The database contains information (basic properties, minimality, Galois orbit, field of values) for all Dirichlet characters of modulus up to $10^6$.
Basic properties are available for all Dirichlet characters of modulus up to $10^{20}$, but this information is not stored in the database and is not searchable.
L-functions are available for characters of modulus up to 2800 (and some of higher modulus).