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are easier to express for versions with primitive characters. Using Euler products of Dirichlet L-functions, we can express the L-function of an imprimitive character as a function of the character that induces it:
: From the factors in this equation we have infinitely many zeros on the line .For primitive Dirichlet character, the L-function satisfies a certain functional equation which allows us to define trivial zeros of as zeros corresponding to poles of the gamma function in this

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