Nimbostratus
A 406 error normally means that the content the server was going to return was not acceptable to the client, so the server logged the error. When using iControl in KSOAP, I ran into this error when first connecting because the first attempt by KSOAP to connect was incomplete (didn't know the servers' security requirements until it talked to the server), immediately attempting to resend resolved it - but leaves this entry in the logs because the error did occur.
Other possible incompatibilities are things like MIME type and language - if the server only returns English and your browser doesn't understand English, for example... But I doubt that is the case here because the connection does indeed go through.
One of the other F5 staffers might have seen the code though and be able to give you a definitive "yep, that's what we're returning when security is enabled and not yet satisfied" - I haven't seen the source, so I can't say positively.
Don.
