Title: Zeros of L-functions and Euler's idoneal numbers Abstract: Assuming the Generalized Riemann Hypothesis, Weinberger showed the only discriminants of definite binary quadratic forms with one class per genus are the examples already known to Euler. Unconditionally there is at most one more such example. Generalizing a technique of Montgomery-Weinberger, we show there is no such example in the range 10^100 < d < 10^28000.