I have to numerically evaluate
$$\int_0^\beta d\tau e^{i \nu_n \tau} G(\tau)$$
for a large number on $\nu_n$. $G(\tau)$ is expensive to evaluate. Currently I'm using Quadpacks dqawo (double qaudpack adaptive weighted oscillatory), which integrals of the type
$$\int_a^b dx \sin(\omega x) f(x)$$
and
$$\int_a^b dx \cos(\omega x) f(x).$$
I use these routines to integrate the real and imaginary part seperatly, but since these routines are adaptive they will calculate two different sets of $G(\tau)$ for each $\nu_n$. So I am considering evaluating a fixed grid of $G(\tau_i)$ once, which I then evaluate by something like Simpsons rule for all $\nu_n$.
Is there something like Simpsons rule, which is adapted especially for oscillatory integrals and which uses an equidistant grid, such that I can evaluate only one set of $G(\tau_i)$