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Production and decay angular distributions were extracted from measurementsof exclusive electroproduction of the rho^0(770) meson over a range in thevirtual photon negative four-momentum squared 0.5< Q^2 <4 GeV^2 and thephoton-nucleon invariant mass range 3.8< W <6.5 GeV. The experiment wasperformed with the HERMES spectrometer, using a longitudinally polarizedpositron beam and a ^3He gas target internal to the HERA e^{+-} storage ring.The event sample combines rho^0 mesons produced incoherently off individualnucleons and coherently off the nucleus as a whole. The distributions in oneproduction angle and two angles describing the rho^0 -> pi+ pi- decay yieldedmeasurements of eight elements of the spin-density matrix, including one thathad not been measured before. The results are consistent with the dominance ofhelicity-conserving amplitudes and natural parity exchange. The improvedprecision achieved at 4< W <7 GeV, in combination with other data at W>7 GeV,reveals evidence for an energy dependence in the ratio R of the longitudinal totransverse cross sections at constant Q^2.Comment: 15 pages, 15 embedded figures, LaTeX for SVJour(epj) document class  Revision: Fig. 15 corrected, recent data added to Figs. 10,12,14,15; minor  changes to tex

Measurement of angular distributions and $R=\sigma_L/\sigma_T$ in diffractive electroproduction of $ \rho^0$ mesons