A fast new algorithm is used compute the zeros of 10 6 quadratic character L-functions for negative fundamental discrim-inants 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… (More)
An algorithm is given to efficiently compute L-functions with large conductor in a restricted range of the critical strip. Examples are included for about 24000 dihedral Galois representations with conductor near 10 7. The data shows good agreement with a symplectic random matrix model.