  Hecke eigenvalues of classical modular forms often encode a wealth of
arithmetic data. The Satake $p$-parameters of a Siegel modular form play a role
analogous to the one played by Hecke eigenvalues in the characterization of
classical modular forms. In this paper we present an algorithm by which we can
compute the Satake $p$-parameters of a Siegel modular form $F$ if we are given
the Hecke eigenvalues of $F$ with respect to the generators of the local Hecke
algebra. We compute explicit examples and relate our computations to the
Ramanujan-Petersson Conjecture.
