Let ϑ(t) be the Riemann-Siegel function. The unique value g_n such that ϑ(g_n) = π n where n = 0, 1, ... is then known as a Gram point. An excellent approximation for Gram point g_n can be obtained by using the first few terms in the asymptotic expansion for ϑ(t) and inverting to obtain g_n≈2π exp[1 + W((8n + 1)/(8e))], where W(z) is the Lambert W-function. This approximation gives as error of 2.2×10^(-3) for n = 0, decreasing to 3.5×10^(-4) by n = 10. The following table gives the first few Gram points.

Gram's law | Riemann-Siegel functions | Riemann zeta function