  Let $\chi$ be a real primitive character to the modulus $D$. It is proved
that $$ L(1,\chi)\gg (\log D)^{-2022} $$ where the implied constant is absolute
and effectively computable.
  In the proof, the lower bound for $L(1,\chi)$ is first related to the
distribution of zeros of a family of Dirichlet $L$-functions in a certain
region, and some results on the gaps between consecutive zeros are derived.
Then, by evaluating certain discrete means of the large sieve type, a
contradiction can be obtained if $L(1,\chi)$ is too small.
