[Exim] need root password of the mailserver?

I have set up exim and fetchmail on a Debian potato. I can read messages,
but I can't send them, the mailserver sends me an error

SMTP error from remote mailer after RCPT TO:<ghigi@???>:
    host mida.sns.it [192.167.206.47]:
    550 <ghigi@???>... Relaying denied

What should I do to let the mailserver relay my messages? Should I do some
configuration on the mailserver, in particular something which requires
root privileges?

Thank you
Alessandro