Amplifying and Reading a 0-1 V signal into Arduino
Just to move things forward I'm posting an idea (not an answer): -



I believe that the waveform shown above is current into a device containing a bridge rectifier, charging capacitor and load. It's too similar to the stereotype to be anything else (within reason) and the only conclusion of this is that the OP is incorrect about the sampling rate because between AC current peaks there are pretty much 56 samples, and, at 60Hz this must mean the sampling time is approximately 300 microseconds or the sampling rate is about 3.3kHz.

The OP is invited to state what the load is and, if it is a device that rectifies the AC supply then, he should recalculate the sampling frequency based on the diagram he has provided and if necessary amend his figure or amend the x axis of the graph.