Class Numbers up to Ten Thousand and Zero-Free Half-Planes

Explicit two-sided bounds for L(1,chi) from a zero-free half-plane Re s > B; under B = 7/8 every imaginary quadratic field of class number at most 10798 has discriminant below 2^40. Unconditionally, by Tatuzawa's theorem, the same holds for class numbers up to 2900 with at most one possible exceptional field. Exact counts of fields for class numbers up to 1000.