principal character

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Where [chi] denotes a Dirichlet character modulo d, L(n, [chi]) denotes the Dirichlet L-function corresponding to[chi], [empty set](d) and [zeta](s) are the Euler function and Riemann zeta-function, respectively.
Let [chi] be the Dirichlet character with conductor f [member of] N = {1, 2,.
where [chi] be the Dirichlet character mod p, L(1, [chi]) be the Dirichlet L-function corresponding character [chi] and a/p = [p.
Let p be an odd prime and [chi] be the Dirichlet character mod p.
For any positive integer number q > 3, let [chi] denote a Dirichlet character modulo q.