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]
4	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]