Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^54 - 374139666052908334342450417765769/269406514469750166223704016775*t^52 + 240508958363437571882851396930078119/269406514469750166223704016775*t^50 - 3805067529518682995578750059063706053/10776260578790006648948160671*t^48 + 1038273824426543753414001499051990397778/10776260578790006648948160671*t^46 - 207728351344465512729482664659739247542270/10776260578790006648948160671*t^44 + 2874320968134456048532493939225269586004414/979660052617273331722560061*t^42 - 340857874740783488996915571254296024740063834/979660052617273331722560061*t^40 + 31996991364100316192372602828428679314154512735/979660052617273331722560061*t^38 - 64938495430945622438152534636856269789655914605/26477298719385765722231353*t^36 + 3926650572873806373621663188062875644714095046475/26477298719385765722231353*t^34 - 191870972613499965215625551394194120926673241114585/26477298719385765722231353*t^32 + 7583954328431346622230579581483505470881008907503060/26477298719385765722231353*t^30 - 242169244472657091289512063217156881954222528791340300/26477298719385765722231353*t^28 + 6225328156336854769779947014916950721258981968684419300/26477298719385765722231353*t^26 - 128095212091425974952766480331031088644669039300057427500/26477298719385765722231353*t^24 + 2092568418723296665665188374595362226170537345056179535375/26477298719385765722231353*t^22 - 26843483121697259167310635091998895177290782297944183006625/26477298719385765722231353*t^20 + 266555794341172560669220865795171289995665260033345432729375/26477298719385765722231353*t^18 - 2011255148781985789977626803144431527755208218895991939973125/26477298719385765722231353*t^16 + 11256208143005071022134429279840165479587724484088160793068750/26477298719385765722231353*t^14 - 45261170037712318319080090210192881101458198504134936433961250/26477298719385765722231353*t^12 + 125236314367207986626732960623235135374108772731663528293873750/26477298719385765722231353*t^10 - 224391753824241557536093664248483618911866641208326135994081250/26477298719385765722231353*t^8 + 237715258737212070573922299215164185846208659844978292590753125/26477298719385765722231353*t^6 - 128184082807685394413441194084258489777143742968145655913046875/26477298719385765722231353*t^4 + 26247463932240818419045155839865800318437451545224077601148125/26477298719385765722231353*t^2 - 848666136225655543176212164056226036888725103337290740429375/26477298719385765722231353
-------------------------------------------------
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
Positive weights:   54 out of 54
Indefinite weights: 0 out of 54
Negative weights:   0 out of 54
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-10.431951551886178907 + 1.8927681304038291553e-599j)  +/-  (1.07e-242, 1.07e-242j)
| (12.509090829354308004 + 8.9869287313971182734e-609j)  +/-  (1.28e-244, 1.28e-244j)
| (-12.509090829354308004 - 3.7745676449127298283e-618j)  +/-  (1.32e-244, 1.32e-244j)
| (9.8387955901631722927 + 3.7352107837725651368e-631j)  +/-  (2.49e-242, 2.49e-242j)
| (9.2739100128714206611 + 2.5982260856318199467e-657j)  +/-  (3.46e-242, 3.46e-242j)
| (11.062367038603437738 - 2.9542088118478735407e-688j)  +/-  (3.96e-243, 3.96e-243j)
| (3.0955129454152609643 - 1.8151355250171408622e-719j)  +/-  (5.05e-247, 5.05e-247j)
| (11.745036961464313027 - 1.6249040720914054203e-721j)  +/-  (9.64e-244, 9.64e-244j)
| (7.697799766263641935 - 1.3080176487986687435e-741j)  +/-  (3.66e-242, 3.66e-242j)
| (-9.2739100128714206611 - 1.7663655836267972356e-752j)  +/-  (3.69e-242, 3.69e-242j)
| (13.430904323339364811 - 1.1299382786374768391e-754j)  +/-  (7.24e-246, 7.24e-246j)
| (2.2423759293463206638 - 1.9512680843462876467e-763j)  +/-  (9.52e-249, 9.52e-249j)
| (-11.745036961464313027 + 4.4905773829125096037e-755j)  +/-  (9.63e-244, 9.63e-244j)
| (-3.5288515742408722283 - 8.1485482837863057217e-761j)  +/-  (3.24e-246, 3.24e-246j)
| (-3.966802906508797071 + 8.9407907500020302199e-761j)  +/-  (1.53e-245, 1.53e-245j)
| (5.7721309871336952084 + 1.1550857320622946383e-757j)  +/-  (2.56e-243, 2.56e-243j)
| (-13.430904323339364811 + 5.498881300076476479e-760j)  +/-  (8.18e-246, 8.18e-246j)
| (-6.7158694323119959596 + 3.6224385816034906319e-758j)  +/-  (1.38e-242, 1.38e-242j)
| (-3.0955129454152609643 - 4.353157159786543889e-763j)  +/-  (5.29e-247, 5.29e-247j)
| (-11.062367038603437738 + 4.2711739764423836647e-757j)  +/-  (3.66e-243, 3.66e-243j)
| (4.409636998176837208 - 8.3755012868499426902e-764j)  +/-  (7.95e-245, 7.95e-245j)
| (1.8228871937355235918 + 8.0587402285576966706e-772j)  +/-  (1.02e-249, 1.02e-249j)
| (-5.7721309871336952084 - 4.3004725398100659475e-763j)  +/-  (2.56e-243, 2.56e-243j)
| (8.2070247308553776342 + 6.5220075580789279976e-765j)  +/-  (4.46e-242, 4.46e-242j)
| (-2.2423759293463206638 - 1.4241578617981916951e-786j)  +/-  (1.06e-248, 1.06e-248j)
| (-6.2398588621411733879 + 5.1532121925256407191e-781j)  +/-  (6.24e-243, 6.24e-243j)
| (3.5288515742408722283 - 2.5303352464419356294e-784j)  +/-  (3.21e-246, 3.21e-246j)
| (7.2013596156247353986 + 3.3195734557044964906e-779j)  +/-  (2.6e-242, 2.6e-242j)
| (-7.697799766263641935 + 4.8231688182751525251e-783j)  +/-  (3.68e-242, 3.68e-242j)
| (-1.8228871937355235918 + 3.9553298411257919592e-795j)  +/-  (1.09e-249, 1.09e-249j)
| (-4.857758788142464054 - 2.9350889246439750158e-789j)  +/-  (3.15e-244, 3.15e-244j)
| (2.6666685821775507099 - 3.1941201422439074328e-793j)  +/-  (7.72e-248, 7.72e-248j)
| (1.4086221888588021554 + 2.540354812070723764e-797j)  +/-  (8.53e-251, 8.53e-251j)
| (-8.7313733314427589523 + 1.4115087609924761663e-786j)  +/-  (4.82e-242, 4.82e-242j)
| (-1.4086221888588021554 - 1.100000375063535163e-801j)  +/-  (8.73e-251, 8.73e-251j)
| (-5.3117016085699399054 + 1.551358217572855665e-793j)  +/-  (8.73e-244, 8.73e-244j)
| (-7.2013596156247353986 + 9.6737846849761245853e-792j)  +/-  (2.38e-242, 2.38e-242j)
| (0.59699197188257449644 - 5.661365464016531537e-807j)  +/-  (4.99e-253, 4.99e-253j)
| (5.3117016085699399054 - 2.1197275557400853967e-795j)  +/-  (9.42e-244, 9.42e-244j)
| (-0.19842016157452860181 - 2.6913984724016113287e-846j)  +/-  (2.27e-254, 2.27e-254j)
| (-1 + 3.0891632807834319362e-813j)  +/-  (7.07e-252, 7.07e-252j)
| (10.431951551886178907 - 4.8373817556462388146e-802j)  +/-  (1.07e-242, 1.07e-242j)
| (6.7158694323119959596 - 3.3651016572325894477e-812j)  +/-  (1.45e-242, 1.45e-242j)
| (6.2398588621411733879 - 7.1310478372376793325e-823j)  +/-  (7.01e-243, 7.01e-243j)
| (8.7313733314427589523 - 4.2570156066077634067e-834j)  +/-  (4.43e-242, 4.43e-242j)
| (1 + 3.9162292335378726707e-852j)  +/-  (6.6e-252, 6.6e-252j)
| (-4.409636998176837208 + 2.7846851231907726354e-844j)  +/-  (6.95e-245, 6.95e-245j)
| (-8.2070247308553776342 + 3.3194434298074487123e-840j)  +/-  (4.33e-242, 4.33e-242j)
| (0.19842016157452860181 - 1.1058985690295975466e-883j)  +/-  (4.33e-254, 4.33e-254j)
| (3.966802906508797071 + 2.1796743091545694303e-846j)  +/-  (1.61e-245, 1.61e-245j)
| (-9.8387955901631722927 - 1.4587905215819745583e-841j)  +/-  (2.38e-242, 2.38e-242j)
| (-0.59699197188257449644 - 1.8484046953357066997e-855j)  +/-  (4.99e-253, 4.99e-253j)
| (-2.6666685821775507099 + 1.0936107542022871328e-851j)  +/-  (7.63e-248, 7.63e-248j)
| (4.857758788142464054 - 2.4066010983255670077e-848j)  +/-  (2.69e-244, 2.69e-244j)
-------------------------------------------------
The weights are:
| (5.6886313196864588691e-25 + 5.7166285820872418058e-623j)  +/-  (4.46e-68, 1.23e-187j)
| (3.445706583629362038e-35 + 3.0587516269089085597e-630j)  +/-  (1.01e-72, 2.78e-192j)
| (3.445706583629362038e-35 + 3.3782496661554393492e-629j)  +/-  (1.11e-72, 3.07e-192j)
| (2.2001433213546471951e-22 + 1.1057577358671970019e-623j)  +/-  (1.11e-67, 3.07e-187j)
| (4.6528594992176480206e-20 - 1.7515878682171392825e-622j)  +/-  (1.27e-66, 3.5e-186j)
| (6.9568685471518239335e-28 + 1.6544227626861927574e-626j)  +/-  (1.15e-70, 3.16e-190j)
| (0.0014279899287823010619 + 1.1891906557702625752e-613j)  +/-  (2.87e-47, 7.91e-167j)
| (3.17378574487511583e-31 - 3.2301972778980208789e-628j)  +/-  (4.22e-72, 1.16e-191j)
| (2.7210382191299875151e-14 + 1.7408753132505378785e-619j)  +/-  (6.5e-65, 1.79e-184j)
| (4.6528594992176480206e-20 + 2.9805967132200480013e-621j)  +/-  (1.41e-71, 3.89e-191j)
| (2.8640459800951226715e-40 - 7.9058239223887519404e-633j)  +/-  (2.26e-76, 6.23e-196j)
| (0.013623838414846746299 + 4.9087328568244727123e-613j)  +/-  (1.19e-44, 3.27e-164j)
| (3.17378574487511583e-31 - 5.4555512844229027127e-627j)  +/-  (3.82e-76, 1.05e-195j)
| (0.000343494707263600685 + 1.0312705158741179894e-613j)  +/-  (2.45e-55, 6.77e-175j)
| (6.7261790850119303657e-05 - 4.4250180715101318815e-614j)  +/-  (1.78e-57, 4.89e-177j)
| (1.077854615088083312e-08 + 1.6050888504467563899e-616j)  +/-  (4.15e-63, 1.14e-182j)
| (2.8640459800951226715e-40 - 6.2907138328635919157e-632j)  +/-  (3.47e-80, 9.55e-200j)
| (3.0807771345047889343e-11 - 3.2512465290934430068e-617j)  +/-  (5.94e-68, 1.64e-187j)
| (0.0014279899287823010619 - 2.1927170987658808832e-613j)  +/-  (2.57e-55, 7.08e-175j)
| (6.9568685471518239335e-28 + 5.640833814174098715e-625j)  +/-  (1.85e-75, 5.1e-195j)
| (1.0647654341065482485e-05 - 7.0067413181289580326e-615j)  +/-  (1.29e-61, 3.56e-181j)
| (0.031581877265039573614 - 8.7108562103745362163e-613j)  +/-  (4.95e-49, 1.36e-168j)
| (1.077854615088083312e-08 - 5.5815437211972425291e-616j)  +/-  (4.4e-66, 1.21e-185j)
| (4.8735214913864057891e-16 - 2.1317261478326751992e-620j)  +/-  (1.13e-70, 3.11e-190j)
| (0.013623838414846746299 - 7.5968390320553171046e-613j)  +/-  (2.53e-54, 6.97e-174j)
| (6.6032231318984450355e-10 + 1.4290584286467603388e-616j)  +/-  (3.21e-67, 8.86e-187j)
| (0.000343494707263600685 - 5.0992506740203320753e-614j)  +/-  (3.82e-60, 1.05e-179j)
| (1.0728907653654470705e-12 - 1.1973036104072486023e-618j)  +/-  (2.3e-69, 6.33e-189j)
| (2.7210382191299875151e-14 - 1.1543483676036179531e-618j)  +/-  (1.7e-71, 4.69e-191j)
| (0.031581877265039573614 + 1.2399737503805691652e-612j)  +/-  (3.12e-55, 8.61e-175j)
| (1.3515128857388858629e-06 - 6.1055163239459690363e-615j)  +/-  (2.25e-65, 6.2e-185j)
| (0.0048614345417642836821 - 2.5279669405073773516e-613j)  +/-  (2.8e-59, 7.71e-179j)
| (0.060870856473252671374 + 1.4099673834711336319e-612j)  +/-  (2.37e-54, 6.54e-174j)
| (5.9277788532023397421e-18 - 2.4280826963471440268e-620j)  +/-  (6.94e-74, 1.91e-193j)
| (0.060870856473252671374 - 1.8501843504063382278e-612j)  +/-  (2.96e-56, 8.16e-176j)
| (1.3622496225591380523e-07 + 1.9479139633489930449e-615j)  +/-  (9.97e-67, 2.75e-186j)
| (1.0728907653654470705e-12 + 6.5351575008039001962e-618j)  +/-  (1.58e-70, 4.36e-190j)
| (0.1336849019040389452 + 2.7346407419724683172e-612j)  +/-  (4.15e-58, 1.14e-177j)
| (1.3622496225591380523e-07 - 6.3351283585655105605e-616j)  +/-  (7.89e-70, 2.17e-189j)
| (0.15534917118543772211 + 3.3389986498765997772e-612j)  +/-  (6.78e-59, 1.87e-178j)
| (0.098177026925758146497 + 2.509731099758384289e-612j)  +/-  (1.17e-59, 3.22e-179j)
| (5.6886313196864588691e-25 - 5.1607122665232870655e-625j)  +/-  (5.18e-79, 1.43e-198j)
| (3.0807771345047889343e-11 + 7.0457343263760251614e-618j)  +/-  (8.76e-73, 2.41e-192j)
| (6.6032231318984450355e-10 - 3.5933382417232876279e-617j)  +/-  (3.91e-72, 1.08e-191j)
| (5.9277788532023397421e-18 + 2.1547119698604753858e-621j)  +/-  (2.8e-76, 7.71e-196j)
| (0.098177026925758146497 - 2.0706580179022396992e-612j)  +/-  (4.48e-64, 1.23e-183j)
| (1.0647654341065482485e-05 + 1.7267641999261775796e-614j)  +/-  (6.39e-70, 1.76e-189j)
| (4.8735214913864057891e-16 + 1.7858202227229090384e-619j)  +/-  (1.38e-76, 3.8e-196j)
| (0.15534917118543772211 - 3.2143511456380169677e-612j)  +/-  (5.39e-66, 1.51e-185j)
| (6.7261790850119303657e-05 + 1.9868662719027273775e-614j)  +/-  (1.88e-70, 5.31e-190j)
| (2.2001433213546471951e-22 - 3.7788603521778116239e-622j)  +/-  (4.53e-80, 1.24e-199j)
| (0.1336849019040389452 - 3.066631647610737107e-612j)  +/-  (1.38e-67, 3.8e-187j)
| (0.0048614345417642836821 + 4.2642204790664586464e-613j)  +/-  (2.49e-69, 6.61e-189j)
| (1.3515128857388858629e-06 + 2.225897296612536034e-615j)  +/-  (7.97e-72, 2.32e-191j)
