Polynomial root density in a sieve

For an integer polynomial $F$ and squarefree $d$, let ${\rho }_F(d)$ count the roots of $F$ modulo $d$. The Chinese remainder theorem makes ${\rho }_F$ multiplicative, andThus $g(d)={\rho }_F(d)/d$ and $r_d=O({\rho }_F(d))$ define a sieve distribution.