  An amplitude analysis of the $B^0 \to K^{*0} \mu^+\mu^-$ decay is presented.
The analysis is based on data collected by the LHCb experiment from
proton-proton collisions at $\sqrt{s} = 7,\,8$ and $13$ TeV, corresponding to
an integrated luminosity of $4.7$ fb$^{-1}$. For the first time, Wilson
coefficients and non-local hadronic contributions are accessed directly from
the unbinned data, where the latter are parameterised as a function of $q^2$
with a polynomial expansion. Wilson coefficients and non-local hadronic
parameters are determined under two alternative hypotheses: the first relies on
experimental information alone, while the second one includes information from
theoretical predictions for the non-local contributions. Both models obtain
similar results for the parameters of interest. The overall level of
compatibility with the Standard Model is evaluated to be between 1.8 and 1.9
standard deviations when looking at the $\mathcal{C}_9$ Wilson coefficient
alone, and between 1.3 and 1.4 standard deviations when considering the full
set of $\mathcal{C}_9, \, \mathcal{C}_{10}, \, \mathcal{C}_9^\prime$ and
$\mathcal{C}_{10}^\prime$ Wilson coefficients. The ranges reflect the
theoretical assumptions made in the analysis.
