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Collinear laser spectroscopy was performed on Zn (Z=30) isotopes at ISOLDE, CERN. The study of hyperfine spectra of nuclei across the Zn isotopic chain, N=33–49, allowed the measurement of nuclear spins for the ground and isomeric states in odd-A neutron-rich nuclei up to N=50. Exactly one long-lived (>10 ms) isomeric state has been established in each 69–79Zn isotope. The nuclear magnetic dipole moments and spectroscopic quadrupole moments are well reproduced by large-scale shell–model calculations in the f5pg9 and fpg9d5 model spaces, thus establishing the dominant term in their wave function. The magnetic moment of the intruder Iπ=1/2+ isomer in 79Zn is reproduced only if the νs1/2 orbital is added to the valence space, as realized in the recently developed PFSDG-U interaction. The spin and moments of the low-lying isomeric state in 73Zn suggest a strong onset of deformation at N=43, while the progression towards 79Zn points to the stability of the Z=28 and N=50 shell gaps, supporting the magicity of 78Ni. Keywords: Zinc, Magnetic dipole moment, Quadrupole moment, Laser, Shell closure