i got banned for no reason

Contact player support to ask them. They're pretty quick to respond. If live-chat is an option at the time, use it.

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i check my email and nothing and i try to login again nothing the same message

Go to the riot support site by going to the top left part of the site and hitting the drop down menu and select "support" or use this link directly: https://support.riotgames.com/

Submit a support ticket and inquire what the ban was about.

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i got banned for no reason look the photo

Just because a reason isn't listed, does not mean it was for no reason