Really simple Nginx rewrite to index.php needed, unable to find the solution

I used the .htaccess to nginx rewrite converter and the solution is not working. In fact I'm unable to get any of my rewrites working no matter what I try. I am obviously doing something wrong here. Here's my minimalistic Nginx.conf file:

worker_processes  1;
 events {
     worker_connections  1024;
 }
 
 http {
     include       mime.types;
     default_type  application/octet-stream;
     sendfile        on;
     keepalive_timeout  65;
     server {
         listen       80;
         server_name  localhost;
 
         location / {
             root   html;
             index  index.html index.htm;
         }
 
         # Make sure to set this as your actual server WWW root
         root html;
         # Index file
         index index.php;
         # Rewrite that directs everything to index file
         rewrite /!^(.*).php$ /./index.php last;
 
         location ~ \.php$ {
             root           html;
             fastcgi_pass   127.0.0.1:9000;
             fastcgi_index  index.php;
             fastcgi_param  SCRIPT_FILENAME  $document_root$fastcgi_script_name;
             include        fastcgi_params;
         }
     }
 }
 

I even tried things like "rewrite index.php" with no success. I also tried to put the rewrite in a separate location tag, but that made no difference either.

What am I doing wrong?

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