Starting with polynomial:
P : 2*t
Extension levels are: 1 84
-------------------------------------------------
Trying to find an order 84 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^85 - 42*t^83 + 3403/8*t^81 - 5535/2*t^79 + 415935/32*t^77 - 1502501/32*t^75 + 277962685/2048*t^73 - 330237765/1024*t^71 + 21042072975/32768*t^69 - 35616668975/32768*t^67 + 828931106355/524288*t^65 - 65309723531/32768*t^63 + 1149098108613/524288*t^61 - 1107929156355/524288*t^59 + 30089948992435/16777216*t^57 - 11273135819701/8388608*t^55 + 478303048350171/536870912*t^53 - 280946973839103/536870912*t^51 + 2341224781992525/8589934592*t^49 - 270353529420975/2147483648*t^47 + 1771225244267115/34359738368*t^45 - 642312451217745/34359738368*t^43 + 52728013040874885/8796093022208*t^41 - 7459794805644825/4398046511104*t^39 + 59437719903041025/140737488355328*t^37 - 12978859493582073/140737488355328*t^35 + 39602161018878633/2251799813685248*t^33 - 820383749920273/281474976710656*t^31 + 1879204156221315/4503599627370496*t^29 - 230779457781565/4503599627370496*t^27 + 771462758869803/144115188075855872*t^25 - 33935311973745/72057594037927936*t^23 + 317986441828055/9223372036854775808*t^21 - 19090095135475/9223372036854775808*t^19 + 14771069086725/147573952589676412928*t^17 - 140676848445/36893488147419103232*t^15 + 65649195941/590295810358705651712*t^13 - 1412200023/590295810358705651712*t^11 + 1362649145/37778931862957161709568*t^9 - 6690585/18889465931478580854784*t^7 + 1221759/604462909807314587353088*t^5 - 3311/604462909807314587353088*t^3 + 43/9671406556917033397649408*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:   85 out of 85
Indefinite weights: 0 out of 85
Negative weights:   0 out of 85
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.98934336807511019779 - 5.6398925361053215537e-1763j)  +/-  (6.05e-480, 6.05e-480j)
| (-0.93401610873254799935 + 2.0176866371703329378e-1783j)  +/-  (1.47e-480, 1.47e-480j)
| (-0.90544823749314661572 + 1.7923112937835913084e-1784j)  +/-  (3.5e-481, 3.5e-481j)
| (-0.97607587755592715901 + 1.3627762722168687864e-1781j)  +/-  (6.49e-480, 6.49e-480j)
| (0.90544823749314661572 - 1.4079711656268518264e-1784j)  +/-  (3.61e-481, 3.61e-481j)
| (0.94643977315760935387 - 1.2996544813890254723e-1815j)  +/-  (2.45e-480, 2.45e-480j)
| (0.99733228366355167281 - 5.2048853831406782273e-1842j)  +/-  (2.47e-480, 2.47e-480j)
| (-0.92034618356915944631 + 1.4446205523420652424e-1861j)  +/-  (7.45e-481, 7.45e-481j)
| (-0.98934336807511019779 + 3.9440564652575778268e-1859j)  +/-  (6.55e-480, 6.55e-480j)
| (-0.99733228366355167281 + 9.7358860960948569652e-1860j)  +/-  (2.58e-480, 2.58e-480j)
| (0.88934214888251890342 - 7.5176885894349139519e-1863j)  +/-  (1.51e-481, 1.51e-481j)
| (0.99400097523994591879 + 2.2032042974018005364e-1868j)  +/-  (4.55e-480, 4.55e-480j)
| (-0.87204940814380760813 + 1.2771595844376632446e-1891j)  +/-  (5.94e-482, 5.94e-482j)
| (-0.88934214888251890342 - 7.1087743270958175256e-1892j)  +/-  (1.54e-481, 1.54e-481j)
| (0.99933284837023937207 - 4.2129864833953332588e-1887j)  +/-  (7.25e-481, 7.25e-481j)
| (0.83399781788987793962 - 1.2506410634341156243e-1905j)  +/-  (6.17e-483, 6.17e-483j)
| (0.92034618356915944631 - 1.3955774143187605979e-1902j)  +/-  (7.37e-481, 7.37e-481j)
| (0.98336567682946611968 + 4.4618730393945425837e-1903j)  +/-  (6.68e-480, 6.68e-480j)
| (-0.76864713977853207117 + 3.1522993646675539113e-1921j)  +/-  (1.14e-484, 1.14e-484j)
| (-0.96748369705742525451 + 2.7440209117224009658e-1915j)  +/-  (5.29e-480, 5.29e-480j)
| (0.93401610873254799935 + 2.9528230304959771392e-1915j)  +/-  (1.48e-480, 1.48e-480j)
| (0.76864713977853207117 - 6.6368546643669826032e-1924j)  +/-  (1.14e-484, 1.14e-484j)
| (-0.99400097523994591879 - 2.3290830589171230488e-1916j)  +/-  (4.93e-480, 4.93e-480j)
| (-0.79149648842925410245 - 7.2272371032739517744e-1923j)  +/-  (4.41e-484, 4.41e-484j)
| (-0.81328974073556535201 + 5.860177979825517085e-1923j)  +/-  (1.77e-483, 1.77e-483j)
| (-0.98336567682946611968 - 4.1254794349226750036e-1918j)  +/-  (6.73e-480, 6.73e-480j)
| (0.74477218274378185418 - 1.0924098931258475048e-1923j)  +/-  (2.54e-485, 2.54e-485j)
| (0.85359308903734644834 - 7.0711285793363731574e-1921j)  +/-  (2.03e-482, 2.03e-482j)
| (-0.83399781788987793962 - 7.4214868274629237545e-1922j)  +/-  (5.89e-483, 5.89e-483j)
| (-0.63967302155889127364 - 3.0962815209777706507e-1929j)  +/-  (1.9e-488, 1.9e-488j)
| (-0.94643977315760935387 - 6.0810522477674749536e-1918j)  +/-  (2.44e-480, 2.44e-480j)
| (0.79149648842925410245 - 2.0140807679945315294e-1922j)  +/-  (4.52e-484, 4.52e-484j)
| (0.71990347375799584864 - 1.6056239501916702398e-1925j)  +/-  (5.25e-486, 5.25e-486j)
| (-0.99933284837023937207 + 3.6395025319344443486e-1919j)  +/-  (7.55e-481, 7.55e-481j)
| (-0.71990347375799584864 - 1.0069508589146748745e-1925j)  +/-  (5.2e-486, 5.2e-486j)
| (-0.74477218274378185418 - 6.5921611176700116376e-1925j)  +/-  (2.53e-485, 2.53e-485j)
| (0.97607587755592715901 - 5.091907014609876468e-1917j)  +/-  (6.76e-480, 6.76e-480j)
| (0.61117371409784929225 + 3.2087957335442728838e-1944j)  +/-  (2.44e-489, 2.44e-489j)
| (0.81328974073556535201 - 8.094932135087419602e-1938j)  +/-  (1.83e-483, 1.83e-483j)
| (-0.95760059990840595223 + 1.8302280870920934929e-1935j)  +/-  (4.07e-480, 4.07e-480j)
| (-0.55176774077044590495 - 2.8472123401648558671e-1948j)  +/-  (3.61e-491, 3.61e-491j)
| (0.95760059990840595223 + 8.581846382075126774e-1937j)  +/-  (4.04e-480, 4.04e-480j)
| (0.69407419522063387436 + 2.0047476044271135916e-1959j)  +/-  (6.94e-487, 6.94e-487j)
| (0.58185891555795283842 + 1.9272393215474899806e-1963j)  +/-  (3.01e-490, 3.01e-490j)
| (0.3572308898011327812 - 9.7978281828539595498e-1972j)  +/-  (1.41e-497, 1.41e-497j)
| (-0.58185891555795283842 - 1.3164262748374203218e-1963j)  +/-  (3.07e-490, 3.07e-490j)
| (-0.69407419522063387436 + 8.2409655398666190326e-1960j)  +/-  (7.06e-487, 7.06e-487j)
| (0.87204940814380760813 - 6.117876137685822321e-1954j)  +/-  (6.02e-482, 6.02e-482j)
| (0.48941784781108550916 + 3.1991178040263799393e-1983j)  +/-  (2.74e-493, 2.74e-493j)
| (0.96748369705742525451 - 1.5519546234485248738e-1977j)  +/-  (5.21e-480, 5.21e-480j)
| (-0.66731881122223941583 + 8.6219263024327775045e-2007j)  +/-  (1.21e-487, 1.21e-487j)
| (-0.48941784781108550916 + 1.8580606175239447819e-2013j)  +/-  (2.67e-493, 2.67e-493j)
| (-0.85359308903734644834 + 4.7302918174477010859e-2013j)  +/-  (2.1e-482, 2.1e-482j)
| (0.66731881122223941583 + 4.1440112538960359021e-2018j)  +/-  (1.22e-487, 1.22e-487j)
| (0.55176774077044590495 - 3.2710713366976153294e-2023j)  +/-  (3.67e-491, 3.67e-491j)
| (-0.1456011677350048724 - 1.0569489769327403962e-2038j)  +/-  (3.02e-505, 3.02e-505j)
| (-0.4244566988758150854 - 1.8568944203735995794e-2028j)  +/-  (2.35e-495, 2.35e-495j)
| (-0.61117371409784929225 + 8.7398047160387499219e-2023j)  +/-  (2.48e-489, 2.48e-489j)
| (0.52094034048793028618 + 4.5644772560985101336e-2024j)  +/-  (4.34e-492, 4.34e-492j)
| (0.39110472049015601574 - 1.6879153451016026349e-2028j)  +/-  (1.84e-496, 1.84e-496j)
| (0.63967302155889127364 + 3.5561844003509508172e-2030j)  +/-  (1.94e-488, 1.94e-488j)
| (-0.52094034048793028618 + 1.8505839985648483512e-2035j)  +/-  (4.31e-492, 4.31e-492j)
| (-0.45724232330463852282 - 3.4271634702812069787e-2037j)  +/-  (2.66e-494, 2.66e-494j)
| (-0.036522023057658834968 + 1.9963761004223391246e-2053j)  +/-  (1.32e-509, 1.32e-509j)
| (0.4244566988758150854 + 2.4370116443396487063e-2037j)  +/-  (2.36e-495, 2.36e-495j)
| (0.45724232330463852282 - 8.3685257132385911333e-2037j)  +/-  (2.74e-494, 2.74e-494j)
| (-0.07299531466090752529 + 5.3402658755930662189e-2052j)  +/-  (6.87e-508, 6.87e-508j)
| (-0.39110472049015601574 + 2.4039265474169323779e-2040j)  +/-  (1.79e-496, 1.79e-496j)
| (-0.1816368509794364397 + 2.0856872708767612358e-2047j)  +/-  (7.01e-504, 7.01e-504j)
| (0.1456011677350048724 + 9.1120631418643048112e-2049j)  +/-  (3.07e-505, 3.07e-505j)
| (0.32288040477144621663 - 2.1590772436809225809e-2041j)  +/-  (6.91e-499, 6.91e-499j)
| (0.10937120837787438699 - 3.3379682834777816452e-2050j)  +/-  (1.75e-506, 1.75e-506j)
| (-0.32288040477144621663 - 1.8098543173550074067e-2043j)  +/-  (6.85e-499, 6.85e-499j)
| (-0.3572308898011327812 - 1.0004252203660045009e-2040j)  +/-  (1.43e-497, 1.43e-497j)
| (0.07299531466090752529 - 1.070866592738551218e-2051j)  +/-  (6.07e-508, 6.07e-508j)
| (0.28809909936523756893 + 4.2488286556811829534e-2043j)  +/-  (4.46e-500, 4.46e-500j)
| (0.1816368509794364397 + 5.6963410236314094551e-2047j)  +/-  (6.86e-504, 6.86e-504j)
| (-1.4068565271469924507e-2076 - 1.1931317448367775993e-2077j)  +/-  (1.2e-2074, 1.2e-2074j)
| (-0.28809909936523756893 + 5.4719579764290876018e-2043j)  +/-  (4.43e-500, 4.43e-500j)
| (-0.10937120837787438699 + 3.5080412824328012464e-2050j)  +/-  (1.75e-506, 1.75e-506j)
| (0.21743017558155696835 - 7.8727231356446304351e-2046j)  +/-  (1.32e-502, 1.32e-502j)
| (0.25293338239168074656 - 2.0156626301463099629e-2044j)  +/-  (3.26e-501, 3.26e-501j)
| (0.036522023057658834968 + 4.3765028413324383641e-2053j)  +/-  (1.32e-509, 1.32e-509j)
| (-0.21743017558155696835 - 5.6238890793081144554e-2047j)  +/-  (1.32e-502, 1.32e-502j)
| (-0.25293338239168074656 - 3.0057569991531440025e-2044j)  +/-  (3.27e-501, 3.27e-501j)
-------------------------------------------------
The weights are:
| (0.00024650814006740725447 + 9.7321923440443846615e-1765j)  +/-  (3.95e-131, 4.14e-363j)
| (0.0014838826584663845687 + 4.3512088254200043158e-1766j)  +/-  (1.93e-131, 2.02e-363j)
| (0.002094924293262260037 + 6.2355922680648136191e-1766j)  +/-  (1.06e-131, 1.11e-363j)
| (0.00054971954945844990859 + 1.5774543730726821115e-1766j)  +/-  (2.25e-132, 2.36e-364j)
| (0.002094924293262260037 + 1.4083234394316143025e-1764j)  +/-  (3.28e-133, 3.44e-365j)
| (0.0012122297184345691718 - 1.5935367080988727293e-1764j)  +/-  (2.42e-133, 2.54e-365j)
| (6.1957162354010477951e-05 - 4.3739570615092520031e-1765j)  +/-  (1.72e-133, 1.81e-365j)
| (0.0017786383998800356142 - 5.2528587315548797166e-1766j)  +/-  (6.52e-132, 6.84e-364j)
| (0.00024650814006740725447 + 7.0262735068429059445e-1767j)  +/-  (4.54e-134, 4.76e-366j)
| (6.1957162354010477951e-05 + 1.7588766299765144238e-1767j)  +/-  (1.42e-134, 1.49e-366j)
| (0.0024310528165235300092 - 1.3710709474834745546e-1764j)  +/-  (7.22e-135, 7.58e-367j)
| (0.00013909373513995837787 + 1.6842848502929314837e-1764j)  +/-  (2.36e-134, 2.48e-366j)
| (0.0027852305785585448478 + 8.4390577593480375683e-1766j)  +/-  (2.35e-135, 2.46e-367j)
| (0.0024310528165235300092 - 7.2981222833891174889e-1766j)  +/-  (9.29e-135, 9.75e-367j)
| (1.5509978700280972059e-05 + 8.7566730723238323931e-1766j)  +/-  (1e-134, 1.05e-366j)
| (0.003540088834359558048 + 1.2852457357322023346e-1764j)  +/-  (1.02e-137, 1.07e-369j)
| (0.0017786383998800356142 - 1.4538751845806925824e-1764j)  +/-  (4.63e-136, 4.86e-368j)
| (0.00038362727481076744564 - 3.6194853747728973199e-1764j)  +/-  (9.81e-136, 1.03e-367j)
| (0.0047579252850032765134 - 1.5264125251164772967e-1765j)  +/-  (4.48e-140, 4.7e-372j)
| (0.00074389878986158367368 - 2.1440367967692465221e-1766j)  +/-  (7.58e-138, 7.95e-370j)
| (0.0014838826584663845687 + 1.5126248488333526517e-1764j)  +/-  (2.36e-136, 2.48e-368j)
| (0.0047579252850032765134 - 1.215887897557369605e-1764j)  +/-  (2.06e-140, 2.17e-372j)
| (0.00013909373513995837787 - 3.9553077168821578099e-1767j)  +/-  (2.97e-138, 3.12e-370j)
| (0.0043434105674902282177 + 1.3755514709174010442e-1765j)  +/-  (1e-140, 1.05e-372j)
| (0.0039367418327241499033 - 1.2316871786296699154e-1765j)  +/-  (1.21e-140, 1.27e-372j)
| (0.00038362727481076744564 - 1.0967743111637278733e-1766j)  +/-  (1.7e-138, 1.78e-370j)
| (0.0051780743698960791454 + 1.194081099562561772e-1764j)  +/-  (7.04e-144, 7.39e-376j)
| (0.0031555678877637295185 - 1.3110148946670974691e-1764j)  +/-  (6.52e-142, 6.84e-374j)
| (0.003540088834359558048 + 1.0950073824766684108e-1765j)  +/-  (1e-140, 1.05e-372j)
| (0.0068699816917409095332 + 2.3784879460380995061e-1765j)  +/-  (1.09e-145, 1.15e-377j)
| (0.0012122297184345691718 - 3.5318239917568627084e-1766j)  +/-  (1.96e-139, 2.05e-371j)
| (0.0043434105674902282177 + 1.2381478487139836876e-1764j)  +/-  (7.25e-144, 7.6e-376j)
| (0.0056016161450136114246 - 1.1725254408393905991e-1764j)  +/-  (1.49e-145, 1.56e-377j)
| (1.5509978700280972059e-05 - 4.3986352521087256509e-1768j)  +/-  (1.57e-140, 1.64e-372j)
| (0.0056016161450136114246 - 1.8483294696339758858e-1765j)  +/-  (2.82e-145, 2.95e-377j)
| (0.0051780743698960791454 + 1.6840736464409431955e-1765j)  +/-  (2.3e-144, 2.41e-376j)
| (0.00054971954945844990859 + 2.3368090442266998011e-1764j)  +/-  (3.24e-143, 3.4e-375j)
| (0.0072844964092539578288 - 1.0863848142164192069e-1764j)  +/-  (1.53e-149, 1.6e-381j)
| (0.0039367418327241499033 - 1.261138507310230499e-1764j)  +/-  (1.83e-144, 1.92e-376j)
| (0.00096512896575652360687 + 2.7957782760368331733e-1766j)  +/-  (3.19e-140, 3.35e-372j)
| (0.0080878181423846279985 - 2.9598401382481736925e-1765j)  +/-  (5.52e-150, 5.8e-382j)
| (0.00096512896575652360687 + 1.7147917351640410551e-1764j)  +/-  (1.18e-143, 1.23e-375j)
| (0.0060262908317305746219 + 1.1510728449470759119e-1764j)  +/-  (1.18e-147, 1.23e-379j)
| (0.0076911651440200361432 + 1.0645153360270987303e-1764j)  +/-  (1.18e-150, 1.24e-382j)
| (0.010144024318277801478 - 9.0507953892865108018e-1765j)  +/-  (2.07e-154, 2.17e-386j)
| (0.0076911651440200361432 + 2.7607740481010090521e-1765j)  +/-  (8.89e-151, 9.33e-383j)
| (0.0060262908317305746219 + 2.0189662638268569076e-1765j)  +/-  (2.95e-148, 3.1e-380j)
| (0.0027852305785585448478 + 1.3392335940013306323e-1764j)  +/-  (1.24e-145, 1.3e-377j)
| (0.0088426763981856411987 - 9.9758349185661134239e-1765j)  +/-  (6.61e-154, 6.94e-386j)
| (0.00074389878986158367368 - 1.9192920283035685869e-1764j)  +/-  (4.39e-145, 4.6e-377j)
| (0.0064498326068481069011 - 2.1957622521400168008e-1765j)  +/-  (1.27e-149, 1.33e-381j)
| (0.0088426763981856411987 - 3.3725353411730252057e-1765j)  +/-  (1.17e-154, 1.23e-386j)
| (0.0031555678877637295185 - 9.6569058084927287229e-1766j)  +/-  (1.5e-146, 1.58e-378j)
| (0.0064498326068481069011 - 1.1296145590260465032e-1764j)  +/-  (7.27e-151, 7.63e-383j)
| (0.0080878181423846279985 - 1.0424352346949385941e-1764j)  +/-  (1.68e-153, 1.77e-385j)
| (0.011381398836676778792 - 5.6557712138411151031e-1765j)  +/-  (3.01e-160, 3.16e-392j)
| (0.0095329826834819260095 - 3.802871363512054631e-1765j)  +/-  (2.77e-157, 2.91e-389j)
| (0.0072844964092539578288 - 2.5669064944973642105e-1765j)  +/-  (1.7e-152, 1.78e-384j)
| (0.008472339088980456528 + 1.0201275221774857939e-1764j)  +/-  (9.21e-155, 9.67e-387j)
| (0.0098492685768641504323 + 9.2853941411173162197e-1765j)  +/-  (5.04e-158, 5.28e-390j)
| (0.0068699816917409095332 + 1.1080710404087008749e-1764j)  +/-  (1.29e-152, 1.36e-384j)
| (0.008472339088980456528 + 3.1638480717478871912e-1765j)  +/-  (1.58e-155, 1.65e-387j)
| (0.0091968541602206560373 + 3.5856340514750227587e-1765j)  +/-  (3.95e-157, 4.14e-389j)
| (0.011612396998043905074 + 6.3841388667222816095e-1765j)  +/-  (3.76e-163, 3.95e-395j)
| (0.0095329826834819260095 - 9.5178379690922406362e-1765j)  +/-  (2.05e-158, 2.15e-390j)
| (0.0091968541602206560373 + 9.7480111425550949201e-1765j)  +/-  (9.5e-158, 9.97e-390j)
| (0.011565949814390175569 - 6.1402935891544831593e-1765j)  +/-  (1.09e-163, 1.14e-395j)
| (0.0098492685768641504323 + 4.0239699553270460983e-1765j)  +/-  (2.77e-161, 2.91e-393j)
| (0.011244279701933418601 + 5.4156789442624040267e-1765j)  +/-  (1.03e-163, 1.08e-395j)
| (0.011381398836676778792 - 7.607758190065254959e-1765j)  +/-  (2.85e-165, 2.99e-397j)
| (0.010415677258309616875 + 8.8141882838366867294e-1765j)  +/-  (3.65e-163, 3.82e-395j)
| (0.011488813241604227669 + 7.3633775041616473601e-1765j)  +/-  (1.73e-165, 1.82e-397j)
| (0.010415677258309616875 + 4.476622177038659481e-1765j)  +/-  (1.09e-164, 1.15e-396j)
| (0.010144024318277801478 - 4.2486485022338698369e-1765j)  +/-  (6.62e-164, 6.95e-396j)
| (0.011565949814390175569 - 7.1185521470914989943e-1765j)  +/-  (1.83e-166, 1.92e-398j)
| (0.01066277801098766244 - 8.5757452576340196811e-1765j)  +/-  (1.06e-165, 1.11e-397j)
| (0.011244279701933418601 + 7.8514321504853101431e-1765j)  +/-  (1.19e-166, 1.25e-398j)
| (0.011627906976744186047 - 6.6286536994997812333e-1765j)  +/-  (2.81e-167, 2.95e-399j)
| (0.01066277801098766244 - 4.7076031720485646201e-1765j)  +/-  (1.98e-167, 2.07e-399j)
| (0.011488813241604227669 + 5.8974071554792336403e-1765j)  +/-  (2.05e-167, 2.15e-399j)
| (0.011078187427285736138 - 8.094146750218477316e-1765j)  +/-  (1.44e-167, 1.51e-399j)
| (0.010884008186882602373 + 8.3356605327859648531e-1765j)  +/-  (1.67e-167, 1.75e-399j)
| (0.011612396998043905074 + 6.8735520565358591994e-1765j)  +/-  (3.85e-168, 4.04e-400j)
| (0.011078187427285736138 - 5.1774242908411352659e-1765j)  +/-  (2.29e-169, 2.41e-401j)
| (0.010884008186882602373 + 4.9413012449152619306e-1765j)  +/-  (2.21e-169, 2.31e-401j)
