L = Q[x]/(x^2-41)
[L:Q] = 2, discriminant = 41.
Minimal polynomial:  x^2-41
Ramified primes:  41
Inert primes: 3, 7, 11, 13, 17, 19, 29
Split primes: 2, 5, 23, 31, 37
 
 

k	factor(k)	zL(1-k)	denominator of zL(1-k)
2	2	4/3	[3, 1]
4	22	448/15	[3, 1; 5, 1]
6	2*3	733924/63	[3, 2; 7, 1]
8	23	324649814/15	[3, 1; 5, 1]
10	2*5	3970068530764/33	[3, 1; 11, 1]
12	22*3	6419998586927832328/4095	[3, 2; 5, 1; 7, 1; 13, 1]
14	2*7	123407242075130286004/3	[3, 1]
16	24	498892114387951583457289649/255	[3, 1; 5, 1; 17, 1]
18	2*32	560606297292308330570657275519348/3591	[3, 3; 7, 1; 19, 1]
20	22*5	666159673951002284358170884495203519568/33825	[3, 1; 5, 2; 11, 1; 41, 1]
22	2*11	258544809927042393527437248353417044884172/69	[3, 1; 23, 1]
24	23*3	4237305315191737531693797080486099851545364991834/4095	[3, 2; 5, 1; 7, 1; 13, 1]
26	2*13	1205335113210720999099053080674507703268775833425444/3	[3, 1]
28	22*7	3203319572341859771873441135349548114989623635687280592504/15	[3, 1; 5, 1]
30	2*3*5	3262603011651575071608873923836328530577245128911004709237729463764/21483	[3, 2; 7, 1; 11, 1; 31, 1]
32	25	72252622819452126528953616703345956974563213860732415492125070382882909/510	[2, 1; 3, 1; 5, 1; 17, 1]
34	2*17	511188142951485403129238972414935140271972584689043096443896209790071318404/3	[3, 1]
36	22*32	2247668015835430789938983115747200624215868535674792286250128960057137277428710307960224/8636355	[3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1]