This paper presents algorithms for calculating the quadratic character and
the norms of prime ideals in the ring of integers of any quadratic field. The
norms of prime ideals are obtained by means of a sieve algorithm using the
quadratic character for the field considered.

A quadratic field, and its ring of integers, can be represented naturally in
a plane. Using such a representation, the prime numbers - which generate the
principal prime ideals in the ring - are displayed in a given bounded region of
the plane.