Starting with polynomial:
P : 4194304*t^22 - 484442112*t^20 + 23011000320*t^18 - 586780508160*t^16 + 8801707622400*t^14 - 80095539363840*t^12 + 440525466501120*t^10 - 1415974713753600*t^8 + 2477955749068800*t^6 - 2064963124224000*t^4 + 619488937267200*t^2 - 28158588057600
Extension levels are: 22 37
-------------------------------------------------
Trying to find an order 37 Kronrod extension for:
P1 : 4194304*t^22 - 484442112*t^20 + 23011000320*t^18 - 586780508160*t^16 + 8801707622400*t^14 - 80095539363840*t^12 + 440525466501120*t^10 - 1415974713753600*t^8 + 2477955749068800*t^6 - 2064963124224000*t^4 + 619488937267200*t^2 - 28158588057600
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4194304*t^59 - 279325036772780096144295912500424081408/104779331696056756994688859075*t^57 + 82482997721619777113631780878544998498304/104779331696056756994688859075*t^55 - 69235346295860368108655627321195723118870528/481984925801861082175568751745*t^53 + 8759644347745647732383011942222007803433582592/481984925801861082175568751745*t^51 - 163460527630173756758876412787239877131542003712/96396985160372216435113750349*t^49 + 58397786134090882530654704072156152917152736411648/481984925801861082175568751745*t^47 - 3275610035450479204757118787191826306265735393869824/481984925801861082175568751745*t^45 + 29339333176022379181695613424311555068498507047043072/96396985160372216435113750349*t^43 - 1061428330441921189167091916311683274024380692254359552/96396985160372216435113750349*t^41 + 2405247767161080175758202152659787414911216818208716800/7415152704644016648854903873*t^39 - 57992530227424766665977910422336953294249007645253395456/7415152704644016648854903873*t^37 + 1147673738387699611530435806970025964213992662043416150528/7415152704644016648854903873*t^35 - 18658881013263940801186840040181235492170333270206403982080/7415152704644016648854903873*t^33 + 248997243169937666526454926082986966454550396951718298022400/7415152704644016648854903873*t^31 - 2720416755167107848449122065776029593220809902561944886419200/7415152704644016648854903873*t^29 + 24230486942202833887165428416928360435521302553537339335867200/7415152704644016648854903873*t^27 - 174883076366786838494338139254312375078231943780097850234543200/7415152704644016648854903873*t^25 + 1014606231423454269509566252562459553618110496273380653659903000/7415152704644016648854903873*t^23 - 203601257036508811181048510459969191972683789912214056431659500/322397943680174636906734951*t^21 + 737784117794120474352467421592075515386916409449357609578088750/322397943680174636906734951*t^19 - 2064232006794952016469249466129428640028999622463207992397711125/322397943680174636906734951*t^17 + 4365178114891828375976909398129475327882323198305898034429827125/322397943680174636906734951*t^15 - 13573226541764359512112877067644374622643025796184740306915821875/644795887360349273813469902*t^13 + 14955957100230567436520307496580240256684107881931787413640763125/644795887360349273813469902*t^11 - 22211906932349895616595030350494398490633106080930340186936865625/1289591774720698547626939804*t^9 + 82690123261719371557722400654468672889829855720797022720678384375/10316734197765588381015518432*t^7 - 43059770877605033865122550893866932647923414272348478771780115625/20633468395531176762031036864*t^5 + 10260314917027782078966752663381082515573578632233123841373265625/41266936791062353524062073728*t^3 - 704503478680034222476782987315170565972480441964681437177046875/82533873582124707048124147456*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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: 1
  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
-------------------------------------------------
The nodes are:
| (-8.3783914088827398892 - 2.4104834629720665691e-917j)  +/-  (1.13e-244, 1.13e-244j)
| (-7.346665409228234584 - 3.3876609419614707486e-914j)  +/-  (4.17e-243, 4.17e-243j)
| (-5.225480247699243493 + 1.3300489465208851688e-919j)  +/-  (5.76e-241, 5.76e-241j)
| (6.4785676926706087822 + 2.1292004647702747969e-936j)  +/-  (4.14e-242, 4.14e-242j)
| (-6.4785676926706087822 - 3.1631176228702832319e-935j)  +/-  (4.27e-242, 4.27e-242j)
| (-6.0818043589372239753 + 5.2419033796420478323e-946j)  +/-  (9.6e-242, 9.6e-242j)
| (4.6125617748040441619 - 1.3010971917846023403e-953j)  +/-  (1.17e-241, 1.17e-241j)
| (-7.8331207646149021633 - 4.6537770577651444944e-956j)  +/-  (8.83e-244, 8.83e-244j)
| (6.8985205073108195358 + 8.5880095645171608112e-956j)  +/-  (1.45e-242, 1.45e-242j)
| (2.6456374410581727008 - 3.9904991863690336677e-957j)  +/-  (1.64e-244, 1.64e-244j)
| (9.0368837457701775812 + 6.2970009722237495178e-959j)  +/-  (5.98e-246, 5.98e-246j)
| (4.2943124805931615158 + 7.1654184582404482861e-955j)  +/-  (5.72e-242, 5.72e-242j)
| (-6.8985205073108195358 - 1.1268711296457075004e-953j)  +/-  (1.58e-242, 1.58e-242j)
| (-2.1442335927985344636 + 2.1233678193341680681e-959j)  +/-  (6.59e-246, 6.59e-246j)
| (7.346665409228234584 + 2.5014721346162946372e-958j)  +/-  (4.14e-243, 4.14e-243j)
| (8.3783914088827398892 + 2.3430587843356380097e-959j)  +/-  (1.13e-244, 1.13e-244j)
| (-9.0368837457701775812 + 1.4097636624134558811e-960j)  +/-  (5.56e-246, 5.56e-246j)
| (-1.419023274754022707 - 1.3168937558364325743e-962j)  +/-  (2.4e-248, 2.4e-248j)
| (-1.1767139584812444474 + 4.2133305183259712944e-963j)  +/-  (2.67e-249, 2.67e-249j)
| (-3.4370868186202271168 - 1.2846545017984232224e-957j)  +/-  (5.61e-243, 5.61e-243j)
| (7.8331207646149021633 + 2.1002351124474724047e-958j)  +/-  (8.68e-244, 8.68e-244j)
| (1.8948407704933347393 + 1.2392168293997489972e-960j)  +/-  (1.18e-246, 1.18e-246j)
| (2.3966372598465089177 + 2.7458675897298936987e-959j)  +/-  (3.74e-245, 3.74e-245j)
| (3.4370868186202271168 + 1.314952397245194294e-957j)  +/-  (5.59e-243, 5.59e-243j)
| (-4.2943124805931615158 + 6.3726387991789334262e-955j)  +/-  (6.06e-242, 6.06e-242j)
| (5.3986485900436757648 + 6.5666636004110166879e-962j)  +/-  (5.56e-241, 5.56e-241j)
| (4.9398341310601758879 - 3.5978286862899786544e-962j)  +/-  (2.74e-241, 2.74e-241j)
| (3.165265909202137447 + 4.9129274397239100331e-965j)  +/-  (1.83e-243, 1.83e-243j)
| (3.9935122350435742932 + 1.376182781393620064e-963j)  +/-  (2.93e-242, 2.93e-242j)
| (-0.93667771335154254488 - 1.0550761421966145926e-970j)  +/-  (2.91e-250, 2.91e-250j)
| (-4.6125617748040441619 + 1.2057130098900517455e-960j)  +/-  (1.2e-241, 1.2e-241j)
| (5.7092013532052637774 - 8.4925426983074403059e-982j)  +/-  (2.4e-241, 2.4e-241j)
| (1.419023274754022707 + 3.1815075470645372752e-989j)  +/-  (2.51e-248, 2.51e-248j)
| (-5.7092013532052637774 - 9.9494124026067377453e-981j)  +/-  (2.35e-241, 2.35e-241j)
| (-5.3986485900436757648 + 1.4144771735873673705e-999j)  +/-  (5.55e-241, 5.55e-241j)
| (-3.9935122350435742932 + 8.444448819916373759e-1012j)  +/-  (2.9e-242, 2.9e-242j)
| (-3.7107015328778049148 + 9.6619689784733011149e-1014j)  +/-  (1.49e-242, 1.49e-242j)
| (-3.1004150684263014244e-1053 - 2.5362442158008008485e-1053j)  +/-  (2.36e-1051, 2.36e-1051j)
| (-2.6456374410581727008 - 6.8572065095824129926e-1022j)  +/-  (1.64e-244, 1.64e-244j)
| (5.225480247699243493 - 2.0092593821176525828e-1022j)  +/-  (5.78e-241, 5.78e-241j)
| (-0.2341791399309906351 + 8.5421495263293220993e-1036j)  +/-  (8.3e-254, 8.3e-254j)
| (1.1767139584812444474 + 4.721244990300772811e-1032j)  +/-  (2.68e-249, 2.68e-249j)
| (2.1442335927985344636 + 3.8310550658696185983e-1028j)  +/-  (7.42e-246, 7.42e-246j)
| (3.7107015328778049148 - 3.2147796948008986717e-1025j)  +/-  (1.39e-242, 1.39e-242j)
| (-4.9398341310601758879 - 3.1401766719159086822e-1026j)  +/-  (2.51e-241, 2.51e-241j)
| (-2.3966372598465089177 - 4.2553141901366079947e-1038j)  +/-  (3.55e-245, 3.55e-245j)
| (6.0818043589372239753 + 9.7568550999154899315e-1038j)  +/-  (1.11e-241, 1.11e-241j)
| (-0.47028969960893441992 + 1.7591903535330430711e-1048j)  +/-  (1.49e-252, 1.49e-252j)
| (0.47028969960893441992 - 3.1730396848050789762e-1049j)  +/-  (1.38e-252, 1.38e-252j)
| (0.93667771335154254488 + 1.4827409587739012361e-1046j)  +/-  (2.72e-250, 2.72e-250j)
| (-2.8995393192379396479 + 3.9861335909744153418e-1039j)  +/-  (6e-244, 6e-244j)
| (-1.6558743732864224954 - 1.6265358599173545026e-1044j)  +/-  (1.73e-247, 1.73e-247j)
| (0.70368609717000693217 - 2.449097442530247209e-1048j)  +/-  (1.97e-251, 1.97e-251j)
| (1.6558743732864224954 - 1.2763656670637935006e-1044j)  +/-  (1.88e-247, 1.88e-247j)
| (-3.165265909202137447 + 8.8473940078948955358e-1044j)  +/-  (1.88e-243, 1.88e-243j)
| (-1.8948407704933347393 + 6.9505478327244837901e-1047j)  +/-  (1.04e-246, 1.04e-246j)
| (-0.70368609717000693217 + 1.2332310025967581945e-1050j)  +/-  (2e-251, 2e-251j)
| (0.2341791399309906351 + 3.6419895407646240516e-1053j)  +/-  (7.45e-254, 7.45e-254j)
| (2.8995393192379396479 + 2.6055267157882397712e-1048j)  +/-  (5.88e-244, 5.88e-244j)
-------------------------------------------------
The weights are:
| (1.0808867671606702996e-31 + 1.7784383307074752428e-942j)  +/-  (2.7e-70, 1.11e-189j)
| (9.5176435166503861426e-25 - 2.9889866580567475785e-937j)  +/-  (3.69e-67, 1.52e-186j)
| (1.6096442321556575538e-13 - 3.6311978382541189418e-930j)  +/-  (9.68e-60, 3.99e-179j)
| (1.3608699530411253459e-19 - 5.8335198990331059499e-936j)  +/-  (1.76e-67, 7.25e-187j)
| (1.3608699530411253459e-19 - 9.3378470469104695277e-935j)  +/-  (9.45e-65, 3.89e-184j)
| (1.878562410500981606e-17 + 2.2573155345792283862e-933j)  +/-  (2.04e-63, 8.42e-183j)
| (1.0552387660453771377e-10 - 1.5777194305214563787e-929j)  +/-  (4.73e-61, 1.95e-180j)
| (6.4941098470080751016e-28 - 7.1425544489840942447e-940j)  +/-  (1.37e-69, 5.64e-189j)
| (5.2466036568024398576e-22 + 1.3212884703259253664e-937j)  +/-  (2.92e-70, 1.2e-189j)
| (0.0001283088252310737838 + 9.1322459692980668935e-925j)  +/-  (2.09e-50, 8.59e-170j)
| (1.4648275330595902194e-36 + 1.5575188061250781017e-946j)  +/-  (4.1e-78, 1.69e-197j)
| (1.7152654432944180453e-09 + 1.090807433744700017e-928j)  +/-  (1.04e-60, 4.27e-180j)
| (5.2466036568024398576e-22 + 4.2164925088495611129e-936j)  +/-  (1.6e-68, 6.61e-188j)
| (0.0014372328298033886494 + 1.2041648053204452307e-923j)  +/-  (1.16e-48, 4.8e-168j)
| (9.5176435166503861426e-25 - 2.1874018777555528787e-939j)  +/-  (1.37e-72, 5.65e-192j)
| (1.0808867671606702996e-31 - 1.1642282977196247086e-943j)  +/-  (1.61e-76, 6.62e-196j)
| (1.4648275330595902194e-36 - 1.5126323696922548169e-945j)  +/-  (6.05e-78, 2.49e-197j)
| (0.018067667793631100033 - 9.3250497521352715519e-923j)  +/-  (2.28e-44, 9.41e-164j)
| (0.034331038905204970247 + 1.4838869602848557106e-922j)  +/-  (1.43e-41, 5.87e-161j)
| (1.1381543651314730052e-06 - 4.8236327277170737494e-926j)  +/-  (5.38e-60, 2.22e-179j)
| (6.4941098470080751016e-28 + 2.2828559510486303338e-941j)  +/-  (9.71e-75, 4e-194j)
| (0.0038020039638061130392 - 1.6037438668244201823e-923j)  +/-  (2.38e-51, 9.81e-171j)
| (0.00045267670037102584171 - 2.560888739499759973e-924j)  +/-  (8.35e-55, 3.44e-174j)
| (1.1381543651314730052e-06 - 1.7532750391353017874e-926j)  +/-  (4.02e-61, 1.65e-180j)
| (1.7152654432944180453e-09 + 4.1367853786301191947e-928j)  +/-  (6.97e-66, 2.87e-185j)
| (2.8286225855219478636e-14 + 1.6478977727307670487e-931j)  +/-  (3.9e-69, 1.61e-188j)
| (4.6269971592536019603e-12 + 2.5590393400257537931e-930j)  +/-  (2.34e-67, 9.63e-187j)
| (6.7916208668100064072e-06 + 7.3074398727428439291e-926j)  +/-  (3.11e-61, 1.28e-180j)
| (1.946534713913972222e-08 - 7.0181894321750413047e-928j)  +/-  (2.57e-64, 1.06e-183j)
| (0.055380981172343974052 - 2.2339997275667477308e-922j)  +/-  (1.56e-51, 6.42e-171j)
| (1.0552387660453771377e-10 - 6.8400486011743561242e-929j)  +/-  (1.01e-69, 4.18e-189j)
| (1.4036412905402351232e-15 - 7.0455352118496818503e-933j)  +/-  (6.76e-71, 2.79e-190j)
| (0.018067667793631100033 - 6.3099954836791656724e-923j)  +/-  (2.13e-55, 8.78e-175j)
| (1.4036412905402351232e-15 - 5.6876708297248862451e-932j)  +/-  (7e-73, 2.88e-192j)
| (2.8286225855219478636e-14 + 1.114754797062630686e-930j)  +/-  (6.12e-72, 2.52e-191j)
| (1.946534713913972222e-08 - 2.3638612233522611453e-927j)  +/-  (2.32e-69, 9.56e-189j)
| (1.6321353086929720171e-07 + 1.1548170337375255563e-926j)  +/-  (7.41e-69, 3.05e-188j)
| (0.13161589425991599701 - 4.081059031394402382e-922j)  +/-  (3.56e-60, 1.47e-179j)
| (0.0001283088252310737838 + 1.9381858418975785287e-924j)  +/-  (6.96e-67, 2.87e-186j)
| (1.6096442321556575538e-13 - 6.2477533552285726559e-931j)  +/-  (1.4e-72, 5.76e-192j)
| (0.12582552851831580602 + 4.0161253595116237247e-922j)  +/-  (1.68e-60, 6.93e-180j)
| (0.034331038905204970247 + 1.0747287755988699694e-922j)  +/-  (4.3e-61, 1.77e-180j)
| (0.0014372328298033886494 + 6.6078408624575426433e-924j)  +/-  (2.33e-64, 9.61e-184j)
| (1.6321353086929720171e-07 + 3.8094303045356080372e-927j)  +/-  (9.66e-69, 3.98e-188j)
| (4.6269971592536019603e-12 + 1.2806512147672807063e-929j)  +/-  (9.23e-73, 3.8e-192j)
| (0.00045267670037102584171 - 5.0342007903034757406e-924j)  +/-  (1.13e-67, 4.65e-187j)
| (1.878562410500981606e-17 + 2.1108924094641453691e-934j)  +/-  (9.46e-77, 3.89e-196j)
| (0.10649991347469592623 - 3.6415668393374568645e-922j)  +/-  (4.4e-63, 1.81e-182j)
| (0.10649991347469592623 - 3.204036980870884902e-922j)  +/-  (6.73e-64, 2.77e-183j)
| (0.055380981172343974052 - 1.7294689343367114964e-922j)  +/-  (3.35e-64, 1.38e-183j)
| (3.2738712768286969964e-05 - 6.4060662042138452602e-925j)  +/-  (2.32e-69, 9.58e-189j)
| (0.0085607568720535448778 + 5.4076192614415752997e-923j)  +/-  (4.25e-67, 1.75e-186j)
| (0.079665090822099851565 + 2.4995511211933345315e-922j)  +/-  (4.46e-65, 1.82e-184j)
| (0.0085607568720535448778 + 3.4209953281611036934e-923j)  +/-  (7.92e-67, 3.23e-186j)
| (6.7916208668100064072e-06 + 1.833181346925518708e-925j)  +/-  (3.56e-70, 1.47e-189j)
| (0.0038020039638061130392 - 2.7160285102171563372e-923j)  +/-  (7.12e-68, 2.93e-187j)
| (0.079665090822099851565 + 3.0281826972373036904e-922j)  +/-  (1.52e-66, 6.57e-186j)
| (0.12582552851831580602 + 3.7683765533301172295e-922j)  +/-  (1.02e-66, 4.78e-186j)
| (3.2738712768286969964e-05 - 2.7853462212316300031e-925j)  +/-  (6.7e-70, 2.55e-189j)
