The totally real subfield L of Q(exp(2*Pi*I/8))
[L:Q] = 2, discriminant = 23.
Minimal polynomial:  x^2-2
Ramified primes:  2
Inert primes: 3, 5, 11, 13, 19, 29, 37
Split primes: 7, 17, 23, 31
 
 
k factor(k) zL(1-k) denominator of zL(k)
2 2 1/12 [2, 2; 3, 1]
22 11/120 [2, 3; 3, 1; 5, 1]
6 2*3 361/252 [2, 2; 3, 2; 7, 1]
8 23 24611/240 [2, 4; 3, 1; 5, 1]
10 2*5 2873041/132 [2, 2; 3, 1; 11, 1]
12 22*3 27233033477/2520 [2, 3; 3, 2; 5, 1; 7, 1]
14 2*7 129570724921/12 [2, 2; 3, 1]
16 24 159549339299844787/8160 [2, 5; 3, 1; 5, 1; 17, 1]
18 2*32 853244674392953815867/14364 [2, 2; 3, 3; 7, 1; 19, 1]
20 22*5 1883014201750720442753521/6600 [2, 3; 3, 1; 5, 2; 11, 1]
22 2*11 570397367814021408569126923/276 [2, 2; 3, 1; 23, 1]
24 23*3 109511675519893842297200129361077/5040 [2, 4; 3, 2; 5, 1; 7, 1]
26 2*13 3854553830778219905574569395190491/12 [2, 2; 3, 1]
28 22*7 22620741302181663024236570255435200710817/3480 [2, 3; 3, 1; 5, 1; 29, 1]
30 2*3*5 487857934646005911764739665381199198181718311/2772 [2, 2; 3, 2; 7, 1; 11, 1]
32 25 102010928071772976385504537152795193127593261481587/16320 [2, 6; 3, 1; 5, 1; 17, 1]
34 2*17 3434757869192636734100930146655497570361814688585871/12 [2, 2; 3, 1]
36 22*32 88459896110093779093586793692246545522548443631029537081731931/5314680   [2, 3; 3, 3; 5, 1; 7, 1; 19, 1; 37, 1]