  Let $p$ be an odd prime. In this paper we write down the functional equations
of Siegel Eisenstein series of degree $n$, level $p$ with quadratic or trivial
characters. First we study the $U(p)$ action in the space of Siegel Eisenstein
series to get $U(p)$-eigen functions. Secondly we show that the functional
equations for $U(p)$-eigen Eisenstein series are quite simple and easy to write
down. Consequently the matrix that represents functional equations of Siegel
Eisenstein series are given by the products of simple matrices.
