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The coherent photoproduction of J/ψ and ψ′ mesons was measured in ultra-peripheral Pb–Pb collisions at a center-of-mass energy sNN−−−√ = 5.02 TeV with the ALICE detector. Charmonia are detected in the central rapidity region for events where the hadronic interactions are strongly suppressed. The J/ψ is reconstructed using the dilepton (l+l−) and proton–antiproton decay channels, while for the ψ′ the dilepton and the l+l−π+π− decay channels are studied. The analysis is based on an event sample corresponding to an integrated luminosity of about 233 μb−1. The results are compared with theoretical models for coherent J/ψ and ψ′ photoproduction. The coherent cross section is found to be in a good agreement with models incorporating moderate nuclear gluon shadowing of about 0.64 at a Bjorken-x of around 6×10−4, such as the EPS09 parametrization, however none of the models is able to fully describe the rapidity dependence of the coherent J/ψ cross section including ALICE measurements at forward rapidity. The ratio of ψ′ to J/ψ coherent photoproduction cross sections was also measured and found to be consistent with the one for photoproduction off protons.