Starting with polynomial:
P : t
Extension levels are: 1 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 53/4*t^51 + 1325/16*t^49 - 2597/8*t^47 + 57293/64*t^45 - 1890669/1024*t^43 + 12108327/4096*t^41 - 15417435/4096*t^39 + 253873763/65536*t^37 - 853939021/262144*t^35 + 2363226593/1048576*t^33 - 337603799/262144*t^31 + 1276307045/2097152*t^29 - 3986005079/16777216*t^27 + 5124863673/67108864*t^25 - 1348648335/67108864*t^23 + 9221838615/2147483648*t^21 - 6328712775/8589934592*t^19 + 3435586935/34359738368*t^17 - 180820365/17179869184*t^15 + 115067505/137438953472*t^13 - 213696795/4398046511104*t^11 + 34467225/17592186044416*t^9 - 899145/17592186044416*t^7 + 217035/281474976710656*t^5 - 6201/1125899906842624*t^3 + 53/4503599627370496*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:
| (0.99956083650879434943 + 1.2693834727467204736e-828j)  +/-  (2.34e-237, 2.34e-237j)
| (0.98904018732216397911 + 2.4201138544731482472e-830j)  +/-  (6.78e-237, 6.78e-237j)
| (-0.90279782996574351572 + 7.3131088169254564821e-836j)  +/-  (1.06e-237, 1.06e-237j)
| (-0.99956083650879434943 + 4.5363699695770458515e-856j)  +/-  (2.06e-237, 2.06e-237j)
| (0.92668960743183343805 - 2.1504507631857763417e-874j)  +/-  (1.86e-237, 1.86e-237j)
| (0.90279782996574351572 + 6.4090996442433004687e-882j)  +/-  (9.3e-238, 9.3e-238j)
| (-0.98904018732216397911 + 1.16675355979172151e-888j)  +/-  (7.67e-237, 7.67e-237j)
| (-0.92668960743183343805 - 3.0483226870136469645e-904j)  +/-  (1.8e-237, 1.8e-237j)
| (-0.99604984261521692498 - 7.6593814520340992858e-907j)  +/-  (5.61e-237, 5.61e-237j)
| (0.99604984261521692498 - 1.1340333624002230886e-917j)  +/-  (6.67e-237, 6.67e-237j)
| (0.84559600350182605991 + 1.654408548795669044e-920j)  +/-  (1.2e-238, 1.2e-238j)
| (-0.29205677063697582044 + 8.7377391761685050382e-932j)  +/-  (1.74e-249, 1.74e-249j)
| (-0.87573494219563680773 - 6.8225808887086228292e-919j)  +/-  (4.04e-238, 4.04e-238j)
| (-0.84559600350182605991 + 8.100695459263855905e-920j)  +/-  (1.15e-238, 1.15e-238j)
| (-0.97855649229950400214 - 1.7551204743423045478e-916j)  +/-  (6.63e-237, 6.63e-237j)
| (0.87573494219563680773 + 2.7456351038263906998e-928j)  +/-  (3.59e-238, 3.59e-238j)
| (0.77652386271804241942 - 7.3596809821171434054e-931j)  +/-  (7.35e-240, 7.35e-240j)
| (-0.94732635385419138443 + 3.1919778591598922798e-926j)  +/-  (3.25e-237, 3.25e-237j)
| (-0.73783327904172728401 - 3.3278318456331066831e-941j)  +/-  (1.58e-240, 1.58e-240j)
| (-0.96463558190835867291 + 5.3356685502483897252e-937j)  +/-  (6.15e-237, 6.15e-237j)
| (0.96463558190835867291 - 1.8153831663953999494e-940j)  +/-  (4.83e-237, 4.83e-237j)
| (0.69655102906299702757 - 4.8649336268190471244e-951j)  +/-  (2.63e-241, 2.63e-241j)
| (0.97855649229950400214 + 1.4176912192782116797e-949j)  +/-  (6.1e-237, 6.1e-237j)
| (-0.81248687800568128041 + 2.0856437165440125775e-952j)  +/-  (3.26e-239, 3.26e-239j)
| (-0.77652386271804241942 + 2.0018212066758331323e-953j)  +/-  (8.38e-240, 8.38e-240j)
| (0.81248687800568128041 + 6.8279201356228322325e-950j)  +/-  (2.96e-239, 2.96e-239j)
| (0.73783327904172728401 + 3.5263528621554937746e-952j)  +/-  (1.73e-240, 1.73e-240j)
| (0.29205677063697582044 - 2.2931322496983949515e-962j)  +/-  (2.13e-249, 2.13e-249j)
| (-0.17689027512257296266 - 3.1618521783248788592e-965j)  +/-  (4.82e-252, 4.82e-252j)
| (-0.60680014581859337038 + 6.2499679001446952096e-957j)  +/-  (6.54e-243, 6.54e-243j)
| (-0.23488604578098367943 - 7.2306283132199181094e-965j)  +/-  (1e-250, 1e-250j)
| (0.55864676580365245686 - 2.8818562348140868754e-956j)  +/-  (7.2e-244, 7.2e-244j)
| (0.60680014581859337038 - 2.1609956478883067245e-955j)  +/-  (5.97e-243, 5.97e-243j)
| (0.94732635385419138443 - 7.3341192646876870132e-955j)  +/-  (3.82e-237, 3.82e-237j)
| (-0.65282211819052162401 - 1.8308953924235263667e-957j)  +/-  (4.44e-242, 4.44e-242j)
| (-0.69655102906299702757 - 4.2369816371434830563e-960j)  +/-  (3.09e-241, 3.09e-241j)
| (0.11827317092136580395 + 7.4807896398668399279e-972j)  +/-  (2.12e-253, 2.12e-253j)
| (0.65282211819052162401 - 8.2834848346764797122e-965j)  +/-  (4.67e-242, 4.67e-242j)
| (0.40312342928797221419 + 3.7852859975191523536e-969j)  +/-  (5.21e-247, 5.21e-247j)
| (-0.40312342928797221419 + 2.4106084606805945363e-969j)  +/-  (4.53e-247, 4.53e-247j)
| (-0.55864676580365245686 + 6.4579090660439715534e-967j)  +/-  (6.55e-244, 6.55e-244j)
| (-0.11827317092136580395 - 3.2793129285173460364e-976j)  +/-  (1.95e-253, 1.95e-253j)
| (0.34820163543439878724 + 7.2887913738082154856e-972j)  +/-  (3.29e-248, 3.29e-248j)
| (0.50853111864922048501 - 1.7219159693043536105e-968j)  +/-  (7.3e-245, 7.3e-245j)
| (0.059240627893714287219 + 2.8265975510591722433e-978j)  +/-  (1.04e-254, 1.04e-254j)
| (-0.50853111864922048501 + 2.7896431369154411436e-969j)  +/-  (7.4e-245, 7.4e-245j)
| (-0.34820163543439878724 - 1.328613664983931978e-973j)  +/-  (3.56e-248, 3.56e-248j)
| (0.23488604578098367943 + 3.4082480381972821532e-977j)  +/-  (9.63e-251, 9.63e-251j)
| (0.45662923739371306445 + 4.5475061091372041271e-971j)  +/-  (7.09e-246, 7.09e-246j)
| (0.17689027512257296266 + 1.1185877454927252624e-976j)  +/-  (4.25e-252, 4.25e-252j)
| (-0.059240627893714287219 - 2.1675956168790548153e-979j)  +/-  (1.28e-254, 1.28e-254j)
| (-0.45662923739371306445 - 7.4718898693284919346e-971j)  +/-  (6.78e-246, 6.78e-246j)
| (3.2085308027789199551e-1094 + 6.2290478642646269678e-1094j)  +/-  (3.71e-1092, 3.71e-1092j)
-------------------------------------------------
The weights are:
| (0.018867924528301886792 - 1.3622528582084317685e-827j)  +/-  (4.08e-61, 9.97e-174j)
| (0.018867924528301886792 - 1.1353082122529118646e-827j)  +/-  (2.53e-61, 6.18e-174j)
| (0.018867924528301886792 + 1.834198405022238093e-829j)  +/-  (5.75e-62, 1.4e-174j)
| (0.018867924528301886792 - 1.2026662265723678243e-830j)  +/-  (2.14e-62, 5.23e-175j)
| (0.018867924528301886792 - 4.187038908796430475e-828j)  +/-  (2.69e-62, 6.57e-175j)
| (0.018867924528301886792 + 3.6076304963438887063e-828j)  +/-  (1.2e-62, 2.93e-175j)
| (0.018867924528301886792 - 6.0239262418125922707e-830j)  +/-  (1.01e-62, 2.47e-175j)
| (0.018867924528301886792 - 1.5829968312973993688e-829j)  +/-  (2.47e-63, 6.03e-176j)
| (0.018867924528301886792 + 3.6101147185309966318e-830j)  +/-  (1.81e-62, 4.42e-175j)
| (0.018867924528301886792 + 2.0401692131261119295e-827j)  +/-  (5.16e-63, 1.26e-175j)
| (0.018867924528301886792 + 2.8137962734267681287e-828j)  +/-  (1.61e-64, 3.92e-177j)
| (0.018867924528301886792 + 6.0077914833960688469e-829j)  +/-  (3.31e-67, 8.09e-180j)
| (0.018867924528301886792 - 2.0887916596670801288e-829j)  +/-  (2.86e-64, 6.99e-177j)
| (0.018867924528301886792 + 2.3473024103864745312e-829j)  +/-  (5.68e-65, 1.39e-177j)
| (0.018867924528301886792 + 8.448392753558059927e-830j)  +/-  (5.14e-64, 1.26e-176j)
| (0.018867924528301886792 - 3.1644457688315166431e-828j)  +/-  (7.23e-66, 1.77e-178j)
| (0.018867924528301886792 + 2.292457953763613186e-828j)  +/-  (1.34e-67, 3.28e-180j)
| (0.018867924528301886792 + 1.3346868691461263023e-829j)  +/-  (1.45e-64, 3.54e-177j)
| (0.018867924528301886792 - 3.1520985545851603435e-829j)  +/-  (2.6e-68, 6.36e-181j)
| (0.018867924528301886792 - 1.0887881882848995736e-829j)  +/-  (1.11e-64, 2.7e-177j)
| (0.018867924528301886792 - 6.1332823366207207008e-828j)  +/-  (6.43e-67, 1.57e-179j)
| (0.018867924528301886792 + 1.9214290393595055008e-828j)  +/-  (9.69e-70, 2.37e-182j)
| (0.018867924528301886792 + 7.9866814343354643403e-828j)  +/-  (8.17e-67, 2e-179j)
| (0.018867924528301886792 - 2.6102886514661371302e-829j)  +/-  (1.77e-67, 4.33e-180j)
| (0.018867924528301886792 + 2.8783427706459972491e-829j)  +/-  (2.99e-68, 7.3e-181j)
| (0.018867924528301886792 - 2.5289122736244826925e-828j)  +/-  (3.11e-68, 7.59e-181j)
| (0.018867924528301886792 - 2.0927044864711743105e-828j)  +/-  (2.01e-69, 4.91e-182j)
| (0.018867924528301886792 + 1.0968096378187152241e-828j)  +/-  (5.34e-74, 1.3e-186j)
| (0.018867924528301886792 + 6.7878635606075138249e-829j)  +/-  (9.98e-74, 2.44e-186j)
| (0.018867924528301886792 + 4.0146766863710957156e-829j)  +/-  (4.78e-73, 1.17e-185j)
| (0.018867924528301886792 - 6.3887151284191092239e-829j)  +/-  (2e-73, 4.88e-186j)
| (0.018867924528301886792 - 1.5263309470423385641e-828j)  +/-  (1.15e-73, 2.81e-186j)
| (0.018867924528301886792 + 1.6421028234147689148e-828j)  +/-  (3.33e-73, 8.13e-186j)
| (0.018867924528301886792 + 4.9793343416209075078e-828j)  +/-  (6.96e-70, 1.7e-182j)
| (0.018867924528301886792 - 3.7194968040972700667e-829j)  +/-  (2.09e-73, 5.11e-186j)
| (0.018867924528301886792 + 3.4322376171733510617e-829j)  +/-  (8e-73, 1.96e-185j)
| (0.018867924528301886792 - 9.1419425129902608531e-829j)  +/-  (2.14e-77, 5.23e-190j)
| (0.018867924528301886792 - 1.7726938453991457371e-828j)  +/-  (8.63e-74, 2.11e-186j)
| (0.018867924528301886792 + 1.2449452442470064542e-828j)  +/-  (8.79e-77, 2.15e-189j)
| (0.018867924528301886792 + 5.2934399223037130504e-829j)  +/-  (3.05e-77, 7.46e-190j)
| (0.018867924528301886792 - 4.318651353819607654e-829j)  +/-  (3.62e-76, 8.83e-189j)
| (0.018867924528301886792 - 7.2073330018332609071e-829j)  +/-  (6.34e-78, 1.55e-190j)
| (0.018867924528301886792 - 1.1677123631991633996e-828j)  +/-  (7.42e-78, 1.81e-190j)
| (0.018867924528301886792 + 1.4228162349276105483e-828j)  +/-  (3.42e-77, 8.34e-190j)
| (0.018867924528301886792 + 8.6134026504232370915e-829j)  +/-  (3.09e-79, 7.56e-192j)
| (0.018867924528301886792 + 4.6323797735332883811e-829j)  +/-  (3.14e-78, 7.67e-191j)
| (0.018867924528301886792 - 5.643245208582049238e-829j)  +/-  (2e-78, 4.88e-191j)
| (0.018867924528301886792 - 1.031378370856842021e-828j)  +/-  (1.56e-79, 3.81e-192j)
| (0.018867924528301886792 - 1.3295523222527339471e-828j)  +/-  (6.17e-79, 1.51e-191j)
| (0.018867924528301886792 + 9.707056051335367494e-829j)  +/-  (7.7e-80, 1.88e-192j)
| (0.018867924528301886792 + 7.6495144523304453474e-829j)  +/-  (6.92e-81, 1.7e-193j)
| (0.018867924528301886792 - 4.9569190401463473e-829j)  +/-  (6.71e-81, 1.81e-193j)
| (0.018867924528301886792 - 8.1171500459705746942e-829j)  +/-  (6.68e-81, 1.61e-193j)
