Sine wave comes in on A0-A6

First off, I have google photos which doesn't host images but webpages with images in them. Here is that link.

I was bored with a potentially defective NANO and found some spurious input, these were not pulled up. It was only a few mV so could be anything and I thought it was 60hz hum, but it's not 60hz. Each A0-6 had a slightly different non-sine wave, but they added up to a perfect sine in the 3-8 Hz range. No code other than the Serial.print was going at time. I'm not sure of the axis values as it was a month ago and very late.

What do you think?

I think it was 60Hz hum, as the quality of your evidence to the contrary is unconvincing.

It might have been aliased down to a different frequency if you weren't sampling at greater than 120Hz.

The evidence is very circumstantial and the axis values are not known. Your explanation is satisfactory. I can not explain it otherwise. I was sampling at 50ms and saw it rise and fall and thought it odd at the time, but perhaps it was a artifact of sample rate being a factor of the 60hz.

MarkT mentioned "aliased down", that is the keyword here.
If you sample the mains 60 Hz electrical noise with a fixed delay, you can capture a sample of the sine wave and a few waves later a new sample at a slightly different position in the wave.
It can be reproduced, if you have enough mains electrical noise. That is often disturbed by computers and monitors and other devices, so you need some luck to receive a clean 60 Hz out of the air. The human body is a big collector of 60 Hz noise, perhaps you were sitting in a position that helped, or you hand was nearby the analog pins.