The totally real cubic subfield L of Q(exp(2*Pi*I/13))
[L:Q] = 3, discriminant = 132.
Minimal polynomial:  x^3-9*x^2+14*x-1
Ramified primes: 13
Inert primes: 2, 3, 7, 11, 17, 19, 23, 29, 37
Split primes: 5, 31

 k factor(k) zL(1-k) denominator of zL(k) 2 2 -1/3 [3, 1] 4 22 11227/390 [2, 1; 3, 1; 5, 1; 13, 1] 6 2*3 -6701911/63 [3, 2; 7, 1] 8 23 2853073794787/780 [2, 2; 3, 1; 5, 1; 13, 1] 10 2*5 -20913215006301031/33 [3, 1; 11, 1] 12 22*3 3206733659326104097826029/8190 [2, 1; 3, 2; 5, 1; 7, 1; 13, 1] 14 2*7 -2069989928154737842614201751/3 [3, 1] 16 24 78663375875812483572166748601502733219/26520 [2, 3; 3, 1; 5, 1; 13, 1; 17, 1] 18 2*32 -99498235030131603936258919545898850571482557/3591 [3, 3; 7, 1; 19, 1] 20 22*5 11035697452453804037380841545936906133399775925684937/21450 [2, 1; 3, 1; 5, 2; 11, 1; 13, 1] 22 2*11 -1220853774162853604685947884218211298056565169424023204853/69 [3, 1; 23, 1] 24 23*3 17429069689173335643022300384188550385494167711590331996185818375189/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] 26 2*13 -320058609371745754403712171765753516350752662343108103846629668989005741/3 [3, 1] 28 22*7 193765476022909705561402481827166487595307510955032529745651903066835620836071953289/11310 [2, 1; 3, 1; 5, 1; 13, 1; 29, 1] 30 2*3*5 -91468384756151564145750345376001129130328398108372299216993719932884543319032897506955251831/21483 [3, 2; 7, 1; 11, 1; 31, 1] 32 25 84318455276942504224836344287772092043662372093675996265781422866294967736174496729820736747884732099/53040 [2, 4; 3, 1; 5, 1; 13, 1; 17, 1] 34 2*17 -2606911780445990223088578532053271669923637612957651984261484058123295573323961943458945520677451817519401/3 [3, 1] 36 22*32 11740879874841876871751314199085032620670699087508252372925803215044533425041311829081844046719442477361958966667955788547/17272710 [2, 1; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1]