Twitter 1.1 user_timline with Bearer Authorization returns 400 in node.js

I have a bearer token and try to get a user's timeline from behind a proxy with the following code.

var parsedUrl = url.parse( 'https://api.twitter.com/1.1/statuses/user_timeline.json:443/?count=2&screen_name=twitterapi', true, true );
var options = {
    'host': parsedUrl.host,
    'path': parsedUrl.path,
    'method': 'GET',
    'headers': {
        'Host': parsedUrl.host,
        'Authorization': 'Bearer ' + settings.accessToken
    }
};

var adapter = https;
if(settings.proxy)
{
    options.host = settings.proxy;
    options.port = settings.proxyPort;
    options.path = parsedUrl.path;

    options.headers['Proxy-Connection'] = 'Keep-Alive';

    adapter = http;
}

var body = '';
var req = adapter.request(options, function(res) {

    res.on('data', function (chunk) {
        body += chunk;
    });

    res.on('end', function () {
        try
        {
            var result = JSON.parse( body );
        }
        catch(ex)
        {
         //...
        }
    });

});
req.end();

This request always return a 400 with no body or error message. If try the acces with cUrl it works like a charm. I retrieve the bearer token in the same way. Why does Twitter respond with a 400?

curl --get 'https://api.twitter.com/1.1/statuses/user_timeline.json' --data 'count=2&screen_name=twitterapi' --header 'Authorization: Bearer <token>' --verbose --proxy http://proxy.example.com:8080

What does cUrl differently?

EDIT: The status code is NOT 404 but 400! Sorry.

EDIT2: When I leave the Authorization header out I still get 400 even though I expect a authorization failed message. Is any special enconding needed?

EDIT3: Now the status code is 401. Something smelly goes on :(

Here is the trick: You have to tunnel the HTTPS connection on the HTTP request using CONNECT to get through the proxy. The initial way is wrong.

var http = require('http');
var https = require('https');

var connectReq = http.request({ // establishing a tunnel
  host: 'localhost',
  port: 3128,
  method: 'CONNECT',
  path: 'github.com:443',
}).on('connect', function(res, socket, head) {
  // should check res.statusCode here
  var req = https.get({
    host: 'github.com',
    socket: socket, // using a tunnel
    agent: false    // cannot use a default agent
  }, function(res) {
    res.setEncoding('utf8');
    res.on('data', console.log);
  });
}).end();

See following node.js bug/issue for details: HTTPS request not working with proxy