Starting with polynomial:
P : 2*t
Extension levels are: 1 2 64
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 64 Kronrod extension for:
P2 : 2*t^3 - 1*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^67 - 33*t^65 + 260*t^63 - 1302*t^61 + 595665/128*t^59 - 3235501/256*t^57 + 13881343/512*t^55 - 48275865/1024*t^53 + 2217471399/32768*t^51 - 5324436975/65536*t^49 + 5397877485/65536*t^47 - 9306388455/131072*t^45 + 219364870725/4194304*t^43 - 277044025545/8388608*t^41 + 300497488025/16777216*t^39 - 280086337895/33554432*t^37 + 7174519270695/2147483648*t^35 - 4923689695575/4294967296*t^33 + 722141155351/2147483648*t^31 - 360682746765/4294967296*t^29 + 4881239839553/274877906944*t^27 - 1735881645069/549755813888*t^25 + 514589420475/1099511627776*t^23 - 125788525005/2199023255552*t^21 + 400236215925/70368744177664*t^19 - 63665481789/140737488355328*t^17 + 3964517181/140737488355328*t^15 - 376038215/281474976710656*t^13 + 419014011/9007199254740992*t^11 - 20376455/18014398509481984*t^9 + 643467/36028797018963968*t^7 - 11781/72057594037927936*t^5 + 6545/9223372036854775808*t^3 - 17/18446744073709551616*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
Sufficient bits for target precision reached
Positive weights:   67 out of 67
Indefinite weights: 0 out of 67
Negative weights:   0 out of 67
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99893297480237244441 - 5.4529397570530270165e-861j)  +/-  (6.68e-233, 6.68e-233j)
| (-0.99573417629503452187 + 2.0596679418074119733e-859j)  +/-  (2.41e-232, 2.41e-232j)
| (-0.93247222940435580457 - 2.3672465361822196396e-875j)  +/-  (1.95e-232, 1.95e-232j)
| (-0.99041043087520515835 + 1.7245950698363094332e-888j)  +/-  (4.25e-232, 4.25e-232j)
| (0.91479386848802097 - 3.4504191009561970893e-906j)  +/-  (8.84e-233, 8.84e-233j)
| (0.93247222940435580457 - 2.1194331079494247035e-905j)  +/-  (1.79e-232, 1.79e-232j)
| (0.97343805436069282581 + 1.1243371187783397042e-904j)  +/-  (4.96e-232, 4.96e-232j)
| (-0.89516329135506232207 - 8.5855306760368381112e-907j)  +/-  (3.71e-233, 3.71e-233j)
| (-0.98297309968390177828 - 6.0279401621165845584e-916j)  +/-  (5.13e-232, 5.13e-232j)
| (-0.97343805436069282581 - 4.4140620371681379005e-928j)  +/-  (4.7e-232, 4.7e-232j)
| (0.89516329135506232207 + 2.7122726799130715384e-933j)  +/-  (4.53e-233, 4.53e-233j)
| (0.09226835946330199524 + 5.9775203115415567288e-954j)  +/-  (2.51e-253, 2.51e-253j)
| (-0.91479386848802097 - 5.5250604721319259379e-932j)  +/-  (8.87e-233, 8.87e-233j)
| (-0.82499747459830231554 + 6.8633948411465661016e-935j)  +/-  (1.83e-234, 1.83e-234j)
| (0.7071067811865475244 + 4.5241555181960015478e-938j)  +/-  (4.38e-237, 4.38e-237j)
| (0.82499747459830231554 + 1.471534299766316046e-934j)  +/-  (1.77e-234, 1.77e-234j)
| (0.85021713572961415213 + 4.7221468690050438246e-934j)  +/-  (6.24e-234, 6.24e-234j)
| (-0.94816064759096585893 + 2.9109751863088379581e-932j)  +/-  (2.5e-232, 2.5e-232j)
| (-0.79801722728023950333 - 7.0017249877303332807e-938j)  +/-  (5.53e-235, 5.53e-235j)
| (-0.96182564317281907041 + 6.6976008970692078493e-935j)  +/-  (4.52e-232, 4.52e-232j)
| (0.98297309968390177828 - 1.8073590833866352628e-940j)  +/-  (5e-232, 5e-232j)
| (0.79801722728023950333 + 1.2428529454626445566e-945j)  +/-  (5.32e-235, 5.32e-235j)
| (-0.31779141958190162617 + 1.1550421058977887884e-958j)  +/-  (6.67e-247, 6.67e-247j)
| (-0.85021713572961415213 - 5.391560617945971703e-946j)  +/-  (5.36e-234, 5.36e-234j)
| (-0.76933397098287890812 + 1.7400396410471451881e-947j)  +/-  (1.26e-235, 1.26e-235j)
| (0.96182564317281907041 + 4.5722913144351778457e-942j)  +/-  (3.98e-232, 3.98e-232j)
| (0.76933397098287890812 - 3.6351059426792849382e-946j)  +/-  (1.22e-235, 1.22e-235j)
| (0.73900891722065911592 + 3.8922293167880069873e-947j)  +/-  (2.35e-236, 2.35e-236j)
| (0.99041043087520515835 + 4.6626778737319344019e-941j)  +/-  (4.09e-232, 4.09e-232j)
| (-0.63884680565196131707 - 6.0242279695255581487e-953j)  +/-  (1.3e-238, 1.3e-238j)
| (-0.046183458645739591949 + 4.5570967183120427712e-969j)  +/-  (1.29e-254, 1.29e-254j)
| (0.4457383557765382674 + 9.4336107416334091086e-957j)  +/-  (1.88e-243, 1.88e-243j)
| (0.67369564364655721171 + 1.2224166802118836808e-950j)  +/-  (8.61e-238, 8.61e-238j)
| (0.94816064759096585893 + 2.6179573369271916753e-943j)  +/-  (2.8e-232, 2.8e-232j)
| (-0.67369564364655721171 - 2.7887978528048828487e-953j)  +/-  (8.04e-238, 8.04e-238j)
| (-0.7071067811865475244 + 1.7875756064788850007e-952j)  +/-  (5.67e-237, 5.67e-237j)
| (0.52643216287735580024 - 6.097996794128889024e-957j)  +/-  (2.13e-241, 2.13e-241j)
| (0.63884680565196131707 - 3.5357843412338042818e-956j)  +/-  (1.49e-238, 1.49e-238j)
| (0.99573417629503452187 - 1.3270654561399883963e-948j)  +/-  (2.3e-232, 2.3e-232j)
| (-0.73900891722065911592 + 6.7355987523012249271e-952j)  +/-  (2.43e-236, 2.43e-236j)
| (-0.60263463637925638918 + 6.5808449752759837698e-956j)  +/-  (1.95e-239, 1.95e-239j)
| (-0.87362239064636953713 - 2.9277375030483563849e-951j)  +/-  (1.62e-233, 1.62e-233j)
| (0.87362239064636953713 - 1.9806215784173542979e-965j)  +/-  (1.54e-233, 1.54e-233j)
| (0.60263463637925638918 + 3.6492064199259879599e-971j)  +/-  (1.85e-239, 1.85e-239j)
| (-0.36124166618715294874 + 1.6284218429134438075e-977j)  +/-  (9.16e-246, 9.16e-246j)
| (-0.56513641442259188898 + 1.5778653701975690131e-971j)  +/-  (2.19e-240, 2.19e-240j)
| (-0.52643216287735580024 + 1.0815150011889818965e-973j)  +/-  (2.32e-241, 2.32e-241j)
| (0.56513641442259188898 + 1.8408895341212219467e-973j)  +/-  (2.28e-240, 2.28e-240j)
| (0.48660447856685628729 + 2.3182179436690416306e-976j)  +/-  (2.1e-242, 2.1e-242j)
| (0.13815635495188219823 - 1.101332948410197247e-985j)  +/-  (5.35e-252, 5.35e-252j)
| (-0.99893297480237244441 + 3.6301163892496947651e-981j)  +/-  (8.26e-233, 8.26e-233j)
| (-0.48660447856685628729 - 2.4865414977152794833e-1002j)  +/-  (2.13e-242, 2.13e-242j)
| (-0.13815635495188219823 - 1.9774500958929462685e-1014j)  +/-  (5.86e-252, 5.86e-252j)
| (0.27366299007208286354 - 3.885522802688335102e-1009j)  +/-  (3.72e-248, 3.72e-248j)
| (0.31779141958190162617 + 1.1972996897102317984e-1009j)  +/-  (6.81e-247, 6.81e-247j)
| (-0.09226835946330199524 + 2.5594835311042361314e-1017j)  +/-  (2.22e-253, 2.22e-253j)
| (-0.4457383557765382674 - 6.7087201564961463861e-1005j)  +/-  (2.04e-243, 2.04e-243j)
| (-0.22895054995013407691 - 1.8519021841601838779e-1011j)  +/-  (1.79e-249, 1.79e-249j)
| (0.18374951781657033157 + 1.0753489475443443467e-1012j)  +/-  (1.15e-250, 1.15e-250j)
| (0.40392100487189496264 + 2.6923728641640628958e-1005j)  +/-  (1.38e-244, 1.38e-244j)
| (6.4378725711329124786e-1046 - 2.0181912357720540336e-1047j)  +/-  (4.32e-1044, 4.32e-1044j)
| (-0.27366299007208286354 + 9.7590222033366928024e-1010j)  +/-  (3.99e-248, 3.99e-248j)
| (-0.40392100487189496264 - 4.003620284569984137e-1006j)  +/-  (1.52e-244, 1.52e-244j)
| (0.046183458645739591949 + 1.3497936689429232153e-1016j)  +/-  (1.17e-254, 1.17e-254j)
| (0.36124166618715294874 + 3.5257560340151020269e-1007j)  +/-  (1.02e-245, 1.02e-245j)
| (0.22895054995013407691 + 1.20229329559075193e-1010j)  +/-  (2.07e-249, 2.07e-249j)
| (-0.18374951781657033157 + 1.163550663749237457e-1012j)  +/-  (1.19e-250, 1.19e-250j)
-------------------------------------------------
The weights are:
| (3.1366350771804986241e-05 + 1.1691823872210042769e-862j)  +/-  (4.56e-39, 1.19e-148j)
| (0.0001251977964418986891 + 4.523661624977815017e-861j)  +/-  (2.24e-39, 5.83e-149j)
| (0.0019190520792598594417 + 6.2425876347083521977e-861j)  +/-  (4.75e-40, 1.24e-149j)
| (0.00028069380019985977641 - 1.0858803626039136027e-860j)  +/-  (1.75e-39, 4.56e-149j)
| (0.0023992967378929616786 - 1.0316397459346701215e-862j)  +/-  (3.48e-41, 9.06e-151j)
| (0.0019190520792598594417 + 4.7535473061496116981e-863j)  +/-  (3.03e-41, 7.89e-151j)
| (0.00077085815180101233774 + 8.4245359194049171288e-863j)  +/-  (8.04e-42, 2.09e-151j)
| (0.002921804144270173609 + 5.9753741741589077633e-861j)  +/-  (3.88e-42, 1.01e-151j)
| (0.0004965277249679720252 + 8.0127087702461473062e-861j)  +/-  (1.58e-41, 4.11e-151j)
| (0.00077085815180101233774 - 7.1188911732832495878e-861j)  +/-  (6.27e-42, 1.63e-151j)
| (0.002921804144270173609 + 1.647223491340715565e-862j)  +/-  (9.82e-44, 2.56e-153j)
| (0.014580684556499277781 + 2.6725372486402903053e-861j)  +/-  (3.09e-46, 8.06e-156j)
| (0.0023992967378929616786 - 6.0985943988809861265e-861j)  +/-  (1.54e-42, 4.01e-152j)
| (0.0046967524545062283181 - 5.6518463853111998934e-861j)  +/-  (1.88e-44, 4.89e-154j)
| (0.0073529411764705882353 - 7.5197963653820871001e-862j)  +/-  (2.45e-46, 6.38e-156j)
| (0.0046967524545062283181 - 3.8406630142914947915e-862j)  +/-  (7.63e-46, 1.99e-155j)
| (0.004075453266348983328 + 3.0529525417840232656e-862j)  +/-  (1.45e-45, 3.78e-155j)
| (0.0014851674464688271814 - 6.4257858089845626261e-861j)  +/-  (6.61e-44, 1.72e-153j)
| (0.0053407133082935083563 + 5.547350744975352131e-861j)  +/-  (4.96e-47, 1.29e-156j)
| (0.001101344590223425352 + 6.6867108641167742796e-861j)  +/-  (7.07e-44, 1.84e-153j)
| (0.0004965277249679720252 - 1.1796206362061181356e-862j)  +/-  (1.23e-48, 3.19e-158j)
| (0.0053407133082935083563 + 4.6829603444050519868e-862j)  +/-  (1.86e-48, 4.85e-158j)
| (0.013220714906472349289 - 3.9618541631881444437e-861j)  +/-  (9.84e-52, 2.56e-161j)
| (0.004075453266348983328 + 5.7564338031895984256e-861j)  +/-  (7.47e-47, 1.95e-156j)
| (0.0060018417807605122678 - 5.4416462106296462557e-861j)  +/-  (1.88e-48, 4.91e-158j)
| (0.001101344590223425352 - 4.5963929399629828261e-863j)  +/-  (1.35e-48, 3.51e-158j)
| (0.0060018417807605122678 - 5.578155048179809897e-862j)  +/-  (2.31e-49, 6.01e-159j)
| (0.0066744973568874853291 + 6.5244184500150685039e-862j)  +/-  (5.8e-50, 1.51e-159j)
| (0.00028069380019985977641 + 1.5048655681513762866e-862j)  +/-  (9.68e-50, 2.52e-159j)
| (0.0087040405721806642028 - 4.9942949456331212044e-861j)  +/-  (3.32e-53, 8.65e-163j)
| (0.014674516002169371484 - 3.1064804560230239157e-861j)  +/-  (4.29e-55, 1.12e-164j)
| (0.011784078208671002862 + 1.5676264973352465894e-861j)  +/-  (7.76e-55, 2.02e-164j)
| (0.0080313849960536911415 + 8.5622194209639152353e-862j)  +/-  (4.4e-52, 1.15e-161j)
| (0.0014851674464688271814 + 2.1447440595343224905e-864j)  +/-  (3.75e-50, 9.77e-160j)
| (0.0080313849960536911415 + 5.1104649776372712186e-861j)  +/-  (1.79e-53, 4.65e-163j)
| (0.0073529411764705882353 - 5.2236151538149344747e-861j)  +/-  (2.65e-53, 6.91e-163j)
| (0.010630429086592193143 + 1.3157391275333274604e-861j)  +/-  (2.28e-55, 5.94e-165j)
| (0.0087040405721806642028 - 9.6495115007889547875e-862j)  +/-  (8.8e-54, 2.29e-163j)
| (0.0001251977964418986891 - 2.0047411554588928385e-862j)  +/-  (1.12e-51, 2.92e-161j)
| (0.0066744973568874853291 + 5.3339065240465740834e-861j)  +/-  (5.42e-53, 1.41e-162j)
| (0.0093651690446476681143 + 4.875048809934005304e-861j)  +/-  (1.3e-55, 3.38e-165j)
| (0.0034821164494312073511 - 5.8631698884977437197e-861j)  +/-  (1.77e-52, 4.62e-162j)
| (0.0034821164494312073511 - 2.3213593836688529078e-862j)  +/-  (1.31e-51, 3.4e-161j)
| (0.0093651690446476681143 + 1.0779397145952102558e-861j)  +/-  (5.58e-55, 1.45e-164j)
| (0.012786830273681317029 + 4.0995548245964576426e-861j)  +/-  (6.85e-59, 1.79e-168j)
| (0.010009129898434948153 - 4.7527474593430708105e-861j)  +/-  (6.17e-57, 1.61e-166j)
| (0.010630429086592193143 + 4.6274698855808570703e-861j)  +/-  (6.9e-58, 1.8e-167j)
| (0.010009129898434948153 - 1.1949508384599990791e-861j)  +/-  (1.44e-56, 3.74e-166j)
| (0.011223765903509969119 - 1.4400512336982655744e-861j)  +/-  (5.02e-58, 1.31e-167j)
| (0.014425188552741316694 - 2.5288970329396200915e-861j)  +/-  (7.75e-62, 2.02e-171j)
| (3.1366350771804986241e-05 + 2.0197272664614918565e-861j)  +/-  (3.02e-57, 7.86e-167j)
| (0.011223765903509969119 - 4.4993397654039236187e-861j)  +/-  (2.46e-59, 6.42e-169j)
| (0.014425188552741316694 - 3.3953603622486992836e-861j)  +/-  (1.49e-62, 3.88e-172j)
| (0.013604537762717751119 + 2.1051267192217982768e-861j)  +/-  (1.57e-62, 4.08e-172j)
| (0.013220714906472349289 - 1.9672286760340282664e-861j)  +/-  (2.62e-62, 6.83e-172j)
| (0.014580684556499277781 + 3.2511557982452832196e-861j)  +/-  (4.87e-63, 1.27e-172j)
| (0.011784078208671002862 + 4.3685157790521936623e-861j)  +/-  (7.22e-62, 1.88e-171j)
| (0.013935024201140164133 - 3.6812214192401140644e-861j)  +/-  (1.33e-63, 3.45e-173j)
| (0.014209354627973204445 + 2.3862525062974259769e-861j)  +/-  (6.61e-64, 1.72e-173j)
| (0.012306585615048214792 - 1.6981975963303934186e-861j)  +/-  (3.09e-63, 8.05e-173j)
| (0.014705882352941176471 + 2.961623704472707591e-861j)  +/-  (2.88e-64, 7.51e-174j)
| (0.013604537762717751119 + 3.822324800295928187e-861j)  +/-  (3.56e-64, 9.27e-174j)
| (0.012306585615048214792 - 4.2351844646038685156e-861j)  +/-  (1.02e-63, 2.66e-173j)
| (0.014674516002169371484 - 2.8168778804737574761e-861j)  +/-  (1.07e-64, 2.8e-174j)
| (0.012786830273681317029 + 1.83149120638006795e-861j)  +/-  (5.05e-65, 1.32e-174j)
| (0.013935024201140164133 - 2.2448981277452966746e-861j)  +/-  (3.71e-65, 9.77e-175j)
| (0.014209354627973204445 + 3.5388088777952241411e-861j)  +/-  (3.49e-65, 8.81e-175j)
