Starting with polynomial:
P : t
Extension levels are: 1 76
-------------------------------------------------
Trying to find an order 76 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^77 - 2926*t^75 + 4059825*t^73 - 3556406700*t^71 + 2209417662375*t^69 - 1036658767186350*t^67 + 382008755708169975*t^65 - 113511173124713364000*t^63 + 27710915139070649986500*t^61 - 5634552744944365497255000*t^59 + 964071974659980936580330500*t^57 - 139878079232484506798382498000*t^55 + 17309912305019957716299834127500*t^53 - 1834850704332115517927782417515000*t^51 + 167102474858817663239851613023687500*t^49 - 13100834028931304798004366461057100000*t^47 + 885125099079671280415170009025170318750*t^45 - 51545520475816151035942253466759918562500*t^43 + 2585866943870110243636436382249122581218750*t^41 - 111600573367025810514835675444435816663125000*t^39 + 4134801243248306279574661775216347007368781250*t^37 - 131132268000160570580796416299718433662267062500*t^35 + 3546531793640706340707903077196930364956768281250*t^33 - 81416034219230128169294470641738227508572767500000*t^31 + 1577435662997583733280080368683678157978597370312500*t^29 - 25617555167080759828468505187422933285572421293875000*t^27 + 345836994755590257684324820030209599355227687467312500*t^25 - 3842633275062113974270275778113439992835863194081250000*t^23 + 34720936378239815553227848995096439935266906717948437500*t^21 - 251427470325184871247512009964491461600208634854109375000*t^19 + 1433136580853553766110818456797601331121189218668423437500*t^17 - 6287308870841397167453913229821734872015539798029212500000*t^15 + 20630232232448334455708152785352567548800989962283353515625*t^13 - 48762367094877881440764724765378796024438703547215199218750*t^11 + 78880299712302455271825290061642170039533196914612822265625*t^9 - 81134022561225382565306012634831946326377002540744617187500*t^7 + 47328179827381473163095174036985302023719918148767693359375*t^5 - 12791399953346344098133830820806838384789167067234511718750*t^3 + 1009847364737869270905302433221592504062302663202724609375*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:   77 out of 77
Indefinite weights: 0 out of 77
Negative weights:   0 out of 77
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-13.669053480117322936 - 7.3473014642362396924e-1257j)  +/-  (3.63e-493, 3.63e-493j)
| (16.467057331771378705 - 3.5162154951869530755e-1267j)  +/-  (3.15e-497, 3.15e-497j)
| (-16.467057331771378705 - 2.0113348513256605386e-1266j)  +/-  (2.94e-497, 2.94e-497j)
| (12.596882276318064679 - 7.1913521302864283867e-1263j)  +/-  (3.65e-492, 3.65e-492j)
| (-14.254762154604086397 + 6.1170816795291108112e-1261j)  +/-  (7.64e-494, 7.64e-494j)
| (-14.890555534365297146 - 1.0051176506419250981e-1262j)  +/-  (9.82e-495, 9.82e-495j)
| (12.0963272441909875 + 5.1358836431584513236e-1268j)  +/-  (8.56e-492, 8.56e-492j)
| (-4.3262177748601627088 + 1.3053218051919738239e-1273j)  +/-  (3.91e-497, 3.91e-497j)
| (1.4289991902668753391 - 7.0623297922417114039e-1281j)  +/-  (9.61e-505, 9.61e-505j)
| (-11.61366154160407123 + 7.1130352716588397934e-1266j)  +/-  (1.65e-491, 1.65e-491j)
| (11.61366154160407123 + 1.4235379880185529754e-1285j)  +/-  (1.67e-491, 1.67e-491j)
| (-12.596882276318064679 + 7.8342728689002822885e-1284j)  +/-  (3.66e-492, 3.66e-492j)
| (13.669053480117322936 + 1.94292858245883668e-1305j)  +/-  (3.91e-493, 3.91e-493j)
| (-15.603952221982934883 - 1.5873030637945431657e-1303j)  +/-  (6.37e-496, 6.37e-496j)
| (-13.119258863486208731 - 6.3901771927130210119e-1328j)  +/-  (1.3e-492, 1.3e-492j)
| (6.9665738139027985269 + 1.0683612100536576385e-1346j)  +/-  (5.59e-493, 5.59e-493j)
| (14.254762154604086397 - 1.1478098845500429717e-1344j)  +/-  (7.06e-494, 7.06e-494j)
| (11.145988658308416001 + 1.422386376220121722e-1344j)  +/-  (1.79e-491, 1.79e-491j)
| (-1.7873605283198567717 - 3.7339660157396950079e-1374j)  +/-  (1.16e-503, 1.16e-503j)
| (13.119258863486208731 - 3.911585309369611045e-1365j)  +/-  (1.39e-492, 1.39e-492j)
| (4.695402894232470889 + 1.2963880052691075297e-1383j)  +/-  (1.96e-496, 1.96e-496j)
| (-12.0963272441909875 - 6.9103335828305596799e-1403j)  +/-  (8.62e-492, 8.62e-492j)
| (-5.4407217977754342435 + 2.3738469078243152283e-1421j)  +/-  (4.14e-495, 4.14e-495j)
| (15.603952221982934883 + 8.9401731500014490399e-1436j)  +/-  (7.62e-496, 7.62e-496j)
| (10.247245803464717138 + 1.3330696489677217496e-1465j)  +/-  (3.1e-491, 3.1e-491j)
| (-9.8130378914757847718 - 1.7057627072826224161e-1512j)  +/-  (2.81e-491, 2.81e-491j)
| (14.890555534365297146 - 1.7968226024685039533e-1545j)  +/-  (9.64e-495, 9.64e-495j)
| (5.8173522721323987268 + 1.921679729212318376e-1553j)  +/-  (2.21e-494, 2.21e-494j)
| (-10.247245803464717138 - 8.8138189606446257373e-1555j)  +/-  (3.01e-491, 3.01e-491j)
| (-1.4289991902668753391 + 9.1087738315477109815e-1581j)  +/-  (1.01e-504, 1.01e-504j)
| (8.5576993868166801366 - 1.6468617385406331838e-1568j)  +/-  (1.1e-491, 1.1e-491j)
| (4.3262177748601627088 + 3.2162375896049418984e-1574j)  +/-  (3.86e-497, 3.86e-497j)
| (7.3572155498719514997 - 3.5765776000386565392e-1570j)  +/-  (1.22e-492, 1.22e-492j)
| (-6.9665738139027985269 + 1.9651455659585593072e-1568j)  +/-  (5.46e-493, 5.46e-493j)
| (-1.0712329064392394604 - 6.4167541209309191541e-1583j)  +/-  (7.43e-506, 7.43e-506j)
| (-2.8675851315715495049 + 1.9755944758608789823e-1577j)  +/-  (1.93e-500, 1.93e-500j)
| (8.9691486249361082631 - 9.3666981780261612031e-1569j)  +/-  (1.57e-491, 1.57e-491j)
| (1.0712329064392394604 - 4.2130949712334175632e-1582j)  +/-  (7.1e-506, 7.1e-506j)
| (7.7522968661923361604 + 5.0891980594135825513e-1569j)  +/-  (2.51e-492, 2.51e-492j)
| (-7.7522968661923361604 - 1.1282701563351941117e-1566j)  +/-  (2.34e-492, 2.34e-492j)
| (-8.1522826606366504936 - 1.5232643100756066332e-1583j)  +/-  (7.6e-492, 7.6e-492j)
| (9.3873246922870788478 + 1.0271896941444792768e-1599j)  +/-  (2.09e-491, 2.09e-491j)
| (2.8675851315715495049 + 8.2791153871933434415e-1635j)  +/-  (1.89e-500, 1.89e-500j)
| (3.9590464804253638433 + 5.1662669688575861868e-1629j)  +/-  (4.73e-498, 4.73e-498j)
| (3.5936801634928907926 - 5.1882564173298707398e-1629j)  +/-  (9.97e-499, 9.97e-499j)
| (-2.506491889225198204 - 1.212711076078621049e-1632j)  +/-  (1.72e-501, 1.72e-501j)
| (-8.9691486249361082631 - 9.1380089577926679938e-1630j)  +/-  (1.67e-491, 1.67e-491j)
| (-11.145988658308416001 - 4.616336944880430999e-1675j)  +/-  (1.85e-491, 1.85e-491j)
| (6.5799576973794367095 - 5.6931733970636730308e-1700j)  +/-  (1.99e-493, 1.99e-493j)
| (5.0668245922874758726 + 8.6126454245242267662e-1702j)  +/-  (1.06e-495, 1.06e-495j)
| (10.691096357328416743 + 2.2723397742662667352e-1696j)  +/-  (2.6e-491, 2.6e-491j)
| (-3.5936801634928907926 + 3.3805176457063534447e-1706j)  +/-  (9.66e-499, 9.66e-499j)
| (-5.8173522721323987268 + 2.6214850409817235301e-1701j)  +/-  (2.16e-494, 2.16e-494j)
| (6.1969957516456103212 - 7.5092635828129893977e-1702j)  +/-  (6.62e-494, 6.62e-494j)
| (1.7873605283198567717 + 9.7314581197574164172e-1711j)  +/-  (1.21e-503, 1.21e-503j)
| (-2.1464717539023013483 + 1.2265688716617783282e-1709j)  +/-  (1.91e-502, 1.91e-502j)
| (-3.9590464804253638433 + 8.2405594479678129966e-1705j)  +/-  (4.52e-498, 4.52e-498j)
| (-7.3572155498719514997 - 8.4357924412471565082e-1699j)  +/-  (1.28e-492, 1.28e-492j)
| (5.4407217977754342435 - 6.5093292463729331568e-1719j)  +/-  (4.14e-495, 4.14e-495j)
| (-10.691096357328416743 + 1.9454554365890510318e-1713j)  +/-  (2.6e-491, 2.6e-491j)
| (-8.5576993868166801366 + 3.0055249602574199317e-1729j)  +/-  (1.09e-491, 1.09e-491j)
| (-4.695402894232470889 + 5.9508980716543655141e-1750j)  +/-  (1.91e-496, 1.91e-496j)
| (2.9445115654602530297e-1814 - 6.3095163113013575434e-1815j)  +/-  (2.32e-1812, 2.32e-1812j)
| (-5.0668245922874758726 + 2.1713971595320518329e-1750j)  +/-  (1.13e-495, 1.13e-495j)
| (0.71391011625077910063 + 2.9078059662205478886e-1764j)  +/-  (5.14e-507, 5.14e-507j)
| (3.2299219283980426818 + 5.2193000051440378557e-1755j)  +/-  (1.35e-499, 1.35e-499j)
| (-3.2299219283980426818 - 7.7502354079010814116e-1753j)  +/-  (1.45e-499, 1.45e-499j)
| (-0.35688166905672581735 - 7.5824854014193948686e-1762j)  +/-  (1.22e-508, 1.22e-508j)
| (8.1522826606366504936 - 7.6700914303559358545e-1747j)  +/-  (7.22e-492, 7.22e-492j)
| (-6.1969957516456103212 - 4.4366286010915859739e-1745j)  +/-  (6.73e-494, 6.73e-494j)
| (0.35688166905672581735 + 2.128966690056193195e-1803j)  +/-  (1.22e-508, 1.22e-508j)
| (-9.3873246922870788478 - 7.0811678697960665456e-1744j)  +/-  (2.07e-491, 2.07e-491j)
| (-0.71391011625077910063 + 1.1596682472465901797e-1767j)  +/-  (5.08e-507, 5.08e-507j)
| (-6.5799576973794367095 + 5.03917100766108921e-1753j)  +/-  (1.98e-493, 1.98e-493j)
| (9.8130378914757847718 - 1.3646343190252118223e-1752j)  +/-  (2.56e-491, 2.56e-491j)
| (2.1464717539023013483 + 6.8951867152423353692e-1764j)  +/-  (1.84e-502, 1.84e-502j)
| (2.506491889225198204 - 6.3788423743071024601e-1762j)  +/-  (1.58e-501, 1.58e-501j)
-------------------------------------------------
The weights are:
| (6.0433421504904167707e-42 - 4.2572774483131390615e-1297j)  +/-  (6.22e-158, 1.92e-401j)
| (5.2184705636769467762e-60 + 4.9664237214678928012e-1307j)  +/-  (2.45e-165, 7.55e-409j)
| (5.2184705636769467762e-60 - 7.2677317184936441797e-1307j)  +/-  (1.16e-164, 3.56e-408j)
| (7.1094797815049000609e-36 + 7.1693414677094319464e-1295j)  +/-  (2.48e-157, 7.63e-401j)
| (1.8224090828528017019e-45 + 6.813554282751268196e-1300j)  +/-  (1.02e-159, 3.15e-403j)
| (1.8967886101450954632e-49 - 1.2714935931905084808e-1301j)  +/-  (2.3e-161, 7.09e-405j)
| (3.3022583246728153431e-33 - 1.5877157757710823949e-1293j)  +/-  (2.68e-157, 8.24e-401j)
| (1.2669609886617577466e-05 + 3.5704589152296910665e-1278j)  +/-  (2.86e-127, 8.81e-371j)
| (0.051453686366146929097 + 1.8041826872670995769e-1277j)  +/-  (3.53e-95, 1.09e-338j)
| (9.753928293773677805e-31 - 7.1604768636141364682e-1292j)  +/-  (1.62e-155, 4.99e-399j)
| (9.753928293773677805e-31 + 2.8101352147345817693e-1292j)  +/-  (8.41e-157, 2.59e-400j)
| (7.1094797815049000609e-36 - 1.9472308405303054485e-1294j)  +/-  (1.61e-157, 4.95e-401j)
| (6.0433421504904167707e-42 + 6.1803795029284737668e-1298j)  +/-  (1.15e-162, 3.55e-406j)
| (4.1204126561639811776e-54 + 6.4680529248911057057e-1304j)  +/-  (2.4e-164, 7.38e-408j)
| (9.0146830726145794649e-39 + 8.1364482320566910135e-1296j)  +/-  (1.94e-158, 5.96e-402j)
| (4.4826264565655956756e-12 - 8.5263458218180329766e-1283j)  +/-  (1.04e-146, 3.2e-390j)
| (1.8224090828528017019e-45 - 1.03936408956247938e-1299j)  +/-  (8.85e-165, 2.73e-408j)
| (1.9395690716184472957e-28 - 4.0826419509235858155e-1291j)  +/-  (5.09e-158, 1.57e-401j)
| (0.028969609809574659344 - 3.0889845290297439806e-1277j)  +/-  (7.27e-115, 2.24e-358j)
| (9.0146830726145794649e-39 - 2.461178094598282501e-1296j)  +/-  (9.73e-162, 3e-405j)
| (2.4100116625816924372e-06 - 7.8427877176831319721e-1280j)  +/-  (5.02e-140, 1.55e-383j)
| (3.3022583246728153431e-33 + 4.0969408989614609388e-1293j)  +/-  (2.56e-160, 7.89e-404j)
| (5.5888323279589364922e-08 + 9.9073238428797266074e-1280j)  +/-  (2.82e-144, 8.7e-388j)
| (4.1204126561639811776e-54 - 4.6056378240797327786e-1304j)  +/-  (2.93e-169, 9.01e-413j)
| (2.7632652261350233683e-24 - 5.1754958825525409607e-1289j)  +/-  (2.77e-158, 8.54e-402j)
| (2.1077291104141965554e-22 - 1.2973123257663213771e-1287j)  +/-  (3.58e-159, 1.1e-402j)
| (1.8967886101450954632e-49 + 1.0250980175007691868e-1301j)  +/-  (2.86e-167, 8.82e-411j)
| (6.759211128150306357e-09 + 3.6898232271718634919e-1281j)  +/-  (3.81e-148, 1.17e-391j)
| (2.7632652261350233683e-24 + 1.3920511505906231516e-1288j)  +/-  (4.41e-160, 1.36e-403j)
| (0.051453686366146929097 + 3.6042808807055876623e-1277j)  +/-  (1.99e-120, 6.12e-364j)
| (2.0384881057776112456e-17 - 1.5917212848253696363e-1285j)  +/-  (4.02e-156, 1.24e-399j)
| (1.2669609886617577466e-05 + 1.8757119223252305106e-1279j)  +/-  (1.43e-143, 4.42e-387j)
| (2.761775110176846291e-13 + 2.0449411069947797972e-1283j)  +/-  (3.03e-153, 9.33e-397j)
| (4.4826264565655956756e-12 + 3.7826568219577673623e-1282j)  +/-  (3.89e-156, 1.2e-399j)
| (0.080357177736003871144 - 4.0057759095833379298e-1277j)  +/-  (7.77e-121, 2.39e-364j)
| (0.0023639069757304043772 + 1.5405857831126917687e-1277j)  +/-  (6.75e-139, 2.08e-382j)
| (5.6245234965401644635e-19 + 2.5614170090449462993e-1286j)  +/-  (1.63e-157, 5.02e-401j)
| (0.080357177736003871144 - 2.4056399565707882031e-1277j)  +/-  (1.65e-123, 5.07e-367j)
| (1.4127196117968260555e-14 - 4.4723433743992317604e-1284j)  +/-  (1.1e-154, 3.4e-398j)
| (1.4127196117968260555e-14 + 1.6481180533104762963e-1283j)  +/-  (5.2e-159, 1.6e-402j)
| (5.9463298287192859918e-16 - 3.0409861479267430954e-1284j)  +/-  (5.22e-160, 1.61e-403j)
| (1.2319562570455697905e-20 - 3.6742411376284010776e-1287j)  +/-  (4.42e-159, 1.36e-402j)
| (0.0023639069757304043772 + 3.0871499255404040689e-1278j)  +/-  (3.62e-143, 1.12e-386j)
| (5.7689061536278805487e-05 - 4.1816450478817956036e-1279j)  +/-  (2.75e-147, 8.46e-391j)
| (0.00022818530663290889431 + 8.7040583493165538129e-1279j)  +/-  (2.62e-146, 8.05e-390j)
| (0.0062175915613133015819 - 2.0005411003172927245e-1277j)  +/-  (1.16e-143, 3.58e-387j)
| (5.6245234965401644635e-19 - 7.792925991651175749e-1286j)  +/-  (8.27e-164, 2.55e-407j)
| (1.9395690716184472957e-28 + 1.0482929867923762267e-1290j)  +/-  (2.45e-167, 7.54e-411j)
| (6.088264954292204719e-11 + 3.2547500359739462638e-1282j)  +/-  (6.15e-156, 1.89e-399j)
| (3.9574516733997994766e-07 + 3.0512348574584048164e-1280j)  +/-  (9.14e-153, 2.82e-396j)
| (2.7129145316346265226e-26 + 4.9755039614242987136e-1290j)  +/-  (3.03e-164, 9.32e-408j)
| (0.00022818530663290889431 + 9.5540062616254527093e-1278j)  +/-  (5.65e-153, 1.74e-396j)
| (6.759211128150306357e-09 - 2.5806048468686344857e-1280j)  +/-  (1.22e-159, 3.75e-403j)
| (6.9673351711161180261e-10 - 1.1415064799202331244e-1281j)  +/-  (7.65e-156, 2.36e-399j)
| (0.028969609809574659344 - 1.2735989575595403789e-1277j)  +/-  (7.22e-146, 2.22e-389j)
| (0.014327962022984623326 + 2.5327075134604882721e-1277j)  +/-  (1.13e-147, 3.47e-391j)
| (5.7689061536278805487e-05 - 9.5970810891820850753e-1278j)  +/-  (1.35e-154, 4.17e-398j)
| (2.761775110176846291e-13 - 8.2060213354103712315e-1283j)  +/-  (1.24e-162, 3.82e-406j)
| (5.5888323279589364922e-08 - 1.1023273020895848847e-1280j)  +/-  (6.09e-156, 1.87e-399j)
| (2.7129145316346265226e-26 - 1.3020986808312983376e-1289j)  +/-  (7.34e-169, 2.26e-412j)
| (2.0384881057776112456e-17 + 5.1168723383540945853e-1285j)  +/-  (4.9e-165, 1.51e-408j)
| (2.4100116625816924372e-06 + 1.9568512294947335311e-1278j)  +/-  (8.61e-159, 2.65e-402j)
| (0.14236543797973869594 + 4.0024860031202653632e-1277j)  +/-  (2.09e-150, 6.42e-394j)
| (3.9574516733997994766e-07 - 3.959759217002481409e-1279j)  +/-  (1.17e-159, 3.6e-403j)
| (0.11043046816321127857 + 3.0218043552887579846e-1277j)  +/-  (5.98e-152, 1.84e-395j)
| (0.00078608827064711509288 - 1.6940693958219980691e-1278j)  +/-  (4.05e-157, 1.25e-400j)
| (0.00078608827064711509288 - 1.1834036635988680326e-1277j)  +/-  (1.75e-156, 5.4e-400j)
| (0.1336093769597086214 - 4.2290963622602556174e-1277j)  +/-  (6.44e-153, 1.98e-396j)
| (5.9463298287192859918e-16 + 8.8787264137529899955e-1285j)  +/-  (5.51e-165, 1.7e-408j)
| (6.9673351711161180261e-10 + 6.6193069454987908709e-1281j)  +/-  (1.5e-162, 4.61e-406j)
| (0.1336093769597086214 - 3.5795341017768886108e-1277j)  +/-  (1.87e-155, 5.74e-399j)
| (1.2319562570455697905e-20 + 1.0657215849418137402e-1286j)  +/-  (2.45e-168, 7.55e-412j)
| (0.11043046816321127857 + 4.2280037349306741777e-1277j)  +/-  (2.31e-156, 7.12e-400j)
| (6.088264954292204719e-11 - 1.6284382841195375649e-1281j)  +/-  (2.67e-163, 8.21e-407j)
| (2.1077291104141965554e-22 + 4.6600272765191709705e-1288j)  +/-  (7.86e-170, 2.42e-413j)
| (0.014327962022984623326 + 8.4555562040552474327e-1278j)  +/-  (2.47e-160, 7.64e-404j)
| (0.0062175915613133015819 - 5.2739070258319155772e-1278j)  +/-  (1.44e-160, 4.41e-404j)
