An electron electric dipole moment (eEDM) directly violates time-reversal symmetry, which has far reaching implications for physics beyond the Standard Model. An experiment using trapped molecular ions offers high sensitivity because of the large effective electric fields and long coherence times that are possible. We demonstrate precision spectroscopy on many trapped HfF+ ions in a radiofrequency quadrupole trap with rotating electric and magnetic fields. The spectroscopy performed is a Ramsey type experiment between spin states of the metastable 3∆1 electronic state and has a coherence time exceeding 1 second. We have collected and analyzed over 200 hours of Ramsey spectroscopy data taken under a variety of experimental conditions. We identify several systematic errors that could potentially affect an eEDM measurement and estimate the size of these interloping effects. By collecting data under pairs of conditions where the eEDM has opposing signs (e.g. performing Ramsey spectroscopy on the two Λ-doublets) we are able to take frequency differences that can suppress some of these systematic effects. Although our data set includes runs where we have intentionally varied experimental parameters to study systematic effects, we achieve a 1σ statistical sensitivity of 2.76 × 10−28 e·cm and place a 1σ upper bound on the size of systematic effects of 2.82 × 10−28 e·cm. Finally we present a preliminary upper bound on the eEDM of |de|
< 4.6 × 10−28 e·cm with 90% confidence.