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The electric quadrupole moment of $^{49}$Sc was measured by collinear laser spectroscopy at CERN-ISOLDE to be $Q_{\rm s}=-0.159(8)$ $e$b, and a nearly tenfold improvement in precision was reached for the electromagnetic moments of $^{47,49}$Sc. The single-particle behavior and nucleon-nucleon correlations are investigated with the electromagnetic moments of $Z=21$ isotopes and $N=28$ isotones as valence neutrons and protons fill the distinctive $0f_{7/2}$ orbit, respectively, located between magic numbers, 20 and 28. The experimental data are interpreted with shell-model calculations using an effective interaction, and ab-initio valence-space in-medium similarity renormalization group calculations based on chiral interactions. These results highlight the sensitivity of nuclear electromagnetic moments to different types of nucleon-nucleon correlations, and establish an important benchmark for further developments of theoretical calculations., Comment: Accepted by Physics Letters B (2022)