Starting with polynomial:
P : 2*t
Extension levels are: 1 16 18 36
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : 2*t^17 - 8*t^15 + 105/8*t^13 - 91/8*t^11 + 715/128*t^9 - 99/64*t^7 + 231/1024*t^5 - 15/1024*t^3 + 9/32768*t
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P3 : 2*t^35 - 17*t^33 + 66*t^31 - 155*t^29 + 31465/128*t^27 - 71253/256*t^25 + 118755/512*t^23 - 148005/1024*t^21 + 2220075/32768*t^19 - 1562275/65536*t^17 + 408595/65536*t^15 - 156009/131072*t^13 + 676039/4194304*t^11 - 124355/8388608*t^9 + 14535/16777216*t^7 - 969/33554432*t^5 + 969/2147483648*t^3 - 9/4294967296*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^71 - 35*t^69 + 1173/4*t^67 - 12529/8*t^65 + 47905/8*t^63 - 279279/16*t^61 + 2581215/64*t^59 - 9706503/128*t^57 + 3872894697/32768*t^55 - 10143295635/65536*t^53 + 45088585113/262144*t^51 - 85675031325/524288*t^49 + 279871768995/2097152*t^47 - 394447695285/4194304*t^45 + 961830587025/16777216*t^43 - 1015828093665/33554432*t^41 + 29749251314475/2147483648*t^39 - 23576679383985/4294967296*t^37 + 32308782859535/17179869184*t^35 - 19090095135475/34359738368*t^33 + 9691894453395/68719476736*t^31 - 4207965378925/137438953472*t^29 + 3106243534261/549755813888*t^27 - 967428110493/1099511627776*t^25 + 8061900920775/70368744177664*t^23 - 1735881645069/140737488355328*t^21 + 609590544255/562949953421312*t^19 - 85794224747/1125899906842624*t^17 + 18941582087/4503599627370496*t^15 - 1594920705/9007199254740992*t^13 + 197466373/36028797018963968*t^11 - 8544965/72057594037927936*t^9 + 15380937/9223372036854775808*t^7 - 250971/18446744073709551616*t^5 + 3885/73786976294838206464*t^3 - 9/147573952589676412928*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:   71 out of 71
Indefinite weights: 0 out of 71
Negative weights:   0 out of 71
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.97629600711993336597 + 1.320207470768757903e-801j)  +/-  (1.66e-230, 1.66e-230j)
| (-0.84339144581288570127 - 1.3585515678275196969e-816j)  +/-  (9.98e-233, 9.98e-233j)
| (-0.90630778703664996324 - 1.0469941700245706582e-814j)  +/-  (1.76e-231, 1.76e-231j)
| (-0.99144486137381041114 + 2.7822125156177536864e-822j)  +/-  (1.32e-230, 1.32e-230j)
| (0.92387953251128675613 - 4.468207547194616781e-838j)  +/-  (3.73e-231, 3.73e-231j)
| (0.93969262078590838405 + 1.2326499369457734796e-838j)  +/-  (7.27e-231, 7.27e-231j)
| (-0.9961946980917455323 + 8.5524422006781727508e-837j)  +/-  (7.25e-231, 7.25e-231j)
| (-0.92387953251128675613 - 3.3961757352945088491e-845j)  +/-  (3.58e-231, 3.58e-231j)
| (0.9990482215818577624 + 1.9761766187918484716e-850j)  +/-  (2.06e-231, 2.06e-231j)
| (0.9961946980917455323 + 7.3834486210380395424e-852j)  +/-  (7.31e-231, 7.31e-231j)
| (0.86602540378443864676 - 3.3308130526527017253e-855j)  +/-  (2.74e-232, 2.74e-232j)
| (0.98480775301220805937 - 2.8520854577191885882e-852j)  +/-  (1.74e-230, 1.74e-230j)
| (-0.95371695074822692114 + 4.5454365100668920745e-852j)  +/-  (1.02e-230, 1.02e-230j)
| (-0.86602540378443864676 + 8.2949036041019732165e-861j)  +/-  (2.93e-232, 2.93e-232j)
| (0.97629600711993336597 + 2.6787322970523389391e-858j)  +/-  (1.98e-230, 1.98e-230j)
| (0.84339144581288570127 + 1.0569432661453748204e-861j)  +/-  (8.2e-233, 8.2e-233j)
| (0.96592582628906828675 + 2.5059206557143953638e-859j)  +/-  (1.51e-230, 1.51e-230j)
| (-0.9990482215818577624 - 1.4401825144024868657e-857j)  +/-  (2.18e-231, 2.18e-231j)
| (-0.79335334029123516458 - 1.9097055444135949533e-871j)  +/-  (7.74e-234, 7.74e-234j)
| (-0.93969262078590838405 + 1.477714932068194676e-867j)  +/-  (5.82e-231, 5.82e-231j)
| (0.88701083317822170105 + 1.8966637793352715589e-876j)  +/-  (7.37e-232, 7.37e-232j)
| (0.7660444431189780352 - 1.3681948900563287697e-881j)  +/-  (1.7e-234, 1.7e-234j)
| (-0.88701083317822170105 + 2.1017546009563510373e-875j)  +/-  (7.25e-232, 7.25e-232j)
| (-0.73727733681012404138 - 6.9991359008348789931e-883j)  +/-  (3.32e-235, 3.32e-235j)
| (-0.7660444431189780352 + 1.1473897387943392511e-881j)  +/-  (1.76e-234, 1.76e-234j)
| (0.99144486137381041114 + 5.4340274200991847627e-876j)  +/-  (1.21e-230, 1.21e-230j)
| (0.73727733681012404138 + 3.7146025524472768655e-885j)  +/-  (3.55e-235, 3.55e-235j)
| (0.90630778703664996324 + 8.9897998121030965003e-880j)  +/-  (1.79e-231, 1.79e-231j)
| (0.21643961393810287976 + 5.2062454782137127215e-900j)  +/-  (2.09e-249, 2.09e-249j)
| (-0.64278760968653932632 - 1.0873615673932163699e-886j)  +/-  (2.23e-237, 2.23e-237j)
| (0.25881904510252076235 - 6.3165818410922096363e-899j)  +/-  (3.71e-248, 3.71e-248j)
| (0.95371695074822692114 + 2.409642371733109286e-880j)  +/-  (1.08e-230, 1.08e-230j)
| (0.7071067811865475244 - 4.8624573553127417308e-887j)  +/-  (6.29e-236, 6.29e-236j)
| (-0.17364817766693034885 - 1.5357970565927147998e-901j)  +/-  (1.09e-250, 1.09e-250j)
| (-0.7071067811865475244 - 2.8721749584973719828e-885j)  +/-  (6.81e-236, 6.81e-236j)
| (-0.81915204428899178968 + 6.163063471050117463e-882j)  +/-  (2.82e-233, 2.82e-233j)
| (0.79335334029123516458 - 4.999781368482551652e-885j)  +/-  (8.67e-234, 8.67e-234j)
| (0.60876142900872063942 - 2.1033214076137473933e-889j)  +/-  (2.81e-238, 2.81e-238j)
| (0.81915204428899178968 + 3.379461425130196508e-884j)  +/-  (2.99e-233, 2.99e-233j)
| (-0.98480775301220805937 + 1.1675027871924369625e-886j)  +/-  (1.7e-230, 1.7e-230j)
| (-0.57357643635104609611 - 2.3096293889245387268e-913j)  +/-  (3.21e-239, 3.21e-239j)
| (-0.96592582628906828675 - 3.7904994091648981822e-915j)  +/-  (1.44e-230, 1.44e-230j)
| (0.67559020761566024435 - 4.6289716660180110196e-931j)  +/-  (1.07e-236, 1.07e-236j)
| (0.57357643635104609611 + 9.5639299634235125067e-934j)  +/-  (3.03e-239, 3.03e-239j)
| (1.4722442522361976649e-968 + 7.6443178943199508342e-968j)  +/-  (5.53e-966, 5.53e-966j)
| (-0.60876142900872063942 - 2.1330338149109531872e-931j)  +/-  (2.76e-238, 2.76e-238j)
| (-0.53729960834682383184 + 1.4315128476165683734e-934j)  +/-  (3.88e-240, 3.88e-240j)
| (-0.13052619222005159155 + 3.9889687315951182675e-948j)  +/-  (6.04e-252, 6.04e-252j)
| (0.5 - 1.6068172303421868432e-937j)  +/-  (4.27e-241, 4.27e-241j)
| (0.13052619222005159155 + 3.8096441833671737665e-948j)  +/-  (5.06e-252, 5.06e-252j)
| (-0.5 + 2.4706374950115728465e-935j)  +/-  (4.12e-241, 4.12e-241j)
| (-0.46174861323503393056 - 1.186835248916490354e-936j)  +/-  (3.09e-242, 3.09e-242j)
| (-0.30070579950427312162 - 3.6161380068350853715e-942j)  +/-  (8.17e-247, 8.17e-247j)
| (0.53729960834682383184 - 1.1416265125497768431e-935j)  +/-  (3.33e-240, 3.33e-240j)
| (0.46174861323503393056 - 2.6573769095605418314e-939j)  +/-  (3.06e-242, 3.06e-242j)
| (0.087155742747658173558 + 6.55620068847118636e-950j)  +/-  (2.46e-253, 2.46e-253j)
| (-0.42261826174069943619 + 8.7479011223956529345e-939j)  +/-  (3.03e-243, 3.03e-243j)
| (-0.67559020761566024435 + 9.7672307243097253582e-935j)  +/-  (1.35e-236, 1.35e-236j)
| (0.043619387365335999782 - 1.832697049124486035e-950j)  +/-  (1.11e-254, 1.11e-254j)
| (0.42261826174069943619 - 1.1414407509151248201e-938j)  +/-  (2.74e-243, 2.74e-243j)
| (0.64278760968653932632 - 1.5637637806167667382e-942j)  +/-  (2.13e-237, 2.13e-237j)
| (-0.25881904510252076235 + 4.9295088630951387751e-952j)  +/-  (4.38e-248, 4.38e-248j)
| (-0.38268343236508977173 + 1.1681600844771819259e-947j)  +/-  (1.92e-244, 1.92e-244j)
| (-0.043619387365335999782 + 4.3227254553885714226e-958j)  +/-  (1.69e-254, 1.69e-254j)
| (0.38268343236508977173 - 8.0983802960689709711e-949j)  +/-  (1.97e-244, 1.97e-244j)
| (0.30070579950427312162 + 1.0162073966280192817e-950j)  +/-  (8.5e-247, 8.5e-247j)
| (-0.087155742747658173558 + 3.9110517928246524828e-956j)  +/-  (2.77e-253, 2.77e-253j)
| (-0.34202014332566873304 - 2.2805226564159658178e-949j)  +/-  (1.11e-245, 1.11e-245j)
| (-0.21643961393810287976 - 5.8721244908365663991e-953j)  +/-  (2.09e-249, 2.09e-249j)
| (0.17364817766693034885 - 1.2906313797793800452e-954j)  +/-  (1.17e-250, 1.17e-250j)
| (0.34202014332566873304 + 1.5060297981146241929e-951j)  +/-  (1.18e-245, 1.18e-245j)
-------------------------------------------------
The weights are:
| (0.00065064036780104192193 + 2.6852360047529126796e-803j)  +/-  (1.1e-28, 3.21e-137j)
| (0.0040095954045784761376 + 3.9829316284006006537e-803j)  +/-  (4.29e-29, 1.25e-137j)
| (0.0024806415993990324561 - 4.679303985627040546e-803j)  +/-  (4.66e-29, 1.35e-137j)
| (0.00023662620632591467535 - 2.0621736808326282852e-803j)  +/-  (8.98e-30, 2.61e-138j)
| (0.0020339806862045310805 + 1.4131728576234353856e-804j)  +/-  (3.16e-31, 9.17e-140j)
| (0.0016246913672293192 - 1.1194897764368349473e-804j)  +/-  (2.42e-31, 7.03e-140j)
| (0.00010550171519299958773 + 6.9996640871514421967e-804j)  +/-  (4.97e-30, 1.44e-138j)
| (0.0020339806862045310805 + 5.1229628039177410683e-803j)  +/-  (6.28e-30, 1.83e-138j)
| (2.6425707696211581285e-05 + 1.7661436530391999288e-806j)  +/-  (9.43e-33, 2.74e-141j)
| (0.00010550171519299958773 - 7.0613337851840356248e-806j)  +/-  (9.92e-33, 2.88e-141j)
| (0.0034722222222222222222 - 2.4881943459025401735e-804j)  +/-  (3.59e-34, 1.04e-142j)
| (0.00041880124454230288851 - 2.819353789698466994e-805j)  +/-  (2.54e-33, 7.38e-142j)
| (0.001255888581326445905 + 7.3432364055654293589e-803j)  +/-  (1.83e-33, 5.31e-142j)
| (0.0034722222222222222222 - 4.1570949820608671783e-803j)  +/-  (5.61e-34, 1.63e-142j)
| (0.00065064036780104192193 + 4.3991794911090728695e-805j)  +/-  (1.23e-33, 3.58e-142j)
| (0.0040095954045784761376 + 2.9090148417264740033e-804j)  +/-  (5.47e-36, 1.59e-144j)
| (0.00093037914038584273081 - 6.3241668415857252808e-805j)  +/-  (5.94e-34, 1.73e-142j)
| (2.6425707696211581285e-05 - 1.5333635668420060284e-804j)  +/-  (8.54e-35, 2.48e-143j)
| (0.0051470899645658280392 + 3.7144022997666218344e-803j)  +/-  (3.41e-37, 9.9e-146j)
| (0.0016246913672293192 - 5.8599214322299788614e-803j)  +/-  (1.12e-34, 3.26e-143j)
| (0.0029612747475621798881 + 2.0981498914613555185e-804j)  +/-  (1.16e-36, 3.36e-145j)
| (0.005738554321757428133 - 4.3482215464596927435e-804j)  +/-  (2.63e-39, 7.65e-148j)
| (0.0029612747475621798881 + 4.3786631891249382486e-803j)  +/-  (2.63e-35, 7.65e-144j)
| (0.0063391962309190404614 + 3.5014228017759676162e-803j)  +/-  (2.69e-39, 7.81e-148j)
| (0.005738554321757428133 - 3.6033417030671670686e-803j)  +/-  (1.86e-38, 5.42e-147j)
| (0.00023662620632591467535 + 1.5875854914285460325e-805j)  +/-  (5.16e-37, 1.5e-145j)
| (0.0063391962309190404614 + 4.8839778305227593993e-804j)  +/-  (8.79e-42, 2.56e-150j)
| (0.0024806415993990324561 - 1.7395915072474554291e-804j)  +/-  (4e-38, 1.16e-146j)
| (0.013238248521087846967 + 1.4653066688770150752e-803j)  +/-  (4.87e-46, 1.42e-154j)
| (0.0081503345671314607559 - 3.226345323716115701e-803j)  +/-  (6.51e-44, 1.89e-152j)
| (0.012958509748503046158 - 1.3851277538251265911e-803j)  +/-  (5.5e-46, 1.6e-154j)
| (0.001255888581326445905 + 8.5907894077141527228e-805j)  +/-  (4.21e-38, 1.22e-146j)
| (0.0069444444444444444444 - 5.4461757456859764264e-804j)  +/-  (1.91e-43, 5.54e-152j)
| (0.013470087644346586 - 2.215580692730083763e-803j)  +/-  (4.66e-48, 1.36e-156j)
| (0.0069444444444444444444 - 3.4058225785618463246e-803j)  +/-  (1.33e-43, 3.87e-152j)
| (0.0045693045602384115761 - 3.8387920910045578166e-803j)  +/-  (1.22e-41, 3.55e-150j)
| (0.0051470899645658280392 + 3.8398717993935024768e-804j)  +/-  (4.16e-42, 1.21e-150j)
| (0.0087417989243230608496 + 7.2811167499634987242e-804j)  +/-  (1.4e-46, 4.06e-155j)
| (0.0045693045602384115761 - 3.359846592003162474e-804j)  +/-  (8.53e-42, 2.48e-150j)
| (0.00041880124454230288851 + 6.4957828723931436252e-803j)  +/-  (8.37e-42, 2.43e-150j)
| (0.0093195843286504773128 - 3.0551743069387253907e-803j)  +/-  (5.59e-48, 1.63e-156j)
| (0.00093037914038584273081 - 1.1844475152535248916e-802j)  +/-  (9.65e-42, 2.81e-150j)
| (0.0075496926579698484275 + 6.033805815527085746e-804j)  +/-  (1.51e-45, 4.38e-154j)
| (0.0093195843286504773128 - 7.9385790146640471958e-804j)  +/-  (8.76e-48, 2.55e-156j)
| (0.013888888888888888889 - 1.8781409263243387607e-803j)  +/-  (6.37e-52, 1.85e-160j)
| (0.0087417989243230608496 + 3.1401095121881313641e-803j)  +/-  (5.2e-48, 1.51e-156j)
| (0.0098792934843104127513 + 2.9710305370058208544e-803j)  +/-  (1.11e-49, 3.22e-158j)
| (0.013652262682562974214 + 2.1310549122106317817e-803j)  +/-  (1.1e-52, 3.19e-161j)
| (0.010416666666666666667 - 9.3153141968263418288e-804j)  +/-  (1.44e-51, 4.2e-160j)
| (0.013652262682562974214 + 1.6284294981765406015e-803j)  +/-  (5.56e-53, 1.62e-161j)
| (0.010416666666666666667 - 2.8873139703603759541e-803j)  +/-  (3.52e-51, 1.02e-159j)
| (0.010927614141326709001 + 2.8037685154977782819e-803j)  +/-  (3.84e-52, 1.12e-160j)
| (0.012633000307562442984 + 2.4686831153357300225e-803j)  +/-  (3.16e-54, 9.19e-163j)
| (0.0098792934843104127513 + 8.6170420491623339203e-804j)  +/-  (1.25e-52, 3.64e-161j)
| (0.010927614141326709001 + 1.0032176764791859024e-803j)  +/-  (5.51e-54, 1.6e-162j)
| (0.013783387173695889301 - 1.7111195427041028242e-803j)  +/-  (2.14e-55, 6.22e-164j)
| (0.011408247289489856433 - 2.720220096555856786e-803j)  +/-  (1.37e-54, 3.97e-163j)
| (0.0075496926579698484275 + 3.314588765993922996e-803j)  +/-  (3.22e-52, 9.37e-161j)
| (0.013862463181192677308 + 1.7943966287816706637e-803j)  +/-  (1.17e-55, 3.4e-164j)
| (0.011408247289489856433 - 1.0766387644490931065e-803j)  +/-  (9.23e-56, 2.68e-164j)
| (0.0081503345671314607559 - 6.6458164810637027587e-804j)  +/-  (1.65e-53, 4.8e-162j)
| (0.012958509748503046158 - 2.3844558481572242574e-803j)  +/-  (1.11e-56, 3.21e-165j)
| (0.011854908202684357808 + 2.6365577550183794843e-803j)  +/-  (5.81e-56, 1.69e-164j)
| (0.013862463181192677308 + 1.9622371856908285242e-803j)  +/-  (4.16e-57, 1.21e-165j)
| (0.011854908202684357808 + 1.1516685182811768473e-803j)  +/-  (1.73e-57, 5.03e-166j)
| (0.012633000307562442984 + 1.3060421134687834691e-803j)  +/-  (6.03e-58, 1.76e-166j)
| (0.013783387173695889301 - 2.0465759395183838242e-803j)  +/-  (9.27e-58, 2.7e-166j)
| (0.012264197521659569689 - 2.55271974156846035e-803j)  +/-  (7.83e-58, 2.28e-166j)
| (0.013238248521087846967 + 2.3000707441903316726e-803j)  +/-  (4.55e-58, 1.32e-166j)
| (0.013470087644346586 - 1.5464498690668042516e-803j)  +/-  (8.45e-59, 2.5e-167j)
| (0.012264197521659569689 - 1.2281792334567997624e-803j)  +/-  (6.91e-59, 1.96e-167j)
