The totally real cubic subfield L of Q(exp(2pi/19))
[L:Q] = 3, discriminant = 19^2.
Minimal polynomial:  x^3 - 354315*x^2 + 39645147398*x - 1424861898171643
Ramified primes: 19
Inert primes: 2, 3, 5, 13, 17, 23, 29
Split primes: 7, 11, 31, 37
 
 

k	factor(k)	zL(1-k)	denominator of zL(k)
2	2	-1	1
4	22	4087/10	[2, 1; 5, 1]
6	2*3	-2758494229/399	[3, 1; 7, 1; 19, 1]
8	23	21696966762367/20	[2, 2; 5, 1]
10	2*5	-9433962448200800551/11	[11, 1]
12	22*3	125409648387935611859681662663/51870	[2, 1; 3, 1; 5, 1; 7, 1; 13, 1; 19, 1]
14	2*7	-19441227878944562710748606969911	1
16	24	259313831060432392490226493319685940181759/680	[2, 3; 5, 1; 17, 1]
18	2*32	-19455967175251474562833273219570517539567228701757/1197	[3, 2; 7, 1; 19, 1]
20	22*5	757416698800862135086999717821959149253902537676096929277/550	[2, 1; 5, 2; 11, 1]
22	2*11	-4970305542360347874402919688376721171964467489250088528234487573/23	[23, 1]
24	23*3	6151602135166085469209053469292246449331322831489633040864095794273646637023/103740	[2, 2; 3, 1; 5, 1; 7, 1; 13, 1; 19, 1]
26	2*13	-27128822257312678255789674288911903341787466155945159675721756812133478163527021	1
28	22*7	5764683500176888379941162702868902900915276598413135479553832307577930176481477186979562749/290	[2, 1; 5, 1; 29, 1]
30	2*3*5	-3066959395677233749164961158094253244747692391432756387431226672220108625676617447897331025678143324469/136059	[3, 1; 7, 1; 11, 1; 19, 1; 31, 1]
32	25	52228036540900642093213435165483604957808574416125683305640152151212155636542795125004355205037840758662176799/1360	[2, 4; 5, 1; 17, 1]
34	2*17	-95783728652636865832254296923246204263689826550726282847151327613830434636645404367431064496246497835759165748830761	1
36	22*32	1968371389087061160723662750483439811179265537775687542390887543705989124558914958164670894663263159955424454674901520065940890629171/5757570	[2, 1; 3, 2; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1]