While studying Dirichlet L-functions and Dedekind zeta functions I stumbled across mentions of the so called Siegel-Klingen theorem on the internet. However, I have doubts whether the thesis of the Siegel-Klingen theorem is that
1) For all number fields K $\zeta_K(-k)\in\mathbb{Q},k\geq0$;
or if it is
2) For all completely real K $\zeta_K(2k),k\geq1$, is a rational multiple of $|\mathrm{disc}(K)|^{\frac{1}{2}}\pi^{2k N},\, N=[K:\mathbb{Q}]$;
the second statement follows from the first (restricted to when K is completely real) considering the functional equation for $\zeta_K$, and I know how to prove the first statement when K is abelian over $\mathbb{Q}$, by using the analogous fact for Dirichlet L-functions L(s,$\chi$) and the factorization of $\zeta_K$ as product of some of them.
I have done a quick search on google, but I could not find a satisfactory reference in english, so I'd appreciate if someone pointed me out one,if it exists. Thanks in advance!