Jacobi-Kubota symbols

In their work on the primes of the form $X^2+Y^4$, Friedlander and Iwaniec associated to each odd primary element $r+si$ of the Gaussian integers the Jacobi symbol $$ \left(\frac{s}{|r|}\right), $$ and named it the Jacobi-Kubota symbol. They proceeded to prove, via a variant of Vinogradov's method, that this symbol is equidistributed (in the set $\{-1, 1\}$) as $r+si$ varies among primes in the Gaussian integers. We will consider a generalization of this symbol to arbitrary quadratic rings, and prove a similar equidistribution result. We will also discuss the applications of this result to arithmetic statistics.