Starting with polynomial:
P : 2*t
Extension levels are: 1 60
-------------------------------------------------
Trying to find an order 60 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^61 - 1830*t^59 + 1565565/2*t^57 - 208220145*t^55 + 309206915325/8*t^53 - 42608712931785/8*t^51 + 18108702996008625/32*t^49 - 380282762916181125/8*t^47 + 411085666712391796125/128*t^45 - 22609711669181548786875/128*t^43 + 4083313927454187710909625/512*t^41 - 76098123193464407339679375/256*t^39 + 18796236428785708612900805625/2048*t^37 - 481472825445049305238151405625/2048*t^35 + 40925190162829190945242869478125/8192*t^33 - 90035418358224220079534312851875/1024*t^31 + 41866469536574262336983455476121875/32768*t^29 - 499934900936739720847508321273690625/32768*t^27 + 19497461136532849113052824529673934375/131072*t^25 - 76963662381050720183103254722397109375/65536*t^23 + 3894361316481166441265024688953293734375/524288*t^21 - 19471806582405832206325123444766468671875/524288*t^19 + 302698084144672482480145100823187831171875/2097152*t^17 - 223733366541714443572281161478008396953125/524288*t^15 + 7830667828960005525029840651730293893359375/8388608*t^13 - 12215841813177608619046551416699258473640625/8388608*t^11 + 51682407671136036465196948301419939696171875/33554432*t^9 - 17227469223712012155065649433806646565390625/16777216*t^7 + 51682407671136036465196948301419939696171875/134217728*t^5 - 8910759943299316631930508327831024085546875/134217728*t^3 + 1782151988659863326386101665566204817109375/536870912*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: 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:   61 out of 61
Indefinite weights: 0 out of 61
Negative weights:   0 out of 61
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (7.7766963448476243544 + 5.9267281294976367435e-902j)  +/-  (3.12e-241, 3.12e-241j)
| (-8.6185407332142506273 - 2.4808614372500837146e-902j)  +/-  (4.12e-242, 4.12e-242j)
| (-4.6745377615999188766 + 2.4904069409254894547e-905j)  +/-  (1.32e-241, 1.32e-241j)
| (6.307195800219425988 - 7.8359427706356581918e-911j)  +/-  (1.19e-240, 1.19e-240j)
| (8.1846218361099518091 + 5.8636989896965662954e-916j)  +/-  (1.16e-241, 1.16e-241j)
| (-7.7766963448476243544 - 9.0971921848781419215e-919j)  +/-  (3.23e-241, 3.23e-241j)
| (-6.656292358498873288 + 3.3407803029518697835e-931j)  +/-  (1.22e-240, 1.22e-240j)
| (9.0888424760573392158 + 2.08785722539217504e-939j)  +/-  (6.36e-243, 6.36e-243j)
| (9.6157041046875608106 + 3.5922547191058239169e-939j)  +/-  (7.94e-244, 7.94e-244j)
| (2.5726263447097192688 - 2.3340307455326103885e-941j)  +/-  (9.89e-246, 9.89e-246j)
| (-9.6157041046875608106 + 4.6580273682161301087e-940j)  +/-  (9.87e-244, 9.87e-244j)
| (7.0160284848388694043 - 2.2493047821220550238e-935j)  +/-  (8.55e-241, 8.55e-241j)
| (8.6185407332142506273 - 2.4459956163171026392e-938j)  +/-  (4.03e-242, 4.03e-242j)
| (-2.5726263447097192688 + 8.3167908479361128876e-942j)  +/-  (1.11e-245, 1.11e-245j)
| (6.656292358498873288 - 2.5924948373817195214e-936j)  +/-  (1.28e-240, 1.28e-240j)
| (-8.1846218361099518091 - 4.5122679131636910618e-940j)  +/-  (1.2e-241, 1.2e-241j)
| (4.9892473314939936227 + 3.3444569456508633373e-938j)  +/-  (3.08e-241, 3.08e-241j)
| (-2.2823160084101850486 - 3.2783678370662069593e-943j)  +/-  (1.47e-246, 1.47e-246j)
| (7.3885339440499835311 + 2.1768757841751631528e-937j)  +/-  (5.61e-241, 5.61e-241j)
| (-1.4202064526026657481 + 1.7818033032027507325e-946j)  +/-  (2.56e-249, 2.56e-249j)
| (-4.9892473314939936227 + 5.4644846181828471128e-937j)  +/-  (2.42e-241, 2.42e-241j)
| (-10.252011649196144911 + 2.3271124589458153959e-943j)  +/-  (3.71e-245, 3.71e-245j)
| (2.2823160084101850486 - 4.1957323984080578415e-945j)  +/-  (1.38e-246, 1.38e-246j)
| (1.9936301908281087054 - 5.2805936602144727275e-946j)  +/-  (1.91e-247, 1.91e-247j)
| (4.3643428074654232117 + 6.7879051958892985193e-941j)  +/-  (4.74e-242, 4.74e-242j)
| (5.9671093310413951706 + 4.068855125496886486e-939j)  +/-  (9.58e-241, 9.58e-241j)
| (5.3090795734924509512 - 1.1075325190034965495e-939j)  +/-  (5.19e-241, 5.19e-241j)
| (5.6347492296736760809 + 3.1471160835503311478e-941j)  +/-  (7.63e-241, 7.63e-241j)
| (1.7063340915790623931 - 5.3547223547666797712e-947j)  +/-  (2.4e-248, 2.4e-248j)
| (-5.9671093310413951706 + 1.8715610826497336263e-938j)  +/-  (1.04e-240, 1.04e-240j)
| (3.1591458858192855896 + 4.5763849080165789048e-951j)  +/-  (3.08e-244, 3.08e-244j)
| (1.4202064526026657481 - 1.7398344708717109187e-956j)  +/-  (2.56e-249, 2.56e-249j)
| (-3.1591458858192855896 - 4.0415420473417692475e-950j)  +/-  (2.83e-244, 2.83e-244j)
| (-9.0888424760573392158 - 1.6075066723235340747e-948j)  +/-  (7.11e-243, 7.11e-243j)
| (-2.8648125198053047142 + 1.5889111487259707974e-951j)  +/-  (5.68e-245, 5.68e-245j)
| (-5.6347492296736760809 - 1.112824455043168507e-945j)  +/-  (8.42e-241, 8.42e-241j)
| (-1.7063340915790623931 + 1.7371512257054922546e-970j)  +/-  (2.56e-248, 2.56e-248j)
| (1.1350369935815598925 + 1.0320357103244276213e-972j)  +/-  (2.04e-250, 2.04e-250j)
| (10.252011649196144911 - 2.4751636071024839035e-968j)  +/-  (4.05e-245, 4.05e-245j)
| (-7.3885339440499835311 - 1.2754440668070634432e-961j)  +/-  (6.63e-241, 6.63e-241j)
| (-0.56677314117022046542 - 3.0939337513567065012e-1001j)  +/-  (1.02e-252, 1.02e-252j)
| (-6.307195800219425988 - 7.1527977296425765576e-988j)  +/-  (1.17e-240, 1.17e-240j)
| (-7.0160284848388694043 - 3.7860538787730436368e-1008j)  +/-  (8.69e-241, 8.69e-241j)
| (3.7554659075853780481 + 9.7915197618781035561e-1018j)  +/-  (5.33e-243, 5.33e-243j)
| (-4.0581381112767337185 + 7.7326703744675751386e-1015j)  +/-  (2.06e-242, 2.06e-242j)
| (-1.9936301908281087054 + 6.2056305919595949542e-1023j)  +/-  (1.78e-247, 1.78e-247j)
| (-0.85062416477081462473 - 1.0913948907068387943e-1026j)  +/-  (1.85e-251, 1.85e-251j)
| (-5.3090795734924509512 - 3.73561490425961507e-1016j)  +/-  (5.16e-241, 5.16e-241j)
| (0.85062416477081462473 - 3.8623522921260625678e-1032j)  +/-  (1.49e-251, 1.49e-251j)
| (4.6745377615999188766 - 4.4284745546237574166e-1022j)  +/-  (1.29e-241, 1.29e-241j)
| (-3.7554659075853780481 - 2.4897756467423566824e-1022j)  +/-  (5.43e-243, 5.43e-243j)
| (-4.3643428074654232117 - 1.0062847353204639658e-1024j)  +/-  (5.18e-242, 5.18e-242j)
| (-3.4559220338316390818 - 2.742711507451596186e-1027j)  +/-  (1.52e-243, 1.52e-243j)
| (2.8648125198053047142 - 1.83198329349846811e-1027j)  +/-  (6.3e-245, 6.3e-245j)
| (-0.28329399584293825691 + 2.6827094172835170631e-1038j)  +/-  (5.99e-254, 5.99e-254j)
| (-1.5017767088226587339e-1059 - 1.8127267948793483714e-1058j)  +/-  (1.11e-1056, 1.11e-1056j)
| (-1.1350369935815598925 + 6.7765501249691789794e-1035j)  +/-  (2.22e-250, 2.22e-250j)
| (0.28329399584293825691 - 6.3611423327649833617e-1038j)  +/-  (5.99e-254, 5.99e-254j)
| (4.0581381112767337185 + 3.8753304263568409058e-1026j)  +/-  (2.08e-242, 2.08e-242j)
| (0.56677314117022046542 - 1.562808416543701936e-1038j)  +/-  (9.7e-253, 9.7e-253j)
| (3.4559220338316390818 + 2.2723113191008484651e-1034j)  +/-  (1.29e-243, 1.29e-243j)
-------------------------------------------------
The weights are:
| (1.2179530564067152341e-27 - 5.2774534171339801588e-925j)  +/-  (5.05e-59, 2.54e-177j)
| (1.3977653698327198173e-33 + 1.7829452638515970732e-927j)  +/-  (1.91e-62, 9.58e-181j)
| (5.7039803251286354776e-11 + 6.640290685987781793e-915j)  +/-  (6.35e-47, 3.19e-165j)
| (1.0277368048053693301e-18 - 1.7364610962817745817e-920j)  +/-  (1.76e-54, 8.86e-173j)
| (1.9132142559222252681e-30 + 2.0224508205872980085e-926j)  +/-  (1.2e-60, 6.01e-179j)
| (1.2179530564067152341e-27 + 2.1159706847727036749e-924j)  +/-  (1.75e-60, 8.78e-179j)
| (1.1444908106729465443e-20 - 1.0153480763003905798e-920j)  +/-  (7.02e-57, 3.53e-175j)
| (3.7088060732095639449e-37 + 8.3214917369161524922e-930j)  +/-  (1.54e-64, 7.76e-183j)
| (2.2364824894989936017e-41 - 6.2239398714294540986e-932j)  +/-  (1.9e-66, 9.56e-185j)
| (0.00021942509449102738995 - 3.84451031710399082e-913j)  +/-  (9.01e-39, 4.53e-157j)
| (2.2364824894989936017e-41 + 1.8001606240530102549e-931j)  +/-  (1.55e-68, 7.79e-187j)
| (8.6411169244947932162e-23 - 1.4958295880417220104e-922j)  +/-  (5.52e-59, 2.78e-177j)
| (1.3977653698327198173e-33 - 5.2890232867884980432e-928j)  +/-  (2.09e-63, 1.05e-181j)
| (0.00021942509449102738995 - 1.3255283967636619639e-912j)  +/-  (6.64e-43, 3.34e-161j)
| (1.1444908106729465443e-20 + 1.7760372017064065204e-921j)  +/-  (2.6e-58, 1.31e-176j)
| (1.9132142559222252681e-30 - 7.4117804306912850394e-926j)  +/-  (6.47e-66, 3.25e-184j)
| (2.7668880796351236181e-12 - 3.2376091417950918786e-917j)  +/-  (2.48e-55, 1.25e-173j)
| (0.00089286291334885392657 + 2.3493700114031491709e-912j)  +/-  (2.73e-42, 1.37e-160j)
| (4.1939484179227371596e-25 + 1.0100929995988674791e-923j)  +/-  (3.64e-60, 1.83e-178j)
| (0.021440700089215401467 - 8.4628907581458939292e-912j)  +/-  (8.89e-35, 4.47e-153j)
| (2.7668880796351236181e-12 + 9.9413429557422776465e-916j)  +/-  (3.02e-57, 1.52e-175j)
| (9.3712287678835697734e-47 - 3.2645143471038703806e-934j)  +/-  (4.2e-73, 2.11e-191j)
| (0.00089286291334885392657 + 8.0787634678724365091e-913j)  +/-  (9.11e-44, 4.58e-162j)
| (0.0030522259632903189842 - 1.55835588918183911e-912j)  +/-  (5.43e-42, 2.73e-160j)
| (9.2880342218154709459e-10 - 6.3418977266395101676e-916j)  +/-  (9.31e-55, 4.68e-173j)
| (6.5184766419075549797e-17 + 1.4270908200802349349e-919j)  +/-  (1.27e-58, 6.36e-177j)
| (1.0446062071534588904e-13 + 6.0892951361874279121e-918j)  +/-  (1.05e-57, 5.28e-176j)
| (3.0158661318419225693e-15 - 1.0019815220317212714e-918j)  +/-  (2.5e-58, 1.26e-176j)
| (0.0087970077780564754112 + 2.7647241996358046625e-912j)  +/-  (4.42e-45, 2.22e-163j)
| (6.5184766419075549797e-17 - 1.1748362405765737753e-918j)  +/-  (6.27e-66, 3.15e-184j)
| (7.7204093582151220506e-06 - 6.6714704351731486009e-914j)  +/-  (3.5e-53, 1.76e-171j)
| (0.021440700089215401467 - 4.5188497871828434169e-912j)  +/-  (3.95e-44, 1.99e-162j)
| (7.7204093582151220506e-06 - 3.4486982725110574066e-913j)  +/-  (7.67e-57, 3.85e-175j)
| (3.7088060732095639449e-37 - 2.5948535484794757427e-929j)  +/-  (3.85e-74, 1.93e-192j)
| (4.5111525791571676646e-05 + 6.9805759167209066974e-913j)  +/-  (1.54e-55, 7.74e-174j)
| (3.0158661318419225693e-15 + 1.0757172338053858641e-917j)  +/-  (2.32e-65, 1.17e-183j)
| (0.0087970077780564754112 + 5.9433952584797362665e-912j)  +/-  (3.78e-51, 1.9e-169j)
| (0.04429919014155633415 + 6.8142341876109558784e-912j)  +/-  (1.1e-47, 5.51e-166j)
| (9.3712287678835697734e-47 + 1.2197459267653121218e-934j)  +/-  (2.25e-77, 1.13e-195j)
| (4.1939484179227371596e-25 - 4.4880819469604991856e-923j)  +/-  (3.25e-70, 1.63e-188j)
| (0.1160576513452515956 + 1.5598865682176051608e-911j)  +/-  (1.28e-50, 6.42e-169j)
| (1.0277368048053693301e-18 + 1.1678968744287840028e-919j)  +/-  (1e-67, 5.04e-186j)
| (8.6411169244947932162e-23 + 7.4670845312435556175e-922j)  +/-  (1.71e-69, 8.59e-188j)
| (1.2734244397327137293e-07 - 7.9621098848895388242e-915j)  +/-  (1.17e-62, 5.89e-181j)
| (1.2096242825343146554e-08 + 3.3560037781123393066e-914j)  +/-  (2.86e-64, 1.44e-182j)
| (0.0030522259632903189842 - 3.8760300803398696817e-912j)  +/-  (3.95e-58, 1.99e-176j)
| (0.077742307060467862788 - 1.3714566570998275992e-911j)  +/-  (3.88e-56, 1.95e-174j)
| (1.0446062071534588904e-13 - 9.5802127179686763404e-917j)  +/-  (2.55e-66, 1.28e-184j)
| (0.077742307060467862788 - 9.4917620048365914834e-912j)  +/-  (1.79e-57, 8.97e-176j)
| (5.7039803251286354776e-11 + 1.5194767609611341877e-916j)  +/-  (6.9e-66, 3.47e-184j)
| (1.2734244397327137293e-07 - 7.3029248652807092612e-914j)  +/-  (5.08e-64, 2.55e-182j)
| (9.2880342218154709459e-10 - 1.8479347150618942885e-914j)  +/-  (3.51e-65, 1.76e-183j)
| (1.0935537165661110849e-06 + 1.6140356673272682843e-913j)  +/-  (1.65e-63, 8.28e-182j)
| (4.5111525791571676646e-05 + 1.6756237060148083852e-913j)  +/-  (2.54e-64, 1.27e-182j)
| (0.14753749310915864445 - 1.6452260758145980998e-911j)  +/-  (4.54e-61, 2.26e-179j)
| (0.15981414117778535617 + 1.6085372755331391865e-911j)  +/-  (1.63e-61, 8.12e-180j)
| (0.04429919014155633415 + 1.1184513749196817444e-911j)  +/-  (9.79e-62, 4.94e-180j)
| (0.14753749310915864445 - 1.4572091960208397133e-911j)  +/-  (4.2e-62, 2.09e-180j)
| (1.2096242825343146554e-08 + 2.3689093994856455816e-915j)  +/-  (2.3e-67, 1.17e-185j)
| (0.1160576513452515956 + 1.2225306816069013372e-911j)  +/-  (3.57e-63, 1.5e-181j)
| (1.0935537165661110849e-06 + 2.4192083291130029454e-914j)  +/-  (2.25e-66, 1.16e-184j)
