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A recent proposal to associate 60 TeV to 2 PeV IceCube neutrino events with gamma-ray bursts (GRBs) indicates the Lorentz violation of cosmic neutrinos and leads further to the CPT symmetry violation between neutrinos and antineutrinos. Here we find that another 12 northern hemisphere track events possibly correlated with GRBs from three-year IceCube data satisfy the same regularity at a lower energy scale around 1 TeV. The combined fitting indicates a Lorentz violation scale ELV=(6.4±1.5)×1017 GeV and an intrinsic time difference Δtin=(−2.8±0.7)×102 s, from which we find an earlier emission of neutrinos than photons at the GRB source. We also suggest analyzing neutrino events detected a few minutes before the GRB trigger time to test the CPT violation of ultrahigh-energy neutrinos.