Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 68
-------------------------------------------------
Trying to find an order 68 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^70 - 35*t^68 + 2345/8*t^66 - 25025/16*t^64 + 47775/8*t^62 - 277977/16*t^60 + 82003215/2048*t^58 - 307372595/4096*t^56 + 3817369325/32768*t^54 - 9950192175/65536*t^52 + 87959698827/524288*t^50 - 166025625675/1048576*t^48 + 269076014025/2097152*t^46 - 375834918375/4194304*t^44 + 3627957477375/67108864*t^42 - 3786268349115/134217728*t^40 + 27345271410275/2147483648*t^38 - 21335988680825/4294967296*t^36 + 57443046448375/34359738368*t^34 - 33256500575375/68719476736*t^32 + 8247612142693/68719476736*t^30 - 3486599885395/137438953472*t^28 + 19968708434535/4398046511104*t^26 - 6003543238875/8796093022208*t^24 + 6003543238875/70368744177664*t^22 - 1232727545049/140737488355328*t^20 + 818944872585/1125899906842624*t^18 - 107922967705/2251799813685248*t^16 + 11012547725/4503599627370496*t^14 - 842844275/9007199254740992*t^12 + 370851481/144115188075855872*t^10 - 13803405/288230376151711744*t^8 + 5085465/9223372036854775808*t^6 - 62475/18446744073709551616*t^4 + 1225/147573952589676412928*t^2 - 1/295147905179352825856
-------------------------------------------------
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: 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:   70 out of 70
Indefinite weights: 0 out of 70
Negative weights:   0 out of 70
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99371220989324258353 + 1.1444670939039137605e-830j)  +/-  (2.48e-230, 2.48e-230j)
| (-0.96968952037668685821 - 7.8134667510171164418e-837j)  +/-  (1.63e-230, 1.63e-230j)
| (-0.92811498851903892969 - 1.0176229679959298614e-838j)  +/-  (2.95e-231, 2.95e-231j)
| (-0.99974823494250657451 - 1.5097889449404220568e-836j)  +/-  (6.69e-231, 6.69e-231j)
| (0.92811498851903892969 - 1.0808833231291460675e-836j)  +/-  (2.95e-231, 2.95e-231j)
| (0.9438833303083675629 - 8.5422387665640571353e-841j)  +/-  (6.95e-231, 6.95e-231j)
| (0.97967539842323555163 - 1.1054661724603815396e-848j)  +/-  (2.03e-230, 2.03e-230j)
| (-0.91047754665881591206 + 3.5921996457799956401e-858j)  +/-  (1.53e-231, 1.53e-231j)
| (0.56948449316845199552 - 1.0513526757501674841e-866j)  +/-  (1.16e-239, 1.16e-239j)
| (0.99974823494250657451 + 2.3839127003873365678e-854j)  +/-  (7.34e-231, 7.34e-231j)
| (0.86974113315569539755 + 4.5347427805443078558e-873j)  +/-  (1.65e-232, 1.65e-232j)
| (0.96968952037668685821 + 4.3814631589438642898e-872j)  +/-  (1.6e-230, 1.6e-230j)
| (-0.86974113315569539755 + 5.3587560976340553266e-893j)  +/-  (1.77e-232, 1.77e-232j)
| (-0.79562454888178101872 + 4.4101623077862472213e-895j)  +/-  (4.33e-234, 4.33e-234j)
| (0.9977348750464561052 + 1.4748232169766758264e-888j)  +/-  (1.78e-230, 1.78e-230j)
| (0.84672419922828416835 - 7.6387873077361134915e-904j)  +/-  (5.3e-233, 5.3e-233j)
| (0.91047754665881591206 - 1.6099077056557081838e-900j)  +/-  (1.35e-231, 1.35e-231j)
| (-0.98768834059513772619 + 7.523693657055501007e-901j)  +/-  (2.49e-230, 2.49e-230j)
| (-0.76764474035801113148 - 3.7461022818780258964e-907j)  +/-  (8.21e-235, 8.21e-235j)
| (-0.97967539842323555163 - 1.2321720719794274324e-901j)  +/-  (2.21e-230, 2.21e-230j)
| (0.89100652418836786236 + 3.5085136095789910938e-906j)  +/-  (5.59e-232, 5.59e-232j)
| (0.76764474035801113148 - 6.4692754470193726575e-920j)  +/-  (1.01e-234, 1.01e-234j)
| (-0.28759932743201725807 + 3.8109750157682697282e-931j)  +/-  (1.63e-247, 1.63e-247j)
| (-0.82200207544790989563 - 9.3442774360496136761e-918j)  +/-  (1.55e-233, 1.55e-233j)
| (-0.73811899748734062094 + 9.3723354114057645178e-920j)  +/-  (1.76e-235, 1.76e-235j)
| (0.98768834059513772619 - 4.8027725864379319735e-912j)  +/-  (2.55e-230, 2.55e-230j)
| (0.7071067811865475244 + 1.8413357681218816319e-936j)  +/-  (3.49e-236, 3.49e-236j)
| (0.82200207544790989563 + 1.0792098918901099674e-932j)  +/-  (1.79e-233, 1.79e-233j)
| (-0.84672419922828416835 + 1.6078624652103490637e-930j)  +/-  (5.89e-233, 5.89e-233j)
| (-0.64087561398502414541 + 4.1597869101022756647e-936j)  +/-  (7.08e-238, 7.08e-238j)
| (0.95775081668493048874 - 9.6445809654919416352e-928j)  +/-  (9.75e-231, 9.75e-231j)
| (-0.9977348750464561052 + 1.0654909565508658036e-927j)  +/-  (1.91e-230, 1.91e-230j)
| (0.6746705459320743536 + 3.1868321846678011221e-942j)  +/-  (5e-237, 5e-237j)
| (-0.9438833303083675629 - 1.6883600955146035497e-934j)  +/-  (5.5e-231, 5.5e-231j)
| (-0.7071067811865475244 - 1.5208323651180766804e-943j)  +/-  (3.13e-236, 3.13e-236j)
| (-0.89100652418836786236 + 8.9474167633190810845e-938j)  +/-  (5.43e-232, 5.43e-232j)
| (0.79562454888178101872 - 1.7183617585363242586e-943j)  +/-  (3.75e-234, 3.75e-234j)
| (0.64087561398502414541 + 4.6508127236255049101e-945j)  +/-  (8.55e-238, 8.55e-238j)
| (0.73811899748734062094 - 4.7510998926546722369e-943j)  +/-  (1.84e-235, 1.84e-235j)
| (-0.95775081668493048874 - 1.4919124112068396404e-937j)  +/-  (1.11e-230, 1.11e-230j)
| (-0.56948449316845199552 - 1.1268922763686094995e-952j)  +/-  (1.06e-239, 1.06e-239j)
| (-0.99371220989324258353 - 1.1573722598586350653e-952j)  +/-  (2.57e-230, 2.57e-230j)
| (0.53203207651533656356 + 5.7753790306891065311e-966j)  +/-  (1.05e-240, 1.05e-240j)
| (0.60579004384081985861 - 2.6164124171079479798e-963j)  +/-  (1.02e-238, 1.02e-238j)
| (0.49350821806434685556 + 2.0231346615195699368e-967j)  +/-  (8.92e-242, 8.92e-242j)
| (-0.53203207651533656356 - 2.1404443488895417335e-965j)  +/-  (1.09e-240, 1.09e-240j)
| (-0.45399049973954679156 - 1.9172945615360913051e-967j)  +/-  (8.7e-243, 8.7e-243j)
| (-0.6746705459320743536 + 1.5116493074929798834e-962j)  +/-  (5.17e-237, 5.17e-237j)
| (0.45399049973954679156 + 3.976908967901176367e-970j)  +/-  (8.5e-243, 8.5e-243j)
| (0.15643446504023086901 + 2.1953925684936021548e-978j)  +/-  (2.72e-251, 2.72e-251j)
| (-0.60579004384081985861 + 5.1280781620646903276e-970j)  +/-  (9.77e-239, 9.77e-239j)
| (-0.49350821806434685556 - 7.6761500770404616625e-976j)  +/-  (8.33e-242, 8.33e-242j)
| (-0.067269005612039653337 + 2.4265604774723247236e-987j)  +/-  (6.74e-254, 6.74e-254j)
| (0.37229365840194516497 - 5.9618084545340159249e-979j)  +/-  (5.55e-245, 5.55e-245j)
| (0.33027906195516708177 + 3.0355770977137010704e-979j)  +/-  (2.68e-246, 2.68e-246j)
| (-0.022438064295804937237 - 1.2330776358493159173e-988j)  +/-  (2.91e-255, 2.91e-255j)
| (-0.4135585049665206605 - 2.6540882534300832699e-979j)  +/-  (8.24e-244, 8.24e-244j)
| (-0.24434040613789402966 + 9.1824244295815270804e-983j)  +/-  (9.78e-249, 9.78e-249j)
| (0.20058941578327277445 - 2.1150338045919268602e-983j)  +/-  (5.03e-250, 5.03e-250j)
| (0.4135585049665206605 - 4.0751806382171015589e-977j)  +/-  (7.15e-244, 7.15e-244j)
| (0.067269005612039653337 - 3.8668005506083493117e-987j)  +/-  (4.96e-254, 4.96e-254j)
| (-0.20058941578327277445 - 1.2269951771090524696e-984j)  +/-  (5.24e-250, 5.24e-250j)
| (-0.33027906195516708177 - 2.885083375390138287e-982j)  +/-  (3.47e-246, 3.47e-246j)
| (0.022438064295804937237 + 1.4383930350465103816e-988j)  +/-  (2.91e-255, 2.91e-255j)
| (0.28759932743201725807 + 8.0197398604966469235e-981j)  +/-  (1.6e-247, 1.6e-247j)
| (0.24434040613789402966 - 8.6289598542276777103e-983j)  +/-  (1.04e-248, 1.04e-248j)
| (-0.11196447610330785847 - 7.1680254981427574234e-987j)  +/-  (9.7e-253, 9.7e-253j)
| (-0.37229365840194516497 + 5.2267337809926465193e-980j)  +/-  (5.28e-245, 5.28e-245j)
| (-0.15643446504023086901 + 9.0213236859282447393e-986j)  +/-  (2.24e-251, 2.24e-251j)
| (0.11196447610330785847 + 2.8175729526597151042e-986j)  +/-  (1.1e-252, 1.1e-252j)
-------------------------------------------------
The weights are:
| (0.014285714285714285714 - 6.4800060147140522334e-831j)  +/-  (8.4e-26, 1.03e-133j)
| (0.014285714285714285714 - 1.8164625859466614759e-832j)  +/-  (3.74e-26, 4.59e-134j)
| (0.014285714285714285714 + 2.8283018742363710263e-832j)  +/-  (2.82e-26, 3.46e-134j)
| (0.014285714285714285714 + 1.6221762024727730118e-833j)  +/-  (9.22e-27, 1.13e-134j)
| (0.014285714285714285714 - 8.2875296133081328603e-831j)  +/-  (3.7e-27, 4.54e-135j)
| (0.014285714285714285714 + 9.6788834065532417325e-831j)  +/-  (3.75e-27, 4.61e-135j)
| (0.014285714285714285714 - 2.0867219230119714296e-830j)  +/-  (9.1e-28, 1.12e-135j)
| (0.014285714285714285714 - 3.1709900665618200975e-832j)  +/-  (2.12e-28, 2.6e-136j)
| (0.014285714285714285714 + 2.8294238550041006399e-831j)  +/-  (9.81e-30, 1.2e-137j)
| (0.014285714285714285714 + 5.4282441180384701574e-831j)  +/-  (2.05e-28, 2.52e-136j)
| (0.014285714285714285714 + 5.8129768215155431624e-831j)  +/-  (4.27e-30, 5.24e-138j)
| (0.014285714285714285714 + 1.4852471206593460542e-830j)  +/-  (1.16e-28, 1.43e-136j)
| (0.014285714285714285714 - 3.8668940483233548792e-832j)  +/-  (1.02e-31, 1.26e-139j)
| (0.014285714285714285714 + 4.943462649636466547e-832j)  +/-  (2.15e-32, 2.64e-140j)
| (0.014285714285714285714 - 2.4418902494749309405e-830j)  +/-  (2.85e-28, 3.5e-136j)
| (0.014285714285714285714 - 5.2854319200054122054e-831j)  +/-  (2.56e-31, 3.14e-139j)
| (0.014285714285714285714 + 7.2553279370073957656e-831j)  +/-  (5.69e-30, 6.99e-138j)
| (0.014285714285714285714 - 1.1515960408709057174e-832j)  +/-  (2.06e-34, 2.53e-142j)
| (0.014285714285714285714 - 5.3128889102082080945e-832j)  +/-  (3.14e-35, 3.85e-143j)
| (0.014285714285714285714 + 1.4832437767812596043e-832j)  +/-  (3.78e-34, 4.64e-142j)
| (0.014285714285714285714 - 6.4547110724145783491e-831j)  +/-  (2.5e-31, 3.07e-139j)
| (0.014285714285714285714 + 4.1396170724662171369e-831j)  +/-  (1.19e-34, 1.46e-142j)
| (0.014285714285714285714 + 1.0914850494055750264e-831j)  +/-  (1.76e-38, 2.16e-146j)
| (0.014285714285714285714 - 4.579644093747827562e-832j)  +/-  (2.13e-35, 2.61e-143j)
| (0.014285714285714285714 + 5.6884397186795381785e-832j)  +/-  (2.09e-36, 2.56e-144j)
| (0.014285714285714285714 + 3.7921187011633410904e-830j)  +/-  (2.15e-31, 2.64e-139j)
| (0.014285714285714285714 + 3.6026742113277258669e-831j)  +/-  (5.11e-37, 6.28e-145j)
| (0.014285714285714285714 + 4.8429561453718083759e-831j)  +/-  (9.81e-35, 1.2e-142j)
| (0.014285714285714285714 + 4.2209432478162945576e-832j)  +/-  (4.02e-36, 4.93e-144j)
| (0.014285714285714285714 - 6.8574800946722009398e-832j)  +/-  (1.76e-39, 2.16e-147j)
| (0.014285714285714285714 - 1.1678215225535740421e-830j)  +/-  (2.27e-32, 2.79e-140j)
| (0.014285714285714285714 - 4.900320243539765611e-833j)  +/-  (2.39e-37, 2.93e-145j)
| (0.014285714285714285714 - 3.3783397682224697382e-831j)  +/-  (1.2e-38, 1.47e-146j)
| (0.014285714285714285714 - 2.4885936343069167232e-832j)  +/-  (3.69e-37, 4.52e-145j)
| (0.014285714285714285714 - 6.070661965010415619e-832j)  +/-  (2.25e-39, 2.76e-147j)
| (0.014285714285714285714 + 3.5170516851456601761e-832j)  +/-  (6.13e-37, 7.53e-145j)
| (0.014285714285714285714 - 4.4656968768543624934e-831j)  +/-  (2.76e-37, 3.39e-145j)
| (0.014285714285714285714 + 3.1769540703588339014e-831j)  +/-  (8.11e-41, 9.95e-149j)
| (0.014285714285714285714 - 3.8544896675236807096e-831j)  +/-  (1.58e-38, 1.94e-146j)
| (0.014285714285714285714 + 2.1515025207593725036e-832j)  +/-  (1.56e-38, 1.91e-146j)
| (0.014285714285714285714 - 7.6784632809362357034e-832j)  +/-  (2.1e-45, 2.58e-153j)
| (0.014285714285714285714 + 8.2084463028963617549e-833j)  +/-  (1.26e-38, 1.55e-146j)
| (0.014285714285714285714 - 2.6780879727607309705e-831j)  +/-  (1.19e-44, 1.46e-152j)
| (0.014285714285714285714 - 2.9949376846966251511e-831j)  +/-  (4.86e-43, 5.97e-151j)
| (0.014285714285714285714 + 2.5390240871697221215e-831j)  +/-  (7.5e-46, 9.21e-154j)
| (0.014285714285714285714 + 8.1035674604848990142e-832j)  +/-  (1.51e-47, 1.85e-155j)
| (0.014285714285714285714 + 8.9870918389199647701e-832j)  +/-  (3.02e-49, 3.7e-157j)
| (0.014285714285714285714 + 6.4601361109907146701e-832j)  +/-  (1.11e-45, 1.37e-153j)
| (0.014285714285714285714 - 2.4106539036220917139e-831j)  +/-  (1.81e-48, 2.23e-156j)
| (0.014285714285714285714 + 1.7225557763694007285e-831j)  +/-  (8.33e-53, 1.02e-160j)
| (0.014285714285714285714 + 7.2633536742858310225e-832j)  +/-  (6.49e-47, 7.97e-155j)
| (0.014285714285714285714 - 8.5394829985455908894e-832j)  +/-  (9.58e-49, 1.18e-156j)
| (0.014285714285714285714 - 1.3731856297498509507e-831j)  +/-  (5.04e-54, 6.19e-162j)
| (0.014285714285714285714 - 2.1809274541277485105e-831j)  +/-  (7.52e-52, 9.23e-160j)
| (0.014285714285714285714 + 2.0775174148744745362e-831j)  +/-  (1.44e-52, 1.77e-160j)
| (0.014285714285714285714 + 1.436662531363779313e-831j)  +/-  (8.4e-55, 1.03e-162j)
| (0.014285714285714285714 - 9.4473489257270666614e-832j)  +/-  (1.08e-52, 1.32e-160j)
| (0.014285714285714285714 - 1.1437050321160002569e-831j)  +/-  (1.38e-54, 1.69e-162j)
| (0.014285714285714285714 - 1.8037022886237731757e-831j)  +/-  (5.25e-55, 6.44e-163j)
| (0.014285714285714285714 + 2.2916586672516420473e-831j)  +/-  (9.82e-53, 1.21e-160j)
| (0.014285714285714285714 + 1.572602190032841784e-831j)  +/-  (7.18e-56, 8.82e-164j)
| (0.014285714285714285714 + 1.1978129462803666367e-831j)  +/-  (4.58e-56, 5.63e-164j)
| (0.014285714285714285714 - 1.0410047400968242866e-831j)  +/-  (1.94e-55, 2.38e-163j)
| (0.014285714285714285714 - 1.5030420077585334222e-831j)  +/-  (3.46e-56, 4.24e-164j)
| (0.014285714285714285714 - 1.9806228518479359969e-831j)  +/-  (5.81e-56, 7.14e-164j)
| (0.014285714285714285714 + 1.8895509112395140681e-831j)  +/-  (3.05e-56, 3.75e-164j)
| (0.014285714285714285714 + 1.3123629878457620306e-831j)  +/-  (1.52e-57, 1.87e-165j)
| (0.014285714285714285714 + 9.9212911237305502836e-832j)  +/-  (2.32e-57, 2.84e-165j)
| (0.014285714285714285714 - 1.2539721099202392588e-831j)  +/-  (1.08e-57, 1.33e-165j)
| (0.014285714285714285714 - 1.6456557852147455622e-831j)  +/-  (9.78e-58, 1.16e-165j)
