  Eisenstein polynomials, which were defined by the second author, are
analogues of the concept of an Eisenstein series. The second author conjectured
that there exist some analogous properties between Eisenstein series and
Eisenstein polynomials. In the previous paper, the first author provided new
analogous properties of Eisenstein polynomials and zeta polynomials for the
Type II case. In this paper, the analogous properties of Eisenstein polynomials
and zeta polynomials are shown to also hold for the Type I, Type III, and Type
IV cases. These properties are finite analogies of certain properties of
Eisenstein series.
