Starting with polynomial:
P : t
Extension levels are: 1 70
-------------------------------------------------
Trying to find an order 70 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^71 - 71/4*t^69 + 1207/8*t^67 - 52327/64*t^65 + 50765/16*t^63 - 600873/64*t^61 + 2819481/128*t^59 - 689161713/16384*t^57 + 4364690849/65536*t^55 - 23231419035/262144*t^53 + 52480156443/524288*t^51 - 405528481605/4194304*t^49 + 336794840655/4194304*t^47 - 965716771215/16777216*t^45 + 1198069678575/33554432*t^43 - 10303399235745/536870912*t^41 + 38403578969595/4294967296*t^39 - 61997934676405/17179869184*t^37 + 43281577038245/34359738368*t^35 - 104261288816825/274877906944*t^33 + 13492637376295/137438953472*t^31 - 11950621676147/549755813888*t^29 + 4500883488419/1099511627776*t^27 - 22895798615001/35184372088832*t^25 + 12178616284575/140737488355328*t^23 - 5358591165213/562949953421312*t^21 + 961798414269/1125899906842624*t^19 - 553762723367/9007199254740992*t^17 + 31275635539/9007199254740992*t^15 - 5392350955/36028797018963968*t^13 + 341953963/72057594037927936*t^11 - 121338503/1152921504606846976*t^9 + 28001193/18446744073709551616*t^7 - 937839/73786976294838206464*t^5 + 7455/147573952589676412928*t^3 - 71/1180591620717411303424*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:
| (-0.99779820878257107827 - 1.0560920917537879423e-818j)  +/-  (3.86e-230, 3.86e-230j)
| (-0.97053313512356730533 + 7.1995565985751092812e-826j)  +/-  (3.71e-230, 3.71e-230j)
| (-0.95892439509704013515 + 2.0375439444083459367e-832j)  +/-  (2.35e-230, 2.35e-230j)
| (-0.99975527668524300879 + 7.5955734018707840595e-836j)  +/-  (1.43e-230, 1.43e-230j)
| (0.9129445576913887139 + 3.791083016604037643e-839j)  +/-  (3.14e-231, 3.14e-231j)
| (0.93010189568289619909 - 7.6263541502200607887e-845j)  +/-  (6.67e-231, 6.67e-231j)
| (0.97053313512356730533 + 2.8381231519434726558e-850j)  +/-  (3.62e-230, 3.62e-230j)
| (-0.87330557086689273783 - 1.6740576141204084607e-861j)  +/-  (4.26e-232, 4.26e-232j)
| (0.98024201096180283547 - 3.0178533406022646123e-865j)  +/-  (4.44e-230, 4.44e-230j)
| (-0.99388790402955070957 + 1.517764621478284339e-866j)  +/-  (4.77e-230, 4.77e-230j)
| (0.89400008785627571442 - 5.797501918076187815e-875j)  +/-  (1.32e-231, 1.32e-231j)
| (0.99388790402955070957 + 2.9258217126805944387e-872j)  +/-  (5.23e-230, 5.23e-230j)
| (-0.82683178387890870872 - 4.7899642375193986818e-880j)  +/-  (4.21e-233, 4.21e-233j)
| (-0.89400008785627571442 - 1.1362833182604279299e-885j)  +/-  (1.29e-231, 1.29e-231j)
| (0.98803201703136405766 + 1.8840960090247898897e-889j)  +/-  (6e-230, 6e-230j)
| (0.82683178387890870872 + 6.0055044255413888877e-893j)  +/-  (4.53e-233, 4.53e-233j)
| (0.85090151721206211152 - 1.3160008710912132161e-892j)  +/-  (1.36e-232, 1.36e-232j)
| (-0.9129445576913887139 - 2.0843450699404728596e-888j)  +/-  (2.85e-231, 2.85e-231j)
| (-0.74511542576142850554 + 3.5165547047784503082e-895j)  +/-  (5.49e-235, 5.49e-235j)
| (-0.93010189568289619909 - 2.7213264337791118945e-890j)  +/-  (6.41e-231, 6.41e-231j)
| (0.99779820878257107827 + 1.0658685239882907224e-893j)  +/-  (4.34e-230, 4.34e-230j)
| (0.80114348850074812512 - 3.0520688366223023225e-900j)  +/-  (1.04e-233, 1.04e-233j)
| (-0.94543851553597029631 - 5.2124728236330145621e-893j)  +/-  (1.41e-230, 1.41e-230j)
| (-0.85090151721206211152 - 1.2941466361860741311e-898j)  +/-  (1.45e-232, 1.45e-232j)
| (-0.80114348850074812512 - 2.7733192604023703419e-901j)  +/-  (1.21e-233, 1.21e-233j)
| (0.95892439509704013515 + 1.9947464288989277892e-901j)  +/-  (2.33e-230, 2.33e-230j)
| (0.7148853359641624715 + 5.9212431432520485593e-909j)  +/-  (1.01e-235, 1.01e-235j)
| (0.74511542576142850554 - 3.1639474109516944256e-909j)  +/-  (5.52e-235, 5.52e-235j)
| (0.99975527668524300879 + 4.0192033684778479535e-901j)  +/-  (1.3e-230, 1.3e-230j)
| (-0.61604882012036416457 - 3.3090868613606372356e-910j)  +/-  (3.24e-238, 3.24e-238j)
| (-0.13235385426422243225 - 1.0097131163190732651e-924j)  +/-  (5.01e-252, 5.01e-252j)
| (0.65028880777493690969 - 5.3925511141555881411e-910j)  +/-  (2.71e-237, 2.71e-237j)
| (0.68325582455069347583 - 7.8805596081514869418e-909j)  +/-  (1.59e-236, 1.59e-236j)
| (-0.98803201703136405766 + 1.3440329815769438875e-900j)  +/-  (5.46e-230, 5.46e-230j)
| (-0.65028880777493690969 - 2.009163484698022302e-926j)  +/-  (2.59e-237, 2.59e-237j)
| (-0.77388691712210681703 + 9.5660814883506034504e-924j)  +/-  (2.53e-234, 2.53e-234j)
| (0.77388691712210681703 - 3.9353817621344882567e-925j)  +/-  (2.42e-234, 2.42e-234j)
| (0.61604882012036416457 + 1.9194507543287305688e-927j)  +/-  (3.35e-238, 3.35e-238j)
| (0.94543851553597029631 - 3.7404067386197622308e-921j)  +/-  (1.24e-230, 1.24e-230j)
| (-0.7148853359641624715 + 1.7668004842967086952e-926j)  +/-  (9.38e-236, 9.38e-236j)
| (-0.58060288797072069431 + 4.9770170078641601679e-931j)  +/-  (4.28e-239, 4.28e-239j)
| (-0.98024201096180283547 + 1.4460056930604789629e-929j)  +/-  (5.43e-230, 5.43e-230j)
| (0.54402039840273227085 + 2.9855678544350324284e-944j)  +/-  (4.21e-240, 4.21e-240j)
| (0.58060288797072069431 + 4.6743365742012524155e-942j)  +/-  (3.93e-239, 3.93e-239j)
| (-0.088380104597342480341 - 2.261520810069921713e-957j)  +/-  (3.17e-253, 3.17e-253j)
| (-0.54402039840273227085 - 2.5891515201812169516e-945j)  +/-  (3.52e-240, 3.52e-240j)
| (-0.68325582455069347583 - 7.8583924761129588377e-942j)  +/-  (1.67e-236, 1.67e-236j)
| (0.87330557086689273783 + 1.5922699139217792375e-952j)  +/-  (4.19e-232, 4.19e-232j)
| (0.50637296335764387271 - 1.6838653076475644073e-961j)  +/-  (4.11e-241, 4.11e-241j)
| (0.17606851504603618592 + 5.3252429166404951596e-972j)  +/-  (1.15e-250, 1.15e-250j)
| (-0.38778750559790211841 + 5.4485739035278490529e-964j)  +/-  (1.62e-244, 1.62e-244j)
| (-0.50637296335764387271 + 6.2636617643862104605e-963j)  +/-  (4.35e-241, 4.35e-241j)
| (0.04423334672537885331 + 9.5809799885335764277e-977j)  +/-  (1.33e-254, 1.33e-254j)
| (0.42817998374045524792 + 9.9727036633988409418e-965j)  +/-  (2.47e-243, 2.47e-243j)
| (0.46773427945748179746 + 2.6690998976799100798e-964j)  +/-  (4.02e-242, 4.02e-242j)
| (-6.3090061107502105666e-1000 + 3.2498196195387631164e-999j)  +/-  (2.35e-997, 2.35e-997j)
| (-0.46773427945748179746 - 3.7522567444422512012e-965j)  +/-  (3.41e-242, 3.41e-242j)
| (-0.42817998374045524792 + 3.291469623122994966e-966j)  +/-  (2.84e-243, 2.84e-243j)
| (0.13235385426422243225 - 1.5244215650480607071e-974j)  +/-  (5.57e-252, 5.57e-252j)
| (0.38778750559790211841 + 1.9370468346372661869e-966j)  +/-  (1.64e-244, 1.64e-244j)
| (0.088380104597342480341 + 3.1154811419068321287e-975j)  +/-  (3.23e-253, 3.23e-253j)
| (-0.26237895064197910638 + 4.123858994789642935e-970j)  +/-  (3.99e-248, 3.99e-248j)
| (-0.34663591520261936244 + 8.579925577173958375e-968j)  +/-  (1.3e-245, 1.3e-245j)
| (-0.04423334672537885331 + 1.1283747907409899733e-976j)  +/-  (1.33e-254, 1.33e-254j)
| (0.30480576872528660325 - 4.7235076197091958473e-969j)  +/-  (7.43e-247, 7.43e-247j)
| (0.26237895064197910638 + 4.9482037026161226213e-971j)  +/-  (3.86e-248, 3.86e-248j)
| (-0.17606851504603618592 - 4.2300288886809281958e-973j)  +/-  (1.17e-250, 1.17e-250j)
| (-0.30480576872528660325 + 1.2299478073839259908e-969j)  +/-  (7.39e-247, 7.39e-247j)
| (-0.21943851344146056304 - 1.0958497010544489081e-971j)  +/-  (2.28e-249, 2.28e-249j)
| (0.21943851344146056304 + 6.8699869772638352831e-972j)  +/-  (2.26e-249, 2.26e-249j)
| (0.34663591520261936244 - 4.4965268992442951302e-968j)  +/-  (1.21e-245, 1.21e-245j)
-------------------------------------------------
The weights are:
| (0.014084507042253521127 - 1.687051787292334557e-818j)  +/-  (2.83e-22, 1.33e-130j)
| (0.014084507042253521127 - 1.9821281265853586731e-818j)  +/-  (1.05e-22, 4.92e-131j)
| (0.014084507042253521127 + 1.6365271313508546787e-818j)  +/-  (7.57e-23, 3.55e-131j)
| (0.014084507042253521127 - 2.5351272805984439156e-818j)  +/-  (9.53e-23, 4.47e-131j)
| (0.014084507042253521127 - 4.7899004449440132598e-820j)  +/-  (2.01e-24, 9.42e-133j)
| (0.014084507042253521127 + 4.2728519663080089752e-820j)  +/-  (1.63e-24, 7.66e-133j)
| (0.014084507042253521127 - 2.7456184520476320434e-820j)  +/-  (2.15e-25, 1.01e-133j)
| (0.014084507042253521127 - 8.7764514863336218823e-819j)  +/-  (6.76e-26, 3.17e-134j)
| (0.014084507042253521127 + 2.2427194186120424383e-820j)  +/-  (7.73e-26, 3.62e-134j)
| (0.014084507042253521127 + 6.3316137254542063273e-818j)  +/-  (3.21e-24, 1.51e-132j)
| (0.014084507042253521127 + 5.3118704708523700091e-820j)  +/-  (5.33e-26, 2.5e-134j)
| (0.014084507042253521127 + 1.2430944081442535523e-820j)  +/-  (4.9e-27, 2.3e-135j)
| (0.014084507042253521127 - 7.3782284111349048522e-819j)  +/-  (1.19e-27, 5.58e-136j)
| (0.014084507042253521127 + 9.6812806962520737133e-819j)  +/-  (7.81e-27, 3.66e-135j)
| (0.014084507042253521127 - 1.7420459573947009933e-820j)  +/-  (1.31e-26, 6.12e-135j)
| (0.014084507042253521127 - 6.9133432135799148324e-820j)  +/-  (6.9e-29, 3.24e-137j)
| (0.014084507042253521127 + 6.3729637362767526272e-820j)  +/-  (2.21e-28, 1.03e-136j)
| (0.014084507042253521127 - 1.0785944306220784205e-818j)  +/-  (3.46e-28, 1.62e-136j)
| (0.014084507042253521127 + 5.9195372650848151497e-819j)  +/-  (1.36e-31, 6.38e-140j)
| (0.014084507042253521127 + 1.2168508553881038145e-818j)  +/-  (1.85e-28, 8.65e-137j)
| (0.014084507042253521127 - 7.4536795564916664939e-821j)  +/-  (3.71e-30, 1.74e-138j)
| (0.014084507042253521127 + 7.4611630769900418711e-820j)  +/-  (4.26e-32, 2e-140j)
| (0.014084507042253521127 - 1.3955143214249996647e-818j)  +/-  (1.74e-28, 8.15e-137j)
| (0.014084507042253521127 + 8.0203959258676287743e-819j)  +/-  (5.95e-30, 2.79e-138j)
| (0.014084507042253521127 + 6.8252606972930140824e-819j)  +/-  (2.28e-31, 1.07e-139j)
| (0.014084507042253521127 + 3.2512556177361594775e-820j)  +/-  (3.42e-31, 1.6e-139j)
| (0.014084507042253521127 - 9.1565053149637273366e-820j)  +/-  (1.14e-35, 5.33e-144j)
| (0.014084507042253521127 + 8.581980906236553394e-820j)  +/-  (3.61e-35, 1.69e-143j)
| (0.014084507042253521127 + 2.4837463316979283253e-821j)  +/-  (5.63e-32, 2.64e-140j)
| (0.014084507042253521127 + 4.6277133184319240206e-819j)  +/-  (8.64e-39, 4.05e-147j)
| (0.014084507042253521127 + 2.5686374442534705089e-819j)  +/-  (3.6e-41, 1.69e-149j)
| (0.014084507042253521127 - 1.0337943666225690276e-819j)  +/-  (1.03e-37, 4.85e-146j)
| (0.014084507042253521127 + 9.7415320792624366173e-820j)  +/-  (7.49e-37, 3.51e-145j)
| (0.014084507042253521127 - 3.5422278275088281317e-818j)  +/-  (3.59e-34, 1.68e-142j)
| (0.014084507042253521127 - 4.9028402290605537137e-819j)  +/-  (4.71e-39, 2.21e-147j)
| (0.014084507042253521127 - 6.3435062349950752903e-819j)  +/-  (2.15e-36, 1.01e-144j)
| (0.014084507042253521127 - 8.0171281975813214001e-820j)  +/-  (2.25e-36, 1.05e-144j)
| (0.014084507042253521127 + 1.0946680202994045306e-819j)  +/-  (1.06e-39, 4.97e-148j)
| (0.014084507042253521127 - 3.7601545064846993918e-820j)  +/-  (8.6e-35, 4.03e-143j)
| (0.014084507042253521127 - 5.5431185571284742573e-819j)  +/-  (1.25e-38, 5.88e-147j)
| (0.014084507042253521127 - 4.3768758739472960647e-819j)  +/-  (2.12e-41, 9.94e-150j)
| (0.014084507042253521127 + 2.526850911468219856e-818j)  +/-  (2.61e-35, 1.23e-143j)
| (0.014084507042253521127 + 1.2205216793232738524e-819j)  +/-  (1.17e-42, 5.49e-151j)
| (0.014084507042253521127 - 1.1568745991969873537e-819j)  +/-  (1.29e-41, 6.06e-150j)
| (0.014084507042253521127 - 2.4564795617475052846e-819j)  +/-  (8.85e-47, 4.15e-155j)
| (0.014084507042253521127 + 4.1470142236725030031e-819j)  +/-  (2.05e-43, 9.61e-152j)
| (0.014084507042253521127 + 5.2063068729461299251e-819j)  +/-  (2.14e-40, 1.01e-148j)
| (0.014084507042253521127 - 5.8393532972454547338e-820j)  +/-  (4.64e-39, 2.18e-147j)
| (0.014084507042253521127 - 1.2857247991345104661e-819j)  +/-  (1.38e-44, 6.48e-153j)
| (0.014084507042253521127 - 1.8807134298715046395e-819j)  +/-  (6.85e-49, 3.21e-157j)
| (0.014084507042253521127 + 3.3888682254504002757e-819j)  +/-  (1.17e-47, 5.47e-156j)
| (0.014084507042253521127 - 3.9353903665042770179e-819j)  +/-  (1.97e-45, 9.22e-154j)
| (0.014084507042253521127 + 2.1501729866735252372e-819j)  +/-  (1.67e-49, 7.85e-158j)
| (0.014084507042253521127 - 1.4213067552341605225e-819j)  +/-  (6.99e-48, 3.28e-156j)
| (0.014084507042253521127 + 1.3526083783787269592e-819j)  +/-  (6.52e-47, 3.06e-155j)
| (0.014084507042253521127 - 2.2476921883882845373e-819j)  +/-  (3.86e-50, 1.81e-158j)
| (0.014084507042253521127 + 3.7397215909255785873e-819j)  +/-  (4.12e-48, 1.93e-156j)
| (0.014084507042253521127 - 3.5580891684588387567e-819j)  +/-  (8.5e-49, 3.99e-157j)
| (0.014084507042253521127 + 1.9670032449139690206e-819j)  +/-  (1.76e-51, 8.24e-160j)
| (0.014084507042253521127 + 1.4919653607771989206e-819j)  +/-  (6.74e-51, 3.16e-159j)
| (0.014084507042253521127 - 2.0567221410257147791e-819j)  +/-  (1.97e-51, 9.26e-160j)
| (0.014084507042253521127 - 2.9427683787060225713e-819j)  +/-  (7.43e-53, 3.48e-161j)
| (0.014084507042253521127 - 3.2306732615809269129e-819j)  +/-  (6.27e-52, 2.94e-160j)
| (0.014084507042253521127 + 2.3496546390908521806e-819j)  +/-  (2.65e-52, 1.24e-160j)
| (0.014084507042253521127 + 1.6398086394731731448e-819j)  +/-  (1.09e-53, 5.1e-162j)
| (0.014084507042253521127 - 1.7173526138192038061e-819j)  +/-  (8.22e-54, 3.85e-162j)
| (0.014084507042253521127 - 2.6866583120640754341e-819j)  +/-  (5.56e-54, 2.61e-162j)
| (0.014084507042253521127 + 3.0823153787483280047e-819j)  +/-  (4.5e-54, 2.11e-162j)
| (0.014084507042253521127 + 2.8111416509572371478e-819j)  +/-  (3.01e-54, 1.41e-162j)
| (0.014084507042253521127 + 1.7975791558042741432e-819j)  +/-  (3.94e-55, 1.86e-163j)
| (0.014084507042253521127 - 1.5647420533261852665e-819j)  +/-  (3.44e-55, 1.59e-163j)
