L = Q[x]/(x^2-44)
[L:Q] = 2, discriminant = 44.
Minimal polynomial  x^2-44
Ramified primes:  2, 11
Inert primes: 3, 11, 13, 17, 23, 29, 31
Split primes: 5, 7, 19, 37
 
 

k	factor(k)	zL(1-k)	denominator of zL(1-k)
2	2	7/6	[2, 1; 3, 1]
4	22	2153/60	[2, 2; 3, 1; 5, 1]
6	2*3	2130727/126	[2, 1; 3, 2; 7, 1]
8	23	4393611593/120	[2, 3; 3, 1; 5, 1]
10	2*5	15515203176007/66	[2, 1; 3, 1; 11, 1]
12	22*3	57833610972825439403/16380	[2, 2; 3, 2; 5, 1; 7, 1; 13, 1]
14	2*7	640284813520180963687/6	[2, 1; 3, 1]
16	24	23849907642936468917264806441/4080	[2, 4; 3, 1; 5, 1; 17, 1]
18	2*32	3858252593190828124973590079348989/7182	[2, 1; 3, 3; 7, 1; 19, 1]
20	22*5	257570454888069177671400223300084538443/3300	[2, 2; 3, 1; 5, 2; 11, 1]
22	2*11	2360181170214245276197461642177962807357701/138	[2, 1; 3, 1; 23, 1]
24	23*3	178195602951418769387248613782238554963197881783123/32760	[2, 3; 3, 2; 5, 1; 7, 1; 13, 1]
26	2*13	14594616971473493215520156507649856776365301930628237/6	[2, 1; 3, 1]
28	22*7	2590900879751548185461971322384417102931821687710198139310571/1740	[2, 2; 3, 1; 5, 1; 29, 1]
30	2*3*5	52399170394895627715682952998769642135319661333469727999989000524807/42966	[2, 1; 3, 2; 7, 1; 11, 1; 31, 1]
32	25	10691568483016382137593722574105500990769954492520571787854701471842530761/8160	[2, 5; 3, 1; 5, 1; 17, 1]
34	2*17	10889707874192178568357333572044524510856826605968841320249856684620427584937/6	[2, 1; 3, 1]
36	22*32	110289777018090342826754595437522916167936202996315571094040801777700666145501213104319429/34545420	[2, 2; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1]