Stark, The Gauss class-number problems, available at http://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/stark.pdf writes, on page 251, "We define the Epstein zeta functions, $$\zeta(s,Q)=(1/2)\sum_{m,n\ne0,0}Q(m,n)^{-s}$$ ... Theorem 4.1 (Folk Theorem.) Let $c\gt1/4$ be a real number and set $$Q(x,y)=x^2+xy+cy^2,$$ with discriminant $d=1-4c\lt0$. Then for $c\gt41$, $\zeta(s,Q)$ has a zero $s$ with $\sigma\gt1$."