用C#写一个用私钥对 content 的 base64 内容进行签名。 签名算法：SHA1withRSA，模数长度：1024。

好的，以下是用 C# 实现对 content 进行签名的代码：

using System;
using System.Security.Cryptography;
using System.Text;

class Program
{
    static void Main(string[] args)
    {
        string content = "待签名的内容";
        string privateKey = "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";
        byte[] privateKeyBytes = Convert.FromBase64String(privateKey);
        RSACryptoServiceProvider rsa = new RSACryptoServiceProvider();
        rsa.ImportCspBlob(privateKeyBytes);

        byte[] contentBytes = Encoding.UTF8.GetBytes(content);
        byte[] signatureBytes = rsa.SignData(contentBytes, new SHA1CryptoServiceProvider());
        string signature = Convert.ToBase64String(signatureBytes);

        Console.WriteLine($"签名结果：{signature}");
    }
}

需要注意的是，私钥的长度必须是 1024 位，否则无法进行签名。