Extreme Values of Dirichlet L-Functions At Critical Points of the Zeta Function

We estimate large and small values of |L(ρ^,χ)|, where χ is a primitive character mod q for q > 2 and ρ^ runs over critical points of the Riemann zeta function in the right half of the one-line and on the one-line, that is, the points where ζ^(ρ^)=0 and 1≤ ρ^.