The totally real subfield L of Q(exp(2*Pi*I/12))
[L:Q] = 2, discriminant = 12.
Minimal polynomial:  x^2-3
Ramified primes:  2, 3
Inert primes: 5, 7, 17, 19, 29, 31
Split primes: 11, 13, 23, 37

 k factor(k) zL(1-k) denominator of zL(k) 2 2 1/6 [2, 1; 3, 1] 4 22 23/60 [2, 2; 3, 1; 5, 1] 6 2*3 1681/126 [2, 1; 3, 2; 7, 1] 8 23 257543/120 [2, 3; 3, 1; 5, 1] 10 2*5 67637281/66 [2, 1; 3, 1; 11, 1] 12 22*3 18752521534133/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] 14 2*7 15442193173681/6 [2, 1; 3, 1] 16 24 42783818174313146311/4080 [2, 4; 3, 1; 5, 1; 17, 1] 18 2*32 514802473837215246476827/7182 [2, 1; 3, 3; 7, 1; 19, 1] 20 22*5 2556248976935265966594188533/3300 [2, 2; 3, 1; 5, 2; 11, 1] 22 2*11 1742246443991808605483768362723/138 [2, 1; 3, 1; 23, 1] 24 23*3 9784043347352101537435984662493577693/32760 [2, 3; 3, 2; 5, 1; 7, 1; 13, 1] 26 2*13 59603426243912408678663547473670548011/6 [2, 1; 3, 1] 28 22*7 787021254910761302606269484108127241457524021/1740 [2, 2; 3, 1; 5, 1; 29, 1] 30 2*3*5 1183905977142282240924625045967870444850942156438481/42966 [2, 1; 3, 2; 7, 1; 11, 1; 31, 1] 32 25 17967653479516058193170206595247961216400601193448372071/8160 [2, 5; 3, 1; 5, 1; 17, 1] 34 2*17 1361204292314783105732805341719017219109085563241077649231/6 [2, 1; 3, 1] 36 22*32 1025414556106448459132233693924027659685077471949823090581301163897659/34545420 [2, 2; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1]