Starting with polynomial:
P : 4294967296*t^32 - 1065151889408*t^30 + 115835267973120*t^28 - 7297621882306560*t^26 + 296465888968704000*t^24 - 8182458535536230400*t^22 + 157512326809072435200*t^20 - 2137667292408840192000*t^18 + 20441443483659534336000*t^16 - 136276289891063562240000*t^14 + 620057119004339208192000*t^12 - 1860171357013017624576000*t^10 + 3487821294399408046080000*t^8 - 3756115240122439434240000*t^6 + 2012204592922735411200000*t^4 - 402440918584547082240000*t^2 + 12576278705767096320000
Extension levels are: 32
-------------------------------------------------
Ending with final polynomial:
P : 4294967296*t^32 - 1065151889408*t^30 + 115835267973120*t^28 - 7297621882306560*t^26 + 296465888968704000*t^24 - 8182458535536230400*t^22 + 157512326809072435200*t^20 - 2137667292408840192000*t^18 + 20441443483659534336000*t^16 - 136276289891063562240000*t^14 + 620057119004339208192000*t^12 - 1860171357013017624576000*t^10 + 3487821294399408046080000*t^8 - 3756115240122439434240000*t^6 + 2012204592922735411200000*t^4 - 402440918584547082240000*t^2 + 12576278705767096320000
-------------------------------------------------
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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   32 out of 32
Indefinite weights: 0 out of 32
Negative weights:   0 out of 32
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.8122259495159138328 + 6.3163925493047145986e-472j)  +/-  (1.98e-120, 1.98e-120j)
| (5.2755509865158801278 - 9.7257703081158006946e-479j)  +/-  (3.57e-120, 3.57e-120j)
| (-7.1258139098307275728 + 2.9638226502804860906e-484j)  +/-  (5.94e-122, 5.94e-122j)
| (-5.8122259495159138328 + 1.5996937831155812104e-481j)  +/-  (1.81e-120, 1.81e-120j)
| (6.4094981492696604122 - 9.1042205696584516248e-483j)  +/-  (4.94e-121, 4.94e-121j)
| (-5.2755509865158801278 + 3.487725169779878282e-483j)  +/-  (3.51e-120, 3.51e-120j)
| (7.1258139098307275728 - 4.4076173870077237025e-486j)  +/-  (6.4e-122, 6.4e-122j)
| (-1.7676541094632016046 - 2.5195193263192612353e-488j)  +/-  (6.49e-123, 6.49e-123j)
| (-6.4094981492696604122 + 5.3033906240424929304e-487j)  +/-  (5.88e-121, 5.88e-121j)
| (3.8537554854714446439 - 1.5153717632241738479e-485j)  +/-  (3.14e-120, 3.14e-120j)
| (0.58497876543593244847 - 5.7769878496297274947e-493j)  +/-  (8.63e-126, 8.63e-126j)
| (2.577249537732317454 + 2.356202101708400556e-487j)  +/-  (1.46e-121, 1.46e-121j)
| (4.777164503502596393 - 3.8962877354106767621e-488j)  +/-  (4.24e-120, 4.24e-120j)
| (-2.1694991836061121733 - 2.1514583287895282596e-493j)  +/-  (4.21e-122, 4.21e-122j)
| (3.4171674928185707359 - 2.9428965532888947371e-490j)  +/-  (1.55e-120, 1.55e-120j)
| (1.3703764109528718382 + 1.695154957477655237e-497j)  +/-  (7.21e-124, 7.21e-124j)
| (0.97650046358968283848 + 2.1571162120304303067e-500j)  +/-  (9.24e-125, 9.24e-125j)
| (-4.777164503502596393 + 3.00106457093224021e-494j)  +/-  (5.01e-120, 5.01e-120j)
| (-1.3703764109528718382 - 3.241210888040960333e-508j)  +/-  (7.71e-124, 7.71e-124j)
| (-4.3055479533511984453 + 1.0243032434171109956e-503j)  +/-  (5.16e-120, 5.16e-120j)
| (-3.8537554854714446439 - 4.9068802102785695562e-515j)  +/-  (3.27e-120, 3.27e-120j)
| (1.7676541094632016046 + 2.2749748652420743767e-520j)  +/-  (5.95e-123, 5.95e-123j)
| (0.19484074156939932671 + 1.1326354915916420872e-524j)  +/-  (6.23e-127, 6.23e-127j)
| (-2.9924908250023742063 - 4.3166572473842362436e-519j)  +/-  (6.15e-121, 6.15e-121j)
| (-0.19484074156939932671 + 7.104719378953524751e-527j)  +/-  (6.23e-127, 6.23e-127j)
| (-0.97650046358968283848 - 6.4456415644009207539e-525j)  +/-  (9.21e-125, 9.21e-125j)
| (2.1694991836061121733 - 2.8433807249823073462e-520j)  +/-  (3.67e-122, 3.67e-122j)
| (4.3055479533511984453 + 1.3946469354868076041e-524j)  +/-  (4.22e-120, 4.22e-120j)
| (-3.4171674928185707359 - 9.3625251720074606451e-531j)  +/-  (1.49e-120, 1.49e-120j)
| (-0.58497876543593244847 - 9.8793396077161421504e-539j)  +/-  (8.63e-126, 8.63e-126j)
| (-2.577249537732317454 - 1.6042358190673455712e-538j)  +/-  (1.42e-121, 1.42e-121j)
| (2.9924908250023742063 + 2.7083026249681806891e-538j)  +/-  (5.72e-121, 5.72e-121j)
-------------------------------------------------
The weights are:
| (6.7552902236701187406e-16 - 2.4800201620659761029e-486j)  +/-  (7.05e-39, 9.43e-98j)
| (2.3780648557778086759e-13 + 1.4917470350629167413e-485j)  +/-  (1.29e-37, 1.72e-96j)
| (4.1246074890182693364e-23 + 8.1492052180474272057e-492j)  +/-  (3.19e-43, 4.27e-102j)
| (6.7552902236701187406e-16 + 3.6706414395090598314e-488j)  +/-  (7.4e-41, 9.9e-100j)
| (5.2084495919608612944e-19 - 1.9836895765246034418e-488j)  +/-  (1.26e-41, 1.68e-100j)
| (2.3780648557778086759e-13 - 7.2203758241963845201e-487j)  +/-  (3.57e-40, 4.77e-99j)
| (4.1246074890182693364e-23 + 8.0264621676449711209e-491j)  +/-  (1.23e-43, 1.65e-102j)
| (0.0099034617023205918768 - 2.1553790099996847103e-481j)  +/-  (4.38e-30, 5.86e-89j)
| (5.2084495919608612944e-19 - 9.6942493437739312435e-490j)  +/-  (2.69e-42, 3.6e-101j)
| (8.8812907131058950894e-08 - 2.4981232592697290004e-483j)  +/-  (7.29e-38, 9.75e-97j)
| (0.15653899375759844489 - 1.2425982800587305439e-480j)  +/-  (3.8e-31, 5.08e-90j)
| (0.00030255702581706249216 + 8.8272438614813192207e-482j)  +/-  (4.29e-35, 5.74e-94j)
| (3.3475012398012070049e-11 - 9.1767302444277097102e-485j)  +/-  (1.34e-39, 1.8e-98j)
| (0.0020620510513078847176 + 9.3399682710836096334e-482j)  +/-  (6.11e-35, 8.17e-94j)
| (2.0596221039534288761e-06 + 9.8371748221327705931e-483j)  +/-  (2.87e-37, 3.85e-96j)
| (0.034109847726092050511 - 6.8260362801950514543e-481j)  +/-  (4.99e-32, 6.68e-91j)
| (0.08534480827208076015 + 9.9178935857421321834e-481j)  +/-  (2.69e-31, 3.6e-90j)
| (3.3475012398012070049e-11 + 8.9697812374000415208e-486j)  +/-  (1.03e-41, 1.37e-100j)
| (0.034109847726092050511 + 4.2213420309373163214e-481j)  +/-  (1.63e-33, 2.19e-92j)
| (2.312518412074240541e-09 - 7.8027927664880845581e-485j)  +/-  (1.85e-41, 2.47e-100j)
| (8.8812907131058950894e-08 + 5.0615616748533225024e-484j)  +/-  (3.81e-41, 5.1e-100j)
| (0.0099034617023205918768 + 4.0393689613379945019e-481j)  +/-  (3.21e-37, 4.29e-96j)
| (0.21170556988047931757 + 1.3446970169834497872e-480j)  +/-  (3.15e-35, 4.2e-94j)
| (3.0559803060896301541e-05 + 1.0307476167351427277e-482j)  +/-  (3.38e-40, 4.53e-99j)
| (0.21170556988047931757 - 1.2574658079103248861e-480j)  +/-  (8.5e-36, 1.14e-94j)
| (0.08534480827208076015 - 7.0646837902980961795e-481j)  +/-  (2.29e-36, 3.06e-95j)
| (0.0020620510513078847176 - 2.046518611961808104e-481j)  +/-  (1.45e-38, 1.94e-97j)
| (2.312518412074240541e-09 + 5.2398061685849571743e-484j)  +/-  (2.31e-42, 3.09e-101j)
| (2.0596221039534288761e-06 - 2.5527780812976860735e-483j)  +/-  (3.35e-41, 4.49e-100j)
| (0.15653899375759844489 + 1.0153447053764331498e-480j)  +/-  (6.6e-38, 8.96e-97j)
| (0.00030255702581706249216 - 3.4037783367067457483e-482j)  +/-  (5.29e-40, 7.08e-99j)
| (3.0559803060896301541e-05 - 3.2185453291192112741e-482j)  +/-  (1.1e-40, 1.46e-99j)
