We report on a measurement of the parity violating asymmetry in the elastic scattering of polarized electrons off unpolarized protons with the A4 apparatus at MAMI in Mainz at a four momentum transfer value of $Q^2$ = Qsquare (GeV/c)$^2$ and at a forward electron scattering angle of 30$^circ < theta_e < 40^circ$. The measured asymmetry is $A_{LR}(vec{e}p)$ = (Aphys $pm$ Deltastat$_{stat}$ $pm$ Deltasyst$_{syst}$) $times$ 10$^{-6}$. The expectation from the Standard Model assuming no strangeness contribution to the vector current is A$_0$ = (Azero $pm$ DeltaAzero) $times$ 10$^{-6}$. We have improved the statistical accuracy by a factor of 3 as compared to our previous measurements at a higher $Q^2$. We have extracted the strangeness contribution to the electromagnetic form factors from our data to be $G_E^s$ + FakGMs $G_M^s$ = GEsGMs $pm $ DeltaGEsGMs at $Q^2$ = Qsquare (GeV/c)$^2$. As in our previous measurement at higher momentum transfer for $G_E^s$ + 0.230 $G_M^s$, we again find the value for $G_E^s$ + FakGMs $G_M^s$ to be positive, this time at an improved significance level of 2 $sigma$.
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