  The $k$-th moment of the mean empirical spectral distribution of the squared
unimodular random matrix of dimension $N$ can be expressed in the form
$N^{-2k-1} Q_k(N)$, where $Q_k(x)$ is a polynomial of degree $k+1$ with integer
coefficients. We use tools from traffic-free probability to express the
coefficients of this polynomial in terms of the number of quotients, with a
certain property, of some colored directed graphs. The obtained result
disproves the formula conjectured in A. Lakshminarayan, Z. Puchala, K.
Zyczkowski (2014).
