Measurements are presented of the $CP$ violation observables $S$ and $C$ in the decays of $B^0$ and $overline{B}{}^0$ mesons to the $J/psi K^0_S$ final state. The data sample corresponds to an integrated luminosity of $3.0,text{fb}^{-1}$ collected with the LHCb experiment in proton-proton collisions at center-of-mass energies of $7$ and $8,text{TeV}$. The analysis of the time evolution of $41500$ $B^0$ and $overline{B}{}^0$ decays yields $S = 0.731 pm 0.035 , text{(stat)} pm 0.020 ,text{(syst)}$ and $C = -0.038 pm 0.032 , text{(stat)} pm 0.005,text{(syst)}$. In the Standard Model, $S$ equals $sin(2beta)$ to a good level of precision. The values are consistent with the current world averages and with the Standard Model expectations.
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