The recoil proton polarization has been measured in the p (vec e,evec p) pi^0 reaction in parallel kinematics around W = 1232 MeV, Q^2 = 0.121 (GeV/c)^2 and epsilon = 0.718 using the polarized c.w. electron beam of the Mainz Microtron. Due to the spin precession in a magnetic spectrometer, all three proton polarization components P_x/P_e = (-11.4 pm 1.3 pm 1.4) %, P_y = (-43.1 pm 1.3 pm 2.2) %, and P_z/P_e = (56.2 pm 1.5 pm 2.6) % could be measured simultaneously. The Coulomb quadrupole to magnetic dipole ratio CMR = (-6.4pm 0.7_{stat}pm 0.8_{syst}) % was determined from P_x in the framework of the Mainz Unitary Isobar Model. The consistency among the reduced polarizations and the extraction of the ratio of longitudinal to transverse response is discussed.
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