x^128 - 24744*x^124 + 318263348*x^120 - 4908783454048*x^116 + 70365514719842
906*x^112 - 664951036082412593672*x^108 + 4463003605812657475887568*x^104 -
29117506764711911281675568216*x^100 + 200165383706633501807266315567171*x^96
- 638656470413424881875191732251560392*x^92 - 40394679385796315248477248083
90748037904*x^88 + 49705977334740225212797113076467432277609832*x^84 - 13600
8434606352219420850355464811214338694510278*x^80 - 5837162339201745610992485
70605733460035609736564512*x^76 + 573751376055927644006900021942573145518484
5811906098932*x^72 - 1666033124257131799360759760109486349232970799402866557
4392*x^68 + 15611321264070057869443398525428470474531587759431929536622177*x
^64 + 41671759284875771863744470472818868099409964243213065077165416192*x^60
- 5362216985058993248300440480986425469071571390466426012069336067424*x^56
- 26489530631714445718357963598763622388539245328126581994749267416726016*x^
52 + 41667470831823461898186644724140534106347144893277289318131848494558688
64*x^48 + 649570727218432913865673780433647425904155643882121284283800795369
4038069248*x^44 - 1369546197468588106388642080137000292262714755907725023133
501300527558898500096*x^40 - 61613053106915320488778113804734851464486398733
7377452528588918812081081489641472*x^36 + 1958197287783726777380269951911856
12180120724094578171465886350410610092763921409536*x^32 - 522868850847745590
7187358180354718054146517446147172770121259841280516467720876130304*x^28 - 9
9249876125558218503085529841337319831975151855563906384679038058504138036517
9998543872*x^24 - 1124011837386053693628927441408771599107812947087629922629
64816716417738416605872660807680*x^20 + 258550303314306655686082694256980478
48466707234049941211154803508680808662178168320198819840*x^16 - 679959640868
0815726678896554493737727631356385185659224682877675655504896276160181819044
528128*x^12 + 57740717806831774171616584849651964026128382472069488005984202
721923244144627188879389917839360*x^8 + 732890044636684366116759828590467183
46055267621347064592139434459925865091137569189035779746693120*x^4 + 2968393
5454107535914952547762124621750060810977789725149141877139915645447322613169
72553546655399936
x^128 + 72*x^124 + 97244*x^120 + 6305904*x^116 + 4474491398*x^112 + 21245066
3592*x^108 + 77356958612120*x^104 + 4717963098509752*x^100 + 304571637129377
265*x^96 + 9523624355823921064*x^92 + 960937109432614682824*x^88 - 182221806
930477490768600*x^84 + 16240354327321393671801334*x^80 - 5991642039586462657
60006896*x^76 + 12957213594155705011858581860*x^72 - 91671414671045613984781
519080*x^68 - 17505084636311203518847045180*x^64 + 1504843143185030371002977
4500968*x^60 - 144562251724578643705279898281980*x^56 + 16429512450866898071
77703608812016*x^52 + 10457530382596818823814308246264022*x^48 - 17024155298
1703038852433060611361192*x^44 + 618757876424162521918492459357585416*x^40 +
11173843551821992746142770702047029848*x^36 + 18088876540020424479807643058
611350577*x^32 - 31462390484164950206024293324833300312*x^28 + 5431124475238
18127330327169378088491544*x^24 - 250002696862357027775219783338121547016*x^
20 + 751472242213567478663440513772891772006*x^16 + 332794182402309742374439
5331305440312048*x^12 + 1756542571511582451971278846041012726972*x^8 - 34506
4330125954756518709614653268319656*x^4 + 14712240920408219482556913763542000
481
P1 and P2 are isomorphic. galoisinit(P1) takes 6min. galoisinit(P2) takes 90min. I understand that the most likely explanation for the huge (15x) performance slowdown is the probabilistic nature of algorithm, but perhaps there's some room for improvement in the edge cases like P2?