Genderize打电话.io API来自c#

我试图调用http://genderize.io/，但我得到一个错误从。net说:

{"You must provide a request body if you set ContentLength>0 or SendChunked==true.  Do this by calling [Begin]GetRequestStream before [Begin]GetResponse."}

如何调用这个web服务"http://api.genderize.io/"?name=peter"从c#和得到JSON字符串回来吗?

HttpWebRequest request;
                string postData = "name=peter"
    URL = "http://api.genderize.io/?"
                Uri uri = new Uri(URL + postData);
                request = (HttpWebRequest)WebRequest.Create(uri);
                request.Method = "POST";
                request.ContentType = "application/x-www-form-urlencoded";
                request.ContentLength = postData.Length;
                request.AllowAutoRedirect = true;
                UTF8Encoding enc = new UTF8Encoding();
                string result = string.Empty;
                HttpWebResponse Response;
                try
                {
                    using (Response = (HttpWebResponse)request.GetResponse())
                    {
                        using (Stream responseStream = Response.GetResponseStream())
                        {
                            using (StreamReader readStream = new StreamReader(responseStream, Encoding.UTF8))
                            {
                                return readStream.ReadToEnd();
                            }
                        }
                    }
                }
                catch (Exception ex)
                {
                    Debug.WriteLine("Error: " + ex.Message);
                    throw ex;
                }