Asymmetries in the time-dependent rates of $D^0 to K^+K^-$ and $D^0 to pi^+pi^-$ decays are measured in a $pp$ collision data sample collected with the LHCb detector during LHC Run 1, corresponding to an integrated luminosity of $3,mathrm{fb}^{-1}$. The asymmetries in effective decay widths between $D^0$ and $overline{D}^0$ decays, sensitive to indirect $CP$ violation, are measured to be $A_Gamma(K^+ K^-) = (-0.30 pm 0.32 pm 0.10)times 10^{-3}$ and $A_Gamma(pi^+pi^-) = (0.46 pm 0.58 pm 0.12)times 10^{-3}$, where the first uncertainty is statistical and the second systematic. These measurements show no evidence for $C!P$ violation and improve on the precision of the previous best measurements by nearly a factor of two.
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