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I was hired at the end of April to fill a role for project that is just now starting to ramp up. The first two weeks on the job I spent time completing administrative tasks and various new-hire hr requirements. After that, however, until this week there was not much for me to do but wait until I was needed as a project contributor. I periodically asked our project leads for work or ways to contribute, but was simply told to wait it out and study up on documentation. I guess my question is, what is the best way to remain productive during times like this and demonstrate value to the company? I don't want to come off as unproductive to coworkers passing by, but also don't want to pester my superiors for work and come off as someone who can't create value (which is especially hard a a new hire). I realize the answer might be industry specific, but there has to be some way to properly handle genuinely not having much to do. If this question is too broad I apologize! Thanks!
Edit: This is no longer a problem, but wanted to know in case this happens again in the future.