Let \(\mathfrak D\) be a principal ideal domain and \(\mathfrak F\) the field of quotients. Let \(I_n\) be the identity matrix in \(M_n(\mathfrak D)\) and \(J=\left(\begin{smallmatrix} 0&I_n\\-I_n&0\end{smallmatrix}\right)\). The set of unimodular matrices \(X\) in \(M_{2n}(\mathfrak D)\) such that \(X^tJX=J\) will be denoted by \(\text{Sp}_{2n}(\mathfrak D)\). The matrices \(X\) and \(Y\) in \(M_{2n}(\mathfrak D)\) are conjugate if there is some \(Q\in\text{Sp}_{2n}(\mathfrak D)\) such that \(Q^{-1}XQ=Y\). The characteristic polynomial of \(X\) is \(f_X(x)=|xI-X|\). Let \(f(x)\in\mathfrak D[x]\) be a separable, irreducible, palindromic, and monic polynomial of degree \(2n\). Define \(M_f=\{X\in\text{Sp}_{2n}(\mathfrak D)\mid f_X(x)=f(x)\}\) and let \(\mathfrak M_f\) be the set of conjugacy classes of \(M_f\) in \(\text{Sp}_{2n}(\mathfrak D)\). For a root \(\zeta\) of \(f(x)\) let \(\mathfrak R=\mathfrak D[\zeta]\) and \(\mathfrak S=\mathfrak F[\zeta]\). Two ideals \(\mathfrak{a,b}\subset\mathfrak R\) are equivalent if there are \(\lambda,\mu\in\mathfrak R\) such that \(\lambda\mathfrak a=\mu\mathfrak b\). Let \(P_f\) be the set of pairs \((\mathfrak a,a)\), where \(\mathfrak a\subset\mathfrak R\) and \(a\in\mathfrak R\) with certain additional conditions. Let \(\mathfrak P_f\) be the set of all classes of \(P_f\). Using an eigenvalue of \(X\), the author defines a mapping \(\Psi\colon\mathfrak M_f \to\mathfrak P_f\) and shows that \(\Psi\) is a bijection. He considers a short exact sequence containing \(\mathfrak P_f\) and also gives formulas for the number of elements \(q_m\) in \(\mathfrak M_f\) if \(f(x)\) is the \(m\)-th cyclotomic polynomial.