Starting with polynomial:
P : 2*t
Extension levels are: 1 54
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^55 - 1485*t^53 + 1023165/2*t^51 - 434845125/4*t^49 + 63922233375/4*t^47 - 13819986855675/8*t^45 + 2280297831186375/16*t^43 - 294158420223042375/32*t^41 + 60302476145723686875/128*t^39 - 4964903869331250219375/256*t^37 + 330662597697461264610375/512*t^35 - 17885840511817222949379375/1024*t^33 + 196744245629989452443173125/512*t^31 - 7037390324457315029698115625/1024*t^29 + 204084319409262135861245353125/2048*t^27 - 4775573074176733979153141263125/4096*t^25 + 358167980563255048436485594734375/32768*t^23 - 5330382298970795720848873851046875/65536*t^21 + 62187793487992616743236861595546875/131072*t^19 - 559690141391933550689131754359921875/262144*t^17 + 1902946480732574072343047964823734375/262144*t^15 - 9514732403662870361715239824118671875/524288*t^13 + 33734051249350176736990395740057109375/1048576*t^11 - 80668383422359118284107468074049609375/2097152*t^9 + 242005150267077354852322404222148828125/8388608*t^7 - 203284326224344978075950819546605015625/16777216*t^5 + 78186279317055760798442622902540390625/33554432*t^3 - 8687364368561751199826958100282265625/67108864*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
-------------------------------------------------
The nodes are:
| (-8.4965875649075647286 - 2.4518672252413812422e-779j)  +/-  (7.58e-244, 7.58e-244j)
| (-9.0338717801824065451 + 1.1031187320991142064e-782j)  +/-  (1.01e-244, 1.01e-244j)
| (-3.0238424864191802206 - 3.3220956851902869665e-787j)  +/-  (2.47e-245, 2.47e-245j)
| (-7.1563802343429105315 - 5.4117304684739626511e-785j)  +/-  (2.06e-242, 2.06e-242j)
| (8.4965875649075647286 + 9.976116938304655113e-793j)  +/-  (8.37e-244, 8.37e-244j)
| (5.3022190388457906044 + 3.7807918019969855129e-791j)  +/-  (2.89e-242, 2.89e-242j)
| (-9.6821899525637261032 + 2.6292210931426976823e-794j)  +/-  (5.82e-246, 5.82e-246j)
| (9.6821899525637261032 + 4.7818198212199293331e-796j)  +/-  (5.34e-246, 5.34e-246j)
| (3.652709346413297785 - 9.6340629307702648747e-794j)  +/-  (3.94e-244, 3.94e-244j)
| (5.6512779962558643625 + 4.0820735721033241432e-792j)  +/-  (3.47e-242, 3.47e-242j)
| (8.0165891148558295997 - 1.1748958231759324794e-792j)  +/-  (3.3e-243, 3.3e-243j)
| (-6.0092815232536672601 - 3.0186883334134863127e-792j)  +/-  (4.28e-242, 4.28e-242j)
| (-7.5733727465412007382 + 8.4936207560101953346e-801j)  +/-  (9.66e-243, 9.66e-243j)
| (-2.4065354826206520698 + 5.6513048225761155847e-816j)  +/-  (9.26e-247, 9.26e-247j)
| (9.0338717801824065451 + 6.5915270904135674079e-811j)  +/-  (9.69e-245, 9.69e-245j)
| (1.7978466126036981391 - 3.9820490194305621946e-823j)  +/-  (1.64e-248, 1.64e-248j)
| (-4.6259383469194118935 - 4.2659648792710964272e-816j)  +/-  (7.62e-243, 7.62e-243j)
| (-5.3022190388457906044 - 1.3243143302160226469e-824j)  +/-  (2.64e-242, 2.64e-242j)
| (-2.7139409275561001054 + 7.8106190218576213854e-842j)  +/-  (5.4e-246, 5.4e-246j)
| (4.9607928202275563211 - 1.4367509817448667747e-837j)  +/-  (1.6e-242, 1.6e-242j)
| (-8.0165891148558295997 + 5.6211624437754224909e-838j)  +/-  (2.75e-243, 2.75e-243j)
| (0.8956218604622908624 + 6.9552679104709482824e-855j)  +/-  (1.15e-251, 1.15e-251j)
| (6.0092815232536672601 + 1.9029224122067251318e-845j)  +/-  (4.31e-242, 4.31e-242j)
| (-5.6512779962558643625 - 2.0401530481755667057e-858j)  +/-  (3.58e-242, 3.58e-242j)
| (-0.8956218604622908624 - 2.2926891893511452575e-883j)  +/-  (1.57e-251, 1.57e-251j)
| (3.9725795904787464401 + 2.9521635801410228539e-874j)  +/-  (1.35e-243, 1.35e-243j)
| (2.4065354826206520698 - 2.8271004366457791834e-881j)  +/-  (1.07e-246, 1.07e-246j)
| (3.336623318934166081 - 8.2490444453557484232e-879j)  +/-  (1.19e-244, 1.19e-244j)
| (-6.3778918319127679183 - 4.1061918577056810725e-877j)  +/-  (4.5e-242, 4.5e-242j)
| (-0.59668052547571689328 - 2.0361850251636927667e-897j)  +/-  (9.89e-253, 9.89e-253j)
| (-1.7978466126036981391 + 2.7237193323688295827e-893j)  +/-  (1.84e-248, 1.84e-248j)
| (3.0238424864191802206 + 1.3258121795592854763e-889j)  +/-  (2.74e-245, 2.74e-245j)
| (6.7592785186840849948 - 4.1676219626233710711e-886j)  +/-  (3.5e-242, 3.5e-242j)
| (-3.9725795904787464401 - 1.1271249845935316288e-889j)  +/-  (1.37e-243, 1.37e-243j)
| (7.5733727465412007382 + 5.3098179827151137089e-889j)  +/-  (9.28e-243, 9.28e-243j)
| (-2.1012775733291406293 - 2.7208898199234778801e-898j)  +/-  (1.3e-247, 1.3e-247j)
| (-6.7592785186840849948 + 1.772885290409784804e-891j)  +/-  (3.21e-242, 3.21e-242j)
| (4.2967794840336987762 - 1.2993658064591370166e-897j)  +/-  (3.4e-243, 3.4e-243j)
| (2.7139409275561001054 + 2.4516175094749079671e-900j)  +/-  (5.6e-246, 5.6e-246j)
| (-3.336623318934166081 - 1.4612077394149825665e-898j)  +/-  (1.07e-244, 1.07e-244j)
| (3.3302975070212390417e-939 + 3.9630761298615961228e-939j)  +/-  (2.85e-937, 2.85e-937j)
| (-4.2967794840336987762 - 3.9367428240851999469e-897j)  +/-  (3.72e-243, 3.72e-243j)
| (6.3778918319127679183 - 6.7349062044942417627e-898j)  +/-  (4.35e-242, 4.35e-242j)
| (0.59668052547571689328 - 6.1444413666592986182e-910j)  +/-  (1.02e-252, 1.02e-252j)
| (4.6259383469194118935 + 1.2181606326160883879e-900j)  +/-  (7.42e-243, 7.42e-243j)
| (-4.9607928202275563211 + 9.8820104432195442418e-902j)  +/-  (1.64e-242, 1.64e-242j)
| (-3.652709346413297785 - 4.5578872303604324833e-904j)  +/-  (4.53e-244, 4.53e-244j)
| (7.1563802343429105315 - 2.0285160765281367625e-909j)  +/-  (1.72e-242, 1.72e-242j)
| (0.2982205504927666893 + 9.1733663045854033657e-921j)  +/-  (5.92e-254, 5.92e-254j)
| (2.1012775733291406293 - 7.4942579969620536769e-915j)  +/-  (1.3e-247, 1.3e-247j)
| (-1.1952915904152335333 - 4.916108167330846013e-917j)  +/-  (1.49e-250, 1.49e-250j)
| (-0.2982205504927666893 - 1.2747625101168578021e-920j)  +/-  (5.92e-254, 5.92e-254j)
| (-1.4959445977962446857 - 4.2056762613727518638e-917j)  +/-  (1.72e-249, 1.72e-249j)
| (1.4959445977962446857 - 1.7285702948600736361e-916j)  +/-  (1.9e-249, 1.9e-249j)
| (1.1952915904152335333 + 2.2437652759253342352e-917j)  +/-  (1.63e-250, 1.63e-250j)
-------------------------------------------------
The weights are:
| (1.2621982459866922792e-32 - 2.9551601222767216528e-806j)  +/-  (8.93e-75, 2.26e-196j)
| (1.1759544331197208047e-36 + 2.5971265694063232928e-808j)  +/-  (2.54e-76, 6.43e-198j)
| (1.8773395812165767626e-05 - 1.8858801627765613777e-791j)  +/-  (5.42e-53, 1.37e-174j)
| (1.3131616407495595689e-23 + 1.2621955373580204576e-801j)  +/-  (1.73e-71, 4.38e-193j)
| (1.2621982459866922792e-32 + 1.4037125458873466531e-806j)  +/-  (4.13e-78, 1.05e-199j)
| (1.201584756290999617e-13 + 5.9926731126678203819e-797j)  +/-  (4.05e-68, 1.02e-189j)
| (8.1816673003541132554e-42 - 6.1834877674856007853e-811j)  +/-  (2.47e-79, 6.25e-201j)
| (8.1816673003541132554e-42 + 3.2403655871315082711e-811j)  +/-  (1.27e-81, 3.22e-203j)
| (2.8788921476249844369e-07 - 1.1567598646839560716e-793j)  +/-  (1.12e-61, 2.84e-183j)
| (2.688531753864499695e-15 - 8.6033051091641495391e-798j)  +/-  (6.78e-70, 1.72e-191j)
| (3.186394189538746436e-29 - 7.3594743731909490945e-805j)  +/-  (2.98e-77, 7.54e-199j)
| (4.2492757974395330313e-17 - 3.1429223956906476515e-798j)  +/-  (3e-72, 7.6e-194j)
| (2.9805284545398795103e-26 - 5.4622098689932013438e-803j)  +/-  (6.47e-76, 1.64e-197j)
| (0.00052766643123977635857 - 5.356264387929018931e-791j)  +/-  (5.65e-57, 1.43e-178j)
| (1.1759544331197208047e-36 - 1.2945336207935645082e-808j)  +/-  (6.96e-81, 1.76e-202j)
| (0.0067386218635711245757 - 2.4505834251280770035e-791j)  +/-  (1.79e-53, 4.52e-175j)
| (9.5235164169590773964e-11 - 8.7678686443840681116e-795j)  +/-  (1e-68, 2.54e-190j)
| (1.201584756290999617e-13 - 2.1899579855998974696e-796j)  +/-  (7.47e-71, 1.89e-192j)
| (0.00011016039915215328869 + 4.8749762450756126692e-791j)  +/-  (2.49e-60, 6.3e-182j)
| (3.9134694306753897513e-12 - 3.5662270754836046396e-796j)  +/-  (2.06e-71, 5.21e-193j)
| (3.186394189538746436e-29 + 1.6274317164952638108e-804j)  +/-  (5.4e-78, 1.37e-199j)
| (0.075703318917566572724 + 1.0104479648267887075e-790j)  +/-  (4.74e-58, 1.2e-179j)
| (4.2492757974395330313e-17 + 1.0387299996172575202e-798j)  +/-  (7.07e-75, 1.79e-196j)
| (2.688531753864499695e-15 + 2.8405977917028160771e-797j)  +/-  (4.45e-72, 1.12e-193j)
| (0.075703318917566572724 + 1.8609047580751857977e-790j)  +/-  (2.38e-59, 6.02e-181j)
| (2.5434728215500947928e-08 + 3.2811115536973182855e-794j)  +/-  (5.41e-69, 1.37e-190j)
| (0.00052766643123977635857 - 6.0888149374005144023e-792j)  +/-  (1.31e-63, 3.31e-185j)
| (2.5931384967000675019e-06 + 3.6442381674464631672e-793j)  +/-  (2.96e-67, 7.48e-189j)
| (4.5599345458077143773e-19 + 2.8979739630617163277e-799j)  +/-  (1.37e-75, 3.47e-197j)
| (0.11802697453147851199 - 2.0373947923858734953e-790j)  +/-  (3.32e-60, 8.41e-182j)
| (0.0067386218635711245757 - 9.637845223544870309e-791j)  +/-  (1.05e-61, 2.65e-183j)
| (1.8773395812165767626e-05 - 1.0312530641286059421e-792j)  +/-  (1.16e-66, 2.92e-188j)
| (3.1552135089755289118e-21 + 8.264566724828623587e-801j)  +/-  (5.04e-79, 1.28e-200j)
| (2.5434728215500947928e-08 - 2.4196434771462255423e-793j)  +/-  (1.27e-71, 3.22e-193j)
| (2.9805284545398795103e-26 + 2.3449737813563711739e-803j)  +/-  (2.83e-81, 7.16e-203j)
| (0.0020756177757301351151 + 7.1082091941628898024e-791j)  +/-  (2.62e-65, 6.63e-187j)
| (3.1552135089755289118e-21 - 2.1645013715766332173e-800j)  +/-  (1.94e-77, 4.91e-199j)
| (1.7673215155940583538e-09 - 8.2659555966557506345e-795j)  +/-  (2.13e-72, 5.38e-194j)
| (0.00011016039915215328869 + 2.6330048569769996721e-792j)  +/-  (2.16e-68, 5.45e-190j)
| (2.5931384967000675019e-06 - 7.4106504199854668556e-792j)  +/-  (1.46e-70, 3.68e-192j)
| (0.16823046163605511761 - 1.9524342752160743603e-790j)  +/-  (1.08e-65, 2.73e-187j)
| (1.7673215155940583538e-09 + 4.753731596329461605e-794j)  +/-  (7.14e-73, 1.81e-194j)
| (4.5599345458077143773e-19 - 1.0338427554513753964e-799j)  +/-  (1.27e-78, 3.21e-200j)
| (0.11802697453147851199 - 1.3658485813706044079e-790j)  +/-  (4.04e-68, 1.02e-189j)
| (9.5235164169590773964e-11 + 1.8362544547090176719e-795j)  +/-  (4.94e-74, 1.25e-195j)
| (3.9134694306753897513e-12 + 1.470098555387894405e-795j)  +/-  (7.51e-75, 1.9e-196j)
| (2.8788921476249844369e-07 + 1.2281110616513940655e-792j)  +/-  (2.6e-72, 6.58e-194j)
| (1.3131616407495595689e-23 - 5.1237146864815234443e-802j)  +/-  (3.72e-81, 9.42e-203j)
| (0.15397650652511948678 + 1.7002101787570066282e-790j)  +/-  (4.56e-69, 1.15e-190j)
| (0.0020756177757301351151 + 1.2795367848435671003e-791j)  +/-  (1.8e-71, 4.56e-193j)
| (0.040572443299451616654 - 1.5855936085074231725e-790j)  +/-  (3.02e-70, 7.63e-192j)
| (0.15397650652511948678 + 2.0722631548955683103e-790j)  +/-  (7.61e-70, 1.92e-191j)
| (0.018131777713818180713 + 1.2685548408577142102e-790j)  +/-  (1.44e-70, 3.65e-192j)
| (0.018131777713818180713 + 4.2883022658821639364e-791j)  +/-  (1.13e-71, 2.88e-193j)
| (0.040572443299451616654 - 6.8718781019488271923e-791j)  +/-  (1.71e-71, 4.27e-193j)
