= Imprimitive Dirichlet L-function Euler correction
{title2=$L(s,\chi)=L(s,\chi_0)\prod_{p\mid q,\ p\nmid q_0}(1-\chi_0(p)p^{-s})$}
The inducing <primitive Dirichlet character> has <conductor of a Dirichlet character> $q_0$. Increasing the modulus removes Euler factors only at new <prime> divisors. The correction creates zeros on the imaginary axis; raising the exponents of <primes> already dividing the <conductor of a Dirichlet character> changes no Euler factor. Primitive gamma factors continue to use $q_0$. For real-even characters this includes principal primitive <conductor of a Dirichlet character> one, with its <Riemann zeta function> <pole> treated separately.
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