= Solution
The Dirichlet-series coefficients are
$$
a_n=\sum_{d\mid n}\chi_D(d).
$$
They are multiplicative. At a <prime power>, their values are $k+1$ if $\chi_D(p)=1$, one for even $k$ and zero for odd $k$ if $\chi_D(p)=-1$, and one if $\chi_D(p)=0$. Thus every $a_n$ is nonnegative. In particular $a_{m^2}\ge1$. This is the <nonnegative zeta-times-real-L coefficients> identity. The same Euler expansion gives $-\zeta'/\zeta(\sigma)-L'/L(\sigma,\chi_D)\ge0$ for $\sigma>1$, with coefficients $\Lambda(n)(1+\chi_D(n))\ge0$.
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