The NA60 experiment studies muon pair production at the CERN SPS. In this letter we report on a precision measurement of J/psi in In-In collisions. We have studied the J/psi centrality distribution, and we have compared it with the one expected if absorption in cold nuclear matter were the only active suppression mechanism. For collisions involving more than ~80 participant nucleons, we find that an extra suppression is present. This result is in qualitative agreement with previous Pb-Pb measurements by the NA50 experiment, but no theoretical explanation is presently able to coherently describe both results.
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