  Let $\mathbf{K}$ be a number field and $\mathfrak{q}$ an integral ideal in
$\mathcal{O}_{\mathbf{K}}$. A result of Tatuzawa from 1973, computes the
asymptotic (with an error term) for the number of ideals with norm at most $x$
in a class of the narrow ray class group of $\mathbf{K}$ modulo $\mathfrak{q}$.
This result bounds the error term with a constant whose dependence on
$\mathfrak{q}$ is explicit but dependence on $\mathbf{K}$ is not explicit. The
aim of this paper is to prove this asymptotic with a fully explicit bound for
the error term.

Number Theory