[Plugin: W3 Total Cache] 500 Internal Error, what rules can I change?

I’m getting the 500 Internal Error immediately when I active the plugin. It has to do with other rewrite rules in htaccess, I know, but how can I keep the rewrite rules I currently have, and make this work? Here is my current htaccess file:

ErrorDocument 401 default

RewriteEngine On
# Redirect HTTP with www to HTTPS with www
RewriteCond %{HTTPS} off
RewriteCond %{HTTP_HOST} ^www\. [NC]
RewriteRule .* https://%{HTTP_HOST}%{REQUEST_URI} [R=301,L]
# Redirect HTTP without www to HTTPS with www
RewriteCond %{HTTPS} off
RewriteCond %{HTTP_HOST} !^www\. [NC]
RewriteRule .* https://www.%{HTTP_HOST}%{REQUEST_URI} [R=301,L]
# Redirect HTTPS without www to HTTPS with www
RewriteCond %{HTTPS} on
RewriteCond %{HTTP_HOST} !^www\. [NC]
RewriteRule .* https://www.%{HTTP_HOST}%{REQUEST_URI} [R=301,L]

<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>

However, when the plugin adds the code below, I get the 500 error:

# BEGIN W3TC Browser Cache
<IfModule mod_deflate.c>
    <IfModule mod_headers.c>
        Header append Vary User-Agent env=!dont-vary
    </IfModule>
    <IfModule mod_filter.c>
        AddOutputFilterByType DEFLATE text/css text/x-component application/x-javascript application/javascript text/javascript text/x-js text/html text/richtext image/svg+xml text/plain text/xsd text/xsl text/xml image/x-icon application/json
    <IfModule mod_mime.c>
        # DEFLATE by extension
        AddOutputFilter DEFLATE js css htm html xml
    </IfModule>
    </IfModule>
</IfModule>
# END W3TC Browser Cache

Any advice on solving this would be appreciated.

Thanks.