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In this paper, we consider the distribution of the continuous paths of Dirichlet character sums modulo prime   $q$   on the complex plane. We also find a limiting distribution as   $q \rightarrow \infty $   using Steinhaus random multiplicative functions, stating properties of this random process. This is motivated by Kowalski and Sawin’s work on Kloosterman paths.

The Limiting Distribution of Character Sums