Starting with polynomial:
P : t
Extension levels are: 1 82
-------------------------------------------------
Trying to find an order 82 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^83 - 3403*t^81 + 5512860*t^79 - 5661707220*t^77 + 4141538831430*t^75 - 2298554051443650*t^73 + 1006766674532318700*t^71 - 357402169458973138500*t^69 + 104808186193843872865125*t^67 - 25747877741620978100532375*t^65 + 5355558570257163444910734000*t^63 - 950855080701112746173696682000*t^61 + 145005399806919693791488744005000*t^59 - 19084941466895353544402864691735000*t^57 + 2175683327226070304061926574857790000*t^55 - 215392649395380960102130730910921210000*t^53 + 18550691929177185188796009199703089211250*t^51 - 1391301894688288889159700689977731690843750*t^49 + 90898390452968207425100445078545137135125000*t^47 - 5171640004192559590870188480521436486477375000*t^45 + 255996180207531699748074329785811106080630062500*t^43 - 11007835748923863089167196180789877561467092687500*t^41 + 410292059732616715141686403102168163654682545625000*t^39 - 13218539837472564605216940204291591707309555056875000*t^37 + 366814480489863667794770090669091669877840152828281250*t^35 - 8730184635658755293515528157924381743092595637313093750*t^33 + 177289903370300876729853802591695136936649634480819750000*t^31 - 3053326113599626210347482155745860691686743704947451250000*t^29 + 44273228647194580050038491258314980029457783721738043125000*t^27 - 535858732936734399915983118333398551391023520218277694375000*t^25 + 5358587329367343999159831183333985513910235202182776943750000*t^23 - 43732986913868968767336686754306397903848048585556211831250000*t^21 + 286997726622265107535647006825135736244002818842712640142578125*t^19 - 1487170037951737375411989035366612451446196424912238226193359375*t^17 + 5948680151806949501647956141466449805784785699648952904773437500*t^15 - 17846040455420848504943868424399349417354357098946858714320312500*t^13 + 38666420986745171760711714919531923737601107047718193881027343750*t^11 - 57477112277594174238895792447952859609947591557418936850175781250*t^9 + 54452001105089217700006540213850077525213507791238992805429687500*t^7 - 29320308287355732607695829345919272513576504195282534587539062500*t^5 + 7330077071838933151923957336479818128394126048820633646884765625*t^3 - 536347102817482913555411512425352545980058003572241486357421875*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
Positive weights:   83 out of 83
Indefinite weights: 0 out of 83
Negative weights:   0 out of 83
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (15.595096275507712852 + 3.0813271892427477918e-1217j)  +/-  (9.2e-494, 9.2e-494j)
| (-16.298682806682770332 + 5.0889479285945034088e-1218j)  +/-  (1.06e-494, 1.06e-494j)
| (17.150345541912654317 + 2.2361797497827448715e-1220j)  +/-  (2.54e-496, 2.54e-496j)
| (13.335350551702226366 - 2.5567922029010476272e-1214j)  +/-  (5.62e-491, 5.62e-491j)
| (-14.968330032009443381 + 2.2266963683151788022e-1215j)  +/-  (8.25e-493, 8.25e-493j)
| (-13.84965897407668806 - 4.4879126056837784595e-1213j)  +/-  (1.87e-491, 1.87e-491j)
| (-14.391186335084795215 - 1.4173808715574656869e-1214j)  +/-  (4.53e-492, 4.53e-492j)
| (-17.150345541912654317 + 4.2537415308062802248e-1219j)  +/-  (2.71e-496, 2.71e-496j)
| (-8.5773186131023563132 - 1.587520178304760775e-1211j)  +/-  (2.28e-490, 2.28e-490j)
| (10.598402445600750372 - 5.6247544232640009105e-1216j)  +/-  (9.13e-490, 9.13e-490j)
| (2.067201362652794349 + 6.3969529017977572979e-1228j)  +/-  (2.64e-502, 2.64e-502j)
| (-8.9692326561211520103 + 2.895397478068236882e-1214j)  +/-  (3.56e-490, 3.56e-490j)
| (11.908033415906101647 - 3.973193493607698743e-1230j)  +/-  (5.52e-490, 5.52e-490j)
| (-5.9514790315015529679 + 1.1181617133289372237e-1233j)  +/-  (2.62e-493, 2.62e-493j)
| (-9.7701887842151328654 - 1.7781226072263112259e-1234j)  +/-  (7.29e-490, 7.29e-490j)
| (12.367911451744731514 + 2.091536055423541676e-1252j)  +/-  (3.11e-490, 3.11e-490j)
| (9.7701887842151328654 - 4.0735384734309250894e-1258j)  +/-  (7.17e-490, 7.17e-490j)
| (-10.598402445600750372 - 1.0016671070840672491e-1297j)  +/-  (9.01e-490, 9.01e-490j)
| (-2.7609173254183997214 - 1.0920993195440471276e-1359j)  +/-  (2.19e-500, 2.19e-500j)
| (-13.335350551702226366 + 9.2841860493582169583e-1371j)  +/-  (5.57e-491, 5.57e-491j)
| (-12.367911451744731514 - 1.3798169916932792318e-1425j)  +/-  (3.11e-490, 3.11e-490j)
| (5.9514790315015529679 + 1.448044459276666195e-1453j)  +/-  (2.71e-493, 2.71e-493j)
| (4.8714791631163448674 + 5.9826020172587415972e-1455j)  +/-  (2.69e-495, 2.69e-495j)
| (-5.5891415545461454926 - 3.2858309446544632499e-1450j)  +/-  (5.36e-494, 5.36e-494j)
| (16.298682806682770332 + 5.812699031607739136e-1453j)  +/-  (1.03e-494, 1.03e-494j)
| (-4.5157446065853503557 - 2.7499143505846093125e-1455j)  +/-  (5.26e-496, 5.26e-496j)
| (13.84965897407668806 + 2.4404432486307675622e-1449j)  +/-  (1.84e-491, 1.84e-491j)
| (-3.4587326824195342652 - 1.8928514707339160413e-1467j)  +/-  (1.8e-498, 1.8e-498j)
| (5.2292122600311196315 + 4.1043017470992250383e-1464j)  +/-  (1.29e-494, 1.29e-494j)
| (-4.8714791631163448674 - 4.3380280698309925601e-1459j)  +/-  (2.72e-495, 2.72e-495j)
| (-7.8080251702695524225 + 2.7309760952007953929e-1464j)  +/-  (4.1e-491, 4.1e-491j)
| (3.1092413666939979881 + 1.9839993964172810531e-1484j)  +/-  (2.37e-499, 2.37e-499j)
| (3.8095410686381154775 - 1.3596925266826202263e-1483j)  +/-  (1.15e-497, 1.15e-497j)
| (14.391186335084795215 - 1.7171586648368218327e-1475j)  +/-  (4.53e-492, 4.53e-492j)
| (8.19040105611860002 + 7.898007919723141811e-1477j)  +/-  (1.33e-490, 1.33e-490j)
| (12.842729957107753192 - 2.3076557045933553103e-1476j)  +/-  (1.51e-490, 1.51e-490j)
| (4.5157446065853503557 - 3.1631399212303068549e-1491j)  +/-  (5.25e-496, 5.25e-496j)
| (-15.595096275507712852 + 1.3911171552050631082e-1484j)  +/-  (9.49e-494, 9.49e-494j)
| (10.180504027326547598 - 1.3145772716539053203e-1489j)  +/-  (9.03e-490, 9.03e-490j)
| (1.0319411461815301009 - 4.1229338890241423674e-1518j)  +/-  (1.2e-505, 1.2e-505j)
| (-1.3764925316769409912 + 2.0132122020328061866e-1517j)  +/-  (1.32e-504, 1.32e-504j)
| (11.024827460546718582 - 1.4045478862586275579e-1502j)  +/-  (8.03e-490, 8.03e-490j)
| (-11.908033415906101647 - 1.6795436351799814197e-1523j)  +/-  (5.61e-490, 5.61e-490j)
| (4.1618233754045301348 + 7.0475209398267235855e-1554j)  +/-  (1.02e-496, 1.02e-496j)
| (14.968330032009443381 - 3.2673645751215216625e-1550j)  +/-  (8.64e-493, 8.64e-493j)
| (-3.1092413666939979881 + 1.2175784500182035367e-1556j)  +/-  (2.33e-499, 2.33e-499j)
| (-11.024827460546718582 + 8.8537615684158815283e-1548j)  +/-  (7.78e-490, 7.78e-490j)
| (-8.19040105611860002 - 2.5753940345649791184e-1556j)  +/-  (1.41e-490, 1.41e-490j)
| (11.460910957330330398 - 2.9042404580395818209e-1571j)  +/-  (8.74e-490, 8.74e-490j)
| (5.5891415545461454926 - 5.3769627725170270846e-1576j)  +/-  (5.02e-494, 5.02e-494j)
| (-9.3666591844227521161 - 1.0269876949157191433e-1570j)  +/-  (5.25e-490, 5.25e-490j)
| (-1.0319411461815301009 + 1.7668371051853488448e-1606j)  +/-  (1.17e-505, 1.17e-505j)
| (6.3164532042036952353 - 3.9458028097602783956e-1595j)  +/-  (8.34e-493, 8.34e-493j)
| (7.8080251702695524225 - 1.8499816834556881998e-1592j)  +/-  (4.39e-491, 4.39e-491j)
| (7.4297868429540199748 - 1.3640878057946573648e-1592j)  +/-  (2.03e-491, 2.03e-491j)
| (-7.0553243536893348518 - 3.1742730578080757486e-1590j)  +/-  (8.23e-492, 8.23e-492j)
| (-2.067201362652794349 + 6.9718797761942173952e-1614j)  +/-  (2.57e-502, 2.57e-502j)
| (-5.2292122600311196315 - 5.3846840430431930661e-1606j)  +/-  (1.27e-494, 1.27e-494j)
| (8.5773186131023563132 + 9.5525551036399923265e-1600j)  +/-  (2.33e-490, 2.33e-490j)
| (0.68775739911216287967 + 2.4430742238435766259e-1621j)  +/-  (4.15e-507, 4.15e-507j)
| (-4.1618233754045301348 + 4.6911242762738138386e-1612j)  +/-  (1.01e-496, 1.01e-496j)
| (6.68431170415856585 + 2.2817405726713331504e-1606j)  +/-  (2.76e-492, 2.76e-492j)
| (-2.4136168353313809222 + 1.7063884786412442785e-1616j)  +/-  (2.64e-501, 2.64e-501j)
| (2.7609173254183997214 - 4.0624213678080400389e-1615j)  +/-  (2.35e-500, 2.35e-500j)
| (-1.7215367604059473641 - 4.4461757761314517012e-1618j)  +/-  (1.66e-503, 1.66e-503j)
| (3.4587326824195342652 + 3.0901887545026424089e-1613j)  +/-  (1.77e-498, 1.77e-498j)
| (8.9692326561211520103 - 4.2507596137947434957e-1604j)  +/-  (3.53e-490, 3.53e-490j)
| (-0.68775739911216287967 - 2.3935686070984986196e-1651j)  +/-  (3.93e-507, 3.93e-507j)
| (-12.842729957107753192 + 1.9676939135493560381e-1632j)  +/-  (1.5e-490, 1.5e-490j)
| (-10.180504027326547598 - 1.2300105279791240418e-1675j)  +/-  (8.71e-490, 8.71e-490j)
| (1.7215367604059473641 - 1.6089333749790780966e-1713j)  +/-  (1.64e-503, 1.64e-503j)
| (-11.460910957330330398 + 3.4946251678308919446e-1699j)  +/-  (8.49e-490, 8.49e-490j)
| (-6.3164532042036952353 + 5.8503032800818489239e-1708j)  +/-  (8.8e-493, 8.8e-493j)
| (-1.387573640892603467e-1784 - 1.024396733394408224e-1784j)  +/-  (1.43e-1782, 1.43e-1782j)
| (-3.8095410686381154775 + 5.2481760048753583015e-1713j)  +/-  (1.22e-497, 1.22e-497j)
| (0.34381780246899930026 - 8.6555919315175590589e-1723j)  +/-  (1.03e-508, 1.03e-508j)
| (7.0553243536893348518 - 2.8457218522498590825e-1707j)  +/-  (7.97e-492, 7.97e-492j)
| (-0.34381780246899930026 - 2.6526896456538148868e-1776j)  +/-  (1.15e-508, 1.15e-508j)
| (-7.4297868429540199748 + 6.6308031413890292085e-1706j)  +/-  (2.03e-491, 2.03e-491j)
| (-6.68431170415856585 - 1.0191638864666639525e-1707j)  +/-  (2.69e-492, 2.69e-492j)
| (2.4136168353313809222 + 4.4458264439144032252e-1717j)  +/-  (2.64e-501, 2.64e-501j)
| (1.3764925316769409912 + 5.2231000679331945888e-1720j)  +/-  (1.21e-504, 1.21e-504j)
| (9.3666591844227521161 + 3.1313581273397155355e-1706j)  +/-  (5.32e-490, 5.32e-490j)
-------------------------------------------------
The weights are:
| (4.0544430534687449239e-54 + 5.3618940820356572611e-1248j)  +/-  (6.17e-156, 3.66e-400j)
| (6.2550892758622243539e-59 + 6.5933375485405657428e-1250j)  +/-  (1.77e-158, 1.05e-402j)
| (5.2955140842001696722e-65 + 1.8206501889126650674e-1253j)  +/-  (1.5e-159, 8.93e-404j)
| (4.8594747313331045597e-40 + 6.4754777600346444382e-1241j)  +/-  (5.7e-151, 3.38e-395j)
| (5.3240473055003372283e-50 + 2.3239974357086069668e-1245j)  +/-  (6.13e-156, 3.64e-400j)
| (4.6869593991794793723e-43 + 8.3585045145263466671e-1242j)  +/-  (5.69e-154, 3.37e-398j)
| (2.3696500979544480181e-46 - 1.7043635735636282743e-1243j)  +/-  (5.96e-155, 3.54e-399j)
| (5.2955140842001696722e-65 - 5.4638865321223740396e-1253j)  +/-  (5.77e-162, 3.42e-406j)
| (1.6429548776854720758e-17 - 1.1187974073974414262e-1227j)  +/-  (3.12e-141, 1.85e-385j)
| (6.8375812482760403332e-26 + 8.7775181829805528552e-1234j)  +/-  (1.31e-149, 7.79e-394j)
| (0.016295541586602304412 - 7.7193050828645877178e-1222j)  +/-  (4.6e-99, 2.73e-343j)
| (5.3477399374868958323e-19 - 1.1999831485171999398e-1228j)  +/-  (8.67e-143, 5.14e-387j)
| (2.9203099082861514161e-32 - 5.3696168068364875405e-1237j)  +/-  (3.03e-153, 1.8e-397j)
| (2.9524038960487724008e-09 + 1.3319137259127202147e-1224j)  +/-  (1.76e-132, 1.05e-376j)
| (3.0349815734773980157e-22 - 9.4022046332999081598e-1231j)  +/-  (5.4e-146, 3.21e-390j)
| (1.132894129228898374e-34 + 3.2710097924841466273e-1238j)  +/-  (1.45e-154, 8.6e-399j)
| (3.0349815734773980157e-22 + 6.1118536145680680671e-1232j)  +/-  (1.57e-148, 9.3e-393j)
| (6.8375812482760403332e-26 - 8.3286812114989325615e-1233j)  +/-  (3.28e-149, 1.95e-393j)
| (0.003068916436716661888 - 6.1306158763546604077e-1222j)  +/-  (8.34e-115, 4.95e-359j)
| (4.8594747313331045597e-40 - 2.9823258089581822352e-1240j)  +/-  (7.35e-156, 4.36e-400j)
| (1.132894129228898374e-34 - 1.807502685347011168e-1237j)  +/-  (3.39e-154, 2.01e-398j)
| (2.9524038960487724008e-09 + 2.4072955421307309106e-1225j)  +/-  (3.86e-139, 2.29e-383j)
| (1.0000627695384993322e-06 - 4.7863127601267840651e-1224j)  +/-  (6.91e-134, 4.1e-378j)
| (2.3723504629839399159e-08 - 3.3177334042724427073e-1224j)  +/-  (1.83e-135, 1.08e-379j)
| (6.2550892758622243539e-59 - 2.0464866472381771554e-1250j)  +/-  (1.46e-167, 8.68e-412j)
| (5.2824532289692202139e-06 + 3.6423849351139662951e-1223j)  +/-  (1.71e-131, 1.01e-375j)
| (4.6869593991794793723e-43 - 1.9649311532539129904e-1242j)  +/-  (8.23e-162, 4.89e-406j)
| (0.00035272516569553686191 - 2.3617450733068462831e-1222j)  +/-  (5.17e-126, 3.07e-370j)
| (1.6517387651290830913e-07 + 1.8947727155367763984e-1224j)  +/-  (1.43e-137, 8.5e-382j)
| (1.0000627695384993322e-06 - 1.7369540111537724537e-1223j)  +/-  (2.41e-133, 1.43e-377j)
| (8.7606138649225398626e-15 - 7.8307250234290582149e-1227j)  +/-  (7.77e-145, 4.61e-389j)
| (0.0011075029274131003031 + 1.8329729761065820529e-1222j)  +/-  (3.31e-127, 1.96e-371j)
| (9.896613223853563407e-05 + 5.1695489324365080281e-1223j)  +/-  (1.09e-131, 6.45e-376j)
| (2.3696500979544480181e-46 + 4.3140178077943467406e-1244j)  +/-  (6.41e-164, 3.8e-408j)
| (4.1598247740561635745e-16 + 7.8295212938134356867e-1229j)  +/-  (4.26e-151, 2.53e-395j)
| (2.9490145732226834318e-37 - 1.631888131025943446e-1239j)  +/-  (4.33e-160, 2.57e-404j)
| (5.2824532289692202139e-06 + 1.1299191410469356805e-1223j)  +/-  (1.95e-137, 1.16e-381j)
| (4.0544430534687449239e-54 - 1.8469255959652502725e-1247j)  +/-  (4.87e-168, 2.89e-412j)
| (5.1541064032524119721e-24 - 7.7905180380548995524e-1233j)  +/-  (2.43e-155, 1.44e-399j)
| (0.080661361638098404053 + 1.9024454028017555398e-1221j)  +/-  (9.09e-115, 5.39e-359j)
| (0.053335000008510907116 - 2.0643883945707595383e-1221j)  +/-  (1.28e-119, 7.61e-364j)
| (6.9482947491399404281e-28 - 8.6558077378249137521e-1235j)  +/-  (3.51e-157, 2.08e-401j)
| (2.9203099082861514161e-32 + 3.3027144562753999684e-1236j)  +/-  (4.49e-161, 2.67e-405j)
| (2.4412765589851721215e-05 - 2.4965427098927549742e-1223j)  +/-  (9.64e-139, 5.72e-383j)
| (5.3240473055003372283e-50 - 6.3078724291398611791e-1246j)  +/-  (1.03e-166, 6.13e-411j)
| (0.0011075029274131003031 + 3.9174476356020186278e-1222j)  +/-  (7.74e-136, 4.6e-380j)
| (6.9482947491399404281e-28 + 6.932933506740504825e-1234j)  +/-  (2.54e-159, 1.5e-403j)
| (4.1598247740561635745e-16 + 3.3925178529608176292e-1227j)  +/-  (8.71e-153, 5.17e-397j)
| (5.2827856976275878181e-30 + 7.3831949718645337709e-1236j)  +/-  (1.11e-158, 6.61e-403j)
| (2.3723504629839399159e-08 - 6.9984068514386614805e-1225j)  +/-  (1.88e-146, 1.12e-390j)
| (1.419424616430391347e-20 + 9.7186859088761817471e-1230j)  +/-  (7.27e-156, 4.31e-400j)
| (0.080661361638098404053 + 2.4228119382406946402e-1221j)  +/-  (9.52e-127, 5.65e-371j)
| (3.1709125245935780363e-10 - 7.6958877862014364741e-1226j)  +/-  (1.15e-149, 6.81e-394j)
| (8.7606138649225398626e-15 - 3.6769128105342499851e-1228j)  +/-  (2.69e-154, 1.6e-398j)
| (1.5471507548272158546e-13 + 1.5817034174810450246e-1227j)  +/-  (1.24e-153, 7.38e-398j)
| (2.3077256569653772179e-12 - 6.4242846260575162593e-1226j)  +/-  (7.91e-155, 4.69e-399j)
| (0.016295541586602304412 - 1.2621542428164120161e-1221j)  +/-  (3.19e-140, 1.89e-384j)
| (1.6517387651290830913e-07 + 7.8132445757780423052e-1224j)  +/-  (7.96e-150, 4.73e-394j)
| (1.6429548776854720758e-17 - 1.5209083663207806902e-1229j)  +/-  (6.93e-157, 4.11e-401j)
| (0.10834469619534734768 - 2.2867779786882696277e-1221j)  +/-  (2.58e-136, 1.53e-380j)
| (2.4412765589851721215e-05 - 7.2026510905958598782e-1223j)  +/-  (2.08e-148, 1.23e-392j)
| (2.9258349448162527932e-11 + 2.2813680774535090687e-1226j)  +/-  (6.06e-153, 3.59e-397j)
| (0.0075167835944291675202 + 9.054006867509433809e-1222j)  +/-  (1.18e-143, 7.02e-388j)
| (0.003068916436716661888 - 3.1449751199024873651e-1222j)  +/-  (1.05e-145, 6.26e-390j)
| (0.031303378762543260981 + 1.6611385138579098023e-1221j)  +/-  (6.96e-142, 4.13e-386j)
| (0.00035272516569553686191 - 1.0043952220165040084e-1222j)  +/-  (8.29e-147, 4.92e-391j)
| (5.3477399374868958323e-19 + 2.6826573896393151118e-1230j)  +/-  (4.5e-158, 2.67e-402j)
| (0.10834469619534734768 - 2.6854629968598959524e-1221j)  +/-  (5.26e-142, 3.12e-386j)
| (2.9490145732226834318e-37 + 8.1953394419795230231e-1239j)  +/-  (3.8e-169, 2.26e-413j)
| (5.1541064032524119721e-24 + 9.1162055677350657438e-1232j)  +/-  (3.32e-163, 1.97e-407j)
| (0.031303378762543260981 + 1.1057994821371946362e-1221j)  +/-  (3.75e-148, 2.23e-392j)
| (5.2827856976275878181e-30 - 5.1309177755578963806e-1235j)  +/-  (4.2e-166, 2.49e-410j)
| (3.1709125245935780363e-10 - 5.0695716907525437365e-1225j)  +/-  (2.64e-157, 1.57e-401j)
| (0.13715536747171093363 - 2.779224152134976359e-1221j)  +/-  (1.17e-148, 6.95e-393j)
| (9.896613223853563407e-05 + 1.3430476388674190002e-1222j)  +/-  (5.19e-153, 3.1e-397j)
| (0.12930655633635467228 + 2.5945320361959417604e-1221j)  +/-  (1.85e-149, 1.11e-393j)
| (2.3077256569653772179e-12 - 6.2550551319111904541e-1227j)  +/-  (1.84e-158, 1.1e-402j)
| (0.12930655633635467228 + 2.8112159287229992523e-1221j)  +/-  (1.04e-150, 6.12e-395j)
| (1.5471507548272158546e-13 + 2.2061761307993757749e-1226j)  +/-  (1.87e-159, 1.11e-403j)
| (2.9258349448162527932e-11 + 1.8391754522711882445e-1225j)  +/-  (2.98e-158, 1.77e-402j)
| (0.0075167835944291675202 + 5.0775169831912265415e-1222j)  +/-  (4.21e-154, 2.34e-398j)
| (0.053335000008510907116 - 1.4934349255664943612e-1221j)  +/-  (2.43e-153, 1.25e-397j)
| (1.419424616430391347e-20 - 4.2737523818609544348e-1231j)  +/-  (7.87e-164, 5.33e-408j)
