  In this article, we define the orbit data of birational maps of
$\mathbf{P}^2(\mathbb{C})$ and show that the orbit data determine the dynamical
degree by providing the minimal polynomials of the dynamical degree in terms of
orbit data. Using this, we determine all Salem numbers and Pisot numbers that
appear in the Weyl Spectrum of Coxeter group $W_n$ associated to $E_n$ and the
Dynamical Spectrum of $\mathbf{P}^2(\mathbb{C})$.
