  In this article, we prove an omega-result for the Hecke eigenvalues
$\lambda_F(n)$ of Maass forms $F$ which are Hecke eigenforms in the space of
Siegel modular forms of weight $k$, genus two for the Siegel modular group
$Sp_2(\Z)$. In particular, we prove $$ \lambda_F(n)= \Omega(n^{k-1}\text{exp}
(c \frac{\sqrt{\log n}}{\log\log n})), $$ when $c>0$ is an absolute constant.
This improves the earlier result $$ \lambda_F(n)= \Omega(n^{k-1}
(\frac{\sqrt{\log n}}{\log\log n})) $$ of Das and the third author. We also
show that for any $n \ge 3$, one has $$ \lambda_F(n) \leq n^{k-1}\text{exp}
\left(c_1\sqrt{\frac{\log n}{\log\log n}}\right), $$ where $c_1>0$ is an
absolute constant. This improves an earlier result of Pitale and Schmidt.
Further, we investigate the limit points of the sequence
$\{\frac{\lambda_F(n)}{n^{k-1}}\}_{n \in \N}$ and show that it has infinitely
many limit points. Finally, we show that $\lambda_F(n) >0$ for all $n$, a
result earlier proved by Breulmann by a different technique.
