I'm halfway into my 4-month internship at a software development company of 50+ employees. So far I've have done every task they have assigned to me, but they're fairly small tasks, so I'm constantly without any specific tasks to do.
My supervisor is rather senior and very busy, so I don't like to keep asking him multiple times for new tasks (even though I report to him every single time I finish the ask given and also say "I am open to new tasks" or something similar).
This week I asked him and his supervisor for a feedback, and they said that they are very satisfied with me/my work. When I asked if there was something that I could improve, they said that I am okay and that they don't have any complaints.
The problem is that I am only have enough work to fill around 40% of my working hours.
I thought about trying to engage some project here, but that doesn't seem like a good thing to do, because I think I would be bypassing my supervisor doing it.
How can I ask for more tasks without being annoying/rude here? Is it okay to ask for more tasks?