Starting with polynomial:
P : t
Extension levels are: 1 72
-------------------------------------------------
Trying to find an order 72 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^73 - 73/4*t^71 + 2555/16*t^69 - 28543/32*t^67 + 914617/256*t^65 - 699413/64*t^63 + 6795789/256*t^61 - 26918385/512*t^59 + 708574719/8192*t^57 - 31413479209/262144*t^55 + 148092116271/1048576*t^53 - 299224246659/2097152*t^51 + 2084759095575/16777216*t^49 - 1571587625895/16777216*t^47 + 4113525965115/67108864*t^45 - 4680908856855/134217728*t^43 + 74155450837545/4294967296*t^41 - 127746785056275/17179869184*t^39 + 191233066114545/68719476736*t^37 - 124133744670845/137438953472*t^35 + 278715388977935/1099511627776*t^33 - 33690871195135/549755813888*t^31 + 27925588423775/2199023255552*t^29 - 9858946869611/4398046511104*t^27 + 23540750688663/70368744177664*t^25 - 23540750688663/562949953421312*t^23 + 9747643083849/2251799813685248*t^21 - 1648152212245/4503599627370496*t^19 + 894711200933/36028797018963968*t^17 - 47680534219/36028797018963968*t^15 + 7761947431/144115188075855872*t^13 - 465001459/288230376151711744*t^11 + 623782445/18446744073709551616*t^9 - 34024497/73786976294838206464*t^7 + 1077699/295147905179352825856*t^5 - 8103/590295810358705651712*t^3 + 73/4722366482869645213696*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
-------------------------------------------------
The nodes are:
| (0.99791716086539217467 + 1.8364470386098502386e-796j)  +/-  (2.43e-229, 2.43e-229j)
| (-0.043022233004530474283 + 1.3722624810759645437e-839j)  +/-  (1.09e-254, 1.09e-254j)
| (-0.89963086965224337564 + 6.0349299271089973557e-811j)  +/-  (8.96e-231, 8.96e-231j)
| (-0.99791716086539217467 - 1.0593026407470164966e-808j)  +/-  (2.64e-229, 2.64e-229j)
| (0.93383722882292518406 - 4.8356472585717469573e-811j)  +/-  (4.34e-230, 4.34e-230j)
| (0.97211819662906132344 + 2.2816541832116330554e-809j)  +/-  (2.21e-229, 2.21e-229j)
| (0.98867759023234040753 + 3.0724465391977594138e-824j)  +/-  (3.85e-229, 3.85e-229j)
| (-0.88001220397353559613 - 1.043669861591913522e-836j)  +/-  (2.97e-231, 2.97e-231j)
| (-0.66806386421353346464 + 8.324521553445841147e-843j)  +/-  (2.42e-236, 2.42e-236j)
| (-0.99976850197989083904 - 5.5647269239560159279e-833j)  +/-  (1.01e-229, 1.01e-229j)
| (0.88001220397353559613 + 1.0505890829152833741e-842j)  +/-  (3.71e-231, 3.71e-231j)
| (-0.98867759023234040753 + 1.5420997319678093273e-838j)  +/-  (3.53e-229, 3.53e-229j)
| (-0.9175836260593937212 + 3.5384219513311111895e-845j)  +/-  (2.25e-230, 2.25e-230j)
| (-0.85876395827580301159 + 6.5557047721722882808e-847j)  +/-  (1.07e-231, 1.07e-231j)
| (0.66806386421353346464 - 5.2354885103214974453e-853j)  +/-  (2.3e-236, 2.3e-236j)
| (0.85876395827580301159 + 1.5618164875679712326e-847j)  +/-  (1.03e-231, 1.03e-231j)
| (-0.96112978387230075879 - 1.88484560437704585e-843j)  +/-  (1.87e-229, 1.87e-229j)
| (-0.97211819662906132344 - 1.5963911630514775998e-843j)  +/-  (2.22e-229, 2.22e-229j)
| (-0.78564985507871435614 - 3.7856109629608069551e-851j)  +/-  (2.21e-233, 2.21e-233j)
| (-0.98130647027160934869 - 7.7638406222497755849e-847j)  +/-  (2.97e-229, 2.97e-229j)
| (0.99421790689395191598 - 3.4892309804539851057e-847j)  +/-  (3.45e-229, 3.45e-229j)
| (0.75830580847856251639 - 3.7866353278517558773e-868j)  +/-  (4.9e-234, 4.9e-234j)
| (0.96112978387230075879 + 2.1873671711535828616e-862j)  +/-  (1.64e-229, 1.64e-229j)
| (-0.83592547941863689659 + 9.0476477429018703861e-870j)  +/-  (3.13e-232, 3.13e-232j)
| (-0.75830580847856251639 + 3.6309825871617167834e-872j)  +/-  (4.77e-234, 4.77e-234j)
| (0.085964798737446473645 - 4.5643986442084728563e-892j)  +/-  (2.5e-253, 2.5e-253j)
| (0.72955755408648751191 - 7.437808474319496365e-874j)  +/-  (8.71e-235, 8.71e-235j)
| (0.9175836260593937212 + 1.6677056630461017628e-865j)  +/-  (2.26e-230, 2.26e-230j)
| (0.9483615800121715507 - 1.9072540462978320375e-865j)  +/-  (9.06e-230, 9.06e-230j)
| (-0.63543230089017746396 + 6.6516432813304170429e-883j)  +/-  (3.28e-237, 3.28e-237j)
| (-0.6994583270516470882 - 3.0066455522429161987e-881j)  +/-  (1.65e-235, 1.65e-235j)
| (0.99976850197989083904 + 2.7907851556444001703e-873j)  +/-  (9.97e-230, 9.97e-230j)
| (0.6994583270516470882 - 6.169514707763684973e-893j)  +/-  (1.59e-235, 1.59e-235j)
| (-0.9483615800121715507 - 3.4998740442908728604e-884j)  +/-  (9.45e-230, 9.45e-230j)
| (-0.72955755408648751191 + 6.5595946340789099008e-892j)  +/-  (9.73e-235, 9.73e-235j)
| (-0.93383722882292518406 + 3.0665907740030584219e-886j)  +/-  (4.73e-230, 4.73e-230j)
| (-0.81153905900736103094 - 3.5499527310731008056e-890j)  +/-  (7.75e-233, 7.75e-233j)
| (0.60162406322492252865 + 8.4756063982770148569e-898j)  +/-  (3.8e-238, 3.8e-238j)
| (0.81153905900736103094 - 1.1932705802082028294e-891j)  +/-  (8.8e-233, 8.8e-233j)
| (0.25535329511618703742 + 1.5776110120116500703e-907j)  +/-  (4.37e-248, 4.37e-248j)
| (-0.60162406322492252865 + 6.1417149472511106597e-897j)  +/-  (4e-238, 4e-238j)
| (-0.99421790689395191598 - 1.2958269798056606477e-887j)  +/-  (3.7e-229, 3.7e-229j)
| (0.29671281927349024938 - 6.1405929126818089955e-911j)  +/-  (7.59e-247, 7.59e-247j)
| (0.63543230089017746396 + 5.067897584630224112e-900j)  +/-  (3.5e-237, 3.5e-237j)
| (0.89963086965224337564 - 7.1939709752360601474e-896j)  +/-  (8.53e-231, 8.53e-231j)
| (-0.56670175629111761656 + 1.1396008864339715219e-906j)  +/-  (5.07e-239, 5.07e-239j)
| (-0.4559066935084587905 + 1.1808018875231605754e-909j)  +/-  (3.56e-242, 3.56e-242j)
| (0.98130647027160934869 + 1.7660203389142542377e-902j)  +/-  (3.35e-229, 3.35e-229j)
| (0.49377555015997726157 - 7.073992298836179478e-926j)  +/-  (4.67e-241, 4.67e-241j)
| (0.41719360261231682966 - 1.3137855377924985267e-928j)  +/-  (2.66e-243, 2.66e-243j)
| (-0.17129314418147759322 + 5.9153783114550423011e-938j)  +/-  (1.11e-250, 1.11e-250j)
| (-0.5307300481619333258 - 1.5997496067065251217e-926j)  +/-  (5.26e-240, 5.26e-240j)
| (0.56670175629111761656 - 3.1424018800189302522e-924j)  +/-  (4.95e-239, 4.95e-239j)
| (0.21352091543979605088 - 9.6479259575527395741e-936j)  +/-  (2.38e-249, 2.38e-249j)
| (0.4559066935084587905 + 1.9200602790230268901e-928j)  +/-  (3.96e-242, 3.96e-242j)
| (-0.29671281927349024938 + 2.716865208399507847e-934j)  +/-  (7.79e-247, 7.79e-247j)
| (-0.41719360261231682966 + 1.0403548764483124003e-929j)  +/-  (2.81e-243, 2.81e-243j)
| (0.83592547941863689659 - 2.055448704261566229e-917j)  +/-  (2.86e-232, 2.86e-232j)
| (-0.12874817745258079194 + 4.4424350930504029743e-938j)  +/-  (5.32e-252, 5.32e-252j)
| (0.37770796520396485042 - 2.0522111615197120276e-930j)  +/-  (2.22e-244, 2.22e-244j)
| (3.2466179547611367348e-962 + 1.1360443259243396245e-961j)  +/-  (8.63e-960, 8.63e-960j)
| (-0.49377555015997726157 - 5.153829723636823356e-928j)  +/-  (4.42e-241, 4.42e-241j)
| (-0.37770796520396485042 - 2.9093542306858434552e-931j)  +/-  (1.84e-244, 1.84e-244j)
| (0.043022233004530474283 - 2.3653776015152205509e-941j)  +/-  (1.09e-254, 1.09e-254j)
| (0.78564985507871435614 - 1.6401427012541499651e-931j)  +/-  (2.22e-233, 2.22e-233j)
| (0.5307300481619333258 - 2.5386638376921934706e-940j)  +/-  (4.7e-240, 4.7e-240j)
| (-0.085964798737446473645 - 1.2927273091354463676e-954j)  +/-  (2.35e-253, 2.35e-253j)
| (-0.33752289959411328449 + 2.3402938569978791934e-947j)  +/-  (1.21e-245, 1.21e-245j)
| (-0.25535329511618703742 + 4.9209377628354878158e-951j)  +/-  (4.45e-248, 4.45e-248j)
| (0.12874817745258079194 - 1.6233375563214023333e-952j)  +/-  (5.56e-252, 5.56e-252j)
| (0.33752289959411328449 + 3.750895160937240941e-946j)  +/-  (1.25e-245, 1.25e-245j)
| (0.17129314418147759322 - 9.5990256870139873425e-952j)  +/-  (1.21e-250, 1.21e-250j)
| (-0.21352091543979605088 + 7.5301001980642743472e-952j)  +/-  (2.26e-249, 2.26e-249j)
-------------------------------------------------
The weights are:
| (0.01369863013698630137 - 3.0163854501840052487e-796j)  +/-  (2.27e-28, 4.38e-136j)
| (0.01369863013698630137 - 3.7429257116392623782e-797j)  +/-  (1.22e-28, 2.35e-136j)
| (0.01369863013698630137 + 8.9738923866525067104e-798j)  +/-  (3.5e-29, 6.75e-137j)
| (0.01369863013698630137 - 1.2604657850425889479e-798j)  +/-  (2.49e-29, 4.81e-137j)
| (0.01369863013698630137 + 2.1768760651872423128e-796j)  +/-  (1.49e-29, 2.88e-137j)
| (0.01369863013698630137 - 3.5445701408410850931e-796j)  +/-  (1.34e-29, 2.59e-137j)
| (0.01369863013698630137 - 6.333427146294608949e-796j)  +/-  (1.23e-29, 2.38e-137j)
| (0.01369863013698630137 - 9.8629893525589528563e-798j)  +/-  (2.85e-30, 5.51e-138j)
| (0.01369863013698630137 - 1.7418168934696407015e-797j)  +/-  (1.54e-31, 2.97e-139j)
| (0.01369863013698630137 + 4.2002514872744221795e-799j)  +/-  (1.01e-30, 1.95e-138j)
| (0.01369863013698630137 - 1.5709260932161228664e-796j)  +/-  (5.15e-32, 9.93e-140j)
| (0.01369863013698630137 - 2.9456509659255409808e-798j)  +/-  (3.27e-31, 6.31e-139j)
| (0.01369863013698630137 - 8.0935772841535372819e-798j)  +/-  (2.43e-31, 4.7e-139j)
| (0.01369863013698630137 + 1.0761839582983336302e-797j)  +/-  (1.43e-31, 2.75e-139j)
| (0.01369863013698630137 - 8.7973469512931266241e-797j)  +/-  (6.37e-35, 1.23e-142j)
| (0.01369863013698630137 + 1.43592127158798301e-796j)  +/-  (1.47e-33, 2.84e-141j)
| (0.01369863013698630137 + 5.4961141897531290244e-798j)  +/-  (1.88e-32, 3.62e-140j)
| (0.01369863013698630137 - 4.6418577185872339877e-798j)  +/-  (1.56e-32, 3e-140j)
| (0.01369863013698630137 - 1.3527251200000810583e-797j)  +/-  (1.3e-35, 2.51e-143j)
| (0.01369863013698630137 + 3.791975849801048242e-798j)  +/-  (1.89e-32, 3.64e-140j)
| (0.01369863013698630137 + 1.1320188075534905874e-795j)  +/-  (1.78e-36, 3.43e-144j)
| (0.01369863013698630137 + 1.0609914073559140193e-796j)  +/-  (8.33e-39, 1.61e-146j)
| (0.01369863013698630137 + 2.9268587736107910467e-796j)  +/-  (5.68e-37, 1.1e-144j)
| (0.01369863013698630137 - 1.1671454325238986383e-797j)  +/-  (1.93e-35, 3.72e-143j)
| (0.01369863013698630137 + 1.4475701003009815326e-797j)  +/-  (6.84e-37, 1.32e-144j)
| (0.01369863013698630137 + 4.2604564185163971476e-797j)  +/-  (2.28e-41, 4.39e-149j)
| (0.01369863013698630137 - 9.9386348545033632727e-797j)  +/-  (1.28e-39, 2.47e-147j)
| (0.01369863013698630137 - 1.9298607603985669469e-796j)  +/-  (1.8e-38, 3.47e-146j)
| (0.01369863013698630137 - 2.4961324444614300591e-796j)  +/-  (6.09e-38, 1.17e-145j)
| (0.01369863013698630137 + 1.8435936789808839228e-797j)  +/-  (9.83e-41, 1.9e-148j)
| (0.01369863013698630137 + 1.6419828939379550349e-797j)  +/-  (1.02e-39, 1.96e-147j)
| (0.01369863013698630137 - 4.5322723705443431104e-796j)  +/-  (8.68e-39, 1.67e-146j)
| (0.01369863013698630137 + 9.3381773296071592535e-797j)  +/-  (1.31e-41, 2.53e-149j)
| (0.01369863013698630137 - 6.355579526027971886e-798j)  +/-  (5.45e-38, 1.05e-145j)
| (0.01369863013698630137 - 1.5439462693134716505e-797j)  +/-  (6.1e-40, 1.18e-147j)
| (0.01369863013698630137 + 7.2211079767233982385e-798j)  +/-  (3.57e-38, 6.89e-146j)
| (0.01369863013698630137 + 1.2592889543633589021e-797j)  +/-  (4.42e-39, 8.53e-147j)
| (0.01369863013698630137 - 7.8604838225430940398e-797j)  +/-  (1.05e-46, 2.02e-154j)
| (0.01369863013698630137 + 1.2225836664078098863e-796j)  +/-  (1.54e-44, 2.97e-152j)
| (0.01369863013698630137 + 5.0776557356202017147e-797j)  +/-  (3.08e-49, 5.93e-157j)
| (0.01369863013698630137 - 1.9474680840231514861e-797j)  +/-  (3.7e-45, 7.14e-153j)
| (0.01369863013698630137 + 2.1020788894591800444e-798j)  +/-  (3.81e-40, 7.35e-148j)
| (0.01369863013698630137 - 5.3110770425140222847e-797j)  +/-  (2.28e-49, 4.4e-157j)
| (0.01369863013698630137 + 8.30719590180359554e-797j)  +/-  (8.73e-47, 1.68e-154j)
| (0.01369863013698630137 + 1.7325296960541586007e-796j)  +/-  (2.09e-44, 4.03e-152j)
| (0.01369863013698630137 + 2.0536053999114691851e-797j)  +/-  (9.28e-47, 1.79e-154j)
| (0.01369863013698630137 - 2.3874298382782787957e-797j)  +/-  (2.29e-49, 4.42e-157j)
| (0.01369863013698630137 + 4.5182758463514463618e-796j)  +/-  (6.65e-44, 1.28e-151j)
| (0.01369863013698630137 + 6.7266778969692904141e-797j)  +/-  (2.5e-50, 4.82e-158j)
| (0.01369863013698630137 + 6.1030404341165900303e-797j)  +/-  (3.28e-51, 6.33e-159j)
| (0.01369863013698630137 + 3.2860909324586860286e-797j)  +/-  (1.68e-53, 3.25e-161j)
| (0.01369863013698630137 - 2.162182530969552091e-797j)  +/-  (1.44e-49, 2.77e-157j)
| (0.01369863013698630137 + 7.4512872754215058201e-797j)  +/-  (4.68e-50, 9.02e-158j)
| (0.01369863013698630137 - 4.8570285970531769801e-797j)  +/-  (1.09e-52, 2.1e-160j)
| (0.01369863013698630137 - 6.4037553858577572402e-797j)  +/-  (4.56e-51, 8.8e-159j)
| (0.01369863013698630137 - 2.8766136563152992523e-797j)  +/-  (3.83e-54, 7.39e-162j)
| (0.01369863013698630137 + 2.5045243443394610921e-797j)  +/-  (6.89e-53, 1.33e-160j)
| (0.01369863013698630137 - 1.3212783782756761936e-796j)  +/-  (4.44e-50, 8.57e-158j)
| (0.01369863013698630137 - 3.4325304003574734121e-797j)  +/-  (1.58e-54, 3.05e-162j)
| (0.01369863013698630137 - 5.8220569536423496564e-797j)  +/-  (5.33e-53, 1.03e-160j)
| (0.01369863013698630137 + 3.9079091053325485665e-797j)  +/-  (7.69e-55, 1.48e-162j)
| (0.01369863013698630137 + 2.2733892876292698989e-797j)  +/-  (7.97e-53, 1.54e-160j)
| (0.01369863013698630137 - 2.6249108073758510925e-797j)  +/-  (2.57e-54, 4.96e-162j)
| (0.01369863013698630137 - 4.0801963733346439068e-797j)  +/-  (2.59e-55, 4.99e-163j)
| (0.01369863013698630137 - 1.1366215332682030533e-796j)  +/-  (5.5e-53, 1.06e-160j)
| (0.01369863013698630137 - 7.0747120404122342634e-797j)  +/-  (6.64e-54, 1.28e-161j)
| (0.01369863013698630137 + 3.5846461509827666513e-797j)  +/-  (8.95e-56, 1.73e-163j)
| (0.01369863013698630137 + 2.7488471622082914031e-797j)  +/-  (8.64e-56, 1.67e-163j)
| (0.01369863013698630137 + 3.0085155634144802712e-797j)  +/-  (1.65e-56, 3.19e-164j)
| (0.01369863013698630137 - 4.4494374495730603749e-797j)  +/-  (2.61e-57, 5.05e-165j)
| (0.01369863013698630137 + 5.558680375906829223e-797j)  +/-  (2.78e-57, 5.37e-165j)
| (0.01369863013698630137 + 4.6479793763594016362e-797j)  +/-  (1.71e-57, 3.31e-165j)
| (0.01369863013698630137 - 3.1448862884308514685e-797j)  +/-  (1.52e-57, 2.87e-165j)
