Deriving the WPA passphrase is supposed to be VERY HARD. This is why no one uses WEP anymore, deriving the key was possible.
How many wi-fi devices do you have? If you enumerate all of them, including levels, someone may have an idea, because all the working devices have to know the passphrase. For example, if one of them is a Windows device, well, the passcode is somewhere on the windows device so that the driver can get it and it is possible to reconstruct it, I am just not sure how. Someone might know or it might be possible to find the procedure with a web search.
But what I would do is just change the passcode and then reconfigure all the devices you own to use the new one. Then I would write the passcode on a piece of paper and tape it to the router. You mostly care about the passcode to stop over the air attacks, (from people sitting in your front yard) and if someone can physically get to the router, they are allowed to know the over-the-air encryption code.
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