Polynomial Cipher

You've just received a message from Alice! Before you can read it though, you'll have to decipher it.

The encrypted message you received was "13417108788227".

You know Alice encrypted it using the following method:

  1. Convert each letter into a two digit number corresponding to its position in the alphabet. 'A' turns into "01", 'B' into "02", and 'Z' into "26". The word "CAR" becomes "030118".

  2. Pass the converted words through the encryption function: \[E(x) = 2x^4 + 3x^3 +x^2 + 4x + 1\]For example, "CAR" becomes E(30118).

Let M be Alice's original unencrypted message. What is the alphabetic position of the first letter of M? ('A' is in position 1, 'B' is in position 2, and 'Z' is in 26).


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