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New measurements of directed flow for charged hadrons, characterized by the Fourier coefficient v1, are presented for transverse momenta pT, and centrality intervals in Au+Au collisions recorded by the STAR experiment for the center-of-mass energy range √sN N = 7.7–200 GeV. The measurements underscore the importance of momentum conservation, and the characteristic dependencies on √sN N , centrality and pT are consistent with the expectations of geometric fluctuations generated in the initial stages of the collision, acting in concert with a hydrodynamic-like expansion. The centrality and pT dependencies of veven 1 , as well as an observed similarity between its excitation function and that for v3, could serve as constraints for initial-state models. The veven 1 excitation function could also provide an important supplement to the flow measurements employed for precision extraction of the temperature dependence of the specific shear viscosity.