On the distribution of norms of prime ideals of the given class in arithmetic progressions

Let $\mathcal C$ be a class of ideals of the ring of algebraic numbers of the imaginary quadratic field. Let $l$ and $q$ be relatively prime integers, $1\le q\le\log^{A_1}x$, $A_1>1$. The asymptotic formula for the number $\pi_1(x,q,l,\mathcal C)$ of prime ideals belonging to the class $\mathcal C$ whose norms do not exceed $x$ and lie in an arithmetic progression got in this paper.