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In a previous work we apply lattice point theorems on hyperbolic spacesobtaining asymptotic formulas for the number of integral representations ofnegative integers by quadratic and hermitian forms of signature (n,1) lying inEuclidean balls of increasing radius. This formula involves an error term thatdepends on the first nonzero eigenvalue of the Laplace-Beltrami operator on thecorresponding congruence hyperbolic manifolds. The aim of this paper is tocompare the error term obtained by experimental computations, with the errorterm mentioned above, for several choices of quadratic and hermitian forms.  Our numerical results give evidences of the existence of exceptionaleigenvalues for some arithmetic subgroups of SU(3,1), SU(4,1) and SU(5,1), thusthey contradicts the generalized Selberg (and Ramanujan) conjecture in thesecases. Furthermore, for several arithmetic subgroups of SO(4,1), SO(6,1),SO(8,1) and SU(2,1), there are evidences of a lower bound on the first nonzeroeigenvalue better than the already known lower bound for congruences subgroups.

A numerical study on exceptional eigenvalues of certain congruence subgroups of SO(n,1) and SU(n,1)