  We compute the fluctuation moments $\alpha_{m_1,\dots,m_r}$ of a Complex
Wigner Matrix $X_N$ given by the limit
$\lim_{N\rightarrow\infty}N^{r-2}k_r(Tr(X_N^{m_1}),\dots,Tr(X_N^{m_r}))$. We
prove the limit exists and characterize the leading order via planar graphs
that result to be trees. We prove these graphs can be counted by the set of
non-crossing partitioned permutations which permit us to express the moments
$\alpha_{m_1,\dots,m_r}$ in terms of simpler quantities
$\overline{\kappa}_{m_1,\dots,m_r}$ which we call the pseudo-cumulants. We
prove the pseudo-cumulants coincide with the higher order free cumulants up to
$r=4$ which permit us to find the higher order free cumulants
$\kappa_{m_1,\dots,m_r}$ associated to the moment sequence
$\alpha_{m_1,\dots,m_r}$ up to order 4.
