Starting with polynomial:
P : 1024*t^10 - 2304*t^8 + 1792*t^6 - 560*t^4 + 60*t^2 - 1
Extension levels are: 10 55
-------------------------------------------------
Trying to find an order 55 Kronrod extension for:
P1 : 1024*t^10 - 2304*t^8 + 1792*t^6 - 560*t^4 + 60*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1024*t^65 - 16384*t^63 + 124992*t^61 - 605120*t^59 + 2087420*t^57 - 5461512*t^55 + 22528737/2*t^53 - 37584261/2*t^51 + 1652411475/64*t^49 - 473498025/16*t^47 + 14624324715/512*t^45 - 11965356585/512*t^43 + 133391567855/8192*t^41 - 39688347475/4096*t^39 + 323176543725/65536*t^37 - 140676848445/65536*t^35 + 3348108992991/4194304*t^33 - 132638171391/524288*t^31 + 2284324062845/33554432*t^29 - 519280833995/33554432*t^27 + 1584935415063/536870912*t^25 - 125788525005/268435456*t^23 + 263012370465/4294967296*t^21 - 27923456925/4294967296*t^19 + 75792240225/137438953472*t^17 - 1257042033/34359738368*t^15 + 2030606361/1099511627776*t^13 - 75207643/1099511627776*t^11 + 31100905/17592186044416*t^9 - 260865/8796093022208*t^7 + 40579/140737488355328*t^5 - 187/140737488355328*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
-------------------------------------------------
The nodes are:
| (0.99547192257308460473 + 4.8090283715415611798e-892j)  +/-  (3.73e-233, 3.73e-233j)
| (-0.97181156832354168738 + 1.598308606745583026e-888j)  +/-  (6.9e-233, 6.9e-233j)
| (-0.9283679330160726102 + 8.6328876999866783019e-900j)  +/-  (2.57e-233, 2.57e-233j)
| (-0.9819286972627067004 - 1.8154430072514883769e-913j)  +/-  (7.92e-233, 7.92e-233j)
| (0.9283679330160726102 + 1.2236192377670497028e-936j)  +/-  (2.42e-233, 2.42e-233j)
| (0.90963199535451837141 + 1.2698247594056728448e-938j)  +/-  (1.33e-233, 1.33e-233j)
| (-0.99886733918300797666 - 8.0805901768851883188e-938j)  +/-  (1.07e-233, 1.07e-233j)
| (-0.90963199535451837141 + 2.7932398950840992182e-965j)  +/-  (1.28e-233, 1.28e-233j)
| (-0.28173255684142969771 + 1.1115581333640578504e-988j)  +/-  (4.27e-248, 4.27e-248j)
| (-0.99547192257308460473 - 1.3040606142778780608e-972j)  +/-  (3.78e-233, 3.78e-233j)
| (0.86602540378443864676 - 4.4031722256001108048e-986j)  +/-  (2.23e-234, 2.23e-234j)
| (0.94500081871466848739 + 7.9436167332471748966e-983j)  +/-  (4.15e-233, 4.15e-233j)
| (-0.88883544865492346631 - 1.3348713578889126249e-985j)  +/-  (5.86e-234, 5.86e-234j)
| (-0.84125353283118116886 + 2.4797832083561938288e-987j)  +/-  (7.45e-235, 7.45e-235j)
| (0.95949297361449738989 - 3.2620032643908858967e-983j)  +/-  (6.21e-233, 6.21e-233j)
| (0.88883544865492346631 - 1.400438181963284451e-985j)  +/-  (6.04e-234, 6.04e-234j)
| (0.98982144188093273238 + 1.760093174539436292e-983j)  +/-  (6.6e-233, 6.6e-233j)
| (-0.98982144188093273238 + 7.4042292606085878893e-984j)  +/-  (6.9e-233, 6.9e-233j)
| (-0.75574957435425828377 - 1.0063947419479461189e-994j)  +/-  (1.71e-236, 1.71e-236j)
| (-0.95949297361449738989 - 7.0702961249907009767e-990j)  +/-  (6.05e-233, 6.05e-233j)
| (0.84125353283118116886 - 4.7863372817242264005e-996j)  +/-  (8.59e-235, 8.59e-235j)
| (0.75574957435425828377 - 3.85487564782189433e-998j)  +/-  (1.68e-236, 1.68e-236j)
| (-0.94500081871466848739 + 7.9693499829139513226e-995j)  +/-  (4.64e-233, 4.64e-233j)
| (-0.81457595205033570778 + 1.5563789039146486167e-1000j)  +/-  (2.67e-235, 2.67e-235j)
| (-0.78605309474278746976 - 2.7832160413934989088e-1002j)  +/-  (5.94e-236, 5.94e-236j)
| (0.9819286972627067004 - 4.3513267786604333514e-997j)  +/-  (7.36e-233, 7.36e-233j)
| (0.78605309474278746976 + 2.1736608833687165796e-1003j)  +/-  (6.5e-236, 6.5e-236j)
| (0.81457595205033570778 - 1.7062030886388348809e-1002j)  +/-  (2.51e-235, 2.51e-235j)
| (0.97181156832354168738 - 3.7880342302333424862e-1000j)  +/-  (7.81e-233, 7.81e-233j)
| (-0.65486073394528506406 + 1.936188701464840575e-1007j)  +/-  (9.49e-239, 9.49e-239j)
| (0.99886733918300797666 + 2.2458424422688268187e-1003j)  +/-  (1.13e-233, 1.13e-233j)
| (0.54064081745559758211 - 3.2559534205799874684e-1012j)  +/-  (1.81e-241, 1.81e-241j)
| (0.65486073394528506406 + 8.3669350381150585761e-1010j)  +/-  (8.84e-239, 8.84e-239j)
| (0.72373403810507016164 - 9.4854699176378894616e-1008j)  +/-  (2.92e-237, 2.92e-237j)
| (-0.61815898622060521322 + 1.1078652751975740005e-1009j)  +/-  (1.35e-239, 1.35e-239j)
| (-0.72373403810507016164 + 1.0799362765609244412e-1006j)  +/-  (3.46e-237, 3.46e-237j)
| (0.04758191582374229745 - 5.6659910651077898286e-1025j)  +/-  (1.02e-254, 1.02e-254j)
| (0.61815898622060521322 - 1.9641508180302807196e-1010j)  +/-  (1.51e-239, 1.51e-239j)
| (0.28173255684142969771 + 6.5357202092962008092e-1019j)  +/-  (4.05e-248, 4.05e-248j)
| (-0.69007901148211198967 - 1.3758098862723060841e-1006j)  +/-  (5.19e-238, 5.19e-238j)
| (-0.5 + 6.1522209389104136367e-1012j)  +/-  (2.23e-242, 2.23e-242j)
| (-0.86602540378443864676 + 1.1264669287573127059e-1012j)  +/-  (2.25e-234, 2.25e-234j)
| (0.69007901148211198967 + 9.0794637312244332372e-1021j)  +/-  (5.84e-238, 5.84e-238j)
| (0.5800569095711981792 + 3.8916818485762843063e-1026j)  +/-  (1.9e-240, 1.9e-240j)
| (-3.8083229657765671509e-1061 - 4.6729636239999764406e-1061j)  +/-  (3.92e-1059, 3.92e-1059j)
| (-0.54064081745559758211 + 1.0394814658335223229e-1023j)  +/-  (1.84e-241, 1.84e-241j)
| (-0.5800569095711981792 - 4.5782574120128970612e-1028j)  +/-  (1.64e-240, 1.64e-240j)
| (0.23575893550942722825 + 2.4593715591310225751e-1036j)  +/-  (2.34e-249, 2.34e-249j)
| (0.5 + 3.1782633641881568886e-1030j)  +/-  (2.26e-242, 2.26e-242j)
| (0.18925124436041020362 - 3.4436479269918556562e-1039j)  +/-  (1.2e-250, 1.2e-250j)
| (-0.32706796331742163634 - 2.7356121540087809835e-1035j)  +/-  (5.96e-247, 5.96e-247j)
| (-0.45822652172741039456 - 1.7433883838603233545e-1031j)  +/-  (2.06e-243, 2.06e-243j)
| (-0.14231483827328514044 + 5.9560829895292302923e-1042j)  +/-  (5.89e-252, 5.89e-252j)
| (0.45822652172741039456 + 2.0299049175753201017e-1032j)  +/-  (1.97e-243, 1.97e-243j)
| (0.41541501300188642553 + 8.0177154941591142947e-1033j)  +/-  (1.38e-244, 1.38e-244j)
| (-0.095056043304182663632 + 3.6751337559140294376e-1042j)  +/-  (2.25e-253, 2.25e-253j)
| (-0.41541501300188642553 + 3.7957295824128843181e-1033j)  +/-  (1.43e-244, 1.43e-244j)
| (-0.18925124436041020362 - 2.5412604573985536628e-1041j)  +/-  (1.17e-250, 1.17e-250j)
| (0.14231483827328514044 - 7.7886150499278177591e-1041j)  +/-  (5.16e-252, 5.16e-252j)
| (0.37166245566032751915 - 1.013438957181545924e-1034j)  +/-  (9.44e-246, 9.44e-246j)
| (0.095056043304182663632 + 1.5630020165773811211e-1042j)  +/-  (2.12e-253, 2.12e-253j)
| (-0.23575893550942722825 + 3.0196682180222026365e-1038j)  +/-  (2.14e-249, 2.14e-249j)
| (-0.37166245566032751915 + 2.0679818709000887063e-1034j)  +/-  (9.25e-246, 9.25e-246j)
| (-0.04758191582374229745 + 7.6369697573719246186e-1044j)  +/-  (1.02e-254, 1.02e-254j)
| (0.32706796331742163634 + 1.6066859229477646411e-1035j)  +/-  (5.86e-247, 5.86e-247j)
-------------------------------------------------
The weights are:
| (0.00013690380861585833031 - 1.2210686299607903376e-892j)  +/-  (4.58e-34, 6.76e-145j)
| (0.00084215569200815555825 + 3.5301451178620450735e-890j)  +/-  (2.25e-34, 3.33e-145j)
| (0.0020929239537494684724 - 7.7000027120544986833e-890j)  +/-  (8.13e-35, 1.2e-145j)
| (0.00054266717412066204393 + 8.5730673690906085992e-890j)  +/-  (1.31e-34, 1.94e-145j)
| (0.0020929239537494684724 - 1.7754318303990470015e-891j)  +/-  (3.14e-36, 4.64e-147j)
| (0.0026146914095054161814 + 2.2358596833289115731e-891j)  +/-  (2.96e-36, 4.37e-147j)
| (3.4303616870571176316e-05 - 2.0264638761326769118e-891j)  +/-  (4.77e-36, 7.04e-147j)
| (0.0026146914095054161814 + 6.7210574536356217196e-890j)  +/-  (1.05e-36, 1.55e-147j)
| (0.013948890400236220976 + 3.2312612909492852453e-890j)  +/-  (1.14e-39, 1.68e-150j)
| (0.00013690380861585833031 + 9.2481182186657224661e-891j)  +/-  (7.48e-36, 1.1e-146j)
| (0.0037878787878787878788 + 3.3082704458963012345e-891j)  +/-  (2.27e-38, 3.35e-149j)
| (0.0016208098883122161382 + 1.3669343772230114835e-891j)  +/-  (3.11e-38, 4.58e-149j)
| (0.003181387048703044097 - 6.128155537914619342e-890j)  +/-  (5.75e-38, 8.49e-149j)
| (0.0044286741439251028369 - 5.4217569693035689973e-890j)  +/-  (2.02e-39, 2.98e-150j)
| (0.0012026247512789305389 - 1.0113424954935804865e-891j)  +/-  (6.96e-39, 1.03e-149j)
| (0.003181387048703044097 - 2.7471806237622208664e-891j)  +/-  (8.86e-39, 1.31e-149j)
| (0.00030687141201138340992 + 2.7615144399488598581e-892j)  +/-  (9.52e-40, 1.4e-150j)
| (0.00030687141201138340992 - 2.7233610423050518851e-890j)  +/-  (2.74e-37, 4.05e-148j)
| (0.0064976148615660216633 + 4.8067589709769824339e-890j)  +/-  (1.24e-41, 1.83e-152j)
| (0.0012026247512789305389 - 1.5603802059580491261e-889j)  +/-  (3.5e-38, 5.16e-149j)
| (0.0044286741439251028369 - 3.9179103363192989472e-891j)  +/-  (5.3e-42, 7.82e-153j)
| (0.0064976148615660216633 + 6.0245115677284921004e-891j)  +/-  (5.97e-44, 8.81e-155j)
| (0.0016208098883122161382 + 9.6624122845713719376e-890j)  +/-  (1.29e-38, 1.91e-149j)
| (0.0050979699748680179065 + 5.1822497023161810024e-890j)  +/-  (7.75e-42, 1.14e-152j)
| (0.0057897050340194906951 - 4.9817515850650372614e-890j)  +/-  (1.96e-42, 2.89e-153j)
| (0.00054266717412066204393 - 4.6321258011170327344e-892j)  +/-  (5.12e-43, 7.55e-154j)
| (0.0057897050340194906951 - 5.2774863245013482388e-891j)  +/-  (8.65e-45, 1.28e-155j)
| (0.0050979699748680179065 + 4.5747854610390438959e-891j)  +/-  (3.16e-44, 4.67e-155j)
| (0.00084215569200815555825 + 7.0965081958340126205e-892j)  +/-  (3.8e-43, 5.61e-154j)
| (0.0086539002899491298518 - 4.3642108105663425465e-890j)  +/-  (8.78e-49, 1.3e-159j)
| (3.4303616870571176316e-05 + 2.2963243208673312542e-893j)  +/-  (2.74e-44, 4.04e-155j)
| (0.010722841007590048678 + 1.1342873766726370488e-890j)  +/-  (4.06e-51, 5.99e-162j)
| (0.0086539002899491298518 - 8.5152236530512235515e-891j)  +/-  (1.14e-49, 1.69e-160j)
| (0.0072152885164868007769 - 6.8142716489910509986e-891j)  +/-  (5.17e-48, 7.63e-159j)
| (0.0093618101174956608201 + 4.2312849257439369301e-890j)  +/-  (1.74e-51, 2.57e-162j)
| (0.0072152885164868007769 - 4.648852484833194169e-890j)  +/-  (7.8e-50, 1.15e-160j)
| (0.015117211534644580339 - 2.3709968714217304531e-890j)  +/-  (9.15e-56, 1.35e-166j)
| (0.0093618101174956608201 + 9.4228369629646105764e-891j)  +/-  (2.62e-51, 3.86e-162j)
| (0.013948890400236220976 + 1.7794677136097343852e-890j)  +/-  (2.01e-55, 2.97e-166j)
| (0.0079362266350283507383 + 4.5025599449641615684e-890j)  +/-  (1.03e-50, 1.52e-161j)
| (0.011363636363636363636 - 3.849910246675810693e-890j)  +/-  (1.29e-54, 1.9e-165j)
| (0.0037878787878787878788 + 5.7231518065241349781e-890j)  +/-  (5.39e-49, 7.96e-160j)
| (0.0079362266350283507383 + 7.6450931584489240124e-891j)  +/-  (3.61e-51, 5.32e-162j)
| (0.010053545176647133609 - 1.0366038955801314729e-890j)  +/-  (4.52e-53, 6.67e-164j)
| (0.015151515151515151515 + 2.4926550665608042072e-890j)  +/-  (2.38e-57, 3.52e-168j)
| (0.010722841007590048678 + 3.9751899804697513826e-890j)  +/-  (1.66e-54, 2.44e-165j)
| (0.010053545176647133609 - 4.1020239557775314869e-890j)  +/-  (8.15e-54, 1.2e-164j)
| (0.014309359459506995957 - 1.8948550310605790466e-890j)  +/-  (5.55e-58, 8.18e-169j)
| (0.011363636363636363636 - 1.2351330518821059966e-890j)  +/-  (2.15e-56, 3.17e-167j)
| (0.014608847977394489471 + 2.0119122536134900379e-890j)  +/-  (2.16e-58, 3.19e-169j)
| (0.013530705263202935377 - 3.3547311949139883018e-890j)  +/-  (4.78e-59, 7.06e-170j)
| (0.011970128102812107418 + 3.7255742999970644469e-890j)  +/-  (9.97e-58, 1.47e-168j)
| (0.014844643739503768105 - 2.8609547832952415311e-890j)  +/-  (1.98e-60, 2.92e-171j)
| (0.011970128102812107418 + 1.3389350572755810536e-890j)  +/-  (1.29e-58, 1.9e-169j)
| (0.012536823742009735334 - 1.4454835360153022526e-890j)  +/-  (2.57e-59, 3.79e-170j)
| (0.015014611342899293185 + 2.7377971392327421394e-890j)  +/-  (3.57e-61, 5.27e-172j)
| (0.012536823742009735334 - 3.601764009309911403e-890j)  +/-  (3.26e-60, 4.81e-171j)
| (0.014608847977394489471 + 2.9843179296079504838e-890j)  +/-  (2.59e-61, 3.82e-172j)
| (0.014844643739503768105 - 2.1304265132206147069e-890j)  +/-  (9.31e-62, 1.37e-172j)
| (0.013058591197765683043 + 1.5545654872620661893e-890j)  +/-  (1.02e-61, 1.5e-172j)
| (0.015014611342899293185 + 2.2501890248583102368e-890j)  +/-  (5.87e-62, 8.68e-173j)
| (0.014309359459506995957 - 3.1077786012346967869e-890j)  +/-  (2.07e-62, 3.05e-173j)
| (0.013058591197765683043 + 3.4782048393877457267e-890j)  +/-  (2.39e-62, 3.52e-173j)
| (0.015117211534644580339 - 2.614978968227789652e-890j)  +/-  (1.16e-62, 1.74e-173j)
| (0.013530705263202935377 - 1.6659656899763437569e-890j)  +/-  (8.51e-63, 1.18e-173j)
