Testing general relativity with LISA including spin precession and higher harmonics in the waveform

We compute the accuracy at which a Laser Interferometer Space Antenna-like space-based gravitational wave detector will be able to observe deviations from general relativity in the low frequency approximation. To do so, we introduce six correction parameters that account for modified gravity in the second post-Newtonian gravitational wave phase for inspiralling supermassive black hole binaries with spin precession on quasicircular orbits. Our implementation can be regarded as a subset of the parametrized post-Einsteinian formalism developed by Yunes and Pretorius, being able to investigate also next-to-leading order effects. In order to find error distributions for the alternative theory parameters, we use the Fisher information formalism and carry out Monte Carlo simulations for 17 different binary black hole mass configurations in the range 105Msun<M