Starting with polynomial:
P : 4*t^2 - 1
Extension levels are: 2 36 39
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P1 : 4*t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 39 Kronrod extension for:
P2 : 4*t^38 - 37*t^36 + 315/2*t^34 - 6545/16*t^32 + 5797/8*t^30 - 29667/32*t^28 + 56637/64*t^26 - 2629575/4096*t^24 + 5852925/16384*t^22 - 10015005/65536*t^20 + 6561555/131072*t^18 - 13037895/1048576*t^16 + 2414425/1048576*t^14 - 1300075/4194304*t^12 + 245157/8388608*t^10 - 245157/134217728*t^8 + 74613/1073741824*t^6 - 5985/4294967296*t^4 + 95/8589934592*t^2 - 1/68719476736
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^77 - 76*t^75 + 2775/4*t^73 - 8103/2*t^71 + 544215/32*t^69 - 1748943/32*t^67 + 143218999/1024*t^65 - 18730855/64*t^63 + 1045181709/2048*t^61 - 1540002035/2048*t^59 + 30999335081/32768*t^57 - 16782543687/16384*t^55 + 251738155305/262144*t^53 - 205263418941/262144*t^51 + 37387265592825/67108864*t^49 - 5815796869995/16777216*t^47 + 202802465047245/1073741824*t^45 - 96805419670575/1073741824*t^43 + 647520696018735/17179869184*t^41 - 118413686604675/8589934592*t^39 + 605134770855615/137438953472*t^37 - 168345763320735/137438953472*t^35 + 1300853625660225/4398046511104*t^33 - 33935311973745/549755813888*t^31 + 194813827997425/17592186044416*t^29 - 29846948742247/17592186044416*t^27 + 61989816618513/281474976710656*t^25 - 3376351667675/140737488355328*t^23 + 4881239839553/2251799813685248*t^21 - 360682746765/2251799813685248*t^19 + 1370594437707/144115188075855872*t^17 - 15991836267/36028797018963968*t^15 + 73006209045/4611686018427387904*t^13 - 1917334783/4611686018427387904*t^11 + 563921995/73786976294838206464*t^9 - 3372291/36893488147419103232*t^7 + 374699/590295810358705651712*t^5 - 1235/590295810358705651712*t^3 + 39/18889465931478580854784*t
-------------------------------------------------
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
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.99675730813420998559 + 1.1584073694544946707e-1869j)  +/-  (2.24e-483, 2.24e-483j)
| (-0.96051811163137229844 - 1.1030671756804850732e-1873j)  +/-  (3.88e-483, 3.88e-483j)
| (-0.94853644194714552616 + 2.7986750607575159483e-1882j)  +/-  (2.63e-483, 2.63e-483j)
| (-0.99675730813420998559 + 8.3846204663882056809e-1888j)  +/-  (2.28e-483, 2.28e-483j)
| (0.94853644194714552616 + 1.7173254171573411112e-1892j)  +/-  (2.76e-483, 2.76e-483j)
| (0.90345043461038227502 - 2.1401971079820090754e-1897j)  +/-  (3.92e-484, 3.92e-484j)
| (0.8854560256532098959 - 3.2169905075428745512e-1897j)  +/-  (1.7e-484, 1.7e-484j)
| (-0.90345043461038227502 + 1.8996865153398611581e-1896j)  +/-  (4.18e-484, 4.18e-484j)
| (0.72120244734381453129 + 4.5367431791407125202e-1902j)  +/-  (2.08e-488, 2.08e-488j)
| (-0.98705026263791286379 - 2.4426720507785635481e-1895j)  +/-  (4.99e-483, 4.99e-483j)
| (0.86602540378443864676 + 1.0737914193095835202e-1897j)  +/-  (6.59e-485, 6.59e-485j)
| (-0.9927088740980539928 - 5.4352582142983854513e-1897j)  +/-  (4.04e-483, 4.04e-483j)
| (-0.93501624268541482344 + 7.8775312614074209026e-1898j)  +/-  (1.61e-483, 1.61e-483j)
| (-0.8854560256532098959 + 1.3476822569468072493e-1898j)  +/-  (1.7e-484, 1.7e-484j)
| (0.9991889981715696377 - 5.3572857514297897367e-1895j)  +/-  (6.28e-484, 6.28e-484j)
| (0.84519008554379475254 - 1.9278084902629593227e-1903j)  +/-  (2.39e-485, 2.39e-485j)
| (0.82298386589365639458 + 3.5392721746454559991e-1903j)  +/-  (6.48e-486, 6.48e-486j)
| (-0.9991889981715696377 - 1.3389711021860217675e-1902j)  +/-  (6.26e-484, 6.26e-484j)
| (-0.77460496182765458307 - 6.8241955780890359886e-1906j)  +/-  (4.26e-487, 4.26e-487j)
| (-0.91997944365882420313 - 8.5230463455141170804e-1903j)  +/-  (8.42e-484, 8.42e-484j)
| (0.97094181742605202716 + 8.4802851565810219099e-1900j)  +/-  (5e-483, 5e-483j)
| (0.77460496182765458307 - 9.2776947347576464899e-1920j)  +/-  (4.62e-487, 4.62e-487j)
| (0.97979065204226770147 + 1.4224791731475829265e-1914j)  +/-  (5.53e-483, 5.53e-483j)
| (-0.82298386589365639458 - 1.95711094548295679e-1928j)  +/-  (6.37e-486, 6.37e-486j)
| (-0.79944276340350114978 - 1.7377754936310579704e-1929j)  +/-  (1.92e-486, 1.92e-486j)
| (0.79944276340350114978 - 4.0615468137153663973e-1929j)  +/-  (1.83e-486, 1.83e-486j)
| (0.74851074817110109863 - 1.3171568001820116729e-1930j)  +/-  (1.03e-487, 1.03e-487j)
| (0.93501624268541482344 - 8.3212460243905607205e-1925j)  +/-  (1.67e-483, 1.67e-483j)
| (-0.53446582612780109204 - 1.0950423831297554517e-1939j)  +/-  (1.55e-493, 1.55e-493j)
| (-0.63244537559537723782 + 1.9817544304931448334e-1936j)  +/-  (8.18e-491, 8.18e-491j)
| (-0.97094181742605202716 + 2.7969081452850985232e-1927j)  +/-  (4.96e-483, 4.96e-483j)
| (0.91997944365882420313 - 3.1595093355365025654e-1928j)  +/-  (8.84e-484, 8.84e-484j)
| (0.66312265824079520238 - 1.1032193486457439952e-1940j)  +/-  (5.12e-490, 5.12e-490j)
| (-0.97979065204226770147 + 2.9147324625762996987e-1933j)  +/-  (5.3e-483, 5.3e-483j)
| (-0.6927243535095993926 - 1.1137393029905488226e-1956j)  +/-  (2.86e-489, 2.86e-489j)
| (-0.74851074817110109863 - 1.6168184569168650634e-1955j)  +/-  (1.01e-487, 1.01e-487j)
| (0.46472317204376854566 - 5.1838721185650211857e-1963j)  +/-  (1.14e-495, 1.14e-495j)
| (0.63244537559537723782 + 9.0592383764271531861e-1958j)  +/-  (8.24e-491, 8.24e-491j)
| (0.96051811163137229844 - 2.7818992956811082674e-1948j)  +/-  (3.8e-483, 3.8e-483j)
| (-0.72120244734381453129 + 2.1836179573220681745e-1986j)  +/-  (2.35e-488, 2.35e-488j)
| (-0.56806474673115580251 + 1.5739455088275095333e-1992j)  +/-  (1.34e-492, 1.34e-492j)
| (-0.080466568716725880436 + 4.350813206434235249e-2008j)  +/-  (5.49e-508, 5.49e-508j)
| (0.6927243535095993926 - 3.5005574862299313993e-1981j)  +/-  (3.03e-489, 3.03e-489j)
| (0.60074226423797891692 + 1.2646593653852183784e-1988j)  +/-  (1.16e-491, 1.16e-491j)
| (0.98705026263791286379 + 6.9198162365178184011e-2015j)  +/-  (5.2e-483, 5.2e-483j)
| (-0.60074226423797891692 + 2.8580810868186863986e-2064j)  +/-  (1.19e-491, 1.19e-491j)
| (-0.66312265824079520238 + 7.5458410648600802891e-2062j)  +/-  (5.27e-490, 5.27e-490j)
| (0.9927088740980539928 + 1.1799509522790791978e-2079j)  +/-  (3.79e-483, 3.79e-483j)
| (0.5 + 2.0357598491792854419e-2116j)  +/-  (1.04e-494, 1.04e-494j)
| (0.39196660986007507588 + 2.0364427405951099788e-2119j)  +/-  (7.4e-498, 7.4e-498j)
| (1.3830246092256768834e-2146 + 6.0134288342646283311e-2146j)  +/-  (4.75e-2144, 4.75e-2144j)
| (-0.5 - 3.7370547232839423807e-2117j)  +/-  (1.04e-494, 1.04e-494j)
| (-0.84519008554379475254 + 6.5301288868256445337e-2107j)  +/-  (2.23e-485, 2.23e-485j)
| (0.56806474673115580251 - 1.1646139626611201375e-2117j)  +/-  (1.33e-492, 1.33e-492j)
| (0.53446582612780109204 + 4.83327411873525923e-2119j)  +/-  (1.6e-493, 1.6e-493j)
| (-0.12053668025532305335 - 2.7652895770099582846e-2131j)  +/-  (1.02e-506, 1.02e-506j)
| (-0.46472317204376854566 + 7.5832033647833694144e-2120j)  +/-  (1.1e-495, 1.1e-495j)
| (-0.31666799380147249909 - 9.2748057069383199981e-2125j)  +/-  (3.28e-500, 3.28e-500j)
| (0.20002569377604442753 - 3.3857340870552541405e-2129j)  +/-  (5.6e-504, 5.6e-504j)
| (0.42869256140305418307 - 1.1826929217275966334e-2123j)  +/-  (9.75e-497, 9.75e-497j)
| (-0.86602540378443864676 - 1.7075887111418782388e-2128j)  +/-  (6.79e-485, 6.79e-485j)
| (-0.27821746391645263455 + 1.2951824946816689942e-2145j)  +/-  (1.98e-501, 1.98e-501j)
| (-0.42869256140305418307 - 2.4310837008133776976e-2141j)  +/-  (1.02e-496, 1.02e-496j)
| (-0.040265940109415143362 + 2.7992740646665413875e-2153j)  +/-  (1.31e-509, 1.31e-509j)
| (0.35460488704253562597 - 6.4595193813224929435e-2143j)  +/-  (6.26e-499, 6.26e-499j)
| (0.12053668025532305335 + 5.3593964891252341474e-2151j)  +/-  (1.02e-506, 1.02e-506j)
| (-0.39196660986007507588 - 7.8793442018400760306e-2142j)  +/-  (7e-498, 7e-498j)
| (-0.35460488704253562597 - 1.3027926560516485509e-2143j)  +/-  (6.12e-499, 6.12e-499j)
| (-0.16041128085776024037 + 1.4074959651888297895e-2149j)  +/-  (2.32e-505, 2.32e-505j)
| (0.16041128085776024037 + 5.1348489270246449399e-2149j)  +/-  (2.05e-505, 2.05e-505j)
| (0.31666799380147249909 + 1.6273094604994608326e-2144j)  +/-  (3.08e-500, 3.08e-500j)
| (0.040265940109415143362 - 8.8254585441178710279e-2153j)  +/-  (1.31e-509, 1.31e-509j)
| (-0.20002569377604442753 - 1.3574319191018323705e-2149j)  +/-  (5.73e-504, 5.73e-504j)
| (-0.23931566428755776715 - 3.0958602493755768713e-2147j)  +/-  (9.67e-503, 9.67e-503j)
| (0.080466568716725880436 - 5.4657939009081301041e-2152j)  +/-  (5.49e-508, 5.49e-508j)
| (0.27821746391645263455 - 3.902089238585821939e-2145j)  +/-  (2.13e-501, 2.13e-501j)
| (0.23931566428755776715 + 2.3619492522455441662e-2146j)  +/-  (9.55e-503, 9.55e-503j)
-------------------------------------------------
The weights are:
| (8.3011136936456001342e-05 - 2.220482246210841295e-1871j)  +/-  (2.35e-142, 3.7e-377j)
| (0.00099237124651413620168 + 5.8529430491976921427e-1873j)  +/-  (1.14e-142, 1.8e-377j)
| (0.0012856233115160182706 - 7.537429097068340041e-1873j)  +/-  (1.03e-142, 1.62e-377j)
| (8.3011136936456001342e-05 - 4.8489446919315466429e-1874j)  +/-  (1.05e-143, 1.66e-378j)
| (0.0012856233115160182706 - 3.0884387903139073692e-1871j)  +/-  (3.31e-144, 5.21e-379j)
| (0.0023561193872091202704 + 2.9251146764123777778e-1871j)  +/-  (1.86e-144, 2.93e-379j)
| (0.0027688157260823345993 - 2.8817261178923235333e-1871j)  +/-  (1.43e-144, 2.25e-379j)
| (0.0023561193872091202704 + 1.4317867118899786108e-1872j)  +/-  (2.18e-145, 3.44e-380j)
| (0.0061521414095550311323 + 2.5862634874288459087e-1871j)  +/-  (4.56e-146, 7.19e-381j)
| (0.00032989460290291329381 - 1.9400731838070249597e-1873j)  +/-  (1.92e-145, 3.02e-380j)
| (0.0032051282051282051282 + 2.8400250472639561927e-1871j)  +/-  (3.14e-146, 4.94e-381j)
| (0.00018627040111505110797 + 1.0909803517166660457e-1873j)  +/-  (2.23e-145, 3.52e-380j)
| (0.0016121105886467878293 + 9.5974518841964874567e-1873j)  +/-  (6.84e-146, 1.08e-380j)
| (0.0027688157260823345993 - 1.6999975375956841019e-1872j)  +/-  (3.09e-147, 4.87e-382j)
| (2.0786486319166759069e-05 - 9.9022578586742778879e-1872j)  +/-  (3.98e-149, 6.26e-384j)
| (0.0036622271704932424162 - 2.7989673243284740658e-1871j)  +/-  (1.04e-147, 1.63e-382j)
| (0.0041371481599837459874 + 2.7578773780484908381e-1871j)  +/-  (2.58e-148, 4.06e-383j)
| (2.0786486319166759069e-05 + 1.2123353858220028302e-1874j)  +/-  (9.39e-147, 1.48e-381j)
| (0.005128040424512535721 + 3.3505118585088342082e-1872j)  +/-  (5.16e-151, 8.13e-386j)
| (0.0019697156826307731243 - 1.1850663017061475633e-1872j)  +/-  (7.47e-147, 1.18e-381j)
| (0.00073425624581275707756 - 3.2947921590653697972e-1871j)  +/-  (2.27e-150, 3.58e-385j)
| (0.005128040424512535721 + 2.6739701357165511787e-1871j)  +/-  (7.31e-151, 1.15e-385j)
| (0.00051295228423830639017 + 3.5022057867445544594e-1871j)  +/-  (1.58e-150, 2.49e-385j)
| (0.0041371481599837459874 + 2.6302997725237056694e-1872j)  +/-  (8.7e-152, 1.37e-386j)
| (0.00462681112874068824 - 2.9807597278017832903e-1872j)  +/-  (4.97e-152, 7.82e-387j)
| (0.00462681112874068824 - 2.716310091068268825e-1871j)  +/-  (2.9e-151, 4.56e-386j)
| (0.005637585382978698376 - 2.6306628882112491179e-1871j)  +/-  (2.21e-152, 3.47e-387j)
| (0.0016121105886467878293 + 3.0246886420678175907e-1871j)  +/-  (7.51e-152, 1.18e-386j)
| (0.0091582856500195780966 + 6.9260936827809619772e-1872j)  +/-  (1.26e-157, 1.98e-392j)
| (0.0076924723960002847919 - 5.4669704462373110836e-1872j)  +/-  (8.57e-157, 1.35e-391j)
| (0.00073425624581275707756 - 4.4003531035546106421e-1873j)  +/-  (1.49e-151, 2.35e-386j)
| (0.0019697156826307731243 - 2.971851727263241971e-1871j)  +/-  (2.41e-152, 3.8e-387j)
| (0.0071829274375341221369 + 2.4939235985284673213e-1871j)  +/-  (1.04e-156, 1.64e-391j)
| (0.00051295228423830639017 + 3.03564926426425879e-1873j)  +/-  (1.32e-151, 2.09e-386j)
| (0.0066683714109577893805 - 4.569478410535310508e-1872j)  +/-  (1.4e-157, 2.2e-392j)
| (0.005637585382978698376 - 3.7389678797919075266e-1872j)  +/-  (1.66e-156, 2.61e-391j)
| (0.010051697094430485914 + 2.188496057433555883e-1871j)  +/-  (8.84e-162, 1.39e-396j)
| (0.0076924723960002847919 - 2.4459321414471986068e-1871j)  +/-  (5.73e-159, 9.02e-394j)
| (0.00099237124651413620168 + 3.1721677386281304127e-1871j)  +/-  (1.46e-155, 2.3e-390j)
| (0.0061521414095550311323 + 4.1455070997793787024e-1872j)  +/-  (1.26e-157, 1.98e-392j)
| (0.0086833646605290745254 - 6.4256855477616812083e-1872j)  +/-  (1.26e-160, 1.99e-395j)
| (0.012737501683576364511 + 1.3695849406466690656e-1871j)  +/-  (9.95e-166, 1.57e-400j)
| (0.0066683714109577893805 - 2.5406967224629444605e-1871j)  +/-  (5.67e-158, 8.93e-393j)
| (0.0081937016917721322728 + 2.3967309611947437267e-1871j)  +/-  (2.03e-160, 3.2e-395j)
| (0.00032989460290291329381 - 3.936853473276087796e-1871j)  +/-  (1.7e-157, 2.68e-392j)
| (0.0081937016917721322728 + 5.9390508682765670985e-1872j)  +/-  (9.59e-162, 1.51e-396j)
| (0.0071829274375341221369 + 5.0102019247229850709e-1872j)  +/-  (1.08e-160, 1.7e-395j)
| (0.00018627040111505110797 + 5.3298870834634026253e-1871j)  +/-  (9.83e-158, 1.55e-392j)
| (0.0096153846153846153846 - 2.2421756995918683295e-1871j)  +/-  (1.4e-164, 2.21e-399j)
| (0.010850797137882047388 + 2.0782575161798107339e-1871j)  +/-  (6.46e-167, 1.02e-401j)
| (0.012820512820512820513 + 1.4898219321743450099e-1871j)  +/-  (9.27e-170, 1.46e-404j)
| (0.0096153846153846153846 - 7.4394727080991701623e-1872j)  +/-  (6.18e-166, 9.73e-401j)
| (0.0036622271704932424162 - 2.2996851202442987392e-1872j)  +/-  (9.26e-162, 1.46e-396j)
| (0.0086833646605290745254 - 2.3463446522527335899e-1871j)  +/-  (5.55e-164, 8.75e-399j)
| (0.0091582856500195780966 + 2.2948104416000282137e-1871j)  +/-  (1.39e-164, 2.19e-399j)
| (0.012634242419397769405 - 1.3097489056279518494e-1871j)  +/-  (8.87e-171, 1.4e-405j)
| (0.010051697094430485914 + 7.964999717443178944e-1872j)  +/-  (2.52e-168, 3.97e-403j)
| (0.011534889508996802242 + 1.0171499973334888027e-1871j)  +/-  (3.42e-171, 5.39e-406j)
| (0.012307560536274514123 - 1.7893399169779774301e-1871j)  +/-  (2.23e-172, 3.52e-407j)
| (0.010464393433303700242 - 2.1338339574292696023e-1871j)  +/-  (9.45e-169, 1.49e-403j)
| (0.0032051282051282051282 + 1.9894292846332246141e-1872j)  +/-  (3.6e-165, 5.68e-400j)
| (0.011828141573998684311 - 1.0744815197265277462e-1871j)  +/-  (1.03e-171, 1.62e-406j)
| (0.010464393433303700242 - 8.5018329177531995853e-1872j)  +/-  (4.48e-170, 7.05e-405j)
| (0.012799726334193653754 - 1.4296406841363902308e-1871j)  +/-  (1.65e-172, 2.59e-407j)
| (0.011208402231866032684 - 2.0218396168856684916e-1871j)  +/-  (6.64e-172, 1.05e-406j)
| (0.012634242419397769405 - 1.6701809430902770322e-1871j)  +/-  (6.63e-174, 1.04e-408j)
| (0.010850797137882047388 + 9.0491131186195012794e-1872j)  +/-  (1.77e-171, 2.79e-406j)
| (0.011208402231866032684 - 9.6059652590642901065e-1872j)  +/-  (6.03e-172, 9.5e-407j)
| (0.012490618217609907219 + 1.2502267745378600328e-1871j)  +/-  (6.09e-174, 9.59e-409j)
| (0.012490618217609907219 + 1.7299294453755359309e-1871j)  +/-  (3.93e-175, 6.19e-410j)
| (0.011534889508996802242 + 1.9646571712864439849e-1871j)  +/-  (6.08e-175, 9.58e-410j)
| (0.012799726334193653754 - 1.5500346788289732686e-1871j)  +/-  (3.18e-175, 5.02e-410j)
| (0.012307560536274514123 - 1.1911125361863433763e-1871j)  +/-  (5.63e-175, 8.87e-410j)
| (0.012086256574700063435 + 1.1324997816944733978e-1871j)  +/-  (6.55e-175, 1.03e-409j)
| (0.012737501683576364511 + 1.6101853323624922707e-1871j)  +/-  (4.79e-176, 7.55e-411j)
| (0.011828141573998684311 - 1.9067905085292620454e-1871j)  +/-  (4.57e-177, 7.22e-412j)
| (0.012086256574700063435 + 1.8483228599464412867e-1871j)  +/-  (4.69e-177, 7.36e-412j)
