L = Q[x]/(x^2-13)
[L:Q] = 2, discriminant = 13.
Minimal polynomial:  x^2-13
Ramified primes:  13
Inert primes: 2, 5, 7, 11, 19, 31, 37
Split primes: 3, 17, 23, 29
 
 

k	factor(k)	zL(1-k)	denominator of zL(k)
2	2	1/6	[2, 1; 3, 1]
4	22	29/60	[2, 2; 3, 1; 5, 1]
6	2*3	33463/1638	[2, 1; 3, 2; 7, 1; 13, 1]
8	23	467669/120	[2, 3; 3, 1; 5, 1]
10	2*5	144547171/66	[2, 1; 3, 1; 11, 1]
12	22*3	47067236077919/16380	[2, 2; 3, 2; 5, 1; 7, 1; 13, 1]
14	2*7	45495767916691/6	[2, 1; 3, 1]
16	24	147939984968716630933/4080	[2, 4; 3, 1; 5, 1; 17, 1]
18	2*32	27159338094720360855345181/93366	[2, 1; 3, 3; 7, 1; 13, 1; 19, 1]
20	22*5	12174855335880619308295189279/3300	[2, 2; 3, 1; 5, 2; 11, 1]
22	2*11	9738560526887500711761231871273/138	[2, 1; 3, 1; 23, 1]
24	23*3	64184156678679131455067913889018026839/32760	[2, 3; 3, 2; 5, 1; 7, 1; 13, 1]
26	2*13	458886127252695004415215453937104183681/6	[2, 1; 3, 1]
28	22*7	7111224376757111074805747134193347871898539743/1740	[2, 2; 3, 1; 5, 1; 29, 1]
30	2*3*5	163208472336761293665410529395434958347731151528481623/558558	[2, 1; 3, 2; 7, 1; 11, 1; 13, 1; 31, 1]
32	25	223613340952997516543979434097249313411112078292443739253/8160	[2, 5; 3, 1; 5, 1; 17, 1]
34	2*17	19881716170300177604943960879958666096944395349276789711341/6	[2, 1; 3, 1]
36	22*32	17577384395118304860229267936743101792367686188967360624051800379960177/34545420	[2, 2; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1]