L = Q[x]/(x^2-24)
[L:Q] = 2, discriminant = 24.
Minimal polynomial:  x^2-24
Ramified primes:  2, 3
Inert primes: 7, 11, 13, 17, 31, 37
Split primes: 5, 19, 23, 29
 
 

k	factor(k)	zL(1-k)	denominator of zL(1-k)
2	2	1/2	[2, 1]
4	22	87/20	[2, 2; 5, 1]
6	2*3	3623/6	[2, 1; 3, 1]
8	23	15540167/40	[2, 3; 5, 1]
10	2*5	16324877601/22	[2, 1; 11, 1]
12	22*3	2586338303951011/780	[2, 2; 3, 1; 5, 1; 13, 1]
14	2*7	59633825180769841/2	[2, 1]
16	24	660880926452517181569159/1360	[2, 4; 5, 1; 17, 1]
18	2*32	4544082991633386942201552461/342	[2, 1; 3, 2; 19, 1]
20	22*5	631781365642564377262812035249077/1100	[2, 2; 5, 2; 11, 1]
22	2*11	1722396914545775335671336811132998243/46	[2, 1; 23, 1]
24	23*3	5527184623827320720804884942579502766150331/1560	[2, 3; 3, 1; 5, 1; 13, 1]
26	2*13	942789767203372848785249600906315045590165291/2	[2, 1]
28	22*7	49795498846995002717120976487518848181828208151855349/580	[2, 2; 5, 1; 29, 1]
30	2*3*5	42803845767925533625901559679513737511976953587525759879143/2046	[2, 1; 3, 1; 11, 1; 31, 1]
32	25	18189257533562225887976804252771500706059403491007010114263580199/2720	[2, 5; 5, 1; 17, 1]
34	2*17	5511970821772721584086223746242599677014403850712665374289138080591/2	[2, 1]
36	22*32	2372712014916573736857334377402291123253402254747327583217143214909606512470253/1645020	[2, 2; 3, 2; 5, 1; 13, 1; 19, 1; 37, 1]