In this article we prove that all completely multiplicative automatic sequences $(a_n)_{n \in \mathbf{N}}$ defined on $\mathbf{C}$, vanishing or not, can be written in the form $a_n=b_nχ_n$ where $(b_n)_{n \in \mathbf{N}}$ is an almost constant sequence, and $(χ_n)_{n \in \mathbf{N}}$ is a Dirichlet character.
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