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

k	factor(k)	zL(1-k)	denominator of zL(1-k)
2	2	5/6	[2, 1; 3, 1]
4	22	1129/60	[2, 2; 3, 1; 5, 1]
6	2*3	115865/18	[2, 1; 3, 2]
8	23	1193648689/120	[2, 3; 3, 1; 5, 1]
10	2*5	2988574807055/66	[2, 1; 3, 1; 11, 1]
12	22*3	1126138824426408037/2340	[2, 2; 3, 2; 5, 1; 13, 1]
14	2*7	61724704374047728655/6	[2, 1; 3, 1]
16	24	1625886902325466618525254353/4080	[2, 4; 3, 1; 5, 1; 17, 1]
18	2*32	983107522010748251749534394373935/37962	[2, 1; 3, 3; 19, 1; 37, 1]
20	22*5	8780152495032015611104972776926106659/3300	[2, 2; 3, 1; 5, 2; 11, 1]
22	2*11	56891811270123946109776919715889222866365/138	[2, 1; 3, 1; 23, 1]
24	23*3	433911874930178370627361990523141469876914594077/4680	[2, 3; 3, 2; 5, 1; 13, 1]
26	2*13	175911166485334350140633936023221162252822595543205/6	[2, 1; 3, 1]
28	22*7	22082569468039048855099345948162953549100473737499786154883/1740	[2, 2; 3, 1; 5, 1; 29, 1]
30	2*3*5	45115240238382314357179807313418320850080812921254585950553043865/6138	[2, 1; 3, 2; 11, 1; 31, 1]
32	25	45565529434948529023674033156713910264466057785696102264822266218754033/8160	[2, 5; 3, 1; 5, 1; 17, 1]
34	2*17	32817789385672302405698899493694670283958202718161570082249370089698415905/6	[2, 1; 3, 1]
36	22*32	33575957599937117078539644693724914606758605879233451973775731915824573141246719647851/4935060	[2, 2; 3, 3; 5, 1; 13, 1; 19, 1; 37, 1]