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Collinear laser spectroscopy measurements were performed on $^{69,71,73}$Ge isotopes ($Z = 32$) at ISOLDE-CERN. The hyperfine structure of the $4s^2 4p^2 \, ^3P_1 \rightarrow 4s^2 4p 5s \, ^3P_1^o$ transition of the germanium atom was probed with laser light of 269 nm, produced by combining the frequency-mixing and frequency-doubling techniques. The hyperfine fields for both atomic levels were calculated using state-of-the-art atomic relativistic Fock-space coupled-cluster calculations. A new $^{73}$Ge quadrupole moment was determined from these calculations and previously measured precision hyperfine parameters, yielding $Q_{\rm s}$ = $-$0.198(4) b, in excellent agreement with the literature value from molecular calculations. The moments of $^{69}$Ge have been revised: $μ$ = +0.920(5) $μ_{N}$ and $Q_{\rm s}$= +0.114(8) b, and those of $^{71}$Ge have been confirmed. The experimental moments around $N = 40$ are interpreted with large-scale shell-model calculations using the JUN45 interaction, revealing rather mixed wave function configurations, although their $g$-factors are lying close to the effective single-particle values. Through a comparison with neighboring isotones, the structural change from the single-particle nature of nickel to deformation in germanium is further investigated around $N = 40$.