Starting with polynomial:
P : 218266320541953276229/17179869184*t^37 - 995653215622882753209/8589934592*t^35 + 8343854412614299129005/17179869184*t^33 - 1330179688967496962595/1073741824*t^31 + 9231844109998299815025/4294967296*t^29 - 5766351859475861115231/2147483648*t^27 + 10708939167598027785429/4294967296*t^25 - 1880961212107381929525/1073741824*t^23 + 8065816723104536070675/8589934592*t^21 - 1650898159699758844875/4294967296*t^19 + 1026558492031486408995/8589934592*t^17 - 29933952597830650005/1073741824*t^15 + 20542908645570053925/4294967296*t^13 - 1257729100749186975/2147483648*t^11 + 210258664258982625/4294967296*t^9 - 2803448856786435/1073741824*t^7 + 1369126185872445/17179869184*t^5 - 9821565178425/8589934592*t^3 + 83945001525/17179869184*t
Extension levels are: 37
-------------------------------------------------
Ending with final polynomial:
P : 218266320541953276229/17179869184*t^37 - 995653215622882753209/8589934592*t^35 + 8343854412614299129005/17179869184*t^33 - 1330179688967496962595/1073741824*t^31 + 9231844109998299815025/4294967296*t^29 - 5766351859475861115231/2147483648*t^27 + 10708939167598027785429/4294967296*t^25 - 1880961212107381929525/1073741824*t^23 + 8065816723104536070675/8589934592*t^21 - 1650898159699758844875/4294967296*t^19 + 1026558492031486408995/8589934592*t^17 - 29933952597830650005/1073741824*t^15 + 20542908645570053925/4294967296*t^13 - 1257729100749186975/2147483648*t^11 + 210258664258982625/4294967296*t^9 - 2803448856786435/1073741824*t^7 + 1369126185872445/17179869184*t^5 - 9821565178425/8589934592*t^3 + 83945001525/17179869184*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:
| (-0.99794458247791364894 + 3.8745727233591811975e-889j)  +/-  (1.24e-243, 1.24e-243j)
| (-0.98918596321431918668 + 8.7938011408479510953e-891j)  +/-  (3.75e-243, 3.75e-243j)
| (-0.92178143741246374267 - 4.3251725916466183214e-893j)  +/-  (2.72e-243, 2.72e-243j)
| (0.99794458247791364894 + 1.5571163619166277475e-894j)  +/-  (1.39e-243, 1.39e-243j)
| (0.92178143741246374267 + 2.4634124445547090985e-922j)  +/-  (2.97e-243, 2.97e-243j)
| (0.95097234326209482133 - 7.8744317618753923969e-940j)  +/-  (4.07e-243, 4.07e-243j)
| (0.083670408954769901943 + 2.5033341527654123401e-964j)  +/-  (9.66e-255, 9.66e-255j)
| (-0.88612496215548607895 + 3.3079688678675617645e-952j)  +/-  (1.47e-243, 1.47e-243j)
| (-0.97349303005648574433 - 1.6842131902484224454e-952j)  +/-  (5.13e-243, 5.13e-243j)
| (0.98918596321431918668 - 1.4035023779229675365e-958j)  +/-  (4.38e-243, 4.38e-243j)
| (0.88612496215548607895 - 1.658926075914964485e-977j)  +/-  (1.34e-243, 1.34e-243j)
| (0.97349303005648574433 + 1.5630209196836220552e-995j)  +/-  (4.95e-243, 4.95e-243j)
| (-0.95097234326209482133 + 4.9703208397780112252e-1005j)  +/-  (4.8e-243, 4.8e-243j)
| (-0.84425298734055596799 - 1.2247516990021720931e-1007j)  +/-  (5.17e-244, 5.17e-244j)
| (0.48171087780320555415 + 5.8967350364305012348e-1014j)  +/-  (1.12e-248, 1.12e-248j)
| (0.84425298734055596799 - 2.8618449631122442698e-1006j)  +/-  (5.39e-244, 5.39e-244j)
| (0.79645920050990229339 + 1.0118417479629161196e-1010j)  +/-  (1.73e-244, 1.73e-244j)
| (-0.3288374298837069995 + 9.3928868033156234725e-1021j)  +/-  (7.09e-251, 7.09e-251j)
| (-0.79645920050990229339 + 4.739573927594155297e-1013j)  +/-  (1.38e-244, 1.38e-244j)
| (-0.74307883398196526255 - 2.7619717387909273875e-1015j)  +/-  (3.32e-245, 3.32e-245j)
| (0.74307883398196526255 + 5.1537218162121616705e-1017j)  +/-  (3.27e-245, 3.27e-245j)
| (0.68448630913095935745 + 2.7056256736225720158e-1018j)  +/-  (6.69e-246, 6.69e-246j)
| (0.24866779279136575881 - 7.6377439297630785352e-1026j)  +/-  (4.23e-252, 4.23e-252j)
| (-0.68448630913095935745 + 7.7132752884455410547e-1018j)  +/-  (5.85e-246, 5.85e-246j)
| (-0.55334239186158178124 + 9.0221875926205078643e-1020j)  +/-  (1.16e-247, 1.16e-247j)
| (-7.9793385351888420652e-1031 - 1.5024797943812797085e-1030j)  +/-  (6.29e-1029, 6.29e-1029j)
| (0.62109260840892448315 - 6.5829627112506761945e-1021j)  +/-  (9.28e-247, 9.28e-247j)
| (0.4067005093183261101 + 9.3092594399599570399e-1025j)  +/-  (1.05e-249, 1.05e-249j)
| (-0.24866779279136575881 - 2.395338078844723047e-1026j)  +/-  (3.75e-252, 3.75e-252j)
| (-0.62109260840892448315 - 7.46046734128546513e-1024j)  +/-  (1.01e-246, 1.01e-246j)
| (-0.16675393023985197697 + 1.1431569275347005333e-1031j)  +/-  (2.45e-253, 2.45e-253j)
| (0.3288374298837069995 - 5.5942062305651565137e-1031j)  +/-  (6.41e-251, 6.41e-251j)
| (0.55334239186158178124 + 1.5947084078875896293e-1026j)  +/-  (1.22e-247, 1.22e-247j)
| (-0.083670408954769901943 - 1.6473863705078372067e-1033j)  +/-  (9.66e-255, 9.66e-255j)
| (-0.48171087780320555415 - 2.1991092246282043407e-1027j)  +/-  (1.15e-248, 1.15e-248j)
| (-0.4067005093183261101 - 2.1288723624751432834e-1028j)  +/-  (1.19e-249, 1.19e-249j)
| (0.16675393023985197697 + 2.1438514993065151945e-1032j)  +/-  (2.95e-253, 2.95e-253j)
-------------------------------------------------
The weights are:
| (0.0052730572794979393517 + 5.0001390099618579816e-889j)  +/-  (7.28e-80, 1.67e-198j)
| (0.012238780100307556526 - 8.084073275383996601e-889j)  +/-  (5.51e-80, 1.27e-198j)
| (0.032461639847521481067 + 3.957976924572821146e-889j)  +/-  (1.3e-80, 2.99e-199j)
| (0.0052730572794979393517 + 1.0060690114736972059e-891j)  +/-  (7.56e-82, 1.74e-200j)
| (0.032461639847521481067 + 1.5731084960533620661e-890j)  +/-  (5.13e-82, 1.18e-200j)
| (0.025886036990558933523 - 1.1037303244346334198e-890j)  +/-  (4.8e-82, 1.1e-200j)
| (0.083474573625862787252 - 1.1508075007415265774e-889j)  +/-  (2.33e-83, 5.35e-202j)
| (0.038809602501934544489 - 3.5255191392124931043e-889j)  +/-  (3.76e-82, 8.64e-201j)
| (0.019129044489083966044 + 5.5464550956284740588e-889j)  +/-  (2.08e-81, 4.77e-200j)
| (0.012238780100307556526 - 3.5271467317194735328e-891j)  +/-  (1.99e-82, 4.57e-201j)
| (0.038809602501934544489 - 2.0950392734454394121e-890j)  +/-  (1.47e-83, 3.38e-202j)
| (0.019129044489083966044 + 6.9353728211513183627e-891j)  +/-  (1.86e-82, 4.28e-201j)
| (0.025886036990558933523 - 4.5650192816904937034e-889j)  +/-  (5.48e-83, 1.26e-201j)
| (0.044885364662437166657 + 3.1914012298351156608e-889j)  +/-  (2.1e-84, 4.83e-203j)
| (0.073406777248488172725 + 6.9376317539408441375e-890j)  +/-  (6.98e-87, 1.6e-205j)
| (0.044885364662437166657 + 2.6647972698344718884e-890j)  +/-  (5.29e-85, 1.21e-203j)
| (0.050646297654824601604 - 3.2788425822858302062e-890j)  +/-  (7.58e-86, 1.74e-204j)
| (0.079108861837529380767 + 1.7161555839968661292e-889j)  +/-  (1.93e-88, 4.44e-207j)
| (0.050646297654824601604 - 2.9183085545155489908e-889j)  +/-  (1.85e-86, 4.26e-205j)
| (0.056051987998274917809 + 2.6864471074140078832e-889j)  +/-  (3.09e-87, 7.1e-206j)
| (0.056051987998274917809 + 3.9344539828035260332e-890j)  +/-  (2.68e-87, 6.15e-206j)
| (0.061064516523225986131 - 4.6295264711123553641e-890j)  +/-  (4.69e-88, 1.08e-206j)
| (0.08113662450846503051 - 9.5685674033823000429e-890j)  +/-  (4.53e-90, 1.04e-208j)
| (0.061064516523225986131 - 2.4839396761773351603e-889j)  +/-  (3.07e-89, 7.05e-208j)
| (0.069772451555700344885 - 2.1391173308209507025e-889j)  +/-  (1.67e-90, 3.85e-209j)
| (0.083768360993138904797 + 1.2538713606245309078e-889j)  +/-  (4.25e-91, 9.76e-210j)
| (0.065648722872751249484 + 5.3624561095758501396e-890j)  +/-  (8.16e-90, 1.87e-208j)
| (0.076526207570529237886 - 7.7787705250804888055e-890j)  +/-  (8.91e-91, 2.05e-209j)
| (0.08113662450846503051 - 1.5918616630741317548e-889j)  +/-  (4.06e-92, 9.32e-211j)
| (0.065648722872751249484 + 2.3031941562914580578e-889j)  +/-  (1.66e-91, 3.8e-210j)
| (0.082595272236437250891 + 1.4738754759060084322e-889j)  +/-  (2.19e-92, 5.04e-211j)
| (0.079108861837529380767 + 8.6555685077132925206e-890j)  +/-  (3.49e-92, 8.01e-211j)
| (0.069772451555700344885 - 6.1320768216621475666e-890j)  +/-  (8.13e-92, 1.87e-210j)
| (0.083474573625862787252 - 1.3614107344731669738e-889j)  +/-  (9.98e-93, 2.29e-211j)
| (0.073406777248488172725 + 1.9881640873536026025e-889j)  +/-  (1.29e-93, 2.96e-212j)
| (0.076526207570529237886 - 1.8477959808560617879e-889j)  +/-  (1.16e-93, 2.66e-212j)
| (0.082595272236437250891 + 1.0518838825000918791e-889j)  +/-  (1.22e-93, 2.78e-212j)
