  We study the magic manifold $N$ which is a hyperbolic and fibered
$3$-manifold. We give an explicit construction of a fiber $F_a$ and its
monodromy $:F_a \rightarrow F_a$ of the fibration associated to each fibered
class $a$ of $N$. Let $\delta_g$ (resp. $\delta_g^+$) be the minimal dilatation
of pseudo-Anosovs (resp. pseudo-Anosovs with orientable invariant foliations)
defined on an orientable closed surface of genus $g$. As a consequence of our
result, we obtain the first explicit construction of the following
pseudo-Anosovs; a minimizer of $\delta_7^+$ and conjectural minimizers of
$\delta_g$ for large $g$.
