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Nevermind, I resolved it by deleting /var/log/exim4/paniclog
Sent an email and got this:

2014-11-03 19:38:27 1XlMWJ-0007ye-AQ <= alvaro@alvr.me H=(correo.alvr.me) [84.200.69.35] P=esmtpsa X=TLS1.2:DHE_RSA_AES_256_CBC_SHA256:256 A=login:alvaro@alvr.me S=1945 id=e13d231f47f01196fdc6ee2091796454@alvr.me
2014-11-03 19:38:27 1XlMWJ-0007ye-AQ => alvaro.sg93@gmail.com R=dnslookup T=remote_smtp H=gmail-smtp-in.l.google.com [173.194.67.26] X=TLS1.2:RSA_ARCFOUR_SHA1:128
2014-11-03 19:38:27 1XlMWJ-0007ye-AQ Completed
Nov 3 12:25:12 alvr imapd-ssl: Connection, ip=[::ffff:84.200.69.35]
Nov 3 12:25:12 alvr imapd-ssl: LOGIN, user=alvaro@alvr.me, ip=[::ffff:84.200.69.35], port=[49070], protocol=IMAP
Nov 3 12:25:12 alvr imapd-ssl: LOGOUT, user=alvaro@alvr.me, ip=[::ffff:84.200.69.35], headers=0, body=0, rcvd=52, sent=310, time=0, starttls=1


This is the part that repeats the most.