# Numerical analytical theory – Non-trivial real zeros of Dirichlet L functions

When dealing with the theorem of prime numbers in arithmetic progressions, the possible presence of a real zero close to $$1$$ at most one real character mod $$q$$. On the other hand, it is also known that the Riemann $$zeta$$ The function does not disappear (0, 1).

Is there any result that shows that some Dirichlet L functions (associated with a non-main character) do not disappear? far since $$1$$ ? I think it does not fade in $$1/2$$ It is still open in general, but it may be known in some cases.