L = Q[x]/(x^2-40)
[L:Q] = 2, discriminant = 40.
Minimal polynomial:  x^2-40
Ramified primes:  2, 5
Inert primes: 7, 11, 17, 19, 23, 29
Split primes: 3, 13, 31, 37
 
 

k	factor(k)	zL(1-k)	denominator of zL(1-k)
2	2	7/6	[2, 1; 3, 1]
4	22	1577/60	[2, 2; 3, 1; 5, 1]
6	2*3	1264807/126	[2, 1; 3, 2; 7, 1]
8	23	2150342537/120	[2, 3; 3, 1; 5, 1]
10	2*5	6273958190407/66	[2, 1; 3, 1; 11, 1]
12	22*3	19327071911053422827/16380	[2, 2; 3, 2; 5, 1; 7, 1; 13, 1]
14	2*7	176836590584822968807/6	[2, 1; 3, 1]
16	24	5443774185448827969118891369/4080	[2, 4; 3, 1; 5, 1; 17, 1]
18	2*32	727811089794971859689502345571069/7182	[2, 1; 3, 3; 7, 1; 19, 1]
20	22*5	40154912568352747611033023042162274187/3300	[2, 2; 3, 1; 5, 2; 11, 1]
22	2*11	304090330290887531809755216310777086459781/138	[2, 1; 3, 1; 23, 1]
24	23*3	18974436285039855244365922390662114802894020172307/32760	[2, 3; 3, 2; 5, 1; 7, 1; 13, 1]
26	2*13	1284337697708472979372679882122257485773034425490317/6	[2, 1; 3, 1]
28	22*7	188430828053950266672225355211898845875545322299932105450539/1740	[2, 2; 3, 1; 5, 1; 29, 1]
30	2*3*5	3149489747561981724204704081586571990837347499024599495197940316807/42966	[2, 1; 3, 2; 7, 1; 11, 1; 31, 1]
32	25	531094543673857504216340861327958747347181609388965009640737833983210249/8160	[2, 5; 3, 1; 5, 1; 17, 1]
34	2*17	447055329671540958752211046354104758009806750016023773935137726413340895657/6	[2, 1; 3, 1]
36	22*32	3741923767377165307720777117618025575397471808964339741031674319977996641447013880739461/34545420	[2, 2; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1]