  In \cite{indice}, we show the following result, conjectured by D. Panyushev
\cite{Panyushev}, for $\g$ a semisimple Lie algebra: {\rm ind} \n(\g^{e}) =
{\rm rk} \g-\dim \z(\g^{e}, where $\n(\g^{e})$ and $\z(\g^{e})$ are,
respectively, the normaliser and the centre of the centraliser $\g^{e}$ of a
nilpotent element $e$. This result is proved in \cite{indice} when $\g$ is a
classical simple Lie algebra and when $e$ satisfies a certain property $(P)$.
We present in this paper the computations, made using GAP4, which prove that
distinguished, non-regular, nilpotent orbits in $E\_6$, $E\_7$, $E\_8$ and
$F\_4$ satisfy the property $(P)$. This work completes the proof, presented in
\cite{indice}, of the equality (\ref{princ}). The complete proof of this result
was already presented in \cite{indice\_arxiv}.
