Starting with polynomial:
P : t
Extension levels are: 1 36 38
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P2 : t^37 - 37/4*t^35 + 629/16*t^33 - 407/4*t^31 + 5735/32*t^29 - 232841/1024*t^27 + 878787/4096*t^25 - 627705/4096*t^23 + 5476185/65536*t^21 - 9126975/262144*t^19 + 11560835/1048576*t^17 - 1374365/524288*t^15 + 1924111/4194304*t^13 - 1924111/33554432*t^11 + 657305/134217728*t^9 - 35853/134217728*t^7 + 35853/4294967296*t^5 - 2109/17179869184*t^3 + 37/68719476736*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^75 - 19*t^73 + 2773/16*t^71 - 8085/8*t^69 + 1083461/256*t^67 - 3470533/256*t^65 + 8843263/256*t^63 - 2300727/32*t^61 + 1020317415/8192*t^59 - 1491565961/8192*t^57 + 237967863049/1048576*t^55 - 127436677887/524288*t^53 + 3775144262643/16777216*t^51 - 3033774827175/16777216*t^49 + 8491494002145/67108864*t^47 - 1296042427365/16777216*t^45 + 176912705973465/4294967296*t^43 - 82401584774355/4294967296*t^41 + 536069842313775/68719476736*t^39 - 94996094126115/34359738368*t^37 + 936954702926515/1099511627776*t^35 - 250352961919515/1099511627776*t^33 + 115505564632885/2199023255552*t^31 - 715187791675/68719476736*t^29 + 123844579170319/70368744177664*t^27 - 17736182025705/70368744177664*t^25 + 68191278865263/2251799813685248*t^23 - 3397580313853/1125899906842624*t^21 + 8860027645865/36028797018963968*t^19 - 580273254077/36028797018963968*t^17 + 119527914549/144115188075855872*t^15 - 1176468391/36028797018963968*t^13 + 17472589069/18446744073709551616*t^11 - 355004455/18446744073709551616*t^9 + 75149997/295147905179352825856*t^7 - 288933/147573952589676412928*t^5 + 33781/4722366482869645213696*t^3 - 37/4722366482869645213696*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
  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:   75 out of 75
Indefinite weights: 0 out of 75
Negative weights:   0 out of 75
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99909896620468147236 + 9.917533145140330435e-1862j)  +/-  (2.45e-482, 2.45e-482j)
| (-0.96773294693349883869 - 3.8923104186080495957e-1884j)  +/-  (4.76e-483, 4.76e-483j)
| (-0.92788902729650932713 - 8.9261189429356082761e-1887j)  +/-  (6.15e-484, 6.15e-484j)
| (-0.99190043525887688731 + 1.1444981041834900226e-1884j)  +/-  (1.6e-482, 1.6e-482j)
| (0.94287744546108417004 + 1.7970999554339664645e-1884j)  +/-  (1.29e-483, 1.29e-483j)
| (0.92788902729650932713 - 5.6788212335558540499e-1890j)  +/-  (5.7e-484, 5.7e-484j)
| (0.99190043525887688731 + 2.3024274853451384952e-1916j)  +/-  (1.56e-482, 1.56e-482j)
| (-0.94287744546108417004 - 9.2810388624570823285e-1948j)  +/-  (1.27e-483, 1.27e-483j)
| (-0.89292585814956848973 - 1.3143027934785005315e-1951j)  +/-  (9.15e-485, 9.15e-485j)
| (0.99639748854252650165 + 8.1152159965111251051e-1969j)  +/-  (2.07e-482, 2.07e-482j)
| (0.85152913773331129989 - 1.2200247782124184217e-2003j)  +/-  (8.74e-486, 8.74e-486j)
| (1 - 3.5676361031482401294e-2013j)  +/-  (1.25e-482, 1.25e-482j)
| (-0.91122849038813570283 - 6.9757880473011393917e-2042j)  +/-  (2.43e-484, 2.43e-484j)
| (-0.82850964924384212353 + 5.6578109318667704522e-2044j)  +/-  (2.3e-486, 2.3e-486j)
| (0.98561591034770846226 + 3.5123779752215188537e-2038j)  +/-  (1.19e-482, 1.19e-482j)
| (0.87301411316118815875 - 1.1243739005633381921e-2058j)  +/-  (2.91e-485, 2.91e-485j)
| (0.89292585814956848973 - 4.6563668625496206629e-2057j)  +/-  (8.85e-485, 8.85e-485j)
| (-1 - 2.6363333737653949134e-2051j)  +/-  (2.06e-482, 2.06e-482j)
| (-0.75067230525272435529 - 1.34820153324679569e-2063j)  +/-  (2.55e-488, 2.55e-488j)
| (-0.85152913773331129989 - 5.0281063384865447521e-2061j)  +/-  (8.77e-486, 8.77e-486j)
| (0.82850964924384212353 + 4.1508354306646493381e-2063j)  +/-  (2.24e-486, 2.24e-486j)
| (0.77803575431843950714 - 1.1377099909223889148e-2063j)  +/-  (1.25e-487, 1.25e-487j)
| (-0.95616673473925093551 + 8.5825231127097660614e-2058j)  +/-  (2.59e-483, 2.59e-483j)
| (-0.87301411316118815875 - 1.27992324548556848e-2060j)  +/-  (3e-485, 3e-485j)
| (-0.77803575431843950714 - 9.8905769047561523861e-2063j)  +/-  (1.21e-487, 1.21e-487j)
| (-0.99909896620468147236 + 4.5093880669876273316e-2055j)  +/-  (2.28e-482, 2.28e-482j)
| (0.75067230525272435529 - 4.990639425338201647e-2064j)  +/-  (2.63e-488, 2.63e-488j)
| (0.80399713036694054483 + 4.2554367011066622983e-2063j)  +/-  (6.24e-487, 6.24e-487j)
| (-0.99639748854252650165 - 4.6042440116764777301e-2057j)  +/-  (1.99e-482, 1.99e-482j)
| (-0.66067472339008144191 + 3.015153522727043022e-2067j)  +/-  (1.11e-490, 1.11e-490j)
| (0.97755523894768619434 - 5.22936434445100476e-2057j)  +/-  (8.05e-483, 8.05e-483j)
| (0.91122849038813570283 - 3.2008066498739122253e-2073j)  +/-  (2.34e-484, 2.34e-484j)
| (0.66067472339008144191 - 7.1008435542776752621e-2083j)  +/-  (1.02e-490, 1.02e-490j)
| (-0.80399713036694054483 + 1.1056646880191961487e-2078j)  +/-  (6.02e-487, 6.02e-487j)
| (-0.72195609395452446235 + 8.3054502425097733246e-2081j)  +/-  (5.35e-489, 5.35e-489j)
| (-0.69193886897754620001 + 8.1567799368943079437e-2082j)  +/-  (6.18e-490, 6.18e-490j)
| (-0.97755523894768619434 - 1.5080221740198860972e-2072j)  +/-  (7.61e-483, 7.61e-483j)
| (0.62821999729564231679 + 1.4196788490606775423e-2084j)  +/-  (1.31e-491, 1.31e-491j)
| (0.72195609395452446235 - 4.003124408999688499e-2084j)  +/-  (5.74e-489, 5.74e-489j)
| (-0.98561591034770846226 - 2.1346267219718298462e-2074j)  +/-  (1.16e-482, 1.16e-482j)
| (-0.55997478613759539038 - 7.5596793959070007121e-2087j)  +/-  (1.89e-493, 1.89e-493j)
| (0.96773294693349883869 + 1.4197117126186840753e-2082j)  +/-  (4.7e-483, 4.7e-483j)
| (0.55997478613759539038 - 1.5170874779369868123e-2105j)  +/-  (1.87e-493, 1.87e-493j)
| (0.59463317630428661613 + 1.3921278076373700804e-2105j)  +/-  (1.76e-492, 1.76e-492j)
| (0.21067926999572632036 - 2.9652163095270716024e-2116j)  +/-  (6.21e-504, 6.21e-504j)
| (-0.62821999729564231679 - 1.5373003527864884659e-2104j)  +/-  (1.38e-491, 1.38e-491j)
| (-0.59463317630428661613 + 1.2216323140009502804e-2105j)  +/-  (1.77e-492, 1.77e-492j)
| (0.69193886897754620001 - 5.9106446900497186256e-2106j)  +/-  (6.12e-490, 6.12e-490j)
| (0.5243072835572316878 - 1.2811512610051469083e-2110j)  +/-  (2.06e-494, 2.06e-494j)
| (0.95616673473925093551 - 2.3492871359326188986e-2121j)  +/-  (2.51e-483, 2.51e-483j)
| (-0.5243072835572316878 + 7.0185652822737445613e-2133j)  +/-  (2.03e-494, 2.03e-494j)
| (-0.48769494381363454535 + 5.2142013028738513021e-2136j)  +/-  (1.22e-495, 1.22e-495j)
| (-0.084805924475509191089 - 3.9323156126085650931e-2149j)  +/-  (6.19e-508, 6.19e-508j)
| (0.45020374481767329246 - 7.8570149588492765956e-2138j)  +/-  (1.05e-496, 1.05e-496j)
| (0.48769494381363454535 + 8.1672158189245562411e-2137j)  +/-  (1.22e-495, 1.22e-495j)
| (-0.12701781974687874737 - 8.0150767535167796814e-2148j)  +/-  (1.69e-506, 1.69e-506j)
| (-0.45020374481767329246 - 3.01299234061188458e-2137j)  +/-  (1.1e-496, 1.1e-496j)
| (-0.41190124824399267538 - 9.331794778761969703e-2139j)  +/-  (8.69e-498, 8.69e-498j)
| (0.25197806138512519445 - 2.5861189887391901401e-2143j)  +/-  (1.69e-502, 1.69e-502j)
| (0.41190124824399267538 + 5.328382286639853892e-2139j)  +/-  (8.44e-498, 8.44e-498j)
| (0.12701781974687874737 + 7.1865116196779198619e-2148j)  +/-  (1.6e-506, 1.6e-506j)
| (-0.29282277127655037995 - 1.2537343214837511274e-2142j)  +/-  (2.28e-501, 2.28e-501j)
| (-0.3331397947420575668 - 3.1953581309415738754e-2141j)  +/-  (3.65e-500, 3.65e-500j)
| (1.3474976133684105419e-2176 + 1.8452141461840645111e-2177j)  +/-  (1.02e-2174, 1.02e-2174j)
| (0.3331397947420575668 - 1.4061559506920244794e-2143j)  +/-  (3.7e-500, 3.7e-500j)
| (0.29282277127655037995 + 3.044284505128426331e-2142j)  +/-  (2.25e-501, 2.25e-501j)
| (-0.042441203196148305878 - 3.9500509234652033968e-2150j)  +/-  (1.32e-509, 1.32e-509j)
| (-0.37285647778030861083 - 8.450371725380492996e-2140j)  +/-  (6.29e-499, 6.29e-499j)
| (-0.16900082032184907409 - 3.9965963663667000365e-2146j)  +/-  (1.97e-505, 1.97e-505j)
| (0.16900082032184907409 + 3.5852509102126558979e-2146j)  +/-  (2.09e-505, 2.09e-505j)
| (0.37285647778030861083 + 3.7067538028730635876e-2141j)  +/-  (6.26e-499, 6.26e-499j)
| (0.042441203196148305878 + 3.7556190276066908522e-2150j)  +/-  (1.32e-509, 1.32e-509j)
| (-0.21067926999572632036 + 5.7034082704363668609e-2145j)  +/-  (6.5e-504, 6.5e-504j)
| (-0.25197806138512519445 + 1.3672653575320843725e-2143j)  +/-  (1.62e-502, 1.62e-502j)
| (0.084805924475509191089 - 2.7304488318696512654e-2149j)  +/-  (5.64e-508, 5.64e-508j)
-------------------------------------------------
The weights are:
| (0.013513513513513513514 + 3.7168503851234790174e-1861j)  +/-  (1.97e-139, 9.2e-373j)
| (0.013513513513513513514 + 6.8140402482963154409e-1864j)  +/-  (9.09e-140, 4.24e-373j)
| (0.013513513513513513514 - 6.9549327047993988242e-1864j)  +/-  (5.96e-140, 2.78e-373j)
| (0.013513513513513513514 - 6.7313289034168019349e-1864j)  +/-  (3.13e-140, 1.46e-373j)
| (0.013513513513513513514 + 2.383797457005550092e-1862j)  +/-  (5.65e-141, 2.64e-374j)
| (0.013513513513513513514 - 1.8820507394395705756e-1862j)  +/-  (4.62e-141, 2.16e-374j)
| (0.013513513513513513514 - 1.8617787321686986189e-1861j)  +/-  (1.36e-141, 6.36e-375j)
| (0.013513513513513513514 + 6.9012536595443669961e-1864j)  +/-  (4.68e-142, 2.19e-375j)
| (0.013513513513513513514 - 7.0834545325436437249e-1864j)  +/-  (1.24e-142, 5.79e-376j)
| (0.013513513513513513514 + 4.9610152271502999596e-1861j)  +/-  (1.51e-141, 7.06e-375j)
| (0.013513513513513513514 - 9.081850915315878099e-1863j)  +/-  (1.15e-144, 5.38e-378j)
| (0.0067567567567567567568 - 7.4370527983466976971e-1861j)  +/-  (1.43e-141, 6.69e-375j)
| (0.013513513513513513514 + 7.0155887523391391722e-1864j)  +/-  (2.71e-144, 1.27e-377j)
| (0.013513513513513513514 + 7.3331191943785657305e-1864j)  +/-  (6.1e-146, 2.85e-379j)
| (0.013513513513513513514 + 9.939936435719856179e-1862j)  +/-  (8e-143, 3.73e-376j)
| (0.013513513513513513514 + 1.0629406700528985904e-1862j)  +/-  (2.87e-145, 1.34e-378j)
| (0.013513513513513513514 - 1.26228496681102849e-1862j)  +/-  (4.53e-145, 2.12e-378j)
| (0.0067567567567567567568 + 3.3520280997396622126e-1864j)  +/-  (3.57e-148, 1.67e-381j)
| (0.013513513513513513514 - 7.6593278426582316995e-1864j)  +/-  (3.04e-149, 1.42e-382j)
| (0.013513513513513513514 - 7.2419044049091419754e-1864j)  +/-  (1.76e-147, 8.22e-381j)
| (0.013513513513513513514 + 7.8563371121497579253e-1863j)  +/-  (6.01e-148, 2.8e-381j)
| (0.013513513513513513514 + 6.0625518390883794451e-1863j)  +/-  (2.02e-149, 9.42e-383j)
| (0.013513513513513513514 - 6.8543481386121394896e-1864j)  +/-  (1.5e-147, 7.02e-381j)
| (0.013513513513513513514 + 7.1587939668135922374e-1864j)  +/-  (8.67e-148, 4.05e-381j)
| (0.013513513513513513514 + 7.5413932680422462611e-1864j)  +/-  (3.36e-150, 1.57e-383j)
| (0.013513513513513513514 - 6.7070792139182203863e-1864j)  +/-  (1.07e-148, 4.99e-382j)
| (0.013513513513513513514 - 5.3947799992163526803e-1863j)  +/-  (8.08e-153, 3.77e-386j)
| (0.013513513513513513514 - 6.8692699687886161293e-1863j)  +/-  (2.88e-151, 1.35e-384j)
| (0.013513513513513513514 + 6.7161591722572089333e-1864j)  +/-  (6.45e-149, 3.01e-382j)
| (0.013513513513513513514 + 8.074638067693039579e-1864j)  +/-  (8.43e-155, 3.94e-388j)
| (0.013513513513513513514 - 6.2208696099257996535e-1862j)  +/-  (1.07e-150, 4.97e-384j)
| (0.013513513513513513514 + 1.5252076073581053643e-1862j)  +/-  (1.01e-150, 4.73e-384j)
| (0.013513513513513513514 + 3.9601394114957953983e-1863j)  +/-  (3.8e-156, 1.78e-389j)
| (0.013513513513513513514 - 7.4328106212639956211e-1864j)  +/-  (2.36e-152, 1.1e-385j)
| (0.013513513513513513514 + 7.7871255417693880694e-1864j)  +/-  (1e-154, 4.68e-388j)
| (0.013513513513513513514 - 7.925353022224357657e-1864j)  +/-  (1.37e-155, 6.4e-389j)
| (0.013513513513513513514 - 6.7801802575398477676e-1864j)  +/-  (4.81e-152, 2.24e-385j)
| (0.013513513513513513514 - 3.6135971411860136411e-1863j)  +/-  (1.14e-159, 5.34e-393j)
| (0.013513513513513513514 + 4.8357988458963914785e-1863j)  +/-  (8.78e-158, 4.1e-391j)
| (0.013513513513513513514 + 6.7526434028839873736e-1864j)  +/-  (1.01e-152, 4.71e-386j)
| (0.013513513513513513514 - 8.5961756444315607074e-1864j)  +/-  (1.17e-161, 5.48e-395j)
| (0.013513513513513513514 + 4.2727997142022694454e-1862j)  +/-  (6.87e-155, 3.21e-388j)
| (0.013513513513513513514 - 3.052000419496310995e-1863j)  +/-  (5.76e-162, 2.69e-395j)
| (0.013513513513513513514 + 3.3135241972028447279e-1863j)  +/-  (5.03e-161, 2.35e-394j)
| (0.013513513513513513514 + 1.6998651710757423085e-1863j)  +/-  (1.17e-166, 5.47e-400j)
| (0.013513513513513513514 - 8.2356760526711189327e-1864j)  +/-  (1.37e-160, 6.42e-394j)
| (0.013513513513513513514 + 8.409237324321447891e-1864j)  +/-  (1.67e-161, 7.78e-395j)
| (0.013513513513513513514 - 4.3632203332214701389e-1863j)  +/-  (5.66e-160, 2.64e-393j)
| (0.013513513513513513514 + 2.8227267468180845362e-1863j)  +/-  (9.89e-164, 4.61e-397j)
| (0.013513513513513513514 - 3.1216806954347774508e-1862j)  +/-  (2.27e-157, 1.06e-390j)
| (0.013513513513513513514 + 8.7974378599613579564e-1864j)  +/-  (1.96e-164, 9.14e-398j)
| (0.013513513513513513514 - 9.0140750022254942738e-1864j)  +/-  (1.22e-165, 5.71e-399j)
| (0.013513513513513513514 - 1.236461974938308875e-1863j)  +/-  (1.01e-170, 4.72e-404j)
| (0.013513513513513513514 + 2.4416448341254255625e-1863j)  +/-  (2.25e-167, 1.05e-400j)
| (0.013513513513513513514 - 2.6206426291088615689e-1863j)  +/-  (2.61e-166, 1.22e-399j)
| (0.013513513513513513514 + 1.1901138483103733633e-1863j)  +/-  (3.05e-171, 1.42e-404j)
| (0.013513513513513513514 + 9.2472550529511036557e-1864j)  +/-  (2.2e-168, 1.03e-401j)
| (0.013513513513513513514 - 9.4982776618456073852e-1864j)  +/-  (1.8e-169, 8.4e-403j)
| (0.013513513513513513514 - 1.7938290484582351759e-1863j)  +/-  (5.24e-172, 2.45e-405j)
| (0.013513513513513513514 - 2.2823780487945345794e-1863j)  +/-  (3.79e-170, 1.77e-403j)
| (0.013513513513513513514 + 1.5367918309200240881e-1863j)  +/-  (2.94e-173, 1.37e-406j)
| (0.013513513513513513514 + 1.0373748988763260393e-1863j)  +/-  (5.6e-173, 2.61e-406j)
| (0.013513513513513513514 - 1.0059812257851727944e-1863j)  +/-  (1.84e-172, 8.6e-406j)
| (0.013513513513513513514 - 1.3414158427836440773e-1863j)  +/-  (1.37e-174, 6.39e-408j)
| (0.013513513513513513514 - 2.0124464669992726698e-1863j)  +/-  (2.81e-173, 1.31e-406j)
| (0.013513513513513513514 + 1.89756810635830148e-1863j)  +/-  (2e-173, 9.35e-407j)
| (0.013513513513513513514 + 1.2867551546732044914e-1863j)  +/-  (4.88e-175, 2.28e-408j)
| (0.013513513513513513514 + 9.7685911568887867113e-1864j)  +/-  (6.54e-174, 3.05e-407j)
| (0.013513513513513513514 - 1.1473396341942408031e-1863j)  +/-  (1.32e-175, 6.15e-409j)
| (0.013513513513513513514 - 1.6145165344880668597e-1863j)  +/-  (1.9e-175, 8.85e-409j)
| (0.013513513513513513514 + 2.1400770572876392002e-1863j)  +/-  (1.29e-174, 6.01e-408j)
| (0.013513513513513513514 + 1.4009264687937999728e-1863j)  +/-  (2.85e-176, 1.33e-409j)
| (0.013513513513513513514 + 1.1078122763928662013e-1863j)  +/-  (1.04e-176, 4.9e-410j)
| (0.013513513513513513514 - 1.0712427390323219641e-1863j)  +/-  (1.03e-176, 4.89e-410j)
| (0.013513513513513513514 - 1.4658398572530210654e-1863j)  +/-  (1.01e-176, 4.59e-410j)
