Dirichlet L-function for the Legendre symbol

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Suppose  is a prime number. The Dirichlet L-function for the Legendred symbol mod  is defined as the Dirichlet L-function for the Legendre symbol mod . In other words, it is the function given by the following L-series:
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The numerator here is the Legendre symbol, which is  if  divides ,  if  is a quadratic residue modulo , and  if  is a quadratic nonresidue modulo .