A pseudo-Anosov surface automorphism $\phi$ has associated to it an algebraic
unit $\lambda_\phi$ called the dilatation of $\phi$. It is known that in many
cases $\lambda_\phi$ appears as the spectral radius of a Perron-Frobenius
matrix preserving a symplectic form $L$. We investigate what algebraic units
could potentially appear as dilatations by first showing that every algebraic
unit $\lambda$ appears as an eigenvalue for some integral symplectic matrix.