  In the Coxeter group W(R) generated by the root system R, let T(R) be the
number of conjugacy classes having no eigenvalue 1 and let S(R) be the number
of conjugacy classes having no eigenvalue -1. The algebra H{R) of observables
of the rational Calogero model based on the root system R possesses T(R)
independent traces, the same algebra considered as an associative superalgebra
with respect to a certain natural parity possesses S(R) even independent
supertraces and no odd trace or supertrace. The numbers T(R) and S(R) are
determined for all irreducible root systems (hence for all root systems). It is
shown that T(R) =< S(R), and T(R) = S(R) if and only if superalgebra H(R)
contains a Klein operator (or, equivalently, W(R) containes -1).
