Any tips for riding with no hands?

Right now I'm mainly riding my road bike. Generally, I feel comfortable using my right hand to do stuff: eat, take photos... whatever... But when I take my left hand off the handlebars, I start to feel jittery...

Taking both hands off, I don't know, I haven't got the hang of it yet. I still feel the fear that somehow I'm going to crash. Lately I've been trying it for a couple seconds here and there, and it isn't so bad...

But I'm wondering, what advice do you have for riding with no hands?

Does it matter if you're pedaling or not? The bike wants to stay upright, yes, while it's moving?