Suppose $V$ is a smooth projective variety over number field $\mathbb{Q}$. For every prime integer $p$ and positive integer $j$, let \begin{equation} Z_p(H^j(V), T):=\det(1-{\rm Frob}_p\cdot T|H^j_{et}(X, \mathbb{Q}_{\ell})^{I_p}) \end{equation} where $I_p$ is the corresponding inertia group. Then according to the famous Weil-conjecture, we know that when $p$ is a "good" prime, i.e. when $H^j_{et}(X, \mathbb{Q}_{\ell})^{I_p}=H^j_{et}(X, \mathbb{Q}_{\ell})$, then all roots of $Z_p(H^j(V), T)$ has absolute value $p^{j/2}$.
My question is: How about when $p$ is "bad", i.e. when $H^j_{et}(X, \mathbb{Q}_{\ell})^{I_p}\neq H^j_{et}(X, \mathbb{Q}_{\ell})$, can we still say something about the absolute value of its roots?
Any hint or reference is appreaciated.