LetXXbe a smooth projective variety over an algebraically closed field, andf:X→Xf\colon X\to Xa surjective self-morphism ofXX. Theii-th cohomological dynamical degreeχi(f)\chi _i(f)is defined as the spectral radius of the pullbackf∗f^{*}on the étale cohomology groupHe´ti(X,Qℓ)H^i_{\acute {\mathrm {e}}\mathrm {t}}(X, \mathbf {Q}_\ell )and thekk-th numerical dynamical degreeλk(f)\lambda _k(f)as the spectral radius of the pullbackf∗f^{*}on the vector spaceNk(X)R\mathsf {N}^k(X)_{\mathbf {R}}of real algebraic cycles of codimensionkkonXXmodulo numerical equivalence. Truong conjectured thatχ2k(f)=λk(f)\chi _{2k}(f) = \lambda _k(f)for all0≤k≤dimX0 \le k \le \dim Xas a generalization of Weil’s Riemann hypothesis. We prove this conjecture in the case of abelian varieties. In the course of the proof we also obtain a new parity result on the eigenvalues of self-maps of abelian varieties in prime characteristic, which is of independent interest.