Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 44
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^46 - 23*t^44 + 989/8*t^42 - 6601/16*t^40 + 61295/64*t^38 - 210197/128*t^36 + 4414137/2048*t^34 - 9070809/4096*t^32 + 14799741/8192*t^30 - 19332995/16384*t^28 + 81198579/131072*t^26 - 68544255/262144*t^24 + 92736345/1048576*t^22 - 49934955/2097152*t^20 + 677688675/134217728*t^18 - 222981435/268435456*t^16 + 222981435/2147483648*t^14 - 41158845/4294967296*t^12 + 21559395/34359738368*t^10 - 1891175/68719476736*t^8 + 203665/274877906944*t^6 - 5819/549755813888*t^4 + 529/8796093022208*t^2 - 1/17592186044416
-------------------------------------------------
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
Positive weights:   46 out of 46
Indefinite weights: 0 out of 46
Negative weights:   0 out of 46
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.98545951771719686801 - 2.6157591574888990832e-869j)  +/-  (2.22e-239, 2.22e-239j)
| (-0.95314476681416082173 - 5.5863314182902514966e-888j)  +/-  (1.32e-239, 1.32e-239j)
| (-0.90307473232453270466 - 9.9543216028582030284e-889j)  +/-  (3.72e-240, 3.72e-240j)
| (0.4294834430300819004 - 2.0342387292434956961e-895j)  +/-  (9.43e-248, 9.43e-248j)
| (0.93027844333783315439 + 7.1441576955227629027e-885j)  +/-  (8.07e-240, 8.07e-240j)
| (0.95314476681416082173 + 1.2978826284929541903e-903j)  +/-  (1.33e-239, 1.33e-239j)
| (-0.99941702236617402895 - 4.9433211107229329681e-916j)  +/-  (6.73e-240, 6.73e-240j)
| (-0.87166047003275122082 + 1.3795617102291902515e-919j)  +/-  (1.3e-240, 1.3e-240j)
| (-0.98545951771719686801 + 1.9013138551584985829e-916j)  +/-  (1.97e-239, 1.97e-239j)
| (0.99941702236617402895 + 8.5933933981624439166e-918j)  +/-  (6.32e-240, 6.32e-240j)
| (0.87166047003275122082 + 2.633950266041846956e-932j)  +/-  (1.11e-240, 1.11e-240j)
| (-0.99475727885809482918 - 8.134047443155322364e-938j)  +/-  (1.84e-239, 1.84e-239j)
| (-0.30251455088107578749 + 2.8099416034202605495e-952j)  +/-  (4.36e-250, 4.36e-250j)
| (-0.83618212425471087022 - 2.3617613716558053557e-943j)  +/-  (4.13e-241, 4.13e-241j)
| (0.99475727885809482918 + 4.2388205888886340982e-939j)  +/-  (1.77e-239, 1.77e-239j)
| (0.83618212425471087022 + 1.0876004560556335371e-954j)  +/-  (3.97e-241, 3.97e-241j)
| (0.7968051114159045953 - 1.3214557789250749203e-958j)  +/-  (1.02e-241, 1.02e-241j)
| (-0.93027844333783315439 + 2.4016945457122476953e-963j)  +/-  (5.83e-240, 5.83e-240j)
| (-0.7968051114159045953 - 1.0254652536471499817e-966j)  +/-  (8.98e-242, 8.98e-242j)
| (-0.49011021717801722536 + 1.3309322991384301588e-971j)  +/-  (1.16e-246, 1.16e-246j)
| (0.97156708939794148293 - 9.480216705459746234e-964j)  +/-  (1.99e-239, 1.99e-239j)
| (0.7071067811865475244 + 6.80346106335443776e-982j)  +/-  (4.61e-243, 4.61e-243j)
| (0.90307473232453270466 - 5.2681357254956955145e-983j)  +/-  (3.4e-240, 3.4e-240j)
| (-0.75371302532736111352 - 1.4134940070953195327e-991j)  +/-  (2.3e-242, 2.3e-242j)
| (-0.7071067811865475244 - 1.1703154083603757641e-992j)  +/-  (5.04e-243, 5.04e-243j)
| (0.034141110185967895283 + 1.6345385094727986561e-1005j)  +/-  (4.44e-255, 4.44e-255j)
| (0.75371302532736111352 + 1.0783117577509997244e-994j)  +/-  (2.66e-242, 2.66e-242j)
| (0.3668542188130565157 + 9.2095205974707483712e-1000j)  +/-  (5.77e-249, 5.77e-249j)
| (-0.97156708939794148293 + 3.7973287538855624233e-996j)  +/-  (1.84e-239, 1.84e-239j)
| (-0.65720367881797246116 + 1.4307195218816661386e-1001j)  +/-  (8.26e-244, 8.26e-244j)
| (-0.23676442046644673699 - 6.5116676912334453868e-1009j)  +/-  (2.49e-251, 2.49e-251j)
| (0.65720367881797246116 + 8.0440210124216258944e-1000j)  +/-  (7.57e-244, 7.57e-244j)
| (0.60423638952109452076 + 6.9156495385538690169e-1003j)  +/-  (9.03e-245, 9.03e-245j)
| (0.10226414894203423714 + 6.623397616085649079e-1013j)  +/-  (6.2e-254, 6.2e-254j)
| (-0.60423638952109452076 - 3.4356606355910671295e-1004j)  +/-  (9.96e-245, 9.96e-245j)
| (-0.3668542188130565157 - 1.5346734528042542977e-1008j)  +/-  (5.85e-249, 5.85e-249j)
| (0.16991038502866666211 - 1.3621017950235991626e-1012j)  +/-  (1.24e-252, 1.24e-252j)
| (0.54845187124931871364 - 5.5830242134399123576e-1007j)  +/-  (1.15e-245, 1.15e-245j)
| (0.23676442046644673699 - 9.4310371902923523785e-1013j)  +/-  (2.13e-251, 2.13e-251j)
| (-0.16991038502866666211 - 2.3330614798552611998e-1013j)  +/-  (1.14e-252, 1.14e-252j)
| (-0.54845187124931871364 + 1.9269146391687296956e-1007j)  +/-  (1.15e-245, 1.15e-245j)
| (-0.10226414894203423714 - 2.0594195303157697127e-1015j)  +/-  (5.68e-254, 5.68e-254j)
| (0.30251455088107578749 + 2.3579231817019803293e-1011j)  +/-  (3.84e-250, 3.84e-250j)
| (0.49011021717801722536 + 3.7693045363296389783e-1009j)  +/-  (1.24e-246, 1.24e-246j)
| (-0.034141110185967895283 - 2.0976678059681138891e-1016j)  +/-  (4.44e-255, 4.44e-255j)
| (-0.4294834430300819004 - 3.6052034315692193243e-1009j)  +/-  (8.91e-248, 8.91e-248j)
-------------------------------------------------
The weights are:
| (0.021739130434782608696 + 9.705297831422644821e-870j)  +/-  (3.3e-71, 1.95e-186j)
| (0.021739130434782608696 - 5.2224837751161779458e-871j)  +/-  (1.35e-71, 7.94e-187j)
| (0.021739130434782608696 - 7.6109971487781157702e-871j)  +/-  (1.25e-71, 7.39e-187j)
| (0.021739130434782608696 + 5.4361018719258513342e-870j)  +/-  (2.55e-72, 1.5e-187j)
| (0.021739130434782608696 - 2.2249659266807510891e-869j)  +/-  (1.69e-72, 9.98e-188j)
| (0.021739130434782608696 + 3.1330365048193871604e-869j)  +/-  (2.35e-72, 1.39e-187j)
| (0.021739130434782608696 - 5.7565746281023719064e-872j)  +/-  (1.24e-73, 7.32e-189j)
| (0.021739130434782608696 + 8.8322995667105836261e-871j)  +/-  (1.12e-73, 6.61e-189j)
| (0.021739130434782608696 - 2.8851682128127225639e-871j)  +/-  (1.04e-73, 6.15e-189j)
| (0.021739130434782608696 - 8.1863414828931354572e-870j)  +/-  (8.5e-75, 5.02e-190j)
| (0.021739130434782608696 - 1.4413688336493336616e-869j)  +/-  (1.84e-75, 1.09e-190j)
| (0.021739130434782608696 + 1.728345913695605753e-871j)  +/-  (9.86e-74, 5.82e-189j)
| (0.021739130434782608696 - 2.4766905507159093262e-870j)  +/-  (2.8e-77, 1.65e-192j)
| (0.021739130434782608696 - 1.0076172080814321779e-870j)  +/-  (4.68e-75, 2.76e-190j)
| (0.021739130434782608696 + 3.6809932592673258712e-869j)  +/-  (1.28e-74, 7.56e-190j)
| (0.021739130434782608696 + 1.2296017654340156295e-869j)  +/-  (2.95e-76, 1.74e-191j)
| (0.021739130434782608696 - 1.0719139480585225667e-869j)  +/-  (7.48e-77, 4.42e-192j)
| (0.021739130434782608696 + 6.4088102228817128552e-871j)  +/-  (1.39e-75, 8.22e-191j)
| (0.021739130434782608696 + 1.1346311101702995312e-870j)  +/-  (2.39e-77, 1.41e-192j)
| (0.021739130434782608696 + 1.9770042861846352507e-870j)  +/-  (3.79e-80, 2.23e-195j)
| (0.021739130434782608696 - 5.7037210025893776432e-869j)  +/-  (6.2e-76, 3.66e-191j)
| (0.021739130434782608696 - 8.5017730117100465597e-870j)  +/-  (2.32e-79, 1.37e-194j)
| (0.021739130434782608696 + 1.7446945724176522462e-869j)  +/-  (1.35e-76, 7.96e-192j)
| (0.021739130434782608696 - 1.2646702841081935378e-870j)  +/-  (8.67e-79, 5.12e-194j)
| (0.021739130434782608696 + 1.3981678500302534979e-870j)  +/-  (1.38e-79, 8.12e-195j)
| (0.021739130434782608696 + 3.5159350253674223938e-870j)  +/-  (6.04e-83, 3.56e-198j)
| (0.021739130434782608696 + 9.4908872684271029803e-870j)  +/-  (2.45e-79, 1.45e-194j)
| (0.021739130434782608696 - 5.032911809013436183e-870j)  +/-  (2.88e-82, 1.7e-197j)
| (0.021739130434782608696 + 4.0489247766697601657e-871j)  +/-  (1.41e-78, 8.3e-194j)
| (0.021739130434782608696 - 1.5355978391848961622e-870j)  +/-  (5.56e-81, 3.28e-196j)
| (0.021739130434782608696 + 2.6603697956537662621e-870j)  +/-  (2.94e-83, 1.74e-198j)
| (0.021739130434782608696 + 7.6844636292436731398e-870j)  +/-  (6.49e-82, 3.83e-197j)
| (0.021739130434782608696 - 6.9950829579663831021e-870j)  +/-  (1.23e-82, 7.25e-198j)
| (0.021739130434782608696 - 3.7694704342586540846e-870j)  +/-  (5.58e-85, 3.29e-200j)
| (0.021739130434782608696 + 1.6774827154583971279e-870j)  +/-  (1.62e-83, 9.55e-199j)
| (0.021739130434782608696 + 2.3022659830116153486e-870j)  +/-  (1.32e-84, 7.78e-200j)
| (0.021739130434782608696 + 4.043976813312837967e-870j)  +/-  (1.48e-85, 8.77e-201j)
| (0.021739130434782608696 + 6.4037127365602258482e-870j)  +/-  (6.72e-85, 3.97e-200j)
| (0.021739130434782608696 - 4.3429797531848384149e-870j)  +/-  (7.1e-86, 4.19e-201j)
| (0.021739130434782608696 - 2.8545505425332657513e-870j)  +/-  (1.31e-86, 7.71e-202j)
| (0.021739130434782608696 - 1.82440227759574236e-870j)  +/-  (4.16e-86, 2.45e-201j)
| (0.021739130434782608696 + 3.0606843744580676175e-870j)  +/-  (4.86e-87, 2.87e-202j)
| (0.021739130434782608696 + 4.6708202859190486986e-870j)  +/-  (4.65e-87, 2.74e-202j)
| (0.021739130434782608696 - 5.8891931153972180899e-870j)  +/-  (5.12e-87, 3.01e-202j)
| (0.021739130434782608696 - 3.2804743521926046928e-870j)  +/-  (2.15e-87, 1.27e-202j)
| (0.021739130434782608696 - 2.136017255958086279e-870j)  +/-  (1.42e-87, 7.97e-203j)
