(Please check working) Given RSA encoding function $E: x\to x^{11} \pmod{3737}$ find the decoding function $D$

Question

Please check the working and final answer to the question:

Question:
Given RSA encoding function $E: x\to x^{11} \pmod{3737}$ find the decoding function $D$

My working:
$\phi(3737) = \phi(37) \times \phi(101)$
$= 36 \times 100 = 3600$

Using euclid's algorithm (Skipping the fairly long gory details) we show:

$1 = 4\times3600 - 1309 \times 11$

Taking the coefficient of 11 (power of $x$), we get $-1309$ but we want this in positive congruent mod $3600$ so $3600-1309 = 2291$ and finally we have

$D:x\to x^{2291}\pmod{3737}$