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]