The Quadratic Character Experiment

A fast new algorithm is used compute the zeros of 10 6 quadratic character L-functions for negative fundamental discriminants with absolute value d > 10 12 . These are compared to the 1-level density, including various lower-order terms. These terms come from, on the one hand, the explicit formula, and on the other, the L-functions ratios conjecture. The latter give a much better fit to the data, providing numerical evidence for the conjecture.