624308723954e-902j)  +/-  (1.38e-234, 1.38e-234j)
| (-0.65486073394528506406 + 2.5168777351384296511e-906j)  +/-  (2.33e-238, 2.33e-238j)
| (-0.84125353283118116886 - 2.0335005587520123516e-902j)  +/-  (5.13e-234, 5.13e-234j)
| (-0.81457595205033570778 + 2.2032462755964489171e-902j)  +/-  (1.12e-234, 1.12e-234j)
| (0.9819286972627067004 + 1.0603457122346409597e-897j)  +/-  (4.41e-231, 4.41e-231j)
| (0.72373403810507016164 - 1.1459789512243894661e-904j)  +/-  (1.04e-236, 1.04e-236j)
| (0.75574957435425828377 + 3.3138403127445373553e-904j)  +/-  (5.23e-236, 5.23e-236j)
| (0.99886733918300797666 - 1.5613356987658235047e-899j)  +/-  (1.03e-230, 1.03e-230j)
| (-0.61815898622060521322 + 1.8496072985042351765e-910j)  +/-  (3.1e-239, 3.1e-239j)
| (-0.18925124436041020362 - 5.5275174243540203346e-923j)  +/-  (1.23e-250, 1.23e-250j)
| (0.18925124436041020362 + 6.6942978410234005516e-924j)  +/-  (1.35e-250, 1.35e-250j)
| (0.69007901148211198967 - 4.5755343905681321069e-911j)  +/-  (1.58e-237, 1.58e-237j)
| (-0.95949297361449738989 - 1.5570789421469151996e-903j)  +/-  (1.53e-231, 1.53e-231j)
| (-0.69007901148211198967 - 1.5494598587083215854e-918j)  +/-  (1.49e-237, 1.49e-237j)
| (-0.75574957435425828377 - 3.6578998454430859952e-916j)  +/-  (5.95e-236, 5.95e-236j)
| (0.61815898622060521322 - 5.5342421138994715737e-920j)  +/-  (3.11e-239, 3.11e-239j)
| (0.5800569095711981792 + 3.7406785079231481785e-921j)  +/-  (3.73e-240, 3.73e-240j)
| (0.04758191582374229745 - 9.3864768190980272092e-939j)  +/-  (1.51e-254, 1.51e-254j)
| (0.97181156832354168738 + 1.4449309762091985075e-913j)  +/-  (3.13e-231, 3.13e-231j)
| (-0.54064081745559758211 + 4.0607643742619588316e-924j)  +/-  (4.17e-241, 4.17e-241j)
| (-0.14231483827328514044 + 9.8746682333604500684e-937j)  +/-  (5.17e-252, 5.17e-252j)
| (0.23575893550942722825 + 5.4208691944956281296e-933j)  +/-  (2.41e-249, 2.41e-249j)
| (0.54064081745559758211 + 1.9058161234327833601e-925j)  +/-  (3.89e-241, 3.89e-241j)
| (-0.095056043304182663632 + 3.2338694740179882157e-937j)  +/-  (2.64e-253, 2.64e-253j)
| (-0.5800569095711981792 - 1.4216230368096063035e-922j)  +/-  (3.72e-240, 3.72e-240j)
| (-0.90963199535451837141 + 2.0321253880373718962e-917j)  +/-  (1.33e-232, 1.33e-232j)
| (0.78605309474278746976 + 1.6413614447041850975e-919j)  +/-  (2.95e-235, 2.95e-235j)
| (0.5 - 8.9622057393377110826e-928j)  +/-  (3.4e-242, 3.4e-242j)
| (-0.28173255684142969771 + 2.8755734425739473593e-934j)  +/-  (5.97e-248, 5.97e-248j)
| (-0.72373403810507016164 - 6.1086551912113550027e-922j)  +/-  (9.22e-237, 9.22e-237j)
| (-0.5 + 4.6929495780458975764e-928j)  +/-  (3.56e-242, 3.56e-242j)
| (-0.23575893550942722825 - 8.040249326689105612e-935j)  +/-  (2.63e-249, 2.63e-249j)
| (0.45822652172741039456 - 4.8649375718166509533e-929j)  +/-  (2.5e-243, 2.5e-243j)
| (0.37166245566032751915 - 3.5898770415767597622e-931j)  +/-  (1.3e-245, 1.3e-245j)
| (0.9283679330160726102 - 2.4939499506436743876e-935j)  +/-  (3.66e-232, 3.66e-232j)
| (-0.45822652172741039456 + 9.4392106805613582683e-950j)  +/-  (2.55e-243, 2.55e-243j)
| (-0.41541501300188642553 - 2.1748199171666967546e-951j)  +/-  (2.07e-244, 2.07e-244j)
| (0.095056043304182663632 - 8.1470436361516628672e-960j)  +/-  (2.61e-253, 2.61e-253j)
| (0.41541501300188642553 + 3.4809789214498372778e-952j)  +/-  (2.1e-244, 2.1e-244j)
| (0.14231483827328514044 + 2.2468180150510758365e-958j)  +/-  (4.9e-252, 4.9e-252j)
| (-0.37166245566032751915 - 2.3543827911894422407e-952j)  +/-  (1.28e-245, 1.28e-245j)
| (-0.32706796331742163634 + 5.3773007778648555107e-953j)  +/-  (8.05e-247, 8.05e-247j)
| (-0.04758191582374229745 + 2.6745697459770595815e-961j)  +/-  (1.03e-254, 1.03e-254j)
| (0.32706796331742163634 + 1.4936985135685881411e-953j)  +/-  (7.19e-247, 7.19e-247j)
| (0.28173255684142969771 - 1.1141553499584084902e-954j)  +/-  (5.36e-248, 5.36e-248j)
| (2.0924719956290565541e-1080 - 2.625849424050884347e-1080j)  +/-  (2.25e-1078, 2.25e-1078j)
-------------------------------------------------
The weights are:
| (0.015151515151515151515 + 2.262632252665595985e-802j)  +/-  (2.06e-36, 3.7e-145j)
| (0.015151515151515151515 - 2.064458294016249286e-804j)  +/-  (1.01e-36, 1.81e-145j)
| (0.015151515151515151515 + 2.1162398307014532627e-804j)  +/-  (2.18e-37, 3.91e-146j)
| (0.015151515151515151515 + 2.0669506959550020648e-804j)  +/-  (4.87e-37, 8.73e-146j)
| (0.015151515151515151515 - 3.8518420444880937771e-803j)  +/-  (1.32e-38, 2.37e-147j)
| (0.015151515151515151515 + 8.1382593011216729286e-803j)  +/-  (1.35e-38, 2.43e-147j)
| (0.0075757575757575757576 + 4.5355562925575950544e-802j)  +/-  (1.07e-38, 1.92e-147j)
| (0.015151515151515151515 - 2.1346636084847333783e-804j)  +/-  (1.41e-38, 2.53e-147j)
| (0.0075757575757575757576 - 1.0319670056511403663e-804j)  +/-  (2.5e-37, 4.49e-146j)
| (0.015151515151515151515 + 2.0645100768912139909e-804j)  +/-  (4.43e-38, 7.94e-147j)
| (0.015151515151515151515 + 3.173100559880869665e-803j)  +/-  (3.42e-41, 6.13e-150j)
| (0.015151515151515151515 + 7.2692397494245139998e-802j)  +/-  (1.35e-40, 2.42e-149j)
| (0.015151515151515151515 - 2.179594926070492933e-804j)  +/-  (7.2e-41, 1.29e-149j)
| (0.015151515151515151515 + 2.2063471372230690918e-804j)  +/-  (2.53e-41, 4.53e-150j)
| (0.015151515151515151515 - 1.2059101161014112576e-803j)  +/-  (6.76e-44, 1.21e-152j)
| (0.015151515151515151515 - 2.6634098939365830502e-803j)  +/-  (3.12e-42, 5.59e-151j)
| (0.015151515151515151515 + 4.7850329788281564716e-803j)  +/-  (7.07e-42, 1.27e-150j)
| (0.015151515151515151515 - 2.0753549319605731026e-804j)  +/-  (3.76e-40, 6.73e-149j)
| (0.015151515151515151515 - 2.3054723128605663763e-804j)  +/-  (1.63e-44, 2.91e-153j)
| (0.015151515151515151515 + 2.0868292055889541362e-804j)  +/-  (8.28e-41, 1.48e-149j)
| (0.015151515151515151515 - 1.1416313188072530679e-802j)  +/-  (1.52e-43, 2.72e-152j)
| (0.015151515151515151515 + 2.270624070899405075e-803j)  +/-  (4.43e-44, 7.93e-153j)
| (0.015151515151515151515 - 2.4888003173103211762e-804j)  +/-  (8.06e-47, 1.44e-155j)
| (0.015151515151515151515 - 2.2361378210418857658e-804j)  +/-  (8.62e-44, 1.54e-152j)
| (0.015151515151515151515 + 2.269121753320370333e-804j)  +/-  (2.47e-44, 4.42e-153j)
| (0.015151515151515151515 - 3.0328593747432846411e-802j)  +/-  (6.72e-45, 1.2e-153j)
| (0.015151515151515151515 - 1.5115544158923283085e-803j)  +/-  (4.19e-48, 7.5e-157j)
| (0.015151515151515151515 + 1.7134266178457253813e-803j)  +/-  (1.02e-47, 1.83e-156j)
| (0.015151515151515151515 - 1.2097101684520635116e-801j)  +/-  (1.17e-44, 2.1e-153j)
| (0.015151515151515151515 + 2.5454164744428559903e-804j)  +/-  (1.31e-50, 2.35e-159j)
| (0.015151515151515151515 + 3.4669982125680782362e-804j)  +/-  (1.08e-53, 1.94e-162j)
| (0.015151515151515151515 + 5.09470049609473258e-804j)  +/-  (6.26e-54, 1.12e-162j)
| (0.015151515151515151515 + 1.344977326991687112e-803j)  +/-  (4.3e-49, 7.71e-158j)
| (0.015151515151515151515 - 2.1003483057991865234e-804j)  +/-  (7.69e-46, 1.38e-154j)
| (0.015151515151515151515 + 2.4367887380139460126e-804j)  +/-  (2.63e-50, 4.71e-159j)
| (0.015151515151515151515 + 2.3453839220144775412e-804j)  +/-  (2.26e-49, 4.04e-158j)
| (0.015151515151515151515 + 1.0886093998720772909e-803j)  +/-  (8.05e-52, 1.44e-160j)
| (0.015151515151515151515 - 9.8876141091747306186e-804j)  +/-  (8.26e-53, 1.48e-161j)
| (0.015151515151515151515 - 4.3332529465637776803e-804j)  +/-  (1.77e-56, 3.17e-165j)
| (0.015151515151515151515 + 1.7360135911329329697e-802j)  +/-  (4.78e-49, 8.56e-158j)
| (0.015151515151515151515 + 2.6738826822580525461e-804j)  +/-  (7.59e-55, 1.36e-163j)
| (0.015151515151515151515 - 3.6100231175109012042e-804j)  +/-  (1.29e-56, 2.32e-165j)
| (0.015151515151515151515 - 5.4065871601893373647e-804j)  +/-  (6.45e-57, 1.15e-165j)
| (0.015151515151515151515 + 9.0307423663091181199e-804j)  +/-  (6.38e-55, 1.14e-163j)
| (0.015151515151515151515 + 3.7664688204144470794e-804j)  +/-  (4.13e-57, 7.39e-166j)
| (0.015151515151515151515 - 2.6069817023778173349e-804j)  +/-  (2.8e-55, 5.02e-164j)
| (0.015151515151515151515 + 2.1557424259748175358e-804j)  +/-  (8.34e-52, 1.49e-160j)
| (0.015151515151515151515 - 1.961364721054440445e-803j)  +/-  (3.63e-53, 6.51e-162j)
| (0.015151515151515151515 - 8.2899988071840000403e-804j)  +/-  (2.13e-56, 3.81e-165j)
| (0.015151515151515151515 + 3.2159494766529271365e-804j)  +/-  (1.14e-58, 2.03e-167j)
| (0.015151515151515151515 - 2.3890745945466229157e-804j)  +/-  (1.75e-54, 3.14e-163j)
| (0.015151515151515151515 - 2.7465539114663814386e-804j)  +/-  (1.22e-57, 2.19e-166j)
| (0.015151515151515151515 - 3.3360350609556214969e-804j)  +/-  (1.5e-58, 2.69e-167j)
| (0.015151515151515151515 + 7.6454087483788877706e-804j)  +/-  (6.18e-59, 1.11e-167j)
| (0.015151515151515151515 + 6.5844760790404391149e-804j)  +/-  (3.51e-60, 6.29e-169j)
| (0.015151515151515151515 - 6.1210504901121155337e-803j)  +/-  (9.53e-56, 1.71e-164j)
| (0.015151515151515151515 + 2.8254842746193119878e-804j)  +/-  (2.66e-59, 4.76e-168j)
| (0.015151515151515151515 - 2.9112247413217193344e-804j)  +/-  (5.58e-60, 1e-168j)
| (0.015151515151515151515 + 4.5617245800911903249e-804j)  +/-  (5.36e-62, 9.61e-171j)
| (0.015151515151515151515 - 7.0811321744668063224e-804j)  +/-  (3.5e-61, 6.27e-170j)
| (0.015151515151515151515 - 4.8144136949363366706e-804j)  +/-  (4.92e-62, 8.81e-171j)
| (0.015151515151515151515 + 3.0043974148124813266e-804j)  +/-  (1.22e-61, 2.19e-170j)
| (0.015151515151515151515 - 3.1057062065920214872e-804j)  +/-  (7.72e-62, 1.38e-170j)
| (0.015151515151515151515 - 3.9379006216893460113e-804j)  +/-  (2.25e-63, 4.03e-172j)
| (0.015151515151515151515 - 6.1451719792450405007e-804j)  +/-  (1.22e-63, 2.17e-172j)
| (0.015151515151515151515 + 5.754840125535382614e-804j)  +/-  (9.8e-64, 1.73e-172j)
| (0.015151515151515151515 + 4.1261283050216666466e-804j)  +/-  (7.32e-64, 1.34e-172j)
