The totally real subfield L of Q(exp(2pi/9))
[L:Q] = 3
Minimal polynomial  x^3 - 3*x + 1
Ramified primes:  3
Inert primes:
Split primes:

 k factor(k) zL(1-k) denominator of zL(k) 2 -1/9 [3, 2] 4 22 199/90 [2, 1; 3, 2; 5, 1] 6 2*3 -50353/27 [3, 3] 8 23 2648750959/180 [2, 2; 3, 2; 5, 1] 10 2*5 -57973999723111/99 [3, 2; 11, 1] 12 22*3 291720890751434104747/3510 [2, 1; 3, 3; 5, 1; 13, 1] 14 2*7 -302807634262249042876951/9 [3, 2] 16 24 203340723290875963356476808592943/6120 [2, 3; 3, 2; 5, 1; 17, 1] 18 2*32 -109725885024970496508485353263175846171/1539 [3, 4; 19, 1] 20 22*5 1505375405471479277033590026464694005548856429/4950 [2, 1; 3, 2; 5, 2; 11, 1] 22 2*11 -497334585142124563981977742725220753042250099846773/207 [3, 2; 23, 1] 24 23*3 233001011478375646922914852684472233719019739985105394945987/7020 [2, 2; 3, 3; 5, 1; 13, 1] 26 2*13 -6880306453075003853011546950459213981969421264506666076002518701/9 [3, 2] 28 22*7 73605106310824909669795040156964037021274661432100401011898012297587126573/2610 [2, 1; 3, 2; 5, 1; 29, 1] 30 2*3*5 -14823286255915094308037893888123137308859995503700960041475387278252283804406813073/9207 [3, 3; 11, 1; 31, 1] 32 25 1690236373468982177735401213606887434271003697089940477647269894291973419552058160312937423/12240 [2, 4; 3, 2; 5, 1; 17, 1] 34 2*17 -156059825587317105003363304069294155533519186925702977386601799959520154353405206177762617724201/9 [3, 2] 36 22*32 23065560670265700639067447283880696130646623752789813419820819835254540406174745738881723784737711767806737381/7402590 [2, 1; 3, 4; 5, 1; 13, 1; 19, 1; 37, 1]