I've been having trouble with finding the curvature computations of globally symmetric spaces of rank $1$.

More specifically, I need to use results about the eigenvalues of the operator $R:T_pM \rightarrow T_pM$; $X \mapsto -[[X,c],c]$ for a given $c \in T_pM$. The fact is, using the book of Besse "Manifolds all of whose geodesics are closed", it seems some eigenvalues are $-4$, but the results used in "The free loop space of globally symmetric spaces" imply eigenvalues $\frac{1}{4}$. I think I'm computing something wrong, but I don't know where to find the right computations done explicitly. Any reference?