Problem placing Application made in Laravel 5.2 in production

I'm not putting my system into production. I created a VirtualHost in the http.conf Apache file with the following configuration:

<VirtualHost *:80>
DocumentRoot /var/www/html/dna/public
ServerName www.dna.com
<Directory "/var/www/html/dna/public">
       Options Indexes FollowSymLinks Includes ExecCGI
       AllowOverride All
       Require all granted
   </Directory>
</VirtualHost>

When I access the www.dna.com address the home page appears normally, but when I try to login, erro 500 appears:

The file .htaccess of the folder /public of the project:

<IfModule mod_rewrite.c>
    <IfModule mod_negotiation.c>
        Options -MultiViews
    </IfModule>

    RewriteEngine On


    # Redirect Trailing Slashes If Not A Folder...
    RewriteCond %{REQUEST_FILENAME} !-d
    RewriteRule ^(.*)/$ /$1 [L,R=301]

    # Handle Front Controller...
    RewriteCond %{REQUEST_FILENAME} !-d
    RewriteCond %{REQUEST_FILENAME} !-f
    RewriteRule ^ index.php [L]

    # Handle Authorization Header
    RewriteCond %{HTTP:Authorization} .
    RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]
</IfModule>