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The first measurements of the Fourier coefficients (V-n Delta) of the azimuthal distributions of charged hadrons emitted from photon-proton (gamma p) interactions are presented. The data are extracted from 68.8nb(-1) of ultra-peripheral proton-lead (pPb) collisions at root s(NN)= 8.16 TeV using the CMS detector. The high energy lead ions produce a flux of photons that can interact with the oncoming proton. This gamma p system provides a set of unique initial conditions with multiplicity lower than in photon-lead collisions but comparable to recent electron-positron and electron-proton data. The V-n Delta coefficients are presented in ranges of event multiplicity and transverse momentum (p(T)) and are compared to corresponding hadronic minimum bias pPb results. For a given multiplicity range, the mean p(T) of charged particles is smaller in gamma p than in pPb collisions. For both the gamma p and pPb samples, V-1 Delta is negative, V-2 Delta is positive, and V-3 Delta consistent with 0. For each multiplicity and p(T) range, V-2 Delta is larger for gamma p events. The gamma p data are consistent with model predictions that have no collective effects.