  There is a natural conjugation action on the set of endomorphism of $\P^N$ of
fixed degree $d \geq 2$. The quotient by this action forms the moduli of degree
$d$ endomorphisms of $\P^N$, denoted $\mathcal{M}_d^N$. We construct invariant
functions on this moduli space coming from to set of multiplier matrices of the
periodic points. The basic properties of these functions are demonstrated such
as that they are in the ring of regular functions of $\mathcal{M}_d^N$, methods
of computing them, as well as the existence of relations. The main part of the
article examines to what extend these invariant functions determine the
conjugacy class in the moduli space. Several different types of isospectral
families are constructed and a generalization of McMullen's theorem on the
multiplier mapping of dimension 1 is proposed. Finally, this generalization is
shown to hold when restricted to several specific families in
$\mathcal{M}_d^N$.
