Starting with polynomial:
P : 16*t^4 - 12*t^2 + 1
Extension levels are: 4 40
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : 16*t^4 - 12*t^2 + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^44 - 172*t^42 + 861*t^40 - 2665*t^38 + 45695/8*t^36 - 575757/64*t^34 + 2760681/256*t^32 - 643467/64*t^30 + 7565085/1024*t^28 - 17651865/4096*t^26 + 32782035/16384*t^24 - 12096045/16384*t^22 + 28224105/131072*t^20 - 206253075/4194304*t^18 + 145422675/16777216*t^16 - 9694845/8388608*t^14 + 30421755/268435456*t^12 - 8436285/1073741824*t^10 + 1562275/4294967296*t^8 - 44275/4294967296*t^6 + 5313/34359738368*t^4 - 253/274877906944*t^2 + 1/1099511627776
-------------------------------------------------
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:   44 out of 44
Indefinite weights: 0 out of 44
Negative weights:   0 out of 44
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.97814760073380563793 + 7.3453686253814302857e-936j)  +/-  (1.12e-240, 1.12e-240j)
| (0.97814760073380563793 - 3.0843535571063316862e-934j)  +/-  (1.16e-240, 1.16e-240j)
| (-0.88294759285892694203 + 1.8907655149674420815e-942j)  +/-  (2.73e-241, 2.73e-241j)
| (0.99756405025982424761 + 8.1978709170725941912e-940j)  +/-  (2.73e-241, 2.73e-241j)
| (0.96126169593831886192 + 8.0814845523858705427e-944j)  +/-  (1.35e-240, 1.35e-240j)
| (0.88294759285892694203 + 1.9283672826274715366e-946j)  +/-  (2.43e-241, 2.43e-241j)
| (-0.99026806874157031508 - 2.0448146619383330988e-948j)  +/-  (9.23e-241, 9.23e-241j)
| (-0.9135454576426008955 + 1.58042480155984976e-949j)  +/-  (6.57e-241, 6.57e-241j)
| (0.99026806874157031508 + 1.2858045698019972429e-946j)  +/-  (8.78e-241, 8.78e-241j)
| (-0.99756405025982424761 + 1.1072514011106167468e-949j)  +/-  (2.42e-241, 2.42e-241j)
| (0.84804809615642597039 - 1.5677735477657340965e-949j)  +/-  (1.04e-241, 1.04e-241j)
| (-0.24192189559966772256 - 1.3151927574088615259e-965j)  +/-  (2.22e-251, 2.22e-251j)
| (-0.84804809615642597039 + 1.882403371671030327e-955j)  +/-  (9.9e-242, 9.9e-242j)
| (-0.8090169943749474241 - 1.3068090835571595078e-955j)  +/-  (3.29e-242, 3.29e-242j)
| (0.9135454576426008955 - 6.784556655816398089e-953j)  +/-  (5.5e-241, 5.5e-241j)
| (0.8090169943749474241 - 1.3317978760131594631e-961j)  +/-  (3.43e-242, 3.43e-242j)
| (0.93969262078590838405 + 1.8726083395552996183e-970j)  +/-  (8.48e-241, 8.48e-241j)
| (-0.96126169593831886192 + 7.767887127644694565e-972j)  +/-  (1.22e-240, 1.22e-240j)
| (-0.7660444431189780352 - 9.4194636899943649218e-983j)  +/-  (9.61e-243, 9.61e-243j)
| (-0.93969262078590838405 + 8.0097626513386162234e-987j)  +/-  (9.71e-241, 9.71e-241j)
| (0.37460659341591203541 - 1.2564752505933495718e-995j)  +/-  (4.83e-249, 4.83e-249j)
| (0.7660444431189780352 - 5.5781695428433838597e-1014j)  +/-  (9.04e-243, 9.04e-243j)
| (0.17364817766693034885 + 6.6112017780005724828e-1030j)  +/-  (1.06e-252, 1.06e-252j)
| (-0.66913060635885821383 + 8.0802895014478472107e-1032j)  +/-  (3.7e-244, 3.7e-244j)
| (-0.71933980033865113936 + 2.1888515968542580571e-1033j)  +/-  (2.17e-243, 2.17e-243j)
| (0.1045284632676534714 + 6.5274127351568555988e-1037j)  +/-  (6.34e-254, 6.34e-254j)
| (0.66913060635885821383 + 3.4291685370291218385e-1046j)  +/-  (4.16e-244, 4.16e-244j)
| (0.71933980033865113936 + 1.1714397505402255221e-1059j)  +/-  (2.32e-243, 2.32e-243j)
| (-0.17364817766693034885 - 1.0121141959154687533e-1071j)  +/-  (1.1e-252, 1.1e-252j)
| (-0.61566147532565827967 - 2.7604473836543780062e-1064j)  +/-  (6.01e-245, 6.01e-245j)
| (-0.37460659341591203541 - 9.4033185091403188643e-1069j)  +/-  (4.66e-249, 4.66e-249j)
| (0.24192189559966772256 + 2.5222161857636576188e-1069j)  +/-  (2.25e-251, 2.25e-251j)
| (0.55919290347074683016 - 8.8511808419772361324e-1064j)  +/-  (6.91e-246, 6.91e-246j)
| (0.034899496702500971646 + 2.0660017212988075669e-1075j)  +/-  (2.86e-255, 2.86e-255j)
| (-0.5 + 4.9362638077990727176e-1068j)  +/-  (7.16e-247, 7.16e-247j)
| (-0.43837114678907741745 + 2.4940092984604738123e-1069j)  +/-  (7.08e-248, 7.08e-248j)
| (-0.1045284632676534714 + 4.7249806333453943217e-1075j)  +/-  (6.34e-254, 6.34e-254j)
| (0.61566147532565827967 + 2.7065068153692423716e-1068j)  +/-  (5.54e-245, 5.54e-245j)
| (0.3090169943749474241 + 4.0460581901432799134e-1075j)  +/-  (3.9e-250, 3.9e-250j)
| (-0.3090169943749474241 + 1.5135733567723978869e-1075j)  +/-  (3.66e-250, 3.66e-250j)
| (-0.55919290347074683016 - 4.5918323085798014245e-1072j)  +/-  (6.87e-246, 6.87e-246j)
| (-0.034899496702500971646 + 3.2378807131574056833e-1080j)  +/-  (2.86e-255, 2.86e-255j)
| (0.5 - 3.064219951472408569e-1071j)  +/-  (8.42e-247, 8.42e-247j)
| (0.43837114678907741745 - 2.0981587049137101849e-1073j)  +/-  (6.03e-248, 6.03e-248j)
-------------------------------------------------
The weights are:
| (0.00096060602619332338331 + 8.8043515329259523009e-938j)  +/-  (9.05e-74, 1.57e-189j)
| (0.00096060602619332338331 + 1.0052862721735118964e-935j)  +/-  (3.71e-74, 6.44e-190j)
| (0.0048978566281028129982 - 4.3380415518530775058e-937j)  +/-  (1.51e-74, 2.63e-190j)
| (0.00010813256953810761018 - 1.7181432979688631914e-936j)  +/-  (1.29e-74, 2.24e-190j)
| (0.0016883544871508225513 - 3.0832792326921631706e-935j)  +/-  (1.5e-74, 2.61e-190j)
| (0.0048978566281028129982 + 1.5849037750711989678e-935j)  +/-  (1.86e-75, 3.22e-191j)
| (0.00043042560068534597871 + 3.2829503515501858289e-937j)  +/-  (9.25e-76, 1.6e-191j)
| (0.003676326596012686513 + 1.814092943403908495e-937j)  +/-  (4.23e-76, 7.34e-192j)
| (0.00043042560068534597871 + 1.0954901003592228149e-935j)  +/-  (6.41e-75, 1.11e-190j)
| (0.00010813256953810761018 - 5.7788167927813034543e-938j)  +/-  (3.73e-76, 6.47e-192j)
| (0.0062403205912324731394 - 1.4769199639389574402e-935j)  +/-  (1.08e-76, 1.87e-192j)
| (0.0209216399206547438 - 5.0802708445667865466e-936j)  +/-  (1.48e-78, 2.57e-194j)
| (0.0062403205912324731394 + 7.0162982010766145805e-937j)  +/-  (7.94e-77, 1.38e-192j)
| (0.0076775889513894730655 - 9.9158361543055723728e-937j)  +/-  (2.13e-77, 3.7e-193j)
| (0.003676326596012686513 - 1.7537879278840139743e-935j)  +/-  (5.34e-77, 9.26e-193j)
| (0.0076775889513894730655 + 1.3969661062314111873e-935j)  +/-  (1.63e-78, 2.83e-194j)
| (0.00259950618756691072 + 2.0839832366587395459e-935j)  +/-  (6.42e-77, 1.11e-192j)
| (0.0016883544871508225513 - 4.6592619852271030984e-937j)  +/-  (9.05e-78, 1.57e-193j)
| (0.0091816869148118850128 + 1.3056732269661408471e-936j)  +/-  (7.04e-80, 1.22e-195j)
| (0.00259950618756691072 + 7.8474471119520812e-938j)  +/-  (6.88e-78, 1.19e-193j)
| (0.019103775559318345993 + 9.6590917061007713367e-936j)  +/-  (2.52e-83, 4.37e-199j)
| (0.0091816869148118850128 - 1.3313090605910996008e-935j)  +/-  (7.27e-81, 1.26e-196j)
| (0.021552140230954537601 - 8.1253637427372893517e-936j)  +/-  (1.01e-83, 1.75e-199j)
| (0.012272538480751705238 + 2.0061767764405129748e-936j)  +/-  (3.8e-82, 6.58e-198j)
| (0.010723338925527766982 - 1.6440923430220056742e-936j)  +/-  (2.63e-81, 4.56e-197j)
| (0.021979417785931173755 + 7.6107984653426131167e-936j)  +/-  (1.5e-84, 2.61e-200j)
| (0.012272538480751705238 - 1.2194683786613708327e-935j)  +/-  (1.32e-83, 2.3e-199j)
| (0.010723338925527766982 + 1.2733153565679978523e-935j)  +/-  (7.42e-83, 1.29e-198j)
| (0.021552140230954537601 + 5.5745781948267797917e-936j)  +/-  (1.33e-85, 2.3e-201j)
| (0.013799132173329641362 - 2.3907895694029923256e-936j)  +/-  (1.65e-84, 2.86e-200j)
| (0.019103775559318345993 - 4.1232522008872993977e-936j)  +/-  (4.18e-86, 7.25e-202j)
| (0.0209216399206547438 + 8.6389586364956895979e-936j)  +/-  (2.47e-86, 4.29e-202j)
| (0.015273406593510133727 - 1.1171310545139404389e-935j)  +/-  (1.03e-86, 1.78e-202j)
| (0.022195156113998047196 - 7.0967057922018351849e-936j)  +/-  (1.32e-86, 2.29e-202j)
| (0.016666666666666666667 - 3.2216791052618910523e-936j)  +/-  (7.2e-87, 1.25e-202j)
| (0.017951794170285091996 + 3.664554798213103986e-936j)  +/-  (5.96e-87, 1.03e-202j)
| (0.021979417785931173755 - 6.0767304776636592311e-936j)  +/-  (9.03e-88, 1.57e-203j)
| (0.013799132173329641362 + 1.1677900400099290535e-935j)  +/-  (6.27e-88, 1.09e-203j)
| (0.020100188826388304712 - 9.1504418580367225418e-936j)  +/-  (2.75e-88, 4.77e-204j)
| (0.020100188826388304712 + 4.5958228216786919645e-936j)  +/-  (5.89e-88, 1.02e-203j)
| (0.015273406593510133727 + 2.7965001635675453328e-936j)  +/-  (3.85e-88, 6.69e-204j)
| (0.022195156113998047196 + 6.5847454483324941616e-936j)  +/-  (3.43e-88, 5.94e-204j)
| (0.016666666666666666667 + 1.0668201787032401881e-935j)  +/-  (1.5e-89, 2.62e-205j)
| (0.017951794170285091996 - 1.0164775480137521994e-935j)  +/-  (1.63e-89, 2.82e-205j)
