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The inclusive cross-section for jet production in association with a Z boson decaying into an electronpositron pair is measured as a function of the transverse momentum and the absolute rapidity of jets using 19.9 fb(-1) of root s = 8 TeV proton-proton collision data collected with the ATLAS detector at the Large Hadron Collider. The measured Z + jets cross-section is unfolded to the particle level. The cross-section is compared with state-of-the-art Standard Model calculations, including the next-to-leading-order and next-to-next-to-leading-order perturbative QCD calculations, corrected for non-perturbative and QED radiation effects. The results of the measurements cover final-state jets with transverse momenta up to 1 TeV, and show good agreement with fixed-order calculations.