You need to share your code. What happens when you run this:

use strict;
use warnings;
use LWP::UserAgent;
use HTTP::Request;
my $ua = LWP::UserAgent->new;
my $req = HTTP::Request->new( GET => 'https://mysite.com:443/');
my $response = $ua->request($req);
print $response->code."\n";
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