  A square matrix of order $n$ with $n\geq 2$ is called a \textit{permutative
matrix} or permutative when all its rows (up to the first one) are permutations
of precisely its first row. In this paper, the spectra of a class of
permutative matrices are studied. In particular, spectral results for matrices
partitioned into $2$-by-$2$ symmetric blocks are presented and, using these
results sufficient conditions on a given list to be the list of eigenvalues of
a nonnegative permutative matrix are obtained and the corresponding permutative
matrices are constructed. Guo perturbations on given lists are exhibited.
