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We present updated measurements of time-dependent CP asymmetries in fully-reconstructed neutral B decays to several CP eigenstates containing a charmonium meson. The measurements use a data sample of (383+/-4)x10(6) Upsilon(4S)-->BB[over] decays collected with the BABAR detector at the PEP-II B factory. We determine sin2beta = 0.714+/-0.032(stat)+/-0.018(syst) and |lambda|=0.952+/-0.022(stat)+/-0.017(syst).