Maximum length/legal characters for JSESSIONID cookie

While there is no prescribed standard limit for cookie sizes, RFC 6265 recommends that a "user-agent" should at least be able to handle 4096 bytes per cookie. Hopefully you don't have cookies that big, but nonetheless it's nothing that the BIG-IP persistence table can't handle. I'd also add that the example JSESSIONID value that you've provided is not uncommonly long.