Inspired by Gill's work to factorize the Coulomb operator, we have developed a related approach that is scalable to arbitrary system size and requires only simple trigonometric function evaluations. After a somewhat involved derivation, using dual angular and radial numerical integration, the final working equations are remarkably simple and we have described a linearithmic scaling scheme to implement them; alternative algorithms are surely possible. For example, we have implemented the method using spherical t-designs to perform angular integration due to their simple even-weight nature and antipodal structure, but the same could be achieved with the Lebedev-Laikov scheme that is ubiquitous in the density functional theory community. While PME generates structure factors on a rectilinear grid via an interpolation scheme, to enable the FFT algorithm to efficiently carry out the Fourier transform, SGT instead uses cubature to evaluate the Fourier integral on a spherical grid. Supplanting the FFT in this way offers many possibilities to parallelize the method, which has proven to be problematic in implementing Fourier space methods on modern supercomputing hardware.