Exponential congruence for a public key

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I have this formula as a public key for "T" = 19:

$c \equiv 19^{13}(mod 697)$

But I do not know how to solve it. I tried the exponential property: $716\equiv 19(mod 697) \Rightarrow 716^{13}\equiv 19^{13}(mod 697)$

But as it turns out, c = 15. So, how to solve it? Thank you for your attention.