Nonnegative zeta-times-real-L coefficients ($a_n={\sum }_{d\mid n}\chi (d)\ge 0(\chi \text{ real})$)

The coefficients of $\zeta (s)L(s,\chi )$ are multiplicative. On $p^k$, their values are $k+1$ when $\chi (p)=1$, alternating one and zero when $\chi (p)=-1$, and one when $\chi (p)=0$. In particular $a_{m^2}\ge 1$. Their logarithmic Euler coefficients $\Lambda (n)(1+\chi (n))$ are also nonnegative, supporting uniqueness of a possible exceptional real Dirichlet zero.