There are two ways to authenticate to an HTTP Server in CURL.
The most common way to authenticate is the encoded username and password in the URL, i.e https://USERNAME:PASSWORD@api.sipgate.net/RPC2
Here, however, problems occur when control characters like '@' and ':' are present in the authentication data.
Instead, please use the less common option with the button 'u'.
curl -u firstname.lastname@example.org: PASSWORD https://api.sipgate.net/RPC2