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We measure the complete set of angular coefficients $J_i$ for exclusive$\bar{B} \to D^* \ell \bar{\nu}_\ell$ decays ($\ell = e, \mu$). Our analysisuses the full $711\,\mathrm{fb}^{-1}$ Belle data set with hadronic tag-sidereconstruction. The results allow us to extract the form factors describing the$B \to D^*$ transition and the Cabibbo-Kobayashi-Maskawa matrix element$|V_{\rm cb}|$. Using recent lattice QCD calculations for the hadronic formfactors, we find $|V_{\rm cb}| = (41.0 \pm 0.7) \times 10^3 $ using the BGLparameterization, compatible with determinations from inclusive semileptonicdecays. We search for lepton flavor universality violation as a function of thehadronic recoil parameter $w$, and investigate the differences of the electronand muon angular distributions. We find no deviation from Standard Modelexpectations.

Measurement of Angular Coefficients of $\bar{B} \to D^* \ell \bar{\nu}_\ell$: Implications for $|V_{cb}|$ and Tests of Lepton Flavor Universality