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Electronic band structure calculations for the CeIn3 compound utilizing the full potential linearized augmented plane waves method were performed with the aim to compute the hyperfine fields acting on Ce and In atoms. The latter are found to be in reasonable agreement with the values measured at low temperatures. The 4f orbital contribution dominates the magnetic hyperfine field at Ce ions while the contact field is negligible due to an almost complete cancellation of valence and core contributions. A non-zero magnetic hyperfine field appears at In sites due to the spin-polarization of the 5p sub-shells through the hybridization with the extended 6s, 6p and 5d Ce states which, in turn, are spin-polarized by the Ce 4f states. No net magnetic moment at In is observed since the sum of its 5p sub-shell spins is zero. The 5p shell of In is responsible for the presence of an electric field gradient at In nuclei.