RSA implementation not working with large values for plaintext

While implementing RSA encryption/decryption (using python), the plaintext doesn't match with the decrypted ciphertext for large values of plaintext. Works fine for smaller values for plaintext (numeric value).

Input: p=53 q=59 e=3 plaintext = 1000 (private key computed as 2011)

Here, the decryption gives 1000 as the plaintext, which is correct. Now, if

Input: p=53 q=59 e=3 plaintext = 10000 (private key computed as 2011)

Here, after the decryption, the computed plaintext is 619 (which should be 10000)

The code for the same is here,

    def encrypt(plaintext):
            ciphertext = (plaintext**publicKey) % (self.n)
            return ciphertext
   def decrypt(ciphertext):
            plaintext = (ciphertext**privateKey) % (self.n)
            return plaintext

Considering the algorithm will be used to encrypt/decrypt alphanumeric text, which will produce large numeric values, what modifications are needed or am I missing something?

ps: Checking for multiple values of plaintext,it may be happening because n=3127 and any plaintext greater than 3127 will not produce the original plaintext upon decryption. I might be wrong.

How to make it work for plaintext greater than n, here 3127?