  From pulsating stars to transiting exoplanets, the search for periodic
signals in K2 data, Kepler's 2-wheeled extension, is relevant to a long list of
scientific goals. Systematics affecting K2 light curves due to the decreased
spacecraft pointing precision inhibit the easy extraction of periodic signals
from the data. We here develop a method for producing periodograms of K2 light
curves that are insensitive to pointing-induced systematics; the
Systematics-Insensitive Periodogram (SIP). Traditional sine-fitting
periodograms use a generative model to find the frequency of a sinusoid that
best describes the data. We extend this principle by including systematic
trends, based on a set of 'Eigen light curves', following Foreman-Mackey et al.
(2015), in our generative model as well as a sum of sine and cosine functions
over a grid of frequencies. Using this method we are able to produce
periodograms with vastly reduced systematic features. The quality of the
resulting periodograms are such that we can recover acoustic oscillations in
giant stars and measure stellar rotation periods without the need for any
detrending. The algorithm is also applicable to the detection of other periodic
phenomena such as variable stars, eclipsing binaries and short-period exoplanet
candidates. The SIP code is available at https://github.com/RuthAngus/SIPK2.
