Let $K$ be a real quadratic number field of discriminant $D_K$ and let $\zeta(s,K)$ be the Dedekind zeta function associated to $K$ By the Siegel-Klingen Theorem, if $n>0$ then $\zeta(-n,K)$ is a rational number. On the other hand, $K$ is obviously an abelian number field, thus the factorization of the Dedekind zeta function of an abelian number field tells us that: $$\zeta(s,K)=\zeta(s)L(s,\chi)$$ where $\zeta(s)$ is the famous Riemann zeta function and $L(s,\chi)$ is the Dirichlet L-function associated to $\chi$ where $\chi$ is the unique Dirichlet character with conductor $D_K$ such that the group of characters of $K/\Rats$ is $\{ \chi_0, \chi \}$ and $\chi_0$ is the trivial character. In fact, the values of $\chi$ are simply given by $$\chi(a)=\left(\frac{D_K}{a}\right)$$ where the parentheses denote the Kronecker symbol.

Furthermore, if $k$ is a positive integer then:

1. Putting the values of the Riemann zeta function in terms of Bernoulli numbers one gets: $$\zeta(1-k)=-\frac{B_k}{k}$$ where $B_k$ is the $k$ Bernoulli number;
2. The values of Dirichlet L-series at negative integers can be written in terms of generalized Bernoulli numbers as follows: $$L(1-k,\chi)= -\frac{B_{k,\chi}}{k}$$ where $B_{k,\chi}$ is the $k$ generalized Bernoulli number associated to $\chi$

Therefore: $$\zeta(1-k,K)=\zeta(1-k)L(1-k,\chi)=\frac{B_k \cdot B_{k,\chi}}{k^2}.$$ The interested reader can find tables of values at the author's personal website.