We consider the fluctuations of regular functions $f$ of a Wigner matrix $W$
    viewed as an entire matrix $f(W)$. Going beyond the well studied tracial mode,
    $\mathrm{Tr}[f(W)]$, which is equivalent to the customary linear statistics of
    eigenvalues, we show that $\mathrm{Tr}[f(W)]$ is asymptotically normal for any
    non-trivial bounded deterministic matrix $A$. We identify three different and
    asymptotically independent modes of this fluctuation, corresponding to the
    tracial part, the traceless diagonal part and the off-diagonal part of $f(W)$
    in the entire mesoscopic regime, where we find that the off-diagonal modes
    fluctuate on a much smaller scale than the tracial mode. In addition, we
    determine the fluctuations in the Eigenstate Thermalisation Hypothesis [Deutsch
    1991], i.e. prove that the eigenfunction overlaps with any deterministic matrix
    are asymptotically Gaussian after a small spectral averaging. In particular, in
    the macroscopic regime our result generalises [Lytova 2013] to complex $W$ and
    to all crossover ensembles in between. The main technical inputs are the recent
    multi-resolvent local laws with traceless deterministic matrices from the
    companion paper [Cipolloni, Erd\H{o}s, Schr\”oder 2020].

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